LMFDB - Embedded newform 14.15.d.a.5.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [14,15,Mod(3,14)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(14, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 15, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("14.3");

S:= CuspForms(chi, 15);

N := Newforms(S);

Level:	$ N $	$=$	$ 14 = 2 \cdot 7 $
Weight:	$ k $	$=$	$ 15 $
Character orbit:	$[\chi]$	$=$	14.d (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$17.4060555413$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 4 x^{19} + 5366534 x^{18} + 786490608 x^{17} + 19826027932115 x^{16} + \cdots + 13\!\cdots\!24 $ x^20 - 4x^19 + 5366534x^18 + 786490608x^17 + 19826027932115x^16 + 3116508483645696x^15 + 38794655189396647126x^14 + 6995731541198679243060x^13 + 54561557157067963809187457x^12 + 6630233353755658208901796272x^11 + 34794459335155646904361009621528x^10 - 507937593458729410665953593711872x^9 + 15479722701777718863087638126396034896x^8 - 883719083612311978219332637069278729984x^7 + 3763299771642320209476548571825975912308608x^6 - 633899212255257611286599422411160802422874624x^5 + 597491591633081375797803556549613553954788912384x^4 - 42265294259314426139494021682209240856866274451456x^3 + 11534106439702605092537039760142524539554443571202048x^2 + 525642005044107600688521330249536141111741609738240000*x + 136102482846251121074713416730051821278073355281841537024
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{76}\cdot 3^{12}\cdot 7^{14} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.8
Root			$-48.0702 + 83.2600i$ of defining polynomial
Character	$\chi$	$=$	14.5
Dual form			14.15.d.a.3.8

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(45.2548 - 78.3837i) q^{2} +(-262.346 + 151.465i) q^{3} +(-4096.00 - 7094.48i) q^{4} +(106192. + 61309.7i) q^{5} +27418.1i q^{6} +(-789690. - 233694. i) q^{7} -741455. q^{8} +(-2.34560e6 + 4.06270e6i) q^{9} +O(q^{10})$	\(q+(45.2548 - 78.3837i) q^{2} +(-262.346 + 151.465i) q^{3} +(-4096.00 - 7094.48i) q^{4} +(106192. + 61309.7i) q^{5} +27418.1i q^{6} +(-789690. - 233694. i) q^{7} -741455. q^{8} +(-2.34560e6 + 4.06270e6i) q^{9} +(9.61136e6 - 5.54912e6i) q^{10} +(9.98984e6 + 1.73029e7i) q^{11} +(2.14913e6 + 1.24080e6i) q^{12} +4.33468e7i q^{13} +(-5.40551e7 + 5.13230e7i) q^{14} -3.71452e7 q^{15} +(-3.35544e7 + 5.81180e7i) q^{16} +(4.48694e8 - 2.59054e8i) q^{17} +(2.12300e8 + 3.67714e8i) q^{18} +(8.44187e8 + 4.87392e8i) q^{19} -1.00450e9i q^{20} +(2.42568e8 - 5.83021e7i) q^{21} +1.80835e9 q^{22} +(-1.28289e9 + 2.22203e9i) q^{23} +(1.94517e8 - 1.12305e8i) q^{24} +(4.46600e9 + 7.73534e9i) q^{25} +(3.39768e9 + 1.96165e9i) q^{26} -2.87002e9i q^{27} +(1.57663e9 + 6.55965e9i) q^{28} +3.33710e10 q^{29} +(-1.68100e9 + 2.91157e9i) q^{30} +(-3.94945e10 + 2.28021e10i) q^{31} +(3.03700e9 + 5.26024e9i) q^{32} +(-5.24158e9 - 3.02623e9i) q^{33} -4.68938e10i q^{34} +(-6.95307e10 - 7.32320e10i) q^{35} +3.84303e10 q^{36} +(-4.05505e10 + 7.02355e10i) q^{37} +(7.64071e10 - 4.41137e10i) q^{38} +(-6.56553e9 - 1.13718e10i) q^{39} +(-7.87363e10 - 4.54584e10i) q^{40} -2.23592e11i q^{41} +(6.40745e9 - 2.16518e10i) q^{42} -3.64930e11 q^{43} +(8.18368e10 - 1.41745e11i) q^{44} +(-4.98166e11 + 2.87616e11i) q^{45} +(1.16114e11 + 2.01116e11i) q^{46} +(-3.54734e10 - 2.04806e10i) q^{47} -2.03293e10i q^{48} +(5.68997e11 + 3.69091e11i) q^{49} +8.08433e11 q^{50} +(-7.84753e10 + 1.35923e11i) q^{51} +(3.07523e11 - 1.77548e11i) q^{52} +(-4.00430e11 - 6.93564e11i) q^{53} +(-2.24962e11 - 1.29882e11i) q^{54} +2.44990e12i q^{55} +(5.85520e11 + 1.73274e11i) q^{56} -2.95292e11 q^{57} +(1.51020e12 - 2.61574e12i) q^{58} +(8.72791e11 - 5.03906e11i) q^{59} +(1.52147e11 + 2.63526e11i) q^{60} +(1.17721e12 + 6.79660e11i) q^{61} +4.12763e12i q^{62} +(2.80173e12 - 2.66012e12i) q^{63} +5.49756e11 q^{64} +(-2.65758e12 + 4.60306e12i) q^{65} +(-4.74414e11 + 2.73903e11i) q^{66} +(-2.43262e12 - 4.21342e12i) q^{67} +(-3.67570e12 - 2.12217e12i) q^{68} -7.77254e11i q^{69} +(-8.88679e12 + 2.13597e12i) q^{70} +4.67641e12 q^{71} +(1.73916e12 - 3.01231e12i) q^{72} +(-4.73238e12 + 2.73224e12i) q^{73} +(3.67021e12 + 6.35699e12i) q^{74} +(-2.34327e12 - 1.35289e12i) q^{75} -7.98543e12i q^{76} +(-3.84529e12 - 1.59985e13i) q^{77} -1.18849e12 q^{78} +(-1.42899e12 + 2.47508e12i) q^{79} +(-7.12639e12 + 4.11442e12i) q^{80} +(-1.07842e13 - 1.86788e13i) q^{81} +(-1.75260e13 - 1.01186e13i) q^{82} -5.45017e12i q^{83} +(-1.40718e12 - 1.48209e12i) q^{84} +6.35301e13 q^{85} +(-1.65149e13 + 2.86046e13i) q^{86} +(-8.75474e12 + 5.05455e12i) q^{87} +(-7.40702e12 - 1.28293e13i) q^{88} +(3.25912e13 + 1.88165e13i) q^{89} +5.20641e13i q^{90} +(1.01299e13 - 3.42305e13i) q^{91} +2.10189e13 q^{92} +(6.90746e12 - 1.19641e13i) q^{93} +(-3.21069e12 + 1.85369e12i) q^{94} +(5.97637e13 + 1.03514e14i) q^{95} +(-1.59349e12 - 9.20000e11i) q^{96} +1.14678e14i q^{97} +(5.46806e13 - 2.78969e13i) q^{98} -9.37287e13 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4374 q^{3} - 81920 q^{4} + 3354 q^{5} + 1455616 q^{7} + 17547432 q^{9}+O(q^{10}) $ 20 * q - 4374 * q^3 - 81920 * q^4 + 3354 * q^5 + 1455616 * q^7 + 17547432 * q^9	\( 20 q - 4374 q^{3} - 81920 q^{4} + 3354 q^{5} + 1455616 q^{7} + 17547432 q^{9} - 3933696 q^{10} + 8400426 q^{11} + 35831808 q^{12} - 114693888 q^{14} + 562720524 q^{15} - 671088640 q^{16} + 2180481042 q^{17} - 251755008 q^{18} - 3919727442 q^{19} + 7585509006 q^{21} + 5394565632 q^{22} - 6905098386 q^{23} - 2371878912 q^{24} + 14165082644 q^{25} + 12652202496 q^{26} - 17334943744 q^{28} + 27884908704 q^{29} + 54103511808 q^{30} + 45638710782 q^{31} - 37041090498 q^{33} - 18274367202 q^{35} - 287497125888 q^{36} - 27026027926 q^{37} - 354043974912 q^{38} - 126125404380 q^{39} + 32224837632 q^{40} - 298475364864 q^{42} + 726682953656 q^{43} + 68816289792 q^{44} + 498861631944 q^{45} - 286664984832 q^{46} - 2044625353338 q^{47} + 2939974016204 q^{49} + 1161106642944 q^{50} - 2419609945602 q^{51} + 1314350333952 q^{52} + 1546271487546 q^{53} - 5213176950528 q^{54} + 1720927125504 q^{56} + 14789884876092 q^{57} - 2365863040512 q^{58} - 6798944731566 q^{59} - 2304903266304 q^{60} - 2214453865554 q^{61} - 4417730390688 q^{63} + 10995116277760 q^{64} + 7516703932836 q^{65} - 8476063570944 q^{66} - 4655820763226 q^{67} - 17862500696064 q^{68} + 20497461621504 q^{70} + 96606137494152 q^{71} - 2062377025536 q^{72} - 65348368908666 q^{73} - 566532483072 q^{74} - 186663280957308 q^{75} + 77525241691422 q^{77} + 88663911671808 q^{78} - 60517474082978 q^{79} - 225083129856 q^{80} - 107180264511342 q^{81} - 43979002397184 q^{82} + 18842436550656 q^{84} + 416326699526124 q^{85} + 2363335174656 q^{86} - 126768392660088 q^{87} - 22096140828672 q^{88} - 237147002561826 q^{89} + 203506111374408 q^{91} + 113133131956224 q^{92} - 94175068190130 q^{93} - 221058962902272 q^{94} + 25202514515490 q^{95} + 19430432047104 q^{96} + 165606984015360 q^{98} + 10\!\cdots\!68 q^{99}+O(q^{100}) \) 20 * q - 4374 * q^3 - 81920 * q^4 + 3354 * q^5 + 1455616 * q^7 + 17547432 * q^9 - 3933696 * q^10 + 8400426 * q^11 + 35831808 * q^12 - 114693888 * q^14 + 562720524 * q^15 - 671088640 * q^16 + 2180481042 * q^17 - 251755008 * q^18 - 3919727442 * q^19 + 7585509006 * q^21 + 5394565632 * q^22 - 6905098386 * q^23 - 2371878912 * q^24 + 14165082644 * q^25 + 12652202496 * q^26 - 17334943744 * q^28 + 27884908704 * q^29 + 54103511808 * q^30 + 45638710782 * q^31 - 37041090498 * q^33 - 18274367202 * q^35 - 287497125888 * q^36 - 27026027926 * q^37 - 354043974912 * q^38 - 126125404380 * q^39 + 32224837632 * q^40 - 298475364864 * q^42 + 726682953656 * q^43 + 68816289792 * q^44 + 498861631944 * q^45 - 286664984832 * q^46 - 2044625353338 * q^47 + 2939974016204 * q^49 + 1161106642944 * q^50 - 2419609945602 * q^51 + 1314350333952 * q^52 + 1546271487546 * q^53 - 5213176950528 * q^54 + 1720927125504 * q^56 + 14789884876092 * q^57 - 2365863040512 * q^58 - 6798944731566 * q^59 - 2304903266304 * q^60 - 2214453865554 * q^61 - 4417730390688 * q^63 + 10995116277760 * q^64 + 7516703932836 * q^65 - 8476063570944 * q^66 - 4655820763226 * q^67 - 17862500696064 * q^68 + 20497461621504 * q^70 + 96606137494152 * q^71 - 2062377025536 * q^72 - 65348368908666 * q^73 - 566532483072 * q^74 - 186663280957308 * q^75 + 77525241691422 * q^77 + 88663911671808 * q^78 - 60517474082978 * q^79 - 225083129856 * q^80 - 107180264511342 * q^81 - 43979002397184 * q^82 + 18842436550656 * q^84 + 416326699526124 * q^85 + 2363335174656 * q^86 - 126768392660088 * q^87 - 22096140828672 * q^88 - 237147002561826 * q^89 + 203506111374408 * q^91 + 113133131956224 * q^92 - 94175068190130 * q^93 - 221058962902272 * q^94 + 25202514515490 * q^95 + 19430432047104 * q^96 + 165606984015360 * q^98 + 1056686373672768 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/14\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	45.2548	−	78.3837i	0.353553	−	0.612372i
$2$	45.2548	−	78.3837i	0.353553	−	0.612372i
$3$	−262.346	+	151.465i	−0.119957	+	0.0692571i	−0.558778	−	0.829317i	$-0.688730\pi$
$3$	−262.346	+	151.465i	−0.119957	+	0.0692571i	0.438821	+	0.898574i	$0.355396\pi$
$4$	−4096.00	−	7094.48i	−0.250000	−	0.433013i
$5$	106192.	+	61309.7i	1.35925	+	0.784764i	0.989523	−	0.144376i	$-0.0461173\pi$
$5$	106192.	+	61309.7i	1.35925	+	0.784764i	0.369729	+	0.929140i	$0.379451\pi$
$6$			27418.1i			0.0979443i
$7$	−789690.	−	233694.i	−0.958893	−	0.283766i
$7$	−789690.	−	233694.i	−0.958893	−	0.283766i
$8$	−741455.			−0.353553
$9$	−2.34560e6	+	4.06270e6i	−0.490407	+	0.849410i
$10$	9.61136e6	−	5.54912e6i	0.961136	−	0.554912i
$11$	9.98984e6	+	1.73029e7i	0.512637	+	0.887913i	0.999893	+	0.0146537i	$0.00466458\pi$
$11$	9.98984e6	+	1.73029e7i	0.512637	+	0.887913i	−0.487256	+	0.873259i	$0.662002\pi$
$12$	2.14913e6	+	1.24080e6i	0.0599784	+	0.0346285i
$13$			4.33468e7i			0.690801i	0.938455	+	0.345401i	$0.112257\pi$
$13$			4.33468e7i			0.690801i	−0.938455	+	0.345401i	$0.887743\pi$
$14$	−5.40551e7	+	5.13230e7i	−0.512791	+	0.486873i
$15$	−3.71452e7			−0.217402
$16$	−3.35544e7	+	5.81180e7i	−0.125000	+	0.216506i
$17$	4.48694e8	−	2.59054e8i	1.09347	−	0.631317i	0.158974	−	0.987283i	$-0.449181\pi$
$17$	4.48694e8	−	2.59054e8i	1.09347	−	0.631317i	0.934499	+	0.355966i	$0.115848\pi$
$18$	2.12300e8	+	3.67714e8i	0.346770	+	0.600623i
$19$	8.44187e8	+	4.87392e8i	0.944417	+	0.545259i	0.891342	−	0.453331i	$-0.149765\pi$
$19$	8.44187e8	+	4.87392e8i	0.944417	+	0.545259i	0.0530745	+	0.998591i	$0.483098\pi$
$20$		−	1.00450e9i		−	0.784764i
