LMFDB - Embedded newform 231.2.be.a.2.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(2,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 10, 3]))

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

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

chi := DirichletCharacter("231.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.be (of order $30$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			2.4
Character	$\chi$	$=$	231.2
Dual form			231.2.be.a.116.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41473 - 1.57122i) q^{2} +(-1.63740 + 0.564721i) q^{3} +(-0.258206 + 2.45666i) q^{4} +(-0.705701 + 3.32006i) q^{5} +(3.20379 + 1.77379i) q^{6} +(-0.181035 - 2.63955i) q^{7} +(0.804266 - 0.584333i) q^{8} +(2.36218 - 1.84935i) q^{9} +O(q^{10})$	\(q+(-1.41473 - 1.57122i) q^{2} +(-1.63740 + 0.564721i) q^{3} +(-0.258206 + 2.45666i) q^{4} +(-0.705701 + 3.32006i) q^{5} +(3.20379 + 1.77379i) q^{6} +(-0.181035 - 2.63955i) q^{7} +(0.804266 - 0.584333i) q^{8} +(2.36218 - 1.84935i) q^{9} +(6.21493 - 3.58819i) q^{10} +(-0.190758 - 3.31113i) q^{11} +(-0.964542 - 4.16836i) q^{12} +(1.12657 + 0.366043i) q^{13} +(-3.89120 + 4.01870i) q^{14} +(-0.719391 - 5.83481i) q^{15} +(2.77650 + 0.590162i) q^{16} +(4.47832 - 4.97367i) q^{17} +(-6.24759 - 1.09517i) q^{18} +(-0.167965 + 0.0176539i) q^{19} +(-7.97406 - 2.59093i) q^{20} +(1.78704 + 4.21977i) q^{21} +(-4.93265 + 4.98409i) q^{22} +(-5.56650 - 3.21382i) q^{23} +(-0.986922 + 1.41097i) q^{24} +(-5.95708 - 2.65226i) q^{25} +(-1.01865 - 2.28793i) q^{26} +(-2.82348 + 4.36211i) q^{27} +(6.53123 + 0.236805i) q^{28} +(3.12357 + 2.26940i) q^{29} +(-8.15002 + 9.38501i) q^{30} +(6.02551 - 1.28076i) q^{31} +(-3.99485 - 6.91928i) q^{32} +(2.18221 + 5.31394i) q^{33} -14.1504 q^{34} +(8.89123 + 1.26169i) q^{35} +(3.93331 + 6.28060i) q^{36} +(4.40516 - 1.96130i) q^{37} +(0.265364 + 0.238935i) q^{38} +(-2.05135 + 0.0368343i) q^{39} +(1.37245 + 3.08258i) q^{40} +(6.82831 - 4.96106i) q^{41} +(4.10201 - 8.77768i) q^{42} -7.93464i q^{43} +(8.18360 + 0.386327i) q^{44} +(4.47297 + 9.14768i) q^{45} +(2.82549 + 13.2929i) q^{46} +(0.185690 - 0.0195168i) q^{47} +(-4.87952 + 0.601611i) q^{48} +(-6.93445 + 0.955702i) q^{49} +(4.26039 + 13.1121i) q^{50} +(-4.52407 + 10.6729i) q^{51} +(-1.19013 + 2.67308i) q^{52} +(-0.128162 - 0.602956i) q^{53} +(10.8483 - 1.73491i) q^{54} +(11.1278 + 1.70334i) q^{55} +(-1.68798 - 2.01711i) q^{56} +(0.265057 - 0.123760i) q^{57} +(-0.853278 - 8.11840i) q^{58} +(-1.20138 - 0.126270i) q^{59} +(14.5199 - 0.260721i) q^{60} +(-0.907825 + 4.27098i) q^{61} +(-10.5368 - 7.65546i) q^{62} +(-5.30909 - 5.90030i) q^{63} +(-3.46576 + 10.6665i) q^{64} +(-2.01031 + 3.48195i) q^{65} +(5.26211 - 10.9465i) q^{66} +(-0.957449 - 1.65835i) q^{67} +(11.0623 + 12.2859i) q^{68} +(10.9295 + 2.11880i) q^{69} +(-10.5963 - 15.7550i) q^{70} +(7.07684 - 2.29940i) q^{71} +(0.819183 - 2.86767i) q^{72} +(-10.9372 - 1.14954i) q^{73} +(-9.31376 - 4.14675i) q^{74} +(11.2519 + 0.978738i) q^{75} -0.417192i q^{76} +(-8.70537 + 1.10295i) q^{77} +(2.95999 + 3.17102i) q^{78} +(-2.52078 + 2.26972i) q^{79} +(-3.91875 + 8.80167i) q^{80} +(2.15980 - 8.73701i) q^{81} +(-17.4551 - 3.71020i) q^{82} +(2.27363 + 6.99752i) q^{83} +(-10.8280 + 3.30058i) q^{84} +(13.3526 + 18.3782i) q^{85} +(-12.4671 + 11.2254i) q^{86} +(-6.39612 - 1.95199i) q^{87} +(-2.08823 - 2.55157i) q^{88} +(1.52478 + 0.880330i) q^{89} +(8.04495 - 19.9695i) q^{90} +(0.762242 - 3.03989i) q^{91} +(9.33257 - 12.8452i) q^{92} +(-9.14291 + 5.49985i) q^{93} +(-0.293367 - 0.264149i) q^{94} +(0.0599213 - 0.570113i) q^{95} +(10.4486 + 9.07368i) q^{96} +(-0.310343 + 0.955137i) q^{97} +(11.3120 + 9.54348i) q^{98} +(-6.57406 - 7.46872i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q - 3 q^{3} + 18 q^{4} - 20 q^{6} - 20 q^{7} - 9 q^{9}+O(q^{10}) $ 224 * q - 3 * q^3 + 18 * q^4 - 20 * q^6 - 20 * q^7 - 9 * q^9	$ 224 q - 3 q^{3} + 18 q^{4} - 20 q^{6} - 20 q^{7} - 9 q^{9} - 16 q^{12} - 40 q^{13} + 12 q^{15} + 34 q^{16} - 5 q^{18} - 10 q^{19} - 76 q^{22} - 25 q^{24} - 18 q^{25} + 6 q^{27} + 10 q^{28} - 35 q^{30} - 8 q^{33} - 96 q^{34} - 48 q^{36} - 10 q^{37} - 45 q^{39} - 120 q^{40} + 34 q^{42} - 24 q^{45} - 50 q^{46} + 14 q^{48} - 56 q^{49} - 45 q^{51} - 10 q^{52} + 48 q^{55} + 60 q^{57} + 44 q^{58} - 47 q^{60} - 50 q^{61} + 60 q^{63} - 72 q^{64} + 77 q^{66} - 80 q^{67} + 78 q^{69} + 36 q^{70} + 55 q^{72} - 70 q^{73} - 11 q^{75} + 36 q^{78} - 90 q^{79} + 23 q^{81} - 6 q^{82} + 125 q^{84} + 160 q^{85} + 86 q^{88} + 30 q^{90} - 128 q^{91} - 38 q^{93} - 210 q^{94} + 135 q^{96} + 40 q^{97} + 80 q^{99}+O(q^{100}) $ 224 * q - 3 * q^3 + 18 * q^4 - 20 * q^6 - 20 * q^7 - 9 * q^9 - 16 * q^12 - 40 * q^13 + 12 * q^15 + 34 * q^16 - 5 * q^18 - 10 * q^19 - 76 * q^22 - 25 * q^24 - 18 * q^25 + 6 * q^27 + 10 * q^28 - 35 * q^30 - 8 * q^33 - 96 * q^34 - 48 * q^36 - 10 * q^37 - 45 * q^39 - 120 * q^40 + 34 * q^42 - 24 * q^45 - 50 * q^46 + 14 * q^48 - 56 * q^49 - 45 * q^51 - 10 * q^52 + 48 * q^55 + 60 * q^57 + 44 * q^58 - 47 * q^60 - 50 * q^61 + 60 * q^63 - 72 * q^64 + 77 * q^66 - 80 * q^67 + 78 * q^69 + 36 * q^70 + 55 * q^72 - 70 * q^73 - 11 * q^75 + 36 * q^78 - 90 * q^79 + 23 * q^81 - 6 * q^82 + 125 * q^84 + 160 * q^85 + 86 * q^88 + 30 * q^90 - 128 * q^91 - 38 * q^93 - 210 * q^94 + 135 * q^96 + 40 * q^97 + 80 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{10}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.41473	−	1.57122i	−1.00037	−	1.11102i	−0.993816	−	0.111041i	$-0.964581\pi$
$2$	−1.41473	−	1.57122i	−1.00037	−	1.11102i	−0.00655073	−	0.999979i	$-0.502085\pi$
$3$	−1.63740	+	0.564721i	−0.945355	+	0.326042i
$3$	−1.63740	+	0.564721i	−0.945355	+	0.326042i
$4$	−0.258206	+	2.45666i	−0.129103	+	1.22833i
$5$	−0.705701	+	3.32006i	−0.315599	+	1.48478i	0.479092	+	0.877764i	$0.340966\pi$
$5$	−0.705701	+	3.32006i	−0.315599	+	1.48478i	−0.794692	+	0.607013i	$0.792367\pi$
$6$	3.20379	+	1.77379i	1.30794	+	0.724147i
$7$	−0.181035	−	2.63955i	−0.0684248	−	0.997656i
$7$	−0.181035	−	2.63955i	−0.0684248	−	0.997656i
$8$	0.804266	−	0.584333i	0.284351	−	0.206593i
$9$	2.36218	−	1.84935i	0.787394	−	0.616451i
$10$	6.21493	−	3.58819i	1.96533	−	1.13468i
$11$	−0.190758	−	3.31113i	−0.0575156	−	0.998345i
$11$	−0.190758	−	3.31113i	−0.0575156	−	0.998345i
$12$	−0.964542	−	4.16836i	−0.278439	−	1.20330i
$13$	1.12657	+	0.366043i	0.312453	+	0.101522i	0.461046	−	0.887376i	$-0.347474\pi$
$13$	1.12657	+	0.366043i	0.312453	+	0.101522i	−0.148593	+	0.988898i	$0.547474\pi$
$14$	−3.89120	+	4.01870i	−1.03997	+	1.07404i
$15$	−0.719391	−	5.83481i	−0.185746	−	1.50654i
$16$	2.77650	+	0.590162i	0.694124	+	0.147541i
$17$	4.47832	−	4.97367i	1.08615	−	1.20629i	0.108935	−	0.994049i	$-0.465256\pi$
$17$	4.47832	−	4.97367i	1.08615	−	1.20629i	0.977217	−	0.212244i	$-0.0680773\pi$
$18$	−6.24759	−	1.09517i	−1.47257	−	0.258133i
$19$	−0.167965	+	0.0176539i	−0.0385339	+	0.00405007i	−0.123776	−	0.992310i	$-0.539500\pi$
$19$	−0.167965	+	0.0176539i	−0.0385339	+	0.00405007i	0.0852419	+	0.996360i	$0.472834\pi$
$20$	−7.97406	−	2.59093i	−1.78305	−	0.579350i
$21$	1.78704	+	4.21977i	0.389963	+	0.920830i
$22$	−4.93265	+	4.98409i	−1.05164	+	1.06261i
$23$	−5.56650	−	3.21382i	−1.16069	−	0.670127i	−0.209224	−	0.977868i	$-0.567094\pi$
$23$	−5.56650	−	3.21382i	−1.16069	−	0.670127i	−0.951470	+	0.307740i	$0.900427\pi$
$24$	−0.986922	+	1.41097i	−0.201455	+	0.288014i
$25$	−5.95708	−	2.65226i	−1.19142	−	0.530453i
$26$	−1.01865	−	2.28793i	−0.199774	−	0.448701i
$27$	−2.82348	+	4.36211i	−0.543378	+	0.839488i
$28$	6.53123	+	0.236805i	1.23429	+	0.0447519i
$29$	3.12357	+	2.26940i	0.580032	+	0.421418i	0.838735	−	0.544539i	$-0.183295\pi$
$29$	3.12357	+	2.26940i	0.580032	+	0.421418i	−0.258704	+	0.965957i	$0.583295\pi$
$30$	−8.15002	+	9.38501i	−1.48798	+	1.71346i
$31$	6.02551	−	1.28076i	1.08221	−	0.230031i	0.367905	−	0.929863i	$-0.380075\pi$
$31$	6.02551	−	1.28076i	1.08221	−	0.230031i	0.714308	+	0.699832i	$0.246742\pi$
$32$	−3.99485	−	6.91928i	−0.706196	−	1.22317i
$33$	2.18221	+	5.31394i	0.379875	+	0.925038i
$34$	−14.1504			−2.42677
$35$	8.89123	+	1.26169i	1.50289	+	0.213264i
$36$	3.93331	+	6.28060i	0.655551	+	1.04677i
$37$	4.40516	−	1.96130i	0.724204	−	0.322437i	−0.0113190	−	0.999936i	$-0.503603\pi$
$37$	4.40516	−	1.96130i	0.724204	−	0.322437i	0.735523	+	0.677499i	$0.236936\pi$
$38$	0.265364	+	0.238935i	0.0430477	+	0.0387603i
$39$	−2.05135	+	0.0368343i	−0.328480	+	0.00589822i
$40$	1.37245	+	3.08258i	0.217004	+	0.487398i
$41$	6.82831	−	4.96106i	1.06640	−	0.774787i	0.0911407	−	0.995838i	$-0.470949\pi$
$41$	6.82831	−	4.96106i	1.06640	−	0.774787i	0.975262	+	0.221051i	$0.0709487\pi$
$42$	4.10201	−	8.77768i	0.632954	−	1.35442i
$43$		−	7.93464i		−	1.21002i	−0.796217	−	0.605011i	$-0.793169\pi$
$43$		−	7.93464i		−	1.21002i	0.796217	−	0.605011i	$-0.206831\pi$
$44$	8.18360	+	0.386327i	1.23372	+	0.0582409i
$45$	4.47297	+	9.14768i	0.666791	+	1.36366i
$46$	2.82549	+	13.2929i	0.416595	+	1.95993i
$47$	0.185690	−	0.0195168i	0.0270857	−	0.00284682i	−0.0909759	−	0.995853i	$-0.528999\pi$
$47$	0.185690	−	0.0195168i	0.0270857	−	0.00284682i	0.118062	+	0.993006i	$0.462332\pi$
$48$	−4.87952	+	0.601611i	−0.704298	+	0.0868351i
$49$	−6.93445	+	0.955702i	−0.990636	+	0.136529i
$50$	4.26039	+	13.1121i	0.602510	+	1.85433i
$51$	−4.52407	+	10.6729i	−0.633497	+	1.49451i
$52$	−1.19013	+	2.67308i	−0.165041	+	0.370689i
$53$	−0.128162	−	0.602956i	−0.0176044	−	0.0828224i	0.968468	−	0.249136i	$-0.0801468\pi$
$53$	−0.128162	−	0.602956i	−0.0176044	−	0.0828224i	−0.986073	+	0.166314i	$0.946813\pi$
$54$	10.8483	−	1.73491i	1.47627	−	0.236092i
$55$	11.1278	+	1.70334i	1.50047	+	0.229679i
$56$	−1.68798	−	2.01711i	−0.225565	−	0.269548i
$57$	0.265057	−	0.123760i	0.0351077	−	0.0163924i
$58$	−0.853278	−	8.11840i	−0.112041	−	1.06600i
