LMFDB - Embedded newform 891.2.n.l.190.5

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			190.5
Character	$\chi$	$=$	891.190
Dual form			891.2.n.l.136.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.05062 - 0.467766i) q^{2} +(-0.453266 - 0.503403i) q^{4} +(-3.57276 + 1.59069i) q^{5} +(-4.48724 + 0.953792i) q^{7} +(0.951502 + 2.92842i) q^{8} +4.49768 q^{10} +(-2.66817 + 1.96999i) q^{11} +(0.0609944 + 0.580323i) q^{13} +(5.16053 + 1.09690i) q^{14} +(0.228535 - 2.17437i) q^{16} +(-1.01351 - 0.736358i) q^{17} +(-0.681632 - 2.09785i) q^{19} +(2.42017 + 1.07753i) q^{20} +(3.72472 - 0.821635i) q^{22} +(-3.65244 + 6.32621i) q^{23} +(6.88865 - 7.65062i) q^{25} +(0.207373 - 0.638229i) q^{26} +(2.51406 + 1.82657i) q^{28} +(1.21630 - 0.258533i) q^{29} +(-0.906619 - 8.62591i) q^{31} +(1.82193 - 3.15567i) q^{32} +(0.720369 + 1.24772i) q^{34} +(14.5146 - 10.5455i) q^{35} +(-2.36110 + 7.26672i) q^{37} +(-0.265166 + 2.52288i) q^{38} +(-8.05772 - 8.94900i) q^{40} +(-1.61139 - 0.342512i) q^{41} +(-2.89432 - 5.01312i) q^{43} +(2.20109 + 0.450233i) q^{44} +(6.79650 - 4.93795i) q^{46} +(-0.353367 + 0.392454i) q^{47} +(12.8308 - 5.71263i) q^{49} +(-10.8160 + 4.81561i) q^{50} +(0.264490 - 0.293745i) q^{52} +(1.07638 - 0.782035i) q^{53} +(6.39907 - 11.2826i) q^{55} +(-7.06272 - 12.2330i) q^{56} +(-1.39880 - 0.297325i) q^{58} +(-0.371858 - 0.412991i) q^{59} +(-1.17120 + 11.1433i) q^{61} +(-3.08239 + 9.48662i) q^{62} +(-6.92785 + 5.03338i) q^{64} +(-1.14103 - 1.97633i) q^{65} +(-3.73086 + 6.46203i) q^{67} +(0.0887048 + 0.843970i) q^{68} +(-20.1822 + 4.28985i) q^{70} +(-4.14062 - 3.00833i) q^{71} +(0.117434 - 0.361425i) q^{73} +(5.87974 - 6.53011i) q^{74} +(-0.747102 + 1.29402i) q^{76} +(10.0937 - 11.3847i) q^{77} +(12.4607 + 5.54788i) q^{79} +(2.64225 + 8.13202i) q^{80} +(1.53274 + 1.11360i) q^{82} +(0.104355 - 0.992868i) q^{83} +(4.79235 + 1.01864i) q^{85} +(0.695868 + 6.62074i) q^{86} +(-8.30774 - 5.93907i) q^{88} -3.33068 q^{89} +(-0.827203 - 2.54587i) q^{91} +(4.84016 - 1.02881i) q^{92} +(0.554831 - 0.247027i) q^{94} +(5.77234 + 6.41083i) q^{95} +(14.3779 + 6.40147i) q^{97} -16.1524 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$.

$n$	$244$	$650$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.05062	−	0.467766i	−0.742900	−	0.330760i	0.000146925	−	1.00000i	$-0.499953\pi$
$2$	−1.05062	−	0.467766i	−0.742900	−	0.330760i	−0.743047	+	0.669240i	$0.766620\pi$
$3$		0			0
$3$		0			0
$4$	−0.453266	−	0.503403i	−0.226633	−	0.251702i
$5$	−3.57276	+	1.59069i	−1.59779	+	0.711380i	−0.996173	−	0.0874067i	$-0.972142\pi$
$5$	−3.57276	+	1.59069i	−1.59779	+	0.711380i	−0.601614	+	0.798787i	$0.705475\pi$
$6$		0			0
$7$	−4.48724	+	0.953792i	−1.69602	+	0.360499i	−0.951629	−	0.307249i	$-0.900592\pi$
$7$	−4.48724	+	0.953792i	−1.69602	+	0.360499i	−0.744387	+	0.667748i	$0.767258\pi$
$8$	0.951502	+	2.92842i	0.336407	+	1.03535i
$9$		0			0
$10$	4.49768			1.42229
$11$	−2.66817	+	1.96999i	−0.804483	+	0.593975i
$11$	−2.66817	+	1.96999i	−0.804483	+	0.593975i
$12$		0			0
$13$	0.0609944	+	0.580323i	0.0169168	+	0.160953i	0.999719	−	0.0237094i	$-0.00754764\pi$
$13$	0.0609944	+	0.580323i	0.0169168	+	0.160953i	−0.982802	+	0.184662i	$0.940881\pi$
$14$	5.16053	+	1.09690i	1.37921	+	0.293160i
$15$		0			0
$16$	0.228535	−	2.17437i	0.0571338	−	0.543592i
$17$	−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	$0.981425\pi$
$20$	2.42017	+	1.07753i	0.541167	+	0.240943i
$21$		0			0
$22$	3.72472	−	0.821635i	0.794114	−	0.175173i
$23$	−3.65244	+	6.32621i	−0.761586	+	1.31911i	0.180447	+	0.983585i	$0.442246\pi$
$23$	−3.65244	+	6.32621i	−0.761586	+	1.31911i	−0.942033	+	0.335521i	$0.891088\pi$
$24$		0			0
$25$	6.88865	−	7.65062i	1.37773	−	1.53012i
$26$	0.207373	−	0.638229i	0.0406692	−	0.125167i
$27$		0			0
$28$	2.51406	+	1.82657i	0.475112	+	0.345189i
$29$	1.21630	−	0.258533i	0.225862	−	0.0480084i	−0.0935904	−	0.995611i	$-0.529834\pi$
$29$	1.21630	−	0.258533i	0.225862	−	0.0480084i	0.319452	+	0.947602i	$0.396501\pi$
$30$		0			0
$31$	−0.906619	−	8.62591i	−0.162834	−	1.54926i	−0.705134	−	0.709074i	$-0.749113\pi$
$31$	−0.906619	−	8.62591i	−0.162834	−	1.54926i	0.542300	−	0.840185i	$-0.317553\pi$
$32$	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	$0.883849\pi$
$38$	−0.265166	+	2.52288i	−0.0430155	+	0.409265i
$39$		0			0
$40$	−8.05772	−	8.94900i	−1.27404	−	1.41496i
$41$	−1.61139	−	0.342512i	−0.251657	−	0.0534914i	0.0803557	−	0.996766i	$-0.474394\pi$
$41$	−1.61139	−	0.342512i	−0.251657	−	0.0534914i	−0.332013	+	0.943275i	$0.607728\pi$
$42$		0			0
$43$	−2.89432	−	5.01312i	−0.441380	−	0.764493i	0.556412	−	0.830907i	$-0.312178\pi$
$43$	−2.89432	−	5.01312i	−0.441380	−	0.764493i	−0.997792	+	0.0664134i	$0.978844\pi$
$44$	2.20109	+	0.450233i	0.331827	+	0.0678752i
$45$		0			0
$46$	6.79650	−	4.93795i	1.00209	−	0.728060i
$47$	−0.353367	+	0.392454i	−0.0515439	+	0.0572453i	−0.768365	−	0.640011i	$-0.778930\pi$
$47$	−0.353367	+	0.392454i	−0.0515439	+	0.0572453i	0.716821	+	0.697257i	$0.245596\pi$
$48$		0			0
$49$	12.8308	−	5.71263i	1.83297	−	0.816089i
$50$	−10.8160	+	4.81561i	−1.52962	+	0.681030i
$51$		0			0
$52$	0.264490	−	0.293745i	0.0366781	−	0.0407352i
$53$	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
$58$	−1.39880	−	0.297325i	−0.183672	−	0.0390407i
$59$	−0.371858	−	0.412991i	−0.0484119	−	0.0537668i	0.718452	−	0.695576i	$-0.244851\pi$
$59$	−0.371858	−	0.412991i	−0.0484119	−	0.0537668i	−0.766864	+	0.641809i	$0.778184\pi$
$60$		0			0
$61$	−1.17120	+	11.1433i	−0.149957	+	1.42675i	0.617965	+	0.786206i	$0.287957\pi$
$61$	−1.17120	+	11.1433i	−0.149957	+	1.42675i	−0.767922	+	0.640543i	$0.778709\pi$
$62$	−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	−0.998734	−	0.0503104i	$-0.983979\pi$
$67$	−3.73086	+	6.46203i	−0.455797	+	0.789463i	0.542937	+	0.839774i	$0.317312\pi$
$68$	0.0887048	+	0.843970i	0.0107570	+	0.102346i
$69$		0			0
$70$	−20.1822	+	4.28985i	−2.41223	+	0.512735i
$71$	−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	$0.0929204\pi$
$74$	5.87974	−	6.53011i	0.683506	−	0.759110i
$75$		0			0
$76$	−0.747102	+	1.29402i	−0.0856985	+	0.148434i
$77$	10.0937	−	11.3847i	1.15029	−	1.29741i
$78$		0			0
$79$	12.4607	+	5.54788i	1.40194	+	0.624186i	0.961803	−	0.273743i	$-0.0882618\pi$
