LMFDB - Embedded newform 570.2.bf.a.269.36

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(29,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 17]))

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

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

chi := DirichletCharacter("570.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.bf (of order $18$, degree $6$, 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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$40$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			269.36
Character	$\chi$	$=$	570.269
Dual form			570.2.bf.a.89.36

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.642788 - 0.766044i) q^{2} +(1.40021 + 1.01952i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(-0.722849 + 2.11601i) q^{5} +(1.68103 - 0.417284i) q^{6} +(-4.02623 + 2.32455i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(0.921151 + 2.85508i) q^{9} +O(q^{10})$	\(q+(0.642788 - 0.766044i) q^{2} +(1.40021 + 1.01952i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(-0.722849 + 2.11601i) q^{5} +(1.68103 - 0.417284i) q^{6} +(-4.02623 + 2.32455i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(0.921151 + 2.85508i) q^{9} +(1.15632 + 1.91388i) q^{10} +(-0.0906937 - 0.0523621i) q^{11} +(0.760890 - 1.55597i) q^{12} +(-1.33336 - 0.485303i) q^{13} +(-0.807307 + 4.57846i) q^{14} +(-3.16945 + 2.22589i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(3.79975 + 3.18837i) q^{17} +(2.77922 + 1.12957i) q^{18} +(3.84452 + 2.05419i) q^{19} +(2.20938 + 0.344426i) q^{20} +(-8.00748 - 0.849989i) q^{21} +(-0.0984085 + 0.0358178i) q^{22} +(0.445860 + 2.52860i) q^{23} +(-0.702853 - 1.58303i) q^{24} +(-3.95498 - 3.05911i) q^{25} +(-1.22883 + 0.709466i) q^{26} +(-1.62101 + 4.93683i) q^{27} +(2.98838 + 3.56141i) q^{28} +(5.99196 - 5.02786i) q^{29} +(-0.332157 + 3.85871i) q^{30} +(-2.96451 + 1.71156i) q^{31} +(-0.342020 + 0.939693i) q^{32} +(-0.0736056 - 0.165782i) q^{33} +(4.88487 - 0.861334i) q^{34} +(-2.00840 - 10.1998i) q^{35} +(2.65175 - 1.40294i) q^{36} -4.83826 q^{37} +(4.04481 - 1.62467i) q^{38} +(-1.37220 - 2.03891i) q^{39} +(1.68401 - 1.47109i) q^{40} +(-0.912946 + 0.332285i) q^{41} +(-5.79824 + 5.58772i) q^{42} +(3.52133 + 0.620906i) q^{43} +(-0.0358178 + 0.0984085i) q^{44} +(-6.70722 - 0.114628i) q^{45} +(2.22361 + 1.28380i) q^{46} +(4.06112 - 3.40768i) q^{47} +(-1.66446 - 0.479138i) q^{48} +(7.30704 - 12.6562i) q^{49} +(-4.88562 + 1.06333i) q^{50} +(2.06982 + 8.33830i) q^{51} +(-0.246395 + 1.39737i) q^{52} +(3.46921 - 0.611716i) q^{53} +(2.73986 + 4.41510i) q^{54} +(0.176356 - 0.154059i) q^{55} +4.64909 q^{56} +(3.28883 + 6.79585i) q^{57} -7.82195i q^{58} +(-1.98984 - 1.66967i) q^{59} +(2.74244 + 2.73478i) q^{60} +(-2.42070 - 13.7285i) q^{61} +(-0.594418 + 3.37111i) q^{62} +(-10.3455 - 9.35396i) q^{63} +(0.500000 + 0.866025i) q^{64} +(1.99072 - 2.47060i) q^{65} +(-0.174309 - 0.0501773i) q^{66} +(5.34450 - 4.48457i) q^{67} +(2.48011 - 4.29568i) q^{68} +(-1.95366 + 3.99512i) q^{69} +(-9.10450 - 5.01780i) q^{70} +(-2.73413 + 15.5060i) q^{71} +(0.629800 - 2.93315i) q^{72} +(2.57642 + 7.07867i) q^{73} +(-3.10997 + 3.70632i) q^{74} +(-2.41896 - 8.31557i) q^{75} +(1.35538 - 4.14282i) q^{76} +0.486872 q^{77} +(-2.44393 - 0.259422i) q^{78} +(-1.78665 - 4.90879i) q^{79} +(-0.0444616 - 2.23563i) q^{80} +(-7.30296 + 5.25992i) q^{81} +(-0.332285 + 0.912946i) q^{82} +(2.49077 + 4.31413i) q^{83} +(0.553409 + 8.03343i) q^{84} +(-9.49326 + 5.73559i) q^{85} +(2.73911 - 2.29839i) q^{86} +(13.5160 - 0.931093i) q^{87} +(0.0523621 + 0.0906937i) q^{88} +(16.3079 + 5.93559i) q^{89} +(-4.39913 + 5.06435i) q^{90} +(6.49653 - 1.14551i) q^{91} +(2.41276 - 0.878173i) q^{92} +(-5.89589 - 0.625844i) q^{93} -5.30141i q^{94} +(-7.12568 + 6.65017i) q^{95} +(-1.43694 + 0.967066i) q^{96} +(7.91209 + 6.63904i) q^{97} +(-4.99831 - 13.7327i) q^{98} +(0.0659552 - 0.307171i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q+O(q^{10}) $ 240 * q	$ 240 q - 30 q^{15} + 48 q^{19} + 12 q^{25} - 48 q^{39} + 36 q^{45} - 72 q^{46} + 216 q^{49} - 180 q^{51} + 36 q^{54} + 60 q^{55} + 6 q^{60} - 72 q^{61} + 120 q^{64} - 156 q^{66} + 48 q^{79} - 120 q^{81} - 108 q^{84} - 48 q^{85} - 36 q^{90} - 24 q^{91} - 216 q^{99}+O(q^{100}) $ 240 * q - 30 * q^15 + 48 * q^19 + 12 * q^25 - 48 * q^39 + 36 * q^45 - 72 * q^46 + 216 * q^49 - 180 * q^51 + 36 * q^54 + 60 * q^55 + 6 * q^60 - 72 * q^61 + 120 * q^64 - 156 * q^66 + 48 * q^79 - 120 * q^81 - 108 * q^84 - 48 * q^85 - 36 * q^90 - 24 * q^91 - 216 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{13}{18}\right)$	$-1$

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 $

$2$	0.642788	−	0.766044i	0.454519	−	0.541675i
$2$	0.642788	−	0.766044i	0.454519	−	0.541675i
$3$	1.40021	+	1.01952i	0.808409	+	0.588621i
$3$	1.40021	+	1.01952i	0.808409	+	0.588621i
$4$	−0.173648	−	0.984808i	−0.0868241	−	0.492404i
$5$	−0.722849	+	2.11601i	−0.323268	+	0.946308i
$5$	−0.722849	+	2.11601i	−0.323268	+	0.946308i
$6$	1.68103	−	0.417284i	0.686279	−	0.170355i
$7$	−4.02623	+	2.32455i	−1.52177	+	0.878596i	−0.522104	+	0.852882i	$0.674853\pi$
$7$	−4.02623	+	2.32455i	−1.52177	+	0.878596i	−0.999669	+	0.0257143i	$0.991814\pi$
$8$	−0.866025	−	0.500000i	−0.306186	−	0.176777i
$9$	0.921151	+	2.85508i	0.307050	+	0.951693i
$10$	1.15632	+	1.91388i	0.365660	+	0.605221i
$11$	−0.0906937	−	0.0523621i	−0.0273452	−	0.0157878i	0.486265	−	0.873811i	$-0.338359\pi$
$11$	−0.0906937	−	0.0523621i	−0.0273452	−	0.0157878i	−0.513610	+	0.858024i	$0.671692\pi$
$12$	0.760890	−	1.55597i	0.219650	−	0.449170i
$13$	−1.33336	−	0.485303i	−0.369807	−	0.134599i	0.150430	−	0.988621i	$-0.451934\pi$
$13$	−1.33336	−	0.485303i	−0.369807	−	0.134599i	−0.520237	+	0.854022i	$0.674156\pi$
$14$	−0.807307	+	4.57846i	−0.215762	+	1.22365i
$15$	−3.16945	+	2.22589i	−0.818349	+	0.574721i
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	3.79975	+	3.18837i	0.921575	+	0.773293i	0.974286	−	0.225317i	$-0.0723416\pi$
$17$	3.79975	+	3.18837i	0.921575	+	0.773293i	−0.0527106	+	0.998610i	$0.516786\pi$
$18$	2.77922	+	1.12957i	0.655069	+	0.266242i
$19$	3.84452	+	2.05419i	0.881993	+	0.471262i
$19$	3.84452	+	2.05419i	0.881993	+	0.471262i
$20$	2.20938	+	0.344426i	0.494033	+	0.0770161i
$21$	−8.00748	−	0.849989i	−1.74738	−	0.185483i
$22$	−0.0984085	+	0.0358178i	−0.0209808	+	0.00763637i
$23$	0.445860	+	2.52860i	0.0929682	+	0.527249i	0.995351	+	0.0963137i	$0.0307052\pi$
$23$	0.445860	+	2.52860i	0.0929682	+	0.527249i	−0.902383	+	0.430935i	$0.858184\pi$
$24$	−0.702853	−	1.58303i	−0.143469	−	0.323136i
$25$	−3.95498	−	3.05911i	−0.790996	−	0.611822i
$26$	−1.22883	+	0.709466i	−0.240993	+	0.139138i
$27$	−1.62101	+	4.93683i	−0.311964	+	0.950094i
$28$	2.98838	+	3.56141i	0.564751	+	0.673044i
$29$	5.99196	−	5.02786i	1.11268	−	0.933649i	0.114468	−	0.993427i	$-0.463484\pi$
$29$	5.99196	−	5.02786i	1.11268	−	0.933649i	0.998212	+	0.0597776i	$0.0190392\pi$
$30$	−0.332157	+	3.85871i	−0.0606434	+	0.704502i
$31$	−2.96451	+	1.71156i	−0.532441	+	0.307405i	−0.742010	−	0.670389i	$-0.766127\pi$
$31$	−2.96451	+	1.71156i	−0.532441	+	0.307405i	0.209569	+	0.977794i	$0.432794\pi$
$32$	−0.342020	+	0.939693i	−0.0604612	+	0.166116i
$33$	−0.0736056	−	0.165782i	−0.0128131	−	0.0288589i
$34$	4.88487	−	0.861334i	0.837748	−	0.147718i
$35$	−2.00840	−	10.1998i	−0.339482	−	1.72409i
$36$	2.65175	−	1.40294i	0.441958	−	0.233823i
$37$	−4.83826			−0.795405			−0.397702	−	0.917514i	$-0.630192\pi$
$37$	−4.83826			−0.795405			−0.397702	+	0.917514i	$0.630192\pi$
$38$	4.04481	−	1.62467i	0.656154	−	0.263556i
$39$	−1.37220	−	2.03891i	−0.219728	−	0.326487i
$40$	1.68401	−	1.47109i	0.266265	−	0.232600i
$41$	−0.912946	+	0.332285i	−0.142578	+	0.0518942i	−0.412324	−	0.911037i	$-0.635283\pi$
$41$	−0.912946	+	0.332285i	−0.142578	+	0.0518942i	0.269745	+	0.962932i	$0.413060\pi$
$42$	−5.79824	+	5.58772i	−0.894688	+	0.862204i
$43$	3.52133	+	0.620906i	0.536998	+	0.0946873i	0.435569	−	0.900155i	$-0.356547\pi$
$43$	3.52133	+	0.620906i	0.536998	+	0.0946873i	0.101429	+	0.994843i	$0.467658\pi$
$44$	−0.0358178	+	0.0984085i	−0.00539973	+	0.0148356i
$45$	−6.70722	−	0.114628i	−0.999854	−	0.0170877i
$46$	2.22361	+	1.28380i	0.327854	+	0.189286i
$47$	4.06112	−	3.40768i	0.592375	−	0.497061i	−0.296610	−	0.954999i	$-0.595856\pi$
$47$	4.06112	−	3.40768i	0.592375	−	0.497061i	0.888984	+	0.457937i	$0.151412\pi$
$48$	−1.66446	−	0.479138i	−0.240244	−	0.0691577i
$49$	7.30704	−	12.6562i	1.04386	−	1.80802i
$50$	−4.88562	+	1.06333i	−0.690932	+	0.150378i
$51$	2.06982	+	8.33830i	0.289833	+	1.16760i
$52$	−0.246395	+	1.39737i	−0.0341688	+	0.193781i
$53$	3.46921	−	0.611716i	0.476533	−	0.0840257i	0.0697774	−	0.997563i	$-0.477771\pi$
$53$	3.46921	−	0.611716i	0.476533	−	0.0840257i	0.406756	+	0.913537i	$0.366660\pi$
$54$	2.73986	+	4.41510i	0.372848	+	0.600820i
$55$	0.176356	−	0.154059i	0.0237799	−	0.0207733i
$56$	4.64909			0.621261
$57$	3.28883	+	6.79585i	0.435616	+	0.900133i
$58$		−	7.82195i		−	1.02707i
$59$	−1.98984	−	1.66967i	−0.259055	−	0.217373i	0.504005	−	0.863701i	$-0.331859\pi$
$59$	−1.98984	−	1.66967i	−0.259055	−	0.217373i	−0.763060	+	0.646328i	$0.776304\pi$
$60$	2.74244	+	2.73478i	0.354047	+	0.353059i
$61$	−2.42070	−	13.7285i	−0.309939	−	1.75775i	−0.599293	−	0.800530i	$-0.704552\pi$
$61$	−2.42070	−	13.7285i	−0.309939	−	1.75775i	0.289354	−	0.957222i	$-0.406559\pi$
$62$	−0.594418	+	3.37111i	−0.0754911	+	0.428132i
$63$	−10.3455	−	9.35396i	−1.30342	−	1.17849i
$64$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$65$	1.99072	−	2.47060i	0.246919	−	0.306440i
