LMFDB - Embedded newform 336.2.bo.a.5.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(5,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 6, 10]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("336.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.bo (of order $12$, degree $4$, 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:	$2.68297350792$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$60$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			5.1
Character	$\chi$	$=$	336.5
Dual form			336.2.bo.a.269.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41011 - 0.107640i) q^{2} +(-1.45943 + 0.932779i) q^{3} +(1.97683 + 0.303568i) q^{4} +(4.12446 - 1.10515i) q^{5} +(2.15836 - 1.15823i) q^{6} +(2.48663 + 0.903685i) q^{7} +(-2.75487 - 0.640850i) q^{8} +(1.25985 - 2.72264i) q^{9} +O(q^{10})$	\(q+(-1.41011 - 0.107640i) q^{2} +(-1.45943 + 0.932779i) q^{3} +(1.97683 + 0.303568i) q^{4} +(4.12446 - 1.10515i) q^{5} +(2.15836 - 1.15823i) q^{6} +(2.48663 + 0.903685i) q^{7} +(-2.75487 - 0.640850i) q^{8} +(1.25985 - 2.72264i) q^{9} +(-5.93491 + 1.11442i) q^{10} +(-0.900067 - 0.241172i) q^{11} +(-3.16819 + 1.40091i) q^{12} +(-3.15920 - 3.15920i) q^{13} +(-3.40916 - 1.54196i) q^{14} +(-4.98849 + 5.46009i) q^{15} +(3.81569 + 1.20020i) q^{16} +(-0.617276 - 1.06915i) q^{17} +(-2.06959 + 3.70362i) q^{18} +(5.03645 - 1.34951i) q^{19} +(8.48883 - 0.932628i) q^{20} +(-4.47200 + 1.00062i) q^{21} +(1.24323 + 0.436963i) q^{22} +(-0.751039 + 1.30084i) q^{23} +(4.61830 - 1.63441i) q^{24} +(11.4597 - 6.61626i) q^{25} +(4.11477 + 4.79488i) q^{26} +(0.700977 + 5.14865i) q^{27} +(4.64132 + 2.54129i) q^{28} +(0.0310193 + 0.0310193i) q^{29} +(7.62204 - 7.16238i) q^{30} +(-0.910147 + 0.525473i) q^{31} +(-5.25136 - 2.10314i) q^{32} +(1.53854 - 0.487591i) q^{33} +(0.755344 + 1.57407i) q^{34} +(11.2547 + 0.979120i) q^{35} +(3.31700 - 4.99975i) q^{36} +(0.677396 - 0.181508i) q^{37} +(-7.24722 + 1.36084i) q^{38} +(7.55746 + 1.66378i) q^{39} +(-12.0706 + 0.401374i) q^{40} +8.51301i q^{41} +(6.41372 - 0.929622i) q^{42} +(-3.09050 - 3.09050i) q^{43} +(-1.70606 - 0.749987i) q^{44} +(2.18726 - 12.6218i) q^{45} +(1.19907 - 1.75348i) q^{46} +(-3.11429 + 5.39411i) q^{47} +(-6.68824 + 1.80759i) q^{48} +(5.36671 + 4.49427i) q^{49} +(-16.8716 + 8.09615i) q^{50} +(1.89815 + 0.984567i) q^{51} +(-5.28617 - 7.20423i) q^{52} +(5.03575 + 1.34932i) q^{53} +(-0.434255 - 7.33563i) q^{54} -3.97882 q^{55} +(-6.27123 - 4.08310i) q^{56} +(-6.09153 + 6.66741i) q^{57} +(-0.0404017 - 0.0470795i) q^{58} +(2.80729 - 10.4770i) q^{59} +(-11.5189 + 9.27931i) q^{60} +(0.360681 - 0.0966443i) q^{61} +(1.33997 - 0.643008i) q^{62} +(5.59319 - 5.63172i) q^{63} +(7.17862 + 3.53092i) q^{64} +(-16.5214 - 9.53863i) q^{65} +(-2.22200 + 0.521949i) q^{66} +(-10.3271 - 2.76713i) q^{67} +(-0.895687 - 2.30092i) q^{68} +(-0.117309 - 2.59903i) q^{69} +(-15.7650 - 2.59212i) q^{70} +4.38335 q^{71} +(-5.21552 + 6.69316i) q^{72} +(5.81636 + 10.0742i) q^{73} +(-0.974740 + 0.183031i) q^{74} +(-10.5531 + 20.3453i) q^{75} +(10.3659 - 1.13885i) q^{76} +(-2.02019 - 1.41308i) q^{77} +(-10.4778 - 3.15960i) q^{78} +(-0.738936 + 1.27988i) q^{79} +(17.0641 + 0.733293i) q^{80} +(-5.82558 - 6.86022i) q^{81} +(0.916339 - 12.0043i) q^{82} +(-8.71723 + 8.71723i) q^{83} +(-9.14412 + 0.620499i) q^{84} +(-3.72750 - 3.72750i) q^{85} +(4.02529 + 4.69061i) q^{86} +(-0.0742045 - 0.0163362i) q^{87} +(2.32501 + 1.24121i) q^{88} +(7.08244 + 4.08905i) q^{89} +(-4.44289 + 17.5626i) q^{90} +(-5.00086 - 10.7107i) q^{91} +(-1.87957 + 2.34354i) q^{92} +(0.838140 - 1.61586i) q^{93} +(4.97212 - 7.27108i) q^{94} +(19.2812 - 11.1320i) q^{95} +(9.62574 - 1.82899i) q^{96} +9.28533i q^{97} +(-7.08389 - 6.91509i) q^{98} +(-1.79057 + 2.14672i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 6 q^{3} - 4 q^{4}+O(q^{10}) $ 240 * q - 6 * q^3 - 4 * q^4	$ 240 q - 6 q^{3} - 4 q^{4} - 12 q^{10} - 6 q^{12} - 16 q^{15} - 20 q^{16} - 4 q^{18} - 12 q^{19} + 2 q^{21} - 40 q^{22} - 6 q^{24} - 12 q^{28} + 22 q^{30} - 24 q^{31} - 12 q^{33} - 64 q^{36} - 4 q^{37} + 48 q^{40} - 18 q^{42} - 16 q^{43} - 6 q^{45} + 12 q^{46} - 16 q^{49} - 10 q^{51} - 48 q^{52} - 90 q^{54} - 4 q^{58} - 18 q^{60} - 12 q^{61} - 36 q^{63} + 32 q^{64} - 66 q^{66} - 36 q^{67} - 76 q^{70} - 46 q^{72} + 24 q^{75} - 76 q^{78} - 8 q^{79} - 4 q^{81} + 72 q^{82} - 24 q^{84} + 24 q^{85} + 12 q^{88} - 88 q^{91} - 14 q^{93} + 24 q^{94} + 96 q^{96} + 28 q^{99}+O(q^{100}) $ 240 * q - 6 * q^3 - 4 * q^4 - 12 * q^10 - 6 * q^12 - 16 * q^15 - 20 * q^16 - 4 * q^18 - 12 * q^19 + 2 * q^21 - 40 * q^22 - 6 * q^24 - 12 * q^28 + 22 * q^30 - 24 * q^31 - 12 * q^33 - 64 * q^36 - 4 * q^37 + 48 * q^40 - 18 * q^42 - 16 * q^43 - 6 * q^45 + 12 * q^46 - 16 * q^49 - 10 * q^51 - 48 * q^52 - 90 * q^54 - 4 * q^58 - 18 * q^60 - 12 * q^61 - 36 * q^63 + 32 * q^64 - 66 * q^66 - 36 * q^67 - 76 * q^70 - 46 * q^72 + 24 * q^75 - 76 * q^78 - 8 * q^79 - 4 * q^81 + 72 * q^82 - 24 * q^84 + 24 * q^85 + 12 * q^88 - 88 * q^91 - 14 * q^93 + 24 * q^94 + 96 * q^96 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−1.41011	−	0.107640i	−0.997099	−	0.0761128i
$2$	−1.41011	−	0.107640i	−0.997099	−	0.0761128i
$3$	−1.45943	+	0.932779i	−0.842600	+	0.538540i
$3$	−1.45943	+	0.932779i	−0.842600	+	0.538540i
$4$	1.97683	+	0.303568i	0.988414	+	0.151784i
$5$	4.12446	−	1.10515i	1.84452	−	0.494236i	0.845317	−	0.534266i	$-0.179412\pi$
$5$	4.12446	−	1.10515i	1.84452	−	0.494236i	0.999199	+	0.0400293i	$0.0127451\pi$
$6$	2.15836	−	1.15823i	0.881145	−	0.472846i
$7$	2.48663	+	0.903685i	0.939860	+	0.341561i
$7$	2.48663	+	0.903685i	0.939860	+	0.341561i
$8$	−2.75487	−	0.640850i	−0.973994	−	0.226575i
$9$	1.25985	−	2.72264i	0.419948	−	0.907548i
$10$	−5.93491	+	1.11442i	−1.87678	+	0.352411i
$11$	−0.900067	−	0.241172i	−0.271380	−	0.0727161i	0.120562	−	0.992706i	$-0.461530\pi$
$11$	−0.900067	−	0.241172i	−0.271380	−	0.0727161i	−0.391943	+	0.919990i	$0.628197\pi$
$12$	−3.16819	+	1.40091i	−0.914579	+	0.404408i
$13$	−3.15920	−	3.15920i	−0.876205	−	0.876205i	0.116934	−	0.993140i	$-0.462693\pi$
$13$	−3.15920	−	3.15920i	−0.876205	−	0.876205i	−0.993140	+	0.116934i	$0.962693\pi$
$14$	−3.40916	−	1.54196i	−0.911136	−	0.412105i
$15$	−4.98849	+	5.46009i	−1.28802	+	1.40979i
$16$	3.81569	+	1.20020i	0.953923	+	0.300051i
$17$	−0.617276	−	1.06915i	−0.149711	−	0.259308i	0.781409	−	0.624019i	$-0.214501\pi$
$17$	−0.617276	−	1.06915i	−0.149711	−	0.259308i	−0.931121	+	0.364711i	$0.881168\pi$
$18$	−2.06959	+	3.70362i	−0.487806	+	0.872952i
$19$	5.03645	−	1.34951i	1.15544	−	0.309600i	0.370297	−	0.928913i	$-0.379256\pi$
$19$	5.03645	−	1.34951i	1.15544	−	0.309600i	0.785144	+	0.619314i	$0.212589\pi$
$20$	8.48883	−	0.932628i	1.89816	−	0.208542i
$21$	−4.47200	+	1.00062i	−0.975870	+	0.218353i
$22$	1.24323	+	0.436963i	0.265059	+	0.0931607i
$23$	−0.751039	+	1.30084i	−0.156602	+	0.271243i	−0.933641	−	0.358209i	$-0.883387\pi$
$23$	−0.751039	+	1.30084i	−0.156602	+	0.271243i	0.777039	+	0.629453i	$0.216721\pi$
$24$	4.61830	−	1.63441i	0.942706	−	0.333623i
$25$	11.4597	−	6.61626i	2.29194	−	1.32325i
$26$	4.11477	+	4.79488i	0.806973	+	0.940354i
$27$	0.700977	+	5.14865i	0.134903	+	0.990859i
$28$	4.64132	+	2.54129i	0.877127	+	0.480259i
$29$	0.0310193	+	0.0310193i	0.00576014	+	0.00576014i	0.709981	−	0.704221i	$-0.248704\pi$
$29$	0.0310193	+	0.0310193i	0.00576014	+	0.00576014i	−0.704221	+	0.709981i	$0.748704\pi$
$30$	7.62204	−	7.16238i	1.39159	−	1.30766i
$31$	−0.910147	+	0.525473i	−0.163467	+	0.0943778i	−0.579502	−	0.814971i	$-0.696753\pi$
$31$	−0.910147	+	0.525473i	−0.163467	+	0.0943778i	0.416035	+	0.909349i	$0.363419\pi$
$32$	−5.25136	−	2.10314i	−0.928318	−	0.371786i
$33$	1.53854	−	0.487591i	0.267826	−	0.0848787i
$34$	0.755344	+	1.57407i	0.129540	+	0.269950i
$35$	11.2547	+	0.979120i	1.90240	+	0.165501i
$36$	3.31700	−	4.99975i	0.552834	−	0.833291i
$37$	0.677396	−	0.181508i	0.111363	−	0.0298397i	−0.202707	−	0.979239i	$-0.564974\pi$
$37$	0.677396	−	0.181508i	0.111363	−	0.0298397i	0.314070	+	0.949400i	$0.398307\pi$
$38$	−7.24722	+	1.36084i	−1.17565	+	0.220758i
$39$	7.55746	+	1.66378i	1.21016	+	0.266418i
$40$	−12.0706	+	0.401374i	−1.90853	+	0.0634628i
$41$			8.51301i			1.32951i	0.747062	+	0.664755i	$0.231464\pi$
$41$			8.51301i			1.32951i	−0.747062	+	0.664755i	$0.768536\pi$
$42$	6.41372	−	0.929622i	0.989658	−	0.143444i
$43$	−3.09050	−	3.09050i	−0.471297	−	0.471297i	0.431037	−	0.902334i	$-0.358148\pi$
$43$	−3.09050	−	3.09050i	−0.471297	−	0.471297i	−0.902334	+	0.431037i	$0.858148\pi$
$44$	−1.70606	−	0.749987i	−0.257199	−	0.113065i
$45$	2.18726	−	12.6218i	0.326058	−	1.88154i
$46$	1.19907	−	1.75348i	0.176793	−	0.258537i
$47$	−3.11429	+	5.39411i	−0.454266	+	0.786812i	−0.998646	−	0.0520269i	$-0.983432\pi$
$47$	−3.11429	+	5.39411i	−0.454266	+	0.786812i	0.544379	+	0.838839i	$0.316765\pi$
$48$	−6.68824	+	1.80759i	−0.965365	+	0.260904i
$49$	5.36671	+	4.49427i	0.766672	+	0.642039i
$50$	−16.8716	+	8.09615i	−2.38601	+	1.14497i
$51$	1.89815	+	0.984567i	0.265794	+	0.137867i
$52$	−5.28617	−	7.20423i	−0.733059	−	0.999047i
$53$	5.03575	+	1.34932i	0.691713	+	0.185344i	0.587516	−	0.809213i	$-0.300106\pi$
$53$	5.03575	+	1.34932i	0.691713	+	0.185344i	0.104197	+	0.994557i	$0.466773\pi$
$54$	−0.434255	−	7.33563i	−0.0590947	−	0.998252i
$55$	−3.97882			−0.536504
$56$	−6.27123	−	4.08310i	−0.838028	−	0.545627i
$57$	−6.09153	+	6.66741i	−0.806842	+	0.883120i
$58$	−0.0404017	−	0.0470795i	−0.00530501	−	0.00618185i
$59$	2.80729	−	10.4770i	0.365479	−	1.36398i	−0.501292	−	0.865278i	$-0.667142\pi$
$59$	2.80729	−	10.4770i	0.365479	−	1.36398i	0.866771	−	0.498707i	$-0.166191\pi$
$60$	−11.5189	+	9.27931i	−1.48708	+	1.19795i