$79$	12.4607	+	5.54788i	1.40194	+	0.624186i	0.440141	+	0.897929i	$0.354928\pi$
$80$	2.64225	+	8.13202i	0.295413	+	0.909187i
$81$		0			0
$82$	1.53274	+	1.11360i	0.169263	+	0.122977i
$83$	0.104355	−	0.992868i	0.0114544	−	0.108981i	−0.987301	−	0.158862i	$-0.949217\pi$
$83$	0.104355	−	0.992868i	0.0114544	−	0.108981i	0.998755	+	0.0498807i	$0.0158841\pi$
$84$		0			0
$85$	4.79235	+	1.01864i	0.519803	+	0.110488i
$86$	0.695868	+	6.62074i	0.0750374	+	0.713933i
$87$		0			0
$88$	−8.30774	−	5.93907i	−0.885609	−	0.633107i
$89$	−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
$92$	4.84016	−	1.02881i	0.504621	−	0.107261i
$93$		0			0
$94$	0.554831	−	0.247027i	0.0572264	−	0.0254788i
$95$	5.77234	+	6.41083i	0.592230	+	0.657738i
$96$		0			0
$97$	14.3779	+	6.40147i	1.45986	+	0.649971i	0.974509	−	0.224349i	$-0.0720256\pi$
$97$	14.3779	+	6.40147i	1.45986	+	0.649971i	0.485350	+	0.874320i	$0.338692\pi$
$98$	−16.1524			−1.63164
$99$		0			0
$100$	−6.97373			−0.697373
$101$	−13.9178	−	6.19661i	−1.38487	−	0.616586i	−0.427125	−	0.904192i	$-0.640474\pi$
$101$	−13.9178	−	6.19661i	−1.38487	−	0.616586i	−0.957749	+	0.287607i	$0.907140\pi$
$102$		0			0
$103$	2.32985	+	2.58756i	0.229567	+	0.254960i	0.846913	−	0.531732i	$-0.178459\pi$
$103$	2.32985	+	2.58756i	0.229567	+	0.254960i	−0.617346	+	0.786692i	$0.711792\pi$
$104$	−1.64139	+	0.730796i	−0.160952	+	0.0716604i
$105$		0			0
$106$	−1.49667	+	0.318128i	−0.145370	+	0.0308993i
$107$	−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	$0.494195\pi$
$110$	−12.0006	+	8.86040i	−1.14421	+	0.844806i
$111$		0			0
$112$	1.04840	+	9.97487i	0.0990646	+	0.942537i
$113$	12.1557	+	2.58378i	1.14352	+	0.243062i	0.740451	−	0.672110i	$-0.234612\pi$
$113$	12.1557	+	2.58378i	1.14352	+	0.243062i	0.403064	+	0.915172i	$0.367945\pi$
$114$		0			0
$115$	2.98621	−	28.4119i	0.278466	−	2.64943i
$116$	−0.681456	−	0.495107i	−0.0632716	−	0.0459695i
$117$		0			0
$118$	0.197499	+	0.607838i	0.0181812	+	0.0559561i
$119$	5.25019	+	2.33754i	0.481284	+	0.214282i
$120$		0			0
$121$	3.23825	−	10.5126i	0.294386	−	0.955687i
$122$	6.44293	−	11.1595i	0.583315	−	1.01033i
$123$		0			0
$124$	−3.93137	+	4.36623i	−0.353047	+	0.392099i
$125$	−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	$0.693812\pi$
$128$	2.50450	−	0.532348i	0.221369	−	0.0470534i
$129$		0			0
$130$	0.274333	+	2.61011i	0.0240606	+	0.228921i
$131$	4.06152	−	7.03476i	0.354857	−	0.614630i	−0.632237	−	0.774775i	$-0.717863\pi$
$131$	4.06152	−	7.03476i	0.354857	−	0.614630i	0.987093	+	0.160145i	$0.0511963\pi$
$132$		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
$137$	0.701945	−	6.67856i	0.0599712	−	0.570588i	−0.922737	−	0.385429i	$-0.874053\pi$
$137$	0.701945	−	6.67856i	0.0599712	−	0.570588i	0.982709	−	0.185159i	$-0.0592800\pi$
$138$		0			0
$139$	−2.00414	−	2.22582i	−0.169989	−	0.188792i	0.652131	−	0.758106i	$-0.273875\pi$
$139$	−2.00414	−	2.22582i	−0.169989	−	0.188792i	−0.822120	+	0.569315i	$0.807209\pi$
$140$	−11.8876	−	2.52679i	−1.00469	−	0.213553i
$141$		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
$146$	−0.292440	+	0.324788i	−0.0242025	+	0.0268796i
$147$		0			0
$148$	4.72830	−	2.10517i	0.388664	−	0.173044i
$149$	0.234607	−	0.104454i	0.0192198	−	0.00855719i	−0.397104	−	0.917774i	$-0.629985\pi$
$149$	0.234607	−	0.104454i	0.0192198	−	0.00855719i	0.416324	+	0.909216i	$0.363318\pi$
$150$		0			0
$151$	−4.24694	+	4.71671i	−0.345611	+	0.383840i	−0.890741	−	0.454512i	$-0.849814\pi$
$151$	−4.24694	+	4.71671i	−0.345611	+	0.383840i	0.545129	+	0.838352i	$0.316480\pi$
$152$	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
$157$	8.88811	+	1.88923i	0.709349	+	0.150777i	0.548437	−	0.836192i	$-0.315223\pi$
$157$	8.88811	+	1.88923i	0.709349	+	0.150777i	0.160912	+	0.986969i	$0.448557\pi$
$158$	−10.4964	−	11.6574i	−0.835048	−	0.927414i
$159$		0			0
$160$	−1.48960	+	14.1726i	−0.117763	+	1.12044i
$161$	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
$167$	1.42595	+	13.5670i	0.110343	+	1.04984i	0.899879	+	0.436140i	$0.143655\pi$
$167$	1.42595	+	13.5670i	0.110343	+	1.04984i	−0.789536	+	0.613704i	$0.789679\pi$
$168$		0			0
$169$	12.3829	−	2.63206i	0.952528	−	0.202466i
$170$	−4.55844	−	3.31190i	−0.349616	−	0.254011i
$171$		0			0
$172$	−1.21172	+	3.72929i	−0.0923927	+	0.284356i
$173$	14.2011	−	15.7719i	1.07969	−	1.19912i	0.100763	−	0.994910i	$-0.467872\pi$
$173$	14.2011	−	15.7719i	1.07969	−	1.19912i	0.978928	−	0.204207i	$-0.0654616\pi$
$174$		0			0
$175$	−23.6139	+	40.9005i	−1.78504	+	3.09178i
$176$	3.67372	+	6.25179i	0.276917	+	0.471246i
$177$		0			0
$178$	3.49927	+	1.55798i	0.262281	+	0.116775i
$179$	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	$0.703444\pi$
$182$	−0.321795	+	3.06168i	−0.0238530	+	0.226946i
$183$		0			0
$184$	−22.0011	−	4.67648i	−1.62194	−	0.344755i
$185$	−3.12349	−	29.7180i	−0.229644	−	2.18491i
$186$		0			0
$187$	4.15483	−	0.0318807i	0.303832	−	0.00233135i
$188$	0.357732			0.0260903
$189$		0			0
$190$	−3.06576	−	9.43545i	−0.222414	−	0.684519i
$191$	−0.443235	+	0.0942126i	−0.0320714	+	0.00681698i	−0.223919	−	0.974608i	$-0.571885\pi$
$191$	−0.443235	+	0.0942126i	−0.0320714	+	0.00681698i	0.191848	+	0.981425i	$0.438552\pi$
$192$		0			0
$193$	−16.0244	+	7.13453i	−1.15346	+	0.513554i	−0.892168	−	0.451705i	$-0.850816\pi$
$193$	−16.0244	+	7.13453i	−1.15346	+	0.513554i	−0.261295	+	0.965259i	$0.584149\pi$
$194$	−12.1113	−	13.4510i	−0.869544	−	0.965726i
$195$		0			0
$196$	−8.69151	−	3.86971i	−0.620822	−	0.276408i
$197$	−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	$0.655240\pi$
$200$	28.9588	+	12.8933i	2.04770	+	0.911693i
$201$		0			0
$202$	11.7238	+	13.0205i	0.824880	+	0.916122i
$203$	−5.21126	+	2.32020i	−0.365759	+	0.162846i
$204$		0			0
$205$	6.30195	−	1.33952i	0.440147	−	0.0935561i
$206$	−1.23741	−	3.80836i	−0.0862146	−	0.265341i
$207$		0			0
$208$	1.27577			0.0884590
$209$	5.95146	+	4.25460i	0.411671	+	0.294297i
$210$		0			0
$211$	−1.17723	−	11.2005i	−0.0810435	−	0.771078i	−0.957273	−	0.289184i	$-0.906616\pi$
$211$	−1.17723	−	11.2005i	−0.0810435	−	0.771078i	0.876230	−	0.481893i	$-0.160051\pi$
$212$	−0.881565	−	0.187382i	−0.0605461	−	0.0128695i
$213$		0			0
$214$	−1.15768	+	11.0146i	−0.0791373	+	0.752941i
