LMFDB - Embedded newform 483.2.r.a.34.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(34,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 9]))

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

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

chi := DirichletCharacter("483.34");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.r (of order $22$, degree $10$, 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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$32$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			34.15
Character	$\chi$	$=$	483.34
Dual form			483.2.r.a.412.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.129024 + 0.0829186i) q^{2} +(-0.989821 - 0.142315i) q^{3} +(-0.821058 + 1.79787i) q^{4} +(-3.74200 + 1.09875i) q^{5} +(0.139511 - 0.0637126i) q^{6} +(-0.158342 - 2.64101i) q^{7} +(-0.0867944 - 0.603668i) q^{8} +(0.959493 + 0.281733i) q^{9} +O(q^{10})$	\(q+(-0.129024 + 0.0829186i) q^{2} +(-0.989821 - 0.142315i) q^{3} +(-0.821058 + 1.79787i) q^{4} +(-3.74200 + 1.09875i) q^{5} +(0.139511 - 0.0637126i) q^{6} +(-0.158342 - 2.64101i) q^{7} +(-0.0867944 - 0.603668i) q^{8} +(0.959493 + 0.281733i) q^{9} +(0.391701 - 0.452047i) q^{10} +(0.170830 - 0.265816i) q^{11} +(1.06856 - 1.66272i) q^{12} +(1.14921 + 0.995794i) q^{13} +(0.239419 + 0.327624i) q^{14} +(3.86028 - 0.555025i) q^{15} +(-2.52738 - 2.91675i) q^{16} +(2.42691 + 5.31419i) q^{17} +(-0.147158 + 0.0432096i) q^{18} +(3.19164 - 6.98871i) q^{19} +(1.09699 - 7.62976i) q^{20} +(-0.219124 + 2.63666i) q^{21} +0.0484616i q^{22} +(-1.47490 - 4.56341i) q^{23} +0.609876i q^{24} +(8.58907 - 5.51986i) q^{25} +(-0.230845 - 0.0331905i) q^{26} +(-0.909632 - 0.415415i) q^{27} +(4.87819 + 1.88374i) q^{28} +(2.19928 + 4.81575i) q^{29} +(-0.452047 + 0.391701i) q^{30} +(4.53470 - 0.651992i) q^{31} +(1.73829 + 0.510408i) q^{32} +(-0.206920 + 0.238799i) q^{33} +(-0.753775 - 0.484422i) q^{34} +(3.49433 + 9.70869i) q^{35} +(-1.29432 + 1.49372i) q^{36} +(0.789895 - 2.69013i) q^{37} +(0.167697 + 1.16636i) q^{38} +(-0.995794 - 1.14921i) q^{39} +(0.988067 + 2.16356i) q^{40} +(-2.21110 - 7.53031i) q^{41} +(-0.190356 - 0.358362i) q^{42} +(-7.04710 - 1.01322i) q^{43} +(0.337641 + 0.525380i) q^{44} -3.89998 q^{45} +(0.568688 + 0.466492i) q^{46} -8.31829i q^{47} +(2.08656 + 3.24675i) q^{48} +(-6.94986 + 0.836365i) q^{49} +(-0.650496 + 1.42439i) q^{50} +(-1.64592 - 5.60549i) q^{51} +(-2.73387 + 1.24852i) q^{52} +(-0.237530 + 0.205821i) q^{53} +(0.151810 - 0.0218270i) q^{54} +(-0.347179 + 1.18238i) q^{55} +(-1.58055 + 0.324811i) q^{56} +(-4.15375 + 6.46336i) q^{57} +(-0.683075 - 0.438986i) q^{58} +(0.835725 + 0.724160i) q^{59} +(-2.17166 + 7.39599i) q^{60} +(0.591132 + 4.11141i) q^{61} +(-0.531023 + 0.460134i) q^{62} +(0.592130 - 2.57864i) q^{63} +(7.13956 - 2.09637i) q^{64} +(-5.39447 - 2.46357i) q^{65} +(0.00689680 - 0.0479683i) q^{66} +(-7.91252 - 12.3121i) q^{67} -11.5468 q^{68} +(0.810443 + 4.72686i) q^{69} +(-1.25588 - 0.962907i) q^{70} +(-1.38621 + 0.890866i) q^{71} +(0.0867944 - 0.603668i) q^{72} +(8.12885 + 3.71232i) q^{73} +(0.121147 + 0.412588i) q^{74} +(-9.28720 + 4.24132i) q^{75} +(9.94426 + 11.4763i) q^{76} +(-0.729072 - 0.409073i) q^{77} +(0.223772 + 0.0657054i) q^{78} +(3.66239 + 3.17348i) q^{79} +(12.6623 + 8.13754i) q^{80} +(0.841254 + 0.540641i) q^{81} +(0.909687 + 0.788248i) q^{82} +(-5.94289 - 1.74499i) q^{83} +(-4.56045 - 2.55881i) q^{84} +(-14.9205 - 17.2192i) q^{85} +(0.993258 - 0.453606i) q^{86} +(-1.49154 - 5.07972i) q^{87} +(-0.175292 - 0.0800531i) q^{88} +(1.08210 - 7.52618i) q^{89} +(0.503190 - 0.323381i) q^{90} +(2.44793 - 3.19274i) q^{91} +(9.41537 + 1.09516i) q^{92} -4.58134 q^{93} +(0.689741 + 1.07326i) q^{94} +(-4.26427 + 29.6586i) q^{95} +(-1.64796 - 0.752597i) q^{96} +(18.1980 - 5.34340i) q^{97} +(0.827347 - 0.684183i) q^{98} +(0.238799 - 0.206920i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q + 4 q^{2} - 36 q^{4} + 12 q^{8} + 32 q^{9}+O(q^{10}) $ 320 * q + 4 * q^2 - 36 * q^4 + 12 * q^8 + 32 * q^9	$ 320 q + 4 q^{2} - 36 q^{4} + 12 q^{8} + 32 q^{9} - 4 q^{18} + 52 q^{23} - 68 q^{25} - 88 q^{28} + 24 q^{32} + 28 q^{35} + 14 q^{36} - 44 q^{37} + 110 q^{42} - 44 q^{43} - 154 q^{44} + 40 q^{46} - 16 q^{49} - 166 q^{50} - 44 q^{51} + 110 q^{56} - 44 q^{57} - 62 q^{58} - 84 q^{64} + 72 q^{70} - 40 q^{71} - 12 q^{72} + 22 q^{74} + 72 q^{77} - 8 q^{78} - 88 q^{79} - 32 q^{81} - 304 q^{85} + 330 q^{88} - 412 q^{92} + 24 q^{93} + 148 q^{95} - 60 q^{98} + 44 q^{99}+O(q^{100}) $ 320 * q + 4 * q^2 - 36 * q^4 + 12 * q^8 + 32 * q^9 - 4 * q^18 + 52 * q^23 - 68 * q^25 - 88 * q^28 + 24 * q^32 + 28 * q^35 + 14 * q^36 - 44 * q^37 + 110 * q^42 - 44 * q^43 - 154 * q^44 + 40 * q^46 - 16 * q^49 - 166 * q^50 - 44 * q^51 + 110 * q^56 - 44 * q^57 - 62 * q^58 - 84 * q^64 + 72 * q^70 - 40 * q^71 - 12 * q^72 + 22 * q^74 + 72 * q^77 - 8 * q^78 - 88 * q^79 - 32 * q^81 - 304 * q^85 + 330 * q^88 - 412 * q^92 + 24 * q^93 + 148 * q^95 - 60 * q^98 + 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$-1$	$e\left(\frac{9}{22}\right)$

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 $

$2$	−0.129024	+	0.0829186i	−0.0912336	+	0.0586323i	−0.585462	−	0.810700i	$-0.699087\pi$
$2$	−0.129024	+	0.0829186i	−0.0912336	+	0.0586323i	0.494229	+	0.869332i	$0.335451\pi$
$3$	−0.989821	−	0.142315i	−0.571474	−	0.0821655i
$3$	−0.989821	−	0.142315i	−0.571474	−	0.0821655i
$4$	−0.821058	+	1.79787i	−0.410529	+	0.898934i
$5$	−3.74200	+	1.09875i	−1.67347	+	0.491377i	−0.974616	−	0.223883i	$-0.928127\pi$
$5$	−3.74200	+	1.09875i	−1.67347	+	0.491377i	−0.698859	+	0.715260i	$0.746308\pi$
$6$	0.139511	−	0.0637126i	0.0569552	−	0.0260106i
$7$	−0.158342	−	2.64101i	−0.0598476	−	0.998208i
$7$	−0.158342	−	2.64101i	−0.0598476	−	0.998208i
$8$	−0.0867944	−	0.603668i	−0.0306865	−	0.213429i
$9$	0.959493	+	0.281733i	0.319831	+	0.0939109i
$10$	0.391701	−	0.452047i	0.123867	−	0.142950i
$11$	0.170830	−	0.265816i	0.0515071	−	0.0801466i	−0.814545	−	0.580100i	$-0.803013\pi$
$11$	0.170830	−	0.265816i	0.0515071	−	0.0801466i	0.866052	+	0.499954i	$0.166650\pi$
$12$	1.06856	−	1.66272i	0.308468	−	0.479986i
$13$	1.14921	+	0.995794i	0.318733	+	0.276184i	0.799502	−	0.600664i	$-0.205097\pi$
$13$	1.14921	+	0.995794i	0.318733	+	0.276184i	−0.480769	+	0.876847i	$0.659642\pi$
$14$	0.239419	+	0.327624i	0.0639873	+	0.0875611i
$15$	3.86028	−	0.555025i	0.996721	−	0.143307i
$16$	−2.52738	−	2.91675i	−0.631845	−	0.729188i
$17$	2.42691	+	5.31419i	0.588612	+	1.28888i	0.936277	+	0.351262i	$0.114247\pi$
$17$	2.42691	+	5.31419i	0.588612	+	1.28888i	−0.347665	+	0.937619i	$0.613025\pi$
$18$	−0.147158	+	0.0432096i	−0.0346856	+	0.0101846i
$19$	3.19164	−	6.98871i	0.732212	−	1.60332i	−0.0637435	−	0.997966i	$-0.520304\pi$
$19$	3.19164	−	6.98871i	0.732212	−	1.60332i	0.795956	−	0.605355i	$-0.206969\pi$
$20$	1.09699	−	7.62976i	0.245295	−	1.70607i
$21$	−0.219124	+	2.63666i	−0.0478169	+	0.575367i
$22$			0.0484616i			0.0103320i
$23$	−1.47490	−	4.56341i	−0.307537	−	0.951536i
$23$	−1.47490	−	4.56341i	−0.307537	−	0.951536i
$24$			0.609876i			0.124490i
$25$	8.58907	−	5.51986i	1.71781	−	1.10397i
$26$	−0.230845	−	0.0331905i	−0.0452725	−	0.00650920i
$27$	−0.909632	−	0.415415i	−0.175059	−	0.0799467i
$28$	4.87819	+	1.88374i	0.921891	+	0.355994i
$29$	2.19928	+	4.81575i	0.408396	+	0.894263i	0.996349	+	0.0853679i	$0.0272066\pi$
$29$	2.19928	+	4.81575i	0.408396	+	0.894263i	−0.587953	+	0.808895i	$0.700066\pi$
$30$	−0.452047	+	0.391701i	−0.0825321	+	0.0715145i
$31$	4.53470	−	0.651992i	0.814457	−	0.117101i	0.277516	−	0.960721i	$-0.410489\pi$
$31$	4.53470	−	0.651992i	0.814457	−	0.117101i	0.536941	+	0.843620i	$0.319580\pi$
$32$	1.73829	+	0.510408i	0.307289	+	0.0902282i
$33$	−0.206920	+	0.238799i	−0.0360202	+	0.0415696i
$34$	−0.753775	−	0.484422i	−0.129271	−	0.0830776i