$59$	−1.20138	−	0.126270i	−0.156406	−	0.0164389i	0.0260019	−	0.999662i	$-0.491722\pi$
$59$	−1.20138	−	0.126270i	−0.156406	−	0.0164389i	−0.182408	+	0.983223i	$0.558389\pi$
$60$	14.5199	−	0.260721i	1.87451	−	0.0336590i
$61$	−0.907825	+	4.27098i	−0.116235	+	0.546843i	0.881038	+	0.473045i	$0.156845\pi$
$61$	−0.907825	+	4.27098i	−0.116235	+	0.546843i	−0.997273	+	0.0737979i	$0.976488\pi$
$62$	−10.5368	−	7.65546i	−1.33818	−	0.972244i
$63$	−5.30909	−	5.90030i	−0.668883	−	0.743368i
$64$	−3.46576	+	10.6665i	−0.433220	+	1.33332i
$65$	−2.01031	+	3.48195i	−0.249348	+	0.431883i
$66$	5.26211	−	10.9465i	0.647721	−	1.34743i
$67$	−0.957449	−	1.65835i	−0.116971	−	0.202600i	0.801595	−	0.597868i	$-0.203985\pi$
$67$	−0.957449	−	1.65835i	−0.116971	−	0.202600i	−0.918566	+	0.395268i	$0.870652\pi$
$68$	11.0623	+	12.2859i	1.34150	+	1.48989i
$69$	10.9295	+	2.11880i	1.31576	+	0.255074i
$70$	−10.5963	−	15.7550i	−1.26650	−	1.88309i
$71$	7.07684	−	2.29940i	0.839866	−	0.272889i	0.142671	−	0.989770i	$-0.454431\pi$
$71$	7.07684	−	2.29940i	0.839866	−	0.272889i	0.697195	+	0.716881i	$0.254431\pi$
$72$	0.819183	−	2.86767i	0.0965417	−	0.337958i
$73$	−10.9372	−	1.14954i	−1.28010	−	0.134544i	−0.560045	−	0.828462i	$-0.689216\pi$
$73$	−10.9372	−	1.14954i	−1.28010	−	0.134544i	−0.720054	+	0.693918i	$0.755883\pi$
$74$	−9.31376	−	4.14675i	−1.08270	−	0.482050i
$75$	11.2519	+	0.978738i	1.29926	+	0.113015i
$76$		−	0.417192i		−	0.0478552i
$77$	−8.70537	+	1.10295i	−0.992069	+	0.125692i
$78$	2.95999	+	3.17102i	0.335153	+	0.359047i
$79$	−2.52078	+	2.26972i	−0.283609	+	0.255363i	−0.798640	−	0.601808i	$-0.794447\pi$
$79$	−2.52078	+	2.26972i	−0.283609	+	0.255363i	0.515031	+	0.857172i	$0.327780\pi$
$80$	−3.91875	+	8.80167i	−0.438130	+	0.984056i
$81$	2.15980	−	8.73701i	0.239977	−	0.970778i
$82$	−17.4551	−	3.71020i	−1.92760	−	0.409724i
$83$	2.27363	+	6.99752i	0.249563	+	0.768077i	0.994852	+	0.101335i	$0.0323115\pi$
$83$	2.27363	+	6.99752i	0.249563	+	0.768077i	−0.745289	+	0.666742i	$0.767688\pi$
$84$	−10.8280	+	3.30058i	−1.18143	+	0.360123i
$85$	13.3526	+	18.3782i	1.44829	+	1.99340i
$86$	−12.4671	+	11.2254i	−1.34436	+	1.21046i
$87$	−6.39612	−	1.95199i	−0.685736	−	0.209275i
$88$	−2.08823	−	2.55157i	−0.222606	−	0.271998i
$89$	1.52478	+	0.880330i	0.161626	+	0.0933148i	0.578631	−	0.815589i	$-0.303587\pi$
$89$	1.52478	+	0.880330i	0.161626	+	0.0933148i	−0.417005	+	0.908904i	$0.636920\pi$
$90$	8.04495	−	19.9695i	0.848013	−	2.10497i
$91$	0.762242	−	3.03989i	0.0799046	−	0.318667i
$92$	9.33257	−	12.8452i	0.972988	−	1.33920i
$93$	−9.14291	+	5.49985i	−0.948076	+	0.570308i
$94$	−0.293367	−	0.264149i	−0.0302585	−	0.0272449i
$95$	0.0599213	−	0.570113i	0.00614780	−	0.0584924i
$96$	10.4486	+	9.07368i	1.06641	+	0.926079i
$97$	−0.310343	+	0.955137i	−0.0315105	+	0.0969795i	−0.965575	−	0.260125i	$-0.916236\pi$
$97$	−0.310343	+	0.955137i	−0.0315105	+	0.0969795i	0.934064	+	0.357105i	$0.116236\pi$
$98$	11.3120	+	9.54348i	1.14269	+	0.964037i
$99$	−6.57406	−	7.46872i	−0.660718	−	0.750635i
$100$	8.05387	−	13.9497i	0.805387	−	1.39497i
$101$	−3.76207	+	0.799653i	−0.374340	+	0.0795684i	−0.391240	−	0.920289i	$-0.627954\pi$
$101$	−3.76207	+	0.799653i	−0.374340	+	0.0795684i	0.0168998	+	0.999857i	$0.494620\pi$
$102$	23.1698	−	7.99100i	2.29416	−	0.791227i
$103$	1.01854	−	0.453483i	0.100360	−	0.0446830i	−0.355943	−	0.934508i	$-0.615840\pi$
$103$	1.01854	−	0.453483i	0.100360	−	0.0446830i	0.456302	+	0.889825i	$0.349174\pi$
$104$	1.11995	−	0.363893i	0.109820	−	0.0356827i
$105$	−15.2710	+	2.95517i	−1.49030	+	0.288395i
$106$	−0.766060	+	1.05439i	−0.0744064	+	0.102412i
$107$	−0.880790	−	8.38016i	−0.0851492	−	0.810140i	−0.950865	−	0.309605i	$-0.899803\pi$
$107$	−0.880790	−	8.38016i	−0.0851492	−	0.810140i	0.865716	−	0.500535i	$-0.166863\pi$
$108$	−9.98719	−	8.06265i	−0.961018	−	0.775829i
$109$	−8.66436	+	5.00237i	−0.829895	+	0.479140i	−0.853817	−	0.520574i	$-0.825718\pi$
$109$	−8.66436	+	5.00237i	−0.829895	+	0.479140i	0.0239216	+	0.999714i	$0.492385\pi$
$110$	−13.0665	−	19.8940i	−1.24584	−	1.89682i
$111$	−6.10544	+	5.69913i	−0.579503	+	0.540938i
$112$	1.05512	−	7.43554i	0.0996995	−	0.702593i
$113$	−9.25318	−	12.7359i	−0.870466	−	1.19809i	−0.978971	−	0.203997i	$-0.934607\pi$
$113$	−9.25318	−	12.7359i	−0.870466	−	1.19809i	0.108506	−	0.994096i	$-0.465393\pi$
$114$	−0.569439	−	0.241376i	−0.0533328	−	0.0226069i
$115$	14.5984	−	16.2131i	1.36130	−	1.51188i
$116$	−6.38168	+	7.08758i	−0.592524	+	0.658065i
$117$	3.33809	−	1.21875i	0.308607	−	0.112674i
$118$	1.50123	+	2.06626i	0.138199	+	0.190215i
$119$	−13.9390	−	10.9203i	−1.27779	−	1.00107i
$120$	−3.98805	−	4.27237i	−0.364058	−	0.390012i
$121$	−10.9272	+	1.26325i	−0.993384	+	0.114841i
$122$	7.99498	−	4.61590i	0.723831	−	0.417904i
$123$	−8.37909	+	11.9793i	−0.755517	+	1.08014i
$124$	1.59058	+	15.1333i	0.142838	+	1.35901i
$125$	3.03420	−	4.17621i	0.271387	−	0.373532i
$126$	−1.75971	+	16.6891i	−0.156768	+	1.48678i
$127$	4.45869	−	1.44871i	0.395644	−	0.128553i	−0.104436	−	0.994532i	$-0.533304\pi$
$127$	4.45869	−	1.44871i	0.395644	−	0.128553i	0.500080	+	0.865979i	$0.333304\pi$
$128$	7.06466	−	3.14539i	0.624433	−	0.278016i
$129$	4.48086	+	12.9922i	0.394517	+	1.14390i
$130$	8.31495	−	1.76740i	0.729269	−	0.155011i
$131$	3.76680	−	6.52429i	0.329107	−	0.570030i	−0.653228	−	0.757161i	$-0.726586\pi$
$131$	3.76680	−	6.52429i	0.329107	−	0.570030i	0.982335	+	0.187132i	$0.0599191\pi$
$132$	−13.6180	+	3.98888i	−1.18530	+	0.347187i
$133$	0.0770058	+	0.440157i	0.00667725	+	0.0381664i
$134$	−1.25110	+	3.85048i	−0.108078	+	0.332631i
$135$	−12.4899	−	12.4525i	−1.07496	−	1.07174i
$136$	0.695473	−	6.61698i	0.0596363	−	0.567402i
$137$	9.56176	+	8.60944i	0.816916	+	0.735554i	0.967453	−	0.253050i	$-0.0814337\pi$
$137$	9.56176	+	8.60944i	0.816916	+	0.735554i	−0.150537	+	0.988604i	$0.548100\pi$
$138$	−12.1332	−	20.1702i	−1.03285	−	1.71700i
$139$	0.985502	−	1.35643i	0.0835892	−	0.115051i	−0.765175	−	0.643823i	$-0.777347\pi$
$139$	0.985502	−	1.35643i	0.0835892	−	0.115051i	0.848764	+	0.528772i	$0.177347\pi$
$140$	−5.39531	+	21.5170i	−0.455987	+	1.81852i
$141$	−0.293028	+	0.136820i	−0.0246774	+	0.0115223i
$142$	−13.6247	−	7.86622i	−1.14336	−	0.660119i
$143$	0.997117	−	3.80003i	0.0833831	−	0.317775i
$144$	7.65000	−	3.74065i	0.637500	−	0.311721i
$145$	−9.73887	+	8.76892i	−0.808769	+	0.728219i
$146$	13.6670	+	18.8110i	1.13109	+	1.55681i
$147$	10.8148	−	5.48090i	0.891989	−	0.452057i
$148$	3.68083	+	11.3284i	0.302562	+	0.931191i
$149$	12.2438	+	2.60251i	1.00305	+	0.213206i	0.680029	−	0.733185i	$-0.261967\pi$
$149$	12.2438	+	2.60251i	1.00305	+	0.213206i	0.323024	+	0.946391i	$0.395300\pi$
$150$	−14.3807	−	19.0639i	−1.17418	−	1.55656i
$151$	8.04655	−	18.0729i	0.654819	−	1.47075i	−0.214615	−	0.976699i	$-0.568850\pi$
$151$	8.04655	−	18.0729i	0.654819	−	1.47075i	0.869434	−	0.494049i	$-0.164484\pi$
$152$	−0.124773	+	0.112346i	−0.0101204	+	0.00911246i
$153$	1.38052	−	20.0307i	0.111608	−	1.61939i
$154$	14.0487	+	12.1177i	1.13208	+	0.976470i
$155$			20.9089i			1.67944i
$156$	0.439182	−	5.04900i	0.0351627	−	0.404243i
$157$	8.76981	+	3.90457i	0.699907	+	0.311619i	0.725664	−	0.688050i	$-0.241533\pi$
$157$	8.76981	+	3.90457i	0.699907	+	0.311619i	−0.0257567	+	0.999668i	$0.508200\pi$
$158$	7.13244	+	0.749650i	0.567427	+	0.0596390i
$159$	0.550355	+	0.914906i	0.0436460	+	0.0725568i
$160$	25.7916	−	8.38021i	2.03901	−	0.662514i
$161$	−7.47530	+	15.2749i	−0.589136	+	1.20383i
$162$	−16.7833	+	8.96701i	−1.31862	+	0.704515i
$163$	12.0276	+	13.3580i	0.942074	+	1.04628i	0.998852	+	0.0478926i	$0.0152505\pi$
$163$	12.0276	+	13.3580i	0.942074	+	1.04628i	−0.0567782	+	0.998387i	$0.518083\pi$
$164$	10.4245	+	18.0558i	0.814020	+	1.40992i
$165$	−19.1826	+	3.49504i	−1.49336	+	0.272088i
$166$	7.77805	−	13.4720i	0.603694	−	1.04563i
$167$	−4.68490	+	14.4186i	−0.362528	+	1.11575i	0.588986	+	0.808143i	$0.299527\pi$
$167$	−4.68490	+	14.4186i	−0.362528	+	1.11575i	−0.951515	+	0.307604i	$0.900473\pi$
$168$	3.90301	+	2.34960i	0.301123	+	0.181275i
$169$	−9.38206	−	6.81647i	−0.721697	−	0.524343i
$170$	9.98592	−	46.9801i	0.765885	−	3.60321i
$171$	−0.364116	+	0.352328i	−0.0278446	+	0.0269432i
$172$	19.4927	+	2.04877i	1.48631	+	0.156217i
$173$	−1.23354	−	11.7363i	−0.0937842	−	0.892297i	−0.935726	−	0.352728i	$-0.885254\pi$
$173$	−1.23354	−	11.7363i	−0.0937842	−	0.892297i	0.841942	−	0.539569i	$-0.181413\pi$
$174$	5.98179	+	12.8112i	0.453478	+	0.971217i
$175$	−5.92234	+	16.2042i	−0.447687	+	1.22492i
$176$	1.42447	−	9.30593i	0.107373	−	0.701461i
$177$	2.03844	−	0.471688i	0.153219	−	0.0354542i
$178$	−0.773958	−	3.64119i	−0.0580106	−	0.272918i
$179$	0.0937235	−	0.210506i	0.00700522	−	0.0157340i	−0.910009	−	0.414589i	$-0.863926\pi$
$179$	0.0937235	−	0.210506i	0.00700522	−	0.0157340i	0.917014	+	0.398855i	$0.130592\pi$
$180$	−23.6277	+	8.62660i	−1.76111	+	0.642989i
$181$	−4.24250	−	13.0571i	−0.315342	−	0.970524i	−0.975613	−	0.219496i	$-0.929559\pi$
$181$	−4.24250	−	13.0571i	−0.315342	−	0.970524i	0.660271	−	0.751027i	$-0.270441\pi$
$182$	−5.85470	+	3.10298i	−0.433980	+	0.230008i
$183$	−0.925436	−	7.50599i	−0.0684102	−	0.554859i
$184$	−6.35488	+	0.667925i	−0.468488	+	0.0492401i
$185$	3.40293	+	16.0095i	0.250188	+	1.17704i
$186$	21.5762	+	6.58470i	1.58205	+	0.482814i
$187$	−17.3228	−	13.8795i	−1.26677	−	1.01497i
$188$			0.461218i			0.0336378i
$189$	12.0252	+	6.66301i	0.874701	+	0.484663i
$190$	−0.980546	+	0.712408i	−0.0711363	+	0.0516835i
$191$	6.25794	+	14.0556i	0.452809	+	1.01703i	0.985338	+	0.170614i	$0.0545750\pi$
$191$	6.25794	+	14.0556i	0.452809	+	1.01703i	−0.532529	+	0.846412i	$0.678758\pi$
$192$	−0.348754	−	19.4226i	−0.0251692	−	1.40170i
$193$	4.60368	+	4.14517i	0.331380	+	0.298376i	0.817977	−	0.575250i	$-0.195095\pi$
$193$	4.60368	+	4.14517i	0.331380	+	0.298376i	−0.486597	+	0.873626i	$0.661762\pi$
$194$	1.93978	−	0.863646i	0.139268	−	0.0620062i
