LMFDB - Embedded newform 945.2.ch.a.107.2

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			107.2
Character	$\chi$	$=$	945.107
Dual form			945.2.ch.a.53.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.650762 - 2.42868i) q^{2} +(-3.74293 + 2.16098i) q^{4} +(-1.11718 + 1.93699i) q^{5} +(-2.56343 - 0.654856i) q^{7} +(4.12826 + 4.12826i) q^{8} +O(q^{10})$	\(q+(-0.650762 - 2.42868i) q^{2} +(-3.74293 + 2.16098i) q^{4} +(-1.11718 + 1.93699i) q^{5} +(-2.56343 - 0.654856i) q^{7} +(4.12826 + 4.12826i) q^{8} +(5.43133 + 1.45275i) q^{10} +(-4.33235 + 2.50128i) q^{11} +(4.46310 - 4.46310i) q^{13} +(0.0777484 + 6.65190i) q^{14} +(3.01772 - 5.22685i) q^{16} +(0.985130 + 0.263965i) q^{17} +(5.51117 + 3.18187i) q^{19} +(-0.00427246 - 9.66421i) q^{20} +(8.89413 + 8.89413i) q^{22} +(0.265791 - 0.0712184i) q^{23} +(-2.50383 - 4.32791i) q^{25} +(-13.7438 - 7.93501i) q^{26} +(11.0099 - 3.08844i) q^{28} +4.05409 q^{29} +(-2.12640 - 3.68302i) q^{31} +(-3.37955 - 0.905549i) q^{32} -2.56434i q^{34} +(4.13225 - 4.23373i) q^{35} +(1.30258 - 0.349026i) q^{37} +(4.14129 - 15.4555i) q^{38} +(-12.6084 + 3.38438i) q^{40} +2.13805i q^{41} +(1.22969 - 1.22969i) q^{43} +(10.8104 - 18.7242i) q^{44} +(-0.345933 - 0.599174i) q^{46} +(-2.02246 - 7.54793i) q^{47} +(6.14233 + 3.35735i) q^{49} +(-8.88171 + 8.89743i) q^{50} +(-7.06040 + 26.3498i) q^{52} +(-0.0108921 + 0.0406498i) q^{53} +(-0.00494526 - 11.1861i) q^{55} +(-7.87908 - 13.2859i) q^{56} +(-2.63825 - 9.84608i) q^{58} +(-5.17288 - 8.95970i) q^{59} +(1.02281 - 1.77155i) q^{61} +(-7.56110 + 7.56110i) q^{62} -3.27376i q^{64} +(3.65888 + 13.6310i) q^{65} +(3.66938 - 13.6943i) q^{67} +(-4.25770 + 1.14085i) q^{68} +(-12.9715 - 7.28075i) q^{70} -5.23525i q^{71} +(10.0585 + 2.69518i) q^{73} +(-1.69534 - 2.93642i) q^{74} -27.5039 q^{76} +(12.7436 - 3.57479i) q^{77} +(12.5365 + 7.23793i) q^{79} +(6.75300 + 11.6846i) q^{80} +(5.19263 - 1.39136i) q^{82} +(9.98593 + 9.98593i) q^{83} +(-1.61186 + 1.61329i) q^{85} +(-3.78676 - 2.18628i) q^{86} +(-28.2110 - 7.55911i) q^{88} +(-2.39266 + 4.14421i) q^{89} +(-14.3635 + 8.51815i) q^{91} +(-0.840935 + 0.840935i) q^{92} +(-17.0154 + 9.82382i) q^{94} +(-12.3202 + 7.12033i) q^{95} +(0.238144 + 0.238144i) q^{97} +(4.15673 - 17.1026i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.650762	−	2.42868i	−0.460158	−	1.71733i	−0.672463	−	0.740131i	$-0.734764\pi$
$2$	−0.650762	−	2.42868i	−0.460158	−	1.71733i	0.212305	−	0.977204i	$-0.431903\pi$
$3$		0			0
$3$		0			0
$4$	−3.74293	+	2.16098i	−1.87147	+	1.08049i
$5$	−1.11718	+	1.93699i	−0.499617	+	0.866246i
$5$	−1.11718	+	1.93699i	−0.499617	+	0.866246i
$6$		0			0
$7$	−2.56343	−	0.654856i	−0.968885	−	0.247512i
$7$	−2.56343	−	0.654856i	−0.968885	−	0.247512i
$8$	4.12826	+	4.12826i	1.45956	+	1.45956i
$9$		0			0
$10$	5.43133	+	1.45275i	1.71754	+	0.459399i
$11$	−4.33235	+	2.50128i	−1.30625	+	0.754165i	−0.981468	−	0.191624i	$-0.938625\pi$
$11$	−4.33235	+	2.50128i	−1.30625	+	0.754165i	−0.324783	+	0.945789i	$0.605291\pi$
$12$		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
$17$	0.985130	+	0.263965i	0.238929	+	0.0640209i	0.376296	−	0.926499i	$-0.377197\pi$
$17$	0.985130	+	0.263965i	0.238929	+	0.0640209i	−0.137367	+	0.990520i	$0.543864\pi$
$18$		0			0
$19$	5.51117	+	3.18187i	1.26435	+	0.729972i	0.973913	−	0.226922i	$-0.0728664\pi$
$19$	5.51117	+	3.18187i	1.26435	+	0.729972i	0.290436	+	0.956894i	$0.406200\pi$
$20$	−0.00427246	−	9.66421i	−0.000955351	−	2.16098i
$21$		0			0
$22$	8.89413	+	8.89413i	1.89624	+	1.89624i
$23$	0.265791	−	0.0712184i	0.0554212	−	0.0148501i	−0.231002	−	0.972953i	$-0.574200\pi$
$23$	0.265791	−	0.0712184i	0.0554212	−	0.0148501i	0.286423	+	0.958103i	$0.407534\pi$
$24$		0			0
$25$	−2.50383	−	4.32791i	−0.500766	−	0.865583i
$26$	−13.7438	−	7.93501i	−2.69539	−	1.55618i
$27$		0			0
$28$	11.0099	−	3.08844i	2.08067	−	0.583661i
$29$	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	$0.958068\pi$
$32$	−3.37955	−	0.905549i	−0.597426	−	0.160080i
$33$		0			0
$34$		−	2.56434i		−	0.439781i
$35$	4.13225	−	4.23373i	0.698478	−	0.715632i
$36$		0			0
$37$	1.30258	−	0.349026i	0.214143	−	0.0573795i	−0.150153	−	0.988663i	$-0.547976\pi$
$37$	1.30258	−	0.349026i	0.214143	−	0.0573795i	0.364296	+	0.931283i	$0.381310\pi$
$38$	4.14129	−	15.4555i	0.671805	−	2.50721i
$39$		0			0
$40$	−12.6084	+	3.38438i	−1.99356	+	0.535117i
$41$			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
$47$	−2.02246	−	7.54793i	−0.295007	−	1.10098i	−0.941212	−	0.337816i	$-0.890312\pi$
$47$	−2.02246	−	7.54793i	−0.295007	−	1.10098i	0.646206	−	0.763163i	$-0.276355\pi$
$48$		0			0
$49$	6.14233	+	3.35735i	0.877475	+	0.479622i
$50$	−8.88171	+	8.89743i	−1.25606	+	1.25829i
$51$		0			0
$52$	−7.06040	+	26.3498i	−0.979101	+	3.65405i
$53$	−0.0108921	+	0.0406498i	−0.00149614	+	0.00558367i	−0.966670	−	0.256026i	$-0.917587\pi$
$53$	−0.0108921	+	0.0406498i	−0.00149614	+	0.00558367i	0.965174	+	0.261610i	$0.0842534\pi$
$54$		0			0
$55$	−0.00494526	−	11.1861i	−0.000666819	−	1.50833i
$56$	−7.87908	−	13.2859i	−1.05289	−	1.77540i
$57$		0			0
$58$	−2.63825	−	9.84608i	−0.346419	−	1.29285i
$59$	−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
$65$	3.65888	+	13.6310i	0.453829	+	1.69072i
$66$		0			0
$67$	3.66938	−	13.6943i	0.448286	−	1.67303i	−0.258824	−	0.965924i	$-0.583335\pi$
$67$	3.66938	−	13.6943i	0.448286	−	1.67303i	0.707111	−	0.707103i	$-0.249998\pi$
$68$	−4.25770	+	1.14085i	−0.516322	+	0.138348i
