LMFDB - Embedded newform 750.2.o.b.229.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [750,2,Mod(19,750)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(750, base_ring=CyclotomicField(50))

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

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

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

chi := DirichletCharacter("750.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 750 = 2 \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	750.o (of order $50$, degree $20$, 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:	$5.98878015160$
Analytic rank:	$0$
Dimension:	$280$
Relative dimension:	$14$ over $\Q(\zeta_{50})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{50}]$

Embedding invariants

Embedding label			229.4
Character	$\chi$	$=$	750.229
Dual form			750.2.o.b.619.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.248690 - 0.968583i) q^{2} +(0.982287 - 0.187381i) q^{3} +(-0.876307 + 0.481754i) q^{4} +(0.522565 - 2.17415i) q^{5} +(-0.425779 - 0.904827i) q^{6} +(-0.991752 + 1.36503i) q^{7} +(0.684547 + 0.728969i) q^{8} +(0.929776 - 0.368125i) q^{9} +O(q^{10})$	\(q+(-0.248690 - 0.968583i) q^{2} +(0.982287 - 0.187381i) q^{3} +(-0.876307 + 0.481754i) q^{4} +(0.522565 - 2.17415i) q^{5} +(-0.425779 - 0.904827i) q^{6} +(-0.991752 + 1.36503i) q^{7} +(0.684547 + 0.728969i) q^{8} +(0.929776 - 0.368125i) q^{9} +(-2.23580 + 0.0345414i) q^{10} +(2.10639 - 0.540829i) q^{11} +(-0.770513 + 0.637424i) q^{12} +(1.70311 + 4.30157i) q^{13} +(1.56878 + 0.621125i) q^{14} +(0.105914 - 2.23356i) q^{15} +(0.535827 - 0.844328i) q^{16} +(3.82580 - 6.95911i) q^{17} +(-0.587785 - 0.809017i) q^{18} +(1.33073 - 6.97594i) q^{19} +(0.589477 + 2.15697i) q^{20} +(-0.718404 + 1.52669i) q^{21} +(-1.04768 - 1.90572i) q^{22} +(3.06920 + 0.193098i) q^{23} +(0.809017 + 0.587785i) q^{24} +(-4.45385 - 2.27227i) q^{25} +(3.74288 - 2.71936i) q^{26} +(0.844328 - 0.535827i) q^{27} +(0.211471 - 1.67396i) q^{28} +(-7.25457 - 0.916466i) q^{29} +(-2.18973 + 0.452877i) q^{30} +(-3.42840 - 1.88478i) q^{31} +(-0.951057 - 0.309017i) q^{32} +(1.96774 - 0.925948i) q^{33} +(-7.69191 - 1.97495i) q^{34} +(2.44952 + 2.86953i) q^{35} +(-0.637424 + 0.770513i) q^{36} +(1.92551 + 1.22196i) q^{37} +(-7.08772 + 0.445922i) q^{38} +(2.47898 + 3.90625i) q^{39} +(1.94261 - 1.10737i) q^{40} +(0.320264 + 5.09044i) q^{41} +(1.65738 + 0.316163i) q^{42} +(-1.21012 + 0.393192i) q^{43} +(-1.58530 + 1.48869i) q^{44} +(-0.314489 - 2.21384i) q^{45} +(-0.576248 - 3.02080i) q^{46} +(4.77375 - 5.08353i) q^{47} +(0.368125 - 0.929776i) q^{48} +(1.28339 + 3.94985i) q^{49} +(-1.09325 + 4.87902i) q^{50} +(2.45403 - 7.55273i) q^{51} +(-3.56475 - 2.94902i) q^{52} +(-9.39033 - 4.41876i) q^{53} +(-0.728969 - 0.684547i) q^{54} +(-0.0751176 - 4.86223i) q^{55} +(-1.67396 + 0.211471i) q^{56} -7.10174i q^{57} +(0.916466 + 7.25457i) q^{58} +(7.59591 + 9.18187i) q^{59} +(0.983212 + 2.00831i) q^{60} +(0.0187279 - 0.297671i) q^{61} +(-0.972957 + 3.78942i) q^{62} +(-0.419607 + 1.63426i) q^{63} +(-0.0627905 + 0.998027i) q^{64} +(10.2422 - 1.45497i) q^{65} +(-1.38621 - 1.67565i) q^{66} +(-1.41679 - 11.2150i) q^{67} +7.94141i q^{68} +(3.05102 - 0.385433i) q^{69} +(2.17021 - 3.08619i) q^{70} +(1.55801 + 1.46307i) q^{71} +(0.904827 + 0.425779i) q^{72} +(-2.81321 - 2.32729i) q^{73} +(0.704719 - 2.16890i) q^{74} +(-4.80074 - 1.39745i) q^{75} +(2.19456 + 6.75415i) q^{76} +(-1.35077 + 3.41166i) q^{77} +(3.16703 - 3.37254i) q^{78} +(1.38816 + 7.27699i) q^{79} +(-1.55569 - 1.60618i) q^{80} +(0.728969 - 0.684547i) q^{81} +(4.85087 - 1.57614i) q^{82} +(15.1645 + 2.89278i) q^{83} +(-0.105945 - 1.68394i) q^{84} +(-13.1309 - 11.9545i) q^{85} +(0.681784 + 1.07432i) q^{86} +(-7.29780 + 0.459139i) q^{87} +(1.83617 + 1.16527i) q^{88} +(-11.0470 + 13.3536i) q^{89} +(-2.06608 + 0.855169i) q^{90} +(-7.56084 - 1.94129i) q^{91} +(-2.78258 + 1.30939i) q^{92} +(-3.72085 - 1.20898i) q^{93} +(-6.11100 - 3.35955i) q^{94} +(-14.4714 - 6.53860i) q^{95} +(-0.992115 - 0.125333i) q^{96} +(0.796645 - 6.30609i) q^{97} +(3.50660 - 2.22535i) q^{98} +(1.75938 - 1.27826i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 280 q+O(q^{10}) $ 280 * q	$ 280 q - 10 q^{11} - 20 q^{13} + 30 q^{17} + 10 q^{19} + 20 q^{22} + 60 q^{23} + 70 q^{24} + 20 q^{25} + 20 q^{29} + 10 q^{30} + 20 q^{31} + 20 q^{33} - 10 q^{34} + 30 q^{35} - 20 q^{37} + 90 q^{38} - 40 q^{41} - 10 q^{46} - 100 q^{47} + 120 q^{49} - 20 q^{50} - 30 q^{51} + 80 q^{52} - 30 q^{53} - 10 q^{55} + 30 q^{58} + 20 q^{59} + 60 q^{61} - 50 q^{62} - 10 q^{63} + 20 q^{65} + 40 q^{66} + 50 q^{67} + 10 q^{69} + 20 q^{70} + 80 q^{71} - 20 q^{73} + 80 q^{75} - 30 q^{76} - 100 q^{77} - 100 q^{79} + 100 q^{82} + 30 q^{83} - 20 q^{86} - 10 q^{87} - 60 q^{89} - 10 q^{90} + 70 q^{91} - 120 q^{92} + 50 q^{93} + 30 q^{94} - 20 q^{95} + 10 q^{97} + 40 q^{98} + 20 q^{99}+O(q^{100}) $ 280 * q - 10 * q^11 - 20 * q^13 + 30 * q^17 + 10 * q^19 + 20 * q^22 + 60 * q^23 + 70 * q^24 + 20 * q^25 + 20 * q^29 + 10 * q^30 + 20 * q^31 + 20 * q^33 - 10 * q^34 + 30 * q^35 - 20 * q^37 + 90 * q^38 - 40 * q^41 - 10 * q^46 - 100 * q^47 + 120 * q^49 - 20 * q^50 - 30 * q^51 + 80 * q^52 - 30 * q^53 - 10 * q^55 + 30 * q^58 + 20 * q^59 + 60 * q^61 - 50 * q^62 - 10 * q^63 + 20 * q^65 + 40 * q^66 + 50 * q^67 + 10 * q^69 + 20 * q^70 + 80 * q^71 - 20 * q^73 + 80 * q^75 - 30 * q^76 - 100 * q^77 - 100 * q^79 + 100 * q^82 + 30 * q^83 - 20 * q^86 - 10 * q^87 - 60 * q^89 - 10 * q^90 + 70 * q^91 - 120 * q^92 + 50 * q^93 + 30 * q^94 - 20 * q^95 + 10 * q^97 + 40 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{21}{50}\right)$	$1$

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 $

$2$	−0.248690	−	0.968583i	−0.175850	−	0.684892i
$2$	−0.248690	−	0.968583i	−0.175850	−	0.684892i
$3$	0.982287	−	0.187381i	0.567124	−	0.108185i
$3$	0.982287	−	0.187381i	0.567124	−	0.108185i
$4$	−0.876307	+	0.481754i	−0.438153	+	0.240877i
$5$	0.522565	−	2.17415i	0.233698	−	0.972309i
$5$	0.522565	−	2.17415i	0.233698	−	0.972309i
$6$	−0.425779	−	0.904827i	−0.173824	−	0.369394i
$7$	−0.991752	+	1.36503i	−0.374847	+	0.515933i	−0.954210	−	0.299137i	$-0.903301\pi$
$7$	−0.991752	+	1.36503i	−0.374847	+	0.515933i	0.579363	+	0.815070i	$0.303301\pi$
$8$	0.684547	+	0.728969i	0.242024	+	0.257729i
$9$	0.929776	−	0.368125i	0.309925	−	0.122708i
$10$	−2.23580	+	0.0345414i	−0.707022	+	0.0109229i
$11$	2.10639	−	0.540829i	0.635101	−	0.163066i	0.0826058	−	0.996582i	$-0.473676\pi$
$11$	2.10639	−	0.540829i	0.635101	−	0.163066i	0.552495	+	0.833516i	$0.313676\pi$
$12$	−0.770513	+	0.637424i	−0.222428	+	0.184008i
$13$	1.70311	+	4.30157i	0.472359	+	1.19304i	0.949374	+	0.314147i	$0.101718\pi$
$13$	1.70311	+	4.30157i	0.472359	+	1.19304i	−0.477016	+	0.878895i	$0.658282\pi$
$14$	1.56878	+	0.621125i	0.419275	+	0.166003i
$15$	0.105914	−	2.23356i	0.0273469	−	0.576702i
$16$	0.535827	−	0.844328i	0.133957	−	0.211082i
$17$	3.82580	−	6.95911i	0.927893	−	1.68783i	0.227897	−	0.973685i	$-0.426815\pi$
$17$	3.82580	−	6.95911i	0.927893	−	1.68783i	0.699997	−	0.714146i	$-0.253185\pi$
$18$	−0.587785	−	0.809017i	−0.138542	−	0.190687i
$19$	1.33073	−	6.97594i	0.305291	−	1.60039i	−0.417070	−	0.908875i	$-0.636943\pi$
$19$	1.33073	−	6.97594i	0.305291	−	1.60039i	0.722360	−	0.691517i	$-0.243057\pi$
$20$	0.589477	+	2.15697i	0.131811	+	0.482313i
$21$	−0.718404	+	1.52669i	−0.156769	+	0.333150i
$22$	−1.04768	−	1.90572i	−0.223365	−	0.406300i
$23$	3.06920	+	0.193098i	0.639972	+	0.0402636i	0.379462	−	0.925207i	$-0.376109\pi$
$23$	3.06920	+	0.193098i	0.639972	+	0.0402636i	0.260510	+	0.965471i	$0.416109\pi$
$24$	0.809017	+	0.587785i	0.165140	+	0.119981i
$25$	−4.45385	−	2.27227i	−0.890770	−	0.454454i
$26$	3.74288	−	2.71936i	0.734040	−	0.533311i
$27$	0.844328	−	0.535827i	0.162491	−	0.103120i
$28$	0.211471	−	1.67396i	0.0399643	−	0.316350i
$29$	−7.25457	−	0.916466i	−1.34714	−	0.170183i	−0.581550	−	0.813511i	$-0.697553\pi$
$29$	−7.25457	−	0.916466i	−1.34714	−	0.170183i	−0.765591	+	0.643328i	$0.777553\pi$
$30$	−2.18973	+	0.452877i	−0.399788	+	0.0826836i
$31$	−3.42840	−	1.88478i	−0.615759	−	0.338516i	0.143162	−	0.989699i	$-0.454273\pi$
$31$	−3.42840	−	1.88478i	−0.615759	−	0.338516i	−0.758921	+	0.651183i	$0.774273\pi$
$32$	−0.951057	−	0.309017i	−0.168125	−	0.0546270i
$33$	1.96774	−	0.925948i	0.342540	−	0.161187i
$34$	−7.69191	−	1.97495i	−1.31915	−	0.338701i
$35$	2.44952	+	2.86953i	0.414045	+	0.485040i
$36$	−0.637424	+	0.770513i	−0.106237	+	0.128419i
$37$	1.92551	+	1.22196i	0.316551	+	0.200890i	0.684604	−	0.728916i	$-0.259975\pi$
$37$	1.92551	+	1.22196i	0.316551	+	0.200890i	−0.368052	+	0.929805i	$0.619975\pi$
$38$	−7.08772	+	0.445922i	−1.14978	+	0.0723380i
$39$	2.47898	+	3.90625i	0.396955	+	0.625500i
$40$	1.94261	−	1.10737i	0.307153	−	0.175091i
$41$	0.320264	+	5.09044i	0.0500168	+	0.794994i	0.940461	+	0.339902i	$0.110394\pi$
$41$	0.320264	+	5.09044i	0.0500168	+	0.794994i	−0.890444	+	0.455092i	$0.849606\pi$
$42$	1.65738	+	0.316163i	0.255740	+	0.0487850i
$43$	−1.21012	+	0.393192i	−0.184542	+	0.0599612i	−0.399830	−	0.916589i	$-0.630931\pi$
$43$	−1.21012	+	0.393192i	−0.184542	+	0.0599612i	0.215288	+	0.976551i	$0.430931\pi$
$44$	−1.58530	+	1.48869i	−0.238993	+	0.224429i
$45$	−0.314489	−	2.21384i	−0.0468813	−	0.330020i
$46$	−0.576248	−	3.02080i	−0.0849631	−	0.445392i
$47$	4.77375	−	5.08353i	0.696323	−	0.741509i	−0.279482	−	0.960151i	$-0.590163\pi$
$47$	4.77375	−	5.08353i	0.696323	−	0.741509i	0.975805	+	0.218642i	$0.0701627\pi$
$48$	0.368125	−	0.929776i	0.0531342	−	0.134202i
$49$	1.28339	+	3.94985i	0.183341	+	0.564265i
$50$	−1.09325	+	4.87902i	−0.154609	+	0.689997i
$51$	2.45403	−	7.55273i	0.343633	−	1.05759i
$52$	−3.56475	−	2.94902i	−0.494342	−	0.408955i
$53$	−9.39033	−	4.41876i	−1.28986	−	0.606963i	−0.346289	−	0.938128i	$-0.612558\pi$
