LMFDB - Embedded newform 891.2.n.l.784.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [891,2,Mod(136,891)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(891, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 6]))

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

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

chi := DirichletCharacter("891.136");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 891 = 3^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	891.n (of order $15$, degree $8$, 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:	$7.11467082010$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$12$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			784.8
Character	$\chi$	$=$	891.784
Dual form			891.2.n.l.433.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.120212 + 1.14375i) q^{2} +(0.662593 - 0.140839i) q^{4} +(0.408797 - 3.88945i) q^{5} +(3.06963 + 3.40917i) q^{7} +(0.951502 + 2.92842i) q^{8} +4.49768 q^{10} +(3.04015 + 1.32570i) q^{11} +(-0.533071 - 0.237339i) q^{13} +(-3.53021 + 3.92070i) q^{14} +(-1.99732 + 0.889266i) q^{16} +(-1.01351 - 0.736358i) q^{17} +(-0.681632 - 2.09785i) q^{19} +(-0.276918 - 2.63470i) q^{20} +(-1.15080 + 3.63652i) q^{22} +(-3.65244 - 6.32621i) q^{23} +(-10.0699 - 2.14043i) q^{25} +(0.207373 - 0.638229i) q^{26} +(2.51406 + 1.82657i) q^{28} +(-0.832048 - 0.924083i) q^{29} +(7.92356 + 3.52780i) q^{31} +(1.82193 + 3.15567i) q^{32} +(0.720369 - 1.24772i) q^{34} +(14.5146 - 10.5455i) q^{35} +(-2.36110 + 7.26672i) q^{37} +(2.31746 - 1.03180i) q^{38} +(11.7789 - 2.50369i) q^{40} +(1.10232 - 1.22425i) q^{41} +(-2.89432 + 5.01312i) q^{43} +(2.20109 + 0.450233i) q^{44} +(6.79650 - 4.93795i) q^{46} +(0.516559 + 0.109798i) q^{47} +(-1.46810 + 13.9681i) q^{49} +(1.23758 - 11.7748i) q^{50} +(-0.386636 - 0.0821820i) q^{52} +(1.07638 - 0.782035i) q^{53} +(6.39907 - 11.2826i) q^{55} +(-7.06272 + 12.2330i) q^{56} +(0.956893 - 1.06274i) q^{58} +(0.543590 - 0.115544i) q^{59} +(10.2360 - 4.55734i) q^{61} +(-3.08239 + 9.48662i) q^{62} +(-6.92785 + 5.03338i) q^{64} +(-1.14103 + 1.97633i) q^{65} +(-3.73086 - 6.46203i) q^{67} +(-0.775252 - 0.345164i) q^{68} +(13.8062 + 15.3333i) q^{70} +(-4.14062 - 3.00833i) q^{71} +(0.117434 - 0.361425i) q^{73} +(-8.59511 - 1.82695i) q^{74} +(-0.747102 - 1.29402i) q^{76} +(4.81257 + 14.4338i) q^{77} +(-1.42577 - 13.5653i) q^{79} +(2.64225 + 8.13202i) q^{80} +(1.53274 + 1.11360i) q^{82} +(-0.912026 + 0.406060i) q^{83} +(-3.27834 + 3.64097i) q^{85} +(-6.08166 - 2.70773i) q^{86} +(-0.989516 + 10.1643i) q^{88} -3.33068 q^{89} +(-0.827203 - 2.54587i) q^{91} +(-3.31105 - 3.67730i) q^{92} +(-0.0634841 + 0.604011i) q^{94} +(-8.43812 + 1.79358i) q^{95} +(-1.64513 - 15.6524i) q^{97} -16.1524 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 8 q^{4} + 14 q^{7} + 64 q^{10} + 14 q^{13} + 4 q^{16} - 16 q^{19} - 16 q^{22} + 20 q^{25} - 36 q^{28} + 4 q^{31} - 84 q^{34} - 24 q^{37} + 106 q^{40} - 84 q^{43} - 76 q^{46} + 54 q^{49} - 52 q^{52}+ \cdots + 66 q^{97}+O(q^{100}) $ 96 * q + 8 * q^4 + 14 * q^7 + 64 * q^10 + 14 * q^13 + 4 * q^16 - 16 * q^19 - 16 * q^22 + 20 * q^25 - 36 * q^28 + 4 * q^31 - 84 * q^34 - 24 * q^37 + 106 * q^40 - 84 * q^43 - 76 * q^46 + 54 * q^49 - 52 * q^52 - 72 * q^55 + 10 * q^58 + 6 * q^61 - 104 * q^64 - 76 * q^67 + 8 * q^70 - 92 * q^73 - 204 * q^76 + 102 * q^79 + 24 * q^82 - 54 * q^85 + 44 * q^91 + 118 * q^94 + 66 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$.

$n$	$244$	$650$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.120212	+	1.14375i	0.0850031	+	0.808750i	0.951102	+	0.308877i	$0.0999532\pi$
$2$	0.120212	+	1.14375i	0.0850031	+	0.808750i	−0.866099	+	0.499873i	$0.833380\pi$
$3$		0			0
$3$		0			0
$4$	0.662593	−	0.140839i	0.331297	−	0.0704193i
$5$	0.408797	−	3.88945i	0.182820	−	1.73941i	−0.390963	−	0.920406i	$-0.627858\pi$
$5$	0.408797	−	3.88945i	0.182820	−	1.73941i	0.573783	−	0.819008i	$-0.305475\pi$
$6$		0			0
$7$	3.06963	+	3.40917i	1.16021	+	1.28854i	0.950481	+	0.310784i	$0.100592\pi$
$7$	3.06963	+	3.40917i	1.16021	+	1.28854i	0.209729	+	0.977759i	$0.432742\pi$
$8$	0.951502	+	2.92842i	0.336407	+	1.03535i
$9$		0			0
$10$	4.49768			1.42229
$11$	3.04015	+	1.32570i	0.916639	+	0.399715i
$11$	3.04015	+	1.32570i	0.916639	+	0.399715i
$12$		0			0
$13$	−0.533071	−	0.237339i	−0.147847	−	0.0658259i	0.331479	−	0.943463i	$-0.392452\pi$
$13$	−0.533071	−	0.237339i	−0.147847	−	0.0658259i	−0.479327	+	0.877637i	$0.659119\pi$
$14$	−3.53021	+	3.92070i	−0.943488	+	1.04785i
$15$		0			0
$16$	−1.99732	+	0.889266i	−0.499331	+	0.222316i
$17$	−1.01351	−	0.736358i	−0.245812	−	0.178593i	0.458057	−	0.888923i	$-0.348546\pi$
$17$	−1.01351	−	0.736358i	−0.245812	−	0.178593i	−0.703869	+	0.710330i	$0.748546\pi$
$18$		0			0
$19$	−0.681632	−	2.09785i	−0.156377	−	0.481279i	0.841921	−	0.539601i	$-0.181425\pi$
$19$	−0.681632	−	2.09785i	−0.156377	−	0.481279i	−0.998298	+	0.0583220i	$0.981425\pi$
$20$	−0.276918	−	2.63470i	−0.0619207	−	0.589136i
$21$		0			0
$22$	−1.15080	+	3.63652i	−0.245352	+	0.775309i
$23$	−3.65244	−	6.32621i	−0.761586	−	1.31911i	−0.942033	−	0.335521i	$-0.891088\pi$
$23$	−3.65244	−	6.32621i	−0.761586	−	1.31911i	0.180447	−	0.983585i	$-0.442246\pi$
$24$		0			0
$25$	−10.0699	−	2.14043i	−2.01399	−	0.428087i
$26$	0.207373	−	0.638229i	0.0406692	−	0.125167i
$27$		0			0
$28$	2.51406	+	1.82657i	0.475112	+	0.345189i
$29$	−0.832048	−	0.924083i	−0.154507	−	0.171598i	0.660922	−	0.750455i	$-0.270166\pi$
$29$	−0.832048	−	0.924083i	−0.154507	−	0.171598i	−0.815429	+	0.578857i	$0.803499\pi$
$30$		0			0
$31$	7.92356	+	3.52780i	1.42311	+	0.633611i	0.966643	−	0.256127i	$-0.0824465\pi$
$31$	7.92356	+	3.52780i	1.42311	+	0.633611i	0.456471	+	0.889738i	$0.349113\pi$
$32$	1.82193	+	3.15567i	0.322075	+	0.557850i
$33$		0			0
$34$	0.720369	−	1.24772i	0.123542	−	0.213982i
$35$	14.5146	−	10.5455i	2.45342	−	1.78251i
$36$		0			0
$37$	−2.36110	+	7.26672i	−0.388163	+	1.19464i	0.545997	+	0.837787i	$0.316151\pi$
$37$	−2.36110	+	7.26672i	−0.388163	+	1.19464i	−0.934160	+	0.356855i	$0.883849\pi$
$38$	2.31746	−	1.03180i	0.375942	−	0.167380i
$39$		0			0
$40$	11.7789	−	2.50369i	1.86241	−	0.395868i
$41$	1.10232	−	1.22425i	0.172153	−	0.191196i	−0.650894	−	0.759169i	$-0.725606\pi$
$41$	1.10232	−	1.22425i	0.172153	−	0.191196i	0.823047	+	0.567973i	$0.192272\pi$
$42$		0			0
$43$	−2.89432	+	5.01312i	−0.441380	+	0.764493i	−0.997792	−	0.0664134i	$-0.978844\pi$
$43$	−2.89432	+	5.01312i	−0.441380	+	0.764493i	0.556412	+	0.830907i	$0.312178\pi$
$44$	2.20109	+	0.450233i	0.331827	+	0.0678752i
$45$		0			0
$46$	6.79650	−	4.93795i	1.00209	−	0.728060i
$47$	0.516559	+	0.109798i	0.0753478	+	0.0160157i	0.245431	−	0.969414i	$-0.421070\pi$
$47$	0.516559	+	0.109798i	0.0753478	+	0.0160157i	−0.170083	+	0.985430i	$0.554404\pi$
$48$		0			0
$49$	−1.46810	+	13.9681i	−0.209729	+	1.99544i
$50$	1.23758	−	11.7748i	0.175020	−	1.66520i
$51$		0			0
$52$	−0.386636	−	0.0821820i	−0.0536167	−	0.0113966i
$53$	1.07638	−	0.782035i	0.147852	−	0.107421i	−0.511400	−	0.859343i	$-0.670873\pi$
$53$	1.07638	−	0.782035i	0.147852	−	0.107421i	0.659252	+	0.751922i	$0.270873\pi$
$54$		0			0
$55$	6.39907	−	11.2826i	0.862850	−	1.52134i
$56$	−7.06272	+	12.2330i	−0.943796	+	1.63470i
$57$		0			0
$58$	0.956893	−	1.06274i	0.125646	−	0.139544i
$59$	0.543590	−	0.115544i	0.0707693	−	0.0150425i	−0.172391	−	0.985029i	$-0.555149\pi$
$59$	0.543590	−	0.115544i	0.0707693	−	0.0150425i	0.243160	+	0.969986i	$0.421816\pi$
$60$		0			0
$61$	10.2360	−	4.55734i	1.31058	−	0.583508i	0.371892	−	0.928276i	$-0.378709\pi$
$61$	10.2360	−	4.55734i	1.31058	−	0.583508i	0.938688	+	0.344768i	$0.112043\pi$
$62$	−3.08239	+	9.48662i	−0.391464	+	1.20480i
$63$		0			0
$64$	−6.92785	+	5.03338i	−0.865981	+	0.629172i
$65$	−1.14103	+	1.97633i	−0.141528	+	0.245134i
$66$		0			0
$67$	−3.73086	−	6.46203i	−0.455797	−	0.789463i	0.542937	−	0.839774i	$-0.317312\pi$
