LMFDB - Embedded newform 891.2.u.e.512.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [891,2,Mod(107,891)]

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([5, 9]))

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

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

chi := DirichletCharacter("891.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 891 = 3^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	891.u (of order $30$, 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:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{30})$
Twist minimal:	no (minimal twist has level 297)
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			512.5
Character	$\chi$	$=$	891.512
Dual form			891.2.u.e.134.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.607139 + 0.129051i) q^{2} +(-1.47513 - 0.656769i) q^{4} +(0.776244 + 3.65194i) q^{5} +(2.20625 - 0.231886i) q^{7} +(-1.81517 - 1.31880i) q^{8} +O(q^{10})$	\(q+(0.607139 + 0.129051i) q^{2} +(-1.47513 - 0.656769i) q^{4} +(0.776244 + 3.65194i) q^{5} +(2.20625 - 0.231886i) q^{7} +(-1.81517 - 1.31880i) q^{8} +2.31741i q^{10} +(-3.15510 - 1.02242i) q^{11} +(4.58440 + 4.12782i) q^{13} +(1.36942 + 0.143932i) q^{14} +(1.22906 + 1.36501i) q^{16} +(0.0962825 - 0.296327i) q^{17} +(1.44540 - 1.98943i) q^{19} +(1.25342 - 5.89689i) q^{20} +(-1.78364 - 1.02792i) q^{22} +(-7.72848 + 4.46204i) q^{23} +(-8.16640 + 3.63592i) q^{25} +(2.25067 + 3.09778i) q^{26} +(-3.40679 - 1.10693i) q^{28} +(0.690036 + 6.56526i) q^{29} +(-0.721480 + 0.801285i) q^{31} +(2.81373 + 4.87352i) q^{32} +(0.0966983 - 0.167486i) q^{34} +(2.55942 + 7.87708i) q^{35} +(-3.01593 + 2.19120i) q^{37} +(1.13430 - 1.02133i) q^{38} +(3.40716 - 7.65260i) q^{40} +(-0.436738 + 4.15528i) q^{41} +(4.12066 + 2.37906i) q^{43} +(3.98268 + 3.58037i) q^{44} +(-5.26809 + 1.71171i) q^{46} +(0.585996 + 1.31617i) q^{47} +(-2.03329 + 0.432188i) q^{49} +(-5.42736 + 1.15362i) q^{50} +(-4.05156 - 9.09995i) q^{52} +(5.61052 - 1.82297i) q^{53} +(1.28469 - 12.3159i) q^{55} +(-4.31052 - 2.48868i) q^{56} +(-0.428307 + 4.07507i) q^{58} +(2.27545 - 5.11074i) q^{59} +(1.11847 - 1.00708i) q^{61} +(-0.541446 + 0.393383i) q^{62} +(-0.0558176 - 0.171789i) q^{64} +(-11.5159 + 19.9462i) q^{65} +(-1.39875 - 2.42271i) q^{67} +(-0.336647 + 0.373885i) q^{68} +(0.537375 + 5.11278i) q^{70} +(6.47873 + 2.10507i) q^{71} +(5.66251 + 7.79378i) q^{73} +(-2.11386 + 0.941153i) q^{74} +(-3.43875 + 1.98536i) q^{76} +(-7.19801 - 1.52409i) q^{77} +(1.03441 - 4.86651i) q^{79} +(-4.03089 + 5.54804i) q^{80} +(-0.801405 + 2.46647i) q^{82} +(-8.96283 - 9.95424i) q^{83} +(1.15691 + 0.121596i) q^{85} +(2.19479 + 1.97620i) q^{86} +(4.37867 + 6.01680i) q^{88} -3.05090i q^{89} +(11.0715 + 8.04392i) q^{91} +(14.3310 - 1.50625i) q^{92} +(0.185928 + 0.874721i) q^{94} +(8.38726 + 3.73425i) q^{95} +(14.3958 + 3.05992i) q^{97} -1.29026 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 8 q^{4}+O(q^{10}) $ 64 * q + 8 * q^4	$ 64 q + 8 q^{4} + 4 q^{16} - 36 q^{22} - 8 q^{25} - 200 q^{28} - 8 q^{31} + 64 q^{34} - 24 q^{37} + 60 q^{40} - 40 q^{46} - 100 q^{52} + 16 q^{55} - 24 q^{58} - 60 q^{61} + 72 q^{64} + 24 q^{67} - 8 q^{70} + 160 q^{73} + 60 q^{79} + 144 q^{82} + 20 q^{85} + 24 q^{88} + 48 q^{91} - 20 q^{94} + 24 q^{97}+O(q^{100}) $ 64 * q + 8 * q^4 + 4 * q^16 - 36 * q^22 - 8 * q^25 - 200 * q^28 - 8 * q^31 + 64 * q^34 - 24 * q^37 + 60 * q^40 - 40 * q^46 - 100 * q^52 + 16 * q^55 - 24 * q^58 - 60 * q^61 + 72 * q^64 + 24 * q^67 - 8 * q^70 + 160 * q^73 + 60 * q^79 + 144 * q^82 + 20 * q^85 + 24 * q^88 + 48 * q^91 - 20 * q^94 + 24 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$244$	$650$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.607139	+	0.129051i	0.429312	+	0.0912531i	0.417500	−	0.908677i	$-0.362907\pi$
$2$	0.607139	+	0.129051i	0.429312	+	0.0912531i	0.0118125	+	0.999930i	$0.496240\pi$
$3$		0			0
$3$		0			0
$4$	−1.47513	−	0.656769i	−0.737564	−	0.328385i
$5$	0.776244	+	3.65194i	0.347147	+	1.63320i	0.712033	+	0.702146i	$0.247775\pi$
$5$	0.776244	+	3.65194i	0.347147	+	1.63320i	−0.364886	+	0.931052i	$0.618892\pi$
$6$		0			0
$7$	2.20625	−	0.231886i	0.833882	−	0.0876446i	0.322042	−	0.946725i	$-0.395631\pi$
$7$	2.20625	−	0.231886i	0.833882	−	0.0876446i	0.511840	+	0.859081i	$0.328964\pi$
$8$	−1.81517	−	1.31880i	−0.641759	−	0.466265i
$9$		0			0
$10$			2.31741i			0.732830i
$11$	−3.15510	−	1.02242i	−0.951298	−	0.308271i
$11$	−3.15510	−	1.02242i	−0.951298	−	0.308271i
$12$		0			0
$13$	4.58440	+	4.12782i	1.27148	+	1.14485i	0.982247	+	0.187593i	$0.0600685\pi$
$13$	4.58440	+	4.12782i	1.27148	+	1.14485i	0.289238	+	0.957257i	$0.406598\pi$
$14$	1.36942	+	0.143932i	0.365994	+	0.0384675i
$15$		0			0
$16$	1.22906	+	1.36501i	0.307265	+	0.341253i
$17$	0.0962825	−	0.296327i	0.0233519	−	0.0718699i	−0.938701	−	0.344731i	$-0.887970\pi$
$17$	0.0962825	−	0.296327i	0.0233519	−	0.0718699i	0.962053	+	0.272861i	$0.0879700\pi$
$18$		0			0
$19$	1.44540	−	1.98943i	0.331598	−	0.456406i	−0.610366	−	0.792120i	$-0.708977\pi$
$19$	1.44540	−	1.98943i	0.331598	−	0.456406i	0.941964	+	0.335714i	$0.108977\pi$
$20$	1.25342	−	5.89689i	0.280274	−	1.31859i
$21$		0			0
$22$	−1.78364	−	1.02792i	−0.380273	−	0.219154i
$23$	−7.72848	+	4.46204i	−1.61150	+	0.930399i	−0.622475	+	0.782639i	$0.713873\pi$
$23$	−7.72848	+	4.46204i	−1.61150	+	0.930399i	−0.989023	+	0.147760i	$0.952794\pi$
$24$		0			0
$25$	−8.16640	+	3.63592i	−1.63328	+	0.727183i
$26$	2.25067	+	3.09778i	0.441393	+	0.607525i
$27$		0			0
$28$	−3.40679	−	1.10693i	−0.643822	−	0.209191i
$29$	0.690036	+	6.56526i	0.128136	+	1.21914i	0.849880	+	0.526977i	$0.176674\pi$
$29$	0.690036	+	6.56526i	0.128136	+	1.21914i	−0.721743	+	0.692161i	$0.756659\pi$
$30$		0			0
$31$	−0.721480	+	0.801285i	−0.129582	+	0.143915i	−0.804444	−	0.594029i	$-0.797536\pi$
$31$	−0.721480	+	0.801285i	−0.129582	+	0.143915i	0.674862	+	0.737944i	$0.264203\pi$
$32$	2.81373	+	4.87352i	0.497401	+	0.861524i
$33$		0			0
$34$	0.0966983	−	0.167486i	0.0165836	−	0.0287237i
$35$	2.55942	+	7.87708i	0.432621	+	1.33147i
$36$		0			0
$37$	−3.01593	+	2.19120i	−0.495815	+	0.360231i	−0.807416	−	0.589982i	$-0.799135\pi$
$37$	−3.01593	+	2.19120i	−0.495815	+	0.360231i	0.311601	+	0.950213i	$0.399135\pi$
$38$	1.13430	−	1.02133i	0.184008	−	0.165681i
$39$		0			0
$40$	3.40716	−	7.65260i	0.538719	−	1.20998i
$41$	−0.436738	+	4.15528i	−0.0682070	+	0.648946i	0.905998	+	0.423282i	$0.139122\pi$
$41$	−0.436738	+	4.15528i	−0.0682070	+	0.648946i	−0.974205	+	0.225664i	$0.927545\pi$
$42$		0			0
$43$	4.12066	+	2.37906i	0.628394	+	0.362803i	0.780130	−	0.625618i	$-0.215153\pi$
$43$	4.12066	+	2.37906i	0.628394	+	0.362803i	−0.151736	+	0.988421i	$0.548486\pi$
$44$	3.98268	+	3.58037i	0.600412	+	0.539762i
$45$		0			0
$46$	−5.26809	+	1.71171i	−0.776738	+	0.252377i
$47$	0.585996	+	1.31617i	0.0854763	+	0.191983i	0.951226	−	0.308494i	$-0.0998248\pi$
$47$	0.585996	+	1.31617i	0.0854763	+	0.191983i	−0.865750	+	0.500477i	$0.833158\pi$
$48$		0			0
$49$	−2.03329	+	0.432188i	−0.290469	+	0.0617412i
$50$	−5.42736	+	1.15362i	−0.767545	+	0.163147i
$51$		0			0
$52$	−4.05156	−	9.09995i	−0.561850	−	1.26194i
$53$	5.61052	−	1.82297i	0.770664	−	0.250404i	0.102815	−	0.994701i	$-0.467215\pi$
$53$	5.61052	−	1.82297i	0.770664	−	0.250404i	0.667849	+	0.744297i	$0.267215\pi$
$54$		0			0
$55$	1.28469	−	12.3159i	0.173228	−	1.66067i
$56$	−4.31052	−	2.48868i	−0.576017	−	0.332564i
$57$		0			0
$58$	−0.428307	+	4.07507i	−0.0562395	+	0.535083i
$59$	2.27545	−	5.11074i	0.296238	−	0.665361i	−0.702698	−	0.711489i	$-0.748021\pi$
$59$	2.27545	−	5.11074i	0.296238	−	0.665361i	0.998936	+	0.0461273i	$0.0146880\pi$
$60$		0			0
$61$	1.11847	−	1.00708i	0.143206	−	0.128943i	−0.594414	−	0.804159i	$-0.702616\pi$
$61$	1.11847	−	1.00708i	0.143206	−	0.128943i	0.737620	+	0.675216i	$0.235949\pi$
$62$	−0.541446	+	0.393383i	−0.0687637	+	0.0499597i
$63$		0			0
$64$	−0.0558176	−	0.171789i	−0.00697720	−	0.0214736i