$21$	2.42568e8	−	5.83021e7i	0.134679	−	0.0323705i
$22$	1.80835e9			0.724978
$23$	−1.28289e9	+	2.22203e9i	−0.376786	+	0.652613i	−0.990593	−	0.136843i	$-0.956304\pi$
$23$	−1.28289e9	+	2.22203e9i	−0.376786	+	0.652613i	0.613806	+	0.789457i	$0.289638\pi$
$24$	1.94517e8	−	1.12305e8i	0.0424111	−	0.0244861i
$25$	4.46600e9	+	7.73534e9i	0.731710	+	1.26736i
$26$	3.39768e9	+	1.96165e9i	0.423028	+	0.244235i
$27$		−	2.87002e9i		−	0.274371i
$28$	1.57663e9	+	6.55965e9i	0.116849	+	0.486155i
$29$	3.33710e10			1.93457			0.967283	−	0.253700i	$-0.0816476\pi$
$29$	3.33710e10			1.93457			0.967283	+	0.253700i	$0.0816476\pi$
$30$	−1.68100e9	+	2.91157e9i	−0.0768632	+	0.133131i
$31$	−3.94945e10	+	2.28021e10i	−1.43550	+	0.828788i	−0.997533	−	0.0702007i	$-0.977636\pi$
$31$	−3.94945e10	+	2.28021e10i	−1.43550	+	0.828788i	−0.437971	+	0.898989i	$0.644303\pi$
$32$	3.03700e9	+	5.26024e9i	0.0883883	+	0.153093i
$33$	−5.24158e9	−	3.02623e9i	−0.122989	−	0.0710075i
$34$		−	4.68938e10i		−	0.892817i
$35$	−6.95307e10	−	7.32320e10i	−1.08069	−	1.13822i
$36$	3.84303e10			0.490407
$37$	−4.05505e10	+	7.02355e10i	−0.427153	+	0.739851i	−0.996619	−	0.0821641i	$-0.973817\pi$
$37$	−4.05505e10	+	7.02355e10i	−0.427153	+	0.739851i	0.569466	+	0.822015i	$0.307150\pi$
$38$	7.64071e10	−	4.41137e10i	0.667803	−	0.385556i
$39$	−6.56553e9	−	1.13718e10i	−0.0478429	−	0.0828663i
$40$	−7.87363e10	−	4.54584e10i	−0.480568	−	0.277456i
$41$		−	2.23592e11i		−	1.14807i	−0.818830	−	0.574037i	$-0.805377\pi$
$41$		−	2.23592e11i		−	1.14807i	0.818830	−	0.574037i	$-0.194623\pi$
$42$	6.40745e9	−	2.16518e10i	0.0277933	−	0.0939182i
$43$	−3.64930e11			−1.34255			−0.671275	−	0.741208i	$-0.734253\pi$
$43$	−3.64930e11			−1.34255			−0.671275	+	0.741208i	$0.734253\pi$
$44$	8.18368e10	−	1.41745e11i	0.256318	−	0.443956i
$45$	−4.98166e11	+	2.87616e11i	−1.33317	+	0.769708i
$46$	1.16114e11	+	2.01116e11i	0.266428	+	0.461467i
$47$	−3.54734e10	−	2.04806e10i	−0.0700194	−	0.0404257i	0.464582	−	0.885530i	$-0.346205\pi$
$47$	−3.54734e10	−	2.04806e10i	−0.0700194	−	0.0404257i	−0.534601	+	0.845105i	$0.679538\pi$
$48$		−	2.03293e10i		−	0.0346285i
$49$	5.68997e11	+	3.69091e11i	0.838953	+	0.544204i
$50$	8.08433e11			1.03479
$51$	−7.84753e10	+	1.35923e11i	−0.0874464	+	0.151462i
$52$	3.07523e11	−	1.77548e11i	0.299126	−	0.172700i
$53$	−4.00430e11	−	6.93564e11i	−0.340875	−	0.590413i	0.643721	−	0.765261i	$-0.277390\pi$
$53$	−4.00430e11	−	6.93564e11i	−0.340875	−	0.590413i	−0.984595	+	0.174848i	$0.944057\pi$
$54$	−2.24962e11	−	1.29882e11i	−0.168017	−	0.0970047i
$55$			2.44990e12i			1.60920i
$56$	5.85520e11	+	1.73274e11i	0.339020	+	0.100327i
$57$	−2.95292e11			−0.151052
$58$	1.51020e12	−	2.61574e12i	0.683972	−	1.18467i
$59$	8.72791e11	−	5.03906e11i	0.350708	−	0.202481i	−0.314289	−	0.949327i	$-0.601766\pi$
$59$	8.72791e11	−	5.03906e11i	0.350708	−	0.202481i	0.664997	+	0.746846i	$0.268433\pi$
$60$	1.52147e11	+	2.63526e11i	0.0543505	+	0.0941378i
$61$	1.17721e12	+	6.79660e11i	0.374579	+	0.216263i	0.675457	−	0.737399i	$-0.263946\pi$
$61$	1.17721e12	+	6.79660e11i	0.374579	+	0.216263i	−0.300878	+	0.953663i	$0.597280\pi$
$62$			4.12763e12i			1.17208i
$63$	2.80173e12	−	2.66012e12i	0.711282	−	0.675332i
$64$	5.49756e11			0.125000
$65$	−2.65758e12	+	4.60306e12i	−0.542116	+	0.938973i
$66$	−4.74414e11	+	2.73903e11i	−0.0869660	+	0.0502099i
$67$	−2.43262e12	−	4.21342e12i	−0.401375	−	0.695202i	0.592517	−	0.805558i	$-0.298134\pi$
$67$	−2.43262e12	−	4.21342e12i	−0.401375	−	0.695202i	−0.993892	+	0.110356i	$0.964801\pi$
$68$	−3.67570e12	−	2.12217e12i	−0.546737	−	0.315659i
$69$		−	7.77254e11i		−	0.104381i
$70$	−8.88679e12	+	2.13597e12i	−1.07909	+	0.259363i
$71$	4.67641e12			0.514167			0.257083	−	0.966389i	$-0.417238\pi$
$71$	4.67641e12			0.514167			0.257083	+	0.966389i	$0.417238\pi$
$72$	1.73916e12	−	3.01231e12i	0.173385	−	0.300312i
$73$	−4.73238e12	+	2.73224e12i	−0.428371	+	0.247320i	−0.698652	−	0.715461i	$-0.746217\pi$
$73$	−4.73238e12	+	2.73224e12i	−0.428371	+	0.247320i	0.270282	+	0.962781i	$0.412883\pi$
$74$	3.67021e12	+	6.35699e12i	0.302043	+	0.523154i
$75$	−2.34327e12	−	1.35289e12i	−0.175547	−	0.101352i
$76$		−	7.98543e12i		−	0.545259i
$77$	−3.84529e12	−	1.59985e13i	−0.239604	−	0.996883i
$78$	−1.18849e12			−0.0676601
$79$	−1.42899e12	+	2.47508e12i	−0.0744113	+	0.128884i	−0.900830	−	0.434172i	$-0.857041\pi$
$79$	−1.42899e12	+	2.47508e12i	−0.0744113	+	0.128884i	0.826419	+	0.563056i	$0.190374\pi$
$80$	−7.12639e12	+	4.11442e12i	−0.339813	+	0.196191i
$81$	−1.07842e13	−	1.86788e13i	−0.471405	−	0.816497i
$82$	−1.75260e13	−	1.01186e13i	−0.703049	−	0.405905i
$83$		−	5.45017e12i		−	0.200846i	−0.994945	−	0.100423i	$-0.967980\pi$
$83$		−	5.45017e12i		−	0.200846i	0.994945	−	0.100423i	$-0.0320196\pi$
$84$	−1.40718e12	−	1.48209e12i	−0.0476865	−	0.0502249i
$85$	6.35301e13			1.98174
$86$	−1.65149e13	+	2.86046e13i	−0.474663	+	0.822141i
$87$	−8.75474e12	+	5.05455e12i	−0.232064	+	0.133982i
$88$	−7.40702e12	−	1.28293e13i	−0.181244	−	0.313925i
$89$	3.25912e13	+	1.88165e13i	0.736835	+	0.425412i	0.820917	−	0.571047i	$-0.193463\pi$
$89$	3.25912e13	+	1.88165e13i	0.736835	+	0.425412i	−0.0840827	+	0.996459i	$0.526796\pi$
$90$			5.20641e13i			1.08853i
$91$	1.01299e13	−	3.42305e13i	0.196026	−	0.662405i
$92$	2.10189e13			0.376786
$93$	6.90746e12	−	1.19641e13i	0.114799	−	0.198838i
$94$	−3.21069e12	+	1.85369e12i	−0.0495112	+	0.0285853i
$95$	5.97637e13	+	1.03514e14i	0.855800	+	1.48229i
$96$	−1.59349e12	−	9.20000e11i	−0.0212056	−	0.0122430i
$97$			1.14678e14i			1.41932i	0.704547	+	0.709658i	$0.251150\pi$
$97$			1.14678e14i			1.41932i	−0.704547	+	0.709658i	$0.748850\pi$
$98$	5.46806e13	−	2.78969e13i	0.629870	−	0.321347i
$99$	−9.37287e13			−1.00560
$100$	3.65855e13	−	6.33679e13i	0.365855	−	0.633679i
$101$	−1.14451e13	+	6.60783e12i	−0.106750	+	0.0616324i	−0.552425	−	0.833563i	$-0.686297\pi$
$101$	−1.14451e13	+	6.60783e12i	−0.106750	+	0.0616324i	0.445674	+	0.895195i	$0.352964\pi$
$102$	7.10278e12	+	1.23024e13i	0.0618339	+	0.107100i
$103$	−8.74064e13	−	5.04641e13i	−0.710694	−	0.410320i	0.100624	−	0.994925i	$-0.467916\pi$
$103$	−8.74064e13	−	5.04641e13i	−0.710694	−	0.410320i	−0.811318	+	0.584605i	$0.801249\pi$
$104$		−	3.21397e13i		−	0.244235i
$105$	2.93332e13	+	8.68060e12i	0.208465	+	0.0616914i
$106$	−7.24855e13			−0.482070
$107$	1.17926e14	−	2.04253e14i	0.734382	−	1.27199i	−0.220613	−	0.975362i	$-0.570806\pi$
$107$	1.17926e14	−	2.04253e14i	0.734382	−	1.27199i	0.954994	−	0.296625i	$-0.0958610\pi$
$108$	−2.03613e13	+	1.17556e13i	−0.118806	+	0.0685927i
$109$	−6.05767e13	−	1.04922e14i	−0.331375	−	0.573959i	0.651406	−	0.758729i	$-0.274179\pi$
$109$	−6.05767e13	−	1.04922e14i	−0.331375	−	0.573959i	−0.982782	+	0.184770i	$0.940846\pi$
$110$	1.92032e14	+	1.10870e14i	0.985427	+	0.568937i
$111$		−	2.45679e13i		−	0.118334i
$112$	4.00794e13	−	3.80537e13i	0.181299	−	0.172136i
$113$	−1.34624e14			−0.572235			−0.286117	−	0.958195i	$-0.592365\pi$
$113$	−1.34624e14			−0.572235			−0.286117	+	0.958195i	$0.592365\pi$
$114$	−1.33634e13	+	2.31460e13i	−0.0534050	+	0.0925002i
$115$	−2.72465e14	+	1.57307e14i	−1.02430	+	0.591377i
$116$	−1.36688e14	−	2.36750e14i	−0.483641	−	0.837692i
$117$	−1.76105e14	−	1.01674e14i	−0.586773	−	0.338774i
$118$		−	9.12167e13i		−	0.286352i
$119$	−4.14869e14	+	9.97151e13i	−1.22767	+	0.295075i
$120$	2.75415e13			0.0768632
$121$	−9.71891e12	+	1.68336e13i	−0.0255929	+	0.0443283i
$122$	1.06548e14	−	6.15158e13i	0.264867	−	0.152921i
$123$	3.38665e13	+	5.86584e13i	0.0795122	+	0.137719i
$124$	3.23539e14	+	1.86795e14i	0.717752	+	0.414394i
$125$			3.46828e14i			0.727351i
$126$	−8.17184e13	−	3.39993e14i	−0.162079	−	0.674335i
$127$	3.44488e14			0.646470			0.323235	−	0.946319i	$-0.395230\pi$
$127$	3.44488e14			0.646470			0.323235	+	0.946319i	$0.395230\pi$
$128$	2.48791e13	−	4.30919e13i	0.0441942	−	0.0765466i
$129$	9.57378e13	−	5.52742e13i	0.161048	−	0.0929811i
$130$	2.40536e14	+	4.16621e14i	0.383334	+	0.663954i
$131$	8.29443e14	+	4.78879e14i	1.25282	+	0.723314i	0.971668	−	0.236351i	$-0.0759514\pi$
$131$	8.29443e14	+	4.78879e14i	1.25282	+	0.723314i	0.281148	+	0.959664i	$0.409285\pi$
$132$			4.95817e13i			0.0710075i
$133$	−5.52746e14	−	5.82170e14i	−0.750869	−	0.790839i
$134$	−4.40351e14			−0.567630
$135$	1.75960e14	−	3.04771e14i	0.215316	−	0.372939i
$136$	−3.32687e14	+	1.92077e14i	−0.386601	+	0.223204i
$137$	5.69577e14	+	9.86536e14i	0.628794	+	1.08910i	0.987794	+	0.155766i	$0.0497844\pi$
$137$	5.69577e14	+	9.86536e14i	0.628794	+	1.08910i	−0.359000	+	0.933338i	$0.616882\pi$
$138$	−6.09240e13	−	3.51745e13i	−0.0639198	−	0.0369041i
$139$		−	1.74371e15i		−	1.73928i	−0.493686	−	0.869640i	$-0.664351\pi$
$139$		−	1.74371e15i		−	1.73928i	0.493686	−	0.869640i	$-0.335649\pi$
$140$	−2.34745e14	+	7.93242e14i	−0.222690	+	0.752505i
$141$	1.24084e13			0.0111991
$142$	2.11630e14	−	3.66554e14i	0.181785	−	0.314862i
$143$	−7.50025e14	+	4.33027e14i	−0.613372	+	0.354130i
$144$	−1.57411e14	−	2.72643e14i	−0.122602	−	0.212352i
$145$	3.54372e15	+	2.04597e15i	2.62956	+	1.51818i
$146$			4.94589e14i			0.349763i
$147$	−2.05178e14	−	1.06461e13i	−0.138328	−	0.00717746i
$148$	6.64379e14			0.427153
$149$	1.43228e15	−	2.48078e15i	0.878465	−	1.52155i	0.0254388	−	0.999676i	$-0.491902\pi$
$149$	1.43228e15	−	2.48078e15i	0.878465	−	1.52155i	0.853026	−	0.521869i	$-0.174765\pi$
$150$	−2.12089e14	+	1.22450e14i	−0.124131	+	0.0716668i
$151$	−4.88056e14	−	8.45337e14i	−0.272666	−	0.472271i	0.696878	−	0.717190i	$-0.254572\pi$
$151$	−4.88056e14	−	8.45337e14i	−0.272666	−	0.472271i	−0.969544	+	0.244919i	$0.921239\pi$
$152$	−6.25927e14	−	3.61379e14i	−0.333902	−	0.192778i
$153$			2.43055e15i			1.23841i
$154$	−1.42804e15	−	4.22601e14i	−0.695177	−	0.205724i
$155$	−5.59197e15			−2.60161
$156$	−5.37848e13	+	9.31580e13i	−0.0239215	+	0.0414332i
$157$	−5.23736e14	+	3.02379e14i	−0.222749	+	0.128604i	−0.607222	−	0.794532i	$-0.707716\pi$
$157$	−5.23736e14	+	3.02379e14i	−0.222749	+	0.128604i	0.384474	+	0.923136i	$0.374383\pi$
$158$	1.29337e14	+	2.24019e14i	0.0526167	+	0.0911349i
$159$	2.10102e14	+	1.21302e14i	0.0817805	+	0.0472160i
$160$			7.44790e14i			0.277456i
$161$	1.53236e15	−	1.45491e15i	0.546488	−	0.518867i
$162$	−1.95215e15			−0.666667
$163$	1.65902e15	−	2.87351e15i	0.542674	−	0.939938i	−0.456076	−	0.889941i	$-0.650745\pi$
$163$	1.65902e15	−	2.87351e15i	0.542674	−	0.939938i	0.998749	−	0.0499975i	$-0.0159213\pi$
$164$	−1.58627e15	+	9.15834e14i	−0.497130	+	0.287018i
$165$	−3.71074e14	−	6.42720e14i	−0.111448	−	0.193034i
$166$	−4.27204e14	−	2.46646e14i	−0.122993	−	0.0710098i
$167$		−	7.57679e14i		−	0.209156i	−0.994517	−	0.104578i	$-0.966651\pi$
