LMFDB - Embedded newform 585.2.i.f.391.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(196,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 0]))

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

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

chi := DirichletCharacter("585.196");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} + 11 x^{14} - 4 x^{13} + 74 x^{12} - 18 x^{11} + 289 x^{10} - 4 x^{9} + 784 x^{8} + \cdots + 81 $ x^16 - x^15 + 11x^14 - 4x^13 + 74x^12 - 18x^11 + 289x^10 - 4x^9 + 784x^8 - 9x^7 + 1221x^6 + 133x^5 + 1245x^4 - 14x^3 + 391x^2 + 63x + 81
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			391.5
Root			$0.316605 + 0.548376i$ of defining polynomial
Character	$\chi$	$=$	585.391
Dual form			585.2.i.f.196.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.316605 + 0.548376i) q^{2} +(-1.15302 - 1.29250i) q^{3} +(0.799523 - 1.38481i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.343725 - 1.04150i) q^{6} +(0.896323 + 1.55248i) q^{7} +2.27895 q^{8} +(-0.341107 + 2.98054i) q^{9} +O(q^{10})$	\(q+(0.316605 + 0.548376i) q^{2} +(-1.15302 - 1.29250i) q^{3} +(0.799523 - 1.38481i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.343725 - 1.04150i) q^{6} +(0.896323 + 1.55248i) q^{7} +2.27895 q^{8} +(-0.341107 + 2.98054i) q^{9} -0.633210 q^{10} +(2.02789 + 3.51241i) q^{11} +(-2.71173 + 0.563330i) q^{12} +(-0.500000 + 0.866025i) q^{13} +(-0.567560 + 0.983044i) q^{14} +(1.69585 - 0.352292i) q^{15} +(-0.877517 - 1.51990i) q^{16} +7.09008 q^{17} +(-1.74246 + 0.756600i) q^{18} -1.65636 q^{19} +(0.799523 + 1.38481i) q^{20} +(0.973100 - 2.94853i) q^{21} +(-1.28408 + 2.22409i) q^{22} +(4.07356 - 7.05562i) q^{23} +(-2.62767 - 2.94554i) q^{24} +(-0.500000 - 0.866025i) q^{25} -0.633210 q^{26} +(4.24565 - 2.99573i) q^{27} +2.86652 q^{28} +(-0.816509 - 1.41423i) q^{29} +(0.730101 + 0.818423i) q^{30} +(-2.17278 + 3.76337i) q^{31} +(2.83460 - 4.90968i) q^{32} +(2.20160 - 6.67091i) q^{33} +(2.24475 + 3.88803i) q^{34} -1.79265 q^{35} +(3.85478 + 2.85538i) q^{36} +0.729336 q^{37} +(-0.524411 - 0.908307i) q^{38} +(1.69585 - 0.352292i) q^{39} +(-1.13948 + 1.97363i) q^{40} +(-0.439625 + 0.761453i) q^{41} +(1.92499 - 0.399894i) q^{42} +(-2.76981 - 4.79745i) q^{43} +6.48538 q^{44} +(-2.41067 - 1.78568i) q^{45} +5.15884 q^{46} +(4.67619 + 8.09941i) q^{47} +(-0.952684 + 2.88667i) q^{48} +(1.89321 - 3.27914i) q^{49} +(0.316605 - 0.548376i) q^{50} +(-8.17497 - 9.16392i) q^{51} +(0.799523 + 1.38481i) q^{52} +5.39044 q^{53} +(2.98698 + 1.37975i) q^{54} -4.05578 q^{55} +(2.04268 + 3.53802i) q^{56} +(1.90981 + 2.14084i) q^{57} +(0.517022 - 0.895508i) q^{58} +(-6.45122 + 11.1738i) q^{59} +(0.868008 - 2.63009i) q^{60} +(2.54766 + 4.41268i) q^{61} -2.75165 q^{62} +(-4.93297 + 2.14197i) q^{63} +0.0797303 q^{64} +(-0.500000 - 0.866025i) q^{65} +(4.35521 - 0.904743i) q^{66} +(-2.18533 + 3.78510i) q^{67} +(5.66868 - 9.81843i) q^{68} +(-13.8163 + 2.87017i) q^{69} +(-0.567560 - 0.983044i) q^{70} -2.80901 q^{71} +(-0.777367 + 6.79252i) q^{72} -5.00513 q^{73} +(0.230911 + 0.399950i) q^{74} +(-0.542829 + 1.64479i) q^{75} +(-1.32430 + 2.29375i) q^{76} +(-3.63529 + 6.29651i) q^{77} +(0.730101 + 0.818423i) q^{78} +(-3.41146 - 5.90883i) q^{79} +1.75503 q^{80} +(-8.76729 - 2.03337i) q^{81} -0.556750 q^{82} +(-3.25768 - 5.64247i) q^{83} +(-3.30514 - 3.70497i) q^{84} +(-3.54504 + 6.14019i) q^{85} +(1.75387 - 3.03779i) q^{86} +(-0.886449 + 2.68597i) q^{87} +(4.62147 + 8.00461i) q^{88} +7.59275 q^{89} +(0.215993 - 1.88731i) q^{90} -1.79265 q^{91} +(-6.51381 - 11.2823i) q^{92} +(7.36940 - 1.53090i) q^{93} +(-2.96101 + 5.12863i) q^{94} +(0.828179 - 1.43445i) q^{95} +(-9.61410 + 1.99722i) q^{96} +(6.27213 + 10.8637i) q^{97} +2.39760 q^{98} +(-11.1606 + 4.84611i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + q^{2} - 2 q^{3} - 5 q^{4} - 8 q^{5} - 13 q^{6} + 6 q^{7} - 12 q^{8} + 4 q^{9}+O(q^{10}) $ 16 * q + q^2 - 2 * q^3 - 5 * q^4 - 8 * q^5 - 13 * q^6 + 6 * q^7 - 12 * q^8 + 4 * q^9	\( 16 q + q^{2} - 2 q^{3} - 5 q^{4} - 8 q^{5} - 13 q^{6} + 6 q^{7} - 12 q^{8} + 4 q^{9} - 2 q^{10} + 9 q^{11} - 16 q^{12} - 8 q^{13} - 3 q^{14} + q^{15} + 13 q^{16} + 12 q^{17} + 23 q^{18} - 22 q^{19} - 5 q^{20} + 15 q^{21} + 4 q^{22} + 3 q^{23} - 12 q^{24} - 8 q^{25} - 2 q^{26} + 22 q^{27} - 26 q^{28} + 8 q^{29} + 8 q^{30} + 18 q^{31} + 3 q^{32} - 26 q^{33} + 9 q^{34} - 12 q^{35} + 5 q^{36} - 36 q^{37} - 8 q^{38} + q^{39} + 6 q^{40} - 17 q^{41} - 45 q^{42} + 17 q^{43} + 10 q^{44} + q^{45} + 6 q^{46} + 11 q^{47} + 35 q^{48} + 16 q^{49} + q^{50} - 16 q^{51} - 5 q^{52} + 20 q^{53} + 44 q^{54} - 18 q^{55} - q^{56} - 25 q^{57} + 10 q^{58} + 7 q^{59} + 5 q^{60} + 21 q^{61} - 58 q^{62} - 30 q^{63} - 20 q^{64} - 8 q^{65} + 68 q^{66} + 13 q^{67} - 16 q^{68} - 13 q^{69} - 3 q^{70} - 68 q^{71} + 36 q^{72} - 32 q^{73} - 4 q^{74} + q^{75} + 2 q^{76} + 18 q^{77} + 8 q^{78} + 37 q^{79} - 26 q^{80} - 32 q^{81} + 2 q^{82} + 3 q^{83} + 27 q^{84} - 6 q^{85} - 2 q^{86} - 20 q^{87} + 19 q^{88} + 28 q^{89} - 16 q^{90} - 12 q^{91} - 14 