$65$	−11.5159	+	19.9462i	−1.42838	+	2.47402i
$66$		0			0
$67$	−1.39875	−	2.42271i	−0.170885	−	0.295981i	0.767845	−	0.640636i	$-0.221329\pi$
$67$	−1.39875	−	2.42271i	−0.170885	−	0.295981i	−0.938729	+	0.344655i	$0.887996\pi$
$68$	−0.336647	+	0.373885i	−0.0408245	+	0.0453402i
$69$		0			0
$70$	0.537375	+	5.11278i	0.0642286	+	0.611094i
$71$	6.47873	+	2.10507i	0.768884	+	0.249826i	0.667087	−	0.744980i	$-0.267541\pi$
$71$	6.47873	+	2.10507i	0.768884	+	0.249826i	0.101797	+	0.994805i	$0.467541\pi$
$72$		0			0
$73$	5.66251	+	7.79378i	0.662747	+	0.912193i	0.999568	−	0.0293753i	$-0.00935180\pi$
$73$	5.66251	+	7.79378i	0.662747	+	0.912193i	−0.336821	+	0.941569i	$0.609352\pi$
$74$	−2.11386	+	0.941153i	−0.245732	+	0.109407i
$75$		0			0
$76$	−3.43875	+	1.98536i	−0.394452	+	0.227737i
$77$	−7.19801	−	1.52409i	−0.820289	−	0.173686i
$78$		0			0
$79$	1.03441	−	4.86651i	0.116380	−	0.547525i	−0.880866	−	0.473365i	$-0.843039\pi$
$79$	1.03441	−	4.86651i	0.116380	−	0.547525i	0.997246	−	0.0741597i	$-0.0236275\pi$
$80$	−4.03089	+	5.54804i	−0.450667	+	0.620290i
$81$		0			0
$82$	−0.801405	+	2.46647i	−0.0885004	+	0.272376i
$83$	−8.96283	−	9.95424i	−0.983799	−	1.09262i	−0.995695	−	0.0926900i	$-0.970453\pi$
$83$	−8.96283	−	9.95424i	−0.983799	−	1.09262i	0.0118962	−	0.999929i	$-0.496213\pi$
$84$		0			0
$85$	1.15691	+	0.121596i	0.125484	+	0.0131889i
$86$	2.19479	+	1.97620i	0.236670	+	0.213099i
$87$		0			0
$88$	4.37867	+	6.01680i	0.466768	+	0.641393i
$89$		−	3.05090i		−	0.323394i	−0.986840	−	0.161697i	$-0.948303\pi$
$89$		−	3.05090i		−	0.323394i	0.986840	−	0.161697i	$-0.0516968\pi$
$90$		0			0
$91$	11.0715	+	8.04392i	1.16061	+	0.843231i
$92$	14.3310	−	1.50625i	1.49411	−	0.157037i
$93$		0			0
$94$	0.185928	+	0.874721i	0.0191770	+	0.0902206i
$95$	8.38726	+	3.73425i	0.860515	+	0.383126i
$96$		0			0
$97$	14.3958	+	3.05992i	1.46167	+	0.310688i	0.869022	−	0.494774i	$-0.164749\pi$
$97$	14.3958	+	3.05992i	1.46167	+	0.310688i	0.592648	+	0.805461i	$0.298082\pi$
$98$	−1.29026			−0.130336
$99$		0			0
$100$	14.4344			1.44344
$101$	6.41057	+	1.36261i	0.637876	+	0.135585i	0.515487	−	0.856898i	$-0.327611\pi$
$101$	6.41057	+	1.36261i	0.637876	+	0.135585i	0.122389	+	0.992482i	$0.460944\pi$
$102$		0			0
$103$	−8.00445	−	3.56381i	−0.788702	−	0.351153i	−0.0274620	−	0.999623i	$-0.508743\pi$
$103$	−8.00445	−	3.56381i	−0.788702	−	0.351153i	−0.761240	+	0.648470i	$0.775409\pi$
$104$	−2.87771	−	13.5386i	−0.282183	−	1.32757i
$105$		0			0
$106$	3.64162	−	0.382750i	0.353705	−	0.0371759i
$107$	−0.618545	−	0.449399i	−0.0597970	−	0.0434451i	0.557485	−	0.830187i	$-0.311766\pi$
$107$	−0.618545	−	0.449399i	−0.0597970	−	0.0434451i	−0.617282	+	0.786742i	$0.711766\pi$
$108$		0			0
$109$		−	4.39272i		−	0.420746i	−0.977621	−	0.210373i	$-0.932532\pi$
$109$		−	4.39272i		−	0.420746i	0.977621	−	0.210373i	$-0.0674678\pi$
$110$	2.36937	−	7.31167i	0.225911	−	0.697140i
$111$		0			0
$112$	3.02814	+	2.72655i	0.286132	+	0.257634i
$113$	−5.98198	−	0.628732i	−0.562738	−	0.0591461i	−0.181111	−	0.983463i	$-0.557969\pi$
$113$	−5.98198	−	0.628732i	−0.562738	−	0.0591461i	−0.381627	+	0.924317i	$0.624636\pi$
$114$		0			0
$115$	−22.2943	−	24.7603i	−2.07895	−	2.30891i
$116$	3.29397	−	10.1378i	0.305837	−	0.941269i
$117$		0			0
$118$	2.04106	−	2.80928i	0.187895	−	0.258615i
$119$	0.143709	−	0.676097i	0.0131738	−	0.0619777i
$120$		0			0
$121$	8.90931	+	6.45168i	0.809937	+	0.586516i
$122$	0.809034	−	0.467096i	0.0732465	−	0.0422889i
$123$		0			0
$124$	1.59053	−	0.708152i	0.142834	−	0.0635939i
$125$	−8.64472	−	11.8984i	−0.773207	−	1.06423i
$126$		0			0
$127$	−10.7264	−	3.48521i	−0.951811	−	0.309262i	−0.208360	−	0.978052i	$-0.566813\pi$
$127$	−10.7264	−	3.48521i	−0.951811	−	0.309262i	−0.743451	+	0.668790i	$0.766813\pi$
$128$	−1.18818	−	11.3048i	−0.105021	−	0.999208i
$129$		0			0
$130$	−9.56585	+	10.6240i	−0.838981	+	0.931782i
$131$	8.59104	+	14.8801i	0.750603	+	1.30008i	0.947531	+	0.319664i	$0.103570\pi$
$131$	8.59104	+	14.8801i	0.750603	+	1.30008i	−0.196928	+	0.980418i	$0.563097\pi$
$132$		0			0
$133$	2.72760	−	4.72433i	0.236513	−	0.409652i
$134$	−0.536583	−	1.65143i	−0.0463537	−	0.142662i
$135$		0			0
$136$	−0.565564	+	0.410906i	−0.0484967	+	0.0352349i
$137$	1.01033	−	0.909706i	0.0863184	−	0.0777214i	−0.624842	−	0.780751i	$-0.714837\pi$
$137$	1.01033	−	0.909706i	0.0863184	−	0.0777214i	0.711160	+	0.703030i	$0.248170\pi$
$138$		0			0
$139$	4.90673	−	11.0207i	0.416183	−	0.934763i	−0.576841	−	0.816856i	$-0.695715\pi$
$139$	4.90673	−	11.0207i	0.416183	−	0.934763i	0.993025	−	0.117907i	$-0.0376185\pi$
$140$	1.39795	−	13.3006i	0.118149	−	1.12411i
$141$		0			0
$142$	3.66183	+	2.11416i	0.307294	+	0.177416i
$143$	−10.2439	−	17.7109i	−0.856637	−	1.48106i
$144$		0			0
$145$	−23.4403	+	7.61622i	−1.94661	+	0.632492i
$146$	2.43213	+	5.46266i	0.201285	+	0.452093i
$147$		0			0
$148$	5.88799	−	1.25153i	0.483990	−	0.102875i
$149$	14.3002	−	3.03960i	1.17152	−	0.249013i	0.419249	−	0.907872i	$-0.362294\pi$
$149$	14.3002	−	3.03960i	1.17152	−	0.249013i	0.752267	+	0.658858i	$0.228960\pi$
$150$		0			0
$151$	−1.13147	−	2.54132i	−0.0920775	−	0.206809i	0.861636	−	0.507527i	$-0.169440\pi$
$151$	−1.13147	−	2.54132i	−0.0920775	−	0.206809i	−0.953713	+	0.300718i	$0.902774\pi$
$152$	−5.24730	+	1.70495i	−0.425613	+	0.138290i
$153$		0			0
$154$	−4.17351	−	1.85425i	−0.336311	−	0.149419i
$155$	−3.48629	−	2.01281i	−0.280026	−	0.161673i
$156$		0			0
$157$	1.85052	−	17.6065i	0.147688	−	1.40516i	−0.630044	−	0.776559i	$-0.716963\pi$
$157$	1.85052	−	17.6065i	0.147688	−	1.40516i	0.777732	−	0.628596i	$-0.216370\pi$
$158$	1.25606	−	2.82115i	0.0999266	−	0.224439i
$159$		0			0
$160$	−15.6137	+	14.0586i	−1.23437	+	1.11143i
$161$	−16.0162	+	11.6365i	−1.26226	+	0.917083i
$162$		0			0
$163$	0.454189	+	1.39785i	0.0355748	+	0.109488i	0.967267	−	0.253761i	$-0.0816675\pi$
$163$	0.454189	+	1.39785i	0.0355748	+	0.109488i	−0.931692	+	0.363249i	$0.881668\pi$
$164$	3.37330	−	5.84273i	0.263411	−	0.456241i
$165$		0			0
$166$	−4.15708	−	7.20027i	−0.322652	−	0.558849i
$167$	6.01213	−	6.67715i	0.465233	−	0.516693i	−0.464177	−	0.885742i	$-0.653650\pi$
$167$	6.01213	−	6.67715i	0.465233	−	0.516693i	0.929410	+	0.369049i	$0.120317\pi$
$168$		0			0
$169$	2.61903	+	24.9184i	0.201463	+	1.91680i
$170$	0.686712	+	0.223126i	0.0526684	+	0.0171130i
$171$		0			0
$172$	−4.51600	−	6.21574i	−0.344342	−	0.473946i
$173$	6.02423	−	2.68216i	0.458014	−	0.203921i	−0.164743	−	0.986337i	$-0.552679\pi$
$173$	6.02423	−	2.68216i	0.458014	−	0.203921i	0.622757	+	0.782416i	$0.286013\pi$
$174$		0			0
$175$	−17.1740	+	9.91540i	−1.29823	+	0.749534i
$176$	−2.48219	−	5.56336i	−0.187102	−	0.419354i
$177$		0			0
$178$	0.393722	−	1.85232i	0.0295107	−	0.138837i
$179$	0.750385	−	1.03282i	0.0560864	−	0.0771963i	−0.780053	−	0.625714i	$-0.784808\pi$
$179$	0.750385	−	1.03282i	0.0560864	−	0.0771963i	0.836139	+	0.548518i	$0.184808\pi$
$180$		0			0
$181$	6.39068	−	19.6685i	0.475016	−	1.46195i	−0.370921	−	0.928664i	$-0.620958\pi$
$181$	6.39068	−	19.6685i	0.475016	−	1.46195i	0.845937	−	0.533283i	$-0.179042\pi$
$182$	5.68386	+	6.31257i	0.421316	+	0.467919i
$183$		0			0
$184$	19.9130	+	2.09294i	1.46801	+	0.154294i
$185$	−10.3432	−	9.31309i	−0.760450	−	0.684712i
$186$		0			0
$187$	−0.606752	+	0.836500i	−0.0443701	+	0.0611709i
$188$		−	2.32638i		−	0.169669i
$189$		0			0
$190$	4.61032	+	3.34960i	0.334468	+	0.243005i
$191$	6.69305	−	0.703468i	0.484292	−	0.0509012i	0.140763	−	0.990043i	$-0.455044\pi$
$191$	6.69305	−	0.703468i	0.484292	−	0.0509012i	0.343529	+	0.939142i	$0.388378\pi$
$192$		0			0
$193$	−3.28299	−	15.4453i	−0.236315	−	1.11177i	−0.922994	−	0.384814i	$-0.874266\pi$
$193$	−3.28299	−	15.4453i	−0.236315	−	1.11177i	0.686679	−	0.726961i	$-0.259068\pi$
$194$	8.34535	+	3.71559i	0.599161	+	0.266764i
$195$		0			0
$196$	3.28320	+	0.697867i	0.234515	+	0.0498476i
$197$	−2.09103			−0.148980			−0.0744900	−	0.997222i	$-0.523733\pi$