$167$		−	7.57679e14i		−	0.209156i	0.994517	−	0.104578i	$-0.0333492\pi$
$168$	−1.79853e14	+	4.32284e13i	−0.0476161	+	0.0114447i
$169$	2.05843e15			0.522793
$170$	2.87504e15	−	4.97972e15i	0.700651	−	1.21356i
$171$	−3.96025e15	+	2.28645e15i	−0.926297	+	0.534798i
$172$	1.49475e15	+	2.58899e15i	0.335638	+	0.581341i
$173$	−1.13933e14	−	6.57792e13i	−0.0245656	−	0.0141829i	0.487667	−	0.873030i	$-0.337848\pi$
$173$	−1.13933e14	−	6.57792e13i	−0.0245656	−	0.0141829i	−0.512232	+	0.858847i	$0.671181\pi$
$174$			9.14971e14i			0.189480i
$175$	−1.71906e15	−	7.15220e15i	−0.341998	−	1.42290i
$176$	−1.34081e15			−0.256318
$177$	−1.52648e14	+	2.64395e14i	−0.0280466	+	0.0485781i
$178$	2.94982e15	−	1.70308e15i	0.521021	−	0.300811i
$179$	1.19317e15	+	2.06663e15i	0.202642	+	0.350987i	0.949379	−	0.314133i	$-0.101714\pi$
$179$	1.19317e15	+	2.06663e15i	0.202642	+	0.350987i	−0.746737	+	0.665120i	$0.768380\pi$
$180$	4.08098e15	+	2.35615e15i	0.666586	+	0.384854i
$181$			6.33443e15i			0.995308i	0.867376	+	0.497654i	$0.165805\pi$
$181$			6.33443e15i			0.995308i	−0.867376	+	0.497654i	$0.834195\pi$
$182$	−2.22469e15	−	2.34311e15i	−0.336333	−	0.354237i
$183$	−4.11780e14			−0.0599111
$184$	9.51207e14	−	1.64754e15i	0.133214	−	0.230734i
$185$	−8.61223e15	+	4.97227e15i	−1.16122	+	0.670429i
$186$	−6.25192e14	−	1.08286e15i	−0.0811751	−	0.140599i
$187$	8.96477e15	+	5.17581e15i	1.12111	+	0.647273i
$188$			3.35554e14i			0.0404257i
$189$	−6.70705e14	+	2.26642e15i	−0.0778572	+	0.263092i
$190$	1.08184e16			1.21028
$191$	−1.11716e15	+	1.93499e15i	−0.120471	+	0.208662i	−0.919954	−	0.392027i	$-0.871774\pi$
$191$	−1.11716e15	+	1.93499e15i	−0.120471	+	0.208662i	0.799482	+	0.600690i	$0.205107\pi$
$192$	−1.44226e14	+	8.32689e13i	−0.0149946	+	0.00865714i
$193$	5.18959e15	+	8.98863e15i	0.520273	+	0.901140i	0.999722	+	0.0235700i	$0.00750327\pi$
$193$	5.18959e15	+	8.98863e15i	0.520273	+	0.901140i	−0.479449	+	0.877570i	$0.659163\pi$
$194$	8.98890e15	+	5.18975e15i	0.869150	+	0.501804i
$195$		−	1.61012e15i		−	0.150182i
$196$	2.87898e14	−	5.54854e15i	0.0259088	−	0.499328i
$197$	7.07208e15			0.614163			0.307082	−	0.951683i	$-0.400648\pi$
$197$	7.07208e15			0.614163			0.307082	+	0.951683i	$0.400648\pi$
$198$	−4.24168e15	+	7.34680e15i	−0.355534	+	0.615803i
$199$	−2.69790e15	+	1.55763e15i	−0.218300	+	0.126036i	−0.605163	−	0.796102i	$-0.706892\pi$
$199$	−2.69790e15	+	1.55763e15i	−0.218300	+	0.126036i	0.386863	+	0.922137i	$0.373559\pi$
$200$	−3.31134e15	−	5.73541e15i	−0.258699	−	0.448079i
$201$	1.27637e15	+	7.36914e14i	0.0962953	+	0.0555961i
$202$			1.19614e15i			0.0871614i
$203$	−2.63528e16	−	7.79860e15i	−1.85504	−	0.548965i
$204$	1.28574e15			0.0874464
$205$	1.37084e16	−	2.37436e16i	0.900967	−	1.56052i
$206$	−7.91113e15	+	4.56749e15i	−0.502537	+	0.290140i
$207$	−6.01831e15	−	1.04240e16i	−0.369557	−	0.640092i
$208$	−2.51923e15	−	1.45448e15i	−0.149563	−	0.0863502i
$209$			1.94759e16i			1.11808i
$210$	2.00788e15	−	1.90640e15i	0.111482	−	0.105847i
$211$	6.76121e15			0.363117			0.181559	−	0.983380i	$-0.441886\pi$
$211$	6.76121e15			0.363117			0.181559	+	0.983380i	$0.441886\pi$
$212$	−3.28032e15	+	5.68168e15i	−0.170437	+	0.295206i
$213$	−1.22684e15	+	7.08314e14i	−0.0616778	+	0.0356097i
$214$	−1.06734e16	−	1.84869e16i	−0.519286	−	0.899430i
$215$	−3.87525e16	−	2.23738e16i	−1.82486	−	1.05359i
$216$			2.12799e15i			0.0970047i
$217$	3.65171e16	−	8.77701e15i	1.61168	−	0.387372i
$218$	−1.09656e16			−0.468636
$219$	8.27680e14	−	1.43358e15i	0.0342573	−	0.0593354i
$220$	1.73807e16	−	1.00348e16i	0.696802	−	0.402299i
$221$	1.12291e16	+	1.94495e16i	0.436115	+	0.755373i
$222$	−1.92573e15	−	1.11182e15i	−0.0724642	−	0.0418372i
$223$		−	1.24304e16i		−	0.453264i	−0.973980	−	0.226632i	$-0.927228\pi$
$223$		−	1.24304e16i		−	0.453264i	0.973980	−	0.226632i	$-0.0727715\pi$
$224$	−1.16900e15	−	4.86369e15i	−0.0413123	−	0.171882i
$225$	−4.19018e16			−1.43534
$226$	−6.09240e15	+	1.05523e16i	−0.202315	+	0.350421i
$227$	−2.07574e16	+	1.19843e16i	−0.668332	+	0.385862i	−0.795444	−	0.606027i	$-0.792763\pi$
$227$	−2.07574e16	+	1.19843e16i	−0.668332	+	0.385862i	0.127112	+	0.991888i	$0.459429\pi$
$228$	1.20951e15	+	2.09494e15i	0.0377631	+	0.0654075i
$229$	3.04032e16	+	1.75533e16i	0.920598	+	0.531508i	0.883826	−	0.467816i	$-0.154959\pi$
$229$	3.04032e16	+	1.75533e16i	0.920598	+	0.531508i	0.0367725	+	0.999324i	$0.488292\pi$
$230$			2.84757e16i			0.836333i
$231$	3.43201e15	+	3.61471e15i	0.0977834	+	0.102989i
$232$	−2.47431e16			−0.683972
$233$	1.74556e16	−	3.02340e16i	0.468213	−	0.810969i	−0.531127	−	0.847292i	$-0.678231\pi$
$233$	1.74556e16	−	3.02340e16i	0.468213	−	0.810969i	0.999340	+	0.0363233i	$0.0115646\pi$
$234$	−1.59392e16	+	9.20250e15i	−0.414911	+	0.239549i
$235$	−2.51132e15	−	4.34973e15i	−0.0634493	−	0.109897i
$236$	−7.14990e15	−	4.12800e15i	−0.175354	−	0.101241i
$237$		−	8.65768e14i		−	0.0206140i
$238$	−1.09588e16	+	3.70315e16i	−0.253352	+	0.856117i
$239$	7.26933e16			1.63196			0.815979	−	0.578082i	$-0.196199\pi$
$239$	7.26933e16			1.63196			0.815979	+	0.578082i	$0.196199\pi$
$240$	1.24638e15	−	2.15880e15i	0.0271752	−	0.0470689i
$241$	4.20008e16	−	2.42492e16i	0.889484	−	0.513544i	0.0157101	−	0.999877i	$-0.494999\pi$
$241$	4.20008e16	−	2.42492e16i	0.889484	−	0.513544i	0.873774	+	0.486333i	$0.161666\pi$
$242$	8.79655e14	+	1.52361e15i	0.0180969	+	0.0313448i
$243$	1.75465e16	+	1.01305e16i	0.350709	+	0.202482i
$244$		−	1.11355e16i		−	0.216263i
$245$	3.77938e16	+	7.40794e16i	0.713277	+	1.39809i
$246$	6.13048e15			0.112447
$247$	−2.11269e16	+	3.65928e16i	−0.376666	+	0.652404i
$248$	2.92834e16	−	1.69068e16i	0.507527	−	0.293021i
$249$	8.25511e14	+	1.42983e15i	0.0139100	+	0.0240929i
$250$	2.71856e16	+	1.56956e16i	0.445409	+	0.257157i
$251$		−	9.46547e16i		−	1.50809i	−0.656825	−	0.754043i	$-0.728101\pi$
$251$		−	9.46547e16i		−	1.50809i	0.656825	−	0.754043i	$-0.271899\pi$
$252$	−3.03480e16	−	8.98093e15i	−0.470248	−	0.139161i
$253$	−5.12635e16			−0.772618
$254$	1.55897e16	−	2.70022e16i	0.228561	−	0.395880i
$255$	−1.66668e16	+	9.62260e15i	−0.237723	+	0.137250i
$256$	−2.25180e15	−	3.90023e15i	−0.0312500	−	0.0541266i
$257$	−6.50584e16	−	3.75615e16i	−0.878560	−	0.507237i	−0.00837648	−	0.999965i	$-0.502666\pi$
$257$	−6.50584e16	−	3.75615e16i	−0.878560	−	0.507237i	−0.870183	+	0.492728i	$0.836000\pi$
$258$		−	1.00057e16i		−	0.131495i
$259$	4.84359e16	−	4.59878e16i	0.619539	−	0.588227i
$260$	4.35418e16			0.542116
$261$	−7.82751e16	+	1.35576e17i	−0.948724	+	1.64324i
$262$	7.50726e16	−	4.33432e16i	0.885875	−	0.511460i
$263$	7.85625e16	+	1.36074e17i	0.902661	+	1.56346i	0.824026	+	0.566552i	$0.191723\pi$
$263$	7.85625e16	+	1.36074e17i	0.902661	+	1.56346i	0.0786350	+	0.996903i	$0.474944\pi$
$264$	3.88640e15	+	2.24381e15i	0.0434830	+	0.0251049i
$265$		−	9.82009e16i		−	1.07003i
$266$	−7.06470e16	+	1.69802e16i	−0.749760	+	0.180207i
$267$	−1.14002e16			−0.117851
$268$	−1.99280e16	+	3.45163e16i	−0.200688	+	0.347601i
$269$	1.99591e16	−	1.15234e16i	0.195828	−	0.113061i	−0.398880	−	0.917003i	$-0.630601\pi$
$269$	1.99591e16	−	1.15234e16i	0.195828	−	0.113061i	0.594708	+	0.803942i	$0.297268\pi$
$270$	−1.59261e16	−	2.75848e16i	−0.152252	−	0.263708i
$271$	−5.83170e16	−	3.36693e16i	−0.543263	−	0.313653i	0.203137	−	0.979150i	$-0.434886\pi$
$271$	−5.83170e16	−	3.36693e16i	−0.543263	−	0.313653i	−0.746400	+	0.665497i	$0.768220\pi$
$272$			3.47696e16i			0.315659i
$273$	2.52721e15	+	1.05145e16i	0.0223616	+	0.0930362i
$274$	1.03104e17			0.889249
$275$	−8.92293e16	+	1.54550e17i	−0.750203	+	1.29939i
$276$	−5.51422e15	+	3.18363e15i	−0.0451981	+	0.0260951i
$277$	−8.29569e16	−	1.43686e17i	−0.662970	−	1.14830i	−0.979831	−	0.199826i	$-0.935962\pi$
$277$	−8.29569e16	−	1.43686e17i	−0.662970	−	1.14830i	0.316861	−	0.948472i	$-0.397371\pi$
$278$	−1.36678e17	−	7.89111e16i	−1.06509	−	0.614929i
$279$		−	2.13939e17i		−	1.62577i
$280$	5.15539e16	+	5.42982e16i	0.382081	+	0.402420i
$281$	−1.57534e17			−1.13875			−0.569376	−	0.822077i	$-0.692815\pi$
$281$	−1.57534e17			−1.13875			−0.569376	+	0.822077i	$0.692815\pi$
$282$	5.61540e14	−	9.72616e14i	0.00395947	−	0.00685800i
$283$	−4.18892e16	+	2.41847e16i	−0.288136	+	0.166355i	−0.637101	−	0.770781i	$-0.719866\pi$
$283$	−4.18892e16	+	2.41847e16i	−0.288136	+	0.166355i	0.348965	+	0.937136i	$0.386533\pi$
$284$	−1.91546e16	−	3.31767e16i	−0.128542	−	0.222641i
$285$	−3.13575e16	−	1.81042e16i	−0.205318	−	0.118540i
$286$			7.83863e16i			0.500816i
$287$	−5.22521e16	+	1.76569e17i	−0.325785	+	1.10088i
$288$	−2.84944e16			−0.173385
$289$	5.00289e16	−	8.66526e16i	0.297123	−	0.514632i
$290$	3.20741e17	−	1.85180e17i	1.85938	−	1.07351i
$291$	−1.73698e16	−	3.00853e16i	−0.0982977	−	0.170257i
$292$	3.87677e16	+	2.23825e16i	0.214185	+	0.123660i
$293$			1.19860e17i			0.646550i	0.946305	+	0.323275i	$0.104784\pi$
$293$			1.19860e17i			0.646550i	−0.946305	+	0.323275i	$0.895216\pi$
$294$	−1.01198e16	+	1.56009e16i	−0.0533016	+	0.0821707i
$295$	1.23577e17			0.635601
$296$	3.00663e16	−	5.20764e16i	0.151021	−	0.261577i
$297$	4.96596e16	−	2.86710e16i	0.243617	−	0.140653i
$298$	−1.29635e17	−	2.24535e17i	−0.621168	−	1.07589i
$299$	−9.63180e16	−	5.56092e16i	−0.450826	−	0.260285i
$300$			2.21657e16i			0.101352i
$301$	2.88182e17	+	8.52819e16i	1.28736	+	0.380971i
$302$	−8.83475e16			−0.385608
$303$	2.00171e15	−	3.46707e15i	0.00853696	−	0.0147865i
$304$	−5.66524e16	+	3.27083e16i	−0.236104	+	0.136315i
$305$	8.33395e16	+	1.44348e17i	0.339431	+	0.587912i
$306$	1.90515e17	+	1.09994e17i	0.758368	+	0.437844i
$307$			1.36486e17i			0.531030i	0.964107	+	0.265515i	$0.0855419\pi$
$307$			1.36486e17i			0.531030i	−0.964107	+	0.265515i	$0.914458\pi$
$308$	−9.77507e16	+	9.28102e16i	−0.371762	+	0.352972i
$309$	3.05742e16			0.113670
$310$	−2.53064e17	+	4.38319e17i	−0.919810	+	1.59316i
$311$	8.05827e16	−	4.65244e16i	0.286364	−	0.165333i	−0.349937	−	0.936773i	$-0.613797\pi$
$311$	8.05827e16	−	4.65244e16i	0.286364	−	0.165333i	0.636301	+	0.771441i	$0.280464\pi$
$312$	4.86805e15	+	8.43170e15i	0.0169150	+	0.0292977i
$313$	−4.32110e17	−	2.49479e17i	−1.46820	−	0.847664i	−0.468832	−	0.883287i	$-0.655325\pi$
$313$	−4.32110e17	−	2.49479e17i	−1.46820	−	0.847664i	−0.999365	+	0.0356233i	$0.988658\pi$
$314$			5.47365e16i			0.181874i
$315$	4.60611e17	−	1.10709e17i	1.49679	−	0.359758i
$316$	2.34125e16			0.0744113
$317$	2.21555e17	−	3.83744e17i	0.688757	−	1.19296i	−0.283483	−	0.958977i	$-0.591490\pi$
$317$	2.21555e17	−	3.83744e17i	0.688757	−	1.19296i	0.972240	−	0.233985i	$-0.0751766\pi$
$318$	1.90162e16	−	1.09790e16i	0.0578276	−	0.0333868i
$319$	3.33371e17	+	5.77416e17i	0.991730	+	1.71773i
