LMFDB - Embedded newform 945.2.ch.a.863.31

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			863.31
Character	$\chi$	$=$	945.863
Dual form			945.2.ch.a.242.31

$q$-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 $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

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

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	0.740131	−	0.672463i	$-0.234764\pi$
$2$	2.42868	−	0.650762i	1.71733	−	0.460158i	0.977204	+	0.212305i	$0.0680970\pi$
$3$		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	0.324783	−	0.945789i	$-0.394709\pi$
$11$	4.33235	−	2.50128i	1.30625	−	0.754165i	0.981468	+	0.191624i	$0.0613754\pi$
$12$		0			0
$13$	4.46310	+	4.46310i	1.23784	+	1.23784i	0.960882	+	0.276960i	$0.0893268\pi$
$13$	4.46310	+	4.46310i	1.23784	+	1.23784i	0.276960	+	0.960882i	$0.410673\pi$
$14$	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	−0.990520	−	0.137367i	$-0.956136\pi$
$17$	−0.263965	+	0.985130i	−0.0640209	+	0.238929i	0.926499	+	0.376296i	$0.122803\pi$
$18$		0			0
$19$	−5.51117	−	3.18187i	−1.26435	−	0.729972i	−0.290436	−	0.956894i	$-0.593800\pi$
$19$	−5.51117	−	3.18187i	−1.26435	−	0.729972i	−0.973913	+	0.226922i	$0.927134\pi$
$20$	−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	0.958103	−	0.286423i	$-0.0924663\pi$
$23$	−0.0712184	−	0.265791i	−0.0148501	−	0.0554212i	−0.972953	+	0.231002i	$0.925800\pi$
$24$		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	0.609424	−	0.792845i	$-0.291401\pi$
$31$	−2.12640	−	3.68302i	−0.381912	−	0.661491i	−0.991336	+	0.131354i	$0.958068\pi$
$32$	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	0.931283	−	0.364296i	$-0.118690\pi$
$37$	−0.349026	−	1.30258i	−0.0573795	−	0.214143i	−0.988663	+	0.150153i	$0.952024\pi$
$38$	−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	$-0.946607\pi$
$41$		−	2.13805i		−	0.333907i	0.985965	−	0.166953i	$-0.0533930\pi$
$42$		0			0
$43$	1.22969	+	1.22969i	0.187526	+	0.187526i	0.794626	−	0.607100i	$-0.207667\pi$
$43$	1.22969	+	1.22969i	0.187526	+	0.187526i	−0.607100	+	0.794626i	$0.707667\pi$
$44$	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	0.337816	−	0.941212i	$-0.390312\pi$
$47$	7.54793	−	2.02246i	1.10098	−	0.295007i	0.763163	+	0.646206i	$0.223645\pi$
$48$		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	0.261610	−	0.965174i	$-0.415747\pi$
$53$	0.0406498	+	0.0108921i	0.00558367	+	0.00149614i	−0.256026	+	0.966670i	$0.582413\pi$
$54$		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	−0.976919	−	0.213611i	$-0.931477\pi$
$59$	−5.17288	−	8.95970i	−0.673452	−	1.16645i	0.303467	−	0.952842i	$-0.401856\pi$
$60$		0			0
$61$	1.02281	−	1.77155i	0.130957	−	0.226824i	−0.793089	−	0.609106i	$-0.791528\pi$
$61$	1.02281	−	1.77155i	0.130957	−	0.226824i	0.924046	+	0.382282i	$0.124862\pi$
$62$	−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	−0.707103	−	0.707111i	$-0.749998\pi$
$67$	−13.6943	−	3.66938i	−1.67303	−	0.448286i	−0.965924	+	0.258824i	$0.916665\pi$
$68$	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	$0.100548\pi$
$71$			5.23525i			0.621310i	−0.950523	+	0.310655i	$0.899452\pi$
$72$		0			0
$73$	−2.69518	+	10.0585i	−0.315447	+	1.17726i	0.608126	+	0.793841i	$0.291922\pi$
$73$	−2.69518	+	10.0585i	−0.315447	+	1.17726i	−0.923573	+	0.383423i	$0.874745\pi$
$74$	−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	−0.415031	−	0.909807i	$-0.636229\pi$
$79$	−12.5365	−	7.23793i	−1.41046	−	0.814331i	−0.995432	+	0.0954764i	$0.969563\pi$
$80$	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	0.101235	−	0.994863i	$-0.467721\pi$
