LMFDB - Embedded newform 300.2.w.a.223.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,2,Mod(67,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 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("300.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	300.w (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.39551206064$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			223.11
Character	$\chi$	$=$	300.223
Dual form			300.2.w.a.187.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.632122 + 1.26508i) q^{2} +(-0.453990 - 0.891007i) q^{3} +(-1.20084 - 1.59937i) q^{4} +(-0.590092 + 2.15680i) q^{5} +(1.41417 - 0.0111084i) q^{6} +(-1.77479 - 1.77479i) q^{7} +(2.78240 - 0.508165i) q^{8} +(-0.587785 + 0.809017i) q^{9} +O(q^{10})$	\(q+(-0.632122 + 1.26508i) q^{2} +(-0.453990 - 0.891007i) q^{3} +(-1.20084 - 1.59937i) q^{4} +(-0.590092 + 2.15680i) q^{5} +(1.41417 - 0.0111084i) q^{6} +(-1.77479 - 1.77479i) q^{7} +(2.78240 - 0.508165i) q^{8} +(-0.587785 + 0.809017i) q^{9} +(-2.35551 - 2.10987i) q^{10} +(-0.582275 - 0.801432i) q^{11} +(-0.879875 + 1.79606i) q^{12} +(-0.710606 - 4.48659i) q^{13} +(3.36714 - 1.12337i) q^{14} +(2.18962 - 0.453391i) q^{15} +(-1.11595 + 3.84118i) q^{16} +(-3.22163 - 1.64150i) q^{17} +(-0.651917 - 1.25499i) q^{18} +(-0.911162 - 2.80427i) q^{19} +(4.15813 - 1.64621i) q^{20} +(-0.775613 + 2.38709i) q^{21} +(1.38194 - 0.230020i) q^{22} +(1.25105 - 7.89882i) q^{23} +(-1.71596 - 2.24844i) q^{24} +(-4.30358 - 2.54542i) q^{25} +(6.12507 + 1.93710i) q^{26} +(0.987688 + 0.156434i) q^{27} +(-0.707297 + 4.96979i) q^{28} +(0.616890 + 0.200440i) q^{29} +(-0.810532 + 3.05664i) q^{30} +(-6.41357 + 2.08390i) q^{31} +(-4.15397 - 3.83986i) q^{32} +(-0.449734 + 0.882653i) q^{33} +(4.11309 - 3.03798i) q^{34} +(4.87517 - 2.78058i) q^{35} +(1.99975 - 0.0314184i) q^{36} +(4.16075 - 0.658998i) q^{37} +(4.12358 + 0.619949i) q^{38} +(-3.67497 + 2.67002i) q^{39} +(-0.545863 + 6.30095i) q^{40} +(9.50896 + 6.90867i) q^{41} +(-2.52957 - 2.49014i) q^{42} +(-1.10111 + 1.10111i) q^{43} +(-0.582564 + 1.89367i) q^{44} +(-1.39804 - 1.74513i) q^{45} +(9.20181 + 6.57569i) q^{46} +(-8.43980 + 4.30030i) q^{47} +(3.92915 - 0.749540i) q^{48} -0.700218i q^{49} +(5.94055 - 3.83535i) q^{50} +3.61572i q^{51} +(-6.32237 + 6.52421i) q^{52} +(-5.38846 + 2.74556i) q^{53} +(-0.822241 + 1.15062i) q^{54} +(2.07213 - 0.782931i) q^{55} +(-5.84008 - 4.03630i) q^{56} +(-2.08496 + 2.08496i) q^{57} +(-0.643521 + 0.653711i) q^{58} +(5.91350 + 4.29641i) q^{59} +(-3.35453 - 2.95755i) q^{60} +(1.00189 - 0.727914i) q^{61} +(1.41787 - 9.43094i) q^{62} +(2.47904 - 0.392641i) q^{63} +(7.48354 - 2.82784i) q^{64} +(10.0960 + 1.11487i) q^{65} +(-0.832338 - 1.12689i) q^{66} +(2.66543 - 5.23120i) q^{67} +(1.24331 + 7.12376i) q^{68} +(-7.60587 + 2.47130i) q^{69} +(0.435954 + 7.92514i) q^{70} +(-11.9160 - 3.87174i) q^{71} +(-1.22434 + 2.54970i) q^{72} +(-8.37438 - 1.32637i) q^{73} +(-1.79642 + 5.68024i) q^{74} +(-0.314203 + 4.99012i) q^{75} +(-3.39089 + 4.82477i) q^{76} +(-0.388959 + 2.45579i) q^{77} +(-1.05476 - 6.33690i) q^{78} +(-2.78730 + 8.57843i) q^{79} +(-7.62615 - 4.67353i) q^{80} +(-0.309017 - 0.951057i) q^{81} +(-14.7508 + 7.66246i) q^{82} +(-3.13531 - 1.59752i) q^{83} +(4.74923 - 1.62603i) q^{84} +(5.44146 - 5.97978i) q^{85} +(-0.696954 - 2.08902i) q^{86} +(-0.101469 - 0.640650i) q^{87} +(-2.02738 - 1.93402i) q^{88} +(3.29356 + 4.53320i) q^{89} +(3.09146 - 0.665495i) q^{90} +(-6.70159 + 9.22394i) q^{91} +(-14.1354 + 7.48436i) q^{92} +(4.76846 + 4.76846i) q^{93} +(-0.105221 - 13.3953i) q^{94} +(6.58592 - 0.310418i) q^{95} +(-1.53547 + 5.44448i) q^{96} +(3.83895 + 7.53437i) q^{97} +(0.885830 + 0.442623i) q^{98} +0.990625 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 12 q^{8}+O(q^{10}) $ 240 * q + 12 * q^8	$ 240 q + 12 q^{8} + 8 q^{10} + 8 q^{12} + 4 q^{13} + 20 q^{17} - 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} - 8 q^{30} - 20 q^{32} - 8 q^{33} - 4 q^{37} - 76 q^{38} - 92 q^{40} - 20 q^{42} - 140 q^{44} - 4 q^{45} - 16 q^{48} - 164 q^{50} - 172 q^{52} - 4 q^{53} - 120 q^{58} + 20 q^{60} - 44 q^{62} - 60 q^{64} - 20 q^{65} + 16 q^{68} - 44 q^{70} + 12 q^{72} - 44 q^{73} - 48 q^{77} + 24 q^{78} - 4 q^{80} + 60 q^{81} + 24 q^{82} + 80 q^{84} - 64 q^{85} + 60 q^{88} - 260 q^{89} + 48 q^{90} + 144 q^{92} - 64 q^{93} + 40 q^{94} - 20 q^{96} - 180 q^{97} + 256 q^{98}+O(q^{100}) $ 240 * q + 12 * q^8 + 8 * q^10 + 8 * q^12 + 4 * q^13 + 20 * q^17 - 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 - 8 * q^30 - 20 * q^32 - 8 * q^33 - 4 * q^37 - 76 * q^38 - 92 * q^40 - 20 * q^42 - 140 * q^44 - 4 * q^45 - 16 * q^48 - 164 * q^50 - 172 * q^52 - 4 * q^53 - 120 * q^58 + 20 * q^60 - 44 * q^62 - 60 * q^64 - 20 * q^65 + 16 * q^68 - 44 * q^70 + 12 * q^72 - 44 * q^73 - 48 * q^77 + 24 * q^78 - 4 * q^80 + 60 * q^81 + 24 * q^82 + 80 * q^84 - 64 * q^85 + 60 * q^88 - 260 * q^89 + 48 * q^90 + 144 * q^92 - 64 * q^93 + 40 * q^94 - 20 * q^96 - 180 * q^97 + 256 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$1$	$-1$	$e\left(\frac{11}{20}\right)$

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 $

$2$	−0.632122	+	1.26508i	−0.446978	+	0.894545i
$2$	−0.632122	+	1.26508i	−0.446978	+	0.894545i
$3$	−0.453990	−	0.891007i	−0.262112	−	0.514423i
$3$	−0.453990	−	0.891007i	−0.262112	−	0.514423i
$4$	−1.20084	−	1.59937i	−0.600422	−	0.799684i
$5$	−0.590092	+	2.15680i	−0.263897	+	0.964551i
$5$	−0.590092	+	2.15680i	−0.263897	+	0.964551i
$6$	1.41417	−	0.0111084i	0.577332	−	0.00453500i
$7$	−1.77479	−	1.77479i	−0.670809	−	0.670809i	0.287094	−	0.957903i	$-0.407311\pi$
$7$	−1.77479	−	1.77479i	−0.670809	−	0.670809i	−0.957903	+	0.287094i	$0.907311\pi$
$8$	2.78240	−	0.508165i	0.983728	−	0.179664i
$9$	−0.587785	+	0.809017i	−0.195928	+	0.269672i
$10$	−2.35551	−	2.10987i	−0.744878	−	0.667201i
$11$	−0.582275	−	0.801432i	−0.175562	−	0.241641i	0.712163	−	0.702014i	$-0.247716\pi$
$11$	−0.582275	−	0.801432i	−0.175562	−	0.241641i	−0.887726	+	0.460373i	$0.847716\pi$
$12$	−0.879875	+	1.79606i	−0.253998	+	0.518477i
$13$	−0.710606	−	4.48659i	−0.197087	−	1.24436i	−0.865631	−	0.500683i	$-0.833082\pi$
$13$	−0.710606	−	4.48659i	−0.197087	−	1.24436i	0.668544	−	0.743673i	$-0.266918\pi$
$14$	3.36714	−	1.12337i	0.899905	−	0.300232i
$15$	2.18962	−	0.453391i	0.565357	−	0.117065i
$16$	−1.11595	+	3.84118i	−0.278987	+	0.960295i
$17$	−3.22163	−	1.64150i	−0.781361	−	0.398123i	0.0173417	−	0.999850i	$-0.494480\pi$
$17$	−3.22163	−	1.64150i	−0.781361	−	0.398123i	−0.798702	+	0.601727i	$0.794480\pi$
$18$	−0.651917	−	1.25499i	−0.153658	−	0.295804i
$19$	−0.911162	−	2.80427i	−0.209035	−	0.643343i	−0.999524	−	0.0308666i	$-0.990173\pi$
$19$	−0.911162	−	2.80427i	−0.209035	−	0.643343i	0.790489	−	0.612477i	$-0.209827\pi$
$20$	4.15813	−	1.64621i	0.929785	−	0.368103i
$21$	−0.775613	+	2.38709i	−0.169253	+	0.520906i
$22$	1.38194	−	0.230020i	0.294631	−	0.0490404i
$23$	1.25105	−	7.89882i	0.260862	−	1.64702i	−0.414877	−	0.909877i	$-0.636175\pi$
$23$	1.25105	−	7.89882i	0.260862	−	1.64702i	0.675739	−	0.737141i	$-0.263825\pi$
$24$	−1.71596	−	2.24844i	−0.350270	−	0.458960i
$25$	−4.30358	−	2.54542i	−0.860716	−	0.509085i
$26$	6.12507	+	1.93710i	1.20123	+	0.379896i
$27$	0.987688	+	0.156434i	0.190081	+	0.0301058i
$28$	−0.707297	+	4.96979i	−0.133667	+	0.939203i
$29$	0.616890	+	0.200440i	0.114554	+	0.0372207i	0.365733	−	0.930720i	$-0.380818\pi$
$29$	0.616890	+	0.200440i	0.114554	+	0.0372207i	−0.251179	+	0.967941i	$0.580818\pi$
$30$	−0.810532	+	3.05664i	−0.147982	+	0.558063i
$31$	−6.41357	+	2.08390i	−1.15191	+	0.374279i	−0.821863	−	0.569685i	$-0.807065\pi$
$31$	−6.41357	+	2.08390i	−1.15191	+	0.374279i	−0.330048	+	0.943964i	$0.607065\pi$
$32$	−4.15397	−	3.83986i	−0.734326	−	0.678797i
$33$	−0.449734	+	0.882653i	−0.0782887	+	0.153650i
$34$	4.11309	−	3.03798i	0.705390	−	0.521010i
$35$	4.87517	−	2.78058i	0.824054	−	0.470005i
$36$	1.99975	−	0.0314184i	0.333292	−	0.00523640i
$37$	4.16075	−	0.658998i	0.684023	−	0.108339i	0.195255	−	0.980752i	$-0.437447\pi$
$37$	4.16075	−	0.658998i	0.684023	−	0.108339i	0.488768	+	0.872414i	$0.337447\pi$
$38$	4.12358	+	0.619949i	0.668934	+	0.100569i
$39$	−3.67497	+	2.67002i	−0.588466	+	0.427546i
$40$	−0.545863	+	6.30095i	−0.0863086	+	0.996268i
$41$	9.50896	+	6.90867i	1.48505	+	1.07895i	0.975885	+	0.218283i	$0.0700457\pi$
$41$	9.50896	+	6.90867i	1.48505	+	1.07895i	0.509165	+	0.860669i	$0.329954\pi$
$42$	−2.52957	−	2.49014i	−0.390322	−	0.384238i
$43$	−1.10111	+	1.10111i	−0.167918	+	0.167918i	−0.786063	−	0.618146i	$-0.787884\pi$
$43$	−1.10111	+	1.10111i	−0.167918	+	0.167918i	0.618146	+	0.786063i	$0.287884\pi$
$44$	−0.582564	+	1.89367i	−0.0878248	+	0.285481i
$45$	−1.39804	−	1.74513i	−0.208408	−	0.260149i
$46$	9.20181	+	6.57569i	1.35673	+	0.969533i
$47$	−8.43980	+	4.30030i	−1.23107	+	0.627262i	−0.943778	−	0.330580i	$-0.892756\pi$
$47$	−8.43980	+	4.30030i	−1.23107	+	0.627262i	−0.287294	+	0.957842i	$0.592756\pi$
$48$	3.92915	−	0.749540i	0.567123	−	0.108187i
$49$		−	0.700218i		−	0.100031i
$50$	5.94055	−	3.83535i	0.840120	−	0.542400i
$51$			3.61572i			0.506302i
$52$	−6.32237	+	6.52421i	−0.876756	+	0.904745i
$53$	−5.38846	+	2.74556i	−0.740162	+	0.377131i	−0.783058	−	0.621948i	$-0.786341\pi$
$53$	−5.38846	+	2.74556i	−0.740162	+	0.377131i	0.0428967	+	0.999080i	$0.486341\pi$
$54$	−0.822241	+	1.15062i	−0.111893	+	0.156579i
$55$	2.07213	−	0.782931i	0.279405	−	0.105570i
$56$	−5.84008	−	4.03630i	−0.780413	−	0.539374i
$57$	−2.08496	+	2.08496i	−0.276160	+	0.276160i
$58$	−0.643521	+	0.653711i	−0.0844985	+	0.0858365i
$59$	5.91350	+	4.29641i	0.769872	+	0.559345i	0.901922	−	0.431898i	$-0.142156\pi$
$59$	5.91350	+	4.29641i	0.769872	+	0.559345i	−0.132051	+	0.991243i	$0.542156\pi$
$60$	−3.35453	−	2.95755i	−0.433068	−	0.381819i