$320$	5.83794e16	+	3.37054e16i	0.169906	+	0.0980955i
$321$			7.14465e16i			0.203445i
$322$	−4.46947e16	−	1.85954e17i	−0.124527	−	0.518101i
$323$	5.05043e17			1.37693
$324$	−8.83444e16	+	1.53017e17i	−0.235702	+	0.408249i
$325$	−3.35302e17	+	1.93587e17i	−0.875493	+	0.505466i
$326$	−1.50157e17	−	2.60080e17i	−0.383728	−	0.664637i
$327$	3.17841e16	+	1.83505e16i	0.0795015	+	0.0459002i
$328$			1.65784e17i			0.405905i
$329$	2.32268e16	+	2.44632e16i	0.0556697	+	0.0586331i
$330$	−6.71716e16			−0.157612
$331$	−2.74168e17	+	4.74874e17i	−0.629827	+	1.09089i	0.357759	+	0.933814i	$0.383541\pi$
$331$	−2.74168e17	+	4.74874e17i	−0.629827	+	1.09089i	−0.987586	+	0.157079i	$0.949792\pi$
$332$	−3.86661e16	+	2.23239e16i	−0.0869689	+	0.0502115i
$333$	−1.90230e17	−	3.29489e17i	−0.418958	−	0.725656i
$334$	−5.93897e16	−	3.42886e16i	−0.128081	−	0.0739478i
$335$		−	5.96573e17i		−	1.25994i
$336$	−4.75084e15	+	1.60539e16i	−0.00982642	+	0.0332051i
$337$	7.64047e16			0.154779			0.0773893	−	0.997001i	$-0.475342\pi$
$337$	7.64047e16			0.154779			0.0773893	+	0.997001i	$0.475342\pi$
$338$	9.31541e16	−	1.61348e17i	0.184835	−	0.320144i
$339$	3.53181e16	−	2.03909e16i	0.0686434	−	0.0396313i
$340$	−2.60219e17	−	4.50713e17i	−0.495435	−	0.858119i
$341$	−7.89087e17	−	4.55579e17i	−1.47178	−	0.849735i
$342$			4.13892e17i			0.756318i
$343$	−3.63077e17	−	4.24439e17i	−0.650040	−	0.759900i
$344$	2.70579e17			0.474663
$345$	4.76532e16	−	8.25378e16i	0.0819141	−	0.141879i
$346$	−1.03120e16	+	5.95366e15i	−0.0173705	+	0.0100288i
$347$	2.81212e17	+	4.87074e17i	0.464224	+	0.804060i	0.999166	−	0.0408287i	$-0.0129998\pi$
$347$	2.81212e17	+	4.87074e17i	0.464224	+	0.804060i	−0.534942	+	0.844889i	$0.679666\pi$
$348$	7.17188e16	+	4.14069e16i	0.116032	+	0.0669912i
$349$		−	6.65335e17i		−	1.05502i	−0.849547	−	0.527512i	$-0.823125\pi$
$349$		−	6.65335e17i		−	1.05502i	0.849547	−	0.527512i	$-0.176875\pi$
$350$	−6.38411e17	−	1.88926e17i	−0.992257	−	0.293640i
$351$	1.24406e17			0.189536
$352$	−6.06783e16	+	1.05098e17i	−0.0906222	+	0.156962i
$353$	−6.22159e17	+	3.59204e17i	−0.910916	+	0.525918i	−0.880726	−	0.473627i	$-0.842945\pi$
$353$	−6.22159e17	+	3.59204e17i	−0.910916	+	0.525918i	−0.0301902	+	0.999544i	$0.509611\pi$
$354$	1.38162e16	+	2.39303e16i	0.0198319	+	0.0343499i
$355$	4.96595e17	+	2.86709e17i	0.698882	+	0.403500i
$356$		−	3.08290e17i		−	0.425412i
$357$	9.37356e16	−	8.89980e16i	0.126831	−	0.120421i
$358$	2.15986e17			0.286579
$359$	4.26233e17	−	7.38257e17i	0.554607	−	0.960608i	−0.443327	−	0.896360i	$-0.646202\pi$
$359$	4.26233e17	−	7.38257e17i	0.554607	−	0.960608i	0.997934	−	0.0642478i	$-0.0204648\pi$
$360$	3.69368e17	−	2.13255e17i	0.471348	−	0.272133i
$361$	7.55981e16	+	1.30940e17i	0.0946151	+	0.163878i
$362$	4.96516e17	+	2.86664e17i	0.609499	+	0.351895i
$363$		−	5.88831e15i		−	0.00708997i
$364$	−2.84340e17	+	6.83420e16i	−0.335836	+	0.0807194i
$365$	−6.70052e17			−0.776352
$366$	−1.86350e16	+	3.22768e16i	−0.0211818	+	0.0366879i
$367$	−1.02807e18	+	5.93559e17i	−1.14647	+	0.661913i	−0.948024	−	0.318199i	$-0.896922\pi$
$367$	−1.02807e18	+	5.93559e17i	−1.14647	+	0.661913i	−0.198444	+	0.980112i	$0.563589\pi$
$368$	−8.60934e16	−	1.49118e17i	−0.0941966	−	0.163153i
$369$	9.08388e17	+	5.24458e17i	0.975185	+	0.563023i
$370$			9.00078e17i			0.948130i
$371$	1.54133e17	+	6.41279e17i	0.159323	+	0.662872i
$372$	−1.13172e17			−0.114799
$373$	−1.89839e17	+	3.28811e17i	−0.188984	+	0.327329i	−0.944912	−	0.327325i	$-0.893853\pi$
$373$	−1.89839e17	+	3.28811e17i	−0.188984	+	0.327329i	0.755928	+	0.654655i	$0.227186\pi$
$374$	8.11399e17	−	4.68461e17i	0.792744	−	0.457691i
$375$	−5.25324e16	−	9.09887e16i	−0.0503742	−	0.0872507i
$376$	2.63020e16	+	1.51854e16i	0.0247556	+	0.0142926i
$377$			1.44653e18i			1.33640i
$378$	1.47298e17	+	1.55139e17i	0.133584	+	0.140695i
$379$	−1.86804e18			−1.66307			−0.831537	−	0.555470i	$-0.812539\pi$
$379$	−1.86804e18			−1.66307			−0.831537	+	0.555470i	$0.812539\pi$
$380$	4.89584e17	−	8.47985e17i	0.427900	−	0.741144i
$381$	−9.03749e16	+	5.21780e16i	−0.0775484	+	0.0447726i
$382$	1.01114e17	+	1.75135e17i	0.0851861	+	0.147547i
$383$	1.23661e18	+	7.13958e17i	1.02292	+	0.590584i	0.914949	−	0.403570i	$-0.132231\pi$
$383$	1.23661e18	+	7.13958e17i	1.02292	+	0.590584i	0.107972	+	0.994154i	$0.465564\pi$
$384$			1.50733e16i			0.0122430i
$385$	5.72526e17	−	1.93466e18i	0.456636	−	1.54305i
$386$	9.39415e17			0.735778
$387$	8.55981e17	−	1.48260e18i	0.658396	−	1.14038i
$388$	8.13583e17	−	4.69722e17i	0.614582	−	0.354829i
$389$	9.21907e17	+	1.59679e18i	0.683974	+	1.18468i	0.973758	+	0.227586i	$0.0730834\pi$
$389$	9.21907e17	+	1.59679e18i	0.683974	+	1.18468i	−0.289783	+	0.957092i	$0.593583\pi$
$390$	−1.26207e17	−	7.28658e16i	−0.0919671	−	0.0530972i
$391$			1.32935e18i			0.951487i
$392$	−4.21886e17	−	2.73665e17i	−0.296615	−	0.192405i
$393$	−2.90134e17			−0.200378
$394$	3.20046e17	−	5.54336e17i	0.217140	−	0.376097i
$395$	−3.03493e17	+	1.75222e17i	−0.202287	+	0.116791i
$396$	3.83913e17	+	6.64957e17i	0.251401	+	0.435439i
$397$	4.98429e17	+	2.87768e17i	0.320678	+	0.185144i	0.651695	−	0.758481i	$-0.274058\pi$
$397$	4.98429e17	+	2.87768e17i	0.320678	+	0.185144i	−0.331017	+	0.943625i	$0.607392\pi$
$398$			2.81962e17i			0.178242i
$399$	2.33189e17	+	6.90079e16i	0.144843	+	0.0428636i
$400$	−5.99417e17			−0.365855
$401$	3.23678e17	−	5.60626e17i	0.194134	−	0.336250i	−0.752482	−	0.658613i	$-0.771144\pi$
$401$	3.23678e17	−	5.60626e17i	0.194134	−	0.336250i	0.946616	+	0.322362i	$0.104477\pi$
$402$	1.15524e17	−	6.66979e16i	0.0680911	−	0.0393124i
$403$	−9.88399e17	−	1.71196e18i	−0.572528	−	0.991648i
$404$	9.37582e16	+	5.41313e16i	0.0533752	+	0.0308162i
$405$		−	2.64471e18i		−	1.47977i
$406$	−1.80387e18	+	1.71270e18i	−0.992028	+	0.941888i
$407$	−1.62037e18			−0.875898
$408$	5.81859e16	−	1.00781e17i	0.0309170	−	0.0535498i
$409$	−1.80402e18	+	1.04155e18i	−0.942278	+	0.544025i	−0.890674	−	0.454643i	$-0.849767\pi$
$409$	−1.80402e18	+	1.04155e18i	−0.942278	+	0.544025i	−0.0516046	+	0.998668i	$0.516434\pi$
$410$	−1.24074e18	−	2.14903e18i	−0.637080	−	1.10345i
$411$	−2.98852e17	−	1.72542e17i	−0.150856	−	0.0870969i
$412$			8.26804e17i			0.410320i
$413$	−8.06994e17	+	1.93964e17i	−0.393749	+	0.0946389i
$414$	−1.08943e18			−0.522633
$415$	3.34148e17	−	5.78762e17i	0.157617	−	0.273000i
$416$	−2.28014e17	+	1.31644e17i	−0.105757	+	0.0610588i
$417$	2.64111e17	+	4.57453e17i	0.120458	+	0.208639i
$418$	1.52659e18	+	8.81377e17i	0.684681	+	0.395301i
$419$		−	5.16197e17i		−	0.227676i	−0.993499	−	0.113838i	$-0.963686\pi$
$419$		−	5.16197e17i		−	0.227676i	0.993499	−	0.113838i	$-0.0363145\pi$
$420$	−5.85643e16	−	2.43659e17i	−0.0254032	−	0.105691i
$421$	1.69789e18			0.724328			0.362164	−	0.932114i	$-0.382038\pi$
$421$	1.69789e18			0.724328			0.362164	+	0.932114i	$0.382038\pi$
$422$	3.05977e17	−	5.29968e17i	0.128381	−	0.222363i
$423$	1.66413e17	−	9.60786e16i	0.0686760	−	0.0396501i
$424$	2.96901e17	+	5.14247e17i	0.120517	+	0.208742i
$425$	4.00774e18	+	2.31387e18i	1.60021	+	0.923882i
$426$			1.28218e17i			0.0503597i
$427$	−7.70795e17	−	8.11826e17i	−0.297813	−	0.313666i
$428$	−1.93209e18			−0.734382
$429$	1.31177e17	−	2.27206e17i	0.0490521	−	0.0849607i
$430$	−3.50748e18	+	2.02504e18i	−1.29037	+	0.744997i
$431$	1.38643e18	+	2.40137e18i	0.501832	+	0.869198i	0.999998	+	0.00211633i	$0.000673649\pi$
$431$	1.38643e18	+	2.40137e18i	0.501832	+	0.869198i	−0.498166	+	0.867082i	$0.665993\pi$
$432$	1.66800e17	+	9.63017e16i	0.0594030	+	0.0342964i
$433$		−	5.15442e18i		−	1.80619i	−0.429436	−	0.903097i	$-0.641288\pi$
$433$		−	5.15442e18i		−	1.80619i	0.429436	−	0.903097i	$-0.358712\pi$
$434$	9.64601e17	−	3.25955e18i	0.332598	−	1.12390i
$435$	−1.23957e18			−0.420578
$436$	−4.96244e17	+	8.59521e17i	−0.165688	+	0.286979i
$437$	−2.16600e18	+	1.25054e18i	−0.711687	+	0.410892i
$438$	−7.49130e16	−	1.29753e17i	−0.0242236	−	0.0419565i
$439$	−4.08508e18	−	2.35852e18i	−1.30002	−	0.750566i	−0.319611	−	0.947549i	$-0.603552\pi$
$439$	−4.08508e18	−	2.35852e18i	−1.30002	−	0.750566i	−0.980407	+	0.196983i	$0.936886\pi$
$440$		−	1.81649e18i		−	0.568937i
$441$	−2.83415e18	+	1.44592e18i	−0.873680	+	0.445734i
$442$	2.03269e18			0.616760
$443$	9.99797e17	−	1.73170e18i	0.298597	−	0.517185i	−0.677218	−	0.735782i	$-0.736815\pi$
$443$	9.99797e17	−	1.73170e18i	0.298597	−	0.517185i	0.975815	+	0.218597i	$0.0701480\pi$
$444$	−1.74297e17	+	1.00630e17i	−0.0512399	+	0.0295834i
$445$	2.30727e18	+	3.99631e18i	0.667696	+	1.15648i
$446$	−9.74341e17	−	5.62536e17i	−0.277567	−	0.160253i
$447$			8.67763e17i			0.243360i
$448$	−4.34137e17	−	1.28475e17i	−0.119862	−	0.0354708i
$449$	4.78871e18			1.30165			0.650825	−	0.759228i	$-0.274423\pi$
$449$	4.78871e18			1.30165			0.650825	+	0.759228i	$0.274423\pi$
$450$	−1.89626e18	+	3.28442e18i	−0.507470	+	0.878964i
$451$	3.86880e18	−	2.23365e18i	1.01939	−	0.588545i
$452$	5.51421e17	+	9.55089e17i	0.143059	+	0.247785i
$453$	2.56079e17	+	1.47847e17i	0.0654163	+	0.0377681i
$454$			2.16939e18i			0.545691i
$455$	3.17437e18	−	3.01393e18i	0.786281	−	0.746541i
$456$	2.18946e17			0.0534050
$457$	1.31456e18	−	2.27689e18i	0.315768	−	0.546927i	−0.663832	−	0.747882i	$-0.731071\pi$
$457$	1.31456e18	−	2.27689e18i	0.315768	−	0.546927i	0.979601	+	0.200955i	$0.0644044\pi$
$458$	2.75178e18	−	1.58874e18i	0.650961	−	0.375833i
$459$	−7.43489e17	−	1.28776e18i	−0.173215	−	0.300017i
$460$	2.23203e18	+	1.28866e18i	0.512148	+	0.295689i
$461$			6.70171e18i			1.51453i	0.653105	+	0.757267i	$0.273466\pi$
$461$			6.70171e18i			1.51453i	−0.653105	+	0.757267i	$0.726534\pi$
$462$	4.38649e17	−	1.05431e17i	0.0976390	−	0.0234679i
$463$	1.64820e18			0.361363			0.180681	−	0.983542i	$-0.442170\pi$
$463$	1.64820e18			0.361363			0.180681	+	0.983542i	$0.442170\pi$
$464$	−1.11975e18	+	1.93946e18i	−0.241821	+	0.418846i
$465$	1.46703e18	−	8.46989e17i	0.312081	−	0.180180i
$466$	−1.57990e18	−	2.73647e18i	−0.331077	−	0.573442i
$467$	8.69730e16	+	5.02139e16i	0.0179542	+	0.0103659i	0.508950	−	0.860796i	$-0.330034\pi$
$467$	8.69730e16	+	5.02139e16i	0.0179542	+	0.0103659i	−0.490996	+	0.871162i	$0.663367\pi$
$468$			1.66583e18i			0.338774i
$469$	9.36364e17	+	3.89578e18i	0.187601	+	0.780521i
$470$	−4.54597e17			−0.0897309
$471$	9.15999e16	−	1.58656e17i	0.0178135	−	0.0308539i
$472$	−6.47135e17	+	3.73624e17i	−0.123994	+	0.0715880i
$473$	−3.64559e18	−	6.31435e18i	−0.688241	−	1.19207i
$474$	−6.78621e16	−	3.91802e16i	−0.0126235	−	0.00728816i
$475$			8.70677e18i			1.59589i
$476$	2.40673e18	+	2.53485e18i	0.434689	+	0.457828i
$477$	3.75699e18			0.668670
$478$	3.28972e18	−	5.69797e18i	0.576984	−	0.999366i
