LMFDB - Embedded newform 336.2.bo.a.5.60

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			5.60
Character	$\chi$	$=$	336.5
Dual form			336.2.bo.a.269.60

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.41011 + 0.107640i) q^{2} +(0.797510 + 1.53752i) q^{3} +(1.97683 + 0.303568i) q^{4} +(-4.12446 + 1.10515i) q^{5} +(0.959079 + 2.25392i) q^{6} +(2.48663 + 0.903685i) q^{7} +(2.75487 + 0.640850i) q^{8} +(-1.72796 + 2.45238i) q^{9} +O(q^{10})$	\(q+(1.41011 + 0.107640i) q^{2} +(0.797510 + 1.53752i) q^{3} +(1.97683 + 0.303568i) q^{4} +(-4.12446 + 1.10515i) q^{5} +(0.959079 + 2.25392i) q^{6} +(2.48663 + 0.903685i) q^{7} +(2.75487 + 0.640850i) q^{8} +(-1.72796 + 2.45238i) q^{9} +(-5.93491 + 1.11442i) q^{10} +(0.900067 + 0.241172i) q^{11} +(1.10980 + 3.28152i) 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} +(-2.70058 + 3.27213i) q^{18} +(5.03645 - 1.34951i) q^{19} +(-8.48883 + 0.932628i) q^{20} +(0.593678 + 4.54396i) q^{21} +(1.24323 + 0.436963i) q^{22} +(0.751039 - 1.30084i) q^{23} +(1.21171 + 4.74676i) q^{24} +(11.4597 - 6.61626i) q^{25} +(-4.11477 - 4.79488i) q^{26} +(-5.14865 - 0.700977i) q^{27} +(4.64132 + 2.54129i) q^{28} +(-0.0310193 - 0.0310193i) q^{29} +(-6.44660 - 8.23629i) q^{30} +(-0.910147 + 0.525473i) q^{31} +(5.25136 + 2.10314i) q^{32} +(0.347004 + 1.57621i) q^{33} +(0.755344 + 1.57407i) q^{34} +(-11.2547 - 0.979120i) q^{35} +(-4.16034 + 4.32338i) q^{36} +(0.677396 - 0.181508i) q^{37} +(7.24722 - 1.36084i) q^{38} +(2.33785 - 7.37684i) q^{39} +(-12.0706 + 0.401374i) q^{40} -8.51301i q^{41} +(0.348042 + 6.47139i) q^{42} +(-3.09050 - 3.09050i) q^{43} +(1.70606 + 0.749987i) q^{44} +(4.41665 - 12.0244i) q^{45} +(1.19907 - 1.75348i) q^{46} +(3.11429 - 5.39411i) q^{47} +(1.19771 + 6.82389i) q^{48} +(5.36671 + 4.49427i) q^{49} +(16.8716 - 8.09615i) q^{50} +(-1.15156 + 1.80174i) q^{51} +(-5.28617 - 7.20423i) q^{52} +(-5.03575 - 1.34932i) q^{53} +(-7.18472 - 1.54265i) 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} +(-8.20387 - 12.3080i) q^{60} +(0.360681 - 0.0966443i) q^{61} +(-1.33997 + 0.643008i) q^{62} +(-6.51298 + 4.53664i) q^{63} +(7.17862 + 3.53092i) q^{64} +(16.5214 + 9.53863i) q^{65} +(0.319652 + 2.25998i) q^{66} +(-10.3271 - 2.76713i) q^{67} +(0.895687 + 2.30092i) q^{68} +(2.59903 + 0.117309i) q^{69} +(-15.7650 - 2.59212i) q^{70} -4.38335 q^{71} +(-6.33190 + 5.64863i) q^{72} +(5.81636 + 10.0742i) q^{73} +(0.974740 - 0.183031i) q^{74} +(19.3119 + 12.3430i) q^{75} +(10.3659 - 1.13885i) q^{76} +(2.02019 + 1.41308i) q^{77} +(4.09068 - 10.1505i) q^{78} +(-0.738936 + 1.27988i) q^{79} +(-17.0641 - 0.733293i) q^{80} +(-3.02833 - 8.47521i) q^{81} +(0.916339 - 12.0043i) q^{82} +(8.71723 - 8.71723i) q^{83} +(-0.205800 + 9.16284i) q^{84} +(-3.72750 - 3.72750i) q^{85} +(-4.02529 - 4.69061i) q^{86} +(0.0229547 - 0.0724310i) q^{87} +(2.32501 + 1.24121i) q^{88} +(-7.08244 - 4.08905i) q^{89} +(7.52227 - 16.4803i) q^{90} +(-5.00086 - 10.7107i) q^{91} +(1.87957 - 2.34354i) q^{92} +(-1.53378 - 0.980302i) q^{93} +(4.97212 - 7.27108i) q^{94} +(-19.2812 + 11.1320i) q^{95} +(0.954385 + 9.75137i) q^{96} +9.28533i q^{97} +(7.08389 + 6.91509i) q^{98} +(-2.14672 + 1.79057i) 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
$3$	0.797510	+	1.53752i	0.460442	+	0.887690i
$3$	0.797510	+	1.53752i	0.460442	+	0.887690i
$4$	1.97683	+	0.303568i	0.988414	+	0.151784i
$5$	−4.12446	+	1.10515i	−1.84452	+	0.494236i	−0.999199	−	0.0400293i	$-0.987255\pi$
$5$	−4.12446	+	1.10515i	−1.84452	+	0.494236i	−0.845317	+	0.534266i	$0.820588\pi$
$6$	0.959079	+	2.25392i	0.391542	+	0.920160i
$7$	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
$9$	−1.72796	+	2.45238i	−0.575985	+	0.817460i
$10$	−5.93491	+	1.11442i	−1.87678	+	0.352411i
$11$	0.900067	+	0.241172i	0.271380	+	0.0727161i	0.391943	−	0.919990i	$-0.371803\pi$
$11$	0.900067	+	0.241172i	0.271380	+	0.0727161i	−0.120562	+	0.992706i	$0.538470\pi$
$12$	1.10980	+	3.28152i	0.320371	+	0.947292i
$13$	−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	0.931121	−	0.364711i	$-0.118832\pi$
$17$	0.617276	+	1.06915i	0.149711	+	0.259308i	−0.781409	+	0.624019i	$0.785499\pi$
$18$	−2.70058	+	3.27213i	−0.636534	+	0.771249i
$19$	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
$21$	0.593678	+	4.54396i	0.129551	+	0.991573i
$22$	1.24323	+	0.436963i	0.265059	+	0.0931607i
$23$	0.751039	−	1.30084i	0.156602	−	0.271243i	−0.777039	−	0.629453i	$-0.783279\pi$
$23$	0.751039	−	1.30084i	0.156602	−	0.271243i	0.933641	+	0.358209i	$0.116613\pi$
$24$	1.21171	+	4.74676i	0.247340	+	0.968929i
$25$	11.4597	−	6.61626i	2.29194	−	1.32325i
$26$	−4.11477	−	4.79488i	−0.806973	−	0.940354i
$27$	−5.14865	−	0.700977i	−0.990859	−	0.134903i
$28$	4.64132	+	2.54129i	0.877127	+	0.480259i
$29$	−0.0310193	−	0.0310193i	−0.00576014	−	0.00576014i	0.704221	−	0.709981i	$-0.251296\pi$
$29$	−0.0310193	−	0.0310193i	−0.00576014	−	0.00576014i	−0.709981	+	0.704221i	$0.751296\pi$
$30$	−6.44660	−	8.23629i	−1.17698	−	1.50373i
$31$	−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
$33$	0.347004	+	1.57621i	0.0604057	+	0.274383i
$34$	0.755344	+	1.57407i	0.129540	+	0.269950i
$35$	−11.2547	−	0.979120i	−1.90240	−	0.165501i
$36$	−4.16034	+	4.32338i	−0.693389	+	0.720563i
$37$	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
$39$	2.33785	−	7.37684i	0.374356	−	1.18124i
$40$	−12.0706	+	0.401374i	−1.90853	+	0.0634628i
$41$		−	8.51301i		−	1.32951i	−0.747062	−	0.664755i	$-0.768536\pi$
$41$		−	8.51301i		−	1.32951i	0.747062	−	0.664755i	$-0.231464\pi$
$42$	0.348042	+	6.47139i	0.0537041	+	0.998557i
$43$	−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
$45$	4.41665	−	12.0244i	0.658395	−	1.79249i
$46$	1.19907	−	1.75348i	0.176793	−	0.258537i
$47$	3.11429	−	5.39411i	0.454266	−	0.786812i	−0.544379	−	0.838839i	$-0.683235\pi$
$47$	3.11429	−	5.39411i	0.454266	−	0.786812i	0.998646	+	0.0520269i	$0.0165681\pi$
$48$	1.19771	+	6.82389i	0.172875	+	0.984944i
$49$	5.36671	+	4.49427i	0.766672	+	0.642039i
$50$	16.8716	−	8.09615i	2.38601	−	1.14497i
$51$	−1.15156	+	1.80174i	−0.161251	+	0.252293i
$52$	−5.28617	−	7.20423i	−0.733059	−	0.999047i
$53$	−5.03575	−	1.34932i	−0.691713	−	0.185344i	−0.104197	−	0.994557i	$-0.533227\pi$
$53$	−5.03575	−	1.34932i	−0.691713	−	0.185344i	−0.587516	+	0.809213i	$0.699894\pi$
$54$	−7.18472	−	1.54265i	−0.977717	−	0.209929i
$55$	−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	$0.332858\pi$
$59$	−2.80729	+	10.4770i	−0.365479	+	1.36398i	−0.866771	+	0.498707i	$0.833809\pi$
$60$	−8.20387	−	12.3080i	−1.05911	−	1.58896i
$61$	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
$63$	−6.51298	+	4.53664i	−0.820558	+	0.571563i
$64$	7.17862	+	3.53092i	0.897328	+	0.441365i
$65$	16.5214	+	9.53863i	2.04923	+	1.18312i
$66$	0.319652	+	2.25998i	0.0393464	+	0.278185i
$67$	−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
$69$	2.59903	+	0.117309i	0.312886	+	0.0141224i
$70$	−15.7650	−	2.59212i	−1.88428	−	0.309818i
$71$	−4.38335			−0.520208			−0.260104	−	0.965581i	$-0.583757\pi$
$71$	−4.38335			−0.520208			−0.260104	+	0.965581i	$0.583757\pi$
$72$	−6.33190	+	5.64863i	−0.746222	+	0.665697i
$73$	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