$67$	−3.73086	−	6.46203i	−0.455797	−	0.789463i	−0.998734	+	0.0503104i	$0.983979\pi$
$68$	−0.775252	−	0.345164i	−0.0940131	−	0.0418573i
$69$		0			0
$70$	13.8062	+	15.3333i	1.65016	+	1.83268i
$71$	−4.14062	−	3.00833i	−0.491401	−	0.357024i	0.314322	−	0.949316i	$-0.398223\pi$
$71$	−4.14062	−	3.00833i	−0.491401	−	0.357024i	−0.805723	+	0.592293i	$0.798223\pi$
$72$		0			0
$73$	0.117434	−	0.361425i	0.0137446	−	0.0423015i	−0.943949	−	0.330091i	$-0.892920\pi$
$73$	0.117434	−	0.361425i	0.0137446	−	0.0423015i	0.957694	+	0.287790i	$0.0929204\pi$
$74$	−8.59511	−	1.82695i	−0.999162	−	0.212378i
$75$		0			0
$76$	−0.747102	−	1.29402i	−0.0856985	−	0.148434i
$77$	4.81257	+	14.4338i	0.548444	+	1.64488i
$78$		0			0
$79$	−1.42577	−	13.5653i	−0.160411	−	1.52621i	−0.717970	−	0.696074i	$-0.754928\pi$
$79$	−1.42577	−	13.5653i	−0.160411	−	1.52621i	0.557559	−	0.830138i	$-0.311738\pi$
$80$	2.64225	+	8.13202i	0.295413	+	0.909187i
$81$		0			0
$82$	1.53274	+	1.11360i	0.169263	+	0.122977i
$83$	−0.912026	+	0.406060i	−0.100108	+	0.0445709i	−0.456180	−	0.889888i	$-0.650783\pi$
$83$	−0.912026	+	0.406060i	−0.100108	+	0.0445709i	0.356072	+	0.934459i	$0.384116\pi$
$84$		0			0
$85$	−3.27834	+	3.64097i	−0.355586	+	0.394919i
$86$	−6.08166	−	2.70773i	−0.655803	−	0.291982i
$87$		0			0
$88$	−0.989516	+	10.1643i	−0.105483	+	1.08351i
$89$	−3.33068			−0.353051			−0.176525	−	0.984296i	$-0.556486\pi$
$89$	−3.33068			−0.353051			−0.176525	+	0.984296i	$0.556486\pi$
$90$		0			0
$91$	−0.827203	−	2.54587i	−0.0867145	−	0.266880i
$92$	−3.31105	−	3.67730i	−0.345201	−	0.383385i
$93$		0			0
$94$	−0.0634841	+	0.604011i	−0.00654788	+	0.0622989i
$95$	−8.43812	+	1.79358i	−0.865732	+	0.184017i
$96$		0			0
$97$	−1.64513	−	15.6524i	−0.167038	−	1.58926i	−0.681547	−	0.731775i	$-0.738692\pi$
$97$	−1.64513	−	15.6524i	−0.167038	−	1.58926i	0.514509	−	0.857485i	$-0.327974\pi$
$98$	−16.1524			−1.63164
$99$		0			0
$100$	−6.97373			−0.697373
$101$	1.59248	+	15.1515i	0.158458	+	1.50763i	0.727949	+	0.685631i	$0.240474\pi$
$101$	1.59248	+	15.1515i	0.158458	+	1.50763i	−0.569491	+	0.821998i	$0.692860\pi$
$102$		0			0
$103$	−3.40582	+	0.723929i	−0.335585	+	0.0713309i	−0.372622	−	0.927983i	$-0.621541\pi$
$103$	−3.40582	+	0.723929i	−0.335585	+	0.0713309i	0.0370371	+	0.999314i	$0.488208\pi$
$104$	0.187809	−	1.78689i	0.0184162	−	0.175219i
$105$		0			0
$106$	1.02384	+	1.13709i	0.0994444	+	0.110444i
$107$	−2.97592	−	9.15893i	−0.287693	−	0.885428i	−0.985579	−	0.169218i	$-0.945876\pi$
$107$	−2.97592	−	9.15893i	−0.287693	−	0.885428i	0.697886	−	0.716209i	$-0.254124\pi$
$108$		0			0
$109$	0.380750			0.0364692			0.0182346	−	0.999834i	$-0.494195\pi$
$109$	0.380750			0.0364692			0.0182346	+	0.999834i	$0.494195\pi$
$110$	13.6736	+	5.96260i	1.30373	+	0.568511i
$111$		0			0
$112$	−9.16269	−	4.07949i	−0.865793	−	0.385476i
$113$	−8.31549	+	9.23528i	−0.782255	+	0.868782i	−0.994094	−	0.108522i	$-0.965388\pi$
$113$	−8.31549	+	9.23528i	−0.782255	+	0.868782i	0.211839	+	0.977305i	$0.432055\pi$
$114$		0			0
$115$	−26.0986	+	11.6198i	−2.43370	+	1.08355i
$116$	−0.681456	−	0.495107i	−0.0632716	−	0.0459695i
$117$		0			0
$118$	0.197499	+	0.607838i	0.0181812	+	0.0559561i
$119$	−0.600730	−	5.71557i	−0.0550688	−	0.523945i
$120$		0			0
$121$	7.48501	+	8.06068i	0.680456	+	0.732789i
$122$	6.44293	+	11.1595i	0.583315	+	1.01033i
$123$		0			0
$124$	5.74695	+	1.22155i	0.516091	+	0.109699i
$125$	−6.39905	+	19.6942i	−0.572348	+	1.76151i
$126$		0			0
$127$	0.354450	+	0.257523i	0.0314523	+	0.0228515i	0.603400	−	0.797438i	$-0.293812\pi$
$127$	0.354450	+	0.257523i	0.0314523	+	0.0228515i	−0.571948	+	0.820290i	$0.693812\pi$
$128$	−1.71328	−	1.90279i	−0.151434	−	0.168184i
$129$		0			0
$130$	−2.39758	−	1.06747i	−0.210282	−	0.0936236i
$131$	4.06152	+	7.03476i	0.354857	+	0.614630i	0.987093	−	0.160145i	$-0.0511963\pi$
$131$	4.06152	+	7.03476i	0.354857	+	0.614630i	−0.632237	+	0.774775i	$0.717863\pi$
$132$		0			0
$133$	5.05955	−	8.76340i	0.438719	−	0.759884i
$134$	6.94243	−	5.04397i	0.599734	−	0.435732i
$135$		0			0
$136$	1.19201	−	3.66863i	0.102214	−	0.314583i
$137$	−6.13478	+	2.73138i	−0.524129	+	0.233357i	−0.651707	−	0.758471i	$-0.725947\pi$
$137$	−6.13478	+	2.73138i	−0.524129	+	0.233357i	0.127577	+	0.991829i	$0.459280\pi$
$138$		0			0
$139$	2.92969	−	0.622724i	0.248493	−	0.0528188i	−0.0819812	−	0.996634i	$-0.526125\pi$
$139$	2.92969	−	0.622724i	0.248493	−	0.0528188i	0.330474	+	0.943815i	$0.392791\pi$
$140$	8.13208	−	9.03159i	0.687286	−	0.763309i
$141$		0			0
$142$	2.94301	−	5.09745i	0.246972	−	0.427768i
$143$	−1.30598	−	1.42824i	−0.109211	−	0.119435i
$144$		0			0
$145$	−3.93431	+	2.85845i	−0.326727	+	0.237381i
$146$	0.427495	+	0.0908668i	0.0353797	+	0.00752019i
$147$		0			0
$148$	−0.541015	+	5.14741i	−0.0444712	+	0.423115i
$149$	−0.0268439	+	0.255402i	−0.00219914	+	0.0209234i	−0.995566	−	0.0940610i	$-0.970015\pi$
$149$	−0.0268439	+	0.255402i	−0.00219914	+	0.0209234i	0.993367	+	0.114984i	$0.0366818\pi$
$150$		0			0
$151$	6.20826	+	1.31961i	0.505221	+	0.107388i	0.453469	−	0.891272i	$-0.350186\pi$
$151$	6.20826	+	1.31961i	0.505221	+	0.107388i	0.0517519	+	0.998660i	$0.483520\pi$
$152$	5.49481	−	3.99221i	0.445688	−	0.323811i
$153$		0			0
$154$	−15.9301	+	7.23948i	−1.28368	+	0.583374i
$155$	16.9603	−	29.3761i	1.36229	−	2.35955i
$156$		0			0
$157$	−6.08017	+	6.75272i	−0.485251	+	0.538926i	−0.935196	−	0.354131i	$-0.884777\pi$
$157$	−6.08017	+	6.75272i	−0.485251	+	0.538926i	0.449945	+	0.893056i	$0.351443\pi$
$158$	15.3438	−	3.26143i	1.22069	−	0.259465i
$159$		0			0
$160$	13.0186	−	5.79627i	1.02921	−	0.458235i
$161$	10.3555	−	31.8709i	0.816125	−	2.51178i
$162$		0			0
$163$	−5.00952	+	3.63963i	−0.392376	+	0.285078i	−0.766428	−	0.642330i	$-0.777968\pi$
$163$	−5.00952	+	3.63963i	−0.392376	+	0.285078i	0.374053	+	0.927408i	$0.377968\pi$
$164$	0.557968	−	0.966429i	0.0435700	−	0.0754654i
$165$		0			0
$166$	−0.574066	−	0.994312i	−0.0445562	−	0.0771736i
$167$	−12.4623	−	5.54858i	−0.964363	−	0.429362i	−0.136716	−	0.990610i	$-0.543655\pi$
$167$	−12.4623	−	5.54858i	−0.964363	−	0.429362i	−0.827648	+	0.561248i	$0.810321\pi$
$168$		0			0
$169$	−8.47086	−	9.40785i	−0.651605	−	0.723680i
$170$	−4.55844	−	3.31190i	−0.349616	−	0.254011i
$171$		0			0
$172$	−1.21172	+	3.72929i	−0.0923927	+	0.284356i
$173$	−20.7594	−	4.41256i	−1.57831	−	0.335480i	−0.666312	−	0.745673i	$-0.732128\pi$
$173$	−20.7594	−	4.41256i	−1.57831	−	0.335480i	−0.911999	+	0.410192i	$0.865462\pi$
$174$		0			0
$175$	−23.6139	−	40.9005i	−1.78504	−	3.09178i
$176$	−7.25107	+	0.0556386i	−0.546570	+	0.00419392i
$177$		0			0
$178$	−0.400389	−	3.80944i	−0.0300104	−	0.285530i
$179$	4.48218	+	13.7947i	0.335014	+	1.03107i	0.966715	+	0.255855i	$0.0823568\pi$
$179$	4.48218	+	13.7947i	0.335014	+	1.03107i	−0.631702	+	0.775212i	$0.717643\pi$
$180$		0			0
$181$	−0.235532	−	0.171124i	−0.0175070	−	0.0127195i	0.578997	−	0.815329i	$-0.303444\pi$
$181$	−0.235532	−	0.171124i	−0.0175070	−	0.0127195i	−0.596504	+	0.802610i	$0.703444\pi$
$182$	2.81239	−	1.25216i	0.208468	−	0.0928159i
$183$		0			0
$184$	15.0505	−	16.7153i	1.10954	−	1.23227i
$185$	27.2983	+	12.1540i	2.00701	+	0.893580i
$186$		0			0
$187$	−2.10503	−	3.58225i	−0.153935	−	0.261960i
$188$	0.357732			0.0260903
$189$		0			0
$190$	−3.06576	−	9.43545i	−0.222414	−	0.684519i
$191$	0.303208	+	0.336747i	0.0219394	+	0.0243661i	0.754015	−	0.656858i	$-0.228115\pi$
$191$	0.303208	+	0.336747i	0.0219394	+	0.0243661i	−0.732075	+	0.681224i	$0.761448\pi$
$192$		0			0
$193$	1.83352	−	17.4448i	0.131980	−	1.25570i	−0.705292	−	0.708917i	$-0.749184\pi$
$193$	1.83352	−	17.4448i	0.131980	−	1.25570i	0.837271	−	0.546787i	$-0.184149\pi$
$194$	17.7046	−	3.76323i	1.27112	−	0.270184i
$195$		0			0
$196$	0.994488	+	9.46192i	0.0710349	+	0.675851i
$197$	−17.6706			−1.25898			−0.629489	−	0.777010i	$-0.716736\pi$
$197$	−17.6706			−1.25898			−0.629489	+	0.777010i	$0.716736\pi$
$198$		0			0
$199$	−13.2207			−0.937192			−0.468596	−	0.883413i	$-0.655240\pi$