$479$	−8.64178e18	+	4.98933e18i	−1.49367	+	0.862370i	−0.999974	−	0.00726427i	$-0.997688\pi$
$479$	−8.64178e18	+	4.98933e18i	−1.49367	+	0.862370i	−0.493696	+	0.869635i	$0.664354\pi$
$480$	−1.12810e17	−	1.95392e17i	−0.0192158	−	0.0332827i
$481$	−3.04448e18	−	1.75773e18i	−0.511090	−	0.295078i
$482$		−	4.38957e18i		−	0.726260i
$483$	−1.81640e17	+	6.13790e17i	−0.0296197	+	0.100090i
$484$	1.59235e17			0.0255929
$485$	−7.03089e18	+	1.21779e19i	−1.11383	+	1.92921i
$486$	1.58813e18	−	9.16906e17i	0.247988	−	0.143176i
$487$	−1.85394e18	−	3.21112e18i	−0.285360	−	0.494258i	0.687336	−	0.726339i	$-0.258780\pi$
$487$	−1.85394e18	−	3.21112e18i	−0.285360	−	0.494258i	−0.972696	+	0.232081i	$0.925447\pi$
$488$	−8.72845e17	−	5.03937e17i	−0.132434	−	0.0764606i
$489$			1.00514e18i			0.150336i
$490$	7.51697e18	+	3.90035e17i	1.10833	+	0.0575083i
$491$	−8.22467e18			−1.19550			−0.597748	−	0.801684i	$-0.703938\pi$
$491$	−8.22467e18			−1.19550			−0.597748	+	0.801684i	$0.703938\pi$
$492$	2.77434e17	−	4.80530e17i	0.0397561	−	0.0688596i
$493$	1.49734e19	−	8.64489e18i	2.11540	−	1.22132i
$494$	1.91218e18	+	3.31200e18i	0.266343	+	0.461320i
$495$	−9.95320e18	−	5.74648e18i	−1.36687	−	0.789161i
$496$		−	3.06045e18i		−	0.414394i
$497$	−3.69291e18	−	1.09285e18i	−0.493031	−	0.145903i
$498$	1.49434e17			0.0196717
$499$	6.57038e17	−	1.13802e18i	0.0852877	−	0.147723i	−0.820226	−	0.572040i	$-0.806152\pi$
$499$	6.57038e17	−	1.13802e18i	0.0852877	−	0.147723i	0.905514	+	0.424317i	$0.139486\pi$
$500$	2.46056e18	−	1.42061e18i	0.314952	−	0.181838i
$501$	1.14762e17	+	1.98774e17i	0.0144855	+	0.0250897i
$502$	−7.41938e18	−	4.28358e18i	−0.923510	−	0.533189i
$503$		−	7.73353e18i		−	0.949297i	−0.880175	−	0.474649i	$-0.842575\pi$
$503$		−	7.73353e18i		−	0.949297i	0.880175	−	0.474649i	$-0.157425\pi$
$504$	−2.07735e18	+	1.97236e18i	−0.251476	+	0.238766i
$505$	−1.62050e18			−0.193468
$506$	−2.31992e18	+	4.01822e18i	−0.273162	+	0.473130i
$507$	−5.40021e17	+	3.11781e17i	−0.0627126	+	0.0362071i
$508$	−1.41102e18	−	2.44396e18i	−0.161617	−	0.279930i
$509$	7.89384e17	+	4.55751e17i	0.0891792	+	0.0514877i	0.543926	−	0.839133i	$-0.316937\pi$
$509$	7.89384e17	+	4.55751e17i	0.0891792	+	0.0514877i	−0.454747	+	0.890621i	$0.650270\pi$
$510$			1.74188e18i			0.194100i
$511$	4.37562e18	−	1.05170e18i	0.480943	−	0.115596i
$512$	−4.07619e17			−0.0441942
$513$	1.39882e18	−	2.42283e18i	0.149603	−	0.259120i
$514$	−5.88841e18	+	3.39968e18i	−0.621236	+	0.358671i
$515$	−6.18788e18	−	1.07177e19i	−0.644008	−	1.11545i
$516$	−7.84284e17	−	4.52807e17i	−0.0805240	−	0.0464906i
$517$		−	8.18392e17i		−	0.0828948i
$518$	−1.41274e18	−	5.87775e18i	−0.141174	−	0.587358i
$519$	3.98531e16			0.00392908
$520$	1.97047e18	−	3.41296e18i	0.191667	−	0.331977i
$521$	−2.88677e18	+	1.66668e18i	−0.277044	+	0.159951i	−0.632084	−	0.774899i	$-0.717800\pi$
$521$	−2.88677e18	+	1.66668e18i	−0.277044	+	0.159951i	0.355040	+	0.934851i	$0.384467\pi$
$522$	7.08465e18	+	1.22710e19i	0.670850	+	1.16195i
$523$	−2.04274e18	−	1.17938e18i	−0.190854	−	0.110190i	0.401528	−	0.915847i	$-0.368479\pi$
$523$	−2.04274e18	−	1.17938e18i	−0.190854	−	0.110190i	−0.592382	+	0.805657i	$0.701812\pi$
$524$		−	7.84595e18i		−	0.723314i
$525$	1.53430e18	+	1.61597e18i	0.139571	+	0.147000i
$526$	1.42213e19			1.27656
$527$	−1.18140e19	+	2.04624e19i	−1.04646	+	1.81252i
$528$	3.51756e17	−	2.03087e17i	0.0307471	−	0.0177519i
$529$	2.50479e18	+	4.33843e18i	0.216064	+	0.374234i
$530$	−7.69734e18	−	4.44406e18i	−0.655254	−	0.378311i
$531$			4.72785e18i			0.397193i
$532$	−1.86615e18	+	6.30601e18i	−0.154726	+	0.522845i
$533$	9.69200e18			0.793091
$534$	−5.15914e17	+	8.93589e17i	−0.0416667	+	0.0721688i
$535$	2.50454e19	−	1.44600e19i	1.99642	−	1.15263i
$536$	1.80368e18	+	3.12406e18i	0.141908	+	0.245791i
$537$	−6.26044e17	−	3.61447e17i	−0.0486166	−	0.0280688i
$538$		−	2.08595e18i		−	0.159893i
$539$	−7.02162e17	+	1.35325e19i	−0.0531271	+	1.02390i
$540$	−2.88293e18			−0.215316
$541$	−1.21947e19	+	2.11219e19i	−0.899065	+	1.55723i	−0.0703728	+	0.997521i	$0.522419\pi$
$541$	−1.21947e19	+	2.11219e19i	−0.899065	+	1.55723i	−0.828692	+	0.559705i	$0.810914\pi$
$542$	−5.27825e18	+	3.04740e18i	−0.384145	+	0.221786i
$543$	−9.59446e17	−	1.66181e18i	−0.0689322	−	0.119394i
$544$	2.72537e18	+	1.57349e18i	0.193301	+	0.111602i
$545$		−	1.48558e19i		−	1.04021i
$546$	9.38537e17	+	2.77742e17i	0.0648788	+	0.0191997i
$547$	2.32496e19			1.58673			0.793367	−	0.608743i	$-0.208326\pi$
$547$	2.32496e19			1.58673			0.793367	+	0.608743i	$0.208326\pi$
$548$	4.66597e18	−	8.08170e18i	0.314397	−	0.544552i
$549$	−5.52251e18	+	3.18842e18i	−0.367392	+	0.212114i
$550$	8.07612e18	+	1.39882e19i	0.530473	+	0.918807i
$551$	2.81714e19	+	1.62648e19i	1.82704	+	1.05484i
$552$			5.76299e17i			0.0369041i
$553$	1.70687e18	−	1.62060e18i	0.107926	−	0.102471i
$554$	−1.50168e19			−0.937582
$555$	1.50625e18	−	2.60891e18i	0.0928640	−	0.160845i
$556$	−1.23707e19	+	7.14222e18i	−0.753131	+	0.434820i
$557$	−7.09209e18	−	1.22839e19i	−0.426371	−	0.738496i	0.570176	−	0.821522i	$-0.306875\pi$
$557$	−7.09209e18	−	1.22839e19i	−0.426371	−	0.738496i	−0.996547	+	0.0830259i	$0.973542\pi$
$558$	−1.67693e19	−	9.68177e18i	−0.995579	−	0.574798i
$559$		−	1.58185e19i		−	0.927436i
$560$	6.58916e18	−	1.58373e18i	0.381517	−	0.0916988i
$561$	−3.13582e18			−0.179313
$562$	−7.12916e18	+	1.23481e19i	−0.402610	+	0.697340i
$563$	1.65687e19	−	9.56594e18i	0.924123	−	0.533542i	0.0391746	−	0.999232i	$-0.487527\pi$
$563$	1.65687e19	−	9.56594e18i	0.924123	−	0.533542i	0.884948	+	0.465690i	$0.154194\pi$
$564$	−5.08248e16	−	8.80311e16i	−0.00279977	−	0.00484934i
$565$	−1.42960e19	−	8.25377e18i	−0.777811	−	0.449069i
$566$			4.37791e18i			0.235262i
$567$	4.15107e18	+	1.72707e19i	0.220332	+	0.916702i
$568$	−3.46735e18			−0.181785
$569$	1.29329e19	−	2.24005e19i	0.669746	−	1.16003i	−0.308229	−	0.951312i	$-0.599736\pi$
$569$	1.29329e19	−	2.24005e19i	0.669746	−	1.16003i	0.977975	−	0.208722i	$-0.0669304\pi$
$570$	−2.83815e18	+	1.63861e18i	−0.145182	+	0.0838207i
$571$	6.26423e18	+	1.08500e19i	0.316530	+	0.548246i	0.979762	−	0.200168i	$-0.0641488\pi$
$571$	6.26423e18	+	1.08500e19i	0.316530	+	0.548246i	−0.663231	+	0.748414i	$0.730815\pi$
$572$	6.14421e18	+	3.54736e18i	0.306686	+	0.177065i
$573$		−	6.76847e17i		−	0.0333740i
$574$	1.14754e19	+	1.20863e19i	0.558966	+	0.588722i
$575$	−2.29176e19			−1.10279
$576$	−1.28951e18	+	2.23349e18i	−0.0613009	+	0.106176i
$577$	1.42233e19	−	8.21181e18i	0.667988	−	0.385663i	−0.127326	−	0.991861i	$-0.540639\pi$
$577$	1.42233e19	−	8.21181e18i	0.667988	−	0.385663i	0.795314	+	0.606198i	$0.207306\pi$
$578$	−4.52810e18	−	7.84290e18i	−0.210098	−	0.363900i
$579$	−2.72293e18	−	1.57208e18i	−0.124821	−	0.0720652i
$580$		−	3.35211e19i		−	1.51818i
$581$	−1.27367e18	+	4.30394e18i	−0.0569934	+	0.192590i
$582$	−3.14426e18			−0.139014
$583$	8.00045e18	−	1.38572e19i	0.349490	−	0.605334i
$584$	3.50885e18	−	2.02584e18i	0.151452	−	0.0874408i
$585$	−1.24672e19	−	2.15939e19i	−0.531715	−	0.920958i
$586$	9.39509e18	+	5.42426e18i	0.395929	+	0.228590i
$587$			3.59730e19i			1.49799i	0.662574	+	0.748996i	$0.269464\pi$
$587$			3.59730e19i			1.49799i	−0.662574	+	0.748996i	$0.730536\pi$
$588$	7.64882e17	+	1.49924e18i	0.0314741	+	0.0616922i
$589$	−4.44543e19			−1.80762
$590$	5.59247e18	−	9.68644e18i	0.224719	−	0.389225i
$591$	−1.85533e18	+	1.07118e18i	−0.0736731	+	0.0425352i
$592$	−2.72130e18	−	4.71342e18i	−0.106788	−	0.184963i
$593$	−1.16787e19	−	6.74272e18i	−0.452911	−	0.261488i	0.256148	−	0.966638i	$-0.417547\pi$
$593$	−1.16787e19	−	6.74272e18i	−0.452911	−	0.261488i	−0.709059	+	0.705149i	$0.750880\pi$
$594$		−	5.19001e18i		−	0.198913i
$595$	−5.01691e19	−	1.48466e19i	−1.90028	−	0.562352i
$596$	−2.34665e19			−0.878465
$597$	4.71855e17	−	8.17277e17i	0.0174577	−	0.0302377i
$598$	−8.71771e18	+	5.03317e18i	−0.318782	+	0.184049i
$599$	3.51764e18	+	6.09273e18i	0.127135	+	0.220204i	0.922565	−	0.385841i	$-0.126089\pi$
$599$	3.51764e18	+	6.09273e18i	0.127135	+	0.220204i	−0.795431	+	0.606045i	$0.792755\pi$
$600$	1.73743e18	+	1.00311e18i	0.0620653	+	0.0358334i
$601$			3.63144e19i			1.28220i	0.767455	+	0.641102i	$0.221523\pi$
$601$			3.63144e19i			1.28220i	−0.767455	+	0.641102i	$0.778477\pi$
$602$	1.97263e19	−	1.87293e19i	0.688447	−	0.653652i
$603$	2.28238e19			0.787348
$604$	−3.99815e18	+	6.92500e18i	−0.136333	+	0.236136i
$605$	−2.06413e18	+	1.19173e18i	−0.0695745	+	0.0401688i
$606$	−1.81174e17	−	3.13803e17i	−0.00603655	−	0.0104556i
$607$	1.05984e19	+	6.11900e18i	0.349076	+	0.201539i	0.664278	−	0.747485i	$-0.268739\pi$
$607$	1.05984e19	+	6.11900e18i	0.349076	+	0.201539i	−0.315202	+	0.949025i	$0.602072\pi$
$608$			5.92084e18i			0.192778i
$609$	8.09475e18	−	1.94560e18i	0.260545	−	0.0626228i
$610$	1.50861e19			0.480029
$611$	8.87768e17	−	1.53766e18i	0.0279261	−	0.0483695i
$612$	1.72435e19	−	9.95552e18i	0.536247	−	0.309602i
$613$	−1.29404e19	−	2.24135e19i	−0.397856	−	0.689106i	0.595605	−	0.803277i	$-0.296912\pi$
$613$	−1.29404e19	−	2.24135e19i	−0.397856	−	0.689106i	−0.993461	+	0.114171i	$0.963579\pi$
$614$	1.06983e19	+	6.17664e18i	0.325188	+	0.187747i
$615$			8.30537e18i			0.249593i
$616$	2.85111e18	+	1.18622e19i	0.0847129	+	0.352451i
$617$	1.38916e19			0.408091			0.204045	−	0.978961i	$-0.434591\pi$
$617$	1.38916e19			0.408091			0.204045	+	0.978961i	$0.434591\pi$
$618$	1.38363e18	−	2.39652e18i	0.0401885	−	0.0696085i
$619$	−1.19128e19	+	6.87784e18i	−0.342120	+	0.197523i	−0.661209	−	0.750202i	$-0.729956\pi$
$619$	−1.19128e19	+	6.87784e18i	−0.342120	+	0.197523i	0.319089	+	0.947725i	$0.396623\pi$
$620$	2.29047e19	+	3.96721e19i	0.650404	+	1.12653i
$621$	6.37727e18	+	3.68192e18i	0.179058	+	0.103379i
$622$		−	8.42182e18i		−	0.233816i
$623$	−2.13396e19	−	2.24756e19i	−0.585828	−	0.617013i
$624$	8.81210e17			0.0239215
$625$	5.99441e18	−	1.03826e19i	0.160911	−	0.278706i
$626$	−3.91102e19	+	2.25803e19i	−1.03817	+	0.599389i
$627$	−2.94992e18	−	5.10941e18i	−0.0774349	−	0.134121i
$628$	4.29045e18	+	2.47709e18i	0.111374	+	0.0643020i
$629$			4.20190e19i			1.07868i
$630$	1.21671e19	−	4.11145e19i	0.308889	−	1.04379i
$631$	1.52607e19			0.383149			0.191575	−	0.981478i	$-0.438641\pi$
$631$	1.52607e19			0.383149			0.191575	+	0.981478i	$0.438641\pi$
$632$	1.05953e18	−	1.83516e18i	0.0263084	−	0.0455674i
$633$	−1.77377e18	+	1.02409e18i	−0.0435584	+	0.0251485i
$634$	−2.00528e19	−	3.47325e19i	−0.487025	−	0.843551i
$635$	3.65817e19	+	2.11205e19i	0.878715	+	0.507326i
$636$		−	1.98742e18i		−	0.0472160i
$637$	−1.59989e19	+	2.46642e19i	−0.375937	+	0.579550i
$638$	6.03466e19			1.40252
