LMFDB - Embedded newform 127.2.c.a.107.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [127,2,Mod(19,127)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("127.19"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(127, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 127 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	127.c (of order $3$, degree $2$, 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:	$1.01410010567$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - x^{17} + 12 x^{16} - 7 x^{15} + 92 x^{14} - 46 x^{13} + 388 x^{12} - 105 x^{11} + 1128 x^{10} + \cdots + 9 $ x^18 - x^17 + 12x^16 - 7x^15 + 92x^14 - 46x^13 + 388x^12 - 105x^11 + 1128x^10 - 250x^9 + 1865x^8 - 14x^7 + 1885x^6 - 360x^5 + 552x^4 - 129x^3 + 126x^2 - 27x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			107.9
Root			$-1.14539 + 1.98387i$ of defining polynomial
Character	$\chi$	$=$	127.107
Dual form			127.2.c.a.19.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.29077 q^{2} +(0.483029 + 0.836631i) q^{3} +3.24763 q^{4} -4.03893 q^{5} +(1.10651 + 1.91653i) q^{6} +(0.0980034 + 0.169747i) q^{7} +2.85803 q^{8} +(1.03337 - 1.78984i) q^{9} -9.25226 q^{10} +(1.05139 - 1.82107i) q^{11} +(1.56870 + 2.71707i) q^{12} +(-1.12015 - 1.94016i) q^{13} +(0.224503 + 0.388851i) q^{14} +(-1.95092 - 3.37909i) q^{15} +0.0518359 q^{16} +(-3.12095 + 5.40565i) q^{17} +(2.36720 - 4.10012i) q^{18} +2.17425 q^{19} -13.1169 q^{20} +(-0.0946770 + 0.163985i) q^{21} +(2.40850 - 4.17165i) q^{22} +(3.86745 + 6.69862i) q^{23} +(1.38051 + 2.39112i) q^{24} +11.3130 q^{25} +(-2.56601 - 4.44447i) q^{26} +4.89476 q^{27} +(0.318279 + 0.551275i) q^{28} +(-2.53526 + 4.39120i) q^{29} +(-4.46911 - 7.74073i) q^{30} +(-3.42896 - 5.93913i) q^{31} -5.59732 q^{32} +2.03142 q^{33} +(-7.14938 + 12.3831i) q^{34} +(-0.395829 - 0.685595i) q^{35} +(3.35599 - 5.81274i) q^{36} +(1.06283 - 1.84087i) q^{37} +4.98070 q^{38} +(1.08213 - 1.87431i) q^{39} -11.5434 q^{40} +(-0.903577 + 1.56504i) q^{41} +(-0.216883 + 0.375653i) q^{42} +(-2.82883 + 4.89969i) q^{43} +(3.41454 - 5.91415i) q^{44} +(-4.17369 + 7.22904i) q^{45} +(8.85943 + 15.3450i) q^{46} -1.13665 q^{47} +(0.0250382 + 0.0433675i) q^{48} +(3.48079 - 6.02891i) q^{49} +25.9154 q^{50} -6.03004 q^{51} +(-3.63784 - 6.30093i) q^{52} +(4.46561 - 7.73466i) q^{53} +11.2128 q^{54} +(-4.24651 + 7.35517i) q^{55} +(0.280097 + 0.485142i) q^{56} +(1.05022 + 1.81904i) q^{57} +(-5.80770 + 10.0592i) q^{58} +(3.31019 - 5.73342i) q^{59} +(-6.33587 - 10.9740i) q^{60} -3.84677 q^{61} +(-7.85495 - 13.6052i) q^{62} +0.405093 q^{63} -12.9258 q^{64} +(4.52422 + 7.83618i) q^{65} +4.65351 q^{66} +(-6.16321 - 10.6750i) q^{67} +(-10.1357 + 17.5555i) q^{68} +(-3.73618 + 6.47126i) q^{69} +(-0.906753 - 1.57054i) q^{70} +(-5.76341 - 9.98251i) q^{71} +(2.95339 - 5.11542i) q^{72} +15.5578 q^{73} +(2.43469 - 4.21700i) q^{74} +(5.46449 + 9.46477i) q^{75} +7.06114 q^{76} +0.412161 q^{77} +(2.47892 - 4.29362i) q^{78} +(5.01100 + 8.67931i) q^{79} -0.209361 q^{80} +(-0.735785 - 1.27442i) q^{81} +(-2.06989 + 3.58515i) q^{82} +(-3.65263 + 6.32654i) q^{83} +(-0.307476 + 0.532564i) q^{84} +(12.6053 - 21.8330i) q^{85} +(-6.48021 + 11.2241i) q^{86} -4.89842 q^{87} +(3.00492 - 5.20467i) q^{88} +5.40131 q^{89} +(-9.56097 + 16.5601i) q^{90} +(0.219558 - 0.380285i) q^{91} +(12.5600 + 21.7546i) q^{92} +(3.31257 - 5.73754i) q^{93} -2.60381 q^{94} -8.78162 q^{95} +(-2.70367 - 4.68289i) q^{96} +(6.27345 + 10.8659i) q^{97} +(7.97369 - 13.8108i) q^{98} +(-2.17295 - 3.76366i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 2 q^{2} + q^{3} + 10 q^{4} - 8 q^{5} + 5 q^{7} - 6 q^{8} - 2 q^{9} - 4 q^{10} + 5 q^{12} - 8 q^{14} + 3 q^{15} - 6 q^{16} - 6 q^{17} + 16 q^{19} - 32 q^{20} + 3 q^{21} + 6 q^{22} + 13 q^{23} - 6 q^{24}+ \cdots + 17 q^{99}+O(q^{100}) $ 18 * q - 2 * q^2 + q^3 + 10 * q^4 - 8 * q^5 + 5 * q^7 - 6 * q^8 - 2 * q^9 - 4 * q^10 + 5 * q^12 - 8 * q^14 + 3 * q^15 - 6 * q^16 - 6 * q^17 + 16 * q^19 - 32 * q^20 + 3 * q^21 + 6 * q^22 + 13 * q^23 - 6 * q^24 + 6 * q^25 - 14 * q^26 + 10 * q^27 - 2 * q^28 - 5 * q^29 - 23 * q^30 - 11 * q^31 - 4 * q^32 - 16 * q^33 - 2 * q^34 - 16 * q^35 + 15 * q^36 - 4 * q^37 + 4 * q^38 - 7 * q^39 - 36 * q^40 - 11 * q^41 + 9 * q^43 - 15 * q^44 + 14 * q^45 + 15 * q^46 - 10 * q^47 + 20 * q^48 + 12 * q^49 + 32 * q^50 + 4 * q^51 + 26 * q^52 - 2 * q^53 + 2 * q^54 - q^55 + 12 * q^56 + 28 * q^57 + 10 * q^58 + 6 * q^60 + 28 * q^61 + 8 * q^62 - 12 * q^63 - 50 * q^64 + 15 * q^65 + 36 * q^66 - 12 * q^67 - 41 * q^68 + 33 * q^69 + 21 * q^70 - 4 * q^71 + 31 * q^72 + 52 * q^73 + 13 * q^74 - 11 * q^75 + 26 * q^76 - 40 * q^77 + q^78 - 35 * q^79 + 26 * q^80 + 27 * q^81 - 26 * q^82 + 13 * q^83 + 22 * q^84 + 15 * q^85 - 5 * q^86 - 64 * q^87 - q^88 + 8 * q^89 - 30 * q^90 - 16 * q^91 + 11 * q^92 - 6 * q^93 - 62 * q^94 - 38 * q^95 - 31 * q^96 + 28 * q^97 + 32 * q^98 + 17 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/127\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	2.29077			1.61982			0.809910	−	0.586555i	$-0.199516\pi$
$2$	2.29077			1.61982			0.809910	+	0.586555i	$0.199516\pi$
$3$	0.483029	+	0.836631i	0.278877	+	0.483029i	0.971106	−	0.238649i	$-0.0767045\pi$
$3$	0.483029	+	0.836631i	0.278877	+	0.483029i	−0.692229	+	0.721678i	$0.743371\pi$
$4$	3.24763			1.62381
$5$	−4.03893			−1.80626			−0.903132	−	0.429363i	$-0.858738\pi$
$5$	−4.03893			−1.80626			−0.903132	+	0.429363i	$0.858738\pi$
$6$	1.10651	+	1.91653i	0.451730	+	0.782420i
$7$	0.0980034	+	0.169747i	0.0370418	+	0.0641583i	0.883952	−	0.467578i	$-0.154873\pi$
$7$	0.0980034	+	0.169747i	0.0370418	+	0.0641583i	−0.846910	+	0.531736i	$0.821540\pi$
$8$	2.85803			1.01047
$9$	1.03337	−	1.78984i	0.344455	−	0.596614i
$10$	−9.25226			−2.92582
$11$	1.05139	−	1.82107i	0.317007	−	0.549073i	−0.662855	−	0.748748i	$-0.730655\pi$
$11$	1.05139	−	1.82107i	0.317007	−	0.549073i	0.979862	+	0.199675i	$0.0639887\pi$
$12$	1.56870	+	2.71707i	0.452845	+	0.784350i
$13$	−1.12015	−	1.94016i	−0.310675	−	0.538104i	0.667834	−	0.744310i	$-0.267222\pi$
$13$	−1.12015	−	1.94016i	−0.310675	−	0.538104i	−0.978509	+	0.206206i	$0.933888\pi$
$14$	0.224503	+	0.388851i	0.0600010	+	0.103925i
$15$	−1.95092	−	3.37909i	−0.503726	−	0.872478i
$16$	0.0518359			0.0129590
$17$	−3.12095	+	5.40565i	−0.756942	+	1.31106i	0.187462	+	0.982272i	$0.439974\pi$
$17$	−3.12095	+	5.40565i	−0.756942	+	1.31106i	−0.944403	+	0.328790i	$0.893359\pi$
$18$	2.36720	−	4.10012i	0.557955	−	0.966407i
$19$	2.17425			0.498806			0.249403	−	0.968400i	$-0.419766\pi$
$19$	2.17425			0.498806			0.249403	+	0.968400i	$0.419766\pi$
$20$	−13.1169			−2.93304
$21$	−0.0946770	+	0.163985i	−0.0206602	+	0.0357845i
$22$	2.40850	−	4.17165i	0.513495	−	0.889399i
$23$	3.86745	+	6.69862i	0.806419	+	1.39676i	0.915329	+	0.402706i	$0.131930\pi$
$23$	3.86745	+	6.69862i	0.806419	+	1.39676i	−0.108911	+	0.994052i	$0.534736\pi$
$24$	1.38051	+	2.39112i	0.281796	+	0.488085i
$25$	11.3130			2.26259
$26$	−2.56601	−	4.44447i	−0.503237	−	0.871632i
$27$	4.89476			0.941997
$28$	0.318279	+	0.551275i	0.0601490	+	0.104181i
$29$	−2.53526	+	4.39120i	−0.470786	+	0.815425i	−0.999442	−	0.0334112i	$-0.989363\pi$
$29$	−2.53526	+	4.39120i	−0.470786	+	0.815425i	0.528656	+	0.848836i	$0.322696\pi$
$30$	−4.46911	−	7.74073i	−0.815945	−	1.41326i
$31$	−3.42896	−	5.93913i	−0.615859	−	1.06670i	−0.990233	−	0.139421i	$-0.955476\pi$
$31$	−3.42896	−	5.93913i	−0.615859	−	1.06670i	0.374374	−	0.927278i	$-0.377857\pi$
$32$	−5.59732			−0.989476
$33$	2.03142			0.353624
$34$	−7.14938	+	12.3831i	−1.22611	+	2.12368i
$35$	−0.395829	−	0.685595i	−0.0669073	−	0.115887i
$36$	3.35599	−	5.81274i	0.559331	−	0.968790i
$37$	1.06283	−	1.84087i	0.174727	−	0.302637i	−0.765340	−	0.643627i	$-0.777429\pi$
$37$	1.06283	−	1.84087i	0.174727	−	0.302637i	0.940067	+	0.340990i	$0.110762\pi$
$38$	4.98070			0.807976
$39$	1.08213	−	1.87431i	0.173280	−	0.300130i
$40$	−11.5434			−1.82517
$41$	−0.903577	+	1.56504i	−0.141115	+	0.244418i	−0.927917	−	0.372787i	$-0.878402\pi$
$41$	−0.903577	+	1.56504i	−0.141115	+	0.244418i	0.786802	+	0.617206i	$0.211735\pi$
$42$	−0.216883	+	0.375653i	−0.0334658	+	0.0579645i
$43$	−2.82883	+	4.89969i	−0.431393	+	0.747195i	−0.996994	−	0.0774845i	$-0.975311\pi$
$43$	−2.82883	+	4.89969i	−0.431393	+	0.747195i	0.565600	+	0.824680i	$0.308645\pi$
$44$	3.41454	−	5.91415i	0.514761	−	0.891592i
$45$	−4.17369	+	7.22904i	−0.622177	+	1.07764i
$46$	8.85943	+	15.3450i	1.30625	+	2.26250i
$47$	−1.13665			−0.165798			−0.0828990	−	0.996558i	$-0.526418\pi$
$47$	−1.13665			−0.165798			−0.0828990	+	0.996558i	$0.526418\pi$
$48$	0.0250382	+	0.0433675i	0.00361396	+	0.00625956i
$49$	3.48079	−	6.02891i	0.497256	−	0.861272i
$50$	25.9154			3.66499
