LMFDB - Embedded newform 572.2.bk.a.31.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(31,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 12, 15]))

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

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

chi := DirichletCharacter("572.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.bk (of order $20$, degree $8$, 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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$640$
Relative dimension:	$80$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			31.8
Character	$\chi$	$=$	572.31
Dual form			572.2.bk.a.203.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.35684 - 0.398721i) q^{2} +(-1.82403 - 2.51057i) q^{3} +(1.68204 + 1.08200i) q^{4} +(-2.67101 - 1.36095i) q^{5} +(1.47391 + 4.13373i) q^{6} +(-2.81984 + 0.446619i) q^{7} +(-1.85085 - 2.13877i) q^{8} +(-2.04880 + 6.30555i) q^{9} +O(q^{10})$	\(q+(-1.35684 - 0.398721i) q^{2} +(-1.82403 - 2.51057i) q^{3} +(1.68204 + 1.08200i) q^{4} +(-2.67101 - 1.36095i) q^{5} +(1.47391 + 4.13373i) q^{6} +(-2.81984 + 0.446619i) q^{7} +(-1.85085 - 2.13877i) q^{8} +(-2.04880 + 6.30555i) q^{9} +(3.08150 + 2.91158i) q^{10} +(-3.18471 - 0.926083i) q^{11} +(-0.351662 - 6.19649i) q^{12} +(3.26739 + 1.52453i) q^{13} +(4.00416 + 0.518339i) q^{14} +(1.45526 + 9.18816i) q^{15} +(1.65854 + 3.63995i) q^{16} +(3.36744 - 1.09415i) q^{17} +(5.29405 - 7.73875i) q^{18} +(-6.44543 - 1.02086i) q^{19} +(-3.02020 - 5.17921i) q^{20} +(6.26476 + 6.26476i) q^{21} +(3.95190 + 2.52636i) q^{22} +0.595326 q^{23} +(-1.99352 + 8.54788i) q^{24} +(2.34319 + 3.22512i) q^{25} +(-3.82547 - 3.37132i) q^{26} +(10.7136 - 3.48104i) q^{27} +(-5.22634 - 2.29985i) q^{28} +(-8.06247 - 5.85773i) q^{29} +(1.68895 - 13.0471i) q^{30} +(1.73450 - 0.883773i) q^{31} +(-0.799050 - 5.60014i) q^{32} +(3.48402 + 9.68463i) q^{33} +(-5.00534 + 0.141917i) q^{34} +(8.13965 + 2.64473i) q^{35} +(-10.2688 + 8.38941i) q^{36} +(-0.428374 - 2.70465i) q^{37} +(8.33840 + 3.95507i) q^{38} +(-2.13240 - 10.9838i) q^{39} +(2.03288 + 8.23159i) q^{40} +(-0.771756 + 4.87268i) q^{41} +(-6.00240 - 10.9982i) q^{42} +4.83437 q^{43} +(-4.35479 - 5.00358i) q^{44} +(14.0539 - 14.0539i) q^{45} +(-0.807764 - 0.237369i) q^{46} +(0.296621 - 1.87279i) q^{47} +(6.11312 - 10.8033i) q^{48} +(1.09465 - 0.355673i) q^{49} +(-1.89341 - 5.31026i) q^{50} +(-8.88925 - 6.45842i) q^{51} +(3.84634 + 6.09964i) q^{52} +(2.90071 - 8.92746i) q^{53} +(-15.9246 + 0.451511i) q^{54} +(7.24604 + 6.80780i) q^{55} +(6.17432 + 5.20438i) q^{56} +(9.19376 + 18.0438i) q^{57} +(8.60391 + 11.1627i) q^{58} +(12.3355 - 1.95375i) q^{59} +(-7.49381 + 17.0295i) q^{60} +(2.73429 + 8.41528i) q^{61} +(-2.70583 + 0.507558i) q^{62} +(2.96111 - 18.6957i) q^{63} +(-1.14871 + 7.91710i) q^{64} +(-6.65242 - 8.51876i) q^{65} +(-0.865805 - 14.5297i) q^{66} +(2.47404 + 2.47404i) q^{67} +(6.84804 + 1.80318i) q^{68} +(-1.08590 - 1.49461i) q^{69} +(-9.98971 - 6.83394i) q^{70} +(-1.95297 + 3.83292i) q^{71} +(17.2782 - 7.28872i) q^{72} +(0.132251 + 0.834998i) q^{73} +(-0.497163 + 3.84058i) q^{74} +(3.82283 - 11.7655i) q^{75} +(-9.73692 - 8.69110i) q^{76} +(9.39398 + 1.18906i) q^{77} +(-1.48613 + 15.7535i) q^{78} +(-0.216356 - 0.0702984i) q^{79} +(0.523811 - 11.9795i) q^{80} +(-12.1898 - 8.85642i) q^{81} +(2.98999 - 6.30374i) q^{82} +(-3.72865 + 7.31789i) q^{83} +(3.75911 + 17.3161i) q^{84} +(-10.4835 - 1.66043i) q^{85} +(-6.55947 - 1.92756i) q^{86} +30.9261i q^{87} +(3.91374 + 8.52541i) q^{88} +(8.76427 + 8.76427i) q^{89} +(-24.6725 + 13.4653i) q^{90} +(-9.89440 - 2.83965i) q^{91} +(1.00136 + 0.644145i) q^{92} +(-5.38256 - 2.74255i) q^{93} +(-1.14919 + 2.42282i) q^{94} +(15.8265 + 11.4986i) q^{95} +(-12.6020 + 12.2209i) q^{96} +(-4.64452 - 9.11539i) q^{97} +(-1.62708 + 0.0461328i) q^{98} +(12.3643 - 18.1840i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 640 q - 6 q^{2} - 12 q^{5} - 14 q^{6} - 6 q^{8} + 120 q^{9}+O(q^{10}) $ 640 * q - 6 * q^2 - 12 * q^5 - 14 * q^6 - 6 * q^8 + 120 * q^9	$ 640 q - 6 q^{2} - 12 q^{5} - 14 q^{6} - 6 q^{8} + 120 q^{9} - 12 q^{13} + 4 q^{14} - 36 q^{16} - 10 q^{18} - 60 q^{20} - 56 q^{21} - 44 q^{22} - 14 q^{24} + 26 q^{26} - 14 q^{28} - 24 q^{29} - 16 q^{32} - 28 q^{33} + 12 q^{34} - 12 q^{37} + 4 q^{40} - 36 q^{41} - 8 q^{42} + 26 q^{44} - 16 q^{45} - 50 q^{46} + 48 q^{48} + 36 q^{50} - 52 q^{52} - 40 q^{53} + 116 q^{54} - 36 q^{57} - 70 q^{58} + 52 q^{60} - 8 q^{61} - 48 q^{65} - 228 q^{66} - 44 q^{68} - 68 q^{70} - 38 q^{72} - 12 q^{73} - 12 q^{74} + 108 q^{76} + 108 q^{78} + 62 q^{80} - 168 q^{81} - 36 q^{84} - 52 q^{85} - 62 q^{86} + 16 q^{89} - 80 q^{92} - 4 q^{93} - 124 q^{94} - 132 q^{96} - 4 q^{97} - 108 q^{98}+O(q^{100}) $ 640 * q - 6 * q^2 - 12 * q^5 - 14 * q^6 - 6 * q^8 + 120 * q^9 - 12 * q^13 + 4 * q^14 - 36 * q^16 - 10 * q^18 - 60 * q^20 - 56 * q^21 - 44 * q^22 - 14 * q^24 + 26 * q^26 - 14 * q^28 - 24 * q^29 - 16 * q^32 - 28 * q^33 + 12 * q^34 - 12 * q^37 + 4 * q^40 - 36 * q^41 - 8 * q^42 + 26 * q^44 - 16 * q^45 - 50 * q^46 + 48 * q^48 + 36 * q^50 - 52 * q^52 - 40 * q^53 + 116 * q^54 - 36 * q^57 - 70 * q^58 + 52 * q^60 - 8 * q^61 - 48 * q^65 - 228 * q^66 - 44 * q^68 - 68 * q^70 - 38 * q^72 - 12 * q^73 - 12 * q^74 + 108 * q^76 + 108 * q^78 + 62 * q^80 - 168 * q^81 - 36 * q^84 - 52 * q^85 - 62 * q^86 + 16 * q^89 - 80 * q^92 - 4 * q^93 - 124 * q^94 - 132 * q^96 - 4 * q^97 - 108 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−1.35684	−	0.398721i	−0.959433	−	0.281938i
$2$	−1.35684	−	0.398721i	−0.959433	−	0.281938i
$3$	−1.82403	−	2.51057i	−1.05311	−	1.44948i	−0.886084	−	0.463524i	$-0.846585\pi$
$3$	−1.82403	−	2.51057i	−1.05311	−	1.44948i	−0.167022	−	0.985953i	$-0.553415\pi$
$4$	1.68204	+	1.08200i	0.841022	+	0.541002i
$5$	−2.67101	−	1.36095i	−1.19451	−	0.608634i	−0.260360	−	0.965512i	$-0.583841\pi$
$5$	−2.67101	−	1.36095i	−1.19451	−	0.608634i	−0.934151	+	0.356877i	$0.883841\pi$
$6$	1.47391	+	4.13373i	0.601722	+	1.68759i
$7$	−2.81984	+	0.446619i	−1.06580	+	0.168806i	−0.664611	−	0.747189i	$-0.731403\pi$
$7$	−2.81984	+	0.446619i	−1.06580	+	0.168806i	−0.401189	+	0.915995i	$0.631403\pi$
$8$	−1.85085	−	2.13877i	−0.654374	−	0.756171i
$9$	−2.04880	+	6.30555i	−0.682933	+	2.10185i
$10$	3.08150	+	2.91158i	0.974456	+	0.920722i
$11$	−3.18471	−	0.926083i	−0.960226	−	0.279224i
$11$	−3.18471	−	0.926083i	−0.960226	−	0.279224i
$12$	−0.351662	−	6.19649i	−0.101516	−	1.78877i
$13$	3.26739	+	1.52453i	0.906210	+	0.422827i
$13$	3.26739	+	1.52453i	0.906210	+	0.422827i
$14$	4.00416	+	0.518339i	1.07016	+	0.138532i
$15$	1.45526	+	9.18816i	0.375747	+	2.37237i
$16$	1.65854	+	3.63995i	0.414635	+	0.909988i
$17$	3.36744	−	1.09415i	0.816723	−	0.265370i	0.129281	−	0.991608i	$-0.458733\pi$
$17$	3.36744	−	1.09415i	0.816723	−	0.265370i	0.687443	+	0.726239i	$0.258733\pi$
$18$	5.29405	−	7.73875i	1.24782	−	1.82404i
$19$	−6.44543	−	1.02086i	−1.47868	−	0.234200i	−0.635615	−	0.772006i	$-0.719253\pi$
$19$	−6.44543	−	1.02086i	−1.47868	−	0.234200i	−0.843069	+	0.537806i	$0.819253\pi$
$20$	−3.02020	−	5.17921i	−0.675338	−	1.15811i
$21$	6.26476	+	6.26476i	1.36708	+	1.36708i
$22$	3.95190	+	2.52636i	0.842548	+	0.538622i
$23$	0.595326			0.124134			0.0620670	−	0.998072i	$-0.480231\pi$
$23$	0.595326			0.124134			0.0620670	+	0.998072i	$0.480231\pi$
$24$	−1.99352	+	8.54788i	−0.406926	+	1.74483i
$25$	2.34319	+	3.22512i	0.468637	+	0.645024i
$26$	−3.82547	−	3.37132i	−0.750236	−	0.661170i
$27$	10.7136	−	3.48104i	2.06182	−	0.669927i
$28$	−5.22634	−	2.29985i	−0.987686	−	0.434630i
$29$	−8.06247	−	5.85773i	−1.49716	−	1.08775i	−0.971494	−	0.237065i	$-0.923815\pi$
$29$	−8.06247	−	5.85773i	−1.49716	−	1.08775i	−0.525670	−	0.850689i	$-0.676185\pi$
$30$	1.68895	−	13.0471i	0.308359	−	2.38207i
$31$	1.73450	−	0.883773i	0.311526	−	0.158730i	−0.291237	−	0.956651i	$-0.594067\pi$
$31$	1.73450	−	0.883773i	0.311526	−	0.158730i	0.602762	+	0.797921i	$0.294067\pi$
$32$	−0.799050	−	5.60014i	−0.141253	−	0.989973i
$33$	3.48402	+	9.68463i	0.606491	+	1.68588i
$34$	−5.00534	+	0.141917i	−0.858409	+	0.0243385i
$35$	8.13965	+	2.64473i	1.37585	+	0.447041i
$36$	−10.2688	+	8.38941i	−1.71147	+	1.39823i
$37$	−0.428374	−	2.70465i	−0.0704242	−	0.444641i	−0.997554	−	0.0699005i	$-0.977732\pi$
$37$	−0.428374	−	2.70465i	−0.0704242	−	0.444641i	0.927130	−	0.374740i	$-0.122268\pi$
$38$	8.33840	+	3.95507i	1.35267	+	0.641597i
$39$	−2.13240	−	10.9838i	−0.341457	−	1.75881i
$40$	2.03288	+	8.23159i	0.321427	+	1.30153i
$41$	−0.771756	+	4.87268i	−0.120528	+	0.760984i	0.851193	+	0.524853i	$0.175880\pi$
$41$	−0.771756	+	4.87268i	−0.120528	+	0.760984i	−0.971721	+	0.236131i	$0.924120\pi$
$42$	−6.00240	−	10.9982i	−0.926190	−	1.69706i
$43$	4.83437			0.737234			0.368617	−	0.929581i	$-0.379831\pi$
$43$	4.83437			0.737234			0.368617	+	0.929581i	$0.379831\pi$
$44$	−4.35479	−	5.00358i	−0.656510	−	0.754318i
$45$	14.0539	−	14.0539i	2.09503	−	2.09503i
$46$	−0.807764	−	0.237369i	−0.119098	−	0.0349981i
$47$	0.296621	−	1.87279i	0.0432667	−	0.273175i	−0.956565	−	0.291519i	$-0.905839\pi$
$47$	0.296621	−	1.87279i	0.0432667	−	0.273175i	0.999832	+	0.0183439i	$0.00583936\pi$
$48$	6.11312	−	10.8033i	0.882352	−	1.55932i
$49$	1.09465	−	0.355673i	0.156378	−	0.0508104i
$50$	−1.89341	−	5.31026i	−0.267769	−	0.750984i
$51$	−8.88925	−	6.45842i	−1.24474	−	0.904359i
$52$	3.84634	+	6.09964i	0.533392	+	0.845868i
$53$	2.90071	−	8.92746i	0.398443	−	1.22628i	−0.527805	−	0.849366i	$-0.676985\pi$
$53$	2.90071	−	8.92746i	0.398443	−	1.22628i	0.926248	−	0.376915i	$-0.123015\pi$
$54$	−15.9246	+	0.451511i	−2.16706	+	0.0614428i
$55$	7.24604	+	6.80780i	0.977055	+	0.917963i
$56$	6.17432	+	5.20438i	0.825079	+	0.695465i
$57$	9.19376	+	18.0438i	1.21774	+	2.38996i