$66$	−0.174309	−	0.0501773i	−0.0214560	−	0.00617640i
$67$	5.34450	−	4.48457i	0.652935	−	0.547877i	−0.255025	−	0.966934i	$-0.582084\pi$
$67$	5.34450	−	4.48457i	0.652935	−	0.547877i	0.907960	+	0.419057i	$0.137639\pi$
$68$	2.48011	−	4.29568i	0.300758	−	0.520928i
$69$	−1.95366	+	3.99512i	−0.235194	+	0.480956i
$70$	−9.10450	−	5.01780i	−1.08820	−	0.599742i
$71$	−2.73413	+	15.5060i	−0.324482	+	1.84023i	0.188808	+	0.982014i	$0.439538\pi$
$71$	−2.73413	+	15.5060i	−0.324482	+	1.84023i	−0.513290	+	0.858215i	$0.671573\pi$
$72$	0.629800	−	2.93315i	0.0742226	−	0.345675i
$73$	2.57642	+	7.07867i	0.301548	+	0.828495i	0.994232	+	0.107254i	$0.0342059\pi$
$73$	2.57642	+	7.07867i	0.301548	+	0.828495i	−0.692684	+	0.721241i	$0.743572\pi$
$74$	−3.10997	+	3.70632i	−0.361527	+	0.430851i
$75$	−2.41896	−	8.31557i	−0.279317	−	0.960199i
$76$	1.35538	−	4.14282i	0.155473	−	0.475214i
$77$	0.486872			0.0554842
$78$	−2.44393	−	0.259422i	−0.276721	−	0.0293737i
$79$	−1.78665	−	4.90879i	−0.201014	−	0.552282i	0.797696	−	0.603060i	$-0.206052\pi$
$79$	−1.78665	−	4.90879i	−0.201014	−	0.552282i	−0.998710	+	0.0507779i	$0.983830\pi$
$80$	−0.0444616	−	2.23563i	−0.00497096	−	0.249951i
$81$	−7.30296	+	5.25992i	−0.811440	+	0.584436i
$82$	−0.332285	+	0.912946i	−0.0366947	+	0.100818i
$83$	2.49077	+	4.31413i	0.273397	+	0.473538i	0.969729	−	0.244182i	$-0.0785193\pi$
$83$	2.49077	+	4.31413i	0.273397	+	0.473538i	−0.696332	+	0.717719i	$0.745186\pi$
$84$	0.553409	+	8.03343i	0.0603819	+	0.876519i
$85$	−9.49326	+	5.73559i	−1.02969	+	0.622113i
$86$	2.73911	−	2.29839i	0.295366	−	0.247841i
$87$	13.5160	−	0.931093i	1.44907	−	0.0998237i
$88$	0.0523621	+	0.0906937i	0.00558181	+	0.00966798i
$89$	16.3079	+	5.93559i	1.72863	+	0.629171i	0.998532	−	0.0541685i	$-0.0172508\pi$
$89$	16.3079	+	5.93559i	1.72863	+	0.629171i	0.730101	+	0.683339i	$0.239473\pi$
$90$	−4.39913	+	5.06435i	−0.463709	+	0.533829i
$91$	6.49653	−	1.14551i	0.681021	−	0.120082i
$92$	2.41276	−	0.878173i	0.251548	−	0.0915558i
$93$	−5.89589	−	0.625844i	−0.611375	−	0.0648970i
$94$		−	5.30141i		−	0.546799i
$95$	−7.12568	+	6.65017i	−0.731079	+	0.682293i
$96$	−1.43694	+	0.967066i	−0.146657	+	0.0987007i
$97$	7.91209	+	6.63904i	0.803351	+	0.674092i	0.949011	−	0.315243i	$-0.102086\pi$
$97$	7.91209	+	6.63904i	0.803351	+	0.674092i	−0.145660	+	0.989335i	$0.546530\pi$
$98$	−4.99831	−	13.7327i	−0.504905	−	1.38722i
$99$	0.0659552	−	0.307171i	0.00662875	−	0.0308719i
$100$	−2.32586	+	4.42610i	−0.232586	+	0.442610i
$101$	−0.0861922	+	0.236811i	−0.00857645	+	0.0235636i	−0.943907	−	0.330211i	$-0.892880\pi$
$101$	−0.0861922	+	0.236811i	−0.00857645	+	0.0235636i	0.935331	+	0.353775i	$0.115102\pi$
$102$	7.71796	+	3.77418i	0.764192	+	0.373700i
$103$	7.45112	−	12.9057i	0.734180	−	1.27164i	−0.220902	−	0.975296i	$-0.570900\pi$
$103$	7.45112	−	12.9057i	0.734180	−	1.27164i	0.955082	−	0.296341i	$-0.0957666\pi$
$104$	0.912071	+	1.08696i	0.0894360	+	0.106586i
$105$	7.58678	−	16.3295i	0.740394	−	1.59359i
$106$	1.76137	−	3.05078i	0.171079	−	0.296318i
$107$	−8.47883	+	4.89525i	−0.819679	+	0.473242i	−0.850306	−	0.526289i	$-0.823583\pi$
$107$	−8.47883	+	4.89525i	−0.819679	+	0.473242i	0.0306267	+	0.999531i	$0.490250\pi$
$108$	5.14332	+	0.739116i	0.494916	+	0.0711215i
$109$	9.47129	+	1.67004i	0.907185	+	0.159961i	0.607725	−	0.794148i	$-0.292082\pi$
$109$	9.47129	+	1.67004i	0.907185	+	0.159961i	0.299460	+	0.954109i	$0.403193\pi$
$110$	−0.00465620	−	0.234124i	−0.000443951	−	0.0223228i
$111$	−6.77456	−	4.93271i	−0.643012	−	0.468192i
$112$	2.98838	−	3.56141i	0.282375	−	0.336522i
$113$			1.39050i			0.130807i	0.997859	+	0.0654036i	$0.0208335\pi$
$113$			1.39050i			0.130807i	−0.997859	+	0.0654036i	$0.979167\pi$
$114$	7.31994	+	1.84890i	0.685576	+	0.173165i
$115$	−5.67282	−	0.884351i	−0.528993	−	0.0824661i
$116$	−5.99196	−	5.02786i	−0.556340	−	0.466825i
$117$	0.157354	−	4.25388i	0.0145473	−	0.393272i
$118$	−2.55809	+	0.451060i	−0.235491	+	0.0415235i
$119$	−22.7102	−	4.00442i	−2.08184	−	0.367085i
$120$	3.85777	−	0.342947i	0.352165	−	0.0313067i
$121$	−5.49452	−	9.51678i	−0.499501	−	0.865162i
$122$	−12.0726	−	6.97013i	−1.09300	−	0.631046i
$123$	−1.61708	−	0.465501i	−0.145807	−	0.0419728i
$124$	2.20034	+	2.62226i	0.197596	+	0.235486i
$125$	9.33195	−	6.15749i	0.834675	−	0.550743i
$126$	−13.8155	+	1.91253i	−1.23079	+	0.170382i
$127$	−3.69581	−	1.34517i	−0.327950	−	0.119364i	0.172798	−	0.984957i	$-0.444719\pi$
$127$	−3.69581	−	1.34517i	−0.327950	−	0.119364i	−0.500748	+	0.865593i	$0.666942\pi$
$128$	0.984808	+	0.173648i	0.0870455	+	0.0153485i
$129$	4.29756	+	4.45947i	0.378379	+	0.392635i
$130$	−0.612976	−	3.11305i	−0.0537616	−	0.273033i
$131$	5.21813	−	6.21873i	0.455910	−	0.543333i	−0.488300	−	0.872676i	$-0.662383\pi$
$131$	5.21813	−	6.21873i	0.455910	−	0.543333i	0.944210	+	0.329343i	$0.106827\pi$
$132$	−0.150482	+	0.101275i	−0.0130978	+	0.00881487i
$133$	−20.2540	+	0.666134i	−1.75624	+	0.0577611i
$134$		−	6.97675i		−	0.602699i
$135$	−9.27463	−	6.99866i	−0.798233	−	0.602349i
$136$	−1.69650	−	4.66108i	−0.145473	−	0.399685i
$137$	−1.52264	−	8.63533i	−0.130088	−	0.737766i	−0.978155	−	0.207877i	$-0.933345\pi$
$137$	−1.52264	−	8.63533i	−0.130088	−	0.737766i	0.848067	−	0.529889i	$-0.177767\pi$
$138$	1.80465	+	4.06461i	0.153622	+	0.346002i
$139$	13.7768	+	5.01436i	1.16854	+	0.425312i	0.852139	−	0.523315i	$-0.175305\pi$
$139$	13.7768	+	5.01436i	1.16854	+	0.425312i	0.316396	+	0.948627i	$0.397527\pi$
$140$	−9.69612	+	3.74907i	−0.819472	+	0.316854i
$141$	9.16060	−	0.631058i	0.771462	−	0.0531447i
$142$	10.1209	+	12.0616i	0.849323	+	1.01218i
$143$	0.0955159	+	0.113831i	0.00798744	+	0.00951906i
$144$	−1.84209	−	2.36785i	−0.153508	−	0.197320i
$145$	6.30770	+	16.3134i	0.523826	+	1.35476i
$146$	7.07867	+	2.57642i	0.585835	+	0.213226i
$147$	23.1346	−	10.2715i	1.90811	−	0.847183i
$148$	0.840155	+	4.76475i	0.0690603	+	0.391660i
$149$	5.04115	+	13.8504i	0.412987	+	1.13467i	0.955594	+	0.294686i	$0.0952149\pi$
$149$	5.04115	+	13.8504i	0.412987	+	1.13467i	−0.542607	+	0.839986i	$0.682563\pi$
$150$	−7.92497	−	3.49211i	−0.647071	−	0.285130i
$151$			17.8106i			1.44941i	0.689059	+	0.724705i	$0.258024\pi$
$151$			17.8106i			1.44941i	−0.689059	+	0.724705i	$0.741976\pi$
$152$	−2.30236	−	3.70124i	−0.186746	−	0.300210i
$153$	−5.60290	+	13.7856i	−0.452968	+	1.11450i
$154$	0.312955	−	0.372966i	0.0252187	−	0.0300544i
$155$	−1.47878	−	7.51011i	−0.118779	−	0.603227i
$156$	−1.76966	+	1.70541i	−0.141686	+	0.136542i
$157$	−17.7541	−	3.13052i	−1.41693	−	0.249843i	−0.587848	−	0.808972i	$-0.700025\pi$
$157$	−17.7541	−	3.13052i	−1.41693	−	0.249843i	−0.829081	+	0.559129i	$0.811136\pi$
$158$	−4.90879	−	1.78665i	−0.390523	−	0.142139i
$159$	5.48127	+	2.68041i	0.434693	+	0.212570i
$160$	−1.74117	−	1.40297i	−0.137651	−	0.110915i
$161$	−7.67298	−	9.14430i	−0.604716	−	0.720672i
$162$	−0.664920	+	8.97540i	−0.0522411	+	0.705174i
$163$	−12.5756	−	7.26050i	−0.984993	−	0.568686i	−0.0812193	−	0.996696i	$-0.525881\pi$
$163$	−12.5756	−	7.26050i	−0.984993	−	0.568686i	−0.903774	+	0.428010i	$0.859215\pi$
$164$	0.485768	+	0.841375i	0.0379321	+	0.0657004i
$165$	0.404001	−	0.0359149i	0.0314515	−	0.00279597i
$166$	4.90585	+	0.865034i	0.380768	+	0.0671397i
$167$	−14.3743	+	2.53457i	−1.11232	+	0.196131i	−0.699464	−	0.714667i	$-0.746578\pi$
$167$	−14.3743	+	2.53457i	−1.11232	+	0.196131i	−0.412851	+	0.910799i	$0.635467\pi$
$168$	6.50969	+	4.73985i	0.502233	+	0.365688i
$169$	−8.41625	−	7.06207i	−0.647404	−	0.543236i
$170$	−1.70843	+	10.9590i	−0.131031	+	0.840519i
$171$	−2.32348	+	12.8686i	−0.177681	+	0.984088i
$172$		−	3.57565i		−	0.272641i
$173$	−2.45142	+	2.92149i	−0.186378	+	0.222117i	−0.851140	−	0.524938i	$-0.824088\pi$
$173$	−2.45142	+	2.92149i	−0.186378	+	0.222117i	0.664762	+	0.747055i	$0.268533\pi$
$174$	7.97465	−	10.9523i	0.604557	−	0.830295i
$175$	23.0347	+	3.12315i	1.74126	+	0.236088i
$176$	0.103133	+	0.0181851i	0.00777395	+	0.00137076i
$177$	−1.08392	−	4.36657i	−0.0814722	−	0.328212i
$178$	15.0294	−	8.67725i	1.12650	−	0.650387i
$179$	−12.0121	+	20.8056i	−0.897830	+	1.55509i	−0.0675672	+	0.997715i	$0.521524\pi$
$179$	−12.0121	+	20.8056i	−0.897830	+	1.55509i	−0.830263	+	0.557372i	$0.811810\pi$
$180$	1.05181	+	6.62523i	0.0783973	+	0.493816i
$181$	−2.84819	−	3.39434i	−0.211704	−	0.252299i	0.649734	−	0.760162i	$-0.274880\pi$
$181$	−2.84819	−	3.39434i	−0.211704	−	0.252299i	−0.861438	+	0.507863i	$0.830436\pi$
$182$	3.29837	−	5.71295i	0.244492	−	0.423472i
$183$	10.6070	−	21.6906i	0.784092	−	1.60342i
$184$	0.878173	−	2.41276i	0.0647398	−	0.177871i
$185$	3.49733	−	10.2378i	0.257129	−	0.752698i
$186$	−4.26923	+	4.11423i	−0.313035	+	0.301670i
$187$	−0.177664	−	0.488128i	−0.0129921	−	0.0356954i
$188$	−4.06112	−	3.40768i	−0.296187	−	0.248531i
$189$	−4.94931	−	23.6450i	−0.360010	−	1.71992i
$190$	0.514025	+	9.73323i	0.0372913	+	0.706123i
$191$		−	8.06560i		−	0.583606i	−0.956478	−	0.291803i	$-0.905745\pi$
$191$		−	8.06560i		−	0.583606i	0.956478	−	0.291803i	$-0.0942552\pi$
$192$	−0.182829	+	1.72237i	−0.0131945	+	0.124302i
$193$	16.0842	−	5.85417i	1.15777	−	0.421392i	0.309467	−	0.950910i	$-0.399849\pi$
$193$	16.0842	−	5.85417i	1.15777	−	0.421392i	0.848299	+	0.529518i	$0.177627\pi$
$194$	10.1716	−	1.79353i	0.730278	−	0.128768i
$195$	5.30625	−	1.42976i	0.379988	−	0.102387i
$196$	−13.7327	−	4.99831i	−0.980910	−	0.357022i
$197$	−11.8521	−	20.5284i	−0.844424	−	1.46258i	−0.886121	−	0.463455i	$-0.846610\pi$
$197$	−11.8521	−	20.5284i	−0.844424	−	1.46258i	0.0416969	−	0.999130i	$-0.486724\pi$
$198$	−0.192912	−	0.247970i	−0.0137096	−	0.0176225i
$199$	−4.91779	+	4.12652i	−0.348613	+	0.292521i	−0.800233	−	0.599689i	$-0.795291\pi$
