LMFDB - Embedded newform 58.2.d.b.7.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [58,2,Mod(7,58)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(58, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([6])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("58.7"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 58 = 2 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	58.d (of order $7$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$0.463132331723$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{7})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 13 x^{10} - 9 x^{9} - 5 x^{8} + 35 x^{7} + 197 x^{6} - 140 x^{5} - 80 x^{4} + \cdots + 4096 $ x^12 - 3x^11 + 13x^10 - 9x^9 - 5x^8 + 35x^7 + 197x^6 - 140x^5 - 80x^4 + 576x^3 + 3328x^2 + 3072*x + 4096
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			7.1
Root			$2.06920 - 0.996473i$ of defining polynomial
Character	$\chi$	$=$	58.7
Dual form			58.2.d.b.25.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.222521 - 0.974928i) q^{2} +(-2.06920 - 0.996473i) q^{3} +(-0.900969 + 0.433884i) q^{4} +(-0.788529 - 3.45477i) q^{5} +(-0.511050 + 2.23905i) q^{6} +(3.72857 + 1.79558i) q^{7} +(0.623490 + 0.781831i) q^{8} +(1.41815 + 1.77830i) q^{9} +(-3.19269 + 1.53752i) q^{10} +(-1.14832 + 1.43995i) q^{11} +2.29664 q^{12} +(2.09403 - 2.62583i) q^{13} +(0.920880 - 4.03464i) q^{14} +(-1.81096 + 7.93435i) q^{15} +(0.623490 - 0.781831i) q^{16} +3.52078 q^{17} +(1.41815 - 1.77830i) q^{18} +(-2.45556 + 1.18253i) q^{19} +(2.20941 + 2.77051i) q^{20} +(-5.92589 - 7.43083i) q^{21} +(1.65937 + 0.799109i) q^{22} +(0.679736 - 2.97812i) q^{23} +(-0.511050 - 2.23905i) q^{24} +(-6.80881 + 3.27895i) q^{25} +(-3.02595 - 1.45722i) q^{26} +(0.370748 + 1.62435i) q^{27} -4.13840 q^{28} +(0.127372 + 5.38366i) q^{29} +8.13840 q^{30} +(-0.196643 - 0.861548i) q^{31} +(-0.900969 - 0.433884i) q^{32} +(3.81096 - 1.83526i) q^{33} +(-0.783447 - 3.43250i) q^{34} +(3.26324 - 14.2972i) q^{35} +(-2.04929 - 0.986885i) q^{36} +(3.04846 + 3.82264i) q^{37} +(1.69930 + 2.13085i) q^{38} +(-6.94952 + 3.34671i) q^{39} +(2.20941 - 2.77051i) q^{40} -3.01488 q^{41} +(-5.92589 + 7.43083i) q^{42} +(-0.409830 + 1.79558i) q^{43} +(0.409830 - 1.79558i) q^{44} +(5.02538 - 6.30163i) q^{45} -3.05470 q^{46} +(1.25592 - 1.57487i) q^{47} +(-2.06920 + 0.996473i) q^{48} +(6.31365 + 7.91707i) q^{49} +(4.71184 + 5.90847i) q^{50} +(-7.28518 - 3.50836i) q^{51} +(-0.747349 + 3.27435i) q^{52} +(1.47479 + 6.46147i) q^{53} +(1.50113 - 0.722904i) q^{54} +(5.88016 + 2.83174i) q^{55} +(0.920880 + 4.03464i) q^{56} +6.25940 q^{57} +(5.22034 - 1.32216i) q^{58} +6.12406 q^{59} +(-1.81096 - 7.93435i) q^{60} +(-1.64476 - 0.792074i) q^{61} +(-0.796190 + 0.383425i) q^{62} +(2.09457 + 9.17693i) q^{63} +(-0.222521 + 0.974928i) q^{64} +(-10.7228 - 5.16384i) q^{65} +(-2.63727 - 3.30703i) q^{66} +(-0.0862879 - 0.108202i) q^{67} +(-3.17211 + 1.52761i) q^{68} +(-4.37412 + 5.48497i) q^{69} -14.6649 q^{70} +(-8.17273 + 10.2483i) q^{71} +(-0.506132 + 2.21751i) q^{72} +(3.42387 - 15.0009i) q^{73} +(3.04846 - 3.82264i) q^{74} +17.3562 q^{75} +(1.69930 - 2.13085i) q^{76} +(-6.86712 + 3.30703i) q^{77} +(4.80921 + 6.03056i) q^{78} +(-9.90051 - 12.4148i) q^{79} +(-3.19269 - 1.53752i) q^{80} +(2.36987 - 10.3831i) q^{81} +(0.670875 + 2.93929i) q^{82} +(0.0422914 - 0.0203665i) q^{83} +(8.56316 + 4.12380i) q^{84} +(-2.77623 - 12.1635i) q^{85} +1.84176 q^{86} +(5.10111 - 11.2668i) q^{87} -1.84176 q^{88} +(0.800961 + 3.50924i) q^{89} +(-7.26188 - 3.49714i) q^{90} +(12.5226 - 6.03056i) q^{91} +(0.679736 + 2.97812i) q^{92} +(-0.451617 + 1.97866i) q^{93} +(-1.81485 - 0.873987i) q^{94} +(6.02166 + 7.55092i) q^{95} +(1.43193 + 1.79558i) q^{96} +(-4.71887 + 2.27249i) q^{97} +(6.31365 - 7.91707i) q^{98} -4.18915 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} - 3 q^{3} - 2 q^{4} + 4 q^{6} + q^{7} - 2 q^{8} - 11 q^{9} - 7 q^{10} - 2 q^{11} + 4 q^{12} + q^{13} + q^{14} - 9 q^{15} - 2 q^{16} - 12 q^{17} - 11 q^{18} - 6 q^{19} + 7 q^{20} - 13 q^{21}+ \cdots - 8 q^{99}+O(q^{100}) $ 12 * q - 2 * q^2 - 3 * q^3 - 2 * q^4 + 4 * q^6 + q^7 - 2 * q^8 - 11 * q^9 - 7 * q^10 - 2 * q^11 + 4 * q^12 + q^13 + q^14 - 9 * q^15 - 2 * q^16 - 12 * q^17 - 11 * q^18 - 6 * q^19 + 7 * q^20 - 13 * q^21 - 2 * q^22 + 35 * q^23 + 4 * q^24 - 6 * q^25 + 8 * q^26 + 39 * q^27 - 6 * q^28 - 14 * q^29 + 54 * q^30 - 8 * q^31 - 2 * q^32 + 33 * q^33 - 5 * q^34 - 18 * q^35 - 4 * q^36 + 31 * q^37 + q^38 - 22 * q^39 + 7 * q^40 - 30 * q^41 - 13 * q^42 - 5 * q^43 + 5 * q^44 - 20 * q^45 - 28 * q^46 - 33 * q^47 - 3 * q^48 + 37 * q^49 + q^50 - 15 * q^51 - 6 * q^52 + 13 * q^53 - 24 * q^54 + 36 * q^55 + q^56 - 38 * q^57 + 38 * q^59 - 9 * q^60 - 5 * q^61 - 8 * q^62 + 4 * q^63 - 2 * q^64 - 20 * q^65 - 30 * q^66 - 7 * q^67 - 19 * q^68 + 20 * q^69 - 18 * q^70 + 3 * q^71 + 3 * q^72 - 22 * q^73 + 31 * q^74 - 2 * q^75 + q^76 + 10 * q^77 + 41 * q^78 - 60 * q^79 - 7 * q^80 + 88 * q^81 + 26 * q^82 - 39 * q^83 + 43 * q^84 + 38 * q^85 + 2 * q^86 + 9 * q^87 - 2 * q^88 + 39 * q^89 - 34 * q^90 + 61 * q^91 + 35 * q^92 - 54 * q^93 + 16 * q^94 + 55 * q^95 - 3 * q^96 - 19 * q^97 + 37 * q^98 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/58\mathbb{Z}\right)^\times$.

$n$	$31$
$\chi(n)$	$e\left(\frac{3}{7}\right)$

Coefficient data

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

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

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

$2$	−0.222521	−	0.974928i	−0.157346	−	0.689378i
$2$	−0.222521	−	0.974928i	−0.157346	−	0.689378i
$3$	−2.06920	−	0.996473i	−1.19465	−	0.575314i	−0.272505	−	0.962154i	$-0.587852\pi$
$3$	−2.06920	−	0.996473i	−1.19465	−	0.575314i	−0.922147	+	0.386840i	$0.873566\pi$
$4$	−0.900969	+	0.433884i	−0.450484	+	0.216942i
$5$	−0.788529	−	3.45477i	−0.352641	−	1.54502i	−0.771058	−	0.636765i	$-0.780272\pi$
$5$	−0.788529	−	3.45477i	−0.352641	−	1.54502i	0.418417	−	0.908255i	$-0.362585\pi$
$6$	−0.511050	+	2.23905i	−0.208635	+	0.914090i
$7$	3.72857	+	1.79558i	1.40927	+	0.678666i	0.975018	−	0.222127i	$-0.0713001\pi$
$7$	3.72857	+	1.79558i	1.40927	+	0.678666i	0.434247	+	0.900794i	$0.357014\pi$
$8$	0.623490	+	0.781831i	0.220437	+	0.276419i
$9$	1.41815	+	1.77830i	0.472717	+	0.592768i
$10$	−3.19269	+	1.53752i	−1.00962	+	0.486206i
$11$	−1.14832	+	1.43995i	−0.346231	+	0.434160i	−0.924206	−	0.381895i	$-0.875272\pi$
$11$	−1.14832	+	1.43995i	−0.346231	+	0.434160i	0.577975	+	0.816055i	$0.303843\pi$
$12$	2.29664			0.662982
$13$	2.09403	−	2.62583i	0.580778	−	0.728273i	−0.401467	−	0.915873i	$-0.631500\pi$
$13$	2.09403	−	2.62583i	0.580778	−	0.728273i	0.982245	+	0.187601i	$0.0600710\pi$
$14$	0.920880	−	4.03464i	0.246115	−	1.07830i
$15$	−1.81096	+	7.93435i	−0.467589	+	2.04864i
$16$	0.623490	−	0.781831i	0.155872	−	0.195458i
$17$	3.52078			0.853914			0.426957	−	0.904272i	$-0.359586\pi$
$17$	3.52078			0.853914			0.426957	+	0.904272i	$0.359586\pi$
$18$	1.41815	−	1.77830i	0.334261	−	0.419150i
$19$	−2.45556	+	1.18253i	−0.563344	+	0.271292i	−0.693807	−	0.720161i	$-0.744068\pi$
$19$	−2.45556	+	1.18253i	−0.563344	+	0.271292i	0.130463	+	0.991453i	$0.458354\pi$
$20$	2.20941	+	2.77051i	0.494039	+	0.619505i
$21$	−5.92589	−	7.43083i	−1.29313	−	1.62154i
$22$	1.65937	+	0.799109i	0.353778	+	0.170371i
$23$	0.679736	−	2.97812i	0.141735	−	0.620980i	−0.853297	−	0.521425i	$-0.825401\pi$
$23$	0.679736	−	2.97812i	0.141735	−	0.620980i	0.995032	−	0.0995556i	$-0.0317421\pi$
$24$	−0.511050	−	2.23905i	−0.104318	−	0.457045i
$25$	−6.80881	+	3.27895i	−1.36176	+	0.655790i
$26$	−3.02595	−	1.45722i	−0.593439	−	0.285785i
$27$	0.370748	+	1.62435i	0.0713504	+	0.312607i
$28$	−4.13840			−0.782083
$29$	0.127372	+	5.38366i	0.0236524	+	0.999720i
$29$	0.127372	+	5.38366i	0.0236524	+	0.999720i
$30$	8.13840			1.48586
$31$	−0.196643	−	0.861548i	−0.0353181	−	0.154739i	0.954194	−	0.299188i	$-0.0967159\pi$
$31$	−0.196643	−	0.861548i	−0.0353181	−	0.154739i	−0.989512	+	0.144450i	$0.953859\pi$
$32$	−0.900969	−	0.433884i	−0.159270	−	0.0767005i
$33$	3.81096	−	1.83526i	0.663404	−	0.319478i
$34$	−0.783447	−	3.43250i	−0.134360	−	0.588670i
$35$	3.26324	−	14.2972i	0.551589	−	2.41667i
$36$	−2.04929	−	0.986885i	−0.341548	−	0.164481i
$37$	3.04846	+	3.82264i	0.501163	+	0.628439i	0.966491	−	0.256700i	$-0.0826351\pi$
$37$	3.04846	+	3.82264i	0.501163	+	0.628439i	−0.465328	+	0.885138i	$0.654064\pi$
$38$	1.69930	+	2.13085i	0.275663	+	0.345670i
$39$	−6.94952	+	3.34671i	−1.11281	+	0.535903i
$40$	2.20941	−	2.77051i	0.349338	−	0.438056i
$41$	−3.01488			−0.470846			−0.235423	−	0.971893i	$-0.575647\pi$
$41$	−3.01488			−0.470846			−0.235423	+	0.971893i	$0.575647\pi$
$42$	−5.92589	+	7.43083i	−0.914384	+	1.14660i
$43$	−0.409830	+	1.79558i	−0.0624985	+	0.273824i	−0.996516	−	0.0834039i	$-0.973421\pi$
$43$	−0.409830	+	1.79558i	−0.0624985	+	0.273824i	0.934017	+	0.357228i	$0.116278\pi$
$44$	0.409830	−	1.79558i	0.0617842	−	0.270694i
$45$	5.02538	−	6.30163i	0.749139	−	0.939391i
$46$	−3.05470			−0.450392
$47$	1.25592	−	1.57487i	0.183194	−	0.229718i	−0.681751	−	0.731584i	$-0.738781\pi$
$47$	1.25592	−	1.57487i	0.183194	−	0.229718i	0.864946	+	0.501866i	$0.167353\pi$
$48$	−2.06920	+	0.996473i	−0.298663	+	0.143828i
$49$	6.31365	+	7.91707i	0.901950	+	1.13101i
$50$	4.71184	+	5.90847i	0.666355	+	0.835583i
$51$	−7.28518	−	3.50836i	−1.02013	−	0.491269i
$52$	−0.747349	+	3.27435i	−0.103639	+	0.454071i
$53$	1.47479	+	6.46147i	0.202578	+	0.887551i	0.969360	+	0.245644i	$0.0789993\pi$
