LMFDB - Embedded newform 637.2.r.g.324.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [637,2,Mod(116,637)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(637, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("637.116"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.r (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,0,20,0,0,0,0,-16,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(12)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			324.14
Character	$\chi$	$=$	637.324
Dual form			637.2.r.g.116.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.43372 + 0.827759i) q^{2} +(0.247488 + 0.428663i) q^{3} +(0.370370 + 0.641500i) q^{4} +(-2.48886 - 1.43695i) q^{5} +0.819443i q^{6} -2.08473i q^{8} +(1.37750 - 2.38590i) q^{9} +(-2.37889 - 4.12036i) q^{10} +(2.23554 - 1.29069i) q^{11} +(-0.183325 + 0.317527i) q^{12} +(3.54562 + 0.654682i) q^{13} -1.42251i q^{15} +(2.46639 - 4.27192i) q^{16} +(-1.13792 - 1.97093i) q^{17} +(3.94990 - 2.28047i) q^{18} +(-3.80679 - 2.19785i) q^{19} -2.12881i q^{20} +4.27352 q^{22} +(-3.58463 + 6.20876i) q^{23} +(0.893645 - 0.515946i) q^{24} +(1.62963 + 2.82260i) q^{25} +(4.54150 + 3.87355i) q^{26} +2.84859 q^{27} +6.19574 q^{29} +(1.17750 - 2.03948i) q^{30} +(5.93577 - 3.42702i) q^{31} +(3.46138 - 1.99843i) q^{32} +(1.10654 + 0.638861i) q^{33} -3.76769i q^{34} +2.04074 q^{36} +(-5.10298 - 2.94621i) q^{37} +(-3.63859 - 6.30221i) q^{38} +(0.596861 + 1.68190i) q^{39} +(-2.99564 + 5.18860i) q^{40} +3.98014i q^{41} +1.31425 q^{43} +(1.65595 + 0.956065i) q^{44} +(-6.85682 + 3.95878i) q^{45} +(-10.2787 + 5.93442i) q^{46} +(-1.17094 - 0.676040i) q^{47} +2.44161 q^{48} +5.39576i q^{50} +(0.563244 - 0.975567i) q^{51} +(0.893211 + 2.51699i) q^{52} +(4.14389 + 7.17742i) q^{53} +(4.08408 + 2.35795i) q^{54} -7.41860 q^{55} -2.17577i q^{57} +(8.88296 + 5.12858i) q^{58} +(-8.32324 + 4.80543i) q^{59} +(0.912540 - 0.526855i) q^{60} +(4.77650 - 8.27315i) q^{61} +11.3470 q^{62} -3.24870 q^{64} +(-7.88381 - 6.72427i) q^{65} +(1.05765 + 1.83190i) q^{66} +(-13.7781 + 7.95477i) q^{67} +(0.842903 - 1.45995i) q^{68} -3.54862 q^{69} -4.79396i q^{71} +(-4.97395 - 2.87171i) q^{72} +(4.94074 - 2.85253i) q^{73} +(-4.87750 - 8.44808i) q^{74} +(-0.806629 + 1.39712i) q^{75} -3.25607i q^{76} +(-0.536475 + 2.90543i) q^{78} +(1.00713 - 1.74440i) q^{79} +(-12.2770 + 7.08815i) q^{80} +(-3.42750 - 5.93661i) q^{81} +(-3.29460 + 5.70641i) q^{82} -3.11798i q^{83} +6.54052i q^{85} +(1.88427 + 1.08789i) q^{86} +(1.53337 + 2.65588i) q^{87} +(-2.69074 - 4.66049i) q^{88} +(11.3089 + 6.52918i) q^{89} -13.1077 q^{90} -5.31056 q^{92} +(2.93807 + 1.69629i) q^{93} +(-1.11920 - 1.93850i) q^{94} +(6.31639 + 10.9403i) q^{95} +(1.71330 + 0.989176i) q^{96} +14.0382i q^{97} -7.11169i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 20 q^{4} - 16 q^{9} - 28 q^{16} - 16 q^{22} + 36 q^{23} + 44 q^{25} + 72 q^{29} + 104 q^{36} - 32 q^{39} - 72 q^{43} + 72 q^{51} - 12 q^{53} - 328 q^{64} + 24 q^{65} - 96 q^{74} + 48 q^{78} - 36 q^{79}+ \cdots + 84 q^{95}+O(q^{100}) $ 32 * q + 20 * q^4 - 16 * q^9 - 28 * q^16 - 16 * q^22 + 36 * q^23 + 44 * q^25 + 72 * q^29 + 104 * q^36 - 32 * q^39 - 72 * q^43 + 72 * q^51 - 12 * q^53 - 328 * q^64 + 24 * q^65 - 96 * q^74 + 48 * q^78 - 36 * q^79 - 16 * q^81 - 136 * q^88 + 48 * q^92 + 84 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.43372	+	0.827759i	1.01379	+	0.585314i	0.912300	−	0.409522i	$-0.134305\pi$
$2$	1.43372	+	0.827759i	1.01379	+	0.585314i	0.101493	+	0.994836i	$0.467638\pi$
$3$	0.247488	+	0.428663i	0.142888	+	0.247488i	0.928583	−	0.371125i	$-0.121028\pi$
$3$	0.247488	+	0.428663i	0.142888	+	0.247488i	−0.785695	+	0.618614i	$0.787695\pi$
$4$	0.370370	+	0.641500i	0.185185	+	0.320750i
$5$	−2.48886	−	1.43695i	−1.11305	−	0.642622i	−0.173435	−	0.984845i	$-0.555487\pi$
$5$	−2.48886	−	1.43695i	−1.11305	−	0.642622i	−0.939619	+	0.342223i	$0.888820\pi$
$6$			0.819443i			0.334536i
$7$		0			0
$7$		0			0
$8$		−	2.08473i		−	0.737063i
$9$	1.37750	−	2.38590i	0.459166	−	0.795299i
$10$	−2.37889	−	4.12036i	−0.752271	−	1.30297i
$11$	2.23554	−	1.29069i	0.674040	−	0.389157i	−0.123565	−	0.992336i	$-0.539433\pi$
$11$	2.23554	−	1.29069i	0.674040	−	0.389157i	0.797606	+	0.603179i	$0.206100\pi$
$12$	−0.183325	+	0.317527i	−0.0529212	+	0.0916623i
$13$	3.54562	+	0.654682i	0.983377	+	0.181576i
$13$	3.54562	+	0.654682i	0.983377	+	0.181576i
$14$		0			0
$15$		−	1.42251i		−	0.367291i
$16$	2.46639	−	4.27192i	0.616598	−	1.06798i
$17$	−1.13792	−	1.97093i	−0.275986	−	0.478022i	0.694397	−	0.719592i	$-0.255671\pi$
$17$	−1.13792	−	1.97093i	−0.275986	−	0.478022i	−0.970383	+	0.241570i	$0.922338\pi$
$18$	3.94990	−	2.28047i	0.931000	−	0.537513i
$19$	−3.80679	−	2.19785i	−0.873338	−	0.504222i	−0.00488206	−	0.999988i	$-0.501554\pi$
$19$	−3.80679	−	2.19785i	−0.873338	−	0.504222i	−0.868456	+	0.495766i	$0.834887\pi$
$20$		−	2.12881i		−	0.476016i
$21$		0			0
$22$	4.27352			0.911117
$23$	−3.58463	+	6.20876i	−0.747447	+	1.29462i	0.201595	+	0.979469i	$0.435387\pi$
$23$	−3.58463	+	6.20876i	−0.747447	+	1.29462i	−0.949043	+	0.315148i	$0.897946\pi$
$24$	0.893645	−	0.515946i	0.182414	−	0.105317i
$25$	1.62963	+	2.82260i	0.325926	+	0.564520i
$26$	4.54150	+	3.87355i	0.890662	+	0.759665i
$27$	2.84859			0.548212
$28$		0			0
$29$	6.19574			1.15052			0.575260	−	0.817971i	$-0.304901\pi$
$29$	6.19574			1.15052			0.575260	+	0.817971i	$0.304901\pi$
$30$	1.17750	−	2.03948i	0.214980	−	0.372357i
$31$	5.93577	−	3.42702i	1.06610	−	0.615511i	0.138983	−	0.990295i	$-0.455617\pi$
$31$	5.93577	−	3.42702i	1.06610	−	0.615511i	0.927112	+	0.374784i	$0.122283\pi$
$32$	3.46138	−	1.99843i	0.611891	−	0.353276i
$33$	1.10654	+	0.638861i	0.192624	+	0.111211i
$34$		−	3.76769i		−	0.646154i
$35$		0			0
$36$	2.04074			0.340123
$37$	−5.10298	−	2.94621i	−0.838925	−	0.484353i	0.0179738	−	0.999838i	$-0.494278\pi$
$37$	−5.10298	−	2.94621i	−0.838925	−	0.484353i	−0.856899	+	0.515485i	$0.827612\pi$
$38$	−3.63859	−	6.30221i	−0.590256	−	1.02235i
$39$	0.596861	+	1.68190i	0.0955743	+	0.269319i
$40$	−2.99564	+	5.18860i	−0.473653	+	0.820390i
$41$			3.98014i			0.621594i	0.950476	+	0.310797i	$0.100596\pi$
$41$			3.98014i			0.621594i	−0.950476	+	0.310797i	$0.899404\pi$
$42$		0			0
$43$	1.31425			0.200422			0.100211	−	0.994966i	$-0.468048\pi$
$43$	1.31425			0.200422			0.100211	+	0.994966i	$0.468048\pi$
$44$	1.65595	+	0.956065i	0.249644	+	0.144132i
$45$	−6.85682	+	3.95878i	−1.02215	+	0.590141i
$46$	−10.2787	+	5.93442i	−1.51551	+	0.874983i
$47$	−1.17094	−	0.676040i	−0.170799	−	0.0986106i	0.412164	−	0.911110i	$-0.364773\pi$
$47$	−1.17094	−	0.676040i	−0.170799	−	0.0986106i	−0.582962	+	0.812499i	$0.698106\pi$
$48$	2.44161			0.352417
$49$		0			0
$50$			5.39576i			0.763076i
$51$	0.563244	−	0.975567i	0.0788699	−	0.136607i
$52$	0.893211	+	2.51699i	0.123866	+	0.349043i
$53$	4.14389	+	7.17742i	0.569207	+	0.985895i	0.996645	+	0.0818503i	$0.0260830\pi$
$53$	4.14389	+	7.17742i	0.569207	+	0.985895i	−0.427438	+	0.904045i	$0.640584\pi$
$54$	4.08408	+	2.35795i	0.555773	+	0.320876i
$55$	−7.41860			−1.00032
$56$		0			0
$57$		−	2.17577i		−	0.288188i
$58$	8.88296	+	5.12858i	1.16639	+	0.673416i
$59$	−8.32324	+	4.80543i	−1.08359	+	0.625613i	−0.931864	−	0.362809i	$-0.881818\pi$
$59$	−8.32324	+	4.80543i	−1.08359	+	0.625613i	−0.151730	+	0.988422i	$0.548485\pi$
$60$	0.912540	−	0.526855i	0.117808	−	0.0680167i
$61$	4.77650	−	8.27315i	0.611569	−	1.05927i	−0.379407	−	0.925230i	$-0.623872\pi$
$61$	4.77650	−	8.27315i	0.611569	−	1.05927i	0.990976	−	0.134038i	$-0.0427946\pi$
$62$	11.3470			1.44107
$63$		0			0
$64$	−3.24870			−0.406087
$65$	−7.88381	−	6.72427i	−0.977867	−	0.834044i
$66$	1.05765	+	1.83190i	0.130187	+	0.225491i
$67$	−13.7781	+	7.95477i	−1.68326	+	0.971830i	−0.723787	+	0.690024i	$0.757600\pi$
$67$	−13.7781	+	7.95477i	−1.68326	+	0.971830i	−0.959471	+	0.281806i	$0.909067\pi$
$68$	0.842903	−	1.45995i	0.102217	−	0.177045i
$69$	−3.54862			−0.427204
$70$		0			0
$71$		−	4.79396i		−	0.568938i	−0.958685	−	0.284469i	$-0.908183\pi$
$71$		−	4.79396i		−	0.568938i	0.958685	−	0.284469i	$-0.0918173\pi$