$61$	0.360681	−	0.0966443i	0.0461805	−	0.0123740i	−0.235655	−	0.971837i	$-0.575723\pi$
$61$	0.360681	−	0.0966443i	0.0461805	−	0.0123740i	0.281835	+	0.959463i	$0.409057\pi$
$62$	1.33997	−	0.643008i	0.170176	−	0.0816621i
$63$	5.59319	−	5.63172i	0.704675	−	0.709530i
$64$	7.17862	+	3.53092i	0.897328	+	0.441365i
$65$	−16.5214	−	9.53863i	−2.04923	−	1.18312i
$66$	−2.22200	+	0.521949i	−0.273509	+	0.0642475i
$67$	−10.3271	−	2.76713i	−1.26165	−	0.338058i	−0.434824	−	0.900515i	$-0.643190\pi$
$67$	−10.3271	−	2.76713i	−1.26165	−	0.338058i	−0.826827	+	0.562457i	$0.809856\pi$
$68$	−0.895687	−	2.30092i	−0.108618	−	0.279027i
$69$	−0.117309	−	2.59903i	−0.0141224	−	0.312886i
$70$	−15.7650	−	2.59212i	−1.88428	−	0.309818i
$71$	4.38335			0.520208			0.260104	−	0.965581i	$-0.416243\pi$
$71$	4.38335			0.520208			0.260104	+	0.965581i	$0.416243\pi$
$72$	−5.21552	+	6.69316i	−0.614654	+	0.788797i
$73$	5.81636	+	10.0742i	0.680753	+	1.17910i	0.974751	+	0.223293i	$0.0716806\pi$
$73$	5.81636	+	10.0742i	0.680753	+	1.17910i	−0.293999	+	0.955806i	$0.594986\pi$
$74$	−0.974740	+	0.183031i	−0.113311	+	0.0212769i
$75$	−10.5531	+	20.3453i	−1.21856	+	2.34928i
$76$	10.3659	−	1.13885i	1.18905	−	0.130635i
$77$	−2.02019	−	1.41308i	−0.230222	−	0.161036i
$78$	−10.4778	−	3.15960i	−1.18637	−	0.357754i
$79$	−0.738936	+	1.27988i	−0.0831368	+	0.143997i	−0.904596	−	0.426270i	$-0.859827\pi$
$79$	−0.738936	+	1.27988i	−0.0831368	+	0.143997i	0.821459	+	0.570268i	$0.193161\pi$
$80$	17.0641	+	0.733293i	1.90782	+	0.0819847i
$81$	−5.82558	−	6.86022i	−0.647287	−	0.762247i
$82$	0.916339	−	12.0043i	0.101193	−	1.32565i
$83$	−8.71723	+	8.71723i	−0.956840	+	0.956840i	−0.999106	−	0.0422664i	$-0.986542\pi$
$83$	−8.71723	+	8.71723i	−0.956840	+	0.956840i	0.0422664	+	0.999106i	$0.486542\pi$
$84$	−9.14412	+	0.620499i	−0.997706	+	0.0677020i
$85$	−3.72750	−	3.72750i	−0.404304	−	0.404304i
$86$	4.02529	+	4.69061i	0.434058	+	0.505802i
$87$	−0.0742045	−	0.0163362i	−0.00795555	−	0.00175142i
$88$	2.32501	+	1.24121i	0.247847	+	0.132313i
$89$	7.08244	+	4.08905i	0.750737	+	0.433438i	0.825960	−	0.563728i	$-0.190633\pi$
$89$	7.08244	+	4.08905i	0.750737	+	0.433438i	−0.0752229	+	0.997167i	$0.523967\pi$
$90$	−4.44289	+	17.5626i	−0.468321	+	1.85126i
$91$	−5.00086	−	10.7107i	−0.524233	−	1.12279i
$92$	−1.87957	+	2.34354i	−0.195958	+	0.244331i
$93$	0.838140	−	1.61586i	0.0869111	−	0.167556i
$94$	4.97212	−	7.27108i	0.512835	−	0.749954i
$95$	19.2812	−	11.1320i	1.97821	−	1.14212i
$96$	9.62574	−	1.82899i	0.982423	−	0.186670i
$97$			9.28533i			0.942782i	0.881924	+	0.471391i	$0.156248\pi$
$97$			9.28533i			0.942782i	−0.881924	+	0.471391i	$0.843752\pi$
$98$	−7.08389	−	6.91509i	−0.715581	−	0.698530i
$99$	−1.79057	+	2.14672i	−0.179959	+	0.215754i
$100$	24.6623	−	9.60041i	2.46623	−	0.960041i
$101$	−2.03334	+	7.58853i	−0.202325	+	0.755087i	0.787923	+	0.615773i	$0.211156\pi$
$101$	−2.03334	+	7.58853i	−0.202325	+	0.755087i	−0.990248	+	0.139314i	$0.955510\pi$
$102$	−2.57063	−	1.59266i	−0.254530	−	0.157697i
$103$	0.192570	−	0.333540i	0.0189745	−	0.0328647i	−0.856382	−	0.516342i	$-0.827293\pi$
$103$	0.192570	−	0.333540i	0.0189745	−	0.0328647i	0.875357	+	0.483478i	$0.160627\pi$
$104$	6.67862	+	10.7278i	0.654893	+	1.05194i
$105$	−17.3387	+	9.06923i	−1.69209	+	0.885066i
$106$	−6.95572	−	2.44474i	−0.675599	−	0.237454i
$107$	−0.604394	−	2.25563i	−0.0584290	−	0.218060i	0.930538	−	0.366195i	$-0.119340\pi$
$107$	−0.604394	−	2.25563i	−0.0584290	−	0.218060i	−0.988967	+	0.148135i	$0.952673\pi$
$108$	−0.177257	+	10.3908i	−0.0170565	+	0.999855i
$109$	−13.7955	−	3.69648i	−1.32136	−	0.354059i	−0.471876	−	0.881665i	$-0.656423\pi$
$109$	−13.7955	−	3.69648i	−1.32136	−	0.354059i	−0.849489	+	0.527606i	$0.823090\pi$
$110$	5.61058	+	0.428279i	0.534948	+	0.0408348i
$111$	−0.819302	+	0.896757i	−0.0777647	+	0.0851164i
$112$	8.40363	+	6.43265i	0.794068	+	0.607829i
$113$			6.07877i			0.571842i	0.958253	+	0.285921i	$0.0922996\pi$
$113$			6.07877i			0.571842i	−0.958253	+	0.285921i	$0.907700\pi$
$114$	9.30741	−	8.74610i	0.871719	−	0.819147i
$115$	−1.66001	+	6.19526i	−0.154797	+	0.577711i
$116$	0.0519033	+	0.0707362i	0.00481910	+	0.00656769i
$117$	−12.5815	+	4.62128i	−1.16316	+	0.427237i
$118$	−5.08633	+	14.4715i	−0.468235	+	1.33221i
$119$	−0.568761	−	3.21641i	−0.0521383	−	0.294848i
$120$	17.2417	−	11.8450i	1.57395	−	1.08129i
$121$	−8.77432	−	5.06586i	−0.797666	−	0.460533i
$122$	−0.519003	+	0.0974555i	−0.0469884	+	0.00882321i
$123$	−7.94076	−	12.4241i	−0.715995	−	1.12024i
$124$	−1.95872	+	0.762479i	−0.175898	+	0.0684726i
$125$	24.8566	−	24.8566i	2.22324	−	2.22324i
$126$	−8.49321	+	7.33930i	−0.756636	+	0.653837i
$127$	−7.12876			−0.632575			−0.316288	−	0.948663i	$-0.602436\pi$
$127$	−7.12876			−0.632575			−0.316288	+	0.948663i	$0.602436\pi$
$128$	−9.74259	−	5.75169i	−0.861131	−	0.508382i
$129$	7.39311	+	1.62760i	0.650927	+	0.143302i
$130$	22.2703	+	15.2289i	1.95323	+	1.33566i
$131$	−2.67074	−	9.96733i	−0.233343	−	0.870850i	−0.978889	−	0.204395i	$-0.934477\pi$
$131$	−2.67074	−	9.96733i	−0.233343	−	0.870850i	0.745545	−	0.666455i	$-0.232189\pi$
$132$	3.18945	−	0.496832i	0.277606	−	0.0432436i
$133$	13.7433	+	1.19562i	1.19170	+	0.103673i
$134$	14.2644	+	5.01356i	1.23226	+	0.433106i
$135$	8.58116	+	20.4607i	0.738549	+	1.76098i
$136$	1.01535	+	3.34096i	0.0870654	+	0.286485i
$137$	−6.36656	−	11.0272i	−0.543932	−	0.942118i	−0.998673	−	0.0514945i	$-0.983602\pi$
$137$	−6.36656	−	11.0272i	−0.543932	−	0.942118i	0.454741	−	0.890624i	$-0.349732\pi$
$138$	−0.114340	+	3.67755i	−0.00973324	+	0.313054i
$139$	−12.4403	+	12.4403i	−1.05517	+	1.05517i	−0.0567825	+	0.998387i	$0.518084\pi$
$139$	−12.4403	+	12.4403i	−1.05517	+	1.05517i	−0.998387	+	0.0567825i	$0.981916\pi$
$140$	21.9514	+	5.35213i	1.85523	+	0.452337i
$141$	−0.486440	−	10.7773i	−0.0409656	−	0.907608i
$142$	−6.18102	−	0.471823i	−0.518699	−	0.0395945i
$143$	2.08158	+	3.60541i	0.174071	+	0.301499i
$144$	8.07491	−	8.87670i	0.672909	−	0.739725i
$145$	0.162219	+	0.0936570i	0.0134715	+	0.00777779i
$146$	−7.11732	−	14.8318i	−0.589034	−	1.22749i
$147$	−12.0245	−	1.55310i	−0.991762	−	0.128097i
$148$	1.39419	−	0.153174i	0.114602	−	0.0125908i
$149$	−5.61925	−	20.9713i	−0.460347	−	1.71804i	−0.671872	−	0.740667i	$-0.734510\pi$
$149$	−5.61925	−	20.9713i	−0.460347	−	1.71804i	0.211525	−	0.977373i	$-0.432157\pi$
$150$	17.0710	−	27.5532i	1.39384	−	2.24971i
$151$	−2.16074	+	1.24750i	−0.175838	+	0.101520i	−0.585336	−	0.810791i	$-0.699037\pi$
$151$	−2.16074	+	1.24750i	−0.175838	+	0.101520i	0.409498	+	0.912311i	$0.365704\pi$
$152$	−14.7396	+	0.490125i	−1.19554	+	0.0397544i
$153$	−3.68859	+	0.333655i	−0.298205	+	0.0269744i
$154$	2.69659	+	2.21006i	0.217298	+	0.178092i
$155$	−3.17314	+	3.17314i	−0.254873	+	0.254873i
$156$	14.4347	+	5.58321i	1.15570	+	0.447015i
$157$	−0.00877407	+	0.0327453i	−0.000700247	+	0.00261336i	−0.966275	−	0.257512i	$-0.917097\pi$
$157$	−0.00877407	+	0.0327453i	−0.000700247	+	0.00261336i	0.965575	+	0.260125i	$0.0837639\pi$
$158$	1.17975	−	1.72523i	0.0938557	−	0.137252i
$159$	−8.60792	+	2.72800i	−0.682652	+	0.216345i
$160$	−23.9833	−	2.87080i	−1.89605	−	0.226956i
$161$	−3.04311	+	2.55600i	−0.239830	+	0.201441i
$162$	7.47629	+	10.3007i	0.587392	+	0.809302i
$163$	−2.84108	−	10.6030i	−0.222530	−	0.830495i	−0.983379	−	0.181565i	$-0.941884\pi$
$163$	−2.84108	−	10.6030i	−0.222530	−	0.830495i	0.760848	−	0.648930i	$-0.224783\pi$
$164$	−2.58428	+	16.8288i	−0.201798	+	1.31411i
$165$	5.80679	−	3.71136i	0.452058	−	0.288929i
$166$	13.2306	−	11.3539i	1.02689	−	0.881237i
$167$			8.36244i			0.647105i	0.946210	+	0.323552i	$0.104877\pi$
$167$			8.36244i			0.647105i	−0.946210	+	0.323552i	$0.895123\pi$
$168$	12.9610	+	0.109298i	0.999964	+	0.00843254i
$169$			6.96113i			0.535472i
$170$	4.85496	+	5.65741i	0.372359	+	0.433904i
$171$	2.67090	−	15.4126i	0.204249	−	1.17863i
$172$	−5.17121	−	7.04757i	−0.394301	−	0.537372i
$173$	−1.20237	−	4.48731i	−0.0914145	−	0.341164i	0.905037	−	0.425333i	$-0.139843\pi$
$173$	−1.20237	−	4.48731i	−0.0914145	−	0.341164i	−0.996451	+	0.0841694i	$0.973176\pi$
$174$	0.102878	+	0.0310232i	0.00779917	+	0.00235186i
$175$	34.4751	−	6.09627i	2.60607	−	0.460834i
$176$	−3.14492	−	2.00050i	−0.237057	−	0.150794i
$177$	5.67566	+	17.9089i	0.426609	+	1.34612i
$178$	−9.54689	−	6.52837i	−0.715569	−	0.489322i
$179$	−4.40547	+	16.4414i	−0.329280	+	1.22889i	0.580659	+	0.814147i	$0.302795\pi$
$179$	−4.40547	+	16.4414i	−0.329280	+	1.22889i	−0.909939	+	0.414743i	$0.863872\pi$
$180$	8.15540	−	24.2870i	0.607868	−	1.81025i
$181$	3.20849	−	3.20849i	0.238485	−	0.238485i	−0.577738	−	0.816223i	$-0.696064\pi$
$181$	3.20849	−	3.20849i	0.238485	−	0.238485i	0.816223	+	0.577738i	$0.196064\pi$
$182$	5.89887	+	15.6416i	0.437253	+	1.15943i
$183$	−0.436240	+	0.477481i	−0.0322478	+	0.0352964i
$184$	2.90266	−	3.10233i	0.213987	−	0.228707i
$185$	2.59330	−	1.49724i	0.190663	−	0.110079i
$186$	−1.35580	+	2.18832i	−0.0994122	+	0.160455i
$187$	0.297739	+	1.11118i	0.0217729	+	0.0812574i
$188$	−7.79390	+	9.71783i	−0.568428	+	0.708746i
$189$	−2.90969	+	13.4363i	−0.211649	+	0.977346i
$190$	−28.3869	+	13.6220i	−2.05941	+	0.988242i
$191$	1.78760	+	1.03207i	0.129346	+	0.0746779i	0.563277	−	0.826268i	$-0.309540\pi$
$191$	1.78760	+	1.03207i	0.129346	+	0.0746779i	−0.433931	+	0.900946i	$0.642874\pi$
$192$	−13.7702	+	1.54296i	−0.993781	+	0.111354i
$193$	2.03453	+	3.52392i	0.146449	+	0.253657i	0.929913	−	0.367781i	$-0.119882\pi$
$193$	2.03453	+	3.52392i	0.146449	+	0.253657i	−0.783464	+	0.621438i	$0.786549\pi$
$194$	0.999470	−	13.0933i	0.0717578	−	0.940048i
$195$	33.0092	−	1.48990i	2.36384	−	0.106694i
$196$	9.24473	+	10.5136i	0.660338	+	0.750968i
$197$	−1.05279	+	1.05279i	−0.0750085	+	0.0750085i	−0.743616	−	0.668607i	$-0.766891\pi$