$69$		0			0
$70$	−12.9715	−	7.28075i	−1.55039	−	0.870216i
$71$		−	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
$73$	10.0585	+	2.69518i	1.17726	+	0.315447i	0.793841	−	0.608126i	$-0.208078\pi$
$73$	10.0585	+	2.69518i	1.17726	+	0.315447i	0.383423	+	0.923573i	$0.374745\pi$
$74$	−1.69534	−	2.93642i	−0.197079	−	0.341352i
$75$		0			0
$76$	−27.5039			−3.15491
$77$	12.7436	−	3.57479i	1.45227	−	0.407385i
$78$		0			0
$79$	12.5365	+	7.23793i	1.41046	+	0.814331i	0.995432	−	0.0954764i	$-0.0304374\pi$
$79$	12.5365	+	7.23793i	1.41046	+	0.814331i	0.415031	+	0.909807i	$0.363771\pi$
$80$	6.75300	+	11.6846i	0.755009	+	1.30638i
$81$		0			0
$82$	5.19263	−	1.39136i	0.573430	−	0.153650i
$83$	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
$88$	−28.2110	−	7.55911i	−3.00730	−	0.805803i
$89$	−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
$95$	−12.3202	+	7.12033i	−1.26403	+	0.730531i
$96$		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	$0.744557\pi$
$98$	4.15673	−	17.1026i	0.419893	−	1.72762i
$99$		0			0
$100$	18.7242	+	10.7884i	1.87242	+	1.07884i
$101$	9.68543	−	5.59189i	0.963736	−	0.556413i	0.0664154	−	0.997792i	$-0.478844\pi$
$101$	9.68543	−	5.59189i	0.963736	−	0.556413i	0.897321	+	0.441379i	$0.145510\pi$
$102$		0			0
$103$	2.73780	+	10.2176i	0.269763	+	1.00677i	0.959270	+	0.282490i	$0.0911605\pi$
$103$	2.73780	+	10.2176i	0.269763	+	1.00677i	−0.689507	+	0.724279i	$0.742173\pi$
$104$	36.8496			3.61340
$105$		0			0
$106$	0.105813			0.0102775
$107$	3.59435	+	13.4143i	0.347479	+	1.29681i	0.889690	+	0.456565i	$0.150921\pi$
$107$	3.59435	+	13.4143i	0.347479	+	1.29681i	−0.542211	+	0.840242i	$0.682413\pi$
$108$		0			0
$109$	−3.36589	+	1.94330i	−0.322394	+	0.186134i	−0.652459	−	0.757824i	$-0.726263\pi$
$109$	−3.36589	+	1.94330i	−0.322394	+	0.186134i	0.330065	+	0.943958i	$0.392929\pi$
$110$	−27.1641	+	7.29148i	−2.59000	+	0.695215i
$111$		0			0
$112$	−11.1586	+	11.4225i	−1.05438	+	1.07932i
$113$	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
$115$	−0.158986	+	0.594397i	−0.0148256	+	0.0554278i
$116$	−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
$122$	−4.96813	−	1.33121i	−0.449794	−	0.120522i
$123$		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	$0.797231\pi$
$128$	−14.7100	+	3.94153i	−1.30019	+	0.348386i
$129$		0			0
$130$	30.7243	−	17.7568i	2.69470	−	1.55738i
$131$	−4.13205	−	2.38564i	−0.361019	−	0.208435i	0.308509	−	0.951222i	$-0.400170\pi$
$131$	−4.13205	−	2.38564i	−0.361019	−	0.208435i	−0.669528	+	0.742787i	$0.733503\pi$
$132$		0			0
$133$	−12.0438	−	11.7655i	−1.04433	−	1.02020i
$134$	−35.6470			−3.07943
$135$		0			0
$136$	2.97716	+	5.15658i	0.255289	+	0.442173i
$137$	0.751559	+	0.201380i	0.0642100	+	0.0172050i	0.290781	−	0.956790i	$-0.406085\pi$
$137$	0.751559	+	0.201380i	0.0642100	+	0.0172050i	−0.226571	+	0.973995i	$0.572752\pi$
$138$		0			0
$139$			1.14654i			0.0972483i	0.998817	+	0.0486241i	$0.0154837\pi$
$139$			1.14654i			0.0972483i	−0.998817	+	0.0486241i	$0.984516\pi$
$140$	−6.31771	+	24.7763i	−0.533944	+	2.09398i
$141$		0			0
$142$	−12.7147	+	3.40691i	−1.06700	+	0.285901i
$143$	−8.17223	+	30.4992i	−0.683396	+	2.55047i
$144$		0			0
$145$	−4.52914	+	7.85272i	−0.376125	+	0.652133i
$146$		−	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	$0.659535\pi$
$152$	9.61592	+	35.8871i	0.779954	+	2.91083i
$153$		0			0
$154$	−16.9751	−	28.6238i	−1.36789	−	2.30657i
$155$	9.50953	−	0.00420408i	0.763824	−	0.000337680i
$156$		0			0
$157$	−1.36639	+	5.09943i	−0.109050	+	0.406979i	−0.998773	−	0.0495210i	$-0.984231\pi$
$157$	−1.36639	+	5.09943i	−0.109050	+	0.406979i	0.889723	+	0.456500i	$0.150897\pi$
$158$	9.42034	−	35.1572i	0.749442	−	2.79696i
$159$		0			0
$160$	5.52960	−	5.53449i	0.437153	−	0.437540i
$161$	−0.727973	+	0.00850867i	−0.0573723	+	0.000670577i
$162$		0			0
$163$	−2.18961	−	8.17175i	−0.171504	−	0.640061i	−0.997121	−	0.0758299i	$-0.975839\pi$
$163$	−2.18961	−	8.17175i	−0.171504	−	0.640061i	0.825617	−	0.564231i	$-0.190827\pi$
$164$	−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
$170$	4.96709	+	2.86483i	0.380959	+	0.219722i
$171$		0			0
$172$	−1.94531	+	7.25998i	−0.148328	+	0.553569i
$173$	15.4098	−	4.12905i	1.17159	−	0.313926i	0.380003	−	0.924985i	$-0.375923\pi$
$173$	15.4098	−	4.12905i	1.17159	−	0.313926i	0.791585	+	0.611060i	$0.209256\pi$
$174$		0			0
$175$	3.58422	+	12.7339i	0.270942	+	0.962596i
$176$			30.1927i			2.27586i
$177$		0			0
$178$	11.6220	+	3.11411i	0.871106	+	0.233412i
$179$	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	$0.615519\pi$
$182$	30.0351	+	29.3411i	2.22635	+	2.17491i
$183$		0			0
$184$	1.39126	+	0.803244i	0.102565	+	0.0592160i
$185$	−0.779157	+	2.91300i	−0.0572848	+	0.214168i
$186$		0			0
$187$	−4.92818	+	1.32050i	−0.360384	+	0.0965646i
$188$	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	$-0.585169\pi$
$191$	−17.0237	−	9.82861i	−1.23179	−	0.711173i	−0.967403	+	0.253243i	$0.918503\pi$
$192$		0			0
$193$	5.35533	+	1.43496i	0.385485	+	0.103290i	0.446356	−	0.894855i	$-0.352721\pi$
$193$	5.35533	+	1.43496i	0.385485	+	0.103290i	−0.0608716	+	0.998146i	$0.519388\pi$
$194$	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	$-0.759144\pi$
$199$	−6.99916	+	4.04097i	−0.496157	+	0.286457i	0.230968	+	0.972961i	$0.425811\pi$
$200$	7.53030	−	28.2032i	0.532473	−	1.99427i
$201$		0			0
$202$	−19.8838	−	19.8838i	−1.39902	−	1.39902i
$203$	−10.3924	−	2.65485i	−0.729402	−	0.186334i
