LMFDB - Embedded newform 538.2.e.a.9.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [538,2,Mod(9,538)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(538, base_ring=CyclotomicField(134))

chi = DirichletCharacter(H, H._module([109]))

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

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

chi := DirichletCharacter("538.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 538 = 2 \cdot 269 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	538.e (of order $134$, degree $66$, 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:	$4.29595162874$
Analytic rank:	$0$
Dimension:	$1452$
Relative dimension:	$22$ over $\Q(\zeta_{134})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{134}]$

Embedding invariants

Embedding label			9.6
Character	$\chi$	$=$	538.9
Dual form			538.2.e.a.299.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.833094 + 0.553131i) q^{2} +(0.283306 - 0.499678i) q^{3} +(0.388092 - 0.921621i) q^{4} +(-0.723479 - 0.505183i) q^{5} +(0.0403669 + 0.572984i) q^{6} +(-0.341899 - 2.41448i) q^{7} +(0.186460 + 0.982463i) q^{8} +(1.37101 + 2.29119i) q^{9} +(0.882159 + 0.0206858i) q^{10} +(-3.95285 - 1.14238i) q^{11} +(-0.350565 - 0.455022i) q^{12} +(0.0912267 - 3.89043i) q^{13} +(1.62036 + 1.82238i) q^{14} +(-0.457395 + 0.218386i) q^{15} +(-0.698769 - 0.715347i) q^{16} +(-0.695955 - 2.40813i) q^{17} +(-2.40951 - 1.15043i) q^{18} +(1.84077 + 5.40538i) q^{19} +(-0.746363 + 0.470716i) q^{20} +(-1.30333 - 0.513198i) q^{21} +(3.92498 - 1.23473i) q^{22} +(-4.57177 - 2.59209i) q^{23} +(0.543740 + 0.185167i) q^{24} +(-1.45412 - 3.96301i) q^{25} +(2.07592 + 3.29155i) q^{26} +(3.25601 - 0.0763503i) q^{27} +(-2.35793 - 0.621940i) q^{28} +(-8.91811 - 3.27226i) q^{29} +(0.260257 - 0.434935i) q^{30} +(-1.07150 + 1.69896i) q^{31} +(0.977821 + 0.209440i) q^{32} +(-1.69069 + 1.65151i) q^{33} +(1.91181 + 1.62125i) q^{34} +(-0.972398 + 1.91955i) q^{35} +(2.64369 - 0.374355i) q^{36} +(0.425576 - 2.56986i) q^{37} +(-4.52342 - 3.48500i) q^{38} +(-1.91812 - 1.14777i) q^{39} +(0.361423 - 0.804988i) q^{40} +(5.45616 - 8.21775i) q^{41} +(1.36966 - 0.293368i) q^{42} +(-0.723726 + 1.97242i) q^{43} +(-2.58691 + 3.19968i) q^{44} +(0.165575 - 2.35024i) q^{45} +(5.24248 - 0.369335i) q^{46} +(-11.7414 - 1.10434i) q^{47} +(-0.555409 + 0.146498i) q^{48} +(1.01196 - 0.292460i) q^{49} +(3.40349 + 2.49724i) q^{50} +(-1.40046 - 0.334485i) q^{51} +(-3.55009 - 1.59392i) q^{52} +(-0.199606 - 0.931908i) q^{53} +(-2.67033 + 1.86461i) q^{54} +(2.28269 + 2.82340i) q^{55} +(2.30839 - 0.786108i) q^{56} +(3.22245 + 0.611584i) q^{57} +(9.23961 - 2.20678i) q^{58} +(13.5021 + 5.68570i) q^{59} +(0.0237574 + 0.506298i) q^{60} +(3.17233 - 2.95670i) q^{61} +(-0.0470874 - 2.00807i) q^{62} +(5.06330 - 4.09363i) q^{63} +(-0.930465 + 0.366380i) q^{64} +(-2.03138 + 2.76856i) q^{65} +(0.495002 - 2.31103i) q^{66} +(-4.59892 - 10.9213i) q^{67} +(-2.48948 - 0.293170i) q^{68} +(-2.59042 + 1.55006i) q^{69} +(-0.251664 - 2.13703i) q^{70} +(-1.75039 - 1.55635i) q^{71} +(-1.99537 + 1.77418i) q^{72} +(0.688488 - 5.84636i) q^{73} +(1.06693 + 2.37634i) q^{74} +(-2.39219 - 0.396153i) q^{75} +(5.69610 + 0.401292i) q^{76} +(-1.40678 + 9.93466i) q^{77} +(2.23284 - 0.104773i) q^{78} +(0.103815 + 0.330007i) q^{79} +(0.144164 + 0.870545i) q^{80} +(-2.90202 + 5.41022i) q^{81} +9.86413i q^{82} +(12.3414 + 6.61987i) q^{83} +(-0.978784 + 1.00200i) q^{84} +(-0.713037 + 2.09382i) q^{85} +(-0.488075 - 2.04353i) q^{86} +(-4.16163 + 3.52913i) q^{87} +(0.385298 - 4.09653i) q^{88} +(-15.0363 - 7.61701i) q^{89} +(1.16205 + 2.04956i) q^{90} +(-9.42456 + 1.10987i) q^{91} +(-4.16319 + 3.20747i) q^{92} +(0.545371 + 1.01673i) q^{93} +(10.3926 - 5.57454i) q^{94} +(1.39895 - 4.84061i) q^{95} +(0.381675 - 0.429260i) q^{96} +(3.00236 + 2.79829i) q^{97} +(-0.681293 + 0.803395i) q^{98} +(-2.80196 - 10.6229i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1452 q + 22 q^{4} - 2 q^{5} + 2 q^{6} + 20 q^{9} + 2 q^{11} - 10 q^{13} + 12 q^{14} - 22 q^{16} + 2 q^{20} + 12 q^{21} - 4 q^{23} - 2 q^{24} - 24 q^{25} - 8 q^{30} - 12 q^{34} - 20 q^{36} - 396 q^{37} - 2 q^{38}+ \cdots + 18 q^{99}+O(q^{100}) $ 1452 * q + 22 * q^4 - 2 * q^5 + 2 * q^6 + 20 * q^9 + 2 * q^11 - 10 * q^13 + 12 * q^14 - 22 * q^16 + 2 * q^20 + 12 * q^21 - 4 * q^23 - 2 * q^24 - 24 * q^25 - 8 * q^30 - 12 * q^34 - 20 * q^36 - 396 * q^37 - 2 * q^38 + 24 * q^41 + 14 * q^43 - 2 * q^44 - 42 * q^45 - 402 * q^47 + 22 * q^49 + 12 * q^51 + 10 * q^52 - 10 * q^53 - 8 * q^54 - 4 * q^55 - 12 * q^56 + 16 * q^57 - 18 * q^58 - 268 * q^60 - 2 * q^61 + 4 * q^62 + 22 * q^64 + 16 * q^65 + 40 * q^66 + 6 * q^67 - 106 * q^73 + 40 * q^78 + 40 * q^79 - 2 * q^80 - 14 * q^81 - 402 * q^83 - 12 * q^84 - 100 * q^87 + 4 * q^92 - 340 * q^93 + 2 * q^96 - 64 * q^97 + 18 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/538\mathbb{Z}\right)^\times$.

$n$	$271$
$\chi(n)$	$e\left(\frac{109}{134}\right)$

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 $

$2$	−0.833094	+	0.553131i	−0.589087	+	0.391123i
$2$	−0.833094	+	0.553131i	−0.589087	+	0.391123i
$3$	0.283306	−	0.499678i	0.163567	−	0.288489i	−0.776081	−	0.630634i	$-0.782795\pi$
$3$	0.283306	−	0.499678i	0.163567	−	0.288489i	0.939647	+	0.342145i	$0.111153\pi$
$4$	0.388092	−	0.921621i	0.194046	−	0.460810i
$5$	−0.723479	−	0.505183i	−0.323550	−	0.225925i	0.399479	−	0.916742i	$-0.369191\pi$
$5$	−0.723479	−	0.505183i	−0.323550	−	0.225925i	−0.723029	+	0.690818i	$0.757251\pi$
$6$	0.0403669	+	0.572984i	0.0164797	+	0.233920i
$7$	−0.341899	−	2.41448i	−0.129226	−	0.912589i	−0.943327	−	0.331865i	$-0.892322\pi$
$7$	−0.341899	−	2.41448i	−0.129226	−	0.912589i	0.814101	−	0.580723i	$-0.197230\pi$
$8$	0.186460	+	0.982463i	0.0659236	+	0.347353i
$9$	1.37101	+	2.29119i	0.457002	+	0.763731i
$10$	0.882159	+	0.0206858i	0.278963	+	0.00654141i
$11$	−3.95285	−	1.14238i	−1.19183	−	0.344441i	−0.378143	−	0.925747i	$-0.623437\pi$
$11$	−3.95285	−	1.14238i	−1.19183	−	0.344441i	−0.813685	+	0.581307i	$0.802542\pi$
$12$	−0.350565	−	0.455022i	−0.101199	−	0.131353i
$13$	0.0912267	−	3.89043i	0.0253017	−	1.07901i	−0.829005	−	0.559241i	$-0.811093\pi$
$13$	0.0912267	−	3.89043i	0.0253017	−	1.07901i	0.854307	−	0.519769i	$-0.173982\pi$
$14$	1.62036	+	1.82238i	0.433059	+	0.487051i
$15$	−0.457395	+	0.218386i	−0.118099	+	0.0563869i
$16$	−0.698769	−	0.715347i	−0.174692	−	0.178837i
$17$	−0.695955	−	2.40813i	−0.168794	−	0.584058i	−0.999621	−	0.0275272i	$-0.991237\pi$
$17$	−0.695955	−	2.40813i	−0.168794	−	0.584058i	0.830827	−	0.556530i	$-0.187868\pi$
$18$	−2.40951	−	1.15043i	−0.567926	−	0.271159i
$19$	1.84077	+	5.40538i	0.422302	+	1.24008i	0.926435	+	0.376454i	$0.122857\pi$
$19$	1.84077	+	5.40538i	0.422302	+	1.24008i	−0.504134	+	0.863625i	$0.668188\pi$
$20$	−0.746363	+	0.470716i	−0.166892	+	0.105255i
$21$	−1.30333	−	0.513198i	−0.284409	−	0.111989i
$22$	3.92498	−	1.23473i	0.836808	−	0.263246i
$23$	−4.57177	−	2.59209i	−0.953280	−	0.540488i	−0.0640492	−	0.997947i	$-0.520401\pi$
$23$	−4.57177	−	2.59209i	−0.953280	−	0.540488i	−0.889231	+	0.457459i	$0.848760\pi$
$24$	0.543740	+	0.185167i	0.110990	+	0.0377972i
$25$	−1.45412	−	3.96301i	−0.290824	−	0.792603i
$26$	2.07592	+	3.29155i	0.407121	+	0.645527i
$27$	3.25601	−	0.0763503i	0.626620	−	0.0146936i
$28$	−2.35793	−	0.621940i	−0.445606	−	0.117536i
$29$	−8.91811	−	3.27226i	−1.65605	−	0.607643i	−0.665700	−	0.746220i	$-0.731867\pi$
$29$	−8.91811	−	3.27226i	−1.65605	−	0.607643i	−0.990352	+	0.138576i	$0.955747\pi$
$30$	0.260257	−	0.434935i	0.0475162	−	0.0794079i
$31$	−1.07150	+	1.69896i	−0.192447	+	0.305142i	−0.928181	−	0.372128i	$-0.878628\pi$
$31$	−1.07150	+	1.69896i	−0.192447	+	0.305142i	0.735734	+	0.677270i	$0.236837\pi$
$32$	0.977821	+	0.209440i	0.172856	+	0.0370242i
$33$	−1.69069	+	1.65151i	−0.294311	+	0.287490i
$34$	1.91181	+	1.62125i	0.327872	+	0.278041i
$35$	−0.972398	+	1.91955i	−0.164365	+	0.324463i
$36$	2.64369	−	0.374355i	0.440614	−	0.0623926i
$37$	0.425576	−	2.56986i	0.0699642	−	0.422483i	−0.928701	−	0.370830i	$-0.879073\pi$
$37$	0.425576	−	2.56986i	0.0699642	−	0.422483i	0.998665	−	0.0516532i	$-0.0164490\pi$
$38$	−4.52342	−	3.48500i	−0.733795	−	0.565342i
$39$	−1.91812	−	1.14777i	−0.307144	−	0.183790i
$40$	0.361423	−	0.804988i	0.0571460	−	0.127280i
$41$	5.45616	−	8.21775i	0.852109	−	1.28340i	−0.105235	−	0.994447i	$-0.533560\pi$
$41$	5.45616	−	8.21775i	0.852109	−	1.28340i	0.957344	−	0.288950i	$-0.0933061\pi$
$42$	1.36966	−	0.293368i	0.211343	−	0.0452677i
$43$	−0.723726	+	1.97242i	−0.110367	+	0.300791i	−0.981857	−	0.189622i	$-0.939274\pi$
$43$	−0.723726	+	1.97242i	−0.110367	+	0.300791i	0.871490	+	0.490413i	$0.163154\pi$
$44$	−2.58691	+	3.19968i	−0.389991	+	0.482369i
$45$	0.165575	−	2.35024i	0.0246825	−	0.350353i
$46$	5.24248	−	0.369335i	0.772962	−	0.0544554i
$47$	−11.7414	−	1.10434i	−1.71266	−	0.161084i	−0.808565	−	0.588406i	$-0.799756\pi$
$47$	−11.7414	−	1.10434i	−1.71266	−	0.161084i	−0.904099	+	0.427322i	$0.859457\pi$
$48$	−0.555409	+	0.146498i	−0.0801663	+	0.0211451i
$49$	1.01196	−	0.292460i	0.144566	−	0.0417800i
$50$	3.40349	+	2.49724i	0.481326	+	0.353164i
$51$	−1.40046	−	0.334485i	−0.196103	−	0.0468372i
$52$	−3.55009	−	1.59392i	−0.492310	−	0.221037i
$53$	−0.199606	−	0.931908i	−0.0274180	−	0.128007i	0.962015	−	0.272995i	$-0.0880142\pi$
$53$	−0.199606	−	0.931908i	−0.0274180	−	0.128007i	−0.989434	+	0.144987i	$0.953686\pi$
$54$	−2.67033	+	1.86461i	−0.363386	+	0.253741i
$55$	2.28269	+	2.82340i	0.307798	+	0.380707i
$56$	2.30839	−	0.786108i	0.308471	−	0.105048i
$57$	3.22245	+	0.611584i	0.426824	+	0.0810063i
$58$	9.23961	−	2.20678i	1.21322	−	0.289765i
$59$	13.5021	+	5.68570i	1.75782	+	0.740215i	0.995684	+	0.0928031i	$0.0295827\pi$
$59$	13.5021	+	5.68570i	1.75782	+	0.740215i	0.762140	+	0.647412i	$0.224149\pi$