q^{92} + 19 q^{93} + 44 q^{94} + 11 q^{95} - 35 q^{96} + 17 q^{97} + 90 q^{98} - 44 q^{99}+O(q^{100}) \) 16 * q + q^2 - 2 * q^3 - 5 * q^4 - 8 * q^5 - 13 * q^6 + 6 * q^7 - 12 * q^8 + 4 * q^9 - 2 * q^10 + 9 * q^11 - 16 * q^12 - 8 * q^13 - 3 * q^14 + q^15 + 13 * q^16 + 12 * q^17 + 23 * q^18 - 22 * q^19 - 5 * q^20 + 15 * q^21 + 4 * q^22 + 3 * q^23 - 12 * q^24 - 8 * q^25 - 2 * q^26 + 22 * q^27 - 26 * q^28 + 8 * q^29 + 8 * q^30 + 18 * q^31 + 3 * q^32 - 26 * q^33 + 9 * q^34 - 12 * q^35 + 5 * q^36 - 36 * q^37 - 8 * q^38 + q^39 + 6 * q^40 - 17 * q^41 - 45 * q^42 + 17 * q^43 + 10 * q^44 + q^45 + 6 * q^46 + 11 * q^47 + 35 * q^48 + 16 * q^49 + q^50 - 16 * q^51 - 5 * q^52 + 20 * q^53 + 44 * q^54 - 18 * q^55 - q^56 - 25 * q^57 + 10 * q^58 + 7 * q^59 + 5 * q^60 + 21 * q^61 - 58 * q^62 - 30 * q^63 - 20 * q^64 - 8 * q^65 + 68 * q^66 + 13 * q^67 - 16 * q^68 - 13 * q^69 - 3 * q^70 - 68 * q^71 + 36 * q^72 - 32 * q^73 - 4 * q^74 + q^75 + 2 * q^76 + 18 * q^77 + 8 * q^78 + 37 * q^79 - 26 * q^80 - 32 * q^81 + 2 * q^82 + 3 * q^83 + 27 * q^84 - 6 * q^85 - 2 * q^86 - 20 * q^87 + 19 * q^88 + 28 * q^89 - 16 * q^90 - 12 * q^91 - 14 * q^92 + 19 * q^93 + 44 * q^94 + 11 * q^95 - 35 * q^96 + 17 * q^97 + 90 * q^98 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	0.316605	+	0.548376i	0.223874	+	0.387760i	0.955981	−	0.293429i	$-0.0947964\pi$
$2$	0.316605	+	0.548376i	0.223874	+	0.387760i	−0.732107	+	0.681189i	$0.761463\pi$
$3$	−1.15302	−	1.29250i	−0.665694	−	0.746225i
$3$	−1.15302	−	1.29250i	−0.665694	−	0.746225i
$4$	0.799523	−	1.38481i	0.399761	−	0.692407i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	0.343725	−	1.04150i	0.140325	−	0.425190i
$7$	0.896323	+	1.55248i	0.338778	+	0.586781i	0.984203	−	0.177043i	$-0.0566531\pi$
$7$	0.896323	+	1.55248i	0.338778	+	0.586781i	−0.645425	+	0.763824i	$0.723320\pi$
$8$	2.27895			0.805731
$9$	−0.341107	+	2.98054i	−0.113702	+	0.993515i
$10$	−0.633210			−0.200239
$11$	2.02789	+	3.51241i	0.611432	+	1.05903i	0.990999	+	0.133867i	$0.0427396\pi$
$11$	2.02789	+	3.51241i	0.611432	+	1.05903i	−0.379567	+	0.925164i	$0.623927\pi$
$12$	−2.71173	+	0.563330i	−0.782810	+	0.162619i
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i
$14$	−0.567560	+	0.983044i	−0.151687	+	0.262729i
$15$	1.69585	−	0.352292i	0.437865	−	0.0909613i
$16$	−0.877517	−	1.51990i	−0.219379	−	0.379976i
$17$	7.09008			1.71960			0.859798	−	0.510634i	$-0.170589\pi$
$17$	7.09008			1.71960			0.859798	+	0.510634i	$0.170589\pi$
$18$	−1.74246	+	0.756600i	−0.410701	+	0.178332i
