LMFDB - Embedded newform 5.19.c.a.2.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5,19,Mod(2,5)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 19, names="a")

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

chi := DirichletCharacter("5.2");

S:= CuspForms(chi, 19);

N := Newforms(S);

Level:	$ N $	$=$	$ 5 $
Weight:	$ k $	$=$	$ 19 $
Character orbit:	$[\chi]$	$=$	5.c (of order $4$, 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:	$10.2693068855$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 1365649 x^{14} + 735328563216 x^{12} + \cdots + 22\!\cdots\!00 $ x^16 + 1365649x^14 + 735328563216x^12 + 196541937723225664x^10 + 26804517896227604816896x^8 + 1698608176414048875695308800x^6 + 38033703783600508125786931200000x^4 + 174469353400289826571825446912000000*x^2 + 223860255706571447791285331558400000000
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{39}\cdot 3^{12}\cdot 5^{25} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			2.8
Root			$-590.308i$ of defining polynomial
Character	$\chi$	$=$	5.2
Dual form			5.19.c.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)

$f(q)$	$=$	$q+(622.308 + 622.308i) q^{2} +(-24393.6 + 24393.6i) q^{3} +512390. i q^{4} +(1.93064e6 + 295511. i) q^{5} -3.03607e7 q^{6} +(-3.63215e6 - 3.63215e6i) q^{7} +(-1.55730e8 + 1.55730e8i) q^{8} -8.02680e8i q^{9} +O(q^{10})$	\(q+(622.308 + 622.308i) q^{2} +(-24393.6 + 24393.6i) q^{3} +512390. i q^{4} +(1.93064e6 + 295511. i) q^{5} -3.03607e7 q^{6} +(-3.63215e6 - 3.63215e6i) q^{7} +(-1.55730e8 + 1.55730e8i) q^{8} -8.02680e8i q^{9} +(1.01755e9 + 1.38535e9i) q^{10} +1.61251e9 q^{11} +(-1.24991e10 - 1.24991e10i) q^{12} +(-6.40234e9 + 6.40234e9i) q^{13} -4.52063e9i q^{14} +(-5.43039e10 + 3.98868e10i) q^{15} -5.95041e10 q^{16} +(6.97717e9 + 6.97717e9i) q^{17} +(4.99514e11 - 4.99514e11i) q^{18} +1.05230e11i q^{19} +(-1.51417e11 + 9.89241e11i) q^{20} +1.77203e11 q^{21} +(1.00348e12 + 1.00348e12i) q^{22} +(-1.83599e12 + 1.83599e12i) q^{23} -7.59765e12i q^{24} +(3.64004e12 + 1.14105e12i) q^{25} -7.96845e12 q^{26} +(1.01297e13 + 1.01297e13i) q^{27} +(1.86108e12 - 1.86108e12i) q^{28} -1.51916e13i q^{29} +(-5.86156e13 - 8.97192e12i) q^{30} +2.32707e13 q^{31} +(3.79385e12 + 3.79385e12i) q^{32} +(-3.93349e13 + 3.93349e13i) q^{33} +8.68389e12i q^{34} +(-5.93903e12 - 8.08570e12i) q^{35} +4.11285e14 q^{36} +(1.21070e13 + 1.21070e13i) q^{37} +(-6.54854e13 + 6.54854e13i) q^{38} -3.12353e14i q^{39} +(-3.46679e14 + 2.54639e14i) q^{40} -4.41756e14 q^{41} +(1.10275e14 + 1.10275e14i) q^{42} +(1.75004e14 - 1.75004e14i) q^{43} +8.26233e14i q^{44} +(2.37200e14 - 1.54969e15i) q^{45} -2.28511e15 q^{46} +(1.26772e15 + 1.26772e15i) q^{47} +(1.45152e15 - 1.45152e15i) q^{48} -1.60203e15i q^{49} +(1.55514e15 + 2.97531e15i) q^{50} -3.40397e14 q^{51} +(-3.28049e15 - 3.28049e15i) q^{52} +(1.11472e15 - 1.11472e15i) q^{53} +1.26076e16i q^{54} +(3.11317e15 + 4.76513e14i) q^{55} +1.13127e15 q^{56} +(-2.56694e15 - 2.56694e15i) q^{57} +(9.45384e15 - 9.45384e15i) q^{58} +6.28063e15i q^{59} +(-2.04376e16 - 2.78248e16i) q^{60} +5.12455e15 q^{61} +(1.44815e16 + 1.44815e16i) q^{62} +(-2.91545e15 + 2.91545e15i) q^{63} +2.03205e16i q^{64} +(-1.42526e16 + 1.04686e16i) q^{65} -4.89569e16 q^{66} +(-3.69810e15 - 3.69810e15i) q^{67} +(-3.57503e15 + 3.57503e15i) q^{68} -8.95732e16i q^{69} +(1.33589e15 - 8.72770e15i) q^{70} +8.23007e16 q^{71} +(1.25001e17 + 1.25001e17i) q^{72} +(2.68205e16 - 2.68205e16i) q^{73} +1.50686e16i q^{74} +(-1.16628e17 + 6.09596e16i) q^{75} -5.39188e16 q^{76} +(-5.85686e15 - 5.85686e15i) q^{77} +(1.94380e17 - 1.94380e17i) q^{78} +1.50642e17i q^{79} +(-1.14881e17 - 1.75841e16i) q^{80} -1.83225e17 q^{81} +(-2.74908e17 - 2.74908e17i) q^{82} +(-6.69322e16 + 6.69322e16i) q^{83} +9.07968e16i q^{84} +(1.14086e16 + 1.55322e16i) q^{85} +2.17813e17 q^{86} +(3.70578e17 + 3.70578e17i) q^{87} +(-2.51116e17 + 2.51116e17i) q^{88} -2.86724e17i q^{89} +(1.11199e18 - 8.16770e17i) q^{90} +4.65084e16 q^{91} +(-9.40745e17 - 9.40745e17i) q^{92} +(-5.67658e17 + 5.67658e17i) q^{93} +1.57783e18i q^{94} +(-3.10966e16 + 2.03161e17i) q^{95} -1.85092e17 q^{96} +(8.46795e17 + 8.46795e17i) q^{97} +(9.96955e17 - 9.96955e17i) q^{98} -1.29433e18i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 510 q^{2} - 20130 q^{3} + 3145170 q^{5} - 30766728 q^{6} + 78767350 q^{7} - 217339260 q^{8}+O(q^{10}) $ 16 * q + 510 * q^2 - 20130 * q^3 + 3145170 * q^5 - 30766728 * q^6 + 78767350 * q^7 - 217339260 * q^8	$ 16 q + 510 q^{2} - 20130 q^{3} + 3145170 q^{5} - 30766728 q^{6} + 78767350 q^{7} - 217339260 q^{8} - 635093930 q^{10} + 4719921012 q^{11} - 22715951880 q^{12} + 8689116940 q^{13} - 59706310410 q^{15} + 10530345976 q^{16} - 221748184620 q^{17} + 654304109970 q^{18} - 878373508140 q^{20} + 1431507507492 q^{21} + 2209421844320 q^{22} - 3507966822690 q^{23} + 10464353188900 q^{25} - 23324455191468 q^{26} + 11679867134280 q^{27} + 8077754165240 q^{28} - 80865025845360 q^{30} + 53033402941772 q^{31} + 20394786468360 q^{32} - 4953707733660 q^{33} - 82375887392730 q^{35} + 263454471040956 q^{36} - 29247362581160 q^{37} + 391580910829560 q^{38} - 918259855204500 q^{40} - 717170436410748 q^{41} + 11\!\cdots\!80 q^{42}+ \cdots - 43\!\cdots\!90 q^{98}+O(q^{100}) $ 16 * q + 510 * q^2 - 20130 * q^3 + 3145170 * q^5 - 30766728 * q^6 + 78767350 * q^7 - 217339260 * q^8 - 635093930 * q^10 + 4719921012 * q^11 - 22715951880 * q^12 + 8689116940 * q^13 - 59706310410 * q^15 + 10530345976 * q^16 - 221748184620 * q^17 + 654304109970 * q^18 - 878373508140 * q^20 + 1431507507492 * q^21 + 2209421844320 * q^22 - 3507966822690 * q^23 + 10464353188900 * q^25 - 23324455191468 * q^26 + 11679867134280 * q^27 + 8077754165240 * q^28 - 80865025845360 * q^30 + 53033402941772 * q^31 + 20394786468360 * q^32 - 4953707733660 * q^33 - 82375887392730 * q^35 + 263454471040956 * q^36 - 29247362581160 * q^37 + 391580910829560 * q^38 - 918259855204500 * q^40 - 717170436410748 * q^41 + 1119760897992480 * q^42 + 1295649718427950 * q^43 - 2413910465914410 * q^45 - 6165422784262408 * q^46 + 5324712362382270 * q^47 + 7675815427929360 * q^48 - 10266398091964350 * q^50 - 5996743906200468 * q^51 + 5457051468349900 * q^52 + 25019175284457720 * q^53 - 28447209909214060 * q^55 - 22879869030140400 * q^56 + 26327201869272960 * q^57 + 72036625362175440 * q^58 - 129993967558538280 * q^60 - 55112667981951388 * q^61 + 98952816959518920 * q^62 + 129200567352114030 * q^63 - 145786436727900960 * q^65 - 217789774433419296 * q^66 + 132604737823930030 * q^67 + 291394918710173220 * q^68 - 344767752141139080 * q^70 - 148288220084109108 * q^71 + 428373837658219140 * q^72 + 357896091854250160 * q^73 - 656924515001553450 * q^75 - 254554257141486000 * q^76 + 201286979542193700 * q^77 + 866949362074211400 * q^78 - 608571216720410880 * q^80 - 330578957555881164 * q^81 - 167911799138733280 * q^82 + 314012877447835830 * q^83 - 37755360901186580 * q^85 - 149686440788368488 * q^86 + 359090097519437040 * q^87 - 966828856938988320 * q^88 + 2368537241357586390 * q^90 + 498102030062089052 * q^91 - 1299658879961370120 * q^92 - 3025937916654554460 * q^93 + 2986575636848949000 * q^95 + 3531977749160666592 * q^96 - 1689002222572272080 * q^97 - 4330619740553781090 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/5\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	622.308	+	622.308i	1.21544	+	1.21544i	0.969210	+	0.246235i	$0.0791934\pi$
$2$	622.308	+	622.308i	1.21544	+	1.21544i	0.246235	+	0.969210i	$0.420807\pi$
$3$	−24393.6	+	24393.6i	−1.23933	+	1.23933i	−0.279049	+	0.960277i	$0.590019\pi$
$3$	−24393.6	+	24393.6i	−1.23933	+	1.23933i	−0.960277	+	0.279049i	$0.909981\pi$
$4$			512390.i			1.95461i
$5$	1.93064e6	+	295511.i	0.988488	+	0.151301i
$5$	1.93064e6	+	295511.i	0.988488	+	0.151301i
$6$	−3.03607e7			−3.01266
$7$	−3.63215e6	−	3.63215e6i	−0.0900080	−	0.0900080i	0.660669	−	0.750677i	$-0.270273\pi$
$7$	−3.63215e6	−	3.63215e6i	−0.0900080	−	0.0900080i	−0.750677	+	0.660669i	$0.770273\pi$
$8$	−1.55730e8	+	1.55730e8i	−1.16028	+	1.16028i
$9$		−	8.02680e8i		−	2.07186i
$10$	1.01755e9	+	1.38535e9i	1.01755	+	1.38535i
$11$	1.61251e9			0.683861			0.341930	−	0.939725i	$-0.388919\pi$
$11$	1.61251e9			0.683861			0.341930	+	0.939725i	$0.388919\pi$
$12$	−1.24991e10	−	1.24991e10i	−2.42240	−	2.42240i
$13$	−6.40234e9	+	6.40234e9i	−0.603738	+	0.603738i	−0.941302	−	0.337565i	$-0.890397\pi$
$13$	−6.40234e9	+	6.40234e9i	−0.603738	+	0.603738i	0.337565	+	0.941302i	$0.390397\pi$
$14$		−	4.52063e9i		−	0.218799i
$15$	−5.43039e10	+	3.98868e10i	−1.41257	+	1.03755i
$16$	−5.95041e10			−0.865898
$17$	6.97717e9	+	6.97717e9i	0.0588354	+	0.0588354i	0.735912	−	0.677077i	$-0.236754\pi$
$17$	6.97717e9	+	6.97717e9i	0.0588354	+	0.0588354i	−0.677077	+	0.735912i	$0.736754\pi$
$18$	4.99514e11	−	4.99514e11i	2.51823	−	2.51823i
$19$			1.05230e11i			0.326105i	0.986617	+	0.163052i	$0.0521339\pi$
$19$			1.05230e11i			0.326105i	−0.986617	+	0.163052i	$0.947866\pi$
$20$	−1.51417e11	+	9.89241e11i	−0.295736	+	1.93211i
$21$	1.77203e11			0.223098
$22$	1.00348e12	+	1.00348e12i	0.831195	+	0.831195i
$23$	−1.83599e12	+	1.83599e12i	−1.01934	+	1.01934i	−0.0195353	+	0.999809i	$0.506219\pi$
$23$	−1.83599e12	+	1.83599e12i	−1.01934	+	1.01934i	−0.999809	+	0.0195353i	$0.993781\pi$
$24$		−	7.59765e12i		−	2.87593i
$25$	3.64004e12	+	1.14105e12i	0.954216	+	0.299119i
$26$	−7.96845e12			−1.46762
$27$	1.01297e13	+	1.01297e13i	1.32838	+	1.32838i
$28$	1.86108e12	−	1.86108e12i	0.175931	−	0.175931i
$29$		−	1.51916e13i		−	1.04718i	−0.851971	−	0.523590i	$-0.824593\pi$
$29$		−	1.51916e13i		−	1.04718i	0.851971	−	0.523590i	$-0.175407\pi$
$30$	−5.86156e13	−	8.97192e12i	−2.97798	−	0.455821i
$31$	2.32707e13			0.880145			0.440073	−	0.897962i	$-0.354953\pi$
