LMFDB - Embedded newform 483.2.u.a.113.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(113,483)]

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([11, 0, 13]))

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

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

chi := DirichletCharacter("483.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.u (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:	$480$
Relative dimension:	$48$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			113.19
Character	$\chi$	$=$	483.113
Dual form			483.2.u.a.218.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.497545 + 0.774196i) q^{2} +(-0.368438 - 1.69241i) q^{3} +(0.479003 + 1.04887i) q^{4} +(-0.349963 - 0.102758i) q^{5} +(1.49357 + 0.556808i) q^{6} +(0.755750 + 0.654861i) q^{7} +(-2.87220 - 0.412960i) q^{8} +(-2.72851 + 1.24710i) q^{9} +O(q^{10})$	\(q+(-0.497545 + 0.774196i) q^{2} +(-0.368438 - 1.69241i) q^{3} +(0.479003 + 1.04887i) q^{4} +(-0.349963 - 0.102758i) q^{5} +(1.49357 + 0.556808i) q^{6} +(0.755750 + 0.654861i) q^{7} +(-2.87220 - 0.412960i) q^{8} +(-2.72851 + 1.24710i) q^{9} +(0.253678 - 0.219813i) q^{10} +(-2.91049 + 1.87046i) q^{11} +(1.59863 - 1.19711i) q^{12} +(1.55140 + 1.79042i) q^{13} +(-0.883010 + 0.259275i) q^{14} +(-0.0449698 + 0.630141i) q^{15} +(0.238559 - 0.275312i) q^{16} +(-2.87508 + 6.29555i) q^{17} +(0.392059 - 2.73289i) q^{18} +(2.18751 - 0.999000i) q^{19} +(-0.0598530 - 0.416287i) q^{20} +(0.829846 - 1.52031i) q^{21} -3.18392i q^{22} +(4.79288 + 0.168282i) q^{23} +(0.359329 + 5.01309i) q^{24} +(-4.09435 - 2.63128i) q^{25} +(-2.15803 + 0.310277i) q^{26} +(3.11589 + 4.15828i) q^{27} +(-0.324857 + 1.10636i) q^{28} +(-0.448929 - 0.205019i) q^{29} +(-0.465478 - 0.348339i) q^{30} +(-0.541841 + 3.76859i) q^{31} +(-1.54057 - 5.24671i) q^{32} +(4.23791 + 4.23659i) q^{33} +(-3.44351 - 5.35820i) q^{34} +(-0.197192 - 0.306837i) q^{35} +(-2.61500 - 2.26448i) q^{36} +(2.32790 + 7.92809i) q^{37} +(-0.314961 + 2.19060i) q^{38} +(2.45852 - 3.28527i) q^{39} +(0.962728 + 0.439663i) q^{40} +(-1.44492 + 4.92093i) q^{41} +(0.764134 + 1.39889i) q^{42} +(-9.35016 + 1.34435i) q^{43} +(-3.35599 - 2.15677i) q^{44} +(1.08303 - 0.156061i) q^{45} +(-2.51496 + 3.62690i) q^{46} +4.97537i q^{47} +(-0.553835 - 0.302305i) q^{48} +(0.142315 + 0.989821i) q^{49} +(4.07425 - 1.86065i) q^{50} +(11.7139 + 2.54630i) q^{51} +(-1.13479 + 2.48483i) q^{52} +(1.41612 - 1.63429i) q^{53} +(-4.76961 + 0.343374i) q^{54} +(1.21077 - 0.355513i) q^{55} +(-1.90023 - 2.19298i) q^{56} +(-2.49668 - 3.33409i) q^{57} +(0.382087 - 0.245552i) q^{58} +(-4.49456 + 3.89456i) q^{59} +(-0.682476 + 0.254672i) q^{60} +(4.51883 + 0.649709i) q^{61} +(-2.64803 - 2.29454i) q^{62} +(-2.87874 - 0.844299i) q^{63} +(5.52755 + 1.62304i) q^{64} +(-0.358954 - 0.785999i) q^{65} +(-5.38850 + 1.17308i) q^{66} +(-2.73050 + 4.24874i) q^{67} -7.98038 q^{68} +(-1.48108 - 8.17352i) q^{69} +0.335663 q^{70} +(7.99744 - 12.4443i) q^{71} +(8.35181 - 2.45514i) q^{72} +(-5.97002 - 13.0725i) q^{73} +(-7.29613 - 2.14234i) q^{74} +(-2.94469 + 7.89879i) q^{75} +(2.09564 + 1.81588i) q^{76} +(-3.42449 - 0.492367i) q^{77} +(1.32022 + 3.53795i) q^{78} +(5.47772 - 4.74647i) q^{79} +(-0.111778 + 0.0718351i) q^{80} +(5.88950 - 6.80542i) q^{81} +(-3.09085 - 3.56703i) q^{82} +(13.9341 - 4.09141i) q^{83} +(1.99211 + 0.142166i) q^{84} +(1.65309 - 1.90777i) q^{85} +(3.61134 - 7.90773i) q^{86} +(-0.181574 + 0.835309i) q^{87} +(9.13191 - 4.17040i) q^{88} +(-2.03220 - 14.1343i) q^{89} +(-0.418033 + 0.916121i) q^{90} +2.36906i q^{91} +(2.11929 + 5.10771i) q^{92} +(6.57764 - 0.471473i) q^{93} +(-3.85191 - 2.47547i) q^{94} +(-0.868202 + 0.124829i) q^{95} +(-8.31199 + 4.54037i) q^{96} +(-3.02692 + 10.3087i) q^{97} +(-0.837123 - 0.382301i) q^{98} +(5.60864 - 8.73321i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q + 4 q^{3} + 40 q^{4} - 6 q^{6} - 4 q^{9}+O(q^{10}) $ 480 * q + 4 * q^3 + 40 * q^4 - 6 * q^6 - 4 * q^9	$ 480 q + 4 q^{3} + 40 q^{4} - 6 q^{6} - 4 q^{9} - 22 q^{12} + 8 q^{13} - 22 q^{15} - 24 q^{16} - 30 q^{18} - 120 q^{24} - 88 q^{25} + 16 q^{27} - 44 q^{30} + 8 q^{31} - 22 q^{33} - 44 q^{34} + 10 q^{36} - 44 q^{37} - 308 q^{40} - 44 q^{43} - 184 q^{46} + 98 q^{48} + 48 q^{49} - 28 q^{52} + 28 q^{54} - 44 q^{55} + 66 q^{57} + 4 q^{58} + 220 q^{60} + 84 q^{64} + 176 q^{66} + 44 q^{67} + 102 q^{69} - 8 q^{70} - 60 q^{72} + 4 q^{73} - 8 q^{75} + 176 q^{76} + 18 q^{78} - 16 q^{81} + 20 q^{82} - 154 q^{84} + 84 q^{85} + 28 q^{87} - 418 q^{90} - 188 q^{93} + 12 q^{94} - 412 q^{96} - 132 q^{97}+O(q^{100}) $ 480 * q + 4 * q^3 + 40 * q^4 - 6 * q^6 - 4 * q^9 - 22 * q^12 + 8 * q^13 - 22 * q^15 - 24 * q^16 - 30 * q^18 - 120 * q^24 - 88 * q^25 + 16 * q^27 - 44 * q^30 + 8 * q^31 - 22 * q^33 - 44 * q^34 + 10 * q^36 - 44 * q^37 - 308 * q^40 - 44 * q^43 - 184 * q^46 + 98 * q^48 + 48 * q^49 - 28 * q^52 + 28 * q^54 - 44 * q^55 + 66 * q^57 + 4 * q^58 + 220 * q^60 + 84 * q^64 + 176 * q^66 + 44 * q^67 + 102 * q^69 - 8 * q^70 - 60 * q^72 + 4 * q^73 - 8 * q^75 + 176 * q^76 + 18 * q^78 - 16 * q^81 + 20 * q^82 - 154 * q^84 + 84 * q^85 + 28 * q^87 - 418 * q^90 - 188 * q^93 + 12 * q^94 - 412 * q^96 - 132 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$323$	$346$	$442$
$\chi(n)$	$-1$	$1$	$e\left(\frac{13}{22}\right)$

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 $

$2$	−0.497545	+	0.774196i	−0.351818	+	0.547439i	−0.971387	−	0.237503i	$-0.923671\pi$
$2$	−0.497545	+	0.774196i	−0.351818	+	0.547439i	0.619569	+	0.784942i	$0.287307\pi$
$3$	−0.368438	−	1.69241i	−0.212718	−	0.977114i
$3$	−0.368438	−	1.69241i	−0.212718	−	0.977114i
$4$	0.479003	+	1.04887i	0.239501	+	0.524435i
$5$	−0.349963	−	0.102758i	−0.156508	−	0.0459550i	0.202540	−	0.979274i	$-0.435080\pi$
$5$	−0.349963	−	0.102758i	−0.156508	−	0.0459550i	−0.359048	+	0.933319i	$0.616899\pi$
$6$	1.49357	+	0.556808i	0.609748	+	0.227316i
$7$	0.755750	+	0.654861i	0.285646	+	0.247514i
$7$	0.755750	+	0.654861i	0.285646	+	0.247514i
$8$	−2.87220	−	0.412960i	−1.01548	−	0.146003i
$9$	−2.72851	+	1.24710i	−0.909502	+	0.415699i
$10$	0.253678	−	0.219813i	0.0802199	−	0.0695109i
$11$	−2.91049	+	1.87046i	−0.877544	+	0.563963i	−0.900052	−	0.435783i	$-0.856471\pi$
$11$	−2.91049	+	1.87046i	−0.877544	+	0.563963i	0.0225074	+	0.999747i	$0.492835\pi$
$12$	1.59863	−	1.19711i	0.461486	−	0.345577i
$13$	1.55140	+	1.79042i	0.430282	+	0.496572i	0.928942	−	0.370226i	$-0.120720\pi$
$13$	1.55140	+	1.79042i	0.430282	+	0.496572i	−0.498660	+	0.866798i	$0.666174\pi$
$14$	−0.883010	+	0.259275i	−0.235994	+	0.0692942i
$15$	−0.0449698	+	0.630141i	−0.0116111	+	0.162702i
$16$	0.238559	−	0.275312i	0.0596398	−	0.0688280i
$17$	−2.87508	+	6.29555i	−0.697310	+	1.52690i	0.145893	+	0.989300i	$0.453394\pi$
$17$	−2.87508	+	6.29555i	−0.697310	+	1.52690i	−0.843203	+	0.537595i	$0.819333\pi$
$18$	0.392059	−	2.73289i	0.0924092	−	0.644147i
$19$	2.18751	−	0.999000i	0.501848	−	0.229186i	−0.148373	−	0.988931i	$-0.547404\pi$
$19$	2.18751	−	0.999000i	0.501848	−	0.229186i	0.650221	+	0.759745i	$0.274676\pi$
$20$	−0.0598530	−	0.416287i	−0.0133835	−	0.0930846i
$21$	0.829846	−	1.52031i	0.181087	−	0.331760i
$22$		−	3.18392i		−	0.678814i
$23$	4.79288	+	0.168282i	0.999384	+	0.0350892i
$23$	4.79288	+	0.168282i	0.999384	+	0.0350892i
$24$	0.359329	+	5.01309i	0.0733478	+	1.02329i
$25$	−4.09435	−	2.63128i	−0.818871	−	0.526256i
$26$	−2.15803	+	0.310277i	−0.423224	+	0.0608504i
$27$	3.11589	+	4.15828i	0.599652	+	0.800261i
$28$	−0.324857	+	1.10636i	−0.0613923	+	0.209083i
$29$	−0.448929	−	0.205019i	−0.0833640	−	0.0380711i	0.373297	−	0.927712i	$-0.378227\pi$
$29$	−0.448929	−	0.205019i	−0.0833640	−	0.0380711i	−0.456661	+	0.889641i	$0.650955\pi$
$30$	−0.465478	−	0.348339i	−0.0849843	−	0.0635977i
$31$	−0.541841	+	3.76859i	−0.0973176	+	0.676859i	0.881509	+	0.472167i	$0.156528\pi$
$31$	−0.541841	+	3.76859i	−0.0973176	+	0.676859i	−0.978827	+	0.204691i	$0.934381\pi$
$32$	−1.54057	−	5.24671i	−0.272338	−	0.927496i
$33$	4.23791	+	4.23659i	0.737726	+	0.737495i
$34$	−3.44351	−	5.35820i	−0.590556	−	0.918923i
$35$	−0.197192	−	0.306837i	−0.0333315	−	0.0518649i
$36$	−2.61500	−	2.26448i	−0.435834	−	0.377414i
$37$	2.32790	+	7.92809i	0.382704	+	1.30337i	0.895577	+	0.444906i	$0.146763\pi$
$37$	2.32790	+	7.92809i	0.382704	+	1.30337i	−0.512873	+	0.858464i	$0.671419\pi$
$38$	−0.314961	+	2.19060i	−0.0510935	+	0.355363i
$39$	2.45852	−	3.28527i	0.393679	−	0.526064i
$40$	0.962728	+	0.439663i	0.152221	+	0.0695168i
$41$	−1.44492	+	4.92093i	−0.225658	+	0.768520i	0.766359	+	0.642413i	$0.222067\pi$
$41$	−1.44492	+	4.92093i	−0.225658	+	0.768520i	−0.992017	+	0.126107i	$0.959752\pi$
$42$	0.764134	+	1.39889i	0.117908	+	0.215853i
$43$	−9.35016	+	1.34435i	−1.42589	+	0.205012i	−0.811665	−	0.584123i	$-0.801439\pi$
$43$	−9.35016	+	1.34435i	−1.42589	+	0.205012i	−0.614221	+	0.789134i	$0.710530\pi$
$44$	−3.35599	−	2.15677i	−0.505935	−	0.325145i
$45$	1.08303	−	0.156061i	0.161448	−	0.0232641i
$46$	−2.51496	+	3.62690i	−0.370810	+	0.534757i
$47$			4.97537i			0.725732i	0.931841	+	0.362866i	$0.118202\pi$
$47$			4.97537i			0.725732i	−0.931841	+	0.362866i	$0.881798\pi$
$48$	−0.553835	−	0.302305i	−0.0799392	−	0.0436339i
$49$	0.142315	+	0.989821i	0.0203307	+	0.141403i
$50$	4.07425	−	1.86065i	0.576186	−	0.263135i
$51$	11.7139	+	2.54630i	1.64028	+	0.356553i
$52$	−1.13479	+	2.48483i	−0.157367	+	0.344585i
$53$	1.41612	−	1.63429i	0.194519	−	0.224486i	−0.650109	−	0.759841i	$-0.725277\pi$
$53$	1.41612	−	1.63429i	0.194519	−	0.224486i	0.844627	+	0.535355i	$0.179822\pi$
$54$	−4.76961	+	0.343374i	−0.649062	+	0.0467273i
$55$	1.21077	−	0.355513i	0.163260	−	0.0479374i
$56$	−1.90023	−	2.19298i	−0.253929	−	0.293050i
$57$	−2.49668	−	3.33409i	−0.330693	−	0.441611i
