LMFDB - Embedded newform 637.2.r.g.116.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(116,637)]

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

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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			116.3
Character	$\chi$	$=$	637.116
Dual form			637.2.r.g.324.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.43372 + 0.827759i) q^{2} +(-0.247488 + 0.428663i) q^{3} +(0.370370 - 0.641500i) q^{4} +(-2.48886 + 1.43695i) q^{5} -0.819443i q^{6} -2.08473i q^{8} +(1.37750 + 2.38590i) q^{9} +O(q^{10})$	\(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} +(5.62534 - 1.99628i) 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} +(1.15814 - 1.35785i) 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} +(-1.73317 + 2.03204i) 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} +(9.76530 - 3.46545i) 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}+O(q^{10}) $ 32 * q + 20 * q^4 - 16 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$248$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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	$-0.865695\pi$
$2$	−1.43372	+	0.827759i	−1.01379	+	0.585314i	−0.101493	+	0.994836i	$0.532362\pi$
$3$	−0.247488	+	0.428663i	−0.142888	+	0.247488i	−0.928583	−	0.371125i	$-0.878972\pi$
$3$	−0.247488	+	0.428663i	−0.142888	+	0.247488i	0.785695	+	0.618614i	$0.212305\pi$
$4$	0.370370	−	0.641500i	0.185185	−	0.320750i
$5$	−2.48886	+	1.43695i	−1.11305	+	0.642622i	−0.939619	−	0.342223i	$-0.888820\pi$
$5$	−2.48886	+	1.43695i	−1.11305	+	0.642622i	−0.173435	+	0.984845i	$0.555487\pi$
$6$		−	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	$-0.460567\pi$
$11$	−2.23554	−	1.29069i	−0.674040	−	0.389157i	−0.797606	+	0.603179i	$0.793900\pi$
$12$	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	$-0.744329\pi$
$17$	1.13792	−	1.97093i	0.275986	−	0.478022i	0.970383	+	0.241570i	$0.0776623\pi$
$18$	−3.94990	−	2.28047i	−0.931000	−	0.537513i
$19$	−3.80679	+	2.19785i	−0.873338	+	0.504222i	−0.868456	−	0.495766i	$-0.834887\pi$
$19$	−3.80679	+	2.19785i	−0.873338	+	0.504222i	−0.00488206	+	0.999988i	$0.501554\pi$
$20$			2.12881i			0.476016i
$21$		0			0
$22$	4.27352			0.911117
$23$	−3.58463	−	6.20876i	−0.747447	−	1.29462i	−0.949043	−	0.315148i	$-0.897946\pi$
$23$	−3.58463	−	6.20876i	−0.747447	−	1.29462i	0.201595	−	0.979469i	$-0.435387\pi$
$24$	0.893645	+	0.515946i	0.182414	+	0.105317i
$25$	1.62963	−	2.82260i	0.325926	−	0.564520i
$26$	5.62534	−	1.99628i	1.10322	−	0.391504i
$27$	−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	0.927112	−	0.374784i	$-0.122283\pi$
$31$	5.93577	+	3.42702i	1.06610	+	0.615511i	0.138983	+	0.990295i	$0.455617\pi$
$32$	−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	$-0.505722\pi$
$37$	5.10298	−	2.94621i	0.838925	−	0.484353i	0.856899	+	0.515485i	$0.172388\pi$
$38$	3.63859	−	6.30221i	0.590256	−	1.02235i
$39$	1.15814	−	1.35785i	0.185450	−	0.217429i
$40$	2.99564	+	5.18860i	0.473653	+	0.820390i
$41$		−	3.98014i		−	0.621594i	−0.950476	−	0.310797i	$-0.899404\pi$
$41$		−	3.98014i		−	0.621594i	0.950476	−	0.310797i	$-0.100596\pi$
$42$		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	−0.582962	−	0.812499i	$-0.698106\pi$
$47$	−1.17094	+	0.676040i	−0.170799	+	0.0986106i	0.412164	+	0.911110i	$0.364773\pi$
$48$	−2.44161			−0.352417
$49$		0			0
$50$			5.39576i			0.763076i
$51$	0.563244	+	0.975567i	0.0788699	+	0.136607i
$52$	−1.73317	+	2.03204i	−0.240347	+	0.281793i
$53$	4.14389	−	7.17742i	0.569207	−	0.985895i	−0.427438	−	0.904045i	$-0.640584\pi$
$53$	4.14389	−	7.17742i	0.569207	−	0.985895i	0.996645	−	0.0818503i	$-0.0260830\pi$
$54$	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	−0.151730	−	0.988422i	$-0.548485\pi$
$59$	−8.32324	−	4.80543i	−1.08359	−	0.625613i	−0.931864	+	0.362809i	$0.881818\pi$
$60$	−0.912540	−	0.526855i	−0.117808	−	0.0680167i
$61$	−4.77650	−	8.27315i	−0.611569	−	1.05927i	−0.990976	−	0.134038i	$-0.957205\pi$
$61$	−4.77650	−	8.27315i	−0.611569	−	1.05927i	0.379407	−	0.925230i	$-0.376128\pi$
$62$	−11.3470			−1.44107
$63$		0			0
