LMFDB - Embedded newform 300.2.w.a.127.25

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			127.25
Character	$\chi$	$=$	300.127
Dual form			300.2.w.a.163.25

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.18105 + 0.777895i) q^{2} +(-0.891007 + 0.453990i) q^{3} +(0.789760 + 1.83747i) q^{4} +(2.16584 - 0.556007i) q^{5} +(-1.40548 - 0.156924i) q^{6} +(3.13412 - 3.13412i) q^{7} +(-0.496609 + 2.78449i) q^{8} +(0.587785 - 0.809017i) q^{9} +O(q^{10})$	\(q+(1.18105 + 0.777895i) q^{2} +(-0.891007 + 0.453990i) q^{3} +(0.789760 + 1.83747i) q^{4} +(2.16584 - 0.556007i) q^{5} +(-1.40548 - 0.156924i) q^{6} +(3.13412 - 3.13412i) q^{7} +(-0.496609 + 2.78449i) q^{8} +(0.587785 - 0.809017i) q^{9} +(2.99048 + 1.02812i) q^{10} +(0.0527296 + 0.0725760i) q^{11} +(-1.53787 - 1.27865i) q^{12} +(-5.12177 + 0.811209i) q^{13} +(6.13957 - 1.26354i) q^{14} +(-1.67735 + 1.47868i) q^{15} +(-2.75256 + 2.90231i) q^{16} +(-1.36594 + 2.68082i) q^{17} +(1.32353 - 0.498255i) q^{18} +(0.464955 + 1.43098i) q^{19} +(2.73213 + 3.54054i) q^{20} +(-1.36966 + 4.21538i) q^{21} +(0.00581977 + 0.126734i) q^{22} +(2.09335 + 0.331555i) q^{23} +(-0.821650 - 2.70645i) q^{24} +(4.38171 - 2.40844i) q^{25} +(-6.68011 - 3.02612i) q^{26} +(-0.156434 + 0.987688i) q^{27} +(8.23404 + 3.28364i) q^{28} +(-6.04881 - 1.96538i) q^{29} +(-3.13129 + 0.441585i) q^{30} +(-3.95945 + 1.28650i) q^{31} +(-5.50860 + 1.28658i) q^{32} +(-0.0799312 - 0.0407270i) q^{33} +(-3.69864 + 2.10362i) q^{34} +(5.04540 - 8.53059i) q^{35} +(1.95075 + 0.441106i) q^{36} +(-1.26010 - 7.95598i) q^{37} +(-0.564019 + 2.05175i) q^{38} +(4.19525 - 3.04803i) q^{39} +(0.472619 + 6.30687i) q^{40} +(8.23695 + 5.98450i) q^{41} +(-4.89676 + 3.91313i) q^{42} +(-7.85946 - 7.85946i) q^{43} +(-0.0917123 + 0.154206i) q^{44} +(0.823229 - 2.07901i) q^{45} +(2.21444 + 2.01999i) q^{46} +(-3.49688 - 6.86301i) q^{47} +(1.13493 - 3.83561i) q^{48} -12.6454i q^{49} +(7.04854 + 0.564022i) q^{50} -3.00875i q^{51} +(-5.53554 - 8.77042i) q^{52} +(1.47153 + 2.88805i) q^{53} +(-0.953075 + 1.04482i) q^{54} +(0.154557 + 0.127870i) q^{55} +(7.17049 + 10.2834i) q^{56} +(-1.06393 - 1.06393i) q^{57} +(-5.61510 - 7.02655i) q^{58} +(11.4383 + 8.31042i) q^{59} +(-4.04172 - 1.91428i) q^{60} +(-9.26103 + 6.72853i) q^{61} +(-5.67708 - 1.56061i) q^{62} +(-0.693367 - 4.37774i) q^{63} +(-7.50676 - 2.76560i) q^{64} +(-10.6419 + 4.60469i) q^{65} +(-0.0627215 - 0.110279i) q^{66} +(1.84223 + 0.938661i) q^{67} +(-6.00467 - 0.392675i) q^{68} +(-2.01571 + 0.654945i) q^{69} +(12.5948 - 6.15026i) q^{70} +(-2.37497 - 0.771676i) q^{71} +(1.96080 + 2.03845i) q^{72} +(1.16183 - 7.33551i) q^{73} +(4.70067 - 10.3766i) q^{74} +(-2.81073 + 4.13519i) q^{75} +(-2.26218 + 1.98447i) q^{76} +(0.392723 + 0.0622012i) q^{77} +(7.32585 - 0.336411i) q^{78} +(-0.395606 + 1.21755i) q^{79} +(-4.34789 + 7.81638i) q^{80} +(-0.309017 - 0.951057i) q^{81} +(5.07295 + 13.4755i) q^{82} +(1.03260 - 2.02659i) q^{83} +(-8.82732 + 0.812434i) q^{84} +(-1.46786 + 6.56569i) q^{85} +(-3.16858 - 15.3962i) q^{86} +(6.28180 - 0.994939i) q^{87} +(-0.228273 + 0.110783i) q^{88} +(7.66814 + 10.5543i) q^{89} +(2.58953 - 1.81503i) q^{90} +(-13.5098 + 18.5947i) q^{91} +(1.04403 + 4.10831i) q^{92} +(2.94384 - 2.94384i) q^{93} +(1.20871 - 10.8258i) q^{94} +(1.80265 + 2.84076i) q^{95} +(4.32411 - 3.64720i) q^{96} +(3.93972 - 2.00739i) q^{97} +(9.83679 - 14.9349i) q^{98} +0.0897089 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 $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

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

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 $

$2$	1.18105	+	0.777895i	0.835129	+	0.550055i
$2$	1.18105	+	0.777895i	0.835129	+	0.550055i
$3$	−0.891007	+	0.453990i	−0.514423	+	0.262112i
$3$	−0.891007	+	0.453990i	−0.514423	+	0.262112i
$4$	0.789760	+	1.83747i	0.394880	+	0.918733i
$5$	2.16584	−	0.556007i	0.968592	−	0.248654i
$5$	2.16584	−	0.556007i	0.968592	−	0.248654i
$6$	−1.40548	−	0.156924i	−0.573785	−	0.0640638i
$7$	3.13412	−	3.13412i	1.18459	−	1.18459i	0.206043	−	0.978543i	$-0.433941\pi$
$7$	3.13412	−	3.13412i	1.18459	−	1.18459i	0.978543	−	0.206043i	$-0.0660586\pi$
$8$	−0.496609	+	2.78449i	−0.175578	+	0.984466i
$9$	0.587785	−	0.809017i	0.195928	−	0.269672i
$10$	2.99048	+	1.02812i	0.945672	+	0.325121i
$11$	0.0527296	+	0.0725760i	0.0158986	+	0.0218825i	0.816892	−	0.576790i	$-0.195695\pi$
$11$	0.0527296	+	0.0725760i	0.0158986	+	0.0218825i	−0.800994	+	0.598673i	$0.795695\pi$
$12$	−1.53787	−	1.27865i	−0.443946	−	0.369115i
$13$	−5.12177	+	0.811209i	−1.42052	+	0.224989i	−0.818967	−	0.573841i	$-0.805453\pi$
$13$	−5.12177	+	0.811209i	−1.42052	+	0.224989i	−0.601557	+	0.798830i	$0.705453\pi$
$14$	6.13957	−	1.26354i	1.64087	−	0.337695i
$15$	−1.67735	+	1.47868i	−0.433091	+	0.381792i
$16$	−2.75256	+	2.90231i	−0.688140	+	0.725578i
$17$	−1.36594	+	2.68082i	−0.331290	+	0.650193i	−0.995226	−	0.0975960i	$-0.968885\pi$
$17$	−1.36594	+	2.68082i	−0.331290	+	0.650193i	0.663936	+	0.747789i	$0.268885\pi$
$18$	1.32353	−	0.498255i	0.311960	−	0.117440i
$19$	0.464955	+	1.43098i	0.106668	+	0.328290i	0.990118	−	0.140235i	$-0.0447857\pi$
$19$	0.464955	+	1.43098i	0.106668	+	0.328290i	−0.883450	+	0.468525i	$0.844786\pi$
$20$	2.73213	+	3.54054i	0.610924	+	0.791689i
$21$	−1.36966	+	4.21538i	−0.298884	+	0.919871i
$22$	0.00581977	+	0.126734i	0.00124078	+	0.0270198i
$23$	2.09335	+	0.331555i	0.436494	+	0.0691339i	0.370815	−	0.928707i	$-0.379078\pi$
$23$	2.09335	+	0.331555i	0.436494	+	0.0691339i	0.0656796	+	0.997841i	$0.479078\pi$
$24$	−0.821650	−	2.70645i	−0.167719	−	0.552453i
$25$	4.38171	−	2.40844i	0.876343	−	0.481688i
$26$	−6.68011	−	3.02612i	−1.31008	−	0.593471i
$27$	−0.156434	+	0.987688i	−0.0301058	+	0.190081i
$28$	8.23404	+	3.28364i	1.55609	+	0.620549i
$29$	−6.04881	−	1.96538i	−1.12324	−	0.364962i	−0.312235	−	0.950005i	$-0.601078\pi$
$29$	−6.04881	−	1.96538i	−1.12324	−	0.364962i	−0.811002	+	0.585043i	$0.801078\pi$
$30$	−3.13129	+	0.441585i	−0.571693	+	0.0806220i
$31$	−3.95945	+	1.28650i	−0.711139	+	0.231063i	−0.642177	−	0.766556i	$-0.721969\pi$
$31$	−3.95945	+	1.28650i	−0.711139	+	0.231063i	−0.0689619	+	0.997619i	$0.521969\pi$
$32$	−5.50860	+	1.28658i	−0.973793	+	0.227436i
$33$	−0.0799312	−	0.0407270i	−0.0139142	−	0.00708966i
$34$	−3.69864	+	2.10362i	−0.634312	+	0.360768i
$35$	5.04540	−	8.53059i	0.852829	−	1.44193i
$36$	1.95075	+	0.441106i	0.325125	+	0.0735177i
$37$	−1.26010	−	7.95598i	−0.207160	−	1.30796i	−0.843743	−	0.536747i	$-0.819653\pi$
$37$	−1.26010	−	7.95598i	−0.207160	−	1.30796i	0.636583	−	0.771208i	$-0.280347\pi$
$38$	−0.564019	+	2.05175i	−0.0914960	+	0.332838i
$39$	4.19525	−	3.04803i	0.671778	−	0.488075i
$40$	0.472619	+	6.30687i	0.0747277	+	0.997204i
$41$	8.23695	+	5.98450i	1.28640	+	0.934621i	0.999726	−	0.0234081i	$-0.00745171\pi$
$41$	8.23695	+	5.98450i	1.28640	+	0.934621i	0.286670	+	0.958029i	$0.407452\pi$
$42$	−4.89676	+	3.91313i	−0.755586	+	0.603808i
$43$	−7.85946	−	7.85946i	−1.19856	−	1.19856i	−0.974599	−	0.223957i	$-0.928103\pi$
$43$	−7.85946	−	7.85946i	−1.19856	−	1.19856i	−0.223957	−	0.974599i	$-0.571897\pi$
$44$	−0.0917123	+	0.154206i	−0.0138261	+	0.0232475i
$45$	0.823229	−	2.07901i	0.122720	−	0.309921i
$46$	2.21444	+	2.01999i	0.326501	+	0.297831i
$47$	−3.49688	−	6.86301i	−0.510072	−	1.00107i	−0.992163	−	0.124952i	$-0.960122\pi$
$47$	−3.49688	−	6.86301i	−0.510072	−	1.00107i	0.482091	−	0.876121i	$-0.339878\pi$
$48$	1.13493	−	3.83561i	0.163813	−	0.553623i
$49$		−	12.6454i		−	1.80649i
$50$	7.04854	+	0.564022i	0.996814	+	0.0797647i
$51$		−	3.00875i		−	0.421309i
$52$	−5.53554	−	8.77042i	−0.767641	−	1.21624i
$53$	1.47153	+	2.88805i	0.202131	+	0.396704i	0.969713	−	0.244246i	$-0.0785406\pi$
$53$	1.47153	+	2.88805i	0.202131	+	0.396704i	−0.767583	+	0.640950i	$0.778541\pi$
$54$	−0.953075	+	1.04482i	−0.129697	+	0.142182i
$55$	0.154557	+	0.127870i	0.0208404	+	0.0172420i
$56$	7.17049	+	10.2834i	0.958197	+	1.37417i
$57$	−1.06393	−	1.06393i	−0.140921	−	0.140921i
$58$	−5.61510	−	7.02655i	−0.737298	−	0.922632i
$59$	11.4383	+	8.31042i	1.48914	+	1.08192i	0.974465	+	0.224539i	$0.0720877\pi$
$59$	11.4383	+	8.31042i	1.48914	+	1.08192i	0.514676	+	0.857385i	$0.327912\pi$
$60$	−4.04172	−	1.91428i	−0.521784	−	0.247133i
$61$	−9.26103	+	6.72853i	−1.18575	+	0.861500i	−0.992809	−	0.119710i	$-0.961804\pi$
$61$	−9.26103	+	6.72853i	−1.18575	+	0.861500i	−0.192944	+	0.981210i	$0.561804\pi$
$62$	−5.67708	−	1.56061i	−0.720990	−	0.198198i
$63$	−0.693367	−	4.37774i	−0.0873560	−	0.551544i
$64$	−7.50676	−	2.76560i	−0.938345	−	0.345701i
$65$	−10.6419	+	4.60469i	−1.31996	+	0.571141i
$66$	−0.0627215	−	0.110279i	−0.00772048	−	0.0135744i
$67$	1.84223	+	0.938661i	0.225064	+	0.114676i	0.562887	−	0.826534i	$-0.309691\pi$
$67$	1.84223	+	0.938661i	0.225064	+	0.114676i	−0.337823	+	0.941210i	$0.609691\pi$
$68$	−6.00467	−	0.392675i	−0.728174	−	0.0476188i
$69$	−2.01571	+	0.654945i	−0.242663	+	0.0788461i
$70$	12.5948	−	6.15026i	1.50536	−	0.735096i
$71$	−2.37497	−	0.771676i	−0.281857	−	0.0915810i	0.164677	−	0.986348i	$-0.447342\pi$
$71$	−2.37497	−	0.771676i	−0.281857	−	0.0915810i	−0.446534	+	0.894767i	$0.647342\pi$
$72$	1.96080	+	2.03845i	0.231082	+	0.240233i
$73$	1.16183	−	7.33551i	0.135982	−	0.858556i	−0.821531	−	0.570164i	$-0.806880\pi$
$73$	1.16183	−	7.33551i	0.135982	−	0.858556i	0.957513	−	0.288392i	$-0.0931205\pi$
$74$	4.70067	−	10.3766i	0.546442	−	1.20626i