$58$	8.60391	+	11.1627i	1.12975	+	1.46573i
$59$	12.3355	−	1.95375i	1.60595	−	0.254357i	0.711884	−	0.702297i	$-0.247842\pi$
$59$	12.3355	−	1.95375i	1.60595	−	0.254357i	0.894063	+	0.447940i	$0.147842\pi$
$60$	−7.49381	+	17.0295i	−0.967447	+	2.19850i
$61$	2.73429	+	8.41528i	0.350090	+	1.07747i	0.958802	+	0.284075i	$0.0916865\pi$
$61$	2.73429	+	8.41528i	0.350090	+	1.07747i	−0.608712	+	0.793391i	$0.708314\pi$
$62$	−2.70583	+	0.507558i	−0.343640	+	0.0644600i
$63$	2.96111	−	18.6957i	0.373065	−	2.35544i
$64$	−1.14871	+	7.91710i	−0.143588	+	0.989638i
$65$	−6.65242	−	8.51876i	−0.825131	−	1.05662i
$66$	−0.865805	−	14.5297i	−0.106573	−	1.78848i
$67$	2.47404	+	2.47404i	0.302252	+	0.302252i	0.841894	−	0.539643i	$-0.181441\pi$
$67$	2.47404	+	2.47404i	0.302252	+	0.302252i	−0.539643	+	0.841894i	$0.681441\pi$
$68$	6.84804	+	1.80318i	0.830447	+	0.218667i
$69$	−1.08590	−	1.49461i	−0.130726	−	0.179929i
$70$	−9.98971	−	6.83394i	−1.19400	−	0.816812i
$71$	−1.95297	+	3.83292i	−0.231775	+	0.454884i	−0.977376	−	0.211508i	$-0.932162\pi$
$71$	−1.95297	+	3.83292i	−0.231775	+	0.454884i	0.745601	+	0.666392i	$0.232162\pi$
$72$	17.2782	−	7.28872i	2.03625	−	0.858984i
$73$	0.132251	+	0.834998i	0.0154788	+	0.0977292i	0.994218	−	0.107378i	$-0.0342456\pi$
$73$	0.132251	+	0.834998i	0.0154788	+	0.0977292i	−0.978739	+	0.205107i	$0.934246\pi$
$74$	−0.497163	+	3.84058i	−0.0577941	+	0.446458i
$75$	3.82283	−	11.7655i	0.441422	−	1.35856i
$76$	−9.73692	−	8.69110i	−1.11690	−	0.996938i
$77$	9.39398	+	1.18906i	1.07054	+	0.135506i
$78$	−1.48613	+	15.7535i	−0.168272	+	1.78373i
$79$	−0.216356	−	0.0702984i	−0.0243420	−	0.00790918i	0.296821	−	0.954933i	$-0.404074\pi$
$79$	−0.216356	−	0.0702984i	−0.0243420	−	0.00790918i	−0.321163	+	0.947024i	$0.604074\pi$
$80$	0.523811	−	11.9795i	0.0585639	−	1.33935i
$81$	−12.1898	−	8.85642i	−1.35442	−	0.984046i
$82$	2.98999	−	6.30374i	0.330189	−	0.696131i
$83$	−3.72865	+	7.31789i	−0.409273	+	0.803243i	−0.999993	−	0.00363295i	$-0.998844\pi$
$83$	−3.72865	+	7.31789i	−0.409273	+	0.803243i	0.590720	+	0.806876i	$0.298844\pi$
$84$	3.75911	+	17.3161i	0.410152	+	1.88934i
$85$	−10.4835	−	1.66043i	−1.13710	−	0.180099i
$86$	−6.55947	−	1.92756i	−0.707326	−	0.207854i
$87$			30.9261i			3.31563i
$88$	3.91374	+	8.52541i	0.417206	+	0.908812i
$89$	8.76427	+	8.76427i	0.929010	+	0.929010i	0.997642	−	0.0686317i	$-0.0218633\pi$
$89$	8.76427	+	8.76427i	0.929010	+	0.929010i	−0.0686317	+	0.997642i	$0.521863\pi$
$90$	−24.6725	+	13.4653i	−2.60071	+	1.41937i
$91$	−9.89440	−	2.83965i	−1.03722	−	0.297676i
$92$	1.00136	+	0.644145i	0.104399	+	0.0671567i
$93$	−5.38256	−	2.74255i	−0.558146	−	0.284390i
$94$	−1.14919	+	2.42282i	−0.118530	+	0.249895i
$95$	15.8265	+	11.4986i	1.62376	+	1.17973i
$96$	−12.6020	+	12.2209i	−1.28619	+	1.24729i
$97$	−4.64452	−	9.11539i	−0.471580	−	0.925528i	−0.997198	−	0.0748069i	$-0.976166\pi$
$97$	−4.64452	−	9.11539i	−0.471580	−	0.925528i	0.525618	−	0.850721i	$-0.323834\pi$
$98$	−1.62708	+	0.0461328i	−0.164360	+	0.00466011i
$99$	12.3643	−	18.1840i	1.24266	−	1.82756i
$100$	0.451751	+	7.96012i	0.0451751	+	0.796012i
$101$	−14.8125	−	4.81288i	−1.47390	−	0.478900i	−0.541617	−	0.840625i	$-0.682188\pi$
$101$	−14.8125	−	4.81288i	−1.47390	−	0.478900i	−0.932285	+	0.361726i	$0.882188\pi$
$102$	9.48621	+	12.3074i	0.939274	+	1.21861i
$103$	4.03745	+	2.93338i	0.397822	+	0.289035i	0.768653	−	0.639666i	$-0.220927\pi$
$103$	4.03745	+	2.93338i	0.397822	+	0.289035i	−0.370831	+	0.928700i	$0.620927\pi$
$104$	−2.78683	−	9.80987i	−0.273271	−	0.961937i
$105$	−8.20722	−	25.2592i	−0.800943	−	2.46505i
$106$	−7.49537	+	10.9566i	−0.728014	+	1.06420i
$107$	1.94868	+	2.68213i	0.188386	+	0.259291i	0.892755	−	0.450543i	$-0.148770\pi$
$107$	1.94868	+	2.68213i	0.188386	+	0.259291i	−0.704368	+	0.709835i	$0.748770\pi$
$108$	21.7872	+	5.73683i	2.09647	+	0.552027i
$109$	1.07731	−	1.07731i	0.103188	−	0.103188i	−0.653628	−	0.756816i	$-0.726754\pi$
$109$	1.07731	−	1.07731i	0.103188	−	0.103188i	0.756816	+	0.653628i	$0.226754\pi$
$110$	−7.11732	−	12.1263i	−0.678610	−	1.15619i
$111$	−6.00883	+	6.00883i	−0.570333	+	0.570333i
$112$	−6.30249	−	9.52336i	−0.595529	−	0.899873i
$113$	−6.84599	+	4.97390i	−0.644016	+	0.467905i	−0.861228	−	0.508219i	$-0.830304\pi$
$113$	−6.84599	+	4.97390i	−0.644016	+	0.467905i	0.217211	+	0.976125i	$0.430304\pi$
$114$	−5.28005	−	28.1483i	−0.494522	−	2.63633i
$115$	−1.59012	−	0.810207i	−0.148280	−	0.0755522i
$116$	−7.22335	−	18.5766i	−0.670671	−	1.72479i
$117$	−16.3072	+	17.4792i	−1.50760	+	1.61596i
$118$	−17.5164	−	2.26749i	−1.61251	−	0.208740i
$119$	−9.00698	+	4.58928i	−0.825668	+	0.420699i
$120$	16.9579	−	20.1184i	1.54804	−	1.83655i
$121$	9.28474	+	5.89861i	0.844067	+	0.536237i
$122$	−0.354652	−	12.5084i	−0.0321087	−	1.13246i
$123$	13.6409	−	6.95038i	1.22996	−	0.626695i
$124$	3.87375	+	0.390193i	0.347873	+	0.0350403i
$125$	0.475297	+	3.00091i	0.0425118	+	0.268409i
$126$	−11.4721	+	24.1865i	−1.02202	+	2.15470i
$127$	2.65577	+	8.17361i	0.235661	+	0.725290i	0.997033	+	0.0769749i	$0.0245261\pi$
$127$	2.65577	+	8.17361i	0.235661	+	0.725290i	−0.761372	+	0.648315i	$0.775474\pi$
$128$	4.71533	−	10.2842i	0.416780	−	0.909007i
$129$	−8.81805	−	12.1370i	−0.776386	−	1.06860i
$130$	5.62968	+	14.2111i	0.493755	+	1.24639i
$131$			17.7333i			1.54936i	0.632351	+	0.774682i	$0.282090\pi$
$131$			17.7333i			1.54936i	−0.632351	+	0.774682i	$0.717910\pi$
$132$	−4.61853	+	20.0597i	−0.401991	+	1.74597i
$133$	18.6310			1.61552
$134$	−2.37043	−	4.34333i	−0.204774	−	0.375206i
$135$	−33.3535	−	5.28268i	−2.87061	−	0.454661i
$136$	−8.57275	−	5.17708i	−0.735108	−	0.443931i
$137$	2.07896	−	4.08019i	0.177618	−	0.348594i	−0.784984	−	0.619517i	$-0.787329\pi$
$137$	2.07896	−	4.08019i	0.177618	−	0.348594i	0.962601	+	0.270922i	$0.0873287\pi$
$138$	0.877458	+	2.46091i	0.0746942	+	0.209487i
$139$	−0.977178	+	1.34497i	−0.0828831	+	0.114079i	−0.848445	−	0.529283i	$-0.822461\pi$
$139$	−0.977178	+	1.34497i	−0.0828831	+	0.114079i	0.765562	+	0.643362i	$0.222461\pi$
$140$	10.8296	+	13.2557i	0.915271	+	1.12031i
$141$	−5.24282	+	2.67135i	−0.441525	+	0.224968i
$142$	4.17814	−	4.42198i	0.350622	−	0.371084i
$143$	−8.99384	−	7.88104i	−0.752103	−	0.659046i
$144$	−26.3499	+	3.00047i	−2.19583	+	0.250040i
$145$	13.5629	+	26.6187i	1.12634	+	2.21056i
$146$	0.153488	−	1.18569i	0.0127028	−	0.0981286i
$147$	−2.88962	−	2.09943i	−0.238332	−	0.173158i
$148$	2.20589	−	5.01283i	0.181323	−	0.412052i
$149$	−2.63629	−	1.34325i	−0.215973	−	0.110044i	0.342657	−	0.939460i	$-0.388673\pi$
$149$	−2.63629	−	1.34325i	−0.215973	−	0.110044i	−0.558630	+	0.829417i	$0.688673\pi$
$150$	−9.87811	+	14.4396i	−0.806544	+	1.17899i
$151$	−1.64871	+	10.4096i	−0.134171	+	0.847119i	0.825173	+	0.564880i	$0.191077\pi$
$151$	−1.64871	+	10.4096i	−0.134171	+	0.847119i	−0.959344	+	0.282240i	$0.908923\pi$
$152$	9.74615	+	15.6748i	0.790517	+	1.27139i
$153$			23.4752i			1.89786i
$154$	−12.2721	−	5.35894i	−0.988910	−	0.431836i
$155$	−5.83564			−0.468730
$156$	8.29770	−	20.7825i	0.664348	−	1.66393i
$157$	−12.3308	+	8.95883i	−0.984103	+	0.714993i	−0.958622	−	0.284683i	$-0.908112\pi$
$157$	−12.3308	+	8.95883i	−0.984103	+	0.714993i	−0.0254812	+	0.999675i	$0.508112\pi$
$158$	0.265532	+	0.181650i	0.0211246	+	0.0144513i
$159$	−27.7040	+	9.00157i	−2.19707	+	0.713871i
$160$	−5.48722	+	16.0455i	−0.433803	+	1.26851i
$161$	−1.67873	+	0.265884i	−0.132302	+	0.0209546i
$162$	13.0084	+	16.8771i	1.02204	+	1.32599i
$163$	−5.16674	−	10.1403i	−0.404691	−	0.794250i	0.595266	−	0.803528i	$-0.297047\pi$
$163$	−5.16674	−	10.1403i	−0.404691	−	0.794250i	−0.999957	+	0.00927834i	$0.997047\pi$
$164$	−6.57038	+	7.36101i	−0.513060	+	0.574798i
$165$	3.87442	−	30.6093i	0.301623	−	2.38293i
$166$	7.97699	−	8.44254i	0.619135	−	0.655268i
$167$	−2.39184	−	4.69426i	−0.185086	−	0.363253i	0.779755	−	0.626085i	$-0.215344\pi$
$167$	−2.39184	−	4.69426i	−0.185086	−	0.363253i	−0.964842	+	0.262832i	$0.915344\pi$
$168$	1.80377	−	24.9940i	0.139164	−	1.92833i
$169$	8.35164	+	9.96243i	0.642434	+	0.766341i
$170$	13.5625	+	6.43294i	1.04019	+	0.493384i
$171$	19.6425	−	38.5505i	1.50210	−	2.94803i
$172$	8.13161	+	5.23080i	0.620030	+	0.398845i
$173$	3.40386	+	4.68501i	0.258790	+	0.356194i	0.918566	−	0.395269i	$-0.129349\pi$
$173$	3.40386	+	4.68501i	0.258790	+	0.356194i	−0.659775	+	0.751463i	$0.729349\pi$
$174$	12.3309	−	41.9618i	0.934802	−	3.18112i
$175$	−8.04782	−	8.04782i	−0.608358	−	0.608358i
$176$	−1.91106	−	13.1281i	−0.144052	−	0.989570i
$177$	−27.4054	−	27.4054i	−2.05992	−	2.05992i
$178$	−8.39723	−	15.3862i	−0.629399	−	1.15325i
$179$	7.50466	−	5.45245i	0.560924	−	0.407535i	−0.270873	−	0.962615i	$-0.587312\pi$
$179$	7.50466	−	5.45245i	0.560924	−	0.407535i	0.831797	+	0.555080i	$0.187312\pi$
$180$	38.8456	−	8.43289i	2.89538	−	0.628551i
$181$	6.13952	−	1.99485i	0.456347	−	0.148276i	−0.0718185	−	0.997418i	$-0.522880\pi$
$181$	6.13952	−	1.99485i	0.456347	−	0.148276i	0.528165	+	0.849142i	$0.322880\pi$
$182$	12.2929	+	7.79806i	0.911212	+	0.578031i
$183$	16.1397	−	22.2144i	1.19308	−	1.64213i
$184$	−1.10186	−	1.27327i	−0.0812302	−	0.0938665i
$185$	−2.53669	+	7.80713i	−0.186501	+	0.573991i
$186$	6.20978	+	5.86735i	0.455323	+	0.430215i
$187$	−11.7376	+	0.366013i	−0.858337	+	0.0267655i
$188$	2.52530	−	2.82918i	0.184176	−	0.206339i
$189$	−28.6558	+	14.6009i	−2.08441	+	1.06206i
$190$	−16.8893	−	21.9121i	−1.22528	−	1.58967i
$191$	6.74297	−	9.28090i	0.487904	−	0.671543i	−0.492096	−	0.870541i	$-0.663769\pi$
$191$	6.74297	−	9.28090i	0.487904	−	0.671543i	0.980000	+	0.198999i	$0.0637689\pi$
$192$	21.9717	−	11.5572i	1.58567	−	0.834066i
$193$	5.62685	−	11.0433i	0.405030	−	0.794915i	−0.594931	−	0.803777i	$-0.702821\pi$
$193$	5.62685	−	11.0433i	0.405030	−	0.794915i	0.999961	+	0.00886127i	$0.00282067\pi$
$194$	2.66739	+	14.2200i	0.191507	+	1.02094i
