LMFDB - Embedded newform 945.2.ch.a.242.31

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [945,2,Mod(53,945)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(945, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 8]))

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

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

chi := DirichletCharacter("945.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 945 = 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	945.ch (of order $12$, degree $4$, 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:	$7.54586299101$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			242.31
Character	$\chi$	$=$	945.242
Dual form			945.2.ch.a.863.31

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.42868 + 0.650762i) q^{2} +(3.74293 + 2.16098i) q^{4} +(-1.11889 - 1.93600i) q^{5} +(-0.654856 - 2.56343i) q^{7} +(4.12826 + 4.12826i) q^{8} +O(q^{10})$	\(q+(2.42868 + 0.650762i) q^{2} +(3.74293 + 2.16098i) q^{4} +(-1.11889 - 1.93600i) q^{5} +(-0.654856 - 2.56343i) q^{7} +(4.12826 + 4.12826i) q^{8} +(-1.45755 - 5.43004i) q^{10} +(4.33235 + 2.50128i) q^{11} +(4.46310 - 4.46310i) q^{13} +(0.0777484 - 6.65190i) q^{14} +(3.01772 + 5.22685i) q^{16} +(-0.263965 - 0.985130i) q^{17} +(-5.51117 + 3.18187i) q^{19} +(-0.00427246 - 9.66421i) q^{20} +(8.89413 + 8.89413i) q^{22} +(-0.0712184 + 0.265791i) q^{23} +(-2.49617 + 4.33234i) q^{25} +(13.7438 - 7.93501i) q^{26} +(3.08844 - 11.0099i) q^{28} +4.05409 q^{29} +(-2.12640 + 3.68302i) q^{31} +(0.905549 + 3.37955i) q^{32} -2.56434i q^{34} +(-4.23008 + 4.13599i) q^{35} +(-0.349026 + 1.30258i) q^{37} +(-15.4555 + 4.14129i) q^{38} +(3.37323 - 12.6114i) q^{40} +2.13805i q^{41} +(1.22969 - 1.22969i) q^{43} +(10.8104 + 18.7242i) q^{44} +(-0.345933 + 0.599174i) q^{46} +(7.54793 + 2.02246i) q^{47} +(-6.14233 + 3.35735i) q^{49} +(-8.88171 + 8.89743i) q^{50} +(26.3498 - 7.06040i) q^{52} +(0.0406498 - 0.0108921i) q^{53} +(-0.00494526 - 11.1861i) q^{55} +(7.87908 - 13.2859i) q^{56} +(9.84608 + 2.63825i) q^{58} +(-5.17288 + 8.95970i) q^{59} +(1.02281 + 1.77155i) q^{61} +(-7.56110 + 7.56110i) q^{62} -3.27376i q^{64} +(-13.6343 - 3.64683i) q^{65} +(-13.6943 + 3.66938i) q^{67} +(1.14085 - 4.25770i) q^{68} +(-12.9650 + 7.29222i) q^{70} -5.23525i q^{71} +(-2.69518 - 10.0585i) q^{73} +(-1.69534 + 2.93642i) q^{74} -27.5039 q^{76} +(3.57479 - 12.7436i) q^{77} +(-12.5365 + 7.23793i) q^{79} +(6.74267 - 11.6906i) q^{80} +(-1.39136 + 5.19263i) q^{82} +(9.98593 + 9.98593i) q^{83} +(-1.61186 + 1.61329i) q^{85} +(3.78676 - 2.18628i) q^{86} +(7.55911 + 28.2110i) q^{88} +(-2.39266 - 4.14421i) q^{89} +(-14.3635 - 8.51815i) q^{91} +(-0.840935 + 0.840935i) q^{92} +(17.0154 + 9.82382i) q^{94} +(12.3265 + 7.10944i) q^{95} +(0.238144 + 0.238144i) q^{97} +(-17.1026 + 4.15673i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q - 8 q^{7}+O(q^{10}) $ 128 * q - 8 * q^7	$ 128 q - 8 q^{7} - 8 q^{10} + 64 q^{16} - 8 q^{25} + 8 q^{28} + 16 q^{31} - 8 q^{37} + 40 q^{40} - 32 q^{43} + 80 q^{52} + 32 q^{55} + 16 q^{58} - 24 q^{61} - 16 q^{67} - 80 q^{70} + 64 q^{73} - 160 q^{76} - 40 q^{82} - 64 q^{85} - 48 q^{88} - 136 q^{91} - 208 q^{97}+O(q^{100}) $ 128 * q - 8 * q^7 - 8 * q^10 + 64 * q^16 - 8 * q^25 + 8 * q^28 + 16 * q^31 - 8 * q^37 + 40 * q^40 - 32 * q^43 + 80 * q^52 + 32 * q^55 + 16 * q^58 - 24 * q^61 - 16 * q^67 - 80 * q^70 + 64 * q^73 - 160 * q^76 - 40 * q^82 - 64 * q^85 - 48 * q^88 - 136 * q^91 - 208 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

$n$	$136$	$596$	$757$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	2.42868	+	0.650762i	1.71733	+	0.460158i	0.977204	−	0.212305i	$-0.0680970\pi$
$2$	2.42868	+	0.650762i	1.71733	+	0.460158i	0.740131	+	0.672463i	$0.234764\pi$
$3$		0			0
$3$		0			0
$4$	3.74293	+	2.16098i	1.87147	+	1.08049i
$5$	−1.11889	−	1.93600i	−0.500383	−	0.865804i
$5$	−1.11889	−	1.93600i	−0.500383	−	0.865804i
$6$		0			0
$7$	−0.654856	−	2.56343i	−0.247512	−	0.968885i
$7$	−0.654856	−	2.56343i	−0.247512	−	0.968885i
$8$	4.12826	+	4.12826i	1.45956	+	1.45956i
$9$		0			0
$10$	−1.45755	−	5.43004i	−0.460917	−	1.71713i
$11$	4.33235	+	2.50128i	1.30625	+	0.754165i	0.981468	−	0.191624i	$-0.0613754\pi$
$11$	4.33235	+	2.50128i	1.30625	+	0.754165i	0.324783	+	0.945789i	$0.394709\pi$
$12$		0			0
$13$	4.46310	−	4.46310i	1.23784	−	1.23784i	0.276960	−	0.960882i	$-0.410673\pi$
$13$	4.46310	−	4.46310i	1.23784	−	1.23784i	0.960882	−	0.276960i	$-0.0893268\pi$
$14$	0.0777484	−	6.65190i	0.0207791	−	1.77779i
$15$		0			0
$16$	3.01772	+	5.22685i	0.754431	+	1.30671i
$17$	−0.263965	−	0.985130i	−0.0640209	−	0.238929i	0.926499	−	0.376296i	$-0.122803\pi$
$17$	−0.263965	−	0.985130i	−0.0640209	−	0.238929i	−0.990520	+	0.137367i	$0.956136\pi$
$18$		0			0
$19$	−5.51117	+	3.18187i	−1.26435	+	0.729972i	−0.973913	−	0.226922i	$-0.927134\pi$
$19$	−5.51117	+	3.18187i	−1.26435	+	0.729972i	−0.290436	+	0.956894i	$0.593800\pi$
$20$	−0.00427246	−	9.66421i	−0.000955351	−	2.16098i
$21$		0			0
$22$	8.89413	+	8.89413i	1.89624	+	1.89624i
$23$	−0.0712184	+	0.265791i	−0.0148501	+	0.0554212i	−0.972953	−	0.231002i	$-0.925800\pi$
$23$	−0.0712184	+	0.265791i	−0.0148501	+	0.0554212i	0.958103	+	0.286423i	$0.0924663\pi$
$24$		0			0
$25$	−2.49617	+	4.33234i	−0.499234	+	0.866467i
$26$	13.7438	−	7.93501i	2.69539	−	1.55618i
$27$		0			0
$28$	3.08844	−	11.0099i	0.583661	−	2.08067i
$29$	4.05409			0.752826			0.376413	−	0.926452i	$-0.377157\pi$
$29$	4.05409			0.752826			0.376413	+	0.926452i	$0.377157\pi$
$30$		0			0
$31$	−2.12640	+	3.68302i	−0.381912	+	0.661491i	−0.991336	−	0.131354i	$-0.958068\pi$
$31$	−2.12640	+	3.68302i	−0.381912	+	0.661491i	0.609424	+	0.792845i	$0.291401\pi$
$32$	0.905549	+	3.37955i	0.160080	+	0.597426i
$33$		0			0
$34$		−	2.56434i		−	0.439781i
$35$	−4.23008	+	4.13599i	−0.715014	+	0.699110i
$36$		0			0
$37$	−0.349026	+	1.30258i	−0.0573795	+	0.214143i	−0.988663	−	0.150153i	$-0.952024\pi$
$37$	−0.349026	+	1.30258i	−0.0573795	+	0.214143i	0.931283	+	0.364296i	$0.118690\pi$
$38$	−15.4555	+	4.14129i	−2.50721	+	0.671805i
$39$		0			0
$40$	3.37323	−	12.6114i	0.533354	−	1.99403i
$41$			2.13805i			0.333907i	0.985965	+	0.166953i	$0.0533930\pi$
$41$			2.13805i			0.333907i	−0.985965	+	0.166953i	$0.946607\pi$
$42$		0			0
$43$	1.22969	−	1.22969i	0.187526	−	0.187526i	−0.607100	−	0.794626i	$-0.707667\pi$
$43$	1.22969	−	1.22969i	0.187526	−	0.187526i	0.794626	+	0.607100i	$0.207667\pi$
$44$	10.8104	+	18.7242i	1.62974	+	2.82279i
$45$		0			0
$46$	−0.345933	+	0.599174i	−0.0510051	+	0.0883433i
$47$	7.54793	+	2.02246i	1.10098	+	0.295007i	0.763163	−	0.646206i	$-0.223645\pi$
$47$	7.54793	+	2.02246i	1.10098	+	0.295007i	0.337816	+	0.941212i	$0.390312\pi$
$48$		0			0
$49$	−6.14233	+	3.35735i	−0.877475	+	0.479622i
$50$	−8.88171	+	8.89743i	−1.25606	+	1.25829i
$51$		0			0
$52$	26.3498	−	7.06040i	3.65405	−	0.979101i
$53$	0.0406498	−	0.0108921i	0.00558367	−	0.00149614i	−0.256026	−	0.966670i	$-0.582413\pi$
$53$	0.0406498	−	0.0108921i	0.00558367	−	0.00149614i	0.261610	+	0.965174i	$0.415747\pi$
$54$		0			0
$55$	−0.00494526	−	11.1861i	−0.000666819	−	1.50833i
$56$	7.87908	−	13.2859i	1.05289	−	1.77540i
$57$		0			0
$58$	9.84608	+	2.63825i	1.29285	+	0.346419i
$59$	−5.17288	+	8.95970i	−0.673452	+	1.16645i	0.303467	+	0.952842i	$0.401856\pi$
$59$	−5.17288	+	8.95970i	−0.673452	+	1.16645i	−0.976919	+	0.213611i	$0.931477\pi$
$60$		0			0
$61$	1.02281	+	1.77155i	0.130957	+	0.226824i	0.924046	−	0.382282i	$-0.124862\pi$
$61$	1.02281	+	1.77155i	0.130957	+	0.226824i	−0.793089	+	0.609106i	$0.791528\pi$
$62$	−7.56110	+	7.56110i	−0.960261	+	0.960261i
$63$		0			0
$64$		−	3.27376i		−	0.409220i
$65$	−13.6343	−	3.64683i	−1.69112	−	0.452334i
$66$		0			0