$58$	0.382087	−	0.245552i	0.0501705	−	0.0322426i
$59$	−4.49456	+	3.89456i	−0.585142	+	0.507028i	−0.896370	−	0.443307i	$-0.853805\pi$
$59$	−4.49456	+	3.89456i	−0.585142	+	0.507028i	0.311228	+	0.950335i	$0.399260\pi$
$60$	−0.682476	+	0.254672i	−0.0881073	+	0.0328780i
$61$	4.51883	+	0.649709i	0.578577	+	0.0831868i	0.425389	−	0.905010i	$-0.360137\pi$
$61$	4.51883	+	0.649709i	0.578577	+	0.0831868i	0.153187	+	0.988197i	$0.451046\pi$
$62$	−2.64803	−	2.29454i	−0.336301	−	0.291406i
$63$	−2.87874	−	0.844299i	−0.362687	−	0.106372i
$64$	5.52755	+	1.62304i	0.690944	+	0.202880i
$65$	−0.358954	−	0.785999i	−0.0445227	−	0.0974912i
$66$	−5.38850	+	1.17308i	−0.663279	+	0.144396i
$67$	−2.73050	+	4.24874i	−0.333584	+	0.519067i	−0.967011	−	0.254736i	$-0.918011\pi$
$67$	−2.73050	+	4.24874i	−0.333584	+	0.519067i	0.633427	+	0.773803i	$0.281648\pi$
$68$	−7.98038			−0.967764
$69$	−1.48108	−	8.17352i	−0.178301	−	0.983976i
$70$	0.335663			0.0401195
$71$	7.99744	−	12.4443i	0.949122	−	1.47686i	0.0715386	−	0.997438i	$-0.477209\pi$
$71$	7.99744	−	12.4443i	0.949122	−	1.47686i	0.877583	−	0.479424i	$-0.159155\pi$
$72$	8.35181	−	2.45514i	0.984270	−	0.289342i
$73$	−5.97002	−	13.0725i	−0.698737	−	1.53002i	−0.841496	−	0.540264i	$-0.818324\pi$
$73$	−5.97002	−	13.0725i	−0.698737	−	1.53002i	0.142758	−	0.989758i	$-0.454403\pi$
$74$	−7.29613	−	2.14234i	−0.848158	−	0.249042i
$75$	−2.94469	+	7.89879i	−0.340024	+	0.912074i
$76$	2.09564	+	1.81588i	0.240387	+	0.208296i
$77$	−3.42449	−	0.492367i	−0.390256	−	0.0561104i
$78$	1.32022	+	3.53795i	0.149485	+	0.400594i
$79$	5.47772	−	4.74647i	0.616291	−	0.534019i	−0.289808	−	0.957085i	$-0.593591\pi$
$79$	5.47772	−	4.74647i	0.616291	−	0.534019i	0.906099	+	0.423066i	$0.139046\pi$
$80$	−0.111778	+	0.0718351i	−0.0124971	+	0.00803140i
$81$	5.88950	−	6.80542i	0.654389	−	0.756158i
$82$	−3.09085	−	3.56703i	−0.341327	−	0.393913i
$83$	13.9341	−	4.09141i	1.52946	−	0.449090i	0.594576	−	0.804040i	$-0.297320\pi$
$83$	13.9341	−	4.09141i	1.52946	−	0.449090i	0.934886	+	0.354949i	$0.115502\pi$
$84$	1.99211	+	0.142166i	0.217357	+	0.0155116i
$85$	1.65309	−	1.90777i	0.179303	−	0.206927i
$86$	3.61134	−	7.90773i	0.389421	−	0.852712i
$87$	−0.181574	+	0.835309i	−0.0194667	+	0.0895545i
$88$	9.13191	−	4.17040i	0.973465	−	0.444566i
$89$	−2.03220	−	14.1343i	−0.215413	−	1.49823i	−0.754679	−	0.656095i	$-0.772207\pi$
$89$	−2.03220	−	14.1343i	−0.215413	−	1.49823i	0.539266	−	0.842136i	$-0.318702\pi$
$90$	−0.418033	+	0.916121i	−0.0440646	+	0.0965677i
$91$			2.36906i			0.248345i
$92$	2.11929	+	5.10771i	0.220952	+	0.532516i
$93$	6.57764	−	0.471473i	0.682069	−	0.0488895i
$94$	−3.85191	−	2.47547i	−0.397294	−	0.255325i
$95$	−0.868202	+	0.124829i	−0.0890756	+	0.0128071i
$96$	−8.31199	+	4.54037i	−0.848338	+	0.463400i
$97$	−3.02692	+	10.3087i	−0.307337	+	1.04669i	0.650530	+	0.759480i	$0.274547\pi$
$97$	−3.02692	+	10.3087i	−0.307337	+	1.04669i	−0.957867	+	0.287212i	$0.907271\pi$
$98$	−0.837123	−	0.382301i	−0.0845622	−	0.0386183i
$99$	5.60864	−	8.73321i	0.563690	−	0.877720i
$100$	0.798664	−	5.55483i	0.0798664	−	0.555483i
$101$	−1.19989	−	4.08644i	−0.119393	−	0.406616i	0.878009	−	0.478643i	$-0.158871\pi$
$101$	−1.19989	−	4.08644i	−0.119393	−	0.406616i	−0.997403	+	0.0720274i	$0.977053\pi$
$102$	−7.79955	+	7.80199i	−0.772271	+	0.772512i
$103$	3.44495	+	5.36045i	0.339441	+	0.528181i	0.968447	−	0.249220i	$-0.0801742\pi$
$103$	3.44495	+	5.36045i	0.339441	+	0.528181i	−0.629006	+	0.777401i	$0.716538\pi$
$104$	−3.71657	−	5.78310i	−0.364440	−	0.567079i
$105$	−0.446641	+	0.446780i	−0.0435877	+	0.0436013i
$106$	0.560675	+	1.90948i	0.0544576	+	0.185465i
$107$	−0.0480800	+	0.334404i	−0.00464807	+	0.0323280i	−0.992013	−	0.126132i	$-0.959744\pi$
$107$	−0.0480800	+	0.334404i	−0.00464807	+	0.0323280i	0.987365	+	0.158460i	$0.0506529\pi$
$108$	−2.86897	+	5.25998i	−0.276067	+	0.506142i
$109$	3.33526	+	1.52316i	0.319460	+	0.145892i	0.568690	−	0.822552i	$-0.307450\pi$
$109$	3.33526	+	1.52316i	0.319460	+	0.145892i	−0.249230	+	0.968444i	$0.580178\pi$
$110$	−0.327175	+	1.11425i	−0.0311949	+	0.106240i
$111$	12.5599	−	6.86077i	1.19213	−	0.651195i
$112$	0.360582	−	0.0518439i	0.0340718	−	0.00489879i
$113$	−8.32256	−	5.34858i	−0.782920	−	0.503152i	0.0870813	−	0.996201i	$-0.472246\pi$
$113$	−8.32256	−	5.34858i	−0.782920	−	0.503152i	−0.870002	+	0.493049i	$0.835882\pi$
$114$	3.82345	−	0.274058i	0.358099	−	0.0256679i
$115$	−1.66004	−	0.551401i	−0.154799	−	0.0514184i
$116$		−	0.569072i		−	0.0528370i
$117$	−6.46584	−	2.95041i	−0.597767	−	0.272766i
$118$	−0.778903	−	5.41739i	−0.0717038	−	0.498711i
$119$	−6.29555	+	2.87508i	−0.577112	+	0.263558i
$120$	0.389385	−	1.79132i	0.0355458	−	0.163524i
$121$	0.402756	−	0.881912i	0.0366142	−	0.0801738i
$122$	−2.75132	+	3.17520i	−0.249093	+	0.287469i
$123$	8.86060	+	0.632333i	0.798933	+	0.0570155i
$124$	−4.21230	+	1.23684i	−0.378276	+	0.111072i
$125$	2.35675	+	2.71983i	0.210794	+	0.243269i
$126$	2.08596	−	1.80863i	0.185832	−	0.161126i
$127$	−7.30444	+	4.69428i	−0.648165	+	0.416550i	−0.822995	−	0.568048i	$-0.807699\pi$
$127$	−7.30444	+	4.69428i	−0.648165	+	0.416550i	0.174831	+	0.984599i	$0.444062\pi$
$128$	4.25844	−	3.68996i	0.376397	−	0.326150i
$129$	5.72015	+	15.3290i	0.503631	+	1.34964i
$130$	0.787113	+	0.113170i	0.0690344	+	0.00992565i
$131$	8.70955	+	7.54687i	0.760957	+	0.659373i	0.946296	−	0.323302i	$-0.104793\pi$
$131$	8.70955	+	7.54687i	0.760957	+	0.659373i	−0.185339	+	0.982675i	$0.559338\pi$
$132$	−2.41366	+	6.47435i	−0.210082	+	0.563520i
$133$	2.30741	+	0.677517i	0.200078	+	0.0587482i
$134$	−1.93081	−	4.22789i	−0.166797	−	0.365234i
$135$	−0.663147	−	1.77543i	−0.0570746	−	0.152804i
$136$	10.8576	−	16.8948i	0.931033	−	1.44871i
$137$	−4.50090			−0.384538			−0.192269	−	0.981342i	$-0.561585\pi$
$137$	−4.50090			−0.384538			−0.192269	+	0.981342i	$0.561585\pi$
$138$	7.06480	+	2.92005i	0.601396	+	0.248571i
$139$	15.4776			1.31279			0.656397	−	0.754416i	$-0.272080\pi$
$139$	15.4776			1.31279			0.656397	+	0.754416i	$0.272080\pi$
$140$	0.227376	−	0.353804i	0.0192168	−	0.0299019i
$141$	8.42036	−	1.83311i	0.709122	−	0.154376i
$142$	5.65520	+	12.3832i	0.474574	+	1.03917i
$143$	−7.86423	−	2.30915i	−0.657640	−	0.193101i
$144$	−0.307570	+	1.04870i	−0.0256308	+	0.0873914i
$145$	0.136041	+	0.117880i	0.0112976	+	0.00978942i
$146$	13.0910	+	1.88221i	1.08342	+	0.155773i
$147$	1.62275	−	0.605543i	0.133842	−	0.0499443i
$148$	−7.20046	+	6.23924i	−0.591874	+	0.512862i
$149$	18.4059	−	11.8288i	1.50787	−	0.969050i	0.514086	−	0.857738i	$-0.328131\pi$
$149$	18.4059	−	11.8288i	1.50787	−	0.969050i	0.993786	−	0.111312i	$-0.0355053\pi$
$150$	−4.65009	−	6.20977i	−0.379678	−	0.507026i
$151$	−8.65963	−	9.99374i	−0.704710	−	0.813279i	0.284670	−	0.958625i	$-0.408116\pi$
$151$	−8.65963	−	9.99374i	−0.704710	−	0.813279i	−0.989381	+	0.145346i	$0.953570\pi$
$152$	−6.69549	+	1.96597i	−0.543076	+	0.159462i
$153$	−0.00647990	−	20.7630i	−0.000523869	−	1.67859i
$154$	2.08502	−	2.40625i	0.168016	−	0.193901i
$155$	0.576879	−	1.26319i	0.0463360	−	0.101462i
$156$	4.62346	+	1.00502i	0.370173	+	0.0804657i
$157$	3.22869	−	1.47449i	0.257678	−	0.117677i	−0.282388	−	0.959300i	$-0.591127\pi$
$157$	3.22869	−	1.47449i	0.257678	−	0.117677i	0.540066	+	0.841623i	$0.318399\pi$
$158$	0.949283	+	6.60241i	0.0755209	+	0.525259i
$159$	−3.28763	−	1.79452i	−0.260726	−	0.142315i
$160$			1.99446i			0.157676i
$161$	3.51201	+	3.26585i	0.276786	+	0.257385i
$162$	2.33844	+	7.94563i	0.183725	+	0.624268i
$163$	−7.62974	−	4.90333i	−0.597607	−	0.384059i	0.206585	−	0.978429i	$-0.433765\pi$
$163$	−7.62974	−	4.90333i	−0.597607	−	0.384059i	−0.804192	+	0.594370i	$0.797401\pi$
$164$	−5.85353	+	0.841611i	−0.457084	+	0.0657187i
$165$	−1.04777	−	1.91813i	−0.0815686	−	0.149326i
$166$	−3.76527	+	12.8233i	−0.292242	+	0.995285i
$167$	20.9700	+	9.57669i	1.62271	+	0.741066i	0.999170	−	0.0407266i	$-0.0129673\pi$
$167$	20.9700	+	9.57669i	1.62271	+	0.741066i	0.623538	+	0.781793i	$0.285695\pi$
$168$	−3.01131	+	4.02395i	−0.232328	+	0.310454i
$169$	1.05136	−	7.31236i	0.0808737	−	0.562489i
$170$	0.654499	+	2.22902i	0.0501978	+	0.170958i
$171$	−4.72277	+	5.45381i	−0.361160	+	0.417063i
$172$	−5.88880	−	9.16315i	−0.449017	−	0.698684i
$173$	1.84031	+	2.86357i	0.139916	+	0.217713i	0.904139	−	0.427239i	$-0.140514\pi$
$173$	1.84031	+	2.86357i	0.139916	+	0.217713i	−0.764223	+	0.644952i	$0.776877\pi$
$174$	−0.556351	−	0.556177i	−0.0421769	−	0.0421637i
$175$	−1.37118	−	4.66982i	−0.103652	−	0.353005i
$176$	−0.179364	+	1.24751i	−0.0135201	+	0.0940343i
$177$	8.24716	+	6.17174i	0.619894	+	0.463896i
$178$	11.9538	+	5.45912i	0.895976	+	0.409178i
$179$	−7.38001	+	25.1340i	−0.551608	+	1.87860i	−0.0800031	+	0.996795i	$0.525493\pi$
$179$	−7.38001	+	25.1340i	−0.551608	+	1.87860i	−0.471605	+	0.881810i	$0.656325\pi$
$180$	0.682459	+	1.06120i	0.0508675	+	0.0790971i
$181$	−14.4604	+	2.07910i	−1.07484	+	0.154538i	−0.656929	−	0.753952i	$-0.728145\pi$
$181$	−14.4604	+	2.07910i	−1.07484	+	0.154538i	−0.417906	+	0.908490i	$0.637236\pi$
$182$	−1.83412	−	1.17871i	−0.135954	−	0.0873722i
$183$	−0.565333	−	7.88709i	−0.0417906	−	0.583031i
$184$	−13.6966	−	2.46260i	−1.00973	−	0.181546i
$185$		−	3.01375i		−	0.221575i
$186$	−2.90766	+	5.32696i	−0.213200	+	0.390591i
$187$	−3.40766	−	23.7008i	−0.249193	−	1.73318i
$188$	−5.21851	+	2.38321i	−0.380599	+	0.173814i
$189$	−0.368263	+	5.18309i	−0.0267872	+	0.377014i
$190$	0.335328	−	0.734266i	0.0243272	−	0.0532692i
$191$	8.33971	−	9.62454i	0.603440	−	0.696407i	−0.369035	−	0.929416i	$-0.620312\pi$
$191$	8.33971	−	9.62454i	0.603440	−	0.696407i	0.972475	+	0.233009i	$0.0748571\pi$
$192$	0.710283	−	9.95288i	0.0512603	−	0.718287i
$193$	−7.71827	+	2.26629i	−0.555573	+	0.163131i	−0.547454	−	0.836836i	$-0.684403\pi$
