LMFDB - Embedded newform 945.2.ch.a.53.2

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			53.2
Character	$\chi$	$=$	945.53
Dual form			945.2.ch.a.107.2

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

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

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 $

$2$	−0.650762	+	2.42868i	−0.460158	+	1.71733i	0.212305	+	0.977204i	$0.431903\pi$
$2$	−0.650762	+	2.42868i	−0.460158	+	1.71733i	−0.672463	+	0.740131i	$0.734764\pi$
$3$		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	−0.324783	−	0.945789i	$-0.605291\pi$
$11$	−4.33235	−	2.50128i	−1.30625	−	0.754165i	−0.981468	+	0.191624i	$0.938625\pi$
$12$		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
$17$	0.985130	−	0.263965i	0.238929	−	0.0640209i	−0.137367	−	0.990520i	$-0.543864\pi$
$17$	0.985130	−	0.263965i	0.238929	−	0.0640209i	0.376296	+	0.926499i	$0.377197\pi$
$18$		0			0
$19$	5.51117	−	3.18187i	1.26435	−	0.729972i	0.290436	−	0.956894i	$-0.406200\pi$
$19$	5.51117	−	3.18187i	1.26435	−	0.729972i	0.973913	+	0.226922i	$0.0728664\pi$
$20$	−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	0.286423	−	0.958103i	$-0.407534\pi$
$23$	0.265791	+	0.0712184i	0.0554212	+	0.0148501i	−0.231002	+	0.972953i	$0.574200\pi$
$24$		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	−0.991336	−	0.131354i	$-0.958068\pi$
$31$	−2.12640	+	3.68302i	−0.381912	+	0.661491i	0.609424	+	0.792845i	$0.291401\pi$
$32$	−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	0.364296	−	0.931283i	$-0.381310\pi$
$37$	1.30258	+	0.349026i	0.214143	+	0.0573795i	−0.150153	+	0.988663i	$0.547976\pi$
$38$	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	$-0.946607\pi$
$41$		−	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
$47$	−2.02246	+	7.54793i	−0.295007	+	1.10098i	0.646206	+	0.763163i	$0.276355\pi$
$47$	−2.02246	+	7.54793i	−0.295007	+	1.10098i	−0.941212	+	0.337816i	$0.890312\pi$
$48$		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	0.965174	−	0.261610i	$-0.0842534\pi$
$53$	−0.0108921	−	0.0406498i	−0.00149614	−	0.00558367i	−0.966670	+	0.256026i	$0.917587\pi$
$54$		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	0.303467	+	0.952842i	$0.401856\pi$
$59$	−5.17288	+	8.95970i	−0.673452	+	1.16645i	−0.976919	+	0.213611i	$0.931477\pi$
$60$		0			0
$61$	1.02281	+	1.77155i	0.130957	+	0.226824i	0.924046	−	0.382282i	$-0.124862\pi$
$61$	1.02281	+	1.77155i	0.130957	+	0.226824i	−0.793089	+	0.609106i	$0.791528\pi$
$62$	−7.56110	−	7.56110i	−0.960261	−	0.960261i
$63$		0			0
$64$			3.27376i			0.409220i
$65$	3.65888	−	13.6310i	0.453829	−	1.69072i
$66$		0			0
$67$	3.66938	+	13.6943i	0.448286	+	1.67303i	0.707111	+	0.707103i	$0.249998\pi$
$67$	3.66938	+	13.6943i	0.448286	+	1.67303i	−0.258824	+	0.965924i	$0.583335\pi$
$68$	−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	$0.100548\pi$
$71$			5.23525i			0.621310i	−0.950523	+	0.310655i	$0.899452\pi$
$72$		0			0
$73$	10.0585	−	2.69518i	1.17726	−	0.315447i	0.383423	−	0.923573i	$-0.374745\pi$
$73$	10.0585	−	2.69518i	1.17726	−	0.315447i	0.793841	+	0.608126i	$0.208078\pi$
$74$	−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	0.415031	−	0.909807i	$-0.363771\pi$
$79$	12.5365	−	7.23793i	1.41046	−	0.814331i	0.995432	+	0.0954764i	$0.0304374\pi$
$80$	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	0.101235	−	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
$88$	−28.2110	+	7.55911i	−3.00730	+	0.805803i
$89$	−2.39266	−	4.14421i	−0.253622	−	0.439285i	0.710899	−	0.703294i	$-0.248288\pi$