$195$	1.32535	−	6.83662i	0.0949103	−	0.489581i
$196$	−0.557323	−	17.2824i	−0.0398088	−	1.23446i
$197$	−1.57501			−0.112214			−0.0561072	−	0.998425i	$-0.517869\pi$
$197$	−1.57501			−0.112214			−0.0561072	+	0.998425i	$0.517869\pi$
$198$	−2.43447	+	20.8955i	−0.173010	+	1.48498i
$199$	−1.60255	−	2.77570i	−0.113602	−	0.196764i	0.803618	−	0.595145i	$-0.202906\pi$
$199$	−1.60255	−	2.77570i	−0.113602	−	0.196764i	−0.917220	+	0.398381i	$0.869572\pi$
$200$	−6.34088	+	1.34780i	−0.448368	+	0.0953036i
$201$	2.50424	+	2.17470i	0.176635	+	0.153391i
$202$	6.57875	+	4.77974i	0.462879	+	0.336301i
$203$	5.42473	−	8.65565i	0.380741	−	0.607508i
$204$	−25.0516	−	13.8699i	−1.75396	−	0.971090i
$205$	11.6523	+	26.1715i	0.813831	+	1.82789i
$206$	−2.15348	−	0.958791i	−0.150040	−	0.0668021i
$207$	−19.0925	+	2.70279i	−1.32702	+	0.187857i
$208$	2.91188	+	1.68117i	0.201902	+	0.116568i
$209$	0.0904949	+	0.552788i	0.00625966	+	0.0382371i
$210$	26.2476	+	19.8134i	1.81126	+	1.36725i
$211$	5.54922	+	1.80305i	0.382024	+	0.124127i	0.493732	−	0.869614i	$-0.335632\pi$
$211$	5.54922	+	1.80305i	0.382024	+	0.124127i	−0.111708	+	0.993741i	$0.535632\pi$
$212$	1.51435	−	0.159165i	0.104006	−	0.0109315i
$213$	−10.2891	+	7.76149i	−0.704999	+	0.531809i
$214$	−11.9210	+	13.2396i	−0.814901	+	0.905040i
$215$	26.3435	+	5.59949i	1.79661	+	0.381882i
$216$	0.278100	+	5.15814i	0.0189223	+	0.350967i
$217$	−4.47146	−	15.6728i	−0.303543	−	1.06394i
$218$	20.1176	+	6.53659i	1.36253	+	0.442714i
$219$	18.5577	−	4.29418i	1.25402	−	0.290174i
$220$	−7.05781	+	26.8974i	−0.475837	+	1.81342i
$221$	6.86570	−	3.96391i	0.461837	−	0.266642i
$222$	17.5921	+	1.53023i	1.18071	+	0.102703i
$223$	−15.0184	+	10.9115i	−1.00571	+	0.730690i	−0.963305	−	0.268411i	$-0.913502\pi$
$223$	−15.0184	+	10.9115i	−1.00571	+	0.730690i	−0.0424036	+	0.999101i	$0.513502\pi$
$224$	−17.5406	+	11.7972i	−1.17198	+	0.788236i
$225$	−18.9767	+	4.75161i	−1.26511	+	0.316774i
$226$	−6.92013	+	32.5567i	−0.460320	+	2.16564i
$227$	1.30455	−	12.4120i	0.0865860	−	0.823811i	−0.861918	−	0.507047i	$-0.830737\pi$
$227$	1.30455	−	12.4120i	0.0865860	−	0.823811i	0.948504	−	0.316764i	$-0.102596\pi$
$228$	0.235597	+	0.683112i	0.0156028	+	0.0452402i
$229$	−8.10560	−	9.00218i	−0.535633	−	0.594881i	0.413207	−	0.910637i	$-0.364409\pi$
$229$	−8.10560	−	9.00218i	−0.535633	−	0.594881i	−0.948840	+	0.315756i	$0.897742\pi$
$230$	−46.1271			−3.04153
$231$	13.6314	−	6.72207i	0.896877	−	0.442280i
$232$	3.83826			0.251994
$233$	−9.69361	−	10.7658i	−0.635050	−	0.705294i	0.336619	−	0.941641i	$-0.390717\pi$
$233$	−9.69361	−	10.7658i	−0.635050	−	0.705294i	−0.971669	+	0.236347i	$0.924050\pi$
$234$	−6.63744	−	3.52066i	−0.433903	−	0.230153i
$235$	−0.0662448	+	0.630277i	−0.00432133	+	0.0411147i
$236$	0.620404	−	2.91877i	0.0403849	−	0.189996i
$237$	2.84577	−	5.13998i	0.184853	−	0.333877i
$238$	2.56171	+	37.3506i	0.166051	+	2.42108i
$239$	1.41552	−	1.02843i	0.0915621	−	0.0665237i	−0.541062	−	0.840982i	$-0.681978\pi$
$239$	1.41552	−	1.02843i	0.0915621	−	0.0665237i	0.632624	+	0.774459i	$0.281978\pi$
$240$	1.44610	−	16.6249i	0.0933452	−	1.07313i
$241$	9.26910	−	5.35152i	0.597076	−	0.344722i	−0.170815	−	0.985303i	$-0.554640\pi$
$241$	9.26910	−	5.35152i	0.597076	−	0.344722i	0.767890	+	0.640581i	$0.221307\pi$
$242$	17.4439	+	15.3819i	1.12134	+	0.988786i
$243$	1.39751	+	15.5257i	0.0896504	+	0.995973i
$244$	−10.2580	−	3.33301i	−0.656699	−	0.213374i
$245$	1.72066	−	23.6973i	0.109929	−	1.51396i
$246$	30.6763	−	3.78218i	1.95585	−	0.241143i
$247$	−0.195686	−	0.0415943i	−0.0124512	−	0.00264658i
$248$	4.09772	−	4.55097i	0.260205	−	0.288987i
$249$	−7.67449	−	10.1738i	−0.486351	−	0.644738i
$250$	−10.8543	+	1.14083i	−0.686487	+	0.0721527i
$251$	−27.3065	−	8.87242i	−1.72357	−	0.560022i	−0.731074	−	0.682298i	$-0.760981\pi$
$251$	−27.3065	−	8.87242i	−1.72357	−	0.560022i	−0.992496	+	0.122276i	$0.960981\pi$
$252$	15.8659	−	11.5192i	0.999457	−	0.725639i
$253$	−9.57953	+	19.0445i	−0.602260	+	1.19732i
$254$	−8.58409	−	4.95603i	−0.538614	−	0.310969i
$255$	−32.2421	−	22.5521i	−2.01908	−	1.41227i
$256$	5.55495	+	2.47322i	0.347184	+	0.154576i
$257$	7.55325	+	16.9649i	0.471159	+	1.05824i	0.980292	+	0.197552i	$0.0632991\pi$
$257$	7.55325	+	16.9649i	0.471159	+	1.05824i	−0.509134	+	0.860687i	$0.670034\pi$
$258$	14.0744	−	25.4209i	0.876233	−	1.58264i
$259$	−5.97445	−	11.2726i	−0.371234	−	0.700444i
$260$	−8.03491	−	5.83770i	−0.498304	−	0.362039i
$261$	11.5754	−	0.415831i	0.716496	−	0.0257393i
$262$	−15.5801	+	3.31165i	−0.962542	+	0.204595i
$263$	5.52584	+	9.57104i	0.340738	+	0.590176i	0.984570	−	0.174991i	$-0.0559898\pi$
$263$	5.52584	+	9.57104i	0.340738	+	0.590176i	−0.643832	+	0.765167i	$0.722656\pi$
$264$	4.86019	+	2.99868i	0.299124	+	0.184556i
$265$	2.09230			0.128529
$266$	0.582640	−	0.743697i	0.0357239	−	0.0455990i
$267$	−2.99381	−	0.580382i	−0.183218	−	0.0355188i
$268$	4.32123	−	1.92393i	0.263961	−	0.117523i
$269$	4.36611	+	3.93126i	0.266206	+	0.239693i	0.791414	−	0.611281i	$-0.209345\pi$
$269$	4.36611	+	3.93126i	0.266206	+	0.239693i	−0.525207	+	0.850974i	$0.676012\pi$
$270$	−1.89562	+	37.2413i	−0.115364	+	2.26644i
$271$	−9.10515	−	20.4505i	−0.553099	−	1.24228i	−0.946438	−	0.322886i	$-0.895347\pi$
$271$	−9.10515	−	20.4505i	−0.553099	−	1.24228i	0.393339	−	0.919394i	$-0.371320\pi$
$272$	15.3693	−	11.1665i	0.931901	−	0.677066i
$273$	0.468593	+	5.40798i	0.0283605	+	0.327306i
$274$		−	27.2037i		−	1.64343i
$275$	−7.64564	+	20.2306i	−0.461050	+	1.21995i
$276$	−8.02724	+	26.3030i	−0.483183	+	1.58326i
$277$	−2.80393	−	13.1915i	−0.168472	−	0.792599i	−0.978506	−	0.206216i	$-0.933885\pi$
$277$	−2.80393	−	13.1915i	−0.168472	−	0.792599i	0.810034	−	0.586382i	$-0.199448\pi$
$278$	−3.52546	+	0.370541i	−0.211443	+	0.0222236i
$279$	11.8648	−	14.1687i	0.710324	−	0.848256i
$280$	7.88816	−	4.18071i	0.471408	−	0.249845i
$281$	1.13759	+	3.50115i	0.0678631	+	0.208861i	0.979237	−	0.202718i	$-0.0649774\pi$
$281$	1.13759	+	3.50115i	0.0678631	+	0.208861i	−0.911374	+	0.411579i	$0.864977\pi$
$282$	0.629531	+	0.266848i	0.0374880	+	0.0158906i
$283$	−1.19368	+	2.68105i	−0.0709569	+	0.159372i	−0.945542	−	0.325500i	$-0.894467\pi$
$283$	−1.19368	+	2.68105i	−0.0709569	+	0.159372i	0.874585	+	0.484872i	$0.161134\pi$
$284$	3.82158	+	17.9791i	0.226769	+	1.06687i
$285$	0.223840	+	0.967345i	0.0132591	+	0.0573005i
$286$	−7.38134	+	3.80934i	−0.436468	+	0.225251i
$287$	−14.3311	−	17.1255i	−0.845940	−	1.01089i
$288$	−22.2327	−	8.95672i	−1.31008	−	0.527780i
$289$	−2.90513	−	27.6405i	−0.170890	−	1.62591i
$290$	27.5558	+	2.89623i	1.61813	+	0.170072i
$291$	−0.0312293	−	1.73920i	−0.00183069	−	0.101954i
$292$	5.64808	−	26.5721i	0.330529	−	1.55502i
$293$	19.8801	+	14.4437i	1.16141	+	0.843812i	0.989955	−	0.141380i	$-0.0451539\pi$
$293$	19.8801	+	14.4437i	1.16141	+	0.843812i	0.171453	+	0.985192i	$0.445154\pi$
$294$	−23.9117	−	9.23840i	−1.39456	−	0.538795i
$295$	1.26704	−	3.89954i	0.0737697	−	0.227040i
$296$	2.39687	−	4.15149i	0.139315	−	0.241301i
$297$	14.9821	+	8.51680i	0.869351	+	0.494195i
$298$	−13.2326	−	22.9196i	−0.766545	−	1.32770i
$299$	−5.09462	−	5.65815i	−0.294630	−	0.327219i
$300$	−5.30974	+	27.3895i	−0.306558	+	1.58133i
$301$	−20.9439	+	1.43645i	−1.20719	+	0.0827955i
$302$	−39.7801	+	12.9253i	−2.28909	+	0.743770i
$303$	5.70845	−	3.43387i	0.327942	−	0.197271i
$304$	−0.476773	−	0.0501109i	−0.0273448	−	0.00287406i
$305$	−13.5393	−	6.02807i	−0.775257	−	0.345167i
$306$	−33.4257	+	26.1690i	−1.91082	+	1.49598i
$307$			22.8529i			1.30428i	0.758097	+	0.652142i	$0.226129\pi$
$307$			22.8529i			1.30428i	−0.758097	+	0.652142i	$0.773871\pi$
$308$	−0.461789	−	21.6710i	−0.0263129	−	1.23482i
$309$	−1.41167	+	1.31772i	−0.0803070	+	0.0749627i
$310$	32.8525	−	29.5805i	1.86589	−	1.68006i
$311$	−7.87572	+	17.6892i	−0.446591	+	1.00306i	0.540270	+	0.841492i	$0.318322\pi$
$311$	−7.87572	+	17.6892i	−0.446591	+	1.00306i	−0.986861	+	0.161569i	$0.948345\pi$
$312$	−1.62831	+	1.22830i	−0.0921849	+	0.0695387i
$313$	28.9672	+	6.15717i	1.63732	+	0.348024i	0.932447	−	0.361307i	$-0.117669\pi$
$313$	28.9672	+	6.15717i	1.63732	+	0.348024i	0.704876	+	0.709331i	$0.251003\pi$
$314$	−6.27199	−	19.3032i	−0.353949	−	1.08934i
$315$	23.3360	−	13.4627i	1.31483	−	0.758536i
$316$	−4.92505	−	6.77875i	−0.277056	−	0.381335i
$317$	11.0591	−	9.95763i	0.621139	−	0.559276i	−0.297327	−	0.954776i	$-0.596095\pi$
$317$	11.0591	−	9.95763i	0.621139	−	0.559276i	0.918466	+	0.395500i	$0.129429\pi$
$318$	0.658913	−	2.15908i	0.0369500	−	0.121075i
$319$	6.91846	−	10.7755i	0.387359	−	0.603309i
$320$	−32.9677	−	19.0339i	−1.84295	−	1.06403i
$321$	6.17466	+	13.2243i	0.344636	+	0.738108i
$322$	34.5757	−	9.86449i	1.92683	−	0.549727i
$323$	−0.664397	+	0.914464i	−0.0369680	+	0.0508821i
$324$	20.9062	+	7.56184i	1.16146	+	0.420102i
$325$	−5.74020	−	5.16850i	−0.318409	−	0.286697i
$326$	3.97252	−	37.7960i	0.220017	−	2.09333i
$327$	11.3621	−	13.0838i	0.628326	−	0.723538i
$328$	2.59286	−	7.98002i	0.143167	−	0.440623i
$329$	−0.0851321	−	0.486606i	−0.00469349	−	0.0268274i
$330$	32.6297	+	25.1955i	1.79621	+	1.38697i
$331$	−8.04186	+	13.9289i	−0.442021	+	0.765602i	−0.997839	−	0.0657014i	$-0.979072\pi$
$331$	−8.04186	+	13.9289i	−0.442021	+	0.765602i	0.555819	+	0.831303i	$0.312405\pi$
$332$	−17.7776	+	3.77875i	−0.975673	+	0.207386i
$333$	6.77865	−	12.7797i	0.371468	−	0.700321i
$334$	29.2827	−	13.0375i	1.60228	−	0.713380i
$335$	6.18150	−	2.00849i	0.337732	−	0.109736i
$336$	2.47135	+	12.7708i	0.134823	+	0.696706i
$337$	19.5978	−	26.9740i	1.06756	−	1.46937i	0.195034	−	0.980796i	$-0.437518\pi$
$337$	19.5978	−	26.9740i	1.06756	−	1.46937i	0.872524	−	0.488571i	$-0.162482\pi$
$338$	2.56294	+	24.3847i	0.139406	+	1.32636i
$339$	22.3434	+	15.6284i	1.21353	+	0.848816i
$340$	−48.5968	+	28.0574i	−2.63553	+	1.52163i
$341$	−5.39018	−	19.7069i	−0.291895	−	1.06719i