$197$	−2.09103			−0.148980			−0.0744900	+	0.997222i	$0.523733\pi$
$198$		0			0
$199$	−3.76773			−0.267087			−0.133544	−	0.991043i	$-0.542636\pi$
$199$	−3.76773			−0.267087			−0.133544	+	0.991043i	$0.542636\pi$
$200$	19.6184	+	4.17003i	1.38723	+	0.294865i
$201$		0			0
$202$	3.71626	+	1.65459i	0.261475	+	0.116416i
$203$	3.04478	+	14.3246i	0.213702	+	1.00539i
$204$		0			0
$205$	−15.5139	+	1.63057i	−1.08354	+	0.113884i
$206$	−4.39990	−	3.19671i	−0.306556	−	0.222726i
$207$		0			0
$208$			11.3311i			0.785670i
$209$	−6.59443	+	4.79903i	−0.456146	+	0.331956i
$210$		0			0
$211$	8.09236	+	7.28640i	0.557101	+	0.501616i	0.898898	−	0.438158i	$-0.144369\pi$
$211$	8.09236	+	7.28640i	0.557101	+	0.501616i	−0.341797	+	0.939774i	$0.611035\pi$
$212$	−9.47350	−	0.995705i	−0.650642	−	0.0683853i
$213$		0			0
$214$	−0.317547	−	0.352672i	−0.0217071	−	0.0241082i
$215$	−5.48956	+	16.8951i	−0.374385	+	1.15224i
$216$		0			0
$217$	−1.40596	+	1.93513i	−0.0954425	+	0.131365i
$218$	0.566886	−	2.66699i	0.0383944	−	0.180631i
$219$		0			0
$220$	−9.98378	+	17.3238i	−0.673107	+	1.16797i
$221$	1.66458	−	0.961046i	0.111972	−	0.0646470i
$222$		0			0
$223$	10.3750	−	4.61926i	0.694764	−	0.309329i	−0.0288010	−	0.999585i	$-0.509169\pi$
$223$	10.3750	−	4.61926i	0.694764	−	0.309329i	0.723565	+	0.690256i	$0.242502\pi$
$224$	7.33787	+	10.0997i	0.490282	+	0.674815i
$225$		0			0
$226$	−3.55076	−	1.15371i	−0.236193	−	0.0767437i
$227$	1.11988	+	10.6550i	0.0743292	+	0.707195i	0.966704	+	0.255899i	$0.0823714\pi$
$227$	1.11988	+	10.6550i	0.0743292	+	0.707195i	−0.892374	+	0.451296i	$0.850962\pi$
$228$		0			0
$229$	−13.1650	+	14.6213i	−0.869971	+	0.966200i	−0.999679	−	0.0253520i	$-0.991929\pi$
$229$	−13.1650	+	14.6213i	−0.869971	+	0.966200i	0.129708	+	0.991552i	$0.458596\pi$
$230$	−10.3404	−	17.9101i	−0.681825	−	1.18095i
$231$		0			0
$232$	7.40571	−	12.8271i	0.486209	−	0.842138i
$233$	−6.22888	−	19.1705i	−0.408068	−	1.25590i	−0.918306	−	0.395871i	$-0.870443\pi$
$233$	−6.22888	−	19.1705i	−0.408068	−	1.25590i	0.510238	−	0.860033i	$-0.329557\pi$
$234$		0			0
$235$	−4.35170	+	3.16169i	−0.283874	+	0.206246i
$236$	−6.71315	+	6.04454i	−0.436989	+	0.393466i
$237$		0			0
$238$	0.174502	−	0.391939i	0.0113113	−	0.0254056i
$239$	1.79773	−	17.1043i	0.116286	−	1.10638i	−0.768327	−	0.640058i	$-0.778910\pi$
$239$	1.79773	−	17.1043i	0.116286	−	1.10638i	0.884612	−	0.466327i	$-0.154423\pi$
$240$		0			0
$241$	17.7792	+	10.2648i	1.14526	+	0.661215i	0.947727	−	0.319081i	$-0.103374\pi$
$241$	17.7792	+	10.2648i	1.14526	+	0.661215i	0.197531	+	0.980297i	$0.436708\pi$
$242$	4.57659	+	5.06683i	0.294194	+	0.325708i
$243$		0			0
$244$	−2.31131	+	0.750990i	−0.147966	+	0.0480772i
$245$	−3.15665	−	7.08996i	−0.201671	−	0.452961i
$246$		0			0
$247$	14.8383	−	3.15398i	0.944139	−	0.200683i
$248$	2.36634	−	0.502981i	0.150263	−	0.0319394i
$249$		0			0
$250$	−3.71304	−	8.33962i	−0.234833	−	0.527444i
$251$	−6.04667	+	1.96468i	−0.381662	+	0.124010i	−0.493563	−	0.869710i	$-0.664306\pi$
$251$	−6.04667	+	1.96468i	−0.381662	+	0.124010i	0.111901	+	0.993719i	$0.464306\pi$
$252$		0			0
$253$	28.9462	−	6.17642i	1.81983	−	0.388308i
$254$	−6.06263	−	3.50026i	−0.380403	−	0.219626i
$255$		0			0
$256$	0.699743	−	6.65761i	0.0437339	−	0.416101i
$257$	5.63007	−	12.6453i	0.351194	−	0.788794i	−0.648427	−	0.761276i	$-0.724573\pi$
$257$	5.63007	−	12.6453i	0.351194	−	0.788794i	0.999621	−	0.0275179i	$-0.00876032\pi$
$258$		0			0
$259$	−6.14577	+	5.53367i	−0.381879	+	0.343846i
$260$	30.0875	−	21.8598i	1.86595	−	1.35569i
$261$		0			0
$262$	3.29566	+	10.1430i	0.203606	+	0.626636i
$263$	7.71773	−	13.3675i	0.475896	−	0.824275i	−0.523723	−	0.851889i	$-0.675457\pi$
$263$	7.71773	−	13.3675i	0.475896	−	0.824275i	0.999619	+	0.0276132i	$0.00879066\pi$
$264$		0			0
$265$	11.0125	+	19.0742i	0.676493	+	1.17172i
$266$	2.26571	−	2.51633i	0.138920	−	0.154286i
$267$		0			0
$268$	0.472177	+	4.49247i	0.0288428	+	0.274421i
$269$	−5.84229	−	1.89827i	−0.356211	−	0.115740i	0.125445	−	0.992101i	$-0.459964\pi$
$269$	−5.84229	−	1.89827i	−0.356211	−	0.115740i	−0.481655	+	0.876361i	$0.659964\pi$
$270$		0			0
$271$	11.0715	+	15.2386i	0.672546	+	0.925680i	0.999815	−	0.0192514i	$-0.00612829\pi$
$271$	11.0715	+	15.2386i	0.672546	+	0.925680i	−0.327269	+	0.944931i	$0.606128\pi$
$272$	0.522826	−	0.232777i	0.0317010	−	0.0141142i
$273$		0			0
$274$	0.730810	−	0.421933i	0.0441498	−	0.0254899i
$275$	29.4833	−	3.12218i	1.77791	−	0.188275i
$276$		0			0
$277$	−1.14030	+	5.36469i	−0.0685140	+	0.322333i	−0.999036	−	0.0439036i	$-0.986021\pi$
$277$	−1.14030	+	5.36469i	−0.0685140	+	0.322333i	0.930522	+	0.366236i	$0.119354\pi$
$278$	4.40130	−	6.05787i	0.263973	−	0.363327i
$279$		0			0
$280$	5.74250	−	17.6736i	0.343180	−	1.05620i
$281$	17.4638	+	19.3955i	1.04180	+	1.15704i	0.987356	+	0.158521i	$0.0506727\pi$
$281$	17.4638	+	19.3955i	1.04180	+	1.15704i	0.0544463	+	0.998517i	$0.482661\pi$
$282$		0			0
$283$	−17.1513	−	1.80267i	−1.01954	−	0.107158i	−0.420017	−	0.907516i	$-0.637976\pi$
$283$	−17.1513	−	1.80267i	−1.01954	−	0.107158i	−0.599522	+	0.800359i	$0.704642\pi$
$284$	−8.17442	−	7.36028i	−0.485062	−	0.436752i
$285$		0			0
$286$	−3.93385	−	12.0749i	−0.232614	−	0.714006i
$287$			9.26884i			0.547122i
$288$		0			0
$289$	13.6747	+	9.93529i	0.804397	+	0.584429i
$290$	−15.2144	+	1.59910i	−0.893420	+	0.0939023i
$291$		0			0
$292$	−3.23422	−	15.2158i	−0.189268	−	0.890437i
$293$	−24.8046	−	11.0437i	−1.44910	−	0.645182i	−0.476822	−	0.879000i	$-0.658211\pi$
$293$	−24.8046	−	11.0437i	−1.44910	−	0.645182i	−0.972280	+	0.233818i	$0.924878\pi$
$294$		0			0
$295$	20.4304	+	4.34262i	1.18951	+	0.252837i
$296$	8.36416			0.486157
$297$		0			0
$298$	9.07446			0.525669
$299$	−53.8489	−	11.4459i	−3.11416	−	0.661936i
$300$		0			0
$301$	9.64285	+	4.29327i	0.555804	+	0.247460i
$302$	−0.358997	−	1.68895i	−0.0206580	−	0.0971882i
$303$		0			0
$304$	4.49208	−	0.472136i	0.257638	−	0.0270789i
$305$	4.54600	+	3.30286i	0.260303	+	0.189121i
$306$		0			0
$307$			14.5585i			0.830895i	0.909617	+	0.415448i	$0.136375\pi$
$307$			14.5585i			0.830895i	−0.909617	+	0.415448i	$0.863625\pi$
$308$	9.61701	+	6.97565i	0.547980	+	0.397475i
$309$		0			0
$310$	−1.85691	−	1.67197i	−0.105465	−	0.0949614i
$311$	4.35726	+	0.457966i	0.247078	+	0.0259689i	0.227258	−	0.973835i	$-0.427024\pi$
$311$	4.35726	+	0.457966i	0.247078	+	0.0259689i	0.0198199	+	0.999804i	$0.493691\pi$
$312$		0			0
$313$	−3.77269	−	4.18999i	−0.213245	−	0.236832i	0.627027	−	0.778997i	$-0.284271\pi$
$313$	−3.77269	−	4.18999i	−0.213245	−	0.236832i	−0.840272	+	0.542165i	$0.817605\pi$
$314$	3.39567	−	10.4508i	0.191629	−	0.589773i
$315$		0			0
$316$	−4.72205	+	6.49935i	−0.265636	+	0.365617i
$317$	−3.30773	+	15.5617i	−0.185781	+	0.874030i	0.782204	+	0.623022i	$0.214095\pi$
$317$	−3.30773	+	15.5617i	−0.185781	+	0.874030i	−0.967985	+	0.251008i	$0.919238\pi$
$318$		0			0
$319$	4.53532	−	21.4195i	0.253929	−	1.19926i
$320$	0.584035	−	0.337193i	0.0326486	−	0.0188497i
$321$		0			0
$322$	−11.2258	+	4.99804i	−0.625588	+	0.278530i
$323$	−0.450354	−	0.619859i	−0.0250584	−	0.0344899i
$324$		0			0
$325$	−52.4465	−	17.0409i	−2.90921	−	0.945259i
$326$	0.0953614	+	0.907303i	0.00528158	+	0.0502509i
$327$		0			0
$328$	6.27273	−	6.96657i	0.346353	−	0.384664i
$329$	1.59805	+	2.76791i	0.0881035	+	0.152600i
$330$		0			0
$331$	−9.89275	+	17.1347i	−0.543755	+	0.941811i	0.454930	+	0.890527i	$0.349664\pi$
$331$	−9.89275	+	17.1347i	−0.543755	+	0.941811i	−0.998684	+	0.0512832i	$0.983669\pi$
$332$	6.68369	+	20.5703i	0.366815	+	1.12894i
$333$		0			0
$334$	4.51189	−	3.27808i	0.246880	−	0.179369i
$335$	7.76183	−	6.98878i	0.424074	−	0.381838i
$336$		0			0
$337$	−9.70893	+	21.8066i	−0.528879	+	1.18788i	0.429678	+	0.902982i	$0.358627\pi$
$337$	−9.70893	+	21.8066i	−0.528879	+	1.18788i	−0.958557	+	0.284900i	$0.908040\pi$
$338$	−1.62564	+	15.4669i	−0.0884230	+	0.841288i
$339$		0			0
$340$	−1.62673	−	0.939191i	−0.0882216	−	0.0509348i