$67$	−13.6943	+	3.66938i	−1.67303	+	0.448286i	−0.965924	−	0.258824i	$-0.916665\pi$
$67$	−13.6943	+	3.66938i	−1.67303	+	0.448286i	−0.707103	+	0.707111i	$0.749998\pi$
$68$	1.14085	−	4.25770i	0.138348	−	0.516322i
$69$		0			0
$70$	−12.9650	+	7.29222i	−1.54962	+	0.871587i
$71$		−	5.23525i		−	0.621310i	−0.950523	−	0.310655i	$-0.899452\pi$
$71$		−	5.23525i		−	0.621310i	0.950523	−	0.310655i	$-0.100548\pi$
$72$		0			0
$73$	−2.69518	−	10.0585i	−0.315447	−	1.17726i	−0.923573	−	0.383423i	$-0.874745\pi$
$73$	−2.69518	−	10.0585i	−0.315447	−	1.17726i	0.608126	−	0.793841i	$-0.291922\pi$
$74$	−1.69534	+	2.93642i	−0.197079	+	0.341352i
$75$		0			0
$76$	−27.5039			−3.15491
$77$	3.57479	−	12.7436i	0.407385	−	1.45227i
$78$		0			0
$79$	−12.5365	+	7.23793i	−1.41046	+	0.814331i	−0.995432	−	0.0954764i	$-0.969563\pi$
$79$	−12.5365	+	7.23793i	−1.41046	+	0.814331i	−0.415031	+	0.909807i	$0.636229\pi$
$80$	6.74267	−	11.6906i	0.753853	−	1.30705i
$81$		0			0
$82$	−1.39136	+	5.19263i	−0.153650	+	0.573430i
$83$	9.98593	+	9.98593i	1.09610	+	1.09610i	0.994863	+	0.101235i	$0.0322795\pi$
$83$	9.98593	+	9.98593i	1.09610	+	1.09610i	0.101235	+	0.994863i	$0.467721\pi$
$84$		0			0
$85$	−1.61186	+	1.61329i	−0.174831	+	0.174986i
$86$	3.78676	−	2.18628i	0.408336	−	0.235753i
$87$		0			0
$88$	7.55911	+	28.2110i	0.805803	+	3.00730i
$89$	−2.39266	−	4.14421i	−0.253622	−	0.439285i	0.710899	−	0.703294i	$-0.248288\pi$
$89$	−2.39266	−	4.14421i	−0.253622	−	0.439285i	−0.964520	+	0.264009i	$0.914955\pi$
$90$		0			0
$91$	−14.3635	−	8.51815i	−1.50571	−	0.892945i
$92$	−0.840935	+	0.840935i	−0.0876735	+	0.0876735i
$93$		0			0
$94$	17.0154	+	9.82382i	1.75500	+	1.01325i
$95$	12.3265	+	7.10944i	1.26467	+	0.729413i
$96$		0			0
$97$	0.238144	+	0.238144i	0.0241798	+	0.0241798i	0.719093	−	0.694914i	$-0.244557\pi$
$97$	0.238144	+	0.238144i	0.0241798	+	0.0241798i	−0.694914	+	0.719093i	$0.744557\pi$
$98$	−17.1026	+	4.15673i	−1.72762	+	0.419893i
$99$		0			0
$100$	−18.7051	+	10.8215i	−1.87051	+	1.08215i
$101$	−9.68543	−	5.59189i	−0.963736	−	0.556413i	−0.0664154	−	0.997792i	$-0.521156\pi$
$101$	−9.68543	−	5.59189i	−0.963736	−	0.556413i	−0.897321	+	0.441379i	$0.854490\pi$
$102$		0			0
$103$	−10.2176	−	2.73780i	−1.00677	−	0.269763i	−0.282490	−	0.959270i	$-0.591160\pi$
$103$	−10.2176	−	2.73780i	−1.00677	−	0.269763i	−0.724279	+	0.689507i	$0.757827\pi$
$104$	36.8496			3.61340
$105$		0			0
$106$	0.105813			0.0102775
$107$	−13.4143	−	3.59435i	−1.29681	−	0.347479i	−0.456565	−	0.889690i	$-0.650921\pi$
$107$	−13.4143	−	3.59435i	−1.29681	−	0.347479i	−0.840242	+	0.542211i	$0.817587\pi$
$108$		0			0
$109$	3.36589	+	1.94330i	0.322394	+	0.186134i	0.652459	−	0.757824i	$-0.273737\pi$
$109$	3.36589	+	1.94330i	0.322394	+	0.186134i	−0.330065	+	0.943958i	$0.607071\pi$
$110$	7.26746	−	27.1706i	0.692925	−	2.59061i
$111$		0			0
$112$	11.4225	−	11.1586i	1.07932	−	1.05438i
$113$	12.1383	+	12.1383i	1.14187	+	1.14187i	0.988107	+	0.153768i	$0.0491408\pi$
$113$	12.1383	+	12.1383i	1.14187	+	1.14187i	0.153768	+	0.988107i	$0.450859\pi$
$114$		0			0
$115$	0.594256	−	0.159512i	0.0554146	−	0.0148746i
$116$	15.1742	+	8.76082i	1.40889	+	0.813422i
$117$		0			0
$118$	−18.3939	+	18.3939i	−1.69330	+	1.69330i
$119$	−2.35245	+	1.32177i	−0.215649	+	0.121167i
$120$		0			0
$121$	7.01282	+	12.1466i	0.637529	+	1.10423i
$122$	1.33121	+	4.96813i	0.120522	+	0.449794i
$123$		0			0
$124$	−15.9179	+	9.19021i	−1.42947	+	0.825305i
$125$	11.1803	−	0.0148282i	0.999999	−	0.00132627i
$126$		0			0
$127$	−2.35613	−	2.35613i	−0.209072	−	0.209072i	0.594801	−	0.803873i	$-0.297231\pi$
$127$	−2.35613	−	2.35613i	−0.209072	−	0.209072i	−0.803873	+	0.594801i	$0.797231\pi$
$128$	3.94153	−	14.7100i	0.348386	−	1.30019i
$129$		0			0
$130$	−30.7400	−	17.7296i	−2.69608	−	1.55499i
$131$	4.13205	−	2.38564i	0.361019	−	0.208435i	−0.308509	−	0.951222i	$-0.599830\pi$
$131$	4.13205	−	2.38564i	0.361019	−	0.208435i	0.669528	+	0.742787i	$0.266497\pi$
$132$		0			0
$133$	11.7655	+	12.0438i	1.02020	+	1.04433i
$134$	−35.6470			−3.07943
$135$		0			0
$136$	2.97716	−	5.15658i	0.255289	−	0.442173i
$137$	−0.201380	−	0.751559i	−0.0172050	−	0.0642100i	0.956790	−	0.290781i	$-0.0939151\pi$
$137$	−0.201380	−	0.751559i	−0.0172050	−	0.0642100i	−0.973995	+	0.226571i	$0.927248\pi$
$138$		0			0
$139$			1.14654i			0.0972483i	0.998817	+	0.0486241i	$0.0154837\pi$
$139$			1.14654i			0.0972483i	−0.998817	+	0.0486241i	$0.984516\pi$
$140$	−24.7707	+	6.33961i	−2.09351	+	0.535795i
$141$		0			0
$142$	3.40691	−	12.7147i	0.285901	−	1.06700i
$143$	30.4992	−	8.17223i	2.55047	−	0.683396i
$144$		0			0
$145$	−4.53608	−	7.84871i	−0.376701	−	0.651800i
$146$		−	26.1829i		−	2.16691i
$147$		0			0
$148$	−4.12123	+	4.12123i	−0.338763	+	0.338763i
$149$	9.23325	+	15.9925i	0.756418	+	1.31015i	0.944666	+	0.328032i	$0.106386\pi$
$149$	9.23325	+	15.9925i	0.756418	+	1.31015i	−0.188249	+	0.982121i	$0.560281\pi$
$150$		0			0
$151$	6.38096	−	11.0522i	0.519275	−	0.899411i	−0.480474	−	0.877009i	$-0.659535\pi$
$151$	6.38096	−	11.0522i	0.519275	−	0.899411i	0.999749	−	0.0224023i	$-0.00713146\pi$
$152$	−35.8871	−	9.61592i	−2.91083	−	0.779954i
$153$		0			0
$154$	16.9751	−	28.6238i	1.36789	−	2.30657i
$155$	9.50953	−	0.00420408i	0.763824	−	0.000337680i
$156$		0			0
$157$	5.09943	−	1.36639i	0.406979	−	0.109050i	−0.0495210	−	0.998773i	$-0.515769\pi$
$157$	5.09943	−	1.36639i	0.406979	−	0.109050i	0.456500	+	0.889723i	$0.349103\pi$
$158$	−35.1572	+	9.42034i	−2.79696	+	0.749442i
$159$		0			0
$160$	5.52960	−	5.53449i	0.437153	−	0.437540i
$161$	0.727973	+	0.00850867i	0.0573723	+	0.000670577i
$162$		0			0
$163$	8.17175	+	2.18961i	0.640061	+	0.171504i	0.564231	−	0.825617i	$-0.309173\pi$
$163$	8.17175	+	2.18961i	0.640061	+	0.171504i	0.0758299	+	0.997121i	$0.475839\pi$
$164$	−4.62028	+	8.00256i	−0.360783	+	0.624895i
$165$		0			0
$166$	17.7541	+	30.7511i	1.37799	+	2.38674i
$167$	0.227335	−	0.227335i	0.0175917	−	0.0175917i	−0.698256	−	0.715848i	$-0.746040\pi$
$167$	0.227335	−	0.227335i	0.0175917	−	0.0175917i	0.715848	+	0.698256i	$0.246040\pi$
$168$		0			0
$169$		−	26.8385i		−	2.06450i
$170$	−4.96456	+	2.86922i	−0.380764	+	0.220059i
$171$		0			0
$172$	7.25998	−	1.94531i	0.553569	−	0.148328i
$173$	−4.12905	+	15.4098i	−0.313926	+	1.17159i	0.611060	+	0.791585i	$0.290744\pi$
$173$	−4.12905	+	15.4098i	−0.313926	+	1.17159i	−0.924985	+	0.380003i	$0.875923\pi$
$174$		0			0
$175$	12.7403	+	3.56170i	0.963073	+	0.269239i
$176$			30.1927i			2.27586i
$177$		0			0
$178$	−3.11411	−	11.6220i	−0.233412	−	0.871106i
$179$	2.02163	−	3.50157i	0.151104	−	0.261720i	−0.780530	−	0.625119i	$-0.785050\pi$
$179$	2.02163	−	3.50157i	0.151104	−	0.261720i	0.931634	+	0.363399i	$0.118384\pi$
$180$		0			0
$181$	−9.55204			−0.709998			−0.354999	−	0.934867i	$-0.615519\pi$
$181$	−9.55204			−0.709998			−0.354999	+	0.934867i	$0.615519\pi$
$182$	−29.3411	−	30.0351i	−2.17491	−	2.22635i
$183$		0			0
$184$	−1.39126	+	0.803244i	−0.102565	+	0.0592160i
$185$	2.91231	−	0.781733i	0.214118	−	0.0574741i
$186$		0			0
$187$	1.32050	−	4.92818i	0.0965646	−	0.360384i
$188$	23.8809	+	23.8809i	1.74169	+	1.74169i
$189$		0			0
$190$	25.3105	+	25.2881i	1.83622	+	1.83459i
$191$	17.0237	−	9.82861i	1.23179	−	0.711173i	0.264386	−	0.964417i	$-0.414831\pi$
$191$	17.0237	−	9.82861i	1.23179	−	0.711173i	0.967403	+	0.253243i	$0.0814974\pi$
$192$		0			0
$193$	−1.43496	−	5.35533i	−0.103290	−	0.385485i	0.894855	−	0.446356i	$-0.147279\pi$
$193$	−1.43496	−	5.35533i	−0.103290	−	0.385485i	−0.998146	+	0.0608716i	$0.980612\pi$
$194$	0.423399	+	0.733349i	0.0303983	+	0.0526514i
$195$		0			0
$196$	−30.2455	−	0.707125i	−2.16039	−	0.0505089i
$197$	7.68996	−	7.68996i	0.547887	−	0.547887i	−0.377942	−	0.925829i	$-0.623368\pi$
$197$	7.68996	−	7.68996i	0.547887	−	0.547887i	0.925829	+	0.377942i	$0.123368\pi$