$215$	18.3151	+	13.3067i	1.24908	+	0.907508i
$216$		0			0
$217$	12.2955	+	37.8418i	0.834675	+	2.56887i
$218$	−0.400023	−	0.178102i	−0.0270930	−	0.0120626i
$219$		0			0
$220$	−8.58016	+	1.89269i	−0.578474	+	0.127605i
$221$	0.365507	−	0.633076i	0.0245866	−	0.0425853i
$222$		0			0
$223$	−10.5592	+	11.7271i	−0.707093	+	0.785306i	−0.984488	−	0.175449i	$-0.943862\pi$
$223$	−10.5592	+	11.7271i	−0.707093	+	0.785306i	0.277395	+	0.960756i	$0.410529\pi$
$224$	−5.16557	+	15.8980i	−0.345139	+	1.06223i
$225$		0			0
$226$	−11.5624	−	8.40060i	−0.769122	−	0.558800i
$227$	−7.81368	+	1.66085i	−0.518612	+	0.110234i	−0.459779	−	0.888033i	$-0.652071\pi$
$227$	−7.81368	+	1.66085i	−0.518612	+	0.110234i	−0.0588332	+	0.998268i	$0.518738\pi$
$228$		0			0
$229$	2.05942	+	19.5940i	0.136090	+	1.29481i	0.822989	+	0.568057i	$0.192305\pi$
$229$	2.05942	+	19.5940i	0.136090	+	1.29481i	−0.686899	+	0.726753i	$0.741029\pi$
$230$	−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
$236$	−0.0393499	+	0.374389i	−0.00256146	+	0.0243707i
$237$		0			0
$238$	−4.42253	−	4.91172i	−0.286670	−	0.318379i
$239$	9.80723	+	2.08459i	0.634377	+	0.134841i	0.513865	−	0.857871i	$-0.328213\pi$
$239$	9.80723	+	2.08459i	0.634377	+	0.134841i	0.120512	+	0.992712i	$0.461546\pi$
$240$		0			0
$241$	−8.59826	−	14.8926i	−0.553863	−	0.959318i	−0.997991	−	0.0633552i	$-0.979820\pi$
$241$	−8.59826	−	14.8926i	−0.553863	−	0.959318i	0.444128	−	0.895963i	$-0.353513\pi$
$242$	−8.31957	+	9.52994i	−0.534802	+	0.612608i
$243$		0			0
$244$	6.14042	−	4.46128i	0.393100	−	0.285604i
$245$	−36.7542	+	40.8197i	−2.34814	+	2.60787i
$246$		0			0
$247$	1.17585	−	0.523523i	0.0748177	−	0.0333110i
$248$	24.3977	−	10.8625i	1.54925	−	0.689772i
$249$		0			0
$250$	15.9352	−	17.6979i	1.00783	−	1.11931i
$251$	−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
$256$	13.8720	+	2.94859i	0.867002	+	0.184287i
$257$	10.8355	+	12.0340i	0.675898	+	0.750661i	0.979347	−	0.202187i	$-0.0648048\pi$
$257$	10.8355	+	12.0340i	0.675898	+	0.750661i	−0.303449	+	0.952848i	$0.598138\pi$
$258$		0			0
$259$	3.66388	−	34.8595i	0.227663	−	2.16606i
$260$	−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	−0.963026	−	0.269408i	$-0.913172\pi$
$263$	−11.5926	−	20.0789i	−0.714828	−	1.23812i	0.248198	−	0.968709i	$-0.420161\pi$
$264$		0			0
$265$	−2.60166	+	4.50621i	−0.159819	+	0.276814i
$266$	−1.21644	−	11.5737i	−0.0745849	−	0.709628i
$267$		0			0
$268$	4.94408	−	1.05090i	0.302008	−	0.0641937i
$269$	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	$-0.163321\pi$
$272$	−1.83273	+	2.03546i	−0.111126	+	0.123418i
$273$		0			0
$274$	−3.86148	+	6.68828i	−0.233280	+	0.404054i
$275$	−3.30840	+	33.9837i	−0.199504	+	2.04930i
$276$		0			0
$277$	−7.86170	−	3.50025i	−0.472364	−	0.210310i	0.156727	−	0.987642i	$-0.449906\pi$
$277$	−7.86170	−	3.50025i	−0.472364	−	0.210310i	−0.629090	+	0.777332i	$0.716572\pi$
$278$	1.06442	+	3.27596i	0.0638398	+	0.196479i
$279$		0			0
$280$	44.6924	+	32.4709i	2.67088	+	1.94051i
$281$	−0.922113	+	8.77332i	−0.0550087	+	0.523372i	0.931972	+	0.362531i	$0.118087\pi$
$281$	−0.922113	+	8.77332i	−0.0550087	+	0.523372i	−0.986980	+	0.160841i	$0.948579\pi$
$282$		0			0
$283$	19.6317	+	4.17284i	1.16698	+	0.248050i	0.750360	−	0.661030i	$-0.229880\pi$
$283$	19.6317	+	4.17284i	1.16698	+	0.248050i	0.416622	+	0.909080i	$0.363214\pi$
$284$	0.362397	+	3.44798i	0.0215043	+	0.204600i
$285$		0			0
$286$	0.704000	+	2.11143i	0.0416284	+	0.124851i
$287$	7.55738			0.446098
$288$		0			0
$289$	−4.76831	−	14.6753i	−0.280489	−	0.863256i
$290$	5.47054	−	1.16280i	0.321241	−	0.0682820i
$291$		0			0
$292$	−0.235171	+	0.104705i	−0.0137623	+	0.00612739i
$293$	−1.13974	−	1.26581i	−0.0665842	−	0.0739492i	0.708932	−	0.705276i	$-0.249177\pi$
$293$	−1.13974	−	1.26581i	−0.0665842	−	0.0739492i	−0.775517	+	0.631327i	$0.782510\pi$
$294$		0			0
$295$	1.98550	+	0.884003i	0.115600	+	0.0514686i
$296$	−23.5266			−1.36746
$297$		0			0
$298$	−0.295342			−0.0171087
$299$	−3.89402	−	1.73373i	−0.225197	−	0.100264i
$300$		0			0
$301$	17.7690	+	19.7345i	1.02419	+	1.13748i
$302$	6.66823	−	2.96889i	0.383714	−	0.170840i
$303$		0			0
$304$	−4.71727	+	1.00269i	−0.270554	+	0.0575080i
$305$	−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	$0.691008\pi$
$308$	−10.3063	+	0.0790816i	−0.587253	+	0.00450609i
$309$		0			0
$310$	−4.07768	−	38.7966i	−0.231597	−	2.20350i
$311$	−26.6914	−	5.67343i	−1.51353	−	0.321710i	−0.625034	−	0.780597i	$-0.714915\pi$
$311$	−26.6914	−	5.67343i	−1.51353	−	0.321710i	−0.888495	+	0.458887i	$0.848248\pi$
$312$		0			0
$313$	−0.943695	+	8.97866i	−0.0533408	+	0.507504i	0.934934	+	0.354821i	$0.115458\pi$
$313$	−0.943695	+	8.97866i	−0.0533408	+	0.507504i	−0.988275	+	0.152683i	$0.951209\pi$
$314$	−8.45430	−	6.14241i	−0.477104	−	0.346636i
$315$		0			0
$316$	−2.85522	−	8.78745i	−0.160618	−	0.494333i
$317$	22.8882	+	10.1905i	1.28553	+	0.572353i	0.931792	−	0.362992i	$-0.118245\pi$
$317$	22.8882	+	10.1905i	1.28553	+	0.572353i	0.353735	+	0.935346i	$0.384912\pi$
$318$		0			0
$319$	−2.73599	+	3.08592i	−0.153186	+	0.172778i
$320$	16.7450	−	29.0031i	0.936072	−	1.62132i
$321$		0			0
$322$	−25.7877	+	28.6402i	−1.43709	+	1.59606i
$323$	−0.853926	+	2.62811i	−0.0475137	+	0.146232i
$324$		0			0
$325$	4.85999	+	3.53099i	0.269584	+	0.195864i
$326$	6.96559	−	1.48058i	0.385788	−	0.0820018i
$327$		0			0
$328$	−0.530223	−	5.04474i	−0.0292767	−	0.278549i
$329$	1.21132	−	2.09807i	0.0667824	−	0.115671i
$330$		0			0
$331$	4.65092	+	8.05563i	0.255638	+	0.442777i	0.965069	−	0.261998i	$-0.0843813\pi$
$331$	4.65092	+	8.05563i	0.255638	+	0.442777i	−0.709431	+	0.704775i	$0.751048\pi$
$332$	−0.547113	+	0.397501i	−0.0300268	+	0.0218157i
$333$		0			0
$334$	4.84804	−	14.9207i	0.265273	−	0.816426i
$335$	3.05033	−	29.0219i	0.166657	−	1.58564i
$336$		0			0
$337$	−9.48759	−	10.5370i	−0.516822	−	0.573989i	0.427080	−	0.904214i	$-0.359542\pi$
$337$	−9.48759	−	10.5370i	−0.516822	−	0.573989i	−0.943902	+	0.330225i	$0.892875\pi$
$338$	−14.2409	−	3.02699i	−0.774600	−	0.164646i
$339$		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
$344$	11.9266	−	13.2458i	0.643038	−	0.714166i
$345$		0			0
$346$	−22.2975	+	9.92749i	−1.19872	+	0.533705i
$347$	1.35386	−	0.602777i	0.0726789	−	0.0323587i	−0.370075	−	0.929002i	$-0.620668\pi$