$64$	−3.24870			−0.406087
$65$	9.76530	−	3.46545i	1.21124	−	0.429836i
$66$	−1.05765	+	1.83190i	−0.130187	+	0.225491i
$67$	13.7781	+	7.95477i	1.68326	+	0.971830i	0.959471	+	0.281806i	$0.0909334\pi$
$67$	13.7781	+	7.95477i	1.68326	+	0.971830i	0.723787	+	0.690024i	$0.242400\pi$
$68$	−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	0.760445	−	0.649402i	$-0.224981\pi$
$73$	4.94074	+	2.85253i	0.578269	+	0.333864i	−0.182176	+	0.983266i	$0.558314\pi$
$74$	−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	0.917103	−	0.398650i	$-0.130521\pi$
$79$	1.00713	+	1.74440i	0.113311	+	0.196260i	−0.803792	+	0.594910i	$0.797188\pi$
$80$	−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	$0.0547391\pi$
$83$			3.11798i			0.342243i	−0.985250	+	0.171122i	$0.945261\pi$
$84$		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	0.238464	−	0.971151i	$-0.423356\pi$
$89$	11.3089	−	6.52918i	1.19874	−	0.692092i	0.960274	+	0.279060i	$0.0900227\pi$
$90$	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	$-0.747480\pi$
$97$		−	14.0382i		−	1.42536i	0.701488	−	0.712682i	$-0.252520\pi$
$98$		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	−0.00413039	+	0.999991i	$0.501315\pi$
$101$	−8.72413	+	15.1106i	−0.868083	+	1.50356i	−0.863953	+	0.503573i	$0.832019\pi$
$102$	−1.61507	−	0.932461i	−0.159916	−	0.0923274i
$103$	−3.27849	−	5.67851i	−0.323039	−	0.559520i	0.658074	−	0.752953i	$-0.271371\pi$
$103$	−3.27849	−	5.67851i	−0.323039	−	0.559520i	−0.981114	+	0.193433i	$0.938038\pi$
$104$	−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	−0.945794	−	0.324766i	$-0.894715\pi$
$107$	−7.80102	−	13.5118i	−0.754153	−	1.30623i	0.191642	−	0.981465i	$-0.438619\pi$
$108$	−1.05503	+	1.82737i	−0.101521	+	0.175839i
$109$	−8.67508	−	5.00856i	−0.830922	−	0.479733i	0.0232461	−	0.999730i	$-0.492600\pi$
$109$	−8.67508	−	5.00856i	−0.830922	−	0.479733i	−0.854168	+	0.519997i	$0.825933\pi$
$110$	−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
$117$	−3.32208	−	9.36130i	−0.307126	−	0.865453i
$118$	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
$130$	−11.1322	+	13.0518i	−0.976355	+	1.14472i
$131$	−1.06773	−	1.84936i	−0.0932878	−	0.161579i	0.815605	−	0.578609i	$-0.196404\pi$
$131$	−1.06773	−	1.84936i	−0.0932878	−	0.161579i	−0.908893	+	0.417030i	$0.863071\pi$
$132$		−	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	$-0.339170\pi$
$137$	−0.371707	−	0.214605i	−0.0317570	−	0.0183349i	−0.515794	+	0.856712i	$0.672503\pi$
$138$	−5.08773	+	2.93740i	−0.433096	+	0.250048i
$139$	−19.4858			−1.65276			−0.826381	−	0.563112i	$-0.809604\pi$
$139$	−19.4858			−1.65276			−0.826381	+	0.563112i	$0.809604\pi$
$140$		0			0
$141$		−	0.669248i		−	0.0563609i
$142$	3.96824	+	6.87319i	0.333007	+	0.576786i
$143$	7.08137	+	6.03985i	0.592174	+	0.505078i
$144$	−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	−0.639097	+	0.769126i	$0.720692\pi$
$149$	−19.8323	+	11.4502i	−1.62473	+	0.938037i	−0.985631	+	0.168911i	$0.945975\pi$
$150$	−2.31296	−	1.33539i	−0.188853	−	0.109034i
$151$	−9.71744	−	5.61037i	−0.790794	−	0.456565i	0.0494478	−	0.998777i	$-0.484254\pi$
$151$	−9.71744	−	5.61037i	−0.790794	−	0.456565i	−0.840242	+	0.542211i	$0.817587\pi$
$152$	4.58192	+	7.93613i	0.371643	+	0.643705i
$153$	6.26993			0.506894
$154$		0			0
$155$	−19.6978			−1.58216
$156$	−0.442119	−	1.24585i	−0.0353978	−	0.0997478i
$157$	1.89400	−	3.28050i	0.151157	−	0.261812i	−0.780496	−	0.625161i	$-0.785033\pi$
$157$	1.89400	−	3.28050i	0.151157	−	0.261812i	0.931653	+	0.363349i	$0.118367\pi$
$158$	−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	$-0.945466\pi$
$163$	−16.9853	+	9.80649i	−1.33039	+	0.768103i	−0.345034	+	0.938590i	$0.612133\pi$
$164$	−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	$0.130371\pi$
$167$			10.2922i			0.796435i	−0.917291	+	0.398217i	$0.869629\pi$
$168$		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	$-0.0933654\pi$
$173$	3.00220	+	5.19995i	0.228253	+	0.395345i	−0.729038	+	0.684474i	$0.760032\pi$
$174$		−	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	−0.973733	−	0.227692i	$-0.926882\pi$