$83$	9.98593	−	9.98593i	1.09610	−	1.09610i	0.994863	−	0.101235i	$-0.0322795\pi$
$84$		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	−0.964520	−	0.264009i	$-0.914955\pi$
$89$	−2.39266	+	4.14421i	−0.253622	+	0.439285i	0.710899	+	0.703294i	$0.248288\pi$
$90$		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	−0.694914	−	0.719093i	$-0.744557\pi$
$97$	0.238144	−	0.238144i	0.0241798	−	0.0241798i	0.719093	+	0.694914i	$0.244557\pi$
$98$	−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	−0.897321	−	0.441379i	$-0.854490\pi$
$101$	−9.68543	+	5.59189i	−0.963736	+	0.556413i	−0.0664154	+	0.997792i	$0.521156\pi$
$102$		0			0
$103$	−10.2176	+	2.73780i	−1.00677	+	0.269763i	−0.724279	−	0.689507i	$-0.757827\pi$
$103$	−10.2176	+	2.73780i	−1.00677	+	0.269763i	−0.282490	+	0.959270i	$0.591160\pi$
$104$	36.8496			3.61340
$105$		0			0
$106$	0.105813			0.0102775
$107$	−13.4143	+	3.59435i	−1.29681	+	0.347479i	−0.840242	−	0.542211i	$-0.817587\pi$
$107$	−13.4143	+	3.59435i	−1.29681	+	0.347479i	−0.456565	+	0.889690i	$0.650921\pi$
$108$		0			0
$109$	3.36589	−	1.94330i	0.322394	−	0.186134i	−0.330065	−	0.943958i	$-0.607071\pi$
$109$	3.36589	−	1.94330i	0.322394	−	0.186134i	0.652459	+	0.757824i	$0.273737\pi$
$110$	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	0.153768	−	0.988107i	$-0.450859\pi$
$113$	12.1383	−	12.1383i	1.14187	−	1.14187i	0.988107	−	0.153768i	$-0.0491408\pi$
$114$		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	−0.803873	−	0.594801i	$-0.797231\pi$
$127$	−2.35613	+	2.35613i	−0.209072	+	0.209072i	0.594801	+	0.803873i	$0.297231\pi$
$128$	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	0.669528	−	0.742787i	$-0.266497\pi$
$131$	4.13205	+	2.38564i	0.361019	+	0.208435i	−0.308509	+	0.951222i	$0.599830\pi$
$132$		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	−0.973995	−	0.226571i	$-0.927248\pi$
$137$	−0.201380	+	0.751559i	−0.0172050	+	0.0642100i	0.956790	+	0.290781i	$0.0939151\pi$
$138$		0			0
$139$		−	1.14654i		−	0.0972483i	−0.998817	−	0.0486241i	$-0.984516\pi$
$139$		−	1.14654i		−	0.0972483i	0.998817	−	0.0486241i	$-0.0154837\pi$
$140$	−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	−0.188249	−	0.982121i	$-0.560281\pi$
$149$	9.23325	−	15.9925i	0.756418	−	1.31015i	0.944666	−	0.328032i	$-0.106386\pi$
$150$		0			0
$151$	6.38096	+	11.0522i	0.519275	+	0.899411i	0.999749	+	0.0224023i	$0.00713146\pi$
$151$	6.38096	+	11.0522i	0.519275	+	0.899411i	−0.480474	+	0.877009i	$0.659535\pi$
$152$	−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	0.456500	−	0.889723i	$-0.349103\pi$
$157$	5.09943	+	1.36639i	0.406979	+	0.109050i	−0.0495210	+	0.998773i	$0.515769\pi$
$158$	−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	0.0758299	−	0.997121i	$-0.475839\pi$
$163$	8.17175	−	2.18961i	0.640061	−	0.171504i	0.564231	+	0.825617i	$0.309173\pi$
$164$	−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	0.715848	−	0.698256i	$-0.246040\pi$
$167$	0.227335	+	0.227335i	0.0175917	+	0.0175917i	−0.698256	+	0.715848i	$0.746040\pi$
$168$		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	−0.924985	−	0.380003i	$-0.875923\pi$
$173$	−4.12905	−	15.4098i	−0.313926	−	1.17159i	0.611060	−	0.791585i	$-0.290744\pi$
$174$		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	0.931634	−	0.363399i	$-0.118384\pi$
$179$	2.02163	+	3.50157i	0.151104	+	0.261720i	−0.780530	+	0.625119i	$0.785050\pi$
$180$		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	0.967403	−	0.253243i	$-0.0814974\pi$
$191$	17.0237	+	9.82861i	1.23179	+	0.711173i	0.264386	+	0.964417i	$0.414831\pi$
$192$		0			0
