LMFDB - Embedded newform 460.2.g.c.459.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(459,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("460.459");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.g (of order $2$, degree $1$, 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:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$56$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			459.16
Character	$\chi$	$=$	460.459
Dual form			460.2.g.c.459.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.968186 + 1.03083i) q^{2} +0.281229 q^{3} +(-0.125231 - 1.99608i) q^{4} +(1.92344 + 1.14033i) q^{5} +(-0.272282 + 0.289900i) q^{6} +0.654652i q^{7} +(2.17887 + 1.80348i) q^{8} -2.92091 q^{9} +O(q^{10})$	\(q+(-0.968186 + 1.03083i) q^{2} +0.281229 q^{3} +(-0.125231 - 1.99608i) q^{4} +(1.92344 + 1.14033i) q^{5} +(-0.272282 + 0.289900i) q^{6} +0.654652i q^{7} +(2.17887 + 1.80348i) q^{8} -2.92091 q^{9} +(-3.03775 + 0.878693i) q^{10} -3.83142 q^{11} +(-0.0352186 - 0.561354i) q^{12} +5.53192i q^{13} +(-0.674837 - 0.633825i) q^{14} +(0.540928 + 0.320695i) q^{15} +(-3.96863 + 0.499942i) q^{16} +5.39216 q^{17} +(2.82798 - 3.01097i) q^{18} +7.15249 q^{19} +(2.03532 - 3.98215i) q^{20} +0.184107i q^{21} +(3.70952 - 3.94955i) q^{22} +(-2.92031 + 3.80418i) q^{23} +(0.612760 + 0.507190i) q^{24} +(2.39928 + 4.38674i) q^{25} +(-5.70248 - 5.35593i) q^{26} -1.66513 q^{27} +(1.30674 - 0.0819830i) q^{28} -1.36806 q^{29} +(-0.854301 + 0.247114i) q^{30} +6.50560i q^{31} +(3.32702 - 4.57503i) q^{32} -1.07750 q^{33} +(-5.22062 + 5.55842i) q^{34} +(-0.746523 + 1.25919i) q^{35} +(0.365789 + 5.83036i) q^{36} +0.364169 q^{37} +(-6.92494 + 7.37302i) q^{38} +1.55573i q^{39} +(2.13436 + 5.95353i) q^{40} -5.98276 q^{41} +(-0.189784 - 0.178250i) q^{42} -2.05553i q^{43} +(0.479813 + 7.64780i) q^{44} +(-5.61821 - 3.33081i) q^{45} +(-1.09407 - 6.69350i) q^{46} -5.64904 q^{47} +(-1.11609 + 0.140598i) q^{48} +6.57143 q^{49} +(-6.84494 - 1.77393i) q^{50} +1.51643 q^{51} +(11.0421 - 0.692769i) q^{52} +4.91027 q^{53} +(1.61216 - 1.71647i) q^{54} +(-7.36951 - 4.36910i) q^{55} +(-1.18065 + 1.42640i) q^{56} +2.01149 q^{57} +(1.32453 - 1.41024i) q^{58} -8.55081i q^{59} +(0.572390 - 1.11989i) q^{60} -6.21530i q^{61} +(-6.70619 - 6.29864i) q^{62} -1.91218i q^{63} +(1.49492 + 7.85908i) q^{64} +(-6.30824 + 10.6403i) q^{65} +(1.04322 - 1.11073i) q^{66} +8.19725i q^{67} +(-0.675268 - 10.7632i) q^{68} +(-0.821275 + 1.06985i) q^{69} +(-0.575239 - 1.98867i) q^{70} +5.98091i q^{71} +(-6.36427 - 5.26780i) q^{72} -6.53524i q^{73} +(-0.352583 + 0.375397i) q^{74} +(0.674745 + 1.23368i) q^{75} +(-0.895716 - 14.2769i) q^{76} -2.50825i q^{77} +(-1.60370 - 1.50624i) q^{78} -2.65782 q^{79} +(-8.20355 - 3.56396i) q^{80} +8.29445 q^{81} +(5.79242 - 6.16722i) q^{82} +15.6753i q^{83} +(0.367492 - 0.0230560i) q^{84} +(10.3715 + 6.14887i) q^{85} +(2.11891 + 1.99014i) q^{86} -0.384737 q^{87} +(-8.34814 - 6.90988i) q^{88} -16.2942i q^{89} +(8.87298 - 2.56658i) q^{90} -3.62148 q^{91} +(7.95915 + 5.35275i) q^{92} +1.82956i q^{93} +(5.46932 - 5.82322i) q^{94} +(13.7574 + 8.15623i) q^{95} +(0.935654 - 1.28663i) q^{96} +13.6570 q^{97} +(-6.36237 + 6.77404i) q^{98} +11.1912 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{4} - 8 q^{6} + 16 q^{9}+O(q^{10}) $ 56 * q - 8 * q^4 - 8 * q^6 + 16 * q^9	$ 56 q - 8 q^{4} - 8 q^{6} + 16 q^{9} - 8 q^{16} - 100 q^{24} - 24 q^{25} - 24 q^{26} - 16 q^{29} + 104 q^{41} - 8 q^{46} + 32 q^{49} - 32 q^{50} + 52 q^{54} - 92 q^{64} + 32 q^{69} - 44 q^{70} + 24 q^{81} + 56 q^{85} + 28 q^{94} + 88 q^{96}+O(q^{100}) $ 56 * q - 8 * q^4 - 8 * q^6 + 16 * q^9 - 8 * q^16 - 100 * q^24 - 24 * q^25 - 24 * q^26 - 16 * q^29 + 104 * q^41 - 8 * q^46 + 32 * q^49 - 32 * q^50 + 52 * q^54 - 92 * q^64 + 32 * q^69 - 44 * q^70 + 24 * q^81 + 56 * q^85 + 28 * q^94 + 88 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	−0.968186	+	1.03083i	−0.684611	+	0.728909i
$2$	−0.968186	+	1.03083i	−0.684611	+	0.728909i
$3$	0.281229			0.162367			0.0811837	−	0.996699i	$-0.474130\pi$
$3$	0.281229			0.162367			0.0811837	+	0.996699i	$0.474130\pi$
$4$	−0.125231	−	1.99608i	−0.0626157	−	0.998038i
$5$	1.92344	+	1.14033i	0.860190	+	0.509973i
$5$	1.92344	+	1.14033i	0.860190	+	0.509973i
$6$	−0.272282	+	0.289900i	−0.111159	+	0.118351i
$7$			0.654652i			0.247435i	0.992317	+	0.123718i	$0.0394817\pi$
$7$			0.654652i			0.247435i	−0.992317	+	0.123718i	$0.960518\pi$
$8$	2.17887	+	1.80348i	0.770346	+	0.637626i
$9$	−2.92091			−0.973637
$10$	−3.03775	+	0.878693i	−0.960620	+	0.277867i
$11$	−3.83142			−1.15522			−0.577608	−	0.816314i	$-0.696014\pi$
$11$	−3.83142			−1.15522			−0.577608	+	0.816314i	$0.696014\pi$
$12$	−0.0352186	−	0.561354i	−0.0101667	−	0.162049i
$13$			5.53192i			1.53428i	0.641481	+	0.767139i	$0.278320\pi$
$13$			5.53192i			1.53428i	−0.641481	+	0.767139i	$0.721680\pi$
$14$	−0.674837	−	0.633825i	−0.180358	−	0.169397i
$15$	0.540928	+	0.320695i	0.139667	+	0.0828030i
$16$	−3.96863	+	0.499942i	−0.992159	+	0.124986i
$17$	5.39216			1.30779			0.653896	−	0.756585i	$-0.273133\pi$
$17$	5.39216			1.30779			0.653896	+	0.756585i	$0.273133\pi$
$18$	2.82798	−	3.01097i	0.666562	−	0.709692i
$19$	7.15249			1.64089			0.820447	−	0.571722i	$-0.193725\pi$
$19$	7.15249			1.64089			0.820447	+	0.571722i	$0.193725\pi$
$20$	2.03532	−	3.98215i	0.455111	−	0.890435i
$21$			0.184107i			0.0401755i
$22$	3.70952	−	3.94955i	0.790873	−	0.842046i
$23$	−2.92031	+	3.80418i	−0.608927	+	0.793227i
$23$	−2.92031	+	3.80418i	−0.608927	+	0.793227i
$24$	0.612760	+	0.507190i	0.125079	+	0.103530i
$25$	2.39928	+	4.38674i	0.479855	+	0.877348i
$26$	−5.70248	−	5.35593i	−1.11835	−	1.05038i
$27$	−1.66513			−0.320454
$28$	1.30674	−	0.0819830i	0.246950	−	0.0154933i
$29$	−1.36806			−0.254042			−0.127021	−	0.991900i	$-0.540542\pi$
$29$	−1.36806			−0.254042			−0.127021	+	0.991900i	$0.540542\pi$
$30$	−0.854301	+	0.247114i	−0.155973	+	0.0451166i
$31$			6.50560i			1.16844i	0.811595	+	0.584221i	$0.198600\pi$
$31$			6.50560i			1.16844i	−0.811595	+	0.584221i	$0.801400\pi$
$32$	3.32702	−	4.57503i	0.588140	−	0.808759i
$33$	−1.07750			−0.187569
$34$	−5.22062	+	5.55842i	−0.895328	+	0.953261i
$35$	−0.746523	+	1.25919i	−0.126185	+	0.212842i
$36$	0.365789	+	5.83036i	0.0609649	+	0.971726i
$37$	0.364169			0.0598690			0.0299345	−	0.999552i	$-0.490470\pi$
$37$	0.364169			0.0598690			0.0299345	+	0.999552i	$0.490470\pi$
$38$	−6.92494	+	7.37302i	−1.12337	+	1.19606i
$39$			1.55573i			0.249117i
$40$	2.13436	+	5.95353i	0.337472	+	0.941336i
$41$	−5.98276			−0.934350			−0.467175	−	0.884165i	$-0.654728\pi$
$41$	−5.98276			−0.934350			−0.467175	+	0.884165i	$0.654728\pi$
$42$	−0.189784	−	0.178250i	−0.0292842	−	0.0275046i
$43$		−	2.05553i		−	0.313466i	−0.987641	−	0.156733i	$-0.949904\pi$
$43$		−	2.05553i		−	0.313466i	0.987641	−	0.156733i	$-0.0500962\pi$
$44$	0.479813	+	7.64780i	0.0723346	+	1.15295i
$45$	−5.61821	−	3.33081i	−0.837513	−	0.496528i
$46$	−1.09407	−	6.69350i	−0.161312	−	0.986903i
$47$	−5.64904			−0.823997			−0.411999	−	0.911184i	$-0.635169\pi$
$47$	−5.64904			−0.823997			−0.411999	+	0.911184i	$0.635169\pi$
$48$	−1.11609	+	0.140598i	−0.161094	+	0.0202936i
$49$	6.57143			0.938776
$50$	−6.84494	−	1.77393i	−0.968020	−	0.250871i
$51$	1.51643			0.212343
$52$	11.0421	−	0.692769i	1.53127	−	0.0960698i
$53$	4.91027			0.674478			0.337239	−	0.941419i	$-0.390507\pi$
$53$	4.91027			0.674478			0.337239	+	0.941419i	$0.390507\pi$
$54$	1.61216	−	1.71647i	0.219387	−	0.233582i
$55$	−7.36951	−	4.36910i	−0.993705	−	0.589129i
$56$	−1.18065	+	1.42640i	−0.157771	+	0.190611i
$57$	2.01149			0.266428
$58$	1.32453	−	1.41024i	0.173920	−	0.185173i
$59$		−	8.55081i		−	1.11322i	−0.830774	−	0.556610i	$-0.812102\pi$
$59$		−	8.55081i		−	1.11322i	0.830774	−	0.556610i	$-0.187898\pi$
$60$	0.572390	−	1.11989i	0.0738952	−	0.144578i
$61$		−	6.21530i		−	0.795787i	−0.917432	−	0.397894i	$-0.869741\pi$
$61$		−	6.21530i		−	0.795787i	0.917432	−	0.397894i	$-0.130259\pi$
$62$	−6.70619	−	6.29864i	−0.851687	−	0.799928i
$63$		−	1.91218i		−	0.240912i
$64$	1.49492	+	7.85908i	0.186865	+	0.982386i
$65$	−6.30824	+	10.6403i	−0.782440	+	1.31977i
$66$	1.04322	−	1.11073i	0.128412	−	0.136721i
$67$			8.19725i			1.00145i	0.865605	+	0.500727i	$0.166934\pi$