$193$	−7.71827	+	2.26629i	−0.555573	+	0.163131i	−0.00811966	+	0.999967i	$0.502585\pi$
$194$	−6.47494	−	7.47248i	−0.464874	−	0.536493i
$195$	−1.19798	+	0.897089i	−0.0857892	+	0.0642419i
$196$	−0.970024	+	0.623397i	−0.0692874	+	0.0445283i
$197$	−7.57294	+	6.56199i	−0.539550	+	0.467522i	−0.881492	−	0.472198i	$-0.843461\pi$
$197$	−7.57294	+	6.56199i	−0.539550	+	0.467522i	0.341943	+	0.939721i	$0.388915\pi$
$198$	3.97066	+	8.68735i	0.282182	+	0.617383i
$199$	12.1154	+	1.74193i	0.858837	+	0.123482i	0.557643	−	0.830081i	$-0.311706\pi$
$199$	12.1154	+	1.74193i	0.858837	+	0.123482i	0.301194	+	0.953563i	$0.402615\pi$
$200$	10.6732	+	9.24836i	0.754707	+	0.653958i
$201$	8.19664	+	3.05573i	0.578146	+	0.215535i
$202$	3.76070	+	1.10424i	0.264602	+	0.0776942i
$203$	−0.205019	−	0.448929i	−0.0143895	−	0.0315086i
$204$	2.94028	+	13.5061i	0.205861	+	0.945615i
$205$	1.01133	−	1.57367i	0.0706346	−	0.109910i
$206$	−5.86405			−0.408568
$207$	−13.2873	+	5.51802i	−0.923529	+	0.383529i
$208$	0.863025			0.0598400
$209$	−4.49812	+	6.99921i	−0.311141	+	0.484145i
$210$	−0.123671	−	0.568080i	−0.00853412	−	0.0392013i
$211$	1.33269	+	2.91819i	0.0917464	+	0.200897i	0.949942	−	0.312426i	$-0.101142\pi$
$211$	1.33269	+	2.91819i	0.0917464	+	0.200897i	−0.858196	+	0.513323i	$0.828414\pi$
$212$	2.39248	+	0.702494i	0.164316	+	0.0482475i
$213$	−24.0074	−	8.95002i	−1.64496	−	0.613245i
$214$	−0.234972	−	0.203604i	−0.0160624	−	0.0139181i
$215$	3.41035	+	0.490335i	0.232584	+	0.0334406i
$216$	−7.23224	−	13.2301i	−0.492091	−	0.900196i
$217$	−2.87740	+	2.49328i	−0.195330	+	0.169255i
$218$	−2.83867	+	1.82430i	−0.192259	+	0.123557i
$219$	−19.9245	+	14.9201i	−1.34637	+	1.00821i
$220$	0.952847	+	1.09964i	0.0642410	+	0.0741380i
$221$	−15.7321	+	4.61935i	−1.05825	+	0.310731i
$222$	−0.937542	+	13.1374i	−0.0629237	+	0.881722i
$223$	−11.4476	+	13.2113i	−0.766589	+	0.884691i	−0.996065	−	0.0886232i	$-0.971753\pi$
$223$	−11.4476	+	13.2113i	−0.766589	+	0.884691i	0.229476	+	0.973314i	$0.426299\pi$
$224$	2.27158	−	4.97406i	0.151776	−	0.332343i
$225$	14.4529	+	2.07341i	0.963529	+	0.138228i
$226$	8.28170	−	3.78212i	0.550890	−	0.251583i
$227$	2.01992	+	14.0489i	0.134067	+	0.932455i	0.940176	+	0.340689i	$0.110660\pi$
$227$	2.01992	+	14.0489i	0.134067	+	0.932455i	−0.806109	+	0.591767i	$0.798431\pi$
$228$	2.30111	−	4.21573i	0.152395	−	0.279193i
$229$			5.48338i			0.362352i	0.983451	+	0.181176i	$0.0579904\pi$
$229$			5.48338i			0.362352i	−0.983451	+	0.181176i	$0.942010\pi$
$230$	1.25284	−	1.01085i	0.0826096	−	0.0666533i
$231$	0.428424	+	5.97704i	0.0281882	+	0.393260i
$232$	1.20475	+	0.774244i	0.0790955	+	0.0508316i
$233$	−14.9562	+	2.15037i	−0.979811	+	0.140876i	−0.613567	−	0.789643i	$-0.710266\pi$
$233$	−14.9562	+	2.15037i	−0.979811	+	0.140876i	−0.366245	+	0.930519i	$0.619357\pi$
$234$	5.50124	−	3.53786i	0.359628	−	0.231277i
$235$	0.511261	−	1.74119i	0.0333510	−	0.113583i
$236$	−6.23779	−	2.84870i	−0.406045	−	0.185435i
$237$	−10.0512	−	7.52176i	−0.652894	−	0.488591i
$238$	0.906446	−	6.30447i	0.0587562	−	0.408658i
$239$	−1.96157	−	6.68048i	−0.126883	−	0.432124i	0.871408	−	0.490559i	$-0.163207\pi$
$239$	−1.96157	−	6.68048i	−0.126883	−	0.432124i	−0.998291	+	0.0584344i	$0.981389\pi$
$240$	0.162757	+	0.162707i	0.0105060	+	0.0105027i
$241$	−1.70434	−	2.65201i	−0.109786	−	0.170831i	0.782013	−	0.623262i	$-0.214193\pi$
$241$	−1.70434	−	2.65201i	−0.109786	−	0.170831i	−0.891799	+	0.452431i	$0.850557\pi$
$242$	0.482383	+	0.750603i	0.0310088	+	0.0482506i
$243$	−13.6875	−	7.46008i	−0.878053	−	0.478564i
$244$	1.48307	+	5.05087i	0.0949438	+	0.323349i
$245$	0.0519075	−	0.361025i	0.00331625	−	0.0230650i
$246$	−4.89810	+	6.54522i	−0.312291	+	0.417308i
$247$	5.18233	+	2.36669i	0.329744	+	0.150589i
$248$	3.11255	−	10.6004i	0.197647	−	0.673124i
$249$	−12.0582	−	22.0747i	−0.764156	−	1.39893i
$250$	−3.27827	+	0.471344i	−0.207336	+	0.0298104i
$251$	18.7268	+	12.0350i	1.18202	+	0.759640i	0.975757	−	0.218856i	$-0.0702325\pi$
$251$	18.7268	+	12.0350i	1.18202	+	0.759640i	0.206266	+	0.978496i	$0.433869\pi$
$252$	−0.493365	−	3.42385i	−0.0310791	−	0.215682i
$253$	−14.2644	+	8.47508i	−0.896793	+	0.532824i
$254$		−	7.99069i		−	0.501380i
$255$	−3.83779	−	2.09482i	−0.240332	−	0.131183i
$256$	2.37771	+	16.5373i	0.148607	+	1.03358i
$257$	−7.06984	+	3.22869i	−0.441004	+	0.201400i	−0.623527	−	0.781802i	$-0.714301\pi$
$257$	−7.06984	+	3.22869i	−0.441004	+	0.201400i	0.182523	+	0.983202i	$0.441574\pi$
$258$	−14.7137	−	3.19836i	−0.916034	−	0.199121i
$259$	−3.43249	+	7.51610i	−0.213284	+	0.467028i
$260$	0.652471	−	0.752991i	0.0404645	−	0.0466985i
$261$	1.48058		0.000462075i	0.0916458		2.86017e-5i
$262$	−10.1761	+	2.98799i	−0.628685	+	0.184598i
$263$	11.0549	+	12.7581i	0.681677	+	0.786697i	0.986156	−	0.165822i	$-0.0530277\pi$
$263$	11.0549	+	12.7581i	0.681677	+	0.786697i	−0.304479	+	0.952519i	$0.598482\pi$
$264$	−10.4226	−	13.9184i	−0.641465	−	0.856619i
$265$	−0.663525	+	0.426422i	−0.0407600	+	0.0261949i
$266$	−1.67257	+	1.44929i	−0.102552	+	0.0888618i
$267$	−23.1723	+	8.64693i	−1.41812	+	0.529183i
$268$	−5.76430	−	0.828781i	−0.352110	−	0.0506258i
$269$	−23.9725	−	20.7723i	−1.46163	−	1.26651i	−0.897639	−	0.440732i	$-0.854719\pi$
$269$	−23.9725	−	20.7723i	−1.46163	−	1.26651i	−0.563993	−	0.825779i	$-0.690736\pi$
$270$	1.70447	+	0.369950i	0.103731	+	0.0225144i
$271$	16.4796	+	4.83884i	1.00106	+	0.293939i	0.740892	−	0.671624i	$-0.234403\pi$
$271$	16.4796	+	4.83884i	1.00106	+	0.293939i	0.260171	+	0.965563i	$0.416221\pi$
$272$	1.04736	+	2.29341i	0.0635058	+	0.139058i
$273$	4.00942	−	0.872852i	0.242661	−	0.0528274i
$274$	2.23940	−	3.48458i	0.135287	−	0.210511i
$275$	16.8382			1.01538
$276$	7.86351	−	5.46859i	0.473328	−	0.329171i
$277$	19.0079			1.14208			0.571038	−	0.820924i	$-0.306541\pi$
$277$	19.0079			1.14208			0.571038	+	0.820924i	$0.306541\pi$
$278$	−7.70081	+	11.9827i	−0.461864	+	0.718674i
$279$	−3.22138	−	10.9584i	−0.192859	−	0.656059i
$280$	0.439663	+	0.962728i	0.0262749	+	0.0575340i
$281$	11.4351	+	3.35764i	0.682159	+	0.200300i	0.604411	−	0.796673i	$-0.293409\pi$
$281$	11.4351	+	3.35764i	0.682159	+	0.200300i	0.0777486	+	0.996973i	$0.475227\pi$
$282$	−2.77032	+	7.43106i	−0.164970	+	0.442513i
$283$	−5.37652	−	4.65878i	−0.319601	−	0.276936i	0.480253	−	0.877130i	$-0.340545\pi$
$283$	−5.37652	−	4.65878i	−0.319601	−	0.276936i	−0.799855	+	0.600194i	$0.795090\pi$
$284$	16.8832	+	2.42744i	1.00183	+	0.144042i
$285$	0.531140	+	1.42336i	0.0314620	+	0.0843127i
$286$	5.70054	−	4.93955i	0.337080	−	0.292082i
$287$	−4.31452	+	2.77277i	−0.254678	+	0.163672i
$288$	10.7466	+	12.3944i	0.633251	+	0.730350i
$289$	−20.2352	−	23.3527i	−1.19031	−	1.37369i
$290$	−0.158949	+	0.0466716i	−0.00933380	+	0.00274065i
$291$	18.5618	+	1.32466i	1.08811	+	0.0776528i
$292$	10.8517	−	12.5235i	0.635048	−	0.732884i
$293$	−10.6830	+	23.3925i	−0.624106	+	1.36660i	0.288389	+	0.957513i	$0.406881\pi$
$293$	−10.6830	+	23.3925i	−0.624106	+	1.36660i	−0.912495	+	0.409088i	$0.865847\pi$
$294$	−0.338583	+	1.55761i	−0.0197466	+	0.0908417i
$295$	1.97313	−	0.901097i	0.114880	−	0.0524639i
$296$	−3.41220	−	23.7324i	−0.198330	−	1.37942i
$297$	−16.8466	−	6.27448i	−0.977539	−	0.364082i
$298$			20.1351i			1.16640i
$299$	7.13440	+	8.84232i	0.412593	+	0.511365i
$300$	−9.69531	+	0.694943i	−0.559759	+	0.0401226i
$301$	−7.94674	−	5.10706i	−0.458043	−	0.294366i
$302$	12.0457	−	1.73191i	0.693150	−	0.0996600i
$303$	−6.47385	+	3.53630i	−0.371913	+	0.203155i
$304$	0.246813	−	0.840567i	0.0141557	−	0.0482098i
$305$	−1.51466	−	0.691722i	−0.0867292	−	0.0396079i
$306$	16.0778	+	10.3255i	0.919108	+	0.590269i
$307$	1.84814	−	12.8541i	0.105479	−	0.733621i	−0.866606	−	0.498992i	$-0.833704\pi$
$307$	1.84814	−	12.8541i	0.105479	−	0.733621i	0.972085	−	0.234628i	$-0.0753873\pi$
$308$	−1.12391	−	3.82768i	−0.0640407	−	0.218102i
$309$	7.80283	−	7.80526i	0.443887	−	0.444026i
$310$	0.690931	+	1.07511i	0.0392423	+	0.0610622i
$311$	3.88042	+	6.03805i	0.220038	+	0.342387i	0.933670	−	0.358135i	$-0.116587\pi$
$311$	3.88042	+	6.03805i	0.220038	+	0.342387i	−0.713631	+	0.700521i	$0.752951\pi$
$312$	−8.41805	+	8.42068i	−0.476578	+	0.476727i
$313$	−1.98320	−	6.75415i	−0.112097	−	0.381767i	0.884265	−	0.466985i	$-0.154660\pi$
$313$	−1.98320	−	6.75415i	−0.112097	−	0.381767i	−0.996362	+	0.0852175i	$0.972842\pi$
$314$	−0.464873	+	3.23327i	−0.0262343	+	0.182464i
$315$	0.920695	+	0.591289i	0.0518753	+	0.0333153i
$316$	7.60226	+	3.47184i	0.427661	+	0.195306i
$317$	−1.48248	+	5.04888i	−0.0832646	+	0.283573i	−0.990591	−	0.136853i	$-0.956301\pi$
$317$	−1.48248	+	5.04888i	−0.0832646	+	0.283573i	0.907327	+	0.420426i	$0.138119\pi$
$318$	3.02506	−	1.65242i	0.169637	−	0.0926630i
$319$	1.69008	−	0.242997i	0.0946263	−	0.0136052i
$320$	−1.76766	−	1.13601i	−0.0988151	−	0.0635046i
$321$	0.583663	−	0.0418359i	0.0325769	−	0.00233505i
$322$	−4.27579	+	1.09408i	−0.238280	+	0.0609707i
$323$			16.6438i			0.926084i
$324$	9.95909	+	2.91750i	0.553283	+	0.162083i
$325$	−1.64091	−	11.4128i	−0.0910213	−	0.633067i
$326$	7.59228	−	3.46728i	0.420497	−	0.192035i
$327$	1.34898	−	6.20582i	0.0745987	−	0.343183i
$328$	6.18223	−	13.5372i	0.341356	−	0.747466i
$329$	−3.25817	+	3.76013i	−0.179629	+	0.207303i
$330$	2.00632	+	0.143180i	0.110444	+	0.00788181i
$331$	13.5558	−	3.98033i	0.745092	−	0.218779i	0.112917	−	0.993604i	$-0.463981\pi$
$331$	13.5558	−	3.98033i	0.745092	−	0.218779i	0.632175	+	0.774826i	$0.282162\pi$
$332$	10.9658	+	12.6552i	0.601826	+	0.694545i
$333$	−16.2388	−	18.7287i	−0.889880	−	1.02633i
$334$	−17.8478	+	11.4701i	−0.976586	+	0.627614i
$335$	1.39217	−	1.20632i	0.0760623	−	0.0659084i
$336$	−0.220593	−	0.591152i	−0.0120343	−	0.0322500i
$337$	25.3909	+	3.65066i	1.38313	+	0.198864i	0.793383	−	0.608722i	$-0.208318\pi$
$337$	25.3909	+	3.65066i	1.38313	+	0.198864i	0.589749	+	0.807587i	$0.299227\pi$