$75$	19.3119	+	12.3430i	2.22994	+	1.42525i
$76$	10.3659	−	1.13885i	1.18905	−	0.130635i
$77$	2.02019	+	1.41308i	0.230222	+	0.161036i
$78$	4.09068	−	10.1505i	0.463178	−	1.14932i
$79$	−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
$81$	−3.02833	−	8.47521i	−0.336481	−	0.941690i
$82$	0.916339	−	12.0043i	0.101193	−	1.32565i
$83$	8.71723	−	8.71723i	0.956840	−	0.956840i	−0.0422664	−	0.999106i	$-0.513458\pi$
$83$	8.71723	−	8.71723i	0.956840	−	0.956840i	0.999106	+	0.0422664i	$0.0134578\pi$
$84$	−0.205800	+	9.16284i	−0.0224547	+	0.999748i
$85$	−3.72750	−	3.72750i	−0.404304	−	0.404304i
$86$	−4.02529	−	4.69061i	−0.434058	−	0.505802i
$87$	0.0229547	−	0.0724310i	0.00246100	−	0.00776542i
$88$	2.32501	+	1.24121i	0.247847	+	0.132313i
$89$	−7.08244	−	4.08905i	−0.750737	−	0.433438i	0.0752229	−	0.997167i	$-0.476033\pi$
$89$	−7.08244	−	4.08905i	−0.750737	−	0.433438i	−0.825960	+	0.563728i	$0.809367\pi$
$90$	7.52227	−	16.4803i	0.792917	−	1.73718i
$91$	−5.00086	−	10.7107i	−0.524233	−	1.12279i
$92$	1.87957	−	2.34354i	0.195958	−	0.244331i
$93$	−1.53378	−	0.980302i	−0.159045	−	0.101653i
$94$	4.97212	−	7.27108i	0.512835	−	0.749954i
$95$	−19.2812	+	11.1320i	−1.97821	+	1.14212i
$96$	0.954385	+	9.75137i	0.0974065	+	0.995245i
$97$			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
$99$	−2.14672	+	1.79057i	−0.215754	+	0.179959i
$100$	24.6623	−	9.60041i	2.46623	−	0.960041i
$101$	2.03334	−	7.58853i	0.202325	−	0.755087i	−0.787923	−	0.615773i	$-0.788844\pi$
$101$	2.03334	−	7.58853i	0.202325	−	0.755087i	0.990248	−	0.139314i	$-0.0444897\pi$
$102$	−1.81777	+	2.41669i	−0.179986	+	0.239288i
$103$	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
$105$	−7.47034	−	18.0853i	−0.729030	−	1.76494i
$106$	−6.95572	−	2.44474i	−0.675599	−	0.237454i
$107$	0.604394	+	2.25563i	0.0584290	+	0.218060i	0.988967	−	0.148135i	$-0.0473270\pi$
$107$	0.604394	+	2.25563i	0.0584290	+	0.218060i	−0.930538	+	0.366195i	$0.880660\pi$
$108$	−9.96520	−	2.94868i	−0.958902	−	0.283736i
$109$	−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	$-0.907700\pi$
$113$		−	6.07877i		−	0.571842i	0.958253	−	0.285921i	$-0.0922996\pi$
$114$	7.87205	+	10.0575i	0.737285	+	0.941970i
$115$	−1.66001	+	6.19526i	−0.154797	+	0.577711i
$116$	−0.0519033	−	0.0707362i	−0.00481910	−	0.00656769i
$117$	13.2065	−	2.28860i	1.22094	−	0.211581i
$118$	−5.08633	+	14.4715i	−0.468235	+	1.33221i
$119$	0.568761	+	3.21641i	0.0521383	+	0.294848i
$120$	−10.2435	−	18.2387i	−0.935102	−	1.66496i
$121$	−8.77432	−	5.06586i	−0.797666	−	0.460533i
$122$	0.519003	−	0.0974555i	0.0469884	−	0.00882321i
$123$	13.0890	−	6.78921i	1.18019	−	0.612163i
$124$	−1.95872	+	0.762479i	−0.175898	+	0.0684726i
$125$	−24.8566	+	24.8566i	−2.22324	+	2.22324i
$126$	−9.67234	+	5.69612i	−0.861681	+	0.507451i
$127$	−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
$129$	2.28701	−	7.21642i	0.201360	−	0.635371i
$130$	22.2703	+	15.2289i	1.95323	+	1.33566i
$131$	2.67074	+	9.96733i	0.233343	+	0.870850i	0.978889	+	0.204395i	$0.0655225\pi$
$131$	2.67074	+	9.96733i	0.233343	+	0.870850i	−0.745545	+	0.666455i	$0.767811\pi$
$132$	0.207480	+	3.22124i	0.0180588	+	0.280373i
$133$	13.7433	+	1.19562i	1.19170	+	0.103673i
$134$	−14.2644	−	5.01356i	−1.23226	−	0.433106i
$135$	22.0101	−	2.79886i	1.89433	−	0.240888i
$136$	1.01535	+	3.34096i	0.0870654	+	0.286485i
$137$	6.36656	+	11.0272i	0.543932	+	0.942118i	0.998673	+	0.0514945i	$0.0163984\pi$
$137$	6.36656	+	11.0272i	0.543932	+	0.942118i	−0.454741	+	0.890624i	$0.650268\pi$
$138$	3.65229	+	0.445178i	0.310904	+	0.0378961i
$139$	−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
$141$	10.7773	+	0.486440i	0.907608	+	0.0409656i
$142$	−6.18102	−	0.471823i	−0.518699	−	0.0395945i
$143$	−2.08158	−	3.60541i	−0.174071	−	0.301499i
$144$	−9.53670	+	7.28363i	−0.794725	+	0.606969i
$145$	0.162219	+	0.0936570i	0.0134715	+	0.00777779i
$146$	7.11732	+	14.8318i	0.589034	+	1.22749i
$147$	−2.63005	+	11.8357i	−0.216923	+	0.976189i
$148$	1.39419	−	0.153174i	0.114602	−	0.0125908i
$149$	5.61925	+	20.9713i	0.460347	+	1.71804i	0.671872	+	0.740667i	$0.265490\pi$
$149$	5.61925	+	20.9713i	0.460347	+	1.71804i	−0.211525	+	0.977373i	$0.567843\pi$
$150$	25.9033	+	19.4838i	2.11500	+	1.59084i
$151$	−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
$156$	6.86091	−	13.8731i	0.549312	−	1.11073i
$157$	−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
$159$	−1.94144	−	8.81868i	−0.153966	−	0.699366i
$160$	−23.9833	−	2.87080i	−1.89605	−	0.226956i
$161$	3.04311	−	2.55600i	0.239830	−	0.201441i
$162$	−3.35802	−	12.2770i	−0.263831	−	0.964569i
$163$	−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
$165$	−3.17315	−	6.11753i	−0.247029	−	0.476249i
$166$	13.2306	−	11.3539i	1.02689	−	0.881237i
$167$		−	8.36244i		−	0.647105i	−0.946210	−	0.323552i	$-0.895123\pi$
$167$		−	8.36244i		−	0.647105i	0.946210	−	0.323552i	$-0.104877\pi$
$168$	−1.27649	+	12.8985i	−0.0984831	+	0.995139i
$169$			6.96113i			0.535472i
$170$	−4.85496	−	5.65741i	−0.372359	−	0.433904i
$171$	−5.39325	+	14.6832i	−0.412432	+	1.12285i
$172$	−5.17121	−	7.04757i	−0.394301	−	0.537372i
$173$	1.20237	+	4.48731i	0.0914145	+	0.341164i	0.996451	−	0.0841694i	$-0.0268237\pi$
$173$	1.20237	+	4.48731i	0.0914145	+	0.341164i	−0.905037	+	0.425333i	$0.860157\pi$
$174$	0.0401651	−	0.0996650i	0.00304491	−	0.00755558i
$175$	34.4751	−	6.09627i	2.60607	−	0.460834i
$176$	3.14492	+	2.00050i	0.237057	+	0.150794i
$177$	−18.3474	+	4.03920i	−1.37908	+	0.303605i
$178$	−9.54689	−	6.52837i	−0.715569	−	0.489322i
$179$	4.40547	−	16.4414i	0.329280	−	1.22889i	−0.580659	−	0.814147i	$-0.697205\pi$
$179$	4.40547	−	16.4414i	0.329280	−	1.22889i	0.909939	−	0.414743i	$-0.136128\pi$
$180$	12.3812	−	22.4294i	0.922838	−	1.67179i
$181$	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
$186$	−2.05728	−	1.54743i	−0.150847	−	0.113463i
$187$	0.297739	+	1.11118i	0.0217729	+	0.0812574i
$188$	7.79390	−	9.71783i	0.568428	−	0.708746i
$189$	−12.1694	−	6.39583i	−0.885191	−	0.465229i
$190$	−28.3869	+	13.6220i	−2.05941	+	0.988242i
$191$	−1.78760	−	1.03207i	−0.129346	−	0.0746779i	0.433931	−	0.900946i	$-0.357126\pi$
$191$	−1.78760	−	1.03207i	−0.129346	−	0.0746779i	−0.563277	+	0.826268i	$0.690460\pi$
$192$	0.296155	+	13.8532i	0.0213731	+	0.999772i
$193$	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
$195$	−1.48990	+	33.0092i	−0.106694	+	2.36384i
$196$	9.24473	+	10.5136i	0.660338	+	0.750968i
$197$	1.05279	−	1.05279i	0.0750085	−	0.0750085i	−0.668607	−	0.743616i	$-0.733109\pi$
$197$	1.05279	−	1.05279i	0.0750085	−	0.0750085i	0.743616	+	0.668607i	$0.233109\pi$
$198$	−3.21985	+	2.29383i	−0.228825	+	0.163015i
$199$	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
$201$	−3.98141	−	18.0849i	−0.280827	−	1.27561i
$202$	3.68407	−	10.4818i	0.259210	−	0.737497i
$203$	−0.0491020	−	0.105165i	−0.00344628	−	0.00738116i
$204$	−2.82339	+	3.21214i	−0.197677	+	0.224895i
$205$	9.40812	+	35.1116i	0.657092	+	2.45230i
$206$	0.307447	−	0.449601i	0.0214208	−	0.0313252i
$207$	1.89238	+	4.08962i	0.131530	+	0.284248i
$208$	−8.26286	−	15.8462i	−0.572927	−	1.09874i
$209$	4.85861			0.336077
$210$	−8.58732	−	26.3064i	−0.592581	−	1.81531i