$51$	−6.03004			−0.844375
$52$	−3.63784	−	6.30093i	−0.504478	−	0.873782i
$53$	4.46561	−	7.73466i	0.613398	−	1.06244i	−0.377265	−	0.926105i	$-0.623135\pi$
$53$	4.46561	−	7.73466i	0.613398	−	1.06244i	0.990663	−	0.136332i	$-0.0435313\pi$
$54$	11.2128			1.52586
$55$	−4.24651	+	7.35517i	−0.572599	+	0.991771i
$56$	0.280097	+	0.485142i	0.0374295	+	0.0648298i
$57$	1.05022	+	1.81904i	0.139106	+	0.240938i
$58$	−5.80770	+	10.0592i	−0.762588	+	1.32084i
$59$	3.31019	−	5.73342i	0.430950	−	0.746428i	−0.566005	−	0.824402i	$-0.691512\pi$
$59$	3.31019	−	5.73342i	0.430950	−	0.746428i	0.996955	+	0.0779739i	$0.0248451\pi$
$60$	−6.33587	−	10.9740i	−0.817957	−	1.41674i
$61$	−3.84677			−0.492528			−0.246264	−	0.969203i	$-0.579203\pi$
$61$	−3.84677			−0.492528			−0.246264	+	0.969203i	$0.579203\pi$
$62$	−7.85495	−	13.6052i	−0.997580	−	1.72786i
$63$	0.405093			0.0510369
$64$	−12.9258			−1.61573
$65$	4.52422	+	7.83618i	0.561161	+	0.971959i
$66$	4.65351			0.572807
$67$	−6.16321	−	10.6750i	−0.752956	−	1.30416i	−0.946384	−	0.323043i	$-0.895294\pi$
$67$	−6.16321	−	10.6750i	−0.752956	−	1.30416i	0.193429	−	0.981114i	$-0.438039\pi$
$68$	−10.1357	+	17.5555i	−1.22913	+	2.12892i
$69$	−3.73618	+	6.47126i	−0.449783	+	0.779048i
$70$	−0.906753	−	1.57054i	−0.108378	−	0.187716i
$71$	−5.76341	−	9.98251i	−0.683991	−	1.18471i	−0.973753	−	0.227608i	$-0.926910\pi$
$71$	−5.76341	−	9.98251i	−0.683991	−	1.18471i	0.289762	−	0.957099i	$-0.406424\pi$
$72$	2.95339	−	5.11542i	0.348060	−	0.602858i
$73$	15.5578			1.82091			0.910454	−	0.413610i	$-0.135732\pi$
$73$	15.5578			1.82091			0.910454	+	0.413610i	$0.135732\pi$
$74$	2.43469	−	4.21700i	0.283027	−	0.490217i
$75$	5.46449	+	9.46477i	0.630985	+	1.09290i
$76$	7.06114			0.809969
$77$	0.412161			0.0469701
$78$	2.47892	−	4.29362i	0.280682	−	0.486156i
$79$	5.01100	+	8.67931i	0.563782	+	0.976499i	0.997162	+	0.0752876i	$0.0239875\pi$
$79$	5.01100	+	8.67931i	0.563782	+	0.976499i	−0.433380	+	0.901211i	$0.642679\pi$
$80$	−0.209361			−0.0234073
$81$	−0.735785	−	1.27442i	−0.0817539	−	0.141602i
$82$	−2.06989	+	3.58515i	−0.228581	+	0.395913i
$83$	−3.65263	+	6.32654i	−0.400928	+	0.694428i	−0.993838	−	0.110841i	$-0.964646\pi$
$83$	−3.65263	+	6.32654i	−0.400928	+	0.694428i	0.592910	+	0.805269i	$0.297979\pi$
$84$	−0.307476	+	0.532564i	−0.0335484	+	0.0581075i
$85$	12.6053	−	21.8330i	1.36724	−	2.36812i
$86$	−6.48021	+	11.2241i	−0.698779	+	1.21032i
$87$	−4.89842			−0.525166
$88$	3.00492	−	5.20467i	0.320325	−	0.554820i
$89$	5.40131			0.572537			0.286269	−	0.958149i	$-0.407585\pi$
$89$	5.40131			0.572537			0.286269	+	0.958149i	$0.407585\pi$
$90$	−9.56097	+	16.5601i	−1.00781	+	1.74559i
$91$	0.219558	−	0.380285i	0.0230159	−	0.0398647i
$92$	12.5600	+	21.7546i	1.30947	+	2.26808i
$93$	3.31257	−	5.73754i	0.343498	−	0.594956i
$94$	−2.60381			−0.268563
$95$	−8.78162			−0.900976
$96$	−2.70367	−	4.68289i	−0.275942	−	0.477946i
$97$	6.27345	+	10.8659i	0.636973	+	1.10327i	0.986094	+	0.166191i	$0.0531469\pi$
$97$	6.27345	+	10.8659i	0.636973	+	1.10327i	−0.349121	+	0.937078i	$0.613520\pi$
$98$	7.97369	−	13.8108i	0.805465	−	1.39511i
$99$	−2.17295	−	3.76366i	−0.218390	−	0.378262i
$100$	36.7403			3.67403
$101$	0.463054	+	0.802033i	0.0460756	+	0.0798052i	0.888143	−	0.459566i	$-0.151995\pi$
$101$	0.463054	+	0.802033i	0.0460756	+	0.0798052i	−0.842068	+	0.539372i	$0.818662\pi$
$102$	−13.8134			−1.36773
$103$	−0.0315208	−	0.0545956i	−0.00310584	−	0.00537947i	0.864468	−	0.502687i	$-0.167655\pi$
$103$	−0.0315208	−	0.0545956i	−0.00310584	−	0.00537947i	−0.867574	+	0.497308i	$0.834322\pi$
$104$	−3.20143	−	5.54505i	−0.313926	−	0.543737i
$105$	0.382394	−	0.662325i	0.0373178	−	0.0646363i
$106$	10.2297	−	17.7183i	0.993594	−	1.72096i
$107$	−15.3210			−1.48113			−0.740566	−	0.671983i	$-0.765443\pi$
$107$	−15.3210			−1.48113			−0.740566	+	0.671983i	$0.765443\pi$
$108$	15.8964			1.52963
$109$	−5.33182	+	9.23497i	−0.510695	+	0.884550i	0.489228	+	0.872156i	$0.337279\pi$
$109$	−5.33182	+	9.23497i	−0.510695	+	0.884550i	−0.999923	+	0.0123942i	$0.996055\pi$
$110$	−9.72777	+	16.8490i	−0.927507	+	1.60649i
$111$	2.05350			0.194910
$112$	0.00508009	+	0.00879898i	0.000480023	+	0.000831425i
$113$	5.85614	+	10.1431i	0.550899	+	0.954185i	0.998210	+	0.0598064i	$0.0190483\pi$
$113$	5.85614	+	10.1431i	0.550899	+	0.954185i	−0.447311	+	0.894378i	$0.647618\pi$
$114$	2.40582	+	4.16701i	0.225326	+	0.390276i
$115$	−15.6203	−	27.0552i	−1.45661	−	2.52291i
$116$	−8.23358	+	14.2610i	−0.764469	+	1.32410i
$117$	−4.63011			−0.428054
$118$	7.58289	−	13.1340i	0.698062	−	1.20908i
$119$	−1.22345			−0.112154
$120$	−5.57579	−	9.65756i	−0.508998	−	0.881610i
$121$	3.28914	+	5.69696i	0.299013	+	0.517905i
$122$	−8.81206			−0.797807
$123$	−1.74582			−0.157415
$124$	−11.1360	−	19.2881i	−1.00004	−	1.73212i
$125$	−25.4976			−2.28057
$126$	0.927976			0.0826706
$127$	−9.20080	−	6.50732i	−0.816439	−	0.577431i
$127$	−9.20080	−	6.50732i	−0.816439	−	0.577431i
$128$	−18.4155			−1.62772
$129$	−5.46564			−0.481223
$130$	10.3640	+	17.9509i	0.908979	+	1.57440i
$131$	−0.219763			−0.0192008			−0.00960038	−	0.999954i	$-0.503056\pi$
$131$	−0.219763			−0.0192008			−0.00960038	+	0.999954i	$0.503056\pi$
$132$	6.59729			0.574220
$133$	0.213083	+	0.369071i	0.0184767	+	0.0320025i
$134$	−14.1185	−	24.4539i	−1.21965	−	2.11250i
$135$	−19.7696			−1.70149
$136$	−8.91977	+	15.4495i	−0.764864	+	1.32478i
$137$	−9.25296			−0.790534			−0.395267	−	0.918566i	$-0.629348\pi$
$137$	−9.25296			−0.790534			−0.395267	+	0.918566i	$0.629348\pi$
$138$	−8.55873	+	14.8242i	−0.728568	+	1.26192i
$139$	−3.77088	−	6.53136i	−0.319842	−	0.553983i	0.660613	−	0.750727i	$-0.270296\pi$
$139$	−3.77088	−	6.53136i	−0.319842	−	0.553983i	−0.980455	+	0.196744i	$0.936963\pi$
$140$	−1.28550	−	2.22656i	−0.108645	−	0.188179i
$141$	−0.549037	−	0.950961i	−0.0462373	−	0.0800853i
$142$	−13.2026	−	22.8676i	−1.10794	−	1.91901i
$143$	−4.71089			−0.393945
$144$	0.0535654	−	0.0927780i	0.00446378	−	0.00773150i
$145$	10.2397	−	17.7357i	0.850364	−	1.47287i
$146$	35.6395			2.94954
$147$	6.72529			0.554693
$148$	3.45166	−	5.97845i	0.283725	−	0.491426i
$149$	3.59996	−	6.23532i	0.294921	−	0.510817i	−0.680046	−	0.733170i	$-0.738040\pi$
$149$	3.59996	−	6.23532i	0.294921	−	0.510817i	0.974966	+	0.222352i	$0.0713735\pi$
$150$	12.5179	+	21.6816i	1.02208	+	1.77030i
$151$	7.61514	+	13.1898i	0.619711	+	1.07337i	0.989538	+	0.144271i	$0.0460837\pi$
$151$	7.61514	+	13.1898i	0.619711	+	1.07337i	−0.369827	+	0.929101i	$0.620583\pi$
$152$	6.21406			0.504027
$153$	6.45017	+	11.1720i	0.521465	+	0.903204i
$154$	0.944166			0.0760830
$155$	13.8493	+	23.9877i	1.11240	+	1.92674i
$156$	3.51437	−	6.08707i	0.281375	−	0.487355i
$157$	0.909296	+	1.57495i	0.0725697	+	0.125694i	0.900027	−	0.435834i	$-0.143547\pi$
$157$	0.909296	+	1.57495i	0.0725697	+	0.125694i	−0.827457	+	0.561529i	$0.810213\pi$
$158$	11.4791	+	19.8823i	0.913225	+	1.58175i
$159$	8.62808			0.684251
$160$	22.6072			1.78725
$161$	−0.758046	+	1.31297i	−0.0597424	+	0.103477i
$162$	−1.68551	−	2.91940i	−0.132427	−	0.229369i
$163$	2.92926	−	5.07363i	0.229438	−	0.397398i	−0.728204	−	0.685360i	$-0.759645\pi$
$163$	2.92926	−	5.07363i	0.229438	−	0.397398i	0.957642	+	0.287963i	$0.0929780\pi$
$164$	−2.93448	+	5.08267i	−0.229145	+	0.396890i
$165$	−8.20475			−0.638739
$166$	−8.36733	+	14.4926i	−0.649431	+	1.12485i
$167$	−14.8075			−1.14584			−0.572918	−	0.819613i	$-0.694189\pi$
$167$	−14.8075			−1.14584			−0.572918	+	0.819613i	$0.694189\pi$
$168$	−0.270590	+	0.468675i	−0.0208765	+	0.0361591i
$169$	3.99051	−	6.91177i	0.306962	−	0.531675i
$170$	28.8758	−	50.0144i	2.21468	−	3.83593i
$171$	2.24679	−	3.89155i	0.171816	−	0.297595i
$172$	−9.18701	+	15.9124i	−0.700503	+	1.21331i
$173$	−6.75967	−	11.7081i	−0.513928	−	0.890150i	−0.999869	−	0.0161581i	$-0.994856\pi$
$173$	−6.75967	−	11.7081i	−0.513928	−	0.890150i	0.485941	−	0.873991i	$-0.338477\pi$
$174$	−11.2212			−0.850673
$175$	1.10871	+	1.92034i	0.0838104	+	0.145164i
$176$	0.0545000	−	0.0943967i	0.00410809	−	0.00711542i
$177$	6.39568			0.480729
$178$	12.3732			0.927407
$179$	−2.59343	−	4.49195i	−0.193842	−	0.335744i	0.752678	−	0.658388i	$-0.228762\pi$
$179$	−2.59343	−	4.49195i	−0.193842	−	0.335744i	−0.946520	+	0.322644i	$0.895428\pi$
$180$	−13.5546	+	23.4773i	−1.01030	+	1.74989i
$181$	−19.3594			−1.43897			−0.719485	−	0.694508i	$-0.755622\pi$
$181$	−19.3594			−1.43897			−0.719485	+	0.694508i	$0.755622\pi$
$182$	0.502956	−	0.871146i	0.0372816	−	0.0645736i
$183$	−1.85810	−	3.21833i	−0.137355	−	0.237906i
$184$	11.0533	+	19.1449i	0.814859	+	1.41138i
$185$	−4.29268	+	7.43513i	−0.315604	+	0.546642i
$186$	7.58834	−	13.1434i	0.556404	−	0.963721i
$187$	6.56270	+	11.3669i	0.479912	+	0.831232i
$188$	−3.69143			−0.269225
