LMFDB - Embedded newform 14.15.d.a.3.1

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			3.1
Root			$753.046 + 1304.31i$ of defining polynomial
Character	$\chi$	$=$	14.3
Dual form			14.15.d.a.5.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-45.2548 - 78.3837i) q^{2} +(-3571.50 - 2062.01i) q^{3} +(-4096.00 + 7094.48i) q^{4} +(81056.3 - 46797.9i) q^{5} +373263. i q^{6} +(587107. + 577519. i) q^{7} +741455. q^{8} +(6.11227e6 + 1.05868e7i) q^{9} +O(q^{10})$	\(q+(-45.2548 - 78.3837i) q^{2} +(-3571.50 - 2062.01i) q^{3} +(-4096.00 + 7094.48i) q^{4} +(81056.3 - 46797.9i) q^{5} +373263. i q^{6} +(587107. + 577519. i) q^{7} +741455. q^{8} +(6.11227e6 + 1.05868e7i) q^{9} +(-7.33638e6 - 4.23566e6i) q^{10} +(1.07193e7 - 1.85664e7i) q^{11} +(2.92577e7 - 1.68920e7i) q^{12} +9.80750e6i q^{13} +(1.86987e7 - 7.21551e7i) q^{14} -3.85991e8 q^{15} +(-3.35544e7 - 5.81180e7i) q^{16} +(5.15718e8 + 2.97750e8i) q^{17} +(5.53219e8 - 9.58204e8i) q^{18} +(-1.96957e8 + 1.13713e8i) q^{19} +7.66737e8i q^{20} +(-9.06004e8 - 3.27323e9i) q^{21} -1.94041e9 q^{22} +(-7.21245e8 - 1.24923e9i) q^{23} +(-2.64811e9 - 1.52889e9i) q^{24} +(1.32833e9 - 2.30073e9i) q^{25} +(7.68748e8 - 4.43837e8i) q^{26} -3.06891e10i q^{27} +(-6.50199e9 + 1.79970e9i) q^{28} +1.54449e10 q^{29} +(1.74679e10 + 3.02554e10i) q^{30} +(2.91870e10 + 1.68511e10i) q^{31} +(-3.03700e9 + 5.26024e9i) q^{32} +(-7.65682e10 + 4.42067e10i) q^{33} -5.38984e10i q^{34} +(7.46154e10 + 1.93362e10i) q^{35} -1.00143e11 q^{36} +(-1.75374e10 - 3.03757e10i) q^{37} +(1.78265e10 + 1.02921e10i) q^{38} +(2.02231e10 - 3.50275e10i) q^{39} +(6.00996e10 - 3.46985e10i) q^{40} +9.80369e10i q^{41} +(-2.15567e11 + 2.19145e11i) q^{42} -3.91868e11 q^{43} +(8.78127e10 + 1.52096e11i) q^{44} +(9.90876e11 + 5.72083e11i) q^{45} +(-6.52796e10 + 1.13068e11i) q^{46} +(6.95210e11 - 4.01380e11i) q^{47} +2.76758e11i q^{48} +(1.11658e10 + 6.78131e11i) q^{49} -2.40453e11 q^{50} +(-1.22792e12 - 2.12683e12i) q^{51} +(-6.95791e10 - 4.01715e10i) q^{52} +(9.24571e11 - 1.60140e12i) q^{53} +(-2.40553e12 + 1.38883e12i) q^{54} -2.00657e12i q^{55} +(4.35313e11 + 4.28205e11i) q^{56} +9.37908e11 q^{57} +(-6.98959e11 - 1.21063e12i) q^{58} +(-9.16901e11 - 5.29373e11i) q^{59} +(1.58102e12 - 2.73840e12i) q^{60} +(-5.05142e11 + 2.91644e11i) q^{61} -3.05038e12i q^{62} +(-2.52550e12 + 9.74551e12i) q^{63} +5.49756e11 q^{64} +(4.58970e11 + 7.94960e11i) q^{65} +(6.93016e12 + 4.00113e12i) q^{66} +(5.19561e12 - 8.99907e12i) q^{67} +(-4.22476e12 + 2.43917e12i) q^{68} +5.94885e12i q^{69} +(-1.86106e12 - 6.72369e12i) q^{70} -5.47020e12 q^{71} +(4.53197e12 + 7.84961e12i) q^{72} +(2.19550e12 + 1.26757e12i) q^{73} +(-1.58730e12 + 2.74929e12i) q^{74} +(-9.48825e12 + 5.47805e12i) q^{75} -1.86307e12i q^{76} +(1.70159e13 - 4.70985e12i) q^{77} -3.66078e12 q^{78} +(-3.31121e12 - 5.73519e12i) q^{79} +(-5.43960e12 - 3.14055e12i) q^{80} +(-3.40465e13 + 5.89702e13i) q^{81} +(7.68449e12 - 4.43664e12i) q^{82} -1.05545e13i q^{83} +(2.69329e13 + 6.97953e12i) q^{84} +5.57362e13 q^{85} +(1.77339e13 + 3.07160e13i) q^{86} +(-5.51617e13 - 3.18476e13i) q^{87} +(7.94790e12 - 1.37662e13i) q^{88} +(-2.07604e13 + 1.19860e13i) q^{89} -1.03558e14i q^{90} +(-5.66402e12 + 5.75805e12i) q^{91} +1.18169e13 q^{92} +(-6.94943e13 - 1.20368e14i) q^{93} +(-6.29232e13 - 3.63287e13i) q^{94} +(-1.06431e13 + 1.84343e13i) q^{95} +(2.16933e13 - 1.25246e13i) q^{96} +1.03644e14i q^{97} +(5.26491e13 - 3.15639e13i) q^{98} +2.62078e14 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 $\left(\mathbb{Z}/14\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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
$3$	−3571.50	−	2062.01i	−1.63306	−	0.942848i	−0.983142	−	0.182843i	$-0.941470\pi$
$3$	−3571.50	−	2062.01i	−1.63306	−	0.942848i	−0.649918	−	0.760004i	$-0.725197\pi$
$4$	−4096.00	+	7094.48i	−0.250000	+	0.433013i
$5$	81056.3	−	46797.9i	1.03752	−	0.599013i	0.118391	−	0.992967i	$-0.462226\pi$
$5$	81056.3	−	46797.9i	1.03752	−	0.599013i	0.919130	+	0.393954i	$0.128893\pi$
$6$			373263.i			1.33339i
$7$	587107.	+	577519.i	0.712904	+	0.701262i
$7$	587107.	+	577519.i	0.712904	+	0.701262i
$8$	741455.			0.353553
$9$	6.11227e6	+	1.05868e7i	1.27792	+	2.21343i
$10$	−7.33638e6	−	4.23566e6i	−0.733638	−	0.423566i
$11$	1.07193e7	−	1.85664e7i	0.550071	−	0.952751i	−0.448198	−	0.893934i	$-0.647934\pi$
$11$	1.07193e7	−	1.85664e7i	0.550071	−	0.952751i	0.998269	−	0.0588166i	$-0.0187327\pi$
$12$	2.92577e7	−	1.68920e7i	0.816530	−	0.471424i
$13$			9.80750e6i			0.156299i	0.996942	+	0.0781493i	$0.0249011\pi$
$13$			9.80750e6i			0.156299i	−0.996942	+	0.0781493i	$0.975099\pi$
$14$	1.86987e7	−	7.21551e7i	0.177384	−	0.684496i
$15$	−3.85991e8			−2.25911
$16$	−3.35544e7	−	5.81180e7i	−0.125000	−	0.216506i
$17$	5.15718e8	+	2.97750e8i	1.25681	+	0.725619i	0.972453	−	0.233099i	$-0.0748867\pi$
$17$	5.15718e8	+	2.97750e8i	1.25681	+	0.725619i	0.284357	+	0.958719i	$0.408220\pi$
$18$	5.53219e8	−	9.58204e8i	0.903628	−	1.56513i
$19$	−1.96957e8	+	1.13713e8i	−0.220341	+	0.127214i	−0.606108	−	0.795382i	$-0.707270\pi$
$19$	−1.96957e8	+	1.13713e8i	−0.220341	+	0.127214i	0.385767	+	0.922596i	$0.373937\pi$
$20$			7.66737e8i			0.599013i
$21$	−9.06004e8	−	3.27323e9i	−0.503031	−	1.81736i
$22$	−1.94041e9			−0.777918
$23$	−7.21245e8	−	1.24923e9i	−0.211830	−	0.366901i	0.740457	−	0.672104i	$-0.234609\pi$
$23$	−7.21245e8	−	1.24923e9i	−0.211830	−	0.366901i	−0.952287	+	0.305203i	$0.901276\pi$
$24$	−2.64811e9	−	1.52889e9i	−0.577374	−	0.333347i
$25$	1.32833e9	−	2.30073e9i	0.217633	−	0.376952i
$26$	7.68748e8	−	4.43837e8i	0.0957129	−	0.0552599i
$27$		−	3.06891e10i		−	2.93385i
$28$	−6.50199e9	+	1.79970e9i	−0.481881	+	0.133381i
$29$	1.54449e10			0.895366			0.447683	−	0.894192i	$-0.352249\pi$
$29$	1.54449e10			0.895366			0.447683	+	0.894192i	$0.352249\pi$
$30$	1.74679e10	+	3.02554e10i	0.798717	+	1.38342i
$31$	2.91870e10	+	1.68511e10i	1.06086	+	0.612488i	0.925670	−	0.378332i	$-0.123502\pi$
$31$	2.91870e10	+	1.68511e10i	1.06086	+	0.612488i	0.135190	+	0.990820i	$0.456836\pi$
$32$	−3.03700e9	+	5.26024e9i	−0.0883883	+	0.153093i
$33$	−7.65682e10	+	4.42067e10i	−1.79660	+	1.03727i
$34$		−	5.38984e10i		−	1.02618i
$35$	7.46154e10	+	1.93362e10i	1.15972	+	0.300535i
$36$	−1.00143e11			−1.27792
$37$	−1.75374e10	−	3.03757e10i	−0.184737	−	0.319973i	0.758751	−	0.651381i	$-0.225810\pi$
$37$	−1.75374e10	−	3.03757e10i	−0.184737	−	0.319973i	−0.943488	+	0.331407i	$0.892477\pi$
$38$	1.78265e10	+	1.02921e10i	0.155805	+	0.0899538i
$39$	2.02231e10	−	3.50275e10i	0.147366	−	0.255245i
$40$	6.00996e10	−	3.46985e10i	0.366819	−	0.211783i
$41$			9.80369e10i			0.503388i	0.967807	+	0.251694i	$0.0809876\pi$
$41$			9.80369e10i			0.503388i	−0.967807	+	0.251694i	$0.919012\pi$
$42$	−2.15567e11	+	2.19145e11i	−0.935054	+	0.950577i
$43$	−3.91868e11			−1.44165			−0.720826	−	0.693116i	$-0.756237\pi$
$43$	−3.91868e11			−1.44165			−0.720826	+	0.693116i	$0.756237\pi$
$44$	8.78127e10	+	1.52096e11i	0.275036	+	0.476376i
$45$	9.90876e11	+	5.72083e11i	2.65174	+	1.53099i
$46$	−6.52796e10	+	1.13068e11i	−0.149787	+	0.259438i
$47$	6.95210e11	−	4.01380e11i	1.37224	−	0.792265i	0.381032	−	0.924562i	$-0.375569\pi$
$47$	6.95210e11	−	4.01380e11i	1.37224	−	0.792265i	0.991210	+	0.132297i	$0.0422353\pi$
$48$			2.76758e11i			0.471424i
$49$	1.11658e10	+	6.78131e11i	0.0164634	+	0.999864i
$50$	−2.40453e11			−0.307780
$51$	−1.22792e12	−	2.12683e12i	−1.36830	−	2.36996i
$52$	−6.95791e10	−	4.01715e10i	−0.0676792	−	0.0390746i
$53$	9.24571e11	−	1.60140e12i	0.787063	−	1.36323i	−0.140696	−	0.990053i	$-0.544934\pi$
$53$	9.24571e11	−	1.60140e12i	0.787063	−	1.36323i	0.927759	−	0.373180i	$-0.121732\pi$
$54$	−2.40553e12	+	1.38883e12i	−1.79661	+	1.03727i
$55$		−	2.00657e12i		−	1.31800i
$56$	4.35313e11	+	4.28205e11i	0.252050	+	0.247934i
$57$	9.37908e11			0.479773
$58$	−6.98959e11	−	1.21063e12i	−0.316560	−	0.548297i
$59$	−9.16901e11	−	5.29373e11i	−0.368433	−	0.212715i	0.304341	−	0.952563i	$-0.401564\pi$
$59$	−9.16901e11	−	5.29373e11i	−0.368433	−	0.212715i	−0.672774	+	0.739848i	$0.734897\pi$
$60$	1.58102e12	−	2.73840e12i	0.564778	−	0.978224i
$61$	−5.05142e11	+	2.91644e11i	−0.160733	+	0.0927991i	−0.578209	−	0.815889i	$-0.696248\pi$
$61$	−5.05142e11	+	2.91644e11i	−0.160733	+	0.0927991i	0.417476	+	0.908688i	$0.362915\pi$
$62$		−	3.05038e12i		−	0.866188i
$63$	−2.52550e12	+	9.74551e12i	−0.641157	+	2.47412i
$64$	5.49756e11			0.125000
$65$	4.58970e11	+	7.94960e11i	0.0936249	+	0.162163i
$66$	6.93016e12	+	4.00113e12i	1.27039	+	0.733458i
$67$	5.19561e12	−	8.99907e12i	0.857262	−	1.48482i	−0.0172695	−	0.999851i	$-0.505497\pi$
$67$	5.19561e12	−	8.99907e12i	0.857262	−	1.48482i	0.874531	−	0.484970i	$-0.161169\pi$
$68$	−4.22476e12	+	2.43917e12i	−0.628405	+	0.362810i
$69$			5.94885e12i			0.798894i
$70$	−1.86106e12	−	6.72369e12i	−0.225983	−	0.816434i
$71$	−5.47020e12			−0.601443			−0.300722	−	0.953712i	$-0.597228\pi$
$71$	−5.47020e12			−0.601443			−0.300722	+	0.953712i	$0.597228\pi$
$72$	4.53197e12	+	7.84961e12i	0.451814	+	0.782565i
$73$	2.19550e12	+	1.26757e12i	0.198734	+	0.114739i	0.596065	−	0.802936i	$-0.296730\pi$
$73$	2.19550e12	+	1.26757e12i	0.198734	+	0.114739i	−0.397331	+	0.917676i	$0.630063\pi$
$74$	−1.58730e12	+	2.74929e12i	−0.130629	+	0.226255i
$75$	−9.48825e12	+	5.47805e12i	−0.710816	+	0.410390i
$76$		−	1.86307e12i		−	0.127214i