$199$	−4.91779	+	4.12652i	−0.348613	+	0.292521i	0.451620	+	0.892211i	$0.350846\pi$
$200$	1.89556	+	4.62675i	0.134036	+	0.327161i
$201$	12.0555	−	0.830483i	0.850330	−	0.0585778i
$202$	0.126005	+	0.218246i	0.00886566	+	0.0153558i
$203$	−12.4376	+	34.1719i	−0.872946	+	2.39840i
$204$	7.85220	−	3.48631i	0.549764	−	0.244090i
$205$	−0.0431960	−	2.17199i	−0.00301694	−	0.151699i
$206$	−5.09686	−	14.0035i	−0.355115	−	0.975671i
$207$	−6.80864	+	3.60219i	−0.473233	+	0.250369i
$208$	1.41893			0.0983852
$209$	−0.241112	−	0.387609i	−0.0166781	−	0.0268114i
$210$	−7.63242	−	16.3082i	−0.526687	−	1.12537i
$211$	−4.41320	+	5.25944i	−0.303817	+	0.362075i	−0.896254	−	0.443542i	$-0.853722\pi$
$211$	−4.41320	+	5.25944i	−0.303817	+	0.362075i	0.592437	+	0.805617i	$0.298166\pi$
$212$	−1.20485	−	3.31029i	−0.0827491	−	0.227351i
$213$	−19.6371	+	18.9241i	−1.34551	+	1.29666i
$214$	−1.70010	+	9.64177i	−0.116217	+	0.659098i
$215$	−3.85923	+	7.00235i	−0.263198	+	0.477556i
$216$	3.87226	−	3.46491i	0.263474	−	0.235758i
$217$	7.95719	−	13.7823i	0.540169	−	0.935601i
$218$	7.36735	−	6.18194i	0.498980	−	0.418694i
$219$	−3.60933	+	12.5383i	−0.243896	+	0.847261i
$220$	−0.182342	−	0.146925i	−0.0122935	−	0.00990569i
$221$	−3.51911	−	6.09527i	−0.236721	−	0.410012i
$222$	−8.13328	+	2.01893i	−0.545870	+	0.135502i
$223$	−2.42000	+	13.7245i	−0.162055	+	0.919061i	0.789994	+	0.613115i	$0.210084\pi$
$223$	−2.42000	+	13.7245i	−0.162055	+	0.919061i	−0.952049	+	0.305946i	$0.901027\pi$
$224$	−0.807307	−	4.57846i	−0.0539404	−	0.305911i
$225$	5.09086	−	14.1097i	0.339391	−	0.940645i
$226$	1.06518	+	0.893796i	0.0708550	+	0.0594544i
$227$		−	1.58854i		−	0.105435i	−0.998609	−	0.0527176i	$-0.983212\pi$
$227$		−	1.58854i		−	0.105435i	0.998609	−	0.0527176i	$-0.0167883\pi$
$228$	6.12151	−	4.41895i	0.405407	−	0.292652i
$229$	16.9141			1.11771			0.558857	−	0.829264i	$-0.311240\pi$
$229$	16.9141			1.11771			0.558857	+	0.829264i	$0.311240\pi$
$230$	−4.32387	+	3.77718i	−0.285108	+	0.249060i
$231$	0.681721	+	0.496377i	0.0448540	+	0.0326592i
$232$	−7.70312	+	1.35827i	−0.505735	+	0.0891747i
$233$	−2.53356	+	14.3685i	−0.165979	+	0.941314i	0.782070	+	0.623190i	$0.214164\pi$
$233$	−2.53356	+	14.3685i	−0.165979	+	0.941314i	−0.948049	+	0.318124i	$0.896947\pi$
$234$	−3.15752	−	2.85488i	−0.206414	−	0.186630i
$235$	4.27511	+	11.0566i	0.278877	+	0.721253i
$236$	−1.29878	+	2.24955i	−0.0845431	+	0.146433i
$237$	2.50294	−	8.69485i	0.162583	−	0.564791i
$238$	−17.6654	+	14.8230i	−1.14508	+	0.960834i
$239$	15.6740	+	9.04939i	1.01387	+	0.585356i	0.912322	−	0.409474i	$-0.134288\pi$
$239$	15.6740	+	9.04939i	1.01387	+	0.585356i	0.101546	+	0.994831i	$0.467621\pi$
$240$	2.21701	−	3.17567i	0.143108	−	0.204988i
$241$	8.06391	−	22.1554i	0.519442	−	1.42716i	−0.351695	−	0.936115i	$-0.614394\pi$
$241$	8.06391	−	22.1554i	0.519442	−	1.42716i	0.871137	−	0.491041i	$-0.163383\pi$
$242$	−10.8221	−	1.90823i	−0.695670	−	0.122665i
$243$	−15.5882	−	0.0805574i	−0.999987	−	0.00516776i
$244$	−13.0996	+	4.76785i	−0.838614	+	0.305230i
$245$	21.4987	+	24.6102i	1.37350	+	1.57229i
$246$	−1.39604	+	0.939540i	−0.0890080	+	0.0599029i
$247$	−4.12922	−	4.60472i	−0.262736	−	0.292992i
$248$	3.42312			0.217368
$249$	−0.910768	+	8.58007i	−0.0577176	+	0.543740i
$250$	1.28155	−	11.1066i	0.0810521	−	0.702446i
$251$	10.2777	−	1.81223i	0.648721	−	0.114387i	0.160401	−	0.987052i	$-0.448721\pi$
$251$	10.2777	−	1.81223i	0.648721	−	0.114387i	0.488320	+	0.872665i	$0.337610\pi$
$252$	−7.41537	+	11.8127i	−0.467124	+	0.744128i
$253$	0.0919659	−	0.252674i	0.00578184	−	0.0158855i
$254$	−3.40608	+	1.96650i	−0.213716	+	0.123389i
$255$	−19.1401	−	1.64758i	−1.19860	−	0.103175i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	−6.00519	−	7.15671i	−0.374593	−	0.446423i	0.545507	−	0.838107i	$-0.316337\pi$
$257$	−6.00519	−	7.15671i	−0.374593	−	0.446423i	−0.920100	+	0.391683i	$0.871893\pi$
$258$	6.17857	−	0.425631i	0.384661	−	0.0264986i
$259$	19.4800	−	11.2468i	1.21043	−	0.698840i
$260$	−2.77875	−	1.53146i	−0.172331	−	0.0949774i
$261$	19.8744	+	12.4761i	1.23020	+	0.772253i
$262$	−1.40967	−	7.99464i	−0.0870897	−	0.493910i
$263$	12.1414	−	4.41912i	0.748672	−	0.272494i	0.0606254	−	0.998161i	$-0.480691\pi$
$263$	12.1414	−	4.41912i	0.748672	−	0.272494i	0.688047	+	0.725666i	$0.258468\pi$
$264$	−0.0191466	+	0.180374i	−0.00117839	+	0.0111013i
$265$	−1.21332	+	7.78306i	−0.0745338	+	0.478110i
$266$	−12.5087	+	15.9436i	−0.766959	+	0.977567i
$267$	16.7829	+	24.9373i	1.02710	+	1.52614i
$268$	−5.34450	−	4.48457i	−0.326467	−	0.273939i
$269$	26.0845	−	9.49400i	1.59040	−	0.578859i	0.612970	−	0.790106i	$-0.289975\pi$
$269$	26.0845	−	9.49400i	1.59040	−	0.578859i	0.977433	+	0.211247i	$0.0677524\pi$
$270$	−11.3229	+	2.60612i	−0.689090	+	0.158604i
$271$	−0.913695	+	5.18182i	−0.0555030	+	0.314773i	−0.999902	−	0.0140297i	$-0.995534\pi$
$271$	−0.913695	+	5.18182i	−0.0555030	+	0.314773i	0.944399	+	0.328803i	$0.106645\pi$
$272$	−4.66108	−	1.69650i	−0.282620	−	0.102865i
$273$	10.2643	+	5.01939i	0.621226	+	0.303788i
$274$	−7.59379	−	4.38427i	−0.458757	−	0.264864i
$275$	0.198511	+	0.484533i	0.0119706	+	0.0292184i
$276$	4.27368	+	1.23024i	0.257245	+	0.0740517i
$277$	12.6467	+	7.30156i	0.759865	+	0.438708i	0.829247	−	0.558882i	$-0.188769\pi$
$277$	12.6467	+	7.30156i	0.759865	+	0.438708i	−0.0693823	+	0.997590i	$0.522103\pi$
$278$	12.6968	−	7.33050i	0.761503	−	0.439654i
$279$	−7.61739	−	6.88730i	−0.456041	−	0.412332i
$280$	−3.36059	+	9.83752i	−0.200834	+	0.587904i
$281$	−1.01731	−	5.76945i	−0.0606876	−	0.344177i	−0.999999	−	0.00111193i	$-0.999646\pi$
$281$	−1.01731	−	5.76945i	−0.0606876	−	0.344177i	0.939312	−	0.343065i	$-0.111465\pi$
$282$	5.40490	−	7.42307i	0.321857	−	0.442037i
$283$	−21.0306	+	25.0633i	−1.25014	+	1.48986i	−0.446451	+	0.894808i	$0.647312\pi$
$283$	−21.0306	+	25.0633i	−1.25014	+	1.48986i	−0.803688	+	0.595051i	$0.797132\pi$
$284$	15.7453			0.934309
$285$	−16.7574	+	2.04682i	−0.992623	+	0.121243i
$286$	0.148596			0.00878668
$287$	2.90332	−	3.46004i	0.171378	−	0.204240i
$288$	−2.99795	−	0.110896i	−0.176656	−	0.00653460i
$289$	1.32039	+	7.48829i	0.0776699	+	0.440488i
$290$	16.5513	+	5.65409i	0.971927	+	0.332020i
$291$	4.30992	+	17.3626i	0.252652	+	1.01781i
$292$	6.52374	−	3.76648i	0.381773	−	0.220417i
$293$	20.8904	+	12.0611i	1.22043	+	0.704616i	0.965010	−	0.262214i	$-0.0844525\pi$
$293$	20.8904	+	12.0611i	1.22043	+	0.704616i	0.255421	+	0.966830i	$0.417786\pi$
$294$	7.00217	−	24.3245i	0.408375	−	1.41864i
$295$	4.97140	−	3.00360i	0.289446	−	0.174876i
$296$	4.19005	+	2.41913i	0.243542	+	0.140609i
$297$	0.405519	−	0.362860i	0.0235306	−	0.0210553i
$298$	13.8504	+	5.04115i	0.802334	+	0.292026i
$299$	0.632645	−	3.58791i	0.0365868	−	0.207494i
$300$	−7.76919	+	3.82619i	−0.448554	+	0.220905i
$301$	−15.6210	+	5.68559i	−0.900381	+	0.327712i
$302$	13.6437	+	11.4485i	0.785109	+	0.658785i
$303$	−0.362121	+	0.243710i	−0.0208033	+	0.0140007i
$304$	−4.31524	−	0.615400i	−0.247496	−	0.0352956i
$305$	30.7994	+	4.80139i	1.76357	+	0.274927i
$306$	6.95888	+	13.1533i	0.397812	+	0.751922i
$307$	6.04000	−	2.19838i	0.344721	−	0.125468i	−0.163857	−	0.986484i	$-0.552394\pi$
$307$	6.04000	−	2.19838i	0.344721	−	0.125468i	0.508578	+	0.861016i	$0.330171\pi$
$308$	−0.0845445	−	0.479476i	−0.00481737	−	0.0273207i
$309$	23.5907	−	10.4741i	1.34203	−	0.595849i
$310$	−6.70362	−	3.69460i	−0.380740	−	0.209839i
$311$	6.75652	−	3.90088i	0.383127	−	0.221198i	−0.296051	−	0.955172i	$-0.595670\pi$
$311$	6.75652	−	3.90088i	0.383127	−	0.221198i	0.679178	+	0.733974i	$0.262336\pi$
$312$	0.168904	+	2.45185i	0.00956229	+	0.138809i
$313$	−20.1201	−	23.9782i	−1.13725	−	1.35533i	−0.925833	−	0.377933i	$-0.876635\pi$
$313$	−20.1201	−	23.9782i	−1.13725	−	1.35533i	−0.211422	−	0.977395i	$-0.567809\pi$
$314$	−13.8102	+	11.5881i	−0.779355	+	0.653957i
$315$	27.2713	−	15.1297i	1.53656	−	0.852464i
$316$	−4.52397	+	2.61191i	−0.254493	+	0.146932i
$317$	−5.96589	+	16.3911i	−0.335078	+	0.920618i	0.651691	+	0.758484i	$0.274060\pi$
$317$	−5.96589	+	16.3911i	−0.335078	+	0.920618i	−0.986769	+	0.162134i	$0.948162\pi$
$318$	5.57661	−	2.47596i	0.312721	−	0.138845i
$319$	−0.806702	+	0.142243i	−0.0451667	+	0.00796410i
$320$	−2.19394	+	0.431998i	−0.122645	+	0.0241494i
$321$	−16.8629	−	1.78999i	−0.941196	−	0.0999073i
$322$	−11.9370			−0.665225
$323$	8.05871	+	20.0631i	0.448399	+	1.11634i
$324$	6.44816	+	6.27864i	0.358231	+	0.348813i
$325$	3.78881	+	5.99825i	0.210166	+	0.332723i
$326$	−13.6453	+	4.96647i	−0.755742	+	0.275067i
$327$	11.5591	+	11.9946i	0.639220	+	0.663302i
$328$	0.956777	+	0.168706i	0.0528292	+	0.00931521i
$329$	−8.42969	+	23.1604i	−0.464744	+	1.27687i
$330$	0.232175	−	0.332569i	0.0127808	−	0.0183073i
$331$	−0.121709	−	0.0702690i	−0.00668975	−	0.00386233i	0.496651	−	0.867950i	$-0.334563\pi$
$331$	−0.121709	−	0.0702690i	−0.00668975	−	0.00386233i	−0.503341	+	0.864088i	$0.667896\pi$
$332$	3.81608	−	3.20207i	0.209434	−	0.175736i
$333$	−4.45677	−	13.8136i	−0.244229	−	0.756981i
$334$	−7.29801	+	12.6405i	−0.399330	+	0.691659i
$335$	5.62611	+	14.5507i	0.307387	+	0.794988i
$336$	7.81528	−	1.93999i	0.426359	−	0.105835i
$337$	−2.54126	+	14.4122i	−0.138431	+	0.785083i	0.833977	+	0.551799i	$0.186058\pi$
$337$	−2.54126	+	14.4122i	−0.138431	+	0.785083i	−0.972409	+	0.233284i	$0.925053\pi$
$338$	−10.8197	+	1.90781i	−0.588515	+	0.103771i
$339$	−1.41764	+	1.94699i	−0.0769959	+	0.105746i
$340$	7.29695	+	8.35306i	0.395732	+	0.453008i
$341$	0.358483			0.0194129
$342$	8.36443	+	10.0517i	0.452297	+	0.543533i
$343$			35.3985i			1.91134i
$344$	−2.73911	−	2.29839i	−0.147683	−	0.123921i