$60$	0.0237574	+	0.506298i	0.00306707	+	0.0653628i
$61$	3.17233	−	2.95670i	0.406175	−	0.378566i	−0.451919	−	0.892059i	$-0.649260\pi$
$61$	3.17233	−	2.95670i	0.406175	−	0.378566i	0.858094	+	0.513492i	$0.171649\pi$
$62$	−0.0470874	−	2.00807i	−0.00598010	−	0.255026i
$63$	5.06330	−	4.09363i	0.637915	−	0.515749i
$64$	−0.930465	+	0.366380i	−0.116308	+	0.0457975i
$65$	−2.03138	+	2.76856i	−0.251961	+	0.343397i
$66$	0.495002	−	2.31103i	0.0609305	−	0.284468i
$67$	−4.59892	−	10.9213i	−0.561847	−	1.33425i	−0.916794	−	0.399360i	$-0.869232\pi$
$67$	−4.59892	−	10.9213i	−0.561847	−	1.33425i	0.354947	−	0.934886i	$-0.384499\pi$
$68$	−2.48948	−	0.293170i	−0.301894	−	0.0355520i
$69$	−2.59042	+	1.55006i	−0.311850	+	0.186605i
$70$	−0.251664	−	2.13703i	−0.0300796	−	0.255424i
$71$	−1.75039	−	1.55635i	−0.207733	−	0.184705i	0.554156	−	0.832413i	$-0.313041\pi$
$71$	−1.75039	−	1.55635i	−0.207733	−	0.184705i	−0.761889	+	0.647708i	$0.775728\pi$
$72$	−1.99537	+	1.77418i	−0.235157	+	0.209089i
$73$	0.688488	−	5.84636i	0.0805814	−	0.684265i	−0.892054	−	0.451929i	$-0.850736\pi$
$73$	0.688488	−	5.84636i	0.0805814	−	0.684265i	0.972636	−	0.232336i	$-0.0746369\pi$
$74$	1.06693	+	2.37634i	0.124028	+	0.276244i
$75$	−2.39219	−	0.396153i	−0.276227	−	0.0457438i
$76$	5.69610	+	0.401292i	0.653387	+	0.0460314i
$77$	−1.40678	+	9.93466i	−0.160318	+	1.13216i
$78$	2.23284	−	0.104773i	0.252819	−	0.0118632i
$79$	0.103815	+	0.330007i	0.0116801	+	0.0371287i	0.959572	−	0.281463i	$-0.0908198\pi$
$79$	0.103815	+	0.330007i	0.0116801	+	0.0371287i	−0.947892	+	0.318592i	$0.896790\pi$
$80$	0.144164	+	0.870545i	0.0161181	+	0.0973299i
$81$	−2.90202	+	5.41022i	−0.322447	+	0.601135i
$82$			9.86413i			1.08931i
$83$	12.3414	+	6.61987i	1.35464	+	0.726625i	0.979709	−	0.200427i	$-0.0642331\pi$
$83$	12.3414	+	6.61987i	1.35464	+	0.726625i	0.374932	+	0.927052i	$0.377666\pi$
$84$	−0.978784	+	1.00200i	−0.106794	+	0.109328i
$85$	−0.713037	+	2.09382i	−0.0773397	+	0.227106i
$86$	−0.488075	−	2.04353i	−0.0526304	−	0.220359i
$87$	−4.16163	+	3.52913i	−0.446174	+	0.378363i
$88$	0.385298	−	4.09653i	0.0410729	−	0.436692i
$89$	−15.0363	−	7.61701i	−1.59384	−	0.807401i	−0.999996	−	0.00282103i	$-0.999102\pi$
$89$	−15.0363	−	7.61701i	−1.59384	−	0.807401i	−0.593844	−	0.804580i	$-0.702390\pi$
$90$	1.16205	+	2.04956i	0.122491	+	0.216042i
$91$	−9.42456	+	1.10987i	−0.987962	+	0.116346i
$92$	−4.16319	+	3.20747i	−0.434042	+	0.334402i
$93$	0.545371	+	1.01673i	0.0565523	+	0.105430i
$94$	10.3926	−	5.57454i	1.07191	−	0.574970i
$95$	1.39895	−	4.84061i	0.143529	−	0.496636i
$96$	0.381675	−	0.429260i	0.0389546	−	0.0438112i
$97$	3.00236	+	2.79829i	0.304844	+	0.284123i	0.819265	−	0.573414i	$-0.194381\pi$
$97$	3.00236	+	2.79829i	0.304844	+	0.284123i	−0.514422	+	0.857537i	$0.671993\pi$
$98$	−0.681293	+	0.803395i	−0.0688210	+	0.0811552i
$99$	−2.80196	−	10.6229i	−0.281608	−	1.06765i
$100$	−4.21673	−	0.197865i	−0.421673	−	0.0197865i
$101$	−2.34756	+	12.3694i	−0.233591	+	1.23080i	0.649049	+	0.760747i	$0.275167\pi$
$101$	−2.34756	+	12.3694i	−0.233591	+	1.23080i	−0.882640	+	0.470050i	$0.844236\pi$
$102$	1.35173	−	0.495980i	0.133841	−	0.0491093i
$103$	10.0907	−	0.949083i	0.994271	−	0.0935159i	0.416003	−	0.909363i	$-0.363430\pi$
$103$	10.0907	−	0.949083i	0.994271	−	0.0935159i	0.578268	+	0.815847i	$0.303729\pi$
$104$	3.83921	−	0.635783i	0.376465	−	0.0623436i
$105$	0.683671	+	1.02971i	0.0667195	+	0.100489i
$106$	0.681758	+	0.665959i	0.0662182	+	0.0646837i
$107$	0.926374	+	9.84931i	0.0895560	+	0.952168i	0.919178	+	0.393843i	$0.128855\pi$
$107$	0.926374	+	9.84931i	0.0895560	+	0.952168i	−0.829622	+	0.558326i	$0.811444\pi$
$108$	1.19327	−	3.03044i	0.114822	−	0.291604i
$109$	8.17367	+	8.76977i	0.782896	+	0.839992i	0.990398	−	0.138243i	$-0.0441454\pi$
$109$	8.17367	+	8.76977i	0.782896	+	0.839992i	−0.207502	+	0.978234i	$0.566533\pi$
$110$	−3.46341	−	1.08953i	−0.330223	−	0.103882i
$111$	−1.16354	−	0.940708i	−0.110438	−	0.0892881i
$112$	−1.48828	+	1.93174i	−0.140630	+	0.182533i
$113$	14.4615	−	10.6108i	1.36042	−	0.998182i	0.362616	−	0.931938i	$-0.381884\pi$
$113$	14.4615	−	10.6108i	1.36042	−	0.998182i	0.997803	−	0.0662440i	$-0.0211016\pi$
$114$	−3.02289	+	1.27293i	−0.283120	+	0.119221i
$115$	1.99810	+	4.18490i	0.186324	+	0.390244i
$116$	−6.47683	+	6.94918i	−0.601358	+	0.645215i
$117$	9.03879	−	5.12478i	0.835636	−	0.473787i
$118$	−14.3935	+	2.73171i	−1.32503	+	0.251475i
$119$	−5.57645	+	2.50371i	−0.511192	+	0.229515i
$120$	−0.299841	−	0.408653i	−0.0273717	−	0.0373047i
$121$	5.01580	+	3.16336i	0.455982	+	0.287579i
$122$	−1.00741	+	4.21792i	−0.0912062	+	0.381873i
$123$	−2.56047	−	5.05446i	−0.230870	−	0.455745i
$124$	1.14996	+	1.64687i	0.103269	+	0.147893i
$125$	−2.07527	+	7.86786i	−0.185618	+	0.703722i
$126$	−1.95389	+	6.21105i	−0.174066	+	0.553324i
$127$	−1.65235	−	0.233979i	−0.146622	−	0.0207622i	0.0665089	−	0.997786i	$-0.478814\pi$
$127$	−1.65235	−	0.233979i	−0.146622	−	0.0207622i	−0.213131	+	0.977024i	$0.568366\pi$
$128$	0.572509	−	0.819898i	0.0506031	−	0.0724695i
$129$	0.780539	+	0.920428i	0.0687226	+	0.0810392i
$130$	0.160953	−	3.43009i	0.0141165	−	0.300839i
$131$	−0.159618	+	0.334309i	−0.0139459	+	0.0292087i	−0.909272	−	0.416203i	$-0.863361\pi$
$131$	−0.159618	+	0.334309i	−0.0139459	+	0.0292087i	0.895326	+	0.445412i	$0.146943\pi$
$132$	0.865921	+	2.19911i	0.0753687	+	0.191408i
$133$	12.4218	−	6.29260i	1.07711	−	0.545638i
$134$	9.87223	+	6.55465i	0.852831	+	0.566235i
$135$	−2.39423	−	1.58964i	−0.206062	−	0.136815i
$136$	2.23613	−	1.13277i	0.191747	−	0.0971342i
$137$	5.72745	+	14.5455i	0.489329	+	1.24271i	0.937257	+	0.348639i	$0.113356\pi$
$137$	5.72745	+	14.5455i	0.489329	+	1.24271i	−0.447928	+	0.894070i	$0.647838\pi$
$138$	1.30068	−	2.72419i	0.110721	−	0.231898i
$139$	−0.630112	+	13.4284i	−0.0534454	+	1.13898i	0.793937	+	0.608000i	$0.208028\pi$
$139$	−0.630112	+	13.4284i	−0.0534454	+	1.13898i	−0.847383	+	0.530983i	$0.821823\pi$
$140$	1.39172	+	1.64114i	0.117622	+	0.138702i
$141$	−3.87823	+	5.55407i	−0.326606	+	0.467737i
$142$	2.31910	+	0.328393i	0.194615	+	0.0275581i
$143$	−4.80495	+	15.2740i	−0.401810	+	1.27728i
$144$	0.680979	−	2.58176i	0.0567483	−	0.215147i
$145$	4.79898	+	6.87269i	0.398534	+	0.570746i
$146$	2.66023	+	5.25139i	0.220162	+	0.434608i
$147$	0.140560	−	0.588512i	0.0115932	−	0.0485396i
$148$	−2.20328	−	1.38956i	−0.181108	−	0.114221i
$149$	7.83004	+	10.6715i	0.641462	+	0.874247i	0.998201	−	0.0599575i	$-0.0190965\pi$
$149$	7.83004	+	10.6715i	0.641462	+	0.874247i	−0.356739	+	0.934204i	$0.616111\pi$
$150$	2.21205	−	0.993163i	0.180613	−	0.0810914i
$151$	−16.8965	+	3.20676i	−1.37502	+	0.260962i	−0.820708	−	0.571348i	$-0.806421\pi$
$151$	−16.8965	+	3.20676i	−1.37502	+	0.260962i	−0.554310	+	0.832310i	$0.687018\pi$
$152$	−4.96735	+	2.81637i	−0.402905	+	0.228438i
$153$	4.56333	−	4.89613i	0.368923	−	0.395829i
$154$	−4.32319	−	9.05464i	−0.348372	−	0.729644i
$155$	1.63349	−	0.687860i	0.131205	−	0.0552502i
$156$	−1.80221	+	1.32234i	−0.144292	+	0.105872i
$157$	8.94832	−	11.6146i	0.714154	−	0.926948i	−0.285350	−	0.958423i	$-0.592110\pi$
$157$	8.94832	−	11.6146i	0.714154	−	0.926948i	0.999505	+	0.0314750i	$0.0100205\pi$
$158$	−0.269025	−	0.217504i	−0.0214025	−	0.0173037i
$159$	−0.522204	−	0.164276i	−0.0414134	−	0.0130280i
$160$	−0.601628	−	0.645504i	−0.0475629	−	0.0510316i
$161$	−4.69547	+	11.9247i	−0.370055	+	0.939798i
$162$	−0.574902	−	6.11242i	−0.0451686	−	0.480237i
$163$	9.65123	+	9.42757i	0.755943	+	0.738424i	0.971234	−	0.238125i	$-0.0765329\pi$
$163$	9.65123	+	9.42757i	0.755943	+	0.738424i	−0.215292	+	0.976550i	$0.569070\pi$
$164$	−5.45616	−	8.21775i	−0.426054	−	0.641699i
$165$	2.05749	−	0.340725i	0.160175	−	0.0265254i
$166$	−13.9432	+	1.31142i	−1.08220	+	0.101786i
$167$	−11.8899	+	4.36269i	−0.920070	+	0.337595i	−0.760309	−	0.649561i	$-0.774953\pi$
$167$	−11.8899	+	4.36269i	−0.920070	+	0.337595i	−0.159760	+	0.987156i	$0.551072\pi$
$168$	0.261179	−	1.37616i	0.0201504	−	0.106173i
$169$	−2.14139	−	0.100482i	−0.164723	−	0.00772942i
$170$	−0.564129	−	2.13875i	−0.0432667	−	0.164035i
$171$	−9.86105	+	11.6284i	−0.754093	+	0.889243i
$172$	1.53695	+	1.43248i	0.117191	+	0.109226i
$173$	−2.35843	+	2.65246i	−0.179308	+	0.201663i	−0.830134	−	0.557564i	$-0.811736\pi$
$173$	−2.35843	+	2.65246i	−0.179308	+	0.201663i	0.650826	+	0.759227i	$0.274423\pi$
$174$	1.51496	−	5.24203i	0.114849	−	0.397397i
$175$	−9.07147	+	4.86590i	−0.685738	+	0.367828i
$176$	1.94493	+	3.62592i	0.146605	+	0.273314i
$177$	6.66625	−	5.13591i	0.501066	−	0.386039i
$178$	16.7398	−	1.97134i	1.25470	−	0.147758i
$179$	−7.99507	−	14.1012i	−0.597579	−	1.05397i	−0.990903	−	0.134575i	$-0.957033\pi$
$179$	−7.99507	−	14.1012i	−0.597579	−	1.05397i	0.393324	−	0.919400i	$-0.371325\pi$
$180$	−2.10177	−	1.06471i	−0.156657	−	0.0793585i
$181$	0.680227	−	7.23224i	0.0505609	−	0.537568i	−0.933357	−	0.358949i	$-0.883135\pi$
$181$	0.680227	−	7.23224i	0.0505609	−	0.537568i	0.983918	−	0.178620i	$-0.0571632\pi$
$182$	7.23764	−	6.13764i	0.536490	−	0.454952i
$183$	−0.578658	−	2.42279i	−0.0427756	−	0.179098i
$184$	1.69418	−	4.97491i	0.124896	−	0.366756i
$185$	−1.60615	+	1.64425i	−0.118086	+	0.120888i
$186$	−1.01673	−	0.545371i	−0.0745503	−	0.0399885i
$187$			10.3140i			0.754236i
$188$	−5.57454	+	10.3926i	−0.406565	+	0.757956i
$189$	−1.29757	−	7.83548i	−0.0943847	−	0.569947i
$190$	1.51204	+	4.80648i	0.109695	+	0.348699i
$191$	2.23283	−	0.104773i	0.161562	−	0.00758112i	0.0340623	−	0.999420i	$-0.489156\pi$
$191$	2.23283	−	0.104773i	0.161562	−	0.00758112i	0.127500	+	0.991839i	$0.459305\pi$
$192$	−0.0805343	+	0.568731i	−0.00581206	+	0.0410446i
$193$	−13.1333	−	0.925245i	−0.945354	−	0.0666006i	−0.410792	−	0.911729i	$-0.634748\pi$
$193$	−13.1333	−	0.925245i	−0.945354	−	0.0666006i	−0.534563	+	0.845129i	$0.679524\pi$