$77$	1.70159e13	−	4.70985e12i	1.06028	−	0.293476i
$78$	−3.66078e12			−0.208407
$79$	−3.31121e12	−	5.73519e12i	−0.172424	−	0.298647i	0.766843	−	0.641835i	$-0.221827\pi$
$79$	−3.31121e12	−	5.73519e12i	−0.172424	−	0.298647i	−0.939267	+	0.343188i	$0.888493\pi$
$80$	−5.43960e12	−	3.14055e12i	−0.259380	−	0.149753i
$81$	−3.40465e13	+	5.89702e13i	−1.48825	+	2.57773i
$82$	7.68449e12	−	4.43664e12i	0.308261	−	0.177974i
$83$		−	1.05545e13i		−	0.388949i	−0.980908	−	0.194475i	$-0.937700\pi$
$83$		−	1.05545e13i		−	0.388949i	0.980908	−	0.194475i	$-0.0623002\pi$
$84$	2.69329e13	+	6.97953e12i	0.912699	+	0.236522i
$85$	5.57362e13			1.73862
$86$	1.77339e13	+	3.07160e13i	0.509701	+	0.882828i
$87$	−5.51617e13	−	3.18476e13i	−1.46219	−	0.844193i
$88$	7.94790e12	−	1.37662e13i	0.194479	−	0.336848i
$89$	−2.07604e13	+	1.19860e13i	−0.469360	+	0.270985i	−0.715972	−	0.698129i	$-0.754016\pi$
$89$	−2.07604e13	+	1.19860e13i	−0.469360	+	0.270985i	0.246612	+	0.969114i	$0.420683\pi$
$90$		−	1.03558e14i		−	2.16514i
$91$	−5.66402e12	+	5.75805e12i	−0.109606	+	0.111426i
$92$	1.18169e13			0.211830
$93$	−6.94943e13	−	1.20368e14i	−1.15497	−	2.00046i
$94$	−6.29232e13	−	3.63287e13i	−0.970322	−	0.560216i
$95$	−1.06431e13	+	1.84343e13i	−0.152406	+	0.263974i
$96$	2.16933e13	−	1.25246e13i	0.288687	−	0.166673i
$97$			1.03644e14i			1.28275i	0.767228	+	0.641375i	$0.221636\pi$
$97$			1.03644e14i			1.28275i	−0.767228	+	0.641375i	$0.778364\pi$
$98$	5.26491e13	−	3.15639e13i	0.606469	−	0.363587i
$99$	2.62078e14			2.81179
$100$	1.08817e13	+	1.88476e13i	0.108817	+	0.188476i
$101$	−8.45267e12	−	4.88015e12i	−0.0788395	−	0.0455180i	0.460062	−	0.887887i	$-0.347827\pi$
$101$	−8.45267e12	−	4.88015e12i	−0.0788395	−	0.0455180i	−0.538902	+	0.842369i	$0.681161\pi$
$102$	−1.11139e14	+	1.92498e14i	−0.967532	+	1.67581i
$103$	2.36669e13	−	1.36641e13i	0.192433	−	0.111101i	−0.400688	−	0.916215i	$-0.631229\pi$
$103$	2.36669e13	−	1.36641e13i	0.192433	−	0.111101i	0.593121	+	0.805113i	$0.297895\pi$
$104$			7.27182e12i			0.0552599i
$105$	−2.26618e14	−	2.22917e14i	−1.61053	−	1.58423i
$106$	−1.67365e14			−1.11307
$107$	6.38437e13	+	1.10580e14i	0.397586	+	0.688640i	0.993428	−	0.114463i	$-0.0365146\pi$
$107$	6.38437e13	+	1.10580e14i	0.397586	+	0.688640i	−0.595841	+	0.803102i	$0.703181\pi$
$108$	2.17724e14	+	1.25703e14i	1.27040	+	0.733463i
$109$	1.12213e14	−	1.94359e14i	0.613845	−	1.06321i	−0.376741	−	0.926318i	$-0.622955\pi$
$109$	1.12213e14	−	1.94359e14i	0.613845	−	1.06321i	0.990586	−	0.136892i	$-0.0437112\pi$
$110$	−1.57282e14	+	9.08069e13i	−0.807106	+	0.465983i
$111$			1.44649e14i			0.696714i
$112$	1.38642e13	−	5.34998e13i	0.0627147	−	0.242006i
$113$	1.41467e14			0.601322			0.300661	−	0.953731i	$-0.402793\pi$
$113$	1.41467e14			0.601322			0.300661	+	0.953731i	$0.402793\pi$
$114$	−4.24449e13	−	7.35167e13i	−0.169626	−	0.293800i
$115$	−1.16923e14	−	6.75055e13i	−0.439556	−	0.253778i
$116$	−6.32625e13	+	1.09574e14i	−0.223841	+	0.387705i
$117$	−1.03830e14	+	5.99461e13i	−0.345956	+	0.199738i
$118$			9.58267e13i			0.300824i
$119$	1.30825e14	+	4.72648e14i	0.387135	+	1.39865i
$120$	−2.86195e14			−0.798717
$121$	−3.99331e13	−	6.91662e13i	−0.105156	−	0.182136i
$122$	4.57202e13	+	2.63966e13i	0.113655	+	0.0656188i
$123$	2.02153e14	−	3.50139e14i	0.474618	−	0.822062i
$124$	−2.39100e14	+	1.38045e14i	−0.530430	+	0.306244i
$125$			3.22612e14i			0.676565i
$126$	8.78180e14	−	2.43073e14i	1.74177	−	0.482107i
$127$	3.21826e14			0.603941			0.301971	−	0.953317i	$-0.402356\pi$
$127$	3.21826e14			0.603941			0.301971	+	0.953317i	$0.402356\pi$
$128$	−2.48791e13	−	4.30919e13i	−0.0441942	−	0.0765466i
$129$	1.39956e15	+	8.08035e14i	2.35430	+	1.35926i
$130$	4.15413e13	−	7.19516e13i	0.0662028	−	0.114667i
$131$	−8.71082e14	+	5.02919e14i	−1.31571	+	0.759625i	−0.983035	−	0.183417i	$-0.941284\pi$
$131$	−8.71082e14	+	5.02919e14i	−1.31571	+	0.759625i	−0.332674	+	0.943042i	$0.607951\pi$
$132$		−	7.24282e14i		−	1.03727i
$133$	−1.81306e14	−	4.69846e13i	−0.246292	−	0.0638255i
$134$	−9.40507e14			−1.21235
$135$	−1.43619e15	−	2.48755e15i	−1.75742	−	3.04393i
$136$	3.82381e14	+	2.20768e14i	0.444349	+	0.256545i
$137$	2.66400e14	−	4.61419e14i	0.294097	−	0.509391i	−0.680677	−	0.732583i	$-0.738314\pi$
$137$	2.66400e14	−	4.61419e14i	0.294097	−	0.509391i	0.974774	+	0.223192i	$0.0716477\pi$
$138$	4.66293e14	−	2.69214e14i	0.489221	−	0.282452i
$139$		−	6.09093e13i		−	0.0607547i	−0.999539	−	0.0303774i	$-0.990329\pi$
$139$		−	6.09093e13i		−	0.0607547i	0.999539	−	0.0303774i	$-0.00967090\pi$
$140$	−4.42805e14	+	4.50156e14i	−0.420065	+	0.427039i
$141$	−3.31059e15			−2.98794
$142$	2.47553e14	+	4.28774e14i	0.212642	+	0.368307i
$143$	1.82090e14	+	1.05130e14i	0.148914	+	0.0859753i
$144$	4.10187e14	−	7.10465e14i	0.319481	−	0.553357i
$145$	1.25191e15	−	7.22791e14i	0.928961	−	0.536336i
$146$		−	2.29455e14i		−	0.162266i
$147$	1.35843e15	−	2.44497e15i	0.915834	−	1.64836i
$148$	2.87333e14			0.184737
$149$	2.56774e14	+	4.44745e14i	0.157488	+	0.272777i	0.933962	−	0.357372i	$-0.116327\pi$
$149$	2.56774e14	+	4.44745e14i	0.157488	+	0.272777i	−0.776474	+	0.630149i	$0.782994\pi$
$150$	8.58779e14	+	4.95816e14i	0.502623	+	0.290190i
$151$	2.58809e14	−	4.48270e14i	0.144591	−	0.250439i	−0.784629	−	0.619965i	$-0.787147\pi$
$151$	2.58809e14	−	4.48270e14i	0.144591	−	0.250439i	0.929220	+	0.369527i	$0.120480\pi$
$152$	−1.46034e14	+	8.43130e13i	−0.0779023	+	0.0449769i
$153$			7.27970e15i			3.70914i
$154$	−1.13923e15	−	1.12062e15i	−0.554581	−	0.545524i
$155$	3.15439e15			1.46755
$156$	1.65668e14	+	2.86945e14i	0.0736828	+	0.127622i
$157$	2.63860e15	+	1.52340e15i	1.12222	+	0.647911i	0.941965	−	0.335710i	$-0.108976\pi$
$157$	2.63860e15	+	1.52340e15i	1.12222	+	0.647911i	0.180250	+	0.983621i	$0.442309\pi$
$158$	−2.99697e14	+	5.19090e14i	−0.121922	+	0.211175i
$159$	−6.60422e15	+	3.81295e15i	−2.57064	+	1.48416i
$160$			5.68501e14i			0.211783i
$161$	2.98008e14	−	1.14997e15i	0.106279	−	0.410113i
$162$	6.16307e15			2.10471
$163$	−2.04361e15	−	3.53963e15i	−0.668474	−	1.15783i	−0.978331	−	0.207048i	$-0.933614\pi$
$163$	−2.04361e15	−	3.53963e15i	−0.668474	−	1.15783i	0.309857	−	0.950783i	$-0.399719\pi$
$164$	−6.95521e14	−	4.01559e14i	−0.217973	−	0.125847i
$165$	−4.13756e15	+	7.16646e15i	−1.24267	+	2.15237i
$166$	−8.27304e14	+	4.77644e14i	−0.238182	+	0.137514i
$167$		−	5.67759e15i		−	1.56729i	−0.621210	−	0.783644i	$-0.713359\pi$
$167$		−	5.67759e15i		−	1.56729i	0.621210	−	0.783644i	$-0.286641\pi$
$168$	−6.71761e14	−	2.42695e15i	−0.177848	−	0.642535i
$169$	3.84119e15			0.975571
$170$	−2.52233e15	−	4.36881e15i	−0.614696	−	1.06468i
$171$	−2.40770e15	−	1.39009e15i	−0.563158	−	0.325139i
$172$	1.60509e15	−	2.78010e15i	0.360413	−	0.624254i
$173$	9.10944e14	−	5.25934e14i	0.196412	−	0.113399i	−0.398569	−	0.917139i	$-0.630493\pi$
$173$	9.10944e14	−	5.25934e14i	0.196412	−	0.113399i	0.594981	+	0.803740i	$0.297160\pi$
$174$			5.76503e15i			1.19387i
$175$	2.10859e15	−	5.83640e14i	0.419494	−	0.116112i
$176$	−1.43872e15			−0.275036
$177$	2.18314e15	+	3.78131e15i	0.401115	+	0.694752i
$178$	1.87902e15	+	1.08485e15i	0.331888	+	0.191616i
$179$	−2.01054e15	+	3.48235e15i	−0.341461	+	0.591427i	−0.984704	−	0.174234i	$-0.944255\pi$
$179$	−2.01054e15	+	3.48235e15i	−0.341461	+	0.591427i	0.643243	+	0.765662i	$0.277588\pi$
$180$	−8.11726e15	+	4.68650e15i	−1.32587	+	0.765493i
$181$		−	7.07907e15i		−	1.11231i	−0.831078	−	0.556156i	$-0.812276\pi$
$181$		−	7.07907e15i		−	1.11231i	0.831078	−	0.556156i	$-0.187724\pi$
$182$	7.07661e14	+	1.83387e14i	0.106986	+	0.0277249i
$183$	2.40549e15			0.349982
$184$	−5.34771e14	−	9.26250e14i	−0.0748933	−	0.129719i
$185$	−2.84303e15	−	1.64143e15i	−0.383336	−	0.221319i
$186$	−6.28991e15	+	1.08944e16i	−0.816684	+	1.41454i
$187$	1.10563e16	−	6.38335e15i	1.38267	−	0.798284i
$188$			6.57620e15i			0.792265i
$189$	1.77236e16	−	1.80178e16i	2.05740	−	2.09155i
$190$	1.92660e15			0.215534
$191$	−3.50585e15	−	6.07230e15i	−0.378059	−	0.654817i	0.612721	−	0.790299i	$-0.290075\pi$
$191$	−3.50585e15	−	6.07230e15i	−0.378059	−	0.654817i	−0.990780	+	0.135482i	$0.956742\pi$
$192$	−1.96345e15	−	1.13360e15i	−0.204133	−	0.117856i
$193$	2.24518e15	−	3.88877e15i	0.225087	−	0.389862i	−0.731259	−	0.682100i	$-0.761067\pi$
$193$	2.24518e15	−	3.88877e15i	0.225087	−	0.389862i	0.956345	+	0.292239i	$0.0944001\pi$
$194$	8.12399e15	−	4.69039e15i	0.785520	−	0.453520i
$195$		−	3.78560e15i		−	0.353096i
$196$	−4.85672e15	−	2.69841e15i	−0.437070	−	0.242837i
$197$	−1.68442e16			−1.46281			−0.731404	−	0.681945i	$-0.761134\pi$
$197$	−1.68442e16			−1.46281			−0.731404	+	0.681945i	$0.761134\pi$
$198$	−1.18603e16	−	2.05426e16i	−0.994120	−	1.72187i
$199$	7.61929e15	+	4.39900e15i	0.616514	+	0.355944i	0.775510	−	0.631335i	$-0.217493\pi$
$199$	7.61929e15	+	4.39900e15i	0.616514	+	0.355944i	−0.158997	+	0.987279i	$0.550826\pi$
$200$	9.84896e14	−	1.70589e15i	0.0769450	−	0.133273i
$201$	−3.71123e16	+	2.14268e16i	−2.79992	+	1.61653i
$202$			8.83401e14i			0.0643722i
$203$	9.06783e15	+	8.91976e15i	0.638310	+	0.627886i
$204$	2.01183e16			1.36830
$205$	4.58792e15	+	7.94651e15i	0.301536	+	0.522275i
$206$	−2.14208e15	−	1.23673e15i	−0.136071	−	0.0785606i
$207$	8.81688e15	−	1.52713e16i	0.541405	−	0.937742i
$208$	5.69992e14	−	3.29085e14i	0.0338396	−	0.0195373i
$209$			4.87571e15i			0.279907i
$210$	−7.21751e15	+	2.78512e16i	−0.400730	+	1.54635i
$211$	3.79686e15			0.203914			0.101957	−	0.994789i	$-0.467490\pi$