$639$	−1.09690e19	+	1.89989e19i	−0.252151	+	0.436738i
$640$	5.28390e18	−	3.05066e18i	0.120142	−	0.0693640i
$641$	3.71311e18	+	6.43129e18i	0.0835086	+	0.144641i	0.904755	−	0.425933i	$-0.140054\pi$
$641$	3.71311e18	+	6.43129e18i	0.0835086	+	0.144641i	−0.821246	+	0.570574i	$0.806721\pi$
$642$	5.60024e18	+	3.23330e18i	0.124584	+	0.0719285i
$643$		−	7.17838e19i		−	1.57961i	−0.613359	−	0.789804i	$-0.710182\pi$
$643$		−	7.17838e19i		−	1.57961i	0.613359	−	0.789804i	$-0.289818\pi$
$644$	−1.65984e19	−	4.91199e18i	−0.361298	−	0.106919i
$645$	1.35554e19			0.291873
$646$	2.28556e19	−	3.95871e19i	0.486817	−	0.843191i
$647$	−3.96155e19	+	2.28720e19i	−0.834709	+	0.481919i	−0.855462	−	0.517865i	$-0.826727\pi$
$647$	−3.96155e19	+	2.28720e19i	−0.834709	+	0.481919i	0.0207534	+	0.999785i	$0.493394\pi$
$648$	7.99602e18	+	1.38495e19i	0.166667	+	0.288675i
$649$	1.74381e19	+	1.00679e19i	0.359572	+	0.207599i
$650$			3.50430e19i			0.714837i
$651$	−8.25069e18	+	7.83368e18i	−0.166503	+	0.158088i
$652$	−2.71814e19			−0.542674
$653$	3.50394e19	−	6.06900e19i	0.692092	−	1.19874i	−0.279059	−	0.960274i	$-0.590022\pi$
$653$	3.50394e19	−	6.06900e19i	0.692092	−	1.19874i	0.971151	−	0.238465i	$-0.0766442\pi$
$654$	2.87676e18	−	1.66090e18i	0.0562160	−	0.0324563i
$655$	5.87199e19	+	1.01706e20i	1.13526	+	1.96633i
$656$	1.29947e19	+	7.50251e18i	0.248565	+	0.143509i
$657$		−	2.56350e19i		−	0.485150i
$658$	2.96865e18	−	7.13524e17i	0.0555875	−	0.0133606i
$659$	8.31252e19			1.54005			0.770025	−	0.638014i	$-0.220244\pi$
$659$	8.31252e19			1.54005			0.770025	+	0.638014i	$0.220244\pi$
$660$	−3.03984e18	+	5.26516e18i	−0.0557241	+	0.0965170i
$661$	−4.42710e19	+	2.55599e19i	−0.802988	+	0.463605i	−0.844515	−	0.535532i	$-0.820111\pi$
$661$	−4.42710e19	+	2.55599e19i	−0.802988	+	0.463605i	0.0415269	+	0.999137i	$0.486778\pi$
$662$	2.48149e19	+	4.29807e19i	0.445355	+	0.771378i
$663$	−5.89183e18	−	3.40165e18i	−0.104630	−	0.0604081i
$664$			4.04106e18i			0.0710098i
$665$	−2.30043e19	−	9.57102e19i	−0.399997	−	1.66420i
$666$	−3.44354e19			−0.592496
$667$	−4.28114e19	+	7.41515e19i	−0.728918	+	1.26252i
$668$	−5.37534e18	+	3.10345e18i	−0.0905671	+	0.0522890i
$669$	1.88278e18	+	3.26106e18i	0.0313918	+	0.0543721i
$670$	−4.67615e19	−	2.69978e19i	−0.771552	−	0.445456i
$671$			2.71588e19i			0.443458i
$672$	1.04336e18	+	1.09890e18i	0.0168597	+	0.0177572i
$673$	−1.21090e20			−1.93644			−0.968219	−	0.250104i	$-0.919535\pi$
$673$	−1.21090e20			−1.93644			−0.968219	+	0.250104i	$0.919535\pi$
$674$	3.45768e18	−	5.98888e18i	0.0547225	−	0.0947821i
$675$	2.22006e19	−	1.28175e19i	0.347726	−	0.200760i
$676$	−8.43135e18	−	1.46035e19i	−0.130698	−	0.226376i
$677$	1.25953e18	+	7.27191e17i	0.0193236	+	0.0111565i	0.509631	−	0.860393i	$-0.329782\pi$
$677$	1.25953e18	+	7.27191e17i	0.0193236	+	0.0111565i	−0.490307	+	0.871550i	$0.663115\pi$
$678$		−	3.69115e18i		−	0.0560471i
$679$	2.67996e19	−	9.05603e19i	0.402754	−	1.36097i
$680$	−4.71047e19			−0.700651
$681$	3.63041e18	−	6.28806e18i	0.0534473	−	0.0925735i
$682$	−7.14200e19	+	4.12343e19i	−1.04071	+	0.600853i
$683$	−6.49060e19	−	1.12420e20i	−0.936138	−	1.62144i	−0.772593	−	0.634902i	$-0.781041\pi$
$683$	−6.49060e19	−	1.12420e20i	−0.936138	−	1.62144i	−0.163545	−	0.986536i	$-0.552293\pi$
$684$	3.24424e19	+	1.87306e19i	0.463148	+	0.267399i
$685$			1.39682e20i			1.97382i
$686$	−4.97001e19	+	9.25140e18i	−0.695166	+	0.129401i
$687$	−1.06348e19			−0.147243
$688$	1.22450e19	−	2.12090e19i	0.167819	−	0.290671i
$689$	3.00638e19	−	1.73573e19i	0.407858	−	0.235477i
$690$	−4.31308e18	−	7.47047e18i	−0.0579220	−	0.100324i
$691$	5.86115e19	+	3.38393e19i	0.779177	+	0.449858i	0.836139	−	0.548518i	$-0.184808\pi$
$691$	5.86115e19	+	3.38393e19i	0.779177	+	0.449858i	−0.0569615	+	0.998376i	$0.518141\pi$
$692$			1.07773e18i			0.0141829i
$693$	7.40166e19	+	2.19038e19i	0.964266	+	0.285356i
$694$	5.09049e19			0.656512
$695$	1.06906e20	−	1.85167e20i	1.36493	−	2.36412i
$696$	6.49125e18	−	3.74772e18i	0.0820471	−	0.0473699i
$697$	−5.79224e19	−	1.00325e20i	−0.724799	−	1.25539i
$698$	−5.21514e19	−	3.01096e19i	−0.646068	−	0.373007i
$699$			1.05757e19i			0.129708i
$700$	−4.36999e19	+	4.14912e19i	−0.530633	+	0.503814i
$701$	3.16145e19			0.380067			0.190033	−	0.981778i	$-0.439140\pi$
$701$	3.16145e19			0.380067			0.190033	+	0.981778i	$0.439140\pi$
$702$	5.62997e18	−	9.75139e18i	0.0670110	−	0.116066i
$703$	−6.84644e19	+	3.95279e19i	−0.806821	+	0.465818i
$704$	5.49197e18	+	9.51238e18i	0.0640796	+	0.110989i
$705$	1.31767e18	+	7.60755e17i	0.0152224	+	0.00878863i
$706$			6.50228e19i			0.743760i
$707$	1.05823e19	−	2.54349e18i	0.119852	−	0.0288067i
$708$	2.50099e18			0.0280466
$709$	−2.68391e19	+	4.64867e19i	−0.298020	+	0.516185i	−0.975683	−	0.219187i	$-0.929659\pi$
$709$	−2.68391e19	+	4.64867e19i	−0.298020	+	0.516185i	0.677663	+	0.735372i	$0.262993\pi$
$710$	4.49467e19	−	2.59500e19i	0.494184	−	0.285317i
$711$	−6.70367e18	−	1.16111e19i	−0.0729836	−	0.126411i
$712$	−2.41649e19	−	1.39516e19i	−0.260510	−	0.150406i
$713$		−	1.17011e20i		−	1.24910i
$714$	−2.73400e18	−	1.13749e19i	−0.0289009	−	0.120243i
$715$	−1.06195e20			−1.11164
$716$	9.77442e18	−	1.69298e19i	0.101321	−	0.175493i
$717$	−1.90708e19	+	1.10105e19i	−0.195764	+	0.113025i
$718$	−3.85782e19	−	6.68194e19i	−0.392167	−	0.679252i
$719$	−3.56296e19	−	2.05707e19i	−0.358681	−	0.207084i	0.309821	−	0.950795i	$-0.399731\pi$
$719$	−3.56296e19	−	2.05707e19i	−0.358681	−	0.207084i	−0.668502	+	0.743710i	$0.733064\pi$
$720$		−	3.86032e19i		−	0.384854i
$721$	5.72308e19	+	6.02774e19i	0.565045	+	0.595124i
$722$	1.36847e19			0.133806
$723$	−7.34581e18	+	1.27233e19i	−0.0711331	+	0.123206i
$724$	4.49395e19	−	2.59458e19i	0.430981	−	0.248827i
$725$	1.49035e20	+	2.58136e20i	1.41554	+	2.45179i
$726$	−4.61547e17	−	2.66474e17i	−0.00434170	−	0.00250668i
$727$			2.36120e19i			0.219985i	0.993932	+	0.109992i	$0.0350826\pi$
$727$			2.36120e19i			0.219985i	−0.993932	+	0.109992i	$0.964917\pi$
$728$	−7.51085e18	+	2.53804e19i	−0.0693058	+	0.234196i
$729$	9.70236e19			0.886716
$730$	−3.03231e19	+	5.25211e19i	−0.274482	+	0.475416i
$731$	−1.63742e20	+	9.45366e19i	−1.46804	+	0.847575i
$732$	1.68665e18	+	2.92136e18i	0.0149778	+	0.0259423i
$733$	1.32075e20	+	7.62537e19i	1.16170	+	0.670707i	0.951711	−	0.306997i	$-0.0993241\pi$
$733$	1.32075e20	+	7.62537e19i	1.16170	+	0.670707i	0.209988	+	0.977704i	$0.432657\pi$
$734$			1.07446e20i			0.936087i
$735$	−2.11355e19	−	1.37100e19i	−0.182390	−	0.118311i
$736$	−1.55846e19			−0.133214
$737$	4.86029e19	−	8.41828e19i	0.411519	−	0.712772i
$738$	8.22179e19	−	4.74685e19i	0.689560	−	0.398118i
$739$	−1.38430e19	−	2.39767e19i	−0.115005	−	0.199195i	0.802776	−	0.596280i	$-0.203355\pi$
$739$	−1.38430e19	−	2.39767e19i	−0.115005	−	0.199195i	−0.917782	+	0.397085i	$0.870022\pi$
$740$	7.05514e19	+	4.07329e19i	0.580609	+	0.335215i
$741$		−	1.27999e19i		−	0.104347i
$742$	5.72411e19	+	1.69394e19i	0.462254	+	0.136795i
$743$	−6.54827e19			−0.523848			−0.261924	−	0.965089i	$-0.584357\pi$
$743$	−6.54827e19			−0.523848			−0.261924	+	0.965089i	$0.584357\pi$
$744$	−5.12157e18	+	8.87083e18i	−0.0405876	+	0.0702997i
$745$	3.04192e20	−	1.75625e20i	2.38811	−	1.37878i
$746$	1.71823e19	+	2.97606e19i	0.133632	+	0.231457i
$747$	2.21424e19	+	1.27839e19i	0.170601	+	0.0984963i
$748$		−	8.48005e19i		−	0.647273i
$749$	−1.40857e20	+	1.33738e20i	−1.06514	+	1.01131i
$750$	−9.50937e18			−0.0712399
$751$	−7.40212e19	+	1.28208e20i	−0.549384	+	0.951562i	0.448932	+	0.893566i	$0.351804\pi$
$751$	−7.40212e19	+	1.28208e20i	−0.549384	+	0.951562i	−0.998317	+	0.0579959i	$0.981529\pi$
$752$	2.38058e18	−	1.37443e18i	0.0175048	−	0.0101064i
$753$	1.43369e19	+	2.48322e19i	0.104446	+	0.180905i
$754$	1.13384e20	+	6.54623e19i	0.818375	+	0.472489i
$755$		−	1.19690e20i		−	0.855914i
$756$	1.88263e19	−	4.52496e18i	0.133387	−	0.0320599i
$757$	1.06274e19			0.0746029			0.0373014	−	0.999304i	$-0.488124\pi$
$757$	1.06274e19			0.0746029			0.0373014	+	0.999304i	$0.488124\pi$
$758$	−8.45378e19	+	1.46424e20i	−0.587985	+	1.01842i
$759$	1.34488e19	−	7.76465e18i	0.0926808	−	0.0535093i
$760$	−4.43121e19	−	7.67508e19i	−0.302571	−	0.524068i
$761$	−1.24646e20	−	7.19646e19i	−0.843310	−	0.486885i	0.0150781	−	0.999886i	$-0.495200\pi$
$761$	−1.24646e20	−	7.19646e19i	−0.843310	−	0.486885i	−0.858388	+	0.513001i	$0.828534\pi$
$762$			9.44522e18i			0.0633180i
$763$	2.33172e19	+	9.70122e19i	0.154883	+	0.644399i
$764$	1.83036e19			0.120471
$765$	−1.49016e20	+	2.58104e20i	−0.971859	+	1.68331i
$766$	1.11925e20	−	6.46201e19i	0.723314	−	0.417606i
$767$	2.18427e19	+	3.78326e19i	0.139875	+	0.242270i
$768$	1.18150e18	+	6.82139e17i	0.00749730	+	0.00432857i
$769$		−	2.54467e20i		−	1.60010i	−0.599934	−	0.800049i	$-0.704807\pi$
$769$		−	2.54467e20i		−	1.60010i	0.599934	−	0.800049i	$-0.295193\pi$
$770$	−1.25736e20	−	1.32429e20i	−0.783475	−	0.825181i
$771$	2.27570e19			0.140519
$772$	4.25131e19	−	7.36348e19i	0.260137	−	0.450570i
$773$	−1.54579e20	+	8.92463e19i	−0.937334	+	0.541170i	−0.889124	−	0.457667i	$-0.848685\pi$
$773$	−1.54579e20	+	8.92463e19i	−0.937334	+	0.541170i	−0.0482107	+	0.998837i	$0.515352\pi$
$774$	−7.74745e19	−	1.34190e20i	−0.465556	−	0.806367i
$775$	−3.52765e20	−	2.03669e20i	−2.10074	−	1.21287i
$776$		−	8.50288e19i		−	0.501804i
$777$	−5.74138e18	+	1.94011e19i	−0.0335791	+	0.113469i
$778$	1.66883e20			0.967286
$779$	1.08977e20	−	1.88754e20i	0.625998	−	1.08426i
$780$	−1.14230e19	+	6.59506e18i	−0.0650305	+	0.0375454i
$781$	4.67166e19	+	8.09155e19i	0.263581	+	0.456536i
$782$	1.04200e20	+	6.01596e19i	0.582664	+	0.336401i
$783$		−	9.57754e19i		−	0.530788i
$784$	−4.05432e19	+	2.06843e19i	−0.222693	+	0.113613i
$785$	−7.41552e19			−0.403695
$786$	−1.31300e19	+	2.27418e19i	−0.0708445	+	0.122706i
$787$	−1.60532e19	+	9.26830e18i	−0.0858495	+	0.0495652i	−0.542310	−	0.840178i	$-0.682450\pi$
$787$	−1.60532e19	+	9.26830e18i	−0.0858495	+	0.0495652i	0.456461	+	0.889744i	$0.349117\pi$
$788$	−2.89673e19	−	5.01728e19i	−0.153541	−	0.265941i
$789$	−4.12210e19	−	2.37990e19i	−0.216561	−	0.125031i
$790$			3.17185e19i			0.165167i
$791$	1.06311e20	+	3.14609e19i	0.548712	+	0.162381i
$792$	6.94956e19			0.355534
$793$	−2.94611e19	+	5.10281e19i	−0.149395	+	0.258760i
$794$	4.51126e19	−	2.60458e19i	0.226754	−	0.130916i
$795$	1.48740e19	+	2.57626e19i	0.0741069	+	0.128357i
$796$	2.21012e19	+	1.27601e19i	0.109150	+	0.0630179i
$797$		−	1.10066e19i		−	0.0538824i	−0.999637	−	0.0269412i	$-0.991423\pi$
$797$		−	1.10066e19i		−	0.0538824i	0.999637	−	0.0269412i	$-0.00857669\pi$
$798$	1.59620e19	−	1.51553e19i	0.0774582	−	0.0735433i
