LMFDB - Embedded newform 58.2.e.a.33.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [58,2,Mod(5,58)] 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([11])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("58.5"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 58 = 2 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	58.e (of order $14$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == 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 $\Q(\zeta_{14})$
Coefficient field:	$\Q(\zeta_{28})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{10} + x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^12 - x^10 + x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			33.1
Root			$0.781831 - 0.623490i$ of defining polynomial
Character	$\chi$	$=$	58.33
Dual form			58.2.e.a.51.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.974928 - 0.222521i) q^{2} +(0.626980 + 1.30194i) q^{3} +(0.900969 + 0.433884i) q^{4} +(-0.308457 + 1.35144i) q^{5} +(-0.321552 - 1.40881i) q^{6} +(1.78967 - 0.861862i) q^{7} +(-0.781831 - 0.623490i) q^{8} +(0.568532 - 0.712916i) q^{9} +(0.601447 - 1.24892i) q^{10} +(-2.70097 + 2.15395i) q^{11} +1.44504i q^{12} +(-3.81172 - 4.77974i) q^{13} +(-1.93659 + 0.442013i) q^{14} +(-1.95288 + 0.445733i) q^{15} +(0.623490 + 0.781831i) q^{16} -4.25956i q^{17} +(-0.712916 + 0.568532i) q^{18} +(-0.940908 + 1.95381i) q^{19} +(-0.864277 + 1.08377i) q^{20} +(2.24418 + 1.78967i) q^{21} +(3.11255 - 1.49893i) q^{22} +(0.127108 + 0.556895i) q^{23} +(0.321552 - 1.40881i) q^{24} +(2.77361 + 1.33570i) q^{25} +(2.65256 + 5.50809i) q^{26} +(5.51107 + 1.25786i) q^{27} +1.98639 q^{28} +(-4.17344 - 3.40329i) q^{29} +2.00311 q^{30} +(5.88393 + 1.34297i) q^{31} +(-0.433884 - 0.900969i) q^{32} +(-4.49776 - 2.16601i) q^{33} +(-0.947841 + 4.15276i) q^{34} +(0.612715 + 2.68448i) q^{35} +(0.821552 - 0.395639i) q^{36} +(-2.12207 - 1.69229i) q^{37} +(1.35208 - 1.69546i) q^{38} +(3.83306 - 7.95942i) q^{39} +(1.08377 - 0.864277i) q^{40} +9.14522i q^{41} +(-1.78967 - 2.24418i) q^{42} +(-10.7813 + 2.46076i) q^{43} +(-3.36805 + 0.768736i) q^{44} +(0.788095 + 0.988239i) q^{45} -0.571217i q^{46} +(-3.89807 + 3.10861i) q^{47} +(-0.626980 + 1.30194i) q^{48} +(-1.90430 + 2.38792i) q^{49} +(-2.40684 - 1.91939i) q^{50} +(5.54568 - 2.67066i) q^{51} +(-1.36039 - 5.96024i) q^{52} +(2.32017 - 10.1653i) q^{53} +(-5.09299 - 2.45265i) q^{54} +(-2.07780 - 4.31459i) q^{55} +(-1.93659 - 0.442013i) q^{56} -3.13368 q^{57} +(3.31150 + 4.24664i) q^{58} +9.01438 q^{59} +(-1.95288 - 0.445733i) q^{60} +(4.16364 + 8.64589i) q^{61} +(-5.43757 - 2.61859i) q^{62} +(0.403051 - 1.76588i) q^{63} +(0.222521 + 0.974928i) q^{64} +(7.63528 - 3.67696i) q^{65} +(3.90301 + 3.11255i) q^{66} +(-7.82616 + 9.81369i) q^{67} +(1.84815 - 3.83773i) q^{68} +(-0.645349 + 0.514648i) q^{69} -2.75352i q^{70} +(-2.66783 - 3.34535i) q^{71} +(-0.888992 + 0.202907i) q^{72} +(6.80675 - 1.55360i) q^{73} +(1.69229 + 2.12207i) q^{74} +4.44852i q^{75} +(-1.69546 + 1.35208i) q^{76} +(-2.97745 + 6.18273i) q^{77} +(-5.50809 + 6.90693i) q^{78} +(-9.09164 - 7.25034i) q^{79} +(-1.24892 + 0.601447i) q^{80} +(1.20895 + 5.29674i) q^{81} +(2.03500 - 8.91593i) q^{82} +(9.76203 + 4.70114i) q^{83} +(1.24543 + 2.58615i) q^{84} +(5.75653 + 1.31389i) q^{85} +11.0585 q^{86} +(1.81420 - 7.56736i) q^{87} +3.45467 q^{88} +(-2.78013 - 0.634546i) q^{89} +(-0.548431 - 1.13883i) q^{90} +(-10.9412 - 5.26901i) q^{91} +(-0.127108 + 0.556895i) q^{92} +(1.94065 + 8.50252i) q^{93} +(4.49206 - 2.16326i) q^{94} +(-2.35023 - 1.87425i) q^{95} +(0.900969 - 1.12978i) q^{96} +(-1.05219 + 2.18489i) q^{97} +(2.38792 - 1.90430i) q^{98} +3.15015i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{4} - 2 q^{5} - 12 q^{6} + 4 q^{7} - 4 q^{9} - 26 q^{13} - 14 q^{15} - 2 q^{16} + 2 q^{20} + 14 q^{21} + 4 q^{22} - 16 q^{23} + 12 q^{24} + 22 q^{25} + 14 q^{26} - 4 q^{28} + 18 q^{29} + 16 q^{30}+ \cdots - 28 q^{97}+O(q^{100}) $ 12 * q + 2 * q^4 - 2 * q^5 - 12 * q^6 + 4 * q^7 - 4 * q^9 - 26 * q^13 - 14 * q^15 - 2 * q^16 + 2 * q^20 + 14 * q^21 + 4 * q^22 - 16 * q^23 + 12 * q^24 + 22 * q^25 + 14 * q^26 - 4 * q^28 + 18 * q^29 + 16 * q^30 + 28 * q^31 - 10 * q^33 - 4 * q^34 + 4 * q^35 + 18 * q^36 - 28 * q^37 + 22 * q^38 + 28 * q^39 - 14 * q^40 - 4 * q^42 - 28 * q^43 - 28 * q^44 - 4 * q^45 - 14 * q^47 - 8 * q^49 - 28 * q^50 - 4 * q^51 - 2 * q^52 + 30 * q^53 - 32 * q^54 + 28 * q^55 - 20 * q^57 - 10 * q^58 - 48 * q^59 - 14 * q^60 - 28 * q^61 + 10 * q^62 + 22 * q^63 + 2 * q^64 + 2 * q^65 - 16 * q^67 - 14 * q^68 - 28 * q^69 + 30 * q^71 + 42 * q^73 + 2 * q^74 + 28 * q^76 + 14 * q^77 - 16 * q^78 + 28 * q^79 - 2 * q^80 + 26 * q^81 - 20 * q^82 + 28 * q^85 + 52 * q^86 + 4 * q^87 - 4 * q^88 + 14 * q^89 + 70 * q^90 - 4 * q^91 + 16 * q^92 + 66 * q^93 - 8 * q^94 + 2 * q^96 - 28 * q^97

Character values

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

$n$	$31$
$\chi(n)$	$e\left(\frac{1}{14}\right)$

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 $

$2$	−0.974928	−	0.222521i	−0.689378	−	0.157346i
$2$	−0.974928	−	0.222521i	−0.689378	−	0.157346i
$3$	0.626980	+	1.30194i	0.361987	+	0.751674i	0.999829	−	0.0184933i	$-0.00588693\pi$
$3$	0.626980	+	1.30194i	0.361987	+	0.751674i	−0.637842	+	0.770167i	$0.720173\pi$
$4$	0.900969	+	0.433884i	0.450484	+	0.216942i
$5$	−0.308457	+	1.35144i	−0.137946	+	0.604381i	0.857939	+	0.513752i	$0.171745\pi$
$5$	−0.308457	+	1.35144i	−0.137946	+	0.604381i	−0.995885	+	0.0906292i	$0.971112\pi$
$6$	−0.321552	−	1.40881i	−0.131273	−	0.575145i
$7$	1.78967	−	0.861862i	0.676433	−	0.325753i	−0.0639355	−	0.997954i	$-0.520365\pi$
$7$	1.78967	−	0.861862i	0.676433	−	0.325753i	0.740369	+	0.672201i	$0.234651\pi$
$8$	−0.781831	−	0.623490i	−0.276419	−	0.220437i
$9$	0.568532	−	0.712916i	0.189511	−	0.237639i
$10$	0.601447	−	1.24892i	0.190194	−	0.394942i
$11$	−2.70097	+	2.15395i	−0.814373	+	0.649441i	−0.939442	−	0.342707i	$-0.888656\pi$
$11$	−2.70097	+	2.15395i	−0.814373	+	0.649441i	0.125069	+	0.992148i	$0.460085\pi$
$12$			1.44504i			0.417148i
$13$	−3.81172	−	4.77974i	−1.05718	−	1.32566i	−0.943217	−	0.332177i	$-0.892217\pi$
$13$	−3.81172	−	4.77974i	−1.05718	−	1.32566i	−0.113963	−	0.993485i	$-0.536355\pi$
$14$	−1.93659	+	0.442013i	−0.517574	+	0.118133i
$15$	−1.95288	+	0.445733i	−0.504233	+	0.115088i
$16$	0.623490	+	0.781831i	0.155872	+	0.195458i
$17$		−	4.25956i		−	1.03309i	−0.856259	−	0.516547i	$-0.827217\pi$
$17$		−	4.25956i		−	1.03309i	0.856259	−	0.516547i	$-0.172783\pi$
$18$	−0.712916	+	0.568532i	−0.168036	+	0.134004i
$19$	−0.940908	+	1.95381i	−0.215859	+	0.448236i	−0.980578	−	0.196128i	$-0.937163\pi$
$19$	−0.940908	+	1.95381i	−0.215859	+	0.448236i	0.764719	+	0.644363i	$0.222878\pi$
$20$	−0.864277	+	1.08377i	−0.193258	+	0.242338i
$21$	2.24418	+	1.78967i	0.489720	+	0.390539i
$22$	3.11255	−	1.49893i	0.663598	−	0.319572i
$23$	0.127108	+	0.556895i	0.0265038	+	0.116121i	0.986449	−	0.164066i	$-0.0524609\pi$
$23$	0.127108	+	0.556895i	0.0265038	+	0.116121i	−0.959946	+	0.280186i	$0.909604\pi$
$24$	0.321552	−	1.40881i	0.0656365	−	0.287572i
$25$	2.77361	+	1.33570i	0.554721	+	0.267140i
$26$	2.65256	+	5.50809i	0.520209	+	1.08023i
$27$	5.51107	+	1.25786i	1.06061	+	0.242076i
$28$	1.98639			0.375392
$29$	−4.17344	−	3.40329i	−0.774989	−	0.631975i
$29$	−4.17344	−	3.40329i	−0.774989	−	0.631975i
$30$	2.00311			0.365716
$31$	5.88393	+	1.34297i	1.05678	+	0.241204i	0.715397	−	0.698718i	$-0.246246\pi$
$31$	5.88393	+	1.34297i	1.05678	+	0.241204i	0.341388	+	0.939923i	$0.389103\pi$
$32$	−0.433884	−	0.900969i	−0.0767005	−	0.159270i
$33$	−4.49776	−	2.16601i	−0.782960	−	0.377054i
$34$	−0.947841	+	4.15276i	−0.162553	+	0.712193i
$35$	0.612715	+	2.68448i	0.103568	+	0.453760i
$36$	0.821552	−	0.395639i	0.136925	−	0.0659398i
$37$	−2.12207	−	1.69229i	−0.348866	−	0.278211i	0.433341	−	0.901230i	$-0.357335\pi$
$37$	−2.12207	−	1.69229i	−0.348866	−	0.278211i	−0.782207	+	0.623019i	$0.785906\pi$
$38$	1.35208	−	1.69546i	0.219337	−	0.275039i
$39$	3.83306	−	7.95942i	0.613780	−	1.27453i
$40$	1.08377	−	0.864277i	0.171359	−	0.136654i
$41$			9.14522i			1.42824i	0.700021	+	0.714122i	$0.253174\pi$
$41$			9.14522i			1.42824i	−0.700021	+	0.714122i	$0.746826\pi$
$42$	−1.78967	−	2.24418i	−0.276153	−	0.346285i
$43$	−10.7813	+	2.46076i	−1.64413	+	0.375262i	−0.941690	−	0.336481i	$-0.890763\pi$
$43$	−10.7813	+	2.46076i	−1.64413	+	0.375262i	−0.702440	+	0.711743i	$0.747906\pi$
$44$	−3.36805	+	0.768736i	−0.507753	+	0.115891i
$45$	0.788095	+	0.988239i	0.117482	+	0.147318i
$46$		−	0.571217i		−	0.0842213i
$47$	−3.89807	+	3.10861i	−0.568592	+	0.453437i	−0.865104	−	0.501592i	$-0.832748\pi$
$47$	−3.89807	+	3.10861i	−0.568592	+	0.453437i	0.296513	+	0.955029i	$0.404176\pi$
$48$	−0.626980	+	1.30194i	−0.0904968	+	0.187919i
$49$	−1.90430	+	2.38792i	−0.272043	+	0.341131i
$50$	−2.40684	−	1.91939i	−0.340379	−	0.271443i
$51$	5.54568	−	2.67066i	0.776551	−	0.373967i
$52$	−1.36039	−	5.96024i	−0.188652	−	0.826537i
$53$	2.32017	−	10.1653i	0.318700	−	1.39632i	−0.521134	−	0.853475i	$-0.674491\pi$
$53$	2.32017	−	10.1653i	0.318700	−	1.39632i	0.839834	−	0.542843i	$-0.182652\pi$
$54$	−5.09299	−	2.45265i	−0.693068	−	0.333764i
$55$	−2.07780	−	4.31459i	−0.280170	−	0.581780i
$56$	−1.93659	−	0.442013i	−0.258787	−	0.0590665i
$57$	−3.13368			−0.415066
$58$	3.31150	+	4.24664i	0.434822	+	0.557611i
$59$	9.01438			1.17357			0.586786	−	0.809742i	$-0.300393\pi$