$67$			8.19725i			1.00145i	−0.865605	+	0.500727i	$0.833066\pi$
$68$	−0.675268	−	10.7632i	−0.0818882	−	1.30523i
$69$	−0.821275	+	1.06985i	−0.0988699	+	0.128794i
$70$	−0.575239	−	1.98867i	−0.0687542	−	0.237691i
$71$			5.98091i			0.709803i	0.934904	+	0.354901i	$0.115486\pi$
$71$			5.98091i			0.709803i	−0.934904	+	0.354901i	$0.884514\pi$
$72$	−6.36427	−	5.26780i	−0.750037	−	0.620817i
$73$		−	6.53524i		−	0.764892i	−0.923978	−	0.382446i	$-0.875082\pi$
$73$		−	6.53524i		−	0.764892i	0.923978	−	0.382446i	$-0.124918\pi$
$74$	−0.352583	+	0.375397i	−0.0409870	+	0.0436390i
$75$	0.674745	+	1.23368i	0.0779129	+	0.142453i
$76$	−0.895716	−	14.2769i	−0.102746	−	1.63767i
$77$		−	2.50825i		−	0.285841i
$78$	−1.60370	−	1.50624i	−0.181583	−	0.170548i
$79$	−2.65782			−0.299028			−0.149514	−	0.988760i	$-0.547771\pi$
$79$	−2.65782			−0.299028			−0.149514	+	0.988760i	$0.547771\pi$
$80$	−8.20355	−	3.56396i	−0.917185	−	0.398463i
$81$	8.29445			0.921605
$82$	5.79242	−	6.16722i	0.639666	−	0.681056i
$83$			15.6753i			1.72059i	0.509794	+	0.860296i	$0.329722\pi$
$83$			15.6753i			1.72059i	−0.509794	+	0.860296i	$0.670278\pi$
$84$	0.367492	−	0.0230560i	0.0400966	−	0.00251561i
$85$	10.3715	+	6.14887i	1.12495	+	0.666938i
$86$	2.11891	+	1.99014i	0.228488	+	0.214602i
$87$	−0.384737			−0.0412481
$88$	−8.34814	−	6.90988i	−0.889915	−	0.736596i
$89$		−	16.2942i		−	1.72719i	−0.504190	−	0.863593i	$-0.668209\pi$
$89$		−	16.2942i		−	1.72719i	0.504190	−	0.863593i	$-0.331791\pi$
$90$	8.87298	−	2.56658i	0.935295	−	0.270542i
$91$	−3.62148			−0.379635
$92$	7.95915	+	5.35275i	0.829798	+	0.558063i
$93$			1.82956i			0.189717i
$94$	5.46932	−	5.82322i	0.564118	−	0.600619i
$95$	13.7574	+	8.15623i	1.41148	+	0.836812i
$96$	0.935654	−	1.28663i	0.0954947	−	0.131316i
$97$	13.6570			1.38666			0.693329	−	0.720622i	$-0.256143\pi$
$97$	13.6570			1.38666			0.693329	+	0.720622i	$0.256143\pi$
$98$	−6.36237	+	6.77404i	−0.642696	+	0.684282i
$99$	11.1912			1.12476
$100$	8.45580	−	5.33849i	0.845580	−	0.533849i
$101$	0.609219			0.0606195			0.0303098	−	0.999541i	$-0.490351\pi$
$101$	0.609219			0.0606195			0.0303098	+	0.999541i	$0.490351\pi$
$102$	−1.46819	+	1.56319i	−0.145372	+	0.154779i
$103$		−	11.2690i		−	1.11037i	−0.831727	−	0.555185i	$-0.812648\pi$
$103$		−	11.2690i		−	1.11037i	0.831727	−	0.555185i	$-0.187352\pi$
$104$	−9.97670	+	12.0533i	−0.978296	+	1.18192i
$105$	−0.209944	+	0.354120i	−0.0204884	+	0.0345585i
$106$	−4.75406	+	5.06167i	−0.461755	+	0.491633i
$107$		−	6.95955i		−	0.672805i	−0.941718	−	0.336403i	$-0.890790\pi$
$107$		−	6.95955i		−	0.672805i	0.941718	−	0.336403i	$-0.109210\pi$
$108$	0.208526	+	3.32373i	0.0200655	+	0.319826i
$109$		−	11.3619i		−	1.08827i	−0.838998	−	0.544135i	$-0.816858\pi$
$109$		−	11.3619i		−	1.08827i	0.838998	−	0.544135i	$-0.183142\pi$
$110$	11.6389	−	3.36664i	1.10972	−	0.320996i
$111$	0.102415			0.00972077
$112$	−0.327288	−	2.59808i	−0.0309259	−	0.245495i
$113$	−6.43268			−0.605136			−0.302568	−	0.953128i	$-0.597844\pi$
$113$	−6.43268			−0.605136			−0.302568	+	0.953128i	$0.597844\pi$
$114$	−1.94749	+	2.07351i	−0.182399	+	0.194202i
$115$	−9.95509	+	3.98700i	−0.928317	+	0.371790i
$116$	0.171324	+	2.73074i	0.0159070	+	0.253543i
$117$		−	16.1582i		−	1.49383i
$118$	8.81445	+	8.27877i	0.811436	+	0.762123i
$119$			3.52999i			0.323594i
$120$	0.600243	+	1.67430i	0.0547944	+	0.152842i
$121$	3.67975			0.334523
$122$	6.40693	+	6.01757i	0.580056	+	0.544805i
$123$	−1.68252			−0.151708
$124$	12.9857	−	0.814705i	1.16615	−	0.0731627i
$125$	−0.387477	+	11.1736i	−0.0346570	+	0.999399i
$126$	1.97114	+	1.85135i	0.175603	+	0.164931i
$127$	16.4339			1.45827			0.729135	−	0.684370i	$-0.239923\pi$
$127$	16.4339			1.45827			0.729135	+	0.684370i	$0.239923\pi$
$128$	−9.54876	−	6.06805i	−0.843999	−	0.536344i
$129$		−	0.578075i		−	0.0508967i
$130$	−4.86086	−	16.8046i	−0.426325	−	1.47386i
$131$		−	14.0422i		−	1.22688i	−0.789743	−	0.613438i	$-0.789786\pi$
$131$		−	14.0422i		−	1.22688i	0.789743	−	0.613438i	$-0.210214\pi$
$132$	0.134937	+	2.15078i	0.0117448	+	0.187201i
$133$			4.68240i			0.406015i
$134$	−8.44999	−	7.93646i	−0.729968	−	0.685606i
$135$	−3.20278	−	1.89881i	−0.275652	−	0.163423i
$136$	11.7488	+	9.72466i	1.00745	+	0.833883i
$137$	−4.19694			−0.358568			−0.179284	−	0.983797i	$-0.557378\pi$
$137$	−4.19694			−0.358568			−0.179284	+	0.983797i	$0.557378\pi$
$138$	−0.307684	−	1.88241i	−0.0261918	−	0.160241i
$139$		−	18.2867i		−	1.55106i	−0.631311	−	0.775530i	$-0.717483\pi$
$139$		−	18.2867i		−	1.55106i	0.631311	−	0.775530i	$-0.282517\pi$
$140$	2.60692	+	1.33243i	0.220325	+	0.112611i
$141$	−1.58867			−0.133790
$142$	−6.16531	−	5.79063i	−0.517381	−	0.485939i
$143$		−	21.1951i		−	1.77242i
$144$	11.5920	−	1.46029i	0.966002	−	0.121691i
$145$	−2.63138	−	1.56004i	−0.218524	−	0.129554i
$146$	6.73673	+	6.32733i	0.557536	+	0.523653i
$147$	1.84807			0.152427
$148$	−0.0456053	−	0.726908i	−0.00374873	−	0.0597515i
$149$			12.9235i			1.05873i	0.848393	+	0.529367i	$0.177570\pi$
$149$			12.9235i			1.05873i	−0.848393	+	0.529367i	$0.822430\pi$
$150$	−1.92499	−	0.498880i	−0.157175	−	0.0407334i
$151$			2.56990i			0.209136i	0.994518	+	0.104568i	$0.0333459\pi$
$151$			2.56990i			0.209136i	−0.994518	+	0.104568i	$0.966654\pi$
$152$	15.5843	+	12.8994i	1.26406	+	1.04628i
$153$	−15.7500			−1.27331
$154$	2.58558	+	2.42845i	0.208352	+	0.195690i
$155$	−7.41856	+	12.5132i	−0.595873	+	1.00508i
$156$	3.10536	−	0.194827i	0.248628	−	0.0155986i
$157$	2.58579			0.206369			0.103184	−	0.994662i	$-0.467097\pi$
$157$	2.58579			0.206369			0.103184	+	0.994662i	$0.467097\pi$
$158$	2.57327	−	2.73977i	0.204718	−	0.217964i
$159$	1.38091			0.109513
$160$	11.6164	−	5.00591i	0.918358	−	0.395752i
$161$	−2.49042	−	1.91179i	−0.196272	−	0.150670i
$162$	−8.03057	+	8.55019i	−0.630941	+	0.671766i
$163$	−1.76864			−0.138530			−0.0692652	−	0.997598i	$-0.522065\pi$
$163$	−1.76864			−0.138530			−0.0692652	+	0.997598i	$0.522065\pi$
$164$	0.749228	+	11.9420i	0.0585049	+	0.932516i
$165$	−2.07252	−	1.22872i	−0.161345	−	0.0956553i
$166$	−16.1587	−	15.1767i	−1.25415	−	1.17794i
$167$	13.2066			1.02196			0.510978	−	0.859594i	$-0.329283\pi$
$167$	13.2066			1.02196			0.510978	+	0.859594i	$0.329283\pi$
$168$	−0.332033	+	0.401145i	−0.0256169	+	0.0309490i
$169$	−17.6021			−1.35401
$170$	−16.3800	+	4.73806i	−1.25629	+	0.363392i
$171$	−20.8918			−1.59764
$172$	−4.10300	+	0.257417i	−0.312851	+	0.0196279i
$173$			2.53152i			0.192468i	0.995359	+	0.0962341i	$0.0306797\pi$
$173$			2.53152i			0.192468i	−0.995359	+	0.0962341i	$0.969320\pi$
$174$	0.372497	−	0.396599i	0.0282389	−	0.0300661i
$175$	−2.87179	+	1.57069i	−0.217087	+	0.118733i
$176$	15.2055	−	1.91549i	1.14616	−	0.144385i
$177$		−	2.40473i		−	0.180751i
$178$	16.7966	+	15.7759i	1.25896	+	1.18245i
$179$		−	6.62757i		−	0.495368i	−0.968841	−	0.247684i	$-0.920331\pi$
$179$		−	6.62757i		−	0.495368i	0.968841	−	0.247684i	$-0.0796694\pi$
$180$	−5.94498	+	11.6315i	−0.443113	+	0.866960i
$181$			7.00488i			0.520668i	0.965519	+	0.260334i	$0.0838327\pi$
$181$			7.00488i			0.520668i	−0.965519	+	0.260334i	$0.916167\pi$
$182$	3.50627	−	3.73314i	0.259902	−	0.276719i
$183$		−	1.74792i		−	0.129210i
$184$	−13.2237	+	3.02208i	−0.974866	+	0.222791i
$185$	0.700458	+	0.415274i	0.0514987	+	0.0305316i
$186$	−1.88597	−	1.77136i	−0.138286	−	0.129882i
$187$	−20.6596			−1.51078
$188$	0.707437	+	11.2759i	0.0515951	+	0.822381i
$189$		−	1.09008i		−	0.0792918i
$190$	−21.7275	+	6.28484i	−1.57628	+	0.455951i
$191$	22.3243			1.61533			0.807664	−	0.589644i	$-0.200732\pi$
$191$	22.3243			1.61533			0.807664	+	0.589644i	$0.200732\pi$
$192$	0.420414	+	2.21020i	0.0303408	+	0.159507i
$193$		−	0.678683i		−	0.0488527i	−0.999702	−	0.0244263i	$-0.992224\pi$
$193$		−	0.678683i		−	0.0488527i	0.999702	−	0.0244263i	$-0.00777592\pi$
$194$	−13.2225	+	14.0781i	−0.949321	+	1.01075i
$195$	−1.77406	+	2.99237i	−0.127043	+	0.214288i
$196$	−0.822949	−	13.1171i	−0.0587821	−	0.936934i
$197$		−	9.91923i		−	0.706716i	−0.935488	−	0.353358i	$-0.885040\pi$
$197$		−	9.91923i		−	0.706716i	0.935488	−	0.353358i	$-0.114960\pi$
$198$	−10.8352	+	11.5363i	−0.770023	+	0.819847i
$199$	19.4256			1.37704			0.688521	−	0.725216i	$-0.258260\pi$
$199$	19.4256			1.37704			0.688521	+	0.725216i	$0.258260\pi$
$200$	−2.68370	+	13.8852i	−0.189766	+	0.981829i
