LMFDB - Embedded newform 380.2.bj.a.23.2

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			23.2
Character	$\chi$	$=$	380.23
Dual form			380.2.bj.a.347.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41416 + 0.0118355i) q^{2} +(-0.0933215 - 0.0653444i) q^{3} +(1.99972 - 0.0334747i) q^{4} +(1.39136 - 1.75046i) q^{5} +(0.132745 + 0.0913032i) q^{6} +(4.78721 - 1.28273i) q^{7} +(-2.82754 + 0.0710065i) q^{8} +(-1.02162 - 2.80688i) q^{9} +O(q^{10})$	\(q+(-1.41416 + 0.0118355i) q^{2} +(-0.0933215 - 0.0653444i) q^{3} +(1.99972 - 0.0334747i) q^{4} +(1.39136 - 1.75046i) q^{5} +(0.132745 + 0.0913032i) q^{6} +(4.78721 - 1.28273i) q^{7} +(-2.82754 + 0.0710065i) q^{8} +(-1.02162 - 2.80688i) q^{9} +(-1.94689 + 2.49191i) q^{10} +(0.466282 - 0.269208i) q^{11} +(-0.188804 - 0.127547i) q^{12} +(-2.77779 + 1.94503i) q^{13} +(-6.75472 + 1.87065i) q^{14} +(-0.244227 + 0.0724381i) q^{15} +(3.99776 - 0.133880i) q^{16} +(-5.45758 + 2.54491i) q^{17} +(1.47796 + 3.95730i) q^{18} +(2.75906 - 3.37455i) q^{19} +(2.72373 - 3.54701i) q^{20} +(-0.530569 - 0.193111i) q^{21} +(-0.656213 + 0.386223i) q^{22} +(1.00799 - 0.0881880i) q^{23} +(0.268510 + 0.178137i) q^{24} +(-1.12823 - 4.87105i) q^{25} +(3.90523 - 2.78347i) q^{26} +(-0.176532 + 0.658828i) q^{27} +(9.53014 - 2.72535i) q^{28} +(1.38341 + 3.80089i) q^{29} +(0.344519 - 0.105330i) q^{30} +(-0.138683 - 0.0800689i) q^{31} +(-5.65190 + 0.236644i) q^{32} +(-0.0611054 - 0.00534603i) q^{33} +(7.68779 - 3.66351i) q^{34} +(4.41536 - 10.1646i) q^{35} +(-2.13692 - 5.57878i) q^{36} +(3.38813 - 3.38813i) q^{37} +(-3.86183 + 4.80482i) q^{38} +0.386325 q^{39} +(-3.80983 + 5.04829i) q^{40} +(-1.76413 - 10.0049i) q^{41} +(0.752597 + 0.266811i) q^{42} +(-0.818125 + 9.35121i) q^{43} +(0.923421 - 0.553949i) q^{44} +(-6.33478 - 2.11707i) q^{45} +(-1.42442 + 0.136642i) q^{46} +(1.90980 + 0.890557i) q^{47} +(-0.381825 - 0.248737i) q^{48} +(15.2098 - 8.78138i) q^{49} +(1.65316 + 6.87510i) q^{50} +(0.675605 + 0.119127i) q^{51} +(-5.48970 + 3.98250i) q^{52} +(0.411241 + 4.70050i) q^{53} +(0.241848 - 0.933780i) q^{54} +(0.177528 - 1.19077i) q^{55} +(-13.4449 + 3.96688i) q^{56} +(-0.477988 + 0.134628i) q^{57} +(-2.00136 - 5.35871i) q^{58} +(10.8840 + 3.96146i) q^{59} +(-0.485960 + 0.153031i) q^{60} +(3.37282 + 2.83013i) q^{61} +(0.197069 + 0.111589i) q^{62} +(-8.49118 - 12.1267i) q^{63} +(7.98992 - 0.401547i) q^{64} +(-0.460207 + 7.56866i) q^{65} +(0.0864763 + 0.00683694i) q^{66} +(-6.00106 - 2.79834i) q^{67} +(-10.8284 + 5.27180i) q^{68} +(-0.0998301 - 0.0576369i) q^{69} +(-6.12374 + 14.4266i) q^{70} +(-4.11104 - 4.89935i) q^{71} +(3.08798 + 7.86402i) q^{72} +(-2.80477 + 4.00563i) q^{73} +(-4.75128 + 4.83148i) q^{74} +(-0.213007 + 0.528297i) q^{75} +(5.40439 - 6.84051i) q^{76} +(1.88687 - 1.88687i) q^{77} +(-0.546326 + 0.00457235i) q^{78} +(1.74573 + 9.90050i) q^{79} +(5.32797 - 7.18420i) q^{80} +(-6.80505 + 5.71011i) q^{81} +(2.61318 + 14.1277i) q^{82} +(-0.0751360 - 0.280411i) q^{83} +(-1.06745 - 0.368408i) q^{84} +(-3.13869 + 13.0942i) q^{85} +(1.04629 - 13.2338i) q^{86} +(0.119265 - 0.445103i) q^{87} +(-1.29931 + 0.794304i) q^{88} +(-6.80756 - 1.20036i) q^{89} +(8.98348 + 2.91891i) q^{90} +(-10.8029 + 12.8744i) q^{91} +(2.01275 - 0.210094i) 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} +(-21.4052 + 12.5983i) 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 $

$2$	−1.41416	+	0.0118355i	−0.999965	+	0.00836898i
$2$	−1.41416	+	0.0118355i	−0.999965	+	0.00836898i
$3$	−0.0933215	−	0.0653444i	−0.0538792	−	0.0377266i	0.546327	−	0.837572i	$-0.316026\pi$
$3$	−0.0933215	−	0.0653444i	−0.0538792	−	0.0377266i	−0.600206	+	0.799846i	$0.704915\pi$
$4$	1.99972	−	0.0334747i	0.999860	−	0.0167374i
$5$	1.39136	−	1.75046i	0.622235	−	0.782830i
$5$	1.39136	−	1.75046i	0.622235	−	0.782830i
$6$	0.132745	+	0.0913032i	0.0541930	+	0.0372744i
$7$	4.78721	−	1.28273i	1.80939	−	0.484826i	0.814015	−	0.580844i	$-0.197277\pi$
$7$	4.78721	−	1.28273i	1.80939	−	0.484826i	0.995380	+	0.0960182i	$0.0306107\pi$
$8$	−2.82754	+	0.0710065i	−0.999685	+	0.0251046i
$9$	−1.02162	−	2.80688i	−0.340540	−	0.935627i
$10$	−1.94689	+	2.49191i	−0.615662	+	0.788010i
$11$	0.466282	−	0.269208i	0.140589	−	0.0811692i	−0.428056	−	0.903752i	$-0.640801\pi$
$11$	0.466282	−	0.269208i	0.140589	−	0.0811692i	0.568645	+	0.822583i	$0.307468\pi$
$12$	−0.188804	−	0.127547i	−0.0545031	−	0.0368195i
$13$	−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	$0.461394\pi$
$14$	−6.75472	+	1.87065i	−1.80527	+	0.499952i
$15$	−0.244227	+	0.0724381i	−0.0630591	+	0.0187034i
$16$	3.99776	−	0.133880i	0.999440	−	0.0334701i
$17$	−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	$0.621706\pi$
$18$	1.47796	+	3.95730i	0.348359	+	0.932745i
$19$	2.75906	−	3.37455i	0.632972	−	0.774174i
$19$	2.75906	−	3.37455i	0.632972	−	0.774174i
$20$	2.72373	−	3.54701i	0.609045	−	0.793135i
$21$	−0.530569	−	0.193111i	−0.115780	−	0.0421403i
$22$	−0.656213	+	0.386223i	−0.139905	+	0.0823430i
$23$	1.00799	−	0.0881880i	0.210181	−	0.0183885i	0.0184212	−	0.999830i	$-0.494136\pi$
$23$	1.00799	−	0.0881880i	0.210181	−	0.0183885i	0.191760	+	0.981442i	$0.438580\pi$
$24$	0.268510	+	0.178137i	0.0548093	+	0.0363621i
$25$	−1.12823	−	4.87105i	−0.225647	−	0.974209i
$26$	3.90523	−	2.78347i	0.765879	−	0.545883i
$27$	−0.176532	+	0.658828i	−0.0339737	+	0.126791i
$28$	9.53014	−	2.72535i	1.80103	−	0.515042i
$29$	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	$0.766342\pi$
$30$	0.344519	−	0.105330i	0.0629003	−	0.0192305i
$31$	−0.138683	−	0.0800689i	−0.0249083	−	0.0143808i	0.487494	−	0.873126i	$-0.337911\pi$
$31$	−0.138683	−	0.0800689i	−0.0249083	−	0.0143808i	−0.512402	+	0.858745i	$0.671244\pi$
$32$	−5.65190	+	0.236644i	−0.999125	+	0.0418332i
$33$	−0.0611054	−	0.00534603i	−0.0106371	−	0.000930624i
$34$	7.68779	−	3.66351i	1.31844	−	0.628287i
$35$	4.41536	−	10.1646i	0.746333	−	1.71812i
$36$	−2.13692	−	5.57878i	−0.356153	−	0.929796i
$37$	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	$0.121139\pi$
$38$	−3.86183	+	4.80482i	−0.626471	+	0.779445i
$39$	0.386325			0.0618614
$40$	−3.80983	+	5.04829i	−0.602386	+	0.798205i
$41$	−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	$-0.347195\pi$
$42$	0.752597	+	0.266811i	0.116128	+	0.0411699i
$43$	−0.818125	+	9.35121i	−0.124763	+	1.42605i	0.633321	+	0.773889i	$0.281691\pi$
$43$	−0.818125	+	9.35121i	−0.124763	+	1.42605i	−0.758084	+	0.652157i	$0.773864\pi$
$44$	0.923421	−	0.553949i	0.139211	−	0.0835110i
$45$	−6.33478	−	2.11707i	−0.944334	−	0.315595i
$46$	−1.42442	+	0.136642i	−0.210020	+	0.0201468i
$47$	1.90980	+	0.890557i	0.278574	+	0.129901i	0.556884	−	0.830590i	$-0.311997\pi$
$47$	1.90980	+	0.890557i	0.278574	+	0.129901i	−0.278311	+	0.960491i	$0.589774\pi$
$48$	−0.381825	−	0.248737i	−0.0551117	−	0.0359021i
$49$	15.2098	−	8.78138i	2.17283	−	1.25448i
$50$	1.65316	+	6.87510i	0.233792	+	0.972287i
$51$	0.675605	+	0.119127i	0.0946036	+	0.0166812i
$52$	−5.48970	+	3.98250i	−0.761284	+	0.552274i
$53$	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	$0.867173\pi$
$54$	0.241848	−	0.933780i	0.0329114	−	0.127071i
$55$	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
$58$	−2.00136	−	5.35871i	−0.262791	−	0.703633i
$59$	10.8840	+	3.96146i	1.41698	+	0.515739i	0.933170	−	0.359434i	$-0.117030\pi$
$59$	10.8840	+	3.96146i	1.41698	+	0.515739i	0.483810	+	0.875173i	$0.339252\pi$
$60$	−0.485960	+	0.153031i	−0.0627372	+	0.0197563i
$61$	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	$0.631269\pi$
$62$	0.197069	+	0.111589i	0.0250278	+	0.0141718i
$63$	−8.49118	−	12.1267i	−1.06979	−	1.52782i
$64$	7.98992	−	0.401547i	0.998740	−	0.0501934i
$65$	−0.460207	+	7.56866i	−0.0570816	+	0.938776i
$66$	0.0864763	+	0.00683694i	0.0106445	+	0.000841570i
$67$	−6.00106	−	2.79834i	−0.733146	−	0.341872i	0.0199332	−	0.999801i	$-0.493655\pi$
$67$	−6.00106	−	2.79834i	−0.733146	−	0.341872i	−0.753079	+	0.657930i	$0.771432\pi$
$68$	−10.8284	+	5.27180i	−1.31314	+	0.639299i
$69$	−0.0998301	−	0.0576369i	−0.0120181	−	0.00693867i
$70$	−6.12374	+	14.4266i	−0.731927	+	1.72431i
$71$	−4.11104	−	4.89935i	−0.487891	−	0.581445i	0.464789	−	0.885421i	$-0.346130\pi$
$71$	−4.11104	−	4.89935i	−0.487891	−	0.581445i	−0.952680	+	0.303976i	$0.901686\pi$
$72$	3.08798	+	7.86402i	0.363922	+	0.926783i
$73$	−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	$0.286825\pi$