$211$	3.79686e15			0.203914			0.101957	+	0.994789i	$0.467490\pi$
$212$	7.57409e15	+	1.31187e16i	0.393531	+	0.681616i
$213$	1.95368e16	+	1.12796e16i	0.982193	+	0.567069i
$214$	5.77847e15	−	1.00086e16i	0.281136	−	0.486942i
$215$	−3.17634e16	+	1.83386e16i	−1.49574	+	0.863568i
$216$		−	2.27546e16i		−	1.03727i
$217$	7.40404e15	+	2.67495e16i	0.326777	+	1.18059i
$218$	−2.03128e16			−0.868107
$219$	−5.22748e15	−	9.05426e15i	−0.216363	−	0.374752i
$220$	1.42356e16	+	8.21890e15i	0.570710	+	0.329500i
$221$	−2.92018e15	+	5.05790e15i	−0.113413	+	0.196437i
$222$	1.13381e16	−	6.54607e15i	0.426648	−	0.246326i
$223$		−	6.03134e15i		−	0.219928i	−0.993936	−	0.109964i	$-0.964926\pi$
$223$		−	6.03134e15i		−	0.219928i	0.993936	−	0.109964i	$-0.0350735\pi$
$224$	−4.82093e15	+	1.33440e15i	−0.170371	+	0.0471573i
$225$	3.24764e16			1.11247
$226$	−6.40208e15	−	1.10887e16i	−0.212599	−	0.368233i
$227$	2.39287e16	+	1.38152e16i	0.770438	+	0.444812i	0.833031	−	0.553227i	$-0.186604\pi$
$227$	2.39287e16	+	1.38152e16i	0.770438	+	0.444812i	−0.0625930	+	0.998039i	$0.519937\pi$
$228$	−3.84167e15	+	6.65397e15i	−0.119943	+	0.207748i
$229$	−1.95108e16	+	1.12646e16i	−0.590782	+	0.341088i	−0.765407	−	0.643547i	$-0.777462\pi$
$229$	−1.95108e16	+	1.12646e16i	−0.590782	+	0.341088i	0.174625	+	0.984635i	$0.444129\pi$
$230$			1.22198e16i			0.358896i
$231$	−7.04839e16	−	1.82656e16i	−2.00820	−	0.520415i
$232$	1.14517e16			0.316560
$233$	−1.16047e16	−	2.01000e16i	−0.311274	−	0.539143i	0.667364	−	0.744732i	$-0.267423\pi$
$233$	−1.16047e16	−	2.01000e16i	−0.311274	−	0.539143i	−0.978639	+	0.205588i	$0.934089\pi$
$234$	9.39759e15	+	5.42570e15i	0.244628	+	0.141236i
$235$	3.75674e16	−	6.50687e16i	0.949154	−	1.64398i
$236$	7.51125e15	−	4.33662e15i	0.184216	−	0.106357i
$237$			2.73110e16i			0.650278i
$238$	3.11274e16	−	3.16441e16i	0.719622	−	0.731568i
$239$	−6.95548e16			−1.56150			−0.780750	−	0.624844i	$-0.785163\pi$
$239$	−6.95548e16			−1.56150			−0.780750	+	0.624844i	$0.785163\pi$
$240$	1.29517e16	+	2.24330e16i	0.282389	+	0.489112i
$241$	−3.62973e16	−	2.09563e16i	−0.768697	−	0.443807i	0.0637126	−	0.997968i	$-0.479706\pi$
$241$	−3.62973e16	−	2.09563e16i	−0.768697	−	0.443807i	−0.832410	+	0.554161i	$0.813039\pi$
$242$	−3.61433e15	+	6.26021e15i	−0.0743568	+	0.128790i
$243$	1.16074e17	−	6.70155e16i	2.32002	−	1.33947i
$244$		−	4.77829e15i		−	0.0927991i
$245$	3.26402e16	+	5.44443e16i	0.616013	+	1.02752i
$246$	−3.65936e16			−0.671211
$247$	−1.11524e15	−	1.93165e15i	−0.0198833	−	0.0344390i
$248$	2.16409e16	+	1.24944e16i	0.375071	+	0.216547i
$249$	−2.17635e16	+	3.76956e16i	−0.366720	+	0.635177i
$250$	2.52875e16	−	1.45997e16i	0.414310	−	0.239202i
$251$			1.11790e17i			1.78110i	0.454888	+	0.890549i	$0.349679\pi$
$251$			1.11790e17i			1.78110i	−0.454888	+	0.890549i	$0.650321\pi$
$252$	−5.87949e16	−	5.78348e16i	−0.911036	−	0.896159i
$253$	−3.09250e16			−0.466087
$254$	−1.45642e16	−	2.52259e16i	−0.213525	−	0.369837i
$255$	−1.99062e17	−	1.14929e17i	−2.83927	−	1.63926i
$256$	−2.25180e15	+	3.90023e15i	−0.0312500	+	0.0541266i
$257$	9.85962e16	−	5.69246e16i	1.33146	−	0.768719i	0.345937	−	0.938258i	$-0.387561\pi$
$257$	9.85962e16	−	5.69246e16i	1.33146	−	0.768719i	0.985524	+	0.169538i	$0.0542277\pi$
$258$		−	1.46270e17i		−	1.92228i
$259$	7.24621e15	−	2.79619e16i	0.0926856	−	0.357659i
$260$	−7.51977e15			−0.0936249
$261$	9.44037e16	+	1.63512e17i	1.14421	+	1.98183i
$262$	7.88413e16	+	4.55191e16i	0.930347	+	0.537136i
$263$	−2.19392e16	+	3.79999e16i	−0.252076	+	0.436608i	−0.964097	−	0.265550i	$-0.914447\pi$
$263$	−2.19392e16	+	3.79999e16i	−0.252076	+	0.436608i	0.712021	+	0.702158i	$0.247780\pi$
$264$	−5.67719e16	+	3.27773e16i	−0.635193	+	0.366729i
$265$		−	1.73072e17i		−	1.88584i
$266$	4.52215e15	+	1.63377e16i	0.0479925	+	0.173388i
$267$	9.88613e16			1.02199
$268$	4.25625e16	+	7.37204e16i	0.428631	+	0.742410i
$269$	−6.98866e16	−	4.03490e16i	−0.685690	−	0.395883i	0.116305	−	0.993213i	$-0.462895\pi$
$269$	−6.98866e16	−	4.03490e16i	−0.685690	−	0.395883i	−0.801995	+	0.597330i	$0.796228\pi$
$270$	−1.29989e17	+	2.25147e17i	−1.24268	+	2.15239i
$271$	3.46851e16	−	2.00254e16i	0.323115	−	0.186551i	−0.329665	−	0.944098i	$-0.606936\pi$
$271$	3.46851e16	−	2.00254e16i	0.323115	−	0.186551i	0.652780	+	0.757547i	$0.273602\pi$
$272$		−	3.99633e16i		−	0.362810i
$273$	3.21022e16	−	8.88563e15i	0.284051	−	0.0786231i
$274$	−4.82236e16			−0.415916
$275$	−2.84776e16	−	4.93246e16i	−0.239428	−	0.414701i
$276$	−4.22040e16	−	2.43665e16i	−0.345931	−	0.199724i
$277$	2.04422e16	−	3.54069e16i	0.163369	−	0.282963i	−0.772706	−	0.634764i	$-0.781097\pi$
$277$	2.04422e16	−	3.54069e16i	0.163369	−	0.282963i	0.936075	+	0.351801i	$0.114431\pi$
$278$	−4.77429e15	+	2.75644e15i	−0.0372045	+	0.0214800i
$279$			4.11995e17i			3.13085i
$280$	5.53240e16	+	1.43370e16i	0.410022	+	0.106255i
$281$	1.23659e17			0.893881			0.446941	−	0.894564i	$-0.352513\pi$
$281$	1.23659e17			0.893881			0.446941	+	0.894564i	$0.352513\pi$
$282$	1.49820e17	+	2.59496e17i	1.05640	+	1.82973i
$283$	1.10380e17	+	6.37281e16i	0.759254	+	0.438355i	0.829028	−	0.559208i	$-0.188895\pi$
$283$	1.10380e17	+	6.37281e16i	0.759254	+	0.438355i	−0.0697741	+	0.997563i	$0.522228\pi$
$284$	2.24059e16	−	3.88082e16i	0.150361	−	0.260433i
$285$	7.60234e16	−	4.38921e16i	0.497775	−	0.287391i
$286$		−	1.90305e16i		−	0.121587i
$287$	−5.66182e16	+	5.75581e16i	−0.353007	+	0.358867i
$288$	−7.42518e16			−0.451814
$289$	9.31208e16	+	1.61290e17i	0.553047	+	0.957905i
$290$	−1.13310e17	−	6.54196e16i	−0.656874	−	0.379247i
$291$	2.13715e17	−	3.70165e17i	1.20944	−	2.09481i
$292$	−1.79855e16	+	1.03839e16i	−0.0993671	+	0.0573696i
$293$		−	3.42111e16i		−	0.184541i	−0.995734	−	0.0922706i	$-0.970588\pi$
$293$		−	3.42111e16i		−	0.184541i	0.995734	−	0.0922706i	$-0.0294125\pi$
$294$	−2.53121e17	+	4.16779e15i	−1.33321	+	0.0219520i
$295$	−9.90942e16			−0.509676
$296$	−1.30032e16	−	2.25222e16i	−0.0653143	−	0.113128i
$297$	−5.69788e17	−	3.28967e17i	−2.79523	−	1.61383i
$298$	2.32405e16	−	4.02538e16i	0.111361	−	0.192882i
$299$	1.22518e16	−	7.07361e15i	0.0573460	−	0.0331087i
$300$		−	8.97523e16i		−	0.410390i
$301$	−2.30068e17	−	2.26311e17i	−1.02776	−	1.01098i
$302$	−4.68494e16			−0.204482
$303$	2.01258e16	+	3.48589e16i	0.0858331	+	0.148667i
$304$	1.32175e16	+	7.63115e15i	0.0550852	+	0.0318035i
$305$	−2.72966e16	+	4.72791e16i	−0.111176	+	0.192562i
$306$	5.70610e17	−	3.29442e17i	2.27138	−	1.31138i
$307$			7.49508e16i			0.291614i	0.989313	+	0.145807i	$0.0465778\pi$
$307$			7.49508e16i			0.291614i	−0.989313	+	0.145807i	$0.953422\pi$
$308$	−3.62830e16	+	1.40010e17i	−0.137990	+	0.532482i
$309$	−1.12702e17			−0.419007
$310$	−1.42751e17	−	2.47253e17i	−0.518858	−	0.898689i
$311$	3.34357e17	+	1.93041e17i	1.18819	+	0.686004i	0.957896	−	0.287116i	$-0.0926965\pi$
$311$	3.34357e17	+	1.93041e17i	1.18819	+	0.686004i	0.230298	+	0.973120i	$0.426030\pi$
$312$	1.49946e16	−	2.59713e16i	0.0521016	−	0.0902427i
$313$	−1.17520e17	+	6.78504e16i	−0.399303	+	0.230538i	−0.686183	−	0.727429i	$-0.740715\pi$
$313$	−1.17520e17	+	6.78504e16i	−0.399303	+	0.230538i	0.286880	+	0.957966i	$0.407382\pi$
$314$		−	2.75764e17i		−	0.916285i
$315$	2.51361e17	+	9.08124e17i	0.816817	+	2.95101i
$316$	5.42509e16			0.172424
$317$	−1.48908e17	−	2.57916e17i	−0.462917	−	0.801797i	0.536187	−	0.844099i	$-0.319864\pi$
$317$	−1.48908e17	−	2.57916e17i	−0.462917	−	0.801797i	−0.999105	+	0.0423024i	$0.986531\pi$
$318$	5.97745e17	+	3.45109e17i	1.81772	+	1.04946i
$319$	1.65559e17	−	2.86757e17i	0.492515	−	0.853061i
$320$	4.45612e16	−	2.57274e16i	0.129690	−	0.0748766i
$321$		−	5.26585e17i		−	1.49945i
$322$	−1.03625e17	+	2.86825e16i	−0.288717	+	0.0799146i
$323$	−1.35432e17			−0.369236
$324$	−2.78909e17	−	4.83084e17i	−0.744127	−	1.28887i
$325$	2.25644e16	+	1.30276e16i	0.0589170	+	0.0340158i
$326$	−1.84966e17	+	3.20371e17i	−0.472682	+	0.818710i
$327$	−8.01539e17	+	4.62769e17i	−2.00489	+	1.15752i
$328$			7.26900e16i			0.177974i
$329$	6.39967e17	+	1.65844e17i	1.53386	+	0.397493i
$330$	7.48978e17			1.75740
$331$	3.09882e17	+	5.36732e17i	0.711870	+	1.23299i	0.964154	+	0.265342i	$0.0854847\pi$
$331$	3.09882e17	+	5.36732e17i	0.711870	+	1.23299i	−0.252285	+	0.967653i	$0.581182\pi$
$332$	7.48790e16	+	4.32314e16i	0.168420	+	0.0972373i
$333$	2.14387e17	−	3.71328e17i	0.472159	−	0.817803i
$334$	−4.45030e17	+	2.56938e17i	−0.959764	+	0.554120i
$335$		−	9.72575e17i		−	2.05404i
$336$	−1.59833e17	+	1.62487e17i	−0.330592	+	0.336080i
$337$	−8.73043e17			−1.76859			−0.884294	−	0.466931i	$-0.845360\pi$
$337$	−8.73043e17			−1.76859			−0.884294	+	0.466931i	$0.845360\pi$
$338$	−1.73832e17	−	3.01087e17i	−0.344916	−	0.597413i
$339$	−5.05251e17	−	2.91707e17i	−0.981994	−	0.566955i
$340$	−2.28296e17	+	3.95420e17i	−0.434655	+	0.752845i
$341$	6.25731e17	−	3.61266e17i	1.16710	−	0.673823i
$342$			2.51633e17i			0.459816i
$343$	−3.85078e17	+	4.04584e17i	−0.689430	+	0.724352i
$344$	−2.90552e17			−0.509701
$345$	2.78394e17	+	4.82192e17i	0.478548	+	0.828870i
$346$	−8.24493e16	−	4.76021e16i	−0.138885	−	0.0801851i
$347$	−2.32098e17	+	4.02006e17i	−0.383147	+	0.663630i	−0.991510	−	0.130029i	$-0.958493\pi$
$347$	−2.32098e17	+	4.02006e17i	−0.383147	+	0.663630i	0.608363	+	0.793659i	$0.291826\pi$
$348$	4.51884e17	−	2.60896e17i	0.731093	−	0.422097i
$349$			1.22129e18i			1.93660i	0.249790	+	0.968300i	$0.419638\pi$