$201$			2.30530i			0.162603i
$202$	−0.589837	+	0.628003i	−0.0415008	+	0.0441861i
$203$		−	0.895602i		−	0.0628589i
$204$	−0.189905	−	3.02691i	−0.0132960	−	0.211926i
$205$	−11.5075	−	6.82234i	−0.803719	−	0.476493i
$206$	11.6165	+	10.9105i	0.809358	+	0.760171i
$207$	8.52996	−	11.1117i	0.592873	−	0.772315i
$208$	−2.76564	−	21.9542i	−0.191763	−	1.52225i
$209$	−27.4042			−1.89559
$210$	−0.161774	−	0.559271i	−0.0111634	−	0.0385933i
$211$		−	4.05469i		−	0.279136i	−0.990212	−	0.139568i	$-0.955429\pi$
$211$		−	4.05469i		−	0.279136i	0.990212	−	0.139568i	$-0.0445715\pi$
$212$	−0.614920	−	9.80127i	−0.0422329	−	0.673154i
$213$			1.68200i			0.115249i
$214$	7.17413	+	6.73814i	0.490414	+	0.460610i
$215$	2.34400	−	3.95370i	0.159859	−	0.269640i
$216$	−3.62810	−	3.00303i	−0.246861	−	0.204330i
$217$	−4.25891			−0.289114
$218$	11.7122	+	11.0004i	0.793249	+	0.745042i
$219$		−	1.83790i		−	0.124194i
$220$	−7.79815	+	15.2573i	−0.525751	+	1.02864i
$221$			29.8290i			2.00652i
$222$	−0.0991565	+	0.105572i	−0.00665495	+	0.00708556i
$223$	3.45116			0.231107			0.115553	−	0.993301i	$-0.463136\pi$
$223$	3.45116			0.231107			0.115553	+	0.993301i	$0.463136\pi$
$224$	2.99506	+	2.17804i	0.200116	+	0.145527i
$225$	−7.00807	−	12.8133i	−0.467205	−	0.854218i
$226$	6.22803	−	6.63102i	0.414283	−	0.441089i
$227$		−	21.6513i		−	1.43705i	−0.695501	−	0.718525i	$-0.744818\pi$
$227$		−	21.6513i		−	1.43705i	0.695501	−	0.718525i	$-0.255182\pi$
$228$	−0.251901	−	4.01508i	−0.0166826	−	0.265905i
$229$		−	20.8162i		−	1.37557i	−0.725914	−	0.687786i	$-0.758583\pi$
$229$		−	20.8162i		−	1.37557i	0.725914	−	0.687786i	$-0.241417\pi$
$230$	5.52845	−	14.1222i	0.364535	−	0.931190i
$231$		−	0.705391i		−	0.0464113i
$232$	−2.98081	−	2.46726i	−0.195700	−	0.161984i
$233$		−	5.50864i		−	0.360883i	−0.983586	−	0.180442i	$-0.942247\pi$
$233$		−	5.50864i		−	0.360883i	0.983586	−	0.180442i	$-0.0577527\pi$
$234$	16.6564	+	15.6442i	1.08887	+	1.02269i
$235$	−10.8656	−	6.44180i	−0.708795	−	0.420216i
$236$	−17.0681	+	1.07083i	−1.11104	+	0.0697050i
$237$	−0.747456			−0.0485525
$238$	−3.63883	−	3.41769i	−0.235870	−	0.221536i
$239$			22.0392i			1.42560i	0.701369	+	0.712798i	$0.252572\pi$
$239$			22.0392i			1.42560i	−0.701369	+	0.712798i	$0.747428\pi$
$240$	−2.30707	−	1.00229i	−0.148921	−	0.0646974i
$241$			11.4536i			0.737793i	0.929470	+	0.368897i	$0.120264\pi$
$241$			11.4536i			0.737793i	−0.929470	+	0.368897i	$0.879736\pi$
$242$	−3.56268	+	3.79320i	−0.229018	+	0.243836i
$243$	7.32803			0.470093
$244$	−12.4062	+	0.778350i	−0.794226	+	0.0498287i
$245$	12.6398	+	7.49363i	0.807526	+	0.478750i
$246$	1.62900	−	1.73440i	0.103861	−	0.110581i
$247$			39.5670i			2.51759i
$248$	−11.7327	+	14.1748i	−0.745029	+	0.900104i
$249$			4.40836i			0.279368i
$250$	−11.1430	−	11.2176i	−0.704744	−	0.709461i
$251$	−12.9871			−0.819740			−0.409870	−	0.912144i	$-0.634426\pi$
$251$	−12.9871			−0.819740			−0.409870	+	0.912144i	$0.634426\pi$
$252$	−3.81686	+	0.239465i	−0.240439	+	0.0150849i
$253$	11.1889	−	14.5754i	0.703441	−	0.916348i
$254$	−15.9110	+	16.9406i	−0.998348	+	1.06295i
$255$	2.91677	+	1.72924i	0.182655	+	0.108289i
$256$	15.5001	−	3.96818i	0.968757	−	0.248011i
$257$			17.1866i			1.07207i	0.844195	+	0.536036i	$0.180079\pi$
$257$			17.1866i			1.07207i	−0.844195	+	0.536036i	$0.819921\pi$
$258$	0.595899	+	0.559684i	0.0370990	+	0.0348444i
$259$			0.238404i			0.0148137i
$260$	22.0289	+	11.2592i	1.36617	+	0.698267i
$261$	3.99597			0.247344
$262$	14.4752	+	13.5955i	0.894281	+	0.839933i
$263$			10.8553i			0.669367i	0.942331	+	0.334684i	$0.108629\pi$
$263$			10.8553i			0.669367i	−0.942331	+	0.334684i	$0.891371\pi$
$264$	−2.34774	−	1.94326i	−0.144493	−	0.119599i
$265$	9.44463	+	5.59935i	0.580179	+	0.343965i
$266$	−4.82677	−	4.53343i	−0.295948	−	0.277963i
$267$		−	4.58241i		−	0.280439i
$268$	16.3623	−	1.02655i	0.999488	−	0.0627067i
$269$	−27.3295			−1.66631			−0.833156	−	0.553038i	$-0.813468\pi$
$269$	−27.3295			−1.66631			−0.833156	+	0.553038i	$0.813468\pi$
$270$	5.05824	−	1.46314i	0.307835	−	0.0890437i
$271$			25.0950i			1.52441i	0.647335	+	0.762206i	$0.275884\pi$
$271$			25.0950i			1.52441i	−0.647335	+	0.762206i	$0.724116\pi$
$272$	−21.3995	+	2.69577i	−1.29754	+	0.163455i
$273$	−1.01847			−0.0616403
$274$	4.06342	−	4.32634i	0.245480	−	0.261364i
$275$	−9.19262	−	16.8074i	−0.554336	−	1.01353i
$276$	2.23834	+	1.50535i	0.134732	+	0.0906113i
$277$			6.08201i			0.365433i	0.983166	+	0.182716i	$0.0584890\pi$
$277$			6.08201i			0.365433i	−0.983166	+	0.182716i	$0.941511\pi$
$278$	18.8505	+	17.7050i	1.13058	+	1.06187i
$279$		−	19.0023i		−	1.13764i
$280$	−3.89749	+	1.39726i	−0.232920	+	0.0835024i
$281$			19.5601i			1.16686i	0.812163	+	0.583430i	$0.198290\pi$
$281$			19.5601i			1.16686i	−0.812163	+	0.583430i	$0.801710\pi$
$282$	1.53813	−	1.63766i	0.0915944	−	0.0975210i
$283$			18.8637i			1.12133i	0.828042	+	0.560666i	$0.189455\pi$
$283$			18.8637i			1.12133i	−0.828042	+	0.560666i	$0.810545\pi$
$284$	11.9383	−	0.748997i	0.708410	−	0.0444448i
$285$	3.86898	+	2.29377i	0.229179	+	0.135871i
$286$	21.8486	+	20.5208i	1.29193	+	1.21342i
$287$		−	3.91663i		−	0.231191i
$288$	−9.71793	+	13.3633i	−0.572634	+	0.787438i
$289$	12.0754			0.710319
$290$	4.15581	−	1.20210i	0.244037	−	0.0705898i
$291$	3.84074			0.225148
$292$	−13.0448	+	0.818416i	−0.763391	+	0.0478942i
$293$	−20.6808			−1.20818			−0.604092	−	0.796914i	$-0.706464\pi$
$293$	−20.6808			−1.20818			−0.604092	+	0.796914i	$0.706464\pi$
$294$	−1.78928	+	1.90506i	−0.104353	+	0.111105i
$295$	9.75078	−	16.4470i	0.567712	−	0.957581i
$296$	0.793475	+	0.656771i	0.0461198	+	0.0381740i
$297$	6.37981			0.370194
$298$	−13.3219	−	12.5123i	−0.771720	−	0.724820i
$299$	−21.0444	−	16.1549i	−1.21703	−	0.934263i
$300$	2.37801	−	1.50134i	0.137295	−	0.0866797i
$301$	1.34566			0.0775626
$302$	−2.64914	−	2.48814i	−0.152441	−	0.143177i
$303$	0.171330			0.00984264
$304$	−28.3856	+	3.57583i	−1.62803	+	0.205088i
$305$	7.08752	−	11.9548i	0.405830	−	0.684529i
$306$	15.2490	−	16.2356i	0.871725	−	0.928130i
$307$	−7.19481			−0.410630			−0.205315	−	0.978696i	$-0.565822\pi$
$307$	−7.19481			−0.410630			−0.205315	+	0.978696i	$0.565822\pi$
$308$	−5.00665	+	0.314111i	−0.285280	+	0.0178981i
$309$		−	3.16917i		−	0.180288i
$310$	−5.71643	−	19.7624i	−0.324671	−	1.12243i
$311$		−	25.6535i		−	1.45468i	−0.686279	−	0.727338i	$-0.740757\pi$
$311$		−	25.6535i		−	1.45468i	0.686279	−	0.727338i	$-0.259243\pi$
$312$	−2.80574	+	3.38974i	−0.158843	+	0.191906i
$313$	30.7114			1.73591			0.867954	−	0.496644i	$-0.165435\pi$
$313$	30.7114			1.73591			0.867954	+	0.496644i	$0.165435\pi$
$314$	−2.50353	+	2.66552i	−0.141282	+	0.150424i
$315$	2.18053	−	3.67797i	0.122859	−	0.207230i
$316$	0.332842	+	5.30521i	0.0187238	+	0.298441i
$317$		−	5.69841i		−	0.320055i	−0.987113	−	0.160027i	$-0.948842\pi$
$317$		−	5.69841i		−	0.320055i	0.987113	−	0.160027i	$-0.0511582\pi$
$318$	−1.33698	+	1.42349i	−0.0749740	+	0.0798252i
$319$	5.24159			0.293473
$320$	−6.08659	+	16.8212i	−0.340251	+	0.940335i
$321$		−	1.95723i		−	0.109242i
$322$	4.38192	−	0.716236i	0.244195	−	0.0399143i
$323$	38.5674			2.14595
$324$	−1.03872	−	16.5563i	−0.0577069	−	0.919797i
$325$	−24.2671	+	13.2726i	−1.34610	+	0.736231i
$326$	1.71237	−	1.82317i	0.0948395	−	0.100976i
$327$		−	3.19528i		−	0.176700i
$328$	−13.0356	−	10.7898i	−0.719772	−	0.595766i
$329$		−	3.69816i		−	0.203886i
$330$	3.27318	−	0.946795i	0.180183	−	0.0521194i
$331$		−	0.289786i		−	0.0159281i	−0.999968	−	0.00796403i	$-0.997465\pi$
$331$		−	0.289786i		−	0.0159281i	0.999968	−	0.00796403i	$-0.00253506\pi$
$332$	31.2892	−	1.96304i	1.71722	−	0.107736i
$333$	−1.06370			−0.0582906
$334$	−12.7864	+	13.6138i	−0.699643	+	0.744913i
$335$	−9.34760	+	15.7670i	−0.510714	+	0.861441i
$336$	−0.0920429	−	0.730654i	−0.00502135	−	0.0398604i
$337$	−19.0234			−1.03627			−0.518134	−	0.855299i	$-0.673373\pi$
$337$	−19.0234			−1.03627			−0.518134	+	0.855299i	$0.673373\pi$
$338$	17.0421	−	18.1448i	0.926969	−	0.986949i
$339$	−1.80905			−0.0982544
$340$	10.9748	−	21.4724i	0.595190	−	1.16450i
$341$		−	24.9257i		−	1.34980i
$342$	20.2271	−	21.5359i	1.09376	−	1.16453i
$343$			8.88457i			0.479722i
$344$	3.70711	−	4.47873i	0.199874	−	0.241477i
$345$	−2.79966	+	1.12126i	−0.150728	+	0.0603666i
$346$	−2.60958	−	2.45099i	−0.140292	−	0.131766i