$338$	5.13810	+	4.45219i	0.279476	+	0.242167i
$339$	−5.98565	+	16.0558i	−0.325096	+	0.872032i
$340$	2.79284	+	0.820051i	0.151463	+	0.0444735i
$341$	−5.47196	−	11.9819i	−0.296323	−	0.648857i
$342$	−1.87252	−	6.36987i	−0.101254	−	0.344443i
$343$	−0.540641	+	0.841254i	−0.0291919	+	0.0454234i
$344$	27.4107			1.47788
$345$	−0.321576	+	3.01262i	−0.0173131	+	0.162194i
$346$	−3.13260			−0.168410
$347$	−4.50660	+	7.01241i	−0.241927	+	0.376446i	−0.940890	−	0.338712i	$-0.890009\pi$
$347$	−4.50660	+	7.01241i	−0.241927	+	0.376446i	0.698963	+	0.715158i	$0.253645\pi$
$348$	−0.963104	+	0.209668i	−0.0516278	+	0.0112394i
$349$	0.541140	+	1.18493i	0.0289666	+	0.0634280i	0.923562	−	0.383448i	$-0.125264\pi$
$349$	0.541140	+	1.18493i	0.0289666	+	0.0634280i	−0.894596	+	0.446876i	$0.852536\pi$
$350$	4.29758	+	1.26188i	0.229715	+	0.0674505i
$351$	−2.61105	+	12.0299i	−0.139367	+	0.642109i
$352$	14.2976	+	12.3889i	0.762062	+	0.660331i
$353$	20.5795	+	2.95889i	1.09534	+	0.157486i	0.666214	−	0.745760i	$-0.267914\pi$
$353$	20.5795	+	2.95889i	1.09534	+	0.157486i	0.429123	+	0.903246i	$0.358823\pi$
$354$	−8.88147	+	3.31419i	−0.472045	+	0.176147i
$355$	−4.07756	+	3.53323i	−0.216414	+	0.187524i
$356$	13.8516	−	8.90187i	0.734132	−	0.471798i
$357$	7.18534	+	9.59537i	0.380289	+	0.507841i
$358$	−15.7868	−	18.2189i	−0.834356	−	0.962898i
$359$	−18.5347	+	5.44228i	−0.978224	+	0.287233i	−0.731491	−	0.681851i	$-0.761175\pi$
$359$	−18.5347	+	5.44228i	−0.978224	+	0.287233i	−0.246733	+	0.969083i	$0.579357\pi$
$360$	−3.17511		0.000990919i	−0.167343		5.22260e-5i
$361$	−8.65518	+	9.98861i	−0.455536	+	0.525716i
$362$	5.58509	−	12.2296i	0.293546	−	0.642776i
$363$	−1.64095	−	0.356698i	−0.0861274	−	0.0187218i
$364$	−2.48483	+	1.13479i	−0.130241	+	0.0594789i
$365$	0.745974	+	5.18836i	0.0390461	+	0.271571i
$366$	6.38743	+	3.48651i	0.333876	+	0.182243i
$367$			33.2236i			1.73426i	0.498083	+	0.867129i	$0.334037\pi$
$367$			33.2236i			1.73426i	−0.498083	+	0.867129i	$0.665963\pi$
$368$	1.18972	−	1.27939i	0.0620182	−	0.0666929i
$369$	−2.19441	−	15.2287i	−0.114237	−	0.792777i
$370$	2.33323	+	1.49948i	0.121299	+	0.0779541i
$371$	2.14046	−	0.307752i	0.111127	−	0.0159777i
$372$	3.64522	+	6.67324i	0.188996	+	0.345992i
$373$	3.35863	−	11.4384i	0.173903	−	0.592260i	−0.825700	−	0.564109i	$-0.809220\pi$
$373$	3.35863	−	11.4384i	0.173903	−	0.592260i	0.999604	−	0.0281512i	$-0.00896199\pi$
$374$	20.0445	+	9.15403i	1.03648	+	0.473344i
$375$	3.73476	−	4.99067i	0.192862	−	0.257717i
$376$	2.05463	−	14.2902i	0.105959	−	0.736962i
$377$	−0.329401	−	1.12184i	−0.0169650	−	0.0577775i
$378$	−3.82949	−	2.86393i	−0.196968	−	0.147305i
$379$	20.8733	+	32.4795i	1.07219	+	1.66836i	0.644967	+	0.764210i	$0.276871\pi$
$379$	20.8733	+	32.4795i	1.07219	+	1.66836i	0.427221	+	0.904147i	$0.359493\pi$
$380$	−0.546800	−	0.850837i	−0.0280502	−	0.0436470i
$381$	10.6359	+	10.6326i	0.544893	+	0.544723i
$382$	3.30189	+	11.2452i	0.168939	+	0.575355i
$383$	0.977421	−	6.79812i	0.0499439	−	0.347367i	−0.949492	−	0.313791i	$-0.898401\pi$
$383$	0.977421	−	6.79812i	0.0499439	−	0.347367i	0.999436	−	0.0335769i	$-0.0106899\pi$
$384$	−7.81390	−	5.84751i	−0.398752	−	0.298405i
$385$	1.14785	+	0.524205i	0.0584998	+	0.0267160i
$386$	2.08564	−	7.10303i	0.106156	−	0.361535i
$387$	23.8354	−	15.3286i	1.21162	−	0.779198i
$388$	−12.2624	+	1.76307i	−0.622529	+	0.0895062i
$389$	4.10203	+	2.63621i	0.207981	+	0.133661i	0.640485	−	0.767971i	$-0.278733\pi$
$389$	4.10203	+	2.63621i	0.207981	+	0.133661i	−0.432504	+	0.901632i	$0.642370\pi$
$390$	−0.0984726	−	1.37381i	−0.00498636	−	0.0695658i
$391$	−14.8393	+	29.6900i	−0.750458	+	1.50149i
$392$		−	2.90173i		−	0.146560i
$393$	9.56347	−	17.5207i	0.482413	−	0.883802i
$394$	−1.31238	−	9.12782i	−0.0661169	−	0.459853i
$395$	−2.40474	+	1.09821i	−0.120995	+	0.0552568i
$396$	11.8465	+	1.69950i	0.595311	+	0.0854032i
$397$	0.0457843	−	0.100254i	0.00229785	−	0.00503159i	−0.908480	−	0.417929i	$-0.862756\pi$
$397$	0.0457843	−	0.100254i	0.00229785	−	0.00503159i	0.910777	+	0.412898i	$0.135483\pi$
$398$	−7.37654	+	8.51299i	−0.369753	+	0.426717i
$399$	0.296499	−	4.15471i	0.0148435	−	0.207996i
$400$	−1.70117	+	0.499508i	−0.0850585	+	0.0249754i
$401$	−2.40730	−	2.77817i	−0.120215	−	0.138735i	0.692452	−	0.721464i	$-0.256530\pi$
$401$	−2.40730	−	2.77817i	−0.120215	−	0.138735i	−0.812667	+	0.582729i	$0.801985\pi$
$402$	−6.44393	+	4.82544i	−0.321394	+	0.240671i
$403$	−7.58796	+	4.87649i	−0.377983	+	0.242915i
$404$	3.71139	−	3.21594i	0.184649	−	0.159999i
$405$	−2.76042	+	1.77645i	−0.137166	+	0.0882725i
$406$	0.449565	+	0.0646377i	0.0223115	+	0.00320791i
$407$	−21.6045	−	18.7204i	−1.07089	−	0.927934i
$408$	−32.5933	−	12.1509i	−1.61361	−	0.601557i
$409$	33.8535	+	9.94028i	1.67395	+	0.491515i	0.974728	−	0.223393i	$-0.0717133\pi$
$409$	33.8535	+	9.94028i	1.67395	+	0.491515i	0.699218	+	0.714908i	$0.253532\pi$
$410$	0.715141	+	1.56594i	0.0353183	+	0.0773363i
$411$	1.65830	+	7.61737i	0.0817980	+	0.375737i
$412$	−3.97227	+	6.18097i	−0.195700	+	0.304515i
$413$	−5.94715			−0.292640
$414$	2.33899	−	13.0324i	0.114955	−	0.640508i
$415$	−5.29683			−0.260011
$416$	7.00375	−	10.8980i	0.343387	−	0.534320i
$417$	−5.70254	−	26.1945i	−0.279255	−	1.28275i
$418$	−3.18074	−	6.96484i	−0.155575	−	0.340662i
$419$	22.8830	+	6.71904i	1.11791	+	0.328247i	0.787944	−	0.615747i	$-0.211146\pi$
$419$	22.8830	+	6.71904i	1.11791	+	0.328247i	0.329962	+	0.943994i	$0.392964\pi$
$420$	−0.682556	−	0.254459i	−0.0333053	−	0.0124163i
$421$	10.6158	+	9.19862i	0.517381	+	0.448313i	0.873992	−	0.485940i	$-0.161523\pi$
$421$	10.6158	+	9.19862i	0.517381	+	0.448313i	−0.356611	+	0.934253i	$0.616068\pi$
$422$	−2.92233	−	0.420167i	−0.142257	−	0.0204534i
$423$	−6.20476	−	13.5753i	−0.301686	−	0.660055i
$424$	−4.74226	+	4.10919i	−0.230305	+	0.199560i
$425$	28.3370	−	18.2111i	1.37454	−	0.883366i
$426$	18.8738	−	14.1334i	0.914439	−	0.684763i
$427$	2.98963	+	3.45022i	0.144679	+	0.166968i
$428$	−0.373776	+	0.109751i	−0.0180672	+	0.00530500i
$429$	−1.01054	+	14.1603i	−0.0487895	+	0.683665i
$430$	−2.07642	+	2.39632i	−0.100134	+	0.115561i
$431$	10.4560	−	22.8955i	0.503648	−	1.10284i	−0.471618	−	0.881803i	$-0.656330\pi$
$431$	10.4560	−	22.8955i	0.503648	−	1.10284i	0.975266	−	0.221033i	$-0.0709428\pi$
$432$	1.88815	+	0.134155i	0.0908435	+	0.00645451i
$433$	20.1448	−	9.19984i	0.968099	−	0.442116i	0.132335	−	0.991205i	$-0.457753\pi$
$433$	20.1448	−	9.19984i	0.968099	−	0.442116i	0.835764	+	0.549089i	$0.185025\pi$
$434$	−0.498650	−	3.46819i	−0.0239360	−	0.166478i
$435$	0.149379	−	0.273669i	0.00716218	−	0.0131214i
$436$			4.22785i			0.202477i
$437$	10.6526	−	4.41997i	0.509581	−	0.211436i
$438$	−1.63777	−	22.8489i	−0.0782556	−	1.09176i
$439$	−19.0214	−	12.2243i	−0.907841	−	0.583434i	0.00126474	−	0.999999i	$-0.499597\pi$
$439$	−19.0214	−	12.2243i	−0.907841	−	0.583434i	−0.909106	+	0.416565i	$0.863234\pi$
$440$	−3.62437	+	0.521106i	−0.172785	+	0.0248428i
$441$	−1.62271	−	2.52325i	−0.0772719	−	0.120155i
$442$	4.25114	−	14.4780i	0.202206	−	0.688650i
$443$	−3.95576	−	1.80653i	−0.187944	−	0.0858310i	0.319220	−	0.947680i	$-0.396579\pi$
$443$	−3.95576	−	1.80653i	−0.187944	−	0.0858310i	−0.507164	+	0.861849i	$0.669306\pi$
$444$	13.2123	+	9.88737i	0.627027	+	0.469234i
$445$	−0.741220	+	5.15530i	−0.0351372	+	0.244385i
$446$	−4.53239	−	15.4359i	−0.214615	−	0.730911i
$447$	−26.8006	−	26.7922i	−1.26762	−	1.26723i
$448$	3.11458	+	4.84639i	0.147150	+	0.228970i
$449$	−16.8645	−	26.2416i	−0.795884	−	1.23842i	−0.967404	−	0.253239i	$-0.918504\pi$
$449$	−16.8645	−	26.2416i	−0.795884	−	1.23842i	0.171520	−	0.985181i	$-0.445132\pi$
$450$	−8.79622	+	10.1578i	−0.414658	+	0.478842i
$451$	−4.99897	−	17.0249i	−0.235393	−	0.801673i
$452$	1.62344	−	11.2913i	0.0763601	−	0.531096i
$453$	−13.7230	+	18.3377i	−0.644762	+	0.861581i
$454$	−11.8816	−	5.42613i	−0.557629	−	0.254661i
$455$	0.243441	−	0.829083i	0.0114127	−	0.0388680i
$456$	5.79411	+	10.6072i	0.271334	+	0.496727i
$457$	16.1216	−	2.31794i	0.754138	−	0.108429i	0.245485	−	0.969400i	$-0.421053\pi$
$457$	16.1216	−	2.31794i	0.754138	−	0.108429i	0.508653	+	0.860972i	$0.330144\pi$
$458$	−4.24521	−	2.72823i	−0.198366	−	0.127482i
$459$	−35.1371	+	7.66083i	−1.64006	+	0.357577i
$460$	−0.216815	−	2.00528i	−0.0101090	−	0.0934969i
$461$			6.74852i			0.314310i	0.987574	+	0.157155i	$0.0502322\pi$
$461$			6.74852i			0.314310i	−0.987574	+	0.157155i	$0.949768\pi$
$462$	−4.84056	−	2.64217i	−0.225203	−	0.122925i
$463$	−1.58874	−	11.0499i	−0.0738350	−	0.513534i	−0.992855	−	0.119324i	$-0.961927\pi$
$463$	−1.58874	−	11.0499i	−0.0738350	−	0.513534i	0.919020	−	0.394210i	$-0.128982\pi$
$464$	−0.163540	+	0.0746863i	−0.00759217	+	0.00346723i
$465$	−2.35038	−	0.510909i	−0.108996	−	0.0236928i
$466$	5.77656	−	12.6489i	0.267594	−	0.585949i
$467$	−16.0561	+	18.5297i	−0.742986	+	0.857452i	−0.993869	−	0.110566i	$-0.964734\pi$
$467$	−16.0561	+	18.5297i	−0.742986	+	0.857452i	0.250883	+	0.968017i	$0.419279\pi$
$468$	−0.00255760	−	8.19508i	−0.000118225	−	0.378818i
$469$	−4.84591	+	1.42289i	−0.223763	+	0.0657029i
$470$	1.09365	+	1.26214i	0.0504463	+	0.0582181i
$471$	−3.68502	−	4.92101i	−0.169797	−	0.226748i
$472$	14.5176	−	9.32987i	0.668225	−	0.429442i
$473$	24.6990	−	21.4018i	1.13566	−	0.984055i
$474$	10.8242	−	4.03915i	0.497173	−	0.185524i
$475$	−11.5851	−	1.66568i	−0.531559	−	0.0764267i
$476$	−6.03117	−	5.22604i	−0.276438	−	0.239535i
$477$	−1.82577	+	6.22520i	−0.0835964	+	0.285032i
$478$	6.14797	+	1.80521i	0.281202	+	0.0825682i
$479$	5.04304	+	11.0427i	0.230422	+	0.504554i	0.989160	−	0.146842i	$-0.0469109\pi$
$479$	5.04304	+	11.0427i	0.230422	+	0.504554i	−0.758738	+	0.651396i	$0.774184\pi$
$480$	3.37545	−	0.734836i	0.154067	−	0.0335405i