$189$	0.479703	+	0.830870i	0.0348932	+	0.0604369i
$190$	−20.1167			−1.45942
$191$	13.8955			1.00544			0.502721	−	0.864449i	$-0.332332\pi$
$191$	13.8955			1.00544			0.502721	+	0.864449i	$0.332332\pi$
$192$	−6.24356	−	10.8142i	−0.450590	−	0.780445i
$193$	8.23013			0.592418			0.296209	−	0.955123i	$-0.404278\pi$
$193$	8.23013			0.592418			0.296209	+	0.955123i	$0.404278\pi$
$194$	14.3710	+	24.8914i	1.03178	+	1.78710i
$195$	−4.37066	+	7.57021i	−0.312990	+	0.542114i
$196$	11.3043	−	19.5797i	0.807451	−	1.39855i
$197$	5.62470	+	9.74227i	0.400743	+	0.694108i	0.993816	−	0.111041i	$-0.0354186\pi$
$197$	5.62470	+	9.74227i	0.400743	+	0.694108i	−0.593073	+	0.805149i	$0.702085\pi$
$198$	−4.97773	−	8.62168i	−0.353752	−	0.612716i
$199$	−2.50451	+	4.33794i	−0.177540	+	0.307509i	−0.941037	−	0.338302i	$-0.890147\pi$
$199$	−2.50451	+	4.33794i	−0.177540	+	0.307509i	0.763497	+	0.645811i	$0.223481\pi$
$200$	32.3328			2.28627
$201$	5.95402	−	10.3127i	0.419964	−	0.727399i
$202$	1.06075	+	1.83727i	0.0746341	+	0.129270i
$203$	−0.993856			−0.0697550
$204$	−19.5833			−1.37111
$205$	3.64948	−	6.32109i	0.254891	−	0.441484i
$206$	−0.0722069	−	0.125066i	−0.00503090	−	0.00871377i
$207$	15.9859			1.11110
$208$	−0.0580641	−	0.100570i	−0.00402602	−	0.00697328i
$209$	2.28599	−	3.95945i	0.158125	−	0.273881i
$210$	0.875976	−	1.51724i	0.0604481	−	0.104699i
$211$	−7.73138	+	13.3911i	−0.532250	+	0.921884i	0.467041	+	0.884236i	$0.345320\pi$
$211$	−7.73138	+	13.3911i	−0.532250	+	0.921884i	−0.999291	+	0.0376483i	$0.988013\pi$
$212$	14.5026	−	25.1193i	0.996045	−	1.72520i
$213$	5.56779	−	9.64369i	0.381499	−	0.660775i
$214$	−35.0968			−2.39917
$215$	11.4255	−	19.7895i	0.779210	−	1.34963i
$216$	13.9894			0.951856
$217$	0.672099	−	1.16411i	0.0456250	−	0.0790249i
$218$	−12.2140	+	21.1552i	−0.827234	+	1.43281i
$219$	7.51490	+	13.0162i	0.507810	+	0.879552i
$220$	−13.7911	+	23.8869i	−0.929795	+	1.61045i
$221$	13.9838			0.940650
$222$	4.70410			0.315719
$223$	10.5780	+	18.3217i	0.708358	+	1.22691i	0.965466	+	0.260529i	$0.0838969\pi$
$223$	10.5780	+	18.3217i	0.708358	+	1.22691i	−0.257108	+	0.966383i	$0.582770\pi$
$224$	−0.548556	−	0.950127i	−0.0366519	−	0.0634830i
$225$	11.6904	−	20.2484i	0.779361	−	1.34989i
$226$	13.4151	+	23.2356i	0.892357	+	1.54561i
$227$	15.2122			1.00967			0.504833	−	0.863217i	$-0.331554\pi$
$227$	15.2122			1.00967			0.504833	+	0.863217i	$0.331554\pi$
$228$	3.41074	+	5.90757i	0.225882	+	0.391238i
$229$	−3.41189			−0.225464			−0.112732	−	0.993625i	$-0.535960\pi$
$229$	−3.41189			−0.225464			−0.112732	+	0.993625i	$0.535960\pi$
$230$	−35.7826	−	61.9773i	−2.35944	−	4.08666i
$231$	0.199086	+	0.344827i	0.0130989	+	0.0226879i
$232$	−7.24585	+	12.5502i	−0.475713	+	0.823960i
$233$	−2.54006	+	4.39951i	−0.166405	+	0.288222i	−0.937153	−	0.348918i	$-0.886549\pi$
$233$	−2.54006	+	4.39951i	−0.166405	+	0.288222i	0.770748	+	0.637140i	$0.219883\pi$
$234$	−10.6065			−0.693370
$235$	4.59087			0.299475
$236$	10.7503	−	18.6200i	0.699783	−	1.21206i
$237$	−4.84092	+	8.38472i	−0.314452	+	0.544646i
$238$	−2.80265			−0.181669
$239$	0.667352	+	1.15589i	0.0431674	+	0.0747681i	0.886802	−	0.462150i	$-0.152922\pi$
$239$	0.667352	+	1.15589i	0.0431674	+	0.0747681i	−0.843634	+	0.536918i	$0.819588\pi$
$240$	−0.101128	−	0.175158i	−0.00652777	−	0.0113064i
$241$	−3.26175	−	5.64952i	−0.210108	−	0.363918i	0.741640	−	0.670798i	$-0.234048\pi$
$241$	−3.26175	−	5.64952i	−0.210108	−	0.363918i	−0.951748	+	0.306880i	$0.900715\pi$
$242$	7.53466	+	13.0504i	0.484347	+	0.838913i
$243$	8.05295	−	13.9481i	0.516597	−	0.894772i
$244$	−12.4929			−0.799775
$245$	−14.0587	+	24.3503i	−0.898175	+	1.55569i
$246$	−3.99926			−0.254984
$247$	−2.43549	−	4.21839i	−0.154966	−	0.268410i
$248$	−9.80007	−	16.9742i	−0.622305	−	1.07786i
$249$	−7.05731			−0.447239
$250$	−58.4091			−3.69411
$251$	−1.14257	−	1.97898i	−0.0721181	−	0.124912i	0.827711	−	0.561154i	$-0.189643\pi$
$251$	−1.14257	−	1.97898i	−0.0721181	−	0.124912i	−0.899829	+	0.436242i	$0.856309\pi$
$252$	1.31559			0.0828745
$253$	16.2649			1.02256
$254$	−21.0769	−	14.9068i	−1.32248	−	0.935335i
$255$	24.3549			1.52516
$256$	−16.3340			−1.02088
$257$	−3.97362	−	6.88252i	−0.247868	−	0.429320i	0.715066	−	0.699057i	$-0.246397\pi$
$257$	−3.97362	−	6.88252i	−0.247868	−	0.429320i	−0.962934	+	0.269737i	$0.913063\pi$
$258$	−12.5205			−0.779494
$259$	0.416642			0.0258889
$260$	14.6930	+	25.4490i	0.911221	+	1.57828i
$261$	5.23970	+	9.07543i	0.324329	+	0.561755i
$262$	−0.503426			−0.0311018
$263$	−1.75362	+	3.03735i	−0.108133	+	0.187291i	−0.915014	−	0.403423i	$-0.867820\pi$
$263$	−1.75362	+	3.03735i	−0.108133	+	0.187291i	0.806881	+	0.590714i	$0.201154\pi$
$264$	5.80585			0.357326
$265$	−18.0363	+	31.2397i	−1.10796	+	1.91904i
$266$	0.488125	+	0.845457i	0.0299289	+	0.0518383i
$267$	2.60899	+	4.51890i	0.159668	+	0.276552i
$268$	−20.0158	−	34.6684i	−1.22266	−	2.11771i
$269$	14.6943	+	25.4513i	0.895930	+	1.55180i	0.832650	+	0.553800i	$0.186823\pi$
$269$	14.6943	+	25.4513i	0.895930	+	1.55180i	0.0632797	+	0.997996i	$0.479844\pi$
$270$	−45.2876			−2.75611
$271$	2.81358	−	4.87326i	0.170913	−	0.296030i	−0.767826	−	0.640658i	$-0.778662\pi$
$271$	2.81358	−	4.87326i	0.170913	−	0.296030i	0.938739	+	0.344628i	$0.111995\pi$
$272$	−0.161777	+	0.280206i	−0.00980918	+	0.0169900i
$273$	0.424211			0.0256744
$274$	−21.1964			−1.28052
$275$	11.8944	−	20.6017i	0.717258	−	1.24233i
$276$	−12.1337	+	21.0162i	−0.730365	+	1.26503i
$277$	2.37513	+	4.11385i	0.142708	+	0.247177i	0.928515	−	0.371294i	$-0.121086\pi$
$277$	2.37513	+	4.11385i	0.142708	+	0.247177i	−0.785808	+	0.618471i	$0.787752\pi$
$278$	−8.63822	−	14.9618i	−0.518086	−	0.897352i
$279$	−14.1735			−0.848543
$280$	−1.13129	−	1.95945i	−0.0676076	−	0.117100i
$281$	−26.3749			−1.57340			−0.786699	−	0.617337i	$-0.788211\pi$
$281$	−26.3749			−1.57340			−0.786699	+	0.617337i	$0.788211\pi$
$282$	−1.25772	−	2.17843i	−0.0748960	−	0.129724i
$283$	11.0033	−	19.0583i	0.654078	−	1.13290i	−0.328046	−	0.944662i	$-0.606390\pi$
$283$	11.0033	−	19.0583i	0.654078	−	1.13290i	0.982124	−	0.188235i	$-0.0602765\pi$
$284$	−18.7174	−	32.4195i	−1.11067	−	1.92374i
$285$	−4.24178	−	7.34698i	−0.251261	−	0.435198i
$286$	−10.7916			−0.638119
$287$	−0.354214			−0.0209086
$288$	−5.78408	+	10.0183i	−0.340830	+	0.590335i
$289$	−10.9807	−	19.0191i	−0.645921	−	1.11877i
$290$	23.4569	−	40.6285i	1.37744	−	2.38579i
$291$	−6.06052	+	10.4971i	−0.355274	+	0.615353i
$292$	50.5261			2.95682
$293$	0.852791	−	1.47708i	0.0498206	−	0.0862918i	−0.840040	−	0.542525i	$-0.817468\pi$
$293$	0.852791	−	1.47708i	0.0498206	−	0.0862918i	0.889860	+	0.456233i	$0.150802\pi$
$294$	15.4061			0.898502
$295$	−13.3696	+	23.1569i	−0.778410	+	1.34825i
$296$	3.03759	−	5.26126i	0.176556	−	0.305804i
$297$	5.14632	−	8.91369i	0.298620	−	0.517225i
$298$	8.24669	−	14.2837i	0.477718	−	0.827432i
$299$	8.66427	−	15.0070i	0.501068	−	0.867875i
$300$	17.7466	+	30.7381i	1.02460	+	1.77466i
$301$	−1.10894			−0.0639183
$302$	17.4445	+	30.2148i	1.00382	+	1.73867i
$303$	−0.447337	+	0.774810i	−0.0256988	+	0.0445117i
$304$	0.112704			0.00646401
$305$	15.5368			0.889636
$306$	14.7758	+	25.5925i	0.844679	+	1.46303i
$307$	7.86393	−	13.6207i	0.448818	−	0.777375i	−0.549491	−	0.835499i	$-0.685179\pi$
$307$	7.86393	−	13.6207i	0.448818	−	0.777375i	0.998309	+	0.0581239i	$0.0185118\pi$
$308$	1.33855			0.0762707
$309$	0.0304509	−	0.0527426i	0.00173229	−	0.00300042i
$310$	31.7256	+	54.9503i	1.80189	+	3.12097i
$311$	−9.46136	−	16.3876i	−0.536505	−	0.929253i	−0.999089	−	0.0426779i	$-0.986411\pi$
$311$	−9.46136	−	16.3876i	−0.536505	−	0.929253i	0.462584	−	0.886575i	$-0.346922\pi$
$312$	3.09277	−	5.35684i	0.175094	−	0.303271i
$313$	3.44226	−	5.96217i	0.194568	−	0.337002i	−0.752191	−	0.658945i	$-0.771003\pi$
$313$	3.44226	−	5.96217i	0.194568	−	0.337002i	0.946759	+	0.321944i	$0.104336\pi$
$314$	2.08299	+	3.60784i	0.117550	+	0.203602i
$315$	−1.63614			−0.0921862
$316$	16.2739	+	28.1872i	0.915477	+	1.58565i
$317$	13.6422			0.766221			0.383110	−	0.923703i	$-0.374853\pi$
$317$	13.6422			0.766221			0.383110	+	0.923703i	$0.374853\pi$
$318$	19.7649			1.10836
$319$	5.33112	+	9.23376i	0.298485	+	0.516991i
$320$	52.2066			2.91844
$321$	−7.40047	−	12.8180i	−0.413054	−	0.715430i
$322$	−1.73651	+	3.00772i	−0.0967719	+	0.167614i
$323$	−6.78571	+	11.7532i	−0.377567	+	0.653965i
$324$	−2.38956	−	4.13883i	−0.132753	−	0.229935i
$325$	−12.6722	−	21.9490i	−0.702929	−	1.21751i
$326$	6.71027	−	11.6225i	0.371647	−	0.643712i
$327$	−10.3017			−0.569685
$328$	−2.58245	+	4.47294i	−0.142592	+	0.246977i
$329$	−0.111396	−	0.192943i	−0.00614146	−	0.0106373i
$330$	−18.7952			−1.03464
$331$	−22.3751			−1.22984			−0.614922	−	0.788588i	$-0.710813\pi$