$347$	−15.5843			−0.836607			−0.418304	−	0.908307i	$-0.637375\pi$
$347$	−15.5843			−0.836607			−0.418304	+	0.908307i	$0.637375\pi$
$348$	0.0481811	+	0.767964i	0.00258278	+	0.0411672i
$349$	12.3741			0.662369			0.331185	−	0.943566i	$-0.392552\pi$
$349$	12.3741			0.662369			0.331185	+	0.943566i	$0.392552\pi$
$350$	1.16131	−	4.48106i	0.0620745	−	0.239523i
$351$		−	9.21136i		−	0.491666i
$352$	−12.7472	+	17.5289i	−0.679428	+	0.934291i
$353$			19.9365i			1.06111i	0.847650	+	0.530556i	$0.178017\pi$
$353$			19.9365i			1.06111i	−0.847650	+	0.530556i	$0.821983\pi$
$354$	2.47888	+	2.32823i	0.131751	+	0.123744i
$355$	−6.82023	+	11.5039i	−0.361980	+	0.610566i
$356$	−32.5245	+	2.04055i	−1.72380	+	0.108149i
$357$			0.992735i			0.0525411i
$358$	6.83191	+	6.41672i	0.361078	+	0.339134i
$359$	26.9051			1.42000			0.709999	−	0.704203i	$-0.248695\pi$
$359$	26.9051			1.42000			0.709999	+	0.704203i	$0.248695\pi$
$360$	−6.23427	−	17.3897i	−0.328575	−	0.916519i
$361$	32.1581			1.69253
$362$	−7.22086	−	6.78203i	−0.379520	−	0.356455i
$363$	1.03485			0.0543156
$364$	0.453523	+	7.22875i	0.0237711	+	0.378890i
$365$	7.45236	−	12.5702i	0.390074	−	0.657952i
$366$	1.80181	+	1.69231i	0.0941823	+	0.0884586i
$367$		−	18.1969i		−	0.949871i	−0.880020	−	0.474936i	$-0.842471\pi$
$367$		−	18.1969i		−	0.949871i	0.880020	−	0.474936i	$-0.157529\pi$
$368$	9.68777	−	16.5574i	0.505010	−	0.863114i
$369$	17.4751			0.909717
$370$	−1.10625	+	0.319992i	−0.0575113	+	0.0166356i
$371$			3.21452i			0.166890i
$372$	3.65195	−	0.229119i	0.189345	−	0.0118792i
$373$	−12.5810			−0.651418			−0.325709	−	0.945470i	$-0.605603\pi$
$373$	−12.5810			−0.651418			−0.325709	+	0.945470i	$0.605603\pi$
$374$	20.0024	−	21.2966i	1.03430	−	1.10122i
$375$	−0.108970	+	3.14234i	−0.00562717	+	0.162270i
$376$	−12.3085	−	10.1879i	−0.634763	−	0.525403i
$377$		−	7.56798i		−	0.389771i
$378$	1.12369	+	1.05540i	0.0577965	+	0.0542840i
$379$	10.9642			0.563192			0.281596	−	0.959533i	$-0.409136\pi$
$379$	10.9642			0.563192			0.281596	+	0.959533i	$0.409136\pi$
$380$	14.5576	−	28.4823i	0.746789	−	1.46111i
$381$	4.62168			0.236776
$382$	−21.6140	+	23.0126i	−1.10587	+	1.17743i
$383$		−	4.76207i		−	0.243330i	−0.992571	−	0.121665i	$-0.961177\pi$
$383$		−	4.76207i		−	0.243330i	0.992571	−	0.121665i	$-0.0388234\pi$
$384$	−2.68539	−	1.70651i	−0.137038	−	0.0870849i
$385$	2.86024	−	4.82447i	0.145771	−	0.245878i
$386$	0.699609	+	0.657091i	0.0356091	+	0.0334451i
$387$			6.00403i			0.305202i
$388$	−1.71028	−	27.2604i	−0.0868264	−	1.38394i
$389$		−	22.6828i		−	1.15006i	−0.818132	−	0.575031i	$-0.804990\pi$
$389$		−	22.6828i		−	1.15006i	0.818132	−	0.575031i	$-0.195010\pi$
$390$	−1.36701	−	4.72592i	−0.0692214	−	0.239307i
$391$	−15.7468	+	20.5128i	−0.796349	+	1.03738i
$392$	14.3183	+	11.8514i	0.723182	+	0.598588i
$393$		−	3.94908i		−	0.199205i
$394$	10.2251	+	9.60367i	0.515132	+	0.483826i
$395$	−5.11217	−	3.03080i	−0.257221	−	0.152496i
$396$	−1.40149	−	22.3385i	−0.0704276	−	1.12255i
$397$			21.3718i			1.07262i	0.844021	+	0.536310i	$0.180182\pi$
$397$			21.3718i			1.07262i	−0.844021	+	0.536310i	$0.819818\pi$
$398$	−18.8076	+	20.0245i	−0.942738	+	1.00374i
$399$			1.31682i			0.0659237i
$400$	−11.7150	−	16.2099i	−0.585748	−	0.810493i
$401$		−	32.0721i		−	1.60160i	−0.598930	−	0.800801i	$-0.704407\pi$
$401$		−	32.0721i		−	1.60160i	0.598930	−	0.800801i	$-0.295593\pi$
$402$	−2.37638	−	2.23196i	−0.118523	−	0.111320i
$403$	−35.9885			−1.79271
$404$	−0.0762933	−	1.21605i	−0.00379573	−	0.0605006i
$405$	15.9539	+	9.45844i	0.792756	+	0.469994i
$406$	0.923215	+	0.867109i	0.0458184	+	0.0430339i
$407$	−1.39528			−0.0691616
$408$	3.30410	+	2.73485i	0.163577	+	0.135395i
$409$	18.9559			0.937308			0.468654	−	0.883382i	$-0.344739\pi$
$409$	18.9559			0.937308			0.468654	+	0.883382i	$0.344739\pi$
$410$	18.1741	−	5.25701i	0.897555	−	0.259625i
$411$	−1.18030			−0.0582199
$412$	−22.4938	+	1.41123i	−1.10819	+	0.0695265i
$413$	5.59781			0.275450
$414$	3.19568	+	19.5511i	0.157059	+	0.960886i
$415$	−17.8751	+	30.1507i	−0.877456	+	1.48004i
$416$	25.3087	+	18.4048i	1.24086	+	0.902370i
$417$		−	5.14275i		−	0.251842i
$418$	26.5323	−	28.2491i	1.29774	−	1.38171i
$419$	1.24267			0.0607086			0.0303543	−	0.999539i	$-0.490336\pi$
$419$	1.24267			0.0607086			0.0303543	+	0.999539i	$0.490336\pi$
$420$	0.733141	+	0.374716i	0.0357736	+	0.0182843i
$421$			6.09732i			0.297165i	0.988900	+	0.148583i	$0.0474711\pi$
$421$			6.09732i			0.297165i	−0.988900	+	0.148583i	$0.952529\pi$
$422$	4.17971	+	3.92570i	0.203465	+	0.191100i
$423$	16.5003			0.802274
$424$	10.6988	+	8.85558i	0.519581	+	0.430065i
$425$	12.9373	+	23.6540i	0.627550	+	1.14739i
$426$	−1.73386	−	1.62849i	−0.0840059	−	0.0789007i
$427$	4.06886			0.196906
$428$	−13.8918	+	0.871554i	−0.671485	+	0.0421282i
$429$		−	5.96066i		−	0.287784i
$430$	1.80618	+	6.24419i	0.0871019	+	0.301122i
$431$	12.3343			0.594124			0.297062	−	0.954858i	$-0.403993\pi$
$431$	12.3343			0.594124			0.297062	+	0.954858i	$0.403993\pi$
$432$	6.60829	−	0.832469i	0.317942	−	0.0400522i
$433$	28.5488			1.37197			0.685983	−	0.727617i	$-0.259372\pi$
$433$	28.5488			1.37197			0.685983	+	0.727617i	$0.259372\pi$
$434$	4.12342	−	4.39022i	0.197930	−	0.210737i
$435$	−0.740020	−	0.438729i	−0.0354812	−	0.0210354i
$436$	−22.6792	+	1.42286i	−1.08613	+	0.0681427i
$437$	−20.8875	+	27.2094i	−0.999184	+	1.30160i
$438$	1.89456	+	1.77943i	0.0905257	+	0.0850243i
$439$		−	8.91781i		−	0.425624i	−0.977093	−	0.212812i	$-0.931738\pi$
$439$		−	8.91781i		−	0.425624i	0.977093	−	0.212812i	$-0.0682621\pi$
$440$	−8.17761	−	22.8104i	−0.389852	−	1.08745i
$441$	−19.1946			−0.914027
$442$	−30.7487	−	28.8800i	−1.46257	−	1.37368i
$443$	−37.6705			−1.78978			−0.894889	−	0.446289i	$-0.852745\pi$
$443$	−37.6705			−1.78978			−0.894889	+	0.446289i	$0.852745\pi$
$444$	−0.0128255	−	0.204427i	−0.000608673	−	0.00970170i
$445$	18.5809	−	31.3411i	0.880818	−	1.48571i
$446$	−3.34137	+	3.55757i	−0.158218	+	0.168456i
$447$			3.63446i			0.171904i
$448$	−5.14497	+	0.978653i	−0.243077	+	0.0462370i
$449$	−16.8125			−0.793431			−0.396715	−	0.917942i	$-0.629850\pi$
$449$	−16.8125			−0.793431			−0.396715	+	0.917942i	$0.629850\pi$
$450$	19.9935	+	5.18149i	0.942500	+	0.244258i
$451$	22.9224			1.07938
$452$	0.805573	+	12.8401i	0.0378910	+	0.603948i
$453$			0.722730i			0.0339568i
$454$	22.3189	+	20.9625i	1.04748	+	0.983820i
$455$	−6.96572	−	4.12970i	−0.326558	−	0.193603i
$456$	4.38276	+	3.62768i	0.205242	+	0.169881i
$457$	−23.2244			−1.08639			−0.543196	−	0.839606i	$-0.682786\pi$
$457$	−23.2244			−1.08639			−0.543196	+	0.839606i	$0.682786\pi$
$458$	21.4580	+	20.1539i	1.00267	+	0.941731i
$459$	−8.97865			−0.419088
$460$	9.20504	+	19.3718i	0.429187	+	0.903215i
$461$	−2.97543			−0.138579			−0.0692897	−	0.997597i	$-0.522073\pi$
$461$	−2.97543			−0.138579			−0.0692897	+	0.997597i	$0.522073\pi$
$462$	0.727140	+	0.682950i	0.0338296	+	0.0317737i
$463$	−13.7510			−0.639063			−0.319532	−	0.947576i	$-0.603526\pi$
$463$	−13.7510			−0.639063			−0.319532	+	0.947576i	$0.603526\pi$
$464$	5.42932	−	0.683949i	0.252050	−	0.0317516i
$465$	−2.08631	+	3.51906i	−0.0967505	+	0.163193i
$466$	5.67849	+	5.33339i	0.263051	+	0.247064i
$467$			5.53901i			0.256315i	0.991754	+	0.128157i	$0.0409063\pi$
$467$			5.53901i			0.256315i	−0.991754	+	0.128157i	$0.959094\pi$
$468$	−32.2531	+	2.02352i	−1.49090	+	0.0935371i
$469$	−5.36635			−0.247795
$470$	17.1604	−	4.96377i	0.791548	−	0.228962i
$471$	0.727199			0.0335076
$472$	15.4212	−	18.6311i	0.709819	−	0.857564i
$473$			7.87561i			0.362121i
$474$	0.723676	−	0.770501i	0.0332395	−	0.0353903i
$475$	17.1608	+	31.3761i	0.787391	+	1.43963i
$476$	7.04613	−	0.442066i	0.322959	−	0.0202620i
$477$	−14.3425			−0.656696
$478$	−22.7187	−	21.3380i	−1.03913	−	0.975979i
$479$	9.33772			0.426651			0.213326	−	0.976981i	$-0.431570\pi$
$479$	9.33772			0.426651			0.213326	+	0.976981i	$0.431570\pi$
$480$	3.26687	−	1.40781i	0.149111	−	0.0642572i
$481$			2.01455i			0.0918556i
$482$	−11.8068	−	11.0892i	−0.537784	−	0.505101i
$483$	−0.700377	−	0.537650i	−0.0318682	−	0.0244639i
$484$	−0.460820	−	7.34506i	−0.0209463	−	0.333866i
$485$	26.2685	+	15.5735i	1.19279	+	0.707158i
$486$	−7.09489	+	7.55397i	−0.321831	+	0.342655i
$487$	16.6129			0.752801			0.376401	−	0.926457i	$-0.377162\pi$