$72$	−4.97395	−	2.87171i	−0.586185	−	0.338434i
$73$	4.94074	−	2.85253i	0.578269	−	0.333864i	−0.182176	−	0.983266i	$-0.558314\pi$
$73$	4.94074	−	2.85253i	0.578269	−	0.333864i	0.760445	+	0.649402i	$0.224981\pi$
$74$	−4.87750	−	8.44808i	−0.566998	−	0.982069i
$75$	−0.806629	+	1.39712i	−0.0931415	+	0.161326i
$76$		−	3.25607i		−	0.373497i
$77$		0			0
$78$	−0.536475	+	2.90543i	−0.0607438	+	0.328975i
$79$	1.00713	−	1.74440i	0.113311	−	0.196260i	−0.803792	−	0.594910i	$-0.797188\pi$
$79$	1.00713	−	1.74440i	0.113311	−	0.196260i	0.917103	+	0.398650i	$0.130521\pi$
$80$	−12.2770	+	7.08815i	−1.37261	+	0.792479i
$81$	−3.42750	−	5.93661i	−0.380834	−	0.659623i
$82$	−3.29460	+	5.70641i	−0.363828	+	0.630168i
$83$		−	3.11798i		−	0.342243i	−0.985250	−	0.171122i	$-0.945261\pi$
$83$		−	3.11798i		−	0.342243i	0.985250	−	0.171122i	$-0.0547391\pi$
$84$		0			0
$85$			6.54052i			0.709419i
$86$	1.88427	+	1.08789i	0.203187	+	0.117310i
$87$	1.53337	+	2.65588i	0.164395	+	0.284740i
$88$	−2.69074	−	4.66049i	−0.286833	−	0.496810i
$89$	11.3089	+	6.52918i	1.19874	+	0.692092i	0.960274	−	0.279060i	$-0.0900227\pi$
$89$	11.3089	+	6.52918i	1.19874	+	0.692092i	0.238464	+	0.971151i	$0.423356\pi$
$90$	−13.1077			−1.38167
$91$		0			0
$92$	−5.31056			−0.553664
$93$	2.93807	+	1.69629i	0.304663	+	0.175898i
$94$	−1.11920	−	1.93850i	−0.115436	−	0.199942i
$95$	6.31639	+	10.9403i	0.648048	+	1.12245i
$96$	1.71330	+	0.989176i	0.174863	+	0.100957i
$97$			14.0382i			1.42536i	0.701488	+	0.712682i	$0.252520\pi$
$97$			14.0382i			1.42536i	−0.701488	+	0.712682i	$0.747480\pi$
$98$		0			0
$99$		−	7.11169i		−	0.714752i
$100$	−1.20713	+	2.09081i	−0.120713	+	0.209081i
$101$	8.72413	+	15.1106i	0.868083	+	1.50356i	0.863953	+	0.503573i	$0.167981\pi$
$101$	8.72413	+	15.1106i	0.868083	+	1.50356i	0.00413039	+	0.999991i	$0.498685\pi$
$102$	1.61507	−	0.932461i	0.159916	−	0.0923274i
$103$	3.27849	−	5.67851i	0.323039	−	0.559520i	−0.658074	−	0.752953i	$-0.728629\pi$
$103$	3.27849	−	5.67851i	0.323039	−	0.559520i	0.981114	+	0.193433i	$0.0619621\pi$
$104$	1.36483	−	7.39164i	0.133833	−	0.724810i
$105$		0			0
$106$			13.7206i			1.33266i
$107$	−7.80102	+	13.5118i	−0.754153	+	1.30623i	0.191642	+	0.981465i	$0.438619\pi$
$107$	−7.80102	+	13.5118i	−0.754153	+	1.30623i	−0.945794	+	0.324766i	$0.894715\pi$
$108$	1.05503	+	1.82737i	0.101521	+	0.175839i
$109$	8.67508	−	5.00856i	0.830922	−	0.479733i	−0.0232461	−	0.999730i	$-0.507400\pi$
$109$	8.67508	−	5.00856i	0.830922	−	0.479733i	0.854168	+	0.519997i	$0.174067\pi$
$110$	−10.6362	−	6.14082i	−1.01412	−	0.585504i
$111$		−	2.91661i		−	0.276832i
$112$		0			0
$113$	−3.95074			−0.371654			−0.185827	−	0.982582i	$-0.559496\pi$
$113$	−3.95074			−0.371654			−0.185827	+	0.982582i	$0.559496\pi$
$114$	1.80102	−	3.11945i	0.168681	−	0.292163i
$115$	17.8433	−	10.3018i	1.66390	−	0.960652i
$116$	2.29472	+	3.97457i	0.213059	+	0.369029i
$117$	6.44609	−	7.55765i	0.595941	−	0.698705i
$118$	−15.9109			−1.46472
$119$		0			0
$120$	−2.96555			−0.270716
$121$	−2.16824	+	3.75551i	−0.197113	+	0.341410i
$122$	13.6963	−	7.90759i	1.24001	−	0.715920i
$123$	−1.70614	+	0.985039i	−0.153837	+	0.0888180i
$124$	4.39686	+	2.53853i	0.394850	+	0.227967i
$125$			5.00270i			0.447455i
$126$		0			0
$127$	−2.37353			−0.210616			−0.105308	−	0.994440i	$-0.533583\pi$
$127$	−2.37353			−0.210616			−0.105308	+	0.994440i	$0.533583\pi$
$128$	−11.5805	−	6.68600i	−1.02358	−	0.590964i
$129$	0.325263	+	0.563372i	0.0286378	+	0.0496021i
$130$	−5.73711	−	16.1666i	−0.503178	−	1.41791i
$131$	1.06773	−	1.84936i	0.0932878	−	0.161579i	−0.815605	−	0.578609i	$-0.803596\pi$
$131$	1.06773	−	1.84936i	0.0932878	−	0.161579i	0.908893	+	0.417030i	$0.136929\pi$
$132$			0.946460i			0.0823788i
$133$		0			0
$134$	−26.3385			−2.27530
$135$	−7.08976	−	4.09327i	−0.610189	−	0.352293i
$136$	−4.10886	+	2.37225i	−0.352332	+	0.203419i
$137$	0.371707	−	0.214605i	0.0317570	−	0.0183349i	−0.484037	−	0.875047i	$-0.660830\pi$
$137$	0.371707	−	0.214605i	0.0317570	−	0.0183349i	0.515794	+	0.856712i	$0.327497\pi$
$138$	−5.08773	−	2.93740i	−0.433096	−	0.250048i
$139$	19.4858			1.65276			0.826381	−	0.563112i	$-0.190396\pi$
$139$	19.4858			1.65276			0.826381	+	0.563112i	$0.190396\pi$
$140$		0			0
$141$		−	0.669248i		−	0.0563609i
$142$	3.96824	−	6.87319i	0.333007	−	0.576786i
$143$	8.77135	−	3.11272i	0.733497	−	0.260299i
$144$	−6.79491	−	11.7691i	−0.566242	−	0.980760i
$145$	−15.4204	−	8.90295i	−1.28059	−	0.739350i
$146$	9.44485			0.781661
$147$		0			0
$148$		−	4.36475i		−	0.358780i
$149$	19.8323	+	11.4502i	1.62473	+	0.938037i	0.985631	+	0.168911i	$0.0540251\pi$
$149$	19.8323	+	11.4502i	1.62473	+	0.938037i	0.639097	+	0.769126i	$0.279308\pi$
$150$	−2.31296	+	1.33539i	−0.188853	+	0.109034i
$151$	9.71744	−	5.61037i	0.790794	−	0.456565i	−0.0494478	−	0.998777i	$-0.515746\pi$
$151$	9.71744	−	5.61037i	0.790794	−	0.456565i	0.840242	+	0.542211i	$0.182413\pi$
$152$	−4.58192	+	7.93613i	−0.371643	+	0.643705i
$153$	−6.26993			−0.506894
$154$		0			0
$155$	−19.6978			−1.58216
$156$	−0.857878	+	1.00581i	−0.0686852	+	0.0805293i
$157$	−1.89400	−	3.28050i	−0.151157	−	0.261812i	0.780496	−	0.625161i	$-0.214967\pi$
$157$	−1.89400	−	3.28050i	−0.151157	−	0.261812i	−0.931653	+	0.363349i	$0.881633\pi$
$158$	2.88788	−	1.66732i	0.229748	−	0.132645i
$159$	−2.05113	+	3.55266i	−0.162665	+	0.281744i
$160$	−11.4865			−0.908091
$161$		0			0
$162$		−	11.3486i		−	0.891629i
$163$	16.9853	+	9.80649i	1.33039	+	0.768103i	0.985360	−	0.170487i	$-0.0545340\pi$
$163$	16.9853	+	9.80649i	1.33039	+	0.768103i	0.345034	+	0.938590i	$0.387867\pi$
$164$	−2.55326	+	1.47413i	−0.199376	+	0.115110i
$165$	−1.83602	−	3.18008i	−0.142934	−	0.247569i
$166$	2.58094	−	4.47032i	0.200320	−	0.346964i
$167$		−	10.2922i		−	0.796435i	−0.917291	−	0.398217i	$-0.869629\pi$
$167$		−	10.2922i		−	0.796435i	0.917291	−	0.398217i	$-0.130371\pi$
$168$		0			0
$169$	12.1428	+	4.64250i	0.934060	+	0.357116i
$170$	−5.41397	+	9.37728i	−0.415233	+	0.719204i
$171$	−10.4877	+	6.05508i	−0.802015	+	0.463044i
$172$	0.486761	+	0.843094i	0.0371151	+	0.0642853i
$173$	−3.00220	+	5.19995i	−0.228253	+	0.395345i	−0.957290	−	0.289128i	$-0.906635\pi$
$173$	−3.00220	+	5.19995i	−0.228253	+	0.395345i	0.729038	+	0.684474i	$0.239968\pi$
$174$			5.07706i			0.384891i
$175$		0			0
$176$		−	12.7334i		−	0.959815i
$177$	−4.11981	−	2.37858i	−0.309664	−	0.178785i
$178$	10.8092	+	18.7220i	0.810182	+	1.40328i
$179$	−3.87565	−	6.71282i	−0.289680	−	0.501740i	0.684054	−	0.729432i	$-0.260215\pi$
$179$	−3.87565	−	6.71282i	−0.289680	−	0.501740i	−0.973733	+	0.227692i	$0.926882\pi$
$180$	−5.07912	−	2.93243i	−0.378575	−	0.218570i
$181$	−19.9999			−1.48658			−0.743289	−	0.668970i	$-0.766735\pi$
$181$	−19.9999			−1.48658			−0.743289	+	0.668970i	$0.766735\pi$
$182$		0			0
$183$	4.72852			0.349542
$184$	12.9436	+	7.47298i	0.954213	+	0.550915i
$185$	8.46708	+	14.6654i	0.622512	+	1.07822i
$186$	2.80825	+	4.86402i	0.205911	+	0.356648i
$187$	−5.08773	−	2.93740i	−0.372052	−	0.214804i
$188$		−	1.00154i		−	0.0730448i
$189$		0			0
$190$			20.9138i			1.51725i
$191$	−10.2418	+	17.7392i	−0.741068	+	1.28357i	0.210942	+	0.977499i	$0.432347\pi$
$191$	−10.2418	+	17.7392i	−0.741068	+	1.28357i	−0.952010	+	0.306068i	$0.900986\pi$
$192$	−0.804015	−	1.39260i	−0.0580248	−	0.100502i
$193$	10.7672	−	6.21647i	0.775043	−	0.447471i	−0.0596279	−	0.998221i	$-0.518991\pi$
$193$	10.7672	−	6.21647i	0.775043	−	0.447471i	0.834671	+	0.550750i	$0.185658\pi$
$194$	−11.6202	+	20.1269i	−0.834285	+	1.44502i
$195$	0.931292	−	5.04368i	0.0666912	−	0.361185i
$196$		0			0
$197$		−	18.9805i		−	1.35231i	−0.736761	−	0.676154i	$-0.763646\pi$
$197$		−	18.9805i		−	1.35231i	0.736761	−	0.676154i	$-0.236354\pi$
$198$	5.88677	−	10.1962i	0.418354	−	0.724611i
$199$	−6.40940	−	11.1014i	−0.454350	−	0.786958i	0.544300	−	0.838891i	$-0.316795\pi$
$199$	−6.40940	−	11.1014i	−0.454350	−	0.786958i	−0.998651	+	0.0519325i	$0.983462\pi$
$200$	5.88436	−	3.39734i	0.416087	−	0.240228i
$201$	−6.81982	−	3.93743i	−0.481033	−	0.277725i
$202$			28.8859i			2.03241i
$203$		0			0
$204$	0.834435			0.0584221