$61$	1.00189	−	0.727914i	0.128279	−	0.0931999i	−0.521796	−	0.853070i	$-0.674738\pi$
$61$	1.00189	−	0.727914i	0.128279	−	0.0931999i	0.650074	+	0.759871i	$0.274738\pi$
$62$	1.41787	−	9.43094i	0.180070	−	1.19773i
$63$	2.47904	−	0.392641i	0.312329	−	0.0494681i
$64$	7.48354	−	2.82784i	0.935442	−	0.353480i
$65$	10.0960	+	1.11487i	1.25225	+	0.138282i
$66$	−0.832338	−	1.12689i	−0.102454	−	0.138711i
$67$	2.66543	−	5.23120i	0.325634	−	0.639093i	−0.668918	−	0.743336i	$-0.733242\pi$
$67$	2.66543	−	5.23120i	0.325634	−	0.639093i	0.994552	+	0.104244i	$0.0332422\pi$
$68$	1.24331	+	7.12376i	0.150773	+	0.863883i
$69$	−7.60587	+	2.47130i	−0.915639	+	0.297509i
$70$	0.435954	+	7.92514i	0.0521065	+	0.947235i
$71$	−11.9160	−	3.87174i	−1.41417	−	0.459491i	−0.500423	−	0.865781i	$-0.666822\pi$
$71$	−11.9160	−	3.87174i	−1.41417	−	0.459491i	−0.913744	+	0.406291i	$0.866822\pi$
$72$	−1.22434	+	2.54970i	−0.144290	+	0.300485i
$73$	−8.37438	−	1.32637i	−0.980147	−	0.155240i	−0.354254	−	0.935149i	$-0.615265\pi$
$73$	−8.37438	−	1.32637i	−0.980147	−	0.155240i	−0.625893	+	0.779909i	$0.715265\pi$
$74$	−1.79642	+	5.68024i	−0.208829	+	0.660314i
$75$	−0.314203	+	4.99012i	−0.0362811	+	0.576209i
$76$	−3.39089	+	4.82477i	−0.388962	+	0.553439i
$77$	−0.388959	+	2.45579i	−0.0443260	+	0.279864i
$78$	−1.05476	−	6.33690i	−0.119428	−	0.717513i
$79$	−2.78730	+	8.57843i	−0.313596	+	0.965149i	0.662732	+	0.748856i	$0.269397\pi$
$79$	−2.78730	+	8.57843i	−0.313596	+	0.965149i	−0.976328	+	0.216293i	$0.930603\pi$
$80$	−7.62615	−	4.67353i	−0.852629	−	0.522517i
$81$	−0.309017	−	0.951057i	−0.0343352	−	0.105673i
$82$	−14.7508	+	7.66246i	−1.62896	+	0.846177i
$83$	−3.13531	−	1.59752i	−0.344145	−	0.175351i	0.273372	−	0.961908i	$-0.411861\pi$
$83$	−3.13531	−	1.59752i	−0.344145	−	0.175351i	−0.617516	+	0.786558i	$0.711861\pi$
$84$	4.74923	−	1.62603i	0.518183	−	0.177415i
$85$	5.44146	−	5.97978i	0.590209	−	0.648598i
$86$	−0.696954	−	2.08902i	−0.0751544	−	0.225265i
$87$	−0.101469	−	0.640650i	−0.0108786	−	0.0686849i
$88$	−2.02738	−	1.93402i	−0.216120	−	0.206167i
$89$	3.29356	+	4.53320i	0.349117	+	0.480518i	0.947076	−	0.321008i	$-0.104022\pi$
$89$	3.29356	+	4.53320i	0.349117	+	0.480518i	−0.597960	+	0.801526i	$0.704022\pi$
$90$	3.09146	−	0.665495i	0.325868	−	0.0701494i
$91$	−6.70159	+	9.22394i	−0.702517	+	0.966932i
$92$	−14.1354	+	7.48436i	−1.47372	+	0.780298i
$93$	4.76846	+	4.76846i	0.494467	+	0.494467i
$94$	−0.105221	−	13.3953i	−0.0108528	−	1.38162i
$95$	6.58592	−	0.310418i	0.675701	−	0.0318482i
$96$	−1.53547	+	5.44448i	−0.156714	+	0.555675i
$97$	3.83895	+	7.53437i	0.389786	+	0.764999i	0.999621	−	0.0275298i	$-0.00876413\pi$
$97$	3.83895	+	7.53437i	0.389786	+	0.764999i	−0.609835	+	0.792529i	$0.708764\pi$
$98$	0.885830	+	0.442623i	0.0894823	+	0.0447117i
$99$	0.990625			0.0995615
$100$	1.09686	+	9.93966i	0.109686	+	0.993966i
$101$	−6.21954			−0.618867			−0.309434	−	0.950921i	$-0.600139\pi$
$101$	−6.21954			−0.618867			−0.309434	+	0.950921i	$0.600139\pi$
$102$	−4.57417	−	2.28558i	−0.452910	−	0.226306i
$103$	−6.88277	−	13.5082i	−0.678180	−	1.33100i	−0.931543	−	0.363632i	$-0.881537\pi$
$103$	−6.88277	−	13.5082i	−0.678180	−	1.33100i	0.253363	−	0.967371i	$-0.418463\pi$
$104$	−4.25712	−	12.1224i	−0.417445	−	1.18870i
$105$	−4.69080	−	3.08145i	−0.457775	−	0.300718i
$106$	−0.0671795	−	8.55234i	−0.00652505	−	0.830677i
$107$	12.1376	+	12.1376i	1.17338	+	1.17338i	0.981398	+	0.191983i	$0.0614920\pi$
$107$	12.1376	+	12.1376i	1.17338	+	1.17338i	0.191983	+	0.981398i	$0.438508\pi$
$108$	−0.935863	−	1.76753i	−0.0900535	−	0.170081i
$109$	9.77725	−	13.4572i	0.936490	−	1.28897i	−0.0207832	−	0.999784i	$-0.506616\pi$
$109$	9.77725	−	13.4572i	0.936490	−	1.28897i	0.957273	−	0.289184i	$-0.0933840\pi$
$110$	−0.319367	+	3.11631i	−0.0304504	+	0.297128i
$111$	−2.47611	−	3.40808i	−0.235022	−	0.323480i
$112$	8.79788	−	4.83672i	0.831321	−	0.457027i
$113$	−1.31076	−	8.27580i	−0.123306	−	0.778522i	−0.969400	−	0.245488i	$-0.921052\pi$
$113$	−1.31076	−	8.27580i	−0.123306	−	0.778522i	0.846094	−	0.533034i	$-0.178948\pi$
$114$	−1.31969	−	3.95559i	−0.123600	−	0.370475i
$115$	16.2980	+	7.35930i	1.51979	+	0.686258i
$116$	−0.420211	−	1.22733i	−0.0390157	−	0.113955i
$117$	4.04741	+	2.06226i	0.374183	+	0.190656i
$118$	−9.17334	+	4.76518i	−0.844474	+	0.438670i
$119$	2.80440	+	8.63106i	0.257079	+	0.791208i
$120$	5.86201	−	2.37421i	0.535126	−	0.216734i
$121$	3.09594	−	9.52831i	0.281449	−	0.866210i
$122$	0.287553	+	1.72760i	0.0260338	+	0.156409i
$123$	1.83869	−	11.6090i	0.165789	−	1.04675i
$124$	11.0346	+	7.75522i	0.990937	+	0.696439i
$125$	8.02948	−	7.77994i	0.718179	−	0.695859i
$126$	−1.07033	+	3.38437i	−0.0953527	+	0.301504i
$127$	16.4029	+	2.59797i	1.45552	+	0.230532i	0.833523	−	0.552484i	$-0.186320\pi$
$127$	16.4029	+	2.59797i	1.45552	+	0.230532i	0.622001	+	0.783017i	$0.286320\pi$
$128$	−1.15307	+	11.2548i	−0.101918	+	0.994793i
$129$	1.48099	+	0.481202i	0.130394	+	0.0423675i
$130$	−7.79230	+	12.0675i	−0.683430	+	1.05839i
$131$	14.3823	−	4.67308i	1.25658	−	0.408289i	0.396308	−	0.918118i	$-0.370291\pi$
$131$	14.3823	−	4.67308i	1.25658	−	0.408289i	0.860276	+	0.509829i	$0.170291\pi$
$132$	1.95175	−	0.340638i	0.169878	−	0.0296487i
$133$	−3.35987	+	6.59412i	−0.291338	+	0.571783i
$134$	4.93300	+	6.67873i	0.426146	+	0.576955i
$135$	−0.920225	+	2.03794i	−0.0792004	+	0.175398i
$136$	−9.79803	−	2.93020i	−0.840175	−	0.251263i
$137$	−8.05142	+	1.27522i	−0.687880	+	0.108949i	−0.490583	−	0.871394i	$-0.663216\pi$
$137$	−8.05142	+	1.27522i	−0.687880	+	0.108949i	−0.197296	+	0.980344i	$0.563216\pi$
$138$	1.68145	−	11.1842i	0.143135	−	0.952060i
$139$	1.71761	−	1.24792i	0.145686	−	0.105847i	−0.512555	−	0.858654i	$-0.671301\pi$
$139$	1.71761	−	1.24792i	0.145686	−	0.105847i	0.658241	+	0.752807i	$0.271301\pi$
$140$	−10.3015	−	4.45814i	−0.870635	−	0.376781i
$141$	7.66318	+	5.56763i	0.645356	+	0.468879i
$142$	12.4304	−	12.6272i	1.04314	−	1.05965i
$143$	−3.18193	+	3.18193i	−0.266086	+	0.266086i
$144$	−2.45164	−	3.16061i	−0.204303	−	0.263384i
$145$	−0.796330	+	1.21223i	−0.0661316	+	0.100670i
$146$	6.97160	−	9.75582i	0.576973	−	0.807397i
$147$	−0.623899	+	0.317892i	−0.0514583	+	0.0262193i
$148$	−6.05039	−	5.86321i	−0.497339	−	0.481953i
$149$		−	6.70318i		−	0.549146i	−0.961566	−	0.274573i	$-0.911463\pi$
$149$		−	6.70318i		−	0.549146i	0.961566	−	0.274573i	$-0.0885365\pi$
$150$	−6.11427	−	3.55186i	−0.499228	−	0.290008i
$151$		−	3.66896i		−	0.298576i	−0.988794	−	0.149288i	$-0.952302\pi$
$151$		−	3.66896i		−	0.298576i	0.988794	−	0.149288i	$-0.0476982\pi$
$152$	−3.96025	−	7.33959i	−0.321219	−	0.595319i
$153$	3.22163	−	1.64150i	0.260454	−	0.132708i
$154$	−2.86090	−	2.04442i	−0.230538	−	0.164744i
$155$	−0.709950	−	15.0625i	−0.0570245	−	1.20985i
$156$	8.68341	+	2.67135i	0.695229	+	0.213879i
$157$	12.4337	−	12.4337i	0.992319	−	0.992319i	−0.00765190	−	0.999971i	$-0.502436\pi$
$157$	12.4337	−	12.4337i	0.992319	−	0.992319i	0.999971	+	0.00765190i	$0.00243570\pi$
$158$	−9.09047	−	8.94877i	−0.723199	−	0.711926i
$159$	4.89262	+	3.55469i	0.388010	+	0.281906i
$160$	10.7330	−	6.69342i	0.848521	−	0.529162i
$161$	−16.2391	+	11.7984i	−1.27982	+	0.929846i
$162$	1.39850	+	0.210253i	0.109876	+	0.0165191i
$163$	9.09281	−	1.44016i	0.712204	−	0.112802i	0.210189	−	0.977661i	$-0.432592\pi$
$163$	9.09281	−	1.44016i	0.712204	−	0.112802i	0.502015	+	0.864859i	$0.332592\pi$
$164$	−0.369284	−	23.5045i	−0.0288362	−	1.83540i
$165$	−1.63832	−	1.49083i	−0.127543	−	0.116061i
$166$	4.00288	−	2.95658i	0.310684	−	0.229475i
$167$	−7.73498	+	15.1807i	−0.598550	+	1.17472i	0.370725	+	0.928743i	$0.379109\pi$
$167$	−7.73498	+	15.1807i	−0.598550	+	1.17472i	−0.969275	+	0.245979i	$0.920891\pi$
$168$	−0.945031	+	7.03599i	−0.0729108	+	0.542839i
$169$	−7.26078	+	2.35917i	−0.558521	+	0.181475i
$170$	4.12522	+	10.6638i	0.316390	+	0.817877i
$171$	2.80427	+	0.911162i	0.214448	+	0.0696783i
$172$	3.08334	+	0.438818i	0.235102	+	0.0334596i
$173$	−14.7932	−	2.34301i	−1.12470	−	0.178136i	−0.433749	−	0.901034i	$-0.642810\pi$
$173$	−14.7932	−	2.34301i	−1.12470	−	0.178136i	−0.690955	+	0.722898i	$0.742810\pi$
$174$	0.874613	+	0.276603i	0.0663043	+	0.0209692i
$175$	3.12037	+	12.1556i	0.235878	+	0.918875i
$176$	3.72823	−	1.34226i	0.281026	−	0.101177i
$177$	1.14346	−	7.21949i	0.0859474	−	0.542650i
$178$	−7.81678	+	1.30108i	−0.585893	+	0.0975199i
$179$	0.284605	−	0.875924i	0.0212724	−	0.0654696i	−0.939857	−	0.341569i	$-0.889042\pi$
$179$	0.284605	−	0.875924i	0.0212724	−	0.0654696i	0.961129	+	0.276099i	$0.0890418\pi$
$180$	−1.11228	+	4.33161i	−0.0829041	+	0.322859i
$181$	−3.55067	−	10.9278i	−0.263919	−	0.812259i	−0.991940	−	0.126705i	$-0.959560\pi$
$181$	−3.55067	−	10.9278i	−0.263919	−	0.812259i	0.728022	−	0.685554i	$-0.240440\pi$
$182$	−7.43279	−	14.3087i	−0.550955	−	1.06063i
$183$	−1.10342	−	0.562223i	−0.0815675	−	0.0415607i
$184$	−0.532980	−	22.6134i	−0.0392918	−	1.66709i
$185$	−1.03390	+	9.36278i	−0.0760137	+	0.688365i
$186$	−9.04673	+	3.01823i	−0.663338	+	0.221307i
$187$	0.560321	+	3.53772i	0.0409747	+	0.258704i
$188$	17.0126	+	8.33436i	1.24077	+	0.607846i
$189$	−1.47530	−	2.03058i	−0.107313	−	0.147703i
$190$	−3.77040	+	8.52792i	−0.273534	+	0.618681i
$191$	−12.4464	+	17.1310i	−0.900587	+	1.23955i	0.0696930	+	0.997568i	$0.477798\pi$
$191$	−12.4464	+	17.1310i	−0.900587	+	1.23955i	−0.970280	+	0.241984i	$0.922202\pi$
$192$	−5.91708	−	5.38407i	−0.427028	−	0.388562i
$193$	10.4449	+	10.4449i	0.751839	+	0.751839i	0.974822	−	0.222983i	$-0.0715794\pi$
$193$	10.4449	+	10.4449i	0.751839	+	0.751839i	−0.222983	+	0.974822i	$0.571579\pi$
$194$	−11.9582	+	0.0939331i	−0.858552	+	0.00674400i
$195$	−3.59014	−	9.50174i	−0.257095	−	0.680434i
$196$	−1.11991	+	0.840852i	−0.0799932	+	0.0600609i