$198$		0			0
$199$	6.99916	+	4.04097i	0.496157	+	0.286457i	0.727125	−	0.686505i	$-0.240856\pi$
$199$	6.99916	+	4.04097i	0.496157	+	0.286457i	−0.230968	+	0.972961i	$0.574189\pi$
$200$	−28.1898	+	7.58016i	−1.99332	+	0.535998i
$201$		0			0
$202$	−19.8838	−	19.8838i	−1.39902	−	1.39902i
$203$	−2.65485	−	10.3924i	−0.186334	−	0.729402i
$204$		0			0
$205$	4.13925	−	2.39224i	0.289098	−	0.167081i
$206$	−23.0336	−	13.2984i	−1.60483	−	0.926546i
$207$		0			0
$208$	36.7964	+	9.85956i	2.55137	+	0.683637i
$209$	−31.8351			−2.20208
$210$		0			0
$211$	13.4885			0.928590			0.464295	−	0.885681i	$-0.346308\pi$
$211$	13.4885			0.928590			0.464295	+	0.885681i	$0.346308\pi$
$212$	0.175687	+	0.0470751i	0.0120662	+	0.00323313i
$213$		0			0
$214$	−30.2399	−	17.4590i	−2.06716	−	1.19347i
$215$	−3.75656	−	1.00479i	−0.256196	−	0.0685260i
$216$		0			0
$217$	10.8337	+	3.03901i	0.735436	+	0.206302i
$218$	6.91003	+	6.91003i	0.468006	+	0.468006i
$219$		0			0
$220$	24.1544	−	41.8794i	1.62849	−	2.82351i
$221$	−5.57484	−	3.21863i	−0.375004	−	0.216509i
$222$		0			0
$223$	−2.94364	+	2.94364i	−0.197121	+	0.197121i	−0.798765	−	0.601644i	$-0.794513\pi$
$223$	−2.94364	+	2.94364i	−0.197121	+	0.197121i	0.601644	+	0.798765i	$0.294513\pi$
$224$	8.07024	−	4.53443i	0.539215	−	0.302969i
$225$		0			0
$226$	21.5809	+	37.3792i	1.43554	+	2.48642i
$227$	5.05613	+	18.8697i	0.335587	+	1.25243i	0.903231	+	0.429155i	$0.141189\pi$
$227$	5.05613	+	18.8697i	0.335587	+	1.25243i	−0.567644	+	0.823274i	$0.692145\pi$
$228$		0			0
$229$	−6.00222	+	3.46538i	−0.396638	+	0.228999i	−0.685032	−	0.728513i	$-0.740212\pi$
$229$	−6.00222	+	3.46538i	−0.396638	+	0.228999i	0.288394	+	0.957512i	$0.406879\pi$
$230$	1.54706		0.000683942i	0.102010		4.50978e-5i
$231$		0			0
$232$	16.7363	+	16.7363i	1.09879	+	1.09879i
$233$	−5.51176	+	20.5702i	−0.361088	+	1.34760i	0.511560	+	0.859247i	$0.329068\pi$
$233$	−5.51176	+	20.5702i	−0.361088	+	1.34760i	−0.872648	+	0.488350i	$0.837599\pi$
$234$		0			0
$235$	−4.52983	−	16.8757i	−0.295493	−	1.10085i
$236$	−38.7235	+	22.3570i	−2.52069	+	1.45532i
$237$		0			0
$238$	−6.57351	+	1.67927i	−0.426097	+	0.108851i
$239$	−0.787711			−0.0509528			−0.0254764	−	0.999675i	$-0.508110\pi$
$239$	−0.787711			−0.0509528			−0.0254764	+	0.999675i	$0.508110\pi$
$240$		0			0
$241$	−0.438601	+	0.759678i	−0.0282527	+	0.0489352i	−0.879806	−	0.475333i	$-0.842328\pi$
$241$	−0.438601	+	0.759678i	−0.0282527	+	0.0489352i	0.851553	+	0.524268i	$0.175661\pi$
$242$	9.12735	+	34.0637i	0.586728	+	2.18970i
$243$		0			0
$244$			8.84107i			0.565991i
$245$	13.3724	+	8.13502i	0.854332	+	0.519727i
$246$		0			0
$247$	−10.3959	+	38.7979i	−0.661473	+	2.46865i
$248$	−23.9828	+	6.42617i	−1.52291	+	0.408062i
$249$		0			0
$250$	27.1631	+	7.23972i	1.71794	+	0.457880i
$251$		−	1.76477i		−	0.111391i	−0.998448	−	0.0556957i	$-0.982262\pi$
$251$		−	1.76477i		−	0.111391i	0.998448	−	0.0556957i	$-0.0177377\pi$
$252$		0			0
$253$	−0.973360	+	0.973360i	−0.0611946	+	0.0611946i
$254$	−4.18899	−	7.25555i	−0.262841	−	0.455254i
$255$		0			0
$256$	15.8717	−	27.4905i	0.991980	−	1.71816i
$257$	2.54666	+	0.682377i	0.158857	+	0.0425655i	0.337371	−	0.941372i	$-0.390462\pi$
$257$	2.54666	+	0.682377i	0.158857	+	0.0425655i	−0.178514	+	0.983937i	$0.557129\pi$
$258$		0			0
$259$	3.56763	+	0.0416991i	0.221682	+	0.00259106i
$260$	−43.1514	−	43.1132i	−2.67614	−	2.67377i
$261$		0			0
$262$	11.5879	−	3.10497i	0.715903	−	0.191826i
$263$	−26.8646	+	7.19835i	−1.65654	+	0.443869i	−0.961434	−	0.275036i	$-0.911310\pi$
$263$	−26.8646	+	7.19835i	−1.65654	+	0.443869i	−0.695108	+	0.718905i	$0.744644\pi$
$264$		0			0
$265$	−0.0665696	−	0.0665108i	−0.00408934	−	0.00408573i
$266$	20.7370	+	36.9071i	1.27147	+	2.26292i
$267$		0			0
$268$	−59.1864	−	15.8589i	−3.61538	−	0.968739i
$269$	10.0436	−	17.3961i	0.612370	−	1.06066i	−0.378470	−	0.925614i	$-0.623550\pi$
$269$	10.0436	−	17.3961i	0.612370	−	1.06066i	0.990840	−	0.135043i	$-0.0431171\pi$
$270$		0			0
$271$	−0.546081	−	0.945841i	−0.0331721	−	0.0574557i	0.848963	−	0.528453i	$-0.177228\pi$
$271$	−0.546081	−	0.945841i	−0.0331721	−	0.0574557i	−0.882135	+	0.470997i	$0.843894\pi$
$272$	4.35256	−	4.35256i	0.263913	−	0.263913i
$273$		0			0
$274$		−	1.95634i		−	0.118187i
$275$	−21.6507	+	12.5256i	−1.30558	+	0.755319i
$276$		0			0
$277$	−3.97197	+	1.06429i	−0.238653	+	0.0639468i	−0.376163	−	0.926554i	$-0.622757\pi$
$277$	−3.97197	+	1.06429i	−0.238653	+	0.0639468i	0.137510	+	0.990500i	$0.456090\pi$
$278$	−0.746125	+	2.78458i	−0.0447496	+	0.167008i
$279$		0			0
$280$	−34.5373	−	0.388407i	−2.06400	−	0.0232117i
$281$		−	7.91764i		−	0.472327i	−0.971713	−	0.236163i	$-0.924110\pi$
$281$		−	7.91764i		−	0.472327i	0.971713	−	0.236163i	$-0.0758900\pi$
$282$		0			0
$283$	5.53409	+	20.6535i	0.328967	+	1.22772i	0.910263	+	0.414030i	$0.135879\pi$
$283$	5.53409	+	20.6535i	0.328967	+	1.22772i	−0.581296	+	0.813692i	$0.697454\pi$
$284$	11.3133	−	19.5952i	0.671320	−	1.16276i
$285$		0			0
$286$	79.3908			4.69448
$287$	5.48073	−	1.40011i	0.323517	−	0.0826460i
$288$		0			0
$289$	13.8216	−	7.97992i	0.813037	−	0.469407i
$290$	−5.90904	−	22.0139i	−0.346991	−	1.29270i
$291$		0			0
$292$	11.6485	−	43.4727i	0.681675	−	2.54405i
$293$	−20.6685	−	20.6685i	−1.20747	−	1.20747i	−0.971845	−	0.235620i	$-0.924288\pi$
$293$	−20.6685	−	20.6685i	−1.20747	−	1.20747i	−0.235620	−	0.971845i	$-0.575712\pi$
$294$		0			0
$295$	23.1338	−	0.0102273i	1.34690	−	0.000595455i
$296$	−6.81826	+	3.93652i	−0.396303	+	0.228806i
$297$		0			0
$298$	12.0173	+	44.8492i	0.696144	+	2.59804i
$299$	0.868396	+	1.50411i	0.0502206	+	0.0869847i
$300$		0			0
$301$	−3.95749	−	2.34695i	−0.228106	−	0.135276i
$302$	22.6896	−	22.6896i	1.30564	−	1.30564i
$303$		0			0
$304$	−33.2624	−	19.2040i	−1.90773	−	1.10143i
$305$	2.28531	−	3.96232i	0.130857	−	0.226882i
$306$		0			0
$307$	−10.4383	−	10.4383i	−0.595743	−	0.595743i	0.343434	−	0.939177i	$-0.388410\pi$
$307$	−10.4383	−	10.4383i	−0.595743	−	0.595743i	−0.939177	+	0.343434i	$0.888410\pi$
$308$	40.9190	−	39.9735i	2.33158	−	2.27770i
$309$		0			0
$310$	23.0983	+	6.17823i	1.31190	+	0.350900i
$311$	16.8933	+	9.75337i	0.957933	+	0.553063i	0.895536	−	0.444988i	$-0.146792\pi$
$311$	16.8933	+	9.75337i	0.957933	+	0.553063i	0.0623969	+	0.998051i	$0.480126\pi$
$312$		0			0
$313$	−14.5869	−	3.90856i	−0.824502	−	0.220925i	−0.178188	−	0.983996i	$-0.557024\pi$
$313$	−14.5869	−	3.90856i	−0.824502	−	0.220925i	−0.646314	+	0.763072i	$0.723690\pi$
$314$	13.2741			0.749099
$315$		0			0
$316$	−62.5642			−3.51951
$317$	15.9783	+	4.28137i	0.897431	+	0.240466i	0.677912	−	0.735143i	$-0.262885\pi$
$317$	15.9783	+	4.28137i	0.897431	+	0.240466i	0.219518	+	0.975608i	$0.429551\pi$
$318$		0			0
$319$	17.5637	+	10.1404i	0.983380	+	0.567755i
$320$	−6.33799	+	3.66298i	−0.354304	+	0.204767i
$321$		0			0
$322$	1.76248	+	0.494402i	0.0982189	+	0.0275520i
$323$	4.58931	+	4.58931i	0.255356	+	0.255356i
$324$		0			0
$325$	8.19499	+	30.4763i	0.454576	+	1.69052i
$326$	18.4216	+	10.6357i	1.02028	+	0.589059i
$327$		0			0
$328$	−8.82641	+	8.82641i	−0.487357	+	0.487357i
$329$	0.241629	−	20.6730i	0.0133215	−	1.13974i
$330$		0			0
$331$	−13.3963	−	23.2031i	−0.736328	−	1.27536i	−0.954138	−	0.299367i	$-0.903225\pi$
$331$	−13.3963	−	23.2031i	−0.736328	−	1.27536i	0.217810	−	0.975991i	$-0.430109\pi$
$332$	15.7972	+	58.9560i	0.866985	+	3.23563i
$333$		0			0
$334$	0.700063	−	0.404182i	0.0383058	−	0.0221158i
$335$	22.4263	+	22.4065i	1.22528	+	1.22420i
$336$		0			0
$337$	−3.48628	−	3.48628i	−0.189910	−	0.189910i	0.605747	−	0.795657i	$-0.292874\pi$
$337$	−3.48628	−	3.48628i	−0.189910	−	0.189910i	−0.795657	+	0.605747i	$0.792874\pi$
$338$	17.4655	−	65.1821i	0.949998	−	3.54544i
$339$		0			0