$193$	−1.43496	+	5.35533i	−0.103290	+	0.385485i	−0.998146	−	0.0608716i	$-0.980612\pi$
$193$	−1.43496	+	5.35533i	−0.103290	+	0.385485i	0.894855	+	0.446356i	$0.147279\pi$
$194$	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	0.925829	−	0.377942i	$-0.123368\pi$
$197$	7.68996	+	7.68996i	0.547887	+	0.547887i	−0.377942	+	0.925829i	$0.623368\pi$
$198$		0			0
$199$	6.99916	−	4.04097i	0.496157	−	0.286457i	−0.230968	−	0.972961i	$-0.574189\pi$
$199$	6.99916	−	4.04097i	0.496157	−	0.286457i	0.727125	+	0.686505i	$0.240856\pi$
$200$	−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	0.601644	−	0.798765i	$-0.294513\pi$
$223$	−2.94364	−	2.94364i	−0.197121	−	0.197121i	−0.798765	+	0.601644i	$0.794513\pi$
$224$	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	−0.567644	−	0.823274i	$-0.692145\pi$
$227$	5.05613	−	18.8697i	0.335587	−	1.25243i	0.903231	−	0.429155i	$-0.141189\pi$
$228$		0			0
$229$	−6.00222	−	3.46538i	−0.396638	−	0.228999i	0.288394	−	0.957512i	$-0.406879\pi$
$229$	−6.00222	−	3.46538i	−0.396638	−	0.228999i	−0.685032	+	0.728513i	$0.740212\pi$
$230$	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	−0.872648	−	0.488350i	$-0.837599\pi$
$233$	−5.51176	−	20.5702i	−0.361088	−	1.34760i	0.511560	−	0.859247i	$-0.329068\pi$
$234$		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	0.851553	−	0.524268i	$-0.175661\pi$
$241$	−0.438601	−	0.759678i	−0.0282527	−	0.0489352i	−0.879806	+	0.475333i	$0.842328\pi$
$242$	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	$0.0177377\pi$
$251$			1.76477i			0.111391i	−0.998448	+	0.0556957i	$0.982262\pi$
$252$		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	−0.178514	−	0.983937i	$-0.557129\pi$
$257$	2.54666	−	0.682377i	0.158857	−	0.0425655i	0.337371	+	0.941372i	$0.390462\pi$
$258$		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	−0.695108	−	0.718905i	$-0.744644\pi$
$263$	−26.8646	−	7.19835i	−1.65654	−	0.443869i	−0.961434	+	0.275036i	$0.911310\pi$
$264$		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	0.990840	+	0.135043i	$0.0431171\pi$
$269$	10.0436	+	17.3961i	0.612370	+	1.06066i	−0.378470	+	0.925614i	$0.623550\pi$
$270$		0			0
$271$	−0.546081	+	0.945841i	−0.0331721	+	0.0574557i	−0.882135	−	0.470997i	$-0.843894\pi$
$271$	−0.546081	+	0.945841i	−0.0331721	+	0.0574557i	0.848963	+	0.528453i	$0.177228\pi$
$272$	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	0.137510	−	0.990500i	$-0.456090\pi$
$277$	−3.97197	−	1.06429i	−0.238653	−	0.0639468i	−0.376163	+	0.926554i	$0.622757\pi$
$278$	−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	$0.0758900\pi$
$281$			7.91764i			0.472327i	−0.971713	+	0.236163i	$0.924110\pi$
$282$		0			0
$283$	5.53409	−	20.6535i	0.328967	−	1.22772i	−0.581296	−	0.813692i	$-0.697454\pi$
$283$	5.53409	−	20.6535i	0.328967	−	1.22772i	0.910263	−	0.414030i	$-0.135879\pi$
$284$	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	−0.235620	+	0.971845i	$0.575712\pi$
$293$	−20.6685	+	20.6685i	−1.20747	+	1.20747i	−0.971845	+	0.235620i	$0.924288\pi$
$294$		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	−0.939177	−	0.343434i	$-0.888410\pi$
$307$	−10.4383	+	10.4383i	−0.595743	+	0.595743i	0.343434	+	0.939177i	$0.388410\pi$
$308$	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	0.0623969	−	0.998051i	$-0.480126\pi$
$311$	16.8933	−	9.75337i	0.957933	−	0.553063i	0.895536	+	0.444988i	$0.146792\pi$
$312$		0			0
$313$	−14.5869	+	3.90856i	−0.824502	+	0.220925i	−0.646314	−	0.763072i	$-0.723690\pi$
$313$	−14.5869	+	3.90856i	−0.824502	+	0.220925i	−0.178188	+	0.983996i	$0.557024\pi$
$314$	13.2741			0.749099
$315$		0			0
$316$	−62.5642			−3.51951
