LMFDB - Embedded newform 380.2.bj.a.23.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(23,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([18, 27, 4]))

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

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

chi := DirichletCharacter("380.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.bj (of order $36$, degree $12$, 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:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$672$
Relative dimension:	$56$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			23.16
Character	$\chi$	$=$	380.23
Dual form			380.2.bj.a.347.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.918074 + 1.07570i) q^{2} +(0.0933215 + 0.0653444i) q^{3} +(-0.314282 - 1.97515i) q^{4} +(1.39136 - 1.75046i) q^{5} +(-0.155967 + 0.0403954i) q^{6} +(-4.78721 + 1.28273i) q^{7} +(2.41321 + 1.47526i) q^{8} +(-1.02162 - 2.80688i) q^{9} +O(q^{10})$	\(q+(-0.918074 + 1.07570i) q^{2} +(0.0933215 + 0.0653444i) q^{3} +(-0.314282 - 1.97515i) q^{4} +(1.39136 - 1.75046i) q^{5} +(-0.155967 + 0.0403954i) q^{6} +(-4.78721 + 1.28273i) q^{7} +(2.41321 + 1.47526i) q^{8} +(-1.02162 - 2.80688i) q^{9} +(0.605609 + 3.10375i) q^{10} +(-0.466282 + 0.269208i) q^{11} +(0.0997360 - 0.204861i) q^{12} +(-2.77779 + 1.94503i) q^{13} +(3.01517 - 6.32726i) q^{14} +(0.244227 - 0.0724381i) q^{15} +(-3.80245 + 1.24151i) q^{16} +(-5.45758 + 2.54491i) q^{17} +(3.95730 + 1.47796i) q^{18} +(-2.75906 + 3.37455i) q^{19} +(-3.89471 - 2.19801i) q^{20} +(-0.530569 - 0.193111i) q^{21} +(0.138493 - 0.748734i) q^{22} +(-1.00799 + 0.0881880i) q^{23} +(0.128805 + 0.295364i) q^{24} +(-1.12823 - 4.87105i) q^{25} +(0.457939 - 4.77377i) q^{26} +(0.176532 - 0.658828i) q^{27} +(4.03812 + 9.05233i) q^{28} +(1.38341 + 3.80089i) q^{29} +(-0.146296 + 0.329219i) q^{30} +(0.138683 + 0.0800689i) q^{31} +(2.15544 - 5.23011i) q^{32} +(-0.0611054 - 0.00534603i) q^{33} +(2.27289 - 8.20716i) q^{34} +(-4.41536 + 10.1646i) q^{35} +(-5.22294 + 2.90001i) q^{36} +(3.38813 - 3.38813i) q^{37} +(-1.09699 - 6.06602i) q^{38} -0.386325 q^{39} +(5.94004 - 2.17162i) q^{40} +(-1.76413 - 10.0049i) q^{41} +(0.694832 - 0.393445i) q^{42} +(0.818125 - 9.35121i) q^{43} +(0.678270 + 0.836371i) q^{44} +(-6.33478 - 2.11707i) q^{45} +(0.830548 - 1.16527i) q^{46} +(-1.90980 - 0.890557i) q^{47} +(-0.435976 - 0.132610i) q^{48} +(15.2098 - 8.78138i) q^{49} +(6.27561 + 3.25833i) q^{50} +(-0.675605 - 0.119127i) q^{51} +(4.71474 + 4.87528i) q^{52} +(0.411241 + 4.70050i) q^{53} +(0.546634 + 0.794749i) q^{54} +(-0.177528 + 1.19077i) q^{55} +(-13.4449 - 3.96688i) q^{56} +(-0.477988 + 0.134628i) q^{57} +(-5.35871 - 2.00136i) q^{58} +(-10.8840 - 3.96146i) q^{59} +(-0.219832 - 0.459619i) q^{60} +(3.37282 + 2.83013i) q^{61} +(-0.213452 + 0.0756733i) q^{62} +(8.49118 + 12.1267i) q^{63} +(3.64721 + 7.12024i) q^{64} +(-0.460207 + 7.56866i) q^{65} +(0.0618500 - 0.0608233i) q^{66} +(6.00106 + 2.79834i) q^{67} +(6.74180 + 9.97973i) q^{68} +(-0.0998301 - 0.0576369i) q^{69} +(-6.88044 - 14.0814i) q^{70} +(4.11104 + 4.89935i) q^{71} +(1.67549 - 8.28077i) q^{72} +(-2.80477 + 4.00563i) q^{73} +(0.534075 + 6.75519i) q^{74} +(0.213007 - 0.528297i) q^{75} +(7.53237 + 4.38901i) q^{76} +(1.88687 - 1.88687i) q^{77} +(0.354674 - 0.415571i) q^{78} +(-1.74573 - 9.90050i) q^{79} +(-3.11737 + 8.38344i) q^{80} +(-6.80505 + 5.71011i) q^{81} +(12.3819 + 7.28754i) q^{82} +(0.0751360 + 0.280411i) q^{83} +(-0.214676 + 1.10865i) q^{84} +(-3.13869 + 13.0942i) q^{85} +(9.30805 + 9.46517i) q^{86} +(-0.119265 + 0.445103i) q^{87} +(-1.52239 - 0.0382310i) q^{88} +(-6.80756 - 1.20036i) q^{89} +(8.09314 - 4.87073i) q^{90} +(10.8029 - 12.8744i) q^{91} +(0.490979 + 1.96323i) q^{92} +(0.00771009 + 0.0165343i) q^{93} +(2.71132 - 1.23679i) q^{94} +(2.06817 + 9.52485i) q^{95} +(0.542907 - 0.347236i) q^{96} +(2.84664 - 1.32741i) q^{97} +(-4.51754 + 24.4232i) q^{98} +(1.23200 + 1.03377i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8}+O(q^{10}) $ 672 * q - 12 * q^2 - 24 * q^5 - 36 * q^6 - 6 * q^8	$ 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8} - 12 q^{10} - 6 q^{12} - 24 q^{13} - 36 q^{16} - 24 q^{17} - 24 q^{18} + 36 q^{20} - 48 q^{21} - 24 q^{22} - 24 q^{25} - 60 q^{26} - 24 q^{28} - 6 q^{30} + 18 q^{32} - 60 q^{33} + 24 q^{36} - 48 q^{37} - 114 q^{38} - 42 q^{40} - 24 q^{41} - 48 q^{42} - 12 q^{45} - 12 q^{46} - 96 q^{48} - 6 q^{50} - 12 q^{52} - 24 q^{53} - 48 q^{56} - 24 q^{57} + 120 q^{58} - 12 q^{60} - 48 q^{61} + 36 q^{62} - 12 q^{65} - 96 q^{66} - 6 q^{68} - 12 q^{70} + 120 q^{72} - 24 q^{73} - 96 q^{76} - 360 q^{77} - 126 q^{78} + 48 q^{80} - 48 q^{81} + 228 q^{82} - 24 q^{85} - 132 q^{86} - 102 q^{88} + 78 q^{90} + 108 q^{92} - 60 q^{93} - 144 q^{96} - 24 q^{97} + 18 q^{98}+O(q^{100}) $ 672 * q - 12 * q^2 - 24 * q^5 - 36 * q^6 - 6 * q^8 - 12 * q^10 - 6 * q^12 - 24 * q^13 - 36 * q^16 - 24 * q^17 - 24 * q^18 + 36 * q^20 - 48 * q^21 - 24 * q^22 - 24 * q^25 - 60 * q^26 - 24 * q^28 - 6 * q^30 + 18 * q^32 - 60 * q^33 + 24 * q^36 - 48 * q^37 - 114 * q^38 - 42 * q^40 - 24 * q^41 - 48 * q^42 - 12 * q^45 - 12 * q^46 - 96 * q^48 - 6 * q^50 - 12 * q^52 - 24 * q^53 - 48 * q^56 - 24 * q^57 + 120 * q^58 - 12 * q^60 - 48 * q^61 + 36 * q^62 - 12 * q^65 - 96 * q^66 - 6 * q^68 - 12 * q^70 + 120 * q^72 - 24 * q^73 - 96 * q^76 - 360 * q^77 - 126 * q^78 + 48 * q^80 - 48 * q^81 + 228 * q^82 - 24 * q^85 - 132 * q^86 - 102 * q^88 + 78 * q^90 + 108 * q^92 - 60 * q^93 - 144 * q^96 - 24 * q^97 + 18 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	−0.918074	+	1.07570i	−0.649176	+	0.760638i
$2$	−0.918074	+	1.07570i	−0.649176	+	0.760638i
$3$	0.0933215	+	0.0653444i	0.0538792	+	0.0377266i	0.600206	−	0.799846i	$-0.295085\pi$
$3$	0.0933215	+	0.0653444i	0.0538792	+	0.0377266i	−0.546327	+	0.837572i	$0.683974\pi$
$4$	−0.314282	−	1.97515i	−0.157141	−	0.987576i
$5$	1.39136	−	1.75046i	0.622235	−	0.782830i
$5$	1.39136	−	1.75046i	0.622235	−	0.782830i
$6$	−0.155967	+	0.0403954i	−0.0636734	+	0.0164914i
$7$	−4.78721	+	1.28273i	−1.80939	+	0.484826i	−0.995380	−	0.0960182i	$-0.969389\pi$
$7$	−4.78721	+	1.28273i	−1.80939	+	0.484826i	−0.814015	+	0.580844i	$0.802723\pi$
$8$	2.41321	+	1.47526i	0.853200	+	0.521584i
$9$	−1.02162	−	2.80688i	−0.340540	−	0.935627i
$10$	0.605609	+	3.10375i	0.191510	+	0.981491i
$11$	−0.466282	+	0.269208i	−0.140589	+	0.0811692i	−0.568645	−	0.822583i	$-0.692532\pi$
$11$	−0.466282	+	0.269208i	−0.140589	+	0.0811692i	0.428056	+	0.903752i	$0.359199\pi$
$12$	0.0997360	−	0.204861i	0.0287913	−	0.0591382i
$13$	−2.77779	+	1.94503i	−0.770421	+	0.539454i	−0.891409	−	0.453199i	$-0.850283\pi$
$13$	−2.77779	+	1.94503i	−0.770421	+	0.539454i	0.120988	+	0.992654i	$0.461394\pi$
$14$	3.01517	−	6.32726i	0.805839	−	1.69103i
$15$	0.244227	−	0.0724381i	0.0630591	−	0.0187034i
$16$	−3.80245	+	1.24151i	−0.950614	+	0.310377i
$17$	−5.45758	+	2.54491i	−1.32366	+	0.617231i	−0.950554	−	0.310559i	$-0.899484\pi$
$17$	−5.45758	+	2.54491i	−1.32366	+	0.617231i	−0.373103	+	0.927790i	$0.621706\pi$
$18$	3.95730	+	1.47796i	0.932745	+	0.348359i
$19$	−2.75906	+	3.37455i	−0.632972	+	0.774174i
$19$	−2.75906	+	3.37455i	−0.632972	+	0.774174i
$20$	−3.89471	−	2.19801i	−0.870883	−	0.491490i
$21$	−0.530569	−	0.193111i	−0.115780	−	0.0421403i
$22$	0.138493	−	0.748734i	0.0295268	−	0.159631i
$23$	−1.00799	+	0.0881880i	−0.210181	+	0.0183885i	−0.191760	−	0.981442i	$-0.561420\pi$
$23$	−1.00799	+	0.0881880i	−0.210181	+	0.0183885i	−0.0184212	+	0.999830i	$0.505864\pi$
$24$	0.128805	+	0.295364i	0.0262922	+	0.0602909i
$25$	−1.12823	−	4.87105i	−0.225647	−	0.974209i
$26$	0.457939	−	4.77377i	0.0898092	−	0.936212i
$27$	0.176532	−	0.658828i	0.0339737	−	0.126791i
$28$	4.03812	+	9.05233i	0.763132	+	1.71073i
$29$	1.38341	+	3.80089i	0.256893	+	0.705808i	0.999355	+	0.0359192i	$0.0114359\pi$
$29$	1.38341	+	3.80089i	0.256893	+	0.705808i	−0.742462	+	0.669889i	$0.766342\pi$
$30$	−0.146296	+	0.329219i	−0.0267099	+	0.0601070i
$31$	0.138683	+	0.0800689i	0.0249083	+	0.0143808i	0.512402	−	0.858745i	$-0.328756\pi$
$31$	0.138683	+	0.0800689i	0.0249083	+	0.0143808i	−0.487494	+	0.873126i	$0.662089\pi$
$32$	2.15544	−	5.23011i	0.381031	−	0.924562i
$33$	−0.0611054	−	0.00534603i	−0.0106371	−	0.000930624i
$34$	2.27289	−	8.20716i	0.389797	−	1.40752i
$35$	−4.41536	+	10.1646i	−0.746333	+	1.71812i
$36$	−5.22294	+	2.90001i	−0.870490	+	0.483335i
$37$	3.38813	−	3.38813i	0.557006	−	0.557006i	−0.371448	−	0.928454i	$-0.621139\pi$
$37$	3.38813	−	3.38813i	0.557006	−	0.557006i	0.928454	+	0.371448i	$0.121139\pi$
$38$	−1.09699	−	6.06602i	−0.177956	−	0.984038i
$39$	−0.386325			−0.0618614
$40$	5.94004	−	2.17162i	0.939203	−	0.343363i
$41$	−1.76413	−	10.0049i	−0.275511	−	1.56250i	−0.737334	−	0.675528i	$-0.763916\pi$
$41$	−1.76413	−	10.0049i	−0.275511	−	1.56250i	0.461823	−	0.886972i	$-0.347195\pi$
$42$	0.694832	−	0.393445i	0.107215	−	0.0607099i
$43$	0.818125	−	9.35121i	0.124763	−	1.42605i	−0.633321	−	0.773889i	$-0.718309\pi$
$43$	0.818125	−	9.35121i	0.124763	−	1.42605i	0.758084	−	0.652157i	$-0.226136\pi$
$44$	0.678270	+	0.836371i	0.102253	+	0.126088i
$45$	−6.33478	−	2.11707i	−0.944334	−	0.315595i
$46$	0.830548	−	1.16527i	0.122458	−	0.171809i
$47$	−1.90980	−	0.890557i	−0.278574	−	0.129901i	0.278311	−	0.960491i	$-0.410226\pi$
$47$	−1.90980	−	0.890557i	−0.278574	−	0.129901i	−0.556884	+	0.830590i	$0.688003\pi$
$48$	−0.435976	−	0.132610i	−0.0629278	−	0.0191406i
$49$	15.2098	−	8.78138i	2.17283	−	1.25448i
$50$	6.27561	+	3.25833i	0.887505	+	0.460798i
$51$	−0.675605	−	0.119127i	−0.0946036	−	0.0166812i
$52$	4.71474	+	4.87528i	0.653817	+	0.676079i
$53$	0.411241	+	4.70050i	0.0564883	+	0.645664i	0.970679	+	0.240380i	$0.0772719\pi$
$53$	0.411241	+	4.70050i	0.0564883	+	0.645664i	−0.914191	+	0.405284i	$0.867173\pi$
$54$	0.546634	+	0.794749i	0.0743875	+	0.108152i
$55$	−0.177528	+	1.19077i	−0.0239378	+	0.160564i
$56$	−13.4449	−	3.96688i	−1.79665	−	0.530097i
$57$	−0.477988	+	0.134628i	−0.0633110	+	0.0178320i