$349$			1.22129e18i			1.93660i	−0.249790	+	0.968300i	$0.580362\pi$
$350$	−1.41172e17	−	1.38866e17i	−0.219417	−	0.215834i
$351$	3.00984e17			0.458557
$352$	6.51092e16	+	1.12772e17i	0.0972397	+	0.168424i
$353$	2.26555e17	+	1.30801e17i	0.331703	+	0.191509i	0.656597	−	0.754241i	$-0.271995\pi$
$353$	2.26555e17	+	1.30801e17i	0.331703	+	0.191509i	−0.324894	+	0.945751i	$0.605329\pi$
$354$	1.97595e17	−	3.42245e17i	0.283631	−	0.491264i
$355$	−4.43394e17	+	2.55994e17i	−0.624010	+	0.360272i
$356$		−	1.96379e17i		−	0.270985i
$357$	5.07361e17	−	1.95783e18i	0.686499	−	2.64909i
$358$	3.63946e17			0.482898
$359$	4.19101e17	+	7.25904e17i	0.545328	+	0.944536i	0.998586	+	0.0531564i	$0.0169282\pi$
$359$	4.19101e17	+	7.25904e17i	0.545328	+	0.944536i	−0.453258	+	0.891379i	$0.649738\pi$
$360$	7.34690e17	+	4.24174e17i	0.937533	+	0.541285i
$361$	−3.73642e17	+	6.47167e17i	−0.467633	+	0.809965i
$362$	−5.54884e17	+	3.20362e17i	−0.681149	+	0.393261i
$363$			3.29370e17i			0.396586i
$364$	−1.76505e16	−	6.37683e16i	−0.0208472	−	0.0753173i
$365$	2.37279e17			0.274921
$366$	−1.08860e17	−	1.88551e17i	−0.123737	−	0.214319i
$367$	4.29158e17	+	2.47774e17i	0.478580	+	0.276308i	0.719825	−	0.694156i	$-0.244222\pi$
$367$	4.29158e17	+	2.47774e17i	0.478580	+	0.276308i	−0.241244	+	0.970464i	$0.577556\pi$
$368$	−4.84019e16	+	8.38346e16i	−0.0529575	+	0.0917251i
$369$	−1.03789e18	+	5.99228e17i	−1.11421	+	0.643291i
$370$			2.97130e17i			0.312993i
$371$	1.46766e18	−	4.06238e17i	1.51708	−	0.419916i
$372$	1.13860e18			1.15497
$373$	−1.70503e17	−	2.95319e17i	−0.169734	−	0.293988i	0.768592	−	0.639739i	$-0.220958\pi$
$373$	−1.70503e17	−	2.95319e17i	−0.169734	−	0.293988i	−0.938326	+	0.345751i	$0.887624\pi$
$374$	−1.00070e18	−	5.77755e17i	−0.977695	−	0.564472i
$375$	6.65227e17	−	1.15221e18i	0.637898	−	1.10487i
$376$	5.15467e17	−	2.97605e17i	0.485161	−	0.280108i
$377$			1.51476e17i			0.139944i
$378$	−2.21438e18	−	5.73846e17i	−2.00821	−	0.520419i
$379$	−7.24986e17			−0.645439			−0.322720	−	0.946495i	$-0.604597\pi$
$379$	−7.24986e17			−0.645439			−0.322720	+	0.946495i	$0.604597\pi$
$380$	−8.71879e16	−	1.51014e17i	−0.0762028	−	0.131987i
$381$	−1.14940e18	−	6.63607e17i	−0.986272	−	0.569424i
$382$	−3.17313e17	+	5.49602e17i	−0.267328	+	0.463026i
$383$	6.44614e17	−	3.72168e17i	0.533223	−	0.307856i	−0.209105	−	0.977893i	$-0.567055\pi$
$383$	6.44614e17	−	3.72168e17i	0.533223	−	0.307856i	0.742328	+	0.670037i	$0.233722\pi$
$384$			2.05204e17i			0.166673i
$385$	1.15883e18	−	1.17807e18i	0.924263	−	0.939606i
$386$	−4.06421e17			−0.318321
$387$	−2.39520e18	−	4.14861e18i	−1.84232	−	3.19099i
$388$	−7.35300e17	−	4.24526e17i	−0.555447	−	0.320687i
$389$	−1.61294e17	+	2.79370e17i	−0.119666	+	0.207268i	−0.919635	−	0.392773i	$-0.871516\pi$
$389$	−1.61294e17	+	2.79370e17i	−0.119666	+	0.207268i	0.799969	+	0.600041i	$0.204849\pi$
$390$	−2.96729e17	+	1.71317e17i	−0.216226	+	0.124838i
$391$		−	8.59001e17i		−	0.614832i
$392$	8.27896e15	+	5.02804e17i	0.00582067	+	0.353505i
$393$	4.14809e18			2.86484
$394$	7.62282e17	+	1.32031e18i	0.517181	+	0.895783i
$395$	−5.36790e17	−	3.09916e17i	−0.357787	−	0.206568i
$396$	−1.07347e18	+	1.85930e18i	−0.702949	+	1.21754i
$397$	1.62278e16	−	9.36914e15i	0.0104406	−	0.00602790i	−0.494771	−	0.869024i	$-0.664748\pi$
$397$	1.62278e16	−	9.36914e15i	0.0104406	−	0.00602790i	0.505211	+	0.862996i	$0.331415\pi$
$398$		−	7.96304e17i		−	0.503381i
$399$	5.50652e17	+	5.41660e17i	0.342032	+	0.336447i
$400$	−1.78285e17			−0.108817
$401$	4.61751e17	+	7.99776e17i	0.276947	+	0.479686i	0.970625	−	0.240599i	$-0.0773440\pi$
$401$	4.61751e17	+	7.99776e17i	0.276947	+	0.479686i	−0.693677	+	0.720286i	$0.744011\pi$
$402$	3.35902e18	+	1.93933e18i	1.97984	+	1.14306i
$403$	−1.65268e17	+	2.86252e17i	−0.0957309	+	0.165811i
$404$	6.92442e16	−	3.99782e16i	0.0394198	−	0.0227590i
$405$			6.37321e18i			3.56593i
$406$	2.88800e17	−	1.11443e18i	0.158824	−	0.612874i
$407$	−7.51956e17			−0.406473
$408$	−9.10451e17	−	1.57695e18i	−0.483766	−	0.837907i
$409$	−2.44973e18	−	1.41435e18i	−1.27954	−	0.738744i	−0.302778	−	0.953061i	$-0.597914\pi$
$409$	−2.44973e18	−	1.41435e18i	−1.27954	−	0.738744i	−0.976764	+	0.214317i	$0.931247\pi$
$410$	4.15251e17	−	7.19236e17i	0.213218	−	0.369304i
$411$	−1.90290e18	+	1.09864e18i	−0.960557	+	0.554578i
$412$			2.23872e17i			0.111101i
$413$	−2.32596e17	−	8.40326e17i	−0.113488	−	0.410013i
$414$	−1.59603e18			−0.765663
$415$	−4.93930e17	−	8.55512e17i	−0.232986	−	0.403543i
$416$	−5.15898e16	−	2.97854e16i	−0.0239282	−	0.0138150i
$417$	−1.25595e17	+	2.17538e17i	−0.0572824	+	0.0992161i
$418$	3.82176e17	−	2.20649e17i	0.171407	−	0.0989620i
$419$			2.85613e18i			1.25973i	0.776703	+	0.629867i	$0.216891\pi$
$419$			2.85613e18i			1.25973i	−0.776703	+	0.629867i	$0.783109\pi$
$420$	2.50971e18	−	6.94667e17i	1.08862	−	0.301322i
$421$	−3.25299e18			−1.38774			−0.693870	−	0.720101i	$-0.744096\pi$
$421$	−3.25299e18			−1.38774			−0.693870	+	0.720101i	$0.744096\pi$
$422$	−1.71826e17	−	2.97612e17i	−0.0720946	−	0.124872i
$423$	8.49862e18	+	4.90668e18i	3.50724	+	2.02491i
$424$	6.85528e17	−	1.18737e18i	0.278269	−	0.481975i
$425$	1.37008e18	−	7.91019e17i	0.547047	−	0.315838i
$426$		−	2.04182e18i		−	0.801957i
$427$	−4.65002e17	−	1.20503e17i	−0.179663	−	0.0465589i
$428$	−1.04601e18			−0.397586
$429$	−4.33557e17	−	7.50943e17i	−0.162123	−	0.280806i
$430$	2.87489e18	+	1.65982e18i	1.05765	+	0.610635i
$431$	9.71533e17	−	1.68275e18i	0.351655	−	0.609084i	−0.634885	−	0.772607i	$-0.718952\pi$
$431$	9.71533e17	−	1.68275e18i	0.351655	−	0.609084i	0.986540	+	0.163523i	$0.0522857\pi$
$432$	−1.78359e18	+	1.02976e18i	−0.635198	+	0.366732i
$433$		−	3.35910e18i		−	1.17709i	−0.808466	−	0.588543i	$-0.799702\pi$
$433$		−	3.35910e18i		−	1.17709i	0.808466	−	0.588543i	$-0.200298\pi$
$434$	1.76165e18	−	1.79090e18i	0.607425	−	0.617509i
$435$	−5.96160e18			−2.02273
$436$	9.19251e17	+	1.59219e18i	0.306922	+	0.531605i
$437$	2.84108e17	+	1.64030e17i	0.0933497	+	0.0538955i
$438$	−4.73138e17	+	8.19498e17i	−0.152992	+	0.264990i
$439$	−1.64053e18	+	9.47162e17i	−0.522075	+	0.301420i	−0.737783	−	0.675038i	$-0.764127\pi$
$439$	−1.64053e18	+	9.47162e17i	−0.522075	+	0.301420i	0.215708	+	0.976458i	$0.430794\pi$
$440$		−	1.48778e18i		−	0.465983i
$441$	−7.11096e18	+	4.26313e18i	−2.19209	+	1.31419i
$442$	5.28609e17			0.160391
$443$	2.60130e18	+	4.50558e18i	0.776897	+	1.34563i	0.933722	+	0.357999i	$0.116541\pi$
$443$	2.60130e18	+	4.50558e18i	0.776897	+	1.34563i	−0.156825	+	0.987626i	$0.550126\pi$
$444$	−1.02621e18	−	5.92482e17i	−0.301686	−	0.174178i
$445$	−1.12184e18	+	1.94309e18i	−0.324647	+	0.562306i
$446$	−4.72759e17	+	2.72947e17i	−0.134678	+	0.0777562i
$447$		−	2.11788e18i		−	0.593948i
$448$	3.22765e17	+	3.17495e17i	0.0891130	+	0.0876577i
$449$	7.07492e18			1.92308			0.961540	−	0.274665i	$-0.0885669\pi$
$449$	7.07492e18			1.92308			0.961540	+	0.274665i	$0.0885669\pi$
$450$	−1.46971e18	−	2.54562e18i	−0.393319	−	0.681249i
$451$	1.82019e18	+	1.05089e18i	0.479603	+	0.276899i
$452$	−5.79450e17	+	1.00364e18i	−0.150330	+	0.260380i
$453$	−1.84867e18	+	1.06733e18i	−0.472251	+	0.272654i
$454$		−	2.50082e18i		−	0.629060i
$455$	−1.89640e17	+	7.31791e17i	−0.0469732	+	0.181262i
$456$	6.95417e17			0.169626
$457$	−1.74544e18	−	3.02320e18i	−0.419269	−	0.726195i	0.576597	−	0.817029i	$-0.304380\pi$
$457$	−1.74544e18	−	3.02320e18i	−0.419269	−	0.726195i	−0.995866	+	0.0908335i	$0.971047\pi$
$458$	1.76592e18	+	1.01955e18i	0.417746	+	0.241186i
$459$	9.13768e18	−	1.58269e19i	2.12886	−	3.68729i
$460$	9.57832e17	−	5.53005e17i	0.219778	−	0.126889i
$461$		−	4.04428e18i		−	0.913975i	−0.889473	−	0.456988i	$-0.848928\pi$
$461$		−	4.04428e18i		−	0.913975i	0.889473	−	0.456988i	$-0.151072\pi$
$462$	1.75802e18	+	6.35140e18i	0.391317	+	1.41376i
$463$	−2.42585e18			−0.531859			−0.265930	−	0.963992i	$-0.585679\pi$
$463$	−2.42585e18			−0.531859			−0.265930	+	0.963992i	$0.585679\pi$
$464$	−5.18246e17	−	8.97629e17i	−0.111921	−	0.193852i
$465$	−1.12659e19	−	6.50438e18i	−2.39660	−	1.38368i
$466$	−1.05034e18	+	1.81924e18i	−0.220104	+	0.381232i
$467$	−5.93098e18	+	3.42425e18i	−1.22436	+	0.706883i	−0.965844	−	0.259125i	$-0.916566\pi$
$467$	−5.93098e18	+	3.42425e18i	−1.22436	+	0.706883i	−0.258513	+	0.966008i	$0.583233\pi$
$468$		−	9.82156e17i		−	0.199738i
$469$	8.24752e18	−	2.28285e18i	1.65239	−	0.457369i
$470$	−6.80043e18			−1.34231
$471$	−6.28251e18	−	1.08816e19i	−1.22176	−	2.11616i
$472$	−6.79841e17	−	3.92506e17i	−0.130261	−	0.0752060i
$473$	−4.20056e18	+	7.27558e18i	−0.793011	+	1.37354i
$474$	2.14074e18	−	1.23595e18i	0.398212	−	0.229908i
$475$			6.04192e17i			0.110744i
$476$	−3.88905e18	−	1.00783e18i	−0.702417	−	0.182028i
$477$	2.26049e19			4.02322
$478$	3.14769e18	+	5.45196e18i	0.552073	+	0.956219i
$479$	6.42258e17	+	3.70808e17i	0.111010	+	0.0640914i	0.554477	−	0.832199i	$-0.312918\pi$
$479$	6.42258e17	+	3.70808e17i	0.111010	+	0.0640914i	−0.443467	+	0.896291i	$0.646252\pi$
$480$	1.17225e18	−	2.03040e18i	0.199679	−	0.345855i
$481$	2.97909e17	−	1.71998e17i	0.0500113	−	0.0288741i
$482$			3.79349e18i			0.627639i
$483$	−3.43558e18	+	3.49261e18i	−0.560234	+	0.569535i
$484$	6.54264e17			0.105156
$485$	4.85032e18	+	8.40100e18i	0.768383	+	1.33088i
$486$	−1.05058e19	−	6.06555e18i	−1.64050	−	0.947145i
$487$	−2.57598e18	+	4.46173e18i	−0.396497	+	0.686753i	−0.993291	−	0.115641i	$-0.963108\pi$