$31$	2.32707e13			0.880145			0.440073	+	0.897962i	$0.354953\pi$
$32$	3.79385e12	+	3.79385e12i	0.107828	+	0.107828i
$33$	−3.93349e13	+	3.93349e13i	−0.847526	+	0.847526i
$34$			8.68389e12i			0.143022i
$35$	−5.93903e12	−	8.08570e12i	−0.0753534	−	0.102590i
$36$	4.11285e14			4.04968
$37$	1.21070e13	+	1.21070e13i	0.0931584	+	0.0931584i	0.752150	−	0.658992i	$-0.229017\pi$
$37$	1.21070e13	+	1.21070e13i	0.0931584	+	0.0931584i	−0.658992	+	0.752150i	$0.729017\pi$
$38$	−6.54854e13	+	6.54854e13i	−0.396362	+	0.396362i
$39$		−	3.12353e14i		−	1.49646i
$40$	−3.46679e14	+	2.54639e14i	−1.32247	+	0.971370i
$41$	−4.41756e14			−1.34936			−0.674680	−	0.738111i	$-0.735718\pi$
$41$	−4.41756e14			−1.34936			−0.674680	+	0.738111i	$0.735718\pi$
$42$	1.10275e14	+	1.10275e14i	0.271164	+	0.271164i
$43$	1.75004e14	−	1.75004e14i	0.348202	−	0.348202i	−0.511237	−	0.859440i	$-0.670813\pi$
$43$	1.75004e14	−	1.75004e14i	0.348202	−	0.348202i	0.859440	+	0.511237i	$0.170813\pi$
$44$			8.26233e14i			1.33668i
$45$	2.37200e14	−	1.54969e15i	0.313475	−	2.04800i
$46$	−2.28511e15			−2.47791
$47$	1.26772e15	+	1.26772e15i	1.13277	+	1.13277i	0.989714	+	0.143060i	$0.0456941\pi$
$47$	1.26772e15	+	1.26772e15i	1.13277	+	1.13277i	0.143060	+	0.989714i	$0.454306\pi$
$48$	1.45152e15	−	1.45152e15i	1.07313	−	1.07313i
$49$		−	1.60203e15i		−	0.983797i
$50$	1.55514e15	+	2.97531e15i	0.796234	+	1.52336i
$51$	−3.40397e14			−0.145832
$52$	−3.28049e15	−	3.28049e15i	−1.18007	−	1.18007i
$53$	1.11472e15	−	1.11472e15i	0.337818	−	0.337818i	−0.517727	−	0.855546i	$-0.673222\pi$
$53$	1.11472e15	−	1.11472e15i	0.337818	−	0.337818i	0.855546	+	0.517727i	$0.173222\pi$
$54$			1.26076e16i			3.22914i
$55$	3.11317e15	+	4.76513e14i	0.675988	+	0.103469i
$56$	1.13127e15			0.208869
$57$	−2.56694e15	−	2.56694e15i	−0.404150	−	0.404150i
$58$	9.45384e15	−	9.45384e15i	1.27279	−	1.27279i
$59$			6.28063e15i			0.724995i	0.931985	+	0.362497i	$0.118076\pi$
$59$			6.28063e15i			0.724995i	−0.931985	+	0.362497i	$0.881924\pi$
$60$	−2.04376e16	−	2.78248e16i	−2.02800	−	2.76103i
$61$	5.12455e15			0.438215			0.219108	−	0.975701i	$-0.429685\pi$
$61$	5.12455e15			0.438215			0.219108	+	0.975701i	$0.429685\pi$
$62$	1.44815e16	+	1.44815e16i	1.06977	+	1.06977i
$63$	−2.91545e15	+	2.91545e15i	−0.186484	+	0.186484i
$64$			2.03205e16i			1.12802i
$65$	−1.42526e16	+	1.04686e16i	−0.688134	+	0.505441i
$66$	−4.89569e16			−2.06024
$67$	−3.69810e15	−	3.69810e15i	−0.135927	−	0.135927i	0.635870	−	0.771797i	$-0.280642\pi$
$67$	−3.69810e15	−	3.69810e15i	−0.135927	−	0.135927i	−0.771797	+	0.635870i	$0.780642\pi$
$68$	−3.57503e15	+	3.57503e15i	−0.115000	+	0.115000i
$69$		−	8.95732e16i		−	2.52660i
$70$	1.33589e15	−	8.72770e15i	0.0331047	−	0.216281i
$71$	8.23007e16			1.79506			0.897529	−	0.440956i	$-0.145361\pi$
$71$	8.23007e16			1.79506			0.897529	+	0.440956i	$0.145361\pi$
$72$	1.25001e17	+	1.25001e17i	2.40393	+	2.40393i
$73$	2.68205e16	−	2.68205e16i	0.455577	−	0.455577i	−0.441624	−	0.897200i	$-0.645597\pi$
$73$	2.68205e16	−	2.68205e16i	0.455577	−	0.455577i	0.897200	+	0.441624i	$0.145597\pi$
$74$			1.50686e16i			0.226458i
$75$	−1.16628e17	+	6.09596e16i	−1.55329	+	0.811878i
$76$	−5.39188e16			−0.637408
$77$	−5.85686e15	−	5.85686e15i	−0.0615529	−	0.0615529i
$78$	1.94380e17	−	1.94380e17i	1.81886	−	1.81886i
$79$			1.50642e17i			1.25691i	0.777848	+	0.628453i	$0.216312\pi$
$79$			1.50642e17i			1.25691i	−0.777848	+	0.628453i	$0.783688\pi$
$80$	−1.14881e17	−	1.75841e16i	−0.855930	−	0.131012i
$81$	−1.83225e17			−1.22073
$82$	−2.74908e17	−	2.74908e17i	−1.64007	−	1.64007i
$83$	−6.69322e16	+	6.69322e16i	−0.358040	+	0.358040i	−0.863090	−	0.505050i	$-0.831474\pi$
$83$	−6.69322e16	+	6.69322e16i	−0.358040	+	0.358040i	0.505050	+	0.863090i	$0.331474\pi$
$84$			9.07968e16i			0.436071i
$85$	1.14086e16	+	1.55322e16i	0.0492562	+	0.0670600i
$86$	2.17813e17			0.846441
$87$	3.70578e17	+	3.70578e17i	1.29780	+	1.29780i
$88$	−2.51116e17	+	2.51116e17i	−0.793469	+	0.793469i
$89$		−	2.86724e17i		−	0.818377i	−0.912450	−	0.409188i	$-0.865812\pi$
$89$		−	2.86724e17i		−	0.818377i	0.912450	−	0.409188i	$-0.134188\pi$
$90$	1.11199e18	−	8.16770e17i	2.87025	−	2.10823i
$91$	4.65084e16			0.108682
$92$	−9.40745e17	−	9.40745e17i	−1.99242	−	1.99242i
$93$	−5.67658e17	+	5.67658e17i	−1.09079	+	1.09079i
$94$			1.57783e18i			2.75365i
$95$	−3.10966e16	+	2.03161e17i	−0.0493401	+	0.322350i
$96$	−1.85092e17			−0.267267
$97$	8.46795e17	+	8.46795e17i	1.11387	+	1.11387i	0.992623	+	0.121243i	$0.0386880\pi$
$97$	8.46795e17	+	8.46795e17i	1.11387	+	1.11387i	0.121243	+	0.992623i	$0.461312\pi$
$98$	9.96955e17	−	9.96955e17i	1.19575	−	1.19575i
$99$		−	1.29433e18i		−	1.41686i
$100$	−5.84662e17	+	1.86512e18i	−0.584662	+	1.86512i
$101$	−3.70254e17			−0.338538			−0.169269	−	0.985570i	$-0.554141\pi$
$101$	−3.70254e17			−0.338538			−0.169269	+	0.985570i	$0.554141\pi$
$102$	−2.11832e17	−	2.11832e17i	−0.177251	−	0.177251i
$103$	1.03050e18	−	1.03050e18i	0.789796	−	0.789796i	−0.191664	−	0.981461i	$-0.561388\pi$
$103$	1.03050e18	−	1.03050e18i	0.789796	−	0.789796i	0.981461	+	0.191664i	$0.0613885\pi$
$104$		−	1.99407e18i		−	1.40101i
$105$	3.42114e17	+	5.23653e16i	0.220530	+	0.0337551i
$106$	1.38740e18			0.821199
$107$	−2.13275e18	−	2.13275e18i	−1.16008	−	1.16008i	−0.984458	−	0.175619i	$-0.943807\pi$
$107$	−2.13275e18	−	2.13275e18i	−1.16008	−	1.16008i	−0.175619	−	0.984458i	$-0.556193\pi$
$108$	−5.19035e18	+	5.19035e18i	−2.59647	+	2.59647i
$109$		−	3.04401e18i		−	1.40155i	−0.713384	−	0.700774i	$-0.752838\pi$
$109$		−	3.04401e18i		−	1.40155i	0.713384	−	0.700774i	$-0.247162\pi$
$110$	1.64081e18	+	2.23389e18i	0.695865	+	0.947387i
$111$	−5.90669e17			−0.230907
$112$	2.16127e17	+	2.16127e17i	0.0779377	+	0.0779377i
$113$	1.67873e17	−	1.67873e17i	0.0558823	−	0.0558823i	−0.678613	−	0.734496i	$-0.737419\pi$
$113$	1.67873e17	−	1.67873e17i	0.0558823	−	0.0558823i	0.734496	+	0.678613i	$0.237419\pi$
$114$		−	3.19486e18i		−	0.982444i
$115$	−4.08720e18	+	3.00209e18i	−1.16184	+	0.853381i
$116$	7.78401e18			2.04683
$117$	5.13903e18	+	5.13903e18i	1.25086	+	1.25086i
$118$	−3.90848e18	+	3.90848e18i	−0.881191	+	0.881191i
$119$		−	5.06842e16i		−	0.0105913i
$120$	2.24519e18	−	1.46683e19i	0.435132	−	2.84282i
$121$	−2.95974e18			−0.532335
$122$	3.18905e18	+	3.18905e18i	0.532626	+	0.532626i
$123$	1.07760e19	−	1.07760e19i	1.67230	−	1.67230i
$124$			1.19237e19i			1.72034i
$125$	6.69042e18	+	3.27863e18i	0.897973	+	0.440050i
$126$	−3.62861e18			−0.453321
$127$	−6.42294e18	−	6.42294e18i	−0.747310	−	0.747310i	0.226663	−	0.973973i	$-0.427218\pi$
$127$	−6.42294e18	−	6.42294e18i	−0.747310	−	0.747310i	−0.973973	+	0.226663i	$0.927218\pi$
$128$	−1.16511e19	+	1.16511e19i	−1.26321	+	1.26321i
$129$			8.53797e18i			0.863072i
$130$	−1.53842e19	−	2.35476e18i	−1.45072	−	0.222053i
$131$	−1.48921e18			−0.131073			−0.0655366	−	0.997850i	$-0.520876\pi$
$131$	−1.48921e18			−0.131073			−0.0655366	+	0.997850i	$0.520876\pi$
$132$	−2.01548e19	−	2.01548e19i	−1.65659	−	1.65659i
$133$	3.82211e17	−	3.82211e17i	0.0293520	−	0.0293520i
$134$		−	4.60272e18i		−	0.330424i
$135$	1.65633e19	+	2.25502e19i	1.11210	+	1.51407i
$136$	−2.17311e18			−0.136531
$137$	−8.39955e18	−	8.39955e18i	−0.494050	−	0.494050i	0.415530	−	0.909580i	$-0.363596\pi$
$137$	−8.39955e18	−	8.39955e18i	−0.494050	−	0.494050i	−0.909580	+	0.415530i	$0.863596\pi$
$138$	5.57421e19	−	5.57421e19i	3.07094	−	3.07094i
$139$			8.28997e18i			0.427976i	0.976836	+	0.213988i	$0.0686454\pi$
$139$			8.28997e18i			0.427976i	−0.976836	+	0.213988i	$0.931355\pi$
$140$	4.14303e18	−	3.04310e18i	0.200524	−	0.147287i
$141$	−6.18487e19			−2.80775
$142$	5.12164e19	+	5.12164e19i	2.18179	+	2.18179i
$143$	−1.03238e19	+	1.03238e19i	−0.412873	+	0.412873i
$144$			4.77627e19i			1.79402i
$145$	4.48928e18	−	2.93295e19i	0.158440	−	1.03512i
$146$	3.33812e19			1.10746
$147$	3.90793e19	+	3.90793e19i	1.21925	+	1.21925i
$148$	−6.20352e18	+	6.20352e18i	−0.182089	+	0.182089i
$149$		−	5.75268e19i		−	1.58926i	−0.607096	−	0.794628i	$-0.707666\pi$
$149$		−	5.75268e19i		−	1.58926i	0.607096	−	0.794628i	$-0.292334\pi$
$150$	−1.10514e20	−	3.46431e19i	−2.87473	−	0.901146i
$151$	−3.67875e19			−0.901379			−0.450689	−	0.892681i	$-0.648822\pi$
$151$	−3.67875e19			−0.901379			−0.450689	+	0.892681i	$0.648822\pi$
$152$	−1.63875e19	−	1.63875e19i	−0.378372	−	0.378372i
$153$	5.60043e18	−	5.60043e18i	0.121898	−	0.121898i
$154$		−	7.28954e18i		−	0.149628i
$155$	4.49274e19	+	6.87675e18i	0.870013	+	0.133167i
$156$	1.60046e20			2.92499
$157$	7.10154e18	+	7.10154e18i	0.122534	+	0.122534i	0.765714	−	0.643181i	$-0.222386\pi$
$157$	7.10154e18	+	7.10154e18i	0.122534	+	0.122534i	−0.643181	+	0.765714i	$0.722386\pi$
$158$	−9.37458e19	+	9.37458e19i	−1.52770	+	1.52770i
$159$			5.43842e19i			0.837333i
$160$	6.20344e18	+	8.44568e18i	0.0902719	+	0.122901i
$161$	1.33372e19			0.183498
$162$	−1.14023e20	−	1.14023e20i	−1.48373	−	1.48373i
$163$	3.42433e19	−	3.42433e19i	0.421587	−	0.421587i	−0.464163	−	0.885750i	$-0.653645\pi$
$163$	3.42433e19	−	3.42433e19i	0.421587	−	0.421587i	0.885750	+	0.464163i	$0.153645\pi$
$164$		−	2.26351e20i		−	2.63747i
$165$	−8.75655e19	+	6.43177e19i	−0.966001	+	0.709537i
$166$	−8.33048e19			−0.870357
$167$	4.92075e19	+	4.92075e19i	0.487061	+	0.487061i	0.907377	−	0.420317i	$-0.138081\pi$
$167$	4.92075e19	+	4.92075e19i	0.487061	+	0.487061i	−0.420317	+	0.907377i	$0.638081\pi$
$168$	−2.75958e19	+	2.75958e19i	−0.258856	+	0.258856i
$169$			3.04755e19i			0.271001i
$170$	−2.56618e18	+	1.67655e19i	−0.0216395	+	0.141376i
$171$	8.44659e19			0.675642
$172$	8.96702e19	+	8.96702e19i	0.680600	+	0.680600i
$173$	5.37211e19	−	5.37211e19i	0.387017	−	0.387017i	−0.486605	−	0.873622i	$-0.661765\pi$
$173$	5.37211e19	−	5.37211e19i	0.387017	−	0.387017i	0.873622	+	0.486605i	$0.161765\pi$
$174$			4.61227e20i			3.15480i