$35$	3.49433	+	9.70869i	0.590649	+	1.64107i
$36$	−1.29432	+	1.49372i	−0.215720	+	0.248954i
$37$	0.789895	−	2.69013i	0.129858	−	0.442255i	−0.868736	−	0.495276i	$-0.835067\pi$
$37$	0.789895	−	2.69013i	0.129858	−	0.442255i	0.998593	+	0.0530210i	$0.0168850\pi$
$38$	0.167697	+	1.16636i	0.0272040	+	0.189208i
$39$	−0.995794	−	1.14921i	−0.159455	−	0.184021i
$40$	0.988067	+	2.16356i	0.156227	+	0.342090i
$41$	−2.21110	−	7.53031i	−0.345315	−	1.17604i	−0.930854	−	0.365392i	$-0.880935\pi$
$41$	−2.21110	−	7.53031i	−0.345315	−	1.17604i	0.585538	−	0.810645i	$-0.300883\pi$
$42$	−0.190356	−	0.358362i	−0.0293726	−	0.0552964i
$43$	−7.04710	−	1.01322i	−1.07467	−	0.154515i	−0.417817	−	0.908531i	$-0.637205\pi$
$43$	−7.04710	−	1.01322i	−1.07467	−	0.154515i	−0.656855	+	0.754017i	$0.728114\pi$
$44$	0.337641	+	0.525380i	0.0509013	+	0.0792040i
$45$	−3.89998			−0.581375
$46$	0.568688	+	0.466492i	0.0838485	+	0.0687805i
$47$		−	8.31829i		−	1.21335i	−0.794951	−	0.606674i	$-0.792503\pi$
$47$		−	8.31829i		−	1.21335i	0.794951	−	0.606674i	$-0.207497\pi$
$48$	2.08656	+	3.24675i	0.301169	+	0.468628i
$49$	−6.94986	+	0.836365i	−0.992837	+	0.119481i
$50$	−0.650496	+	1.42439i	−0.0919940	+	0.201439i
$51$	−1.64592	−	5.60549i	−0.230475	−	0.784925i
$52$	−2.73387	+	1.24852i	−0.379120	+	0.173138i
$53$	−0.237530	+	0.205821i	−0.0326273	+	0.0282717i	−0.671022	−	0.741438i	$-0.734144\pi$
$53$	−0.237530	+	0.205821i	−0.0326273	+	0.0282717i	0.638395	+	0.769709i	$0.279599\pi$
$54$	0.151810	−	0.0218270i	0.0206587	−	0.00297027i
$55$	−0.347179	+	1.18238i	−0.0468137	+	0.159433i
$56$	−1.58055	+	0.324811i	−0.211210	+	0.0434047i
$57$	−4.15375	+	6.46336i	−0.550178	+	0.856093i
$58$	−0.683075	−	0.438986i	−0.0896921	−	0.0576416i
$59$	0.835725	+	0.724160i	0.108802	+	0.0942776i	0.707563	−	0.706650i	$-0.249795\pi$
$59$	0.835725	+	0.724160i	0.108802	+	0.0942776i	−0.598761	+	0.800928i	$0.704340\pi$
$60$	−2.17166	+	7.39599i	−0.280360	+	0.954818i
$61$	0.591132	+	4.11141i	0.0756867	+	0.526413i	0.992028	+	0.126015i	$0.0402188\pi$
$61$	0.591132	+	4.11141i	0.0756867	+	0.526413i	−0.916342	+	0.400397i	$0.868872\pi$
$62$	−0.531023	+	0.460134i	−0.0674400	+	0.0584371i
$63$	0.592130	−	2.57864i	0.0746014	−	0.324878i
$64$	7.13956	−	2.09637i	0.892446	−	0.262046i
$65$	−5.39447	−	2.46357i	−0.669102	−	0.305569i
$66$	0.00689680	−	0.0479683i	0.000848938	−	0.00590449i
$67$	−7.91252	−	12.3121i	−0.966668	−	1.50417i	−0.860268	−	0.509842i	$-0.829704\pi$
$67$	−7.91252	−	12.3121i	−0.966668	−	1.50417i	−0.106400	−	0.994323i	$-0.533932\pi$
$68$	−11.5468			−1.40026
$69$	0.810443	+	4.72686i	0.0975659	+	0.569047i
$70$	−1.25588	−	0.962907i	−0.150107	−	0.115089i
$71$	−1.38621	+	0.890866i	−0.164513	+	0.105726i	−0.620307	−	0.784359i	$-0.712992\pi$
$71$	−1.38621	+	0.890866i	−0.164513	+	0.105726i	0.455793	+	0.890086i	$0.349356\pi$
$72$	0.0867944	−	0.603668i	0.0102288	−	0.0711430i
$73$	8.12885	+	3.71232i	0.951410	+	0.434495i	0.829786	−	0.558082i	$-0.188462\pi$
$73$	8.12885	+	3.71232i	0.951410	+	0.434495i	0.121624	+	0.992576i	$0.461190\pi$
$74$	0.121147	+	0.412588i	0.0140830	+	0.0479624i
$75$	−9.28720	+	4.24132i	−1.07239	+	0.489746i
$76$	9.94426	+	11.4763i	1.14068	+	1.31642i
$77$	−0.729072	−	0.409073i	−0.0830855	−	0.0466182i
$78$	0.223772	+	0.0657054i	0.0253372	+	0.00743967i
$79$	3.66239	+	3.17348i	0.412051	+	0.357044i	0.836083	−	0.548603i	$-0.184840\pi$
$79$	3.66239	+	3.17348i	0.412051	+	0.357044i	−0.424032	+	0.905647i	$0.639386\pi$
$80$	12.6623	+	8.13754i	1.41568	+	0.909804i
$81$	0.841254	+	0.540641i	0.0934726	+	0.0600712i
$82$	0.909687	+	0.788248i	0.100458	+	0.0870474i
$83$	−5.94289	−	1.74499i	−0.652317	−	0.191538i	−0.0612029	−	0.998125i	$-0.519494\pi$
$83$	−5.94289	−	1.74499i	−0.652317	−	0.191538i	−0.591114	+	0.806588i	$0.701312\pi$
$84$	−4.56045	−	2.55881i	−0.497586	−	0.279189i
$85$	−14.9205	−	17.2192i	−1.61835	−	1.86768i
$86$	0.993258	−	0.453606i	0.107106	−	0.0489136i
$87$	−1.49154	−	5.07972i	−0.159910	−	0.544604i
$88$	−0.175292	−	0.0800531i	−0.0186862	−	0.00853369i
$89$	1.08210	−	7.52618i	0.114702	−	0.797773i	−0.848538	−	0.529134i	$-0.822517\pi$
$89$	1.08210	−	7.52618i	0.114702	−	0.797773i	0.963241	−	0.268639i	$-0.0865740\pi$
$90$	0.503190	−	0.323381i	0.0530409	−	0.0340873i
$91$	2.44793	−	3.19274i	0.256613	−	0.334691i
$92$	9.41537	+	1.09516i	0.981621	+	0.114178i
$93$	−4.58134			−0.475062
$94$	0.689741	+	1.07326i	0.0711414	+	0.110698i
$95$	−4.26427	+	29.6586i	−0.437504	+	3.04291i
$96$	−1.64796	−	0.752597i	−0.168194	−	0.0768116i
$97$	18.1980	−	5.34340i	1.84772	−	0.542540i	0.847797	−	0.530321i	$-0.177929\pi$
$97$	18.1980	−	5.34340i	1.84772	−	0.542540i	0.999925	−	0.0122191i	$-0.00388957\pi$
$98$	0.827347	−	0.684183i	0.0835747	−	0.0691130i
$99$	0.238799	−	0.206920i	0.0240002	−	0.0207963i
$100$	2.87185	+	19.9741i	0.287185	+	1.99741i
$101$	−3.31144	+	11.2777i	−0.329500	+	1.12217i	0.613587	+	0.789627i	$0.289726\pi$
$101$	−3.31144	+	11.2777i	−0.329500	+	1.12217i	−0.943087	+	0.332547i	$0.892092\pi$
$102$	0.677162	+	0.586764i	0.0670490	+	0.0580983i
$103$	−5.19284	−	3.33724i	−0.511666	−	0.328828i	0.259201	−	0.965823i	$-0.416541\pi$
$103$	−5.19284	−	3.33724i	−0.511666	−	0.328828i	−0.770868	+	0.636995i	$0.780177\pi$
$104$	0.501385	−	0.780170i	0.0491648	−	0.0765020i
$105$	−2.07707	−	10.1072i	−0.202701	−	0.986358i
$106$	0.0135807	−	0.0462515i	0.00131907	−	0.00449234i
$107$	1.77582	−	0.255324i	0.171675	−	0.0246831i	−0.0559414	−	0.998434i	$-0.517816\pi$
$107$	1.77582	−	0.255324i	0.171675	−	0.0246831i	0.227616	+	0.973751i	$0.426907\pi$
$108$	1.49372	−	1.29432i	0.143733	−	0.124546i
$109$	8.57293	−	3.91513i	0.821138	−	0.375001i	0.0398763	−	0.999205i	$-0.487304\pi$
$109$	8.57293	−	3.91513i	0.821138	−	0.375001i	0.781262	+	0.624203i	$0.214576\pi$
$110$	−0.0532472	−	0.181343i	−0.00507693	−	0.0172904i
$111$	−1.16470	+	2.55034i	−0.110548	+	0.242067i
$112$	−7.30298	+	7.13668i	−0.690067	+	0.674353i
$113$	−9.35373	−	14.5547i	−0.879925	−	1.36919i	−0.928877	−	0.370388i	$-0.879225\pi$
$113$	−9.35373	−	14.5547i	−0.879925	−	1.36919i	0.0489522	−	0.998801i	$-0.484412\pi$
$114$		−	1.17835i		−	0.110363i
$115$	10.5331	+	15.4557i	0.982218	+	1.44126i
$116$	−10.4638			−0.971541
$117$	0.822109	+	1.27923i	0.0760040	+	0.118265i
$118$	−0.167875	−	0.0241367i	−0.0154541	−	0.00222197i
$119$	13.6505	−	7.25095i	1.25134	−	0.664694i
$120$	−0.670102	−	2.28216i	−0.0611717	−	0.208332i
$121$	4.52809	+	9.91513i	0.411645	+	0.901376i
$122$	−0.417183	−	0.481455i	−0.0377699	−	0.0435888i
$123$	1.11692	+	7.76833i	0.100709	+	0.700447i
$124$	−2.55106	+	8.68812i	−0.229092	+	0.780216i
$125$	−13.3057	+	15.3555i	−1.19009	+	1.37344i
$126$	0.137418	+	0.381805i	0.0122422	+	0.0340139i
$127$	2.74020	+	1.76102i	0.243154	+	0.156265i	0.656542	−	0.754289i	$-0.272018\pi$
$127$	2.74020	+	1.76102i	0.243154	+	0.156265i	−0.413388	+	0.910555i	$0.635655\pi$
$128$	−3.12014	+	3.60083i	−0.275784	+	0.318271i
$129$	6.83117	+	2.00581i	0.601451	+	0.176602i
$130$	0.900291	−	0.129442i	0.0789608	−	0.0113528i
$131$	6.23455	−	5.40227i	0.544715	−	0.471999i	−0.338500	−	0.940966i	$-0.609919\pi$
$131$	6.23455	−	5.40227i	0.544715	−	0.471999i	0.883215	+	0.468968i	$0.155374\pi$
$132$	−0.259435	−	0.568083i	−0.0225809	−	0.0494453i
$133$	−18.9626	−	7.32254i	−1.64427	−	0.634945i
$134$	2.04181	+	0.932462i	0.176385	+	0.0805525i
$135$	3.86028	+	0.555025i	0.332240	+	0.0477690i
$136$	2.99737	−	1.92629i	0.257022	−	0.165178i
$137$		−	21.9063i		−	1.87158i	−0.352558	−	0.935790i	$-0.614688\pi$
$137$		−	21.9063i		−	1.87158i	0.352558	−	0.935790i	$-0.385312\pi$
$138$	−0.496511	−	0.542677i	−0.0422658	−	0.0461957i
$139$		−	3.29935i		−	0.279848i	−0.990162	−	0.139924i	$-0.955314\pi$
$139$		−	3.29935i		−	0.279848i	0.990162	−	0.139924i	$-0.0446857\pi$
$140$	−20.3240	−	1.68906i	−1.71769	−	0.142752i
$141$	−1.18382	+	8.23362i	−0.0996953	+	0.693396i