$205$	5.71925	−	9.90603i	0.399450	−	0.691867i
$206$	9.40088	−	5.42760i	0.654990	−	0.378159i
$207$	9.87565	+	17.1051i	0.686405	+	1.18889i
$208$	11.5416	−	13.5319i	0.800268	−	0.938267i
$209$	−11.3470			−0.784887
$210$		0			0
$211$	−7.86926			−0.541743			−0.270871	−	0.962616i	$-0.587312\pi$
$211$	−7.86926			−0.541743			−0.270871	+	0.962616i	$0.587312\pi$
$212$	−3.06954	+	5.31660i	−0.210817	+	0.365146i
$213$	2.05499	−	1.18645i	0.140806	−	0.0812941i
$214$	−22.3690	+	12.9147i	−1.52911	+	0.882832i
$215$	−3.27100	−	1.88851i	−0.223080	−	0.128796i
$216$		−	5.93854i		−	0.404066i
$217$		0			0
$218$	16.5835			1.12318
$219$	2.44555	+	1.41194i	0.165255	+	0.0954100i
$220$	−2.74763	−	4.75903i	−0.185245	−	0.320854i
$221$	−2.74429	−	7.73315i	−0.184601	−	0.520188i
$222$	2.41425	−	4.18160i	0.162034	−	0.280651i
$223$			7.77059i			0.520357i	0.965560	+	0.260179i	$0.0837815\pi$
$223$			7.77059i			0.520357i	−0.965560	+	0.260179i	$0.916219\pi$
$224$		0			0
$225$	8.97925			0.598617
$226$	−5.66426	−	3.27026i	−0.376781	−	0.217534i
$227$	−22.1210	+	12.7716i	−1.46822	+	0.847678i	−0.999366	−	0.0355975i	$-0.988667\pi$
$227$	−22.1210	+	12.7716i	−1.46822	+	0.847678i	−0.468855	+	0.883275i	$0.655333\pi$
$228$	1.39576	−	0.805841i	0.0924363	−	0.0533681i
$229$	11.1705	+	6.44929i	0.738167	+	0.426181i	0.821402	−	0.570349i	$-0.193192\pi$
$229$	11.1705	+	6.44929i	0.738167	+	0.426181i	−0.0832356	+	0.996530i	$0.526525\pi$
$230$	34.1098			2.24913
$231$		0			0
$232$		−	12.9164i		−	0.848005i
$233$	4.07139	−	7.05186i	0.266726	−	0.461983i	−0.701289	−	0.712877i	$-0.747392\pi$
$233$	4.07139	−	7.05186i	0.266726	−	0.461983i	0.968014	+	0.250895i	$0.0807249\pi$
$234$	15.4978	−	5.49976i	1.01312	−	0.359531i
$235$	1.94287	+	3.36514i	0.126739	+	0.219518i
$236$	−6.16536	−	3.55957i	−0.401331	−	0.231708i
$237$	0.997011			0.0647628
$238$		0			0
$239$			23.8122i			1.54028i	0.637875	+	0.770140i	$0.279814\pi$
$239$			23.8122i			1.54028i	−0.637875	+	0.770140i	$0.720186\pi$
$240$	−6.07685	−	3.50847i	−0.392259	−	0.226471i
$241$	0.249889	−	0.144273i	0.0160967	−	0.00929346i	−0.491930	−	0.870635i	$-0.663708\pi$
$241$	0.249889	−	0.144273i	0.0160967	−	0.00929346i	0.508027	+	0.861341i	$0.330375\pi$
$242$	−6.21731	+	3.58957i	−0.399664	+	0.230746i
$243$	5.96942	−	10.3393i	0.382939	−	0.663269i
$244$	7.07630			0.453013
$245$		0			0
$246$	−3.26150			−0.207946
$247$	−12.0585	−	10.2850i	−0.767266	−	0.654418i
$248$	−7.14440	−	12.3745i	−0.453670	−	0.785779i
$249$	1.33656	−	0.771665i	0.0847012	−	0.0489023i
$250$	−4.14103	+	7.17247i	−0.261902	+	0.453627i
$251$	−7.61843			−0.480871			−0.240435	−	0.970665i	$-0.577290\pi$
$251$	−7.61843			−0.480871			−0.240435	+	0.970665i	$0.577290\pi$
$252$		0			0
$253$			18.5066i			1.16350i
$254$	−3.40297	−	1.96471i	−0.213522	−	0.123277i
$255$	−2.80368	+	1.61870i	−0.175573	+	0.101367i
$256$	−7.82009	−	13.5448i	−0.488756	−	0.846550i
$257$	5.82801	−	10.0944i	0.363541	−	0.629672i	−0.625000	−	0.780625i	$-0.714901\pi$
$257$	5.82801	−	10.0944i	0.363541	−	0.629672i	0.988541	+	0.150953i	$0.0482343\pi$
$258$			1.07696i			0.0670484i
$259$		0			0
$260$	1.39369	−	7.54793i	0.0864331	−	0.468103i
$261$	8.53463	−	14.7824i	0.528280	−	0.915008i
$262$	3.06165	−	1.76764i	0.189149	−	0.109205i
$263$	6.77638	+	11.7370i	0.417850	+	0.723737i	0.995723	−	0.0923895i	$-0.0294505\pi$
$263$	6.77638	+	11.7370i	0.417850	+	0.723737i	−0.577873	+	0.816127i	$0.696117\pi$
$264$	1.33185	−	2.30684i	0.0819698	−	0.141976i
$265$		−	23.8182i		−	1.46314i
$266$		0			0
$267$			6.46359i			0.395565i
$268$	−10.2060	−	5.89241i	−0.623428	−	0.359936i
$269$	−8.91662	−	15.4440i	−0.543656	−	0.941640i	−0.998690	−	0.0511657i	$-0.983706\pi$
$269$	−8.91662	−	15.4440i	−0.543656	−	0.941640i	0.455034	−	0.890474i	$-0.349627\pi$
$270$	−6.77649	−	11.7372i	−0.412404	−	0.714304i
$271$	26.3049	+	15.1872i	1.59791	+	0.922555i	0.991889	+	0.127107i	$0.0405693\pi$
$271$	26.3049	+	15.1872i	1.59791	+	0.922555i	0.606023	+	0.795447i	$0.292764\pi$
$272$	−11.2262			−0.680690
$273$		0			0
$274$	0.710564			0.0429268
$275$	7.28620	+	4.20669i	0.439375	+	0.253673i
$276$	−1.31430	−	2.27644i	−0.0791117	−	0.137025i
$277$	2.60712	+	4.51567i	0.156647	+	0.271320i	0.933657	−	0.358167i	$-0.116598\pi$
$277$	2.60712	+	4.51567i	0.156647	+	0.271320i	−0.777011	+	0.629487i	$0.783265\pi$
$278$	27.9372	+	16.1295i	1.67556	+	0.967385i
$279$		−	18.8829i		−	1.13049i
$280$		0			0
$281$		−	1.66255i		−	0.0991794i	−0.998770	−	0.0495897i	$-0.984209\pi$
$281$		−	1.66255i		−	0.0991794i	0.998770	−	0.0495897i	$-0.0157914\pi$
$282$	0.553976	−	0.959515i	0.0329888	−	0.0571383i
$283$	6.89783	+	11.9474i	0.410033	+	0.710198i	0.994893	−	0.100936i	$-0.0321838\pi$
$283$	6.89783	+	11.9474i	0.410033	+	0.710198i	−0.584860	+	0.811134i	$0.698850\pi$
$284$	3.07532	−	1.77554i	0.182487	−	0.105359i
$285$	−3.12647	+	5.41520i	−0.185196	+	0.320769i
$286$	15.1523	+	2.79780i	0.895972	+	0.165437i
$287$		0			0
$288$		−	11.0113i		−	0.648849i
$289$	5.91028	−	10.2369i	0.347663	−	0.602171i
$290$	−14.7390	−	25.5287i	−0.865503	−	1.49910i
$291$	−6.01765	+	3.47429i	−0.352761	+	0.203667i
$292$	3.65980	+	2.11299i	0.214174	+	0.123653i
$293$		−	12.8576i		−	0.751149i	−0.926792	−	0.375574i	$-0.877445\pi$
$293$		−	12.8576i		−	0.751149i	0.926792	−	0.375574i	$-0.122555\pi$
$294$		0			0
$295$	27.6206			1.60813
$296$	−6.14204	+	10.6383i	−0.356999	+	0.618340i
$297$	6.36814	−	3.67665i	0.369517	−	0.213341i
$298$	18.9560	+	32.8328i	1.09809	+	1.90195i
$299$	−16.7745	+	19.6671i	−0.970094	+	1.13738i
$300$	−1.19500			−0.0689936
$301$		0			0
$302$	18.5761			1.06894
$303$	−4.31824	+	7.47941i	−0.248077	+	0.429681i
$304$	−18.7781	+	10.8415i	−1.07700	+	0.621805i
$305$	−23.7761	+	13.7272i	−1.36142	+	0.786015i
$306$	−8.98933	−	5.18999i	−0.513886	−	0.296692i
$307$			20.9016i			1.19292i	0.802644	+	0.596458i	$0.203426\pi$
$307$			20.9016i			1.19292i	−0.802644	+	0.596458i	$0.796574\pi$
$308$		0			0
$309$	3.24555			0.184633
$310$	−28.2411	−	16.3050i	−1.60399	−	0.926062i
$311$	−8.56961	−	14.8430i	−0.485938	−	0.841669i	0.513931	−	0.857831i	$-0.328189\pi$
$311$	−8.56961	−	14.8430i	−0.485938	−	0.841669i	−0.999869	+	0.0161620i	$0.994855\pi$
$312$	3.50630	−	1.24429i	0.198505	−	0.0704442i
$313$	−1.27633	+	2.21067i	−0.0721424	+	0.124954i	−0.899840	−	0.436220i	$-0.856317\pi$
$313$	−1.27633	+	2.21067i	−0.0721424	+	0.124954i	0.827698	+	0.561174i	$0.189650\pi$
$314$		−	6.27109i		−	0.353898i
$315$		0			0
$316$	1.49204			0.0839339
$317$	−23.6328	−	13.6444i	−1.32735	−	0.766345i	−0.342459	−	0.939533i	$-0.611260\pi$
$317$	−23.6328	−	13.6444i	−1.32735	−	0.766345i	−0.984889	+	0.173188i	$0.944593\pi$
$318$	−5.88149	+	3.39568i	−0.329818	+	0.190420i
$319$	13.8508	−	7.99678i	0.775497	−	0.447733i
$320$	8.08557	+	4.66821i	0.451997	+	0.260961i
$321$	−7.72264			−0.431036
$322$		0			0
$323$			10.0039i			0.556633i
$324$	2.53889	−	4.39748i	0.141049	−	0.244305i
$325$	3.93014	+	11.0748i	0.218005	+	0.614317i
$326$	16.2348	+	28.1195i	0.899163	+	1.55740i
$327$	4.29397	+	2.47912i	0.237457	+	0.137096i
$328$	8.29751			0.458154
$329$		0			0
$330$		−	6.07912i		−	0.334645i
$331$	8.39444	+	4.84653i	0.461400	+	0.266390i	0.712633	−	0.701537i	$-0.247503\pi$
$331$	8.39444	+	4.84653i	0.461400	+	0.266390i	−0.251233	+	0.967927i	$0.580836\pi$
$332$	2.00018	−	1.15481i	0.109774	−	0.0633783i
$333$	−14.0587	+	8.11679i	−0.770412	+	0.444798i
$334$	8.51947	−	14.7561i	0.466164	−	0.807421i
$335$	45.7223			2.49808
$336$		0			0
$337$	6.31370			0.343929			0.171965	−	0.985103i	$-0.444988\pi$
$337$	6.31370			0.343929			0.171965	+	0.985103i	$0.444988\pi$
$338$	13.5665	+	16.7073i	0.737920	+	0.908760i
$339$	−0.977762	−	1.69353i	−0.0531048	−	0.0919801i
$340$	−4.19574	+	2.42241i	−0.227546	+	0.131374i
$341$	8.84643	−	15.3225i	0.479061	−	0.829758i
$342$	−20.0486			−1.08410
$343$		0			0
$344$		−	2.73986i		−	0.147724i
$345$	8.83203	+	5.09918i	0.475501	+	0.274530i
$346$	−8.60862	+	4.97019i	−0.462802	+	0.267199i
$347$	−14.5600	−	25.2187i	−0.781622	−	1.35381i	−0.930997	−	0.365028i	$-0.881059\pi$
$347$	−14.5600	−	25.2187i	−0.781622	−	1.35381i	0.149375	−	0.988781i	$-0.452274\pi$