$195$	−9.25269	+	32.2399i	−0.662599	+	2.30875i
$196$	2.22609	+	0.586157i	0.159006	+	0.0418683i
$197$	−10.3317	+	10.3317i	−0.736102	+	0.736102i	−0.971821	−	0.235719i	$-0.924256\pi$
$197$	−10.3317	+	10.3317i	−0.736102	+	0.736102i	0.235719	+	0.971821i	$0.424256\pi$
$198$	−24.0267	+	19.7429i	−1.70751	+	1.40307i
$199$	−26.7111			−1.89350			−0.946749	−	0.321971i	$-0.895655\pi$
$199$	−26.7111			−1.89350			−0.946749	+	0.321971i	$0.895655\pi$
$200$	2.56091	−	10.9808i	0.181084	−	0.776457i
$201$	1.69851	−	10.7240i	0.119804	−	0.756410i
$202$	18.1793	+	12.4364i	1.27909	+	0.875021i
$203$	25.3511	+	12.9170i	1.77930	+	0.906597i
$204$	−7.96407	−	20.4815i	−0.557597	−	1.43399i
$205$	8.69282	−	11.9646i	0.607133	−	0.835647i
$206$	−4.30859	−	5.58995i	−0.300194	−	0.389471i
$207$	−1.21970	+	3.75386i	−0.0847752	+	0.260911i
$208$	−0.130115	+	14.4216i	−0.00902184	+	0.999959i
$209$	19.5814	+	9.22013i	1.35448	+	0.637770i
$210$	1.06452	+	37.5452i	0.0734590	+	2.59086i
$211$	14.9939	+	4.87180i	1.03222	+	0.335389i	0.775668	−	0.631141i	$-0.217413\pi$
$211$	14.9939	+	4.87180i	1.03222	+	0.335389i	0.256553	+	0.966530i	$0.417413\pi$
$212$	14.5387	−	11.8778i	0.998519	−	0.815770i
$213$	13.1851	−	2.08831i	0.903428	−	0.143089i
$214$	−1.57463	−	4.41621i	−0.107640	−	0.301886i
$215$	−12.9126	−	6.57932i	−0.880634	−	0.448706i
$216$	−27.2744	−	16.4710i	−1.85578	−	1.12071i
$217$	−4.49631	+	3.26676i	−0.305230	+	0.221762i
$218$	−1.89129	+	1.03219i	−0.128094	+	0.0699090i
$219$	1.85509	−	1.85509i	0.125355	−	0.125355i
$220$	4.82209	+	19.2912i	0.325105	+	1.30062i
$221$	12.6708	+	1.55874i	0.852329	+	0.104853i
$222$	10.5489	−	5.75719i	0.707994	−	0.386397i
$223$	1.10819	+	0.175519i	0.0742096	+	0.0117536i	0.193429	−	0.981114i	$-0.438039\pi$
$223$	1.10819	+	0.175519i	0.0742096	+	0.0117536i	−0.119219	+	0.992868i	$0.538039\pi$
$224$	4.75432	+	15.4346i	0.317662	+	1.03127i
$225$	−25.1369	+	8.16747i	−1.67579	+	0.544498i
$226$	11.2721	−	4.01916i	0.749811	−	0.267351i
$227$	3.06070	+	19.3245i	0.203146	+	1.28261i	0.852742	+	0.522332i	$0.174938\pi$
$227$	3.06070	+	19.3245i	0.203146	+	1.28261i	−0.649597	+	0.760279i	$0.725062\pi$
$228$	−4.05912	+	40.2981i	−0.268821	+	2.66881i
$229$	13.4223	−	6.83898i	0.886968	−	0.451933i	0.0497245	−	0.998763i	$-0.484166\pi$
$229$	13.4223	−	6.83898i	0.886968	−	0.451933i	0.837244	+	0.546830i	$0.184166\pi$
$230$	1.83450	+	1.73334i	0.120963	+	0.114293i
$231$	−14.1497	−	25.7531i	−0.930985	−	1.69443i
$232$	2.39407	+	28.0856i	0.157179	+	1.84391i
$233$	−12.1027	−	3.93239i	−0.792872	−	0.257620i	−0.115545	−	0.993302i	$-0.536861\pi$
$233$	−12.1027	−	3.93239i	−0.792872	−	0.257620i	−0.677326	+	0.735683i	$0.736861\pi$
$234$	29.0956	−	17.2146i	1.90204	−	1.12535i
$235$	−3.34105	+	4.59856i	−0.217946	+	0.299977i
$236$	22.8628	+	10.0608i	1.48824	+	0.654900i
$237$	0.218152	+	0.671403i	0.0141705	+	0.0436123i
$238$	14.0509	−	2.63566i	0.910784	−	0.170845i
$239$	4.49950	+	0.712651i	0.291048	+	0.0460975i	0.300251	−	0.953860i	$-0.402929\pi$
$239$	4.49950	+	0.712651i	0.291048	+	0.0460975i	−0.00920293	+	0.999958i	$0.502929\pi$
$240$	−31.0309	+	20.5360i	−2.00303	+	1.32559i
$241$	11.4359	+	11.4359i	0.736653	+	0.736653i	0.971929	−	0.235276i	$-0.0755993\pi$
$241$	11.4359	+	11.4359i	0.736653	+	0.736653i	−0.235276	+	0.971929i	$0.575599\pi$
$242$	−10.2460	−	11.7055i	−0.658640	−	0.752458i
$243$			12.9631i			0.831582i
$244$	−4.50617	+	17.1134i	−0.288478	+	1.09557i
$245$	−3.40787	−	0.539754i	−0.217721	−	0.0344836i
$246$	−21.2798	+	3.99166i	−1.35675	+	0.254499i
$247$	−19.5034	−	13.1618i	−1.24097	−	0.837463i
$248$	−5.10049	−	2.07398i	−0.323882	−	0.131698i
$249$	25.1733	−	3.98705i	1.59529	−	0.252669i
$250$	0.551621	−	4.26127i	0.0348876	−	0.269506i
$251$	−8.64557	+	26.6083i	−0.545704	+	1.67950i	0.173607	+	0.984815i	$0.444458\pi$
$251$	−8.64557	+	26.6083i	−0.545704	+	1.67950i	−0.719311	+	0.694688i	$0.755542\pi$
$252$	25.2095	−	28.2431i	1.58805	−	1.77915i
$253$	−1.89594	−	0.551321i	−0.119197	−	0.0346613i
$254$	−0.344467	−	12.1492i	−0.0216138	−	0.762309i
$255$	14.9537	+	29.3483i	0.936437	+	1.83786i
$256$	−10.4985	+	12.0740i	−0.656156	+	0.754625i
$257$	−5.00906	+	6.89438i	−0.312457	+	0.430060i	−0.936145	−	0.351613i	$-0.885633\pi$
$257$	−5.00906	+	6.89438i	−0.312457	+	0.430060i	0.623689	+	0.781673i	$0.285633\pi$
$258$	7.12543	+	19.9839i	0.443610	+	1.24415i
$259$	2.41589	+	7.43536i	0.150116	+	0.462011i
$260$	−1.97233	−	21.5269i	−0.122319	−	1.33504i
$261$	53.4546	−	38.8371i	3.30876	−	2.40395i
$262$	7.07063	−	24.0613i	0.436825	−	1.48651i
$263$		−	21.2646i		−	1.31123i	−0.755096	−	0.655615i	$-0.772410\pi$
$263$		−	21.2646i		−	1.31123i	0.755096	−	0.655615i	$-0.227590\pi$
$264$	14.2648	−	25.3763i	0.877940	−	1.56181i
$265$	−19.8976	+	19.8976i	−1.22230	+	1.22230i
$266$	−25.2794	−	7.42859i	−1.54998	−	0.455476i
$267$	6.01696	−	37.9896i	0.368232	−	2.32493i
$268$	1.48452	+	6.83835i	0.0906815	+	0.417719i
$269$	−6.61107	−	20.3468i	−0.403084	−	1.24056i	−0.922485	−	0.386034i	$-0.873845\pi$
$269$	−6.61107	−	20.3468i	−0.403084	−	1.24056i	0.519401	−	0.854531i	$-0.326155\pi$
$270$	43.1492	+	20.4665i	2.62597	+	1.24555i
$271$	6.66758	−	1.05604i	0.405026	−	0.0641499i	0.0494023	−	0.998779i	$-0.484268\pi$
$271$	6.66758	−	1.05604i	0.405026	−	0.0641499i	0.355624	+	0.934629i	$0.384268\pi$
$272$	9.56766	+	10.4426i	0.580125	+	0.633177i
$273$	10.9186	+	30.0202i	0.660824	+	1.81690i
$274$	−4.44768	+	4.70725i	−0.268694	+	0.284375i
$275$	−4.47564	−	12.4411i	−0.269891	−	0.750224i
$276$	−0.209354	−	3.68893i	−0.0126016	−	0.222048i
$277$	10.1273	+	3.29057i	0.608492	+	0.197711i	0.597024	−	0.802223i	$-0.296350\pi$
$277$	10.1273	+	3.29057i	0.608492	+	0.197711i	0.0114675	+	0.999934i	$0.496350\pi$
$278$	1.86214	−	1.43529i	0.111684	−	0.0860830i
$279$	2.01903	+	12.7477i	0.120876	+	0.763183i
$280$	−9.40879	−	22.3039i	−0.562283	−	1.33291i
$281$	−4.67917	+	9.18338i	−0.279136	+	0.547835i	−0.987425	−	0.158088i	$-0.949467\pi$
$281$	−4.67917	+	9.18338i	−0.279136	+	0.547835i	0.708289	+	0.705922i	$0.249467\pi$
$282$	8.17881	−	1.53418i	0.487041	−	0.0913591i
$283$	12.3118	−	8.94502i	0.731859	−	0.531726i	−0.158292	−	0.987392i	$-0.550599\pi$
$283$	12.3118	−	8.94502i	0.731859	−	0.531726i	0.890151	+	0.455666i	$0.150599\pi$
$284$	−7.43221	+	4.33402i	−0.441021	+	0.257177i
$285$		−	60.7073i		−	3.59599i
$286$	9.06089	+	14.2794i	0.535781	+	0.844357i
$287$		−	14.0849i		−	0.831403i
$288$	36.9491	+	6.43510i	2.17724	+	0.379192i
$289$	−3.61081	+	2.62341i	−0.212401	+	0.154318i
$290$	−7.78928	−	41.5251i	−0.457402	−	2.43844i
$291$	−14.4130	+	28.2872i	−0.844907	+	1.65822i
$292$	−0.681019	+	1.54760i	−0.0398536	+	0.0905664i
$293$	1.90975	+	12.0577i	0.111569	+	0.704419i	0.978539	+	0.206059i	$0.0660640\pi$
$293$	1.90975	+	12.0577i	0.111569	+	0.704419i	−0.866971	+	0.498359i	$0.833936\pi$
$294$	3.08367	+	4.00075i	0.179843	+	0.233328i
$295$	−35.6072	−	11.5695i	−2.07313	−	0.673602i
$296$	−4.99177	+	5.92209i	−0.290141	+	0.344214i
$297$	−37.3433	+	1.16447i	−2.16688	+	0.0675697i
$298$	3.04144	+	2.87373i	0.176186	+	0.166471i
$299$	1.94516	+	0.907590i	0.112492	+	0.0524873i
$300$	19.1604	−	15.6537i	1.10623	−	0.903766i
$301$	−13.6322	+	2.15912i	−0.785744	+	0.124450i
$302$	6.38756	−	13.4668i	0.367563	−	0.774926i
$303$	14.9355	+	45.9667i	0.858022	+	2.64072i
$304$	−6.97413	−	25.1542i	−0.399994	−	1.44269i
$305$	4.14944	−	26.1985i	0.237596	−	1.50012i
$306$	9.36007	−	31.8522i	0.535080	−	1.82087i
$307$	−5.70243	+	5.70243i	−0.325455	+	0.325455i	−0.850855	−	0.525400i	$-0.823916\pi$
$307$	−5.70243	+	5.70243i	−0.325455	+	0.325455i	0.525400	+	0.850855i	$0.323916\pi$
$308$	14.5145	+	12.1644i	0.827042	+	0.693129i
$309$		−	15.4869i		−	0.881018i
$310$	7.91804	+	2.32679i	0.449715	+	0.132153i
$311$	−7.86095	+	5.71132i	−0.445754	+	0.323859i	−0.787917	−	0.615781i	$-0.788840\pi$
$311$	−7.86095	+	5.71132i	−0.445754	+	0.323859i	0.342163	+	0.939641i	$0.388840\pi$
$312$	−19.5451	+	24.8901i	−1.10652	+	1.40912i
$313$	−5.39567	−	16.6062i	−0.304981	−	0.938636i	−0.979684	−	0.200546i	$-0.935728\pi$
$313$	−5.39567	−	16.6062i	−0.304981	−	0.938636i	0.674703	−	0.738089i	$-0.264272\pi$
$314$	20.3030	−	7.23919i	1.14576	−	0.408531i
$315$	−33.3530	+	45.9065i	−1.87923	+	2.58654i
$316$	−0.287857	−	0.352343i	−0.0161932	−	0.0198208i
$317$	0.220340	+	0.432442i	0.0123755	+	0.0242884i	0.897112	−	0.441804i	$-0.145661\pi$
$317$	0.220340	+	0.432442i	0.0123755	+	0.0242884i	−0.884736	+	0.466093i	$0.845661\pi$
$318$	41.1790	−	1.16755i	2.30921	−	0.0654731i
$319$	20.2519	+	26.1217i	1.13389	+	1.46253i
$320$	13.8430	−	19.5833i	0.773845	−	1.09474i
$321$	3.17921	−	9.78460i	0.177446	−	0.546123i
$322$	2.38378	+	0.308580i	0.132843	+	0.0171965i
$323$	−22.8215	+	3.61458i	−1.26983	+	0.201121i
$324$	−10.9211	−	28.0863i	−0.606729	−	1.56035i
$325$	2.73932	+	14.1100i	0.151950	+	0.782680i
$326$	2.96731	+	15.8189i	0.164344	+	0.876127i
$327$	−4.66971	−	0.739609i	−0.258235	−	0.0409005i
$328$	11.8500	−	7.36798i	0.654304	−	0.406829i
$329$			5.41346i			0.298454i
$330$	−17.4615	+	39.9872i	−0.961227	+	2.20122i
$331$	12.3767	+	12.3767i	0.680284	+	0.680284i	0.960064	−	0.279780i	$-0.0902616\pi$
$331$	12.3767	+	12.3767i	0.680284	+	0.680284i	−0.279780	+	0.960064i	$0.590262\pi$
$332$	−14.1897	+	8.27460i	−0.778763	+	0.454128i
$333$	17.9319	+	2.84014i	0.982664	+	0.155639i
$334$	1.37366	+	7.32305i	0.0751631	+	0.400699i
$335$	−3.24114	−	9.97520i	−0.177082	−	0.545004i
$336$	−12.4131	+	33.1938i	−0.677189	+	1.81087i
$337$	−5.45493	+	7.50807i	−0.297149	+	0.408991i	−0.931320	−	0.364202i	$-0.881342\pi$
$337$	−5.45493	+	7.50807i	−0.297149	+	0.408991i	0.634171	+	0.773193i	$0.281342\pi$
$338$	−7.35963	−	16.8474i	−0.400311	−	0.916379i
$339$	24.9746	+	8.11475i	1.35644	+	0.440733i
$340$	−15.8372	−	14.1361i	−0.858891	−	0.766639i