$341$	3.09559	−	1.79048i	0.167636	−	0.0969598i
$342$		0			0
$343$	−19.1545	+	6.22366i	−1.03424	+	0.336046i
$344$	−4.34218	−	9.75271i	−0.234115	−	0.525831i
$345$		0			0
$346$	4.00368	−	0.851009i	0.215239	−	0.0457505i
$347$	−16.9727	+	3.60765i	−0.911141	+	0.193669i	−0.639555	−	0.768745i	$-0.720881\pi$
$347$	−16.9727	+	3.60765i	−0.911141	+	0.193669i	−0.271586	+	0.962414i	$0.587548\pi$
$348$		0			0
$349$	−4.53784	−	10.1921i	−0.242905	−	0.545573i	0.750415	−	0.660967i	$-0.229854\pi$
$349$	−4.53784	−	10.1921i	−0.242905	−	0.545573i	−0.993320	+	0.115394i	$0.963187\pi$
$350$	−11.7066	+	3.80370i	−0.625743	+	0.203316i
$351$		0			0
$352$	−3.89480	−	18.2532i	−0.207594	−	0.972901i
$353$	20.3046	+	11.7228i	1.08070	+	0.623944i	0.931086	−	0.364800i	$-0.118863\pi$
$353$	20.3046	+	11.7228i	1.08070	+	0.623944i	0.149617	+	0.988744i	$0.452196\pi$
$354$		0			0
$355$	−2.65851	+	25.2940i	−0.141099	+	1.34247i
$356$	−2.00373	+	4.50046i	−0.106198	+	0.238524i
$357$		0			0
$358$	0.588874	−	0.530225i	0.0311230	−	0.0280232i
$359$	14.8582	−	10.7951i	0.784184	−	0.569743i	−0.122048	−	0.992524i	$-0.538946\pi$
$359$	14.8582	−	10.7951i	0.784184	−	0.569743i	0.906232	+	0.422781i	$0.138946\pi$
$360$		0			0
$361$	4.00269	+	12.3190i	0.210668	+	0.648370i
$362$	6.41828	−	11.1168i	0.337337	−	0.584285i
$363$		0			0
$364$	−11.0489	−	19.1372i	−0.579119	−	1.00306i
$365$	−24.0670	+	26.7291i	−1.25972	+	1.39906i
$366$		0			0
$367$	−1.41118	−	13.4265i	−0.0736632	−	0.700859i	−0.967570	−	0.252605i	$-0.918713\pi$
$367$	−1.41118	−	13.4265i	−0.0736632	−	0.700859i	0.893906	−	0.448254i	$-0.147954\pi$
$368$	−15.5895	−	5.06533i	−0.812659	−	0.264049i
$369$		0			0
$370$	−5.07791	−	6.98915i	−0.263988	−	0.363348i
$371$	11.9555	−	5.32291i	0.620696	−	0.276352i
$372$		0			0
$373$	24.4937	−	14.1414i	1.26823	−	0.732215i	0.293581	−	0.955934i	$-0.405153\pi$
$373$	24.4937	−	14.1414i	1.26823	−	0.732215i	0.974654	+	0.223719i	$0.0718197\pi$
$374$	−0.476334	+	0.429570i	−0.0246307	+	0.0222125i
$375$		0			0
$376$	0.672078	−	3.16188i	0.0346598	−	0.163061i
$377$	−23.9368	+	32.9461i	−1.23281	+	1.69681i
$378$		0			0
$379$	−0.0682032	+	0.209908i	−0.00350336	+	0.0107822i	−0.952793	−	0.303621i	$-0.901804\pi$
$379$	−0.0682032	+	0.209908i	−0.00350336	+	0.0107822i	0.949290	+	0.314403i	$0.101804\pi$
$380$	−9.91974	−	11.0170i	−0.508872	−	0.565160i
$381$		0			0
$382$	4.15440	+	0.436645i	0.212557	+	0.0223407i
$383$	28.6768	+	25.8207i	1.46532	+	1.31938i	0.844672	+	0.535284i	$0.179795\pi$
$383$	28.6768	+	25.8207i	1.46532	+	1.31938i	0.620644	+	0.784093i	$0.286871\pi$
$384$		0			0
$385$	−0.0215298	−	27.4698i	−0.00109726	−	1.39999i
$386$		−	9.80110i		−	0.498863i
$387$		0			0
$388$	−19.2260	−	13.9685i	−0.976050	−	0.709142i
$389$	−36.1590	+	3.80046i	−1.83333	+	0.192691i	−0.957210	−	0.289395i	$-0.906546\pi$
$389$	−36.1590	+	3.80046i	−1.83333	+	0.192691i	−0.876124	+	0.482086i	$0.839879\pi$
$390$		0			0
$391$	0.578105	+	2.71977i	0.0292360	+	0.137545i
$392$	4.26073	+	1.89700i	0.215199	+	0.0958128i
$393$		0			0
$394$	−1.26955	−	0.269851i	−0.0639589	−	0.0135949i
$395$	18.5752			0.934617
$396$		0			0
$397$	22.4527			1.12687			0.563434	−	0.826161i	$-0.309480\pi$
$397$	22.4527			1.12687			0.563434	+	0.826161i	$0.309480\pi$
$398$	−2.28753	−	0.486230i	−0.114664	−	0.0243725i
$399$		0			0
$400$	−15.0001	−	6.67846i	−0.750004	−	0.333923i
$401$	5.72301	+	26.9246i	0.285793	+	1.34455i	0.853402	+	0.521253i	$0.174535\pi$
$401$	5.72301	+	26.9246i	0.285793	+	1.34455i	−0.567609	+	0.823298i	$0.692131\pi$
$402$		0			0
$403$	−6.61511	+	0.695277i	−0.329522	+	0.0346342i
$404$	−8.56149	−	6.22029i	−0.425950	−	0.309471i
$405$		0			0
$406$			9.08993i			0.451126i
$407$	11.7559	−	3.82991i	0.582717	−	0.189841i
$408$		0			0
$409$	−29.6933	−	26.7360i	−1.46824	−	1.32201i	−0.838082	−	0.545544i	$-0.816323\pi$
$409$	−29.6933	−	26.7360i	−1.46824	−	1.32201i	−0.630158	−	0.776467i	$-0.717010\pi$
$410$	−9.62950	−	1.01210i	−0.475567	−	0.0499841i
$411$		0			0
$412$	9.46699	+	10.5142i	0.466405	+	0.517995i
$413$	3.83509	−	11.8032i	0.188712	−	0.580797i
$414$		0			0
$415$	29.3949	−	40.4587i	1.44294	−	1.98604i
$416$	−7.21772	+	33.9567i	−0.353878	+	1.66486i
$417$		0			0
$418$	−4.62305	+	2.06266i	−0.226121	+	0.100888i
$419$	21.9499	−	12.6728i	1.07232	−	0.619105i	0.143507	−	0.989649i	$-0.454162\pi$
$419$	21.9499	−	12.6728i	1.07232	−	0.619105i	0.928815	+	0.370544i	$0.120829\pi$
$420$		0			0
$421$	−13.6093	+	6.05927i	−0.663278	+	0.295311i	−0.710628	−	0.703568i	$-0.751589\pi$
$421$	−13.6093	+	6.05927i	−0.663278	+	0.295311i	0.0473497	+	0.998878i	$0.484922\pi$
$422$	3.97287	+	5.46819i	0.193396	+	0.266187i
$423$		0			0
$424$	−12.5882	−	4.09014i	−0.611335	−	0.198635i
$425$	0.291139	+	2.77000i	0.0141223	+	0.134365i
$426$		0			0
$427$	2.23410	−	2.48122i	0.108116	−	0.120075i
$428$	0.617281	+	1.06916i	0.0298374	+	0.0516799i
$429$		0			0
$430$	−5.51327	+	9.54926i	−0.265873	+	0.460506i
$431$	−4.81473	−	14.8182i	−0.231917	−	0.713768i	−0.997515	−	0.0704489i	$-0.977557\pi$
$431$	−4.81473	−	14.8182i	−0.231917	−	0.713768i	0.765598	−	0.643319i	$-0.222443\pi$
$432$		0			0
$433$	−8.59479	+	6.24448i	−0.413039	+	0.300091i	−0.774831	−	0.632168i	$-0.782165\pi$
$433$	−8.59479	+	6.24448i	−0.413039	+	0.300091i	0.361792	+	0.932259i	$0.382165\pi$
$434$	−1.10334	+	0.993454i	−0.0529621	+	0.0476873i
$435$		0			0
$436$	−2.88500	+	6.47982i	−0.138166	+	0.310327i
$437$	−2.29387	+	21.8247i	−0.109731	+	1.04402i
$438$		0			0
$439$	15.4266	+	8.90653i	0.736270	+	0.425085i	0.820711	−	0.571343i	$-0.193577\pi$
$439$	15.4266	+	8.90653i	0.736270	+	0.425085i	−0.0844418	+	0.996428i	$0.526911\pi$
$440$	−18.5741	+	20.6612i	−0.885486	+	0.984983i
$441$		0			0
$442$	1.13466	−	0.368672i	0.0539701	−	0.0175359i
$443$	−7.45041	−	16.7339i	−0.353980	−	0.795051i	−0.999510	−	0.0313162i	$-0.990030\pi$
$443$	−7.45041	−	16.7339i	−0.353980	−	0.795051i	0.645530	−	0.763735i	$-0.276637\pi$
$444$		0			0
$445$	11.1417	−	2.36824i	0.528167	−	0.112265i
$446$	6.89521	−	1.46562i	0.326498	−	0.0693992i
$447$		0			0
$448$	−0.162983	−	0.366065i	−0.00770021	−	0.0172950i
$449$	13.4434	−	4.36802i	0.634433	−	0.206140i	0.0258953	−	0.999665i	$-0.491756\pi$
$449$	13.4434	−	4.36802i	0.634433	−	0.206140i	0.608538	+	0.793525i	$0.291756\pi$
$450$		0			0
$451$	5.62640	−	12.6638i	0.264937	−	0.596315i
$452$	8.41126	+	4.85624i	0.395632	+	0.228418i
$453$		0			0
$454$	−0.695114	+	6.61357i	−0.0326233	+	0.310390i
$455$	−20.7817	+	46.6765i	−0.974263	+	2.18823i
$456$		0			0
$457$	−6.43116	+	5.79065i	−0.300837	+	0.270875i	−0.805699	−	0.592325i	$-0.798210\pi$
$457$	−6.43116	+	5.79065i	−0.300837	+	0.270875i	0.504862	+	0.863200i	$0.331543\pi$
$458$	−9.87990	+	7.17817i	−0.461658	+	0.335414i
$459$		0			0
$460$	16.6251	+	51.1668i	0.775150	+	2.38567i
$461$	18.1341	−	31.4092i	0.844590	−	1.46287i	−0.0413877	−	0.999143i	$-0.513178\pi$
$461$	18.1341	−	31.4092i	0.844590	−	1.46287i	0.885977	−	0.463729i	$-0.153489\pi$
$462$		0			0
$463$	14.1514	+	24.5109i	0.657669	+	1.13912i	0.981217	+	0.192905i	$0.0617908\pi$
$463$	14.1514	+	24.5109i	0.657669	+	1.13912i	−0.323548	+	0.946212i	$0.604876\pi$
$464$	−8.11354	+	9.01100i	−0.376662	+	0.418325i
$465$		0			0
$466$	−1.30781	−	12.4430i	−0.0605833	−	0.576412i
$467$	26.4483	+	8.59356i	1.22388	+	0.397662i	0.848493	−	0.529206i	$-0.177510\pi$
$467$	26.4483	+	8.59356i	1.22388	+	0.397662i	0.375386	+	0.926869i	$0.377510\pi$
$468$		0			0
$469$	−3.64778	−	5.02074i	−0.168439	−	0.231836i
$470$	−3.05011	+	1.35800i	−0.140691	+	0.0626396i
$471$		0			0
$472$	−10.8703	+	6.27600i	−0.500348	+	0.288876i
$473$	−10.5687	−	11.7192i	−0.485948	−	0.538850i
$474$		0			0
$475$	−4.57036	+	21.5018i	−0.209702	+	0.986572i
$476$	−0.656028	+	0.902945i	−0.0300690	+	0.0413864i
$477$		0			0
$478$	3.29881	−	10.1527i	0.150884	−	0.464373i
$479$	4.96151	+	5.51031i	0.226697	+	0.251773i	0.845753	−	0.533574i	$-0.179151\pi$
$479$	4.96151	+	5.51031i	0.226697	+	0.251773i	−0.619056	+	0.785347i	$0.712485\pi$
$480$		0			0