$211$	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
$213$	−3.49577	−	6.73951i	−0.239526	−	0.461784i
$214$	0.609467	+	3.24574i	0.0416623	+	0.221875i
$215$	16.1621	+	9.33120i	1.10225	+	0.636383i
$216$	−13.7347	−	5.23061i	−0.934525	−	0.355898i
$217$	−2.73806	+	0.484174i	−0.185872	+	0.0328679i
$218$	−19.0552	−	6.69739i	−1.29058	−	0.453604i
$219$	−10.8508	+	16.9771i	−0.733226	+	1.14720i
$220$	−7.86544	−	1.20784i	−0.530288	−	0.0814327i
$221$	1.42757	−	5.32777i	0.0960289	−	0.358385i
$222$	1.05878	+	1.35272i	0.0710606	+	0.0907884i
$223$		−	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	0.395533	−	0.918452i	$-0.370560\pi$
$227$	4.20128	+	1.12573i	0.278849	+	0.0747173i	−0.116684	+	0.993169i	$0.537227\pi$
$228$	10.0179	+	15.0295i	0.663451	+	0.995354i
$229$	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
$231$	−0.561526	+	4.23304i	−0.0369457	+	0.278514i
$232$	−0.0655754	−	0.105333i	−0.00430524	−	0.00691544i
$233$	−0.356818	+	0.618027i	−0.0233759	+	0.0404883i	−0.877477	−	0.479619i	$-0.840775\pi$
$233$	−0.356818	+	0.618027i	−0.0233759	+	0.0404883i	0.854101	+	0.520108i	$0.174108\pi$
$234$	18.8690	−	1.80563i	1.23351	−	0.118038i
$235$	−6.88350	+	25.6896i	−0.449030	+	1.67580i
$236$	−8.73001	+	19.8589i	−0.568275	+	1.29271i
$237$	−2.55715	−	0.115419i	−0.166105	−	0.00749726i
$238$	0.455803	+	4.59672i	0.0295453	+	0.297961i
$239$			10.4030i			0.672913i	0.941699	+	0.336457i	$0.109229\pi$
$239$			10.4030i			0.672913i	−0.941699	+	0.336457i	$0.890771\pi$
$240$	−12.4813	−	26.8212i	−0.805665	−	1.73130i
$241$	−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
$243$	10.6157	−	11.4152i	0.680998	−	0.732285i
$244$	0.742343	−	0.0815577i	0.0475236	−	0.00522120i
$245$	−27.1016	−	12.6055i	−1.73146	−	0.805333i
$246$	19.1877	−	8.16465i	1.22336	−	0.520559i
$247$	−20.1746	−	11.6478i	−1.28368	−	0.741131i
$248$	−2.84409	+	0.864344i	−0.180600	+	0.0548859i
$249$	20.3550	+	6.45087i	1.28995	+	0.408807i
$250$	−37.7261	+	32.3750i	−2.38601	+	2.04758i
$251$	−11.3421	−	11.3421i	−0.715904	−	0.715904i	0.251860	−	0.967764i	$-0.418958\pi$
$251$	−11.3421	−	11.3421i	−0.715904	−	0.715904i	−0.967764	+	0.251860i	$0.918958\pi$
$252$	−14.2522	+	6.99103i	−0.897805	+	0.440394i
$253$	0.989711	−	0.989711i	0.0622226	−	0.0622226i
$254$	−10.0523	−	0.767338i	−0.630740	−	0.0481471i
$255$	2.75840	−	8.70383i	0.172738	−	0.545055i
$256$	13.1190	+	9.15921i	0.819939	+	0.572451i
$257$	14.0333	−	24.3064i	0.875373	−	1.51619i	0.0190088	−	0.999819i	$-0.493949\pi$
$257$	14.0333	−	24.3064i	0.875373	−	1.51619i	0.856365	−	0.516372i	$-0.172718\pi$
$258$	4.00172	−	9.92979i	0.249136	−	0.618202i
$259$	1.84846	+	0.160809i	0.114858	+	0.00999220i
$260$	29.7643	+	23.8716i	1.84590	+	1.48045i
$261$	0.129671	−	0.0224711i	0.00802643	−	0.00139093i
$262$	2.69316	+	14.3425i	0.166384	+	0.886084i
$263$	3.68184	+	6.37713i	0.227032	+	0.393231i	0.956927	−	0.290328i	$-0.0937645\pi$
$263$	3.68184	+	6.37713i	0.227032	+	0.393231i	−0.729895	+	0.683559i	$0.760431\pi$
$264$	−0.0541629	+	4.56463i	−0.00333350	+	0.280934i
$265$	22.2609			1.36748
$266$	19.2510	+	3.16529i	1.18035	+	0.194076i
$267$	0.638693	−	14.1505i	0.0390874	−	0.865995i
$268$	−19.5748	−	8.60510i	−1.19572	−	0.525640i
$269$	19.9270	+	5.33942i	1.21497	+	0.325550i	0.808710	−	0.588207i	$-0.200166\pi$
$269$	19.9270	+	5.33942i	1.21497	+	0.325550i	0.406260	+	0.913757i	$0.366833\pi$
$270$	31.3380	−	1.57755i	1.90717	−	0.0960064i
$271$	−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
$273$	12.4797	−	16.2308i	0.755308	−	0.982335i
$274$	7.79060	+	16.2349i	0.470647	+	0.980785i
$275$	11.9102	−	3.19132i	0.718210	−	0.192444i
$276$	5.10222	+	1.02088i	0.307117	+	0.0614499i
$277$	−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	$-0.572791\pi$
$281$	−7.60012			−0.453385			−0.226692	+	0.973966i	$0.572791\pi$
$282$	15.1448	+	1.84600i	0.901858	+	0.109927i
$283$	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
$285$	−32.4927	−	20.7675i	−1.92470	−	1.23016i
$286$	−2.54718	−	5.30808i	−0.150618	−	0.313874i
$287$	7.69308	−	21.1688i	0.454108	−	1.24955i
$288$	−14.2318	+	9.24420i	−0.838618	+	0.544720i
$289$	7.73794	−	13.4025i	0.455173	−	0.788383i
$290$	0.218665	+	0.149528i	0.0128405	+	0.00878058i
$291$	−14.2764	+	7.40514i	−0.836898	+	0.434097i
$292$	8.43972	+	21.6807i	0.493897	+	1.26876i
$293$	−11.2933	−	11.2933i	−0.659764	−	0.659764i	0.295560	−	0.955324i	$-0.404494\pi$
$293$	−11.2933	−	11.2933i	−0.659764	−	0.659764i	−0.955324	+	0.295560i	$0.904494\pi$
$294$	−4.98264	+	16.4065i	−0.290594	+	0.956847i
$295$		−	46.3143i		−	2.69652i
$296$	1.98246	−	0.0659211i	0.115228	−	0.00383158i
$297$	−4.46508	−	1.87264i	−0.259090	−	0.108661i
$298$	5.66642	+	30.1768i	0.328247	+	1.74809i
$299$	−6.48229	+	1.73693i	−0.374881	+	0.100449i
$300$	34.4293	+	30.2625i	1.98778	+	1.74721i
$301$	−4.89211	−	10.4778i	−0.281976	−	0.603930i
$302$	−3.18116	+	1.52653i	−0.183055	+	0.0878422i
$303$	13.2892	−	2.92562i	0.763442	−	0.168072i
$304$	20.8372	+	0.895437i	1.19510	+	0.0513568i
$305$	−1.38081	+	0.797211i	−0.0790649	+	0.0456482i
$306$	−5.16541	−	0.867530i	−0.295287	−	0.0495934i
$307$	−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
$309$	0.666402	+	0.0300786i	0.0379103	+	0.00171111i
$310$	4.81604	−	4.13292i	0.273532	−	0.234734i
$311$	−3.74561	+	2.16253i	−0.212394	+	0.122626i	−0.602424	−	0.798177i	$-0.705798\pi$
$311$	−3.74561	+	2.16253i	−0.212394	+	0.122626i	0.390029	+	0.920802i	$0.372465\pi$
$312$	11.1679	−	18.8240i	0.632260	−	1.06570i
$313$	−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
$315$	21.8489	−	25.9090i	1.23104	−	1.45981i
$316$	−1.84928	+	2.30577i	−0.104030	+	0.129710i
$317$	10.4434	−	2.79830i	0.586559	−	0.157168i	0.0466790	−	0.998910i	$-0.485136\pi$
$317$	10.4434	−	2.79830i	0.586559	−	0.157168i	0.539880	+	0.841742i	$0.318470\pi$
$318$	−1.78841	−	12.6443i	−0.100289	−	0.709057i
$319$	−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
$324$	−3.41369	−	17.6733i	−0.189649	−	0.981852i
$325$	−57.1057	−	15.3014i	−3.16765	−	0.848770i
$326$	−2.86493	−	15.2573i	−0.158674	−	0.845023i
$327$	−5.31858	−	24.1588i	−0.294118	−	1.33599i
$328$	5.45556	−	23.4523i	0.301233	−	1.29493i
$329$	12.6187	−	10.5988i	0.695691	−	0.584333i
$330$	−3.81600	−	8.96796i	−0.210064	−	0.493670i
$331$	−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
$333$	−0.725384	+	1.97487i	−0.0397508	+	0.108222i
$334$	0.900130	−	11.7920i	0.0492529	−	0.645228i
$335$	45.6516			2.49422
$336$	−3.18838	+	18.0509i	−0.173940	+	0.984756i
$337$	−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
$339$	9.34625	−	4.84788i	0.507619	−	0.263301i
$340$	−6.23707	−	8.50017i	−0.338253	−	0.460986i
$341$	−0.945922	+	0.253459i	−0.0512246	+	0.0137256i
$342$	−9.18558	+	20.1244i	−0.496699	+	1.08820i
$343$	9.28363	+	16.0254i	0.501269	+	0.865291i
$344$	−6.53339	−	10.4945i	−0.352257	−	0.565824i
$345$	−10.8492	+	2.38847i	−0.584103	+	0.128591i
$346$	1.21246	+	6.45702i	0.0651824	+	0.347132i
$347$	−18.9843	−	5.08684i	−1.01913	−	0.273076i	−0.289692	−	0.957120i	$-0.593553\pi$
$347$	−18.9843	−	5.08684i	−1.01913	−	0.273076i	−0.729441	+	0.684044i	$0.760220\pi$
$348$	0.0673652	−	0.136215i	0.00361115	−	0.00730191i
$349$	−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	0.630126	−	0.776493i	$-0.283003\pi$