$204$		0			0
$205$	−4.14137	−	2.38858i	−0.289246	−	0.166826i
$206$	23.0336	−	13.2984i	1.60483	−	0.926546i
$207$		0			0
$208$	−9.85956	−	36.7964i	−0.683637	−	2.55137i
$209$	−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	$0.346308\pi$
$212$	−0.0470751	−	0.175687i	−0.00323313	−	0.0120662i
$213$		0			0
$214$	30.2399	−	17.4590i	2.06716	−	1.19347i
$215$	1.00811	+	3.75567i	0.0687525	+	0.256135i
$216$		0			0
$217$	3.03901	+	10.8337i	0.206302	+	0.735436i
$218$	6.91003	+	6.91003i	0.468006	+	0.468006i
$219$		0			0
$220$	24.1914	+	41.8580i	1.63098	+	2.82207i
$221$	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
$227$	−18.8697	−	5.05613i	−1.25243	−	0.335587i	−0.429155	−	0.903231i	$-0.641189\pi$
$227$	−18.8697	−	5.05613i	−1.25243	−	0.335587i	−0.823274	+	0.567644i	$0.807855\pi$
$228$		0			0
$229$	6.00222	+	3.46538i	0.396638	+	0.228999i	0.685032	−	0.728513i	$-0.259788\pi$
$229$	6.00222	+	3.46538i	0.396638	+	0.228999i	−0.288394	+	0.957512i	$0.593121\pi$
$230$	1.54706		0.000683942i	0.102010		4.50978e-5i
$231$		0			0
$232$	16.7363	+	16.7363i	1.09879	+	1.09879i
$233$	20.5702	−	5.51176i	1.34760	−	0.361088i	0.488350	−	0.872648i	$-0.337599\pi$
$233$	20.5702	−	5.51176i	1.34760	−	0.361088i	0.859247	+	0.511560i	$0.170932\pi$
$234$		0			0
$235$	16.8797	+	4.51490i	1.10111	+	0.294520i
$236$	38.7235	+	22.3570i	2.52069	+	1.45532i
$237$		0			0
$238$	−1.67927	+	6.57351i	−0.108851	+	0.426097i
$239$	−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	$0.842328\pi$
$242$	−34.0637	−	9.12735i	−2.18970	−	0.586728i
$243$		0			0
$244$			8.84107i			0.565991i
$245$	−13.3652	+	8.14684i	−0.853872	+	0.520483i
$246$		0			0
$247$	38.7979	−	10.3959i	2.46865	−	0.661473i
$248$	6.42617	−	23.9828i	0.408062	−	1.52291i
$249$		0			0
$250$	−7.31175	−	27.1438i	−0.462436	−	1.71672i
$251$		−	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
$257$	−0.682377	−	2.54666i	−0.0425655	−	0.158857i	0.941372	−	0.337371i	$-0.109538\pi$
$257$	−0.682377	−	2.54666i	−0.0425655	−	0.158857i	−0.983937	+	0.178514i	$0.942871\pi$
$258$		0			0
$259$	−3.56763	+	0.0416991i	−0.221682	+	0.00259106i
$260$	−43.1514	−	43.1132i	−2.67614	−	2.67377i
$261$		0			0
$262$	−3.10497	+	11.5879i	−0.191826	+	0.715903i
$263$	7.19835	−	26.8646i	0.443869	−	1.65654i	−0.275036	−	0.961434i	$-0.588690\pi$
$263$	7.19835	−	26.8646i	0.443869	−	1.65654i	0.718905	−	0.695108i	$-0.244644\pi$
$264$		0			0
$265$	−0.0665696	−	0.0665108i	−0.00408934	−	0.00408573i
$266$	−20.7370	+	36.9071i	−1.27147	+	2.26292i
$267$		0			0
$268$	15.8589	+	59.1864i	0.968739	+	3.61538i
$269$	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
$275$	21.6728	+	12.4872i	1.30692	+	0.753009i
$276$		0			0
$277$	1.06429	−	3.97197i	0.0639468	−	0.238653i	−0.926554	−	0.376163i	$-0.877243\pi$
$277$	1.06429	−	3.97197i	0.0639468	−	0.238653i	0.990500	+	0.137510i	$0.0439100\pi$
$278$	2.78458	−	0.746125i	0.167008	−	0.0447496i
$279$		0			0
$280$	34.5369	−	0.418944i	2.06398	−	0.0250367i
$281$		−	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
$283$	−20.6535	−	5.53409i	−1.22772	−	0.328967i	−0.414030	−	0.910263i	$-0.635879\pi$
$283$	−20.6535	−	5.53409i	−1.22772	−	0.328967i	−0.813692	+	0.581296i	$0.802546\pi$
$284$	11.3133	+	19.5952i	0.671320	+	1.16276i
$285$		0			0
$286$	79.3908			4.69448
$287$	1.40011	−	5.48073i	0.0826460	−	0.323517i
$288$		0			0
$289$	−13.8216	−	7.97992i	−0.813037	−	0.469407i
$290$	22.0191	+	5.88957i	1.29301	+	0.345848i
$291$		0			0
$292$	−43.4727	+	11.6485i	−2.54405	+	0.681675i
$293$	−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
$298$	−44.8492	−	12.0173i	−2.59804	−	0.696144i
$299$	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
$305$	2.28882	+	3.96030i	0.131057	+	0.226766i
$306$		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	$0.888410\pi$
$308$	−39.9735	+	40.9190i	−2.27770	+	2.33158i
$309$		0			0
$310$	−6.19865	−	23.0928i	−0.352060	−	1.31159i
$311$	−16.8933	+	9.75337i	−0.957933	+	0.553063i	−0.895536	−	0.444988i	$-0.853208\pi$
$311$	−16.8933	+	9.75337i	−0.957933	+	0.553063i	−0.0623969	+	0.998051i	$0.519874\pi$
$312$		0			0
$313$	3.90856	+	14.5869i	0.220925	+	0.824502i	0.983996	+	0.178188i	$0.0570236\pi$
$313$	3.90856	+	14.5869i	0.220925	+	0.824502i	−0.763072	+	0.646314i	$0.776310\pi$
$314$	13.2741			0.749099
$315$		0			0
$316$	−62.5642			−3.51951
$317$	−4.28137	−	15.9783i	−0.240466	−	0.897431i	−0.975608	−	0.219518i	$-0.929551\pi$
$317$	−4.28137	−	15.9783i	−0.240466	−	0.897431i	0.735143	−	0.677912i	$-0.237115\pi$
$318$		0			0
$319$	−17.5637	+	10.1404i	−0.983380	+	0.567755i
$320$	6.34122	+	3.65737i	0.354485	+	0.204453i
$321$		0			0
$322$	0.494402	+	1.76248i	0.0275520	+	0.0982189i
$323$	4.58931	+	4.58931i	0.255356	+	0.255356i
$324$		0			0
$325$	−30.4907	−	8.14108i	−1.69132	−	0.451586i
$326$	−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	$0.903225\pi$
$332$	−58.9560	−	15.7972i	−3.23563	−	0.866985i
$333$		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	$0.792874\pi$
$338$	−65.1821	+	17.4655i	−3.54544	+	0.949998i
$339$		0			0
$340$	2.54680	−	9.52163i	0.138120	−	0.516383i
$341$	18.4246	+	10.6374i	0.997746	+	0.576049i
$342$		0			0
$343$	−13.5468	−	12.6287i	−0.731460	−	0.681884i
$344$	10.1530			0.547410
$345$		0			0
$346$	−20.0563	−	34.7385i	−1.07823	−	1.86755i
$347$	23.4263	+	6.27705i	1.25759	+	0.336970i	0.825263	−	0.564748i	$-0.191027\pi$
$347$	23.4263	+	6.27705i	1.25759	+	0.336970i	0.432325	+	0.901718i	$0.357693\pi$