$59$	9.01438			1.17357			0.586786	+	0.809742i	$0.300393\pi$
$60$	−1.95288	−	0.445733i	−0.252116	−	0.0575439i
$61$	4.16364	+	8.64589i	0.533100	+	1.10699i	0.977455	+	0.211142i	$0.0677184\pi$
$61$	4.16364	+	8.64589i	0.533100	+	1.10699i	−0.444356	+	0.895850i	$0.646567\pi$
$62$	−5.43757	−	2.61859i	−0.690572	−	0.332562i
$63$	0.403051	−	1.76588i	0.0507797	−	0.222480i
$64$	0.222521	+	0.974928i	0.0278151	+	0.121866i
$65$	7.63528	−	3.67696i	0.947040	−	0.456070i
$66$	3.90301	+	3.11255i	0.480428	+	0.383128i
$67$	−7.82616	+	9.81369i	−0.956118	+	1.19893i	0.0238376	+	0.999716i	$0.492412\pi$
$67$	−7.82616	+	9.81369i	−0.956118	+	1.19893i	−0.979955	+	0.199218i	$0.936160\pi$
$68$	1.84815	−	3.83773i	0.224121	−	0.465393i
$69$	−0.645349	+	0.514648i	−0.0776909	+	0.0619564i
$70$		−	2.75352i		−	0.329108i
$71$	−2.66783	−	3.34535i	−0.316613	−	0.397020i	0.597904	−	0.801568i	$-0.296000\pi$
$71$	−2.66783	−	3.34535i	−0.316613	−	0.397020i	−0.914517	+	0.404548i	$0.867429\pi$
$72$	−0.888992	+	0.202907i	−0.104769	+	0.0239128i
$73$	6.80675	−	1.55360i	0.796670	−	0.181835i	0.195235	−	0.980756i	$-0.437453\pi$
$73$	6.80675	−	1.55360i	0.796670	−	0.181835i	0.601435	+	0.798922i	$0.294596\pi$
$74$	1.69229	+	2.12207i	0.196725	+	0.246686i
$75$			4.44852i			0.513671i
$76$	−1.69546	+	1.35208i	−0.194482	+	0.155094i
$77$	−2.97745	+	6.18273i	−0.339312	+	0.704588i
$78$	−5.50809	+	6.90693i	−0.623669	+	0.782056i
$79$	−9.09164	−	7.25034i	−1.02289	−	0.815727i	−0.0398656	−	0.999205i	$-0.512693\pi$
$79$	−9.09164	−	7.25034i	−1.02289	−	0.815727i	−0.983024	+	0.183478i	$0.941264\pi$
$80$	−1.24892	+	0.601447i	−0.139633	+	0.0672438i
$81$	1.20895	+	5.29674i	0.134327	+	0.588527i
$82$	2.03500	−	8.91593i	0.224729	−	0.984600i
$83$	9.76203	+	4.70114i	1.07152	+	0.516018i	0.884597	−	0.466357i	$-0.154434\pi$
$83$	9.76203	+	4.70114i	1.07152	+	0.516018i	0.186925	+	0.982374i	$0.440148\pi$
$84$	1.24543	+	2.58615i	0.135887	+	0.282173i
$85$	5.75653	+	1.31389i	0.624383	+	0.142511i
$86$	11.0585			1.19247
$87$	1.81420	−	7.56736i	0.194503	−	0.811306i
$88$	3.45467			0.368269
$89$	−2.78013	−	0.634546i	−0.294693	−	0.0672617i	0.0726184	−	0.997360i	$-0.476864\pi$
$89$	−2.78013	−	0.634546i	−0.294693	−	0.0672617i	−0.367311	+	0.930098i	$0.619722\pi$
$90$	−0.548431	−	1.13883i	−0.0578097	−	0.120043i
$91$	−10.9412	−	5.26901i	−1.14695	−	0.552342i
$92$	−0.127108	+	0.556895i	−0.0132519	+	0.0580603i
$93$	1.94065	+	8.50252i	0.201236	+	0.881671i
$94$	4.49206	−	2.16326i	0.463321	−	0.223124i
$95$	−2.35023	−	1.87425i	−0.241129	−	0.192294i
$96$	0.900969	−	1.12978i	0.0919548	−	0.115308i
$97$	−1.05219	+	2.18489i	−0.106833	+	0.221842i	−0.947532	−	0.319662i	$-0.896431\pi$
$97$	−1.05219	+	2.18489i	−0.106833	+	0.221842i	0.840698	+	0.541504i	$0.182145\pi$
$98$	2.38792	−	1.90430i	0.241216	−	0.192363i
$99$			3.15015i			0.316602i
$100$	1.91939	+	2.40684i	0.191939	+	0.240684i
$101$	7.05659	−	1.61062i	0.702157	−	0.160263i	0.143486	−	0.989652i	$-0.454169\pi$
$101$	7.05659	−	1.61062i	0.702157	−	0.160263i	0.558671	+	0.829390i	$0.311312\pi$
$102$	−6.00092	+	1.36967i	−0.594179	+	0.135618i
$103$	−4.95154	−	6.20903i	−0.487889	−	0.611794i	0.475560	−	0.879683i	$-0.342245\pi$
$103$	−4.95154	−	6.20903i	−0.487889	−	0.611794i	−0.963450	+	0.267889i	$0.913674\pi$
$104$			6.11352i			0.599480i
$105$	−3.11087	+	2.48083i	−0.303590	+	0.242105i
$106$	−4.52400	+	9.39419i	−0.439410	+	0.912445i
$107$	8.17962	−	10.2569i	0.790754	−	0.991574i	−0.209153	−	0.977883i	$-0.567071\pi$
$107$	8.17962	−	10.2569i	0.790754	−	0.991574i	0.999906	−	0.0136908i	$-0.00435806\pi$
$108$	4.41953	+	3.52446i	0.425270	+	0.339141i
$109$	4.71858	−	2.27235i	0.451958	−	0.217652i	−0.194035	−	0.980995i	$-0.562158\pi$
$109$	4.71858	−	2.27235i	0.451958	−	0.217652i	0.645993	+	0.763343i	$0.276443\pi$
$110$	1.06562	+	4.66877i	0.101603	+	0.445150i
$111$	0.872766	−	3.82384i	0.0828393	−	0.362942i
$112$	1.78967	+	0.861862i	0.169108	+	0.0814383i
$113$	0.0602769	+	0.125166i	0.00567037	+	0.0117746i	0.903785	−	0.427987i	$-0.140777\pi$
$113$	0.0602769	+	0.125166i	0.00567037	+	0.0117746i	−0.898114	+	0.439762i	$0.855063\pi$
$114$	3.05511	+	0.697308i	0.286137	+	0.0653089i
$115$	−0.791817			−0.0738373
$116$	−2.28351	−	4.87705i	−0.212019	−	0.452822i
$117$	−5.57464			−0.515375
$118$	−8.78837	−	2.00589i	−0.809035	−	0.184657i
$119$	−3.67115	−	7.62322i	−0.336534	−	0.698820i
$120$	1.80474	+	0.869115i	0.164749	+	0.0793390i
$121$	0.208000	−	0.911307i	0.0189091	−	0.0828461i
$122$	−2.13536	−	9.35562i	−0.193326	−	0.847018i
$123$	−11.9065	+	5.73387i	−1.07357	+	0.517006i
$124$	4.71854	+	3.76291i	0.423738	+	0.337920i
$125$	−6.98204	+	8.75520i	−0.624492	+	0.783089i
$126$	−0.785892	+	1.63192i	−0.0700128	+	0.145383i
$127$	5.07520	−	4.04734i	0.450352	−	0.359143i	−0.371895	−	0.928275i	$-0.621292\pi$
$127$	5.07520	−	4.04734i	0.450352	−	0.359143i	0.822247	+	0.569131i	$0.192720\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−9.96340	−	12.4937i	−0.877229	−	1.10001i
$130$	−8.26204	+	1.88576i	−0.724629	+	0.165392i
$131$	−2.19402	+	0.500771i	−0.191692	+	0.0437525i	−0.317289	−	0.948329i	$-0.602773\pi$
$131$	−2.19402	+	0.500771i	−0.191692	+	0.0437525i	0.125597	+	0.992081i	$0.459915\pi$
$132$	−3.11255	−	3.90301i	−0.270913	−	0.339714i
$133$			4.30762i			0.373518i
$134$	9.81369	−	7.82616i	0.847774	−	0.676077i
$135$	−3.39985	+	7.05987i	−0.292613	+	0.607617i
$136$	−2.65579	+	3.33026i	−0.227732	+	0.285567i
$137$	−5.91244	−	4.71502i	−0.505134	−	0.402831i	0.337493	−	0.941328i	$-0.390421\pi$
$137$	−5.91244	−	4.71502i	−0.505134	−	0.402831i	−0.842628	+	0.538497i	$0.818992\pi$
$138$	0.743689	−	0.358142i	0.0633070	−	0.0304870i
$139$	−1.38693	−	6.07655i	−0.117638	−	0.515406i	−0.999071	−	0.0430969i	$-0.986278\pi$
$139$	−1.38693	−	6.07655i	−0.117638	−	0.515406i	0.881433	−	0.472310i	$-0.156580\pi$
$140$	−0.612715	+	2.68448i	−0.0517839	+	0.226880i
$141$	−6.49122	−	3.12601i	−0.546659	−	0.263257i
$142$	1.85653	+	3.85512i	0.155796	+	0.323515i
$143$	20.5907	+	4.69969i	1.72188	+	0.393007i
$144$	0.911854			0.0759878
$145$	5.88666	−	4.59038i	0.488860	−	0.381211i
$146$	−6.98180			−0.577818
$147$	−4.30288	−	0.982104i	−0.354895	−	0.0810026i
$148$	−1.17766	−	2.44544i	−0.0968030	−	0.201014i
$149$	−0.653328	−	0.314626i	−0.0535227	−	0.0257752i	0.406931	−	0.913459i	$-0.366599\pi$
$149$	−0.653328	−	0.314626i	−0.0535227	−	0.0257752i	−0.460454	+	0.887684i	$0.652313\pi$
$150$	0.989888	−	4.33698i	0.0808240	−	0.354113i
$151$	2.08373	+	9.12944i	0.169572	+	0.742943i	0.986170	+	0.165737i	$0.0530001\pi$
$151$	2.08373	+	9.12944i	0.169572	+	0.742943i	−0.816598	+	0.577207i	$0.804143\pi$
$152$	1.95381	−	0.940908i	0.158475	−	0.0763177i
$153$	−3.03671	−	2.42169i	−0.245503	−	0.195782i
$154$	4.27858	−	5.36518i	0.344778	−	0.432338i
$155$	−3.62988	+	7.53752i	−0.291559	+	0.605428i
$156$	6.90693	−	5.50809i	0.552997	−	0.441000i
$157$			11.8225i			0.943535i	0.881723	+	0.471767i	$0.156384\pi$
$157$			11.8225i			0.943535i	−0.881723	+	0.471767i	$0.843616\pi$
$158$	7.25034	+	9.09164i	0.576806	+	0.723292i
$159$	14.6893	−	3.35275i	1.16494	−	0.265890i
$160$	1.35144	−	0.308457i	0.106841	−	0.0243857i
$161$	0.707448	+	0.887112i	0.0557547	+	0.0699142i
$162$		−	5.43296i		−	0.426854i
$163$	10.6024	−	8.45516i	0.830447	−	0.662259i	−0.113069	−	0.993587i	$-0.536068\pi$
$163$	10.6024	−	8.45516i	0.830447	−	0.662259i	0.943516	+	0.331328i	$0.107497\pi$
$164$	−3.96796	+	8.23956i	−0.309846	+	0.643402i
$165$	4.31459	−	5.41033i	0.335891	−	0.421194i
$166$	−8.47117	−	6.75553i	−0.657490	−	0.524331i
$167$	−4.18305	+	2.01445i	−0.323694	+	0.155883i	−0.588673	−	0.808371i	$-0.700349\pi$
$167$	−4.18305	+	2.01445i	−0.323694	+	0.155883i	0.264979	+	0.964254i	$0.414635\pi$
$168$	−0.638727	−	2.79845i	−0.0492789	−	0.215905i
$169$	−5.42398	+	23.7640i	−0.417229	+	1.82800i
$170$	−5.31983	−	2.56190i	−0.408013	−	0.196489i
$171$	0.857970	+	1.78159i	0.0656106	+	0.136242i
$172$	−10.7813	−	2.46076i	−0.822065	−	0.187631i
$173$	9.49522			0.721908			0.360954	−	0.932584i	$-0.382451\pi$
$173$	9.49522			0.721908			0.360954	+	0.932584i	$0.382451\pi$
$174$	−3.45261	+	6.97393i	−0.261742	+	0.528692i
$175$	6.11504			0.462253
$176$	−3.36805	−	0.768736i	−0.253877	−	0.0579457i
$177$	5.65184	+	11.7362i	0.424818	+	0.882144i
$178$	2.56922	+	1.23727i	0.192571	+	0.0927375i
$179$	−1.67604	+	7.34323i	−0.125273	+	0.548859i	0.872870	+	0.487953i	$0.162256\pi$
$179$	−1.67604	+	7.34323i	−0.125273	+	0.548859i	−0.998144	+	0.0609061i	$0.980601\pi$
$180$	0.281268	+	1.23231i	0.0209645	+	0.0918513i
$181$	16.6497	−	8.01808i	1.23756	−	0.595980i	0.303414	−	0.952859i	$-0.401874\pi$
$181$	16.6497	−	8.01808i	1.23756	−	0.595980i	0.934150	+	0.356879i	$0.116159\pi$
$182$	9.49443	+	7.57155i	0.703774	+	0.561241i
$183$	−8.64589	+	10.8416i	−0.639123	+	0.801434i
$184$	0.247842	−	0.514648i	0.0182711	−	0.0379404i
$185$	2.94160	−	2.34585i	0.216271	−	0.172470i
$186$		−	8.72118i		−	0.639468i
$187$	9.17488	+	11.5049i	0.670934	+	0.841324i
$188$	−4.86081	+	1.10945i	−0.354511	+	0.0809148i
$189$	10.9471	−	2.49861i	0.796286	−	0.181747i
$190$	1.87425	+	2.35023i	0.135972	+	0.170504i
$191$		−	11.8574i		−	0.857973i	−0.903311	−	0.428986i	$-0.858871\pi$
$191$		−	11.8574i		−	0.857973i	0.903311	−	0.428986i	$-0.141129\pi$
$192$	−1.12978	+	0.900969i	−0.0815348	+	0.0650218i
$193$	7.35713	−	15.2772i	0.529578	−	1.09968i	−0.448949	−	0.893558i	$-0.648201\pi$
$193$	7.35713	−	15.2772i	0.529578	−	1.09968i	0.978526	−	0.206122i	$-0.0660843\pi$
$194$	1.51199	−	1.89597i	0.108554	−	0.136123i