$481$	−22.8711	−	2.40385i	−1.04283	−	0.109606i
$482$	9.46975	+	8.52660i	0.431335	+	0.388376i
$483$		0			0
$484$	−8.90511	−	15.3684i	−0.404778	−	0.698564i
$485$			54.9478i			2.49505i
$486$		0			0
$487$	15.0683	+	10.9477i	0.682808	+	0.496089i	0.874288	−	0.485408i	$-0.161329\pi$
$487$	15.0683	+	10.9477i	0.682808	+	0.496089i	−0.191480	+	0.981496i	$0.561329\pi$
$488$	−3.35835	+	0.352977i	−0.152025	+	0.0159785i
$489$		0			0
$490$	−1.00156	−	4.71196i	−0.0452458	−	0.212865i
$491$	−19.5154	−	8.68880i	−0.880716	−	0.392120i	−0.0839943	−	0.996466i	$-0.526768\pi$
$491$	−19.5154	−	8.68880i	−0.880716	−	0.392120i	−0.796722	+	0.604346i	$0.793434\pi$
$492$		0			0
$493$	2.01190	+	0.427643i	0.0906115	+	0.0192601i
$494$	9.41594			0.423643
$495$		0			0
$496$	−1.98051			−0.0889273
$497$	14.7818	+	3.14197i	0.663055	+	0.140937i
$498$		0			0
$499$	10.9153	+	4.85982i	0.488637	+	0.217555i	0.636240	−	0.771491i	$-0.280489\pi$
$499$	10.9153	+	4.85982i	0.488637	+	0.217555i	−0.147602	+	0.989047i	$0.547156\pi$
$500$	4.93754	+	23.2293i	0.220813	+	1.03885i
$501$		0			0
$502$	−3.92471	+	0.412504i	−0.175168	+	0.0184109i
$503$	21.5801	+	15.6789i	0.962210	+	0.699087i	0.953663	−	0.300877i	$-0.0972792\pi$
$503$	21.5801	+	15.6789i	0.962210	+	0.699087i	0.00854739	+	0.999963i	$0.497279\pi$
$504$		0			0
$505$			24.4688i			1.08885i
$506$	18.3714	−	0.0143988i	0.816710	−	0.000640106i
$507$		0			0
$508$	13.5338	+	12.1859i	0.600465	+	0.540661i
$509$	−25.7218	−	2.70347i	−1.14010	−	0.119829i	−0.484395	−	0.874849i	$-0.660960\pi$
$509$	−25.7218	−	2.70347i	−1.14010	−	0.119829i	−0.655702	+	0.755020i	$0.727627\pi$
$510$		0			0
$511$	14.3002	+	15.8819i	0.632602	+	0.702576i
$512$	−5.74119	+	17.6696i	−0.253727	+	0.780892i
$513$		0			0
$514$	5.05013	−	6.95091i	0.222752	−	0.306591i
$515$	6.80143	−	31.9982i	0.299707	−	1.41001i
$516$		0			0
$517$	−0.503198	−	4.75178i	−0.0221306	−	0.208983i
$518$	−4.44546	+	2.56659i	−0.195322	+	0.112769i
$519$		0			0
$520$	47.2083	−	21.0185i	2.07022	−	0.921722i
$521$	−13.0853	−	18.0103i	−0.573276	−	0.789047i	0.419662	−	0.907680i	$-0.362149\pi$
$521$	−13.0853	−	18.0103i	−0.573276	−	0.789047i	−0.992938	+	0.118634i	$0.962149\pi$
$522$		0			0
$523$	−27.2570	−	8.85633i	−1.19186	−	0.387260i	−0.355103	−	0.934827i	$-0.615554\pi$
$523$	−27.2570	−	8.85633i	−1.19186	−	0.387260i	−0.836762	+	0.547567i	$0.815554\pi$
$524$	−2.90008	−	27.5924i	−0.126691	−	1.20538i
$525$		0			0
$526$	6.41083	−	7.11995i	0.279525	−	0.310444i
$527$	0.167977	+	0.290944i	0.00731717	+	0.0126737i
$528$		0			0
$529$	28.3196	−	49.0509i	1.23129	−	2.13265i
$530$	4.22457	+	13.0019i	0.183503	+	0.564766i
$531$		0			0
$532$	−7.12635	+	5.17759i	−0.308966	+	0.224477i
$533$	−19.1544	+	17.2467i	−0.829670	+	0.747038i
$534$		0			0
$535$	1.16104	−	2.60774i	0.0501961	−	0.112742i
$536$	−0.656092	+	6.24230i	−0.0283389	+	0.269626i
$537$		0			0
$538$	−3.30211	−	1.90647i	−0.142364	−	0.0821938i
$539$	6.85710	+	0.715277i	0.295356	+	0.0308092i
$540$		0			0
$541$	27.0426	−	8.78666i	1.16265	−	0.377768i	0.336755	−	0.941592i	$-0.390670\pi$
$541$	27.0426	−	8.78666i	1.16265	−	0.377768i	0.825895	+	0.563824i	$0.190670\pi$
$542$	4.75538	+	10.6807i	0.204261	+	0.458777i
$543$		0			0
$544$	1.71507	−	0.364549i	0.0735329	−	0.0156299i
$545$	16.0419	−	3.40982i	0.687161	−	0.146061i
$546$		0			0
$547$	7.26651	+	16.3209i	0.310694	+	0.697830i	0.999636	−	0.0269869i	$-0.00859123\pi$
$547$	7.26651	+	16.3209i	0.310694	+	0.697830i	−0.688942	+	0.724816i	$0.741925\pi$
$548$	−2.08783	+	0.678378i	−0.0891878	+	0.0289789i
$549$		0			0
$550$	18.3034	+	1.90926i	0.780458	+	0.0814110i
$551$	14.0585	+	8.11667i	0.598911	+	0.345782i
$552$		0			0
$553$	1.15368	−	10.9766i	0.0490596	−	0.466771i
$554$	−1.38464	+	3.10995i	−0.0588277	+	0.132129i
$555$		0			0
$556$	−14.4761	+	13.0343i	−0.613924	+	0.552779i
$557$	−27.7784	+	20.1822i	−1.17701	+	0.855148i	−0.991831	−	0.127556i	$-0.959287\pi$
$557$	−27.7784	+	20.1822i	−1.17701	+	0.855148i	−0.185179	+	0.982705i	$0.559287\pi$
$558$		0			0
$559$	9.07042	+	27.9159i	0.383638	+	1.18072i
$560$	−7.60662	+	13.1750i	−0.321438	+	0.556747i
$561$		0			0
$562$	8.09993	+	14.0295i	0.341675	+	0.591798i
$563$	0.0657990	−	0.0730772i	0.00277310	−	0.00307984i	−0.741757	−	0.670669i	$-0.766007\pi$
$563$	0.0657990	−	0.0730772i	0.00277310	−	0.00307984i	0.744530	+	0.667589i	$0.232674\pi$
$564$		0			0
$565$	−2.34739	−	22.3339i	−0.0987554	−	0.939595i
$566$	−10.1806	−	3.30787i	−0.427922	−	0.139040i
$567$		0			0
$568$	−8.98384	−	12.3652i	−0.376953	−	0.518832i
$569$	−31.9277	+	14.2151i	−1.33848	+	0.595930i	−0.946100	−	0.323873i	$-0.895015\pi$
$569$	−31.9277	+	14.2151i	−1.33848	+	0.595930i	−0.392380	+	0.919803i	$0.628348\pi$
$570$		0			0
$571$	−7.73170	+	4.46390i	−0.323562	+	0.186808i	−0.652979	−	0.757376i	$-0.726481\pi$
$571$	−7.73170	+	4.46390i	−0.323562	+	0.186808i	0.329417	+	0.944184i	$0.393148\pi$
$572$	3.47909	+	32.8536i	0.145468	+	1.37368i
$573$		0			0
$574$	−1.19616	+	5.62748i	−0.0499266	+	0.234886i
$575$	46.8903	−	64.5389i	1.95546	−	2.69146i
$576$		0			0
$577$	−1.57214	+	4.83854i	−0.0654489	+	0.201431i	−0.978433	−	0.206564i	$-0.933772\pi$
$577$	−1.57214	+	4.83854i	−0.0654489	+	0.201431i	0.912984	+	0.407995i	$0.133772\pi$
$578$	7.02031	+	7.79685i	0.292006	+	0.324306i
$579$		0			0
$580$	39.5795	+	4.15998i	1.64345	+	0.172734i
$581$	−22.0825	−	19.8831i	−0.916135	−	0.824891i
$582$		0			0
$583$	−19.5656	+	0.0153347i	−0.810324	+	0.000635100i
$584$		−	21.6147i		−	0.894424i
$585$		0			0
$586$	−13.6347	−	9.90616i	−0.563242	−	0.409220i
$587$	3.40633	−	0.358020i	0.140594	−	0.0147771i	−0.0339698	−	0.999423i	$-0.510815\pi$
$587$	3.40633	−	0.358020i	0.140594	−	0.0147771i	0.174564	+	0.984646i	$0.444148\pi$
$588$		0			0
$589$	0.551268	+	2.59351i	0.0227146	+	0.106864i
$590$	11.8437	+	5.27315i	0.487597	+	0.217092i
$591$		0			0
$592$	−6.69777	−	1.42365i	−0.275277	−	0.0585118i
$593$	−16.6897			−0.685365			−0.342683	−	0.939451i	$-0.611336\pi$
$593$	−16.6897			−0.685365			−0.342683	+	0.939451i	$0.611336\pi$
$594$		0			0
$595$	2.58062			0.105795
$596$	−23.0909	−	4.90812i	−0.945840	−	0.201044i
$597$		0			0
$598$	−31.2167	−	13.8986i	−1.27654	−	0.568354i
$599$	−10.0293	−	47.1839i	−0.409784	−	1.92788i	−0.370992	−	0.928636i	$-0.620982\pi$
$599$	−10.0293	−	47.1839i	−0.409784	−	1.92788i	−0.0387921	−	0.999247i	$-0.512351\pi$
$600$		0			0
$601$	−18.8072	+	1.97671i	−0.767161	+	0.0806318i	−0.480021	−	0.877257i	$-0.659371\pi$
$601$	−18.8072	+	1.97671i	−0.767161	+	0.0806318i	−0.287139	+	0.957889i	$0.592704\pi$
$602$	5.30050	+	3.85104i	0.216032	+	0.156956i
$603$		0			0
$604$			4.49188i			0.182772i
$605$	−16.6454	+	37.5444i	−0.676730	+	1.52640i
$606$		0			0
$607$	−26.6309	−	23.9786i	−1.08092	−	0.973261i	−0.0811909	−	0.996699i	$-0.525872\pi$
$607$	−26.6309	−	23.9786i	−1.08092	−	0.973261i	−0.999725	+	0.0234373i	$0.992539\pi$
$608$	13.7625	+	1.44649i	0.558142	+	0.0586631i
$609$		0			0
$610$	2.33382	+	2.59196i	0.0944934	+	0.104946i
$611$	−2.74646	+	8.45274i	−0.111110	+	0.341961i
$612$		0			0
$613$	−0.393669	+	0.541839i	−0.0159002	+	0.0218847i	−0.816893	−	0.576789i	$-0.804305\pi$
$613$	−0.393669	+	0.541839i	−0.0159002	+	0.0218847i	0.800993	+	0.598674i	$0.204305\pi$
$614$	−1.87879	+	8.83901i	−0.0758218	+	0.356713i
$615$		0			0
$616$	11.0556	+	12.2592i	0.445444	+	0.493937i
$617$	−9.40017	+	5.42719i	−0.378436	+	0.218490i	−0.677138	−	0.735856i	$-0.736780\pi$
$617$	−9.40017	+	5.42719i	−0.378436	+	0.218490i	0.298701	+	0.954347i	$0.403447\pi$
$618$		0			0
$619$	25.3410	−	11.2825i	1.01854	−	0.453483i	0.171597	−	0.985167i	$-0.445107\pi$
$619$	25.3410	−	11.2825i	1.01854	−	0.453483i	0.846943	+	0.531684i	$0.178441\pi$
$620$	3.82077	+	5.25884i	0.153446	+	0.211200i
$621$		0			0
$622$	2.58636	+	0.840360i	0.103704	+	0.0336953i
$623$	−0.707459	−	6.73102i	−0.0283438	−	0.269673i
$624$		0			0
$625$	6.83439	−	7.59036i	0.273376	−	0.303614i
$626$	−1.74982	−	3.03078i	−0.0699369	−	0.121134i
$627$		0			0
$628$	−14.2932	+	24.7565i	−0.570360	+	0.987893i