$348$		0			0
$349$		−	0.641866i		−	0.0343583i	−0.999852	−	0.0171792i	$-0.994531\pi$
$349$		−	0.641866i		−	0.0343583i	0.999852	−	0.0171792i	$-0.00546857\pi$
$350$	28.5942	−	16.9917i	1.52842	−	0.908244i
$351$		0			0
$352$	16.9064	−	4.53006i	0.901116	−	0.241453i
$353$	0.504151	−	1.88152i	0.0268332	−	0.100143i	−0.951211	−	0.308543i	$-0.900159\pi$
$353$	0.504151	−	1.88152i	0.0268332	−	0.100143i	0.978044	+	0.208400i	$0.0668254\pi$
$354$		0			0
$355$	10.1406	+	5.84871i	0.538208	+	0.310417i
$356$		−	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
$362$	6.21611	+	23.1988i	0.326711	+	1.21930i
$363$		0			0
$364$	35.3541	−	62.9222i	1.85306	−	3.29802i
$365$	−16.4577	+	16.4723i	−0.861436	+	0.862198i
$366$		0			0
$367$	−8.43689	+	31.4869i	−0.440402	+	1.64360i	0.287397	+	0.957811i	$0.407210\pi$
$367$	−8.43689	+	31.4869i	−0.440402	+	1.64360i	−0.727799	+	0.685790i	$0.759457\pi$
$368$	0.429835	−	1.60417i	0.0224067	−	0.0836230i
$369$		0			0
$370$	7.58179	−	0.00335185i	0.394159	−	0.000174254i
$371$	0.0545408	−	0.0970700i	0.00283162	−	0.00503962i
$372$		0			0
$373$	−4.81293	−	17.9621i	−0.249204	−	0.930043i	−0.971224	−	0.238170i	$-0.923453\pi$
$373$	−4.81293	−	17.9621i	−0.249204	−	0.930043i	0.722019	−	0.691873i	$-0.243214\pi$
$374$	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	$0.902888\pi$
$380$	30.7267	−	53.2747i	1.57625	−	2.73293i
$381$		0			0
$382$	−12.7922	+	47.7411i	−0.654505	+	2.44264i
$383$	8.16722	−	2.18840i	0.417326	−	0.111822i	−0.0440451	−	0.999030i	$-0.514025\pi$
$383$	8.16722	−	2.18840i	0.417326	−	0.111822i	0.461371	+	0.887207i	$0.347358\pi$
$384$		0			0
$385$	−7.31259	+	28.6779i	−0.372684	+	1.46156i
$386$		−	13.9402i		−	0.709536i
$387$		0			0
$388$	−1.40598	−	0.376731i	−0.0713778	−	0.0191256i
$389$	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
$392$	11.4971	+	39.2171i	0.580691	+	1.98076i
$393$		0			0
$394$	−23.6808	−	13.6721i	−1.19302	−	0.688790i
$395$	−28.0252	+	16.1969i	−1.41010	+	0.814954i
$396$		0			0
$397$	−8.22953	+	2.20510i	−0.413028	+	0.110671i	−0.459349	−	0.888256i	$-0.651917\pi$
$397$	−8.22953	+	2.20510i	−0.413028	+	0.110671i	0.0463203	+	0.998927i	$0.485251\pi$
$398$	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	$-0.230616\pi$
$401$	10.9993	+	6.35044i	0.549278	+	0.317126i	−0.199553	+	0.979887i	$0.563949\pi$
$402$		0			0
$403$	−25.9280	−	6.94739i	−1.29157	−	0.346074i
$404$	−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	$-0.439810\pi$
$409$	22.9042	−	13.2237i	1.13254	−	0.653871i	0.944572	+	0.328304i	$0.106477\pi$
$410$	−3.10604	+	11.6124i	−0.153396	+	0.573498i
$411$		0			0
$412$	−32.3274	−	32.3274i	−1.59266	−	1.59266i
$413$	7.39301	+	26.3550i	0.363786	+	1.29685i
$414$		0			0
$415$	−30.4987	+	8.18654i	−1.49712	+	0.401862i
$416$	−19.1248	+	11.0417i	−0.937672	+	0.541365i
$417$		0			0
$418$	20.7170	+	77.3171i	1.01330	+	3.78170i
$419$	−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	$0.612106\pi$
$422$	−8.77784	−	32.7593i	−0.427298	−	1.59470i
$423$		0			0
$424$	−0.212778	+	0.122847i	−0.0103334	+	0.00596600i
$425$	−1.32418	−	4.92448i	−0.0642321	−	0.238872i
$426$		0			0
$427$	−3.78200	+	3.87146i	−0.183024	+	0.187353i
$428$	−42.4414	−	42.4414i	−2.05148	−	2.05148i
$429$		0			0
$430$	8.46528	−	4.89242i	0.408232	−	0.235934i
$431$	14.4168	−	8.32354i	0.694432	−	0.400931i	−0.110838	−	0.993838i	$-0.535353\pi$
$431$	14.4168	−	8.32354i	0.694432	−	0.400931i	0.805270	+	0.592908i	$0.202020\pi$
$432$		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
$437$	1.69143	+	0.453216i	0.0809119	+	0.0216803i
$438$		0			0
$439$	28.2457	+	16.3077i	1.34810	+	0.778324i	0.987980	−	0.154584i	$-0.0494036\pi$
$439$	28.2457	+	16.3077i	1.34810	+	0.778324i	0.360116	+	0.932907i	$0.382737\pi$
$440$	46.1585	−	46.1994i	2.20052	−	2.20247i
$441$		0			0
$442$	−11.4449	−	11.4449i	−0.544379	−	0.544379i
$443$	−12.7017	+	3.40342i	−0.603477	+	0.161701i	−0.547605	−	0.836737i	$-0.684460\pi$
$443$	−12.7017	+	3.40342i	−0.603477	+	0.161701i	−0.0558717	+	0.998438i	$0.517794\pi$
$444$		0			0
$445$	−5.35425	−	9.26437i	−0.253816	−	0.439173i
$446$	9.06477	+	5.23355i	0.429229	+	0.247816i
$447$		0			0
$448$	−2.14384	+	8.39204i	−0.101287	+	0.396487i
$449$	−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
$452$	−71.6635	−	19.2022i	−3.37077	−	0.903194i
$453$		0			0
$454$			49.1189i			2.30526i
$455$	−0.452924	−	37.3382i	−0.0212334	−	1.75044i
$456$		0			0
$457$	−6.88267	+	1.84421i	−0.321958	+	0.0862684i	−0.416178	−	0.909283i	$-0.636631\pi$
$457$	−6.88267	+	1.84421i	−0.321958	+	0.0862684i	0.0942205	+	0.995551i	$0.469964\pi$
$458$	4.51028	−	16.8326i	0.210751	−	0.786535i
$459$		0			0
$460$	−0.689405	−	2.56835i	−0.0321437	−	0.119750i
$461$		−	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
$467$	−2.38672	−	8.90737i	−0.110444	−	0.412184i	0.888461	−	0.458951i	$-0.151775\pi$
$467$	−2.38672	−	8.90737i	−0.110444	−	0.412184i	−0.998906	+	0.0467673i	$0.985108\pi$
$468$		0			0
$469$	−18.3740	+	32.7015i	−0.848432	+	1.51001i
$470$	−0.0194226	−	43.9335i	−0.000895898	−	2.02650i
$471$		0			0
$472$	15.6329	−	58.3429i	0.719564	−	2.68545i
$473$	−2.25164	+	8.40324i	−0.103531	+	0.386382i
$474$		0			0
$475$	−0.0281336	−	31.8187i	−0.00129086	−	1.45994i
$476$	11.6614	−	0.136300i	0.534499	−	0.00624731i
$477$		0			0
$478$	0.512613	+	1.91310i	0.0234464	+	0.0875030i
$479$	−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
$485$	−0.727329	+	0.195232i	−0.0330263	+	0.00886503i
$486$		0			0