$341$	−6.34233	+	1.20827i	−0.343457	+	0.0654313i
$342$	−42.0226	+	44.4751i	−2.27232	+	2.40494i
$343$	14.8788	−	7.58114i	0.803381	−	0.409343i
$344$	−8.94769	−	10.3396i	−0.482427	−	0.557475i
$345$	0.866356	+	5.46995i	0.0466430	+	0.294492i
$346$	−2.75049	−	7.71400i	−0.147867	−	0.414707i
$347$	15.8428	−	5.14762i	0.850483	−	0.276339i	0.148835	−	0.988862i	$-0.452448\pi$
$347$	15.8428	−	5.14762i	0.850483	−	0.276339i	0.701649	+	0.712523i	$0.252448\pi$
$348$	−33.4621	+	52.0190i	−1.79376	+	2.78851i
$349$	−31.7834	−	5.03399i	−1.70133	−	0.269463i	−0.771170	−	0.636629i	$-0.780328\pi$
$349$	−31.7834	−	5.03399i	−1.70133	−	0.269463i	−0.930156	+	0.367166i	$0.880328\pi$
$350$	7.71079	+	14.1285i	0.412159	+	0.755198i
$351$	40.3123	+	4.95917i	2.15171	+	0.264701i
$352$	−2.64145	+	18.5748i	−0.140790	+	0.990040i
$353$	21.2278	−	21.2278i	1.12984	−	1.12984i	0.139641	−	0.990202i	$-0.455405\pi$
$353$	21.2278	−	21.2278i	1.12984	−	1.12984i	0.990202	−	0.139641i	$-0.0445950\pi$
$354$	26.2577	+	48.1120i	1.39558	+	2.55712i
$355$	10.4328	−	7.57988i	0.553716	−	0.402298i
$356$	5.25891	+	24.2248i	0.278722	+	1.28391i
$357$	27.9507	+	14.2416i	1.47931	+	0.753746i
$358$	−12.3566	+	4.40586i	−0.653069	+	0.232857i
$359$	−25.0365	+	3.96539i	−1.32138	+	0.209285i	−0.776970	−	0.629537i	$-0.783245\pi$
$359$	−25.0365	+	3.96539i	−1.32138	+	0.209285i	−0.544405	+	0.838822i	$0.683245\pi$
$360$	−56.0697	−	4.04644i	−2.95513	−	0.213266i
$361$	22.4314	+	7.28839i	1.18060	+	0.383600i
$362$	−9.12574	+	0.258743i	−0.479638	+	0.0135992i
$363$	−2.12683	−	34.0692i	−0.111630	−	1.78817i
$364$	−13.5703	−	15.4822i	−0.711277	−	0.811487i
$365$	0.783146	−	2.41027i	0.0409917	−	0.126160i
$366$	−30.7564	+	23.7062i	−1.60766	+	1.23914i
$367$	12.7152	−	17.5009i	0.663727	−	0.913542i	−0.335870	−	0.941908i	$-0.609030\pi$
$367$	12.7152	−	17.5009i	0.663727	−	0.913542i	0.999598	+	0.0283661i	$0.00903042\pi$
$368$	0.987371	+	2.16696i	0.0514703	+	0.112961i
$369$	−29.1437	−	14.8495i	−1.51716	−	0.773033i
$370$	6.55475	−	9.58161i	0.340765	−	0.498124i
$371$	−4.19236	+	26.4695i	−0.217657	+	1.37423i
$372$	−6.08625	−	10.4370i	−0.315558	−	0.541136i
$373$	−30.0670			−1.55681			−0.778405	−	0.627762i	$-0.783971\pi$
$373$	−30.0670			−1.55681			−0.778405	+	0.627762i	$0.783971\pi$
$374$	16.0720	+	4.18340i	0.831062	+	0.216318i
$375$	6.66702	−	6.66702i	0.344283	−	0.344283i
$376$	−4.55449	+	2.83186i	−0.234880	+	0.146042i
$377$	−17.4130	−	31.4309i	−0.896813	−	1.61878i
$378$	44.7031	−	8.38541i	2.29928	−	0.431299i
$379$	15.8937	−	31.1932i	0.816407	−	1.60229i	0.0182535	−	0.999833i	$-0.494189\pi$
$379$	15.8937	−	31.1932i	0.816407	−	1.60229i	0.798153	−	0.602455i	$-0.205811\pi$
$380$	14.1793	+	36.4654i	0.727382	+	1.87064i
$381$	15.6762	−	21.5764i	0.803115	−	1.10539i
$382$	−12.8496	+	9.90416i	−0.657445	+	0.506741i
$383$	−3.91249	+	1.99351i	−0.199919	+	0.101864i	−0.551084	−	0.834450i	$-0.685786\pi$
$383$	−3.91249	+	1.99351i	−0.199919	+	0.101864i	0.351165	+	0.936314i	$0.385786\pi$
$384$	−34.4202	+	6.92066i	−1.75650	+	0.353169i
$385$	−23.4732	−	15.9607i	−1.19630	−	0.813432i
$386$	−12.0380	+	12.7405i	−0.612716	+	0.648474i
$387$	−9.90464	+	30.4834i	−0.503481	+	1.54956i
$388$	2.05059	−	20.3579i	0.104103	−	1.03351i
$389$	1.70281	−	2.34372i	0.0863360	−	0.118831i	−0.763664	−	0.645614i	$-0.776602\pi$
$389$	1.70281	−	2.34372i	0.0863360	−	0.118831i	0.850000	+	0.526782i	$0.176602\pi$
$390$	25.4092	−	40.0552i	1.28664	−	2.02827i
$391$	2.00472	−	0.651374i	0.101383	−	0.0329414i
$392$	−2.78674	−	1.68291i	−0.140751	−	0.0849998i
$393$	44.5206	−	32.3461i	2.24577	−	1.63165i
$394$	18.1379	−	9.89902i	0.913776	−	0.498705i
$395$	0.482217	+	0.482217i	0.0242630	+	0.0242630i
$396$	40.4724	−	17.2081i	2.03382	−	0.864738i
$397$	3.35859	+	3.35859i	0.168563	+	0.168563i	0.786347	−	0.617784i	$-0.211970\pi$
$397$	3.35859	+	3.35859i	0.168563	+	0.168563i	−0.617784	+	0.786347i	$0.711970\pi$
$398$	36.2427	+	10.6503i	1.81668	+	0.533850i
$399$	−33.9837	−	46.7745i	−1.70131	−	2.34165i
$400$	−7.85302	+	13.8781i	−0.392651	+	0.693903i
$401$	−1.52127	+	2.98566i	−0.0759685	+	0.149096i	−0.925867	−	0.377850i	$-0.876663\pi$
$401$	−1.52127	+	2.98566i	−0.0759685	+	0.149096i	0.849898	+	0.526947i	$0.176663\pi$
$402$	−6.58048	+	13.8735i	−0.328204	+	0.691947i
$403$	7.01463	−	0.243335i	0.349423	−	0.0121214i
$404$	−19.7078	−	24.1227i	−0.980497	−	1.20015i
$405$	20.5060	+	40.2453i	1.01895	+	1.99980i
$406$	−29.2471	−	27.6344i	−1.45151	−	1.37147i
$407$	−1.14048	+	9.01022i	−0.0565315	+	0.446620i
$408$	2.63958	+	30.9657i	0.130678	+	1.53303i
$409$	11.0773	+	21.7405i	0.547739	+	1.07500i	0.984494	+	0.175418i	$0.0561277\pi$
$409$	11.0773	+	21.7405i	0.547739	+	1.07500i	−0.436755	+	0.899581i	$0.643872\pi$
$410$	−16.5653	+	12.7681i	−0.818104	+	0.630573i
$411$	−14.0357	+	2.22304i	−0.692330	+	0.109654i
$412$	3.61724	+	9.30261i	0.178209	+	0.458307i
$413$	−33.9116	+	11.0186i	−1.66868	+	0.542188i
$414$	3.15169	−	4.60708i	0.154897	−	0.226425i
$415$	19.9185	−	14.4717i	0.977762	−	0.710386i
$416$	5.92675	−	19.5160i	0.290583	−	0.956850i
$417$	5.15904			0.252639
$418$	−22.8926	−	20.3178i	−1.11972	−	0.993776i
$419$			1.47714i			0.0721630i	0.999349	+	0.0360815i	$0.0114876\pi$
$419$			1.47714i			0.0721630i	−0.999349	+	0.0360815i	$0.988512\pi$
$420$	13.5257	−	51.3674i	0.659985	−	2.50647i
$421$	0.638858	−	4.03359i	0.0311360	−	0.196585i	−0.967217	−	0.253951i	$-0.918270\pi$
$421$	0.638858	−	4.03359i	0.0311360	−	0.196585i	0.998353	+	0.0573653i	$0.0182700\pi$
$422$	−18.4018	−	12.5886i	−0.895787	−	0.612805i
$423$	11.2013	+	5.70734i	0.544625	+	0.277500i
$424$	−24.4626	+	10.3194i	−1.18801	+	0.501156i
$425$	11.4193	+	8.29660i	0.553917	+	0.402444i
$426$	−18.7227	−	2.42366i	−0.907120	−	0.117427i
$427$	−11.4687	−	22.5086i	−0.555009	−	1.08927i
$428$	0.375693	+	6.61994i	0.0181598	+	0.319987i
$429$	−3.38082	+	36.9549i	−0.163228	+	1.78420i
$430$	14.8971	+	14.0756i	0.718402	+	0.678787i
$431$	−34.5098	+	17.5836i	−1.66228	+	0.846974i	−0.667537	+	0.744576i	$0.732652\pi$
$431$	−34.5098	+	17.5836i	−1.66228	+	0.846974i	−0.994744	+	0.102398i	$0.967348\pi$
$432$	30.4397	+	33.2234i	1.46453	+	1.59846i
$433$	14.0828	−	19.3833i	0.676775	−	0.931501i	−0.323115	−	0.946360i	$-0.604730\pi$
$433$	14.0828	−	19.3833i	0.676775	−	0.931501i	0.999890	+	0.0148591i	$0.00472998\pi$
$434$	7.40332	−	2.63971i	0.355371	−	0.126710i
$435$	42.0888	−	82.6039i	2.01800	−	3.96055i
$436$	2.97773	−	0.646429i	0.142608	−	0.0309583i
$437$	−3.83713	−	0.607742i	−0.183555	−	0.0290723i
$438$	−3.25673	+	1.77740i	−0.155613	+	0.0849275i
$439$	20.4297			0.975059			0.487529	−	0.873107i	$-0.337898\pi$
$439$	20.4297			0.975059			0.487529	+	0.873107i	$0.337898\pi$
$440$	1.14901	−	28.0978i	0.0547768	−	1.33951i
$441$			7.63107i			0.363384i
$442$	−16.5707	−	7.16708i	−0.788190	−	0.340903i
$443$	−3.80091	−	5.23151i	−0.180587	−	0.248557i	0.709121	−	0.705087i	$-0.249092\pi$
$443$	−3.80091	−	5.23151i	−0.180587	−	0.248557i	−0.889708	+	0.456530i	$0.849092\pi$
$444$	−16.6087	+	3.60554i	−0.788213	+	0.171111i
$445$	−11.4817	−	35.3371i	−0.544286	−	1.67514i
$446$	−1.43365	−	0.680009i	−0.0678853	−	0.0321993i
$447$	1.43634	+	9.06872i	0.0679367	+	0.428936i
$448$	−0.296757	−	22.8380i	−0.0140205	−	1.07899i
$449$	10.3501	−	5.27363i	0.488450	−	0.248878i	−0.192378	−	0.981321i	$-0.561620\pi$
$449$	10.3501	−	5.27363i	0.488450	−	0.248878i	0.680828	+	0.732443i	$0.261620\pi$
$450$	37.3633	−	1.05937i	1.76132	−	0.0499390i
$451$	6.97032	−	14.8033i	0.328220	−	0.697062i
$452$	−16.8970	+	0.958936i	−0.794769	+	0.0451046i
$453$	29.1413	−	14.8482i	1.36918	−	0.697630i
$454$	3.55219	−	27.4406i	0.166713	−	1.28785i
$455$	22.5634	+	21.0505i	1.05779	+	0.986862i
$456$	21.5753	−	53.0597i	1.01035	−	2.48475i
$457$	16.3923	+	8.35231i	0.766801	+	0.390705i	0.793211	−	0.608946i	$-0.208408\pi$
$457$	16.3923	+	8.35231i	0.766801	+	0.390705i	−0.0264101	+	0.999651i	$0.508408\pi$
$458$	−20.9387	+	3.92769i	−0.978403	+	0.183529i
$459$	32.2684	−	23.4444i	1.50616	−	1.09429i
$460$	−1.79801	−	3.08332i	−0.0838325	−	0.143761i
$461$	−25.2631	+	25.2631i	−1.17662	+	1.17662i	−0.196019	+	0.980600i	$0.562801\pi$
$461$	−25.2631	+	25.2631i	−1.17662	+	1.17662i	−0.980600	+	0.196019i	$0.937199\pi$
$462$	8.93067	+	40.5847i	0.415492	+	1.88817i
$463$	−11.9448	+	11.9448i	−0.555122	+	0.555122i	−0.927915	−	0.372793i	$-0.878400\pi$
$463$	−11.9448	+	11.9448i	−0.555122	+	0.555122i	0.372793	+	0.927915i	$0.378400\pi$
$464$	7.94994	−	39.0623i	0.369066	−	1.81342i
$465$	10.6444	+	14.6508i	0.493623	+	0.679413i
$466$	14.8535	+	10.1612i	0.688074	+	0.470709i
$467$	6.53155	+	20.1020i	0.302244	+	0.930212i	0.980691	+	0.195562i	$0.0626532\pi$
$467$	6.53155	+	20.1020i	0.302244	+	0.930212i	−0.678447	+	0.734649i	$0.737347\pi$
$468$	−46.3420	+	11.7564i	−2.14216	+	0.543440i
$469$	−8.08134	−	5.87144i	−0.373162	−	0.271118i
$470$	6.36683	−	4.90738i	0.293680	−	0.226361i
$471$	44.9835	+	14.6160i	2.07273	+	0.673471i
$472$	−27.0098	−	22.7668i	−1.24323	−	1.04793i
$473$	−15.3960	−	4.47702i	−0.707911	−	0.205854i
$474$	−0.0282955	−	0.997970i	−0.00129966	−	0.0458383i
$475$	−11.8105	−	23.1793i	−0.541901	−	1.06354i
$476$	−20.1157	−	2.02620i	−0.922004	−	0.0928709i
$477$	50.3496	+	36.5811i	2.30535	+	1.67493i
$478$	−5.82096	−	2.76100i	−0.266245	−	0.126285i
$479$	−14.8530	−	7.56797i	−0.678650	−	0.345789i	0.0804547	−	0.996758i	$-0.474363\pi$
$479$	−14.8530	−	7.56797i	−0.678650	−	0.345789i	−0.759104	+	0.650969i	$0.774363\pi$
$480$	50.2921	−	15.4915i	2.29551	−	0.707086i
$481$	2.72364	−	9.49019i	0.124187	−	0.432716i
$482$	−10.9570	−	20.0765i	−0.499078	−	0.914459i
$483$	3.72957	+	3.72957i	0.169701	+	0.169701i
$484$	9.23502	+	19.9678i	0.419774	+	0.907629i
$485$			30.6682i			1.39257i
$486$	5.16865	−	17.5889i	0.234455	−	0.797847i
$487$	−24.7659	−	3.92253i	−1.12225	−	0.177747i	−0.432388	−	0.901688i	$-0.642329\pi$