$195$	9.57433	+	7.63528i	0.685632	+	0.546774i
$196$	−2.75179	+	1.32519i	−0.196557	+	0.0946567i
$197$	−0.319942	−	1.40176i	−0.0227949	−	0.0998711i	0.962251	−	0.272164i	$-0.0877395\pi$
$197$	−0.319942	−	1.40176i	−0.0227949	−	0.0998711i	−0.985046	+	0.172293i	$0.944882\pi$
$198$	0.700975	−	3.07117i	0.0498161	−	0.218259i
$199$	−4.08909	−	1.96920i	−0.289868	−	0.139593i	0.283299	−	0.959032i	$-0.408571\pi$
$199$	−4.08909	−	1.96920i	−0.289868	−	0.139593i	−0.573167	+	0.819439i	$0.694285\pi$
$200$	−1.33570	−	2.77361i	−0.0944481	−	0.196123i
$201$	−17.6837	−	4.03618i	−1.24731	−	0.284690i
$202$	−7.23806			−0.509268
$203$	−10.4023	−	2.49384i	−0.730096	−	0.175034i
$204$	6.15524			0.430953
$205$	−12.3592	−	2.82091i	−0.863204	−	0.197021i
$206$	3.44575	+	7.15518i	0.240077	+	0.498525i
$207$	0.469284	+	0.225995i	0.0326175	+	0.0157078i
$208$	1.36039	−	5.96024i	0.0943258	−	0.413268i
$209$	−1.66706	−	7.30386i	−0.115313	−	0.505219i
$210$	3.58491	−	1.72640i	0.247382	−	0.119133i
$211$	−8.19766	−	6.53742i	−0.564350	−	0.450054i	0.299290	−	0.954162i	$-0.403250\pi$
$211$	−8.19766	−	6.53742i	−0.564350	−	0.450054i	−0.863641	+	0.504108i	$0.831821\pi$
$212$	6.50098	−	8.15197i	0.446489	−	0.559880i
$213$	2.68276	−	5.57081i	0.183820	−	0.381706i
$214$	−10.2569	+	8.17962i	−0.701149	+	0.559147i
$215$		−	15.3293i		−	1.04545i
$216$	−3.52446	−	4.41953i	−0.239809	−	0.300711i
$217$	11.6878	−	2.66766i	0.793417	−	0.181092i
$218$	−5.10592	+	1.16539i	−0.345817	+	0.0789304i
$219$	6.29038	+	7.88789i	0.425065	+	0.533014i
$220$		−	4.78884i		−	0.322863i
$221$	−20.3596	+	16.2362i	−1.36953	+	1.09217i
$222$	−1.70177	+	3.53376i	−0.114215	+	0.237170i
$223$	−13.5812	+	17.0303i	−0.909463	+	1.14043i	0.0801653	+	0.996782i	$0.474455\pi$
$223$	−13.5812	+	17.0303i	−0.909463	+	1.14043i	−0.989629	+	0.143649i	$0.954116\pi$
$224$	−1.55302	−	1.23849i	−0.103766	−	0.0827503i
$225$	2.52912	−	1.21796i	0.168608	−	0.0811974i
$226$	−0.0309135	−	0.135441i	−0.00205633	−	0.00900939i
$227$	−4.25726	+	18.6523i	−0.282564	+	1.23800i	0.611928	+	0.790913i	$0.290394\pi$
$227$	−4.25726	+	18.6523i	−0.282564	+	1.23800i	−0.894493	+	0.447082i	$0.852463\pi$
$228$	−2.82334	−	1.35965i	−0.186981	−	0.0900451i
$229$	−11.1057	−	23.0613i	−0.733886	−	1.52393i	−0.847728	−	0.530432i	$-0.822030\pi$
$229$	−11.1057	−	23.0613i	−0.733886	−	1.52393i	0.113841	−	0.993499i	$-0.463684\pi$
$230$	0.771964	+	0.176196i	0.0509018	+	0.0116180i
$231$	−9.91633			−0.652447
$232$	1.14102	+	5.26290i	0.0749113	+	0.345526i
$233$	−27.0319			−1.77092			−0.885461	−	0.464714i	$-0.846157\pi$
$233$	−27.0319			−1.77092			−0.885461	+	0.464714i	$0.846157\pi$
$234$	5.43487	+	1.24047i	0.355289	+	0.0810923i
$235$	−2.99870	−	6.22687i	−0.195614	−	0.406196i
$236$	8.12168	+	3.91119i	0.528676	+	0.254597i
$237$	3.73921	−	16.3826i	0.242888	−	1.06416i
$238$	1.88278	+	8.24900i	0.122043	+	0.534703i
$239$	−23.4837	+	11.3092i	−1.51904	+	0.731530i	−0.992909	−	0.118876i	$-0.962071\pi$
$239$	−23.4837	+	11.3092i	−1.51904	+	0.731530i	−0.526128	+	0.850405i	$0.676357\pi$
$240$	−1.56609	−	1.24892i	−0.101091	−	0.0806172i
$241$	11.7956	−	14.7912i	0.759820	−	0.952784i	−0.240018	−	0.970768i	$-0.577153\pi$
$241$	11.7956	−	14.7912i	0.759820	−	0.952784i	0.999838	+	0.0179841i	$0.00572484\pi$
$242$	−0.405570	+	0.842175i	−0.0260710	+	0.0541370i
$243$	7.12055	−	5.67845i	0.456783	−	0.364273i
$244$			9.59621i			0.614335i
$245$	−2.63973	−	3.31011i	−0.168646	−	0.211475i
$246$	12.8839	−	2.94067i	0.821447	−	0.187490i
$247$	12.9252	−	2.95009i	0.822411	−	0.187710i
$248$	−3.76291	−	4.71854i	−0.238945	−	0.299628i
$249$			15.6571i			0.992227i
$250$	8.75520	−	6.98204i	0.553727	−	0.441583i
$251$	10.0957	−	20.9640i	0.637236	−	1.32323i	−0.292944	−	0.956129i	$-0.594635\pi$
$251$	10.0957	−	20.9640i	0.637236	−	1.32323i	0.930180	−	0.367104i	$-0.119651\pi$
$252$	1.12932	−	1.41613i	0.0711408	−	0.0892077i
$253$	−1.54284	−	1.23037i	−0.0969975	−	0.0773529i
$254$	−5.84858	+	2.81653i	−0.366972	+	0.176725i
$255$	1.89863	+	8.31843i	0.118897	+	0.520920i
$256$	−0.222521	+	0.974928i	−0.0139076	+	0.0609330i
$257$	10.3369	+	4.97797i	0.644796	+	0.310517i	0.727552	−	0.686053i	$-0.240658\pi$
$257$	10.3369	+	4.97797i	0.644796	+	0.310517i	−0.0827562	+	0.996570i	$0.526372\pi$
$258$	6.93349	+	14.3975i	0.431660	+	0.896352i
$259$	−5.25634	−	1.19972i	−0.326613	−	0.0745472i
$260$	8.47452			0.525567
$261$	−4.79899	+	1.04044i	−0.297050	+	0.0644016i
$262$	2.25044			0.139033
$263$	21.0789	+	4.81113i	1.29978	+	0.296667i	0.815761	−	0.578389i	$-0.196318\pi$
$263$	21.0789	+	4.81113i	1.29978	+	0.296667i	0.484022	+	0.875056i	$0.339176\pi$
$264$	2.16601	+	4.49776i	0.133309	+	0.276818i
$265$	13.0222	+	6.27114i	0.799945	+	0.385233i
$266$	0.958537	−	4.19962i	0.0587717	−	0.257495i
$267$	−0.916945	−	4.01740i	−0.0561161	−	0.245861i
$268$	−11.3091	+	5.44619i	−0.690815	+	0.332679i
$269$	−3.55799	−	2.83740i	−0.216934	−	0.172999i	0.508993	−	0.860771i	$-0.330018\pi$
$269$	−3.55799	−	2.83740i	−0.216934	−	0.172999i	−0.725928	+	0.687771i	$0.758589\pi$
$270$	4.88558	−	6.12632i	0.297327	−	0.372836i
$271$	−3.48439	+	7.23542i	−0.211662	+	0.439520i	−0.979587	−	0.201019i	$-0.935575\pi$
$271$	−3.48439	+	7.23542i	−0.211662	+	0.439520i	0.767926	+	0.640539i	$0.221289\pi$
$272$	3.33026	−	2.65579i	0.201926	−	0.161031i
$273$		−	17.5483i		−	1.06207i
$274$	4.71502	+	5.91244i	0.284845	+	0.357184i
$275$	−10.3685	+	2.36653i	−0.625241	+	0.142707i
$276$	−0.804737	+	0.183676i	−0.0484395	+	0.0110560i
$277$	17.7525	+	22.2609i	1.06664	+	1.33753i	0.938310	+	0.345795i	$0.112391\pi$
$277$	17.7525	+	22.2609i	1.06664	+	1.33753i	0.128332	+	0.991731i	$0.459038\pi$
$278$			6.23282i			0.373820i
$279$	4.30262	−	3.43123i	0.257591	−	0.205422i
$280$	1.19471	−	2.48083i	0.0713974	−	0.148258i
$281$	12.4526	−	15.6151i	0.742862	−	0.931520i	−0.256525	−	0.966538i	$-0.582577\pi$
$281$	12.4526	−	15.6151i	0.742862	−	0.931520i	0.999387	+	0.0350182i	$0.0111489\pi$
$282$	5.63287	+	4.49206i	0.335433	+	0.267499i
$283$	3.85838	−	1.85810i	0.229357	−	0.110453i	−0.315676	−	0.948867i	$-0.602231\pi$
$283$	3.85838	−	1.85810i	0.229357	−	0.110453i	0.545033	+	0.838414i	$0.316517\pi$
$284$	−0.952137	−	4.17158i	−0.0564989	−	0.247538i
$285$	0.966604	−	4.23497i	0.0572567	−	0.250858i
$286$	−19.0286	−	9.16371i	−1.12519	−	0.541861i
$287$	7.88192	+	16.3670i	0.465255	+	0.966112i
$288$	−0.888992	−	0.202907i	−0.0523844	−	0.0119564i
$289$	−1.14384			−0.0672846
$290$	−6.76053	+	3.16539i	−0.396992	+	0.185878i
$291$	−3.50429			−0.205425
$292$	6.80675	+	1.55360i	0.398335	+	0.0909174i
$293$	−1.32028	−	2.74160i	−0.0771318	−	0.160166i	0.858837	−	0.512249i	$-0.171188\pi$
$293$	−1.32028	−	2.74160i	−0.0771318	−	0.160166i	−0.935969	+	0.352083i	$0.885473\pi$
$294$	3.97646	+	1.91496i	0.231912	+	0.111683i
$295$	−2.78055	+	12.1824i	−0.161890	+	0.709286i
$296$	0.603973	+	2.64618i	0.0351052	+	0.153806i
$297$	−17.5946	+	8.47311i	−1.02094	+	0.491660i
$298$	0.566937	+	0.452117i	0.0328418	+	0.0261904i
$299$	2.17732	−	2.73027i	0.125917	−	0.157896i
$300$	−1.93014	+	4.00798i	−0.111437	+	0.231401i
$301$	−17.1742	+	13.6959i	−0.989902	+	0.789420i
$302$		−	9.36422i		−	0.538850i
$303$	6.52127	+	8.17741i	0.374637	+	0.469780i
$304$	−2.11420	+	0.482552i	−0.121258	+	0.0276763i
$305$	−12.9687	+	2.96002i	−0.742585	+	0.169490i
$306$	2.42169	+	3.03671i	0.138439	+	0.173597i
$307$		−	23.6143i		−	1.34774i	−0.738850	−	0.673870i	$-0.764631\pi$
$307$		−	23.6143i		−	1.34774i	0.738850	−	0.673870i	$-0.235369\pi$
$308$	−5.36518	+	4.27858i	−0.305709	+	0.243795i
$309$	4.97926	−	10.3395i	0.283260	−	0.588195i
$310$	5.21612	−	6.54081i	0.296256	−	0.371493i
$311$	10.8163	+	8.62575i	0.613339	+	0.489121i	0.880193	−	0.474615i	$-0.157413\pi$
$311$	10.8163	+	8.62575i	0.613339	+	0.489121i	−0.266854	+	0.963737i	$0.585984\pi$
$312$	−7.95942	+	3.83306i	−0.450614	+	0.217004i
$313$	1.91326	+	8.38254i	0.108144	+	0.473809i	0.999778	+	0.0210534i	$0.00670200\pi$
$313$	1.91326	+	8.38254i	0.108144	+	0.473809i	−0.891634	+	0.452756i	$0.850441\pi$
$314$	2.63074	−	11.5260i	0.148461	−	0.650452i
$315$	2.26216	+	1.08940i	0.127458	+	0.0613806i
$316$	−5.04548	−	10.4770i	−0.283830	−	0.589380i
$317$	−12.3647	−	2.82217i	−0.694473	−	0.158509i	−0.139308	−	0.990249i	$-0.544488\pi$
$317$	−12.3647	−	2.82217i	−0.694473	−	0.158509i	−0.555165	+	0.831740i	$0.687345\pi$
$318$	−15.0671			−0.844922
$319$	18.6029	+	0.202779i	1.04156	+	0.0113535i
$320$	−1.38619			−0.0774905
$321$	18.4823	+	4.21847i	1.03158	+	0.235452i
$322$	−0.492310	−	1.02229i	−0.0274354	−	0.0569701i
$323$	8.32239	+	4.00785i	0.463070	+	0.223003i
$324$	−1.20895	+	5.29674i	−0.0671637	+	0.294264i
$325$	−4.18791	−	18.3484i	−0.232303	−	1.01779i
$326$	−12.2181	+	5.88391i	−0.676696	+	0.325879i
$327$	5.91691	+	4.71858i	0.327206	+	0.260938i
$328$	5.70195	−	7.15002i	0.314838	−	0.394794i
$329$	−4.29708	+	8.92299i	−0.236906	+	0.491940i
$330$	−5.41033	+	4.31459i	−0.297829	+	0.237511i
$331$		−	5.21791i		−	0.286802i	−0.989665	−	0.143401i	$-0.954196\pi$
$331$		−	5.21791i		−	0.286802i	0.989665	−	0.143401i	$-0.0458039\pi$
$332$	6.75553	+	8.47117i	0.370758	+	0.464916i
$333$	−2.41293	+	0.550735i	−0.132228	+	0.0301801i
$334$	4.52643	−	1.03313i	0.247675	−	0.0565302i
$335$	−10.8486	−	13.6037i	−0.592721	−	0.743248i
$336$			2.87041i			0.156594i
$337$	2.88315	−	2.29923i	0.157055	−	0.125247i	−0.541809	−	0.840501i	$-0.682261\pi$
$337$	2.88315	−	2.29923i	0.157055	−	0.125247i	0.698864	+	0.715254i	$0.253689\pi$