$53$	−9.39033	−	4.41876i	−1.28986	−	0.606963i	−0.943573	+	0.331165i	$0.892558\pi$
$54$	−0.728969	−	0.684547i	−0.0992001	−	0.0931551i
$55$	−0.0751176	−	4.86223i	−0.0101289	−	0.655623i
$56$	−1.67396	+	0.211471i	−0.223693	+	0.0282590i
$57$		−	7.10174i		−	0.940648i
$58$	0.916466	+	7.25457i	0.120338	+	0.952572i
$59$	7.59591	+	9.18187i	0.988903	+	1.19538i	0.980721	+	0.195412i	$0.0626043\pi$
$59$	7.59591	+	9.18187i	0.988903	+	1.19538i	0.00818143	+	0.999967i	$0.497396\pi$
$60$	0.983212	+	2.00831i	0.126932	+	0.259271i
$61$	0.0187279	−	0.297671i	0.00239786	−	0.0381128i	−0.996646	−	0.0818355i	$-0.973922\pi$
$61$	0.0187279	−	0.297671i	0.00239786	−	0.0381128i	0.999044	+	0.0437227i	$0.0139218\pi$
$62$	−0.972957	+	3.78942i	−0.123566	+	0.481256i
$63$	−0.419607	+	1.63426i	−0.0528655	+	0.205898i
$64$	−0.0627905	+	0.998027i	−0.00784881	+	0.124753i
$65$	10.2422	−	1.45497i	1.27039	−	0.180467i
$66$	−1.38621	−	1.67565i	−0.170631	−	0.206258i
$67$	−1.41679	−	11.2150i	−0.173088	−	1.37013i	−0.804161	−	0.594411i	$-0.797385\pi$
$67$	−1.41679	−	11.2150i	−0.173088	−	1.37013i	0.631073	−	0.775723i	$-0.282615\pi$
$68$			7.94141i			0.963037i
$69$	3.05102	−	0.385433i	0.367299	−	0.0464007i
$70$	2.17021	−	3.08619i	0.259390	−	0.368870i
$71$	1.55801	+	1.46307i	0.184901	+	0.173634i	0.771470	−	0.636265i	$-0.219522\pi$
$71$	1.55801	+	1.46307i	0.184901	+	0.173634i	−0.586569	+	0.809899i	$0.699522\pi$
$72$	0.904827	+	0.425779i	0.106635	+	0.0501786i
$73$	−2.81321	−	2.32729i	−0.329261	−	0.272388i	0.458074	−	0.888914i	$-0.348540\pi$
$73$	−2.81321	−	2.32729i	−0.329261	−	0.272388i	−0.787335	+	0.616526i	$0.788540\pi$
$74$	0.704719	−	2.16890i	0.0819219	−	0.252130i
$75$	−4.80074	−	1.39745i	−0.554342	−	0.161364i
$76$	2.19456	+	6.75415i	0.251733	+	0.774754i
$77$	−1.35077	+	3.41166i	−0.153935	+	0.388794i
$78$	3.16703	−	3.37254i	0.358595	−	0.381865i
$79$	1.38816	+	7.27699i	0.156180	+	0.818725i	0.971013	+	0.239029i	$0.0768289\pi$
$79$	1.38816	+	7.27699i	0.156180	+	0.818725i	−0.814832	+	0.579697i	$0.803171\pi$
$80$	−1.55569	−	1.60618i	−0.173932	−	0.179577i
$81$	0.728969	−	0.684547i	0.0809965	−	0.0760608i
$82$	4.85087	−	1.57614i	0.535689	−	0.174056i
$83$	15.1645	+	2.89278i	1.66452	+	0.317524i	0.931791	−	0.362996i	$-0.118246\pi$
$83$	15.1645	+	2.89278i	1.66452	+	0.317524i	0.732729	+	0.680520i	$0.238246\pi$
$84$	−0.105945	−	1.68394i	−0.0115595	−	0.183733i
$85$	−13.1309	−	11.9545i	−1.42425	−	1.29664i
$86$	0.681784	+	1.07432i	0.0735187	+	0.115847i
$87$	−7.29780	+	0.459139i	−0.782407	+	0.0492249i
$88$	1.83617	+	1.16527i	0.195737	+	0.124218i
$89$	−11.0470	+	13.3536i	−1.17098	+	1.41548i	−0.280865	+	0.959747i	$0.590621\pi$
$89$	−11.0470	+	13.3536i	−1.17098	+	1.41548i	−0.890118	+	0.455729i	$0.849379\pi$
$90$	−2.06608	+	0.855169i	−0.217784	+	0.0901427i
$91$	−7.56084	−	1.94129i	−0.792592	−	0.203503i
$92$	−2.78258	+	1.30939i	−0.290105	+	0.136513i
$93$	−3.72085	−	1.20898i	−0.385834	−	0.125365i
$94$	−6.11100	−	3.35955i	−0.630302	−	0.346511i
$95$	−14.4714	−	6.53860i	−1.48473	−	0.670846i
$96$	−0.992115	−	0.125333i	−0.101257	−	0.0127918i
$97$	0.796645	−	6.30609i	0.0808870	−	0.640287i	−0.898598	−	0.438772i	$-0.855414\pi$
$97$	0.796645	−	6.30609i	0.0808870	−	0.640287i	0.979485	−	0.201515i	$-0.0645864\pi$
$98$	3.50660	−	2.22535i	0.354220	−	0.224795i
$99$	1.75938	−	1.27826i	0.176824	−	0.128470i
$100$	4.99761	−	0.154455i	0.499761	−	0.0154455i
$101$	3.27905	+	2.38237i	0.326277	+	0.237054i	0.738849	−	0.673871i	$-0.235369\pi$
$101$	3.27905	+	2.38237i	0.326277	+	0.237054i	−0.412572	+	0.910925i	$0.635369\pi$
$102$	−7.92574	−	0.498645i	−0.784765	−	0.0493732i
$103$	6.34740	+	11.5459i	0.625428	+	1.13765i	0.979311	+	0.202360i	$0.0648610\pi$
$103$	6.34740	+	11.5459i	0.625428	+	1.13765i	−0.353883	+	0.935290i	$0.615139\pi$
$104$	−1.96985	+	4.18615i	−0.193160	+	0.410485i
$105$	2.94383	+	2.35971i	0.287289	+	0.230284i
$106$	−1.94465	+	10.1942i	−0.188881	+	0.990150i
$107$	5.32535	+	7.32971i	0.514821	+	0.708590i	0.984723	−	0.174129i	$-0.0557109\pi$
$107$	5.32535	+	7.32971i	0.514821	+	0.708590i	−0.469902	+	0.882718i	$0.655711\pi$
$108$	−0.481754	+	0.876307i	−0.0463568	+	0.0843226i
$109$	−1.08637	+	1.71185i	−0.104056	+	0.163965i	−0.892366	−	0.451312i	$-0.850956\pi$
$109$	−1.08637	+	1.71185i	−0.104056	+	0.163965i	0.788311	+	0.615278i	$0.210956\pi$
$110$	−4.69079	+	1.28194i	−0.447249	+	0.122229i
$111$	2.12037	+	0.839515i	0.201257	+	0.0796832i
$112$	0.621125	+	1.56878i	0.0586908	+	0.148236i
$113$	12.9270	−	10.6942i	1.21607	−	1.00602i	0.216515	−	0.976279i	$-0.430531\pi$
$113$	12.9270	−	10.6942i	1.21607	−	1.00602i	0.999558	−	0.0297435i	$-0.00946905\pi$
$114$	−6.87862	+	1.76613i	−0.644242	+	0.165413i
$115$	2.02368	−	6.57199i	0.188709	−	0.612841i
$116$	6.79874	−	2.69181i	0.631247	−	0.249929i
$117$	3.16703	+	3.37254i	0.292792	+	0.311792i
$118$	7.00438	−	9.64071i	0.644806	−	0.887499i
$119$	5.70514	+	12.1240i	0.522989	+	1.11141i
$120$	1.70070	−	1.45177i	0.155252	−	0.132528i
$121$	−5.49499	+	3.02089i	−0.499544	+	0.274627i
$122$	−0.292976	+	0.0558882i	−0.0265248	+	0.00505988i
$123$	1.26845	+	4.94027i	0.114372	+	0.445449i
$124$	3.91233			0.351338
$125$	−7.26768	+	8.49593i	−0.650041	+	0.759899i
$126$	1.68727			0.150314
$127$	−1.54829	−	6.03021i	−0.137389	−	0.535094i	−0.999593	−	0.0285331i	$-0.990916\pi$
$127$	−1.54829	−	6.03021i	−0.137389	−	0.535094i	0.862204	−	0.506561i	$-0.169084\pi$
$128$	0.982287	−	0.187381i	0.0868227	−	0.0165623i
$129$	−1.11501	+	0.612982i	−0.0981711	+	0.0539700i
$130$	−3.95640	−	9.55863i	−0.347000	−	0.838348i
$131$	−4.75180	−	10.0981i	−0.415167	−	0.882275i	−0.997590	−	0.0693888i	$-0.977895\pi$
$131$	−4.75180	−	10.0981i	−0.415167	−	0.882275i	0.582423	−	0.812886i	$-0.302105\pi$
$132$	−1.27826	+	1.75938i	−0.111259	+	0.153134i
$133$	8.20261	+	8.73490i	0.711257	+	0.757412i
$134$	−10.5104	+	4.16134i	−0.907956	+	0.359485i
$135$	−0.723751	−	2.11570i	−0.0622906	−	0.182090i
$136$	7.69191	−	1.97495i	0.659576	−	0.169350i
$137$	0.208050	−	0.172114i	0.0177749	−	0.0147047i	−0.628494	−	0.777814i	$-0.716328\pi$
$137$	0.208050	−	0.172114i	0.0177749	−	0.0147047i	0.646269	+	0.763110i	$0.276328\pi$
$138$	−1.13208	−	2.85931i	−0.0963692	−	0.243401i
$139$	8.00899	+	3.17098i	0.679313	+	0.268959i	0.682339	−	0.731036i	$-0.260963\pi$
$139$	8.00899	+	3.17098i	0.679313	+	0.268959i	−0.00302529	+	0.999995i	$0.500963\pi$
$140$	−3.52894	−	1.33452i	−0.298250	−	0.112788i
$141$	3.73664	−	5.88800i	0.314682	−	0.495859i
$142$	1.02964	−	1.87291i	0.0864055	−	0.157171i
$143$	5.91384	+	8.13970i	0.494540	+	0.680676i
$144$	0.187381	−	0.982287i	0.0156151	−	0.0818573i
$145$	−5.78352	+	15.2936i	−0.480295	+	1.27007i
$146$	−1.55455	+	3.30360i	−0.128656	+	0.273408i
$147$	2.00078	+	3.63941i	0.165022	+	0.300173i
$148$	−2.27602	−	0.143195i	−0.187088	−	0.0117706i
$149$	1.41479	+	1.02791i	0.115904	+	0.0842094i	0.644227	−	0.764834i	$-0.277179\pi$
$149$	1.41479	+	1.02791i	0.115904	+	0.0842094i	−0.528323	+	0.849043i	$0.677179\pi$
$150$	−0.159652	+	4.99745i	−0.0130356	+	0.408040i
$151$	−6.74197	+	4.89833i	−0.548654	+	0.398620i	−0.827289	−	0.561777i	$-0.810118\pi$
$151$	−6.74197	+	4.89833i	−0.548654	+	0.398620i	0.278635	+	0.960397i	$0.410118\pi$
$152$	5.99619	−	3.80530i	0.486355	−	0.308651i
$153$	0.995322	−	7.87879i	0.0804670	−	0.636962i
$154$	3.64040	+	0.459889i	0.293351	+	0.0370589i
$155$	−5.88935	+	6.46894i	−0.473044	+	0.519598i
$156$	−4.05420	−	2.22881i	−0.324596	−	0.178448i
$157$	4.81808	+	1.56549i	0.384525	+	0.124940i	0.494899	−	0.868950i	$-0.335205\pi$
$157$	4.81808	+	1.56549i	0.384525	+	0.124940i	−0.110374	+	0.993890i	$0.535205\pi$
$158$	6.70315	−	3.15426i	0.533274	−	0.250940i
$159$	−10.0520	−	2.58091i	−0.797175	−	0.204680i
$160$	−1.16884	+	1.90626i	−0.0924048	+	0.150703i
$161$	−3.30747	+	3.99804i	−0.260665	+	0.315090i
$162$	−0.844328	−	0.535827i	−0.0663367	−	0.0420985i
$163$	−5.17317	+	0.325468i	−0.405194	+	0.0254926i	−0.264080	−	0.964501i	$-0.585068\pi$
$163$	−5.17317	+	0.325468i	−0.405194	+	0.0254926i	−0.141114	+	0.989993i	$0.545068\pi$
$164$	−2.73299	−	4.30650i	−0.213411	−	0.336281i
$165$	−0.984878	−	4.76203i	−0.0766726	−	0.370723i
$166$	−0.969357	−	15.4075i	−0.0752367	−	1.19585i
$167$	−14.2401	−	2.71645i	−1.10194	−	0.210205i	−0.395838	−	0.918320i	$-0.629546\pi$
$167$	−14.2401	−	2.71645i	−1.10194	−	0.210205i	−0.706097	+	0.708115i	$0.749546\pi$
$168$	−1.60469	+	0.521395i	−0.123804	+	0.0402265i
$169$	−6.12634	+	5.75302i	−0.471257	+	0.442540i
$170$	−8.31336	+	15.6913i	−0.637605	+	1.20347i
$171$	−1.33073	−	6.97594i	−0.101764	−	0.533464i
$172$	0.871015	−	0.927537i	0.0664143	−	0.0707240i
$173$	−6.81607	+	17.2154i	−0.518216	+	1.30886i	0.401349	+	0.915925i	$0.368542\pi$
$173$	−6.81607	+	17.2154i	−0.518216	+	1.30886i	−0.919565	+	0.392939i	$0.871458\pi$
$174$	2.25960	+	6.95435i	0.171300	+	0.527208i
$175$	7.51883	−	3.82611i	0.568370	−	0.289227i
$176$	0.672024	−	2.06828i	0.0506557	−	0.155902i
$177$	9.18187	+	7.59591i	0.690152	+	0.570943i
$178$	15.6813	+	7.37908i	1.17537	+	0.553085i
$179$	−1.09426	−	1.02758i	−0.0817888	−	0.0768048i	0.642575	−	0.766223i	$-0.277866\pi$
$179$	−1.09426	−	1.02758i	−0.0817888	−	0.0768048i	−0.724364	+	0.689418i	$0.757866\pi$
$180$	1.34212	+	1.78850i	0.100035	+	0.133307i
$181$	−1.39331	+	0.176016i	−0.103564	+	0.0130832i	−0.176944	−	0.984221i	$-0.556621\pi$
$181$	−1.39331	+	0.176016i	−0.103564	+	0.0130832i	0.0733804	+	0.997304i	$0.476621\pi$
$182$			7.80608i			0.578625i
$183$	−0.0373818	−	0.295908i	−0.00276334	−	0.0218741i
$184$	1.96025	+	2.36953i	0.144511	+	0.174684i
$185$	3.66293	−	3.54778i	0.269304	−	0.260838i
$186$	−0.245657	+	3.90461i	−0.0180125	+	0.286300i
$187$	4.29495	−	16.7277i	0.314078	−	1.22325i
$188$	−1.73426	+	6.75450i	−0.126484	+	0.492623i
$189$	−0.105945	+	1.68394i	−0.00770633	+	0.122489i
$190$	−2.73429	+	15.6428i	−0.198367	+	1.13485i
$191$	6.15790	+	7.44363i	0.445570	+	0.538602i	0.944705	−	0.327923i	$-0.106349\pi$