$348$	−1.13583	+	1.96732i	−0.0608870	+	0.105459i
$349$		−	20.3297i		−	1.08822i	−0.839013	−	0.544112i	$-0.816867\pi$
$349$		−	20.3297i		−	1.08822i	0.839013	−	0.544112i	$-0.183133\pi$
$350$		0			0
$351$	10.1000	+	1.86492i	0.539099	+	0.0995421i
$352$	5.15870	−	8.93513i	0.274960	−	0.476244i
$353$	−12.2958	+	7.09900i	−0.654441	+	0.377841i	−0.790155	−	0.612907i	$-0.790000\pi$
$353$	−12.2958	+	7.09900i	−0.654441	+	0.377841i	0.135715	+	0.990748i	$0.456667\pi$
$354$	−3.93777	−	6.82043i	−0.209290	−	0.362502i
$355$	−6.88866	+	11.9315i	−0.365612	+	0.633259i
$356$			9.67285i			0.512660i
$357$		0			0
$358$		−	12.8324i		−	0.678214i
$359$	6.49661	+	3.75082i	0.342878	+	0.197961i	0.661544	−	0.749906i	$-0.269902\pi$
$359$	6.49661	+	3.75082i	0.342878	+	0.197961i	−0.318666	+	0.947867i	$0.603235\pi$
$360$	8.25299	+	14.2946i	0.434971	+	0.753391i
$361$	0.161114	+	0.279058i	0.00847971	+	0.0146873i
$362$	−28.6742	−	16.5551i	−1.50708	−	0.870115i
$363$	−2.14646			−0.112660
$364$		0			0
$365$	−16.3958			−0.858193
$366$	6.77938	+	3.91407i	0.354364	+	0.204592i
$367$	−14.2942	−	24.7582i	−0.746149	−	1.29237i	−0.949656	−	0.313294i	$-0.898567\pi$
$367$	−14.2942	−	24.7582i	−0.746149	−	1.29237i	0.203507	−	0.979073i	$-0.434766\pi$
$368$	17.6822	+	30.6265i	0.921749	+	1.59652i
$369$	9.49621	+	5.48264i	0.494353	+	0.285415i
$370$			28.0348i			1.45746i
$371$		0			0
$372$			2.51303i			0.130294i
$373$	3.95602	−	6.85203i	0.204835	−	0.354784i	−0.745245	−	0.666791i	$-0.767668\pi$
$373$	3.95602	−	6.85203i	0.204835	−	0.354784i	0.950080	+	0.312006i	$0.101001\pi$
$374$	−4.86292	−	8.42283i	−0.251456	−	0.435534i
$375$	−2.14447	+	1.23811i	−0.110740	+	0.0639357i
$376$	−1.40936	+	2.44108i	−0.0726822	+	0.125889i
$377$	21.9677	+	4.05624i	1.13139	+	0.208907i
$378$		0			0
$379$		−	1.78091i		−	0.0914791i	−0.998953	−	0.0457395i	$-0.985436\pi$
$379$		−	1.78091i		−	0.0914791i	0.998953	−	0.0457395i	$-0.0145644\pi$
$380$	−4.67880	+	8.10393i	−0.240018	+	0.415723i
$381$	−0.587421	−	1.01744i	−0.0300945	−	0.0521251i
$382$	−29.3676	+	16.9554i	−1.50258	+	0.867515i
$383$	12.2973	+	7.09987i	0.628364	+	0.362786i	0.780118	−	0.625632i	$-0.215159\pi$
$383$	12.2973	+	7.09987i	0.628364	+	0.362786i	−0.151754	+	0.988418i	$0.548492\pi$
$384$		−	6.61883i		−	0.337766i
$385$		0			0
$386$	20.5829			1.04764
$387$	1.81038	−	3.13568i	0.0920270	−	0.159395i
$388$	−9.00550	+	5.19933i	−0.457185	+	0.263956i
$389$	−3.38749	−	5.86731i	−0.171753	−	0.297485i	0.767280	−	0.641312i	$-0.221610\pi$
$389$	−3.38749	−	5.86731i	−0.171753	−	0.297485i	−0.939033	+	0.343828i	$0.888276\pi$
$390$	5.51016	−	6.46034i	0.279018	−	0.327132i
$391$	16.3161			0.825140
$392$		0			0
$393$	1.05700			0.0533187
$394$	15.7113	−	27.2128i	0.791524	−	1.37096i
$395$	−5.01321	+	2.89438i	−0.252242	+	0.145632i
$396$	4.56215	−	2.63396i	0.229257	−	0.132361i
$397$	−25.1167	−	14.5011i	−1.26057	−	0.727792i	−0.287387	−	0.957815i	$-0.592787\pi$
$397$	−25.1167	−	14.5011i	−1.26057	−	0.727792i	−0.973185	+	0.230023i	$0.926120\pi$
$398$		−	21.2218i		−	1.06375i
$399$		0			0
$400$	16.0772			0.803861
$401$	19.0183	+	10.9802i	0.949728	+	0.548326i	0.892997	−	0.450064i	$-0.148599\pi$
$401$	19.0183	+	10.9802i	0.949728	+	0.548326i	0.0567318	+	0.998389i	$0.481932\pi$
$402$	−6.51848	−	11.2903i	−0.325112	−	0.563111i
$403$	23.2896	−	8.26485i	1.16014	−	0.411701i
$404$	−6.46231	+	11.1930i	−0.321512	+	0.556875i
$405$			19.7006i			0.978928i
$406$		0			0
$407$	−15.2105			−0.753959
$408$	−2.03379	−	1.17421i	−0.100688	−	0.0581321i
$409$	3.46661	−	2.00145i	0.171413	−	0.0989653i	−0.411839	−	0.911257i	$-0.635113\pi$
$409$	3.46661	−	2.00145i	0.171413	−	0.0989653i	0.583252	+	0.812291i	$0.301780\pi$
$410$	16.3996	−	9.46832i	0.809919	−	0.467607i
$411$	0.183986	+	0.106224i	0.00907537	+	0.00523967i
$412$	4.85702			0.239288
$413$		0			0
$414$			32.6986i			1.60705i
$415$	−4.48037	+	7.76024i	−0.219933	+	0.380935i
$416$	13.5811	−	4.81956i	0.665866	−	0.236298i
$417$	4.82250	+	8.35282i	0.236159	+	0.409039i
$418$	−16.2684	−	9.39256i	−0.795713	−	0.459405i
$419$	−1.75047			−0.0855162			−0.0427581	−	0.999085i	$-0.513614\pi$
$419$	−1.75047			−0.0855162			−0.0427581	+	0.999085i	$0.513614\pi$
$420$		0			0
$421$		−	16.2204i		−	0.790533i	−0.918566	−	0.395267i	$-0.870652\pi$
$421$		−	16.2204i		−	0.790533i	0.918566	−	0.395267i	$-0.129348\pi$
$422$	−11.2823	−	6.51385i	−0.549215	−	0.317089i
$423$	−3.22593	+	1.86249i	−0.156850	+	0.0905573i
$424$	14.9630	−	8.63888i	0.726666	−	0.419541i
$425$	3.70878	−	6.42379i	0.179902	−	0.311600i
$426$	3.92837			0.190330
$427$		0			0
$428$	−11.5570			−0.558631
$429$	3.50512	+	2.98959i	0.169229	+	0.144339i
$430$	−3.12647	−	5.41520i	−0.150772	−	0.261144i
$431$	10.1149	−	5.83984i	0.487217	−	0.281295i	−0.236202	−	0.971704i	$-0.575903\pi$
$431$	10.1149	−	5.83984i	0.487217	−	0.281295i	0.723419	+	0.690409i	$0.242569\pi$
$432$	7.02574	−	12.1689i	0.338026	−	0.585479i
$433$	−31.6289			−1.51999			−0.759994	−	0.649930i	$-0.774798\pi$
$433$	−31.6289			−1.51999			−0.759994	+	0.649930i	$0.774798\pi$
$434$		0			0
$435$		−	8.81351i		−	0.422575i
$436$	6.42598	+	3.71004i	0.307749	+	0.177679i
$437$	27.2919	−	15.7570i	1.30555	−	0.753759i
$438$	2.33749	+	4.04865i	0.111690	+	0.193452i
$439$	−4.85769	+	8.41377i	−0.231845	+	0.401567i	−0.958351	−	0.285593i	$-0.907810\pi$
$439$	−4.85769	+	8.41377i	−0.231845	+	0.401567i	0.726506	+	0.687160i	$0.241143\pi$
$440$			15.4658i			0.737302i
$441$		0			0
$442$	2.46664	−	13.3588i	0.117326	−	0.635413i
$443$	−10.5582	+	18.2873i	−0.501633	+	0.868854i	0.498365	+	0.866967i	$0.333934\pi$
$443$	−10.5582	+	18.2873i	−0.501633	+	0.868854i	−0.999998	+	0.00188659i	$0.999399\pi$
$444$	1.87100	−	1.08022i	0.0887939	−	0.0512652i
$445$	−18.7642	−	32.5005i	−0.889507	−	1.54067i
$446$	−6.43218	+	11.1409i	−0.304573	+	0.527535i
$447$			11.3352i			0.536135i
$448$		0			0
$449$			13.4710i			0.635735i	0.948135	+	0.317867i	$0.102967\pi$
$449$			13.4710i			0.635735i	−0.948135	+	0.317867i	$0.897033\pi$
$450$	12.8737	+	7.43266i	0.606874	+	0.350379i
$451$	5.13713	+	8.89776i	0.241898	+	0.418979i
$452$	−1.46323	−	2.53440i	−0.0688248	−	0.119208i
$453$	4.80991	+	2.77700i	0.225989	+	0.130475i
$454$	−42.2871			−1.98463
$455$		0			0
$456$	−4.53589			−0.212413
$457$	−8.10237	−	4.67791i	−0.379013	−	0.218823i	0.298376	−	0.954449i	$-0.403555\pi$
$457$	−8.10237	−	4.67791i	−0.379013	−	0.218823i	−0.677389	+	0.735625i	$0.736888\pi$
$458$	10.6769	+	18.4929i	0.498899	+	0.864119i
$459$	−3.24147	−	5.61439i	−0.151299	−	0.262057i
$460$	13.2173	+	7.63099i	0.616258	+	0.355797i
$461$		−	8.14109i		−	0.379168i	−0.981864	−	0.189584i	$-0.939286\pi$
$461$		−	8.14109i		−	0.379168i	0.981864	−	0.189584i	$-0.0607140\pi$
$462$		0			0
$463$		−	24.3018i		−	1.12940i	−0.825296	−	0.564700i	$-0.808992\pi$
$463$		−	24.3018i		−	1.12940i	0.825296	−	0.564700i	$-0.191008\pi$
$464$	15.2811	−	26.4677i	0.709408	−	1.22873i
$465$	−4.87497	−	8.44369i	−0.226071	−	0.391567i
$466$	11.6745	−	6.74026i	0.540810	−	0.312237i
$467$	−16.3968	+	28.4000i	−0.758751	+	1.31420i	0.184736	+	0.982788i	$0.440857\pi$
$467$	−16.3968	+	28.4000i	−0.758751	+	1.31420i	−0.943488	+	0.331408i	$0.892476\pi$
$468$	7.23567	+	1.33603i	0.334469	+	0.0617582i
$469$		0			0
$470$			6.43290i			0.296728i
$471$	0.937484	−	1.62377i	0.0431970	−	0.0748194i
$472$	10.0180	+	17.3517i	0.461116	+	0.798677i
$473$	2.93807	−	1.69629i	0.135093	−	0.0779957i
$474$	1.42944	+	0.825285i	0.0656561	+	0.0379066i
$475$		−	14.3267i		−	0.657356i
$476$		0			0
$477$	22.8328			1.04544
$478$	−19.7107	+	34.1400i	−0.901548	+	1.56153i
$479$	2.14868	−	1.24054i	0.0981759	−	0.0566819i	−0.450108	−	0.892974i	$-0.648615\pi$
$479$	2.14868	−	1.24054i	0.0981759	−	0.0566819i	0.548284	+	0.836292i	$0.315281\pi$
$480$	−2.84279	−	4.92385i	−0.129755	−	0.224742i
$481$	−16.1644	−	13.7869i	−0.737032	−	0.628631i
$482$	0.477694			0.0217584
$483$		0			0
$484$	−3.21221			−0.146009
$485$	20.1721	−	34.9392i	0.915970	−	1.58651i
$486$	17.1170	−	9.88248i	0.776441	−	0.448279i
$487$	19.8506	−	11.4608i	0.899519	−	0.519337i	0.0224747	−	0.999747i	$-0.492845\pi$
$487$	19.8506	−	11.4608i	0.899519	−	0.519337i	0.877044	+	0.480410i	$0.159512\pi$