$347$	1.35386	−	0.602777i	0.0726789	−	0.0323587i	0.442754	+	0.896643i	$0.354001\pi$
$348$		0			0
$349$	1.35085	−	1.50027i	0.0723092	−	0.0803076i	−0.705905	−	0.708307i	$-0.749459\pi$
$349$	1.35085	−	1.50027i	0.0723092	−	0.0803076i	0.778214	+	0.627999i	$0.216126\pi$
$350$	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	0.779860	−	0.625954i	$-0.215290\pi$
$353$	−2.85887	−	4.95171i	−0.152162	−	0.263553i	−0.932022	+	0.362401i	$0.881957\pi$
$354$		0			0
$355$	19.5788	+	4.16160i	1.03913	+	0.220875i
$356$	1.50968	+	1.67667i	0.0800130	+	0.0888635i
$357$		0			0
$358$	1.74364	−	16.5896i	0.0921541	−	0.876788i
$359$	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
$365$	0.155353	+	1.47808i	0.00813155	+	0.0773665i
$366$		0			0
$367$	17.6763	−	3.75721i	0.922695	−	0.196125i	0.278015	−	0.960577i	$-0.410324\pi$
$367$	17.6763	−	3.75721i	0.922695	−	0.196125i	0.644681	+	0.764452i	$0.276990\pi$
$368$	12.9208	+	9.38750i	0.673542	+	0.489357i
$369$		0			0
$370$	−10.6195	+	32.6834i	−0.552080	+	1.69913i
$371$	−4.08407	+	4.53582i	−0.212034	+	0.235488i
$372$		0			0
$373$	12.2370	−	21.1952i	0.633610	−	1.09744i	−0.353198	−	0.935548i	$-0.614906\pi$
$373$	12.2370	−	21.1952i	0.633610	−	1.09744i	0.986808	−	0.161895i	$-0.0517607\pi$
$374$	−4.38006	−	1.90999i	−0.226487	−	0.0987634i
$375$		0			0
$376$	−1.48550	−	0.661388i	−0.0766089	−	0.0341085i
$377$	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	$0.777000\pi$
$380$	0.610827	−	5.81163i	0.0313348	−	0.298130i
$381$		0			0
$382$	0.509741	+	0.108349i	0.0260806	+	0.00554361i
$383$	−2.60432	−	24.7785i	−0.133075	−	1.26612i	−0.833550	−	0.552444i	$-0.813695\pi$
$383$	−2.60432	−	24.7785i	−0.133075	−	1.26612i	0.700475	−	0.713677i	$-0.252971\pi$
$384$		0			0
$385$	−17.9529	+	56.7309i	−0.914965	+	2.89127i
$386$	20.1728			1.02677
$387$		0			0
$388$	−3.29451	−	10.1395i	−0.167254	−	0.514754i
$389$	−21.8352	+	4.64121i	−1.10709	+	0.235319i	−0.724960	−	0.688791i	$-0.758142\pi$
$389$	−21.8352	+	4.64121i	−1.10709	+	0.235319i	−0.382128	+	0.924110i	$0.624809\pi$
$390$		0			0
$391$	8.36013	−	3.72217i	0.422790	−	0.188238i
$392$	28.9375	+	32.1383i	1.46156	+	1.62323i
$393$		0			0
$394$	18.5651	+	8.26569i	0.935294	+	0.416420i
$395$	−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	$0.0599524\pi$
$398$	13.8899	+	6.18420i	0.696240	+	0.309986i
$399$		0			0
$400$	−15.0609	−	16.7269i	−0.753047	−	0.836344i
$401$	−30.3571	+	13.5158i	−1.51596	+	0.674949i	−0.985017	−	0.172458i	$-0.944829\pi$
$401$	−30.3571	+	13.5158i	−1.51596	+	0.674949i	−0.530943	+	0.847407i	$0.678162\pi$
$402$		0			0
$403$	4.95051	−	1.05226i	0.246603	−	0.0524170i
$404$	3.18908	+	9.81498i	0.158663	+	0.488314i
$405$		0			0
$406$	6.56035			0.325585
$407$	−8.01558	−	24.0402i	−0.397318	−	1.19163i
$408$		0			0
$409$	−3.79453	−	36.1026i	−0.187628	−	1.78516i	−0.532422	−	0.846479i	$-0.678718\pi$
$409$	−3.79453	−	36.1026i	−0.187628	−	1.78516i	0.344794	−	0.938678i	$-0.387949\pi$
$410$	−7.24752	−	1.54051i	−0.357930	−	0.0760803i
$411$		0			0
$412$	0.246544	−	2.34571i	0.0121463	−	0.115565i
$413$	2.06252	+	1.49851i	0.101490	+	0.0737369i
$414$		0			0
$415$	1.20652	+	3.71328i	0.0592256	+	0.182278i
$416$	1.94244	+	0.864829i	0.0952358	+	0.0424017i
$417$		0			0
$418$	−4.26255	−	7.25385i	−0.208488	−	0.354797i
$419$	−2.99011	+	5.17903i	−0.146077	+	0.253012i	−0.929774	−	0.368131i	$-0.879998\pi$
$419$	−2.99011	+	5.17903i	−0.146077	+	0.253012i	0.783697	+	0.621143i	$0.213331\pi$
$420$		0			0
$421$	−10.5851	+	11.7559i	−0.515884	+	0.572947i	−0.943651	−	0.330942i	$-0.892634\pi$
$421$	−10.5851	+	11.7559i	−0.515884	+	0.572947i	0.427767	+	0.903889i	$0.359300\pi$
$422$	−4.00242	+	12.3182i	−0.194835	+	0.599639i
$423$		0			0
$424$	3.31431	+	2.40798i	0.160957	+	0.116942i
$425$	−12.6153	+	2.68146i	−0.611932	+	0.130070i
$426$		0			0
$427$	−5.37288	−	51.1196i	−0.260012	−	2.47385i
$428$	−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	$-0.00718112\pi$
$434$	4.78316	−	45.5087i	0.229599	−	2.18449i
$435$		0			0
$436$	−0.172581	−	0.191671i	−0.00826513	−	0.00917936i
$437$	15.7610	+	3.35011i	0.753952	+	0.160258i
$438$		0			0
$439$	−7.85940	−	13.6129i	−0.375109	−	0.649707i	0.615235	−	0.788344i	$-0.289061\pi$
$439$	−7.85940	−	13.6129i	−0.375109	−	0.649707i	−0.990343	+	0.138637i	$0.955728\pi$
$440$	39.1288	+	8.00379i	1.86539	+	0.381566i
$441$		0			0
$442$	−0.680139	+	0.494150i	−0.0323509	+	0.0235043i
$443$	10.9667	−	12.1798i	0.521046	−	0.578680i	−0.423982	−	0.905671i	$-0.639368\pi$
$443$	10.9667	−	12.1798i	0.521046	−	0.578680i	0.945028	+	0.326991i	$0.106035\pi$
$444$		0			0
$445$	11.8997	−	5.29809i	0.564100	−	0.251154i
$446$	16.5792	−	7.38153i	0.785047	−	0.349526i
$447$		0			0
$448$	26.2861	−	29.1937i	1.24190	−	1.37927i
$449$	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
$454$	8.98609	+	1.91005i	0.421738	+	0.0896432i
$455$	7.00510	+	7.77995i	0.328404	+	0.364730i
$456$		0			0
$457$	0.469498	−	4.46698i	0.0219622	−	0.208956i	−0.978038	−	0.208428i	$-0.933165\pi$
$457$	0.469498	−	4.46698i	0.0219622	−	0.208956i	1.00000		0.000528143i	$-0.000168113\pi$
$458$	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	0.742036	−	0.670360i	$-0.233860\pi$
$461$	−4.49882	−	7.79219i	−0.209531	−	0.362918i	−0.951567	+	0.307442i	$0.900527\pi$
$462$		0			0
$463$	3.15033	−	5.45653i	0.146408	−	0.253586i	−0.783489	−	0.621405i	$-0.786562\pi$
$463$	3.15033	−	5.45653i	0.146408	−	0.253586i	0.929897	+	0.367819i	$0.119895\pi$
$464$	−0.284178	−	2.70377i	−0.0131926	−	0.125520i
$465$		0			0
$466$	20.1041	−	4.27326i	0.931304	−	0.197955i
$467$	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
$470$	−1.58933	+	1.76513i	−0.0733104	+	0.0814195i
$471$		0			0
$472$	0.855587	−	1.48192i	0.0393816	−	0.0682109i
$473$	17.5984	+	7.67404i	0.809173	+	0.352853i
$474$		0			0
$475$	−20.7453	−	9.23642i	−0.951862	−	0.423796i
$476$	−1.20301	−	3.70249i	−0.0551399	−	0.169703i
$477$		0			0
$478$	−9.32856	−	6.77759i	−0.426678	−	0.310000i
$479$	2.28072	−	21.6996i	0.104209	−	0.991478i	−0.810054	−	0.586356i	$-0.800562\pi$
$479$	2.28072	−	21.6996i	0.104209	−	0.991478i	0.914262	−	0.405123i	$-0.132771\pi$
$480$		0			0
$481$	−4.36106	−	0.926972i	−0.198847	−	0.0422663i
$482$	2.06724	+	19.6684i	0.0941600	+	0.895873i
$483$		0			0