$353$	−6.71494	−	11.6306i	−0.357400	−	0.619035i	−0.987526	+	0.157458i	$0.949670\pi$
$354$	−26.3067	+	3.72081i	−1.39818	+	0.197759i
$355$	18.0790	−	4.84425i	0.959532	−	0.257106i
$356$	−12.7595	−	10.2333i	−0.676250	−	0.542366i
$357$	−4.49172	+	3.43961i	−0.237727	+	0.182043i
$358$	7.98195	−	22.7100i	0.421859	−	1.20026i
$359$	−6.04080	+	10.4630i	−0.318821	+	0.552215i	−0.980242	−	0.197800i	$-0.936620\pi$
$359$	−6.04080	+	10.4630i	−0.318821	+	0.552215i	0.661421	+	0.750015i	$0.269954\pi$
$360$	19.8731	−	30.2952i	1.04741	−	1.59670i
$361$	7.09017	−	4.09351i	0.373167	−	0.215448i
$362$	4.86969	−	4.17896i	0.255945	−	0.219642i
$363$	0.791267	−	17.5308i	0.0415307	−	0.920128i
$364$	−6.63441	−	22.6913i	−0.347737	−	1.18935i
$365$	−35.1228	−	35.1228i	−1.83841	−	1.83841i
$366$	0.563750	+	0.720258i	0.0294677	+	0.0376485i
$367$	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
$369$	20.8771	+	14.7101i	1.08682	+	0.765778i
$370$	−3.81800	+	1.83214i	−0.198489	+	0.0952482i
$371$	−11.3027	−	7.90601i	−0.586807	−	0.410459i
$372$	−2.73443	−	2.40349i	−0.141773	−	0.124615i
$373$	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
$375$	−58.0410	−	18.3942i	−2.99722	−	0.949873i
$376$	12.0363	−	12.8643i	0.620724	−	0.663425i
$377$			0.195992i			0.0100941i
$378$	−16.4717	−	10.3287i	−0.847213	−	0.531253i
$379$	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
$381$	−5.68526	−	10.9606i	−0.291265	−	0.561530i
$382$	−2.40962	−	1.64775i	−0.123287	−	0.0843061i
$383$	−15.4102	+	26.6912i	−0.787424	+	1.36386i	0.140117	+	0.990135i	$0.455252\pi$
$383$	−15.4102	+	26.6912i	−0.787424	+	1.36386i	−0.927540	+	0.373723i	$0.878081\pi$
$384$	−1.07355	+	19.5665i	−0.0547843	+	0.998498i
$385$	−9.89388	−	3.59560i	−0.504239	−	0.183249i
$386$	2.48961	+	5.18811i	0.126718	+	0.264068i
$387$	12.9193	−	2.23883i	0.656727	−	0.113806i
$388$	−2.81873	+	18.3555i	−0.143099	+	0.931859i
$389$	23.8769	+	6.39781i	1.21061	+	0.324382i	0.807001	−	0.590550i	$-0.201089\pi$
$389$	23.8769	+	6.39781i	1.21061	+	0.324382i	0.403608	+	0.914932i	$0.367756\pi$
$390$	−5.65402	+	46.3862i	−0.286302	+	2.34886i
$391$	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
$396$	−4.78726	+	2.88797i	−0.240569	+	0.145126i
$397$	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
$399$	9.12216	+	22.0842i	0.456679	+	1.10559i
$400$	51.6676	−	11.4917i	2.58338	−	0.574583i
$401$	−16.3825	−	9.45842i	−0.818101	−	0.472331i	0.0316601	−	0.999499i	$-0.489921\pi$
$401$	−16.3825	−	9.45842i	−0.818101	−	0.472331i	−0.849761	+	0.527168i	$0.823254\pi$
$402$	−3.66757	−	25.9303i	−0.182922	−	1.29329i
$403$	4.53542	+	1.21526i	0.225925	+	0.0605365i
$404$	6.32320	−	14.3840i	0.314591	−	0.715629i
$405$	21.8566	+	31.6089i	1.08606	+	1.57066i
$406$	−0.0579193	−	0.153580i	−0.00287448	−	0.00762205i
$407$	0.653476			0.0323916
$408$	−4.32705	+	4.22557i	−0.214221	+	0.209197i
$409$	−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
$411$	−11.8772	+	18.5830i	−0.585859	+	0.916634i
$412$	0.481929	−	0.600894i	0.0237429	−	0.0296039i
$413$	−16.4486	+	23.5155i	−0.809382	+	1.15712i
$414$	2.22827	+	5.97052i	0.109513	+	0.293435i
$415$	−26.3201	+	45.5877i	−1.29200	+	2.23781i
$416$	−9.94587	−	23.2344i	−0.487637	−	1.13916i
$417$	−29.0484	−	9.20596i	−1.42251	−	0.450818i
$418$	6.85118	+	0.522979i	0.335102	+	0.0255798i
$419$	6.74790	−	6.74790i	0.329656	−	0.329656i	−0.522799	−	0.852456i	$-0.675112\pi$
$419$	6.74790	−	6.74790i	0.329656	−	0.329656i	0.852456	+	0.522799i	$0.175112\pi$
$420$	−9.27746	−	38.0192i	−0.452694	−	1.85515i
$421$	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
$423$	7.84705	+	16.9582i	0.381537	+	0.824537i
$424$	−13.0081	−	6.94437i	−0.631730	−	0.337248i
$425$	14.1476	+	8.16812i	0.686259	+	0.396212i
$426$	−4.20398	−	9.87974i	−0.203684	−	0.478675i
$427$	0.984219	+	0.0856234i	0.0476297	+	0.00414361i
$428$	0.510046	+	4.64246i	0.0246540	+	0.224402i
$429$	3.88331	−	6.07583i	0.187488	−	0.293344i
$430$	21.7860	+	14.8977i	1.05061	+	0.718432i
$431$	−11.2910	+	6.51888i	−0.543870	+	0.314003i	−0.746646	−	0.665222i	$-0.768337\pi$
$431$	−11.2910	+	6.51888i	−0.543870	+	0.314003i	0.202776	+	0.979225i	$0.435004\pi$
$432$	−18.8044	−	8.85414i	−0.904725	−	0.425995i
$433$		−	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
$435$	−0.0146288	+	0.324107i	−0.000701399	+	0.0155398i
$436$	−26.1491	−	11.4952i	−1.25231	−	0.550518i
$437$	2.02707	−	7.56514i	0.0969681	−	0.361890i
$438$	−17.1282	+	22.7716i	−0.818416	+	1.08807i
$439$	−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
$441$	−20.2951	+	5.39530i	−0.966433	+	0.256919i
$442$	2.58651	−	7.35908i	0.123028	−	0.350036i
$443$	3.13148	+	11.6868i	0.148781	+	0.555258i	0.999558	+	0.0297311i	$0.00946509\pi$
$443$	3.13148	+	11.6868i	0.148781	+	0.555258i	−0.850777	+	0.525527i	$0.823868\pi$
$444$	1.34739	+	2.02145i	0.0639444	+	0.0959337i
$445$	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	$-0.941665\pi$
$449$		−	7.72323i		−	0.364482i	0.983254	−	0.182241i	$-0.0583351\pi$
$450$	−9.29861	+	55.3654i	−0.438341	+	2.60995i
$451$	2.05310	−	7.66228i	0.0966768	−	0.360803i
$452$	1.84532	−	12.0167i	0.0867965	−	0.565217i
$453$	−3.64127	−	2.32729i	−0.171082	−	0.109346i
$454$	5.80310	+	2.03963i	0.272353	+	0.0957246i
$455$	32.4628	+	38.6492i	1.52188	+	1.81190i
$456$	12.5086	+	22.2716i	0.585767	+	1.04296i
$457$	−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
$459$	−2.42869	−	5.93739i	−0.113361	−	0.277134i
$460$	−5.16225	+	11.7430i	−0.240691	+	0.547522i
$461$	17.8566	−	17.8566i	0.831666	−	0.831666i	−0.156079	−	0.987745i	$-0.549885\pi$
$461$	17.8566	−	17.8566i	0.831666	−	0.831666i	0.987745	+	0.156079i	$0.0498854\pi$
$462$	−1.24746	+	5.90862i	−0.0580370	+	0.274894i
$463$	−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
$465$	7.40939	+	2.34817i	0.343602	+	0.108894i
$466$	−0.569677	+	0.833078i	−0.0263898	+	0.0385916i
$467$	−3.58040	−	13.3623i	−0.165681	−	0.618331i	−0.997952	−	0.0639622i	$-0.979626\pi$
$467$	−3.58040	−	13.3623i	−0.165681	−	0.618331i	0.832271	−	0.554369i	$-0.187040\pi$
$468$	26.8018	−	0.515088i	1.23891	−	0.0238100i
$469$	−23.1790	−	16.2132i	−1.07031	−	0.748658i
$470$	−12.4717	+	35.4842i	−0.575277	+	1.63676i
$471$	−0.0573440	+	0.0126243i	−0.00264227	+	0.000581699i
$472$	−14.4479	+	27.0636i	−0.665018	+	1.24570i
$473$	−2.03632	−	3.52700i	−0.0936299	−	0.162172i
$474$	−3.59344	−	0.438004i	−0.165052	−	0.0201182i
$475$	48.7875	−	48.7875i	2.23852	−	2.23852i
$476$	0.147943	+	6.53095i	0.00678093	+	0.299346i
$477$	12.0106	−	10.0180i	0.549928	−	0.458692i
$478$	−1.11977	+	14.6694i	−0.0512173	+	0.670961i
$479$	−3.30633	−	5.72673i	−0.151070	−	0.261661i	0.780551	−	0.625092i	$-0.214939\pi$
$479$	−3.30633	−	5.72673i	−0.151070	−	0.261661i	−0.931621	+	0.363431i	$0.881605\pi$
$480$	−14.7130	−	39.1644i	−0.671554	−	1.78760i
$481$	−2.71345	−	1.56661i	−0.123723	−	0.0714313i
$482$	−28.2086	+	13.5364i	−1.28487	+	0.616566i
$483$	6.35682	+	2.64041i	0.289245	+	0.120143i
$484$	−15.8075	−	12.6779i	−0.718522	−	0.576270i
$485$	−10.2616	−	38.2970i	−0.465957	−	1.73898i
$486$	16.1981	−	14.9540i	0.734759	−	0.678328i
$487$	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	−0.331875	−	0.943323i	$-0.607681\pi$