$175$	−9.07671e18	−	1.73656e19i	−0.0589639	−	0.112810i
$176$	−9.59508e19			−0.592154
$177$	−1.53207e20	−	1.53207e20i	−0.898504	−	0.898504i
$178$	1.78430e20	−	1.78430e20i	0.994692	−	0.994692i
$179$		−	2.43429e20i		−	1.29031i	−0.764051	−	0.645156i	$-0.776792\pi$
$179$		−	2.43429e20i		−	1.29031i	0.764051	−	0.645156i	$-0.223208\pi$
$180$	7.94043e20	+	1.21539e20i	4.00306	+	0.612722i
$181$	−4.05960e17			−0.00194704			−0.000973522	−	1.00000i	$-0.500310\pi$
$181$	−4.05960e17			−0.00194704			−0.000973522		1.00000i	$0.500310\pi$
$182$	2.89426e19	+	2.89426e19i	0.132098	+	0.132098i
$183$	−1.25007e20	+	1.25007e20i	−0.543091	+	0.543091i
$184$		−	5.71839e20i		−	2.36545i
$185$	1.97966e19	+	2.69521e19i	0.0779909	+	0.106181i
$186$	−7.06515e20			−2.65158
$187$	1.12507e19	+	1.12507e19i	0.0402352	+	0.0402352i
$188$	−6.49568e20	+	6.49568e20i	−2.21413	+	2.21413i
$189$		−	7.35850e19i		−	0.239129i
$190$	−1.45780e20	+	1.07077e20i	−0.451769	+	0.331829i
$191$	3.39662e20			1.00403			0.502014	−	0.864859i	$-0.332592\pi$
$191$	3.39662e20			1.00403			0.502014	+	0.864859i	$0.332592\pi$
$192$	−4.95692e20	−	4.95692e20i	−1.39798	−	1.39798i
$193$	−1.07293e20	+	1.07293e20i	−0.288772	+	0.288772i	−0.836594	−	0.547823i	$-0.815457\pi$
$193$	−1.07293e20	+	1.07293e20i	−0.288772	+	0.288772i	0.547823	+	0.836594i	$0.315457\pi$
$194$			1.05393e21i			2.70769i
$195$	9.23036e19	−	6.03041e20i	0.226416	−	1.47923i
$196$	8.20863e20			1.92294
$197$	−9.25616e19	−	9.25616e19i	−0.207126	−	0.207126i	0.595919	−	0.803045i	$-0.296788\pi$
$197$	−9.25616e19	−	9.25616e19i	−0.207126	−	0.207126i	−0.803045	+	0.595919i	$0.796788\pi$
$198$	8.05470e20	−	8.05470e20i	1.72212	−	1.72212i
$199$		−	1.74927e20i		−	0.357420i	−0.983902	−	0.178710i	$-0.942808\pi$
$199$		−	1.74927e20i		−	0.357420i	0.983902	−	0.178710i	$-0.0571924\pi$
$200$	−7.44560e20	+	3.89168e20i	−1.45422	+	0.760095i
$201$	1.80420e20			0.336916
$202$	−2.30412e20	−	2.30412e20i	−0.411474	−	0.411474i
$203$	−5.51780e19	+	5.51780e19i	−0.0942545	+	0.0942545i
$204$		−	1.74416e20i		−	0.285046i
$205$	−8.52871e20	−	1.30544e20i	−1.33382	−	0.204160i
$206$	1.28258e21			1.91991
$207$	1.47372e21	+	1.47372e21i	2.11194	+	2.11194i
$208$	3.80965e20	−	3.80965e20i	0.522775	−	0.522775i
$209$			1.69684e20i			0.223010i
$210$	1.80313e20	+	2.45488e20i	0.227015	+	0.309070i
$211$	−3.59108e20			−0.433194			−0.216597	−	0.976261i	$-0.569496\pi$
$211$	−3.59108e20			−0.433194			−0.216597	+	0.976261i	$0.569496\pi$
$212$	5.71171e20	+	5.71171e20i	0.660304	+	0.660304i
$213$	−2.00761e21	+	2.00761e21i	−2.22466	+	2.22466i
$214$		−	2.65446e21i		−	2.82002i
$215$	3.89585e20	−	2.86154e20i	0.396877	−	0.291510i
$216$	−3.15499e21			−3.08258
$217$	−8.45226e19	−	8.45226e19i	−0.0792201	−	0.0792201i
$218$	1.89431e21	−	1.89431e21i	1.70350	−	1.70350i
$219$			1.30850e21i			1.12922i
$220$	−2.44161e20	+	1.59516e21i	−0.202242	+	1.32129i
$221$	−8.93403e19			−0.0710423
$222$	−3.67578e20	−	3.67578e20i	−0.280655	−	0.280655i
$223$	1.63575e20	−	1.63575e20i	0.119942	−	0.119942i	−0.644588	−	0.764530i	$-0.722971\pi$
$223$	1.63575e20	−	1.63575e20i	0.119942	−	0.119942i	0.764530	+	0.644588i	$0.222971\pi$
$224$		−	2.75596e19i		−	0.0194107i
$225$	9.15897e20	−	2.92179e21i	0.619732	−	1.97700i
$226$	2.08937e20			0.135844
$227$	2.23800e19	+	2.23800e19i	0.0139839	+	0.0139839i	0.714064	−	0.700080i	$-0.246852\pi$
$227$	2.23800e19	+	2.23800e19i	0.0139839	+	0.0139839i	−0.700080	+	0.714064i	$0.746852\pi$
$228$	1.31528e21	−	1.31528e21i	0.789956	−	0.789956i
$229$			3.12885e20i			0.180661i	0.995912	+	0.0903307i	$0.0287924\pi$
$229$			3.12885e20i			0.180661i	−0.995912	+	0.0903307i	$0.971208\pi$
$230$	−4.41172e21	−	6.75274e20i	−2.44939	−	0.374912i
$231$	2.85741e20			0.152568
$232$	2.36579e21	+	2.36579e21i	1.21502	+	1.21502i
$233$	1.70610e21	−	1.70610e21i	0.842949	−	0.842949i	−0.146292	−	0.989241i	$-0.546734\pi$
$233$	1.70610e21	−	1.70610e21i	0.842949	−	0.842949i	0.989241	+	0.146292i	$0.0467340\pi$
$234$			6.39611e21i			3.04070i
$235$	2.07289e21	+	2.82214e21i	0.948343	+	1.29112i
$236$	−3.21813e21			−1.41708
$237$	−3.67471e21	−	3.67471e21i	−1.55772	−	1.55772i
$238$	3.15411e19	−	3.15411e19i	0.0128732	−	0.0128732i
$239$			1.00998e21i			0.396946i	0.980106	+	0.198473i	$0.0635981\pi$
$239$			1.00998e21i			0.396946i	−0.980106	+	0.198473i	$0.936402\pi$
$240$	3.23130e21	−	2.37342e21i	1.22314	−	0.898409i
$241$	−2.26889e21			−0.827295			−0.413648	−	0.910437i	$-0.635745\pi$
$241$	−2.26889e21			−0.827295			−0.413648	+	0.910437i	$0.635745\pi$
$242$	−1.84187e21	−	1.84187e21i	−0.647023	−	0.647023i
$243$	5.45088e20	−	5.45088e20i	0.184506	−	0.184506i
$244$			2.62577e21i			0.856541i
$245$	4.73417e20	−	3.09294e21i	0.148850	−	0.972471i
$246$	1.34120e22			4.06517
$247$	−6.73718e20	−	6.73718e20i	−0.196882	−	0.196882i
$248$	−3.62395e21	+	3.62395e21i	−1.02121	+	1.02121i
$249$		−	3.26544e21i		−	0.887457i
$250$	2.12319e21	+	6.20382e21i	0.556580	+	1.62629i
$251$	4.80359e21			1.21479			0.607396	−	0.794399i	$-0.292214\pi$
$251$	4.80359e21			1.21479			0.607396	+	0.794399i	$0.292214\pi$
$252$	−1.49385e21	−	1.49385e21i	−0.364503	−	0.364503i
$253$	−2.96056e21	+	2.96056e21i	−0.697090	+	0.697090i
$254$		−	7.99410e21i		−	1.81663i
$255$	−6.57184e20	−	1.00591e20i	−0.144154	−	0.0220647i
$256$	−9.17422e21			−1.94272
$257$	5.42937e21	+	5.42937e21i	1.11007	+	1.11007i	0.993140	+	0.116932i	$0.0373058\pi$
$257$	5.42937e21	+	5.42937e21i	1.11007	+	1.11007i	0.116932	+	0.993140i	$0.462694\pi$
$258$	−5.31324e21	+	5.31324e21i	−1.04902	+	1.04902i
$259$		−	8.79490e19i		−	0.0167700i
$260$	−5.36403e21	−	7.30287e21i	−0.987941	−	1.34504i
$261$	−1.21940e22			−2.16960
$262$	−9.26746e20	−	9.26746e20i	−0.159312	−	0.159312i
$263$	4.37793e21	−	4.37793e21i	0.727222	−	0.727222i	−0.242843	−	0.970066i	$-0.578080\pi$
$263$	4.37793e21	−	4.37793e21i	0.727222	−	0.727222i	0.970066	+	0.242843i	$0.0780800\pi$
$264$		−	1.22513e22i		−	1.96673i
$265$	2.48153e21	−	1.82271e21i	0.385041	−	0.282817i
$266$	4.75705e20			0.0713515
$267$	6.99423e21	+	6.99423e21i	1.01424	+	1.01424i
$268$	1.89487e21	−	1.89487e21i	0.265685	−	0.265685i
$269$			3.81640e21i			0.517468i	0.965949	+	0.258734i	$0.0833053\pi$
$269$			3.81640e21i			0.517468i	−0.965949	+	0.258734i	$0.916695\pi$
$270$	−3.72567e21	+	2.43407e22i	−0.488574	+	3.19197i
$271$	−9.97918e21			−1.26582			−0.632909	−	0.774226i	$-0.718139\pi$
$271$	−9.97918e21			−1.26582			−0.632909	+	0.774226i	$0.718139\pi$
$272$	−4.15170e20	−	4.15170e20i	−0.0509455	−	0.0509455i
$273$	−1.13451e21	+	1.13451e21i	−0.134693	+	0.134693i
$274$		−	1.04542e22i		−	1.20098i
$275$	5.86960e21	+	1.83995e21i	0.652551	+	0.204556i
$276$	4.58964e22			4.93852
$277$	7.85415e21	+	7.85415e21i	0.818053	+	0.818053i	0.985826	−	0.167773i	$-0.0536575\pi$
$277$	7.85415e21	+	7.85415e21i	0.818053	+	0.818053i	−0.167773	+	0.985826i	$0.553657\pi$
$278$	−5.15891e21	+	5.15891e21i	−0.520181	+	0.520181i
$279$		−	1.86789e22i		−	1.82353i
$280$	2.18407e21	+	3.34302e20i	0.206464	+	0.0316021i
$281$	1.61885e22			1.48201			0.741004	−	0.671500i	$-0.234350\pi$
$281$	1.61885e22			1.48201			0.741004	+	0.671500i	$0.234350\pi$
$282$	−3.84889e22	−	3.84889e22i	−3.41267	−	3.41267i
$283$	−3.88499e21	+	3.88499e21i	−0.333666	+	0.333666i	−0.853977	−	0.520311i	$-0.825816\pi$
$283$	−3.88499e21	+	3.88499e21i	−0.333666	+	0.333666i	0.520311	+	0.853977i	$0.325816\pi$
$284$			4.21700e22i			3.50864i
$285$	−4.19728e21	−	5.71440e21i	−0.338349	−	0.460646i
$286$	−1.28492e22			−1.00365
$287$	1.60452e21	+	1.60452e21i	0.121453	+	0.121453i
$288$	3.04525e21	−	3.04525e21i	0.223404	−	0.223404i
$289$		−	1.39657e22i		−	0.993077i
$290$	2.10457e22	−	1.54582e22i	1.45071	−	1.06556i
$291$	−4.13129e22			−2.76089
$292$	1.37426e22	+	1.37426e22i	0.890476	+	0.890476i
$293$	−2.09887e22	+	2.09887e22i	−1.31879	+	1.31879i	−0.404059	+	0.914733i	$0.632401\pi$
$293$	−2.09887e22	+	2.09887e22i	−1.31879	+	1.31879i	−0.914733	+	0.404059i	$0.867599\pi$
$294$			4.86387e22i			2.96385i
$295$	−1.85599e21	+	1.21256e22i	−0.109693	+	0.716648i
$296$	−3.77086e21			−0.216179
$297$	1.63342e22	+	1.63342e22i	0.908426	+	0.908426i
$298$	3.57994e22	−	3.57994e22i	1.93165	−	1.93165i
$299$		−	2.35093e22i		−	1.23083i
$300$	−3.12351e22	−	5.97592e22i	−1.58691	−	3.03608i
$301$	−1.27128e21			−0.0626819
$302$	−2.28931e22	−	2.28931e22i	−1.09558	−	1.09558i
$303$	9.03184e21	−	9.03184e21i	0.419559	−	0.419559i
$304$		−	6.26161e21i		−	0.282373i
$305$	9.89367e21	+	1.51436e21i	0.433170	+	0.0663026i
$306$	6.97038e21			0.296322
$307$	−1.15443e21	−	1.15443e21i	−0.0476567	−	0.0476567i	0.682877	−	0.730534i	$-0.260729\pi$
$307$	−1.15443e21	−	1.15443e21i	−0.0476567	−	0.0476567i	−0.730534	+	0.682877i	$0.760729\pi$
$308$	3.00100e21	−	3.00100e21i	0.120312	−	0.120312i
$309$			5.02755e22i			1.95763i
$310$	2.36792e22	+	3.22381e22i	0.895595	+	1.21931i
$311$	−1.39389e22			−0.512134			−0.256067	−	0.966659i	$-0.582427\pi$
$311$	−1.39389e22			−0.512134			−0.256067	+	0.966659i	$0.582427\pi$
$312$	4.86427e22	+	4.86427e22i	1.73631	+	1.73631i
$313$	2.27399e22	−	2.27399e22i	0.788660	−	0.788660i	−0.192615	−	0.981274i	$-0.561697\pi$
$313$	2.27399e22	−	2.27399e22i	0.788660	−	0.788660i	0.981274	+	0.192615i	$0.0616967\pi$
$314$			8.83868e21i			0.297866i
$315$	−6.49023e21	+	4.76714e21i	−0.212552	+	0.156121i
$316$	−7.71875e22			−2.45676
$317$	−3.57070e22	−	3.57070e22i	−1.10464	−	1.10464i	−0.993843	−	0.110796i	$-0.964660\pi$
$317$	−3.57070e22	−	3.57070e22i	−1.10464	−	1.10464i	−0.110796	−	0.993843i	$-0.535340\pi$
$318$	−3.38437e22	+	3.38437e22i	−1.01773	+	1.01773i
$319$		−	2.44965e22i		−	0.716125i
$320$	−6.00493e21	+	3.92316e22i	−0.170670	+	1.11503i
$321$	1.04051e23			2.87543
$322$	8.29985e21	+	8.29985e21i	0.223032	+	0.223032i
$323$	−7.34207e20	+	7.34207e20i	−0.0191865	+	0.0191865i
$324$		−	9.38829e22i		−	2.38606i
$325$	−3.06102e22	+	1.59994e22i	−0.756686	+	0.395506i