$338$	10.5760	−	21.9612i	0.575257	−	1.19453i
$339$	−0.125166	+	0.156953i	−0.00679809	+	0.00852454i
$340$	4.61638	+	3.68144i	0.250358	+	0.199654i
$341$	−18.7850	+	9.04638i	−1.01726	+	0.489889i
$342$	−0.440017	−	1.92784i	−0.0237934	−	0.104246i
$343$	−4.44411	+	19.4709i	−0.239960	+	1.05133i
$344$	9.96340	+	4.79812i	0.537191	+	0.258697i
$345$	−0.496453	−	1.03090i	−0.0267281	−	0.0555016i
$346$	−9.25716	−	2.11289i	−0.497668	−	0.113589i
$347$	3.61233			0.193920			0.0969599	−	0.995288i	$-0.469088\pi$
$347$	3.61233			0.193920			0.0969599	+	0.995288i	$0.469088\pi$
$348$	4.91789	−	6.03080i	0.263627	−	0.323285i
$349$	14.2824			0.764521			0.382260	−	0.924055i	$-0.375146\pi$
$349$	14.2824			0.764521			0.382260	+	0.924055i	$0.375146\pi$
$350$	−5.96172	−	1.36072i	−0.318667	−	0.0727337i
$351$	−14.9944	−	31.1361i	−0.800339	−	1.66192i
$352$	3.11255	+	1.49893i	0.165899	+	0.0798930i
$353$	0.271865	−	1.19112i	0.0144699	−	0.0633968i	−0.967178	−	0.254102i	$-0.918220\pi$
$353$	0.271865	−	1.19112i	0.0144699	−	0.0633968i	0.981647	+	0.190705i	$0.0610774\pi$
$354$	−2.89859	−	12.6996i	−0.154059	−	0.674974i
$355$	5.34394	−	2.57351i	0.283627	−	0.136588i
$356$	−2.22949	−	1.77796i	−0.118163	−	0.0942316i
$357$	7.62322	−	9.55922i	0.403464	−	0.505927i
$358$	3.26804	−	6.78616i	0.172722	−	0.358660i
$359$	−24.3681	+	19.4329i	−1.28610	+	1.02563i	−0.288420	+	0.957504i	$0.593130\pi$
$359$	−24.3681	+	19.4329i	−1.28610	+	1.02563i	−0.997677	+	0.0681245i	$0.978299\pi$
$360$		−	1.26401i		−	0.0666189i
$361$	8.91422	+	11.1781i	0.469170	+	0.588320i
$362$	−18.0165	+	4.11214i	−0.946925	+	0.216129i
$363$	1.31688	−	0.300569i	0.0691181	−	0.0157758i
$364$	−7.57155	−	9.49443i	−0.396857	−	0.497643i
$365$			9.67812i			0.506576i
$366$	10.8416	−	8.64589i	0.566700	−	0.451928i
$367$	2.09608	−	4.35256i	0.109415	−	0.227202i	−0.839071	−	0.544022i	$-0.816901\pi$
$367$	2.09608	−	4.35256i	0.109415	−	0.227202i	0.948486	+	0.316820i	$0.102615\pi$
$368$	−0.356148	+	0.446595i	−0.0185655	+	0.0232804i
$369$	6.51978	+	5.19935i	0.339406	+	0.270667i
$370$	−3.38984	+	1.63246i	−0.176230	+	0.0848677i
$371$	−4.60877	−	20.1923i	−0.239275	−	1.04833i
$372$	−1.94065	+	8.50252i	−0.100618	+	0.440835i
$373$	0.843840	+	0.406372i	0.0436924	+	0.0210411i	0.455602	−	0.890183i	$-0.349424\pi$
$373$	0.843840	+	0.406372i	0.0436924	+	0.0210411i	−0.411910	+	0.911225i	$0.635138\pi$
$374$	−6.38476	−	13.2581i	−0.330148	−	0.685559i
$375$	−15.7763	−	3.60084i	−0.814686	−	0.185947i
$376$	4.98582			0.257124
$377$	−0.358846	+	32.9204i	−0.0184815	+	1.69548i
$378$	−11.2286			−0.577539
$379$	1.40960	+	0.321733i	0.0724065	+	0.0165263i	0.258571	−	0.965992i	$-0.416749\pi$
$379$	1.40960	+	0.321733i	0.0724065	+	0.0165263i	−0.186164	+	0.982519i	$0.559606\pi$
$380$	−1.30428	−	2.70836i	−0.0669081	−	0.138936i
$381$	8.45144	+	4.07000i	0.432980	+	0.208512i
$382$	−2.63852	+	11.5601i	−0.134999	+	0.591468i
$383$	1.75701	+	7.69797i	0.0897791	+	0.393348i	0.999774	−	0.0212722i	$-0.00677165\pi$
$383$	1.75701	+	7.69797i	0.0897791	+	0.393348i	−0.909995	+	0.414620i	$0.863915\pi$
$384$	1.30194	−	0.626980i	0.0664392	−	0.0319954i
$385$	−7.43717	−	5.93094i	−0.379033	−	0.302269i
$386$	−10.5722	+	13.2571i	−0.538109	+	0.674768i
$387$	−4.37519	+	9.08517i	−0.222403	+	0.461825i
$388$	−1.89597	+	1.51199i	−0.0962535	+	0.0767596i
$389$		−	8.04652i		−	0.407975i	−0.978974	−	0.203987i	$-0.934610\pi$
$389$		−	8.04652i		−	0.407975i	0.978974	−	0.203987i	$-0.0653901\pi$
$390$	−7.63528	−	9.57433i	−0.386627	−	0.484815i
$391$	2.37213	−	0.541423i	0.119964	−	0.0273809i
$392$	2.97768	−	0.679637i	0.150396	−	0.0343268i
$393$	−2.02758	−	2.54250i	−0.102278	−	0.128252i
$394$			1.43781i			0.0724356i
$395$	12.6028	−	10.0504i	0.634114	−	0.505689i
$396$	−1.36680	+	2.83819i	−0.0686843	+	0.142624i
$397$	−1.60063	+	2.00712i	−0.0803332	+	0.100735i	−0.820374	−	0.571827i	$-0.806235\pi$
$397$	−1.60063	+	2.00712i	−0.0803332	+	0.100735i	0.740041	+	0.672562i	$0.234806\pi$
$398$	3.54838	+	2.82974i	0.177864	+	0.141842i
$399$	−5.60826	+	2.70080i	−0.280764	+	0.135209i
$400$	0.685024	+	3.00129i	0.0342512	+	0.150064i
$401$	1.69714	−	7.43566i	0.0847512	−	0.371319i	−0.914711	−	0.404108i	$-0.867582\pi$
$401$	1.69714	−	7.43566i	0.0847512	−	0.371319i	0.999462	+	0.0327891i	$0.0104390\pi$
$402$	16.3422	+	7.86997i	0.815073	+	0.392519i
$403$	−16.0088	−	33.2427i	−0.797457	−	1.65594i
$404$	7.05659	+	1.61062i	0.351078	+	0.0801314i
$405$	−7.53113			−0.374225
$406$	9.58653	+	4.74604i	0.475771	+	0.235542i
$407$	9.37676			0.464789
$408$	−6.00092	−	1.36967i	−0.297090	−	0.0678088i
$409$	0.943573	+	1.95935i	0.0466567	+	0.0968836i	0.922994	−	0.384814i	$-0.125735\pi$
$409$	0.943573	+	1.95935i	0.0466567	+	0.0968836i	−0.876337	+	0.481698i	$0.840020\pi$
$410$	11.4216	+	5.50036i	0.564074	+	0.271644i
$411$	2.43167	−	10.6539i	0.119946	−	0.525516i
$412$	−1.76718	−	7.74253i	−0.0870629	−	0.381447i
$413$	16.1328	−	7.76915i	0.793844	−	0.382295i
$414$	−0.407230	−	0.324755i	−0.0200142	−	0.0159608i
$415$	−9.36447	+	11.7427i	−0.459684	+	0.576425i
$416$	−2.65256	+	5.50809i	−0.130052	+	0.270056i
$417$	7.04171	−	5.61558i	0.344834	−	0.274996i
$418$			7.49170i			0.366431i
$419$	6.88565	+	8.63433i	0.336386	+	0.421815i	0.921040	−	0.389468i	$-0.127341\pi$
$419$	6.88565	+	8.63433i	0.336386	+	0.421815i	−0.584654	+	0.811283i	$0.698770\pi$
$420$	−3.87919	+	0.885399i	−0.189285	+	0.0432031i
$421$	3.56740	−	0.814236i	0.173864	−	0.0396834i	−0.134702	−	0.990886i	$-0.543008\pi$
$421$	3.56740	−	0.814236i	0.173864	−	0.0396834i	0.308567	+	0.951203i	$0.400151\pi$
$422$	6.53742	+	8.19766i	0.318237	+	0.399056i
$423$			4.54634i			0.221050i
$424$	−8.15197	+	6.50098i	−0.395895	+	0.315716i
$425$	5.68948	−	11.8143i	0.275980	−	0.573079i
$426$	−3.85512	+	4.83417i	−0.186781	+	0.234216i
$427$	14.9031	+	11.8848i	0.721213	+	0.575148i
$428$	11.8199	−	5.69216i	0.571336	−	0.275141i
$429$	6.79124	+	29.7544i	0.327884	+	1.43655i
$430$	−3.41108	+	14.9449i	−0.164497	+	0.720709i
$431$	−5.73298	−	2.76086i	−0.276148	−	0.132986i	0.290684	−	0.956819i	$-0.406117\pi$
$431$	−5.73298	−	2.76086i	−0.276148	−	0.132986i	−0.566832	+	0.823833i	$0.691831\pi$
$432$	2.45265	+	5.09299i	0.118003	+	0.245037i
$433$	−21.3175	−	4.86557i	−1.02445	−	0.233824i	−0.322893	−	0.946436i	$-0.604655\pi$
$433$	−21.3175	−	4.86557i	−1.02445	−	0.233824i	−0.701559	+	0.712611i	$0.747512\pi$
$434$	−11.9883			−0.575459
$435$	9.66721	+	4.78598i	0.463507	+	0.229470i
$436$	5.23723			0.250818
$437$	−1.20767	−	0.275642i	−0.0577705	−	0.0131857i
$438$	−4.37745	−	9.08987i	−0.209163	−	0.434331i
$439$	18.6130	+	8.96353i	0.888349	+	0.427806i	0.821667	−	0.569968i	$-0.193044\pi$
$439$	18.6130	+	8.96353i	0.888349	+	0.427806i	0.0666819	+	0.997774i	$0.478759\pi$
$440$	−1.06562	+	4.66877i	−0.0508013	+	0.222575i
$441$	0.619730	+	2.71521i	0.0295109	+	0.129296i
$442$	23.4620	−	11.2987i	1.11598	−	0.537425i
$443$	2.00330	+	1.59758i	0.0951798	+	0.0759034i	0.669924	−	0.742430i	$-0.266327\pi$
$443$	2.00330	+	1.59758i	0.0951798	+	0.0759034i	−0.574744	+	0.818333i	$0.694898\pi$
$444$	2.44544	−	3.06648i	0.116055	−	0.145529i
$445$	1.71510	−	3.56144i	0.0813035	−	0.168828i
$446$	17.0303	−	13.5812i	0.806406	−	0.643088i
$447$		−	1.04786i		−	0.0495619i
$448$	1.23849	+	1.55302i	0.0585133	+	0.0733734i
$449$	39.7431	−	9.07111i	1.87559	−	0.428092i	0.876971	−	0.480544i	$-0.159561\pi$
$449$	39.7431	−	9.07111i	1.87559	−	0.428092i	0.998623	+	0.0524518i	$0.0167036\pi$
$450$	−2.73673	+	0.624642i	−0.129011	+	0.0294459i
$451$	−19.6984	−	24.7010i	−0.927560	−	1.16312i
$452$			0.138924i			0.00653443i
$453$	−10.5795	+	8.43687i	−0.497068	+	0.396399i
$454$	8.30105	−	17.2373i	0.389587	−	0.808987i
$455$	10.4956	−	13.1611i	0.492043	−	0.617002i
$456$	2.45001	+	1.95381i	0.114732	+	0.0914958i
$457$	−22.7103	+	10.9367i	−1.06234	+	0.511598i	−0.881632	−	0.471938i	$-0.843555\pi$
$457$	−22.7103	+	10.9367i	−1.06234	+	0.511598i	−0.180713	+	0.983536i	$0.557841\pi$
$458$	5.69566	+	24.9543i	0.266141	+	1.16604i
$459$	5.35795	−	23.4747i	0.250088	−	1.09571i
$460$	−0.713402	−	0.343556i	−0.0332625	−	0.0160184i
$461$	17.8174	+	36.9982i	0.829838	+	1.72318i	0.678379	+	0.734712i	$0.262683\pi$
$461$	17.8174	+	36.9982i	0.829838	+	1.72318i	0.151459	+	0.988464i	$0.451603\pi$
$462$	9.66771	+	2.20659i	0.449783	+	0.102660i
$463$	−33.1170			−1.53908			−0.769539	−	0.638600i	$-0.779514\pi$
$463$	−33.1170			−1.53908			−0.769539	+	0.638600i	$0.779514\pi$
$464$	0.0586971	−	5.38484i	0.00272495	−	0.249985i
$465$	−12.0892			−0.560625
$466$	26.3542	+	6.01517i	1.22083	+	0.278648i
$467$	−6.56154	−	13.6252i	−0.303632	−	0.630498i	0.692200	−	0.721706i	$-0.256642\pi$
$467$	−6.56154	−	13.6252i	−0.303632	−	0.630498i	−0.995832	+	0.0912076i	$0.970927\pi$
$468$	−5.02258	−	2.41874i	−0.232169	−	0.111807i
$469$	−5.54823	+	24.3084i	−0.256193	+	1.12246i
$470$	1.53791	+	6.73802i	0.0709385	+	0.310802i
$471$	−15.3921	+	7.41244i	−0.709230	+	0.341547i
$472$	−7.04773	−	5.62038i	−0.324398	−	0.258699i
$473$	23.8196	−	29.8688i	1.09522	−	1.37337i
$474$	−7.29093	+	15.1398i	−0.334883	+	0.695393i
$475$	−5.21941	+	4.16234i	−0.239483	+	0.190981i
$476$		−	8.46114i		−	0.387816i
$477$	−5.92795	−	7.43341i	−0.271422	−	0.340352i
$478$	25.4115	−	5.80001i	1.16229	−	0.265286i
$479$	−23.9257	+	5.46090i	−1.09320	+	0.249515i	−0.730856	−	0.682532i	$-0.760879\pi$
$479$	−23.9257	+	5.46090i	−1.09320	+	0.249515i	−0.362339	+	0.932046i	$0.618022\pi$
$480$	1.24892	+	1.56609i	0.0570050	+	0.0714820i
$481$			16.5935i			0.756598i