$199$	−13.2207			−0.937192			−0.468596	+	0.883413i	$0.655240\pi$
$200$	−3.31349	−	31.5257i	−0.234299	−	2.22920i
$201$		0			0
$202$	−17.1380	+	3.64279i	−1.20583	+	0.256306i
$203$	0.596275	−	5.67318i	0.0418503	−	0.398179i
$204$		0			0
$205$	−4.31103	−	4.78788i	−0.301095	−	0.334400i
$206$	−1.23741	−	3.80836i	−0.0862146	−	0.265341i
$207$		0			0
$208$	1.27577			0.0884590
$209$	0.708864	−	7.28141i	0.0490331	−	0.503666i
$210$		0			0
$211$	10.2886	+	4.58077i	0.708295	+	0.315353i	0.729078	−	0.684431i	$-0.239949\pi$
$211$	10.2886	+	4.58077i	0.708295	+	0.315353i	−0.0207832	+	0.999784i	$0.506616\pi$
$212$	0.603060	−	0.669766i	0.0414184	−	0.0459998i
$213$		0			0
$214$	10.1177	−	4.50471i	0.691635	−	0.307936i
$215$	18.3151	+	13.3067i	1.24908	+	0.907508i
$216$		0			0
$217$	12.2955	+	37.8418i	0.834675	+	2.56887i
$218$	0.0457709	+	0.435481i	0.00309999	+	0.0294945i
$219$		0			0
$220$	2.65096	−	8.37698i	0.178728	−	0.564776i
$221$	0.365507	+	0.633076i	0.0245866	+	0.0425853i
$222$		0			0
$223$	15.4356	+	3.28093i	1.03364	+	0.219707i	0.693341	−	0.720609i	$-0.256138\pi$
$223$	15.4356	+	3.28093i	1.03364	+	0.219707i	0.340301	+	0.940317i	$0.389471\pi$
$224$	−5.16557	+	15.8980i	−0.345139	+	1.06223i
$225$		0			0
$226$	−11.5624	−	8.40060i	−0.769122	−	0.558800i
$227$	5.34518	+	5.93642i	0.354772	+	0.394014i	0.893942	−	0.448183i	$-0.147929\pi$
$227$	5.34518	+	5.93642i	0.354772	+	0.394014i	−0.539170	+	0.842197i	$0.681262\pi$
$228$		0			0
$229$	−17.9986	−	8.01351i	−1.18938	−	0.529547i	−0.285937	−	0.958249i	$-0.592305\pi$
$229$	−17.9986	−	8.01351i	−1.18938	−	0.529547i	−0.903446	+	0.428701i	$0.858971\pi$
$230$	−16.4275	−	28.4533i	−1.08320	−	1.87615i
$231$		0			0
$232$	1.91441	−	3.31586i	0.125687	−	0.217697i
$233$	−14.4585	+	10.5047i	−0.947207	+	0.688186i	−0.950145	−	0.311810i	$-0.899065\pi$
$233$	−14.4585	+	10.5047i	−0.947207	+	0.688186i	0.00293795	+	0.999996i	$0.499065\pi$
$234$		0			0
$235$	0.638221	−	1.96424i	0.0416330	−	0.128133i
$236$	0.343906	−	0.153117i	0.0223864	−	0.00996705i
$237$		0			0
$238$	6.46494	−	1.37416i	0.419060	−	0.0890739i
$239$	−6.70892	+	7.45101i	−0.433964	+	0.481966i	−0.919970	−	0.391990i	$-0.871787\pi$
$239$	−6.70892	+	7.45101i	−0.433964	+	0.481966i	0.486005	+	0.873956i	$0.338454\pi$
$240$		0			0
$241$	−8.59826	+	14.8926i	−0.553863	+	0.959318i	0.444128	+	0.895963i	$0.353513\pi$
$241$	−8.59826	+	14.8926i	−0.553863	+	0.959318i	−0.997991	+	0.0633552i	$0.979820\pi$
$242$	−8.31957	+	9.52994i	−0.534802	+	0.612608i
$243$		0			0
$244$	6.14042	−	4.46128i	0.393100	−	0.285604i
$245$	53.7280	+	11.4202i	3.43255	+	0.729612i
$246$		0			0
$247$	−0.134542	+	1.28008i	−0.00856069	+	0.0814495i
$248$	−2.79160	+	26.5603i	−0.177267	+	1.68658i
$249$		0			0
$250$	−23.2944	−	4.95139i	−1.47327	−	0.313153i
$251$	−4.20229	+	3.05314i	−0.265246	+	0.192713i	−0.712457	−	0.701716i	$-0.752417\pi$
$251$	−4.20229	+	3.05314i	−0.265246	+	0.192713i	0.447211	+	0.894429i	$0.352417\pi$
$252$		0			0
$253$	−2.71727	−	24.0747i	−0.170833	−	1.51356i
$254$	−0.251931	+	0.436358i	−0.0158076	+	0.0273795i
$255$		0			0
$256$	−9.48957	+	10.5392i	−0.593098	+	0.658702i
$257$	−15.8395	+	3.36679i	−0.988041	+	0.210015i	−0.673466	−	0.739218i	$-0.735195\pi$
$257$	−15.8395	+	3.36679i	−0.988041	+	0.210015i	−0.314575	+	0.949233i	$0.601862\pi$
$258$		0			0
$259$	−32.0212	+	14.2567i	−1.98970	+	0.885871i
$260$	−0.477698	+	1.47020i	−0.0296256	+	0.0911782i
$261$		0			0
$262$	−7.55773	+	5.49101i	−0.466918	+	0.339236i
$263$	−11.5926	+	20.0789i	−0.714828	+	1.23812i	0.248198	+	0.968709i	$0.420161\pi$
$263$	−11.5926	+	20.0789i	−0.714828	+	1.23812i	−0.963026	+	0.269408i	$0.913172\pi$
$264$		0			0
$265$	−2.60166	−	4.50621i	−0.159819	−	0.276814i
$266$	10.6313	+	4.73337i	0.651848	+	0.290222i
$267$		0			0
$268$	−3.38214	−	3.75625i	−0.206597	−	0.229450i
$269$	6.98259	+	5.07315i	0.425736	+	0.309315i	0.779942	−	0.625852i	$-0.215249\pi$
$269$	6.98259	+	5.07315i	0.425736	+	0.309315i	−0.354206	+	0.935168i	$0.615249\pi$
$270$		0			0
$271$	7.48888	−	23.0484i	0.454917	−	1.40009i	−0.416315	−	0.909220i	$-0.636679\pi$
$271$	7.48888	−	23.0484i	0.454917	−	1.40009i	0.871232	−	0.490871i	$-0.163321\pi$
$272$	2.67912	+	0.569466i	0.162446	+	0.0345289i
$273$		0			0
$274$	−3.86148	−	6.68828i	−0.233280	−	0.404054i
$275$	−27.7766	−	19.8570i	−1.67499	−	1.19742i
$276$		0			0
$277$	0.899541	+	8.55856i	0.0540482	+	0.514234i	0.987735	+	0.156142i	$0.0499058\pi$
$277$	0.899541	+	8.55856i	0.0540482	+	0.514234i	−0.933686	+	0.358092i	$0.883428\pi$
$278$	1.06442	+	3.27596i	0.0638398	+	0.196479i
$279$		0			0
$280$	44.6924	+	32.4709i	2.67088	+	1.94051i
$281$	8.05898	−	3.58809i	0.480758	−	0.214047i	−0.152025	−	0.988377i	$-0.548579\pi$
$281$	8.05898	−	3.58809i	0.480758	−	0.214047i	0.632783	+	0.774329i	$0.281913\pi$
$282$		0			0
$283$	−13.4296	+	14.9151i	−0.798308	+	0.886611i	−0.995597	−	0.0937342i	$-0.970120\pi$
$283$	−13.4296	+	14.9151i	−0.798308	+	0.886611i	0.197289	+	0.980345i	$0.436786\pi$
$284$	−3.16723	−	1.41014i	−0.187941	−	0.0836766i
$285$		0			0
$286$	1.47655	−	1.66540i	0.0873101	−	0.0984769i
$287$	7.55738			0.446098
$288$		0			0
$289$	−4.76831	−	14.6753i	−0.280489	−	0.863256i
$290$	−3.74229	−	4.15623i	−0.219755	−	0.244062i
$291$		0			0
$292$	0.0269084	−	0.256017i	0.00157470	−	0.0149822i
$293$	1.66609	−	0.354138i	0.0973340	−	0.0206890i	−0.158987	−	0.987281i	$-0.550823\pi$
$293$	1.66609	−	0.354138i	0.0973340	−	0.0206890i	0.256321	+	0.966592i	$0.417490\pi$
$294$		0			0
$295$	−0.227183	−	2.16150i	−0.0132271	−	0.125847i
$296$	−23.5266			−1.36746
$297$		0			0
$298$	−0.295342			−0.0171087
$299$	0.445556	+	4.23918i	0.0257672	+	0.245158i
$300$		0			0
$301$	−25.9750	+	5.52117i	−1.49718	+	0.318235i
$302$	−0.762983	+	7.25930i	−0.0439048	+	0.417726i
$303$		0			0
$304$	3.22698	+	3.58393i	0.185080	+	0.205552i
$305$	−13.5411	−	41.6752i	−0.775361	−	2.38632i
$306$		0			0
$307$	−19.7887			−1.12940			−0.564699	−	0.825297i	$-0.691008\pi$
$307$	−19.7887			−1.12940			−0.564699	+	0.825297i	$0.691008\pi$
$308$	5.22161	+	8.88594i	0.297529	+	0.506323i
$309$		0			0
$310$	35.6377	+	15.8669i	2.02408	+	0.901180i
$311$	18.2590	−	20.2787i	1.03537	−	1.14990i	0.0468395	−	0.998902i	$-0.485085\pi$
$311$	18.2590	−	20.2787i	1.03537	−	1.14990i	0.988534	−	0.150997i	$-0.0482483\pi$
$312$		0			0
$313$	8.24759	−	3.67206i	0.466181	−	0.207557i	−0.160184	−	0.987087i	$-0.551209\pi$
$313$	8.24759	−	3.67206i	0.466181	−	0.207557i	0.626365	+	0.779530i	$0.284542\pi$
$314$	−8.45430	−	6.14241i	−0.477104	−	0.346636i
$315$		0			0
$316$	−2.85522	−	8.78745i	−0.160618	−	0.494333i
$317$	−2.61888	−	24.9170i	−0.147091	−	1.39948i	−0.780257	−	0.625459i	$-0.784912\pi$
$317$	−2.61888	−	24.9170i	−0.147091	−	1.39948i	0.633166	−	0.774016i	$-0.281755\pi$
$318$		0			0
$319$	−1.30449	−	3.91240i	−0.0730374	−	0.219052i
$320$	16.7450	+	29.0031i	0.936072	+	1.62132i
$321$		0			0
$322$	37.6970	+	8.01274i	2.10077	+	0.446533i
$323$	−0.853926	+	2.62811i	−0.0475137	+	0.146232i
$324$		0			0
$325$	4.85999	+	3.53099i	0.269584	+	0.195864i
$326$	−4.76502	−	5.29209i	−0.263910	−	0.293101i
$327$		0			0
$328$	4.63398	+	2.06318i	0.255869	+	0.113920i
$329$	1.21132	+	2.09807i	0.0667824	+	0.115671i
$330$		0			0
$331$	4.65092	−	8.05563i	0.255638	−	0.442777i	−0.709431	−	0.704775i	$-0.751048\pi$
$331$	4.65092	−	8.05563i	0.255638	−	0.442777i	0.965069	+	0.261998i	$0.0843813\pi$
$332$	−0.547113	+	0.397501i	−0.0300268	+	0.0218157i
$333$		0			0
$334$	4.84804	−	14.9207i	0.265273	−	0.816426i
$335$	−26.6589	+	11.8693i	−1.45653	+	0.648490i
$336$		0			0
$337$	13.8691	−	2.94798i	0.755500	−	0.160586i	0.185968	−	0.982556i	$-0.440458\pi$
$337$	13.8691	−	2.94798i	0.755500	−	0.160586i	0.569532	+	0.821969i	$0.307125\pi$
$338$	9.74188	−	10.8194i	0.529888	−	0.588500i
$339$		0			0
$340$	−1.65942	+	2.87420i	−0.0899947	+	0.155875i
$341$	19.4120	+	21.2293i	1.05122	+	1.14963i
$342$		0			0
$343$	−26.1466	+	18.9966i	−1.41178	+	1.02572i