$487$	−24.7659	−	3.92253i	−1.12225	−	0.177747i	−0.689862	+	0.723941i	$0.742329\pi$
$488$	12.9376	−	21.4235i	0.585659	−	0.969794i
$489$	−16.0336	+	31.4677i	−0.725065	+	1.42302i
$490$	4.40873	+	2.09115i	0.199166	+	0.0944685i
$491$	−8.75735	−	6.36259i	−0.395214	−	0.287140i	0.372375	−	0.928082i	$-0.378544\pi$
$491$	−8.75735	−	6.36259i	−0.395214	−	0.287140i	−0.767589	+	0.640943i	$0.778544\pi$
$492$	30.4649	+	3.06865i	1.37346	+	0.138345i
$493$	−33.5591	−	10.9040i	−1.51143	−	0.491092i
$494$	21.2152	+	25.6349i	0.954516	+	1.15337i
$495$	−57.7726	+	31.7425i	−2.59669	+	1.42672i
$496$	6.09363	+	4.84773i	0.273612	+	0.217670i
$497$	3.79521	−	11.6805i	0.170239	−	0.523941i
$498$	−35.7459	−	4.62731i	−1.60181	−	0.207355i
$499$	−2.15582	−	13.6113i	−0.0965078	−	0.609326i	−0.987780	−	0.155857i	$-0.950186\pi$
$499$	−2.15582	−	13.6113i	−0.0965078	−	0.609326i	0.891272	−	0.453469i	$-0.149814\pi$
$500$	−2.44752	+	5.56193i	−0.109456	+	0.248737i
$501$	−7.42245	+	14.5674i	−0.331611	+	0.650822i
$502$	22.3400	−	32.6562i	0.997082	−	1.45752i
$503$	−6.23353	−	8.57972i	−0.277939	−	0.382551i	0.647111	−	0.762396i	$-0.275977\pi$
$503$	−6.23353	−	8.57972i	−0.277939	−	0.382551i	−0.925050	+	0.379845i	$0.875977\pi$
$504$	−45.4665	+	28.2698i	−2.02524	+	1.25924i
$505$	33.0143	+	33.0143i	1.46912	+	1.46912i
$506$	2.35267	+	1.50401i	0.104589	+	0.0668613i
$507$	9.77769	−	39.1392i	0.434242	−	1.73823i
$508$	−4.37676	+	16.6219i	−0.194187	+	0.737478i
$509$	−3.30042	+	20.8381i	−0.146289	+	0.923631i	0.799928	+	0.600096i	$0.204871\pi$
$509$	−3.30042	+	20.8381i	−0.146289	+	0.923631i	−0.946216	+	0.323534i	$0.895129\pi$
$510$	−8.58804	−	45.7834i	−0.380285	−	2.02732i
$511$	−0.745853	−	2.29550i	−0.0329946	−	0.101547i
$512$	19.0590	−	12.1965i	0.842295	−	0.539016i
$513$	−72.6071	+	11.4998i	−3.20568	+	0.507730i
$514$	9.54544	−	7.35737i	0.421031	−	0.324520i
$515$	−6.79190	−	13.3298i	−0.299287	−	0.587383i
$516$	−1.70006	−	29.9561i	−0.0748411	−	1.31874i
$517$	−2.67902	+	5.68961i	−0.117823	+	0.250229i
$518$	−0.313355	−	11.0519i	−0.0137680	−	0.485592i
$519$	5.55327	−	17.0912i	0.243762	−	0.750221i
$520$	−5.90707	+	29.9950i	−0.259042	+	1.31537i
$521$	−7.41693	−	5.38871i	−0.324942	−	0.236084i	0.413340	−	0.910577i	$-0.364362\pi$
$521$	−7.41693	−	5.38871i	−0.324942	−	0.236084i	−0.738281	+	0.674493i	$0.764362\pi$
$522$	−88.0147	+	31.3823i	−3.85230	+	1.37357i
$523$	−31.7160	+	10.3051i	−1.38684	+	0.450613i	−0.904913	−	0.425597i	$-0.860064\pi$
$523$	−31.7160	+	10.3051i	−1.38684	+	0.450613i	−0.481930	+	0.876210i	$0.660064\pi$
$524$	−19.1875	+	29.8281i	−0.838208	+	1.30305i
$525$	−5.52510	+	34.8841i	−0.241135	+	1.52247i
$526$	−8.47863	+	28.8527i	−0.369686	+	1.25804i
$527$	4.87385	−	4.87385i	0.212308	−	0.212308i
$528$	−29.4732	+	28.7440i	−1.28266	+	1.25092i
$529$	−22.6456			−0.984591
$530$	34.9315	−	19.0643i	1.51733	−	0.828102i
$531$	−12.9535	+	81.7851i	−0.562133	+	3.54917i
$532$	31.3382	+	20.1588i	1.35868	+	0.873997i
$533$	−9.95015	+	14.7444i	−0.430989	+	0.638649i
$534$	−23.3113	+	49.1468i	−1.00878	+	2.12679i
$535$	−1.55471	−	9.81605i	−0.0672160	−	0.424385i
$536$	0.712333	−	9.87047i	0.0307681	−	0.426339i
$537$	−27.3775	−	8.89549i	−1.18143	−	0.383869i
$538$	0.857492	+	30.2433i	0.0369691	+	1.30388i
$539$	−3.81552	+	0.118979i	−0.164346	+	0.00512480i
$540$	−50.3862	−	44.9743i	−2.16828	−	1.93539i
$541$	−4.41990	+	2.25205i	−0.190026	+	0.0968232i	−0.546415	−	0.837515i	$-0.684008\pi$
$541$	−4.41990	+	2.25205i	−0.190026	+	0.0968232i	0.356389	+	0.934338i	$0.384008\pi$
$542$	−9.46792	−	1.22562i	−0.406682	−	0.0526450i
$543$	−16.2069	−	11.7750i	−0.695504	−	0.505313i
$544$	−8.81812	−	17.9838i	−0.378074	−	0.771050i
$545$	−4.34366	+	1.41134i	−0.186062	+	0.0604553i
$546$	−2.84515	−	45.0861i	−0.121761	−	1.92951i
$547$	−7.30541	−	10.0550i	−0.312357	−	0.429922i	0.623758	−	0.781618i	$-0.285605\pi$
$547$	−7.30541	−	10.0550i	−0.312357	−	0.429922i	−0.936114	+	0.351696i	$0.885605\pi$
$548$	7.91168	−	4.61362i	0.337970	−	0.197084i
$549$	−58.6650			−2.50376
$550$	1.11223	+	18.6651i	0.0474256	+	0.795882i
$551$	45.9862	+	45.9862i	1.95908	+	1.95908i
$552$	−1.18680	+	5.08878i	−0.0505134	+	0.216593i
$553$	0.641487	+	0.101602i	0.0272788	+	0.00432054i
$554$	−12.4292	−	8.50275i	−0.528064	−	0.361247i
$555$	24.2273	−	7.87194i	1.02839	−	0.334145i
$556$	−3.09892	+	1.20499i	−0.131423	+	0.0511029i
$557$	−1.30450	−	8.23629i	−0.0552734	−	0.348983i	−0.999789	−	0.0205175i	$-0.993469\pi$
$557$	−1.30450	−	8.23629i	−0.0552734	−	0.348983i	0.944516	−	0.328465i	$-0.106531\pi$
$558$	2.34325	−	18.1016i	0.0991979	−	0.766302i
$559$	15.7957	+	7.37012i	0.668089	+	0.311723i
$560$	3.87322	+	34.0143i	0.163674	+	1.43737i
$561$	22.3286	+	28.8004i	0.942716	+	1.21595i
$562$	10.0105	−	10.5947i	0.422267	−	0.446911i
$563$	−0.541112	+	1.66537i	−0.0228051	+	0.0701870i	−0.961811	−	0.273713i	$-0.911748\pi$
$563$	−0.541112	+	1.66537i	−0.0228051	+	0.0701870i	0.939006	+	0.343900i	$0.111748\pi$
$564$	−11.7091	−	1.17942i	−0.493041	−	0.0496626i
$565$	25.0549	−	3.96831i	1.05407	−	0.166948i
$566$	−20.2717	+	7.22803i	−0.852083	+	0.303817i
$567$	38.3288	+	19.5295i	1.60966	+	0.820162i
$568$	11.8124	−	2.91720i	0.495638	−	0.122403i
$569$	4.96721	+	6.83678i	0.208236	+	0.286613i	0.900342	−	0.435184i	$-0.143317\pi$
$569$	4.96721	+	6.83678i	0.208236	+	0.286613i	−0.692105	+	0.721796i	$0.743317\pi$
$570$	−24.2053	+	82.3702i	−1.01385	+	3.45011i
$571$	−19.8121			−0.829109			−0.414555	−	0.910024i	$-0.636063\pi$
$571$	−19.8121			−0.829109			−0.414555	+	0.910024i	$0.636063\pi$
$572$	−6.60071	−	22.9876i	−0.275990	−	0.961161i
$573$	−35.5997			−1.48720
$574$	−5.61593	+	19.1109i	−0.234404	+	0.797675i
$575$	1.39496	+	1.92000i	0.0581738	+	0.0800694i
$576$	−47.5682	−	23.4638i	−1.98201	−	0.977657i
$577$	22.0645	+	11.2424i	0.918555	+	0.468027i	0.848308	−	0.529502i	$-0.177621\pi$
$577$	22.0645	+	11.2424i	0.918555	+	0.468027i	0.0702468	+	0.997530i	$0.477621\pi$
$578$	5.94531	−	2.11985i	0.247292	−	0.0881740i
$579$	−37.9886	+	6.01680i	−1.57875	+	0.250050i
$580$	−5.98812	+	59.4488i	−0.248643	+	2.46848i
$581$	7.24590	−	22.3006i	0.300611	−	0.925185i
$582$	30.8349	−	32.6345i	1.27815	−	1.35274i
$583$	−17.5055	+	25.7451i	−0.725003	+	1.06625i
$584$	1.54110	−	1.82831i	0.0637710	−	0.0756561i
$585$	67.3450	−	24.4940i	2.78437	−	1.01270i
$586$	2.21643	−	17.1219i	0.0915597	−	0.707298i
$587$	0.932250	+	5.88599i	0.0384781	+	0.242941i	0.999429	−	0.0337765i	$-0.0107534\pi$
$587$	0.932250	+	5.88599i	0.0384781	+	0.242941i	−0.960951	+	0.276717i	$0.910753\pi$
$588$	−2.58887	−	6.65791i	−0.106763	−	0.274568i
$589$	−12.0818	+	3.92562i	−0.497823	+	0.161752i
$590$	43.7004	+	29.8953i	1.79912	+	1.23077i
$591$	44.7838	+	7.09305i	1.84216	+	0.291769i
$592$	9.13431	−	6.04502i	0.375418	−	0.248449i
$593$	11.4290	+	11.4290i	0.469335	+	0.469335i	0.901699	−	0.432364i	$-0.142321\pi$
$593$	11.4290	+	11.4290i	0.469335	+	0.469335i	−0.432364	+	0.901699i	$0.642321\pi$
$594$	51.1333	+	13.3095i	2.09802	+	0.546097i
$595$	30.3035			1.24232
$596$	−2.98094	−	5.11188i	−0.122104	−	0.209391i
$597$	48.7219	+	67.0600i	1.99406	+	2.74458i
$598$	−2.27740	−	2.00703i	−0.0931299	−	0.0820737i
$599$	0.745169	−	0.242120i	0.0304468	−	0.00989276i	−0.293754	−	0.955881i	$-0.594905\pi$
$599$	0.745169	−	0.242120i	0.0304468	−	0.00989276i	0.324201	+	0.945988i	$0.394905\pi$
$600$	−32.2391	+	13.5999i	−1.31616	+	0.555215i
$601$	13.1486	+	9.55301i	0.536342	+	0.389675i	0.822725	−	0.568440i	$-0.192453\pi$
$601$	13.1486	+	9.55301i	0.536342	+	0.389675i	−0.286383	+	0.958115i	$0.592453\pi$
$602$	19.3576	+	2.50584i	0.788956	+	0.102130i
$603$	−20.6690	+	10.5314i	−0.841705	+	0.428870i
$604$	−14.0364	+	15.7254i	−0.571133	+	0.639859i
$605$	−16.7719	−	28.3913i	−0.681876	−	1.15427i
$606$	−1.93721	−	68.3247i	−0.0786940	−	2.77550i
$607$	−0.0124567	−	0.00404743i	−0.000505603	−	0.000164280i	0.308764	−	0.951139i	$-0.400085\pi$
$607$	−0.0124567	−	0.00404743i	−0.000505603	−	0.000164280i	−0.309270	+	0.950974i	$0.600085\pi$
$608$	−0.566710	+	36.9110i	−0.0229831	+	1.49694i
$609$	−13.8122	−	87.2067i	−0.559698	−	3.53379i
$610$	−16.0760	+	33.8928i	−0.650899	+	1.37228i
$611$	3.82430	−	5.66694i	0.154715	−	0.229260i
$612$	−25.4003	+	39.4864i	−1.02675	+	1.59614i
$613$	−1.62556	+	10.2634i	−0.0656557	+	0.414534i	0.932868	+	0.360218i	$0.117298\pi$
$613$	−1.62556	+	10.2634i	−0.0656557	+	0.414534i	−0.998524	+	0.0543158i	$0.982702\pi$
$614$	10.0110	−	5.46362i	0.404010	−	0.220494i
$615$	−45.8940			−1.85063
$616$	−14.8437	−	22.2924i	−0.598071	−	0.898185i
$617$	5.13453	−	5.13453i	0.206709	−	0.206709i	−0.596158	−	0.802867i	$-0.703307\pi$
$617$	5.13453	−	5.13453i	0.206709	−	0.206709i	0.802867	+	0.596158i	$0.203307\pi$
$618$	−6.17495	+	21.0133i	−0.248393	+	0.845278i
$619$	−6.05791	+	38.2481i	−0.243488	+	1.53732i	0.498489	+	0.866896i	$0.333889\pi$
$619$	−6.05791	+	38.2481i	−0.243488	+	1.53732i	−0.741976	+	0.670426i	$0.766111\pi$
$620$	−9.81580	−	6.31418i	−0.394212	−	0.253584i
$621$	6.37806	−	2.07236i	0.255943	−	0.0831608i
$622$	12.9433	−	4.61503i	0.518979	−	0.185046i
$623$	−28.6281	−	20.7996i	−1.14696	−	0.833317i
$624$	36.4438	−	25.9789i	1.45892	−	1.03999i
$625$	8.97398	−	27.6191i	0.358959	−	1.10476i
$626$	0.699848	+	24.6833i	0.0279715	+	0.986543i
$627$	−12.5694	−	65.9783i	−0.501974	−	2.63492i
$628$	−30.4344	+	1.72721i	−1.21446	+	0.0689230i
$629$	−4.40180	−	8.63902i	−0.175511	−	0.344460i
$630$	63.5587	−	48.9893i	2.53224	−	1.95178i
$631$	25.9623	−	4.11202i	1.03354	−	0.163697i	0.383457	−	0.923559i	$-0.374733\pi$
$631$	25.9623	−	4.11202i	1.03354	−	0.163697i	0.650085	+	0.759862i	$0.274733\pi$
$632$	0.250090	+	0.592848i	0.00994806	+	0.0235822i
$633$	−15.1183	−	46.5295i	−0.600900	−	1.84938i
$634$	−0.126543	−	0.674610i	−0.00502567	−	0.0267922i
$635$	4.03027	−	25.4461i	0.159936	−	1.00980i