$179$	−3.87565	+	6.71282i	−0.289680	+	0.501740i	0.684054	+	0.729432i	$0.260215\pi$
$180$	−5.07912	+	2.93243i	−0.378575	+	0.218570i
$181$	19.9999			1.48658			0.743289	−	0.668970i	$-0.233265\pi$
$181$	19.9999			1.48658			0.743289	+	0.668970i	$0.233265\pi$
$182$		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	−0.952010	−	0.306068i	$-0.900986\pi$
$191$	−10.2418	−	17.7392i	−0.741068	−	1.28357i	0.210942	−	0.977499i	$-0.432347\pi$
$192$	0.804015	−	1.39260i	0.0580248	−	0.100502i
$193$	−10.7672	−	6.21647i	−0.775043	−	0.447471i	0.0596279	−	0.998221i	$-0.481009\pi$
$193$	−10.7672	−	6.21647i	−0.775043	−	0.447471i	−0.834671	+	0.550750i	$0.814342\pi$
$194$	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	$-0.683205\pi$
$199$	6.40940	−	11.1014i	0.454350	−	0.786958i	0.998651	+	0.0519325i	$0.0165381\pi$
$200$	−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
$208$	−5.94813	−	16.7613i	−0.412429	−	1.16219i
$209$	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
$221$	−5.32496	+	6.24320i	−0.358196	+	0.419963i
$222$	−2.41425	−	4.18160i	−0.162034	−	0.280651i
$223$		−	7.77059i		−	0.520357i	−0.965560	−	0.260179i	$-0.916219\pi$
$223$		−	7.77059i		−	0.520357i	0.965560	−	0.260179i	$-0.0837815\pi$
$224$		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	−0.468855	−	0.883275i	$-0.655333\pi$
$227$	−22.1210	−	12.7716i	−1.46822	−	0.847678i	−0.999366	+	0.0355975i	$0.988667\pi$
$228$	−1.39576	−	0.805841i	−0.0924363	−	0.0533681i
$229$	11.1705	−	6.44929i	0.738167	−	0.426181i	−0.0832356	−	0.996530i	$-0.526525\pi$
$229$	11.1705	−	6.44929i	0.738167	−	0.426181i	0.821402	+	0.570349i	$0.193192\pi$
$230$	−34.1098			−2.24913
$231$		0			0
$232$		−	12.9164i		−	0.848005i
$233$	4.07139	+	7.05186i	0.266726	+	0.461983i	0.968014	−	0.250895i	$-0.0807249\pi$
$233$	4.07139	+	7.05186i	0.266726	+	0.461983i	−0.701289	+	0.712877i	$0.747392\pi$
$234$	12.5118	+	10.6716i	0.817924	+	0.697625i
$235$	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	0.508027	−	0.861341i	$-0.330375\pi$
$241$	0.249889	+	0.144273i	0.0160967	+	0.00929346i	−0.491930	+	0.870635i	$0.663708\pi$
$242$	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
$247$	14.9363	−	5.30050i	0.950375	−	0.337263i
$248$	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	$-0.422710\pi$
$251$	7.61843			0.480871			0.240435	+	0.970665i	$0.422710\pi$
$252$		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	$-0.285099\pi$
$257$	−5.82801	−	10.0944i	−0.363541	−	0.629672i	−0.988541	+	0.150953i	$0.951766\pi$
$258$		−	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	−0.577873	−	0.816127i	$-0.696117\pi$
$263$	6.77638	−	11.7370i	0.417850	−	0.723737i	0.995723	+	0.0923895i	$0.0294505\pi$
$264$	−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	−0.455034	−	0.890474i	$-0.650373\pi$
$269$	8.91662	−	15.4440i	0.543656	−	0.941640i	0.998690	−	0.0511657i	$-0.0162937\pi$
$270$	−6.77649	+	11.7372i	−0.412404	+	0.714304i
$271$	26.3049	−	15.1872i	1.59791	−	0.922555i	0.606023	−	0.795447i	$-0.292764\pi$
$271$	26.3049	−	15.1872i	1.59791	−	0.922555i	0.991889	−	0.127107i	$-0.0405693\pi$
$272$	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	−0.777011	−	0.629487i	$-0.783265\pi$
$277$	2.60712	−	4.51567i	0.156647	−	0.271320i	0.933657	+	0.358167i	$0.116598\pi$
$278$	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	$-0.967816\pi$
$283$	−6.89783	+	11.9474i	−0.410033	+	0.710198i	0.584860	+	0.811134i	$0.301150\pi$
$284$	−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	$0.122555\pi$
$293$			12.8576i			0.751149i	−0.926792	+	0.375574i	$0.877445\pi$
$294$		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
$299$	8.64496	+	24.3607i	0.499951	+	1.40881i
$300$	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	$-0.796574\pi$
$307$		−	20.9016i		−	1.19292i	0.802644	−	0.596458i	$-0.203426\pi$
$308$		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	$-0.671811\pi$
$311$	8.56961	−	14.8430i	0.485938	−	0.841669i	0.999869	+	0.0161620i	$0.00514476\pi$
$312$	−2.83074	−	2.41440i	−0.160259	−	0.136688i
$313$	1.27633	+	2.21067i	0.0721424	+	0.124954i	0.899840	−	0.436220i	$-0.143683\pi$