$197$	−1.05279	+	1.05279i	−0.0750085	+	0.0750085i	0.668607	+	0.743616i	$0.266891\pi$
$198$	2.75598	−	2.83438i	0.195859	−	0.201431i
$199$	8.29969	+	14.3755i	0.588349	+	1.01905i	0.994449	+	0.105222i	$0.0335554\pi$
$199$	8.29969	+	14.3755i	0.588349	+	1.01905i	−0.406099	+	0.913829i	$0.633111\pi$
$200$	−35.8100	+	10.8830i	−2.53215	+	0.769544i
$201$	17.6527	−	5.59445i	1.24512	−	0.394602i
$202$	3.68407	−	10.4818i	0.259210	−	0.737497i
$203$	0.0491020	+	0.105165i	0.00344628	+	0.00738116i
$204$	3.45343	+	2.52254i	0.241789	+	0.176613i
$205$	9.40812	+	35.1116i	0.657092	+	2.45230i
$206$	−0.307447	+	0.449601i	−0.0214208	+	0.0313252i
$207$	2.59552	+	3.68366i	0.180401	+	0.256032i
$208$	−8.26286	−	15.8462i	−0.572927	−	1.09874i
$209$	−4.85861			−0.336077
$210$	25.4258	−	10.9223i	1.75454	−	0.753709i
$211$	7.08853	−	7.08853i	0.487994	−	0.487994i	−0.419679	−	0.907673i	$-0.637857\pi$
$211$	7.08853	−	7.08853i	0.487994	−	0.487994i	0.907673	+	0.419679i	$0.137857\pi$
$212$	9.54519	+	4.19607i	0.655566	+	0.288187i
$213$	−6.39718	+	4.08870i	−0.438327	+	0.280153i
$214$	0.609467	+	3.24574i	0.0416623	+	0.221875i
$215$	−16.1621	−	9.33120i	−1.10225	−	0.636383i
$216$	1.36841	−	14.6331i	0.0931088	−	0.995656i
$217$	−2.73806	+	0.484174i	−0.185872	+	0.0328679i
$218$	19.0552	+	6.69739i	1.29058	+	0.453604i
$219$	−17.8856	−	9.27720i	−1.20859	−	0.626895i
$220$	−7.86544	−	1.20784i	−0.530288	−	0.0814327i
$221$	−1.42757	+	5.32777i	−0.0960289	+	0.358385i
$222$	1.25183	−	1.17634i	0.0840175	−	0.0789507i
$223$		−	28.1014i		−	1.88181i	−0.338669	−	0.940906i	$-0.609977\pi$
$223$		−	28.1014i		−	1.88181i	0.338669	−	0.940906i	$-0.390023\pi$
$224$	−11.1576	−	9.97532i	−0.745501	−	0.666504i
$225$	−3.57628	−	39.5362i	−0.238419	−	2.63574i
$226$	0.654317	−	8.57174i	0.0435245	−	0.570184i
$227$	−4.20128	−	1.12573i	−0.278849	−	0.0747173i	0.116684	−	0.993169i	$-0.462773\pi$
$227$	−4.20128	−	1.12573i	−0.278849	−	0.0747173i	−0.395533	+	0.918452i	$0.629440\pi$
$228$	−14.0659	+	11.3311i	−0.931538	+	0.750422i
$229$	4.46227	+	16.6534i	0.294875	+	1.10049i	0.941316	+	0.337525i	$0.109590\pi$
$229$	4.46227	+	16.6534i	0.294875	+	1.10049i	−0.646441	+	0.762964i	$0.723743\pi$
$230$	3.00766	−	8.55732i	0.198319	−	0.564253i
$231$	4.26642	+	0.177896i	0.280710	+	0.0117047i
$232$	−0.0655754	−	0.105333i	−0.00430524	−	0.00691544i
$233$	0.356818	−	0.618027i	0.0233759	−	0.0404883i	−0.854101	−	0.520108i	$-0.825892\pi$
$233$	0.356818	−	0.618027i	0.0233759	−	0.0404883i	0.877477	+	0.479619i	$0.159225\pi$
$234$	18.2387	−	5.16225i	1.19230	−	0.337467i
$235$	−6.88350	+	25.6896i	−0.449030	+	1.67580i
$236$	8.73001	−	19.8589i	0.568275	−	1.29271i
$237$	−0.115419	−	2.55715i	−0.00749726	−	0.166105i
$238$	0.455803	+	4.59672i	0.0295453	+	0.297961i
$239$		−	10.4030i		−	0.672913i	−0.941699	−	0.336457i	$-0.890771\pi$
$239$		−	10.4030i		−	0.672913i	0.941699	−	0.336457i	$-0.109229\pi$
$240$	−25.5877	+	14.8468i	−1.65168	+	0.958359i
$241$	−19.1601	+	11.0621i	−1.23421	+	0.712573i	−0.967905	−	0.251316i	$-0.919137\pi$
$241$	−19.1601	+	11.0621i	−1.23421	+	0.712573i	−0.266307	+	0.963888i	$0.585803\pi$
$242$	11.8275	+	8.08789i	0.760299	+	0.519909i
$243$	14.9011	+	4.57800i	0.955904	+	0.293679i
$244$	0.742343	−	0.0815577i	0.0475236	−	0.00522120i
$245$	27.1016	+	12.6055i	1.73146	+	0.805333i
$246$	9.86003	+	18.3741i	0.628653	+	1.17149i
$247$	−20.1746	−	11.6478i	−1.28368	−	0.741131i
$248$	2.84409	−	0.864344i	0.180600	−	0.0548859i
$249$	4.59089	−	20.8534i	0.290936	−	1.32153i
$250$	−37.7261	+	32.3750i	−2.38601	+	2.04758i
$251$	11.3421	+	11.3421i	0.715904	+	0.715904i	0.967764	−	0.251860i	$-0.0810421\pi$
$251$	11.3421	+	11.3421i	0.715904	+	0.715904i	−0.251860	+	0.967764i	$0.581042\pi$
$252$	12.7664	−	9.43502i	0.804206	−	0.594351i
$253$	0.989711	−	0.989711i	0.0622226	−	0.0622226i
$254$	10.0523	+	0.767338i	0.630740	+	0.0481471i
$255$	8.91694	+	1.96307i	0.558400	+	0.122932i
$256$	13.1190	+	9.15921i	0.819939	+	0.572451i
$257$	−14.0333	+	24.3064i	−0.875373	+	1.51619i	−0.0190088	+	0.999819i	$0.506051\pi$
$257$	−14.0333	+	24.3064i	−0.875373	+	1.51619i	−0.856365	+	0.516372i	$0.827282\pi$
$258$	−10.2499	−	3.09089i	−0.638132	−	0.192430i
$259$	1.84846	+	0.160809i	0.114858	+	0.00999220i
$260$	−29.7643	−	23.8716i	−1.84590	−	1.48045i
$261$	0.123534	−	0.0453750i	0.00764656	−	0.00280864i
$262$	2.69316	+	14.3425i	0.166384	+	0.886084i
$263$	−3.68184	−	6.37713i	−0.227032	−	0.393231i	0.729895	−	0.683559i	$-0.239569\pi$
$263$	−3.68184	−	6.37713i	−0.227032	−	0.393231i	−0.956927	+	0.290328i	$0.906236\pi$
$264$	−4.55095	+	0.357277i	−0.280092	+	0.0219888i
$265$	22.2609			1.36748
$266$	−19.2510	−	3.16529i	−1.18035	−	0.194076i
$267$	−14.1505	+	0.638693i	−0.865995	+	0.0390874i
$268$	−19.5748	−	8.60510i	−1.19572	−	0.525640i
$269$	−19.9270	−	5.33942i	−1.21497	−	0.325550i	−0.406260	−	0.913757i	$-0.633167\pi$
$269$	−19.9270	−	5.33942i	−1.21497	−	0.325550i	−0.808710	+	0.588207i	$0.799834\pi$
$270$	−9.89801	−	29.7756i	−0.602374	−	1.81208i
$271$	−18.9549	−	10.9436i	−1.15143	−	0.664779i	−0.202195	−	0.979345i	$-0.564808\pi$
$271$	−18.9549	−	10.9436i	−1.15143	−	0.664779i	−0.949235	+	0.314566i	$0.898141\pi$
$272$	−1.07213	−	4.82041i	−0.0650077	−	0.292281i
$273$	17.2891	+	10.9668i	1.04638	+	0.663740i
$274$	7.79060	+	16.2349i	0.470647	+	0.980785i
$275$	−11.9102	+	3.19132i	−0.718210	+	0.192444i
$276$	0.557082	−	5.17344i	0.0335324	−	0.311405i
$277$	−0.727534	+	2.71519i	−0.0437133	+	0.163140i	−0.984332	−	0.176324i	$-0.943579\pi$
$277$	−0.727534	+	2.71519i	−0.0437133	+	0.163140i	0.940619	+	0.339465i	$0.110246\pi$
$278$	18.8812	−	16.2031i	1.13242	−	0.971796i
$279$	0.284033	+	3.14002i	0.0170046	+	0.187988i
$280$	−30.3779	−	9.90994i	−1.81542	−	0.592232i
$281$	7.60012			0.453385			0.226692	−	0.973966i	$-0.427209\pi$
$281$	7.60012			0.453385			0.226692	+	0.973966i	$0.427209\pi$
$282$	−0.474126	+	15.2495i	−0.0282338	+	0.908094i
$283$	13.9261	+	3.73148i	0.827820	+	0.221814i	0.647762	−	0.761843i	$-0.275705\pi$
$283$	13.9261	+	3.73148i	0.827820	+	0.221814i	0.180057	+	0.983656i	$0.442372\pi$
$284$	8.66513	+	1.33065i	0.514181	+	0.0789593i
$285$	−17.7558	+	34.2315i	−1.05176	+	2.02770i
$286$	−2.54718	−	5.30808i	−0.150618	−	0.313874i
$287$	−7.69308	+	21.1688i	−0.454108	+	1.24955i
$288$	−12.3420	+	11.6480i	−0.727260	+	0.686363i
$289$	7.73794	−	13.4025i	0.455173	−	0.788383i
$290$	−0.218665	−	0.149528i	−0.0128405	−	0.00878058i
$291$	−8.66116	−	13.5512i	−0.507726	−	0.794388i
$292$	8.43972	+	21.6807i	0.493897	+	1.26876i
$293$	11.2933	+	11.2933i	0.659764	+	0.659764i	0.955324	−	0.295560i	$-0.0955063\pi$
$293$	11.2933	+	11.2933i	0.659764	+	0.659764i	−0.295560	+	0.955324i	$0.595506\pi$
$294$	16.7887	+	3.48435i	0.979135	+	0.203212i
$295$		−	46.3143i		−	2.69652i
$296$	−1.98246	+	0.0659211i	−0.115228	+	0.00383158i
$297$	0.610786	−	4.80319i	0.0354414	−	0.278709i
$298$	5.66642	+	30.1768i	0.328247	+	1.74809i
$299$	6.48229	−	1.73693i	0.374881	−	0.100449i
$300$	−27.0378	+	37.0156i	−1.56103	+	2.13710i
$301$	−4.89211	−	10.4778i	−0.281976	−	0.603930i
$302$	3.18116	−	1.52653i	0.183055	−	0.0878422i
$303$	−4.11092	−	12.9716i	−0.236166	−	0.745196i
$304$	20.8372	+	0.895437i	1.19510	+	0.0513568i
$305$	1.38081	−	0.797211i	0.0790649	−	0.0456482i
$306$	5.23724	−	0.0734514i	0.299393	−	0.00419894i
$307$	−10.9814	−	10.9814i	−0.626740	−	0.626740i	0.320506	−	0.947246i	$-0.396147\pi$
$307$	−10.9814	−	10.9814i	−0.626740	−	0.626740i	−0.947246	+	0.320506i	$0.896147\pi$
$308$	−3.56461	−	3.40669i	−0.203112	−	0.194114i
$309$	0.0300786	+	0.666402i	0.00171111	+	0.0379103i
$310$	4.81604	−	4.13292i	0.273532	−	0.234734i
$311$	3.74561	−	2.16253i	0.212394	−	0.122626i	−0.390029	−	0.920802i	$-0.627535\pi$
$311$	3.74561	−	2.16253i	0.212394	−	0.122626i	0.602424	+	0.798177i	$0.294202\pi$
$312$	−19.7536	−	9.42670i	−1.11833	−	0.533682i
$313$	−9.77200	+	16.9256i	−0.552346	+	0.956692i	0.445759	+	0.895153i	$0.352934\pi$
$313$	−9.77200	+	16.9256i	−0.552346	+	0.956692i	−0.998105	+	0.0615384i	$0.980399\pi$
$314$	0.0158971	−	0.0452300i	0.000897126	−	0.00255248i
$315$	16.8450	−	29.4091i	0.949109	−	1.65701i
$316$	−1.84928	+	2.30577i	−0.104030	+	0.129710i
$317$	−10.4434	+	2.79830i	−0.586559	+	0.157168i	−0.539880	−	0.841742i	$-0.681530\pi$
$317$	−10.4434	+	2.79830i	−0.586559	+	0.157168i	−0.0466790	+	0.998910i	$0.514864\pi$
$318$	12.4318	−	2.92023i	0.697139	−	0.163759i
$319$	−0.0204384	−	0.0354004i	−0.00114433	−	0.00198204i
$320$	33.5101	+	6.62970i	1.87327	+	0.370612i
$321$	2.98607	+	2.72816i	0.166666	+	0.152271i
$322$	4.56625	−	3.27669i	0.254467	−	0.182603i
$323$	−4.55171	−	4.55171i	−0.253264	−	0.253264i
$324$	−9.43363	−	15.3299i	−0.524090	−	0.851663i
$325$	−57.1057	−	15.3014i	−3.16765	−	0.848770i
$326$	2.86493	+	15.2573i	0.158674	+	0.845023i
$327$	23.5814	−	7.47338i	1.30406	−	0.413279i
$328$	5.45556	−	23.4523i	0.301233	−	1.29493i
$329$	−12.6187	+	10.5988i	−0.695691	+	0.584333i
$330$	−8.58771	+	4.60839i	−0.472738	+	0.253684i
$331$	−7.07456	+	1.89562i	−0.388853	+	0.104193i	−0.447948	−	0.894060i	$-0.647845\pi$
$331$	−7.07456	+	1.89562i	−0.388853	+	0.104193i	0.0590952	+	0.998252i	$0.481178\pi$
$332$	−19.8787	+	14.5862i	−1.09099	+	0.800521i
$333$	0.359233	−	2.07298i	0.0196858	−	0.113599i
$334$	0.900130	−	11.7920i	0.0492529	−	0.645228i
$335$	−45.6516			−2.49422
$336$	−18.2647	−	1.54924i	−0.996422	−	0.0845182i
$337$	−29.7098			−1.61839			−0.809197	−	0.587538i	$-0.800097\pi$
$337$	−29.7098			−1.61839			−0.809197	+	0.587538i	$0.800097\pi$
$338$	0.749295	−	9.81597i	0.0407563	−	0.533919i
$339$	−5.67015	−	8.87151i	−0.307960	−	0.481834i
$340$	−6.23707	−	8.50017i	−0.338253	−	0.460986i
$341$	0.945922	−	0.253459i	0.0512246	−	0.0137256i
$342$	−5.42528	+	21.4460i	−0.293366	+	1.15967i