$491$	13.5488	−	13.5488i	0.611448	−	0.611448i	0.943323	+	0.331875i	$0.107681\pi$
$492$	27.9356	−	9.44771i	1.25943	−	0.425936i
$493$	0.0140169	−	0.0523118i	0.000631289	−	0.00235600i
$494$	−27.1946	−	18.5963i	−1.22354	−	0.836685i
$495$	6.87523	−	9.75758i	0.309019	−	0.438571i
$496$	−4.10351	+	0.912684i	−0.184253	+	0.0409807i
$497$	−10.8998	−	3.96117i	−0.488923	−	0.177683i
$498$	28.0085	+	11.2874i	1.25509	+	0.505803i
$499$	−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
$501$	12.8574	−	6.66912i	0.574428	−	0.297955i
$502$	−14.7727	−	17.2144i	−0.659338	−	0.768317i
$503$			26.1076i			1.16408i	0.813160	+	0.582040i	$0.197745\pi$
$503$			26.1076i			1.16408i	−0.813160	+	0.582040i	$0.802255\pi$
$504$	−20.8497	+	8.32403i	−0.928720	+	0.370782i
$505$			33.5457i			1.49277i
$506$	1.50213	−	1.28907i	0.0667780	−	0.0573062i
$507$	−10.7029	+	5.55157i	−0.475333	+	0.246554i
$508$	−14.0923	−	2.16406i	−0.625246	−	0.0960148i
$509$	5.36218	+	20.0119i	0.237675	+	0.887014i	0.976925	+	0.213583i	$0.0685134\pi$
$509$	5.36218	+	20.0119i	0.237675	+	0.887014i	−0.739250	+	0.673431i	$0.764820\pi$
$510$	4.82653	−	11.9765i	0.213722	−	0.530327i
$511$	5.35923	+	30.3071i	0.237078	+	1.34071i
$512$	17.5134	+	14.3276i	0.773990	+	0.633198i
$513$	−26.8769	+	3.41774i	−1.18664	+	0.150897i
$514$	22.4049	−	32.7642i	0.988236	−	1.44517i
$515$	−0.425635	+	1.58849i	−0.0187557	+	0.0699973i
$516$	6.71171	−	13.5714i	0.295466	−	0.597446i
$517$	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	−0.190909	−	0.981608i	$-0.561143\pi$
$521$	12.8675	−	7.42904i	0.563734	−	0.325472i	0.754643	+	0.656136i	$0.227810\pi$
$522$	0.185269	−	0.0177290i	0.00810902	−	0.000775977i
$523$	−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
$525$	36.8674	+	48.1445i	1.60903	+	2.10120i
$526$	4.50537	+	9.38878i	0.196444	+	0.409370i
$527$	−1.12362	−	0.648724i	−0.0489458	−	0.0282588i
$528$	−0.567712	+	6.43081i	−0.0247065	+	0.279865i
$529$	10.3719	+	17.9646i	0.450951	+	0.781071i
$530$	31.3904	+	2.39616i	1.36351	+	0.104083i
$531$	−20.8426	−	24.9883i	−0.904492	−	1.08440i
$532$	26.8053	+	6.53558i	1.16216	+	0.283353i
$533$	−26.8943	+	26.8943i	−1.16492	+	1.16492i
$534$	2.42378	−	19.8850i	0.104887	−	0.860508i
$535$	−4.98560	−	8.63531i	−0.215546	−	0.373337i
$536$	−26.6764	−	14.2412i	−1.15224	−	0.615125i
$537$	28.7925	−	6.33869i	1.24249	−	0.273535i
$538$	27.5246	+	9.67412i	1.18667	+	0.417081i
$539$	3.74650	+	5.33944i	0.161373	+	0.229986i
$540$	44.3598	+	1.14869i	1.90894	+	0.0494319i
$541$	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
$543$	7.49193	+	2.37433i	0.321509	+	0.101892i
$544$	0.992960	+	6.91272i	0.0425728	+	0.296381i
$545$	60.9840			2.61227
$546$	19.3449	−	21.5440i	0.827885	−	0.921997i
$547$	−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
$549$	−0.386233	+	1.05152i	−0.0164840	+	0.0448780i
$550$	17.1382	−	3.21811i	0.730774	−	0.137221i
$551$	−0.198088	−	0.114366i	−0.00843883	−	0.00487216i
$552$	7.08481	+	1.98876i	0.301549	+	0.0846472i
$553$	−2.99407	+	2.51482i	−0.127321	+	0.106941i
$554$	−1.31817	+	3.75041i	−0.0560035	+	0.159340i
$555$	−4.37023	−	2.79319i	−0.185506	−	0.118564i
$556$	−28.3687	+	20.8158i	−1.20310	+	0.882786i
$557$	−5.48140	+	20.4569i	−0.232254	+	0.866785i	0.747113	+	0.664697i	$0.231439\pi$
$557$	−5.48140	+	20.4569i	−0.232254	+	0.866785i	−0.979367	+	0.202088i	$0.935227\pi$
$558$	0.738510	−	4.39720i	0.0312636	−	0.186149i
$559$			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	0.148711	−	0.988881i	$-0.452488\pi$
$563$	−5.14751	−	1.37927i	−0.216942	−	0.0581294i	−0.365653	+	0.930751i	$0.619154\pi$
$564$	21.1571	+	4.23324i	0.890875	+	0.178251i
$565$	6.71793	+	25.0716i	0.282625	+	1.05477i
$566$	19.2357	+	6.76080i	0.808535	+	0.284178i
$567$	0.128564	−	23.8114i	0.00539916	−	0.999985i
$568$	−12.0756	−	2.80907i	−0.506680	−	0.117866i
$569$	−12.4010	+	21.4791i	−0.519876	+	0.900451i	0.479857	+	0.877347i	$0.340688\pi$
$569$	−12.4010	+	21.4791i	−0.519876	+	0.900451i	−0.999733	+	0.0231046i	$0.992645\pi$
$570$	−43.5830	−	32.7819i	−1.82549	−	1.37308i
$571$	−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
$573$	0.161205	−	3.57155i	0.00673444	−	0.149204i
$574$	13.1267	−	29.0222i	0.547898	−	1.21136i
$575$		−	19.8763i		−	0.828898i
$576$	−21.0635	+	11.5034i	−0.877646	+	0.479310i
$577$	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
$579$	−3.79554	+	5.93850i	−0.157737	+	0.246796i
$580$	0.292247	+	0.234388i	0.0121349	+	0.00973243i
$581$	29.5542	−	13.7989i	1.22611	−	0.572476i
$582$	−20.9284	+	8.90536i	−0.867511	+	0.369139i
$583$	−4.20709	−	2.42896i	−0.174240	−	0.100597i
$584$	9.56724	+	31.4806i	0.395895	+	1.30268i
$585$	−51.9406	+	24.0344i	−2.14748	+	0.993700i
$586$	−14.7093	−	17.1405i	−0.607634	−	0.708067i
$587$	−17.0199	−	17.0199i	−0.702486	−	0.702486i	0.262457	−	0.964944i	$-0.415467\pi$
$587$	−17.0199	−	17.0199i	−0.702486	−	0.702486i	−0.964944	+	0.262457i	$0.915467\pi$
$588$	−8.79207	+	22.5987i	−0.362579	+	0.931953i
$589$	−3.87478	+	3.87478i	−0.159657	+	0.159657i
$590$	4.98526	−	65.3083i	0.205240	−	2.68870i
$591$	2.45831	+	0.779082i	0.101121	+	0.0320472i
$592$	2.80258	+	0.120435i	0.115185	+	0.00494985i
$593$	−18.9683	+	32.8540i	−0.778934	+	1.34915i	0.153622	+	0.988130i	$0.450906\pi$
$593$	−18.9683	+	32.8540i	−0.778934	+	1.34915i	−0.932556	+	0.361024i	$0.882427\pi$
$594$	−6.09468	−	3.12125i	−0.250068	−	0.128066i
$595$	−5.90044	−	12.6374i	−0.241895	−	0.518083i
$596$	4.74207	+	43.1626i	0.194243	+	1.76801i
$597$	−15.4836	+	24.2256i	−0.633700	+	0.991486i
$598$	−9.32772	+	1.75151i	−0.381439	+	0.0716244i
$599$	5.47198	+	9.47774i	0.223579	+	0.387250i	0.955892	−	0.293718i	$-0.0948926\pi$
$599$	5.47198	+	9.47774i	0.223579	+	0.387250i	−0.732313	+	0.680968i	$0.761559\pi$
$600$	45.2917	+	46.3795i	1.84903	+	1.89343i
$601$	−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
$603$	24.6308	−	20.5444i	1.00304	−	0.836632i
$604$	−4.65010	+	1.81016i	−0.189210	+	0.0736546i
$605$	41.7879	+	11.1970i	1.69892	+	0.455224i
$606$	19.0541	−	2.69501i	0.774020	−	0.109477i
$607$	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
$609$	0.122535	−	0.159366i	0.00496536	−	0.00645783i
$610$	−2.03291	+	0.975526i	−0.0823100	+	0.0394979i
$611$	−26.8798	+	7.20242i	−1.08744	+	0.291379i
$612$	−7.19043	−	1.77932i	−0.290656	−	0.0719246i
$613$	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	$-0.401177\pi$
$617$	15.1768			0.610995			0.305497	+	0.952193i	$0.401177\pi$
$618$	0.936464	+	0.114146i	0.0376701	+	0.00459161i
$619$	−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
$621$	−4.77869	+	6.17110i	−0.191762	+	0.247638i
$622$	−5.51451	+	2.64623i	−0.221112	+	0.106104i
$623$	−13.9162	−	16.5683i	−0.557542	−	0.663794i
$624$	17.7742	−	25.3419i	0.711539	−	1.01449i
$625$	41.9686	−	72.6917i	1.67874	−	2.90767i
$626$	−15.6015	+	22.8151i	−0.623560	+	0.911876i
$627$	3.87479	+	7.47022i	0.154744	+	0.298332i
$628$	−0.0272852	+	0.0620682i	−0.00108880	+	0.00247679i
$629$	0.612199	+	0.612199i	0.0244100	+	0.0244100i
$630$	33.5982	−	34.1828i	1.33858	−	1.36187i
$631$			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
$633$	16.5519	+	5.24561i	0.657881	+	0.208494i
$634$	15.0275	−	2.82179i	0.596820	−	0.112067i