$487$	16.6129			0.752801			0.376401	+	0.926457i	$0.377162\pi$
$488$	11.2092	−	13.5423i	0.507415	−	0.613031i
$489$	−0.497392			−0.0224928
$490$	−19.9623	+	5.77427i	−0.901806	+	0.260855i
$491$			12.0468i			0.543664i	0.962345	+	0.271832i	$0.0876295\pi$
$491$			12.0468i			0.543664i	−0.962345	+	0.271832i	$0.912370\pi$
$492$	0.210705	+	3.35844i	0.00949930	+	0.151410i
$493$	−7.37678			−0.332234
$494$	−40.7869	−	38.3082i	−1.83509	−	1.72357i
$495$	21.5257	+	12.7617i	0.967508	+	0.573597i
$496$	−3.25243	−	25.8184i	−0.146038	−	1.15928i
$497$	−3.91541			−0.175630
$498$	−4.54428	−	4.26811i	−0.203634	−	0.191259i
$499$			27.5819i			1.23474i	0.786675	+	0.617368i	$0.211801\pi$
$499$			27.5819i			1.23474i	−0.786675	+	0.617368i	$0.788199\pi$
$500$	22.3519	−	0.625854i	0.999608	−	0.0279890i
$501$	3.71407			0.165933
$502$	12.5739	−	13.3875i	0.561203	−	0.597515i
$503$		−	27.9969i		−	1.24832i	−0.781296	−	0.624161i	$-0.785441\pi$
$503$		−	27.9969i		−	1.24832i	0.781296	−	0.624161i	$-0.214559\pi$
$504$	3.44858	−	4.16639i	0.153612	−	0.185586i
$505$	1.17180	+	0.694713i	0.0521443	+	0.0309143i
$506$	4.19184	+	25.6456i	0.186350	+	1.14009i
$507$	−4.95022			−0.219847
$508$	−2.05803	−	32.8032i	−0.0913105	−	1.45541i
$509$	34.9389			1.54864			0.774319	−	0.632795i	$-0.218092\pi$
$509$	34.9389			1.54864			0.774319	+	0.632795i	$0.218092\pi$
$510$	−4.60653	+	1.33248i	−0.203981	+	0.0590031i
$511$	4.27831			0.189261
$512$	−10.9165	+	19.8200i	−0.482444	+	0.875927i
$513$	−11.9098			−0.525832
$514$	−17.7165	−	16.6399i	−0.781443	−	0.733953i
$515$	12.8504	−	21.6753i	0.566258	−	0.955129i
$516$	−1.15388	+	0.0723931i	−0.0507968	+	0.00318693i
$517$	21.6438			0.951895
$518$	−0.245755	−	0.230819i	−0.0107978	−	0.0101416i
$519$			0.711937i			0.0312506i
$520$	−32.9344	+	11.8071i	−1.44427	+	0.517775i
$521$		−	14.5055i		−	0.635496i	−0.948175	−	0.317748i	$-0.897073\pi$
$521$		−	14.5055i		−	0.635496i	0.948175	−	0.317748i	$-0.102927\pi$
$522$	−3.86884	+	4.11918i	−0.169335	+	0.180291i
$523$			36.8502i			1.61135i	0.592359	+	0.805674i	$0.298197\pi$
$523$			36.8502i			1.61135i	−0.592359	+	0.805674i	$0.701803\pi$
$524$	−28.0294	+	1.75853i	−1.22447	+	0.0768217i
$525$	−0.807630	+	0.441724i	−0.0352479	+	0.0192784i
$526$	−11.1900	−	10.5100i	−0.487908	−	0.458256i
$527$			35.0793i			1.52808i
$528$	4.27622	−	0.538690i	0.186099	−	0.0234435i
$529$	−5.94359	−	22.2188i	−0.258417	−	0.966033i
$530$	−14.9162	+	4.31462i	−0.647916	+	0.187415i
$531$			24.9761i			1.08387i
$532$	9.34642	−	0.586383i	0.405219	−	0.0254229i
$533$		−	33.0961i		−	1.43355i
$534$	4.72369	+	4.43662i	0.204414	+	0.191991i
$535$	7.93622	−	13.3863i	0.343113	−	0.578741i
$536$	−14.7836	+	17.8607i	−0.638553	+	0.771465i
$537$		−	1.86386i		−	0.0804316i
$538$	26.4601	−	28.1722i	1.14078	−	1.21459i
$539$	−25.1779			−1.08449
$540$	−3.38907	+	6.63079i	−0.145842	+	0.285344i
$541$	−11.3540			−0.488145			−0.244073	−	0.969757i	$-0.578484\pi$
$541$	−11.3540			−0.488145			−0.244073	+	0.969757i	$0.578484\pi$
$542$	−25.8687	−	24.2966i	−1.11116	−	1.04363i
$543$			1.96997i			0.0845396i
$544$	17.9398	−	24.6693i	0.769164	−	1.05769i
$545$	12.9563	−	21.8539i	0.554988	−	0.936119i
$546$	0.986064	−	1.04987i	0.0421996	−	0.0449302i
$547$	−2.81699			−0.120446			−0.0602229	−	0.998185i	$-0.519181\pi$
$547$	−2.81699			−0.120446			−0.0602229	+	0.998185i	$0.519181\pi$
$548$	0.525588	+	8.37740i	0.0224520	+	0.357865i
$549$			18.1543i			0.774808i
$550$	26.2258	+	6.79666i	1.11827	+	0.289811i
$551$	−9.78502			−0.416856
$552$	−3.71889	+	0.849897i	−0.158287	+	0.0361740i
$553$		−	1.73995i		−	0.0739902i
$554$	−6.26954	−	5.88852i	−0.266367	−	0.250179i
$555$	0.196989	+	0.116787i	0.00836172	+	0.00495733i
$556$	−36.5017	+	2.29007i	−1.54802	+	0.0971206i
$557$	6.66780			0.282524			0.141262	−	0.989972i	$-0.454884\pi$
$557$	6.66780			0.282524			0.141262	+	0.989972i	$0.454884\pi$
$558$	19.5882	+	18.3978i	0.829234	+	0.778839i
$559$	11.3710			0.480944
$560$	2.33315	−	5.37047i	0.0985938	−	0.226944i
$561$	−5.81008			−0.245302
$562$	−20.1632	−	18.9379i	−0.850535	−	0.798846i
$563$		−	17.4556i		−	0.735666i	−0.929892	−	0.367833i	$-0.880100\pi$
$563$		−	17.4556i		−	0.735666i	0.929892	−	0.367833i	$-0.119900\pi$
$564$	0.198952	+	3.17111i	0.00837737	+	0.133528i
$565$	−12.3729	−	7.33541i	−0.520532	−	0.308603i
$566$	−19.4454	−	18.2636i	−0.817349	−	0.767677i
$567$			5.42998i			0.228038i
$568$	−10.7864	+	13.0316i	−0.452589	+	0.546794i
$569$		−	0.914134i		−	0.0383225i	−0.999816	−	0.0191613i	$-0.993900\pi$
$569$		−	0.914134i		−	0.0383225i	0.999816	−	0.0191613i	$-0.00609959\pi$
$570$	−6.11038	+	1.76748i	−0.255936	+	0.0740315i
$571$	2.39490			0.100224			0.0501118	−	0.998744i	$-0.484042\pi$
$571$	2.39490			0.100224			0.0501118	+	0.998744i	$0.484042\pi$
$572$	−42.3070	+	2.65429i	−1.76894	+	0.110981i
$573$	6.27822			0.262277
$574$	4.03739	+	3.79202i	0.168517	+	0.158276i
$575$	−23.6946	−	3.68336i	−0.988132	−	0.153607i
$576$	−4.36653	−	22.9557i	−0.181939	−	0.956487i
$577$			21.6501i			0.901307i	0.892699	+	0.450654i	$0.148809\pi$
$577$			21.6501i			0.901307i	−0.892699	+	0.450654i	$0.851191\pi$
$578$	−11.6913	+	12.4477i	−0.486292	+	0.517757i
$579$		−	0.190865i		−	0.00793209i
$580$	−2.78443	+	5.44780i	−0.115617	+	0.226208i
$581$	−10.2619			−0.425736
$582$	−3.71855	+	3.95916i	−0.154139	+	0.164112i
$583$	−18.8133			−0.779167
$584$	11.7862	−	14.2394i	0.487715	−	0.589231i
$585$	18.4258	−	31.0795i	0.761813	−	1.28498i
$586$	20.0229	−	21.3184i	0.827137	−	0.880656i
$587$	−27.9584			−1.15396			−0.576982	−	0.816757i	$-0.695770\pi$
$587$	−27.9584			−1.15396			−0.576982	+	0.816757i	$0.695770\pi$
$588$	−0.231437	−	3.68890i	−0.00954429	−	0.152128i
$589$			46.5313i			1.91729i
$590$	7.51353	+	25.9752i	0.309327	+	1.06938i
$591$		−	2.78957i		−	0.114748i
$592$	−1.44525	+	0.182063i	−0.0593995	+	0.00748276i
$593$			22.7821i			0.935547i	0.883848	+	0.467773i	$0.154944\pi$
$593$			22.7821i			0.935547i	−0.883848	+	0.467773i	$0.845056\pi$
$594$	−6.17684	+	6.57651i	−0.253439	+	0.269838i
$595$	−4.02537	+	6.78974i	−0.165024	+	0.278352i
$596$	25.7963	−	1.61842i	1.05666	−	0.0662933i
$597$	5.46303			0.223587
$598$	37.0279	−	6.05231i	1.51418	−	0.247497i
$599$			25.3111i			1.03418i	0.855930	+	0.517092i	$0.172985\pi$
$599$			25.3111i			1.03418i	−0.855930	+	0.517092i	$0.827015\pi$
$600$	−0.754732	+	3.90491i	−0.0308118	+	0.159417i
$601$	−19.2016			−0.783251			−0.391625	−	0.920125i	$-0.628087\pi$
$601$	−19.2016			−0.783251			−0.391625	+	0.920125i	$0.628087\pi$
$602$	−1.30285	+	1.38715i	−0.0531002	+	0.0565360i
$603$		−	23.9434i		−	0.975052i
$604$	5.12972	−	0.321832i	0.208725	−	0.0130952i
$605$	7.07779	+	4.19614i	0.287753	+	0.170597i
$606$	−0.165879	+	0.176612i	−0.00673838	+	0.00717439i
$607$	−32.0992			−1.30286			−0.651432	−	0.758707i	$-0.725832\pi$
$607$	−32.0992			−1.30286			−0.651432	+	0.758707i	$0.725832\pi$
$608$	23.7965	−	32.7229i	0.965075	−	1.32709i
$609$		−	0.251869i		−	0.0102062i
$610$	5.46134	+	18.8805i	0.221123	+	0.764449i
$611$		−	31.2500i		−	1.26424i
$612$	1.97240	+	31.4382i	0.0797294	+	1.27082i
$613$	34.4018			1.38947			0.694737	−	0.719264i	$-0.255521\pi$
$613$	34.4018			1.38947			0.694737	+	0.719264i	$0.255521\pi$
$614$	6.96592	−	7.41665i	0.281122	−	0.299311i
$615$	−3.23624	−	1.91864i	−0.130498	−	0.0773670i
$616$	4.52357	−	5.46513i	0.182260	−	0.220197i
$617$	24.5692			0.989117			0.494559	−	0.869144i	$-0.335330\pi$
$617$	24.5692			0.989117			0.494559	+	0.869144i	$0.335330\pi$
$618$	3.26688	+	3.06835i	0.131413	+	0.123427i
$619$	11.3810			0.457441			0.228720	−	0.973492i	$-0.426546\pi$
$619$	11.3810			0.457441			0.228720	+	0.973492i	$0.426546\pi$
$620$	25.9063	+	13.2410i	1.04042	+	0.531770i
$621$	4.86269	−	6.33446i	0.195133	−	0.254193i
$622$	26.4445	+	24.8374i	1.06033	+	0.995887i
$623$	10.6671			0.427367
$624$	−0.777777	−	6.17414i	−0.0311360	−	0.247163i
$625$	−13.4870	+	21.0500i	−0.539478	+	0.842000i
$626$	−29.7343	+	31.6583i	−1.18842	+	1.26532i
$627$	−7.70684			−0.307782
$628$	−0.323822	−	5.16144i	−0.0129219	−	0.205964i
$629$	1.96366			0.0782961
$630$	1.68022	+	5.80872i	0.0669416	+	0.231425i
$631$	−35.3367			−1.40673			−0.703366	−	0.710828i	$-0.748320\pi$
$631$	−35.3367			−1.40673			−0.703366	+	0.710828i	$0.748320\pi$
$632$	−5.79104	−	4.79333i	−0.230355	−	0.190668i