$326$	4.26197e22			1.02483
$327$	7.42545e22	+	7.42545e22i	1.73697	+	1.73697i
$328$	6.87946e22	−	6.87946e22i	1.56563	−	1.56563i
$329$		−	9.20910e21i		−	0.203917i
$330$	−9.45181e22	−	1.44673e22i	−2.03652	−	0.311718i
$331$	−6.14668e22			−1.28881			−0.644405	−	0.764685i	$-0.722895\pi$
$331$	−6.14668e22			−1.28881			−0.644405	+	0.764685i	$0.722895\pi$
$332$	−3.42954e22	−	3.42954e22i	−0.699830	−	0.699830i
$333$	9.71806e21	−	9.71806e21i	0.193011	−	0.193011i
$334$			6.12444e22i			1.18399i
$335$	−6.04688e21	−	8.23253e21i	−0.113796	−	0.154928i
$336$	−1.05443e22			−0.193180
$337$	−3.53317e22	−	3.53317e22i	−0.630225	−	0.630225i	0.317899	−	0.948124i	$-0.397023\pi$
$337$	−3.53317e22	−	3.53317e22i	−0.630225	−	0.630225i	−0.948124	+	0.317899i	$0.897023\pi$
$338$	−1.89652e22	+	1.89652e22i	−0.329387	+	0.329387i
$339$			8.19006e21i			0.138513i
$340$	−7.95855e21	+	5.84564e21i	−0.131076	+	0.0962768i
$341$	3.75242e22			0.601897
$342$	5.25638e22	+	5.25638e22i	0.821206	+	0.821206i
$343$	−1.17334e22	+	1.17334e22i	−0.178558	+	0.178558i
$344$			5.45067e22i			0.808024i
$345$	2.64699e22	−	1.72934e23i	0.382278	−	2.49751i
$346$	6.68621e22			0.940795
$347$	−5.68349e22	−	5.68349e22i	−0.779202	−	0.779202i	0.200493	−	0.979695i	$-0.435746\pi$
$347$	−5.68349e22	−	5.68349e22i	−0.779202	−	0.779202i	−0.979695	+	0.200493i	$0.935746\pi$
$348$	−1.89880e23	+	1.89880e23i	−2.53669	+	2.53669i
$349$		−	2.48541e22i		−	0.323571i	−0.986826	−	0.161785i	$-0.948275\pi$
$349$		−	2.48541e22i		−	0.323571i	0.986826	−	0.161785i	$-0.0517252\pi$
$350$	5.15826e21	−	1.64553e22i	0.0654471	−	0.208782i
$351$	−1.29707e23			−1.60399
$352$	6.11761e21	+	6.11761e21i	0.0737391	+	0.0737391i
$353$	−1.12896e23	+	1.12896e23i	−1.32649	+	1.32649i	−0.418082	+	0.908409i	$0.637298\pi$
$353$	−1.12896e23	+	1.12896e23i	−1.32649	+	1.32649i	−0.908409	+	0.418082i	$0.862702\pi$
$354$		−	1.90684e23i		−	2.18417i
$355$	1.58893e23	+	2.43207e22i	1.77439	+	0.271595i
$356$	1.46914e23			1.59961
$357$	1.23637e21	+	1.23637e21i	0.0131261	+	0.0131261i
$358$	1.51488e23	−	1.51488e23i	1.56830	−	1.56830i
$359$			2.18161e22i			0.220255i	0.993917	+	0.110128i	$0.0351260\pi$
$359$			2.18161e22i			0.220255i	−0.993917	+	0.110128i	$0.964874\pi$
$360$	2.04393e23	+	2.78272e23i	2.01254	+	2.73998i
$361$	9.30540e22			0.893656
$362$	−2.52632e20	−	2.52632e20i	−0.00236653	−	0.00236653i
$363$	7.21988e22	−	7.21988e22i	0.659736	−	0.659736i
$364$			2.38305e22i			0.212432i
$365$	5.97065e22	−	4.38550e22i	0.519261	−	0.381403i
$366$	−1.55585e23			−1.32020
$367$	−8.39097e22	−	8.39097e22i	−0.694733	−	0.694733i	0.268537	−	0.963269i	$-0.413460\pi$
$367$	−8.39097e22	−	8.39097e22i	−0.694733	−	0.694733i	−0.963269	+	0.268537i	$0.913460\pi$
$368$	1.09249e23	−	1.09249e23i	0.882648	−	0.882648i
$369$			3.54588e23i			2.79568i
$370$	−4.45293e21	+	2.90920e22i	−0.0342634	+	0.223851i
$371$	−8.09765e21			−0.0608126
$372$	−2.90862e23	−	2.90862e23i	−2.13207	−	2.13207i
$373$	−5.06563e22	+	5.06563e22i	−0.362455	+	0.362455i	−0.864716	−	0.502261i	$-0.832502\pi$
$373$	−5.06563e22	+	5.06563e22i	−0.362455	+	0.362455i	0.502261	+	0.864716i	$0.332502\pi$
$374$			1.40028e22i			0.0978074i
$375$	−2.43182e23	+	8.32261e22i	−1.65825	+	0.567516i
$376$	−3.94845e23			−2.62867
$377$	9.72616e22	+	9.72616e22i	0.632222	+	0.632222i
$378$	4.57925e22	−	4.57925e22i	0.290649	−	0.290649i
$379$		−	1.14751e23i		−	0.711218i	−0.934635	−	0.355609i	$-0.884273\pi$
$379$		−	1.14751e23i		−	0.711218i	0.934635	−	0.355609i	$-0.115727\pi$
$380$	−1.04098e23	−	1.59336e22i	−0.630070	−	0.0964408i
$381$	3.13358e23			1.85232
$382$	2.11374e23	+	2.11374e23i	1.22034	+	1.22034i
$383$	6.33293e22	−	6.33293e22i	0.357121	−	0.357121i	−0.505629	−	0.862751i	$-0.668740\pi$
$383$	6.33293e22	−	6.33293e22i	0.357121	−	0.357121i	0.862751	+	0.505629i	$0.168740\pi$
$384$		−	5.68425e23i		−	3.13106i
$385$	−9.57673e21	−	1.30383e22i	−0.0515312	−	0.0701573i
$386$	−1.33538e23			−0.701972
$387$	−1.40472e23	−	1.40472e23i	−0.721425	−	0.721425i
$388$	−4.33890e23	+	4.33890e23i	−2.17718	+	2.17718i
$389$			2.75999e23i			1.35320i	0.736352	+	0.676598i	$0.236547\pi$
$389$			2.75999e23i			1.35320i	−0.736352	+	0.676598i	$0.763453\pi$
$390$	4.32718e23	−	3.17836e23i	2.07312	−	1.52272i
$391$	−2.56201e22			−0.119947
$392$	2.49484e23	+	2.49484e23i	1.14148	+	1.14148i
$393$	3.63272e22	−	3.63272e22i	0.162442	−	0.162442i
$394$		−	1.15204e23i		−	0.503501i
$395$	−4.45164e22	+	2.90836e23i	−0.190172	+	1.24244i
$396$	6.63200e23			2.76941
$397$	−3.96269e22	−	3.96269e22i	−0.161762	−	0.161762i	0.621585	−	0.783347i	$-0.286489\pi$
$397$	−3.96269e22	−	3.96269e22i	−0.161762	−	0.161762i	−0.783347	+	0.621585i	$0.786489\pi$
$398$	1.08858e23	−	1.08858e23i	0.434424	−	0.434424i
$399$			1.86470e22i			0.0727534i
$400$	−2.16597e23	−	6.78971e22i	−0.826254	−	0.259007i
$401$	−1.66355e23			−0.620494			−0.310247	−	0.950656i	$-0.600412\pi$
$401$	−1.66355e23			−0.620494			−0.310247	+	0.950656i	$0.600412\pi$
$402$	1.12277e23	+	1.12277e23i	0.409502	+	0.409502i
$403$	−1.48987e23	+	1.48987e23i	−0.531377	+	0.531377i
$404$		−	1.89714e23i		−	0.661711i
$405$	−3.53742e23	−	5.41451e22i	−1.20668	−	0.184699i
$406$	−6.86754e22			−0.229122
$407$	1.95227e22	+	1.95227e22i	0.0637074	+	0.0637074i
$408$	5.30100e22	−	5.30100e22i	0.169206	−	0.169206i
$409$		−	4.47799e23i		−	1.39821i	−0.715018	−	0.699107i	$-0.753581\pi$
$409$		−	4.47799e23i		−	1.39821i	0.715018	−	0.699107i	$-0.246419\pi$
$410$	−4.49510e23	−	6.11987e23i	−1.37305	−	1.86934i
$411$	4.09791e23			1.22458
$412$	5.28020e23	+	5.28020e23i	1.54375	+	1.54375i
$413$	2.28121e22	−	2.28121e22i	0.0652553	−	0.0652553i
$414$			1.83421e24i			5.13388i
$415$	−1.49001e23	+	1.09443e23i	−0.408091	+	0.299746i
$416$	−4.85790e22			−0.130199
$417$	−2.02223e23	−	2.02223e23i	−0.530402	−	0.530402i
$418$	−1.05596e23	+	1.05596e23i	−0.271057	+	0.271057i
$419$		−	5.93809e23i		−	1.49183i	−0.666039	−	0.745917i	$-0.732012\pi$
$419$		−	5.93809e23i		−	1.49183i	0.666039	−	0.745917i	$-0.267988\pi$
$420$	−2.68314e22	+	1.75296e23i	−0.0659782	+	0.431051i
$421$	4.76273e23			1.14635			0.573175	−	0.819433i	$-0.305711\pi$
$421$	4.76273e23			1.14635			0.573175	+	0.819433i	$0.305711\pi$
$422$	−2.23476e23	−	2.23476e23i	−0.526524	−	0.526524i
$423$	1.01757e24	−	1.01757e24i	2.34694	−	2.34694i
$424$			3.47191e23i			0.783927i
$425$	1.74359e22	+	3.33585e22i	0.0385429	+	0.0737405i
$426$	−2.49871e24			−5.40790
$427$	−1.86131e22	−	1.86131e22i	−0.0394429	−	0.0394429i
$428$	1.09280e24	−	1.09280e24i	2.26750	−	2.26750i
$429$		−	5.03671e23i		−	1.02337i
$430$	4.20518e23	+	6.43659e22i	0.836697	+	0.128068i
$431$	−7.59177e22			−0.147927			−0.0739636	−	0.997261i	$-0.523565\pi$
$431$	−7.59177e22			−0.147927			−0.0739636	+	0.997261i	$0.523565\pi$
$432$	−6.02757e23	−	6.02757e23i	−1.15024	−	1.15024i
$433$	−5.82274e23	+	5.82274e23i	−1.08827	+	1.08827i	−0.0925632	+	0.995707i	$0.529506\pi$
$433$	−5.82274e23	+	5.82274e23i	−1.08827	+	1.08827i	−0.995707	+	0.0925632i	$0.970494\pi$
$434$		−	1.05198e23i		−	0.192575i
$435$	6.05943e23	+	8.24963e23i	1.08650	+	1.47921i
$436$	1.55972e24			2.73948
$437$	−1.93202e23	−	1.93202e23i	−0.332413	−	0.332413i
$438$	−8.14290e23	+	8.14290e23i	−1.37250	+	1.37250i
$439$			7.39853e23i			1.22170i	0.791746	+	0.610850i	$0.209172\pi$
$439$			7.39853e23i			1.22170i	−0.791746	+	0.610850i	$0.790828\pi$
$440$	−5.59022e23	+	4.10607e23i	−0.904388	+	0.664281i
$441$	−1.28592e24			−2.03829
$442$	−5.55972e22	−	5.55972e22i	−0.0863480	−	0.0863480i
$443$	−5.19135e23	+	5.19135e23i	−0.790035	+	0.790035i	−0.981500	−	0.191464i	$-0.938676\pi$
$443$	−5.19135e23	+	5.19135e23i	−0.790035	+	0.790035i	0.191464	+	0.981500i	$0.438676\pi$
$444$		−	3.02653e23i		−	0.451334i
$445$	8.47299e22	−	5.53560e23i	0.123822	−	0.808955i
$446$	2.03587e23			0.291566
$447$	1.40329e24	+	1.40329e24i	1.96961	+	1.96961i
$448$	7.38071e22	−	7.38071e22i	0.101530	−	0.101530i
$449$			2.01668e23i			0.271907i	0.990715	+	0.135954i	$0.0434098\pi$
$449$			2.01668e23i			0.271907i	−0.990715	+	0.135954i	$0.956590\pi$
$450$	2.38822e24	−	1.24828e24i	3.15618	−	1.64968i
$451$	−7.12335e23			−0.922774
$452$	8.60163e22	+	8.60163e22i	0.109228	+	0.109228i
$453$	8.97380e23	−	8.97380e23i	1.11710	−	1.11710i
$454$			2.78545e22i			0.0339933i
$455$	8.97911e22	+	1.37437e22i	0.107431	+	0.0164438i
$456$	7.99500e23			0.937853
$457$	−8.60567e23	−	8.60567e23i	−0.989780	−	0.989780i	0.0101681	−	0.999948i	$-0.496763\pi$
$457$	−8.60567e23	−	8.60567e23i	−0.989780	−	0.989780i	−0.999948	+	0.0101681i	$0.996763\pi$
$458$	−1.94711e23	+	1.94711e23i	−0.219584	+	0.219584i
$459$			1.41353e23i			0.156311i
$460$	−1.53824e24	−	2.09424e24i	−1.66803	−	2.27094i
$461$	9.16818e23			0.974933			0.487466	−	0.873142i	$-0.337921\pi$
$461$	9.16818e23			0.974933			0.487466	+	0.873142i	$0.337921\pi$
$462$	1.77819e23	+	1.77819e23i	0.185438	+	0.185438i
$463$	3.64839e23	−	3.64839e23i	0.373140	−	0.373140i	−0.495480	−	0.868620i	$-0.665008\pi$
$463$	3.64839e23	−	3.64839e23i	0.373140	−	0.373140i	0.868620	+	0.495480i	$0.165008\pi$
$464$			9.03961e23i			0.906750i
$465$	−1.26369e24	+	9.28193e23i	−1.24327	+	0.913192i
$466$	2.12344e24			2.04912
$467$	3.81305e23	+	3.81305e23i	0.360928	+	0.360928i	0.864154	−	0.503227i	$-0.167854\pi$
$467$	3.81305e23	+	3.81305e23i	0.360928	+	0.360928i	−0.503227	+	0.864154i	$0.667854\pi$
$468$	−2.63319e24	+	2.63319e24i	−2.44494	+	2.44494i
$469$			2.68641e22i			0.0244690i
$470$	−4.66265e23	+	3.04621e24i	−0.416631	+	2.72195i
$471$	−3.46465e23			−0.303718
$472$	−9.78082e23	−	9.78082e23i	−0.841196	−	0.841196i
$473$	2.82195e23	−	2.82195e23i	0.238122	−	0.238122i
$474$		−	4.57360e24i		−	3.78663i
$475$	−1.20073e23	+	3.83042e23i	−0.0975442	+	0.311174i
$476$	2.59701e22			0.0207019
$477$	−8.94763e23	−	8.94763e23i	−0.699911	−	0.699911i
$478$	−6.28517e23	+	6.28517e23i	−0.482465	+	0.482465i