$74$	−4.75128	+	4.83148i	−0.552325	+	0.561648i
$75$	−0.213007	+	0.528297i	−0.0245960	+	0.0610025i
$76$	5.40439	−	6.84051i	0.619926	−	0.784660i
$77$	1.88687	−	1.88687i	0.215028	−	0.215028i
$78$	−0.546326	+	0.00457235i	−0.0618593	+	0.000517717i
$79$	1.74573	+	9.90050i	0.196409	+	1.11389i	0.910397	+	0.413735i	$0.135776\pi$
$79$	1.74573	+	9.90050i	0.196409	+	1.11389i	−0.713988	+	0.700158i	$0.753113\pi$
$80$	5.32797	−	7.18420i	0.595685	−	0.803218i
$81$	−6.80505	+	5.71011i	−0.756116	+	0.634457i
$82$	2.61318	+	14.1277i	0.288578	+	1.56014i
$83$	−0.0751360	−	0.280411i	−0.00824725	−	0.0307792i	0.961680	−	0.274176i	$-0.0884050\pi$
$83$	−0.0751360	−	0.280411i	−0.00824725	−	0.0307792i	−0.969927	+	0.243397i	$0.921738\pi$
$84$	−1.06745	−	0.368408i	−0.116469	−	0.0401966i
$85$	−3.13869	+	13.0942i	−0.340438	+	1.42026i
$86$	1.04629	−	13.2338i	0.112824	−	1.42704i
$87$	0.119265	−	0.445103i	0.0127865	−	0.0477201i
$88$	−1.29931	+	0.794304i	−0.138507	+	0.0846731i
$89$	−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	$0.674954\pi$
$90$	8.98348	+	2.91891i	0.946942	+	0.307681i
$91$	−10.8029	+	12.8744i	−1.13245	+	1.34961i
$92$	2.01275	−	0.210094i	0.209844	−	0.0219038i
$93$	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	$0.310137\pi$
$98$	−21.4052	+	12.5983i	−2.16225	+	1.27262i
$99$	−1.23200	−	1.03377i	−0.123820	−	0.103898i
$100$	−2.41921	−	9.70296i	−0.241921	−	0.970296i
$101$	−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	$0.905993\pi$
$102$	−0.956826	−	0.160470i	−0.0947399	−	0.0158889i
$103$	10.3198	+	2.76517i	1.01684	+	0.272460i	0.728483	−	0.685064i	$-0.240226\pi$
$103$	10.3198	+	2.76517i	1.01684	+	0.272460i	0.288353	+	0.957524i	$0.406892\pi$
$104$	7.71620	−	5.69689i	0.756635	−	0.558626i
$105$	−1.07625	+	0.660053i	−0.105031	+	0.0644146i
$106$	−0.637195	−	6.64242i	−0.0618898	−	0.645168i
$107$	10.9203	−	2.92609i	1.05571	−	0.282875i	0.311098	−	0.950378i	$-0.399303\pi$
$107$	10.9203	−	2.92609i	1.05571	−	0.282875i	0.744608	+	0.667503i	$0.232637\pi$
$108$	−0.330961	+	1.32338i	−0.0318467	+	0.127342i
$109$	−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	$0.789763\pi$
$110$	−0.236960	+	1.68605i	−0.0225932	+	0.160759i
$111$	−0.537581	+	0.0947901i	−0.0510250	+	0.00899708i
$112$	18.9664	−	5.76895i	1.79215	−	0.545115i
$113$	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	$0.649295\pi$
$114$	0.674360	−	0.196044i	0.0631596	−	0.0183612i
$115$	1.24811	−	1.88716i	0.116387	−	0.175978i
$116$	2.89367	+	7.55441i	0.268670	+	0.701409i
$117$	8.29732	+	5.80985i	0.767088	+	0.537121i
$118$	−15.4387	−	5.47334i	−1.42125	−	0.503862i
$119$	−22.8621	+	19.1836i	−2.09577	+	1.75856i
$120$	0.685416	−	0.222163i	0.0625697	−	0.0202806i
$121$	−5.35505	+	9.27523i	−0.486823	+	0.843202i
$122$	−4.80321	−	3.96235i	−0.434862	−	0.358734i
$123$	−0.489132	+	1.04895i	−0.0441035	+	0.0945803i
$124$	−0.280008	−	0.155473i	−0.0251455	−	0.0139619i
$125$	−10.0964	−	4.80245i	−0.903046	−	0.429544i
$126$	12.1514	+	17.0486i	1.08254	+	1.51881i
$127$	−13.8511	+	9.69862i	−1.22908	+	0.860613i	−0.993786	−	0.111310i	$-0.964495\pi$
$127$	−13.8511	+	9.69862i	−1.22908	+	0.860613i	−0.235297	+	0.971923i	$0.575606\pi$
$128$	−11.2943	+	0.662418i	−0.998284	+	0.0585500i
$129$	0.687398	−	0.819210i	0.0605221	−	0.0721274i
$130$	0.561229	−	10.7088i	0.0492230	−	0.939221i
$131$	−1.47594	+	4.05511i	−0.128954	+	0.354297i	−0.987321	−	0.158739i	$-0.949257\pi$
$131$	−1.47594	+	4.05511i	−0.128954	+	0.354297i	0.858367	+	0.513036i	$0.171479\pi$
$132$	−0.122373	−	0.00864507i	−0.0106512	−	0.000752457i
$133$	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
$136$	15.2508	−	7.58335i	1.30774	−	0.650267i
$137$	−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	$0.501542\pi$
$138$	0.141858	+	0.0803265i	0.0120758	+	0.00683785i
$139$	−1.28196	+	7.27036i	−0.108734	+	0.616664i	0.880928	+	0.473250i	$0.156919\pi$
$139$	−1.28196	+	7.27036i	−0.108734	+	0.616664i	−0.989663	+	0.143414i	$0.954192\pi$
$140$	8.48923	−	20.4741i	0.717471	−	1.73038i
$141$	−0.120033	−	0.207903i	−0.0101086	−	0.0175086i
$142$	5.87167	+	6.87982i	0.492740	+	0.577342i
$143$	−0.771616	+	1.65474i	−0.0645258	+	0.138376i
$144$	−4.45998	−	11.0845i	−0.371665	−	0.923705i
$145$	8.57814	+	2.86680i	0.712376	+	0.238075i
$146$	3.91900	−	5.69782i	0.324339	−	0.471555i
$147$	−1.99321	−	0.174384i	−0.164398	−	0.0143829i
$148$	6.66190	−	6.88874i	0.547605	−	0.566251i
$149$	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	$0.377818\pi$
$150$	0.294974	−	0.749620i	0.0240846	−	0.0612062i
$151$		−	19.8959i		−	1.61910i	−0.587049	−	0.809551i	$-0.699710\pi$
$151$		−	19.8959i		−	1.61910i	0.587049	−	0.809551i	$-0.300290\pi$
$152$	−7.56173	+	9.73756i	−0.613338	+	0.789821i
$153$	12.7188	+	12.7188i	1.02826	+	1.02826i
$154$	−2.64601	+	2.69067i	−0.213221	+	0.216821i
$155$	−0.333116	+	0.131355i	−0.0267565	+	0.0105507i
$156$	0.772541	−	0.0129321i	0.0618528	−	0.00103540i
$157$	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	$-0.178403\pi$
$158$	−2.58592	−	13.9803i	−0.205725	−	1.11221i
$159$	0.268774	−	0.465530i	0.0213152	−	0.0369190i
$160$	−7.44960	+	10.2227i	−0.588942	+	0.808175i
$161$	4.71235	−	1.71516i	0.371386	−	0.135173i
$162$	9.55587	−	8.15558i	0.750780	−	0.640763i
$163$	6.16061	+	1.65073i	0.482536	+	0.129295i	0.491883	−	0.870661i	$-0.336309\pi$
$163$	6.16061	+	1.65073i	0.482536	+	0.129295i	−0.00934727	+	0.999956i	$0.502975\pi$
$164$	−3.86268	−	19.9479i	−0.301624	−	1.55767i
$165$	−0.0943776	+	0.0995243i	−0.00734728	+	0.00774796i
$166$	0.109573	+	0.395659i	0.00850455	+	0.0307091i
$167$	−1.28396	−	14.6758i	−0.0993562	−	1.13565i	−0.868202	−	0.496212i	$-0.834724\pi$
$167$	−1.28396	−	14.6758i	−0.0993562	−	1.13565i	0.768845	−	0.639435i	$-0.220832\pi$
$168$	1.51391	+	0.508355i	0.116801	+	0.0392204i
$169$	−0.513279	+	1.41022i	−0.0394830	+	0.108479i
$170$	4.28364	−	18.5544i	0.328540	−	1.42306i
$171$	−12.2907	−	4.29685i	−0.939891	−	0.328589i
$172$	−1.32299	+	18.7272i	−0.100877	+	1.42794i
$173$	−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	$-0.293466\pi$
$174$	−0.163392	+	0.630860i	−0.0123867	+	0.0478254i
$175$	−11.6493	−	21.8715i	−0.880606	−	1.65333i
$176$	1.82804	−	1.13865i	0.137794	−	0.0858293i
$177$	−0.756855	−	1.08090i	−0.0568887	−	0.0812455i
$178$	9.64122	+	1.61693i	0.722640	+	0.121194i
$179$	8.26327	+	14.3124i	0.617626	+	1.06976i	0.989918	+	0.141644i	$0.0452387\pi$
$179$	8.26327	+	14.3124i	0.617626	+	1.06976i	−0.372292	+	0.928116i	$0.621428\pi$
$180$	−12.7387	−	4.02150i	−0.949484	−	0.299745i
$181$	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	$0.357329\pi$
$182$	15.1247	−	18.3344i	1.12112	−	1.35904i
$183$	−0.129823	−	0.484506i	−0.00959680	−	0.0358157i
$184$	−2.84388	+	0.320929i	−0.209653	+	0.0236592i
$185$	−1.21668	−	10.6449i	−0.0894525	−	0.782630i
$186$	−0.0110990	−	0.0232910i	−0.000813820	−	0.00170778i
$187$	−1.85966	+	2.65587i	−0.135992	+	0.194216i
$188$	3.84889	+	1.71693i	0.280709	+	0.125220i
$189$			3.38039i			0.245887i
$190$	3.03746	+	13.4452i	0.220360	+	0.975419i
$191$			4.97986i			0.360330i	0.983636	+	0.180165i	$0.0576631\pi$
$191$			4.97986i			0.360330i	−0.983636	+	0.180165i	$0.942337\pi$
$192$	−0.771870	−	0.484623i	−0.0557049	−	0.0349747i
$193$	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	$0.140827\pi$
$194$	−4.00991	+	1.91087i	−0.287894	+	0.137192i
$195$	0.537517	−	0.676247i	0.0384924	−	0.0484270i
$196$	30.1214	−	18.0694i	2.15153	−	1.29067i
$197$	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	$0.787144\pi$
$198$	1.75448	+	1.44734i	0.124686	+	0.102858i
$199$	7.44457	−	2.70960i	0.527731	−	0.192079i	−0.0643937	−	0.997925i	$-0.520511\pi$
$199$	7.44457	−	2.70960i	0.527731	−	0.192079i	0.592125	+	0.805846i	$0.298289\pi$
$200$	3.53600	+	13.6929i	0.250033	+	0.968237i
$201$	0.377172	+	0.653281i	0.0266037	+	0.0460789i
$202$	2.12870	−	12.6927i	0.149775	−	0.893057i
$203$	11.4982	+	16.4211i	0.807015	+	1.15254i
$204$	1.35501	+	0.215606i	0.0948696	+	0.0150954i
$205$	−19.9677	−	10.8324i	−1.39461	−	0.756564i
$206$	−14.6266	−	3.78827i	−1.01908	−	0.263941i
$207$	−1.27732	−	2.73922i	−0.0887800	−	0.190389i
$208$	−10.8445	+	8.14766i	−0.751934	+	0.564938i
$209$	0.378046	−	2.31625i	0.0261500	−	0.160218i
$210$	1.51418	−	0.946161i	0.104488	−	0.0652913i
$211$	−7.81684	+	21.4766i	−0.538133	+	1.47851i	0.311041	+	0.950396i	$0.399322\pi$