$194$	−4.04907	−	0.670536i	−0.290706	−	0.0481417i
$195$	0.807886	+	1.79938i	0.0578540	+	0.128857i
$196$	0.123198	−	1.04615i	0.00879987	−	0.0747249i
$197$	19.4486	−	17.2926i	1.38565	−	1.23205i	0.443757	−	0.896147i	$-0.353645\pi$
$197$	19.4486	−	17.2926i	1.38565	−	1.23205i	0.941897	−	0.335902i	$-0.109041\pi$
$198$	8.21018	+	7.30005i	0.583472	+	0.518792i
$199$	−2.42917	−	20.6275i	−0.172199	−	1.46224i	−0.758247	−	0.651968i	$-0.773944\pi$
$199$	−2.42917	−	20.6275i	−0.172199	−	1.46224i	0.586048	−	0.810276i	$-0.300683\pi$
$200$	3.62238	−	2.16756i	0.256141	−	0.153270i
$201$	−6.76002	−	0.796084i	−0.476815	−	0.0561514i
$202$	−4.88614	−	11.6033i	−0.343787	−	0.816409i
$203$	−4.85172	+	22.6514i	−0.340524	+	1.58982i
$204$	−0.851774	+	1.16088i	−0.0596361	+	0.0812779i
$205$	−8.09888	+	3.18902i	−0.565651	+	0.222731i
$206$	−7.88158	+	6.37218i	−0.549135	+	0.443971i
$207$	−0.328956	−	14.0286i	−0.0228640	−	0.975053i
$208$	−2.84675	+	2.65325i	−0.197387	+	0.183970i
$209$	−1.10128	−	23.4695i	−0.0761770	−	1.62342i
$210$	−1.13912	−	0.479682i	−0.0786071	−	0.0331012i
$211$	24.9233	−	5.95265i	1.71579	−	0.409797i	0.748430	−	0.663214i	$-0.230808\pi$
$211$	24.9233	−	5.95265i	1.71579	−	0.409797i	0.967357	+	0.253416i	$0.0815543\pi$
$212$	−0.936332	−	0.177705i	−0.0643075	−	0.0122048i
$213$	−1.27357	+	0.433706i	−0.0872635	+	0.0297171i
$214$	−6.21971	−	7.69299i	−0.425171	−	0.525882i
$215$	1.52003	−	1.06139i	0.103665	−	0.0723863i
$216$	0.682127	+	3.18467i	0.0464129	+	0.216690i
$217$	4.46846	+	2.00625i	0.303339	+	0.136193i
$218$	−11.6603	−	2.78493i	−0.789733	−	0.188619i
$219$	−2.72624	−	2.00033i	−0.184223	−	0.135170i
$220$	3.48800	−	1.00804i	0.235161	−	0.0679619i
$221$	−9.43215	+	2.48788i	−0.634475	+	0.167353i
$222$	1.48967	+	0.140111i	0.0999801	+	0.00940361i
$223$	10.5041	−	0.740016i	0.703405	−	0.0495551i	0.285939	−	0.958248i	$-0.407694\pi$
$223$	10.5041	−	0.740016i	0.703405	−	0.0495551i	0.417466	+	0.908693i	$0.362918\pi$
$224$	0.171373	−	2.43254i	0.0114504	−	0.162531i
$225$	7.08641	−	8.76499i	0.472428	−	0.584333i
$226$	−6.17858	+	16.8389i	−0.410993	+	1.12011i
$227$	−2.57258	+	0.551024i	−0.170748	+	0.0365727i	−0.294015	−	0.955801i	$-0.594991\pi$
$227$	−2.57258	+	0.551024i	−0.170748	+	0.0365727i	0.123266	+	0.992374i	$0.460663\pi$
$228$	1.81425	−	2.73253i	0.120152	−	0.180966i
$229$	6.07423	−	13.5290i	0.401397	−	0.894020i	−0.594549	−	0.804059i	$-0.702669\pi$
$229$	6.07423	−	13.5290i	0.401397	−	0.894020i	0.995945	−	0.0899601i	$-0.0286740\pi$
$230$	−3.97941	−	2.38120i	−0.262394	−	0.157012i
$231$	4.56558	+	3.51749i	0.300393	+	0.231434i
$232$	1.55200	−	9.37185i	0.101894	−	0.615292i
$233$	23.3145	−	3.30142i	1.52738	−	0.216283i	0.674457	−	0.738314i	$-0.264378\pi$
$233$	23.3145	−	3.30142i	1.52738	−	0.216283i	0.852927	+	0.522031i	$0.174825\pi$
$234$	−4.69548	+	9.26906i	−0.306953	+	0.605938i
$235$	7.93680	+	6.73054i	0.517740	+	0.439052i
$236$	10.4801	−	10.2372i	0.682197	−	0.666388i
$237$	0.194309	+	0.0416191i	0.0126217	+	0.00270345i
$238$	3.26082	−	5.17033i	0.211368	−	0.335143i
$239$	6.40816	−	10.7092i	0.414509	−	0.692717i	−0.577844	−	0.816147i	$-0.696106\pi$
$239$	6.40816	−	10.7092i	0.414509	−	0.692717i	0.992353	+	0.123430i	$0.0393894\pi$
$240$	0.475835	+	0.174595i	0.0307150	+	0.0112700i
$241$	−0.677190	−	0.178619i	−0.0436216	−	0.0115059i	0.233167	−	0.972437i	$-0.425091\pi$
$241$	−0.677190	−	0.178619i	−0.0436216	−	0.0115059i	−0.276789	+	0.960931i	$0.589270\pi$
$242$	−5.92839	+	0.139015i	−0.381091	+	0.00893622i
$243$	7.09339	+	11.2472i	0.455041	+	0.721509i
$244$	−1.49380	−	4.07115i	−0.0956308	−	0.260629i
$245$	−0.879881	−	0.299638i	−0.0562135	−	0.0191432i
$246$	4.92889	+	2.79457i	0.314255	+	0.178175i
$247$	21.1972	−	6.66827i	1.34874	−	0.424292i
$248$	−1.86896	−	0.735921i	−0.118679	−	0.0467310i
$249$	6.80418	−	4.29126i	0.431198	−	0.271948i
$250$	−2.62306	−	7.70256i	−0.165897	−	0.487153i
$251$	−24.1769	−	11.5434i	−1.52603	−	0.728612i	−0.532963	−	0.846139i	$-0.678921\pi$
$251$	−24.1769	−	11.5434i	−1.52603	−	0.728612i	−0.993070	+	0.117527i	$0.962503\pi$
$252$	−1.80775	−	6.25514i	−0.113877	−	0.394037i
$253$	15.1103	+	15.4688i	0.949979	+	0.972517i
$254$	1.50598	−	0.719040i	0.0944938	−	0.0451166i
$255$	0.844227	+	0.949480i	0.0528676	+	0.0594587i
$256$	−0.0234426	+	0.999725i	−0.00146516	+	0.0624828i
$257$	−6.72121	−	8.72391i	−0.419257	−	0.544182i	0.534339	−	0.845270i	$-0.320561\pi$
$257$	−6.72121	−	8.72391i	−0.419257	−	0.544182i	−0.953596	+	0.301088i	$0.902650\pi$
$258$	−1.15938	−	0.335063i	−0.0721798	−	0.0208601i
$259$	−6.35039	−	0.148911i	−0.394594	−	0.00925285i
$260$	1.76320	+	2.94661i	0.109349	+	0.182741i
$261$	−4.72941	−	24.9194i	−0.292743	−	1.54247i
$262$	−0.0519403	−	0.366801i	−0.00320888	−	0.0226610i
$263$	0.609612	+	8.65308i	0.0375903	+	0.533572i	0.979985	+	0.199070i	$0.0637920\pi$
$263$	0.609612	+	8.65308i	0.0375903	+	0.533572i	−0.942395	+	0.334502i	$0.891432\pi$
$264$	−1.93779	−	1.35310i	−0.119263	−	0.0832773i
$265$	−0.326373	+	0.775054i	−0.0200489	+	0.0476112i
$266$	−6.86793	+	12.1132i	−0.421100	+	0.742710i
$267$	−8.06591	+	5.35535i	−0.493626	+	0.327742i
$268$	−11.8501			−0.723859
$269$	8.28219	−	14.1565i	0.504974	−	0.863134i
$269$	8.28219	−	14.1565i	0.504974	−	0.863134i
$270$	2.87390			0.174900
$271$	−9.65881	+	6.41295i	−0.586731	+	0.389559i	−0.811067	−	0.584953i	$-0.801113\pi$
$271$	−9.65881	+	6.41295i	−0.586731	+	0.389559i	0.224336	+	0.974512i	$0.427979\pi$
$272$	−1.23634	+	2.18058i	−0.0749640	+	0.132217i
$273$	−2.11546	+	5.02368i	−0.128033	+	0.304047i
$274$	−12.8171	−	8.94977i	−0.774309	−	0.540675i
$275$	1.22065	+	17.3263i	0.0736078	+	1.04482i
$276$	0.423246	+	2.98895i	0.0254764	+	0.179914i
$277$	−2.19287	−	11.5543i	−0.131757	−	0.694229i	−0.984978	−	0.172680i	$-0.944757\pi$
$277$	−2.19287	−	11.5543i	−0.131757	−	0.694229i	0.853221	−	0.521549i	$-0.174646\pi$
$278$	−6.90273	−	11.5357i	−0.413998	−	0.691863i
$279$	−5.36168	−	0.125726i	−0.320995	−	0.00752703i
$280$	−2.06720	−	0.597425i	−0.123539	−	0.0357030i
$281$	−0.816677	−	1.06002i	−0.0487188	−	0.0632354i	0.767172	−	0.641442i	$-0.221663\pi$
$281$	−0.816677	−	1.06002i	−0.0487188	−	0.0632354i	−0.815891	+	0.578206i	$0.803753\pi$
$282$	0.158802	−	6.77224i	0.00945654	−	0.403281i
$283$	−15.4814	−	17.4116i	−0.920275	−	1.03501i	−0.999273	−	0.0381348i	$-0.987858\pi$
$283$	−15.4814	−	17.4116i	−0.920275	−	1.03501i	0.0789971	−	0.996875i	$-0.474828\pi$
$284$	−2.11368	+	1.00919i	−0.125424	+	0.0598841i
$285$	−2.02241	−	2.07039i	−0.119798	−	0.122640i
$286$	−4.44557	−	15.3825i	−0.262872	−	0.909585i
$287$	−21.7071	−	10.3642i	−1.28133	−	0.611777i
$288$	0.860732	+	2.52752i	0.0507191	+	0.148936i
$289$	9.06440	−	5.71674i	0.533200	−	0.336279i
$290$	−7.79950	−	3.07113i	−0.458002	−	0.180343i
$291$	2.24883	−	0.707443i	0.131829	−	0.0414710i
$292$	−5.12093	−	2.90345i	−0.299680	−	0.169912i
$293$	−22.6179	−	7.70241i	−1.32135	−	0.449979i	−0.429813	−	0.902918i	$-0.641420\pi$
$293$	−22.6179	−	7.70241i	−1.32135	−	0.449979i	−0.891542	+	0.452939i	$0.850376\pi$
$294$	0.208425	+	0.568034i	0.0121556	+	0.0331284i
$295$	−6.89618	−	10.9345i	−0.401511	−	0.636632i
$296$	2.60415	−	0.0610647i	0.151363	−	0.00354931i
$297$	−12.9577	−	3.41780i	−0.751884	−	0.198321i
$298$	−12.4259	−	4.55936i	−0.719814	−	0.264117i
$299$	−10.5014	+	17.5497i	−0.607312	+	1.01492i
$300$	−1.29349	+	2.05095i	−0.0746798	+	0.118412i
$301$	5.00981	+	1.07306i	0.288761	+	0.0618499i
$302$	12.3026	−	12.0175i	0.707936	−	0.691530i
$303$	5.51562	+	4.67734i	0.316864	+	0.268706i
$304$	2.58045	−	5.09390i	0.147999	−	0.292155i
$305$	−3.78879	+	0.536506i	−0.216945	+	0.0307202i
$306$	−1.09348	+	6.60306i	−0.0625102	+	0.377472i
$307$	4.16591	+	3.20957i	0.237761	+	0.183180i	0.722279	−	0.691602i	$-0.243095\pi$
$307$	4.16591	+	3.20957i	0.237761	+	0.183180i	−0.484518	+	0.874781i	$0.661005\pi$
$308$	8.61002	+	5.15208i	0.490602	+	0.293567i
$309$	2.38453	−	5.31101i	0.135651	−	0.302133i
$310$	−0.980378	+	1.47659i	−0.0556817	+	0.0838646i
$311$	−10.6423	+	2.27948i	−0.603469	+	0.129257i	−0.500954	−	0.865474i	$-0.667017\pi$
$311$	−10.6423	+	2.27948i	−0.603469	+	0.129257i	−0.102515	+	0.994731i	$0.532689\pi$
$312$	0.769984	−	2.09849i	0.0435918	−	0.118804i
$313$	8.51116	−	10.5272i	0.481079	−	0.595034i	−0.477934	−	0.878396i	$-0.658614\pi$
$313$	8.51116	−	10.5272i	0.481079	−	0.595034i	0.959013	+	0.283362i	$0.0914499\pi$
$314$	−1.03038	+	14.6257i	−0.0581480	+	0.825375i
$315$	−5.73122	+	0.403767i	−0.322918	+	0.0227497i
$316$	0.344431	+	0.0323954i	0.0193758	+	0.00182238i
$317$	27.7953	−	7.33144i	1.56114	−	0.411775i	0.630047	−	0.776557i	$-0.283036\pi$
$317$	27.7953	−	7.33144i	1.56114	−	0.411775i	0.931093	+	0.364782i	$0.118857\pi$
$318$	0.525911	−	0.151989i	0.0294916	−	0.00852314i
$319$	31.5137	+	23.1226i	1.76443	+	1.29462i
$320$	0.858261	+	0.204987i	0.0479783	+	0.0114591i
$321$	5.18393	+	2.32748i	0.289339	+	0.129907i
$322$	−2.68415	−	12.5316i	−0.149582	−	0.698359i
$323$	11.7358	−	8.19472i	0.652996	−	0.455966i
$324$	3.85992	+	4.77423i	0.214440	+	0.265235i
$325$	−15.5505	+	5.29562i	−0.862585	+	0.293748i
$326$	−13.2551	−	2.51566i	−0.734130	−	0.139329i
$327$	6.69771	−	1.59968i	0.370384	−	0.0884623i
$328$	9.09099	+	3.82819i	0.501966	+	0.211376i
$329$	1.34798	+	28.7271i	0.0743168	+	1.58377i
$330$	−1.52562	+	1.42192i	−0.0839825	+	0.0782740i
$331$	0.816360	+	34.8142i	0.0448712	+	1.91356i	0.312295	+	0.949985i	$0.398902\pi$
$331$	0.816360	+	34.8142i	0.0448712	+	1.91356i	−0.267424	+	0.963579i	$0.586172\pi$
$332$	10.8906	−	8.80494i	0.597699	−	0.483234i
$333$	6.47152	−	2.54822i	0.354637	−	0.139642i
$334$	7.49229	−	10.2112i	0.409960	−	0.558733i
$335$	−2.19002	+	10.2246i	−0.119653	+	0.558630i
$336$	0.543610	+	1.29094i	0.0296564	+	0.0704264i
$337$	−14.8777	−	1.75205i	−0.810442	−	0.0954405i	−0.298444	−	0.954427i	$-0.596468\pi$