$345$	−7.04150	−	7.02184i	−0.379102	−	0.378043i
$346$	0.662248	+	3.75580i	0.0356027	+	0.201913i
$347$	1.52821	−	8.66689i	0.0820384	−	0.465263i	−0.915918	−	0.401365i	$-0.868536\pi$
$347$	1.52821	−	8.66689i	0.0820384	−	0.465263i	0.997956	−	0.0638975i	$-0.0203531\pi$
$348$	−3.26397	−	13.1490i	−0.174967	−	0.704859i
$349$	3.32939	+	5.76668i	0.178218	+	0.308683i	0.941270	−	0.337654i	$-0.109633\pi$
$349$	3.32939	+	5.76668i	0.178218	+	0.308683i	−0.763052	+	0.646337i	$0.776300\pi$
$350$	17.1989	−	15.6381i	0.919320	−	0.835891i
$351$	4.55725	−	5.79589i	0.243248	−	0.309362i
$352$	0.0802233	−	0.0673154i	0.00427592	−	0.00358792i
$353$	7.74392	−	13.4129i	0.412167	−	0.713895i	−0.582959	−	0.812502i	$-0.698105\pi$
$353$	7.74392	−	13.4129i	0.412167	−	0.713895i	0.995126	+	0.0986066i	$0.0314386\pi$
$354$	−4.04172	−	1.97645i	−0.214815	−	0.105047i
$355$	−30.8346	−	16.9940i	−1.63653	−	0.901947i
$356$	3.01358	−	17.0908i	0.159719	−	0.905813i
$357$	−27.7164	−	28.7606i	−1.46691	−	1.52217i
$358$	8.21679	+	22.5754i	0.434271	+	1.19315i
$359$	6.53170	−	7.78418i	0.344730	−	0.410833i	−0.565624	−	0.824663i	$-0.691365\pi$
$359$	6.53170	−	7.78418i	0.344730	−	0.410833i	0.910354	+	0.413830i	$0.135809\pi$
$360$	5.75131	+	3.45288i	0.303121	+	0.181983i
$361$	10.5606	+	15.7947i	0.555823	+	0.831300i
$362$	−4.43099			−0.232888
$363$	2.00911	−	18.9272i	0.105451	−	0.993422i
$364$	−2.25622	−	6.19891i	−0.118258	−	0.324911i
$365$	−16.8409	+	0.334927i	−0.881492	+	0.0175309i
$366$	−9.79795	−	22.0679i	−0.512147	−	1.15351i
$367$	−1.30970	+	3.59838i	−0.0683659	+	0.187834i	−0.969171	−	0.246391i	$-0.920755\pi$
$367$	−1.30970	+	3.59838i	−0.0683659	+	0.187834i	0.900805	+	0.434225i	$0.142978\pi$
$368$	−1.28380	−	2.22361i	−0.0669228	−	0.115914i
$369$	−1.78966	−	2.30045i	−0.0931660	−	0.119757i
$370$	−5.59456	−	9.25984i	−0.290848	−	0.481396i
$371$	−12.5459	+	10.5273i	−0.651351	+	0.546548i
$372$	0.407474	+	5.91499i	0.0211265	+	0.306678i
$373$	−5.25856	−	9.10809i	−0.272278	−	0.471599i	0.697167	−	0.716909i	$-0.254444\pi$
$373$	−5.25856	−	9.10809i	−0.272278	−	0.471599i	−0.969445	+	0.245310i	$0.921110\pi$
$374$	−0.488128	−	0.177664i	−0.0252405	−	0.00918679i
$375$	19.3443	+	0.892366i	0.998938	+	0.0460816i
$376$	−5.22087	+	0.920580i	−0.269246	+	0.0474753i
$377$	−10.4295	+	3.79602i	−0.537145	+	0.195505i
$378$	−21.2945	−	11.4073i	−1.09527	−	0.586728i
$379$			30.9672i			1.59068i	0.606164	+	0.795340i	$0.292708\pi$
$379$			30.9672i			1.59068i	−0.606164	+	0.795340i	$0.707292\pi$
$380$	7.78650	+	5.86263i	0.399439	+	0.300747i
$381$	−3.80347	−	5.65147i	−0.194858	−	0.289533i
$382$	−6.17861	−	5.18447i	−0.316125	−	0.265260i
$383$	−2.05062	−	5.63403i	−0.104782	−	0.287885i	0.876212	−	0.481926i	$-0.160063\pi$
$383$	−2.05062	−	5.63403i	−0.104782	−	0.287885i	−0.980993	+	0.194041i	$0.937840\pi$
$384$	1.20190	+	1.24718i	0.0613340	+	0.0636447i
$385$	−0.351935	+	1.03023i	−0.0179363	+	0.0525051i
$386$	5.85417	−	16.0842i	0.297969	−	0.818664i
$387$	1.47094	+	10.6256i	0.0747723	+	0.540131i
$388$	5.16425	−	8.94475i	0.262175	−	0.454101i
$389$	−22.0311	−	26.2557i	−1.11702	−	1.33121i	−0.937709	−	0.347423i	$-0.887057\pi$
$389$	−22.0311	−	26.2557i	−1.11702	−	1.33121i	−0.179313	−	0.983792i	$-0.557387\pi$
$390$	2.31553	−	4.98385i	0.117251	−	0.252367i
$391$	−6.36795	+	11.0296i	−0.322041	+	0.557791i
$392$	−12.6562	+	7.30704i	−0.639233	+	0.369061i
$393$	13.6466	−	3.38750i	0.688379	−	0.170877i
$394$	−23.3440	−	4.11617i	−1.17605	−	0.207370i
$395$	11.6785	−	0.232260i	0.587611	−	0.0116863i
$396$	−0.313958	−	0.0116135i	−0.0157770	−	0.000583599i
$397$	15.4770	−	18.4447i	0.776767	−	0.925715i	−0.222015	−	0.975043i	$-0.571264\pi$
$397$	15.4770	−	18.4447i	0.776767	−	0.925715i	0.998783	+	0.0493280i	$0.0157080\pi$
$398$			6.41972i			0.321792i
$399$	−29.0389	−	19.7166i	−1.45376	−	0.987067i
$400$	4.76274	+	1.52194i	0.238137	+	0.0760969i
$401$	−9.20553	−	7.72436i	−0.459702	−	0.385736i	0.383319	−	0.923616i	$-0.374781\pi$
$401$	−9.20553	−	7.72436i	−0.459702	−	0.385736i	−0.843022	+	0.537880i	$0.819225\pi$
$402$	7.11295	−	9.76888i	0.354762	−	0.487228i
$403$	4.78337	−	0.843438i	0.238277	−	0.0420146i
$404$	0.248181	+	0.0437610i	0.0123475	+	0.00217719i
$405$	−5.85110	−	19.2553i	−0.290743	−	0.956801i
$406$	18.1825	+	31.4930i	0.902382	+	1.56297i
$407$	0.438800	+	0.253341i	0.0217505	+	0.0125577i
$408$	2.37663	−	8.25609i	0.117661	−	0.408737i
$409$	−17.7789	−	21.1881i	−0.879110	−	1.04768i	−0.998495	−	0.0548348i	$-0.982537\pi$
$409$	−17.7789	−	21.1881i	−0.879110	−	1.04768i	0.119385	−	0.992848i	$-0.461908\pi$
$410$	−1.69161	−	1.36304i	−0.0835426	−	0.0673157i
$411$	6.67190	−	13.6436i	0.329100	−	0.672990i
$412$	−14.0035	−	5.09686i	−0.689904	−	0.251104i
$413$	11.8928	+	2.09702i	0.585206	+	0.103188i
$414$	−1.61708	+	7.53117i	−0.0794750	+	0.370137i
$415$	−10.9292	+	2.15201i	−0.536493	+	0.105638i
$416$	0.912071	−	1.08696i	0.0447180	−	0.0532928i
$417$	14.1782	+	21.0669i	0.694307	+	1.03165i
$418$	−0.451909	−	0.0644472i	−0.0221036	−	0.00315222i
$419$		−	37.9671i		−	1.85481i	−0.374054	−	0.927407i	$-0.622033\pi$
$419$		−	37.9671i		−	1.85481i	0.374054	−	0.927407i	$-0.377967\pi$
$420$	−17.3988	−	4.63594i	−0.848976	−	0.226211i
$421$	−4.75919	−	13.0758i	−0.231949	−	0.637274i	0.768046	−	0.640394i	$-0.221229\pi$
$421$	−4.75919	−	13.0758i	−0.231949	−	0.637274i	−0.999995	+	0.00312012i	$0.999007\pi$
$422$	1.19222	+	6.76141i	0.0580363	+	0.329140i
$423$	13.4701	+	8.45582i	0.654939	+	0.411136i
$424$	−3.31029	−	1.20485i	−0.160762	−	0.0585125i
$425$	−5.27437	−	24.2338i	−0.255844	−	1.17551i
$426$	1.87425	+	27.2071i	0.0908077	+	1.31819i
$427$	41.6588	+	49.6470i	2.01601	+	2.40259i
$428$	6.29322	+	7.49996i	0.304194	+	0.362524i
$429$	0.0176883	+	0.256768i	0.000853999	+	0.0123969i
$430$	2.88344	+	7.45737i	0.139052	+	0.359626i
$431$	−18.0503	−	6.56979i	−0.869454	−	0.316455i	−0.131508	−	0.991315i	$-0.541982\pi$
$431$	−18.0503	−	6.56979i	−0.869454	−	0.316455i	−0.737946	+	0.674860i	$0.764204\pi$
$432$	−0.165241	−	5.19352i	−0.00795014	−	0.249874i
$433$	−5.83374	−	33.0848i	−0.280352	−	1.58995i	−0.721431	−	0.692486i	$-0.756515\pi$
$433$	−5.83374	−	33.0848i	−0.280352	−	1.58995i	0.441080	−	0.897468i	$-0.354596\pi$
$434$	−5.44304	−	14.9546i	−0.261274	−	0.717845i
$435$	−7.79982	+	29.2730i	−0.373973	+	1.40353i
$436$		−	9.61740i		−	0.460590i
$437$	−3.48009	+	10.6371i	−0.166475	+	0.508842i
$438$	7.28487	+	10.8244i	0.348085	+	0.517209i
$439$	−17.0937	+	20.3715i	−0.815839	+	0.972279i	−0.999944	−	0.0106276i	$-0.996617\pi$
$439$	−17.0937	+	20.3715i	−0.815839	+	0.972279i	0.184105	+	0.982907i	$0.441061\pi$
$440$	−0.229759	+	0.0452407i	−0.0109533	+	0.00215676i
$441$	42.8652	+	9.20394i	2.04120	+	0.438283i
$442$	−6.93129	−	1.22217i	−0.329688	−	0.0581329i
$443$	−28.5078	−	10.3760i	−1.35445	−	0.492979i	−0.440115	−	0.897941i	$-0.645062\pi$
$443$	−28.5078	−	10.3760i	−1.35445	−	0.492979i	−0.914333	+	0.404962i	$0.867285\pi$
$444$	−3.68138	+	7.52819i	−0.174711	+	0.357272i
$445$	−24.3479	+	30.2171i	−1.15420	+	1.43243i
$446$	8.95803	+	10.6758i	0.424175	+	0.505512i
$447$	−7.06218	+	24.5330i	−0.334030	+	1.16037i
$448$	−4.02623	−	2.32455i	−0.190222	−	0.109825i
$449$	2.16458	+	3.74916i	0.102153	+	0.176934i	0.912571	−	0.408917i	$-0.134094\pi$
$449$	2.16458	+	3.74916i	0.102153	+	0.176934i	−0.810419	+	0.585851i	$0.800760\pi$
$450$	−7.53630	−	12.9694i	−0.355265	−	0.611381i
$451$	0.100198	+	0.0176675i	0.00471812	+	0.000831932i
$452$	1.36938	−	0.241458i	0.0644100	−	0.0113572i
$453$	−18.1583	+	24.9386i	−0.853153	+	1.17172i
$454$	−1.21689	−	1.02109i	−0.0571116	−	0.0479223i
$455$	−2.27209	+	14.5747i	−0.106517	+	0.683274i
$456$	0.549716	−	7.52979i	0.0257428	−	0.352615i
$457$		−	24.4038i		−	1.14156i	−0.821103	−	0.570781i	$-0.806641\pi$
$457$		−	24.4038i		−	1.14156i	0.821103	−	0.570781i	$-0.193359\pi$
$458$	10.8722	−	12.9569i	0.508023	−	0.605438i
$459$	−21.8999	+	13.5903i	−1.02220	+	0.634343i
$460$	0.114160	+	5.74021i	0.00532273	+	0.267638i
$461$	34.5470	+	6.09156i	1.60901	+	0.283712i	0.904659	−	0.426137i	$-0.140126\pi$
$461$	34.5470	+	6.09156i	1.60901	+	0.283712i	0.704353	+	0.709849i	$0.251237\pi$
$462$	0.818449	−	0.203164i	0.0380777	−	0.00945204i
$463$	13.9124	−	8.03232i	0.646563	−	0.373294i	−0.140575	−	0.990070i	$-0.544895\pi$
$463$	13.9124	−	8.03232i	0.646563	−	0.373294i	0.787138	+	0.616776i	$0.211562\pi$
$464$	−3.91098	+	6.77401i	−0.181563	+	0.314476i
$465$	5.58613	−	12.0234i	0.259050	−	0.557570i
$466$	9.37839	+	11.1767i	0.434446	+	0.517752i
$467$	11.8739	−	20.5661i	0.549457	−	0.951687i	−0.448855	−	0.893605i	$-0.648168\pi$
$467$	11.8739	−	20.5661i	0.549457	−	0.951687i	0.998312	−	0.0580824i	$-0.0184986\pi$
$468$	−4.21658	+	0.583716i	−0.194912	+	0.0269823i
$469$	−11.0936	+	30.4795i	−0.512256	+	1.40741i
$470$	11.2178	+	3.83212i	0.517440	+	0.176762i
$471$	−21.6677	−	22.4840i	−0.998395	−	1.03601i
$472$	0.888415	+	2.44090i	0.0408926	+	0.112352i
$473$	−0.286851	−	0.240696i	−0.0131894	−	0.0110672i
$474$	−5.05179	−	7.50631i	−0.232036	−	0.344776i
$475$	−8.92102	−	19.8851i	−0.409324	−	0.912389i
$476$			23.0605i			1.05698i
$477$	4.94217	+	9.34140i	0.226286	+	0.427713i
$478$	17.0073	−	6.19015i	0.777895	−	0.283131i
$479$	−28.3407	+	4.99723i	−1.29492	+	0.228329i	−0.778304	−	0.627888i	$-0.783920\pi$
$479$	−28.3407	+	4.99723i	−1.29492	+	0.228329i	−0.516616	+	0.856217i	$0.672809\pi$
$480$	−1.00763	−	3.73961i	−0.0459919	−	0.170689i
$481$	6.45114	+	2.34802i	0.294147	+	0.107061i
$482$	−11.7886	−	20.4185i	−0.536958	−	0.930039i
$483$	−1.42094	−	20.6267i	−0.0646548	−	0.938546i
$484$	−8.41809	+	7.06361i	−0.382640	+	0.321073i
$485$	−19.7675	+	11.9430i	−0.897596	+	0.542305i