$484$	−6.75984	+	3.13484i	−0.307265	+	0.142493i
$485$	−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	$0.851568\pi$
$488$	−33.7466	+	7.17306i	−1.52764	+	0.324709i
$489$		0			0
$490$	57.7087	−	25.6936i	2.60701	−	1.16072i
$491$	−18.1076	−	20.1105i	−0.817183	−	0.907574i	0.179916	−	0.983682i	$-0.442417\pi$
$491$	−18.1076	−	20.1105i	−0.817183	−	0.907574i	−0.997100	+	0.0761080i	$0.975751\pi$
$492$		0			0
$493$	−1.42311	−	0.633609i	−0.0640936	−	0.0285363i
$494$	−1.48026			−0.0666000
$495$		0			0
$496$	−18.9631			−0.851467
$497$	21.4493	+	9.54982i	0.962131	+	0.428368i
$498$		0			0
$499$	19.0935	+	21.2055i	0.854742	+	0.949287i	0.999191	−	0.0402249i	$-0.0128074\pi$
$499$	19.0935	+	21.2055i	0.854742	+	0.949287i	−0.144448	+	0.989512i	$0.546141\pi$
$500$	12.8146	−	5.70543i	0.573087	−	0.255155i
$501$		0			0
$502$	5.84316	−	1.24200i	0.260793	−	0.0554332i
$503$	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
$506$	−8.40648	+	26.5643i	−0.373714	+	1.18093i
$507$		0			0
$508$	−0.0310223	−	0.295158i	−0.00137639	−	0.0130955i
$509$	24.0540	+	5.11284i	1.06617	+	0.226622i	0.707408	−	0.706805i	$-0.249864\pi$
$509$	24.0540	+	5.11284i	1.06617	+	0.226622i	0.358766	+	0.933427i	$0.383197\pi$
$510$		0			0
$511$	−0.182230	+	1.73381i	−0.00806139	+	0.0766990i
$512$	−17.3379	−	12.5967i	−0.766233	−	0.556701i
$513$		0			0
$514$	−5.75485	−	17.7116i	−0.253836	−	0.781226i
$515$	−12.4400	−	5.53865i	−0.548173	−	0.244062i
$516$		0			0
$517$	0.169711	−	1.74326i	0.00746389	−	0.0766687i
$518$	−20.1554	+	34.9102i	−0.885579	+	1.53387i
$519$		0			0
$520$	4.70183	−	5.22191i	0.206189	−	0.228996i
$521$	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	$0.841853\pi$
$524$	−5.38227	+	1.14404i	−0.235126	+	0.0499775i
$525$		0			0
$526$	2.78714	+	26.5179i	0.121525	+	1.15623i
$527$	−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
$533$	0.100482	−	0.956018i	0.00435234	−	0.0414097i
$534$		0			0
$535$	25.2013	+	27.9889i	1.08955	+	1.21007i
$536$	−22.4735	−	4.77689i	−0.970707	−	0.206330i
$537$		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	$0.398378\pi$
$542$	−18.6492	+	20.7120i	−0.801052	+	0.889659i
$543$		0			0
$544$	−4.17025	+	1.85671i	−0.178798	+	0.0796060i
$545$	−1.36033	+	0.605657i	−0.0582700	+	0.0259435i
$546$		0			0
$547$	−11.0931	+	12.3202i	−0.474309	+	0.526773i	−0.932058	−	0.362308i	$-0.881989\pi$
$547$	−11.0931	+	12.3202i	−0.474309	+	0.526773i	0.457750	+	0.889081i	$0.348656\pi$
$548$	−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
$553$	−61.2059	−	13.0097i	−2.60274	−	0.553229i
$554$	6.62235	+	7.35486i	0.281357	+	0.312478i
$555$		0			0
$556$	−0.212077	+	2.01778i	−0.00899407	+	0.0855729i
$557$	−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
$563$	−4.24022	−	40.3430i	−0.178704	−	1.70026i	−0.605449	−	0.795884i	$-0.707006\pi$
$563$	−4.24022	−	40.3430i	−0.178704	−	1.70026i	0.426745	−	0.904372i	$-0.359660\pi$
$564$		0			0
$565$	−47.5395	+	10.1048i	−2.00000	+	0.425114i
$566$	−18.6735	−	13.5671i	−0.784905	−	0.570267i
$567$		0			0
$568$	4.86987	−	14.9879i	0.204335	−	0.628879i
$569$	6.71998	−	7.46329i	0.281716	−	0.312878i	−0.585634	−	0.810575i	$-0.699155\pi$
$569$	6.71998	−	7.46329i	0.281716	−	0.312878i	0.867350	+	0.497698i	$0.165821\pi$
$570$		0			0
$571$	−17.8106	+	30.8488i	−0.745348	+	1.29098i	0.204683	+	0.978828i	$0.434384\pi$
$571$	−17.8106	+	30.8488i	−0.745348	+	1.29098i	−0.950032	+	0.312153i	$0.898950\pi$
$572$	−0.127026	+	1.30481i	−0.00531123	+	0.0545566i
$573$		0			0
$574$	−7.93993	−	3.53508i	−0.331406	−	0.147552i
$575$	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	$0.484075\pi$
$578$	−1.85495	+	17.6486i	−0.0771556	+	0.734087i
$579$		0			0
$580$	3.22224	+	0.684909i	0.133796	+	0.0284393i
$581$	0.478725	+	4.55477i	0.0198609	+	0.188964i
$582$		0			0
$583$	−1.33136	+	4.20706i	−0.0551391	+	0.174239i
$584$	1.17014			0.0484209
$585$		0			0
$586$	0.605329	+	1.86301i	0.0250059	+	0.0769602i
$587$	−20.1482	+	4.28262i	−0.831603	+	0.176763i	−0.603993	−	0.796990i	$-0.706425\pi$
$587$	−20.1482	+	4.28262i	−0.831603	+	0.176763i	−0.227610	+	0.973752i	$0.573091\pi$
$588$		0			0
$589$	−17.4779	+	7.78164i	−0.720162	+	0.320637i
$590$	−1.67250	−	1.85750i	−0.0688558	−	0.0764721i
$591$		0			0
$592$	15.2609	+	6.79460i	0.627220	+	0.279256i
$593$	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
$596$	−0.158922	−	0.0707565i	−0.00650969	−	0.00289830i
$597$		0			0
$598$	3.28015	+	3.64298i	0.134135	+	0.148972i
$599$	−26.1839	+	11.6578i	−1.06985	+	0.476327i	−0.864640	−	0.502392i	$-0.832453\pi$
$599$	−26.1839	+	11.6578i	−1.06985	+	0.476327i	−0.205207	+	0.978719i	$0.565787\pi$
$600$		0			0
$601$	18.2629	−	3.88189i	0.744957	−	0.158346i	0.180232	−	0.983624i	$-0.442315\pi$
$601$	18.2629	−	3.88189i	0.744957	−	0.158346i	0.564726	+	0.825279i	$0.308982\pi$
$602$	−9.43733	−	29.0451i	−0.384637	−	1.18379i
$603$		0			0
$604$	4.29940			0.174940
$605$	5.15278	+	42.7099i	0.209490	+	1.73640i
$606$		0			0
$607$	−3.30683	−	31.4624i	−0.134220	−	1.27702i	−0.829592	−	0.558370i	$-0.811427\pi$
$607$	−3.30683	−	31.4624i	−0.134220	−	1.27702i	0.695372	−	0.718650i	$-0.255240\pi$
$608$	−7.86201	−	1.67112i	−0.318847	−	0.0677729i
$609$		0			0
$610$	−5.26770	+	50.1188i	−0.213283	+	2.02925i
$611$	−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	$0.656709\pi$
$614$	20.7903	+	9.25645i	0.839029	+	0.373560i
$615$		0			0
$616$	42.9435	+	18.7262i	1.73024	+	0.754499i
$617$	−9.68326	+	16.7719i	−0.389833	+	0.675211i	−0.992427	−	0.122837i	$-0.960801\pi$
$617$	−9.68326	+	16.7719i	−0.389833	+	0.675211i	0.602594	+	0.798048i	$0.294134\pi$
$618$		0			0
$619$	25.2167	−	28.0060i	1.01355	−	1.12566i	0.0215023	−	0.999769i	$-0.493155\pi$
$619$	25.2167	−	28.0060i	1.01355	−	1.12566i	0.992044	−	0.125889i	$-0.0401782\pi$
$620$	7.10050	−	21.8531i	0.285163	−	0.877641i
$621$		0			0
$622$	25.3886	+	18.4459i	1.01799	+	0.739614i
$623$	14.9455	−	3.17677i	0.598780	−	0.127275i
$624$		0			0
$625$	−3.08471	−	29.3491i	−0.123389	−	1.17396i
$626$	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	$0.798525\pi$
$632$	−4.39012	+	41.7692i	−0.174629	+	1.66149i
$633$		0			0
$634$	−19.2800	−	21.4126i	−0.765706	−	0.850402i
$635$	−1.67600	−	0.356246i	−0.0665102	−	0.0141372i
$636$		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