$331$	−22.3751			−1.22984			−0.614922	+	0.788588i	$0.710813\pi$
$332$	−11.8624	+	20.5462i	−0.651033	+	1.12762i
$333$	−2.19657	−	3.80458i	−0.120372	−	0.208490i
$334$	−33.9205			−1.85605
$335$	24.8928	+	43.1155i	1.36004	+	2.35565i
$336$	−0.00490767	+	0.00850033i	−0.000267735	+	0.000463731i
$337$	−15.6868	+	27.1704i	−0.854515	+	1.48006i	0.0225785	+	0.999745i	$0.492812\pi$
$337$	−15.6868	+	27.1704i	−0.854515	+	1.48006i	−0.877094	+	0.480319i	$0.840521\pi$
$338$	9.14135	−	15.8333i	0.497224	−	0.861217i
$339$	−5.65737	+	9.79885i	−0.307266	+	0.532201i
$340$	40.9373	−	70.9055i	2.22014	−	3.84539i
$341$	−14.4207			−0.780927
$342$	5.14688	−	8.91466i	0.278311	−	0.482049i
$343$	2.73656			0.147761
$344$	−8.08490	+	14.0035i	−0.435909	+	0.755016i
$345$	15.0902	−	26.1369i	0.812427	−	1.40717i
$346$	−15.4848	−	26.8205i	−0.832471	−	1.44188i
$347$	14.9278	−	25.8558i	0.801369	−	1.38801i	−0.117346	−	0.993091i	$-0.537439\pi$
$347$	14.9278	−	25.8558i	0.801369	−	1.38801i	0.918715	−	0.394921i	$-0.129228\pi$
$348$	−15.9082			−0.852771
$349$	12.0868			0.646991			0.323496	−	0.946230i	$-0.395142\pi$
$349$	12.0868			0.646991			0.323496	+	0.946230i	$0.395142\pi$
$350$	2.53979	+	4.39905i	0.135758	+	0.235139i
$351$	−5.48288	−	9.49663i	−0.292655	−	0.506893i
$352$	−5.88499	+	10.1931i	−0.313671	+	0.543294i
$353$	15.7376	+	27.2584i	0.837629	+	1.45082i	0.891872	+	0.452288i	$0.149392\pi$
$353$	15.7376	+	27.2584i	0.837629	+	1.45082i	−0.0542429	+	0.998528i	$0.517275\pi$
$354$	14.6510			0.778694
$355$	23.2780	+	40.3187i	1.23547	+	2.13989i
$356$	17.5414			0.929694
$357$	−0.590964	−	1.02358i	−0.0312772	−	0.0541736i
$358$	−5.94095	−	10.2900i	−0.313989	−	0.543844i
$359$	14.6979	−	25.4575i	0.775724	−	1.34359i	−0.158663	−	0.987333i	$-0.550718\pi$
$359$	14.6979	−	25.4575i	0.775724	−	1.34359i	0.934387	−	0.356260i	$-0.115948\pi$
$360$	−11.9285	+	20.6608i	−0.628689	+	1.08892i
$361$	−14.2727			−0.751193
$362$	−44.3479			−2.33087
$363$	−3.17750	+	5.50359i	−0.166776	+	0.288864i
$364$	0.713042	−	1.23502i	0.0373735	−	0.0647329i
$365$	−62.8371			−3.28904
$366$	−4.25648	−	7.37245i	−0.222490	−	0.385364i
$367$	5.97466	+	10.3484i	0.311875	+	0.540183i	0.978768	−	0.204970i	$-0.0657097\pi$
$367$	5.97466	+	10.3484i	0.311875	+	0.540183i	−0.666893	+	0.745153i	$0.732376\pi$
$368$	0.200473	+	0.347229i	0.0104504	+	0.0181005i
$369$	1.86745	+	3.23452i	0.0972155	+	0.168382i
$370$	−9.83354	+	17.0322i	−0.511221	+	0.885461i
$371$	1.75058			0.0908855
$372$	10.7580	−	18.6334i	0.557777	−	0.966097i
$373$	21.7720			1.12731			0.563655	−	0.826010i	$-0.309395\pi$
$373$	21.7720			1.12731			0.563655	+	0.826010i	$0.309395\pi$
$374$	15.0336	+	26.0390i	0.777371	+	1.34645i
$375$	−12.3161	−	21.3321i	−0.635999	−	1.10158i
$376$	−3.24859			−0.167533
$377$	11.3595			0.585045
$378$	1.09889	+	1.90333i	0.0565208	+	0.0978968i
$379$	−17.9436			−0.921699			−0.460850	−	0.887478i	$-0.652455\pi$
$379$	−17.9436			−0.921699			−0.460850	+	0.887478i	$0.652455\pi$
$380$	−28.5195			−1.46302
$381$	0.999972	−	10.8409i	0.0512301	−	0.555396i
$382$	31.8314			1.62863
$383$	−0.445217			−0.0227496			−0.0113748	−	0.999935i	$-0.503621\pi$
$383$	−0.445217			−0.0227496			−0.0113748	+	0.999935i	$0.503621\pi$
$384$	−8.89523	−	15.4070i	−0.453933	−	0.786234i
$385$	−1.66469			−0.0848404
$386$	18.8533			0.959610
$387$	5.84644	+	10.1263i	0.297191	+	0.514750i
$388$	20.3738	+	35.2885i	1.03433	+	1.79150i
$389$	−3.91158			−0.198325			−0.0991626	−	0.995071i	$-0.531616\pi$
$389$	−3.91158			−0.198325			−0.0991626	+	0.995071i	$0.531616\pi$
$390$	−10.0122	+	17.3416i	−0.506987	+	0.878127i
$391$	−48.2805			−2.44165
$392$	9.94821	−	17.2308i	0.502460	−	0.870287i
$393$	−0.106152	−	0.183860i	−0.00535465	−	0.00927453i
$394$	12.8849	+	22.3173i	0.649132	+	1.12433i
$395$	−20.2391	−	35.0551i	−1.01834	−	1.76381i
$396$	−7.05693	−	12.2230i	−0.354624	−	0.614227i
$397$	17.4764			0.877114			0.438557	−	0.898703i	$-0.355490\pi$
$397$	17.4764			0.877114			0.438557	+	0.898703i	$0.355490\pi$
$398$	−5.73726	+	9.93723i	−0.287583	+	0.498108i
$399$	−0.205851	+	0.356544i	−0.0103054	+	0.0178495i
$400$	0.586417			0.0293208
$401$	8.56031			0.427482			0.213741	−	0.976890i	$-0.431435\pi$
$401$	8.56031			0.427482			0.213741	+	0.976890i	$0.431435\pi$
$402$	13.6393	−	23.6239i	0.680266	−	1.17826i
$403$	−7.68191	+	13.3055i	−0.382663	+	0.662793i
$404$	1.50383	+	2.60470i	0.0748182	+	0.129589i
$405$	2.97178	+	5.14728i	0.147669	+	0.255770i
$406$	−2.27670			−0.112991
$407$	−2.23490	−	3.87096i	−0.110780	−	0.191876i
$408$	−17.2340			−0.853213
$409$	2.19831	+	3.80759i	0.108700	+	0.188273i	0.915244	−	0.402901i	$-0.131998\pi$
$409$	2.19831	+	3.80759i	0.108700	+	0.188273i	−0.806544	+	0.591174i	$0.798665\pi$
$410$	8.36013	−	14.4802i	0.412877	−	0.715124i
$411$	−4.46945	−	7.74132i	−0.220462	−	0.381851i
$412$	−0.102368	−	0.177306i	−0.00504330	−	0.00873526i
$413$	1.29764			0.0638527
$414$	36.6201			1.79978
$415$	14.7527	−	25.5524i	0.724182	−	1.25432i
$416$	6.26986	+	10.8597i	0.307405	+	0.532441i
$417$	3.64289	−	6.30967i	0.178393	−	0.308986i
$418$	5.23668	−	9.07019i	0.256134	−	0.443637i
$419$	−12.8908			−0.629758			−0.314879	−	0.949132i	$-0.601964\pi$
$419$	−12.8908			−0.629758			−0.314879	+	0.949132i	$0.601964\pi$
$420$	1.24187	−	2.15099i	0.0605972	−	0.104957i
$421$	−0.628897			−0.0306506			−0.0153253	−	0.999883i	$-0.504878\pi$
$421$	−0.628897			−0.0306506			−0.0153253	+	0.999883i	$0.504878\pi$
$422$	−17.7108	+	30.6760i	−0.862149	+	1.49329i
$423$	−1.17458	+	2.03443i	−0.0571100	+	0.0989174i
$424$	12.7628	−	22.1059i	0.619819	−	1.07356i
$425$	−35.3072	+	61.1538i	−1.71265	+	2.96639i
$426$	12.7545	−	22.0915i	0.617959	−	1.07034i
$427$	−0.376996	−	0.652977i	−0.0182441	−	0.0315998i
$428$	−49.7568			−2.40508
$429$	−2.27550	−	3.94128i	−0.109862	−	0.190287i
$430$	26.1731	−	45.3332i	1.26218	−	2.18616i
$431$	−12.0526			−0.580553			−0.290276	−	0.956943i	$-0.593747\pi$
$431$	−12.0526			−0.580553			−0.290276	+	0.956943i	$0.593747\pi$
$432$	0.253724			0.0122073
$433$	−5.83676	−	10.1096i	−0.280497	−	0.485834i	0.691011	−	0.722845i	$-0.257166\pi$
$433$	−5.83676	−	10.1096i	−0.280497	−	0.485834i	−0.971507	+	0.237010i	$0.923832\pi$
$434$	1.53962	−	2.66671i	0.0739043	−	0.128006i
$435$	19.7844			0.948588
$436$	−17.3158	+	29.9918i	−0.829274	+	1.43635i
$437$	8.40878	+	14.5644i	0.402246	+	0.696711i
$438$	17.2149	+	29.8171i	0.822560	+	1.42472i
$439$	7.42256	−	12.8562i	0.354259	−	0.613595i	−0.632732	−	0.774371i	$-0.718066\pi$
$439$	7.42256	−	12.8562i	0.354259	−	0.613595i	0.986991	+	0.160776i	$0.0513997\pi$
$440$	−12.1367	+	21.0213i	−0.578592	+	1.00215i
$441$	−7.19386	−	12.4601i	−0.342565	−	0.593339i
$442$	32.0336			1.52368
$443$	9.89563	+	17.1397i	0.470156	+	0.814334i	0.999418	−	0.0341250i	$-0.0108644\pi$
$443$	9.89563	+	17.1397i	0.470156	+	0.814334i	−0.529262	+	0.848459i	$0.677531\pi$
$444$	6.66901			0.316497
$445$	−21.8155			−1.03415
$446$	24.2319	+	41.9708i	1.14741	+	1.98737i
$447$	6.95555			0.328986
$448$	−1.26678	−	2.19412i	−0.0598496	−	0.103662i
$449$	12.6142	−	21.8484i	0.595300	−	1.03109i	−0.398204	−	0.917297i	$-0.630367\pi$
$449$	12.6142	−	21.8484i	0.595300	−	1.03109i	0.993504	−	0.113793i	$-0.0363001\pi$
$450$	26.7801	−	46.3844i	1.26242	−	2.18658i
$451$	1.90003	+	3.29095i	0.0894690	+	0.154965i
$452$	19.0186	+	32.9411i	0.894558	+	1.54942i
$453$	−7.35667	+	12.7421i	−0.345647	+	0.598678i
$454$	34.8476			1.63548
$455$	−0.886778	+	1.53594i	−0.0415728	+	0.0720062i
$456$	3.00157	+	5.19888i	0.140562	+	0.243460i
$457$	18.9512			0.886500			0.443250	−	0.896398i	$-0.353825\pi$
$457$	18.9512			0.886500			0.443250	+	0.896398i	$0.353825\pi$
$458$	−7.81585			−0.365211
$459$	−15.2763	+	26.4593i	−0.713037	+	1.23502i
$460$	−50.7291	−	87.8654i	−2.36526	−	4.09674i
$461$	−14.3130			−0.666624			−0.333312	−	0.942817i	$-0.608166\pi$
$461$	−14.3130			−0.666624			−0.333312	+	0.942817i	$0.608166\pi$
$462$	0.456060	+	0.789919i	0.0212178	+	0.0367503i
$463$	18.0830	−	31.3206i	0.840386	−	1.45559i	−0.0491823	−	0.998790i	$-0.515662\pi$
$463$	18.0830	−	31.3206i	0.840386	−	1.45559i	0.889568	−	0.456802i	$-0.151005\pi$
$464$	−0.131417	+	0.227622i	−0.00610090	+	0.0105671i
$465$	−13.3792	+	23.1735i	−0.620448	+	1.07465i
$466$	−5.81869	+	10.0783i	−0.269546	+	0.466867i
$467$	3.55041	−	6.14948i	0.164293	−	0.284564i	−0.772111	−	0.635488i	$-0.780799\pi$
$467$	3.55041	−	6.14948i	0.164293	−	0.284564i	0.936404	+	0.350924i	$0.114132\pi$
$468$	−15.0369			−0.695080
$469$	1.20803	−	2.09237i	0.0557817	−	0.0966167i
$470$	10.5166			0.485096
$471$	−0.878433	+	1.52149i	−0.0404761	+	0.0701066i
$472$	9.46063	−	16.3863i	0.435461	−	0.754240i
$473$	5.94844	+	10.3030i	0.273510	+	0.473733i
$474$	−11.0894	+	19.2075i	−0.509355	+	0.882229i
$475$	24.5971			1.12859
$476$	−3.97333			−0.182117