$342$	1.06871	+	0.0736558i	0.0577893	+	0.00398285i
$343$	3.77800	+	18.1308i	0.203993	+	0.978972i
$344$	−4.63647	−	6.38156i	−0.249982	−	0.344071i
$345$	−14.7475	+	34.7914i	−0.793980	+	1.87311i
$346$	−16.6952	+	18.5419i	−0.897541	+	0.996820i
$347$	−5.32814	+	5.91750i	−0.286030	+	0.317668i	−0.868987	−	0.494834i	$-0.835229\pi$
$347$	−5.32814	+	5.91750i	−0.286030	+	0.317668i	0.582958	+	0.812503i	$0.301895\pi$
$348$	6.44689	−	15.2091i	0.345589	−	0.815293i
$349$	8.60651	+	11.8458i	0.460696	+	0.634094i	0.974653	−	0.223722i	$-0.0718209\pi$
$349$	8.60651	+	11.8458i	0.460696	+	0.634094i	−0.513957	+	0.857816i	$0.671821\pi$
$350$	33.8388	−	13.6193i	1.80876	−	0.727980i
$351$	−4.77755	+	3.88068i	−0.255007	+	0.207136i
$352$	−22.1486	+	14.5474i	−1.18053	+	0.775379i
$353$	17.6551	−	10.1932i	0.939684	−	0.542527i	0.0498231	−	0.998758i	$-0.484134\pi$
$353$	17.6551	−	10.1932i	0.939684	−	0.542527i	0.889861	+	0.456231i	$0.150801\pi$
$354$	−3.62498	−	2.53553i	−0.192665	−	0.134762i
$355$	2.64003	+	25.1182i	0.140118	+	1.33314i
$356$	−2.55638	+	3.51855i	−0.135488	+	0.186483i
$357$	28.9907	+	10.0094i	1.53435	+	0.529751i
$358$	−0.463345	+	0.150550i	−0.0244886	+	0.00795682i
$359$	22.5438	−	10.0372i	1.18982	−	0.529741i	0.286237	−	0.958159i	$-0.407595\pi$
$359$	22.5438	−	10.0372i	1.18982	−	0.529741i	0.903581	+	0.428418i	$0.140929\pi$
$360$	8.94275	+	4.74346i	0.471324	+	0.250002i
$361$	−18.5569	+	3.94439i	−0.976679	+	0.207600i
$362$	−14.5135	+	25.1381i	−0.762813	+	1.32123i
$363$	17.1789	−	8.23928i	0.901658	−	0.432450i
$364$	7.27118	+	2.65749i	0.381113	+	0.139290i
$365$	11.5349	−	35.5009i	0.603766	−	1.85820i
$366$	−10.4843	+	12.0730i	−0.548024	+	0.631067i
$367$	−3.08846	+	29.3847i	−0.161216	+	1.53387i	0.552547	+	0.833482i	$0.313656\pi$
$367$	−3.08846	+	29.3847i	−0.161216	+	1.53387i	−0.713763	+	0.700388i	$0.753011\pi$
$368$	−13.5587	−	12.2083i	−0.706795	−	0.636401i
$369$	6.95496	−	24.3469i	0.362061	−	1.26745i
$370$	20.3402	−	27.9959i	1.05744	−	1.45544i
$371$	−1.56833	+	0.447447i	−0.0814237	+	0.0232303i
$372$	−11.1505	−	23.8812i	−0.578128	−	1.23818i
$373$	14.1124	+	8.14778i	0.730711	+	0.421876i	0.818682	−	0.574247i	$-0.194705\pi$
$373$	14.1124	+	8.14778i	0.730711	+	0.421876i	−0.0879712	+	0.996123i	$0.528038\pi$
$374$	2.69929	+	46.8537i	0.139577	+	2.42275i
$375$	−2.60981	+	8.55162i	−0.134770	+	0.441604i
$376$	0.137940	−	0.124202i	0.00711371	−	0.00640522i
$377$	2.68820	+	3.69999i	0.138449	+	0.190559i
$378$	−6.54331	−	28.3205i	−0.336552	−	1.45665i
$379$	2.53652	+	7.80661i	0.130292	+	0.400999i	0.994828	−	0.101573i	$-0.0323874\pi$
$379$	2.53652	+	7.80661i	0.130292	+	0.400999i	−0.864536	+	0.502571i	$0.832387\pi$
$380$	1.38510	+	0.294413i	0.0710544	+	0.0151031i
$381$	−6.48255	+	4.89004i	−0.332111	+	0.250524i
$382$	13.2311	−	29.7175i	0.676960	−	1.52048i
$383$	−9.98508	+	8.99061i	−0.510214	+	0.459399i	−0.883577	−	0.468287i	$-0.844871\pi$
$383$	−9.98508	+	8.99061i	−0.510214	+	0.459399i	0.373363	+	0.927685i	$0.378205\pi$
$384$	−9.79143	+	9.13983i	−0.499667	+	0.466415i
$385$	2.48154	−	29.6807i	0.126471	−	1.51267i
$386$		−	13.0977i		−	0.666655i
$387$	−14.6739	−	18.7431i	−0.745918	−	0.952763i
$388$	−2.26632	−	1.00903i	−0.115055	−	0.0512257i
$389$	−30.0025	−	3.15339i	−1.52119	−	0.159883i	−0.693246	−	0.720701i	$-0.743820\pi$
$389$	−30.0025	−	3.15339i	−1.52119	−	0.159883i	−0.827939	+	0.560818i	$0.810487\pi$
$390$	−12.6168	+	7.58957i	−0.638879	+	0.384313i
$391$	−40.9130	+	13.2934i	−2.06906	+	0.672278i
$392$	−5.01869	+	4.82067i	−0.253482	+	0.243481i
$393$	−2.48337	+	12.8101i	−0.125269	+	0.646183i
$394$	2.22821	+	2.47468i	0.112256	+	0.124672i
$395$	−5.75669	−	9.97088i	−0.289650	−	0.501689i
$396$	20.0456	−	14.2218i	1.00733	−	0.714671i
$397$	−10.3401	+	17.9096i	−0.518955	+	0.898857i	0.480802	+	0.876829i	$0.340346\pi$
$397$	−10.3401	+	17.9096i	−0.518955	+	0.898857i	−0.999757	+	0.0220280i	$0.992988\pi$
$398$	−2.09406	+	6.44484i	−0.104966	+	0.323051i
$399$	−0.374655	−	0.677227i	−0.0187562	−	0.0339038i
$400$	−14.9745	−	10.8796i	−0.748727	−	0.543982i
$401$	0.144897	−	0.681686i	0.00723580	−	0.0340418i	−0.974382	−	0.224901i	$-0.927794\pi$
$401$	0.144897	−	0.681686i	0.00723580	−	0.0340418i	0.981617	+	0.190859i	$0.0611274\pi$
$402$	−0.125896	−	7.01132i	−0.00627912	−	0.349693i
$403$	7.25694	+	0.762735i	0.361494	+	0.0379945i
$404$	−0.993090	−	9.44862i	−0.0494080	−	0.470086i
$405$	27.4832	+	13.3364i	1.36565	+	0.662690i
$406$	−21.2745	+	3.72199i	−1.05583	+	0.184719i
$407$	−7.33446	−	14.2120i	−0.363556	−	0.704460i
$408$	2.59798	+	11.2274i	0.128619	+	0.555840i
$409$	6.05004	+	28.4632i	0.299155	+	1.40741i	0.828966	+	0.559298i	$0.188929\pi$
$409$	6.05004	+	28.4632i	0.299155	+	1.40741i	−0.529811	+	0.848115i	$0.677737\pi$
$410$	24.6362	−	55.3339i	1.21670	−	2.73275i
$411$	−20.5184	−	8.69741i	−1.01210	−	0.429012i
$412$	0.851062	+	2.61930i	0.0419288	+	0.129044i
$413$	−0.115804	+	3.19395i	−0.00569835	+	0.157164i
$414$	31.2575	+	26.1749i	1.53622	+	1.28642i
$415$	−24.8367	+	2.61044i	−1.21919	+	0.128142i
$416$	−1.96770	−	9.25731i	−0.0964745	−	0.453877i
$417$	−0.847662	+	2.77755i	−0.0415102	+	0.136017i
$418$	0.740524	−	0.924234i	0.0362202	−	0.0452057i
$419$			29.9904i			1.46513i	0.680699	+	0.732564i	$0.261676\pi$
$419$			29.9904i			1.46513i	−0.680699	+	0.732564i	$0.738324\pi$
$420$	−3.31680	−	38.2788i	−0.161843	−	1.86782i
$421$	24.6054	−	17.8769i	1.19920	−	0.871267i	0.204990	−	0.978764i	$-0.434284\pi$
$421$	24.6054	−	17.8769i	1.19920	−	0.871267i	0.994205	+	0.107497i	$0.0342837\pi$
$422$	−5.01767	−	11.2699i	−0.244256	−	0.548609i
$423$	0.402541	−	0.389509i	0.0195722	−	0.0189386i
$424$	−0.455404	−	0.410047i	−0.0221164	−	0.0199137i
$425$	−39.8692	+	17.7509i	−1.93394	+	0.861046i
$426$	26.7513	+	5.18603i	1.29611	+	0.251264i
$427$	11.4378	+	1.62305i	0.553515	+	0.0785450i
$428$	20.8146			1.00611
$429$	0.513275	+	6.78528i	0.0247811	+	0.327597i
$430$	−28.4710	−	49.3132i	−1.37299	−	2.37809i
$431$	−9.65243	+	2.05169i	−0.464941	+	0.0988263i	−0.434425	−	0.900708i	$-0.643048\pi$
$431$	−9.65243	+	2.05169i	−0.464941	+	0.0988263i	−0.0305162	+	0.999534i	$0.509715\pi$
$432$	−10.4137	+	10.4451i	−0.501030	+	0.502538i
$433$	6.12151	+	4.44754i	0.294181	+	0.213735i	0.725079	−	0.688665i	$-0.241803\pi$
$433$	6.12151	+	4.44754i	0.294181	+	0.213735i	−0.430898	+	0.902401i	$0.641803\pi$
$434$	−18.2994	+	29.1984i	−0.878401	+	1.40157i
$435$	10.9945	−	19.8580i	0.527144	−	0.952118i
$436$	−10.0520	−	22.5771i	−0.481401	−	1.08125i
$437$	0.991714	+	0.441539i	0.0474401	+	0.0211217i
$438$	−33.0013	−	23.0832i	−1.57686	−	1.10296i
$439$	5.63401	+	3.25280i	0.268897	+	0.155248i	0.628386	−	0.777902i	$-0.283716\pi$
$439$	5.63401	+	3.25280i	0.268897	+	0.155248i	−0.359489	+	0.933149i	$0.617049\pi$
$440$	9.94502	−	5.13240i	0.474110	−	0.244678i
$441$	−14.6130	+	15.0818i	−0.695857	+	0.718180i
$442$	−15.9413	−	5.17964i	−0.758250	−	0.246370i
$443$	−23.8596	+	2.50774i	−1.13360	+	0.119146i	−0.652692	−	0.757624i	$-0.726360\pi$
$443$	−23.8596	+	2.50774i	−1.13360	+	0.119146i	−0.480910	+	0.876770i	$0.659694\pi$
$444$	−12.4244	−	16.4706i	−0.589636	−	0.781658i
$445$	−3.99879	+	4.44110i	−0.189561	+	0.210528i
$446$	38.3914	+	8.16035i	1.81789	+	0.386404i
$447$	−21.5178	+	2.65299i	−1.01776	+	0.125482i
$448$	28.7822	+	7.21704i	1.35983	+	0.340973i
$449$	18.9823	+	6.16772i	0.895830	+	0.291073i	0.720515	−	0.693440i	$-0.243906\pi$
$449$	18.9823	+	6.16772i	0.895830	+	0.291073i	0.175315	+	0.984512i	$0.443906\pi$
$450$	34.3127	+	23.0942i	1.61752	+	1.08867i
$451$	−17.7293	−	21.6631i	−0.834839	−	1.02008i
$452$	33.6771	−	19.4435i	1.58404	−	0.914543i
$453$	−2.96934	+	34.1366i	−0.139512	+	1.60388i
$454$	−21.3475	+	15.5099i	−1.00189	+	0.727914i
$455$	9.55472	+	4.67595i	0.447932	+	0.219212i
$456$	0.140859	−	0.254418i	0.00659635	−	0.0119142i
$457$	0.718221	−	3.37896i	0.0335970	−	0.158061i	−0.958151	−	0.286263i	$-0.907587\pi$
$457$	0.718221	−	3.37896i	0.0335970	−	0.158061i	0.991748	+	0.128201i	$0.0409204\pi$
$458$	−2.67715	+	25.4713i	−0.125095	+	1.19020i
$459$	9.05129	+	33.5780i	0.422478	+	1.56728i
$460$	36.0608	+	40.0496i	1.68134	+	1.86732i
$461$	−4.98910			−0.232366			−0.116183	−	0.993228i	$-0.537066\pi$
$461$	−4.98910			−0.232366			−0.116183	+	0.993228i	$0.537066\pi$
$462$	−29.8466	−	11.9079i	−1.38859	−	0.554006i
$463$	−15.2100			−0.706871			−0.353435	−	0.935459i	$-0.614987\pi$
$463$	−15.2100			−0.706871			−0.353435	+	0.935459i	$0.614987\pi$
$464$	7.33325	+	8.14440i	0.340438	+	0.378094i
$465$	−11.8077	−	34.2363i	−0.547569	−	1.58767i
$466$	−3.20164	+	30.4616i	−0.148313	+	1.41111i
$467$	−5.81809	+	27.3719i	−0.269229	+	1.26662i	0.610831	+	0.791761i	$0.290835\pi$
$467$	−5.81809	+	27.3719i	−0.269229	+	1.26662i	−0.880060	+	0.474862i	$0.842498\pi$
$468$	2.13216	+	8.51526i	0.0985589	+	0.393618i
$469$	−4.20397	+	2.82745i	−0.194121	+	0.130560i
$470$	1.08402	−	0.787588i	0.0500022	−	0.0363287i
$471$	−16.5647	−	1.44086i	−0.763261	−	0.0663915i
$472$	−1.04001	+	0.600449i	−0.0478703	+	0.0276379i
$473$	−26.2727	+	1.51359i	−1.20802	+	0.0695951i
$474$	−12.1020	+	2.80036i	−0.555865	+	0.128625i
$475$	1.04740	+	0.340322i	0.0480582	+	0.0156151i
$476$	30.4267	−	31.4237i	1.39461	−	1.44030i
$477$	−1.41782	−	1.18727i	−0.0649175	−	0.0543615i
$478$	−3.61847	−	0.769129i	−0.165505	−	0.0351791i
$479$	5.48722	−	6.09417i	0.250717	−	0.278450i	−0.604628	−	0.796508i	$-0.706678\pi$
$479$	5.48722	−	6.09417i	0.250717	−	0.278450i	0.855345	+	0.518058i	$0.173345\pi$
$480$	−37.4988	+	28.2869i	−1.71158	+	1.29111i
$481$	5.68062	−	0.597058i	0.259014	−	0.0272235i
$482$	−21.5217	−	6.99283i	−0.980287	−	0.318515i
$483$	3.61406	−	29.2326i	0.164445	−	1.33013i
$484$	−0.281904	−	27.1707i	−0.0128138	−	1.23503i
$485$	−2.95211	−	1.70440i	−0.134048	−	0.0773928i
$486$	22.4172	−	24.1605i	1.01686	−	1.09594i
$487$	22.6772	+	10.0966i	1.02760	+	0.457518i	0.850111	−	0.526604i	$-0.176535\pi$