$337$	−14.8777	−	1.75205i	−0.810442	−	0.0954405i	−0.511998	+	0.858987i	$0.671094\pi$
$338$	1.83956	−	1.10076i	0.100059	−	0.0598735i
$339$	−1.20498	−	10.2322i	−0.0654454	−	0.555736i
$340$	1.65298	+	1.46974i	0.0896455	+	0.0797080i
$341$	6.17634	−	5.49167i	0.334467	−	0.297391i
$342$	1.78317	−	15.1420i	0.0964229	−	0.818785i
$343$	−8.04383	−	17.9158i	−0.434326	−	0.967363i
$344$	−2.07277	−	0.343257i	−0.111757	−	0.0185072i
$345$	2.65718	+	0.187199i	0.143058	+	0.0100785i
$346$	0.497634	−	3.51427i	0.0267530	−	0.188929i
$347$	10.8521	−	0.509224i	0.582573	−	0.0273366i	0.246451	−	0.969155i	$-0.420735\pi$
$347$	10.8521	−	0.509224i	0.582573	−	0.0273366i	0.336122	+	0.941819i	$0.390885\pi$
$348$	1.63743	+	5.20507i	0.0877753	+	0.279021i
$349$	1.69048	+	10.2081i	0.0904896	+	0.546427i	0.993223	+	0.116226i	$0.0370796\pi$
$349$	1.69048	+	10.2081i	0.0904896	+	0.546427i	−0.902733	+	0.430201i	$0.858443\pi$
$350$	4.86590	−	9.07147i	0.260093	−	0.484890i
$351$		−	12.6742i		−	0.676501i
$352$	−3.62592	−	1.94493i	−0.193262	−	0.103665i
$353$	−12.5425	+	12.8401i	−0.667570	+	0.683407i	−0.962243	−	0.272191i	$-0.912252\pi$
$353$	−12.5425	+	12.8401i	−0.667570	+	0.683407i	0.294673	+	0.955598i	$0.404789\pi$
$354$	−2.71278	+	7.96601i	−0.144182	+	0.423389i
$355$	0.480127	+	2.01025i	0.0254825	+	0.106693i
$356$	−12.8554	+	10.9016i	−0.681337	+	0.577785i
$357$	−0.328791	+	3.49574i	−0.0174015	+	0.185014i
$358$	14.4605	+	7.32532i	0.764259	+	0.387155i
$359$	−7.66453	−	13.5182i	−0.404518	−	0.713465i	0.591138	−	0.806570i	$-0.298679\pi$
$359$	−7.66453	−	13.5182i	−0.404518	−	0.713465i	−0.995656	+	0.0931053i	$0.970321\pi$
$360$	2.33989	−	0.275554i	0.123323	−	0.0145230i
$361$	−10.7786	+	8.30422i	−0.567295	+	0.437064i
$362$	3.43369	+	6.40139i	0.180471	+	0.336450i
$363$	3.00167	−	1.61009i	0.157547	−	0.0845075i
$364$	−2.63472	+	9.11660i	−0.138097	+	0.477840i
$365$	−3.45159	+	3.88191i	−0.180664	+	0.203188i
$366$	1.82220	+	1.69834i	0.0952479	+	0.0887737i
$367$	13.6905	−	16.1441i	0.714638	−	0.842717i	−0.278405	−	0.960464i	$-0.589806\pi$
$367$	13.6905	−	16.1441i	0.714638	−	0.842717i	0.993044	+	0.117747i	$0.0375671\pi$
$368$	1.34037	+	5.08167i	0.0698716	+	0.264901i
$369$	26.3089	+	1.23451i	1.36959	+	0.0642662i
$370$	0.428585	−	2.25822i	0.0222811	−	0.117399i
$371$	−2.18183	+	0.800564i	−0.113275	+	0.0415632i
$372$	1.14869	−	0.108040i	0.0595570	−	0.00560162i
$373$	−9.48291	+	1.57039i	−0.491006	+	0.0813119i	−0.403741	−	0.914873i	$-0.632290\pi$
$373$	−9.48291	+	1.57039i	−0.491006	+	0.0813119i	−0.0872652	+	0.996185i	$0.527813\pi$
$374$	−5.70500	−	8.59255i	−0.294999	−	0.444310i
$375$	3.34346	+	3.26598i	0.172655	+	0.168654i
$376$	−1.10434	−	11.7414i	−0.0569519	−	0.605518i
$377$	−13.5441	+	34.3967i	−0.697555	+	1.77152i
$378$	5.41505	+	5.80996i	0.278520	+	0.298832i
$379$	−23.8013	−	7.48749i	−1.22259	−	0.384606i	−0.380926	−	0.924606i	$-0.624395\pi$
$379$	−23.8013	−	7.48749i	−1.22259	−	0.384606i	−0.841665	+	0.539999i	$0.818424\pi$
$380$	−3.91828	−	3.16790i	−0.201004	−	0.162510i
$381$	−0.585034	+	0.759355i	−0.0299722	+	0.0389029i
$382$	−1.80221	+	1.32234i	−0.0922089	+	0.0676566i
$383$	15.2567	−	6.42455i	0.779580	−	0.328279i	0.0381177	−	0.999273i	$-0.487864\pi$
$383$	15.2567	−	6.42455i	0.779580	−	0.328279i	0.741463	+	0.670994i	$0.234132\pi$
$384$	−0.247490	−	0.518352i	−0.0126297	−	0.0264521i
$385$	6.03659	−	6.47684i	0.307653	−	0.330090i
$386$	11.4530	−	6.49361i	0.582945	−	0.330516i
$387$	−5.51142	+	1.04600i	−0.280161	+	0.0531714i
$388$	3.74415	−	1.68105i	0.190080	−	0.0853422i
$389$	−0.664952	−	0.906261i	−0.0337144	−	0.0459493i	0.789067	−	0.614307i	$-0.210564\pi$
$389$	−0.664952	−	0.906261i	−0.0337144	−	0.0459493i	−0.822782	+	0.568357i	$0.807579\pi$
$390$	−1.66834	−	1.05219i	−0.0844797	−	0.0532797i
$391$	−3.06034	+	12.8134i	−0.154768	+	0.648001i
$392$	0.476022	+	0.939685i	0.0240427	+	0.0474613i
$393$	0.121826	+	0.174469i	0.00614532	+	0.00880081i
$394$	−6.63740	+	25.1640i	−0.334387	+	1.26774i
$395$	0.0916062	−	0.291199i	0.00460921	−	0.0146518i
$396$	−10.8777	−	1.54033i	−0.546627	−	0.0774043i
$397$	−20.7551	+	29.7237i	−1.04167	+	1.49179i	−0.180428	+	0.983588i	$0.557748\pi$
$397$	−20.7551	+	29.7237i	−1.04167	+	1.49179i	−0.861240	+	0.508199i	$0.830311\pi$
$398$	13.4334	+	15.8410i	0.673357	+	0.794037i
$399$	0.374905	−	7.98965i	0.0187687	−	0.399983i
$400$	−1.81883	+	3.80943i	−0.0909417	+	0.190472i
$401$	6.18395	+	15.7049i	0.308812	+	0.784264i	0.998206	+	0.0598773i	$0.0190710\pi$
$401$	6.18395	+	15.7049i	0.308812	+	0.784264i	−0.689394	+	0.724387i	$0.742123\pi$
$402$	6.07207	−	3.07597i	0.302848	−	0.153415i
$403$	6.51194	+	4.32359i	0.324383	+	0.215373i
$404$	10.4888	+	6.96401i	0.521836	+	0.346472i
$405$	4.83270	−	2.44813i	0.240139	−	0.121649i
$406$	−8.48726	−	21.5544i	−0.421216	−	1.06973i
$407$	−4.61800	+	9.67210i	−0.228906	+	0.479428i
$408$	0.0674890	−	1.43827i	0.00334120	−	0.0712048i
$409$	−3.10951	−	3.66680i	−0.153755	−	0.181312i	0.680400	−	0.732841i	$-0.261806\pi$
$409$	−3.10951	−	3.66680i	−0.153755	−	0.181312i	−0.834156	+	0.551529i	$0.814045\pi$
$410$	4.98319	−	7.13650i	0.246102	−	0.352446i
$411$	8.89071	+	1.25896i	0.438546	+	0.0620997i
$412$	3.04144	−	9.66817i	0.149841	−	0.476317i
$413$	9.11166	−	34.5445i	0.448356	−	1.69983i
$414$	8.03369	+	11.5052i	0.394834	+	0.565448i
$415$	−5.58448	−	11.0240i	−0.274131	−	0.541146i
$416$	0.904016	−	3.78504i	0.0443230	−	0.185577i
$417$	6.53137	+	4.11920i	0.319842	+	0.201718i
$418$	13.8992	+	18.9431i	0.679831	+	0.926539i
$419$	10.5928	−	4.75596i	0.517493	−	0.232344i	−0.134024	−	0.990978i	$-0.542790\pi$
$419$	10.5928	−	4.75596i	0.517493	−	0.232344i	0.651517	+	0.758634i	$0.274133\pi$
$420$	1.21433	−	0.230465i	0.0592530	−	0.0112455i
$421$	−28.4398	+	16.1247i	−1.38607	+	0.785869i	−0.991137	−	0.132841i	$-0.957590\pi$
$421$	−28.4398	+	16.1247i	−1.38607	+	0.785869i	−0.394931	+	0.918711i	$0.629232\pi$
$422$	−17.4708	+	18.7449i	−0.850466	+	0.912490i
$423$	−13.5673	−	28.4159i	−0.659667	−	1.38163i
$424$	0.878346	−	0.369869i	0.0426563	−	0.0179624i
$425$	−8.53145	+	6.25979i	−0.413836	+	0.303645i
$426$	0.821106	−	1.06577i	0.0397827	−	0.0516367i
$427$	−8.22352	−	6.64864i	−0.397964	−	0.321750i
$428$	9.43684	+	2.96867i	0.456147	+	0.143496i
$429$	6.27083	+	6.72816i	0.302759	+	0.324838i
$430$	−0.679243	+	1.72502i	−0.0327560	+	0.0831877i
$431$	0.0512928	+	0.545350i	0.00247069	+	0.0262686i	0.996755	−	0.0804990i	$-0.0256514\pi$
$431$	0.0512928	+	0.545350i	0.00247069	+	0.0262686i	−0.994284	+	0.106768i	$0.965950\pi$
$432$	−2.32982	−	2.27583i	−0.112093	−	0.109496i
$433$	−8.97606	−	13.5192i	−0.431362	−	0.649692i	0.551470	−	0.834195i	$-0.314067\pi$
$433$	−8.97606	−	13.5192i	−0.431362	−	0.649692i	−0.982832	+	0.184502i	$0.940933\pi$
$434$	−4.83236	+	0.800251i	−0.231961	+	0.0384133i
$435$	4.79371	−	0.450871i	0.229841	−	0.0216176i
$436$	11.2545	−	4.12955i	0.538995	−	0.197770i
$437$	5.59565	−	29.4836i	0.267676	−	1.41039i
$438$	3.37766	+	0.158493i	0.161391	+	0.00757309i
$439$	1.85388	+	7.02851i	0.0884809	+	0.335453i	0.996512	−	0.0834501i	$-0.0265939\pi$
$439$	1.85388	+	7.02851i	0.0884809	+	0.335453i	−0.908031	+	0.418903i	$0.862415\pi$
$440$	−2.34825	+	2.76911i	−0.111949	+	0.132012i
$441$	2.05749	+	1.91764i	0.0979758	+	0.0913162i
$442$	6.48175	−	7.28985i	0.308305	−	0.346743i
$443$	0.0924829	−	0.320008i	0.00439400	−	0.0152040i	−0.958458	−	0.285233i	$-0.907929\pi$
$443$	0.0924829	−	0.320008i	0.00439400	−	0.0152040i	0.962852	+	0.270029i	$0.0870334\pi$
$444$	−1.31853	+	0.707258i	−0.0625749	+	0.0335650i
$445$	7.03045	+	13.1068i	0.333275	+	0.621322i
$446$	−8.34156	+	6.42663i	−0.394984	+	0.304310i
$447$	7.55063	−	0.889189i	0.357133	−	0.0420572i
$448$	1.20274	+	2.12133i	0.0568243	+	0.100223i
$449$	12.7673	+	6.46758i	0.602524	+	0.305224i	0.726613	−	0.687047i	$-0.241093\pi$
$449$	12.7673	+	6.46758i	0.602524	+	0.305224i	−0.124089	+	0.992271i	$0.539601\pi$
$450$	−1.05546	+	11.2218i	−0.0497549	+	0.529000i
$451$	−30.9552	+	26.2505i	−1.45762	+	1.23609i
$452$	−4.16678	−	17.4460i	−0.195989	−	0.820589i
$453$	−3.18453	+	9.35130i	−0.149622	+	0.439363i
$454$	1.83842	−	1.88203i	0.0862812	−	0.0883281i
$455$	7.37916	+	3.95816i	0.345941	+	0.185561i
$456$			3.27997i			0.153599i
$457$	−7.29217	+	13.5947i	−0.341113	+	0.635935i	−0.992422	−	0.122878i	$-0.960788\pi$
$457$	−7.29217	+	13.5947i	−0.341113	+	0.635935i	0.651308	+	0.758813i	$0.274220\pi$
$458$	2.42289	+	14.6308i	0.113214	+	0.683650i
$459$	−2.44990	−	7.78777i	−0.114351	−	0.363502i
$460$	4.63234	−	0.217367i	0.215984	−	0.0101348i
$461$	3.16226	−	22.3318i	0.147281	−	1.04009i	−0.768911	−	0.639356i	$-0.779201\pi$
$461$	3.16226	−	22.3318i	0.147281	−	1.04009i	0.916192	−	0.400739i	$-0.131247\pi$
$462$	−5.74919	−	0.405032i	−0.267476	−	0.0188438i
$463$	18.2581	+	3.02359i	0.848527	+	0.140518i	0.571762	−	0.820419i	$-0.306260\pi$
$463$	18.2581	+	3.02359i	0.848527	+	0.140518i	0.276765	+	0.960938i	$0.410738\pi$
$464$	3.89090	+	8.66610i	0.180631	+	0.402313i
$465$	0.119070	−	1.01110i	0.00552175	−	0.0468885i
$466$	−17.5971	+	15.6464i	−0.815168	+	0.724804i
$467$	15.8700	+	14.1108i	0.734377	+	0.652969i	0.945920	−	0.324400i	$-0.105162\pi$
$467$	15.8700	+	14.1108i	0.734377	+	0.652969i	−0.211543	+	0.977369i	$0.567849\pi$
$468$	−1.21523	−	10.3192i	−0.0561739	−	0.477006i
$469$	−24.7969	+	14.8380i	−1.14501	+	0.685155i
$470$	−10.3350	−	1.21708i	−0.476717	−	0.0561398i
$471$	−3.26846	−	7.76177i	−0.150603	−	0.357644i
$472$	−3.06838	+	14.3255i	−0.141234	+	0.659383i
$473$	5.11403	−	6.96990i	0.235143	−	0.320476i
$474$	−0.184898	+	0.0728055i	−0.00849266	+	0.00334407i
$475$	18.7449	−	15.1551i	0.860075	−	0.695362i
$476$	0.143298	+	6.11104i	0.00656804	+	0.280099i
$477$	1.86152	−	1.73499i	0.0852331	−	0.0794397i
$478$	0.584966	+	12.4663i	0.0267557	+	0.570195i
$479$	−3.98967	−	1.68004i	−0.182293	−	0.0767630i	0.295043	−	0.955484i	$-0.404666\pi$