$313$	1.27633	+	2.21067i	0.0721424	+	0.124954i	−0.827698	+	0.561174i	$0.810350\pi$
$314$			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	$-0.388740\pi$
$317$	23.6328	−	13.6444i	1.32735	−	0.766345i	0.984889	+	0.173188i	$0.0554068\pi$
$318$	−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
$325$	−7.62595	+	8.94097i	−0.423012	+	0.495956i
$326$	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	$-0.752497\pi$
$331$	−8.39444	+	4.84653i	−0.461400	+	0.266390i	0.251233	+	0.967927i	$0.419164\pi$
$332$	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	$0.444988\pi$
$338$	−21.2522	+	3.39525i	−1.15597	+	0.184677i
$339$	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	0.149375	+	0.988781i	$0.452274\pi$
$347$	−14.5600	+	25.2187i	−0.781622	+	1.35381i	−0.930997	+	0.365028i	$0.881059\pi$
$348$	1.13583	+	1.96732i	0.0608870	+	0.105459i
$349$			20.3297i			1.08822i	0.839013	+	0.544112i	$0.183133\pi$
$349$			20.3297i			1.08822i	−0.839013	+	0.544112i	$0.816867\pi$
$350$		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	0.135715	−	0.990748i	$-0.456667\pi$
$353$	−12.2958	−	7.09900i	−0.654441	−	0.377841i	−0.790155	+	0.612907i	$0.790000\pi$
$354$	−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	$-0.730098\pi$
$359$	−6.49661	+	3.75082i	−0.342878	+	0.197961i	0.318666	+	0.947867i	$0.396765\pi$
$360$	−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	−0.203507	−	0.979073i	$-0.565234\pi$
$367$	14.2942	−	24.7582i	0.746149	−	1.29237i	0.949656	−	0.313294i	$-0.101433\pi$
$368$	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	0.950080	−	0.312006i	$-0.101001\pi$
$373$	3.95602	+	6.85203i	0.204835	+	0.354784i	−0.745245	+	0.666791i	$0.767668\pi$
$374$	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	−0.151754	−	0.988418i	$-0.548492\pi$
$383$	12.2973	−	7.09987i	0.628364	−	0.362786i	0.780118	+	0.625632i	$0.215159\pi$
$384$			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	−0.939033	−	0.343828i	$-0.888276\pi$
$389$	−3.38749	+	5.86731i	−0.171753	+	0.297485i	0.767280	+	0.641312i	$0.221610\pi$
$390$	−2.83974	−	8.00211i	−0.143796	−	0.405202i
$391$	−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	−0.973185	−	0.230023i	$-0.926120\pi$
$397$	−25.1167	+	14.5011i	−1.26057	+	0.727792i	−0.287387	+	0.957815i	$0.592787\pi$
$398$			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	$-0.851401\pi$
$401$	−19.0183	+	10.9802i	−0.949728	+	0.548326i	−0.0567318	+	0.998389i	$0.518068\pi$
$402$	6.51848	−	11.2903i	0.325112	−	0.563111i
$403$	−18.8023	−	16.0369i	−0.936612	−	0.798856i
$404$	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	0.583252	−	0.812291i	$-0.301780\pi$
$409$	3.46661	+	2.00145i	0.171413	+	0.0989653i	−0.411839	+	0.911257i	$0.635113\pi$
$410$	−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
$416$	10.9644	+	9.35176i	0.537573	+	0.458508i
$417$	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	$-0.486386\pi$
$419$	1.75047			0.0855162			0.0427581	+	0.999085i	$0.486386\pi$
$420$		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
$429$	−4.34162	+	1.54072i	−0.209615	+	0.0743869i
$430$	3.12647	−	5.41520i	0.150772	−	0.261144i
$431$	−10.1149	−	5.83984i	−0.487217	−	0.281295i	0.236202	−	0.971704i	$-0.424097\pi$
$431$	−10.1149	−	5.83984i	−0.487217	−	0.281295i	−0.723419	+	0.690409i	$0.757431\pi$
$432$	−7.02574	−	12.1689i	−0.338026	−	0.585479i
$433$	31.6289			1.51999			0.759994	−	0.649930i	$-0.225202\pi$
$433$	31.6289			1.51999			0.759994	+	0.649930i	$0.225202\pi$
$434$		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	$-0.0921904\pi$
$439$	4.85769	+	8.41377i	0.231845	+	0.401567i	−0.726506	+	0.687160i	$0.758857\pi$
$440$		−	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	−0.999998	−	0.00188659i	$-0.999399\pi$
$443$	−10.5582	−	18.2873i	−0.501633	−	0.868854i	0.498365	−	0.866967i	$-0.333934\pi$
$444$	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	$-0.596445\pi$
$457$	8.10237	−	4.67791i	0.379013	−	0.218823i	0.677389	+	0.735625i	$0.263112\pi$
$458$	−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	$0.0607140\pi$
$461$			8.14109i			0.379168i	−0.981864	+	0.189584i	$0.939286\pi$