$487$	22.6772	+	10.0966i	1.02760	+	0.457518i	0.177492	+	0.984122i	$0.443202\pi$
$488$	1.76554	+	3.96548i	0.0799224	+	0.179509i
$489$	−27.2376	−	15.0802i	−1.23173	−	0.681950i
$490$	−39.6679	+	30.8217i	−1.79201	+	1.39238i
$491$	−25.1259	−	18.2550i	−1.13391	−	0.823837i	−0.147654	−	0.989039i	$-0.547172\pi$
$491$	−25.1259	−	18.2550i	−1.13391	−	0.823837i	−0.986260	+	0.165202i	$0.947172\pi$
$492$	−27.2657	−	23.6777i	−1.22923	−	1.06747i
$493$	25.2756	−	5.37249i	1.13836	−	0.241965i
$494$	0.211489	+	0.366310i	0.00951535	+	0.0164811i
$495$	29.4359	−	16.5556i	1.32305	−	0.744119i
$496$	17.4857			0.785129
$497$	−7.35055	−	18.2634i	−0.329717	−	0.819225i
$498$	−5.12790	+	26.4515i	−0.229787	+	1.18532i
$499$	29.3937	−	13.0869i	1.31584	−	0.585851i	0.375735	−	0.926727i	$-0.377390\pi$
$499$	29.3937	−	13.0869i	1.31584	−	0.585851i	0.940108	+	0.340876i	$0.110724\pi$
$500$	9.47610	+	8.53232i	0.423784	+	0.381577i
$501$	−0.471434	−	26.2548i	−0.0210621	−	1.17298i
$502$	24.6909	+	55.4566i	1.10201	+	2.47515i
$503$	0.195747	−	0.142218i	0.00872791	−	0.00634119i	−0.583413	−	0.812176i	$-0.698283\pi$
$503$	0.195747	−	0.142218i	0.00872791	−	0.00634119i	0.592141	+	0.805835i	$0.298283\pi$
$504$	−7.71766	−	1.64313i	−0.343772	−	0.0731907i
$505$		−	13.0546i		−	0.580923i
$506$	43.4755	−	11.8913i	1.93272	−	0.528632i
$507$	19.2116	+	5.86306i	0.853218	+	0.260388i
$508$	2.40775	+	11.3276i	0.106826	+	0.502579i
$509$	21.6961	−	2.28035i	0.961661	−	0.101075i	0.389331	−	0.921098i	$-0.372706\pi$
$509$	21.6961	−	2.28035i	0.961661	−	0.101075i	0.572330	+	0.820023i	$0.306040\pi$
$510$	10.1796	+	82.5646i	0.450762	+	3.65602i
$511$	−1.05427	+	29.0773i	−0.0466380	+	1.28631i
$512$	−8.75219	−	26.9365i	−0.386796	−	1.19043i
$513$	0.397238	−	0.782527i	0.0175385	−	0.0345494i
$514$	15.9697	−	35.8685i	0.704393	−	1.58209i
$515$	0.786807	+	3.70164i	0.0346709	+	0.163114i
$516$	−33.0745	+	7.65329i	−1.45602	+	0.336917i
$517$	−0.100045	−	0.611123i	−0.00439996	−	0.0268771i
$518$	−9.25945	+	25.3349i	−0.406837	+	1.11315i
$519$	8.64755	+	18.5205i	0.379585	+	0.812960i
$520$	0.417800	+	3.97510i	0.0183217	+	0.174320i
$521$	−20.2304	−	2.12630i	−0.886311	−	0.0931551i	−0.349578	−	0.936907i	$-0.613675\pi$
$521$	−20.2304	−	2.12630i	−0.886311	−	0.0931551i	−0.536733	+	0.843752i	$0.680342\pi$
$522$	−17.0294	−	17.5991i	−0.745356	−	0.770293i
$523$	−3.66915	+	17.2620i	−0.160441	+	0.754814i	0.822186	+	0.569219i	$0.192754\pi$
$523$	−3.66915	+	17.2620i	−0.160441	+	0.754814i	−0.982626	+	0.185595i	$0.940579\pi$
$524$	15.0554	+	10.9384i	0.657697	+	0.477845i
$525$	0.546433	−	29.8772i	0.0238483	−	1.30395i
$526$	7.22061	−	22.2228i	0.314834	−	0.968958i
$527$	20.6140	−	35.7046i	0.897962	−	1.55532i
$528$	2.92282	+	16.0420i	0.127199	+	0.698138i
$529$	9.15725	+	15.8608i	0.398141	+	0.689601i
$530$	−2.96004	−	3.28746i	−0.128576	−	0.142798i
$531$	−3.07138	+	1.92349i	−0.133287	+	0.0834726i
$532$	−1.10120	+	0.0755264i	−0.0477431	+	0.00327449i
$533$	9.50850	−	3.08950i	0.411859	−	0.133821i
$534$	3.32354	+	5.52502i	0.143823	+	0.239091i
$535$	28.4442	+	2.98961i	1.22975	+	0.129252i
$536$	−1.73907	−	0.774285i	−0.0751165	−	0.0334440i
$537$	−0.0345858	+	0.397612i	−0.00149249	+	0.0171582i
$538$		−	12.4218i		−	0.535542i
$539$	4.48726	+	22.7786i	0.193280	+	0.981144i
$540$	33.8165	−	27.4683i	1.45523	−	1.18205i
$541$	−15.0542	+	13.5548i	−0.647229	+	0.582768i	−0.925969	−	0.377599i	$-0.876750\pi$
$541$	−15.0542	+	13.5548i	−0.647229	+	0.582768i	0.278740	+	0.960367i	$0.410083\pi$
$542$	−19.2509	+	43.2382i	−0.826896	+	1.85724i
$543$	14.3203	+	18.9838i	0.614542	+	0.814675i
$544$	−52.3045	−	11.1177i	−2.24254	−	0.476666i
$545$	−10.4937	−	32.2964i	−0.449502	−	1.38343i
$546$	7.83419	−	8.38711i	0.335273	−	0.358935i
$547$	−12.0745	−	16.6191i	−0.516266	−	0.710580i	0.468694	−	0.883361i	$-0.344725\pi$
$547$	−12.0745	−	16.6191i	−0.516266	−	0.710580i	−0.984960	+	0.172781i	$0.944725\pi$
$548$	−23.6194	+	21.2670i	−1.00897	+	0.908482i
$549$	5.75410	+	11.7677i	0.245579	+	0.502234i
$550$	42.6033	−	16.6080i	1.81661	−	0.708165i
$551$	−0.564714	−	0.326038i	−0.0240576	−	0.0138897i
$552$	10.0283	−	4.68240i	0.426833	−	0.199296i
$553$	6.44738	+	6.24282i	0.274171	+	0.265472i
$554$	−16.7599	+	23.0680i	−0.712059	+	0.980065i
$555$	−14.6129	−	24.2923i	−0.620282	−	1.03115i
$556$	3.07782	+	2.77128i	0.130529	+	0.117529i
$557$	−4.83998	+	46.0494i	−0.205077	+	1.95117i	0.0906040	+	0.995887i	$0.471120\pi$
$557$	−4.83998	+	46.0494i	−0.205077	+	1.95117i	−0.295681	+	0.955287i	$0.595546\pi$
$558$	−39.0475	+	1.40274i	−1.65301	+	0.0593826i
$559$	2.90442	−	8.93889i	0.122844	−	0.378075i
$560$	23.9419	+	8.75034i	1.01173	+	0.369769i
$561$	36.2024	+	12.9439i	1.52847	+	0.546491i
$562$	3.89168	−	6.74059i	0.164161	−	0.284335i
$563$	36.6904	−	7.79878i	1.54632	−	0.328680i	0.645801	−	0.763506i	$-0.276523\pi$
$563$	36.6904	−	7.79878i	1.54632	−	0.328680i	0.900515	+	0.434826i	$0.143190\pi$
$564$	−0.260459	−	0.755200i	−0.0109673	−	0.0317997i
$565$	48.8140	−	21.7334i	2.05362	−	0.914331i
$566$	5.90125	−	1.91743i	0.248048	−	0.0805957i
$567$	−23.4528	−	4.11919i	−0.984924	−	0.172990i
$568$	4.34804	−	5.98456i	0.182440	−	0.251107i
$569$	0.211716	+	2.01434i	0.00887559	+	0.0844456i	0.998063	−	0.0622114i	$-0.0198153\pi$
$569$	0.211716	+	2.01434i	0.00887559	+	0.0844456i	−0.989187	+	0.146657i	$0.953149\pi$
$570$	1.20324	−	1.72023i	0.0503981	−	0.0720527i
$571$	−3.99938	+	2.30904i	−0.167369	+	0.0966303i	−0.581345	−	0.813658i	$-0.697473\pi$
$571$	−3.99938	+	2.30904i	−0.167369	+	0.0966303i	0.413976	+	0.910288i	$0.364140\pi$
$572$	9.07794	+	3.43077i	0.379568	+	0.143448i
$573$	−18.1842	−	19.4806i	−0.759658	−	0.813816i
$574$	−6.63328	+	46.7454i	−0.276868	+	1.95112i
$575$	24.6362	+	33.9088i	1.02740	+	1.41409i
$576$	11.5394	+	31.6057i	0.480808	+	1.31690i
$577$	−20.7631	+	23.0598i	−0.864380	+	0.959991i	−0.999524	−	0.0308351i	$-0.990183\pi$
$577$	−20.7631	+	23.0598i	−0.864380	+	0.959991i	0.135145	+	0.990826i	$0.456850\pi$
$578$	−39.3193	+	43.6685i	−1.63547	+	1.81637i
$579$	−9.87895	−	4.18753i	−0.410555	−	0.174028i
$580$	−19.0276	−	26.1893i	−0.790080	−	1.08745i
$581$	18.0587	−	7.26816i	0.749201	−	0.301534i
$582$	−2.68849	+	2.50957i	−0.111441	+	0.104025i
$583$	−1.97202	+	0.539381i	−0.0816727	+	0.0223389i
$584$	−9.46811	+	5.46642i	−0.391793	+	0.226202i
$585$	1.69065	+	11.9428i	0.0698997	+	0.493772i
$586$	−5.43074	−	51.6700i	−0.224342	−	2.13447i
$587$	−1.47931	+	2.03609i	−0.0610575	+	0.0840385i	−0.838454	−	0.544973i	$-0.816540\pi$
$587$	−1.47931	+	2.03609i	−0.0610575	+	0.0840385i	0.777396	+	0.629011i	$0.216540\pi$
$588$	10.6723	+	27.9835i	0.440118	+	1.15402i
$589$	−0.989465	+	0.321497i	−0.0407702	+	0.0132470i
$590$	−7.91954	+	3.52601i	−0.326042	+	0.145163i
$591$	2.57892	−	0.889438i	0.106083	−	0.0365866i
$592$	13.3884	−	2.84579i	0.550260	−	0.116961i
$593$	−3.12250	+	5.40833i	−0.128226	+	0.222094i	−0.922989	−	0.384826i	$-0.874262\pi$
$593$	−3.12250	+	5.40833i	−0.128226	+	0.222094i	0.794763	+	0.606919i	$0.207595\pi$
$594$	−7.81393	−	35.5892i	−0.320609	−	1.46024i
$595$	46.0930	−	38.5719i	1.88963	−	1.58129i
$596$	−9.55491	+	29.4070i	−0.391384	+	1.20456i
$597$	4.19152	+	3.63995i	0.171548	+	0.148973i
$598$	−1.68267	+	16.0095i	−0.0688095	+	0.654679i
$599$	35.7055	+	32.1494i	1.45889	+	1.31359i	0.857341	+	0.514748i	$0.172115\pi$
$599$	35.7055	+	32.1494i	1.45889	+	1.31359i	0.601545	+	0.798839i	$0.294552\pi$
$600$	9.62145	−	5.78771i	0.392794	−	0.236282i
$601$	−16.9076	+	23.2714i	−0.689677	+	0.949258i	−0.999999	−	0.00137289i	$-0.999563\pi$
$601$	−16.9076	+	23.2714i	−0.689677	+	0.949258i	0.310322	+	0.950631i	$0.399563\pi$
$602$	31.8869	+	30.8752i	1.29962	+	1.25838i
$603$	−5.32854	−	2.14666i	−0.216995	−	0.0874189i
$604$	42.3213	+	24.4342i	1.72203	+	0.994213i
$605$	3.51729	−	37.1706i	0.142998	−	1.51120i
$606$	−13.4713	−	4.11121i	−0.547234	−	0.167006i
$607$	21.6979	−	19.5369i	0.880692	−	0.792979i	−0.0986642	−	0.995121i	$-0.531457\pi$
$607$	21.6979	−	19.5369i	0.880692	−	0.792979i	0.979356	+	0.202142i	$0.0647903\pi$
$608$	0.793148	+	1.09167i	0.0321664	+	0.0442732i
$609$	−3.99445	+	17.2362i	−0.161863	+	0.698448i
$610$	9.68302	+	29.8013i	0.392054	+	1.20662i
$611$	0.216336	+	0.0459837i	0.00875203	+	0.00186030i
$612$	48.8522	+	8.56352i	1.97473	+	0.346160i
$613$	−2.27909	+	5.11891i	−0.0920515	+	0.206751i	−0.953703	−	0.300749i	$-0.902763\pi$
$613$	−2.27909	+	5.11891i	−0.0920515	+	0.206751i	0.861652	+	0.507500i	$0.169430\pi$
$614$	35.9069	−	32.3307i	1.44909	−	1.30476i
$615$	−33.8591	−	36.2729i	−1.36533	−	1.46267i
$616$	−6.35694	+	5.97390i	−0.256129	+	0.240695i
$617$			35.1197i			1.41387i	0.707281	+	0.706933i	$0.249922\pi$
$617$			35.1197i			1.41387i	−0.707281	+	0.706933i	$0.750078\pi$
$618$	4.06756	+	0.353813i	0.163621	+	0.0142324i
$619$	−39.4619	−	17.5696i	−1.58611	−	0.706181i	−0.591158	−	0.806555i	$-0.701329\pi$
$619$	−39.4619	−	17.5696i	−1.58611	−	0.706181i	−0.994950	+	0.100375i	$0.967996\pi$
$620$	−51.3661	−	5.39880i	−2.06291	−	0.216821i
$621$	29.7359	−	15.2075i	1.19326	−	0.610257i
$622$	38.9356	−	12.6509i	1.56118	−	0.507257i
$623$	2.04764	−	4.18409i	0.0820368	−	0.167632i
$624$	−5.71731	−	1.10836i	−0.228876	−	0.0443700i
$625$	−10.0924	−	11.2088i	−0.403696	−	0.448350i
$626$	−31.3066	−	54.2245i	−1.25126	−	2.16725i
$627$	−0.460347	−	0.854032i	−0.0183845	−	0.0341068i
$628$	−11.8566	+	20.5363i	−0.473131	+	0.819487i
$629$	9.97282	−	30.6932i	0.397642	−	1.22382i
$630$	−54.1670	−	17.6199i	−2.15807	−	0.701993i
$631$	−8.00283	−	5.81440i	−0.318588	−	0.231468i	0.416985	−	0.908913i	$-0.363087\pi$
$631$	−8.00283	−	5.81440i	−0.318588	−	0.231468i	−0.735573	+	0.677446i	$0.763087\pi$
$632$	−0.701103	+	3.29843i	−0.0278884	+	0.131204i
$633$	−10.1045	+	0.181438i	−0.401619	+	0.00721152i
$634$	−31.2912	−	3.28884i	−1.24273	−	0.130617i
$635$	1.66332	+	15.8255i	0.0660070	+	0.628015i