$636$	−56.3390	−	14.8348i	−2.23399	−	0.588237i
$637$	4.11888	+	0.506700i	0.163196	+	0.0200762i
$638$	−17.0634	−	43.5179i	−0.675545	−	1.72289i
$639$	−20.1674	−	20.1674i	−0.797812	−	0.797812i
$640$	−26.5910	+	21.0520i	−1.05110	+	0.832153i
$641$	20.7734	+	28.5922i	0.820501	+	1.12932i	0.989618	+	0.143726i	$0.0459084\pi$
$641$	20.7734	+	28.5922i	0.820501	+	1.12932i	−0.169117	+	0.985596i	$0.554092\pi$
$642$	−8.21501	+	12.0085i	−0.324221	+	0.473939i
$643$	−19.7055	+	38.6742i	−0.777109	+	1.52516i	0.0722727	+	0.997385i	$0.476975\pi$
$643$	−19.7055	+	38.6742i	−0.777109	+	1.52516i	−0.849382	+	0.527778i	$0.823025\pi$
$644$	−3.11138	−	1.36916i	−0.122605	−	0.0539524i
$645$	7.03527	+	44.4189i	0.277014	+	1.74899i
$646$	32.4065	+	4.19502i	1.27502	+	0.165051i
$647$	−7.43449	+	22.8810i	−0.292280	+	0.899545i	0.691842	+	0.722049i	$0.256800\pi$
$647$	−7.43449	+	22.8810i	−0.292280	+	0.899545i	−0.984122	+	0.177496i	$0.943200\pi$
$648$	3.61965	+	42.4632i	0.142193	+	1.66811i
$649$	−41.0944	−	5.20157i	−1.61309	−	0.204180i
$650$	1.90911	−	20.2372i	0.0748816	−	0.793769i
$651$	16.4029	+	5.32961i	0.642879	+	0.208884i
$652$	2.28116	−	22.6469i	0.0893370	−	0.886920i
$653$	29.7606	+	21.6224i	1.16462	+	0.846149i	0.990356	−	0.138549i	$-0.0442439\pi$
$653$	29.7606	+	21.6224i	1.16462	+	0.846149i	0.174269	+	0.984698i	$0.444244\pi$
$654$	6.04116	+	2.86544i	0.236228	+	0.112048i
$655$	24.1341	−	47.3657i	0.942995	−	1.85073i
$656$	−19.0163	+	5.27236i	−0.742461	+	0.205851i
$657$	−5.53608	−	0.876829i	−0.215983	−	0.0342084i
$658$	2.15846	−	7.34522i	0.0841456	−	0.286346i
$659$		−	5.06255i		−	0.197209i	−0.995127	−	0.0986045i	$-0.968562\pi$
$659$		−	5.06255i		−	0.197209i	0.995127	−	0.0986045i	$-0.0314379\pi$
$660$	39.6363	−	47.2941i	1.54284	−	1.84092i
$661$	2.17151	+	2.17151i	0.0844618	+	0.0844618i	0.748075	−	0.663614i	$-0.230978\pi$
$661$	2.17151	+	2.17151i	0.0844618	+	0.0844618i	−0.663614	+	0.748075i	$0.730978\pi$
$662$	−11.8584	−	21.7281i	−0.460888	−	0.844485i
$663$	−19.1986	−	34.6540i	−0.745612	−	1.34585i
$664$	22.5525	−	5.56958i	0.875207	−	0.216142i
$665$	−49.7637	−	25.3559i	−1.92975	−	0.983258i
$666$	−23.1984	−	11.0035i	−0.898920	−	0.426376i
$667$	−4.79980	−	3.48726i	−0.185849	−	0.135027i
$668$	1.05602	−	10.4839i	0.0408585	−	0.405635i
$669$	−1.58071	−	3.10233i	−0.0611140	−	0.119943i
$670$	0.420394	+	14.8271i	0.0162412	+	0.572820i
$671$	−0.914672	−	29.3324i	−0.0353105	−	1.13236i
$672$	30.0776	−	40.0894i	1.16027	−	1.54648i
$673$	−1.18793	−	0.385982i	−0.0457913	−	0.0148785i	0.286032	−	0.958220i	$-0.407664\pi$
$673$	−1.18793	−	0.385982i	−0.0457913	−	0.0148785i	−0.331823	+	0.943342i	$0.607664\pi$
$674$	10.3951	−	8.01227i	0.400405	−	0.308621i
$675$	36.3306	+	26.3958i	1.39837	+	1.01597i
$676$	3.26843	+	25.7937i	0.125709	+	0.992067i
$677$	12.1428	+	37.3718i	0.466687	+	1.43631i	0.856848	+	0.515568i	$0.172419\pi$
$677$	12.1428	+	37.3718i	0.466687	+	1.43631i	−0.390161	+	0.920747i	$0.627581\pi$
$678$	−30.6511	−	20.9683i	−1.17715	−	0.805285i
$679$	17.1679	+	23.6296i	0.658845	+	0.906822i
$680$	15.8522	+	25.4951i	0.607903	+	0.977693i
$681$	42.9326	−	42.9326i	1.64518	−	1.64518i
$682$	9.08731	+	0.889393i	0.347971	+	0.0340566i
$683$	−28.0564	+	28.0564i	−1.07355	+	1.07355i	−0.0764775	+	0.997071i	$0.524367\pi$
$683$	−28.0564	+	28.0564i	−1.07355	+	1.07355i	−0.997071	+	0.0764775i	$0.975633\pi$
$684$	74.7512	−	43.5904i	2.85818	−	1.66672i
$685$	−11.1058	+	8.06887i	−0.424333	+	0.308296i
$686$	−23.2110	+	4.35391i	−0.886200	+	0.166233i
$687$	−41.6524	−	21.2230i	−1.58914	−	0.809706i
$688$	8.01798	+	17.5969i	0.305683	+	0.670874i
$689$	23.0879	−	24.7473i	0.879578	−	0.942795i
$690$	1.00548	−	7.76730i	0.0382779	−	0.295696i
$691$	30.5780	−	15.5803i	1.16324	−	0.592702i	0.237698	−	0.971339i	$-0.423607\pi$
$691$	30.5780	−	15.5803i	1.16324	−	0.592702i	0.925545	+	0.378637i	$0.123607\pi$
$692$	0.656241	+	11.5634i	0.0249466	+	0.439573i
$693$	−26.7440	+	56.7981i	−1.01592	+	2.15758i
$694$	−23.5486	+	0.667675i	−0.893892	+	0.0253446i
$695$	4.44048	−	2.26254i	0.168437	−	0.0858230i
$696$	66.1439	−	57.2396i	2.50718	−	2.16966i
$697$	2.73258	+	17.2528i	0.103504	+	0.653498i
$698$	41.1179	+	19.5030i	1.55633	+	0.738201i
$699$	12.2031	+	37.5574i	0.461565	+	1.42055i
$700$	−4.82901	−	22.2445i	−0.182520	−	0.840765i
$701$	20.6212	+	28.3827i	0.778854	+	1.07200i	0.995407	+	0.0957293i	$0.0305183\pi$
$701$	20.6212	+	28.3827i	0.778854	+	1.07200i	−0.216554	+	0.976271i	$0.569482\pi$
$702$	−52.7201	−	22.8022i	−1.98979	−	0.860612i
$703$			17.8699i			0.673977i
$704$	10.9902	−	24.1499i	0.414208	−	0.910182i
$705$	17.6392			0.664331
$706$	−37.2668	+	20.3388i	−1.40255	+	0.765462i
$707$	43.9185	+	6.95601i	1.65173	+	0.261608i
$708$	−16.4444	−	75.7499i	−0.618017	−	2.84685i
$709$	13.2138	−	25.9336i	0.496256	−	0.973957i	−0.498025	−	0.867163i	$-0.665941\pi$
$709$	13.2138	−	25.9336i	0.496256	−	0.973957i	0.994281	−	0.106794i	$-0.0340587\pi$
$710$	−17.1779	+	6.12492i	−0.644676	+	0.229864i
$711$	0.886540	−	1.22022i	0.0332479	−	0.0457618i
$712$	2.52344	−	34.9661i	0.0945699	−	1.31041i
$713$	1.03259	−	0.526133i	0.0386710	−	0.0197038i
$714$	−32.2463	−	30.4682i	−1.20679	−	1.14024i
$715$	13.2969	+	33.2905i	0.497278	+	1.24499i
$716$	18.5227	−	1.05120i	0.692227	−	0.0392851i
$717$	−6.41808	−	12.5962i	−0.239688	−	0.470414i
$718$	35.5517	+	4.60216i	1.32678	+	0.171751i
$719$	31.0711	+	22.5745i	1.15876	+	0.841887i	0.989620	−	0.143706i	$-0.0459020\pi$
$719$	31.0711	+	22.5745i	1.15876	+	0.841887i	0.169137	+	0.985593i	$0.445902\pi$
$720$	74.4644	+	27.8466i	2.77512	+	1.03778i
$721$	−12.6951	−	6.46847i	−0.472790	−	0.240898i
$722$	−27.5298	−	18.8331i	−1.02455	−	0.700894i
$723$	7.85115	−	49.5702i	0.291987	−	1.84354i
$724$	12.4854	+	3.28755i	0.464015	+	0.122181i
$725$		−	39.7282i		−	1.47547i
$726$	−10.6983	+	47.0746i	−0.397053	+	1.74710i
$727$	17.1864			0.637407			0.318704	−	0.947854i	$-0.396753\pi$
$727$	17.1864			0.637407			0.318704	+	0.947854i	$0.396753\pi$
$728$	12.2397	+	26.4176i	0.453633	+	0.979103i
$729$	−4.02476	+	2.92416i	−0.149065	+	0.108302i
$730$	−2.02363	+	2.95811i	−0.0748980	+	0.109484i
$731$	16.2794	−	5.28951i	0.602116	−	0.195639i
$732$	51.1837	−	19.9024i	1.89180	−	0.735612i
$733$	2.57642	−	0.408065i	0.0951624	−	0.0150722i	−0.108672	−	0.994078i	$-0.534660\pi$
$733$	2.57642	−	0.408065i	0.0951624	−	0.0150722i	0.203834	+	0.979005i	$0.434660\pi$
$734$	−24.2305	+	18.6762i	−0.894364	+	0.689352i
$735$	4.86099	+	9.54022i	0.179300	+	0.351896i
$736$	−0.475695	−	3.33391i	−0.0175344	−	0.122889i
$737$	−5.58792	−	10.1702i	−0.205834	−	0.374626i
$738$	33.6227	+	31.7686i	1.23767	+	1.16942i
$739$	−2.64910	−	5.19915i	−0.0974488	−	0.191254i	0.837136	−	0.546995i	$-0.184228\pi$
$739$	−2.64910	−	5.19915i	−0.0974488	−	0.191254i	−0.934584	+	0.355741i	$0.884228\pi$
$740$	−12.7142	+	10.3872i	−0.467382	+	0.381842i
$741$	2.53138	+	72.9721i	0.0929925	+	2.68070i
$742$	16.2423	−	34.2434i	0.596275	−	1.25712i
$743$	−0.835937	+	1.64062i	−0.0306676	+	0.0601885i	−0.905832	−	0.423637i	$-0.860753\pi$
$743$	−0.835937	+	1.64062i	−0.0306676	+	0.0601885i	0.875164	+	0.483826i	$0.160753\pi$
$744$	4.09662	+	16.5881i	0.150189	+	0.608151i
$745$	5.21344	+	7.17569i	0.191006	+	0.262897i
$746$	40.7962	+	11.9883i	1.49365	+	0.438925i
$747$	−38.5041	−	38.5041i	−1.40879	−	1.40879i
$748$	−20.1391	−	12.0844i	−0.736360	−	0.441851i
$749$	−6.69287	−	6.69287i	−0.244552	−	0.244552i
$750$	−11.7044	+	6.38782i	−0.427383	+	0.233250i
$751$	23.4524	−	17.0392i	0.855790	−	0.621768i	−0.0709464	−	0.997480i	$-0.522602\pi$
$751$	23.4524	−	17.0392i	0.855790	−	0.621768i	0.926736	+	0.375712i	$0.122602\pi$
$752$	7.30884	−	2.02641i	0.266526	−	0.0738957i
$753$	82.5719	−	26.8292i	3.00909	−	0.977711i
$754$	11.0945	+	49.5897i	0.404037	+	1.80595i
$755$	18.5706	−	25.5603i	0.675854	−	0.930233i
$756$	−63.9986	−	6.44640i	−2.32760	−	0.234453i
$757$	6.37522	−	19.6209i	0.231711	−	0.713134i	−0.765829	−	0.643044i	$-0.777671\pi$
$757$	6.37522	−	19.6209i	0.231711	−	0.713134i	0.997541	−	0.0700904i	$-0.0223288\pi$
$758$	−34.0027	+	35.9871i	−1.23503	+	1.30711i
$759$	2.07413	+	5.76552i	0.0752862	+	0.209275i
$760$	−4.69952	−	55.1314i	−0.170469	−	1.99983i
$761$	−48.0866	+	24.5014i	−1.74314	+	0.888173i	−0.777259	+	0.629181i	$0.783391\pi$
$761$	−48.0866	+	24.5014i	−1.74314	+	0.888173i	−0.965879	+	0.258993i	$0.916609\pi$
$762$	−29.8731	+	23.0254i	−1.08219	+	0.834121i
$763$	−2.55670	+	3.51899i	−0.0925586	+	0.127396i
$764$	21.3839	−	8.31496i	0.773644	−	0.300825i
$765$	31.9486	−	62.7026i	1.15510	−	2.26702i
$766$	6.10349	−	1.14489i	0.220528	−	0.0413666i
$767$	43.2834	+	12.4221i	1.56287	+	0.448538i
$768$	49.4622	+	4.33381i	1.78481	+	0.156383i
$769$	26.9344	−	26.9344i	0.971281	−	0.971281i	−0.0283182	−	0.999599i	$-0.509015\pi$
$769$	26.9344	−	26.9344i	0.971281	−	0.971281i	0.999599	+	0.0283182i	$0.00901516\pi$
$770$	25.4855	+	31.0154i	0.918435	+	1.11772i
$771$	26.4455			0.952412
$772$	21.4135	−	12.4871i	0.770689	−	0.449419i
$773$	4.30806	−	27.2000i	0.154950	−	0.978317i	−0.780576	−	0.625061i	$-0.785074\pi$
$773$	4.30806	−	27.2000i	0.154950	−	0.978317i	0.935526	−	0.353257i	$-0.114926\pi$
$774$	25.5934	−	37.4119i	0.919936	−	1.34474i
$775$	6.91454	+	3.52313i	0.248377	+	0.126555i
$776$	−10.8994	+	26.8048i	−0.391267	+	0.962236i
$777$	14.2603	−	19.6276i	0.511585	−	0.704137i
$778$	−3.24494	+	2.50111i	−0.116337	+	0.0896692i
$779$	9.94860	−	30.6186i	0.356446	−	1.09703i
$780$	−50.4471	+	44.2174i	−1.80629	+	1.58324i
$781$	9.76925	−	10.3981i	0.349571	−	0.372074i
$782$	−2.97981	+	0.0844868i	−0.106558	+	0.00302124i
$783$	−106.769	−	34.6913i	−3.81560	−	1.23977i
$784$	3.11015	+	3.39457i	0.111077	+	0.121235i
$785$	45.1281	−	7.14759i	1.61069	−	0.255108i
$786$	−73.3045	+	26.1373i	−2.61469	+	0.932286i