$53$	1.47479	+	6.46147i	0.202578	+	0.887551i	−0.766783	+	0.641907i	$0.778144\pi$
$54$	1.50113	−	0.722904i	0.204277	−	0.0983748i
$55$	5.88016	+	2.83174i	0.792881	+	0.381831i
$56$	0.920880	+	4.03464i	0.123058	+	0.539151i
$57$	6.25940			0.829077
$58$	5.22034	−	1.32216i	0.685464	−	0.173607i
$59$	6.12406			0.797285			0.398642	−	0.917106i	$-0.369481\pi$
$59$	6.12406			0.797285			0.398642	+	0.917106i	$0.369481\pi$
$60$	−1.81096	−	7.93435i	−0.233794	−	1.02432i
$61$	−1.64476	−	0.792074i	−0.210590	−	0.101415i	0.325616	−	0.945502i	$-0.394428\pi$
$61$	−1.64476	−	0.792074i	−0.210590	−	0.101415i	−0.536205	+	0.844088i	$0.680143\pi$
$62$	−0.796190	+	0.383425i	−0.101116	+	0.0486950i
$63$	2.09457	+	9.17693i	0.263892	+	1.15618i
$64$	−0.222521	+	0.974928i	−0.0278151	+	0.121866i
$65$	−10.7228	−	5.16384i	−1.33000	−	0.640495i
$66$	−2.63727	−	3.30703i	−0.324625	−	0.407067i
$67$	−0.0862879	−	0.108202i	−0.0105417	−	0.0132189i	0.776533	−	0.630077i	$-0.216977\pi$
$67$	−0.0862879	−	0.108202i	−0.0105417	−	0.0132189i	−0.787074	+	0.616858i	$0.788405\pi$
$68$	−3.17211	+	1.52761i	−0.384675	+	0.185250i
$69$	−4.37412	+	5.48497i	−0.526582	+	0.660313i
$70$	−14.6649			−1.75279
$71$	−8.17273	+	10.2483i	−0.969925	+	1.21625i	0.00640935	+	0.999979i	$0.497960\pi$
$71$	−8.17273	+	10.2483i	−0.969925	+	1.21625i	−0.976334	+	0.216268i	$0.930612\pi$
$72$	−0.506132	+	2.21751i	−0.0596482	+	0.261336i
$73$	3.42387	−	15.0009i	0.400733	−	1.75573i	−0.223709	−	0.974656i	$-0.571817\pi$
$73$	3.42387	−	15.0009i	0.400733	−	1.75573i	0.624442	−	0.781071i	$-0.285326\pi$
$74$	3.04846	−	3.82264i	0.354376	−	0.444373i
$75$	17.3562			2.00412
$76$	1.69930	−	2.13085i	0.194923	−	0.244426i
$77$	−6.86712	+	3.30703i	−0.782581	+	0.376871i
$78$	4.80921	+	6.03056i	0.544536	+	0.682827i
$79$	−9.90051	−	12.4148i	−1.11389	−	1.39678i	−0.908390	−	0.418123i	$-0.862688\pi$
$79$	−9.90051	−	12.4148i	−1.11389	−	1.39678i	−0.205504	−	0.978656i	$-0.565883\pi$
$80$	−3.19269	−	1.53752i	−0.356953	−	0.171900i
$81$	2.36987	−	10.3831i	0.263319	−	1.15367i
$82$	0.670875	+	2.93929i	0.0740857	+	0.324591i
$83$	0.0422914	−	0.0203665i	0.00464209	−	0.00223551i	−0.431561	−	0.902084i	$-0.642037\pi$
$83$	0.0422914	−	0.0203665i	0.00464209	−	0.00223551i	0.436203	+	0.899848i	$0.356323\pi$
$84$	8.56316	+	4.12380i	0.934317	+	0.449943i
$85$	−2.77623	−	12.1635i	−0.301125	−	1.31931i
$86$	1.84176			0.198602
$87$	5.10111	−	11.2668i	0.546897	−	1.20793i
$88$	−1.84176			−0.196332
$89$	0.800961	+	3.50924i	0.0849017	+	0.371979i	0.999474	−	0.0324449i	$-0.0103293\pi$
$89$	0.800961	+	3.50924i	0.0849017	+	0.371979i	−0.914572	+	0.404423i	$0.867472\pi$
$90$	−7.26188	−	3.49714i	−0.765470	−	0.368631i
$91$	12.5226	−	6.03056i	1.31272	−	0.632175i
$92$	0.679736	+	2.97812i	0.0708673	+	0.310490i
$93$	−0.451617	+	1.97866i	−0.0468305	+	0.205178i
$94$	−1.81485	−	0.873987i	−0.187188	−	0.0901449i
$95$	6.02166	+	7.55092i	0.617809	+	0.774708i
$96$	1.43193	+	1.79558i	0.146146	+	0.183261i
$97$	−4.71887	+	2.27249i	−0.479129	+	0.230736i	−0.657829	−	0.753167i	$-0.728525\pi$
$97$	−4.71887	+	2.27249i	−0.479129	+	0.230736i	0.178700	+	0.983904i	$0.442811\pi$
$98$	6.31365	−	7.91707i	0.637775	−	0.799745i
$99$	−4.18915			−0.421025
$100$	4.71184	−	5.90847i	0.471184	−	0.590847i
$101$	−2.14719	+	9.40747i	−0.213654	+	0.936079i	0.748406	+	0.663241i	$0.230819\pi$
$101$	−2.14719	+	9.40747i	−0.213654	+	0.936079i	−0.962060	+	0.272838i	$0.912038\pi$
$102$	−1.79929	+	7.88321i	−0.178156	+	0.780554i
$103$	−9.84264	+	12.3423i	−0.969824	+	1.21612i	0.00653753	+	0.999979i	$0.497919\pi$
$103$	−9.84264	+	12.3423i	−0.969824	+	1.21612i	−0.976362	+	0.216143i	$0.930652\pi$
$104$	3.35856			0.329334
$105$	−20.9991	+	26.3320i	−2.04930	+	2.56974i
$106$	5.97129	−	2.87562i	0.579983	−	0.279305i
$107$	−10.6232	−	13.3211i	−1.02699	−	1.28780i	−0.956950	−	0.290254i	$-0.906260\pi$
$107$	−10.6232	−	13.3211i	−1.02699	−	1.28780i	−0.0700358	−	0.997544i	$-0.522311\pi$
$108$	−1.03881	−	1.30263i	−0.0999597	−	0.125346i
$109$	18.0142	+	8.67517i	1.72545	+	0.830931i	0.987797	+	0.155746i	$0.0497780\pi$
$109$	18.0142	+	8.67517i	1.72545	+	0.830931i	0.737648	+	0.675185i	$0.235936\pi$
$110$	1.45228	−	6.36285i	0.138469	−	0.606674i
$111$	−2.49870	−	10.9475i	−0.237166	−	1.03909i
$112$	3.72857	−	1.79558i	0.352316	−	0.169667i
$113$	−9.91629	−	4.77544i	−0.932847	−	0.449235i	−0.0952063	−	0.995458i	$-0.530351\pi$
$113$	−9.91629	−	4.77544i	−0.932847	−	0.449235i	−0.837640	+	0.546222i	$0.816065\pi$
$114$	−1.39285	−	6.10246i	−0.130452	−	0.571548i
$115$	−10.8247			−1.00941
$116$	−2.45064	−	4.79524i	−0.227536	−	0.445227i
$117$	7.63916			0.706241
$118$	−1.36273	−	5.97052i	−0.125450	−	0.549631i
$119$	13.1274	+	6.32185i	1.20339	+	0.579523i
$120$	−7.33244	+	3.53112i	−0.669357	+	0.322345i
$121$	1.69292	+	7.41718i	0.153902	+	0.674289i
$122$	−0.406222	+	1.77977i	−0.0367776	+	0.161133i
$123$	6.23839	+	3.00425i	0.562497	+	0.270884i
$124$	0.550981	+	0.690908i	0.0494795	+	0.0620453i
$125$	5.64992	+	7.08478i	0.505345	+	0.633682i
$126$	8.48076	−	4.08412i	0.755526	−	0.363842i
$127$	−1.41252	+	1.77125i	−0.125341	+	0.157173i	−0.840543	−	0.541746i	$-0.817764\pi$
$127$	−1.41252	+	1.77125i	−0.125341	+	0.157173i	0.715201	+	0.698919i	$0.246335\pi$
$128$	1.00000			0.0883883
$129$	2.63727	−	3.30703i	0.232199	−	0.291168i
$130$	−2.64832	+	11.6030i	−0.232273	+	1.01765i
$131$	−0.622714	+	2.72829i	−0.0544068	+	0.238372i	−0.994819	−	0.101666i	$-0.967583\pi$
$131$	−0.622714	+	2.72829i	−0.0544068	+	0.238372i	0.940412	+	0.340038i	$0.110440\pi$
$132$	−2.63727	+	3.30703i	−0.229545	+	0.287840i
$133$	−11.2790			−0.978017
$134$	−0.0862879	+	0.108202i	−0.00745414	+	0.00934719i
$135$	5.31942	−	2.56170i	0.457822	−	0.220476i
$136$	2.19517	+	2.75265i	0.188234	+	0.236038i
$137$	−0.165560	−	0.207606i	−0.0141448	−	0.0177370i	0.774709	−	0.632318i	$-0.217896\pi$
$137$	−0.165560	−	0.207606i	−0.0141448	−	0.0177370i	−0.788854	+	0.614581i	$0.789325\pi$
$138$	6.32079	+	3.04393i	0.538061	+	0.259117i
$139$	1.42402	−	6.23904i	0.120784	−	0.529189i	−0.877944	−	0.478763i	$-0.841085\pi$
$139$	1.42402	−	6.23904i	0.120784	−	0.529189i	0.998728	−	0.0504252i	$-0.0160577\pi$
$140$	3.26324	+	14.2972i	0.275794	+	1.20833i
$141$	−4.16806	+	2.00723i	−0.351014	+	0.169039i
$142$	11.8099	+	5.68737i	0.991068	+	0.477273i
$143$	1.37644	+	6.03056i	0.115103	+	0.504301i
$144$	2.27454			0.189545
$145$	18.4989	−	4.68521i	1.53625	−	0.389085i
$146$	−15.3867			−1.27341
$147$	−5.17505	−	22.6734i	−0.426831	−	1.87007i
$148$	−4.40515	−	2.12141i	−0.362101	−	0.174379i
$149$	−9.33977	+	4.49780i	−0.765144	+	0.368474i	−0.775397	−	0.631474i	$-0.782450\pi$
$149$	−9.33977	+	4.49780i	−0.765144	+	0.368474i	0.0102535	+	0.999947i	$0.496736\pi$
$150$	−3.86211	−	16.9210i	−0.315340	−	1.38159i
$151$	−2.41525	+	10.5819i	−0.196550	+	0.861143i	0.776421	+	0.630215i	$0.217033\pi$
$151$	−2.41525	+	10.5819i	−0.196550	+	0.861143i	−0.972971	+	0.230928i	$0.925824\pi$
$152$	−2.45556	−	1.18253i	−0.199172	−	0.0959162i
$153$	4.99299	+	6.26101i	0.403659	+	0.506173i
$154$	4.75219	+	5.95906i	0.382943	+	0.480195i
$155$	−2.82139	+	1.35871i	−0.226620	+	0.109134i
$156$	4.80921	−	6.03056i	0.385045	−	0.482832i
$157$	24.3534			1.94362			0.971808	−	0.235772i	$-0.0757619\pi$
$157$	24.3534			1.94362			0.971808	+	0.235772i	$0.0757619\pi$
$158$	−9.90051	+	12.4148i	−0.787642	+	0.987672i
$159$	3.38705	−	14.8396i	0.268611	−	1.17686i
$160$	−0.788529	+	3.45477i	−0.0623387	+	0.273124i
$161$	7.88189	−	9.88358i	0.621180	−	0.778935i
$162$	−10.6501			−0.836750
$163$	8.34151	−	10.4599i	0.653358	−	0.819285i	−0.339244	−	0.940698i	$-0.610171\pi$
$163$	8.34151	−	10.4599i	0.653358	−	0.819285i	0.992602	+	0.121414i	$0.0387427\pi$
$164$	2.71632	−	1.30811i	0.212109	−	0.102146i
$165$	−9.34547	−	11.7188i	−0.727543	−	0.912311i
$166$	−0.0292666	−	0.0366991i	−0.00227153	−	0.00284841i
$167$	9.05074	+	4.35860i	0.700367	+	0.337279i	0.749953	−	0.661491i	$-0.230076\pi$
$167$	9.05074	+	4.35860i	0.700367	+	0.337279i	−0.0495862	+	0.998770i	$0.515790\pi$
$168$	2.11493	−	9.26609i	0.163170	−	0.714895i
$169$	0.382758	+	1.67697i	0.0294429	+	0.128998i
$170$	−11.2407	+	5.41326i	−0.862126	+	0.415178i
$171$	−5.58526	−	2.68972i	−0.427115	−	0.205688i
$172$	−0.409830	−	1.79558i	−0.0312492	−	0.136912i
$173$	−16.3814			−1.24545			−0.622727	−	0.782439i	$-0.713975\pi$
$173$	−16.3814			−1.24545			−0.622727	+	0.782439i	$0.713975\pi$
$174$	−12.1194	−	2.46612i	−0.918769	−	0.186956i
$175$	−31.2747			−2.36415
$176$	0.409830	+	1.79558i	0.0308921	+	0.135347i
$177$	−12.6719	−	6.10246i	−0.952478	−	0.458689i
$178$	3.24302	−	1.56176i	0.243075	−	0.117059i
$179$	−1.89387	−	8.29757i	−0.141554	−	0.620189i	−0.995075	−	0.0991299i	$-0.968394\pi$
$179$	−1.89387	−	8.29757i	−0.141554	−	0.620189i	0.853520	−	0.521060i	$-0.174463\pi$
$180$	−1.79354	+	7.85800i	−0.133682	+	0.585701i
$181$	−7.65851	−	3.68815i	−0.569253	−	0.274138i	0.127038	−	0.991898i	$-0.459453\pi$
$181$	−7.65851	−	3.68815i	−0.569253	−	0.274138i	−0.696290	+	0.717760i	$0.745167\pi$
$182$	−8.66591	−	10.8667i	−0.642360	−	0.805494i
$183$	2.61405	+	3.27792i	0.193236	+	0.242310i
$184$	2.75219	−	1.32539i	0.202894	−	0.0977088i
$185$	10.8026	−	13.5460i	0.794220	−	0.995920i
$186$	2.02955			0.148814
$187$	−4.04297	+	5.06973i	−0.295651	+	0.370735i
$188$	−0.448232	+	1.96383i	−0.0326907	+	0.143227i
$189$	−1.53430	+	6.72221i	−0.111604	+	0.488969i
$190$	6.02166	−	7.55092i	0.436857	−	0.547802i
$191$	24.4078			1.76609			0.883044	−	0.469291i	$-0.155490\pi$