$481$	−10.5831	+	16.4676i	−0.482547	+	0.750857i
$482$	2.90116			0.132144
$483$	4.23319	−	7.14703i	0.192617	−	0.325201i
$484$	1.11793			0.0508151
$485$	2.11862	−	3.29663i	0.0962014	−	0.149692i
$486$	12.5857	−	6.88507i	0.570899	−	0.312313i
$487$	−11.8463	−	25.9399i	−0.536809	−	1.17545i	−0.962675	−	0.270661i	$-0.912758\pi$
$487$	−11.8463	−	25.9399i	−0.536809	−	1.17545i	0.425866	−	0.904786i	$-0.359969\pi$
$488$	−12.7107	−	3.73219i	−0.575385	−	0.168948i
$489$	−5.48737	+	14.7192i	−0.248147	+	0.665626i
$490$	0.253678	+	0.219813i	0.0114600	+	0.00993013i
$491$	−24.1362	−	3.47026i	−1.08925	−	0.156611i	−0.425790	−	0.904822i	$-0.640004\pi$
$491$	−24.1362	−	3.47026i	−1.08925	−	0.156611i	−0.663460	+	0.748211i	$0.730913\pi$
$492$	3.58101	+	9.59650i	0.161445	+	0.432643i
$493$	2.58141	−	2.23681i	0.116261	−	0.100741i
$494$	−4.41073	+	2.83460i	−0.198448	+	0.127535i
$495$	−2.86023	+	2.47996i	−0.128558	+	0.111466i
$496$	0.908277	+	1.04821i	0.0407828	+	0.0470659i
$497$	14.1933	−	4.16754i	0.636658	−	0.186940i
$498$	23.0896	+	1.64778i	1.03467	+	0.0738389i
$499$	−8.86126	+	10.2264i	−0.396685	+	0.457798i	−0.918594	−	0.395202i	$-0.870674\pi$
$499$	−8.86126	+	10.2264i	−0.396685	+	0.457798i	0.521909	+	0.853001i	$0.325220\pi$
$500$	−1.72386	+	3.77473i	−0.0770933	+	0.168811i
$501$	8.48153	−	39.0183i	0.378927	−	1.74321i
$502$	−18.6348	+	8.51024i	−0.831713	+	0.379831i
$503$	2.70347	+	18.8030i	0.120542	+	0.838386i	0.956945	+	0.290271i	$0.0937454\pi$
$503$	2.70347	+	18.8030i	0.120542	+	0.838386i	−0.836403	+	0.548115i	$0.815346\pi$
$504$	7.91965	+	3.61380i	0.352769	+	0.160971i
$505$			1.55340i			0.0691254i
$506$	0.535797	−	15.2601i	0.0238191	−	0.678396i
$507$	−12.7629	+	0.914820i	−0.566819	+	0.0406286i
$508$	−8.42253	−	5.41283i	−0.373690	−	0.240156i
$509$	−4.85937	+	0.698672i	−0.215388	+	0.0309681i	−0.249164	−	0.968461i	$-0.580156\pi$
$509$	−4.85937	+	0.698672i	−0.215388	+	0.0309681i	0.0337761	+	0.999429i	$0.489247\pi$
$510$	3.53127	−	1.92894i	0.156367	−	0.0854148i
$511$	4.04884	−	13.7891i	0.179110	−	0.609993i
$512$	−3.73509	−	1.70576i	−0.165069	−	0.0753847i
$513$	10.9701	+	5.98348i	0.484343	+	0.264177i
$514$	1.01793	−	7.07985i	0.0448989	−	0.312279i
$515$	−0.654774	−	2.22996i	−0.0288528	−	0.0982636i
$516$	−13.3382	+	13.3423i	−0.587180	+	0.587363i
$517$	−9.30620	−	14.4807i	−0.409286	−	0.636862i
$518$	−4.11111	−	6.39702i	−0.180632	−	0.281069i
$519$	4.16830	−	4.16960i	0.182968	−	0.183025i
$520$	0.706400	+	2.40578i	0.0309777	+	0.105500i
$521$	−1.87260	+	13.0242i	−0.0820400	+	0.570601i	0.906793	+	0.421575i	$0.138523\pi$
$521$	−1.87260	+	13.0242i	−0.0820400	+	0.570601i	−0.988833	+	0.149025i	$0.952386\pi$
$522$	−0.736300	+	1.14649i	−0.0322270	+	0.0501806i
$523$	3.44148	+	1.57167i	0.150485	+	0.0687243i	0.489234	−	0.872153i	$-0.337276\pi$
$523$	3.44148	+	1.57167i	0.150485	+	0.0687243i	−0.338749	+	0.940877i	$0.610004\pi$
$524$	−3.74378	+	12.7502i	−0.163548	+	0.556993i
$525$	−7.39806	+	4.04114i	−0.322878	+	0.176370i
$526$	−15.3776	+	2.21096i	−0.670495	+	0.0964026i
$527$	−22.1675	−	14.2462i	−0.965632	−	0.620574i
$528$	2.17738	−	0.156071i	0.0947582	−	0.00679210i
$529$	22.9434	+	1.61311i	0.997537	+	0.0701353i
$530$		−	0.725862i		−	0.0315295i
$531$	7.40655	−	16.2315i	0.321417	−	0.704386i
$532$	0.394629	+	2.74471i	0.0171093	+	0.118998i
$533$	−11.0522	+	5.04735i	−0.478722	+	0.218625i
$534$	4.83484	−	22.2421i	0.209224	−	0.962510i
$535$	0.0511890	−	0.112088i	0.00221309	−	0.00484600i
$536$	9.59710	−	11.0756i	0.414532	−	0.478395i
$537$	45.2562	+	3.22969i	1.95295	+	0.139371i
$538$	28.0093	−	8.22427i	1.20757	−	0.354573i
$539$	−2.26562	−	2.61467i	−0.0975872	−	0.112622i
$540$	1.54454	−	1.54599i	0.0664665	−	0.0665287i
$541$	−33.5867	+	21.5849i	−1.44400	+	0.928005i	−0.444525	+	0.895767i	$0.646627\pi$
$541$	−33.5867	+	21.5849i	−1.44400	+	0.928005i	−0.999480	+	0.0322388i	$0.989736\pi$
$542$	−11.9456	+	10.3509i	−0.513105	+	0.444608i
$543$	8.84646	+	23.7070i	0.379638	+	1.01736i
$544$	37.4602	+	5.38597i	1.60609	+	0.230921i
$545$	−1.01070	−	0.875776i	−0.0432936	−	0.0375141i
$546$	−1.31911	+	3.53836i	−0.0564528	+	0.151428i
$547$	−6.51831	−	1.91395i	−0.278703	−	0.0818345i	0.139394	−	0.990237i	$-0.455485\pi$
$547$	−6.51831	−	1.91395i	−0.278703	−	0.0818345i	−0.418097	+	0.908403i	$0.637303\pi$
$548$	−2.15594	−	4.72086i	−0.0920973	−	0.201665i
$549$	−13.1399	+	3.86268i	−0.560798	+	0.164855i
$550$	−8.37779	+	13.0361i	−0.357230	+	0.555861i
$551$	−1.18685			−0.0505614
$552$	0.878609	+	24.0876i	0.0373961	+	1.02524i
$553$	7.24806			0.308219
$554$	−9.45731	+	14.7159i	−0.401802	+	0.625217i
$555$	−5.10050	+	1.11038i	−0.216504	+	0.0471330i
$556$	7.41381	+	16.2340i	0.314416	+	0.688475i
$557$	−28.2442	−	8.29324i	−1.19674	−	0.351396i	−0.378137	−	0.925750i	$-0.623435\pi$
$557$	−28.2442	−	8.29324i	−1.19674	−	0.351396i	−0.818607	+	0.574354i	$0.805253\pi$
$558$	10.0867	+	2.95830i	0.427004	+	0.125235i
$559$	−16.9128	−	14.6551i	−0.715337	−	0.619843i
$560$	−0.131518	−	0.0189094i	−0.00555764	−	0.000799068i
$561$	−38.8560	+	14.4995i	−1.64050	+	0.612167i
$562$	−8.28894	+	7.18240i	−0.349648	+	0.302971i
$563$	26.8518	−	17.2566i	1.13167	−	0.727280i	0.165762	−	0.986166i	$-0.446992\pi$
$563$	26.8518	−	17.2566i	1.13167	−	0.727280i	0.965908	+	0.258885i	$0.0833552\pi$
$564$	5.95607	+	7.95379i	0.250796	+	0.334915i
$565$	2.36297	+	2.72702i	0.0994111	+	0.114727i
$566$	6.28187	−	1.84452i	0.264047	−	0.0775312i
$567$	8.90759	−	1.28639i	0.374084	−	0.0540235i
$568$	−28.1092	+	32.4398i	−1.17944	+	1.36114i
$569$	−8.68073	+	19.0081i	−0.363915	+	0.796863i	0.635773	+	0.771876i	$0.280682\pi$
$569$	−8.68073	+	19.0081i	−0.363915	+	0.796863i	−0.999688	+	0.0249866i	$0.992046\pi$
$570$	−1.36623	−	0.296981i	−0.0572249	−	0.0124392i
$571$	13.2058	−	6.03087i	0.552644	−	0.252384i	−0.119462	−	0.992839i	$-0.538117\pi$
$571$	13.2058	−	6.03087i	0.552644	−	0.252384i	0.672106	+	0.740455i	$0.265390\pi$
$572$	−1.34499	−	9.35464i	−0.0562370	−	0.391137i
$573$	−19.3613	−	10.5682i	−0.808831	−	0.441491i
$574$		−	4.71986i		−	0.197003i
$575$	−19.1809	−	13.3004i	−0.799900	−	0.554666i
$576$	−17.1061	+	2.46493i	−0.712752	+	0.102705i
$577$	−24.1984	−	15.5514i	−1.00739	−	0.647413i	−0.0706765	−	0.997499i	$-0.522516\pi$
$577$	−24.1984	−	15.5514i	−1.00739	−	0.647413i	−0.936717	+	0.350087i	$0.886152\pi$
$578$	28.1475	−	4.04700i	1.17078	−	0.168333i
$579$	6.67920	+	12.2275i	0.277578	+	0.508157i
$580$	−0.0584769	+	0.199154i	−0.00242812	+	0.00826943i
$581$	13.2100	+	6.03279i	0.548041	+	0.250282i
$582$	−10.2609	+	13.7114i	−0.425328	+	0.568356i
$583$	−1.06473	+	7.40535i	−0.0440966	+	0.306698i
$584$	11.7486	+	40.0122i	0.486162	+	1.65572i
$585$	1.95963	+	1.69695i	0.0810205	+	0.0701604i
$586$	−12.7951	−	19.9095i	−0.528560	−	0.822455i
$587$	7.11331	+	11.0685i	0.293598	+	0.456847i	0.956447	−	0.291906i	$-0.0942894\pi$
$587$	7.11331	+	11.0685i	0.293598	+	0.456847i	−0.662849	+	0.748753i	$0.730653\pi$
$588$	1.41244	+	1.41200i	0.0582479	+	0.0582297i
$589$	2.57954	+	8.78511i	0.106288	+	0.361984i
$590$	−0.284095	+	1.97592i	−0.0116960	+	0.0813475i
$591$	13.8957	+	10.3988i	0.571594	+	0.427751i
$592$	2.73804	+	1.25042i	0.112533	+	0.0513920i
$593$	1.97280	−	6.71873i	0.0810131	−	0.275905i	−0.909017	−	0.416758i	$-0.863166\pi$
$593$	1.97280	−	6.71873i	0.0810131	−	0.275905i	0.990031	+	0.140853i	$0.0449844\pi$
$594$	13.2396	−	9.92073i	0.543228	−	0.407053i
$595$	2.49865	−	0.359252i	0.102435	−	0.0147279i
$596$	21.2233	+	13.6394i	0.869341	+	0.558691i
$597$	−1.51571	−	21.1460i	−0.0620338	−	0.865448i
$598$	−10.3954	+	1.12396i	−0.425098	+	0.0459623i
$599$			41.6537i			1.70192i	0.525228	+	0.850962i	$0.323980\pi$
$599$			41.6537i			1.70192i	−0.525228	+	0.850962i	$0.676020\pi$
$600$	11.7196	−	21.4708i	0.478451	−	0.876543i
$601$	−0.614034	−	4.27070i	−0.0250470	−	0.174205i	0.973458	−	0.228865i	$-0.0735016\pi$
$601$	−0.614034	−	4.27070i	−0.0250470	−	0.174205i	−0.998505	+	0.0546600i	$0.982592\pi$
$602$	7.90773	−	3.61134i	0.322295	−	0.147187i
$603$	2.15160	−	14.9979i	0.0876199	−	0.610763i
$604$	6.33415	−	13.8698i	0.257733	−	0.564356i
$605$	−0.231573	+	0.267250i	−0.00941480	+	0.0108653i
$606$	0.483245	−	6.77150i	0.0196305	−	0.275073i
$607$	18.9219	−	5.55596i	0.768015	−	0.225510i	0.125822	−	0.992053i	$-0.459843\pi$
$607$	18.9219	−	5.55596i	0.768015	−	0.225510i	0.642193	+	0.766543i	$0.278025\pi$
$608$	−8.61148	−	9.93818i	−0.349242	−	0.403046i
$609$	−0.684235	+	0.512379i	−0.0277266	+	0.0207626i
$610$	1.28914	−	0.828480i	0.0521957	−	0.0335442i
$611$	−8.90798	+	7.71881i	−0.360378	+	0.312269i
$612$	21.7745	−	9.95231i	0.880183	−	0.402298i
$613$	33.3218	+	4.79095i	1.34586	+	0.193505i	0.777295	−	0.629136i	$-0.216591\pi$
$613$	33.3218	+	4.79095i	1.34586	+	0.193505i	0.568561	+	0.822641i	$0.307500\pi$
$614$	9.03203	+	7.82630i	0.364503	+	0.315844i
$615$	−3.03590	−	1.13179i	−0.122419	−	0.0456383i
$616$	9.63247	+	2.82835i	0.388103	+	0.113957i
$617$	−13.7389	−	30.0840i	−0.553107	−	1.21113i	−0.955316	−	0.295587i	$-0.904485\pi$
$617$	−13.7389	−	30.0840i	−0.553107	−	1.21113i	0.402209	−	0.915548i	$-0.368242\pi$
$618$	2.16054	+	9.92438i	0.0869097	+	0.399217i
$619$	5.05676	−	7.86848i	0.203248	−	0.316261i	−0.724634	−	0.689134i	$-0.757991\pi$
$619$	5.05676	−	7.86848i	0.203248	−	0.316261i	0.927882	+	0.372873i	$0.121627\pi$
$620$	1.60125			0.0643076
$621$	14.2343	+	20.4545i	0.571203	+	0.820809i
$622$	−6.60532			−0.264849
$623$	7.72015	−	12.0128i	0.309301	−	0.481282i
$624$	−0.317971	−	1.46059i	−0.0127290	−	0.0584705i
$625$	9.56377	+	20.9417i	0.382551	+	0.837669i
$626$	6.21577	+	1.82511i	0.248432	+	0.0729462i
$627$	13.5028	+	5.03389i	0.539250	+	0.201034i
$628$	3.09310	+	2.68019i	0.123428	+	0.106951i
$629$	−56.6046	−	8.13851i	−2.25697	−	0.324504i
$630$	−0.915860	+	0.418605i	−0.0364887	+	0.0166776i