$479$		−	3.41833e23i		−	0.257510i	−0.991676	−	0.128755i	$-0.958902\pi$
$479$		−	3.41833e23i		−	0.257510i	0.991676	−	0.128755i	$-0.0410981\pi$
$480$	−3.57345e23	−	5.46966e22i	−0.264190	−	0.0404379i
$481$	−1.55027e23			−0.112487
$482$	−1.41195e24	−	1.41195e24i	−1.00553	−	1.00553i
$483$	−3.25343e23	+	3.25343e23i	−0.227414	+	0.227414i
$484$		−	1.51654e24i		−	1.04051i
$485$	1.38462e24	+	1.88509e24i	0.932513	+	1.26957i
$486$	6.78425e23			0.448513
$487$	−1.56878e24	−	1.56878e24i	−1.01813	−	1.01813i	−0.999833	−	0.0182958i	$-0.994176\pi$
$487$	−1.56878e24	−	1.56878e24i	−1.01813	−	1.01813i	−0.0182958	−	0.999833i	$-0.505824\pi$
$488$	−7.98047e23	+	7.98047e23i	−0.508452	+	0.508452i
$489$			1.67064e24i			1.04497i
$490$	2.21937e24	−	1.63015e24i	1.36290	−	1.00107i
$491$	2.14063e24			1.29065			0.645324	−	0.763909i	$-0.276723\pi$
$491$	2.14063e24			1.29065			0.645324	+	0.763909i	$0.276723\pi$
$492$	5.52153e24	+	5.52153e24i	3.26869	+	3.26869i
$493$	1.05994e23	−	1.05994e23i	0.0616112	−	0.0616112i
$494$		−	8.38520e23i		−	0.478598i
$495$	3.82488e23	−	2.49888e24i	0.214373	−	1.40055i
$496$	−1.38470e24			−0.762116
$497$	−2.98928e23	−	2.98928e23i	−0.161569	−	0.161569i
$498$	2.03211e24	−	2.03211e24i	1.07866	−	1.07866i
$499$			7.01278e23i			0.365582i	0.983152	+	0.182791i	$0.0585132\pi$
$499$			7.01278e23i			0.365582i	−0.983152	+	0.182791i	$0.941487\pi$
$500$	−1.67994e24	+	3.42811e24i	−0.860127	+	1.75519i
$501$	−2.40070e24			−1.20725
$502$	2.98931e24	+	2.98931e24i	1.47651	+	1.47651i
$503$	4.92485e23	−	4.92485e23i	0.238936	−	0.238936i	−0.577473	−	0.816409i	$-0.695961\pi$
$503$	4.92485e23	−	4.92485e23i	0.238936	−	0.238936i	0.816409	+	0.577473i	$0.195961\pi$
$504$		−	9.08046e23i		−	0.432746i
$505$	−7.14827e23	−	1.09414e23i	−0.334641	−	0.0512213i
$506$	−3.68475e24			−1.69455
$507$	−7.43410e23	−	7.43410e23i	−0.335859	−	0.335859i
$508$	3.29105e24	−	3.29105e24i	1.46070	−	1.46070i
$509$			3.49695e23i			0.152486i	0.997089	+	0.0762428i	$0.0242924\pi$
$509$			3.49695e23i			0.152486i	−0.997089	+	0.0762428i	$0.975708\pi$
$510$	−3.46372e23	−	4.71569e23i	−0.148392	−	0.202029i
$511$	−1.94832e23			−0.0820111
$512$	−2.65493e24	−	2.65493e24i	−1.09805	−	1.09805i
$513$	−1.06595e24	+	1.06595e24i	−0.433191	+	0.433191i
$514$			6.75747e24i			2.69846i
$515$	2.29406e24	−	1.68501e24i	0.900201	−	0.661206i
$516$	−4.37477e24			−1.68697
$517$	2.04421e24	+	2.04421e24i	0.774659	+	0.774659i
$518$	5.47313e22	−	5.47313e22i	0.0203830	−	0.0203830i
$519$			2.62091e24i			0.959280i
$520$	5.89270e23	−	3.84984e24i	0.211975	−	1.38488i
$521$	1.20747e24			0.426911			0.213456	−	0.976953i	$-0.431528\pi$
$521$	1.20747e24			0.426911			0.213456	+	0.976953i	$0.431528\pi$
$522$	−7.58840e24	−	7.58840e24i	−2.63704	−	2.63704i
$523$	−3.92939e24	+	3.92939e24i	−1.34218	+	1.34218i	−0.448290	+	0.893888i	$0.647967\pi$
$523$	−3.92939e24	+	3.92939e24i	−1.34218	+	1.34218i	−0.893888	+	0.448290i	$0.852033\pi$
$524$		−	7.63055e23i		−	0.256197i
$525$	6.45025e23	+	2.02197e23i	0.212884	+	0.0667330i
$526$	5.44884e24			1.76780
$527$	1.62364e23	+	1.62364e23i	0.0517837	+	0.0517837i
$528$	2.34059e24	−	2.34059e24i	0.733871	−	0.733871i
$529$		−	3.49760e24i		−	1.07813i
$530$	2.67857e24	+	4.09991e23i	0.811745	+	0.124249i
$531$	5.04133e24			1.50208
$532$	1.95841e23	+	1.95841e23i	0.0573718	+	0.0573718i
$533$	2.82827e24	−	2.82827e24i	0.814659	−	0.814659i
$534$			8.70513e24i			2.46549i
$535$	−3.48733e24	−	4.74783e24i	−0.971200	−	1.32224i
$536$	1.15181e24			0.315427
$537$	5.93812e24	+	5.93812e24i	1.59912	+	1.59912i
$538$	−2.37497e24	+	2.37497e24i	−0.628954	+	0.628954i
$539$		−	2.58328e24i		−	0.672780i
$540$	−1.15545e25	+	8.48689e24i	−2.95942	+	2.17373i
$541$	−4.59430e24			−1.15729			−0.578647	−	0.815578i	$-0.696419\pi$
$541$	−4.59430e24			−1.15729			−0.578647	+	0.815578i	$0.696419\pi$
$542$	−6.21012e24	−	6.21012e24i	−1.53853	−	1.53853i
$543$	9.90284e21	−	9.90284e21i	0.00241302	−	0.00241302i
$544$			5.29406e22i			0.0126882i
$545$	8.99538e23	−	5.87689e24i	0.212056	−	1.38541i
$546$	−1.41203e24			−0.327424
$547$	−3.41070e24	−	3.41070e24i	−0.777961	−	0.777961i	0.201523	−	0.979484i	$-0.435411\pi$
$547$	−3.41070e24	−	3.41070e24i	−0.777961	−	0.777961i	−0.979484	+	0.201523i	$0.935411\pi$
$548$	4.30384e24	−	4.30384e24i	0.965676	−	0.965676i
$549$		−	4.11337e24i		−	0.907919i
$550$	2.50768e24	+	4.79771e24i	0.544513	+	1.04177i
$551$	1.59861e24			0.341490
$552$	1.39492e25	+	1.39492e25i	2.93156	+	2.93156i
$553$	5.47154e23	−	5.47154e23i	0.113132	−	0.113132i
$554$			9.77540e24i			1.98860i
$555$	−1.14037e24	−	1.74549e23i	−0.228249	−	0.0349366i
$556$	−4.24770e24			−0.836528
$557$	2.60790e24	+	2.60790e24i	0.505351	+	0.505351i	0.913096	−	0.407745i	$-0.133685\pi$
$557$	2.60790e24	+	2.60790e24i	0.505351	+	0.505351i	−0.407745	+	0.913096i	$0.633685\pi$
$558$	1.16240e25	−	1.16240e25i	2.21641	−	2.21641i
$559$			2.24087e24i			0.420446i
$560$	3.53396e23	+	4.81132e23i	0.0652484	+	0.0888326i
$561$	−5.48893e23			−0.0997291
$562$	1.00743e25	+	1.00743e25i	1.80130	+	1.80130i
$563$	−7.31957e24	+	7.31957e24i	−1.28798	+	1.28798i	−0.351971	+	0.936011i	$0.614489\pi$
$563$	−7.31957e24	+	7.31957e24i	−1.28798	+	1.28798i	−0.936011	+	0.351971i	$0.885511\pi$
$564$		−	3.16907e25i		−	5.48807i
$565$	3.73710e23	−	2.74494e23i	0.0636940	−	0.0467839i
$566$	−4.83532e24			−0.811106
$567$	6.65501e23	+	6.65501e23i	0.109876	+	0.109876i
$568$	−1.28167e25	+	1.28167e25i	−2.08277	+	2.08277i
$569$		−	3.09833e24i		−	0.495584i	−0.968813	−	0.247792i	$-0.920295\pi$
$569$		−	3.09833e24i		−	0.495584i	0.968813	−	0.247792i	$-0.0797049\pi$
$570$	9.44114e23	−	6.16812e24i	0.148645	−	0.971134i
$571$	1.26522e24			0.196083			0.0980415	−	0.995182i	$-0.468742\pi$
$571$	1.26522e24			0.196083			0.0980415	+	0.995182i	$0.468742\pi$
$572$	−5.28982e24	−	5.28982e24i	−0.807006	−	0.807006i
$573$	−8.28558e24	+	8.28558e24i	−1.24432	+	1.24432i
$574$			1.99701e24i			0.295239i
$575$	−8.77806e24	+	4.58814e24i	−1.27758	+	0.667769i
$576$	1.63109e25			2.33709
$577$	−1.27729e24	−	1.27729e24i	−0.180180	−	0.180180i	0.611254	−	0.791434i	$-0.290665\pi$
$577$	−1.27729e24	−	1.27729e24i	−0.180180	−	0.180180i	−0.791434	+	0.611254i	$0.790665\pi$
$578$	8.69098e24	−	8.69098e24i	1.20703	−	1.20703i
$579$		−	5.23452e24i		−	0.715764i
$580$	1.50281e25	+	2.30026e24i	2.02327	+	0.309688i
$581$	4.86215e23			0.0644530
$582$	−2.57093e25	−	2.57093e25i	−3.35570	−	3.35570i
$583$	1.79749e24	−	1.79749e24i	0.231021	−	0.231021i
$584$			8.35352e24i			1.05719i
$585$	8.40297e24	+	1.14402e25i	1.04720	+	1.42571i
$586$	−2.61228e25			−3.20584
$587$	1.46830e22	+	1.46830e22i	0.00177448	+	0.00177448i	0.707993	−	0.706219i	$-0.249601\pi$
$587$	1.46830e22	+	1.46830e22i	0.00177448	+	0.00177448i	−0.706219	+	0.707993i	$0.749601\pi$
$588$	−2.00239e25	+	2.00239e25i	−2.38315	+	2.38315i
$589$			2.44878e24i			0.287020i
$590$	−8.70087e24	+	6.39087e24i	−1.00437	+	0.737721i
$591$	4.51583e24			0.513393
$592$	−7.20417e23	−	7.20417e23i	−0.0806657	−	0.0806657i
$593$	1.24863e25	−	1.24863e25i	1.37702	−	1.37702i	0.527407	−	0.849613i	$-0.323164\pi$
$593$	1.24863e25	−	1.24863e25i	1.37702	−	1.37702i	0.849613	−	0.527407i	$-0.176836\pi$
$594$			2.03298e25i			2.20828i
$595$	1.49777e22	−	9.78529e22i	0.00160248	−	0.0104694i
$596$	2.94762e25			3.10638
$597$	4.26710e24	+	4.26710e24i	0.442960	+	0.442960i
$598$	1.46300e25	−	1.46300e25i	1.49601	−	1.49601i
$599$			1.93289e25i			1.94700i	0.228693	+	0.973499i	$0.426555\pi$
$599$			1.93289e25i			1.94700i	−0.228693	+	0.973499i	$0.573445\pi$
$600$	8.66929e24	−	2.76558e25i	0.860245	−	2.74426i
$601$	2.12695e24			0.207916			0.103958	−	0.994582i	$-0.466849\pi$
$601$	2.12695e24			0.207916			0.103958	+	0.994582i	$0.466849\pi$
$602$	−7.91127e23	−	7.91127e23i	−0.0761865	−	0.0761865i
$603$	−2.96839e24	+	2.96839e24i	−0.281621	+	0.281621i
$604$		−	1.88495e25i		−	1.76185i
$605$	−5.71419e24	−	8.74634e23i	−0.526206	−	0.0805430i
$606$	1.12412e25			1.01990
$607$	−2.97673e24	−	2.97673e24i	−0.266098	−	0.266098i	0.561428	−	0.827526i	$-0.310252\pi$
$607$	−2.97673e24	−	2.97673e24i	−0.266098	−	0.266098i	−0.827526	+	0.561428i	$0.810252\pi$
$608$	−3.99227e23	+	3.99227e23i	−0.0351631	+	0.0351631i
$609$		−	2.69199e24i		−	0.233624i
$610$	5.21451e24	+	7.09930e24i	0.445908	+	0.607082i
$611$	−1.62328e25			−1.36780
$612$	2.86960e24	+	2.86960e24i	0.238264	+	0.238264i
$613$	4.60147e24	−	4.60147e24i	0.376489	−	0.376489i	−0.493345	−	0.869834i	$-0.664226\pi$
$613$	4.60147e24	−	4.60147e24i	0.376489	−	0.376489i	0.869834	+	0.493345i	$0.164226\pi$
$614$		−	1.43683e24i		−	0.115848i
$615$	2.39891e25	−	1.76202e25i	1.90606	−	1.40002i
$616$	1.82418e24			0.142837
$617$	9.13299e24	+	9.13299e24i	0.704768	+	0.704768i	0.965430	−	0.260662i	$-0.0839408\pi$
$617$	9.13299e24	+	9.13299e24i	0.704768	+	0.704768i	−0.260662	+	0.965430i	$0.583941\pi$
$618$	−3.12869e25	+	3.12869e25i	−2.37939	+	2.37939i
$619$			2.29659e24i			0.172135i	0.996289	+	0.0860673i	$0.0274300\pi$
$619$			2.29659e24i			0.172135i	−0.996289	+	0.0860673i	$0.972570\pi$
$620$	−3.52358e24	+	2.30203e25i	−0.260291	+	1.70054i
$621$	−3.71961e25			−2.70815
$622$	−8.67426e24	−	8.67426e24i	−0.622470	−	0.622470i
$623$	−1.04142e24	+	1.04142e24i	−0.0736604	+	0.0736604i
$624$			1.85863e25i			1.29578i
$625$	1.19479e25	+	8.30694e24i	0.821055	+	0.570849i
$626$	2.83024e25			1.91715
$627$	−4.13921e24	−	4.13921e24i	−0.276382	−	0.276382i
$628$	−3.63876e24	+	3.63876e24i	−0.239506	+	0.239506i
$629$			1.68945e23i			0.0109620i
$630$	−7.00555e24	−	1.07229e24i	−0.448102	−	0.0685881i
$631$	−1.44627e25			−0.911979			−0.455990	−	0.889985i	$-0.650715\pi$
$631$	−1.44627e25			−0.911979			−0.455990	+	0.889985i	$0.650715\pi$
$632$	−2.34595e25	−	2.34595e25i	−1.45836	−	1.45836i
$633$	8.75995e24	−	8.75995e24i	0.536869	−	0.536869i
$634$		−	4.44415e25i		−	2.68526i
$635$	−1.05023e25	−	1.42984e25i	−0.625637	−	0.851775i