$482$	−14.7912	+	11.7956i	−0.673720	+	0.537274i
$483$	−0.711408	+	1.47725i	−0.0323702	+	0.0672174i
$484$	0.582803	−	0.730812i	0.0264910	−	0.0332187i
$485$	−2.62819	−	2.09591i	−0.119340	−	0.0951703i
$486$	−8.20560	+	3.95161i	−0.372213	+	0.179249i
$487$	−6.32313	−	27.7034i	−0.286528	−	1.25536i	−0.889254	−	0.457414i	$-0.848776\pi$
$487$	−6.32313	−	27.7034i	−0.286528	−	1.25536i	0.602726	−	0.797948i	$-0.294081\pi$
$488$	2.13536	−	9.35562i	0.0966631	−	0.423509i
$489$	17.6556	+	8.50249i	0.798414	+	0.384496i
$490$	1.83697	+	3.81452i	0.0829860	+	0.172322i
$491$	21.8879	+	4.99578i	0.987789	+	0.225456i	0.685748	−	0.727839i	$-0.259475\pi$
$491$	21.8879	+	4.99578i	0.987789	+	0.225456i	0.302040	+	0.953295i	$0.402332\pi$
$492$	−13.2152			−0.595789
$493$	−14.4965	+	17.7770i	−0.652890	+	0.800637i
$494$	−13.2576			−0.596488
$495$	−4.25724	−	0.971687i	−0.191349	−	0.0436741i
$496$	2.61859	+	5.43757i	0.117578	+	0.244154i
$497$	−7.65777	−	3.68779i	−0.343498	−	0.165420i
$498$	3.48403	−	15.2645i	0.156123	−	0.684020i
$499$	−4.36675	−	19.1320i	−0.195482	−	0.856464i	−0.973585	−	0.228327i	$-0.926675\pi$
$499$	−4.36675	−	19.1320i	−0.195482	−	0.856464i	0.778102	−	0.628138i	$-0.216183\pi$
$500$	−10.0893	+	4.85877i	−0.451209	+	0.217291i
$501$	−5.24538	−	4.18305i	−0.234346	−	0.186885i
$502$	−14.5075	+	18.1918i	−0.647502	+	0.811942i
$503$	2.80317	−	5.82085i	0.124987	−	0.259539i	−0.829081	−	0.559129i	$-0.811136\pi$
$503$	2.80317	−	5.82085i	0.124987	−	0.259539i	0.954068	+	0.299590i	$0.0968499\pi$
$504$	−1.41613	+	1.12932i	−0.0630794	+	0.0503041i
$505$			10.0334i			0.446478i
$506$	1.23037	+	1.54284i	0.0546968	+	0.0685876i
$507$	−34.3400	+	7.83787i	−1.52509	+	0.348092i
$508$	6.32868	−	1.44448i	0.280790	−	0.0640884i
$509$	−20.2260	−	25.3626i	−0.896501	−	1.12418i	−0.991681	−	0.128717i	$-0.958914\pi$
$509$	−20.2260	−	25.3626i	−0.896501	−	1.12418i	0.0951802	−	0.995460i	$-0.469657\pi$
$510$		−	8.53235i		−	0.377819i
$511$	10.8429	−	8.64691i	0.479661	−	0.382517i
$512$	0.433884	−	0.900969i	0.0191751	−	0.0398176i
$513$	−7.64304	+	9.58407i	−0.337448	+	0.423147i
$514$	−8.96999	−	7.15333i	−0.395649	−	0.315520i
$515$	9.91846	−	4.77648i	0.437059	−	0.210477i
$516$	−3.55590	−	15.5794i	−0.156540	−	0.685845i
$517$	3.83278	−	16.7925i	0.168565	−	0.738533i
$518$	4.85758	+	2.33929i	0.213430	+	0.102782i
$519$	5.95332	+	12.3622i	0.261322	+	0.542640i
$520$	−8.26204	−	1.88576i	−0.362315	−	0.0826959i
$521$	−22.9436			−1.00518			−0.502588	−	0.864526i	$-0.667619\pi$
$521$	−22.9436			−1.00518			−0.502588	+	0.864526i	$0.667619\pi$
$522$	4.91019	+	0.0535232i	0.214913	+	0.00234265i
$523$	−36.0578			−1.57670			−0.788349	−	0.615228i	$-0.789064\pi$
$523$	−36.0578			−1.57670			−0.788349	+	0.615228i	$0.789064\pi$
$524$	−2.19402	−	0.500771i	−0.0958462	−	0.0218763i
$525$	3.83401	+	7.96140i	0.167330	+	0.347464i
$526$	−19.4799	−	9.38101i	−0.849362	−	0.409031i
$527$	5.72045	−	25.0629i	0.249187	−	1.09176i
$528$	−1.11086	−	4.86698i	−0.0483438	−	0.211808i
$529$	20.4283	−	9.83775i	0.888187	−	0.427728i
$530$	−11.3002	−	9.01162i	−0.490850	−	0.391440i
$531$	5.12496	−	6.42650i	0.222404	−	0.278886i
$532$	−1.86901	+	3.88104i	−0.0810318	+	0.168264i
$533$	43.7118	−	34.8590i	1.89337	−	1.50991i
$534$			4.12071i			0.178321i
$535$	11.3385	+	14.2181i	0.490207	+	0.614701i
$536$	12.2375	−	2.79312i	0.528578	−	0.120645i
$537$	−10.6113	+	2.42195i	−0.457910	+	0.104515i
$538$	2.83740	+	3.55799i	0.122329	+	0.153396i
$539$		−	10.5515i		−	0.454484i
$540$	−6.12632	+	4.88558i	−0.263635	+	0.210242i
$541$	−5.76003	+	11.9608i	−0.247643	+	0.514236i	−0.987323	−	0.158723i	$-0.949262\pi$
$541$	−5.76003	+	11.9608i	−0.247643	+	0.514236i	0.739680	+	0.672958i	$0.234977\pi$
$542$	5.00707	−	6.27866i	0.215072	−	0.269692i
$543$	20.8781	+	16.6497i	0.895965	+	0.714508i
$544$	−3.83773	+	1.84815i	−0.164541	+	0.0792389i
$545$	1.61546	+	7.07779i	0.0691987	+	0.303179i
$546$	−3.90487	+	17.1084i	−0.167113	+	0.732170i
$547$	−23.6479	−	11.3882i	−1.01111	−	0.486926i	−0.146417	−	0.989223i	$-0.546774\pi$
$547$	−23.6479	−	11.3882i	−1.01111	−	0.486926i	−0.864695	+	0.502297i	$0.832489\pi$
$548$	−3.28116	−	6.81340i	−0.140164	−	0.291054i
$549$	8.53096	+	1.94714i	0.364092	+	0.0831017i
$550$	10.6351			0.453482
$551$	10.5762	−	4.95196i	0.450562	−	0.210961i
$552$	0.825432			0.0351327
$553$	−22.5199	−	5.14001i	−0.957642	−	0.218576i
$554$	−12.3539	−	25.6530i	−0.524865	−	1.08989i
$555$	4.89847	+	2.35898i	0.207928	+	0.100133i
$556$	1.38693	−	6.07655i	0.0588191	−	0.257703i
$557$	1.55348	+	6.80622i	0.0658229	+	0.288389i	0.997117	−	0.0758791i	$-0.0241763\pi$
$557$	1.55348	+	6.80622i	0.0658229	+	0.288389i	−0.931294	+	0.364268i	$0.881319\pi$
$558$	−4.95827	+	2.38778i	−0.209900	+	0.101083i
$559$	52.8570	+	42.1521i	2.23561	+	1.78284i
$560$	−1.71679	+	2.15279i	−0.0725476	+	0.0909718i
$561$	−9.22624	+	19.1585i	−0.389532	+	0.808872i
$562$	−15.6151	+	12.4526i	−0.658684	+	0.525283i
$563$			23.7025i			0.998942i	0.866331	+	0.499471i	$0.166472\pi$
$563$			23.7025i			0.998942i	−0.866331	+	0.499471i	$0.833528\pi$
$564$	−4.49206	−	5.63287i	−0.189150	−	0.237187i
$565$	−0.187747	+	0.0428521i	−0.00789858	+	0.00180280i
$566$	−4.17511	+	0.952942i	−0.175493	+	0.0400551i
$567$	6.72868	+	8.43750i	0.282578	+	0.354342i
$568$			4.27886i			0.179537i
$569$	3.47276	−	2.76943i	0.145586	−	0.116101i	−0.547989	−	0.836486i	$-0.684606\pi$
$569$	3.47276	−	2.76943i	0.145586	−	0.116101i	0.693574	+	0.720385i	$0.256035\pi$
$570$	−1.88474	+	3.91370i	−0.0789430	+	0.163927i
$571$	−14.8581	+	18.6314i	−0.621791	+	0.779701i	−0.988595	−	0.150597i	$-0.951880\pi$
$571$	−14.8581	+	18.6314i	−0.621791	+	0.779701i	0.366805	+	0.930298i	$0.380452\pi$
$572$	16.5124	+	13.1682i	0.690419	+	0.550591i
$573$	15.4376	−	7.43437i	0.644916	−	0.310575i
$574$	−4.04231	−	17.7105i	−0.168723	−	0.739222i
$575$	−0.391297	+	1.71438i	−0.0163182	+	0.0714948i
$576$	0.821552	+	0.395639i	0.0342313	+	0.0164849i
$577$	−12.7689	−	26.5150i	−0.531578	−	1.10383i	−0.977922	−	0.208971i	$-0.932988\pi$
$577$	−12.7689	−	26.5150i	−0.531578	−	1.10383i	0.446344	−	0.894862i	$-0.352726\pi$
$578$	1.11516	+	0.254528i	0.0463845	+	0.0105870i
$579$	24.5028			1.01830
$580$	7.29539	−	1.58167i	0.302925	−	0.0656752i
$581$	21.5226			0.892907
$582$	3.41643	+	0.779777i	0.141615	+	0.0323228i
$583$	15.6289	+	32.4538i	0.647285	+	1.34410i
$584$	−6.29038	−	3.02929i	−0.260298	−	0.125353i
$585$	1.71954	−	7.53378i	0.0710941	−	0.311483i
$586$	0.677119	+	2.96665i	0.0279715	+	0.122551i
$587$	−15.7028	+	7.56209i	−0.648125	+	0.312121i	−0.728909	−	0.684611i	$-0.759972\pi$
$587$	−15.7028	+	7.56209i	−0.648125	+	0.312121i	0.0807832	+	0.996732i	$0.474258\pi$
$588$	−3.45064	−	2.75179i	−0.142302	−	0.113482i
$589$	−8.16015	+	10.2325i	−0.336233	+	0.421623i
$590$	5.42167	−	11.2582i	0.223207	−	0.463493i
$591$	1.62440	−	1.29542i	0.0668190	−	0.0532864i
$592$		−	2.71423i		−	0.111554i
$593$	18.6471	+	23.3827i	0.765745	+	0.960214i	0.999928	−	0.0119783i	$-0.00381290\pi$
$593$	18.6471	+	23.3827i	0.765745	+	0.960214i	−0.234183	+	0.972193i	$0.575241\pi$
$594$	19.0389	−	4.34551i	0.781176	−	0.178298i
$595$	11.4347	−	2.60990i	0.468777	−	0.106995i
$596$	−0.452117	−	0.566937i	−0.0185194	−	0.0232226i
$597$		−	6.55839i		−	0.268417i
$598$	−2.73027	+	2.17732i	−0.111649	+	0.0890371i
$599$	−11.6209	+	24.1310i	−0.474817	+	0.985967i	0.516722	+	0.856153i	$0.327152\pi$
$599$	−11.6209	+	24.1310i	−0.474817	+	0.985967i	−0.991538	+	0.129814i	$0.958562\pi$
$600$	2.77361	−	3.47799i	0.113232	−	0.141988i
$601$	−20.1052	−	16.0333i	−0.820107	−	0.654013i	0.120801	−	0.992677i	$-0.461454\pi$
$601$	−20.1052	−	16.0333i	−0.820107	−	0.654013i	−0.940908	+	0.338663i	$0.890025\pi$
$602$	19.7912	−	9.53094i	0.806629	−	0.388452i
$603$	2.54692	+	11.1588i	0.103719	+	0.454421i
$604$	−2.08373	+	9.12944i	−0.0847860	+	0.371472i
$605$	1.16742	+	0.562198i	0.0474622	+	0.0228566i
$606$	−4.53812	−	9.42351i	−0.184349	−	0.382804i
$607$	−16.2163	−	3.70126i	−0.658198	−	0.150229i	−0.119639	−	0.992817i	$-0.538174\pi$
$607$	−16.2163	−	3.70126i	−0.658198	−	0.150229i	−0.538559	+	0.842588i	$0.681031\pi$
$608$	2.16857			0.0879472
$609$	−3.27519	−	15.1067i	−0.132717	−	0.612154i
$610$	13.3022			0.538590
$611$	29.7167	+	6.78263i	1.20221	+	0.274396i
$612$	−1.68525	−	3.49945i	−0.0681220	−	0.141457i
$613$	−0.722463	−	0.347920i	−0.0291800	−	0.0140524i	0.419237	−	0.907877i	$-0.362298\pi$
$613$	−0.722463	−	0.347920i	−0.0291800	−	0.0140524i	−0.448417	+	0.893825i	$0.648012\pi$
$614$	−5.25468	+	23.0223i	−0.212062	+	0.929103i
$615$	−4.07633	−	17.8596i	−0.164373	−	0.720167i
$616$	6.18273	−	2.97745i	0.249109	−	0.119965i
$617$	−4.56314	−	3.63899i	−0.183705	−	0.146500i	0.527319	−	0.849667i	$-0.323197\pi$
$617$	−4.56314	−	3.63899i	−0.183705	−	0.146500i	−0.711025	+	0.703167i	$0.751769\pi$
$618$	−7.15518	+	8.97231i	−0.287823	+	0.360919i
$619$	8.05404	−	16.7244i	0.323719	−	0.672210i	−0.674070	−	0.738668i	$-0.735455\pi$
$619$	8.05404	−	16.7244i	0.323719	−	0.672210i	0.997789	+	0.0664574i	$0.0211697\pi$
$620$	−6.54081	+	5.21612i	−0.262685	+	0.209485i
$621$			3.22897i			0.129574i
$622$	−8.62575	−	10.8163i	−0.345861	−	0.433696i
$623$	−5.52241	+	1.26045i	−0.221251	+	0.0504990i
$624$	8.61280	−	1.96582i	0.344788	−	0.0786956i
$625$	−0.0814774	−	0.102169i	−0.00325910	−	0.00408678i
$626$		−	8.59812i		−	0.343650i
$627$	8.46396	−	6.74979i	0.338018	−	0.269560i
$628$	−5.12957	+	10.6517i	−0.204692	+	0.425048i
$629$	−7.20842	+	9.03908i	−0.287419	+	0.360412i