$191$	6.15790	+	7.44363i	0.445570	+	0.538602i	−0.499134	+	0.866525i	$0.666349\pi$
$192$	0.125333	+	0.992115i	0.00904515	+	0.0715997i
$193$			18.7407i			1.34898i	0.738283	+	0.674491i	$0.235637\pi$
$193$			18.7407i			1.34898i	−0.738283	+	0.674491i	$0.764363\pi$
$194$	−6.30609	+	0.796645i	−0.452751	+	0.0571957i
$195$	9.78820	−	3.34841i	0.700947	−	0.239784i
$196$	−3.02750	−	2.84301i	−0.216250	−	0.203072i
$197$	23.2005	+	10.9173i	1.65297	+	0.777827i	0.999787	+	0.0206230i	$0.00656496\pi$
$197$	23.2005	+	10.9173i	1.65297	+	0.777827i	0.653179	+	0.757204i	$0.273435\pi$
$198$	−1.67565	−	1.38621i	−0.119083	−	0.0985140i
$199$	0.675257	−	2.07823i	0.0478677	−	0.147322i	−0.924266	−	0.381750i	$-0.875322\pi$
$199$	0.675257	−	2.07823i	0.0478677	−	0.147322i	0.972134	+	0.234428i	$0.0753217\pi$
$200$	−1.39246	−	4.80219i	−0.0984617	−	0.339566i
$201$	−3.49318	−	10.7509i	−0.246390	−	0.758310i
$202$	1.49205	−	3.76850i	0.104981	−	0.265151i
$203$	8.44574	−	8.99380i	0.592775	−	0.631241i
$204$	1.48807	+	7.80074i	0.104186	+	0.546161i
$205$	11.2347	+	1.96379i	0.784669	+	0.137157i
$206$	9.60461	−	9.01933i	0.669185	−	0.628407i
$207$	2.92475	−	0.950310i	0.203284	−	0.0660511i
$208$	4.54451	+	0.866912i	0.315105	+	0.0601095i
$209$	−0.969752	−	15.4138i	−0.0670792	−	1.06619i
$210$	1.55348	−	3.43818i	0.107200	−	0.237257i
$211$	2.77087	+	4.36619i	0.190754	+	0.300581i	0.926222	−	0.376979i	$-0.123037\pi$
$211$	2.77087	+	4.36619i	0.190754	+	0.300581i	−0.735467	+	0.677560i	$0.763037\pi$
$212$	10.3576	−	0.651643i	0.711360	−	0.0447550i
$213$	1.80456	+	1.14521i	0.123646	+	0.0784685i
$214$	5.77507	−	6.98086i	0.394776	−	0.477202i
$215$	0.222492	+	2.83645i	0.0151738	+	0.193444i
$216$	0.968583	+	0.248690i	0.0659037	+	0.0169212i
$217$	5.97290	−	2.81064i	0.405467	−	0.190798i
$218$	1.92824	+	0.626522i	0.130597	+	0.0424335i
$219$	−3.19947	−	1.75892i	−0.216200	−	0.118857i
$220$	2.40822	+	4.22461i	0.162362	+	0.284823i
$221$	36.4509	+	4.60482i	2.45195	+	0.309754i
$222$	0.285825	−	2.26254i	0.0191833	−	0.151851i
$223$	−7.04047	+	4.46802i	−0.471465	+	0.299201i	−0.750252	−	0.661152i	$-0.770068\pi$
$223$	−7.04047	+	4.46802i	−0.471465	+	0.299201i	0.278787	+	0.960353i	$0.410068\pi$
$224$	1.36503	−	0.991752i	0.0912049	−	0.0662642i
$225$	−4.97756	−	0.473130i	−0.331838	−	0.0315420i
$226$	−13.5730	−	9.86137i	−0.902863	−	0.655969i
$227$	17.9344	+	1.12834i	1.19035	+	0.0748902i	0.645577	−	0.763696i	$-0.276617\pi$
$227$	17.9344	+	1.12834i	1.19035	+	0.0748902i	0.544770	+	0.838586i	$0.316617\pi$
$228$	3.42129	+	6.22330i	0.226580	+	0.412148i
$229$	−12.2890	+	26.1154i	−0.812080	+	1.72576i	−0.133730	+	0.991018i	$0.542696\pi$
$229$	−12.2890	+	26.1154i	−0.812080	+	1.72576i	−0.678350	+	0.734739i	$0.737304\pi$
$230$	−6.86879	−	0.325714i	−0.452914	−	0.0214769i
$231$	−0.687564	+	3.60433i	−0.0452384	+	0.237148i
$232$	−4.29802	−	5.91572i	−0.282179	−	0.388386i
$233$	−7.69772	+	14.0021i	−0.504294	+	0.917308i	0.494546	+	0.869152i	$0.335334\pi$
$233$	−7.69772	+	14.0021i	−0.504294	+	0.917308i	−0.998840	+	0.0481561i	$0.984666\pi$
$234$	2.47898	−	3.90625i	0.162056	−	0.255359i
$235$	−8.55776	−	13.0353i	−0.558246	−	0.850331i
$236$	−11.0797	−	4.38678i	−0.721230	−	0.285555i
$237$	2.72714	+	6.88798i	0.177147	+	0.447422i
$238$	10.3243	−	8.54103i	0.669227	−	0.553633i
$239$	23.3360	−	5.99168i	1.50948	−	0.387569i	0.598876	−	0.800842i	$-0.295614\pi$
$239$	23.3360	−	5.99168i	1.50948	−	0.387569i	0.910607	+	0.413272i	$0.135614\pi$
$240$	−1.82910	−	1.28623i	−0.118068	−	0.0830256i
$241$	−17.1298	+	6.78218i	−1.10343	+	0.436878i	−0.848025	−	0.529956i	$-0.822208\pi$
$241$	−17.1298	+	6.78218i	−1.10343	+	0.436878i	−0.255404	+	0.966834i	$0.582208\pi$
$242$	4.29253	+	4.57108i	0.275935	+	0.293840i
$243$	0.587785	−	0.809017i	0.0377064	−	0.0518985i
$244$	0.126993	+	0.269873i	0.00812987	+	0.0172769i
$245$	9.25822	−	0.726216i	0.591486	−	0.0463962i
$246$	4.46961	−	2.45719i	0.284972	−	0.156665i
$247$	32.2739	−	6.15658i	2.05354	−	0.391734i
$248$	−0.972957	−	3.78942i	−0.0617828	−	0.240628i
$249$	15.4379			0.978340
$250$	10.0364	+	4.92650i	0.634759	+	0.311579i
$251$	−27.2309			−1.71880			−0.859401	−	0.511303i	$-0.829163\pi$
$251$	−27.2309			−1.71880			−0.859401	+	0.511303i	$0.829163\pi$
$252$	−0.419607	−	1.63426i	−0.0264327	−	0.102949i
$253$	6.56937	−	1.25317i	0.413013	−	0.0787864i
$254$	−5.45571	+	2.99930i	−0.342322	+	0.188193i
$255$	−15.1384	−	9.28222i	−0.948001	−	0.581275i
$256$	−0.425779	−	0.904827i	−0.0266112	−	0.0565517i
$257$	−7.41125	+	10.2007i	−0.462301	+	0.636303i	−0.974984	−	0.222275i	$-0.928652\pi$
$257$	−7.41125	+	10.2007i	−0.462301	+	0.636303i	0.512683	+	0.858578i	$0.328652\pi$
$258$	0.871015	+	0.927537i	0.0542270	+	0.0577459i
$259$	−3.57764	+	1.41649i	−0.222304	+	0.0880163i
$260$	−8.27441	+	6.20924i	−0.513157	+	0.385081i
$261$	−7.08251	+	1.81848i	−0.438396	+	0.112561i
$262$	−8.59912	+	7.11381i	−0.531256	+	0.439493i
$263$	−8.02823	−	20.2770i	−0.495042	−	1.25033i	−0.935744	−	0.352680i	$-0.885271\pi$
$263$	−8.02823	−	20.2770i	−0.495042	−	1.25033i	0.440702	−	0.897653i	$-0.354729\pi$
$264$	2.02200	+	0.800566i	0.124445	+	0.0492714i
$265$	−14.5141	+	18.1069i	−0.891594	+	1.11230i
$266$	6.42057	−	10.1172i	0.393670	−	0.620325i
$267$	−8.34916	+	15.1871i	−0.510960	+	0.929433i
$268$	6.64442	+	9.14526i	0.405873	+	0.558636i
$269$	−1.61938	+	8.48911i	−0.0987356	+	0.517590i	0.898215	+	0.439556i	$0.144864\pi$
$269$	−1.61938	+	8.48911i	−0.0987356	+	0.517590i	−0.996951	+	0.0780340i	$0.975136\pi$
$270$	−1.86924	+	1.22717i	−0.113758	+	0.0746830i
$271$	−8.22307	+	17.4749i	−0.499516	+	1.06153i	0.483047	+	0.875594i	$0.339530\pi$
$271$	−8.22307	+	17.4749i	−0.499516	+	1.06153i	−0.982563	+	0.185931i	$0.940470\pi$
$272$	−3.82580	−	6.95911i	−0.231973	−	0.421958i
$273$	−7.79068	−	0.490148i	−0.471513	−	0.0296651i
$274$	−0.218447	−	0.158711i	−0.0131968	−	0.00958807i
$275$	−10.6105	−	2.37751i	−0.639835	−	0.143369i
$276$	−2.48794	+	1.80760i	−0.149757	+	0.108805i
$277$	−23.6872	+	15.0324i	−1.42323	+	0.903207i	−0.999996	−	0.00281577i	$-0.999104\pi$
$277$	−23.6872	+	15.0324i	−1.42323	+	0.903207i	−0.423230	+	0.906022i	$0.639104\pi$
$278$	1.07961	−	8.54596i	0.0647505	−	0.512553i
$279$	−3.88148	−	0.490345i	−0.232378	−	0.0293562i
$280$	−0.414986	+	3.74996i	−0.0248002	+	0.224103i
$281$	−23.1407	−	12.7217i	−1.38046	−	0.758914i	−0.393415	−	0.919361i	$-0.628706\pi$
$281$	−23.1407	−	12.7217i	−1.38046	−	0.758914i	−0.987044	+	0.160447i	$0.948706\pi$
$282$	−6.63228	−	2.15496i	−0.394946	−	0.128326i
$283$	11.3713	−	5.35093i	0.675954	−	0.318080i	−0.0569841	−	0.998375i	$-0.518148\pi$
$283$	11.3713	−	5.35093i	0.675954	−	0.318080i	0.732938	+	0.680295i	$0.238148\pi$
$284$	−2.07013	−	0.531519i	−0.122840	−	0.0315398i
$285$	−15.4402	−	3.71112i	−0.914600	−	0.219828i
$286$	6.41327	−	7.75231i	0.379224	−	0.458404i
$287$	−7.26623	−	4.61129i	−0.428912	−	0.272196i
$288$	−0.998027	+	0.0627905i	−0.0588093	+	0.00369997i
$289$	−24.6834	−	38.8948i	−1.45196	−	2.28793i
$290$	16.2514	+	1.79845i	0.954317	+	0.105609i
$291$	−0.399110	−	6.34367i	−0.0233962	−	0.371872i
$292$	3.58641	+	0.684144i	0.209879	+	0.0400365i
$293$	2.15790	−	0.701143i	0.126066	−	0.0409612i	−0.245305	−	0.969446i	$-0.578888\pi$
$293$	2.15790	−	0.701143i	0.126066	−	0.0409612i	0.371370	+	0.928485i	$0.378888\pi$
$294$	3.02750	−	2.84301i	0.176567	−	0.165808i
$295$	23.9321	−	11.7165i	1.39338	−	0.682162i
$296$	0.427327	+	2.24012i	0.0248379	+	0.130205i
$297$	1.48869	−	1.58530i	0.0863828	−	0.0919883i
$298$	0.643769	−	1.62597i	0.0372925	−	0.0941901i
$299$	4.39657	+	13.5312i	0.254260	+	0.782532i
$300$	4.88015	−	1.08818i	0.281756	−	0.0628260i
$301$	0.663421	−	2.04180i	0.0382389	−	0.117687i
$302$	6.42110	+	5.31199i	0.369493	+	0.305671i
$303$	3.66738	+	1.72574i	0.210685	+	0.0991410i
$304$	−5.17694	−	4.86147i	−0.296918	−	0.278825i
$305$	−0.637394	−	0.196270i	−0.0364971	−	0.0112384i
$306$	−7.87879	+	0.995322i	−0.450400	+	0.0568988i
$307$			8.26773i			0.471864i	0.971770	+	0.235932i	$0.0758143\pi$
$307$			8.26773i			0.471864i	−0.971770	+	0.235932i	$0.924186\pi$
$308$	−0.459889	−	3.64040i	−0.0262046	−	0.207431i
$309$	8.39845	+	10.1520i	0.477771	+	0.577526i
$310$	7.73033	+	4.09557i	0.439053	+	0.232613i
$311$	0.351042	−	5.57966i	0.0199058	−	0.316393i	−0.975456	−	0.220193i	$-0.929331\pi$
$311$	0.351042	−	5.57966i	0.0199058	−	0.316393i	0.995362	−	0.0961999i	$-0.0306688\pi$
$312$	−1.15055	+	4.48111i	−0.0651373	+	0.253693i
$313$	−3.11996	+	12.1515i	−0.176351	+	0.686841i	0.817482	+	0.575954i	$0.195369\pi$
$313$	−3.11996	+	12.1515i	−0.176351	+	0.686841i	−0.993833	+	0.110887i	$0.964631\pi$
$314$	0.318099	−	5.05603i	0.0179513	−	0.285329i
$315$	3.33386	+	1.76630i	0.187841	+	0.0995195i
$316$	−4.72217	−	5.70812i	−0.265643	−	0.321107i
$317$	−2.55466	−	20.2222i	−0.143484	−	1.13579i	−0.885244	−	0.465128i	$-0.846008\pi$
$317$	−2.55466	−	20.2222i	−0.143484	−	1.13579i	0.741760	−	0.670666i	$-0.233992\pi$
$318$			10.3780i			0.581972i
$319$	−15.7766	+	1.99305i	−0.883321	+	0.111589i
$320$	2.13705	+	0.658050i	0.119465	+	0.0367861i
$321$	6.60447	+	6.20201i	0.368626	+	0.346162i
$322$	4.69497	+	2.20929i	0.261640	+	0.123119i
$323$	−43.4552	−	35.9493i	−2.41791	−	2.00027i
$324$	−0.309017	+	0.951057i	−0.0171676	+	0.0528365i
$325$	2.18892	−	23.0285i	0.121419	−	1.27739i
$326$	1.60176	+	4.92970i	0.0887131	+	0.273031i
$327$	−0.746361	+	1.88509i	−0.0412739	+	0.104246i
$328$	−3.49154	+	3.71811i	−0.192788	+	0.205298i
$329$	2.20479	+	11.5579i	0.121554	+	0.637208i
$330$	−4.36749	+	2.13820i	−0.240423	+	0.117704i
$331$	0.917619	−	0.861702i	0.0504369	−	0.0473634i	−0.658919	−	0.752214i	$-0.728986\pi$
$331$	0.917619	−	0.861702i	0.0504369	−	0.0473634i	0.709356	+	0.704851i	$0.248986\pi$
$332$	−14.6824	+	4.77059i	−0.805799	+	0.261820i
$333$	2.24012	+	0.427327i	0.122758	+	0.0234174i
$334$	0.910269	+	14.4683i	0.0498077	+	0.791671i
$335$	−25.1235	−	2.78027i	−1.37264	−	0.151903i