$75$	−2.81073	+	4.13519i	−0.324555	+	0.477491i
$76$	−2.26218	+	1.98447i	−0.259490	+	0.227634i
$77$	0.392723	+	0.0622012i	0.0447549	+	0.00708848i
$78$	7.32585	−	0.336411i	0.829489	−	0.0380911i
$79$	−0.395606	+	1.21755i	−0.0445091	+	0.136985i	−0.970842	−	0.239722i	$-0.922944\pi$
$79$	−0.395606	+	1.21755i	−0.0445091	+	0.136985i	0.926332	+	0.376707i	$0.122944\pi$
$80$	−4.34789	+	7.81638i	−0.486109	+	0.873898i
$81$	−0.309017	−	0.951057i	−0.0343352	−	0.105673i
$82$	5.07295	+	13.4755i	0.560213	+	1.48812i
$83$	1.03260	−	2.02659i	0.113343	−	0.222447i	−0.827366	−	0.561663i	$-0.810162\pi$
$83$	1.03260	−	2.02659i	0.113343	−	0.222447i	0.940709	+	0.339216i	$0.110162\pi$
$84$	−8.82732	+	0.812434i	−0.963140	+	0.0886438i
$85$	−1.46786	+	6.56569i	−0.159212	+	0.712149i
$86$	−3.16858	−	15.3962i	−0.341677	−	1.66022i
$87$	6.28180	−	0.994939i	0.673479	−	0.106669i
$88$	−0.228273	+	0.110783i	−0.0243340	+	0.0118095i
$89$	7.66814	+	10.5543i	0.812821	+	1.11875i	0.990882	+	0.134733i	$0.0430177\pi$
$89$	7.66814	+	10.5543i	0.812821	+	1.11875i	−0.178061	+	0.984020i	$0.556982\pi$
$90$	2.58953	−	1.81503i	0.272960	−	0.191321i
$91$	−13.5098	+	18.5947i	−1.41621	+	1.94925i
$92$	1.04403	+	4.10831i	0.108847	+	0.428321i
$93$	2.94384	−	2.94384i	0.305262	−	0.305262i
$94$	1.20871	−	10.8258i	0.124669	−	1.11659i
$95$	1.80265	+	2.84076i	0.184948	+	0.291456i
$96$	4.32411	−	3.64720i	0.441328	−	0.372241i
$97$	3.93972	−	2.00739i	0.400018	−	0.203819i	−0.242396	−	0.970177i	$-0.577933\pi$
$97$	3.93972	−	2.00739i	0.400018	−	0.203819i	0.642413	+	0.766358i	$0.277933\pi$
$98$	9.83679	−	14.9349i	0.993666	−	1.50865i
$99$	0.0897089			0.00901609
$100$	7.88593	+	6.14916i	0.788593	+	0.614916i
$101$	6.81825			0.678442			0.339221	−	0.940707i	$-0.389837\pi$
$101$	6.81825			0.678442			0.339221	+	0.940707i	$0.389837\pi$
$102$	2.34049	−	3.55349i	0.231743	−	0.351847i
$103$	−2.20599	+	1.12401i	−0.217363	+	0.110752i	−0.559282	−	0.828978i	$-0.688923\pi$
$103$	−2.20599	+	1.12401i	−0.217363	+	0.110752i	0.341919	+	0.939729i	$0.388923\pi$
$104$	0.284716	−	14.6644i	0.0279187	−	1.43796i
$105$	−0.622683	+	9.89137i	−0.0607677	+	0.965299i
$106$	−0.508641	+	4.55562i	−0.0494036	+	0.442481i
$107$	2.71179	−	2.71179i	0.262159	−	0.262159i	−0.563772	−	0.825931i	$-0.690650\pi$
$107$	2.71179	−	2.71179i	0.262159	−	0.262159i	0.825931	+	0.563772i	$0.190650\pi$
$108$	−1.93839	+	0.492593i	−0.186522	+	0.0473998i
$109$	4.04353	−	5.56544i	0.387300	−	0.533072i	−0.570200	−	0.821506i	$-0.693134\pi$
$109$	4.04353	−	5.56544i	0.387300	−	0.533072i	0.957500	+	0.288433i	$0.0931344\pi$
$110$	0.0830696	+	0.271250i	0.00792038	+	0.0258626i
$111$	4.73470	+	6.51676i	0.449398	+	0.618543i
$112$	0.469342	+	17.7230i	0.0443487	+	1.67467i
$113$	−11.4626	+	1.81550i	−1.07831	+	0.170788i	−0.670228	−	0.742155i	$-0.733804\pi$
$113$	−11.4626	+	1.81550i	−1.07831	+	0.170788i	−0.408086	+	0.912943i	$0.633804\pi$
$114$	−0.428929	−	2.08418i	−0.0401729	−	0.195201i
$115$	4.71821	−	0.445824i	0.439975	−	0.0415733i
$116$	−1.16579	−	12.6667i	−0.108241	−	1.17607i
$117$	−2.35422	+	4.62042i	−0.217648	+	0.427158i
$118$	7.04459	+	18.7128i	0.648507	+	1.72265i
$119$	4.12097	+	12.6830i	0.377768	+	1.16265i
$120$	−3.28437	−	5.40490i	−0.299820	−	0.493398i
$121$	3.39670	−	10.4540i	0.308791	−	0.950361i
$122$	−16.1718	+	0.742628i	−1.46413	+	0.0672344i
$123$	−10.0561	−	1.59273i	−0.906726	−	0.143611i
$124$	−5.49093	−	6.25933i	−0.493100	−	0.562105i
$125$	8.15097	−	7.65256i	0.729045	−	0.684465i
$126$	2.58652	−	5.70970i	0.230426	−	0.508661i
$127$	0.434901	−	2.74586i	0.0385912	−	0.243655i	−0.960850	−	0.277068i	$-0.910637\pi$
$127$	0.434901	−	2.74586i	0.0385912	−	0.243655i	0.999442	+	0.0334122i	$0.0106374\pi$
$128$	−6.71451	−	9.10579i	−0.593485	−	0.804845i
$129$	10.5709	+	3.43471i	0.930720	+	0.302409i
$130$	−16.1506	−	2.83991i	−1.41650	−	0.249076i
$131$	−11.7429	+	3.81550i	−1.02598	+	0.333361i	−0.773200	−	0.634162i	$-0.781345\pi$
$131$	−11.7429	+	3.81550i	−1.02598	+	0.333361i	−0.252781	+	0.967524i	$0.581345\pi$
$132$	0.0117080	−	0.179035i	0.00101905	−	0.0155830i
$133$	5.94209	+	3.02765i	0.515245	+	0.262530i
$134$	1.44558	+	2.54166i	0.124879	+	0.219566i
$135$	0.210349	+	2.22615i	0.0181040	+	0.191597i
$136$	−6.78636	−	5.13477i	−0.581926	−	0.440303i
$137$	0.711394	+	4.49156i	0.0607785	+	0.383740i	0.999262	+	0.0384157i	$0.0122311\pi$
$137$	0.711394	+	4.49156i	0.0607785	+	0.383740i	−0.938483	+	0.345324i	$0.887769\pi$
$138$	−2.89014	−	0.794490i	−0.246025	−	0.0676315i
$139$	−13.0231	+	9.46183i	−1.10460	+	0.802542i	−0.981805	−	0.189889i	$-0.939187\pi$
$139$	−13.0231	+	9.46183i	−1.10460	+	0.802542i	−0.122799	+	0.992432i	$0.539187\pi$
$140$	19.6593	+	2.53365i	1.66152	+	0.214132i
$141$	6.23148	+	4.52744i	0.524786	+	0.381279i
$142$	−2.20468	−	2.75887i	−0.185013	−	0.231519i
$143$	−0.328943	−	0.328943i	−0.0275076	−	0.0275076i
$144$	0.730106	+	3.93280i	0.0608422	+	0.327734i
$145$	−14.1935	−	0.893513i	−1.17871	−	0.0742022i
$146$	7.07843	−	7.75982i	0.585815	−	0.642207i
$147$	5.74089	+	11.2671i	0.473501	+	0.929298i
$148$	13.6237	−	8.59871i	1.11986	−	0.706810i
$149$		−	2.90133i		−	0.237686i	−0.992913	−	0.118843i	$-0.962081\pi$
$149$		−	2.90133i		−	0.237686i	0.992913	−	0.118843i	$-0.0379185\pi$
$150$	−6.53635	+	2.69742i	−0.533691	+	0.220244i
$151$		−	4.02046i		−	0.327180i	−0.986528	−	0.163590i	$-0.947693\pi$
$151$		−	4.02046i		−	0.327180i	0.986528	−	0.163590i	$-0.0523075\pi$
$152$	−4.21546	+	0.584022i	−0.341919	+	0.0473704i
$153$	1.36594	+	2.68082i	0.110430	+	0.216731i
$154$	0.415439	+	0.378960i	0.0334771	+	0.0305374i
$155$	−7.86024	+	4.98784i	−0.631349	+	0.400633i
$156$	8.91389	+	5.30142i	0.713682	+	0.424453i
$157$	−2.31475	−	2.31475i	−0.184737	−	0.184737i	0.608679	−	0.793416i	$-0.291700\pi$
$157$	−2.31475	−	2.31475i	−0.184737	−	0.184737i	−0.793416	+	0.608679i	$0.791700\pi$
$158$	−1.41436	+	1.13025i	−0.112520	+	0.0899176i
$159$	−2.62229	−	1.90521i	−0.207961	−	0.151093i
$160$	−11.2154	+	5.84933i	−0.886656	+	0.462430i
$161$	7.59995	−	5.52169i	0.598960	−	0.435170i
$162$	0.374857	−	1.36363i	0.0294516	−	0.107137i
$163$	1.04062	+	6.57021i	0.0815075	+	0.514618i	0.994337	+	0.106276i	$0.0338929\pi$
$163$	1.04062	+	6.57021i	0.0815075	+	0.514618i	−0.912829	+	0.408342i	$0.866107\pi$
$164$	−4.49109	+	19.8614i	−0.350696	+	1.55092i
$165$	−0.195763	−	0.0437658i	−0.0152401	−	0.00340716i
$166$	2.79603	−	1.59025i	0.217014	−	0.123428i
$167$	2.62863	+	1.33936i	0.203410	+	0.103642i	0.552728	−	0.833362i	$-0.313587\pi$
$167$	2.62863	+	1.33936i	0.203410	+	0.103642i	−0.349318	+	0.937004i	$0.613587\pi$
$168$	−11.0575	−	5.90720i	−0.853104	−	0.455750i
$169$	13.2108	−	4.29244i	1.01621	−	0.330187i
$170$	−6.84103	+	6.61257i	−0.524683	+	0.507161i
$171$	1.43098	+	0.464955i	0.109430	+	0.0355560i
$172$	8.23440	−	20.6486i	0.627867	−	1.57444i
$173$	−1.01770	+	6.42548i	−0.0773739	+	0.488520i	0.918322	+	0.395835i	$0.129545\pi$
$173$	−1.01770	+	6.42548i	−0.0773739	+	0.488520i	−0.995696	+	0.0926847i	$0.970455\pi$
$174$	8.19308	+	3.71150i	0.621115	+	0.281368i
$175$	6.18447	−	21.2812i	0.467502	−	1.60870i
$176$	−0.355780	−	0.0467322i	−0.0268179	−	0.00352257i
$177$	−13.9645	−	2.21175i	−1.04963	−	0.166246i
$178$	0.846333	+	18.4302i	0.0634354	+	1.38140i
$179$	−2.84051	+	8.74220i	−0.212310	+	0.653423i	0.787024	+	0.616923i	$0.211621\pi$
$179$	−2.84051	+	8.74220i	−0.212310	+	0.653423i	−0.999334	+	0.0364999i	$0.988379\pi$
$180$	4.47027	−	0.129265i	0.333194	−	0.00963484i
$181$	1.42108	+	4.37363i	0.105628	+	0.325090i	0.989877	−	0.141925i	$-0.0453293\pi$
$181$	1.42108	+	4.37363i	0.105628	+	0.325090i	−0.884249	+	0.467015i	$0.845329\pi$
$182$	−30.4205	+	11.4520i	−2.25492	+	0.848881i
$183$	5.19695	−	10.1996i	0.384169	−	0.753975i
$184$	−1.96279	+	5.66427i	−0.144699	+	0.417575i
$185$	−7.15276	−	16.5307i	−0.525881	−	1.21536i
$186$	5.76682	−	1.18683i	0.422844	−	0.0870222i
$187$	−0.266589	+	0.0422235i	−0.0194949	+	0.00308769i
$188$	9.84885	−	11.8455i	0.718302	−	0.863924i
$189$	2.60525	+	3.58582i	0.189504	+	0.260830i
$190$	−0.0807892	+	4.75735i	−0.00586107	+	0.345135i
$191$	−2.40696	+	3.31289i	−0.174161	+	0.239712i	−0.887170	−	0.461443i	$-0.847332\pi$
$191$	−2.40696	+	3.31289i	−0.174161	+	0.239712i	0.713009	+	0.701155i	$0.247332\pi$
$192$	7.94413	−	0.943825i	0.573318	−	0.0681147i
$193$	−11.4434	+	11.4434i	−0.823717	+	0.823717i	−0.986639	−	0.162922i	$-0.947908\pi$
$193$	−11.4434	+	11.4434i	−0.823717	+	0.823717i	0.162922	+	0.986639i	$0.447908\pi$
$194$	6.21454	+	0.693861i	0.446178	+	0.0498164i
$195$	7.39151	−	8.93413i	0.529317	−	0.639786i
$196$	23.2355	−	9.98683i	1.65968	−	0.713345i
$197$	7.67379	−	3.90999i	0.546735	−	0.278575i	−0.158728	−	0.987322i	$-0.550739\pi$
$197$	7.67379	−	3.90999i	0.546735	−	0.278575i	0.705463	+	0.708747i	$0.250739\pi$
$198$	0.105951	+	0.0697841i	0.00752959	+	0.00495934i
$199$	21.3364			1.51250			0.756249	−	0.654284i	$-0.227030\pi$
$199$	21.3364			1.51250			0.756249	+	0.654284i	$0.227030\pi$
$200$	4.53028	+	13.3969i	0.320339	+	0.947303i
$201$	−2.06758			−0.145836
$202$	8.05270	+	5.30388i	0.566586	+	0.373180i
$203$	−25.1174	+	12.7980i	−1.76290	+	0.898242i
$204$	5.52848	−	2.37619i	0.387071	−	0.166367i
$205$	21.1673	+	8.38165i	1.47839	+	0.585400i
$206$	−3.47975	−	0.388518i	−0.242445	−	0.0270693i
$207$	1.49868	−	1.49868i	0.104165	−	0.104165i
$208$	11.7436	−	17.0979i	0.814272	−	1.18553i
$209$	−0.0793382	+	0.109200i	−0.00548794	+	0.00755350i
$210$	−8.42987	+	11.1978i	−0.581716	+	0.772724i