$343$	9.28363	+	16.0254i	0.501269	+	0.865291i
$344$	6.53339	+	10.4945i	0.352257	+	0.565824i
$345$	−3.35614	−	10.5899i	−0.180689	−	0.570144i
$346$	1.21246	+	6.45702i	0.0651824	+	0.347132i
$347$	18.9843	+	5.08684i	1.01913	+	0.273076i	0.729441	−	0.684044i	$-0.239780\pi$
$347$	18.9843	+	5.08684i	1.01913	+	0.273076i	0.289692	+	0.957120i	$0.406447\pi$
$348$	−0.141730	−	0.0548199i	−0.00759754	−	0.00293866i
$349$	−4.66251	−	4.66251i	−0.249579	−	0.249579i	0.571219	−	0.820798i	$-0.306471\pi$
$349$	−4.66251	−	4.66251i	−0.249579	−	0.249579i	−0.820798	+	0.571219i	$0.806471\pi$
$350$	−49.2700	+	4.88552i	−2.63359	+	0.261142i
$351$	14.0511	−	18.4802i	0.749993	−	0.986399i
$352$	4.21936	+	3.15945i	0.224893	+	0.168399i
$353$	6.71494	+	11.6306i	0.357400	+	0.619035i	0.987526	−	0.157458i	$-0.0503300\pi$
$353$	6.71494	+	11.6306i	0.357400	+	0.619035i	−0.630126	+	0.776493i	$0.716997\pi$
$354$	−6.07560	−	25.8645i	−0.322914	−	1.37468i
$355$	18.0790	−	4.84425i	0.959532	−	0.257106i
$356$	12.7595	+	10.2333i	0.676250	+	0.542366i
$357$	3.83027	+	4.16359i	0.202719	+	0.220360i
$358$	7.98195	−	22.7100i	0.421859	−	1.20026i
$359$	6.04080	−	10.4630i	0.318821	−	0.552215i	−0.661421	−	0.750015i	$-0.730046\pi$
$359$	6.04080	−	10.4630i	0.318821	−	0.552215i	0.980242	+	0.197800i	$0.0633797\pi$
$360$	−14.1143	+	33.3696i	−0.743888	+	1.75873i
$361$	7.09017	−	4.09351i	0.373167	−	0.215448i
$362$	−4.86969	+	4.17896i	−0.255945	+	0.219642i
$363$	17.5308	−	0.791267i	0.920128	−	0.0415307i
$364$	−6.63441	−	22.6913i	−0.347737	−	1.18935i
$365$	35.1228	+	35.1228i	1.83841	+	1.83841i
$366$	0.666542	−	0.626345i	0.0348407	−	0.0327396i
$367$	12.3381	−	7.12343i	0.644046	−	0.371840i	−0.142126	−	0.989849i	$-0.545394\pi$
$367$	12.3381	−	7.12343i	0.644046	−	0.371840i	0.786171	+	0.618009i	$0.212060\pi$
$368$	−4.42700	+	4.06220i	−0.230773	+	0.211757i
$369$	23.1779	+	10.7251i	1.20659	+	0.558325i
$370$	−3.81800	+	1.83214i	−0.198489	+	0.0952482i
$371$	11.3027	+	7.90601i	0.586807	+	0.410459i
$372$	2.14738	−	2.93983i	0.111336	−	0.152423i
$373$	35.8478	−	9.60540i	1.85613	−	0.497349i	0.856314	−	0.516456i	$-0.172749\pi$
$373$	35.8478	−	9.60540i	1.85613	−	0.497349i	0.999817	+	0.0191072i	$0.00608238\pi$
$374$	−0.300239	−	1.59893i	−0.0155250	−	0.0826789i
$375$	−13.0906	+	59.4621i	−0.675997	+	3.07061i
$376$	12.0363	−	12.8643i	0.620724	−	0.663425i
$377$		−	0.195992i		−	0.0100941i
$378$	5.54926	−	18.6335i	0.285423	−	0.958402i
$379$	17.6449	+	17.6449i	0.906355	+	0.906355i	0.995976	−	0.0896206i	$-0.0285655\pi$
$379$	17.6449	+	17.6449i	0.906355	+	0.906355i	−0.0896206	+	0.995976i	$0.528565\pi$
$380$	41.4950	−	16.1529i	2.12865	−	0.828628i
$381$	10.4039	−	6.64956i	0.533008	−	0.340667i
$382$	−2.40962	−	1.64775i	−0.123287	−	0.0843061i
$383$	15.4102	−	26.6912i	0.787424	−	1.36386i	−0.140117	−	0.990135i	$-0.544748\pi$
$383$	15.4102	−	26.6912i	0.787424	−	1.36386i	0.927540	−	0.373723i	$-0.121919\pi$
$384$	19.5836	−	0.693525i	0.999374	−	0.0353913i
$385$	−9.89388	−	3.59560i	−0.504239	−	0.183249i
$386$	−2.48961	−	5.18811i	−0.126718	−	0.264068i
$387$	−12.3079	+	4.52078i	−0.625645	+	0.229804i
$388$	−2.81873	+	18.3555i	−0.143099	+	0.931859i
$389$	−23.8769	−	6.39781i	−1.21061	−	0.324382i	−0.403608	−	0.914932i	$-0.632244\pi$
$389$	−23.8769	−	6.39781i	−1.21061	−	0.324382i	−0.807001	+	0.590550i	$0.798911\pi$
$390$	−46.7070	−	1.45218i	−2.36510	−	0.0735340i
$391$	1.85439			0.0937806
$392$	−11.9044	−	15.8204i	−0.601264	−	0.799050i
$393$	13.1951	+	12.0554i	0.665603	+	0.608113i
$394$	1.59788	−	1.37123i	0.0805000	−	0.0690818i
$395$	−1.63327	+	6.09543i	−0.0821785	+	0.306694i
$396$	−4.19133	+	3.70014i	−0.210622	+	0.185939i
$397$	30.2212	−	8.09774i	1.51676	−	0.406414i	0.598085	−	0.801433i	$-0.295929\pi$
$397$	30.2212	−	8.09774i	1.51676	−	0.406414i	0.918673	+	0.395019i	$0.129262\pi$
$398$	−10.1561	−	21.1644i	−0.509080	−	1.06088i
$399$	−21.1726	+	11.0746i	−1.05996	+	0.554423i
$400$	51.6676	−	11.4917i	2.58338	−	0.574583i
$401$	16.3825	+	9.45842i	0.818101	+	0.472331i	0.849761	−	0.527168i	$-0.176746\pi$
$401$	16.3825	+	9.45842i	0.818101	+	0.472331i	−0.0316601	+	0.999499i	$0.510079\pi$
$402$	−25.4944	+	5.98867i	−1.27155	+	0.298688i
$403$	4.53542	+	1.21526i	0.225925	+	0.0605365i
$404$	−6.32320	+	14.3840i	−0.314591	+	0.715629i
$405$	−31.6089	−	21.8566i	−1.57066	−	1.08606i
$406$	−0.0579193	−	0.153580i	−0.00287448	−	0.00762205i
$407$	−0.653476			−0.0323916
$408$	−4.59820	−	3.92878i	−0.227645	−	0.194504i
$409$	−5.29476	−	9.17079i	−0.261809	−	0.453467i	0.704914	−	0.709293i	$-0.250986\pi$
$409$	−5.29476	−	9.17079i	−0.261809	−	0.453467i	−0.966723	+	0.255827i	$0.917652\pi$
$410$	−9.48710	−	50.5239i	−0.468534	−	2.49520i
$411$	19.5775	+	10.1548i	0.965686	+	0.500899i
$412$	0.481929	−	0.600894i	0.0237429	−	0.0296039i
$413$	16.4486	−	23.5155i	0.809382	−	1.15712i
$414$	−3.26347	−	5.47376i	−0.160391	−	0.269021i
$415$	−26.3201	+	45.5877i	−1.29200	+	2.23781i
$416$	9.94587	+	23.2344i	0.487637	+	1.13916i
$417$	6.55161	−	29.7597i	0.320834	−	1.45734i
$418$	6.85118	+	0.522979i	0.335102	+	0.0255798i
$419$	−6.74790	+	6.74790i	−0.329656	+	0.329656i	−0.852456	−	0.522799i	$-0.824888\pi$
$419$	−6.74790	+	6.74790i	−0.329656	+	0.329656i	0.522799	+	0.852456i	$0.324888\pi$
$420$	−37.0288	+	12.6648i	−1.80682	+	0.617980i
$421$	13.8240	+	13.8240i	0.673741	+	0.673741i	0.958576	−	0.284835i	$-0.0919389\pi$
$421$	13.8240	+	13.8240i	0.673741	+	0.673741i	−0.284835	+	0.958576i	$0.591939\pi$
$422$	−10.7586	+	9.23260i	−0.523721	+	0.449436i
$423$	10.7627	+	15.2749i	0.523302	+	0.742689i
$424$	−13.0081	−	6.94437i	−0.631730	−	0.337248i
$425$	−14.1476	−	8.16812i	−0.686259	−	0.396212i
$426$	9.46084	−	5.07693i	0.458379	−	0.245978i
$427$	0.984219	+	0.0856234i	0.0476297	+	0.00414361i
$428$	−0.510046	−	4.64246i	−0.0246540	−	0.224402i
$429$	−6.40096	−	3.32016i	−0.309041	−	0.160299i
$430$	21.7860	+	14.8977i	1.05061	+	0.718432i
$431$	11.2910	−	6.51888i	0.543870	−	0.314003i	−0.202776	−	0.979225i	$-0.564996\pi$
$431$	11.2910	−	6.51888i	0.543870	−	0.314003i	0.746646	+	0.665222i	$0.231663\pi$
$432$	−3.50472	+	20.4870i	−0.168621	+	0.985681i
$433$		−	13.1629i		−	0.632569i	−0.948664	−	0.316285i	$-0.897565\pi$
$433$		−	13.1629i		−	0.632569i	0.948664	−	0.316285i	$-0.102435\pi$
$434$	3.91309	−	0.388015i	0.187834	−	0.0186253i
$435$	−0.324107	+	0.0146288i	−0.0155398	+	0.000701399i
$436$	−26.1491	−	11.4952i	−1.25231	−	0.550518i
$437$	−2.02707	+	7.56514i	−0.0969681	+	0.361890i
$438$	24.2220	+	15.0071i	1.15737	+	0.717066i
$439$	−2.44940	+	4.24248i	−0.116903	+	0.202483i	−0.918539	−	0.395330i	$-0.870630\pi$
$439$	−2.44940	+	4.24248i	−0.116903	+	0.202483i	0.801636	+	0.597813i	$0.203963\pi$
$440$	10.9611	+	2.54983i	0.522552	+	0.121558i
$441$	18.9975	−	8.94955i	0.904644	−	0.426169i
$442$	2.58651	−	7.35908i	0.123028	−	0.350036i
$443$	−3.13148	−	11.6868i	−0.148781	−	0.555258i	−0.999558	−	0.0297311i	$-0.990535\pi$
$443$	−3.13148	−	11.6868i	−0.148781	−	0.555258i	0.850777	−	0.525527i	$-0.176132\pi$
$444$	−1.89184	+	1.52402i	−0.0897830	+	0.0723268i
$445$	33.7303	+	9.03800i	1.59897	+	0.428442i
$446$	−3.02483	+	39.6261i	−0.143230	+	1.87635i
$447$	27.7625	+	25.3646i	1.31312	+	1.19970i
$448$	14.6598	+	15.2673i	0.692609	+	0.721313i
$449$			7.72323i			0.364482i	0.983254	+	0.182241i	$0.0583351\pi$
$449$			7.72323i			0.364482i	−0.983254	+	0.182241i	$0.941665\pi$
$450$	0.787289	+	56.1353i	0.0371131	+	2.64625i
$451$	2.05310	−	7.66228i	0.0966768	−	0.360803i
$452$	−1.84532	+	12.0167i	−0.0867965	+	0.565217i
$453$	1.98979	−	3.83613i	0.0934885	−	0.180237i
$454$	5.80310	+	2.03963i	0.272353	+	0.0957246i
$455$	−32.4628	−	38.6492i	−1.52188	−	1.81190i
$456$	21.0542	−	14.4641i	0.985952	−	0.677344i
$457$	−15.6899	−	9.05857i	−0.733943	−	0.423742i	0.0859200	−	0.996302i	$-0.472617\pi$
$457$	−15.6899	−	9.05857i	−0.733943	−	0.423742i	−0.819863	+	0.572560i	$0.805950\pi$
$458$	−4.49973	−	23.9635i	−0.210259	−	1.11974i
$459$	5.07200	−	3.92759i	0.236741	−	0.183324i
$460$	−5.16225	+	11.7430i	−0.240691	+	0.547522i
$461$	−17.8566	+	17.8566i	−0.831666	+	0.831666i	−0.987745	−	0.156079i	$-0.950115\pi$
$461$	−17.8566	+	17.8566i	−0.831666	+	0.831666i	0.156079	+	0.987745i	$0.450115\pi$
$462$	−5.99698	−	0.710089i	−0.279005	−	0.0330363i
$463$	−13.0308			−0.605593			−0.302797	−	0.953055i	$-0.597920\pi$
$463$	−13.0308			−0.605593			−0.302797	+	0.953055i	$0.597920\pi$
$464$	0.0811306	+	0.155589i	0.00376639	+	0.00722306i
$465$	1.67112	−	7.59080i	0.0774964	−	0.352015i
$466$	−0.569677	+	0.833078i	−0.0263898	+	0.0385916i
$467$	3.58040	+	13.3623i	0.165681	+	0.618331i	0.997952	+	0.0639622i	$0.0203737\pi$
$467$	3.58040	+	13.3623i	0.165681	+	0.618331i	−0.832271	+	0.554369i	$0.812960\pi$
$468$	−26.2743	+	5.31613i	−1.21453	+	0.245738i
$469$	−23.1790	−	16.2132i	−1.07031	−	0.748658i
$470$	12.4717	−	35.4842i	0.575277	−	1.63676i
$471$	−0.0177390	−	0.0559735i	−0.000817371	−	0.00257913i
$472$	−14.4479	+	27.0636i	−0.665018	+	1.24570i
$473$	2.03632	+	3.52700i	0.0936299	+	0.162172i
$474$	−0.112497	+	3.61829i	−0.00516717	+	0.166193i
$475$	48.7875	−	48.7875i	2.23852	−	2.23852i
$476$	−0.147943	−	6.53095i	−0.00678093	−	0.299346i
$477$	10.0180	−	12.0106i	0.458692	−	0.549928i
$478$	−1.11977	+	14.6694i	−0.0512173	+	0.670961i
$479$	3.30633	+	5.72673i	0.151070	+	0.261661i	0.931621	−	0.363431i	$-0.118395\pi$
$479$	3.30633	+	5.72673i	0.151070	+	0.261661i	−0.780551	+	0.625092i	$0.785061\pi$
$480$	37.6797	−	18.1814i	1.71983	−	0.829865i
$481$	−2.71345	−	1.56661i	−0.123723	−	0.0714313i
$482$	28.2086	−	13.5364i	1.28487	−	0.616566i
$483$	2.05700	−	6.56885i	0.0935967	−	0.298893i
$484$	−15.8075	−	12.6779i	−0.718522	−	0.576270i
$485$	10.2616	+	38.2970i	0.465957	+	1.73898i
$486$	−20.5194	−	8.05943i	−0.930779	−	0.365583i