$630$	−1.96303	−	1.56546i	−0.0782089	−	0.0623695i
$631$	23.0524	−	11.1015i	0.917702	−	0.441942i	0.0854517	−	0.996342i	$-0.472767\pi$
$631$	23.0524	−	11.1015i	0.917702	−	0.441942i	0.832250	+	0.554400i	$0.187052\pi$
$632$	2.58762	+	11.3371i	0.102930	+	0.450965i
$633$	3.37154	−	14.7717i	0.134007	−	0.587121i
$634$	11.4267	+	5.50283i	0.453814	+	0.218545i
$635$	3.90425	+	8.10726i	0.154935	+	0.321727i
$636$	14.6893	+	3.35275i	0.582471	+	0.132945i
$637$	18.6723			0.739823
$638$	−18.0913	−	4.33722i	−0.716242	−	0.171712i
$639$	−3.90170			−0.154349
$640$	1.35144	+	0.308457i	0.0534203	+	0.0121928i
$641$	7.41067	+	15.3884i	0.292704	+	0.607806i	0.994519	−	0.104553i	$-0.0333412\pi$
$641$	7.41067	+	15.3884i	0.292704	+	0.607806i	−0.701815	+	0.712359i	$0.747627\pi$
$642$	−17.0802	−	8.22541i	−0.674103	−	0.324631i
$643$	−6.59667	+	28.9019i	−0.260147	+	1.13978i	0.660945	+	0.750434i	$0.270156\pi$
$643$	−6.59667	+	28.9019i	−0.260147	+	1.13978i	−0.921092	+	0.389345i	$0.872702\pi$
$644$	0.252485	+	1.10621i	0.00994931	+	0.0435908i
$645$	19.9578	−	9.61115i	0.785836	−	0.378439i
$646$	−7.22190	−	5.75927i	−0.284142	−	0.226596i
$647$	3.63991	−	4.56430i	0.143099	−	0.179441i	−0.705117	−	0.709091i	$-0.749105\pi$
$647$	3.63991	−	4.56430i	0.143099	−	0.179441i	0.848216	+	0.529650i	$0.177677\pi$
$648$	2.35727	−	4.89493i	0.0926024	−	0.192291i
$649$	−24.3476	+	19.4165i	−0.955726	+	0.762166i
$650$			18.8203i			0.738192i
$651$	10.8011	+	13.5442i	0.423329	+	0.530838i
$652$	13.2210	−	3.01761i	0.517775	−	0.118179i
$653$	−3.28521	+	0.749829i	−0.128560	+	0.0293431i	−0.286317	−	0.958135i	$-0.592431\pi$
$653$	−3.28521	+	0.749829i	−0.128560	+	0.0293431i	0.157757	+	0.987478i	$0.449574\pi$
$654$	−4.71858	−	5.91691i	−0.184511	−	0.231370i
$655$		−	3.11955i		−	0.121891i
$656$	−7.15002	+	5.70195i	−0.279161	+	0.222624i
$657$	2.76227	−	5.73591i	0.107766	−	0.223779i
$658$	6.17490	−	7.74308i	0.240723	−	0.301857i
$659$	−31.0020	−	24.7233i	−1.20767	−	0.963082i	−0.207781	−	0.978175i	$-0.566624\pi$
$659$	−31.0020	−	24.7233i	−1.20767	−	0.963082i	−0.999886	+	0.0150934i	$0.995195\pi$
$660$	6.23477	−	3.00251i	0.242688	−	0.116872i
$661$	−4.35944	−	19.1000i	−0.169563	−	0.742902i	−0.986174	−	0.165714i	$-0.947007\pi$
$661$	−4.35944	−	19.1000i	−0.169563	−	0.742902i	0.816611	−	0.577188i	$-0.195850\pi$
$662$	−1.16109	+	5.08708i	−0.0451272	+	0.197715i
$663$	−33.9036	−	16.3271i	−1.31671	−	0.634093i
$664$	−4.70114	−	9.76203i	−0.182440	−	0.378840i
$665$	−5.82149	−	1.32872i	−0.225748	−	0.0515254i
$666$	2.47498			0.0959035
$667$	1.36480	−	2.75675i	0.0528452	−	0.106742i
$668$	−4.64283			−0.179637
$669$	−30.6875	−	7.00422i	−1.18645	−	0.270799i
$670$	7.54947	+	15.6766i	0.291661	+	0.605641i
$671$	−29.8687	−	14.3840i	−1.15307	−	0.555288i
$672$	0.638727	−	2.79845i	0.0246394	−	0.107952i
$673$	−7.16100	−	31.3744i	−0.276036	−	1.20939i	−0.902758	−	0.430150i	$-0.858461\pi$
$673$	−7.16100	−	31.3744i	−0.276036	−	1.20939i	0.626721	−	0.779243i	$-0.284396\pi$
$674$	−3.32249	+	1.60003i	−0.127977	+	0.0616307i
$675$	13.6054	+	10.8499i	0.523672	+	0.417614i
$676$	−15.1976	+	19.0572i	−0.584525	+	0.732971i
$677$	−5.20305	+	10.8043i	−0.199970	+	0.415241i	−0.976705	−	0.214586i	$-0.931160\pi$
$677$	−5.20305	+	10.8043i	−0.199970	+	0.415241i	0.776736	+	0.629827i	$0.216874\pi$
$678$	0.156953	−	0.125166i	0.00602776	−	0.00480698i
$679$			4.81708i			0.184862i
$680$	−3.68144	−	4.61638i	−0.141177	−	0.177030i
$681$	−26.9533	+	6.15192i	−1.03285	+	0.235742i
$682$	20.3270	−	4.63951i	0.778362	−	0.177656i
$683$	22.5294	+	28.2510i	0.862063	+	1.08099i	0.995942	+	0.0899953i	$0.0286852\pi$
$683$	22.5294	+	28.2510i	0.862063	+	1.08099i	−0.133879	+	0.990998i	$0.542743\pi$
$684$			1.97742i			0.0756085i
$685$	8.19579	−	6.53592i	0.313145	−	0.249725i
$686$	8.66538	−	17.9939i	0.330846	−	0.687008i
$687$	23.0613	−	28.9179i	0.879842	−	1.10329i
$688$	−8.64592	−	6.89489i	−0.329623	−	0.262865i
$689$	−57.4316	+	27.6576i	−2.18797	+	1.05367i
$690$	0.254610	+	1.11552i	0.00969285	+	0.0424671i
$691$	−1.12128	+	4.91265i	−0.0426555	+	0.186886i	−0.991767	−	0.128053i	$-0.959127\pi$
$691$	−1.12128	+	4.91265i	−0.0426555	+	0.186886i	0.949112	+	0.314940i	$0.101984\pi$
$692$	8.55490	+	4.11982i	0.325209	+	0.156612i
$693$	2.71500	+	5.63775i	0.103134	+	0.214160i
$694$	−3.52176	−	0.803818i	−0.133684	−	0.0305125i
$695$	8.63989			0.327730
$696$	−6.13657	+	4.78526i	−0.232606	+	0.181385i
$697$	38.9546			1.47551
$698$	−13.9243	−	3.17814i	−0.527044	−	0.120294i
$699$	−16.9485	−	35.1939i	−0.641051	−	1.33116i
$700$	5.50946	+	2.65321i	0.208238	+	0.100282i
$701$	2.27609	−	9.97218i	0.0859666	−	0.376644i	−0.913583	−	0.406652i	$-0.866696\pi$
$701$	2.27609	−	9.97218i	0.0859666	−	0.376644i	0.999550	+	0.0300079i	$0.00955325\pi$
$702$	7.68998	+	33.6920i	0.290240	+	1.27162i
$703$	5.30310	−	2.55384i	0.200010	−	0.0963198i
$704$	−2.70097	−	2.15395i	−0.101797	−	0.0811801i
$705$	6.22687	−	7.80825i	0.234517	−	0.294076i
$706$	−0.530097	+	1.10076i	−0.0199505	+	0.0414276i
$707$	11.2409	−	8.96429i	0.422756	−	0.337137i
$708$			13.0262i			0.489553i
$709$	−28.8557	−	36.1839i	−1.08370	−	1.35892i	−0.928628	−	0.371012i	$-0.879011\pi$
$709$	−28.8557	−	36.1839i	−1.08370	−	1.35892i	−0.155071	−	0.987903i	$-0.549561\pi$
$710$	−5.78262	+	1.31984i	−0.217018	+	0.0495329i
$711$	−10.3378	+	2.35953i	−0.387697	+	0.0884892i
$712$	1.77796	+	2.22949i	0.0666318	+	0.0835536i
$713$			3.44743i			0.129107i
$714$	−9.55922	+	7.62322i	−0.357745	+	0.285292i
$715$	−12.7027	+	26.3774i	−0.475053	+	0.986457i
$716$	−4.69617	+	5.88881i	−0.175504	+	0.220075i
$717$	−29.4477	−	23.4837i	−1.09974	−	0.877017i
$718$	28.0813	−	13.5233i	1.04799	−	0.504683i
$719$	−0.0552738	−	0.242170i	−0.00206136	−	0.00903142i	0.973887	−	0.227034i	$-0.0729029\pi$
$719$	−0.0552738	−	0.242170i	−0.00206136	−	0.00903142i	−0.975948	+	0.218003i	$0.930046\pi$
$720$	−0.281268	+	1.23231i	−0.0104822	+	0.0459256i
$721$	−14.2130	−	6.84460i	−0.529318	−	0.254906i
$722$	−6.20337	−	12.8814i	−0.230865	−	0.479397i
$723$	26.6528	+	6.08333i	0.991228	+	0.226241i
$724$	18.4798			0.686796
$725$	−7.02972	−	15.0138i	−0.261077	−	0.557600i
$726$	−1.35074			−0.0501308
$727$	−20.2197	−	4.61502i	−0.749908	−	0.171162i	−0.169548	−	0.985522i	$-0.554231\pi$
$727$	−20.2197	−	4.61502i	−0.749908	−	0.171162i	−0.580360	+	0.814360i	$0.697088\pi$
$728$	5.26901	+	10.9412i	0.195282	+	0.405508i
$729$	26.5422	+	12.7821i	0.983045	+	0.473409i
$730$	2.15358	−	9.43547i	0.0797077	−	0.349222i
$731$	10.4817	+	45.9235i	0.387681	+	1.69854i
$732$	−12.4937	+	6.01664i	−0.461779	+	0.222381i
$733$	−3.36423	−	2.68289i	−0.124261	−	0.0990947i	0.559388	−	0.828906i	$-0.311036\pi$
$733$	−3.36423	−	2.68289i	−0.124261	−	0.0990947i	−0.683648	+	0.729812i	$0.739608\pi$
$734$	−3.01207	+	3.77701i	−0.111177	+	0.139412i
$735$	2.65450	−	5.51214i	0.0979129	−	0.203318i
$736$	0.446595	−	0.356148i	0.0164617	−	0.0131278i
$737$		−	43.3637i		−	1.59732i
$738$	−5.19935	−	6.51978i	−0.191391	−	0.239996i
$739$	−14.7834	+	3.37422i	−0.543817	+	0.124123i	−0.485600	−	0.874181i	$-0.661399\pi$
$739$	−14.7834	+	3.37422i	−0.543817	+	0.124123i	−0.0582174	+	0.998304i	$0.518542\pi$
$740$	3.66811	−	0.837223i	0.134842	−	0.0307769i
$741$	11.9447	+	14.9782i	0.438799	+	0.550237i
$742$			20.7116i			0.760347i
$743$	−20.6193	+	16.4433i	−0.756448	+	0.603247i	−0.923900	−	0.382633i	$-0.875017\pi$
$743$	−20.6193	+	16.4433i	−0.756448	+	0.603247i	0.167452	+	0.985880i	$0.446446\pi$
$744$	3.78398	−	7.85751i	0.138727	−	0.288070i
$745$	0.626722	−	0.785884i	0.0229613	−	0.0287926i
$746$	−0.732257	−	0.583955i	−0.0268098	−	0.0213801i
$747$	8.90154	−	4.28676i	0.325690	−	0.156844i
$748$	3.27448	+	14.3464i	0.119727	+	0.524557i
$749$	5.79881	−	25.4062i	0.211884	−	0.928324i
$750$	14.5795	+	7.02112i	0.532368	+	0.256375i
$751$	12.2542	+	25.4460i	0.447161	+	0.928540i	0.995719	+	0.0924273i	$0.0294626\pi$
$751$	12.2542	+	25.4460i	0.447161	+	0.928540i	−0.548558	+	0.836112i	$0.684823\pi$
$752$	−4.86081	−	1.10945i	−0.177256	−	0.0404574i
$753$	33.6236			1.22531
$754$	7.67532	−	32.0151i	0.279519	−	1.16592i
$755$	−12.9806			−0.472413
$756$	10.9471	+	2.49861i	0.398143	+	0.0908735i
$757$	17.0082	+	35.3179i	0.618174	+	1.28365i	0.941388	+	0.337326i	$0.109523\pi$
$757$	17.0082	+	35.3179i	0.618174	+	1.28365i	−0.323213	+	0.946326i	$0.604763\pi$
$758$	−1.30267	−	0.627333i	−0.0473151	−	0.0227857i
$759$	0.634540	−	2.78010i	0.0230323	−	0.100911i
$760$	0.668911	+	2.93069i	0.0242639	+	0.106307i
$761$	9.94360	−	4.78858i	0.360455	−	0.173586i	−0.244887	−	0.969552i	$-0.578751\pi$
$761$	9.94360	−	4.78858i	0.360455	−	0.173586i	0.605342	+	0.795966i	$0.293036\pi$
$762$	−7.33388	−	5.84858i	−0.265679	−	0.211872i
$763$	6.48627	−	8.13353i	0.234819	−	0.294453i
$764$	5.14474	−	10.6832i	0.186130	−	0.386503i
$765$	4.20946	−	3.35693i	0.152193	−	0.121370i
$766$		−	7.89594i		−	0.285292i
$767$	−34.3603	−	43.0864i	−1.24068	−	1.55576i
$768$	−1.40881	+	0.321552i	−0.0508361	+	0.0116030i
$769$	20.0150	−	4.56829i	0.721759	−	0.164737i	0.154165	−	0.988045i	$-0.450731\pi$
$769$	20.0150	−	4.56829i	0.721759	−	0.164737i	0.567594	+	0.823308i	$0.307874\pi$
$770$	5.93094	+	7.43717i	0.213736	+	0.268017i
$771$			16.5790i			0.597080i
$772$	13.2571	−	10.5722i	0.477133	−	0.380501i
$773$	−18.9219	+	39.2917i	−0.680573	+	1.41322i	0.218680	+	0.975797i	$0.429825\pi$
$773$	−18.9219	+	39.2917i	−0.680573	+	1.41322i	−0.899253	+	0.437428i	$0.855889\pi$
$774$	6.28713	−	7.88382i	0.225986	−	0.283378i
$775$	14.5259	+	11.5840i	0.521786	+	0.416110i