$197$	−9.78412	−	19.2024i	−0.697090	−	1.36812i	−0.919472	−	0.393156i	$-0.871383\pi$
$197$	−9.78412	−	19.2024i	−0.697090	−	1.36812i	0.222382	−	0.974960i	$-0.428617\pi$
$198$	−0.626196	+	1.25322i	−0.0445018	+	0.0890623i
$199$	−10.7861			−0.764606			−0.382303	−	0.924037i	$-0.624869\pi$
$199$	−10.7861			−0.764606			−0.382303	+	0.924037i	$0.624869\pi$
$200$	−13.2678	−	4.89546i	−0.938175	−	0.346162i
$201$	−5.87111			−0.414116
$202$	3.93151	−	7.86820i	0.276620	−	0.553605i
$203$	−0.739113	−	1.45059i	−0.0518755	−	0.101811i
$204$	5.78287	−	4.34192i	0.404882	−	0.303995i
$205$	−20.5118	+	16.4322i	−1.43261	+	1.14767i
$206$	21.4397	−	0.168411i	1.49377	−	0.0117337i
$207$	5.65493	+	5.65493i	0.393045	+	0.393045i
$208$	18.0268	+	2.27724i	1.24993	+	0.157898i
$209$	−1.71688	+	2.36309i	−0.118759	+	0.163458i
$210$	6.86343	−	3.98637i	0.473622	−	0.275086i
$211$	−13.2828	−	18.2822i	−0.914424	−	1.25860i	−0.965633	−	0.259909i	$-0.916308\pi$
$211$	−13.2828	−	18.2822i	−0.914424	−	1.25860i	0.0512093	−	0.998688i	$-0.483692\pi$
$212$	10.8618	+	5.32114i	0.745995	+	0.365457i
$213$	1.96000	+	12.3749i	0.134297	+	0.847917i
$214$	−23.0274	+	7.68253i	−1.57412	+	0.525167i
$215$	−1.72512	−	3.02463i	−0.117652	−	0.206278i
$216$	2.82764	−	0.0666451i	0.192397	−	0.00453463i
$217$	15.0812	+	7.68428i	1.02378	+	0.521643i
$218$	10.8440	+	20.8756i	0.734450	+	1.41387i
$219$	2.62008	+	8.06379i	0.177049	+	0.544900i
$220$	−3.74049	−	2.37391i	−0.252184	−	0.160049i
$221$	−5.07544	+	15.6206i	−0.341411	+	1.05076i
$222$	5.87669	−	0.978155i	0.394417	−	0.0656494i
$223$	0.0533298	−	0.336711i	0.00357123	−	0.0225478i	−0.985838	−	0.167698i	$-0.946367\pi$
$223$	0.0533298	−	0.336711i	0.00357123	−	0.0225478i	0.989410	+	0.145150i	$0.0463666\pi$
$224$	0.557492	+	14.1874i	0.0372490	+	0.947935i
$225$	4.58887	−	1.98551i	0.305925	−	0.132367i
$226$	11.2981	+	3.57310i	0.751538	+	0.237679i
$227$	14.9903	+	2.37422i	0.994939	+	0.157583i	0.632612	−	0.774469i	$-0.281983\pi$
$227$	14.9903	+	2.37422i	0.994939	+	0.157583i	0.362326	+	0.932051i	$0.381983\pi$
$228$	5.83834	+	0.830907i	0.386653	+	0.0550282i
$229$	17.8213	+	5.79049i	1.17766	+	0.382646i	0.831498	−	0.555527i	$-0.187484\pi$
$229$	17.8213	+	5.79049i	1.17766	+	0.382646i	0.346166	+	0.938173i	$0.387484\pi$
$230$	−19.6124	+	15.9662i	−1.29320	+	1.05278i
$231$	2.36471	−	0.768341i	0.155587	−	0.0505532i
$232$	1.81829	+	0.244222i	0.119377	+	0.0160340i
$233$	8.78825	−	17.2479i	0.575737	−	1.12995i	−0.401114	−	0.916028i	$-0.631377\pi$
$233$	8.78825	−	17.2479i	0.575737	−	1.12995i	0.976851	−	0.213920i	$-0.0686232\pi$
$234$	−5.16737	+	3.81669i	−0.337802	+	0.249505i
$235$	−4.29462	−	20.7406i	−0.280150	−	1.35296i
$236$	−0.229652	−	14.6172i	−0.0149491	−	0.951496i
$237$	8.90885	−	1.41102i	0.578692	−	0.0916558i
$238$	−12.6917	−	1.90810i	−0.822680	−	0.123684i
$239$	0.648942	−	0.471484i	0.0419765	−	0.0304977i	−0.566599	−	0.823994i	$-0.691741\pi$
$239$	0.648942	−	0.471484i	0.0419765	−	0.0304977i	0.608576	+	0.793496i	$0.291741\pi$
$240$	−0.701950	+	8.91668i	−0.0453107	+	0.575570i
$241$	−10.2685	−	7.46048i	−0.661451	−	0.480572i	0.205702	−	0.978615i	$-0.434052\pi$
$241$	−10.2685	−	7.46048i	−0.661451	−	0.480572i	−0.867152	+	0.498043i	$0.834052\pi$
$242$	10.0970	+	9.93966i	0.649063	+	0.638945i
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	−2.36731	−	0.728276i	−0.151552	−	0.0466231i
$245$	1.51023	+	0.413193i	0.0964851	+	0.0263979i
$246$	13.5240	+	9.66440i	0.862261	+	0.616179i
$247$	−11.9341	+	6.08074i	−0.759350	+	0.386908i
$248$	−16.7862	+	9.05739i	−1.06592	+	0.575145i
$249$			3.51884i			0.222997i
$250$	4.76661	+	15.0758i	0.301467	+	0.953477i
$251$		−	5.05741i		−	0.319221i	−0.987180	−	0.159610i	$-0.948976\pi$
$251$		−	5.05741i		−	0.319221i	0.987180	−	0.159610i	$-0.0510238\pi$
$252$	−3.60491	−	3.49339i	−0.227088	−	0.220063i
$253$	−7.05882	+	3.59665i	−0.443784	+	0.226119i
$254$	−13.6553	+	19.1087i	−0.856808	+	1.19899i
$255$	−7.79839	−	2.13361i	−0.488354	−	0.133612i
$256$	−13.5093	−	8.57313i	−0.844332	−	0.535820i
$257$	−5.59294	+	5.59294i	−0.348878	+	0.348878i	−0.859692	−	0.510814i	$-0.829344\pi$
$257$	−5.59294	+	5.59294i	−0.348878	+	0.348878i	0.510814	+	0.859692i	$0.329344\pi$
$258$	−1.54492	+	1.56939i	−0.0961828	+	0.0977058i
$259$	−8.55406	−	6.21489i	−0.531523	−	0.386174i
$260$	−10.3406	−	17.4860i	−0.641299	−	1.08444i
$261$	−0.524758	+	0.381259i	−0.0324817	+	0.0235993i
$262$	−3.17953	+	21.1486i	−0.196432	+	1.30657i
$263$	5.26506	−	0.833904i	0.324658	−	0.0514207i	0.00802154	−	0.999968i	$-0.497447\pi$
$263$	5.26506	−	0.833904i	0.324658	−	0.0514207i	0.316636	+	0.948547i	$0.397447\pi$
$264$	−0.802808	+	2.68444i	−0.0494094	+	0.165216i
$265$	−2.74193	−	13.2420i	−0.168436	−	0.813447i
$266$	−6.21823	−	8.41879i	−0.381264	−	0.516189i
$267$	2.54386	−	4.99262i	0.155682	−	0.305543i
$268$	−11.5674	+	2.01885i	−0.706590	+	0.123321i
$269$	14.5139	−	4.71586i	0.884929	−	0.287531i	0.168926	−	0.985629i	$-0.445970\pi$
$269$	14.5139	−	4.71586i	0.884929	−	0.287531i	0.716002	+	0.698098i	$0.245970\pi$
$270$	−1.99645	−	2.45238i	−0.121500	−	0.149247i
$271$	−15.8393	−	5.14649i	−0.962167	−	0.312627i	−0.214517	−	0.976720i	$-0.568818\pi$
$271$	−15.8393	−	5.14649i	−0.962167	−	0.312627i	−0.747650	+	0.664093i	$0.768818\pi$
$272$	9.90049	−	10.5430i	0.600305	−	0.639265i
$273$	11.2611	+	1.78358i	0.681550	+	0.107947i
$274$	3.47623	−	10.9918i	0.210007	−	0.664037i
$275$	0.465882	+	4.93116i	0.0280938	+	0.297360i
$276$	13.0860	+	9.19693i	0.787682	+	0.553590i
$277$	−2.26929	+	14.3277i	−0.136349	+	0.860871i	0.820788	+	0.571233i	$0.193535\pi$
$277$	−2.26929	+	14.3277i	−0.136349	+	0.860871i	−0.957136	+	0.289638i	$0.906465\pi$
$278$	0.492973	+	2.96175i	0.0295665	+	0.177634i
$279$	2.08390	−	6.41357i	0.124760	−	0.383970i
$280$	12.1517	−	10.2141i	0.726202	−	0.610409i
$281$	0.523806	+	1.61211i	0.0312476	+	0.0961703i	0.965464	−	0.260537i	$-0.0838995\pi$
$281$	0.523806	+	1.61211i	0.0312476	+	0.0961703i	−0.934216	+	0.356707i	$0.883899\pi$
$282$	−11.8875	+	6.17510i	−0.707893	+	0.367722i
$283$	−1.89544	−	0.965777i	−0.112672	−	0.0574095i	0.396746	−	0.917928i	$-0.370139\pi$
$283$	−1.89544	−	0.965777i	−0.112672	−	0.0574095i	−0.509418	+	0.860519i	$0.670139\pi$
$284$	8.11690	+	23.7074i	0.481649	+	1.40677i
$285$	−3.26653	−	5.72717i	−0.193493	−	0.339248i
$286$	−2.01402	−	6.03675i	−0.119091	−	0.356961i
$287$	−4.61499	−	29.1379i	−0.272414	−	1.71996i
$288$	5.54815	−	1.10362i	0.326928	−	0.0650317i
$289$	−2.30797	−	3.17665i	−0.135763	−	0.186862i
$290$	−1.03019	−	1.77370i	−0.0604947	−	0.104155i
$291$	4.97032	−	6.84106i	0.291365	−	0.401030i
$292$	7.93497	+	14.9865i	0.464359	+	0.877017i
$293$	12.5122	+	12.5122i	0.730972	+	0.730972i	0.970812	−	0.239840i	$-0.0770951\pi$
$293$	12.5122	+	12.5122i	0.730972	+	0.730972i	−0.239840	+	0.970812i	$0.577095\pi$
$294$	−0.00777832	−	0.990227i	−0.000453641	−	0.0577512i
$295$	−12.7560	+	10.2190i	−0.742683	+	0.594971i
$296$	11.2420	−	3.94795i	0.653428	−	0.229470i
$297$	−0.449734	−	0.882653i	−0.0260962	−	0.0512167i
$298$	8.48005	+	4.23723i	0.491236	+	0.245456i
$299$	−36.3278			−2.10089
$300$	8.35834	−	5.48982i	0.482569	−	0.316955i
$301$	3.90848			0.225281
$302$	4.64153	+	2.31923i	0.267090	+	0.133457i
$303$	2.82361	+	5.54165i	0.162212	+	0.318360i
$304$	11.7885	−	0.370514i	0.676117	−	0.0212504i
$305$	0.978760	+	2.59041i	0.0560436	+	0.148326i
$306$	0.0401650	+	5.11325i	0.00229608	+	0.292305i
$307$	18.9220	+	18.9220i	1.07994	+	1.07994i	0.996514	+	0.0834227i	$0.0265852\pi$
$307$	18.9220	+	18.9220i	1.07994	+	1.07994i	0.0834227	+	0.996514i	$0.473415\pi$
$308$	4.39479	−	2.32693i	0.250417	−	0.132589i
$309$	−8.91119	+	12.2652i	−0.506940	+	0.697743i
$310$	19.5040	+	8.62319i	1.10775	+	0.489764i
$311$	−1.35781	−	1.86887i	−0.0769945	−	0.105974i	0.768783	−	0.639510i	$-0.220863\pi$
$311$	−1.35781	−	1.86887i	−0.0769945	−	0.105974i	−0.845777	+	0.533536i	$0.820863\pi$
$312$	−8.86844	+	9.29657i	−0.502076	+	0.526315i
$313$	−1.02291	−	6.45842i	−0.0578185	−	0.365052i	−0.999586	−	0.0287858i	$-0.990836\pi$
$313$	−1.02291	−	6.45842i	−0.0578185	−	0.365052i	0.941767	−	0.336266i	$-0.109164\pi$
$314$	7.86999	+	23.5892i	0.444129	+	1.33122i
$315$	−0.616012	+	5.57848i	−0.0347083	+	0.314312i
$316$	17.0672	−	5.84344i	0.960104	−	0.328719i
$317$	−17.7707	−	9.05465i	−0.998105	−	0.508560i	−0.122955	−	0.992412i	$-0.539237\pi$
$317$	−17.7707	−	9.05465i	−0.998105	−	0.508560i	−0.875150	+	0.483853i	$0.839237\pi$
$318$	−7.58970	+	3.94254i	−0.425609	+	0.221087i
$319$	−0.198560	−	0.611106i	−0.0111172	−	0.0342154i
$320$	1.68311	+	17.8092i	0.0940890	+	0.995564i
$321$	5.30431	−	16.3250i	0.296057	−	0.911171i
$322$	−4.66081	−	28.0018i	−0.259737	−	1.56048i
$323$	−1.66779	+	10.5300i	−0.0927982	+	0.585905i
$324$	−1.15001	+	1.63630i	−0.0638893	+	0.0909056i
$325$	−8.36212	+	21.1172i	−0.463847	+	1.17137i
$326$	−3.92585	+	12.4135i	−0.217433	+	0.687518i
$327$	−16.4293	−	2.60214i	−0.908540	−	0.143899i
$328$	29.9685	+	14.3906i	1.65473	+	0.794586i
$329$	22.6110	+	7.34677i	1.24659	+	0.405041i
$330$	2.92164	−	1.13022i	0.160831	−	0.0622164i
$331$	29.5081	−	9.58775i	1.62191	−	0.526990i	0.649518	−	0.760346i	$-0.274971\pi$
$331$	29.5081	−	9.58775i	1.62191	−	0.526990i	0.972392	+	0.233355i	$0.0749705\pi$
$332$	1.20999	+	6.93288i	0.0664071	+	0.380491i
$333$	−1.91249	+	3.75347i	−0.104804	+	0.205689i
$334$	−14.3154	−	19.3814i	−0.783303	−	1.06050i
$335$	9.70981	+	8.83569i	0.530503	+	0.482745i
$336$	−8.30370	−	5.64314i	−0.453004	−	0.307859i
$337$	−19.6994	+	3.12009i	−1.07310	+	0.169962i	−0.667888	−	0.744262i	$-0.732801\pi$
$337$	−19.6994	+	3.12009i	−1.07310	+	0.169962i	−0.405209	+	0.914224i	$0.632801\pi$
$338$	1.60516	−	10.6767i	0.0873094	−	0.580738i
$339$	−6.77872	+	4.92503i	−0.368169	+	0.267491i
$340$	−16.0982	−	1.52211i	−0.873048	−	0.0825478i
$341$	5.40456	+	3.92664i	0.292673	+	0.212640i