$191$	24.4078			1.76609			0.883044	+	0.469291i	$0.155490\pi$
$192$	1.43193	−	1.79558i	0.103341	−	0.129585i
$193$	−4.45144	+	2.14370i	−0.320422	+	0.154307i	−0.587180	−	0.809456i	$-0.699762\pi$
$193$	−4.45144	+	2.14370i	−0.320422	+	0.154307i	0.266758	+	0.963764i	$0.414048\pi$
$194$	3.26556	+	4.09489i	0.234454	+	0.293996i
$195$	17.0420	+	21.3700i	1.22040	+	1.53034i
$196$	−9.12349	−	4.39364i	−0.651678	−	0.313832i
$197$	−0.163605	+	0.716798i	−0.0116563	+	0.0510698i	−0.980422	−	0.196910i	$-0.936909\pi$
$197$	−0.163605	+	0.716798i	−0.0116563	+	0.0510698i	0.968765	+	0.247979i	$0.0797666\pi$
$198$	0.932173	+	4.08412i	0.0662467	+	0.290246i
$199$	1.19231	−	0.574188i	0.0845209	−	0.0407031i	−0.391146	−	0.920329i	$-0.627921\pi$
$199$	1.19231	−	0.574188i	0.0845209	−	0.0407031i	0.475667	+	0.879626i	$0.342207\pi$
$200$	−6.80881	−	3.27895i	−0.481456	−	0.231857i
$201$	0.0707267	+	0.309874i	0.00498868	+	0.0218568i
$202$	9.64941			0.678930
$203$	−9.19189	+	20.3020i	−0.645144	+	1.42492i
$204$	8.08594			0.566129
$205$	2.37732	+	10.4157i	0.166039	+	0.727466i
$206$	14.2230	+	6.84945i	0.990965	+	0.477224i
$207$	6.25997	−	3.01464i	0.435098	−	0.209532i
$208$	−0.747349	−	3.27435i	−0.0518193	−	0.227035i
$209$	1.11698	−	4.89379i	0.0772629	−	0.338511i
$210$	30.3445	+	14.6132i	2.09397	+	1.00840i
$211$	1.89916	+	2.38147i	0.130743	+	0.163947i	0.842894	−	0.538080i	$-0.180850\pi$
$211$	1.89916	+	2.38147i	0.130743	+	0.163947i	−0.712151	+	0.702027i	$0.752279\pi$
$212$	−4.13226	−	5.18169i	−0.283805	−	0.355880i
$213$	27.1231	−	13.0618i	1.85845	−	0.894981i
$214$	−10.6232	+	13.3211i	−0.726188	+	0.910611i
$215$	6.52649			0.445103
$216$	−1.03881	+	1.30263i	−0.0706822	+	0.0886327i
$217$	0.813785	−	3.56543i	0.0552433	−	0.242037i
$218$	4.44914	−	19.4929i	0.301333	−	1.32023i
$219$	−22.0327	+	27.6281i	−1.48883	+	1.86693i
$220$	−6.52649			−0.440016
$221$	7.37260	−	9.24495i	0.495935	−	0.621882i
$222$	−10.1170	+	4.87210i	−0.679010	+	0.326994i
$223$	−5.37834	−	6.74423i	−0.360161	−	0.451627i	0.568431	−	0.822731i	$-0.307551\pi$
$223$	−5.37834	−	6.74423i	−0.360161	−	0.451627i	−0.928591	+	0.371104i	$0.878979\pi$
$224$	−2.58025	−	3.23553i	−0.172400	−	0.216183i
$225$	−15.4869	−	7.45810i	−1.03246	−	0.497206i
$226$	−2.44912	+	10.7303i	−0.162913	+	0.713769i
$227$	0.104102	+	0.456102i	0.00690951	+	0.0302725i	0.978265	−	0.207358i	$-0.0664864\pi$
$227$	0.104102	+	0.456102i	0.00690951	+	0.0302725i	−0.971356	+	0.237630i	$0.923629\pi$
$228$	−5.63952	+	2.71585i	−0.373486	+	0.179862i
$229$	−22.7826	−	10.9715i	−1.50551	−	0.725018i	−0.514341	−	0.857586i	$-0.671963\pi$
$229$	−22.7826	−	10.9715i	−1.50551	−	0.725018i	−0.991174	+	0.132568i	$0.957678\pi$
$230$	2.40872	+	10.5533i	0.158826	+	0.695864i
$231$	17.5048			1.15173
$232$	−4.12970	+	3.45624i	−0.271128	+	0.226913i
$233$	13.2841			0.870270			0.435135	−	0.900365i	$-0.356701\pi$
$233$	13.2841			0.870270			0.435135	+	0.900365i	$0.356701\pi$
$234$	−1.69987	−	7.44763i	−0.111124	−	0.486867i
$235$	−6.43114	−	3.09707i	−0.419521	−	0.202031i
$236$	−5.51759	+	2.65713i	−0.359164	+	0.172964i
$237$	8.11505	+	35.5544i	0.527129	+	2.30950i
$238$	3.24221	−	14.2051i	0.210161	−	0.920777i
$239$	−14.4978	−	6.98177i	−0.937784	−	0.451613i	−0.0983969	−	0.995147i	$-0.531371\pi$
$239$	−14.4978	−	6.98177i	−0.937784	−	0.451613i	−0.839387	+	0.543534i	$0.817086\pi$
$240$	5.07421	+	6.36285i	0.327539	+	0.410720i
$241$	−9.27842	−	11.6348i	−0.597676	−	0.749462i	0.387338	−	0.921938i	$-0.373395\pi$
$241$	−9.27842	−	11.6348i	−0.597676	−	0.749462i	−0.985014	+	0.172476i	$0.944823\pi$
$242$	6.85450	−	3.30095i	0.440624	−	0.212193i
$243$	−12.1337	+	15.2152i	−0.778380	+	0.976058i
$244$	1.82554			0.116869
$245$	22.3732	−	28.0551i	1.42937	−	1.79237i
$246$	1.54075	−	6.75049i	0.0982349	−	0.430395i
$247$	−2.03687	+	8.92412i	−0.129603	+	0.567828i
$248$	0.550981	−	0.690908i	0.0349873	−	0.0438727i
$249$	−0.107804			−0.00683180
$250$	5.64992	−	7.08478i	0.357333	−	0.448081i
$251$	0.327432	−	0.157683i	0.0206673	−	0.00995285i	−0.423522	−	0.905886i	$-0.639206\pi$
$251$	0.327432	−	0.157683i	0.0206673	−	0.00995285i	0.444189	+	0.895933i	$0.353492\pi$
$252$	−5.86887	−	7.35933i	−0.369704	−	0.463594i
$253$	3.50777	+	4.39861i	0.220532	+	0.276538i
$254$	2.04116	+	0.982970i	0.128074	+	0.0616770i
$255$	−6.37600	+	27.9351i	−0.399281	+	1.74936i
$256$	−0.222521	−	0.974928i	−0.0139076	−	0.0609330i
$257$	−4.56869	+	2.20017i	−0.284987	+	0.137243i	−0.570917	−	0.821008i	$-0.693412\pi$
$257$	−4.56869	+	2.20017i	−0.284987	+	0.137243i	0.285929	+	0.958251i	$0.407698\pi$
$258$	−3.81096	−	1.83526i	−0.237260	−	0.114258i
$259$	4.50250	+	19.7267i	0.279772	+	1.22576i
$260$	11.9014			0.738096
$261$	−9.39315	+	7.86134i	−0.581421	+	0.486605i
$262$	2.79845			0.172889
$263$	2.42180	+	10.6106i	0.149335	+	0.654279i	0.993071	+	0.117520i	$0.0374944\pi$
$263$	2.42180	+	10.6106i	0.149335	+	0.654279i	−0.843736	+	0.536759i	$0.819648\pi$
$264$	3.81096	+	1.83526i	0.234549	+	0.112953i
$265$	21.1600	−	10.1901i	1.29985	−	0.625973i
$266$	2.50982	+	10.9963i	0.153887	+	0.674224i
$267$	1.83952	−	8.05944i	0.112577	−	0.493230i
$268$	0.124690	+	0.0600474i	0.00761663	+	0.00366798i
$269$	−16.8131	−	21.0830i	−1.02511	−	1.28545i	−0.957712	−	0.287727i	$-0.907100\pi$
$269$	−16.8131	−	21.0830i	−1.02511	−	1.28545i	−0.0674024	−	0.997726i	$-0.521471\pi$
$270$	−3.68115	−	4.61602i	−0.224028	−	0.280922i
$271$	−12.7323	+	6.13158i	−0.773435	+	0.372467i	−0.778600	−	0.627520i	$-0.784070\pi$
$271$	−12.7323	+	6.13158i	−0.773435	+	0.372467i	0.00516543	+	0.999987i	$0.498356\pi$
$272$	2.19517	−	2.75265i	0.133102	−	0.166904i
$273$	−31.9210			−1.93195
$274$	−0.165560	+	0.207606i	−0.0100019	+	0.0125420i
$275$	3.09717	−	13.5696i	0.186766	−	0.818277i
$276$	1.56111	−	6.83965i	0.0939675	−	0.411699i
$277$	8.12000	−	10.1822i	0.487883	−	0.611786i	−0.475565	−	0.879681i	$-0.657756\pi$
$277$	8.12000	−	10.1822i	0.487883	−	0.611786i	0.963448	+	0.267894i	$0.0863277\pi$
$278$	−6.39949			−0.383816
$279$	1.25323	−	1.57150i	0.0750286	−	0.0940829i
$280$	13.2126	−	6.36285i	0.789604	−	0.380253i
$281$	18.1332	+	22.7384i	1.08174	+	1.35646i	0.929799	+	0.368068i	$0.119981\pi$
$281$	18.1332	+	22.7384i	1.08174	+	1.35646i	0.151940	+	0.988390i	$0.451448\pi$
$282$	2.88438	+	3.61690i	0.171763	+	0.215383i
$283$	−16.9605	−	8.16773i	−1.00820	−	0.485521i	−0.144483	−	0.989507i	$-0.546152\pi$
$283$	−16.9605	−	8.16773i	−1.00820	−	0.485521i	−0.863712	+	0.503986i	$0.831866\pi$
$284$	2.91681	−	12.7794i	0.173081	−	0.758318i
$285$	−4.93571	−	21.6248i	−0.292366	−	1.28094i
$286$	5.57308	−	2.68385i	0.329543	−	0.158700i
$287$	−11.2412	−	5.41347i	−0.663546	−	0.319547i
$288$	−0.506132	−	2.21751i	−0.0298241	−	0.130668i
$289$	−4.60413			−0.270831
$290$	−8.68413	−	16.9925i	−0.509949	−	0.997834i
$291$	12.0288			0.705138
$292$	3.42387	+	15.0009i	0.200367	+	0.877863i
$293$	5.38294	+	2.59229i	0.314475	+	0.151443i	0.584463	−	0.811421i	$-0.301305\pi$
$293$	5.38294	+	2.59229i	0.314475	+	0.151443i	−0.269988	+	0.962864i	$0.587020\pi$
$294$	−20.9533	+	10.0906i	−1.22202	+	0.588496i
$295$	−4.82900	−	21.1572i	−0.281155	−	1.23182i
$296$	−1.08798	+	4.76676i	−0.0632376	+	0.277062i
$297$	−2.76471	−	1.33142i	−0.160425	−	0.0772566i
$298$	6.46332	+	8.10475i	0.374410	+	0.469496i
$299$	−6.39663	−	8.02112i	−0.369927	−	0.463873i
$300$	−15.6374	+	7.53056i	−0.902824	+	0.434777i
$301$	−4.75219	+	5.95906i	−0.273912	+	0.343475i
$302$	10.8540			0.624579
$303$	13.8173	−	17.3263i	0.793781	−	0.995370i
$304$	−0.606473	+	2.65713i	−0.0347836	+	0.152397i
$305$	−1.43949	+	6.30684i	−0.0824252	+	0.361128i
$306$	4.99299	−	6.26101i	0.285430	−	0.357918i
$307$	−11.1008			−0.633556			−0.316778	−	0.948500i	$-0.602601\pi$
$307$	−11.1008			−0.633556			−0.316778	+	0.948500i	$0.602601\pi$
$308$	4.75219	−	5.95906i	0.270781	−	0.339549i
$309$	32.6651	−	15.7307i	1.85825	−	0.894888i
$310$	1.95246	+	2.44831i	0.110892	+	0.139055i
$311$	−0.265341	−	0.332727i	−0.0150461	−	0.0188672i	0.774252	−	0.632878i	$-0.218127\pi$
$311$	−0.265341	−	0.332727i	−0.0150461	−	0.0188672i	−0.789298	+	0.614011i	$0.789555\pi$
$312$	−6.94952	−	3.34671i	−0.393439	−	0.189470i
$313$	−3.00305	+	13.1572i	−0.169743	+	0.743691i	0.816359	+	0.577545i	$0.195989\pi$
$313$	−3.00305	+	13.1572i	−0.169743	+	0.743691i	−0.986101	+	0.166146i	$0.946868\pi$
$314$	−5.41915	−	23.7429i	−0.305820	−	1.33989i
$315$	30.0525	−	14.4725i	1.69327	−	0.815435i
$316$	14.3067	+	6.88972i	0.804812	+	0.387577i
$317$	3.21490	+	14.0854i	0.180567	+	0.791115i	0.981361	+	0.192175i	$0.0615540\pi$
$317$	3.21490	+	14.0854i	0.180567	+	0.791115i	−0.800794	+	0.598940i	$0.795589\pi$
$318$	−15.2213			−0.853566
$319$	−7.89844	−	5.99874i	−0.442228	−	0.335865i
$320$	3.54362			0.198094
$321$	8.70743	+	38.1497i	0.486001	+	2.12931i
$322$	−11.3897	−	5.48497i	−0.634721	−	0.305666i
$323$	−8.64547	+	4.16344i	−0.481047	+	0.231660i
$324$	2.36987	+	10.3831i	0.131659	+	0.576837i
$325$	−5.64788	+	24.7450i	−0.313288	+	1.37260i
$326$	−12.0538	−	5.80482i	−0.667600	−	0.321499i
$327$	−28.6303	−	35.9013i	−1.58326	−	1.98535i
$328$	−1.87975	−	2.35713i	−0.103792	−	0.130151i
$329$	7.51058	−	3.61690i	0.414072	−	0.199406i
$330$	−9.34547	+	11.7188i	−0.514451	+	0.645101i
$331$	9.53743			0.524225			0.262112	−	0.965037i	$-0.415581\pi$
$331$	9.53743			0.524225			0.262112	+	0.965037i	$0.415581\pi$
$332$	−0.0292666	+	0.0366991i	−0.00160621	+	0.00201413i
$333$	−2.47465	+	10.8422i	−0.135610	+	0.594147i
$334$	2.23535	−	9.79370i	0.122313	−	0.535887i
$335$	−0.305771	+	0.383425i	−0.0167061	+	0.0209487i