$336$	0.904084	+	1.42461i	0.0493218	+	0.0777188i
$337$	7.04322	−	0.443122i	0.383669	−	0.0241384i	0.130215	−	0.991486i	$-0.458433\pi$
$337$	7.04322	−	0.443122i	0.383669	−	0.0241384i	0.253454	+	0.967347i	$0.418433\pi$
$338$	7.09584	+	4.50315i	0.385963	+	0.244939i
$339$	10.6942	−	12.9270i	0.580828	−	0.702100i
$340$	17.2658	+	4.14990i	0.936370	+	0.225060i
$341$	−8.24090	−	2.11590i	−0.446270	−	0.114583i
$342$	−6.42584	+	3.02377i	−0.347470	+	0.163507i
$343$	−17.8973	−	5.81518i	−0.966363	−	0.313990i
$344$	−1.11501	−	0.612982i	−0.0601173	−	0.0330498i
$345$	0.756366	−	6.83478i	0.0407214	−	0.367972i
$346$	18.3696	+	2.32063i	0.987558	+	0.124758i
$347$	0.0944589	−	0.747719i	0.00507082	−	0.0401397i	−0.989376	−	0.145377i	$-0.953560\pi$
$347$	0.0944589	−	0.747719i	0.00507082	−	0.0401397i	0.994447	+	0.105238i	$0.0335604\pi$
$348$	6.17392	−	3.91809i	0.330957	−	0.210032i
$349$	27.8999	−	20.2705i	1.49345	−	1.08505i	0.520545	−	0.853834i	$-0.325729\pi$
$349$	27.8999	−	20.2705i	1.49345	−	1.08505i	0.972902	−	0.231218i	$-0.0742712\pi$
$350$	−5.57577	−	6.33110i	−0.298037	−	0.338411i
$351$	3.74288	+	2.71936i	0.199780	+	0.145149i
$352$	−2.17042	−	0.136551i	−0.115684	−	0.00727822i
$353$	−12.7685	−	23.2258i	−0.679599	−	1.23619i	−0.960987	−	0.276592i	$-0.910795\pi$
$353$	−12.7685	−	23.2258i	−0.679599	−	1.23619i	0.281388	−	0.959594i	$-0.409205\pi$
$354$	5.07383	−	10.7824i	0.269671	−	0.573080i
$355$	3.99508	−	2.62279i	0.212037	−	0.139203i
$356$	3.24746	−	17.0238i	0.172115	−	0.902259i
$357$	7.87591	+	10.8403i	0.416837	+	0.573727i
$358$	−0.723164	+	1.31543i	−0.0382204	+	0.0695226i
$359$	−14.0148	+	22.0838i	−0.739672	+	1.16554i	0.241123	+	0.970495i	$0.422484\pi$
$359$	−14.0148	+	22.0838i	−0.739672	+	1.16554i	−0.980795	+	0.195042i	$0.937516\pi$
$360$	1.39854	−	1.74473i	0.0737095	−	0.0919554i
$361$	−29.2272	−	11.5719i	−1.53827	−	0.609045i
$362$	0.516989	+	1.30576i	0.0271723	+	0.0686295i
$363$	−4.83159	+	3.99704i	−0.253593	+	0.209790i
$364$	7.56084	−	1.94129i	0.396296	−	0.101751i
$365$	−6.52995	+	4.90017i	−0.341793	+	0.256487i
$366$	−0.277315	+	0.109797i	−0.0144955	+	0.00573916i
$367$	1.30131	+	1.38575i	0.0679277	+	0.0723356i	0.762035	−	0.647536i	$-0.224201\pi$
$367$	1.30131	+	1.38575i	0.0679277	+	0.0723356i	−0.694107	+	0.719872i	$0.744201\pi$
$368$	1.80760	−	2.48794i	0.0942275	−	0.129693i
$369$	2.17169	+	4.61508i	0.113054	+	0.240251i
$370$	−4.34726	−	2.66556i	−0.226003	−	0.138576i
$371$	15.3446	−	8.43578i	0.796653	−	0.437964i
$372$	3.84303	−	0.733098i	0.199252	−	0.0380093i
$373$	8.70151	+	33.8902i	0.450547	+	1.75477i	0.635582	+	0.772034i	$0.280760\pi$
$373$	8.70151	+	33.8902i	0.450547	+	1.75477i	−0.185034	+	0.982732i	$0.559240\pi$
$374$	−17.2703			−0.893025
$375$	−5.54697	+	9.70727i	−0.286444	+	0.501281i
$376$	6.97359			0.359636
$377$	−8.41312	−	32.7669i	−0.433298	−	1.68758i
$378$	1.65738	−	0.316163i	0.0852466	−	0.0162617i
$379$	−25.7987	+	14.1830i	−1.32519	+	0.728531i	−0.977870	−	0.209215i	$-0.932909\pi$
$379$	−25.7987	+	14.1830i	−1.32519	+	0.728531i	−0.347323	+	0.937746i	$0.612909\pi$
$380$	15.8313	−	1.24181i	0.812130	−	0.0637036i
$381$	−2.65082	−	5.63327i	−0.135805	−	0.288601i
$382$	5.67836	−	7.81560i	0.290530	−	0.399881i
$383$	−0.537561	−	0.572445i	−0.0274681	−	0.0292506i	0.715088	−	0.699035i	$-0.246387\pi$
$383$	−0.537561	−	0.572445i	−0.0274681	−	0.0292506i	−0.742556	+	0.669784i	$0.766387\pi$
$384$	0.929776	−	0.368125i	0.0474475	−	0.0187858i
$385$	6.71158	+	4.71959i	0.342054	+	0.240532i
$386$	18.1519	−	4.66061i	0.923907	−	0.237219i
$387$	−0.980398	+	0.811056i	−0.0498364	+	0.0412283i
$388$	2.33988	+	5.90986i	0.118789	+	0.300027i
$389$	−3.65994	−	1.44907i	−0.185567	−	0.0734710i	0.273504	−	0.961871i	$-0.411817\pi$
$389$	−3.65994	−	1.44907i	−0.185567	−	0.0734710i	−0.459070	+	0.888400i	$0.651817\pi$
$390$	−5.67744	−	8.64797i	−0.287488	−	0.437907i
$391$	13.0859	−	20.6201i	0.661784	−	1.04280i
$392$	−2.00078	+	3.63941i	−0.101055	+	0.183818i
$393$	−6.55983	−	9.02883i	−0.330900	−	0.455444i
$394$	4.80461	−	25.1866i	0.242053	−	1.26888i
$395$	16.5467	+	0.784632i	0.832553	+	0.0394791i
$396$	−0.925948	+	1.96774i	−0.0465306	+	0.0988827i
$397$	6.25786	+	11.3830i	0.314073	+	0.571297i	0.985480	−	0.169792i	$-0.0543097\pi$
$397$	6.25786	+	11.3830i	0.314073	+	0.571297i	−0.671407	+	0.741089i	$0.734310\pi$
$398$	−2.18087	−	0.137208i	−0.109317	−	0.00687764i
$399$	9.69408	+	7.04316i	0.485311	+	0.352599i
$400$	−4.30503	+	2.54297i	−0.215252	+	0.127148i
$401$	5.88723	−	4.27732i	0.293994	−	0.213599i	−0.431004	−	0.902350i	$-0.641841\pi$
$401$	5.88723	−	4.27732i	0.293994	−	0.213599i	0.724998	+	0.688751i	$0.241841\pi$
$402$	−9.54443	+	6.05708i	−0.476033	+	0.302100i
$403$	2.26856	−	17.9575i	0.113005	−	0.894527i
$404$	−4.02116	−	0.507991i	−0.200060	−	0.0252735i
$405$	−1.10737	−	1.94261i	−0.0550259	−	0.0965289i
$406$	−10.8116	−	5.94374i	−0.536572	−	0.294983i
$407$	4.71674	+	1.53256i	0.233800	+	0.0759663i
$408$	7.18560	−	3.38129i	0.355740	−	0.167399i
$409$	−26.6329	−	6.83816i	−1.31691	−	0.338125i	−0.476070	−	0.879407i	$-0.657939\pi$
$409$	−26.6329	−	6.83816i	−1.31691	−	0.338125i	−0.840841	+	0.541282i	$0.817939\pi$
$410$	−0.891877	−	11.3702i	−0.0440466	−	0.561532i
$411$	0.172114	−	0.208050i	0.00848976	−	0.0102624i
$412$	−11.1245	−	7.05985i	−0.548067	−	0.347814i
$413$	−20.0668	+	1.26250i	−0.987422	+	0.0621233i
$414$	−1.64781	−	2.59653i	−0.0809855	−	0.127613i
$415$	14.2138	−	31.4582i	0.697727	−	1.54422i
$416$	−0.290498	−	4.61733i	−0.0142428	−	0.226383i
$417$	8.46131	+	1.61408i	0.414352	+	0.0790419i
$418$	−14.6883	+	4.77253i	−0.718431	+	0.233432i
$419$	26.5195	−	24.9034i	1.29556	−	1.21661i	0.333825	−	0.942635i	$-0.391661\pi$
$419$	26.5195	−	24.9034i	1.29556	−	1.21661i	0.961736	−	0.273978i	$-0.0883394\pi$
$420$	−3.71650	−	0.649629i	−0.181347	−	0.0316986i
$421$	0.763421	+	4.00199i	0.0372069	+	0.195045i	0.996038	−	0.0889329i	$-0.0283457\pi$
$421$	0.763421	+	4.00199i	0.0372069	+	0.195045i	−0.958831	+	0.283978i	$0.908346\pi$
$422$	3.53993	−	3.76964i	0.172321	−	0.183503i
$423$	2.56715	−	6.48388i	0.124819	−	0.315257i
$424$	−3.20699	−	9.87011i	−0.155745	−	0.479335i
$425$	−32.8525	+	22.3016i	−1.59358	+	1.08179i
$426$	0.660454	−	2.03267i	0.0319991	−	0.0984832i
$427$	0.387756	+	0.320780i	0.0187648	+	0.0155236i
$428$	−8.19775	−	3.85757i	−0.396253	−	0.186463i
$429$	7.33432	+	6.88738i	0.354104	+	0.332526i
$430$	2.69201	−	0.920898i	0.129820	−	0.0444097i
$431$	24.7284	−	3.12392i	1.19113	−	0.150474i	0.495324	−	0.868708i	$-0.335049\pi$
$431$	24.7284	−	3.12392i	1.19113	−	0.150474i	0.695801	+	0.718234i	$0.255049\pi$
$432$		−	1.00000i		−	0.0481125i
$433$	−0.549138	−	4.34687i	−0.0263899	−	0.208897i	0.973406	−	0.229085i	$-0.0735735\pi$
$433$	−0.549138	−	4.34687i	−0.0263899	−	0.208897i	−0.999796	+	0.0201881i	$0.993573\pi$
$434$	−4.20774	−	5.08628i	−0.201978	−	0.244149i
$435$	−2.81534	+	16.1064i	−0.134985	+	0.772245i
$436$	0.127306	−	2.02347i	0.00609684	−	0.0969066i
$437$	5.43132	−	21.1536i	0.259815	−	1.01191i
$438$	−0.907987	+	3.53637i	−0.0433853	+	0.168975i
$439$	−0.600663	+	9.54726i	−0.0286681	+	0.455666i	0.957340	+	0.288966i	$0.0933113\pi$
$439$	−0.600663	+	9.54726i	−0.0286681	+	0.455666i	−0.986008	+	0.166701i	$0.946689\pi$
$440$	3.49299	−	3.38318i	0.166522	−	0.161287i
$441$	2.64730	+	3.20004i	0.126062	+	0.152383i
$442$	−4.60482	−	36.4509i	−0.219029	−	1.73379i
$443$		−	33.0760i		−	1.57149i	−0.618552	−	0.785744i	$-0.712280\pi$
$443$		−	33.0760i		−	1.57149i	0.618552	−	0.785744i	$-0.287720\pi$
$444$	−2.26254	+	0.285825i	−0.107375	+	0.0135646i
$445$	23.2599	+	30.9960i	1.10262	+	1.46935i
$446$	6.07854	+	5.70813i	0.287827	+	0.270288i
$447$	1.58234	+	0.744594i	0.0748422	+	0.0352181i
$448$	−1.30006	−	1.07551i	−0.0614222	−	0.0508129i
$449$	0.117343	−	0.361145i	0.00553776	−	0.0170435i	−0.948249	−	0.317526i	$-0.897148\pi$
$449$	0.117343	−	0.361145i	0.00553776	−	0.0170435i	0.953787	+	0.300483i	$0.0971478\pi$
$450$	0.779604	+	4.93885i	0.0367509	+	0.232820i
$451$	3.42766	+	10.5493i	0.161402	+	0.496745i
$452$	−6.17609	+	15.5990i	−0.290499	+	0.733716i
$453$	−5.70470	+	6.07488i	−0.268030	+	0.285423i
$454$	−3.36721	−	17.6515i	−0.158031	−	0.828428i
$455$	−8.17169	+	15.4239i	−0.383095	+	0.723086i
$456$	5.17694	−	4.86147i	0.242433	−	0.227659i
$457$	23.2429	−	7.55207i	1.08726	−	0.353271i	0.290070	−	0.957005i	$-0.406321\pi$
$457$	23.2429	−	7.55207i	1.08726	−	0.353271i	0.797185	+	0.603735i	$0.206321\pi$
$458$	28.3511	+	5.40827i	1.32476	+	0.252712i
$459$	−0.498645	−	7.92574i	−0.0232748	−	0.369942i
$460$	1.39272	+	6.73399i	0.0649358	+	0.313974i
$461$	−18.4848	−	29.1274i	−0.860925	−	1.35660i	−0.933253	−	0.359219i	$-0.883043\pi$
$461$	−18.4848	−	29.1274i	−0.860925	−	1.35660i	0.0723285	−	0.997381i	$-0.476957\pi$
$462$	3.66209	−	0.230399i	0.170376	−	0.0107191i
$463$	7.03607	+	4.46522i	0.326994	+	0.207517i	0.689182	−	0.724589i	$-0.257970\pi$
$463$	7.03607	+	4.46522i	0.326994	+	0.207517i	−0.362188	+	0.932105i	$0.617970\pi$
$464$	−4.66099	+	5.63417i	−0.216381	+	0.261560i
$465$	−4.57288	+	7.45791i	−0.212062	+	0.345852i
$466$	15.4765	+	3.97370i	0.716937	+	0.184078i
$467$	32.3755	−	15.2348i	1.49816	−	0.704981i	0.510253	−	0.860025i	$-0.329552\pi$
$467$	32.3755	−	15.2348i	1.49816	−	0.704981i	0.987908	+	0.155044i	$0.0495519\pi$
$468$	−4.40002	−	1.42965i	−0.203391	−	0.0660858i
$469$	16.7140	+	9.18857i	0.771779	+	0.424289i
$470$	−10.4976	+	11.5307i	−0.484217	+	0.531869i
$471$	5.02608	+	0.634942i	0.231590	+	0.0292566i
$472$	−1.49354	+	11.8226i	−0.0687458	+	0.544179i
$473$	−2.33634	+	1.48269i	−0.107425	+	0.0681739i
$474$	5.99337	−	4.35444i	0.275284	−	0.200006i
$475$	−21.7781	+	28.0460i	−0.999248	+	1.28684i
$476$	−10.8403	−	7.87591i	−0.496862	−	0.360992i
$477$	−10.3576	−	0.651643i	−0.474240	−	0.0298367i
$478$	−11.6069	−	21.1128i	−0.530886	−	0.965679i
$479$	5.69933	−	12.1117i	0.260409	−	0.553398i	−0.731277	−	0.682081i	$-0.761075\pi$