$487$	10.4448	−	6.03029i	0.473298	−	0.273259i	−0.244321	−	0.969694i	$-0.578565\pi$
$487$	10.4448	−	6.03029i	0.473298	−	0.273259i	0.717619	+	0.696436i	$0.245232\pi$
$488$	−1.05556	+	0.0350999i	−0.0477832	+	0.00158890i
$489$	14.0366	+	12.8243i	0.634759	+	0.579933i
$490$	−36.8594	−	20.6923i	−1.66514	−	0.934783i
$491$	−13.5488	+	13.5488i	−0.611448	+	0.611448i	−0.943323	−	0.331875i	$-0.892319\pi$
$491$	−13.5488	+	13.5488i	−0.611448	+	0.611448i	0.331875	+	0.943323i	$0.392319\pi$
$492$	−11.9260	−	26.9709i	−0.537664	−	1.21594i
$493$	0.0140169	−	0.0523118i	0.000631289	−	0.00235600i
$494$	27.1946	+	18.5963i	1.22354	+	0.836685i
$495$	−5.01270	+	10.8329i	−0.225304	+	0.486903i
$496$	−4.10351	+	0.912684i	−0.184253	+	0.0409807i
$497$	10.8998	+	3.96117i	0.488923	+	0.177683i
$498$	−8.71832	+	28.9114i	−0.390677	+	1.29555i
$499$	−0.0450111	−	0.167984i	−0.00201497	−	0.00751998i	0.964911	−	0.262577i	$-0.0845724\pi$
$499$	−0.0450111	−	0.167984i	−0.00201497	−	0.00751998i	−0.966926	+	0.255057i	$0.917906\pi$
$500$	56.6829	−	41.5915i	2.53493	−	1.86003i
$501$	−7.80031	−	12.2044i	−0.348492	−	0.545250i
$502$	−14.7727	−	17.2144i	−0.659338	−	0.768317i
$503$		−	26.1076i		−	1.16408i	−0.813160	−	0.582040i	$-0.802255\pi$
$503$		−	26.1076i		−	1.16408i	0.813160	−	0.582040i	$-0.197745\pi$
$504$	−19.0176	+	11.9303i	−0.847111	+	0.531416i
$505$			33.5457i			1.49277i
$506$	−1.50213	+	1.28907i	−0.0667780	+	0.0573062i
$507$	−6.49320	−	10.1593i	−0.288373	−	0.451188i
$508$	−14.0923	−	2.16406i	−0.625246	−	0.0960148i
$509$	−5.36218	−	20.0119i	−0.237675	−	0.887014i	−0.976925	−	0.213583i	$-0.931487\pi$
$509$	−5.36218	−	20.0119i	−0.237675	−	0.887014i	0.739250	−	0.673431i	$-0.235180\pi$
$510$	−12.3626	−	3.72797i	−0.547424	−	0.165077i
$511$	5.35923	+	30.3071i	0.237078	+	1.34071i
$512$	−17.5134	−	14.3276i	−0.773990	−	0.633198i
$513$	10.4786	+	24.9850i	0.462642	+	1.10311i
$514$	22.4049	−	32.7642i	0.988236	−	1.44517i
$515$	0.425635	−	1.58849i	0.0187557	−	0.0699973i
$516$	14.1208	+	5.46180i	0.621635	+	0.240442i
$517$	4.10398	−	4.10398i	0.180493	−	0.180493i
$518$	−2.58923	−	0.425727i	−0.113764	−	0.0187054i
$519$	5.94044	+	5.42734i	0.260756	+	0.238234i
$520$	39.4015	+	36.8654i	1.72787	+	1.61666i
$521$	−12.8675	+	7.42904i	−0.563734	+	0.325472i	−0.754643	−	0.656136i	$-0.772190\pi$
$521$	−12.8675	+	7.42904i	−0.563734	+	0.325472i	0.190909	+	0.981608i	$0.438857\pi$
$522$	−0.179081	+	0.0506866i	−0.00783815	+	0.00221849i
$523$	−10.8448	−	40.4735i	−0.474212	−	1.76978i	−0.624378	−	0.781122i	$-0.714648\pi$
$523$	−10.8448	−	40.4735i	−0.474212	−	1.76978i	0.150166	−	0.988661i	$-0.452019\pi$
$524$	−2.25383	−	20.5144i	−0.0984588	−	0.896177i
$525$	−44.6274	+	41.0547i	−1.94770	+	1.79178i
$526$	4.50537	+	9.38878i	0.196444	+	0.409370i
$527$	1.12362	+	0.648724i	0.0489458	+	0.0282588i
$528$	6.45581	−	0.0139362i	0.280953	−	0.000606494i
$529$	10.3719	+	17.9646i	0.450951	+	0.781071i
$530$	−31.3904	−	2.39616i	−1.36351	−	0.104083i
$531$	−24.9883	−	20.8426i	−1.08440	−	0.904492i
$532$	26.8053	+	6.53558i	1.16216	+	0.283353i
$533$	26.8943	−	26.8943i	1.16492	−	1.16492i
$534$	20.0225	+	0.622525i	0.866458	+	0.0269393i
$535$	−4.98560	−	8.63531i	−0.215546	−	0.373337i
$536$	26.6764	+	14.2412i	1.15224	+	0.615125i
$537$	−8.90677	−	28.1044i	−0.384356	−	1.21279i
$538$	27.5246	+	9.67412i	1.18667	+	0.417081i
$539$	−3.74650	−	5.33944i	−0.161373	−	0.229986i
$540$	10.7523	+	43.0523i	0.462703	+	1.85268i
$541$	7.87059	+	29.3734i	0.338383	+	1.26286i	0.900155	+	0.435570i	$0.143453\pi$
$541$	7.87059	+	29.3734i	0.338383	+	1.26286i	−0.561772	+	0.827292i	$0.689880\pi$
$542$	25.5506	+	17.4721i	1.09749	+	0.750489i
$543$	−1.68974	+	7.67536i	−0.0725136	+	0.329381i
$544$	0.992960	+	6.91272i	0.0425728	+	0.296381i
$545$	−60.9840			−2.61227
$546$	−23.1991	−	17.3254i	−0.992830	−	0.741458i
$547$	−24.4606	+	24.4606i	−1.04586	+	1.04586i	−0.0469612	+	0.998897i	$0.514954\pi$
$547$	−24.4606	+	24.4606i	−1.04586	+	1.04586i	−0.998897	+	0.0469612i	$0.985046\pi$
$548$	−9.23809	−	23.7316i	−0.394632	−	1.01376i
$549$	0.191275	−	1.10376i	0.00816340	−	0.0471075i
$550$	17.1382	−	3.21811i	0.730774	−	0.137221i
$551$	0.198088	+	0.114366i	0.00843883	+	0.00487216i
$552$	−1.34242	+	7.23516i	−0.0571370	+	0.307949i
$553$	−2.99407	+	2.51482i	−0.127321	+	0.106941i
$554$	1.31817	−	3.75041i	0.0560035	−	0.159340i
$555$	−2.38813	+	4.60409i	−0.101370	+	0.195433i
$556$	−28.3687	+	20.8158i	−1.20310	+	0.882786i
$557$	5.48140	−	20.4569i	0.232254	−	0.866785i	−0.747113	−	0.664697i	$-0.768561\pi$
$557$	5.48140	−	20.4569i	0.232254	−	0.866785i	0.979367	−	0.202088i	$-0.0647727\pi$
$558$	−0.0625276	−	4.45835i	−0.00264701	−	0.188737i
$559$			19.5270i			0.825906i
$560$	41.7695	+	17.2440i	1.76508	+	0.728691i
$561$	−1.47101	−	1.34396i	−0.0621062	−	0.0567419i
$562$	−10.7170	−	0.818075i	−0.452070	−	0.0345084i
$563$	5.14751	+	1.37927i	0.216942	+	0.0581294i	0.365653	−	0.930751i	$-0.380846\pi$
$563$	5.14751	+	1.37927i	0.216942	+	0.0581294i	−0.148711	+	0.988881i	$0.547512\pi$
$564$	2.31002	−	21.4524i	0.0972694	−	0.903311i
$565$	6.71793	+	25.0716i	0.282625	+	1.05477i
$566$	−19.2357	−	6.76080i	−0.808535	−	0.284178i
$567$	−8.28661	−	22.3234i	−0.348005	−	0.937493i
$568$	−12.0756	−	2.80907i	−0.506680	−	0.117866i
$569$	12.4010	−	21.4791i	0.519876	−	0.900451i	−0.479857	−	0.877347i	$-0.659312\pi$
$569$	12.4010	−	21.4791i	0.519876	−	0.900451i	0.999733	−	0.0231046i	$-0.00735507\pi$
$570$	28.7223	−	46.3590i	1.20305	−	1.94176i
$571$	−4.25910	+	15.8952i	−0.178238	+	0.665192i	0.817740	+	0.575588i	$0.195227\pi$
$571$	−4.25910	+	15.8952i	−0.178238	+	0.665192i	−0.995977	+	0.0896041i	$0.971440\pi$
$572$	3.02044	+	7.75917i	0.126291	+	0.324427i
$573$	−3.57155	+	0.161205i	−0.149204	+	0.00673444i
$574$	13.1267	−	29.0222i	0.547898	−	1.21136i
$575$			19.8763i			0.828898i
$576$	18.6574	−	15.0964i	0.777391	−	0.629018i
$577$	11.2253	−	6.48094i	0.467316	−	0.269805i	−0.247799	−	0.968811i	$-0.579707\pi$
$577$	11.2253	−	6.48094i	0.467316	−	0.269805i	0.715115	+	0.699006i	$0.246374\pi$
$578$	−12.3540	+	18.0661i	−0.513859	+	0.751451i
$579$	−6.25629	−	3.24512i	−0.260002	−	0.134863i
$580$	0.292247	+	0.234388i	0.0121349	+	0.00973243i
$581$	−29.5542	+	13.7989i	−1.22611	+	0.572476i
$582$	10.7546	+	20.0411i	0.445791	+	0.830728i
$583$	−4.20709	−	2.42896i	−0.174240	−	0.100597i
$584$	−9.56724	−	31.4806i	−0.395895	−	1.30268i
$585$	−46.7847	+	32.9647i	−1.93431	+	1.36292i
$586$	−14.7093	−	17.1405i	−0.607634	−	0.708067i
$587$	17.0199	+	17.0199i	0.702486	+	0.702486i	0.964944	−	0.262457i	$-0.0845329\pi$
$587$	17.0199	+	17.0199i	0.702486	+	0.702486i	−0.262457	+	0.964944i	$0.584533\pi$
$588$	−23.2988	−	6.72045i	−0.960828	−	0.277147i
$589$	−3.87478	+	3.87478i	−0.159657	+	0.159657i
$590$	−4.98526	+	65.3083i	−0.205240	+	2.68870i
$591$	0.554450	−	2.51850i	0.0228070	−	0.103597i
$592$	2.80258	+	0.120435i	0.115185	+	0.00494985i
$593$	18.9683	−	32.8540i	0.778934	−	1.34915i	−0.153622	−	0.988130i	$-0.549094\pi$
$593$	18.9683	−	32.8540i	0.778934	−	1.34915i	0.932556	−	0.361024i	$-0.117573\pi$
$594$	−1.37829	+	6.70728i	−0.0565519	+	0.275203i
$595$	−5.90044	−	12.6374i	−0.241895	−	0.518083i
$596$	−4.74207	−	43.1626i	−0.194243	−	1.76801i
$597$	−25.5219	−	13.2382i	−1.04454	−	0.541802i
$598$	−9.32772	+	1.75151i	−0.381439	+	0.0716244i
$599$	−5.47198	−	9.47774i	−0.223579	−	0.387250i	0.732313	−	0.680968i	$-0.238441\pi$
$599$	−5.47198	−	9.47774i	−0.223579	−	0.387250i	−0.955892	+	0.293718i	$0.905107\pi$
$600$	42.1106	−	49.2858i	1.71916	−	2.01208i
$601$	−7.61633			−0.310677			−0.155338	−	0.987861i	$-0.549647\pi$
$601$	−7.61633			−0.310677			−0.155338	+	0.987861i	$0.549647\pi$
$602$	5.77059	+	15.3014i	0.235192	+	0.623640i
$603$	−20.5444	+	24.6308i	−0.836632	+	1.00304i
$604$	−4.65010	+	1.81016i	−0.189210	+	0.0736546i
$605$	−41.7879	−	11.1970i	−1.69892	−	0.455224i
$606$	4.40060	+	18.7338i	0.178762	+	0.761010i
$607$	19.1158	+	11.0365i	0.775886	+	0.447958i	0.834970	−	0.550295i	$-0.185485\pi$
$607$	19.1158	+	11.0365i	0.775886	+	0.447958i	−0.0590845	+	0.998253i	$0.518818\pi$
$608$	−29.2864	−	3.50558i	−1.18772	−	0.142170i
$609$	−0.169757	−	0.107680i	−0.00687889	−	0.00436340i
$610$	−2.03291	+	0.975526i	−0.0823100	+	0.0394979i
$611$	26.8798	−	7.20242i	1.08744	−	0.291379i
$612$	−7.39300	−	0.460161i	−0.298844	−	0.0186009i
$613$	3.89225	−	14.5261i	0.157207	−	0.586703i	−0.841700	−	0.539946i	$-0.818445\pi$
$613$	3.89225	−	14.5261i	0.157207	−	0.586703i	0.998906	−	0.0467569i	$-0.0148886\pi$
$614$	14.3029	+	16.6670i	0.577219	+	0.672625i
$615$	−46.4818	−	42.4670i	−1.87433	−	1.71244i
$616$	4.65980	+	5.18751i	0.187749	+	0.209011i
$617$	−15.1768			−0.610995			−0.305497	−	0.952193i	$-0.598823\pi$
$617$	−15.1768			−0.610995			−0.305497	+	0.952193i	$0.598823\pi$
$618$	0.0293172	−	0.942939i	0.00117931	−	0.0379306i
$619$	−4.27523	−	1.14555i	−0.171836	−	0.0460434i	0.171875	−	0.985119i	$-0.445017\pi$
$619$	−4.27523	−	1.14555i	−0.171836	−	0.0460434i	−0.343711	+	0.939075i	$0.611684\pi$
$620$	−7.23601	+	5.30949i	−0.290605	+	0.213234i
$621$	−7.22402	−	2.95498i	−0.289890	−	0.118579i
$622$	−5.51451	+	2.64623i	−0.221112	+	0.106104i
$623$	13.9162	+	16.5683i	0.557542	+	0.663794i
$624$	26.8401	+	15.4190i	1.07446	+	0.617253i
$625$	41.9686	−	72.6917i	1.67874	−	2.90767i
$626$	15.6015	−	22.8151i	0.623560	−	0.911876i
$627$	7.09078	−	4.53201i	0.283178	−	0.180991i
$628$	−0.0272852	+	0.0620682i	−0.00108880	+	0.00247679i
$629$	−0.612199	−	0.612199i	−0.0244100	−	0.0244100i
$630$	−26.9189	+	39.6569i	−1.07248	+	1.57997i
$631$			32.0955i			1.27770i	0.769330	+	0.638852i	$0.220590\pi$
$631$			32.0955i			1.27770i	−0.769330	+	0.638852i	$0.779410\pi$
$632$	2.85588	−	3.05234i	0.113601	−	0.121416i
$633$	−3.73314	+	16.9572i	−0.148379	+	0.673989i
$634$	15.0275	−	2.82179i	0.596820	−	0.112067i