$342$	−2.92533	+	2.97165i	−0.158184	+	0.160689i
$343$	−13.6663	+	13.6663i	−0.737911	+	0.737911i
$344$	−2.50419	+	3.62328i	−0.135017	+	0.195354i
$345$	−0.841931	−	17.8626i	−0.0453280	−	0.961692i
$346$	12.3152	−	17.2335i	0.662068	−	0.926476i
$347$	−3.24564	+	1.65374i	−0.174235	+	0.0887772i	−0.538933	−	0.842349i	$-0.681172\pi$
$347$	−3.24564	+	1.65374i	−0.174235	+	0.0887772i	0.364698	+	0.931126i	$0.381172\pi$
$348$	−0.902787	+	0.931607i	−0.0483944	+	0.0499394i
$349$			24.4825i			1.31052i	0.755405	+	0.655258i	$0.227440\pi$
$349$			24.4825i			1.31052i	−0.755405	+	0.655258i	$0.772560\pi$
$350$	−17.3502	−	3.73629i	−0.927407	−	0.199713i
$351$		−	4.54251i		−	0.242461i
$352$	−0.658632	+	5.56498i	−0.0351052	+	0.296614i
$353$	14.7437	−	7.51230i	0.784729	−	0.399839i	−0.0152379	−	0.999884i	$-0.504851\pi$
$353$	14.7437	−	7.51230i	0.784729	−	0.399839i	0.799966	+	0.600045i	$0.204851\pi$
$354$	8.41042	+	6.01016i	0.447009	+	0.319436i
$355$	15.3821	−	23.4157i	0.816397	−	1.24278i
$356$	3.29520	−	10.7113i	0.174645	−	0.567697i
$357$	6.41716	−	6.41716i	0.339632	−	0.339632i
$358$	0.928207	+	0.913738i	0.0490573	+	0.0482926i
$359$	−6.02704	−	4.37890i	−0.318095	−	0.231109i	0.417267	−	0.908784i	$-0.362988\pi$
$359$	−6.02704	−	4.37890i	−0.318095	−	0.231109i	−0.735362	+	0.677674i	$0.762988\pi$
$360$	−4.77673	−	4.14522i	−0.251756	−	0.218472i
$361$	8.33761	−	6.05763i	0.438822	−	0.318823i
$362$	16.0690	+	2.41585i	0.844568	+	0.126974i
$363$	−9.89532	+	1.56726i	−0.519369	+	0.0822600i
$364$	22.8000	−	0.358215i	1.19505	−	0.0187756i
$365$	7.80238	−	17.2792i	0.408395	−	0.904434i
$366$	1.40875	−	1.04052i	0.0736368	−	0.0543891i
$367$	12.3376	−	24.2139i	0.644018	−	1.26396i	−0.306080	−	0.952006i	$-0.599018\pi$
$367$	12.3376	−	24.2139i	0.644018	−	1.26396i	0.950098	−	0.311951i	$-0.100982\pi$
$368$	28.9447	+	13.6202i	1.50885	+	0.710002i
$369$	−11.1785	+	3.63210i	−0.581927	+	0.189080i
$370$	−11.1911	−	7.22638i	−0.581797	−	0.375682i
$371$	14.4362	+	4.69060i	0.749490	+	0.243524i
$372$	1.90035	−	13.3527i	0.0985283	−	0.692306i
$373$	1.04989	+	0.166286i	0.0543613	+	0.00860998i	0.183556	−	0.983009i	$-0.441239\pi$
$373$	1.04989	+	0.166286i	0.0543613	+	0.00860998i	−0.129195	+	0.991619i	$0.541239\pi$
$374$	−4.82969	−	1.52742i	−0.249737	−	0.0789813i
$375$	−10.5773	−	3.62230i	−0.546209	−	0.187055i
$376$	−21.2977	+	16.2540i	−1.09834	+	0.838235i
$377$	0.460925	−	2.91016i	0.0237388	−	0.149881i
$378$	3.50142	−	0.582799i	0.180093	−	0.0299759i
$379$	−5.91385	+	18.2010i	−0.303774	+	0.934921i	0.676358	+	0.736573i	$0.263557\pi$
$379$	−5.91385	+	18.2010i	−0.303774	+	0.934921i	−0.980132	+	0.198347i	$0.936443\pi$
$380$	−8.40513	−	10.1605i	−0.431174	−	0.521225i
$381$	−5.13196	−	15.7946i	−0.262919	−	0.809180i
$382$	−13.8044	−	26.5745i	−0.706293	−	1.35967i
$383$	−18.3322	−	9.34072i	−0.936731	−	0.477289i	−0.0821581	−	0.996619i	$-0.526181\pi$
$383$	−18.3322	−	9.34072i	−0.936731	−	0.477289i	−0.854573	+	0.519331i	$0.826181\pi$
$384$	10.5516	−	4.08218i	0.538458	−	0.208318i
$385$	−5.06714	−	2.28805i	−0.258245	−	0.116610i
$386$	−19.8160	+	6.61115i	−1.00861	+	0.336499i
$387$	−0.243600	−	1.53803i	−0.0123829	−	0.0781826i
$388$	7.44024	−	15.1875i	0.377721	−	0.771028i
$389$	−7.78730	−	10.7183i	−0.394832	−	0.543439i	0.564606	−	0.825361i	$-0.309028\pi$
$389$	−7.78730	−	10.7183i	−0.394832	−	0.543439i	−0.959438	+	0.281921i	$0.909028\pi$
$390$	14.2898	+	1.46446i	0.723594	+	0.0741558i
$391$	−16.9964	+	23.3935i	−0.859543	+	1.18306i
$392$	−0.355826	−	1.94829i	−0.0179719	−	0.0984034i
$393$	−10.6932	−	10.6932i	−0.539398	−	0.539398i
$394$	30.4773	−	0.239402i	1.53542	−	0.0120609i
$395$	−16.8572	−	11.0737i	−0.848178	−	0.557180i
$396$	−1.18959	−	1.58437i	−0.0597789	−	0.0796177i
$397$	5.75681	+	11.2984i	0.288926	+	0.567049i	0.989156	−	0.146868i	$-0.0469193\pi$
$397$	5.75681	+	11.2984i	0.288926	+	0.567049i	−0.700230	+	0.713917i	$0.746919\pi$
$398$	6.81813	−	13.6453i	0.341762	−	0.683975i
$399$	7.40076			0.370501
$400$	14.5800	−	13.6903i	0.729000	−	0.684513i
$401$	15.1445			0.756281			0.378141	−	0.925748i	$-0.376564\pi$
$401$	15.1445			0.756281			0.378141	+	0.925748i	$0.376564\pi$
$402$	3.71126	−	7.42741i	0.185101	−	0.370446i
$403$	13.9071	+	27.2942i	0.692762	+	1.35962i
$404$	7.46870	+	9.94733i	0.371581	+	0.494898i
$405$	2.23359	−	0.105277i	0.110988	−	0.00523126i
$406$	2.30232	−	0.0180849i	0.114262	−	0.000897540i
$407$	−2.95084	−	2.95084i	−0.146268	−	0.146268i
$408$	1.83738	+	10.0604i	0.0909641	+	0.498064i
$409$	−15.2785	+	21.0290i	−0.755471	+	1.03982i	0.242106	+	0.970250i	$0.422162\pi$
$409$	−15.2785	+	21.0290i	−0.755471	+	1.03982i	−0.997577	+	0.0695670i	$0.977838\pi$
$410$	−7.82205	−	36.3361i	−0.386303	−	1.79451i
$411$	4.79150	+	6.59493i	0.236347	+	0.325304i
$412$	−13.3394	+	27.2293i	−0.657187	+	1.34149i
$413$	−2.87000	−	18.1205i	−0.141223	−	0.891650i
$414$	−10.7285	+	3.57932i	−0.527279	+	0.175914i
$415$	5.29565	−	5.81955i	0.259953	−	0.285671i
$416$	−14.2760	+	21.3658i	−0.699939	+	1.04754i
$417$	−1.89168	−	0.963860i	−0.0926361	−	0.0472004i
$418$	−1.90421	−	3.66575i	−0.0931380	−	0.179298i
$419$	−7.45434	−	22.9421i	−0.364168	−	1.12079i	−0.950500	−	0.310724i	$-0.899429\pi$
$419$	−7.45434	−	22.9421i	−0.364168	−	1.12079i	0.586332	−	0.810071i	$-0.300571\pi$
$420$	0.704549	+	11.2026i	0.0343785	+	0.546633i
$421$	−5.40899	+	16.6472i	−0.263618	+	0.811334i	0.728390	+	0.685162i	$0.240269\pi$
$421$	−5.40899	+	16.6472i	−0.263618	+	0.811334i	−0.992009	+	0.126171i	$0.959731\pi$
$422$	31.5247	−	5.24718i	1.53460	−	0.255429i
$423$	1.48178	−	9.35560i	0.0720466	−	0.454885i
$424$	−13.5977	+	10.3775i	−0.660361	+	0.503975i
$425$	9.68624	+	15.2648i	0.469851	+	0.740450i
$426$	−16.8942	−	5.34293i	−0.818528	−	0.258866i
$427$	−3.07004	−	0.486247i	−0.148570	−	0.0235311i
$428$	4.83710	−	33.9877i	0.233810	−	1.64286i
$429$	4.27968	+	1.39055i	0.206625	+	0.0671366i
$430$	4.91688	−	0.270473i	0.237113	−	0.0130434i
$431$	34.6020	−	11.2429i	1.66672	−	0.541550i	0.684455	−	0.729055i	$-0.260040\pi$
$431$	34.6020	−	11.2429i	1.66672	−	0.541550i	0.982264	+	0.187505i	$0.0600400\pi$
$432$	−1.70310	+	3.61931i	−0.0819406	+	0.174134i
$433$	−16.2768	+	31.9450i	−0.782213	+	1.53518i	0.0613291	+	0.998118i	$0.480466\pi$
$433$	−16.2768	+	31.9450i	−0.782213	+	1.53518i	−0.843542	+	0.537062i	$0.819534\pi$
$434$	−19.2544	+	14.2215i	−0.924241	+	0.682656i
$435$	1.44163	+	0.159194i	0.0691209	+	0.00763278i
$436$	−33.2640	+	0.522616i	−1.59306	+	0.0250287i
$437$	−23.2903	+	3.68883i	−1.11413	+	0.176460i
$438$	−11.8575	−	1.78269i	−0.566575	−	0.0851802i
$439$	13.0760	−	9.50025i	0.624082	−	0.453422i	−0.230263	−	0.973128i	$-0.573959\pi$
$439$	13.0760	−	9.50025i	0.624082	−	0.453422i	0.854345	+	0.519706i	$0.173959\pi$
$440$	5.36763	−	3.23141i	0.255892	−	0.154052i
$441$	0.566488	+	0.411578i	0.0269756	+	0.0195989i
$442$	−16.5530	−	16.2949i	−0.787345	−	0.775072i
$443$	3.16889	−	3.16889i	0.150559	−	0.150559i	−0.627809	−	0.778367i	$-0.716048\pi$
$443$	3.16889	−	3.16889i	0.150559	−	0.150559i	0.778367	+	0.627809i	$0.216048\pi$
$444$	−2.47734	+	8.05278i	−0.117569	+	0.382168i
$445$	−11.7207	+	4.42855i	−0.555615	+	0.209934i
$446$	0.392255	+	0.280309i	0.0185738	+	0.0132730i
$447$	−5.97258	+	3.04318i	−0.282493	+	0.143938i
$448$	−18.3006	−	8.26290i	−0.864620	−	0.390385i
$449$		−	32.0207i		−	1.51115i	−0.655062	−	0.755575i	$-0.727358\pi$
$449$		−	32.0207i		−	1.51115i	0.655062	−	0.755575i	$-0.272642\pi$
$450$	−0.388905	+	7.06036i	−0.0183331	+	0.332829i
$451$		−	11.6435i		−	0.548272i
$452$	−11.6620	+	12.0343i	−0.548536	+	0.566047i
$453$	−3.26907	+	1.66567i	−0.153594	+	0.0782602i
$454$	−12.4793	+	17.4630i	−0.585680	+	0.819581i
$455$	−15.9397	−	19.8970i	−0.747263	−	0.932784i
$456$	−4.74170	+	6.86071i	−0.222051	+	0.321282i
$457$	16.1908	−	16.1908i	0.757374	−	0.757374i	−0.218469	−	0.975844i	$-0.570106\pi$
$457$	16.1908	−	16.1908i	0.757374	−	0.757374i	0.975844	+	0.218469i	$0.0701064\pi$
$458$	−18.5906	+	18.8850i	−0.868684	+	0.882439i
$459$	−2.92518	−	2.12527i	−0.136536	−	0.0991990i
$460$	−7.80107	−	34.9038i	−0.363727	−	1.62740i
$461$	−9.97154	+	7.24475i	−0.464421	+	0.337421i	−0.795263	−	0.606265i	$-0.792667\pi$
$461$	−9.97154	+	7.24475i	−0.464421	+	0.337421i	0.330842	+	0.943686i	$0.392667\pi$
$462$	−0.522775	+	3.47723i	−0.0243217	+	0.161775i
$463$	32.1267	−	5.08837i	1.49306	−	0.236477i	0.644100	−	0.764941i	$-0.277232\pi$
$463$	32.1267	−	5.08837i	1.49306	−	0.236477i	0.848955	+	0.528464i	$0.177232\pi$
$464$	−1.45834	+	2.14590i	−0.0677018	+	0.0996211i
$465$	−13.0985	+	7.47080i	−0.607427	+	0.346450i
$466$	16.2647	+	22.0206i	0.753448	+	1.02008i
$467$	−0.752525	+	1.47691i	−0.0348227	+	0.0683434i	−0.907762	−	0.419485i	$-0.862211\pi$
$467$	−0.752525	+	1.47691i	−0.0348227	+	0.0683434i	0.872940	+	0.487828i	$0.162211\pi$
$468$	−1.56200	−	8.94974i	−0.0722034	−	0.413702i
$469$	−14.0149	+	4.55371i	−0.647147	+	0.210271i
$470$	28.9531	+	7.67753i	1.33551	+	0.354138i
$471$	−16.7233	−	5.43373i	−0.770570	−	0.250373i
$472$	18.6370	+	8.94930i	0.857838	+	0.411925i
$473$	1.52361	+	0.241317i	0.0700558	+	0.0110957i
$474$	−3.84643	+	12.1623i	−0.176672	+	0.558634i
$475$	−3.21679	+	14.3877i	−0.147596	+	0.660153i
$476$	10.4366	−	14.8498i	0.478360	−	0.680640i
$477$	0.946054	−	5.97315i	0.0433168	−	0.273492i
$478$	0.186253	+	1.11900i	0.00851903	+	0.0511817i
$479$	0.416357	−	1.28141i	0.0190238	−	0.0585493i	−0.941094	−	0.338145i	$-0.890200\pi$
$479$	0.416357	−	1.28141i	0.0190238	−	0.0585493i	0.960118	+	0.279596i	$0.0902005\pi$
$480$	−10.8366	−	6.52445i	−0.494620	−	0.297799i
$481$	−5.91331	−	18.1993i	−0.269624	−	0.829816i
$482$	15.9290	−	8.27448i	0.725547	−	0.376892i
$483$	17.8849	+	9.11280i	0.813790	+	0.414647i
$484$	−18.9570	+	6.49047i	−0.861682	+	0.295022i
$485$	−18.5155	+	3.83388i	−0.840744	+	0.174088i
$486$	−0.447567	−	1.34152i	−0.0203021	−	0.0608527i