$58$	−5.35871	−	2.00136i	−0.703633	−	0.262791i
$59$	−10.8840	−	3.96146i	−1.41698	−	0.515739i	−0.483810	−	0.875173i	$-0.660748\pi$
$59$	−10.8840	−	3.96146i	−1.41698	−	0.515739i	−0.933170	+	0.359434i	$0.882970\pi$
$60$	−0.219832	−	0.459619i	−0.0283802	−	0.0593366i
$61$	3.37282	+	2.83013i	0.431845	+	0.362361i	0.832647	−	0.553804i	$-0.186824\pi$
$61$	3.37282	+	2.83013i	0.431845	+	0.362361i	−0.400803	+	0.916164i	$0.631269\pi$
$62$	−0.213452	+	0.0756733i	−0.0271085	+	0.00961052i
$63$	8.49118	+	12.1267i	1.06979	+	1.52782i
$64$	3.64721	+	7.12024i	0.455901	+	0.890030i
$65$	−0.460207	+	7.56866i	−0.0570816	+	0.938776i
$66$	0.0618500	−	0.0608233i	0.00761320	−	0.00748683i
$67$	6.00106	+	2.79834i	0.733146	+	0.341872i	0.753079	−	0.657930i	$-0.228568\pi$
$67$	6.00106	+	2.79834i	0.733146	+	0.341872i	−0.0199332	+	0.999801i	$0.506345\pi$
$68$	6.74180	+	9.97973i	0.817563	+	1.21022i
$69$	−0.0998301	−	0.0576369i	−0.0120181	−	0.00693867i
$70$	−6.88044	−	14.0814i	−0.822370	−	1.68305i
$71$	4.11104	+	4.89935i	0.487891	+	0.581445i	0.952680	−	0.303976i	$-0.0983143\pi$
$71$	4.11104	+	4.89935i	0.487891	+	0.581445i	−0.464789	+	0.885421i	$0.653870\pi$
$72$	1.67549	−	8.28077i	0.197459	−	0.975898i
$73$	−2.80477	+	4.00563i	−0.328274	+	0.468824i	−0.949033	−	0.315178i	$-0.897936\pi$
$73$	−2.80477	+	4.00563i	−0.328274	+	0.468824i	0.620759	+	0.784002i	$0.286825\pi$
$74$	0.534075	+	6.75519i	0.0620850	+	0.785275i
$75$	0.213007	−	0.528297i	0.0245960	−	0.0610025i
$76$	7.53237	+	4.38901i	0.864022	+	0.503454i
$77$	1.88687	−	1.88687i	0.215028	−	0.215028i
$78$	0.354674	−	0.415571i	0.0401590	−	0.0470542i
$79$	−1.74573	−	9.90050i	−0.196409	−	1.11389i	−0.910397	−	0.413735i	$-0.864224\pi$
$79$	−1.74573	−	9.90050i	−0.196409	−	1.11389i	0.713988	−	0.700158i	$-0.246887\pi$
$80$	−3.11737	+	8.38344i	−0.348533	+	0.937297i
$81$	−6.80505	+	5.71011i	−0.756116	+	0.634457i
$82$	12.3819	+	7.28754i	1.36735	+	0.804774i
$83$	0.0751360	+	0.280411i	0.00824725	+	0.0307792i	0.969927	−	0.243397i	$-0.0782617\pi$
$83$	0.0751360	+	0.280411i	0.00824725	+	0.0307792i	−0.961680	+	0.274176i	$0.911595\pi$
$84$	−0.214676	+	1.10865i	−0.0234231	+	0.120963i
$85$	−3.13869	+	13.0942i	−0.340438	+	1.42026i
$86$	9.30805	+	9.46517i	1.00371	+	1.02066i
$87$	−0.119265	+	0.445103i	−0.0127865	+	0.0477201i
$88$	−1.52239	−	0.0382310i	−0.162287	−	0.00407544i
$89$	−6.80756	−	1.20036i	−0.721600	−	0.127238i	−0.199226	−	0.979954i	$-0.563843\pi$
$89$	−6.80756	−	1.20036i	−0.721600	−	0.127238i	−0.522375	+	0.852716i	$0.674954\pi$
$90$	8.09314	−	4.87073i	0.853092	−	0.513420i
$91$	10.8029	−	12.8744i	1.13245	−	1.34961i
$92$	0.490979	+	1.96323i	0.0511881	+	0.204680i
$93$	0.00771009	+	0.0165343i	0.000799499	+	0.00171453i
$94$	2.71132	−	1.23679i	0.279651	−	0.127565i
$95$	2.06817	+	9.52485i	0.212189	+	0.977229i
$96$	0.542907	−	0.347236i	0.0554103	−	0.0354397i
$97$	2.84664	−	1.32741i	0.289033	−	0.134778i	−0.272695	−	0.962101i	$-0.587915\pi$
$97$	2.84664	−	1.32741i	0.289033	−	0.134778i	0.561727	+	0.827323i	$0.310137\pi$
$98$	−4.51754	+	24.4232i	−0.456340	+	2.46712i
$99$	1.23200	+	1.03377i	0.123820	+	0.103898i
$100$	−9.26648	+	3.75931i	−0.926648	+	0.375931i
$101$	−1.58028	+	8.96220i	−0.157244	+	0.891773i	0.799462	+	0.600716i	$0.205118\pi$
$101$	−1.58028	+	8.96220i	−0.157244	+	0.891773i	−0.956706	+	0.291056i	$0.905993\pi$
$102$	0.748401	−	0.617384i	0.0741027	−	0.0611301i
$103$	−10.3198	−	2.76517i	−1.01684	−	0.272460i	−0.288353	−	0.957524i	$-0.593108\pi$
$103$	−10.3198	−	2.76517i	−1.01684	−	0.272460i	−0.728483	+	0.685064i	$0.759774\pi$
$104$	−9.57284	+	0.595808i	−0.938694	+	0.0584237i
$105$	−1.07625	+	0.660053i	−0.105031	+	0.0644146i
$106$	−5.43390	−	3.87303i	−0.527787	−	0.376182i
$107$	−10.9203	+	2.92609i	−1.05571	+	0.282875i	−0.744608	−	0.667503i	$-0.767363\pi$
$107$	−10.9203	+	2.92609i	−1.05571	+	0.282875i	−0.311098	+	0.950378i	$0.600697\pi$
$108$	−1.35677	−	0.141621i	−0.130555	−	0.0136275i
$109$	−0.505235	−	0.602116i	−0.0483928	−	0.0576722i	0.741305	−	0.671168i	$-0.234207\pi$
$109$	−0.505235	−	0.602116i	−0.0483928	−	0.0576722i	−0.789698	+	0.613496i	$0.789763\pi$
$110$	−1.11794	−	1.28419i	−0.106591	−	0.122442i
$111$	0.537581	−	0.0947901i	0.0510250	−	0.00899708i
$112$	16.6106	−	10.8209i	1.56956	−	1.02248i
$113$	4.67720	+	4.67720i	0.439994	+	0.439994i	0.892010	−	0.452016i	$-0.149295\pi$
$113$	4.67720	+	4.67720i	0.439994	+	0.439994i	−0.452016	+	0.892010i	$0.649295\pi$
$114$	0.294007	−	0.637773i	0.0275363	−	0.0597329i
$115$	−1.24811	+	1.88716i	−0.116387	+	0.175978i
$116$	7.07256	−	3.92700i	0.656671	−	0.364613i
$117$	8.29732	+	5.80985i	0.767088	+	0.537121i
$118$	14.2537	−	8.07109i	1.31216	−	0.743004i
$119$	22.8621	−	19.1836i	2.09577	−	1.75856i
$120$	0.696237	+	0.185490i	0.0635574	+	0.0169328i
$121$	−5.35505	+	9.27523i	−0.486823	+	0.843202i
$122$	−6.14087	+	1.02989i	−0.555969	+	0.0932416i
$123$	0.489132	−	1.04895i	0.0441035	−	0.0945803i
$124$	0.114563	−	0.299085i	0.0102880	−	0.0268586i
$125$	−10.0964	−	4.80245i	−0.903046	−	0.429544i
$126$	−20.8402	−	1.99917i	−1.85660	−	0.178100i
$127$	13.8511	−	9.69862i	1.22908	−	0.860613i	0.235297	−	0.971923i	$-0.424394\pi$
$127$	13.8511	−	9.69862i	1.22908	−	0.860613i	0.993786	+	0.111310i	$0.0355047\pi$
$128$	−11.0077	−	2.61359i	−0.972951	−	0.231011i
$129$	0.687398	−	0.819210i	0.0605221	−	0.0721274i
$130$	−7.71914	−	7.44363i	−0.677013	−	0.652850i
$131$	1.47594	−	4.05511i	0.128954	−	0.354297i	−0.858367	−	0.513036i	$-0.828521\pi$
$131$	1.47594	−	4.05511i	0.128954	−	0.354297i	0.987321	+	0.158739i	$0.0507429\pi$
$132$	0.00864507	+	0.122373i	0.000752457	+	0.0106512i
$133$	8.87958	−	19.6938i	0.769957	−	1.70767i
$134$	−8.51960	+	3.88629i	−0.735982	+	0.335724i
$135$	−0.907633	−	1.22568i	−0.0781166	−	0.105490i
$136$	−16.9247	−	1.90994i	−1.45128	−	0.163776i
$137$	−2.14498	+	0.187662i	−0.183258	+	0.0160330i	−0.178415	−	0.983955i	$-0.557097\pi$
$137$	−2.14498	+	0.187662i	−0.183258	+	0.0160330i	−0.00484290	+	0.999988i	$0.501542\pi$
$138$	0.153652	−	0.0544728i	0.0130797	−	0.00463703i
$139$	1.28196	−	7.27036i	0.108734	−	0.616664i	−0.880928	−	0.473250i	$-0.843081\pi$
$139$	1.28196	−	7.27036i	0.108734	−	0.616664i	0.989663	−	0.143414i	$-0.0458081\pi$
$140$	21.4642	+	5.52648i	1.81406	+	0.467073i
$141$	−0.120033	−	0.207903i	−0.0101086	−	0.0175086i
$142$	−9.04449	−	0.0756958i	−0.758996	−	0.00635225i
$143$	0.771616	−	1.65474i	0.0645258	−	0.138376i
$144$	7.36943	+	9.40469i	0.614120	+	0.783724i
$145$	8.57814	+	2.86680i	0.712376	+	0.238075i
$146$	−1.73389	−	6.69458i	−0.143498	−	0.554047i
$147$	1.99321	+	0.174384i	0.164398	+	0.0143829i
$148$	−7.75691	−	5.62725i	−0.637614	−	0.462557i
$149$	4.99565	−	0.880868i	0.409260	−	0.0721635i	0.0347717	−	0.999395i	$-0.488930\pi$
$149$	4.99565	−	0.880868i	0.409260	−	0.0721635i	0.374488	+	0.927232i	$0.377818\pi$
$150$	0.372735	+	0.714149i	0.0304337	+	0.0583100i
$151$			19.8959i			1.61910i	0.587049	+	0.809551i	$0.300290\pi$
$151$			19.8959i			1.61910i	−0.587049	+	0.809551i	$0.699710\pi$
$152$	−11.6366	+	4.07317i	−0.943849	+	0.330378i
$153$	12.7188	+	12.7188i	1.02826	+	1.02826i
$154$	0.297429	+	3.76200i	0.0239675	+	0.303150i
$155$	0.333116	−	0.131355i	0.0267565	−	0.0105507i
$156$	0.121415	+	0.763050i	0.00972095	+	0.0610929i
$157$	1.31786	−	15.0632i	0.105176	−	1.20217i	−0.741830	−	0.670588i	$-0.766042\pi$
$157$	1.31786	−	15.0632i	0.105176	−	1.20217i	0.847006	−	0.531583i	$-0.178403\pi$
$158$	12.2527	+	7.21150i	0.974774	+	0.573716i
$159$	−0.268774	+	0.465530i	−0.0213152	+	0.0369190i
$160$	−6.15613	−	11.0500i	−0.486684	−	0.873578i
$161$	4.71235	−	1.71516i	0.371386	−	0.135173i
$162$	0.105139	−	12.5625i	0.00826052	−	0.987005i
$163$	−6.16061	−	1.65073i	−0.482536	−	0.129295i	0.00934727	−	0.999956i	$-0.497025\pi$
$163$	−6.16061	−	1.65073i	−0.482536	−	0.129295i	−0.491883	+	0.870661i	$0.663691\pi$
$164$	−19.2067	+	6.62878i	−1.49979	+	0.517620i
$165$	−0.0943776	+	0.0995243i	−0.00734728	+	0.00774796i
$166$	−0.370620	−	0.176614i	−0.0287657	−	0.0137079i
$167$	1.28396	+	14.6758i	0.0993562	+	1.13565i	0.868202	+	0.496212i	$0.165276\pi$
$167$	1.28396	+	14.6758i	0.0993562	+	1.13565i	−0.768845	+	0.639435i	$0.779168\pi$
$168$	−0.995486	−	1.24875i	−0.0768034	−	0.0963428i
$169$	−0.513279	+	1.41022i	−0.0394830	+	0.108479i
$170$	−11.2039	−	15.3977i	−0.859301	−	1.18095i
$171$	12.2907	+	4.29685i	0.939891	+	0.328589i
$172$	−18.7272	+	1.32299i	−1.42794	+	0.100877i
$173$	−5.18908	−	11.1280i	−0.394518	−	0.846047i	−0.998786	−	0.0492654i	$-0.984312\pi$
$173$	−5.18908	−	11.1280i	−0.394518	−	0.846047i	0.604268	−	0.796781i	$-0.293466\pi$
$174$	−0.369305	−	0.536931i	−0.0279970	−	0.0407047i
$175$	11.6493	+	21.8715i	0.880606	+	1.65333i
$176$	1.43879	−	1.60254i	0.108453	−	0.120796i
$177$	−0.756855	−	1.08090i	−0.0568887	−	0.0812455i
$178$	7.54107	−	6.22091i	0.565227	−	0.466277i
$179$	−8.26327	−	14.3124i	−0.617626	−	1.06976i	−0.989918	−	0.141644i	$-0.954761\pi$
$179$	−8.26327	−	14.3124i	−0.617626	−	1.06976i	0.372292	−	0.928116i	$-0.378572\pi$
$180$	−2.19064	+	13.1775i	−0.163281	+	0.982194i
$181$	2.50283	−	0.910957i	0.186034	−	0.0677109i	−0.247323	−	0.968933i	$-0.579551\pi$
$181$	2.50283	−	0.910957i	0.186034	−	0.0677109i	0.433358	+	0.901222i	$0.357329\pi$
$182$	3.93120	+	23.4404i	0.291400	+	1.73752i
$183$	0.129823	+	0.484506i	0.00959680	+	0.0358157i
$184$	−2.56261	−	1.27424i	−0.188918	−	0.0939380i
$185$	−1.21668	−	10.6449i	−0.0894525	−	0.782630i
$186$	−0.0248645	−	0.00688596i	−0.00182315	−	0.000504903i
$187$	1.85966	−	2.65587i	0.135992	−	0.194216i
$188$	−1.15877	+	4.05204i	−0.0845119	+	0.295525i
$189$			3.38039i			0.245887i
$190$	−12.1447	−	6.51977i	−0.881066	−	0.472994i
$191$		−	4.97986i		−	0.360330i	−0.983636	−	0.180165i	$-0.942337\pi$
$191$		−	4.97986i		−	0.360330i	0.983636	−	0.180165i	$-0.0576631\pi$
$192$	−0.124905	+	0.902797i	−0.00901426	+	0.0651537i
$193$	2.67179	−	3.81571i	0.192319	−	0.274661i	−0.711399	−	0.702789i	$-0.751938\pi$
$193$	2.67179	−	3.81571i	0.192319	−	0.274661i	0.903718	+	0.428128i	$0.140827\pi$
$194$	−1.18552	+	4.28081i	−0.0851157	+	0.307344i