$479$	5.69933	−	12.1117i	0.260409	−	0.553398i	0.991686	+	0.128683i	$0.0410751\pi$
$480$	−0.790938	+	2.09151i	−0.0361012	+	0.0954640i
$481$	−1.97701	+	10.3638i	−0.0901439	+	0.472551i
$482$	10.8291	+	14.9050i	0.493253	+	0.678904i
$483$	−2.49973	+	4.54698i	−0.113741	+	0.206895i
$484$	3.35997	−	5.29446i	0.152726	−	0.240657i
$485$	−13.2941	−	5.02737i	−0.603653	−	0.228281i
$486$	−0.929776	−	0.368125i	−0.0421755	−	0.0166985i
$487$	−12.4642	−	31.4810i	−0.564807	−	1.42654i	−0.878835	−	0.477125i	$-0.841679\pi$
$487$	−12.4642	−	31.4810i	−0.564807	−	1.42654i	0.314029	−	0.949413i	$-0.398321\pi$
$488$	0.229813	−	0.190118i	0.0104031	−	0.00860622i
$489$	−5.02055	+	1.28906i	−0.227037	+	0.0582932i
$490$	−3.00583	−	8.78676i	−0.135789	−	0.396945i
$491$	−8.80524	+	3.48624i	−0.397375	+	0.157332i	−0.558309	−	0.829633i	$-0.688550\pi$
$491$	−8.80524	+	3.48624i	−0.397375	+	0.157332i	0.160934	+	0.986965i	$0.448550\pi$
$492$	−3.49154	−	3.71811i	−0.157411	−	0.167625i
$493$	−34.1323	+	46.9791i	−1.53724	+	2.11583i
$494$	−13.9894	−	29.7289i	−0.629411	−	1.33757i
$495$	−1.85975	−	4.49313i	−0.0835895	−	0.201951i
$496$	−3.42840	+	1.88478i	−0.153940	+	0.0846291i
$497$	−3.54228	+	0.675727i	−0.158893	+	0.0303105i
$498$	−3.83926	−	14.9529i	−0.172041	−	0.670057i
$499$	20.5695			0.920818			0.460409	−	0.887707i	$-0.347703\pi$
$499$	20.5695			0.920818			0.460409	+	0.887707i	$0.347703\pi$
$500$	2.27577	−	10.9463i	0.101775	−	0.489532i
$501$	−14.4969			−0.647675
$502$	6.77206	+	26.3754i	0.302252	+	1.17719i
$503$	36.5648	−	6.97512i	1.63035	−	0.311005i	0.710623	−	0.703573i	$-0.248413\pi$
$503$	36.5648	−	6.97512i	1.63035	−	0.311005i	0.919723	+	0.392568i	$0.128413\pi$
$504$	−1.47857	+	0.812848i	−0.0658605	+	0.0362071i
$505$	6.89314	−	5.88420i	0.306741	−	0.261843i
$506$	−2.84754	−	6.05133i	−0.126589	−	0.269014i
$507$	−4.93982	+	6.79908i	−0.219385	+	0.301958i
$508$	4.26185	+	4.53841i	0.189089	+	0.201360i
$509$	−5.53922	+	2.19313i	−0.245521	+	0.0972088i	−0.487662	−	0.873032i	$-0.662150\pi$
$509$	−5.53922	+	2.19313i	−0.245521	+	0.0972088i	0.242141	+	0.970241i	$0.422150\pi$
$510$	−5.22584	+	16.9712i	−0.231404	+	0.751496i
$511$	5.96682	−	1.53202i	0.263956	−	0.0677725i
$512$	−0.770513	+	0.637424i	−0.0340522	+	0.0281704i
$513$	−2.61432	−	6.60303i	−0.115425	−	0.291531i
$514$	11.7233	+	4.64160i	0.517094	+	0.204732i
$515$	28.4194	−	7.76673i	1.25231	−	0.342243i
$516$	0.681784	−	1.07432i	0.0300139	−	0.0472943i
$517$	7.30607	−	13.2897i	0.321320	−	0.584480i
$518$	2.26171	+	3.11298i	0.0993738	+	0.136776i
$519$	−3.46949	+	18.1877i	−0.152294	+	0.798351i
$520$	8.07193	+	6.47028i	0.353978	+	0.283741i
$521$	−6.83833	+	14.5322i	−0.299593	+	0.636667i	−0.996777	−	0.0802254i	$-0.974436\pi$
$521$	−6.83833	+	14.5322i	−0.299593	+	0.636667i	0.697184	+	0.716892i	$0.254436\pi$
$522$	3.52270	+	6.40776i	0.154184	+	0.280460i
$523$	15.3710	+	0.967060i	0.672126	+	0.0422866i	0.395187	−	0.918601i	$-0.370680\pi$
$523$	15.3710	+	0.967060i	0.672126	+	0.0422866i	0.276939	+	0.960887i	$0.410680\pi$
$524$	9.02883	+	6.55983i	0.394426	+	0.286568i
$525$	6.66871	−	5.16723i	0.291046	−	0.225516i
$526$	−17.6434	+	12.8187i	−0.769289	+	0.558921i
$527$	−26.2328	+	16.6478i	−1.14272	+	0.725190i
$528$	0.272564	−	2.15757i	0.0118618	−	0.0938960i
$529$	−13.4359	−	1.69735i	−0.584171	−	0.0737980i
$530$	21.1476	+	9.55510i	0.918591	+	0.415047i
$531$	10.4426	+	5.74085i	0.453169	+	0.249132i
$532$	−11.3961	−	3.70281i	−0.494082	−	0.160537i
$533$	−21.3515	+	10.0472i	−0.924835	+	0.435194i
$534$	16.7863	+	4.30998i	0.726413	+	0.186511i
$535$	18.7187	−	7.74785i	0.809281	−	0.334969i
$536$	7.20555	−	8.71001i	0.311232	−	0.376215i
$537$	−1.26743	−	0.804333i	−0.0546935	−	0.0347095i
$538$	8.62513	−	0.542647i	0.371856	−	0.0233952i
$539$	4.83951	+	7.62584i	0.208452	+	0.328468i
$540$	1.65347	+	1.50533i	0.0711542	+	0.0647792i
$541$	0.0690749	+	1.09791i	0.00296976	+	0.0472030i	0.999233	−	0.0391715i	$-0.0124719\pi$
$541$	0.0690749	+	1.09791i	0.00296976	+	0.0472030i	−0.996263	+	0.0863745i	$0.972472\pi$
$542$	18.9709	+	3.61889i	0.814870	+	0.155445i
$543$	−1.33565	+	0.433979i	−0.0573182	+	0.0186238i
$544$	−5.78904	+	5.43627i	−0.248203	+	0.233078i
$545$	3.15411	+	3.25649i	0.135107	+	0.139493i
$546$	1.46271	+	7.66782i	0.0625984	+	0.328152i
$547$	−12.6832	+	13.5063i	−0.542296	+	0.577487i	−0.940493	−	0.339813i	$-0.889636\pi$
$547$	−12.6832	+	13.5063i	−0.542296	+	0.577487i	0.398197	+	0.917300i	$0.369636\pi$
$548$	−0.0993992	+	0.251054i	−0.00424612	+	0.0107245i
$549$	−0.0921672	−	0.283662i	−0.00393360	−	0.0121064i
$550$	0.335896	+	10.8684i	0.0143227	+	0.463429i
$551$	−16.0471	+	49.3879i	−0.683630	+	2.10400i
$552$	2.36953	+	1.96025i	0.100854	+	0.0834337i
$553$	−11.3100	−	5.32209i	−0.480951	−	0.226318i
$554$	20.4509	+	19.2046i	0.868873	+	0.815926i
$555$	2.93326	−	4.17131i	0.124510	−	0.177062i
$556$	−8.54596	+	1.07961i	−0.362429	+	0.0457855i
$557$			3.29110i			0.139448i	0.997566	+	0.0697242i	$0.0222119\pi$
$557$			3.29110i			0.139448i	−0.997566	+	0.0697242i	$0.977788\pi$
$558$	0.490345	+	3.88148i	0.0207580	+	0.164316i
$559$	−3.75232	−	4.53577i	−0.158706	−	0.191843i
$560$	3.73535	−	0.530628i	0.157847	−	0.0224231i
$561$	1.08441	−	17.2362i	0.0457838	−	0.727713i
$562$	−6.56718	+	25.5775i	−0.277020	+	1.07892i
$563$	−1.83316	+	7.13967i	−0.0772583	+	0.300901i	−0.995456	−	0.0952208i	$-0.969644\pi$
$563$	−1.83316	+	7.13967i	−0.0772583	+	0.300901i	0.918198	+	0.396122i	$0.129644\pi$
$564$	−0.437875	+	6.95983i	−0.0184379	+	0.293062i
$565$	−16.4955	−	33.6937i	−0.693971	−	1.41750i
$566$	−8.01075	−	9.68333i	−0.336717	−	0.407021i
$567$	0.211471	+	1.67396i	0.00888095	+	0.0702999i
$568$			2.13728i			0.0896781i
$569$	36.7762	−	4.64592i	1.54174	−	0.194767i	0.691972	−	0.721924i	$-0.256742\pi$
$569$	36.7762	−	4.64592i	1.54174	−	0.194767i	0.849768	+	0.527157i	$0.176742\pi$
$570$	0.245304	+	15.8781i	0.0102746	+	0.665059i
$571$	15.6005	+	14.6498i	0.652859	+	0.613075i	0.938507	−	0.345259i	$-0.112209\pi$
$571$	15.6005	+	14.6498i	0.652859	+	0.613075i	−0.285649	+	0.958334i	$0.592209\pi$
$572$	−9.10367	−	4.28386i	−0.380644	−	0.179117i
$573$	7.44363	+	6.15790i	0.310962	+	0.257250i
$574$	−2.65938	+	8.18473i	−0.111000	+	0.341624i
$575$	−13.2310	−	7.83407i	−0.551770	−	0.326703i
$576$	0.309017	+	0.951057i	0.0128757	+	0.0396274i
$577$	1.21024	−	3.05671i	0.0503829	−	0.127253i	−0.902405	−	0.430888i	$-0.858200\pi$
$577$	1.21024	−	3.05671i	0.0503829	−	0.127253i	0.952788	+	0.303635i	$0.0982004\pi$
$578$	−31.5343	+	33.5806i	−1.31165	+	1.39677i
$579$	3.51165	+	18.4087i	0.145939	+	0.765040i
$580$	−2.29962	−	16.1881i	−0.0954864	−	0.672175i
$581$	−18.9882	+	17.8311i	−0.787762	+	0.739757i
$582$	−6.04512	+	1.96418i	−0.250578	+	0.0814178i
$583$	−22.1695	−	4.22906i	−0.918167	−	0.175150i
$584$	−0.229253	−	3.64388i	−0.00948657	−	0.150785i
$585$	8.98739	−	5.12322i	0.371583	−	0.211819i
$586$	−1.21576	−	1.91573i	−0.0502227	−	0.0791383i
$587$	−38.6433	+	2.43123i	−1.59498	+	0.100348i	−0.835242	−	0.549882i	$-0.814673\pi$
$587$	−38.6433	+	2.43123i	−1.59498	+	0.100348i	−0.759737	+	0.650230i	$0.774673\pi$
$588$	−3.50660	−	2.22535i	−0.144610	−	0.0917720i
$589$	−17.7104	+	21.4082i	−0.729744	+	0.882109i
$590$	−17.3001	−	20.2665i	−0.712233	−	0.834357i
$591$	24.8352	+	6.37661i	1.02159	+	0.262299i
$592$	2.06348	−	0.970998i	0.0848083	−	0.0399078i
$593$	18.3270	+	5.95480i	0.752599	+	0.244534i	0.660099	−	0.751179i	$-0.270514\pi$
$593$	18.3270	+	5.95480i	0.752599	+	0.244534i	0.0924997	+	0.995713i	$0.470514\pi$
$594$	−1.90572	−	1.04768i	−0.0781925	−	0.0429867i
$595$	29.3408	−	6.06823i	1.20286	−	0.248773i
$596$	−1.73499	−	0.219180i	−0.0710679	−	0.00897797i
$597$	0.273875	−	2.16795i	0.0112090	−	0.0887282i
$598$	12.0128	−	7.62353i	0.491238	−	0.311749i
$599$	17.8942	−	13.0009i	0.731138	−	0.531203i	−0.158785	−	0.987313i	$-0.550758\pi$
$599$	17.8942	−	13.0009i	0.731138	−	0.531203i	0.889923	+	0.456110i	$0.150758\pi$
$600$	−2.26764	−	4.45621i	−0.0925758	−	0.181924i
$601$	15.2680	+	11.0928i	0.622795	+	0.452487i	0.853897	−	0.520443i	$-0.174233\pi$
$601$	15.2680	+	11.0928i	0.622795	+	0.452487i	−0.231102	+	0.972930i	$0.574233\pi$
$602$	−2.14264	−	0.134803i	−0.0873274	−	0.00549418i
$603$	−5.44582	−	9.90592i	−0.221771	−	0.403400i
$604$	3.54825	−	7.54041i	0.144376	−	0.306815i
$605$	3.69639	+	13.5255i	0.150280	+	0.549891i
$606$	0.759480	−	3.98133i	0.0308518	−	0.161731i
$607$	−5.03770	−	6.93380i	−0.204474	−	0.281434i	0.694448	−	0.719543i	$-0.255649\pi$
$607$	−5.03770	−	6.93380i	−0.204474	−	0.281434i	−0.898922	+	0.438108i	$0.855649\pi$
$608$	−3.42129	+	6.22330i	−0.138752	+	0.252388i
$609$	6.61087	−	10.4171i	0.267886	−	0.422121i
$610$	−0.0315898	+	0.666180i	−0.00127903	+	0.0269728i
$611$	29.9974	+	11.8768i	1.21357	+	0.480484i
$612$	2.92343	+	7.38373i	0.118173	+	0.298470i
$613$	−33.1704	+	27.4409i	−1.33974	+	1.10833i	−0.354892	+	0.934907i	$0.615482\pi$
$613$	−33.1704	+	27.4409i	−1.33974	+	1.10833i	−0.984848	+	0.173421i	$0.944518\pi$
$614$	8.00798	−	2.05610i	0.323176	−	0.0829775i
$615$	11.4037	−	0.176179i	0.459843	−	0.00710420i
$616$	−3.41166	+	1.35077i	−0.137460	+	0.0544241i
$617$	5.79843	+	6.17470i	0.233436	+	0.248584i	0.835012	−	0.550231i	$-0.185460\pi$
$617$	5.79843	+	6.17470i	0.233436	+	0.248584i	−0.601576	+	0.798815i	$0.705460\pi$
$618$	7.74443	−	10.6593i	0.311527	−	0.428780i
$619$	−1.81463	−	3.85629i	−0.0729361	−	0.154997i	0.865034	−	0.501713i	$-0.167297\pi$
$619$	−1.81463	−	3.85629i	−0.0729361	−	0.154997i	−0.937970	+	0.346716i	$0.887297\pi$
$620$	2.04445	−	8.50599i	0.0821070	−	0.341609i
$621$	2.69488	−	1.48152i	0.108142	−	0.0594514i
$622$	−5.49166	+	1.04759i	−0.220196	+	0.0420045i
$623$	−7.27210	−	28.3230i	−0.291351	−	1.13474i
$624$	4.62646			0.185207
$625$	14.6736	+	20.2407i	0.586944	+	0.809628i
$626$	12.5456			0.501423
$627$	−3.84083	−	14.9590i	−0.153388	−	0.597406i
$628$	−4.97630	+	0.949280i	−0.198576	+	0.0378804i