$633$		−	1.14030i		−	0.0453227i
$634$	5.87411	+	5.51712i	0.233291	+	0.219113i
$635$	31.6096	+	18.7401i	1.25439	+	0.743678i
$636$	−0.172933	−	2.75640i	−0.00685724	−	0.109298i
$637$			36.3526i			1.44034i
$638$	−5.07484	+	5.40321i	−0.200915	+	0.213915i
$639$		−	17.4697i		−	0.691090i
$640$	−11.4469	−	22.5603i	−0.452479	−	0.891775i
$641$		−	16.5488i		−	0.653638i	−0.945087	−	0.326819i	$-0.894023\pi$
$641$		−	16.5488i		−	0.653638i	0.945087	−	0.326819i	$-0.105977\pi$
$642$	2.01757	+	1.89496i	0.0796272	+	0.0747881i
$643$		−	4.87109i		−	0.192097i	−0.995377	−	0.0960486i	$-0.969380\pi$
$643$		−	4.87109i		−	0.192097i	0.995377	−	0.0960486i	$-0.0306204\pi$
$644$	−3.50419	+	5.21048i	−0.138085	+	0.205321i
$645$	0.659199	−	1.11190i	0.0259559	−	0.0437808i
$646$	−37.3404	+	39.7565i	−1.46914	+	1.56420i
$647$	44.4194			1.74631			0.873154	−	0.487444i	$-0.162071\pi$
$647$	44.4194			1.74631			0.873154	+	0.487444i	$0.162071\pi$
$648$	18.0725	+	14.9589i	0.709955	+	0.587640i
$649$			32.7617i			1.28601i
$650$	9.81323	−	37.8656i	0.384906	−	1.48521i
$651$	−1.19773			−0.0469427
$652$	0.221489	+	3.53034i	0.00867417	+	0.138259i
$653$		−	5.52577i		−	0.216240i	−0.994138	−	0.108120i	$-0.965517\pi$
$653$		−	5.52577i		−	0.216240i	0.994138	−	0.108120i	$-0.0344831\pi$
$654$	3.29380	+	3.09363i	0.128798	+	0.120971i
$655$	16.0129	−	27.0095i	0.625674	−	1.05535i
$656$	23.7434	−	2.99103i	0.927023	−	0.116780i
$657$			19.0888i			0.744727i
$658$	3.81218	+	3.58051i	0.148614	+	0.139583i
$659$	−25.2982			−0.985479			−0.492739	−	0.870177i	$-0.664004\pi$
$659$	−25.2982			−0.985479			−0.492739	+	0.870177i	$0.664004\pi$
$660$	−2.19306	+	4.29078i	−0.0853649	+	0.167018i
$661$		−	24.9395i		−	0.970036i	−0.874504	−	0.485018i	$-0.838813\pi$
$661$		−	24.9395i		−	0.970036i	0.874504	−	0.485018i	$-0.161187\pi$
$662$	0.298720	+	0.280566i	0.0116101	+	0.0109045i
$663$			8.38877i			0.325793i
$664$	−28.2702	+	34.1545i	−1.09710	+	1.32545i
$665$	−5.33950	+	9.00633i	−0.207057	+	0.349250i
$666$	1.02986	−	1.09650i	0.0399064	−	0.0424885i
$667$	3.99515	−	5.20434i	0.154693	−	0.201513i
$668$	−1.65388	−	26.3614i	−0.0639905	−	1.01995i
$669$	0.970566			0.0375242
$670$	−7.20286	−	24.9012i	−0.278271	−	0.962016i
$671$			23.8134i			0.919306i
$672$	0.842296	+	0.612528i	0.0324923	+	0.0236288i
$673$			10.5013i			0.404796i	0.979303	+	0.202398i	$0.0648735\pi$
$673$			10.5013i			0.404796i	−0.979303	+	0.202398i	$0.935127\pi$
$674$	18.4181	−	19.6099i	0.709440	−	0.755345i
$675$	−3.99511	−	7.30449i	−0.153772	−	0.281150i
$676$	2.20434	+	35.1351i	0.0847821	+	1.35135i
$677$	−24.8115			−0.953583			−0.476792	−	0.879016i	$-0.658200\pi$
$677$	−24.8115			−0.953583			−0.476792	+	0.879016i	$0.658200\pi$
$678$	1.75150	−	1.86483i	0.0672660	−	0.0716185i
$679$			8.94058i			0.343108i
$680$	11.5088	+	32.1024i	0.441343	+	1.23107i
$681$		−	6.08898i		−	0.233330i
$682$	25.6942	+	24.1327i	0.983882	+	0.924089i
$683$	24.7975			0.948848			0.474424	−	0.880296i	$-0.342656\pi$
$683$	24.7975			0.948848			0.474424	+	0.880296i	$0.342656\pi$
$684$	2.61631	+	41.7016i	0.100037	+	1.59450i
$685$	−8.07257	−	4.78591i	−0.308437	−	0.182860i
$686$	−9.15850	−	8.60192i	−0.349673	−	0.328423i
$687$		−	5.85411i		−	0.223348i
$688$	1.02765	+	8.15766i	0.0391787	+	0.311008i
$689$			27.1632i			1.03484i
$690$	1.55476	−	3.97157i	0.0591887	−	0.151195i
$691$		−	22.3112i		−	0.848756i	−0.905485	−	0.424378i	$-0.860493\pi$
$691$		−	22.3112i		−	0.848756i	0.905485	−	0.424378i	$-0.139507\pi$
$692$	5.05311	−	0.317026i	0.192090	−	0.0120515i
$693$			7.32636i			0.278305i
$694$	15.0885	−	16.0648i	0.572751	−	0.609810i
$695$	20.8530	−	35.1735i	0.790999	−	1.33421i
$696$	−0.838290	−	0.693865i	−0.0317753	−	0.0263009i
$697$	−32.2600			−1.22193
$698$	−11.9804	+	12.7556i	−0.453465	+	0.482807i
$699$		−	1.54919i		−	0.0585957i
$700$	3.49486	+	5.53561i	0.132093	+	0.209226i
$701$			16.5040i			0.623347i	0.950189	+	0.311673i	$0.100890\pi$
$701$			16.5040i			0.623347i	−0.950189	+	0.311673i	$0.899110\pi$
$702$	9.49537	+	8.91831i	0.358380	+	0.336600i
$703$	2.60471			0.0982387
$704$	−5.72766	−	30.1114i	−0.215869	−	1.13487i
$705$	−3.05572	−	1.81162i	−0.115085	−	0.0682295i
$706$	−20.5512	−	19.3022i	−0.773454	−	0.726449i
$707$			0.398827i			0.0149994i
$708$	−4.80003	+	0.301148i	−0.180396	+	0.0113178i
$709$			24.7656i			0.930090i	0.885287	+	0.465045i	$0.153962\pi$
$709$			24.7656i			0.930090i	−0.885287	+	0.465045i	$0.846038\pi$
$710$	−5.25538	−	18.1685i	−0.197231	−	0.681851i
$711$	7.76326			0.291145
$712$	29.3863	−	35.5030i	1.10130	−	1.33053i
$713$	−24.7485	−	18.9984i	−0.926839	−	0.711495i
$714$	−1.02334	−	0.961153i	−0.0382977	−	0.0359702i
$715$	24.1695	−	40.7675i	0.903887	−	1.52462i
$716$	−13.2291	+	0.829979i	−0.494396	+	0.0310178i
$717$			6.19805i			0.231471i
$718$	−26.0492	+	27.7347i	−0.972146	+	1.03505i
$719$			25.2459i			0.941515i	0.882263	+	0.470757i	$0.156019\pi$
$719$			25.2459i			0.941515i	−0.882263	+	0.470757i	$0.843981\pi$
$720$	23.9618	+	10.4100i	0.893005	+	0.387958i
$721$	7.37729			0.274745
$722$	−31.1351	+	33.1497i	−1.15873	+	1.23370i
$723$			3.22109i			0.119794i
$724$	13.9823	−	0.877230i	0.519647	−	0.0326020i
$725$	−3.28234	−	6.00131i	−0.121903	−	0.222883i
$726$	−1.00193	+	1.06676i	−0.0371850	+	0.0395911i
$727$			1.08854i			0.0403716i	0.999796	+	0.0201858i	$0.00642578\pi$
$727$			1.08854i			0.0403716i	−0.999796	+	0.0201858i	$0.993574\pi$
$728$	−7.89073	−	6.53127i	−0.292450	−	0.242065i
$729$	−22.8225			−0.845278
$730$	5.74247	+	19.8524i	0.212538	+	0.734770i
$731$		−	11.0838i		−	0.409948i
$732$	−3.48898	+	0.218894i	−0.128956	+	0.00809057i
$733$	12.6647			0.467782			0.233891	−	0.972263i	$-0.424854\pi$
$733$	12.6647			0.467782			0.233891	+	0.972263i	$0.424854\pi$
$734$	18.7580	+	17.6180i	0.692370	+	0.650292i
$735$	3.55467	+	2.10742i	0.131116	+	0.0777335i
$736$	7.68833	+	26.0171i	0.283396	+	0.959003i
$737$		−	31.4071i		−	1.15689i
$738$	−16.9191	+	18.0139i	−0.622802	+	0.663101i
$739$			2.47297i			0.0909697i	0.998965	+	0.0454849i	$0.0144833\pi$
$739$			2.47297i			0.0909697i	−0.998965	+	0.0454849i	$0.985517\pi$
$740$	0.741199	−	1.45017i	0.0272470	−	0.0533094i
$741$			11.1274i			0.408774i
$742$	−3.31363	−	3.11226i	−0.121647	−	0.114254i
$743$			2.46872i			0.0905687i	0.998974	+	0.0452843i	$0.0144194\pi$
$743$			2.46872i			0.0905687i	−0.998974	+	0.0452843i	$0.985581\pi$
$744$	−3.29958	+	3.98637i	−0.120968	+	0.146148i
$745$	−14.7371	+	24.8576i	−0.539925	+	0.910712i
$746$	12.1807	−	12.9689i	0.445968	−	0.474824i
$747$		−	45.7863i		−	1.67523i
$748$	2.58723	+	41.2382i	0.0945985	+	1.50782i
$749$	4.55609			0.166476
$750$	−3.13373	−	3.15470i	−0.114428	−	0.115193i
$751$	6.97895			0.254666			0.127333	−	0.991860i	$-0.459358\pi$
$751$	6.97895			0.254666			0.127333	+	0.991860i	$0.459358\pi$
$752$	22.4190	−	2.82419i	0.817536	−	0.102988i
$753$	−3.65235			−0.133099
$754$	7.80132	+	7.32721i	0.284107	+	0.266841i
$755$	−2.93055	+	4.94306i	−0.106654	+	0.179896i
$756$	−2.17589	+	0.136512i	−0.0791362	+	0.00496491i
$757$	−12.8118			−0.465653			−0.232827	−	0.972518i	$-0.574797\pi$
$757$	−12.8118			−0.465653			−0.232827	+	0.972518i	$0.574797\pi$
$758$	−10.6154	+	11.3022i	−0.385568	+	0.410516i
$759$	3.14665	−	4.09902i	0.114216	−	0.148785i
$760$	15.2660	+	42.5826i	0.553755	+	1.54463i
$761$	15.7760			0.571879			0.285940	−	0.958248i	$-0.407694\pi$
$761$	15.7760			0.571879			0.285940	+	0.958248i	$0.407694\pi$
$762$	−4.47464	+	4.76417i	−0.162099	+	0.172588i
$763$	7.43808			0.269276
$764$	−2.79570	−	44.5609i	−0.101145	−	1.61216i
$765$	−30.2943	−	17.9603i	−1.09529	−	0.649356i
$766$	4.90889	+	4.61057i	0.177365	+	0.166587i
$767$	47.3024			1.70799
$768$	4.35908	−	1.11597i	0.157295	−	0.0402689i
$769$		−	43.1981i		−	1.55777i	−0.627170	−	0.778883i	$-0.715787\pi$
$769$		−	43.1981i		−	1.55777i	0.627170	−	0.778883i	$-0.284213\pi$
$770$	2.20398	+	7.61941i	0.0794259	+	0.274585i
$771$			4.83337i			0.174070i
$772$	−1.35470	+	0.0849924i	−0.0487568	+	0.00305894i
$773$	−21.0272			−0.756297			−0.378148	−	0.925745i	$-0.623439\pi$
$773$	−21.0272			−0.756297			−0.378148	+	0.925745i	$0.623439\pi$
$774$	−6.18915	−	5.81302i	−0.222464	−	0.208945i
$775$	−28.5384	+	15.6087i	−1.02513	+	0.560682i
$776$	29.7568	+	24.6301i	1.06821	+	0.884169i
$777$			0.0670460i			0.00240526i
$778$	23.3821	+	21.9611i	0.838290	+	0.787345i