$631$	31.0168	−	26.8762i	1.23476	−	1.06992i	0.239678	−	0.970852i	$-0.422958\pi$
$631$	31.0168	−	26.8762i	1.23476	−	1.06992i	0.995080	−	0.0990717i	$-0.0315873\pi$
$632$	−17.6932	+	11.3707i	−0.703797	+	0.452303i
$633$	4.44776	−	3.33064i	0.176783	−	0.132381i
$634$	−3.17121	−	3.65978i	−0.125945	−	0.145348i
$635$	3.03866	−	0.892232i	0.120586	−	0.0354071i
$636$	0.307430	−	4.30788i	0.0121904	−	0.170818i
$637$	−1.55140	+	1.79042i	−0.0614689	+	0.0709389i
$638$	−0.652764	+	1.42935i	−0.0258432	+	0.0565887i
$639$	−6.30188	+	43.9278i	−0.249298	+	1.73776i
$640$	−1.86947	+	0.853759i	−0.0738974	+	0.0337478i
$641$	−3.02644	−	21.0493i	−0.119537	−	0.831399i	−0.958067	−	0.286543i	$-0.907494\pi$
$641$	−3.02644	−	21.0493i	−0.119537	−	0.831399i	0.838530	−	0.544855i	$-0.183415\pi$
$642$	−0.258010	+	0.472685i	−0.0101828	+	0.0186554i
$643$			31.3583i			1.23665i	0.785922	+	0.618326i	$0.212189\pi$
$643$			31.3583i			1.23665i	−0.785922	+	0.618326i	$0.787811\pi$
$644$	−1.74318	+	5.24799i	−0.0686910	+	0.206800i
$645$	−0.426656	−	5.95238i	−0.0167996	−	0.234375i
$646$	−12.8855	−	8.28103i	−0.506974	−	0.325813i
$647$	−10.8626	+	1.56180i	−0.427052	+	0.0614008i	−0.352490	−	0.935816i	$-0.614665\pi$
$647$	−10.8626	+	1.56180i	−0.427052	+	0.0614008i	−0.0745618	+	0.997216i	$0.523756\pi$
$648$	−19.7262	+	17.1144i	−0.774917	+	0.672317i
$649$	5.79675	−	19.7419i	0.227542	−	0.774938i
$650$	9.65215	+	4.40799i	0.378588	+	0.172896i
$651$	5.27980	+	3.95112i	0.206931	+	0.154857i
$652$	1.48829	−	10.3513i	0.0582861	−	0.405388i
$653$	10.1403	+	34.5347i	0.396821	+	1.35145i	0.879604	+	0.475707i	$0.157808\pi$
$653$	10.1403	+	34.5347i	0.396821	+	1.35145i	−0.482783	+	0.875740i	$0.660374\pi$
$654$	4.13334	+	4.13205i	0.161626	+	0.161576i
$655$	−2.27252	−	3.53610i	−0.0887946	−	0.138167i
$656$	1.01009	+	1.57174i	0.0394375	+	0.0613660i
$657$	32.5919	+	28.2232i	1.27153	+	1.10109i
$658$	−1.28999	−	4.39330i	−0.0502890	−	0.171269i
$659$	3.65183	−	25.3991i	0.142255	−	0.989407i	−0.786203	−	0.617969i	$-0.787956\pi$
$659$	3.65183	−	25.3991i	0.142255	−	0.989407i	0.928458	−	0.371438i	$-0.121135\pi$
$660$	1.50998	−	2.01776i	0.0587761	−	0.0785412i
$661$	−18.8998	−	8.63126i	−0.735118	−	0.335717i	0.0124321	−	0.999923i	$-0.496043\pi$
$661$	−18.8998	−	8.63126i	−0.735118	−	0.335717i	−0.747550	+	0.664206i	$0.768770\pi$
$662$	−3.66305	+	12.4752i	−0.142369	+	0.484863i
$663$	13.6141	+	24.9232i	0.528729	+	0.967936i
$664$	−41.7109	+	5.99713i	−1.61870	+	0.232734i
$665$	−0.737888	−	0.474212i	−0.0286141	−	0.0183892i
$666$	22.5792	−	3.25360i	0.874928	−	0.126074i
$667$	−2.11716	−	1.05818i	−0.0819768	−	0.0409728i
$668$			26.5821i			1.02849i
$669$	26.5766	+	14.5065i	1.02751	+	0.560855i
$670$	0.241261	+	1.67801i	0.00932074	+	0.0648272i
$671$	−14.3672	+	6.56130i	−0.554641	+	0.253296i
$672$	−9.25509	−	2.01181i	−0.357023	−	0.0776072i
$673$	−6.03388	+	13.2124i	−0.232589	+	0.509299i	−0.989555	−	0.144155i	$-0.953954\pi$
$673$	−6.03388	+	13.2124i	−0.232589	+	0.509299i	0.756966	+	0.653454i	$0.226681\pi$
$674$	−15.4595	+	17.8412i	−0.595476	+	0.687216i
$675$	−1.81594	−	25.2242i	−0.0698956	−	0.970881i
$676$	8.17331	−	2.39990i	0.314358	−	0.0923039i
$677$	18.2661	+	21.0802i	0.702022	+	0.810177i	0.989024	−	0.147753i	$-0.0472042\pi$
$677$	18.2661	+	21.0802i	0.702022	+	0.810177i	−0.287002	+	0.957930i	$0.592659\pi$
$678$	−9.45220	−	12.6226i	−0.363010	−	0.484766i
$679$	−9.03837	+	5.80861i	−0.346861	+	0.222914i
$680$	−5.53584	+	4.79683i	−0.212290	+	0.183950i
$681$	23.0322	−	8.59467i	0.882596	−	0.329348i
$682$	11.9989	+	1.72518i	0.459461	+	0.0660606i
$683$	15.0554	+	13.0456i	0.576080	+	0.499176i	0.893472	−	0.449118i	$-0.148262\pi$
$683$	15.0554	+	13.0456i	0.576080	+	0.499176i	−0.317392	+	0.948294i	$0.602807\pi$
$684$	−7.98255	−	2.34118i	−0.305221	−	0.0895174i
$685$	1.57515	+	0.462505i	0.0601833	+	0.0176714i
$686$	−0.382301	−	0.837123i	−0.0145963	−	0.0319615i
$687$	9.28013	−	2.02029i	0.354059	−	0.0770787i
$688$	−1.86045	+	2.89492i	−0.0709291	+	0.110368i
$689$	5.12302			0.195172
$690$	−2.17236	−	1.74788i	−0.0827003	−	0.0665406i
$691$	0.385056			0.0146482			0.00732410	−	0.999973i	$-0.497669\pi$
$691$	0.385056			0.0146482			0.00732410	+	0.999973i	$0.497669\pi$
$692$	−2.12200	+	3.30190i	−0.0806664	+	0.125519i
$693$	9.95776	−	2.92724i	0.378264	−	0.111197i
$694$	−3.18674	−	6.97799i	−0.120967	−	0.264881i
$695$	−5.41659	−	1.59045i	−0.205463	−	0.0603294i
$696$	0.866464	−	2.32419i	0.0328432	−	0.0880981i
$697$	−26.8257	−	23.2446i	−1.01610	−	0.880453i
$698$	−1.18661	−	0.170609i	−0.0449139	−	0.00645764i
$699$	9.14973	+	24.5197i	0.346075	+	0.927420i
$700$	4.24123	−	3.67505i	0.160303	−	0.138904i
$701$	−24.9512	+	16.0351i	−0.942393	+	0.605639i	−0.919072	−	0.394089i	$-0.871060\pi$
$701$	−24.9512	+	16.0351i	−0.942393	+	0.605639i	−0.0233204	+	0.999728i	$0.507424\pi$
$702$	−8.01438	−	8.00688i	−0.302483	−	0.302200i
$703$	13.0125	+	15.0172i	0.490774	+	0.566383i
$704$	−19.1237	+	5.61522i	−0.720751	+	0.211632i
$705$	−3.13518	−	0.223741i	−0.118078	−	0.00842657i
$706$	−12.5300	+	14.4604i	−0.471573	+	0.544224i
$707$	1.76923	−	3.87408i	0.0665389	−	0.145700i
$708$	−2.52294	+	11.6065i	−0.0948177	+	0.436198i
$709$	−16.2836	+	7.43647i	−0.611544	+	0.279283i	−0.697013	−	0.717058i	$-0.745488\pi$
$709$	−16.2836	+	7.43647i	−0.611544	+	0.279283i	0.0854697	+	0.996341i	$0.472761\pi$
$710$	−0.706637	−	4.91477i	−0.0265196	−	0.184448i
$711$	−9.02668	+	19.7820i	−0.338527	+	0.741883i
$712$			41.4356i			1.55287i
$713$	−3.23117	+	17.9712i	−0.121008	+	0.673027i
$714$	−11.0037	+	0.788728i	−0.411804	+	0.0295174i
$715$	2.51491	+	1.61623i	0.0940522	+	0.0604437i
$716$	−29.8973	+	4.29859i	−1.11732	+	0.160646i
$717$	−10.5834	+	5.78112i	−0.395244	+	0.215900i
$718$	5.00846	−	17.0573i	0.186914	−	0.636571i
$719$	−29.7206	−	13.5729i	−1.10839	−	0.506185i	−0.224782	−	0.974409i	$-0.572167\pi$
$719$	−29.7206	−	13.5729i	−1.10839	−	0.506185i	−0.883610	+	0.468224i	$0.844894\pi$
$720$	0.215401	−	0.335400i	0.00802750	−	0.0124996i
$721$	−0.906827	+	6.30712i	−0.0337720	+	0.234889i
$722$	−3.42679	−	11.6706i	−0.127532	−	0.434334i
$723$	−3.86034	+	3.86155i	−0.143568	+	0.143612i
$724$	−9.10728	−	14.1712i	−0.338470	−	0.526669i
$725$	1.29861	+	2.02068i	0.0482292	+	0.0750461i
$726$	1.09260	−	1.09294i	0.0405502	−	0.0405628i
$727$	−5.64105	−	19.2116i	−0.209215	−	0.712521i	−0.995509	−	0.0946680i	$-0.969821\pi$
$727$	−5.64105	−	19.2116i	−0.209215	−	0.712521i	0.786294	−	0.617853i	$-0.211997\pi$
$728$	0.978326	−	6.80441i	0.0362592	−	0.252188i
$729$	−7.58252	+	25.9134i	−0.280834	+	0.959756i
$730$	−4.38796	−	2.00392i	−0.162406	−	0.0741683i
$731$	18.4191	−	62.7296i	0.681254	−	2.32014i
$732$	8.00173	−	4.37090i	0.295753	−	0.161553i
$733$	26.8577	−	3.86155i	0.992010	−	0.142630i	0.372848	−	0.927892i	$-0.378381\pi$
$733$	26.8577	−	3.86155i	0.992010	−	0.142630i	0.619163	+	0.785263i	$0.287472\pi$
$734$	−25.7216	−	16.5303i	−0.949401	−	0.610143i
$735$	−0.630127	+	0.0451664i	−0.0232426	+	0.00166599i
$736$	−6.50085	−	25.4061i	−0.239625	−	0.936481i
$737$		−	17.4732i		−	0.643633i
$738$	12.8818	+	5.87808i	0.474187	+	0.216375i
$739$	−6.11324	−	42.5185i	−0.224879	−	1.56407i	−0.719209	−	0.694794i	$-0.755495\pi$
$739$	−6.11324	−	42.5185i	−0.224879	−	1.56407i	0.494330	−	0.869275i	$-0.335414\pi$
$740$	3.16103	−	1.44359i	0.116202	−	0.0530676i
$741$	2.09605	−	9.64261i	0.0770002	−	0.354230i
$742$	−0.826716	+	1.81025i	−0.0303497	+	0.0664566i
$743$	1.59846	−	1.84473i	0.0586420	−	0.0676764i	−0.725671	−	0.688042i	$-0.758470\pi$
$743$	1.59846	−	1.84473i	0.0586420	−	0.0676764i	0.784313	+	0.620366i	$0.213016\pi$
$744$	−19.0870	−	1.36213i	−0.699762	−	0.0499382i
$745$	−7.65690	+	2.24827i	−0.280527	+	0.0823702i
$746$	7.18452	+	8.29138i	0.263044	+	0.303569i
$747$	−32.9168	+	28.5405i	−1.20436	+	1.04424i
$748$	23.2268	−	14.9269i	0.849255	−	0.545783i
$749$	−0.255324	+	0.221240i	−0.00932935	+	0.00808393i
$750$	2.00555	+	5.37452i	0.0732322	+	0.196250i
$751$	34.0454	+	4.89499i	1.24233	+	0.178621i	0.731969	−	0.681338i	$-0.238602\pi$
$751$	34.0454	+	4.89499i	1.24233	+	0.178621i	0.510364	+	0.859958i	$0.329511\pi$
$752$	1.36978	+	1.18692i	0.0499507	+	0.0432825i
$753$	13.4684	−	36.1275i	0.490817	−	1.31656i
$754$	1.03241	+	0.303144i	0.0375983	+	0.0110398i
$755$	2.00361	+	4.38729i	0.0729188	+	0.159670i
$756$	−5.61278	+	2.09645i	−0.204135	+	0.0762472i
$757$	9.73240	−	15.1439i	0.353730	−	0.550415i	−0.618099	−	0.786100i	$-0.712097\pi$
$757$	9.73240	−	15.1439i	0.353730	−	0.550415i	0.971829	+	0.235685i	$0.0757334\pi$
$758$	−35.5309			−1.29054
$759$	19.5989	+	21.0186i	0.711393	+	0.762928i
$760$	2.54520			0.0923239
$761$	0.456685	−	0.710616i	0.0165548	−	0.0257598i	−0.832878	−	0.553457i	$-0.813308\pi$
$761$	0.456685	−	0.710616i	0.0165548	−	0.0257598i	0.849432	+	0.527698i	$0.176945\pi$
$762$	−13.5235	+	2.94407i	−0.489905	+	0.106652i
$763$	1.52316	+	3.33526i	0.0551422	+	0.120744i
$764$	14.0896	+	4.13709i	0.509745	+	0.149675i
$765$	−2.13130	+	7.26693i	−0.0770574	+	0.262737i
$766$	4.77676	+	4.13909i	0.172591	+	0.149551i
$767$	−13.9458	−	2.00510i	−0.503552	−	0.0723999i
$768$	27.1119	−	10.1170i	0.978317	−	0.365067i
$769$	37.5010	−	32.4948i	1.35232	−	1.17179i	0.383640	−	0.923483i	$-0.374670\pi$
$769$	37.5010	−	32.4948i	1.35232	−	1.17179i	0.968681	−	0.248309i	$-0.0798750\pi$
$770$	−0.976944	+	0.627844i	−0.0352066	+	0.0226259i
$771$	8.06906	+	10.7755i	0.290600	+	0.388070i
$772$	−6.07411	−	7.00990i	−0.218612	−	0.252292i
$773$	18.3223	−	5.37992i	0.659008	−	0.193502i	0.0649055	−	0.997891i	$-0.479325\pi$
$773$	18.3223	−	5.37992i	0.659008	−	0.193502i	0.594103	+	0.804389i	$0.297507\pi$
$774$	0.00813929	+	26.0800i	0.000292561	+	0.937426i
$775$	12.1347	−	14.0042i	0.435892	−	0.503046i
$776$	12.9510	−	28.3587i	0.464913	−	1.01802i
$777$	13.9850	+	3.03996i	0.501709	+	0.109058i