$317$	15.9783	−	4.28137i	0.897431	−	0.240466i	0.219518	−	0.975608i	$-0.429551\pi$
$317$	15.9783	−	4.28137i	0.897431	−	0.240466i	0.677912	+	0.735143i	$0.262885\pi$
$318$		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	0.217810	+	0.975991i	$0.430109\pi$
$331$	−13.3963	+	23.2031i	−0.736328	+	1.27536i	−0.954138	+	0.299367i	$0.903225\pi$
$332$	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	−0.795657	−	0.605747i	$-0.792874\pi$
$337$	−3.48628	+	3.48628i	−0.189910	+	0.189910i	0.605747	+	0.795657i	$0.292874\pi$
$338$	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	0.564748	+	0.825263i	$0.308973\pi$
$347$	−6.27705	+	23.4263i	−0.336970	+	1.25759i	−0.901718	+	0.432325i	$0.857693\pi$
$348$		0			0
$349$			0.641866i			0.0343583i	0.999852	+	0.0171792i	$0.00546857\pi$
$349$			0.641866i			0.0343583i	−0.999852	+	0.0171792i	$0.994531\pi$
$350$	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	0.208400	−	0.978044i	$-0.433175\pi$
$353$	−1.88152	−	0.504151i	−0.100143	−	0.0268332i	−0.308543	+	0.951211i	$0.599841\pi$
$354$		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	−0.728174	−	0.685392i	$-0.759631\pi$
$359$	4.34803	−	7.53101i	0.229480	−	0.397471i	0.957654	+	0.287921i	$0.0929641\pi$
$360$		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	0.957811	−	0.287397i	$-0.0927900\pi$
$367$	31.4869	+	8.43689i	1.64360	+	0.440402i	0.685790	+	0.727799i	$0.259457\pi$
$368$	−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	0.238170	−	0.971224i	$-0.423453\pi$
$373$	17.9621	−	4.81293i	0.930043	−	0.249204i	0.691873	+	0.722019i	$0.256786\pi$
$374$	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	$-0.902888\pi$
$379$		−	11.6954i		−	0.600752i	0.953821	−	0.300376i	$-0.0971122\pi$
$380$	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	0.887207	−	0.461371i	$-0.152642\pi$
$383$	−2.18840	−	8.16722i	−0.111822	−	0.417326i	−0.999030	+	0.0440451i	$0.985975\pi$
$384$		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	0.996789	+	0.0800731i	$0.0255154\pi$
$389$	11.1976	+	19.3948i	0.567740	+	0.983354i	−0.429049	+	0.903281i	$0.641151\pi$
$390$		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	0.998927	−	0.0463203i	$-0.0147495\pi$
$397$	2.20510	+	8.22953i	0.110671	+	0.413028i	−0.888256	+	0.459349i	$0.848083\pi$
$398$	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	0.199553	−	0.979887i	$-0.436051\pi$
$401$	−10.9993	−	6.35044i	−0.549278	−	0.317126i	−0.748831	+	0.662761i	$0.769384\pi$
$402$		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	−0.944572	−	0.328304i	$-0.893523\pi$
$409$	−22.9042	+	13.2237i	−1.13254	+	0.653871i	−0.187966	+	0.982175i	$0.560190\pi$
$410$	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	−0.805270	−	0.592908i	$-0.797980\pi$
$431$	−14.4168	+	8.32354i	−0.694432	+	0.400931i	0.110838	+	0.993838i	$0.464647\pi$
$432$		0			0
$433$	8.43208	+	8.43208i	0.405220	+	0.405220i	0.880068	−	0.474848i	$-0.157497\pi$
$433$	8.43208	+	8.43208i	0.405220	+	0.405220i	−0.474848	+	0.880068i	$0.657497\pi$
$434$	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	−0.360116	−	0.932907i	$-0.617263\pi$
$439$	−28.2457	−	16.3077i	−1.34810	−	0.778324i	−0.987980	+	0.154584i	$0.950596\pi$
$440$	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	0.998438	+	0.0558717i	$0.0177938\pi$
$443$	3.40342	+	12.7017i	0.161701	+	0.603477i	−0.836737	+	0.547605i	$0.815540\pi$
$444$		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	0.995551	−	0.0942205i	$-0.0300359\pi$
$457$	1.84421	+	6.88267i	0.0862684	+	0.321958i	−0.909283	+	0.416178i	$0.863369\pi$