$211$	−7.81684	+	21.4766i	−0.538133	+	1.47851i	−0.849174	+	0.528112i	$0.822900\pi$
$212$	0.979714	+	9.38592i	0.0672871	+	0.644628i
$213$	0.0635035	+	0.725848i	0.00435119	+	0.0497343i
$214$	−15.4085	+	4.26721i	−1.05330	+	0.291701i
$215$	15.2306	+	14.4430i	1.03872	+	0.985005i
$216$	0.452370	−	1.87539i	0.0307799	−	0.127604i
$217$	−0.766613	−	0.205413i	−0.0520411	−	0.0139444i
$218$	0.721612	+	0.845511i	0.0488737	+	0.0572652i
$219$	0.523492	−	0.190535i	0.0353743	−	0.0128752i
$220$	0.315145	−	2.38716i	0.0212471	−	0.160942i
$221$	10.2101	−	17.6844i	0.686805	−	1.18958i
$222$	0.759106	−	0.140411i	0.0509479	−	0.00942379i
$223$	0.369258	−	4.22064i	0.0247273	−	0.282635i	−0.973757	−	0.227592i	$-0.926915\pi$
$223$	0.369258	−	4.22064i	0.0247273	−	0.282635i	0.998484	−	0.0550430i	$-0.0175296\pi$
$224$	−26.7533	+	8.38272i	−1.78753	+	0.560094i
$225$	−12.5198	+	8.14318i	−0.834655	+	0.542879i
$226$	−6.66969	−	6.55897i	−0.443661	−	0.436296i
$227$	16.8207	+	16.8207i	1.11643	+	1.11643i	0.992261	+	0.124166i	$0.0396256\pi$
$227$	16.8207	+	16.8207i	1.11643	+	1.11643i	0.124166	+	0.992261i	$0.460374\pi$
$228$	−0.951335	+	0.285220i	−0.0630037	+	0.0188891i
$229$			29.2338i			1.93182i	0.258871	+	0.965912i	$0.416650\pi$
$229$			29.2338i			1.93182i	−0.258871	+	0.965912i	$0.583350\pi$
$230$	−1.74270	+	2.68352i	−0.114910	+	0.176946i
$231$	−0.299382	+	0.0527890i	−0.0196979	+	0.00347326i
$232$	−4.18153	−	10.6489i	−0.274531	−	0.699136i
$233$	−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	$0.684949\pi$
$234$	−11.8025	−	8.11788i	−0.771556	−	0.530682i
$235$	4.21611	−	2.10396i	0.275029	−	0.137247i
$236$	21.8976	+	7.55748i	1.42541	+	0.491950i
$237$	0.484029	−	1.03800i	0.0314410	−	0.0674255i
$238$	32.1038	−	27.3993i	2.08098	−	1.77604i
$239$	−9.48320	−	16.4254i	−0.613417	−	1.06247i	−0.990660	−	0.136356i	$-0.956461\pi$
$239$	−9.48320	−	16.4254i	−0.613417	−	1.06247i	0.377242	−	0.926115i	$-0.376872\pi$
$240$	−0.966662	+	0.322287i	−0.0623977	+	0.0208036i
$241$	−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	$0.942564\pi$
$242$	7.46315	−	13.1801i	0.479749	−	0.847247i
$243$	3.04660	−	0.266543i	0.195440	−	0.0170987i
$244$	6.83942	+	5.54656i	0.437849	+	0.355082i
$245$	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
$248$	0.397818	+	0.216550i	0.0252615	+	0.0137510i
$249$	−0.0113115	+	0.0310781i	−0.000716838	+	0.00196950i
$250$	14.3347	+	6.67196i	0.906609	+	0.421971i
$251$	−4.71883	+	5.62368i	−0.297850	+	0.354963i	−0.894126	−	0.447816i	$-0.852202\pi$
$251$	−4.71883	+	5.62368i	−0.297850	+	0.354963i	0.596276	+	0.802779i	$0.296646\pi$
$252$	−17.3859	−	23.9657i	−1.09521	−	1.50970i
$253$	0.446268	−	0.312480i	0.0280566	−	0.0196455i
$254$	19.4729	−	13.8794i	1.22184	−	0.870869i
$255$	1.14854	−	1.01687i	0.0719242	−	0.0636790i
$256$	15.9642	−	1.07044i	0.997760	−	0.0669026i
$257$	−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	$0.937543\pi$
$258$	−0.962398	+	1.16663i	−0.0599163	+	0.0726314i
$259$	11.8736	−	20.5658i	0.737793	−	1.27789i
$260$	−0.666925	+	15.1506i	−0.0413610	+	0.939600i
$261$	9.25533	−	7.76614i	0.572890	−	0.480712i
$262$	2.03923	−	5.75206i	0.125984	−	0.355364i
$263$	19.0413	+	13.3329i	1.17414	+	0.822140i	0.987083	−	0.160210i	$-0.0512170\pi$
$263$	19.0413	+	13.3329i	1.17414	+	0.822140i	0.187054	+	0.982350i	$0.440106\pi$
$264$	0.173157	+	0.0107772i	0.0106571	+	0.000663291i
$265$	8.80024	+	5.82023i	0.540594	+	0.357534i
$266$	−12.3241	+	27.9553i	−0.755639	+	1.71405i
$267$	0.556855	+	0.556855i	0.0340790	+	0.0340790i
$268$	−12.0941	−	5.39501i	−0.738766	−	0.329553i
$269$	−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	$0.538862\pi$
$270$	−1.29805	−	1.72257i	−0.0789967	−	0.104832i
$271$	−8.61319	−	10.2648i	−0.523214	−	0.623542i	0.438124	−	0.898915i	$-0.355643\pi$
$271$	−8.61319	−	10.2648i	−0.523214	−	0.623542i	−0.961338	+	0.275373i	$0.911199\pi$
$272$	−21.4774	+	10.9046i	−1.30226	+	0.661188i
$273$	1.84942	−	0.495550i	0.111932	−	0.0299920i
$274$	3.03114	−	0.290772i	0.183118	−	0.0175662i
$275$	−1.83740	−	1.96755i	−0.110799	−	0.118648i
$276$	−0.201562	−	0.111916i	−0.0121326	−	0.00673655i
$277$	−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	$0.700337\pi$
$278$	1.72685	−	10.2967i	0.103570	−	0.617552i
$279$	−0.0830620	+	0.471068i	−0.00497279	+	0.0282021i
$280$	−11.7628	+	29.0542i	−0.702965	+	1.73632i
$281$	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	$0.612259\pi$
$282$	0.172207	+	0.292589i	0.0102548	+	0.0174234i
$283$	−19.4090	+	9.05055i	−1.15374	+	0.537999i	−0.902825	−	0.430009i	$-0.858510\pi$
$283$	−19.4090	+	9.05055i	−1.15374	+	0.537999i	−0.250918	+	0.968008i	$0.580733\pi$
$284$	−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
$288$	6.43834	+	15.6225i	0.379383	+	0.920562i
$289$	12.3812	−	14.7553i	0.728305	−	0.867961i
$290$	−12.1648	−	3.95260i	−0.714343	−	0.232105i
$291$	−0.352392	−	0.0621361i	−0.0206576	−	0.00364249i
$292$	−5.47468	+	8.10403i	−0.320381	+	0.474253i
$293$	−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	$0.132518\pi$
$294$	2.82080	+	0.223016i	0.164512	+	0.0130066i
$295$	22.0780	−	13.5403i	1.28543	−	0.788345i
$296$	−9.33949	+	9.82065i	−0.542847	+	0.570814i
$297$	0.0950478	+	0.354723i	0.00551523	+	0.0205831i
$298$	−7.05424	+	1.30482i	−0.408641	+	0.0755861i
$299$	−2.62847	+	2.20555i	−0.152008	+	0.127550i
$300$	−0.408270	+	1.06358i	−0.0235715	+	0.0614056i
$301$	8.07853	+	45.8156i	0.465639	+	2.64077i
$302$	0.235478	+	28.1360i	0.0135502	+	1.61905i
$303$	0.733104	−	0.733104i	0.0421157	−	0.0421157i
$304$	10.5783	−	13.8600i	0.606706	−	0.794926i
$305$	9.64683	−	1.96626i	0.552376	−	0.112588i
$306$	−18.1371	−	17.8360i	−1.03683	−	1.01962i
$307$	−5.80176	+	8.28577i	−0.331124	+	0.472894i	−0.949847	−	0.312715i	$-0.898761\pi$
$307$	−5.80176	+	8.28577i	−0.331124	+	0.472894i	0.618723	+	0.785609i	$0.287650\pi$
$308$	3.71004	−	3.83637i	0.211399	−	0.218597i
$309$	−0.782367	−	0.932389i	−0.0445073	−	0.0530417i
$310$	0.469526	−	0.189701i	0.0266673	−	0.0107743i
$311$	−19.6631	−	11.3525i	−1.11499	−	0.643740i	−0.174873	−	0.984591i	$-0.555951\pi$
$311$	−19.6631	−	11.3525i	−1.11499	−	0.643740i	−0.940117	+	0.340851i	$0.889285\pi$
$312$	−1.09235	+	0.0274316i	−0.0618420	+	0.00155301i
$313$	−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	$0.719205\pi$
$314$	−1.68538	+	21.3174i	−0.0951117	+	1.20301i
$315$	−33.0416	−	2.00907i	−1.86168	−	0.113198i
$316$	3.82238	+	19.7398i	0.215026	+	1.11045i
$317$	−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	$0.848270\pi$
$318$	−0.374581	+	0.661517i	−0.0210054	+	0.0370960i
$319$	1.66829	+	1.39986i	0.0934063	+	0.0783772i
$320$	10.4140	−	14.5447i	0.582158	−	0.813076i
$321$	−1.21030	−	0.440514i	−0.0675525	−	0.0245871i
$322$	−6.64374	+	2.48129i	−0.370241	+	0.138277i
$323$	−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
$326$	−8.73164	−	2.26149i	−0.483601	−	0.125252i
$327$	0.00780440	+	0.0892046i	0.000431584	+	0.00493303i
$328$	5.69855	+	28.1639i	0.314650	+	1.55509i
$329$	10.2850	+	1.81352i	0.567029	+	0.0999825i
$330$	0.132287	−	0.141861i	0.00728218	−	0.00780918i
$331$	5.61891	−	3.24408i	0.308843	−	0.178311i	−0.337565	−	0.941302i	$-0.609603\pi$
$331$	5.61891	−	3.24408i	0.308843	−	0.178311i	0.646409	+	0.762991i	$0.276270\pi$
$332$	−0.159638	−	0.558229i	−0.00876126	−	0.0306368i
$333$	−12.9715	−	6.04870i	−0.710833	−	0.331467i
$334$	1.98943	+	20.7388i	0.108857	+	1.13477i
$335$	−13.2480	+	6.61113i	−0.723817	+	0.361205i
$336$	−2.14694	−	0.700979i	−0.117125	−	0.0382416i
$337$	−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	$0.970185\pi$
$338$	0.709170	−	2.00036i	0.0385738	−	0.108805i
$339$	−0.130854	−	0.742112i	−0.00710704	−	0.0403060i
$340$	−5.83817	+	26.2897i	−0.316619	+	1.42576i
$341$	−0.0862208			−0.00466912
$342$	17.4319	+	5.93099i	0.942608	+	0.320711i
$343$	37.0169	−	37.0169i	1.99873	−	1.99873i
$344$	1.64928	−	26.4990i	0.0889233	−	1.42873i
$345$	−0.239791	+	0.0945550i	−0.0129099	+	0.00509067i
$346$	7.46991	+	15.6754i	0.401585	+	0.842716i
$347$	18.4077	+	1.61047i	0.988178	+	0.0864543i	0.569769	−	0.821805i	$-0.307033\pi$
$347$	18.4077	+	1.61047i	0.988178	+	0.0864543i	0.418408	+	0.908259i	$0.362588\pi$
$348$	0.223597	−	0.894074i	0.0119861	−	0.0479274i
$349$	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	$0.652896\pi$
$350$	16.7329	+	30.7920i	0.894412	+	1.64590i