$488$	−17.2473	−	9.95771i	−0.780747	−	0.450764i
$489$			9.70797i			0.439010i
$490$		0			0
$491$	−22.8735			−1.03227			−0.516134	−	0.856508i	$-0.672629\pi$
$491$	−22.8735			−1.03227			−0.516134	+	0.856508i	$0.672629\pi$
$492$	−1.26380	−	0.729658i	−0.0569767	−	0.0328955i
$493$	−7.05026	−	12.2114i	−0.317528	−	0.549974i
$494$	−8.77508	−	24.7273i	−0.394809	−	1.11254i
$495$	−10.2191	+	17.7000i	−0.459315	+	0.795557i
$496$		−	33.8095i		−	1.51809i
$497$		0			0
$498$	2.55501			0.114493
$499$	7.34465	+	4.24044i	0.328792	+	0.189828i	0.655305	−	0.755365i	$-0.272540\pi$
$499$	7.34465	+	4.24044i	0.328792	+	0.189828i	−0.326513	+	0.945193i	$0.605874\pi$
$500$	−3.20923	+	1.85285i	−0.143521	+	0.0828620i
$501$	4.41188	−	2.54720i	0.197108	−	0.113801i
$502$	−10.9227	−	6.30622i	−0.487504	−	0.281460i
$503$	9.36890			0.417739			0.208869	−	0.977944i	$-0.433022\pi$
$503$	9.36890			0.417739			0.208869	+	0.977944i	$0.433022\pi$
$504$		0			0
$505$		−	50.1444i		−	2.23140i
$506$	−15.3190	+	26.5333i	−0.681012	+	1.17955i
$507$	1.01513	+	6.35412i	0.0450836	+	0.282196i
$508$	−0.879083	−	1.52262i	−0.0390030	−	0.0675552i
$509$	18.6544	+	10.7701i	0.826840	+	0.477376i	0.852770	−	0.522287i	$-0.174921\pi$
$509$	18.6544	+	10.7701i	0.826840	+	0.477376i	−0.0259293	+	0.999664i	$0.508254\pi$
$510$	−5.35958			−0.237326
$511$		0			0
$512$			0.851388i			0.0376264i
$513$	−10.8440	−	6.26078i	−0.478774	−	0.276420i
$514$	16.7115	−	9.64837i	0.737111	−	0.425572i
$515$	−16.3194	+	9.42203i	−0.719120	+	0.415184i
$516$	−0.240935	+	0.417312i	−0.0106066	+	0.0183711i
$517$	−3.49023			−0.153500
$518$		0			0
$519$	−2.97203			−0.130458
$520$	−14.0183	+	16.4356i	−0.614742	+	0.720749i
$521$	7.87350	+	13.6373i	0.344944	+	0.597461i	0.985344	−	0.170581i	$-0.0545645\pi$
$521$	7.87350	+	13.6373i	0.344944	+	0.597461i	−0.640399	+	0.768042i	$0.721231\pi$
$522$	24.4725	−	14.1292i	1.07113	−	0.618420i
$523$	8.97018	−	15.5368i	0.392238	−	0.679377i	−0.600506	−	0.799620i	$-0.705034\pi$
$523$	8.97018	−	15.5368i	0.392238	−	0.679377i	0.992744	+	0.120243i	$0.0383675\pi$
$524$	1.58182			0.0691020
$525$		0			0
$526$			22.4369i			0.978293i
$527$	−13.5089	−	7.79934i	−0.588455	−	0.339745i
$528$	5.45832	−	3.15136i	0.237543	−	0.137146i
$529$	−14.1992	−	24.5937i	−0.617355	−	1.06929i
$530$	19.7157	−	34.1486i	0.856396	−	1.48332i
$531$			26.4779i			1.14904i
$532$		0			0
$533$	−2.60573	+	14.1121i	−0.112867	+	0.611261i
$534$	−5.35029	+	9.26698i	−0.231530	+	0.401021i
$535$	38.8313	−	22.4193i	1.67883	−	0.969270i
$536$	16.5835	+	28.7235i	0.716299	+	1.24067i
$537$	1.91836	−	3.32269i	0.0827832	−	0.143385i
$538$		−	29.5232i		−	1.27284i
$539$		0			0
$540$		−	6.06410i		−	0.260957i
$541$	−8.10237	−	4.67791i	−0.348348	−	0.201119i	0.315609	−	0.948889i	$-0.397791\pi$
$541$	−8.10237	−	4.67791i	−0.348348	−	0.201119i	−0.663958	+	0.747770i	$0.731124\pi$
$542$	25.1426	+	43.5483i	1.07997	+	1.87056i
$543$	−4.94974	−	8.57319i	−0.212413	−	0.367911i
$544$	−7.87755	−	4.54810i	−0.337747	−	0.194998i
$545$	−28.7881			−1.23315
$546$		0			0
$547$	−33.1634			−1.41796			−0.708981	−	0.705227i	$-0.750845\pi$
$547$	−33.1634			−1.41796			−0.708981	+	0.705227i	$0.750845\pi$
$548$	0.275338	+	0.158966i	0.0117619	+	0.00679071i
$549$	−13.1593	−	22.7925i	−0.561624	−	0.972761i
$550$	6.96425	+	12.0624i	0.296957	+	0.514344i
$551$	−23.5859	−	13.6173i	−1.00479	−	0.580118i
$552$			7.39790i			0.314876i
$553$		0			0
$554$			8.63228i			0.366750i
$555$	−4.19101	+	7.25904i	−0.177898	+	0.308129i
$556$	7.21695	+	12.5001i	0.306067	+	0.530123i
$557$	−9.65899	+	5.57662i	−0.409265	+	0.236289i	−0.690474	−	0.723357i	$-0.742598\pi$
$557$	−9.65899	+	5.57662i	−0.409265	+	0.236289i	0.281209	+	0.959647i	$0.409265\pi$
$558$	15.6305	−	27.0727i	0.661690	−	1.14608i
$559$	4.65984	+	0.860419i	0.197090	+	0.0363918i
$560$		0			0
$561$		−	2.90789i		−	0.122771i
$562$	1.37619	−	2.38363i	0.0580511	−	0.100547i
$563$	9.58889	+	16.6085i	0.404124	+	0.699963i	0.994219	−	0.107371i	$-0.0342432\pi$
$563$	9.58889	+	16.6085i	0.404124	+	0.699963i	−0.590095	+	0.807334i	$0.700910\pi$
$564$	0.429323	−	0.247869i	0.0180777	−	0.0104372i
$565$	9.83285	+	5.67700i	0.413671	+	0.238833i
$566$			22.8389i			0.959993i
$567$		0			0
$568$	−9.99409			−0.419343
$569$	6.73361	−	11.6630i	0.282288	−	0.488937i	−0.689660	−	0.724133i	$-0.742240\pi$
$569$	6.73361	−	11.6630i	0.282288	−	0.488937i	0.971948	+	0.235197i	$0.0755734\pi$
$570$	−8.96497	+	5.17593i	−0.375501	+	0.216796i
$571$	12.5804	+	21.7899i	0.526473	+	0.911877i	0.999524	+	0.0308427i	$0.00981909\pi$
$571$	12.5804	+	21.7899i	0.526473	+	0.911877i	−0.473052	+	0.881035i	$0.656848\pi$
$572$	5.24545	+	4.47396i	0.219323	+	0.187066i
$573$	−10.1389			−0.423557
$574$		0			0
$575$	−23.3665			−0.974450
$576$	−4.47508	+	7.75106i	−0.186462	+	0.322961i
$577$	−18.7481	+	10.8242i	−0.780492	+	0.450617i	−0.836605	−	0.547807i	$-0.815463\pi$
$577$	−18.7481	+	10.8242i	−0.780492	+	0.450617i	0.0561126	+	0.998424i	$0.482129\pi$
$578$	16.9474	−	9.78457i	0.704918	−	0.406984i
$579$	5.32953	+	3.07701i	0.221488	+	0.127876i
$580$		−	13.1895i		−	0.547666i
$581$		0			0
$582$	−11.5035			−0.476836
$583$	18.5276	+	10.6969i	0.767337	+	0.443022i
$584$	−5.94676	−	10.3001i	−0.246079	−	0.426221i
$585$	−26.9034	+	9.54729i	−1.11232	+	0.394732i
$586$	10.6430	−	18.4342i	0.439658	−	0.761510i
$587$			34.5576i			1.42634i	0.700989	+	0.713172i	$0.252742\pi$
$587$			34.5576i			1.42634i	−0.700989	+	0.713172i	$0.747258\pi$
$588$		0			0
$589$	−30.1283			−1.24142
$590$	39.6002	+	22.8632i	1.63031	+	0.941262i
$591$	8.13624	−	4.69746i	0.334680	−	0.193228i
$592$	−25.1719	+	14.5330i	−1.03456	+	0.597303i
$593$	−1.09846	−	0.634194i	−0.0451082	−	0.0260432i	0.477276	−	0.878753i	$-0.341624\pi$
$593$	−1.09846	−	0.634194i	−0.0451082	−	0.0260432i	−0.522385	+	0.852710i	$0.674957\pi$
$594$	12.1735			0.499485
$595$		0			0
$596$			16.9632i			0.694842i
$597$	3.17251	−	5.49494i	0.129842	−	0.224893i
$598$	−40.3295	+	14.3119i	−1.64920	+	0.585257i
$599$	−8.75714	−	15.1678i	−0.357807	−	0.619740i	0.629787	−	0.776768i	$-0.283142\pi$
$599$	−8.75714	−	15.1678i	−0.357807	−	0.619740i	−0.987594	+	0.157028i	$0.949809\pi$
$600$	2.91262	+	1.68160i	0.118907	+	0.0686511i
$601$	9.02164			0.368000			0.184000	−	0.982926i	$-0.441095\pi$
$601$	9.02164			0.368000			0.184000	+	0.982926i	$0.441095\pi$
$602$		0			0
$603$			43.8307i			1.78493i
$604$	7.19810	+	4.15582i	0.292886	+	0.169098i
$605$	10.7929	−	6.23130i	0.438795	−	0.253338i
$606$	−12.3823	+	7.14893i	−0.502997	+	0.290405i
$607$	−7.91450	+	13.7083i	−0.321239	+	0.556403i	−0.980744	−	0.195297i	$-0.937433\pi$
$607$	−7.91450	+	13.7083i	−0.321239	+	0.556403i	0.659505	+	0.751701i	$0.270766\pi$
$608$	−17.5690			−0.712517
$609$		0			0
$610$	−45.4511			−1.84026
$611$	−3.70910	−	3.16357i	−0.150054	−	0.127984i
$612$	−2.32219	−	4.02216i	−0.0938692	−	0.162586i
$613$	−15.1853	+	8.76721i	−0.613327	+	0.354104i	−0.774266	−	0.632860i	$-0.781881\pi$
$613$	−15.1853	+	8.76721i	−0.613327	+	0.354104i	0.160940	+	0.986964i	$0.448548\pi$
$614$	−17.3015	+	29.9670i	−0.698230	+	1.20937i
$615$	5.66179			0.228306
$616$		0			0
$617$			7.01448i			0.282392i	0.989982	+	0.141196i	$0.0450948\pi$
$617$			7.01448i			0.282392i	−0.989982	+	0.141196i	$0.954905\pi$
$618$	4.65322	+	2.68654i	0.187180	+	0.108068i
$619$	−33.6245	+	19.4131i	−1.35148	+	0.780280i	−0.988457	−	0.151499i	$-0.951590\pi$
$619$	−33.6245	+	19.4131i	−1.35148	+	0.780280i	−0.363027	+	0.931779i	$0.618257\pi$
$620$	−7.29546	−	12.6361i	−0.292993	−	0.507478i
$621$	−10.2111	+	17.6862i	−0.409759	+	0.709724i
$622$		−	28.3743i		−	1.13771i
$623$		0			0
$624$	8.65703	+	1.59848i	0.346558	+	0.0639904i
$625$	15.3368	−	26.5641i	0.613470	−	1.06256i
$626$	−3.65980	+	2.11299i	−0.146275	+	0.0844519i
$627$	−2.80825	−	4.86402i	−0.112151	−	0.194250i
$628$	1.40296	−	2.42999i	0.0559841	−	0.0969674i
$629$			13.4102i			0.534699i
$630$		0			0
$631$		−	12.7484i		−	0.507506i	−0.967269	−	0.253753i	$-0.918335\pi$
$631$		−	12.7484i		−	0.507506i	0.967269	−	0.253753i	$-0.0816650\pi$
$632$	−3.63660	−	2.09959i	−0.144656	−	0.0835172i