$89$	−2.39266	−	4.14421i	−0.253622	−	0.439285i	−0.964520	+	0.264009i	$0.914955\pi$
$90$		0			0
$91$	−14.3635	−	8.51815i	−1.50571	−	0.892945i
$92$	−0.840935	−	0.840935i	−0.0876735	−	0.0876735i
$93$		0			0
$94$	−17.0154	−	9.82382i	−1.75500	−	1.01325i
$95$	−12.3202	−	7.12033i	−1.26403	−	0.730531i
$96$		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	$0.244557\pi$
$98$	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	0.897321	−	0.441379i	$-0.145510\pi$
$101$	9.68543	+	5.59189i	0.963736	+	0.556413i	0.0664154	+	0.997792i	$0.478844\pi$
$102$		0			0
$103$	2.73780	−	10.2176i	0.269763	−	1.00677i	−0.689507	−	0.724279i	$-0.742173\pi$
$103$	2.73780	−	10.2176i	0.269763	−	1.00677i	0.959270	−	0.282490i	$-0.0911605\pi$
$104$	36.8496			3.61340
$105$		0			0
$106$	0.105813			0.0102775
$107$	3.59435	−	13.4143i	0.347479	−	1.29681i	−0.542211	−	0.840242i	$-0.682413\pi$
$107$	3.59435	−	13.4143i	0.347479	−	1.29681i	0.889690	−	0.456565i	$-0.150921\pi$
$108$		0			0
$109$	−3.36589	−	1.94330i	−0.322394	−	0.186134i	0.330065	−	0.943958i	$-0.392929\pi$
$109$	−3.36589	−	1.94330i	−0.322394	−	0.186134i	−0.652459	+	0.757824i	$0.726263\pi$
$110$	−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	0.153768	−	0.988107i	$-0.450859\pi$
$113$	12.1383	−	12.1383i	1.14187	−	1.14187i	0.988107	−	0.153768i	$-0.0491408\pi$
$114$		0			0
$115$	−0.158986	−	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	−0.803873	−	0.594801i	$-0.797231\pi$
$127$	−2.35613	+	2.35613i	−0.209072	+	0.209072i	0.594801	+	0.803873i	$0.297231\pi$
$128$	−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	−0.669528	−	0.742787i	$-0.733503\pi$
$131$	−4.13205	+	2.38564i	−0.361019	+	0.208435i	0.308509	+	0.951222i	$0.400170\pi$
$132$		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	−0.226571	−	0.973995i	$-0.572752\pi$
$137$	0.751559	−	0.201380i	0.0642100	−	0.0172050i	0.290781	+	0.956790i	$0.406085\pi$
$138$		0			0
$139$		−	1.14654i		−	0.0972483i	−0.998817	−	0.0486241i	$-0.984516\pi$
$139$		−	1.14654i		−	0.0972483i	0.998817	−	0.0486241i	$-0.0154837\pi$
$140$	−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	0.944666	+	0.328032i	$0.106386\pi$
$149$	9.23325	+	15.9925i	0.756418	+	1.31015i	−0.188249	+	0.982121i	$0.560281\pi$
$150$		0			0
$151$	6.38096	−	11.0522i	0.519275	−	0.899411i	−0.480474	−	0.877009i	$-0.659535\pi$
$151$	6.38096	−	11.0522i	0.519275	−	0.899411i	0.999749	−	0.0224023i	$-0.00713146\pi$
$152$	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	0.889723	−	0.456500i	$-0.150897\pi$
$157$	−1.36639	−	5.09943i	−0.109050	−	0.406979i	−0.998773	+	0.0495210i	$0.984231\pi$
$158$	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	0.825617	+	0.564231i	$0.190827\pi$
$163$	−2.18961	+	8.17175i	−0.171504	+	0.640061i	−0.997121	+	0.0758299i	$0.975839\pi$
$164$	−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
$170$	4.96709	−	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	0.791585	−	0.611060i	$-0.209256\pi$
$173$	15.4098	+	4.12905i	1.17159	+	0.313926i	0.380003	+	0.924985i	$0.375923\pi$
$174$		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	−0.780530	−	0.625119i	$-0.785050\pi$
$179$	2.02163	−	3.50157i	0.151104	−	0.261720i	0.931634	+	0.363399i	$0.118384\pi$
$180$		0			0
$181$	−9.55204			−0.709998			−0.354999	−	0.934867i	$-0.615519\pi$
$181$	−9.55204			−0.709998			−0.354999	+	0.934867i	$0.615519\pi$
$182$	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	−0.967403	−	0.253243i	$-0.918503\pi$
$191$	−17.0237	+	9.82861i	−1.23179	+	0.711173i	−0.264386	+	0.964417i	$0.585169\pi$