$462$		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	0.943488	+	0.331408i	$0.107524\pi$
$467$	16.3968	+	28.4000i	0.758751	+	1.31420i	−0.184736	+	0.982788i	$0.559143\pi$
$468$	−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	0.548284	−	0.836292i	$-0.315281\pi$
$479$	2.14868	+	1.24054i	0.0981759	+	0.0566819i	−0.450108	+	0.892974i	$0.648615\pi$
$480$	−2.84279	+	4.92385i	−0.129755	+	0.224742i
$481$	−20.0220	+	7.10529i	−0.912926	+	0.323973i
$482$	−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	$-0.507155\pi$
$487$	−19.8506	−	11.4608i	−0.899519	−	0.519337i	−0.877044	+	0.480410i	$0.840488\pi$
$488$	−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
$494$	−17.0270	+	19.9631i	−0.766080	+	0.898183i
$495$	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	$-0.727460\pi$
$499$	−7.34465	+	4.24044i	−0.328792	+	0.189828i	0.326513	+	0.945193i	$0.394126\pi$
$500$	−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	$-0.566978\pi$
$503$	−9.36890			−0.417739			−0.208869	+	0.977944i	$0.566978\pi$
$504$		0			0
$505$		−	50.1444i		−	2.23140i
$506$	−15.3190	−	26.5333i	−0.681012	−	1.17955i
$507$	−4.99527	+	4.05619i	−0.221848	+	0.180142i
$508$	−0.879083	+	1.52262i	−0.0390030	+	0.0675552i
$509$	18.6544	−	10.7701i	0.826840	−	0.477376i	−0.0259293	−	0.999664i	$-0.508254\pi$
$509$	18.6544	−	10.7701i	0.826840	−	0.477376i	0.852770	+	0.522287i	$0.174921\pi$
$510$	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
$520$	−7.22451	−	20.3580i	−0.316816	−	0.892757i
$521$	−7.87350	+	13.6373i	−0.344944	+	0.597461i	−0.985344	−	0.170581i	$-0.945436\pi$
$521$	−7.87350	+	13.6373i	−0.344944	+	0.597461i	0.640399	+	0.768042i	$0.278769\pi$
$522$	−24.4725	−	14.1292i	−1.07113	−	0.618420i
$523$	−8.97018	−	15.5368i	−0.392238	−	0.679377i	0.600506	−	0.799620i	$-0.294966\pi$
$523$	−8.97018	−	15.5368i	−0.392238	−	0.679377i	−0.992744	+	0.120243i	$0.961633\pi$
$524$	−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	$-0.602209\pi$
$541$	8.10237	−	4.67791i	0.348348	−	0.201119i	0.663958	+	0.747770i	$0.268876\pi$
$542$	−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	$-0.257402\pi$
$557$	9.65899	+	5.57662i	0.409265	+	0.236289i	−0.281209	+	0.959647i	$0.590735\pi$
$558$	−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	$-0.965757\pi$
$563$	−9.58889	+	16.6085i	−0.404124	+	0.699963i	0.590095	+	0.807334i	$0.299090\pi$
$564$	−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	0.971948	−	0.235197i	$-0.0755734\pi$
$569$	6.73361	+	11.6630i	0.282288	+	0.488937i	−0.689660	+	0.724133i	$0.742240\pi$
$570$	−8.96497	−	5.17593i	−0.375501	−	0.216796i
$571$	12.5804	−	21.7899i	0.526473	−	0.911877i	−0.473052	−	0.881035i	$-0.656848\pi$
$571$	12.5804	−	21.7899i	0.526473	−	0.911877i	0.999524	−	0.0308427i	$-0.00981909\pi$
$572$	6.49729	−	2.30572i	0.271665	−	0.0964068i
$573$	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	0.0561126	−	0.998424i	$-0.482129\pi$
$577$	−18.7481	−	10.8242i	−0.780492	−	0.450617i	−0.836605	+	0.547807i	$0.815463\pi$
$578$	−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
$585$	21.7199	+	18.5254i	0.898007	+	0.765929i
$586$	−10.6430	−	18.4342i	−0.439658	−	0.761510i
$587$		−	34.5576i		−	1.42634i	−0.700989	−	0.713172i	$-0.747258\pi$
$587$		−	34.5576i		−	1.42634i	0.700989	−	0.713172i	$-0.252742\pi$
$588$		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	−0.522385	−	0.852710i	$-0.674957\pi$
$593$	−1.09846	+	0.634194i	−0.0451082	+	0.0260432i	0.477276	+	0.878753i	$0.341624\pi$
$594$	−12.1735			−0.499485
$595$		0			0
$596$			16.9632i			0.694842i
$597$	3.17251	+	5.49494i	0.129842	+	0.224893i
$598$	−32.5592	−	27.7705i	−1.33145	−	1.13562i
$599$	−8.75714	+	15.1678i	−0.357807	+	0.619740i	−0.987594	−	0.157028i	$-0.949809\pi$
$599$	−8.75714	+	15.1678i	−0.357807	+	0.619740i	0.629787	+	0.776768i	$0.283142\pi$
$600$	2.91262	−	1.68160i	0.118907	−	0.0686511i
$601$	−9.02164			−0.368000			−0.184000	−	0.982926i	$-0.558905\pi$
$601$	−9.02164			−0.368000			−0.184000	+	0.982926i	$0.558905\pi$
$602$		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	$-0.0625672\pi$