$340$	−9.51937	+	2.55522i	−0.516260	+	0.138576i
$341$	−18.4246	+	10.6374i	−0.997746	+	0.576049i
$342$		0			0
$343$	12.6287	+	13.5468i	0.681884	+	0.731460i
$344$	10.1530			0.547410
$345$		0			0
$346$	−20.0563	+	34.7385i	−1.07823	+	1.86755i
$347$	−6.27705	−	23.4263i	−0.336970	−	1.25759i	−0.901718	−	0.432325i	$-0.857693\pi$
$347$	−6.27705	−	23.4263i	−0.336970	−	1.25759i	0.564748	−	0.825263i	$-0.308973\pi$
$348$		0			0
$349$		−	0.641866i		−	0.0343583i	−0.999852	−	0.0171792i	$-0.994531\pi$
$349$		−	0.641866i		−	0.0343583i	0.999852	−	0.0171792i	$-0.00546857\pi$
$350$	28.6242	+	16.9411i	1.53003	+	0.905540i
$351$		0			0
$352$	−4.53006	+	16.9064i	−0.241453	+	0.901116i
$353$	−1.88152	+	0.504151i	−0.100143	+	0.0268332i	−0.308543	−	0.951211i	$-0.599841\pi$
$353$	−1.88152	+	0.504151i	−0.100143	+	0.0268332i	0.208400	+	0.978044i	$0.433175\pi$
$354$		0			0
$355$	−10.1354	+	5.85767i	−0.537933	+	0.310893i
$356$		−	20.6820i		−	1.09614i
$357$		0			0
$358$	7.18859	−	7.18859i	0.379929	−	0.379929i
$359$	4.34803	+	7.53101i	0.229480	+	0.397471i	0.957654	−	0.287921i	$-0.0929641\pi$
$359$	4.34803	+	7.53101i	0.229480	+	0.397471i	−0.728174	+	0.685392i	$0.759631\pi$
$360$		0			0
$361$	10.7486	−	18.6172i	0.565718	−	0.979853i
$362$	−23.1988	−	6.21611i	−1.21930	−	0.326711i
$363$		0			0
$364$	−35.3541	−	62.9222i	−1.85306	−	3.29802i
$365$	−16.4577	+	16.4723i	−0.861436	+	0.862198i
$366$		0			0
$367$	31.4869	−	8.43689i	1.64360	−	0.440402i	0.685790	−	0.727799i	$-0.259457\pi$
$367$	31.4869	−	8.43689i	1.64360	−	0.440402i	0.957811	+	0.287397i	$0.0927900\pi$
$368$	−1.60417	+	0.429835i	−0.0836230	+	0.0224067i
$369$		0			0
$370$	7.58179	−	0.00335185i	0.394159	−	0.000174254i
$371$	−0.0545408	−	0.0970700i	−0.00283162	−	0.00503962i
$372$		0			0
$373$	17.9621	+	4.81293i	0.930043	+	0.249204i	0.691873	−	0.722019i	$-0.256786\pi$
$373$	17.9621	+	4.81293i	0.930043	+	0.249204i	0.238170	+	0.971224i	$0.423453\pi$
$374$	6.41414	−	11.1096i	0.331667	−	0.574465i
$375$		0			0
$376$	22.8106	+	39.5091i	1.17636	+	2.03752i
$377$	18.0938	−	18.0938i	0.931879	−	0.931879i
$378$		0			0
$379$			11.6954i			0.600752i	0.953821	+	0.300376i	$0.0971122\pi$
$379$			11.6954i			0.600752i	−0.953821	+	0.300376i	$0.902888\pi$
$380$	30.7738	+	53.2475i	1.57866	+	2.73154i
$381$		0			0
$382$	47.7411	−	12.7922i	2.44264	−	0.654505i
$383$	−2.18840	+	8.16722i	−0.111822	+	0.417326i	−0.999030	−	0.0440451i	$-0.985975\pi$
$383$	−2.18840	+	8.16722i	−0.111822	+	0.417326i	0.887207	+	0.461371i	$0.152642\pi$
$384$		0			0
$385$	−28.6714	+	7.33794i	−1.46123	+	0.373976i
$386$		−	13.9402i		−	0.709536i
$387$		0			0
$388$	0.376731	+	1.40598i	0.0191256	+	0.0713778i
$389$	11.1976	−	19.3948i	0.567740	−	0.983354i	−0.429049	−	0.903281i	$-0.641151\pi$
$389$	11.1976	−	19.3948i	0.567740	−	0.983354i	0.996789	−	0.0800731i	$-0.0255154\pi$
$390$		0			0
$391$	0.280638			0.0141925
$392$	−39.2171	−	11.4971i	−1.98076	−	0.580691i
$393$		0			0
$394$	23.6808	−	13.6721i	1.19302	−	0.688790i
$395$	28.0395	+	16.1721i	1.41082	+	0.813707i
$396$		0			0
$397$	2.20510	−	8.22953i	0.110671	−	0.413028i	−0.888256	−	0.459349i	$-0.848083\pi$
$397$	2.20510	−	8.22953i	0.110671	−	0.413028i	0.998927	+	0.0463203i	$0.0147495\pi$
$398$	14.3690	+	14.3690i	0.720253	+	0.720253i
$399$		0			0
$400$	−30.1772	+	0.0266822i	−1.50886	+	0.00133411i
$401$	−10.9993	+	6.35044i	−0.549278	+	0.317126i	−0.748831	−	0.662761i	$-0.769384\pi$
$401$	−10.9993	+	6.35044i	−0.549278	+	0.317126i	0.199553	+	0.979887i	$0.436051\pi$
$402$		0			0
$403$	6.94739	+	25.9280i	0.346074	+	1.29157i
$404$	−24.1679	−	41.8601i	−1.20240	−	2.08262i
$405$		0			0
$406$	0.315199	−	26.9674i	0.0156431	−	1.33837i
$407$	−4.77022	+	4.77022i	−0.236451	+	0.236451i
$408$		0			0
$409$	−22.9042	−	13.2237i	−1.13254	−	0.653871i	−0.187966	−	0.982175i	$-0.560190\pi$
$409$	−22.9042	−	13.2237i	−1.13254	−	0.653871i	−0.944572	+	0.328304i	$0.893523\pi$
$410$	11.6097	−	3.11631i	0.573362	−	0.153904i
$411$		0			0
$412$	−32.3274	−	32.3274i	−1.59266	−	1.59266i
$413$	26.3550	+	7.39301i	1.29685	+	0.363786i
$414$		0			0
$415$	8.15957	−	30.5059i	0.400538	−	1.49747i
$416$	19.1248	+	11.0417i	0.937672	+	0.541365i
$417$		0			0
$418$	−77.3171	−	20.7170i	−3.78170	−	1.01330i
$419$	−2.33746			−0.114192			−0.0570961	−	0.998369i	$-0.518184\pi$
$419$	−2.33746			−0.114192			−0.0570961	+	0.998369i	$0.518184\pi$
$420$		0			0
$421$	−14.1558			−0.689913			−0.344957	−	0.938619i	$-0.612106\pi$
$421$	−14.1558			−0.689913			−0.344957	+	0.938619i	$0.612106\pi$
$422$	32.7593	+	8.77784i	1.59470	+	0.427298i
$423$		0			0
$424$	0.212778	+	0.122847i	0.0103334	+	0.00596600i
$425$	4.92682	+	1.31547i	0.238986	+	0.0638096i
$426$		0			0
$427$	3.87146	−	3.78200i	0.187353	−	0.183024i
$428$	−42.4414	−	42.4414i	−2.05148	−	2.05148i
$429$		0			0
$430$	−8.46960	−	4.88494i	−0.408441	−	0.235573i
$431$	−14.4168	−	8.32354i	−0.694432	−	0.400931i	0.110838	−	0.993838i	$-0.464647\pi$
$431$	−14.4168	−	8.32354i	−0.694432	−	0.400931i	−0.805270	+	0.592908i	$0.797980\pi$
$432$		0			0
$433$	8.43208	−	8.43208i	0.405220	−	0.405220i	−0.474848	−	0.880068i	$-0.657497\pi$
$433$	8.43208	−	8.43208i	0.405220	−	0.405220i	0.880068	+	0.474848i	$0.157497\pi$
$434$	24.3338	+	14.4309i	1.16806	+	0.692706i
$435$		0			0
$436$	8.39886	+	14.5472i	0.402232	+	0.696687i
$437$	−0.453216	−	1.69143i	−0.0216803	−	0.0809119i
$438$		0			0
$439$	−28.2457	+	16.3077i	−1.34810	+	0.778324i	−0.987980	−	0.154584i	$-0.950596\pi$
$439$	−28.2457	+	16.3077i	−1.34810	+	0.778324i	−0.360116	+	0.932907i	$0.617263\pi$
$440$	46.1585	−	46.1994i	2.20052	−	2.20247i
$441$		0			0
$442$	−11.4449	−	11.4449i	−0.544379	−	0.544379i
$443$	3.40342	−	12.7017i	0.161701	−	0.603477i	−0.836737	−	0.547605i	$-0.815540\pi$
$443$	3.40342	−	12.7017i	0.161701	−	0.603477i	0.998438	−	0.0558717i	$-0.0177938\pi$
$444$		0			0
$445$	−5.34606	+	9.26910i	−0.253427	+	0.439398i
$446$	−9.06477	+	5.23355i	−0.429229	+	0.247816i
$447$		0			0
$448$	−8.39204	+	2.14384i	−0.396487	+	0.101287i
$449$	−37.7116			−1.77972			−0.889860	−	0.456234i	$-0.849198\pi$
$449$	−37.7116			−1.77972			−0.889860	+	0.456234i	$0.849198\pi$
$450$		0			0
$451$	−5.34786	+	9.26276i	−0.251821	+	0.436166i
$452$	19.2022	+	71.6635i	0.903194	+	3.37077i
$453$		0			0
$454$			49.1189i			2.30526i
$455$	−0.419910	+	37.3386i	−0.0196857	+	1.75046i
$456$		0			0
$457$	1.84421	−	6.88267i	0.0862684	−	0.321958i	−0.909283	−	0.416178i	$-0.863369\pi$
$457$	1.84421	−	6.88267i	0.0862684	−	0.321958i	0.995551	+	0.0942205i	$0.0300359\pi$
$458$	−16.8326	+	4.51028i	−0.786535	+	0.210751i
$459$		0			0
$460$	2.56896	+	0.687134i	0.119778	+	0.0320378i
$461$		−	23.2822i		−	1.08436i	−0.840262	−	0.542181i	$-0.817599\pi$
$461$		−	23.2822i		−	1.08436i	0.840262	−	0.542181i	$-0.182401\pi$
$462$		0			0
$463$	26.0488	−	26.0488i	1.21059	−	1.21059i	0.239757	−	0.970833i	$-0.422932\pi$
$463$	26.0488	−	26.0488i	1.21059	−	1.21059i	0.970833	−	0.239757i	$-0.0770677\pi$
$464$	12.2341	+	21.1901i	0.567955	+	0.983728i
$465$		0			0
$466$	−26.7726	+	46.3715i	−1.24022	+	2.14812i
$467$	8.90737	+	2.38672i	0.412184	+	0.110444i	0.458951	−	0.888461i	$-0.348225\pi$
$467$	8.90737	+	2.38672i	0.412184	+	0.110444i	−0.0467673	+	0.998906i	$0.514892\pi$
$468$		0			0
$469$	18.3740	+	32.7015i	0.848432	+	1.51001i
$470$	−0.0194226	−	43.9335i	−0.000895898	−	2.02650i
$471$		0			0
$472$	−58.3429	+	15.6329i	−2.68545	+	0.719564i
$473$	8.40324	−	2.25164i	0.386382	−	0.103531i
$474$		0			0
$475$	−0.0281336	−	31.8187i	−0.00129086	−	1.45994i
$476$	−11.6614	−	0.136300i	−0.534499	−	0.00624731i
$477$		0			0
$478$	−1.91310	−	0.512613i	−0.0875030	−	0.0234464i
$479$	−9.04651	+	15.6690i	−0.413346	+	0.715936i	−0.995253	−	0.0973193i	$-0.968973\pi$
$479$	−9.04651	+	15.6690i	−0.413346	+	0.715936i	0.581908	+	0.813255i	$0.302307\pi$