$142$	0.104985	−	0.229886i	0.00881018	−	0.0192916i
$143$	0.461017	−	0.135367i	0.0385522	−	0.0113199i
$144$	−1.60326	−	3.51065i	−0.133605	−	0.292554i
$145$	−13.5210	−	15.6041i	−1.12286	−	1.29585i
$146$	−1.35664	+	0.195055i	−0.112276	+	0.0161429i
$147$	6.99814	+	0.161215i	0.577197	+	0.0132968i
$148$	4.18795	+	3.62888i	0.344248	+	0.298292i
$149$	−4.45738	+	6.93582i	−0.365163	+	0.568204i	−0.974411	−	0.224776i	$-0.927835\pi$
$149$	−4.45738	+	6.93582i	−0.365163	+	0.568204i	0.609248	+	0.792980i	$0.291471\pi$
$150$	0.846586	−	1.31731i	0.0691235	−	0.107558i
$151$	−6.04273	+	6.97369i	−0.491751	+	0.567511i	−0.946333	−	0.323194i	$-0.895243\pi$
$151$	−6.04273	+	6.97369i	−0.491751	+	0.567511i	0.454582	+	0.890705i	$0.349789\pi$
$152$	−4.49588	−	1.32011i	−0.364664	−	0.107075i
$153$	0.831423	+	5.78267i	0.0672165	+	0.467501i
$154$	0.127987	−	0.00767350i	0.0103135	−	0.000618349i
$155$	−16.2525	+	7.42227i	−1.30543	+	0.596171i
$156$	2.88373	−	0.846739i	0.230883	−	0.0677934i
$157$	2.32741	−	5.09631i	0.185747	−	0.406730i	−0.793734	−	0.608265i	$-0.791866\pi$
$157$	2.32741	−	5.09631i	0.185747	−	0.406730i	0.979481	+	0.201535i	$0.0645930\pi$
$158$	−0.735675	−	0.105774i	−0.0585272	−	0.00841494i
$159$	0.264404	−	0.169922i	0.0209686	−	0.0134757i
$160$	−7.06550			−0.558576
$161$	−11.8185	+	4.61779i	−0.931425	+	0.363933i
$162$	−0.153371			−0.0120500
$163$	0.102066	−	0.0655936i	0.00799439	−	0.00513768i	−0.536638	−	0.843813i	$-0.680306\pi$
$163$	0.102066	−	0.0655936i	0.00799439	−	0.00513768i	0.544632	+	0.838675i	$0.316669\pi$
$164$	15.3539	+	2.20756i	1.19894	+	0.172382i
$165$	0.511917	−	1.12094i	0.0398526	−	0.0872651i
$166$	0.911467	−	0.267631i	0.0707436	−	0.0207722i
$167$	1.32577	−	0.605459i	0.102591	−	0.0468518i	−0.363458	−	0.931610i	$-0.618404\pi$
$167$	1.32577	−	0.605459i	0.102591	−	0.0468518i	0.466050	+	0.884759i	$0.345677\pi$
$168$	1.61069	−	0.0965690i	0.124267	−	0.00745046i
$169$	−1.52102	−	10.5789i	−0.117002	−	0.813764i
$170$	3.35289	+	0.984497i	0.257155	+	0.0755074i
$171$	5.03130	−	5.80643i	0.384753	−	0.444029i
$172$	7.60771	−	11.8378i	0.580083	−	0.902626i
$173$	−7.08797	+	11.0291i	−0.538889	+	0.838527i	−0.998777	−	0.0494500i	$-0.984253\pi$
$173$	−7.08797	+	11.0291i	−0.538889	+	0.838527i	0.459888	+	0.887977i	$0.347890\pi$
$174$	0.613648	+	0.531729i	0.0465205	+	0.0403103i
$175$	−15.9380	−	21.8098i	−1.20480	−	1.64866i
$176$	−1.20707	+	0.173551i	−0.0909865	+	0.0130819i
$177$	−0.724160	−	0.835725i	−0.0544312	−	0.0628169i
$178$	0.484443	+	1.06078i	0.0363106	+	0.0795090i
$179$	21.0839	−	6.19079i	1.57588	−	0.462721i	0.627176	−	0.778877i	$-0.284211\pi$
$179$	21.0839	−	6.19079i	1.57588	−	0.462721i	0.948707	+	0.316156i	$0.102392\pi$
$180$	3.20211	−	7.01165i	0.238671	−	0.522617i
$181$	−2.04479	+	14.2218i	−0.151988	+	1.05710i	0.760894	+	0.648877i	$0.224761\pi$
$181$	−2.04479	+	14.2218i	−0.151988	+	1.05710i	−0.912882	+	0.408224i	$0.866148\pi$
$182$	−0.0511040	+	0.614919i	−0.00378808	+	0.0455809i
$183$		−	4.15369i		−	0.307050i
$184$	−2.62677	+	1.28643i	−0.193648	+	0.0948366i
$185$			10.9344i			0.803912i
$186$	0.591102	−	0.379878i	0.0433417	−	0.0278540i
$187$	1.82719	+	0.262710i	0.133617	+	0.0192112i
$188$	14.9552	+	6.82980i	1.09072	+	0.498115i
$189$	−0.953082	+	2.46812i	−0.0693265	+	0.179530i
$190$	−1.90906	−	4.18026i	−0.138498	−	0.303268i
$191$	9.91522	−	8.59159i	0.717440	−	0.621666i	−0.217670	−	0.976022i	$-0.569846\pi$
$191$	9.91522	−	8.59159i	0.717440	−	0.621666i	0.935110	+	0.354357i	$0.115300\pi$
$192$	−7.36524	+	1.05896i	−0.531540	+	0.0764240i
$193$	−2.63741	−	0.774414i	−0.189845	−	0.0557436i	0.185428	−	0.982658i	$-0.440633\pi$
$193$	−2.63741	−	0.774414i	−0.189845	−	0.0557436i	−0.375273	+	0.926914i	$0.622451\pi$
$194$	−1.90490	+	2.19837i	−0.136764	+	0.157834i
$195$	4.98896	+	3.20621i	0.357267	+	0.229601i
$196$	4.20256	−	13.1816i	0.300183	−	0.941544i
$197$	0.419424	−	0.484041i	0.0298827	−	0.0344865i	−0.740611	−	0.671934i	$-0.765464\pi$
$197$	0.419424	−	0.484041i	0.0298827	−	0.0344865i	0.770494	+	0.637447i	$0.220010\pi$
$198$	−0.0136532	+	0.0464986i	−0.000970291	+	0.00330451i
$199$	−3.03849	−	21.1331i	−0.215393	−	1.49809i	−0.754751	−	0.656012i	$-0.772242\pi$
$199$	−3.03849	−	21.1331i	−0.215393	−	1.49809i	0.539358	−	0.842077i	$-0.318667\pi$
$200$	−4.07765	−	4.70586i	−0.288333	−	0.332754i
$201$	6.07978	+	13.3129i	0.428835	+	0.939017i
$202$	−0.507878	−	1.72967i	−0.0357342	−	0.121699i
$203$	12.3702	−	6.57085i	0.868218	−	0.461184i
$204$	11.4293	+	1.64329i	0.800212	+	0.115053i
$205$	16.5479	+	25.7490i	1.15575	+	1.79839i
$206$	0.946720			0.0659611
$207$	−0.129492	−	4.79408i	−0.00900031	−	0.333212i
$208$		−	5.86871i		−	0.406922i
$209$	−1.31249	−	2.04227i	−0.0907866	−	0.141267i
$210$	1.10606	+	1.13184i	0.0763256	+	0.0781042i
$211$	−3.98887	+	8.73440i	−0.274605	+	0.601301i	−0.995813	−	0.0914181i	$-0.970860\pi$
$211$	−3.98887	+	8.73440i	−0.274605	+	0.601301i	0.721208	+	0.692719i	$0.243587\pi$
$212$	−0.175013	−	0.596039i	−0.0120199	−	0.0409361i
$213$	1.49889	−	0.684519i	0.102702	−	0.0469025i
$214$	−0.207951	+	0.180191i	−0.0142153	+	0.0123176i
$215$	27.4835	−	3.95154i	1.87436	−	0.269493i
$216$	−0.171822	+	0.585172i	−0.0116910	+	0.0398159i
$217$	−2.43995	−	11.8730i	−0.165635	−	0.805989i
$218$	−0.781476	+	1.21600i	−0.0529282	+	0.0823579i
$219$	−7.51779	−	4.83139i	−0.508005	−	0.326475i
$220$	−1.84072	−	1.59499i	−0.124101	−	0.107534i
$221$	−2.50282	+	8.52382i	−0.168358	+	0.573374i
$222$	−0.0611963	−	0.425630i	−0.00410723	−	0.0285664i
$223$	−13.0110	+	11.2741i	−0.871284	+	0.754972i	−0.970756	−	0.240068i	$-0.922830\pi$
$223$	−13.0110	+	11.2741i	−0.871284	+	0.754972i	0.0994719	+	0.995040i	$0.468285\pi$
$224$	1.07275	−	4.67166i	0.0716759	−	0.312138i
$225$	9.79628	−	2.87645i	0.653085	−	0.191763i
$226$	2.41371	+	1.10230i	0.160557	+	0.0733241i
$227$	1.70991	−	11.8927i	0.113491	−	0.789344i	−0.850988	−	0.525185i	$-0.823996\pi$
$227$	1.70991	−	11.8927i	0.113491	−	0.789344i	0.964479	−	0.264160i	$-0.0850946\pi$
$228$	−8.20979	−	12.7747i	−0.543707	−	0.846024i
$229$	−13.3906			−0.884875			−0.442437	−	0.896799i	$-0.645886\pi$
$229$	−13.3906			−0.884875			−0.442437	+	0.896799i	$0.645886\pi$
$230$	−2.64059	−	1.12077i	−0.174115	−	0.0739013i
$231$	0.663434	+	0.508667i	0.0436508	+	0.0334678i
$232$	2.71623	−	1.74562i	0.178329	−	0.114605i
$233$	2.54632	−	17.7101i	0.166815	−	1.16022i	−0.718600	−	0.695423i	$-0.755217\pi$
$233$	2.54632	−	17.7101i	0.166815	−	1.16022i	0.885415	−	0.464801i	$-0.153874\pi$
$234$	−0.212143	−	0.0968827i	−0.0138682	−	0.00633342i
$235$	9.13974	+	31.1271i	0.596211	+	2.03051i
$236$	−1.98812	+	0.907945i	−0.129416	+	0.0591022i
$237$	−3.17348	−	3.66239i	−0.206139	−	0.237898i
$238$	−1.16001	+	2.06743i	−0.0751921	+	0.134012i
$239$	22.9840	+	6.74870i	1.48671	+	0.436537i	0.921490	−	0.388403i	$-0.126973\pi$
$239$	22.9840	+	6.74870i	1.48671	+	0.436537i	0.565220	+	0.824940i	$0.308791\pi$
$240$	−11.3753	−	9.85674i	−0.734271	−	0.636250i
$241$	−1.64474	−	1.05701i	−0.105947	−	0.0680882i	0.486594	−	0.873628i	$-0.338239\pi$
$241$	−1.64474	−	1.05701i	−0.105947	−	0.0680882i	−0.592542	+	0.805540i	$0.701875\pi$
$242$	−1.40638	−	0.903826i	−0.0904056	−	0.0581001i
$243$	−0.755750	−	0.654861i	−0.0484814	−	0.0420093i
$244$	−7.87713	−	2.31293i	−0.504281	−	0.148070i
$245$	25.0874	−	10.7658i	1.60278	−	0.687805i
$246$	−0.788248	−	0.909687i	−0.0502569	−	0.0579995i
$247$	10.6272	−	4.85327i	0.676191	−	0.308806i
$248$	−0.787174	−	2.68087i	−0.0499856	−	0.170235i
$249$	5.63407	+	2.57299i	0.357044	+	0.163057i
$250$	0.443487	−	3.08452i	0.0280486	−	0.195082i
$251$	3.36454	−	2.16226i	0.212368	−	0.136481i	−0.430133	−	0.902766i	$-0.641533\pi$
$251$	3.36454	−	2.16226i	0.212368	−	0.136481i	0.642501	+	0.766285i	$0.277897\pi$
$252$	4.14988	+	3.18178i	0.261418	+	0.200434i
$253$	−1.46498	−	0.387514i	−0.0921027	−	0.0243628i