$635$	−29.4023	+	7.87832i	−1.16679	+	0.312642i
$636$	−17.8445	+	2.77970i	−0.707580	+	0.110222i
$637$	−2.75620	−	31.1528i	−0.109205	−	1.23432i
$638$	0.0250100	+	0.0521185i	0.000990155	+	0.00206339i
$639$	5.52235	−	11.9343i	0.218461	−	0.472114i
$640$	−46.5394	−	12.9556i	−1.83963	−	0.512117i
$641$	6.60295	−	3.81222i	0.260801	−	0.150573i	−0.363899	−	0.931438i	$-0.618555\pi$
$641$	6.60295	−	3.81222i	0.260801	−	0.150573i	0.624700	+	0.780865i	$0.285221\pi$
$642$	−3.91704	−	4.16842i	−0.154593	−	0.164515i
$643$	18.8073	+	18.8073i	0.741689	+	0.741689i	0.972903	−	0.231214i	$-0.0742698\pi$
$643$	18.8073	+	18.8073i	0.741689	+	0.741689i	−0.231214	+	0.972903i	$0.574270\pi$
$644$	−6.79162	+	4.12899i	−0.267627	+	0.162705i
$645$	32.2913	−	1.45750i	1.27147	−	0.0573888i
$646$	5.92848	+	6.90837i	0.233253	+	0.271806i
$647$	29.6179	−	17.0999i	1.16440	−	0.672266i	0.212044	−	0.977260i	$-0.431988\pi$
$647$	29.6179	−	17.0999i	1.16440	−	0.672266i	0.952354	+	0.304994i	$0.0986545\pi$
$648$	11.6524	+	22.6323i	0.457748	+	0.889082i
$649$	−5.05350	+	8.75293i	−0.198367	+	0.343582i
$650$	78.8783	+	27.7235i	3.09386	+	1.08741i
$651$	3.54437	−	3.26063i	0.138915	−	0.127794i
$652$	−2.39758	−	21.8229i	−0.0938963	−	0.854649i
$653$	−34.2556	+	9.17876i	−1.34053	+	0.359193i	−0.856629	−	0.515933i	$-0.827445\pi$
$653$	−34.2556	+	9.17876i	−1.34053	+	0.359193i	−0.483896	+	0.875125i	$0.660779\pi$
$654$	−34.0569	+	7.99999i	−1.33173	+	0.312825i
$655$	−22.0307	−	38.1583i	−0.860811	−	1.49097i
$656$	−10.2173	+	32.4830i	−0.398920	+	1.26825i
$657$	34.7562	−	3.14391i	1.35597	−	0.122655i
$658$	18.9346	−	13.5873i	0.738148	−	0.529687i
$659$	−9.16650	−	9.16650i	−0.357076	−	0.357076i	0.505658	−	0.862734i	$-0.331250\pi$
$659$	−9.16650	−	9.16650i	−0.357076	−	0.357076i	−0.862734	+	0.505658i	$0.831250\pi$
$660$	12.6057	−	5.57397i	0.490675	−	0.216966i
$661$	18.0035	+	4.82403i	0.700256	+	0.187633i	0.591345	−	0.806418i	$-0.298597\pi$
$661$	18.0035	+	4.82403i	0.700256	+	0.187633i	0.108911	+	0.994052i	$0.465264\pi$
$662$	10.1800	−	1.91154i	0.395655	−	0.0742939i
$663$	−2.88620	−	9.10709i	−0.112091	−	0.353690i
$664$	29.6013	−	18.4284i	1.14875	−	0.715161i
$665$	58.0052	−	10.2571i	2.24935	−	0.397754i
$666$	−0.729693	+	2.88446i	−0.0282750	+	0.111771i
$667$	−0.0636477	+	0.0170544i	−0.00246445	+	0.000660347i
$668$	−2.53857	+	16.5311i	−0.0982202	+	0.639607i
$669$	26.2124	+	41.0119i	1.01343	+	1.58561i
$670$	64.3739	+	4.91393i	2.48698	+	0.189842i
$671$	−0.347945			−0.0134323
$672$	25.5885	+	4.15061i	0.987099	+	0.160113i
$673$	33.5991			1.29515			0.647576	−	0.762001i	$-0.275783\pi$
$673$	33.5991			1.29515			0.647576	+	0.762001i	$0.275783\pi$
$674$	41.8941	+	3.19795i	1.61370	+	0.123180i
$675$	42.0978	+	54.3642i	1.62035	+	2.09248i
$676$	−2.11318	+	13.7610i	−0.0812761	+	0.529268i
$677$	−4.72337	+	1.26562i	−0.181534	+	0.0486419i	−0.348441	−	0.937331i	$-0.613289\pi$
$677$	−4.72337	+	1.26562i	−0.181534	+	0.0486419i	0.166907	+	0.985973i	$0.446622\pi$
$678$	7.04062	+	13.1201i	0.270393	+	0.503876i
$679$	−8.39102	+	23.0892i	−0.322018	+	0.886083i
$680$	7.88001	+	12.6575i	0.302185	+	0.485395i
$681$	7.18152	−	2.27595i	0.275196	−	0.0872146i
$682$	−1.36114	+	0.255587i	−0.0521207	+	0.00978692i
$683$	45.6186	+	12.2235i	1.74555	+	0.467718i	0.983667	−	0.179998i	$-0.0576091\pi$
$683$	45.6186	+	12.2235i	1.74555	+	0.467718i	0.761882	+	0.647716i	$0.224276\pi$
$684$	9.95870	−	29.6573i	0.380780	−	1.13398i
$685$	−38.4453	−	38.4453i	−1.46892	−	1.46892i
$686$	−11.3660	−	23.5969i	−0.433955	−	0.900934i
$687$	−22.0463	−	20.1421i	−0.841120	−	0.768470i
$688$	−8.08318	−	15.5016i	−0.308168	−	0.590994i
$689$	−11.6462	−	20.1717i	−0.443683	−	0.768482i
$690$	3.59264	+	15.2943i	0.136769	+	0.582242i
$691$	−49.9545	+	13.3853i	−1.90036	+	0.509200i	−0.903637	+	0.428299i	$0.859113\pi$
$691$	−49.9545	+	13.3853i	−1.90036	+	0.509200i	−0.996722	+	0.0809002i	$0.974220\pi$
$692$	−1.01468	−	9.23563i	−0.0385722	−	0.351086i
$693$	−6.39246	+	3.72000i	−0.242829	+	0.141311i
$694$	−26.2225	−	9.21648i	−0.995392	−	0.349853i
$695$	−37.5611	+	65.0577i	−1.42477	+	2.46778i
$696$	0.193955	+	0.0925580i	0.00735183	+	0.00350840i
$697$	9.10171	−	5.25488i	0.344752	−	0.199043i
$698$	6.07279	+	7.07654i	0.229859	+	0.267851i
$699$	0.0557335	+	1.23480i	0.00210803	+	0.0467043i
$700$	70.0020	−	1.58572i	2.64583	−	0.0599346i
$701$	8.08082	+	8.08082i	0.305208	+	0.305208i	0.843048	−	0.537839i	$-0.180759\pi$
$701$	8.08082	+	8.08082i	0.305208	+	0.305208i	−0.537839	+	0.843048i	$0.680759\pi$
$702$	−21.8028	+	24.5466i	−0.822895	+	0.926453i
$703$	3.16672	−	1.82831i	0.119435	−	0.0689559i
$704$	−5.60968	−	4.90935i	−0.211423	−	0.185028i
$705$	−13.9167	−	43.9128i	−0.524135	−	1.65385i
$706$	−8.21689	−	17.1232i	−0.309247	−	0.644442i
$707$	−11.9138	+	17.0324i	−0.448065	+	0.640570i
$708$	5.78322	+	37.1258i	0.217347	+	1.39527i
$709$	−3.24662	+	0.869931i	−0.121930	+	0.0326709i	−0.319268	−	0.947665i	$-0.603437\pi$
$709$	−3.24662	+	0.869931i	−0.121930	+	0.0326709i	0.197338	+	0.980335i	$0.436770\pi$
$710$	−26.0148	+	4.88491i	−0.976318	+	0.183327i
$711$	2.55370	+	3.62430i	0.0957712	+	0.135922i
$712$	−16.8907	−	15.8036i	−0.633007	−	0.592264i
$713$		−	1.57860i		−	0.0591192i
$714$	−4.95294	−	6.28341i	−0.185359	−	0.235151i
$715$	12.5699	+	12.5699i	0.470088	+	0.470088i
$716$	−13.6999	+	31.1645i	−0.511991	+	1.16467i
$717$	9.70369	+	15.1824i	0.362391	+	0.566996i
$718$	−9.64443	+	14.1037i	−0.359927	+	0.526346i
$719$	−12.6815	+	21.9650i	−0.472941	+	0.819157i	−0.999520	−	0.0309684i	$-0.990141\pi$
$719$	−12.6815	+	21.9650i	−0.472941	+	0.819157i	0.526580	+	0.850126i	$0.323474\pi$
$720$	23.4946	−	45.5356i	0.875592	−	1.69701i
$721$	0.780266	−	0.655371i	0.0290586	−	0.0244073i
$722$	−10.4386	+	5.00912i	−0.388483	+	0.186420i
$723$	17.6443	−	34.0165i	0.656197	−	1.26509i
$724$	7.31662	−	5.36863i	0.271920	−	0.199524i
$725$	0.560704	+	0.150240i	0.0208240	+	0.00557978i
$726$	−24.8055	−	0.771236i	−0.920620	−	0.0286233i
$727$	−20.6747			−0.766783			−0.383392	−	0.923586i	$-0.625244\pi$
$727$	−20.6747			−0.766783			−0.383392	+	0.923586i	$0.625244\pi$
$728$	6.91276	+	32.7114i	0.256204	+	1.21237i
$729$	−26.0173	+	7.21817i	−0.963602	+	0.267340i
$730$	−45.7465	−	53.3077i	−1.69315	−	1.97301i
$731$	−1.39653	+	5.21191i	−0.0516524	+	0.192769i
$732$	−1.00732	+	0.811469i	−0.0372316	+	0.0299928i
$733$	−7.67217	+	2.05575i	−0.283378	+	0.0759309i	−0.397708	−	0.917512i	$-0.630194\pi$
$733$	−7.67217	+	2.05575i	−0.283378	+	0.0759309i	0.114330	+	0.993443i	$0.463528\pi$
$734$	−18.1649	+	8.71675i	−0.670479	+	0.321741i
$735$	−51.3109	+	6.88310i	−1.89263	+	0.253887i
$736$	6.67982	−	5.25163i	0.246221	−	0.193578i
$737$	8.62769	+	4.98120i	0.317805	+	0.183485i
$738$	−31.5290	−	17.6184i	−1.16060	−	0.648543i
$739$	43.8922	+	11.7609i	1.61460	+	0.432631i	0.949410	−	0.314040i	$-0.101683\pi$
$739$	43.8922	+	11.7609i	1.61460	+	0.432631i	0.665193	+	0.746672i	$0.268349\pi$
$740$	5.58102	−	2.17255i	0.205162	−	0.0798644i
$741$	40.3081	−	1.81934i	1.48075	−	0.0668350i
$742$	−15.0871	−	12.3650i	−0.553863	−	0.453932i
$743$	−10.5124			−0.385663			−0.192831	−	0.981232i	$-0.561767\pi$
$743$	−10.5124			−0.385663			−0.192831	+	0.981232i	$0.561767\pi$
$744$	−3.34449	+	3.91435i	−0.122615	+	0.143507i
$745$	−46.3528	−	80.2854i	−1.69824	−	2.94143i
$746$	−51.5834	+	9.68603i	−1.88860	+	0.354631i
$747$	12.7516	+	34.7163i	0.466555	+	1.27020i
$748$	0.251261	+	2.28699i	0.00918702	+	0.0836207i
$749$	0.535471	−	6.15511i	0.0195657	−	0.224903i
$750$	24.8597	−	82.4391i	0.907749	−	3.01025i
$751$	1.16092	−	2.01078i	0.0423627	−	0.0733743i	−0.844067	−	0.536238i	$-0.819845\pi$
$751$	1.16092	−	2.01078i	0.0423627	−	0.0733743i	0.886429	+	0.462864i	$0.153178\pi$
$752$	−18.3572	+	16.8445i	−0.669419	+	0.614256i
$753$	−27.1325	−	5.97325i	−0.988764	−	0.217677i
$754$	−0.0210966	+	0.276371i	−0.000768292	+	0.0100648i
$755$	−7.53320	+	7.53320i	−0.274161	+	0.274161i
$756$	−9.83078	+	25.6779i	−0.357542	+	0.933897i
$757$	1.55860	+	1.55860i	0.0566483	+	0.0566483i	0.734863	−	0.678215i	$-0.237246\pi$
$757$	1.55860	+	1.55860i	0.0566483	+	0.0566483i	−0.678215	+	0.734863i	$0.737246\pi$
$758$	−22.9819	−	26.7805i	−0.834741	−	0.972711i
$759$	−0.521227	+	2.36759i	−0.0189193	+	0.0859381i
$760$	−60.2513	+	18.3109i	−2.18554	+	0.664207i
$761$	−28.1161	−	16.2328i	−1.01921	−	0.588440i	−0.105334	−	0.994437i	$-0.533591\pi$
$761$	−28.1161	−	16.2328i	−1.01921	−	0.588440i	−0.913875	+	0.405997i	$0.866924\pi$
$762$	−15.3864	+	8.25675i	−0.557391	+	0.299110i
$763$	−30.9638	−	21.6585i	−1.12096	−	0.784092i
$764$	3.22046	+	2.58288i	0.116512	+	0.0934453i
$765$	−14.8447	+	5.45258i	−0.536712	+	0.197139i
$766$	−24.6031	+	35.9789i	−0.888947	+	1.29997i
$767$	−41.9677	+	24.2300i	−1.51536	+	0.874896i
$768$	−27.6898	−	1.13003i	−0.999168	−	0.0407765i
$769$			50.0632i			1.80533i	0.430348	+	0.902663i	$0.358391\pi$
$769$			50.0632i			1.80533i	−0.430348	+	0.902663i	$0.641609\pi$
$770$	13.5644	+	6.13517i	0.488828	+	0.221096i
$771$	−2.19195	−	48.5633i	−0.0789410	−	1.74897i
$772$	2.95217	+	7.58379i	0.106251	+	0.272947i
$773$	10.1172	−	37.7579i	0.363890	−	1.35806i	−0.505028	−	0.863103i	$-0.668518\pi$
$773$	10.1172	−	37.7579i	0.363890	−	1.35806i	0.868919	−	0.494955i	$-0.164815\pi$
$774$	17.8421	−	5.04999i	0.641321	−	0.181518i
$775$	−6.95334	+	12.0435i	−0.249771	+	0.432617i
$776$	5.95050	−	25.5799i	0.213611	−	0.918264i
$777$	−2.84769	+	1.48952i	−0.102160	+	0.0534361i
$778$	32.9805	+	11.5917i	1.18241	+	0.415584i
$779$	11.4884	+	42.8754i	0.411615	+	1.53617i
$780$	65.7057	+	7.07526i	2.35264	+	0.253335i
$781$	−3.94531	−	1.05714i	−0.141174	−	0.0378275i
$782$	−2.61490	−	0.199606i	−0.0935086	−	0.00713790i
$783$	−0.137964	+	0.181451i	−0.00493042	+	0.00648454i