$344$	−17.4345	−	3.70581i	−0.940005	−	0.199804i
$345$		0			0
$346$	2.55130	−	24.2740i	0.137159	−	1.30498i
$347$	−0.154909	+	1.47386i	−0.00831597	+	0.0791212i	−0.997893	−	0.0648851i	$-0.979332\pi$
$347$	−0.154909	+	1.47386i	−0.00831597	+	0.0791212i	0.989577	+	0.144006i	$0.0459986\pi$
$348$		0			0
$349$	−1.97470	−	0.419734i	−0.105703	−	0.0224679i	0.154756	−	0.987953i	$-0.450541\pi$
$349$	−1.97470	−	0.419734i	−0.105703	−	0.0224679i	−0.260459	+	0.965485i	$0.583874\pi$
$350$	43.9410	−	31.9250i	2.34875	−	1.70646i
$351$		0			0
$352$	1.35544	+	12.0091i	0.0722454	+	0.640085i
$353$	−2.85887	+	4.95171i	−0.152162	+	0.263553i	−0.932022	−	0.362401i	$-0.881957\pi$
$353$	−2.85887	+	4.95171i	−0.152162	+	0.263553i	0.779860	+	0.625954i	$0.215290\pi$
$354$		0			0
$355$	−13.3934	+	14.8749i	−0.710850	+	0.789478i
$356$	−2.20688	+	0.469087i	−0.116965	+	0.0248616i
$357$		0			0
$358$	−15.2388	+	6.78477i	−0.805398	+	0.358586i
$359$	3.39150	−	10.4380i	0.178996	−	0.550894i	−0.820797	−	0.571220i	$-0.806470\pi$
$359$	3.39150	−	10.4380i	0.178996	−	0.550894i	0.999793	+	0.0203256i	$0.00647029\pi$
$360$		0			0
$361$	11.4350	−	8.30800i	0.601841	−	0.437263i
$362$	0.167408	−	0.289960i	0.00879879	−	0.0152399i
$363$		0			0
$364$	−0.906656	−	1.57037i	−0.0475217	−	0.0823099i
$365$	−1.35774	−	0.604503i	−0.0710671	−	0.0316411i
$366$		0			0
$367$	−12.0920	−	13.4295i	−0.631197	−	0.701015i	0.339694	−	0.940536i	$-0.389676\pi$
$367$	−12.0920	−	13.4295i	−0.631197	−	0.701015i	−0.970891	+	0.239521i	$0.923010\pi$
$368$	12.9208	+	9.38750i	0.673542	+	0.489357i
$369$		0			0
$370$	−10.6195	+	32.6834i	−0.552080	+	1.69913i
$371$	5.97017	+	1.26900i	0.309956	+	0.0658831i
$372$		0			0
$373$	12.2370	+	21.1952i	0.633610	+	1.09744i	0.986808	+	0.161895i	$0.0517607\pi$
$373$	12.2370	+	21.1952i	0.633610	+	1.09744i	−0.353198	+	0.935548i	$0.614906\pi$
$374$	3.84413	−	2.83825i	0.198775	−	0.146762i
$375$		0			0
$376$	0.169972	+	1.61718i	0.00876564	+	0.0833995i
$377$	0.224220	+	0.690079i	0.0115479	+	0.0355409i
$378$		0			0
$379$	−7.54577	−	5.48232i	−0.387600	−	0.281608i	0.376871	−	0.926266i	$-0.377000\pi$
$379$	−7.54577	−	5.48232i	−0.387600	−	0.281608i	−0.764471	+	0.644658i	$0.777000\pi$
$380$	−5.33843	+	2.37682i	−0.273856	+	0.121928i
$381$		0			0
$382$	−0.348703	+	0.387274i	−0.0178412	+	0.0198147i
$383$	22.7609	+	10.1338i	1.16303	+	0.517814i	0.895206	−	0.445653i	$-0.147029\pi$
$383$	22.7609	+	10.1338i	1.16303	+	0.517814i	0.267824	+	0.963468i	$0.413695\pi$
$384$		0			0
$385$	58.1068	−	12.8178i	2.96140	−	0.653254i
$386$	20.1728			1.02677
$387$		0			0
$388$	−3.29451	−	10.1395i	−0.167254	−	0.514754i
$389$	14.9370	+	16.5892i	0.757336	+	0.841107i	0.991366	−	0.131122i	$-0.0418581\pi$
$389$	14.9370	+	16.5892i	0.757336	+	0.841107i	−0.234030	+	0.972229i	$0.575191\pi$
$390$		0			0
$391$	−0.956572	+	9.10117i	−0.0483759	+	0.460266i
$392$	−42.3014	+	8.99143i	−2.13654	+	0.454136i
$393$		0			0
$394$	−2.12423	−	20.2107i	−0.107017	−	1.01820i
$395$	−53.3442			−2.68404
$396$		0			0
$397$	39.1450			1.96463			0.982315	−	0.187234i	$-0.0599524\pi$
$397$	39.1450			1.96463			0.982315	+	0.187234i	$0.0599524\pi$
$398$	−1.58930	−	15.1211i	−0.0796642	−	0.757954i
$399$		0			0
$400$	22.0164	−	4.67972i	1.10082	−	0.233986i
$401$	3.47348	−	33.0479i	0.173457	−	1.65033i	−0.468405	−	0.883514i	$-0.655171\pi$
$401$	3.47348	−	33.0479i	0.173457	−	1.65033i	0.641862	−	0.766820i	$-0.278162\pi$
$402$		0			0
$403$	−3.38654	−	3.76114i	−0.168696	−	0.187356i
$404$	3.18908	+	9.81498i	0.158663	+	0.488314i
$405$		0			0
$406$	6.56035			0.325585
$407$	−16.8116	+	18.9618i	−0.833322	+	0.939901i
$408$		0			0
$409$	33.1630	+	14.7651i	1.63981	+	0.730088i	0.999283	−	0.0378514i	$-0.0120514\pi$
$409$	33.1630	+	14.7651i	1.63981	+	0.730088i	0.640522	+	0.767940i	$0.278718\pi$
$410$	4.95788	−	5.50628i	0.244852	−	0.271936i
$411$		0			0
$412$	−2.15472	+	0.959341i	−0.106155	+	0.0472633i
$413$	2.06252	+	1.49851i	0.101490	+	0.0737369i
$414$		0			0
$415$	1.20652	+	3.71328i	0.0592256	+	0.182278i
$416$	−0.222255	−	2.11461i	−0.0108969	−	0.103677i
$417$		0			0
$418$	8.41329	−	0.0645566i	0.411508	−	0.00315757i
$419$	−2.99011	−	5.17903i	−0.146077	−	0.253012i	0.783697	−	0.621143i	$-0.213331\pi$
$419$	−2.99011	−	5.17903i	−0.146077	−	0.253012i	−0.929774	+	0.368131i	$0.879998\pi$
$420$		0			0
$421$	15.4734	+	3.28898i	0.754129	+	0.160295i	0.568907	−	0.822402i	$-0.307366\pi$
$421$	15.4734	+	3.28898i	0.754129	+	0.160295i	0.185222	+	0.982697i	$0.440700\pi$
$422$	−4.00242	+	12.3182i	−0.194835	+	0.599639i
$423$		0			0
$424$	3.31431	+	2.40798i	0.160957	+	0.116942i
$425$	8.62986	+	9.58444i	0.418610	+	0.464913i
$426$		0			0
$427$	46.9573	+	20.9067i	2.27242	+	1.01175i
$428$	−3.26175	−	5.64952i	−0.157663	−	0.273080i
$429$		0			0
$430$	−13.0177	+	22.5474i	−0.627771	+	1.08733i
$431$	24.8603	−	18.0620i	1.19748	−	0.870018i	0.203443	−	0.979087i	$-0.434787\pi$
$431$	24.8603	−	18.0620i	1.19748	−	0.870018i	0.994034	+	0.109069i	$0.0347868\pi$
$432$		0			0
$433$	4.24900	−	13.0771i	0.204194	−	0.628444i	−0.795552	−	0.605886i	$-0.792819\pi$
$433$	4.24900	−	13.0771i	0.204194	−	0.628444i	0.999746	−	0.0225582i	$-0.00718112\pi$
$434$	−41.8033	+	18.6120i	−2.00662	+	0.893405i
$435$		0			0
$436$	0.252282	−	0.0536242i	0.0120821	−	0.00256813i
$437$	−10.7818	+	11.9744i	−0.515763	+	0.572813i
$438$		0			0
$439$	−7.85940	+	13.6129i	−0.375109	+	0.649707i	−0.990343	−	0.138637i	$-0.955728\pi$
$439$	−7.85940	+	13.6129i	−0.375109	+	0.649707i	0.615235	+	0.788344i	$0.289061\pi$
$440$	39.1288	+	8.00379i	1.86539	+	0.381566i
$441$		0			0
$442$	−0.680139	+	0.494150i	−0.0323509	+	0.0235043i
$443$	−16.0314	−	3.40758i	−0.761674	−	0.161899i	−0.189331	−	0.981913i	$-0.560632\pi$
$443$	−16.0314	−	3.40758i	−0.761674	−	0.161899i	−0.572343	+	0.820014i	$0.693965\pi$
$444$		0			0
$445$	−1.36157	+	12.9545i	−0.0645447	+	0.614102i
$446$	−1.89700	+	18.0488i	−0.0898256	+	0.854634i
$447$		0			0
$448$	−38.4255	−	8.16760i	−1.81544	−	0.385883i
$449$	13.3887	−	9.72745i	0.631851	−	0.459067i	−0.225190	−	0.974315i	$-0.572300\pi$
$449$	13.3887	−	9.72745i	0.631851	−	0.459067i	0.857041	+	0.515248i	$0.172300\pi$
$450$		0			0
$451$	4.97421	−	2.26055i	0.234226	−	0.106445i
$452$	−4.20910	+	7.29038i	−0.197979	+	0.342910i
$453$		0			0
$454$	−6.14720	+	6.82715i	−0.288502	+	0.320414i
$455$	−10.2402	+	2.17662i	−0.480067	+	0.102041i
$456$		0			0
$457$	−4.10327	+	1.82689i	−0.191943	+	0.0854584i	−0.500457	−	0.865761i	$-0.666835\pi$
$457$	−4.10327	+	1.82689i	−0.191943	+	0.0854584i	0.308515	+	0.951220i	$0.400168\pi$
$458$	7.00175	−	21.5492i	0.327170	−	1.00693i
$459$		0			0
$460$	−15.6562	+	11.3749i	−0.729974	+	0.530357i
$461$	−4.49882	+	7.79219i	−0.209531	+	0.362918i	−0.951567	−	0.307442i	$-0.900527\pi$
$461$	−4.49882	+	7.79219i	−0.209531	+	0.362918i	0.742036	+	0.670360i	$0.233860\pi$
$462$		0			0
$463$	3.15033	+	5.45653i	0.146408	+	0.253586i	0.929897	−	0.367819i	$-0.119895\pi$
$463$	3.15033	+	5.45653i	0.146408	+	0.253586i	−0.783489	+	0.621405i	$0.786562\pi$
$464$	2.48363	+	1.10578i	0.115299	+	0.0513346i
$465$		0			0
$466$	−13.7528	−	15.2740i	−0.637086	−	0.707555i
$467$	7.41774	+	5.38930i	0.343252	+	0.249387i	0.746033	−	0.665909i	$-0.231956\pi$
$467$	7.41774	+	5.38930i	0.343252	+	0.249387i	−0.402781	+	0.915297i	$0.631956\pi$
$468$		0			0
$469$	10.5778	−	32.5551i	0.488438	−	1.50326i
$470$	2.32332	+	0.493836i	0.107167	+	0.0227790i
$471$		0			0
$472$	0.855587	+	1.48192i	0.0393816	+	0.0682109i
$473$	−15.4451	+	11.4036i	−0.710166	+	0.524338i
$474$		0			0
$475$	2.37370	+	22.5842i	0.108913	+	1.03623i
$476$	−1.20301	−	3.70249i	−0.0551399	−	0.169703i
$477$		0			0
$478$	−9.32856	−	6.77759i	−0.426678	−	0.310000i
$479$	−19.9327	+	8.87462i	−0.910750	+	0.405492i	−0.807978	−	0.589213i	$-0.799438\pi$
$479$	−19.9327	+	8.87462i	−0.910750	+	0.405492i	−0.102772	+	0.994705i	$0.532771\pi$
$480$		0			0
$481$	2.98331	−	3.31330i	0.136027	−	0.151074i
$482$	−18.0670	−	8.04394i	−0.822929	−	0.366391i
$483$		0			0