$629$	15.8704	−	8.72481i	0.632793	−	0.347881i
$630$	0.881708	−	3.66838i	0.0351281	−	0.146152i
$631$	−5.16482	−	10.9758i	−0.205608	−	0.436940i	0.775252	−	0.631652i	$-0.217623\pi$
$631$	−5.16482	−	10.9758i	−0.205608	−	0.436940i	−0.980860	+	0.194712i	$0.937623\pi$
$632$	−4.35444	+	5.99337i	−0.173210	+	0.238403i
$633$	3.53993	+	3.76964i	0.140700	+	0.149830i
$634$	−18.9516	+	7.50347i	−0.752664	+	0.298001i
$635$	−13.9197	+	0.215048i	−0.552385	+	0.00853391i
$636$	10.0520	−	2.58091i	0.398588	−	0.102340i
$637$	−14.8048	+	12.2476i	−0.586589	+	0.485268i
$638$	5.85392	+	14.7853i	0.231759	+	0.585356i
$639$	1.98719	+	0.786784i	0.0786120	+	0.0311247i
$640$	0.105914	−	2.23356i	0.00418662	−	0.0882891i
$641$	7.93150	−	12.4980i	0.313275	−	0.493643i	−0.650808	−	0.759242i	$-0.725570\pi$
$641$	7.93150	−	12.4980i	0.313275	−	0.493643i	0.964084	+	0.265599i	$0.0855698\pi$
$642$	4.36470	−	7.93936i	0.172261	−	0.313341i
$643$	−3.76269	−	5.17890i	−0.148386	−	0.204236i	0.728353	−	0.685202i	$-0.240286\pi$
$643$	−3.76269	−	5.17890i	−0.148386	−	0.204236i	−0.876739	+	0.480966i	$0.840286\pi$
$644$	0.972285	−	5.09690i	0.0383134	−	0.200846i
$645$	0.750049	+	2.74452i	0.0295331	+	0.108065i
$646$	−24.0130	+	51.0302i	−0.944779	+	2.00776i
$647$	0.333651	+	0.606909i	0.0131172	+	0.0238600i	0.882784	−	0.469779i	$-0.155666\pi$
$647$	0.333651	+	0.606909i	0.0131172	+	0.0238600i	−0.869667	+	0.493639i	$0.835666\pi$
$648$	0.998027	+	0.0627905i	0.0392062	+	0.00246664i
$649$	20.9658	+	15.2325i	0.822979	+	0.597929i
$650$	−22.8494	+	3.60681i	−0.896226	+	0.141471i
$651$	5.34045	−	3.88006i	0.209309	−	0.152072i
$652$	4.37649	−	2.77740i	0.171396	−	0.108771i
$653$	0.982250	−	7.77531i	0.0384384	−	0.304271i	−0.961162	−	0.275987i	$-0.910995\pi$
$653$	0.982250	−	7.77531i	0.0384384	−	0.304271i	0.999600	−	0.0282847i	$-0.00900451\pi$
$654$	2.01148	+	0.254109i	0.0786552	+	0.00993646i
$655$	−24.4379	+	5.05422i	−0.954868	+	0.197485i
$656$	4.46961	+	2.45719i	0.174509	+	0.0959371i
$657$	−3.47238	−	1.12825i	−0.135471	−	0.0440171i
$658$	10.6465	−	5.00986i	0.415043	−	0.195305i
$659$	5.91299	+	1.51820i	0.230337	+	0.0591405i	0.362094	−	0.932141i	$-0.382062\pi$
$659$	5.91299	+	1.51820i	0.230337	+	0.0591405i	−0.131757	+	0.991282i	$0.542062\pi$
$660$	3.15718	+	3.69853i	0.122893	+	0.143965i
$661$	−21.8367	+	26.3960i	−0.849348	+	1.02669i	0.149930	+	0.988697i	$0.452095\pi$
$661$	−21.8367	+	26.3960i	−0.849348	+	1.02669i	−0.999278	+	0.0379888i	$0.987905\pi$
$662$	−1.06283	−	0.674494i	−0.0413082	−	0.0262150i
$663$	36.6681	−	2.30696i	1.42407	−	0.0895949i
$664$	8.27207	+	13.0347i	0.321018	+	0.505844i
$665$	23.2774	−	13.2692i	0.902658	−	0.514556i
$666$	−0.143195	−	2.27602i	−0.00554869	−	0.0881939i
$667$	−22.0888	−	4.21366i	−0.855280	−	0.163153i
$668$	13.7874	−	4.47980i	0.533450	−	0.173328i
$669$	−6.07854	+	5.70813i	−0.235010	+	0.220689i
$670$	3.55504	+	25.0256i	0.137343	+	0.966825i
$671$	−0.121541	−	0.637140i	−0.00469204	−	0.0245965i
$672$	1.15502	−	1.22997i	0.0445557	−	0.0474470i
$673$	12.2004	−	30.8146i	0.470289	−	1.18782i	−0.480228	−	0.877144i	$-0.659446\pi$
$673$	12.2004	−	30.8146i	0.470289	−	1.18782i	0.950517	−	0.310672i	$-0.100554\pi$
$674$	−2.18078	−	6.71175i	−0.0840005	−	0.258527i
$675$	−4.97805	+	0.467953i	−0.191605	+	0.0180115i
$676$	2.59702	−	7.99280i	0.0998853	−	0.307415i
$677$	6.57953	+	5.44306i	0.252872	+	0.209194i	0.755220	−	0.655472i	$-0.227530\pi$
$677$	6.57953	+	5.44306i	0.252872	+	0.209194i	−0.502348	+	0.864666i	$0.667530\pi$
$678$	−15.1804	−	7.14337i	−0.583001	−	0.274339i
$679$	7.81793	+	7.34152i	0.300025	+	0.281742i
$680$	−0.274307	−	17.7554i	−0.0105192	−	0.680889i
$681$	17.8281	−	2.25222i	0.683176	−	0.0863052i
$682$			8.50820i			0.325796i
$683$	−0.698678	−	5.53061i	−0.0267342	−	0.211623i	0.973089	−	0.230430i	$-0.0740132\pi$
$683$	−0.698678	−	5.53061i	−0.0267342	−	0.211623i	−0.999823	+	0.0188070i	$0.994013\pi$
$684$	4.52682	+	5.47198i	0.173087	+	0.209226i
$685$	−0.265482	−	0.542273i	−0.0101435	−	0.0207192i
$686$	−1.18161	+	18.7812i	−0.0451142	+	0.717069i
$687$	−7.17778	+	27.9556i	−0.273849	+	1.06657i
$688$	−0.316432	+	1.23242i	−0.0120639	+	0.0469856i
$689$	3.01480	−	47.9188i	0.114855	−	1.82556i
$690$	−6.80816	+	0.967138i	−0.259182	+	0.0368183i
$691$	7.80852	+	9.43888i	0.297050	+	0.359072i	0.897830	−	0.440343i	$-0.145143\pi$
$691$	7.80852	+	9.43888i	0.297050	+	0.359072i	−0.600780	+	0.799415i	$0.705143\pi$
$692$	−2.32063	−	18.3696i	−0.0882170	−	0.698309i
$693$			3.66933i			0.139386i
$694$	−0.747719	+	0.0944589i	−0.0283830	+	0.00358561i
$695$	11.0794	−	15.7557i	0.420266	−	0.597647i
$696$	−5.33039	−	5.00557i	−0.202048	−	0.189736i
$697$	36.6502	+	17.2463i	1.38823	+	0.653250i
$698$	−26.5720	−	21.9823i	−1.00577	−	0.832043i
$699$	−4.93764	+	15.1965i	−0.186759	+	0.574784i
$700$	−4.74556	+	6.97507i	−0.179365	+	0.263633i
$701$	3.48594	+	10.7286i	0.131662	+	0.405214i	0.995056	−	0.0993164i	$-0.0316656\pi$
$701$	3.48594	+	10.7286i	0.131662	+	0.405214i	−0.863394	+	0.504531i	$0.831666\pi$
$702$	1.70311	−	4.30157i	0.0642799	−	0.162352i
$703$	11.0867	−	11.8061i	0.418142	−	0.445276i
$704$	0.407501	+	2.13619i	0.0153583	+	0.0805108i
$705$	−10.8488	−	11.2009i	−0.408588	−	0.421849i
$706$	−19.3207	+	18.1434i	−0.727146	+	0.682835i
$707$	−6.50400	+	2.11328i	−0.244608	+	0.0794780i
$708$	−11.7055	−	2.23294i	−0.439919	−	0.0839191i
$709$	0.103456	+	1.64438i	0.00388536	+	0.0617560i	0.999492	−	0.0318825i	$-0.0101502\pi$
$709$	0.103456	+	1.64438i	0.00388536	+	0.0617560i	−0.995606	+	0.0936385i	$0.970150\pi$
$710$	−3.53393	−	3.21731i	−0.132626	−	0.120743i
$711$	3.96952	+	6.25496i	0.148868	+	0.234579i
$712$	−17.2966	+	1.08821i	−0.648216	+	0.0407823i
$713$	−10.1585	−	6.44678i	−0.380439	−	0.241434i
$714$	8.54103	−	10.3243i	0.319640	−	0.386378i
$715$	20.7873	−	8.60405i	0.777401	−	0.321773i
$716$	1.45395	+	0.373310i	0.0543366	+	0.0139513i
$717$	21.8000	−	10.2583i	0.814135	−	0.383103i
$718$	24.8753	+	8.08247i	0.928338	+	0.301635i
$719$	−32.0113	−	17.5984i	−1.19382	−	0.656309i	−0.244205	−	0.969724i	$-0.578527\pi$
$719$	−32.0113	−	17.5984i	−1.19382	−	0.656309i	−0.949616	+	0.313415i	$0.898527\pi$
$720$	−2.03772	−	0.920704i	−0.0759414	−	0.0343126i
$721$	−22.0555	−	2.78626i	−0.821390	−	0.103766i
$722$	−3.93981	+	31.1868i	−0.146624	+	1.16065i
$723$	−15.5556	+	9.87186i	−0.578517	+	0.367138i
$724$	1.13617	−	0.825477i	0.0422255	−	0.0306786i
$725$	30.2283	+	20.5661i	1.12265	+	0.763807i
$726$	5.07304	+	3.68578i	0.188278	+	0.136792i
$727$	41.9826	+	2.64132i	1.55705	+	0.0979611i	0.817812	−	0.575486i	$-0.195187\pi$
$727$	41.9826	+	2.64132i	1.55705	+	0.0979611i	0.739235	+	0.673447i	$0.235187\pi$
$728$	−3.76061	−	6.84052i	−0.139377	−	0.253527i
$729$	0.425779	−	0.904827i	0.0157696	−	0.0335121i
$730$	6.37016	+	5.10618i	0.235770	+	0.188988i
$731$	−1.89342	+	9.92564i	−0.0700305	+	0.367113i
$732$	0.175312	+	0.241297i	0.00647974	+	0.00891859i
$733$	18.1497	−	33.0141i	0.670374	−	1.21940i	−0.294239	−	0.955732i	$-0.595066\pi$
$733$	18.1497	−	33.0141i	0.670374	−	1.21940i	0.964612	−	0.263673i	$-0.0849340\pi$
$734$	1.01859	−	1.60505i	0.0375970	−	0.0592433i
$735$	8.95816	−	2.44817i	0.330427	−	0.0903021i
$736$	−2.85931	−	1.13208i	−0.105396	−	0.0417291i
$737$	−9.04973	−	22.8570i	−0.333351	−	0.841949i
$738$	3.93001	−	3.25119i	0.144666	−	0.119678i
$739$	−21.2293	+	5.45076i	−0.780932	+	0.200509i	−0.618053	−	0.786137i	$-0.712078\pi$
$739$	−21.2293	+	5.45076i	−0.780932	+	0.200509i	−0.162879	+	0.986646i	$0.552078\pi$
$740$	−1.50069	+	4.87358i	−0.0551666	+	0.179156i
$741$	30.5486	−	12.0951i	1.12223	−	0.444323i
$742$	−11.9868	−	12.7646i	−0.440049	−	0.468605i
$743$	−9.76174	+	13.4359i	−0.358123	+	0.492915i	−0.949625	−	0.313389i	$-0.898535\pi$
$743$	−9.76174	+	13.4359i	−0.358123	+	0.492915i	0.591501	+	0.806304i	$0.298535\pi$
$744$	−1.66579	−	3.53998i	−0.0610708	−	0.129782i
$745$	2.97414	−	2.53882i	0.108964	−	0.0930152i
$746$	30.6615	−	16.8563i	1.12260	−	0.617152i
$747$	15.1645	−	2.89278i	0.554840	−	0.105841i
$748$	4.29495	+	16.7277i	0.157039	+	0.611626i
$749$	−15.2867			−0.558564
$750$	10.7818	+	2.95860i	0.393695	+	0.108033i
$751$	−8.99275			−0.328150			−0.164075	−	0.986448i	$-0.552464\pi$
$751$	−8.99275			−0.328150			−0.164075	+	0.986448i	$0.552464\pi$
$752$	−1.73426	−	6.75450i	−0.0632420	−	0.246311i
$753$	−26.7486	+	5.10257i	−0.974773	+	0.185948i
$754$	−29.6452	+	16.2976i	−1.07962	+	0.593524i
$755$	7.12658	+	17.2177i	0.259363	+	0.626618i
$756$	−0.718404	−	1.52669i	−0.0261281	−	0.0555251i
$757$	12.0704	−	16.6134i	0.438705	−	0.603826i	−0.531219	−	0.847235i	$-0.678266\pi$
$757$	12.0704	−	16.6134i	0.438705	−	0.603826i	0.969924	+	0.243409i	$0.0782657\pi$
$758$	20.1533	+	21.4611i	0.732000	+	0.779501i
$759$	6.21818	−	2.46195i	0.225706	−	0.0893632i
$760$	−5.13989	−	15.0251i	−0.186443	−	0.545019i
$761$	14.5002	−	3.72301i	0.525631	−	0.134959i	0.0234556	−	0.999725i	$-0.492533\pi$
$761$	14.5002	−	3.72301i	0.525631	−	0.134959i	0.502175	+	0.864766i	$0.332533\pi$
$762$	−4.79706	+	3.96848i	−0.173779	+	0.143763i
$763$	−1.25931	−	3.18066i	−0.0455902	−	0.115148i
$764$	−8.98221	−	3.55631i	−0.324965	−	0.128663i
$765$	−16.6095	−	6.28116i	−0.600519	−	0.227096i
$766$	−0.420774	+	0.663034i	−0.0152032	+	0.0239564i
$767$	−26.5598	+	48.3121i	−0.959019	+	1.74445i
$768$	−0.587785	−	0.809017i	−0.0212099	−	0.0291929i
$769$	5.26340	−	27.5917i	0.189803	−	0.994982i	−0.752088	−	0.659063i	$-0.770953\pi$
$769$	5.26340	−	27.5917i	0.189803	−	0.994982i	0.941891	−	0.335919i	$-0.109047\pi$
$770$	2.90221	−	7.67444i	0.104588	−	0.276568i
$771$	−5.36855	+	11.4088i	−0.193344	+	0.410876i
$772$	−9.02838	−	16.4226i	−0.324939	−	0.591061i
$773$	−10.1246	−	0.636983i	−0.364155	−	0.0229107i	−0.120341	−	0.992733i	$-0.538399\pi$
$773$	−10.1246	−	0.636983i	−0.364155	−	0.0229107i	−0.243814	+	0.969822i	$0.578399\pi$
$774$	1.02939	+	0.747896i	0.0370007	+	0.0268826i
$775$	10.9869	+	16.1848i	0.394660	+	0.581374i