$195$	−0.537517	+	0.676247i	−0.0384924	+	0.0484270i
$196$	−22.1247	−	27.2818i	−1.58034	−	1.94870i
$197$	2.87544	+	10.7313i	0.204867	+	0.764573i	0.989490	+	0.144600i	$0.0461896\pi$
$197$	2.87544	+	10.7313i	0.204867	+	0.764573i	−0.784624	+	0.619972i	$0.787144\pi$
$198$	−2.24310	+	0.376190i	−0.159410	+	0.0267347i
$199$	−7.44457	+	2.70960i	−0.527731	+	0.192079i	−0.592125	−	0.805846i	$-0.701711\pi$
$199$	−7.44457	+	2.70960i	−0.527731	+	0.192079i	0.0643937	+	0.997925i	$0.479489\pi$
$200$	4.46340	−	13.4193i	0.315610	−	0.948889i
$201$	0.377172	+	0.653281i	0.0266037	+	0.0460789i
$202$	−8.18987	−	9.92788i	−0.576237	−	0.698523i
$203$	−11.4982	−	16.4211i	−0.807015	−	1.15254i
$204$	−0.0229646	+	1.37186i	−0.00160784	+	0.0960496i
$205$	−19.9677	−	10.8324i	−1.39461	−	0.756564i
$206$	12.4488	−	8.56238i	0.867349	−	0.596570i
$207$	1.27732	+	2.73922i	0.0887800	+	0.190389i
$208$	8.14766	−	10.8445i	0.564938	−	0.751934i
$209$	0.378046	−	2.31625i	0.0261500	−	0.160218i
$210$	0.278051	−	1.76370i	0.0191873	−	0.121707i
$211$	7.81684	−	21.4766i	0.538133	−	1.47851i	−0.311041	−	0.950396i	$-0.600678\pi$
$211$	7.81684	−	21.4766i	0.538133	−	1.47851i	0.849174	−	0.528112i	$-0.177100\pi$
$212$	9.15497	−	2.28954i	0.628766	−	0.157247i
$213$	0.0635035	+	0.725848i	0.00435119	+	0.0497343i
$214$	6.87804	−	14.4334i	0.470173	−	0.986646i
$215$	−15.2306	−	14.4430i	−1.03872	−	0.985005i
$216$	1.39795	−	1.32946i	0.0951187	−	0.0904584i
$217$	−0.766613	−	0.205413i	−0.0520411	−	0.0139444i
$218$	1.11154	+	0.00930280i	0.0752831	+	0.000630065i
$219$	−0.523492	+	0.190535i	−0.0353743	+	0.0128752i
$220$	2.40775	−	0.0235939i	0.162331	−	0.00159070i
$221$	10.2101	−	17.6844i	0.686805	−	1.18958i
$222$	−0.391573	+	0.665303i	−0.0262807	+	0.0446522i
$223$	−0.369258	+	4.22064i	−0.0247273	+	0.282635i	0.973757	+	0.227592i	$0.0730851\pi$
$223$	−0.369258	+	4.22064i	−0.0247273	+	0.282635i	−0.998484	+	0.0550430i	$0.982470\pi$
$224$	−3.60971	+	27.8025i	−0.241184	+	1.85763i
$225$	−12.5198	+	8.14318i	−0.834655	+	0.542879i
$226$	−9.32530	+	0.737272i	−0.620310	+	0.0490426i
$227$	−16.8207	−	16.8207i	−1.11643	−	1.11643i	−0.992261	−	0.124166i	$-0.960374\pi$
$227$	−16.8207	−	16.8207i	−1.11643	−	1.11643i	−0.124166	−	0.992261i	$-0.539626\pi$
$228$	0.416134	+	0.901787i	0.0275592	+	0.0597223i
$229$			29.2338i			1.93182i	0.258871	+	0.965912i	$0.416650\pi$
$229$			29.2338i			1.93182i	−0.258871	+	0.965912i	$0.583350\pi$
$230$	−0.884163	−	3.07515i	−0.0583000	−	0.202769i
$231$	0.299382	−	0.0527890i	0.0196979	−	0.00347326i
$232$	−2.26884	+	11.2133i	−0.148957	+	0.736186i
$233$	−14.4139	−	1.26106i	−0.944288	−	0.0826145i	−0.395399	−	0.918509i	$-0.629394\pi$
$233$	−14.4139	−	1.26106i	−0.944288	−	0.0826145i	−0.548889	+	0.835895i	$0.684949\pi$
$234$	−13.8672	+	3.59160i	−0.906530	+	0.234790i
$235$	−4.21611	+	2.10396i	−0.275029	+	0.137247i
$236$	−4.40385	+	22.7426i	−0.286666	+	1.48042i
$237$	0.484029	−	1.03800i	0.0314410	−	0.0674255i
$238$	−0.353224	+	42.2049i	−0.0228961	+	2.73573i
$239$	9.48320	+	16.4254i	0.613417	+	1.06247i	0.990660	+	0.136356i	$0.0435390\pi$
$239$	9.48320	+	16.4254i	0.613417	+	1.06247i	−0.377242	+	0.926115i	$0.623128\pi$
$240$	−0.838729	+	0.578652i	−0.0541397	+	0.0373518i
$241$	−1.87390	+	10.6274i	−0.120708	+	0.684572i	0.863056	+	0.505108i	$0.168547\pi$
$241$	−1.87390	+	10.6274i	−0.120708	+	0.684572i	−0.983765	+	0.179464i	$0.942564\pi$
$242$	−5.06107	−	14.2758i	−0.325338	−	0.917683i
$243$	−3.04660	+	0.266543i	−0.195440	+	0.0170987i
$244$	4.52992	−	7.55128i	0.289998	−	0.483421i
$245$	5.79083	−	38.8422i	0.369963	−	2.48154i
$246$	0.679298	+	1.48917i	0.0433105	+	0.0949461i
$247$	1.10050	−	14.7403i	0.0700234	−	0.937900i
$248$	0.216550	+	0.397818i	0.0137510	+	0.0252615i
$249$	−0.0113115	+	0.0310781i	−0.000716838	+	0.00196950i
$250$	14.4352	−	6.45170i	0.912963	−	0.408041i
$251$	4.71883	−	5.62368i	0.297850	−	0.354963i	−0.596276	−	0.802779i	$-0.703354\pi$
$251$	4.71883	−	5.62368i	0.297850	−	0.354963i	0.894126	+	0.447816i	$0.147798\pi$
$252$	21.2834	−	20.5826i	1.34073	−	1.29658i
$253$	0.446268	−	0.312480i	0.0280566	−	0.0196455i
$254$	−2.28345	+	23.8037i	−0.143276	+	1.49358i
$255$	−1.14854	+	1.01687i	−0.0719242	+	0.0636790i
$256$	12.9173	−	9.44155i	0.807332	−	0.590097i
$257$	−8.01086	+	17.1793i	−0.499704	+	1.07162i	0.481108	+	0.876661i	$0.340234\pi$
$257$	−8.01086	+	17.1793i	−0.499704	+	1.07162i	−0.980812	+	0.194957i	$0.937543\pi$
$258$	0.250145	+	1.49153i	0.0155734	+	0.0928588i
$259$	−11.8736	+	20.5658i	−0.737793	+	1.27789i
$260$	15.0939	−	1.46971i	0.936083	−	0.0911476i
$261$	9.25533	−	7.76614i	0.572890	−	0.480712i
$262$	3.00708	+	5.31057i	0.185778	+	0.328088i
$263$	−19.0413	−	13.3329i	−1.17414	−	0.822140i	−0.187054	−	0.982350i	$-0.559894\pi$
$263$	−19.0413	−	13.3329i	−1.17414	−	0.822140i	−0.987083	+	0.160210i	$0.948783\pi$
$264$	−0.139574	−	0.103047i	−0.00859016	−	0.00634213i
$265$	8.80024	+	5.82023i	0.540594	+	0.357534i
$266$	13.0326	+	27.6322i	0.799080	+	1.69424i
$267$	−0.556855	−	0.556855i	−0.0340790	−	0.0340790i
$268$	3.64113	−	12.7325i	0.222417	−	0.777760i
$269$	−9.44223	+	1.66492i	−0.575703	+	0.101512i	−0.453916	−	0.891044i	$-0.649973\pi$
$269$	−9.44223	+	1.66492i	−0.575703	+	0.101512i	−0.121787	+	0.992556i	$0.538862\pi$
$270$	2.15174	+	0.148919i	0.130951	+	0.00906295i
$271$	8.61319	+	10.2648i	0.523214	+	0.623542i	0.961338	−	0.275373i	$-0.0888012\pi$
$271$	8.61319	+	10.2648i	0.523214	+	0.623542i	−0.438124	+	0.898915i	$0.644357\pi$
$272$	17.5927	−	16.4525i	1.06671	−	0.997581i
$273$	1.84942	−	0.495550i	0.111932	−	0.0299920i
$274$	1.76738	−	2.47966i	0.106772	−	0.149802i
$275$	1.83740	+	1.96755i	0.110799	+	0.118648i
$276$	−0.0824670	+	0.215294i	−0.00496393	+	0.0129592i
$277$	−11.5542	−	3.09593i	−0.694223	−	0.186016i	−0.105581	−	0.994411i	$-0.533670\pi$
$277$	−11.5542	−	3.09593i	−0.694223	−	0.186016i	−0.588641	+	0.808394i	$0.700337\pi$
$278$	6.64382	+	8.05374i	0.398470	+	0.483031i
$279$	0.0830620	−	0.471068i	0.00497279	−	0.0282021i
$280$	−25.6506	+	18.0155i	−1.53292	+	1.07663i
$281$	8.69686	+	7.29754i	0.518811	+	0.435334i	0.864217	−	0.503119i	$-0.167814\pi$
$281$	8.69686	+	7.29754i	0.518811	+	0.435334i	−0.345406	+	0.938453i	$0.612259\pi$
$282$	0.333842	+	0.0617504i	0.0198800	+	0.00367718i
$283$	19.4090	−	9.05055i	1.15374	−	0.537999i	0.250918	−	0.968008i	$-0.419267\pi$
$283$	19.4090	−	9.05055i	1.15374	−	0.537999i	0.902825	+	0.430009i	$0.141490\pi$
$284$	8.38493	−	9.65970i	0.497554	−	0.573198i
$285$	−0.429391	+	1.02402i	−0.0254349	+	0.0606575i
$286$	1.07161	+	2.34920i	0.0633655	+	0.138911i
$287$	21.2788	+	45.6326i	1.25605	+	2.69360i
$288$	−16.8824	−	0.706861i	−0.994802	−	0.0416522i
$289$	12.3812	−	14.7553i	0.728305	−	0.867961i
$290$	−10.9592	+	6.59561i	−0.643546	+	0.387308i
$291$	0.352392	+	0.0621361i	0.0206576	+	0.00364249i
$292$	8.79322	+	4.28096i	0.514585	+	0.250524i
$293$	−1.36368	+	5.08932i	−0.0796670	+	0.297321i	−0.994251	−	0.107075i	$-0.965852\pi$
$293$	−1.36368	+	5.08932i	−0.0796670	+	0.297321i	0.914584	+	0.404396i	$0.132518\pi$
$294$	−2.01750	+	1.98401i	−0.117663	+	0.115710i
$295$	−22.0780	+	13.5403i	−1.28543	+	0.788345i
$296$	13.1747	−	3.17791i	0.765763	−	0.184712i
$297$	0.0950478	+	0.354723i	0.00551523	+	0.0205831i
$298$	−3.63882	+	6.18255i	−0.210791	+	0.358145i
$299$	2.62847	−	2.20555i	0.152008	−	0.127550i
$300$	−1.11041	−	0.254688i	−0.0641096	−	0.0147044i
$301$	8.07853	+	45.8156i	0.465639	+	2.64077i
$302$	−21.4021	−	18.2659i	−1.23155	−	1.05108i
$303$	−0.733104	+	0.733104i	−0.0421157	+	0.0421157i
$304$	6.30168	−	16.2570i	0.361426	−	0.932401i
$305$	9.64683	−	1.96626i	0.552376	−	0.112588i
$306$	−25.3585	+	2.00488i	−1.44965	+	0.114612i
$307$	5.80176	−	8.28577i	0.331124	−	0.472894i	−0.618723	−	0.785609i	$-0.712350\pi$
$307$	5.80176	−	8.28577i	0.331124	−	0.472894i	0.949847	+	0.312715i	$0.101239\pi$
$308$	−4.31986	−	3.13384i	−0.246147	−	0.178567i
$309$	−0.782367	−	0.932389i	−0.0445073	−	0.0530417i
$310$	−0.164526	+	0.478929i	−0.00934443	+	0.0272013i
$311$	19.6631	+	11.3525i	1.11499	+	0.643740i	0.940117	−	0.340851i	$-0.110715\pi$
$311$	19.6631	+	11.3525i	1.11499	+	0.643740i	0.174873	+	0.984591i	$0.444049\pi$
$312$	−0.932284	−	0.569930i	−0.0527802	−	0.0322659i
$313$	−8.00590	−	3.73321i	−0.452520	−	0.211014i	0.182976	−	0.983117i	$-0.441427\pi$
$313$	−8.00590	−	3.73321i	−0.452520	−	0.211014i	−0.635497	+	0.772104i	$0.719205\pi$
$314$	14.9936	+	15.2467i	0.846139	+	0.860422i
$315$	33.0416	+	2.00907i	1.86168	+	0.113198i
$316$	−19.0063	+	6.55962i	−1.06919	+	0.369007i
$317$	−2.73259	−	3.90254i	−0.153477	−	0.219188i	0.735049	−	0.678014i	$-0.237159\pi$
$317$	−2.73259	−	3.90254i	−0.153477	−	0.219188i	−0.888526	+	0.458826i	$0.848270\pi$
$318$	−0.254019	−	0.716513i	−0.0142447	−	0.0401800i
$319$	−1.66829	−	1.39986i	−0.0934063	−	0.0783772i
$320$	17.5383	+	3.52252i	0.980421	+	0.196915i
$321$	−1.21030	−	0.440514i	−0.0675525	−	0.0245871i
$322$	−2.48129	+	6.64374i	−0.138277	+	0.370241i
$323$	6.46988	−	25.4384i	0.359994	−	1.41543i
$324$	13.4170	+	11.6464i	0.745391	+	0.647024i
$325$	12.6083	+	11.3363i	0.699384	+	0.628825i
$326$	7.43159	−	5.11150i	0.411598	−	0.283100i
$327$	−0.00780440	−	0.0892046i	−0.000431584	−	0.00493303i
$328$	10.5026	−	26.7465i	0.579909	−	1.47683i
$329$	10.2850	+	1.81352i	0.567029	+	0.0999825i
$330$	−0.0204133	−	0.192893i	−0.00112371	−	0.0106184i
$331$	−5.61891	+	3.24408i	−0.308843	+	0.178311i	−0.646409	−	0.762991i	$-0.723730\pi$
$331$	−5.61891	+	3.24408i	−0.308843	+	0.178311i	0.337565	+	0.941302i	$0.390397\pi$
$332$	0.530242	−	0.236533i	0.0291008	−	0.0129814i
$333$	−12.9715	−	6.04870i	−0.710833	−	0.331467i
$334$	−16.9656	−	12.0923i	−0.928315	−	0.661660i
$335$	13.2480	−	6.61113i	0.723817	−	0.361205i
$336$	2.25721	+	0.0755914i	0.123141	+	0.00412385i
$337$	−0.575824	+	6.58170i	−0.0313671	+	0.358528i	0.964249	+	0.264997i	$0.0853710\pi$
$337$	−0.575824	+	6.58170i	−0.0313671	+	0.358528i	−0.995616	+	0.0935309i	$0.970185\pi$
$338$	−1.04576	−	1.84682i	−0.0568816	−	0.100454i
$339$	0.130854	+	0.742112i	0.00710704	+	0.0403060i