$19$	−1.65636			−0.379994			−0.189997	−	0.981785i	$-0.560848\pi$
$19$	−1.65636			−0.379994			−0.189997	+	0.981785i	$0.560848\pi$
$20$	0.799523	+	1.38481i	0.178779	+	0.309654i
$21$	0.973100	−	2.94853i	0.212348	−	0.643421i
$22$	−1.28408	+	2.22409i	−0.273767	+	0.474178i
$23$	4.07356	−	7.05562i	0.849397	−	1.47120i	−0.0323503	−	0.999477i	$-0.510299\pi$
$23$	4.07356	−	7.05562i	0.849397	−	1.47120i	0.881747	−	0.471722i	$-0.156367\pi$
$24$	−2.62767	−	2.94554i	−0.536370	−	0.601256i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−0.633210			−0.124183
$27$	4.24565	−	2.99573i	0.817076	−	0.576529i
$28$	2.86652			0.541721
$29$	−0.816509	−	1.41423i	−0.151622	−	0.262617i	0.780202	−	0.625528i	$-0.215116\pi$
$29$	−0.816509	−	1.41423i	−0.151622	−	0.262617i	−0.931824	+	0.362911i	$0.881783\pi$
$30$	0.730101	+	0.818423i	0.133298	+	0.149423i
$31$	−2.17278	+	3.76337i	−0.390243	+	0.675920i	−0.992481	−	0.122396i	$-0.960942\pi$
$31$	−2.17278	+	3.76337i	−0.390243	+	0.675920i	0.602239	+	0.798316i	$0.294276\pi$
$32$	2.83460	−	4.90968i	0.501092	−	0.867917i
$33$	2.20160	−	6.67091i	0.383249	−	1.16126i
$34$	2.24475	+	3.88803i	0.384972	+	0.666791i
$35$	−1.79265			−0.303012
$36$	3.85478	+	2.85538i	0.642463	+	0.475897i
$37$	0.729336			0.119902			0.0599510	−	0.998201i	$-0.480906\pi$
$37$	0.729336			0.119902			0.0599510	+	0.998201i	$0.480906\pi$
$38$	−0.524411	−	0.908307i	−0.0850707	−	0.147347i
$39$	1.69585	−	0.352292i	0.271553	−	0.0564118i
$40$	−1.13948	+	1.97363i	−0.180167	+	0.312058i
$41$	−0.439625	+	0.761453i	−0.0686579	+	0.118919i	−0.898311	−	0.439361i	$-0.855205\pi$
$41$	−0.439625	+	0.761453i	−0.0686579	+	0.118919i	0.829653	+	0.558280i	$0.188538\pi$
$42$	1.92499	−	0.399894i	0.297032	−	0.0617049i
$43$	−2.76981	−	4.79745i	−0.422392	−	0.731604i	0.573781	−	0.819009i	$-0.305476\pi$
$43$	−2.76981	−	4.79745i	−0.422392	−	0.731604i	−0.996173	+	0.0874045i	$0.972143\pi$
$44$	6.48538			0.977708
$45$	−2.41067	−	1.78568i	−0.359362	−	0.266193i
$46$	5.15884			0.760630
$47$	4.67619	+	8.09941i	0.682093	+	1.18142i	0.974341	+	0.225077i	$0.0722634\pi$
$47$	4.67619	+	8.09941i	0.682093	+	1.18142i	−0.292248	+	0.956343i	$0.594403\pi$
$48$	−0.952684	+	2.88667i	−0.137508	+	0.416654i
$49$	1.89321	−	3.27914i	0.270459	−	0.468448i
$50$	0.316605	−	0.548376i	0.0447747	−	0.0775521i
$51$	−8.17497	−	9.16392i	−1.14473	−	1.28320i
$52$	0.799523	+	1.38481i	0.110874	+	0.192039i
$53$	5.39044			0.740433			0.370217	−	0.928945i	$-0.379283\pi$
$53$	5.39044			0.740433			0.370217	+	0.928945i	$0.379283\pi$
$54$	2.98698	+	1.37975i	0.406477	+	0.187760i