$635$	29.4023	−	7.87832i	1.16679	−	0.312642i
$636$	−1.16082	−	18.0224i	−0.0460296	−	0.714633i
$637$	−2.75620	−	31.1528i	−0.109205	−	1.23432i
$638$	−0.0250100	−	0.0521185i	−0.000990155	−	0.00206339i
$639$	7.57424	−	10.7496i	0.299632	−	0.425249i
$640$	−46.5394	−	12.9556i	−1.83963	−	0.512117i
$641$	−6.60295	+	3.81222i	−0.260801	+	0.150573i	−0.624700	−	0.780865i	$-0.714779\pi$
$641$	−6.60295	+	3.81222i	−0.260801	+	0.150573i	0.363899	+	0.931438i	$0.381445\pi$
$642$	−4.50435	+	3.52558i	−0.177773	+	0.139144i
$643$	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
$645$	−1.45750	+	32.2913i	−0.0573888	+	1.27147i
$646$	5.92848	+	6.90837i	0.233253	+	0.271806i
$647$	−29.6179	+	17.0999i	−1.16440	+	0.672266i	−0.952354	−	0.304994i	$-0.901345\pi$
$647$	−29.6179	+	17.0999i	−1.16440	+	0.672266i	−0.212044	+	0.977260i	$0.568012\pi$
$648$	−2.91133	−	25.2888i	−0.114368	−	0.993438i
$649$	−5.05350	+	8.75293i	−0.198367	+	0.343582i
$650$	−78.8783	−	27.7235i	−3.09386	−	1.08741i
$651$	−2.92806	−	3.82370i	−0.114760	−	0.149863i
$652$	−2.39758	−	21.8229i	−0.0938963	−	0.854649i
$653$	34.2556	−	9.17876i	1.34053	−	0.359193i	0.483896	−	0.875125i	$-0.339221\pi$
$653$	34.2556	−	9.17876i	1.34053	−	0.359193i	0.856629	+	0.515933i	$0.172555\pi$
$654$	−4.89935	−	34.6391i	−0.191580	−	1.35450i
$655$	−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	0.862734	−	0.505658i	$-0.168750\pi$
$659$	9.16650	+	9.16650i	0.357076	+	0.357076i	−0.505658	+	0.862734i	$0.668750\pi$
$660$	−4.41568	−	13.0566i	−0.171880	−	0.508226i
$661$	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
$663$	9.33007	−	2.05402i	0.362350	−	0.0797717i
$664$	29.6013	−	18.4284i	1.14875	−	0.715161i
$665$	−58.0052	+	10.2571i	−2.24935	+	0.397754i
$666$	−1.23545	+	2.70670i	−0.0478726	+	0.104883i
$667$	−0.0636477	+	0.0170544i	−0.00246445	+	0.000660347i
$668$	2.53857	−	16.5311i	0.0982202	−	0.639607i
$669$	43.2066	−	22.4112i	1.67046	−	0.866466i
$670$	64.3739	+	4.91393i	2.48698	+	0.189842i
$671$	0.347945			0.0134323
$672$	−6.43896	+	25.1106i	−0.248388	+	0.968661i
$673$	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
$675$	−63.6399	+	26.0319i	−2.44950	+	1.00197i
$676$	−2.11318	+	13.7610i	−0.0812761	+	0.529268i
$677$	4.72337	−	1.26562i	0.181534	−	0.0486419i	−0.166907	−	0.985973i	$-0.553378\pi$
$677$	4.72337	−	1.26562i	0.181534	−	0.0486419i	0.348441	+	0.937331i	$0.386711\pi$
$678$	13.7011	−	5.83002i	0.526187	−	0.223900i
$679$	−8.39102	+	23.0892i	−0.322018	+	0.886083i
$680$	−7.88001	−	12.6575i	−0.302185	−	0.485395i
$681$	1.61973	+	7.35735i	0.0620681	+	0.281934i
$682$	−1.36114	+	0.255587i	−0.0521207	+	0.00978692i
$683$	−45.6186	−	12.2235i	−1.74555	−	0.467718i	−0.761882	−	0.647716i	$-0.775724\pi$
$683$	−45.6186	−	12.2235i	−1.74555	−	0.467718i	−0.983667	+	0.179998i	$0.942391\pi$
$684$	−15.1189	+	27.3889i	−0.578084	+	1.04724i
$685$	−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
$690$	−15.5557	+	2.20020i	−0.592196	+	0.0837601i
$691$	−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
$693$	−6.95623	+	2.51253i	−0.264245	+	0.0954433i
$694$	−26.2225	−	9.21648i	−0.995392	−	0.349853i
$695$	37.5611	−	65.0577i	1.42477	−	2.46778i
$696$	0.109655	−	0.184828i	0.00415645	−	0.00700587i
$697$	9.10171	−	5.25488i	0.344752	−	0.199043i
$698$	−6.07279	−	7.07654i	−0.229859	−	0.267851i
$699$	−1.23480	−	0.0557335i	−0.0467043	−	0.00210803i
$700$	70.0020	−	1.58572i	2.64583	−	0.0599346i
$701$	−8.08082	−	8.08082i	−0.305208	−	0.305208i	0.537839	−	0.843048i	$-0.319241\pi$
$701$	−8.08082	−	8.08082i	−0.305208	−	0.305208i	−0.843048	+	0.537839i	$0.819241\pi$
$702$	17.8244	+	27.5716i	0.672740	+	1.04062i
$703$	3.16672	−	1.82831i	0.119435	−	0.0689559i
$704$	5.60968	+	4.90935i	0.211423	+	0.185028i
$705$	−44.9880	+	9.90414i	−1.69434	+	0.373011i
$706$	−8.21689	−	17.1232i	−0.309247	−	0.644442i
$707$	11.9138	−	17.0324i	0.448065	−	0.640570i
$708$	−37.4959	+	2.41511i	−1.40918	+	0.0907655i
$709$	−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
$711$	−1.86189	−	4.02372i	−0.0698263	−	0.150901i
$712$	−16.8907	−	15.8036i	−0.633007	−	0.592264i
$713$			1.57860i			0.0591192i
$714$	−6.70406	+	4.36674i	−0.250893	+	0.163421i
$715$	12.5699	+	12.5699i	0.470088	+	0.470088i
$716$	13.6999	−	31.1645i	0.511991	−	1.16467i
$717$	−15.9948	+	8.29648i	−0.597338	+	0.309838i
$718$	−9.64443	+	14.1037i	−0.359927	+	0.526346i
$719$	12.6815	−	21.9650i	0.472941	−	0.819157i	−0.526580	−	0.850126i	$-0.676526\pi$
$719$	12.6815	−	21.9650i	0.472941	−	0.819157i	0.999520	+	0.0309684i	$0.00985912\pi$
$720$	31.2843	−	40.5805i	1.16590	−	1.51235i
$721$	0.780266	−	0.655371i	0.0290586	−	0.0244073i
$722$	10.4386	−	5.00912i	0.388483	−	0.186420i
$723$	−32.2886	−	20.6370i	−1.20083	−	0.767498i
$724$	7.31662	−	5.36863i	0.271920	−	0.199524i
$725$	−0.560704	−	0.150240i	−0.0208240	−	0.00557978i
$726$	3.00278	−	24.6352i	0.111444	−	0.914298i
$727$	−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
$732$	0.717422	+	1.07633i	0.0265167	+	0.0397822i
$733$	−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
$735$	−2.23261	−	51.7223i	−0.0823511	−	1.90781i
$736$	6.67982	−	5.25163i	0.246221	−	0.193578i
$737$	−8.62769	−	4.98120i	−0.317805	−	0.183485i
$738$	27.8557	+	22.9901i	1.02538	+	0.846278i
$739$	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
$741$	1.81934	−	40.3081i	0.0668350	−	1.48075i
$742$	−15.0871	−	12.3650i	−0.553863	−	0.453932i
$743$	10.5124			0.385663			0.192831	−	0.981232i	$-0.438233\pi$
$743$	10.5124			0.385663			0.192831	+	0.981232i	$0.438233\pi$
$744$	−3.59713	−	3.68353i	−0.131877	−	0.135045i
$745$	−46.3528	−	80.2854i	−1.69824	−	2.94143i
$746$	51.5834	−	9.68603i	1.88860	−	0.354631i
$747$	6.31496	+	36.4409i	0.231052	+	1.33330i
$748$	0.251261	+	2.28699i	0.00918702	+	0.0836207i
$749$	−0.535471	+	6.15511i	−0.0195657	+	0.224903i
$750$	−79.8643	−	32.1854i	−2.91623	−	1.17525i
$751$	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
$753$	8.39328	−	26.4841i	0.305868	−	0.965134i
$754$	−0.0210966	+	0.276371i	−0.000768292	+	0.0100648i
$755$	7.53320	−	7.53320i	0.274161	−	0.274161i
$756$	−22.1152	−	16.3377i	−0.804320	−	0.594196i
$757$	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
$759$	2.31101	+	0.732399i	0.0838843	+	0.0265844i
$760$	−60.2513	+	18.3109i	−2.18554	+	0.664207i
$761$	28.1161	+	16.2328i	1.01921	+	0.588440i	0.913875	−	0.405997i	$-0.133076\pi$
$761$	28.1161	+	16.2328i	1.01921	+	0.588440i	0.105334	+	0.994437i	$0.466409\pi$
$762$	−6.83704	−	16.0677i	−0.247680	−	0.582071i
$763$	−30.9638	−	21.6585i	−1.12096	−	0.784092i
$764$	−3.22046	−	2.58288i	−0.116512	−	0.0934453i
$765$	15.5822	−	2.70029i	0.563376	−	0.0976291i
$766$	−24.6031	+	35.9789i	−0.888947	+	1.29997i
$767$	41.9677	−	24.2300i	1.51536	−	0.874896i
$768$	−3.61995	+	27.4754i	−0.130624	+	0.991432i
$769$			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
$771$	48.5633	+	2.19195i	1.74897	+	0.0789410i
$772$	2.95217	+	7.58379i	0.106251	+	0.272947i
$773$	−10.1172	+	37.7579i	−0.363890	+	1.35806i	0.505028	+	0.863103i	$0.331482\pi$
$773$	−10.1172	+	37.7579i	−0.363890	+	1.35806i	−0.868919	+	0.494955i	$0.835185\pi$
$774$	18.4587	−	1.76637i	0.663484	−	0.0634908i
$775$	−6.95334	+	12.0435i	−0.249771	+	0.432617i