$633$	−1.94755	−	3.37326i	−0.0774082	−	0.134075i
$634$	−22.5885	−	39.1245i	−0.897105	−	1.55383i
$635$	5.90739	+	3.41063i	0.234427	+	0.135347i
$636$	−3.03871			−0.120493
$637$		0			0
$638$	26.4776			1.04826
$639$	−11.4379	−	6.60367i	−0.452476	−	0.261237i
$640$	19.2148	+	33.2811i	0.759533	+	1.31555i
$641$	−4.85715	−	8.41282i	−0.191846	−	0.332287i	0.754016	−	0.656856i	$-0.228114\pi$
$641$	−4.85715	−	8.41282i	−0.191846	−	0.332287i	−0.945862	+	0.324569i	$0.894781\pi$
$642$	−11.0721	−	6.39249i	−0.436982	−	0.252291i
$643$			0.458279i			0.0180728i	0.999959	+	0.00903639i	$0.00287641\pi$
$643$			0.458279i			0.0180728i	−0.999959	+	0.00903639i	$0.997124\pi$
$644$		0			0
$645$		−	1.86954i		−	0.0736131i
$646$	−8.28084	+	14.3428i	−0.325805	+	0.564311i
$647$	3.08861	+	5.34963i	0.121426	+	0.210316i	0.920330	−	0.391142i	$-0.127920\pi$
$647$	3.08861	+	5.34963i	0.121426	+	0.210316i	−0.798904	+	0.601458i	$0.794587\pi$
$648$	−12.3762	+	7.14541i	−0.486184	+	0.280698i
$649$	−12.4046	+	21.4854i	−0.486924	+	0.843377i
$650$	−3.53251	+	19.1313i	−0.138556	+	0.750392i
$651$		0			0
$652$			14.5281i			0.568965i
$653$	−14.2193	+	24.6285i	−0.556443	+	0.963787i	0.441347	+	0.897337i	$0.354501\pi$
$653$	−14.2193	+	24.6285i	−0.556443	+	0.963787i	−0.997790	+	0.0664508i	$0.978832\pi$
$654$	4.10423	+	7.10874i	0.160488	+	0.277974i
$655$	−5.31486	+	3.06854i	−0.207669	+	0.119898i
$656$	17.0028	+	9.81659i	0.663849	+	0.383274i
$657$		−	15.7175i		−	0.613196i
$658$		0			0
$659$	−25.9818			−1.01211			−0.506054	−	0.862502i	$-0.668897\pi$
$659$	−25.9818			−1.01211			−0.506054	+	0.862502i	$0.668897\pi$
$660$	1.36001	−	2.35561i	0.0529384	−	0.0916920i
$661$	−32.2812	+	18.6376i	−1.25560	+	0.724918i	−0.972215	−	0.234090i	$-0.924789\pi$
$661$	−32.2812	+	18.6376i	−1.25560	+	0.724918i	−0.283380	+	0.959008i	$0.591456\pi$
$662$	8.02353	+	13.8972i	0.311843	+	0.540128i
$663$	2.63573	−	3.09024i	0.102363	−	0.120015i
$664$	−6.50015			−0.252255
$665$		0			0
$666$	−26.8750			−1.04139
$667$	−22.2094	+	38.4679i	−0.859953	+	1.48948i
$668$	6.60245	−	3.81192i	0.255456	−	0.147488i
$669$	−3.33096	+	1.92313i	−0.128782	+	0.0743526i
$670$	65.5530	+	37.8470i	2.53253	+	1.46216i
$671$		−	24.6599i		−	0.951986i
$672$		0			0
$673$	41.7078			1.60772			0.803859	−	0.594820i	$-0.202777\pi$
$673$	41.7078			1.60772			0.803859	+	0.594820i	$0.202777\pi$
$674$	9.05209	+	5.22623i	0.348673	+	0.201307i
$675$	4.64215	+	8.04044i	0.178676	+	0.309477i
$676$	1.51916	+	9.50903i	0.0584292	+	0.365732i
$677$	9.10347	−	15.7677i	0.349875	−	0.606001i	−0.636352	−	0.771399i	$-0.719557\pi$
$677$	9.10347	−	15.7677i	0.349875	−	0.606001i	0.986227	+	0.165398i	$0.0528908\pi$
$678$		−	3.23741i		−	0.124332i
$679$		0			0
$680$	13.6352			0.522886
$681$	−10.9494	−	6.32162i	−0.419581	−	0.242245i
$682$	25.3666	−	14.6454i	0.971338	−	0.560802i
$683$	−23.6736	+	13.6680i	−0.905847	+	0.522991i	−0.879093	−	0.476651i	$-0.841850\pi$
$683$	−23.6736	+	13.6680i	−0.905847	+	0.522991i	−0.0267542	+	0.999642i	$0.508517\pi$
$684$	−7.76866	−	4.48524i	−0.297042	−	0.171497i
$685$	−1.23350			−0.0471297
$686$		0			0
$687$			6.38449i			0.243584i
$688$	3.24147	−	5.61439i	0.123580	−	0.214047i
$689$	9.99370	+	28.1613i	0.380730	+	1.07286i
$690$	8.44178	+	14.6216i	0.321373	+	0.556634i
$691$	−7.27098	−	4.19790i	−0.276601	−	0.159696i	0.355283	−	0.934759i	$-0.384385\pi$
$691$	−7.27098	−	4.19790i	−0.276601	−	0.159696i	−0.631884	+	0.775063i	$0.717718\pi$
$692$	−4.44769			−0.169076
$693$		0			0
$694$		−	48.2087i		−	1.82998i
$695$	−48.4974	−	28.0000i	−1.83961	−	1.06210i
$696$	5.53679	−	3.19667i	0.209872	−	0.121169i
$697$	7.84460	−	4.52908i	0.297135	−	0.171551i
$698$	16.8281	−	29.1471i	0.636953	−	1.10323i
$699$	4.03049			0.152447
$700$		0			0
$701$	27.4998			1.03865			0.519327	−	0.854576i	$-0.326183\pi$
$701$	27.4998			1.03865			0.519327	+	0.854576i	$0.326183\pi$
$702$	12.9369	+	11.0341i	0.488271	+	0.416457i
$703$	12.9507	+	22.4312i	0.488443	+	0.846009i
$704$	−7.26259	+	4.19306i	−0.273719	+	0.158032i
$705$	−0.961674	+	1.66567i	−0.0362187	+	0.0627327i
$706$	−23.5050			−0.884623
$707$		0			0
$708$		−	3.52381i		−	0.132433i
$709$	−25.0991	−	14.4910i	−0.942618	−	0.544221i	−0.0518380	−	0.998656i	$-0.516508\pi$
$709$	−25.0991	−	14.4910i	−0.942618	−	0.544221i	−0.890780	+	0.454435i	$0.849841\pi$
$710$	−19.7528	+	11.4043i	−0.741310	+	0.427996i
$711$	−2.77464	−	4.80581i	−0.104057	−	0.180232i
$712$	13.6116	−	23.5759i	0.510115	−	0.883545i
$713$			49.1384i			1.84025i
$714$		0			0
$715$	−26.3035	−	4.85683i	−0.983696	−	0.181635i
$716$	2.87085	−	4.97246i	0.107289	−	0.185829i
$717$	−10.2074	+	5.89323i	−0.381202	+	0.220087i
$718$	6.20955	+	10.7552i	0.231738	+	0.401382i
$719$	8.77612	−	15.2007i	0.327294	−	0.566890i	−0.654680	−	0.755906i	$-0.727197\pi$
$719$	8.77612	−	15.2007i	0.327294	−	0.566890i	0.981974	+	0.189016i	$0.0605299\pi$
$720$			39.0557i			1.45552i
$721$		0			0
$722$			0.533456i			0.0198532i
$723$	0.123689	+	0.0714119i	0.00460005	+	0.00265584i
$724$	−7.40735	−	12.8299i	−0.275292	−	0.476820i
$725$	10.0968	+	17.4881i	0.374984	+	0.649492i
$726$	−3.07743	−	1.77675i	−0.114214	−	0.0659415i
$727$	22.1403			0.821139			0.410569	−	0.911829i	$-0.365330\pi$
$727$	22.1403			0.821139			0.410569	+	0.911829i	$0.365330\pi$
$728$		0			0
$729$	−14.6556			−0.542799
$730$	−23.5069	−	13.5717i	−0.870031	−	0.502313i
$731$	−1.49552	−	2.59031i	−0.0553137	−	0.0958061i
$732$	1.75130	+	3.03334i	0.0647300	+	0.112116i
$733$	−44.4629	−	25.6707i	−1.64228	−	0.948169i	−0.980022	−	0.198889i	$-0.936267\pi$
$733$	−44.4629	−	25.6707i	−1.64228	−	0.948169i	−0.662254	−	0.749279i	$-0.730400\pi$
$734$		−	47.3285i		−	1.74693i
$735$		0			0
$736$			28.6545i			1.05622i
$737$	−20.5343	+	35.5664i	−0.756389	+	1.31010i
$738$	9.07661	+	15.7212i	0.334115	+	0.578704i
$739$	−19.7270	+	11.3894i	−0.725668	+	0.418965i	−0.816835	−	0.576871i	$-0.804274\pi$
$739$	−19.7270	+	11.3894i	−0.725668	+	0.418965i	0.0911674	+	0.995836i	$0.470940\pi$
$740$	−6.27191	+	10.8633i	−0.230560	+	0.399341i
$741$	1.42444	−	7.71445i	0.0523281	−	0.283398i
$742$		0			0
$743$			27.6199i			1.01328i	0.862159	+	0.506638i	$0.169112\pi$
$743$			27.6199i			1.01328i	−0.862159	+	0.506638i	$0.830888\pi$
$744$	3.53631	−	6.12507i	0.129647	−	0.224556i
$745$	−32.9067	−	56.9960i	−1.20561	−	2.08817i
$746$	11.3437	−	6.54926i	0.415321	−	0.239785i
$747$	−7.43919	−	4.29502i	−0.272186	−	0.157147i
$748$		−	4.35170i		−	0.159114i
$749$		0			0
$750$	−4.09943			−0.149690
$751$	20.5586	−	35.6085i	0.750194	−	1.29937i	−0.197534	−	0.980296i	$-0.563293\pi$
$751$	20.5586	−	35.6085i	0.750194	−	1.29937i	0.947728	−	0.319078i	$-0.103373\pi$
$752$	−5.77597	+	3.33476i	−0.210628	+	0.121606i
$753$	−1.88547	−	3.26573i	−0.0687104	−	0.119010i
$754$	28.1380	+	23.9995i	1.02472	+	0.874010i
$755$	−32.2472			−1.17360
$756$		0			0
$757$	14.0143			0.509357			0.254678	−	0.967026i	$-0.418030\pi$
$757$	14.0143			0.509357			0.254678	+	0.967026i	$0.418030\pi$
$758$	1.47416	−	2.55332i	0.0535440	−	0.0927409i
$759$	−7.93308	+	4.58016i	−0.287952	+	0.166249i
$760$	22.8076	−	13.1680i	0.827318	−	0.477652i
$761$	29.5876	+	17.0824i	1.07255	+	0.619236i	0.928877	−	0.370389i	$-0.120776\pi$
$761$	29.5876	+	17.0824i	1.07255	+	0.619236i	0.143672	+	0.989625i	$0.454109\pi$
$762$		−	1.94497i		−	0.0704588i
$763$		0			0
$764$	−15.1730			−0.548938
$765$	15.6050	+	9.00956i	0.564200	+	0.325741i
$766$	11.7540	+	20.3584i	0.424688	+	0.735581i
$767$	−32.6571	+	11.5891i	−1.17918	+	0.418459i
$768$	3.87076	−	6.70436i	0.139674	−	0.241923i
$769$		−	52.9061i		−	1.90784i	−0.300059	−	0.953921i	$-0.597006\pi$
$769$		−	52.9061i		−	1.90784i	0.300059	−	0.953921i	$-0.402994\pi$
$770$		0			0
$771$	5.76946			0.207782
$772$	7.97572	+	4.60478i	0.287052	+	0.165730i
$773$	39.7621	−	22.9567i	1.43014	−	0.825694i	0.433013	−	0.901388i	$-0.357451\pi$
$773$	39.7621	−	22.9567i	1.43014	−	0.825694i	0.997131	+	0.0756940i	$0.0241172\pi$
$774$	5.19117	−	2.99712i	0.186593	−	0.107729i
$775$	19.3462	+	11.1695i	0.694937	+	0.401222i
$776$	29.2658			1.05058
$777$		0			0
$778$		−	11.2161i		−	0.402117i
$779$	8.74777	−	15.1516i	0.313421	−	0.542862i