$458$	−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	$0.182401\pi$
$461$			23.2822i			1.08436i	−0.840262	+	0.542181i	$0.817599\pi$
$462$		0			0
$463$	26.0488	+	26.0488i	1.21059	+	1.21059i	0.970833	+	0.239757i	$0.0770677\pi$
$463$	26.0488	+	26.0488i	1.21059	+	1.21059i	0.239757	+	0.970833i	$0.422932\pi$
$464$	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	−0.0467673	−	0.998906i	$-0.514892\pi$
$467$	8.90737	−	2.38672i	0.412184	−	0.110444i	0.458951	+	0.888461i	$0.348225\pi$
$468$		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	0.581908	−	0.813255i	$-0.302307\pi$
$479$	−9.04651	−	15.6690i	−0.413346	−	0.715936i	−0.995253	+	0.0973193i	$0.968973\pi$
$480$		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	0.205354	−	0.978688i	$-0.434165\pi$
$487$	−2.34247	−	0.627663i	−0.106148	−	0.0284421i	−0.311502	+	0.950246i	$0.600832\pi$
$488$	−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	$-0.888054\pi$
$491$		−	15.2664i		−	0.688965i	0.938793	−	0.344483i	$-0.111946\pi$
$492$		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	0.504293	−	0.863533i	$-0.331753\pi$
$499$	0.192077	+	0.110896i	0.00859855	+	0.00496437i	−0.495695	+	0.868497i	$0.665086\pi$
$500$	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	−0.972007	−	0.234951i	$-0.924507\pi$
$503$	−16.5305	+	16.5305i	−0.737057	+	0.737057i	0.234951	+	0.972007i	$0.424507\pi$
$504$		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	−0.900944	−	0.433935i	$-0.857125\pi$
$509$	−1.68470	+	2.91798i	−0.0746729	+	0.129337i	0.826271	+	0.563273i	$0.190458\pi$
$510$		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	−0.914604	−	0.404351i	$-0.867497\pi$
$521$	−23.3214	+	13.4646i	−1.02173	+	0.589895i	−0.107124	+	0.994246i	$0.534164\pi$
$522$		0			0
$523$	15.0465	−	4.03169i	0.657936	−	0.176294i	0.0856218	−	0.996328i	$-0.472712\pi$
$523$	15.0465	−	4.03169i	0.657936	−	0.176294i	0.572315	+	0.820034i	$0.306046\pi$
$524$	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	−0.944281	−	0.329142i	$-0.893241\pi$
$541$	−4.35172	+	7.53741i	−0.187095	+	0.324059i	0.757185	+	0.653200i	$0.226574\pi$
$542$	−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	−0.879218	−	0.476420i	$-0.841934\pi$
$547$	−9.42064	+	9.42064i	−0.402798	+	0.402798i	0.476420	+	0.879218i	$0.341934\pi$
$548$	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	0.167943	+	0.985797i	$0.446288\pi$
$557$	−11.1018	+	41.4325i	−0.470398	+	1.75555i	−0.638341	+	0.769754i	$0.720379\pi$
$558$		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	0.260521	−	0.965468i	$-0.416106\pi$
$563$	0.0807657	+	0.0216411i	0.00340387	+	0.000912064i	−0.257117	+	0.966380i	$0.582772\pi$
$564$		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	−0.973409	−	0.229074i	$-0.926430\pi$
$569$	−6.87752	+	11.9122i	−0.288321	+	0.499386i	0.685088	+	0.728460i	$0.259764\pi$
$570$		0			0
$571$	11.2197	+	19.4331i	0.469530	+	0.813251i	0.999393	−	0.0348328i	$-0.0110899\pi$
$571$	11.2197	+	19.4331i	0.469530	+	0.813251i	−0.529863	+	0.848083i	$0.677757\pi$
$572$	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	−0.154644	−	0.987970i	$-0.549423\pi$
$577$	−18.7976	−	5.03680i	−0.782554	−	0.209685i	−0.627910	+	0.778286i	$0.716090\pi$
$578$	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	0.947560	−	0.319578i	$-0.103541\pi$
$587$	15.2148	+	15.2148i	0.627982	+	0.627982i	−0.319578	+	0.947560i	$0.603541\pi$
$588$		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	0.925700	+	0.378259i	$0.123477\pi$
$593$	7.62569	+	28.4595i	0.313150	+	1.16869i	−0.612550	+	0.790432i	$0.709856\pi$
$594$		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	−0.932527	−	0.361101i	$-0.882401\pi$