$607$	7.91450	+	13.7083i	0.321239	+	0.556403i	−0.659505	+	0.751701i	$0.729234\pi$
$608$	17.5690			0.712517
$609$		0			0
$610$	−45.4511			−1.84026
$611$	4.59428	−	1.63039i	0.185865	−	0.0659584i
$612$	2.32219	−	4.02216i	0.0938692	−	0.162586i
$613$	15.1853	+	8.76721i	0.613327	+	0.354104i	0.774266	−	0.632860i	$-0.218119\pi$
$613$	15.1853	+	8.76721i	0.613327	+	0.354104i	−0.160940	+	0.986964i	$0.551452\pi$
$614$	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	−0.363027	−	0.931779i	$-0.618257\pi$
$619$	−33.6245	−	19.4131i	−1.35148	−	0.780280i	−0.988457	+	0.151499i	$0.951590\pi$
$620$	−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	−0.945862	−	0.324569i	$-0.894781\pi$
$641$	−4.85715	+	8.41282i	−0.191846	+	0.332287i	0.754016	+	0.656856i	$0.228114\pi$
$642$	−11.0721	+	6.39249i	−0.436982	+	0.252291i
$643$		−	0.458279i		−	0.0180728i	−0.999959	−	0.00903639i	$-0.997124\pi$
$643$		−	0.458279i		−	0.0180728i	0.999959	−	0.00903639i	$-0.00287641\pi$
$644$		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	$-0.872080\pi$
$647$	−3.08861	+	5.34963i	−0.121426	+	0.210316i	0.798904	+	0.601458i	$0.205413\pi$
$648$	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	−0.997790	−	0.0664508i	$-0.978832\pi$
$653$	−14.2193	−	24.6285i	−0.556443	−	0.963787i	0.441347	−	0.897337i	$-0.354501\pi$
$654$	−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	−0.283380	−	0.959008i	$-0.591456\pi$
$661$	−32.2812	−	18.6376i	−1.25560	−	0.724918i	−0.972215	+	0.234090i	$0.924789\pi$
$662$	8.02353	−	13.8972i	0.311843	−	0.540128i
$663$	−1.35836	−	3.82773i	−0.0527544	−	0.148657i
$664$	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
$676$	7.47548	−	6.07015i	0.287519	−	0.233467i
$677$	−9.10347	−	15.7677i	−0.349875	−	0.606001i	0.636352	−	0.771399i	$-0.280443\pi$
$677$	−9.10347	−	15.7677i	−0.349875	−	0.606001i	−0.986227	+	0.165398i	$0.947109\pi$
$678$			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	$-0.158150\pi$
$683$	23.6736	+	13.6680i	0.905847	+	0.522991i	0.0267542	+	0.999642i	$0.491483\pi$
$684$	−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
$689$	−19.3916	+	22.7355i	−0.738760	+	0.866152i
$690$	8.44178	−	14.6216i	0.321373	−	0.556634i
$691$	−7.27098	+	4.19790i	−0.276601	+	0.159696i	−0.631884	−	0.775063i	$-0.717718\pi$
$691$	−7.27098	+	4.19790i	−0.276601	+	0.159696i	0.355283	+	0.934759i	$0.384385\pi$
$692$	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	$0.326183\pi$
$702$	−16.0243	+	5.68660i	−0.604798	+	0.214627i
$703$	−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	$-0.483492\pi$
$709$	25.0991	−	14.4910i	0.942618	−	0.544221i	0.890780	+	0.454435i	$0.150159\pi$
$710$	−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	$-0.272803\pi$
$719$	−8.77612	−	15.2007i	−0.327294	−	0.566890i	−0.981974	+	0.189016i	$0.939470\pi$
$720$		−	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	$-0.634670\pi$
$727$	−22.1403			−0.821139			−0.410569	+	0.911829i	$0.634670\pi$
$728$		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	−0.662254	+	0.749279i	$0.730400\pi$
$733$	−44.4629	+	25.6707i	−1.64228	+	0.948169i	−0.980022	+	0.198889i	$0.936267\pi$
$734$			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	$-0.195726\pi$
$739$	19.7270	+	11.3894i	0.725668	+	0.418965i	−0.0911674	+	0.995836i	$0.529060\pi$
$740$	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	0.947728	+	0.319078i	$0.103373\pi$
$751$	20.5586	+	35.6085i	0.750194	+	1.29937i	−0.197534	+	0.980296i	$0.563293\pi$
$752$	−5.77597	−	3.33476i	−0.210628	−	0.121606i
$753$	−1.88547	+	3.26573i	−0.0687104	+	0.119010i
$754$	34.8532	−	12.3685i	1.26928	−	0.450433i
$755$	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	0.143672	−	0.989625i	$-0.454109\pi$
$761$	29.5876	−	17.0824i	1.07255	−	0.619236i	0.928877	+	0.370389i	$0.120776\pi$
$762$			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
$767$	26.3650	+	22.4873i	0.951985	+	0.811969i
$768$	−3.87076	−	6.70436i	−0.139674	−	0.241923i
$769$			52.9061i			1.90784i	0.300059	+	0.953921i	$0.402994\pi$
$769$			52.9061i			1.90784i	−0.300059	+	0.953921i	$0.597006\pi$