$641$	31.4874	−	34.9703i	1.24368	−	1.38124i	0.347421	−	0.937709i	$-0.387057\pi$
$641$	31.4874	−	34.9703i	1.24368	−	1.38124i	0.896257	−	0.443535i	$-0.146276\pi$
$642$		0			0
$643$	−17.5608	+	7.81858i	−0.692531	+	0.308335i	−0.722652	−	0.691212i	$-0.757077\pi$
$643$	−17.5608	+	7.81858i	−0.692531	+	0.308335i	0.0301216	+	0.999546i	$0.490411\pi$
$644$	−20.7377	+	9.23301i	−0.817179	+	0.363831i
$645$		0			0
$646$	2.12649	−	2.36171i	0.0836657	−	0.0929201i
$647$	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
$652$	4.10285	+	0.872087i	0.160680	+	0.0341536i
$653$	14.5613	+	16.1719i	0.569826	+	0.632856i	0.957325	−	0.289014i	$-0.0933275\pi$
$653$	14.5613	+	16.1719i	0.569826	+	0.632856i	−0.387499	+	0.921870i	$0.626661\pi$
$654$		0			0
$655$	−3.32068	+	31.5941i	−0.129750	+	1.23449i
$656$	−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	0.679049	−	0.734093i	$-0.262392\pi$
$659$	−7.60422	−	13.1709i	−0.296218	−	0.513065i	−0.975268	+	0.221028i	$0.929059\pi$
$660$		0			0
$661$	8.83930	−	15.3101i	0.343809	−	0.595495i	−0.641328	−	0.767267i	$-0.721616\pi$
$661$	8.83930	−	15.3101i	0.343809	−	0.595495i	0.985137	+	0.171772i	$0.0549494\pi$
$662$	−1.11820	−	10.6389i	−0.0434600	−	0.413494i
$663$		0			0
$664$	3.00683	−	0.639122i	0.116688	−	0.0248027i
$665$	−32.0165	−	23.2613i	−1.24155	−	0.902036i
$666$		0			0
$667$	−2.80694	+	8.63886i	−0.108685	+	0.334498i
$668$	6.18333	−	6.86728i	0.239240	−	0.265703i
$669$		0			0
$670$	−16.7802	+	29.0642i	−0.648276	+	1.12285i
$671$	−18.8272	−	32.0394i	−0.726816	−	1.23687i
$672$		0			0
$673$	13.0461	+	5.80851i	0.502892	+	0.223902i	0.642472	−	0.766309i	$-0.277909\pi$
$673$	13.0461	+	5.80851i	0.502892	+	0.223902i	−0.139581	+	0.990211i	$0.544575\pi$
$674$	5.03898	+	15.5084i	0.194094	+	0.597360i
$675$		0			0
$676$	−6.93772	−	5.04055i	−0.266835	−	0.193867i
$677$	−3.21158	+	30.5562i	−0.123431	+	1.17437i	0.740960	+	0.671549i	$0.234371\pi$
$677$	−3.21158	+	30.5562i	−0.123431	+	1.17437i	−0.864391	+	0.502820i	$0.832296\pi$
$678$		0			0
$679$	−70.6229	−	15.0114i	−2.71026	−	0.576083i
$680$	1.57691	+	15.0033i	0.0604716	+	0.575349i
$681$		0			0
$682$	−10.4643	−	31.3842i	−0.400697	−	1.20176i
$683$	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
$686$	36.3560	−	7.72771i	1.38808	−	0.295045i
$687$		0			0
$688$	−11.5618	+	5.14765i	−0.440790	+	0.196252i
$689$	0.519486	+	0.576947i	0.0197908	+	0.0219799i
$690$		0			0
$691$	−24.7608	−	11.0242i	−0.941944	−	0.419380i	−0.122454	−	0.992474i	$-0.539076\pi$
$691$	−24.7608	−	11.0242i	−0.941944	−	0.419380i	−0.819490	+	0.573094i	$0.805743\pi$
$692$	−14.3765			−0.546513
$693$		0			0
$694$	−1.70435			−0.0646961
$695$	10.7009	+	4.76435i	0.405908	+	0.180722i
$696$		0			0
$697$	1.38095	+	1.53370i	0.0523072	+	0.0580930i
$698$	−2.12100	+	0.944330i	−0.0802811	+	0.0357434i
$699$		0			0
$700$	31.2928	−	6.65149i	1.18276	−	0.251403i
$701$	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
$704$	8.56895	−	27.0777i	0.322954	−	1.02053i
$705$		0			0
$706$	0.687344	+	6.53964i	0.0258685	+	0.246123i
$707$	68.3628	+	14.5310i	2.57105	+	0.546493i
$708$		0			0
$709$	4.19836	−	39.9447i	0.157673	−	1.50015i	−0.574201	−	0.818714i	$-0.694687\pi$
$709$	4.19836	−	39.9447i	0.157673	−	1.50015i	0.731874	−	0.681440i	$-0.238646\pi$
$710$	−18.6232	−	13.5305i	−0.698915	−	0.507792i
$711$		0			0
$712$	−3.16915	−	9.75363i	−0.118769	−	0.365533i
$713$	57.8806	+	25.7701i	2.16765	+	0.965099i
$714$		0			0
$715$	6.93783	+	3.02535i	0.259460	+	0.113142i
$716$	4.91269	−	8.50903i	0.183596	−	0.317997i
$717$		0			0
$718$	−8.44569	+	9.37989i	−0.315190	+	0.350054i
$719$	−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
$722$	−15.9000	+	3.37965i	−0.591737	+	0.125778i
$723$		0			0
$724$	0.0206143	+	0.196132i	0.000766126	+	0.00728920i
$725$	6.40074	−	11.0864i	0.237718	−	0.411739i
$726$		0			0
$727$	6.61792	+	11.4626i	0.245445	+	0.425123i	0.962257	−	0.272144i	$-0.0877326\pi$
$727$	6.61792	+	11.4626i	0.245445	+	0.425123i	−0.716812	+	0.697267i	$0.754399\pi$
$728$	6.66830	−	4.84480i	0.247144	−	0.179560i
$729$		0			0
$730$	0.528180	−	1.62557i	0.0195488	−	0.0601651i
$731$	−0.758022	+	7.21210i	−0.0280365	+	0.266749i
$732$		0			0
$733$	21.9688	+	24.3988i	0.811436	+	0.901191i	0.996673	−	0.0815025i	$-0.0259719\pi$
$733$	21.9688	+	24.3988i	0.811436	+	0.901191i	−0.185237	+	0.982694i	$0.559305\pi$
$734$	−20.3285	−	4.32097i	−0.750340	−	0.159490i
$735$		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	$0.337555\pi$
$740$	−13.5444	+	15.0426i	−0.497902	+	0.552976i
$741$		0			0
$742$	6.41250	−	2.85503i	0.235410	−	0.104811i
$743$	−46.3464	+	20.6348i	−1.70029	+	0.757016i	−0.701259	+	0.712906i	$0.747379\pi$
$743$	−46.3464	+	20.6348i	−1.70029	+	0.757016i	−0.999027	+	0.0441099i	$0.985955\pi$
$744$		0			0
$745$	−0.672040	+	0.746376i	−0.0246216	+	0.0273451i
$746$	−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
$751$	23.0906	+	4.90806i	0.842588	+	0.179098i	0.608933	−	0.793222i	$-0.291598\pi$
$751$	23.0906	+	4.90806i	0.842588	+	0.179098i	0.233655	+	0.972320i	$0.424931\pi$
$752$	0.772582	+	0.858039i	0.0281732	+	0.0312895i
$753$		0			0
$754$	0.0872253	−	0.829893i	0.00317656	−	0.0302229i
$755$	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
$761$	−1.38386	−	13.1666i	−0.0501651	−	0.477289i	−0.990548	−	0.137170i	$-0.956199\pi$
$761$	−1.38386	−	13.1666i	−0.0501651	−	0.477289i	0.940382	−	0.340119i	$-0.110467\pi$
$762$		0			0
$763$	−1.70851	+	0.363156i	−0.0618524	+	0.0131471i
$764$	0.248331	+	0.180423i	0.00898429	+	0.00652747i
$765$		0			0
$766$	−8.85437	+	27.2509i	−0.319921	+	0.984616i
$767$	0.216987	−	0.240988i	0.00783493	−	0.00870157i
$768$		0			0
$769$	11.5333	−	19.9762i	0.415901	−	0.720362i	−0.579622	−	0.814886i	$-0.696800\pi$
$769$	11.5333	−	19.9762i	0.415901	−	0.720362i	0.995523	+	0.0945241i	$0.0301330\pi$
$770$	45.3984	−	51.2048i	1.63605	−	1.84529i
$771$		0			0
$772$	10.8549	+	4.83290i	0.390675	+	0.173940i
$773$	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
$776$	−5.06557	+	48.1957i	−0.181843	+	1.73012i
$777$		0			0
$778$	25.1115	+	5.33760i	0.900289	+	0.191362i
$779$	0.379838	+	3.61392i	0.0136091	+	0.129482i
$780$		0			0
$781$	16.9743	−	0.130246i	0.607387	−	0.00466058i
$782$	−10.5244			−0.376352
$783$		0			0