$351$	−0.791070	−	2.17345i	−0.0422242	−	0.116010i
$352$	−2.57167	+	1.63188i	−0.137071	+	0.0869795i
$353$	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	$-0.101585\pi$
$354$	1.08311	+	1.51961i	0.0575666	+	0.0807665i
$355$	−14.2961	+	0.379463i	−0.758756	+	0.0201398i
$356$	−13.6534	−	2.17250i	−0.723629	−	0.115142i
$357$	3.38707	−	0.296330i	0.179263	−	0.0156835i
$358$	−11.8550	−	20.1423i	−0.626557	−	1.06455i
$359$	12.6991	+	4.62210i	0.670233	+	0.243945i	0.654648	−	0.755934i	$-0.272817\pi$
$359$	12.6991	+	4.62210i	0.670233	+	0.243945i	0.0155851	+	0.999879i	$0.495039\pi$
$360$	18.0622	+	5.53629i	0.951959	+	0.291788i
$361$	−3.77514	−	18.6212i	−0.198692	−	0.980062i
$362$	−3.52864	+	1.31787i	−0.185461	+	0.0692655i
$363$	1.10583	−	0.515655i	0.0580408	−	0.0270649i
$364$	−21.1718	+	26.1069i	−1.10971	+	1.36837i
$365$	3.10926	+	10.4829i	0.162746	+	0.548702i
$366$	0.189326	+	0.683635i	0.00989621	+	0.0357342i
$367$	25.5106	−	17.8627i	1.33164	−	0.932426i	0.331702	−	0.943384i	$-0.392377\pi$
$367$	25.5106	−	17.8627i	1.33164	−	0.932426i	0.999940	+	0.0109586i	$0.00348831\pi$
$368$	4.01791	−	0.487505i	0.209448	−	0.0254129i
$369$	−26.2802	+	15.1729i	−1.36810	+	0.789870i
$370$	1.84658	+	15.0393i	0.0959991	+	0.781854i
$371$	7.99816	+	21.9748i	0.415244	+	1.14087i
$372$	0.0159715	+	0.0328060i	0.000828084	+	0.00170091i
$373$	−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	$0.685509\pi$
$374$	2.59843	−	3.77784i	0.134362	−	0.195348i
$375$	0.628394	+	1.10791i	0.0324501	+	0.0572124i
$376$	−5.46328	−	2.38247i	−0.281747	−	0.122867i
$377$	−11.2357	−	7.86731i	−0.578667	−	0.405187i
$378$	−0.0400087	−	4.78042i	−0.00205782	−	0.245878i
$379$	−36.5913			−1.87957			−0.939784	−	0.341769i	$-0.888974\pi$
$379$	−36.5913			−1.87957			−0.939784	+	0.341769i	$0.888974\pi$
$380$	−4.45459	−	18.9778i	−0.228516	−	0.973540i
$381$	1.92635			0.0986900
$382$	−0.0589392	−	7.04233i	−0.00301559	−	0.360317i
$383$	−13.9897	−	9.79571i	−0.714841	−	0.500537i	0.158676	−	0.987331i	$-0.449278\pi$
$383$	−13.9897	−	9.79571i	−0.714841	−	0.500537i	−0.873517	+	0.486793i	$0.838166\pi$
$384$	1.09729	+	0.676202i	0.0559957	+	0.0345073i
$385$	−0.677577	−	5.92820i	−0.0345325	−	0.302129i
$386$	−3.73318	+	5.42766i	−0.190014	+	0.276261i
$387$	27.0836	−	7.25702i	1.37674	−	0.368895i
$388$	5.64805	−	2.74974i	0.286736	−	0.139597i
$389$	−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	$0.926711\pi$
$390$	−0.752133	+	0.962685i	−0.0380857	+	0.0487475i
$391$	−5.27677	+	3.04655i	−0.266858	+	0.154070i
$392$	−42.3827	+	25.9096i	−2.14065	+	1.30863i
$393$	0.402716	−	0.281985i	0.0203143	−	0.0142243i
$394$	−4.19335	−	15.1418i	−0.211258	−	0.762831i
$395$	19.7594	+	10.7193i	0.994202	+	0.539348i
$396$	−2.49826	−	2.02601i	−0.125542	−	0.101811i
$397$	−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	$0.474158\pi$
$398$	−10.4958	+	3.91993i	−0.526105	+	0.196488i
$399$	−2.11554	+	1.25762i	−0.105909	+	0.0629599i
$400$	−5.16254	−	19.3222i	−0.258127	−	0.966111i
$401$	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	$0.491679\pi$
$402$	−0.541115	−	0.919383i	−0.0269884	−	0.0458546i
$403$	0.540970	−	0.0473288i	0.0269477	−	0.00235761i
$404$	−2.86011	+	17.9748i	−0.142296	+	0.894280i
$405$	0.527063	+	19.8568i	0.0261900	+	0.986692i
$406$	−16.4547	−	23.0861i	−0.816632	−	1.14574i
$407$	0.667713	−	2.49194i	0.0330973	−	0.123521i
$408$	−1.91876	−	0.288865i	−0.0949926	−	0.0143009i
$409$	−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	$-0.329692\pi$
$410$	28.3658	+	15.0824i	1.40089	+	0.744866i
$411$	0.212436	+	0.122650i	0.0104787	+	0.00604987i
$412$	20.7292	+	5.18412i	1.02125	+	0.255403i
$413$	57.1856	+	5.00309i	2.81392	+	0.246186i
$414$	1.83876	+	3.85859i	0.0903702	+	0.189640i
$415$	−0.595391	−	0.258631i	−0.0292266	−	0.0126957i
$416$	15.2395	−	11.6505i	0.747179	−	0.571211i
$417$	0.594712	−	0.594712i	0.0291232	−	0.0291232i
$418$	−0.507205	+	3.28003i	−0.0248082	+	0.160432i
$419$	34.3889			1.68001			0.840005	−	0.542579i	$-0.182552\pi$
$419$	34.3889			1.68001			0.840005	+	0.542579i	$0.182552\pi$
$420$	−2.13009	+	1.35595i	−0.103938	+	0.0661635i
$421$	−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	$-0.210220\pi$
$422$	10.8001	−	30.4639i	0.525741	−	1.48296i
$423$	0.548590	−	6.27041i	0.0266733	−	0.304878i
$424$	−1.49656	−	13.2616i	−0.0726796	−	0.644042i
$425$	18.5538	+	23.7129i	0.899991	+	1.15024i
$426$	−0.0983951	−	1.02572i	−0.00476726	−	0.0496961i
$427$	19.7767	+	9.22200i	0.957059	+	0.446284i
$428$	21.7396	−	6.21691i	1.05082	−	0.300505i
$429$	0.180136	−	0.104002i	0.00869705	−	0.00502125i
$430$	−21.7096	−	20.2445i	−1.04693	−	0.976277i
$431$	31.1593	+	5.49422i	1.50089	+	0.264647i	0.862891	−	0.505391i	$-0.168652\pi$
$431$	31.1593	+	5.49422i	1.50089	+	0.264647i	0.637998	+	0.770038i	$0.279763\pi$
$432$	−0.617530	+	2.65747i	−0.0297109	+	0.127857i
$433$	−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	$-0.298419\pi$
$434$	1.08655	+	0.281415i	0.0521560	+	0.0135084i
$435$	−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
$438$	−0.738048	+	0.275644i	−0.0352653	+	0.0131708i
$439$	−21.8214	−	7.94235i	−1.04148	−	0.379068i	−0.236039	−	0.971744i	$-0.575849\pi$
$439$	−21.8214	−	7.94235i	−1.04148	−	0.379068i	−0.805441	+	0.592676i	$0.798071\pi$
$440$	−0.417413	+	3.37956i	−0.0198994	+	0.161114i
$441$	−40.1869	−	33.7208i	−1.91366	−	1.60575i
$442$	−14.2294	+	25.1295i	−0.676825	+	1.19529i
$443$	−15.0364	−	21.4742i	−0.714401	−	1.02027i	−0.998116	−	0.0613612i	$-0.980456\pi$
$443$	−15.0364	−	21.4742i	−0.714401	−	1.02027i	0.283715	−	0.958909i	$-0.408433\pi$
$444$	−1.07184	+	0.207549i	−0.0508672	+	0.00984984i
$445$	−11.5730	+	10.2463i	−0.548611	+	0.485719i
$446$	−0.472238	+	5.97304i	−0.0223611	+	0.282832i
$447$	−0.523761	−	0.244234i	−0.0247731	−	0.0115519i
$448$	37.7343	−	12.1712i	1.78278	−	0.575034i
$449$	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	$0.496417\pi$
$450$	17.6087	−	11.6640i	0.830082	−	0.549845i
$451$	−3.51598	−	4.19018i	−0.165561	−	0.197308i
$452$	9.50966	+	9.19652i	0.447297	+	0.432568i
$453$	−1.30008	+	1.85671i	−0.0610833	+	0.0872360i
$454$	−23.9863	−	23.5881i	−1.12573	−	1.10705i
$455$	7.50543	+	36.8231i	0.351860	+	1.72629i
$456$	1.34197	−	0.414607i	0.0628434	−	0.0194158i
$457$	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	$-0.00612956\pi$
$458$	−0.345997	−	41.3414i	−0.0161674	−	1.93176i
$459$	−0.713218	−	4.04486i	−0.0332902	−	0.188798i
$460$	2.43270	−	3.81556i	0.113425	−	0.177902i
$461$	−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	$0.541971\pi$
$462$	0.422750	−	0.0781957i	0.0196681	−	0.00363799i
$463$	3.71955	+	13.8815i	0.172862	+	0.645130i	0.996906	+	0.0786038i	$0.0250462\pi$
$463$	3.71955	+	13.8815i	0.172862	+	0.645130i	−0.824044	+	0.566526i	$0.808287\pi$
$464$	6.03941	+	15.0098i	0.280372	+	0.696814i
$465$	0.0396703	+	0.00950901i	0.00183966	+	0.000440970i
$466$	20.3986	+	1.61274i	0.944947	+	0.0747089i
$467$	1.98295	−	7.40048i	0.0917601	−	0.342453i	−0.904748	−	0.425947i	$-0.859941\pi$
$467$	1.98295	−	7.40048i	0.0917601	−	0.342453i	0.996508	+	0.0834934i	$0.0266077\pi$
$468$	16.7868	+	11.3403i	0.775970	+	0.524206i
$469$	−32.3178	−	5.69851i	−1.49230	−	0.263133i
$470$	−5.93737	+	3.02524i	−0.273871	+	0.139544i
$471$	−1.10728	+	1.31960i	−0.0510207	+	0.0608041i
$472$	−31.0563	−	10.4283i	−1.42948	−	0.480004i
$473$	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
$478$	13.6052	+	23.1160i	0.622288	+	1.05730i
$479$	10.6673	+	8.95094i	0.487402	+	0.408979i	0.853094	−	0.521757i	$-0.174723\pi$
$479$	10.6673	+	8.95094i	0.487402	+	0.408979i	−0.365692	+	0.930736i	$0.619168\pi$
$480$	1.36320	−	0.467208i	0.0622214	−	0.0213250i
$481$	−2.82151	+	16.0016i	−0.128650	+	0.729608i
$482$	2.52422	−	15.0511i	0.114975	−	0.685558i
$483$	−0.551840	−	0.147865i	−0.0251096	−	0.00672809i
$484$	−10.3981	+	18.7271i	−0.472642	+	0.851232i
$485$	1.63712	−	6.82984i	0.0743378	−	0.310127i
$486$	−4.30524	+	0.412994i	−0.195290	+	0.0187338i
$487$	−41.2366	+	11.0493i	−1.86861	+	0.500692i	−0.868621	+	0.495477i	$0.834993\pi$
$487$	−41.2366	+	11.0493i	−1.86861	+	0.500692i	−0.999986	+	0.00521503i	$0.998340\pi$
$488$	−9.73771	−	7.76280i	−0.440806	−	0.351405i
$489$	−0.467051	−	0.556610i	−0.0211208	−	0.0251708i
$490$	−7.72947	+	54.9978i	−0.349182	+	2.48455i
$491$	33.2707	−	5.86653i	1.50149	−	0.264753i	0.638360	−	0.769738i	$-0.279613\pi$