$486$	−10.0816	+	11.8895i	−0.457313	+	0.539319i
$487$	−7.34528	−	12.7224i	−0.332847	−	0.576507i	0.650222	−	0.759744i	$-0.274676\pi$
$487$	−7.34528	−	12.7224i	−0.332847	−	0.576507i	−0.983069	+	0.183237i	$0.941342\pi$
$488$	−4.76785	+	13.0996i	−0.215830	+	0.592989i
$489$	−10.2061	−	22.9872i	−0.461537	−	1.03952i
$490$	32.6716	−	0.649765i	1.47595	−	0.0293534i
$491$	6.21043	+	17.0630i	0.280273	+	0.770043i	0.997330	+	0.0730283i	$0.0232663\pi$
$491$	6.21043	+	17.0630i	0.280273	+	0.770043i	−0.717057	+	0.697014i	$0.754511\pi$
$492$	−0.177625	+	1.67335i	−0.00800795	+	0.0754404i
$493$	38.7986			1.74740
$494$	−6.18164	+	0.203308i	−0.278125	+	0.00914726i
$495$	0.602301	+	0.361600i	0.0270714	+	0.0162527i
$496$	2.20034	−	2.62226i	0.0987980	−	0.117743i
$497$	−25.0363	−	68.7866i	−1.12303	−	3.08550i
$498$	5.98728	+	6.21285i	0.268296	+	0.278404i
$499$	−1.06610	+	6.04615i	−0.0477251	+	0.270663i	−0.999327	−	0.0366694i	$-0.988325\pi$
$499$	−1.06610	+	6.04615i	−0.0477251	+	0.270663i	0.951602	+	0.307332i	$0.0994362\pi$
$500$	−7.68442	−	8.12094i	−0.343658	−	0.363179i
$501$	−22.7110	−	11.1060i	−1.01465	−	0.496178i
$502$	5.21811	−	9.03804i	0.232896	−	0.403387i
$503$	−2.08015	+	1.74545i	−0.0927493	+	0.0778259i	−0.687983	−	0.725727i	$-0.741504\pi$
$503$	−2.08015	+	1.74545i	−0.0927493	+	0.0778259i	0.595234	+	0.803552i	$0.297059\pi$
$504$	4.28252	+	13.2735i	0.190759	+	0.591250i
$505$	−0.438791	−	0.353562i	−0.0195259	−	0.0157333i
$506$	−0.134445	−	0.232866i	−0.00597681	−	0.0103521i
$507$	−4.58454	−	18.4689i	−0.203607	−	0.820233i
$508$	−0.682958	+	3.87325i	−0.0303014	+	0.171848i
$509$	3.05486	+	17.3250i	0.135404	+	0.767917i	0.974577	+	0.224052i	$0.0719285\pi$
$509$	3.05486	+	17.3250i	0.135404	+	0.767917i	−0.839173	+	0.543865i	$0.816960\pi$
$510$	−13.5651	+	13.6031i	−0.600674	+	0.602356i
$511$	−26.8280	−	22.5114i	−1.18680	−	0.995843i
$512$		−	1.00000i		−	0.0441942i
$513$	−16.3732	+	15.6499i	−0.722894	+	0.690959i
$514$	−9.34242			−0.412076
$515$	21.9226	+	25.0955i	0.966023	+	1.10584i
$516$	3.64546	−	5.00665i	0.160482	−	0.220406i
$517$	−0.546751	+	0.0964070i	−0.0240461	+	0.00423997i
$518$	3.90596	−	22.1518i	0.171618	−	0.973294i
$519$	−6.41102	+	1.59141i	−0.281412	+	0.0698551i
$520$	−2.95931	+	1.14424i	−0.129775	+	0.0501782i
$521$	−4.11931	+	7.13485i	−0.180470	+	0.312584i	−0.942041	−	0.335498i	$-0.891095\pi$
$521$	−4.11931	+	7.13485i	−0.180470	+	0.312584i	0.761571	+	0.648082i	$0.224429\pi$
$522$	22.3323	−	7.20520i	0.977458	−	0.315363i
$523$	11.6036	−	9.73660i	0.507391	−	0.425752i	−0.352819	−	0.935692i	$-0.614777\pi$
$523$	11.6036	−	9.73660i	0.507391	−	0.425752i	0.860210	+	0.509940i	$0.170332\pi$
$524$	−7.03037	−	4.05898i	−0.307123	−	0.177318i
$525$	29.0692	+	27.8574i	1.26868	+	1.21580i
$526$	4.41912	−	12.1414i	0.192683	−	0.529391i
$527$	−16.7215	−	2.94844i	−0.728398	−	0.128436i
$528$	0.125867	+	0.130609i	0.00547768	+	0.00568404i
$529$	15.4179	−	5.61166i	0.670344	−	0.243985i
$530$	5.18226	+	5.93232i	0.225103	+	0.257683i
$531$	2.93411	−	7.21918i	0.127330	−	0.313286i
$532$	4.17308	+	19.8306i	0.180926	+	0.859766i
$533$	1.37854			0.0597113
$534$	29.8909	+	3.17290i	1.29351	+	0.137305i
$535$	−4.22948	−	21.4798i	−0.182857	−	0.928652i
$536$	−6.87076	+	1.21150i	−0.296771	+	0.0523288i
$537$	−38.0313	+	16.8855i	−1.64117	+	0.728665i
$538$	9.49400	−	26.0845i	0.409315	−	1.12458i
$539$	−1.32540	+	0.765223i	−0.0570892	+	0.0329605i
$540$	−5.28182	+	10.3490i	−0.227293	+	0.445351i
$541$	−22.8092	+	19.1392i	−0.980642	+	0.822856i	−0.984186	−	0.177137i	$-0.943316\pi$
$541$	−22.8092	+	19.1392i	−0.980642	+	0.822856i	0.00354414	+	0.999994i	$0.498872\pi$
$542$	3.38219	+	4.03074i	0.145278	+	0.173135i
$543$	−0.527447	−	7.65656i	−0.0226349	−	0.328574i
$544$	−4.29568	+	2.48011i	−0.184176	+	0.106334i
$545$	−10.3801	+	18.8341i	−0.444636	+	0.806765i
$546$	10.4429	−	4.63654i	0.446914	−	0.198426i
$547$	−2.67401	−	15.1651i	−0.114332	−	0.648411i	−0.987079	−	0.160237i	$-0.948774\pi$
$547$	−2.67401	−	15.1651i	−0.114332	−	0.648411i	0.872746	−	0.488174i	$-0.162337\pi$
$548$	−8.23974	+	2.99902i	−0.351984	+	0.128112i
$549$	36.9661	−	19.5573i	1.57767	−	0.834685i
$550$	0.498774	+	0.159384i	0.0212678	+	0.00679614i
$551$	33.3644	−	7.02108i	1.42137	−	0.299108i
$552$	3.68948	−	2.48304i	0.157035	−	0.105685i
$553$	18.6042	+	15.6108i	0.791132	+	0.663838i
$554$	13.7224	−	4.99456i	0.583011	−	0.212199i
$555$	15.3346	−	10.7694i	0.650919	−	0.457136i
$556$	2.54586	−	14.4383i	0.107968	−	0.612319i
$557$	5.29473	+	1.92712i	0.224345	+	0.0816549i	0.451747	−	0.892146i	$-0.350801\pi$
$557$	5.29473	+	1.92712i	0.224345	+	0.0816549i	−0.227402	+	0.973801i	$0.573023\pi$
$558$	−10.1723	+	1.40819i	−0.430629	+	0.0596135i
$559$	−4.39387	−	2.53680i	−0.185841	−	0.107295i
$560$	5.37583	+	8.89780i	0.227170	+	0.376001i
$561$	0.248891	−	0.864612i	0.0105082	−	0.0365039i
$562$	−5.07357	−	2.92923i	−0.214016	−	0.123562i
$563$	18.1001	−	10.4501i	0.762827	−	0.440418i	−0.0674831	−	0.997720i	$-0.521497\pi$
$563$	18.1001	−	10.4501i	0.762827	−	0.440418i	0.830310	+	0.557302i	$0.188164\pi$
$564$	−2.21219	−	8.91185i	−0.0931501	−	0.375257i
$565$	−2.94231	−	1.00512i	−0.123784	−	0.0422858i
$566$	5.68139	+	32.2208i	0.238807	+	1.35434i
$567$	17.1765	−	38.1537i	0.721345	−	1.60231i
$568$	10.1209	−	12.0616i	0.424662	−	0.506092i
$569$	−17.8675			−0.749045			−0.374522	−	0.927218i	$-0.622193\pi$
$569$	−17.8675			−0.749045			−0.374522	+	0.927218i	$0.622193\pi$
$570$	−9.20350	+	14.1526i	−0.385492	+	0.592786i
$571$	43.7370			1.83034			0.915169	−	0.403070i	$-0.132057\pi$
$571$	43.7370			1.83034			0.915169	+	0.403070i	$0.132057\pi$
$572$	0.0955159	−	0.113831i	0.00399372	−	0.00475953i
$573$	8.22305	−	11.2935i	0.343523	−	0.471793i
$574$	−0.784328	−	4.44814i	−0.0327372	−	0.185662i
$575$	5.97189	−	11.3645i	0.249045	−	0.473932i
$576$	−2.01200	+	2.22528i	−0.0838332	+	0.0927200i
$577$	−9.66319	+	5.57905i	−0.402284	+	0.232259i	−0.687469	−	0.726214i	$-0.741278\pi$
$577$	−9.66319	+	5.57905i	−0.402284	+	0.232259i	0.285185	+	0.958472i	$0.407945\pi$
$578$	6.58509	+	3.80191i	0.273904	+	0.158138i
$579$	28.4896	+	8.20115i	1.18399	+	0.340828i
$580$	14.9703	−	9.04467i	0.621606	−	0.375559i
$581$	−20.0568	−	11.5798i	−0.832097	−	0.480411i
$582$	16.0709	+	7.85885i	0.666159	+	0.325760i
$583$	−0.346667	−	0.126176i	−0.0143575	−	0.00522569i
$584$	1.30808	−	7.41852i	0.0541289	−	0.306980i
$585$	8.88751	+	3.40788i	0.367453	+	0.140898i
$586$	22.6674	−	8.25027i	0.936383	−	0.340816i
$587$	−15.8043	−	13.2614i	−0.652313	−	0.547356i	0.255459	−	0.966820i	$-0.417774\pi$
$587$	−15.8043	−	13.2614i	−0.652313	−	0.547356i	−0.907772	+	0.419464i	$0.862218\pi$
$588$	−14.1328	−	20.9995i	−0.582826	−	0.866004i
$589$	−14.9130	+	0.490473i	−0.614477	+	0.0202096i
$590$	0.894665	−	5.73899i	0.0368328	−	0.236270i
$591$	4.33379	−	40.8273i	0.178268	−	1.67941i
$592$	4.54648	−	1.65478i	0.186859	−	0.0680111i
$593$	−4.71813	−	26.7579i	−0.193751	−	1.09881i	−0.914187	−	0.405293i	$-0.867170\pi$
$593$	−4.71813	−	26.7579i	−0.193751	−	1.09881i	0.720436	−	0.693521i	$-0.243942\pi$
$594$	−0.0173047	−	0.543887i	−0.000710019	−	0.0223160i
$595$	24.8894	−	45.1604i	1.02037	−	1.85139i
$596$	12.7646	−	7.36966i	0.522860	−	0.301873i
$597$	−11.0930	+	0.764178i	−0.454006	+	0.0312757i
$598$	−2.34184	−	2.79090i	−0.0957649	−	0.114128i
$599$	30.3008	−	25.4254i	1.23806	−	1.03885i	0.240382	−	0.970678i	$-0.422727\pi$
$599$	30.3008	−	25.4254i	1.23806	−	1.03885i	0.997673	−	0.0681734i	$-0.0217171\pi$
$600$	−2.06291	+	8.41097i	−0.0842178	+	0.343376i
$601$	23.4964	−	13.5657i	0.958440	−	0.553355i	0.0627471	−	0.998029i	$-0.480014\pi$
$601$	23.4964	−	13.5657i	0.958440	−	0.553355i	0.895692	+	0.444674i	$0.146681\pi$
$602$	−5.68559	+	15.6210i	−0.231727	+	0.636666i
$603$	17.7269	+	11.1280i	0.721895	+	0.453167i
$604$	17.5401	−	3.09279i	0.713695	−	0.125844i
$605$	24.1093	−	4.74725i	0.980182	−	0.193003i
$606$	−0.0460746	+	0.434054i	−0.00187165	+	0.0176323i
$607$	−39.3335			−1.59650			−0.798249	−	0.602327i	$-0.794240\pi$
$607$	−39.3335			−1.59650			−0.798249	+	0.602327i	$0.794240\pi$
$608$	−3.24521	+	2.91009i	−0.131610	+	0.118020i
$609$	−52.2542	+	35.1674i	−2.11745	+	1.42505i
$610$	23.4755	−	20.5074i	0.950497	−	0.830321i
$611$	−7.06869	+	2.57279i	−0.285968	+	0.104084i
$612$	14.5491	+	3.12395i	0.588111	+	0.126278i
$613$	−5.75767	−	1.01523i	−0.232550	−	0.0410049i	0.0561585	−	0.998422i	$-0.482115\pi$
$613$	−5.75767	−	1.01523i	−0.232550	−	0.0410049i	−0.288709	+	0.957417i	$0.593226\pi$
$614$	2.19838	−	6.04000i	0.0887195	−	0.243755i
$615$	2.15391	−	3.08527i	0.0868540	−	0.124410i
$616$	−0.421644	−	0.243436i	−0.0169885	−	0.00980832i
$617$	18.0654	−	15.1587i	0.727286	−	0.610265i	−0.202104	−	0.979364i	$-0.564778\pi$
$617$	18.0654	−	15.1587i	0.727286	−	0.610265i	0.929390	+	0.369099i	$0.120334\pi$
$618$	7.14023	−	24.8042i	0.287222	−	0.997770i
$619$	8.89449	−	15.4057i	0.357500	−	0.619208i	−0.630043	−	0.776561i	$-0.716963\pi$
$619$	8.89449	−	15.4057i	0.357500	−	0.619208i	0.987542	+	0.157353i	$0.0502959\pi$
$620$	−7.13923	+	2.76043i	−0.286718	+	0.110862i
$621$	−13.2060	−	1.89776i	−0.529939	−	0.0761544i
$622$	1.35476	−	7.68323i	0.0543210	−	0.308069i
$623$	−79.4569	+	14.0104i	−3.18337	+	0.561315i
$624$	1.98680	+	1.44663i	0.0795355	+	0.0579116i
$625$	6.28372	+	24.1974i	0.251349	+	0.967897i
$626$	−31.3013			−1.25105
$627$	0.0575685	−	0.788551i	0.00229906	−	0.0314917i
$628$			18.0279i			0.719393i
$629$	−18.3842	−	15.4262i	−0.733025	−	0.615081i
$630$	5.93961	−	30.6162i	0.236640	−	1.21978i
$631$	−1.34554	−	7.63096i	−0.0535652	−	0.303784i	0.946241	−	0.323462i	$-0.104847\pi$
$631$	−1.34554	−	7.63096i	−0.0535652	−	0.303784i	−0.999806	+	0.0196786i	$0.993736\pi$