$599$	−19.0653	−	33.0220i	−0.778986	−	1.34924i	0.153541	−	0.988142i	$-0.450932\pi$
$600$		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	0.982077	−	0.188481i	$-0.0603563\pi$
$607$	0.919787	+	3.43269i	0.0373330	+	0.139329i	−0.944744	+	0.327809i	$0.893690\pi$
$608$	−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	0.585869	+	0.810406i	$0.300753\pi$
$613$	−8.08899	+	30.1885i	−0.326711	+	1.21930i	−0.912580	+	0.408897i	$0.865913\pi$
$614$	−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	0.994604	−	0.103747i	$-0.0330831\pi$
$617$	22.1284	+	22.1284i	0.890857	+	0.890857i	−0.103747	+	0.994604i	$0.533083\pi$
$618$		0			0
$619$	39.9430	−	23.0611i	1.60544	−	0.926903i	0.615072	−	0.788471i	$-0.289127\pi$
$619$	39.9430	−	23.0611i	1.60544	−	0.926903i	0.990372	−	0.138433i	$-0.0442064\pi$
$620$	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	−0.914439	−	0.404724i	$-0.867368\pi$
$641$	−25.8536	+	14.9266i	−1.02116	+	0.589566i	−0.106719	+	0.994289i	$0.534034\pi$
$642$		0			0
$643$	−17.3585	−	17.3585i	−0.684554	−	0.684554i	0.276469	−	0.961023i	$-0.410836\pi$
$643$	−17.3585	−	17.3585i	−0.684554	−	0.684554i	−0.961023	+	0.276469i	$0.910836\pi$
$644$	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	−0.959260	−	0.282525i	$-0.908828\pi$
$647$	0.324212	−	1.20998i	0.0127461	−	0.0475691i	0.972006	+	0.234956i	$0.0754946\pi$
$648$		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	0.997858	−	0.0654169i	$-0.0208377\pi$
$653$	2.58041	+	9.63022i	0.100979	+	0.376859i	−0.896879	+	0.442276i	$0.854171\pi$
$654$		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	0.997511	−	0.0705137i	$-0.0224639\pi$
$661$	11.2529	+	19.4907i	0.437689	+	0.758099i	−0.559822	+	0.828613i	$0.689131\pi$
$662$	−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	0.998137	+	0.0610132i	$0.0194332\pi$
$673$	27.4767	+	27.4767i	1.05915	+	1.05915i	0.0610132	+	0.998137i	$0.480567\pi$
$674$	−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	0.0996090	−	0.995027i	$-0.468241\pi$
$677$	17.7812	−	4.76445i	0.683386	−	0.183113i	0.583777	+	0.811914i	$0.301574\pi$
$678$		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	0.798325	−	0.602226i	$-0.205720\pi$
$683$	31.0627	+	8.32323i	1.18858	+	0.318480i	0.390257	+	0.920706i	$0.372386\pi$
$684$		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	−0.726786	−	0.686864i	$-0.758987\pi$
$691$	6.08405	−	10.5379i	0.231448	−	0.400880i	0.958235	+	0.285984i	$0.0923203\pi$
$692$	−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	$-0.803065\pi$
$701$		−	30.7110i		−	1.15994i	0.814639	−	0.579969i	$-0.196935\pi$
$702$		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	0.404688	−	0.914455i	$-0.367380\pi$
$709$	−4.92357	−	2.84263i	−0.184909	−	0.106757i	−0.589597	+	0.807698i	$0.700713\pi$
$710$	−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	−0.931866	−	0.362802i	$-0.881820\pi$
$719$	−4.06871	+	7.04721i	−0.151737	+	0.262817i	0.780129	+	0.625619i	$0.215153\pi$
$720$		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	0.558666	−	0.829392i	$-0.311313\pi$
$727$	37.4261	−	37.4261i	1.38806	−	1.38806i	0.829392	−	0.558666i	$-0.188687\pi$
$728$	−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	−0.914817	−	0.403868i	$-0.867666\pi$
$733$	−40.7501	+	10.9190i	−1.50514	+	0.403301i	−0.590321	+	0.807168i	$0.700999\pi$
$734$	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	−0.564351	+	0.825535i	$0.690873\pi$
$739$	−42.4476	+	24.5071i	−1.56146	+	0.901510i	−0.997110	+	0.0759743i	$0.975793\pi$