$770$		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	0.997131	−	0.0756940i	$-0.0241172\pi$
$773$	39.7621	+	22.9567i	1.43014	+	0.825694i	0.433013	+	0.901388i	$0.357451\pi$
$774$	−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
$780$	2.89059	+	2.46545i	0.103500	+	0.0882773i
$781$	−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	0.246917	−	0.969037i	$-0.420583\pi$
$787$	−13.1525	−	7.59358i	−0.468835	−	0.270682i	−0.715752	+	0.698355i	$0.753916\pi$
$788$	−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
$793$	11.5194	+	32.4605i	0.409065	+	1.15271i
$794$	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	$-0.406777\pi$
$797$	16.3006			0.577398			0.288699	+	0.957420i	$0.406777\pi$
$798$		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	−0.942755	−	0.333485i	$-0.891775\pi$
$809$	−5.19286	+	8.99430i	−0.182571	+	0.316223i	0.760184	+	0.649708i	$0.225109\pi$
$810$	16.3073	+	28.2451i	0.572981	+	0.992431i
$811$			10.9705i			0.385227i	0.981275	+	0.192614i	$0.0616964\pi$
$811$			10.9705i			0.385227i	−0.981275	+	0.192614i	$0.938304\pi$
$812$		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	$-0.418930\pi$
$821$	34.8423	−	20.1162i	1.21601	−	0.702061i	0.964061	+	0.265681i	$0.0855966\pi$
$822$	−0.175856	+	0.304592i	−0.00613370	+	0.0106239i
$823$	−1.63250	+	2.82757i	−0.0569053	+	0.0985628i	−0.893075	−	0.449908i	$-0.851457\pi$
$823$	−1.63250	+	2.82757i	−0.0569053	+	0.0985628i	0.836169	+	0.548471i	$0.184790\pi$
$824$	−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	0.471796	+	0.881708i	$0.343606\pi$
$829$	−15.1933	+	26.3155i	−0.527683	+	0.913974i	−0.999479	+	0.0322667i	$0.989727\pi$
$830$	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	$0.00835321\pi$
$839$			1.52007i			0.0524787i	−0.999656	+	0.0262394i	$0.991647\pi$
$840$		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
$845$	−36.8928	+	5.89397i	−1.26915	+	0.202759i
$846$	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	$-0.730180\pi$
$853$		−	43.7939i		−	1.49947i	0.661736	−	0.749737i	$-0.269820\pi$
$854$		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	$-0.914971\pi$
$857$	−7.42605	+	12.8623i	−0.253669	+	0.439368i	0.710864	+	0.703329i	$0.248304\pi$
$858$	4.94932	−	5.80278i	0.168967	−	0.198104i
$859$	22.1784	+	38.4141i	0.756717	+	1.31067i	0.944516	+	0.328465i	$0.106531\pi$
$859$	22.1784	+	38.4141i	0.756717	+	1.31067i	−0.187799	+	0.982208i	$0.560135\pi$
$860$			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	$-0.811649\pi$
$863$	−22.3825	+	12.9226i	−0.761910	+	0.439889i	0.0680712	+	0.997680i	$0.478315\pi$
$864$	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
$871$	−43.6439	−	37.2248i	−1.47882	−	1.26131i
$872$	−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	$-0.659288\pi$
$877$	1.18892	−	0.686420i	0.0401468	−	0.0231788i	0.519939	+	0.854203i	$0.325955\pi$
$878$	−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	$-0.411732\pi$
$881$	16.2514			0.547524			0.273762	+	0.961797i	$0.411732\pi$
$882$		0			0
$883$	0.619110			0.0208347			0.0104174	−	0.999946i	$-0.496684\pi$
$883$	0.619110			0.0208347			0.0104174	+	0.999946i	$0.496684\pi$
$884$	2.03281	+	5.72826i	0.0683707	+	0.192662i
$885$	−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	0.999105	+	0.0423000i	$0.0134685\pi$
$887$	15.9690	+	27.6591i	0.536185	+	0.928700i	−0.462920	+	0.886400i	$0.653198\pi$
$888$	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	−0.641394	−	0.767211i	$-0.721644\pi$
$907$	10.3518	−	17.9299i	0.343728	−	0.595354i	0.985122	+	0.171858i	$0.0549770\pi$
$908$	−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	0.724618	−	0.689150i	$-0.242016\pi$
$919$	−7.10925	−	12.3136i	−0.234512	−	0.406187i	−0.959131	+	0.282963i	$0.908683\pi$
$920$	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	−0.849319	−	0.527879i	$-0.822987\pi$
$929$	−24.8963	+	14.3739i	−0.816822	+	0.471593i	0.0324972	+	0.999472i	$0.489654\pi$
$930$			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
$936$	−19.5158	+	6.92563i	−0.637893	+	0.226371i
$937$	−19.8495			−0.648456			−0.324228	−	0.945979i	$-0.605105\pi$
$937$	−19.8495			−0.648456			−0.324228	+	0.945979i	$0.605105\pi$