$211$	15.1542	+	20.8580i	1.04326	+	1.43592i	0.894511	+	0.447047i	$0.147524\pi$
$211$	15.1542	+	20.8580i	1.04326	+	1.43592i	0.148748	+	0.988875i	$0.452476\pi$
$212$	−4.14453	+	4.98475i	−0.284647	+	0.342354i
$213$	2.46645	−	0.390647i	0.168998	−	0.0267667i
$214$	5.31225	−	1.09327i	0.363138	−	0.0747347i
$215$	−21.3922	−	12.6524i	−1.45894	−	0.862887i
$216$	−2.67252	−	0.926085i	−0.181842	−	0.0630121i
$217$	−8.37734	+	16.4415i	−0.568691	+	1.11612i
$218$	9.10493	−	3.42762i	0.616664	−	0.232148i
$219$	2.29505	+	7.06344i	0.155085	+	0.477303i
$220$	−0.112894	+	0.384979i	−0.00761133	+	0.0259553i
$221$	4.82135	−	14.8386i	0.324319	−	0.998152i
$222$	0.522569	+	11.3797i	0.0350725	+	0.763756i
$223$	24.4327	+	3.86975i	1.63613	+	0.259138i	0.905722	−	0.423872i	$-0.139329\pi$
$223$	24.4327	+	3.86975i	1.63613	+	0.259138i	0.730410	+	0.683009i	$0.239329\pi$
$224$	−13.2323	+	21.2969i	−0.884123	+	1.42296i
$225$	0.627037	−	4.96053i	0.0418024	−	0.330702i
$226$	−14.9502	−	6.77253i	−0.994474	−	0.450502i
$227$	−2.96964	+	18.7496i	−0.197102	+	1.24445i	0.668496	+	0.743715i	$0.266938\pi$
$227$	−2.96964	+	18.7496i	−0.197102	+	1.24445i	−0.865598	+	0.500739i	$0.833062\pi$
$228$	1.11469	−	2.79518i	0.0738219	−	0.185116i
$229$	3.82659	+	1.24333i	0.252868	+	0.0821618i	0.432708	−	0.901534i	$-0.357558\pi$
$229$	3.82659	+	1.24333i	0.252868	+	0.0821618i	−0.179840	+	0.983696i	$0.557558\pi$
$230$	5.91925	+	3.14373i	0.390304	+	0.207291i
$231$	−0.378157	+	0.122871i	−0.0248809	+	0.00808430i
$232$	8.47647	−	15.8668i	0.556508	−	1.04171i
$233$	4.12528	+	2.10194i	0.270256	+	0.137702i	0.583867	−	0.811849i	$-0.301539\pi$
$233$	4.12528	+	2.10194i	0.270256	+	0.137702i	−0.313611	+	0.949552i	$0.601539\pi$
$234$	−6.37465	+	3.62561i	−0.416724	+	0.237014i
$235$	−11.3896	−	12.9199i	−0.742973	−	0.842801i
$236$	−6.23659	+	27.5807i	−0.405968	+	1.79535i
$237$	−0.200268	−	1.26445i	−0.0130088	−	0.0821346i
$238$	−4.99899	+	18.1850i	−0.324037	+	1.17876i
$239$	16.3162	−	11.8544i	1.05541	−	0.766798i	0.0821734	−	0.996618i	$-0.473814\pi$
$239$	16.3162	−	11.8544i	1.05541	−	0.766798i	0.973233	+	0.229820i	$0.0738139\pi$
$240$	0.325440	−	8.93835i	0.0210071	−	0.576968i
$241$	5.43945	+	3.95199i	0.350386	+	0.254570i	0.749031	−	0.662535i	$-0.230519\pi$
$241$	5.43945	+	3.95199i	0.350386	+	0.254570i	−0.398645	+	0.917105i	$0.630519\pi$
$242$	12.1438	−	9.70439i	0.780630	−	0.623822i
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$	−19.6774	−	11.7029i	−1.25972	−	0.749201i
$245$	−7.03093	−	27.3879i	−0.449190	−	1.74975i
$246$	−10.6378	−	9.70366i	−0.678239	−	0.618683i
$247$	−3.54222	−	6.95199i	−0.225386	−	0.442345i
$248$	−1.61596	−	11.6639i	−0.102613	−	0.740662i
$249$			2.27450i			0.144140i
$250$	15.5796	−	2.69745i	0.985340	−	0.170602i
$251$		−	27.0687i		−	1.70856i	−0.519811	−	0.854282i	$-0.673997\pi$
$251$		−	27.0687i		−	1.70856i	0.519811	−	0.854282i	$-0.326003\pi$
$252$	7.49636	−	4.73140i	0.472226	−	0.298050i
$253$	0.0863187	+	0.169410i	0.00542681	+	0.0106507i
$254$	2.64963	−	2.90469i	0.166252	−	0.182256i
$255$	−1.67288	−	6.51647i	−0.104760	−	0.408077i
$256$	−0.846832	−	15.9776i	−0.0529270	−	0.998598i
$257$	0.364893	+	0.364893i	0.0227614	+	0.0227614i	0.718396	−	0.695635i	$-0.244877\pi$
$257$	0.364893	+	0.364893i	0.0227614	+	0.0227614i	−0.695635	+	0.718396i	$0.744877\pi$
$258$	9.81298	+	12.2796i	0.610929	+	0.764497i
$259$	−28.8843	−	20.9857i	−1.79478	−	1.30399i
$260$	−16.8655	−	15.9175i	−1.04595	−	0.987163i
$261$	−5.14543	+	3.73837i	−0.318494	+	0.231399i
$262$	−16.8370	−	4.62844i	−1.04019	−	0.285946i
$263$	−2.36297	−	14.9192i	−0.145707	−	0.919957i	−0.946895	−	0.321544i	$-0.895798\pi$
$263$	−2.36297	−	14.9192i	−0.145707	−	0.919957i	0.801188	−	0.598413i	$-0.204202\pi$
$264$	0.153098	−	0.202342i	0.00942256	−	0.0124533i
$265$	4.79287	+	5.43686i	0.294424	+	0.333984i
$266$	4.66272	+	8.19813i	0.285890	+	0.502659i
$267$	−11.6239	−	5.92268i	−0.711372	−	0.362462i
$268$	−0.269842	+	4.12634i	−0.0164832	+	0.252057i
$269$	−18.9244	+	6.14891i	−1.15384	+	0.374906i	−0.822589	−	0.568636i	$-0.807471\pi$
$269$	−18.9244	+	6.14891i	−1.15384	+	0.374906i	−0.331252	+	0.943542i	$0.607471\pi$
$270$	−1.48328	+	2.79283i	−0.0902695	+	0.169966i
$271$	−5.42995	−	1.76430i	−0.329846	−	0.107173i	0.139412	−	0.990234i	$-0.455479\pi$
$271$	−5.42995	−	1.76430i	−0.329846	−	0.107173i	−0.469258	+	0.883061i	$0.655479\pi$
$272$	−4.02072	−	11.3435i	−0.243792	−	0.687801i
$273$	3.59553	−	22.7013i	0.217612	−	1.37395i
$274$	−2.65377	+	5.85815i	−0.160320	+	0.353904i
$275$	0.405841	+	0.191011i	0.0244731	+	0.0115184i
$276$	−2.79537	−	3.18656i	−0.168261	−	0.191808i
$277$	11.6279	+	1.84168i	0.698653	+	0.110656i	0.495650	−	0.868522i	$-0.334930\pi$
$277$	11.6279	+	1.84168i	0.698653	+	0.110656i	0.203003	+	0.979178i	$0.434930\pi$
$278$	−22.7412	+	1.04430i	−1.36393	+	0.0626331i
$279$	−1.28650	+	3.95945i	−0.0770210	+	0.237046i
$280$	21.2477	+	18.2852i	1.26979	+	1.09275i
$281$	−2.40044	−	7.38779i	−0.143198	−	0.440719i	0.853577	−	0.520967i	$-0.174429\pi$
$281$	−2.40044	−	7.38779i	−0.143198	−	0.440719i	−0.996775	+	0.0802486i	$0.974429\pi$
$282$	3.83783	+	10.1946i	0.228539	+	0.607078i
$283$	−8.36586	+	16.4189i	−0.497299	+	0.976004i	0.496835	+	0.867845i	$0.334496\pi$
$283$	−8.36586	+	16.4189i	−0.497299	+	0.976004i	−0.994134	+	0.108159i	$0.965504\pi$
$284$	−0.457731	−	4.97337i	−0.0271613	−	0.295115i
$285$	−2.89585	−	1.71275i	−0.171536	−	0.101454i
$286$	−0.132615	−	0.644382i	−0.00784171	−	0.0381031i
$287$	44.5717	−	7.05947i	2.63099	−	0.416707i
$288$	−2.19702	+	5.21278i	−0.129460	+	0.307166i
$289$	4.67138	+	6.42960i	0.274787	+	0.378212i
$290$	−16.0682	−	12.0963i	−0.943557	−	0.710322i
$291$	−2.59898	+	3.57719i	−0.152355	+	0.209699i
$292$	14.3963	−	3.65846i	0.842480	−	0.214095i
$293$	−16.5382	+	16.5382i	−0.966169	+	0.966169i	−0.999446	−	0.0332770i	$-0.989406\pi$
$293$	−16.5382	+	16.5382i	−0.966169	+	0.966169i	0.0332770	+	0.999446i	$0.489406\pi$
$294$	−1.98436	+	17.7729i	−0.115730	+	1.03653i
$295$	29.3942	+	11.6392i	1.71139	+	0.677663i
$296$	22.7791	+	0.442267i	1.32401	+	0.0257062i
$297$	−0.0799312	+	0.0407270i	−0.00463808	+	0.00236322i
$298$	2.25693	−	3.42662i	0.130740	−	0.198499i
$299$	−10.9906			−0.635605
$300$	−9.81807	−	1.89880i	−0.566847	−	0.109627i
$301$	−49.2649			−2.83958
$302$	3.12749	−	4.74837i	0.179967	−	0.273238i
$303$	−6.07511	+	3.09542i	−0.349006	+	0.177827i
$304$	−5.43297	−	2.58942i	−0.311602	−	0.148514i
$305$	−16.3168	+	19.7221i	−0.934296	+	1.12928i
$306$	−0.472144	+	4.22874i	−0.0269907	+	0.241741i
$307$	22.4411	−	22.4411i	1.28078	−	1.28078i	0.340557	−	0.940224i	$-0.389384\pi$
$307$	22.4411	−	22.4411i	1.28078	−	1.28078i	0.940224	−	0.340557i	$-0.110616\pi$
$308$	0.195864	+	0.770739i	0.0111604	+	0.0439169i
$309$	1.45526	−	2.00300i	0.0827870	−	0.113947i
$310$	−13.1634	−	0.223540i	−0.747628	−	0.0126962i
$311$	−8.54043	−	11.7549i	−0.484284	−	0.666559i	0.495037	−	0.868872i	$-0.335154\pi$
$311$	−8.54043	−	11.7549i	−0.484284	−	0.666559i	−0.979321	+	0.202312i	$0.935154\pi$
$312$	6.40380	+	13.1953i	0.362544	+	0.747037i
$313$	−2.22635	+	0.352619i	−0.125841	+	0.0199312i	−0.219037	−	0.975717i	$-0.570292\pi$
$313$	−2.22635	+	0.352619i	−0.125841	+	0.0199312i	0.0931963	+	0.995648i	$0.470292\pi$
$314$	−0.933204	−	4.53446i	−0.0526637	−	0.255895i
$315$	−3.93577	−	9.09597i	−0.221756	−	0.512500i
$316$	−2.54964	+	0.234659i	−0.143428	+	0.0132006i
$317$	3.60520	−	7.07561i	0.202488	−	0.397406i	−0.767323	−	0.641260i	$-0.778412\pi$
$317$	3.60520	−	7.07561i	0.202488	−	0.397406i	0.969812	+	0.243854i	$0.0784119\pi$
$318$	−1.61501	−	4.29001i	−0.0905651	−	0.240572i
$319$	−0.176312	−	0.542633i	−0.00987158	−	0.0303816i
$320$	−17.7961	−	1.81605i	−0.994833	−	0.101520i
$321$	−1.18510	+	3.64735i	−0.0661456	+	0.203575i
$322$	13.2712	−	0.609429i	0.739576	−	0.0339621i
$323$	−4.47130	−	0.708185i	−0.248790	−	0.0394045i
$324$	1.50348	−	1.31891i	0.0835269	−	0.0732730i
$325$	−20.4884	+	15.8900i	−1.13649	+	0.881417i
$326$	−3.88191	+	8.56924i	−0.214999	+	0.474606i
$327$	−1.07615	+	6.79456i	−0.0595114	+	0.375740i
$328$	−20.7543	+	19.9638i	−1.14597	+	1.10231i
$329$	−32.4691	−	10.5499i	−1.79008	−	0.581633i
$330$	−0.197160	−	0.203972i	−0.0108533	−	0.0112283i
$331$	29.8062	−	9.68463i	1.63830	−	0.532316i	0.662141	−	0.749379i	$-0.269648\pi$
$331$	29.8062	−	9.68463i	1.63830	−	0.532316i	0.976157	+	0.217064i	$0.0696479\pi$
$332$	4.53930	+	0.296847i	0.249126	+	0.0162916i
$333$	−7.17719	−	3.65696i	−0.393308	−	0.200400i
$334$	2.06267	+	3.62665i	0.112864	+	0.198441i
$335$	4.51187	+	1.00870i	0.246510	+	0.0551111i
$336$	−8.46428	−	15.5783i	−0.461764	−	0.849864i
$337$	−5.00654	−	31.6100i	−0.272723	−	1.72191i	−0.620393	−	0.784291i	$-0.713027\pi$
$337$	−5.00654	−	31.6100i	−0.272723	−	1.72191i	0.347669	−	0.937617i	$-0.386973\pi$
$338$	18.9416	+	5.20700i	1.03029	+	0.283223i
$339$	9.38907	−	6.82156i	0.509944	−	0.370496i
$340$	−13.2235	+	2.48817i	−0.717144	+	0.134940i
$341$	−0.302150	−	0.219525i	−0.0163623	−	0.0118879i
$342$	1.32838	+	1.66229i	0.0718304	+	0.0898863i
$343$	−17.6934	−	17.6934i	−0.955352	−	0.955352i
$344$	25.7876	−	17.9815i	1.39038	−	0.969497i
$345$	−4.00156	+	2.53926i	−0.215437	+	0.136709i
$346$	−6.20029	+	6.79715i	−0.333330	+	0.365417i
$347$	4.47490	+	8.78249i	0.240225	+	0.471469i	0.979369	−	0.202079i	$-0.0647697\pi$
$347$	4.47490	+	8.78249i	0.240225	+	0.471469i	−0.739144	+	0.673548i	$0.764770\pi$
$348$	6.78928	+	10.7568i	0.363943	+	0.576626i