$487$	−5.18153	−	32.7149i	−0.234798	−	1.48245i	−0.770171	−	0.637838i	$-0.779829\pi$
$487$	−5.18153	−	32.7149i	−0.234798	−	1.48245i	0.535373	−	0.844616i	$-0.320171\pi$
$488$	2.41776	−	2.53448i	0.109447	−	0.114730i
$489$	−5.41124	−	7.44793i	−0.244705	−	0.336807i
$490$	−1.47737	+	1.64937i	−0.0667408	+	0.0745110i
$491$	1.80230	−	2.48065i	0.0813366	−	0.111950i	−0.766410	−	0.642352i	$-0.777959\pi$
$491$	1.80230	−	2.48065i	0.0813366	−	0.111950i	0.847747	+	0.530402i	$0.177959\pi$
$492$	−20.7751	+	10.9999i	−0.936612	+	0.495913i
$493$	−1.65837	−	1.65837i	−0.0746892	−	0.0746892i
$494$	−0.148786	−	18.9414i	−0.00669421	−	0.852212i
$495$	−0.584560	+	2.13658i	−0.0262740	+	0.0960321i
$496$	−0.847392	−	26.9612i	−0.0380490	−	1.21059i
$497$	14.2769	+	28.0199i	0.640405	+	1.25687i
$498$	−4.45160	−	2.22434i	−0.199481	−	0.0996749i
$499$	38.2306			1.71144			0.855718	−	0.517443i	$-0.173116\pi$
$499$	38.2306			1.71144			0.855718	+	0.517443i	$0.173116\pi$
$500$	−22.0851	−	3.49960i	−0.987677	−	0.156507i
$501$	17.0378			0.761191
$502$	6.39801	+	3.19690i	0.285557	+	0.142685i
$503$	14.4347	+	28.3298i	0.643613	+	1.26316i	0.950295	+	0.311350i	$0.100781\pi$
$503$	14.4347	+	28.3298i	0.643613	+	1.26316i	−0.306682	+	0.951812i	$0.599219\pi$
$504$	6.69815	−	2.35224i	0.298359	−	0.104777i
$505$	3.67010	−	13.4143i	0.163317	−	0.596929i
$506$	−0.0880044	−	11.2035i	−0.00391227	−	0.498056i
$507$	5.39836	+	5.39836i	0.239750	+	0.239750i
$508$	−15.5422	−	29.3540i	−0.689575	−	1.30238i
$509$	0.131687	−	0.181251i	0.00583691	−	0.00803381i	−0.806089	−	0.591795i	$-0.798420\pi$
$509$	0.131687	−	0.181251i	0.00583691	−	0.00803381i	0.811925	+	0.583761i	$0.198420\pi$
$510$	7.62872	−	8.51687i	0.337805	−	0.377133i
$511$	12.5088	+	17.2168i	0.553355	+	0.761628i
$512$	19.3852	−	11.6711i	0.856713	−	0.515793i
$513$	−0.461260	−	2.91228i	−0.0203651	−	0.128580i
$514$	−3.54008	−	10.6109i	−0.156146	−	0.468028i
$515$	33.1960	−	6.87369i	1.46279	−	0.302891i
$516$	−1.00882	−	2.94649i	−0.0444107	−	0.129712i
$517$	8.36068	+	4.25998i	0.367702	+	0.187354i
$518$	13.2695	−	6.89298i	0.583029	−	0.302860i
$519$	4.62833	+	14.2445i	0.203161	+	0.625265i
$520$	28.6577	−	2.02843i	1.25672	−	0.0889526i
$521$	−2.36876	+	7.29029i	−0.103777	+	0.319393i	−0.989441	−	0.144933i	$-0.953703\pi$
$521$	−2.36876	+	7.29029i	−0.103777	+	0.319393i	0.885664	+	0.464326i	$0.153703\pi$
$522$	−0.150611	−	0.904861i	−0.00659207	−	0.0396047i
$523$	−2.40963	+	15.2138i	−0.105366	+	0.665253i	0.877311	+	0.479923i	$0.159335\pi$
$523$	−2.40963	+	15.2138i	−0.105366	+	0.665253i	−0.982676	+	0.185330i	$0.940665\pi$
$524$	−24.7448	−	17.3909i	−1.08098	−	0.759724i
$525$	9.41407	−	8.29878i	0.410864	−	0.362189i
$526$	−2.27321	+	7.18784i	−0.0991166	+	0.313405i
$527$	24.0829	+	3.81435i	1.04907	+	0.166156i
$528$	−2.88855	−	2.71251i	−0.125708	−	0.118047i
$529$	−38.9519	−	12.6563i	−1.69356	−	0.550272i
$530$	18.4853	+	4.90178i	0.802952	+	0.212920i
$531$	−6.95173	+	2.25875i	−0.301679	+	0.0980216i
$532$	14.5811	−	2.54484i	0.632171	−	0.110333i
$533$	24.2392	−	47.5721i	1.04992	−	2.06058i
$534$	4.70801	+	6.37413i	0.203736	+	0.275836i
$535$	−33.3406	+	19.0160i	−1.44144	+	0.822134i
$536$	4.75799	−	15.9098i	0.205514	−	0.687198i
$537$	−0.909662	+	0.144076i	−0.0392548	+	0.00621735i
$538$	−3.20864	+	21.3422i	−0.138334	+	0.920129i
$539$	−0.561177	+	0.407719i	−0.0241716	+	0.0175617i
$540$	4.36446	−	0.975465i	0.187816	−	0.0419773i
$541$	−0.252310	−	0.183314i	−0.0108476	−	0.00788127i	0.582348	−	0.812939i	$-0.302134\pi$
$541$	−0.252310	−	0.183314i	−0.0108476	−	0.00788127i	−0.593196	+	0.805058i	$0.702134\pi$
$542$	16.5231	−	16.7847i	0.709726	−	0.720964i
$543$	−8.12480	+	8.12480i	−0.348668	+	0.348668i
$544$	7.07944	+	19.1894i	0.303528	+	0.822737i
$545$	23.2551	+	29.0286i	0.996138	+	1.24345i
$546$	−9.37472	+	13.1187i	−0.401201	+	0.561427i
$547$	−34.1386	+	17.3945i	−1.45966	+	0.743735i	−0.990258	−	0.139248i	$-0.955532\pi$
$547$	−34.1386	+	17.3945i	−1.45966	+	0.743735i	−0.469405	+	0.882983i	$0.655532\pi$
$548$	11.7080	+	11.3458i	0.500143	+	0.484670i
$549$			1.23840i			0.0528537i
$550$	−6.53280	−	2.52772i	−0.278560	−	0.107782i
$551$		−	1.91256i		−	0.0814777i
$552$	−19.9068	+	10.7412i	−0.847288	+	0.457175i
$553$	20.1718	−	10.2781i	0.857794	−	0.437068i
$554$	−16.6912	−	11.9277i	−0.709143	−	0.506760i
$555$	8.81168	−	3.32940i	0.374035	−	0.141325i
$556$	−4.05846	−	1.24854i	−0.172117	−	0.0529498i
$557$	10.7978	−	10.7978i	0.457518	−	0.457518i	−0.440322	−	0.897840i	$-0.645136\pi$
$557$	10.7978	−	10.7978i	0.457518	−	0.457518i	0.897840	+	0.440322i	$0.145136\pi$
$558$	6.79639	+	6.69045i	0.287714	+	0.283229i
$559$	5.72268	+	4.15777i	0.242044	+	0.175855i
$560$	5.24028	+	21.8294i	0.221442	+	0.922460i
$561$	2.89776	−	2.10534i	0.122343	−	0.0888876i
$562$	−2.37055	−	0.356394i	−0.0999957	−	0.0150336i
$563$	−19.0254	+	3.01333i	−0.801826	+	0.126997i	−0.543881	−	0.839163i	$-0.683046\pi$
$563$	−19.0254	+	3.01333i	−0.801826	+	0.126997i	−0.257946	+	0.966159i	$0.583046\pi$
$564$	−0.297602	−	18.9421i	−0.0125313	−	0.797606i
$565$	18.6227	+	2.05644i	0.783464	+	0.0865151i
$566$	2.41993	−	1.78739i	0.101717	−	0.0751298i
$567$	−1.13949	+	2.23637i	−0.0478540	+	0.0939187i
$568$	−35.1225	−	4.71745i	−1.47371	−	0.197940i
$569$	15.7909	−	5.13076i	0.661987	−	0.215093i	0.0412948	−	0.999147i	$-0.486852\pi$
$569$	15.7909	−	5.13076i	0.661987	−	0.215093i	0.620692	+	0.784054i	$0.286852\pi$
$570$	9.31016	−	0.512143i	0.389960	−	0.0214513i
$571$	18.7027	+	6.07687i	0.782683	+	0.254309i	0.672985	−	0.739656i	$-0.265012\pi$
$571$	18.7027	+	6.07687i	0.782683	+	0.254309i	0.109698	+	0.993965i	$0.465012\pi$
$572$	8.91007	+	1.26807i	0.372549	+	0.0530208i
$573$	20.9143	+	3.31250i	0.873708	+	0.138382i
$574$	39.7789	+	12.5804i	1.66034	+	0.525095i
$575$	−25.4898	+	30.8088i	−1.06300	+	1.28481i
$576$	−2.11094	+	7.71647i	−0.0879559	+	0.321520i
$577$	1.60647	−	10.1429i	0.0668783	−	0.422253i	−0.931420	−	0.363945i	$-0.881430\pi$
$577$	1.60647	−	10.1429i	0.0668783	−	0.422253i	0.998299	−	0.0583078i	$-0.0185705\pi$
$578$	5.47763	−	0.911732i	0.227839	−	0.0379231i
$579$	4.56458	−	14.0483i	0.189698	−	0.583829i
$580$	2.89507	−	0.182075i	0.120211	−	0.00756024i
$581$	2.72926	+	8.39979i	0.113229	+	0.348482i
$582$	5.51262	+	10.6122i	0.228506	+	0.439891i
$583$	5.33794	+	2.71982i	0.221075	+	0.112643i
$584$	−23.9749	+	0.565069i	−0.992089	+	0.0233827i
$585$	−6.83623	+	7.51253i	−0.282643	+	0.310605i
$586$	−23.7382	+	7.91968i	−0.980616	+	0.327159i
$587$	−0.441412	−	2.78696i	−0.0182190	−	0.115030i	0.976903	−	0.213684i	$-0.0685463\pi$
$587$	−0.441412	−	2.78696i	−0.0182190	−	0.115030i	−0.995122	+	0.0986539i	$0.968546\pi$
$588$	1.25763	+	0.616104i	0.0518638	+	0.0254077i
$589$	11.6876	+	16.0866i	0.481579	+	0.662837i
$590$	−4.86443	−	22.5970i	−0.200265	−	0.930302i
$591$	−12.6676	+	17.4354i	−0.521075	+	0.717198i
$592$	−2.11186	+	16.7176i	−0.0867969	+	0.687089i
$593$	−25.1359	−	25.1359i	−1.03221	−	1.03221i	−0.999464	−	0.0327451i	$-0.989575\pi$
$593$	−25.1359	−	25.1359i	−1.03221	−	1.03221i	−0.0327451	−	0.999464i	$-0.510425\pi$
$594$	1.40091	−	0.0110043i	0.0574801	−	0.000451511i
$595$	−20.2703	+	0.955414i	−0.831003	+	0.0391682i
$596$	−10.7209	+	8.04947i	−0.439143	+	0.329719i
$597$	4.89679	+	9.61048i	0.200412	+	0.393331i
$598$	22.9636	−	45.9574i	0.939051	−	1.87934i
$599$	37.4833			1.53153			0.765763	−	0.643123i	$-0.222362\pi$
$599$	37.4833			1.53153			0.765763	+	0.643123i	$0.222362\pi$
$600$	1.66156	+	14.0442i	0.0678331	+	0.573352i
$601$	6.04452			0.246561			0.123280	−	0.992372i	$-0.460659\pi$
$601$	6.04452			0.246561			0.123280	+	0.992372i	$0.460659\pi$
$602$	−2.47064	+	4.94454i	−0.100696	+	0.201524i
$603$	2.66543	+	5.23120i	0.108545	+	0.213031i
$604$	−5.86802	+	4.40585i	−0.238766	+	0.179272i
$605$	18.7238	+	12.2999i	0.761230	+	0.500062i
$606$	−8.79549	+	0.0690894i	−0.357292	+	0.00280656i
$607$	−15.4953	−	15.4953i	−0.628933	−	0.628933i	0.318866	−	0.947800i	$-0.396698\pi$
$607$	−15.4953	−	15.4953i	−0.628933	−	0.628933i	−0.947800	+	0.318866i	$0.896698\pi$
$608$	−6.98305	+	15.1476i	−0.283200	+	0.614316i
$609$	−0.956935	+	1.31711i	−0.0387770	+	0.0533719i
$610$	−3.89577	−	0.399248i	−0.157735	−	0.0161651i
$611$	25.2910	+	34.8101i	1.02317	+	1.40827i
$612$	−6.49404	−	3.18138i	−0.262506	−	0.128600i
$613$	−1.58245	−	9.99119i	−0.0639145	−	0.403540i	−0.998817	−	0.0486348i	$-0.984513\pi$
$613$	−1.58245	−	9.99119i	−0.0639145	−	0.403540i	0.934902	−	0.354906i	$-0.115487\pi$
$614$	−35.8989	+	11.9768i	−1.44876	+	0.483344i
$615$	23.9533	+	10.8161i	0.965892	+	0.436146i
$616$	0.165707	+	7.03066i	0.00667652	+	0.283273i
$617$	4.47285	+	2.27903i	0.180070	+	0.0917504i	0.541702	−	0.840571i	$-0.317780\pi$
$617$	4.47285	+	2.27903i	0.180070	+	0.0917504i	−0.361632	+	0.932321i	$0.617780\pi$
$618$	−9.88347	−	19.0264i	−0.397571	−	0.765356i
$619$	−6.25004	−	19.2356i	−0.251210	−	0.773146i	−0.994553	−	0.104235i	$-0.966761\pi$
$619$	−6.25004	−	19.2356i	−0.251210	−	0.773146i	0.743342	−	0.668911i	$-0.233239\pi$
$620$	−23.2379	+	19.2232i	−0.933257	+	0.772021i
$621$	2.47130	−	7.60587i	0.0991697	−	0.305213i
$622$	3.22257	−	0.536385i	0.129213	−	0.0215071i
$623$	2.20010	−	13.8909i	0.0881452	−	0.556527i
$624$	−6.15495	−	17.0958i	−0.246395	−	0.684381i
$625$	12.0416	+	21.9089i	0.481666	+	0.876355i
$626$	8.81702	+	2.78845i	0.352399	+	0.111449i
$627$	2.88498	+	0.456936i	0.115215	+	0.0182482i
$628$	−34.8170	−	4.95513i	−1.38935	−	0.197731i
$629$	−14.4862	−	4.70684i	−0.577601	−	0.187674i
$630$	−6.66782	−	4.30558i	−0.265652	−	0.171539i
$631$	29.5030	−	9.58611i	1.17450	−	0.381617i	0.344177	−	0.938905i	$-0.388158\pi$
$631$	29.5030	−	9.58611i	1.17450	−	0.381617i	0.830319	+	0.557288i	$0.188158\pi$
$632$	−3.39614	+	25.2851i	−0.135091	+	1.00579i
$633$	−10.2593	+	20.1350i	−0.407770	+	0.800293i