$629$	0.358931	+	1.10467i	0.0143115	+	0.0440463i
$630$		0			0
$631$	−35.5496	+	25.8283i	−1.41521	+	1.02821i	−0.422667	+	0.906285i	$0.638906\pi$
$631$	−35.5496	+	25.8283i	−1.41521	+	1.02821i	−0.992540	+	0.121923i	$0.961094\pi$
$632$	−8.29556	+	7.46935i	−0.329980	+	0.297115i
$633$		0			0
$634$	−4.01651	+	9.02122i	−0.159516	+	0.358279i
$635$	4.40150	−	41.8775i	0.174668	−	1.66186i
$636$		0			0
$637$	−11.1054	−	6.41170i	−0.440012	−	0.254041i
$638$	5.51779	−	12.4193i	0.218451	−	0.491687i
$639$		0			0
$640$	40.3620	−	13.1144i	1.59545	−	0.518392i
$641$	−5.73076	−	12.8715i	−0.226351	−	0.508393i	0.764292	−	0.644870i	$-0.223089\pi$
$641$	−5.73076	−	12.8715i	−0.226351	−	0.508393i	−0.990643	+	0.136477i	$0.956422\pi$
$642$		0			0
$643$	−28.6159	+	6.08250i	−1.12850	+	0.239871i	−0.734083	−	0.679060i	$-0.762388\pi$
$643$	−28.6159	+	6.08250i	−1.12850	+	0.239871i	−0.394419	+	0.918931i	$0.629054\pi$
$644$	31.2685	−	6.64632i	1.23215	−	0.261902i
$645$		0			0
$646$	−0.193434	−	0.434459i	−0.00761055	−	0.0170936i
$647$	39.3432	−	12.7834i	1.54674	−	0.502566i	0.593513	−	0.804824i	$-0.297740\pi$
$647$	39.3432	−	12.7834i	1.54674	−	0.502566i	0.953226	+	0.302258i	$0.0977405\pi$
$648$		0			0
$649$	−12.4046	+	13.7984i	−0.486923	+	0.541635i
$650$	−29.6432	−	17.1145i	−1.16270	−	0.671285i
$651$		0			0
$652$	0.248078	−	2.36030i	0.00971548	−	0.0924367i
$653$	11.1095	−	24.9524i	0.434749	−	0.976463i	−0.554762	−	0.832009i	$-0.687191\pi$
$653$	11.1095	−	24.9524i	0.434749	−	0.976463i	0.989512	−	0.144454i	$-0.0461426\pi$
$654$		0			0
$655$	−47.6726	+	42.9246i	−1.86272	+	1.67720i
$656$	−6.20878	+	4.51094i	−0.242412	+	0.176123i
$657$		0			0
$658$	0.613038	+	1.88674i	0.0238987	+	0.0735526i
$659$	0.320896	−	0.555808i	0.0125003	−	0.0216512i	−0.859708	−	0.510787i	$-0.829354\pi$
$659$	0.320896	−	0.555808i	0.0125003	−	0.0216512i	0.872208	+	0.489135i	$0.162688\pi$
$660$		0			0
$661$	4.12078	+	7.13740i	0.160280	+	0.277613i	0.934969	−	0.354729i	$-0.115427\pi$
$661$	4.12078	+	7.13740i	0.160280	+	0.277613i	−0.774689	+	0.632342i	$0.782094\pi$
$662$	−8.21753	+	9.12650i	−0.319384	+	0.354711i
$663$		0			0
$664$	3.14144	+	29.8888i	0.121911	+	1.15991i
$665$	19.3703	+	6.29378i	0.751147	+	0.244063i
$666$		0			0
$667$	−34.6273	−	47.6604i	−1.34078	−	1.84542i
$668$	−13.2540	+	5.90106i	−0.512813	+	0.228319i
$669$		0			0
$670$	5.61442	−	3.24149i	0.216904	−	0.125230i
$671$	−4.55855	+	2.03388i	−0.175981	+	0.0785171i
$672$		0			0
$673$	−3.08146	+	14.4971i	−0.118782	+	0.558824i	0.878000	+	0.478660i	$0.158878\pi$
$673$	−3.08146	+	14.4971i	−0.118782	+	0.558824i	−0.996782	+	0.0801633i	$0.974456\pi$
$674$	−8.70884	+	11.9867i	−0.335452	+	0.461710i
$675$		0			0
$676$	12.5022	−	38.4778i	0.480854	−	1.47992i
$677$	4.21333	+	4.67938i	0.161931	+	0.179843i	0.818650	−	0.574292i	$-0.194723\pi$
$677$	4.21333	+	4.67938i	0.161931	+	0.179843i	−0.656719	+	0.754136i	$0.728056\pi$
$678$		0			0
$679$	32.4702	+	3.41275i	1.24609	+	0.130969i
$680$	−1.93962	−	1.74644i	−0.0743811	−	0.0669731i
$681$		0			0
$682$	2.11052	−	0.687579i	0.0808160	−	0.0263287i
$683$		−	14.1497i		−	0.541422i	−0.962661	−	0.270711i	$-0.912741\pi$
$683$		−	14.1497i		−	0.541422i	0.962661	−	0.270711i	$-0.0872588\pi$
$684$		0			0
$685$	4.10646	+	2.98352i	0.156900	+	0.113994i
$686$	−12.4326	+	1.30672i	−0.474679	+	0.0498907i
$687$		0			0
$688$	1.81709	+	8.54875i	0.0692760	+	0.325918i
$689$	33.2457	+	14.8020i	1.26656	+	0.563910i
$690$		0			0
$691$	25.1921	+	5.35475i	0.958354	+	0.203704i	0.660432	−	0.750886i	$-0.270373\pi$
$691$	25.1921	+	5.35475i	0.958354	+	0.203704i	0.297922	+	0.954590i	$0.403707\pi$
$692$	−10.6481			−0.404779
$693$		0			0
$694$	−10.7703			−0.408837
$695$	44.0558	+	9.36434i	1.67113	+	0.355210i
$696$		0			0
$697$	1.18927	+	0.529498i	0.0450469	+	0.0200562i
$698$	−1.43979	−	6.77366i	−0.0544967	−	0.256387i
$699$		0			0
$700$	31.8459	−	3.34714i	1.20366	−	0.126510i
$701$	−8.55571	−	6.21609i	−0.323145	−	0.234778i	0.414371	−	0.910108i	$-0.364001\pi$
$701$	−8.55571	−	6.21609i	−0.323145	−	0.234778i	−0.737516	+	0.675329i	$0.764001\pi$
$702$		0			0
$703$			9.16714i			0.345745i
$704$	0.000469536		0.599081i	1.76963e−5		0.0225787i
$705$		0			0
$706$	10.8148	+	9.73773i	0.407022	+	0.366484i
$707$	14.4593	+	1.51973i	0.543796	+	0.0571553i
$708$		0			0
$709$	−17.4499	−	19.3800i	−0.655344	−	0.727833i	0.320270	−	0.947326i	$-0.396226\pi$
$709$	−17.4499	−	19.3800i	−0.655344	−	0.727833i	−0.975614	+	0.219493i	$0.929560\pi$
$710$	−4.87831	+	15.0139i	−0.183080	+	0.563462i
$711$		0			0
$712$	−4.02351	+	5.53789i	−0.150788	+	0.207541i
$713$	2.00058	−	9.41199i	0.0749223	−	0.352482i
$714$		0			0
$715$	56.7273	−	51.1580i	2.12148	−	1.91320i
$716$	−1.78523	+	1.03071i	−0.0667173	+	0.0385193i
$717$		0			0
$718$	10.4141	−	4.63666i	0.388651	−	0.173038i
$719$	−8.91625	−	12.2722i	−0.332520	−	0.457675i	0.609718	−	0.792618i	$-0.291283\pi$
$719$	−8.91625	−	12.2722i	−0.332520	−	0.457675i	−0.942238	+	0.334944i	$0.891283\pi$
$720$		0			0
$721$	−18.4862	−	6.00653i	−0.688461	−	0.223695i
$722$	0.840404	+	7.99591i	0.0312766	+	0.297577i
$723$		0			0
$724$	−22.3447	+	24.8163i	−0.830435	+	0.922292i
$725$	−29.5058	−	51.1056i	−1.09582	−	1.89801i
$726$		0			0
$727$	8.28230	−	14.3454i	0.307174	−	0.532040i	−0.670569	−	0.741847i	$-0.733950\pi$
$727$	8.28230	−	14.3454i	0.307174	−	0.532040i	0.977743	+	0.209807i	$0.0672834\pi$
$728$	−9.48835	−	29.2021i	−0.351662	−	1.08230i
$729$		0			0
$730$	−18.0614	+	13.1224i	−0.668483	+	0.485681i
$731$	1.10173	−	0.991999i	0.0407488	−	0.0366904i
$732$		0			0
$733$	−9.20266	+	20.6695i	−0.339908	+	0.763446i	0.660018	+	0.751250i	$0.270549\pi$
$733$	−9.20266	+	20.6695i	−0.339908	+	0.763446i	−0.999926	+	0.0121956i	$0.996118\pi$
$734$	0.875926	−	8.33388i	0.0323310	−	0.307609i
$735$		0			0
$736$	−43.4916	−	25.1099i	−1.60312	−	0.925563i
$737$	1.93618	+	9.07401i	0.0713199	+	0.334245i
$738$		0			0
$739$	−29.5613	+	9.60506i	−1.08743	+	0.353328i	−0.797253	−	0.603645i	$-0.793714\pi$
$739$	−29.5613	+	9.60506i	−1.08743	+	0.353328i	−0.290178	+	0.956973i	$0.593714\pi$
$740$	9.14104	+	20.5311i	0.336031	+	0.754738i
$741$		0			0
$742$	7.94555	−	1.68888i	0.291690	−	0.0620007i
$743$	−46.0242	+	9.78274i	−1.68846	+	0.358894i	−0.949237	−	0.314562i	$-0.898142\pi$
$743$	−46.0242	+	9.78274i	−1.68846	+	0.358894i	−0.739227	+	0.673456i	$0.764809\pi$
$744$		0			0
$745$	22.2009	+	49.8639i	0.813376	+	1.82687i
$746$	16.6960	−	5.42487i	0.611285	−	0.198619i
$747$		0			0
$748$	1.44442	−	0.835448i	0.0528134	−	0.0305470i
$749$	−1.46887	−	0.848053i	−0.0536714	−	0.0309872i
$750$		0			0
$751$	−3.81772	+	36.3232i	−0.139311	+	1.32545i	0.671875	+	0.740664i	$0.265489\pi$
$751$	−3.81772	+	36.3232i	−0.139311	+	1.32545i	−0.811186	+	0.584788i	$0.801178\pi$
$752$	−1.07636	+	2.41754i	−0.0392508	+	0.0881587i
$753$		0			0
$754$	−18.7847	+	16.9138i	−0.684098	+	0.615964i
$755$	8.40245	−	6.10474i	0.305796	−	0.222174i
$756$		0			0
$757$	−8.52322	−	26.2318i	−0.309782	−	0.953409i	−0.977849	−	0.209309i	$-0.932878\pi$
$757$	−8.52322	−	26.2318i	−0.309782	−	0.953409i	0.668068	−	0.744100i	$-0.267122\pi$
$758$	−0.0684977	+	0.118642i	−0.00248795	+	0.00430925i
$759$		0			0
$760$	−10.2996	−	17.8394i	−0.373605	−	0.647103i
$761$	35.2659	−	39.1668i	1.27839	−	1.41979i	0.419399	−	0.907802i	$-0.362241\pi$
$761$	35.2659	−	39.1668i	1.27839	−	1.41979i	0.858990	−	0.511993i	$-0.171092\pi$
$762$		0			0
$763$	−1.01861	−	9.69141i	−0.0368761	−	0.350853i
$764$	−10.3351	−	3.35808i	−0.373912	−	0.121491i
$765$		0			0
$766$	14.0786	+	19.3775i	0.508681	+	0.700139i
$767$	31.5277	−	14.0371i	1.13840	−	0.506849i
$768$		0			0
$769$	−15.7023	+	9.06575i	−0.566241	+	0.326919i	−0.755647	−	0.654980i	$-0.772677\pi$
$769$	−15.7023	+	9.06575i	−0.566241	+	0.326919i	0.189406	+	0.981899i	$0.439344\pi$
$770$	3.53194	−	16.6808i	0.127282	−	0.601133i
$771$		0			0
$772$	−5.30114	+	24.9399i	−0.190792	+	0.897607i
$773$	−8.15106	+	11.2190i	−0.293173	+	0.403518i	−0.930042	−	0.367454i	$-0.880229\pi$