$632$	−0.907108	+	5.14447i	−0.0360828	+	0.204636i
$633$	−11.5415	+	2.86495i	−0.458733	+	0.113872i
$634$	8.72155	+	15.1062i	0.346377	+	0.599942i
$635$	5.51789	−	6.84801i	0.218971	−	0.271755i
$636$	1.68788	−	5.86345i	0.0669287	−	0.232501i
$637$	−15.8850	+	13.3291i	−0.629386	+	0.528117i
$638$	−0.409574	+	0.709402i	−0.0162152	+	0.0280855i
$639$	−46.7896	+	6.47724i	−1.85097	+	0.256236i
$640$	−1.07931	+	1.95834i	−0.0426634	+	0.0774102i
$641$	−6.12309	+	34.7258i	−0.241847	+	1.37159i	0.585854	+	0.810417i	$0.300759\pi$
$641$	−6.12309	+	34.7258i	−0.241847	+	1.37159i	−0.827702	+	0.561169i	$0.810352\pi$
$642$	−12.2105	+	11.7672i	−0.481909	+	0.464413i
$643$	−7.08140	−	19.4560i	−0.279263	−	0.767269i	−0.997447	−	0.0714154i	$-0.977248\pi$
$643$	−7.08140	−	19.4560i	−0.279263	−	0.767269i	0.718184	−	0.695854i	$-0.244974\pi$
$644$	−7.67298	+	9.14430i	−0.302358	+	0.360336i
$645$	−12.5428	+	5.87015i	−0.493871	+	0.231137i
$646$	20.5493	+	6.72301i	0.808501	+	0.264513i
$647$	39.3673			1.54769			0.773843	−	0.633377i	$-0.218332\pi$
$647$	39.3673			1.54769			0.773843	+	0.633377i	$0.218332\pi$
$648$	8.95451	−	0.903744i	0.351766	−	0.0355024i
$649$	0.0930385	+	0.255621i	0.00365208	+	0.0100340i
$650$	7.03033	+	0.953203i	0.275752	+	0.0373877i
$651$	25.1930	−	11.1855i	0.987392	−	0.438393i
$652$	−4.96647	+	13.6453i	−0.194502	+	0.534390i
$653$	10.7121	+	18.5539i	0.419196	+	0.726069i	0.995859	−	0.0909135i	$-0.0289787\pi$
$653$	10.7121	+	18.5539i	0.419196	+	0.726069i	−0.576663	+	0.816982i	$0.695645\pi$
$654$	16.6184	−	1.14482i	0.649832	−	0.0447658i
$655$	9.38695	+	15.5368i	0.366779	+	0.607073i
$656$	0.744240	−	0.624492i	0.0290577	−	0.0243823i
$657$	−17.8369	+	13.8764i	−0.695883	+	0.541371i
$658$	12.3234	+	21.3447i	0.480415	+	0.832104i
$659$	2.57407	+	0.936884i	0.100271	+	0.0364958i	0.391669	−	0.920106i	$-0.371898\pi$
$659$	2.57407	+	0.936884i	0.100271	+	0.0364958i	−0.291397	+	0.956602i	$0.594120\pi$
$660$	−0.105523	−	0.391627i	−0.00410749	−	0.0152441i
$661$	−35.3289	+	6.22944i	−1.37413	+	0.242297i	−0.811473	−	0.584390i	$-0.801334\pi$
$661$	−35.3289	+	6.22944i	−1.37413	+	0.242297i	−0.562662	+	0.826687i	$0.690223\pi$
$662$	−0.132062	+	0.0480668i	−0.00513275	+	0.00186817i
$663$	1.28679	−	12.1224i	0.0499747	−	0.470797i
$664$		−	4.98153i		−	0.193321i
$665$	13.2310	−	43.3391i	0.513077	−	1.68062i
$666$	−13.4466	−	5.46514i	−0.521045	−	0.211770i
$667$	15.3850	+	12.9095i	0.595710	+	0.499860i
$668$	4.99213	+	13.7158i	0.193152	+	0.530679i
$669$	−17.3809	+	16.7499i	−0.671986	+	0.647588i
$670$	14.7629	+	5.04313i	0.570339	+	0.194833i
$671$	−0.499309	+	1.37184i	−0.0192756	+	0.0529593i
$672$	3.53745	−	7.23386i	0.136460	−	0.279052i
$673$	−6.79756	+	11.7737i	−0.262027	+	0.453843i	−0.966780	−	0.255609i	$-0.917724\pi$
$673$	−6.79756	+	11.7737i	−0.262027	+	0.453843i	0.704754	+	0.709452i	$0.251057\pi$
$674$	9.40690	+	11.2107i	0.362340	+	0.431821i
$675$	21.5134	−	14.5662i	0.828050	−	0.560654i
$676$	−5.49332	+	9.51470i	−0.211281	+	0.365950i
$677$	−20.5592	+	11.8699i	−0.790155	+	0.456196i	−0.840017	−	0.542560i	$-0.817455\pi$
$677$	−20.5592	+	11.8699i	−0.790155	+	0.456196i	0.0498619	+	0.998756i	$0.484122\pi$
$678$	0.580233	+	2.33748i	0.0222837	+	0.0897703i
$679$	−47.2887	−	8.33827i	−1.81477	−	0.319993i
$680$	11.0892	−	0.220539i	0.425252	−	0.00845730i
$681$	1.61955	−	2.22428i	0.0620613	−	0.0852347i
$682$	0.230428	−	0.274614i	0.00882355	−	0.0105155i
$683$			10.3244i			0.395053i	0.980298	+	0.197527i	$0.0632909\pi$
$683$			10.3244i			0.395053i	−0.980298	+	0.197527i	$0.936709\pi$
$684$	13.0766	+	0.0535686i	0.499996	+	0.00204825i
$685$	19.3731	+	3.02012i	0.740207	+	0.115393i
$686$	27.1169	+	22.7537i	1.03533	+	0.868742i
$687$	23.6832	+	17.2443i	0.903571	+	0.657910i
$688$	−3.52133	+	0.620906i	−0.134250	+	0.0236718i
$689$	−4.92258	−	0.867983i	−0.187535	−	0.0330675i
$690$	−9.90523	+	0.880553i	−0.377086	+	0.0335221i
$691$	−21.6242	−	37.4542i	−0.822624	−	1.42483i	−0.903722	−	0.428120i	$-0.859176\pi$
$691$	−21.6242	−	37.4542i	−0.822624	−	1.42483i	0.0810981	−	0.996706i	$-0.474157\pi$
$692$	3.30279	+	1.90687i	0.125553	+	0.0724882i
$693$	0.448483	+	1.39006i	0.0170365	+	0.0528040i
$694$	−5.65691	−	6.74164i	−0.214733	−	0.255909i
$695$	−20.5690	+	25.5273i	−0.780226	+	0.968304i
$696$	−12.1707	−	5.95164i	−0.461331	−	0.225596i
$697$	−4.52841	−	1.64821i	−0.171526	−	0.0624303i
$698$	6.55762	+	1.15629i	0.248210	+	0.0437661i
$699$	−18.1965	+	17.5359i	−0.688256	+	0.663268i
$700$	−0.924235	−	23.2271i	−0.0349328	−	0.877901i
$701$	23.1763	−	27.6204i	0.875355	−	1.04321i	−0.123351	−	0.992363i	$-0.539364\pi$
$701$	23.1763	−	27.6204i	0.875355	−	1.04321i	0.998707	−	0.0508447i	$-0.0161913\pi$
$702$	−1.51056	−	7.21658i	−0.0570124	−	0.272372i
$703$	−18.6008	−	9.93868i	−0.701541	−	0.374844i
$704$		−	0.104724i		−	0.00394694i
$705$	−5.28641	+	19.8401i	−0.199098	+	0.747220i
$706$	−5.29715	−	14.5538i	−0.199361	−	0.547740i
$707$	−0.203449	−	1.15382i	−0.00765148	−	0.0433937i
$708$	−4.11201	+	1.82570i	−0.154539	+	0.0686139i
$709$	20.4424	+	7.44043i	0.767731	+	0.279431i	0.696047	−	0.717996i	$-0.254940\pi$
$709$	20.4424	+	7.44043i	0.767731	+	0.279431i	0.0716841	+	0.997427i	$0.477163\pi$
$710$	−32.8382	+	12.6971i	−1.23240	+	0.476514i
$711$	12.3692	−	9.62278i	0.463882	−	0.360883i
$712$	−11.1553	−	13.2943i	−0.418061	−	0.498225i
$713$	−5.64960	−	6.73293i	−0.211579	−	0.252150i
$714$	−39.8476	+	2.74503i	−1.49126	+	0.102730i
$715$	−0.309912	+	0.119829i	−0.0115900	+	0.00448137i
$716$	22.5754	+	8.21679i	0.843684	+	0.307076i
$717$	12.7208	+	28.6510i	0.475066	+	1.06999i
$718$	−1.76453	−	10.0071i	−0.0658517	−	0.373463i
$719$	−3.97741	−	10.9278i	−0.148332	−	0.407539i	0.843167	−	0.537652i	$-0.180688\pi$
$719$	−3.97741	−	10.9278i	−0.148332	−	0.407539i	−0.991499	+	0.130112i	$0.958466\pi$
$720$	6.34193	−	2.18629i	0.236350	−	0.0814782i
$721$			69.2819i			2.58019i
$722$	18.8877	+	2.06272i	0.702927	+	0.0767664i
$723$	33.8790	−	22.8008i	1.25998	−	0.847971i
$724$	−2.84819	+	3.39434i	−0.105852	+	0.126149i
$725$	−39.0788	+	1.55500i	−1.45135	+	0.0577511i
$726$	−13.2077	−	13.7053i	−0.490182	−	0.508650i
$727$	−17.0160	−	3.00037i	−0.631087	−	0.111278i	−0.151051	−	0.988526i	$-0.548266\pi$
$727$	−17.0160	−	3.00037i	−0.631087	−	0.111278i	−0.480037	+	0.877248i	$0.659377\pi$
$728$	−6.19891	−	2.25622i	−0.229747	−	0.0836211i
$729$	−21.7446	−	16.0054i	−0.805356	−	0.592791i
$730$	−10.5685	+	13.1162i	−0.391159	+	0.485451i
$731$	11.4005	+	13.5866i	0.421663	+	0.502519i
$732$	−23.2030	−	6.67932i	−0.857608	−	0.246875i
$733$	18.0954	+	10.4474i	0.668370	+	0.385883i	0.795459	−	0.606008i	$-0.207230\pi$
$733$	18.0954	+	10.4474i	0.668370	+	0.385883i	−0.127089	+	0.991891i	$0.540563\pi$
$734$	1.91466	+	3.31628i	0.0706713	+	0.122406i
$735$	5.01186	+	56.3777i	0.184865	+	2.07952i
$736$	−2.52860	−	0.445860i	−0.0932054	−	0.0164346i
$737$	−0.719534	+	0.126873i	−0.0265044	+	0.00467343i
$738$	−2.91262	−	0.107739i	−0.107215	−	0.00396594i
$739$	−16.6566	−	13.9765i	−0.612721	−	0.514134i	0.282785	−	0.959183i	$-0.408742\pi$
$739$	−16.6566	−	13.9765i	−0.612721	−	0.514134i	−0.895506	+	0.445049i	$0.853186\pi$
$740$	−10.6896	−	1.66642i	−0.392956	−	0.0612589i
$741$	−1.08714	−	10.6574i	−0.0399372	−	0.391509i
$742$			16.3775i			0.601238i
$743$	10.9830	−	13.0890i	0.402927	−	0.480190i	−0.525983	−	0.850495i	$-0.676303\pi$
$743$	10.9830	−	13.0890i	0.402927	−	0.480190i	0.928910	+	0.370305i	$0.120747\pi$
$744$	4.79307	+	3.48994i	0.175722	+	0.127947i
$745$	−32.9516	+	0.655334i	−1.20725	+	0.0240096i
$746$	−10.3573	−	1.82628i	−0.379209	−	0.0668648i
$747$	−10.0228	+	11.0853i	−0.366716	+	0.405590i
$748$	−0.449861	+	0.259727i	−0.0164486	+	0.00949658i
$749$	22.7585	−	39.4189i	0.831577	−	1.44033i
$750$	13.1179	−	14.2450i	0.478998	−	0.520155i
$751$	3.26720	+	3.89370i	0.119222	+	0.142083i	0.822354	−	0.568976i	$-0.192660\pi$
$751$	3.26720	+	3.89370i	0.119222	+	0.142083i	−0.703132	+	0.711059i	$0.748216\pi$
$752$	−2.65071	+	4.59116i	−0.0966613	+	0.167422i
$753$	16.2385	+	7.94082i	0.591763	+	0.289379i
$754$	−3.79602	+	10.4295i	−0.138243	+	0.379819i
$755$	−37.6875	−	12.8744i	−1.37159	−	0.468548i
$756$	−22.4263	+	8.98003i	−0.815637	+	0.326600i
$757$	7.50444	+	20.6183i	0.272754	+	0.749385i	0.998135	+	0.0610378i	$0.0194410\pi$
$757$	7.50444	+	20.6183i	0.272754	+	0.749385i	−0.725382	+	0.688347i	$0.758337\pi$
$758$	23.7223	+	19.9053i	0.861632	+	0.722995i
$759$	0.386378	−	0.260035i	0.0140246	−	0.00943866i
$760$	9.49610	−	2.19637i	0.344460	−	0.0796708i
$761$			42.6627i			1.54652i	0.634089	+	0.773260i	$0.281375\pi$
$761$			42.6627i			1.54652i	−0.634089	+	0.773260i	$0.718625\pi$
$762$	−6.77410	−	0.719066i	−0.245400	−	0.0260490i
$763$	−42.0157	+	15.2925i	−1.52107	+	0.553624i
$764$	−7.94306	+	1.40058i	−0.287370	+	0.0506711i
$765$	−25.1203	−	21.8207i	−0.908227	−	0.788928i
$766$	−5.63403	−	2.05062i	−0.203566	−	0.0740918i
$767$	1.84287	+	3.19195i	0.0665423	+	0.115255i
$768$	1.72796	−	0.119036i	0.0623522	−	0.00429534i
$769$	−5.51613	+	4.62858i	−0.198917	+	0.166911i	−0.736805	−	0.676105i	$-0.763667\pi$
$769$	−5.51613	+	4.62858i	−0.198917	+	0.166911i	0.537889	+	0.843016i	$0.319222\pi$
$770$	0.562979	+	0.931814i	0.0202884	+	0.0335802i
$771$	−1.11208	−	16.1433i	−0.0400507	−	0.581386i
$772$	−8.55822	−	14.8233i	−0.308017	−	0.533501i
$773$	−0.874302	+	2.40212i	−0.0314465	+	0.0863984i	−0.954422	−	0.298459i	$-0.903527\pi$
$773$	−0.874302	+	2.40212i	−0.0314465	+	0.0863984i	0.922976	+	0.384858i	$0.125749\pi$
$774$	9.08521	+	5.70322i	0.326561	+	0.204998i
$775$	16.9604	+	2.29957i	0.609235	+	0.0826028i
$776$	−3.53256	−	9.70562i	−0.126811	−	0.348411i