$634$	22.6881	−	16.7577i	0.901060	−	0.665535i
$635$	−15.2825	+	33.8448i	−0.606469	+	1.34309i
$636$	−0.190006	−	12.0937i	−0.00753424	−	0.479547i
$637$	−3.14159	+	0.497579i	−0.124474	+	0.0197148i
$638$	0.898611	+	0.135099i	0.0355764	+	0.00534863i
$639$	10.1363	−	7.36448i	0.400987	−	0.291334i
$640$	−23.5939	−	9.12831i	−0.932632	−	0.360828i
$641$	7.01361	+	5.09569i	0.277021	+	0.201267i	0.717617	−	0.696438i	$-0.245233\pi$
$641$	7.01361	+	5.09569i	0.277021	+	0.201267i	−0.440596	+	0.897705i	$0.645233\pi$
$642$	17.2994	+	17.0297i	0.682753	+	0.672110i
$643$	−19.1482	+	19.1482i	−0.755130	+	0.755130i	−0.975432	−	0.220302i	$-0.929296\pi$
$643$	−19.1482	+	19.1482i	−0.755130	+	0.755130i	0.220302	+	0.975432i	$0.429296\pi$
$644$	38.3707	+	11.8043i	1.51202	+	0.465154i
$645$	−1.91178	+	2.91024i	−0.0752762	+	0.114591i
$646$	−12.2670	−	8.76613i	−0.482640	−	0.344899i
$647$	−40.2378	+	20.5022i	−1.58191	+	0.806023i	−0.999974	−	0.00721134i	$-0.997705\pi$
$647$	−40.2378	+	20.5022i	−1.58191	+	0.806023i	−0.581936	+	0.813235i	$0.697705\pi$
$648$	−1.34310	−	2.48919i	−0.0527621	−	0.0977847i
$649$		−	7.24095i		−	0.284232i
$650$	−21.4290	−	23.9274i	−0.840515	−	0.938509i
$651$		−	16.9261i		−	0.663385i
$652$	−13.2224	−	12.8133i	−0.517828	−	0.501809i
$653$	−15.4764	+	7.88563i	−0.605639	+	0.308588i	−0.729786	−	0.683675i	$-0.760380\pi$
$653$	−15.4764	+	7.88563i	−0.605639	+	0.308588i	0.124147	+	0.992264i	$0.460380\pi$
$654$	13.6772	−	19.1394i	0.534821	−	0.748410i
$655$	1.59204	+	33.7772i	0.0622063	+	1.31979i
$656$	−37.1489	+	28.8159i	−1.45042	+	1.12507i
$657$	5.99540	−	5.99540i	0.233903	−	0.233903i
$658$	−23.5872	+	23.9607i	−0.919524	+	0.934084i
$659$	6.41486	+	4.66067i	0.249888	+	0.181554i	0.705677	−	0.708534i	$-0.250643\pi$
$659$	6.41486	+	4.66067i	0.249888	+	0.181554i	−0.455789	+	0.890088i	$0.650643\pi$
$660$	−0.417022	+	4.41054i	−0.0162326	+	0.171680i
$661$	37.5286	−	27.2661i	1.45969	−	1.06053i	0.476248	−	0.879311i	$-0.341996\pi$
$661$	37.5286	−	27.2661i	1.45969	−	1.06053i	0.983443	−	0.181217i	$-0.0580037\pi$
$662$	−6.52345	+	43.3906i	−0.253541	+	1.68642i
$663$	16.2223	−	2.56935i	0.630020	−	0.0997854i
$664$	−9.53550	−	2.85169i	−0.370049	−	0.110667i
$665$	−12.2396	−	11.1377i	−0.474630	−	0.431902i
$666$	−3.53950	−	4.79209i	−0.137153	−	0.185690i
$667$	2.35500	−	4.62194i	0.0911858	−	0.178962i
$668$	33.5681	−	5.85863i	1.29879	−	0.226677i
$669$	−0.324223	+	0.105346i	−0.0125352	+	0.00407293i
$670$	−17.3156	+	6.69843i	−0.668961	+	0.258783i
$671$	−1.16675	−	0.379099i	−0.0450418	−	0.0146350i
$672$	12.3880	−	6.93767i	0.477876	−	0.267627i
$673$	21.4521	+	3.39769i	0.826919	+	0.130971i	0.555528	−	0.831498i	$-0.312516\pi$
$673$	21.4521	+	3.39769i	0.826919	+	0.130971i	0.271391	+	0.962469i	$0.412516\pi$
$674$	8.50530	−	26.8936i	0.327612	−	1.03590i
$675$	−3.85241	−	3.18731i	−0.148279	−	0.122680i
$676$	12.4922	+	8.77965i	0.480471	+	0.337679i
$677$	0.733481	−	4.63102i	0.0281900	−	0.177984i	−0.969576	−	0.244790i	$-0.921281\pi$
$677$	0.733481	−	4.63102i	0.0281900	−	0.177984i	0.997766	+	0.0668060i	$0.0212808\pi$
$678$	−1.94557	−	11.6888i	−0.0747190	−	0.448907i
$679$	6.55860	−	20.1853i	0.251696	−	0.774640i
$680$	12.1016	−	19.4033i	0.464076	−	0.744083i
$681$	−4.68999	−	14.4343i	−0.179721	−	0.553123i
$682$	−8.38385	+	4.35507i	−0.321034	+	0.166764i
$683$	−26.7626	−	13.6362i	−1.02404	−	0.521775i	−0.140476	−	0.990084i	$-0.544863\pi$
$683$	−26.7626	−	13.6362i	−1.02404	−	0.521775i	−0.883565	+	0.468309i	$0.844863\pi$
$684$	−1.91021	−	5.57922i	−0.0730385	−	0.213327i
$685$	2.00069	−	18.1178i	0.0764423	−	0.692246i
$686$	−8.65016	−	25.9277i	−0.330265	−	0.989924i
$687$	−2.93133	−	18.5077i	−0.111837	−	0.706113i
$688$	−3.00078	−	5.45834i	−0.114403	−	0.208097i
$689$	16.1472	+	22.2248i	0.615161	+	0.846697i
$690$	23.1298	+	10.2263i	0.880537	+	0.389307i
$691$	−3.45831	+	4.75996i	−0.131560	+	0.181077i	−0.869715	−	0.493554i	$-0.835697\pi$
$691$	−3.45831	+	4.75996i	−0.131560	+	0.181077i	0.738155	+	0.674632i	$0.235697\pi$
$692$	14.0170	+	26.4733i	0.532845	+	1.00636i
$693$	−1.75815	−	1.75815i	−0.0667867	−	0.0667867i
$694$	−0.0404643	−	5.15135i	−0.00153600	−	0.195543i
$695$	1.67796	+	4.44093i	0.0636487	+	0.168454i
$696$	−0.607884	−	1.73098i	−0.0230418	−	0.0656128i
$697$	−19.2938	−	37.8662i	−0.730804	−	1.43428i
$698$	−30.9722	−	15.4759i	−1.17232	−	0.585772i
$699$	−19.3578			−0.732179
$700$	15.6941	−	19.5876i	0.593183	−	0.740340i
$701$	−32.3819			−1.22305			−0.611524	−	0.791226i	$-0.709443\pi$
$701$	−32.3819			−1.22305			−0.611524	+	0.791226i	$0.709443\pi$
$702$	5.74663	+	2.87142i	0.216893	+	0.108375i
$703$	−5.63913	−	11.0674i	−0.212684	−	0.417415i
$704$	−6.62380	−	4.35097i	−0.249644	−	0.163983i
$705$	−16.5302	+	13.2425i	−0.622565	+	0.498743i
$706$	0.183814	+	23.4006i	0.00691793	+	0.880694i
$707$	11.0384	+	11.0384i	0.415142	+	0.415142i
$708$	−12.9197	+	6.84068i	−0.485553	+	0.257088i
$709$	16.8589	−	23.2043i	0.633149	−	0.871454i	−0.365078	−	0.930977i	$-0.618958\pi$
$709$	16.8589	−	23.2043i	0.633149	−	0.871454i	0.998227	+	0.0595224i	$0.0189578\pi$
$710$	19.8993	+	34.2611i	0.746809	+	1.28580i
$711$	−5.30176	−	7.29725i	−0.198832	−	0.273668i
$712$	11.4676	+	10.9395i	0.429768	+	0.409976i
$713$	8.43662	+	53.2667i	0.315954	+	1.99485i
$714$	4.06178	+	12.1746i	0.152008	+	0.455624i
$715$	−4.98515	−	8.74042i	−0.186434	−	0.326873i
$716$	−1.74269	+	0.596660i	−0.0651274	+	0.0222982i
$717$	−0.714708	−	0.364162i	−0.0266913	−	0.0135999i
$718$	9.34947	−	4.85667i	0.348919	−	0.181249i
$719$	−3.24857	−	9.99806i	−0.121151	−	0.372865i	0.872029	−	0.489454i	$-0.162804\pi$
$719$	−3.24857	−	9.99806i	−0.121151	−	0.372865i	−0.993180	+	0.116589i	$0.962804\pi$
$720$	8.26350	−	3.42265i	0.307963	−	0.127555i
$721$	−11.7588	+	36.1898i	−0.437920	+	1.34778i
$722$	2.39299	+	14.3769i	0.0890577	+	0.535053i
$723$	−1.98555	+	12.5363i	−0.0738434	+	0.466229i
$724$	−13.2138	+	18.8014i	−0.491087	+	0.698749i
$725$	−2.14463	−	2.43285i	−0.0796496	−	0.0903539i
$726$	4.27234	−	13.5090i	0.158561	−	0.501368i
$727$	−19.0292	−	3.01393i	−0.705755	−	0.111781i	−0.206768	−	0.978390i	$-0.566294\pi$
$727$	−19.0292	−	3.01393i	−0.705755	−	0.111781i	−0.498987	+	0.866609i	$0.666294\pi$
$728$	−13.9592	+	29.0702i	−0.517364	+	1.07742i
$729$	0.951057	+	0.309017i	0.0352243	+	0.0114451i
$730$	16.9275	+	20.7932i	0.626514	+	0.769590i
$731$	5.35484	−	1.73989i	0.198056	−	0.0643523i
$732$	0.425839	+	2.43992i	0.0157395	+	0.0901821i
$733$	−16.7661	+	32.9054i	−0.619271	+	1.21539i	0.341979	+	0.939708i	$0.388903\pi$
$733$	−16.7661	+	32.9054i	−0.619271	+	1.21539i	−0.961250	+	0.275680i	$0.911097\pi$
$734$	22.8336	+	30.9142i	0.842804	+	1.14106i
$735$	−0.317473	−	1.53321i	−0.0117102	−	0.0565533i
$736$	−35.5272	+	28.0076i	−1.30955	+	1.03238i
$737$	−5.74446	+	0.909833i	−0.211600	+	0.0335141i
$738$	2.47126	−	16.4375i	0.0909683	−	0.605074i
$739$	0.146989	−	0.106794i	0.00540707	−	0.00392846i	−0.585078	−	0.810977i	$-0.698936\pi$
$739$	0.146989	−	0.106794i	0.00540707	−	0.00392846i	0.590486	+	0.807048i	$0.298936\pi$
$740$	16.2161	−	9.58965i	0.596115	−	0.352523i
$741$	10.8360	+	7.87278i	0.398069	+	0.289214i
$742$	−15.0594	+	15.2979i	−0.552848	+	0.561603i
$743$	14.3370	−	14.3370i	0.525973	−	0.525973i	−0.393396	−	0.919369i	$-0.628700\pi$
$743$	14.3370	−	14.3370i	0.525973	−	0.525973i	0.919369	+	0.393396i	$0.128700\pi$
$744$	15.6910	+	10.8446i	0.575259	+	0.397583i
$745$	14.4574	+	3.95550i	0.529679	+	0.144918i
$746$	−0.874024	+	1.22308i	−0.0320003	+	0.0447801i
$747$	3.13531	−	1.59752i	0.114715	−	0.0584502i
$748$	4.98526	−	5.14441i	0.182279	−	0.188098i
$749$		−	43.0833i		−	1.57423i
$750$	11.2686	−	11.0913i	0.411472	−	0.404999i
$751$			12.5620i			0.458394i	0.973380	+	0.229197i	$0.0736101\pi$
$751$			12.5620i			0.458394i	−0.973380	+	0.229197i	$0.926390\pi$
$752$	−7.09980	−	37.2177i	−0.258903	−	1.35719i
$753$	−4.50618	+	2.29601i	−0.164214	+	0.0836714i
$754$	3.39022	+	2.42268i	0.123465	+	0.0882289i
$755$	7.91323	+	2.16503i	0.287992	+	0.0787934i
$756$	−1.47604	+	4.79796i	−0.0536829	+	0.174500i
$757$	−30.6304	+	30.6304i	−1.11328	+	1.11328i	−0.120579	+	0.992704i	$0.538475\pi$
$757$	−30.6304	+	30.6304i	−1.11328	+	1.11328i	−0.992704	+	0.120579i	$0.961525\pi$
$758$	−19.2874	−	18.9867i	−0.700548	−	0.689629i
$759$	6.40928	+	4.65661i	0.232642	+	0.169024i
$760$	18.1669	−	4.21044i	0.658984	−	0.152729i
$761$	−26.3840	+	19.1691i	−0.956420	+	0.694880i	−0.952317	−	0.305112i	$-0.901306\pi$
$761$	−26.3840	+	19.1691i	−0.956420	+	0.694880i	−0.00410353	+	0.999992i	$0.501306\pi$
$762$	23.2254	+	3.49176i	0.841367	+	0.126493i
$763$	−41.2364	+	6.53120i	−1.49286	+	0.236445i
$764$	42.3448	−	0.665286i	1.53198	−	0.0240692i
$765$	1.63934	+	7.91706i	0.0592703	+	0.286242i
$766$	23.4049	−	17.2872i	0.845654	−	0.624611i
$767$	15.0740	−	29.5845i	0.544292	−	1.06823i
$768$	−1.50561	+	15.9290i	−0.0543291	+	0.574788i
$769$	12.4755	−	4.05354i	0.449879	−	0.146175i	−0.0753100	−	0.997160i	$-0.523995\pi$
$769$	12.4755	−	4.05354i	0.449879	−	0.146175i	0.525189	+	0.850986i	$0.323995\pi$
$770$	6.09761	−	4.96399i	0.219743	−	0.178890i
$771$	7.52249	+	2.44420i	0.270916	+	0.0880259i
$772$	4.16253	−	29.2479i	0.149813	−	1.05265i
$773$	−45.2454	−	7.16616i	−1.62736	−	0.257749i	−0.725007	−	0.688742i	$-0.758163\pi$
$773$	−45.2454	−	7.16616i	−1.62736	−	0.257749i	−0.902355	+	0.430993i	$0.858163\pi$
$774$	2.09972	+	0.664051i	0.0754727	+	0.0238688i
$775$	32.9057	+	7.35704i	1.18201	+	0.264273i
$776$	14.5102	+	19.0128i	0.520886	+	0.682521i
$777$	−1.65404	+	10.4432i	−0.0593385	+	0.374648i
$778$	18.4820	−	3.07627i	0.662612	−	0.110290i
$779$	10.7095	−	32.9606i	0.383709	−	1.18094i
$780$	−10.8856	+	17.1520i	−0.389766	+	0.614142i
$781$	3.83544	+	11.8043i	0.137243	+	0.422390i
$782$	−18.8508	−	36.2893i	−0.674104	−	1.29770i
$783$	0.577939	+	0.294475i	0.0206539	+	0.0105237i