$487$	0.627663	−	2.34247i	0.0284421	−	0.106148i	−0.950246	−	0.311502i	$-0.899168\pi$
$487$	0.627663	−	2.34247i	0.0284421	−	0.106148i	0.978688	+	0.205354i	$0.0658347\pi$
$488$	11.5358	−	3.09102i	0.522203	−	0.139924i
$489$		0			0
$490$	28.4836	+	27.1581i	1.28676	+	1.22688i
$491$			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
$493$	3.99381	+	1.07014i	0.179872	+	0.0481966i
$494$	−50.4964	−	87.4624i	−2.27194	−	3.93512i
$495$		0			0
$496$	−25.6675			−1.15250
$497$	−3.42834	+	13.4202i	−0.153782	+	0.601978i
$498$		0			0
$499$	−0.192077	−	0.110896i	−0.00859855	−	0.00496437i	0.495695	−	0.868497i	$-0.334914\pi$
$499$	−0.192077	−	0.110896i	−0.00859855	−	0.00496437i	−0.504293	+	0.863533i	$0.668247\pi$
$500$	−41.8152	+	24.2160i	−1.87003	+	1.08297i
$501$		0			0
$502$	−4.28606	+	1.14845i	−0.191296	+	0.0512576i
$503$	−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
$508$	13.9104	+	3.72727i	0.617173	+	0.165371i
$509$	−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
$515$	−22.8499	−	6.11179i	−1.00689	−	0.269318i
$516$		0			0
$517$	27.6415	+	27.6415i	1.21567	+	1.21567i
$518$	2.42296	+	8.63750i	0.106459	+	0.379510i
$519$		0			0
$520$	−41.1676	+	71.3772i	−1.80532	+	3.13010i
$521$	23.3214	−	13.4646i	1.02173	−	0.589895i	0.107124	−	0.994246i	$-0.465836\pi$
$521$	23.3214	−	13.4646i	1.02173	−	0.589895i	0.914604	+	0.404351i	$0.132503\pi$
$522$		0			0
$523$	−4.03169	−	15.0465i	−0.176294	−	0.657936i	−0.996328	−	0.0856218i	$-0.972712\pi$
$523$	−4.03169	−	15.0465i	−0.176294	−	0.657936i	0.820034	−	0.572315i	$-0.193954\pi$
$524$	20.6213			0.900847
$525$		0			0
$526$	−69.9299			−3.04909
$527$	−1.12259	−	4.18955i	−0.0489007	−	0.182500i
$528$		0			0
$529$	−19.8530	+	11.4621i	−0.863174	+	0.498354i
$530$	−0.118212	+	0.204959i	−0.00513481	+	0.00890284i
$531$		0			0
$532$	70.5043	+	18.0111i	3.05675	+	0.780880i
$533$	9.54232	+	9.54232i	0.413324	+	0.413324i
$534$		0			0
$535$	−29.9988	−	8.02394i	−1.29696	−	0.346905i
$536$	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	$0.226574\pi$
$542$	2.65251	+	0.710738i	0.113935	+	0.0305288i
$543$		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	$0.841934\pi$
$548$	−3.24821	+	0.870355i	−0.138757	+	0.0371797i
$549$		0			0
$550$	16.2237	−	60.7624i	0.691780	−	2.59092i
$551$	22.3428	+	12.8996i	0.951834	+	0.549542i
$552$		0			0
$553$	−27.3965	−	26.7635i	−1.16502	−	1.13810i
$554$	−10.3392			−0.439272
$555$		0			0
$556$	−2.47765	−	4.29142i	−0.105076	−	0.181997i
$557$	41.4325	+	11.1018i	1.75555	+	0.470398i	0.985797	−	0.167943i	$-0.0537124\pi$
$557$	41.4325	+	11.1018i	1.75555	+	0.470398i	0.769754	+	0.638341i	$0.220379\pi$
$558$		0			0
$559$		−	10.9765i		−	0.464255i
$560$	−9.65910	−	34.3749i	−0.408172	−	1.45261i
$561$		0			0
$562$	−19.2294	+	5.15250i	−0.811143	+	0.217345i
$563$	−0.0216411	+	0.0807657i	−0.000912064	+	0.00340387i	−0.966380	−	0.257117i	$-0.917228\pi$
$563$	−0.0216411	+	0.0807657i	−0.000912064	+	0.00340387i	0.965468	+	0.260521i	$0.0838942\pi$
$564$		0			0
$565$	−37.0723	+	9.95107i	−1.55965	+	0.418645i
$566$			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	$0.677757\pi$
$572$	−35.3201	−	131.816i	−1.47681	−	5.51152i
$573$		0			0
$574$	−14.2221	+	0.166230i	−0.593618	+	0.00693830i
$575$	−0.973722	−	0.972001i	−0.0406070	−	0.0405353i
$576$		0			0
$577$	5.03680	−	18.7976i	0.209685	−	0.782554i	−0.778286	−	0.627910i	$-0.783910\pi$
$577$	5.03680	−	18.7976i	0.209685	−	0.782554i	0.987970	−	0.154644i	$-0.0494229\pi$
$578$	−10.3861	+	38.7613i	−0.432003	+	1.61226i
$579$		0			0
$580$	−0.0173209	−	39.1796i	−0.000719213	−	1.62684i
$581$	−19.0589	−	32.1375i	−0.790695	−	1.33329i
$582$		0			0
$583$	−0.0544883	−	0.203353i	−0.00225667	−	0.00842202i
$584$	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
$590$	−15.0795	−	56.1780i	−0.620812	−	2.31281i
$591$		0			0
$592$	2.10653	−	7.86166i	0.0865777	−	0.323112i
$593$	−28.4595	+	7.62569i	−1.16869	+	0.313150i	−0.790432	−	0.612550i	$-0.790144\pi$
$593$	−28.4595	+	7.62569i	−1.16869	+	0.313150i	−0.378259	+	0.925700i	$0.623477\pi$
$594$		0			0
$595$	5.18836	−	3.08001i	0.212702	−	0.126268i
$596$			79.8116i			3.26921i
$597$		0			0
$598$	−4.21811	−	1.13024i	−0.172491	−	0.0462189i
$599$	−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	$0.485599\pi$
$602$	8.27538	+	8.08416i	0.337279	+	0.329486i
$603$		0			0
$604$	−47.7670	−	27.5783i	−1.94361	−	1.12215i
$605$	15.6931	+	27.1536i	0.638017	+	1.10395i
$606$		0			0
$607$	−3.43269	+	0.919787i	−0.139329	+	0.0373330i	−0.327809	−	0.944744i	$-0.606310\pi$
$607$	−3.43269	+	0.919787i	−0.139329	+	0.0373330i	0.188481	+	0.982077i	$0.439644\pi$
$608$	−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
$613$	30.1885	+	8.08899i	1.21930	+	0.326711i	0.810406	−	0.585869i	$-0.199247\pi$
$613$	30.1885	+	8.08899i	1.21930	+	0.326711i	0.408897	+	0.912580i	$0.365913\pi$
$614$	−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	−0.615072	+	0.788471i	$0.710873\pi$
$619$	−39.9430	+	23.0611i	−1.60544	+	0.926903i	−0.990372	+	0.138433i	$0.955794\pi$
$620$	−35.5844	+	20.5657i	−1.42910	+	0.825937i
$621$		0			0
$622$	34.6813	+	34.6813i	1.39059	+	1.39059i
$623$	8.84728	−	9.05654i	0.354459	−	0.362843i
$624$		0			0
$625$	−12.4617	+	21.6727i	−0.498468	+	0.866908i
$626$	32.8834	−	18.9852i	1.31429	−	0.758803i
$627$		0			0
$628$	−5.90548	−	22.0396i	−0.235654	−	0.879475i
$629$	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	$0.206132\pi$