$799$	−2.12223e19			−0.102086
$800$	−2.71265e19	+	4.69845e19i	−0.129349	+	0.224039i
$801$	−1.52892e20	+	8.82721e19i	−0.722697	+	0.417250i
$802$	−2.92960e19	−	5.07421e19i	−0.137274	−	0.237765i
$803$	−9.45515e19	−	5.45893e19i	−0.439197	−	0.253571i
$804$		−	1.20736e19i		−	0.0555961i
$805$	2.51924e20	−	6.05508e19i	1.15000	−	0.276407i
$806$	−1.78919e20			−0.809677
$807$	−3.49078e18	+	6.04621e18i	−0.0156606	+	0.0271249i
$808$	8.48603e18	−	4.89941e18i	0.0377420	−	0.0217904i
$809$	−3.90760e19	−	6.76815e19i	−0.172294	−	0.298422i	0.766928	−	0.641734i	$-0.221785\pi$
$809$	−3.90760e19	−	6.76815e19i	−0.172294	−	0.298422i	−0.939221	+	0.343312i	$0.888451\pi$
$810$	−2.07302e20	−	1.19686e20i	−0.906168	−	0.523176i
$811$			7.50980e19i			0.325448i	0.986672	+	0.162724i	$0.0520281\pi$
$811$			7.50980e19i			0.325448i	−0.986672	+	0.162724i	$0.947972\pi$
$812$	5.26139e19	+	2.18902e20i	0.226052	+	0.940498i
$813$	2.03989e19			0.0868908
$814$	−7.33296e19	+	1.27011e20i	−0.309677	+	0.536376i
$815$	3.52348e20	−	2.03428e20i	1.47526	−	0.851742i
$816$	−5.26639e18	−	9.12165e18i	−0.0218616	−	0.0378654i
$817$	−3.08069e20	−	1.77864e20i	−1.26793	−	0.732038i
$818$			1.88541e20i			0.769367i
$819$	1.15308e20	+	1.21446e20i	0.466521	+	0.491355i
$820$	−2.24598e20			−0.900967
$821$	−5.92927e19	+	1.02698e20i	−0.235830	+	0.408470i	−0.959514	−	0.281662i	$-0.909114\pi$
$821$	−5.92927e19	+	1.02698e20i	−0.235830	+	0.408470i	0.723683	+	0.690132i	$0.242448\pi$
$822$	−2.70490e19	+	1.56167e19i	−0.106671	+	0.0615868i
$823$	9.29655e19	+	1.61021e20i	0.363515	+	0.629627i	0.988537	−	0.150981i	$-0.0482431\pi$
$823$	9.29655e19	+	1.61021e20i	0.363515	+	0.629627i	−0.625021	+	0.780608i	$0.714910\pi$
$824$	6.48080e19	+	3.74169e19i	0.251268	+	0.145070i
$825$		−	5.40606e19i		−	0.207827i
$826$	−2.13168e19	+	7.20329e19i	−0.0812571	+	0.274581i
$827$	−1.32871e20			−0.502218			−0.251109	−	0.967959i	$-0.580795\pi$
$827$	−1.32871e20			−0.502218			−0.251109	+	0.967959i	$0.580795\pi$
$828$	−4.93020e19	+	8.53935e19i	−0.184779	+	0.320046i
$829$	−6.99071e19	+	4.03609e19i	−0.259800	+	0.149996i	−0.624244	−	0.781230i	$-0.714593\pi$
$829$	−6.99071e19	+	4.03609e19i	−0.259800	+	0.149996i	0.364443	+	0.931226i	$0.381259\pi$
$830$	−3.02436e19	−	5.23835e19i	−0.111452	−	0.193040i
$831$	4.35267e19	+	2.51302e19i	0.159056	+	0.0918308i
$832$			2.38301e19i			0.0863502i
$833$	3.50921e20	+	1.82083e19i	1.26094	+	0.0654266i
$834$	4.78092e19			0.170353
$835$	4.64531e19	−	8.04591e19i	0.164138	−	0.284295i
$836$	1.38171e20	−	7.97731e19i	0.484143	−	0.279520i
$837$	6.54425e19	+	1.13350e20i	0.227395	+	0.393860i
$838$	−4.04614e19	−	2.33604e19i	−0.139422	−	0.0804956i
$839$			1.89707e20i			0.648262i	0.946012	+	0.324131i	$0.105072\pi$
$839$			1.89707e20i			0.648262i	−0.946012	+	0.324131i	$0.894928\pi$
$840$	−2.17492e19	−	6.43627e18i	−0.0737036	−	0.0218112i
$841$	8.16067e20			2.74255
$842$	7.68378e19	−	1.33087e20i	0.256088	−	0.443558i
$843$	4.13283e19	−	2.38609e19i	0.136601	−	0.0788667i
$844$	−2.76939e19	−	4.79672e19i	−0.0907793	−	0.157234i
$845$	2.18588e20	+	1.26202e20i	0.710608	+	0.410270i
$846$		−	1.73921e19i		−	0.0560737i
$847$	1.16088e19	−	1.10221e19i	0.0371198	−	0.0352437i
$848$	5.37447e19			0.170437
$849$	7.32630e18	−	1.26895e19i	0.0230426	−	0.0399109i
$850$	3.62739e20	−	2.09428e20i	1.13152	−	0.653283i
$851$	−1.04044e20	−	1.80209e20i	−0.321891	−	0.557532i
$852$	1.00502e19	+	5.80251e18i	0.0308389	+	0.0178049i
$853$		−	1.23365e20i		−	0.375447i	−0.982222	−	0.187724i	$-0.939889\pi$
$853$		−	1.23365e20i		−	0.375447i	0.982222	−	0.187724i	$-0.0601109\pi$
$854$	−9.85161e19	+	2.36787e19i	−0.297374	+	0.0714747i
$855$	−5.60727e20			−1.67876
$856$	−8.74366e19	+	1.51445e20i	−0.259643	+	0.449715i
$857$	−2.80012e19	+	1.61665e19i	−0.0824730	+	0.0476158i	−0.540669	−	0.841235i	$-0.681829\pi$
$857$	−2.80012e19	+	1.61665e19i	−0.0824730	+	0.0476158i	0.458196	+	0.888851i	$0.348496\pi$
$858$	−1.18728e19	−	2.05643e19i	−0.0346850	−	0.0600763i
$859$	2.44721e20	+	1.41290e20i	0.709120	+	0.409411i	0.810735	−	0.585413i	$-0.199068\pi$
$859$	2.44721e20	+	1.41290e20i	0.709120	+	0.409411i	−0.101615	+	0.994824i	$0.532401\pi$
$860$			3.66572e20i			1.05359i
$861$	−1.30359e19	−	5.42364e19i	−0.0371637	−	0.154621i
$862$	2.50971e20			0.709697
$863$	−1.14283e20	+	1.97945e20i	−0.320559	+	0.555224i	−0.980603	−	0.196002i	$-0.937204\pi$
$863$	−1.14283e20	+	1.97945e20i	−0.320559	+	0.555224i	0.660045	+	0.751226i	$0.270537\pi$
$864$	1.50970e19	−	8.71624e18i	0.0420043	−	0.0242512i
$865$	−8.06581e18	−	1.39704e19i	−0.0222605	−	0.0385563i
$866$	−4.04022e20	−	2.33262e20i	−1.10606	−	0.638586i
$867$			3.03106e19i			0.0823115i
$868$	−2.11842e20	−	2.23119e20i	−0.570656	−	0.601034i
$869$	−5.71014e19			−0.152584
$870$	−5.60966e19	+	9.71622e19i	−0.148697	+	0.257551i
$871$	1.82638e20	−	1.05446e20i	0.480247	−	0.277270i
$872$	4.49149e19	+	7.77949e19i	0.117159	+	0.202925i
$873$	−4.65903e20	−	2.68989e20i	−1.20558	−	0.696042i
$874$			2.26372e20i			0.581090i
$875$	8.10515e19	−	2.73886e20i	0.206398	−	0.697452i
$876$	−1.35607e19			−0.0342573
$877$	−1.45512e20	+	2.52034e20i	−0.364671	+	0.631629i	−0.988723	−	0.149754i	$-0.952152\pi$
$877$	−1.45512e20	+	2.52034e20i	−0.364671	+	0.631629i	0.624052	+	0.781383i	$0.285485\pi$
$878$	−3.69740e20	+	2.13469e20i	−0.919251	+	0.530730i
$879$	−1.81547e19	−	3.14448e19i	−0.0447782	−	0.0775581i
$880$	−1.42383e20	−	8.22049e19i	−0.348401	−	0.201150i
$881$		−	4.53668e20i		−	1.10130i	−0.834735	−	0.550651i	$-0.814379\pi$
$881$		−	4.53668e20i		−	1.10130i	0.834735	−	0.550651i	$-0.185621\pi$
$882$	−1.49220e19	+	2.87586e20i	−0.0359375	+	0.692608i
$883$	6.73323e20			1.60879			0.804394	−	0.594096i	$-0.202490\pi$
$883$	6.73323e20			1.60879			0.804394	+	0.594096i	$0.202490\pi$
$884$	9.19892e19	−	1.59330e20i	0.218057	−	0.377687i
$885$	−3.24199e19	+	1.87177e19i	−0.0762447	+	0.0440199i
$886$	−9.04913e19	−	1.56735e20i	−0.211140	−	0.365705i
$887$	5.53484e20	+	3.19554e20i	1.28127	+	0.739740i	0.977080	−	0.212872i	$-0.0682819\pi$
$887$	5.53484e20	+	3.19554e20i	1.28127	+	0.739740i	0.304187	+	0.952612i	$0.401615\pi$
$888$			1.82160e19i			0.0418372i
$889$	−2.72039e20	−	8.05047e19i	−0.619895	−	0.183446i
$890$	4.17661e20			0.944264
$891$	2.15465e20	−	3.73197e20i	0.483319	−	0.837133i
$892$	−8.81873e19	+	5.09150e19i	−0.196269	+	0.113316i
$893$	−1.99641e19	−	3.45789e19i	−0.0440850	−	0.0763574i
$894$	6.80185e19	+	3.92705e19i	0.149027	+	0.0860406i
$895$			2.92611e20i			0.636106i
$896$	−2.97171e19	+	2.82151e19i	−0.0640988	+	0.0608592i
$897$	3.36915e19			0.0721062
$898$	2.16712e20	−	3.75357e20i	0.460203	−	0.797095i
$899$	−1.31797e21	+	7.60931e20i	−2.77708	+	1.60335i
$900$	1.71630e20	+	2.97272e20i	0.358836	+	0.621521i
$901$	−3.59341e20	−	2.07466e20i	−0.745475	−	0.430400i
$902$		−	4.04334e20i		−	0.832328i
$903$	−8.85204e19	+	2.12762e19i	−0.180813	+	0.0434590i
$904$	9.98178e19			0.202315
$905$	−3.88362e20	+	6.72663e20i	−0.781082	+	1.35287i
$906$	2.31776e19	−	1.33816e19i	0.0462563	−	0.0267061i
$907$	−3.09468e20	−	5.36014e20i	−0.612865	−	1.06151i	−0.990755	−	0.135663i	$-0.956684\pi$
$907$	−3.09468e20	−	5.36014e20i	−0.612865	−	1.06151i	0.377890	−	0.925850i	$-0.376650\pi$
$908$	1.70045e20	+	9.81754e19i	0.334166	+	0.192931i
$909$		−	6.19973e19i		−	0.120900i
$910$	−9.25874e19	−	3.85214e20i	−0.179169	−	0.745439i
$911$	−2.94910e20			−0.566319			−0.283160	−	0.959073i	$-0.591383\pi$
$911$	−2.94910e20			−0.566319			−0.283160	+	0.959073i	$0.591383\pi$
$912$	9.90834e18	−	1.71618e19i	0.0188815	−	0.0327038i
$913$	9.43038e19	−	5.44463e19i	0.178334	−	0.102961i
$914$	−1.18981e20	−	2.06081e20i	−0.223282	−	0.386736i
$915$	−4.37275e19	−	2.52461e19i	−0.0814342	−	0.0470161i
$916$		−	2.87593e20i		−	0.531508i
$917$	−5.43091e20	−	5.72002e20i	−0.996065	−	1.04909i
$918$	−1.34586e20			−0.244963
$919$	1.77482e20	−	3.07407e20i	0.320586	−	0.555271i	−0.660023	−	0.751245i	$-0.729453\pi$
$919$	1.77482e20	−	3.07407e20i	0.320586	−	0.555271i	0.980609	+	0.195974i	$0.0627868\pi$
$920$	2.02020e20	−	1.16636e20i	0.362143	−	0.209083i
$921$	−2.06729e19	−	3.58064e19i	−0.0367776	−	0.0637006i
$922$	5.25305e20	+	3.03285e20i	0.927459	+	0.535469i
$923$			2.02707e20i			0.355187i
$924$	1.15869e19	−	3.91542e19i	0.0201495	−	0.0680886i
$925$	−7.24394e20			−1.25021
$926$	7.45891e19	−	1.29192e20i	0.127761	−	0.221289i
$927$	4.10041e20	−	2.36737e20i	0.697059	−	0.402447i
$928$	1.01348e20	+	1.75540e20i	0.170993	+	0.296169i
$929$	1.23820e20	+	7.14877e19i	0.207340	+	0.119708i	0.600074	−	0.799944i	$-0.295138\pi$
$929$	1.23820e20	+	7.14877e19i	0.207340	+	0.119708i	−0.392735	+	0.919652i	$0.628471\pi$
$930$		−	1.53321e20i		−	0.254813i
$931$	3.00448e20	+	5.88907e20i	0.495589	+	0.971402i
$932$	−2.85993e20			−0.468213
$933$	−1.40937e19	+	2.44110e19i	−0.0229009	+	0.0396655i
$934$	7.87190e18	−	4.54484e18i	0.0126955	−	0.00732978i
$935$	6.34655e20	+	1.09926e21i	1.01591	+	1.75961i
$936$	1.30574e20	+	7.53869e19i	0.207456	+	0.119775i
$937$		−	2.79349e20i		−	0.440524i	−0.975441	−	0.220262i	$-0.929309\pi$
$937$		−	2.79349e20i		−	0.440524i	0.975441	−	0.220262i	$-0.0706912\pi$
$938$	3.47741e20	+	1.02907e20i	0.544297	+	0.161074i
$939$	1.51150e20			0.234827
$940$	−2.05727e19	+	3.56330e19i	−0.0317247	+	0.0549487i
$941$	4.74677e20	−	2.74055e20i	0.726559	−	0.419479i	−0.0906033	−	0.995887i	$-0.528880\pi$
$941$	4.74677e20	−	2.74055e20i	0.726559	−	0.419479i	0.817162	+	0.576408i	$0.195546\pi$
$942$	−8.29068e18	−	1.43599e19i	−0.0125960	−	0.0218170i
$943$	4.96830e20	+	2.86845e20i	0.749248	+	0.432579i
$944$			6.76331e19i			0.101241i
$945$	−2.10177e20	+	1.99554e20i	−0.312293	+	0.296509i
$946$	−6.59923e20			−0.973319
$947$	4.43840e20	−	7.68754e20i	0.649796	−	1.12548i	−0.333376	−	0.942794i	$-0.608188\pi$
$947$	4.43840e20	−	7.68754e20i	0.649796	−	1.12548i	0.983171	−	0.182685i	$-0.0584789\pi$
$948$	−6.14217e18	+	3.54619e18i	−0.00892614	+	0.00515351i
$949$	−1.18434e20	−	2.05134e20i	−0.170849	−	0.295919i
$950$	6.82469e20	+	3.94024e20i	0.977277	+	0.564231i
$951$			1.34231e20i			0.190805i
$952$	3.07607e20	−	7.39343e19i	0.434047	−	0.104325i
$953$	−5.52988e20			−0.774578			−0.387289	−	0.921958i	$-0.626589\pi$
$953$	−5.52988e20			−0.774578			−0.387289	+	0.921958i	$0.626589\pi$
$954$	1.70022e20	−	2.94487e20i	0.236410	−	0.409475i
$955$	−2.37267e20	+	1.36986e20i	−0.327502	+	0.189083i
$956$	−2.97752e20	−	5.15721e20i	−0.407989	−	0.706658i
$957$	−1.74917e20	−	1.00988e20i	−0.237929	−	0.137369i
$958$			9.03166e20i			1.21958i
$959$	−2.19242e20	−	9.12164e20i	−0.293895	−	1.22276i
$960$	−2.04208e19			−0.0271752
$961$	6.61403e20	−	1.14558e21i	0.873781	−	1.51343i