$349$			19.1891i			1.02717i	0.858039	+	0.513585i	$0.171683\pi$
$349$			19.1891i			1.02717i	−0.858039	+	0.513585i	$0.828317\pi$
$350$	23.8587	−	20.3232i	1.27530	−	1.08632i
$351$		−	5.18562i		−	0.276788i
$352$	−0.383841	−	0.331952i	−0.0204588	−	0.0176931i
$353$	16.1097	+	31.6170i	0.857432	+	1.68281i	0.721862	+	0.692037i	$0.243287\pi$
$353$	16.1097	+	31.6170i	0.857432	+	1.68281i	0.135570	+	0.990768i	$0.456713\pi$
$354$	−14.7722	−	13.4751i	−0.785134	−	0.716192i
$355$	−5.57287	−	0.350824i	−0.295777	−	0.0186198i
$356$	−13.3372	+	22.4253i	−0.706868	+	1.18854i
$357$	−9.42978	−	9.42978i	−0.499077	−	0.499077i
$358$	−10.1553	+	8.11536i	−0.536724	+	0.428910i
$359$	0.644378	+	0.468168i	0.0340090	+	0.0247090i	0.604660	−	0.796484i	$-0.293309\pi$
$359$	0.644378	+	0.468168i	0.0340090	+	0.0247090i	−0.570651	+	0.821193i	$0.693309\pi$
$360$	5.38017	+	3.32473i	0.283560	+	0.175229i
$361$	13.5398	−	9.83724i	0.712621	−	0.517749i
$362$	−1.72386	+	6.27093i	−0.0906041	+	0.329593i
$363$	1.71952	+	10.8566i	0.0902514	+	0.569825i
$364$	−44.8366	−	10.1385i	−2.35008	−	0.531402i
$365$	−1.56225	−	16.5335i	−0.0817721	−	0.865403i
$366$	14.0721	−	8.00354i	0.735558	−	0.418352i
$367$	−24.8460	−	12.6597i	−1.29695	−	0.660830i	−0.337135	−	0.941456i	$-0.609458\pi$
$367$	−24.8460	−	12.6597i	−1.29695	−	0.660830i	−0.959817	+	0.280626i	$0.909458\pi$
$368$	−6.72435	+	5.16294i	−0.350531	+	0.269137i
$369$	9.68312	−	3.14624i	0.504083	−	0.163787i
$370$	4.41141	−	25.0877i	0.229338	−	1.30425i
$371$	13.6634	+	4.43952i	0.709370	+	0.230488i
$372$	7.73413	+	3.08428i	0.400996	+	0.159912i
$373$	0.864521	−	5.45837i	0.0447632	−	0.282624i	−0.955146	−	0.296137i	$-0.904302\pi$
$373$	0.864521	−	5.45837i	0.0447632	−	0.282624i	0.999909	+	0.0135133i	$0.00430155\pi$
$374$	−0.347700	−	0.157510i	−0.0179791	−	0.00814464i
$375$	−3.78838	+	10.5189i	−0.195631	+	0.543196i
$376$	20.8466	−	6.32879i	1.07508	−	0.326382i
$377$	32.5750	+	5.15937i	1.67770	+	0.265721i
$378$	0.287541	+	6.26164i	0.0147895	+	0.322064i
$379$	5.76200	−	17.7336i	0.295974	−	0.910915i	−0.686918	−	0.726735i	$-0.741037\pi$
$379$	5.76200	−	17.7336i	0.295974	−	0.910915i	0.982893	−	0.184180i	$-0.0589630\pi$
$380$	−3.79614	+	5.55583i	−0.194738	+	0.285008i
$381$	0.859093	+	2.64402i	0.0440127	+	0.135457i
$382$	−5.41982	+	2.04033i	−0.277302	+	0.104392i
$383$	8.53445	−	16.7498i	0.436090	−	0.855875i	−0.563468	−	0.826138i	$-0.690533\pi$
$383$	8.53445	−	16.7498i	0.436090	−	0.855875i	0.999558	−	0.0297370i	$-0.00946699\pi$
$384$	10.1166	+	5.06499i	0.516261	+	0.258472i
$385$	0.885158	−	0.0836387i	0.0451118	−	0.00426262i
$386$	−22.4171	+	4.61349i	−1.14100	+	0.234820i
$387$	−10.9781	+	1.73876i	−0.558048	+	0.0883862i
$388$	6.79994	+	5.65374i	0.345214	+	0.287025i
$389$	−3.79524	−	5.22370i	−0.192426	−	0.264852i	0.701892	−	0.712283i	$-0.252339\pi$
$389$	−3.79524	−	5.22370i	−0.192426	−	0.264852i	−0.894318	+	0.447431i	$0.852339\pi$
$390$	15.6796	−	4.80183i	0.793965	−	0.243150i
$391$	−3.74824	+	5.15901i	−0.189557	+	0.260902i
$392$	35.2110	+	6.27982i	1.77842	+	0.317179i
$393$	8.73079	−	8.73079i	0.440410	−	0.440410i
$394$	12.1047	+	1.35150i	0.609825	+	0.0680878i
$395$	−0.179853	+	2.85697i	−0.00904937	+	0.143750i
$396$	0.0708485	+	0.164837i	0.00356027	+	0.00828337i
$397$	8.49393	−	4.32787i	0.426298	−	0.217210i	−0.227660	−	0.973741i	$-0.573107\pi$
$397$	8.49393	−	4.32787i	0.426298	−	0.217210i	0.653958	+	0.756531i	$0.273107\pi$
$398$	25.1994	+	16.5975i	1.26313	+	0.831956i
$399$	−6.66897			−0.333866
$400$	−5.07088	+	19.3465i	−0.253544	+	0.967324i
$401$	−14.2450			−0.711363			−0.355682	−	0.934607i	$-0.615751\pi$
$401$	−14.2450			−0.711363			−0.355682	+	0.934607i	$0.615751\pi$
$402$	−2.44191	−	1.60836i	−0.121792	−	0.0802176i
$403$	19.2358	−	9.80113i	0.958204	−	0.488229i
$404$	5.38478	+	12.5283i	0.267903	+	0.623307i
$405$	−1.19807	−	1.88802i	−0.0595328	−	0.0938164i
$406$	−39.6204	−	4.42367i	−1.96633	−	0.219543i
$407$	0.510969	−	0.510969i	0.0253278	−	0.0253278i
$408$	8.37783	+	1.49417i	0.414765	+	0.0739726i
$409$	−8.16703	+	11.2410i	−0.403834	+	0.555829i	−0.961701	−	0.274101i	$-0.911620\pi$
$409$	−8.16703	+	11.2410i	−0.403834	+	0.555829i	0.557867	+	0.829930i	$0.311620\pi$
$410$	18.4796	+	26.3651i	0.912644	+	1.30208i
$411$	−2.67298	−	3.67905i	−0.131849	−	0.181474i
$412$	−3.80753	−	3.16573i	−0.187583	−	0.155965i
$413$	61.8949	−	9.80318i	3.04565	−	0.482383i
$414$	2.93582	−	0.604199i	0.144288	−	0.0296948i
$415$	1.10965	−	4.96341i	0.0544704	−	0.243644i
$416$	27.1701	−	11.0582i	1.33213	−	0.542172i
$417$	7.30808	−	14.3429i	0.357878	−	0.702376i
$418$	−0.178648	+	0.0672535i	−0.00873797	+	0.00328948i
$419$	−6.15217	−	18.9344i	−0.300553	−	0.925007i	−0.981299	−	0.192488i	$-0.938344\pi$
$419$	−6.15217	−	18.9344i	−0.300553	−	0.925007i	0.680746	−	0.732519i	$-0.261656\pi$
$420$	−18.6668	+	6.66765i	−0.910848	+	0.325348i
$421$	0.345619	−	1.06371i	0.0168444	−	0.0518419i	−0.942281	−	0.334823i	$-0.891323\pi$
$421$	0.345619	−	1.06371i	0.0168444	−	0.0518419i	0.959125	+	0.282981i	$0.0913234\pi$
$422$	1.67257	+	36.4227i	0.0814195	+	1.77303i
$423$	−7.60771	−	1.20494i	−0.369899	−	0.0585863i
$424$	−8.77251	+	2.66324i	−0.426031	+	0.129338i
$425$	0.471412	+	15.0364i	0.0228669	+	0.729371i
$426$	3.21688	+	1.45726i	0.155859	+	0.0706047i
$427$	−7.93715	+	50.1132i	−0.384105	+	2.42515i
$428$	7.12449	+	2.84116i	0.344375	+	0.137333i
$429$	0.442428	+	0.143753i	0.0213606	+	0.00694048i
$430$	−15.4231	−	31.5840i	−0.743766	−	1.52312i
$431$	8.32624	−	2.70536i	0.401061	−	0.130313i	−0.101539	−	0.994832i	$-0.532377\pi$
$431$	8.32624	−	2.70536i	0.401061	−	0.130313i	0.502600	+	0.864519i	$0.332377\pi$
$432$	−2.43598	−	3.17269i	−0.117201	−	0.152646i
$433$	14.4137	+	7.34415i	0.692678	+	0.352937i	0.764629	−	0.644471i	$-0.222922\pi$
$433$	14.4137	+	7.34415i	0.692678	+	0.352937i	−0.0719504	+	0.997408i	$0.522922\pi$
$434$	−22.6838	+	12.9015i	−1.08886	+	0.619292i
$435$	13.0522	−	5.64760i	0.625803	−	0.270782i
$436$	13.4197	+	3.03448i	0.642688	+	0.145325i
$437$	0.498865	+	3.14971i	0.0238640	+	0.150671i
$438$	−2.78404	+	10.1276i	−0.133027	+	0.483915i
$439$	−25.5000	+	18.5268i	−1.21705	+	0.884236i	−0.995852	−	0.0909931i	$-0.970996\pi$
$439$	−25.5000	+	18.5268i	−1.21705	+	0.884236i	−0.221195	+	0.975229i	$0.570996\pi$
$440$	−0.432807	+	0.366860i	−0.0206333	+	0.0174893i
$441$	−10.2303	−	7.43278i	−0.487159	−	0.353942i
$442$	17.2371	−	13.7746i	0.819887	−	0.655192i
$443$	22.7614	+	22.7614i	1.08143	+	1.08143i	0.996377	+	0.0850506i	$0.0271052\pi$
$443$	22.7614	+	22.7614i	1.08143	+	1.08143i	0.0850506	+	0.996377i	$0.472895\pi$
$444$	−8.23504	+	13.8465i	−0.390818	+	0.657127i
$445$	22.4762	+	18.5954i	1.06547	+	0.881504i
$446$	25.8459	+	23.5764i	1.22384	+	1.11638i
$447$	1.31718	+	2.58510i	0.0623003	+	0.122271i
$448$	−32.1948	+	14.8593i	−1.52106	+	0.702038i
$449$			3.21571i			0.151759i	0.997117	+	0.0758794i	$0.0241764\pi$
$449$			3.21571i			0.151759i	−0.997117	+	0.0758794i	$0.975824\pi$
$450$	4.59933	−	5.37086i	0.216814	−	0.253185i
$451$			0.913365i			0.0430087i
$452$	−12.3887	−	19.6284i	−0.582714	−	0.923242i
$453$	1.82525	+	3.58226i	0.0857578	+	0.168309i
$454$	−18.0925	+	19.8341i	−0.849124	+	0.930862i
$455$	−18.9213	+	47.7846i	−0.887046	+	2.24018i
$456$	3.49086	−	2.43414i	0.163474	−	0.113989i
$457$	−4.31437	−	4.31437i	−0.201818	−	0.201818i	0.598961	−	0.800778i	$-0.295581\pi$
$457$	−4.31437	−	4.31437i	−0.201818	−	0.201818i	−0.800778	+	0.598961i	$0.795581\pi$
$458$	3.55221	+	4.44512i	0.165984	+	0.207707i
$459$	−2.43413	−	1.76850i	−0.113615	−	0.0825465i
$460$	4.54544	+	8.31746i	0.211932	+	0.387803i
$461$	19.3859	−	14.0847i	0.902893	−	0.655990i	−0.0363144	−	0.999340i	$-0.511562\pi$
$461$	19.3859	−	14.0847i	0.902893	−	0.655990i	0.939207	+	0.343350i	$0.111562\pi$
$462$	−0.542203	−	0.149050i	−0.0252256	−	0.00693443i
$463$	6.36230	+	40.1700i	0.295681	+	1.86686i	0.470700	+	0.882293i	$0.344001\pi$
$463$	6.36230	+	40.1700i	0.295681	+	1.86686i	−0.175019	+	0.984565i	$0.555999\pi$
$464$	22.3539	−	12.1457i	1.03775	−	0.563851i
$465$	4.73909	−	8.01267i	0.219770	−	0.371579i
$466$	3.23708	+	5.69153i	0.149955	+	0.263655i
$467$	−22.9322	−	11.6845i	−1.06118	−	0.540696i	−0.165870	−	0.986148i	$-0.553043\pi$
$467$	−22.9322	−	11.6845i	−1.06118	−	0.540696i	−0.895306	+	0.445452i	$0.853043\pi$
$468$	−10.3491	−	0.676780i	−0.478389	−	0.0312842i
$469$	8.71563	−	2.83188i	0.402450	−	0.130764i
$470$	−3.40133	−	24.1189i	−0.156891	−	1.11252i
$471$	3.11333	+	1.01158i	0.143455	+	0.0466112i
$472$	−28.8206	+	27.7228i	−1.32658	+	1.27605i
$473$	0.155982	−	0.984834i	0.00717208	−	0.0452827i
$474$	0.747078	−	1.64916i	0.0343144	−	0.0757485i
$475$	5.48374	+	5.15034i	0.251611	+	0.236314i
$476$	−20.0501	+	17.5887i	−0.918993	+	0.806176i
$477$	3.20142	+	0.507056i	0.146583	+	0.0232165i
$478$	28.4917	−	1.30837i	1.30318	−	0.0598435i
$479$	−4.89353	+	15.0607i	−0.223591	+	0.688142i	0.774841	+	0.632157i	$0.217830\pi$
$479$	−4.89353	+	15.0607i	−0.223591	+	0.688142i	−0.998432	+	0.0559855i	$0.982170\pi$
$480$	7.33746	−	10.3035i	0.334908	−	0.470287i
$481$	12.9079	+	39.7265i	0.588551	+	1.81137i
$482$	3.35003	+	8.89882i	0.152590	+	0.405330i
$483$	−4.26481	+	8.37016i	−0.194056	+	0.380856i
$484$	21.8914	−	2.01480i	0.995063	−	0.0915819i
$485$	7.41667	−	6.53819i	0.336774	−	0.296884i
$486$	0.285074	+	1.38518i	0.0129312	+	0.0628332i
$487$	−18.8395	+	2.98389i	−0.853701	+	0.135213i	−0.567922	−	0.823083i	$-0.692252\pi$
$487$	−18.8395	+	2.98389i	−0.853701	+	0.135213i	−0.285779	+	0.958295i	$0.592252\pi$