$484$	6.09477	+	4.28677i	0.277035	+	0.194853i
$485$	−61.5517			−2.79492
$486$		0			0
$487$	2.06718	+	6.36212i	0.0936727	+	0.288295i	0.986906	−	0.161299i	$-0.0515685\pi$
$487$	2.06718	+	6.36212i	0.0936727	+	0.288295i	−0.893233	+	0.449595i	$0.851568\pi$
$488$	23.0854	+	25.6389i	1.04503	+	1.16062i
$489$		0			0
$490$	−6.60306	+	62.8240i	−0.298296	+	2.83810i
$491$	26.4700	−	5.62637i	1.19457	−	0.253914i	0.432638	−	0.901568i	$-0.357583\pi$
$491$	26.4700	−	5.62637i	1.19457	−	0.253914i	0.761935	+	0.647653i	$0.224249\pi$
$492$		0			0
$493$	0.162833	+	1.54925i	0.00733363	+	0.0697748i
$494$	−1.48026			−0.0666000
$495$		0			0
$496$	−18.9631			−0.851467
$497$	−2.45424	−	23.3505i	−0.110088	−	1.04741i
$498$		0			0
$499$	−27.9112	+	5.93271i	−1.24948	+	0.265585i	−0.784719	−	0.619852i	$-0.787193\pi$
$499$	−27.9112	+	5.93271i	−1.24948	+	0.265585i	−0.464760	+	0.885437i	$0.653859\pi$
$500$	−1.46626	+	13.9505i	−0.0655730	+	0.623885i
$501$		0			0
$502$	−3.99718	−	4.43932i	−0.178403	−	0.198137i
$503$	3.95017	+	12.1574i	0.176129	+	0.542071i	0.999683	−	0.0251675i	$-0.00801191\pi$
$503$	3.95017	+	12.1574i	0.176129	+	0.542071i	−0.823554	+	0.567238i	$0.808012\pi$
$504$		0			0
$505$	59.5819			2.65136
$506$	27.2086	−	6.00194i	1.20957	−	0.266819i
$507$		0			0
$508$	0.271125	+	0.120713i	0.0120292	+	0.00535576i
$509$	−16.4548	+	18.2750i	−0.729348	+	0.810023i	−0.987755	−	0.156013i	$-0.950136\pi$
$509$	−16.4548	+	18.2750i	−0.729348	+	0.810023i	0.258407	+	0.966036i	$0.416803\pi$
$510$		0			0
$511$	1.59263	−	0.709087i	0.0704540	−	0.0313681i
$512$	−17.3379	−	12.5967i	−0.766233	−	0.556701i
$513$		0			0
$514$	−5.75485	−	17.7116i	−0.253836	−	0.781226i
$515$	1.42339	+	13.5427i	0.0627223	+	0.596763i
$516$		0			0
$517$	1.42486	+	1.01861i	0.0626651	+	0.0447983i
$518$	−20.1554	−	34.9102i	−0.885579	−	1.53387i
$519$		0			0
$520$	−6.87323	−	1.46095i	−0.301411	−	0.0640669i
$521$	4.75950	−	14.6482i	0.208518	−	0.641751i	−0.791033	−	0.611774i	$-0.790456\pi$
$521$	4.75950	−	14.6482i	0.208518	−	0.641751i	0.999551	−	0.0299778i	$-0.00954365\pi$
$522$		0			0
$523$	−15.9498	−	11.5882i	−0.697434	−	0.506716i	0.181661	−	0.983361i	$-0.441853\pi$
$523$	−15.9498	−	11.5882i	−0.697434	−	0.506716i	−0.879096	+	0.476646i	$0.841853\pi$
$524$	3.68190	+	4.08917i	0.160845	+	0.178636i
$525$		0			0
$526$	−24.3587	−	10.8452i	−1.06209	−	0.472873i
$527$	−5.43289	−	9.41004i	−0.236660	−	0.409908i
$528$		0			0
$529$	−15.1806	+	26.2936i	−0.660026	+	1.14320i
$530$	4.84121	−	3.51734i	0.210289	−	0.152784i
$531$		0			0
$532$	2.11820	−	6.51915i	0.0918356	−	0.282641i
$533$	−0.878177	+	0.390990i	−0.0380381	+	0.0169356i
$534$		0			0
$535$	−36.8397	+	7.83053i	−1.59272	+	0.338543i
$536$	15.3737	−	17.0742i	0.664041	−	0.737492i
$537$		0			0
$538$	−4.96300	+	8.59616i	−0.213970	+	0.370607i
$539$	−22.9808	+	40.5188i	−0.989854	+	1.74527i
$540$		0			0
$541$	−11.4472	+	8.31687i	−0.492153	+	0.357570i	−0.806012	−	0.591899i	$-0.798378\pi$
$541$	−11.4472	+	8.31687i	−0.492153	+	0.357570i	0.313858	+	0.949470i	$0.398378\pi$
$542$	27.2618	+	5.79467i	1.17099	+	0.248902i
$543$		0			0
$544$	0.477163	−	4.53990i	0.0204582	−	0.194647i
$545$	0.155650	−	1.48091i	0.00666729	−	0.0634350i
$546$		0			0
$547$	16.2162	+	3.44685i	0.693353	+	0.147377i	0.541092	−	0.840963i	$-0.318011\pi$
$547$	16.2162	+	3.44685i	0.693353	+	0.147377i	0.152261	+	0.988340i	$0.451344\pi$
$548$	−3.68018	+	2.67381i	−0.157209	+	0.114219i
$549$		0			0
$550$	19.3723	−	34.1564i	0.826037	−	1.45643i
$551$	−1.37143	+	2.37539i	−0.0584251	+	0.101195i
$552$		0			0
$553$	41.8697	−	46.5010i	1.78048	−	1.97742i
$554$	−9.68067	+	2.05769i	−0.411292	+	0.0874229i
$555$		0			0
$556$	1.85349	−	0.825225i	0.0786053	−	0.0349974i
$557$	−4.61081	+	14.1906i	−0.195366	+	0.601275i	0.804606	+	0.593809i	$0.202377\pi$
$557$	−4.61081	+	14.1906i	−0.195366	+	0.601275i	−0.999972	+	0.00746621i	$0.997623\pi$
$558$		0			0
$559$	2.73269	−	1.98541i	0.115580	−	0.0839741i
$560$	−19.6127	+	33.9701i	−0.828786	+	1.43550i
$561$		0			0
$562$	5.07265	+	8.78608i	0.213977	+	0.370618i
$563$	37.0582	+	16.4994i	1.56182	+	0.695366i	0.991980	−	0.126392i	$-0.0403398\pi$
$563$	37.0582	+	16.4994i	1.56182	+	0.695366i	0.569837	+	0.821758i	$0.307006\pi$
$564$		0			0
$565$	32.5208	+	36.1180i	1.36816	+	1.51950i
$566$	−18.6735	−	13.5671i	−0.784905	−	0.570267i
$567$		0			0
$568$	4.86987	−	14.9879i	0.204335	−	0.628879i
$569$	−9.82339	−	2.08803i	−0.411818	−	0.0875346i	−0.00265621	−	0.999996i	$-0.500845\pi$
$569$	−9.82339	−	2.08803i	−0.411818	−	0.0875346i	−0.409162	+	0.912462i	$0.634179\pi$
$570$		0			0
$571$	−17.8106	−	30.8488i	−0.745348	−	1.29098i	−0.950032	−	0.312153i	$-0.898950\pi$
$571$	−17.8106	−	30.8488i	−0.745348	−	1.29098i	0.204683	−	0.978828i	$-0.434384\pi$
$572$	−1.06648	−	0.762410i	−0.0445918	−	0.0318780i
$573$		0			0
$574$	0.908492	+	8.64372i	0.0379197	+	0.360782i
$575$	23.2390	+	71.5224i	0.969135	+	2.98269i
$576$		0			0
$577$	24.3890	+	17.7197i	1.01533	+	0.737680i	0.965320	−	0.261069i	$-0.0840750\pi$
$577$	24.3890	+	17.7197i	1.01533	+	0.737680i	0.0500090	+	0.998749i	$0.484075\pi$
$578$	16.2117	−	7.21789i	0.674316	−	0.300225i
$579$		0			0
$580$	−2.20427	+	2.44809i	−0.0915273	+	0.101651i
$581$	−4.18391	−	1.86280i	−0.173578	−	0.0772818i
$582$		0			0
$583$	4.30910	−	0.950542i	0.178465	−	0.0393674i
$584$	1.17014			0.0484209
$585$		0			0
$586$	0.605329	+	1.86301i	0.0250059	+	0.0769602i
$587$	13.7829	+	15.3075i	0.568883	+	0.631808i	0.957099	−	0.289760i	$-0.0935755\pi$
$587$	13.7829	+	15.3075i	0.568883	+	0.631808i	−0.388217	+	0.921568i	$0.626909\pi$
$588$		0			0
$589$	1.99983	−	19.0271i	0.0824015	−	0.783998i
$590$	2.44489	−	0.519678i	0.100655	−	0.0213948i
$591$		0			0
$592$	−1.74616	−	16.6136i	−0.0717669	−	0.682817i
$593$	43.5253			1.78737			0.893684	−	0.448697i	$-0.148112\pi$
$593$	43.5253			1.78737			0.893684	+	0.448697i	$0.148112\pi$
$594$		0			0
$595$	−22.4760			−0.921425
$596$	0.0181839	+	0.173009i	0.000744843	+	0.00708671i
$597$		0			0
$598$	−4.79498	+	1.01921i	−0.196082	+	0.0416784i
$599$	2.99598	−	28.5049i	0.122413	−	1.16468i	−0.744992	−	0.667074i	$-0.767547\pi$
$599$	2.99598	−	28.5049i	0.122413	−	1.16468i	0.867404	−	0.497604i	$-0.165787\pi$
$600$		0			0
$601$	−12.4932	−	13.8752i	−0.509610	−	0.565979i	0.432349	−	0.901706i	$-0.357685\pi$
$601$	−12.4932	−	13.8752i	−0.509610	−	0.565979i	−0.941959	+	0.335727i	$0.891018\pi$
$602$	−9.43733	−	29.0451i	−0.384637	−	1.18379i
$603$		0			0
$604$	4.29940			0.174940
$605$	34.4115	−	25.8174i	1.39902	−	1.04963i
$606$		0			0
$607$	28.9007	+	12.8674i	1.17304	+	0.522272i	0.898359	−	0.439263i	$-0.144760\pi$
$607$	28.9007	+	12.8674i	1.17304	+	0.522272i	0.274684	+	0.961535i	$0.411427\pi$
$608$	5.37824	−	5.97314i	0.218116	−	0.242243i
$609$		0			0
$610$	46.0380	−	20.4975i	1.86403	−	0.829918i
$611$	−0.249303	−	0.181130i	−0.0100857	−	0.00732772i
$612$		0			0
$613$	10.5896	+	32.5913i	0.427709	+	1.31635i	0.900377	+	0.435111i	$0.143291\pi$
$613$	10.5896	+	32.5913i	0.427709	+	1.31635i	−0.472668	+	0.881241i	$0.656709\pi$
$614$	−2.37884	−	22.6332i	−0.0960023	−	0.913401i
$615$		0			0
$616$	−37.6891	+	27.8270i	−1.51854	+	1.12118i
$617$	−9.68326	−	16.7719i	−0.389833	−	0.675211i	0.602594	−	0.798048i	$-0.294134\pi$
$617$	−9.68326	−	16.7719i	−0.389833	−	0.675211i	−0.992427	+	0.122837i	$0.960801\pi$
$618$		0			0
$619$	−36.8623	−	7.83533i	−1.48162	−	0.314928i	−0.605045	−	0.796191i	$-0.706845\pi$
$619$	−36.8623	−	7.83533i	−1.48162	−	0.314928i	−0.876576	+	0.481263i	$0.840178\pi$
$620$	7.10050	−	21.8531i	0.285163	−	0.877641i
$621$		0			0
$622$	25.3886	+	18.4459i	1.01799	+	0.739614i
$623$	−10.2239	−	11.3548i	−0.409613	−	0.454922i
$624$		0			0
$625$	26.9594	+	12.0031i	1.07838	+	0.480124i
$626$	5.19137	+	8.99171i	0.207489	+	0.359381i
$627$		0			0
$628$	−3.07764	+	5.33063i	−0.122811	+	0.212715i
$629$	7.74391	−	5.62628i	0.308770	−	0.224334i
$630$		0			0
$631$	−12.6020	+	38.7850i	−0.501678	+	1.54401i	0.304606	+	0.952478i	$0.401475\pi$