$487$	−2.57598e18	+	4.46173e18i	−0.396497	+	0.686753i	0.596794	+	0.802395i	$0.296441\pi$
$488$	−3.74540e17	+	2.16241e17i	−0.0568276	+	0.0328094i
$489$			1.68557e19i			2.52108i
$490$	2.79042e18	−	5.02232e18i	0.411431	−	0.740512i
$491$	−1.04726e19			−1.52225			−0.761125	−	0.648605i	$-0.775353\pi$
$491$	−1.04726e19			−1.52225			−0.761125	+	0.648605i	$0.775353\pi$
$492$	1.65604e18	+	2.86834e18i	0.237309	+	0.411031i
$493$	7.96523e18	+	4.59873e18i	1.12530	+	0.649695i
$494$	−1.00940e17	+	1.74833e17i	−0.0140596	+	0.0243520i
$495$	2.12431e19	−	1.22647e19i	2.91730	−	1.68430i
$496$		−	2.26172e18i		−	0.306244i
$497$	−3.21159e18	−	3.15915e18i	−0.428771	−	0.421769i
$498$	3.93962e18			0.518620
$499$	2.74454e18	+	4.75369e18i	0.356259	+	0.617059i	0.987333	−	0.158664i	$-0.0507187\pi$
$499$	2.74454e18	+	4.75369e18i	0.356259	+	0.617059i	−0.631073	+	0.775723i	$0.717385\pi$
$500$	−2.28876e18	−	1.32142e18i	−0.292961	−	0.169141i
$501$	−1.17072e19	+	2.02775e19i	−1.47771	+	2.55948i
$502$	8.76253e18	−	5.05905e18i	1.09069	−	0.629713i
$503$		−	1.60460e19i		−	1.96966i	−0.173510	−	0.984832i	$-0.555511\pi$
$503$		−	1.60460e19i		−	1.96966i	0.173510	−	0.984832i	$-0.444489\pi$
$504$	−1.87255e18	+	7.22586e18i	−0.226683	+	0.874734i
$505$	−9.13523e17			−0.109064
$506$	1.39951e18	+	2.42402e18i	0.164786	+	0.285419i
$507$	−1.37188e19	−	7.92056e18i	−1.59317	−	0.919815i
$508$	−1.31820e18	+	2.28319e18i	−0.150985	+	0.261514i
$509$	4.43731e16	−	2.56188e16i	0.00501297	−	0.00289424i	−0.497491	−	0.867469i	$-0.665745\pi$
$509$	4.43731e16	−	2.56188e16i	0.00501297	−	0.00289424i	0.502504	+	0.864575i	$0.332412\pi$
$510$			2.08043e19i			2.31826i
$511$	5.56945e17	+	2.01214e18i	0.0612161	+	0.221163i
$512$	4.07619e17			0.0441942
$513$	3.48975e18	+	6.04443e18i	0.373227	+	0.646448i
$514$	−8.92391e18	−	5.15222e18i	−0.941485	−	0.543567i
$515$	1.27890e18	−	2.21512e18i	0.133102	−	0.230540i
$516$	−1.14652e19	+	6.61942e18i	−1.17715	+	0.679629i
$517$		−	1.72101e19i		−	1.74321i
$518$	−2.51969e18	+	6.97429e17i	−0.251790	+	0.0696934i
$519$	−4.33792e18			−0.427671
$520$	3.40306e17	+	5.89427e17i	0.0331014	+	0.0573333i
$521$	−6.76022e18	−	3.90301e18i	−0.648779	−	0.374573i	0.139209	−	0.990263i	$-0.455544\pi$
$521$	−6.76022e18	−	3.90301e18i	−0.648779	−	0.374573i	−0.787988	+	0.615690i	$0.788877\pi$
$522$	8.54444e18	−	1.47994e19i	0.809078	−	1.40136i
$523$	2.05634e18	−	1.18723e18i	0.192125	−	0.110923i	−0.400852	−	0.916143i	$-0.631286\pi$
$523$	2.05634e18	−	1.18723e18i	0.192125	−	0.110923i	0.592977	+	0.805219i	$0.297953\pi$
$524$		−	8.23983e18i		−	0.759625i
$525$	−8.73430e18	−	2.26345e18i	−0.794535	−	0.205900i
$526$	3.97143e18			0.356489
$527$	1.00348e19	+	1.73809e19i	0.888866	+	1.53956i
$528$	5.13841e18	+	2.96666e18i	0.449150	+	0.259317i
$529$	4.75603e18	−	8.23769e18i	0.410256	−	0.710584i
$530$	−1.35660e19	+	7.83234e18i	−1.15484	+	0.666746i
$531$		−	1.29427e19i		−	1.08733i
$532$	1.07596e18	−	1.09382e18i	0.0892103	−	0.0906913i
$533$	−9.61497e17			−0.0786787
$534$	−4.47395e18	−	7.74911e18i	−0.361329	−	0.625839i
$535$	1.03499e19	+	5.97550e18i	0.825008	+	0.476319i
$536$	3.85232e18	−	6.67241e18i	0.303088	−	0.524963i
$537$	1.43613e19	−	8.29148e18i	1.11525	−	0.643891i
$538$			7.30395e18i			0.559863i
$539$	1.27102e19	+	7.06180e18i	0.961678	+	0.534311i
$540$	2.35305e19			1.75742
$541$	1.57939e18	+	2.73558e18i	0.116442	+	0.201683i	0.918355	−	0.395757i	$-0.129518\pi$
$541$	1.57939e18	+	2.73558e18i	0.116442	+	0.201683i	−0.801913	+	0.597440i	$0.796185\pi$
$542$	−3.13933e18	−	1.81250e18i	−0.228477	−	0.131911i
$543$	−1.45971e19	+	2.52829e19i	−1.04874	+	1.81647i
$544$	−3.13247e18	+	1.80853e18i	−0.222175	+	0.128273i
$545$		−	2.10054e19i		−	1.47080i
$546$	−2.14927e18	−	2.11417e18i	−0.148574	−	0.146148i
$547$	−1.43454e19			−0.979045			−0.489523	−	0.871991i	$-0.662829\pi$
$547$	−1.43454e19			−0.979045			−0.489523	+	0.871991i	$0.662829\pi$
$548$	2.18235e18	+	3.77995e18i	0.147049	+	0.254696i
$549$	−6.17512e18	−	3.56521e18i	−0.410808	−	0.237180i
$550$	−2.57750e18	+	4.46435e18i	−0.169301	+	0.293238i
$551$	−3.04198e18	+	1.75629e18i	−0.197286	+	0.113903i
$552$			4.41080e18i			0.282452i
$553$	1.36815e18	−	5.27946e18i	0.0865082	−	0.333821i
$554$	−3.70043e18			−0.231038
$555$	6.76927e18	+	1.17247e19i	0.417341	+	0.722855i
$556$	4.32120e17	+	2.49484e17i	0.0263076	+	0.0151887i
$557$	5.88238e18	−	1.01886e19i	0.353644	−	0.612530i	−0.633241	−	0.773955i	$-0.718276\pi$
$557$	5.88238e18	−	1.01886e19i	0.353644	−	0.612530i	0.986885	+	0.161425i	$0.0516091\pi$
$558$	3.22937e19	−	1.86447e19i	1.91725	−	1.10692i
$559$		−	3.84324e18i		−	0.225328i
$560$	−1.37989e18	−	4.98531e18i	−0.0798969	−	0.288653i
$561$	−5.26501e19			−3.01064
$562$	−5.59615e18	−	9.69281e18i	−0.316035	−	0.547388i
$563$	1.71313e19	+	9.89074e18i	0.955500	+	0.551658i	0.894785	−	0.446497i	$-0.147329\pi$
$563$	1.71313e19	+	9.89074e18i	0.955500	+	0.551658i	0.0607150	+	0.998155i	$0.480662\pi$
$564$	1.35602e19	−	2.34869e19i	0.746985	−	1.29382i
$565$	1.14668e19	−	6.62037e18i	0.623884	−	0.360200i
$566$		−	1.15360e19i		−	0.619928i
$567$	−5.40453e19	+	1.49593e19i	−2.86865	+	0.794018i
$568$	−4.05591e18			−0.212642
$569$	−1.80896e18	−	3.13321e18i	−0.0936791	−	0.162257i	0.815377	−	0.578930i	$-0.196529\pi$
$569$	−1.80896e18	−	3.13321e18i	−0.0936791	−	0.162257i	−0.909057	+	0.416673i	$0.863196\pi$
$570$	−6.88085e18	−	3.97266e18i	−0.351980	−	0.203216i
$571$	1.28101e19	−	2.21878e19i	0.647292	−	1.12114i	−0.336475	−	0.941693i	$-0.609235\pi$
$571$	1.28101e19	−	2.21878e19i	0.647292	−	1.12114i	0.983767	−	0.179451i	$-0.0574321\pi$
$572$	−1.49168e18	+	8.61223e17i	−0.0744568	+	0.0429876i
$573$			2.89163e19i			1.42581i
$574$	7.07386e18	+	1.83316e18i	0.344567	+	0.0892929i
$575$	−3.83220e18			−0.184405
$576$	3.36026e18	+	5.82013e18i	0.159740	+	0.276679i
$577$	1.64243e19	+	9.48255e18i	0.771356	+	0.445343i	0.833358	−	0.552733i	$-0.186415\pi$
$577$	1.64243e19	+	9.48255e18i	0.771356	+	0.445343i	−0.0620020	+	0.998076i	$0.519749\pi$
$578$	8.42834e18	−	1.45983e19i	0.391063	−	0.677341i
$579$	−1.60373e19	+	9.25916e18i	−0.735160	+	0.424445i
$580$			1.18422e19i			0.536336i
$581$	6.09545e18	−	6.19664e18i	0.272755	−	0.277283i
$582$	−3.86865e19			−1.71040
$583$	−1.98216e19	−	3.43320e19i	−0.865881	−	1.49975i
$584$	1.62786e18	+	9.39847e17i	0.0702632	+	0.0405665i
$585$	−5.61070e18	+	9.71802e18i	−0.239291	+	0.414464i
$586$	−2.68159e18	+	1.54822e18i	−0.113008	+	0.0652452i
$587$			3.57631e19i			1.48925i	0.667482	+	0.744626i	$0.267372\pi$
$587$			3.57631e19i			1.48925i	−0.667482	+	0.744626i	$0.732628\pi$
$588$	1.17817e19	+	1.96520e19i	0.484803	+	0.808658i
$589$	−7.66477e18			−0.311668
$590$	4.48449e18	+	7.76736e18i	0.180198	+	0.312111i
$591$	6.01592e19	+	3.47329e19i	2.38885	+	1.37920i
$592$	−1.17691e18	+	2.03848e18i	−0.0461842	+	0.0799933i
$593$	2.82910e19	−	1.63338e19i	1.09715	−	0.633439i	0.161677	−	0.986844i	$-0.448310\pi$
$593$	2.82910e19	−	1.63338e19i	1.09715	−	0.633439i	0.935470	+	0.353405i	$0.114976\pi$
$594$			5.95494e19i			2.28230i
$595$	3.27231e19	+	3.21888e19i	1.23947	+	1.21923i
$596$	−4.20698e18			−0.157488
$597$	−1.81415e19	−	3.14221e19i	−0.671203	−	1.16256i
$598$	−1.10891e18	−	6.40230e17i	−0.0405498	−	0.0234114i
$599$	−1.48780e19	+	2.57694e19i	−0.537719	+	0.931357i	0.461307	+	0.887241i	$0.347381\pi$
$599$	−1.48780e19	+	2.57694e19i	−0.537719	+	0.931357i	−0.999026	+	0.0441167i	$0.985953\pi$
$600$	−7.03512e18	+	4.06173e18i	−0.251312	+	0.145095i
$601$		−	1.99622e19i		−	0.704835i	−0.935843	−	0.352417i	$-0.885360\pi$
$601$		−	1.99622e19i		−	0.704835i	0.935843	−	0.352417i	$-0.114640\pi$
$602$	−7.32741e18	+	2.82753e19i	−0.255726	+	0.986805i
$603$	1.27028e20			4.38206
$604$	2.12016e18	+	3.67223e18i	0.0722954	+	0.125219i
$605$	−6.47366e18	−	3.73757e18i	−0.218204	−	0.125980i
$606$	1.82158e18	−	3.15507e18i	0.0606932	−	0.105124i
$607$	−3.71152e19	+	2.14285e19i	−1.22245	+	0.705781i	−0.965439	−	0.260628i	$-0.916070\pi$
$607$	−3.71152e19	+	2.14285e19i	−1.22245	+	0.705781i	−0.257009	+	0.966409i	$0.582737\pi$
$608$		−	1.38138e18i		−	0.0449769i
$609$	−1.39932e19	−	5.05549e19i	−0.450397	−	1.62720i
$610$	4.94121e18			0.157226
$611$	3.93653e18	+	6.81827e18i	0.123830	+	0.214479i
$612$	−5.16457e19	−	2.98177e19i	−1.60611	−	0.927286i
$613$	1.39762e19	−	2.42076e19i	0.429702	−	0.744265i	−0.567145	−	0.823618i	$-0.691952\pi$
$613$	1.39762e19	−	2.42076e19i	0.429702	−	0.744265i	0.996847	+	0.0793529i	$0.0252854\pi$
$614$	5.87492e18	−	3.39189e18i	0.178576	−	0.103101i
$615$		−	3.78413e19i		−	1.13721i
$616$	1.26165e19	−	3.49215e18i	0.374864	−	0.103759i
$617$	−3.32537e19			−0.976885			−0.488443	−	0.872596i	$-0.662435\pi$
$617$	−3.32537e19			−0.976885			−0.488443	+	0.872596i	$0.662435\pi$
$618$	5.10030e18	+	8.83398e18i	0.148141	+	0.256588i
$619$	−4.03508e19	−	2.32965e19i	−1.15882	−	0.669047i	−0.207801	−	0.978171i	$-0.566631\pi$
$619$	−4.03508e19	−	2.32965e19i	−1.15882	−	0.669047i	−0.951022	+	0.309124i	$0.899964\pi$
$620$	−1.29204e19	+	2.23788e19i	−0.366888	+	0.635469i
$621$	−3.83379e19	+	2.21344e19i	−1.07643	+	0.621479i
$622$		−	3.49441e19i		−	0.970156i
$623$	−1.91108e19	−	4.95247e18i	−0.524640	−	0.135958i
$624$	−2.71430e18			−0.0736828
$625$	2.32050e19	+	4.01923e19i	0.622905	+	1.07890i
$626$	1.06367e19	+	6.14111e18i	0.282350	+	0.163015i
$627$	1.00537e19	−	1.74136e19i	0.263909	−	0.457105i
$628$	−2.16154e19	+	1.24797e19i	−0.561108	+	0.323956i
$629$		−	2.08870e19i		−	0.536194i