$336$	−9.50439			−0.518507
$337$	9.46514	−	11.8689i	0.515599	−	0.646541i	−0.454069	−	0.890967i	$-0.650028\pi$
$337$	9.46514	−	11.8689i	0.515599	−	0.646541i	0.969668	+	0.244426i	$0.0785994\pi$
$338$	1.54976	−	0.746323i	0.0842956	−	0.0405946i
$339$	15.7602	+	19.7626i	0.855975	+	1.07336i
$340$	7.77883	+	9.75435i	0.421867	+	0.529004i
$341$	1.46639	+	0.706176i	0.0794095	+	0.0382416i
$342$	−1.37944	+	6.04374i	−0.0745918	+	0.326808i
$343$	2.87896	+	12.6135i	0.155449	+	0.681067i
$344$	−1.65937	+	0.799109i	−0.0894671	+	0.0430851i
$345$	22.3984	+	10.7865i	1.20589	+	0.580727i
$346$	3.64520	+	15.9707i	0.195967	+	0.858589i
$347$	21.6519			1.16234			0.581168	−	0.813784i	$-0.302596\pi$
$347$	21.6519			1.16234			0.581168	+	0.813784i	$0.302596\pi$
$348$	0.292527	+	12.3643i	0.0156811	+	0.662796i
$349$	−28.7253			−1.53763			−0.768815	−	0.639471i	$-0.779153\pi$
$349$	−28.7253			−1.53763			−0.768815	+	0.639471i	$0.779153\pi$
$350$	6.95928	+	30.4906i	0.371989	+	1.62979i
$351$	5.04162	+	2.42792i	0.269102	+	0.129593i
$352$	1.65937	−	0.799109i	0.0884446	−	0.0425927i
$353$	−3.44192	−	15.0800i	−0.183195	−	0.802629i	−0.980097	−	0.198520i	$-0.936386\pi$
$353$	−3.44192	−	15.0800i	−0.183195	−	0.802629i	0.796902	−	0.604109i	$-0.206471\pi$
$354$	−3.12970	+	13.7121i	−0.166342	+	0.728790i
$355$	41.8499	+	20.1538i	2.22116	+	1.06965i
$356$	−2.24424	−	2.81419i	−0.118945	−	0.149152i
$357$	−20.8637	−	26.1623i	−1.10423	−	1.38466i
$358$	−7.66811	+	3.69277i	−0.405272	+	0.195169i
$359$	15.2177	−	19.0824i	0.803158	−	1.00713i	−0.196488	−	0.980506i	$-0.562954\pi$
$359$	15.2177	−	19.0824i	0.803158	−	1.00713i	0.999646	−	0.0266219i	$-0.00847502\pi$
$360$	8.06008			0.424804
$361$	−7.21493	+	9.04724i	−0.379733	+	0.476170i
$362$	−1.89150	+	8.28719i	−0.0994149	+	0.435565i
$363$	3.88803	−	17.0346i	0.204068	−	0.894082i
$364$	−8.66591	+	10.8667i	−0.454217	+	0.569570i
$365$	−54.5246			−2.85395
$366$	2.61405	−	3.27792i	0.136639	−	0.171339i
$367$	−10.1869	+	4.90574i	−0.531751	+	0.256078i	−0.680437	−	0.732807i	$-0.738210\pi$
$367$	−10.1869	+	4.90574i	−0.531751	+	0.256078i	0.148686	+	0.988884i	$0.452496\pi$
$368$	−1.90458	−	2.38826i	−0.0992829	−	0.124497i
$369$	−4.27556	−	5.36138i	−0.222577	−	0.279102i
$370$	−15.6101	−	7.51745i	−0.811533	−	0.390814i
$371$	−6.10325	+	26.7401i	−0.316865	+	1.38828i
$372$	−0.451617	−	1.97866i	−0.0234152	−	0.102589i
$373$	30.8098	−	14.8372i	1.59527	−	0.768241i	0.595876	−	0.803076i	$-0.296805\pi$
$373$	30.8098	−	14.8372i	1.59527	−	0.768241i	0.999393	+	0.0348353i	$0.0110907\pi$
$374$	5.84226	+	2.81349i	0.302096	+	0.145482i
$375$	−4.63102	−	20.2898i	−0.239145	−	1.04776i
$376$	2.01433			0.103881
$377$	14.4033	+	10.9391i	0.741806	+	0.563390i
$378$	6.89508			0.354645
$379$	0.797796	+	3.49537i	0.0409800	+	0.179545i	0.991276	−	0.131803i	$-0.0420766\pi$
$379$	0.797796	+	3.49537i	0.0409800	+	0.179545i	−0.950296	+	0.311348i	$0.899219\pi$
$380$	−8.70155	−	4.19045i	−0.446380	−	0.214965i
$381$	4.68780	−	2.25752i	0.240163	−	0.115656i
$382$	−5.43125	−	23.7959i	−0.277887	−	1.21750i
$383$	5.78965	−	25.3661i	0.295837	−	1.29615i	−0.580425	−	0.814314i	$-0.697114\pi$
$383$	5.78965	−	25.3661i	0.295837	−	1.29615i	0.876262	−	0.481834i	$-0.160029\pi$
$384$	−2.06920	−	0.996473i	−0.105593	−	0.0508511i
$385$	16.8399	+	21.1166i	0.858243	+	1.07620i
$386$	3.08049	+	3.86282i	0.156793	+	0.196612i
$387$	−3.77429	+	1.81760i	−0.191858	+	0.0923940i
$388$	3.26556	−	4.09489i	0.165784	−	0.207886i
$389$	−7.48891			−0.379703			−0.189851	−	0.981813i	$-0.560801\pi$
$389$	−7.48891			−0.379703			−0.189851	+	0.981813i	$0.560801\pi$
$390$	17.0420	−	21.3700i	0.862956	−	1.08211i
$391$	2.39320	−	10.4853i	0.121029	−	0.530264i
$392$	−2.25332	+	9.87243i	−0.113810	+	0.498633i
$393$	4.00719	−	5.02485i	0.202136	−	0.253470i
$394$	0.735232			0.0370405
$395$	−35.0836	+	43.9935i	−1.76525	+	2.21355i
$396$	3.77429	−	1.81760i	0.189665	−	0.0913380i
$397$	−7.47716	−	9.37606i	−0.375268	−	0.470571i	0.557954	−	0.829872i	$-0.311587\pi$
$397$	−7.47716	−	9.37606i	−0.375268	−	0.470571i	−0.933222	+	0.359301i	$0.883015\pi$
$398$	−0.825107	−	1.03465i	−0.0413589	−	0.0518624i
$399$	23.3386	+	11.2393i	1.16839	+	0.562667i
$400$	−1.68164	+	7.36774i	−0.0840819	+	0.368387i
$401$	−0.802492	−	3.51595i	−0.0400745	−	0.175578i	0.950930	−	0.309406i	$-0.100130\pi$
$401$	−0.802492	−	3.51595i	−0.0400745	−	0.175578i	−0.991005	+	0.133828i	$0.957273\pi$
$402$	0.286367	−	0.137907i	0.0142827	−	0.00687817i
$403$	−2.67405	−	1.28775i	−0.133204	−	0.0641476i
$404$	−2.14719	−	9.40747i	−0.106827	−	0.468039i
$405$	−37.7398			−1.87531
$406$	21.8384	+	4.44380i	1.08382	+	0.220542i
$407$	−9.00499			−0.446361
$408$	−1.79929	−	7.88321i	−0.0890782	−	0.390277i
$409$	16.8495	+	8.11431i	0.833156	+	0.401227i	0.801298	−	0.598266i	$-0.204143\pi$
$409$	16.8495	+	8.11431i	0.833156	+	0.401227i	0.0318582	+	0.999492i	$0.489857\pi$
$410$	9.62558	−	4.63543i	0.475373	−	0.228928i
$411$	0.135703	+	0.594555i	0.00669375	+	0.0293272i
$412$	3.51280	−	15.3906i	0.173063	−	0.758239i
$413$	22.8340	+	10.9963i	1.12359	+	0.541090i
$414$	−4.33203	−	5.43219i	−0.212908	−	0.266978i
$415$	−0.103710	−	0.130048i	−0.00509090	−	0.00638379i
$416$	−3.02595	+	1.45722i	−0.148360	+	0.0714462i
$417$	−9.16361	+	11.4908i	−0.448744	+	0.562707i
$418$	−5.01965			−0.245519
$419$	20.8170	−	26.1037i	1.01698	−	1.27525i	0.0560586	−	0.998427i	$-0.482147\pi$
$419$	20.8170	−	26.1037i	1.01698	−	1.27525i	0.960921	−	0.276824i	$-0.0892819\pi$
$420$	7.49448	−	32.8355i	0.365693	−	1.60221i
$421$	−1.76150	+	7.71764i	−0.0858503	+	0.376135i	−0.999542	−	0.0302742i	$-0.990362\pi$
$421$	−1.76150	+	7.71764i	−0.0858503	+	0.376135i	0.913691	+	0.406409i	$0.133219\pi$
$422$	1.89916	−	2.38147i	0.0924496	−	0.115928i
$423$	4.58168			0.222769
$424$	−4.13226	+	5.18169i	−0.200680	+	0.251645i
$425$	−23.9723	+	11.5445i	−1.16283	+	0.559988i
$426$	−18.7698	−	23.5366i	−0.909399	−	1.14035i
$427$	−4.71036	−	5.90660i	−0.227950	−	0.285840i
$428$	15.3510	+	7.39265i	0.742018	+	0.357337i
$429$	3.16117	−	13.8500i	0.152623	−	0.668685i
$430$	−1.45228	−	6.36285i	−0.0700351	−	0.306844i
$431$	−4.91253	+	2.36575i	−0.236628	+	0.113954i	−0.548440	−	0.836190i	$-0.684778\pi$
$431$	−4.91253	+	2.36575i	−0.236628	+	0.113954i	0.311812	+	0.950144i	$0.399064\pi$
$432$	1.50113	+	0.722904i	0.0722230	+	0.0347808i
$433$	−8.51733	−	37.3169i	−0.409317	−	1.79333i	−0.587376	−	0.809314i	$-0.699839\pi$
$433$	−8.51733	−	37.3169i	−0.409317	−	1.79333i	0.178059	−	0.984020i	$-0.443018\pi$
$434$	−3.65712			−0.175547
$435$	−42.9465	−	8.73899i	−2.05913	−	0.419003i
$436$	−19.9942			−0.957550
$437$	1.85259	+	8.11675i	0.0886216	+	0.388277i
$438$	31.8381	+	15.3324i	1.52129	+	0.732613i
$439$	−10.4170	+	5.01658i	−0.497178	+	0.239428i	−0.665631	−	0.746281i	$-0.731837\pi$
$439$	−10.4170	+	5.01658i	−0.497178	+	0.239428i	0.168452	+	0.985710i	$0.446123\pi$
$440$	1.45228	+	6.36285i	0.0692347	+	0.303337i
$441$	−5.12525	+	22.4552i	−0.244060	+	1.06930i
$442$	−10.6537	−	5.13056i	−0.506745	−	0.244036i
$443$	16.8781	+	21.1644i	0.801902	+	1.00555i	0.999680	+	0.0253059i	$0.00805599\pi$
$443$	16.8781	+	21.1644i	0.801902	+	1.00555i	−0.197778	+	0.980247i	$0.563373\pi$
$444$	7.00120	+	8.77922i	0.332262	+	0.416643i
$445$	11.4920	−	5.53427i	0.544775	−	0.262350i
$446$	−5.37834	+	6.74423i	−0.254672	+	0.319349i
$447$	23.8078			1.12607
$448$	−2.58025	+	3.23553i	−0.121905	+	0.152864i
$449$	−0.814923	+	3.57041i	−0.0384586	+	0.168498i	−0.990510	−	0.137439i	$-0.956113\pi$
$449$	−0.814923	+	3.57041i	−0.0384586	+	0.168498i	0.952052	+	0.305938i	$0.0989699\pi$
$450$	−3.82495	+	16.7582i	−0.180310	+	0.789989i
$451$	3.46204	−	4.34127i	0.163021	−	0.204422i
$452$	11.0063			0.517691
$453$	15.5422	−	19.4893i	0.730236	−	0.915687i
$454$	0.421501	−	0.202984i	0.0197820	−	0.00952653i
$455$	−30.7086	−	38.5074i	−1.43964	−	1.80526i
$456$	3.90267	+	4.89379i	0.182759	+	0.229173i
$457$	−29.7907	−	14.3464i	−1.39355	−	0.671098i	−0.421708	−	0.906732i	$-0.638569\pi$
$457$	−29.7907	−	14.3464i	−1.39355	−	0.671098i	−0.971842	+	0.235633i	$0.924284\pi$
$458$	−5.62683	+	24.6528i	−0.262924	+	1.15195i
$459$	1.30532	+	5.71898i	0.0609271	+	0.266939i
$460$	9.75272	−	4.69666i	0.454723	−	0.218983i
$461$	29.7228	+	14.3137i	1.38433	+	0.666657i	0.969917	−	0.243434i	$-0.0782739\pi$
$461$	29.7228	+	14.3137i	1.38433	+	0.666657i	0.414409	+	0.910091i	$0.363988\pi$
$462$	−3.89518	−	17.0659i	−0.181220	−	0.793978i
$463$	29.1773			1.35599			0.677993	−	0.735069i	$-0.262850\pi$
$463$	29.1773			1.35599			0.677993	+	0.735069i	$0.262850\pi$
$464$	4.28853	+	3.25707i	0.199090	+	0.151206i
$465$	7.19193			0.333518
$466$	−2.95599	−	12.9510i	−0.136934	−	0.599945i
$467$	−14.1160	−	6.79792i	−0.653212	−	0.314570i	0.0777658	−	0.996972i	$-0.475221\pi$
$467$	−14.1160	−	6.79792i	−0.653212	−	0.314570i	−0.730978	+	0.682401i	$0.760936\pi$
$468$	−6.88265	+	3.31451i	−0.318150	+	0.153213i
$469$	−0.127445	−	0.558374i	−0.00588487	−	0.0257833i
$470$	−1.58836	+	6.95906i	−0.0732656	+	0.320998i
$471$	−50.3921	−	24.2676i	−2.32195	−	1.11819i
$472$	3.81829	+	4.78798i	0.175751	+	0.220385i
$473$	−2.11493	−	2.65203i	−0.0972444	−	0.121941i
$474$	32.8572	−	15.8232i	1.50918	−	0.726783i
$475$	12.8420	−	16.1033i	0.589229	−	0.738870i
$476$	−14.5704			−0.667832
$477$	−9.39898	+	11.7860i	−0.430350	+	0.539642i
$478$	−3.58066	+	15.6879i	−0.163775	+	0.717547i
$479$	0.856371	−	3.75200i	0.0391286	−	0.171433i	−0.951588	−	0.307376i	$-0.900549\pi$
$479$	0.856371	−	3.75200i	0.0391286	−	0.171433i	0.990717	+	0.135942i	$0.0434062\pi$