$777$	38.7423	+	4.11246i	1.38987	+	0.147534i
$778$	−34.2743			−1.22879
$779$	−4.19241	−	0.597884i	−0.150209	−	0.0214214i
$780$	−2.32946	−	4.97736i	−0.0834080	−	0.178218i
$781$	1.05990	−	1.26314i	0.0379261	−	0.0451986i
$782$	4.35593	+	11.9678i	0.155768	+	0.427969i
$783$	15.1086	+	37.7316i	0.539938	+	1.34842i
$784$	−2.53771	+	14.3921i	−0.0906324	+	0.514002i
$785$	19.4577	−	35.3048i	0.694475	−	1.26008i
$786$	6.17688	−	12.6313i	0.220322	−	0.450545i
$787$	0.218345	−	0.378184i	0.00778315	−	0.0134808i	−0.862108	−	0.506725i	$-0.830856\pi$
$787$	0.218345	−	0.378184i	0.00778315	−	0.0134808i	0.869891	+	0.493244i	$0.164189\pi$
$788$	−18.1584	+	15.2367i	−0.646866	+	0.542785i
$789$	21.5059	+	6.19077i	0.765630	+	0.220397i
$790$	7.32889	−	9.09556i	0.260750	−	0.323606i
$791$	−3.23228	−	5.59848i	−0.114927	−	0.199059i
$792$	−0.210704	+	0.233040i	−0.00748706	+	0.00828073i
$793$	−3.43481	+	19.4798i	−0.121974	+	0.691747i
$794$	−4.18108	−	23.7121i	−0.148381	−	0.841511i
$795$	−9.63390	+	9.66088i	−0.341679	+	0.342636i
$796$	4.91779	+	4.12652i	0.174307	+	0.146261i
$797$			14.2821i			0.505898i	0.967480	+	0.252949i	$0.0814005\pi$
$797$			14.2821i			0.505898i	−0.967480	+	0.252949i	$0.918600\pi$
$798$	−33.7697	+	9.57145i	−1.19543	+	0.338826i
$799$	26.2962			0.930292
$800$	4.22730	−	2.67019i	0.149458	−	0.0944054i
$801$	−1.92454	+	52.0279i	−0.0680003	+	1.83832i
$802$	−11.8344	+	2.08673i	−0.417887	+	0.0736848i
$803$	0.136988	−	0.776898i	0.00483420	−	0.0274161i
$804$	−2.91128	−	11.7281i	−0.102673	−	0.413620i
$805$	24.8958	−	9.62614i	0.877462	−	0.339277i
$806$	2.42858	−	4.20643i	0.0855432	−	0.148165i
$807$	46.2031	+	13.3002i	1.62642	+	0.468190i
$808$	0.193050	−	0.161988i	0.00679149	−	0.00569873i
$809$	−16.2829	−	9.40094i	−0.572476	−	0.330519i	0.185661	−	0.982614i	$-0.440557\pi$
$809$	−16.2829	−	9.40094i	−0.572476	−	0.330519i	−0.758138	+	0.652094i	$0.773891\pi$
$810$	−18.5114	−	7.89484i	−0.650424	−	0.277396i
$811$	−0.0966504	+	0.265545i	−0.00339386	+	0.00932454i	−0.941378	−	0.337354i	$-0.890468\pi$
$811$	−0.0966504	+	0.265545i	−0.00339386	+	0.00932454i	0.937984	+	0.346678i	$0.112690\pi$
$812$	35.8125	+	6.31472i	1.25677	+	0.221603i
$813$	−6.56234	+	6.32408i	−0.230151	+	0.221795i
$814$	0.476126	−	0.173296i	0.0166882	−	0.00607401i
$815$	24.4535	−	21.3617i	0.856569	−	0.748269i
$816$	−4.79686	−	7.12752i	−0.167924	−	0.249513i
$817$	12.2624	+	9.62055i	0.429006	+	0.336581i
$818$	−27.6591			−0.967077
$819$	9.25481	+	17.4929i	0.323389	+	0.611252i
$820$	−2.13149	+	0.419702i	−0.0744350	+	0.0146566i
$821$	5.42717	−	0.956956i	0.189410	−	0.0333980i	−0.0781386	−	0.996943i	$-0.524898\pi$
$821$	5.42717	−	0.956956i	0.189410	−	0.0333980i	0.267548	+	0.963544i	$0.413787\pi$
$822$	−6.16300	−	13.8809i	−0.214959	−	0.484152i
$823$	−1.02518	+	2.81666i	−0.0357355	+	0.0981824i	−0.956277	−	0.292462i	$-0.905526\pi$
$823$	−1.02518	+	2.81666i	−0.0357355	+	0.0981824i	0.920542	+	0.390644i	$0.127748\pi$
$824$	−12.9057	+	7.45112i	−0.449592	+	0.259572i
$825$	−0.216036	+	0.880831i	−0.00752140	+	0.0306666i
$826$	9.25096	−	7.76247i	0.321882	−	0.270091i
$827$	20.5422	+	24.4813i	0.714324	+	0.851298i	0.994066	−	0.108777i	$-0.0346936\pi$
$827$	20.5422	+	24.4813i	0.714324	+	0.851298i	−0.279743	+	0.960075i	$0.590249\pi$
$828$	4.72977	+	6.07969i	0.164371	+	0.211284i
$829$	32.0273	−	18.4910i	1.11235	−	0.642217i	0.172915	−	0.984937i	$-0.444681\pi$
$829$	32.0273	−	18.4910i	1.11235	−	0.642217i	0.939438	+	0.342719i	$0.111348\pi$
$830$	−5.37661	+	9.75553i	−0.186625	+	0.338620i
$831$	10.2638	+	23.1172i	0.356049	+	0.801928i
$832$	−0.246395	−	1.39737i	−0.00854220	−	0.0484452i
$833$	68.1174	−	24.7927i	2.36013	−	0.859017i
$834$	25.2517	+	2.68045i	0.874396	+	0.0928165i
$835$	5.02725	−	32.2482i	0.173975	−	1.11600i
$836$	−0.339851	+	0.304757i	−0.0117540	+	0.0105402i
$837$	−3.64417	−	17.4097i	−0.125961	−	0.601768i
$838$	−29.0845	−	24.4048i	−1.00471	−	0.843049i
$839$	−23.3399	+	8.49502i	−0.805782	+	0.293281i	−0.711880	−	0.702301i	$-0.752156\pi$
$839$	−23.3399	+	8.49502i	−0.805782	+	0.293281i	−0.0939019	+	0.995581i	$0.529934\pi$
$840$	−14.7351	+	10.3484i	−0.508409	+	0.357052i
$841$	5.58851	−	31.6940i	0.192707	−	1.09290i
$842$	−13.0758	−	4.75919i	−0.450621	−	0.164013i
$843$	4.45764	−	9.11559i	0.153529	−	0.313958i
$844$	5.94588	+	3.43286i	0.204666	+	0.118164i
$845$	21.0271	−	12.7040i	0.723353	−	0.437032i
$846$	15.1360	−	4.88340i	0.520385	−	0.167895i
$847$	44.2444	+	25.5445i	1.52026	+	0.877720i
$848$	−3.05078	+	1.76137i	−0.104764	+	0.0604856i
$849$	−54.9997	+	13.6526i	−1.88759	+	0.468556i
$850$	−21.9545	−	11.5368i	−0.753032	−	0.395708i
$851$	−2.15719	−	12.2340i	−0.0739474	−	0.419376i
$852$	22.0466	+	16.0526i	0.755304	+	0.549954i
$853$	8.70427	−	10.3733i	0.298029	−	0.355177i	−0.596161	−	0.802865i	$-0.703308\pi$
$853$	8.70427	−	10.3733i	0.298029	−	0.355177i	0.894190	+	0.447688i	$0.147753\pi$
$854$	64.8096			2.21774
$855$	−25.5506	−	14.2186i	−0.873811	−	0.486265i
$856$	9.79051			0.334633
$857$	−3.60871	+	4.30070i	−0.123271	+	0.146909i	−0.824150	−	0.566371i	$-0.808347\pi$
$857$	−3.60871	+	4.30070i	−0.123271	+	0.146909i	0.700879	+	0.713280i	$0.252791\pi$
$858$	0.208065	+	0.151497i	0.00710323	+	0.00517203i
$859$	−8.00419	−	45.3940i	−0.273100	−	1.54882i	−0.744935	−	0.667138i	$-0.767519\pi$
$859$	−8.00419	−	45.3940i	−0.273100	−	1.54882i	0.471835	−	0.881687i	$-0.343592\pi$
$860$	7.56611	+	2.58466i	0.258002	+	0.0881361i
$861$	7.59283	−	1.88477i	0.258763	−	0.0642329i
$862$	−16.6353	+	9.60439i	−0.566600	+	0.327127i
$863$	−32.7774	−	18.9240i	−1.11575	−	0.644181i	−0.175441	−	0.984490i	$-0.556135\pi$
$863$	−32.7774	−	18.9240i	−1.11575	−	0.644181i	−0.940314	+	0.340309i	$0.889468\pi$
$864$	−4.08469	−	3.21175i	−0.138964	−	0.109266i
$865$	−4.40989	−	7.29902i	−0.149941	−	0.248174i
$866$	−29.0943	−	16.7976i	−0.988664	−	0.570805i
$867$	−5.78566	+	11.8313i	−0.196491	+	0.401812i
$868$	−14.9546	−	5.44304i	−0.507593	−	0.184749i
$869$	−0.0949961	+	0.538750i	−0.00322252	+	0.0182758i
$870$	17.4108	+	24.7913i	0.590281	+	0.840504i
$871$	−9.30251	+	3.38584i	−0.315204	+	0.114725i
$872$	−7.36735	−	6.18194i	−0.249490	−	0.209347i
$873$	−11.6667	+	28.7052i	−0.394859	+	0.971524i
$874$	5.91155	+	9.50331i	0.199961	+	0.321454i
$875$	−23.2592	+	46.4841i	−0.786305	+	1.57145i
$876$	12.9746	+	1.37724i	0.438370	+	0.0465327i
$877$	31.1984	−	11.3553i	1.05349	−	0.383441i	0.243514	−	0.969897i	$-0.421700\pi$
$877$	31.1984	−	11.3553i	1.05349	−	0.383441i	0.809980	+	0.586457i	$0.199478\pi$
$878$	4.61785	+	26.1891i	0.155845	+	0.883840i
$879$	16.9543	+	38.1862i	0.571856	+	1.28799i
$880$	−0.113030	+	0.205085i	−0.00381023	+	0.00691343i
$881$	10.6331	−	6.13903i	0.358239	−	0.206829i	−0.310069	−	0.950714i	$-0.600352\pi$
$881$	10.6331	−	6.13903i	0.358239	−	0.206829i	0.668308	+	0.743885i	$0.267019\pi$
$882$	34.6039	−	26.9205i	1.16517	−	0.906460i
$883$	1.21639	+	1.44963i	0.0409346	+	0.0487840i	0.786123	−	0.618070i	$-0.212085\pi$
$883$	1.21639	+	1.44963i	0.0409346	+	0.0487840i	−0.745189	+	0.666854i	$0.767641\pi$
$884$	−5.39159	+	4.52408i	−0.181339	+	0.152161i
$885$	10.0232	+	0.862796i	0.336927	+	0.0290026i
$886$	−26.2730	+	15.1687i	−0.882658	+	0.509603i
$887$	−11.6872	+	32.1104i	−0.392419	+	1.07816i	0.573474	+	0.819224i	$0.305595\pi$
$887$	−11.6872	+	32.1104i	−0.392419	+	1.07816i	−0.965894	+	0.258939i	$0.916627\pi$
$888$	3.40058	+	7.65913i	0.114116	+	0.257024i
$889$	18.0071	−	3.17514i	0.603939	−	0.106491i
$890$	7.49711	+	38.0747i	0.251304	+	1.27627i
$891$	0.937753	−	0.0946438i	0.0314159	−	0.00317069i
$892$	13.9362			0.466619
$893$	22.6130	−	4.75861i	0.756717	−	0.159241i
$894$	14.2539	+	21.1795i	0.476722	+	0.708347i
$895$	−35.3419	−	40.4571i	−1.18135	−	1.35233i
$896$	−4.36872	+	1.59008i	−0.145949	+	0.0531210i
$897$	4.54378	−	4.37881i	0.151712	−	0.146204i
$898$	4.26339	+	0.751751i	0.142271	+	0.0250863i
$899$	−9.15775	+	25.1607i	−0.305428	+	0.839156i
$900$	−14.7793	−	2.56340i	−0.492645	−	0.0854467i
$901$	15.1325	+	8.73677i	0.504138	+	0.291064i
$902$	0.0779399	−	0.0653993i	0.00259511	−	0.00217756i
$903$	−27.6692	−	7.96499i	−0.920775	−	0.265058i
$904$	0.695250	−	1.20421i	0.0231237	−	0.0400514i
$905$	9.24125	−	3.57319i	0.307190	−	0.118777i
$906$	7.43209	+	29.9403i	0.246915	+	0.994700i
$907$	6.05787	−	34.3559i	0.201148	−	1.14077i	−0.702239	−	0.711941i	$-0.747816\pi$
$907$	6.05787	−	34.3559i	0.201148	−	1.14077i	0.903387	−	0.428826i	$-0.141073\pi$
$908$	−1.56441	+	0.275847i	−0.0519167	+	0.00915431i
$909$	−0.755511	−	0.0279468i	−0.0250587	−	0.000926936i
$910$	9.70442	+	11.1090i	0.321698	+	0.368259i
$911$	−39.7431			−1.31675			−0.658374	−	0.752691i	$-0.728755\pi$
$911$	−39.7431			−1.31675			−0.658374	+	0.752691i	$0.728755\pi$
$912$	−5.41481	−	5.26117i	−0.179302	−	0.174215i
$913$		−	0.521687i		−	0.0172653i
$914$	−18.6944	−	15.6865i	−0.618356	−	0.518862i
$915$	38.2303	+	38.1236i	1.26386	+	1.26033i
$916$	−2.93710	−	16.6571i	−0.0970445	−	0.550367i
$917$	−6.55369	+	37.1678i	−0.216422	+	1.22739i
$918$	−3.66618	+	25.5120i	−0.121002	+	0.842021i
$919$	10.2652	+	17.7799i	0.338618	+	0.586504i	0.984173	−	0.177210i	$-0.0567072\pi$
$919$	10.2652	+	17.7799i	0.338618	+	0.586504i	−0.645555	+	0.763714i	$0.723374\pi$
$920$	4.47063	+	3.60228i	0.147392	+	0.118764i
$921$	10.6985	+	3.07973i	0.352529	+	0.101481i
$922$	26.8728	−	22.5489i	0.885007	−	0.742609i
$923$	11.1707	−	19.3482i	0.367689	−	0.636855i
$924$	0.370456	−	0.757559i	0.0121871	−	0.0249219i
$925$	19.1352	+	14.8008i	0.629162	+	0.486646i
$926$	2.78960	−	15.8206i	0.0916718	−	0.519897i
$927$	43.7104	+	9.38542i	1.43564	+	0.308258i
$928$	2.67527	+	7.35023i	0.0878199	+	0.241283i