$630$	5.98068e19	−	6.07996e19i	1.51833	−	1.54354i
$631$	−2.24319e19			−0.563197			−0.281598	−	0.959532i	$-0.590865\pi$
$631$	−2.24319e19			−0.563197			−0.281598	+	0.959532i	$0.590865\pi$
$632$	−2.45512e18	−	4.25239e18i	−0.0609611	−	0.105588i
$633$	−1.35605e19	−	7.82916e18i	−0.333004	−	0.192260i
$634$	−1.34776e19	+	2.33439e19i	−0.327332	+	0.566956i
$635$	2.60860e19	−	1.50608e19i	0.626602	−	0.361769i
$636$		−	6.24713e19i		−	1.48416i
$637$	−6.65077e18	+	1.09509e17i	−0.156277	+	0.00257320i
$638$	−2.99695e19			−0.696521
$639$	−3.34353e19	−	5.79117e19i	−0.768598	−	1.33125i
$640$	−4.03322e18	−	2.32858e18i	−0.0917048	−	0.0529458i
$641$	−4.38504e18	+	7.59511e18i	−0.0986205	+	0.170816i	−0.911114	−	0.412155i	$-0.864776\pi$
$641$	−4.38504e18	+	7.59511e18i	−0.0986205	+	0.170816i	0.812493	+	0.582970i	$0.198110\pi$
$642$	−4.12756e19	+	2.38305e19i	−0.918224	+	0.530137i
$643$			6.40419e19i			1.40925i	0.709581	+	0.704624i	$0.248884\pi$
$643$			6.40419e19i			1.40925i	−0.709581	+	0.704624i	$0.751116\pi$
$644$	6.93777e18	+	6.82447e18i	0.151014	+	0.148548i
$645$	1.51257e20			3.25685
$646$	6.12895e18	+	1.06157e19i	0.130544	+	0.226110i
$647$	−2.46942e19	−	1.42572e19i	−0.520314	−	0.300403i	0.216749	−	0.976227i	$-0.430455\pi$
$647$	−2.46942e19	−	1.42572e19i	−0.520314	−	0.300403i	−0.737063	+	0.675824i	$0.763788\pi$
$648$	−2.52439e19	+	4.37238e19i	−0.526177	+	0.911365i
$649$	−1.96571e19	+	1.13490e19i	−0.405328	+	0.234016i
$650$		−	2.35824e18i		−	0.0481055i
$651$	2.87141e19	−	1.10803e20i	0.579466	−	2.23607i
$652$	3.34825e19			0.668474
$653$	5.89280e18	+	1.02066e19i	0.116394	+	0.201600i	0.918336	−	0.395802i	$-0.129533\pi$
$653$	5.89280e18	+	1.02066e19i	0.116394	+	0.201600i	−0.801942	+	0.597401i	$0.796200\pi$
$654$	7.25471e19	+	4.18851e19i	1.41767	+	0.818493i
$655$	−4.70711e19	+	8.15296e19i	−0.910050	+	1.57625i
$656$	5.69771e18	−	3.28957e18i	0.108987	−	0.0629234i
$657$			3.09909e19i			0.586512i
$658$	−1.59621e19	−	5.76682e19i	−0.298888	−	1.07983i
$659$	−2.53878e19			−0.470356			−0.235178	−	0.971952i	$-0.575567\pi$
$659$	−2.53878e19			−0.470356			−0.235178	+	0.971952i	$0.575567\pi$
$660$	−3.38949e19	−	5.87077e19i	−0.621336	−	1.07619i
$661$	7.58071e19	+	4.37673e19i	1.37499	+	0.793851i	0.991551	−	0.129715i	$-0.0414061\pi$
$661$	7.58071e19	+	4.37673e19i	1.37499	+	0.793851i	0.383439	+	0.923566i	$0.374739\pi$
$662$	2.80473e19	−	4.85794e19i	0.503368	−	0.871859i
$663$	2.08589e19	−	1.20429e19i	0.370421	−	0.213863i
$664$		−	7.82572e18i		−	0.137514i
$665$	−1.68948e19	+	4.67634e18i	−0.293766	+	0.0813120i
$666$	−3.88081e19			−0.667733
$667$	−1.11396e19	−	1.92943e19i	−0.189665	−	0.328510i
$668$	4.02796e19	+	2.32554e19i	0.678656	+	0.391822i
$669$	−1.24367e19	+	2.15410e19i	−0.207358	+	0.359155i
$670$	−7.62340e19	+	4.40137e19i	−1.25784	+	0.726214i
$671$			1.25049e19i			0.204184i
$672$	1.99695e19	+	5.17501e18i	0.322688	+	0.0836230i
$673$	−2.10595e19			−0.336777			−0.168388	−	0.985721i	$-0.553856\pi$
$673$	−2.10595e19			−0.336777			−0.168388	+	0.985721i	$0.553856\pi$
$674$	3.95094e19	+	6.84323e19i	0.625290	+	1.08303i
$675$	−7.06075e19	−	4.07653e19i	−1.10592	−	0.638504i
$676$	−1.57335e19	+	2.72512e19i	−0.243893	+	0.422435i
$677$	3.61924e19	−	2.08957e19i	0.555260	−	0.320579i	−0.195981	−	0.980608i	$-0.562789\pi$
$677$	3.61924e19	−	2.08957e19i	0.555260	−	0.320579i	0.751241	+	0.660028i	$0.229456\pi$
$678$			5.28045e19i			0.801795i
$679$	−5.98564e19	+	6.08501e19i	−0.899543	+	0.914477i
$680$	4.13259e19			0.614696
$681$	−5.69742e19	−	9.86822e19i	−0.838781	−	1.45281i
$682$	−5.66347e19	−	3.26980e19i	−0.825262	−	0.476465i
$683$	−1.34232e19	+	2.32496e19i	−0.193602	+	0.335328i	−0.946441	−	0.322876i	$-0.895350\pi$
$683$	−1.34232e19	+	2.32496e19i	−0.193602	+	0.335328i	0.752839	+	0.658204i	$0.228684\pi$
$684$	1.97239e19	−	1.13876e19i	0.281579	−	0.162570i
$685$		−	4.98679e19i		−	0.704672i
$686$	4.91394e19	+	1.18745e19i	0.687324	+	0.166091i
$687$	9.29106e19			1.28638
$688$	1.31489e19	+	2.27746e19i	0.180207	+	0.312127i
$689$	1.57058e19	+	9.06773e18i	0.213071	+	0.123017i
$690$	2.51973e19	−	4.36430e19i	0.338385	−	0.586099i
$691$	−3.23281e19	+	1.86646e19i	−0.429768	+	0.248127i	−0.699248	−	0.714879i	$-0.746482\pi$
$691$	−3.23281e19	+	1.86646e19i	−0.429768	+	0.248127i	0.269480	+	0.963006i	$0.413148\pi$
$692$			8.61690e18i			0.113399i
$693$	1.53868e20	+	1.51355e20i	2.00454	+	1.97180i
$694$	4.20142e19			0.541851
$695$	−2.85043e18	−	4.93708e18i	−0.0363929	−	0.0630343i
$696$	−4.08999e19	−	2.36136e19i	−0.516961	−	0.298467i
$697$	−2.91905e19	+	5.05593e19i	−0.365268	+	0.632662i
$698$	9.57290e19	−	5.52692e19i	1.18592	−	0.684692i
$699$			9.57162e19i			1.17394i
$700$	−4.49615e18	+	1.73499e19i	−0.0545952	+	0.210674i
$701$	−6.45088e19			−0.775520			−0.387760	−	0.921760i	$-0.626751\pi$
$701$	−6.45088e19			−0.775520			−0.387760	+	0.921760i	$0.626751\pi$
$702$	−1.36210e19	−	2.35922e19i	−0.162124	−	0.280808i
$703$	6.90821e18	+	3.98846e18i	0.0814101	+	0.0470021i
$704$	5.89301e18	−	1.02070e19i	0.0687589	−	0.119094i
$705$	−2.68344e20	+	1.54929e20i	−3.10005	+	1.78981i
$706$		−	2.36776e19i		−	0.270835i
$707$	−2.14424e18	−	7.74675e18i	−0.0242849	−	0.0877371i
$708$	−3.57686e19			−0.401115
$709$	−7.99624e19	−	1.38499e20i	−0.887896	−	1.53788i	−0.842358	−	0.538919i	$-0.818833\pi$
$709$	−7.99624e19	−	1.38499e20i	−0.887896	−	1.53788i	−0.0455384	−	0.998963i	$-0.514500\pi$
$710$	4.01315e19	+	2.31699e19i	0.441242	+	0.254751i
$711$	4.04781e19	−	7.01101e19i	0.440689	−	0.763296i
$712$	−1.53929e19	+	8.88711e18i	−0.165944	+	0.0958078i
$713$		−	4.86152e19i		−	0.518973i
$714$	−1.76422e20	+	4.88322e19i	−1.86494	+	0.516201i
$715$	1.96794e19			0.206001
$716$	−1.64703e19	−	2.85274e19i	−0.170730	−	0.295714i
$717$	2.48415e20	+	1.43423e20i	2.55002	+	1.47226i
$718$	3.79327e19	−	6.57014e19i	0.385605	−	0.667887i
$719$	1.16507e20	−	6.72651e19i	1.17287	−	0.677154i	0.218512	−	0.975834i	$-0.429880\pi$
$719$	1.16507e20	−	6.72651e19i	1.17287	−	0.677154i	0.954353	+	0.298680i	$0.0965463\pi$
$720$		−	7.67836e19i		−	0.765493i
$721$	2.17863e19	+	5.64581e18i	0.215098	+	0.0557416i
$722$	6.76364e19			0.661333
$723$	8.64240e19	+	1.49691e20i	0.836886	+	1.44953i
$724$	5.02223e19	+	2.89959e19i	0.481645	+	0.278078i
$725$	2.05160e19	−	3.55347e19i	0.194861	−	0.337510i
$726$	2.58172e19	−	1.49056e19i	0.242858	−	0.140214i
$727$			9.40833e19i			0.876540i	0.898843	+	0.438270i	$0.144409\pi$
$727$			9.40833e19i			0.876540i	−0.898843	+	0.438270i	$0.855591\pi$
$728$	−4.19962e18	+	4.26934e18i	−0.0387516	+	0.0393950i
$729$	−2.27060e20			−2.07514
$730$	−1.07380e19	−	1.85988e19i	−0.0971994	−	0.168354i
$731$	−2.02093e20	−	1.16679e20i	−1.81188	−	1.04609i
$732$	−9.85287e18	+	1.70657e19i	−0.0874954	+	0.151546i
$733$	−4.38708e19	+	2.53288e19i	−0.385876	+	0.222786i	−0.680372	−	0.732867i	$-0.738182\pi$
$733$	−4.38708e19	+	2.53288e19i	−0.385876	+	0.222786i	0.294496	+	0.955653i	$0.404848\pi$
$734$		−	4.48520e19i		−	0.390759i
$735$	−4.30990e18	−	2.61752e20i	−0.0371926	−	2.25881i
$736$	8.76168e18			0.0748933
$737$	−1.11387e20	−	1.92928e20i	−0.943110	−	1.63351i
$738$	9.39393e19	+	5.42359e19i	0.787867	+	0.454875i
$739$	8.93230e19	−	1.54712e20i	0.742083	−	1.28533i	−0.209463	−	0.977817i	$-0.567171\pi$
$739$	8.93230e19	−	1.54712e20i	0.742083	−	1.28533i	0.951545	−	0.307508i	$-0.0994952\pi$
$740$	2.32901e19	−	1.34466e19i	0.191668	−	0.110660i
$741$			9.19853e18i			0.0749879i
$742$	−9.82613e19	−	9.66567e19i	−0.793515	−	0.780557i
$743$	−7.81429e19			−0.625126			−0.312563	−	0.949897i	$-0.601188\pi$
$743$	−7.81429e19			−0.625126			−0.312563	+	0.949897i	$0.601188\pi$
$744$	−5.15269e19	−	8.92473e19i	−0.408342	−	0.707269i
$745$	4.16263e19	+	2.40330e19i	0.326794	+	0.188675i
$746$	−1.54322e19	+	2.67293e19i	−0.120020	+	0.207881i
$747$	1.11738e20	−	6.45122e19i	0.860911	−	0.497047i
$748$			1.04585e20i			0.798284i
$749$	−2.63793e19	+	1.01793e20i	−0.199476	+	0.769746i
$750$	−1.20419e20			−0.902124
$751$	1.10806e20	+	1.91922e20i	0.822404	+	1.42444i	0.903888	+	0.427770i	$0.140701\pi$
$751$	1.10806e20	+	1.91922e20i	0.822404	+	1.42444i	−0.0814841	+	0.996675i	$0.525966\pi$
$752$	−4.66547e19	−	2.69361e19i	−0.343061	−	0.198066i
$753$	2.30512e20	−	3.99259e20i	1.67930	−	2.90864i
$754$	1.18733e19	−	6.85504e18i	0.0856981	−	0.0494778i
$755$		−	4.84468e19i		−	0.346447i
$756$	5.52312e19	+	1.99540e20i	0.391320	+	1.41377i
$757$	−8.00521e19			−0.561955			−0.280977	−	0.959714i	$-0.590659\pi$
$757$	−8.00521e19			−0.561955			−0.280977	+	0.959714i	$0.590659\pi$
$758$	3.28091e19	+	5.68271e19i	0.228197	+	0.395249i
$759$	1.10449e20	+	6.37677e19i	0.761147	+	0.439449i
$760$	−7.89135e18	+	1.36682e19i	−0.0538835	+	0.0933290i
$761$	3.11614e19	−	1.79910e19i	0.210826	−	0.121720i	−0.390869	−	0.920446i	$-0.627826\pi$
$761$	3.11614e19	−	1.79910e19i	0.210826	−	0.121720i	0.601695	+	0.798726i	$0.294492\pi$
$762$			1.20126e20i			0.805288i
$763$	1.78127e20	−	4.93042e19i	1.18320	−	0.327501i
$764$	5.74398e19			0.378059
$765$	3.40675e20	+	5.90066e20i	2.22183	+	3.84831i
$766$	−5.83438e19	−	3.36848e19i	−0.377045	−	0.217687i
$767$	5.19182e18	−	8.99250e18i	0.0332470	−	0.0575855i
$768$	1.60846e19	−	9.28646e18i	0.102066	−	0.0589280i
$769$		−	8.21908e19i		−	0.516820i	−0.966035	−	0.258410i	$-0.916802\pi$
$769$		−	8.21908e19i		−	0.516820i	0.966035	−	0.258410i	$-0.0831985\pi$
$770$	−1.44784e20	−	3.75201e19i	−0.902165	−	0.233792i
$771$	−4.69515e20			−2.89914