$776$	5.14228	−	3.73609i	0.184597	−	0.134118i
$777$	−3.24885	+	2.06178i	−0.116552	+	0.0739660i
$778$	−0.493358	+	3.90533i	−0.0176877	+	0.140013i
$779$	35.9368	+	4.53988i	1.28757	+	0.162658i
$780$	−6.96436	+	7.64973i	−0.249364	+	0.273904i
$781$	4.07304	+	2.23917i	0.145745	+	0.0801239i
$782$	−23.2267	−	7.54680i	−0.830583	−	0.269873i
$783$	−6.61631	+	3.11340i	−0.236447	+	0.111264i
$784$	4.02264	+	1.03284i	0.143666	+	0.0368871i
$785$	5.92137	−	9.65716i	0.211343	−	0.344679i
$786$	−7.11381	+	8.59912i	−0.253741	+	0.306721i
$787$	−36.5648	−	23.2048i	−1.30340	−	0.827160i	−0.311019	−	0.950404i	$-0.600670\pi$
$787$	−36.5648	−	23.2048i	−1.30340	−	0.827160i	−0.992376	+	0.123243i	$0.960670\pi$
$788$	−25.5902	+	1.61000i	−0.911613	+	0.0573538i
$789$	−11.6856	−	18.4135i	−0.416017	−	0.655538i
$790$	−3.35501	−	16.2219i	−0.119366	−	0.577151i
$791$	1.77745	+	28.2517i	0.0631988	+	1.00452i
$792$	2.13619	+	0.407501i	0.0759063	+	0.0144799i
$793$	1.31235	−	0.426408i	0.0466029	−	0.0151422i
$794$	9.46912	−	8.89210i	0.336047	−	0.315569i
$795$	−10.8641	+	20.5059i	−0.385310	+	0.727268i
$796$	0.409462	+	2.14647i	0.0145130	+	0.0760797i
$797$	4.96103	−	5.28296i	0.175729	−	0.187132i	−0.635074	−	0.772451i	$-0.719031\pi$
$797$	4.96103	−	5.28296i	0.175729	−	0.187132i	0.810803	+	0.585319i	$0.199031\pi$
$798$	4.41107	−	11.1411i	0.156150	−	0.394390i
$799$	−17.1134	−	52.6696i	−0.605429	−	1.86332i
$800$	3.53370	+	3.53737i	0.124935	+	0.125065i
$801$	−5.35550	+	16.4825i	−0.189227	+	0.582382i
$802$	−5.60703	−	4.63854i	−0.197991	−	0.163793i
$803$	−7.18438	−	3.38071i	−0.253531	−	0.119303i
$804$	8.24038	+	7.73824i	0.290616	+	0.272907i
$805$	6.96397	+	9.28017i	0.245448	+	0.327083i
$806$	−17.9575	+	2.26856i	−0.632526	+	0.0799067i
$807$			8.64219i			0.304219i
$808$	0.507991	+	4.02116i	0.0178711	+	0.141464i
$809$	−3.66534	−	4.43064i	−0.128867	−	0.155773i	0.702133	−	0.712045i	$-0.252231\pi$
$809$	−3.66534	−	4.43064i	−0.128867	−	0.155773i	−0.831000	+	0.556273i	$0.812231\pi$
$810$	−1.60618	+	1.55569i	−0.0564355	+	0.0546614i
$811$	−0.290244	+	4.61329i	−0.0101918	+	0.161995i	0.989639	+	0.143581i	$0.0458616\pi$
$811$	−0.290244	+	4.61329i	−0.0101918	+	0.161995i	−0.999830	+	0.0184139i	$0.994138\pi$
$812$	−3.06826	+	11.9501i	−0.107675	+	0.419366i
$813$	−4.80294	+	18.7062i	−0.168447	+	0.656056i
$814$	0.311408	−	4.94969i	0.0109148	−	0.173487i
$815$	−1.99570	+	11.4173i	−0.0699063	+	0.399931i
$816$	−5.06204	−	6.11896i	−0.177207	−	0.214206i
$817$	1.13254	+	8.96497i	0.0396225	+	0.313645i
$818$			27.4967i			0.961401i
$819$	−7.74453	+	0.978362i	−0.270616	+	0.0341867i
$820$	−10.7911	+	3.69150i	−0.376843	+	0.128913i
$821$	28.3358	+	26.6091i	0.988926	+	0.928663i	0.997455	−	0.0713006i	$-0.0227150\pi$
$821$	28.3358	+	26.6091i	0.988926	+	0.928663i	−0.00852918	+	0.999964i	$0.502715\pi$
$822$	−0.244317	−	0.114967i	−0.00852153	−	0.00400993i
$823$	11.4732	+	9.49143i	0.399929	+	0.330850i	0.815549	−	0.578688i	$-0.196435\pi$
$823$	11.4732	+	9.49143i	0.399929	+	0.330850i	−0.415619	+	0.909539i	$0.636435\pi$
$824$	−4.07149	+	12.5308i	−0.141837	+	0.436530i
$825$	−10.8680	−	0.347198i	−0.378376	−	0.0120879i
$826$	6.21324	+	19.1224i	0.216186	+	0.665353i
$827$	−5.69360	+	14.3804i	−0.197986	+	0.500055i	−0.994521	−	0.104537i	$-0.966664\pi$
$827$	−5.69360	+	14.3804i	−0.197986	+	0.500055i	0.796535	+	0.604592i	$0.206664\pi$
$828$	−2.10517	+	2.24177i	−0.0731595	+	0.0779070i
$829$	−9.66394	−	50.6601i	−0.335642	−	1.75950i	−0.604776	−	0.796396i	$-0.706737\pi$
$829$	−9.66394	−	50.6601i	−0.335642	−	1.75950i	0.269133	−	0.963103i	$-0.413263\pi$
$830$	−34.0047	−	5.94389i	−1.18032	−	0.206315i
$831$	−20.4509	+	19.2046i	−0.709432	+	0.666201i
$832$	−4.40002	+	1.42965i	−0.152543	+	0.0495644i
$833$	32.3974	+	6.18014i	1.12250	+	0.214129i
$834$	−0.540870	−	8.59689i	−0.0187288	−	0.297686i
$835$	−13.3474	+	29.5407i	−0.461905	+	1.02230i
$836$	8.27544	+	13.0400i	0.286212	+	0.450998i
$837$	−3.90461	+	0.245657i	−0.134963	+	0.00849116i
$838$	−30.7162	−	19.4931i	−1.06107	−	0.673377i
$839$	11.9513	−	14.4467i	0.412606	−	0.498755i	−0.522738	−	0.852493i	$-0.675090\pi$
$839$	11.9513	−	14.4467i	0.412606	−	0.498755i	0.935345	+	0.353738i	$0.115090\pi$
$840$	0.295036	+	3.76130i	0.0101797	+	0.129777i
$841$	23.7000	+	6.08513i	0.817242	+	0.209832i
$842$	3.68641	−	1.73469i	0.127042	−	0.0597815i
$843$	−25.1146	−	8.16024i	−0.864994	−	0.281054i
$844$	−4.53156	−	2.49125i	−0.155983	−	0.0857522i
$845$	9.30651	+	16.3259i	0.320154	+	0.561628i
$846$	−6.91860	−	0.874023i	−0.237866	−	0.0300495i
$847$	1.32605	−	10.4968i	0.0455637	−	0.360674i
$848$	−8.76247	+	5.56083i	−0.300905	+	0.190960i
$849$	10.1672	−	7.38692i	0.348938	−	0.253519i
$850$	29.7710	+	26.2742i	1.02114	+	0.901198i
$851$	5.67380	+	4.12226i	0.194495	+	0.141309i
$852$	−2.13306	−	0.134201i	−0.0730774	−	0.00459764i
$853$	10.8712	+	19.7747i	0.372224	+	0.677073i	0.994386	−	0.105816i	$-0.0337454\pi$
$853$	10.8712	+	19.7747i	0.372224	+	0.677073i	−0.622162	+	0.782889i	$0.713745\pi$
$854$	0.214271	−	0.455349i	0.00733220	−	0.0155817i
$855$	−15.8621	−	0.752173i	−0.542474	−	0.0257238i
$856$	−1.69768	+	8.89954i	−0.0580254	+	0.304180i
$857$	14.2788	+	19.6531i	0.487754	+	0.671336i	0.979972	−	0.199136i	$-0.0638136\pi$
$857$	14.2788	+	19.6531i	0.487754	+	0.671336i	−0.492218	+	0.870472i	$0.663814\pi$
$858$	4.84703	−	8.81672i	0.165475	−	0.300998i
$859$	18.0533	−	28.4474i	0.615969	−	0.970612i	−0.382933	−	0.923776i	$-0.625086\pi$
$859$	18.0533	−	28.4474i	0.615969	−	0.970612i	0.998903	−	0.0468362i	$-0.0149139\pi$
$860$	−1.56144	−	2.37842i	−0.0532447	−	0.0811033i
$861$	−8.00159	−	3.16806i	−0.272694	−	0.107967i
$862$	−9.17548	−	23.1746i	−0.312518	−	0.789331i
$863$	−27.4772	+	22.7311i	−0.935336	+	0.773777i	−0.974251	−	0.225465i	$-0.927610\pi$
$863$	−27.4772	+	22.7311i	−0.935336	+	0.773777i	0.0389154	+	0.999243i	$0.487610\pi$
$864$	−0.968583	+	0.248690i	−0.0329519	+	0.00846060i
$865$	33.8671	+	23.8153i	1.15151	+	0.809745i
$866$	−4.07374	+	1.61291i	−0.138431	+	0.0548089i
$867$	−31.5343	−	33.5806i	−1.07096	−	1.14046i
$868$	−3.88006	+	5.34045i	−0.131698	+	0.181267i
$869$	6.85962	+	14.5774i	0.232697	+	0.494505i
$870$	16.3006	−	1.27862i	0.552641	−	0.0433493i
$871$	45.8293	−	25.1949i	1.55287	−	0.853696i
$872$	−1.99156	+	0.379910i	−0.0674426	+	0.0128654i
$873$	−1.58073	−	6.15652i	−0.0534995	−	0.208367i
$874$	−21.8397			−0.738740
$875$	−4.38946	−	18.3465i	−0.148391	−	0.620223i
$876$	3.65108			0.123359
$877$	5.67903	+	22.1184i	0.191767	+	0.746884i	0.989581	+	0.143980i	$0.0459901\pi$
$877$	5.67903	+	22.1184i	0.191767	+	0.746884i	−0.797813	+	0.602905i	$0.794010\pi$
$878$	9.39670	−	1.79252i	0.317123	−	0.0604945i
$879$	1.98829	−	1.09307i	0.0670635	−	0.0368684i
$880$	−4.14557	−	2.54189i	−0.139747	−	0.0856870i
$881$	−12.3903	−	26.3308i	−0.417441	−	0.887107i	−0.997373	−	0.0724417i	$-0.976921\pi$
$881$	−12.3903	−	26.3308i	−0.417441	−	0.887107i	0.579932	−	0.814665i	$-0.303079\pi$
$882$	2.44114	−	3.35995i	0.0821976	−	0.113135i
$883$	15.6935	+	16.7119i	0.528130	+	0.562401i	0.936613	−	0.350365i	$-0.113942\pi$
$883$	15.6935	+	16.7119i	0.528130	+	0.562401i	−0.408484	+	0.912766i	$0.633942\pi$
$884$	−34.1605	+	13.5251i	−1.14894	+	0.454899i
$885$	21.3128	−	15.9934i	0.716421	−	0.537613i
$886$	−32.0369	+	8.22567i	−1.07630	+	0.276347i
$887$	−16.6184	+	13.7480i	−0.557993	+	0.461612i	−0.873166	−	0.487422i	$-0.837937\pi$
$887$	−16.6184	+	13.7480i	−0.557993	+	0.461612i	0.315174	+	0.949034i	$0.397937\pi$
$888$	0.839515	+	2.12037i	0.0281723	+	0.0711551i
$889$	9.76694	+	3.86700i	0.327572	+	0.129695i
$890$	24.2377	−	30.2375i	0.812451	−	1.01356i
$891$	1.16527	−	1.83617i	0.0390380	−	0.0615141i
$892$	4.01713	−	7.30713i	0.134503	−	0.244661i
$893$	−29.1098	−	40.0662i	−0.974123	−	1.34077i
$894$	0.327689	−	1.71780i	0.0109595	−	0.0574519i
$895$	−2.80593	+	1.84211i	−0.0937919	+	0.0615749i
$896$	−0.718404	+	1.52669i	−0.0240002	+	0.0510030i
$897$	6.85420	+	12.4677i	0.228855	+	0.416286i
$898$	−0.378981	−	0.0238434i	−0.0126467	−	0.000795666i
$899$	23.1443	+	16.8153i	0.771904	+	0.560821i
$900$	4.58981	−	1.98335i	0.152994	−	0.0661118i
$901$	−66.6762	+	48.4431i	−2.22130	+	1.61387i
$902$	9.36541	−	5.94347i	0.311834	−	0.197896i
$903$	0.269075	−	2.12995i	0.00895425	−	0.0708802i
$904$	16.6449	+	2.10274i	0.553600	+	0.0699360i
$905$	−0.345410	+	3.12125i	−0.0114818	+	0.103754i
$906$	7.30273	+	4.01471i	0.242617	+	0.133380i
$907$	−23.6840	−	7.69541i	−0.786416	−	0.255522i	−0.111839	−	0.993726i	$-0.535674\pi$
$907$	−23.6840	−	7.69541i	−0.786416	−	0.255522i	−0.674577	+	0.738204i	$0.735674\pi$
$908$	−16.2596	+	7.65118i	−0.539594	+	0.253913i
$909$	3.92579	+	1.00797i	0.130210	+	0.0334323i
$910$	16.9716	+	4.07919i	0.562603	+	0.135224i
$911$	−12.3449	+	14.9224i	−0.409005	+	0.494402i	−0.934285	−	0.356528i	$-0.883961\pi$
$911$	−12.3449	+	14.9224i	−0.409005	+	0.494402i	0.525280	+	0.850929i	$0.323961\pi$
$912$	−5.99619	−	3.80530i	−0.198554	−	0.126006i
$913$	33.5069	−	2.10807i	1.10892	−	0.0697671i
$914$	−13.0951	−	20.6345i	−0.433146	−	0.682530i
$915$	−0.662882	−	0.0733573i	−0.0219142	−	0.00242512i
$916$	−1.81228	−	28.8054i	−0.0598795	−	0.951757i
$917$	18.4968	+	3.52846i	0.610819	+	0.116520i
$918$	−7.55273	+	2.45403i	−0.249277	+	0.0809950i
$919$	31.1888	−	29.2882i	1.02882	−	0.966130i	0.0293827	−	0.999568i	$-0.490646\pi$
$919$	31.1888	−	29.2882i	1.02882	−	0.966130i	0.999441	+	0.0334387i	$0.0106459\pi$
$920$	6.17608	−	3.02364i	0.203619	−	0.0996864i
$921$	1.54922	+	8.12129i	0.0510485	+	0.267605i
$922$	−23.6154	+	25.1478i	−0.777730	+	0.828199i
$923$	−3.64002	+	9.19365i	−0.119813	+	0.302613i
$924$	−1.13388	−	3.48974i	−0.0373021	−	0.114804i
$925$	−5.79929	−	9.81771i	−0.190679	−	0.322804i
$926$	2.57514	−	7.92547i	0.0846244	−	0.260447i
$927$	10.1520	+	8.39845i	0.333435	+	0.275841i
$928$	6.61631	+	3.11340i	0.217191	+	0.102202i
$929$	25.1097	+	23.5795i	0.823822	+	0.773620i	0.976696	−	0.214626i	$-0.0688532\pi$