$480$		0			0
$481$	4.25581	+	7.37129i	0.194048	+	0.336102i
$482$	−1.55959	+	1.55959i	−0.0710373	+	0.0710373i
$483$		0			0
$484$			60.6183i			2.75538i
$485$	0.194589	−	0.727502i	0.00883582	−	0.0330342i
$486$		0			0
$487$	−2.34247	+	0.627663i	−0.106148	+	0.0284421i	−0.311502	−	0.950246i	$-0.600832\pi$
$487$	−2.34247	+	0.627663i	−0.106148	+	0.0284421i	0.205354	+	0.978688i	$0.434165\pi$
$488$	−3.09102	+	11.5358i	−0.139924	+	0.522203i
$489$		0			0
$490$	27.1833	+	28.4596i	1.22802	+	1.28567i
$491$			15.2664i			0.688965i	0.938793	+	0.344483i	$0.111946\pi$
$491$			15.2664i			0.688965i	−0.938793	+	0.344483i	$0.888054\pi$
$492$		0			0
$493$	−1.07014	−	3.99381i	−0.0481966	−	0.179872i
$494$	−50.4964	+	87.4624i	−2.27194	+	3.93512i
$495$		0			0
$496$	−25.6675			−1.15250
$497$	−13.4202	+	3.42834i	−0.601978	+	0.153782i
$498$		0			0
$499$	0.192077	−	0.110896i	0.00859855	−	0.00496437i	−0.495695	−	0.868497i	$-0.665086\pi$
$499$	0.192077	−	0.110896i	0.00859855	−	0.00496437i	0.504293	+	0.863533i	$0.331753\pi$
$500$	41.8792	+	24.1050i	1.87290	+	1.07801i
$501$		0			0
$502$	1.14845	−	4.28606i	0.0512576	−	0.191296i
$503$	−16.5305	−	16.5305i	−0.737057	−	0.737057i	0.234951	−	0.972007i	$-0.424507\pi$
$503$	−16.5305	−	16.5305i	−0.737057	−	0.737057i	−0.972007	+	0.234951i	$0.924507\pi$
$504$		0			0
$505$	0.0110557	+	25.0077i	0.000491971	+	1.11283i
$506$	−2.99740	+	1.73055i	−0.133251	+	0.0769324i
$507$		0			0
$508$	−3.72727	−	13.9104i	−0.165371	−	0.617173i
$509$	−1.68470	−	2.91798i	−0.0746729	−	0.129337i	0.826271	−	0.563273i	$-0.190458\pi$
$509$	−1.68470	−	2.91798i	−0.0746729	−	0.129337i	−0.900944	+	0.433935i	$0.857125\pi$
$510$		0			0
$511$	−24.0194	+	13.4958i	−1.06256	+	0.597019i
$512$	34.9000	−	34.9000i	1.54238	−	1.54238i
$513$		0			0
$514$	5.74096	+	3.31455i	0.253223	+	0.146198i
$515$	6.13200	+	22.8445i	0.270208	+	1.00665i
$516$		0			0
$517$	27.6415	+	27.6415i	1.21567	+	1.21567i
$518$	8.63750	+	2.42296i	0.379510	+	0.106459i
$519$		0			0
$520$	−41.2307	−	71.3408i	−1.80809	−	3.12850i
$521$	−23.3214	−	13.4646i	−1.02173	−	0.589895i	−0.107124	−	0.994246i	$-0.534164\pi$
$521$	−23.3214	−	13.4646i	−1.02173	−	0.589895i	−0.914604	+	0.404351i	$0.867497\pi$
$522$		0			0
$523$	15.0465	+	4.03169i	0.657936	+	0.176294i	0.572315	−	0.820034i	$-0.306046\pi$
$523$	15.0465	+	4.03169i	0.657936	+	0.176294i	0.0856218	+	0.996328i	$0.472712\pi$
$524$	20.6213			0.900847
$525$		0			0
$526$	−69.9299			−3.04909
$527$	4.18955	+	1.12259i	0.182500	+	0.0489007i
$528$		0			0
$529$	19.8530	+	11.4621i	0.863174	+	0.498354i
$530$	−0.118393	−	0.204854i	−0.00514268	−	0.00889830i
$531$		0			0
$532$	18.0111	+	70.5043i	0.780880	+	3.05675i
$533$	9.54232	+	9.54232i	0.413324	+	0.413324i
$534$		0			0
$535$	8.05046	+	29.9917i	0.348052	+	1.29665i
$536$	−71.6818	−	41.3855i	−3.09618	−	1.78758i
$537$		0			0
$538$	35.7134	−	35.7134i	1.53971	−	1.53971i
$539$	−35.0084	−	0.818479i	−1.50792	−	0.0352544i
$540$		0			0
$541$	−4.35172	−	7.53741i	−0.187095	−	0.324059i	0.757185	−	0.653200i	$-0.226574\pi$
$541$	−4.35172	−	7.53741i	−0.187095	−	0.324059i	−0.944281	+	0.329142i	$0.893241\pi$
$542$	−0.710738	−	2.65251i	−0.0305288	−	0.113935i
$543$		0			0
$544$	3.09027	−	1.78417i	0.132494	−	0.0764955i
$545$	−0.00384208	−	8.69068i	−0.000164576	−	0.372268i
$546$		0			0
$547$	−9.42064	−	9.42064i	−0.402798	−	0.402798i	0.476420	−	0.879218i	$-0.341934\pi$
$547$	−9.42064	−	9.42064i	−0.402798	−	0.402798i	−0.879218	+	0.476420i	$0.841934\pi$
$548$	0.870355	−	3.24821i	0.0371797	−	0.138757i
$549$		0			0
$550$	−60.7336	+	16.3311i	−2.58969	+	0.696360i
$551$	−22.3428	+	12.8996i	−0.951834	+	0.549542i
$552$		0			0
$553$	26.7635	+	27.3965i	1.13810	+	1.16502i
$554$	−10.3392			−0.439272
$555$		0			0
$556$	−2.47765	+	4.29142i	−0.105076	+	0.181997i
$557$	−11.1018	−	41.4325i	−0.470398	−	1.75555i	−0.638341	−	0.769754i	$-0.720379\pi$
$557$	−11.1018	−	41.4325i	−0.470398	−	1.75555i	0.167943	−	0.985797i	$-0.446288\pi$
$558$		0			0
$559$		−	10.9765i		−	0.464255i
$560$	−34.3834	−	9.62871i	−1.45297	−	0.406887i
$561$		0			0
$562$	5.15250	−	19.2294i	0.217345	−	0.811143i
$563$	0.0807657	−	0.0216411i	0.00340387	−	0.000912064i	−0.257117	−	0.966380i	$-0.582772\pi$
$563$	0.0807657	−	0.0216411i	0.00340387	−	0.000912064i	0.260521	+	0.965468i	$0.416106\pi$
$564$		0			0
$565$	9.91829	−	37.0811i	0.417266	−	1.56001i
$566$			53.7620i			2.25979i
$567$		0			0
$568$	21.6125	−	21.6125i	0.906839	−	0.906839i
$569$	−6.87752	−	11.9122i	−0.288321	−	0.499386i	0.685088	−	0.728460i	$-0.259764\pi$
$569$	−6.87752	−	11.9122i	−0.288321	−	0.499386i	−0.973409	+	0.229074i	$0.926430\pi$
$570$		0			0
$571$	11.2197	−	19.4331i	0.469530	−	0.813251i	−0.529863	−	0.848083i	$-0.677757\pi$
$571$	11.2197	−	19.4331i	0.469530	−	0.813251i	0.999393	+	0.0348328i	$0.0110899\pi$
$572$	131.816	+	35.3201i	5.51152	+	1.47681i
$573$		0			0
$574$	14.2221	+	0.166230i	0.593618	+	0.00693830i
$575$	−0.973722	−	0.972001i	−0.0406070	−	0.0405353i
$576$		0			0
$577$	−18.7976	+	5.03680i	−0.782554	+	0.209685i	−0.627910	−	0.778286i	$-0.716090\pi$
$577$	−18.7976	+	5.03680i	−0.782554	+	0.209685i	−0.154644	+	0.987970i	$0.549423\pi$
$578$	38.7613	−	10.3861i	1.61226	−	0.432003i
$579$		0			0
$580$	−0.0173209	−	39.1796i	−0.000719213	−	1.62684i
$581$	19.0589	−	32.1375i	0.790695	−	1.33329i
$582$		0			0
$583$	0.203353	+	0.0544883i	0.00842202	+	0.00225667i
$584$	30.3979	−	52.6506i	1.25787	−	2.17870i
$585$		0			0
$586$	−36.7468	−	63.6473i	−1.51800	−	2.62925i
$587$	15.2148	−	15.2148i	0.627982	−	0.627982i	−0.319578	−	0.947560i	$-0.603541\pi$
$587$	15.2148	−	15.2148i	0.627982	−	0.627982i	0.947560	+	0.319578i	$0.103541\pi$
$588$		0			0
$589$		−	27.0637i		−	1.11514i
$590$	56.1913	+	15.0298i	2.31336	+	0.618767i
$591$		0			0
$592$	−7.86166	+	2.10653i	−0.323112	+	0.0865777i
$593$	7.62569	−	28.4595i	0.313150	−	1.16869i	−0.612550	−	0.790432i	$-0.709856\pi$
$593$	7.62569	−	28.4595i	0.313150	−	1.16869i	0.925700	−	0.378259i	$-0.123477\pi$
$594$		0			0
$595$	5.19108	+	3.07542i	0.212814	+	0.126080i
$596$			79.8116i			3.26921i
$597$		0			0
$598$	1.13024	+	4.21811i	0.0462189	+	0.172491i
$599$	−19.0653	+	33.0220i	−0.778986	+	1.34924i	0.153541	+	0.988142i	$0.450932\pi$
$599$	−19.0653	+	33.0220i	−0.778986	+	1.34924i	−0.932527	+	0.361101i	$0.882401\pi$
$600$		0			0
$601$	2.21756			0.0904563			0.0452282	−	0.998977i	$-0.485599\pi$
$601$	2.21756			0.0904563			0.0452282	+	0.998977i	$0.485599\pi$
$602$	−8.08416	−	8.27538i	−0.329486	−	0.337279i
$603$		0			0
$604$	47.7670	−	27.5783i	1.94361	−	1.12215i
$605$	15.6691	−	27.1675i	0.637041	−	1.10451i
$606$		0			0
$607$	0.919787	−	3.43269i	0.0373330	−	0.139329i	−0.944744	−	0.327809i	$-0.893690\pi$
$607$	0.919787	−	3.43269i	0.0373330	−	0.139329i	0.982077	+	0.188481i	$0.0603563\pi$
$608$	−15.7439	−	15.7439i	−0.638501	−	0.638501i
$609$		0			0
$610$	8.12882	−	8.13601i	0.329126	−	0.329417i
$611$	42.7136	−	24.6607i	1.72801	−	0.997666i
$612$		0			0
$613$	−8.08899	−	30.1885i	−0.326711	−	1.21930i	−0.912580	−	0.408897i	$-0.865913\pi$
$613$	−8.08899	−	30.1885i	−0.326711	−	1.21930i	0.585869	−	0.810406i	$-0.300753\pi$
$614$	−18.5584	−	32.1440i	−0.748954	−	1.29723i
$615$		0			0
$616$	67.3667	−	37.8513i	2.71428	−	1.52507i
$617$	22.1284	−	22.1284i	0.890857	−	0.890857i	−0.103747	−	0.994604i	$-0.533083\pi$
$617$	22.1284	−	22.1284i	0.890857	−	0.890857i	0.994604	+	0.103747i	$0.0330831\pi$
$618$		0			0
$619$	39.9430	+	23.0611i	1.60544	+	0.926903i	0.990372	+	0.138433i	$0.0442064\pi$
$619$	39.9430	+	23.0611i	1.60544	+	0.926903i	0.615072	+	0.788471i	$0.289127\pi$
$620$	35.6026	+	20.5342i	1.42983	+	0.824673i
$621$		0			0
$622$	34.6813	+	34.6813i	1.39059	+	1.39059i
$623$	−9.05654	+	8.84728i	−0.362843	+	0.354459i
$624$		0			0
$625$	−12.5383	−	21.6285i	−0.501531	−	0.865140i