$779$	−42.7916			−1.53317
$780$	6.19516	+	3.16641i	0.221822	+	0.113376i
$781$		−	22.9153i		−	0.819975i
$782$	−5.89941	−	36.0925i	−0.210962	−	1.29066i
$783$	2.27799			0.0814088
$784$	−26.0796	+	3.28534i	−0.931414	+	0.117333i
$785$	4.97363	+	2.94867i	0.177516	+	0.105242i
$786$	4.07084	+	3.82345i	0.145202	+	0.136378i
$787$		−	35.5684i		−	1.26788i	−0.773384	−	0.633938i	$-0.781438\pi$
$787$		−	35.5684i		−	1.26788i	0.773384	−	0.633938i	$-0.218562\pi$
$788$	−19.7995	+	1.24220i	−0.705329	+	0.0442515i
$789$			3.05283i			0.108683i
$790$	8.07378	−	2.33541i	0.287252	−	0.0830901i
$791$		−	4.21117i		−	0.149732i
$792$	24.3842	+	20.1831i	0.866454	+	0.717177i
$793$	34.3825			1.22096
$794$	−22.0307	−	20.6919i	−0.781842	−	0.734327i
$795$	2.65610	+	1.57470i	0.0942022	+	0.0558488i
$796$	−2.43269	−	38.7749i	−0.0862244	−	1.37434i
$797$	15.6053			0.552767			0.276383	−	0.961047i	$-0.410864\pi$
$797$	15.6053			0.552767			0.276383	+	0.961047i	$0.410864\pi$
$798$	−1.35743	−	1.27493i	−0.0480523	−	0.0451321i
$799$	−30.4606			−1.07762
$800$	28.0519	+	3.61800i	0.991785	+	0.127916i
$801$			47.5940i			1.68165i
$802$	33.0609	+	31.0517i	1.16742	+	1.09647i
$803$			25.0392i			0.883615i
$804$	4.60156	−	0.288696i	0.162284	−	0.0101815i
$805$	−2.61010	−	6.51712i	−0.0919940	−	0.229698i
$806$	34.8435	−	37.0981i	1.22731	−	1.30672i
$807$	−7.68585			−0.270555
$808$	1.32741	+	1.09871i	0.0466980	+	0.0386526i
$809$	24.0021			0.843871			0.421935	−	0.906626i	$-0.361351\pi$
$809$	24.0021			0.843871			0.421935	+	0.906626i	$0.361351\pi$
$810$	−25.1964	+	7.28827i	−0.885312	+	0.256084i
$811$		−	4.16792i		−	0.146356i	−0.997319	−	0.0731778i	$-0.976686\pi$
$811$		−	4.16792i		−	0.146356i	0.997319	−	0.0731778i	$-0.0233140\pi$
$812$	−1.78769	+	0.112157i	−0.0627356	+	0.00393595i
$813$			7.05743i			0.247515i
$814$	1.35089	−	1.43830i	0.0473488	−	0.0504125i
$815$	−3.40188	−	2.01684i	−0.119163	−	0.0706468i
$816$	−6.01816	+	0.758128i	−0.210678	+	0.0265398i
$817$		−	14.7022i		−	0.514365i
$818$	−18.3528	+	19.5403i	−0.641691	+	0.683212i
$819$	10.5780			0.369626
$820$	−12.1768	+	23.8242i	−0.425233	+	0.831977i
$821$	−40.5578			−1.41548			−0.707738	−	0.706475i	$-0.750284\pi$
$821$	−40.5578			−1.41548			−0.707738	+	0.706475i	$0.750284\pi$
$822$	1.14275	−	1.21669i	0.0398580	−	0.0424370i
$823$	0.0128583			0.000448212			0.000224106	−	1.00000i	$-0.499929\pi$
$823$	0.0128583			0.000448212			0.000224106		1.00000i	$0.499929\pi$
$824$	20.3234	−	24.5537i	0.708001	−	0.855368i
$825$	−2.58523	−	4.72673i	−0.0900061	−	0.164564i
$826$	−5.41972	+	5.77040i	−0.188576	+	0.200778i
$827$			13.9930i			0.486585i	0.969953	+	0.243293i	$0.0782275\pi$
$827$			13.9930i			0.486585i	−0.969953	+	0.243293i	$0.921772\pi$
$828$	−23.2480	−	15.6349i	−0.807922	−	0.543351i
$829$	−38.6058			−1.34083			−0.670417	−	0.741985i	$-0.733885\pi$
$829$	−38.6058			−1.34083			−0.670417	+	0.741985i	$0.733885\pi$
$830$	−13.7738	−	47.6177i	−0.478096	−	1.65283i
$831$			1.71044i			0.0593344i
$832$	−43.4758	+	8.26977i	−1.50725	+	0.286703i
$833$	35.4342			1.22772
$834$	5.30132	+	4.97914i	0.183570	+	0.172414i
$835$	25.4021	+	15.0599i	0.879078	+	0.521170i
$836$	3.43186	+	54.7008i	0.118693	+	1.89187i
$837$		−	10.8327i		−	0.374432i
$838$	−1.20314	+	1.28099i	−0.0415618	+	0.0442511i
$839$	10.3705			0.358028			0.179014	−	0.983847i	$-0.442709\pi$
$839$	10.3705			0.358028			0.179014	+	0.983847i	$0.442709\pi$
$840$	−1.09609	+	0.392950i	−0.0378186	+	0.0135581i
$841$	−27.1284			−0.935463
$842$	−6.28532	−	5.90334i	−0.216606	−	0.203443i
$843$			5.50088i			0.189460i
$844$	−8.09347	+	0.507774i	−0.278589	+	0.0174783i
$845$	−33.8567	−	20.0723i	−1.16471	−	0.690508i
$846$	−15.9754	+	17.0091i	−0.549246	+	0.584785i
$847$			2.40896i			0.0827727i
$848$	−19.4871	+	2.45485i	−0.669189	+	0.0843000i
$849$			5.30502i			0.182068i
$850$	−36.9090	−	9.56531i	−1.26597	−	0.328088i
$851$	−1.06349	+	1.38536i	−0.0364558	+	0.0474897i
$852$	3.35740	−	0.210639i	0.115023	−	0.00721639i
$853$		−	3.93487i		−	0.134727i	−0.997728	−	0.0673637i	$-0.978541\pi$
$853$		−	3.93487i		−	0.134727i	0.997728	−	0.0673637i	$-0.0214588\pi$
$854$	−3.93941	+	4.19431i	−0.134804	+	0.143526i
$855$	−40.1842	−	23.8236i	−1.37427	−	0.814751i
$856$	12.5514	−	15.1639i	0.428999	−	0.518293i
$857$		−	45.7555i		−	1.56298i	−0.623919	−	0.781489i	$-0.714461\pi$
$857$		−	45.7555i		−	1.56298i	0.623919	−	0.781489i	$-0.285539\pi$
$858$	6.14445	+	5.77103i	0.209768	+	0.197020i
$859$		−	29.0704i		−	0.991870i	−0.868360	−	0.495935i	$-0.834825\pi$
$859$		−	29.0704i		−	0.991870i	0.868360	−	0.495935i	$-0.165175\pi$
$860$	−8.18543	−	4.18366i	−0.279121	−	0.142662i
$861$		−	1.10147i		−	0.0375379i
$862$	−11.9419	+	12.7146i	−0.406744	+	0.433062i
$863$	5.33774			0.181699			0.0908494	−	0.995865i	$-0.471042\pi$
$863$	5.33774			0.181699			0.0908494	+	0.995865i	$0.471042\pi$
$864$	−5.53992	+	7.61803i	−0.188472	+	0.259171i
$865$	−2.88678	+	4.86924i	−0.0981536	+	0.165559i
$866$	−27.6405	+	29.4290i	−0.939263	+	1.00004i
$867$	3.39595			0.115333
$868$	0.533349	+	8.50111i	0.0181030	+	0.288546i
$869$	10.1832			0.345442
$870$	1.16873	−	0.338066i	0.0396238	−	0.0114615i
$871$	−45.3465			−1.53651
$872$	20.4909	−	24.7560i	0.693910	−	0.838344i
$873$	−39.8908			−1.35010
$874$	−7.82533	−	47.8752i	−0.264696	−	1.61940i
$875$	−7.31484	−	0.253663i	−0.247287	−	0.00857537i
$876$	−3.66858	+	0.230162i	−0.123950	+	0.00777646i
$877$		−	27.5698i		−	0.930968i	−0.885056	−	0.465484i	$-0.845880\pi$
$877$		−	27.5698i		−	0.930968i	0.885056	−	0.465484i	$-0.154120\pi$
$878$	9.19276	+	8.63410i	0.310241	+	0.291387i
$879$	−5.81603			−0.196170
$880$	31.4312	+	13.6550i	1.05955	+	0.460310i
$881$			46.8772i			1.57933i	0.613536	+	0.789667i	$0.289747\pi$
$881$			46.8772i			1.57933i	−0.613536	+	0.789667i	$0.710253\pi$
$882$	18.5839	−	19.7864i	0.625753	−	0.666242i
$883$	55.5718			1.87014			0.935071	−	0.354461i	$-0.115336\pi$
$883$	55.5718			1.87014			0.935071	+	0.354461i	$0.115336\pi$
$884$	59.5409	−	3.73552i	2.00258	−	0.125639i
$885$	2.74220	−	4.62537i	0.0921780	−	0.155480i
$886$	36.4720	−	38.8319i	1.22530	−	1.30458i
$887$	0.0901431			0.00302671			0.00151335	−	0.999999i	$-0.499518\pi$
$887$	0.0901431			0.00302671			0.00151335	+	0.999999i	$0.499518\pi$
$888$	0.223148	+	0.184703i	0.00748836	+	0.00619822i
$889$			10.7585i			0.360828i
$890$	14.3176	+	49.4977i	0.479928	+	1.65917i
$891$	−31.7795			−1.06465
$892$	−0.432193	−	6.88878i	−0.0144709	−	0.230653i
$893$	−40.4047			−1.35209
$894$	−3.74652	−	3.51883i	−0.125302	−	0.117687i
$895$	7.55765	−	12.7478i	0.252624	−	0.426111i
$896$	3.97246	−	6.25112i	0.132711	−	0.208835i
$897$	−5.91829	−	4.54322i	−0.197606	−	0.151694i
$898$	16.2776	−	17.3309i	0.543191	−	0.578339i
$899$		−	8.90004i		−	0.296833i
$900$	−24.6986	+	15.5933i	−0.823288	+	0.519775i
$901$	26.4770			0.882076
$902$	−22.1932	+	23.6292i	−0.738952	+	0.786766i
$903$	0.378438			0.0125936
$904$	−14.0160	−	11.6012i	−0.466164	−	0.385851i
$905$	−7.98790	+	13.4735i	−0.265527	+	0.447874i
$906$	−0.745014	−	0.699737i	−0.0247514	−	0.0232472i
$907$			3.39752i			0.112813i	0.998408	+	0.0564064i	$0.0179642\pi$
$907$			3.39752i			0.112813i	−0.998408	+	0.0564064i	$0.982036\pi$
$908$	−43.2177	+	2.71143i	−1.43423	+	0.0899818i
$909$	−1.77947			−0.0590214
$910$	11.0011	−	3.18217i	0.364684	−	0.105488i
$911$	51.6267			1.71047			0.855234	−	0.518242i	$-0.173413\pi$
$911$	51.6267			1.71047			0.855234	+	0.518242i	$0.173413\pi$
$912$	−7.98285	+	1.00563i	−0.264339	+	0.0332996i
$913$		−	60.0588i		−	1.98766i
$914$	22.4855	−	23.9405i	0.743755	−	0.791880i
$915$	1.99321	−	3.36203i	0.0658936	−	0.111145i
$916$	−41.5507	+	2.60684i	−1.37287	+	0.0861323i
$917$	9.19279			0.303573
$918$	8.69301	−	9.25549i	0.286912	−	0.305477i
$919$	−43.0368			−1.41965			−0.709827	−	0.704376i	$-0.751227\pi$
$919$	−43.0368			−1.41965			−0.709827	+	0.704376i	$0.751227\pi$
$920$	−28.8813	−	9.26666i	−0.952188	−	0.305513i
$921$	−2.02339			−0.0666729
$922$	2.88077	−	3.06716i	0.0948730	−	0.101012i
$923$	−33.0859			−1.08903
$924$	−1.40801	+	0.0883370i	−0.0463202	+	0.00290607i
$925$	0.873741	+	1.59751i	0.0287284	+	0.0525259i
$926$	13.3135	−	14.1750i	0.437510	−	0.465819i
$927$			32.9158i			1.08110i
$928$	−4.55155	+	6.25891i	−0.149412	+	0.205459i
$929$	49.5176			1.62462			0.812310	−	0.583226i	$-0.198210\pi$