$778$	−4.08189	+	1.86414i	−0.146343	+	0.0668325i
$779$	1.75525	+	12.2080i	0.0628884	+	0.437398i
$780$	−1.51477	−	0.826818i	−0.0542373	−	0.0296048i
$781$			51.1777i			1.83128i
$782$	−15.6026	−	26.2607i	−0.557948	−	0.939080i
$783$	−0.546285	−	2.50559i	−0.0195226	−	0.0895423i
$784$	0.306460	+	0.196950i	0.0109450	+	0.00703393i
$785$	−1.28144	+	0.184243i	−0.0457365	+	0.00657592i
$786$	8.80618	+	16.1213i	0.314106	+	0.575029i
$787$	−0.911824	+	3.10539i	−0.0325030	+	0.110695i	−0.974147	−	0.225916i	$-0.927463\pi$
$787$	−0.911824	+	3.10539i	−0.0325030	+	0.110695i	0.941644	+	0.336611i	$0.109281\pi$
$788$	−10.5101	−	4.79981i	−0.374408	−	0.170986i
$789$	17.5189	−	23.4101i	0.623688	−	0.833421i
$790$	0.346239	−	2.40814i	0.0123186	−	0.0856779i
$791$	−2.78719	−	9.49230i	−0.0991011	−	0.337507i
$792$	−19.7156	+	22.7673i	−0.700563	+	0.809002i
$793$	5.84728	+	9.09855i	0.207643	+	0.323099i
$794$	0.0548362	+	0.0853268i	0.00194606	+	0.00302813i
$795$	0.966149	+	0.965847i	0.0342658	+	0.0342551i
$796$	3.97624	+	13.5418i	0.140934	+	0.479978i
$797$	−5.19980	+	36.1654i	−0.184186	+	1.28105i	0.662544	+	0.749023i	$0.269477\pi$
$797$	−5.19980	+	36.1654i	−0.184186	+	1.28105i	−0.846730	+	0.532022i	$0.821432\pi$
$798$	3.06904	+	2.29671i	0.108643	+	0.0813025i
$799$	−31.3227	−	14.3046i	−1.10812	−	0.506060i
$800$	−7.49792	+	25.5356i	−0.265092	+	0.902819i
$801$	23.1717	+	36.0311i	0.818731	+	1.27310i
$802$	3.34859	−	0.481454i	0.118243	−	0.0170007i
$803$	41.8272	+	26.8807i	1.47605	+	0.948599i
$804$	0.721148	+	10.0609i	0.0254329	+	0.354821i
$805$	−0.893482	−	1.50381i	−0.0314911	−	0.0530025i
$806$		−	8.30084i		−	0.292385i
$807$	−26.3229	+	48.2247i	−0.926611	+	1.69759i
$808$	1.75878	+	12.2326i	0.0618736	+	0.430340i
$809$	28.5016	−	13.0163i	1.00206	−	0.457627i	0.154313	−	0.988022i	$-0.450684\pi$
$809$	28.5016	−	13.0163i	1.00206	−	0.457627i	0.847751	+	0.530395i	$0.177956\pi$
$810$	−0.00188563	−	3.02097i	−6.62542e−5	−	0.106146i
$811$	14.6019	−	31.9736i	0.512741	−	1.12275i	−0.459375	−	0.888243i	$-0.651927\pi$
$811$	14.6019	−	31.9736i	0.512741	−	1.12275i	0.972115	−	0.234503i	$-0.0753462\pi$
$812$	0.372663	−	0.430076i	0.0130779	−	0.0150927i
$813$	2.11760	−	29.6730i	0.0742676	−	1.04068i
$814$	25.2424	−	7.41184i	0.884746	−	0.259785i
$815$	2.16627	+	2.50000i	0.0758810	+	0.0875714i
$816$	3.49550	−	2.61755i	0.122367	−	0.0916325i
$817$	−19.1105	+	12.2816i	−0.668593	+	0.429678i
$818$	−24.5394	+	21.2635i	−0.857999	+	0.743460i
$819$	−2.95445	−	6.46400i	−0.103237	−	0.225870i
$820$	2.13500	+	0.306967i	0.0745575	+	0.0107197i
$821$	−28.4309	−	24.6355i	−0.992246	−	0.859786i	−0.00212437	−	0.999998i	$-0.500676\pi$
$821$	−28.4309	−	24.6355i	−0.992246	−	0.859786i	−0.990122	+	0.140212i	$0.955222\pi$
$822$	−6.72242	−	2.50614i	−0.234471	−	0.0874115i
$823$	−48.4412	−	14.2236i	−1.68855	−	0.495804i	−0.710420	−	0.703778i	$-0.751495\pi$
$823$	−48.4412	−	14.2236i	−1.68855	−	0.495804i	−0.978134	+	0.207973i	$0.933313\pi$
$824$	−7.68093	−	16.8189i	−0.267578	−	0.585914i
$825$	−6.20385	−	28.4972i	−0.215990	−	0.992146i
$826$	2.95898	−	4.60426i	0.102956	−	0.160203i
$827$	−46.5297			−1.61800			−0.808998	−	0.587811i	$-0.799990\pi$
$827$	−46.5297			−1.61800			−0.808998	+	0.587811i	$0.799990\pi$
$828$	−12.1523	−	11.2935i	−0.422322	−	0.392475i
$829$	7.39916			0.256983			0.128492	−	0.991711i	$-0.458986\pi$
$829$	7.39916			0.256983			0.128492	+	0.991711i	$0.458986\pi$
$830$	2.63541	−	4.10078i	0.0914765	−	0.142340i
$831$	−7.00324	−	32.1692i	−0.242940	−	1.11594i
$832$	5.66956	+	12.4146i	0.196557	+	0.430399i
$833$	−6.64064	−	1.94987i	−0.230085	−	0.0675589i
$834$	23.1169	+	8.61805i	0.800473	+	0.298419i
$835$	−6.35464	−	5.50633i	−0.219912	−	0.190554i
$836$	−9.49586	−	1.36530i	−0.328421	−	0.0472198i
$837$	−17.3592	+	9.48937i	−0.600020	+	0.328000i
$838$	−16.5872	+	14.3729i	−0.572994	+	0.496502i
$839$	−4.42394	+	2.84309i	−0.152731	+	0.0981544i	−0.614774	−	0.788703i	$-0.710753\pi$
$839$	−4.42394	+	2.84309i	−0.152731	+	0.0981544i	0.462043	+	0.886857i	$0.347117\pi$
$840$	1.46734	−	1.09880i	0.0506281	−	0.0379121i
$841$	−18.8315	−	21.7327i	−0.649361	−	0.749402i
$842$	−12.4034	+	3.64195i	−0.427448	+	0.125510i
$843$	1.46939	−	20.5899i	0.0506085	−	0.709154i
$844$	−2.42244	+	2.79564i	−0.0833838	+	0.0962300i
$845$	−1.11934	+	2.45102i	−0.0385066	+	0.0843176i
$846$	13.5971	+	1.95064i	0.467478	+	0.0670643i
$847$	0.881912	−	0.402756i	0.0303029	−	0.0138389i
$848$	−0.112111	−	0.779748i	−0.00384990	−	0.0267767i
$849$	−5.90366	+	10.8158i	−0.202613	+	0.371196i
$850$			30.9992i			1.06326i
$851$	9.82317	+	38.3901i	0.336734	+	1.31600i
$852$	−2.11219	−	29.4677i	−0.0723625	−	1.00955i
$853$	8.95610	+	5.75574i	0.306651	+	0.197073i	0.684911	−	0.728627i	$-0.259841\pi$
$853$	8.95610	+	5.75574i	0.306651	+	0.197073i	−0.378260	+	0.925699i	$0.623477\pi$
$854$	−4.15862	+	0.597920i	−0.142305	+	0.0204604i
$855$	2.21322	−	1.42333i	0.0756906	−	0.0486768i
$856$	0.276190	−	0.940618i	0.00944000	−	0.0321497i
$857$	−35.9011	−	16.3955i	−1.22636	−	0.560059i	−0.306336	−	0.951923i	$-0.599103\pi$
$857$	−35.9011	−	16.3955i	−1.22636	−	0.560059i	−0.920023	+	0.391864i	$0.871830\pi$
$858$	−10.4600	−	7.82774i	−0.357100	−	0.267235i
$859$	−2.29197	+	15.9410i	−0.0782009	+	0.543899i	0.912630	+	0.408788i	$0.134048\pi$
$859$	−2.29197	+	15.9410i	−0.0782009	+	0.543899i	−0.990830	+	0.135111i	$0.956861\pi$
$860$	1.11927	+	3.81189i	0.0381668	+	0.129984i
$861$	6.28230	+	6.28034i	0.214100	+	0.214033i
$862$	12.5232	+	19.4865i	0.426543	+	0.663714i
$863$	−12.0873	−	18.8082i	−0.411457	−	0.640240i	0.572237	−	0.820088i	$-0.306076\pi$
$863$	−12.0873	−	18.8082i	−0.411457	−	0.640240i	−0.983694	+	0.179848i	$0.942439\pi$
$864$	17.0170	−	22.7543i	0.578931	−	0.774116i
$865$	−0.349783	−	1.19125i	−0.0118930	−	0.0405038i
$866$	−2.90049	+	20.1734i	−0.0985628	+	0.685519i
$867$	−32.0670	+	42.8504i	−1.08905	+	1.45528i
$868$	−3.99341	−	1.82373i	−0.135545	−	0.0619013i
$869$	−7.06475	+	24.0603i	−0.239655	+	0.816191i
$870$	0.137550	+	0.251811i	0.00466339	+	0.00853720i
$871$	−11.8431	+	1.70279i	−0.401289	+	0.0576967i
$872$	−8.95052	−	5.75215i	−0.303103	−	0.194792i
$873$	−4.59702	−	31.9023i	−0.155586	−	1.07973i
$874$	−1.87821	+	10.4463i	−0.0635314	+	0.353351i
$875$			3.59885i			0.121663i
$876$	−25.1931	−	13.7514i	−0.851197	−	0.464616i
$877$	−5.11562	−	35.5799i	−0.172742	−	1.20145i	−0.873058	−	0.487616i	$-0.837867\pi$
$877$	−5.11562	−	35.5799i	−0.172742	−	1.20145i	0.700316	−	0.713833i	$-0.253042\pi$
$878$	18.9280	−	8.64413i	0.638789	−	0.291725i
$879$	43.5257	+	9.46131i	1.46808	+	0.319122i
$880$	0.190963	−	0.418150i	0.00643735	−	0.0140958i
$881$	16.5857	−	19.1409i	0.558785	−	0.644873i	−0.404122	−	0.914705i	$-0.632423\pi$
$881$	16.5857	−	19.1409i	0.558785	−	0.644873i	0.962907	+	0.269832i	$0.0869683\pi$
$882$	2.76086		0.000861637i	0.0929631		2.90128e-5i
$883$	5.60149	−	1.64475i	0.188505	−	0.0553501i	−0.186117	−	0.982528i	$-0.559590\pi$
$883$	5.60149	−	1.64475i	0.188505	−	0.0553501i	0.374623	+	0.927177i	$0.377772\pi$
$884$	−12.3808	−	14.2882i	−0.416411	−	0.480564i
$885$	−2.25200	−	3.00734i	−0.0757002	−	0.101091i
$886$	3.36678	−	2.16370i	0.113109	−	0.0726909i
$887$	23.8570	−	20.6722i	0.801041	−	0.694106i	−0.154814	−	0.987944i	$-0.549478\pi$
$887$	23.8570	−	20.6722i	0.801041	−	0.694106i	0.955855	+	0.293837i	$0.0949324\pi$
$888$	−38.9077	+	14.5187i	−1.30566	+	0.487217i
$889$	−8.59443	−	1.23569i	−0.288248	−	0.0414438i
$890$	−3.62242	−	3.13884i	−0.121424	−	0.105214i
$891$	−4.41206	+	30.8231i	−0.147810	+	1.03261i
$892$	−19.3403	−	5.67883i	−0.647562	−	0.190141i
$893$	4.97039	+	10.8836i	0.166328	+	0.364207i
$894$	34.0769	−	7.41855i	1.13970	−	0.248113i
$895$	5.16546	−	8.03762i	0.172662	−	0.268668i
$896$	5.63473			0.188243
$897$	12.3363	−	15.3322i	0.411896	−	0.511927i
$898$	28.7070			0.957965
$899$	1.01588	−	1.58074i	0.0338815	−	0.0527207i
$900$	4.74825	+	16.1524i	0.158275	+	0.538414i
$901$	6.21728	+	13.6139i	0.207128	+	0.453546i
$902$	15.6679	+	4.60050i	0.521682	+	0.153180i
$903$	−5.71536	+	15.3308i	−0.190195	+	0.510177i
$904$	21.6953	+	18.7991i	0.721574	+	0.625248i
$905$	5.27426	+	0.758324i	0.175322	+	0.0252075i
$906$	−7.36918	−	19.7481i	−0.244824	−	0.656087i
$907$	−41.9776	+	36.3738i	−1.39384	+	1.20777i	−0.443613	+	0.896218i	$0.646303\pi$
$907$	−41.9776	+	36.3738i	−1.39384	+	1.20777i	−0.950229	+	0.311552i	$0.899151\pi$
$908$	−13.7679	+	8.84807i	−0.456903	+	0.293633i
$909$	8.37008	+	9.65350i	0.277618	+	0.320186i
$910$	0.520750	+	0.600977i	0.0172627	+	0.0199222i
$911$	31.6868	−	9.30409i	1.04983	−	0.308258i	0.289082	−	0.957304i	$-0.406650\pi$
$911$	31.6868	−	9.30409i	1.04983	−	0.308258i	0.760749	+	0.649046i	$0.224832\pi$
$912$	−1.51352	−	0.108012i	−0.0501177	−	0.00357663i
$913$	−32.9021	+	37.9710i	−1.08890	+	1.25666i
$914$	−6.22670	+	13.6346i	−0.205961	+	0.450992i
$915$	−0.612619	+	2.81828i	−0.0202526	+	0.0931696i
$916$	−5.75135	+	2.62655i	−0.190030	+	0.0867838i
$917$	1.64009	+	11.4071i	0.0541606	+	0.376695i
$918$	11.5513	−	31.0146i	0.381250	−	1.02363i
$919$			8.05906i			0.265844i	0.991127	+	0.132922i	$0.0424360\pi$
$919$			8.05906i			0.265844i	−0.991127	+	0.132922i	$0.957564\pi$
$920$	4.54025	+	2.26926i	0.149688	+	0.0748153i
$921$	−22.4353	+	1.60812i	−0.739268	+	0.0529894i
$922$	−5.22468	−	3.35770i	−0.172066	−	0.110580i
$923$	34.6877	−	4.98734i	1.14176	−	0.164160i
$924$	−6.06392	+	3.31238i	−0.199488	+	0.108969i
$925$	11.3298	−	38.5858i	0.372522	−	1.26869i
$926$	9.34528	+	4.26785i	0.307105	+	0.140250i
$927$	−16.0846	−	10.3298i	−0.528286	−	0.339276i
$928$	−0.384067	+	2.67125i	−0.0126076	+	0.0876880i
$929$	−0.836484	−	2.84880i	−0.0274441	−	0.0934662i	0.944632	−	0.328131i	$-0.106419\pi$
$929$	−0.836484	−	2.84880i	−0.0274441	−	0.0934662i	−0.972076	+	0.234665i	$0.924601\pi$
$930$	1.56496	−	1.56545i	0.0513171	−	0.0513332i