$773$	−8.15106	+	11.2190i	−0.293173	+	0.403518i	0.636868	+	0.770973i	$0.280229\pi$
$774$		0			0
$775$	2.97849	−	9.16686i	0.106991	−	0.329283i
$776$	−22.0954	−	24.5394i	−0.793177	−	0.880913i
$777$		0			0
$778$	−22.4440	−	2.35896i	−0.804656	−	0.0845727i
$779$	7.63537	+	6.87492i	0.273565	+	0.246319i
$780$		0			0
$781$	−18.2888	−	13.2657i	−0.654424	−	0.474684i
$782$			1.72589i			0.0617175i
$783$		0			0
$784$	−3.08897	−	2.24427i	−0.110320	−	0.0801525i
$785$	65.7346	−	6.90898i	2.34617	−	0.246592i
$786$		0			0
$787$	0.139682	+	0.657150i	0.00497911	+	0.0234249i	0.980567	−	0.196184i	$-0.0628551\pi$
$787$	0.139682	+	0.657150i	0.00497911	+	0.0234249i	−0.975588	+	0.219609i	$0.929522\pi$
$788$	3.08454	+	1.37333i	0.109882	+	0.0489227i
$789$		0			0
$790$	11.2777	+	2.39715i	0.401243	+	0.0852867i
$791$	−13.3435			−0.474441
$792$		0			0
$793$	9.28457			0.329705
$794$	13.6319	+	2.89755i	0.483778	+	0.102830i
$795$		0			0
$796$	5.55788	+	2.47453i	0.196994	+	0.0877073i
$797$	−1.09274	−	5.14095i	−0.0387069	−	0.182102i	0.954547	−	0.298060i	$-0.0963395\pi$
$797$	−1.09274	−	5.14095i	−0.0387069	−	0.182102i	−0.993254	+	0.115958i	$0.963006\pi$
$798$		0			0
$799$	0.446438	−	0.0469225i	0.0157938	−	0.00166000i
$800$	−40.6977	−	29.5686i	−1.43888	−	1.04541i
$801$		0			0
$802$			17.0856i			0.603312i
$803$	−9.89727	−	30.3796i	−0.349267	−	1.07207i
$804$		0			0
$805$	−54.9282	−	49.4576i	−1.93597	−	1.74315i
$806$	−4.10602	−	0.431560i	−0.144628	−	0.0152011i
$807$		0			0
$808$	−9.83926	−	10.9276i	−0.346144	−	0.384432i
$809$	8.82483	−	27.1600i	0.310265	−	0.954896i	−0.667395	−	0.744704i	$-0.732591\pi$
$809$	8.82483	−	27.1600i	0.310265	−	0.954896i	0.977660	−	0.210193i	$-0.0674091\pi$
$810$		0			0
$811$	13.6775	−	18.8255i	0.480283	−	0.661053i	−0.498276	−	0.867018i	$-0.666033\pi$
$811$	13.6775	−	18.8255i	0.480283	−	0.661053i	0.978559	+	0.205965i	$0.0660335\pi$
$812$	4.91649	−	23.1303i	0.172535	−	0.811713i
$813$		0			0
$814$	7.63171	−	0.808173i	0.267491	−	0.0283264i
$815$	−4.75231	+	2.74375i	−0.166466	+	0.0961092i
$816$		0			0
$817$	10.6890	−	4.75904i	0.373960	−	0.166498i
$818$	−14.5777	−	20.0644i	−0.509696	−	0.701536i
$819$		0			0
$820$	23.9558	+	7.78372i	0.836574	+	0.271819i
$821$	−2.24547	−	21.3642i	−0.0783675	−	0.745617i	−0.961186	−	0.275902i	$-0.911023\pi$
$821$	−2.24547	−	21.3642i	−0.0783675	−	0.745617i	0.882818	−	0.469715i	$-0.155643\pi$
$822$		0			0
$823$	32.4175	−	36.0033i	1.13000	−	1.25500i	0.166867	−	0.985979i	$-0.446635\pi$
$823$	32.4175	−	36.0033i	1.13000	−	1.25500i	0.963136	−	0.269016i	$-0.0866984\pi$
$824$	9.82949	+	17.0252i	0.342426	+	0.593100i
$825$		0			0
$826$	3.85165	−	6.67125i	0.134016	−	0.232122i
$827$	12.2819	+	37.7998i	0.427084	+	1.31443i	0.900985	+	0.433851i	$0.142845\pi$
$827$	12.2819	+	37.7998i	0.427084	+	1.31443i	−0.473901	+	0.880578i	$0.657155\pi$
$828$		0			0
$829$	27.8772	−	20.2540i	0.968215	−	0.703450i	0.0131712	−	0.999913i	$-0.495807\pi$
$829$	27.8772	−	20.2540i	0.968215	−	0.703450i	0.955044	+	0.296464i	$0.0958074\pi$
$830$	23.0681	−	20.7706i	0.800704	−	0.720957i
$831$		0			0
$832$	0.453223	−	1.01795i	0.0157127	−	0.0352912i
$833$	−0.0677008	+	0.644130i	−0.00234569	+	0.0223178i
$834$		0			0
$835$	29.0514	+	16.7729i	1.00537	+	0.580449i
$836$	12.8795	−	2.74817i	0.445446	−	0.0950474i
$837$		0			0
$838$	14.9621	−	4.86147i	0.516856	−	0.167937i
$839$	10.6838	+	23.9961i	0.368844	+	0.828438i	0.998663	+	0.0516955i	$0.0164625\pi$
$839$	10.6838	+	23.9961i	0.368844	+	0.828438i	−0.629819	+	0.776742i	$0.716871\pi$
$840$		0			0
$841$	−14.2601	+	3.03109i	−0.491729	+	0.104520i
$842$	−9.04471	+	1.92251i	−0.311701	+	0.0662542i
$843$		0			0
$844$	−7.15179	−	16.0632i	−0.246175	−	0.552917i
$845$	−88.9674	+	28.9073i	−3.06057	+	0.994440i
$846$		0			0
$847$	21.1522	+	12.1680i	0.726797	+	0.418099i
$848$	9.38404	+	5.41788i	0.322249	+	0.186051i
$849$		0			0
$850$	−0.180711	+	1.71935i	−0.00619833	+	0.0589731i
$851$	13.5313	−	30.3918i	0.463847	−	1.04182i
$852$		0			0
$853$	30.3073	−	27.2888i	1.03770	−	0.934350i	0.0398060	−	0.999207i	$-0.487326\pi$
$853$	30.3073	−	27.2888i	1.03770	−	0.934350i	0.997895	+	0.0648576i	$0.0206593\pi$
$854$	1.67661	−	1.21813i	0.0573726	−	0.0416836i
$855$		0			0
$856$	0.530097	+	1.63147i	0.0181183	+	0.0557625i
$857$	−22.9703	+	39.7858i	−0.784651	+	1.35906i	0.144556	+	0.989497i	$0.453825\pi$
$857$	−22.9703	+	39.7858i	−0.784651	+	1.35906i	−0.929207	+	0.369559i	$0.879509\pi$
$858$		0			0
$859$	9.12751	+	15.8093i	0.311427	+	0.539407i	0.978671	−	0.205432i	$-0.0658598\pi$
$859$	9.12751	+	15.8093i	0.311427	+	0.539407i	−0.667245	+	0.744838i	$0.732527\pi$
$860$	19.1940	−	21.3171i	0.654510	−	0.726907i
$861$		0			0
$862$	−1.01090	−	9.61806i	−0.0344314	−	0.327592i
$863$	−18.5553	−	6.02899i	−0.631631	−	0.205229i	−0.0243334	−	0.999704i	$-0.507746\pi$
$863$	−18.5553	−	6.02899i	−0.631631	−	0.205229i	−0.607297	+	0.794475i	$0.707746\pi$
$864$		0			0
$865$	14.4714	+	19.9181i	0.492042	+	0.677237i
$866$	−6.02409	+	2.68210i	−0.204707	+	0.0911414i
$867$		0			0
$868$	3.34490	−	1.93118i	0.113533	−	0.0655485i
$869$	−8.23928	+	14.2967i	−0.279498	+	0.484983i
$870$		0			0
$871$	3.58806	−	16.8805i	0.121577	−	0.571973i
$872$	−5.79310	+	7.97352i	−0.196179	+	0.270017i
$873$		0			0
$874$	−4.20920	+	12.9546i	−0.142378	+	0.438196i
$875$	−21.8314	−	24.2463i	−0.738038	−	0.819674i
$876$		0			0
$877$	−20.3710	−	2.14108i	−0.687880	−	0.0722991i	−0.245861	−	0.969305i	$-0.579071\pi$
$877$	−20.3710	−	2.14108i	−0.687880	−	0.0722991i	−0.442018	+	0.897006i	$0.645737\pi$
$878$	8.21667	+	7.39832i	0.277299	+	0.249681i
$879$		0			0
$880$	18.3903	−	13.3834i	0.619936	−	0.451153i
$881$		−	38.0577i		−	1.28220i	−0.767459	−	0.641099i	$-0.778479\pi$
$881$		−	38.0577i		−	1.28220i	0.767459	−	0.641099i	$-0.221521\pi$
$882$		0			0
$883$	17.6981	+	12.8584i	0.595590	+	0.432721i	0.844311	−	0.535854i	$-0.180010\pi$
$883$	17.6981	+	12.8584i	0.595590	+	0.432721i	−0.248721	+	0.968575i	$0.580010\pi$
$884$	−3.08665	+	0.324420i	−0.103815	+	0.0109114i
$885$		0			0
$886$	−2.36390	−	11.1213i	−0.0794168	−	0.373627i
$887$	−30.9486	−	13.7792i	−1.03915	−	0.462660i	−0.185030	−	0.982733i	$-0.559238\pi$
$887$	−30.9486	−	13.7792i	−1.03915	−	0.462660i	−0.854122	+	0.520073i	$0.825905\pi$
$888$		0			0
$889$	−24.4732	−	5.20193i	−0.820804	−	0.174467i
$890$	7.07018			0.236993
$891$		0			0
$892$	−18.3383			−0.614011
$893$	3.46542	+	0.736599i	0.115966	+	0.0246493i
$894$		0			0
$895$	4.35427	+	1.93864i	0.145547	+	0.0648017i
$896$	−5.24282	−	24.6655i	−0.175150	−	0.824018i
$897$		0			0
$898$	8.72571	−	0.917109i	0.291181	−	0.0306043i
$899$	−5.75849	−	4.18379i	−0.192056	−	0.139537i
$900$		0			0
$901$		−	1.83807i		−	0.0612349i
$902$	5.05029	−	6.96259i	0.168156	−	0.231829i
$903$		0			0
$904$	10.0291	+	9.03028i	0.333564	+	0.300343i
$905$	76.7889	+	8.07084i	2.55255	+	0.268284i
$906$		0			0
$907$	−10.8902	−	12.0948i	−0.361602	−	0.401600i	0.534701	−	0.845041i	$-0.320424\pi$
$907$	−10.8902	−	12.0948i	−0.361602	−	0.401600i	−0.896303	+	0.443441i	$0.853757\pi$
$908$	5.34588	−	16.4529i	0.177409	−	0.546010i
$909$		0			0
$910$	−18.6411	+	25.6572i	−0.617945	+	0.850529i
$911$	3.44054	−	16.1865i	0.113990	−	0.536282i	−0.883682	−	0.468088i	$-0.844943\pi$
$911$	3.44054	−	16.1865i	0.113990	−	0.536282i	0.997672	−	0.0681939i	$-0.0217236\pi$
$912$		0			0
$913$	18.1012	+	40.5704i	0.599063	+	1.34268i
$914$	−4.65190	+	2.68578i	−0.153871	+	0.0888376i
$915$		0			0
$916$	29.0229	−	12.9218i	0.958944	−	0.426949i
$917$	22.4044	+	30.8371i	0.739860	+	1.01833i
$918$		0			0
$919$	30.9592	+	10.0592i	1.02125	+	0.331824i	0.771325	−	0.636441i	$-0.219594\pi$
$919$	30.9592	+	10.0592i	1.02125	+	0.331824i	0.249924	+	0.968265i	$0.419594\pi$
$920$	7.81406	+	74.3458i	0.257622	+	2.45111i
$921$		0			0
$922$	15.0633	−	16.7295i	0.496084	−	0.550957i
$923$	21.0118	+	36.3935i	0.691612	+	1.19791i
$924$		0			0
$925$	16.6623	−	28.8599i	0.547852	−	0.948907i