$776$	2.18489	−	1.05219i	0.0784329	−	0.0377713i
$777$	−1.73365	−	7.59562i	−0.0621944	−	0.272492i
$778$	−1.79052	+	7.84477i	−0.0641932	+	0.281249i
$779$	−17.8681	−	8.60481i	−0.640190	−	0.308299i
$780$	5.31335	+	11.0333i	0.190249	+	0.395055i
$781$	14.4114	+	3.28932i	0.515682	+	0.117701i
$782$	−2.43313			−0.0870086
$783$	−18.7192	−	24.0054i	−0.668971	−	0.857882i
$784$	−3.05426			−0.109081
$785$	−15.9773	−	3.64672i	−0.570255	−	0.130157i
$786$	1.41098	+	2.92994i	0.0503281	+	0.104507i
$787$	−3.36633	−	1.62114i	−0.119997	−	0.0577874i	0.372922	−	0.927863i	$-0.378356\pi$
$787$	−3.36633	−	1.62114i	−0.119997	−	0.0577874i	−0.492919	+	0.870075i	$0.664070\pi$
$788$	0.319942	−	1.40176i	0.0113975	−	0.0499355i
$789$	6.95228	+	30.4599i	0.247508	+	1.08440i
$790$	−14.5232	+	6.99401i	−0.516713	+	0.248836i
$791$	0.215752	+	0.172056i	0.00767125	+	0.00611762i
$792$	1.96409	−	2.46289i	0.0697909	−	0.0875150i
$793$	25.4545	−	52.8568i	0.903916	−	1.87700i
$794$	2.00712	−	1.60063i	0.0712301	−	0.0568041i
$795$			20.8859i			0.740747i
$796$	−2.82974	−	3.54838i	−0.100297	−	0.125769i
$797$	−11.2403	+	2.56553i	−0.398153	+	0.0908759i	−0.416909	−	0.908948i	$-0.636887\pi$
$797$	−11.2403	+	2.56553i	−0.398153	+	0.0908759i	0.0187558	+	0.999824i	$0.494029\pi$
$798$	6.06863	−	1.38513i	0.214827	−	0.0490329i
$799$	13.2413	+	16.6040i	0.468443	+	0.587409i
$800$		−	3.07847i		−	0.108840i
$801$	−2.03297	+	1.62124i	−0.0718314	+	0.0572836i
$802$	−3.30918	+	6.87159i	−0.116851	+	0.242644i
$803$	−15.0385	+	18.8576i	−0.530696	+	0.665471i
$804$	−14.1812	−	11.3091i	−0.500132	−	0.398842i
$805$	−1.41709	+	0.682436i	−0.0499460	+	0.0240527i
$806$	8.21026	+	35.9715i	0.289194	+	1.26704i
$807$	1.46333	−	6.41127i	0.0515117	−	0.225688i
$808$	−6.52127	−	3.14048i	−0.229417	−	0.110482i
$809$	20.0908	+	41.7190i	0.706355	+	1.46676i	0.876530	+	0.481347i	$0.159852\pi$
$809$	20.0908	+	41.7190i	0.706355	+	1.46676i	−0.170175	+	0.985414i	$0.554433\pi$
$810$	7.34231	+	1.67583i	0.257982	+	0.0588828i
$811$	31.6055			1.10982			0.554909	−	0.831911i	$-0.312753\pi$
$811$	31.6055			1.10982			0.554909	+	0.831911i	$0.312753\pi$
$812$	−8.29008	−	6.76025i	−0.290925	−	0.237238i
$813$	−11.6047			−0.406995
$814$	−9.14167	−	2.08653i	−0.320415	−	0.0731327i
$815$	8.15623	+	16.9366i	0.285700	+	0.593263i
$816$	5.54568	+	2.67066i	0.194138	+	0.0934918i
$817$	5.33633	−	23.3800i	0.186694	−	0.817962i
$818$	−0.483920	−	2.12019i	−0.0169199	−	0.0741307i
$819$	−9.97679	+	4.80457i	−0.348617	+	0.167885i
$820$	−9.91131	−	7.90401i	−0.346118	−	0.276020i
$821$	6.20641	−	7.78260i	0.216605	−	0.271615i	−0.661643	−	0.749819i	$-0.730141\pi$
$821$	6.20641	−	7.78260i	0.216605	−	0.271615i	0.878249	+	0.478204i	$0.158712\pi$
$822$	−4.74141	+	9.84564i	−0.165376	+	0.343406i
$823$	15.6004	−	12.4409i	0.543796	−	0.433663i	−0.312673	−	0.949861i	$-0.601225\pi$
$823$	15.6004	−	12.4409i	0.543796	−	0.433663i	0.856469	+	0.516198i	$0.172653\pi$
$824$			7.94165i			0.276660i
$825$	−9.58189	−	12.0153i	−0.333599	−	0.418319i
$826$	−17.4571	+	3.98447i	−0.607411	+	0.138638i
$827$	−31.3640	+	7.15863i	−1.09063	+	0.248930i	−0.729773	−	0.683689i	$-0.760374\pi$
$827$	−31.3640	+	7.15863i	−1.09063	+	0.248930i	−0.360861	+	0.932620i	$0.617517\pi$
$828$	0.324755	+	0.407230i	0.0112860	+	0.0141522i
$829$			18.4924i			0.642269i	0.947034	+	0.321134i	$0.104064\pi$
$829$			18.4924i			0.642269i	−0.947034	+	0.321134i	$0.895936\pi$
$830$	11.7427	−	9.36447i	0.407594	−	0.325046i
$831$	−17.8518	+	37.0697i	−0.619273	+	1.28593i
$832$	3.81172	−	4.77974i	0.132148	−	0.165708i
$833$	10.1715	+	8.11148i	0.352421	+	0.281046i
$834$	−8.11475	+	3.90786i	−0.280991	+	0.135318i
$835$	−1.43211	−	6.27450i	−0.0495604	−	0.217138i
$836$	1.66706	−	7.30386i	0.0576565	−	0.252609i
$837$	30.7374	+	14.8024i	1.06244	+	0.511645i
$838$	−4.79169	−	9.95005i	−0.165526	−	0.343719i
$839$	−11.0565	−	2.52358i	−0.381714	−	0.0871236i	0.0273586	−	0.999626i	$-0.491290\pi$
$839$	−11.0565	−	2.52358i	−0.381714	−	0.0871236i	−0.409072	+	0.912502i	$0.634148\pi$
$840$	3.97895			0.137287
$841$	5.83527	+	28.4069i	0.201216	+	0.979547i
$842$	−3.65914			−0.126102
$843$	28.1375	+	6.42219i	0.969106	+	0.221192i
$844$	−4.54936	−	9.44684i	−0.156595	−	0.325174i
$845$	−30.4425	−	14.6603i	−1.04725	−	0.504331i
$846$	1.01165	−	4.43235i	0.0347814	−	0.152387i
$847$	−0.413169	−	1.81021i	−0.0141966	−	0.0621996i
$848$	9.39419	−	4.52400i	0.322598	−	0.155355i
$849$	4.83826	+	3.85838i	0.166049	+	0.132419i
$850$	−8.17577	+	10.2521i	−0.280427	+	0.351644i
$851$	0.672699	−	1.39687i	0.0230598	−	0.0478842i
$852$	4.83417	−	3.85512i	0.165616	−	0.132074i
$853$		−	20.9622i		−	0.717733i	−0.933389	−	0.358867i	$-0.883163\pi$
$853$		−	20.9622i		−	0.717733i	0.933389	−	0.358867i	$-0.116837\pi$
$854$	−11.8848	−	14.9031i	−0.406691	−	0.509974i
$855$	−2.67236	+	0.609949i	−0.0913928	+	0.0208598i
$856$	−12.7902	+	2.91927i	−0.437159	+	0.0997787i
$857$	9.70850	+	12.1741i	0.331636	+	0.415858i	0.919493	−	0.393107i	$-0.128600\pi$
$857$	9.70850	+	12.1741i	0.331636	+	0.415858i	−0.587857	+	0.808965i	$0.700028\pi$
$858$		−	30.5196i		−	1.04192i
$859$	34.5004	−	27.5131i	1.17714	−	0.938735i	0.178162	−	0.984001i	$-0.442985\pi$
$859$	34.5004	−	27.5131i	1.17714	−	0.938735i	0.998975	+	0.0452658i	$0.0144135\pi$
$860$	6.65112	−	13.8112i	0.226801	−	0.470958i
$861$	−16.3670	+	20.5235i	−0.557785	+	0.699440i
$862$	4.97490	+	3.96735i	0.169446	+	0.135128i
$863$	36.0787	−	17.3746i	1.22813	−	0.591437i	0.296567	−	0.955012i	$-0.404158\pi$
$863$	36.0787	−	17.3746i	1.22813	−	0.591437i	0.931565	+	0.363575i	$0.118444\pi$
$864$	−1.25786	−	5.51107i	−0.0427934	−	0.187490i
$865$	−2.92887	+	12.8322i	−0.0995845	+	0.436308i
$866$	19.7003	+	9.48716i	0.669443	+	0.322387i
$867$	−0.717164	−	1.48921i	−0.0243562	−	0.0505761i
$868$	11.6878	+	2.66766i	0.396709	+	0.0905462i
$869$	40.1731			1.36278
$870$	−8.35985	−	6.81715i	−0.283426	−	0.231123i
$871$	76.7380			2.60017
$872$	−5.10592	−	1.16539i	−0.172908	−	0.0394652i
$873$	0.959440	+	1.99230i	0.0324721	+	0.0674291i
$874$	1.11605	+	0.537462i	0.0377510	+	0.0181799i
$875$	−4.94980	+	21.6865i	−0.167334	+	0.733137i
$876$	2.24501	+	9.83604i	0.0758519	+	0.332329i
$877$	10.4404	−	5.02783i	0.352547	−	0.169778i	−0.249225	−	0.968446i	$-0.580176\pi$
$877$	10.4404	−	5.02783i	0.352547	−	0.169778i	0.601772	+	0.798668i	$0.294462\pi$
$878$	−16.1517	−	12.8806i	−0.545095	−	0.434698i
$879$	2.74160	−	3.43785i	0.0924718	−	0.115956i
$880$	2.07780	−	4.31459i	0.0700426	−	0.145445i
$881$	2.62020	−	2.08954i	0.0882766	−	0.0703983i	−0.578357	−	0.815784i	$-0.696306\pi$
$881$	2.62020	−	2.08954i	0.0882766	−	0.0703983i	0.666634	+	0.745385i	$0.267735\pi$
$882$		−	2.78504i		−	0.0937772i
$883$	32.0436	+	40.1814i	1.07835	+	1.35221i	0.931784	+	0.363013i	$0.118252\pi$
$883$	32.0436	+	40.1814i	1.07835	+	1.35221i	0.146570	+	0.989200i	$0.453177\pi$
$884$	−25.3880	+	5.79464i	−0.853891	+	0.194895i
$885$	−17.6041	+	4.01801i	−0.591754	+	0.135064i
$886$	−1.59758	−	2.00330i	−0.0536718	−	0.0673023i
$887$		−	42.3730i		−	1.42275i	−0.702814	−	0.711374i	$-0.748073\pi$
$887$		−	42.3730i		−	1.42275i	0.702814	−	0.711374i	$-0.251927\pi$
$888$	−3.06648	+	2.44544i	−0.102904	+	0.0820634i
$889$	5.59472	−	11.6175i	0.187641	−	0.389640i
$890$	−2.46459	+	3.09050i	−0.0826133	+	0.103594i
$891$	−14.6743	−	11.7023i	−0.491606	−	0.392043i
$892$	−19.6254	+	9.45108i	−0.657106	+	0.316446i
$893$	−2.40592	−	10.5410i	−0.0805110	−	0.352742i
$894$	−0.233170	+	1.02159i	−0.00779838	+	0.0341669i
$895$	−9.40693	−	4.53014i	−0.314439	−	0.151426i
$896$	−0.861862	−	1.78967i	−0.0287928	−	0.0597888i
$897$	4.91977	+	1.12291i	0.164266	+	0.0374928i
$898$	−40.7652			−1.36035
$899$	−19.9857	−	25.6295i	−0.666562	−	0.854792i
$900$	2.80711			0.0935705
$901$	−43.2999	−	9.88292i	−1.44253	−	0.329248i
$902$	13.7080	+	28.4650i	0.456427	+	0.947780i
$903$	−28.5991	−	13.7726i	−0.951719	−	0.458324i
$904$	0.0309135	−	0.135441i	0.00102817	−	0.00450470i
$905$	5.70022	+	24.9743i	0.189482	+	0.830174i
$906$	12.1916	−	5.87118i	0.405040	−	0.195057i
$907$	−31.3801	−	25.0248i	−1.04196	−	0.830935i	−0.0560861	−	0.998426i	$-0.517862\pi$
$907$	−31.3801	−	25.0248i	−1.04196	−	0.830935i	−0.985874	+	0.167491i	$0.946434\pi$
$908$	−11.9286	+	14.9580i	−0.395864	+	0.496398i
$909$	2.86366	−	5.94645i	0.0949815	−	0.197231i
$910$	−13.1611	+	10.4956i	−0.436286	+	0.347927i
$911$		−	39.7506i		−	1.31700i	−0.752582	−	0.658499i	$-0.771192\pi$
$911$		−	39.7506i		−	1.31700i	0.752582	−	0.658499i	$-0.228808\pi$
$912$	−1.95381	−	2.45001i	−0.0646973	−	0.0811278i
$913$	−36.4930	+	8.32928i	−1.20774	+	0.275659i
$914$	24.5746	−	5.60899i	0.812855	−	0.185529i
$915$	−11.9849	−	15.0286i	−0.396208	−	0.496829i
$916$		−	25.5961i		−	0.845718i
$917$	−3.49499	+	2.78716i	−0.115415	+	0.0920401i
$918$	−10.4472	+	21.6939i	−0.344810	+	0.716005i
$919$	−18.6228	+	23.3523i	−0.614310	+	0.770321i	−0.987531	−	0.157422i	$-0.949682\pi$
$919$	−18.6228	+	23.3523i	−0.614310	+	0.770321i	0.373221	+	0.927742i	$0.378253\pi$
$920$	0.619067	+	0.493690i	0.0204100	+	0.0162765i
$921$	30.7444	−	14.8057i	1.01306	−	0.487865i
$922$	−9.13779	−	40.0353i	−0.300937	−	1.31849i
$923$	−5.82091	+	25.5031i	−0.191597	+	0.839443i
$924$	−8.93431	−	4.30254i	−0.293917	−	0.141543i
$925$	−3.62539	−	7.52820i	−0.119202	−	0.247526i
$926$	32.2867	+	7.36923i	1.06101	+	0.242168i
$927$	−7.24162			−0.237846
$928$	−1.25547	+	5.23677i	−0.0412127	+	0.171906i
$929$	−0.307389			−0.0100851			−0.00504256	−	0.999987i	$-0.501605\pi$