$626$	−32.8834	−	18.9852i	−1.31429	−	0.758803i
$627$		0			0
$628$	22.0396	+	5.90548i	0.879475	+	0.235654i
$629$	1.37534			0.0548385
$630$		0			0
$631$	40.0682			1.59509			0.797545	−	0.603260i	$-0.206132\pi$
$631$	40.0682			1.59509			0.797545	+	0.603260i	$0.206132\pi$
$632$	−81.6338	−	21.8737i	−3.24722	−	0.870089i
$633$		0			0
$634$	36.0200	+	20.7961i	1.43054	+	0.825920i
$635$	−1.92521	+	7.19770i	−0.0763996	+	0.285632i
$636$		0			0
$637$	−12.4296	+	42.3980i	−0.492480	+	1.67987i
$638$	36.0576	+	36.0576i	1.42754	+	1.42754i
$639$		0			0
$640$	−32.8887	+	8.82808i	−1.30004	+	0.348961i
$641$	−25.8536	−	14.9266i	−1.02116	−	0.589566i	−0.106719	−	0.994289i	$-0.534034\pi$
$641$	−25.8536	−	14.9266i	−1.02116	−	0.589566i	−0.914439	+	0.404724i	$0.867368\pi$
$642$		0			0
$643$	−17.3585	+	17.3585i	−0.684554	+	0.684554i	−0.961023	−	0.276469i	$-0.910836\pi$
$643$	−17.3585	+	17.3585i	−0.684554	+	0.684554i	0.276469	+	0.961023i	$0.410836\pi$
$644$	2.70637	+	1.60498i	0.106646	+	0.0632453i
$645$		0			0
$646$	8.15941	+	14.1325i	0.321028	+	0.556036i
$647$	0.324212	+	1.20998i	0.0127461	+	0.0475691i	0.972006	−	0.234956i	$-0.0754946\pi$
$647$	0.324212	+	1.20998i	0.0127461	+	0.0475691i	−0.959260	+	0.282525i	$0.908828\pi$
$648$		0			0
$649$	−44.8215	+	25.8777i	−1.75940	+	1.01579i
$650$	0.0701600	+	79.3501i	0.00275190	+	3.11237i
$651$		0			0
$652$	25.8546	+	25.8546i	1.01254	+	1.01254i
$653$	2.58041	−	9.63022i	0.100979	−	0.376859i	−0.896879	−	0.442276i	$-0.854171\pi$
$653$	2.58041	−	9.63022i	0.100979	−	0.376859i	0.997858	+	0.0654169i	$0.0208377\pi$
$654$		0			0
$655$	−9.24191	−	5.33037i	−0.361111	−	0.208275i
$656$	−11.1753	+	6.45204i	−0.436321	+	0.251910i
$657$		0			0
$658$	14.0401	−	50.0508i	0.547338	−	1.95118i
$659$	−40.7659			−1.58801			−0.794007	−	0.607908i	$-0.792009\pi$
$659$	−40.7659			−1.58801			−0.794007	+	0.607908i	$0.792009\pi$
$660$		0			0
$661$	11.2529	−	19.4907i	0.437689	−	0.758099i	−0.559822	−	0.828613i	$-0.689131\pi$
$661$	11.2529	−	19.4907i	0.437689	−	0.758099i	0.997511	+	0.0705137i	$0.0224639\pi$
$662$	−17.4356	−	65.0707i	−0.677655	−	2.52904i
$663$		0			0
$664$			82.4489i			3.19964i
$665$	10.1525	−	36.2537i	0.393696	−	1.40586i
$666$		0			0
$667$	−0.288726	+	1.07754i	−0.0111795	+	0.0417225i
$668$	1.34216	−	0.359632i	0.0519299	−	0.0139146i
$669$		0			0
$670$	39.8850	+	69.0124i	1.54089	+	2.66618i
$671$			10.2333i			0.395052i
$672$		0			0
$673$	27.4767	−	27.4767i	1.05915	−	1.05915i	0.0610132	−	0.998137i	$-0.480567\pi$
$673$	27.4767	−	27.4767i	1.05915	−	1.05915i	0.998137	−	0.0610132i	$-0.0194332\pi$
$674$	−6.19831	−	10.7358i	−0.238750	−	0.413527i
$675$		0			0
$676$	57.9976	−	100.455i	2.23068	−	3.86364i
$677$	17.7812	+	4.76445i	0.683386	+	0.183113i	0.583777	−	0.811914i	$-0.301574\pi$
$677$	17.7812	+	4.76445i	0.683386	+	0.183113i	0.0996090	+	0.995027i	$0.468241\pi$
$678$		0			0
$679$	0.454514	−	0.766414i	0.0174427	−	0.0294123i
$680$	−13.3142	+	0.00588611i	−0.510578	+	0.000225722i
$681$		0			0
$682$	−51.6697	+	13.8449i	−1.97854	+	0.530147i
$683$	31.0627	−	8.32323i	1.18858	−	0.318480i	0.390257	−	0.920706i	$-0.372386\pi$
$683$	31.0627	−	8.32323i	1.18858	−	0.318480i	0.798325	+	0.602226i	$0.205720\pi$
$684$		0			0
$685$	−1.22969	+	1.23078i	−0.0469842	+	0.0470257i
$686$	21.8552	+	41.1191i	0.834435	+	1.56994i
$687$		0			0
$688$	10.1383	+	2.71654i	0.386518	+	0.103567i
$689$	0.132812	−	0.230036i	0.00505972	−	0.00876369i
$690$		0			0
$691$	6.08405	+	10.5379i	0.231448	+	0.400880i	0.958235	−	0.285984i	$-0.0923203\pi$
$691$	6.08405	+	10.5379i	0.231448	+	0.400880i	−0.726786	+	0.686864i	$0.758987\pi$
$692$	−48.7551	+	48.7551i	−1.85339	+	1.85339i
$693$		0			0
$694$		−	60.9797i		−	2.31476i
$695$	2.21970	−	1.28285i	0.0841980	−	0.0486614i
$696$		0			0
$697$	2.10625	−	0.564369i	0.0797801	−	0.0213770i
$698$	0.417702	−	1.55889i	0.0158103	−	0.0590047i
$699$		0			0
$700$	39.9892	+	40.8627i	1.51145	+	1.54446i
$701$			30.7110i			1.15994i	0.814639	+	0.579969i	$0.196935\pi$
$701$			30.7110i			1.15994i	−0.814639	+	0.579969i	$0.803065\pi$
$702$		0			0
$703$	−2.22111	−	8.28930i	−0.0837708	−	0.312637i
$704$	8.18859	−	14.1831i	0.308619	−	0.534544i
$705$		0			0
$706$	−4.89768			−0.184326
$707$	−7.99184	+	28.4898i	−0.300564	+	1.07147i
$708$		0			0
$709$	−4.92357	+	2.84263i	−0.184909	+	0.106757i	−0.589597	−	0.807698i	$-0.700713\pi$
$709$	−4.92357	+	2.84263i	−0.184909	+	0.106757i	0.404688	+	0.914455i	$0.367380\pi$
$710$	−28.4277	+	7.63064i	−1.06687	+	0.286373i
$711$		0			0
$712$	7.23085	−	26.9859i	0.270987	−	1.01134i
$713$	−0.827475	−	0.827475i	−0.0309892	−	0.0309892i
$714$		0			0
$715$	−49.9466	−	49.9025i	−1.86790	−	1.86625i
$716$	15.1337	−	8.73743i	0.565572	−	0.326533i
$717$		0			0
$718$	5.65906	+	21.1199i	0.211194	+	0.788188i
$719$	−4.06871	−	7.04721i	−0.151737	−	0.262817i	0.780129	−	0.625619i	$-0.215153\pi$
$719$	−4.06871	−	7.04721i	−0.151737	−	0.262817i	−0.931866	+	0.362802i	$0.881820\pi$
$720$		0			0
$721$	−0.327092	+	27.9849i	−0.0121816	+	1.04221i
$722$	38.2204	−	38.2204i	1.42241	−	1.42241i
$723$		0			0
$724$	−35.7526	−	20.6418i	−1.32874	−	0.767146i
$725$	−10.1197	+	17.5637i	−0.375836	+	0.652299i
$726$		0			0
$727$	37.4261	+	37.4261i	1.38806	+	1.38806i	0.829392	+	0.558666i	$0.188687\pi$
$727$	37.4261	+	37.4261i	1.38806	+	1.38806i	0.558666	+	0.829392i	$0.311313\pi$
$728$	−24.1312	−	94.4614i	−0.894362	−	3.50097i
$729$		0			0
$730$	−50.6900	+	29.2958i	−1.87612	+	1.08428i
$731$	−1.53600	−	0.886810i	−0.0568110	−	0.0327998i
$732$		0			0
$733$	−40.7501	−	10.9190i	−1.50514	−	0.403301i	−0.590321	−	0.807168i	$-0.700999\pi$
$733$	−40.7501	−	10.9190i	−1.50514	−	0.403301i	−0.914817	+	0.403868i	$0.867666\pi$
$734$	81.9619			3.02527
$735$		0			0
$736$	−0.962746			−0.0354873
$737$	−68.5067	−	18.3563i	−2.52348	−	0.676163i
$738$		0			0
$739$	−42.4476	−	24.5071i	−1.56146	−	0.901510i	−0.997110	−	0.0759743i	$-0.975793\pi$
$739$	−42.4476	−	24.5071i	−1.56146	−	0.901510i	−0.564351	−	0.825535i	$-0.690873\pi$
$740$	12.5899	+	3.36749i	0.462814	+	0.123791i
$741$		0			0
$742$	−0.0692925	−	0.271245i	−0.00254381	−	0.00995771i
$743$	28.7264	+	28.7264i	1.05387	+	1.05387i	0.998464	+	0.0554047i	$0.0176449\pi$
$743$	28.7264	+	28.7264i	1.05387	+	1.05387i	0.0554047	+	0.998464i	$0.482355\pi$
$744$		0			0
$745$	20.6304	−	35.7694i	0.755838	−	1.31049i
$746$	40.4921	+	23.3781i	1.48252	+	0.855934i
$747$		0			0
$748$	15.5922	−	15.5922i	0.570109	−	0.570109i
$749$	−0.429427	+	36.7403i	−0.0156909	+	1.34246i
$750$		0			0
$751$	4.29587	+	7.44067i	0.156759	+	0.271514i	0.933698	−	0.358061i	$-0.116562\pi$
$751$	4.29587	+	7.44067i	0.156759	+	0.271514i	−0.776939	+	0.629575i	$0.783229\pi$
$752$	12.2065	+	45.5552i	0.445124	+	1.66123i
$753$		0			0
$754$	55.7188	−	32.1693i	2.02916	−	1.17154i
$755$	−28.5365	+	0.0126158i	−1.03855	+	0.000459134i
$756$		0			0
$757$	1.94682	+	1.94682i	0.0707583	+	0.0707583i	0.741600	−	0.670842i	$-0.234067\pi$
$757$	1.94682	+	1.94682i	0.0707583	+	0.0707583i	−0.670842	+	0.741600i	$0.734067\pi$
$758$	−7.61092	+	28.4044i	−0.276441	+	1.03169i
$759$		0			0
$760$	21.5373	+	80.2365i	0.781241	+	2.91048i
$761$	17.3244	−	10.0023i	0.628011	−	0.362582i	−0.151971	−	0.988385i	$-0.548562\pi$
$761$	17.3244	−	10.0023i	0.628011	−	0.362582i	0.779981	+	0.625803i	$0.215229\pi$
$762$		0			0
$763$	2.77733	−	9.90079i	0.100546	−	0.358433i
$764$	84.9578			3.07367
$765$		0			0
$766$	−10.6298	+	18.4114i	−0.384072	+	0.665232i
$767$	16.9009	+	63.0751i	0.610257	+	2.27751i
$768$		0			0
$769$			31.7665i			1.14553i	0.819720	+	0.572764i	$0.194129\pi$
$769$			31.7665i			1.14553i	−0.819720	+	0.572764i	$0.805871\pi$
$770$	−74.4089	−	0.836804i	−2.68151	−	0.0301563i
$771$		0			0
$772$	6.20183	−	23.1455i	0.223209	−	0.833026i