$780$	3.58044	−	1.27060i	0.128200	−	0.0454949i
$781$	−6.18751	−	10.7171i	−0.221406	−	0.383487i
$782$	23.3927	+	13.5058i	0.836522	+	0.482966i
$783$	17.6491			0.630728
$784$		0			0
$785$			10.8863i			0.388548i
$786$	1.51545	+	0.874943i	0.0540541	+	0.0312082i
$787$	−13.1525	+	7.59358i	−0.468835	+	0.270682i	−0.715752	−	0.698355i	$-0.753916\pi$
$787$	−13.1525	+	7.59358i	−0.468835	+	0.270682i	0.246917	+	0.969037i	$0.420583\pi$
$788$	12.1760	−	7.02982i	0.433752	−	0.250427i
$789$	−3.35415	+	5.80956i	−0.119411	+	0.206826i
$790$	−9.58340			−0.340962
$791$		0			0
$792$	−14.8259			−0.526817
$793$	22.3519	−	26.2063i	0.793740	−	0.930614i
$794$	−24.0069	−	41.5812i	−0.851973	−	1.47566i
$795$	10.2100	−	5.89472i	0.362110	−	0.209064i
$796$	4.74770	−	8.22326i	0.168278	−	0.291466i
$797$	−16.3006			−0.577398			−0.288699	−	0.957420i	$-0.593223\pi$
$797$	−16.3006			−0.577398			−0.288699	+	0.957420i	$0.593223\pi$
$798$		0			0
$799$			3.07712i			0.108861i
$800$	11.2815	+	6.51340i	0.398863	+	0.230283i
$801$	31.1559	−	17.9879i	1.10084	−	0.635570i
$802$	18.1779	+	31.4851i	0.641886	+	1.11178i
$803$	7.36347	−	12.7539i	0.259851	−	0.450076i
$804$		−	5.83322i		−	0.205722i
$805$		0			0
$806$	40.2320	+	7.42866i	1.41711	+	0.261663i
$807$	4.41352	−	7.64444i	0.155363	−	0.269097i
$808$	31.5016	−	18.1874i	1.10822	−	0.639832i
$809$	−5.19286	−	8.99430i	−0.182571	−	0.316223i	0.760184	−	0.649708i	$-0.225109\pi$
$809$	−5.19286	−	8.99430i	−0.182571	−	0.316223i	−0.942755	+	0.333485i	$0.891775\pi$
$810$	−16.3073	+	28.2451i	−0.572981	+	0.992431i
$811$		−	10.9705i		−	0.385227i	−0.981275	−	0.192614i	$-0.938304\pi$
$811$		−	10.9705i		−	0.385227i	0.981275	−	0.192614i	$-0.0616964\pi$
$812$		0			0
$813$			15.0346i			0.527286i
$814$	−21.8077	−	12.5907i	−0.764359	−	0.441303i
$815$	−28.1828	−	48.8140i	−0.987200	−	1.70988i
$816$	−2.77836	−	4.81226i	−0.0972621	−	0.168463i
$817$	−5.00310	−	2.88854i	−0.175036	−	0.101057i
$818$	6.62687			0.231703
$819$		0			0
$820$	8.47296			0.295888
$821$	−34.8423	−	20.1162i	−1.21601	−	0.702061i	−0.251945	−	0.967742i	$-0.581070\pi$
$821$	−34.8423	−	20.1162i	−1.21601	−	0.702061i	−0.964061	+	0.265681i	$0.914403\pi$
$822$	0.175856	+	0.304592i	0.00613370	+	0.0106239i
$823$	−1.63250	−	2.82757i	−0.0569053	−	0.0985628i	0.836169	−	0.548471i	$-0.184790\pi$
$823$	−1.63250	−	2.82757i	−0.0569053	−	0.0985628i	−0.893075	+	0.449908i	$0.851457\pi$
$824$	−11.8381	−	6.83476i	−0.412401	−	0.238100i
$825$			4.16443i			0.144987i
$826$		0			0
$827$		−	46.0118i		−	1.59999i	−0.600009	−	0.799993i	$-0.704836\pi$
$827$		−	46.0118i		−	1.59999i	0.600009	−	0.799993i	$-0.295164\pi$
$828$	−7.31529	+	12.6705i	−0.254224	+	0.440329i
$829$	15.1933	+	26.3155i	0.527683	+	0.913974i	0.999479	+	0.0322667i	$0.0102726\pi$
$829$	15.1933	+	26.3155i	0.527683	+	0.913974i	−0.471796	+	0.881708i	$0.656394\pi$
$830$	−12.8472	+	7.41734i	−0.445933	+	0.257460i
$831$	−1.29047	+	2.23515i	−0.0447658	+	0.0775366i
$832$	−11.5186	−	2.12686i	−0.399337	−	0.0737358i
$833$		0			0
$834$			15.9675i			0.552909i
$835$	−14.7893	+	25.6159i	−0.511807	+	0.886475i
$836$	−4.20258	−	7.27908i	−0.145349	−	0.251752i
$837$	16.9086	−	9.76217i	0.584446	−	0.337430i
$838$	−2.50969	−	1.44897i	−0.0866958	−	0.0500538i
$839$		−	1.52007i		−	0.0524787i	−0.999656	−	0.0262394i	$-0.991647\pi$
$839$		−	1.52007i		−	0.0524787i	0.999656	−	0.0262394i	$-0.00835321\pi$
$840$		0			0
$841$	9.38720			0.323697
$842$	13.4266	−	23.2555i	0.462710	−	0.801438i
$843$	0.712673	−	0.411462i	0.0245457	−	0.0141715i
$844$	−2.91454	−	5.04813i	−0.100323	−	0.173764i
$845$	−23.5507	−	29.0031i	−0.810169	−	0.997736i
$846$	−6.16677			−0.212018
$847$		0			0
$848$	40.8818			1.40389
$849$	−3.41426	+	5.91368i	−0.117177	+	0.202957i
$850$	10.6347	−	6.13995i	0.364767	−	0.210598i
$851$	36.5846	−	21.1221i	1.25410	−	0.724057i
$852$	1.52221	+	0.878850i	0.0521501	+	0.0301089i
$853$			43.7939i			1.49947i	0.661736	+	0.749737i	$0.269820\pi$
$853$			43.7939i			1.49947i	−0.661736	+	0.749737i	$0.730180\pi$
$854$		0			0
$855$	34.8033			1.19025
$856$	28.1683	+	16.2630i	0.962774	+	0.555858i
$857$	7.42605	+	12.8623i	0.253669	+	0.439368i	0.964533	−	0.263962i	$-0.0850292\pi$
$857$	7.42605	+	12.8623i	0.253669	+	0.439368i	−0.710864	+	0.703329i	$0.751696\pi$
$858$	2.55070	+	7.18763i	0.0870794	+	0.245381i
$859$	−22.1784	+	38.4141i	−0.756717	+	1.31067i	0.187799	+	0.982208i	$0.439865\pi$
$859$	−22.1784	+	38.4141i	−0.756717	+	1.31067i	−0.944516	+	0.328465i	$0.893469\pi$
$860$		−	2.79780i		−	0.0954040i
$861$		0			0
$862$	19.3359			0.658584
$863$	22.3825	+	12.9226i	0.761910	+	0.439889i	0.829981	−	0.557792i	$-0.188351\pi$
$863$	22.3825	+	12.9226i	0.761910	+	0.439889i	−0.0680712	+	0.997680i	$0.521685\pi$
$864$	9.86006	−	5.69271i	0.335446	−	0.193670i
$865$	14.9441	−	8.62799i	0.508115	−	0.293360i
$866$	−45.3470	−	26.1811i	−1.54095	−	0.889670i
$867$	5.85090			0.198707
$868$		0			0
$869$		−	5.19956i		−	0.176383i
$870$	7.29546	−	12.6361i	0.247339	−	0.428404i
$871$	−54.0596	+	19.1843i	−1.83174	+	0.650035i
$872$	−10.4415	−	18.0852i	−0.353593	−	0.612442i
$873$	33.4937	+	19.3376i	1.13359	+	0.654479i
$874$	52.1719			1.76474
$875$		0			0
$876$			2.09176i			0.0706740i
$877$	−1.18892	−	0.686420i	−0.0401468	−	0.0231788i	0.479792	−	0.877382i	$-0.340712\pi$
$877$	−1.18892	−	0.686420i	−0.0401468	−	0.0231788i	−0.519939	+	0.854203i	$0.674045\pi$
$878$	−13.9291	+	8.04200i	−0.470086	+	0.271404i
$879$	5.51157	−	3.18211i	0.185901	−	0.107330i
$880$	−18.2972	+	31.6917i	−0.616798	+	1.06833i
$881$	−16.2514			−0.547524			−0.273762	−	0.961797i	$-0.588268\pi$
$881$	−16.2514			−0.547524			−0.273762	+	0.961797i	$0.588268\pi$
$882$		0			0
$883$	0.619110			0.0208347			0.0104174	−	0.999946i	$-0.496684\pi$
$883$	0.619110			0.0208347			0.0104174	+	0.999946i	$0.496684\pi$
$884$	3.94441	−	4.62459i	0.132665	−	0.155542i
$885$	6.83577	+	11.8399i	0.229782	+	0.397994i
$886$	−30.2749	+	17.4792i	−1.01710	+	0.587226i
$887$	−15.9690	+	27.6591i	−0.536185	+	0.928700i	0.462920	+	0.886400i	$0.346802\pi$
$887$	−15.9690	+	27.6591i	−0.536185	+	0.928700i	−0.999105	+	0.0423000i	$0.986531\pi$
$888$	−6.08034			−0.204043
$889$		0			0
$890$		−	62.1288i		−	2.08256i
$891$	−15.3246	−	8.84768i	−0.513395	−	0.296409i
$892$	−4.98483	+	2.87799i	−0.166905	+	0.0963624i
$893$	2.97167	+	5.14709i	0.0994432	+	0.172241i
$894$	−9.38279	+	16.2515i	−0.313807	+	0.543531i
$895$			22.2764i			0.744618i
$896$		0			0
$897$	−12.5820	−	2.32322i	−0.420102	−	0.0775700i
$898$	−11.1507	+	19.3136i	−0.372105	+	0.644504i
$899$	36.7765	−	21.2329i	1.22656	−	0.708157i
$900$	3.32565	+	5.76019i	0.110855	+	0.192006i
$901$	9.43082	−	16.3347i	0.314186	−	0.544187i
$902$			17.0092i			0.566345i
$903$		0			0
$904$			8.23621i			0.273932i
$905$	49.7769	+	28.7387i	1.65464	+	0.955308i
$906$	4.59738	+	7.96289i	0.152738	+	0.264549i
$907$	10.3518	+	17.9299i	0.343728	+	0.595354i	0.985122	−	0.171858i	$-0.0549770\pi$
$907$	10.3518	+	17.9299i	0.343728	+	0.595354i	−0.641394	+	0.767211i	$0.721644\pi$
$908$	−16.3859	−	9.46040i	−0.543785	−	0.313954i
$909$	48.0699			1.59438
$910$		0			0
$911$	39.4143			1.30585			0.652926	−	0.757421i	$-0.273541\pi$
$911$	39.4143			1.30585			0.652926	+	0.757421i	$0.273541\pi$
$912$	−9.29472	−	5.36631i	−0.307779	−	0.177696i
$913$	−4.02435	−	6.97037i	−0.133186	−	0.230686i
$914$	−7.74436	−	13.4136i	−0.256161	−	0.443683i
$915$	−11.7686	−	6.79463i	−0.389059	−	0.224623i
$916$			9.55449i			0.315689i
$917$		0			0
$918$		−	10.7326i		−	0.354229i
$919$	−7.10925	+	12.3136i	−0.234512	+	0.406187i	−0.959131	−	0.282963i	$-0.908683\pi$
$919$	−7.10925	+	12.3136i	−0.234512	+	0.406187i	0.724618	+	0.689150i	$0.242016\pi$
$920$	−21.4765	−	37.1985i	−0.708061	−	1.22640i
$921$	−8.95972	+	5.17290i	−0.295233	+	0.170453i
$922$	6.73886	−	11.6721i	0.221933	−	0.384399i
$923$	3.13852	−	16.9975i	0.103306	−	0.559480i
$924$		0			0
$925$		−	19.2049i		−	0.631454i
$926$	20.1160	−	34.8420i	0.661053	−	1.14498i
$927$	−9.03223	−	15.6443i	−0.296657	−	0.513826i
$928$	21.4458	−	12.3817i	0.703993	−	0.406451i
$929$	−24.8963	−	14.3739i	−0.816822	−	0.471593i	0.0324972	−	0.999472i	$-0.489654\pi$