$636$	−2.78659e25			−1.63666
$637$	1.02567e25	+	1.02567e25i	0.593956	+	0.593956i
$638$	1.52444e25	−	1.52444e25i	0.870410	−	0.870410i
$639$		−	6.60611e25i		−	3.71910i
$640$	−2.59371e25	+	1.90510e25i	−1.43980	+	1.05754i
$641$	9.26904e24			0.507356			0.253678	−	0.967289i	$-0.418360\pi$
$641$	9.26904e24			0.507356			0.253678	+	0.967289i	$0.418360\pi$
$642$	6.47519e25	+	6.47519e25i	3.49492	+	3.49492i
$643$	2.64464e24	−	2.64464e24i	0.140756	−	0.140756i	−0.633218	−	0.773974i	$-0.718266\pi$
$643$	2.64464e24	−	2.64464e24i	0.140756	−	0.140756i	0.773974	+	0.633218i	$0.218266\pi$
$644$			6.83385e24i			0.358668i
$645$	−2.52306e24	+	1.64837e25i	−0.130584	+	0.853136i
$646$	−9.13805e23			−0.0466403
$647$	−3.44868e24	−	3.44868e24i	−0.173586	−	0.173586i	0.614967	−	0.788553i	$-0.289169\pi$
$647$	−3.44868e24	−	3.44868e24i	−0.173586	−	0.173586i	−0.788553	+	0.614967i	$0.789169\pi$
$648$	2.85337e25	−	2.85337e25i	1.41639	−	1.41639i
$649$			1.01276e25i			0.495795i
$650$	−2.90055e25	−	9.09240e24i	−1.40043	−	0.438994i
$651$	4.12363e24			0.196359
$652$	1.75459e25	+	1.75459e25i	0.824039	+	0.824039i
$653$	−5.78972e24	+	5.78972e24i	−0.268188	+	0.268188i	−0.828370	−	0.560182i	$-0.810731\pi$
$653$	−5.78972e24	+	5.78972e24i	−0.268188	+	0.268188i	0.560182	+	0.828370i	$0.310731\pi$
$654$			9.24184e25i			4.22239i
$655$	−2.87512e24	−	4.40077e23i	−0.129564	−	0.0198316i
$656$	2.62863e25			1.16841
$657$	−2.15283e25	−	2.15283e25i	−0.943890	−	0.943890i
$658$	5.73089e24	−	5.73089e24i	0.247850	−	0.247850i
$659$			3.06925e25i			1.30938i	0.755900	+	0.654688i	$0.227200\pi$
$659$			3.06925e25i			1.30938i	−0.755900	+	0.654688i	$0.772800\pi$
$660$	−3.29558e25	−	4.48677e25i	−1.38687	−	1.88816i
$661$	2.86757e25			1.19042			0.595211	−	0.803570i	$-0.297069\pi$
$661$	2.86757e25			1.19042			0.595211	+	0.803570i	$0.297069\pi$
$662$	−3.82513e25	−	3.82513e25i	−1.56648	−	1.56648i
$663$	2.17934e24	−	2.17934e24i	0.0880446	−	0.0880446i
$664$		−	2.08467e25i		−	0.830854i
$665$	8.50858e23	−	6.24964e23i	0.0334551	−	0.0245731i
$666$	1.20953e25			0.469188
$667$	2.78917e25	+	2.78917e25i	1.06744	+	1.06744i
$668$	−2.52134e25	+	2.52134e25i	−0.952015	+	0.952015i
$669$			7.98036e24i			0.297295i
$670$	1.36015e24	−	8.88619e24i	0.0499936	−	0.326620i
$671$	8.26338e24			0.299678
$672$	6.72280e23	+	6.72280e23i	0.0240562	+	0.0240562i
$673$	2.21113e25	−	2.21113e25i	0.780691	−	0.780691i	−0.199256	−	0.979947i	$-0.563853\pi$
$673$	2.21113e25	−	2.21113e25i	0.780691	−	0.780691i	0.979947	+	0.199256i	$0.0638525\pi$
$674$		−	4.39744e25i		−	1.53201i
$675$	2.53140e25	+	4.84310e25i	0.870216	+	1.66490i
$676$	−1.56154e25			−0.529702
$677$	−2.71432e25	−	2.71432e25i	−0.908580	−	0.908580i	0.0875781	−	0.996158i	$-0.472087\pi$
$677$	−2.71432e25	−	2.71432e25i	−0.908580	−	0.908580i	−0.996158	+	0.0875781i	$0.972087\pi$
$678$	−5.09674e24	+	5.09674e24i	−0.168355	+	0.168355i
$679$		−	6.15137e24i		−	0.200514i
$680$	−4.19549e24	−	6.42177e23i	−0.134959	−	0.0206573i
$681$	−1.09186e24			−0.0346611
$682$	2.33516e25	+	2.33516e25i	0.731572	+	0.731572i
$683$	−1.67180e25	+	1.67180e25i	−0.516888	+	0.516888i	−0.916628	−	0.399740i	$-0.869100\pi$
$683$	−1.67180e25	+	1.67180e25i	−0.516888	+	0.516888i	0.399740	+	0.916628i	$0.369100\pi$
$684$			4.32795e25i			1.32062i
$685$	−1.37343e25	−	1.86987e25i	−0.413612	−	0.563113i
$686$	−1.46036e25			−0.434054
$687$	−7.63241e24	−	7.63241e24i	−0.223898	−	0.223898i
$688$	−1.04134e25	+	1.04134e25i	−0.301508	+	0.301508i
$689$			1.42736e25i			0.407907i
$690$	1.24090e26	−	9.11456e25i	3.50023	−	2.57095i
$691$	−2.42360e24			−0.0674774			−0.0337387	−	0.999431i	$-0.510741\pi$
$691$	−2.42360e24			−0.0674774			−0.0337387	+	0.999431i	$0.510741\pi$
$692$	2.75261e25	+	2.75261e25i	0.756468	+	0.756468i
$693$	−4.70118e24	+	4.70118e24i	−0.127529	+	0.127529i
$694$		−	7.07377e25i		−	1.89415i
$695$	−2.44977e24	+	1.60049e25i	−0.0647534	+	0.423049i
$696$	−1.15420e26			−3.01161
$697$	−3.08220e24	−	3.08220e24i	−0.0793901	−	0.0793901i
$698$	1.54669e25	−	1.54669e25i	0.393282	−	0.393282i
$699$			8.32360e25i			2.08938i
$700$	8.89797e24	−	4.65082e24i	0.220500	−	0.115252i
$701$	−7.79904e24			−0.190800			−0.0954002	−	0.995439i	$-0.530413\pi$
$701$	−7.79904e24			−0.190800			−0.0954002	+	0.995439i	$0.530413\pi$
$702$	−8.07179e25	−	8.07179e25i	−1.94956	−	1.94956i
$703$	−1.27402e24	+	1.27402e24i	−0.0303794	+	0.0303794i
$704$			3.27670e25i			0.771405i
$705$	−1.19408e26	−	1.82770e25i	−2.77543	−	0.424817i
$706$	−1.40512e26			−3.22455
$707$	1.34482e24	+	1.34482e24i	0.0304711	+	0.0304711i
$708$	7.85019e25	−	7.85019e25i	1.75623	−	1.75623i
$709$			9.63065e23i			0.0212735i	0.999943	+	0.0106368i	$0.00338585\pi$
$709$			9.63065e23i			0.0212735i	−0.999943	+	0.0106368i	$0.996614\pi$
$710$	8.37454e25	+	1.14015e26i	1.82657	+	2.48678i
$711$	1.20917e26			2.60413
$712$	4.46515e25	+	4.46515e25i	0.949545	+	0.949545i
$713$	−4.27249e25	+	4.27249e25i	−0.897171	+	0.897171i
$714$			1.53881e24i			0.0319081i
$715$	−2.29824e25	+	1.68808e25i	−0.470588	+	0.345651i
$716$	1.24731e26			2.52206
$717$	−2.46371e25	−	2.46371e25i	−0.491945	−	0.491945i
$718$	−1.35763e25	+	1.35763e25i	−0.267708	+	0.267708i
$719$		−	8.14469e25i		−	1.58604i	−0.609194	−	0.793021i	$-0.708507\pi$
$719$		−	8.14469e25i		−	1.58604i	0.609194	−	0.793021i	$-0.291493\pi$
$720$	−1.41144e25	+	9.22126e25i	−0.271437	+	1.77336i
$721$	−7.48589e24			−0.142176
$722$	5.79082e25	+	5.79082e25i	1.08619	+	1.08619i
$723$	5.53466e25	−	5.53466e25i	1.02529	−	1.02529i
$724$		−	2.08010e23i		−	0.00380572i
$725$	1.73343e25	−	5.52980e25i	0.313232	−	0.999235i
$726$	8.98597e25			1.60375
$727$	−2.64975e25	−	2.64975e25i	−0.467085	−	0.467085i	0.433884	−	0.900969i	$-0.357143\pi$
$727$	−2.64975e25	−	2.64975e25i	−0.467085	−	0.467085i	−0.900969	+	0.433884i	$0.857143\pi$
$728$	−7.24276e24	+	7.24276e24i	−0.126102	+	0.126102i
$729$		−	4.43919e25i		−	0.763407i
$730$	6.44472e25	+	9.86452e24i	1.09471	+	0.167560i
$731$	2.44206e24			0.0409732
$732$	−6.40521e25	−	6.40521e25i	−1.06153	−	1.06153i
$733$	8.48127e24	−	8.48127e24i	0.138843	−	0.138843i	−0.634269	−	0.773112i	$-0.718699\pi$
$733$	8.48127e24	−	8.48127e24i	0.138843	−	0.138843i	0.773112	+	0.634269i	$0.218699\pi$
$734$		−	1.04435e26i		−	1.68882i
$735$	6.38997e25	+	8.69965e25i	1.02074	+	1.38968i
$736$	−1.39310e25			−0.219827
$737$	−5.96322e24	−	5.96322e24i	−0.0929551	−	0.0929551i
$738$	−2.20663e26	+	2.20663e26i	−3.39799	+	3.39799i
$739$			6.86829e25i			1.04484i	0.852689	+	0.522419i	$0.174970\pi$
$739$			6.86829e25i			1.04484i	−0.852689	+	0.522419i	$0.825030\pi$
$740$	−1.38100e25	+	1.01436e25i	−0.207543	+	0.152442i
$741$	3.28689e25			0.488001
$742$	−5.03923e24	−	5.03923e24i	−0.0739144	−	0.0739144i
$743$	−2.29148e25	+	2.29148e25i	−0.332060	+	0.332060i	−0.853369	−	0.521308i	$-0.825444\pi$
$743$	−2.29148e25	+	2.29148e25i	−0.332060	+	0.332060i	0.521308	+	0.853369i	$0.325444\pi$
$744$		−	1.76803e26i		−	2.53123i
$745$	1.69998e25	−	1.11064e26i	0.240457	−	1.57096i
$746$	−6.30476e25			−0.881088
$747$	5.37251e25	+	5.37251e25i	0.741808	+	0.741808i
$748$	−5.76476e24	+	5.76476e24i	−0.0786443	+	0.0786443i
$749$			1.54929e25i			0.208832i
$750$	−2.03126e26	−	9.95415e25i	−2.70529	−	1.32572i
$751$	4.53369e25			0.596612			0.298306	−	0.954470i	$-0.403578\pi$
$751$	4.53369e25			0.596612			0.298306	+	0.954470i	$0.403578\pi$
$752$	−7.54346e25	−	7.54346e25i	−0.980867	−	0.980867i
$753$	−1.17177e26	+	1.17177e26i	−1.50552	+	1.50552i
$754$			1.21053e26i			1.53686i
$755$	−7.10233e25	−	1.08711e25i	−0.891002	−	0.136380i
$756$	3.77042e25			0.467405
$757$	2.83630e25	+	2.83630e25i	0.347447	+	0.347447i	0.859158	−	0.511711i	$-0.170988\pi$
$757$	2.83630e25	+	2.83630e25i	0.347447	+	0.347447i	−0.511711	+	0.859158i	$0.670988\pi$
$758$	7.14103e25	−	7.14103e25i	0.864446	−	0.864446i
$759$		−	1.44438e26i		−	1.72784i
$760$	−2.67956e25	−	3.64810e25i	−0.316768	−	0.431265i
$761$	1.14310e26			1.33543			0.667715	−	0.744417i	$-0.267273\pi$
$761$	1.14310e26			1.33543			0.667715	+	0.744417i	$0.267273\pi$
$762$	1.95005e26	+	1.95005e26i	2.25139	+	2.25139i
$763$	−1.10563e25	+	1.10563e25i	−0.126150	+	0.126150i
$764$			1.74039e26i			1.96249i
$765$	1.24674e25	−	9.15742e24i	0.138939	−	0.102052i
$766$	7.88207e25			0.868123
$767$	−4.02107e25	−	4.02107e25i	−0.437707	−	0.437707i
$768$	2.23793e26	−	2.23793e26i	2.40766	−	2.40766i
$769$			1.51660e26i			1.61263i	0.591488	+	0.806314i	$0.298541\pi$
$769$			1.51660e26i			1.61263i	−0.591488	+	0.806314i	$0.701459\pi$
$770$	2.15414e24	−	1.40735e25i	0.0226390	−	0.147906i
$771$	−2.64884e26			−2.75148
$772$	−5.49757e25	−	5.49757e25i	−0.564437	−	0.564437i
$773$	8.28025e25	−	8.28025e25i	0.840288	−	0.840288i	−0.148608	−	0.988896i	$-0.547479\pi$
$773$	8.28025e25	−	8.28025e25i	0.840288	−	0.840288i	0.988896	+	0.148608i	$0.0474794\pi$
$774$		−	1.74834e26i		−	1.75370i
$775$	8.47064e25	+	2.65530e25i	0.839849	+	0.263268i
$776$	−2.63743e26			−2.58479
$777$	2.14540e24	+	2.14540e24i	0.0207835	+	0.0207835i
$778$	−1.71756e26	+	1.71756e26i	−1.64474	+	1.64474i
$779$		−	4.64859e25i		−	0.440032i
$780$	3.08992e26	+	4.72954e25i	2.89132	+	0.442556i
$781$	1.32710e26			1.22757
$782$	−1.59436e25	−	1.59436e25i	−0.145789	−	0.145789i
$783$	1.53886e26	−	1.53886e26i	1.39105	−	1.39105i
$784$			9.53272e25i			0.851868i
$785$	1.16119e25	+	1.58091e25i	0.102583	+	0.139663i
$786$	4.52134e25			0.394879
$787$	−1.19064e26	−	1.19064e26i	−1.02804	−	1.02804i	−0.999595	−	0.0284429i	$-0.990945\pi$
$787$	−1.19064e26	−	1.19064e26i	−1.02804	−	1.02804i	−0.0284429	−	0.999595i	$-0.509055\pi$
$788$	4.74276e25	−	4.74276e25i	0.404851	−	0.404851i
$789$			2.13587e26i			1.80253i
$790$	−2.08692e26	+	1.53286e26i	−1.74126	+	1.27897i
$791$	−1.21948e24			−0.0100597
$792$	2.01566e26	+	2.01566e26i	1.64395	+	1.64395i
$793$	−3.28091e25	+	3.28091e25i	−0.264567	+	0.264567i