$631$	−12.6020	+	38.7850i	−0.501678	+	1.54401i	−0.806284	+	0.591528i	$0.798525\pi$
$632$	38.3682	−	17.0826i	1.52621	−	0.679511i
$633$		0			0
$634$	28.1838	−	5.99066i	1.11932	−	0.237919i
$635$	1.14652	−	1.27334i	0.0454983	−	0.0505309i
$636$		0			0
$637$	4.09777	−	7.09755i	0.162360	−	0.281215i
$638$	4.31797	−	1.96232i	0.170950	−	0.0776891i
$639$		0			0
$640$	−8.10118	+	5.88585i	−0.320227	+	0.232659i
$641$	−46.0289	−	9.78374i	−1.81803	−	0.386435i	−0.832241	−	0.554414i	$-0.812943\pi$
$641$	−46.0289	−	9.78374i	−1.81803	−	0.386435i	−0.985791	+	0.167979i	$0.946276\pi$
$642$		0			0
$643$	2.00932	−	19.1174i	0.0792398	−	0.753916i	−0.880693	−	0.473687i	$-0.842923\pi$
$643$	2.00932	−	19.1174i	0.0792398	−	0.753916i	0.959933	−	0.280229i	$-0.0904105\pi$
$644$	2.37282	−	22.5759i	0.0935021	−	0.889613i
$645$		0			0
$646$	−3.10854	−	0.660741i	−0.122304	−	0.0259965i
$647$	34.9606	−	25.4004i	1.37444	−	0.998593i	0.377070	−	0.926185i	$-0.376932\pi$
$647$	34.9606	−	25.4004i	1.37444	−	0.998593i	0.997375	−	0.0724077i	$-0.0230683\pi$
$648$		0			0
$649$	1.80577	+	0.369370i	0.0708827	+	0.0144990i
$650$	−3.45432	+	5.98306i	−0.135490	+	0.234675i
$651$		0			0
$652$	−2.80667	+	3.11713i	−0.109918	+	0.122076i
$653$	−21.2859	+	4.52446i	−0.832982	+	0.177056i	−0.604614	−	0.796519i	$-0.706672\pi$
$653$	−21.2859	+	4.52446i	−0.832982	+	0.177056i	−0.228369	+	0.973575i	$0.573339\pi$
$654$		0			0
$655$	29.0217	−	12.9213i	1.13397	−	0.504876i
$656$	−1.11301	+	3.42548i	−0.0434556	+	0.133742i
$657$		0			0
$658$	−2.25405	+	1.63766i	−0.0878718	+	0.0638426i
$659$	−7.60422	+	13.1709i	−0.296218	+	0.513065i	−0.975268	−	0.221028i	$-0.929059\pi$
$659$	−7.60422	+	13.1709i	−0.296218	+	0.513065i	0.679049	+	0.734093i	$0.262392\pi$
$660$		0			0
$661$	8.83930	+	15.3101i	0.343809	+	0.595495i	0.985137	−	0.171772i	$-0.0549494\pi$
$661$	8.83930	+	15.3101i	0.343809	+	0.595495i	−0.641328	+	0.767267i	$0.721616\pi$
$662$	9.77268	+	4.35108i	0.379826	+	0.169109i
$663$		0			0
$664$	−2.05691	−	2.28443i	−0.0798237	−	0.0886532i
$665$	−32.0165	−	23.2613i	−1.24155	−	0.902036i
$666$		0			0
$667$	−2.80694	+	8.63886i	−0.108685	+	0.334498i
$668$	−9.03890	−	1.92128i	−0.349726	−	0.0743365i
$669$		0			0
$670$	−16.7802	−	29.0642i	−0.648276	−	1.12285i
$671$	37.1605	−	0.285139i	1.43457	−	0.0110077i
$672$		0			0
$673$	−1.49275	−	14.2025i	−0.0575412	−	0.547468i	−0.984879	−	0.173243i	$-0.944575\pi$
$673$	−1.49275	−	14.2025i	−0.0575412	−	0.547468i	0.927338	−	0.374225i	$-0.122091\pi$
$674$	5.03898	+	15.5084i	0.194094	+	0.597360i
$675$		0			0
$676$	−6.93772	−	5.04055i	−0.266835	−	0.193867i
$677$	28.0682	−	12.4968i	1.07875	−	0.480290i	0.211099	−	0.977465i	$-0.432296\pi$
$677$	28.0682	−	12.4968i	1.07875	−	0.480290i	0.867651	+	0.497175i	$0.165629\pi$
$678$		0			0
$679$	48.3117	−	53.6555i	1.85403	−	2.05911i
$680$	−13.7817	−	6.13599i	−0.528502	−	0.235304i
$681$		0			0
$682$	−21.9474	+	24.7544i	−0.840409	+	0.947895i
$683$	41.7448			1.59732			0.798660	−	0.601782i	$-0.205542\pi$
$683$	41.7448			1.59732			0.798660	+	0.601782i	$0.205542\pi$
$684$		0			0
$685$	8.11567	+	24.9775i	0.310084	+	0.954340i
$686$	−24.8704	−	27.6214i	−0.949557	−	1.05459i
$687$		0			0
$688$	1.32291	−	12.5866i	0.0504355	−	0.479861i
$689$	−0.759394	+	0.161414i	−0.0289306	+	0.00614939i
$690$		0			0
$691$	2.83314	+	26.9555i	0.107778	+	1.02544i	0.906059	+	0.423152i	$0.139076\pi$
$691$	2.83314	+	26.9555i	0.107778	+	1.02544i	−0.798281	+	0.602285i	$0.794257\pi$
$692$	−14.3765			−0.546513
$693$		0			0
$694$	−1.70435			−0.0646961
$695$	−1.22440	−	11.6494i	−0.0464443	−	0.441888i
$696$		0			0
$697$	−2.01870	+	0.429087i	−0.0764636	+	0.0162528i
$698$	0.242686	−	2.30901i	0.00918581	−	0.0873971i
$699$		0			0
$700$	−21.4068	−	23.7746i	−0.809100	−	0.898596i
$701$	10.8877	+	33.5089i	0.411223	+	1.26561i	0.915586	+	0.402123i	$0.131728\pi$
$701$	10.8877	+	33.5089i	0.411223	+	1.26561i	−0.504363	+	0.863492i	$0.668272\pi$
$702$		0			0
$703$	16.8539			0.635656
$704$	−27.7345	+	6.11793i	−1.04528	+	0.230578i
$705$		0			0
$706$	−6.00717	−	2.67456i	−0.226083	−	0.100659i
$707$	−46.7656	+	51.9384i	−1.75880	+	1.95335i
$708$		0			0
$709$	−36.6923	+	16.3365i	−1.37801	+	0.613529i	−0.956082	−	0.293101i	$-0.905313\pi$
$709$	−36.6923	+	16.3365i	−1.37801	+	0.613529i	−0.421927	+	0.906630i	$0.638646\pi$
$710$	−18.6232	−	13.5305i	−0.698915	−	0.507792i
$711$		0			0
$712$	−3.16915	−	9.75363i	−0.118769	−	0.365533i
$713$	−6.62274	−	63.0112i	−0.248024	−	2.35979i
$714$		0			0
$715$	−6.08895	+	4.49566i	−0.227714	+	0.168128i
$716$	4.91269	+	8.50903i	0.183596	+	0.317997i
$717$		0			0
$718$	12.3461	+	2.62424i	0.460751	+	0.0979357i
$719$	−0.0121049	+	0.0372552i	−0.000451438	+	0.00138938i	−0.951282	−	0.308322i	$-0.900233\pi$
$719$	−0.0121049	+	0.0372552i	−0.000451438	+	0.00138938i	0.950831	+	0.309712i	$0.100233\pi$
$720$		0			0
$721$	−12.9226	−	9.38881i	−0.481262	−	0.349658i
$722$	10.8769	+	12.0800i	0.404795	+	0.449570i
$723$		0			0
$724$	−0.180163	−	0.0802136i	−0.00669569	−	0.00298111i
$725$	6.40074	+	11.0864i	0.237718	+	0.411739i
$726$		0			0
$727$	6.61792	−	11.4626i	0.245445	−	0.425123i	−0.716812	−	0.697267i	$-0.754399\pi$
$727$	6.61792	−	11.4626i	0.245445	−	0.425123i	0.962257	+	0.272144i	$0.0877326\pi$
$728$	6.66830	−	4.84480i	0.247144	−	0.179560i
$729$		0			0
$730$	0.528180	−	1.62557i	0.0195488	−	0.0601651i
$731$	6.62487	−	2.94958i	0.245030	−	0.109094i
$732$		0			0
$733$	−32.1144	+	6.82613i	−1.18617	+	0.252129i	−0.758420	−	0.651767i	$-0.774028\pi$
$733$	−32.1144	+	6.82613i	−1.18617	+	0.252129i	−0.427753	+	0.903895i	$0.640695\pi$
$734$	13.9063	−	15.4446i	0.513292	−	0.570069i
$735$		0			0
$736$	13.3090	−	23.0518i	0.490575	−	0.849701i
$737$	−2.77561	−	24.5916i	−0.102241	−	0.905842i
$738$		0			0
$739$	−5.17751	+	3.76168i	−0.190458	+	0.138376i	−0.678928	−	0.734205i	$-0.737555\pi$
$739$	−5.17751	+	3.76168i	−0.190458	+	0.138376i	0.488470	+	0.872581i	$0.337555\pi$
$740$	19.7994	+	4.20850i	0.727842	+	0.154708i
$741$		0			0
$742$	−0.733722	+	6.98090i	−0.0269358	+	0.256277i
$743$	5.30299	−	50.4546i	0.194548	−	1.85100i	−0.266765	−	0.963762i	$-0.585955\pi$
$743$	5.30299	−	50.4546i	0.194548	−	1.85100i	0.461313	−	0.887237i	$-0.347379\pi$
$744$		0			0
$745$	0.982401	+	0.208816i	0.0359924	+	0.00765042i
$746$	−22.7708	+	16.5440i	−0.833699	+	0.605718i
$747$		0			0
$748$	−1.89930	−	2.07711i	−0.0694451	−	0.0759465i
$749$	22.0894	−	38.2599i	0.807128	−	1.39799i
$750$		0			0
$751$	−15.7958	+	17.5430i	−0.576397	+	0.640153i	−0.958881	−	0.283809i	$-0.908402\pi$
$751$	−15.7958	+	17.5430i	−0.576397	+	0.640153i	0.382484	+	0.923962i	$0.375069\pi$
$752$	−1.12937	+	0.240056i	−0.0411841	+	0.00875394i
$753$		0			0
$754$	−0.762321	+	0.339407i	−0.0277621	+	0.0123605i
$755$	7.67046	−	23.6073i	0.279157	−	0.859156i
$756$		0			0
$757$	−39.2432	+	28.5118i	−1.42632	+	1.03628i	−0.435629	+	0.900126i	$0.643474\pi$
$757$	−39.2432	+	28.5118i	−1.42632	+	1.03628i	−0.990688	+	0.136154i	$0.956526\pi$
$758$	5.36329	−	9.28949i	0.194803	−	0.337409i
$759$		0			0
$760$	−13.2812	−	23.0038i	−0.481761	−	0.834435i
$761$	12.0945	+	5.38484i	0.438427	+	0.195200i	0.614066	−	0.789254i	$-0.289533\pi$
$761$	12.0945	+	5.38484i	0.438427	+	0.195200i	−0.175640	+	0.984455i	$0.556199\pi$
$762$		0			0
$763$	1.16876	+	1.29804i	0.0423119	+	0.0469922i
$764$	0.248331	+	0.180423i	0.00898429	+	0.00652747i
$765$		0			0
$766$	−8.85437	+	27.2509i	−0.319921	+	0.984616i
$767$	−0.317195	−	0.0674219i	−0.0114532	−	0.00243446i
$768$		0			0
$769$	11.5333	+	19.9762i	0.415901	+	0.720362i	0.995523	−	0.0945241i	$-0.0301330\pi$
$769$	11.5333	+	19.9762i	0.415901	+	0.720362i	−0.579622	+	0.814886i	$0.696800\pi$
$770$	21.6454	+	64.9186i	0.780047	+	2.33950i
$771$		0			0
$772$	−1.24202	−	11.8170i	−0.0447013	−	0.425305i
$773$	2.88942	+	8.89271i	0.103925	+	0.319848i	0.989477	−	0.144693i	$-0.0462193\pi$
$773$	2.88942	+	8.89271i	0.103925	+	0.319848i	−0.885552	+	0.464541i	$0.846219\pi$
$774$		0			0