$55$	−4.05578			−0.546882
$56$	2.04268	+	3.53802i	0.272964	+	0.472788i
$57$	1.90981	+	2.14084i	0.252960	+	0.283561i
$58$	0.517022	−	0.895508i	0.0678883	−	0.117586i
$59$	−6.45122	+	11.1738i	−0.839877	+	1.45471i	0.0501198	+	0.998743i	$0.484040\pi$
$59$	−6.45122	+	11.1738i	−0.839877	+	1.45471i	−0.889997	+	0.455967i	$0.849294\pi$
$60$	0.868008	−	2.63009i	0.112059	−	0.339544i
$61$	2.54766	+	4.41268i	0.326195	+	0.564986i	0.981753	−	0.190158i	$-0.0609001\pi$
$61$	2.54766	+	4.41268i	0.326195	+	0.564986i	−0.655559	+	0.755144i	$0.727567\pi$
$62$	−2.75165			−0.349460
$63$	−4.93297	+	2.14197i	−0.621495	+	0.269863i
$64$	0.0797303			0.00996629
$65$	−0.500000	−	0.866025i	−0.0620174	−	0.107417i
$66$	4.35521	−	0.904743i	0.536089	−	0.111366i
$67$	−2.18533	+	3.78510i	−0.266980	+	0.462424i	−0.968081	−	0.250639i	$-0.919359\pi$
$67$	−2.18533	+	3.78510i	−0.266980	+	0.462424i	0.701100	+	0.713063i	$0.252693\pi$
$68$	5.66868	−	9.81843i	0.687428	−	1.19066i
$69$	−13.8163	+	2.87017i	−1.66328	+	0.345527i
$70$	−0.567560	−	0.983044i	−0.0678365	−	0.117496i
$71$	−2.80901			−0.333369			−0.166684	−	0.986010i	$-0.553306\pi$
$71$	−2.80901			−0.333369			−0.166684	+	0.986010i	$0.553306\pi$
$72$	−0.777367	+	6.79252i	−0.0916136	+	0.800506i
$73$	−5.00513			−0.585806			−0.292903	−	0.956142i	$-0.594621\pi$
$73$	−5.00513			−0.585806			−0.292903	+	0.956142i	$0.594621\pi$
$74$	0.230911	+	0.399950i	0.0268429	+	0.0464933i
$75$	−0.542829	+	1.64479i	−0.0626805	+	0.189924i
$76$	−1.32430	+	2.29375i	−0.151907	+	0.263111i
$77$	−3.63529	+	6.29651i	−0.414280	+	0.717553i
$78$	0.730101	+	0.818423i	0.0826677	+	0.0926682i
$79$	−3.41146	−	5.90883i	−0.383820	−	0.664795i	0.607785	−	0.794102i	$-0.292058\pi$
$79$	−3.41146	−	5.90883i	−0.383820	−	0.664795i	−0.991605	+	0.129306i	$0.958725\pi$
$80$	1.75503			0.196219
$81$	−8.76729	−	2.03337i	−0.974143	−	0.225930i
$82$	−0.556750			−0.0614828
$83$	−3.25768	−	5.64247i	−0.357577	−	0.619341i	0.629979	−	0.776613i	$-0.283064\pi$
$83$	−3.25768	−	5.64247i	−0.357577	−	0.619341i	−0.987555	+	0.157271i	$0.949730\pi$
$84$	−3.30514	−	3.70497i	−0.360621	−	0.404246i
$85$	−3.54504	+	6.14019i	−0.384513	+	0.665997i
$86$	1.75387	−	3.03779i	0.189125	−	0.327574i
$87$	−0.886449	+	2.68597i	−0.0950373	+	0.287967i
$88$	4.62147	+	8.00461i	0.492650	+	0.853295i
$89$	7.59275			0.804830			0.402415	−	0.915457i	$-0.368171\pi$
$89$	7.59275			0.804830			0.402415	+	0.915457i	$0.368171\pi$
$90$	0.215993	−	1.88731i	0.0227676	−	0.198940i
$91$	−1.79265			−0.187920