$488$	−14.1364	−	29.1287i	−0.639925	−	1.31859i
$489$	−3.91001	−	5.38167i	−0.176817	−	0.243367i
$490$	13.0010	−	37.8158i	0.587327	−	1.70834i
$491$	−4.08602	+	5.62393i	−0.184400	+	0.253804i	−0.891202	−	0.453607i	$-0.850137\pi$
$491$	−4.08602	+	5.62393i	−0.184400	+	0.253804i	0.706802	+	0.707411i	$0.250137\pi$
$492$	−5.01531	−	19.7356i	−0.226107	−	0.889749i
$493$	13.5312	−	13.5312i	0.609413	−	0.609413i
$494$	1.22438	−	10.9661i	0.0550876	−	0.493389i
$495$	0.194295	−	0.0498788i	0.00873291	−	0.00224188i
$496$	7.16480	−	15.0328i	0.321709	−	0.674991i
$497$	−9.86197	+	5.02493i	−0.442370	+	0.225399i
$498$	−1.76932	+	2.68630i	−0.0792851	+	0.120376i
$499$	0.252832			0.0113183			0.00565916	−	0.999984i	$-0.498199\pi$
$499$	0.252832			0.0113183			0.00565916	+	0.999984i	$0.498199\pi$
$500$	20.4986	+	8.93346i	0.916726	+	0.399516i
$501$	−2.95018			−0.131804
$502$	21.0566	−	31.9695i	0.939803	−	1.42687i
$503$	15.9788	−	8.14160i	0.712459	−	0.363016i	−0.0598984	−	0.998204i	$-0.519078\pi$
$503$	15.9788	−	8.14160i	0.712459	−	0.363016i	0.772357	+	0.635189i	$0.219078\pi$
$504$	12.5341	+	0.243356i	0.558314	+	0.0108399i
$505$	14.7672	−	3.79099i	0.657133	−	0.168697i
$506$	−0.0298364	+	0.267229i	−0.00132639	+	0.0118798i
$507$	−9.82215	+	9.82215i	−0.436217	+	0.436217i
$508$	5.38888	−	1.36945i	0.239093	−	0.0607596i
$509$	−12.4593	+	17.1488i	−0.552249	+	0.760105i	−0.990315	−	0.138837i	$-0.955664\pi$
$509$	−12.4593	+	17.1488i	−0.552249	+	0.760105i	0.438066	+	0.898943i	$0.355664\pi$
$510$	3.09336	−	8.99760i	0.136976	−	0.398421i
$511$	−19.3490	−	26.6317i	−0.855951	−	1.17812i
$512$	11.4287	−	19.5291i	0.505083	−	0.863071i
$513$	−1.48610	+	0.235375i	−0.0656129	+	0.0103921i
$514$	0.147109	+	0.714805i	0.00648868	+	0.0315287i
$515$	−4.15286	+	3.66097i	−0.182997	+	0.161321i
$516$	2.03735	+	22.1363i	0.0896892	+	0.974498i
$517$	0.313701	−	0.615673i	0.0137966	−	0.0270773i
$518$	−17.7892	−	47.2541i	−0.781611	−	2.07623i
$519$	−2.01033	−	6.18716i	−0.0882438	−	0.271586i
$520$	−7.53684	−	31.9190i	−0.330512	−	1.39974i
$521$	3.05487	−	9.40193i	0.133836	−	0.411906i	−0.861571	−	0.507637i	$-0.830519\pi$
$521$	3.05487	−	9.40193i	0.133836	−	0.411906i	0.995407	+	0.0957313i	$0.0305190\pi$
$522$	−8.98507	+	0.412604i	−0.393266	+	0.0180592i
$523$	−19.0721	−	3.02072i	−0.833963	−	0.132087i	−0.275171	−	0.961395i	$-0.588735\pi$
$523$	−19.0721	−	3.02072i	−0.833963	−	0.132087i	−0.558791	+	0.829308i	$0.688735\pi$
$524$	−16.2849	−	18.5638i	−0.711409	−	0.810965i
$525$	4.15104	+	21.7693i	0.181166	+	0.950092i
$526$	8.81478	−	19.4585i	0.384343	−	0.848429i
$527$	1.95951	−	12.3719i	0.0853576	−	0.538927i
$528$	0.338218	−	0.119882i	0.0147190	−	0.00521719i
$529$	−17.6021	−	5.71927i	−0.765309	−	0.248664i
$530$	1.43132	+	10.1496i	0.0621727	+	0.440869i
$531$	13.4465	−	4.36904i	0.583530	−	0.189600i
$532$	−0.870373	+	13.3095i	−0.0377355	+	0.577040i
$533$	−47.0425	−	23.9693i	−2.03764	−	1.03823i
$534$	−9.12120	−	16.0372i	−0.394713	−	0.693996i
$535$	4.36553	−	7.38108i	0.188738	−	0.319112i
$536$	−3.52856	+	4.66351i	−0.152410	+	0.201433i
$537$	−1.43796	−	9.07892i	−0.0620525	−	0.391784i
$538$	−27.1339	−	7.45902i	−1.16982	−	0.321581i
$539$	0.917753	−	0.666787i	0.0395304	−	0.0287205i
$540$	−3.92435	+	2.14463i	−0.168877	+	0.0922904i
$541$	4.14253	+	3.00972i	0.178101	+	0.129398i	0.673264	−	0.739402i	$-0.264892\pi$
$541$	4.14253	+	3.00972i	0.178101	+	0.129398i	−0.495163	+	0.868800i	$0.664892\pi$
$542$	−5.04060	−	6.30765i	−0.216512	−	0.270937i
$543$	−3.25178	−	3.25178i	−0.139547	−	0.139547i
$544$	4.07537	−	16.5249i	0.174730	−	0.708501i
$545$	5.66321	−	14.3021i	0.242585	−	0.612633i
$546$	21.9057	−	24.0144i	0.937479	−	1.02772i
$547$	8.45520	+	16.5943i	0.361518	+	0.709520i	0.998095	−	0.0616937i	$-0.0196502\pi$
$547$	8.45520	+	16.5943i	0.361518	+	0.709520i	−0.636577	+	0.771213i	$0.719650\pi$
$548$	−7.69126	+	4.85442i	−0.328554	+	0.207370i
$549$			11.4473i			0.488557i
$550$	0.330732	+	0.541296i	0.0141025	+	0.0230809i
$551$		−	9.56956i		−	0.407677i
$552$	−0.822666	−	5.93799i	−0.0350150	−	0.252737i
$553$	2.57607	+	5.05582i	0.109546	+	0.214995i
$554$	12.3005	+	11.2204i	0.522598	+	0.476709i
$555$	13.8780	+	11.4817i	0.589086	+	0.487372i
$556$	−27.6709	−	16.4569i	−1.17351	−	0.697929i
$557$	21.1313	+	21.1313i	0.895360	+	0.895360i	0.995021	−	0.0996610i	$-0.0317758\pi$
$557$	21.1313	+	21.1313i	0.895360	+	0.895360i	−0.0996610	+	0.995021i	$0.531776\pi$
$558$	−4.59947	+	3.67555i	−0.194711	+	0.155598i
$559$	46.6300	+	33.8787i	1.97224	+	1.43292i
$560$	10.8706	+	38.1243i	0.459369	+	1.61105i
$561$	0.218363	−	0.158650i	0.00921930	−	0.00669821i
$562$	2.91188	−	10.5926i	0.122830	−	0.446823i
$563$	−0.604217	−	3.81487i	−0.0254647	−	0.160778i	0.971679	−	0.236304i	$-0.0759362\pi$
$563$	−0.604217	−	3.81487i	−0.0254647	−	0.160778i	−0.997144	+	0.0755266i	$0.975936\pi$
$564$	−3.39764	+	15.0257i	−0.143066	+	0.632697i
$565$	−23.8168	+	10.3054i	−1.00198	+	0.433551i
$566$	−22.6527	+	12.8838i	−0.952164	+	0.541547i
$567$	−3.94922	−	2.01223i	−0.165852	−	0.0845056i
$568$	3.32816	−	6.22987i	0.139646	−	0.261399i
$569$	2.43157	−	0.790065i	0.101937	−	0.0331213i	−0.257605	−	0.966250i	$-0.582933\pi$
$569$	2.43157	−	0.790065i	0.101937	−	0.0331213i	0.359541	+	0.933129i	$0.382933\pi$
$570$	−2.08781	−	4.27551i	−0.0874487	−	0.179081i
$571$	−2.33800	−	0.759663i	−0.0978424	−	0.0317909i	0.259687	−	0.965693i	$-0.416381\pi$
$571$	−2.33800	−	0.759663i	−0.0978424	−	0.0317909i	−0.357529	+	0.933902i	$0.616381\pi$
$572$	0.344636	−	0.864208i	0.0144099	−	0.0361344i
$573$	0.640592	−	4.04454i	0.0267611	−	0.168963i
$574$	58.1330	+	26.3345i	2.42642	+	1.09918i
$575$	9.97100	−	3.58894i	0.415820	−	0.149669i
$576$	−6.64978	+	4.44751i	−0.277074	+	0.185313i
$577$	−6.93561	−	1.09849i	−0.288733	−	0.0457308i	0.0103878	−	0.999946i	$-0.496693\pi$
$577$	−6.93561	−	1.09849i	−0.288733	−	0.0457308i	−0.299121	+	0.954215i	$0.596693\pi$
$578$	0.515580	+	11.2275i	0.0214453	+	0.467003i
$579$	5.00097	−	15.3914i	0.207833	−	0.639645i
$580$	−9.56767	−	26.7858i	−0.397276	−	1.11222i
$581$	−3.11529	−	9.58788i	−0.129244	−	0.397772i
$582$	−5.85220	+	2.20311i	−0.242582	+	0.0913218i
$583$	−0.132010	+	0.259083i	−0.00546728	+	0.0107301i
$584$	19.8487	+	6.87798i	0.821343	+	0.284613i
$585$	−2.52988	+	11.3160i	−0.104598	+	0.467861i
$586$	−32.3973	+	6.66745i	−1.33832	+	0.275430i
$587$	−19.2103	+	3.04261i	−0.792893	+	0.125582i	−0.539726	−	0.841841i	$-0.681472\pi$
$587$	−19.2103	+	3.04261i	−0.792893	+	0.125582i	−0.253167	+	0.967423i	$0.581472\pi$
$588$	−16.1691	+	19.4470i	−0.666800	+	0.801982i
$589$	−3.68193	−	5.06775i	−0.151711	−	0.208813i
$590$	25.6619	+	36.6121i	1.05648	+	1.50730i
$591$	−5.06230	+	6.96765i	−0.208235	+	0.286611i
$592$	26.5592	+	18.2421i	1.09158	+	0.749746i
$593$	−26.2991	+	26.2991i	−1.07998	+	1.07998i	−0.0834655	+	0.996511i	$0.526599\pi$
$593$	−26.2991	+	26.2991i	−1.07998	+	1.07998i	−0.996511	+	0.0834655i	$0.973401\pi$
$594$	−0.126084	−	0.0140775i	−0.00517329	−	0.000577605i
$595$	15.9772	+	25.1781i	0.655001	+	1.03220i
$596$	5.33109	−	2.29135i	0.218370	−	0.0938575i
$597$	−19.0109	+	9.68652i	−0.778063	+	0.396443i
$598$	−12.9805	−	8.54956i	−0.530812	−	0.349618i
$599$	−41.8236			−1.70887			−0.854434	−	0.519561i	$-0.826096\pi$
$599$	−41.8236			−1.70887			−0.854434	+	0.519561i	$0.826096\pi$
$600$	−10.1186	−	9.88001i	−0.413089	−	0.403350i
$601$	−37.3005			−1.52152			−0.760759	−	0.649034i	$-0.775173\pi$
$601$	−37.3005			−1.52152			−0.760759	+	0.649034i	$0.775173\pi$
$602$	−58.1844	−	38.3229i	−2.37142	−	1.56193i
$603$	1.84223	−	0.938661i	0.0750212	−	0.0382252i
$604$	7.38746	−	3.17520i	0.300591	−	0.129197i
$605$	1.54423	−	24.5302i	0.0627818	−	0.997294i
$606$	−9.58292	−	1.06995i	−0.389280	−	0.0434636i
$607$	6.86710	−	6.86710i	0.278727	−	0.278727i	−0.553874	−	0.832601i	$-0.686851\pi$
$607$	6.86710	−	6.86710i	0.278727	−	0.278727i	0.832601	+	0.553874i	$0.186851\pi$
$608$	−4.40232	−	7.28452i	−0.178538	−	0.295426i
$609$	16.5696	−	22.8062i	0.671436	−	0.924152i
$610$	−34.6127	+	10.6001i	−1.40143	+	0.429184i
$611$	23.4776	+	32.3141i	0.949800	+	1.30729i
$612$	−3.84714	+	4.62708i	−0.155511	+	0.187038i
$613$	−9.83772	+	1.55814i	−0.397342	+	0.0629328i	−0.351908	−	0.936035i	$-0.614467\pi$
$613$	−9.83772	+	1.55814i	−0.397342	+	0.0629328i	−0.0454338	+	0.998967i	$0.514467\pi$
$614$	43.9609	−	9.04725i	1.77412	−	0.365117i
$615$	−22.6654	+	2.14166i	−0.913958	+	0.0863600i
$616$	−0.368228	+	1.06264i	−0.0148363	+	0.0428151i
$617$	−13.7364	+	26.9593i	−0.553008	+	1.08534i	0.430179	+	0.902743i	$0.358450\pi$
$617$	−13.7364	+	26.9593i	−0.553008	+	1.08534i	−0.983188	+	0.182597i	$0.941550\pi$
$618$	3.27686	−	1.23360i	0.131815	−	0.0496226i
$619$	−10.2938	−	31.6812i	−0.413744	−	1.27337i	−0.913369	−	0.407133i	$-0.866529\pi$
$619$	−10.2938	−	31.6812i	−0.413744	−	1.27337i	0.499625	−	0.866242i	$-0.333471\pi$
$620$	−15.3727	−	10.5037i	−0.617382	−	0.421839i
$621$	−0.654945	+	2.01571i	−0.0262820	+	0.0808878i
$622$	−0.942608	−	20.5267i	−0.0377951	−	0.823045i
$623$	57.1113	+	9.04554i	2.28811	+	0.362402i
$624$	−2.70135	+	20.5658i	−0.108141	+	0.823291i
$625$	13.3988	−	21.1062i	0.535953	−	0.844248i
$626$	−2.90373	−	1.31541i	−0.116057	−	0.0525742i
$627$	0.0211152	−	0.133316i	0.000843262	−	0.00532415i
$628$	2.42518	−	6.08136i	0.0967750	−	0.242673i
$629$	23.0498	+	7.48932i	0.919054	+	0.298619i
$630$	2.42736	−	13.8044i	0.0967083	−	0.549981i