$491$	33.2707	−	5.86653i	1.50149	−	0.264753i	0.863128	+	0.504986i	$0.168502\pi$
$492$	−0.943014	+	2.11397i	−0.0425143	+	0.0953053i
$493$	−17.2230	−	17.2230i	−0.775685	−	0.775685i
$494$	1.38184	−	20.8582i	0.0621717	−	0.938453i
$495$	−3.52373	+	0.718221i	−0.158380	+	0.0322816i
$496$	−0.565143	−	0.301529i	−0.0253757	−	0.0135391i
$497$	−25.9649	−	18.1808i	−1.16469	−	0.815522i
$498$	0.0156285	−	0.0440835i	0.000700331	−	0.00197543i
$499$	14.5362	−	12.1973i	0.650729	−	0.546026i	−0.256563	−	0.966528i	$-0.582590\pi$
$499$	14.5362	−	12.1973i	0.650729	−	0.546026i	0.907292	+	0.420501i	$0.138146\pi$
$500$	−20.3507	−	9.26558i	−0.910109	−	0.414369i
$501$	−0.839159	+	1.45347i	−0.0374909	+	0.0649361i
$502$	6.60663	−	8.00865i	0.294869	−	0.357444i
$503$	5.70320	−	12.2305i	0.254293	−	0.545333i	−0.737172	−	0.675705i	$-0.763839\pi$
$503$	5.70320	−	12.2305i	0.254293	−	0.545333i	0.991465	+	0.130372i	$0.0416171\pi$
$504$	24.8702	+	33.6856i	1.10781	+	1.50048i
$505$	13.4893	+	15.2359i	0.600264	+	0.677987i
$506$	−0.627398	+	0.447180i	−0.0278912	+	0.0198796i
$507$	0.140050	−	0.0980642i	0.00621985	−	0.00435518i
$508$	−27.3736	+	19.8582i	−1.21451	+	0.881064i
$509$	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	$-0.0412599\pi$
$510$	−1.61219	+	1.45162i	−0.0713888	+	0.0642787i
$511$	−8.28890	+	22.7736i	−0.366679	+	1.00744i
$512$	−22.5633	+	1.70272i	−0.997165	+	0.0752505i
$513$	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
$516$	1.34718	−	1.66120i	0.0593064	−	0.0731303i
$517$	1.13025	−	0.0988842i	0.0497084	−	0.00434892i
$518$	−16.5479	+	29.2239i	−0.727072	+	1.28402i
$519$	−0.242901	+	1.37756i	−0.0106622	+	0.0604682i
$520$	0.763827	−	21.4333i	0.0334960	−	0.939914i
$521$	−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	$0.907702\pi$
$522$	−12.9966	+	11.0921i	−0.568847	+	0.485490i
$523$	4.40231	−	9.44078i	0.192500	−	0.412817i	−0.786241	−	0.617920i	$-0.787975\pi$
$523$	4.40231	−	9.44078i	0.192500	−	0.412817i	0.978740	+	0.205104i	$0.0657532\pi$
$524$	−2.81572	+	8.15850i	−0.123005	+	0.356406i
$525$	−0.342048	+	2.80230i	−0.0149282	+	0.122302i
$526$	−27.0853	−	18.6295i	−1.18098	−	0.812285i
$527$	0.960644	+	0.0840455i	0.0418463	+	0.00366108i
$528$	−0.245000	−	0.0131913i	−0.0106623	−	0.000574079i
$529$	−21.6423	+	3.81612i	−0.940970	+	0.165918i
$530$	−12.5139	−	8.12661i	−0.543567	−	0.352997i
$531$		−	34.5973i		−	1.50140i
$532$	17.0974	−	39.6793i	0.741268	−	1.72032i
$533$	24.3602	+	24.3602i	1.05516	+	1.05516i
$534$	−0.794076	−	0.780894i	−0.0343630	−	0.0337926i
$535$	10.0721	−	23.1868i	0.435454	−	1.00245i
$536$	17.1669	+	7.48629i	0.741498	+	0.323359i
$537$	0.164095	−	1.87561i	0.00708122	−	0.0809387i
$538$	13.3332	−	2.46622i	0.574833	−	0.106326i
$539$	4.72803	−	8.18919i	0.203651	−	0.352733i
$540$	1.85604	+	2.42063i	0.0798713	+	0.104167i
$541$	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	$0.124605\pi$
$542$	12.3020	+	14.4142i	0.528414	+	0.619142i
$543$	−0.293094	−	0.0785344i	−0.0125779	−	0.00337023i
$544$	30.2435	−	15.6751i	1.29668	−	0.672064i
$545$	−1.75694	+	0.0466349i	−0.0752592	+	0.00199762i
$546$	−2.60951	+	0.722677i	−0.111677	+	0.0309277i
$547$	−0.721148	−	8.24276i	−0.0308341	−	0.352435i	−0.995902	−	0.0904362i	$-0.971174\pi$
$547$	−0.721148	−	8.24276i	−0.0308341	−	0.352435i	0.965068	−	0.261999i	$-0.0843817\pi$
$548$	−4.28309	+	0.447074i	−0.182964	+	0.0190980i
$549$	4.49809	−	12.3584i	0.191974	−	0.527444i
$550$	2.62167	+	2.76069i	0.111788	+	0.117716i
$551$	16.6432	+	5.81851i	0.709024	+	0.247877i
$552$	0.286366	+	0.155882i	0.0121885	+	0.00663477i
$553$	21.0568	+	45.1565i	0.895426	+	1.92025i
$554$	16.3761	+	4.24140i	0.695755	+	0.180200i
$555$	−0.582043	+	1.07290i	−0.0247063	+	0.0455422i
$556$	−2.32019	+	14.5816i	−0.0983979	+	0.618397i
$557$	−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	$0.883066\pi$
$558$	0.111888	−	0.667151i	0.00473660	−	0.0282427i
$559$	−15.9158	−	27.5670i	−0.673167	−	1.16596i
$560$	16.2907	−	41.2266i	0.688409	−	1.74214i
$561$	0.347092	−	0.126331i	0.0146542	−	0.00533371i
$562$	−12.3852	−	10.2170i	−0.522437	−	0.430977i
$563$	3.03149	+	11.3137i	0.127762	+	0.476814i	0.999923	−	0.0124047i	$-0.00394864\pi$
$563$	3.03149	+	11.3137i	0.127762	+	0.476814i	−0.872161	+	0.489219i	$0.837282\pi$
$564$	−0.246992	−	0.411730i	−0.0104002	−	0.0173370i
$565$	14.6949	−	1.67959i	0.618221	−	0.0706609i
$566$	27.3403	−	13.0287i	1.14920	−	0.547636i
$567$	−25.2527	+	36.0645i	−1.06051	+	1.51457i
$568$	11.9720	+	13.5612i	0.502334	+	0.569014i
$569$			11.4643i			0.480607i	0.970698	+	0.240303i	$0.0772469\pi$
$569$			11.4643i			0.480607i	−0.970698	+	0.240303i	$0.922753\pi$
$570$	0.595110	−	1.45321i	0.0249264	−	0.0608682i
$571$		−	3.14305i		−	0.131533i	−0.997835	−	0.0657663i	$-0.979051\pi$
$571$		−	3.14305i		−	0.131533i	0.997835	−	0.0657663i	$-0.0209492\pi$
$572$	−1.48762	+	3.33484i	−0.0622007	+	0.139437i
$573$	0.325406	−	0.464728i	0.0135940	−	0.0194143i
$574$	30.6318	+	64.2801i	1.27855	+	2.68300i
$575$	−1.56682	−	4.81049i	−0.0653409	−	0.200611i
$576$	−9.28976	−	22.0165i	−0.387074	−	0.917355i
$577$	−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	$-0.339435\pi$
$578$	−17.3344	+	21.0130i	−0.721016	+	0.874025i
$579$	−0.498670	+	0.181501i	−0.0207240	+	0.00754293i
$580$	17.2498	+	5.44564i	0.716260	+	0.226118i
$581$	−0.719384	−	1.24601i	−0.0298451	−	0.0516932i
$582$	0.499075	+	0.0837000i	0.0206873	+	0.00346948i
$583$	1.45717	+	2.08105i	0.0603497	+	0.0861883i
$584$	7.64617	−	11.5252i	0.316401	−	0.476917i
$585$	21.7145	−	6.44056i	0.897783	−	0.266284i
$586$	1.86823	−	7.21328i	0.0771760	−	0.297978i
$587$	−15.7798	−	33.8400i	−0.651304	−	1.39673i	−0.903305	−	0.428998i	$-0.858867\pi$
$587$	−15.7798	−	33.8400i	−0.651304	−	1.39673i	0.252002	−	0.967727i	$-0.418911\pi$
$588$	−3.99171	−	0.281996i	−0.164615	−	0.0116293i
$589$	−0.652833	+	0.247079i	−0.0268995	+	0.0101807i
$590$	−31.0617	+	19.4095i	−1.27879	+	0.799075i
$591$	0.432889	−	1.18935i	0.0178067	−	0.0489235i
$592$	13.0913	−	13.9985i	0.538051	−	0.575337i
$593$	−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	$-0.169801\pi$
$594$	−0.138612	−	0.500512i	−0.00568730	−	0.0205363i
$595$	1.77071	+	66.7106i	0.0725921	+	2.73487i
$596$	9.96042	−	1.92872i	0.407995	−	0.0790034i
$597$	−0.871796	−	0.233597i	−0.0356802	−	0.00956049i
$598$	3.69098	−	3.15011i	0.150935	−	0.128818i
$599$	−6.34756	+	2.31032i	−0.259354	+	0.0943972i	−0.468425	−	0.883503i	$-0.655178\pi$
$599$	−6.34756	+	2.31032i	−0.259354	+	0.0943972i	0.209071	+	0.977901i	$0.432956\pi$
$600$	0.564773	−	1.50890i	0.0230568	−	0.0616007i
$601$	−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	$0.284122\pi$
$602$	−11.9666	−	64.6952i	−0.487723	−	2.63678i
$603$	−1.72380	+	19.7031i	−0.0701985	+	0.802373i
$604$	−0.666009	−	39.7862i	−0.0270995	−	1.61888i
$605$	8.78512	+	22.2790i	0.357166	+	0.905770i
$606$	−1.02805	+	1.04541i	−0.0417618	+	0.0424667i
$607$	−3.60754	−	3.60754i	−0.146426	−	0.146426i	0.630094	−	0.776519i	$-0.283016\pi$
$607$	−3.60754	−	3.60754i	−0.146426	−	0.146426i	−0.776519	+	0.630094i	$0.783016\pi$
$608$	−14.7954	+	19.7255i	−0.600032	+	0.799976i
$609$		−	2.28379i		−	0.0925436i
$610$	−13.6189	+	2.89479i	−0.551414	+	0.117206i
$611$	−7.03720	+	1.24085i	−0.284695	+	0.0501993i
$612$	25.8599	+	25.0084i	1.04532	+	1.01090i
$613$	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	$0.511130\pi$
$614$	8.10657	−	11.7861i	0.327155	−	0.475648i
$615$	1.15558	+	2.31567i	0.0465976	+	0.0933768i
$616$	−5.20120	+	5.46916i	−0.209562	+	0.220359i
$617$	−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	$0.938471\pi$
$618$	1.11743	+	1.30929i	0.0449496	+	0.0526674i
$619$	−11.6073	−	20.1044i	−0.466536	−	0.808064i	0.532733	−	0.846283i	$-0.321165\pi$
$619$	−11.6073	−	20.1044i	−0.466536	−	0.808064i	−0.999269	+	0.0382188i	$0.987832\pi$
$620$	−0.661742	+	0.273825i	−0.0265762	+	0.0109971i
$621$	−0.119843	+	0.679662i	−0.00480912	+	0.0272739i
$622$	27.9412	+	15.8215i	1.12034	+	0.634386i
$623$	−34.1290	+	2.98590i	−1.36735	+	0.119627i
$624$	1.54443	−	0.0517212i	0.0618268	−	0.00207051i
$625$	−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
$628$	2.13111	−	30.1662i	0.0850404	−	1.20376i
$629$	−9.86851	+	27.1135i	−0.393483	+	1.08109i
$630$	46.7500	+	2.45009i	1.86256	+	0.0976138i
$631$	−14.3003	+	17.0425i	−0.569287	+	0.678450i	−0.971485	−	0.237103i	$-0.923802\pi$