$340$	26.8494	+	2.08413i	1.45611	+	0.113028i
$341$	−0.0862208			−0.00466912
$342$	−15.9059	+	9.27631i	−0.860092	+	0.501605i
$343$	−37.0169	+	37.0169i	−1.99873	+	1.99873i
$344$	15.7698	−	21.3595i	0.850250	−	1.15163i
$345$	−0.239791	+	0.0945550i	−0.0129099	+	0.00509067i
$346$	16.7344	+	4.63442i	0.899647	+	0.249148i
$347$	−18.4077	−	1.61047i	−0.988178	−	0.0864543i	−0.418408	−	0.908259i	$-0.637412\pi$
$347$	−18.4077	−	1.61047i	−0.988178	−	0.0864543i	−0.569769	+	0.821805i	$0.692967\pi$
$348$	0.916629	+	0.0956789i	0.0491365	+	0.00512893i
$349$	1.39943	+	0.807963i	0.0749100	+	0.0432493i	0.536987	−	0.843590i	$-0.319562\pi$
$349$	1.39943	+	0.807963i	0.0749100	+	0.0432493i	−0.462077	+	0.886840i	$0.652896\pi$
$350$	−34.2222	−	7.54841i	−1.82925	−	0.403480i
$351$	0.791070	+	2.17345i	0.0422242	+	0.116010i
$352$	0.402947	+	3.01897i	0.0214771	+	0.160912i
$353$	5.33746	−	19.9197i	0.284084	−	1.06022i	−0.665422	−	0.746468i	$-0.731748\pi$
$353$	5.33746	−	19.9197i	0.284084	−	1.06022i	0.949506	−	0.313749i	$-0.101585\pi$
$354$	1.85758	+	0.178194i	0.0987292	+	0.00947091i
$355$	14.2961	−	0.379463i	0.758756	−	0.0201398i
$356$	−0.231397	+	13.8232i	−0.0122640	+	0.732630i
$357$	3.38707	−	0.296330i	0.179263	−	0.0156835i
$358$	22.9822	+	4.25100i	1.21465	+	0.224672i
$359$	−12.6991	−	4.62210i	−0.670233	−	0.243945i	−0.0155851	−	0.999879i	$-0.504961\pi$
$359$	−12.6991	−	4.62210i	−0.670233	−	0.243945i	−0.654648	+	0.755934i	$0.727183\pi$
$360$	−12.1640	−	14.4544i	−0.641097	−	0.761815i
$361$	−3.77514	−	18.6212i	−0.198692	−	0.980062i
$362$	−1.31787	+	3.52864i	−0.0692655	+	0.185461i
$363$	−1.10583	+	0.515655i	−0.0580408	+	0.0270649i
$364$	−28.8241	−	17.2912i	−1.51079	−	0.906306i
$365$	3.10926	+	10.4829i	0.162746	+	0.548702i
$366$	−0.640373	−	0.305161i	−0.0334728	−	0.0159510i
$367$	−25.5106	+	17.8627i	−1.33164	+	0.932426i	−0.999940	−	0.0109586i	$-0.996512\pi$
$367$	−25.5106	+	17.8627i	−1.33164	+	0.932426i	−0.331702	+	0.943384i	$0.607623\pi$
$368$	3.72336	−	1.58676i	0.194094	−	0.0827157i
$369$	−26.2802	+	15.1729i	−1.36810	+	0.789870i
$370$	12.5678	+	8.46402i	0.653368	+	0.440024i
$371$	−7.99816	−	21.9748i	−0.415244	−	1.14087i
$372$	0.0302347	−	0.0204250i	0.00156760	−	0.00105899i
$373$	−27.8969	+	7.47496i	−1.44445	+	0.387039i	−0.894089	−	0.447889i	$-0.852176\pi$
$373$	−27.8969	+	7.47496i	−1.44445	+	0.387039i	−0.550359	+	0.834928i	$0.685509\pi$
$374$	1.14963	+	4.43873i	0.0594458	+	0.229521i
$375$	−0.628394	−	1.10791i	−0.0324501	−	0.0572124i
$376$	−3.29496	−	4.96657i	−0.169925	−	0.256131i
$377$	−11.2357	−	7.86731i	−0.578667	−	0.405187i
$378$	−3.63630	−	3.10344i	−0.187031	−	0.159624i
$379$	36.5913			1.87957			0.939784	−	0.341769i	$-0.111026\pi$
$379$	36.5913			1.87957			0.939784	+	0.341769i	$0.111026\pi$
$380$	18.1630	−	7.07843i	0.931744	−	0.363116i
$381$	1.92635			0.0986900
$382$	5.35686	+	4.57187i	0.274081	+	0.233917i
$383$	13.9897	+	9.79571i	0.714841	+	0.500537i	0.873517	−	0.486793i	$-0.161834\pi$
$383$	13.9897	+	9.79571i	0.714841	+	0.500537i	−0.158676	+	0.987331i	$0.550722\pi$
$384$	−0.856470	−	0.963195i	−0.0437066	−	0.0491528i
$385$	−0.677577	−	5.92820i	−0.0345325	−	0.302129i
$386$	1.65168	+	6.37716i	0.0840682	+	0.324589i
$387$	−27.0836	+	7.25702i	−1.37674	+	0.368895i
$388$	−3.51648	−	5.20537i	−0.178522	−	0.264263i
$389$	−1.59928	−	4.39399i	−0.0810868	−	0.222784i	0.892524	−	0.451001i	$-0.148933\pi$
$389$	−1.59928	−	4.39399i	−0.0810868	−	0.222784i	−0.973610	+	0.228217i	$0.926711\pi$
$390$	−0.233962	−	1.19905i	−0.0118471	−	0.0607164i
$391$	5.27677	−	3.04655i	0.266858	−	0.154070i
$392$	49.6593	+	1.24707i	2.50817	+	0.0629865i
$393$	0.402716	−	0.281985i	0.0203143	−	0.0142243i
$394$	−14.1836	−	6.75899i	−0.714558	−	0.340513i
$395$	−19.7594	−	10.7193i	−0.994202	−	0.539348i
$396$	1.65466	−	2.75828i	0.0831497	−	0.138609i
$397$	−12.5586	+	5.85619i	−0.630300	+	0.293914i	−0.711395	−	0.702793i	$-0.751936\pi$
$397$	−12.5586	+	5.85619i	−0.630300	+	0.293914i	0.0810947	+	0.996706i	$0.474158\pi$
$398$	3.91993	−	10.4958i	0.196488	−	0.526105i
$399$	2.11554	−	1.25762i	0.105909	−	0.0629599i
$400$	10.3375	+	17.1212i	0.516875	+	0.856061i
$401$	13.7918	+	5.01980i	0.688729	+	0.250677i	0.662591	−	0.748981i	$-0.269457\pi$
$401$	13.7918	+	5.01980i	0.688729	+	0.250677i	0.0261384	+	0.999658i	$0.491679\pi$
$402$	−1.04901	−	0.194034i	−0.0523198	−	0.00967756i
$403$	−0.540970	+	0.0473288i	−0.0269477	+	0.00235761i
$404$	18.1984	+	0.304636i	0.905403	+	0.0151562i
$405$	0.527063	+	19.8568i	0.0261900	+	0.986692i
$406$	28.2205	+	2.70714i	1.40056	+	0.134353i
$407$	−0.667713	+	2.49194i	−0.0330973	+	0.123521i
$408$	−1.45464	−	1.28417i	−0.0720152	−	0.0635761i
$409$	−8.77043	−	24.0966i	−0.433670	−	1.19150i	−0.943543	−	0.331249i	$-0.892530\pi$
$409$	−8.77043	−	24.0966i	−0.433670	−	1.19150i	0.509874	−	0.860249i	$-0.329692\pi$
$410$	29.9842	−	11.5345i	1.48082	−	0.569646i
$411$	−0.212436	−	0.122650i	−0.0104787	−	0.00604987i
$412$	−2.21832	+	21.2521i	−0.109289	+	1.04702i
$413$	57.1856	+	5.00309i	2.81392	+	0.246186i
$414$	−4.11927	−	1.14079i	−0.202451	−	0.0560667i
$415$	0.595391	+	0.258631i	0.0292266	+	0.0126957i
$416$	4.18538	+	18.7206i	0.205205	+	0.917851i
$417$	0.594712	−	0.594712i	0.0291232	−	0.0291232i
$418$	2.14453	+	2.53316i	0.104892	+	0.123901i
$419$	−34.3889			−1.68001			−0.840005	−	0.542579i	$-0.817448\pi$
$419$	−34.3889			−1.68001			−0.840005	+	0.542579i	$0.817448\pi$
$420$	1.64195	+	1.91831i	0.0801189	+	0.0936038i
$421$	−3.32779	−	18.8728i	−0.162187	−	0.919806i	−0.951918	−	0.306353i	$-0.900891\pi$
$421$	−3.32779	−	18.8728i	−0.162187	−	0.919806i	0.789731	−	0.613453i	$-0.210220\pi$
$422$	15.9260	+	28.1257i	0.775267	+	1.36914i
$423$	−0.548590	+	6.27041i	−0.0266733	+	0.304878i
$424$	−5.94206	+	11.9500i	−0.288572	+	0.580344i
$425$	18.5538	+	23.7129i	0.899991	+	1.15024i
$426$	−0.839099	−	0.598071i	−0.0406545	−	0.0289766i
$427$	−19.7767	−	9.22200i	−0.957059	−	0.446284i
$428$	9.21151	+	20.6496i	0.445255	+	0.998138i
$429$	0.180136	−	0.104002i	0.00869705	−	0.00502125i
$430$	29.5193	−	3.12393i	1.42355	−	0.150649i
$431$	−31.1593	−	5.49422i	−1.50089	−	0.264647i	−0.637998	−	0.770038i	$-0.720237\pi$
$431$	−31.1593	−	5.49422i	−1.50089	−	0.264647i	−0.862891	+	0.505391i	$0.831348\pi$
$432$	0.146684	+	2.72433i	0.00705731	+	0.131074i
$433$	−2.72562	−	31.1540i	−0.130985	−	1.49716i	−0.722781	−	0.691077i	$-0.757137\pi$
$433$	−2.72562	−	31.1540i	−0.130985	−	1.49716i	0.591796	−	0.806088i	$-0.298419\pi$
$434$	0.924772	−	0.636065i	0.0443905	−	0.0305321i
$435$	0.613195	+	0.828067i	0.0294005	+	0.0397028i
$436$	−1.03048	+	1.18715i	−0.0493513	+	0.0568542i
$437$	2.48352	−	3.64484i	0.118803	−	0.174356i
$438$	0.275644	−	0.738048i	0.0131708	−	0.0352653i
$439$	21.8214	+	7.94235i	1.04148	+	0.379068i	0.805441	−	0.592676i	$-0.201929\pi$
$439$	21.8214	+	7.94235i	1.04148	+	0.379068i	0.236039	+	0.971744i	$0.424151\pi$
$440$	−2.18511	+	2.61169i	−0.104171	+	0.124508i
$441$	−40.1869	−	33.7208i	−1.91366	−	1.60575i
$442$	9.64957	+	27.2186i	0.458983	+	1.29466i
$443$	15.0364	+	21.4742i	0.714401	+	1.02027i	0.998116	+	0.0613612i	$0.0195442\pi$
$443$	15.0364	+	21.4742i	0.714401	+	1.02027i	−0.283715	+	0.958909i	$0.591567\pi$
$444$	−0.356177	−	1.03201i	−0.0169034	−	0.0489772i
$445$	−11.5730	+	10.2463i	−0.548611	+	0.485719i
$446$	−4.20115	−	4.27207i	−0.198930	−	0.202288i
$447$	0.523761	+	0.244234i	0.0247731	+	0.0115519i
$448$	−26.5933	−	29.4077i	−1.25641	−	1.38938i
$449$	18.7074	+	10.8007i	0.882856	+	0.509717i	0.871599	−	0.490219i	$-0.163083\pi$
$449$	18.7074	+	10.8007i	0.882856	+	0.509717i	0.0112571	+	0.999937i	$0.496417\pi$
$450$	2.73446	−	20.9437i	0.128904	−	0.987294i
$451$	3.51598	+	4.19018i	0.165561	+	0.197308i
$452$	7.76823	−	10.7081i	0.365387	−	0.503669i
$453$	−1.30008	+	1.85671i	−0.0610833	+	0.0872360i
$454$	33.5367	−	2.65146i	1.57396	−	0.124439i
$455$	−7.50543	−	36.8231i	−0.351860	−	1.72629i
$456$	−1.35210	−	0.380269i	−0.0633178	−	0.0178078i
$457$	21.7852	−	21.7852i	1.01907	−	1.01907i	0.0192554	−	0.999815i	$-0.493870\pi$
$457$	21.7852	−	21.7852i	1.01907	−	1.01907i	0.999815	−	0.0192554i	$-0.00612956\pi$
$458$	−31.4469	−	26.8388i	−1.46942	−	1.25409i
$459$	0.713218	+	4.04486i	0.0332902	+	0.188798i
$460$	4.11968	+	1.87211i	0.192081	+	0.0872878i
$461$	−24.2742	+	20.3685i	−1.13056	+	0.948655i	−0.999089	−	0.0426652i	$-0.986415\pi$
$461$	−24.2742	+	20.3685i	−1.13056	+	0.948655i	−0.131473	+	0.991320i	$0.541971\pi$
$462$	−0.218069	+	0.370510i	−0.0101455	+	0.0172377i
$463$	−3.71955	−	13.8815i	−0.172862	−	0.645130i	−0.996906	−	0.0786038i	$-0.974954\pi$
$463$	−3.71955	−	13.8815i	−0.172862	−	0.645130i	0.824044	−	0.566526i	$-0.191713\pi$
$464$	−9.97919	−	12.7352i	−0.463272	−	0.591217i
$465$	0.0396703	+	0.00950901i	0.00183966	+	0.000440970i
$466$	14.5896	−	14.3474i	0.675849	−	0.664630i
$467$	−1.98295	+	7.40048i	−0.0917601	+	0.342453i	−0.996508	−	0.0834934i	$-0.973392\pi$
$467$	−1.98295	+	7.40048i	−0.0917601	+	0.342453i	0.904748	+	0.425947i	$0.140059\pi$
$468$	8.86764	−	18.2144i	0.409907	−	0.841961i
$469$	−32.3178	−	5.69851i	−1.49230	−	0.263133i
$470$	1.60747	−	6.46688i	0.0741469	−	0.298295i
$471$	1.10728	−	1.31960i	0.0510207	−	0.0608041i
$472$	−20.4213	−	25.6167i	−0.939967	−	1.17910i
$473$	2.13594	+	4.58055i	0.0982108	+	0.210614i
$474$	0.672211	+	1.47364i	0.0308757	+	0.0676863i
$475$	19.5504	+	9.63224i	0.897036	+	0.441958i
$476$	−45.0757	−	39.1271i	−2.06604	−	1.79339i
$477$	12.7736	−	5.95644i	0.584864	−	0.272727i
$478$	−26.3752	−	4.87859i	−1.20637	−	0.223142i
$479$	−10.6673	−	8.95094i	−0.487402	−	0.408979i	0.365692	−	0.930736i	$-0.380832\pi$
$479$	−10.6673	−	8.95094i	−0.487402	−	0.408979i	−0.853094	+	0.521757i	$0.825277\pi$
$480$	0.147556	−	1.43347i	0.00673497	−	0.0654286i
$481$	−2.82151	+	16.0016i	−0.128650	+	0.729608i
$482$	−9.71158	−	11.7725i	−0.442350	−	0.536223i
$483$	0.551840	+	0.147865i	0.0251096	+	0.00672809i
$484$	20.0030	+	7.66202i	0.909226	+	0.348273i
$485$	1.63712	−	6.82984i	0.0743378	−	0.310127i
$486$	2.51028	−	3.52195i	0.113869	−	0.159759i