$772$	1.83925e19	+	3.18568e19i	0.112543	+	0.194931i
$773$	−1.60909e20	−	9.29009e19i	−0.975717	−	0.563331i	−0.0747430	−	0.997203i	$-0.523814\pi$
$773$	−1.60909e20	−	9.29009e19i	−0.975717	−	0.563331i	−0.900974	+	0.433872i	$0.857147\pi$
$774$	−2.16789e20	+	3.75489e20i	−1.30272	+	2.25637i
$775$	7.75399e19	−	4.47677e19i	0.461757	−	0.266595i
$776$			7.68473e19i			0.453520i
$777$	−8.35376e19	+	8.49244e19i	−0.488579	+	0.496690i
$778$	2.91974e19			0.169234
$779$	−1.11481e19	−	1.93090e19i	−0.0640379	−	0.110917i
$780$	2.68569e19	+	1.55058e19i	0.152895	+	0.0882740i
$781$	−5.86369e19	+	1.01562e20i	−0.330837	+	0.573026i
$782$	−6.73317e19	+	3.88740e19i	−0.376506	+	0.217376i
$783$		−	4.73992e20i		−	2.62687i
$784$	3.90370e19	−	2.34032e19i	0.214419	−	0.128547i
$785$	2.85167e20			1.55243
$786$	−1.87721e20	−	3.25143e20i	−1.01287	−	1.75435i
$787$	−2.18763e20	−	1.26303e20i	−1.16991	−	0.675446i	−0.216249	−	0.976338i	$-0.569382\pi$
$787$	−2.18763e20	−	1.26303e20i	−1.16991	−	0.675446i	−0.953658	+	0.300892i	$0.902716\pi$
$788$	6.89939e19	−	1.19501e20i	0.365702	−	0.633414i
$789$	1.56712e20	−	9.04778e19i	0.823310	−	0.475338i
$790$			5.61007e19i			0.292132i
$791$	8.30564e19	+	8.17001e19i	0.428684	+	0.421684i
$792$	1.94319e20			0.994120
$793$	−2.86029e18	−	4.95418e18i	−0.0145044	−	0.0251223i
$794$	−1.46878e18	−	8.47998e17i	−0.00738265	−	0.00426237i
$795$	−3.56876e20	+	6.18127e20i	−1.77806	+	3.07970i
$796$	−6.24172e19	+	3.60366e19i	−0.308257	+	0.177972i
$797$			2.42561e20i			1.18744i	0.804671	+	0.593721i	$0.202342\pi$
$797$			2.42561e20i			1.18744i	−0.804671	+	0.593721i	$0.797658\pi$
$798$	1.75376e19	−	6.76749e19i	0.0851041	−	0.328403i
$799$	4.78043e20			2.29953
$800$	8.06827e18	+	1.39746e19i	0.0384725	+	0.0666363i
$801$	−2.53787e20	−	1.46524e20i	−1.19961	−	0.692597i
$802$	4.17929e19	−	7.23874e19i	0.195831	−	0.339190i
$803$	4.70685e19	−	2.71750e19i	0.218636	−	0.126230i
$804$		−	3.51057e20i		−	1.61653i
$805$	−2.96605e19	−	1.07158e20i	−0.135397	−	0.489164i
$806$	2.99166e19			0.135384
$807$	1.66400e20	+	2.88213e20i	0.746515	+	1.29300i
$808$	−6.26727e18	−	3.61841e18i	−0.0278740	−	0.0160931i
$809$	−1.73801e20	+	3.01032e20i	−0.766325	+	1.32731i	0.173219	+	0.984883i	$0.444583\pi$
$809$	−1.73801e20	+	3.01032e20i	−0.766325	+	1.32731i	−0.939543	+	0.342430i	$0.888750\pi$
$810$	4.99556e20	−	2.88419e20i	2.18368	−	1.26075i
$811$			1.70153e20i			0.737382i	0.929552	+	0.368691i	$0.120194\pi$
$811$			1.70153e20i			0.737382i	−0.929552	+	0.368691i	$0.879806\pi$
$812$	−1.00423e20	+	2.77962e19i	−0.431460	+	0.119425i
$813$	−1.65170e20			−0.703556
$814$	3.40297e19	+	5.89411e19i	0.143710	+	0.248913i
$815$	−3.31295e20	−	1.91273e20i	−1.38711	−	0.800849i
$816$	−8.24046e19	+	1.42729e20i	−0.342074	+	0.592490i
$817$	7.71810e19	−	4.45604e19i	0.317655	−	0.183398i
$818$			2.56025e20i			1.04474i
$819$	−9.55791e19	−	2.47689e19i	−0.386701	−	0.100212i
$820$	−7.51685e19			−0.301536
$821$	1.27099e20	+	2.20142e20i	0.505521	+	0.875588i	0.999980	+	0.00638711i	$0.00203309\pi$
$821$	1.27099e20	+	2.20142e20i	0.505521	+	0.875588i	−0.494458	+	0.869201i	$0.664634\pi$
$822$	1.72231e20	+	9.94375e19i	0.679216	+	0.392146i
$823$	1.68639e20	−	2.92092e20i	0.659417	−	1.14214i	−0.321350	−	0.946961i	$-0.604136\pi$
$823$	1.68639e20	−	2.92092e20i	0.659417	−	1.14214i	0.980767	−	0.195183i	$-0.0625302\pi$
$824$	1.75479e19	−	1.01313e19i	0.0680355	−	0.0392803i
$825$			2.34884e20i			0.902975i
$826$	−5.53418e19	+	5.62605e19i	−0.210956	+	0.214459i
$827$	2.37468e20			0.897566			0.448783	−	0.893641i	$-0.351858\pi$
$827$	2.37468e20			0.897566			0.448783	+	0.893641i	$0.351858\pi$
$828$	7.22279e19	+	1.25102e20i	0.270703	+	0.468871i
$829$	1.31838e20	+	7.61168e19i	0.489959	+	0.282878i	0.724557	−	0.689214i	$-0.242044\pi$
$829$	1.31838e20	+	7.61168e19i	0.489959	+	0.282878i	−0.234599	+	0.972092i	$0.575378\pi$
$830$	−4.47055e19	+	7.74321e19i	−0.164746	+	0.285348i
$831$	−1.46019e20	+	8.43040e19i	−0.533582	+	0.308064i
$832$			5.39173e18i			0.0195373i
$833$	−1.96155e20	+	3.53049e20i	−0.704830	+	1.26859i
$834$	2.27352e19			0.0810096
$835$	−2.65699e20	−	4.60205e20i	−0.938826	−	1.62609i
$836$	−3.45906e19	−	1.99709e19i	−0.121203	−	0.0699767i
$837$	5.17147e20	−	8.95725e20i	1.79695	−	3.11241i
$838$	2.23874e20	−	1.29253e20i	0.771427	−	0.445383i
$839$			4.22865e19i			0.144500i	0.997387	+	0.0722500i	$0.0230179\pi$
$839$			4.22865e19i			0.144500i	−0.997387	+	0.0722500i	$0.976982\pi$
$840$	−1.68027e20	−	1.65283e20i	−0.569408	−	0.560110i
$841$	−5.90118e19			−0.198320
$842$	1.47213e20	+	2.54981e20i	0.490640	+	0.849813i
$843$	−4.41647e20	−	2.54985e20i	−1.45976	−	0.842794i
$844$	−1.55520e19	+	2.69368e19i	−0.0509786	+	0.0882975i
$845$	3.11353e20	−	1.79760e20i	1.01218	−	0.584380i
$846$		−	8.88204e20i		−	2.86365i
$847$	1.64998e19	−	6.36701e19i	0.0527588	−	0.203588i
$848$	−1.24094e20			−0.393531
$849$	−2.62816e20	−	4.55210e20i	−0.826604	−	1.43172i
$850$	−1.24006e20	−	7.15948e19i	−0.386821	−	0.223331i
$851$	−2.52975e19	+	4.38166e19i	−0.0782656	+	0.135560i
$852$	−1.60046e20	+	9.24024e19i	−0.491097	+	0.283535i
$853$			6.32395e20i			1.92462i	0.271954	+	0.962310i	$0.412330\pi$
$853$			6.32395e20i			1.92462i	−0.271954	+	0.962310i	$0.587670\pi$
$854$	1.15981e19	+	4.19019e19i	0.0350092	+	0.126482i
$855$	−2.60213e20			−0.779051
$856$	4.73372e19	+	8.19905e19i	0.140568	+	0.243471i
$857$	3.34914e19	+	1.93363e19i	0.0986432	+	0.0569517i	0.548510	−	0.836144i	$-0.315195\pi$
$857$	3.34914e19	+	1.93363e19i	0.0986432	+	0.0569517i	−0.449867	+	0.893096i	$0.648529\pi$
$858$	−3.92411e19	+	6.79676e19i	−0.114638	+	0.198560i
$859$	−8.28701e19	+	4.78451e19i	−0.240130	+	0.138639i	−0.615236	−	0.788343i	$-0.710939\pi$
$859$	−8.28701e19	+	4.78451e19i	−0.240130	+	0.138639i	0.375107	+	0.926982i	$0.377606\pi$
$860$		−	3.00459e20i		−	0.863568i
$861$	3.20897e20	−	8.88218e19i	0.914838	−	0.253220i
$862$	−1.75866e20			−0.497315
$863$	3.22971e19	+	5.59403e19i	0.0905917	+	0.156909i	0.907760	−	0.419489i	$-0.137791\pi$
$863$	3.22971e19	+	5.59403e19i	0.0905917	+	0.156909i	−0.817169	+	0.576399i	$0.804458\pi$
$864$	1.61432e20	+	9.32029e19i	0.449153	+	0.259318i
$865$	4.92252e19	−	8.52606e19i	0.135855	−	0.235307i
$866$	−2.63299e20	+	1.52016e20i	−0.720815	+	0.416163i
$867$		−	7.68064e20i		−	2.08576i
$868$	−2.20101e20	−	5.70381e19i	−0.592903	−	0.153648i
$869$	−1.41976e20			−0.379382
$870$	2.69791e20	+	4.67292e20i	0.715144	+	1.23867i
$871$	8.82584e19	+	5.09560e19i	0.232075	+	0.133989i
$872$	8.32011e19	−	1.44108e20i	0.217027	−	0.375902i
$873$	−1.09725e21	+	6.33499e20i	−2.83927	+	1.63926i
$874$		−	2.96925e19i		−	0.0762197i
$875$	−1.86314e20	+	1.89407e20i	−0.474450	+	0.482326i
$876$	8.56471e19			0.216363
$877$	−2.40619e20	−	4.16764e20i	−0.603021	−	1.04446i	−0.992361	−	0.123369i	$-0.960630\pi$
$877$	−2.40619e20	−	4.16764e20i	−0.603021	−	1.04446i	0.389340	−	0.921094i	$-0.372703\pi$
$878$	1.48484e20	+	8.57273e19i	0.369163	+	0.213136i
$879$	−7.05435e19	+	1.22185e20i	−0.173994	+	0.301367i
$880$	−1.16618e20	+	6.73293e19i	−0.285355	+	0.164750i
$881$		−	5.74170e19i		−	0.139383i	−0.997569	−	0.0696914i	$-0.977799\pi$
$881$		−	5.74170e19i		−	0.139383i	0.997569	−	0.0696914i	$-0.0222015\pi$
$882$	6.55965e20	+	3.64456e20i	1.57979	+	0.877739i
$883$	8.09123e20			1.93326			0.966629	−	0.256181i	$-0.0824643\pi$
$883$	8.09123e20			1.93326			0.966629	+	0.256181i	$0.0824643\pi$
$884$	−2.39221e19	−	4.14343e19i	−0.0567066	−	0.0982187i
$885$	3.53915e20	+	2.04333e20i	0.832331	+	0.480547i
$886$	2.35442e20	−	4.07798e20i	0.549349	−	0.951501i
$887$	−9.74497e19	+	5.62626e19i	−0.225588	+	0.130243i	−0.608535	−	0.793527i	$-0.708242\pi$
$887$	−9.74497e19	+	5.62626e19i	−0.225588	+	0.130243i	0.382947	+	0.923770i	$0.374909\pi$
$888$			1.07251e20i			0.246326i
$889$	1.88946e20	+	1.85861e20i	0.430552	+	0.423521i
$890$	2.03075e20			0.459121
$891$	7.29910e20	+	1.26424e21i	1.63729	+	2.83587i
$892$	4.27892e19	+	2.47044e19i	0.0952315	+	0.0549819i
$893$	−9.12841e19	+	1.58109e20i	−0.201574	+	0.349137i
$894$	−1.66007e20	+	9.58443e19i	−0.363717	+	0.209992i
$895$			3.76356e20i			0.818158i
$896$	1.02797e19	−	3.96677e19i	0.0221730	−	0.0855620i
$897$	−5.83433e19			−0.124866
$898$	−3.20174e20	−	5.54558e20i	−0.679911	−	1.17764i
$899$	4.50792e20	+	2.60265e20i	0.949857	+	0.548400i
$900$	−1.33023e20	+	2.30403e20i	−0.278119	+	0.481716i
$901$	9.53635e20	−	5.50582e20i	1.97838	−	1.14222i
$902$		−	1.90231e20i		−	0.391594i
$903$	3.55034e20	+	1.28267e21i	0.725196	+	2.62000i
$904$	1.04892e20			0.212599
$905$	−3.31286e20	−	5.73804e20i	−0.666289	−	1.15405i
$906$	1.67323e20	+	9.66038e19i	0.333932	+	0.192796i
$907$	−6.83445e19	+	1.18376e20i	−0.135348	+	0.234430i	−0.925730	−	0.378184i	$-0.876549\pi$
$907$	−6.83445e19	+	1.18376e20i	−0.135348	+	0.234430i	0.790382	+	0.612614i	$0.209882\pi$
$908$	−1.96024e20	+	1.13174e20i	−0.385219	+	0.222406i
$909$		−	1.19315e20i		−	0.232674i
$910$	6.59426e19	−	1.82524e19i	0.127607	−	0.0353207i
$911$	−7.70119e20			−1.47887			−0.739434	−	0.673229i	$-0.764907\pi$
$911$	−7.70119e20			−1.47887			−0.739434	+	0.673229i	$0.764907\pi$
$912$	−3.14710e19	−	5.45093e19i	−0.0599717	−	0.103874i
$913$	−1.95960e20	−	1.13138e20i	−0.370572	−	0.213950i
$914$	−1.57980e20	+	2.73629e20i	−0.296468	+	0.513497i
$915$	1.94980e20	−	1.12572e20i	0.363113	−	0.209644i
$916$		−	1.84559e20i		−	0.341088i
$917$	−8.01864e20	−	2.07799e20i	−1.47067	−	0.381117i
$918$	−1.65410e21			−3.01066