$631$	−4.13387	+	1.34318i	−0.164567	+	0.0534710i	−0.390142	−	0.920755i	$-0.627574\pi$
$631$	−4.13387	+	1.34318i	−0.164567	+	0.0534710i	0.225575	+	0.974226i	$0.427574\pi$
$632$	−3.19379	−	1.70621i	−0.127042	−	0.0678692i
$633$	−22.9718	−	11.7047i	−0.913048	−	0.465221i
$634$	9.76201	−	5.55218i	0.387699	−	0.220505i
$635$	−0.584789	−	6.18889i	−0.0232066	−	0.245599i
$636$	1.42977	−	6.32302i	0.0566941	−	0.250724i
$637$	10.2581	+	64.7669i	0.406439	+	2.56616i
$638$	0.213878	−	0.778029i	0.00846750	−	0.0308024i
$639$	−2.02027	+	1.46781i	−0.0799208	+	0.0580658i
$640$	−19.6054	−	15.9884i	−0.774972	−	0.631995i
$641$	23.8819	+	17.3512i	0.943278	+	0.685332i	0.949208	−	0.314651i	$-0.101887\pi$
$641$	23.8819	+	17.3512i	0.943278	+	0.685332i	−0.00592940	+	0.999982i	$0.501887\pi$
$642$	−4.23691	+	3.38583i	−0.167218	+	0.133628i
$643$	−5.10377	−	5.10377i	−0.201273	−	0.201273i	0.599272	−	0.800545i	$-0.295457\pi$
$643$	−5.10377	−	5.10377i	−0.201273	−	0.201273i	−0.800545	+	0.599272i	$0.795457\pi$
$644$	16.1480	+	9.60384i	0.636322	+	0.378444i
$645$	24.8047	+	1.56151i	0.976683	+	0.0614843i
$646$	−4.72994	−	4.31461i	−0.186097	−	0.169756i
$647$	−8.71938	−	17.1127i	−0.342794	−	0.672771i	0.653671	−	0.756779i	$-0.273228\pi$
$647$	−8.71938	−	17.1127i	−0.342794	−	0.672771i	−0.996465	+	0.0840074i	$0.973228\pi$
$648$	2.80167	−	0.388151i	0.110060	−	0.0152480i
$649$			1.26835i			0.0497872i
$650$	−36.5585	+	2.82905i	−1.43394	+	0.110964i
$651$		−	18.4527i		−	0.723218i
$652$	−11.2507	+	7.10098i	−0.440611	+	0.278096i
$653$	−19.9775	−	39.2081i	−0.781781	−	1.53433i	−0.844045	−	0.536272i	$-0.819832\pi$
$653$	−19.9775	−	39.2081i	−0.781781	−	1.53433i	0.0622643	−	0.998060i	$-0.480168\pi$
$654$	−6.55645	+	7.18759i	−0.256377	+	0.281057i
$655$	−23.3118	+	14.7929i	−0.910866	+	0.578005i
$656$	−40.0416	+	7.43352i	−1.56336	+	0.290230i
$657$	−5.25164	−	5.25164i	−0.204886	−	0.204886i
$658$	−30.1410	−	37.7175i	−1.17502	−	1.47038i
$659$	−27.2711	−	19.8136i	−1.06233	−	0.771830i	−0.0878139	−	0.996137i	$-0.527988\pi$
$659$	−27.2711	−	19.8136i	−1.06233	−	0.771830i	−0.974518	+	0.224307i	$0.927988\pi$
$660$	−0.0741872	−	0.394272i	−0.00288773	−	0.0153470i
$661$	36.2595	−	26.3441i	1.41033	−	1.02467i	0.417058	−	0.908880i	$-0.363061\pi$
$661$	36.2595	−	26.3441i	1.41033	−	1.02467i	0.993274	−	0.115787i	$-0.0369389\pi$
$662$	42.7363	+	11.7481i	1.66099	+	0.456602i
$663$	2.44073	+	15.4101i	0.0947899	+	0.598480i
$664$	5.13023	+	3.88169i	0.199091	+	0.150639i
$665$	14.5530	+	3.25355i	0.564341	+	0.126167i
$666$	−5.63189	−	9.90216i	−0.218231	−	0.383701i
$667$	−12.0107	−	6.11974i	−0.465055	−	0.236957i
$668$	−0.385031	+	5.88779i	−0.0148973	+	0.227806i
$669$	−23.5265	+	7.64422i	−0.909587	+	0.295543i
$670$	4.54408	+	4.70108i	0.175553	+	0.181619i
$671$	−0.976660	−	0.317336i	−0.0377035	−	0.0122506i
$672$	2.12151	−	24.9830i	0.0818391	−	0.963742i
$673$	4.08246	−	25.7757i	0.157367	−	0.993579i	−0.774972	−	0.631995i	$-0.782236\pi$
$673$	4.08246	−	25.7757i	0.157367	−	0.993579i	0.932340	−	0.361583i	$-0.117764\pi$
$674$	18.6763	−	41.2276i	0.719384	−	1.58803i
$675$	1.69334	+	4.70453i	0.0651766	+	0.181077i
$676$	18.3205	+	20.8843i	0.704636	+	0.803243i
$677$	8.61245	+	1.36408i	0.331003	+	0.0524258i	0.319724	−	0.947511i	$-0.396410\pi$
$677$	8.61245	+	1.36408i	0.331003	+	0.0524258i	0.0112789	+	0.999936i	$0.496410\pi$
$678$	16.3954	−	0.752896i	0.629662	−	0.0289148i
$679$	6.05616	−	18.6389i	0.232414	−	0.715297i
$680$	−17.5531	−	7.34783i	−0.673132	−	0.281776i
$681$	−5.86617	−	18.0542i	−0.224792	−	0.691838i
$682$	−0.186087	−	0.494310i	−0.00712564	−	0.0189281i
$683$	−1.48416	+	2.91283i	−0.0567898	+	0.111456i	−0.917657	−	0.397373i	$-0.869922\pi$
$683$	−1.48416	+	2.91283i	−0.0567898	+	0.111456i	0.860867	+	0.508830i	$0.169922\pi$
$684$	0.275795	+	2.99658i	0.0105453	+	0.114577i
$685$	4.03810	+	9.33246i	0.154288	+	0.356575i
$686$	−7.13318	−	34.6603i	−0.272346	−	1.32334i
$687$	−3.97398	+	0.629416i	−0.151617	+	0.0240137i
$688$	44.4442	−	1.17697i	1.69442	−	0.0448717i
$689$	−9.87967	−	13.5982i	−0.376385	−	0.518050i
$690$	−6.70131	−	0.113801i	−0.255115	−	0.00433235i
$691$	16.4783	−	22.6804i	0.626864	−	0.862805i	−0.370966	−	0.928647i	$-0.620973\pi$
$691$	16.4783	−	22.6804i	0.626864	−	0.862805i	0.997830	+	0.0658420i	$0.0209733\pi$
$692$	−12.6103	+	3.20460i	−0.479373	+	0.121821i
$693$	0.281158	−	0.281158i	0.0106803	−	0.0106803i
$694$	−1.54677	+	13.8536i	−0.0587145	+	0.525874i
$695$	−22.9451	+	27.7337i	−0.870356	+	1.05200i
$696$	−0.349200	+	17.9857i	−0.0132364	+	0.681746i
$697$	−27.2946	+	13.9073i	−1.03385	+	0.526775i
$698$	−14.9271	+	22.6633i	−0.564999	+	0.857819i
$699$	−4.62991			−0.175119
$700$	43.9876	−	5.44324i	1.66258	−	0.205735i
$701$	23.1470			0.874250			0.437125	−	0.899401i	$-0.355997\pi$
$701$	23.1470			0.874250			0.437125	+	0.899401i	$0.355997\pi$
$702$	4.03386	−	6.12447i	0.152248	−	0.231153i
$703$	10.7990	−	5.50236i	0.407291	−	0.207525i
$704$	−0.195112	−	0.690640i	−0.00735355	−	0.0260295i
$705$	16.0137	+	6.34095i	0.603110	+	0.238814i
$706$	−5.56838	+	49.8729i	−0.209569	+	1.87699i
$707$	21.3692	−	21.3692i	0.803672	−	0.803672i
$708$	−6.96454	−	27.4060i	−0.261744	−	1.02998i
$709$	22.6308	−	31.1487i	0.849919	−	1.16981i	−0.133961	−	0.990987i	$-0.542770\pi$
$709$	22.6308	−	31.1487i	0.849919	−	1.16981i	0.983881	−	0.178827i	$-0.0572302\pi$
$710$	−6.30893	−	4.74944i	−0.236770	−	0.178243i
$711$	0.752487	+	1.03571i	0.0282205	+	0.0388421i
$712$	−33.1964	+	16.1105i	−1.24409	+	0.603766i
$713$	−8.71508	+	1.38033i	−0.326382	+	0.0516939i
$714$	−3.80167	−	18.4724i	−0.142274	−	0.691313i
$715$	−0.895333	−	0.529543i	−0.0334835	−	0.0198038i
$716$	−18.3068	+	1.68489i	−0.684158	+	0.0629673i
$717$	−9.15604	+	17.9697i	−0.341939	+	0.671092i
$718$	0.396857	+	1.05419i	0.0148106	+	0.0393420i
$719$	3.78332	+	11.6439i	0.141094	+	0.434243i	0.996488	−	0.0837350i	$-0.0266849\pi$
$719$	3.78332	+	11.6439i	0.141094	+	0.434243i	−0.855394	+	0.517978i	$0.826685\pi$
$720$	3.76796	+	8.11187i	0.140423	+	0.302312i
$721$	−3.39106	+	10.4366i	−0.126290	+	0.388680i
$722$	23.6435	−	1.08574i	0.879920	−	0.0404069i
$723$	−6.64075	−	1.05179i	−0.246972	−	0.0391165i
$724$	−6.91409	+	6.06531i	−0.256960	+	0.225415i
$725$	−31.2377	+	5.95649i	−1.16014	+	0.221218i
$726$	−6.41447	+	14.1598i	−0.238063	+	0.525520i
$727$	−7.14374	+	45.1038i	−0.264947	+	1.67281i	0.392842	+	0.919606i	$0.371492\pi$
$727$	−7.14374	+	45.1038i	−0.264947	+	1.67281i	−0.657789	+	0.753202i	$0.728508\pi$
$728$	−45.0676	−	46.8522i	−1.67032	−	1.73646i
$729$	−0.951057	−	0.309017i	−0.0352243	−	0.0114451i
$730$	11.0162	−	20.7422i	0.407729	−	0.767702i
$731$	31.8053	−	10.3342i	1.17636	−	0.382223i
$732$	22.8457	+	1.49399i	0.844402	+	0.0552196i
$733$	−37.7569	−	19.2381i	−1.39458	−	0.710575i	−0.414664	−	0.909974i	$-0.636101\pi$
$733$	−37.7569	−	19.2381i	−1.39458	−	0.710575i	−0.979918	+	0.199399i	$0.936101\pi$
$734$	−19.4965	−	34.2793i	−0.719629	−	1.26527i
$735$	18.6985	+	21.2108i	0.689703	+	0.782373i
$736$	−11.9580	+	0.866853i	−0.440779	+	0.0319526i
$737$	0.0290155	+	0.183197i	0.00106880	+	0.00674814i
$738$	13.8837	+	3.81658i	0.511066	+	0.140490i
$739$	8.08428	−	5.87357i	0.297385	−	0.216063i	−0.429080	−	0.903267i	$-0.641162\pi$
$739$	8.08428	−	5.87357i	0.297385	−	0.216063i	0.726465	+	0.687204i	$0.241162\pi$
$740$	24.7257	−	26.1983i	0.908935	−	0.963067i
$741$	6.31228	+	4.58614i	0.231887	+	0.168476i
$742$	12.6837	+	15.8720i	0.465634	+	0.582680i
$743$	16.3290	+	16.3290i	0.599053	+	0.599053i	0.940060	−	0.341008i	$-0.110768\pi$
$743$	16.3290	+	16.3290i	0.599053	+	0.599053i	−0.341008	+	0.940060i	$0.610768\pi$
$744$	6.73515	+	9.65903i	0.246923	+	0.354117i
$745$	−1.61316	−	6.28381i	−0.0591015	−	0.230221i
$746$	5.26708	−	5.77410i	0.192841	−	0.211405i
$747$	−1.03260	−	2.02659i	−0.0377809	−	0.0741491i
$748$	−0.288125	−	0.456501i	−0.0105349	−	0.0166913i
$749$		−	16.9982i		−	0.621099i
$750$	−12.6569	+	9.47644i	−0.462165	+	0.346031i
$751$		−	42.7056i		−	1.55835i	−0.626807	−	0.779174i	$-0.715639\pi$
$751$		−	42.7056i		−	1.55835i	0.626807	−	0.779174i	$-0.284361\pi$
$752$	29.5440	+	8.74181i	1.07736	+	0.318781i
$753$	12.2889	+	24.1184i	0.447834	+	0.878924i
$754$	34.4593	+	31.4334i	1.25493	+	1.14474i
$755$	−2.23540	−	8.70767i	−0.0813546	−	0.316904i
$756$	−4.53130	+	7.61899i	−0.164802	+	0.277100i
$757$	−7.75454	−	7.75454i	−0.281844	−	0.281844i	0.552000	−	0.833844i	$-0.313865\pi$
$757$	−7.75454	−	7.75454i	−0.281844	−	0.281844i	−0.833844	+	0.552000i	$0.813865\pi$
$758$	20.6001	−	16.4621i	0.748229	−	0.597929i
$759$	−0.153821	−	0.111758i	−0.00558335	−	0.00405654i
$760$	−8.80528	+	3.60872i	−0.319401	+	0.130902i
$761$	−13.9344	+	10.1240i	−0.505123	+	0.366993i	−0.810970	−	0.585087i	$-0.801060\pi$
$761$	−13.9344	+	10.1240i	−0.505123	+	0.366993i	0.305847	+	0.952081i	$0.401060\pi$
$762$	−1.04213	+	3.79100i	−0.0377526	+	0.137333i
$763$	−4.76985	−	30.1156i	−0.172680	−	1.09026i
$764$	−7.98824	−	1.80631i	−0.289004	−	0.0653501i
$765$	4.44897	+	5.04674i	0.160853	+	0.182465i
$766$	23.1092	−	13.1435i	0.834970	−	0.474893i
$767$	−65.3259	−	33.2852i	−2.35878	−	1.20186i
$768$	8.00820	+	13.8517i	0.288971	+	0.499829i
$769$	−15.3435	+	4.98540i	−0.553300	+	0.179778i	−0.572304	−	0.820041i	$-0.693950\pi$
$769$	−15.3435	+	4.98540i	−0.553300	+	0.179778i	0.0190041	+	0.999819i	$0.493950\pi$
$770$	1.11048	+	0.589778i	0.0400189	+	0.0212541i
$771$	−0.490780	−	0.159464i	−0.0176750	−	0.00574295i
$772$	−30.0645	−	11.9894i	−1.08205	−	0.431507i