$929$	25.1097	+	23.5795i	0.823822	+	0.773620i	−0.152875	+	0.988246i	$0.548853\pi$
$930$	8.36083	+	2.57451i	0.274163	+	0.0844214i
$931$	29.2618	−	3.69662i	0.959017	−	0.121152i
$932$		−	15.9785i		−	0.523394i
$933$	−0.700699	−	5.54660i	−0.0229399	−	0.181588i
$934$	−22.8076	−	27.5696i	−0.746287	−	0.902106i
$935$	−34.1242	−	18.0792i	−1.11598	−	0.591252i
$936$	−0.290498	+	4.61733i	−0.00949522	+	0.150922i
$937$	0.116192	−	0.452539i	0.00379583	−	0.0147838i	−0.966657	−	0.256075i	$-0.917571\pi$
$937$	0.116192	−	0.452539i	0.00379583	−	0.0147838i	0.970453	+	0.241291i	$0.0775707\pi$
$938$	4.74331	−	18.4740i	0.154874	−	0.603196i
$939$	−0.787744	+	12.5208i	−0.0257071	+	0.408602i
$940$	13.7790	+	7.30021i	0.449423	+	0.238107i
$941$	−7.10986	−	8.59434i	−0.231775	−	0.280168i	0.641785	−	0.766885i	$-0.278194\pi$
$941$	−7.10986	−	8.59434i	−0.231775	−	0.280168i	−0.873560	+	0.486717i	$0.838194\pi$
$942$	−0.634942	−	5.02608i	−0.0206875	−	0.163759i
$943$			15.6854i			0.510788i
$944$	11.8226	−	1.49354i	0.384793	−	0.0486107i
$945$	3.60577	+	1.11031i	0.117296	+	0.0361183i
$946$	2.01713	+	1.89421i	0.0655825	+	0.0615860i
$947$	−34.3403	−	16.1593i	−1.11591	−	0.525107i	−0.222763	−	0.974873i	$-0.571508\pi$
$947$	−34.3403	−	16.1593i	−1.11591	−	0.525107i	−0.893147	+	0.449765i	$0.851508\pi$
$948$	−5.70812	−	4.72217i	−0.185391	−	0.153369i
$949$	5.21978	−	16.0648i	0.169441	−	0.521487i
$950$	32.5809	+	14.1191i	1.05706	+	0.458085i
$951$	−6.29868	−	19.3853i	−0.204249	−	0.628613i
$952$	−4.93261	+	12.4583i	−0.159867	+	0.403777i
$953$	36.8820	−	39.2753i	1.19472	−	1.27225i	0.241359	−	0.970436i	$-0.422407\pi$
$953$	36.8820	−	39.2753i	1.19472	−	1.27225i	0.953366	−	0.301817i	$-0.0975932\pi$
$954$	1.94465	+	10.1942i	0.0629604	+	0.330050i
$955$	19.4015	−	9.49843i	0.627817	−	0.307362i
$956$	−17.5630	+	16.4928i	−0.568029	+	0.533414i
$957$	−15.1237	+	4.91399i	−0.488880	+	0.158847i
$958$	−13.1486	−	2.50822i	−0.424811	−	0.0810369i
$959$	0.0286066	+	0.454689i	0.000923756	+	0.0146827i
$960$	2.22250	+	0.245951i	0.0717309	+	0.00793804i
$961$	−8.40909	−	13.2506i	−0.271261	−	0.427439i
$962$	10.5299	−	0.662486i	0.339498	−	0.0213594i
$963$	7.64963	+	4.85460i	0.246506	+	0.156437i
$964$	11.7436	−	14.1956i	0.378237	−	0.457210i
$965$	40.7450	+	9.79321i	1.31163	+	0.315255i
$966$	5.02579	+	1.29040i	0.161702	+	0.0415180i
$967$	−34.5610	+	16.2632i	−1.11141	+	0.522988i	−0.891723	−	0.452583i	$-0.850503\pi$
$967$	−34.5610	+	16.2632i	−1.11141	+	0.522988i	−0.219685	+	0.975571i	$0.570503\pi$
$968$	−5.96371	−	1.93773i	−0.191681	−	0.0622809i
$969$	−49.4217	−	27.1698i	−1.58765	−	0.872821i
$970$	−1.56332	+	14.1267i	−0.0501951	+	0.453580i
$971$	−48.1630	−	6.08440i	−1.54562	−	0.195258i	−0.694218	−	0.719765i	$-0.744250\pi$
$971$	−48.1630	−	6.08440i	−1.54562	−	0.195258i	−0.851406	+	0.524507i	$0.824250\pi$
$972$	−0.125333	+	0.992115i	−0.00402007	+	0.0318221i
$973$	−12.2714	+	7.78768i	−0.393403	+	0.249661i
$974$	−27.3922	+	19.9016i	−0.877703	+	0.637689i
$975$	−2.16497	−	23.0308i	−0.0693344	−	0.737575i
$976$	−0.241297	−	0.175312i	−0.00772373	−	0.00561162i
$977$	15.6872	+	0.986956i	0.501879	+	0.0315755i	0.311713	−	0.950176i	$-0.399097\pi$
$977$	15.6872	+	0.986956i	0.501879	+	0.0315755i	0.190166	+	0.981752i	$0.439097\pi$
$978$	2.49712	+	4.54224i	0.0798491	+	0.145245i
$979$	−16.0474	+	34.1024i	−0.512877	+	1.08992i
$980$	−7.76319	+	5.09657i	−0.247986	+	0.162804i
$981$	−0.379910	+	1.99156i	−0.0121296	+	0.0635855i
$982$	5.56649	+	7.66162i	0.177634	+	0.244492i
$983$	7.54671	−	13.7274i	0.240703	−	0.437836i	−0.728170	−	0.685397i	$-0.759629\pi$
$983$	7.54671	−	13.7274i	0.240703	−	0.437836i	0.968872	+	0.247560i	$0.0796289\pi$
$984$	−2.73299	+	4.30650i	−0.0871245	+	0.137286i
$985$	35.8596	−	44.7363i	1.14258	−	1.42542i
$986$	53.9916	+	21.3768i	1.71944	+	0.680775i
$987$	4.33147	+	10.9401i	0.137872	+	0.348226i
$988$	−25.3159	+	20.9431i	−0.805406	+	0.666290i
$989$	−3.79003	+	0.973113i	−0.120516	+	0.0309432i
$990$	−3.88947	+	2.91872i	−0.123616	+	0.0927629i
$991$	19.4031	−	7.68223i	0.616360	−	0.244034i	−0.0391347	−	0.999234i	$-0.512460\pi$
$991$	19.4031	−	7.68223i	0.616360	−	0.244034i	0.655495	+	0.755200i	$0.272460\pi$
$992$	2.67817	+	2.85197i	0.0850321	+	0.0905500i
$993$	0.739899	−	1.01838i	0.0234800	−	0.0323174i
$994$	1.53543	+	3.26295i	0.0487008	+	0.103495i
$995$	−4.16551	−	2.55412i	−0.132056	−	0.0809710i
$996$	−13.5284	+	7.43729i	−0.428663	+	0.235659i
$997$	36.3749	−	6.93888i	1.15200	−	0.219756i	0.424217	−	0.905560i	$-0.360549\pi$
$997$	36.3749	−	6.93888i	1.15200	−	0.219756i	0.727786	+	0.685804i	$0.240549\pi$
$998$	−5.11543	−	19.9233i	−0.161926	−	0.630661i
$999$	2.28052			0.0721524

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.o.b.229.4	✓	280
125.119	even	50	inner	750.2.o.b.619.4	yes	280

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
750.2.o.b.229.4	✓	280	1.1	even	1	trivial
750.2.o.b.619.4	yes	280	125.119	even	50	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	750.o (of order \(50\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.248690 - 0.968583i) q^{2} +(0.982287 - 0.187381i) q^{3} +(-0.876307 + 0.481754i) q^{4} +(0.522565 - 2.17415i) q^{5} +(-0.425779 - 0.904827i) q^{6} +(-0.991752 + 1.36503i) q^{7} +(0.684547 + 0.728969i) q^{8} +(0.929776 - 0.368125i) q^{9} +O(q^{10})\)	\(q+(-0.248690 - 0.968583i) q^{2} +(0.982287 - 0.187381i) q^{3} +(-0.876307 + 0.481754i) q^{4} +(0.522565 - 2.17415i) q^{5} +(-0.425779 - 0.904827i) q^{6} +(-0.991752 + 1.36503i) q^{7} +(0.684547 + 0.728969i) q^{8} +(0.929776 - 0.368125i) q^{9} +(-2.23580 + 0.0345414i) q^{10} +(2.10639 - 0.540829i) q^{11} +(-0.770513 + 0.637424i) q^{12} +(1.70311 + 4.30157i) q^{13} +(1.56878 + 0.621125i) q^{14} +(0.105914 - 2.23356i) q^{15} +(0.535827 - 0.844328i) q^{16} +(3.82580 - 6.95911i) q^{17} +(-0.587785 - 0.809017i) q^{18} +(1.33073 - 6.97594i) q^{19} +(0.589477 + 2.15697i) q^{20} +(-0.718404 + 1.52669i) q^{21} +(-1.04768 - 1.90572i) q^{22} +(3.06920 + 0.193098i) q^{23} +(0.809017 + 0.587785i) q^{24} +(-4.45385 - 2.27227i) q^{25} +(3.74288 - 2.71936i) q^{26} +(0.844328 - 0.535827i) q^{27} +(0.211471 - 1.67396i) q^{28} +(-7.25457 - 0.916466i) q^{29} +(-2.18973 + 0.452877i) q^{30} +(-3.42840 - 1.88478i) q^{31} +(-0.951057 - 0.309017i) q^{32} +(1.96774 - 0.925948i) q^{33} +(-7.69191 - 1.97495i) q^{34} +(2.44952 + 2.86953i) q^{35} +(-0.637424 + 0.770513i) q^{36} +(1.92551 + 1.22196i) q^{37} +(-7.08772 + 0.445922i) q^{38} +(2.47898 + 3.90625i) q^{39} +(1.94261 - 1.10737i) q^{40} +(0.320264 + 5.09044i) q^{41} +(1.65738 + 0.316163i) q^{42} +(-1.21012 + 0.393192i) q^{43} +(-1.58530 + 1.48869i) q^{44} +(-0.314489 - 2.21384i) q^{45} +(-0.576248 - 3.02080i) q^{46} +(4.77375 - 5.08353i) q^{47} +(0.368125 - 0.929776i) q^{48} +(1.28339 + 3.94985i) q^{49} +(-1.09325 + 4.87902i) q^{50} +(2.45403 - 7.55273i) q^{51} +(-3.56475 - 2.94902i) q^{52} +(-9.39033 - 4.41876i) q^{53} +(-0.728969 - 0.684547i) q^{54} +(-0.0751176 - 4.86223i) q^{55} +(-1.67396 + 0.211471i) q^{56} -7.10174i q^{57} +(0.916466 + 7.25457i) q^{58} +(7.59591 + 9.18187i) q^{59} +(0.983212 + 2.00831i) q^{60} +(0.0187279 - 0.297671i) q^{61} +(-0.972957 + 3.78942i) q^{62} +(-0.419607 + 1.63426i) q^{63} +(-0.0627905 + 0.998027i) q^{64} +(10.2422 - 1.45497i) q^{65} +(-1.38621 - 1.67565i) q^{66} +(-1.41679 - 11.2150i) q^{67} +7.94141i q^{68} +(3.05102 - 0.385433i) q^{69} +(2.17021 - 3.08619i) q^{70} +(1.55801 + 1.46307i) q^{71} +(0.904827 + 0.425779i) q^{72} +(-2.81321 - 2.32729i) q^{73} +(0.704719 - 2.16890i) q^{74} +(-4.80074 - 1.39745i) q^{75} +(2.19456 + 6.75415i) q^{76} +(-1.35077 + 3.41166i) q^{77} +(3.16703 - 3.37254i) q^{78} +(1.38816 + 7.27699i) q^{79} +(-1.55569 - 1.60618i) q^{80} +(0.728969 - 0.684547i) q^{81} +(4.85087 - 1.57614i) q^{82} +(15.1645 + 2.89278i) q^{83} +(-0.105945 - 1.68394i) q^{84} +(-13.1309 - 11.9545i) q^{85} +(0.681784 + 1.07432i) q^{86} +(-7.29780 + 0.459139i) q^{87} +(1.83617 + 1.16527i) q^{88} +(-11.0470 + 13.3536i) q^{89} +(-2.06608 + 0.855169i) q^{90} +(-7.56084 - 1.94129i) q^{91} +(-2.78258 + 1.30939i) q^{92} +(-3.72085 - 1.20898i) q^{93} +(-6.11100 - 3.35955i) q^{94} +(-14.4714 - 6.53860i) q^{95} +(-0.992115 - 0.125333i) q^{96} +(0.796645 - 6.30609i) q^{97} +(3.50660 - 2.22535i) q^{98} +(1.75938 - 1.27826i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 280 q+O(q^{10}) \) 280 * q	\( 280 q - 10 q^{11} - 20 q^{13} + 30 q^{17} + 10 q^{19} + 20 q^{22} + 60 q^{23} + 70 q^{24} + 20 q^{25} + 20 q^{29} + 10 q^{30} + 20 q^{31} + 20 q^{33} - 10 q^{34} + 30 q^{35} - 20 q^{37} + 90 q^{38} - 40 q^{41} - 10 q^{46} - 100 q^{47} + 120 q^{49} - 20 q^{50} - 30 q^{51} + 80 q^{52} - 30 q^{53} - 10 q^{55} + 30 q^{58} + 20 q^{59} + 60 q^{61} - 50 q^{62} - 10 q^{63} + 20 q^{65} + 40 q^{66} + 50 q^{67} + 10 q^{69} + 20 q^{70} + 80 q^{71} - 20 q^{73} + 80 q^{75} - 30 q^{76} - 100 q^{77} - 100 q^{79} + 100 q^{82} + 30 q^{83} - 20 q^{86} - 10 q^{87} - 60 q^{89} - 10 q^{90} + 70 q^{91} - 120 q^{92} + 50 q^{93} + 30 q^{94} - 20 q^{95} + 10 q^{97} + 40 q^{98} + 20 q^{99}+O(q^{100}) \) 280 * q - 10 * q^11 - 20 * q^13 + 30 * q^17 + 10 * q^19 + 20 * q^22 + 60 * q^23 + 70 * q^24 + 20 * q^25 + 20 * q^29 + 10 * q^30 + 20 * q^31 + 20 * q^33 - 10 * q^34 + 30 * q^35 - 20 * q^37 + 90 * q^38 - 40 * q^41 - 10 * q^46 - 100 * q^47 + 120 * q^49 - 20 * q^50 - 30 * q^51 + 80 * q^52 - 30 * q^53 - 10 * q^55 + 30 * q^58 + 20 * q^59 + 60 * q^61 - 50 * q^62 - 10 * q^63 + 20 * q^65 + 40 * q^66 + 50 * q^67 + 10 * q^69 + 20 * q^70 + 80 * q^71 - 20 * q^73 + 80 * q^75 - 30 * q^76 - 100 * q^77 - 100 * q^79 + 100 * q^82 + 30 * q^83 - 20 * q^86 - 10 * q^87 - 60 * q^89 - 10 * q^90 + 70 * q^91 - 120 * q^92 + 50 * q^93 + 30 * q^94 - 20 * q^95 + 10 * q^97 + 40 * q^98 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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