$787$	15.4654	+	7.88002i	0.551282	+	0.280892i	0.707361	−	0.706852i	$-0.249885\pi$
$787$	15.4654	+	7.88002i	0.551282	+	0.280892i	−0.156079	+	0.987745i	$0.549885\pi$
$788$	−28.5573	+	6.19943i	−1.01731	+	0.220845i
$789$	−53.3861	+	38.7873i	−1.90060	+	1.38086i
$790$	−0.462022	−	0.846562i	−0.0164380	−	0.0301193i
$791$	17.0832	−	17.0832i	0.607408	−	0.607408i
$792$	−61.7759	+	7.21143i	−2.19511	+	0.256247i
$793$	−3.89533	+	31.6645i	−0.138327	+	1.12444i
$794$	−3.21794	−	5.89622i	−0.114200	−	0.209249i
$795$	86.2482	+	13.6604i	3.05891	+	0.484484i
$796$	−44.9292	−	28.9015i	−1.59247	−	1.02439i
$797$	−48.3332	+	15.7044i	−1.71205	+	0.556278i	−0.990672	−	0.136265i	$-0.956490\pi$
$797$	−48.3332	+	15.7044i	−1.71205	+	0.556278i	−0.721377	+	0.692543i	$0.756490\pi$
$798$	27.4605	+	77.0156i	0.972091	+	2.72632i
$799$	−1.05026	−	6.63106i	−0.0371554	−	0.234590i
$800$	16.1888	−	15.6992i	0.572360	−	0.555050i
$801$	−73.2198	+	37.3073i	−2.58709	+	1.31819i
$802$	3.25456	−	3.44450i	0.114923	−	0.121630i
$803$	0.352098	−	2.78170i	0.0124253	−	0.0981641i
$804$	14.4603	−	16.2004i	0.509976	−	0.571343i
$805$	4.84575	+	1.57448i	0.170790	+	0.0554931i
$806$	−9.61476	−	2.46671i	−0.338666	−	0.0868862i
$807$	−39.0231	+	53.7107i	−1.37368	+	1.89071i
$808$	17.1221	+	40.5886i	0.602353	+	1.42790i
$809$	−3.55069	−	10.9279i	−0.124836	−	0.384205i	0.869035	−	0.494750i	$-0.164740\pi$
$809$	−3.55069	−	10.9279i	−0.124836	−	0.384205i	−0.993871	+	0.110545i	$0.964740\pi$
$810$	−11.7768	−	62.7827i	−0.413793	−	2.20596i
$811$	−0.281404	−	0.0445700i	−0.00988142	−	0.00156506i	0.151492	−	0.988459i	$-0.451592\pi$
$811$	−0.281404	−	0.0445700i	−0.00988142	−	0.00156506i	−0.161373	+	0.986893i	$0.551592\pi$
$812$	28.6654	+	49.1569i	1.00596	+	1.72507i
$813$	−14.8131	−	14.8131i	−0.519520	−	0.519520i
$814$	5.14002	−	11.7707i	0.180157	−	0.412563i
$815$			34.1165i			1.19505i
$816$	8.76517	−	43.0680i	0.306842	−	1.50768i
$817$	−31.1596	−	4.93519i	−1.09014	−	0.172661i
$818$	−6.36181	−	33.9152i	−0.222435	−	1.18582i
$819$	38.1772	−	56.5718i	1.33402	−	1.97678i
$820$	27.5675	−	10.7194i	0.962698	−	0.374337i
$821$	−0.0841360	+	0.0133258i	−0.00293637	+	0.000465075i	−0.157902	−	0.987455i	$-0.550473\pi$
$821$	−0.0841360	+	0.0133258i	−0.00293637	+	0.000465075i	0.154966	+	0.987920i	$0.450473\pi$
$822$	19.9306	+	2.58002i	0.695159	+	0.0899884i
$823$	−3.86694	+	11.9012i	−0.134793	+	0.414850i	−0.995558	−	0.0941529i	$-0.969986\pi$
$823$	−3.86694	+	11.9012i	−0.134793	+	0.414850i	0.860765	+	0.509003i	$0.169986\pi$
$824$	−1.19888	−	14.0644i	−0.0417650	−	0.489958i
$825$	−23.0704	+	33.9293i	−0.803208	+	1.18127i
$826$	50.4061	−	1.42917i	1.75385	−	0.0497271i
$827$	−20.1973	−	39.6394i	−0.702328	−	1.37840i	−0.915875	−	0.401463i	$-0.868502\pi$
$827$	−20.1973	−	39.6394i	−0.702328	−	1.37840i	0.213547	−	0.976933i	$-0.431498\pi$
$828$	−6.11328	+	4.99443i	−0.212451	+	0.173569i
$829$	−8.72388	+	12.0074i	−0.302993	+	0.417034i	−0.933180	−	0.359409i	$-0.882978\pi$
$829$	−8.72388	+	12.0074i	−0.302993	+	0.417034i	0.630187	+	0.776443i	$0.282978\pi$
$830$	−32.7965	+	11.6938i	−1.13838	+	0.405899i
$831$	−10.2114	−	31.4274i	−0.354229	−	1.09021i
$832$	−15.8231	+	24.1170i	−0.548567	+	0.836107i
$833$	3.29700	−	2.39541i	0.114234	−	0.0829962i
$834$	−7.00001	−	2.05702i	−0.242390	−	0.0712287i
$835$			15.7936i			0.546559i
$836$	22.9606	+	36.6958i	0.794109	+	1.26915i
$837$	15.5062	−	15.5062i	0.535974	−	0.535974i
$838$	0.588967	−	2.00425i	0.0203455	−	0.0692356i
$839$	0.123341	−	0.778743i	0.00425819	−	0.0268852i	−0.985468	−	0.169863i	$-0.945668\pi$
$839$	0.123341	−	0.778743i	0.00425819	−	0.0268852i	0.989726	+	0.142977i	$0.0456676\pi$
$840$	−38.8334	+	64.3044i	−1.33988	+	2.21871i
$841$	21.7290	+	66.8750i	0.749276	+	2.30603i
$842$	−2.47511	+	5.21822i	−0.0852978	+	0.179832i
$843$	31.5905	−	5.00344i	1.08803	−	0.172328i
$844$	19.9490	+	24.4180i	0.686674	+	0.840502i
$845$	−8.74896	−	37.9759i	−0.300973	−	1.30641i
$846$	−12.9227	−	12.2102i	−0.444293	−	0.419794i
$847$	−28.8159	−	12.4864i	−0.990128	−	0.429038i
$848$	37.3064	−	4.24810i	1.28111	−	0.145880i
$849$	−44.9142	−	14.5935i	−1.54145	−	0.500848i
$850$	−12.1861	−	15.8103i	−0.417981	−	0.542288i
$851$	−0.255022	−	1.61015i	−0.00874204	−	0.0551951i
$852$	24.4375	+	10.7537i	0.837214	+	0.368415i
$853$	0.969313	−	1.90238i	0.0331886	−	0.0651364i	−0.873817	−	0.486255i	$-0.838363\pi$
$853$	0.969313	−	1.90238i	0.0331886	−	0.0651364i	0.907005	+	0.421119i	$0.138363\pi$
$854$	6.58657	+	35.1134i	0.225388	+	1.20156i
$855$	−104.930	+	76.2364i	−3.58854	+	2.60723i
$856$	2.12975	−	9.13201i	0.0727934	−	0.312126i
$857$			17.9582i			0.613440i	0.951800	+	0.306720i	$0.0992316\pi$
$857$			17.9582i			0.613440i	−0.951800	+	0.306720i	$0.900768\pi$
$858$	19.3220	−	48.7940i	0.659641	−	1.66580i
$859$			22.5793i			0.770396i	0.922834	+	0.385198i	$0.125867\pi$
$859$			22.5793i			0.770396i	−0.922834	+	0.385198i	$0.874133\pi$
$860$	−14.6008	−	25.0382i	−0.497882	−	0.853796i
$861$	−35.3610	+	25.6913i	−1.20510	+	0.875556i
$862$	53.8354	−	10.0984i	1.83364	−	0.343954i
$863$	0.273395	−	0.536568i	0.00930647	−	0.0182650i	−0.886306	−	0.463099i	$-0.846737\pi$
$863$	0.273395	−	0.536568i	0.00930647	−	0.0182650i	0.895613	+	0.444834i	$0.146737\pi$
$864$	−28.0550	−	57.2158i	−0.954450	−	1.94652i
$865$	−2.71568	−	17.1462i	−0.0923361	−	0.582987i
$866$	−26.8366	+	20.6850i	−0.911946	+	0.702903i
$867$	13.1725	+	4.28000i	0.447361	+	0.145357i
$868$	−11.0976	+	0.629811i	−0.376678	+	0.0213772i
$869$	0.623929	+	0.424243i	0.0211653	+	0.0143915i
$870$	−90.0437	+	95.2988i	−3.05277	+	3.23093i
$871$	4.31190	+	11.8554i	0.146103	+	0.401704i
$872$	−4.29806	−	0.310183i	−0.145551	−	0.0105041i
$873$	66.9933	−	10.6107i	2.26738	−	0.359118i
$874$	4.96407	+	2.35456i	0.167912	+	0.0796440i
$875$	−2.68052	−	8.24981i	−0.0906183	−	0.278894i
$876$	5.12756	−	1.11313i	0.173244	−	0.0376091i
$877$	5.06858	−	32.0017i	0.171154	−	1.08062i	−0.741219	−	0.671263i	$-0.765752\pi$
$877$	5.06858	−	32.0017i	0.171154	−	1.08062i	0.912373	−	0.409359i	$-0.134248\pi$
$878$	−27.7200	−	8.14577i	−0.935503	−	0.274906i
$879$	26.7882	−	26.7882i	0.903545	−	0.903545i
$880$	−12.7622	+	37.6662i	−0.430214	+	1.26973i
$881$		−	35.4781i		−	1.19529i	−0.801762	−	0.597644i	$-0.796104\pi$
$881$		−	35.4781i		−	1.19529i	0.801762	−	0.597644i	$-0.203896\pi$
$882$	3.04267	−	10.3542i	0.102452	−	0.348643i
$883$	−14.3338	+	10.4141i	−0.482372	+	0.350464i	−0.802243	−	0.596997i	$-0.796360\pi$
$883$	−14.3338	+	10.4141i	−0.482372	+	0.350464i	0.319871	+	0.947461i	$0.396360\pi$
$884$	19.6262	+	16.3317i	0.660101	+	0.549294i
$885$	35.9028	+	110.497i	1.20686	+	3.71433i
$886$	3.07133	+	8.61384i	0.103183	+	0.289388i
$887$	26.4361	−	36.3862i	0.887637	−	1.22173i	−0.0866090	−	0.996242i	$-0.527603\pi$
$887$	26.4361	−	36.3862i	0.887637	−	1.22173i	0.974246	−	0.225486i	$-0.0723969\pi$
$888$	23.9730	+	1.73008i	0.804480	+	0.0580578i
$889$	−11.1393	−	21.8622i	−0.373601	−	0.733234i
$890$	1.48924	+	52.5249i	0.0499196	+	1.76064i
$891$	30.6192	+	39.4939i	1.02578	+	1.32310i
$892$	1.67410	+	1.49429i	0.0560531	+	0.0500326i
$893$	−3.82371	+	11.7682i	−0.127955	+	0.393806i
$894$	1.66700	−	12.8775i	0.0557527	−	0.430689i
$895$	−27.4655	+	4.35011i	−0.918071	+	0.145408i
$896$	−8.70334	+	31.1059i	−0.290758	+	1.03918i
$897$	−1.26947	−	6.53893i	−0.0423865	−	0.218329i
$898$	−16.1461	+	3.02869i	−0.538803	+	0.101069i
$899$	−19.1613	−	3.03485i	−0.639065	−	0.101218i
$900$	−51.1186	−	13.4602i	−1.70395	−	0.448672i
$901$		−	33.2364i		−	1.10727i
$902$	−15.3600	+	17.3066i	−0.511433	+	0.576246i
$903$	30.2861	+	30.2861i	1.00786	+	1.00786i
$904$	23.3089	+	5.43607i	0.775244	+	0.180801i
$905$	−19.1136	−	3.02729i	−0.635357	−	0.100631i
$906$	−45.4604	+	8.52746i	−1.51032	+	0.283306i
$907$	−15.7867	−	48.5865i	−0.524189	−	1.61329i	−0.765913	−	0.642944i	$-0.777713\pi$
$907$	−15.7867	−	48.5865i	−0.524189	−	1.61329i	0.241724	−	0.970345i	$-0.422287\pi$
$908$	−15.7609	+	35.8163i	−0.523045	+	1.18861i
$909$	60.6958	−	83.5406i	2.01315	−	2.77087i
$910$	−22.2218	−	37.5587i	−0.736644	−	1.24506i
$911$	−34.8069	−	11.3094i	−1.15320	−	0.374698i	−0.330854	−	0.943682i	$-0.607337\pi$
$911$	−34.8069	−	11.3094i	−1.15320	−	0.374698i	−0.822349	+	0.568983i	$0.807337\pi$
$912$	−50.4303	+	63.3911i	−1.66991	+	2.09909i
$913$	18.6517	−	19.8523i	0.617280	−	0.657016i
$914$	−18.9116	−	17.8687i	−0.625539	−	0.591045i
$915$	−73.3419	+	37.3695i	−2.42461	+	1.23540i
$916$	29.9766	+	3.01946i	0.990456	+	0.0997659i
$917$	−7.92002	−	50.0051i	−0.261542	−	1.65131i
$918$	−53.1310	+	18.9442i	−1.75358	+	0.625253i
$919$	1.79813	−	0.584247i	0.0593148	−	0.0192725i	−0.279209	−	0.960230i	$-0.590072\pi$
$919$	1.79813	−	0.584247i	0.0593148	−	0.0192725i	0.338524	+	0.940958i	$0.390072\pi$
$920$	1.21023	+	4.90048i	0.0399000	+	0.161564i
$921$	24.7178	+	3.91491i	0.814478	+	0.129001i
$922$	44.3509	−	24.2051i	1.46062	−	0.797152i
$923$	−12.2245	+	9.54628i	−0.402374	+	0.314220i
$924$	4.06447	−	58.6279i	0.133711	−	1.92872i
$925$	7.71905	−	7.71905i	0.253801	−	0.253801i
$926$	20.9698	−	11.4446i	0.689112	−	0.376092i
$927$	−26.7685	+	19.4485i	−0.879194	+	0.638772i
$928$	−26.3618	+	49.8316i	−0.865367	+	1.63580i
$929$	42.2468	+	21.5258i	1.38607	+	0.706239i	0.978367	−	0.206875i	$-0.0663292\pi$
$929$	42.2468	+	21.5258i	1.38607	+	0.706239i	0.407705	+	0.913114i	$0.366329\pi$
$930$	−8.60121	−	24.1229i	−0.282045	−	0.791022i
$931$	−7.41858	+	1.17499i	−0.243134	+	0.0385087i
$932$	−16.1023	−	19.7096i	−0.527449	−	0.645608i
$933$	28.6773	+	9.31782i	0.938852	+	0.305052i
$934$	−0.847178	−	29.8796i	−0.0277205	−	0.977689i
$935$	31.8493	+	14.9966i	1.04158	+	0.490441i
$936$	67.5663	+	2.52596i	2.20847	+	0.0825635i
$937$	1.48563	−	4.57230i	0.0485334	−	0.149371i	−0.923853	−	0.382748i	$-0.874978\pi$
$937$	1.48563	−	4.57230i	0.0485334	−	0.149371i	0.972386	+	0.233377i	$0.0749778\pi$