$632$	21.8737	+	81.6338i	0.870089	+	3.24722i
$633$		0			0
$634$	−36.0200	+	20.7961i	−1.43054	+	0.825920i
$635$	7.19600	−	1.93157i	0.285564	−	0.0766521i
$636$		0			0
$637$	42.3980	−	12.4296i	1.67987	−	0.492480i
$638$	36.0576	+	36.0576i	1.42754	+	1.42754i
$639$		0			0
$640$	8.79900	−	32.8965i	0.347811	−	1.30035i
$641$	25.8536	−	14.9266i	1.02116	−	0.589566i	0.106719	−	0.994289i	$-0.465966\pi$
$641$	25.8536	−	14.9266i	1.02116	−	0.589566i	0.914439	+	0.404724i	$0.132632\pi$
$642$		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
$647$	−1.20998	−	0.324212i	−0.0475691	−	0.0127461i	0.234956	−	0.972006i	$-0.424505\pi$
$647$	−1.20998	−	0.324212i	−0.0475691	−	0.0127461i	−0.282525	+	0.959260i	$0.591172\pi$
$648$		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
$653$	−9.63022	+	2.58041i	−0.376859	+	0.100979i	−0.442276	−	0.896879i	$-0.645829\pi$
$653$	−9.63022	+	2.58041i	−0.376859	+	0.100979i	0.0654169	+	0.997858i	$0.479162\pi$
$654$		0			0
$655$	9.23719	−	5.33854i	0.360927	−	0.208594i
$656$	11.1753	+	6.45204i	0.436321	+	0.251910i
$657$		0			0
$658$	50.0508	−	14.0401i	1.95118	−	0.547338i
$659$	−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	$0.689131\pi$
$662$	65.0707	+	17.4356i	2.52904	+	0.677655i
$663$		0			0
$664$			82.4489i			3.19964i
$665$	36.2447	−	10.1845i	1.40551	−	0.394938i
$666$		0			0
$667$	1.07754	−	0.288726i	0.0417225	−	0.0111795i
$668$	−0.359632	+	1.34216i	−0.0139146	+	0.0519299i
$669$		0			0
$670$	39.8240	−	69.0477i	1.53854	−	2.66754i
$671$			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
$677$	−4.76445	−	17.7812i	−0.183113	−	0.683386i	−0.995027	−	0.0996090i	$-0.968241\pi$
$677$	−4.76445	−	17.7812i	−0.183113	−	0.683386i	0.811914	−	0.583777i	$-0.198426\pi$
$678$		0			0
$679$	−0.454514	−	0.766414i	−0.0174427	−	0.0294123i
$680$	−13.3142	+	0.00588611i	−0.510578	+	0.000225722i
$681$		0			0
$682$	13.8449	−	51.6697i	0.530147	−	1.97854i
$683$	−8.32323	+	31.0627i	−0.318480	+	1.18858i	0.602226	+	0.798325i	$0.294280\pi$
$683$	−8.32323	+	31.0627i	−0.318480	+	1.18858i	−0.920706	+	0.390257i	$0.872386\pi$
$684$		0			0
$685$	−1.22969	+	1.23078i	−0.0469842	+	0.0470257i
$686$	−21.8552	+	41.1191i	−0.834435	+	1.56994i
$687$		0			0
$688$	−2.71654	−	10.1383i	−0.103567	−	0.386518i
$689$	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
$695$	−2.22083	−	1.28089i	−0.0842410	−	0.0485869i
$696$		0			0
$697$	−0.564369	+	2.10625i	−0.0213770	+	0.0797801i
$698$	−1.55889	+	0.417702i	−0.0590047	+	0.0158103i
$699$		0			0
$700$	−40.9333	−	39.9168i	−1.54713	−	1.50871i
$701$			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
$703$	8.28930	+	2.22111i	0.312637	+	0.0837708i
$704$	8.18859	+	14.1831i	0.308619	+	0.534544i
$705$		0			0
$706$	−4.89768			−0.184326
$707$	−28.4898	+	7.99184i	−1.07147	+	0.300564i
$708$		0			0
$709$	4.92357	+	2.84263i	0.184909	+	0.106757i	0.589597	−	0.807698i	$-0.299287\pi$
$709$	4.92357	+	2.84263i	0.184909	+	0.106757i	−0.404688	+	0.914455i	$0.632620\pi$
$710$	7.60550	−	28.4344i	0.285429	−	1.06712i
$711$		0			0
$712$	−26.9859	+	7.23085i	−1.01134	+	0.270987i
$713$	−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
$718$	−21.1199	−	5.65906i	−0.788188	−	0.211194i
$719$	−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
$725$	−10.1507	−	17.5458i	−0.376989	−	0.651633i
$726$		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	$0.311313\pi$
$728$	−94.4614	−	24.1312i	−3.50097	−	0.894362i
$729$		0			0
$730$	50.7159	+	29.2509i	1.87708	+	1.08263i
$731$	1.53600	−	0.886810i	0.0568110	−	0.0327998i
$732$		0			0
$733$	10.9190	+	40.7501i	0.403301	+	1.50514i	0.807168	+	0.590321i	$0.200999\pi$
$733$	10.9190	+	40.7501i	0.403301	+	1.50514i	−0.403868	+	0.914817i	$0.632334\pi$
$734$	81.9619			3.02527
$735$		0			0
$736$	−0.962746			−0.0354873
$737$	18.3563	+	68.5067i	0.676163	+	2.52348i
$738$		0			0
$739$	42.4476	−	24.5071i	1.56146	−	0.901510i	0.564351	−	0.825535i	$-0.309127\pi$
$739$	42.4476	−	24.5071i	1.56146	−	0.901510i	0.997110	−	0.0759743i	$-0.0242067\pi$
$740$	−3.37862	−	12.5869i	−0.124201	−	0.462704i
$741$		0			0
$742$	−0.271245	−	0.0692925i	−0.00995771	−	0.00254381i
$743$	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
$745$	20.6620	+	35.7511i	0.756997	+	1.30982i
$746$	−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	$0.116562\pi$
$752$	−45.5552	−	12.2065i	−1.66123	−	0.445124i
$753$		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	$0.734067\pi$
$758$	28.4044	−	7.61092i	1.03169	−	0.276441i
$759$		0			0
$760$	−80.2555	−	21.4664i	−2.91117	−	0.778667i
$761$	−17.3244	−	10.0023i	−0.628011	−	0.362582i	0.151971	−	0.988385i	$-0.451438\pi$
$761$	−17.3244	−	10.0023i	−0.628011	−	0.362582i	−0.779981	+	0.625803i	$0.784771\pi$
$762$		0			0
$763$	9.90079	−	2.77733i	0.358433	−	0.100546i
$764$	84.9578			3.07367
$765$		0			0
$766$	−10.6298	−	18.4114i	−0.384072	−	0.665232i
$767$	−63.0751	−	16.9009i	−2.27751	−	0.610257i
$768$		0			0
$769$			31.7665i			1.14553i	0.819720	+	0.572764i	$0.194129\pi$
$769$			31.7665i			1.14553i	−0.819720	+	0.572764i	$0.805871\pi$
$770$	74.4082	−	0.902595i	2.68148	−	0.0325272i
$771$		0			0
$772$	−23.1455	+	6.20183i	−0.833026	+	0.223209i
$773$	7.74623	−	28.9093i	0.278613	−	1.03980i	−0.674769	−	0.738029i	$-0.735757\pi$
$773$	7.74623	−	28.9093i	0.278613	−	1.03980i	0.953382	−	0.301768i	$-0.0975766\pi$
$774$		0			0
$775$	−10.6157	+	18.4245i	−0.381327	+	0.661828i
$776$			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