$929$	−0.307389			−0.0100851			−0.00504256	+	0.999987i	$0.501605\pi$
$930$	11.7861	+	2.69011i	0.386483	+	0.0882121i
$931$	−2.87378	−	5.96746i	−0.0941842	−	0.195576i
$932$	−24.3549	−	11.7287i	−0.797773	−	0.384187i
$933$	−4.44855	+	19.4904i	−0.145639	+	0.638087i
$934$	3.36514	+	14.7436i	0.110111	+	0.482427i
$935$	−18.3783	+	8.85051i	−0.601034	+	0.289443i
$936$	4.35843	+	3.47573i	0.142460	+	0.113608i
$937$	−34.0445	+	42.6904i	−1.11218	+	1.39464i	−0.202528	+	0.979277i	$0.564916\pi$
$937$	−34.0445	+	42.6904i	−1.11218	+	1.39464i	−0.909657	+	0.415359i	$0.863656\pi$
$938$	10.8182	−	22.4643i	0.353228	−	0.733486i
$939$	−9.71397	+	7.74664i	−0.317004	+	0.252802i
$940$		−	6.91130i		−	0.225422i
$941$	−17.2687	−	21.6543i	−0.562945	−	0.705911i	0.416154	−	0.909294i	$-0.363378\pi$
$941$	−17.2687	−	21.6543i	−0.562945	−	0.705911i	−0.979099	+	0.203383i	$0.934806\pi$
$942$	16.6556	−	3.80153i	0.542669	−	0.123861i
$943$	−5.09293	+	1.16243i	−0.165849	+	0.0378539i
$944$	5.62038	+	7.04773i	0.182928	+	0.229384i
$945$			15.5651i			0.506332i
$946$	−29.8688	+	23.8196i	−0.971118	+	0.774441i
$947$	−16.3131	+	33.8745i	−0.530104	+	1.10077i	0.448264	+	0.893901i	$0.352042\pi$
$947$	−16.3131	+	33.8745i	−0.530104	+	1.10077i	−0.978368	+	0.206871i	$0.933672\pi$
$948$	10.4770	−	13.1378i	0.340279	−	0.426696i
$949$	−33.3712	−	26.6126i	−1.08328	−	0.863883i
$950$	6.01476	−	2.89656i	0.195145	−	0.0939767i
$951$	−4.07816	−	17.8676i	−0.132243	−	0.579396i
$952$	−1.88278	+	8.24900i	−0.0610213	+	0.267352i
$953$	−13.8761	−	6.68238i	−0.449491	−	0.216463i	0.195422	−	0.980719i	$-0.437392\pi$
$953$	−13.8761	−	6.68238i	−0.449491	−	0.216463i	−0.644913	+	0.764256i	$0.723107\pi$
$954$	4.12523	+	8.56613i	0.133559	+	0.277339i
$955$	16.0246	+	3.65750i	0.518543	+	0.118354i
$956$	−26.0650			−0.843002
$957$	11.3996	+	24.3469i	0.368497	+	0.787024i
$958$	24.5410			0.792885
$959$	−14.6450	−	3.34264i	−0.472913	−	0.107939i
$960$	−0.869115	−	1.80474i	−0.0280506	−	0.0582476i
$961$	4.88702	+	2.35347i	0.157646	+	0.0759182i
$962$	3.69240	−	16.1775i	0.119048	−	0.521582i
$963$	−2.66195	−	11.6628i	−0.0857802	−	0.375827i
$964$	17.0451	−	8.20849i	0.548986	−	0.264378i
$965$	18.3769	+	14.6551i	0.591573	+	0.471763i
$966$	1.02229	−	1.28191i	0.0328917	−	0.0412449i
$967$	18.2882	−	37.9759i	0.588110	−	1.22122i	−0.368439	−	0.929652i	$-0.620108\pi$
$967$	18.2882	−	37.9759i	0.588110	−	1.22122i	0.956549	−	0.291572i	$-0.0941781\pi$
$968$	−0.730812	+	0.582803i	−0.0234892	+	0.0187320i
$969$			13.3481i			0.428802i
$970$	2.09591	+	2.62819i	0.0672956	+	0.0843860i
$971$	21.5190	−	4.91157i	0.690578	−	0.157620i	0.137191	−	0.990545i	$-0.456192\pi$
$971$	21.5190	−	4.91157i	0.690578	−	0.157620i	0.553386	+	0.832925i	$0.313335\pi$
$972$	8.87918	−	2.02661i	0.284800	−	0.0650037i
$973$	−7.71931	−	9.67970i	−0.247470	−	0.310317i
$974$			28.4159i			0.910503i
$975$	21.2628	−	16.9565i	0.680954	−	0.543042i
$976$	−4.16364	+	8.64589i	−0.133275	+	0.276748i
$977$	−17.6347	+	22.1132i	−0.564184	+	0.707464i	−0.979325	−	0.202293i	$-0.935161\pi$
$977$	−17.6347	+	22.1132i	−0.564184	+	0.707464i	0.415141	+	0.909757i	$0.363732\pi$
$978$	−15.3210	−	12.2181i	−0.489910	−	0.390690i
$979$	8.87582	−	4.27437i	0.283672	−	0.136609i
$980$	−0.942108	−	4.12764i	−0.0300945	−	0.131853i
$981$	1.06267	−	4.65585i	0.0339284	−	0.148650i
$982$	−20.2275	−	9.74105i	−0.645485	−	0.310849i
$983$	−1.90738	−	3.96072i	−0.0608360	−	0.126327i	0.868334	−	0.495980i	$-0.165191\pi$
$983$	−1.90738	−	3.96072i	−0.0608360	−	0.126327i	−0.929170	+	0.369653i	$0.879477\pi$
$984$	12.8839	+	2.94067i	0.410724	+	0.0937450i
$985$	1.99308			0.0635047
$986$	18.0888	−	14.1055i	0.576065	−	0.449212i
$987$	−14.3114			−0.455536
$988$	12.9252	+	2.95009i	0.411206	+	0.0938550i
$989$	−2.74077	−	5.69126i	−0.0871514	−	0.180972i
$990$	3.93428	+	1.89465i	0.125040	+	0.0602159i
$991$	−0.219242	+	0.960564i	−0.00696446	+	0.0305133i	−0.978291	−	0.207237i	$-0.933553\pi$
$991$	−0.219242	+	0.960564i	−0.00696446	+	0.0305133i	0.971326	+	0.237750i	$0.0764100\pi$
$992$	−1.34297	−	5.88393i	−0.0426393	−	0.186815i
$993$	6.79339	−	3.27152i	0.215582	−	0.103819i
$994$	6.64516	+	5.29934i	0.210772	+	0.168085i
$995$	3.92256	−	4.91873i	0.124353	−	0.155934i
$996$	−6.79335	+	14.1065i	−0.215256	+	0.446983i
$997$	−3.09163	+	2.46550i	−0.0979130	+	0.0780830i	−0.671223	−	0.741256i	$-0.734231\pi$
$997$	−3.09163	+	2.46550i	−0.0979130	+	0.0780830i	0.573310	+	0.819339i	$0.305659\pi$
$998$			19.6240i			0.621186i
$999$	−9.56619	−	11.9956i	−0.302661	−	0.379525i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	58.2.e.a.33.1	✓	12
3.2	odd	2		522.2.n.a.91.2		12
4.3	odd	2		464.2.y.c.33.1		12
29.6	even	14		1682.2.b.j.1681.4		12
29.14	odd	28		1682.2.a.s.1.3		6
29.15	odd	28		1682.2.a.r.1.3		6
29.22	even	14	inner	58.2.e.a.51.1	yes	12
29.23	even	7		1682.2.b.j.1681.10		12
87.80	odd	14		522.2.n.a.109.2		12
116.51	odd	14		464.2.y.c.225.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
58.2.e.a.33.1	✓	12	1.1	even	1	trivial
58.2.e.a.51.1	yes	12	29.22	even	14	inner
464.2.y.c.33.1		12	4.3	odd	2
464.2.y.c.225.1		12	116.51	odd	14
522.2.n.a.91.2		12	3.2	odd	2
522.2.n.a.109.2		12	87.80	odd	14
1682.2.a.r.1.3		6	29.15	odd	28
1682.2.a.s.1.3		6	29.14	odd	28
1682.2.b.j.1681.4		12	29.6	even	14
1682.2.b.j.1681.10		12	29.23	even	7

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.e (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.974928 - 0.222521i) q^{2} +(0.626980 + 1.30194i) q^{3} +(0.900969 + 0.433884i) q^{4} +(-0.308457 + 1.35144i) q^{5} +(-0.321552 - 1.40881i) q^{6} +(1.78967 - 0.861862i) q^{7} +(-0.781831 - 0.623490i) q^{8} +(0.568532 - 0.712916i) q^{9} +(0.601447 - 1.24892i) q^{10} +(-2.70097 + 2.15395i) q^{11} +1.44504i q^{12} +(-3.81172 - 4.77974i) q^{13} +(-1.93659 + 0.442013i) q^{14} +(-1.95288 + 0.445733i) q^{15} +(0.623490 + 0.781831i) q^{16} -4.25956i q^{17} +(-0.712916 + 0.568532i) q^{18} +(-0.940908 + 1.95381i) q^{19} +(-0.864277 + 1.08377i) q^{20} +(2.24418 + 1.78967i) q^{21} +(3.11255 - 1.49893i) q^{22} +(0.127108 + 0.556895i) q^{23} +(0.321552 - 1.40881i) q^{24} +(2.77361 + 1.33570i) q^{25} +(2.65256 + 5.50809i) q^{26} +(5.51107 + 1.25786i) q^{27} +1.98639 q^{28} +(-4.17344 - 3.40329i) q^{29} +2.00311 q^{30} +(5.88393 + 1.34297i) q^{31} +(-0.433884 - 0.900969i) q^{32} +(-4.49776 - 2.16601i) q^{33} +(-0.947841 + 4.15276i) q^{34} +(0.612715 + 2.68448i) q^{35} +(0.821552 - 0.395639i) q^{36} +(-2.12207 - 1.69229i) q^{37} +(1.35208 - 1.69546i) q^{38} +(3.83306 - 7.95942i) q^{39} +(1.08377 - 0.864277i) q^{40} +9.14522i q^{41} +(-1.78967 - 2.24418i) q^{42} +(-10.7813 + 2.46076i) q^{43} +(-3.36805 + 0.768736i) q^{44} +(0.788095 + 0.988239i) q^{45} -0.571217i q^{46} +(-3.89807 + 3.10861i) q^{47} +(-0.626980 + 1.30194i) q^{48} +(-1.90430 + 2.38792i) q^{49} +(-2.40684 - 1.91939i) q^{50} +(5.54568 - 2.67066i) q^{51} +(-1.36039 - 5.96024i) q^{52} +(2.32017 - 10.1653i) q^{53} +(-5.09299 - 2.45265i) q^{54} +(-2.07780 - 4.31459i) q^{55} +(-1.93659 - 0.442013i) q^{56} -3.13368 q^{57} +(3.31150 + 4.24664i) q^{58} +9.01438 q^{59} +(-1.95288 - 0.445733i) q^{60} +(4.16364 + 8.64589i) q^{61} +(-5.43757 - 2.61859i) q^{62} +(0.403051 - 1.76588i) q^{63} +(0.222521 + 0.974928i) q^{64} +(7.63528 - 3.67696i) q^{65} +(3.90301 + 3.11255i) q^{66} +(-7.82616 + 9.81369i) q^{67} +(1.84815 - 3.83773i) q^{68} +(-0.645349 + 0.514648i) q^{69} -2.75352i q^{70} +(-2.66783 - 3.34535i) q^{71} +(-0.888992 + 0.202907i) q^{72} +(6.80675 - 1.55360i) q^{73} +(1.69229 + 2.12207i) q^{74} +4.44852i q^{75} +(-1.69546 + 1.35208i) q^{76} +(-2.97745 + 6.18273i) q^{77} +(-5.50809 + 6.90693i) q^{78} +(-9.09164 - 7.25034i) q^{79} +(-1.24892 + 0.601447i) q^{80} +(1.20895 + 5.29674i) q^{81} +(2.03500 - 8.91593i) q^{82} +(9.76203 + 4.70114i) q^{83} +(1.24543 + 2.58615i) q^{84} +(5.75653 + 1.31389i) q^{85} +11.0585 q^{86} +(1.81420 - 7.56736i) q^{87} +3.45467 q^{88} +(-2.78013 - 0.634546i) q^{89} +(-0.548431 - 1.13883i) q^{90} +(-10.9412 - 5.26901i) q^{91} +(-0.127108 + 0.556895i) q^{92} +(1.94065 + 8.50252i) q^{93} +(4.49206 - 2.16326i) q^{94} +(-2.35023 - 1.87425i) q^{95} +(0.900969 - 1.12978i) q^{96} +(-1.05219 + 2.18489i) q^{97} +(2.38792 - 1.90430i) q^{98} +3.15015i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{4} - 2 q^{5} - 12 q^{6} + 4 q^{7} - 4 q^{9} - 26 q^{13} - 14 q^{15} - 2 q^{16} + 2 q^{20} + 14 q^{21} + 4 q^{22} - 16 q^{23} + 12 q^{24} + 22 q^{25} + 14 q^{26} - 4 q^{28} + 18 q^{29} + 16 q^{30}+ \cdots - 28 q^{97}+O(q^{100}) \) 12 * q + 2 * q^4 - 2 * q^5 - 12 * q^6 + 4 * q^7 - 4 * q^9 - 26 * q^13 - 14 * q^15 - 2 * q^16 + 2 * q^20 + 14 * q^21 + 4 * q^22 - 16 * q^23 + 12 * q^24 + 22 * q^25 + 14 * q^26 - 4 * q^28 + 18 * q^29 + 16 * q^30 + 28 * q^31 - 10 * q^33 - 4 * q^34 + 4 * q^35 + 18 * q^36 - 28 * q^37 + 22 * q^38 + 28 * q^39 - 14 * q^40 - 4 * q^42 - 28 * q^43 - 28 * q^44 - 4 * q^45 - 14 * q^47 - 8 * q^49 - 28 * q^50 - 4 * q^51 - 2 * q^52 + 30 * q^53 - 32 * q^54 + 28 * q^55 - 20 * q^57 - 10 * q^58 - 48 * q^59 - 14 * q^60 - 28 * q^61 + 10 * q^62 + 22 * q^63 + 2 * q^64 + 2 * q^65 - 16 * q^67 - 14 * q^68 - 28 * q^69 + 30 * q^71 + 42 * q^73 + 2 * q^74 + 28 * q^76 + 14 * q^77 - 16 * q^78 + 28 * q^79 - 2 * q^80 + 26 * q^81 - 20 * q^82 + 28 * q^85 + 52 * q^86 + 4 * q^87 - 4 * q^88 + 14 * q^89 + 70 * q^90 - 4 * q^91 + 16 * q^92 + 66 * q^93 - 8 * q^94 + 2 * q^96 - 28 * q^97

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