$254$	−0.499573			−0.0313460
$255$	12.3181	+	19.1673i	0.771388	+	1.20030i
$256$	−2.01393	+	14.0072i	−0.125870	+	0.875448i
$257$	−23.5165	−	10.7396i	−1.46692	−	0.669919i	−0.487752	−	0.872982i	$-0.662183\pi$
$257$	−23.5165	−	10.7396i	−1.46692	−	0.669919i	−0.979166	+	0.203063i	$0.934910\pi$
$258$	−1.04770	+	0.307633i	−0.0652271	+	0.0191524i
$259$	−7.22974	−	1.66016i	−0.449234	−	0.103157i
$260$	8.85835	−	7.67580i	0.549372	−	0.476033i
$261$	0.753440	+	5.24029i	0.0466368	+	0.324366i
$262$	−0.356457	+	1.21398i	−0.0220220	+	0.0750001i
$263$	1.53497	+	1.33006i	0.0946504	+	0.0820150i	0.700901	−	0.713259i	$-0.252782\pi$
$263$	1.53497	+	1.33006i	0.0946504	+	0.0820150i	−0.606250	+	0.795274i	$0.707327\pi$
$264$	0.162115	+	0.104185i	0.00997749	+	0.00641214i
$265$	0.662693	−	1.03117i	0.0407089	−	0.0633443i
$266$	3.05381	−	0.627572i	0.187241	−	0.0384789i
$267$	−2.14217	+	7.29557i	−0.131099	+	0.446482i
$268$	28.6322	−	4.11669i	1.74899	−	0.251467i
$269$	0.766213	−	0.663927i	0.0467168	−	0.0404803i	−0.631189	−	0.775629i	$-0.717433\pi$
$269$	0.766213	−	0.663927i	0.0467168	−	0.0404803i	0.677906	+	0.735148i	$0.262888\pi$
$270$	−0.544091	+	0.248478i	−0.0331123	+	0.0151219i
$271$	−0.825145	−	2.81019i	−0.0501240	−	0.170707i	0.930627	−	0.365969i	$-0.119262\pi$
$271$	−0.825145	−	2.81019i	−0.0501240	−	0.170707i	−0.980751	+	0.195262i	$0.937444\pi$
$272$	9.36646	−	20.5097i	0.567925	−	1.24358i
$273$	−2.87739	+	2.81187i	−0.174148	+	0.170182i
$274$	1.81644	+	2.82643i	0.109735	+	0.170751i
$275$		−	3.22607i		−	0.194539i
$276$	−9.16368	−	2.42396i	−0.551589	−	0.145905i
$277$	−16.1723			−0.971698			−0.485849	−	0.874043i	$-0.661490\pi$
$277$	−16.1723			−0.971698			−0.485849	+	0.874043i	$0.661490\pi$
$278$	0.273578	+	0.425695i	0.0164081	+	0.0255315i
$279$	4.53470	+	0.651992i	0.271486	+	0.0390337i
$280$	5.55754	−	2.95208i	0.332127	−	0.176420i
$281$	5.61439	+	19.1209i	0.334927	+	1.14065i	0.939055	+	0.343768i	$0.111703\pi$
$281$	5.61439	+	19.1209i	0.334927	+	1.14065i	−0.604128	+	0.796887i	$0.706479\pi$
$282$	−0.529980	−	1.16049i	−0.0315598	−	0.0691064i
$283$	8.87973	+	10.2478i	0.527845	+	0.609166i	0.955578	−	0.294740i	$-0.0952329\pi$
$283$	8.87973	+	10.2478i	0.527845	+	0.609166i	−0.427733	+	0.903905i	$0.640687\pi$
$284$	−0.463496	−	3.22368i	−0.0275034	−	0.191290i
$285$	8.44172	−	28.7499i	0.500044	−	1.70300i
$286$	−0.0482578	+	0.0556924i	−0.00285354	+	0.00329316i
$287$	−19.5375	+	7.03189i	−1.15326	+	0.415079i
$288$	1.52408	+	0.979465i	0.0898071	+	0.0577155i
$289$	−11.2181	+	12.9464i	−0.659890	+	0.761553i
$290$	3.03841	+	0.892156i	0.178421	+	0.0523892i
$291$	−18.7732	+	2.69917i	−1.10050	+	0.158228i
$292$	−13.3485	+	11.5666i	−0.781163	+	0.676882i
$293$	−8.73339	−	19.1234i	−0.510210	−	1.11720i	−0.973015	−	0.230743i	$-0.925884\pi$
$293$	−8.73339	−	19.1234i	−0.510210	−	1.11720i	0.462805	−	0.886460i	$-0.346843\pi$
$294$	−0.916295	+	0.559476i	−0.0534394	+	0.0326293i
$295$	−3.92296	−	1.79155i	−0.228403	−	0.104308i
$296$	−1.69251	−	0.243346i	−0.0983750	−	0.0141442i
$297$	−0.265816	+	0.170830i	−0.0154242	+	0.00991254i
$298$		−	1.26449i		−	0.0732497i
$299$	2.84925	−	6.71300i	0.164777	−	0.388223i
$300$		−	20.1795i		−	1.16507i
$301$	−1.56007	+	18.7719i	−0.0899210	+	1.08199i
$302$	0.201408	−	1.40083i	0.0115898	−	0.0806085i
$303$	4.88272	−	10.6917i	0.280505	−	0.614220i
$304$	−28.4508	+	8.35392i	−1.63177	+	0.479130i
$305$	−6.72944	−	14.7354i	−0.385327	−	0.843747i
$306$	−0.586764	−	0.677162i	−0.0335431	−	0.0387108i
$307$	−7.13795	+	1.02628i	−0.407384	+	0.0585730i	−0.342961	−	0.939350i	$-0.611430\pi$
$307$	−7.13795	+	1.02628i	−0.407384	+	0.0585730i	−0.0644232	+	0.997923i	$0.520521\pi$
$308$	1.33407	−	0.974903i	0.0760157	−	0.0555502i
$309$	4.66505	+	4.04229i	0.265385	+	0.229958i
$310$	1.48152	−	2.30528i	0.0841445	−	0.130931i
$311$	2.05398	−	3.19605i	0.116470	−	0.181232i	−0.778124	−	0.628111i	$-0.783828\pi$
$311$	2.05398	−	3.19605i	0.116470	−	0.181232i	0.894594	+	0.446879i	$0.147465\pi$
$312$	−0.607311	+	0.700874i	−0.0343822	+	0.0396792i
$313$	10.7417	+	3.15405i	0.607156	+	0.178277i	0.570838	−	0.821063i	$-0.306619\pi$
$313$	10.7417	+	3.15405i	0.607156	+	0.178277i	0.0363189	+	0.999340i	$0.488437\pi$
$314$	0.122288	+	0.850531i	0.00690110	+	0.0479982i
$315$	0.617531	+	10.2999i	0.0347939	+	0.580333i
$316$	−8.71252	+	3.97887i	−0.490118	+	0.223829i
$317$	−10.1207	+	2.97171i	−0.568437	+	0.166908i	−0.553307	−	0.832977i	$-0.686634\pi$
$317$	−10.1207	+	2.97171i	−0.568437	+	0.166908i	−0.0151298	+	0.999886i	$0.504816\pi$
$318$	−0.0200247	+	0.0438480i	−0.00112293	+	0.00245887i
$319$	1.65581	+	0.238069i	0.0927074	+	0.0133293i
$320$	−24.4129	+	15.6892i	−1.36472	+	0.877054i
$321$	−1.79408			−0.100136
$322$	1.14196	−	1.57578i	0.0636391	−	0.0878145i
$323$	44.8852			2.49748
$324$	−1.66272	+	1.06856i	−0.0923733	+	0.0593647i
$325$	15.3673	+	2.20948i	0.852423	+	0.122560i
$326$	−0.00772997	+	0.0169263i	−0.000428123	+	0.000937459i
$327$	−9.04285	+	2.65522i	−0.500071	+	0.146834i
$328$	−4.35390	+	1.98836i	−0.240404	+	0.109789i
$329$	−21.9687	+	1.31713i	−1.21117	+	0.0726160i
$330$	0.0268974	+	0.187076i	0.00148065	+	0.0102982i
$331$	−33.0847	−	9.71454i	−1.81850	−	0.533959i	−0.819276	−	0.573399i	$-0.805625\pi$
$331$	−33.0847	−	9.71454i	−1.81850	−	0.533959i	−0.999222	+	0.0394396i	$0.987443\pi$
$332$	8.01672	−	9.25179i	0.439975	−	0.507758i
$333$	1.51580	−	2.35863i	0.0830651	−	0.129252i
$334$	−0.120852	+	0.188050i	−0.00661274	+	0.0102896i
$335$	43.1366	+	37.3781i	2.35681	+	2.04218i
$336$	8.24430	−	6.02472i	0.449764	−	0.328675i
$337$	32.9372	−	4.73565i	1.79420	−	0.257968i	0.836963	−	0.547260i	$-0.184329\pi$
$337$	32.9372	−	4.73565i	1.79420	−	0.257968i	0.957241	+	0.289292i	$0.0934199\pi$
$338$	1.07344	+	1.23881i	0.0583873	+	0.0673826i
$339$	7.18717	+	15.7377i	0.390354	+	0.854755i
$340$	43.2083	−	12.6871i	2.34330	−	0.688055i
$341$	0.601352	−	1.31678i	0.0325650	−	0.0713075i
$342$	−0.167697	+	1.16636i	−0.00906801	+	0.0630694i
$343$	3.30930	+	18.2222i	0.178686	+	0.983906i
$344$			4.34205i			0.234108i
$345$	−8.22632	−	16.7974i	−0.442890	−	0.904344i
$346$		−	2.01074i		−	0.108098i
$347$	5.88422	−	3.78156i	0.315882	−	0.203005i	−0.373086	−	0.927797i	$-0.621700\pi$
$347$	5.88422	−	3.78156i	0.315882	−	0.203005i	0.688968	+	0.724792i	$0.258064\pi$
$348$	10.3573	+	1.48916i	0.555210	+	0.0798272i
$349$	−17.4085	−	7.95020i	−0.931856	−	0.425564i	−0.109146	−	0.994026i	$-0.534812\pi$
$349$	−17.4085	−	7.95020i	−0.931856	−	0.425564i	−0.822710	+	0.568461i	$0.807539\pi$
$350$	3.86482	+	1.49242i	0.206583	+	0.0797735i
$351$	−0.631688	−	1.38320i	−0.0337170	−	0.0738300i
$352$	0.432626	−	0.374873i	0.0230590	−	0.0199808i
$353$	18.1844	−	2.61453i	0.967860	−	0.139157i	0.359784	−	0.933036i	$-0.382850\pi$
$353$	18.1844	−	2.61453i	0.967860	−	0.139157i	0.608076	+	0.793878i	$0.291941\pi$
$354$	0.162731	+	0.0477821i	0.00864905	+	0.00253959i
$355$	4.20838	−	4.85673i	0.223358	−	0.257768i
$356$	12.6426	+	8.12490i	0.670056	+	0.430619i
$357$	−14.5435	+	5.23447i	−0.769725	+	0.277038i
$358$	−2.20699	+	2.54700i	−0.116643	+	0.134613i
$359$	5.72462	−	19.4962i	0.302134	−	1.02897i	−0.658829	−	0.752293i	$-0.728948\pi$
$359$	5.72462	−	19.4962i	0.302134	−	1.02897i	0.960962	−	0.276680i	$-0.0892341\pi$
$360$	0.338497	+	2.35430i	0.0178403	+	0.124082i
$361$	−26.2132	−	30.2517i	−1.37964	−	1.59219i
$362$	−0.915428	−	2.00451i	−0.0481138	−	0.105355i
$363$	−3.07093	−	10.4586i	−0.161182	−	0.548935i
$364$	3.73023	+	7.02249i	0.195517	+	0.368078i
$365$	−34.4971	−	4.95994i	−1.80566	−	0.259615i
$366$	0.344418	+	0.535925i	0.0180030	+	0.0280133i
$367$	5.10405			0.266429			0.133215	−	0.991087i	$-0.457470\pi$
$367$	5.10405			0.266429			0.133215	+	0.991087i	$0.457470\pi$
$368$	−9.58271	+	15.8354i	−0.499533	+	0.825476i
$369$		−	7.84821i		−	0.408562i