$926$	5.42868	+	16.7078i	0.178397	+	0.549051i
$927$		0			0
$928$	−30.0543	+	21.8357i	−0.986581	+	0.716793i
$929$	38.5410	−	34.7024i	1.26449	−	1.13855i	0.280589	−	0.959828i	$-0.409470\pi$
$929$	38.5410	−	34.7024i	1.26449	−	1.13855i	0.983900	−	0.178722i	$-0.0571964\pi$
$930$		0			0
$931$	−2.07911	+	4.66976i	−0.0681401	+	0.153045i
$932$	−3.40222	+	32.3699i	−0.111443	+	1.06031i
$933$		0			0
$934$	14.9488	+	8.63067i	0.489138	+	0.282404i
$935$	−3.52584	−	1.56649i	−0.115307	−	0.0512298i
$936$		0			0
$937$	4.46609	−	1.45112i	0.145901	−	0.0474061i	−0.235156	−	0.971958i	$-0.575560\pi$
$937$	4.46609	−	1.45112i	0.145901	−	0.0474061i	0.381057	+	0.924552i	$0.375560\pi$
$938$	−1.56678	−	3.51904i	−0.0511571	−	0.114901i
$939$		0			0
$940$	8.49581	−	1.80584i	0.277103	−	0.0589000i
$941$	8.81457	−	1.87360i	0.287347	−	0.0610775i	−0.0619832	−	0.998077i	$-0.519743\pi$
$941$	8.81457	−	1.87360i	0.287347	−	0.0610775i	0.349330	+	0.937000i	$0.386409\pi$
$942$		0			0
$943$	−15.1657	−	34.0627i	−0.493863	−	1.10924i
$944$	9.77287	−	3.17540i	0.318080	−	0.103350i
$945$		0			0
$946$	−4.90427	−	8.47910i	−0.159452	−	0.275679i
$947$	28.1466	+	16.2504i	0.914641	+	0.528068i	0.881922	−	0.471396i	$-0.156250\pi$
$947$	28.1466	+	16.2504i	0.914641	+	0.528068i	0.0327198	+	0.999465i	$0.489583\pi$
$948$		0			0
$949$	−6.21205	+	59.1037i	−0.201652	+	1.91859i
$950$	−5.54968	+	12.4648i	−0.180056	+	0.404411i
$951$		0			0
$952$	−1.15249	+	1.03771i	−0.0373524	+	0.0336323i
$953$	9.17192	−	6.66379i	0.297108	−	0.215861i	−0.429237	−	0.903192i	$-0.641218\pi$
$953$	9.17192	−	6.66379i	0.297108	−	0.215861i	0.726345	+	0.687331i	$0.241218\pi$
$954$		0			0
$955$	7.76447	+	23.8966i	0.251252	+	0.773275i
$956$	−13.8855	+	24.0503i	−0.449088	+	0.777843i
$957$		0			0
$958$	2.30121	+	3.98581i	0.0743488	+	0.128776i
$959$	2.01809	−	2.24132i	0.0651675	−	0.0723758i
$960$		0			0
$961$	3.11886	+	29.6740i	0.100608	+	0.957224i
$962$	−13.5757	−	4.41102i	−0.437699	−	0.142217i
$963$		0			0
$964$	−19.4850	−	26.8187i	−0.627568	−	0.863774i
$965$	53.8568	−	23.9786i	1.73371	−	0.771899i
$966$		0			0
$967$	−4.25298	+	2.45546i	−0.136767	+	0.0789623i	−0.566822	−	0.823840i	$-0.691827\pi$
$967$	−4.25298	+	2.45546i	−0.136767	+	0.0789623i	0.430055	+	0.902802i	$0.358494\pi$
$968$	−7.66344	−	23.4605i	−0.246312	−	0.754048i
$969$		0			0
$970$	−7.09109	+	33.3610i	−0.227681	+	1.07116i
$971$	−6.66140	+	9.16863i	−0.213774	+	0.294235i	−0.902415	−	0.430867i	$-0.858208\pi$
$971$	−6.66140	+	9.16863i	−0.213774	+	0.294235i	0.688641	+	0.725103i	$0.258208\pi$
$972$		0			0
$973$	8.26991	−	25.4522i	0.265121	−	0.815959i
$974$	7.73570	+	8.59137i	0.247868	+	0.275285i
$975$		0			0
$976$	2.74934	+	0.288968i	0.0880044	+	0.00924963i
$977$	−22.1946	−	19.9841i	−0.710067	−	0.639347i	0.232797	−	0.972525i	$-0.425212\pi$
$977$	−22.1946	−	19.9841i	−0.710067	−	0.639347i	−0.942864	+	0.333178i	$0.891879\pi$
$978$		0			0
$979$	−3.11930	+	9.62588i	−0.0996932	+	0.307644i
$980$			12.5318i			0.400313i
$981$		0			0
$982$	−10.7272	−	7.79379i	−0.342320	−	0.248710i
$983$	−6.68789	+	0.702926i	−0.213311	+	0.0224199i	−0.210581	−	0.977576i	$-0.567536\pi$
$983$	−6.68789	+	0.702926i	−0.213311	+	0.0224199i	−0.00272968	+	0.999996i	$0.500869\pi$
$984$		0			0
$985$	−1.62315	−	7.63633i	−0.0517179	−	0.243314i
$986$	1.16632	+	0.519277i	0.0371431	+	0.0165372i
$987$		0			0
$988$	−23.9598	−	5.09282i	−0.762264	−	0.162024i
$989$	−42.4618			−1.35021
$990$		0			0
$991$	−6.33993			−0.201395			−0.100697	−	0.994917i	$-0.532107\pi$
$991$	−6.33993			−0.201395			−0.100697	+	0.994917i	$0.532107\pi$
$992$	−5.93513	−	1.26155i	−0.188440	−	0.0400542i
$993$		0			0
$994$	8.56914	+	3.81523i	0.271797	+	0.121012i
$995$	−2.92468	−	13.7595i	−0.0927185	−	0.436206i
$996$		0			0
$997$	−6.71660	+	0.705943i	−0.212717	+	0.0223575i	−0.210287	−	0.977640i	$-0.567440\pi$
$997$	−6.71660	+	0.705943i	−0.212717	+	0.0223575i	−0.00242948	+	0.999997i	$0.500773\pi$
$998$	5.99996	+	4.35922i	0.189925	+	0.137989i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.u.e.512.5		64
3.2	odd	2	inner	891.2.u.e.512.4		64
9.2	odd	6		297.2.k.a.215.5	yes	32
9.4	even	3	inner	891.2.u.e.215.4		64
9.5	odd	6	inner	891.2.u.e.215.5		64
9.7	even	3		297.2.k.a.215.4	yes	32
11.2	odd	10	inner	891.2.u.e.431.5		64
33.2	even	10	inner	891.2.u.e.431.4		64
99.2	even	30		297.2.k.a.134.4	✓	32
99.13	odd	30	inner	891.2.u.e.134.4		64
99.68	even	30	inner	891.2.u.e.134.5		64
99.79	odd	30		297.2.k.a.134.5	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
297.2.k.a.134.4	✓	32	99.2	even	30
297.2.k.a.134.5	yes	32	99.79	odd	30
297.2.k.a.215.4	yes	32	9.7	even	3
297.2.k.a.215.5	yes	32	9.2	odd	6
891.2.u.e.134.4		64	99.13	odd	30	inner
891.2.u.e.134.5		64	99.68	even	30	inner
891.2.u.e.215.4		64	9.4	even	3	inner
891.2.u.e.215.5		64	9.5	odd	6	inner
891.2.u.e.431.4		64	33.2	even	10	inner
891.2.u.e.431.5		64	11.2	odd	10	inner
891.2.u.e.512.4		64	3.2	odd	2	inner
891.2.u.e.512.5		64	1.1	even	1	trivial

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.u (of order \(30\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.607139 + 0.129051i) q^{2} +(-1.47513 - 0.656769i) q^{4} +(0.776244 + 3.65194i) q^{5} +(2.20625 - 0.231886i) q^{7} +(-1.81517 - 1.31880i) q^{8} +O(q^{10})\)	\(q+(0.607139 + 0.129051i) q^{2} +(-1.47513 - 0.656769i) q^{4} +(0.776244 + 3.65194i) q^{5} +(2.20625 - 0.231886i) q^{7} +(-1.81517 - 1.31880i) q^{8} +2.31741i q^{10} +(-3.15510 - 1.02242i) q^{11} +(4.58440 + 4.12782i) q^{13} +(1.36942 + 0.143932i) q^{14} +(1.22906 + 1.36501i) q^{16} +(0.0962825 - 0.296327i) q^{17} +(1.44540 - 1.98943i) q^{19} +(1.25342 - 5.89689i) q^{20} +(-1.78364 - 1.02792i) q^{22} +(-7.72848 + 4.46204i) q^{23} +(-8.16640 + 3.63592i) q^{25} +(2.25067 + 3.09778i) q^{26} +(-3.40679 - 1.10693i) q^{28} +(0.690036 + 6.56526i) q^{29} +(-0.721480 + 0.801285i) q^{31} +(2.81373 + 4.87352i) q^{32} +(0.0966983 - 0.167486i) q^{34} +(2.55942 + 7.87708i) q^{35} +(-3.01593 + 2.19120i) q^{37} +(1.13430 - 1.02133i) q^{38} +(3.40716 - 7.65260i) q^{40} +(-0.436738 + 4.15528i) q^{41} +(4.12066 + 2.37906i) q^{43} +(3.98268 + 3.58037i) q^{44} +(-5.26809 + 1.71171i) q^{46} +(0.585996 + 1.31617i) q^{47} +(-2.03329 + 0.432188i) q^{49} +(-5.42736 + 1.15362i) q^{50} +(-4.05156 - 9.09995i) q^{52} +(5.61052 - 1.82297i) q^{53} +(1.28469 - 12.3159i) q^{55} +(-4.31052 - 2.48868i) q^{56} +(-0.428307 + 4.07507i) q^{58} +(2.27545 - 5.11074i) q^{59} +(1.11847 - 1.00708i) q^{61} +(-0.541446 + 0.393383i) q^{62} +(-0.0558176 - 0.171789i) q^{64} +(-11.5159 + 19.9462i) q^{65} +(-1.39875 - 2.42271i) q^{67} +(-0.336647 + 0.373885i) q^{68} +(0.537375 + 5.11278i) q^{70} +(6.47873 + 2.10507i) q^{71} +(5.66251 + 7.79378i) q^{73} +(-2.11386 + 0.941153i) q^{74} +(-3.43875 + 1.98536i) q^{76} +(-7.19801 - 1.52409i) q^{77} +(1.03441 - 4.86651i) q^{79} +(-4.03089 + 5.54804i) q^{80} +(-0.801405 + 2.46647i) q^{82} +(-8.96283 - 9.95424i) q^{83} +(1.15691 + 0.121596i) q^{85} +(2.19479 + 1.97620i) q^{86} +(4.37867 + 6.01680i) q^{88} -3.05090i q^{89} +(11.0715 + 8.04392i) q^{91} +(14.3310 - 1.50625i) q^{92} +(0.185928 + 0.874721i) q^{94} +(8.38726 + 3.73425i) q^{95} +(14.3958 + 3.05992i) q^{97} -1.29026 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 8 q^{4}+O(q^{10}) \) 64 * q + 8 * q^4	\( 64 q + 8 q^{4} + 4 q^{16} - 36 q^{22} - 8 q^{25} - 200 q^{28} - 8 q^{31} + 64 q^{34} - 24 q^{37} + 60 q^{40} - 40 q^{46} - 100 q^{52} + 16 q^{55} - 24 q^{58} - 60 q^{61} + 72 q^{64} + 24 q^{67} - 8 q^{70} + 160 q^{73} + 60 q^{79} + 144 q^{82} + 20 q^{85} + 24 q^{88} + 48 q^{91} - 20 q^{94} + 24 q^{97}+O(q^{100}) \) 64 * q + 8 * q^4 + 4 * q^16 - 36 * q^22 - 8 * q^25 - 200 * q^28 - 8 * q^31 + 64 * q^34 - 24 * q^37 + 60 * q^40 - 40 * q^46 - 100 * q^52 + 16 * q^55 - 24 * q^58 - 60 * q^61 + 72 * q^64 + 24 * q^67 - 8 * q^70 + 160 * q^73 + 60 * q^79 + 144 * q^82 + 20 * q^85 + 24 * q^88 + 48 * q^91 - 20 * q^94 + 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more