$773$	−28.9093	+	7.74623i	−1.03980	+	0.278613i	−0.738029	−	0.674769i	$-0.764243\pi$
$773$	−28.9093	+	7.74623i	−1.03980	+	0.278613i	−0.301768	+	0.953382i	$0.597577\pi$
$774$		0			0
$775$	−10.6483	−	18.4057i	−0.382497	−	0.661153i
$776$			1.96624i			0.0705837i
$777$		0			0
$778$	39.8167	−	39.8167i	1.42750	−	1.42750i
$779$	−6.80300	−	11.7831i	−0.243743	−	0.422175i
$780$		0			0
$781$	13.0948	−	22.6809i	0.468570	−	0.811588i
$782$	0.681578	+	0.182628i	0.0243732	+	0.00653078i
$783$		0			0
$784$	−36.0842	−	21.9735i	−1.28872	−	0.784767i
$785$	−8.35103	−	8.34365i	−0.298061	−	0.297798i
$786$		0			0
$787$	−2.61451	+	0.700556i	−0.0931973	+	0.0249721i	−0.305116	−	0.952315i	$-0.598695\pi$
$787$	−2.61451	+	0.700556i	−0.0931973	+	0.0249721i	0.211919	+	0.977287i	$0.432029\pi$
$788$	45.4008	−	12.1651i	1.61734	−	0.433364i
$789$		0			0
$790$	57.5748	+	57.5239i	2.04842	+	2.04661i
$791$	23.1668	−	39.0645i	0.823717	−	1.38897i
$792$		0			0
$793$	12.4715	+	3.34173i	0.442876	+	0.118668i
$794$	10.7109	−	18.5519i	0.380117	−	0.658382i
$795$		0			0
$796$	17.4649	+	30.2501i	0.619028	+	1.07219i
$797$	19.5221	−	19.5221i	0.691508	−	0.691508i	−0.271056	−	0.962564i	$-0.587373\pi$
$797$	19.5221	−	19.5221i	0.691508	−	0.691508i	0.962564	+	0.271056i	$0.0873728\pi$
$798$		0			0
$799$		−	7.96956i		−	0.281943i
$800$	−16.9018	−	4.51280i	−0.597568	−	0.159552i
$801$		0			0
$802$	−30.8463	+	8.26525i	−1.08922	+	0.291856i
$803$	13.4828	−	50.3185i	0.475798	−	1.77570i
$804$		0			0
$805$	−0.798049	−	1.41887i	−0.0281275	−	0.0500088i
$806$			67.4919i			2.37730i
$807$		0			0
$808$	−16.8992	−	63.0687i	−0.594512	−	2.21875i
$809$	2.93046	−	5.07571i	0.103030	−	0.178452i	−0.809902	−	0.586565i	$-0.800480\pi$
$809$	2.93046	−	5.07571i	0.103030	−	0.178452i	0.912931	+	0.408113i	$0.133813\pi$
$810$		0			0
$811$	−16.1090			−0.565662			−0.282831	−	0.959170i	$-0.591274\pi$
$811$	−16.1090			−0.565662			−0.282831	+	0.959170i	$0.591274\pi$
$812$	12.5208	−	44.6350i	0.439395	−	1.56638i
$813$		0			0
$814$	−14.6896	+	8.48105i	−0.514871	+	0.297261i
$815$	−4.90420	−	18.2704i	−0.171787	−	0.639985i
$816$		0			0
$817$	−2.86431	+	10.6897i	−0.100210	+	0.373987i
$818$	−47.0213	−	47.0213i	−1.64406	−	1.64406i
$819$		0			0
$820$	20.6625	−	0.00913472i	0.721567	−	0.000318998i
$821$	−36.8611	+	21.2817i	−1.28646	+	0.742738i	−0.978021	−	0.208507i	$-0.933140\pi$
$821$	−36.8611	+	21.2817i	−1.28646	+	0.742738i	−0.308439	+	0.951244i	$0.599806\pi$
$822$		0			0
$823$	−8.56545	−	31.9667i	−0.298573	−	1.11429i	−0.938338	−	0.345719i	$-0.887635\pi$
$823$	−8.56545	−	31.9667i	−0.298573	−	1.11429i	0.639765	−	0.768570i	$-0.279032\pi$
$824$	−30.8785	−	53.4832i	−1.07570	−	1.86317i
$825$		0			0
$826$	59.1968	+	35.1061i	2.05972	+	1.22150i
$827$	7.78145	−	7.78145i	0.270587	−	0.270587i	−0.558749	−	0.829337i	$-0.688719\pi$
$827$	7.78145	−	7.78145i	0.270587	−	0.270587i	0.829337	+	0.558749i	$0.188719\pi$
$828$		0			0
$829$	−32.4643	−	18.7432i	−1.12753	−	0.650980i	−0.184218	−	0.982885i	$-0.558975\pi$
$829$	−32.4643	−	18.7432i	−1.12753	−	0.650980i	−0.943313	+	0.331906i	$0.892308\pi$
$830$	39.6690	−	68.7790i	1.37693	−	2.38735i
$831$		0			0
$832$	−14.6111	−	14.6111i	−0.506549	−	0.506549i
$833$	4.92879	+	5.16477i	0.170772	+	0.178949i
$834$		0			0
$835$	−0.694482	−	0.185757i	−0.0240335	−	0.00642838i
$836$	−119.156	−	68.7950i	−4.12111	−	2.37932i
$837$		0			0
$838$	−5.67693	−	1.52113i	−0.196106	−	0.0525465i
$839$	−0.118993			−0.00410811			−0.00205406	−	0.999998i	$-0.500654\pi$
$839$	−0.118993			−0.00410811			−0.00205406	+	0.999998i	$0.500654\pi$
$840$		0			0
$841$	−12.5643			−0.433253
$842$	−34.3800	−	9.21208i	−1.18481	−	0.317469i
$843$		0			0
$844$	50.4867	+	29.1485i	1.73782	+	1.00333i
$845$	−51.9593	+	30.0294i	−1.78745	+	1.03304i
$846$		0			0
$847$	26.5444	−	25.9311i	0.912078	−	0.891003i
$848$	0.179601	+	0.179601i	0.00616753	+	0.00616753i
$849$		0			0
$850$	11.1096	+	6.40103i	0.381056	+	0.219554i
$851$	−0.321357	−	0.185536i	−0.0110160	−	0.00636008i
$852$		0			0
$853$	6.51907	−	6.51907i	0.223209	−	0.223209i	−0.586639	−	0.809848i	$-0.699549\pi$
$853$	6.51907	−	6.51907i	0.223209	−	0.223209i	0.809848	+	0.586639i	$0.199549\pi$
$854$	11.8637	−	6.66587i	0.405968	−	0.228101i
$855$		0			0
$856$	−40.5392	−	70.2160i	−1.38560	−	2.39993i
$857$	7.94363	+	29.6460i	0.271349	+	1.01269i	0.958249	+	0.285936i	$0.0923046\pi$
$857$	7.94363	+	29.6460i	0.271349	+	1.01269i	−0.686899	+	0.726752i	$0.741029\pi$
$858$		0			0
$859$	30.5614	−	17.6447i	1.04274	−	0.602028i	0.122134	−	0.992514i	$-0.461026\pi$
$859$	30.5614	−	17.6447i	1.04274	−	0.602028i	0.920609	+	0.390486i	$0.127693\pi$
$860$	−11.8892	−	11.8787i	−0.405419	−	0.405061i
$861$		0			0
$862$	−29.5971	−	29.5971i	−1.00808	−	1.00808i
$863$	−13.4253	+	50.1038i	−0.457002	+	1.70555i	0.225134	+	0.974328i	$0.427718\pi$
$863$	−13.4253	+	50.1038i	−0.457002	+	1.70555i	−0.682136	+	0.731225i	$0.738949\pi$
$864$		0			0
$865$	34.4533	−	9.24807i	1.17145	−	0.314444i
$866$	25.9661	−	14.9915i	0.882363	−	0.509433i
$867$		0			0
$868$	33.9824	+	34.7861i	1.15344	+	1.18072i
$869$	−72.4164			−2.45656
$870$		0			0
$871$	−44.7423	+	77.4959i	−1.51603	+	2.62585i
$872$	5.87282	+	21.9177i	0.198879	+	0.742226i
$873$		0			0
$874$		−	4.40286i		−	0.148929i
$875$	−7.35952	−	28.6503i	−0.248797	−	0.968556i
$876$		0			0
$877$	5.32717	−	19.8813i	0.179886	−	0.671343i	−0.815782	−	0.578360i	$-0.803693\pi$
$877$	5.32717	−	19.8813i	0.179886	−	0.671343i	0.995668	−	0.0929832i	$-0.0296403\pi$
$878$	−79.2122	+	21.2249i	−2.67328	+	0.716304i
$879$		0			0
$880$	58.4530	−	33.7823i	1.97045	−	1.13880i
$881$			18.4194i			0.620564i	0.950645	+	0.310282i	$0.100423\pi$
$881$			18.4194i			0.620564i	−0.950645	+	0.310282i	$0.899577\pi$
$882$		0			0
$883$	−14.6058	+	14.6058i	−0.491526	+	0.491526i	−0.908787	−	0.417261i	$-0.862990\pi$
$883$	−14.6058	+	14.6058i	−0.491526	+	0.491526i	0.417261	+	0.908787i	$0.362990\pi$
$884$	−13.9108	−	24.0942i	−0.467871	−	0.810377i
$885$		0			0
$886$	16.5316	−	28.6336i	0.555390	−	0.961963i
$887$	−14.6042	−	3.91318i	−0.490361	−	0.131392i	0.00516191	−	0.999987i	$-0.498357\pi$
$887$	−14.6042	−	3.91318i	−0.490361	−	0.131392i	−0.495523	+	0.868595i	$0.665024\pi$
$888$		0			0
$889$	−4.49684	+	7.58269i	−0.150819	+	0.254315i
$890$	−19.0158	+	19.0326i	−0.637412	+	0.637976i
$891$		0			0
$892$	−17.3790	+	4.65669i	−0.581892	+	0.155918i
$893$	−48.0332	+	12.8704i	−1.60737	+	0.430693i
$894$		0			0
$895$	−9.04102	+	0.00399696i	−0.302208	+	0.000133604i
$896$	−40.2892	−	0.470906i	−1.34597	−	0.0157319i
$897$		0			0
$898$	−91.5893	−	24.5413i	−3.05637	−	0.818953i
$899$	−8.62060	+	14.9313i	−0.287513	+	0.497987i
$900$		0			0
$901$	−0.0214602	−	0.0371702i	−0.000714943	−	0.00123832i
$902$	−19.0161	+	19.0161i	−0.633166	+	0.633166i
$903$		0			0
$904$			100.220i			3.33327i
$905$	10.6877	+	18.4927i	0.355271	+	0.614719i
$906$		0			0
$907$	−30.7656	+	8.24361i	−1.02155	+	0.273725i	−0.730449	−	0.682967i	$-0.760689\pi$
$907$	−30.7656	+	8.24361i	−1.02155	+	0.273725i	−0.291104	+	0.956691i	$0.594023\pi$
$908$	−21.8524	+	81.5544i	−0.725198	+	2.70648i
$909$		0			0
$910$	−25.3184	+	90.4102i	−0.839296	+	2.99707i
$911$			44.5563i			1.47621i	0.674683	+	0.738107i	$0.264280\pi$
$911$			44.5563i			1.47621i	−0.674683	+	0.738107i	$0.735720\pi$
$912$		0			0
$913$	18.2849	+	68.2401i	0.605141	+	2.25842i
$914$	8.95797	−	15.5157i	0.296303	−	0.513212i
$915$		0			0
$916$	−29.9545			−0.989725
$917$	−8.82132	−	9.02997i	−0.291306	−	0.298196i
$918$		0			0
$919$	29.1834	−	16.8490i	0.962671	−	0.555798i	0.0656768	−	0.997841i	$-0.479079\pi$
$919$	29.1834	−	16.8490i	0.962671	−	0.555798i	0.896994	+	0.442043i	$0.145746\pi$
$920$	3.11175	+	1.79473i	0.102591	+	0.0591706i
$921$		0			0
$922$	15.1512	−	56.5450i	0.498978	−	1.86221i