$192$		0			0
$193$	5.35533	−	1.43496i	0.385485	−	0.103290i	−0.0608716	−	0.998146i	$-0.519388\pi$
$193$	5.35533	−	1.43496i	0.385485	−	0.103290i	0.446356	+	0.894855i	$0.352721\pi$
$194$	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	$-0.425811\pi$
$199$	−6.99916	−	4.04097i	−0.496157	−	0.286457i	−0.727125	+	0.686505i	$0.759144\pi$
$200$	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	0.601644	−	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
$227$	−18.8697	+	5.05613i	−1.25243	+	0.335587i	−0.823274	−	0.567644i	$-0.807855\pi$
$227$	−18.8697	+	5.05613i	−1.25243	+	0.335587i	−0.429155	+	0.903231i	$0.641189\pi$
$228$		0			0
$229$	6.00222	−	3.46538i	0.396638	−	0.228999i	−0.288394	−	0.957512i	$-0.593121\pi$
$229$	6.00222	−	3.46538i	0.396638	−	0.228999i	0.685032	+	0.728513i	$0.259788\pi$
$230$	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	0.859247	−	0.511560i	$-0.170932\pi$
$233$	20.5702	+	5.51176i	1.34760	+	0.361088i	0.488350	+	0.872648i	$0.337599\pi$
$234$		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	−0.879806	−	0.475333i	$-0.842328\pi$
$241$	−0.438601	+	0.759678i	−0.0282527	+	0.0489352i	0.851553	+	0.524268i	$0.175661\pi$
$242$	−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	$0.0177377\pi$
$251$			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
$257$	−0.682377	+	2.54666i	−0.0425655	+	0.158857i	−0.983937	−	0.178514i	$-0.942871\pi$
$257$	−0.682377	+	2.54666i	−0.0425655	+	0.158857i	0.941372	+	0.337371i	$0.109538\pi$
$258$		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	0.718905	+	0.695108i	$0.244644\pi$
$263$	7.19835	+	26.8646i	0.443869	+	1.65654i	−0.275036	+	0.961434i	$0.588690\pi$
$264$		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	−0.378470	−	0.925614i	$-0.623550\pi$
$269$	10.0436	−	17.3961i	0.612370	−	1.06066i	0.990840	−	0.135043i	$-0.0431171\pi$
$270$		0			0
$271$	−0.546081	−	0.945841i	−0.0331721	−	0.0574557i	0.848963	−	0.528453i	$-0.177228\pi$
$271$	−0.546081	−	0.945841i	−0.0331721	−	0.0574557i	−0.882135	+	0.470997i	$0.843894\pi$
$272$	4.35256	+	4.35256i	0.263913	+	0.263913i
$273$		0			0
$274$			1.95634i			0.118187i
$275$	21.6728	−	12.4872i	1.30692	−	0.753009i
$276$		0			0
$277$	1.06429	+	3.97197i	0.0639468	+	0.238653i	0.990500	−	0.137510i	$-0.0439100\pi$
$277$	1.06429	+	3.97197i	0.0639468	+	0.238653i	−0.926554	+	0.376163i	$0.877243\pi$
$278$	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	$0.0758900\pi$
$281$			7.91764i			0.472327i	−0.971713	+	0.236163i	$0.924110\pi$
$282$		0			0
$283$	−20.6535	+	5.53409i	−1.22772	+	0.328967i	−0.813692	−	0.581296i	$-0.802546\pi$
$283$	−20.6535	+	5.53409i	−1.22772	+	0.328967i	−0.414030	+	0.910263i	$0.635879\pi$
$284$	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	−0.235620	+	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
$298$	−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	−0.939177	−	0.343434i	$-0.888410\pi$
$307$	−10.4383	+	10.4383i	−0.595743	+	0.595743i	0.343434	+	0.939177i	$0.388410\pi$
$308$	−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	−0.0623969	−	0.998051i	$-0.519874\pi$
$311$	−16.8933	−	9.75337i	−0.957933	−	0.553063i	−0.895536	+	0.444988i	$0.853208\pi$
$312$		0			0
$313$	3.90856	−	14.5869i	0.220925	−	0.824502i	−0.763072	−	0.646314i	$-0.776310\pi$
$313$	3.90856	−	14.5869i	0.220925	−	0.824502i	0.983996	−	0.178188i	$-0.0570236\pi$
$314$	13.2741			0.749099
$315$		0			0
$316$	−62.5642			−3.51951
$317$	−4.28137	+	15.9783i	−0.240466	+	0.897431i	0.735143	+	0.677912i	$0.237115\pi$