$794$		−	4.93202e25i		−	0.393225i
$795$	−1.60711e25	+	1.04996e26i	−0.126690	+	0.827694i
$796$	8.96308e25			0.698618
$797$	−8.58745e25	−	8.58745e25i	−0.661819	−	0.661819i	0.293989	−	0.955809i	$-0.405017\pi$
$797$	−8.58745e25	−	8.58745e25i	−0.661819	−	0.661819i	−0.955809	+	0.293989i	$0.905017\pi$
$798$	−1.16042e25	+	1.16042e25i	−0.0884278	+	0.0884278i
$799$			1.76902e25i			0.133294i
$800$	9.48081e24	+	1.81388e25i	0.0706376	+	0.135144i
$801$	−2.30147e26			−1.69556
$802$	−1.03524e26	−	1.03524e26i	−0.754176	−	0.754176i
$803$	4.32483e25	−	4.32483e25i	0.311551	−	0.311551i
$804$			9.24456e25i			0.658540i
$805$	2.57493e25	+	3.94129e24i	0.181386	+	0.0277636i
$806$	−1.85431e26			−1.29172
$807$	−9.30959e25	−	9.30959e25i	−0.641311	−	0.641311i
$808$	5.76597e25	−	5.76597e25i	0.392798	−	0.392798i
$809$			8.56511e25i			0.577027i	0.957476	+	0.288514i	$0.0931610\pi$
$809$			8.56511e25i			0.577027i	−0.957476	+	0.288514i	$0.906839\pi$
$810$	−1.86442e26	−	2.53831e26i	−1.24216	−	1.69114i
$811$	1.16592e26			0.768210			0.384105	−	0.923289i	$-0.374510\pi$
$811$	1.16592e26			0.768210			0.384105	+	0.923289i	$0.374510\pi$
$812$	−2.82727e25	−	2.82727e25i	−0.184231	−	0.184231i
$813$	2.43429e26	−	2.43429e26i	1.56876	−	1.56876i
$814$			2.42982e25i			0.154866i
$815$	7.62307e25	−	5.59922e25i	0.480520	−	0.352947i
$816$	2.02550e25			0.126276
$817$	1.84156e25	+	1.84156e25i	0.113550	+	0.113550i
$818$	2.78669e26	−	2.78669e26i	1.69945	−	1.69945i
$819$		−	3.73314e25i		−	0.225174i
$820$	6.68892e25	−	4.37003e26i	0.399054	−	2.60711i
$821$	6.74408e25			0.397955			0.198978	−	0.980004i	$-0.436238\pi$
$821$	6.74408e25			0.397955			0.198978	+	0.980004i	$0.436238\pi$
$822$	2.55016e26	+	2.55016e26i	1.48841	+	1.48841i
$823$	−1.15147e26	+	1.15147e26i	−0.664746	+	0.664746i	−0.956495	−	0.291749i	$-0.905763\pi$
$823$	−1.15147e26	+	1.15147e26i	−0.664746	+	0.664746i	0.291749	+	0.956495i	$0.405763\pi$
$824$			3.20961e26i			1.83277i
$825$	−1.88064e26	+	9.82978e25i	−1.06223	+	0.555211i
$826$	2.83924e25			0.158628
$827$	1.86919e26	+	1.86919e26i	1.03301	+	1.03301i	0.999436	+	0.0335706i	$0.0106879\pi$
$827$	1.86919e26	+	1.86919e26i	1.03301	+	1.03301i	0.0335706	+	0.999436i	$0.489312\pi$
$828$	−7.55117e26	+	7.55117e26i	−4.12802	+	4.12802i
$829$		−	2.04538e26i		−	1.10607i	−0.833157	−	0.553036i	$-0.813469\pi$
$829$		−	2.04538e26i		−	1.10607i	0.833157	−	0.553036i	$-0.186531\pi$
$830$	−1.60832e26	−	2.46175e25i	−0.860337	−	0.131686i
$831$	−3.83183e26			−2.02767
$832$	−1.30099e26	−	1.30099e26i	−0.681026	−	0.681026i
$833$	1.11776e25	−	1.11776e25i	0.0578821	−	0.0578821i
$834$		−	2.51689e26i		−	1.28935i
$835$	8.04606e25	+	1.09543e26i	0.407761	+	0.555147i
$836$	−8.69444e25			−0.435898
$837$	2.35725e26	+	2.35725e26i	1.16917	+	1.16917i
$838$	3.69532e26	−	3.69532e26i	1.81324	−	1.81324i
$839$		−	1.70699e26i		−	0.828656i	−0.910128	−	0.414328i	$-0.864017\pi$
$839$		−	1.70699e26i		−	0.828656i	0.910128	−	0.414328i	$-0.135983\pi$
$840$	−6.14323e25	+	4.51226e25i	−0.295042	+	0.216711i
$841$	−2.03268e25			−0.0965841
$842$	2.96389e26	+	2.96389e26i	1.39333	+	1.39333i
$843$	−3.94897e26	+	3.94897e26i	−1.83669	+	1.83669i
$844$		−	1.84003e26i		−	0.846727i
$845$	−9.00585e24	+	5.88373e25i	−0.0410029	+	0.267881i
$846$	1.26649e27			5.70516
$847$	1.07502e25	+	1.07502e25i	0.0479143	+	0.0479143i
$848$	−6.63304e25	+	6.63304e25i	−0.292516	+	0.292516i
$849$		−	1.89538e26i		−	0.827042i
$850$	−9.90875e24	+	3.16097e25i	−0.0427808	+	0.136474i
$851$	−4.44569e25			−0.189921
$852$	−1.02868e27	−	1.02868e27i	−4.34835	−	4.34835i
$853$	−2.02406e26	+	2.02406e26i	−0.846607	+	0.846607i	−0.989708	−	0.143101i	$-0.954293\pi$
$853$	−2.02406e26	+	2.02406e26i	−0.846607	+	0.846607i	0.143101	+	0.989708i	$0.454293\pi$
$854$		−	2.31662e25i		−	0.0958812i
$855$	1.63073e26	+	2.49606e25i	0.667864	+	0.102226i
$856$	6.64268e26			2.69203
$857$	5.60488e25	+	5.60488e25i	0.224770	+	0.224770i	0.810504	−	0.585733i	$-0.199193\pi$
$857$	5.60488e25	+	5.60488e25i	0.224770	+	0.224770i	−0.585733	+	0.810504i	$0.699193\pi$
$858$	3.13439e26	−	3.13439e26i	1.24385	−	1.24385i
$859$			2.06187e26i			0.809698i	0.914384	+	0.404849i	$0.132676\pi$
$859$			2.06187e26i			0.809698i	−0.914384	+	0.404849i	$0.867324\pi$
$860$	1.46622e26	+	1.99619e26i	0.569789	+	0.775741i
$861$	−7.82803e25			−0.301040
$862$	−4.72442e25	−	4.72442e25i	−0.179797	−	0.179797i
$863$	−1.11113e26	+	1.11113e26i	−0.418472	+	0.418472i	−0.884677	−	0.466205i	$-0.845621\pi$
$863$	−1.11113e26	+	1.11113e26i	−0.418472	+	0.418472i	0.466205	+	0.884677i	$0.345621\pi$
$864$			7.68610e25i			0.286472i
$865$	1.19591e26	−	8.78409e25i	0.441117	−	0.324005i
$866$	−7.24708e26			−2.64546
$867$	3.40675e26	+	3.40675e26i	1.23075	+	1.23075i
$868$	4.33085e25	−	4.33085e25i	0.154845	−	0.154845i
$869$			2.42912e26i			0.859548i
$870$	−1.36298e26	+	8.90464e26i	−0.477326	+	3.11848i
$871$	4.73530e25			0.164129
$872$	4.74044e26	+	4.74044e26i	1.62619	+	1.62619i
$873$	6.79705e26	−	6.79705e26i	2.30777	−	2.30777i
$874$		−	2.40462e26i		−	0.808059i
$875$	−1.23921e25	−	3.62090e25i	−0.0412167	−	0.120433i
$876$	−6.70463e26			−2.20718
$877$	−9.62236e25	−	9.62236e25i	−0.313535	−	0.313535i	0.532743	−	0.846277i	$-0.321161\pi$
$877$	−9.62236e25	−	9.62236e25i	−0.313535	−	0.313535i	−0.846277	+	0.532743i	$0.821161\pi$
$878$	−4.60416e26	+	4.60416e26i	−1.48491	+	1.48491i
$879$		−	1.02398e27i		−	3.26883i
$880$	−1.85246e26	−	2.83545e25i	−0.585337	−	0.0895937i
$881$	2.48703e25			0.0777853			0.0388926	−	0.999243i	$-0.487617\pi$
$881$	2.48703e25			0.0777853			0.0388926	+	0.999243i	$0.487617\pi$
$882$	−8.00235e26	−	8.00235e26i	−2.47742	−	2.47742i
$883$	−9.50646e25	+	9.50646e25i	−0.291321	+	0.291321i	−0.837602	−	0.546281i	$-0.816043\pi$
$883$	−9.50646e25	+	9.50646e25i	−0.291321	+	0.291321i	0.546281	+	0.837602i	$0.316043\pi$
$884$		−	4.57771e25i		−	0.138860i
$885$	−2.50514e26	−	3.41063e26i	−0.752215	−	1.02411i
$886$	−6.46123e26			−1.92049
$887$	−3.62956e25	−	3.62956e25i	−0.106793	−	0.106793i	0.651691	−	0.758484i	$-0.274060\pi$
$887$	−3.62956e25	−	3.62956e25i	−0.106793	−	0.106793i	−0.758484	+	0.651691i	$0.774060\pi$
$888$	9.19849e25	−	9.19849e25i	0.267917	−	0.267917i
$889$			4.66581e25i			0.134528i
$890$	3.97213e26	−	2.91757e26i	1.13374	−	0.832742i
$891$	−2.95452e26			−0.834811
$892$	8.38139e25	+	8.38139e25i	0.234440	+	0.234440i
$893$	−1.33402e26	+	1.33402e26i	−0.369403	+	0.369403i
$894$			1.74656e27i			4.78790i
$895$	7.19359e25	−	4.69974e26i	0.195226	−	1.27546i
$896$	8.46369e25			0.227398
$897$	5.73478e26	+	5.73478e26i	1.52540	+	1.52540i
$898$	−1.25500e26	+	1.25500e26i	−0.330488	+	0.330488i
$899$		−	3.53519e26i		−	0.921670i
$900$	1.49710e27	+	4.69297e26i	3.86427	+	1.21134i
$901$	1.55552e25			0.0397513
$902$	−4.43291e26	−	4.43291e26i	−1.12158	−	1.12158i
$903$	3.10111e25	−	3.10111e25i	0.0776833	−	0.0776833i
$904$			5.22857e25i			0.129678i
$905$	−7.83762e23	−	1.19965e23i	−0.00192463	−	0.000294591i
$906$	1.11689e27			2.71555
$907$	−4.91588e26	−	4.91588e26i	−1.18341	−	1.18341i	−0.978855	−	0.204557i	$-0.934425\pi$
$907$	−4.91588e26	−	4.91588e26i	−1.18341	−	1.18341i	−0.204557	−	0.978855i	$-0.565575\pi$
$908$	−1.14673e25	+	1.14673e25i	−0.0273331	+	0.0273331i
$909$			2.97195e26i			0.701402i
$910$	4.73248e25	+	6.44305e25i	0.110590	+	0.150563i
$911$	6.05377e26			1.40075			0.700374	−	0.713776i	$-0.253016\pi$
$911$	6.05377e26			1.40075			0.700374	+	0.713776i	$0.253016\pi$
$912$	1.52744e26	+	1.52744e26i	0.349953	+	0.349953i
$913$	−1.07929e26	+	1.07929e26i	−0.244850	+	0.244850i
$914$		−	1.07107e27i		−	2.40605i
$915$	−2.78283e26	+	2.04402e26i	−0.619010	+	0.454669i
$916$	−1.60319e26			−0.353123
$917$	5.40902e24	+	5.40902e24i	0.0117976	+	0.0117976i
$918$	−8.79651e25	+	8.79651e25i	−0.189988	+	0.189988i
$919$			5.64170e26i			1.20662i	0.797507	+	0.603310i	$0.206152\pi$
$919$			5.64170e26i			1.20662i	−0.797507	+	0.603310i	$0.793848\pi$
$920$	1.68985e26	−	1.10402e27i	0.357896	−	2.33822i
$921$	5.63217e25			0.118124
$922$	5.70543e26	+	5.70543e26i	1.18498	+	1.18498i
$923$	−5.26917e26	+	5.26917e26i	−1.08374	+	1.08374i
$924$			1.46411e26i			0.298212i
$925$	3.02554e25	+	5.78848e25i	0.0610277	+	0.116759i
$926$	4.54084e26			0.907062
$927$	−8.27165e26	−	8.27165e26i	−1.63634	−	1.63634i
$928$	5.76346e25	−	5.76346e25i	0.112915	−	0.112915i
$929$		−	4.57944e26i		−	0.888527i	−0.895896	−	0.444263i	$-0.853465\pi$
$929$		−	4.57944e26i		−	0.888527i	0.895896	−	0.444263i	$-0.146535\pi$
$930$	−1.36403e27	−	2.08783e26i	−2.62106	−	0.401188i
$931$	1.68581e26			0.320821
$932$	8.74189e26	+	8.74189e26i	1.64764	+	1.64764i
$933$	3.40019e26	−	3.40019e26i	0.634701	−	0.634701i
$934$			4.74578e26i			0.877375i
$935$	1.83964e25	+	2.50458e25i	0.0336844	+	0.0458597i
$936$	−1.60060e27			−2.90269
$937$	3.46364e26	+	3.46364e26i	0.622123	+	0.622123i	0.946074	−	0.323951i	$-0.105011\pi$
$937$	3.46364e26	+	3.46364e26i	0.622123	+	0.622123i	−0.323951	+	0.946074i	$0.605011\pi$
$938$	−1.67177e25	+	1.67177e25i	−0.0297407	+	0.0297407i
$939$			1.10942e27i			1.95481i
$940$	−1.44604e27	+	1.06213e27i	−2.52365	+	1.85364i
$941$	−8.65957e26			−1.49689			−0.748445	−	0.663197i	$-0.769199\pi$
$941$	−8.65957e26			−1.49689			−0.748445	+	0.663197i	$0.769199\pi$
$942$	−2.15608e26	−	2.15608e26i	−0.369153	−	0.369153i
$943$	8.11061e26	−	8.11061e26i	1.37546	−	1.37546i
$944$		−	3.73723e26i		−	0.627771i
$945$	2.17452e25	−	1.42066e26i	0.0361806	−	0.236376i
$946$	3.51224e26			0.578848
$947$	−3.88078e26	−	3.88078e26i	−0.633532	−	0.633532i	0.315420	−	0.948952i	$-0.397855\pi$
$947$	−3.88078e26	−	3.88078e26i	−0.633532	−	0.633532i	−0.948952	+	0.315420i	$0.897855\pi$
$948$	1.88289e27	−	1.88289e27i	3.04473	−	3.04473i
$949$			3.43428e26i			0.550098i
$950$	−3.13092e26	+	1.63648e26i	−0.496775	+	0.259655i
$951$	1.74205e27			2.73802
$952$	7.89305e24	+	7.89305e24i	0.0122889	+	0.0122889i