$784$	−9.48906	−	29.2043i	−0.338895	−	1.04301i
$785$	−34.7603	+	7.38852i	−1.24065	+	0.263708i
$786$		0			0
$787$	−25.0543	+	11.1549i	−0.893090	+	0.397629i	−0.801379	−	0.598156i	$-0.795900\pi$
$787$	−25.0543	+	11.1549i	−0.893090	+	0.397629i	−0.0917107	+	0.995786i	$0.529233\pi$
$788$	8.00948	+	8.89543i	0.285326	+	0.316887i
$789$		0			0
$790$	56.0445	+	24.9526i	1.99397	+	0.887774i
$791$	−57.0101			−2.02704
$792$		0			0
$793$	−6.53813			−0.232176
$794$	−41.1265	−	18.3107i	−1.45952	−	0.649822i
$795$		0			0
$796$	5.99251	+	6.65535i	0.212399	+	0.235893i
$797$	36.4927	−	16.2476i	1.29264	−	0.575519i	0.358865	−	0.933389i	$-0.383164\pi$
$797$	36.4927	−	16.2476i	1.29264	−	0.575519i	0.933771	+	0.357871i	$0.116497\pi$
$798$		0			0
$799$	0.647128	−	0.137551i	0.0228937	−	0.00486621i
$800$	−11.5922	−	35.6772i	−0.409847	−	1.26138i
$801$		0			0
$802$	38.2160			1.34945
$803$	0.398671	+	1.19569i	0.0140688	+	0.0421948i
$804$		0			0
$805$	13.6992	+	130.339i	0.482834	+	4.59386i
$806$	−5.69331	−	1.21015i	−0.200538	−	0.0426257i
$807$		0			0
$808$	4.90346	−	46.6533i	0.172503	−	1.64126i
$809$	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	$-0.260212\pi$
$812$	3.53008	+	1.57169i	0.123882	+	0.0551557i
$813$		0			0
$814$	−2.82386	+	29.0065i	−0.0989761	+	1.01668i
$815$	12.1083	−	20.9721i	0.424134	−	0.734622i
$816$		0			0
$817$	−8.54389	+	9.48895i	−0.298913	+	0.331976i
$818$	−12.9009	+	39.7050i	−0.451071	+	1.38825i
$819$		0			0
$820$	−3.53078	−	2.56526i	−0.123300	−	0.0895828i
$821$	15.2569	−	3.24295i	0.532469	−	0.113180i	0.0661724	−	0.997808i	$-0.478921\pi$
$821$	15.2569	−	3.24295i	0.532469	−	0.113180i	0.466297	+	0.884628i	$0.345588\pi$
$822$		0			0
$823$	0.428256	+	4.07459i	0.0149281	+	0.142031i	0.999447	−	0.0332460i	$-0.0105845\pi$
$823$	0.428256	+	4.07459i	0.0149281	+	0.142031i	−0.984519	+	0.175277i	$0.943918\pi$
$824$	−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	$-0.0868439\pi$
$830$	0.469354	−	4.46560i	0.0162915	−	0.155003i
$831$		0			0
$832$	−3.34354	−	3.71338i	−0.115916	−	0.128738i
$833$	−17.2106	−	3.65823i	−0.596313	−	0.126750i
$834$		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
$839$	−11.7493	+	13.0489i	−0.405629	+	0.450497i	−0.911001	−	0.412405i	$-0.864689\pi$
$839$	−11.7493	+	13.0489i	−0.405629	+	0.450497i	0.505371	+	0.862902i	$0.331356\pi$
$840$		0			0
$841$	−25.0803	+	11.1665i	−0.864837	+	0.385050i
$842$	16.6199	−	7.39964i	0.572758	−	0.255008i
$843$		0			0
$844$	−5.10480	+	5.66945i	−0.175714	+	0.195151i
$845$	−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
$850$	14.5082	+	3.08381i	0.497626	+	0.105774i
$851$	−37.3470	−	41.4781i	−1.28024	−	1.42185i
$852$		0			0
$853$	−4.13338	+	39.3265i	−0.141524	+	1.34651i	0.661221	+	0.750191i	$0.270039\pi$
$853$	−4.13338	+	39.3265i	−0.141524	+	1.34651i	−0.802745	+	0.596322i	$0.796628\pi$
$854$	−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	0.834160	−	0.551523i	$-0.185953\pi$
$857$	−1.77266	−	3.07034i	−0.0605529	−	0.104881i	−0.894713	+	0.446642i	$0.852620\pi$
$858$		0			0
$859$	12.1359	−	21.0200i	0.414071	−	0.717192i	−0.581259	−	0.813718i	$-0.697440\pi$
$859$	12.1359	−	21.0200i	0.414071	−	0.717192i	0.995330	+	0.0965262i	$0.0307731\pi$
$860$	−1.60298	−	15.2513i	−0.0546611	−	0.520066i
$861$		0			0
$862$	−34.5675	+	7.34754i	−1.17737	+	0.250258i
$863$	−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
$866$	−10.5811	+	11.7515i	−0.359560	+	0.399332i
$867$		0			0
$868$	13.4765	−	23.3420i	0.457423	−	0.792279i
$869$	−44.1767	+	9.74491i	−1.49859	+	0.330573i
$870$		0			0
$871$	−3.97763	−	1.77095i	−0.134777	−	0.0600065i
$872$	0.362284	+	1.11500i	0.0122685	+	0.0377585i
$873$		0			0
$874$	−14.9918	−	10.8922i	−0.507104	−	0.368433i
$875$	9.92984	−	94.4761i	0.335690	−	3.19387i
$876$		0			0
$877$	−14.1903	−	3.01624i	−0.479173	−	0.101851i	−0.0380079	−	0.999277i	$-0.512101\pi$
$877$	−14.1903	−	3.01624i	−0.479173	−	0.101851i	−0.441165	+	0.897426i	$0.645435\pi$
$878$	1.88960	+	17.9783i	0.0637708	+	0.606738i
$879$		0			0
$880$	−23.0700	−	16.4924i	−0.777689	−	0.555958i
$881$	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	$-0.296354\pi$
$884$	−0.484364	+	0.102955i	−0.0162909	+	0.00346275i
$885$		0			0
$886$	−17.2192	+	7.66646i	−0.578489	+	0.257560i
$887$	7.12360	+	7.91156i	0.239187	+	0.265644i	0.850772	−	0.525534i	$-0.176135\pi$
$887$	7.12360	+	7.91156i	0.239187	+	0.265644i	−0.611585	+	0.791178i	$0.709468\pi$
$888$		0			0
$889$	−1.83612	−	0.817495i	−0.0615816	−	0.0274179i
$890$	−14.9803			−0.502141
$891$		0			0
$892$	10.6896			0.357914
$893$	1.06417	+	0.473801i	0.0356113	+	0.0158552i
$894$		0			0
$895$	−37.9569	−	42.1555i	−1.26876	−	1.40910i
$896$	−10.7305	+	4.77755i	−0.358482	+	0.159607i
$897$		0			0
$898$	−18.6166	+	3.95707i	−0.621243	+	0.132049i
$899$	−3.33281	−	10.2573i	−0.111155	−	0.342101i
$900$		0			0
$901$	−1.66678			−0.0555284
$902$	−6.28341	+	0.0482136i	−0.209215	+	0.00160534i
$903$		0			0
$904$	3.99981	+	38.0556i	0.133032	+	1.26571i
$905$	1.11370	+	0.236725i	0.0370208	+	0.00786901i
$906$		0			0
$907$	−4.59088	+	43.6793i	−0.152438	+	1.45035i	0.604366	+	0.796707i	$0.293426\pi$
$907$	−4.59088	+	43.6793i	−0.152438	+	1.45035i	−0.756804	+	0.653642i	$0.773240\pi$
$908$	4.37775	+	3.18062i	0.145281	+	0.105553i
$909$		0			0
$910$	−3.72050	−	11.4505i	−0.123333	−	0.379581i
$911$	−43.7288	−	19.4693i	−1.44880	−	0.645048i	−0.476584	−	0.879129i	$-0.658125\pi$
$911$	−43.7288	−	19.4693i	−1.44880	−	0.645048i	−0.972217	+	0.234081i	$0.924792\pi$
$912$		0			0
$913$	1.67751	+	2.85472i	0.0555174	+	0.0944774i
$914$	−2.58276	+	4.47348i	−0.0854302	+	0.147969i
$915$		0			0
$916$	8.93023	−	9.91803i	0.295063	−	0.327701i
$917$	−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	$0.847787\pi$
$920$	86.0435	−	18.2891i	2.83677	−	0.602974i
$921$		0			0
$922$	1.08163	+	10.2910i	0.0356216	+	0.338916i
$923$	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
$929$	−3.75366	+	35.7137i	−0.123154	+	1.17173i	0.742062	+	0.670331i	$0.233848\pi$
$929$	−3.75366	+	35.7137i	−0.123154	+	1.17173i	−0.865216	+	0.501399i	$0.832819\pi$
$930$		0			0
$931$	−20.7301	−	23.0231i	−0.679401	−	0.754551i
$932$	11.8416	+	2.51702i	0.387886	+	0.0824477i
$933$		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	$0.0434970\pi$