$479$	−3.98967	−	1.68004i	−0.182293	−	0.0767630i	−0.477336	+	0.878721i	$0.658397\pi$
$480$	−0.492989	+	0.117745i	−0.0225018	+	0.00537431i
$481$	−9.95904	−	1.89011i	−0.454093	−	0.0861817i
$482$	0.662963	−	0.225768i	0.0301971	−	0.0102835i
$483$	4.62825	+	5.72456i	0.210593	+	0.260476i
$484$	4.86201	−	3.39499i	0.221001	−	0.154318i
$485$	−0.758501	−	3.54124i	−0.0344418	−	0.160800i
$486$	−12.1306	−	5.44641i	−0.550257	−	0.247054i
$487$	6.14388	+	1.46740i	0.278406	+	0.0664943i	0.369117	−	0.929383i	$-0.379660\pi$
$487$	6.14388	+	1.46740i	0.278406	+	0.0664943i	−0.0907109	+	0.995877i	$0.528914\pi$
$488$	3.49636	+	2.56539i	0.158273	+	0.116130i
$489$	7.44500	−	2.15162i	0.336675	−	0.0972996i
$490$	0.898763	−	0.237063i	0.0406020	−	0.0107094i
$491$	−34.3443	−	3.23025i	−1.54994	−	0.145779i	−0.716182	−	0.697913i	$-0.754112\pi$
$491$	−34.3443	−	3.23025i	−1.54994	−	0.145779i	−0.833755	+	0.552134i	$0.813814\pi$
$492$	−5.65199	+	0.398185i	−0.254811	+	0.0179516i
$493$	−1.67343	+	23.7533i	−0.0753675	+	1.06980i
$494$	−13.9708	+	17.2801i	−0.628576	+	0.777469i
$495$	−3.33936	+	9.10098i	−0.150093	+	0.409059i
$496$	1.96408	−	0.420687i	0.0881897	−	0.0188894i
$497$	−3.15932	+	4.75839i	−0.141715	+	0.213443i
$498$	−3.29490	+	7.33863i	−0.147648	+	0.328852i
$499$	−5.95122	−	3.56110i	−0.266413	−	0.159417i	0.374043	−	0.927411i	$-0.377971\pi$
$499$	−5.95122	−	3.56110i	−0.266413	−	0.159417i	−0.640456	+	0.767995i	$0.721255\pi$
$500$	6.44578	+	4.96606i	0.288264	+	0.222089i
$501$	−1.18855	+	7.17711i	−0.0531003	+	0.320649i
$502$	26.5266	−	3.75627i	1.18394	−	0.167650i
$503$	−4.51904	+	8.92076i	−0.201494	+	0.397757i	−0.970364	−	0.241648i	$-0.922312\pi$
$503$	−4.51904	+	8.92076i	−0.201494	+	0.397757i	0.768870	+	0.639405i	$0.220819\pi$
$504$	4.96594	+	4.21120i	0.221201	+	0.187582i
$505$	7.94720	−	7.76303i	0.353646	−	0.345450i
$506$	−21.1446	−	4.52898i	−0.939994	−	0.201338i
$507$	−0.656879	+	1.04154i	−0.0291730	+	0.0462564i
$508$	−0.856903	+	1.43203i	−0.0380189	+	0.0635362i
$509$	31.8688	+	11.6934i	1.41256	+	0.518301i	0.933213	−	0.359323i	$-0.116992\pi$
$509$	31.8688	+	11.6934i	1.41256	+	0.518301i	0.479348	+	0.877625i	$0.340873\pi$
$510$	−1.22851	−	0.324038i	−0.0543992	−	0.0143486i
$511$	−14.3513	+	0.336525i	−0.634865	+	0.0148870i
$512$	−0.533449	−	0.845832i	−0.0235753	−	0.0373808i
$513$	6.40627	+	17.4594i	0.282844	+	0.770853i
$514$	10.4249	+	3.55013i	0.459821	+	0.156589i
$515$	−7.77991	−	4.41103i	−0.342824	−	0.194373i
$516$	1.15121	−	0.362150i	0.0506790	−	0.0159428i
$517$	45.1505	+	17.7785i	1.98572	+	0.781896i
$518$	5.37284	−	3.38854i	0.236069	−	0.148884i
$519$	0.657221	+	1.92991i	0.0288488	+	0.0847138i
$520$	−3.09878	−	1.47953i	−0.135890	−	0.0648815i
$521$	6.43098	+	22.2524i	0.281746	+	0.974893i	0.968709	+	0.248200i	$0.0798392\pi$
$521$	6.43098	+	22.2524i	0.281746	+	0.974893i	−0.686962	+	0.726693i	$0.741056\pi$
$522$	17.7237	+	18.1442i	0.775747	+	0.794151i
$523$	25.3980	−	12.1264i	1.11058	−	0.530250i	0.215652	−	0.976470i	$-0.430812\pi$
$523$	25.3980	−	12.1264i	1.11058	−	0.530250i	0.894923	+	0.446220i	$0.147230\pi$
$524$	0.246160	+	0.276850i	0.0107535	+	0.0120942i
$525$	−0.138615	+	5.91135i	−0.00604967	+	0.257992i
$526$	−5.29415	−	6.87163i	−0.230836	−	0.299617i
$527$	4.83704	+	1.39791i	0.210705	+	0.0608941i
$528$	2.36280	+	0.0554054i	0.102828	+	0.00241121i
$529$	2.37225	+	3.96445i	0.103141	+	0.172367i
$530$	−0.156807	−	0.826220i	−0.00681126	−	0.0358887i
$531$	5.48445	+	38.7310i	0.238005	+	1.68078i
$532$	−0.978579	−	13.8903i	−0.0424268	−	0.602222i
$533$	−31.4728	−	21.9765i	−1.36324	−	0.951907i
$534$	3.75746	−	8.92301i	0.162601	−	0.386137i
$535$	4.30549	−	7.59376i	0.186142	−	0.328307i
$536$	9.87223	−	6.55465i	0.426415	−	0.283118i
$537$	−9.31112			−0.401804
$538$	0.930530	+	16.3748i	0.0401180	+	0.705968i
$539$	−4.33424			−0.186689
$540$	−2.39423	+	1.58964i	−0.103031	+	0.0684073i
$541$	−4.16767	+	7.35069i	−0.179182	+	0.316031i	−0.945026	−	0.326996i	$-0.893964\pi$
$541$	−4.16767	+	7.35069i	−0.179182	+	0.316031i	0.765843	+	0.643027i	$0.222322\pi$
$542$	4.49950	−	10.6852i	0.193270	−	0.458968i
$543$	−3.42108	−	2.38883i	−0.146813	−	0.102515i
$544$	−0.176160	−	2.50048i	−0.00755280	−	0.107207i
$545$	−1.48315	−	10.4739i	−0.0635311	−	0.448655i
$546$	−1.01638	−	5.35532i	−0.0434970	−	0.229187i
$547$	−13.6034	−	22.7336i	−0.581637	−	0.972018i	−0.998024	−	0.0628301i	$-0.979987\pi$
$547$	−13.6034	−	22.7336i	−0.581637	−	0.972018i	0.416387	−	0.909188i	$-0.363296\pi$
$548$	15.6282	+	0.366467i	0.667606	+	0.0156547i
$549$	11.1236	+	3.21476i	0.474746	+	0.137202i
$550$	−10.6007	−	13.7593i	−0.452013	−	0.586698i
$551$	1.27162	−	54.2292i	0.0541729	−	2.31024i
$552$	−2.00588	−	2.25597i	−0.0853761	−	0.0960203i
$553$	0.761303	−	0.363488i	0.0323739	−	0.0154571i
$554$	8.21790	+	8.41286i	0.349145	+	0.357428i
$555$	0.366565	+	1.26838i	0.0155598	+	0.0538398i
$556$	12.1314	+	5.79218i	0.514484	+	0.245643i
$557$	−4.59383	−	13.4897i	−0.194647	−	0.571576i	0.805121	−	0.593110i	$-0.202100\pi$
$557$	−4.59383	−	13.4897i	−0.194647	−	0.571576i	−0.999768	+	0.0215342i	$0.993145\pi$
$558$	4.53633	−	2.86097i	0.192038	−	0.121115i
$559$	7.60753	+	2.99554i	0.321764	+	0.126698i
$560$	2.05263	−	0.645721i	0.0867393	−	0.0272867i
$561$	5.15369	+	2.92202i	0.217589	+	0.123368i
$562$	1.26670	+	0.431367i	0.0534324	+	0.0181961i
$563$	−7.08954	−	19.3216i	−0.298788	−	0.814308i	−0.995307	−	0.0967692i	$-0.969149\pi$
$563$	−7.08954	−	19.3216i	−0.298788	−	0.814308i	0.696518	−	0.717539i	$-0.254731\pi$
$564$	3.61364	+	5.72975i	0.152162	+	0.241266i
$565$	−15.8230	+	0.371033i	−0.665678	+	0.0156095i
$566$	22.5284	+	5.94221i	0.946938	+	0.249770i
$567$	14.0551	+	5.15713i	0.590258	+	0.216579i
$568$	1.20268	−	2.00989i	0.0504633	−	0.0843329i
$569$	7.70692	−	12.2200i	0.323091	−	0.512290i	−0.644570	−	0.764546i	$-0.722963\pi$
$569$	7.70692	−	12.2200i	0.323091	−	0.512290i	0.967661	+	0.252256i	$0.0811724\pi$
$570$	2.83006	+	0.606173i	0.118538	+	0.0253898i
$571$	−12.4117	+	12.1240i	−0.519413	+	0.507376i	−0.910799	−	0.412851i	$-0.864533\pi$
$571$	−12.4117	+	12.1240i	−0.519413	+	0.507376i	0.391386	+	0.920227i	$0.371996\pi$
$572$	12.2121	+	10.3561i	0.510614	+	0.433009i
$573$	0.580222	−	1.14538i	0.0242391	−	0.0478490i
$574$	23.8168	−	3.37254i	0.994093	−	0.140767i
$575$	−3.62457	+	21.8872i	−0.151155	+	0.912759i
$576$	−2.11512	−	1.62956i	−0.0881300	−	0.0678985i
$577$	−22.1900	−	13.2781i	−0.923784	−	0.552775i	−0.0291497	−	0.999575i	$-0.509280\pi$
$577$	−22.1900	−	13.2781i	−0.923784	−	0.552775i	−0.894634	+	0.446800i	$0.852564\pi$
$578$	−4.38940	+	9.77638i	−0.182575	+	0.406644i
$579$	−4.18306	+	6.30029i	−0.173842	+	0.261831i
$580$	8.19646	−	1.75560i	0.340339	−	0.0728975i
$581$	11.7640	−	32.0613i	0.488055	−	1.33013i
$582$	−1.48218	+	1.83326i	−0.0614382	+	0.0759912i
$583$	−0.275582	+	3.91172i	−0.0114134	+	0.162007i
$584$	5.87221	−	0.413699i	0.242994	−	0.0171190i
$585$	−9.12833	−	0.858563i	−0.377410	−	0.0354972i
$586$	23.1033	−	6.09386i	0.954389	−	0.251735i
$587$	−3.80761	+	1.10041i	−0.157157	+	0.0454186i	−0.355288	−	0.934757i	$-0.615617\pi$
$587$	−3.80761	+	1.10041i	−0.157157	+	0.0454186i	0.198131	+	0.980175i	$0.436513\pi$
$588$	−0.487835	−	0.357939i	−0.0201180	−	0.0147612i
$589$	−11.1559	−	2.66447i	−0.459671	−	0.109788i
$590$	11.7934	+	5.29499i	0.485526	+	0.217991i
$591$	−3.13085	−	14.6171i	−0.128786	−	0.601269i
$592$	−2.13572	+	1.49131i	−0.0877777	+	0.0612924i
$593$	−12.7696	−	15.7944i	−0.524386	−	0.648598i	0.444596	−	0.895731i	$-0.353347\pi$
$593$	−12.7696	−	15.7944i	−0.524386	−	0.648598i	−0.968982	+	0.247133i	$0.920512\pi$
$594$	12.6855	−	4.31997i	0.520493	−	0.177251i
$595$	5.29927	+	1.00574i	0.217249	+	0.0412314i
$596$	12.8739	−	3.07479i	0.527335	−	0.125948i
$597$	−10.9953	−	4.63009i	−0.450008	−	0.189497i
$598$	−0.958616	−	20.4292i	−0.0392007	−	0.835411i
$599$	27.1773	−	25.3300i	1.11043	−	1.03496i	0.111282	−	0.993789i	$-0.464504\pi$
$599$	27.1773	−	25.3300i	1.11043	−	1.03496i	0.999152	−	0.0411674i	$-0.0131077\pi$
$600$	−0.0568429	−	2.42411i	−0.00232060	−	0.0989637i
$601$	−2.67668	+	2.16407i	−0.109184	+	0.0882743i	−0.681754	−	0.731582i	$-0.738782\pi$
$601$	−2.67668	+	2.16407i	−0.109184	+	0.0882743i	0.572570	+	0.819856i	$0.305947\pi$
$602$	−4.76719	+	1.87713i	−0.194296	+	0.0765060i
$603$	18.7176	−	25.5102i	0.762239	−	1.03885i
$604$	−3.60198	+	16.8167i	−0.146562	+	0.684261i
$605$	−2.03075	−	4.82252i	−0.0825618	−	0.196063i
$606$	−7.18221	−	0.845802i	−0.291757	−	0.0343584i
$607$	−25.7712	+	15.4210i	−1.04602	+	0.625920i	−0.930088	−	0.367337i	$-0.880269\pi$
$607$	−25.7712	+	15.4210i	−1.04602	+	0.625920i	−0.115933	+	0.993257i	$0.536986\pi$
$608$	0.667840	+	5.67103i	0.0270845	+	0.229991i
$609$	9.94389	+	8.84157i	0.402947	+	0.358279i
$610$	2.85966	−	2.54266i	0.115784	−	0.102949i
$611$	−5.36748	+	45.5785i	−0.217145	+	1.84391i
$612$	−2.74138	−	6.10581i	−0.110814	−	0.246813i
$613$	25.7145	+	4.25838i	1.03860	+	0.171994i	0.658211	−	0.752834i	$-0.271314\pi$
$613$	25.7145	+	4.25838i	1.03860	+	0.171994i	0.380386	+	0.924828i	$0.375791\pi$
$614$	−5.24591	−	0.369576i	−0.211708	−	0.0149149i
$615$	−0.700980	+	4.95030i	−0.0282663	+	0.199615i
$616$	−10.0227	+	0.470305i	−0.403828	+	0.0189491i
$617$	3.42526	+	10.8883i	0.137896	+	0.438345i	0.997340	−	0.0728841i	$-0.0232203\pi$
$617$	3.42526	+	10.8883i	0.137896	+	0.438345i	−0.859445	+	0.511229i	$0.829190\pi$
$618$	0.951142	+	5.74353i	0.0382606	+	0.231039i
$619$	4.51863	−	8.42406i	0.181619	−	0.338591i	−0.774005	−	0.633179i	$-0.781750\pi$
$619$	4.51863	−	8.42406i	0.181619	−	0.338591i	0.955624	+	0.294588i	$0.0951824\pi$
$620$		−	1.77242i		−	0.0711819i
$621$	−15.0836	−	8.09081i	−0.605286	−	0.324673i
$622$	7.60518	−	7.78560i	0.304940	−	0.312174i
$623$	−13.2502	+	38.9090i	−0.530860	+	1.55886i
$624$	0.519271	+	2.17414i	0.0207875	+	0.0870353i