$487$	41.2366	−	11.0493i	1.86861	−	0.500692i	0.868621	−	0.495477i	$-0.165007\pi$
$487$	41.2366	−	11.0493i	1.86861	−	0.500692i	0.999986	−	0.00521503i	$-0.00166000\pi$
$488$	3.96415	+	11.8055i	0.179449	+	0.534409i
$489$	−0.467051	−	0.556610i	−0.0211208	−	0.0251708i
$490$	36.4663	+	41.8892i	1.64738	+	1.89236i
$491$	−33.2707	+	5.86653i	−1.50149	+	0.264753i	−0.863128	−	0.504986i	$-0.831498\pi$
$491$	−33.2707	+	5.86653i	−1.50149	+	0.264753i	−0.638360	+	0.769738i	$0.720387\pi$
$492$	−2.22555	−	0.636445i	−0.100336	−	0.0286932i
$493$	−17.2230	−	17.2230i	−0.775685	−	0.775685i
$494$	14.8458	+	14.7165i	0.667945	+	0.662125i
$495$	3.52373	−	0.718221i	0.158380	−	0.0322816i
$496$	−0.626744	−	0.132282i	−0.0281416	−	0.00593963i
$497$	−25.9649	−	18.1808i	−1.16469	−	0.815522i
$498$	−0.0230461	−	0.0406999i	−0.00103272	−	0.00182381i
$499$	−14.5362	+	12.1973i	−0.650729	+	0.546026i	−0.907292	−	0.420501i	$-0.861854\pi$
$499$	−14.5362	+	12.1973i	−0.650729	+	0.546026i	0.256563	+	0.966528i	$0.417410\pi$
$500$	−6.31247	+	21.4512i	−0.282302	+	0.959326i
$501$	−0.839159	+	1.45347i	−0.0374909	+	0.0649361i
$502$	1.71719	+	10.2390i	0.0766418	+	0.456990i
$503$	−5.70320	+	12.2305i	−0.254293	+	0.545333i	−0.991465	−	0.130372i	$-0.958383\pi$
$503$	−5.70320	+	12.2305i	−0.254293	+	0.545333i	0.737172	+	0.675705i	$0.236161\pi$
$504$	2.60104	+	41.7910i	0.115860	+	1.86152i
$505$	13.4893	+	15.2359i	0.600264	+	0.677987i
$506$	−0.0735705	+	0.766933i	−0.00327061	+	0.0340943i
$507$	−0.140050	+	0.0980642i	−0.00621985	+	0.00435518i
$508$	−23.5094	−	24.3099i	−1.04306	−	1.07858i
$509$	21.3589	−	25.4545i	0.946715	−	1.12825i	−0.0448960	−	0.998992i	$-0.514296\pi$
$509$	21.3589	−	25.4545i	0.946715	−	1.12825i	0.991611	−	0.129259i	$-0.0412599\pi$
$510$	−0.0394114	−	2.16905i	−0.00174517	−	0.0960472i
$511$	8.28890	−	22.7736i	0.366679	−	1.00744i
$512$	−1.70272	+	22.5633i	−0.0752505	+	0.997165i
$513$	1.73618	+	2.41346i	0.0766543	+	0.106557i
$514$	−11.1253	−	24.3892i	−0.490718	−	1.07576i
$515$	−19.1988	+	14.2170i	−0.846001	+	0.626476i
$516$	−1.83410	−	1.10025i	−0.0807418	−	0.0484360i
$517$	1.13025	−	0.0988842i	0.0497084	−	0.00434892i
$518$	−11.2218	−	31.6534i	−0.493058	−	1.39077i
$519$	0.242901	−	1.37756i	0.0106622	−	0.0604682i
$520$	−12.2763	+	17.5859i	−0.538352	+	0.771191i
$521$	−5.28448	−	9.15299i	−0.231517	−	0.401000i	0.726737	−	0.686915i	$-0.241036\pi$
$521$	−5.28448	−	9.15299i	−0.231517	−	0.401000i	−0.958255	+	0.285915i	$0.907702\pi$
$522$	−0.142997	+	17.0859i	−0.00625879	+	0.747829i
$523$	−4.40231	+	9.44078i	−0.192500	+	0.412817i	−0.978740	−	0.205104i	$-0.934247\pi$
$523$	−4.40231	+	9.44078i	−0.192500	+	0.412817i	0.786241	+	0.617920i	$0.212025\pi$
$524$	−8.47333	−	1.64076i	−0.370159	−	0.0716770i
$525$	−0.342048	+	2.80230i	−0.0149282	+	0.122302i
$526$	31.8236	−	8.24227i	1.38757	−	0.359380i
$527$	−0.960644	−	0.0840455i	−0.0418463	−	0.00366108i
$528$	0.238987	−	0.0555348i	0.0104006	−	0.00241684i
$529$	−21.6423	+	3.81612i	−0.940970	+	0.165918i
$530$	−14.3401	+	4.12305i	−0.622895	+	0.179094i
$531$			34.5973i			1.50140i
$532$	−41.6889	−	11.3491i	−1.80744	−	0.492047i
$533$	24.3602	+	24.3602i	1.05516	+	1.05516i
$534$	1.11025	−	0.0877777i	0.0480451	−	0.00379851i
$535$	−10.0721	+	23.1868i	−0.435454	+	1.00245i
$536$	10.3536	+	15.6061i	0.447206	+	0.674082i
$537$	0.164095	−	1.87561i	0.00708122	−	0.0809387i
$538$	6.87770	−	11.6856i	0.296519	−	0.503801i
$539$	−4.72803	+	8.18919i	−0.203651	+	0.352733i
$540$	−2.13565	+	2.17792i	−0.0919038	+	0.0937228i
$541$	32.2655	−	11.7437i	1.38720	−	0.504901i	0.462849	−	0.886437i	$-0.346827\pi$
$541$	32.2655	−	11.7437i	1.38720	−	0.504901i	0.924354	+	0.381536i	$0.124605\pi$
$542$	−18.9494	−	0.158593i	−0.813948	−	0.00681215i
$543$	0.293094	+	0.0785344i	0.0125779	+	0.00337023i
$544$	1.54670	+	34.0291i	0.0663144	+	1.45899i
$545$	−1.75694	+	0.0466349i	−0.0752592	+	0.00199762i
$546$	−1.16484	+	2.44438i	−0.0498503	+	0.104610i
$547$	0.721148	+	8.24276i	0.0308341	+	0.352435i	0.995902	+	0.0904362i	$0.0288261\pi$
$547$	0.721148	+	8.24276i	0.0308341	+	0.352435i	−0.965068	+	0.261999i	$0.915618\pi$
$548$	1.04479	+	4.17769i	0.0446312	+	0.178462i
$549$	4.49809	−	12.3584i	0.191974	−	0.527444i
$550$	−3.80337	+	0.170142i	−0.162176	+	0.00725490i
$551$	−16.6432	−	5.81851i	−0.709024	−	0.247877i
$552$	−0.155882	−	0.286366i	−0.00663477	−	0.0121885i
$553$	21.0568	+	45.1565i	0.895426	+	1.92025i
$554$	13.9379	−	9.58658i	0.592164	−	0.407295i
$555$	0.582043	−	1.07290i	0.0247063	−	0.0455422i
$556$	−14.7630	−	0.247128i	−0.626089	−	0.0104806i
$557$	−6.52769	−	9.32251i	−0.276587	−	0.395008i	0.656692	−	0.754159i	$-0.271955\pi$
$557$	−6.52769	−	9.32251i	−0.276587	−	0.395008i	−0.933279	+	0.359151i	$0.883066\pi$
$558$	0.430473	+	0.521826i	0.0182234	+	0.0220906i
$559$	15.9158	+	27.5670i	0.673167	+	1.16596i
$560$	4.16983	−	44.1320i	0.176208	−	1.86492i
$561$	0.347092	−	0.126331i	0.0146542	−	0.00533371i
$562$	−15.8344	+	2.65558i	−0.667932	+	0.112019i
$563$	−3.03149	−	11.3137i	−0.127762	−	0.476814i	0.872161	−	0.489219i	$-0.162718\pi$
$563$	−3.03149	−	11.3137i	−0.127762	−	0.476814i	−0.999923	+	0.0124047i	$0.996051\pi$
$564$	−0.372916	+	0.302423i	−0.0157026	+	0.0127343i
$565$	14.6949	−	1.67959i	0.618221	−	0.0706609i
$566$	−8.08314	+	29.1874i	−0.339760	+	1.22684i
$567$	25.2527	−	36.0645i	1.06051	−	1.51457i
$568$	2.69300	+	17.8880i	0.112996	+	0.750565i
$569$			11.4643i			0.480607i	0.970698	+	0.240303i	$0.0772469\pi$
$569$			11.4643i			0.480607i	−0.970698	+	0.240303i	$0.922753\pi$
$570$	−0.707326	−	1.40202i	−0.0296266	−	0.0587242i
$571$			3.14305i			0.131533i	0.997835	+	0.0657663i	$0.0209492\pi$
$571$			3.14305i			0.131533i	−0.997835	+	0.0657663i	$0.979051\pi$
$572$	−3.51086	−	1.00401i	−0.146796	−	0.0419796i
$573$	0.325406	−	0.464728i	0.0135940	−	0.0194143i
$574$	−68.6227	−	19.0043i	−2.86425	−	0.793225i
$575$	1.56682	+	4.81049i	0.0653409	+	0.200611i
$576$	16.2596	−	17.5115i	0.677484	−	0.729645i
$577$	−8.95915	−	33.4360i	−0.372974	−	1.39196i	−0.856282	−	0.516508i	$-0.827232\pi$
$577$	−8.95915	−	33.4360i	−0.372974	−	1.39196i	0.483308	−	0.875450i	$-0.339435\pi$
$578$	4.50553	+	26.8650i	0.187405	+	1.11744i
$579$	0.498670	−	0.181501i	0.0207240	−	0.00754293i
$580$	2.96642	−	17.8441i	0.123174	−	0.740936i
$581$	−0.719384	−	1.24601i	−0.0298451	−	0.0516932i
$582$	−0.390362	+	0.322024i	−0.0161810	+	0.0133483i
$583$	−1.45717	−	2.08105i	−0.0603497	−	0.0861883i
$584$	−12.6779	+	5.52868i	−0.524614	+	0.228778i
$585$	21.7145	−	6.44056i	0.897783	−	0.266284i
$586$	−4.22265	−	6.13929i	−0.174436	−	0.253612i
$587$	15.7798	+	33.8400i	0.651304	+	1.39673i	0.903305	+	0.428998i	$0.141133\pi$
$587$	15.7798	+	33.8400i	0.651304	+	1.39673i	−0.252002	+	0.967727i	$0.581089\pi$
$588$	−0.281996	−	3.99171i	−0.0116293	−	0.164615i
$589$	−0.652833	+	0.247079i	−0.0268995	+	0.0101807i
$590$	5.70391	−	36.1804i	0.234826	−	1.48952i
$591$	−0.432889	+	1.18935i	−0.0178067	+	0.0489235i
$592$	−8.67683	+	17.0896i	−0.356616	+	0.702379i
$593$	−1.83171	−	20.9365i	−0.0752192	−	0.859759i	−0.936279	−	0.351256i	$-0.885755\pi$
$593$	−1.83171	−	20.9365i	−0.0752192	−	0.859759i	0.861060	−	0.508503i	$-0.169801\pi$
$594$	−0.468838	−	0.223419i	−0.0192367	−	0.00916698i
$595$	−1.77071	−	66.7106i	−0.0725921	−	2.73487i
$596$	−3.30989	−	9.59033i	−0.135578	−	0.392835i
$597$	−0.871796	−	0.233597i	−0.0356802	−	0.00956049i
$598$	−0.0406103	+	4.85231i	−0.00166068	+	0.198426i
$599$	6.34756	−	2.31032i	0.259354	−	0.0943972i	−0.209071	−	0.977901i	$-0.567044\pi$
$599$	6.34756	−	2.31032i	0.259354	−	0.0943972i	0.468425	+	0.883503i	$0.344822\pi$
$600$	1.29341	−	0.960653i	0.0528032	−	0.0392185i
$601$	−8.84216	+	15.3151i	−0.360679	+	0.624715i	−0.988073	−	0.153988i	$-0.950788\pi$
$601$	−8.84216	+	15.3151i	−0.360679	+	0.624715i	0.627394	+	0.778702i	$0.284122\pi$
$602$	−56.7008	−	33.3720i	−2.31095	−	1.36014i
$603$	1.72380	−	19.7031i	0.0701985	−	0.802373i
$604$	39.2974	−	6.25290i	1.59899	−	0.254427i
$605$	8.78512	+	22.2790i	0.357166	+	0.905770i
$606$	−0.115560	−	1.46165i	−0.00469430	−	0.0593753i
$607$	3.60754	+	3.60754i	0.146426	+	0.146426i	0.776519	−	0.630094i	$-0.216984\pi$
$607$	3.60754	+	3.60754i	0.146426	+	0.146426i	−0.630094	+	0.776519i	$0.716984\pi$
$608$	11.7023	+	21.7038i	0.474590	+	0.880207i
$609$		−	2.28379i		−	0.0925436i
$610$	−6.74139	+	12.1823i	−0.272951	+	0.493247i
$611$	7.03720	−	1.24085i	0.284695	−	0.0501993i
$612$	21.1244	−	29.1189i	0.853901	−	1.17706i
$613$	2.57879	+	0.225615i	0.104156	+	0.00911251i	0.139115	−	0.990276i	$-0.455574\pi$
$613$	2.57879	+	0.225615i	0.104156	+	0.00911251i	−0.0349583	+	0.999389i	$0.511130\pi$
$614$	3.58660	+	13.8479i	0.144743	+	0.558857i
$615$	−1.15558	−	2.31567i	−0.0465976	−	0.0933768i
$616$	7.33704	−	1.76979i	0.295618	−	0.0713070i
$617$	−12.3630	+	26.5125i	−0.497716	+	1.06735i	0.483660	+	0.875256i	$0.339307\pi$
$617$	−12.3630	+	26.5125i	−0.497716	+	1.06735i	−0.981376	+	0.192099i	$0.938471\pi$
$618$	1.72125	+	0.0144056i	0.0692386	+	0.000579477i
$619$	11.6073	+	20.1044i	0.466536	+	0.808064i	0.999269	−	0.0382188i	$-0.0121684\pi$
$619$	11.6073	+	20.1044i	0.466536	+	0.808064i	−0.532733	+	0.846283i	$0.678835\pi$
$620$	−0.364139	−	0.616673i	−0.0146242	−	0.0247662i
$621$	−0.119843	+	0.679662i	−0.00480912	+	0.0272739i
$622$	−30.2641	+	10.7292i	−1.21348	+	0.430204i
$623$	34.1290	−	2.98590i	1.36735	−	0.119627i
$624$	1.46898	−	0.479625i	0.0588063	−	0.0192004i
$625$	−22.4542	+	10.9914i	−0.898167	+	0.439654i
$626$	11.3658	−	5.18462i	0.454270	−	0.207219i
$627$	0.186634	−	0.191453i	0.00745344	−	0.00764589i
$628$	−30.1662	+	2.13111i	−1.20376	+	0.0850404i
$629$	−9.86851	+	27.1135i	−0.393483	+	1.08109i
$630$	−32.4957	+	33.6985i	−1.29466	+	1.34258i
$631$	14.3003	−	17.0425i	0.569287	−	0.678450i	−0.402197	−	0.915553i	$-0.631753\pi$
$631$	14.3003	−	17.0425i	0.569287	−	0.678450i	0.971485	+	0.237103i	$0.0761978\pi$
$632$	10.3930	−	26.4674i	0.413412	−	1.05282i
$633$	2.13285	−	1.49344i	0.0847733	−	0.0593589i
$634$	6.70669	+	0.643361i	0.266357	+	0.0255511i
$635$	2.29475	−	37.7400i	0.0910646	−	1.49767i