$631$	−14.3003	+	17.0425i	−0.569287	+	0.678450i	0.402197	+	0.915553i	$0.368247\pi$
$632$	−5.63910	−	27.8701i	−0.224311	−	1.10861i
$633$	2.13285	−	1.49344i	0.0847733	−	0.0593589i
$634$	3.91051	+	5.48649i	0.155306	+	0.217896i
$635$	−2.29475	+	37.7400i	−0.0910646	+	1.49767i
$636$	0.521889	−	0.939927i	0.0206943	−	0.0372705i
$637$	−25.1696	+	53.9763i	−0.997255	+	2.13862i
$638$	−2.37580	−	1.95989i	−0.0940589	−	0.0775927i
$639$	−9.55196	+	16.5445i	−0.377870	+	0.654489i
$640$	−14.5549	+	20.6919i	−0.575333	+	0.817919i
$641$	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	$0.235712\pi$
$642$	1.71678	+	0.608634i	0.0677559	+	0.0240209i
$643$	13.3316	+	9.33487i	0.525746	+	0.368131i	0.806113	−	0.591761i	$-0.201567\pi$
$643$	13.3316	+	9.33487i	0.525746	+	0.368131i	−0.280367	+	0.959893i	$0.590456\pi$
$644$	9.36597	−	3.58758i	0.369071	−	0.141370i
$645$	−0.477576	−	2.34308i	−0.0188045	−	0.0922587i
$646$	8.84839	−	36.0507i	0.348135	−	1.41839i
$647$	−11.2388	−	11.2388i	−0.441844	−	0.441844i	0.450788	−	0.892631i	$-0.351143\pi$
$647$	−11.2388	−	11.2388i	−0.441844	−	0.441844i	−0.892631	+	0.450788i	$0.851143\pi$
$648$	18.8361	−	16.6288i	0.739950	−	0.653239i
$649$	6.14149	−	1.08291i	0.241074	−	0.0425079i
$650$	−17.9644	−	15.8822i	−0.704623	−	0.622950i
$651$	0.0581189	+	0.0692634i	0.00227786	+	0.00271465i
$652$	12.3747	+	3.09477i	0.484632	+	0.121201i
$653$	−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	$0.595448\pi$
$654$	−0.0120925	−	0.126058i	−0.000472853	−	0.00492924i
$655$	5.04476	+	8.22570i	0.197115	+	0.321405i
$656$	−8.39203	−	39.7609i	−0.327654	−	1.55240i
$657$	14.1088	+	3.78043i	0.550435	+	0.147489i
$658$	−14.5661	−	2.44288i	−0.567846	−	0.0952336i
$659$	−0.704049	+	3.99286i	−0.0274259	+	0.155540i	−0.995445	−	0.0953360i	$-0.969607\pi$
$659$	−0.704049	+	3.99286i	−0.0274259	+	0.155540i	0.968019	+	0.250876i	$0.0807186\pi$
$660$	−0.185397	+	0.202180i	−0.00721657	+	0.00786985i
$661$	−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	$-0.557408\pi$
$662$	−7.90767	+	4.65417i	−0.307340	+	0.180889i
$663$	−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
$668$	−3.05884	−	29.3045i	−0.118350	−	1.13382i
$669$	−0.310255	+	0.369747i	−0.0119951	+	0.0142952i
$670$	18.6566	−	9.50602i	0.720769	−	0.367249i
$671$	2.33458	+	0.411649i	0.0901253	+	0.0158915i
$672$	3.04442	+	0.965889i	0.117441	+	0.0372600i
$673$	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	$0.00715303\pi$
$674$	0.736412	−	9.31442i	0.0283655	−	0.358778i
$675$	3.40835	+	0.116586i	0.131187	+	0.00448738i
$676$	−0.979207	+	2.83723i	−0.0376618	+	0.109124i
$677$	−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	$-0.235548\pi$
$678$	0.193833	+	1.04792i	0.00744411	+	0.0402451i
$679$	11.9248	−	10.0061i	0.457630	−	0.383997i
$680$	7.94498	−	37.2471i	0.304676	−	1.42836i
$681$	−0.470594	−	2.66887i	−0.0180332	−	0.102271i
$682$	0.121930	−	0.00102047i	0.00466895	−	3.90757e-5i
$683$	1.42013	−	1.42013i	0.0543396	−	0.0543396i	−0.679415	−	0.733754i	$-0.737766\pi$
$683$	1.42013	−	1.42013i	0.0543396	−	0.0543396i	0.733754	+	0.679415i	$0.237766\pi$
$684$	−24.7217	−	8.18108i	−0.945259	−	0.312811i
$685$	−2.65595	+	4.01582i	−0.101479	+	0.153437i
$686$	−51.9099	+	52.7861i	−1.98193	+	2.01538i
$687$	1.91027	−	2.72814i	0.0728812	−	0.104085i
$688$	−2.01872	+	37.4934i	−0.0769632	+	1.42942i
$689$	−10.2850	−	12.2571i	−0.391826	−	0.466960i
$690$	0.337984	−	0.136554i	0.0128668	−	0.00519854i
$691$	1.76070	+	1.01654i	0.0669803	+	0.0386711i	0.533116	−	0.846042i	$-0.321021\pi$
$691$	1.76070	+	1.01654i	0.0669803	+	0.0386711i	−0.466136	+	0.884713i	$0.654354\pi$
$692$	−10.7492	−	22.0792i	−0.408623	−	0.839325i
$693$	−7.22388	−	3.36855i	−0.274412	−	0.127961i
$694$	−26.0506	−	2.05960i	−0.988867	−	0.0781813i
$695$	10.9428	+	12.3597i	0.415085	+	0.468831i
$696$	−0.305621	+	1.26701i	−0.0115845	+	0.0480260i
$697$	35.0894	+	50.1129i	1.32911	+	1.89816i
$698$	−1.98859	−	1.12603i	−0.0752693	−	0.0426209i
$699$	1.26273	+	1.05955i	0.0477607	+	0.0400760i
$700$	−24.0275	−	43.3469i	−0.908155	−	1.63836i
$701$	−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	$0.651808\pi$
$702$	1.14443	+	3.06425i	0.0431936	+	0.115653i
$703$	−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
$706$	−7.31228	+	28.2329i	−0.275201	+	1.06256i
$707$	3.93095	+	44.9310i	0.147839	+	1.68980i
$708$	−1.54968	−	2.13616i	−0.0582406	−	0.0802819i
$709$	−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	$0.668535\pi$
$710$	20.2125	−	0.705824i	0.758561	−	0.0264891i
$711$	26.0061	−	15.0146i	0.975304	−	0.563092i
$712$	19.3339	+	2.91067i	0.724567	+	0.109082i
$713$	−0.146853	−	0.0684788i	−0.00549970	−	0.00256455i
$714$	−4.78636	+	0.459147i	−0.179125	+	0.0171832i
$715$	1.82296	+	3.65302i	0.0681747	+	0.136615i
$716$	17.0033	+	28.3442i	0.635444	+	1.05927i
$717$	−0.188321	+	2.15252i	−0.00703297	+	0.0803872i
$718$	−18.0133	−	6.38610i	−0.672252	−	0.238327i
$719$	3.87266	+	21.9629i	0.144426	+	0.819079i	0.967826	+	0.251618i	$0.0809628\pi$
$719$	3.87266	+	21.9629i	0.144426	+	0.819079i	−0.823401	+	0.567460i	$0.807926\pi$
$720$	−25.6084	−	7.61545i	−0.954368	−	0.283811i
$721$	52.9498			1.97195
$722$	5.55906	+	26.2887i	0.206887	+	0.978365i
$723$	0.869317	−	0.869317i	0.0323303	−	0.0323303i
$724$	4.97447	−	1.90544i	0.184875	−	0.0708152i
$725$	16.9535	−	11.0270i	0.629637	−	0.409531i
$726$	−1.55772	+	0.742309i	−0.0578123	+	0.0275497i
$727$	0.879142	+	0.0769150i	0.0326056	+	0.00285262i	0.103447	−	0.994635i	$-0.467013\pi$
$727$	0.879142	+	0.0769150i	0.0326056	+	0.00285262i	−0.0708413	+	0.997488i	$0.522568\pi$
$728$	29.6315	−	37.1700i	1.09822	−	1.37761i
$729$	22.7779	+	13.1508i	0.843626	+	0.487068i
$730$	−4.52107	−	14.7878i	−0.167332	−	0.547320i
$731$	−19.3330	−	53.1170i	−0.715058	−	1.96460i
$732$	−0.275829	−	0.964531i	−0.0101949	−	0.0356501i
$733$	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	$0.0249576\pi$
$734$	−35.8647	+	25.5627i	−1.32379	+	0.943537i
$735$	−3.07853	+	3.24642i	−0.113553	+	0.119746i
$736$	−5.67621	+	0.736966i	−0.209228	+	0.0271649i
$737$	−3.55152	+	0.310718i	−0.130822	+	0.0114454i
$738$	36.9850	−	21.7680i	1.36144	−	0.801292i
$739$	−8.15136	−	2.96685i	−0.299853	−	0.109137i	0.187713	−	0.982224i	$-0.439893\pi$
$739$	−8.15136	−	2.96685i	−0.299853	−	0.109137i	−0.487565	+	0.873087i	$0.662115\pi$
$740$	−2.78936	−	21.2461i	−0.102539	−	0.781023i
$741$	1.06589	−	1.30367i	0.0391566	−	0.0478915i
$742$	−11.5708	−	30.9813i	−0.424777	−	1.13736i
$743$	−9.46099	+	4.41173i	−0.347090	+	0.161851i	−0.588343	−	0.808612i	$-0.700219\pi$
$743$	−9.46099	+	4.41173i	−0.347090	+	0.161851i	0.241253	+	0.970462i	$0.422442\pi$
$744$	−0.0229746	−	0.0462040i	−0.000842290	−	0.00169392i
$745$	5.40882	−	9.97030i	0.198164	−	0.365284i
$746$	39.3624	−	10.9010i	1.44116	−	0.399114i
$747$	−0.710321	+	0.497372i	−0.0259893	+	0.0181979i
$748$	−3.62989	+	5.37324i	−0.132722	+	0.196465i
$749$	48.5244	−	28.0156i	1.77304	−	1.02367i
$750$	−0.901765	−	1.55933i	−0.0329278	−	0.0569388i
$751$	5.09171	+	13.9894i	0.185799	+	0.510479i	0.997264	−	0.0739223i	$-0.0235517\pi$
$751$	5.09171	+	13.9894i	0.185799	+	0.510479i	−0.811465	+	0.584401i	$0.801329\pi$
$752$	7.75417	+	3.30455i	0.282765	+	0.120504i
$753$	0.807844	−	0.216461i	0.0294395	−	0.00788828i
$754$	15.9822	+	10.9927i	0.582038	+	0.400330i
$755$	−34.8270	−	27.6823i	−1.26748	−	1.00746i
$756$	0.113158	+	6.75983i	0.00411550	+	0.245853i
$757$	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	$0.669431\pi$
$758$	51.7461	−	0.433077i	1.87950	−	0.0157301i
$759$	−0.0620653			−0.00225283
$760$	6.52414	+	26.7850i	0.236655	+	0.971594i
$761$	34.6863			1.25738			0.628689	−	0.777657i	$-0.283592\pi$
$761$	34.6863			1.25738			0.628689	+	0.777657i	$0.283592\pi$
$762$	−2.72418	+	0.0227994i	−0.0986866	+	0.000825935i
$763$	−3.19102	−	2.23437i	−0.115523	−	0.0808898i
$764$	0.166699	+	9.95832i	0.00603097	+	0.360279i
$765$	39.9603	−	4.56736i	1.44477	−	0.165133i
$766$	19.8997	+	13.6872i	0.719005	+	0.494537i
$767$	−37.9388	+	10.1657i	−1.36989	+	0.367061i
$768$	−1.55975	−	0.943273i	−0.0562825	−	0.0340374i
$769$	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	$0.755393\pi$
$770$	1.02837	+	8.37543i	0.0370598	+	0.301830i
$771$	1.87016	−	1.07974i	0.0673522	−	0.0388858i
$772$	5.21510	−	7.71978i	0.187695	−	0.277841i
$773$	−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	$0.370173\pi$