$919$	−2.76758e20	−	4.79359e20i	−0.499910	−	0.865870i	0.500090	−	0.865973i	$-0.333300\pi$
$919$	−2.76758e20	−	4.79359e20i	−0.499910	−	0.865870i	−1.00000		0.000103848i	$0.999967\pi$
$920$	−8.66931e19	−	5.00523e19i	−0.155407	−	0.0897241i
$921$	1.54549e20	−	2.67687e20i	0.274947	−	0.476223i
$922$	−3.17005e20	+	1.83023e20i	−0.559693	+	0.323139i
$923$		−	5.36490e19i		−	0.0940047i
$924$	4.18287e20	−	4.25231e20i	0.727395	−	0.739471i
$925$	−9.31817e19			−0.160819
$926$	1.09781e20	+	1.90147e20i	0.188041	+	0.325696i
$927$	2.89317e20	+	1.67037e20i	0.491830	+	0.283958i
$928$	−4.69063e19	+	8.12441e19i	−0.0791399	+	0.137074i
$929$	8.40803e19	−	4.85438e19i	0.140794	−	0.0812875i	−0.427948	−	0.903803i	$-0.640763\pi$
$929$	8.40803e19	−	4.85438e19i	0.140794	−	0.0812875i	0.568742	+	0.822516i	$0.307430\pi$
$930$			1.17742e21i			1.95682i
$931$	−7.93115e19	−	1.32293e20i	−0.130824	−	0.218217i
$932$	1.90132e20			0.311274
$933$	−7.96104e20	−	1.37889e21i	−1.29359	−	2.24057i
$934$	5.36811e20	+	3.09928e20i	0.865751	+	0.499842i
$935$	5.97455e20	−	1.03482e21i	0.956366	−	1.65647i
$936$	−7.69850e19	+	4.44473e19i	−0.122314	+	0.0706179i
$937$			5.22544e19i			0.0824035i	0.999151	+	0.0412018i	$0.0131186\pi$
$937$			5.22544e19i			0.0824035i	−0.999151	+	0.0412018i	$0.986881\pi$
$938$	−5.52178e20	−	5.43161e20i	−0.864289	−	0.850176i
$939$	5.59632e20			0.869447
$940$	3.07752e20	+	5.33043e20i	0.474577	+	0.821991i
$941$	4.41328e20	+	2.54801e20i	0.675513	+	0.390008i	0.798162	−	0.602442i	$-0.205806\pi$
$941$	4.41328e20	+	2.54801e20i	0.675513	+	0.390008i	−0.122649	+	0.992450i	$0.539139\pi$
$942$	−5.68628e20	+	9.84893e20i	−0.863917	+	1.49635i
$943$	1.22471e20	−	7.07086e19i	0.184693	−	0.106633i
$944$			7.10512e19i			0.106357i
$945$	5.93413e20	−	2.28988e21i	0.881727	−	3.40244i
$946$	7.60383e20			1.12149
$947$	2.75477e20	+	4.77140e20i	0.403307	+	0.698548i	0.994123	−	0.108258i	$-0.0345273\pi$
$947$	2.75477e20	+	4.77140e20i	0.403307	+	0.698548i	−0.590816	+	0.806806i	$0.701194\pi$
$948$	−1.93757e20	−	1.11866e20i	−0.281579	−	0.162570i
$949$	−1.24317e19	+	2.15323e19i	−0.0179336	+	0.0310619i
$950$	4.73588e19	−	2.73426e19i	0.0678165	−	0.0391539i
$951$			1.22820e21i			1.74584i
$952$	9.70010e19	+	3.50447e20i	0.136873	+	0.494497i
$953$	5.82301e20			0.815638			0.407819	−	0.913063i	$-0.366289\pi$
$953$	5.82301e20			0.815638			0.407819	+	0.913063i	$0.366289\pi$
$954$	−1.02298e21	−	1.77186e21i	−1.42242	−	2.46371i
$955$	−5.68342e20	−	3.28132e20i	−0.784488	−	0.452924i
$956$	2.84896e20	−	4.93455e20i	0.390375	−	0.676149i
$957$	−1.18259e21	+	6.82770e20i	−1.60861	+	0.928733i
$958$		−	6.71233e19i		−	0.0906390i
$959$	4.22884e20	−	1.17051e20i	0.566880	−	0.156908i
$960$	−2.12201e20			−0.282389
$961$	1.89450e20	+	3.28136e20i	0.250282	+	0.433501i
$962$	−2.69637e19	−	1.55675e19i	−0.0353634	−	0.0204170i
$963$	−7.80459e20	+	1.35179e21i	−1.01617	+	1.76006i
$964$	2.97348e20	−	1.71674e20i	0.384349	−	0.221904i
$965$		−	4.20279e20i		−	0.539320i
$966$	4.29240e20	+	1.11236e20i	0.546840	+	0.141711i
$967$	−1.31306e21			−1.66073			−0.830363	−	0.557224i	$-0.811867\pi$
$967$	−1.31306e21			−1.66073			−0.830363	+	0.557224i	$0.811867\pi$
$968$	−2.96086e19	−	5.12836e19i	−0.0371784	−	0.0643949i
$969$	4.83696e20	+	2.79262e20i	0.602984	+	0.348133i
$970$	4.39001e20	−	7.60371e20i	0.543329	−	0.941074i
$971$	7.24545e20	−	4.18316e20i	0.890288	−	0.514008i	0.0162513	−	0.999868i	$-0.494827\pi$
$971$	7.24545e20	−	4.18316e20i	0.890288	−	0.514008i	0.874037	+	0.485860i	$0.161493\pi$
$972$			1.09798e21i			1.33947i
$973$	3.51763e19	−	3.57603e19i	0.0426050	−	0.0433123i
$974$	4.66303e20			0.560732
$975$	−5.37259e19	−	9.30561e19i	−0.0641434	−	0.111100i
$976$	3.38995e19	+	1.95719e19i	0.0401832	+	0.0231998i
$977$	−2.25762e20	+	3.91031e20i	−0.265698	+	0.460203i	−0.967746	−	0.251927i	$-0.918936\pi$
$977$	−2.25762e20	+	3.91031e20i	−0.265698	+	0.460203i	0.702048	+	0.712130i	$0.252269\pi$
$978$	1.32122e21	−	7.62804e20i	1.54384	−	0.891335i
$979$			5.13929e20i			0.596245i
$980$	−5.19948e20	+	8.56125e18i	−0.598932	+	0.00986176i
$981$	2.74351e21			3.13779
$982$	4.73938e20	+	8.20885e20i	0.538197	+	0.932184i
$983$	1.89854e19	+	1.09612e19i	0.0214064	+	0.0123590i	0.510665	−	0.859780i	$-0.329399\pi$
$983$	1.89854e19	+	1.09612e19i	0.0214064	+	0.0123590i	−0.489259	+	0.872139i	$0.662733\pi$
$984$	1.49887e20	−	2.59612e20i	0.167803	−	0.290643i
$985$	−1.36533e21	+	7.88274e20i	−1.51769	+	0.876241i
$986$		−	8.32459e20i		−	0.918807i
$987$	−1.94367e21	−	1.91193e21i	−2.13011	−	2.09533i
$988$	1.82721e19			0.0198833
$989$	2.82633e20	+	4.89534e20i	0.305385	+	0.528943i
$990$	−1.92270e21	−	1.11007e21i	−2.06284	−	1.19098i
$991$	−2.71489e19	+	4.70233e19i	−0.0289226	+	0.0500954i	−0.880124	−	0.474743i	$-0.842541\pi$
$991$	−2.71489e19	+	4.70233e19i	−0.0289226	+	0.0500954i	0.851202	+	0.524839i	$0.175874\pi$
$992$	−1.77282e20	+	1.02354e20i	−0.187535	+	0.108274i
$993$		−	2.55592e21i		−	2.68474i
$994$	−1.02285e20	+	3.94703e20i	−0.106686	+	0.411686i
$995$	8.23455e20			0.852862
$996$	−1.78287e20	−	3.08802e20i	−0.183360	−	0.317589i
$997$	−5.08133e20	−	2.93371e20i	−0.518933	−	0.299606i	0.217565	−	0.976046i	$-0.430189\pi$
$997$	−5.08133e20	−	2.93371e20i	−0.518933	−	0.299606i	−0.736498	+	0.676440i	$0.763522\pi$
$998$	2.48408e20	−	4.30255e20i	0.251913	−	0.436327i
$999$	−9.32203e20	+	5.38208e20i	−0.938754	+	0.541990i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	14.15.d.a.3.1	✓	20
3.2	odd	2		126.15.n.b.73.6		20
7.2	even	3		98.15.d.b.19.5		20
7.3	odd	6		98.15.b.c.97.11		20
7.4	even	3		98.15.b.c.97.20		20
7.5	odd	6	inner	14.15.d.a.5.1	yes	20
7.6	odd	2		98.15.d.b.31.5		20
21.5	even	6		126.15.n.b.19.6		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.15.d.a.3.1	✓	20	1.1	even	1	trivial
14.15.d.a.5.1	yes	20	7.5	odd	6	inner
98.15.b.c.97.11		20	7.3	odd	6
98.15.b.c.97.20		20	7.4	even	3
98.15.d.b.19.5		20	7.2	even	3
98.15.d.b.31.5		20	7.6	odd	2
126.15.n.b.19.6		20	21.5	even	6
126.15.n.b.73.6		20	3.2	odd	2

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)

\(f(q)\)	\(=\)	\(q+(-45.2548 - 78.3837i) q^{2} +(-3571.50 - 2062.01i) q^{3} +(-4096.00 + 7094.48i) q^{4} +(81056.3 - 46797.9i) q^{5} +373263. i q^{6} +(587107. + 577519. i) q^{7} +741455. q^{8} +(6.11227e6 + 1.05868e7i) q^{9} +O(q^{10})\)	\(q+(-45.2548 - 78.3837i) q^{2} +(-3571.50 - 2062.01i) q^{3} +(-4096.00 + 7094.48i) q^{4} +(81056.3 - 46797.9i) q^{5} +373263. i q^{6} +(587107. + 577519. i) q^{7} +741455. q^{8} +(6.11227e6 + 1.05868e7i) q^{9} +(-7.33638e6 - 4.23566e6i) q^{10} +(1.07193e7 - 1.85664e7i) q^{11} +(2.92577e7 - 1.68920e7i) q^{12} +9.80750e6i q^{13} +(1.86987e7 - 7.21551e7i) q^{14} -3.85991e8 q^{15} +(-3.35544e7 - 5.81180e7i) q^{16} +(5.15718e8 + 2.97750e8i) q^{17} +(5.53219e8 - 9.58204e8i) q^{18} +(-1.96957e8 + 1.13713e8i) q^{19} +7.66737e8i q^{20} +(-9.06004e8 - 3.27323e9i) q^{21} -1.94041e9 q^{22} +(-7.21245e8 - 1.24923e9i) q^{23} +(-2.64811e9 - 1.52889e9i) q^{24} +(1.32833e9 - 2.30073e9i) q^{25} +(7.68748e8 - 4.43837e8i) q^{26} -3.06891e10i q^{27} +(-6.50199e9 + 1.79970e9i) q^{28} +1.54449e10 q^{29} +(1.74679e10 + 3.02554e10i) q^{30} +(2.91870e10 + 1.68511e10i) q^{31} +(-3.03700e9 + 5.26024e9i) q^{32} +(-7.65682e10 + 4.42067e10i) q^{33} -5.38984e10i q^{34} +(7.46154e10 + 1.93362e10i) q^{35} -1.00143e11 q^{36} +(-1.75374e10 - 3.03757e10i) q^{37} +(1.78265e10 + 1.02921e10i) q^{38} +(2.02231e10 - 3.50275e10i) q^{39} +(6.00996e10 - 3.46985e10i) q^{40} +9.80369e10i q^{41} +(-2.15567e11 + 2.19145e11i) q^{42} -3.91868e11 q^{43} +(8.78127e10 + 1.52096e11i) q^{44} +(9.90876e11 + 5.72083e11i) q^{45} +(-6.52796e10 + 1.13068e11i) q^{46} +(6.95210e11 - 4.01380e11i) q^{47} +2.76758e11i q^{48} +(1.11658e10 + 6.78131e11i) q^{49} -2.40453e11 q^{50} +(-1.22792e12 - 2.12683e12i) q^{51} +(-6.95791e10 - 4.01715e10i) q^{52} +(9.24571e11 - 1.60140e12i) q^{53} +(-2.40553e12 + 1.38883e12i) q^{54} -2.00657e12i q^{55} +(4.35313e11 + 4.28205e11i) q^{56} +9.37908e11 q^{57} +(-6.98959e11 - 1.21063e12i) q^{58} +(-9.16901e11 - 5.29373e11i) q^{59} +(1.58102e12 - 2.73840e12i) q^{60} +(-5.05142e11 + 2.91644e11i) q^{61} -3.05038e12i q^{62} +(-2.52550e12 + 9.74551e12i) q^{63} +5.49756e11 q^{64} +(4.58970e11 + 7.94960e11i) q^{65} +(6.93016e12 + 4.00113e12i) q^{66} +(5.19561e12 - 8.99907e12i) q^{67} +(-4.22476e12 + 2.43917e12i) q^{68} +5.94885e12i q^{69} +(-1.86106e12 - 6.72369e12i) q^{70} -5.47020e12 q^{71} +(4.53197e12 + 7.84961e12i) q^{72} +(2.19550e12 + 1.26757e12i) q^{73} +(-1.58730e12 + 2.74929e12i) q^{74} +(-9.48825e12 + 5.47805e12i) q^{75} -1.86307e12i q^{76} +(1.70159e13 - 4.70985e12i) q^{77} -3.66078e12 q^{78} +(-3.31121e12 - 5.73519e12i) q^{79} +(-5.43960e12 - 3.14055e12i) q^{80} +(-3.40465e13 + 5.89702e13i) q^{81} +(7.68449e12 - 4.43664e12i) q^{82} -1.05545e13i q^{83} +(2.69329e13 + 6.97953e12i) q^{84} +5.57362e13 q^{85} +(1.77339e13 + 3.07160e13i) q^{86} +(-5.51617e13 - 3.18476e13i) q^{87} +(7.94790e12 - 1.37662e13i) q^{88} +(-2.07604e13 + 1.19860e13i) q^{89} -1.03558e14i q^{90} +(-5.66402e12 + 5.75805e12i) q^{91} +1.18169e13 q^{92} +(-6.94943e13 - 1.20368e14i) q^{93} +(-6.29232e13 - 3.63287e13i) q^{94} +(-1.06431e13 + 1.84343e13i) q^{95} +(2.16933e13 - 1.25246e13i) q^{96} +1.03644e14i q^{97} +(5.26491e13 - 3.15639e13i) q^{98} +2.62078e14 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

Related objects

Downloads

Learn more