$776$	−5.95050	+	25.5799i	−0.213611	+	0.918264i
$777$	1.22692	+	2.97030i	0.0440154	+	0.106559i
$778$	32.9805	+	11.5917i	1.18241	+	0.415584i
$779$	−11.4884	−	42.8754i	−0.411615	−	1.53617i
$780$	−12.9658	+	64.8012i	−0.464250	+	2.32025i
$781$	−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
$786$	−19.9041	+	15.5791i	−0.709957	+	0.555688i
$787$	−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
$789$	−6.86869	+	10.7467i	−0.244532	+	0.382594i
$790$	2.95920	−	8.41943i	0.105283	−	0.299550i
$791$	5.49329	−	15.1157i	0.195319	−	0.537452i
$792$	−7.06143	+	3.55706i	−0.250917	+	0.126395i
$793$	−1.44478	−	0.834147i	−0.0513058	−	0.0296214i
$794$	43.4869	−	8.16572i	1.54329	−	0.289790i
$795$	17.7533	+	34.2267i	0.629645	+	1.21390i
$796$	12.0431	+	30.9374i	0.426857	+	1.09655i
$797$	−9.72334	+	9.72334i	−0.344418	+	0.344418i	−0.858025	−	0.513607i	$-0.828309\pi$
$797$	−9.72334	+	9.72334i	−0.344418	+	0.344418i	0.513607	+	0.858025i	$0.328309\pi$
$798$	10.4861	+	32.1231i	0.371205	+	1.13715i
$799$	7.68951			0.272035
$800$	74.0940	−	10.6430i	2.61962	−	0.376288i
$801$	22.2661	−	10.3031i	0.786732	−	0.364044i
$802$	−22.0830	−	15.1008i	−0.779778	−	0.533229i
$803$	2.80549	+	10.4702i	0.0990035	+	0.369486i
$804$	−2.38056	−	36.9594i	−0.0839558	−	1.30346i
$805$	−9.72642	+	13.9052i	−0.342811	+	0.490095i
$806$	6.26463	+	2.20184i	0.220662	+	0.0775567i
$807$	7.68249	+	34.8965i	0.270436	+	1.22841i
$808$	10.4647	−	19.6024i	0.368147	−	0.689609i
$809$	25.1034	+	43.4804i	0.882589	+	1.52869i	0.848453	+	0.529271i	$0.177535\pi$
$809$	25.1034	+	43.4804i	0.882589	+	1.52869i	0.0341362	+	0.999417i	$0.489132\pi$
$810$	27.4178	+	46.9247i	0.963365	+	1.64877i
$811$	−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
$813$	1.70935	−	37.8713i	0.0599496	−	1.32821i
$814$	0.921474	+	0.0703400i	0.0322976	+	0.00246541i
$815$	23.4358	+	40.5921i	0.820922	+	1.42188i
$816$	−6.55646	+	5.49276i	−0.229522	+	0.192285i
$817$	−19.7358	−	11.3945i	−0.690469	−	0.398643i
$818$	−6.47906	−	13.5018i	−0.226535	−	0.472078i
$819$	34.9080	+	6.24363i	1.21978	+	0.218170i
$820$	7.93948	+	72.2656i	0.277259	+	2.52362i
$821$	−1.67457	−	6.24959i	−0.0584430	−	0.218112i	0.930528	−	0.366220i	$-0.119348\pi$
$821$	−1.67457	−	6.24959i	−0.0584430	−	0.218112i	−0.988971	+	0.148108i	$0.952682\pi$
$822$	−18.7484	+	24.9257i	−0.653927	+	0.869384i
$823$	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	−0.344555	−	0.938766i	$-0.611970\pi$
$827$	17.0881	−	17.0881i	0.594211	−	0.594211i	0.938766	+	0.344555i	$0.111970\pi$
$828$	2.49944	+	8.65894i	0.0868615	+	0.300919i
$829$	−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
$831$	−4.75489	+	1.04679i	−0.164945	+	0.0363128i
$832$	−11.5238	−	33.8336i	−0.399518	−	1.17297i
$833$	−1.49232	+	8.51203i	−0.0517060	+	0.294924i
$834$	−39.9706	−	16.1082i	−1.38407	−	0.557781i
$835$	9.24171	+	34.4905i	0.319823	+	1.19359i
$836$	9.60463	+	1.47492i	0.332183	+	0.0510111i
$837$	5.05437	−	2.06749i	0.174705	−	0.0714629i
$838$	10.2416	−	8.78895i	0.353791	−	0.303609i
$839$			39.0078i			1.34670i	0.739324	+	0.673350i	$0.235145\pi$
$839$			39.0078i			1.34670i	−0.739324	+	0.673350i	$0.764855\pi$
$840$	−8.98987	−	54.6100i	−0.310180	−	1.88422i
$841$		−	28.9981i		−	0.999934i
$842$	18.0054	+	20.9814i	0.620506	+	0.723067i
$843$	−6.06117	−	11.6854i	−0.208758	−	0.402465i
$844$	16.1646	−	11.8609i	0.556410	−	0.408271i
$845$	−7.69307	−	28.7109i	−0.264650	−	0.987686i
$846$	9.23984	+	24.7576i	0.317672	+	0.851185i
$847$	−17.2406	−	20.5262i	−0.592394	−	0.705287i
$848$	−17.5954	−	11.1925i	−0.604228	−	0.384353i
$849$	5.36894	+	24.3876i	0.184262	+	0.836979i
$850$	19.0705	+	13.0408i	0.654112	+	0.447296i
$851$	0.272638	−	1.01750i	0.00934593	−	0.0348795i
$852$	−4.86463	−	14.3840i	−0.166659	−	0.492789i
$853$	−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	0.0881781	−	0.996105i	$-0.471896\pi$
$857$	29.1258	−	16.8158i	0.994919	−	0.574417i	0.906741	+	0.421688i	$0.138562\pi$
$858$	6.12991	−	8.14959i	0.209272	−	0.278223i
$859$	−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
$861$	38.6828	−	5.05399i	1.31831	−	0.172240i
$862$	−16.6233	+	7.97698i	−0.566192	+	0.271697i
$863$	−43.0182	−	24.8366i	−1.46436	−	0.845447i	−0.465149	−	0.885232i	$-0.653999\pi$
$863$	−43.0182	−	24.8366i	−1.46436	−	0.845447i	−0.999208	+	0.0397850i	$0.987333\pi$
$864$	−25.5632	−	14.5094i	−0.869677	−	0.493621i
$865$	−9.91826	−	17.1789i	−0.337231	−	0.584101i
$866$	1.41685	−	18.5612i	0.0481466	−	0.630734i
$867$	26.7778	+	1.20864i	0.909420	+	0.0410474i
$868$	−5.55966	+	0.125940i	−0.188707	+	0.00427469i
$869$	−0.973762	+	0.973762i	−0.0330326	+	0.0330326i
$870$	−0.0555151	+	0.455453i	−0.00188214	+	0.0154413i
$871$	23.8834	+	41.3672i	0.809257	+	1.40167i
$872$	−35.6358	−	19.0241i	−1.20678	−	0.644239i
$873$	−22.7712	−	16.0446i	−0.770687	−	0.543029i
$874$	3.67271	−	10.4495i	0.124231	−	0.353459i
$875$	−84.2718	+	39.3467i	−2.84891	+	1.33016i
$876$	−26.6038	+	30.2668i	−0.898858	+	1.02262i
$877$	−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
$879$	8.35723	−	26.3703i	0.281882	−	0.889449i
$880$	−15.1820	−	4.77539i	−0.511784	−	0.160978i
$881$	23.4730			0.790824			0.395412	−	0.918504i	$-0.370602\pi$
$881$	23.4730			0.790824			0.395412	+	0.918504i	$0.370602\pi$
$882$	−29.1991	+	5.42341i	−0.983184	+	0.182616i
$883$	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
$885$	71.2093	−	36.9361i	2.39368	−	1.24159i
$886$	3.15776	+	16.8168i	0.106087	+	0.564971i
$887$	−44.4350	−	25.6546i	−1.49198	−	0.861396i	−0.492024	−	0.870582i	$-0.663743\pi$
$887$	−44.4350	−	25.6546i	−1.49198	−	0.861396i	−0.999958	+	0.00918553i	$0.997076\pi$
$888$	1.68238	+	2.99550i	0.0564571	+	0.100522i
$889$	−17.7266	−	6.44216i	−0.594532	−	0.216063i
$890$	46.5906	+	16.3753i	1.56172	+	0.548901i
$891$	−0.681717	−	8.35861i	−0.0228384	−	0.280024i
$892$	8.53070	−	55.5517i	0.285629	−	1.86001i
$893$	8.40556	−	31.3700i	0.281281	−	1.04976i
$894$	−41.8785	+	32.7785i	−1.40063	+	1.09628i
$895$			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
$900$	−19.0716	+	77.0705i	−0.635720	+	2.56902i
$901$	−1.66581	−	6.21689i	−0.0554962	−	0.207114i
$902$	3.71987	−	10.5837i	0.123858	−	0.352398i
$903$	12.2083	−	15.8779i	0.406268	−	0.528383i
$904$	3.89558	−	16.7462i	0.129565	−	0.556971i
$905$	−9.68744	+	16.7791i	−0.322021	+	0.557757i
$906$	−4.88409	−	3.67368i	−0.162263	−	0.122050i
$907$	−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
$909$	15.0964	+	18.0992i	0.500717	+	0.600312i
$910$	41.6159	+	57.9940i	1.37955	+	1.92248i
$911$			34.9864i			1.15915i	0.814918	+	0.579576i	$0.196782\pi$
$911$			34.9864i			1.15915i	−0.814918	+	0.579576i	$0.803218\pi$
$912$	15.2411	+	32.7519i	0.504685	+	1.08452i
$913$	9.94844	−	5.74373i	0.329245	−	0.190090i
$914$	−21.1495	−	14.4625i	−0.699562	−	0.478375i
$915$	−2.32694	−	1.48724i	−0.0769263	−	0.0491668i
$916$	3.76569	+	34.2755i	0.124422	+	1.13250i
$917$	−2.36618	+	27.1986i	−0.0781381	+	0.898177i
$918$	−2.78562	−	8.63381i	−0.0919391	−	0.284958i
$919$	−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
$921$	8.12637	−	25.6419i	0.267773	−	0.844929i
$922$	27.1019	−	23.2577i	0.892554	−	0.765953i
$923$	13.8479	+	13.8479i	0.455809	+	0.455809i