$938$	8.62404	+	11.1888i	0.281585	+	0.365328i
$939$	−31.8490	+	43.8364i	−1.03935	+	1.43055i
$940$	−10.5955	+	4.11995i	−0.345586	+	0.134378i
$941$	−32.4017	−	16.5095i	−1.05626	−	0.538193i	−0.162490	−	0.986710i	$-0.551952\pi$
$941$	−32.4017	−	16.5095i	−1.05626	−	0.538193i	−0.893774	+	0.448517i	$0.851952\pi$
$942$	−55.2078	−	37.7675i	−1.79877	−	1.23053i
$943$	−0.459446	+	2.90083i	−0.0149616	+	0.0944640i
$944$	27.5705	+	41.6603i	0.897343	+	1.35593i
$945$	96.4110			3.13625
$946$	19.1049	+	12.2133i	0.621155	+	0.397090i
$947$	16.2163	−	16.2163i	0.526958	−	0.526958i	−0.392706	−	0.919664i	$-0.628461\pi$
$947$	16.2163	−	16.2163i	0.526958	−	0.526958i	0.919664	+	0.392706i	$0.128461\pi$
$948$	−0.359519	+	1.36537i	−0.0116766	+	0.0443452i
$949$	−0.840862	+	2.92988i	−0.0272955	+	0.0951080i
$950$	6.78285	+	36.1598i	0.220065	+	1.17318i
$951$	0.683767	−	1.34197i	0.0221727	−	0.0435163i
$952$	26.4860	+	10.7698i	0.858416	+	0.349051i
$953$	−23.0335	+	31.7029i	−0.746129	+	1.02696i	0.252113	+	0.967698i	$0.418874\pi$
$953$	−23.0335	+	31.7029i	−0.746129	+	1.02696i	−0.998243	+	0.0592609i	$0.981126\pi$
$954$	−53.7308	−	69.7103i	−1.73960	−	2.25695i
$955$	−30.6414	+	15.6126i	−0.991531	+	0.505210i
$956$	6.79726	+	6.06718i	0.219839	+	0.196227i
$957$	28.6401	−	98.4906i	0.925804	−	3.18375i
$958$	17.1356	+	16.1907i	0.553627	+	0.523099i
$959$	−4.04005	+	12.4340i	−0.130460	+	0.401515i
$960$	−74.4153	+	0.966952i	−2.40174	+	0.0312082i
$961$	−15.9939	+	22.0137i	−0.515932	+	0.710120i
$962$	−7.47949	+	11.7907i	−0.241148	+	0.380148i
$963$	−20.9048	+	6.79238i	−0.673647	+	0.218881i
$964$	6.86201	+	31.6094i	0.221011	+	1.01807i
$965$	−30.0587	+	21.8390i	−0.967625	+	0.703021i
$966$	−3.57338	−	6.54750i	−0.114972	−	0.210662i
$967$	8.04497	+	8.04497i	0.258709	+	0.258709i	0.824529	−	0.565820i	$-0.191440\pi$
$967$	8.04497	+	8.04497i	0.258709	+	0.258709i	−0.565820	+	0.824529i	$0.691440\pi$
$968$	−4.56888	−	30.7754i	−0.146849	−	0.989159i
$969$	50.7019	+	50.7019i	1.62878	+	1.62878i
$970$	12.2281	−	41.6120i	0.392620	−	1.33608i
$971$	20.2510	+	27.8731i	0.649885	+	0.894490i	0.999094	−	0.0425551i	$-0.0135498\pi$
$971$	20.2510	+	27.8731i	0.649885	+	0.894490i	−0.349209	+	0.937045i	$0.613550\pi$
$972$	−14.0261	+	21.8045i	−0.449887	+	0.699378i
$973$	2.15480	−	4.22903i	0.0690797	−	0.135576i
$974$	32.0394	+	15.1969i	1.02661	+	0.486941i
$975$	30.4274	−	32.6143i	0.974457	−	1.04449i
$976$	−26.0963	+	23.9098i	−0.835322	+	0.765333i
$977$	17.1721	+	33.7022i	0.549385	+	1.07823i	0.984093	+	0.177657i	$0.0568517\pi$
$977$	17.1721	+	33.7022i	0.549385	+	1.07823i	−0.434708	+	0.900572i	$0.643148\pi$
$978$	34.3019	−	36.3038i	1.09685	−	1.16087i
$979$	−19.7952	−	36.0281i	−0.632657	−	1.15146i
$980$	−5.14817	−	4.59522i	−0.164452	−	0.146789i
$981$	4.58584	+	9.00022i	0.146415	+	0.287355i
$982$	9.34545	+	12.1248i	0.298225	+	0.386917i
$983$	−27.9897	+	4.43313i	−0.892732	+	0.141395i	−0.585914	−	0.810373i	$-0.699264\pi$
$983$	−27.9897	+	4.43313i	−0.892732	+	0.141395i	−0.306818	+	0.951768i	$0.599264\pi$
$984$	−40.1125	−	16.3107i	−1.27874	−	0.519965i
$985$	41.6569	−	13.5352i	1.32730	−	0.431266i
$986$	41.1867	+	28.1757i	1.31165	+	0.897298i
$987$	13.5909	−	9.87434i	0.432602	−	0.314304i
$988$	−18.5645	−	43.2414i	−0.590615	−	1.37569i
$989$	2.87802			0.0915158
$990$	91.0447	−	20.0344i	2.89359	−	0.636735i
$991$		−	6.77665i		−	0.215268i	−0.994191	−	0.107634i	$-0.965673\pi$
$991$		−	6.77665i		−	0.215268i	0.994191	−	0.107634i	$-0.0343274\pi$
$992$	−6.33520	−	9.00727i	−0.201143	−	0.285981i
$993$	8.49701	−	53.6480i	0.269644	−	1.70247i
$994$	−9.80676	+	14.3353i	−0.311051	+	0.454689i
$995$	71.3456	+	36.3524i	2.26181	+	1.15245i
$996$	46.6565	+	20.5312i	1.47837	+	0.650555i
$997$	−0.537926	−	0.390826i	−0.0170363	−	0.0123776i	0.579235	−	0.815161i	$-0.303352\pi$
$997$	−0.537926	−	0.390826i	−0.0170363	−	0.0123776i	−0.596271	+	0.802783i	$0.703352\pi$
$998$	−2.50201	+	19.3280i	−0.0791997	+	0.611817i
$999$	−14.0044	−	27.4852i	−0.443080	−	0.869593i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bk.a.31.8	✓	640
4.3	odd	2	inner	572.2.bk.a.31.49	yes	640
11.5	even	5	inner	572.2.bk.a.291.71	yes	640
13.8	odd	4	inner	572.2.bk.a.515.48	yes	640
44.27	odd	10	inner	572.2.bk.a.291.48	yes	640
52.47	even	4	inner	572.2.bk.a.515.71	yes	640
143.60	odd	20	inner	572.2.bk.a.203.49	yes	640
572.203	even	20	inner	572.2.bk.a.203.8	yes	640

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bk.a.31.8	✓	640	1.1	even	1	trivial
572.2.bk.a.31.49	yes	640	4.3	odd	2	inner
572.2.bk.a.203.8	yes	640	572.203	even	20	inner
572.2.bk.a.203.49	yes	640	143.60	odd	20	inner
572.2.bk.a.291.48	yes	640	44.27	odd	10	inner
572.2.bk.a.291.71	yes	640	11.5	even	5	inner
572.2.bk.a.515.48	yes	640	13.8	odd	4	inner
572.2.bk.a.515.71	yes	640	52.47	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:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.bk (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.35684 - 0.398721i) q^{2} +(-1.82403 - 2.51057i) q^{3} +(1.68204 + 1.08200i) q^{4} +(-2.67101 - 1.36095i) q^{5} +(1.47391 + 4.13373i) q^{6} +(-2.81984 + 0.446619i) q^{7} +(-1.85085 - 2.13877i) q^{8} +(-2.04880 + 6.30555i) q^{9} +O(q^{10})\)	\(q+(-1.35684 - 0.398721i) q^{2} +(-1.82403 - 2.51057i) q^{3} +(1.68204 + 1.08200i) q^{4} +(-2.67101 - 1.36095i) q^{5} +(1.47391 + 4.13373i) q^{6} +(-2.81984 + 0.446619i) q^{7} +(-1.85085 - 2.13877i) q^{8} +(-2.04880 + 6.30555i) q^{9} +(3.08150 + 2.91158i) q^{10} +(-3.18471 - 0.926083i) q^{11} +(-0.351662 - 6.19649i) q^{12} +(3.26739 + 1.52453i) q^{13} +(4.00416 + 0.518339i) q^{14} +(1.45526 + 9.18816i) q^{15} +(1.65854 + 3.63995i) q^{16} +(3.36744 - 1.09415i) q^{17} +(5.29405 - 7.73875i) q^{18} +(-6.44543 - 1.02086i) q^{19} +(-3.02020 - 5.17921i) q^{20} +(6.26476 + 6.26476i) q^{21} +(3.95190 + 2.52636i) q^{22} +0.595326 q^{23} +(-1.99352 + 8.54788i) q^{24} +(2.34319 + 3.22512i) q^{25} +(-3.82547 - 3.37132i) q^{26} +(10.7136 - 3.48104i) q^{27} +(-5.22634 - 2.29985i) q^{28} +(-8.06247 - 5.85773i) q^{29} +(1.68895 - 13.0471i) q^{30} +(1.73450 - 0.883773i) q^{31} +(-0.799050 - 5.60014i) q^{32} +(3.48402 + 9.68463i) q^{33} +(-5.00534 + 0.141917i) q^{34} +(8.13965 + 2.64473i) q^{35} +(-10.2688 + 8.38941i) q^{36} +(-0.428374 - 2.70465i) q^{37} +(8.33840 + 3.95507i) q^{38} +(-2.13240 - 10.9838i) q^{39} +(2.03288 + 8.23159i) q^{40} +(-0.771756 + 4.87268i) q^{41} +(-6.00240 - 10.9982i) q^{42} +4.83437 q^{43} +(-4.35479 - 5.00358i) q^{44} +(14.0539 - 14.0539i) q^{45} +(-0.807764 - 0.237369i) q^{46} +(0.296621 - 1.87279i) q^{47} +(6.11312 - 10.8033i) q^{48} +(1.09465 - 0.355673i) q^{49} +(-1.89341 - 5.31026i) q^{50} +(-8.88925 - 6.45842i) q^{51} +(3.84634 + 6.09964i) q^{52} +(2.90071 - 8.92746i) q^{53} +(-15.9246 + 0.451511i) q^{54} +(7.24604 + 6.80780i) q^{55} +(6.17432 + 5.20438i) q^{56} +(9.19376 + 18.0438i) q^{57} +(8.60391 + 11.1627i) q^{58} +(12.3355 - 1.95375i) q^{59} +(-7.49381 + 17.0295i) q^{60} +(2.73429 + 8.41528i) q^{61} +(-2.70583 + 0.507558i) q^{62} +(2.96111 - 18.6957i) q^{63} +(-1.14871 + 7.91710i) q^{64} +(-6.65242 - 8.51876i) q^{65} +(-0.865805 - 14.5297i) q^{66} +(2.47404 + 2.47404i) q^{67} +(6.84804 + 1.80318i) q^{68} +(-1.08590 - 1.49461i) q^{69} +(-9.98971 - 6.83394i) q^{70} +(-1.95297 + 3.83292i) q^{71} +(17.2782 - 7.28872i) q^{72} +(0.132251 + 0.834998i) q^{73} +(-0.497163 + 3.84058i) q^{74} +(3.82283 - 11.7655i) q^{75} +(-9.73692 - 8.69110i) q^{76} +(9.39398 + 1.18906i) q^{77} +(-1.48613 + 15.7535i) q^{78} +(-0.216356 - 0.0702984i) q^{79} +(0.523811 - 11.9795i) q^{80} +(-12.1898 - 8.85642i) q^{81} +(2.98999 - 6.30374i) q^{82} +(-3.72865 + 7.31789i) q^{83} +(3.75911 + 17.3161i) q^{84} +(-10.4835 - 1.66043i) q^{85} +(-6.55947 - 1.92756i) q^{86} +30.9261i q^{87} +(3.91374 + 8.52541i) q^{88} +(8.76427 + 8.76427i) q^{89} +(-24.6725 + 13.4653i) q^{90} +(-9.89440 - 2.83965i) q^{91} +(1.00136 + 0.644145i) q^{92} +(-5.38256 - 2.74255i) q^{93} +(-1.14919 + 2.42282i) q^{94} +(15.8265 + 11.4986i) q^{95} +(-12.6020 + 12.2209i) q^{96} +(-4.64452 - 9.11539i) q^{97} +(-1.62708 + 0.0461328i) q^{98} +(12.3643 - 18.1840i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 640 q - 6 q^{2} - 12 q^{5} - 14 q^{6} - 6 q^{8} + 120 q^{9}+O(q^{10}) \) 640 * q - 6 * q^2 - 12 * q^5 - 14 * q^6 - 6 * q^8 + 120 * q^9	\( 640 q - 6 q^{2} - 12 q^{5} - 14 q^{6} - 6 q^{8} + 120 q^{9} - 12 q^{13} + 4 q^{14} - 36 q^{16} - 10 q^{18} - 60 q^{20} - 56 q^{21} - 44 q^{22} - 14 q^{24} + 26 q^{26} - 14 q^{28} - 24 q^{29} - 16 q^{32} - 28 q^{33} + 12 q^{34} - 12 q^{37} + 4 q^{40} - 36 q^{41} - 8 q^{42} + 26 q^{44} - 16 q^{45} - 50 q^{46} + 48 q^{48} + 36 q^{50} - 52 q^{52} - 40 q^{53} + 116 q^{54} - 36 q^{57} - 70 q^{58} + 52 q^{60} - 8 q^{61} - 48 q^{65} - 228 q^{66} - 44 q^{68} - 68 q^{70} - 38 q^{72} - 12 q^{73} - 12 q^{74} + 108 q^{76} + 108 q^{78} + 62 q^{80} - 168 q^{81} - 36 q^{84} - 52 q^{85} - 62 q^{86} + 16 q^{89} - 80 q^{92} - 4 q^{93} - 124 q^{94} - 132 q^{96} - 4 q^{97} - 108 q^{98}+O(q^{100}) \) 640 * q - 6 * q^2 - 12 * q^5 - 14 * q^6 - 6 * q^8 + 120 * q^9 - 12 * q^13 + 4 * q^14 - 36 * q^16 - 10 * q^18 - 60 * q^20 - 56 * q^21 - 44 * q^22 - 14 * q^24 + 26 * q^26 - 14 * q^28 - 24 * q^29 - 16 * q^32 - 28 * q^33 + 12 * q^34 - 12 * q^37 + 4 * q^40 - 36 * q^41 - 8 * q^42 + 26 * q^44 - 16 * q^45 - 50 * q^46 + 48 * q^48 + 36 * q^50 - 52 * q^52 - 40 * q^53 + 116 * q^54 - 36 * q^57 - 70 * q^58 + 52 * q^60 - 8 * q^61 - 48 * q^65 - 228 * q^66 - 44 * q^68 - 68 * q^70 - 38 * q^72 - 12 * q^73 - 12 * q^74 + 108 * q^76 + 108 * q^78 + 62 * q^80 - 168 * q^81 - 36 * q^84 - 52 * q^85 - 62 * q^86 + 16 * q^89 - 80 * q^92 - 4 * q^93 - 124 * q^94 - 132 * q^96 - 4 * q^97 - 108 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more