$784$	2.68966	+	0.781408i	0.0960594	+	0.0279074i
$785$	19.4800	+	34.1541i	0.695272	+	1.21901i
$786$	20.2871	−	6.76829i	0.723615	−	0.241417i
$787$	−1.69779	−	10.7194i	−0.0605197	−	0.382107i	−0.999294	−	0.0375734i	$-0.988037\pi$
$787$	−1.69779	−	10.7194i	−0.0605197	−	0.382107i	0.938774	−	0.344533i	$-0.111963\pi$
$788$	−18.9625	+	38.7075i	−0.675512	+	1.37890i
$789$	−3.13330	−	4.31262i	−0.111548	−	0.153533i
$790$	24.6649	−	14.3257i	0.877539	−	0.509687i
$791$	−12.3615	+	17.0142i	−0.439525	+	0.604954i
$792$	2.75632	−	0.503401i	0.0979415	−	0.0178876i
$793$	−3.97780	−	3.97780i	−0.141256	−	0.141256i
$794$	−17.9323	+	0.140860i	−0.636395	+	0.00499894i
$795$	−10.5539	+	8.45480i	−0.374307	+	0.299861i
$796$	12.9524	+	17.2509i	0.459086	+	0.611443i
$797$	13.5415	+	26.5768i	0.479666	+	0.941397i	0.996361	+	0.0852282i	$0.0271619\pi$
$797$	13.5415	+	26.5768i	0.479666	+	0.941397i	−0.516696	+	0.856169i	$0.672838\pi$
$798$	−4.67818	+	9.36253i	−0.165606	+	0.331430i
$799$	34.2489			1.21164
$800$	8.10290	+	27.0988i	0.286481	+	0.958086i
$801$	−5.60334			−0.197984
$802$	−9.57318	+	19.1590i	−0.338041	+	0.676527i
$803$	3.81319	+	7.48381i	0.134565	+	0.264098i
$804$	7.05029	+	9.39006i	0.248644	+	0.331162i
$805$	−15.8643	−	41.9867i	−0.559142	−	1.47984i
$806$	−43.3203	+	0.340285i	−1.52589	+	0.0119860i
$807$	−10.7910	−	10.7910i	−0.379862	−	0.379862i
$808$	−17.3053	+	3.16055i	−0.608797	+	0.111188i
$809$	4.38125	−	6.03028i	0.154037	−	0.212013i	−0.725023	−	0.688724i	$-0.758171\pi$
$809$	4.38125	−	6.03028i	0.154037	−	0.212013i	0.879060	+	0.476711i	$0.158171\pi$
$810$	−1.27872	+	2.89221i	−0.0449295	+	0.101622i
$811$	0.930193	+	1.28030i	0.0326635	+	0.0449575i	0.825036	−	0.565080i	$-0.191155\pi$
$811$	0.930193	+	1.28030i	0.0326635	+	0.0449575i	−0.792373	+	0.610037i	$0.791155\pi$
$812$	−1.43247	+	2.92404i	−0.0502698	+	0.102614i
$813$	2.60532	+	16.4493i	0.0913726	+	0.576904i
$814$	5.59833	−	1.86775i	0.196222	−	0.0654647i
$815$	−2.25946	+	20.4612i	−0.0791454	+	0.716725i
$816$	−13.8886	−	4.03496i	−0.486199	−	0.141252i
$817$	4.09110	+	2.08452i	0.143129	+	0.0729281i
$818$	−16.9455	−	32.6213i	−0.592484	−	1.14058i
$819$	−3.52323	−	10.8434i	−0.123112	−	0.378899i
$820$	50.9125	+	13.0734i	1.77794	+	0.456542i
$821$	9.93549	−	30.5783i	0.346751	−	1.06719i	−0.613888	−	0.789393i	$-0.710396\pi$
$821$	9.93549	−	30.5783i	0.346751	−	1.06719i	0.960640	−	0.277798i	$-0.0896044\pi$
$822$	−11.3719	+	1.89282i	−0.396641	+	0.0660196i
$823$	4.78704	−	30.2242i	0.166866	−	1.05355i	−0.752053	−	0.659103i	$-0.770936\pi$
$823$	4.78704	−	30.2242i	0.166866	−	1.05355i	0.918919	−	0.394447i	$-0.129064\pi$
$824$	−26.0151	−	34.0877i	−0.906277	−	1.18750i
$825$	4.18219	−	2.65381i	0.145605	−	0.0923937i
$826$	24.7380	+	7.82357i	0.860745	+	0.272217i
$827$	−50.7210	−	8.03342i	−1.76374	−	0.279349i	−0.811425	−	0.584457i	$-0.801308\pi$
$827$	−50.7210	−	8.03342i	−1.76374	−	0.279349i	−0.952318	+	0.305107i	$0.901308\pi$
$828$	2.25362	−	15.8350i	0.0783188	−	0.550304i
$829$	−25.8242	−	8.39079i	−0.896912	−	0.291424i	−0.175950	−	0.984399i	$-0.556300\pi$
$829$	−25.8242	−	8.39079i	−0.896912	−	0.291424i	−0.720962	+	0.692975i	$0.756300\pi$
$830$	4.01469	+	10.3781i	0.139352	+	0.360228i
$831$	13.7964	−	4.48271i	0.478590	−	0.155503i
$832$	−18.0052	−	31.5661i	−0.624218	−	1.09436i
$833$	−1.14941	+	2.25584i	−0.0398247	+	0.0781604i
$834$	2.41513	−	1.78385i	0.0836292	−	0.0617696i
$835$	−28.1775	−	25.6408i	−0.975123	−	0.887338i
$836$	5.84116	−	0.0917713i	0.202021	−	0.00317398i
$837$	−6.66060	+	1.05494i	−0.230224	+	0.0364639i
$838$	33.7356	+	5.07188i	1.16538	+	0.175205i
$839$	12.9256	−	9.39100i	0.446241	−	0.324213i	−0.341869	−	0.939748i	$-0.611060\pi$
$839$	12.9256	−	9.39100i	0.446241	−	0.324213i	0.788110	+	0.615535i	$0.211060\pi$
$840$	−14.6176	−	6.19013i	−0.504354	−	0.213580i
$841$	−23.1211	−	16.7985i	−0.797280	−	0.579258i
$842$	−17.6408	−	17.3658i	−0.607943	−	0.598466i
$843$	1.19860	−	1.19860i	0.0412819	−	0.0412819i
$844$	−13.2894	+	43.1981i	−0.457439	+	1.48694i
$845$	−0.803731	−	17.0522i	−0.0276492	−	0.586613i
$846$	10.8989	+	7.78845i	0.374712	+	0.267772i
$847$	−22.4054	+	11.4161i	−0.769860	+	0.392263i
$848$	−4.53292	−	23.7619i	−0.155661	−	0.815988i
$849$			2.12731i			0.0730089i
$850$	−25.4340	+	2.60465i	−0.872379	+	0.0893388i
$851$		−	33.6895i		−	1.15486i
$852$	17.4384	−	17.9951i	0.597431	−	0.616503i
$853$	45.1378	−	22.9989i	1.54549	−	0.787466i	0.546732	−	0.837308i	$-0.315872\pi$
$853$	45.1378	−	22.9989i	1.54549	−	0.787466i	0.998757	+	0.0498414i	$0.0158716\pi$
$854$	2.55578	−	3.57647i	0.0874570	−	0.122384i
$855$	−3.61997	+	5.51058i	−0.123800	+	0.188458i
$856$	39.9394	+	27.6037i	1.36510	+	0.943475i
$857$	−33.6931	+	33.6931i	−1.15093	+	1.15093i	−0.164569	+	0.986366i	$0.552623\pi$
$857$	−33.6931	+	33.6931i	−1.15093	+	1.15093i	−0.986366	+	0.164569i	$0.947377\pi$
$858$	−4.46444	+	4.53513i	−0.152413	+	0.154827i
$859$	−28.7062	−	20.8562i	−0.979441	−	0.711606i	−0.0218576	−	0.999761i	$-0.506958\pi$
$859$	−28.7062	−	20.8562i	−0.979441	−	0.711606i	−0.957584	+	0.288155i	$0.906958\pi$
$860$	−2.76590	+	6.39120i	−0.0943163	+	0.217938i
$861$	−23.8669	+	17.3403i	−0.813382	+	0.590956i
$862$	−7.64958	+	50.8811i	−0.260546	+	1.73302i
$863$	31.6541	−	5.01352i	1.07752	−	0.170662i	0.407647	−	0.913140i	$-0.366349\pi$
$863$	31.6541	−	5.01352i	1.07752	−	0.170662i	0.669871	+	0.742477i	$0.266349\pi$
$864$	−3.50215	−	4.44241i	−0.119145	−	0.151134i
$865$	13.7827	−	30.5233i	0.468627	−	1.03782i
$866$	−30.1240	−	40.7846i	−1.02366	−	1.38592i
$867$	−1.78262	+	3.49859i	−0.0605409	+	0.118818i
$868$	−5.82023	−	33.3481i	−0.197552	−	1.13191i
$869$	8.49801	−	2.76117i	0.288275	−	0.0936663i
$870$	−1.11268	+	1.72315i	−0.0377234	+	0.0584201i
$871$	−25.3643	−	8.24136i	−0.859437	−	0.279248i
$872$	20.3657	−	42.4119i	0.689671	−	1.43625i
$873$	−8.35191	−	1.32281i	−0.282669	−	0.0447704i
$874$	10.0557	−	31.7959i	0.340138	−	1.07551i
$875$	−28.0584	−	0.442893i	−0.948549	−	0.0149725i
$876$	9.75065	−	13.8738i	0.329444	−	0.468753i
$877$	3.21039	−	20.2696i	0.108407	−	0.684457i	−0.872299	−	0.488972i	$-0.837372\pi$
$877$	3.21039	−	20.2696i	0.108407	−	0.684457i	0.980707	−	0.195485i	$-0.0626280\pi$
$878$	3.75294	+	22.5474i	0.126656	+	0.760939i
$879$	5.46804	−	16.8289i	0.184432	−	0.567625i
$880$	0.694992	+	8.83312i	0.0234282	+	0.297764i
$881$	−10.4735	−	32.2341i	−0.352861	−	1.08599i	−0.957239	−	0.289297i	$-0.906579\pi$
$881$	−10.4735	−	32.2341i	−0.352861	−	1.08599i	0.604379	−	0.796697i	$-0.293421\pi$
$882$	−0.878767	+	0.456484i	−0.0295896	+	0.0153706i
$883$	18.4629	+	9.40734i	0.621327	+	0.316582i	0.736165	−	0.676802i	$-0.236635\pi$
$883$	18.4629	+	9.40734i	0.621327	+	0.316582i	−0.114838	+	0.993384i	$0.536635\pi$
$884$	31.0779	−	10.6404i	1.04526	−	0.357875i
$885$	14.8963	+	6.72637i	0.500732	+	0.226105i
$886$	2.00577	+	6.01202i	0.0673851	+	0.201978i
$887$	−4.49497	−	28.3801i	−0.150926	−	0.952911i	−0.940633	−	0.339426i	$-0.889767\pi$
$887$	−4.49497	−	28.3801i	−0.150926	−	0.952911i	0.789706	−	0.613485i	$-0.210233\pi$
$888$	−8.62141	−	8.22437i	−0.289316	−	0.275992i
$889$	−24.5009	−	33.7227i	−0.821735	−	1.13102i
$890$	1.80646	−	17.6270i	0.0605527	−	0.590859i
$891$	−0.582275	+	0.801432i	−0.0195069	+	0.0268490i
$892$	−0.602565	+	0.319043i	−0.0201754	+	0.0106824i
$893$	19.7492	+	19.7492i	0.660882	+	0.660882i
$894$	−0.0744619	−	9.47944i	−0.00249038	−	0.317040i
$895$	1.72125	+	1.13071i	0.0575351	+	0.0377955i
$896$	22.0214	−	17.9285i	0.735683	−	0.598948i
$897$	16.4925	+	32.3683i	0.550667	+	1.08075i
$898$	40.5087	+	20.2410i	1.35179	+	0.675450i
$899$	−4.37416			−0.145886
$900$	−8.68608	−	4.95501i	−0.289536	−	0.165167i
$901$	21.8665			0.728478
$902$	14.7300	+	7.36013i	0.490454	+	0.245066i
$903$	−1.77441	−	3.48248i	−0.0590488	−	0.115890i
$904$	−7.85253	−	22.3605i	−0.261171	−	0.743700i
$905$	25.6644	−	1.20965i	0.853112	−	0.0402103i
$906$	−0.0407565	−	5.18854i	−0.00135404	−	0.172378i
$907$	1.04173	+	1.04173i	0.0345900	+	0.0345900i	0.724190	−	0.689600i	$-0.242214\pi$
$907$	1.04173	+	1.04173i	0.0345900	+	0.0345900i	−0.689600	+	0.724190i	$0.742214\pi$
$908$	−14.2037	−	26.8260i	−0.471366	−	0.890252i
$909$	3.65575	−	5.03171i	0.121254	−	0.166891i
$910$	35.2470	−	7.58759i	1.16843	−	0.251526i
$911$	−1.07000	−	1.47273i	−0.0354508	−	0.0487938i	0.790924	−	0.611915i	$-0.209600\pi$
$911$	−1.07000	−	1.47273i	−0.0354508	−	0.0487938i	−0.826374	+	0.563121i	$0.809600\pi$
$912$	−5.68200	−	10.3354i	−0.188150	−	0.342240i
$913$	0.545307	+	3.44293i	0.0180470	+	0.113944i
$914$	10.2481	+	30.7172i	0.338976	+	1.01604i
$915$	1.86372	−	2.04810i	0.0616128	−	0.0677082i
$916$	−12.1395	−	35.4563i	−0.401099	−	1.17151i
$917$	−33.8193	−	17.2318i	−1.11681	−	0.569044i
$918$	4.53770	−	2.35715i	0.149766	−	0.0777976i
$919$	11.4266	+	35.1676i	0.376930	+	1.16007i	0.942167	+	0.335144i	$0.108785\pi$
$919$	11.4266	+	35.1676i	0.376930	+	1.16007i	−0.565237	+	0.824929i	$0.691215\pi$
$920$	49.0872	+	12.1945i	1.61836	+	0.402040i
$921$	8.26923	−	25.4501i	0.272480	−	0.838608i
$922$	−2.86194	−	17.1943i	−0.0942529	−	0.566265i
$923$	−8.90332	+	56.2134i	−0.293056	+	1.85029i
$924$	−4.06851	−	2.85938i	−0.133844	−	0.0940668i
$925$	−19.5836	−	7.75482i	−0.643903	−	0.254977i
$926$	−13.8708	+	43.8593i	−0.455824	+	1.44131i
$927$	14.9740	+	2.37164i	0.491809	+	0.0778950i
$928$	−1.79288	−	3.20139i	−0.0588543	−	0.105091i
$929$	−36.8445	−	11.9715i	−1.20883	−	0.392772i	−0.365827	−	0.930683i	$-0.619214\pi$
$929$	−36.8445	−	11.9715i	−1.20883	−	0.392772i	−0.843002	+	0.537911i	$0.819214\pi$
$930$	−1.17131	−	21.2930i	−0.0384088	−	0.698226i
$931$	−1.96360	+	0.638012i	−0.0643544	+	0.0209100i
$932$	−38.1391	+	6.65641i	−1.24929	+	0.218038i
$933$	−1.04874	+	2.05827i	−0.0343342	+	0.0673847i
$934$	−1.39272	−	1.88559i	−0.0455713	−	0.0616985i
$935$	−7.96081	−	0.879084i	−0.260346	−	0.0287491i