$317$	−4.28137	+	15.9783i	−0.240466	+	0.897431i	−0.975608	+	0.219518i	$0.929551\pi$
$318$		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	−0.954138	−	0.299367i	$-0.903225\pi$
$331$	−13.3963	−	23.2031i	−0.736328	−	1.27536i	0.217810	−	0.975991i	$-0.430109\pi$
$332$	−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	−0.795657	−	0.605747i	$-0.792874\pi$
$337$	−3.48628	+	3.48628i	−0.189910	+	0.189910i	0.605747	+	0.795657i	$0.292874\pi$
$338$	−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	0.432325	−	0.901718i	$-0.357693\pi$
$347$	23.4263	−	6.27705i	1.25759	−	0.336970i	0.825263	+	0.564748i	$0.191027\pi$
$348$		0			0
$349$			0.641866i			0.0343583i	0.999852	+	0.0171792i	$0.00546857\pi$
$349$			0.641866i			0.0343583i	−0.999852	+	0.0171792i	$0.994531\pi$
$350$	28.5942	+	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	0.978044	−	0.208400i	$-0.0668254\pi$
$353$	0.504151	+	1.88152i	0.0268332	+	0.100143i	−0.951211	+	0.308543i	$0.900159\pi$
$354$		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	0.957654	−	0.287921i	$-0.0929641\pi$
$359$	4.34803	+	7.53101i	0.229480	+	0.397471i	−0.728174	+	0.685392i	$0.759631\pi$
$360$		0			0
$361$	10.7486	−	18.6172i	0.565718	−	0.979853i
$362$	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	−0.727799	−	0.685790i	$-0.759457\pi$
$367$	−8.43689	−	31.4869i	−0.440402	−	1.64360i	0.287397	−	0.957811i	$-0.407210\pi$
$368$	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	0.722019	+	0.691873i	$0.243214\pi$
$373$	−4.81293	+	17.9621i	−0.249204	+	0.930043i	−0.971224	+	0.238170i	$0.923453\pi$
$374$	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	$-0.0971122\pi$
$380$	30.7267	+	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	0.461371	−	0.887207i	$-0.347358\pi$
$383$	8.16722	+	2.18840i	0.417326	+	0.111822i	−0.0440451	+	0.999030i	$0.514025\pi$
$384$		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	−0.429049	−	0.903281i	$-0.641151\pi$
$389$	11.1976	−	19.3948i	0.567740	−	0.983354i	0.996789	−	0.0800731i	$-0.0255154\pi$
$390$		0			0
$391$	0.280638			0.0141925
$392$	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	0.0463203	−	0.998927i	$-0.485251\pi$
$397$	−8.22953	−	2.20510i	−0.413028	−	0.110671i	−0.459349	+	0.888256i	$0.651917\pi$
$398$	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	$-0.563949\pi$
$401$	10.9993	−	6.35044i	0.549278	−	0.317126i	0.748831	+	0.662761i	$0.230616\pi$
$402$		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	0.944572	−	0.328304i	$-0.106477\pi$
$409$	22.9042	+	13.2237i	1.13254	+	0.653871i	0.187966	+	0.982175i	$0.439810\pi$
$410$	−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	0.805270	−	0.592908i	$-0.202020\pi$
$431$	14.4168	+	8.32354i	0.694432	+	0.400931i	−0.110838	+	0.993838i	$0.535353\pi$
$432$		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
$437$	1.69143	−	0.453216i	0.0809119	−	0.0216803i
$438$		0			0
$439$	28.2457	−	16.3077i	1.34810	−	0.778324i	0.360116	−	0.932907i	$-0.382737\pi$
$439$	28.2457	−	16.3077i	1.34810	−	0.778324i	0.987980	+	0.154584i	$0.0494036\pi$
$440$	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	−0.0558717	−	0.998438i	$-0.517794\pi$
$443$	−12.7017	−	3.40342i	−0.603477	−	0.161701i	−0.547605	+	0.836737i	$0.684460\pi$
$444$		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	0.0942205	−	0.995551i	$-0.469964\pi$
$457$	−6.88267	−	1.84421i	−0.321958	−	0.0862684i	−0.416178	+	0.909283i	$0.636631\pi$
$458$	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	$0.182401\pi$