$929$	−24.8963	−	14.3739i	−0.816822	−	0.471593i	−0.849319	+	0.527879i	$0.822987\pi$
$930$		−	16.1412i		−	0.529291i
$931$		0			0
$932$	6.03168			0.197574
$933$	4.24176	−	7.34694i	0.138869	−	0.240528i
$934$	−47.0167	+	27.1451i	−1.53843	+	0.888215i
$935$	8.44178	+	14.6216i	0.276076	+	0.478177i
$936$	−15.7557	−	13.4383i	−0.514990	−	0.439246i
$937$	19.8495			0.648456			0.324228	−	0.945979i	$-0.394895\pi$
$937$	19.8495			0.648456			0.324228	+	0.945979i	$0.394895\pi$
$938$		0			0
$939$	−1.26351			−0.0412330
$940$	−1.43916	+	2.49270i	−0.0469402	+	0.0813028i
$941$	−39.1720	+	22.6160i	−1.27697	+	0.737260i	−0.976291	−	0.216464i	$-0.930547\pi$
$941$	−39.1720	+	22.6160i	−1.27697	+	0.737260i	−0.300682	+	0.953725i	$0.597214\pi$
$942$	2.68818	−	1.55202i	0.0875857	−	0.0505676i
$943$	−24.7118	−	14.2673i	−0.804726	−	0.464609i
$944$			47.4083i			1.54301i
$945$		0			0
$946$	5.61649			0.182608
$947$	19.1474	+	11.0547i	0.622206	+	0.359231i	0.777727	−	0.628602i	$-0.216372\pi$
$947$	19.1474	+	11.0547i	0.622206	+	0.359231i	−0.155521	+	0.987833i	$0.549706\pi$
$948$	0.369263	+	0.639582i	0.0119931	+	0.0207727i
$949$	19.3855	−	6.87938i	0.629278	−	0.223314i
$950$	11.8591	−	20.5406i	0.384760	−	0.666424i
$951$		−	13.5073i		−	0.438004i
$952$		0			0
$953$	−34.3502			−1.11271			−0.556356	−	0.830944i	$-0.687801\pi$
$953$	−34.3502			−1.11271			−0.556356	+	0.830944i	$0.687801\pi$
$954$	32.7359	+	18.9001i	1.05986	+	0.611912i
$955$	50.9807	−	29.4337i	1.64970	−	0.952453i
$956$	−15.2755	+	8.81931i	−0.494045	+	0.285237i
$957$	6.85584	+	3.95822i	0.221618	+	0.127951i
$958$	4.10749			0.132707
$959$		0			0
$960$			4.62131i			0.149152i
$961$	7.98890	−	13.8372i	0.257706	−	0.446361i
$962$	−11.7629	−	33.1468i	−0.379252	−	1.06870i
$963$	21.4918	+	37.2249i	0.692563	+	1.19955i
$964$	0.185102	+	0.106869i	0.00596175	+	0.00344202i
$965$	−35.7309			−1.15022
$966$		0			0
$967$		−	23.8805i		−	0.767945i	−0.923344	−	0.383973i	$-0.874556\pi$
$967$		−	23.8805i		−	0.767945i	0.923344	−	0.383973i	$-0.125444\pi$
$968$	7.82921	+	4.52020i	0.251640	+	0.145285i
$969$	−4.28831	+	2.47585i	−0.137760	+	0.0795359i
$970$	57.8424	−	33.3953i	1.85721	−	1.07226i
$971$	12.9689	−	22.4627i	0.416190	−	0.720863i	−0.579362	−	0.815070i	$-0.696698\pi$
$971$	12.9689	−	22.4627i	0.416190	−	0.720863i	0.995553	+	0.0942072i	$0.0300316\pi$
$972$	8.84358			0.283658
$973$		0			0
$974$	37.9470			1.21590
$975$	−3.77467	+	4.42557i	−0.120886	+	0.141732i
$976$	−23.5615	−	40.8097i	−0.754184	−	1.30629i
$977$	39.2285	−	22.6486i	1.25503	−	0.724592i	0.282926	−	0.959142i	$-0.408695\pi$
$977$	39.2285	−	22.6486i	1.25503	−	0.724592i	0.972104	+	0.234550i	$0.0753616\pi$
$978$	−8.03586	+	13.9185i	−0.256958	+	0.445065i
$979$	33.7086			1.07733
$980$		0			0
$981$		−	27.5971i		−	0.881109i
$982$	−32.7942	−	18.9338i	−1.04651	−	0.604200i
$983$	1.75891	−	1.01551i	0.0561004	−	0.0323896i	−0.471687	−	0.881766i	$-0.656355\pi$
$983$	1.75891	−	1.01551i	0.0561004	−	0.0323896i	0.527788	+	0.849376i	$0.323022\pi$
$984$	2.05354	+	3.55683i	0.0654644	+	0.113388i
$985$	−27.2740	+	47.2400i	−0.869022	+	1.50519i
$986$		−	23.3437i		−	0.743413i
$987$		0			0
$988$	2.13169	−	11.5448i	0.0678182	−	0.367289i
$989$	−4.71112	+	8.15990i	−0.149805	+	0.259470i
$990$	−29.3027	+	16.9179i	−0.931302	+	0.537687i
$991$	13.4832	+	23.3536i	0.428309	+	0.741853i	0.996723	−	0.0808899i	$-0.0257762\pi$
$991$	13.4832	+	23.3536i	0.428309	+	0.741853i	−0.568414	+	0.822743i	$0.692443\pi$
$992$	13.6973	−	23.7244i	0.434890	−	0.753251i
$993$			4.79785i			0.152255i
$994$		0			0
$995$			36.8399i			1.16790i
$996$	0.990045	+	0.571603i	0.0313708	+	0.0181119i
$997$	3.32787	+	5.76404i	0.105395	+	0.182549i	0.913899	−	0.405941i	$-0.133056\pi$
$997$	3.32787	+	5.76404i	0.105395	+	0.182549i	−0.808505	+	0.588490i	$0.799723\pi$
$998$	7.02012	+	12.1592i	0.222218	+	0.384893i
$999$	−14.5363	−	8.39254i	−0.459908	−	0.265528i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.r.g.324.14		32
7.2	even	3		637.2.c.g.246.3	✓	16
7.3	odd	6	inner	637.2.r.g.116.3		32
7.4	even	3	inner	637.2.r.g.116.4		32
7.5	odd	6		637.2.c.g.246.4	yes	16
7.6	odd	2	inner	637.2.r.g.324.13		32
13.12	even	2	inner	637.2.r.g.324.4		32
91.5	even	12		8281.2.a.cs.1.4		16
91.12	odd	6		637.2.c.g.246.14	yes	16
91.25	even	6	inner	637.2.r.g.116.14		32
91.38	odd	6	inner	637.2.r.g.116.13		32
91.44	odd	12		8281.2.a.cs.1.3		16
91.47	even	12		8281.2.a.cs.1.14		16
91.51	even	6		637.2.c.g.246.13	yes	16
91.86	odd	12		8281.2.a.cs.1.13		16
91.90	odd	2	inner	637.2.r.g.324.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.c.g.246.3	✓	16	7.2	even	3
637.2.c.g.246.4	yes	16	7.5	odd	6
637.2.c.g.246.13	yes	16	91.51	even	6
637.2.c.g.246.14	yes	16	91.12	odd	6
637.2.r.g.116.3		32	7.3	odd	6	inner
637.2.r.g.116.4		32	7.4	even	3	inner
637.2.r.g.116.13		32	91.38	odd	6	inner
637.2.r.g.116.14		32	91.25	even	6	inner
637.2.r.g.324.3		32	91.90	odd	2	inner
637.2.r.g.324.4		32	13.12	even	2	inner
637.2.r.g.324.13		32	7.6	odd	2	inner
637.2.r.g.324.14		32	1.1	even	1	trivial
8281.2.a.cs.1.3		16	91.44	odd	12
8281.2.a.cs.1.4		16	91.5	even	12
8281.2.a.cs.1.13		16	91.86	odd	12
8281.2.a.cs.1.14		16	91.47	even	12

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.r (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.43372 + 0.827759i) q^{2} +(0.247488 + 0.428663i) q^{3} +(0.370370 + 0.641500i) q^{4} +(-2.48886 - 1.43695i) q^{5} +0.819443i q^{6} -2.08473i q^{8} +(1.37750 - 2.38590i) q^{9} +(-2.37889 - 4.12036i) q^{10} +(2.23554 - 1.29069i) q^{11} +(-0.183325 + 0.317527i) q^{12} +(3.54562 + 0.654682i) q^{13} -1.42251i q^{15} +(2.46639 - 4.27192i) q^{16} +(-1.13792 - 1.97093i) q^{17} +(3.94990 - 2.28047i) q^{18} +(-3.80679 - 2.19785i) q^{19} -2.12881i q^{20} +4.27352 q^{22} +(-3.58463 + 6.20876i) q^{23} +(0.893645 - 0.515946i) q^{24} +(1.62963 + 2.82260i) q^{25} +(4.54150 + 3.87355i) q^{26} +2.84859 q^{27} +6.19574 q^{29} +(1.17750 - 2.03948i) q^{30} +(5.93577 - 3.42702i) q^{31} +(3.46138 - 1.99843i) q^{32} +(1.10654 + 0.638861i) q^{33} -3.76769i q^{34} +2.04074 q^{36} +(-5.10298 - 2.94621i) q^{37} +(-3.63859 - 6.30221i) q^{38} +(0.596861 + 1.68190i) q^{39} +(-2.99564 + 5.18860i) q^{40} +3.98014i q^{41} +1.31425 q^{43} +(1.65595 + 0.956065i) q^{44} +(-6.85682 + 3.95878i) q^{45} +(-10.2787 + 5.93442i) q^{46} +(-1.17094 - 0.676040i) q^{47} +2.44161 q^{48} +5.39576i q^{50} +(0.563244 - 0.975567i) q^{51} +(0.893211 + 2.51699i) q^{52} +(4.14389 + 7.17742i) q^{53} +(4.08408 + 2.35795i) q^{54} -7.41860 q^{55} -2.17577i q^{57} +(8.88296 + 5.12858i) q^{58} +(-8.32324 + 4.80543i) q^{59} +(0.912540 - 0.526855i) q^{60} +(4.77650 - 8.27315i) q^{61} +11.3470 q^{62} -3.24870 q^{64} +(-7.88381 - 6.72427i) q^{65} +(1.05765 + 1.83190i) q^{66} +(-13.7781 + 7.95477i) q^{67} +(0.842903 - 1.45995i) q^{68} -3.54862 q^{69} -4.79396i q^{71} +(-4.97395 - 2.87171i) q^{72} +(4.94074 - 2.85253i) q^{73} +(-4.87750 - 8.44808i) q^{74} +(-0.806629 + 1.39712i) q^{75} -3.25607i q^{76} +(-0.536475 + 2.90543i) q^{78} +(1.00713 - 1.74440i) q^{79} +(-12.2770 + 7.08815i) q^{80} +(-3.42750 - 5.93661i) q^{81} +(-3.29460 + 5.70641i) q^{82} -3.11798i q^{83} +6.54052i q^{85} +(1.88427 + 1.08789i) q^{86} +(1.53337 + 2.65588i) q^{87} +(-2.69074 - 4.66049i) q^{88} +(11.3089 + 6.52918i) q^{89} -13.1077 q^{90} -5.31056 q^{92} +(2.93807 + 1.69629i) q^{93} +(-1.11920 - 1.93850i) q^{94} +(6.31639 + 10.9403i) q^{95} +(1.71330 + 0.989176i) q^{96} +14.0382i q^{97} -7.11169i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 20 q^{4} - 16 q^{9} - 28 q^{16} - 16 q^{22} + 36 q^{23} + 44 q^{25} + 72 q^{29} + 104 q^{36} - 32 q^{39} - 72 q^{43} + 72 q^{51} - 12 q^{53} - 328 q^{64} + 24 q^{65} - 96 q^{74} + 48 q^{78} - 36 q^{79}+ \cdots + 84 q^{95}+O(q^{100}) \) 32 * q + 20 * q^4 - 16 * q^9 - 28 * q^16 - 16 * q^22 + 36 * q^23 + 44 * q^25 + 72 * q^29 + 104 * q^36 - 32 * q^39 - 72 * q^43 + 72 * q^51 - 12 * q^53 - 328 * q^64 + 24 * q^65 - 96 * q^74 + 48 * q^78 - 36 * q^79 - 16 * q^81 - 136 * q^88 + 48 * q^92 + 84 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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