$480$	5.07421	−	6.36285i	0.231605	−	0.290423i
$481$	16.4211			0.748740
$482$	−9.27842	+	11.6348i	−0.422621	+	0.529949i
$483$	−26.1579	+	12.5970i	−1.19023	+	0.573183i
$484$	−4.74346	−	5.94811i	−0.215612	−	0.270369i
$485$	11.5719	+	14.5107i	0.525453	+	0.658897i
$486$	17.5338	+	8.44382i	0.795348	+	0.383019i
$487$	−6.37692	+	27.9391i	−0.288966	+	1.26604i	0.596981	+	0.802255i	$0.296367\pi$
$487$	−6.37692	+	27.9391i	−0.288966	+	1.26604i	−0.885947	+	0.463787i	$0.846490\pi$
$488$	−0.406222	−	1.77977i	−0.0183888	−	0.0805666i
$489$	−27.6833	+	13.3316i	−1.25188	+	0.602874i
$490$	−32.3302	−	15.5694i	−1.46053	−	0.703353i
$491$	−3.96577	−	17.3752i	−0.178973	−	0.784130i	−0.982106	−	0.188331i	$-0.939692\pi$
$491$	−3.96577	−	17.3752i	−0.178973	−	0.784130i	0.803133	−	0.595800i	$-0.203165\pi$
$492$	−6.92409			−0.312162
$493$	0.448448	+	18.9547i	0.0201971	+	0.853675i
$494$	9.15362			0.411841
$495$	3.30326	+	14.4725i	0.148471	+	0.650492i
$496$	−0.796190	−	0.383425i	−0.0357500	−	0.0172163i
$497$	−48.8742	+	23.5366i	−2.19231	+	1.05576i
$498$	0.0239886	+	0.105101i	0.00107496	+	0.00470969i
$499$	−5.40765	+	23.6925i	−0.242080	+	1.06062i	0.697040	+	0.717032i	$0.254500\pi$
$499$	−5.40765	+	23.6925i	−0.242080	+	1.06062i	−0.939120	+	0.343589i	$0.888357\pi$
$500$	−8.16438	−	3.93176i	−0.365122	−	0.175833i
$501$	−14.3845	−	18.0376i	−0.642653	−	0.805862i
$502$	−0.226590	−	0.284135i	−0.0101132	−	0.0126815i
$503$	17.1240	−	8.24649i	0.763522	−	0.367693i	−0.0112474	−	0.999937i	$-0.503580\pi$
$503$	17.1240	−	8.24649i	0.763522	−	0.367693i	0.774769	+	0.632244i	$0.217866\pi$
$504$	−5.86887	+	7.35933i	−0.261420	+	0.327810i
$505$	34.1938			1.52160
$506$	3.50777	−	4.39861i	0.155939	−	0.195542i
$507$	0.879056	−	3.85139i	0.0390402	−	0.171046i
$508$	0.504124	−	2.20871i	0.0223669	−	0.0979958i
$509$	−9.56212	+	11.9905i	−0.423833	+	0.531470i	−0.947203	−	0.320636i	$-0.896103\pi$
$509$	−9.56212	+	11.9905i	−0.423833	+	0.531470i	0.523369	+	0.852106i	$0.324675\pi$
$510$	28.6535			1.26880
$511$	39.7015	−	49.7841i	1.75629	−	2.20232i
$512$	−0.900969	+	0.433884i	−0.0398176	+	0.0191751i
$513$	−2.83124	−	3.55027i	−0.125002	−	0.156748i
$514$	3.16163	+	3.96456i	0.139454	+	0.174869i
$515$	50.4009	+	24.2718i	2.22093	+	1.06954i
$516$	−0.941230	+	4.12380i	−0.0414353	+	0.181540i
$517$	0.825535	+	3.61690i	0.0363070	+	0.159071i
$518$	18.2302	−	8.77922i	0.800991	−	0.385737i
$519$	33.8964	+	16.3236i	1.48788	+	0.716528i
$520$	−2.64832	−	11.6030i	−0.116136	−	0.508827i
$521$	−4.82047			−0.211189			−0.105594	−	0.994409i	$-0.533674\pi$
$521$	−4.82047			−0.211189			−0.105594	+	0.994409i	$0.533674\pi$
$522$	9.75442	+	7.40833i	0.426939	+	0.324254i
$523$	23.9143			1.04570			0.522849	−	0.852425i	$-0.324869\pi$
$523$	23.9143			1.04570			0.522849	+	0.852425i	$0.324869\pi$
$524$	−0.622714	−	2.72829i	−0.0272034	−	0.119186i
$525$	64.7136	+	31.1644i	2.82433	+	1.36013i
$526$	9.80569	−	4.72217i	0.427548	−	0.205896i
$527$	−0.692335	−	3.03332i	−0.0301586	−	0.132133i
$528$	0.941230	−	4.12380i	0.0409618	−	0.179465i
$529$	12.3151	+	5.93066i	0.535441	+	0.257855i
$530$	−14.6432	−	18.3619i	−0.636058	−	0.797591i
$531$	8.68484	+	10.8904i	0.376890	+	0.472605i
$532$	10.1621	−	4.89379i	0.440581	−	0.212173i
$533$	−6.31324	+	7.91656i	−0.273457	+	0.342904i
$534$	−8.26671			−0.357735
$535$	−37.6446	+	47.2048i	−1.62752	+	2.04084i
$536$	0.0307958	−	0.134925i	0.00133018	−	0.00582788i
$537$	−4.34952	+	19.0565i	−0.187696	+	0.822349i
$538$	−16.8131	+	21.0830i	−0.724866	+	0.908953i
$539$	−18.6502			−0.803322
$540$	−3.68115	+	4.61602i	−0.158411	+	0.198642i
$541$	2.02943	−	0.977322i	0.0872520	−	0.0420184i	−0.389749	−	0.920921i	$-0.627438\pi$
$541$	2.02943	−	0.977322i	0.0872520	−	0.0420184i	0.477001	+	0.878903i	$0.341724\pi$
$542$	8.81106	+	11.0487i	0.378467	+	0.474583i
$543$	12.1718	+	15.2630i	0.522344	+	0.654998i
$544$	−3.17211	−	1.52761i	−0.136003	−	0.0654957i
$545$	15.7660	−	69.0755i	0.675342	−	2.95887i
$546$	7.10310	+	31.1207i	0.303984	+	1.33184i
$547$	8.15731	−	3.92835i	0.348781	−	0.167964i	−0.251288	−	0.967912i	$-0.580854\pi$
$547$	8.15731	−	3.92835i	0.348781	−	0.167964i	0.600069	+	0.799948i	$0.295140\pi$
$548$	0.239242	+	0.115213i	0.0102199	+	0.00492165i
$549$	−0.923967	−	4.04816i	−0.0394339	−	0.172771i
$550$	−13.9186			−0.593489
$551$	−6.67913	−	13.0693i	−0.284540	−	0.556769i
$552$	−7.01554			−0.298601
$553$	−14.6228	−	64.0668i	−0.621826	−	2.72440i
$554$	−11.7337	−	5.65067i	−0.498519	−	0.240074i
$555$	−35.8508	+	17.2648i	−1.52178	+	0.732852i
$556$	1.42402	+	6.23904i	0.0603919	+	0.264594i
$557$	−2.34742	+	10.2847i	−0.0994633	+	0.435777i	0.900536	+	0.434781i	$0.143174\pi$
$557$	−2.34742	+	10.2847i	−0.0994633	+	0.435777i	−1.00000		0.000996194i	$0.999683\pi$
$558$	−1.81096	−	0.872114i	−0.0766642	−	0.0369195i
$559$	3.85669	+	4.83614i	0.163121	+	0.204547i
$560$	−9.14340	−	11.4655i	−0.386379	−	0.484504i
$561$	13.4176	−	6.46155i	0.566490	−	0.272807i
$562$	18.1332	−	22.7384i	0.764905	−	0.959160i
$563$	−39.1477			−1.64988			−0.824939	−	0.565222i	$-0.808791\pi$
$563$	−39.1477			−1.64988			−0.824939	+	0.565222i	$0.808791\pi$
$564$	2.88438	−	3.61690i	0.121455	−	0.152299i
$565$	−8.67875	+	38.0241i	−0.365118	+	1.59969i
$566$	−4.18889	+	18.3527i	−0.176072	+	0.771422i
$567$	27.4799	−	34.4587i	1.15405	−	1.44713i
$568$	−13.1080			−0.550001
$569$	−5.18890	+	6.50667i	−0.217530	+	0.272774i	−0.878608	−	0.477543i	$-0.841528\pi$
$569$	−5.18890	+	6.50667i	−0.217530	+	0.272774i	0.661079	+	0.750317i	$0.270099\pi$
$570$	−19.9843	+	9.62393i	−0.837050	+	0.403102i
$571$	−26.9622	−	33.8095i	−1.12833	−	1.41488i	−0.897013	−	0.442005i	$-0.854267\pi$
$571$	−26.9622	−	33.8095i	−1.12833	−	1.41488i	−0.231319	−	0.972878i	$-0.574304\pi$
$572$	−3.85669	−	4.83614i	−0.161256	−	0.202209i
$573$	−50.5046	−	24.3217i	−2.10986	−	1.01605i
$574$	−2.77634	+	12.1640i	−0.115882	+	0.507714i
$575$	5.13691	+	22.5063i	0.214224	+	0.938576i
$576$	−2.04929	+	0.986885i	−0.0853870	+	0.0411202i
$577$	−11.5941	−	5.58341i	−0.482668	−	0.232441i	0.176695	−	0.984266i	$-0.443459\pi$
$577$	−11.5941	−	5.58341i	−0.482668	−	0.232441i	−0.659363	+	0.751825i	$0.729174\pi$
$578$	1.02451	+	4.48869i	0.0426142	+	0.186705i
$579$	11.3471			0.471568
$580$	−14.6341	+	12.2476i	−0.607646	+	0.508553i
$581$	0.194256			0.00805910
$582$	−2.67665	−	11.7272i	−0.110951	−	0.486107i
$583$	−10.9977	−	5.29620i	−0.455477	−	0.219346i
$584$	13.8629	−	6.67604i	0.573653	−	0.276257i
$585$	−6.02370	−	26.3915i	−0.249049	−	1.09116i
$586$	1.32948	−	5.82482i	0.0549202	−	0.240621i
$587$	12.3948	+	5.96902i	0.511588	+	0.246368i	0.671824	−	0.740711i	$-0.265511\pi$
$587$	12.3948	+	5.96902i	0.511588	+	0.246368i	−0.160236	+	0.987079i	$0.551226\pi$
$588$	14.5002	+	18.1826i	0.597977	+	0.749839i
$589$	1.50168	+	1.88304i	0.0618755	+	0.0775895i
$590$	−19.5522	+	9.41585i	−0.804952	+	0.387644i
$591$	1.05280	−	1.32017i	0.0433064	−	0.0543045i
$592$	4.88934			0.200951
$593$	−13.3356	+	16.7223i	−0.547626	+	0.686702i	−0.976217	−	0.216797i	$-0.930439\pi$
$593$	−13.3356	+	16.7223i	−0.547626	+	0.686702i	0.428590	+	0.903499i	$0.359010\pi$
$594$	−0.682828	+	2.99166i	−0.0280168	+	0.122749i
$595$	11.4892	−	50.3373i	0.471009	−	2.06363i
$596$	6.46332	−	8.10475i	0.264748	−	0.331984i
$597$	−3.03930			−0.124390
$598$	−6.39663	+	8.02112i	−0.261578	+	0.328008i
$599$	24.5010	−	11.7991i	1.00109	−	0.482097i	0.139779	−	0.990183i	$-0.455361\pi$
$599$	24.5010	−	11.7991i	1.00109	−	0.482097i	0.861307	+	0.508085i	$0.169647\pi$
$600$	10.8214	+	13.5696i	0.441781	+	0.553976i
$601$	−12.2761	−	15.3938i	−0.500754	−	0.627925i	0.465645	−	0.884971i	$-0.345822\pi$
$601$	−12.2761	−	15.3938i	−0.500754	−	0.627925i	−0.966399	+	0.257046i	$0.917251\pi$
$602$	6.86712	+	3.30703i	0.279883	+	0.134784i
$603$	0.0700462	−	0.306892i	0.00285250	−	0.0124976i
$604$	−2.41525	−	10.5819i	−0.0982751	−	0.430571i
$605$	24.2897	−	11.6973i	0.987518	−	0.475563i
$606$	−19.9665	−	9.61537i	−0.811085	−	0.390598i
$607$	5.79688	+	25.3978i	0.235288	+	1.03086i	0.945179	+	0.326553i	$0.105887\pi$
$607$	5.79688	+	25.3978i	0.235288	+	1.03086i	−0.709891	+	0.704312i	$0.751256\pi$
$608$	2.72546			0.110532
$609$	39.2503	−	32.8494i	1.59050	−	1.33113i
$610$	6.46903			0.261923
$611$	−1.50541	−	6.59564i	−0.0609024	−	0.266831i
$612$	−7.21508	−	3.47460i	−0.291652	−	0.140452i
$613$	4.03925	−	1.94520i	0.163144	−	0.0785658i	−0.350530	−	0.936552i	$-0.613999\pi$
$613$	4.03925	−	1.94520i	0.163144	−	0.0785658i	0.513674	+	0.857986i	$0.328284\pi$
$614$	2.47016	+	10.8225i	0.0996875	+	0.436759i
$615$	5.45984	−	23.9211i	0.220162	−	0.964593i
$616$	−6.86712	−	3.30703i	−0.276684	−	0.133244i
$617$	12.3400	+	15.4739i	0.496791	+	0.622956i	0.965502	−	0.260396i	$-0.0838530\pi$
$617$	12.3400	+	15.4739i	0.496791	+	0.622956i	−0.468711	+	0.883351i	$0.655282\pi$
$618$	−22.6050	−	28.3457i	−0.909305	−	1.14023i
$619$	−5.69144	+	2.74085i	−0.228758	+	0.110164i	−0.544752	−	0.838597i	$-0.683376\pi$
$619$	−5.69144	+	2.74085i	−0.228758	+	0.110164i	0.315994	+	0.948761i	$0.397662\pi$
$620$	1.95246	−	2.44831i	0.0784128	−	0.0983265i
$621$	5.08952			0.204235
$622$	−0.265341	+	0.332727i	−0.0106392	+	0.0133411i
$623$	−3.31469	+	14.5226i	−0.132800	+	0.581836i
$624$	−1.71639	+	7.51999i	−0.0687105	+	0.301041i
$625$	−3.53806	+	4.43659i	−0.141523	+	0.177464i
$626$	13.4956			0.539393
$627$	−7.18778	+	9.01319i	−0.287052	+	0.359952i
$628$	−21.9417	+	10.5666i	−0.875569	+	0.421652i
$629$	10.7329	+	13.4587i	0.427950	+	0.536633i