$625$	−10.6218	+	9.00743i	−0.424870	+	0.360297i
$626$	−1.26767	+	13.4780i	−0.0506661	+	0.538687i
$627$	−12.0392	−	6.09876i	−0.480799	−	0.243561i
$628$	−7.23151	−	12.7545i	−0.288569	−	0.508960i
$629$	−6.48475	+	0.763667i	−0.258564	+	0.0304494i
$630$	4.55131	−	3.50649i	0.181329	−	0.139702i
$631$	−8.20539	−	15.2973i	−0.326652	−	0.608974i	0.663628	−	0.748062i	$-0.269016\pi$
$631$	−8.20539	−	15.2973i	−0.326652	−	0.608974i	−0.990280	+	0.139088i	$0.955583\pi$
$632$	−0.304862	+	0.163527i	−0.0121268	+	0.00650476i
$633$	4.08650	−	14.1400i	0.162424	−	0.562015i
$634$	−19.1009	+	21.4822i	−0.758592	+	0.853168i
$635$	1.07724	+	1.00402i	0.0427489	+	0.0398432i
$636$	−0.354064	+	0.417519i	−0.0140395	+	0.0165557i
$637$	−1.04548	−	3.96365i	−0.0414232	−	0.157046i
$638$	−39.0437	−	1.83208i	−1.54576	−	0.0725328i
$639$	1.16611	−	6.14424i	0.0461304	−	0.243062i
$640$	−0.828397	+	0.303958i	−0.0327453	+	0.0120150i
$641$	27.5835	−	2.59436i	1.08948	−	0.102471i	0.466359	−	0.884596i	$-0.345566\pi$
$641$	27.5835	−	2.59436i	1.08948	−	0.102471i	0.623122	+	0.782125i	$0.285864\pi$
$642$	−5.60610	+	0.928384i	−0.221255	+	0.0366404i
$643$	18.6147	+	28.0364i	0.734093	+	1.10565i	0.990289	+	0.139023i	$0.0443963\pi$
$643$	18.6147	+	28.0364i	0.734093	+	1.10565i	−0.256196	+	0.966625i	$0.582469\pi$
$644$	9.16777	+	8.95532i	0.361261	+	0.352889i
$645$	−0.0997193	−	1.06023i	−0.00392644	−	0.0417463i
$646$	−5.24425	+	13.3184i	−0.206332	+	0.524005i
$647$	−9.89986	−	10.6218i	−0.389204	−	0.417588i	0.506500	−	0.862240i	$-0.330939\pi$
$647$	−9.89986	−	10.6218i	−0.389204	−	0.417588i	−0.895703	+	0.444652i	$0.853327\pi$
$648$	−5.85645	−	1.84234i	−0.230063	−	0.0723739i
$649$	−46.8765	−	37.8992i	−1.84006	−	1.48768i
$650$	10.0258	−	13.0132i	0.393246	−	0.510420i
$651$	2.26842	−	1.66441i	0.0889063	−	0.0652333i
$652$	12.4342	−	5.23601i	0.486961	−	0.205058i
$653$	2.60729	+	5.46081i	0.102031	+	0.213698i	0.947085	−	0.320984i	$-0.104014\pi$
$653$	2.60729	+	5.46081i	0.102031	+	0.213698i	−0.845053	+	0.534682i	$0.820431\pi$
$654$	−4.69499	+	5.03739i	−0.183589	+	0.196978i
$655$	0.284367	−	0.161230i	0.0111112	−	0.00629977i
$656$	−9.69114	+	1.83927i	−0.378375	+	0.0718113i
$657$	14.3391	−	6.43794i	0.559420	−	0.251168i
$658$	−17.0128	−	23.1867i	−0.663229	−	0.903913i
$659$	−37.5275	−	23.6678i	−1.46186	−	0.921967i	−0.999375	−	0.0353415i	$-0.988748\pi$
$659$	−37.5275	−	23.6678i	−1.46186	−	0.921967i	−0.462487	−	0.886626i	$-0.653043\pi$
$660$	0.484475	−	2.02846i	0.0188582	−	0.0789576i
$661$	5.54354	+	10.9432i	0.215619	+	0.425640i	0.974120	−	0.226032i	$-0.0725754\pi$
$661$	5.54354	+	10.9432i	0.215619	+	0.425640i	−0.758501	+	0.651672i	$0.774068\pi$
$662$	−19.9369	−	28.5520i	−0.774871	−	1.10970i
$663$	−1.42905	+	5.41787i	−0.0554996	+	0.210413i
$664$	−4.20260	+	13.3593i	−0.163092	+	0.518440i
$665$	−12.1659	−	1.72273i	−0.471772	−	0.0668046i
$666$	−3.98188	+	5.70251i	−0.154295	+	0.220968i
$667$	32.2896	+	38.0765i	1.25026	+	1.47433i
$668$	−0.593639	+	12.6511i	−0.0229686	+	0.489487i
$669$	2.60610	−	5.45831i	0.100758	−	0.211030i
$670$	−3.83106	−	9.72943i	−0.148007	−	0.375881i
$671$	−15.9174	+	8.06337i	−0.614484	+	0.311283i
$672$	−1.16694	−	0.774785i	−0.0450155	−	0.0298880i
$673$	−18.3720	−	12.1981i	−0.708190	−	0.470201i	0.146586	−	0.989198i	$-0.453171\pi$
$673$	−18.3720	−	12.1981i	−0.708190	−	0.470201i	−0.854776	+	0.518997i	$0.826306\pi$
$674$	13.3637	−	6.76971i	0.514749	−	0.260760i
$675$	−5.03721	−	12.7926i	−0.193882	−	0.492387i
$676$	−0.923664	+	1.93456i	−0.0355256	+	0.0744060i
$677$	−0.902908	+	19.2420i	−0.0347016	+	0.739530i	0.910592	+	0.413307i	$0.135627\pi$
$677$	−0.902908	+	19.2420i	−0.0347016	+	0.739530i	−0.945293	+	0.326222i	$0.894224\pi$
$678$	6.66360	+	7.85786i	0.255914	+	0.301779i
$679$	5.72991	−	8.20588i	0.219894	−	0.314913i
$680$	−2.19005	−	0.310119i	−0.0839846	−	0.0118925i
$681$	−0.453494	+	1.44157i	−0.0173779	+	0.0552412i
$682$	−2.10786	+	7.99140i	−0.0807140	+	0.306007i
$683$	−7.21171	−	10.3280i	−0.275948	−	0.395190i	0.657758	−	0.753229i	$-0.271505\pi$
$683$	−7.21171	−	10.3280i	−0.275948	−	0.395190i	−0.933706	+	0.358040i	$0.883445\pi$
$684$	6.88995	+	13.6010i	0.263444	+	0.520048i
$685$	3.20446	−	13.4168i	0.122436	−	0.512630i
$686$	16.6111	+	10.4763i	0.634213	+	0.399986i
$687$	−5.03926	−	6.86800i	−0.192260	−	0.262030i
$688$	1.91668	−	0.860551i	0.0730728	−	0.0328082i
$689$	−3.64373	+	0.691538i	−0.138815	+	0.0263455i
$690$	−2.31723	+	1.31381i	−0.0882153	+	0.0500160i
$691$	19.4071	−	20.8224i	0.738280	−	0.792121i	−0.245900	−	0.969295i	$-0.579084\pi$
$691$	19.4071	−	20.8224i	0.738280	−	0.792121i	0.984180	+	0.177174i	$0.0566955\pi$
$692$	1.52928	+	3.20298i	0.0581344	+	0.121759i
$693$	−24.6909	+	10.3973i	−0.937930	+	0.394960i
$694$	−8.75918	+	6.42688i	−0.332494	+	0.243961i
$695$	7.23967	−	9.39686i	0.274616	−	0.356443i
$696$	−4.24322	−	3.43060i	−0.160839	−	0.130037i
$697$	−23.5867	−	7.41996i	−0.893409	−	0.281051i
$698$	−7.05475	−	7.56924i	−0.267026	−	0.286500i
$699$	4.95549	−	12.5851i	0.187434	−	0.476011i
$700$	0.963955	+	10.2489i	0.0364341	+	0.387371i
$701$	29.4096	+	28.7280i	1.11078	+	1.08504i	0.995789	+	0.0916769i	$0.0292227\pi$
$701$	29.4096	+	28.7280i	1.11078	+	1.08504i	0.114996	+	0.993366i	$0.463315\pi$
$702$	7.01052	+	10.5588i	0.264595	+	0.398518i
$703$	14.6745	−	2.43013i	0.553458	−	0.0916540i
$704$	4.09653	−	0.385298i	0.154394	−	0.0145215i
$705$	5.61164	−	2.05904i	0.211347	−	0.0775480i
$706$	3.34685	−	17.6346i	0.125960	−	0.663688i
$707$	30.6682	+	1.43907i	1.15340	+	0.0541218i
$708$	−2.14625	−	8.13696i	−0.0806610	−	0.305806i
$709$	−11.2113	+	13.2206i	−0.421048	+	0.496509i	−0.931675	−	0.363294i	$-0.881652\pi$
$709$	−11.2113	+	13.2206i	−0.421048	+	0.496509i	0.510627	+	0.859802i	$0.329413\pi$
$710$	−1.51192	−	1.40916i	−0.0567415	−	0.0528847i
$711$	−0.613779	+	0.690301i	−0.0230185	+	0.0258883i
$712$	4.67976	−	16.1928i	0.175381	−	0.606852i
$713$	9.30251	−	4.98984i	0.348382	−	0.186871i
$714$	−1.65969	−	3.09415i	−0.0621123	−	0.115796i
$715$	11.1925	−	8.62308i	0.418575	−	0.322485i
$716$	−16.0988	+	1.89585i	−0.601640	+	0.0708513i
$717$	−3.53566	−	6.23598i	−0.132042	−	0.232887i
$718$	13.8626	+	7.02247i	0.517349	+	0.262076i
$719$	2.64699	−	28.1431i	0.0987162	−	1.04956i	−0.796713	−	0.604357i	$-0.793430\pi$
$719$	2.64699	−	28.1431i	0.0987162	−	1.04956i	0.895430	−	0.445203i	$-0.146869\pi$
$720$	−1.79694	+	1.52383i	−0.0669678	+	0.0567898i
$721$	−5.74157	−	24.0394i	−0.213827	−	0.895276i
$722$	4.38627	−	12.8802i	0.163240	−	0.479351i
$723$	−0.281104	+	0.287773i	−0.0104544	+	0.0107024i
$724$	−6.40139	−	3.43369i	−0.237906	−	0.127612i
$725$			40.1009i			1.48931i
$726$	−1.61009	+	3.00167i	−0.0597559	+	0.111402i
$727$	1.43485	+	8.66440i	0.0532155	+	0.321345i	1.00000		0.000523793i	$-0.000166729\pi$
$727$	1.43485	+	8.66440i	0.0532155	+	0.321345i	−0.946784	+	0.321868i	$0.895689\pi$
$728$	−2.84771	−	9.05233i	−0.105543	−	0.335502i
$729$	−10.7684	+	0.505293i	−0.398828	+	0.0187146i
$730$	0.728292	−	5.14318i	0.0269553	−	0.190358i
$731$	5.25353	+	0.370113i	0.194309	+	0.0136891i
$732$	−2.45747	−	0.406963i	−0.0908306	−	0.0150418i
$733$	10.8877	+	24.2498i	0.402145	+	0.895686i	0.995851	+	0.0910037i	$0.0290075\pi$
$733$	10.8877	+	24.2498i	0.402145	+	0.895686i	−0.593706	+	0.804682i	$0.702336\pi$
$734$	−2.47565	+	21.0222i	−0.0913780	+	0.775945i
$735$	−0.398998	+	0.354768i	−0.0147173	+	0.0130858i
$736$	−3.92749	−	3.49211i	−0.144769	−	0.128721i
$737$	5.70256	+	48.4238i	0.210057	+	1.78371i
$738$	−22.6006	+	13.5238i	−0.831940	+	0.497818i
$739$	−4.01669	−	0.473020i	−0.147756	−	0.0174003i	0.0427531	−	0.999086i	$-0.486387\pi$
$739$	−4.01669	−	0.473020i	−0.147756	−	0.0174003i	−0.190509	+	0.981685i	$0.561014\pi$
$740$	0.892043	+	2.11838i	0.0327921	+	0.0778731i
$741$	2.67330	−	12.4809i	0.0982060	−	0.458498i
$742$	1.37485	−	1.87378i	0.0504725	−	0.0687888i
$743$	−16.6096	+	6.54019i	−0.609347	+	0.239936i	−0.650855	−	0.759202i	$-0.725590\pi$
$743$	−16.6096	+	6.54019i	−0.609347	+	0.239936i	0.0415086	+	0.999138i	$0.486784\pi$
$744$	−0.897210	+	0.725386i	−0.0328933	+	0.0265940i
$745$	−0.273796	−	11.6762i	−0.0100311	−	0.427784i
$746$	7.03152	−	6.55358i	0.257442	−	0.239944i
$747$	1.75271	+	37.3523i	0.0641285	+	1.36665i
$748$	9.50561	+	4.00279i	0.347560	+	0.146356i
$749$	23.4643	−	5.60419i	0.857365	−	0.204772i
$750$	−4.59193	−	0.871495i	−0.167674	−	0.0318225i
$751$	28.8018	−	9.80828i	1.05099	−	0.357909i	0.257366	−	0.966314i	$-0.417146\pi$
$751$	28.8018	−	9.80828i	1.05099	−	0.357909i	0.793627	+	0.608405i	$0.208190\pi$
$752$	7.41457	+	9.17088i	0.270382	+	0.334428i
$753$	−12.6174	+	8.81035i	−0.459805	+	0.321067i
$754$	−7.74243	−	36.1474i	−0.281963	−	1.31641i
$755$	13.8443	+	6.21579i	0.503845	+	0.226216i
$756$	−7.72492	−	1.84501i	−0.280953	−	0.0671025i
$757$	−40.8638	−	29.9830i	−1.48522	−	1.08975i	−0.972974	−	0.230913i	$-0.925829\pi$
$757$	−40.8638	−	29.9830i	−1.48522	−	1.08975i	−0.512245	−	0.858839i	$-0.671186\pi$
$758$	23.9703	−	6.92746i	0.870640	−	0.251617i
$759$	12.0103	−	3.16790i	0.435946	−	0.114987i
$760$	5.01656	+	0.471832i	0.181970	+	0.0171151i
$761$	−50.7274	+	3.57377i	−1.83887	+	0.129549i	−0.946692	−	0.322139i	$-0.895598\pi$
$761$	−50.7274	+	3.57377i	−1.83887	+	0.129549i	−0.892176	+	0.451688i	$0.850822\pi$
$762$	0.0673657	−	0.956215i	0.00244040	−	0.0346400i
$763$	18.3799	−	22.7336i	0.665397	−	0.823011i
$764$	0.769983	−	2.09849i	0.0278570	−	0.0759206i
$765$	−5.77492	+	1.23693i	−0.208793	+	0.0447214i
$766$	−9.15664	+	13.7912i	−0.330843	+	0.498296i
$767$	23.3516	−	52.0103i	0.843176	−	1.87798i
$768$	0.492899	+	0.294942i	0.0177860	+	0.0106428i
$769$	−36.3535	−	28.0080i	−1.31094	−	1.01000i	−0.998189	−	0.0601615i	$-0.980838\pi$
$769$	−36.3535	−	28.0080i	−1.31094	−	1.01000i	−0.312753	−	0.949835i	$-0.601251\pi$
$770$	−1.44651	+	8.73484i	−0.0521287	+	0.314782i