$636$	−2.38972	+	1.11580i	−0.0947586	+	0.0442445i
$637$	−8.16194	−	1.46165i	−0.323388	−	0.0579126i
$638$	−26.7184	+	4.37397i	−1.05779	+	0.173167i
$639$	12.4644	−	18.5192i	0.493083	−	0.732607i
$640$	5.45735	+	25.6748i	0.215721	+	1.01489i
$641$	−8.33038	+	18.7103i	−0.329030	+	0.739014i	−0.999997	−	0.00247346i	$-0.999213\pi$
$641$	−8.33038	+	18.7103i	−0.329030	+	0.739014i	0.670967	+	0.741487i	$0.265879\pi$
$642$	12.0428	−	28.4106i	0.475291	−	1.12128i
$643$	−10.5894	−	32.5909i	−0.417606	−	1.28526i	−0.909899	−	0.414830i	$-0.863841\pi$
$643$	−10.5894	−	32.5909i	−0.417606	−	1.28526i	0.492293	−	0.870430i	$-0.336159\pi$
$644$	−35.5950	−	22.3084i	−1.40264	−	0.879073i
$645$	−46.2971	+	5.70811i	−1.82295	+	0.224757i
$646$	2.37677	−	0.249808i	0.0935126	−	0.00982857i
$647$	3.83634	+	18.0486i	0.150822	+	0.709562i	0.986950	+	0.161028i	$0.0514808\pi$
$647$	3.83634	+	18.0486i	0.150822	+	0.709562i	−0.836128	+	0.548535i	$0.815186\pi$
$648$	−3.36827	−	8.28891i	−0.132318	−	0.325619i
$649$	−0.188924	+	4.00200i	−0.00741593	+	0.157092i
$650$			16.3311i			0.640560i
$651$	16.1723	+	23.1375i	0.633843	+	0.906831i
$652$	−35.9217	+	26.0987i	−1.40680	+	1.02210i
$653$	−3.41852	−	7.67812i	−0.133777	−	0.300468i	0.834219	−	0.551433i	$-0.185919\pi$
$653$	−3.41852	−	7.67812i	−0.133777	−	0.300468i	−0.967996	+	0.250965i	$0.919252\pi$
$654$	−36.6319	+	0.657767i	−1.43242	+	0.0257207i
$655$	19.0028	+	17.1102i	0.742501	+	0.668551i
$656$	21.8866	−	9.74455i	0.854529	−	0.380461i
$657$	−27.9615	+	17.5113i	−1.09088	+	0.683179i
$658$	−0.644125	+	0.822178i	−0.0251106	+	0.0320518i
$659$	4.41965			0.172165			0.0860826	−	0.996288i	$-0.472565\pi$
$659$	4.41965			0.172165			0.0860826	+	0.996288i	$0.472565\pi$
$660$	−3.63307	−	48.0276i	−0.141417	−	1.86947i
$661$	−3.93024	−	6.80738i	−0.152869	−	0.264776i	0.779412	−	0.626511i	$-0.215518\pi$
$661$	−3.93024	−	6.80738i	−0.152869	−	0.264776i	−0.932281	+	0.361735i	$0.882184\pi$
$662$	33.2624	−	7.07015i	1.29278	−	0.274789i
$663$	−9.00341	+	10.3677i	−0.349663	+	0.402649i
$664$	5.91748	+	4.29930i	0.229643	+	0.166845i
$665$	−1.51569	−	0.0549549i	−0.0587760	−	0.00213106i
$666$	−29.6696	+	7.42904i	−1.14967	+	0.287869i
$667$	−10.0939	−	22.6712i	−0.390836	−	0.877832i
$668$	−34.2120	−	15.2322i	−1.32370	−	0.589351i
$669$	18.4293	−	26.3478i	0.712516	−	1.01866i
$670$	−11.9009	−	6.87102i	−0.459774	−	0.265450i
$671$	14.3150	+	2.19121i	0.552623	+	0.0845907i
$672$	22.0589	−	29.2224i	0.850940	−	1.12728i
$673$	−12.2289	−	3.97342i	−0.471390	−	0.153164i	0.0636820	−	0.997970i	$-0.479716\pi$
$673$	−12.2289	−	3.97342i	−0.471390	−	0.153164i	−0.535072	+	0.844806i	$0.679716\pi$
$674$	−70.1076	+	7.36861i	−2.70045	+	0.283828i
$675$	28.3891	−	18.4968i	1.09270	−	0.711943i
$676$	19.1683	−	21.2885i	0.737241	−	0.818789i
$677$	−43.4802	−	9.24199i	−1.67108	−	0.355199i	−0.727438	−	0.686173i	$-0.759289\pi$
$677$	−43.4802	−	9.24199i	−1.67108	−	0.355199i	−0.943640	+	0.330975i	$0.892623\pi$
$678$	−7.05438	−	57.2163i	−0.270922	−	2.19738i
$679$	2.57732	+	0.646252i	0.0989083	+	0.0248009i
$680$	21.4780	+	6.97863i	0.823644	+	0.267618i
$681$	4.87322	+	21.0601i	0.186742	+	0.807025i
$682$	−23.3383	+	36.3492i	−0.893668	+	1.39188i
$683$	28.7629	−	16.6063i	1.10058	−	0.635422i	0.164209	−	0.986426i	$-0.447493\pi$
$683$	28.7629	−	16.6063i	1.10058	−	0.635422i	0.936374	+	0.351004i	$0.114160\pi$
$684$	−0.771535	−	0.985484i	−0.0295004	−	0.0376809i
$685$	−35.3316	+	25.6699i	−1.34995	+	0.980798i
$686$	23.1426	−	31.5863i	0.883590	−	1.20597i
$687$	18.3559	+	10.1628i	0.700320	+	0.387735i
$688$	4.68273	−	22.0305i	0.178527	−	0.839905i
$689$	0.0763248	−	0.726182i	0.00290774	−	0.0276653i
$690$	75.5287	−	26.0490i	2.87533	−	0.991667i
$691$	−4.19564	−	4.65973i	−0.159610	−	0.177265i	0.658036	−	0.752987i	$-0.271388\pi$
$691$	−4.19564	−	4.65973i	−0.159610	−	0.177265i	−0.817645	+	0.575722i	$0.804721\pi$
$692$	29.1507			1.10814
$693$	−18.5239	+	18.7047i	−0.703666	+	0.710531i
$694$	16.8356			0.639070
$695$	3.80795	+	4.22916i	0.144444	+	0.160421i
$696$	−6.28479	+	2.16755i	−0.238224	+	0.0821607i
$697$	5.90465	−	56.1790i	0.223655	−	2.12793i
$698$	6.43651	−	30.2814i	0.243626	−	1.14617i
$699$	21.9521	+	12.1539i	0.830303	+	0.459701i
$700$	−38.2790	−	18.7332i	−1.44681	−	0.708049i
$701$	21.3478	−	15.5101i	0.806296	−	0.585808i	−0.106458	−	0.994317i	$-0.533951\pi$
$701$	21.3478	−	15.5101i	0.806296	−	0.585808i	0.912754	+	0.408509i	$0.133951\pi$
$702$	12.8564	+	2.01645i	0.485232	+	0.0761059i
$703$	−0.705289	+	0.407199i	−0.0266005	+	0.0153578i
$704$	35.9794	+	9.44089i	1.35602	+	0.355817i
$705$	−0.247461	−	1.06943i	−0.00931992	−	0.0402770i
$706$	−40.9929	−	13.3194i	−1.54279	−	0.501282i
$707$	2.79179	+	9.78541i	0.104996	+	0.368018i
$708$	0.632440	+	5.12956i	0.0237685	+	0.192781i
$709$	49.5904	+	10.5408i	1.86241	+	0.395867i	0.994840	−	0.101454i	$-0.0323494\pi$
$709$	49.5904	+	10.5408i	1.86241	+	0.395867i	0.867567	+	0.497321i	$0.165683\pi$
$710$	35.7313	−	39.6837i	1.34097	−	1.48930i
$711$	−1.75702	+	10.0233i	−0.0658935	+	0.375902i
$712$	1.74073	−	0.182958i	0.0652366	−	0.00685665i
$713$	−37.6571	−	12.2355i	−1.41027	−	0.458224i
$714$	−25.2872	−	59.7113i	−0.946349	−	2.23464i
$715$	11.9127	+	5.99218i	0.445509	+	0.224095i
$716$	0.492944	+	0.284601i	0.0184222	+	0.0106360i
$717$	−1.73699	+	2.48333i	−0.0648692	+	0.0927416i
$718$	−47.6641	−	21.2214i	−1.77881	−	0.791976i
$719$	−1.26970	−	2.85179i	−0.0473517	−	0.106354i	0.888321	−	0.459224i	$-0.151872\pi$
$719$	−1.26970	−	2.85179i	−0.0473517	−	0.106354i	−0.935672	+	0.352870i	$0.885206\pi$
$720$	7.02057	+	28.0383i	0.261641	+	1.04493i
$721$	−1.38138	−	2.60639i	−0.0514453	−	0.0970669i
$722$	32.4505	+	23.5767i	1.20768	+	0.877434i
$723$	−12.1552	+	13.9971i	−0.452055	+	0.520556i
$724$	33.1722	−	7.05098i	1.23284	−	0.262047i
$725$	−12.5883	−	21.8035i	−0.467517	−	0.809763i
$726$	−37.2492	−	15.3354i	−1.38245	−	0.569151i
$727$	11.4146			0.423344			0.211672	−	0.977341i	$-0.432109\pi$
$727$	11.4146			0.423344			0.211672	+	0.977341i	$0.432109\pi$
$728$	−1.16326	−	2.89028i	−0.0431135	−	0.107121i
$729$	−11.0560	−	24.6326i	−0.409480	−	0.912319i
$730$	−72.0985	+	32.1003i	−2.66849	+	1.18809i
$731$	−39.4643	−	35.5338i	−1.45964	−	1.31427i
$732$	18.6786	−	0.335396i	0.690382	−	0.0123966i
$733$	−8.18386	−	18.3812i	−0.302278	−	0.678927i	0.696994	−	0.717077i	$-0.254520\pi$
$733$	−8.18386	−	18.3812i	−0.302278	−	0.678927i	−0.999272	+	0.0381498i	$0.987854\pi$
$734$	50.5392	−	36.7189i	1.86543	−	1.35532i
$735$	10.5649	+	39.7737i	0.389693	+	1.46707i
$736$			51.3549i			1.89297i
$737$	−5.30838	+	3.48659i	−0.195537	+	0.128430i
$738$	−48.0937	+	23.5165i	−1.77035	+	0.865655i
$739$	2.10392	+	9.89816i	0.0773939	+	0.364110i	0.999753	−	0.0222240i	$-0.00707470\pi$
$739$	2.10392	+	9.89816i	0.0773939	+	0.364110i	−0.922359	+	0.386334i	$0.873741\pi$
$740$	−40.2087	+	4.22610i	−1.47810	+	0.155355i
$741$	0.343906	−	0.0424012i	0.0126337	−	0.00155765i
$742$	2.92180	+	1.83117i	0.107263	+	0.0672245i
$743$	−6.42880	−	19.7858i	−0.235850	−	0.725871i	−0.997008	−	0.0773044i	$-0.975369\pi$
$743$	−6.42880	−	19.7858i	−0.235850	−	0.725871i	0.761158	−	0.648567i	$-0.224631\pi$
$744$	−4.13958	+	9.76585i	−0.151765	+	0.358033i
$745$	−17.2810	+	38.8137i	−0.633126	+	1.42202i
$746$	−7.16327	−	33.7006i	−0.262266	−	1.23387i
$747$	18.3116	+	12.3247i	0.669986	+	0.450936i
$748$	38.5702	−	38.9725i	1.41027	−	1.42497i
$749$	−21.9604	+	3.84199i	−0.802415	+	0.140383i
$750$	17.1286	−	7.99767i	0.625450	−	0.292033i
$751$	−5.23083	−	49.7680i	−0.190876	−	1.81606i	−0.501090	−	0.865395i	$-0.667068\pi$
$751$	−5.23083	−	49.7680i	−0.190876	−	1.81606i	0.310214	−	0.950667i	$-0.399599\pi$
$752$	0.527087	+	0.0553990i	0.0192209	+	0.00202020i
$753$	49.7222	−	0.892817i	1.81198	−	0.0325361i
$754$	2.01041	−	9.45825i	0.0732149	−	0.344449i
$755$	54.3246	+	39.4691i	1.97707	+	1.43643i
$756$	−19.4737	+	27.8213i	−0.708253	+	1.01185i
$757$	6.48505	−	19.9589i	0.235703	−	0.725419i	−0.761324	−	0.648371i	$-0.775451\pi$
$757$	6.48505	−	19.9589i	0.235703	−	0.725419i	0.997027	−	0.0770481i	$-0.0245495\pi$
$758$	8.67740	−	15.0297i	0.315177	−	0.545903i
$759$	4.93075	−	36.5933i	0.178975	−	1.32825i
$760$	−0.284944	−	0.493537i	−0.0103360	−	0.0179025i
$761$	1.77572	+	1.97213i	0.0643697	+	0.0714898i	0.774470	−	0.632611i	$-0.218017\pi$
$761$	1.77572	+	1.97213i	0.0643697	+	0.0714898i	−0.710100	+	0.704101i	$0.751350\pi$
$762$	16.8544	+	3.26740i	0.610570	+	0.118365i
$763$	14.7726	+	21.9644i	0.534803	+	0.795165i
$764$	−36.1456	+	11.7444i	−1.30770	+	0.424899i
$765$	65.5290	+	18.7191i	2.36921	+	0.676791i
$766$	28.2524	+	2.96945i	1.02080	+	0.107291i
$767$	−1.30721	−	0.582006i	−0.0472005	−	0.0210150i
$768$	−10.4924	−	0.912668i	−0.378611	−	0.0329331i
$769$			7.06043i			0.254606i	0.991864	+	0.127303i	$0.0406320\pi$
$769$			7.06043i			0.254606i	−0.991864	+	0.127303i	$0.959368\pi$
$770$	−50.1457	+	38.0912i	−1.80712	+	1.37271i
$771$	−21.9481	−	23.5129i	−0.790442	−	0.846795i
$772$	−11.3720	+	10.2394i	−0.409287	+	0.368524i
$773$	6.93928	−	15.5859i	0.249589	−	0.560585i	−0.744689	−	0.667411i	$-0.767402\pi$
$773$	6.93928	−	15.5859i	0.249589	−	0.560585i	0.994278	+	0.106826i	$0.0340689\pi$
$774$	−8.68975	+	49.5724i	−0.312347	+	1.78184i
$775$	−39.2913	−	8.35163i	−1.41139	−	0.300000i
$776$	0.308520	+	0.949528i	0.0110752	+	0.0340861i
$777$	16.1485	+	15.0839i	0.579322	+	0.541131i
$778$	37.4908	+	51.6016i	1.34411	+	1.85001i
$779$	−1.05934	+	0.953831i	−0.0379547	+	0.0341745i
$780$	16.4531	+	5.02120i	0.589114	+	0.179788i
$781$	−8.96360	−	22.9937i	−0.320743	−	0.822781i
$782$	78.7679	+	45.4766i	2.81673	+	1.62624i
$783$	−18.7187	+	7.21772i	−0.668951	+	0.257940i
$784$	−19.8175	−	1.43895i	−0.707768	−	0.0513911i
$785$	−19.1523	+	26.3609i	−0.683574	+	0.940860i
$786$	23.6407	−	14.2209i	0.843238	−	0.507243i
$787$	−14.7289	−	13.2620i	−0.525030	−	0.472739i	0.363476	−	0.931603i	$-0.381590\pi$