$461$			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
$467$	−2.38672	+	8.90737i	−0.110444	+	0.412184i	−0.998906	−	0.0467673i	$-0.985108\pi$
$467$	−2.38672	+	8.90737i	−0.110444	+	0.412184i	0.888461	+	0.458951i	$0.151775\pi$
$468$		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	−0.995253	−	0.0973193i	$-0.968973\pi$
$479$	−9.04651	+	15.6690i	−0.413346	+	0.715936i	0.581908	+	0.813255i	$0.302307\pi$
$480$		0			0
$481$	4.25581	+	7.37129i	0.194048	+	0.336102i
$482$	−1.55959	−	1.55959i	−0.0710373	−	0.0710373i
$483$		0			0
$484$		−	60.6183i		−	2.75538i
$485$	−0.727329	−	0.195232i	−0.0330263	−	0.00886503i
$486$		0			0
$487$	0.627663	+	2.34247i	0.0284421	+	0.106148i	0.978688	−	0.205354i	$-0.0658347\pi$
$487$	0.627663	+	2.34247i	0.0284421	+	0.106148i	−0.950246	+	0.311502i	$0.899168\pi$
$488$	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	$-0.888054\pi$
$491$		−	15.2664i		−	0.688965i	0.938793	−	0.344483i	$-0.111946\pi$
$492$		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	−0.504293	−	0.863533i	$-0.668247\pi$
$499$	−0.192077	+	0.110896i	−0.00859855	+	0.00496437i	0.495695	+	0.868497i	$0.334914\pi$
$500$	−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	−0.972007	−	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
$508$	13.9104	−	3.72727i	0.617173	−	0.165371i
$509$	−1.68470	−	2.91798i	−0.0746729	−	0.129337i	0.826271	−	0.563273i	$-0.190458\pi$
$509$	−1.68470	−	2.91798i	−0.0746729	−	0.129337i	−0.900944	+	0.433935i	$0.857125\pi$
$510$		0			0
$511$	−24.0194	+	13.4958i	−1.06256	+	0.597019i
$512$	34.9000	+	34.9000i	1.54238	+	1.54238i
$513$		0			0
$514$	−5.74096	−	3.31455i	−0.253223	−	0.146198i
$515$	−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	0.914604	−	0.404351i	$-0.132503\pi$
$521$	23.3214	+	13.4646i	1.02173	+	0.589895i	0.107124	+	0.994246i	$0.465836\pi$
$522$		0			0
$523$	−4.03169	+	15.0465i	−0.176294	+	0.657936i	0.820034	+	0.572315i	$0.193954\pi$
$523$	−4.03169	+	15.0465i	−0.176294	+	0.657936i	−0.996328	+	0.0856218i	$0.972712\pi$
$524$	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	0.757185	−	0.653200i	$-0.226574\pi$
$541$	−4.35172	−	7.53741i	−0.187095	−	0.324059i	−0.944281	+	0.329142i	$0.893241\pi$
$542$	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	−0.879218	−	0.476420i	$-0.841934\pi$
$547$	−9.42064	+	9.42064i	−0.402798	+	0.402798i	0.476420	+	0.879218i	$0.341934\pi$
$548$	−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	0.769754	−	0.638341i	$-0.220379\pi$
$557$	41.4325	−	11.1018i	1.75555	−	0.470398i	0.985797	+	0.167943i	$0.0537124\pi$
$558$		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	0.965468	−	0.260521i	$-0.0838942\pi$
$563$	−0.0216411	−	0.0807657i	−0.000912064	−	0.00340387i	−0.966380	+	0.257117i	$0.917228\pi$
$564$		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	0.685088	−	0.728460i	$-0.259764\pi$
$569$	−6.87752	−	11.9122i	−0.288321	−	0.499386i	−0.973409	+	0.229074i	$0.926430\pi$
$570$		0			0
$571$	11.2197	−	19.4331i	0.469530	−	0.813251i	−0.529863	−	0.848083i	$-0.677757\pi$
$571$	11.2197	−	19.4331i	0.469530	−	0.813251i	0.999393	+	0.0348328i	$0.0110899\pi$
$572$	−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	0.987970	+	0.154644i	$0.0494229\pi$
$577$	5.03680	+	18.7976i	0.209685	+	0.782554i	−0.778286	+	0.627910i	$0.783910\pi$
$578$	−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	0.947560	−	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
$590$	−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	−0.378259	−	0.925700i	$-0.623477\pi$