$771$	−6.26330	+	0.886906i	−0.225567	+	0.0319411i
$772$	−5.94964	+	11.7448i	−0.214132	+	0.422706i
$773$	11.5495	+	9.79414i	0.415405	+	0.352271i	0.830027	−	0.557723i	$-0.188325\pi$
$773$	11.5495	+	9.79414i	0.415405	+	0.352271i	−0.414622	+	0.909994i	$0.636086\pi$
$774$	4.01296	−	3.91996i	0.144243	−	0.140900i
$775$	8.29110	+	1.77588i	0.297825	+	0.0637914i
$776$	−2.18939	+	3.47148i	−0.0785945	+	0.124619i
$777$	−1.87351	+	3.13097i	−0.0672119	+	0.112323i
$778$	1.05525	+	0.387195i	0.0378325	+	0.0138816i
$779$	54.4636	+	14.3656i	1.95136	+	0.514702i
$780$	1.97188	−	0.0462387i	0.0706048	−	0.00165561i
$781$	5.14106	+	8.15162i	0.183962	+	0.291688i
$782$	−4.53794	−	12.3675i	−0.162276	−	0.442262i
$783$	−29.2873	−	9.97362i	−1.04664	−	0.356428i
$784$	−0.916340	−	0.519544i	−0.0327264	−	0.0185551i
$785$	−12.3414	+	3.88241i	−0.440485	+	0.138569i
$786$	−0.197997	−	0.0779634i	−0.00706232	−	0.00278086i
$787$	−12.9272	+	8.15292i	−0.460805	+	0.290620i	−0.743679	−	0.668537i	$-0.766921\pi$
$787$	−12.9272	+	8.15292i	−0.460805	+	0.290620i	0.282874	+	0.959157i	$0.408712\pi$
$788$	−8.38942	−	24.6353i	−0.298861	−	0.877598i
$789$	4.49646	+	2.14686i	0.160078	+	0.0764302i
$790$	0.0847546	+	0.293266i	0.00301543	+	0.0104339i
$791$	−30.5640	−	31.2891i	−1.08673	−	1.11251i
$792$	9.91418	−	4.73358i	0.352285	−	0.168200i
$793$	−11.2134	−	12.6114i	−0.398200	−	0.447845i
$794$	0.849860	−	36.2429i	0.0301604	−	1.28621i
$795$	0.294814	+	0.382659i	0.0104560	+	0.0135715i
$796$	−19.9535	−	5.76659i	−0.707232	−	0.204391i
$797$	−5.23600	−	0.122779i	−0.185469	−	0.00434905i	−0.0693928	−	0.997589i	$-0.522106\pi$
$797$	−5.23600	−	0.122779i	−0.185469	−	0.00434905i	−0.116076	+	0.993240i	$0.537032\pi$
$798$	4.10699	+	6.86350i	0.145386	+	0.242965i
$799$	5.51212	+	29.0435i	0.195005	+	1.02748i
$800$	−0.591856	−	4.17967i	−0.0209253	−	0.147774i
$801$	−3.16279	−	44.8939i	−0.111752	−	1.58625i
$802$	−13.8387	−	9.66310i	−0.488660	−	0.341216i
$803$	−9.40025	+	22.3232i	−0.331728	+	0.787770i
$804$	−3.35720	+	5.92122i	−0.118399	+	0.208825i
$805$	9.42122	−	6.25520i	0.332055	−	0.220467i
$806$	−7.81657			−0.275327
$807$	−4.72728	−	8.14904i	−0.166408	−	0.286860i
$808$	−12.5902			−0.442920
$809$	13.4095	−	8.90320i	0.471453	−	0.313020i	−0.294800	−	0.955559i	$-0.595253\pi$
$809$	13.4095	−	8.90320i	0.471453	−	0.313020i	0.766253	+	0.642539i	$0.222119\pi$
$810$	−2.67196	+	4.71264i	−0.0938831	+	0.165585i
$811$	−18.5530	+	44.0587i	−0.651484	+	1.54711i	0.175253	+	0.984523i	$0.443926\pi$
$811$	−18.5530	+	44.0587i	−0.651484	+	1.54711i	−0.826737	+	0.562588i	$0.809806\pi$
$812$	18.9931	+	13.2623i	0.666527	+	0.465414i
$813$	0.468010	+	6.64312i	0.0164138	+	0.232984i
$814$	−1.50272	−	10.6121i	−0.0526701	−	0.371955i
$815$	−2.21982	−	11.6963i	−0.0777569	−	0.409703i
$816$	0.739325	+	1.23554i	0.0258816	+	0.0432526i
$817$	−11.9939	−	0.281245i	−0.419613	−	0.00983951i
$818$	4.61874	+	1.33482i	0.161490	+	0.0466710i
$819$	−15.4641	−	20.0718i	−0.540358	−	0.701367i
$820$	−0.204047	+	8.70173i	−0.00712563	+	0.303878i
$821$	29.0428	+	32.6637i	1.01360	+	1.13997i	0.990117	+	0.140245i	$0.0447891\pi$
$821$	29.0428	+	32.6637i	1.01360	+	1.13997i	0.0234833	+	0.999724i	$0.492524\pi$
$822$	−8.10316	+	3.86890i	−0.282630	+	0.134943i
$823$	2.41690	+	2.47424i	0.0842478	+	0.0862465i	0.756170	−	0.654375i	$-0.227068\pi$
$823$	2.41690	+	2.47424i	0.0842478	+	0.0862465i	−0.671922	+	0.740622i	$0.734531\pi$
$824$	2.81396	+	9.73682i	0.0980289	+	0.339198i
$825$	9.00341	+	4.29872i	0.313458	+	0.149662i
$826$	11.5168	+	33.8188i	0.400720	+	1.17671i
$827$	24.6743	−	15.5616i	0.858010	−	0.541130i	−0.0307372	−	0.999527i	$-0.509786\pi$
$827$	24.6743	−	15.5616i	0.858010	−	0.541130i	0.888747	+	0.458398i	$0.151577\pi$
$828$	−13.0567	−	5.14120i	−0.453751	−	0.178669i
$829$	−25.0358	+	7.87582i	−0.869528	+	0.273539i	−0.701869	−	0.712306i	$-0.747651\pi$
$829$	−25.0358	+	7.87582i	−0.869528	+	0.273539i	−0.167659	+	0.985845i	$0.553621\pi$
$830$	10.7501	+	6.09506i	0.373142	+	0.211563i
$831$	−6.39467	−	2.17767i	−0.221829	−	0.0755425i
$832$	1.34049	+	3.65333i	0.0464732	+	0.126656i
$833$	−1.40856	−	2.23340i	−0.0488038	−	0.0773829i
$834$	−7.71970	+	0.181019i	−0.267311	+	0.00626819i
$835$	10.8061	+	2.85027i	0.373959	+	0.0986376i
$836$	−22.0574	−	8.09336i	−0.762870	−	0.279915i
$837$	−3.35910	+	5.61365i	−0.116108	+	0.194036i
$838$	−6.19415	+	9.82138i	−0.213973	+	0.339274i
$839$	4.39112	+	0.940537i	0.151598	+	0.0324710i	0.284609	−	0.958644i	$-0.408136\pi$
$839$	4.39112	+	0.940537i	0.151598	+	0.0324710i	−0.133011	+	0.991115i	$0.542465\pi$
$840$	−0.884170	+	0.863680i	−0.0305068	+	0.0297998i
$841$	46.7071	+	39.6084i	1.61059	+	1.36581i
$842$	14.7739	−	29.1643i	0.509143	−	1.00507i
$843$	−0.761038	+	0.107766i	−0.0262115	+	0.00371165i
$844$	4.18642	−	25.2800i	0.144103	−	0.870172i
$845$	1.49849	+	1.15449i	0.0515497	+	0.0397158i
$846$	27.0206	+	16.1686i	0.928988	+	0.555889i
$847$	5.92299	−	13.1921i	0.203516	−	0.453286i
$848$	−0.527159	+	0.793977i	−0.0181027	+	0.0272653i
$849$	−13.0862	+	2.80293i	−0.449116	+	0.0961964i
$850$	3.64502	−	9.93401i	0.125023	−	0.340734i
$851$	−8.60695	+	10.6457i	−0.295042	+	0.364930i
$852$	−0.0945490	+	1.34207i	−0.00323919	+	0.0459784i
$853$	11.5896	−	0.816490i	0.396820	−	0.0279561i	0.129538	−	0.991574i	$-0.458651\pi$
$853$	11.5896	−	0.816490i	0.396820	−	0.0279561i	0.267282	+	0.963618i	$0.413875\pi$
$854$	10.5285	+	0.990259i	0.360279	+	0.0338860i
$855$	13.0087	−	3.43125i	0.444889	−	0.117346i
$856$	−9.50384	+	2.74663i	−0.324835	+	0.0938779i
$857$	9.91735	+	7.27667i	0.338770	+	0.248566i	0.747755	−	0.663975i	$-0.231132\pi$
$857$	9.91735	+	7.27667i	0.338770	+	0.248566i	−0.408984	+	0.912541i	$0.634117\pi$
$858$	−8.94575	−	2.13660i	−0.305403	−	0.0729422i
$859$	5.98214	+	2.68586i	0.204108	+	0.0916403i	0.509073	−	0.860723i	$-0.329988\pi$
$859$	5.98214	+	2.68586i	0.204108	+	0.0916403i	−0.304965	+	0.952363i	$0.598645\pi$
$860$	−0.388287	−	1.81281i	−0.0132405	−	0.0618164i
$861$	−11.3285	+	7.91032i	−0.386074	+	0.269583i
$862$	−0.344382	−	0.425956i	−0.0117297	−	0.0145081i
$863$	−12.3616	+	4.20968i	−0.420794	+	0.143299i	−0.524698	−	0.851288i	$-0.675822\pi$
$863$	−12.3616	+	4.20968i	−0.420794	+	0.143299i	0.103904	+	0.994587i	$0.466867\pi$
$864$	3.19979	+	0.607283i	0.108859	+	0.0206602i
$865$	3.04625	−	0.727565i	0.103576	−	0.0247380i
$866$	14.9558	+	6.29785i	0.508219	+	0.214010i
$867$	−0.288528	−	6.14887i	−0.00979894	−	0.208826i
$868$	3.58317	−	3.33962i	0.121621	−	0.113354i
$869$	−0.0333694	−	1.42306i	−0.00113198	−	0.0482741i
$870$	−3.74422	+	3.02717i	−0.126941	+	0.102631i
$871$	−42.9080	+	16.8955i	−1.45388	+	0.572480i
$872$	−7.09191	+	9.66554i	−0.240162	+	0.327316i
$873$	−2.29515	+	10.7155i	−0.0776791	+	0.362663i
$874$	11.6466	+	27.6577i	0.393952	+	0.935537i
$875$	19.7063	+	2.32069i	0.666196	+	0.0784536i
$876$	−2.90158	+	1.73625i	−0.0980353	+	0.0586625i
$877$	−1.48003	−	12.5678i	−0.0499771	−	0.424385i	−0.995193	−	0.0979379i	$-0.968775\pi$
$877$	−1.48003	−	12.5678i	−0.0499771	−	0.424385i	0.945215	−	0.326447i	$-0.105852\pi$
$878$	−5.43215	−	4.82998i	−0.183326	−	0.163004i
$879$	−10.2565	+	9.11955i	−0.345944	+	0.307595i
$880$	0.424634	−	3.60582i	0.0143144	−	0.121552i
$881$	−20.1736	−	44.9321i	−0.679666	−	1.51380i	−0.849084	−	0.528258i	$-0.822845\pi$
$881$	−20.1736	−	44.9321i	−0.679666	−	1.51380i	0.169418	−	0.985544i	$-0.445811\pi$
$882$	−2.77479	−	0.459512i	−0.0934320	−	0.0154726i
$883$	11.0063	+	0.775400i	0.370393	+	0.0260943i	0.254251	−	0.967138i	$-0.418171\pi$
$883$	11.0063	+	0.775400i	0.370393	+	0.0260943i	0.116142	+	0.993233i	$0.462947\pi$
$884$	−1.36766	+	9.65839i	−0.0459995	+	0.324847i
$885$	−7.41747	+	0.348056i	−0.249335	+	0.0116998i
$886$	0.0999593	+	0.317752i	0.00335820	+	0.0106751i
$887$	−1.34360	−	8.11339i	−0.0451136	−	0.272421i	0.954559	−	0.298023i	$-0.0963273\pi$
$887$	−1.34360	−	8.11339i	−0.0451136	−	0.272421i	−0.999672	+	0.0256023i	$0.991850\pi$
$888$	0.707258	−	1.31853i	0.0237340	−	0.0442471i
$889$			4.06957i			0.136489i
$890$	−13.1068	−	7.03045i	−0.439341	−	0.235661i
$891$	17.6518	−	18.0705i	0.591357	−	0.605386i
$892$	3.39453	−	9.96797i	0.113657	−	0.333752i
$893$	−15.6439	−	65.4998i	−0.523504	−	2.19187i
$894$	−5.79855	+	4.91727i	−0.193932	+	0.164458i
$895$	−1.33943	+	14.2409i	−0.0447721	+	0.476021i
$896$	−2.17537	−	1.10199i	−0.0726740	−	0.0368149i
$897$	5.79408	+	10.2192i	0.193459	+	0.341211i
$898$	−14.2137	+	1.67386i	−0.474319	+	0.0558575i
$899$	15.1152	−	11.6453i	0.504120	−	0.388392i
$900$	−5.32782	−	9.93261i	−0.177594	−	0.331087i
$901$	−2.10524	+	1.12924i	−0.0701357	+	0.0376206i
$902$	11.2686	−	38.9914i	0.375203	−	1.29827i
$903$	1.95549	−	2.19929i	0.0650747	−	0.0731878i
$904$	13.1212	+	12.2293i	0.436405	+	0.406742i
$905$	−4.14573	+	4.88874i	−0.137809	+	0.162507i
$906$	−2.51948	−	9.55198i	−0.0837042	−	0.317343i
$907$	37.5172	+	1.76045i	1.24574	+	0.0584548i	0.659513	−	0.751693i	$-0.270763\pi$
$907$	37.5172	+	1.76045i	1.24574	+	0.0584548i	0.586225	+	0.810148i	$0.300613\pi$
$908$	−0.490564	+	2.58479i	−0.0162799	+	0.0857794i
$909$	−31.5591	+	11.5798i	−1.04675	+	0.384076i
$910$	−8.33692	+	0.784127i	−0.276366	+	0.0259936i
$911$	2.84079	−	0.470442i	0.0941196	−	0.0155864i	−0.116132	−	0.993234i	$-0.537049\pi$
$911$	2.84079	−	0.470442i	0.0941196	−	0.0155864i	0.210251	+	0.977647i	$0.432572\pi$
$912$	−1.81425	−	2.73253i	−0.0600760	−	0.0904830i
$913$	−41.2211	−	40.2658i	−1.36422	−	1.33260i
$914$	−1.44461	−	15.3592i	−0.0477834	−	0.508038i
$915$	−0.805306	+	2.04517i	−0.0266226	+	0.0676112i
$916$	−10.1112	−	10.8486i	−0.334084	−	0.358449i
$917$	0.861757	+	0.271094i	0.0284577	+	0.00895231i
$918$	6.34865	+	5.13283i	0.209537	+	0.169409i
$919$	−11.4807	+	14.9016i	−0.378713	+	0.491557i	−0.942426	−	0.334413i	$-0.891462\pi$
$919$	−11.4807	+	14.9016i	−0.378713	+	0.491557i	0.563713	+	0.825971i	$0.309372\pi$