$477$	−9.22921	−	15.9855i	−0.422576	−	0.731924i
$478$	1.52875	+	2.64787i	0.0699234	+	0.121111i
$479$	11.2972	−	19.5674i	0.516183	−	0.894056i	−0.483640	−	0.875267i	$-0.660686\pi$
$479$	11.2972	−	19.5674i	0.516183	−	0.894056i	0.999823	−	0.0187889i	$-0.00598106\pi$
$480$	10.9199	+	18.9139i	0.498424	+	0.863296i
$481$	−4.76211			−0.217133
$482$	−7.47193	−	12.9418i	−0.340337	−	0.589481i
$483$	−1.46463			−0.0666431
$484$	10.6819	+	18.5016i	0.485541	+	0.840982i
$485$	−25.3380	−	43.8868i	−1.15054	−	1.99280i
$486$	18.4475	−	31.9519i	0.836794	−	1.44937i
$487$	−14.7068	+	25.4730i	−0.666431	+	1.15429i	0.312464	+	0.949929i	$0.398846\pi$
$487$	−14.7068	+	25.4730i	−0.666431	+	1.15429i	−0.978895	+	0.204363i	$0.934488\pi$
$488$	−10.9942			−0.497683
$489$	5.65968			0.255940
$490$	−32.2052	+	55.7810i	−1.45488	+	2.51993i
$491$	−3.39665	+	5.88317i	−0.153289	+	0.265504i	−0.932435	−	0.361339i	$-0.882320\pi$
$491$	−3.39665	+	5.88317i	−0.153289	+	0.265504i	0.779146	+	0.626843i	$0.215653\pi$
$492$	−5.66976			−0.255613
$493$	−15.8248	−	27.4094i	−0.712715	−	1.23446i
$494$	−5.57914	−	9.66336i	−0.251018	−	0.434775i
$495$	8.77639	+	15.2012i	0.394469	+	0.683241i
$496$	−0.177743	−	0.307860i	−0.00798089	−	0.0138233i
$497$	1.12967	−	1.95664i	0.0506725	−	0.0877673i
$498$	−16.1667			−0.724446
$499$	−9.30823	+	16.1223i	−0.416694	+	0.721735i	−0.995605	−	0.0936561i	$-0.970145\pi$
$499$	−9.30823	+	16.1223i	−0.416694	+	0.721735i	0.578911	+	0.815391i	$0.303478\pi$
$500$	−82.8066			−3.70322
$501$	−7.15244	−	12.3884i	−0.319547	−	0.553472i
$502$	−2.61735	−	4.53339i	−0.116818	−	0.202335i
$503$	−7.65271			−0.341217			−0.170609	−	0.985339i	$-0.554573\pi$
$503$	−7.65271			−0.341217			−0.170609	+	0.985339i	$0.554573\pi$
$504$	1.15777			0.0515711
$505$	−1.87024	−	3.23935i	−0.0832246	−	0.144149i
$506$	37.2590			1.65637
$507$	7.71014			0.342419
$508$	−29.8808	−	21.1334i	−1.32575	−	0.937642i
$509$	−9.59328			−0.425215			−0.212607	−	0.977138i	$-0.568196\pi$
$509$	−9.59328			−0.425215			−0.212607	+	0.977138i	$0.568196\pi$
$510$	55.7915			2.47049
$511$	1.52472	+	2.64090i	0.0674497	+	0.116826i
$512$	−0.586439			−0.0259172
$513$	10.6424			0.469874
$514$	−9.10266	−	15.7663i	−0.401501	−	0.695420i
$515$	0.127310	+	0.220508i	0.00560996	+	0.00971674i
$516$	−17.7504			−0.781416
$517$	−1.19507	+	2.06993i	−0.0525592	+	0.0910352i
$518$	0.954431			0.0419353
$519$	6.53024	−	11.3107i	0.286646	−	0.496485i
$520$	12.9304	+	22.3960i	0.567034	+	0.982132i
$521$	−3.00310	−	5.20153i	−0.131568	−	0.227883i	0.792713	−	0.609595i	$-0.208668\pi$
$521$	−3.00310	−	5.20153i	−0.131568	−	0.227883i	−0.924281	+	0.381712i	$0.875335\pi$
$522$	12.0029	+	20.7897i	0.525355	+	0.909941i
$523$	−2.29949	−	3.98284i	−0.100550	−	0.174157i	0.811362	−	0.584545i	$-0.198727\pi$
$523$	−2.29949	−	3.98284i	−0.100550	−	0.174157i	−0.911911	+	0.410387i	$0.865394\pi$
$524$	−0.713708			−0.0311785
$525$	−1.07108	+	1.85516i	−0.0467456	+	0.0809658i
$526$	−4.01713	+	6.95788i	−0.175155	+	0.303378i
$527$	42.8064			1.86468
$528$	0.105300			0.00458261
$529$	−18.4143	+	31.8945i	−0.800622	+	1.38672i
$530$	−41.3170	+	71.5631i	−1.79469	+	3.10850i
$531$	−6.84128	−	11.8494i	−0.296886	−	0.514222i
$532$	0.692016	+	1.19861i	0.0300027	+	0.0519662i
$533$	4.04858			0.175363
$534$	5.97660	+	10.3518i	0.258633	+	0.447965i
$535$	61.8802			2.67532
$536$	−17.6146	−	30.5095i	−0.760837	−	1.31781i
$537$	2.50540	−	4.33948i	0.108116	−	0.187263i
$538$	33.6614	+	58.3032i	1.45124	+	2.51363i
$539$	−7.31937	−	12.6775i	−0.315267	−	0.546059i
$540$	−64.2043			−2.76291
$541$	−2.03663			−0.0875615			−0.0437808	−	0.999041i	$-0.513940\pi$
$541$	−2.03663			−0.0875615			−0.0437808	+	0.999041i	$0.513940\pi$
$542$	6.44527	−	11.1635i	0.276848	−	0.479515i
$543$	−9.35114	−	16.1967i	−0.401296	−	0.695065i
$544$	17.4690	−	30.2571i	0.748975	−	1.29726i
$545$	21.5348	−	37.2994i	0.922451	−	1.59773i
$546$	0.971770			0.0415879
$547$	−16.0254	+	27.7568i	−0.685198	+	1.18680i	0.288177	+	0.957577i	$0.406951\pi$
$547$	−16.0254	+	27.7568i	−0.685198	+	1.18680i	−0.973375	+	0.229220i	$0.926383\pi$
$548$	−30.0502			−1.28368
$549$	−3.97512	+	6.88511i	−0.169654	+	0.293849i
$550$	27.2473	−	47.1937i	1.16183	−	2.01234i
$551$	−5.51228	+	9.54754i	−0.234831	+	0.406739i
$552$	−10.6781	+	18.4951i	−0.454491	+	0.787202i
$553$	−0.982190	+	1.70120i	−0.0417670	+	0.0723425i
$554$	5.44088	+	9.42389i	0.231161	+	0.400383i
$555$	−8.29395			−0.352059
$556$	−12.2464	−	21.2114i	−0.519364	−	0.899565i
$557$	12.4171	−	21.5070i	0.526128	−	0.911280i	−0.473409	−	0.880843i	$-0.656977\pi$
$557$	12.4171	−	21.5070i	0.526128	−	0.911280i	0.999537	−	0.0304372i	$-0.00968996\pi$
$558$	−32.4681			−1.37449
$559$	12.6749			0.536092
$560$	−0.0205181	−	0.0355384i	−0.000867049	−	0.00150177i
$561$	−6.33995	+	10.9811i	−0.267673	+	0.463623i
$562$	−60.4189			−2.54862
$563$	−5.88558	+	10.1941i	−0.248048	+	0.429631i	−0.962984	−	0.269558i	$-0.913122\pi$
$563$	−5.88558	+	10.1941i	−0.248048	+	0.429631i	0.714936	+	0.699189i	$0.246456\pi$
$564$	−1.78307	−	3.08837i	−0.0750808	−	0.130044i
$565$	−23.6525	−	40.9674i	−0.995069	−	1.72351i
$566$	25.2060	−	43.6581i	1.05949	−	1.83509i
$567$	0.144219	−	0.249794i	0.00605662	−	0.0104904i
$568$	−16.4720	−	28.5303i	−0.691150	−	1.19711i
$569$	1.34809			0.0565148			0.0282574	−	0.999601i	$-0.491004\pi$
$569$	1.34809			0.0565148			0.0282574	+	0.999601i	$0.491004\pi$
$570$	−9.71695	−	16.8302i	−0.406998	−	0.704941i
$571$	11.0148			0.460953			0.230477	−	0.973078i	$-0.425971\pi$
$571$	11.0148			0.460953			0.230477	+	0.973078i	$0.425971\pi$
$572$	−15.2992			−0.639693
$573$	6.71192	+	11.6254i	0.280395	+	0.485658i
$574$	−0.811423			−0.0338682
$575$	43.7522	+	75.7811i	1.82459	+	3.16029i
$576$	−13.3571	+	23.1352i	−0.556547	+	0.963967i
$577$	−10.4841	+	18.1591i	−0.436461	+	0.755972i	−0.997414	−	0.0718755i	$-0.977102\pi$
$577$	−10.4841	+	18.1591i	−0.436461	+	0.755972i	0.560953	+	0.827848i	$0.310435\pi$
$578$	−25.1542	−	43.5683i	−1.04628	−	1.81220i
$579$	3.97539	+	6.88559i	0.165212	+	0.286155i
$580$	33.2549	−	57.5991i	1.38083	−	2.39167i
$581$	−1.43188			−0.0594044
$582$	−13.8833	+	24.0465i	−0.575480	+	0.996760i
$583$	−9.39023	−	16.2644i	−0.388904	−	0.673601i
$584$	44.4648			1.83997
$585$	18.7007			0.773179
$586$	1.95355	−	3.38365i	0.0807004	−	0.139777i
$587$	3.63197	+	6.29076i	0.149908	+	0.259647i	0.931193	−	0.364526i	$-0.118769\pi$
$587$	3.63197	+	6.29076i	0.149908	+	0.259647i	−0.781286	+	0.624174i	$0.785436\pi$
$588$	21.8413			0.900718
$589$	−7.45539	−	12.9131i	−0.307194	−	0.532076i
$590$	−30.6268	+	53.0471i	−1.26088	+	2.18391i
$591$	−5.43379	+	9.41160i	−0.223516	+	0.387141i
$592$	0.0550925	−	0.0954230i	0.00226429	−	0.00392186i
$593$	−10.8990	+	18.8777i	−0.447570	+	0.775213i	−0.998227	−	0.0595178i	$-0.981044\pi$
$593$	−10.8990	+	18.8777i	−0.447570	+	0.775213i	0.550658	+	0.834731i	$0.314377\pi$
$594$	11.7890	−	20.4192i	0.483710	−	0.837811i
$595$	4.94145			0.202580
$596$	11.6913	−	20.2500i	0.478896	−	0.829473i
$597$	−4.83901			−0.198048
$598$	19.8479	−	34.3775i	0.811639	−	1.40580i
$599$	0.542120	−	0.938979i	0.0221504	−	0.0383656i	−0.854738	−	0.519060i	$-0.826282\pi$
$599$	0.542120	−	0.938979i	0.0221504	−	0.0383656i	0.876888	+	0.480695i	$0.159615\pi$
$600$	15.6177	+	27.0506i	0.637589	+	1.10434i
$601$	−8.46487	+	14.6616i	−0.345289	+	0.598059i	−0.985406	−	0.170219i	$-0.945553\pi$
$601$	−8.46487	+	14.6616i	−0.345289	+	0.598059i	0.640117	+	0.768277i	$0.278886\pi$
$602$	−2.54033			−0.103536
$603$	−25.4754			−1.03744
$604$	24.7312	+	42.8356i	1.00630	+	1.74296i
$605$	−13.2846	−	23.0096i	−0.540096	−	0.935474i
$606$	−1.02475	+	1.77491i	−0.0416275	+	0.0721009i
$607$	−17.7666	−	30.7726i	−0.721123	−	1.24902i	−0.960550	−	0.278107i	$-0.910293\pi$
$607$	−17.7666	−	30.7726i	−0.721123	−	1.24902i	0.239427	−	0.970914i	$-0.423040\pi$
$608$	−12.1699			−0.493556
$609$	−0.480062	−	0.831491i	−0.0194531	−	0.0336937i
$610$	35.5913			1.44105
$611$	1.27323	+	2.20529i	0.0515093	+	0.0892167i
$612$	20.9477	+	36.2826i	0.846762	+	1.46664i
$613$	−4.05128	+	7.01703i	−0.163630	+	0.283415i	−0.936168	−	0.351553i	$-0.885654\pi$
$613$	−4.05128	+	7.01703i	−0.163630	+	0.283415i	0.772538	+	0.634968i	$0.218987\pi$
$614$	18.0144	−	31.2019i	0.727004	−	1.25921i
$615$	7.05123			0.284333
$616$	1.17797			0.0474617
$617$	11.7219	−	20.3030i	0.471908	−	0.817369i	−0.527575	−	0.849508i	$-0.676899\pi$
$617$	11.7219	−	20.3030i	0.471908	−	0.817369i	0.999483	+	0.0321397i	$0.0102321\pi$
$618$	0.0697561	−	0.120821i	0.00280600	−	0.00486014i
$619$	43.9360			1.76594			0.882969	−	0.469431i	$-0.155541\pi$
$619$	43.9360			1.76594			0.882969	+	0.469431i	$0.155541\pi$
$620$	44.9774	+	77.9032i	1.80634	+	3.12867i
$621$	18.9302	+	32.7881i	0.759644	+	1.31574i
$622$	−21.6738	−	37.5401i	−0.869040	−	1.50522i