$740$	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	0.0554047	−	0.998464i	$-0.482355\pi$
$743$	28.7264	−	28.7264i	1.05387	−	1.05387i	0.998464	−	0.0554047i	$-0.0176449\pi$
$744$		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	−0.776939	−	0.629575i	$-0.783229\pi$
$751$	4.29587	−	7.44067i	0.156759	−	0.271514i	0.933698	+	0.358061i	$0.116562\pi$
$752$	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	−0.670842	−	0.741600i	$-0.734067\pi$
$757$	1.94682	−	1.94682i	0.0707583	−	0.0707583i	0.741600	+	0.670842i	$0.234067\pi$
$758$	−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	0.779981	−	0.625803i	$-0.215229\pi$
$761$	17.3244	+	10.0023i	0.628011	+	0.362582i	−0.151971	+	0.988385i	$0.548562\pi$
$762$		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	$-0.805871\pi$
$769$		−	31.7665i		−	1.14553i	0.819720	−	0.572764i	$-0.194129\pi$
$770$	−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	−0.301768	−	0.953382i	$-0.597577\pi$
$773$	−28.9093	−	7.74623i	−1.03980	−	0.278613i	−0.738029	+	0.674769i	$0.764243\pi$
$774$		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	0.211919	−	0.977287i	$-0.432029\pi$
$787$	−2.61451	−	0.700556i	−0.0931973	−	0.0249721i	−0.305116	+	0.952315i	$0.598695\pi$
$788$	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	0.962564	−	0.271056i	$-0.0873728\pi$
$797$	19.5221	+	19.5221i	0.691508	+	0.691508i	−0.271056	+	0.962564i	$0.587373\pi$
$798$		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	0.912931	−	0.408113i	$-0.133813\pi$
$809$	2.93046	+	5.07571i	0.103030	+	0.178452i	−0.809902	+	0.586565i	$0.800480\pi$
$810$		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	−0.308439	−	0.951244i	$-0.599806\pi$
$821$	−36.8611	−	21.2817i	−1.28646	−	0.742738i	−0.978021	+	0.208507i	$0.933140\pi$
$822$		0			0
$823$	−8.56545	+	31.9667i	−0.298573	+	1.11429i	0.639765	+	0.768570i	$0.279032\pi$
$823$	−8.56545	+	31.9667i	−0.298573	+	1.11429i	−0.938338	+	0.345719i	$0.887635\pi$
$824$	−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	0.829337	−	0.558749i	$-0.188719\pi$
$827$	7.78145	+	7.78145i	0.270587	+	0.270587i	−0.558749	+	0.829337i	$0.688719\pi$
$828$		0			0
$829$	−32.4643	+	18.7432i	−1.12753	+	0.650980i	−0.943313	−	0.331906i	$-0.892308\pi$
$829$	−32.4643	+	18.7432i	−1.12753	+	0.650980i	−0.184218	+	0.982885i	$0.558975\pi$
$830$	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	0.809848	−	0.586639i	$-0.199549\pi$
$853$	6.51907	+	6.51907i	0.223209	+	0.223209i	−0.586639	+	0.809848i	$0.699549\pi$
$854$	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	−0.686899	−	0.726752i	$-0.741029\pi$
$857$	7.94363	−	29.6460i	0.271349	−	1.01269i	0.958249	−	0.285936i	$-0.0923046\pi$
$858$		0			0
$859$	30.5614	+	17.6447i	1.04274	+	0.602028i	0.920609	−	0.390486i	$-0.127693\pi$
$859$	30.5614	+	17.6447i	1.04274	+	0.602028i	0.122134	+	0.992514i	$0.461026\pi$
$860$	−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	−0.682136	−	0.731225i	$-0.738949\pi$
$863$	−13.4253	−	50.1038i	−0.457002	−	1.70555i	0.225134	−	0.974328i	$-0.427718\pi$
$864$		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	0.995668	+	0.0929832i	$0.0296403\pi$
$877$	5.32717	+	19.8813i	0.179886	+	0.671343i	−0.815782	+	0.578360i	$0.803693\pi$
$878$	−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	$-0.899577\pi$
$881$		−	18.4194i		−	0.620564i	0.950645	−	0.310282i	$-0.100423\pi$
$882$		0			0
$883$	−14.6058	−	14.6058i	−0.491526	−	0.491526i	0.417261	−	0.908787i	$-0.362990\pi$
$883$	−14.6058	−	14.6058i	−0.491526	−	0.491526i	−0.908787	+	0.417261i	$0.862990\pi$
$884$	−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	−0.495523	−	0.868595i	$-0.665024\pi$