$782$	−0.182628	−	0.681578i	−0.00653078	−	0.0243732i
$783$		0			0
$784$	36.0842	−	21.9735i	1.28872	−	0.784767i
$785$	−8.35103	−	8.34365i	−0.298061	−	0.297798i
$786$		0			0
$787$	0.700556	−	2.61451i	0.0249721	−	0.0931973i	−0.952315	−	0.305116i	$-0.901305\pi$
$787$	0.700556	−	2.61451i	0.0249721	−	0.0931973i	0.977287	+	0.211919i	$0.0679713\pi$
$788$	−12.1651	+	45.4008i	−0.433364	+	1.61734i
$789$		0			0
$790$	57.5748	+	57.5239i	2.04842	+	2.04661i
$791$	−23.1668	−	39.0645i	−0.823717	−	1.38897i
$792$		0			0
$793$	−3.34173	−	12.4715i	−0.118668	−	0.442876i
$794$	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
$800$	4.54268	+	16.8938i	0.160608	+	0.597284i
$801$		0			0
$802$	8.26525	−	30.8463i	0.291856	−	1.08922i
$803$	−50.3185	+	13.4828i	−1.77570	+	0.475798i
$804$		0			0
$805$	0.796794	−	1.41958i	0.0280833	−	0.0500336i
$806$			67.4919i			2.37730i
$807$		0			0
$808$	63.0687	+	16.8992i	2.21875	+	0.594512i
$809$	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	$0.591274\pi$
$812$	44.6350	−	12.5208i	1.56638	−	0.439395i
$813$		0			0
$814$	14.6896	+	8.48105i	0.514871	+	0.297261i
$815$	18.2748	+	4.88805i	0.640137	+	0.171221i
$816$		0			0
$817$	10.6897	−	2.86431i	0.373987	−	0.100210i
$818$	−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	$-0.0668602\pi$
$821$	36.8611	+	21.2817i	1.28646	+	0.742738i	0.308439	+	0.951244i	$0.400194\pi$
$822$		0			0
$823$	31.9667	+	8.56545i	1.11429	+	0.298573i	0.768570	−	0.639765i	$-0.220968\pi$
$823$	31.9667	+	8.56545i	1.11429	+	0.298573i	0.345719	+	0.938338i	$0.387635\pi$
$824$	−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	$-0.441025\pi$
$829$	32.4643	−	18.7432i	1.12753	−	0.650980i	0.943313	+	0.331906i	$0.107692\pi$
$830$	39.7298	+	68.7439i	1.37904	+	2.38614i
$831$		0			0
$832$	−14.6111	−	14.6111i	−0.506549	−	0.506549i
$833$	5.16477	+	4.92879i	0.178949	+	0.170772i
$834$		0			0
$835$	0.186371	+	0.694317i	0.00644963	+	0.0240278i
$836$	119.156	−	68.7950i	4.12111	−	2.37932i
$837$		0			0
$838$	1.52113	+	5.67693i	0.0525465	+	0.196106i
$839$	−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
$842$	9.21208	+	34.3800i	0.317469	+	1.18481i
$843$		0			0
$844$	−50.4867	+	29.1485i	−1.73782	+	1.00333i
$845$	51.9858	+	29.9834i	1.78837	+	1.03146i
$846$		0			0
$847$	−25.9311	+	26.5444i	−0.891003	+	0.912078i
$848$	0.179601	+	0.179601i	0.00616753	+	0.00616753i
$849$		0			0
$850$	−11.0983	+	6.42067i	−0.380667	+	0.220227i
$851$	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
$857$	−29.6460	−	7.94363i	−1.01269	−	0.271349i	−0.285936	−	0.958249i	$-0.592305\pi$
$857$	−29.6460	−	7.94363i	−1.01269	−	0.271349i	−0.726752	+	0.686899i	$0.758971\pi$
$858$		0			0
$859$	−30.5614	−	17.6447i	−1.04274	−	0.602028i	−0.122134	−	0.992514i	$-0.538974\pi$
$859$	−30.5614	−	17.6447i	−1.04274	−	0.602028i	−0.920609	+	0.390486i	$0.872307\pi$
$860$	−11.8892	−	11.8787i	−0.405419	−	0.405061i
$861$		0			0
$862$	−29.5971	−	29.5971i	−1.00808	−	1.00808i
$863$	50.1038	−	13.4253i	1.70555	−	0.457002i	0.731225	−	0.682136i	$-0.238949\pi$
$863$	50.1038	−	13.4253i	1.70555	−	0.457002i	0.974328	+	0.225134i	$0.0722821\pi$
$864$		0			0
$865$	−9.21760	+	34.4615i	−0.313408	+	1.17173i
$866$	−25.9661	−	14.9915i	−0.882363	−	0.509433i
$867$		0			0
$868$	−34.7861	−	33.9824i	−1.18072	−	1.15344i
$869$	−72.4164			−2.45656
$870$		0			0
$871$	−44.7423	−	77.4959i	−1.51603	−	2.62585i
$872$	−21.9177	−	5.87282i	−0.742226	−	0.198879i
$873$		0			0
$874$		−	4.40286i		−	0.148929i
$875$	−28.6697	−	7.28349i	−0.969212	−	0.246227i
$876$		0			0
$877$	−19.8813	+	5.32717i	−0.671343	+	0.179886i	−0.578360	−	0.815782i	$-0.696307\pi$
$877$	−19.8813	+	5.32717i	−0.671343	+	0.179886i	−0.0929832	+	0.995668i	$0.529640\pi$
$878$	21.2249	−	79.2122i	0.716304	−	2.67328i
$879$		0			0
$880$	−58.4829	−	33.7306i	−1.97146	−	1.13706i
$881$			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
$887$	3.91318	+	14.6042i	0.131392	+	0.490361i	0.999987	−	0.00516191i	$-0.00164309\pi$
$887$	3.91318	+	14.6042i	0.131392	+	0.490361i	−0.868595	+	0.495523i	$0.834976\pi$
$888$		0			0
$889$	4.49684	+	7.58269i	0.150819	+	0.254315i
$890$	−19.0158	+	19.0326i	−0.637412	+	0.637976i
$891$		0			0
$892$	4.65669	−	17.3790i	0.155918	−	0.581892i
$893$	12.8704	−	48.0332i	0.430693	−	1.60737i
$894$		0			0
$895$	−9.04102	+	0.00399696i	−0.302208	+	0.000133604i
$896$	40.2892	−	0.470906i	1.34597	−	0.0157319i
$897$		0			0
$898$	24.5413	+	91.5893i	0.818953	+	3.05637i
$899$	−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
$905$	10.6713	−	18.5022i	0.354727	−	0.615033i
$906$		0			0
$907$	8.24361	−	30.7656i	0.273725	−	1.02155i	−0.682967	−	0.730449i	$-0.739311\pi$
$907$	8.24361	−	30.7656i	0.273725	−	1.02155i	0.956691	−	0.291104i	$-0.0940227\pi$
$908$	81.5544	−	21.8524i	2.70648	−	0.725198i
$909$		0			0
$910$	−90.3878	+	25.3983i	−2.99632	+	0.841946i
$911$			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
$913$	−68.2401	−	18.2849i	−2.25842	−	0.605141i
$914$	8.95797	+	15.5157i	0.296303	+	0.513212i
$915$		0			0
$916$	−29.9545			−0.989725
$917$	9.02997	+	8.82132i	0.298196	+	0.291306i
$918$		0			0
$919$	−29.1834	−	16.8490i	−0.962671	−	0.555798i	−0.0656768	−	0.997841i	$-0.520921\pi$
$919$	−29.1834	−	16.8490i	−0.962671	−	0.555798i	−0.896994	+	0.442043i	$0.854254\pi$
$920$	−3.11016	+	1.79748i	−0.102539	+	0.0592613i
$921$		0			0
$922$	−56.5450	+	15.1512i	−1.86221	+	0.498978i
$923$	−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