$773$	−4.21620	+	26.6201i	−0.151646	+	0.957457i	0.788091	+	0.615559i	$0.211070\pi$
$773$	−4.21620	+	26.6201i	−0.151646	+	0.957457i	−0.939737	+	0.341898i	$0.888930\pi$
$774$	−14.3183	−	6.48625i	−0.514660	−	0.233143i
$775$	−14.2507	+	15.1732i	−0.511901	+	0.545038i
$776$	3.63305	+	11.9670i	0.130419	+	0.429590i
$777$	35.2634	+	5.58517i	1.26507	+	0.200367i
$778$	−0.418881	−	9.12175i	−0.0150176	−	0.327031i
$779$	−4.73390	+	14.5695i	−0.169610	+	0.522005i
$780$	22.2537	+	6.52584i	0.796809	+	0.233663i
$781$	−0.0692262	−	0.213056i	−0.00247711	−	0.00762375i
$782$	−8.44003	+	3.17731i	−0.301815	+	0.113621i
$783$	2.88742	−	5.66689i	0.103188	−	0.202518i
$784$	36.7009	+	34.8072i	1.31075	+	1.24312i
$785$	−6.30039	−	3.72636i	−0.224870	−	0.132999i
$786$	17.1031	−	3.51987i	0.610049	−	0.125550i
$787$	17.4691	−	2.76683i	0.622705	−	0.0986268i	0.162894	−	0.986644i	$-0.447917\pi$
$787$	17.4691	−	2.76683i	0.622705	−	0.0986268i	0.459811	+	0.888017i	$0.347917\pi$
$788$	13.2449	+	11.0124i	0.471831	+	0.392299i
$789$	8.87859	+	12.2203i	0.316086	+	0.435055i
$790$	−2.43484	+	3.23432i	−0.0866277	+	0.115072i
$791$	−30.2353	+	41.6153i	−1.07504	+	1.47967i
$792$	−0.0445503	+	0.249794i	−0.00158302	+	0.00887603i
$793$	41.9746	−	41.9746i	1.49056	−	1.49056i
$794$	13.3984	+	1.49595i	0.475491	+	0.0530892i
$795$	−6.73877	−	2.66836i	−0.238999	−	0.0946369i
$796$	16.8506	+	39.2049i	0.597255	+	1.38958i
$797$	19.2719	−	9.81954i	0.682647	−	0.347826i	−0.0780351	−	0.996951i	$-0.524865\pi$
$797$	19.2719	−	9.81954i	0.682647	−	0.347826i	0.760682	+	0.649125i	$0.224865\pi$
$798$	−7.87639	−	5.18775i	−0.278821	−	0.183645i
$799$	23.1750			0.819873
$800$	−21.0385	+	18.9046i	−0.743823	+	0.668377i
$801$	13.0458			0.460951
$802$	−16.8241	−	11.0811i	−0.594080	−	0.391289i
$803$	0.593645	−	0.302477i	0.0209493	−	0.0106742i
$804$	−1.63289	−	3.79910i	−0.0575876	−	0.133984i
$805$	13.3902	−	16.1847i	0.471941	−	0.570436i
$806$	30.3427	+	3.38780i	1.06878	+	0.119330i
$807$	14.0702	−	14.0702i	0.495295	−	0.495295i
$808$	−3.38601	+	18.9854i	−0.119119	+	0.667902i
$809$	−17.3745	+	23.9139i	−0.610854	+	0.840768i	−0.996647	−	0.0818172i	$-0.973928\pi$
$809$	−17.3745	+	23.9139i	−0.610854	+	0.840768i	0.385794	+	0.922585i	$0.373928\pi$
$810$	0.0536939	−	3.16182i	0.00188661	−	0.111095i
$811$	15.1413	+	20.8402i	0.531683	+	0.731799i	0.987386	−	0.158333i	$-0.0506120\pi$
$811$	15.1413	+	20.8402i	0.531683	+	0.731799i	−0.455703	+	0.890132i	$0.650612\pi$
$812$	−43.3526	−	36.0451i	−1.52138	−	1.26494i
$813$	5.63909	−	0.893144i	0.197772	−	0.0313239i
$814$	1.00096	−	0.206000i	0.0350836	−	0.00722029i
$815$	5.90689	+	13.6514i	0.206909	+	0.478188i
$816$	8.73233	+	8.28176i	0.305693	+	0.289920i
$817$	7.59246	−	14.9010i	0.265626	−	0.521321i
$818$	−18.3900	+	6.92304i	−0.642990	+	0.242058i
$819$	7.10253	+	21.8593i	0.248183	+	0.763827i
$820$	1.31610	+	45.5137i	0.0459603	+	1.58941i
$821$	−5.90690	+	18.1796i	−0.206152	+	0.634471i	0.793512	+	0.608555i	$0.208250\pi$
$821$	−5.90690	+	18.1796i	−0.206152	+	0.634471i	−0.999664	+	0.0259166i	$0.991750\pi$
$822$	−0.295017	−	6.42444i	−0.0102899	−	0.224078i
$823$	−3.92443	−	0.621568i	−0.136797	−	0.0216665i	0.0876604	−	0.996150i	$-0.472061\pi$
$823$	−3.92443	−	0.621568i	−0.136797	−	0.0216665i	−0.224457	+	0.974484i	$0.572061\pi$
$824$	−2.03427	−	6.70075i	−0.0708673	−	0.233432i
$825$	−0.448324	+	0.0140556i	−0.0156086	+	0.000489354i
$826$	80.7268	+	36.5696i	2.80884	+	1.27242i
$827$	−4.58447	+	28.9452i	−0.159418	+	1.00652i	0.770147	+	0.637866i	$0.220183\pi$
$827$	−4.58447	+	28.9452i	−0.159418	+	1.00652i	−0.929565	+	0.368658i	$0.879817\pi$
$828$	3.93736	+	1.57017i	0.136833	+	0.0545672i
$829$	33.1072	+	10.7572i	1.14986	+	0.373612i	0.821091	−	0.570798i	$-0.193366\pi$
$829$	33.1072	+	10.7572i	1.14986	+	0.373612i	0.328770	+	0.944410i	$0.393366\pi$
$830$	5.17156	−	4.99884i	0.179507	−	0.173512i
$831$	−11.1966	+	3.63801i	−0.388407	+	0.126201i
$832$	40.6914	+	8.07525i	1.41072	+	0.279959i
$833$	33.9000	+	17.2729i	1.17457	+	0.598471i
$834$	19.7885	−	11.2548i	0.685219	−	0.389721i
$835$	6.43789	+	1.43929i	0.222792	+	0.0498087i
$836$	−0.263309	−	0.0595397i	−0.00910672	−	0.00205923i
$837$	−0.651271	−	4.11196i	−0.0225112	−	0.142130i
$838$	7.46297	−	27.1482i	0.257804	−	0.937821i
$839$	21.2823	−	15.4625i	0.734746	−	0.533824i	−0.156315	−	0.987707i	$-0.549962\pi$
$839$	21.2823	−	15.4625i	0.734746	−	0.533824i	0.891061	+	0.453883i	$0.149962\pi$
$840$	−27.2332	−	6.64600i	−0.939634	−	0.229309i
$841$	9.26395	+	6.73065i	0.319447	+	0.232092i
$842$	1.23565	−	0.987435i	0.0425831	−	0.0340293i
$843$	5.49279	+	5.49279i	0.189182	+	0.189182i
$844$	−26.3576	+	44.3181i	−0.907267	+	1.52549i
$845$	26.2258	−	16.6420i	0.902194	−	0.572502i
$846$	−8.04777	−	7.34109i	−0.276688	−	0.252392i
$847$	−22.1183	−	43.4096i	−0.759994	−	1.49157i
$848$	−12.4325	−	3.67867i	−0.426934	−	0.126326i
$849$		−	18.4274i		−	0.632427i
$850$	−11.1399	+	18.1254i	−0.382097	+	0.621696i
$851$		−	17.0725i		−	0.585237i
$852$	2.66570	+	4.22350i	0.0913255	+	0.144695i
$853$	−22.5226	−	44.2032i	−0.771161	−	1.51349i	−0.855933	−	0.517087i	$-0.827016\pi$
$853$	−22.5226	−	44.2032i	−0.771161	−	1.51349i	0.0847720	−	0.996400i	$-0.472984\pi$
$854$	−48.3569	+	53.0119i	−1.65474	+	1.81403i
$855$	3.35780	+	0.211381i	0.114834	+	0.00722906i
$856$	6.20425	+	8.89765i	0.212057	+	0.304116i
$857$	−1.39722	−	1.39722i	−0.0477281	−	0.0477281i	0.682840	−	0.730568i	$-0.260745\pi$
$857$	−1.39722	−	1.39722i	−0.0477281	−	0.0477281i	−0.730568	+	0.682840i	$0.760745\pi$
$858$	0.410704	+	0.513942i	0.0140212	+	0.0175457i
$859$	−8.28918	−	6.02244i	−0.282823	−	0.205483i	0.437325	−	0.899304i	$-0.355926\pi$
$859$	−8.28918	−	6.02244i	−0.282823	−	0.205483i	−0.720148	+	0.693821i	$0.755926\pi$
$860$	6.35364	−	49.2998i	0.216657	−	1.68111i
$861$	−36.5088	+	26.5252i	−1.24422	+	0.903975i
$862$	11.9382	+	3.28177i	0.406616	+	0.111778i
$863$	−3.08157	−	19.4563i	−0.104898	−	0.662299i	−0.982969	−	0.183769i	$-0.941170\pi$
$863$	−3.08157	−	19.4563i	−0.104898	−	0.662299i	0.878072	−	0.478529i	$-0.158830\pi$
$864$	−0.409000	−	5.64205i	−0.0139144	−	0.191946i
$865$	1.36844	+	14.4824i	0.0465285	+	0.492416i
$866$	11.3103	+	19.8862i	0.384341	+	0.675759i
$867$	−7.08120	−	3.60805i	−0.240490	−	0.122536i
$868$	−36.8267	−	2.40828i	−1.24998	−	0.0817423i
$869$	−0.109225	+	0.0354894i	−0.00370521	+	0.00120389i
$870$	19.8085	+	3.48311i	0.671571	+	0.118089i
$871$	−10.1969	−	3.31318i	−0.345509	−	0.112263i
$872$	13.4888	+	14.0230i	0.456790	+	0.474879i
$873$	0.691698	−	4.36721i	0.0234104	−	0.147808i
$874$	−1.86096	+	4.10803i	−0.0629479	+	0.138956i
$875$	1.56210	−	49.5301i	0.0528087	−	1.67442i
$876$	−11.1663	+	9.79550i	−0.377274	+	0.330959i
$877$	−42.7175	−	6.76579i	−1.44247	−	0.228465i	−0.614357	−	0.789028i	$-0.710585\pi$
$877$	−42.7175	−	6.76579i	−1.44247	−	0.228465i	−0.828111	+	0.560564i	$0.810585\pi$
$878$	−44.5287	+	2.04481i	−1.50277	+	0.0690088i
$879$	7.22744	−	22.2438i	0.243775	−	0.750264i
$880$	−0.796545	+	0.0966015i	−0.0268515	+	0.00325644i
$881$	−9.84663	−	30.3048i	−0.331741	−	1.02100i	−0.968305	−	0.249771i	$-0.919645\pi$
$881$	−9.84663	−	30.3048i	−0.331741	−	1.02100i	0.636564	−	0.771224i	$-0.280355\pi$
$882$	−6.30063	−	16.7366i	−0.212153	−	0.563551i
$883$	19.3210	−	37.9195i	0.650202	−	1.27609i	−0.296822	−	0.954933i	$-0.595927\pi$
$883$	19.3210	−	37.9195i	0.650202	−	1.27609i	0.947025	−	0.321161i	$-0.104073\pi$
$884$	31.0731	−	2.85986i	1.04510	−	0.0961873i
$885$	−31.4745	+	2.97403i	−1.05800	+	0.0999710i
$886$	9.17639	+	44.5884i	0.308287	+	1.49797i
$887$	−9.67782	+	1.53282i	−0.324949	+	0.0514669i	−0.316778	−	0.948500i	$-0.602601\pi$
$887$	−9.67782	+	1.53282i	−0.324949	+	0.0514669i	−0.00817134	+	0.999967i	$0.502601\pi$
$888$	−20.4971	+	9.94744i	−0.687839	+	0.333814i
$889$	−7.24281	−	9.96887i	−0.242916	−	0.334345i
$890$	12.0803	+	39.4462i	0.404933	+	1.32224i
$891$	0.0527296	−	0.0725760i	0.00176651	−	0.00243139i
$892$	12.1854	+	47.9503i	0.407997	+	1.60550i
$893$	8.19496	−	8.19496i	0.274234	−	0.274234i
$894$	−0.455287	+	4.07776i	−0.0152271	+	0.136381i
$895$	−1.29137	+	20.5135i	−0.0431658	+	0.685692i
$896$	−49.5827	−	7.49454i	−1.65644	−	0.250375i
$897$	9.79273	−	4.98965i	0.326970	−	0.166599i
$898$	−2.50148	+	3.79792i	−0.0834756	+	0.126738i
$899$	26.4785			0.883107
$900$	9.61001	−	2.76547i	0.320334	−	0.0921822i
$901$	−9.75235			−0.324898
$902$	−0.710502	+	1.07873i	−0.0236571	+	0.0359178i
$903$	43.8954	−	22.3658i	1.46075	−	0.744288i
$904$	0.637200	−	32.8192i	0.0211929	−	1.09155i
$905$	5.50960	+	8.68246i	0.183145	+	0.288615i
$906$	−0.630905	+	5.65068i	−0.0209604	+	0.187731i
$907$	−18.8705	+	18.8705i	−0.626584	+	0.626584i	−0.947207	−	0.320623i	$-0.896108\pi$
$907$	−18.8705	+	18.8705i	−0.626584	+	0.626584i	0.320623	+	0.947207i	$0.396108\pi$
$908$	−36.7970	+	9.35105i	−1.22115	+	0.310326i
$909$	4.00767	−	5.51608i	0.132926	−	0.182957i
$910$	−59.5184	+	41.7172i	−1.97302	+	1.38291i
$911$	−9.42916	−	12.9781i	−0.312402	−	0.429984i	0.623726	−	0.781643i	$-0.285618\pi$
$911$	−9.42916	−	12.9781i	−0.312402	−	0.429984i	−0.936128	+	0.351658i	$0.885618\pi$
$912$	6.01639	−	0.159326i	0.199223	−	0.00527582i
$913$	0.201531	−	0.0319193i	0.00666969	−	0.00105638i
$914$	−1.73936	−	8.45161i	−0.0575329	−	0.279554i
$915$	5.58471	−	24.9802i	0.184625	−	0.825819i
$916$	0.737502	+	8.01316i	0.0243677	+	0.264762i
$917$	−24.8454	+	48.7618i	−0.820467	+	1.61026i
$918$	−1.49912	−	3.98218i	−0.0494785	−	0.131432i