$784$	15.0837	+	23.5899i	0.538702	+	0.842496i
$785$			0.144753i			0.00516646i
$786$	−17.3089	−	18.4197i	−0.617387	−	0.657010i
$787$	−11.4687	+	42.8018i	−0.408815	+	1.52572i	0.388093	+	0.921620i	$0.373134\pi$
$787$	−11.4687	+	42.8018i	−0.408815	+	1.52572i	−0.796909	+	0.604100i	$0.793533\pi$
$788$	−2.40079	+	1.76160i	−0.0855245	+	0.0627543i
$789$	11.3218	+	5.87261i	0.403068	+	0.209070i
$790$	2.95920	−	8.41943i	0.105283	−	0.299550i
$791$	−5.49329	+	15.1157i	−0.195319	+	0.537452i
$792$	6.30852	−	4.76645i	0.224163	−	0.169369i
$793$	−1.44478	−	0.834147i	−0.0513058	−	0.0296214i
$794$	−43.4869	+	8.16572i	−1.54329	+	0.289790i
$795$	−32.4882	+	20.7645i	−1.15224	+	0.736443i
$796$	12.0431	+	30.9374i	0.426857	+	1.09655i
$797$	9.72334	−	9.72334i	0.344418	−	0.344418i	−0.513607	−	0.858025i	$-0.671691\pi$
$797$	9.72334	−	9.72334i	0.344418	−	0.344418i	0.858025	+	0.513607i	$0.171691\pi$
$798$	31.0478	−	13.3374i	1.09908	−	0.472139i
$799$	7.68951			0.272035
$800$	−74.0940	+	10.6430i	−2.61962	+	0.376288i
$801$	20.0558	−	14.1314i	0.708637	−	0.499308i
$802$	−22.0830	−	15.1008i	−0.779778	−	0.533229i
$803$	−2.80549	−	10.4702i	−0.0990035	−	0.369486i
$804$	36.5946	−	5.70047i	1.29059	−	0.201040i
$805$	−9.72642	+	13.9052i	−0.342811	+	0.490095i
$806$	−6.26463	−	2.20184i	−0.220662	−	0.0775567i
$807$	34.0625	−	10.7950i	1.19906	−	0.380002i
$808$	10.4647	−	19.6024i	0.368147	−	0.689609i
$809$	−25.1034	−	43.4804i	−0.882589	−	1.52869i	−0.848453	−	0.529271i	$-0.822465\pi$
$809$	−25.1034	−	43.4804i	−0.882589	−	1.52869i	−0.0341362	−	0.999417i	$-0.510868\pi$
$810$	42.2195	+	34.2226i	1.48344	+	1.20246i
$811$	−1.50664	+	1.50664i	−0.0529054	+	0.0529054i	−0.733065	−	0.680159i	$-0.761911\pi$
$811$	−1.50664	+	1.50664i	−0.0529054	+	0.0529054i	0.680159	+	0.733065i	$0.261911\pi$
$812$	0.0651413	+	0.222799i	0.00228601	+	0.00781873i
$813$	37.8713	−	1.70935i	1.32821	−	0.0599496i
$814$	0.921474	+	0.0703400i	0.0322976	+	0.00246541i
$815$	−23.4358	−	40.5921i	−0.820922	−	1.42188i
$816$	6.06108	+	6.03497i	0.212180	+	0.211266i
$817$	−19.7358	−	11.3945i	−0.690469	−	0.398643i
$818$	6.47906	+	13.5018i	0.226535	+	0.472078i
$819$	−35.4618	+	0.121726i	−1.23913	+	0.00425343i
$820$	7.93948	+	72.2656i	0.277259	+	2.52362i
$821$	1.67457	+	6.24959i	0.0584430	+	0.218112i	0.988971	−	0.148108i	$-0.0473183\pi$
$821$	1.67457	+	6.24959i	0.0584430	+	0.218112i	−0.930528	+	0.366220i	$0.880652\pi$
$822$	−26.5134	−	16.4267i	−0.924760	−	0.572947i
$823$	15.3838	−	8.88182i	0.536244	−	0.309601i	−0.207311	−	0.978275i	$-0.566471\pi$
$823$	15.3838	−	8.88182i	0.536244	−	0.309601i	0.743555	+	0.668674i	$0.233138\pi$
$824$	−0.744254	+	0.795452i	−0.0259273	+	0.0277109i
$825$	14.4052	−	15.7670i	0.501524	−	0.548938i
$826$	−25.7255	+	31.3889i	−0.895106	+	1.09216i
$827$	−17.0881	+	17.0881i	−0.594211	+	0.594211i	−0.938766	−	0.344555i	$-0.888030\pi$
$827$	−17.0881	+	17.0881i	−0.594211	+	0.594211i	0.344555	+	0.938766i	$0.388030\pi$
$828$	4.01266	+	8.06989i	0.139450	+	0.280448i
$829$	−7.97274	+	29.7547i	−0.276905	+	1.03342i	0.677650	+	0.735385i	$0.262999\pi$
$829$	−7.97274	+	29.7547i	−0.276905	+	1.03342i	−0.954554	+	0.298037i	$0.903668\pi$
$830$	42.0212	−	61.4506i	1.45858	−	2.13298i
$831$	−1.47089	−	4.64125i	−0.0510248	−	0.161003i
$832$	−11.5238	−	33.8336i	−0.399518	−	1.17297i
$833$	1.49232	−	8.51203i	0.0517060	−	0.294924i
$834$	−12.4418	+	41.2592i	−0.430825	+	1.42869i
$835$	9.24171	+	34.4905i	0.319823	+	1.19359i
$836$	−9.60463	−	1.47492i	−0.332183	−	0.0510111i
$837$	−3.34347	−	4.31768i	−0.115567	−	0.149241i
$838$	10.2416	−	8.78895i	0.353791	−	0.303609i
$839$		−	39.0078i		−	1.34670i	−0.739324	−	0.673350i	$-0.764855\pi$
$839$		−	39.0078i		−	1.34670i	0.739324	−	0.673350i	$-0.235145\pi$
$840$	53.5780	−	13.8730i	1.84862	−	0.478665i
$841$		−	28.9981i		−	0.999934i
$842$	−18.0054	−	20.9814i	−0.620506	−	0.723067i
$843$	−11.0918	+	7.08923i	−0.382022	+	0.244166i
$844$	16.1646	−	11.8609i	0.556410	−	0.408271i
$845$	7.69307	+	28.7109i	0.264650	+	0.987686i
$846$	−13.5325	−	22.6977i	−0.465255	−	0.780364i
$847$	−17.2406	−	20.5262i	−0.592394	−	0.705287i
$848$	17.5954	+	11.1925i	0.604228	+	0.384353i
$849$	−23.8047	+	7.54414i	−0.816976	+	0.258914i
$850$	19.0705	+	13.0408i	0.654112	+	0.447296i
$851$	−0.272638	+	1.01750i	−0.00934593	+	0.0348795i
$852$	−13.8873	+	6.14068i	−0.475772	+	0.210376i
$853$	−31.7259	+	31.7259i	−1.08627	+	1.08627i	−0.0903645	+	0.995909i	$0.528803\pi$
$853$	−31.7259	+	31.7259i	−1.08627	+	1.08627i	−0.995909	+	0.0903645i	$0.971197\pi$
$854$	−1.37864	−	0.226680i	−0.0471761	−	0.00775681i
$855$	−6.01718	−	66.5206i	−0.205783	−	2.27496i
$856$	0.219508	+	6.60129i	0.00750262	+	0.225627i
$857$	−29.1258	+	16.8158i	−0.994919	+	0.574417i	−0.906741	−	0.421688i	$-0.861438\pi$
$857$	−29.1258	+	16.8158i	−0.994919	+	0.574417i	−0.0881781	+	0.996105i	$0.528104\pi$
$858$	8.66869	+	5.37080i	0.295944	+	0.183356i
$859$	−8.49523	−	31.7046i	−0.289853	−	1.08175i	−0.945219	−	0.326436i	$-0.894152\pi$
$859$	−8.49523	−	31.7046i	−0.289853	−	1.08175i	0.655366	−	0.755312i	$-0.272515\pi$
$860$	−29.1171	−	23.3525i	−0.992883	−	0.796313i
$861$	−8.51830	−	38.0702i	−0.290303	−	1.29743i
$862$	−16.6233	+	7.97698i	−0.566192	+	0.271697i
$863$	43.0182	+	24.8366i	1.46436	+	0.845447i	0.999208	−	0.0397850i	$-0.0126673\pi$
$863$	43.0182	+	24.8366i	1.46436	+	0.845447i	0.465149	+	0.885232i	$0.346001\pi$
$864$	7.14726	−	28.5117i	0.243155	−	0.969988i
$865$	−9.91826	−	17.1789i	−0.337231	−	0.584101i
$866$	−1.41685	+	18.5612i	−0.0481466	+	0.630734i
$867$	1.20864	+	26.7778i	0.0410474	+	0.909420i
$868$	−5.55966	+	0.125940i	−0.188707	+	0.00427469i
$869$	0.973762	−	0.973762i	0.0330326	−	0.0330326i
$870$	0.458602	+	0.0142585i	0.0155481	+	0.000483409i
$871$	23.8834	+	41.3672i	0.809257	+	1.40167i
$872$	35.6358	+	19.0241i	1.20678	+	0.644239i
$873$	25.2806	+	11.6981i	0.855620	+	0.395920i
$874$	3.67271	−	10.4495i	0.124231	−	0.353459i
$875$	84.2718	−	39.3467i	2.84891	−	1.33016i
$876$	−32.5404	−	23.7689i	−1.09944	−	0.803077i
$877$	−3.61759	−	13.5010i	−0.122157	−	0.455898i	0.877565	−	0.479458i	$-0.159167\pi$
$877$	−3.61759	−	13.5010i	−0.122157	−	0.455898i	−0.999722	+	0.0235599i	$0.992500\pi$
$878$	3.91059	−	5.71872i	0.131976	−	0.192998i
$879$	−27.0160	−	5.94759i	−0.911227	−	0.200607i
$880$	−15.1820	−	4.77539i	−0.511784	−	0.160978i
$881$	−23.4730			−0.790824			−0.395412	−	0.918504i	$-0.629398\pi$
$881$	−23.4730			−0.790824			−0.395412	+	0.918504i	$0.629398\pi$
$882$	−27.7519	+	10.5750i	−0.934456	+	0.356078i
$883$	27.7398	−	27.7398i	0.933520	−	0.933520i	−0.0644040	−	0.997924i	$-0.520515\pi$
$883$	27.7398	−	27.7398i	0.933520	−	0.933520i	0.997924	+	0.0644040i	$0.0205146\pi$
$884$	−4.43940	+	10.0987i	−0.149313	+	0.339657i
$885$	43.2010	+	67.5923i	1.45219	+	2.27209i
$886$	3.15776	+	16.8168i	0.106087	+	0.564971i
$887$	44.4350	+	25.6546i	1.49198	+	0.861396i	0.999958	−	0.00918553i	$-0.00292388\pi$
$887$	44.4350	+	25.6546i	1.49198	+	0.861396i	0.492024	+	0.870582i	$0.336257\pi$
$888$	2.83176	−	1.94540i	0.0950275	−	0.0652834i
$889$	−17.7266	−	6.44216i	−0.594532	−	0.216063i
$890$	−46.5906	−	16.3753i	−1.56172	−	0.548901i
$891$	3.58892	+	7.57962i	0.120233	+	0.253927i
$892$	8.53070	−	55.5517i	0.285629	−	1.86001i
$893$	−8.40556	+	31.3700i	−0.281281	+	1.04976i
$894$	−36.4180	−	38.7552i	−1.21800	−	1.29617i
$895$			72.6807i			2.42945i
$896$	−19.0285	−	23.1066i	−0.635699	−	0.771937i
$897$	−7.84026	+	8.58146i	−0.261779	+	0.286527i
$898$	0.831327	−	10.8906i	0.0277417	−	0.363425i
$899$	−0.0445319	−	0.0119323i	−0.00148522	−	0.000397964i
$900$	4.93223	−	79.2418i	0.164408	−	2.64139i
$901$	−1.66581	−	6.21689i	−0.0554962	−	0.207114i
$902$	−3.71987	+	10.5837i	−0.123858	+	0.352398i
$903$	16.9131	+	10.7283i	0.562834	+	0.357015i
$904$	3.89558	−	16.7462i	0.129565	−	0.556971i
$905$	9.68744	−	16.7791i	0.322021	−	0.557757i
$906$	−3.21874	+	5.19518i	−0.106936	+	0.172598i
$907$	−6.67964	+	24.9287i	−0.221794	+	0.827745i	0.761870	+	0.647730i	$0.224281\pi$
$907$	−6.67964	+	24.9287i	−0.221794	+	0.827745i	−0.983664	+	0.180015i	$0.942385\pi$
$908$	−7.96348	−	3.50075i	−0.264277	−	0.116176i
$909$	18.0992	+	15.0964i	0.600312	+	0.500717i
$910$	41.6159	+	57.9940i	1.37955	+	1.92248i
$911$		−	34.9864i		−	1.15915i	−0.814918	−	0.579576i	$-0.803218\pi$
$911$		−	34.9864i		−	1.15915i	0.814918	−	0.579576i	$-0.196782\pi$
$912$	−31.2456	+	18.1297i	−1.03465	+	0.600335i
$913$	9.94844	−	5.74373i	0.329245	−	0.190090i
$914$	21.1495	+	14.4625i	0.699562	+	0.478375i
$915$	−1.27157	+	2.45146i	−0.0420367	+	0.0810428i
$916$	3.76569	+	34.2755i	0.124422	+	1.13250i
$917$	2.36618	−	27.1986i	0.0781381	−	0.898177i
$918$	−7.57485	+	4.99239i	−0.250007	+	0.164773i
$919$	−2.02417	−	1.16865i	−0.0667711	−	0.0385503i	0.466243	−	0.884657i	$-0.345607\pi$
$919$	−2.02417	−	1.16865i	−0.0667711	−	0.0385503i	−0.533014	+	0.846106i	$0.678941\pi$
$920$	8.54336	−	16.0033i	0.281666	−	0.527614i
$921$	26.2697	+	5.78330i	0.865616	+	0.190566i
$922$	27.1019	−	23.2577i	0.892554	−	0.765953i
$923$	−13.8479	−	13.8479i	−0.455809	−	0.455809i
$924$	8.37997	+	1.64682i	0.275681	+	0.0541763i
$925$	6.56185	−	6.56185i	0.215752	−	0.215752i
$926$	18.3749	+	1.40263i	0.603836	+	0.0460934i
$927$	−0.665504	−	0.944508i	−0.0218580	−	0.0310217i
$928$	−0.0976556	−	0.228131i	−0.00320570	−	0.00748878i
$929$	6.66719	−	11.5479i	0.218743	−	0.378875i	−0.735681	−	0.677329i	$-0.763138\pi$
$929$	6.66719	−	11.5479i	0.218743	−	0.378875i	0.954424	+	0.298454i	$0.0964709\pi$
$930$	−3.17354	+	10.5240i	−0.104064	+	0.345095i
$931$	33.0942	+	15.3927i	1.08462	+	0.504476i
$932$	0.892980	−	1.11341i	0.0292505	−	0.0364711i
$933$	−3.44928	+	6.64989i	−0.112924	+	0.217707i
$934$	−3.61046	−	19.2277i	−0.118138	−	0.629148i
$935$	2.45603	+	4.25397i	0.0803207	+	0.139120i