$623$	0.529346	+	0.916855i	0.0212078	+	0.0367330i
$624$	0.0560934	−	0.0971565i	0.00224553	−	0.00388937i
$625$	46.4181			1.85672
$626$	7.88543	−	13.6580i	0.315165	−	0.545882i
$627$	4.41680			0.176390
$628$	2.95306	+	5.11485i	0.117840	+	0.204105i
$629$	6.63405	+	11.4905i	0.264517	+	0.458157i
$630$	−3.74803			−0.149325
$631$	−3.43451			−0.136726			−0.0683628	−	0.997661i	$-0.521778\pi$
$631$	−3.43451			−0.136726			−0.0683628	+	0.997661i	$0.521778\pi$
$632$	14.3216	+	24.8057i	0.569683	+	0.986720i
$633$	−14.9379			−0.593729
$634$	31.2511			1.24114
$635$	37.1614	+	26.2826i	1.47470	+	1.04299i
$636$	28.0208			1.11110
$637$	−15.5961			−0.617939
$638$	12.2124	+	21.1524i	0.483492	+	0.837433i
$639$	−23.8228			−0.942416
$640$	74.3789			2.94008
$641$	−20.4851	−	35.4813i	−0.809115	−	1.40143i	−0.913478	−	0.406888i	$-0.866614\pi$
$641$	−20.4851	−	35.4813i	−0.809115	−	1.40143i	0.104363	−	0.994539i	$-0.466720\pi$
$642$	−16.9528	−	29.3631i	−0.669073	−	1.15887i
$643$	−49.3793			−1.94733			−0.973665	−	0.227984i	$-0.926787\pi$
$643$	−49.3793			−1.94733			−0.973665	+	0.227984i	$0.926787\pi$
$644$	−2.46185	+	4.26405i	−0.0970106	+	0.168027i
$645$	22.0753			0.869215
$646$	−15.5445	+	26.9239i	−0.611590	+	1.05931i
$647$	−14.5468	−	25.1957i	−0.571892	−	0.990546i	−0.996372	−	0.0851082i	$-0.972876\pi$
$647$	−14.5468	−	25.1957i	−0.571892	−	0.990546i	0.424480	−	0.905437i	$-0.360457\pi$
$648$	−2.10290	−	3.64232i	−0.0826096	−	0.143084i
$649$	−6.96064	−	12.0562i	−0.273229	−	0.473246i
$650$	−29.0292	−	50.2800i	−1.13862	−	1.97215i
$651$	1.29857			0.0508951
$652$	9.51316	−	16.4773i	0.372564	−	0.645300i
$653$	−21.5722	+	37.3642i	−0.844186	+	1.46217i	0.0421407	+	0.999112i	$0.486582\pi$
$653$	−21.5722	+	37.3642i	−0.844186	+	1.46217i	−0.886326	+	0.463061i	$0.846751\pi$
$654$	−23.5988			−0.922786
$655$	0.887607			0.0346817
$656$	−0.0468377	+	0.0811253i	−0.00182870	+	0.00316741i
$657$	16.0769	−	27.8461i	0.627221	−	1.08638i
$658$	−0.255183	−	0.441989i	−0.00994805	−	0.0172305i
$659$	4.37577	+	7.57905i	0.170456	+	0.295238i	0.938579	−	0.345064i	$-0.112143\pi$
$659$	4.37577	+	7.57905i	0.170456	+	0.295238i	−0.768124	+	0.640302i	$0.778809\pi$
$660$	−26.6460			−1.03719
$661$	17.8867	+	30.9807i	0.695713	+	1.20501i	0.969940	+	0.243346i	$0.0782449\pi$
$661$	17.8867	+	30.9807i	0.695713	+	1.20501i	−0.274226	+	0.961665i	$0.588422\pi$
$662$	−51.2561			−1.99213
$663$	6.75457	+	11.6993i	0.262326	+	0.454362i
$664$	−10.4393	+	18.0814i	−0.405124	+	0.701696i
$665$	−0.860629	−	1.49065i	−0.0333738	−	0.0578050i
$666$	−5.03185	−	8.71541i	−0.194980	−	0.337715i
$667$	−39.2199			−1.51860
$668$	−48.0891			−1.86062
$669$	−10.2190	+	17.6998i	−0.395089	+	0.684315i
$670$	57.0236	+	98.7678i	2.20301	+	3.81573i
$671$	−4.04447	+	7.00523i	−0.156135	+	0.270434i
$672$	0.529937	−	0.917878i	0.0204428	−	0.0354079i
$673$	12.0114			0.463005			0.231502	−	0.972834i	$-0.425636\pi$
$673$	12.0114			0.463005			0.231502	+	0.972834i	$0.425636\pi$
$674$	−35.9349	+	62.2411i	−1.38416	+	2.39744i
$675$	55.3742			2.13135
$676$	12.9597	−	22.4469i	0.498450	−	0.863341i
$677$	6.99572	−	12.1169i	0.268867	−	0.465692i	−0.699702	−	0.714435i	$-0.746684\pi$
$677$	6.99572	−	12.1169i	0.268867	−	0.465692i	0.968570	+	0.248743i	$0.0800173\pi$
$678$	−12.9597	+	22.4469i	−0.497716	+	0.862069i
$679$	−1.22964	+	2.12980i	−0.0471892	+	0.0817341i
$680$	36.0263	−	62.3995i	1.38155	−	2.39291i
$681$	7.34792	+	12.7270i	0.281573	+	0.487699i
$682$	−33.0346			−1.26496
$683$	−5.77771	−	10.0073i	−0.221078	−	0.382918i	0.734058	−	0.679087i	$-0.237624\pi$
$683$	−5.77771	−	10.0073i	−0.221078	−	0.382918i	−0.955136	+	0.296169i	$0.904291\pi$
$684$	7.29674	−	12.6383i	0.278998	−	0.483238i
$685$	37.3721			1.42791
$686$	6.26884			0.239345
$687$	−1.64804	−	2.85449i	−0.0628767	−	0.108906i
$688$	−0.146635	+	0.253979i	−0.00559041	+	0.00968288i
$689$	−20.0087			−0.762269
$690$	34.5681	−	59.8737i	1.31599	−	2.27935i
$691$	−15.8040	−	27.3733i	−0.601212	−	1.04133i	−0.992638	−	0.121120i	$-0.961351\pi$
$691$	−15.8040	−	27.3733i	−0.601212	−	1.04133i	0.391426	−	0.920210i	$-0.371982\pi$
$692$	−21.9529	−	38.0235i	−0.834524	−	1.44544i
$693$	0.425913	−	0.737703i	0.0161791	−	0.0280230i
$694$	34.1963	−	59.2297i	1.29807	−	2.24833i
$695$	15.2303	+	26.3797i	0.577719	+	1.00064i
$696$	−13.9998			−0.530662
$697$	−5.64004	−	9.76883i	−0.213632	−	0.370021i
$698$	27.6881			1.04801
$699$	−4.90769			−0.185626
$700$	3.60067	+	6.23654i	0.136093	+	0.235719i
$701$	25.8678			0.977012			0.488506	−	0.872561i	$-0.337542\pi$
$701$	25.8678			0.977012			0.488506	+	0.872561i	$0.337542\pi$
$702$	−12.5600	−	21.7546i	−0.474047	−	0.821074i
$703$	2.31084	−	4.00250i	0.0871551	−	0.150957i
$704$	−13.5902	+	23.5388i	−0.512198	+	0.887154i
$705$	2.21752	+	3.84086i	0.0835168	+	0.144655i
$706$	36.0513	+	62.4426i	1.35681	+	2.35006i
$707$	−0.0907617	+	0.157204i	−0.00341344	+	0.00591226i
$708$	20.7708			0.780614
$709$	−7.18674	+	12.4478i	−0.269904	+	0.467487i	−0.968837	−	0.247700i	$-0.920325\pi$
$709$	−7.18674	+	12.4478i	−0.269904	+	0.467487i	0.698933	+	0.715187i	$0.253659\pi$
$710$	53.3245	+	92.3608i	2.00123	+	3.46624i
$711$	20.7128			0.776790
$712$	15.4371			0.578530
$713$	26.5226	−	45.9385i	0.993280	−	1.72041i
$714$	−1.35376	−	2.34479i	−0.0506633	−	0.0877515i
$715$	19.0270			0.711568
$716$	−8.42249	−	14.5882i	−0.314763	−	0.545186i
$717$	−0.644701	+	1.11665i	−0.0240768	+	0.0417022i
$718$	33.6694	−	58.3172i	1.25653	−	2.17638i
$719$	13.5229	−	23.4223i	0.504317	−	0.873503i	−0.495670	−	0.868511i	$-0.665078\pi$
$719$	13.5229	−	23.4223i	0.504317	−	0.873503i	0.999988	−	0.00499235i	$-0.00158912\pi$
$720$	−0.216347	+	0.374724i	−0.00806277	+	0.0139651i
$721$	0.00617829	−	0.0107011i	0.000230092	−	0.000398530i
$722$	−32.6954			−1.21680
$723$	3.15104	−	5.45777i	0.117189	−	0.202977i
$724$	−62.8720			−2.33662
$725$	−28.6813	+	49.6774i	−1.06520	+	1.84497i
$726$	−7.27893	+	12.6075i	−0.270146	+	0.467907i
$727$	4.76044	+	8.24533i	0.176555	+	0.305802i	0.940698	−	0.339244i	$-0.110171\pi$
$727$	4.76044	+	8.24533i	0.176555	+	0.305802i	−0.764143	+	0.645046i	$0.776838\pi$
$728$	0.627503	−	1.08687i	0.0232568	−	0.0402820i
$729$	11.1445			0.412760
$730$	−143.945			−5.32765
$731$	−17.6573	−	30.5834i	−0.653079	−	1.13117i
$732$	−6.03443	−	10.4519i	−0.223039	−	0.386315i
$733$	−7.09897	+	12.2958i	−0.262207	+	0.454155i	−0.966828	−	0.255428i	$-0.917783\pi$
$733$	−7.09897	+	12.2958i	−0.262207	+	0.454155i	0.704621	+	0.709583i	$0.251117\pi$
$734$	13.6866	+	23.7058i	0.505181	+	0.874999i
$735$	−27.1630			−1.00192
$736$	−21.6473	−	37.4943i	−0.797931	−	1.38206i
$737$	−25.9198			−0.954770
$738$	4.27790	+	7.40954i	0.157472	+	0.272749i
$739$	22.0592	+	38.2076i	0.811459	+	1.40549i	0.911843	+	0.410540i	$0.134660\pi$
$739$	22.0592	+	38.2076i	0.811459	+	1.40549i	−0.100383	+	0.994949i	$0.532007\pi$
$740$	−13.9410	+	24.1466i	−0.512482	+	0.887645i
$741$	2.35282	−	4.07521i	0.0864332	−	0.149707i
$742$	4.01017			0.147218
$743$	−12.1824			−0.446928			−0.223464	−	0.974712i	$-0.571737\pi$
$743$	−12.1824			−0.446928			−0.223464	+	0.974712i	$0.571737\pi$
$744$	9.46744	−	16.3981i	0.347093	−	0.601183i
$745$	−14.5400	+	25.1840i	−0.532704	+	0.922671i
$746$	49.8746			1.82604
$747$	7.54900	+	13.0753i	0.276203	+	0.478398i
$748$	21.3132	+	36.9156i	0.779288	+	1.34977i
$749$	−1.50151	−	2.60068i	−0.0548638	−	0.0950269i
$750$	−28.2133	−	48.8668i	−1.03020	−	1.78436i
$751$	−4.99370	+	8.64935i	−0.182223	+	0.315619i	−0.942637	−	0.333819i	$-0.891663\pi$
$751$	−4.99370	+	8.64935i	−0.182223	+	0.315619i	0.760414	+	0.649438i	$0.224996\pi$
$752$	−0.0589195			−0.00214857
$753$	1.10378	−	1.91181i	0.0402242	−	0.0696703i
$754$	26.0220			0.947667
$755$	−30.7570	−	53.2727i	−1.11936	−	1.93879i
$756$	1.55790	+	2.69836i	0.0566602	+	0.0981383i
$757$	−29.1469			−1.05936			−0.529681	−	0.848197i	$-0.677688\pi$
$757$	−29.1469			−1.05936			−0.529681	+	0.848197i	$0.677688\pi$
$758$	−41.1046			−1.49299
$759$	7.85640	+	13.6077i	0.285169	+	0.493928i
$760$	−25.0982			−0.910406
$761$	−13.6940			−0.496407			−0.248204	−	0.968708i	$-0.579840\pi$
$761$	−13.6940			−0.496407			−0.248204	+	0.968708i	$0.579840\pi$
$762$	2.29071	−	24.8340i	0.0829835	−	0.899642i
$763$	−2.09014			−0.0756683
$764$	45.1274			1.63265
$765$	−26.0518	−	45.1230i	−0.941903	−	1.63142i
$766$	−1.01989			−0.0368502
$767$	−14.8317			−0.535541
$768$	−7.88980	−	13.6655i	−0.284699	−	0.493113i
$769$	4.84167	+	8.38602i	0.174595	+	0.302408i	0.940021	−	0.341116i	$-0.110805\pi$
$769$	4.84167	+	8.38602i	0.174595	+	0.302408i	−0.765426	+	0.643524i	$0.777472\pi$
$770$	−3.81342			−0.137426
$771$	3.83875	−	6.64892i	0.138249	−	0.239455i
$772$	26.7284			0.961977
$773$	24.4963	−	42.4288i	0.881069	−	1.52606i	0.0309160	−	0.999522i	$-0.490158\pi$