$774$	−38.2147	+	10.5832i	−1.37360	+	0.380404i
$775$	−0.233552	+	0.765870i	−0.00838944	+	0.0275109i
$776$	−7.95472	+	3.95543i	−0.285558	+	0.141992i
$777$	−2.45192	+	1.14335i	−0.0879623	+	0.0410175i
$778$	2.31365	+	6.19490i	0.0829485	+	0.222098i
$779$	−38.6293	−	21.6510i	−1.38404	−	0.775726i
$780$	1.05225	−	1.37030i	0.0376764	−	0.0490645i
$781$	−3.23585	−	1.17775i	−0.115788	−	0.0421433i
$782$	7.42617	−	4.37077i	0.265559	−	0.156298i
$783$	−2.74835	+	0.240449i	−0.0982180	+	0.00859296i
$784$	59.6294	−	37.1421i	2.12962	−	1.32650i
$785$	−24.5339	−	23.2651i	−0.875652	−	0.830369i
$786$	−0.566169	+	0.403539i	−0.0201946	+	0.0143938i
$787$	−10.3242	+	38.5305i	−0.368018	+	1.37346i	0.495264	+	0.868742i	$0.335071\pi$
$787$	−10.3242	+	38.5305i	−0.368018	+	1.37346i	−0.863283	+	0.504721i	$0.831595\pi$
$788$	6.10930	+	21.3633i	0.217635	+	0.761037i
$789$	−0.905735	−	2.48849i	−0.0322450	−	0.0885925i
$790$	−28.0699	−	14.9250i	−0.998681	−	0.531009i
$791$	28.3903	+	16.3912i	1.00944	+	0.582802i
$792$	3.55692	+	2.83554i	0.126390	+	0.100757i
$793$	−14.8737	−	1.30128i	−0.528179	−	0.0462097i
$794$	17.6907	−	8.43025i	0.627818	−	0.299178i
$795$	−0.440932	−	1.11820i	−0.0156382	−	0.0396584i
$796$	14.7963	−	5.66765i	0.524443	−	0.200884i
$797$	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	$0.162575\pi$
$798$	2.97683	−	1.80352i	0.105379	−	0.0638440i
$799$	−12.6893			−0.448915
$800$	7.52937	+	27.2637i	0.266203	+	0.963917i
$801$	3.58549	+	20.3343i	0.126687	+	0.718478i
$802$	−19.5633	−	6.93559i	−0.690803	−	0.244904i
$803$	−0.229467	+	2.62282i	−0.00809772	+	0.0925574i
$804$	0.776107	+	1.29375i	0.0273712	+	0.0456272i
$805$	3.55427	−	10.6352i	0.125271	−	0.374841i
$806$	−0.764461	+	0.0733333i	−0.0269270	+	0.00258306i
$807$	0.989956	+	0.461624i	0.0348481	+	0.0162499i
$808$	3.83192	−	25.4532i	0.134806	−	0.895439i
$809$	−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	$0.458958\pi$
$810$	−0.980369	−	28.0745i	−0.0344467	−	0.986439i
$811$	22.0698	+	3.89150i	0.774976	+	0.136649i	0.547129	−	0.837048i	$-0.315721\pi$
$811$	22.0698	+	3.89150i	0.774976	+	0.136649i	0.227846	+	0.973697i	$0.426832\pi$
$812$	23.5428	+	32.4527i	0.826192	+	1.13887i
$813$	0.133048	+	1.52075i	0.00466621	+	0.0533350i
$814$	−0.914762	+	3.53191i	−0.0320624	+	0.123793i
$815$	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
$818$	12.6880	+	33.9727i	0.443626	+	1.18783i
$819$	47.1735	+	17.1697i	1.64837	+	0.599959i
$820$	−40.2924	−	20.9933i	−1.40707	−	0.733116i
$821$	−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	$0.841532\pi$
$822$	−0.301871	−	0.170933i	−0.0105289	−	0.00596196i
$823$	−18.6201	−	26.5922i	−0.649055	−	0.926946i	0.350900	−	0.936413i	$-0.385876\pi$
$823$	−18.6201	−	26.5922i	−0.649055	−	0.926946i	−0.999955	+	0.00946653i	$0.996987\pi$
$824$	−29.3758	−	7.08585i	−1.02336	−	0.246847i
$825$	0.0429004	+	0.303679i	0.00149360	+	0.0105727i
$826$	−80.9291	−	6.39837i	−2.81588	−	0.222628i
$827$	−2.66421	−	1.24234i	−0.0926436	−	0.0432004i	0.375744	−	0.926723i	$-0.377387\pi$
$827$	−2.66421	−	1.24234i	−0.0926436	−	0.0432004i	−0.468388	+	0.883523i	$0.655165\pi$
$828$	−2.64598	−	5.43492i	−0.0919541	−	0.188877i
$829$	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	$0.585174\pi$
$830$	0.845041	+	0.358699i	0.0293318	+	0.0124506i
$831$	0.875950	+	1.04392i	0.0303864	+	0.0362131i
$832$	−21.4133	+	16.6560i	−0.742373	+	0.577445i
$833$	−60.6608	+	86.6326i	−2.10177	+	3.00164i
$834$	−0.833981	+	0.848059i	−0.0288784	+	0.0293659i
$835$	−27.4759	−	18.1718i	−0.950841	−	0.628860i
$836$	0.678450	−	4.64451i	0.0234647	−	0.160634i
$837$	0.0772337	−	0.0772337i	0.00266959	−	0.00266959i
$838$	−48.6316	+	0.407011i	−1.67995	+	0.0140600i
$839$	4.32340	+	24.5192i	0.149261	+	0.846498i	0.963847	+	0.266456i	$0.0858528\pi$
$839$	4.32340	+	24.5192i	0.149261	+	0.846498i	−0.814586	+	0.580042i	$0.803036\pi$
$840$	2.99626	−	1.94274i	0.103381	−	0.0670310i
$841$	9.68235	−	8.12445i	0.333874	−	0.280154i
$842$	4.92941	+	26.6499i	0.169879	+	0.918416i
$843$	−0.334751	−	1.24931i	−0.0115294	−	0.0430285i
$844$	−14.9126	+	43.2088i	−0.513311	+	1.48731i
$845$	1.75438	+	2.86060i	0.0603527	+	0.0984077i
$846$	−0.701582	+	8.87388i	−0.0241209	+	0.305090i
$847$	−13.7382	+	51.2715i	−0.472049	+	1.76171i
$848$	2.27335	+	18.7364i	0.0780670	+	0.643411i
$849$	2.40268	+	0.423657i	0.0824596	+	0.0145399i
$850$	−26.5188	−	33.3143i	−0.909586	−	1.14267i
$851$	3.11643	−	3.71401i	0.106830	−	0.127315i
$852$	0.151287	+	1.44937i	0.00518300	+	0.0496545i
$853$	−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	$0.212016\pi$
$858$	−0.253511	+	0.149207i	−0.00865473	+	0.00509386i
$859$	−2.18978	−	1.83745i	−0.0747145	−	0.0626929i	0.604666	−	0.796479i	$-0.293307\pi$
$859$	−2.18978	−	1.83745i	−0.0747145	−	0.0626929i	−0.679380	+	0.733787i	$0.737751\pi$
$860$	30.9405	+	28.3721i	1.05506	+	0.967481i
$861$	−0.996062	+	5.64895i	−0.0339457	+	0.192516i
$862$	−44.1293	−	7.40094i	−1.50305	−	0.252077i
$863$	−51.5534	−	13.8137i	−1.75490	−	0.470224i	−0.769239	−	0.638961i	$-0.779364\pi$
$863$	−51.5534	−	13.8137i	−1.75490	−	0.470224i	−0.985661	+	0.168737i	$0.946031\pi$
$864$	0.841836	−	3.76540i	0.0286398	−	0.128102i
$865$	−26.6990	−	6.39979i	−0.907794	−	0.217599i
$866$	4.22320	+	44.0246i	0.143510	+	1.49602i
$867$	−2.11961	+	0.567948i	−0.0719857	+	0.0192885i
$868$	−1.53989	−	0.385107i	−0.0522672	−	0.0130714i
$869$	3.47929	+	4.14646i	0.118027	+	0.140659i
$870$	0.876959	+	1.16377i	0.0297317	+	0.0394554i
$871$	22.1126	−	3.89904i	0.749255	−	0.132114i
$872$	1.47132	+	1.66663i	0.0498253	+	0.0564392i
$873$	−6.63407	−	6.63407i	−0.224529	−	0.224529i
$874$	−3.46897	+	5.18379i	−0.117340	+	0.175344i
$875$	−54.4936	−	10.0394i	−1.84222	−	0.339395i
$876$	1.04046	−	0.398541i	0.0351538	−	0.0134655i
$877$	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	$0.489233\pi$
$878$	30.9531	+	10.9735i	1.04462	+	0.370338i
$879$	0.459820	−	0.385834i	0.0155093	−	0.0130139i
$880$	0.550292	−	4.78419i	0.0185503	−	0.161275i
$881$	−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	$0.301941\pi$
$882$	57.2300	+	47.2112i	1.92703	+	1.58968i
$883$	−20.9934	+	45.0204i	−0.706483	+	1.51506i	0.144296	+	0.989535i	$0.453908\pi$
$883$	−20.9934	+	45.0204i	−0.706483	+	1.51506i	−0.850779	+	0.525524i	$0.823869\pi$
$884$	19.8253	−	35.7056i	0.666798	−	1.20091i
$885$	−2.94513	−	0.179077i	−0.0989996	−	0.00601960i
$886$	21.5181	+	30.1901i	0.722914	+	1.01426i
$887$	19.8267	−	13.8828i	0.665714	−	0.466138i	−0.191232	−	0.981545i	$-0.561248\pi$
$887$	19.8267	−	13.8828i	0.665714	−	0.466138i	0.856945	+	0.515407i	$0.172359\pi$
$888$	1.51330	−	0.306194i	0.0507830	−	0.0102752i
$889$	−53.8672	+	64.1965i	−1.80665	+	2.15308i
$890$	16.2448	−	14.6269i	0.544526	−	0.490293i
$891$	−1.63586	+	4.49449i	−0.0548034	+	0.150571i
$892$	0.597127	−	8.45245i	0.0199933	−	0.283009i
$893$	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
$896$	−53.2185	+	17.6587i	−1.77790	+	0.589934i
$897$	0.389413	−	0.0340692i	0.0130021	−	0.00113754i
$898$	−26.5831	−	15.0526i	−0.887091	−	0.502311i
$899$	0.112477	−	0.637889i	0.00375132	−	0.0212748i
$900$	−24.7635	+	16.7032i	−0.825452	+	0.556773i
$901$	−14.2067	−	24.6068i	−0.473295	−	0.819771i
$902$	5.02176	+	5.88398i	0.167206	+	0.195915i
$903$	2.23990	−	4.80347i	0.0745391	−	0.159850i
$904$	−13.5571	−	12.8928i	−0.450901	−	0.428810i
$905$	1.88775	−	5.64859i	0.0627509	−	0.187765i
$906$	1.81656	−	2.64108i	0.0603511	−	0.0877441i
$907$	34.3136	+	3.00205i	1.13936	+	0.0996814i	0.641180	−	0.767390i	$-0.278445\pi$
$907$	34.3136	+	3.00205i	1.13936	+	0.0996814i	0.498183	+	0.867072i	$0.334001\pi$
$908$	34.1997	+	33.0736i	1.13496	+	1.09759i
$909$	26.7703	−	4.72032i	0.887915	−	0.156563i
$910$	−11.0497	−	51.9850i	−0.366295	−	1.72329i
$911$		−	6.36317i		−	0.210821i	−0.994429	−	0.105411i	$-0.966384\pi$
$911$		−	6.36317i		−	0.210821i	0.994429	−	0.105411i	$-0.0336157\pi$
$912$	−1.89286	+	0.602205i	−0.0626787	+	0.0199410i
$913$	−0.110524	−	0.110524i	−0.00365780	−	0.00365780i
$914$	−30.5500	+	31.0657i	−1.01051	+	1.02756i
$915$	−1.02874	−	0.446873i	−0.0340091	−	0.0147732i
$916$	0.978594	+	58.4594i	0.0323337	+	1.93155i
$917$	−1.86403	+	21.3059i	−0.0615555	+	0.703583i
$918$	1.05648	+	5.71166i	0.0348691	+	0.188513i
$919$	−11.3413	+	19.6437i	−0.374115	+	0.647986i	−0.990194	−	0.139698i	$-0.955387\pi$