$593$	−28.4595	−	7.62569i	−1.16869	−	0.313150i	−0.790432	+	0.612550i	$0.790144\pi$
$594$		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	0.153541	+	0.988142i	$0.450932\pi$
$599$	−19.0653	+	33.0220i	−0.778986	+	1.34924i	−0.932527	+	0.361101i	$0.882401\pi$
$600$		0			0
$601$	2.21756			0.0904563			0.0452282	−	0.998977i	$-0.485599\pi$
$601$	2.21756			0.0904563			0.0452282	+	0.998977i	$0.485599\pi$
$602$	8.27538	−	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	0.188481	−	0.982077i	$-0.439644\pi$
$607$	−3.43269	−	0.919787i	−0.139329	−	0.0373330i	−0.327809	+	0.944744i	$0.606310\pi$
$608$	−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	0.408897	−	0.912580i	$-0.365913\pi$
$613$	30.1885	−	8.08899i	1.21930	−	0.326711i	0.810406	+	0.585869i	$0.199247\pi$
$614$	−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	−0.990372	−	0.138433i	$-0.955794\pi$
$619$	−39.9430	−	23.0611i	−1.60544	−	0.926903i	−0.615072	−	0.788471i	$-0.710873\pi$
$620$	−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	0.914439	−	0.404724i	$-0.132632\pi$
$641$	25.8536	+	14.9266i	1.02116	+	0.589566i	0.106719	+	0.994289i	$0.465966\pi$
$642$		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
$647$	−1.20998	+	0.324212i	−0.0475691	+	0.0127461i	−0.282525	−	0.959260i	$-0.591172\pi$
$647$	−1.20998	+	0.324212i	−0.0475691	+	0.0127461i	0.234956	+	0.972006i	$0.424505\pi$
$648$		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	0.0654169	−	0.997858i	$-0.479162\pi$
$653$	−9.63022	−	2.58041i	−0.376859	−	0.100979i	−0.442276	+	0.896879i	$0.645829\pi$
$654$		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	−0.559822	−	0.828613i	$-0.689131\pi$
$661$	11.2529	−	19.4907i	0.437689	−	0.758099i	0.997511	+	0.0705137i	$0.0224639\pi$
$662$	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	0.998137	+	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
$677$	−4.76445	+	17.7812i	−0.183113	+	0.683386i	0.811914	+	0.583777i	$0.198426\pi$
$677$	−4.76445	+	17.7812i	−0.183113	+	0.683386i	−0.995027	+	0.0996090i	$0.968241\pi$
$678$		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	−0.920706	−	0.390257i	$-0.872386\pi$
$683$	−8.32323	−	31.0627i	−0.318480	−	1.18858i	0.602226	−	0.798325i	$-0.294280\pi$
$684$		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	0.958235	−	0.285984i	$-0.0923203\pi$
$691$	6.08405	+	10.5379i	0.231448	+	0.400880i	−0.726786	+	0.686864i	$0.758987\pi$
$692$	−48.7551	−	48.7551i	−1.85339	−	1.85339i
$693$		0			0
$694$			60.9797i			2.31476i
$695$	−2.22083	+	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	$-0.803065\pi$
$701$		−	30.7110i		−	1.15994i	0.814639	−	0.579969i	$-0.196935\pi$
$702$		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	−0.404688	−	0.914455i	$-0.632620\pi$
$709$	4.92357	−	2.84263i	0.184909	−	0.106757i	0.589597	+	0.807698i	$0.299287\pi$
$710$	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	0.780129	−	0.625619i	$-0.215153\pi$
$719$	−4.06871	−	7.04721i	−0.151737	−	0.262817i	−0.931866	+	0.362802i	$0.881820\pi$
$720$		0			0
$721$	−0.327092	+	27.9849i	−0.0121816	+	1.04221i
$722$	38.2204	+	38.2204i	1.42241	+	1.42241i
$723$		0			0
$724$	35.7526	+	20.6418i	1.32874	+	0.767146i
$725$	−10.1507	+	17.5458i	−0.376989	+	0.651633i
$726$		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	$-0.188687\pi$
$728$	−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	−0.403868	−	0.914817i	$-0.632334\pi$
$733$	10.9190	−	40.7501i	0.403301	−	1.50514i	0.807168	−	0.590321i	$-0.200999\pi$