$924$	−2.39506	+	8.19754i	−0.0787916	+	0.269679i
$925$	6.56185	−	6.56185i	0.215752	−	0.215752i
$926$	−18.3749	−	1.40263i	−0.603836	−	0.0460934i
$927$	0.485216	+	1.04860i	0.0159366	+	0.0344404i
$928$	−0.0976556	−	0.228131i	−0.00320570	−	0.00748878i
$929$	−6.66719	+	11.5479i	−0.218743	+	0.378875i	−0.954424	−	0.298454i	$-0.903529\pi$
$929$	−6.66719	+	11.5479i	−0.218743	+	0.378875i	0.735681	+	0.677329i	$0.236862\pi$
$930$	10.1953	+	4.10872i	0.334317	+	0.134730i
$931$	33.0942	+	15.3927i	1.08462	+	0.504476i
$932$	−0.892980	+	1.11341i	−0.0292505	+	0.0364711i
$933$	−6.31211	−	4.03433i	−0.206649	−	0.132078i
$934$	−3.61046	−	19.2277i	−0.118138	−	0.629148i
$935$	−2.45603	−	4.25397i	−0.0803207	−	0.139120i
$936$	37.8489	+	2.15861i	1.23713	+	0.0705562i
$937$	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
$939$	−33.8168	−	1.52635i	−1.10357	−	0.0498105i
$940$	−21.4060	+	48.6942i	−0.698187	+	1.58823i
$941$	−33.6529	−	9.01726i	−1.09705	−	0.293954i	−0.335489	−	0.942044i	$-0.608901\pi$
$941$	−33.6529	−	9.01726i	−1.09705	−	0.293954i	−0.761564	+	0.648090i	$0.775568\pi$
$942$	−0.0822203	+	0.0116292i	−0.00267888	+	0.000378901i
$943$	−11.0740	−	6.39360i	−0.360621	−	0.208204i
$944$	−23.2863	+	36.6076i	−0.757903	+	1.19147i
$945$	57.2604	+	12.9305i	1.86268	+	0.420628i
$946$	−2.49179	−	5.19265i	−0.0810149	−	0.168828i
$947$	14.5050	−	3.88660i	0.471349	−	0.126298i	−0.0153227	−	0.999883i	$-0.504878\pi$
$947$	14.5050	−	3.88660i	0.471349	−	0.126298i	0.486671	+	0.873585i	$0.338211\pi$
$948$	−5.02000	−	1.00443i	−0.163042	−	0.0326224i
$949$	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	$-0.603495\pi$
$953$	−19.7228			−0.638884			−0.319442	+	0.947606i	$0.603495\pi$
$954$	18.0146	−	12.8337i	0.583245	−	0.415505i
$955$	8.51345	+	2.28117i	0.275489	+	0.0738170i
$956$	−3.15801	+	20.5649i	−0.102137	+	0.665117i
$957$	0.0381291	−	0.0596567i	0.00123254	−	0.00192843i
$958$	−4.04587	−	8.43122i	−0.130716	−	0.272400i
$959$	5.86619	+	33.1740i	0.189429	+	1.07124i
$960$	−16.5313	−	56.8099i	−0.533547	−	1.83353i
$961$	−14.9478	+	25.8903i	−0.482186	+	0.835170i
$962$	−3.65764	−	2.50117i	−0.117927	−	0.0806410i
$963$	−6.57602	−	2.41542i	−0.211909	−	0.0778360i
$964$	−41.2344	+	16.0515i	−1.32807	+	0.516983i
$965$	−12.2858	−	12.2858i	−0.395494	−	0.395494i
$966$	8.67962	+	4.40752i	0.279262	+	0.141810i
$967$		−	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
$969$	−3.36833	+	10.6284i	−0.108206	+	0.341433i
$970$	−10.3478	−	55.1076i	−0.332247	−	1.76940i
$971$	4.18435	−	1.12119i	0.134282	−	0.0359808i	−0.191052	−	0.981580i	$-0.561190\pi$
$971$	4.18435	−	1.12119i	0.134282	−	0.0359808i	0.325334	+	0.945599i	$0.394523\pi$
$972$	24.4507	−	19.3433i	0.784257	−	0.620436i
$973$	−42.1765	+	19.6923i	−1.35212	+	0.631306i
$974$	15.3774	−	7.37911i	0.492723	−	0.236442i
$975$	−22.0160	−	100.004i	−0.705078	−	3.20270i
$976$	1.49224	+	0.0641260i	0.0477655	+	0.00205262i
$977$	−22.3182	+	12.8854i	−0.714021	+	0.412240i	−0.812548	−	0.582894i	$-0.801920\pi$
$977$	−22.3182	+	12.8854i	−0.714021	+	0.412240i	0.0985269	+	0.995134i	$0.468587\pi$
$978$	21.1736	−	16.5727i	0.677058	−	0.529938i
$979$	−5.38851	−	5.38851i	−0.172217	−	0.172217i
$980$	−49.7486	−	33.1460i	−1.58916	−	1.05881i
$981$	32.9031	−	27.4443i	1.05052	−	0.876230i
$982$	20.5637	−	17.6469i	0.656213	−	0.563135i
$983$	−20.6727	+	11.9354i	−0.659356	+	0.380679i	−0.792032	−	0.610480i	$-0.790977\pi$
$983$	−20.6727	+	11.9354i	−0.659356	+	0.380679i	0.132676	+	0.991160i	$0.457643\pi$
$984$	40.4092	−	10.3153i	1.28820	−	0.328841i
$985$	−3.17872	+	5.50570i	−0.101282	+	0.175426i
$986$	0.0253962	−	0.0722567i	0.000808780	−	0.00230112i
$987$	26.3595	+	10.9488i	0.839032	+	0.348506i
$988$	−36.3457	−	29.1500i	−1.15631	−	0.927386i
$989$	−6.34133	+	1.69915i	−0.201642	+	0.0540299i
$990$	10.7451	−	13.0192i	0.341503	−	0.413778i
$991$	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
$996$	38.2801	+	18.9314i	1.21295	+	0.599864i
$997$	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
$999$	−3.61491	+	0.459681i	−0.114371	+	0.0145437i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(1.41011 + 0.107640i) q^{2} +(0.797510 + 1.53752i) q^{3} +(1.97683 + 0.303568i) q^{4} +(-4.12446 + 1.10515i) q^{5} +(0.959079 + 2.25392i) q^{6} +(2.48663 + 0.903685i) q^{7} +(2.75487 + 0.640850i) q^{8} +(-1.72796 + 2.45238i) q^{9} +O(q^{10})\)	\(q+(1.41011 + 0.107640i) q^{2} +(0.797510 + 1.53752i) q^{3} +(1.97683 + 0.303568i) q^{4} +(-4.12446 + 1.10515i) q^{5} +(0.959079 + 2.25392i) q^{6} +(2.48663 + 0.903685i) q^{7} +(2.75487 + 0.640850i) q^{8} +(-1.72796 + 2.45238i) q^{9} +(-5.93491 + 1.11442i) q^{10} +(0.900067 + 0.241172i) q^{11} +(1.10980 + 3.28152i) 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} +(-2.70058 + 3.27213i) q^{18} +(5.03645 - 1.34951i) q^{19} +(-8.48883 + 0.932628i) q^{20} +(0.593678 + 4.54396i) q^{21} +(1.24323 + 0.436963i) q^{22} +(0.751039 - 1.30084i) q^{23} +(1.21171 + 4.74676i) q^{24} +(11.4597 - 6.61626i) q^{25} +(-4.11477 - 4.79488i) q^{26} +(-5.14865 - 0.700977i) q^{27} +(4.64132 + 2.54129i) q^{28} +(-0.0310193 - 0.0310193i) q^{29} +(-6.44660 - 8.23629i) q^{30} +(-0.910147 + 0.525473i) q^{31} +(5.25136 + 2.10314i) q^{32} +(0.347004 + 1.57621i) q^{33} +(0.755344 + 1.57407i) q^{34} +(-11.2547 - 0.979120i) q^{35} +(-4.16034 + 4.32338i) q^{36} +(0.677396 - 0.181508i) q^{37} +(7.24722 - 1.36084i) q^{38} +(2.33785 - 7.37684i) q^{39} +(-12.0706 + 0.401374i) q^{40} -8.51301i q^{41} +(0.348042 + 6.47139i) q^{42} +(-3.09050 - 3.09050i) q^{43} +(1.70606 + 0.749987i) q^{44} +(4.41665 - 12.0244i) q^{45} +(1.19907 - 1.75348i) q^{46} +(3.11429 - 5.39411i) q^{47} +(1.19771 + 6.82389i) q^{48} +(5.36671 + 4.49427i) q^{49} +(16.8716 - 8.09615i) q^{50} +(-1.15156 + 1.80174i) q^{51} +(-5.28617 - 7.20423i) q^{52} +(-5.03575 - 1.34932i) q^{53} +(-7.18472 - 1.54265i) 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} +(-8.20387 - 12.3080i) q^{60} +(0.360681 - 0.0966443i) q^{61} +(-1.33997 + 0.643008i) q^{62} +(-6.51298 + 4.53664i) q^{63} +(7.17862 + 3.53092i) q^{64} +(16.5214 + 9.53863i) q^{65} +(0.319652 + 2.25998i) q^{66} +(-10.3271 - 2.76713i) q^{67} +(0.895687 + 2.30092i) q^{68} +(2.59903 + 0.117309i) q^{69} +(-15.7650 - 2.59212i) q^{70} -4.38335 q^{71} +(-6.33190 + 5.64863i) q^{72} +(5.81636 + 10.0742i) q^{73} +(0.974740 - 0.183031i) q^{74} +(19.3119 + 12.3430i) q^{75} +(10.3659 - 1.13885i) q^{76} +(2.02019 + 1.41308i) q^{77} +(4.09068 - 10.1505i) q^{78} +(-0.738936 + 1.27988i) q^{79} +(-17.0641 - 0.733293i) q^{80} +(-3.02833 - 8.47521i) q^{81} +(0.916339 - 12.0043i) q^{82} +(8.71723 - 8.71723i) q^{83} +(-0.205800 + 9.16284i) q^{84} +(-3.72750 - 3.72750i) q^{85} +(-4.02529 - 4.69061i) q^{86} +(0.0229547 - 0.0724310i) q^{87} +(2.32501 + 1.24121i) q^{88} +(-7.08244 - 4.08905i) q^{89} +(7.52227 - 16.4803i) q^{90} +(-5.00086 - 10.7107i) q^{91} +(1.87957 - 2.34354i) q^{92} +(-1.53378 - 0.980302i) q^{93} +(4.97212 - 7.27108i) q^{94} +(-19.2812 + 11.1320i) q^{95} +(0.954385 + 9.75137i) q^{96} +9.28533i q^{97} +(7.08389 + 6.91509i) q^{98} +(-2.14672 + 1.79057i) 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

Properties

Related objects

Downloads

Learn more