$929$	−26.2986	+	31.3414i	−0.862829	+	1.02828i	0.136463	+	0.990645i	$0.456427\pi$
$929$	−26.2986	+	31.3414i	−0.862829	+	1.02828i	−0.999292	+	0.0376343i	$0.988018\pi$
$930$	−5.61973	−	12.0077i	−0.184278	−	0.393747i
$931$	54.0901	−	33.6468i	1.77273	−	1.10273i
$932$	14.5902			0.477918
$933$	13.4375	+	1.42639i	0.439925	+	0.0466978i
$934$	−8.12220	−	22.3156i	−0.265766	−	0.730187i
$935$	1.16131	−	0.0230958i	0.0379788	−	0.000755313i
$936$	−2.26321	+	3.60530i	−0.0739755	+	0.117843i
$937$	−6.33194	+	17.3969i	−0.206855	+	0.568331i	−0.999124	−	0.0418416i	$-0.986678\pi$
$937$	−6.33194	+	17.3969i	−0.206855	+	0.568331i	0.792269	+	0.610172i	$0.208900\pi$
$938$	16.2178	+	28.0900i	0.529529	+	0.917172i
$939$	−3.72598	−	54.0873i	−0.121593	−	1.76507i
$940$	10.1463	−	6.13012i	0.330934	−	0.199942i
$941$	−5.42107	+	4.54882i	−0.176722	+	0.148287i	−0.726858	−	0.686788i	$-0.759020\pi$
$941$	−5.42107	+	4.54882i	−0.176722	+	0.148287i	0.550136	+	0.835075i	$0.314576\pi$
$942$	−31.1515	+	2.14597i	−1.01497	+	0.0699196i
$943$	−1.24726	−	2.16032i	−0.0406164	−	0.0703497i
$944$	2.44090	+	0.888415i	0.0794446	+	0.0289155i
$945$	53.6105	+	6.61895i	1.74395	+	0.215314i
$946$	−0.368768	+	0.0650238i	−0.0119897	+	0.00211411i
$947$	−25.2380	+	9.18589i	−0.820126	+	0.298501i	−0.717800	−	0.696250i	$-0.754851\pi$
$947$	−25.2380	+	9.18589i	−0.820126	+	0.298501i	−0.102326	+	0.994751i	$0.532628\pi$
$948$	−8.99739	−	0.955067i	−0.292222	−	0.0310191i
$949$		−	10.6888i		−	0.346972i
$950$	−20.9672	−	5.94797i	−0.680264	−	0.192978i
$951$	−25.0646	+	16.8686i	−0.812775	+	0.547002i
$952$	17.6654	+	14.8230i	0.572539	+	0.480417i
$953$	4.52893	+	12.4431i	0.146706	+	0.403072i	0.991180	−	0.132525i	$-0.0423086\pi$
$953$	4.52893	+	12.4431i	0.146706	+	0.403072i	−0.844473	+	0.535598i	$0.820086\pi$
$954$	10.3327	+	2.21862i	0.334533	+	0.0718303i
$955$	17.0669	+	5.83021i	0.552271	+	0.188661i
$956$	6.19015	−	17.0073i	0.200204	−	0.550055i
$957$	−1.27457	−	0.623281i	−0.0412010	−	0.0201478i
$958$	−14.3890	+	24.9224i	−0.464886	+	0.805206i
$959$	26.2038	+	31.2284i	0.846163	+	1.00842i
$960$	−3.51240	−	1.63188i	−0.113362	−	0.0526688i
$961$	−9.64114	+	16.6989i	−0.311004	+	0.538676i
$962$	5.94540	−	3.43258i	0.191687	−	0.110671i
$963$	−21.7866	−	19.6985i	−0.702064	−	0.634774i
$964$	−23.2191	−	4.09415i	−0.747837	−	0.131864i
$965$	0.761024	+	38.2660i	0.0244982	+	1.23183i
$966$	−16.7143	−	12.1701i	−0.537774	−	0.391566i
$967$	−12.1671	+	14.5002i	−0.391268	+	0.466295i	−0.925337	−	0.379146i	$-0.876218\pi$
$967$	−12.1671	+	14.5002i	−0.391268	+	0.466295i	0.534069	+	0.845441i	$0.320662\pi$
$968$			10.9890i			0.353201i
$969$	−9.17095	+	36.3086i	−0.294613	+	1.16640i
$970$	−3.55741	+	22.8196i	−0.114222	+	0.732694i
$971$	−5.15695	−	4.32719i	−0.165494	−	0.138866i	0.556279	−	0.830995i	$-0.312228\pi$
$971$	−5.15695	−	4.32719i	−0.165494	−	0.138866i	−0.721774	+	0.692129i	$0.756673\pi$
$972$	2.62754	+	15.3654i	0.0842783	+	0.492846i
$973$	−67.1249	+	11.8359i	−2.15192	+	0.379442i
$974$	−14.4674	−	2.55099i	−0.463565	−	0.0817390i
$975$	−0.810232	+	12.2616i	−0.0259482	+	0.392684i
$976$	6.97013	+	12.0726i	0.223108	+	0.386435i
$977$	−17.9327	−	10.3534i	−0.573718	−	0.331236i	0.184915	−	0.982755i	$-0.440799\pi$
$977$	−17.9327	−	10.3534i	−0.573718	−	0.331236i	−0.758633	+	0.651518i	$0.774132\pi$
$978$	−24.1696	−	6.95757i	−0.772859	−	0.222478i
$979$	−1.16822	−	1.39223i	−0.0373366	−	0.0444960i
$980$	20.5032	−	25.4456i	0.654949	−	0.812829i
$981$	3.95638	+	28.5796i	0.126317	+	0.912478i
$982$	17.0630	+	6.21043i	0.544502	+	0.198183i
$983$	−0.184591	−	0.0325483i	−0.00588753	−	0.00103813i	0.170704	−	0.985322i	$-0.445396\pi$
$983$	−0.184591	−	0.0325483i	−0.00588753	−	0.00103813i	−0.176591	+	0.984284i	$0.556507\pi$
$984$	1.16769	+	1.21168i	0.0372244	+	0.0386269i
$985$	52.0054	−	10.2401i	1.65703	−	0.326278i
$986$	24.9393	−	29.7215i	0.794229	−	0.946525i
$987$	−35.4158	+	23.8350i	−1.12730	+	0.758678i
$988$	−3.81774	+	4.86609i	−0.121458	+	0.154811i
$989$			9.18087i			0.291935i
$990$	0.664153	−	0.228957i	0.0211082	−	0.00727674i
$991$	16.4329	+	45.1491i	0.522009	+	1.43421i	0.868281	+	0.496073i	$0.165225\pi$
$991$	16.4329	+	45.1491i	0.522009	+	1.43421i	−0.346272	+	0.938134i	$0.612552\pi$
$992$	−0.594418	−	3.37111i	−0.0188728	−	0.107033i
$993$	−0.0987775	−	0.222476i	−0.00313461	−	0.00706007i
$994$	−68.7866	−	25.0363i	−2.18178	−	0.794102i
$995$	−5.17693	−	13.3889i	−0.164120	−	0.424458i
$996$	8.60787	−	0.592981i	0.272751	−	0.0187893i
$997$	3.10488	+	3.70025i	0.0983325	+	0.117188i	0.812967	−	0.582310i	$-0.197851\pi$
$997$	3.10488	+	3.70025i	0.0983325	+	0.117188i	−0.714634	+	0.699499i	$0.753407\pi$
$998$	3.94634	+	4.70307i	0.124919	+	0.148873i
$999$	7.84289	−	23.8857i	0.248138	−	0.755709i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bf.a.269.36	yes	240
3.2	odd	2	inner	570.2.bf.a.269.12	yes	240
5.4	even	2	inner	570.2.bf.a.269.5	yes	240
15.14	odd	2	inner	570.2.bf.a.269.29	yes	240
19.13	odd	18	inner	570.2.bf.a.89.29	yes	240
57.32	even	18	inner	570.2.bf.a.89.5	✓	240
95.89	odd	18	inner	570.2.bf.a.89.12	yes	240
285.89	even	18	inner	570.2.bf.a.89.36	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bf.a.89.5	✓	240	57.32	even	18	inner
570.2.bf.a.89.12	yes	240	95.89	odd	18	inner
570.2.bf.a.89.29	yes	240	19.13	odd	18	inner
570.2.bf.a.89.36	yes	240	285.89	even	18	inner
570.2.bf.a.269.5	yes	240	5.4	even	2	inner
570.2.bf.a.269.12	yes	240	3.2	odd	2	inner
570.2.bf.a.269.29	yes	240	15.14	odd	2	inner
570.2.bf.a.269.36	yes	240	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.bf (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.642788 - 0.766044i) q^{2} +(1.40021 + 1.01952i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(-0.722849 + 2.11601i) q^{5} +(1.68103 - 0.417284i) q^{6} +(-4.02623 + 2.32455i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(0.921151 + 2.85508i) q^{9} +O(q^{10})\)	\(q+(0.642788 - 0.766044i) q^{2} +(1.40021 + 1.01952i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(-0.722849 + 2.11601i) q^{5} +(1.68103 - 0.417284i) q^{6} +(-4.02623 + 2.32455i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(0.921151 + 2.85508i) q^{9} +(1.15632 + 1.91388i) q^{10} +(-0.0906937 - 0.0523621i) q^{11} +(0.760890 - 1.55597i) q^{12} +(-1.33336 - 0.485303i) q^{13} +(-0.807307 + 4.57846i) q^{14} +(-3.16945 + 2.22589i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(3.79975 + 3.18837i) q^{17} +(2.77922 + 1.12957i) q^{18} +(3.84452 + 2.05419i) q^{19} +(2.20938 + 0.344426i) q^{20} +(-8.00748 - 0.849989i) q^{21} +(-0.0984085 + 0.0358178i) q^{22} +(0.445860 + 2.52860i) q^{23} +(-0.702853 - 1.58303i) q^{24} +(-3.95498 - 3.05911i) q^{25} +(-1.22883 + 0.709466i) q^{26} +(-1.62101 + 4.93683i) q^{27} +(2.98838 + 3.56141i) q^{28} +(5.99196 - 5.02786i) q^{29} +(-0.332157 + 3.85871i) q^{30} +(-2.96451 + 1.71156i) q^{31} +(-0.342020 + 0.939693i) q^{32} +(-0.0736056 - 0.165782i) q^{33} +(4.88487 - 0.861334i) q^{34} +(-2.00840 - 10.1998i) q^{35} +(2.65175 - 1.40294i) q^{36} -4.83826 q^{37} +(4.04481 - 1.62467i) q^{38} +(-1.37220 - 2.03891i) q^{39} +(1.68401 - 1.47109i) q^{40} +(-0.912946 + 0.332285i) q^{41} +(-5.79824 + 5.58772i) q^{42} +(3.52133 + 0.620906i) q^{43} +(-0.0358178 + 0.0984085i) q^{44} +(-6.70722 - 0.114628i) q^{45} +(2.22361 + 1.28380i) q^{46} +(4.06112 - 3.40768i) q^{47} +(-1.66446 - 0.479138i) q^{48} +(7.30704 - 12.6562i) q^{49} +(-4.88562 + 1.06333i) q^{50} +(2.06982 + 8.33830i) q^{51} +(-0.246395 + 1.39737i) q^{52} +(3.46921 - 0.611716i) q^{53} +(2.73986 + 4.41510i) q^{54} +(0.176356 - 0.154059i) q^{55} +4.64909 q^{56} +(3.28883 + 6.79585i) q^{57} -7.82195i q^{58} +(-1.98984 - 1.66967i) q^{59} +(2.74244 + 2.73478i) q^{60} +(-2.42070 - 13.7285i) q^{61} +(-0.594418 + 3.37111i) q^{62} +(-10.3455 - 9.35396i) q^{63} +(0.500000 + 0.866025i) q^{64} +(1.99072 - 2.47060i) q^{65} +(-0.174309 - 0.0501773i) q^{66} +(5.34450 - 4.48457i) q^{67} +(2.48011 - 4.29568i) q^{68} +(-1.95366 + 3.99512i) q^{69} +(-9.10450 - 5.01780i) q^{70} +(-2.73413 + 15.5060i) q^{71} +(0.629800 - 2.93315i) q^{72} +(2.57642 + 7.07867i) q^{73} +(-3.10997 + 3.70632i) q^{74} +(-2.41896 - 8.31557i) q^{75} +(1.35538 - 4.14282i) q^{76} +0.486872 q^{77} +(-2.44393 - 0.259422i) q^{78} +(-1.78665 - 4.90879i) q^{79} +(-0.0444616 - 2.23563i) q^{80} +(-7.30296 + 5.25992i) q^{81} +(-0.332285 + 0.912946i) q^{82} +(2.49077 + 4.31413i) q^{83} +(0.553409 + 8.03343i) q^{84} +(-9.49326 + 5.73559i) q^{85} +(2.73911 - 2.29839i) q^{86} +(13.5160 - 0.931093i) q^{87} +(0.0523621 + 0.0906937i) q^{88} +(16.3079 + 5.93559i) q^{89} +(-4.39913 + 5.06435i) q^{90} +(6.49653 - 1.14551i) q^{91} +(2.41276 - 0.878173i) q^{92} +(-5.89589 - 0.625844i) q^{93} -5.30141i q^{94} +(-7.12568 + 6.65017i) q^{95} +(-1.43694 + 0.967066i) q^{96} +(7.91209 + 6.63904i) q^{97} +(-4.99831 - 13.7327i) q^{98} +(0.0659552 - 0.307171i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q+O(q^{10}) \) 240 * q	\( 240 q - 30 q^{15} + 48 q^{19} + 12 q^{25} - 48 q^{39} + 36 q^{45} - 72 q^{46} + 216 q^{49} - 180 q^{51} + 36 q^{54} + 60 q^{55} + 6 q^{60} - 72 q^{61} + 120 q^{64} - 156 q^{66} + 48 q^{79} - 120 q^{81} - 108 q^{84} - 48 q^{85} - 36 q^{90} - 24 q^{91} - 216 q^{99}+O(q^{100}) \) 240 * q - 30 * q^15 + 48 * q^19 + 12 * q^25 - 48 * q^39 + 36 * q^45 - 72 * q^46 + 216 * q^49 - 180 * q^51 + 36 * q^54 + 60 * q^55 + 6 * q^60 - 72 * q^61 + 120 * q^64 - 156 * q^66 + 48 * q^79 - 120 * q^81 - 108 * q^84 - 48 * q^85 - 36 * q^90 - 24 * q^91 - 216 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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