$734$	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	0.997110	+	0.0759743i	$0.0242067\pi$
$739$	42.4476	+	24.5071i	1.56146	+	0.901510i	0.564351	+	0.825535i	$0.309127\pi$
$740$	−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	0.0554047	−	0.998464i	$-0.482355\pi$
$743$	28.7264	−	28.7264i	1.05387	−	1.05387i	0.998464	−	0.0554047i	$-0.0176449\pi$
$744$		0			0
$745$	20.6620	−	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	0.933698	−	0.358061i	$-0.116562\pi$
$751$	4.29587	+	7.44067i	0.156759	+	0.271514i	−0.776939	+	0.629575i	$0.783229\pi$
$752$	−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	−0.670842	−	0.741600i	$-0.734067\pi$
$757$	1.94682	−	1.94682i	0.0707583	−	0.0707583i	0.741600	+	0.670842i	$0.234067\pi$
$758$	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	−0.779981	−	0.625803i	$-0.784771\pi$
$761$	−17.3244	+	10.0023i	−0.628011	+	0.362582i	0.151971	+	0.988385i	$0.451438\pi$
$762$		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	$-0.805871\pi$
$769$		−	31.7665i		−	1.14553i	0.819720	−	0.572764i	$-0.194129\pi$
$770$	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	0.953382	+	0.301768i	$0.0975766\pi$
$773$	7.74623	+	28.9093i	0.278613	+	1.03980i	−0.674769	+	0.738029i	$0.735757\pi$
$774$		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	0.977287	−	0.211919i	$-0.0679713\pi$
$787$	0.700556	+	2.61451i	0.0249721	+	0.0931973i	−0.952315	+	0.305116i	$0.901305\pi$
$788$	−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	0.962564	−	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
$800$	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	−0.809902	−	0.586565i	$-0.800480\pi$
$809$	2.93046	−	5.07571i	0.103030	−	0.178452i	0.912931	+	0.408113i	$0.133813\pi$
$810$		0			0
$811$	−16.1090			−0.565662			−0.282831	−	0.959170i	$-0.591274\pi$
$811$	−16.1090			−0.565662			−0.282831	+	0.959170i	$0.591274\pi$
$812$	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	0.308439	−	0.951244i	$-0.400194\pi$
$821$	36.8611	−	21.2817i	1.28646	−	0.742738i	0.978021	+	0.208507i	$0.0668602\pi$
$822$		0			0
$823$	31.9667	−	8.56545i	1.11429	−	0.298573i	0.345719	−	0.938338i	$-0.387635\pi$
$823$	31.9667	−	8.56545i	1.11429	−	0.298573i	0.768570	+	0.639765i	$0.220968\pi$
$824$	−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	$-0.107692\pi$
$829$	32.4643	+	18.7432i	1.12753	+	0.650980i	0.184218	+	0.982885i	$0.441025\pi$
$830$	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	0.809848	−	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
$857$	−29.6460	+	7.94363i	−1.01269	+	0.271349i	−0.726752	−	0.686899i	$-0.758971\pi$
$857$	−29.6460	+	7.94363i	−1.01269	+	0.271349i	−0.285936	+	0.958249i	$0.592305\pi$
$858$		0			0
$859$	−30.5614	+	17.6447i	−1.04274	+	0.602028i	−0.920609	−	0.390486i	$-0.872307\pi$
$859$	−30.5614	+	17.6447i	−1.04274	+	0.602028i	−0.122134	+	0.992514i	$0.538974\pi$
$860$	−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	0.974328	−	0.225134i	$-0.0722821\pi$
$863$	50.1038	+	13.4253i	1.70555	+	0.457002i	0.731225	+	0.682136i	$0.238949\pi$
$864$		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	−0.0929832	−	0.995668i	$-0.529640\pi$
$877$	−19.8813	−	5.32717i	−0.671343	−	0.179886i	−0.578360	+	0.815782i	$0.696307\pi$
$878$	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	$-0.899577\pi$
$881$		−	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
$887$	3.91318	−	14.6042i	0.131392	−	0.490361i	−0.868595	−	0.495523i	$-0.834976\pi$
$887$	3.91318	−	14.6042i	0.131392	−	0.490361i	0.999987	+	0.00516191i	$0.00164309\pi$