$962$	−2.75555e20	+	1.59092e20i	−0.361395	+	0.208652i
$963$	5.53213e20	+	9.58193e20i	0.720292	+	1.24758i
$964$	−3.44070e20	−	1.98649e20i	−0.444742	−	0.256772i
$965$			1.27269e21i			1.63317i
$966$	3.98910e19	+	4.20145e19i	0.0508201	+	0.0535254i
$967$	−1.08872e20			−0.137700			−0.0688498	−	0.997627i	$-0.521933\pi$
$967$	−1.08872e20			−0.137700			−0.0688498	+	0.997627i	$0.521933\pi$
$968$	7.20614e18	−	1.24814e19i	0.00904847	−	0.0156724i
$969$	−1.32496e20	+	7.64965e19i	−0.165172	+	0.0953619i
$970$	6.36364e20	+	1.10221e21i	0.787595	+	1.36416i
$971$	8.56441e20	+	4.94466e20i	1.05236	+	0.607578i	0.923308	−	0.384060i	$-0.125475\pi$
$971$	8.56441e20	+	4.94466e20i	1.05236	+	0.607578i	0.129048	+	0.991638i	$0.458808\pi$
$972$		−	1.65978e20i		−	0.202482i
$973$	−4.07493e20	+	1.37699e21i	−0.493549	+	1.66778i
$974$	−3.35599e20			−0.403560
$975$	5.86433e19	−	1.01573e20i	0.0700143	−	0.121268i
$976$	−7.90009e19	+	4.56112e19i	−0.0936448	+	0.0540658i
$977$	−4.67970e20	−	8.10548e20i	−0.550752	−	0.953931i	−0.998220	−	0.0596308i	$-0.981008\pi$
$977$	−4.67970e20	−	8.10548e20i	−0.550752	−	0.953931i	0.447468	−	0.894300i	$-0.352326\pi$
$978$	7.87863e19	+	4.54873e19i	0.0920616	+	0.0531518i
$979$			7.51896e20i			0.872327i
$980$	3.70752e20	−	5.71557e20i	0.427072	−	0.658380i
$981$	5.68355e20			0.650035
$982$	−3.72206e20	+	6.44680e20i	−0.422672	+	0.732089i
$983$	−1.08083e20	+	6.24015e19i	−0.121866	+	0.0703591i	−0.559694	−	0.828700i	$-0.689081\pi$
$983$	−1.08083e20	+	6.24015e19i	−0.121866	+	0.0703591i	0.437828	+	0.899059i	$0.355748\pi$
$984$	−2.51105e19	−	4.34926e19i	−0.0281118	−	0.0486911i
$985$	7.50996e20	+	4.33587e20i	0.834802	+	0.481973i
$986$		−	1.56489e21i		−	1.72721i
$987$	−9.79879e18	−	2.89977e18i	−0.0107387	−	0.00317792i
$988$	3.46142e20			0.376666
$989$	4.68166e20	−	8.10887e20i	0.505855	−	0.876166i
$990$	−9.00860e20	+	5.20112e20i	−0.966521	+	0.558021i
$991$	−3.49441e20	−	6.05249e20i	−0.372270	−	0.644791i	0.617644	−	0.786458i	$-0.288087\pi$
$991$	−3.49441e20	−	6.05249e20i	−0.372270	−	0.644791i	−0.989914	+	0.141667i	$0.954754\pi$
$992$	−2.39889e20	−	1.38500e20i	−0.253764	−	0.146510i
$993$		−	1.66108e20i		−	0.174480i
$994$	−2.52784e20	+	2.40008e20i	−0.263660	+	0.250334i
$995$	−3.81992e20			−0.395634
$996$	6.76259e18	−	1.17131e19i	0.00695501	−	0.0120464i
$997$	−4.09214e20	+	2.36260e20i	−0.417912	+	0.241281i	−0.694183	−	0.719798i	$-0.744234\pi$
$997$	−4.09214e20	+	2.36260e20i	−0.417912	+	0.241281i	0.276272	+	0.961080i	$0.410901\pi$
$998$	−5.94683e19	−	1.03002e20i	−0.0603075	−	0.104456i
$999$	2.01577e20	+	1.16380e20i	0.202994	+	0.117198i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	14.15.d.a.5.8	yes	20
3.2	odd	2		126.15.n.b.19.1		20
7.2	even	3		98.15.b.c.97.5		20
7.3	odd	6	inner	14.15.d.a.3.8	✓	20
7.4	even	3		98.15.d.b.31.8		20
7.5	odd	6		98.15.b.c.97.6		20
7.6	odd	2		98.15.d.b.19.8		20
21.17	even	6		126.15.n.b.73.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.15.d.a.3.8	✓	20	7.3	odd	6	inner
14.15.d.a.5.8	yes	20	1.1	even	1	trivial
98.15.b.c.97.5		20	7.2	even	3
98.15.b.c.97.6		20	7.5	odd	6
98.15.d.b.19.8		20	7.6	odd	2
98.15.d.b.31.8		20	7.4	even	3
126.15.n.b.19.1		20	3.2	odd	2
126.15.n.b.73.1		20	21.17	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 14 = 2 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 15 \)
Character orbit:	\([\chi]\)	\(=\)	14.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(45.2548 - 78.3837i) q^{2} +(-262.346 + 151.465i) q^{3} +(-4096.00 - 7094.48i) q^{4} +(106192. + 61309.7i) q^{5} +27418.1i q^{6} +(-789690. - 233694. i) q^{7} -741455. q^{8} +(-2.34560e6 + 4.06270e6i) q^{9} +O(q^{10})\)	\(q+(45.2548 - 78.3837i) q^{2} +(-262.346 + 151.465i) q^{3} +(-4096.00 - 7094.48i) q^{4} +(106192. + 61309.7i) q^{5} +27418.1i q^{6} +(-789690. - 233694. i) q^{7} -741455. q^{8} +(-2.34560e6 + 4.06270e6i) q^{9} +(9.61136e6 - 5.54912e6i) q^{10} +(9.98984e6 + 1.73029e7i) q^{11} +(2.14913e6 + 1.24080e6i) q^{12} +4.33468e7i q^{13} +(-5.40551e7 + 5.13230e7i) q^{14} -3.71452e7 q^{15} +(-3.35544e7 + 5.81180e7i) q^{16} +(4.48694e8 - 2.59054e8i) q^{17} +(2.12300e8 + 3.67714e8i) q^{18} +(8.44187e8 + 4.87392e8i) q^{19} -1.00450e9i q^{20} +(2.42568e8 - 5.83021e7i) q^{21} +1.80835e9 q^{22} +(-1.28289e9 + 2.22203e9i) q^{23} +(1.94517e8 - 1.12305e8i) q^{24} +(4.46600e9 + 7.73534e9i) q^{25} +(3.39768e9 + 1.96165e9i) q^{26} -2.87002e9i q^{27} +(1.57663e9 + 6.55965e9i) q^{28} +3.33710e10 q^{29} +(-1.68100e9 + 2.91157e9i) q^{30} +(-3.94945e10 + 2.28021e10i) q^{31} +(3.03700e9 + 5.26024e9i) q^{32} +(-5.24158e9 - 3.02623e9i) q^{33} -4.68938e10i q^{34} +(-6.95307e10 - 7.32320e10i) q^{35} +3.84303e10 q^{36} +(-4.05505e10 + 7.02355e10i) q^{37} +(7.64071e10 - 4.41137e10i) q^{38} +(-6.56553e9 - 1.13718e10i) q^{39} +(-7.87363e10 - 4.54584e10i) q^{40} -2.23592e11i q^{41} +(6.40745e9 - 2.16518e10i) q^{42} -3.64930e11 q^{43} +(8.18368e10 - 1.41745e11i) q^{44} +(-4.98166e11 + 2.87616e11i) q^{45} +(1.16114e11 + 2.01116e11i) q^{46} +(-3.54734e10 - 2.04806e10i) q^{47} -2.03293e10i q^{48} +(5.68997e11 + 3.69091e11i) q^{49} +8.08433e11 q^{50} +(-7.84753e10 + 1.35923e11i) q^{51} +(3.07523e11 - 1.77548e11i) q^{52} +(-4.00430e11 - 6.93564e11i) q^{53} +(-2.24962e11 - 1.29882e11i) q^{54} +2.44990e12i q^{55} +(5.85520e11 + 1.73274e11i) q^{56} -2.95292e11 q^{57} +(1.51020e12 - 2.61574e12i) q^{58} +(8.72791e11 - 5.03906e11i) q^{59} +(1.52147e11 + 2.63526e11i) q^{60} +(1.17721e12 + 6.79660e11i) q^{61} +4.12763e12i q^{62} +(2.80173e12 - 2.66012e12i) q^{63} +5.49756e11 q^{64} +(-2.65758e12 + 4.60306e12i) q^{65} +(-4.74414e11 + 2.73903e11i) q^{66} +(-2.43262e12 - 4.21342e12i) q^{67} +(-3.67570e12 - 2.12217e12i) q^{68} -7.77254e11i q^{69} +(-8.88679e12 + 2.13597e12i) q^{70} +4.67641e12 q^{71} +(1.73916e12 - 3.01231e12i) q^{72} +(-4.73238e12 + 2.73224e12i) q^{73} +(3.67021e12 + 6.35699e12i) q^{74} +(-2.34327e12 - 1.35289e12i) q^{75} -7.98543e12i q^{76} +(-3.84529e12 - 1.59985e13i) q^{77} -1.18849e12 q^{78} +(-1.42899e12 + 2.47508e12i) q^{79} +(-7.12639e12 + 4.11442e12i) q^{80} +(-1.07842e13 - 1.86788e13i) q^{81} +(-1.75260e13 - 1.01186e13i) q^{82} -5.45017e12i q^{83} +(-1.40718e12 - 1.48209e12i) q^{84} +6.35301e13 q^{85} +(-1.65149e13 + 2.86046e13i) q^{86} +(-8.75474e12 + 5.05455e12i) q^{87} +(-7.40702e12 - 1.28293e13i) q^{88} +(3.25912e13 + 1.88165e13i) q^{89} +5.20641e13i q^{90} +(1.01299e13 - 3.42305e13i) q^{91} +2.10189e13 q^{92} +(6.90746e12 - 1.19641e13i) q^{93} +(-3.21069e12 + 1.85369e12i) q^{94} +(5.97637e13 + 1.03514e14i) q^{95} +(-1.59349e12 - 9.20000e11i) q^{96} +1.14678e14i q^{97} +(5.46806e13 - 2.78969e13i) q^{98} -9.37287e13 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4374 q^{3} - 81920 q^{4} + 3354 q^{5} + 1455616 q^{7} + 17547432 q^{9}+O(q^{10}) \) 20 * q - 4374 * q^3 - 81920 * q^4 + 3354 * q^5 + 1455616 * q^7 + 17547432 * q^9	\( 20 q - 4374 q^{3} - 81920 q^{4} + 3354 q^{5} + 1455616 q^{7} + 17547432 q^{9} - 3933696 q^{10} + 8400426 q^{11} + 35831808 q^{12} - 114693888 q^{14} + 562720524 q^{15} - 671088640 q^{16} + 2180481042 q^{17} - 251755008 q^{18} - 3919727442 q^{19} + 7585509006 q^{21} + 5394565632 q^{22} - 6905098386 q^{23} - 2371878912 q^{24} + 14165082644 q^{25} + 12652202496 q^{26} - 17334943744 q^{28} + 27884908704 q^{29} + 54103511808 q^{30} + 45638710782 q^{31} - 37041090498 q^{33} - 18274367202 q^{35} - 287497125888 q^{36} - 27026027926 q^{37} - 354043974912 q^{38} - 126125404380 q^{39} + 32224837632 q^{40} - 298475364864 q^{42} + 726682953656 q^{43} + 68816289792 q^{44} + 498861631944 q^{45} - 286664984832 q^{46} - 2044625353338 q^{47} + 2939974016204 q^{49} + 1161106642944 q^{50} - 2419609945602 q^{51} + 1314350333952 q^{52} + 1546271487546 q^{53} - 5213176950528 q^{54} + 1720927125504 q^{56} + 14789884876092 q^{57} - 2365863040512 q^{58} - 6798944731566 q^{59} - 2304903266304 q^{60} - 2214453865554 q^{61} - 4417730390688 q^{63} + 10995116277760 q^{64} + 7516703932836 q^{65} - 8476063570944 q^{66} - 4655820763226 q^{67} - 17862500696064 q^{68} + 20497461621504 q^{70} + 96606137494152 q^{71} - 2062377025536 q^{72} - 65348368908666 q^{73} - 566532483072 q^{74} - 186663280957308 q^{75} + 77525241691422 q^{77} + 88663911671808 q^{78} - 60517474082978 q^{79} - 225083129856 q^{80} - 107180264511342 q^{81} - 43979002397184 q^{82} + 18842436550656 q^{84} + 416326699526124 q^{85} + 2363335174656 q^{86} - 126768392660088 q^{87} - 22096140828672 q^{88} - 237147002561826 q^{89} + 203506111374408 q^{91} + 113133131956224 q^{92} - 94175068190130 q^{93} - 221058962902272 q^{94} + 25202514515490 q^{95} + 19430432047104 q^{96} + 165606984015360 q^{98} + 10\!\cdots\!68 q^{99}+O(q^{100}) \) 20 * q - 4374 * q^3 - 81920 * q^4 + 3354 * q^5 + 1455616 * q^7 + 17547432 * q^9 - 3933696 * q^10 + 8400426 * q^11 + 35831808 * q^12 - 114693888 * q^14 + 562720524 * q^15 - 671088640 * q^16 + 2180481042 * q^17 - 251755008 * q^18 - 3919727442 * q^19 + 7585509006 * q^21 + 5394565632 * q^22 - 6905098386 * q^23 - 2371878912 * q^24 + 14165082644 * q^25 + 12652202496 * q^26 - 17334943744 * q^28 + 27884908704 * q^29 + 54103511808 * q^30 + 45638710782 * q^31 - 37041090498 * q^33 - 18274367202 * q^35 - 287497125888 * q^36 - 27026027926 * q^37 - 354043974912 * q^38 - 126125404380 * q^39 + 32224837632 * q^40 - 298475364864 * q^42 + 726682953656 * q^43 + 68816289792 * q^44 + 498861631944 * q^45 - 286664984832 * q^46 - 2044625353338 * q^47 + 2939974016204 * q^49 + 1161106642944 * q^50 - 2419609945602 * q^51 + 1314350333952 * q^52 + 1546271487546 * q^53 - 5213176950528 * q^54 + 1720927125504 * q^56 + 14789884876092 * q^57 - 2365863040512 * q^58 - 6798944731566 * q^59 - 2304903266304 * q^60 - 2214453865554 * q^61 - 4417730390688 * q^63 + 10995116277760 * q^64 + 7516703932836 * q^65 - 8476063570944 * q^66 - 4655820763226 * q^67 - 17862500696064 * q^68 + 20497461621504 * q^70 + 96606137494152 * q^71 - 2062377025536 * q^72 - 65348368908666 * q^73 - 566532483072 * q^74 - 186663280957308 * q^75 + 77525241691422 * q^77 + 88663911671808 * q^78 - 60517474082978 * q^79 - 225083129856 * q^80 - 107180264511342 * q^81 - 43979002397184 * q^82 + 18842436550656 * q^84 + 416326699526124 * q^85 + 2363335174656 * q^86 - 126768392660088 * q^87 - 22096140828672 * q^88 - 237147002561826 * q^89 + 203506111374408 * q^91 + 113133131956224 * q^92 - 94175068190130 * q^93 - 221058962902272 * q^94 + 25202514515490 * q^95 + 19430432047104 * q^96 + 165606984015360 * q^98 + 1056686373672768 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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