$887$	−14.6042	+	3.91318i	−0.490361	+	0.131392i	0.00516191	+	0.999987i	$0.498357\pi$
$888$		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	−0.291104	−	0.956691i	$-0.594023\pi$
$907$	−30.7656	−	8.24361i	−1.02155	−	0.273725i	−0.730449	+	0.682967i	$0.760689\pi$
$908$	−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	$-0.735720\pi$
$911$		−	44.5563i		−	1.47621i	0.674683	−	0.738107i	$-0.264280\pi$
$912$		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	0.896994	−	0.442043i	$-0.145746\pi$
$919$	29.1834	+	16.8490i	0.962671	+	0.555798i	0.0656768	+	0.997841i	$0.479079\pi$
$920$	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	−0.682924	−	0.730489i	$-0.739292\pi$
$929$	8.87442	−	15.3710i	0.291160	−	0.504305i	0.974084	+	0.226185i	$0.0726253\pi$
$930$		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	−0.999894	−	0.0145268i	$-0.995376\pi$
$937$	−30.1626	+	30.1626i	−0.985368	+	0.985368i	0.0145268	+	0.999894i	$0.495376\pi$
$938$	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	0.0555241	−	0.998457i	$-0.482317\pi$
$941$	29.0798	−	16.7893i	0.947976	−	0.547314i	0.892451	+	0.451143i	$0.148984\pi$
$942$		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	0.238283	−	0.971196i	$-0.423415\pi$
$947$	28.6266	−	7.67048i	0.930240	−	0.249257i	0.691957	+	0.721939i	$0.256749\pi$
$948$		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	−0.396202	−	0.918163i	$-0.629672\pi$
$953$	16.1133	−	16.1133i	0.521961	−	0.521961i	0.918163	+	0.396202i	$0.129672\pi$
$954$		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	0.0626698	−	0.998034i	$-0.480039\pi$
$967$	32.9843	−	32.9843i	1.06070	−	1.06070i	0.998034	−	0.0626698i	$-0.0199615\pi$
$968$	−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	0.928820	−	0.370531i	$-0.120824\pi$
$971$	33.4151	+	19.2922i	1.07234	+	0.619117i	0.143521	+	0.989647i	$0.454158\pi$
$972$		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	−0.975037	−	0.222041i	$-0.928728\pi$
$977$	−0.612947	+	2.28755i	−0.0196099	+	0.0731852i	0.955428	+	0.295226i	$0.0953949\pi$
$978$		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	−0.208727	−	0.977974i	$-0.566932\pi$
$983$	−27.5427	−	7.38005i	−0.878476	−	0.235387i	−0.669750	+	0.742587i	$0.733599\pi$
$984$		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	0.690506	−	0.723327i	$-0.257388\pi$
$991$	−8.85117	−	15.3307i	−0.281167	−	0.486995i	−0.971672	+	0.236332i	$0.924055\pi$
$992$	−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	−0.672704	−	0.739912i	$-0.734867\pi$
$997$	−51.3174	−	13.7505i	−1.62524	−	0.435481i	−0.952535	+	0.304431i	$0.901534\pi$
$998$	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.863.31	yes	128
3.2	odd	2	inner	945.2.ch.a.863.2	yes	128
5.2	odd	4	inner	945.2.ch.a.107.31	yes	128
7.4	even	3	inner	945.2.ch.a.53.2	✓	128
15.2	even	4	inner	945.2.ch.a.107.2	yes	128
21.11	odd	6	inner	945.2.ch.a.53.31	yes	128
35.32	odd	12	inner	945.2.ch.a.242.2	yes	128
105.32	even	12	inner	945.2.ch.a.242.31	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
945.2.ch.a.53.2	✓	128	7.4	even	3	inner
945.2.ch.a.53.31	yes	128	21.11	odd	6	inner
945.2.ch.a.107.2	yes	128	15.2	even	4	inner
945.2.ch.a.107.31	yes	128	5.2	odd	4	inner
945.2.ch.a.242.2	yes	128	35.32	odd	12	inner
945.2.ch.a.242.31	yes	128	105.32	even	12	inner
945.2.ch.a.863.2	yes	128	3.2	odd	2	inner
945.2.ch.a.863.31	yes	128	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:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
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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