$636$	1.00396	+	0.384562i	0.0398098	+	0.0152489i
$637$	−25.1696	+	53.9763i	−0.997255	+	2.13862i
$638$	3.03745	−	0.509411i	0.120254	−	0.0201678i
$639$	9.55196	−	16.5445i	0.377870	−	0.654489i
$640$	−19.8906	+	15.6321i	−0.786247	+	0.617913i
$641$	5.11130	−	4.28889i	0.201884	−	0.169401i	−0.536241	−	0.844065i	$-0.680156\pi$
$641$	5.11130	−	4.28889i	0.201884	−	0.169401i	0.738125	+	0.674664i	$0.235712\pi$
$642$	1.58501	−	0.897504i	0.0625553	−	0.0354216i
$643$	−13.3316	−	9.33487i	−0.525746	−	0.368131i	0.280367	−	0.959893i	$-0.409544\pi$
$643$	−13.3316	−	9.33487i	−0.525746	−	0.368131i	−0.806113	+	0.591761i	$0.798433\pi$
$644$	−4.86870	−	8.76858i	−0.191854	−	0.345530i
$645$	−0.477576	−	2.34308i	−0.0188045	−	0.0922587i
$646$	21.4244	+	30.3140i	0.842932	+	1.19269i
$647$	11.2388	+	11.2388i	0.441844	+	0.441844i	0.892631	−	0.450788i	$-0.148857\pi$
$647$	11.2388	+	11.2388i	0.441844	+	0.441844i	−0.450788	+	0.892631i	$0.648857\pi$
$648$	−24.8459	+	3.74050i	−0.976041	+	0.146941i
$649$	6.14149	−	1.08291i	0.241074	−	0.0425079i
$650$	−23.7699	+	3.15528i	−0.932332	+	0.123760i
$651$	−0.0581189	−	0.0692634i	−0.00227786	−	0.00271465i
$652$	−1.32428	+	12.6869i	−0.0518627	+	0.496859i
$653$	−26.2921	+	7.04494i	−1.02889	+	0.275690i	−0.733501	−	0.679688i	$-0.762115\pi$
$653$	−26.2921	+	7.04494i	−1.02889	+	0.275690i	−0.295387	+	0.955378i	$0.595448\pi$
$654$	0.103123	+	0.0735012i	0.00403242	+	0.00287412i
$655$	−5.04476	−	8.22570i	−0.197115	−	0.321405i
$656$	19.1292	+	35.8529i	0.746868	+	1.39982i
$657$	14.1088	+	3.78043i	0.550435	+	0.147489i
$658$	−11.3932	+	9.39865i	−0.444152	+	0.366398i
$659$	0.704049	−	3.99286i	0.0274259	−	0.155540i	−0.968019	−	0.250876i	$-0.919281\pi$
$659$	0.704049	−	3.99286i	0.0274259	−	0.155540i	0.995445	+	0.0953360i	$0.0303926\pi$
$660$	0.226237	+	0.155131i	0.00880626	+	0.00603848i
$661$	−30.3212	−	25.4425i	−1.17936	−	0.989599i	−0.999983	−	0.00581824i	$-0.998148\pi$
$661$	−30.3212	−	25.4425i	−1.17936	−	0.989599i	−0.179375	−	0.983781i	$-0.557408\pi$
$662$	1.66890	−	9.02260i	0.0648638	−	0.350673i
$663$	2.10840	−	0.983161i	0.0818833	−	0.0381828i
$664$	−0.232361	+	0.787538i	−0.00901735	+	0.0305624i
$665$	−22.1185	−	42.9445i	−0.857720	−	1.66532i
$666$	18.4154	−	8.40033i	0.713582	−	0.325506i
$667$	−1.72966	−	3.70927i	−0.0669728	−	0.143624i
$668$	28.5834	−	7.14835i	1.10592	−	0.276578i
$669$	−0.310255	+	0.369747i	−0.0119951	+	0.0142952i
$670$	−5.05104	+	20.3205i	−0.195139	+	0.785048i
$671$	−2.33458	−	0.411649i	−0.0901253	−	0.0158915i
$672$	−2.15360	+	2.35870i	−0.0830769	+	0.0909886i
$673$	3.18326	−	11.8801i	0.122706	−	0.457944i	−0.877042	−	0.480414i	$-0.840486\pi$
$673$	3.18326	−	11.8801i	0.122706	−	0.457944i	0.999748	+	0.0224700i	$0.00715303\pi$
$674$	−6.55131	−	6.66190i	−0.252347	−	0.256607i
$675$	−3.40835	−	0.116586i	−0.131187	−	0.00448738i
$676$	2.94672	+	0.570597i	0.113335	+	0.0219461i
$677$	−6.19793	−	23.1310i	−0.238206	−	0.888996i	−0.976678	−	0.214711i	$-0.931119\pi$
$677$	−6.19793	−	23.1310i	−0.238206	−	0.888996i	0.738472	−	0.674284i	$-0.235548\pi$
$678$	−0.918428	−	0.540553i	−0.0352720	−	0.0207598i
$679$	−11.9248	+	10.0061i	−0.457630	+	0.383997i
$680$	−26.8916	+	26.9687i	−1.03125	+	1.03420i
$681$	−0.470594	−	2.66887i	−0.0180332	−	0.102271i
$682$	0.0791570	−	0.0927481i	0.00303108	−	0.00355151i
$683$	−1.42013	+	1.42013i	−0.0543396	+	0.0543396i	−0.733754	−	0.679415i	$-0.762234\pi$
$683$	−1.42013	+	1.42013i	−0.0543396	+	0.0543396i	0.679415	+	0.733754i	$0.262234\pi$
$684$	4.62421	−	25.6264i	0.176811	−	0.979849i
$685$	−2.65595	+	4.01582i	−0.101479	+	0.153437i
$686$	−5.83502	−	73.8036i	−0.222782	−	2.81783i
$687$	−1.91027	+	2.72814i	−0.0728812	+	0.104085i
$688$	8.49872	+	36.5733i	0.324011	+	1.39434i
$689$	−10.2850	−	12.2571i	−0.391826	−	0.466960i
$690$	0.118432	−	0.344753i	0.00450864	−	0.0131245i
$691$	−1.76070	−	1.01654i	−0.0669803	−	0.0386711i	0.466136	−	0.884713i	$-0.345646\pi$
$691$	−1.76070	−	1.01654i	−0.0669803	−	0.0386711i	−0.533116	+	0.846042i	$0.678979\pi$
$692$	−20.3487	+	13.7465i	−0.773541	+	0.522565i
$693$	−7.22388	−	3.36855i	−0.274412	−	0.127961i
$694$	18.6320	−	18.3227i	0.707262	−	0.695522i
$695$	−10.9428	−	12.3597i	−0.415085	−	0.468831i
$696$	−0.944455	+	0.898182i	−0.0357995	+	0.0340455i
$697$	35.0894	+	50.1129i	1.32911	+	1.89816i
$698$	−2.15391	+	0.763608i	−0.0815268	+	0.0289030i
$699$	−1.26273	−	1.05955i	−0.0477607	−	0.0400760i
$700$	39.5384	−	29.8830i	1.49441	−	1.12947i
$701$	−6.34464	−	2.30926i	−0.239634	−	0.0872196i	0.219412	−	0.975632i	$-0.429586\pi$
$701$	−6.34464	−	2.30926i	−0.239634	−	0.0872196i	−0.459045	+	0.888413i	$0.651808\pi$
$702$	−3.06425	−	1.14443i	−0.115653	−	0.0431936i
$703$	2.08534	+	20.7815i	0.0786502	+	0.783789i
$704$	−3.61745	−	2.33818i	−0.136338	−	0.0881236i
$705$	−0.530936	−	0.0791551i	−0.0199962	−	0.00298115i
$706$	16.5275	+	24.0293i	0.622021	+	0.904353i
$707$	−3.93095	−	44.9310i	−0.147839	−	1.68980i
$708$	−1.89708	+	1.83461i	−0.0712966	+	0.0689489i
$709$	−18.2263	−	3.21378i	−0.684501	−	0.120696i	−0.179426	−	0.983771i	$-0.557424\pi$
$709$	−18.2263	−	3.21378i	−0.684501	−	0.120696i	−0.505075	+	0.863075i	$0.668535\pi$
$710$	−12.7166	+	15.7267i	−0.477247	+	0.590213i
$711$	−26.0061	+	15.0146i	−0.975304	+	0.563092i
$712$	−14.6573	−	12.9397i	−0.549304	−	0.484934i
$713$	−0.146853	−	0.0684788i	−0.00549970	−	0.00256455i
$714$	−2.79082	+	3.91554i	−0.104444	+	0.146535i
$715$	−1.82296	−	3.65302i	−0.0681747	−	0.136615i
$716$	−25.6722	+	20.8193i	−0.959415	+	0.778055i
$717$	−0.188321	+	2.15252i	−0.00703297	+	0.0803872i
$718$	16.6307	−	9.41707i	0.620653	−	0.351442i
$719$	−3.87266	−	21.9629i	−0.144426	−	0.819079i	−0.967826	−	0.251618i	$-0.919037\pi$
$719$	−3.87266	−	21.9629i	−0.144426	−	0.819079i	0.823401	−	0.567460i	$-0.192074\pi$
$720$	26.7161	+	0.185395i	0.995650	+	0.00690927i
$721$	52.9498			1.97195
$722$	23.4967	+	13.0347i	0.874458	+	0.485100i
$723$	−0.869317	+	0.869317i	−0.0323303	+	0.0323303i
$724$	−2.58587	−	4.65718i	−0.0961033	−	0.173083i
$725$	16.9535	−	11.0270i	0.629637	−	0.409531i
$726$	0.460537	−	1.66295i	0.0170921	−	0.0617179i
$727$	−0.879142	−	0.0769150i	−0.0326056	−	0.00285262i	0.0708413	−	0.997488i	$-0.477432\pi$
$727$	−0.879142	−	0.0769150i	−0.0326056	−	0.00285262i	−0.103447	+	0.994635i	$0.532987\pi$
$728$	45.0629	−	15.1316i	1.67014	−	0.560815i
$729$	22.7779	+	13.1508i	0.843626	+	0.487068i
$730$	−14.1311	−	6.27946i	−0.523014	−	0.232413i
$731$	19.3330	+	53.1170i	0.715058	+	1.96460i
$732$	0.916173	−	0.408692i	0.0338627	−	0.0151057i
$733$	2.55578	−	9.53829i	0.0943998	−	0.352305i	−0.902528	−	0.430631i	$-0.858291\pi$
$733$	2.55578	−	9.53829i	0.0943998	−	0.352305i	0.996928	+	0.0783264i	$0.0249576\pi$
$734$	4.20560	−	43.8411i	0.155232	−	1.61821i
$735$	3.07853	−	3.24642i	0.113553	−	0.119746i
$736$	−1.71143	+	5.46201i	−0.0630843	+	0.201332i
$737$	−3.55152	+	0.310718i	−0.130822	+	0.0114454i
$738$	7.80563	−	42.1996i	0.287329	−	1.55339i
$739$	8.15136	+	2.96685i	0.299853	+	0.109137i	0.487565	−	0.873087i	$-0.337885\pi$
$739$	8.15136	+	2.96685i	0.299853	+	0.109137i	−0.187713	+	0.982224i	$0.560107\pi$
$740$	−20.6429	+	5.74864i	−0.758850	+	0.211324i
$741$	1.06589	−	1.30367i	0.0391566	−	0.0478915i
$742$	30.9813	+	11.5708i	1.13736	+	0.424777i
$743$	9.46099	−	4.41173i	0.347090	−	0.161851i	−0.241253	−	0.970462i	$-0.577558\pi$
$743$	9.46099	−	4.41173i	0.347090	−	0.161851i	0.588343	+	0.808612i	$0.299781\pi$
$744$	−0.00578637	+	0.0512753i	−0.000212139	+	0.00187984i
$745$	5.40882	−	9.97030i	0.198164	−	0.365284i
$746$	17.5706	−	36.8714i	0.643305	−	1.34996i
$747$	0.710321	−	0.497372i	0.0259893	−	0.0181979i
$748$	−5.83020	−	2.83842i	−0.213173	−	0.103783i
$749$	48.5244	−	28.0156i	1.77304	−	1.02367i
$750$	1.76870	+	0.341179i	0.0645838	+	0.0124581i
$751$	−5.09171	−	13.9894i	−0.185799	−	0.510479i	0.811465	−	0.584401i	$-0.198671\pi$
$751$	−5.09171	−	13.9894i	−0.185799	−	0.510479i	−0.997264	+	0.0739223i	$0.976448\pi$
$752$	8.36758	+	1.01526i	0.305134	+	0.0370228i
$753$	0.807844	−	0.216461i	0.0294395	−	0.00788828i
$754$	18.7781	−	4.86351i	0.683857	−	0.177118i
$755$	34.8270	+	27.6823i	1.26748	+	1.00746i
$756$	6.67678	−	1.06239i	0.242832	−	0.0386389i
$757$	3.53849	+	2.47768i	0.128609	+	0.0900528i	0.636111	−	0.771598i	$-0.280542\pi$
$757$	3.53849	+	2.47768i	0.128609	+	0.0900528i	−0.507502	+	0.861651i	$0.669431\pi$
$758$	−33.5935	+	39.3614i	−1.22017	+	1.42967i
$759$	0.0620653			0.00225283
$760$	−9.06071	+	26.0366i	−0.328666	+	0.944446i
$761$	34.6863			1.25738			0.628689	−	0.777657i	$-0.283592\pi$
$761$	34.6863			1.25738			0.628689	+	0.777657i	$0.283592\pi$
$762$	−1.76853	+	2.07219i	−0.0640672	+	0.0750674i
$763$	3.19102	+	2.23437i	0.115523	+	0.0808898i
$764$	−9.83598	+	1.56508i	−0.355853	+	0.0566225i
$765$	39.9603	−	4.56736i	1.44477	−	0.165133i
$766$	−23.3809	+	6.05563i	−0.844786	+	0.218799i
$767$	37.9388	−	10.1657i	1.36989	−	0.367061i
$768$	1.82242	−	0.0370254i	0.0657608	−	0.00133604i
$769$	7.72425	+	21.2222i	0.278543	+	0.765292i	0.997528	+	0.0702660i	$0.0223848\pi$
$769$	7.72425	+	21.2222i	0.278543	+	0.765292i	−0.718985	+	0.695026i	$0.755393\pi$
$770$	6.99906	+	4.71365i	0.252229	+	0.169868i
$771$	−1.87016	+	1.07974i	−0.0673522	+	0.0388858i
$772$	−8.37630	−	4.07798i	−0.301470	−	0.146770i
$773$	−9.18329	+	6.43021i	−0.330300	+	0.231279i	−0.726948	−	0.686692i	$-0.759062\pi$
$773$	−9.18329	+	6.43021i	−0.330300	+	0.231279i	0.396648	+	0.917971i	$0.370173\pi$
$774$	17.0583	−	35.7964i	0.613148	−	1.28668i
$775$	0.233552	−	0.765870i	0.00838944	−	0.0275109i
$776$	8.82783	+	0.996213i	0.316901	+	0.0357620i
$777$	−2.45192	+	1.14335i	−0.0879623	+	0.0410175i
$778$	6.19490	+	2.31365i	0.222098	+	0.0829485i
$779$	38.6293	+	21.6510i	1.38404	+	0.775726i
$780$	1.50462	+	0.849146i	0.0538741	+	0.0304043i
$781$	−3.23585	−	1.17775i	−0.115788	−	0.0421433i
$782$	−1.56728	+	8.47320i	−0.0560459	+	0.303001i
$783$	2.74835	−	0.240449i	0.0982180	−	0.00859296i
$784$	−46.9324	+	52.2739i	−1.67616	+	1.86692i
$785$	−24.5339	−	23.2651i	−0.875652	−	0.830369i