$938$		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	−0.300682	−	0.953725i	$-0.597214\pi$
$941$	−39.1720	−	22.6160i	−1.27697	−	0.737260i	−0.976291	+	0.216464i	$0.930547\pi$
$942$	−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	$-0.783628\pi$
$947$	−19.1474	+	11.0547i	−0.622206	+	0.359231i	0.155521	+	0.987833i	$0.450294\pi$
$948$	−0.369263	+	0.639582i	−0.0119931	+	0.0207727i
$949$	−15.6504	−	13.3486i	−0.508035	−	0.433314i
$950$	−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
$962$	22.8245	−	26.7604i	0.735893	−	0.862791i
$963$	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	$-0.303302\pi$
$971$	−12.9689	−	22.4627i	−0.416190	−	0.720863i	−0.995553	+	0.0942072i	$0.969968\pi$
$972$	−8.84358			−0.283658
$973$		0			0
$974$	37.9470			1.21590
$975$	−1.94533	−	5.48175i	−0.0623003	−	0.175556i
$976$	23.5615	−	40.8097i	0.754184	−	1.30629i
$977$	−39.2285	−	22.6486i	−1.25503	−	0.724592i	−0.282926	−	0.959142i	$-0.591305\pi$
$977$	−39.2285	−	22.6486i	−1.25503	−	0.724592i	−0.972104	+	0.234550i	$0.924638\pi$
$978$	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	0.527788	−	0.849376i	$-0.323022\pi$
$983$	1.75891	+	1.01551i	0.0561004	+	0.0323896i	−0.471687	+	0.881766i	$0.656355\pi$
$984$	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	−0.568414	−	0.822743i	$-0.692443\pi$
$991$	13.4832	−	23.3536i	0.428309	−	0.741853i	0.996723	+	0.0808899i	$0.0257762\pi$
$992$	−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	$-0.866944\pi$
$997$	−3.32787	+	5.76404i	−0.105395	+	0.182549i	0.808505	+	0.588490i	$0.200277\pi$
$998$	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.116.3		32
7.2	even	3	inner	637.2.r.g.324.13		32
7.3	odd	6		637.2.c.g.246.3	✓	16
7.4	even	3		637.2.c.g.246.4	yes	16
7.5	odd	6	inner	637.2.r.g.324.14		32
7.6	odd	2	inner	637.2.r.g.116.4		32
13.12	even	2	inner	637.2.r.g.116.13		32
91.12	odd	6	inner	637.2.r.g.324.4		32
91.18	odd	12		8281.2.a.cs.1.4		16
91.25	even	6		637.2.c.g.246.14	yes	16
91.31	even	12		8281.2.a.cs.1.3		16
91.38	odd	6		637.2.c.g.246.13	yes	16
91.51	even	6	inner	637.2.r.g.324.3		32
91.60	odd	12		8281.2.a.cs.1.14		16
91.73	even	12		8281.2.a.cs.1.13		16
91.90	odd	2	inner	637.2.r.g.116.14		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.c.g.246.3	✓	16	7.3	odd	6
637.2.c.g.246.4	yes	16	7.4	even	3
637.2.c.g.246.13	yes	16	91.38	odd	6
637.2.c.g.246.14	yes	16	91.25	even	6
637.2.r.g.116.3		32	1.1	even	1	trivial
637.2.r.g.116.4		32	7.6	odd	2	inner
637.2.r.g.116.13		32	13.12	even	2	inner
637.2.r.g.116.14		32	91.90	odd	2	inner
637.2.r.g.324.3		32	91.51	even	6	inner
637.2.r.g.324.4		32	91.12	odd	6	inner
637.2.r.g.324.13		32	7.2	even	3	inner
637.2.r.g.324.14		32	7.5	odd	6	inner
8281.2.a.cs.1.3		16	91.31	even	12
8281.2.a.cs.1.4		16	91.18	odd	12
8281.2.a.cs.1.13		16	91.73	even	12
8281.2.a.cs.1.14		16	91.60	odd	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.43372 + 0.827759i) q^{2} +(-0.247488 + 0.428663i) q^{3} +(0.370370 - 0.641500i) q^{4} +(-2.48886 + 1.43695i) q^{5} -0.819443i q^{6} -2.08473i q^{8} +(1.37750 + 2.38590i) q^{9} +O(q^{10})\)	\(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} +(5.62534 - 1.99628i) 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} +(1.15814 - 1.35785i) 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} +(-1.73317 + 2.03204i) 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} +(9.76530 - 3.46545i) 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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 20 q^{4} - 16 q^{9}+O(q^{10}) \) 32 * q + 20 * q^4 - 16 * q^9	\( 32 q + 20 q^{4} - 16 q^{9} - 28 q^{16} - 16 q^{22} + 36 q^{23} + 44 q^{25} + 72 q^{29} + 104 q^{36} - 32 q^{39} - 72 q^{43} + 72 q^{51} - 12 q^{53} - 328 q^{64} + 24 q^{65} - 96 q^{74} + 48 q^{78} - 36 q^{79} - 16 q^{81} - 136 q^{88} + 48 q^{92} + 84 q^{95}+O(q^{100}) \) 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

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Representations

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Database

Properties

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