$938$	−26.3414	+	29.2551i	−0.860078	+	0.955213i
$939$		0			0
$940$	−1.27809	+	0.569043i	−0.0416867	+	0.0185601i
$941$	17.8507	−	7.94765i	0.581917	−	0.259086i	−0.0945975	−	0.995516i	$-0.530156\pi$
$941$	17.8507	−	7.94765i	0.581917	−	0.259086i	0.676514	+	0.736430i	$0.263490\pi$
$942$		0			0
$943$	8.05231	−	8.94299i	0.262219	−	0.291224i
$944$	−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	0.503553	−	0.863965i	$-0.332026\pi$
$947$	−15.2771	−	26.4607i	−0.496439	−	0.859858i	−0.999992	+	0.00410698i	$0.998693\pi$
$948$		0			0
$949$	0.216906	+	0.0461047i	0.00704106	+	0.00149662i
$950$	17.4750	+	19.4079i	0.566963	+	0.629676i
$951$		0			0
$952$	−1.84972	+	17.5989i	−0.0599499	+	0.570385i
$953$	−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
$959$	3.22016	+	30.6378i	0.103985	+	0.989347i
$960$		0			0
$961$	−43.2617	+	9.19557i	−1.39554	+	0.296631i
$962$	4.14820	+	3.01385i	0.133743	+	0.0971703i
$963$		0			0
$964$	−3.59969	+	11.0787i	−0.115938	+	0.356821i
$965$	45.9025	−	50.9799i	1.47765	−	1.64110i
$966$		0			0
$967$	−4.38762	+	7.59958i	−0.141096	+	0.244386i	−0.927910	−	0.372805i	$-0.878396\pi$
$967$	−4.38762	+	7.59958i	−0.141096	+	0.244386i	0.786813	+	0.617191i	$0.211729\pi$
$968$	33.8664	−	0.519756i	1.08851	−	0.0167056i
$969$		0			0
$970$	64.6674	+	28.7918i	2.07634	+	0.924448i
$971$	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
$974$	0.804164	−	7.65111i	0.0257671	−	0.245157i
$975$		0			0
$976$	23.9619	+	5.09326i	0.767001	+	0.163031i
$977$	−3.28931	−	31.2957i	−0.105234	−	1.00124i	−0.911951	−	0.410300i	$-0.865424\pi$
$977$	−3.28931	−	31.2957i	−0.105234	−	1.00124i	0.806716	−	0.590939i	$-0.201243\pi$
$978$		0			0
$979$	8.88681	−	6.56141i	0.284024	−	0.209704i
$980$	37.2082			1.18857
$981$		0			0
$982$	9.61715	+	29.5986i	0.306896	+	0.944528i
$983$	43.1838	−	9.17901i	1.37735	−	0.292765i	0.541029	−	0.841004i	$-0.318035\pi$
$983$	43.1838	−	9.17901i	1.37735	−	0.292765i	0.836321	+	0.548239i	$0.184702\pi$
$984$		0			0
$985$	63.1328	−	28.1085i	2.01158	−	0.895612i
$986$	1.19876	+	1.33136i	0.0381764	+	0.0423992i
$987$		0			0
$988$	−0.796518	−	0.354632i	−0.0253406	−	0.0112824i
$989$	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	$0.448901\pi$
$992$	−28.8724	−	12.8548i	−0.916698	−	0.408140i
$993$		0			0
$994$	−18.0679	−	20.0664i	−0.573079	−	0.636469i
$995$	47.2345	−	21.0301i	1.49743	−	0.666700i
$996$		0			0
$997$	−48.3979	+	10.2873i	−1.53278	+	0.325802i	−0.895581	−	0.444899i	$-0.853239\pi$
$997$	−48.3979	+	10.2873i	−1.53278	+	0.325802i	−0.637197	+	0.770701i	$0.719906\pi$
$998$	−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.190.5		96
3.2	odd	2	inner	891.2.n.l.190.8		96
9.2	odd	6	inner	891.2.n.l.784.5		96
9.4	even	3		891.2.f.g.487.8	yes	48
9.5	odd	6		891.2.f.g.487.5	✓	48
9.7	even	3	inner	891.2.n.l.784.8		96
11.4	even	5	inner	891.2.n.l.433.8		96
33.26	odd	10	inner	891.2.n.l.433.5		96
99.4	even	15		891.2.f.g.730.8	yes	48
99.13	odd	30		9801.2.a.cq.1.16		24
99.31	even	15		9801.2.a.cr.1.9		24
99.59	odd	30		891.2.f.g.730.5	yes	48
99.68	even	30		9801.2.a.cq.1.9		24
99.70	even	15	inner	891.2.n.l.136.5		96
99.86	odd	30		9801.2.a.cr.1.16		24
99.92	odd	30	inner	891.2.n.l.136.8		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
891.2.f.g.487.5	✓	48	9.5	odd	6
891.2.f.g.487.8	yes	48	9.4	even	3
891.2.f.g.730.5	yes	48	99.59	odd	30
891.2.f.g.730.8	yes	48	99.4	even	15
891.2.n.l.136.5		96	99.70	even	15	inner
891.2.n.l.136.8		96	99.92	odd	30	inner
891.2.n.l.190.5		96	1.1	even	1	trivial
891.2.n.l.190.8		96	3.2	odd	2	inner
891.2.n.l.433.5		96	33.26	odd	10	inner
891.2.n.l.433.8		96	11.4	even	5	inner
891.2.n.l.784.5		96	9.2	odd	6	inner
891.2.n.l.784.8		96	9.7	even	3	inner
9801.2.a.cq.1.9		24	99.68	even	30
9801.2.a.cq.1.16		24	99.13	odd	30
9801.2.a.cr.1.9		24	99.31	even	15
9801.2.a.cr.1.16		24	99.86	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)

\(f(q)\)	\(=\)	\(q+(-1.05062 - 0.467766i) q^{2} +(-0.453266 - 0.503403i) q^{4} +(-3.57276 + 1.59069i) q^{5} +(-4.48724 + 0.953792i) q^{7} +(0.951502 + 2.92842i) q^{8} +4.49768 q^{10} +(-2.66817 + 1.96999i) q^{11} +(0.0609944 + 0.580323i) q^{13} +(5.16053 + 1.09690i) q^{14} +(0.228535 - 2.17437i) q^{16} +(-1.01351 - 0.736358i) q^{17} +(-0.681632 - 2.09785i) q^{19} +(2.42017 + 1.07753i) q^{20} +(3.72472 - 0.821635i) q^{22} +(-3.65244 + 6.32621i) q^{23} +(6.88865 - 7.65062i) q^{25} +(0.207373 - 0.638229i) q^{26} +(2.51406 + 1.82657i) q^{28} +(1.21630 - 0.258533i) q^{29} +(-0.906619 - 8.62591i) q^{31} +(1.82193 - 3.15567i) q^{32} +(0.720369 + 1.24772i) q^{34} +(14.5146 - 10.5455i) q^{35} +(-2.36110 + 7.26672i) q^{37} +(-0.265166 + 2.52288i) q^{38} +(-8.05772 - 8.94900i) q^{40} +(-1.61139 - 0.342512i) q^{41} +(-2.89432 - 5.01312i) q^{43} +(2.20109 + 0.450233i) q^{44} +(6.79650 - 4.93795i) q^{46} +(-0.353367 + 0.392454i) q^{47} +(12.8308 - 5.71263i) q^{49} +(-10.8160 + 4.81561i) q^{50} +(0.264490 - 0.293745i) q^{52} +(1.07638 - 0.782035i) q^{53} +(6.39907 - 11.2826i) q^{55} +(-7.06272 - 12.2330i) q^{56} +(-1.39880 - 0.297325i) q^{58} +(-0.371858 - 0.412991i) q^{59} +(-1.17120 + 11.1433i) q^{61} +(-3.08239 + 9.48662i) q^{62} +(-6.92785 + 5.03338i) q^{64} +(-1.14103 - 1.97633i) q^{65} +(-3.73086 + 6.46203i) q^{67} +(0.0887048 + 0.843970i) q^{68} +(-20.1822 + 4.28985i) q^{70} +(-4.14062 - 3.00833i) q^{71} +(0.117434 - 0.361425i) q^{73} +(5.87974 - 6.53011i) q^{74} +(-0.747102 + 1.29402i) q^{76} +(10.0937 - 11.3847i) q^{77} +(12.4607 + 5.54788i) q^{79} +(2.64225 + 8.13202i) q^{80} +(1.53274 + 1.11360i) q^{82} +(0.104355 - 0.992868i) q^{83} +(4.79235 + 1.01864i) q^{85} +(0.695868 + 6.62074i) q^{86} +(-8.30774 - 5.93907i) q^{88} -3.33068 q^{89} +(-0.827203 - 2.54587i) q^{91} +(4.84016 - 1.02881i) q^{92} +(0.554831 - 0.247027i) q^{94} +(5.77234 + 6.41083i) q^{95} +(14.3779 + 6.40147i) q^{97} -16.1524 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 8 q^{4} + 14 q^{7} + 64 q^{10} + 14 q^{13} + 4 q^{16} - 16 q^{19} - 16 q^{22} + 20 q^{25} - 36 q^{28} + 4 q^{31} - 84 q^{34} - 24 q^{37} + 106 q^{40} - 84 q^{43} - 76 q^{46} + 54 q^{49} - 52 q^{52}+ \cdots + 66 q^{97}+O(q^{100}) \) 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

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more