$953$	−6.18013e26	+	6.18013e26i	−0.953150	+	0.953150i	−0.998951	−	0.0458004i	$-0.985416\pi$
$953$	−6.18013e26	+	6.18013e26i	−0.953150	+	0.953150i	0.0458004	+	0.998951i	$0.485416\pi$
$954$		−	1.11364e27i		−	1.70141i
$955$	6.55764e26	+	1.00374e26i	0.992470	+	0.151911i
$956$	−5.17503e26			−0.775875
$957$	5.97560e26	+	5.97560e26i	0.887512	+	0.887512i
$958$	2.12725e26	−	2.12725e26i	0.312990	−	0.312990i
$959$			6.10168e25i			0.0889368i
$960$	−8.10520e26	−	1.10348e27i	−1.17037	−	1.59340i
$961$	−1.57528e26			−0.225344
$962$	−9.64742e25	−	9.64742e25i	−0.136721	−	0.136721i
$963$	−1.71192e27	+	1.71192e27i	−2.40351	+	2.40351i
$964$		−	1.16256e27i		−	1.61704i
$965$	−2.38850e26	+	1.75437e26i	−0.329139	+	0.241756i
$966$	−4.04927e26			−0.552819
$967$	3.76289e26	+	3.76289e26i	0.508959	+	0.508959i	0.914207	−	0.405248i	$-0.132815\pi$
$967$	3.76289e26	+	3.76289e26i	0.508959	+	0.508959i	−0.405248	+	0.914207i	$0.632815\pi$
$968$	4.60920e26	−	4.60920e26i	0.617657	−	0.617657i
$969$		−	3.58200e25i		−	0.0475566i
$970$	−3.11449e26	+	2.03477e27i	−0.409677	+	2.67651i
$971$	1.00379e27			1.30818			0.654091	−	0.756416i	$-0.273051\pi$
$971$	1.00379e27			1.30818			0.654091	+	0.756416i	$0.273051\pi$
$972$	2.79298e26	+	2.79298e26i	0.360638	+	0.360638i
$973$	3.01104e25	−	3.01104e25i	0.0385213	−	0.0385213i
$974$		−	1.95253e27i		−	2.47496i
$975$	3.56410e26	−	1.13698e27i	0.447619	−	1.42794i
$976$	−3.04932e26			−0.379450
$977$	4.67844e25	+	4.67844e25i	0.0576833	+	0.0576833i	0.735360	−	0.677677i	$-0.237013\pi$
$977$	4.67844e25	+	4.67844e25i	0.0576833	+	0.0576833i	−0.677677	+	0.735360i	$0.737013\pi$
$978$	−1.03965e27	+	1.03965e27i	−1.27010	+	1.27010i
$979$		−	4.62344e26i		−	0.559656i
$980$	1.58479e27	+	2.42574e26i	1.90080	+	0.290944i
$981$	−2.44337e27			−2.90381
$982$	1.33213e27	+	1.33213e27i	1.56871	+	1.56871i
$983$	5.61130e25	−	5.61130e25i	0.0654759	−	0.0654759i	−0.673611	−	0.739086i	$-0.735257\pi$
$983$	5.61130e25	−	5.61130e25i	0.0654759	−	0.0654759i	0.739086	+	0.673611i	$0.235257\pi$
$984$			3.35630e27i			3.88066i
$985$	−1.51350e26	−	2.06056e26i	−0.173403	−	0.236080i
$986$	1.31922e26			0.149770
$987$	2.24644e26	+	2.24644e26i	0.252720	+	0.252720i
$988$	3.45206e26	−	3.45206e26i	0.384828	−	0.384828i
$989$			6.42612e26i			0.709876i
$990$	1.79310e27	−	1.31705e27i	1.96285	−	1.44173i
$991$	−1.08001e27			−1.17156			−0.585782	−	0.810469i	$-0.699213\pi$
$991$	−1.08001e27			−1.17156			−0.585782	+	0.810469i	$0.699213\pi$
$992$	8.82856e25	+	8.82856e25i	0.0949041	+	0.0949041i
$993$	1.49940e27	−	1.49940e27i	1.59725	−	1.59725i
$994$		−	3.72051e26i		−	0.392757i
$995$	5.16928e25	−	3.37721e26i	0.0540782	−	0.353305i
$996$	1.67318e27			1.73464
$997$	−1.19573e27	−	1.19573e27i	−1.22851	−	1.22851i	−0.964529	−	0.263976i	$-0.914966\pi$
$997$	−1.19573e27	−	1.19573e27i	−1.22851	−	1.22851i	−0.263976	−	0.964529i	$-0.585034\pi$
$998$	−4.36411e26	+	4.36411e26i	−0.444345	+	0.444345i
$999$			2.45281e26i			0.247499i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.19.c.a.2.8	✓	16
3.2	odd	2		45.19.g.a.37.1		16
5.2	odd	4		25.19.c.b.18.1		16
5.3	odd	4	inner	5.19.c.a.3.8	yes	16
5.4	even	2		25.19.c.b.7.1		16
15.8	even	4		45.19.g.a.28.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.19.c.a.2.8	✓	16	1.1	even	1	trivial
5.19.c.a.3.8	yes	16	5.3	odd	4	inner
25.19.c.b.7.1		16	5.4	even	2
25.19.c.b.18.1		16	5.2	odd	4
45.19.g.a.28.1		16	15.8	even	4
45.19.g.a.37.1		16	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:	\( N \)	\(=\)	\( 5 \)
Weight:	\( k \)	\(=\)	\( 19 \)
Character orbit:	\([\chi]\)	\(=\)	5.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(622.308 + 622.308i) q^{2} +(-24393.6 + 24393.6i) q^{3} +512390. i q^{4} +(1.93064e6 + 295511. i) q^{5} -3.03607e7 q^{6} +(-3.63215e6 - 3.63215e6i) q^{7} +(-1.55730e8 + 1.55730e8i) q^{8} -8.02680e8i q^{9} +O(q^{10})\)	\(q+(622.308 + 622.308i) q^{2} +(-24393.6 + 24393.6i) q^{3} +512390. i q^{4} +(1.93064e6 + 295511. i) q^{5} -3.03607e7 q^{6} +(-3.63215e6 - 3.63215e6i) q^{7} +(-1.55730e8 + 1.55730e8i) q^{8} -8.02680e8i q^{9} +(1.01755e9 + 1.38535e9i) q^{10} +1.61251e9 q^{11} +(-1.24991e10 - 1.24991e10i) q^{12} +(-6.40234e9 + 6.40234e9i) q^{13} -4.52063e9i q^{14} +(-5.43039e10 + 3.98868e10i) q^{15} -5.95041e10 q^{16} +(6.97717e9 + 6.97717e9i) q^{17} +(4.99514e11 - 4.99514e11i) q^{18} +1.05230e11i q^{19} +(-1.51417e11 + 9.89241e11i) q^{20} +1.77203e11 q^{21} +(1.00348e12 + 1.00348e12i) q^{22} +(-1.83599e12 + 1.83599e12i) q^{23} -7.59765e12i q^{24} +(3.64004e12 + 1.14105e12i) q^{25} -7.96845e12 q^{26} +(1.01297e13 + 1.01297e13i) q^{27} +(1.86108e12 - 1.86108e12i) q^{28} -1.51916e13i q^{29} +(-5.86156e13 - 8.97192e12i) q^{30} +2.32707e13 q^{31} +(3.79385e12 + 3.79385e12i) q^{32} +(-3.93349e13 + 3.93349e13i) q^{33} +8.68389e12i q^{34} +(-5.93903e12 - 8.08570e12i) q^{35} +4.11285e14 q^{36} +(1.21070e13 + 1.21070e13i) q^{37} +(-6.54854e13 + 6.54854e13i) q^{38} -3.12353e14i q^{39} +(-3.46679e14 + 2.54639e14i) q^{40} -4.41756e14 q^{41} +(1.10275e14 + 1.10275e14i) q^{42} +(1.75004e14 - 1.75004e14i) q^{43} +8.26233e14i q^{44} +(2.37200e14 - 1.54969e15i) q^{45} -2.28511e15 q^{46} +(1.26772e15 + 1.26772e15i) q^{47} +(1.45152e15 - 1.45152e15i) q^{48} -1.60203e15i q^{49} +(1.55514e15 + 2.97531e15i) q^{50} -3.40397e14 q^{51} +(-3.28049e15 - 3.28049e15i) q^{52} +(1.11472e15 - 1.11472e15i) q^{53} +1.26076e16i q^{54} +(3.11317e15 + 4.76513e14i) q^{55} +1.13127e15 q^{56} +(-2.56694e15 - 2.56694e15i) q^{57} +(9.45384e15 - 9.45384e15i) q^{58} +6.28063e15i q^{59} +(-2.04376e16 - 2.78248e16i) q^{60} +5.12455e15 q^{61} +(1.44815e16 + 1.44815e16i) q^{62} +(-2.91545e15 + 2.91545e15i) q^{63} +2.03205e16i q^{64} +(-1.42526e16 + 1.04686e16i) q^{65} -4.89569e16 q^{66} +(-3.69810e15 - 3.69810e15i) q^{67} +(-3.57503e15 + 3.57503e15i) q^{68} -8.95732e16i q^{69} +(1.33589e15 - 8.72770e15i) q^{70} +8.23007e16 q^{71} +(1.25001e17 + 1.25001e17i) q^{72} +(2.68205e16 - 2.68205e16i) q^{73} +1.50686e16i q^{74} +(-1.16628e17 + 6.09596e16i) q^{75} -5.39188e16 q^{76} +(-5.85686e15 - 5.85686e15i) q^{77} +(1.94380e17 - 1.94380e17i) q^{78} +1.50642e17i q^{79} +(-1.14881e17 - 1.75841e16i) q^{80} -1.83225e17 q^{81} +(-2.74908e17 - 2.74908e17i) q^{82} +(-6.69322e16 + 6.69322e16i) q^{83} +9.07968e16i q^{84} +(1.14086e16 + 1.55322e16i) q^{85} +2.17813e17 q^{86} +(3.70578e17 + 3.70578e17i) q^{87} +(-2.51116e17 + 2.51116e17i) q^{88} -2.86724e17i q^{89} +(1.11199e18 - 8.16770e17i) q^{90} +4.65084e16 q^{91} +(-9.40745e17 - 9.40745e17i) q^{92} +(-5.67658e17 + 5.67658e17i) q^{93} +1.57783e18i q^{94} +(-3.10966e16 + 2.03161e17i) q^{95} -1.85092e17 q^{96} +(8.46795e17 + 8.46795e17i) q^{97} +(9.96955e17 - 9.96955e17i) q^{98} -1.29433e18i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 510 q^{2} - 20130 q^{3} + 3145170 q^{5} - 30766728 q^{6} + 78767350 q^{7} - 217339260 q^{8}+O(q^{10}) \) 16 * q + 510 * q^2 - 20130 * q^3 + 3145170 * q^5 - 30766728 * q^6 + 78767350 * q^7 - 217339260 * q^8	\( 16 q + 510 q^{2} - 20130 q^{3} + 3145170 q^{5} - 30766728 q^{6} + 78767350 q^{7} - 217339260 q^{8} - 635093930 q^{10} + 4719921012 q^{11} - 22715951880 q^{12} + 8689116940 q^{13} - 59706310410 q^{15} + 10530345976 q^{16} - 221748184620 q^{17} + 654304109970 q^{18} - 878373508140 q^{20} + 1431507507492 q^{21} + 2209421844320 q^{22} - 3507966822690 q^{23} + 10464353188900 q^{25} - 23324455191468 q^{26} + 11679867134280 q^{27} + 8077754165240 q^{28} - 80865025845360 q^{30} + 53033402941772 q^{31} + 20394786468360 q^{32} - 4953707733660 q^{33} - 82375887392730 q^{35} + 263454471040956 q^{36} - 29247362581160 q^{37} + 391580910829560 q^{38} - 918259855204500 q^{40} - 717170436410748 q^{41} + 11\!\cdots\!80 q^{42}+ \cdots - 43\!\cdots\!90 q^{98}+O(q^{100}) \) 16 * q + 510 * q^2 - 20130 * q^3 + 3145170 * q^5 - 30766728 * q^6 + 78767350 * q^7 - 217339260 * q^8 - 635093930 * q^10 + 4719921012 * q^11 - 22715951880 * q^12 + 8689116940 * q^13 - 59706310410 * q^15 + 10530345976 * q^16 - 221748184620 * q^17 + 654304109970 * q^18 - 878373508140 * q^20 + 1431507507492 * q^21 + 2209421844320 * q^22 - 3507966822690 * q^23 + 10464353188900 * q^25 - 23324455191468 * q^26 + 11679867134280 * q^27 + 8077754165240 * q^28 - 80865025845360 * q^30 + 53033402941772 * q^31 + 20394786468360 * q^32 - 4953707733660 * q^33 - 82375887392730 * q^35 + 263454471040956 * q^36 - 29247362581160 * q^37 + 391580910829560 * q^38 - 918259855204500 * q^40 - 717170436410748 * q^41 + 1119760897992480 * q^42 + 1295649718427950 * q^43 - 2413910465914410 * q^45 - 6165422784262408 * q^46 + 5324712362382270 * q^47 + 7675815427929360 * q^48 - 10266398091964350 * q^50 - 5996743906200468 * q^51 + 5457051468349900 * q^52 + 25019175284457720 * q^53 - 28447209909214060 * q^55 - 22879869030140400 * q^56 + 26327201869272960 * q^57 + 72036625362175440 * q^58 - 129993967558538280 * q^60 - 55112667981951388 * q^61 + 98952816959518920 * q^62 + 129200567352114030 * q^63 - 145786436727900960 * q^65 - 217789774433419296 * q^66 + 132604737823930030 * q^67 + 291394918710173220 * q^68 - 344767752141139080 * q^70 - 148288220084109108 * q^71 + 428373837658219140 * q^72 + 357896091854250160 * q^73 - 656924515001553450 * q^75 - 254554257141486000 * q^76 + 201286979542193700 * q^77 + 866949362074211400 * q^78 - 608571216720410880 * q^80 - 330578957555881164 * q^81 - 167911799138733280 * q^82 + 314012877447835830 * q^83 - 37755360901186580 * q^85 - 149686440788368488 * q^86 + 359090097519437040 * q^87 - 966828856938988320 * q^88 + 2368537241357586390 * q^90 + 498102030062089052 * q^91 - 1299658879961370120 * q^92 - 3025937916654554460 * q^93 + 2986575636848949000 * q^95 + 3531977749160666592 * q^96 - 1689002222572272080 * q^97 - 4330619740553781090 * q^98

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