$787$	−14.7289	−	13.2620i	−0.525030	−	0.472739i	−0.888506	+	0.458864i	$0.848256\pi$
$788$	0.406675	−	3.86926i	0.0144872	−	0.137837i
$789$	−14.4530	−	12.5511i	−0.514540	−	0.446831i
$790$	−7.52226	+	23.1511i	−0.267630	+	0.823681i
$791$	−31.9419	+	26.7299i	−1.13572	+	0.950405i
$792$	−9.65151	−	2.16540i	−0.342951	−	0.0769440i
$793$	−2.58609	+	4.47924i	−0.0918347	+	0.159062i
$794$	42.7684	−	9.09070i	1.51779	−	0.322617i
$795$	−3.42593	+	1.18156i	−0.121505	+	0.0419057i
$796$	7.23276	−	3.22023i	0.256358	−	0.114138i
$797$	−9.70858	+	3.15451i	−0.343896	+	0.111738i	−0.475872	−	0.879514i	$-0.657868\pi$
$797$	−9.70858	+	3.15451i	−0.343896	+	0.111738i	0.131977	+	0.991253i	$0.457868\pi$
$798$	−0.534036	+	1.54676i	−0.0189047	+	0.0547547i
$799$	0.734510	−	1.01097i	0.0259851	−	0.0357654i
$800$	5.44589	+	51.8141i	0.192541	+	1.83191i
$801$	5.22983	−	0.740349i	0.184787	−	0.0261589i
$802$	−1.27607	+	0.736738i	−0.0450595	+	0.0260151i
$803$	−1.71994	+	36.4337i	−0.0606955	+	1.28572i
$804$	−5.98911	+	5.59054i	−0.211220	+	0.197163i
$805$	−45.4382	−	35.5980i	−1.60149	−	1.25466i
$806$	−9.06820	−	12.4813i	−0.319414	−	0.439635i
$807$	−9.36915	−	3.97143i	−0.329810	−	0.139801i
$808$	−2.55844	+	2.84144i	−0.0900056	+	0.0999613i
$809$	−17.4177	+	19.3443i	−0.612373	+	0.680109i	−0.966964	−	0.254912i	$-0.917953\pi$
$809$	−17.4177	+	19.3443i	−0.612373	+	0.680109i	0.354591	+	0.935022i	$0.384620\pi$
$810$	−17.9271	−	62.0496i	−0.629893	−	2.18020i
$811$	5.04690	+	6.94646i	0.177221	+	0.243923i	0.888381	−	0.459106i	$-0.151830\pi$
$811$	5.04690	+	6.94646i	0.177221	+	0.243923i	−0.711161	+	0.703029i	$0.751830\pi$
$812$	19.8633	+	15.5617i	0.697066	+	0.546108i
$813$	26.4576	+	28.3439i	0.927910	+	0.994063i
$814$	−11.9538	+	31.6301i	−0.418980	+	1.10864i
$815$	−52.8373	+	30.5056i	−1.85081	+	1.06857i
$816$	−18.8598	+	26.9634i	−0.660226	+	0.943906i
$817$	0.140077	+	1.33274i	0.00490067	+	0.0466268i
$818$	36.1627	−	49.7737i	1.26440	−	1.74030i
$819$	−3.82128	−	8.59043i	−0.133526	−	0.300174i
$820$	−67.3031	+	21.8681i	−2.35033	+	0.763668i
$821$	26.6732	−	11.8757i	0.930901	−	0.414464i	0.115465	−	0.993312i	$-0.463164\pi$
$821$	26.6732	−	11.8757i	0.930901	−	0.414464i	0.815436	+	0.578848i	$0.196497\pi$
$822$	15.3625	+	44.5434i	0.535828	+	1.55363i
$823$	11.0557	−	2.34996i	0.385377	−	0.0819145i	−0.0111490	−	0.999938i	$-0.503549\pi$
$823$	11.0557	−	2.34996i	0.385377	−	0.0819145i	0.396526	+	0.918023i	$0.370216\pi$
$824$	0.554191	−	0.959886i	0.0193061	−	0.0334392i
$825$	1.09434	−	37.4434i	0.0381000	−	1.30361i
$826$	5.18223	−	4.33663i	0.180313	−	0.150891i
$827$	−5.80849	+	17.8767i	−0.201981	+	0.621633i	0.797843	+	0.602865i	$0.205974\pi$
$827$	−5.80849	+	17.8767i	−0.201981	+	0.621633i	−0.999824	+	0.0187679i	$0.994026\pi$
$828$	−1.71004	−	47.6018i	−0.0594280	−	1.65428i
$829$	0.215653	−	2.05180i	0.00748992	−	0.0712618i	−0.990138	−	0.140092i	$-0.955260\pi$
$829$	0.215653	−	2.05180i	0.00748992	−	0.0712618i	0.997628	+	0.0688304i	$0.0219267\pi$
$830$	39.2389	+	35.3308i	1.36200	+	1.22635i
$831$	12.0407	+	20.0163i	0.417686	+	0.694359i
$832$	−7.80882	+	10.7479i	−0.270722	+	0.372617i
$833$	−26.3013	+	38.7697i	−0.911287	+	1.34329i
$834$	5.56336	−	2.59763i	0.192643	−	0.0899485i
$835$	−44.5646	−	25.7294i	−1.54222	−	0.890402i
$836$	−1.38138	+	0.0795826i	−0.0477760	+	0.00275242i
$837$	−11.4261	+	29.9001i	−0.394942	+	1.03350i
$838$	47.1215	−	42.4284i	1.62779	−	1.46566i
$839$	−0.851981	−	1.17265i	−0.0294136	−	0.0404844i	0.794057	−	0.607843i	$-0.207965\pi$
$839$	−0.851981	−	1.17265i	−0.0294136	−	0.0404844i	−0.823471	+	0.567359i	$0.807965\pi$
$840$	−10.5552	+	11.3001i	−0.364188	+	0.389891i
$841$	−4.35502	−	13.4034i	−0.150173	−	0.462186i
$842$	−62.8986	−	13.3695i	−2.16763	−	0.460744i
$843$	−3.83987	−	5.09037i	−0.132252	−	0.175322i
$844$	−5.86233	+	13.1670i	−0.201790	+	0.453227i
$845$	29.2520	−	26.3386i	1.00630	−	0.906077i
$846$	−1.18149	−	0.0814286i	−0.0406205	−	0.00279957i
$847$	5.31262	+	28.6143i	0.182544	+	0.983198i
$848$		−	1.74974i		−	0.0600864i
$849$	0.440491	−	5.06405i	0.0151176	−	0.173798i
$850$	84.2948	+	37.5305i	2.89129	+	1.28728i
$851$	−30.8246	−	3.23980i	−1.05665	−	0.111059i
$852$	−16.4107	−	27.2810i	−0.562220	−	0.934631i
$853$	51.8964	−	16.8622i	1.77690	−	0.577349i	0.778183	−	0.628037i	$-0.216141\pi$
$853$	51.8964	−	16.8622i	1.77690	−	0.577349i	0.998715	+	0.0506882i	$0.0161415\pi$
$854$	−13.6313	−	20.2675i	−0.466453	−	0.693540i
$855$	−0.912795	−	1.45753i	−0.0312169	−	0.0498464i
$856$	−5.60519	−	6.22520i	−0.191582	−	0.212773i
$857$	−15.7837	−	27.3382i	−0.539161	−	0.933855i	−0.998949	−	0.0458262i	$-0.985408\pi$
$857$	−15.7837	−	27.3382i	−0.539161	−	0.933855i	0.459788	−	0.888029i	$-0.347925\pi$
$858$	9.93502	−	10.4058i	0.339176	−	0.355249i
$859$	−10.8865	+	18.8559i	−0.371442	+	0.643356i	−0.989788	−	0.142550i	$-0.954470\pi$
$859$	−10.8865	+	18.8559i	−0.371442	+	0.643356i	0.618346	+	0.785906i	$0.287803\pi$
$860$	−20.5581	+	63.2713i	−0.701025	+	2.15753i
$861$	33.1370	+	19.9483i	1.12931	+	0.679838i
$862$	16.8793	+	12.2635i	0.574910	+	0.417696i
$863$	−10.1718	+	47.8546i	−0.346252	+	1.62899i	0.368512	+	0.929623i	$0.379867\pi$
$863$	−10.1718	+	47.8546i	−0.346252	+	1.62899i	−0.714764	+	0.699366i	$0.753466\pi$
$864$	41.4620	+	2.11046i	1.41057	+	0.0717994i
$865$	39.8359	+	4.18692i	1.35446	+	0.142360i
$866$	−1.67224	−	15.9103i	−0.0568251	−	0.540655i
$867$	20.3661	+	43.6181i	0.691667	+	1.48135i
$868$	39.6573	−	6.93808i	1.34606	−	0.235494i
$869$	7.99620	+	7.91366i	0.271252	+	0.268453i
$870$	−46.7555	+	10.8190i	−1.58516	+	0.366799i
$871$	−0.471601	−	2.21871i	−0.0159796	−	0.0751780i
$872$	−4.04540	+	9.08611i	−0.136994	+	0.307694i
$873$	1.03330	+	2.83014i	0.0349719	+	0.0957857i
$874$	−0.709254	−	2.18286i	−0.0239909	−	0.0738363i
$875$	−11.5726	−	7.25287i	−0.391226	−	0.245192i
$876$	5.75765	+	46.6989i	0.194533	+	1.57781i
$877$	−1.72910	+	0.181736i	−0.0583876	+	0.00613679i	−0.133677	−	0.991025i	$-0.542679\pi$
$877$	−1.72910	+	0.181736i	−0.0583876	+	0.00613679i	0.0752896	+	0.997162i	$0.476012\pi$
$878$	−2.85976	−	13.4541i	−0.0965122	−	0.454054i
$879$	−40.7084	−	12.4235i	−1.37306	−	0.419035i
$880$	29.8910	+	11.2965i	1.00763	+	0.380806i
$881$		−	45.8867i		−	1.54596i	−0.634428	−	0.772982i	$-0.718764\pi$
$881$		−	45.8867i		−	1.54596i	0.634428	−	0.772982i	$-0.281236\pi$
$882$	44.3703	+	1.62354i	1.49402	+	0.0546676i
$883$	−45.9552	+	33.3884i	−1.54652	+	1.12361i	−0.600438	+	0.799671i	$0.705007\pi$
$883$	−45.9552	+	33.3884i	−1.54652	+	1.12361i	−0.946078	+	0.323939i	$0.894993\pi$
$884$	7.96523	+	17.8902i	0.267900	+	0.601713i
$885$	0.127500	+	7.10064i	0.00428586	+	0.238685i
$886$	37.6951	+	33.9408i	1.26639	+	1.14026i
$887$	−14.9957	+	6.67652i	−0.503506	+	0.224175i	−0.642740	−	0.766084i	$-0.722203\pi$
$887$	−14.9957	+	6.67652i	−0.503506	+	0.224175i	0.139234	+	0.990259i	$0.455536\pi$
$888$	−1.58020	+	8.15123i	−0.0530281	+	0.273537i
$889$	−4.63113	−	11.5067i	−0.155323	−	0.385921i
$890$	12.6352			0.423531
$891$	−29.3414	−	5.48473i	−0.982974	−	0.183745i
$892$	−22.9281	−	39.7126i	−0.767690	−	1.32968i
$893$	−0.0308450	+	0.00655630i	−0.00103219	+	0.000219398i
$894$	34.6103	+	30.0559i	1.15754	+	1.00522i
$895$	0.632754	+	0.459723i	0.0211506	+	0.0153668i
$896$	−9.58136	−	18.0781i	−0.320091	−	0.603947i
$897$	11.5372	+	6.38764i	0.385217	+	0.213277i
$898$	−17.1640	−	38.5510i	−0.572771	−	1.28646i
$899$	21.7276	+	9.67376i	0.724657	+	0.322638i
$900$	−6.77323	−	47.8462i	−0.225774	−	1.59487i
$901$	−3.57286	−	2.06279i	−0.119029	−	0.0687215i
$902$	−8.95528	+	58.5041i	−0.298178	+	1.94797i
$903$	33.4824	−	14.1795i	1.11422	−	0.471864i
$904$	−14.8840	−	4.83611i	−0.495035	−	0.160847i
$905$	46.3442	−	4.87097i	1.54053	−	0.161917i
$906$	57.8369	−	43.6287i	1.92150	−	1.44947i
$907$	25.8320	−	28.6893i	0.857738	−	0.952614i	−0.141566	−	0.989929i	$-0.545214\pi$
$907$	25.8320	−	28.6893i	0.857738	−	0.952614i	0.999304	+	0.0373148i	$0.0118804\pi$
$908$	30.1552	+	6.40968i	1.00073	+	0.212713i
$909$	−7.40785	+	8.84631i	−0.245703	+	0.293414i
$910$	−6.17043	−	21.6278i	−0.204548	−	0.716954i
$911$	20.3528	+	6.61304i	0.674320	+	0.219100i	0.626107	−	0.779737i	$-0.284647\pi$
$911$	20.3528	+	6.61304i	0.674320	+	0.219100i	0.0482129	+	0.998837i	$0.484647\pi$
$912$	0.808969	−	0.187192i	0.0267876	−	0.00619855i
$913$	22.7360	−	8.86313i	0.752452	−	0.293327i
$914$	−6.32518	+	3.65185i	−0.209218	+	0.120792i
$915$	25.5734	+	2.22448i	0.845432	+	0.0735390i
$916$	24.2082	−	17.5883i	0.799863	−	0.581134i
$917$	−17.9031	−	8.76153i	−0.591213	−	0.289331i
$918$	39.9532	−	61.7254i	1.31865	−	2.03724i
$919$	0.0958020	−	0.450713i	0.00316022	−	0.0148676i	−0.976539	−	0.215340i	$-0.930914\pi$
$919$	0.0958020	−	0.450713i	0.00316022	−	0.0148676i	0.979699	+	0.200472i	$0.0642475\pi$
$920$	2.26709	−	21.5700i	0.0747439	−	0.711141i
$921$	−12.9055	−	37.4194i	−0.425251	−	1.23301i
$922$	7.05824	+	7.83897i	0.232451	+	0.258163i
$923$	8.81420			0.290123
$924$	12.9942	+	35.2233i	0.427477	+	1.15876i
$925$	−31.4438			−1.03387
$926$	21.5181	+	23.8983i	0.707130	+	0.785347i
$927$	1.56732	−	2.95484i	0.0514777	−	0.0970498i
$928$	3.22447	−	30.6788i	0.105848	−	1.00708i
$929$	11.5367	−	54.2759i	0.378507	−	1.78073i	−0.215739	−	0.976451i	$-0.569216\pi$
$929$	11.5367	−	54.2759i	0.378507	−	1.78073i	0.594246	−	0.804284i	$-0.297451\pi$
$930$	−37.0880	+	66.9877i	−1.21616	+	2.19661i
$931$	1.14787	−	0.282944i	0.0376201	−	0.00927313i
$932$	28.9510	−	21.0341i	0.948322	−	0.688996i
$933$	2.90630	−	33.4119i	0.0951479	−	1.09386i
$934$	51.2383	−	29.5825i	1.67657	−	0.967968i
$935$	58.3057	−	47.7179i	1.90680	−	1.56054i
$936$	1.97255	−	2.93076i	0.0644750	−	0.0957949i
$937$	34.2638	+	11.1330i	1.11935	+	0.363698i	0.809519	−	0.587094i	$-0.199728\pi$
$937$	34.2638	+	11.1330i	1.11935	+	0.363698i	0.309830	+	0.950792i	$0.399728\pi$
$938$	10.3900	+	2.60526i	0.339247	+	0.0850649i