$370$	−0.906664	−	1.41080i	−0.0471352	−	0.0733438i
$371$	0.581187	+	0.594729i	0.0301737	+	0.0308768i
$372$	3.76154	−	8.23663i	0.195027	−	0.427049i
$373$	2.72457	+	9.27905i	0.141073	+	0.480451i	0.999471	−	0.0325342i	$-0.0103578\pi$
$373$	2.72457	+	9.27905i	0.141073	+	0.480451i	−0.858397	+	0.512985i	$0.828540\pi$
$374$	−0.257534	+	0.117612i	−0.0133168	+	0.00608157i
$375$	15.3555	−	13.3057i	0.792957	−	0.687101i
$376$	−5.02149	+	0.721981i	−0.258964	+	0.0372333i
$377$	−2.26807	+	7.72433i	−0.116811	+	0.397823i
$378$	−0.0816831	−	0.397475i	−0.00420132	−	0.0204439i
$379$	−10.1725	+	15.8287i	−0.522526	+	0.813066i	−0.997767	−	0.0667894i	$-0.978724\pi$
$379$	−10.1725	+	15.8287i	−0.522526	+	0.813066i	0.475241	+	0.879856i	$0.342361\pi$
$380$	−49.8210	−	32.0180i	−2.55577	−	1.64249i
$381$	−2.46169	−	2.13307i	−0.126116	−	0.109280i
$382$	−0.566898	+	1.93068i	−0.0290050	+	0.0987820i
$383$	1.40157	+	9.74814i	0.0716169	+	0.498107i	0.993785	+	0.111317i	$0.0355069\pi$
$383$	1.40157	+	9.74814i	0.0716169	+	0.498107i	−0.922168	+	0.386790i	$0.873584\pi$
$384$	3.60083	−	3.12014i	0.183754	−	0.159224i
$385$	3.17766	+	0.729683i	0.161949	+	0.0371881i
$386$	0.404502	−	0.118773i	0.0205886	−	0.00604537i
$387$	−6.47618	−	2.95757i	−0.329203	−	0.150342i
$388$	−5.33486	+	37.1047i	−0.270836	+	1.88371i
$389$	−13.1719	−	20.4959i	−0.667842	−	1.03918i	−0.995535	−	0.0943975i	$-0.969908\pi$
$389$	−13.1719	−	20.4959i	−0.667842	−	1.03918i	0.327693	−	0.944784i	$-0.393729\pi$
$390$	−0.909549			−0.0460568
$391$	20.6714	−	18.9129i	1.04540	−	0.956465i
$392$	1.10810	+	4.12282i	0.0559673	+	0.208234i
$393$	−6.93992	+	4.46001i	−0.350072	+	0.224978i
$394$	−0.0139797	+	0.0972309i	−0.000704287	+	0.00489842i
$395$	−17.1915	−	7.85111i	−0.864999	−	0.395032i
$396$	0.175948	+	0.599223i	0.00884170	+	0.0301121i
$397$	18.0218	−	8.23027i	0.904487	−	0.413065i	0.0918078	−	0.995777i	$-0.470735\pi$
$397$	18.0218	−	8.23027i	0.904487	−	0.413065i	0.812679	+	0.582711i	$0.198008\pi$
$398$	2.14437	+	2.47473i	0.107487	+	0.124047i
$399$	17.7275	+	9.94667i	0.887486	+	0.497956i
$400$	−37.8079	−	11.1014i	−1.89040	−	0.555070i
$401$	−0.260144	−	0.225416i	−0.0129910	−	0.0112567i	0.648341	−	0.761350i	$-0.275463\pi$
$401$	−0.260144	−	0.225416i	−0.0129910	−	0.0112567i	−0.661332	+	0.750093i	$0.730009\pi$
$402$	−1.88832	−	1.21355i	−0.0941809	−	0.0605264i
$403$	5.86057	+	3.76636i	0.291936	+	0.187616i
$404$	−17.5569	−	15.2132i	−0.873491	−	0.756884i
$405$	−3.74200	−	1.09875i	−0.185942	−	0.0545974i
$406$	−1.05121	+	1.87352i	−0.0521705	+	0.0929811i
$407$	−0.580144	−	0.669522i	−0.0287567	−	0.0331870i
$408$	−3.24100	+	1.48011i	−0.160453	+	0.0732766i
$409$	−4.68515	−	15.9562i	−0.231666	−	0.788981i	−0.990478	−	0.137672i	$-0.956038\pi$
$409$	−4.68515	−	15.9562i	−0.231666	−	0.788981i	0.758812	−	0.651310i	$-0.225780\pi$
$410$	−4.27014	−	1.95011i	−0.210887	−	0.0963089i
$411$	−3.11759	+	21.6833i	−0.153779	+	1.06956i
$412$	10.2635	−	6.59598i	0.505648	−	0.324960i
$413$	1.78018	−	2.32182i	0.0875970	−	0.114249i
$414$	0.414226	+	0.607814i	0.0203581	+	0.0298724i
$415$	24.1556			1.18575
$416$	1.48939	+	2.31754i	0.0730236	+	0.113627i
$417$	−0.469547	+	3.26577i	−0.0229938	+	0.159925i
$418$	0.338684	+	0.154672i	0.0165656	+	0.00756525i
$419$	−18.9086	+	5.55205i	−0.923744	+	0.271236i	−0.708815	−	0.705394i	$-0.750770\pi$
$419$	−18.9086	+	5.55205i	−0.923744	+	0.271236i	−0.214928	+	0.976630i	$0.568952\pi$
$420$	19.8767	+	4.56427i	0.969885	+	0.222714i
$421$	−10.2287	+	8.86318i	−0.498514	+	0.431965i	−0.867476	−	0.497480i	$-0.834259\pi$
$421$	−10.2287	+	8.86318i	−0.498514	+	0.431965i	0.368961	+	0.929445i	$0.379713\pi$
$422$	−0.209585	−	1.45770i	−0.0102024	−	0.0709596i
$423$	2.34353	−	7.98134i	0.113947	−	0.388066i
$424$	0.144864	+	0.125525i	0.00703522	+	0.00609605i
$425$	50.1785	+	32.2478i	2.43402	+	1.56425i
$426$	−0.136633	+	0.212605i	−0.00661989	+	0.0103007i
$427$	10.7647	−	2.21219i	0.520939	−	0.107056i
$428$	−0.999010	+	3.40232i	−0.0482890	+	0.164457i
$429$	−0.475589	+	0.0683794i	−0.0229617	+	0.00330139i
$430$	−3.21838	+	2.78874i	−0.155204	+	0.134485i
$431$	−31.0510	+	14.1805i	−1.49567	+	0.683051i	−0.984332	−	0.176328i	$-0.943578\pi$
$431$	−31.0510	+	14.1805i	−1.49567	+	0.683051i	−0.511341	+	0.859378i	$0.670851\pi$
$432$	1.08732	+	3.70308i	0.0523139	+	0.178165i
$433$	−11.1572	+	24.4308i	−0.536179	+	1.17407i	0.426764	+	0.904363i	$0.359653\pi$
$433$	−11.1572	+	24.4308i	−0.536179	+	1.17407i	−0.962943	+	0.269705i	$0.913074\pi$
$434$	1.29930	+	1.32958i	0.0623684	+	0.0638217i
$435$	11.1627	+	17.3695i	0.535211	+	0.832805i
$436$			18.6275i			0.892098i
$437$	−36.5997	−	4.25712i	−1.75080	−	0.203646i
$438$	1.37059			0.0654892
$439$	10.2641	+	15.9713i	0.489880	+	0.762268i	0.994903	−	0.100838i	$-0.0321524\pi$
$439$	10.2641	+	15.9713i	0.489880	+	0.762268i	−0.505023	+	0.863106i	$0.668516\pi$
$440$	0.743902	+	0.106957i	0.0354641	+	0.00509897i
$441$	−6.90397	−	1.15551i	−0.328760	−	0.0550245i
$442$	−0.383860	−	1.30731i	−0.0182583	−	0.0621822i
$443$	−1.64179	−	3.59501i	−0.0780036	−	0.170804i	0.866612	−	0.498982i	$-0.166293\pi$
$443$	−1.64179	−	3.59501i	−0.0780036	−	0.170804i	−0.944616	+	0.328178i	$0.893565\pi$
$444$	−3.62888	−	4.18795i	−0.172219	−	0.198751i
$445$	4.22017	+	29.3519i	0.200055	+	1.39142i
$446$	0.743900	−	2.53349i	0.0352247	−	0.119964i
$447$	5.39908	−	6.23087i	0.255368	−	0.294710i
$448$	−6.66701	−	18.5237i	−0.314987	−	0.875163i
$449$	−6.44486	−	4.14186i	−0.304152	−	0.195467i	0.379658	−	0.925127i	$-0.376042\pi$
$449$	−6.44486	−	4.14186i	−0.304152	−	0.195467i	−0.683810	+	0.729660i	$0.739678\pi$
$450$	−1.02544	+	1.18342i	−0.0483398	+	0.0557871i
$451$	−2.37940	−	0.698654i	−0.112042	−	0.0328984i
$452$	33.8473	−	4.86651i	1.59205	−	0.228902i
$453$	6.97369	−	6.04273i	0.327652	−	0.283912i
$454$	0.765505	+	1.67622i	0.0359269	+	0.0786690i
$455$	−5.65215	+	14.6369i	−0.264977	+	0.686190i
$456$	4.26225	+	1.94650i	0.199598	+	0.0911534i
$457$	24.8361	+	3.57089i	1.16178	+	0.167039i	0.696122	−	0.717923i	$-0.254907\pi$
$457$	24.8361	+	3.57089i	1.16178	+	0.167039i	0.465662	+	0.884963i	$0.345816\pi$
$458$	1.72770	−	1.11033i	0.0807303	−	0.0518822i
$459$		−	5.84214i		−	0.272688i
$460$	−36.4357	+	6.24707i	−1.69882	+	0.291271i
$461$			20.4941i			0.954504i	0.878766	+	0.477252i	$0.158367\pi$
$461$			20.4941i			0.954504i	−0.878766	+	0.477252i	$0.841633\pi$
$462$	−0.127777	−	0.0106191i	−0.00594472	−	0.000494046i
$463$	−2.11065	+	14.6799i	−0.0980904	+	0.682234i	0.880140	+	0.474714i	$0.157448\pi$
$463$	−2.11065	+	14.6799i	−0.0980904	+	0.682234i	−0.978231	+	0.207520i	$0.933461\pi$
$464$	8.48794	−	18.5860i	0.394043	−	0.862833i
$465$	17.1434	−	5.03375i	0.795005	−	0.233435i
$466$	1.13996	+	2.49616i	0.0528075	+	0.115632i
$467$	6.73405	+	7.77150i	0.311615	+	0.359622i	0.889855	−	0.456244i	$-0.150806\pi$
$467$	6.73405	+	7.77150i	0.311615	+	0.359622i	−0.578240	+	0.815867i	$0.696260\pi$
$468$	−2.97488	+	0.427723i	−0.137514	+	0.0197715i
$469$	−31.2635	+	22.8466i	−1.44362	+	1.05496i
$470$	−3.76026	−	3.25828i	−0.173448	−	0.150293i
$471$	−3.02900	+	4.71321i	−0.139569	+	0.217173i
$472$	0.364616	−	0.567354i	0.0167828	−	0.0261146i
$473$	−1.47318	+	1.70014i	−0.0677371	+	0.0781727i
$474$	0.713134	+	0.209395i	0.0327553	+	0.00961783i
$475$	−11.1635	−	77.6440i	−0.512217	−	3.56255i
$476$	1.82835	+	30.4953i	0.0838023	+	1.39775i
$477$	−0.285895	+	0.130564i	−0.0130902	+	0.00597811i
$478$	−3.52507	+	1.03506i	−0.161233	+	0.0473423i
$479$	−9.96378	+	21.8176i	−0.455257	+	0.996873i	0.533286	+	0.845935i	$0.320957\pi$
$479$	−9.96378	+	21.8176i	−0.455257	+	0.996873i	−0.988543	+	0.150938i	$0.951770\pi$
$480$	6.99358	+	1.00552i	0.319212	+	0.0458957i
$481$	3.58657	−	2.30495i	0.163534	−	0.105097i
$482$	0.299857			0.0136581
$483$	12.3553	−	2.88885i	0.562188	−	0.131447i
$484$	−21.5439			−0.979269
$485$	−62.2257	+	39.9901i	−2.82553	+	1.81585i