$775$	−72.2389	−	52.4846i	−2.59490	−	1.88530i
$776$	44.2715	−	19.7109i	1.58925	−	0.707581i
$777$		0			0
$778$	−17.1782	+	19.0784i	−0.615869	+	0.683992i
$779$	−3.31967	−	1.47801i	−0.118939	−	0.0529552i
$780$		0			0
$781$	−8.59993	−	14.6350i	−0.307730	−	0.523682i
$782$	−10.5244			−0.376352
$783$		0			0
$784$	−9.48906	−	29.2043i	−0.338895	−	1.04301i
$785$	23.7788	+	26.4090i	0.848701	+	0.942578i
$786$		0			0
$787$	2.86673	−	27.2751i	0.102188	−	0.972253i	−0.816520	−	0.577317i	$-0.804100\pi$
$787$	2.86673	−	27.2751i	0.102188	−	0.972253i	0.918708	−	0.394937i	$-0.129233\pi$
$788$	−11.7084	+	2.48870i	−0.417095	+	0.0886563i
$789$		0			0
$790$	−6.41264	−	61.0122i	−0.228152	−	2.17072i
$791$	−57.0101			−2.02704
$792$		0			0
$793$	−6.53813			−0.232176
$794$	4.70572	+	44.7719i	0.167000	+	1.58889i
$795$		0			0
$796$	−8.75996	+	1.86199i	−0.310489	+	0.0659964i
$797$	−4.17551	+	39.7274i	−0.147904	+	1.40722i	0.628906	+	0.777481i	$0.283503\pi$
$797$	−4.17551	+	39.7274i	−0.147904	+	1.40722i	−0.776811	+	0.629734i	$0.783164\pi$
$798$		0			0
$799$	−0.442687	−	0.491653i	−0.0156611	−	0.0173934i
$800$	−11.5922	−	35.6772i	−0.409847	−	1.26138i
$801$		0			0
$802$	38.2160			1.34945
$803$	0.836159	−	0.943102i	0.0295074	−	0.0332813i
$804$		0			0
$805$	−119.727	−	53.3058i	−4.21981	−	1.87878i
$806$	3.89468	−	4.32548i	0.137184	−	0.152358i
$807$		0			0
$808$	−42.8547	+	19.0801i	−1.50762	+	0.671237i
$809$	9.77203	+	7.09979i	0.343566	+	0.249615i	0.746165	−	0.665761i	$-0.231893\pi$
$809$	9.77203	+	7.09979i	0.343566	+	0.249615i	−0.402599	+	0.915377i	$0.631893\pi$
$810$		0			0
$811$	−8.48931	−	26.1274i	−0.298100	−	0.917458i	−0.982162	−	0.188034i	$-0.939788\pi$
$811$	−8.48931	−	26.1274i	−0.298100	−	0.917458i	0.684062	−	0.729424i	$-0.260212\pi$
$812$	−0.403914	−	3.84299i	−0.0141746	−	0.134862i
$813$		0			0
$814$	−23.7084	−	16.9488i	−0.830980	−	0.594054i
$815$	12.1083	+	20.9721i	0.424134	+	0.734622i
$816$		0			0
$817$	12.4896	+	2.65475i	0.436956	+	0.0928780i
$818$	−12.9009	+	39.7050i	−0.451071	+	1.38825i
$819$		0			0
$820$	−3.53078	−	2.56526i	−0.123300	−	0.0895828i
$821$	−10.4369	−	11.5914i	−0.364251	−	0.404542i	0.532962	−	0.846139i	$-0.321079\pi$
$821$	−10.4369	−	11.5914i	−0.364251	−	0.404542i	−0.897213	+	0.441597i	$0.854412\pi$
$822$		0			0
$823$	−3.74282	−	1.66641i	−0.130467	−	0.0580875i	0.340465	−	0.940257i	$-0.389416\pi$
$823$	−3.74282	−	1.66641i	−0.130467	−	0.0580875i	−0.470932	+	0.882170i	$0.656082\pi$
$824$	−5.36062	−	9.28486i	−0.186746	−	0.323453i
$825$		0			0
$826$	−1.46597	+	2.53914i	−0.0510078	+	0.0883481i
$827$	19.9149	−	14.4690i	0.692509	−	0.503137i	−0.184975	−	0.982743i	$-0.559220\pi$
$827$	19.9149	−	14.4690i	0.692509	−	0.503137i	0.877484	+	0.479606i	$0.159220\pi$
$828$		0			0
$829$	9.85566	−	30.3326i	0.342301	−	1.05350i	−0.620711	−	0.784039i	$-0.713156\pi$
$829$	9.85566	−	30.3326i	0.342301	−	1.05350i	0.963013	−	0.269456i	$-0.0868439\pi$
$830$	−4.10200	+	1.82633i	−0.142383	+	0.0633928i
$831$		0			0
$832$	4.88765	−	1.03890i	0.169449	−	0.0360175i
$833$	11.7734	−	13.0757i	0.407926	−	0.453047i
$834$		0			0
$835$	−26.6755	+	46.2033i	−0.923143	+	1.59893i
$836$	−0.555815	−	4.92445i	−0.0192233	−	0.170316i
$837$		0			0
$838$	5.56404	−	4.04251i	0.192207	−	0.139646i
$839$	17.1753	+	3.65072i	0.592956	+	0.126037i	0.494609	−	0.869115i	$-0.335311\pi$
$839$	17.1753	+	3.65072i	0.592956	+	0.126037i	0.0983470	+	0.995152i	$0.468644\pi$
$840$		0			0
$841$	2.86970	−	27.3034i	0.0989552	−	0.941496i
$842$	−1.90165	+	18.0930i	−0.0655353	+	0.623527i
$843$		0			0
$844$	7.46229	+	1.58616i	0.256862	+	0.0545978i
$845$	−40.0542	+	29.1011i	−1.37791	+	1.00111i
$846$		0			0
$847$	−4.50401	+	50.2609i	−0.154759	+	1.72699i
$848$	−1.45444	+	2.51916i	−0.0499457	+	0.0865084i
$849$		0			0
$850$	−9.92474	+	11.0225i	−0.340416	+	0.378070i
$851$	54.5946	−	11.6044i	1.87148	−	0.397795i
$852$		0			0
$853$	36.1244	−	16.0836i	1.23688	−	0.550693i	0.319074	−	0.947730i	$-0.396628\pi$
$853$	36.1244	−	16.0836i	1.23688	−	0.550693i	0.917803	+	0.397037i	$0.129961\pi$
$854$	−18.2671	+	56.2204i	−0.625088	+	1.92382i
$855$		0			0
$856$	23.9896	−	17.4295i	0.819949	−	0.595728i
$857$	−1.77266	+	3.07034i	−0.0605529	+	0.104881i	−0.894713	−	0.446642i	$-0.852620\pi$
$857$	−1.77266	+	3.07034i	−0.0605529	+	0.104881i	0.834160	+	0.551523i	$0.185953\pi$
$858$		0			0
$859$	12.1359	+	21.0200i	0.414071	+	0.717192i	0.995330	−	0.0965262i	$-0.0307731\pi$
$859$	12.1359	+	21.0200i	0.414071	+	0.717192i	−0.581259	+	0.813718i	$0.697440\pi$
$860$	14.0095	+	6.23744i	0.477721	+	0.212695i
$861$		0			0
$862$	23.6469	+	26.2625i	0.805416	+	0.894506i
$863$	−33.7842	−	24.5457i	−1.15003	−	0.835544i	−0.161543	−	0.986866i	$-0.551647\pi$
$863$	−33.7842	−	24.5457i	−1.15003	−	0.835544i	−0.988485	+	0.151322i	$0.951647\pi$
$864$		0			0
$865$	−25.6488	+	78.9389i	−0.872086	+	2.68400i
$866$	15.4676	+	3.28774i	0.525611	+	0.111722i
$867$		0			0
$868$	13.4765	+	23.3420i	0.457423	+	0.792279i
$869$	13.6490	−	43.1306i	0.463011	−	1.46310i
$870$		0			0
$871$	0.455123	+	4.33020i	0.0154212	+	0.146723i
$872$	0.362284	+	1.11500i	0.0122685	+	0.0377585i
$873$		0			0
$874$	−14.9918	−	10.8922i	−0.507104	−	0.368433i
$875$	−86.7836	+	38.6386i	−2.93382	+	1.30622i
$876$		0			0
$877$	9.70730	−	10.7810i	0.327792	−	0.364050i	−0.556611	−	0.830773i	$-0.687899\pi$
$877$	9.70730	−	10.7810i	0.327792	−	0.364050i	0.884404	+	0.466723i	$0.154565\pi$
$878$	−16.5145	−	7.35271i	−0.557336	−	0.248142i
$879$		0			0
$880$	−2.74781	+	28.2254i	−0.0926288	+	0.951478i
$881$	24.6860			0.831693			0.415847	−	0.909435i	$-0.363485\pi$
$881$	24.6860			0.831693			0.415847	+	0.909435i	$0.363485\pi$
$882$		0			0
$883$	−10.6238	−	32.6968i	−0.357520	−	1.10033i	−0.954534	−	0.298103i	$-0.903646\pi$
$883$	−10.6238	−	32.6968i	−0.357520	−	1.10033i	0.597014	−	0.802231i	$-0.296354\pi$
$884$	0.331344	+	0.367994i	0.0111443	+	0.0123770i
$885$		0			0
$886$	1.97023	−	18.7455i	0.0661911	−	0.629766i
$887$	−10.4134	+	2.21344i	−0.349648	+	0.0743200i	−0.379388	−	0.925238i	$-0.623865\pi$
$887$	−10.4134	+	2.21344i	−0.349648	+	0.0743200i	0.0297400	+	0.999558i	$0.490532\pi$
$888$		0			0
$889$	0.210091	+	1.99888i	0.00704621	+	0.0670402i
$890$	−14.9803			−0.502141
$891$		0			0
$892$	10.6896			0.357914
$893$	−0.121764	−	1.15850i	−0.00407466	−	0.0387678i
$894$		0			0
$895$	55.4862	−	11.7939i	1.85470	−	0.394228i
$896$	1.22780	−	11.6817i	0.0410178	−	0.390258i
$897$		0			0
$898$	12.7352	+	14.1439i	0.424980	+	0.471988i
$899$	−3.33281	−	10.2573i	−0.111155	−	0.342101i
$900$		0			0
$901$	−1.66678			−0.0555284
$902$	3.18346	+	5.41748i	0.105998	+	0.180382i
$903$		0			0
$904$	−34.9570	−	15.5639i	−1.16265	−	0.517647i
$905$	−0.761863	+	0.846134i	−0.0253252	+	0.0281264i
$906$		0			0
$907$	40.1229	−	17.8638i	1.33226	−	0.593159i	0.387785	−	0.921750i	$-0.373240\pi$
$907$	40.1229	−	17.8638i	1.33226	−	0.593159i	0.944472	+	0.328591i	$0.106574\pi$
$908$	4.37775	+	3.18062i	0.145281	+	0.105553i
$909$		0			0
$910$	−3.72050	−	11.4505i	−0.123333	−	0.379581i
$911$	5.00348	+	47.6050i	0.165773	+	1.57722i	0.688829	+	0.724924i	$0.258125\pi$
$911$	5.00348	+	47.6050i	0.165773	+	1.57722i	−0.523056	+	0.852298i	$0.675208\pi$
$912$		0			0
$913$	−3.31101	+	0.0254059i	−0.109579	+	0.000840814i
$914$	−2.58276	−	4.47348i	−0.0854302	−	0.147969i
$915$		0			0
$916$	−13.0544	−	2.77479i	−0.431329	−	0.0916818i
$917$	−11.5153	+	35.4405i	−0.380269	+	1.17035i
$918$		0			0
$919$	−21.9642	−	15.9579i	−0.724531	−	0.526403i	0.163297	−	0.986577i	$-0.447787\pi$
$919$	−21.9642	−	15.9579i	−0.724531	−	0.526403i	−0.887829	+	0.460174i	$0.847787\pi$
$920$	−58.8606	−	65.3713i	−1.94058	−	2.15523i
$921$		0			0
$922$	−9.45309	−	4.20879i	−0.311321	−	0.138609i
$923$	1.49325	+	2.58639i	0.0491509	+	0.0851319i
$924$		0			0
$925$	39.3301	−	68.1218i	1.29317	−	2.23983i
$926$	−5.86217	+	4.25911i	−0.192643	+	0.139963i
$927$		0			0
$928$	1.40017	−	4.30929i	0.0459629	−	0.141459i