$786$	−0.0663906	+	0.692086i	−0.00236807	+	0.0246859i
$787$	10.3242	−	38.5305i	0.368018	−	1.37346i	−0.495264	−	0.868742i	$-0.664929\pi$
$787$	10.3242	−	38.5305i	0.368018	−	1.37346i	0.863283	−	0.504721i	$-0.168405\pi$
$788$	20.2922	−	9.05208i	0.722881	−	0.322467i
$789$	−0.905735	−	2.48849i	−0.0322450	−	0.0885925i
$790$	29.6714	−	11.4141i	1.05566	−	0.406096i
$791$	−28.3903	−	16.3912i	−1.00944	−	0.582802i
$792$	1.44800	+	4.31223i	0.0514523	+	0.153228i
$793$	−14.8737	−	1.30128i	−0.528179	−	0.0462097i
$794$	5.23022	−	18.8858i	0.185614	−	0.670232i
$795$	0.440932	+	1.11820i	0.0156382	+	0.0396584i
$796$	7.69157	+	13.8526i	0.272620	+	0.490992i
$797$	10.8282	−	10.8282i	0.383553	−	0.383553i	−0.488827	−	0.872381i	$-0.662575\pi$
$797$	10.8282	−	10.8282i	0.383553	−	0.383553i	0.872381	+	0.488827i	$0.162575\pi$
$798$	−0.589386	+	3.43028i	−0.0208640	+	0.121431i
$799$	12.6893			0.448915
$800$	−27.9080	−	4.59844i	−0.986695	−	0.162580i
$801$	3.58549	+	20.3343i	0.126687	+	0.718478i
$802$	−18.0617	+	10.2274i	−0.637781	+	0.361140i
$803$	0.229467	−	2.62282i	0.00809772	−	0.0925574i
$804$	1.17179	−	0.950286i	0.0413259	−	0.0335140i
$805$	3.55427	−	10.6352i	0.125271	−	0.374841i
$806$	0.445739	−	0.625376i	0.0157005	−	0.0220279i
$807$	−0.989956	−	0.461624i	−0.0348481	−	0.0162499i
$808$	−17.0351	+	19.2964i	−0.599294	+	0.678845i
$809$	−18.9421	+	10.9362i	−0.665967	+	0.384496i	−0.794547	−	0.607203i	$-0.792292\pi$
$809$	−18.9421	+	10.9362i	−0.665967	+	0.384496i	0.128580	+	0.991699i	$0.458958\pi$
$810$	−21.8439	−	17.6630i	−0.767518	−	0.620616i
$811$	−22.0698	−	3.89150i	−0.774976	−	0.136649i	−0.227846	−	0.973697i	$-0.573168\pi$
$811$	−22.0698	−	3.89150i	−0.774976	−	0.136649i	−0.547129	+	0.837048i	$0.684279\pi$
$812$	−28.8205	+	27.8715i	−1.01140	+	0.978099i
$813$	0.133048	+	1.52075i	0.00466621	+	0.0533350i
$814$	−2.06758	−	3.00604i	−0.0724686	−	0.105362i
$815$	−11.4612	+	8.48715i	−0.401467	+	0.297292i
$816$	2.71685	−	0.385792i	0.0951089	−	0.0135054i
$817$	29.2989	+	28.5614i	1.02504	+	0.999237i
$818$	33.9727	+	12.6880i	1.18783	+	0.443626i
$819$	−47.1735	−	17.1697i	−1.64837	−	0.599959i
$820$	−15.1201	+	42.8437i	−0.528016	+	1.49617i
$821$	−16.0718	−	13.4858i	−0.560910	−	0.470659i	0.317706	−	0.948189i	$-0.397088\pi$
$821$	−16.0718	−	13.4858i	−0.560910	−	0.470659i	−0.878615	+	0.477530i	$0.841532\pi$
$822$	0.326967	−	0.115917i	0.0114043	−	0.00404306i
$823$	18.6201	+	26.5922i	0.649055	+	0.926946i	0.999955	−	0.00946653i	$-0.00301334\pi$
$823$	18.6201	+	26.5922i	0.649055	+	0.926946i	−0.350900	+	0.936413i	$0.614124\pi$
$824$	−20.8244	−	21.8973i	−0.725454	−	0.762828i
$825$	0.0429004	+	0.303679i	0.00149360	+	0.0105727i
$826$	−57.8825	+	56.9216i	−2.01399	+	1.98056i
$827$	2.66421	+	1.24234i	0.0926436	+	0.0432004i	0.468388	−	0.883523i	$-0.344835\pi$
$827$	2.66421	+	1.24234i	0.0926436	+	0.0432004i	−0.375744	+	0.926723i	$0.622613\pi$
$828$	5.00895	−	3.38379i	0.174073	−	0.117595i
$829$	12.6285	+	7.29106i	0.438605	+	0.253229i	0.703006	−	0.711184i	$-0.251841\pi$
$829$	12.6285	+	7.29106i	0.438605	+	0.253229i	−0.264401	+	0.964413i	$0.585174\pi$
$830$	−0.824823	+	0.403023i	−0.0286300	+	0.0139891i
$831$	−0.875950	−	1.04392i	−0.0303864	−	0.0362131i
$832$	−23.9803	−	12.6846i	−0.831367	−	0.439760i
$833$	−60.6608	+	86.6326i	−2.10177	+	3.00164i
$834$	0.0937451	+	1.18572i	0.00324613	+	0.0410582i
$835$	27.4759	+	18.1718i	0.950841	+	0.628860i
$836$	−4.69376	−	0.0187434i	−0.162337	−	0.000648254i
$837$	0.0772337	−	0.0772337i	0.00266959	−	0.00266959i
$838$	31.5716	−	36.9923i	1.09062	−	1.27788i
$839$	−4.32340	−	24.5192i	−0.149261	−	0.846498i	−0.963847	−	0.266456i	$-0.914147\pi$
$839$	−4.32340	−	24.5192i	−0.149261	−	0.846498i	0.814586	−	0.580042i	$-0.196964\pi$
$840$	−3.57096	+	0.00510551i	−0.123210	+	0.000176157i
$841$	9.68235	−	8.12445i	0.333874	−	0.280154i
$842$	23.3568	+	13.7469i	0.804927	+	0.473751i
$843$	0.334751	+	1.24931i	0.0115294	+	0.0430285i
$844$	−44.8762	−	8.68975i	−1.54470	−	0.299114i
$845$	1.75438	+	2.86060i	0.0603527	+	0.0984077i
$846$	−6.24146	−	6.34682i	−0.214586	−	0.218208i
$847$	13.7382	−	51.2715i	0.472049	−	1.76171i
$848$	−7.39944	−	17.3629i	−0.254098	−	0.596244i
$849$	2.40268	+	0.423657i	0.0824596	+	0.0145399i
$850$	−42.5418	−	1.81174i	−1.45917	−	0.0621422i
$851$	−3.11643	+	3.71401i	−0.106830	+	0.127315i
$852$	1.41370	−	0.353550i	0.0484326	−	0.0121124i
$853$	−4.90159	−	10.5115i	−0.167827	−	0.359907i	0.804349	−	0.594157i	$-0.202514\pi$
$853$	−4.90159	−	10.5115i	−0.167827	−	0.359907i	−0.972176	+	0.234250i	$0.924736\pi$
$854$	28.0766	−	12.8074i	0.960761	−	0.438259i
$855$	24.6222	−	15.5359i	0.842063	−	0.531316i
$856$	−30.6698	−	9.04902i	−1.04827	−	0.309289i
$857$	23.9558	−	11.1708i	0.818314	−	0.381586i	0.0320572	−	0.999486i	$-0.489794\pi$
$857$	23.9558	−	11.1708i	0.818314	−	0.381586i	0.786257	+	0.617900i	$0.212016\pi$
$858$	−0.0535032	+	0.289254i	−0.00182657	+	0.00987498i
$859$	2.18978	+	1.83745i	0.0747145	+	0.0626929i	0.679380	−	0.733787i	$-0.262249\pi$
$859$	2.18978	+	1.83745i	0.0747145	+	0.0626929i	−0.604666	+	0.796479i	$0.706693\pi$
$860$	−23.7404	+	34.6220i	−0.809542	+	1.18060i
$861$	−0.996062	+	5.64895i	−0.0339457	+	0.192516i
$862$	34.5167	−	28.4741i	1.17564	−	0.969831i
$863$	51.5534	+	13.8137i	1.75490	+	0.470224i	0.985661	−	0.168737i	$-0.0539690\pi$
$863$	51.5534	+	13.8137i	1.75490	+	0.470224i	0.769239	+	0.638961i	$0.220636\pi$
$864$	−3.06524	−	2.34335i	−0.104282	−	0.0797222i
$865$	−26.6990	−	6.39979i	−0.907794	−	0.217599i
$866$	36.0148	+	25.6697i	1.22383	+	0.872291i
$867$	2.11961	−	0.567948i	0.0719857	−	0.0192885i
$868$	−0.164790	+	1.57874i	−0.00559335	+	0.0535858i
$869$	3.47929	+	4.14646i	0.118027	+	0.140659i
$870$	−1.45371	−	0.100610i	−0.0492855	−	0.00341099i
$871$	−22.1126	+	3.89904i	−0.749255	+	0.132114i
$872$	−0.330963	−	2.19839i	−0.0112078	−	0.0744468i
$873$	−6.63407	−	6.63407i	−0.224529	−	0.224529i
$874$	1.64071	+	6.01777i	0.0554979	+	0.203554i
$875$	54.4936	+	10.0394i	1.84222	+	0.339395i
$876$	0.540860	+	0.974094i	0.0182740	+	0.0329116i
$877$	29.1564	+	20.4155i	0.984541	+	0.689383i	0.950722	−	0.310045i	$-0.100344\pi$
$877$	29.1564	+	20.4155i	0.984541	+	0.689383i	0.0338194	+	0.999428i	$0.489233\pi$
$878$	−28.5773	+	16.1817i	−0.964437	+	0.546108i
$879$	−0.459820	+	0.385834i	−0.0155093	+	0.0130139i
$880$	−0.803314	−	4.74826i	−0.0270797	−	0.160064i
$881$	−12.2377	+	21.1964i	−0.412300	+	0.714124i	−0.995141	−	0.0984619i	$-0.968608\pi$
$881$	−12.2377	+	21.1964i	−0.412300	+	0.714124i	0.582841	+	0.812586i	$0.301941\pi$
$882$	73.1682	−	12.2711i	2.46370	−	0.413188i
$883$	20.9934	−	45.0204i	0.706483	−	1.51506i	−0.144296	−	0.989535i	$-0.546092\pi$
$883$	20.9934	−	45.0204i	0.706483	−	1.51506i	0.850779	−	0.525524i	$-0.176131\pi$
$884$	−38.1382	−	14.6086i	−1.28273	−	0.491340i
$885$	−2.94513	−	0.179077i	−0.0989996	−	0.00601960i
$886$	−36.9044	−	3.54017i	−1.23983	−	0.118934i
$887$	−19.8267	+	13.8828i	−0.665714	+	0.466138i	−0.856945	−	0.515407i	$-0.827641\pi$
$887$	−19.8267	+	13.8828i	−0.665714	+	0.466138i	0.191232	+	0.981545i	$0.438752\pi$
$888$	1.43714	+	0.564324i	0.0482272	+	0.0189375i
$889$	−53.8672	+	64.1965i	−1.80665	+	2.15308i
$890$	−0.397119	−	21.8559i	−0.0133115	−	0.732611i
$891$	1.63586	−	4.49449i	0.0548034	−	0.150571i
$892$	8.45245	−	0.597127i	0.283009	−	0.0199933i
$893$	8.27450	−	3.98763i	0.276896	−	0.133441i
$894$	−0.743575	+	0.339188i	−0.0248689	+	0.0113441i
$895$	−36.5505	−	5.44917i	−1.22175	−	0.182146i
$896$	56.0486	−	1.60808i	1.87245	−	0.0537221i
$897$	0.389413	−	0.0340692i	0.0130021	−	0.00113754i
$898$	−28.7931	+	10.2078i	−0.960840	+	0.340638i
$899$	−0.112477	+	0.637889i	−0.00375132	+	0.0212748i
$900$	20.0188	+	22.1693i	0.667293	+	0.738977i
$901$	−14.2067	−	24.6068i	−0.473295	−	0.819771i
$902$	−7.73532	−	0.0647390i	−0.257558	−	0.00215557i
$903$	−2.23990	+	4.80347i	−0.0745391	+	0.159850i
$904$	4.38700	+	18.1872i	0.145909	+	0.604897i
$905$	1.88775	−	5.64859i	0.0627509	−	0.187765i
$906$	−0.803701	−	3.10311i	−0.0267012	−	0.103094i
$907$	−34.3136	−	3.00205i	−1.13936	−	0.0996814i	−0.498183	−	0.867072i	$-0.665999\pi$
$907$	−34.3136	−	3.00205i	−1.13936	−	0.0996814i	−0.641180	+	0.767390i	$0.721555\pi$
$908$	−27.9370	+	38.5098i	−0.927121	+	1.27799i
$909$	26.7703	−	4.72032i	0.887915	−	0.156563i
$910$	46.5013	+	25.7327i	1.54150	+	0.853029i
$911$			6.36317i			0.210821i	0.994429	+	0.105411i	$0.0336157\pi$
$911$			6.36317i			0.210821i	−0.994429	+	0.105411i	$0.966384\pi$
$912$	1.65038	−	1.10534i	0.0546497	−	0.0366016i
$913$	−0.110524	−	0.110524i	−0.00365780	−	0.00365780i
$914$	3.43403	+	43.4349i	0.113588	+	1.43670i
$915$	1.02874	+	0.446873i	0.0340091	+	0.0147732i
$916$	57.7412	−	9.18764i	1.90782	−	0.303568i
$917$	−1.86403	+	21.3059i	−0.0615555	+	0.703583i
$918$	−5.00586	−	2.94627i	−0.165218	−	0.0972413i
$919$	11.3413	−	19.6437i	0.374115	−	0.647986i	−0.616079	−	0.787684i	$-0.711280\pi$
$919$	11.3413	−	19.6437i	0.374115	−	0.647986i	0.990194	+	0.139698i	$0.0446131\pi$
$920$	−5.79601	+	2.71282i	−0.191089	+	0.0894390i
$921$	1.08286	−	0.394128i	0.0356814	−	0.0129870i
$922$	0.375041	−	44.8116i	0.0123513	−	1.47579i
$923$	−20.9490	−	5.61327i	−0.689544	−	0.184763i
$924$	−0.198356	−	0.574734i	−0.00652545	−	0.0189073i
$925$	−20.3264	−	12.6812i	−0.668327	−	0.416954i
$926$	18.3472	+	8.74314i	0.602928	+	0.287317i
$927$	2.78138	+	31.7913i	0.0913525	+	1.04416i
$928$	22.8609	+	0.957184i	0.750447	+	0.0314211i
$929$	1.07594	−	2.95613i	0.0353006	−	0.0969875i	−0.920790	−	0.390058i	$-0.872455\pi$
$929$	1.07594	−	2.95613i	0.0353006	−	0.0969875i	0.956091	+	0.293071i	$0.0946771\pi$
$930$	−0.0466491	+	0.0339435i	−0.00152968	+	0.00111305i
$931$	−12.3316	+	75.5545i	−0.404152	+	2.47620i
$932$	2.03926	+	28.8660i	0.0667980	+	0.945539i
$933$	1.09317	+	2.34430i	0.0357886	+	0.0767490i
$934$	−6.14024	−	8.92726i	−0.200915	−	0.292109i
$935$	−2.06154	−	6.95053i	−0.0674196	−	0.227307i
$936$	11.4522	+	26.2611i	0.374326	+	0.858372i
$937$	15.2846	+	21.8286i	0.499325	+	0.713111i	0.987144	−	0.159835i	$-0.0510961\pi$