$919$	−4.00489	−	12.3258i	−0.132109	−	0.406591i	0.863020	−	0.505170i	$-0.168570\pi$
$919$	−4.00489	−	12.3258i	−0.132109	−	0.406591i	−0.995129	+	0.0985793i	$0.968570\pi$
$920$	−1.10171	+	13.3592i	−0.0363224	+	0.440440i
$921$	−9.80712	+	30.1832i	−0.323156	+	0.994571i
$922$	33.8522	−	1.55453i	1.11486	−	0.0511957i
$923$	12.7901	+	2.02575i	0.420990	+	0.0666783i
$924$	−0.524424	−	0.597813i	−0.0172523	−	0.0196666i
$925$	−24.6829	−	31.8259i	−0.811570	−	1.04643i
$926$	−23.7338	+	52.3920i	−0.779942	+	1.72171i
$927$	−0.387307	+	2.44536i	−0.0127208	+	0.0803161i
$928$	35.8491	+	3.04424i	1.17681	+	0.0999321i
$929$	13.3466	+	4.33657i	0.437887	+	0.142278i	0.519660	−	0.854373i	$-0.326058\pi$
$929$	13.3466	+	4.33657i	0.437887	+	0.142278i	−0.0817736	+	0.996651i	$0.526058\pi$
$930$	11.8301	−	5.77686i	0.387925	−	0.189431i
$931$	18.0954	−	5.87954i	0.593051	−	0.192694i
$932$	−0.604254	+	9.24009i	−0.0197930	+	0.302669i
$933$	12.9462	+	6.59642i	0.423839	+	0.215957i
$934$	−17.9947	−	31.6389i	−0.588806	−	1.03526i
$935$	−0.553912	+	0.239674i	−0.0181148	+	0.00783819i
$936$	−11.6964	−	8.84984i	−0.382308	−	0.289266i
$937$	−4.98334	−	31.4636i	−0.162799	−	1.02787i	−0.924844	−	0.380347i	$-0.875805\pi$
$937$	−4.98334	−	31.4636i	−0.162799	−	1.02787i	0.762045	−	0.647524i	$-0.224195\pi$
$938$	12.4965	+	3.43525i	0.408025	+	0.112165i
$939$	1.82361	−	1.32493i	0.0595112	−	0.0432374i
$940$	14.7448	−	31.1315i	0.480924	−	1.01540i
$941$	−40.7011	−	29.5711i	−1.32682	−	0.963989i	−0.999820	−	0.0189631i	$-0.993963\pi$
$941$	−40.7011	−	29.5711i	−1.32682	−	0.963989i	−0.326996	−	0.945026i	$-0.606037\pi$
$942$	2.89009	+	3.61657i	0.0941643	+	0.117834i
$943$	15.2587	+	15.2587i	0.496890	+	0.496890i
$944$	−55.6040	+	10.3226i	−1.80976	+	0.335973i
$945$	7.63629	+	6.31777i	0.248408	+	0.205517i
$946$	0.950320	−	1.04180i	0.0308976	−	0.0338719i
$947$	14.5982	+	28.6506i	0.474377	+	0.931018i	0.996922	+	0.0784058i	$0.0249830\pi$
$947$	14.5982	+	28.6506i	0.474377	+	0.931018i	−0.522544	+	0.852612i	$0.675017\pi$
$948$	2.16521	−	1.36659i	0.0703228	−	0.0443849i
$949$			38.5133i			1.25019i
$950$	2.47014	+	10.3486i	0.0801421	+	0.335752i
$951$			7.94115i			0.257509i
$952$	−37.3623	+	5.17628i	−1.21092	+	0.167764i
$953$	−20.3126	−	39.8657i	−0.657989	−	1.29138i	−0.942981	−	0.332846i	$-0.891991\pi$
$953$	−20.3126	−	39.8657i	−0.657989	−	1.29138i	0.284992	−	0.958530i	$-0.408009\pi$
$954$	3.38661	+	3.08923i	0.109645	+	0.100017i
$955$	−3.37109	+	8.51347i	−0.109086	+	0.275489i
$956$	34.6679	+	20.6183i	1.12124	+	0.666844i
$957$	0.403445	+	0.403445i	0.0130415	+	0.0130415i
$958$	−17.4952	+	13.9808i	−0.565243	+	0.451700i
$959$	16.3067	+	11.8475i	0.526570	+	0.382576i
$960$	16.6809	−	6.46116i	0.538375	−	0.208533i
$961$	−11.0573	+	8.03363i	−0.356688	+	0.259149i
$962$	−15.6581	+	56.9600i	−0.504839	+	1.83647i
$963$	−0.599934	−	3.78784i	−0.0193326	−	0.122061i
$964$	−2.96579	+	13.1159i	−0.0955217	+	0.422435i
$965$	−18.4220	+	31.1473i	−0.593026	+	1.00267i
$966$	−11.5481	+	6.56801i	−0.371553	+	0.211322i
$967$	−8.41681	−	4.28858i	−0.270666	−	0.137911i	0.313390	−	0.949625i	$-0.398535\pi$
$967$	−8.41681	−	4.28858i	−0.270666	−	0.137911i	−0.584056	+	0.811713i	$0.698535\pi$
$968$	27.4221	+	14.6496i	0.881381	+	0.470856i
$969$	4.30547	−	1.39893i	0.138312	−	0.0449402i
$970$	13.8455	−	1.95253i	0.444552	−	0.0626921i
$971$	−49.9618	−	16.2336i	−1.60335	−	0.520960i	−0.635417	−	0.772169i	$-0.719172\pi$
$971$	−49.9618	−	16.2336i	−1.60335	−	0.520960i	−0.967933	+	0.251209i	$0.919172\pi$
$972$	−0.740840	+	1.85773i	−0.0237625	+	0.0595867i
$973$	−11.1614	+	70.4704i	−0.357819	+	2.25918i
$974$	−24.5716	−	11.1311i	−0.787325	−	0.356662i
$975$	11.0414	−	23.4596i	0.353608	−	0.751309i
$976$	5.96323	−	45.3991i	0.190878	−	1.45319i
$977$	5.28202	+	0.836590i	0.168987	+	0.0267649i	0.240354	−	0.970685i	$-0.422736\pi$
$977$	5.28202	+	0.836590i	0.168987	+	0.0267649i	−0.0713675	+	0.997450i	$0.522736\pi$
$978$	−0.431548	−	9.39759i	−0.0137994	−	0.300502i
$979$	−0.361651	+	1.11305i	−0.0115584	+	0.0355731i
$980$	44.7716	−	34.5489i	1.43018	−	1.10363i
$981$	−2.12581	−	6.54256i	−0.0678718	−	0.208888i
$982$	−9.20063	+	3.46365i	−0.293604	+	0.110529i
$983$	−4.87976	+	9.57708i	−0.155640	+	0.305461i	−0.955639	−	0.294540i	$-0.904833\pi$
$983$	−4.87976	+	9.57708i	−0.155640	+	0.305461i	0.799999	+	0.600002i	$0.204833\pi$
$984$	9.42887	−	27.2101i	0.300581	−	0.867426i
$985$	14.4462	−	12.7351i	0.460294	−	0.405774i
$986$	26.5068	−	5.45516i	0.844149	−	0.173728i
$987$	33.7197	−	5.34068i	1.07331	−	0.169996i
$988$	9.97655	−	11.9991i	0.317396	−	0.381742i
$989$	−13.8468	−	19.0585i	−0.440302	−	0.606024i
$990$	0.268273	+	0.0922318i	0.00852626	+	0.00293132i
$991$	−9.46784	+	13.0314i	−0.300756	+	0.413955i	−0.932470	−	0.361246i	$-0.882351\pi$
$991$	−9.46784	+	13.0314i	−0.300756	+	0.413955i	0.631715	+	0.775201i	$0.282351\pi$
$992$	20.1559	−	12.1810i	0.639950	−	0.386747i
$993$	−22.1608	+	22.1608i	−0.703252	+	0.703252i
$994$	−15.5563	−	1.73689i	−0.493417	−	0.0550907i
$995$	46.2112	−	11.8632i	1.46499	−	0.376088i
$996$	−4.17931	+	1.79631i	−0.132427	+	0.0569182i
$997$	9.89793	−	5.04325i	0.313471	−	0.159721i	−0.290176	−	0.956973i	$-0.593714\pi$
$997$	9.89793	−	5.04325i	0.313471	−	0.159721i	0.603647	+	0.797252i	$0.293714\pi$
$998$	0.298608	+	0.196677i	0.00945226	+	0.00622570i
$999$	8.05515			0.254854

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.2.w.a.127.25	✓	240
3.2	odd	2		900.2.bj.f.127.6		240
4.3	odd	2	inner	300.2.w.a.127.29	yes	240
12.11	even	2		900.2.bj.f.127.2		240
25.13	odd	20	inner	300.2.w.a.163.29	yes	240
75.38	even	20		900.2.bj.f.163.2		240
100.63	even	20	inner	300.2.w.a.163.25	yes	240
300.263	odd	20		900.2.bj.f.163.6		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.w.a.127.25	✓	240	1.1	even	1	trivial
300.2.w.a.127.29	yes	240	4.3	odd	2	inner
300.2.w.a.163.25	yes	240	100.63	even	20	inner
300.2.w.a.163.29	yes	240	25.13	odd	20	inner
900.2.bj.f.127.2		240	12.11	even	2
900.2.bj.f.127.6		240	3.2	odd	2
900.2.bj.f.163.2		240	75.38	even	20
900.2.bj.f.163.6		240	300.263	odd	20

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)

\(f(q)\)	\(=\)	\(q+(1.18105 + 0.777895i) q^{2} +(-0.891007 + 0.453990i) q^{3} +(0.789760 + 1.83747i) q^{4} +(2.16584 - 0.556007i) q^{5} +(-1.40548 - 0.156924i) q^{6} +(3.13412 - 3.13412i) q^{7} +(-0.496609 + 2.78449i) q^{8} +(0.587785 - 0.809017i) q^{9} +O(q^{10})\)	\(q+(1.18105 + 0.777895i) q^{2} +(-0.891007 + 0.453990i) q^{3} +(0.789760 + 1.83747i) q^{4} +(2.16584 - 0.556007i) q^{5} +(-1.40548 - 0.156924i) q^{6} +(3.13412 - 3.13412i) q^{7} +(-0.496609 + 2.78449i) q^{8} +(0.587785 - 0.809017i) q^{9} +(2.99048 + 1.02812i) q^{10} +(0.0527296 + 0.0725760i) q^{11} +(-1.53787 - 1.27865i) q^{12} +(-5.12177 + 0.811209i) q^{13} +(6.13957 - 1.26354i) q^{14} +(-1.67735 + 1.47868i) q^{15} +(-2.75256 + 2.90231i) q^{16} +(-1.36594 + 2.68082i) q^{17} +(1.32353 - 0.498255i) q^{18} +(0.464955 + 1.43098i) q^{19} +(2.73213 + 3.54054i) q^{20} +(-1.36966 + 4.21538i) q^{21} +(0.00581977 + 0.126734i) q^{22} +(2.09335 + 0.331555i) q^{23} +(-0.821650 - 2.70645i) q^{24} +(4.38171 - 2.40844i) q^{25} +(-6.68011 - 3.02612i) q^{26} +(-0.156434 + 0.987688i) q^{27} +(8.23404 + 3.28364i) q^{28} +(-6.04881 - 1.96538i) q^{29} +(-3.13129 + 0.441585i) q^{30} +(-3.95945 + 1.28650i) q^{31} +(-5.50860 + 1.28658i) q^{32} +(-0.0799312 - 0.0407270i) q^{33} +(-3.69864 + 2.10362i) q^{34} +(5.04540 - 8.53059i) q^{35} +(1.95075 + 0.441106i) q^{36} +(-1.26010 - 7.95598i) q^{37} +(-0.564019 + 2.05175i) q^{38} +(4.19525 - 3.04803i) q^{39} +(0.472619 + 6.30687i) q^{40} +(8.23695 + 5.98450i) q^{41} +(-4.89676 + 3.91313i) q^{42} +(-7.85946 - 7.85946i) q^{43} +(-0.0917123 + 0.154206i) q^{44} +(0.823229 - 2.07901i) q^{45} +(2.21444 + 2.01999i) q^{46} +(-3.49688 - 6.86301i) q^{47} +(1.13493 - 3.83561i) q^{48} -12.6454i q^{49} +(7.04854 + 0.564022i) q^{50} -3.00875i q^{51} +(-5.53554 - 8.77042i) q^{52} +(1.47153 + 2.88805i) q^{53} +(-0.953075 + 1.04482i) q^{54} +(0.154557 + 0.127870i) q^{55} +(7.17049 + 10.2834i) q^{56} +(-1.06393 - 1.06393i) q^{57} +(-5.61510 - 7.02655i) q^{58} +(11.4383 + 8.31042i) q^{59} +(-4.04172 - 1.91428i) q^{60} +(-9.26103 + 6.72853i) q^{61} +(-5.67708 - 1.56061i) q^{62} +(-0.693367 - 4.37774i) q^{63} +(-7.50676 - 2.76560i) q^{64} +(-10.6419 + 4.60469i) q^{65} +(-0.0627215 - 0.110279i) q^{66} +(1.84223 + 0.938661i) q^{67} +(-6.00467 - 0.392675i) q^{68} +(-2.01571 + 0.654945i) q^{69} +(12.5948 - 6.15026i) q^{70} +(-2.37497 - 0.771676i) q^{71} +(1.96080 + 2.03845i) q^{72} +(1.16183 - 7.33551i) q^{73} +(4.70067 - 10.3766i) q^{74} +(-2.81073 + 4.13519i) q^{75} +(-2.26218 + 1.98447i) q^{76} +(0.392723 + 0.0622012i) q^{77} +(7.32585 - 0.336411i) q^{78} +(-0.395606 + 1.21755i) q^{79} +(-4.34789 + 7.81638i) q^{80} +(-0.309017 - 0.951057i) q^{81} +(5.07295 + 13.4755i) q^{82} +(1.03260 - 2.02659i) q^{83} +(-8.82732 + 0.812434i) q^{84} +(-1.46786 + 6.56569i) q^{85} +(-3.16858 - 15.3962i) q^{86} +(6.28180 - 0.994939i) q^{87} +(-0.228273 + 0.110783i) q^{88} +(7.66814 + 10.5543i) q^{89} +(2.58953 - 1.81503i) q^{90} +(-13.5098 + 18.5947i) q^{91} +(1.04403 + 4.10831i) q^{92} +(2.94384 - 2.94384i) q^{93} +(1.20871 - 10.8258i) q^{94} +(1.80265 + 2.84076i) q^{95} +(4.32411 - 3.64720i) q^{96} +(3.93972 - 2.00739i) q^{97} +(9.83679 - 14.9349i) q^{98} +0.0897089 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

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more