$486$	0.151810	+	0.0218270i	0.00688623	+	0.000990091i
$487$	−16.8700	+	36.9401i	−0.764452	+	1.67392i	−0.0259518	+	0.999663i	$0.508262\pi$
$487$	−16.8700	+	36.9401i	−0.764452	+	1.67392i	−0.738500	+	0.674253i	$0.764466\pi$
$488$	2.43062	−	0.713695i	0.110029	−	0.0323075i
$489$	−0.110362	+	0.0504005i	−0.00499072	+	0.00227919i
$490$	−2.34419	+	3.46927i	−0.105900	+	0.156725i
$491$	5.61128	+	39.0273i	0.253234	+	1.76128i	0.578525	+	0.815665i	$0.303629\pi$
$491$	5.61128	+	39.0273i	0.253234	+	1.76128i	−0.325291	+	0.945614i	$0.605462\pi$
$492$	−14.8835	−	4.37018i	−0.670999	−	0.197023i
$493$	−20.2544	+	23.3748i	−0.912211	+	1.05275i
$494$	−0.968733	+	1.50738i	−0.0435854	+	0.0678202i
$495$	−0.666232	+	1.03668i	−0.0299449	+	0.0465952i
$496$	−13.3626	−	11.5788i	−0.600000	−	0.519903i
$497$	2.57228	+	3.51994i	0.115383	+	0.157891i
$498$	−0.940278	+	0.135192i	−0.0421349	+	0.00605808i
$499$	19.2552	+	22.2217i	0.861980	+	0.994778i	0.999991	+	0.00434705i	$0.00138371\pi$
$499$	19.2552	+	22.2217i	0.861980	+	0.994778i	−0.138011	+	0.990431i	$0.544071\pi$
$500$	−16.6825	−	36.5296i	−0.746065	−	1.63365i
$501$	−1.39844	+	0.410620i	−0.0624778	+	0.0183451i
$502$	−0.254815	+	0.557966i	−0.0113729	+	0.0249033i
$503$	1.60036	−	11.1308i	0.0713567	−	0.496297i	−0.922533	−	0.385918i	$-0.873885\pi$
$503$	1.60036	−	11.1308i	0.0713567	−	0.496297i	0.993890	−	0.110378i	$-0.0352063\pi$
$504$	−1.60804	−	0.133639i	−0.0716277	−	0.00595274i
$505$		−	45.8397i		−	2.03984i
$506$	0.221150	−	0.0714758i	0.00983131	−	0.00317749i
$507$			10.6877i			0.474658i
$508$	−5.41595	+	3.48062i	−0.240294	+	0.154428i
$509$	29.6469	+	4.26258i	1.31408	+	0.188936i	0.763478	−	0.645834i	$-0.223490\pi$
$509$	29.6469	+	4.26258i	1.31408	+	0.188936i	0.550599	+	0.834770i	$0.314399\pi$
$510$	−3.17865	−	1.45164i	−0.140753	−	0.0642798i
$511$	8.51714	−	22.0562i	0.376776	−	0.975708i
$512$	−4.86017	−	10.6423i	−0.214791	−	0.470327i
$513$	−5.80643	+	5.03130i	−0.256360	+	0.222137i
$514$	3.92470	−	0.564287i	0.173111	−	0.0248896i
$515$	23.0984	+	6.78231i	1.01784	+	0.298864i
$516$	−9.21497	+	10.6346i	−0.405667	+	0.468164i
$517$	−2.21114	−	1.42101i	−0.0972457	−	0.0624960i
$518$	1.07047	−	0.385280i	0.0470336	−	0.0169282i
$519$	8.58543	−	9.90812i	0.376859	−	0.434918i
$520$	−1.01897	+	3.47030i	−0.0446848	+	0.152183i
$521$	−0.236360	−	1.64392i	−0.0103551	−	0.0720214i	0.983989	−	0.178231i	$-0.0570375\pi$
$521$	−0.236360	−	1.64392i	−0.0103551	−	0.0720214i	−0.994344	+	0.106210i	$0.966128\pi$
$522$	−0.531729	−	0.613648i	−0.0232732	−	0.0268586i
$523$	−17.1434	−	37.5389i	−0.749631	−	1.64146i	−0.767028	−	0.641613i	$-0.778265\pi$
$523$	−17.1434	−	37.5389i	−0.749631	−	1.64146i	0.0173976	−	0.999849i	$-0.494462\pi$
$524$	4.59363	+	15.6445i	0.200674	+	0.683432i
$525$	12.6719	+	23.8560i	0.553048	+	1.04116i
$526$	−0.308335	−	0.0443318i	−0.0134440	−	0.00193296i
$527$	14.4701	+	22.5160i	0.630329	+	0.980811i
$528$	1.21948			0.0530713
$529$	−18.6494	+	13.4611i	−0.810842	+	0.585265i
$530$			0.187995i			0.00816599i
$531$	0.597853	+	0.930277i	0.0259446	+	0.0403706i
$532$	28.7344	−	28.0801i	1.24579	−	1.21742i
$533$	4.95763	−	10.8557i	0.214739	−	0.470212i
$534$	−0.328547	−	1.11893i	−0.0142176	−	0.0484208i
$535$	−6.36457	+	2.90660i	−0.275164	+	0.125663i
$536$	−6.74568	+	5.84516i	−0.291369	+	0.252473i
$537$	−21.7503	+	3.12722i	−0.938596	+	0.134950i
$538$	−0.0438078	+	0.149196i	−0.00188869	+	0.00643228i
$539$	−0.964922	+	1.99026i	−0.0415621	+	0.0857266i
$540$	−4.16738	+	6.48457i	−0.179335	+	0.279051i
$541$	−2.59298	−	1.66641i	−0.111481	−	0.0716446i	0.483712	−	0.875227i	$-0.339288\pi$
$541$	−2.59298	−	1.66641i	−0.111481	−	0.0716446i	−0.595193	+	0.803583i	$0.702925\pi$
$542$	0.339480	+	0.294161i	0.0145819	+	0.0126353i
$543$	4.04796	−	13.7861i	0.173714	−	0.591617i
$544$	1.50627	+	10.4763i	0.0645807	+	0.449168i
$545$	−27.7782	+	24.0699i	−1.18989	+	1.03104i
$546$	0.138096	−	0.601388i	0.00590996	−	0.0257370i
$547$	1.70078	−	0.499393i	0.0727200	−	0.0213525i	−0.245170	−	0.969480i	$-0.578844\pi$
$547$	1.70078	−	0.499393i	0.0727200	−	0.0213525i	0.317890	+	0.948128i	$0.397026\pi$
$548$	39.3846	+	17.9863i	1.68243	+	0.768338i
$549$	−0.591132	+	4.11141i	−0.0252289	+	0.175471i
$550$	0.267501	+	0.416240i	0.0114063	+	0.0177485i
$551$	40.6752			1.73282
$552$	2.78311	−	0.899504i	0.118457	−	0.0382854i
$553$	7.80127	−	10.1749i	0.331744	−	0.432680i
$554$	2.08661	−	1.34098i	0.0886516	−	0.0569729i
$555$	1.55613	−	10.8231i	0.0660539	−	0.459415i
$556$	5.93180	+	2.70896i	0.251564	+	0.114886i
$557$	−4.17107	−	14.2054i	−0.176734	−	0.601900i	−0.999441	−	0.0334347i	$-0.989355\pi$
$557$	−4.17107	−	14.2054i	−0.176734	−	0.601900i	0.822707	−	0.568466i	$-0.192463\pi$
$558$	−0.639147	+	0.291889i	−0.0270573	+	0.0123566i
$559$	−7.08962	−	8.18186i	−0.299859	−	0.346056i
$560$	19.4863	−	34.7296i	0.823448	−	1.46760i
$561$	−1.77120	−	0.520072i	−0.0747802	−	0.0219574i
$562$	−2.30987	−	2.00151i	−0.0974358	−	0.0844286i
$563$	−2.89841	−	1.86269i	−0.122153	−	0.0785032i	0.478137	−	0.878285i	$-0.341312\pi$
$563$	−2.89841	−	1.86269i	−0.122153	−	0.0785032i	−0.600291	+	0.799782i	$0.704948\pi$
$564$	−13.8310	−	8.88863i	−0.582389	−	0.374279i
$565$	50.9937	+	44.1863i	2.14532	+	1.85893i
$566$	−1.99543	−	0.585910i	−0.0838740	−	0.0246276i
$567$	1.29463	−	2.30736i	0.0543694	−	0.0969002i
$568$	0.658103	+	0.759492i	0.0276134	+	0.0318676i
$569$	24.5111	−	11.1938i	1.02756	−	0.469270i	0.170973	−	0.985276i	$-0.445309\pi$
$569$	24.5111	−	11.1938i	1.02756	−	0.469270i	0.856585	+	0.516005i	$0.172582\pi$
$570$	1.29471	+	4.40939i	0.0542296	+	0.184689i
$571$	13.8887	+	6.34274i	0.581223	+	0.265436i	0.684255	−	0.729242i	$-0.260127\pi$
$571$	13.8887	+	6.34274i	0.581223	+	0.265436i	−0.103033	+	0.994678i	$0.532855\pi$
$572$	−0.135150	+	0.939992i	−0.00565092	+	0.0393030i
$573$	−11.0370	+	7.09306i	−0.461078	+	0.296317i
$574$	1.93773	−	2.52730i	0.0808792	−	0.105488i
$575$	−37.8573	−	31.0542i	−1.57876	−	1.29505i
$576$	7.44098			0.310041
$577$	−6.12698	−	9.53377i	−0.255070	−	0.396896i	0.689977	−	0.723831i	$-0.257621\pi$
$577$	−6.12698	−	9.53377i	−0.255070	−	0.396896i	−0.945047	+	0.326935i	$0.893984\pi$
$578$	0.373908	−	2.60059i	0.0155525	−	0.108170i
$579$	2.50036	+	1.14187i	0.103911	+	0.0474547i
$580$	39.1557	−	11.4971i	1.62585	−	0.477393i
$581$	−3.66753	+	15.9715i	−0.152155	+	0.662611i
$582$	2.19837	−	1.90490i	0.0911256	−	0.0789608i
$583$	0.0141334	+	0.0982998i	0.000585344	+	0.00407116i
$584$	1.53547	−	5.22934i	0.0635383	−	0.216392i
$585$	−4.48189	−	3.88358i	−0.185303	−	0.160566i
$586$	2.71250	+	1.74322i	0.112053	+	0.0720118i
$587$	−7.21304	+	11.2237i	−0.297714	+	0.463252i	−0.957595	−	0.288118i	$-0.906970\pi$
$587$	−7.21304	+	11.2237i	−0.297714	+	0.463252i	0.659881	+	0.751370i	$0.270607\pi$
$588$	−6.03573	+	12.4494i	−0.248909	+	0.513403i
$589$	9.91655	−	33.7727i	0.408604	−	1.39158i
$590$	0.654708	−	0.0941328i	0.0269539	−	0.00387539i
$591$	−0.484041	+	0.419424i	−0.0199108	+	0.0172528i
$592$	−9.84282	+	4.49507i	−0.404537	+	0.184746i
$593$	−9.41855	−	32.0766i	−0.386773	−	1.31723i	−0.891136	−	0.453737i	$-0.850091\pi$
$593$	−9.41855	−	32.0766i	−0.386773	−	1.31723i	0.504362	−	0.863492i	$-0.331728\pi$
$594$	0.0201317	−	0.0440822i	0.000826012	−	0.00180872i
$595$	−43.1134	+	42.1317i	−1.76748	+	1.72723i
$596$	−8.80991	−	13.7085i	−0.360868	−	0.561522i
$597$			21.3505i			0.873816i
$598$	0.189011	+	1.10239i	0.00772922	+	0.0450802i
$599$	3.92761			0.160478			0.0802389	−	0.996776i	$-0.474432\pi$
$599$	3.92761			0.160478			0.0802389	+	0.996776i	$0.474432\pi$
$600$	3.36643	+	5.23827i	0.137434	+	0.213851i
$601$	18.1571	+	2.61060i	0.740645	+	0.106489i	0.502302	−	0.864692i	$-0.332487\pi$
$601$	18.1571	+	2.61060i	0.740645	+	0.106489i	0.238343	+	0.971181i	$0.423396\pi$
$602$	−1.35525	−	2.55138i	−0.0552359	−	0.103986i
$603$	−4.12328	−	14.0426i	−0.167913	−	0.571859i