$937$	15.2846	+	21.8286i	0.499325	+	0.713111i	−0.487818	+	0.872945i	$0.662207\pi$
$938$	35.8001	−	29.5328i	1.16891	−	0.964280i
$939$	−0.503178	−	0.871530i	−0.0164206	−	0.0284413i
$940$	5.48068	+	7.66623i	0.178760	+	0.250045i
$941$	−39.6877	+	14.4451i	−1.29378	+	0.470898i	−0.894966	−	0.446134i	$-0.852800\pi$
$941$	−39.6877	+	14.4451i	−1.29378	+	0.470898i	−0.398814	+	0.917032i	$0.630578\pi$
$942$	0.402940	+	2.40260i	0.0131285	+	0.0782808i
$943$	2.66054	+	9.92928i	0.0866392	+	0.323342i
$944$	46.3042	+	1.55067i	1.50707	+	0.0504702i
$945$	5.91724	+	4.70334i	0.192488	+	0.153000i
$946$	−6.88827	−	1.90763i	−0.223957	−	0.0620225i
$947$	−2.02591	+	2.89330i	−0.0658332	+	0.0940195i	−0.850719	−	0.525621i	$-0.823833\pi$
$947$	−2.02591	+	2.89330i	−0.0658332	+	0.0940195i	0.784885	+	0.619641i	$0.212722\pi$
$948$	−2.20234	−	0.629805i	−0.0715285	−	0.0204551i
$949$		−	16.5822i		−	0.538281i
$950$	−28.3102	+	12.1874i	−0.918504	+	0.395411i
$951$		−	0.542750i		−	0.0175999i
$952$	83.4720	−	12.5665i	2.70534	−	0.407284i
$953$	21.7162	−	31.0139i	0.703455	−	1.00464i	−0.295331	−	0.955395i	$-0.595430\pi$
$953$	21.7162	−	31.0139i	0.703455	−	1.00464i	0.998787	−	0.0492435i	$-0.0156810\pi$
$954$	−5.31976	+	19.2091i	−0.172234	+	0.621918i
$955$	−8.71705	−	6.92877i	−0.282077	−	0.224210i
$956$	29.4623	−	23.8930i	0.952877	−	0.772754i
$957$	−0.0642142	−	0.239651i	−0.00207575	−	0.00774680i
$958$	19.4220	−	3.25726i	0.627495	−	0.105237i
$959$	10.0278	−	3.64981i	0.323813	−	0.117858i
$960$	1.40652	+	1.47476i	0.0453953	+	0.0475976i
$961$	−15.4872	−	26.8246i	−0.499586	−	0.865309i
$962$	−14.6226	−	17.7257i	−0.471452	−	0.571500i
$963$	19.3696	+	27.6626i	0.624176	+	0.891416i
$964$	21.5797	+	0.361238i	0.695035	+	0.0116347i
$965$	−2.96183	−	9.98589i	−0.0953448	−	0.321457i
$966$	−0.665689	+	0.457866i	−0.0214182	+	0.0147316i
$967$	−14.6194	−	31.3514i	−0.470129	−	1.00819i	−0.988244	−	0.152884i	$-0.951144\pi$
$967$	−14.6194	−	31.3514i	−0.470129	−	1.00819i	0.518116	−	0.855311i	$-0.326634\pi$
$968$	−26.6063	+	14.4830i	−0.855158	+	0.465501i
$969$	2.26604	−	1.95118i	0.0727956	−	0.0626810i
$970$	5.84390	+	8.03136i	0.187636	+	0.257871i
$971$	8.62170	−	23.6879i	0.276684	−	0.760182i	−0.721049	−	0.692884i	$-0.756340\pi$
$971$	8.62170	−	23.6879i	0.276684	−	0.760182i	0.997733	−	0.0672983i	$-0.0214379\pi$
$972$	1.48395	+	5.93373i	0.0475978	+	0.190325i
$973$	3.18889	+	36.4491i	0.102231	+	1.16851i
$974$	−25.9724	+	54.5025i	−0.832210	+	1.74637i
$975$	0.435864	+	1.88180i	0.0139588	+	0.0602660i
$976$	−16.3386	−	6.57406i	−0.522986	−	0.210430i
$977$	23.5314	+	6.30523i	0.752837	+	0.201722i	0.614776	−	0.788702i	$-0.289246\pi$
$977$	23.5314	+	6.30523i	0.752837	+	0.201722i	0.138061	+	0.990424i	$0.455913\pi$
$978$	1.02754	+	0.00859972i	0.0328569	+	0.000274989i
$979$	3.49739	−	1.27295i	0.111777	−	0.0406835i
$980$	−78.5392	+	0.769616i	−2.50884	+	0.0245845i
$981$	−1.17391	+	2.03327i	−0.0374800	+	0.0649173i
$982$	24.2343	−	41.1754i	0.773349	−	1.31396i
$983$	−4.27770	+	48.8943i	−0.136437	+	1.55949i	0.551784	+	0.833987i	$0.313947\pi$
$983$	−4.27770	+	48.8943i	−0.136437	+	1.55949i	−0.688222	+	0.725500i	$0.741608\pi$
$984$	2.72785	−	1.80974i	0.0869607	−	0.0576923i
$985$	22.7855	+	9.89774i	0.726006	+	0.315368i
$986$	34.3388	−	2.71488i	1.09357	−	0.0864594i
$987$	0.841306	+	0.841306i	0.0267791	+	0.0267791i
$988$	−29.4601	+	2.45893i	−0.937251	+	0.0782288i
$989$			9.49811i			0.302022i
$990$	−2.46245	+	4.44987i	−0.0782617	+	0.141426i
$991$	34.5378	−	6.08995i	1.09713	−	0.193454i	0.404352	−	0.914604i	$-0.367497\pi$
$991$	34.5378	−	6.08995i	1.09713	−	0.193454i	0.692779	+	0.721150i	$0.256386\pi$
$992$	0.717693	−	0.552747i	0.0227868	−	0.0175497i
$993$	−0.736348	−	0.0644221i	−0.0233673	−	0.00204437i
$994$	43.3949	−	11.2392i	1.37640	−	0.356487i
$995$	−5.61502	+	16.8015i	−0.178008	+	0.532642i
$996$	0.0649391	+	0.0125747i	0.00205767	+	0.000398444i
$997$	7.35612	−	15.7752i	0.232971	−	0.499607i	−0.754716	−	0.656051i	$-0.772225\pi$
$997$	7.35612	−	15.7752i	0.232971	−	0.499607i	0.987687	+	0.156444i	$0.0500032\pi$
$998$	0.224587	−	26.8347i	0.00710917	−	0.849437i
$999$	−1.63408	−	2.83031i	−0.0517000	−	0.0895471i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.bj.a.23.16	yes	672
4.3	odd	2	inner	380.2.bj.a.23.2	✓	672
5.2	odd	4	inner	380.2.bj.a.327.15	yes	672
19.5	even	9	inner	380.2.bj.a.43.27	yes	672
20.7	even	4	inner	380.2.bj.a.327.27	yes	672
76.43	odd	18	inner	380.2.bj.a.43.15	yes	672
95.62	odd	36	inner	380.2.bj.a.347.2	yes	672
380.347	even	36	inner	380.2.bj.a.347.16	yes	672

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.bj.a.23.2	✓	672	4.3	odd	2	inner
380.2.bj.a.23.16	yes	672	1.1	even	1	trivial
380.2.bj.a.43.15	yes	672	76.43	odd	18	inner
380.2.bj.a.43.27	yes	672	19.5	even	9	inner
380.2.bj.a.327.15	yes	672	5.2	odd	4	inner
380.2.bj.a.327.27	yes	672	20.7	even	4	inner
380.2.bj.a.347.2	yes	672	95.62	odd	36	inner
380.2.bj.a.347.16	yes	672	380.347	even	36	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:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.bj (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.918074 + 1.07570i) q^{2} +(0.0933215 + 0.0653444i) q^{3} +(-0.314282 - 1.97515i) q^{4} +(1.39136 - 1.75046i) q^{5} +(-0.155967 + 0.0403954i) q^{6} +(-4.78721 + 1.28273i) q^{7} +(2.41321 + 1.47526i) q^{8} +(-1.02162 - 2.80688i) q^{9} +O(q^{10})\)	\(q+(-0.918074 + 1.07570i) q^{2} +(0.0933215 + 0.0653444i) q^{3} +(-0.314282 - 1.97515i) q^{4} +(1.39136 - 1.75046i) q^{5} +(-0.155967 + 0.0403954i) q^{6} +(-4.78721 + 1.28273i) q^{7} +(2.41321 + 1.47526i) q^{8} +(-1.02162 - 2.80688i) q^{9} +(0.605609 + 3.10375i) q^{10} +(-0.466282 + 0.269208i) q^{11} +(0.0997360 - 0.204861i) q^{12} +(-2.77779 + 1.94503i) q^{13} +(3.01517 - 6.32726i) q^{14} +(0.244227 - 0.0724381i) q^{15} +(-3.80245 + 1.24151i) q^{16} +(-5.45758 + 2.54491i) q^{17} +(3.95730 + 1.47796i) q^{18} +(-2.75906 + 3.37455i) q^{19} +(-3.89471 - 2.19801i) q^{20} +(-0.530569 - 0.193111i) q^{21} +(0.138493 - 0.748734i) q^{22} +(-1.00799 + 0.0881880i) q^{23} +(0.128805 + 0.295364i) q^{24} +(-1.12823 - 4.87105i) q^{25} +(0.457939 - 4.77377i) q^{26} +(0.176532 - 0.658828i) q^{27} +(4.03812 + 9.05233i) q^{28} +(1.38341 + 3.80089i) q^{29} +(-0.146296 + 0.329219i) q^{30} +(0.138683 + 0.0800689i) q^{31} +(2.15544 - 5.23011i) q^{32} +(-0.0611054 - 0.00534603i) q^{33} +(2.27289 - 8.20716i) q^{34} +(-4.41536 + 10.1646i) q^{35} +(-5.22294 + 2.90001i) q^{36} +(3.38813 - 3.38813i) q^{37} +(-1.09699 - 6.06602i) q^{38} -0.386325 q^{39} +(5.94004 - 2.17162i) q^{40} +(-1.76413 - 10.0049i) q^{41} +(0.694832 - 0.393445i) q^{42} +(0.818125 - 9.35121i) q^{43} +(0.678270 + 0.836371i) q^{44} +(-6.33478 - 2.11707i) q^{45} +(0.830548 - 1.16527i) q^{46} +(-1.90980 - 0.890557i) q^{47} +(-0.435976 - 0.132610i) q^{48} +(15.2098 - 8.78138i) q^{49} +(6.27561 + 3.25833i) q^{50} +(-0.675605 - 0.119127i) q^{51} +(4.71474 + 4.87528i) q^{52} +(0.411241 + 4.70050i) q^{53} +(0.546634 + 0.794749i) q^{54} +(-0.177528 + 1.19077i) q^{55} +(-13.4449 - 3.96688i) q^{56} +(-0.477988 + 0.134628i) q^{57} +(-5.35871 - 2.00136i) q^{58} +(-10.8840 - 3.96146i) q^{59} +(-0.219832 - 0.459619i) q^{60} +(3.37282 + 2.83013i) q^{61} +(-0.213452 + 0.0756733i) q^{62} +(8.49118 + 12.1267i) q^{63} +(3.64721 + 7.12024i) q^{64} +(-0.460207 + 7.56866i) q^{65} +(0.0618500 - 0.0608233i) q^{66} +(6.00106 + 2.79834i) q^{67} +(6.74180 + 9.97973i) q^{68} +(-0.0998301 - 0.0576369i) q^{69} +(-6.88044 - 14.0814i) q^{70} +(4.11104 + 4.89935i) q^{71} +(1.67549 - 8.28077i) q^{72} +(-2.80477 + 4.00563i) q^{73} +(0.534075 + 6.75519i) q^{74} +(0.213007 - 0.528297i) q^{75} +(7.53237 + 4.38901i) q^{76} +(1.88687 - 1.88687i) q^{77} +(0.354674 - 0.415571i) q^{78} +(-1.74573 - 9.90050i) q^{79} +(-3.11737 + 8.38344i) q^{80} +(-6.80505 + 5.71011i) q^{81} +(12.3819 + 7.28754i) q^{82} +(0.0751360 + 0.280411i) q^{83} +(-0.214676 + 1.10865i) q^{84} +(-3.13869 + 13.0942i) q^{85} +(9.30805 + 9.46517i) q^{86} +(-0.119265 + 0.445103i) q^{87} +(-1.52239 - 0.0382310i) q^{88} +(-6.80756 - 1.20036i) q^{89} +(8.09314 - 4.87073i) q^{90} +(10.8029 - 12.8744i) q^{91} +(0.490979 + 1.96323i) q^{92} +(0.00771009 + 0.0165343i) q^{93} +(2.71132 - 1.23679i) q^{94} +(2.06817 + 9.52485i) q^{95} +(0.542907 - 0.347236i) q^{96} +(2.84664 - 1.32741i) q^{97} +(-4.51754 + 24.4232i) q^{98} +(1.23200 + 1.03377i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8}+O(q^{10}) \) 672 * q - 12 * q^2 - 24 * q^5 - 36 * q^6 - 6 * q^8	\( 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8} - 12 q^{10} - 6 q^{12} - 24 q^{13} - 36 q^{16} - 24 q^{17} - 24 q^{18} + 36 q^{20} - 48 q^{21} - 24 q^{22} - 24 q^{25} - 60 q^{26} - 24 q^{28} - 6 q^{30} + 18 q^{32} - 60 q^{33} + 24 q^{36} - 48 q^{37} - 114 q^{38} - 42 q^{40} - 24 q^{41} - 48 q^{42} - 12 q^{45} - 12 q^{46} - 96 q^{48} - 6 q^{50} - 12 q^{52} - 24 q^{53} - 48 q^{56} - 24 q^{57} + 120 q^{58} - 12 q^{60} - 48 q^{61} + 36 q^{62} - 12 q^{65} - 96 q^{66} - 6 q^{68} - 12 q^{70} + 120 q^{72} - 24 q^{73} - 96 q^{76} - 360 q^{77} - 126 q^{78} + 48 q^{80} - 48 q^{81} + 228 q^{82} - 24 q^{85} - 132 q^{86} - 102 q^{88} + 78 q^{90} + 108 q^{92} - 60 q^{93} - 144 q^{96} - 24 q^{97} + 18 q^{98}+O(q^{100}) \) 672 * q - 12 * q^2 - 24 * q^5 - 36 * q^6 - 6 * q^8 - 12 * q^10 - 6 * q^12 - 24 * q^13 - 36 * q^16 - 24 * q^17 - 24 * q^18 + 36 * q^20 - 48 * q^21 - 24 * q^22 - 24 * q^25 - 60 * q^26 - 24 * q^28 - 6 * q^30 + 18 * q^32 - 60 * q^33 + 24 * q^36 - 48 * q^37 - 114 * q^38 - 42 * q^40 - 24 * q^41 - 48 * q^42 - 12 * q^45 - 12 * q^46 - 96 * q^48 - 6 * q^50 - 12 * q^52 - 24 * q^53 - 48 * q^56 - 24 * q^57 + 120 * q^58 - 12 * q^60 - 48 * q^61 + 36 * q^62 - 12 * q^65 - 96 * q^66 - 6 * q^68 - 12 * q^70 + 120 * q^72 - 24 * q^73 - 96 * q^76 - 360 * q^77 - 126 * q^78 + 48 * q^80 - 48 * q^81 + 228 * q^82 - 24 * q^85 - 132 * q^86 - 102 * q^88 + 78 * q^90 + 108 * q^92 - 60 * q^93 - 144 * q^96 - 24 * q^97 + 18 * q^98

Introduction

L-functions

Modular forms

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