$630$	−20.7970	−	26.0786i	−0.828573	−	1.03900i
$631$	−0.398880	−	0.192091i	−0.0158792	−	0.00764700i	0.425927	−	0.904757i	$-0.359948\pi$
$631$	−0.398880	−	0.192091i	−0.0158792	−	0.00764700i	−0.441806	+	0.897110i	$0.645662\pi$
$632$	3.53345	−	15.4811i	0.140553	−	0.615804i
$633$	−1.55666	−	6.82019i	−0.0618718	−	0.271078i
$634$	13.0169	−	6.26859i	0.516966	−	0.248958i
$635$	7.23308	+	3.48327i	0.287036	+	0.138229i
$636$	3.38705	+	14.8396i	0.134305	+	0.588430i
$637$	34.0098			1.34752
$638$	−4.09077	+	9.03525i	−0.161955	+	0.357709i
$639$	−29.8147			−1.17945
$640$	−0.788529	−	3.45477i	−0.0311693	−	0.136562i
$641$	−18.3361	−	8.83019i	−0.724232	−	0.348772i	0.0351807	−	0.999381i	$-0.488799\pi$
$641$	−18.3361	−	8.83019i	−0.724232	−	0.348772i	−0.759413	+	0.650609i	$0.774514\pi$
$642$	35.2557	−	16.9782i	1.39143	−	0.670077i
$643$	2.10122	+	9.20604i	0.0828640	+	0.363051i	0.999311	−	0.0371042i	$-0.0118134\pi$
$643$	2.10122	+	9.20604i	0.0828640	+	0.363051i	−0.916447	+	0.400155i	$0.868956\pi$
$644$	−2.81301	+	12.3246i	−0.110848	+	0.485658i
$645$	−13.5046	−	6.50347i	−0.531743	−	0.256074i
$646$	5.98285	+	7.50226i	0.235392	+	0.295172i
$647$	11.9421	+	14.9749i	0.469492	+	0.588725i	0.959047	−	0.283248i	$-0.0914119\pi$
$647$	11.9421	+	14.9749i	0.469492	+	0.588725i	−0.489554	+	0.871973i	$0.662840\pi$
$648$	9.59540	−	4.62090i	0.376943	−	0.181526i
$649$	−7.03237	+	8.81831i	−0.276045	+	0.346149i
$650$	25.3813			0.995537
$651$	−5.23673	+	6.56665i	−0.205244	+	0.257367i
$652$	−2.97705	+	13.0433i	−0.116590	+	0.510816i
$653$	−0.433110	+	1.89758i	−0.0169489	+	0.0742581i	−0.982695	−	0.185230i	$-0.940697\pi$
$653$	−0.433110	+	1.89758i	−0.0169489	+	0.0742581i	0.965746	+	0.259489i	$0.0835540\pi$
$654$	−28.6303	+	35.9013i	−1.11953	+	1.40385i
$655$	9.91664			0.387475
$656$	−1.87975	+	2.35713i	−0.0733919	+	0.0920305i
$657$	31.5318	−	15.1849i	1.23017	−	0.592420i
$658$	−5.19748	−	6.51744i	−0.202619	−	0.254076i
$659$	−20.1167	−	25.2256i	−0.783637	−	0.982650i	−0.999980	−	0.00633221i	$-0.997984\pi$
$659$	−20.1167	−	25.2256i	−0.783637	−	0.982650i	0.216343	−	0.976317i	$-0.430587\pi$
$660$	13.5046	+	6.50347i	0.525665	+	0.253147i
$661$	−10.3459	+	45.3284i	−0.402409	+	1.76307i	0.215185	+	0.976573i	$0.430965\pi$
$661$	−10.3459	+	45.3284i	−0.402409	+	1.76307i	−0.617594	+	0.786497i	$0.711893\pi$
$662$	−2.12228	−	9.29831i	−0.0824847	−	0.361389i
$663$	−24.4677	+	11.7830i	−0.950247	+	0.457615i
$664$	0.0422914	+	0.0203665i	0.00164123	+	0.000790373i
$665$	8.89385	+	38.9665i	0.344889	+	1.51106i
$666$	11.1210			0.430930
$667$	16.1197	+	3.28014i	0.624159	+	0.127007i
$668$	−10.0456			−0.388674
$669$	4.40841	+	19.3145i	0.170439	+	0.746742i
$670$	0.441852	+	0.212785i	0.0170702	+	0.00822059i
$671$	3.02925	−	1.45881i	0.116943	−	0.0563167i
$672$	2.11493	+	9.26609i	0.0815850	+	0.357447i
$673$	7.90055	−	34.6146i	0.304544	−	1.33429i	−0.558643	−	0.829408i	$-0.688678\pi$
$673$	7.90055	−	34.6146i	0.304544	−	1.33429i	0.863187	−	0.504885i	$-0.168465\pi$
$674$	−13.6775	−	6.58675i	−0.526839	−	0.253712i
$675$	−7.85052	−	9.84424i	−0.302167	−	0.378905i
$676$	−1.07246	−	1.34483i	−0.0412486	−	0.0517241i
$677$	−2.60268	+	1.25338i	−0.100029	+	0.0481714i	−0.483229	−	0.875494i	$-0.660536\pi$
$677$	−2.60268	+	1.25338i	−0.100029	+	0.0481714i	0.383200	+	0.923665i	$0.374822\pi$
$678$	15.7602	−	19.7626i	0.605266	−	0.758980i
$679$	−21.6751			−0.831813
$680$	7.77883	−	9.75435i	0.298305	−	0.374062i
$681$	0.239085	−	1.04750i	0.00916176	−	0.0401403i
$682$	0.362168	−	1.58676i	0.0138681	−	0.0607603i
$683$	−21.1280	+	26.4936i	−0.808439	+	1.01375i	0.191043	+	0.981582i	$0.438813\pi$
$683$	−21.1280	+	26.4936i	−0.808439	+	1.01375i	−0.999482	+	0.0321690i	$0.989759\pi$
$684$	6.19917			0.237031
$685$	−0.586683	+	0.735677i	−0.0224160	+	0.0281088i
$686$	11.6567	−	5.61355i	0.445053	−	0.214326i
$687$	36.2088	+	45.4044i	1.38145	+	1.73229i
$688$	1.14832	+	1.43995i	0.0437792	+	0.0548974i
$689$	20.0549	+	9.65794i	0.764032	+	0.367938i
$690$	5.53196	−	24.2371i	0.210598	−	0.922690i
$691$	−4.51470	−	19.7802i	−0.171747	−	0.752473i	−0.985279	−	0.170953i	$-0.945315\pi$
$691$	−4.51470	−	19.7802i	−0.171747	−	0.752473i	0.813532	−	0.581520i	$-0.197542\pi$
$692$	14.7591	−	7.10762i	0.561058	−	0.270191i
$693$	−15.6195	−	7.52196i	−0.593336	−	0.285736i
$694$	−4.81801	−	21.1091i	−0.182889	−	0.801289i
$695$	−22.6773			−0.860200
$696$	11.9892	−	3.03651i	0.454450	−	0.115099i
$697$	−10.6147			−0.402062
$698$	6.39198	+	28.0051i	0.241940	+	1.06001i
$699$	−27.4874	−	13.2372i	−1.03967	−	0.500678i
$700$	28.1776	−	13.5696i	1.06501	−	0.512882i
$701$	−2.40132	−	10.5209i	−0.0906965	−	0.397367i	0.909120	−	0.416535i	$-0.136756\pi$
$701$	−2.40132	−	10.5209i	−0.0906965	−	0.397367i	−0.999816	+	0.0191675i	$0.993898\pi$
$702$	1.24518	−	5.45548i	0.0469962	−	0.205904i
$703$	−12.0061	−	5.78182i	−0.452817	−	0.218065i
$704$	−1.14832	−	1.43995i	−0.0432789	−	0.0542700i
$705$	10.2212	+	12.8169i	0.384951	+	0.482713i
$706$	−13.9360	+	6.71125i	−0.524490	+	0.252581i
$707$	−24.8979	+	31.2209i	−0.936380	+	1.17418i
$708$	14.0647			0.528585
$709$	1.54717	−	1.94009i	0.0581053	−	0.0728617i	−0.751930	−	0.659243i	$-0.770877\pi$
$709$	1.54717	−	1.94009i	0.0581053	−	0.0728617i	0.810035	+	0.586382i	$0.199448\pi$
$710$	10.3361	−	45.2853i	0.387906	−	1.69953i
$711$	8.03697	−	35.2122i	0.301410	−	1.32056i
$712$	−2.24424	+	2.81419i	−0.0841065	+	0.105466i
$713$	−2.69945			−0.101095
$714$	−20.8637	+	26.1623i	−0.780806	+	0.979099i
$715$	19.7489	−	9.51055i	0.738565	−	0.355674i
$716$	5.30650	+	6.65413i	0.198313	+	0.248677i
$717$	23.0416	+	28.8933i	0.860506	+	1.07904i
$718$	−21.9902	−	10.5899i	−0.820666	−	0.395212i
$719$	5.52493	−	24.2063i	0.206045	−	0.902742i	−0.761124	−	0.648607i	$-0.775352\pi$
$719$	5.52493	−	24.2063i	0.206045	−	0.902742i	0.967169	−	0.254135i	$-0.0817909\pi$
$720$	−1.79354	−	7.85800i	−0.0668412	−	0.292850i
$721$	−58.8605	+	28.3457i	−2.19208	+	1.05565i
$722$	10.4259	+	5.02084i	0.388011	+	0.186856i
$723$	7.60515	+	33.3203i	0.282839	+	1.23920i
$724$	8.50031			0.315912
$725$	−18.5200	−	36.2387i	−0.687816	−	1.34587i
$726$	−17.4726			−0.648470
$727$	9.47808	+	41.5262i	0.351523	+	1.54012i	0.773667	+	0.633593i	$0.218420\pi$
$727$	9.47808	+	41.5262i	0.351523	+	1.54012i	−0.422144	+	0.906529i	$0.638722\pi$
$728$	12.5226	+	6.03056i	0.464118	+	0.223508i
$729$	11.4825	−	5.52967i	0.425277	−	0.204802i
$730$	12.1329	+	53.1576i	0.449057	+	1.96745i
$731$	−1.44292	+	6.32185i	−0.0533683	+	0.233822i
$732$	−3.77741	−	1.81911i	−0.139617	−	0.0672361i
$733$	15.8494	+	19.8745i	0.585412	+	0.734083i	0.983025	−	0.183470i	$-0.0587330\pi$
$733$	15.8494	+	19.8745i	0.585412	+	0.734083i	−0.397614	+	0.917553i	$0.630162\pi$
$734$	7.04954	+	8.83984i	0.260203	+	0.326285i
$735$	−74.2506	+	35.7572i	−2.73877	+	1.31892i
$736$	−1.90458	+	2.38826i	−0.0702036	+	0.0880326i
$737$	0.254890			0.00938901
$738$	−4.27556	+	5.36138i	−0.157385	+	0.197355i
$739$	0.447605	−	1.96109i	0.0164654	−	0.0721397i	−0.966028	−	0.258438i	$-0.916792\pi$
$739$	0.447605	−	1.96109i	0.0164654	−	0.0721397i	0.982493	+	0.186299i	$0.0596492\pi$
$740$	−3.85539	+	16.8916i	−0.141727	+	0.620946i
$741$	13.1073	−	16.4361i	0.481510	−	0.603795i
$742$	27.4278			1.00691
$743$	−17.7644	+	22.2759i	−0.651714	+	0.817224i	−0.992413	−	0.122949i	$-0.960765\pi$
$743$	−17.7644	+	22.2759i	−0.651714	+	0.817224i	0.340699	+	0.940172i	$0.389336\pi$
$744$	−1.82856	+	0.880587i	−0.0670382	+	0.0322839i
$745$	22.9035	+	28.7201i	0.839120	+	1.05222i
$746$	−21.3210	−	26.7357i	−0.780618	−	0.978864i
$747$	0.0961934	+	0.0463243i	0.00351953	+	0.00169492i
$748$	1.44292	−	6.32185i	0.0527584	−	0.231150i
$749$	−15.6902	−	68.7434i	−0.573309	−	2.51183i
$750$	−18.7506	+	9.02981i	−0.684675	+	0.329722i
$751$	23.1668	+	11.1565i	0.845367	+	0.407107i	0.805856	−	0.592112i	$-0.201706\pi$
$751$	23.1668	+	11.1565i	0.845367	+	0.407107i	0.0395112	+	0.999219i	$0.487420\pi$
$752$	−0.448232	−	1.96383i	−0.0163453	−	0.0716136i
$753$	−0.834648			−0.0304163
$754$	7.45977	−	16.4763i	0.271669	−	0.600032i
$755$	38.4625			1.39979
$756$	−1.53430	−	6.72221i	−0.0558020	−	0.244484i
$757$	−27.4721	−	13.2299i	−0.998491	−	0.480848i	−0.138065	−	0.990423i	$-0.544088\pi$
$757$	−27.4721	−	13.2299i	−0.998491	−	0.480848i	−0.860426	+	0.509575i	$0.829803\pi$
$758$	3.23021	−	1.55559i	0.117327	−	0.0565015i
$759$	−2.87518	−	12.5970i	−0.104362	−	0.457242i
$760$	−2.14911	+	9.41585i	−0.0779563	+	0.341549i
$761$	20.7821	+	10.0081i	0.753350	+	0.362794i	0.770820	−	0.637053i	$-0.219847\pi$
$761$	20.7821	+	10.0081i	0.753350	+	0.362794i	−0.0174701	+	0.999847i	$0.505561\pi$
$762$	−3.24405	−	4.06792i	−0.117520	−	0.147365i
$763$	51.5901	+	64.6919i	1.86769	+	2.34200i
$764$	−21.9907	+	10.5902i	−0.795595	+	0.383138i
$765$	17.6932	−	22.1866i	0.639701	−	0.802159i
$766$	−26.0185			−0.940085
$767$	12.8239	−	16.0807i	0.463046	−	0.580641i
$768$	−0.511050	+	2.23905i	−0.0184409	+	0.0807949i
$769$	−9.64160	+	42.2426i	−0.347685	+	1.52331i	0.434736	+	0.900558i	$0.356842\pi$
$769$	−9.64160	+	42.2426i	−0.347685	+	1.52331i	−0.782421	+	0.622749i	$0.786016\pi$
$770$	16.8399	−	21.1166i	0.606870	−	0.760990i
$771$	11.6459			0.419418
$772$	3.08049	−	3.86282i	0.110869	−	0.139026i
$773$	36.0804	−	17.3754i	1.29772	−	0.624951i	0.347840	−	0.937554i	$-0.386915\pi$
$773$	36.0804	−	17.3754i	1.29772	−	0.624951i	0.949884	+	0.312603i	$0.101201\pi$
$774$	2.61189	+	3.27521i	0.0938825	+	0.117725i
$775$	4.16388	+	5.22134i	0.149571	+	0.187556i
$776$	−4.71887	−	2.27249i	−0.169398	−	0.0815776i