$936$	37.6219	−	4.66818i	1.22971	−	0.152584i
$937$	42.9402			1.40280			0.701398	−	0.712769i	$-0.252559\pi$
$937$	42.9402			1.40280			0.701398	+	0.712769i	$0.252559\pi$
$938$	30.9398	+	25.3575i	1.01022	+	0.827950i
$939$	−1.52635	−	33.8168i	−0.0498105	−	1.10357i
$940$	−21.4060	+	48.6942i	−0.698187	+	1.58823i
$941$	33.6529	+	9.01726i	1.09705	+	0.293954i	0.761564	−	0.648090i	$-0.224432\pi$
$941$	33.6529	+	9.01726i	1.09705	+	0.293954i	0.335489	+	0.942044i	$0.391099\pi$
$942$	0.0189890	+	0.0808384i	0.000618695	+	0.00263386i
$943$	−11.0740	−	6.39360i	−0.360621	−	0.208204i
$944$	23.2863	−	36.6076i	0.757903	−	1.19147i
$945$	2.84815	+	58.6331i	0.0926505	+	1.90733i
$946$	−2.49179	−	5.19265i	−0.0810149	−	0.168828i
$947$	−14.5050	+	3.88660i	−0.471349	+	0.126298i	−0.486671	−	0.873585i	$-0.661789\pi$
$947$	−14.5050	+	3.88660i	−0.471349	+	0.126298i	0.0153227	+	0.999883i	$0.495122\pi$
$948$	0.548105	−	5.09008i	0.0178016	−	0.165318i
$949$	13.4515	−	50.2016i	0.436653	−	1.62961i
$950$	−74.0473	+	63.5443i	−2.40241	+	2.06165i
$951$	12.6312	−	13.8253i	0.409593	−	0.448316i
$952$	−0.494375	+	9.22530i	−0.0160228	+	0.298994i
$953$	19.7228			0.638884			0.319442	−	0.947606i	$-0.396505\pi$
$953$	19.7228			0.638884			0.319442	+	0.947606i	$0.396505\pi$
$954$	−15.4193	+	15.8580i	−0.499218	+	0.513420i
$955$	8.51345	+	2.28117i	0.275489	+	0.0738170i
$956$	3.15801	−	20.5649i	0.102137	−	0.665117i
$957$	0.0628491	+	0.0325997i	0.00203162	+	0.00105380i
$958$	−4.04587	−	8.43122i	−0.130716	−	0.272400i
$959$	−5.86619	−	33.1740i	−0.189429	−	1.07124i
$960$	−55.0896	+	21.5820i	−1.77801	+	0.696556i
$961$	−14.9478	+	25.8903i	−0.482186	+	0.835170i
$962$	3.65764	+	2.50117i	0.117927	+	0.0806410i
$963$	−6.90272	−	1.19619i	−0.222437	−	0.0385468i
$964$	−41.2344	+	16.0515i	−1.32807	+	0.516983i
$965$	12.2858	+	12.2858i	0.395494	+	0.395494i
$966$	−3.60767	+	9.04139i	−0.116075	+	0.290902i
$967$		−	15.3169i		−	0.492559i	−0.969199	−	0.246280i	$-0.920792\pi$
$967$		−	15.3169i		−	0.492559i	0.969199	−	0.246280i	$-0.0792082\pi$
$968$	20.9257	+	19.5788i	0.672577	+	0.629287i
$969$	10.8886	+	2.39714i	0.349793	+	0.0770073i
$970$	−10.3478	−	55.1076i	−0.332247	−	1.76940i
$971$	−4.18435	+	1.12119i	−0.134282	+	0.0359808i	−0.325334	−	0.945599i	$-0.605477\pi$
$971$	−4.18435	+	1.12119i	−0.134282	+	0.0359808i	0.191052	+	0.981580i	$0.438810\pi$
$972$	28.0671	+	13.5734i	0.900253	+	0.435367i
$973$	−42.1765	+	19.6923i	−1.35212	+	0.631306i
$974$	−15.3774	+	7.37911i	−0.492723	+	0.236442i
$975$	97.6143	−	30.9357i	3.12616	−	0.990736i
$976$	1.49224	+	0.0641260i	0.0477655	+	0.00205262i
$977$	22.3182	−	12.8854i	0.714021	−	0.412240i	−0.0985269	−	0.995134i	$-0.531413\pi$
$977$	22.3182	−	12.8854i	0.714021	−	0.412240i	0.812548	+	0.582894i	$0.198080\pi$
$978$	−18.4128	−	19.5945i	−0.588778	−	0.626564i
$979$	−5.38851	−	5.38851i	−0.172217	−	0.172217i
$980$	49.7486	+	33.1460i	1.58916	+	1.05881i
$981$	−27.4443	+	32.9031i	−0.876230	+	1.05052i
$982$	20.5637	−	17.6469i	0.656213	−	0.563135i
$983$	20.6727	−	11.9354i	0.659356	−	0.380679i	−0.132676	−	0.991160i	$-0.542357\pi$
$983$	20.6727	−	11.9354i	0.659356	−	0.380679i	0.792032	+	0.610480i	$0.209023\pi$
$984$	13.9138	+	39.3156i	0.443555	+	1.25334i
$985$	−3.17872	+	5.50570i	−0.101282	+	0.175426i
$986$	−0.0253962	+	0.0722567i	−0.000808780	+	0.00230112i
$987$	8.52965	−	27.2387i	0.271502	−	0.867017i
$988$	−36.3457	−	29.1500i	−1.15631	−	0.927386i
$989$	6.34133	−	1.69915i	0.201642	−	0.0540299i
$990$	8.23451	−	14.7360i	0.261710	−	0.468342i
$991$	15.4084	+	26.6881i	0.489464	+	0.847777i	0.999927	−	0.0121232i	$-0.00385902\pi$
$991$	15.4084	+	26.6881i	0.489464	+	0.847777i	−0.510462	+	0.859900i	$0.670526\pi$
$992$	5.88465	−	0.845285i	0.186838	−	0.0268378i
$993$	8.55660	−	9.36552i	0.271535	−	0.297206i
$994$	−14.9436	−	6.75894i	−0.473981	−	0.214381i
$995$	50.1188	+	50.1188i	1.58887	+	1.58887i
$996$	15.4058	−	39.8299i	0.488152	−	1.26206i
$997$	38.4873	+	10.3126i	1.21890	+	0.326605i	0.810250	−	0.586084i	$-0.199331\pi$
$997$	38.4873	+	10.3126i	1.21890	+	0.326605i	0.408655	+	0.912689i	$0.365998\pi$
$998$	0.0453889	+	0.241721i	0.00143676	+	0.00765154i
$999$	1.40936	+	3.36044i	0.0445901	+	0.106320i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.bo.a.5.1	✓	240
3.2	odd	2	inner	336.2.bo.a.5.60	yes	240
7.3	odd	6	inner	336.2.bo.a.101.41	yes	240
16.13	even	4	inner	336.2.bo.a.173.20	yes	240
21.17	even	6	inner	336.2.bo.a.101.20	yes	240
48.29	odd	4	inner	336.2.bo.a.173.41	yes	240
112.45	odd	12	inner	336.2.bo.a.269.60	yes	240
336.269	even	12	inner	336.2.bo.a.269.1	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.bo.a.5.1	✓	240	1.1	even	1	trivial
336.2.bo.a.5.60	yes	240	3.2	odd	2	inner
336.2.bo.a.101.20	yes	240	21.17	even	6	inner
336.2.bo.a.101.41	yes	240	7.3	odd	6	inner
336.2.bo.a.173.20	yes	240	16.13	even	4	inner
336.2.bo.a.173.41	yes	240	48.29	odd	4	inner
336.2.bo.a.269.1	yes	240	336.269	even	12	inner
336.2.bo.a.269.60	yes	240	112.45	odd	12	inner

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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.bo (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41011 - 0.107640i) q^{2} +(-1.45943 + 0.932779i) q^{3} +(1.97683 + 0.303568i) q^{4} +(4.12446 - 1.10515i) q^{5} +(2.15836 - 1.15823i) q^{6} +(2.48663 + 0.903685i) q^{7} +(-2.75487 - 0.640850i) q^{8} +(1.25985 - 2.72264i) q^{9} +O(q^{10})\)	\(q+(-1.41011 - 0.107640i) q^{2} +(-1.45943 + 0.932779i) q^{3} +(1.97683 + 0.303568i) q^{4} +(4.12446 - 1.10515i) q^{5} +(2.15836 - 1.15823i) q^{6} +(2.48663 + 0.903685i) q^{7} +(-2.75487 - 0.640850i) q^{8} +(1.25985 - 2.72264i) q^{9} +(-5.93491 + 1.11442i) q^{10} +(-0.900067 - 0.241172i) q^{11} +(-3.16819 + 1.40091i) q^{12} +(-3.15920 - 3.15920i) q^{13} +(-3.40916 - 1.54196i) q^{14} +(-4.98849 + 5.46009i) q^{15} +(3.81569 + 1.20020i) q^{16} +(-0.617276 - 1.06915i) q^{17} +(-2.06959 + 3.70362i) q^{18} +(5.03645 - 1.34951i) q^{19} +(8.48883 - 0.932628i) q^{20} +(-4.47200 + 1.00062i) q^{21} +(1.24323 + 0.436963i) q^{22} +(-0.751039 + 1.30084i) q^{23} +(4.61830 - 1.63441i) q^{24} +(11.4597 - 6.61626i) q^{25} +(4.11477 + 4.79488i) q^{26} +(0.700977 + 5.14865i) q^{27} +(4.64132 + 2.54129i) q^{28} +(0.0310193 + 0.0310193i) q^{29} +(7.62204 - 7.16238i) q^{30} +(-0.910147 + 0.525473i) q^{31} +(-5.25136 - 2.10314i) q^{32} +(1.53854 - 0.487591i) q^{33} +(0.755344 + 1.57407i) q^{34} +(11.2547 + 0.979120i) q^{35} +(3.31700 - 4.99975i) q^{36} +(0.677396 - 0.181508i) q^{37} +(-7.24722 + 1.36084i) q^{38} +(7.55746 + 1.66378i) q^{39} +(-12.0706 + 0.401374i) q^{40} +8.51301i q^{41} +(6.41372 - 0.929622i) q^{42} +(-3.09050 - 3.09050i) q^{43} +(-1.70606 - 0.749987i) q^{44} +(2.18726 - 12.6218i) q^{45} +(1.19907 - 1.75348i) q^{46} +(-3.11429 + 5.39411i) q^{47} +(-6.68824 + 1.80759i) q^{48} +(5.36671 + 4.49427i) q^{49} +(-16.8716 + 8.09615i) q^{50} +(1.89815 + 0.984567i) q^{51} +(-5.28617 - 7.20423i) q^{52} +(5.03575 + 1.34932i) q^{53} +(-0.434255 - 7.33563i) q^{54} -3.97882 q^{55} +(-6.27123 - 4.08310i) q^{56} +(-6.09153 + 6.66741i) q^{57} +(-0.0404017 - 0.0470795i) q^{58} +(2.80729 - 10.4770i) q^{59} +(-11.5189 + 9.27931i) q^{60} +(0.360681 - 0.0966443i) q^{61} +(1.33997 - 0.643008i) q^{62} +(5.59319 - 5.63172i) q^{63} +(7.17862 + 3.53092i) q^{64} +(-16.5214 - 9.53863i) q^{65} +(-2.22200 + 0.521949i) q^{66} +(-10.3271 - 2.76713i) q^{67} +(-0.895687 - 2.30092i) q^{68} +(-0.117309 - 2.59903i) q^{69} +(-15.7650 - 2.59212i) q^{70} +4.38335 q^{71} +(-5.21552 + 6.69316i) q^{72} +(5.81636 + 10.0742i) q^{73} +(-0.974740 + 0.183031i) q^{74} +(-10.5531 + 20.3453i) q^{75} +(10.3659 - 1.13885i) q^{76} +(-2.02019 - 1.41308i) q^{77} +(-10.4778 - 3.15960i) q^{78} +(-0.738936 + 1.27988i) q^{79} +(17.0641 + 0.733293i) q^{80} +(-5.82558 - 6.86022i) q^{81} +(0.916339 - 12.0043i) q^{82} +(-8.71723 + 8.71723i) q^{83} +(-9.14412 + 0.620499i) q^{84} +(-3.72750 - 3.72750i) q^{85} +(4.02529 + 4.69061i) q^{86} +(-0.0742045 - 0.0163362i) q^{87} +(2.32501 + 1.24121i) q^{88} +(7.08244 + 4.08905i) q^{89} +(-4.44289 + 17.5626i) q^{90} +(-5.00086 - 10.7107i) q^{91} +(-1.87957 + 2.34354i) q^{92} +(0.838140 - 1.61586i) q^{93} +(4.97212 - 7.27108i) q^{94} +(19.2812 - 11.1320i) q^{95} +(9.62574 - 1.82899i) q^{96} +9.28533i q^{97} +(-7.08389 - 6.91509i) q^{98} +(-1.79057 + 2.14672i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 6 q^{3} - 4 q^{4}+O(q^{10}) \) 240 * q - 6 * q^3 - 4 * q^4	\( 240 q - 6 q^{3} - 4 q^{4} - 12 q^{10} - 6 q^{12} - 16 q^{15} - 20 q^{16} - 4 q^{18} - 12 q^{19} + 2 q^{21} - 40 q^{22} - 6 q^{24} - 12 q^{28} + 22 q^{30} - 24 q^{31} - 12 q^{33} - 64 q^{36} - 4 q^{37} + 48 q^{40} - 18 q^{42} - 16 q^{43} - 6 q^{45} + 12 q^{46} - 16 q^{49} - 10 q^{51} - 48 q^{52} - 90 q^{54} - 4 q^{58} - 18 q^{60} - 12 q^{61} - 36 q^{63} + 32 q^{64} - 66 q^{66} - 36 q^{67} - 76 q^{70} - 46 q^{72} + 24 q^{75} - 76 q^{78} - 8 q^{79} - 4 q^{81} + 72 q^{82} - 24 q^{84} + 24 q^{85} + 12 q^{88} - 88 q^{91} - 14 q^{93} + 24 q^{94} + 96 q^{96} + 28 q^{99}+O(q^{100}) \) 240 * q - 6 * q^3 - 4 * q^4 - 12 * q^10 - 6 * q^12 - 16 * q^15 - 20 * q^16 - 4 * q^18 - 12 * q^19 + 2 * q^21 - 40 * q^22 - 6 * q^24 - 12 * q^28 + 22 * q^30 - 24 * q^31 - 12 * q^33 - 64 * q^36 - 4 * q^37 + 48 * q^40 - 18 * q^42 - 16 * q^43 - 6 * q^45 + 12 * q^46 - 16 * q^49 - 10 * q^51 - 48 * q^52 - 90 * q^54 - 4 * q^58 - 18 * q^60 - 12 * q^61 - 36 * q^63 + 32 * q^64 - 66 * q^66 - 36 * q^67 - 76 * q^70 - 46 * q^72 + 24 * q^75 - 76 * q^78 - 8 * q^79 - 4 * q^81 + 72 * q^82 - 24 * q^84 + 24 * q^85 + 12 * q^88 - 88 * q^91 - 14 * q^93 + 24 * q^94 + 96 * q^96 + 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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