$773$	24.4963	−	42.4288i	0.881069	−	1.52606i	0.850153	−	0.526535i	$-0.176509\pi$
$774$	13.3929	+	23.1971i	0.481396	+	0.833803i
$775$	−38.7916	−	67.1890i	−1.39344	−	2.41350i
$776$	17.9297	+	31.0552i	0.643640	+	1.11482i
$777$	0.201250	+	0.348576i	0.00721981	+	0.0125051i
$778$	−8.96054			−0.321251
$779$	−1.96460	+	3.40278i	−0.0703890	+	0.121917i
$780$	−14.1943	+	24.5852i	−0.508237	+	0.880292i
$781$	−24.2385			−0.867320
$782$	−110.599			−3.95503
$783$	−12.4095	+	21.4939i	−0.443479	+	0.768128i
$784$	0.180430	−	0.312514i	0.00644392	−	0.0111612i
$785$	−3.67258	−	6.36110i	−0.131080	−	0.227037i
$786$	−0.243170	−	0.421182i	−0.00867357	−	0.0150231i
$787$	−38.5688			−1.37483			−0.687414	−	0.726266i	$-0.741254\pi$
$787$	−38.5688			−1.37483			−0.687414	+	0.726266i	$0.741254\pi$
$788$	18.2669	+	31.6393i	0.650733	+	1.12710i
$789$	−3.38819			−0.120623
$790$	−46.3631	−	80.3032i	−1.64953	−	2.85706i
$791$	−1.14784	+	1.98812i	−0.0408126	+	0.0706894i
$792$	−6.21036	−	10.7567i	−0.220675	−	0.382221i
$793$	4.30897	+	7.46336i	0.153016	+	0.265032i
$794$	40.0344			1.42077
$795$	−34.8482			−1.23594
$796$	−8.13373	+	14.0880i	−0.288292	+	0.499337i
$797$	21.9506	+	38.0196i	0.777531	+	1.34672i	0.933361	+	0.358939i	$0.116861\pi$
$797$	21.9506	+	38.0196i	0.777531	+	1.34672i	−0.155831	+	0.987784i	$0.549805\pi$
$798$	−0.471557	+	0.816761i	−0.0166930	+	0.0289130i
$799$	3.54744	−	6.14435i	0.125499	−	0.217371i
$800$	−63.3222			−2.23878
$801$	5.58152	−	9.66748i	0.197213	−	0.341584i
$802$	19.6097			0.692443
$803$	16.3574	−	28.3319i	0.577241	−	0.999811i
$804$	19.3364	−	33.4917i	0.681944	−	1.18116i
$805$	3.06169	−	5.30301i	0.107911	−	0.186907i
$806$	−17.5975	+	30.4798i	−0.619846	+	1.07360i
$807$	−14.1956	+	24.5875i	−0.499708	+	0.865520i
$808$	1.32342	+	2.29223i	0.0465578	+	0.0806405i
$809$	25.4482			0.894710			0.447355	−	0.894357i	$-0.352366\pi$
$809$	25.4482			0.894710			0.447355	+	0.894357i	$0.352366\pi$
$810$	6.80767	+	11.7912i	0.239197	+	0.414302i
$811$	1.19195	−	2.06452i	0.0418551	−	0.0724952i	−0.844339	−	0.535809i	$-0.820007\pi$
$811$	1.19195	−	2.06452i	0.0418551	−	0.0724952i	0.886194	+	0.463314i	$0.153340\pi$
$812$	−3.22768			−0.113269
$813$	5.43617			0.190655
$814$	−5.11964	−	8.86747i	−0.179443	−	0.310805i
$815$	−11.8311	+	20.4920i	−0.414425	+	0.717805i
$816$	−0.312573			−0.0109422
$817$	−6.15058	+	10.6531i	−0.215182	+	0.372705i
$818$	5.03583	+	8.72231i	0.176074	+	0.304969i
$819$	−0.453767	−	0.785947i	−0.0158559	−	0.0274632i
$820$	11.8522	−	20.5285i	0.413896	−	0.716888i
$821$	10.1849	−	17.6407i	0.355454	−	0.615665i	−0.631741	−	0.775179i	$-0.717659\pi$
$821$	10.1849	−	17.6407i	0.355454	−	0.615665i	0.987196	+	0.159514i	$0.0509928\pi$
$822$	−10.2385	−	17.7336i	−0.357108	−	0.618530i
$823$	5.00707			0.174535			0.0872677	−	0.996185i	$-0.472186\pi$
$823$	5.00707			0.174535			0.0872677	+	0.996185i	$0.472186\pi$
$824$	−0.0900875	−	0.156036i	−0.00313835	−	0.00543577i
$825$	22.9813			0.800107
$826$	2.97260			0.103430
$827$	12.9930	+	22.5045i	0.451809	+	0.782556i	0.998498	−	0.0547791i	$-0.0174455\pi$
$827$	12.9930	+	22.5045i	0.451809	+	0.782556i	−0.546689	+	0.837336i	$0.684112\pi$
$828$	51.9164			1.80422
$829$	2.17764	+	3.77178i	0.0756324	+	0.130999i	0.901361	−	0.433068i	$-0.142569\pi$
$829$	2.17764	+	3.77178i	0.0756324	+	0.130999i	−0.825729	+	0.564067i	$0.809236\pi$
$830$	33.7951	−	58.5348i	1.17304	−	2.03177i
$831$	−2.29452	+	3.97422i	−0.0795959	+	0.137864i
$832$	14.4789	+	25.0782i	0.501967	+	0.869432i
$833$	21.7268	+	37.6318i	0.752787	+	1.30387i
$834$	8.34503	−	14.4540i	0.288965	−	0.500502i
$835$	59.8063			2.06968
$836$	7.42404	−	12.8588i	0.256766	−	0.444732i
$837$	−16.7839	−	29.0706i	−0.580137	−	1.00483i
$838$	−29.5299			−1.02009
$839$	−26.4316			−0.912520			−0.456260	−	0.889846i	$-0.650811\pi$
$839$	−26.4316			−0.912520			−0.456260	+	0.889846i	$0.650811\pi$
$840$	1.09289	−	1.89295i	0.0377084	−	0.0653129i
$841$	1.64492	+	2.84908i	0.0567213	+	0.0982443i
$842$	−1.44066			−0.0496484
$843$	−12.7399	−	22.0661i	−0.438784	−	0.759997i
$844$	−25.1086	+	43.4894i	−0.864275	+	1.49697i
$845$	−16.1174	+	27.9162i	−0.554455	+	0.960345i
$846$	−2.69069	+	4.66042i	−0.0925079	+	0.160228i
$847$	−0.644694	+	1.11664i	−0.0221519	+	0.0383683i
$848$	0.231479	−	0.400933i	0.00794901	−	0.0137681i
$849$	21.2597			0.729629
$850$	−80.8806	+	140.089i	−2.77418	+	4.80502i
$851$	16.4417			0.563614
$852$	18.0821	−	31.3191i	0.619483	−	1.07298i
$853$	14.6521	−	25.3781i	0.501677	−	0.868930i	−0.498321	−	0.866992i	$-0.666050\pi$
$853$	14.6521	−	25.3781i	0.501677	−	0.868930i	0.999998	−	0.00193738i	$-0.000616687\pi$
$854$	−0.863612	−	1.49582i	−0.0295522	−	0.0511859i
$855$	−9.07463	+	15.7177i	−0.310346	+	0.537534i
$856$	−43.7878			−1.49663
$857$	−6.86506			−0.234506			−0.117253	−	0.993102i	$-0.537409\pi$
$857$	−6.86506			−0.234506			−0.117253	+	0.993102i	$0.537409\pi$
$858$	−5.21265	−	9.02857i	−0.177957	−	0.308230i
$859$	−23.5362	−	40.7658i	−0.803043	−	1.39091i	−0.917604	−	0.397495i	$-0.869880\pi$
$859$	−23.5362	−	40.7658i	−0.803043	−	1.39091i	0.114561	−	0.993416i	$-0.463454\pi$
$860$	37.1057	−	64.2689i	1.26529	−	2.19155i
$861$	−0.171096	−	0.296347i	−0.00583093	−	0.0100995i
$862$	−27.6097			−0.940391
$863$	−4.73356	−	8.19877i	−0.161132	−	0.279089i	0.774143	−	0.633011i	$-0.218181\pi$
$863$	−4.73356	−	8.19877i	−0.161132	−	0.279089i	−0.935275	+	0.353922i	$0.884848\pi$
$864$	−27.3975			−0.932083
$865$	27.3018	+	47.2881i	0.928290	+	1.60785i
$866$	−13.3707	−	23.1587i	−0.454354	−	0.786964i
$867$	10.6080	−	18.3735i	0.360265	−	0.623998i
$868$	2.18273	−	3.78059i	0.0740866	−	0.128322i
$869$	21.0742			0.714892
$870$	45.3214			1.53654
$871$	−13.8075	+	23.9153i	−0.467849	+	0.810337i
$872$	−15.2385	+	26.3938i	−0.516041	+	0.893808i
$873$	25.9311			0.877634
$874$	19.2626	+	33.3638i	0.651567	+	1.12855i
$875$	−2.49885	−	4.32813i	−0.0844765	−	0.146318i
$876$	24.4056	+	42.2717i	0.824589	+	1.42823i
$877$	0.197358	+	0.341833i	0.00666429	+	0.0115429i	0.869338	−	0.494217i	$-0.164545\pi$
$877$	0.197358	+	0.341833i	0.00666429	+	0.0115429i	−0.862674	+	0.505760i	$0.831212\pi$
$878$	17.0034	−	29.4507i	0.573836	−	0.993913i
$879$	1.64769			0.0555753
$880$	−0.220121	+	0.381262i	−0.00742029	+	0.0128523i
$881$	37.9366			1.27811			0.639057	−	0.769159i	$-0.279325\pi$
$881$	37.9366			1.27811			0.639057	+	0.769159i	$0.279325\pi$
$882$	−16.4795	−	28.5433i	−0.554893	−	0.961103i
$883$	5.05492	+	8.75538i	0.170112	+	0.294642i	0.938459	−	0.345391i	$-0.112254\pi$
$883$	5.05492	+	8.75538i	0.170112	+	0.294642i	−0.768347	+	0.640033i	$0.778920\pi$
$884$	45.4141			1.52744
$885$	−25.8317			−0.868323
$886$	22.6686	+	39.2632i	0.761567	+	1.31907i
$887$	11.0010			0.369376			0.184688	−	0.982797i	$-0.440873\pi$
$887$	11.0010			0.369376			0.184688	+	0.982797i	$0.440873\pi$
$888$	5.86898			0.196950
$889$	0.202888	−	2.19955i	0.00680463	−	0.0737704i
$890$	−49.9743			−1.67514
$891$	−3.09440			−0.103666
$892$	34.3535	+	59.5021i	1.15024	+	1.99228i
$893$	−2.47137			−0.0827011
$894$	15.9336			0.532898
$895$	10.4747	+	18.1427i	0.350130	+	0.606442i
$896$	−1.80478	−	3.12597i	−0.0602935	−	0.104431i
$897$	16.7404			0.558945
$898$	28.8962	−	50.0497i	0.964278	−	1.67018i
$899$	34.7732			1.15975
$900$	37.9661	−	65.7593i	1.26554	−	2.19198i
$901$	27.8739	+	48.2790i	0.928614	+	1.60841i
$902$	4.35253	+	7.53881i	0.144924	+	0.251015i
$903$	−0.535651	−	0.927775i	−0.0178254	−	0.0308744i
$904$	16.7370	+	28.9894i	0.556665	+	0.964172i
$905$	78.1911			2.59916
$906$	−16.8524	+	29.1893i	−0.559885	+	0.969749i
$907$	−10.3231	+	17.8802i	−0.342773	+	0.593701i	−0.984947	−	0.172859i	$-0.944700\pi$
$907$	−10.3231	+	17.8802i	−0.342773	+	0.593701i	0.642173	+	0.766560i	$0.278033\pi$
$908$	49.4035			1.63951
$909$	1.91402			0.0634839
$910$	−2.03140	+	3.51850i	−0.0673404	+	0.116637i
$911$	13.4043	−	23.2170i	0.444105	−	0.769212i	−0.553884	−	0.832594i	$-0.686855\pi$
$911$	13.4043	−	23.2170i	0.444105	−	0.769212i	0.997989	+	0.0633813i	$0.0201884\pi$
$912$	0.0544393	+	0.0942916i	0.00180266	+	0.00312231i
$913$	7.68071	+	13.3034i	0.254194	+	0.440277i
$914$	43.4129			1.43597
$915$	7.50474	+	12.9986i	0.248099	+	0.429720i
$916$	−11.0805			−0.366111
$917$	−0.0215375	−	0.0373040i	−0.000711231	−	0.00123189i
$918$	−34.9945	+	60.6122i	−1.15499	+	2.00050i
$919$	11.1050	+	19.2345i	0.366321	+	0.634486i	0.988987	−	0.148001i	$-0.0472840\pi$
$919$	11.1050	+	19.2345i	0.366321	+	0.634486i	−0.622666	+	0.782487i	$0.713951\pi$
$920$	−44.6434	−	77.3247i	−1.47185	−	2.54932i
$921$	15.1940			0.500660
$922$	−32.7879			−1.07981
$923$	−12.9118	+	22.3639i	−0.424997	+	0.736117i
$924$	0.646557	+	1.11987i	0.0212701	+	0.0368410i
$925$	12.0237	−	20.8256i	0.395336	−	0.684743i
$926$	41.4239	−	71.7483i	1.36127	−	2.35780i