$923$	−23.3655	−	23.3655i	−0.769084	−	0.769084i
$924$		0			0
$925$	−4.77199	−	4.76356i	−0.156902	−	0.156625i
$926$	80.2157	−	46.3125i	2.63605	−	1.52192i
$927$		0			0
$928$	3.67118	+	13.7010i	0.120512	+	0.449758i
$929$	8.87442	+	15.3710i	0.291160	+	0.504305i	0.974084	−	0.226185i	$-0.0726253\pi$
$929$	8.87442	+	15.3710i	0.291160	+	0.504305i	−0.682924	+	0.730489i	$0.739292\pi$
$930$		0			0
$931$	23.1687	−	38.0470i	0.759324	−	1.24694i
$932$	−65.0819	+	65.0819i	−2.13183	+	2.13183i
$933$		0			0
$934$	20.0799	+	11.5932i	0.657036	+	0.379340i
$935$	−11.0184	+	2.95760i	−0.360341	+	0.0967239i
$936$		0			0
$937$	−30.1626	−	30.1626i	−0.985368	−	0.985368i	0.0145268	−	0.999894i	$-0.495376\pi$
$937$	−30.1626	−	30.1626i	−0.985368	−	0.985368i	−0.999894	+	0.0145268i	$0.995376\pi$
$938$	23.3436	+	91.3785i	0.762197	+	2.98361i
$939$		0			0
$940$	19.5133	−	72.9534i	0.636452	−	2.37948i
$941$	29.0798	+	16.7893i	0.947976	+	0.547314i	0.892451	−	0.451143i	$-0.148984\pi$
$941$	29.0798	+	16.7893i	0.947976	+	0.547314i	0.0555241	+	0.998457i	$0.482317\pi$
$942$		0			0
$943$	−0.568273	−	0.152268i	−0.0185055	−	0.00495854i
$944$	−62.4414			−2.03229
$945$		0			0
$946$	21.8741			0.711187
$947$	28.6266	+	7.67048i	0.930240	+	0.249257i	0.691957	−	0.721939i	$-0.256749\pi$
$947$	28.6266	+	7.67048i	0.930240	+	0.249257i	0.238283	+	0.971196i	$0.423415\pi$
$948$		0			0
$949$	−56.9211	−	32.8634i	−1.84774	−	1.06679i
$950$	20.6381	−	77.2957i	0.669588	−	2.50780i
$951$		0			0
$952$	−15.1681	−	4.25490i	−0.491602	−	0.137902i
$953$	16.1133	+	16.1133i	0.521961	+	0.521961i	0.918163	−	0.396202i	$-0.129672\pi$
$953$	16.1133	+	16.1133i	0.521961	+	0.521961i	−0.396202	+	0.918163i	$0.629672\pi$
$954$		0			0
$955$	−38.0758	−	21.9606i	−1.23210	−	0.710629i
$956$	−2.94835	−	1.70223i	−0.0953564	−	0.0550540i
$957$		0			0
$958$	−32.1679	+	32.1679i	−1.03930	+	1.03930i
$959$	−1.79469	+	1.00838i	−0.0579536	+	0.0325624i
$960$		0			0
$961$	6.45689	+	11.1837i	0.208287	+	0.360763i
$962$	5.53905	+	20.6720i	0.178586	+	0.666492i
$963$		0			0
$964$	−3.28330	+	1.89562i	−0.105748	+	0.0610537i
$965$	−8.76234	+	8.77009i	−0.282070	+	0.282319i
$966$		0			0
$967$	32.9843	+	32.9843i	1.06070	+	1.06070i	0.998034	+	0.0626698i	$0.0199615\pi$
$967$	32.9843	+	32.9843i	1.06070	+	1.06070i	0.0626698	+	0.998034i	$0.480039\pi$
$968$	−21.1934	+	79.0948i	−0.681181	+	2.54220i
$969$		0			0
$970$	0.946024	−	1.64024i	0.0303750	−	0.0526648i
$971$	33.4151	−	19.2922i	1.07234	−	0.619117i	0.143521	−	0.989647i	$-0.454158\pi$
$971$	33.4151	−	19.2922i	1.07234	−	0.619117i	0.928820	+	0.370531i	$0.120824\pi$
$972$		0			0
$973$	2.93907	−	0.750819i	0.0942224	−	0.0240701i
$974$	−6.09757			−0.195379
$975$		0			0
$976$	−6.17310	+	10.6921i	−0.197596	+	0.342246i
$977$	−0.612947	−	2.28755i	−0.0196099	−	0.0731852i	0.955428	−	0.295226i	$-0.0953949\pi$
$977$	−0.612947	−	2.28755i	−0.0196099	−	0.0731852i	−0.975037	+	0.222041i	$0.928728\pi$
$978$		0			0
$979$		−	23.9389i		−	0.765090i
$980$	32.4724	+	59.3464i	1.03729	+	1.89575i
$981$		0			0
$982$	−9.93483	+	37.0773i	−0.317033	+	1.18318i
$983$	−27.5427	+	7.38005i	−0.878476	+	0.235387i	−0.669750	−	0.742587i	$-0.733599\pi$
$983$	−27.5427	+	7.38005i	−0.878476	+	0.235387i	−0.208727	+	0.977974i	$0.566932\pi$
$984$		0			0
$985$	−23.4919	−	6.28352i	−0.748516	−	0.200210i
$986$		−	10.3961i		−	0.331078i
$987$		0			0
$988$	−122.753	+	122.753i	−3.90528	+	3.90528i
$989$	0.239264	+	0.414417i	0.00760814	+	0.0131777i
$990$		0			0
$991$	−8.85117	+	15.3307i	−0.281167	+	0.486995i	−0.971672	−	0.236332i	$-0.924055\pi$
$991$	−8.85117	+	15.3307i	−0.281167	+	0.486995i	0.690506	+	0.723327i	$0.257388\pi$
$992$	−14.3725	−	3.85111i	−0.456328	−	0.122273i
$993$		0			0
$994$	−34.8244	−	0.407033i	−1.10456	−	0.0129103i
$995$	−0.00798936	−	18.0718i	−0.000253280	−	0.572913i
$996$		0			0
$997$	−51.3174	+	13.7505i	−1.62524	+	0.435481i	−0.952535	−	0.304431i	$-0.901534\pi$
$997$	−51.3174	+	13.7505i	−1.62524	+	0.435481i	−0.672704	+	0.739912i	$0.734867\pi$
$998$	0.538660	−	0.144333i	0.0170510	−	0.00456880i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.ch.a.242.31	yes	128
3.2	odd	2	inner	945.2.ch.a.242.2	yes	128
5.3	odd	4	inner	945.2.ch.a.53.31	yes	128
7.2	even	3	inner	945.2.ch.a.107.2	yes	128
15.8	even	4	inner	945.2.ch.a.53.2	✓	128
21.2	odd	6	inner	945.2.ch.a.107.31	yes	128
35.23	odd	12	inner	945.2.ch.a.863.2	yes	128
105.23	even	12	inner	945.2.ch.a.863.31	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
945.2.ch.a.53.2	✓	128	15.8	even	4	inner
945.2.ch.a.53.31	yes	128	5.3	odd	4	inner
945.2.ch.a.107.2	yes	128	7.2	even	3	inner
945.2.ch.a.107.31	yes	128	21.2	odd	6	inner
945.2.ch.a.242.2	yes	128	3.2	odd	2	inner
945.2.ch.a.242.31	yes	128	1.1	even	1	trivial
945.2.ch.a.863.2	yes	128	35.23	odd	12	inner
945.2.ch.a.863.31	yes	128	105.23	even	12	inner

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:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.ch (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.42868 + 0.650762i) q^{2} +(3.74293 + 2.16098i) q^{4} +(-1.11889 - 1.93600i) q^{5} +(-0.654856 - 2.56343i) q^{7} +(4.12826 + 4.12826i) q^{8} +O(q^{10})\)	\(q+(2.42868 + 0.650762i) q^{2} +(3.74293 + 2.16098i) q^{4} +(-1.11889 - 1.93600i) q^{5} +(-0.654856 - 2.56343i) q^{7} +(4.12826 + 4.12826i) q^{8} +(-1.45755 - 5.43004i) q^{10} +(4.33235 + 2.50128i) q^{11} +(4.46310 - 4.46310i) q^{13} +(0.0777484 - 6.65190i) q^{14} +(3.01772 + 5.22685i) q^{16} +(-0.263965 - 0.985130i) q^{17} +(-5.51117 + 3.18187i) q^{19} +(-0.00427246 - 9.66421i) q^{20} +(8.89413 + 8.89413i) q^{22} +(-0.0712184 + 0.265791i) q^{23} +(-2.49617 + 4.33234i) q^{25} +(13.7438 - 7.93501i) q^{26} +(3.08844 - 11.0099i) q^{28} +4.05409 q^{29} +(-2.12640 + 3.68302i) q^{31} +(0.905549 + 3.37955i) q^{32} -2.56434i q^{34} +(-4.23008 + 4.13599i) q^{35} +(-0.349026 + 1.30258i) q^{37} +(-15.4555 + 4.14129i) q^{38} +(3.37323 - 12.6114i) q^{40} +2.13805i q^{41} +(1.22969 - 1.22969i) q^{43} +(10.8104 + 18.7242i) q^{44} +(-0.345933 + 0.599174i) q^{46} +(7.54793 + 2.02246i) q^{47} +(-6.14233 + 3.35735i) q^{49} +(-8.88171 + 8.89743i) q^{50} +(26.3498 - 7.06040i) q^{52} +(0.0406498 - 0.0108921i) q^{53} +(-0.00494526 - 11.1861i) q^{55} +(7.87908 - 13.2859i) q^{56} +(9.84608 + 2.63825i) q^{58} +(-5.17288 + 8.95970i) q^{59} +(1.02281 + 1.77155i) q^{61} +(-7.56110 + 7.56110i) q^{62} -3.27376i q^{64} +(-13.6343 - 3.64683i) q^{65} +(-13.6943 + 3.66938i) q^{67} +(1.14085 - 4.25770i) q^{68} +(-12.9650 + 7.29222i) q^{70} -5.23525i q^{71} +(-2.69518 - 10.0585i) q^{73} +(-1.69534 + 2.93642i) q^{74} -27.5039 q^{76} +(3.57479 - 12.7436i) q^{77} +(-12.5365 + 7.23793i) q^{79} +(6.74267 - 11.6906i) q^{80} +(-1.39136 + 5.19263i) q^{82} +(9.98593 + 9.98593i) q^{83} +(-1.61186 + 1.61329i) q^{85} +(3.78676 - 2.18628i) q^{86} +(7.55911 + 28.2110i) q^{88} +(-2.39266 - 4.14421i) q^{89} +(-14.3635 - 8.51815i) q^{91} +(-0.840935 + 0.840935i) q^{92} +(17.0154 + 9.82382i) q^{94} +(12.3265 + 7.10944i) q^{95} +(0.238144 + 0.238144i) q^{97} +(-17.1026 + 4.15673i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 8 q^{7}+O(q^{10}) \) 128 * q - 8 * q^7	\( 128 q - 8 q^{7} - 8 q^{10} + 64 q^{16} - 8 q^{25} + 8 q^{28} + 16 q^{31} - 8 q^{37} + 40 q^{40} - 32 q^{43} + 80 q^{52} + 32 q^{55} + 16 q^{58} - 24 q^{61} - 16 q^{67} - 80 q^{70} + 64 q^{73} - 160 q^{76} - 40 q^{82} - 64 q^{85} - 48 q^{88} - 136 q^{91} - 208 q^{97}+O(q^{100}) \) 128 * q - 8 * q^7 - 8 * q^10 + 64 * q^16 - 8 * q^25 + 8 * q^28 + 16 * q^31 - 8 * q^37 + 40 * q^40 - 32 * q^43 + 80 * q^52 + 32 * q^55 + 16 * q^58 - 24 * q^61 - 16 * q^67 - 80 * q^70 + 64 * q^73 - 160 * q^76 - 40 * q^82 - 64 * q^85 - 48 * q^88 - 136 * q^91 - 208 * q^97

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