$928$	−13.7010	−	3.67118i	−0.449758	−	0.120512i
$929$	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
$935$	2.94786	−	11.0210i	0.0964052	−	0.360427i
$936$		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	$0.995376\pi$
$938$	91.3785	+	23.3436i	2.98361	+	0.762197i
$939$		0			0
$940$	−72.9362	+	19.5777i	−2.37892	+	0.638556i
$941$	−29.0798	+	16.7893i	−0.947976	+	0.547314i	−0.892451	−	0.451143i	$-0.851016\pi$
$941$	−29.0798	+	16.7893i	−0.947976	+	0.547314i	−0.0555241	+	0.998457i	$0.517683\pi$
$942$		0			0
$943$	0.152268	+	0.568273i	0.00495854	+	0.0185055i
$944$	−62.4414			−2.03229
$945$		0			0
$946$	21.8741			0.711187
$947$	−7.67048	−	28.6266i	−0.249257	−	0.930240i	−0.971196	−	0.238283i	$-0.923415\pi$
$947$	−7.67048	−	28.6266i	−0.249257	−	0.930240i	0.721939	−	0.691957i	$-0.243251\pi$
$948$		0			0
$949$	56.9211	−	32.8634i	1.84774	−	1.06679i
$950$	−77.2591	+	20.7748i	−2.50662	+	0.674022i
$951$		0			0
$952$	−4.25490	−	15.1681i	−0.137902	−	0.491602i
$953$	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
$955$	38.0563	−	21.9943i	1.23147	−	0.711718i
$956$	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
$962$	−20.6720	−	5.53905i	−0.666492	−	0.178586i
$963$		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	$0.480039\pi$
$968$	79.0948	−	21.1934i	2.54220	−	0.681181i
$969$		0			0
$970$	0.947474	+	1.63940i	0.0304216	+	0.0526379i
$971$	−33.4151	−	19.2922i	−1.07234	−	0.619117i	−0.143521	−	0.989647i	$-0.545842\pi$
$971$	−33.4151	−	19.2922i	−1.07234	−	0.619117i	−0.928820	+	0.370531i	$0.879176\pi$
$972$		0			0
$973$	0.750819	−	2.93907i	0.0240701	−	0.0942224i
$974$	−6.09757			−0.195379
$975$		0			0
$976$	−6.17310	−	10.6921i	−0.197596	−	0.342246i
$977$	2.28755	+	0.612947i	0.0731852	+	0.0196099i	0.295226	−	0.955428i	$-0.404605\pi$
$977$	2.28755	+	0.612947i	0.0731852	+	0.0196099i	−0.222041	+	0.975037i	$0.571272\pi$
$978$		0			0
$979$		−	23.9389i		−	0.765090i
$980$	32.4199	−	59.3751i	1.03562	−	1.89667i
$981$		0			0
$982$	37.0773	−	9.93483i	1.18318	−	0.317033i
$983$	7.38005	−	27.5427i	0.235387	−	0.878476i	−0.742587	−	0.669750i	$-0.766401\pi$
$983$	7.38005	−	27.5427i	0.235387	−	0.878476i	0.977974	−	0.208727i	$-0.0669319\pi$
$984$		0			0
$985$	6.30429	+	23.4864i	0.200871	+	0.748338i
$986$		−	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	$0.924055\pi$
$992$	3.85111	+	14.3725i	0.122273	+	0.456328i
$993$		0			0
$994$	34.8244	−	0.407033i	1.10456	−	0.0129103i
$995$	−0.00798936	−	18.0718i	−0.000253280	−	0.572913i
$996$		0			0
$997$	13.7505	−	51.3174i	0.435481	−	1.62524i	−0.304431	−	0.952535i	$-0.598466\pi$
$997$	13.7505	−	51.3174i	0.435481	−	1.62524i	0.739912	−	0.672704i	$-0.234867\pi$
$998$	−0.144333	+	0.538660i	−0.00456880	+	0.0170510i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
945.2.ch.a.53.2	✓	128	105.53	even	12	inner
945.2.ch.a.53.31	yes	128	35.18	odd	12	inner
945.2.ch.a.107.2	yes	128	1.1	even	1	trivial
945.2.ch.a.107.31	yes	128	3.2	odd	2	inner
945.2.ch.a.242.2	yes	128	21.11	odd	6	inner
945.2.ch.a.242.31	yes	128	7.4	even	3	inner
945.2.ch.a.863.2	yes	128	5.3	odd	4	inner
945.2.ch.a.863.31	yes	128	15.8	even	4	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)

\(f(q)\)	\(=\)	\(q+(-0.650762 - 2.42868i) q^{2} +(-3.74293 + 2.16098i) q^{4} +(-1.11718 + 1.93699i) q^{5} +(-2.56343 - 0.654856i) q^{7} +(4.12826 + 4.12826i) q^{8} +O(q^{10})\)	\(q+(-0.650762 - 2.42868i) q^{2} +(-3.74293 + 2.16098i) q^{4} +(-1.11718 + 1.93699i) q^{5} +(-2.56343 - 0.654856i) q^{7} +(4.12826 + 4.12826i) q^{8} +(5.43133 + 1.45275i) q^{10} +(-4.33235 + 2.50128i) q^{11} +(4.46310 - 4.46310i) q^{13} +(0.0777484 + 6.65190i) q^{14} +(3.01772 - 5.22685i) q^{16} +(0.985130 + 0.263965i) q^{17} +(5.51117 + 3.18187i) q^{19} +(-0.00427246 - 9.66421i) q^{20} +(8.89413 + 8.89413i) q^{22} +(0.265791 - 0.0712184i) q^{23} +(-2.50383 - 4.32791i) q^{25} +(-13.7438 - 7.93501i) q^{26} +(11.0099 - 3.08844i) q^{28} +4.05409 q^{29} +(-2.12640 - 3.68302i) q^{31} +(-3.37955 - 0.905549i) q^{32} -2.56434i q^{34} +(4.13225 - 4.23373i) q^{35} +(1.30258 - 0.349026i) q^{37} +(4.14129 - 15.4555i) q^{38} +(-12.6084 + 3.38438i) q^{40} +2.13805i q^{41} +(1.22969 - 1.22969i) q^{43} +(10.8104 - 18.7242i) q^{44} +(-0.345933 - 0.599174i) q^{46} +(-2.02246 - 7.54793i) q^{47} +(6.14233 + 3.35735i) q^{49} +(-8.88171 + 8.89743i) q^{50} +(-7.06040 + 26.3498i) q^{52} +(-0.0108921 + 0.0406498i) q^{53} +(-0.00494526 - 11.1861i) q^{55} +(-7.87908 - 13.2859i) q^{56} +(-2.63825 - 9.84608i) q^{58} +(-5.17288 - 8.95970i) q^{59} +(1.02281 - 1.77155i) q^{61} +(-7.56110 + 7.56110i) q^{62} -3.27376i q^{64} +(3.65888 + 13.6310i) q^{65} +(3.66938 - 13.6943i) q^{67} +(-4.25770 + 1.14085i) q^{68} +(-12.9715 - 7.28075i) q^{70} -5.23525i q^{71} +(10.0585 + 2.69518i) q^{73} +(-1.69534 - 2.93642i) q^{74} -27.5039 q^{76} +(12.7436 - 3.57479i) q^{77} +(12.5365 + 7.23793i) q^{79} +(6.75300 + 11.6846i) q^{80} +(5.19263 - 1.39136i) q^{82} +(9.98593 + 9.98593i) q^{83} +(-1.61186 + 1.61329i) q^{85} +(-3.78676 - 2.18628i) q^{86} +(-28.2110 - 7.55911i) q^{88} +(-2.39266 + 4.14421i) q^{89} +(-14.3635 + 8.51815i) q^{91} +(-0.840935 + 0.840935i) q^{92} +(-17.0154 + 9.82382i) q^{94} +(-12.3202 + 7.12033i) q^{95} +(0.238144 + 0.238144i) q^{97} +(4.15673 - 17.1026i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 8 q^{7}+O(q^{10}) \) 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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