$927$	−0.130290			−0.00427929
$928$	14.1907	−	24.5789i	0.465831	−	0.806843i
$929$	6.32303			0.207452			0.103726	−	0.994606i	$-0.466924\pi$
$929$	6.32303			0.207452			0.103726	+	0.994606i	$0.466924\pi$
$930$	−30.6488	+	53.0852i	−1.00501	+	1.74073i
$931$	7.56809	−	13.1083i	0.248034	−	0.429608i
$932$	−8.24917	+	14.2880i	−0.270211	+	0.468019i
$933$	9.14023	−	15.8313i	0.299238	−	0.518295i
$934$	8.13316	−	14.0871i	0.266125	−	0.460942i
$935$	−26.5063	−	45.9102i	−0.866848	−	1.50142i
$936$	−13.2330			−0.432534
$937$	−3.04258	−	5.26990i	−0.0993966	−	0.172160i	0.812038	−	0.583604i	$-0.198358\pi$
$937$	−3.04258	−	5.26990i	−0.0993966	−	0.172160i	−0.911435	+	0.411444i	$0.865025\pi$
$938$	2.76732	−	4.79314i	0.0903562	−	0.156502i
$939$	6.65085			0.217042
$940$	14.9094			0.486292
$941$	−14.0188	−	24.2812i	−0.456998	−	0.791544i	0.541802	−	0.840506i	$-0.317742\pi$
$941$	−14.0188	−	24.2812i	−0.456998	−	0.791544i	−0.998801	+	0.0489616i	$0.984409\pi$
$942$	−2.01229	+	3.48539i	−0.0655639	+	0.113560i
$943$	−13.9781			−0.455191
$944$	0.171587	−	0.297197i	0.00558467	−	0.00967294i
$945$	−1.93749	−	3.35582i	−0.0630264	−	0.109165i
$946$	13.6265	+	23.6018i	0.443036	+	0.767361i
$947$	−16.9952	+	29.4366i	−0.552271	+	0.956562i	0.445839	+	0.895113i	$0.352905\pi$
$947$	−16.9952	+	29.4366i	−0.552271	+	0.956562i	−0.998110	+	0.0614486i	$0.980428\pi$
$948$	−15.7215	+	27.2305i	−0.510611	+	0.884405i
$949$	−17.4272	−	30.1848i	−0.565710	−	0.979839i
$950$	56.3464			1.82812
$951$	6.58957	+	11.4135i	0.213681	+	0.370107i
$952$	−3.49667			−0.113328
$953$	−7.02791			−0.227656			−0.113828	−	0.993500i	$-0.536311\pi$
$953$	−7.02791			−0.227656			−0.113828	+	0.993500i	$0.536311\pi$
$954$	−21.1420	−	36.6190i	−0.684497	−	1.18558i
$955$	−56.1229			−1.81609
$956$	2.16731	+	3.75389i	0.0700958	+	0.121410i
$957$	−5.15017	+	8.92035i	−0.166481	+	0.288354i
$958$	25.8794	−	44.8244i	0.836124	−	1.44821i
$959$	−0.906822	−	1.57066i	−0.0292828	−	0.0507193i
$960$	25.2173	+	43.6776i	0.813885	+	1.40969i
$961$	−8.01548	+	13.8832i	−0.258564	+	0.447846i
$962$	−10.9089			−0.351717
$963$	−15.8321	+	27.4221i	−0.510184	+	0.883664i
$964$	−10.5930	−	18.3476i	−0.341176	−	0.590935i
$965$	−33.2409			−1.07006
$966$	−3.35514			−0.107950
$967$	−6.70528	+	11.6139i	−0.215627	+	0.373477i	−0.953466	−	0.301499i	$-0.902513\pi$
$967$	−6.70528	+	11.6139i	−0.215627	+	0.373477i	0.737839	+	0.674977i	$0.235846\pi$
$968$	9.40046	+	16.2821i	0.302142	+	0.523326i
$969$	−13.1108			−0.421179
$970$	−58.0436	−	100.534i	−1.86367	−	3.22797i
$971$	−8.34883	+	14.4606i	−0.267927	+	0.464062i	−0.968326	−	0.249688i	$-0.919672\pi$
$971$	−8.34883	+	14.4606i	−0.267927	+	0.464062i	0.700400	+	0.713751i	$0.253005\pi$
$972$	26.1530	−	45.2983i	0.838858	−	1.45294i
$973$	0.739118	−	1.28019i	0.0236950	−	0.0410410i
$974$	−33.6900	+	58.3528i	−1.07950	+	1.86974i
$975$	12.2421	−	21.2040i	0.392062	−	0.679071i
$976$	−0.199401			−0.00638266
$977$	19.9544	−	34.5620i	0.638396	−	1.10574i	−0.347388	−	0.937721i	$-0.612931\pi$
$977$	19.9544	−	34.5620i	0.638396	−	1.10574i	0.985785	−	0.168014i	$-0.0537353\pi$
$978$	12.9650			0.414576
$979$	5.67890	−	9.83615i	0.181499	−	0.314365i
$980$	−45.6573	+	79.0808i	−1.45847	+	2.52614i
$981$	11.0194	+	19.0862i	0.351823	+	0.609376i
$982$	−7.78094	+	13.4770i	−0.248300	+	0.430068i
$983$	17.8050			0.567892			0.283946	−	0.958840i	$-0.408356\pi$
$983$	17.8050			0.567892			0.283946	+	0.958840i	$0.408356\pi$
$984$	−4.98960			−0.159063
$985$	−22.7178	−	39.3483i	−0.723848	−	1.25374i
$986$	−36.2511	−	62.7887i	−1.15447	−	1.99960i
$987$	0.107615	−	0.186395i	0.00342542	−	0.00593301i
$988$	−7.90956	−	13.6998i	−0.251637	−	0.435848i
$989$	−43.7615			−1.39153
$990$	20.1047	+	34.8223i	0.638969	+	1.10673i
$991$	5.50326			0.174817			0.0874084	−	0.996173i	$-0.472141\pi$
$991$	5.50326			0.174817			0.0874084	+	0.996173i	$0.472141\pi$
$992$	19.1930	+	33.2432i	0.609377	+	1.05547i
$993$	−10.8078	−	18.7197i	−0.342975	−	0.594051i
$994$	2.58781	−	4.48221i	0.0820803	−	0.142167i
$995$	10.1155	−	17.5206i	0.320684	−	0.555442i
$996$	−22.9195			−0.726233
$997$	38.3183			1.21355			0.606776	−	0.794873i	$-0.292463\pi$
$997$	38.3183			1.21355			0.606776	+	0.794873i	$0.292463\pi$
$998$	−21.3230	+	36.9326i	−0.674969	+	1.16908i
$999$	5.20227	−	9.01060i	0.164593	−	0.285083i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	127.2.c.a.107.9	yes	18
127.19	even	3	inner	127.2.c.a.19.9	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
127.2.c.a.19.9	✓	18	127.19	even	3	inner
127.2.c.a.107.9	yes	18	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 127 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	127.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.29077 q^{2} +(0.483029 + 0.836631i) q^{3} +3.24763 q^{4} -4.03893 q^{5} +(1.10651 + 1.91653i) q^{6} +(0.0980034 + 0.169747i) q^{7} +2.85803 q^{8} +(1.03337 - 1.78984i) q^{9} -9.25226 q^{10} +(1.05139 - 1.82107i) q^{11} +(1.56870 + 2.71707i) q^{12} +(-1.12015 - 1.94016i) q^{13} +(0.224503 + 0.388851i) q^{14} +(-1.95092 - 3.37909i) q^{15} +0.0518359 q^{16} +(-3.12095 + 5.40565i) q^{17} +(2.36720 - 4.10012i) q^{18} +2.17425 q^{19} -13.1169 q^{20} +(-0.0946770 + 0.163985i) q^{21} +(2.40850 - 4.17165i) q^{22} +(3.86745 + 6.69862i) q^{23} +(1.38051 + 2.39112i) q^{24} +11.3130 q^{25} +(-2.56601 - 4.44447i) q^{26} +4.89476 q^{27} +(0.318279 + 0.551275i) q^{28} +(-2.53526 + 4.39120i) q^{29} +(-4.46911 - 7.74073i) q^{30} +(-3.42896 - 5.93913i) q^{31} -5.59732 q^{32} +2.03142 q^{33} +(-7.14938 + 12.3831i) q^{34} +(-0.395829 - 0.685595i) q^{35} +(3.35599 - 5.81274i) q^{36} +(1.06283 - 1.84087i) q^{37} +4.98070 q^{38} +(1.08213 - 1.87431i) q^{39} -11.5434 q^{40} +(-0.903577 + 1.56504i) q^{41} +(-0.216883 + 0.375653i) q^{42} +(-2.82883 + 4.89969i) q^{43} +(3.41454 - 5.91415i) q^{44} +(-4.17369 + 7.22904i) q^{45} +(8.85943 + 15.3450i) q^{46} -1.13665 q^{47} +(0.0250382 + 0.0433675i) q^{48} +(3.48079 - 6.02891i) q^{49} +25.9154 q^{50} -6.03004 q^{51} +(-3.63784 - 6.30093i) q^{52} +(4.46561 - 7.73466i) q^{53} +11.2128 q^{54} +(-4.24651 + 7.35517i) q^{55} +(0.280097 + 0.485142i) q^{56} +(1.05022 + 1.81904i) q^{57} +(-5.80770 + 10.0592i) q^{58} +(3.31019 - 5.73342i) q^{59} +(-6.33587 - 10.9740i) q^{60} -3.84677 q^{61} +(-7.85495 - 13.6052i) q^{62} +0.405093 q^{63} -12.9258 q^{64} +(4.52422 + 7.83618i) q^{65} +4.65351 q^{66} +(-6.16321 - 10.6750i) q^{67} +(-10.1357 + 17.5555i) q^{68} +(-3.73618 + 6.47126i) q^{69} +(-0.906753 - 1.57054i) q^{70} +(-5.76341 - 9.98251i) q^{71} +(2.95339 - 5.11542i) q^{72} +15.5578 q^{73} +(2.43469 - 4.21700i) q^{74} +(5.46449 + 9.46477i) q^{75} +7.06114 q^{76} +0.412161 q^{77} +(2.47892 - 4.29362i) q^{78} +(5.01100 + 8.67931i) q^{79} -0.209361 q^{80} +(-0.735785 - 1.27442i) q^{81} +(-2.06989 + 3.58515i) q^{82} +(-3.65263 + 6.32654i) q^{83} +(-0.307476 + 0.532564i) q^{84} +(12.6053 - 21.8330i) q^{85} +(-6.48021 + 11.2241i) q^{86} -4.89842 q^{87} +(3.00492 - 5.20467i) q^{88} +5.40131 q^{89} +(-9.56097 + 16.5601i) q^{90} +(0.219558 - 0.380285i) q^{91} +(12.5600 + 21.7546i) q^{92} +(3.31257 - 5.73754i) q^{93} -2.60381 q^{94} -8.78162 q^{95} +(-2.70367 - 4.68289i) q^{96} +(6.27345 + 10.8659i) q^{97} +(7.97369 - 13.8108i) q^{98} +(-2.17295 - 3.76366i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 2 q^{2} + q^{3} + 10 q^{4} - 8 q^{5} + 5 q^{7} - 6 q^{8} - 2 q^{9} - 4 q^{10} + 5 q^{12} - 8 q^{14} + 3 q^{15} - 6 q^{16} - 6 q^{17} + 16 q^{19} - 32 q^{20} + 3 q^{21} + 6 q^{22} + 13 q^{23} - 6 q^{24}+ \cdots + 17 q^{99}+O(q^{100}) \) 18 * q - 2 * q^2 + q^3 + 10 * q^4 - 8 * q^5 + 5 * q^7 - 6 * q^8 - 2 * q^9 - 4 * q^10 + 5 * q^12 - 8 * q^14 + 3 * q^15 - 6 * q^16 - 6 * q^17 + 16 * q^19 - 32 * q^20 + 3 * q^21 + 6 * q^22 + 13 * q^23 - 6 * q^24 + 6 * q^25 - 14 * q^26 + 10 * q^27 - 2 * q^28 - 5 * q^29 - 23 * q^30 - 11 * q^31 - 4 * q^32 - 16 * q^33 - 2 * q^34 - 16 * q^35 + 15 * q^36 - 4 * q^37 + 4 * q^38 - 7 * q^39 - 36 * q^40 - 11 * q^41 + 9 * q^43 - 15 * q^44 + 14 * q^45 + 15 * q^46 - 10 * q^47 + 20 * q^48 + 12 * q^49 + 32 * q^50 + 4 * q^51 + 26 * q^52 - 2 * q^53 + 2 * q^54 - q^55 + 12 * q^56 + 28 * q^57 + 10 * q^58 + 6 * q^60 + 28 * q^61 + 8 * q^62 - 12 * q^63 - 50 * q^64 + 15 * q^65 + 36 * q^66 - 12 * q^67 - 41 * q^68 + 33 * q^69 + 21 * q^70 - 4 * q^71 + 31 * q^72 + 52 * q^73 + 13 * q^74 - 11 * q^75 + 26 * q^76 - 40 * q^77 + q^78 - 35 * q^79 + 26 * q^80 + 27 * q^81 - 26 * q^82 + 13 * q^83 + 22 * q^84 + 15 * q^85 - 5 * q^86 - 64 * q^87 - q^88 + 8 * q^89 - 30 * q^90 - 16 * q^91 + 11 * q^92 - 6 * q^93 - 62 * q^94 - 38 * q^95 - 31 * q^96 + 28 * q^97 + 32 * q^98 + 17 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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