$888$		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	0.956691	+	0.291104i	$0.0940227\pi$
$907$	8.24361	+	30.7656i	0.273725	+	1.02155i	−0.682967	+	0.730449i	$0.739311\pi$
$908$	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	$-0.735720\pi$
$911$		−	44.5563i		−	1.47621i	0.674683	−	0.738107i	$-0.264280\pi$
$912$		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	−0.896994	−	0.442043i	$-0.854254\pi$
$919$	−29.1834	+	16.8490i	−0.962671	+	0.555798i	−0.0656768	+	0.997841i	$0.520921\pi$
$920$	−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	0.974084	−	0.226185i	$-0.0726253\pi$
$929$	8.87442	+	15.3710i	0.291160	+	0.504305i	−0.682924	+	0.730489i	$0.739292\pi$
$930$		0			0
$931$	23.1687	−	38.0470i	0.759324	−	1.24694i
$932$	−65.0819	−	65.0819i	−2.13183	−	2.13183i
$933$		0			0
$934$	−20.0799	−	11.5932i	−0.657036	−	0.379340i
$935$	2.94786	+	11.0210i	0.0964052	+	0.360427i
$936$		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	$0.495376\pi$
$938$	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	−0.0555241	−	0.998457i	$-0.517683\pi$
$941$	−29.0798	−	16.7893i	−0.947976	−	0.547314i	−0.892451	+	0.451143i	$0.851016\pi$
$942$		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	0.721939	+	0.691957i	$0.243251\pi$
$947$	−7.67048	+	28.6266i	−0.249257	+	0.930240i	−0.971196	+	0.238283i	$0.923415\pi$
$948$		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	−0.396202	−	0.918163i	$-0.629672\pi$
$953$	16.1133	−	16.1133i	0.521961	−	0.521961i	0.918163	+	0.396202i	$0.129672\pi$
$954$		0			0
$955$	38.0563	+	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	0.0626698	−	0.998034i	$-0.480039\pi$
$967$	32.9843	−	32.9843i	1.06070	−	1.06070i	0.998034	−	0.0626698i	$-0.0199615\pi$
$968$	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	−0.928820	−	0.370531i	$-0.879176\pi$
$971$	−33.4151	+	19.2922i	−1.07234	+	0.619117i	−0.143521	+	0.989647i	$0.545842\pi$
$972$		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	−0.222041	−	0.975037i	$-0.571272\pi$
$977$	2.28755	−	0.612947i	0.0731852	−	0.0196099i	0.295226	+	0.955428i	$0.404605\pi$
$978$		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	0.977974	+	0.208727i	$0.0669319\pi$
$983$	7.38005	+	27.5427i	0.235387	+	0.878476i	−0.742587	+	0.669750i	$0.766401\pi$
$984$		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	−0.971672	−	0.236332i	$-0.924055\pi$
$991$	−8.85117	+	15.3307i	−0.281167	+	0.486995i	0.690506	+	0.723327i	$0.257388\pi$
$992$	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	0.739912	+	0.672704i	$0.234867\pi$
$997$	13.7505	+	51.3174i	0.435481	+	1.62524i	−0.304431	+	0.952535i	$0.598466\pi$
$998$	−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.53.2	✓	128
3.2	odd	2	inner	945.2.ch.a.53.31	yes	128
5.2	odd	4	inner	945.2.ch.a.242.2	yes	128
7.2	even	3	inner	945.2.ch.a.863.31	yes	128
15.2	even	4	inner	945.2.ch.a.242.31	yes	128
21.2	odd	6	inner	945.2.ch.a.863.2	yes	128
35.2	odd	12	inner	945.2.ch.a.107.31	yes	128
105.2	even	12	inner	945.2.ch.a.107.2	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
945.2.ch.a.53.2	✓	128	1.1	even	1	trivial
945.2.ch.a.53.31	yes	128	3.2	odd	2	inner
945.2.ch.a.107.2	yes	128	105.2	even	12	inner
945.2.ch.a.107.31	yes	128	35.2	odd	12	inner
945.2.ch.a.242.2	yes	128	5.2	odd	4	inner
945.2.ch.a.242.31	yes	128	15.2	even	4	inner
945.2.ch.a.863.2	yes	128	21.2	odd	6	inner
945.2.ch.a.863.31	yes	128	7.2	even	3	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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