$920$	−3.73894	+	2.74338i	−0.123269	+	0.0904465i
$921$	2.78398	−	1.17233i	0.0917352	−	0.0386294i
$922$	9.71794	+	20.3536i	0.320043	+	0.670311i
$923$	−6.21455	+	6.66777i	−0.204554	+	0.219472i
$924$	5.01365	−	2.84262i	0.164937	−	0.0935155i
$925$	−10.8032	+	2.05033i	−0.355208	+	0.0674145i
$926$	−16.8832	+	7.58021i	−0.554816	+	0.249101i
$927$	16.0090	+	21.8186i	0.525805	+	0.716618i
$928$	−8.03498	−	5.06750i	−0.263761	−	0.166349i
$929$	4.12251	−	17.2606i	0.135255	−	0.566302i	−0.862888	−	0.505395i	$-0.831347\pi$
$929$	4.12251	−	17.2606i	0.135255	−	0.566302i	0.998143	−	0.0609073i	$-0.0193994\pi$
$930$	0.460072	+	0.908200i	0.0150864	+	0.0297810i
$931$	3.44365	+	4.93170i	0.112861	+	0.161630i
$932$	6.00552	−	22.7684i	0.196717	−	0.745803i
$933$	−1.87602	+	5.96351i	−0.0614181	+	0.195236i
$934$	−21.0263	−	2.97740i	−0.688003	−	0.0974236i
$935$	5.21046	−	7.46198i	0.170400	−	0.244033i
$936$	6.72028	+	7.92470i	0.219659	+	0.259027i
$937$	−2.11448	+	45.0621i	−0.0690772	+	1.47211i	0.640757	+	0.767744i	$0.278621\pi$
$937$	−2.11448	+	45.0621i	−0.0690772	+	1.47211i	−0.709834	+	0.704369i	$0.751230\pi$
$938$	12.4508	−	26.0774i	0.406532	−	0.851456i
$939$	−2.84896	−	7.23526i	−0.0929722	−	0.236114i
$940$	9.28321	−	4.70265i	0.302785	−	0.153384i
$941$	10.9395	+	7.26327i	0.356618	+	0.236776i	0.718622	−	0.695401i	$-0.244773\pi$
$941$	10.9395	+	7.26327i	0.356618	+	0.236776i	−0.362004	+	0.932177i	$0.617907\pi$
$942$	7.01621	+	4.65840i	0.228601	+	0.151779i
$943$	−46.2454	+	23.4268i	−1.50596	+	0.762882i
$944$	−5.36761	−	13.6317i	−0.174701	−	0.443674i
$945$	−3.01958	+	6.32432i	−0.0982270	+	0.205730i
$946$	−0.405202	+	8.63531i	−0.0131743	+	0.280758i
$947$	2.50424	+	2.95305i	0.0813768	+	0.0959613i	0.801863	−	0.597508i	$-0.203842\pi$
$947$	2.50424	+	2.95305i	0.0813768	+	0.0959613i	−0.720486	+	0.693469i	$0.756081\pi$
$948$	0.113767	−	0.162927i	0.00369497	−	0.00529162i
$949$	−22.6820	−	3.21186i	−0.736290	−	0.104261i
$950$	−7.23352	+	22.9940i	−0.234686	+	0.746023i
$951$	4.21121	−	15.9657i	0.136558	−	0.517725i
$952$	−3.49959	−	5.01181i	−0.113422	−	0.162434i
$953$	−24.3485	−	48.0648i	−0.788724	−	1.55697i	−0.829961	−	0.557822i	$-0.811637\pi$
$953$	−24.3485	−	48.0648i	−0.788724	−	1.55697i	0.0412368	−	0.999149i	$-0.486870\pi$
$954$	−0.591145	+	2.47507i	−0.0191390	+	0.0801335i
$955$	−1.66834	−	1.05219i	−0.0539862	−	0.0340480i
$956$	−7.38282	−	10.0620i	−0.238778	−	0.325429i
$957$	20.4819	−	9.19595i	0.662085	−	0.297263i
$958$	4.25305	−	0.807181i	0.137410	−	0.0260788i
$959$	33.1617	−	18.8019i	1.07085	−	0.607146i
$960$	0.345578	−	0.370780i	0.0111535	−	0.0119669i
$961$	11.6184	+	24.3341i	0.374788	+	0.784969i
$962$	9.34230	−	3.93402i	0.301208	−	0.126838i
$963$	−21.2966	+	15.6260i	−0.686273	+	0.503540i
$964$	−0.427431	+	0.554791i	−0.0137666	+	0.0178686i
$965$	9.03424	+	7.30410i	0.290823	+	0.235127i
$966$	−7.02220	−	2.20907i	−0.225936	−	0.0710755i
$967$	19.1015	+	20.4946i	0.614263	+	0.659060i	0.960238	−	0.279183i	$-0.0900637\pi$
$967$	19.1015	+	20.4946i	0.614263	+	0.659060i	−0.345975	+	0.938244i	$0.612452\pi$
$968$	−2.17264	+	5.51768i	−0.0698313	+	0.177345i
$969$	−0.769906	−	8.18572i	−0.0247329	−	0.262963i
$970$	2.59067	+	2.53064i	0.0831816	+	0.0812539i
$971$	−11.8819	−	17.8959i	−0.381309	−	0.574305i	0.591387	−	0.806388i	$-0.298580\pi$
$971$	−11.8819	−	17.8959i	−0.381309	−	0.574305i	−0.972696	+	0.232082i	$0.925446\pi$
$972$	13.1186	−	2.17246i	0.420778	−	0.0696818i
$973$	32.6381	−	3.06977i	1.04633	−	0.0984123i
$974$	−5.93010	+	2.17589i	−0.190013	+	0.0697200i
$975$	−1.75944	+	9.27051i	−0.0563470	+	0.296894i
$976$	−4.33179	−	0.203264i	−0.138657	−	0.00650633i
$977$	−8.57019	−	32.4917i	−0.274185	−	1.03950i	−0.952453	−	0.304687i	$-0.901448\pi$
$977$	−8.57019	−	32.4917i	−0.274185	−	1.03950i	0.678268	−	0.734815i	$-0.262731\pi$
$978$	−5.01226	+	5.91056i	−0.160274	+	0.188999i
$979$	50.7345	+	47.2860i	1.62148	+	1.51127i
$980$	−0.617627	+	0.694629i	−0.0197294	+	0.0221891i
$981$	−8.88706	+	30.7509i	−0.283742	+	0.981800i
$982$	30.3988	−	16.3058i	0.970065	−	0.520339i
$983$	−11.0802	−	20.6568i	−0.353405	−	0.658849i	0.640638	−	0.767843i	$-0.278670\pi$
$983$	−11.0802	−	20.6568i	−0.353405	−	0.658849i	−0.994042	+	0.108994i	$0.965237\pi$
$984$	4.48839	−	3.45802i	0.143085	−	0.110238i
$985$	−22.8066	+	2.68578i	−0.726678	+	0.0855762i
$986$	−11.7446	−	20.7144i	−0.374024	−	0.659680i
$987$	14.7362	+	7.46499i	0.469058	+	0.237613i
$988$	2.08083	−	22.1236i	0.0662002	−	0.703847i
$989$	8.42140	−	7.14149i	0.267785	−	0.227086i
$990$	−2.25203	−	9.42908i	−0.0715744	−	0.299676i
$991$	10.1811	−	29.8966i	0.323414	−	0.949697i	−0.657195	−	0.753721i	$-0.728257\pi$
$991$	10.1811	−	29.8966i	0.323414	−	0.949697i	0.980609	−	0.195976i	$-0.0627876\pi$
$992$	−1.40357	+	1.43687i	−0.0445633	+	0.0456205i
$993$	17.6272	+	9.45516i	0.559382	+	0.300051i
$994$		−	5.71171i		−	0.181164i
$995$	−8.66320	+	16.1507i	−0.274642	+	0.512013i
$996$	−1.31427	−	7.93628i	−0.0416442	−	0.251471i
$997$	−8.32444	−	26.4618i	−0.263638	−	0.838054i	−0.988770	−	0.149445i	$-0.952251\pi$
$997$	−8.32444	−	26.4618i	−0.263638	−	0.838054i	0.725133	−	0.688609i	$-0.241778\pi$
$998$	6.92769	−	0.325074i	0.219292	−	0.0102900i
$999$	1.18947	−	8.40000i	0.0376332	−	0.265764i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	538.2.e.a.9.6	✓	1452
269.30	even	134	inner	538.2.e.a.299.6	yes	1452

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
538.2.e.a.9.6	✓	1452	1.1	even	1	trivial
538.2.e.a.299.6	yes	1452	269.30	even	134	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:	\( N \)	\(=\)	\( 538 = 2 \cdot 269 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	538.e (of order \(134\), degree \(66\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.833094 + 0.553131i) q^{2} +(0.283306 - 0.499678i) q^{3} +(0.388092 - 0.921621i) q^{4} +(-0.723479 - 0.505183i) q^{5} +(0.0403669 + 0.572984i) q^{6} +(-0.341899 - 2.41448i) q^{7} +(0.186460 + 0.982463i) q^{8} +(1.37101 + 2.29119i) q^{9} +(0.882159 + 0.0206858i) q^{10} +(-3.95285 - 1.14238i) q^{11} +(-0.350565 - 0.455022i) q^{12} +(0.0912267 - 3.89043i) q^{13} +(1.62036 + 1.82238i) q^{14} +(-0.457395 + 0.218386i) q^{15} +(-0.698769 - 0.715347i) q^{16} +(-0.695955 - 2.40813i) q^{17} +(-2.40951 - 1.15043i) q^{18} +(1.84077 + 5.40538i) q^{19} +(-0.746363 + 0.470716i) q^{20} +(-1.30333 - 0.513198i) q^{21} +(3.92498 - 1.23473i) q^{22} +(-4.57177 - 2.59209i) q^{23} +(0.543740 + 0.185167i) q^{24} +(-1.45412 - 3.96301i) q^{25} +(2.07592 + 3.29155i) q^{26} +(3.25601 - 0.0763503i) q^{27} +(-2.35793 - 0.621940i) q^{28} +(-8.91811 - 3.27226i) q^{29} +(0.260257 - 0.434935i) q^{30} +(-1.07150 + 1.69896i) q^{31} +(0.977821 + 0.209440i) q^{32} +(-1.69069 + 1.65151i) q^{33} +(1.91181 + 1.62125i) q^{34} +(-0.972398 + 1.91955i) q^{35} +(2.64369 - 0.374355i) q^{36} +(0.425576 - 2.56986i) q^{37} +(-4.52342 - 3.48500i) q^{38} +(-1.91812 - 1.14777i) q^{39} +(0.361423 - 0.804988i) q^{40} +(5.45616 - 8.21775i) q^{41} +(1.36966 - 0.293368i) q^{42} +(-0.723726 + 1.97242i) q^{43} +(-2.58691 + 3.19968i) q^{44} +(0.165575 - 2.35024i) q^{45} +(5.24248 - 0.369335i) q^{46} +(-11.7414 - 1.10434i) q^{47} +(-0.555409 + 0.146498i) q^{48} +(1.01196 - 0.292460i) q^{49} +(3.40349 + 2.49724i) q^{50} +(-1.40046 - 0.334485i) q^{51} +(-3.55009 - 1.59392i) q^{52} +(-0.199606 - 0.931908i) q^{53} +(-2.67033 + 1.86461i) q^{54} +(2.28269 + 2.82340i) q^{55} +(2.30839 - 0.786108i) q^{56} +(3.22245 + 0.611584i) q^{57} +(9.23961 - 2.20678i) q^{58} +(13.5021 + 5.68570i) q^{59} +(0.0237574 + 0.506298i) q^{60} +(3.17233 - 2.95670i) q^{61} +(-0.0470874 - 2.00807i) q^{62} +(5.06330 - 4.09363i) q^{63} +(-0.930465 + 0.366380i) q^{64} +(-2.03138 + 2.76856i) q^{65} +(0.495002 - 2.31103i) q^{66} +(-4.59892 - 10.9213i) q^{67} +(-2.48948 - 0.293170i) q^{68} +(-2.59042 + 1.55006i) q^{69} +(-0.251664 - 2.13703i) q^{70} +(-1.75039 - 1.55635i) q^{71} +(-1.99537 + 1.77418i) q^{72} +(0.688488 - 5.84636i) q^{73} +(1.06693 + 2.37634i) q^{74} +(-2.39219 - 0.396153i) q^{75} +(5.69610 + 0.401292i) q^{76} +(-1.40678 + 9.93466i) q^{77} +(2.23284 - 0.104773i) q^{78} +(0.103815 + 0.330007i) q^{79} +(0.144164 + 0.870545i) q^{80} +(-2.90202 + 5.41022i) q^{81} +9.86413i q^{82} +(12.3414 + 6.61987i) q^{83} +(-0.978784 + 1.00200i) q^{84} +(-0.713037 + 2.09382i) q^{85} +(-0.488075 - 2.04353i) q^{86} +(-4.16163 + 3.52913i) q^{87} +(0.385298 - 4.09653i) q^{88} +(-15.0363 - 7.61701i) q^{89} +(1.16205 + 2.04956i) q^{90} +(-9.42456 + 1.10987i) q^{91} +(-4.16319 + 3.20747i) q^{92} +(0.545371 + 1.01673i) q^{93} +(10.3926 - 5.57454i) q^{94} +(1.39895 - 4.84061i) q^{95} +(0.381675 - 0.429260i) q^{96} +(3.00236 + 2.79829i) q^{97} +(-0.681293 + 0.803395i) q^{98} +(-2.80196 - 10.6229i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1452 q + 22 q^{4} - 2 q^{5} + 2 q^{6} + 20 q^{9} + 2 q^{11} - 10 q^{13} + 12 q^{14} - 22 q^{16} + 2 q^{20} + 12 q^{21} - 4 q^{23} - 2 q^{24} - 24 q^{25} - 8 q^{30} - 12 q^{34} - 20 q^{36} - 396 q^{37} - 2 q^{38}+ \cdots + 18 q^{99}+O(q^{100}) \) 1452 * q + 22 * q^4 - 2 * q^5 + 2 * q^6 + 20 * q^9 + 2 * q^11 - 10 * q^13 + 12 * q^14 - 22 * q^16 + 2 * q^20 + 12 * q^21 - 4 * q^23 - 2 * q^24 - 24 * q^25 - 8 * q^30 - 12 * q^34 - 20 * q^36 - 396 * q^37 - 2 * q^38 + 24 * q^41 + 14 * q^43 - 2 * q^44 - 42 * q^45 - 402 * q^47 + 22 * q^49 + 12 * q^51 + 10 * q^52 - 10 * q^53 - 8 * q^54 - 4 * q^55 - 12 * q^56 + 16 * q^57 - 18 * q^58 - 268 * q^60 - 2 * q^61 + 4 * q^62 + 22 * q^64 + 16 * q^65 + 40 * q^66 + 6 * q^67 - 106 * q^73 + 40 * q^78 + 40 * q^79 - 2 * q^80 - 14 * q^81 - 402 * q^83 - 12 * q^84 - 100 * q^87 + 4 * q^92 - 340 * q^93 + 2 * q^96 - 64 * q^97 + 18 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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