$939$	−50.9081	+	6.27661i	−1.66132	+	0.204829i
$940$	−1.53127	−	0.325482i	−0.0499446	−	0.0106161i
$941$	−20.3278	+	22.5763i	−0.662666	+	0.735965i	−0.976975	−	0.213356i	$-0.931561\pi$
$941$	−20.3278	+	22.5763i	−0.662666	+	0.735965i	0.314309	+	0.949321i	$0.398227\pi$
$942$	21.1707	+	28.0652i	0.689779	+	0.914414i
$943$	−53.9537	+	5.67076i	−1.75697	+	0.184665i
$944$	−3.26110	−	1.05959i	−0.106140	−	0.0344869i
$945$	−30.6078	+	35.2222i	−0.995672	+	1.14578i
$946$	39.5470	+	39.1388i	1.28578	+	1.27251i
$947$	−12.5259	−	7.23184i	−0.407038	−	0.235003i	0.282478	−	0.959274i	$-0.408843\pi$
$947$	−12.5259	−	7.23184i	−0.407038	−	0.235003i	−0.689516	+	0.724270i	$0.742177\pi$
$948$	11.8924	+	8.31827i	0.386247	+	0.270165i
$949$	−11.9007	−	5.29851i	−0.386312	−	0.171997i
$950$	−0.947076	−	2.12717i	−0.0307272	−	0.0690144i
$951$	−12.4849	+	22.5499i	−0.404850	+	0.731232i
$952$	−17.5918	−	0.637830i	−0.570153	−	0.0206722i
$953$	−28.3524	−	20.5992i	−0.918423	−	0.667273i	0.0247081	−	0.999695i	$-0.492134\pi$
$953$	−28.3524	−	20.5992i	−0.918423	−	0.667273i	−0.943131	+	0.332421i	$0.892134\pi$
$954$	0.140368	+	3.90738i	0.00454458	+	0.126506i
$955$	−51.0816	+	10.8577i	−1.65296	+	0.351348i
$956$	2.16102	+	3.74299i	0.0698923	+	0.121057i
$957$	−5.24318	+	21.5508i	−0.169488	+	0.696637i
$958$	−17.3382			−0.560172
$959$	20.9940	−	26.7974i	0.677933	−	0.865332i
$960$	64.7303	+	12.5487i	2.08916	+	0.405006i
$961$	6.34646	−	2.82563i	0.204725	−	0.0911493i
$962$	−8.97467	−	8.08083i	−0.289355	−	0.260536i
$963$	−17.5784	−	18.1666i	−0.566457	−	0.585409i
$964$	10.7535	+	24.1529i	0.346348	+	0.777911i
$965$	−17.0111	+	12.3593i	−0.547605	+	0.397859i
$966$	−51.0437	+	35.6778i	−1.64230	+	1.14791i
$967$			17.1424i			0.551261i	0.961264	+	0.275631i	$0.0888867\pi$
$967$			17.1424i			0.551261i	−0.961264	+	0.275631i	$0.911113\pi$
$968$	−8.05023	+	7.40113i	−0.258744	+	0.237881i
$969$	0.571469	−	1.87254i	0.0183582	−	0.0601548i
$970$	1.49845	+	7.04968i	0.0481125	+	0.226351i
$971$	−12.8970	+	1.35553i	−0.413886	+	0.0435012i	−0.309183	−	0.951002i	$-0.600056\pi$
$971$	−12.8970	+	1.35553i	−0.413886	+	0.0435012i	−0.104702	+	0.994504i	$0.533389\pi$
$972$	−38.5022	−	0.575606i	−1.23496	−	0.0184626i
$973$	−3.75877	−	2.35572i	−0.120501	−	0.0755209i
$974$	−16.2183	−	49.9148i	−0.519668	−	1.59937i
$975$	12.3178	+	5.22131i	0.394485	+	0.167216i
$976$	−5.04115	+	11.3226i	−0.161363	+	0.362428i
$977$	8.67650	+	40.8197i	0.277586	+	1.30594i	0.867081	+	0.498167i	$0.165993\pi$
$977$	8.67650	+	40.8197i	0.277586	+	1.30594i	−0.589495	+	0.807772i	$0.700673\pi$
$978$	14.8396	+	64.1306i	0.474517	+	2.05067i
$979$	2.62403	−	5.21667i	0.0838643	−	0.166725i
$980$	57.7719	+	10.3459i	1.84546	+	0.330486i
$981$	−11.2156	+	27.8400i	−0.358088	+	0.888861i
$982$	6.86374	+	65.3042i	0.219031	+	2.08394i
$983$	35.6014	+	3.74186i	1.13551	+	0.119347i	0.653575	−	0.756861i	$-0.273268\pi$
$983$	35.6014	+	3.74186i	1.13551	+	0.119347i	0.481933	+	0.876208i	$0.339935\pi$
$984$	0.260916	+	14.5308i	0.00831769	+	0.463223i
$985$	1.11148	−	5.22912i	0.0354148	−	0.166614i
$986$	−44.1995	−	32.1128i	−1.40760	−	1.02268i
$987$	0.414192	+	0.748694i	0.0131839	+	0.0238312i
$988$	0.152710	−	0.469994i	0.00485836	−	0.0149525i
$989$	−25.5005	+	44.1681i	−0.810868	+	1.40447i
$990$	−67.6564	−	22.8286i	−2.15026	−	0.725540i
$991$	9.78155	+	16.9421i	0.310721	+	0.538185i	0.978519	−	0.206158i	$-0.0660962\pi$
$991$	9.78155	+	16.9421i	0.310721	+	0.538185i	−0.667798	+	0.744343i	$0.732763\pi$
$992$	−32.9329	−	36.5757i	−1.04562	−	1.16128i
$993$	5.30182	−	27.3486i	0.168248	−	0.867883i
$994$	−18.2967	+	37.3871i	−0.580337	+	1.18585i
$995$	10.3464	−	3.36176i	0.328004	−	0.106575i
$996$	26.9752	−	16.2267i	0.854741	−	0.514163i
$997$	29.0291	+	3.05108i	0.919359	+	0.0966286i	0.552372	−	0.833598i	$-0.313723\pi$
$997$	29.0291	+	3.05108i	0.919359	+	0.0966286i	0.366987	+	0.930226i	$0.380389\pi$
$998$	−62.1467	−	27.6695i	−1.96722	−	0.875862i
$999$	−3.88245	+	24.7535i	−0.122835	+	0.783166i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.be.a.2.4	✓	224
3.2	odd	2	inner	231.2.be.a.2.25	yes	224
7.4	even	3	inner	231.2.be.a.200.25	yes	224
11.6	odd	10	inner	231.2.be.a.149.4	yes	224
21.11	odd	6	inner	231.2.be.a.200.4	yes	224
33.17	even	10	inner	231.2.be.a.149.25	yes	224
77.39	odd	30	inner	231.2.be.a.116.25	yes	224
231.116	even	30	inner	231.2.be.a.116.4	yes	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.be.a.2.4	✓	224	1.1	even	1	trivial
231.2.be.a.2.25	yes	224	3.2	odd	2	inner
231.2.be.a.116.4	yes	224	231.116	even	30	inner
231.2.be.a.116.25	yes	224	77.39	odd	30	inner
231.2.be.a.149.4	yes	224	11.6	odd	10	inner
231.2.be.a.149.25	yes	224	33.17	even	10	inner
231.2.be.a.200.4	yes	224	21.11	odd	6	inner
231.2.be.a.200.25	yes	224	7.4	even	3	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:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.be (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41473 - 1.57122i) q^{2} +(-1.63740 + 0.564721i) q^{3} +(-0.258206 + 2.45666i) q^{4} +(-0.705701 + 3.32006i) q^{5} +(3.20379 + 1.77379i) q^{6} +(-0.181035 - 2.63955i) q^{7} +(0.804266 - 0.584333i) q^{8} +(2.36218 - 1.84935i) q^{9} +O(q^{10})\)	\(q+(-1.41473 - 1.57122i) q^{2} +(-1.63740 + 0.564721i) q^{3} +(-0.258206 + 2.45666i) q^{4} +(-0.705701 + 3.32006i) q^{5} +(3.20379 + 1.77379i) q^{6} +(-0.181035 - 2.63955i) q^{7} +(0.804266 - 0.584333i) q^{8} +(2.36218 - 1.84935i) q^{9} +(6.21493 - 3.58819i) q^{10} +(-0.190758 - 3.31113i) q^{11} +(-0.964542 - 4.16836i) q^{12} +(1.12657 + 0.366043i) q^{13} +(-3.89120 + 4.01870i) q^{14} +(-0.719391 - 5.83481i) q^{15} +(2.77650 + 0.590162i) q^{16} +(4.47832 - 4.97367i) q^{17} +(-6.24759 - 1.09517i) q^{18} +(-0.167965 + 0.0176539i) q^{19} +(-7.97406 - 2.59093i) q^{20} +(1.78704 + 4.21977i) q^{21} +(-4.93265 + 4.98409i) q^{22} +(-5.56650 - 3.21382i) q^{23} +(-0.986922 + 1.41097i) q^{24} +(-5.95708 - 2.65226i) q^{25} +(-1.01865 - 2.28793i) q^{26} +(-2.82348 + 4.36211i) q^{27} +(6.53123 + 0.236805i) q^{28} +(3.12357 + 2.26940i) q^{29} +(-8.15002 + 9.38501i) q^{30} +(6.02551 - 1.28076i) q^{31} +(-3.99485 - 6.91928i) q^{32} +(2.18221 + 5.31394i) q^{33} -14.1504 q^{34} +(8.89123 + 1.26169i) q^{35} +(3.93331 + 6.28060i) q^{36} +(4.40516 - 1.96130i) q^{37} +(0.265364 + 0.238935i) q^{38} +(-2.05135 + 0.0368343i) q^{39} +(1.37245 + 3.08258i) q^{40} +(6.82831 - 4.96106i) q^{41} +(4.10201 - 8.77768i) q^{42} -7.93464i q^{43} +(8.18360 + 0.386327i) q^{44} +(4.47297 + 9.14768i) q^{45} +(2.82549 + 13.2929i) q^{46} +(0.185690 - 0.0195168i) q^{47} +(-4.87952 + 0.601611i) q^{48} +(-6.93445 + 0.955702i) q^{49} +(4.26039 + 13.1121i) q^{50} +(-4.52407 + 10.6729i) q^{51} +(-1.19013 + 2.67308i) q^{52} +(-0.128162 - 0.602956i) q^{53} +(10.8483 - 1.73491i) q^{54} +(11.1278 + 1.70334i) q^{55} +(-1.68798 - 2.01711i) q^{56} +(0.265057 - 0.123760i) q^{57} +(-0.853278 - 8.11840i) q^{58} +(-1.20138 - 0.126270i) q^{59} +(14.5199 - 0.260721i) q^{60} +(-0.907825 + 4.27098i) q^{61} +(-10.5368 - 7.65546i) q^{62} +(-5.30909 - 5.90030i) q^{63} +(-3.46576 + 10.6665i) q^{64} +(-2.01031 + 3.48195i) q^{65} +(5.26211 - 10.9465i) q^{66} +(-0.957449 - 1.65835i) q^{67} +(11.0623 + 12.2859i) q^{68} +(10.9295 + 2.11880i) q^{69} +(-10.5963 - 15.7550i) q^{70} +(7.07684 - 2.29940i) q^{71} +(0.819183 - 2.86767i) q^{72} +(-10.9372 - 1.14954i) q^{73} +(-9.31376 - 4.14675i) q^{74} +(11.2519 + 0.978738i) q^{75} -0.417192i q^{76} +(-8.70537 + 1.10295i) q^{77} +(2.95999 + 3.17102i) q^{78} +(-2.52078 + 2.26972i) q^{79} +(-3.91875 + 8.80167i) q^{80} +(2.15980 - 8.73701i) q^{81} +(-17.4551 - 3.71020i) q^{82} +(2.27363 + 6.99752i) q^{83} +(-10.8280 + 3.30058i) q^{84} +(13.3526 + 18.3782i) q^{85} +(-12.4671 + 11.2254i) q^{86} +(-6.39612 - 1.95199i) q^{87} +(-2.08823 - 2.55157i) q^{88} +(1.52478 + 0.880330i) q^{89} +(8.04495 - 19.9695i) q^{90} +(0.762242 - 3.03989i) q^{91} +(9.33257 - 12.8452i) q^{92} +(-9.14291 + 5.49985i) q^{93} +(-0.293367 - 0.264149i) q^{94} +(0.0599213 - 0.570113i) q^{95} +(10.4486 + 9.07368i) q^{96} +(-0.310343 + 0.955137i) q^{97} +(11.3120 + 9.54348i) q^{98} +(-6.57406 - 7.46872i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q - 3 q^{3} + 18 q^{4} - 20 q^{6} - 20 q^{7} - 9 q^{9}+O(q^{10}) \) 224 * q - 3 * q^3 + 18 * q^4 - 20 * q^6 - 20 * q^7 - 9 * q^9	\( 224 q - 3 q^{3} + 18 q^{4} - 20 q^{6} - 20 q^{7} - 9 q^{9} - 16 q^{12} - 40 q^{13} + 12 q^{15} + 34 q^{16} - 5 q^{18} - 10 q^{19} - 76 q^{22} - 25 q^{24} - 18 q^{25} + 6 q^{27} + 10 q^{28} - 35 q^{30} - 8 q^{33} - 96 q^{34} - 48 q^{36} - 10 q^{37} - 45 q^{39} - 120 q^{40} + 34 q^{42} - 24 q^{45} - 50 q^{46} + 14 q^{48} - 56 q^{49} - 45 q^{51} - 10 q^{52} + 48 q^{55} + 60 q^{57} + 44 q^{58} - 47 q^{60} - 50 q^{61} + 60 q^{63} - 72 q^{64} + 77 q^{66} - 80 q^{67} + 78 q^{69} + 36 q^{70} + 55 q^{72} - 70 q^{73} - 11 q^{75} + 36 q^{78} - 90 q^{79} + 23 q^{81} - 6 q^{82} + 125 q^{84} + 160 q^{85} + 86 q^{88} + 30 q^{90} - 128 q^{91} - 38 q^{93} - 210 q^{94} + 135 q^{96} + 40 q^{97} + 80 q^{99}+O(q^{100}) \) 224 * q - 3 * q^3 + 18 * q^4 - 20 * q^6 - 20 * q^7 - 9 * q^9 - 16 * q^12 - 40 * q^13 + 12 * q^15 + 34 * q^16 - 5 * q^18 - 10 * q^19 - 76 * q^22 - 25 * q^24 - 18 * q^25 + 6 * q^27 + 10 * q^28 - 35 * q^30 - 8 * q^33 - 96 * q^34 - 48 * q^36 - 10 * q^37 - 45 * q^39 - 120 * q^40 + 34 * q^42 - 24 * q^45 - 50 * q^46 + 14 * q^48 - 56 * q^49 - 45 * q^51 - 10 * q^52 + 48 * q^55 + 60 * q^57 + 44 * q^58 - 47 * q^60 - 50 * q^61 + 60 * q^63 - 72 * q^64 + 77 * q^66 - 80 * q^67 + 78 * q^69 + 36 * q^70 + 55 * q^72 - 70 * q^73 - 11 * q^75 + 36 * q^78 - 90 * q^79 + 23 * q^81 - 6 * q^82 + 125 * q^84 + 160 * q^85 + 86 * q^88 + 30 * q^90 - 128 * q^91 - 38 * q^93 - 210 * q^94 + 135 * q^96 + 40 * q^97 + 80 * q^99

Introduction

L-functions

Modular forms

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