$929$	49.5176			1.62462			0.812310	+	0.583226i	$0.198210\pi$
$930$	−1.60762	−	5.55775i	−0.0527161	−	0.182246i
$931$	47.0021			1.54043
$932$	−10.9957	+	0.689854i	−0.360175	+	0.0225969i
$933$		−	7.21450i		−	0.236192i
$934$	−5.70979	−	5.36279i	−0.186830	−	0.175476i
$935$	−39.7376	−	23.5589i	−1.29956	−	0.770457i
$936$	29.1411	−	35.2066i	0.952505	−	1.15077i
$937$	13.4516			0.439444			0.219722	−	0.975562i	$-0.429485\pi$
$937$	13.4516			0.439444			0.219722	+	0.975562i	$0.429485\pi$
$938$	5.19562	−	5.53181i	0.169643	−	0.180620i
$939$	8.63692			0.281855
$940$	−11.4976	+	22.4953i	−0.375010	+	0.733716i
$941$		−	52.1559i		−	1.70023i	−0.526593	−	0.850117i	$-0.676531\pi$
$941$		−	52.1559i		−	1.70023i	0.526593	−	0.850117i	$-0.323469\pi$
$942$	−0.704064	+	0.749621i	−0.0229397	+	0.0244240i
$943$	17.4715	−	22.7595i	0.568950	−	0.741151i
$944$	4.27491	+	33.9350i	0.139136	+	1.10449i
$945$	1.24306	−	2.09671i	0.0404367	−	0.0682060i
$946$	−8.11843	−	7.62505i	−0.263953	−	0.247912i
$947$	23.3276			0.758044			0.379022	−	0.925388i	$-0.376260\pi$
$947$	23.3276			0.758044			0.379022	+	0.925388i	$0.376260\pi$
$948$	0.0936048	+	1.49198i	0.00304014	+	0.0484572i
$949$	36.1524			1.17356
$950$	−48.9584	−	12.6880i	−1.58842	−	0.411653i
$951$		−	1.60256i		−	0.0519665i
$952$	−6.36627	+	7.69138i	−0.206332	+	0.249279i
$953$	−15.3966			−0.498745			−0.249372	−	0.968408i	$-0.580224\pi$
$953$	−15.3966			−0.498745			−0.249372	+	0.968408i	$0.580224\pi$
$954$	13.8862	−	14.7847i	0.449581	−	0.478672i
$955$	42.9395	+	25.4571i	1.38949	+	0.823773i
$956$	43.9919	−	2.76000i	1.42280	−	0.0892646i
$957$	1.47409			0.0476505
$958$	−9.04065	+	9.62562i	−0.292090	+	0.310990i
$959$		−	2.74753i		−	0.0887225i
$960$	−1.71172	+	4.73061i	−0.0552457	+	0.152680i
$961$	−11.3229			−0.365255
$962$	−2.07667	−	1.95046i	−0.0669544	−	0.0628854i
$963$			20.3282i			0.655068i
$964$	22.8623	−	1.43435i	0.736346	−	0.0461974i
$965$	0.773926	−	1.30541i	0.0249135	−	0.0420226i
$966$	1.23232	−	0.201426i	0.0396493	−	0.00648078i
$967$	−44.1352			−1.41929			−0.709646	−	0.704559i	$-0.751145\pi$
$967$	−44.1352			−1.41929			−0.709646	+	0.704559i	$0.751145\pi$
$968$	8.01768	+	6.63635i	0.257698	+	0.213300i
$969$	10.8463			0.348432
$970$	−41.4865	+	12.0003i	−1.33205	+	0.385306i
$971$	13.0702			0.419443			0.209722	−	0.977761i	$-0.432744\pi$
$971$	13.0702			0.419443			0.209722	+	0.977761i	$0.432744\pi$
$972$	−0.917698	−	14.6273i	−0.0294352	−	0.469171i
$973$	11.9714			0.383787
$974$	−16.0844	+	17.1251i	−0.515376	+	0.548723i
$975$	−6.82460	+	3.73263i	−0.218562	+	0.119540i
$976$	3.10729	+	24.6662i	0.0994619	+	0.789547i
$977$	−9.02174			−0.288631			−0.144316	−	0.989532i	$-0.546098\pi$
$977$	−9.02174			−0.288631			−0.144316	+	0.989532i	$0.546098\pi$
$978$	0.481568	−	0.512728i	0.0153988	−	0.0163952i
$979$			62.4300i			1.99527i
$980$	13.3749	−	26.1684i	0.427247	−	0.835919i
$981$			33.1870i			1.05958i
$982$	−12.4182	−	11.6635i	−0.396281	−	0.372198i
$983$			14.2428i			0.454275i	0.973863	+	0.227138i	$0.0729368\pi$
$983$			14.2428i			0.454275i	−0.973863	+	0.227138i	$0.927063\pi$
$984$	−3.66599	−	3.03440i	−0.116868	−	0.0967330i
$985$	11.3112	−	19.0791i	0.360406	−	0.607910i
$986$	7.14210	−	7.60423i	0.227451	−	0.242168i
$987$		−	1.04003i		−	0.0331045i
$988$	78.9787	−	4.95503i	2.51265	−	0.157640i
$989$	7.81962	+	6.00279i	0.248650	+	0.190878i
$990$	−33.9961	+	9.83365i	−1.08047	+	0.312534i
$991$			11.9474i			0.379521i	0.981830	+	0.189760i	$0.0607711\pi$
$991$			11.9474i			0.379521i	−0.981830	+	0.189760i	$0.939229\pi$
$992$	29.7634	+	21.6443i	0.944988	+	0.687206i
$993$		−	0.0814961i		−	0.00258620i
$994$	3.79085	−	4.03614i	0.120238	−	0.128018i
$995$	37.3640	+	22.1516i	1.18452	+	0.702254i
$996$	8.79941	−	0.552064i	0.278820	−	0.0174928i
$997$			4.57956i			0.145036i	0.997367	+	0.0725180i	$0.0231035\pi$
$997$			4.57956i			0.145036i	−0.997367	+	0.0725180i	$0.976897\pi$
$998$	−28.4323	−	26.7044i	−0.900009	−	0.845313i
$999$	−0.606388			−0.0191853

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.g.c.459.16	yes	56
4.3	odd	2	inner	460.2.g.c.459.44	yes	56
5.4	even	2	inner	460.2.g.c.459.41	yes	56
20.19	odd	2	inner	460.2.g.c.459.13	✓	56
23.22	odd	2	inner	460.2.g.c.459.15	yes	56
92.91	even	2	inner	460.2.g.c.459.43	yes	56
115.114	odd	2	inner	460.2.g.c.459.42	yes	56
460.459	even	2	inner	460.2.g.c.459.14	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.g.c.459.13	✓	56	20.19	odd	2	inner
460.2.g.c.459.14	yes	56	460.459	even	2	inner
460.2.g.c.459.15	yes	56	23.22	odd	2	inner
460.2.g.c.459.16	yes	56	1.1	even	1	trivial
460.2.g.c.459.41	yes	56	5.4	even	2	inner
460.2.g.c.459.42	yes	56	115.114	odd	2	inner
460.2.g.c.459.43	yes	56	92.91	even	2	inner
460.2.g.c.459.44	yes	56	4.3	odd	2	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:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.968186 + 1.03083i) q^{2} +0.281229 q^{3} +(-0.125231 - 1.99608i) q^{4} +(1.92344 + 1.14033i) q^{5} +(-0.272282 + 0.289900i) q^{6} +0.654652i q^{7} +(2.17887 + 1.80348i) q^{8} -2.92091 q^{9} +O(q^{10})\)	\(q+(-0.968186 + 1.03083i) q^{2} +0.281229 q^{3} +(-0.125231 - 1.99608i) q^{4} +(1.92344 + 1.14033i) q^{5} +(-0.272282 + 0.289900i) q^{6} +0.654652i q^{7} +(2.17887 + 1.80348i) q^{8} -2.92091 q^{9} +(-3.03775 + 0.878693i) q^{10} -3.83142 q^{11} +(-0.0352186 - 0.561354i) q^{12} +5.53192i q^{13} +(-0.674837 - 0.633825i) q^{14} +(0.540928 + 0.320695i) q^{15} +(-3.96863 + 0.499942i) q^{16} +5.39216 q^{17} +(2.82798 - 3.01097i) q^{18} +7.15249 q^{19} +(2.03532 - 3.98215i) q^{20} +0.184107i q^{21} +(3.70952 - 3.94955i) q^{22} +(-2.92031 + 3.80418i) q^{23} +(0.612760 + 0.507190i) q^{24} +(2.39928 + 4.38674i) q^{25} +(-5.70248 - 5.35593i) q^{26} -1.66513 q^{27} +(1.30674 - 0.0819830i) q^{28} -1.36806 q^{29} +(-0.854301 + 0.247114i) q^{30} +6.50560i q^{31} +(3.32702 - 4.57503i) q^{32} -1.07750 q^{33} +(-5.22062 + 5.55842i) q^{34} +(-0.746523 + 1.25919i) q^{35} +(0.365789 + 5.83036i) q^{36} +0.364169 q^{37} +(-6.92494 + 7.37302i) q^{38} +1.55573i q^{39} +(2.13436 + 5.95353i) q^{40} -5.98276 q^{41} +(-0.189784 - 0.178250i) q^{42} -2.05553i q^{43} +(0.479813 + 7.64780i) q^{44} +(-5.61821 - 3.33081i) q^{45} +(-1.09407 - 6.69350i) q^{46} -5.64904 q^{47} +(-1.11609 + 0.140598i) q^{48} +6.57143 q^{49} +(-6.84494 - 1.77393i) q^{50} +1.51643 q^{51} +(11.0421 - 0.692769i) q^{52} +4.91027 q^{53} +(1.61216 - 1.71647i) q^{54} +(-7.36951 - 4.36910i) q^{55} +(-1.18065 + 1.42640i) q^{56} +2.01149 q^{57} +(1.32453 - 1.41024i) q^{58} -8.55081i q^{59} +(0.572390 - 1.11989i) q^{60} -6.21530i q^{61} +(-6.70619 - 6.29864i) q^{62} -1.91218i q^{63} +(1.49492 + 7.85908i) q^{64} +(-6.30824 + 10.6403i) q^{65} +(1.04322 - 1.11073i) q^{66} +8.19725i q^{67} +(-0.675268 - 10.7632i) q^{68} +(-0.821275 + 1.06985i) q^{69} +(-0.575239 - 1.98867i) q^{70} +5.98091i q^{71} +(-6.36427 - 5.26780i) q^{72} -6.53524i q^{73} +(-0.352583 + 0.375397i) q^{74} +(0.674745 + 1.23368i) q^{75} +(-0.895716 - 14.2769i) q^{76} -2.50825i q^{77} +(-1.60370 - 1.50624i) q^{78} -2.65782 q^{79} +(-8.20355 - 3.56396i) q^{80} +8.29445 q^{81} +(5.79242 - 6.16722i) q^{82} +15.6753i q^{83} +(0.367492 - 0.0230560i) q^{84} +(10.3715 + 6.14887i) q^{85} +(2.11891 + 1.99014i) q^{86} -0.384737 q^{87} +(-8.34814 - 6.90988i) q^{88} -16.2942i q^{89} +(8.87298 - 2.56658i) q^{90} -3.62148 q^{91} +(7.95915 + 5.35275i) q^{92} +1.82956i q^{93} +(5.46932 - 5.82322i) q^{94} +(13.7574 + 8.15623i) q^{95} +(0.935654 - 1.28663i) q^{96} +13.6570 q^{97} +(-6.36237 + 6.77404i) q^{98} +11.1912 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{4} - 8 q^{6} + 16 q^{9}+O(q^{10}) \) 56 * q - 8 * q^4 - 8 * q^6 + 16 * q^9	\( 56 q - 8 q^{4} - 8 q^{6} + 16 q^{9} - 8 q^{16} - 100 q^{24} - 24 q^{25} - 24 q^{26} - 16 q^{29} + 104 q^{41} - 8 q^{46} + 32 q^{49} - 32 q^{50} + 52 q^{54} - 92 q^{64} + 32 q^{69} - 44 q^{70} + 24 q^{81} + 56 q^{85} + 28 q^{94} + 88 q^{96}+O(q^{100}) \) 56 * q - 8 * q^4 - 8 * q^6 + 16 * q^9 - 8 * q^16 - 100 * q^24 - 24 * q^25 - 24 * q^26 - 16 * q^29 + 104 * q^41 - 8 * q^46 + 32 * q^49 - 32 * q^50 + 52 * q^54 - 92 * q^64 + 32 * q^69 - 44 * q^70 + 24 * q^81 + 56 * q^85 + 28 * q^94 + 88 * q^96

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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