$919$	−11.3413	+	19.6437i	−0.374115	+	0.647986i	0.616079	+	0.787684i	$0.288720\pi$
$920$	−3.39508	+	5.42462i	−0.111933	+	0.178845i
$921$	1.08286	−	0.394128i	0.0356814	−	0.0129870i
$922$	34.0866	−	29.0917i	1.12258	−	0.958083i
$923$	20.9490	+	5.61327i	0.689544	+	0.184763i
$924$	−0.596912	+	0.115585i	−0.0196370	+	0.00380247i
$925$	−20.3264	−	12.6812i	−0.668327	−	0.416954i
$926$	−5.42434	−	19.5867i	−0.178255	−	0.643660i
$927$	−2.78138	−	31.7913i	−0.0913525	−	1.04416i
$928$	−8.71836	−	21.1549i	−0.286194	−	0.694443i
$929$	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	$0.0946771\pi$
$930$	−0.0562128	−	0.0129778i	−0.00184329	−	0.000425558i
$931$	12.3316	−	75.5545i	0.404152	−	2.47620i
$932$	−28.8660	−	2.03926i	−0.945539	−	0.0667980i
$933$	1.09317	+	2.34430i	0.0357886	+	0.0767490i
$934$	−2.71663	+	10.4890i	−0.0888909	+	0.343209i
$935$	2.06154	+	6.95053i	0.0674196	+	0.227307i
$936$	−23.8735	−	15.8384i	−0.780330	−	0.517694i
$937$	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	$0.662207\pi$
$938$	45.7702	+	7.67612i	1.49445	+	0.250634i
$939$	0.503178	+	0.871530i	0.0164206	+	0.0284413i
$940$	8.36061	−	4.34845i	0.272693	−	0.141831i
$941$	−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	$0.630578\pi$
$942$	1.55025	−	1.87924i	0.0505100	−	0.0612289i
$943$	−2.66054	−	9.92928i	−0.0866392	−	0.323342i
$944$	44.0421	+	14.3798i	1.43345	+	0.468023i
$945$	5.91724	+	4.70334i	0.192488	+	0.153000i
$946$	−3.07479	−	6.45236i	−0.0999700	−	0.209784i
$947$	2.02591	−	2.89330i	0.0658332	−	0.0940195i	−0.784885	−	0.619641i	$-0.787278\pi$
$947$	2.02591	−	2.89330i	0.0658332	−	0.0940195i	0.850719	+	0.525621i	$0.176167\pi$
$948$	0.933175	−	2.09192i	0.0303081	−	0.0679423i
$949$		−	16.5822i		−	0.538281i
$950$	27.7615	+	13.3902i	0.900703	+	0.434435i
$951$			0.542750i			0.0175999i
$952$	63.2813	−	55.8657i	2.05096	−	1.81062i
$953$	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	$-0.0156810\pi$
$954$	−17.9935	+	8.57456i	−0.582561	+	0.277612i
$955$	8.71705	+	6.92877i	0.282077	+	0.224210i
$956$	−19.5136	−	32.5287i	−0.631115	−	1.05205i
$957$	−0.0642142	−	0.239651i	−0.00207575	−	0.00774680i
$958$	−15.1913	−	12.5319i	−0.490808	−	0.404886i
$959$	−10.0278	+	3.64981i	−0.323813	+	0.117858i
$960$	−1.92226	+	0.676843i	−0.0620408	+	0.0218450i
$961$	−15.4872	−	26.8246i	−0.499586	−	0.865309i
$962$	3.80069	−	22.6622i	0.122539	−	0.730659i
$963$	−19.3696	−	27.6626i	−0.624176	−	0.891416i
$964$	−3.39152	+	21.3146i	−0.109234	+	0.686496i
$965$	−2.96183	−	9.98589i	−0.0953448	−	0.321457i
$966$	0.782142	+	0.202574i	0.0251650	+	0.00651772i
$967$	14.6194	+	31.3514i	0.470129	+	1.00819i	0.988244	+	0.152884i	$0.0488559\pi$
$967$	14.6194	+	31.3514i	0.470129	+	1.00819i	−0.518116	+	0.855311i	$0.673366\pi$
$968$	14.4830	−	26.6063i	0.465501	−	0.855158i
$969$	2.26604	−	1.95118i	0.0727956	−	0.0626810i
$970$	−2.23432	+	9.67789i	−0.0717398	+	0.310738i
$971$	−8.62170	+	23.6879i	−0.276684	+	0.760182i	0.721049	+	0.692884i	$0.243660\pi$
$971$	−8.62170	+	23.6879i	−0.276684	+	0.760182i	−0.997733	+	0.0672983i	$0.978562\pi$
$972$	6.08342	−	0.634996i	0.195126	−	0.0203675i
$973$	3.18889	+	36.4491i	0.102231	+	1.16851i
$974$	58.1845	−	16.1136i	1.86435	−	0.516313i
$975$	−0.435864	−	1.88180i	−0.0139588	−	0.0602660i
$976$	13.8626	+	10.8626i	0.443731	+	0.347704i
$977$	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	$0.455913\pi$
$978$	0.667075	+	0.781610i	0.0213307	+	0.0249931i
$979$	−3.49739	+	1.27295i	−0.111777	+	0.0406835i
$980$	10.2798	−	77.8674i	0.328376	−	2.48738i
$981$	−1.17391	+	2.03327i	−0.0374800	+	0.0649173i
$982$	−46.9808	+	8.69001i	−1.49922	+	0.277309i
$983$	4.27770	−	48.8943i	0.136437	−	1.55949i	−0.551784	−	0.833987i	$-0.686053\pi$
$983$	4.27770	−	48.8943i	0.136437	−	1.55949i	0.688222	−	0.725500i	$-0.258392\pi$
$984$	1.30856	−	3.00067i	0.0417152	−	0.0956577i
$985$	22.7855	+	9.89774i	0.726006	+	0.315368i
$986$	24.5600	+	24.1523i	0.782149	+	0.769166i
$987$	−0.841306	−	0.841306i	−0.0267791	−	0.0267791i
$988$	−1.70727	+	29.5132i	−0.0543156	+	0.938940i
$989$			9.49811i			0.302022i
$990$	4.97463	−	1.05739i	0.158104	−	0.0336060i
$991$	−34.5378	+	6.08995i	−1.09713	+	0.193454i	−0.692779	−	0.721150i	$-0.743614\pi$
$991$	−34.5378	+	6.08995i	−1.09713	+	0.193454i	−0.404352	+	0.914604i	$0.632503\pi$
$992$	0.802773	+	0.419723i	0.0254881	+	0.0133262i
$993$	−0.736348	−	0.0644221i	−0.0233673	−	0.00204437i
$994$	36.9339	+	25.4034i	1.17147	+	0.805746i
$995$	5.61502	−	16.8015i	0.178008	−	0.532642i
$996$	−0.0215795	+	0.0625262i	−0.000683774	+	0.00198122i
$997$	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	$0.0500032\pi$
$998$	−20.4122	+	17.4210i	−0.646137	+	0.551453i
$999$	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.23.2	✓	672
4.3	odd	2	inner	380.2.bj.a.23.16	yes	672
5.2	odd	4	inner	380.2.bj.a.327.27	yes	672
19.5	even	9	inner	380.2.bj.a.43.15	yes	672
20.7	even	4	inner	380.2.bj.a.327.15	yes	672
76.43	odd	18	inner	380.2.bj.a.43.27	yes	672
95.62	odd	36	inner	380.2.bj.a.347.16	yes	672
380.347	even	36	inner	380.2.bj.a.347.2	yes	672

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

\(f(q)\)	\(=\)	\(q+(-1.41416 + 0.0118355i) q^{2} +(-0.0933215 - 0.0653444i) q^{3} +(1.99972 - 0.0334747i) q^{4} +(1.39136 - 1.75046i) q^{5} +(0.132745 + 0.0913032i) q^{6} +(4.78721 - 1.28273i) q^{7} +(-2.82754 + 0.0710065i) q^{8} +(-1.02162 - 2.80688i) q^{9} +O(q^{10})\)	\(q+(-1.41416 + 0.0118355i) q^{2} +(-0.0933215 - 0.0653444i) q^{3} +(1.99972 - 0.0334747i) q^{4} +(1.39136 - 1.75046i) q^{5} +(0.132745 + 0.0913032i) q^{6} +(4.78721 - 1.28273i) q^{7} +(-2.82754 + 0.0710065i) q^{8} +(-1.02162 - 2.80688i) q^{9} +(-1.94689 + 2.49191i) q^{10} +(0.466282 - 0.269208i) q^{11} +(-0.188804 - 0.127547i) q^{12} +(-2.77779 + 1.94503i) q^{13} +(-6.75472 + 1.87065i) q^{14} +(-0.244227 + 0.0724381i) q^{15} +(3.99776 - 0.133880i) q^{16} +(-5.45758 + 2.54491i) q^{17} +(1.47796 + 3.95730i) q^{18} +(2.75906 - 3.37455i) q^{19} +(2.72373 - 3.54701i) q^{20} +(-0.530569 - 0.193111i) q^{21} +(-0.656213 + 0.386223i) q^{22} +(1.00799 - 0.0881880i) q^{23} +(0.268510 + 0.178137i) q^{24} +(-1.12823 - 4.87105i) q^{25} +(3.90523 - 2.78347i) q^{26} +(-0.176532 + 0.658828i) q^{27} +(9.53014 - 2.72535i) q^{28} +(1.38341 + 3.80089i) q^{29} +(0.344519 - 0.105330i) q^{30} +(-0.138683 - 0.0800689i) q^{31} +(-5.65190 + 0.236644i) q^{32} +(-0.0611054 - 0.00534603i) q^{33} +(7.68779 - 3.66351i) q^{34} +(4.41536 - 10.1646i) q^{35} +(-2.13692 - 5.57878i) q^{36} +(3.38813 - 3.38813i) q^{37} +(-3.86183 + 4.80482i) q^{38} +0.386325 q^{39} +(-3.80983 + 5.04829i) q^{40} +(-1.76413 - 10.0049i) q^{41} +(0.752597 + 0.266811i) q^{42} +(-0.818125 + 9.35121i) q^{43} +(0.923421 - 0.553949i) q^{44} +(-6.33478 - 2.11707i) q^{45} +(-1.42442 + 0.136642i) q^{46} +(1.90980 + 0.890557i) q^{47} +(-0.381825 - 0.248737i) q^{48} +(15.2098 - 8.78138i) q^{49} +(1.65316 + 6.87510i) q^{50} +(0.675605 + 0.119127i) q^{51} +(-5.48970 + 3.98250i) q^{52} +(0.411241 + 4.70050i) q^{53} +(0.241848 - 0.933780i) q^{54} +(0.177528 - 1.19077i) q^{55} +(-13.4449 + 3.96688i) q^{56} +(-0.477988 + 0.134628i) q^{57} +(-2.00136 - 5.35871i) q^{58} +(10.8840 + 3.96146i) q^{59} +(-0.485960 + 0.153031i) q^{60} +(3.37282 + 2.83013i) q^{61} +(0.197069 + 0.111589i) q^{62} +(-8.49118 - 12.1267i) q^{63} +(7.98992 - 0.401547i) q^{64} +(-0.460207 + 7.56866i) q^{65} +(0.0864763 + 0.00683694i) q^{66} +(-6.00106 - 2.79834i) q^{67} +(-10.8284 + 5.27180i) q^{68} +(-0.0998301 - 0.0576369i) q^{69} +(-6.12374 + 14.4266i) q^{70} +(-4.11104 - 4.89935i) q^{71} +(3.08798 + 7.86402i) q^{72} +(-2.80477 + 4.00563i) q^{73} +(-4.75128 + 4.83148i) q^{74} +(-0.213007 + 0.528297i) q^{75} +(5.40439 - 6.84051i) q^{76} +(1.88687 - 1.88687i) q^{77} +(-0.546326 + 0.00457235i) q^{78} +(1.74573 + 9.90050i) q^{79} +(5.32797 - 7.18420i) q^{80} +(-6.80505 + 5.71011i) q^{81} +(2.61318 + 14.1277i) q^{82} +(-0.0751360 - 0.280411i) q^{83} +(-1.06745 - 0.368408i) q^{84} +(-3.13869 + 13.0942i) q^{85} +(1.04629 - 13.2338i) q^{86} +(0.119265 - 0.445103i) q^{87} +(-1.29931 + 0.794304i) q^{88} +(-6.80756 - 1.20036i) q^{89} +(8.98348 + 2.91891i) q^{90} +(-10.8029 + 12.8744i) q^{91} +(2.01275 - 0.210094i) 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} +(-21.4052 + 12.5983i) 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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