$936$	12.3095	+	3.68128i	0.402348	+	0.120326i
$937$	14.1890	−	2.24732i	0.463536	−	0.0734168i	0.0797013	−	0.996819i	$-0.474603\pi$
$937$	14.1890	−	2.24732i	0.463536	−	0.0734168i	0.383834	+	0.923402i	$0.374603\pi$
$938$	3.09832	−	20.6084i	0.101164	−	0.672889i
$939$	−5.29010	+	3.84349i	−0.172636	+	0.125427i
$940$	−28.0146	+	31.7748i	−0.913735	+	1.03638i
$941$	28.0766	+	20.3988i	0.915270	+	0.664982i	0.942342	−	0.334651i	$-0.108618\pi$
$941$	28.0766	+	20.3988i	0.915270	+	0.664982i	−0.0270725	+	0.999633i	$0.508618\pi$
$942$	17.4453	−	17.7215i	0.568398	−	0.577398i
$943$	66.4665	−	66.4665i	2.16445	−	2.16445i
$944$	−23.1024	+	17.9202i	−0.751920	+	0.583254i
$945$	5.25013	−	1.98371i	0.170787	−	0.0645300i
$946$	−1.26839	+	1.77495i	−0.0412390	+	0.0577085i
$947$	−2.50903	+	1.27841i	−0.0815325	+	0.0415429i	−0.494281	−	0.869302i	$-0.664569\pi$
$947$	−2.50903	+	1.27841i	−0.0815325	+	0.0415429i	0.412749	+	0.910845i	$0.364569\pi$
$948$	−12.9549	−	12.5541i	−0.420755	−	0.407738i
$949$			38.5149i			1.25025i
$950$	−16.1682	−	13.1643i	−0.524564	−	0.427105i
$951$			19.9446i			0.646747i
$952$	12.1890	+	22.5900i	0.395047	+	0.732146i
$953$	−25.2286	+	12.8546i	−0.817234	+	0.416401i	−0.812052	−	0.583585i	$-0.801649\pi$
$953$	−25.2286	+	12.8546i	−0.817234	+	0.416401i	−0.00518178	+	0.999987i	$0.501649\pi$
$954$	6.95848	+	4.97259i	0.225289	+	0.160994i
$955$	−29.6036	−	36.9532i	−0.957948	−	1.19578i
$956$	−1.53335	−	0.471718i	−0.0495922	−	0.0152564i
$957$	−0.454355	+	0.454355i	−0.0146872	+	0.0146872i
$958$	1.35790	+	1.33673i	0.0438718	+	0.0431879i
$959$	16.5529	+	12.0264i	0.534520	+	0.388351i
$960$	15.1040	−	9.58487i	0.487479	−	0.309350i
$961$	11.7117	−	8.50908i	0.377798	−	0.274486i
$962$	26.7614	+	4.02338i	0.862823	+	0.129719i
$963$	−16.9538	+	2.68521i	−0.546327	+	0.0865297i
$964$	0.398779	+	25.3819i	0.0128438	+	0.817497i
$965$	−28.6910	+	16.3641i	−0.923596	+	0.526779i
$966$	−22.8338	+	16.8654i	−0.734666	+	0.542634i
$967$	−11.2935	+	22.1648i	−0.363175	+	0.712771i	−0.998216	−	0.0597073i	$-0.980983\pi$
$967$	−11.2935	+	22.1648i	−0.363175	+	0.712771i	0.635041	+	0.772479i	$0.280983\pi$
$968$	3.77219	−	28.0849i	0.121243	−	0.902682i
$969$	10.1395	−	3.29451i	0.325726	−	0.105835i
$970$	6.85387	−	25.8470i	0.220065	−	0.829897i
$971$	−13.7509	−	4.46795i	−0.441289	−	0.143383i	0.0799415	−	0.996800i	$-0.474527\pi$
$971$	−13.7509	−	4.46795i	−0.441289	−	0.143383i	−0.521230	+	0.853416i	$0.674527\pi$
$972$	1.98005	+	0.281799i	0.0635101	+	0.00903870i
$973$	−5.26320	−	0.833609i	−0.168730	−	0.0267243i
$974$	44.6622	+	14.1248i	1.43107	+	0.452587i
$975$	22.6119	−	2.13631i	0.724160	−	0.0684165i
$976$	1.67799	+	4.66075i	0.0537112	+	0.149187i
$977$	0.0404109	−	0.255144i	0.00129286	−	0.00816278i	−0.987033	−	0.160515i	$-0.948685\pi$
$977$	0.0404109	−	0.255144i	0.00129286	−	0.00816278i	0.988326	+	0.152352i	$0.0486847\pi$
$978$	12.8428	−	2.13764i	0.410667	−	0.0683541i
$979$	1.71529	−	5.27913i	0.0548211	−	0.168722i
$980$	−1.15270	−	2.91159i	−0.0368218	−	0.0930074i
$981$	5.14020	+	15.8199i	0.164114	+	0.505091i
$982$	1.99894	+	3.84812i	0.0637889	+	0.122799i
$983$	−10.9161	−	5.56205i	−0.348171	−	0.177402i	0.271156	−	0.962536i	$-0.412594\pi$
$983$	−10.9161	−	5.56205i	−0.348171	−	0.177402i	−0.619326	+	0.785134i	$0.712594\pi$
$984$	−0.783328	−	33.2353i	−0.0249716	−	1.05950i
$985$	47.1893	−	9.77120i	1.50358	−	0.311336i
$986$	3.14626	−	1.04967i	0.100197	−	0.0334284i
$987$	−3.71918	−	23.4820i	−0.118383	−	0.747439i
$988$	24.0563	+	11.7850i	0.765334	+	0.374932i
$989$	7.31992	+	10.0750i	0.232760	+	0.320367i
$990$	−2.33343	−	2.09009i	−0.0741612	−	0.0664275i
$991$	9.47852	−	13.0461i	0.301095	−	0.414422i	−0.631483	−	0.775390i	$-0.717553\pi$
$991$	9.47852	−	13.0461i	0.301095	−	0.414422i	0.932578	+	0.360968i	$0.117553\pi$
$992$	34.6437	+	15.9707i	1.09994	+	0.507072i
$993$	−21.9391	−	21.9391i	−0.696217	−	0.696217i
$994$	−44.4721	+	0.349333i	−1.41057	+	0.0110802i
$995$	6.36479	−	23.2635i	0.201778	−	0.737502i
$996$	5.62791	−	4.22557i	0.178327	−	0.133892i
$997$	15.2660	+	29.9612i	0.483479	+	0.948881i	0.995927	+	0.0901629i	$0.0287388\pi$
$997$	15.2660	+	29.9612i	0.483479	+	0.948881i	−0.512448	+	0.858718i	$0.671261\pi$
$998$	−24.1664	+	48.3646i	−0.764973	+	1.53096i
$999$	4.21261			0.133281

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.2.w.a.223.11	yes	240
3.2	odd	2		900.2.bj.f.523.20		240
4.3	odd	2	inner	300.2.w.a.223.18	yes	240
12.11	even	2		900.2.bj.f.523.13		240
25.12	odd	20	inner	300.2.w.a.187.18	yes	240
75.62	even	20		900.2.bj.f.487.13		240
100.87	even	20	inner	300.2.w.a.187.11	✓	240
300.287	odd	20		900.2.bj.f.487.20		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.w.a.187.11	✓	240	100.87	even	20	inner
300.2.w.a.187.18	yes	240	25.12	odd	20	inner
300.2.w.a.223.11	yes	240	1.1	even	1	trivial
300.2.w.a.223.18	yes	240	4.3	odd	2	inner
900.2.bj.f.487.13		240	75.62	even	20
900.2.bj.f.487.20		240	300.287	odd	20
900.2.bj.f.523.13		240	12.11	even	2
900.2.bj.f.523.20		240	3.2	odd	2

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:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	300.w (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.632122 + 1.26508i) q^{2} +(-0.453990 - 0.891007i) q^{3} +(-1.20084 - 1.59937i) q^{4} +(-0.590092 + 2.15680i) q^{5} +(1.41417 - 0.0111084i) q^{6} +(-1.77479 - 1.77479i) q^{7} +(2.78240 - 0.508165i) q^{8} +(-0.587785 + 0.809017i) q^{9} +O(q^{10})\)	\(q+(-0.632122 + 1.26508i) q^{2} +(-0.453990 - 0.891007i) q^{3} +(-1.20084 - 1.59937i) q^{4} +(-0.590092 + 2.15680i) q^{5} +(1.41417 - 0.0111084i) q^{6} +(-1.77479 - 1.77479i) q^{7} +(2.78240 - 0.508165i) q^{8} +(-0.587785 + 0.809017i) q^{9} +(-2.35551 - 2.10987i) q^{10} +(-0.582275 - 0.801432i) q^{11} +(-0.879875 + 1.79606i) q^{12} +(-0.710606 - 4.48659i) q^{13} +(3.36714 - 1.12337i) q^{14} +(2.18962 - 0.453391i) q^{15} +(-1.11595 + 3.84118i) q^{16} +(-3.22163 - 1.64150i) q^{17} +(-0.651917 - 1.25499i) q^{18} +(-0.911162 - 2.80427i) q^{19} +(4.15813 - 1.64621i) q^{20} +(-0.775613 + 2.38709i) q^{21} +(1.38194 - 0.230020i) q^{22} +(1.25105 - 7.89882i) q^{23} +(-1.71596 - 2.24844i) q^{24} +(-4.30358 - 2.54542i) q^{25} +(6.12507 + 1.93710i) q^{26} +(0.987688 + 0.156434i) q^{27} +(-0.707297 + 4.96979i) q^{28} +(0.616890 + 0.200440i) q^{29} +(-0.810532 + 3.05664i) q^{30} +(-6.41357 + 2.08390i) q^{31} +(-4.15397 - 3.83986i) q^{32} +(-0.449734 + 0.882653i) q^{33} +(4.11309 - 3.03798i) q^{34} +(4.87517 - 2.78058i) q^{35} +(1.99975 - 0.0314184i) q^{36} +(4.16075 - 0.658998i) q^{37} +(4.12358 + 0.619949i) q^{38} +(-3.67497 + 2.67002i) q^{39} +(-0.545863 + 6.30095i) q^{40} +(9.50896 + 6.90867i) q^{41} +(-2.52957 - 2.49014i) q^{42} +(-1.10111 + 1.10111i) q^{43} +(-0.582564 + 1.89367i) q^{44} +(-1.39804 - 1.74513i) q^{45} +(9.20181 + 6.57569i) q^{46} +(-8.43980 + 4.30030i) q^{47} +(3.92915 - 0.749540i) q^{48} -0.700218i q^{49} +(5.94055 - 3.83535i) q^{50} +3.61572i q^{51} +(-6.32237 + 6.52421i) q^{52} +(-5.38846 + 2.74556i) q^{53} +(-0.822241 + 1.15062i) q^{54} +(2.07213 - 0.782931i) q^{55} +(-5.84008 - 4.03630i) q^{56} +(-2.08496 + 2.08496i) q^{57} +(-0.643521 + 0.653711i) q^{58} +(5.91350 + 4.29641i) q^{59} +(-3.35453 - 2.95755i) q^{60} +(1.00189 - 0.727914i) q^{61} +(1.41787 - 9.43094i) q^{62} +(2.47904 - 0.392641i) q^{63} +(7.48354 - 2.82784i) q^{64} +(10.0960 + 1.11487i) q^{65} +(-0.832338 - 1.12689i) q^{66} +(2.66543 - 5.23120i) q^{67} +(1.24331 + 7.12376i) q^{68} +(-7.60587 + 2.47130i) q^{69} +(0.435954 + 7.92514i) q^{70} +(-11.9160 - 3.87174i) q^{71} +(-1.22434 + 2.54970i) q^{72} +(-8.37438 - 1.32637i) q^{73} +(-1.79642 + 5.68024i) q^{74} +(-0.314203 + 4.99012i) q^{75} +(-3.39089 + 4.82477i) q^{76} +(-0.388959 + 2.45579i) q^{77} +(-1.05476 - 6.33690i) q^{78} +(-2.78730 + 8.57843i) q^{79} +(-7.62615 - 4.67353i) q^{80} +(-0.309017 - 0.951057i) q^{81} +(-14.7508 + 7.66246i) q^{82} +(-3.13531 - 1.59752i) q^{83} +(4.74923 - 1.62603i) q^{84} +(5.44146 - 5.97978i) q^{85} +(-0.696954 - 2.08902i) q^{86} +(-0.101469 - 0.640650i) q^{87} +(-2.02738 - 1.93402i) q^{88} +(3.29356 + 4.53320i) q^{89} +(3.09146 - 0.665495i) q^{90} +(-6.70159 + 9.22394i) q^{91} +(-14.1354 + 7.48436i) q^{92} +(4.76846 + 4.76846i) q^{93} +(-0.105221 - 13.3953i) q^{94} +(6.58592 - 0.310418i) q^{95} +(-1.53547 + 5.44448i) q^{96} +(3.83895 + 7.53437i) q^{97} +(0.885830 + 0.442623i) q^{98} +0.990625 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 12 q^{8}+O(q^{10}) \) 240 * q + 12 * q^8	\( 240 q + 12 q^{8} + 8 q^{10} + 8 q^{12} + 4 q^{13} + 20 q^{17} - 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} - 8 q^{30} - 20 q^{32} - 8 q^{33} - 4 q^{37} - 76 q^{38} - 92 q^{40} - 20 q^{42} - 140 q^{44} - 4 q^{45} - 16 q^{48} - 164 q^{50} - 172 q^{52} - 4 q^{53} - 120 q^{58} + 20 q^{60} - 44 q^{62} - 60 q^{64} - 20 q^{65} + 16 q^{68} - 44 q^{70} + 12 q^{72} - 44 q^{73} - 48 q^{77} + 24 q^{78} - 4 q^{80} + 60 q^{81} + 24 q^{82} + 80 q^{84} - 64 q^{85} + 60 q^{88} - 260 q^{89} + 48 q^{90} + 144 q^{92} - 64 q^{93} + 40 q^{94} - 20 q^{96} - 180 q^{97} + 256 q^{98}+O(q^{100}) \) 240 * q + 12 * q^8 + 8 * q^10 + 8 * q^12 + 4 * q^13 + 20 * q^17 - 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 - 8 * q^30 - 20 * q^32 - 8 * q^33 - 4 * q^37 - 76 * q^38 - 92 * q^40 - 20 * q^42 - 140 * q^44 - 4 * q^45 - 16 * q^48 - 164 * q^50 - 172 * q^52 - 4 * q^53 - 120 * q^58 + 20 * q^60 - 44 * q^62 - 60 * q^64 - 20 * q^65 + 16 * q^68 - 44 * q^70 + 12 * q^72 - 44 * q^73 - 48 * q^77 + 24 * q^78 - 4 * q^80 + 60 * q^81 + 24 * q^82 + 80 * q^84 - 64 * q^85 + 60 * q^88 - 260 * q^89 + 48 * q^90 + 144 * q^92 - 64 * q^93 + 40 * q^94 - 20 * q^96 - 180 * q^97 + 256 * q^98

Introduction

L-functions

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