$777$	10.3406	−	45.3051i	0.370967	−	1.62531i
$778$	1.66644	+	7.30115i	0.0597447	+	0.261759i
$779$	7.40322	−	3.56520i	0.265248	−	0.127737i
$780$	−24.6264	−	11.8595i	−0.881767	−	0.424637i
$781$	−5.37207	−	23.5366i	−0.192228	−	0.842205i
$782$	−10.7549			−0.384596
$783$	−8.69773	+	2.20288i	−0.310832	+	0.0787244i
$784$	10.1263			0.361654
$785$	−19.2034	−	84.1356i	−0.685398	−	3.00293i
$786$	−5.79055	−	2.78858i	−0.206542	−	0.0994655i
$787$	29.8560	−	14.3779i	1.06425	−	0.512516i	0.182002	−	0.983298i	$-0.441742\pi$
$787$	29.8560	−	14.3779i	1.06425	−	0.512516i	0.882250	+	0.470782i	$0.156028\pi$
$788$	−0.163605	−	0.716798i	−0.00582817	−	0.0255349i
$789$	5.56200	−	24.3687i	0.198013	−	0.867550i
$790$	50.6973	+	24.4145i	1.80373	+	0.868630i
$791$	−28.3989	−	35.6110i	−1.00975	−	1.26618i
$792$	−2.61189	−	3.27521i	−0.0928095	−	0.116379i
$793$	−5.52401	+	2.66023i	−0.196164	+	0.0944674i
$794$	−7.47716	+	9.37606i	−0.265354	+	0.332744i
$795$	−53.9383			−1.91299
$796$	−0.825107	+	1.03465i	−0.0292451	+	0.0366723i
$797$	4.18410	−	18.3318i	0.148209	−	0.649344i	−0.845174	−	0.534491i	$-0.820503\pi$
$797$	4.18410	−	18.3318i	0.148209	−	0.649344i	0.993383	−	0.114853i	$-0.0366396\pi$
$798$	5.76415	−	25.2544i	0.204049	−	0.893996i
$799$	4.42180	−	5.54477i	0.156432	−	0.196160i
$800$	7.55721			0.267188
$801$	−5.10461	+	6.40098i	−0.180363	+	0.226168i
$802$	−3.24922	+	1.56474i	−0.114734	+	0.0552530i
$803$	17.6688	+	22.1560i	0.623520	+	0.781869i
$804$	−0.198172	−	0.248500i	−0.00698898	−	0.00876391i
$805$	−40.3606	−	19.4366i	−1.42252	−	0.685051i
$806$	−0.660436	+	2.89356i	−0.0232628	+	0.101921i
$807$	13.7810	+	60.3787i	0.485116	+	2.12543i
$808$	−8.69381	+	4.18672i	−0.305847	+	0.147288i
$809$	−11.5860	−	5.57950i	−0.407341	−	0.196165i	0.218982	−	0.975729i	$-0.429726\pi$
$809$	−11.5860	−	5.57950i	−0.407341	−	0.196165i	−0.626323	+	0.779564i	$0.715441\pi$
$810$	8.39790	+	36.7936i	0.295072	+	1.29280i
$811$	−22.8504			−0.802385			−0.401193	−	0.915994i	$-0.631404\pi$
$811$	−22.8504			−0.802385			−0.401193	+	0.915994i	$0.631404\pi$
$812$	−0.527116	−	22.2797i	−0.0184981	−	0.781864i
$813$	32.4557			1.13827
$814$	2.00380	+	8.77922i	0.0702331	+	0.307712i
$815$	−42.7142	−	20.5701i	−1.49621	−	0.720538i
$816$	−7.28518	+	3.50836i	−0.255032	+	0.122817i
$817$	−1.11698	−	4.89379i	−0.0390781	−	0.171212i
$818$	4.16149	−	18.2327i	0.145503	−	0.637491i
$819$	28.4831	+	13.7167i	0.995280	+	0.479302i
$820$	−6.66111	−	8.35276i	−0.232616	−	0.291691i
$821$	−16.4283	−	20.6005i	−0.573353	−	0.718961i	0.407610	−	0.913156i	$-0.366362\pi$
$821$	−16.4283	−	20.6005i	−0.573353	−	0.718961i	−0.980963	+	0.194195i	$0.937791\pi$
$822$	0.549451	−	0.264602i	0.0191643	−	0.00922905i
$823$	16.5875	−	20.8001i	0.578204	−	0.725045i	−0.403601	−	0.914935i	$-0.632242\pi$
$823$	16.5875	−	20.8001i	0.578204	−	0.725045i	0.981805	+	0.189890i	$0.0608132\pi$
$824$	−15.7864			−0.549944
$825$	−19.9304	+	24.9919i	−0.693887	+	0.870107i
$826$	5.63952	−	24.7084i	0.196224	−	0.859714i
$827$	8.17418	−	35.8134i	0.284244	−	1.24535i	−0.608050	−	0.793899i	$-0.708048\pi$
$827$	8.17418	−	35.8134i	0.284244	−	1.24535i	0.892294	−	0.451456i	$-0.149095\pi$
$828$	−4.33203	+	5.43219i	−0.150548	+	0.188782i
$829$	−36.8254			−1.27900			−0.639500	−	0.768791i	$-0.720859\pi$
$829$	−36.8254			−1.27900			−0.639500	+	0.768791i	$0.720859\pi$
$830$	−0.103710	+	0.130048i	−0.00359981	+	0.00451402i
$831$	−26.9481	+	12.9775i	−0.934820	+	0.450186i
$832$	2.09403	+	2.62583i	0.0725973	+	0.0910341i
$833$	22.2290	+	27.8742i	0.770188	+	0.965785i
$834$	13.2418	+	6.37692i	0.458526	+	0.220815i
$835$	7.92121	−	34.7051i	0.274125	−	1.20102i
$836$	1.11698	+	4.89379i	0.0386314	+	0.169255i
$837$	1.32655	−	0.638834i	0.0458523	−	0.0220813i
$838$	−30.0815	−	14.4865i	−1.03915	−	0.500427i
$839$	4.65941	+	20.4142i	0.160861	+	0.704776i	0.989445	+	0.144911i	$0.0462897\pi$
$839$	4.65941	+	20.4142i	0.160861	+	0.704776i	−0.828584	+	0.559865i	$0.810853\pi$
$840$	−33.6799			−1.16207
$841$	−28.9676	+	1.37145i	−0.998881	+	0.0472915i
$842$	7.91611			0.272807
$843$	−14.8631	−	65.1195i	−0.511912	−	2.24283i
$844$	−2.74436	−	1.32162i	−0.0944649	−	0.0454919i
$845$	5.49174	−	2.64468i	0.188921	−	0.0909798i
$846$	−1.01952	−	4.46681i	−0.0350518	−	0.153572i
$847$	−7.00598	+	30.6952i	−0.240728	+	1.05470i
$848$	5.97129	+	2.87562i	0.205055	+	0.0987493i
$849$	26.9556	+	33.8013i	0.925115	+	1.16006i
$850$	16.5894	+	20.8024i	0.569010	+	0.713516i
$851$	13.4564	−	6.48027i	0.461280	−	0.222141i
$852$	−18.7698	+	23.5366i	−0.643042	+	0.806350i
$853$	−8.14070			−0.278732			−0.139366	−	0.990241i	$-0.544507\pi$
$853$	−8.14070			−0.278732			−0.139366	+	0.990241i	$0.544507\pi$
$854$	−4.71036	+	5.90660i	−0.161185	+	0.202120i
$855$	−4.88822	+	21.4167i	−0.167174	+	0.732435i
$856$	3.79138	−	16.6111i	0.129587	−	0.567757i
$857$	24.8327	−	31.1392i	0.848268	−	1.06369i	−0.148927	−	0.988848i	$-0.547582\pi$
$857$	24.8327	−	31.1392i	0.848268	−	1.06369i	0.997195	−	0.0748463i	$-0.0238466\pi$
$858$	−14.2062			−0.484991
$859$	27.8901	−	34.9731i	0.951598	−	1.19327i	−0.0294631	−	0.999566i	$-0.509380\pi$
$859$	27.8901	−	34.9731i	0.951598	−	1.19327i	0.981061	−	0.193700i	$-0.0620488\pi$
$860$	−5.88016	+	2.83174i	−0.200512	+	0.0965614i
$861$	17.8659	+	22.4031i	0.608867	+	0.763495i
$862$	3.39958	+	4.26293i	0.115790	+	0.145196i
$863$	1.94440	+	0.936373i	0.0661881	+	0.0318745i	0.466685	−	0.884424i	$-0.345448\pi$
$863$	1.94440	+	0.936373i	0.0661881	+	0.0318745i	−0.400497	+	0.916298i	$0.631162\pi$
$864$	0.370748	−	1.62435i	0.0126131	−	0.0552616i
$865$	12.9172	+	56.5940i	0.439198	+	1.92425i
$866$	−34.4860	+	16.6076i	−1.17188	+	0.564348i
$867$	9.52685	+	4.58789i	0.323549	+	0.155813i
$868$	0.813785	+	3.56543i	0.0276217	+	0.121018i
$869$	29.2456			0.992090
$870$	1.03660	+	43.8143i	0.0351441	+	1.48545i
$871$	−0.464808			−0.0157494
$872$	4.44914	+	19.4929i	0.150667	+	0.660114i
$873$	−10.7333	−	5.16886i	−0.363266	−	0.174939i
$874$	7.50100	−	3.61229i	0.253725	−	0.122188i
$875$	8.34480	+	36.5610i	0.282106	+	1.23599i
$876$	7.86337	−	34.4517i	0.265679	−	1.16401i
$877$	−25.1844	−	12.1282i	−0.850417	−	0.409539i	−0.0426847	−	0.999089i	$-0.513591\pi$
$877$	−25.1844	−	12.1282i	−0.850417	−	0.409539i	−0.807732	+	0.589549i	$0.799305\pi$
$878$	7.20882	+	9.03957i	0.243286	+	0.305071i
$879$	−8.55523	−	10.7279i	−0.288561	−	0.361844i
$880$	5.88016	−	2.83174i	0.198220	−	0.0954578i
$881$	11.8199	−	14.8216i	0.398221	−	0.499353i	−0.541782	−	0.840519i	$-0.682250\pi$
$881$	11.8199	−	14.8216i	0.398221	−	0.499353i	0.940003	+	0.341166i	$0.110822\pi$
$882$	23.0327			0.775550
$883$	27.4634	−	34.4380i	0.924218	−	1.15893i	−0.0627523	−	0.998029i	$-0.519988\pi$
$883$	27.4634	−	34.4380i	0.924218	−	1.15893i	0.986970	−	0.160903i	$-0.0514408\pi$
$884$	−2.63125	+	11.5283i	−0.0884985	+	0.387737i
$885$	−11.0904	+	48.5904i	−0.372801	+	1.63335i
$886$	16.8781	−	21.1644i	0.567030	−	0.711033i
$887$	20.7096			0.695359			0.347679	−	0.937613i	$-0.386970\pi$
$887$	20.7096			0.695359			0.347679	+	0.937613i	$0.386970\pi$
$888$	7.00120	−	8.77922i	0.234945	−	0.294611i
$889$	−8.44712	+	4.06792i	−0.283307	+	0.136434i
$890$	−7.95273	−	9.97241i	−0.266576	−	0.334276i
$891$	12.2297	+	15.3356i	0.409710	+	0.513760i
$892$	7.77193	+	3.74277i	0.260224	+	0.125317i
$893$	−1.22164	+	5.35235i	−0.0408806	+	0.179110i
$894$	−5.29773	−	23.2109i	−0.177182	−	0.776287i
$895$	−27.1728	+	13.0857i	−0.908287	+	0.437408i
$896$	3.72857	+	1.79558i	0.124563	+	0.0599862i
$897$	5.24306	+	22.9713i	0.175061	+	0.766991i
$898$	3.66223			0.122210
$899$	4.61323	−	1.16839i	0.153860	−	0.0389681i
$900$	17.1892			0.572972
$901$	5.19240	+	22.7494i	0.172984	+	0.757892i
$902$	−5.00280	−	2.40922i	−0.166575	−	0.0802183i
$903$	15.7713	−	7.59504i	0.524835	−	0.252747i
$904$	−2.44912	−	10.7303i	−0.0814566	−	0.356885i
$905$	−6.70274	+	29.3666i	−0.222807	+	0.976179i
$906$	−22.4591	−	10.8157i	−0.746155	−	0.359329i
$907$	−28.3949	−	35.6061i	−0.942838	−	1.18228i	−0.983096	−	0.183092i	$-0.941390\pi$
$907$	−28.3949	−	35.6061i	−0.942838	−	1.18228i	0.0402583	−	0.999189i	$-0.487182\pi$
$908$	−0.291688	−	0.365765i	−0.00968001	−	0.0121383i
$909$	−19.7744	+	9.52285i	−0.655875	+	0.315853i
$910$	−30.7086	+	38.5074i	−1.01798	+	1.27651i
$911$	59.3261			1.96556			0.982781	−	0.184775i	$-0.0591556\pi$
$911$	59.3261			1.96556			0.982781	+	0.184775i	$0.0591556\pi$
$912$	3.90267	−	4.89379i	0.129230	−	0.162050i
$913$	−0.0192374	+	0.0842846i	−0.000636665	+	0.00278941i
$914$	−7.35770	+	32.2362i	−0.243371	+	1.06628i
$915$	9.26319	−	11.6157i	0.306232	−	0.384002i
$916$	25.2867			0.835497
$917$	−7.22070	+	9.05447i	−0.238449	+	0.299005i
$918$	5.28513	−	2.54519i	0.174435	−	0.0840036i
$919$	6.28260	+	7.87814i	0.207244	+	0.259876i	0.874580	−	0.484881i	$-0.161137\pi$
$919$	6.28260	+	7.87814i	0.207244	+	0.259876i	−0.667336	+	0.744757i	$0.732566\pi$
$920$	−6.74909	−	8.46309i	−0.222511	−	0.279020i
$921$	22.9697	+	11.0616i	0.756878	+	0.364493i
$922$	7.34091	−	32.1626i	0.241760	−	1.05922i
$923$	9.79628	+	42.9203i	0.322449	+	1.41274i
$924$	−15.7713	+	7.59504i	−0.518837	+	0.249859i
$925$	−33.2906	−	16.0319i	−1.09459	−	0.527126i
$926$	−6.49256	−	28.4458i	−0.213359	−	0.934786i
$927$	−35.9067			−1.17933
$928$	2.22112	−	4.90577i	0.0729120	−	0.161040i
$929$	24.3541			0.799033			0.399517	−	0.916726i	$-0.369178\pi$
$929$	24.3541			0.799033			0.399517	+	0.916726i	$0.369178\pi$
$930$	−1.60036	−	7.01162i	−0.0524777	−	0.229920i
$931$	−24.8657	−	11.9747i	−0.814942	−	0.392455i
$932$	−11.9686	+	5.76375i	−0.392043	+	0.188798i