$931$	1.30015	+	2.02307i	0.0426106	+	0.0663033i
$932$	−9.41950	−	14.6570i	−0.308546	−	0.480107i
$933$	8.78917	−	8.79191i	0.287744	−	0.287834i
$934$	−6.35698	−	21.6499i	−0.208007	−	0.708406i
$935$	−1.24290	+	8.64458i	−0.0406473	+	0.282708i
$936$	17.3528	+	11.1443i	0.567193	+	0.364263i
$937$	30.2636	+	13.8209i	0.988668	+	0.451509i	0.843052	−	0.537832i	$-0.180756\pi$
$937$	30.2636	+	13.8209i	0.988668	+	0.451509i	0.145616	+	0.989341i	$0.453484\pi$
$938$	1.30947	−	4.45963i	0.0427556	−	0.145612i
$939$	−10.7001	+	5.84487i	−0.349185	+	0.190740i
$940$	2.07118	−	0.297791i	0.0675544	−	0.00971286i
$941$	15.2531	+	9.80257i	0.497237	+	0.319555i	0.765110	−	0.643900i	$-0.222685\pi$
$941$	15.2531	+	9.80257i	0.497237	+	0.319555i	−0.267873	+	0.963454i	$0.586321\pi$
$942$	5.64329	−	0.404501i	0.183868	−	0.0131794i
$943$	−7.75341	+	23.3423i	−0.252486	+	0.760129i
$944$			2.16649i			0.0705132i
$945$	0.661484	−	1.77605i	0.0215181	−	0.0577748i
$946$	4.28031	+	29.7702i	0.139165	+	0.967912i
$947$	49.9368	−	22.8054i	1.62273	−	0.741075i	0.623556	−	0.781779i	$-0.285687\pi$
$947$	49.9368	−	22.8054i	1.62273	−	0.741075i	0.999171	+	0.0407039i	$0.0129600\pi$
$948$	3.07481	−	14.1453i	0.0998652	−	0.459418i
$949$	14.1433	−	30.9696i	0.459112	−	1.00531i
$950$	7.05366	−	8.14036i	0.228851	−	0.264108i
$951$	9.09098	+	0.648774i	0.294795	+	0.0210379i
$952$	19.2694	−	5.65799i	0.624524	−	0.183377i
$953$	−2.67212	−	3.08379i	−0.0865583	−	0.0998937i	0.710818	−	0.703376i	$-0.248325\pi$
$953$	−2.67212	−	3.08379i	−0.0865583	−	0.0998937i	−0.797376	+	0.603482i	$0.793779\pi$
$954$	−3.91112	−	4.51082i	−0.126627	−	0.146043i
$955$	−3.90759	+	2.51126i	−0.126447	+	0.0812623i
$956$	6.06736	−	5.25739i	0.196232	−	0.170036i
$957$	−1.03394	−	2.77078i	−0.0334225	−	0.0895666i
$958$	−11.0584	−	1.58995i	−0.357279	−	0.0513690i
$959$	−3.40155	−	2.94746i	−0.109842	−	0.0951785i
$960$	−1.27131	+	3.41015i	−0.0410315	+	0.110062i
$961$	15.8356	+	4.64975i	0.510826	+	0.149992i
$962$	−7.48357	−	16.3867i	−0.241280	−	0.528330i
$963$	−0.285847	−	0.972383i	−0.00921130	−	0.0313346i
$964$	1.96523	−	3.05795i	0.0632956	−	0.0984899i
$965$	2.93399			0.0944485
$966$	3.42699	+	6.83329i	0.110262	+	0.219858i
$967$	−20.3810			−0.655409			−0.327705	−	0.944780i	$-0.606275\pi$
$967$	−20.3810			−0.655409			−0.327705	+	0.944780i	$0.606275\pi$
$968$	−1.52099	+	2.36670i	−0.0488864	+	0.0760687i
$969$	28.1681	−	6.13219i	0.904889	−	0.196994i
$970$	1.49813	+	3.28045i	0.0481021	+	0.105329i
$971$	−10.0039	−	2.93741i	−0.321040	−	0.0942658i	0.117242	−	0.993103i	$-0.462595\pi$
$971$	−10.0039	−	2.93741i	−0.321040	−	0.0942658i	−0.438282	+	0.898838i	$0.644413\pi$
$972$	1.26830	−	17.9298i	0.0406808	−	0.575098i
$973$	11.6972	+	10.1357i	0.374995	+	0.324935i
$974$	25.9766	+	3.73487i	0.832344	+	0.119673i
$975$	−18.7105	+	6.98199i	−0.599217	+	0.223603i
$976$	1.25688	−	1.08909i	0.0402318	−	0.0348610i
$977$	3.49713	−	2.24747i	0.111883	−	0.0719030i	−0.483503	−	0.875343i	$-0.660636\pi$
$977$	3.49713	−	2.24747i	0.111883	−	0.0719030i	0.595386	+	0.803440i	$0.296999\pi$
$978$	−8.66534	−	11.5718i	−0.277087	−	0.370025i
$979$	32.3522	+	37.3365i	1.03398	+	1.19328i
$980$	0.403532	−	0.118488i	0.0128904	−	0.00378495i
$981$	−10.9998	+	0.00343292i	−0.351197	+	0.000109605i
$982$	14.6955	−	16.9595i	0.468952	−	0.541200i
$983$	22.2368	−	48.6918i	0.709244	−	1.55303i	−0.119146	−	0.992877i	$-0.538016\pi$
$983$	22.2368	−	48.6918i	0.709244	−	1.55303i	0.828390	−	0.560152i	$-0.189257\pi$
$984$	−25.1882	−	5.47525i	−0.802972	−	0.174545i
$985$	3.32455	−	1.51827i	0.105929	−	0.0483761i
$986$	0.447357	+	3.11143i	0.0142467	+	0.0990882i
$987$	7.56412	+	4.12879i	0.240769	+	0.131421i
$988$			6.56924i			0.208995i
$989$	−45.0404	+	4.86984i	−1.43220	+	0.154852i
$990$	−0.496885	−	3.44827i	−0.0157920	−	0.109593i
$991$	34.0497	+	21.8824i	1.08162	+	0.695118i	0.954932	−	0.296825i	$-0.0959276\pi$
$991$	34.0497	+	21.8824i	1.08162	+	0.695118i	0.126692	+	0.991942i	$0.459564\pi$
$992$	20.6075	−	2.96290i	0.654287	−	0.0940723i
$993$	−11.7308	−	21.4754i	−0.372266	−	0.681502i
$994$	−3.83533	+	13.0619i	−0.121649	+	0.414300i
$995$	−4.06094	−	1.85457i	−0.128740	−	0.0587938i
$996$	17.3776	−	23.2213i	0.550630	−	0.735795i
$997$	−0.712132	+	4.95299i	−0.0225535	+	0.156863i	−0.997986	−	0.0634360i	$-0.979794\pi$
$997$	−0.712132	+	4.95299i	−0.0225535	+	0.156863i	0.975432	+	0.220299i	$0.0707032\pi$
$998$	−3.50839	−	11.9485i	−0.111056	−	0.378222i
$999$	−25.7137	+	34.3831i	−0.813546	+	1.08783i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.u.a.113.19	✓	480
3.2	odd	2	inner	483.2.u.a.113.30	yes	480
23.11	odd	22	inner	483.2.u.a.218.30	yes	480
69.11	even	22	inner	483.2.u.a.218.19	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.u.a.113.19	✓	480	1.1	even	1	trivial
483.2.u.a.113.30	yes	480	3.2	odd	2	inner
483.2.u.a.218.19	yes	480	69.11	even	22	inner
483.2.u.a.218.30	yes	480	23.11	odd	22	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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.u (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.497545 + 0.774196i) q^{2} +(-0.368438 - 1.69241i) q^{3} +(0.479003 + 1.04887i) q^{4} +(-0.349963 - 0.102758i) q^{5} +(1.49357 + 0.556808i) q^{6} +(0.755750 + 0.654861i) q^{7} +(-2.87220 - 0.412960i) q^{8} +(-2.72851 + 1.24710i) q^{9} +O(q^{10})\)	\(q+(-0.497545 + 0.774196i) q^{2} +(-0.368438 - 1.69241i) q^{3} +(0.479003 + 1.04887i) q^{4} +(-0.349963 - 0.102758i) q^{5} +(1.49357 + 0.556808i) q^{6} +(0.755750 + 0.654861i) q^{7} +(-2.87220 - 0.412960i) q^{8} +(-2.72851 + 1.24710i) q^{9} +(0.253678 - 0.219813i) q^{10} +(-2.91049 + 1.87046i) q^{11} +(1.59863 - 1.19711i) q^{12} +(1.55140 + 1.79042i) q^{13} +(-0.883010 + 0.259275i) q^{14} +(-0.0449698 + 0.630141i) q^{15} +(0.238559 - 0.275312i) q^{16} +(-2.87508 + 6.29555i) q^{17} +(0.392059 - 2.73289i) q^{18} +(2.18751 - 0.999000i) q^{19} +(-0.0598530 - 0.416287i) q^{20} +(0.829846 - 1.52031i) q^{21} -3.18392i q^{22} +(4.79288 + 0.168282i) q^{23} +(0.359329 + 5.01309i) q^{24} +(-4.09435 - 2.63128i) q^{25} +(-2.15803 + 0.310277i) q^{26} +(3.11589 + 4.15828i) q^{27} +(-0.324857 + 1.10636i) q^{28} +(-0.448929 - 0.205019i) q^{29} +(-0.465478 - 0.348339i) q^{30} +(-0.541841 + 3.76859i) q^{31} +(-1.54057 - 5.24671i) q^{32} +(4.23791 + 4.23659i) q^{33} +(-3.44351 - 5.35820i) q^{34} +(-0.197192 - 0.306837i) q^{35} +(-2.61500 - 2.26448i) q^{36} +(2.32790 + 7.92809i) q^{37} +(-0.314961 + 2.19060i) q^{38} +(2.45852 - 3.28527i) q^{39} +(0.962728 + 0.439663i) q^{40} +(-1.44492 + 4.92093i) q^{41} +(0.764134 + 1.39889i) q^{42} +(-9.35016 + 1.34435i) q^{43} +(-3.35599 - 2.15677i) q^{44} +(1.08303 - 0.156061i) q^{45} +(-2.51496 + 3.62690i) q^{46} +4.97537i q^{47} +(-0.553835 - 0.302305i) q^{48} +(0.142315 + 0.989821i) q^{49} +(4.07425 - 1.86065i) q^{50} +(11.7139 + 2.54630i) q^{51} +(-1.13479 + 2.48483i) q^{52} +(1.41612 - 1.63429i) q^{53} +(-4.76961 + 0.343374i) q^{54} +(1.21077 - 0.355513i) q^{55} +(-1.90023 - 2.19298i) q^{56} +(-2.49668 - 3.33409i) q^{57} +(0.382087 - 0.245552i) q^{58} +(-4.49456 + 3.89456i) q^{59} +(-0.682476 + 0.254672i) q^{60} +(4.51883 + 0.649709i) q^{61} +(-2.64803 - 2.29454i) q^{62} +(-2.87874 - 0.844299i) q^{63} +(5.52755 + 1.62304i) q^{64} +(-0.358954 - 0.785999i) q^{65} +(-5.38850 + 1.17308i) q^{66} +(-2.73050 + 4.24874i) q^{67} -7.98038 q^{68} +(-1.48108 - 8.17352i) q^{69} +0.335663 q^{70} +(7.99744 - 12.4443i) q^{71} +(8.35181 - 2.45514i) q^{72} +(-5.97002 - 13.0725i) q^{73} +(-7.29613 - 2.14234i) q^{74} +(-2.94469 + 7.89879i) q^{75} +(2.09564 + 1.81588i) q^{76} +(-3.42449 - 0.492367i) q^{77} +(1.32022 + 3.53795i) q^{78} +(5.47772 - 4.74647i) q^{79} +(-0.111778 + 0.0718351i) q^{80} +(5.88950 - 6.80542i) q^{81} +(-3.09085 - 3.56703i) q^{82} +(13.9341 - 4.09141i) q^{83} +(1.99211 + 0.142166i) q^{84} +(1.65309 - 1.90777i) q^{85} +(3.61134 - 7.90773i) q^{86} +(-0.181574 + 0.835309i) q^{87} +(9.13191 - 4.17040i) q^{88} +(-2.03220 - 14.1343i) q^{89} +(-0.418033 + 0.916121i) q^{90} +2.36906i q^{91} +(2.11929 + 5.10771i) q^{92} +(6.57764 - 0.471473i) q^{93} +(-3.85191 - 2.47547i) q^{94} +(-0.868202 + 0.124829i) q^{95} +(-8.31199 + 4.54037i) q^{96} +(-3.02692 + 10.3087i) q^{97} +(-0.837123 - 0.382301i) q^{98} +(5.60864 - 8.73321i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q + 4 q^{3} + 40 q^{4} - 6 q^{6} - 4 q^{9}+O(q^{10}) \) 480 * q + 4 * q^3 + 40 * q^4 - 6 * q^6 - 4 * q^9	\( 480 q + 4 q^{3} + 40 q^{4} - 6 q^{6} - 4 q^{9} - 22 q^{12} + 8 q^{13} - 22 q^{15} - 24 q^{16} - 30 q^{18} - 120 q^{24} - 88 q^{25} + 16 q^{27} - 44 q^{30} + 8 q^{31} - 22 q^{33} - 44 q^{34} + 10 q^{36} - 44 q^{37} - 308 q^{40} - 44 q^{43} - 184 q^{46} + 98 q^{48} + 48 q^{49} - 28 q^{52} + 28 q^{54} - 44 q^{55} + 66 q^{57} + 4 q^{58} + 220 q^{60} + 84 q^{64} + 176 q^{66} + 44 q^{67} + 102 q^{69} - 8 q^{70} - 60 q^{72} + 4 q^{73} - 8 q^{75} + 176 q^{76} + 18 q^{78} - 16 q^{81} + 20 q^{82} - 154 q^{84} + 84 q^{85} + 28 q^{87} - 418 q^{90} - 188 q^{93} + 12 q^{94} - 412 q^{96} - 132 q^{97}+O(q^{100}) \) 480 * q + 4 * q^3 + 40 * q^4 - 6 * q^6 - 4 * q^9 - 22 * q^12 + 8 * q^13 - 22 * q^15 - 24 * q^16 - 30 * q^18 - 120 * q^24 - 88 * q^25 + 16 * q^27 - 44 * q^30 + 8 * q^31 - 22 * q^33 - 44 * q^34 + 10 * q^36 - 44 * q^37 - 308 * q^40 - 44 * q^43 - 184 * q^46 + 98 * q^48 + 48 * q^49 - 28 * q^52 + 28 * q^54 - 44 * q^55 + 66 * q^57 + 4 * q^58 + 220 * q^60 + 84 * q^64 + 176 * q^66 + 44 * q^67 + 102 * q^69 - 8 * q^70 - 60 * q^72 + 4 * q^73 - 8 * q^75 + 176 * q^76 + 18 * q^78 - 16 * q^81 + 20 * q^82 - 154 * q^84 + 84 * q^85 + 28 * q^87 - 418 * q^90 - 188 * q^93 + 12 * q^94 - 412 * q^96 - 132 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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