$929$	32.8058	−	14.6061i	1.07632	−	0.479211i	0.209492	−	0.977810i	$-0.432819\pi$
$929$	32.8058	−	14.6061i	1.07632	−	0.479211i	0.866832	+	0.498600i	$0.166152\pi$
$930$		0			0
$931$	30.3036	−	6.44123i	0.993161	−	0.211103i
$932$	−8.10062	+	8.99665i	−0.265345	+	0.294695i
$933$		0			0
$934$	−5.27228	+	9.13186i	−0.172514	+	0.298804i
$935$	−14.7935	+	6.72298i	−0.483800	+	0.219865i
$936$		0			0
$937$	35.7303	−	25.9596i	1.16726	−	0.848062i	0.176579	−	0.984287i	$-0.443497\pi$
$937$	35.7303	−	25.9596i	1.16726	−	0.848062i	0.990678	+	0.136225i	$0.0434970\pi$
$938$	38.5064	+	8.18478i	1.25728	+	0.267243i
$939$		0			0
$940$	0.146240	−	1.39138i	0.00476982	−	0.0453818i
$941$	−2.04249	+	19.4330i	−0.0665833	+	0.633498i	0.909441	+	0.415834i	$0.136510\pi$
$941$	−2.04249	+	19.4330i	−0.0665833	+	0.633498i	−0.976024	+	0.217664i	$0.930156\pi$
$942$		0			0
$943$	−11.7710	−	2.50201i	−0.383317	−	0.0814765i
$944$	−0.982976	+	0.714174i	−0.0319931	+	0.0232444i
$945$		0			0
$946$	−14.8995	−	16.2944i	−0.484425	−	0.529777i
$947$	−15.2771	+	26.4607i	−0.496439	+	0.859858i	−0.999992	−	0.00410698i	$-0.998693\pi$
$947$	−15.2771	+	26.4607i	−0.496439	+	0.859858i	0.503553	+	0.863965i	$0.332026\pi$
$948$		0			0
$949$	−0.148381	+	0.164793i	−0.00481664	+	0.00534942i
$950$	−25.5452	+	5.42981i	−0.828797	+	0.176166i
$951$		0			0
$952$	16.1660	−	7.19757i	0.523943	−	0.233274i
$953$	−4.51629	+	13.8997i	−0.146297	+	0.450256i	−0.997175	−	0.0751068i	$-0.976070\pi$
$953$	−4.51629	+	13.8997i	−0.146297	+	0.450256i	0.850879	+	0.525362i	$0.176070\pi$
$954$		0			0
$955$	1.43371	−	1.04165i	0.0463938	−	0.0337070i
$956$	−3.39590	+	5.88186i	−0.109831	+	0.190233i
$957$		0			0
$958$	−12.5465	−	21.7311i	−0.405358	−	0.702101i
$959$	−28.1432	−	12.5302i	−0.908791	−	0.404620i
$960$		0			0
$961$	29.5945	+	32.8680i	0.954660	+	1.06026i
$962$	4.14820	+	3.01385i	0.133743	+	0.0971703i
$963$		0			0
$964$	−3.59969	+	11.0787i	−0.115938	+	0.356821i
$965$	−67.1011	−	14.2628i	−2.16006	−	0.459135i
$966$		0			0
$967$	−4.38762	−	7.59958i	−0.141096	−	0.244386i	0.786813	−	0.617191i	$-0.211729\pi$
$967$	−4.38762	−	7.59958i	−0.141096	−	0.244386i	−0.927910	+	0.372805i	$0.878396\pi$
$968$	−16.4831	+	29.5890i	−0.529786	+	0.951028i
$969$		0			0
$970$	−7.39928	−	70.3995i	−0.237577	−	2.26039i
$971$	3.46730	+	10.6713i	0.111271	+	0.342457i	0.991151	−	0.132739i	$-0.0423771\pi$
$971$	3.46730	+	10.6713i	0.111271	+	0.342457i	−0.879880	+	0.475196i	$0.842377\pi$
$972$		0			0
$973$	11.1160	+	8.07626i	0.356363	+	0.258913i
$974$	−7.02814	+	3.12913i	−0.225196	+	0.100264i
$975$		0			0
$976$	−16.3918	+	18.2050i	−0.524690	+	0.582727i
$977$	28.7475	+	12.7992i	0.919715	+	0.409483i	0.811305	−	0.584623i	$-0.198757\pi$
$977$	28.7475	+	12.7992i	0.919715	+	0.409483i	0.108410	+	0.994106i	$0.465424\pi$
$978$		0			0
$979$	−10.1258	−	4.41549i	−0.323620	−	0.141120i
$980$	37.2082			1.18857
$981$		0			0
$982$	9.61715	+	29.5986i	0.306896	+	0.944528i
$983$	−29.5412	−	32.8088i	−0.942217	−	1.04644i	−0.998845	−	0.0480425i	$-0.984702\pi$
$983$	−29.5412	−	32.8088i	−0.942217	−	1.04644i	0.0566285	−	0.998395i	$-0.481965\pi$
$984$		0			0
$985$	−7.22369	+	68.7288i	−0.230166	+	2.18988i
$986$	−1.75238	+	0.372479i	−0.0558070	+	0.0118621i
$987$		0			0
$988$	0.0911381	+	0.867121i	0.00289949	+	0.0275868i
$989$	42.2854			1.34460
$990$		0			0
$991$	10.0638			0.319687			0.159844	−	0.987142i	$-0.448901\pi$
$991$	10.0638			0.319687			0.159844	+	0.987142i	$0.448901\pi$
$992$	3.30359	+	31.4316i	0.104889	+	0.997954i
$993$		0			0
$994$	26.4120	−	5.61405i	0.837738	−	0.178067i
$995$	−5.40460	+	51.4213i	−0.171337	+	1.63017i
$996$		0			0
$997$	33.1080	+	36.7702i	1.04854	+	1.16452i	0.986045	+	0.166478i	$0.0532394\pi$
$997$	33.1080	+	36.7702i	1.04854	+	1.16452i	0.0624960	+	0.998045i	$0.480094\pi$
$998$	−10.1408	−	31.2101i	−0.321001	−	0.987940i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.n.l.784.8		96
3.2	odd	2	inner	891.2.n.l.784.5		96
9.2	odd	6		891.2.f.g.487.5	✓	48
9.4	even	3	inner	891.2.n.l.190.5		96
9.5	odd	6	inner	891.2.n.l.190.8		96
9.7	even	3		891.2.f.g.487.8	yes	48
11.4	even	5	inner	891.2.n.l.136.5		96
33.26	odd	10	inner	891.2.n.l.136.8		96
99.2	even	30		9801.2.a.cq.1.9		24
99.4	even	15	inner	891.2.n.l.433.8		96
99.20	odd	30		9801.2.a.cr.1.16		24
99.59	odd	30	inner	891.2.n.l.433.5		96
99.70	even	15		891.2.f.g.730.8	yes	48
99.79	odd	30		9801.2.a.cq.1.16		24
99.92	odd	30		891.2.f.g.730.5	yes	48
99.97	even	15		9801.2.a.cr.1.9		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
891.2.f.g.487.5	✓	48	9.2	odd	6
891.2.f.g.487.8	yes	48	9.7	even	3
891.2.f.g.730.5	yes	48	99.92	odd	30
891.2.f.g.730.8	yes	48	99.70	even	15
891.2.n.l.136.5		96	11.4	even	5	inner
891.2.n.l.136.8		96	33.26	odd	10	inner
891.2.n.l.190.5		96	9.4	even	3	inner
891.2.n.l.190.8		96	9.5	odd	6	inner
891.2.n.l.433.5		96	99.59	odd	30	inner
891.2.n.l.433.8		96	99.4	even	15	inner
891.2.n.l.784.5		96	3.2	odd	2	inner
891.2.n.l.784.8		96	1.1	even	1	trivial
9801.2.a.cq.1.9		24	99.2	even	30
9801.2.a.cq.1.16		24	99.79	odd	30
9801.2.a.cr.1.9		24	99.97	even	15
9801.2.a.cr.1.16		24	99.20	odd	30

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:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	891.n (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.120212 + 1.14375i) q^{2} +(0.662593 - 0.140839i) q^{4} +(0.408797 - 3.88945i) q^{5} +(3.06963 + 3.40917i) q^{7} +(0.951502 + 2.92842i) q^{8} +4.49768 q^{10} +(3.04015 + 1.32570i) q^{11} +(-0.533071 - 0.237339i) q^{13} +(-3.53021 + 3.92070i) q^{14} +(-1.99732 + 0.889266i) q^{16} +(-1.01351 - 0.736358i) q^{17} +(-0.681632 - 2.09785i) q^{19} +(-0.276918 - 2.63470i) q^{20} +(-1.15080 + 3.63652i) q^{22} +(-3.65244 - 6.32621i) q^{23} +(-10.0699 - 2.14043i) q^{25} +(0.207373 - 0.638229i) q^{26} +(2.51406 + 1.82657i) q^{28} +(-0.832048 - 0.924083i) q^{29} +(7.92356 + 3.52780i) q^{31} +(1.82193 + 3.15567i) q^{32} +(0.720369 - 1.24772i) q^{34} +(14.5146 - 10.5455i) q^{35} +(-2.36110 + 7.26672i) q^{37} +(2.31746 - 1.03180i) q^{38} +(11.7789 - 2.50369i) q^{40} +(1.10232 - 1.22425i) q^{41} +(-2.89432 + 5.01312i) q^{43} +(2.20109 + 0.450233i) q^{44} +(6.79650 - 4.93795i) q^{46} +(0.516559 + 0.109798i) q^{47} +(-1.46810 + 13.9681i) q^{49} +(1.23758 - 11.7748i) q^{50} +(-0.386636 - 0.0821820i) q^{52} +(1.07638 - 0.782035i) q^{53} +(6.39907 - 11.2826i) q^{55} +(-7.06272 + 12.2330i) q^{56} +(0.956893 - 1.06274i) q^{58} +(0.543590 - 0.115544i) q^{59} +(10.2360 - 4.55734i) q^{61} +(-3.08239 + 9.48662i) q^{62} +(-6.92785 + 5.03338i) q^{64} +(-1.14103 + 1.97633i) q^{65} +(-3.73086 - 6.46203i) q^{67} +(-0.775252 - 0.345164i) q^{68} +(13.8062 + 15.3333i) q^{70} +(-4.14062 - 3.00833i) q^{71} +(0.117434 - 0.361425i) q^{73} +(-8.59511 - 1.82695i) q^{74} +(-0.747102 - 1.29402i) q^{76} +(4.81257 + 14.4338i) q^{77} +(-1.42577 - 13.5653i) q^{79} +(2.64225 + 8.13202i) q^{80} +(1.53274 + 1.11360i) q^{82} +(-0.912026 + 0.406060i) q^{83} +(-3.27834 + 3.64097i) q^{85} +(-6.08166 - 2.70773i) q^{86} +(-0.989516 + 10.1643i) q^{88} -3.33068 q^{89} +(-0.827203 - 2.54587i) q^{91} +(-3.31105 - 3.67730i) q^{92} +(-0.0634841 + 0.604011i) q^{94} +(-8.43812 + 1.79358i) q^{95} +(-1.64513 - 15.6524i) q^{97} -16.1524 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 8 q^{4} + 14 q^{7} + 64 q^{10} + 14 q^{13} + 4 q^{16} - 16 q^{19} - 16 q^{22} + 20 q^{25} - 36 q^{28} + 4 q^{31} - 84 q^{34} - 24 q^{37} + 106 q^{40} - 84 q^{43} - 76 q^{46} + 54 q^{49} - 52 q^{52}+ \cdots + 66 q^{97}+O(q^{100}) \) 96 * q + 8 * q^4 + 14 * q^7 + 64 * q^10 + 14 * q^13 + 4 * q^16 - 16 * q^19 - 16 * q^22 + 20 * q^25 - 36 * q^28 + 4 * q^31 - 84 * q^34 - 24 * q^37 + 106 * q^40 - 84 * q^43 - 76 * q^46 + 54 * q^49 - 52 * q^52 - 72 * q^55 + 10 * q^58 + 6 * q^61 - 104 * q^64 - 76 * q^67 + 8 * q^70 - 92 * q^73 - 204 * q^76 + 102 * q^79 + 24 * q^82 - 54 * q^85 + 44 * q^91 + 118 * q^94 + 66 * q^97

Introduction

L-functions

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