$933$	0.217489	+	0.952883i	0.00712028	+	0.0311960i
$934$	−3.48637	+	15.2748i	−0.114078	+	0.499806i
$935$	20.7027	+	9.96991i	0.677052	+	0.326051i
$936$	4.76294	+	5.97254i	0.155682	+	0.195218i
$937$	17.0680	+	21.4026i	0.557588	+	0.699194i	0.978110	−	0.208089i	$-0.0667243\pi$
$937$	17.0680	+	21.4026i	0.557588	+	0.699194i	−0.420521	+	0.907283i	$0.638153\pi$
$938$	−0.516015	+	0.248500i	−0.0168485	+	0.00811380i
$939$	19.3247	−	24.2325i	0.630639	−	0.790797i
$940$	7.13803			0.232817
$941$	−19.3916	+	24.3163i	−0.632147	+	0.792688i	−0.989997	−	0.141092i	$-0.954939\pi$
$941$	−19.3916	+	24.3163i	−0.632147	+	0.792688i	0.357849	+	0.933779i	$0.383510\pi$
$942$	−12.4458	+	54.5287i	−0.405507	+	1.77664i
$943$	−2.04932	+	8.97867i	−0.0667352	+	0.292386i
$944$	3.81829	−	4.78798i	0.124275	−	0.155836i
$945$	24.4335			0.794823
$946$	−2.11493	+	2.65203i	−0.0687621	+	0.0862250i
$947$	−42.7271	+	20.5763i	−1.38844	+	0.668640i	−0.970782	−	0.239963i	$-0.922865\pi$
$947$	−42.7271	+	20.5763i	−1.38844	+	0.668640i	−0.417663	+	0.908602i	$0.637151\pi$
$948$	−22.7379	−	28.5124i	−0.738492	−	0.926039i
$949$	−32.2202	−	40.4028i	−1.04591	−	1.31153i
$950$	−18.5572	−	8.93666i	−0.602074	−	0.289944i
$951$	7.38345	−	32.3490i	0.239425	−	1.04899i
$952$	3.24221	+	14.2051i	0.105081	+	0.460389i
$953$	−44.7043	+	21.5285i	−1.44812	+	0.697375i	−0.982267	−	0.187489i	$-0.939965\pi$
$953$	−44.7043	+	21.5285i	−1.44812	+	0.697375i	−0.465848	+	0.884865i	$0.654251\pi$
$954$	13.5819	+	6.54071i	0.439731	+	0.211763i
$955$	−19.2463	−	84.3234i	−0.622794	−	2.72864i
$956$	16.0913			0.520431
$957$	10.3658	+	20.2832i	0.335080	+	0.655662i
$958$	−3.84849			−0.124339
$959$	−0.244529	−	1.07135i	−0.00789625	−	0.0345957i
$960$	−7.33244	−	3.53112i	−0.236654	−	0.113966i
$961$	27.2264	−	13.1116i	0.878272	−	0.422954i
$962$	−3.65405	−	16.0094i	−0.117811	−	0.516165i
$963$	8.62364	−	37.7826i	0.277893	−	1.21753i
$964$	13.4077	+	6.45681i	0.431833	+	0.207960i
$965$	10.9161	+	13.6883i	0.351401	+	0.440643i
$966$	18.1018	+	22.6990i	0.582417	+	0.730328i
$967$	−8.78018	+	4.22831i	−0.282351	+	0.135973i	−0.569700	−	0.821853i	$-0.692941\pi$
$967$	−8.78018	+	4.22831i	−0.282351	+	0.135973i	0.287348	+	0.957826i	$0.407226\pi$
$968$	−4.74346	+	5.94811i	−0.152461	+	0.191180i
$969$	22.0379			0.707961
$970$	11.5719	−	14.5107i	0.371551	−	0.465910i
$971$	7.78130	−	34.0921i	0.249714	−	1.09407i	−0.682137	−	0.731225i	$-0.738949\pi$
$971$	7.78130	−	34.0921i	0.249714	−	1.09407i	0.931850	−	0.362843i	$-0.118194\pi$
$972$	4.33048	−	18.9731i	0.138900	−	0.608562i
$973$	16.5123	−	20.7057i	0.529359	−	0.663795i
$974$	28.6576			0.918250
$975$	36.3443	−	45.5743i	1.16395	−	1.45954i
$976$	−1.64476	+	0.792074i	−0.0526474	+	0.0253537i
$977$	13.8566	+	17.3756i	0.443312	+	0.555896i	0.952413	−	0.304811i	$-0.0985933\pi$
$977$	13.8566	+	17.3756i	0.443312	+	0.555896i	−0.509101	+	0.860707i	$0.670022\pi$
$978$	19.1574	+	24.0226i	0.612587	+	0.768160i
$979$	−5.97287	−	2.87638i	−0.190894	−	0.0919296i
$980$	−7.98489	+	34.9841i	−0.255068	+	1.11753i
$981$	10.1197	+	44.3374i	0.323098	+	1.41558i
$982$	−16.0571	+	7.73268i	−0.512402	+	0.246760i
$983$	−35.5825	−	17.1356i	−1.13491	−	0.546542i	−0.230440	−	0.973087i	$-0.574017\pi$
$983$	−35.5825	−	17.1356i	−1.13491	−	0.546542i	−0.904467	+	0.426544i	$0.859731\pi$
$984$	1.54075	+	6.75049i	0.0491175	+	0.215198i
$985$	2.60538			0.0830143
$986$	18.3796	−	4.65501i	0.585327	−	0.148246i
$987$	−19.1450			−0.609393
$988$	−2.03687	−	8.92412i	−0.0648015	−	0.283914i
$989$	5.06888	+	2.44104i	0.161181	+	0.0776206i
$990$	13.3746	−	6.44089i	0.425074	−	0.204705i
$991$	−0.424816	−	1.86124i	−0.0134947	−	0.0591242i	0.967732	−	0.251981i	$-0.0810820\pi$
$991$	−0.424816	−	1.86124i	−0.0134947	−	0.0591242i	−0.981227	+	0.192856i	$0.938225\pi$
$992$	−0.196643	+	0.861548i	−0.00624341	+	0.0273542i
$993$	−19.7348	−	9.50379i	−0.626266	−	0.301594i
$994$	33.8220	+	42.4114i	1.07277	+	1.34521i
$995$	−2.92386	−	3.66641i	−0.0926927	−	0.116233i
$996$	0.0971280	−	0.0467744i	0.00307762	−	0.00148210i
$997$	−0.922744	+	1.15708i	−0.0292236	+	0.0366452i	−0.796229	−	0.604996i	$-0.793175\pi$
$997$	−0.922744	+	1.15708i	−0.0292236	+	0.0366452i	0.767005	+	0.641641i	$0.221746\pi$
$998$	24.3018			0.769259
$999$	−5.07911	+	6.36900i	−0.160696	+	0.201506i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	58.2.d.b.7.1	✓	12
3.2	odd	2		522.2.k.h.181.2		12
4.3	odd	2		464.2.u.h.65.2		12
29.2	odd	28		1682.2.b.i.1681.2		12
29.5	even	14		1682.2.a.q.1.2		6
29.24	even	7		1682.2.a.t.1.5		6
29.25	even	7	inner	58.2.d.b.25.1	yes	12
29.27	odd	28		1682.2.b.i.1681.11		12
87.83	odd	14		522.2.k.h.199.2		12
116.83	odd	14		464.2.u.h.257.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
58.2.d.b.7.1	✓	12	1.1	even	1	trivial
58.2.d.b.25.1	yes	12	29.25	even	7	inner
464.2.u.h.65.2		12	4.3	odd	2
464.2.u.h.257.2		12	116.83	odd	14
522.2.k.h.181.2		12	3.2	odd	2
522.2.k.h.199.2		12	87.83	odd	14
1682.2.a.q.1.2		6	29.5	even	14
1682.2.a.t.1.5		6	29.24	even	7
1682.2.b.i.1681.2		12	29.2	odd	28
1682.2.b.i.1681.11		12	29.27	odd	28

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 58 = 2 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	58.d (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.222521 - 0.974928i) q^{2} +(-2.06920 - 0.996473i) q^{3} +(-0.900969 + 0.433884i) q^{4} +(-0.788529 - 3.45477i) q^{5} +(-0.511050 + 2.23905i) q^{6} +(3.72857 + 1.79558i) q^{7} +(0.623490 + 0.781831i) q^{8} +(1.41815 + 1.77830i) q^{9} +(-3.19269 + 1.53752i) q^{10} +(-1.14832 + 1.43995i) q^{11} +2.29664 q^{12} +(2.09403 - 2.62583i) q^{13} +(0.920880 - 4.03464i) q^{14} +(-1.81096 + 7.93435i) q^{15} +(0.623490 - 0.781831i) q^{16} +3.52078 q^{17} +(1.41815 - 1.77830i) q^{18} +(-2.45556 + 1.18253i) q^{19} +(2.20941 + 2.77051i) q^{20} +(-5.92589 - 7.43083i) q^{21} +(1.65937 + 0.799109i) q^{22} +(0.679736 - 2.97812i) q^{23} +(-0.511050 - 2.23905i) q^{24} +(-6.80881 + 3.27895i) q^{25} +(-3.02595 - 1.45722i) q^{26} +(0.370748 + 1.62435i) q^{27} -4.13840 q^{28} +(0.127372 + 5.38366i) q^{29} +8.13840 q^{30} +(-0.196643 - 0.861548i) q^{31} +(-0.900969 - 0.433884i) q^{32} +(3.81096 - 1.83526i) q^{33} +(-0.783447 - 3.43250i) q^{34} +(3.26324 - 14.2972i) q^{35} +(-2.04929 - 0.986885i) q^{36} +(3.04846 + 3.82264i) q^{37} +(1.69930 + 2.13085i) q^{38} +(-6.94952 + 3.34671i) q^{39} +(2.20941 - 2.77051i) q^{40} -3.01488 q^{41} +(-5.92589 + 7.43083i) q^{42} +(-0.409830 + 1.79558i) q^{43} +(0.409830 - 1.79558i) q^{44} +(5.02538 - 6.30163i) q^{45} -3.05470 q^{46} +(1.25592 - 1.57487i) q^{47} +(-2.06920 + 0.996473i) q^{48} +(6.31365 + 7.91707i) q^{49} +(4.71184 + 5.90847i) q^{50} +(-7.28518 - 3.50836i) q^{51} +(-0.747349 + 3.27435i) q^{52} +(1.47479 + 6.46147i) q^{53} +(1.50113 - 0.722904i) q^{54} +(5.88016 + 2.83174i) q^{55} +(0.920880 + 4.03464i) q^{56} +6.25940 q^{57} +(5.22034 - 1.32216i) q^{58} +6.12406 q^{59} +(-1.81096 - 7.93435i) q^{60} +(-1.64476 - 0.792074i) q^{61} +(-0.796190 + 0.383425i) q^{62} +(2.09457 + 9.17693i) q^{63} +(-0.222521 + 0.974928i) q^{64} +(-10.7228 - 5.16384i) q^{65} +(-2.63727 - 3.30703i) q^{66} +(-0.0862879 - 0.108202i) q^{67} +(-3.17211 + 1.52761i) q^{68} +(-4.37412 + 5.48497i) q^{69} -14.6649 q^{70} +(-8.17273 + 10.2483i) q^{71} +(-0.506132 + 2.21751i) q^{72} +(3.42387 - 15.0009i) q^{73} +(3.04846 - 3.82264i) q^{74} +17.3562 q^{75} +(1.69930 - 2.13085i) q^{76} +(-6.86712 + 3.30703i) q^{77} +(4.80921 + 6.03056i) q^{78} +(-9.90051 - 12.4148i) q^{79} +(-3.19269 - 1.53752i) q^{80} +(2.36987 - 10.3831i) q^{81} +(0.670875 + 2.93929i) q^{82} +(0.0422914 - 0.0203665i) q^{83} +(8.56316 + 4.12380i) q^{84} +(-2.77623 - 12.1635i) q^{85} +1.84176 q^{86} +(5.10111 - 11.2668i) q^{87} -1.84176 q^{88} +(0.800961 + 3.50924i) q^{89} +(-7.26188 - 3.49714i) q^{90} +(12.5226 - 6.03056i) q^{91} +(0.679736 + 2.97812i) q^{92} +(-0.451617 + 1.97866i) q^{93} +(-1.81485 - 0.873987i) q^{94} +(6.02166 + 7.55092i) q^{95} +(1.43193 + 1.79558i) q^{96} +(-4.71887 + 2.27249i) q^{97} +(6.31365 - 7.91707i) q^{98} -4.18915 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} - 3 q^{3} - 2 q^{4} + 4 q^{6} + q^{7} - 2 q^{8} - 11 q^{9} - 7 q^{10} - 2 q^{11} + 4 q^{12} + q^{13} + q^{14} - 9 q^{15} - 2 q^{16} - 12 q^{17} - 11 q^{18} - 6 q^{19} + 7 q^{20} - 13 q^{21}+ \cdots - 8 q^{99}+O(q^{100}) \) 12 * q - 2 * q^2 - 3 * q^3 - 2 * q^4 + 4 * q^6 + q^7 - 2 * q^8 - 11 * q^9 - 7 * q^10 - 2 * q^11 + 4 * q^12 + q^13 + q^14 - 9 * q^15 - 2 * q^16 - 12 * q^17 - 11 * q^18 - 6 * q^19 + 7 * q^20 - 13 * q^21 - 2 * q^22 + 35 * q^23 + 4 * q^24 - 6 * q^25 + 8 * q^26 + 39 * q^27 - 6 * q^28 - 14 * q^29 + 54 * q^30 - 8 * q^31 - 2 * q^32 + 33 * q^33 - 5 * q^34 - 18 * q^35 - 4 * q^36 + 31 * q^37 + q^38 - 22 * q^39 + 7 * q^40 - 30 * q^41 - 13 * q^42 - 5 * q^43 + 5 * q^44 - 20 * q^45 - 28 * q^46 - 33 * q^47 - 3 * q^48 + 37 * q^49 + q^50 - 15 * q^51 - 6 * q^52 + 13 * q^53 - 24 * q^54 + 36 * q^55 + q^56 - 38 * q^57 + 38 * q^59 - 9 * q^60 - 5 * q^61 - 8 * q^62 + 4 * q^63 - 2 * q^64 - 20 * q^65 - 30 * q^66 - 7 * q^67 - 19 * q^68 + 20 * q^69 - 18 * q^70 + 3 * q^71 + 3 * q^72 - 22 * q^73 + 31 * q^74 - 2 * q^75 + q^76 + 10 * q^77 + 41 * q^78 - 60 * q^79 - 7 * q^80 + 88 * q^81 + 26 * q^82 - 39 * q^83 + 43 * q^84 + 38 * q^85 + 2 * q^86 + 9 * q^87 - 2 * q^88 + 39 * q^89 - 34 * q^90 + 61 * q^91 + 35 * q^92 - 54 * q^93 + 16 * q^94 + 55 * q^95 - 3 * q^96 - 19 * q^97 + 37 * q^98 - 8 * q^99

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