$604$	−7.57632	−	16.5898i	−0.308276	−	0.675031i
$605$	−27.8384	−	32.1272i	−1.13179	−	1.30616i
$606$	0.256550	+	1.78435i	0.0104216	+	0.0724841i
$607$	9.63264	−	32.8057i	0.390977	−	1.33154i	−0.495434	−	0.868645i	$-0.664991\pi$
$607$	9.63264	−	32.8057i	0.390977	−	1.33154i	0.886411	−	0.462899i	$-0.153191\pi$
$608$	9.11509	−	10.5194i	0.369666	−	0.426617i
$609$	−13.1794	+	4.74351i	−0.534057	+	0.192217i
$610$	2.09010	+	1.34322i	0.0846256	+	0.0543856i
$611$	8.28331	−	9.55945i	0.335107	−	0.386734i
$612$	−11.0791	−	3.25312i	−0.447847	−	0.131500i
$613$	−3.90188	+	0.561006i	−0.157595	+	0.0226588i	−0.220661	−	0.975351i	$-0.570821\pi$
$613$	−3.90188	+	0.561006i	−0.157595	+	0.0226588i	0.0630654	+	0.998009i	$0.479912\pi$
$614$	0.835867	−	0.724283i	0.0337329	−	0.0292297i
$615$	−12.7150	−	27.8419i	−0.512717	−	1.12269i
$616$	−0.183665	+	0.475623i	−0.00740007	+	0.0191634i
$617$	37.6375	+	17.1885i	1.51523	+	0.691982i	0.987527	−	0.157447i	$-0.0503265\pi$
$617$	37.6375	+	17.1885i	1.51523	+	0.691982i	0.527702	+	0.849430i	$0.323054\pi$
$618$	−0.937084	−	0.134732i	−0.0376950	−	0.00541973i
$619$	23.0166	−	14.7919i	0.925115	−	0.594535i	0.0109778	−	0.999940i	$-0.496506\pi$
$619$	23.0166	−	14.7919i	0.925115	−	0.594535i	0.914138	+	0.405404i	$0.132869\pi$
$620$		−	35.3140i		−	1.41824i
$621$	−0.554095	+	4.76371i	−0.0222351	+	0.191161i
$622$			0.582680i			0.0233633i
$623$	−20.0480	−	1.66613i	−0.803208	−	0.0667520i
$624$	−0.835204	+	5.80897i	−0.0334349	+	0.232545i
$625$	11.7113	−	25.6441i	0.468451	−	1.02576i
$626$	−1.64746	+	0.483739i	−0.0658459	+	0.0193341i
$627$	1.00848	+	2.20827i	0.0402749	+	0.0881897i
$628$	7.25155	+	8.36874i	0.289368	+	0.333949i
$629$	16.2129	−	2.33106i	0.646451	−	0.0929456i
$630$	−0.933728	−	1.27773i	−0.0372006	−	0.0509058i
$631$	−27.4594	−	23.7937i	−1.09314	−	0.947213i	−0.0943108	−	0.995543i	$-0.530065\pi$
$631$	−27.4594	−	23.7937i	−1.09314	−	0.947213i	−0.998831	+	0.0483296i	$0.984610\pi$
$632$	1.59785	−	2.48631i	0.0635592	−	0.0989000i
$633$	5.19130	−	8.07782i	0.206336	−	0.321064i
$634$	1.05940	−	1.22262i	0.0420743	−	0.0485564i
$635$	−12.1888	−	3.57895i	−0.483697	−	0.142026i
$636$	0.0884063	+	0.614879i	0.00350554	+	0.0243815i
$637$	−8.81968	−	5.95947i	−0.349448	−	0.236123i
$638$	−0.233379	+	0.106581i	−0.00923956	+	0.00421957i
$639$	−1.58105	+	0.464238i	−0.0625453	+	0.0183650i
$640$	7.71914	−	16.9026i	0.305126	−	0.668133i
$641$	28.0494	+	4.03289i	1.10788	+	0.159290i	0.671883	−	0.740657i	$-0.265486\pi$
$641$	28.0494	+	4.03289i	1.10788	+	0.159290i	0.436000	+	0.899947i	$0.356395\pi$
$642$	0.231479	−	0.148762i	0.00913573	−	0.00587118i
$643$	−19.9096			−0.785158			−0.392579	−	0.919718i	$-0.628417\pi$
$643$	−19.9096			−0.785158			−0.392579	+	0.919718i	$0.628417\pi$
$644$	1.40147	−	25.0395i	0.0552257	−	0.986694i
$645$	−27.7662			−1.09329
$646$	−5.79126	+	3.72182i	−0.227854	+	0.146433i
$647$	−15.6964	−	2.25680i	−0.617089	−	0.0887240i	−0.173320	−	0.984866i	$-0.555450\pi$
$647$	−15.6964	−	2.25680i	−0.617089	−	0.0887240i	−0.443768	+	0.896142i	$0.646359\pi$
$648$	0.253352	−	0.554763i	0.00995259	−	0.0217931i
$649$	0.335260	−	0.0984412i	0.0131601	−	0.00386416i
$650$	−2.16595	+	0.989157i	−0.0849556	+	0.0387979i
$651$	0.725418	+	12.0993i	0.0284314	+	0.474211i
$652$	0.0341267	+	0.237356i	0.00133650	+	0.00929560i
$653$	−2.02618	−	0.594939i	−0.0792904	−	0.0232818i	0.241847	−	0.970314i	$-0.422247\pi$
$653$	−2.02618	−	0.594939i	−0.0792904	−	0.0232818i	−0.321137	+	0.947033i	$0.604065\pi$
$654$	0.946577	−	1.09241i	0.0370141	−	0.0427165i
$655$	−17.3940	+	27.0655i	−0.679638	+	1.05754i
$656$	−16.3758	+	25.4812i	−0.639366	+	0.994873i
$657$	6.75370	+	5.85211i	0.263487	+	0.228313i
$658$	2.72527	−	1.99155i	0.106242	−	0.0776389i
$659$	−1.85554	+	0.266787i	−0.0722817	+	0.0103925i	−0.178361	−	0.983965i	$-0.557079\pi$
$659$	−1.85554	+	0.266787i	−0.0722817	+	0.0103925i	0.106079	+	0.994358i	$0.466170\pi$
$660$	1.59499	+	1.84072i	0.0620849	+	0.0716498i
$661$	−1.37331	−	3.00712i	−0.0534154	−	0.116963i	0.881042	−	0.473037i	$-0.156842\pi$
$661$	−1.37331	−	3.00712i	−0.0534154	−	0.116963i	−0.934458	+	0.356074i	$0.884115\pi$
$662$	5.07423	−	1.48993i	0.197215	−	0.0579077i
$663$	3.69041	−	8.08087i	0.143324	−	0.313835i
$664$	−0.537586	+	3.73899i	−0.0208624	+	0.145101i
$665$	79.0039	+	6.56576i	3.06364	+	0.254609i
$666$			0.430007i			0.0166624i
$667$	18.7325	−	17.1389i	0.725326	−	0.663623i
$668$			2.88068i			0.111457i
$669$	14.4831	−	9.30772i	0.559949	−	0.359857i
$670$	−8.66500	−	1.24584i	−0.334758	−	0.0481309i
$671$	1.19386	+	0.545219i	0.0460886	+	0.0210479i
$672$	−1.72667	+	4.47144i	−0.0666079	+	0.172489i
$673$	4.91787	+	10.7686i	0.189570	+	0.415100i	0.980422	−	0.196907i	$-0.0630897\pi$
$673$	4.91787	+	10.7686i	0.189570	+	0.415100i	−0.790852	+	0.612007i	$0.790362\pi$
$674$	−3.85701	+	3.34212i	−0.148567	+	0.128734i
$675$	−10.1059	+	1.45301i	−0.388977	+	0.0559265i
$676$	20.2684	+	5.95133i	0.779552	+	0.228897i
$677$	−14.4340	+	16.6578i	−0.554746	+	0.640211i	−0.961982	−	0.273112i	$-0.911947\pi$
$677$	−14.4340	+	16.6578i	−0.554746	+	0.640211i	0.407237	+	0.913323i	$0.366492\pi$
$678$	−2.23227	−	1.43459i	−0.0857297	−	0.0550951i
$679$	−16.9935	−	47.2149i	−0.652150	−	1.81194i
$680$	−9.09965	+	10.5016i	−0.348956	+	0.402716i
$681$	−3.38501	+	11.5283i	−0.129714	+	0.441765i
$682$	0.0315966	+	0.219759i	0.00120990	+	0.00841501i
$683$	−7.06958	−	8.15873i	−0.270510	−	0.312185i	0.604199	−	0.796833i	$-0.293493\pi$
$683$	−7.06958	−	8.15873i	−0.270510	−	0.312185i	−0.874709	+	0.484648i	$0.838948\pi$
$684$	6.30820	+	13.8130i	0.241200	+	0.528155i
$685$	24.0696	+	81.9734i	0.919651	+	3.13204i
$686$	−1.93794	−	2.07670i	−0.0739908	−	0.0792886i
$687$	13.2543	+	1.90568i	0.505682	+	0.0727062i
$688$	14.8554	+	23.1154i	0.566356	+	0.881268i
$689$	−0.477927			−0.0182076
$690$	2.45421	+	1.48516i	0.0934303	+	0.0565389i
$691$			44.6466i			1.69844i	0.528040	+	0.849219i	$0.322927\pi$
$691$			44.6466i			1.69844i	−0.528040	+	0.849219i	$0.677073\pi$
$692$	−14.0092	−	21.7988i	−0.532551	−	0.828665i
$693$	−0.584291	−	0.597906i	−0.0221954	−	0.0227126i
$694$	−0.445643	+	0.975823i	−0.0169164	+	0.0370417i
$695$	3.62517	+	12.3462i	0.137511	+	0.468318i
$696$	−2.93701	+	1.34129i	−0.111327	+	0.0508414i
$697$	34.6514	−	30.0256i	1.31251	−	1.13730i
$698$	2.90533	−	0.417724i	0.109968	−	0.0158111i
$699$	−5.04081	+	17.1674i	−0.190661	+	0.649331i
$700$	52.2971	−	10.7473i	1.97665	−	0.406210i
$701$	14.0858	−	21.9179i	0.532012	−	0.827827i	−0.466376	−	0.884587i	$-0.654441\pi$
$701$	14.0858	−	21.9179i	0.532012	−	0.827827i	0.998388	+	0.0567598i	$0.0180769\pi$
$702$	0.196196	+	0.126088i	0.00740495	+	0.00475887i
$703$	−16.2795	−	14.1063i	−0.613994	−	0.532029i
$704$	0.662402	−	2.25593i	0.0249652	−	0.0850237i
$705$	−4.61686	−	32.1110i	−0.173881	−	1.20937i
$706$	−2.12943	+	1.84516i	−0.0801423	+	0.0694437i
$707$	30.3089	+	6.95979i	1.13988	+	0.261750i
$708$	2.09710	−	0.615764i	0.0788138	−	0.0231418i
$709$	27.0919	+	12.3724i	1.01746	+	0.464657i	0.853102	−	0.521744i	$-0.174718\pi$
$709$	27.0919	+	12.3724i	1.01746	+	0.464657i	0.164355	+	0.986401i	$0.447446\pi$
$710$	−0.140268	+	0.975587i	−0.00526417	+	0.0366131i
$711$	2.61996	+	4.07674i	0.0982563	+	0.152890i
$712$	−4.63724			−0.173788
$713$	−9.66352	−	19.7321i	−0.361902	−	0.738972i
$714$	1.44243	−	1.88130i	0.0539815	−	0.0704059i
$715$	−1.57639	+	1.01309i	−0.0589538	+	0.0378873i
$716$	−6.18089	+	42.9890i	−0.230991	+	1.60657i
$717$	−21.7896	−	9.95097i	−0.813747	−	0.371626i
$718$	0.877990	+	2.99016i	0.0327663	+	0.111592i
$719$	−4.61158	+	2.10604i	−0.171983	+	0.0785420i	−0.499546	−	0.866287i	$-0.666500\pi$
$719$	−4.61158	+	2.10604i	−0.171983	+	0.0785420i	0.327563	+	0.944829i	$0.393773\pi$
$720$	9.85674	+	11.3753i	0.367339	+	0.423932i
$721$	−7.99143	+	14.2428i	−0.297616	+	0.530429i
$722$	5.89056	+	1.72962i	0.219224	+	0.0643699i
$723$	1.47758	+	1.28033i	0.0549516	+	0.0476158i
$724$	−23.8901	−	15.3532i	−0.887868	−	0.570598i
$725$	45.4720	+	29.2231i	1.68879	+	1.08532i
$726$	1.26344	+	1.09478i	0.0468906	+	0.0406309i
$727$	−34.5922	−	10.1572i	−1.28295	−	0.376709i	−0.431964	−	0.901891i	$-0.642179\pi$
$727$	−34.5922	−	10.1572i	−1.28295	−	0.376709i	−0.850990	+	0.525182i	$0.823997\pi$
$728$	−2.13983	−	1.20063i	−0.0793072	−	0.0444982i
$729$	0.654861	+	0.755750i	0.0242541	+	0.0279907i
$730$	4.86222	−	2.22050i	0.179959	−	0.0821845i
$731$	−11.7182	−	39.9086i	−0.433414	−	1.47607i
$732$	7.46779	+	3.41042i	0.276017	+	0.126053i
$733$	4.83254	−	33.6111i	0.178494	−	1.24145i	−0.681756	−	0.731580i	$-0.738783\pi$
$733$	4.83254	−	33.6111i	0.178494	−	1.24145i	0.860250	−	0.509873i	$-0.170308\pi$
$734$	−0.658544	+	0.423221i	−0.0243073	+	0.0156214i
$735$	−26.3642	+	7.08595i	−0.972459	+	0.261369i
$736$	−0.234597	−	8.68532i	−0.00864736	−	0.320145i
$737$	−4.62445			−0.170344
$738$	0.650763	+	1.01261i	0.0239549	+	0.0372746i
$739$	−0.126099	+	0.877040i	−0.00463864	+	0.0322624i	−0.992009	−	0.126165i	$-0.959733\pi$
$739$	−0.126099	+	0.877040i	−0.00463864	+	0.0322624i	0.987371	+	0.158427i	$0.0506423\pi$
$740$	−19.6586	−	8.97777i	−0.722664	−	0.330029i
$741$	−11.2097	+	3.29147i	−0.411799	+	0.120915i
$742$	−0.124301	−	0.0285431i	−0.00456324	−	0.00104785i
$743$	−17.4389	+	15.1109i	−0.639771	+	0.554364i	−0.913192	−	0.407530i	$-0.866390\pi$
$743$	−17.4389	+	15.1109i	−0.639771	+	0.554364i	0.273421	+	0.961894i	$0.411845\pi$
$744$	0.397634	+	2.76561i	0.0145780	+	0.101392i
$745$	9.05879	−	30.8514i	0.331888	−	1.13031i
$746$	−1.12094	−	0.971301i	−0.0410406	−	0.0355618i
$747$	−5.21054	−	3.34861i	−0.190644	−	0.122519i
$748$	−1.97254	+	3.06934i	−0.0721234	+	0.112226i
$749$	−0.955498	−	4.64952i	−0.0349131	−	0.169890i
$750$	−0.877945	+	2.99001i	−0.0320580	+	0.109180i
$751$	33.5767	−	4.82761i	1.22523	−	0.176162i	0.500834	−	0.865543i	$-0.333027\pi$
$751$	33.5767	−	4.82761i	1.22523	−	0.176162i	0.724399	+	0.689381i	$0.242118\pi$
$752$	−24.2624	+	21.0235i	−0.884759	+	0.766648i
$753$	−3.63802	+	1.66143i	−0.132577	+	0.0605458i
$754$	−0.347856	−	1.18469i	−0.0126682	−	0.0431438i
$755$	14.9496	−	32.7350i	0.544071	−	1.19135i
$756$	−3.65482	−	3.73999i	−0.132925	−	0.136022i
$757$	−10.2213	−	15.9046i	−0.371498	−	0.578062i	0.604294	−	0.796761i	$-0.293455\pi$
$757$	−10.2213	−	15.9046i	−0.371498	−	0.578062i	−0.975792	+	0.218699i	$0.929819\pi$
$758$		−	2.88577i		−	0.104816i
$759$	1.39492	+	0.592059i	0.0506325	+	0.0214904i
$760$	18.2741			0.662871
$761$	9.45502	+	14.7123i	0.342744	+	0.533320i	0.969244	−	0.246101i	$-0.0791496\pi$
$761$	9.45502	+	14.7123i	0.342744	+	0.533320i	−0.626500	+	0.779421i	$0.715513\pi$
$762$	0.494488	+	0.0710967i	0.0179134	+	0.00257556i
$763$	−11.6973	−	22.0213i	−0.423472	−	0.797223i
$764$	7.30556	+	24.8804i	0.264306	+	0.900143i
$765$	−9.46490	−	20.7252i	−0.342204	−	0.749323i
$766$	−0.989138	−	1.14153i	−0.0357390	−	0.0412450i
$767$	0.239307	+	1.66442i	0.00864089	+	0.0600987i
$768$	3.98686	−	13.5780i	0.143863	−	0.489953i
$769$	−8.44912	+	9.75080i	−0.304683	+	0.351623i	−0.887357	−	0.461083i	$-0.847461\pi$
$769$	−8.44912	+	9.75080i	−0.304683	+	0.351623i	0.582674	+

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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.r (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.129024 + 0.0829186i) q^{2} +(-0.989821 - 0.142315i) q^{3} +(-0.821058 + 1.79787i) q^{4} +(-3.74200 + 1.09875i) q^{5} +(0.139511 - 0.0637126i) q^{6} +(-0.158342 - 2.64101i) q^{7} +(-0.0867944 - 0.603668i) q^{8} +(0.959493 + 0.281733i) q^{9} +O(q^{10})\)	\(q+(-0.129024 + 0.0829186i) q^{2} +(-0.989821 - 0.142315i) q^{3} +(-0.821058 + 1.79787i) q^{4} +(-3.74200 + 1.09875i) q^{5} +(0.139511 - 0.0637126i) q^{6} +(-0.158342 - 2.64101i) q^{7} +(-0.0867944 - 0.603668i) q^{8} +(0.959493 + 0.281733i) q^{9} +(0.391701 - 0.452047i) q^{10} +(0.170830 - 0.265816i) q^{11} +(1.06856 - 1.66272i) q^{12} +(1.14921 + 0.995794i) q^{13} +(0.239419 + 0.327624i) q^{14} +(3.86028 - 0.555025i) q^{15} +(-2.52738 - 2.91675i) q^{16} +(2.42691 + 5.31419i) q^{17} +(-0.147158 + 0.0432096i) q^{18} +(3.19164 - 6.98871i) q^{19} +(1.09699 - 7.62976i) q^{20} +(-0.219124 + 2.63666i) q^{21} +0.0484616i q^{22} +(-1.47490 - 4.56341i) q^{23} +0.609876i q^{24} +(8.58907 - 5.51986i) q^{25} +(-0.230845 - 0.0331905i) q^{26} +(-0.909632 - 0.415415i) q^{27} +(4.87819 + 1.88374i) q^{28} +(2.19928 + 4.81575i) q^{29} +(-0.452047 + 0.391701i) q^{30} +(4.53470 - 0.651992i) q^{31} +(1.73829 + 0.510408i) q^{32} +(-0.206920 + 0.238799i) q^{33} +(-0.753775 - 0.484422i) q^{34} +(3.49433 + 9.70869i) q^{35} +(-1.29432 + 1.49372i) q^{36} +(0.789895 - 2.69013i) q^{37} +(0.167697 + 1.16636i) q^{38} +(-0.995794 - 1.14921i) q^{39} +(0.988067 + 2.16356i) q^{40} +(-2.21110 - 7.53031i) q^{41} +(-0.190356 - 0.358362i) q^{42} +(-7.04710 - 1.01322i) q^{43} +(0.337641 + 0.525380i) q^{44} -3.89998 q^{45} +(0.568688 + 0.466492i) q^{46} -8.31829i q^{47} +(2.08656 + 3.24675i) q^{48} +(-6.94986 + 0.836365i) q^{49} +(-0.650496 + 1.42439i) q^{50} +(-1.64592 - 5.60549i) q^{51} +(-2.73387 + 1.24852i) q^{52} +(-0.237530 + 0.205821i) q^{53} +(0.151810 - 0.0218270i) q^{54} +(-0.347179 + 1.18238i) q^{55} +(-1.58055 + 0.324811i) q^{56} +(-4.15375 + 6.46336i) q^{57} +(-0.683075 - 0.438986i) q^{58} +(0.835725 + 0.724160i) q^{59} +(-2.17166 + 7.39599i) q^{60} +(0.591132 + 4.11141i) q^{61} +(-0.531023 + 0.460134i) q^{62} +(0.592130 - 2.57864i) q^{63} +(7.13956 - 2.09637i) q^{64} +(-5.39447 - 2.46357i) q^{65} +(0.00689680 - 0.0479683i) q^{66} +(-7.91252 - 12.3121i) q^{67} -11.5468 q^{68} +(0.810443 + 4.72686i) q^{69} +(-1.25588 - 0.962907i) q^{70} +(-1.38621 + 0.890866i) q^{71} +(0.0867944 - 0.603668i) q^{72} +(8.12885 + 3.71232i) q^{73} +(0.121147 + 0.412588i) q^{74} +(-9.28720 + 4.24132i) q^{75} +(9.94426 + 11.4763i) q^{76} +(-0.729072 - 0.409073i) q^{77} +(0.223772 + 0.0657054i) q^{78} +(3.66239 + 3.17348i) q^{79} +(12.6623 + 8.13754i) q^{80} +(0.841254 + 0.540641i) q^{81} +(0.909687 + 0.788248i) q^{82} +(-5.94289 - 1.74499i) q^{83} +(-4.56045 - 2.55881i) q^{84} +(-14.9205 - 17.2192i) q^{85} +(0.993258 - 0.453606i) q^{86} +(-1.49154 - 5.07972i) q^{87} +(-0.175292 - 0.0800531i) q^{88} +(1.08210 - 7.52618i) q^{89} +(0.503190 - 0.323381i) q^{90} +(2.44793 - 3.19274i) q^{91} +(9.41537 + 1.09516i) q^{92} -4.58134 q^{93} +(0.689741 + 1.07326i) q^{94} +(-4.26427 + 29.6586i) q^{95} +(-1.64796 - 0.752597i) q^{96} +(18.1980 - 5.34340i) q^{97} +(0.827347 - 0.684183i) q^{98} +(0.238799 - 0.206920i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q + 4 q^{2} - 36 q^{4} + 12 q^{8} + 32 q^{9}+O(q^{10}) \) 320 * q + 4 * q^2 - 36 * q^4 + 12 * q^8 + 32 * q^9	\( 320 q + 4 q^{2} - 36 q^{4} + 12 q^{8} + 32 q^{9} - 4 q^{18} + 52 q^{23} - 68 q^{25} - 88 q^{28} + 24 q^{32} + 28 q^{35} + 14 q^{36} - 44 q^{37} + 110 q^{42} - 44 q^{43} - 154 q^{44} + 40 q^{46} - 16 q^{49} - 166 q^{50} - 44 q^{51} + 110 q^{56} - 44 q^{57} - 62 q^{58} - 84 q^{64} + 72 q^{70} - 40 q^{71} - 12 q^{72} + 22 q^{74} + 72 q^{77} - 8 q^{78} - 88 q^{79} - 32 q^{81} - 304 q^{85} + 330 q^{88} - 412 q^{92} + 24 q^{93} + 148 q^{95} - 60 q^{98} + 44 q^{99}+O(q^{100}) \) 320 * q + 4 * q^2 - 36 * q^4 + 12 * q^8 + 32 * q^9 - 4 * q^18 + 52 * q^23 - 68 * q^25 - 88 * q^28 + 24 * q^32 + 28 * q^35 + 14 * q^36 - 44 * q^37 + 110 * q^42 - 44 * q^43 - 154 * q^44 + 40 * q^46 - 16 * q^49 - 166 * q^50 - 44 * q^51 + 110 * q^56 - 44 * q^57 - 62 * q^58 - 84 * q^64 + 72 * q^70 - 40 * q^71 - 12 * q^72 + 22 * q^74 + 72 * q^77 - 8 * q^78 - 88 * q^79 - 32 * q^81 - 304 * q^85 + 330 * q^88 - 412 * q^92 + 24 * q^93 + 148 * q^95 - 60 * q^98 + 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more