$92$	−6.51381	−	11.2823i	−0.679112	−	1.17626i
$93$	7.36940	−	1.53090i	0.764171	−	0.158747i
$94$	−2.96101	+	5.12863i	−0.305405	+	0.528977i
$95$	0.828179	−	1.43445i	0.0849693	−	0.147171i
$96$	−9.61410	+	1.99722i	−0.981235	+	0.203840i
$97$	6.27213	+	10.8637i	0.636839	+	1.10304i	0.986122	+	0.166020i	$0.0530916\pi$
$97$	6.27213	+	10.8637i	0.636839	+	1.10304i	−0.349284	+	0.937017i	$0.613575\pi$
$98$	2.39760			0.242194
$99$	−11.1606	+	4.84611i	−1.12169	+	0.487052i
$100$	−1.59905			−0.159905
$101$	2.61592	+	4.53090i	0.260294	+	0.450842i	0.966320	−	0.257344i	$-0.0828473\pi$
$101$	2.61592	+	4.53090i	0.260294	+	0.450842i	−0.706026	+	0.708186i	$0.749514\pi$
$102$	2.43703	−	7.38430i	0.241302	−	0.731155i
$103$	8.58590	−	14.8712i	0.845994	−	1.46531i	−0.0387607	−	0.999249i	$-0.512341\pi$
$103$	8.58590	−	14.8712i	0.845994	−	1.46531i	0.884755	−	0.466057i	$-0.154326\pi$
$104$	−1.13948	+	1.97363i	−0.111735	+	0.193530i
$105$	2.06695	+	2.31699i	0.201714	+	0.226115i
$106$	1.70664	+	2.95599i	0.165763	+	0.287111i
$107$	−4.98432			−0.481852			−0.240926	−	0.970543i	$-0.577451\pi$
$107$	−4.98432			−0.481852			−0.240926	+	0.970543i	$0.577451\pi$
$108$	−0.754039	−	8.27460i	−0.0725574	−	0.796223i
$109$	−4.81126			−0.460835			−0.230417	−	0.973092i	$-0.574009\pi$
$109$	−4.81126			−0.460835			−0.230417	+	0.973092i	$0.574009\pi$
$110$	−1.28408	−	2.22409i	−0.122432	−	0.212059i
$111$	−0.840936	−	0.942666i	−0.0798181	−	0.0894739i
$112$	1.57308	−	2.72465i	0.148642	−	0.257455i
$113$	−4.70502	+	8.14933i	−0.442611	+	0.766625i	−0.997882	−	0.0650446i	$-0.979281\pi$
$113$	−4.70502	+	8.14933i	−0.442611	+	0.766625i	0.555271	+	0.831669i	$0.312614\pi$
$114$	−0.569331	+	1.72509i	−0.0533227	+	0.161570i
$115$	4.07356	+	7.05562i	0.379862	+	0.657940i
$116$	−2.61127			−0.242450
$117$	−2.41067	−	1.78568i	−0.222867	−	0.165086i
$118$	−8.16995			−0.752105
$119$	6.35499	+	11.0072i	0.582561	+	1.00903i
$120$	3.86475	−	0.802856i	0.352802	−	0.0732904i
$121$	−2.72469	+	4.71930i	−0.247699	+	0.429027i
$122$	−1.61321	+	2.79415i	−0.146053	+	0.252971i
$123$	1.49107	−	0.309753i	0.134445	−	0.0279295i
$124$	3.47437	+	6.01779i	0.312008	+	0.540414i
$125$	1.00000			0.0894427
$126$	−2.73641	−	2.02696i	−0.243778	−	0.180576i
$127$	−9.51514			−0.844332			−0.422166	−	0.906519i	$-0.638730\pi$
$127$	−9.51514			−0.844332			−0.422166	+	0.906519i	$0.638730\pi$
$128$	−5.64397	−	9.77564i	−0.498861	−	0.864052i
$129$	−3.00707	+	9.11151i	−0.264757	+	0.802224i
$130$	0.316605	−	0.548376i	0.0277681	−	0.0480958i
$131$	4.04845	−	7.01212i	0.353715	−	0.612652i	−0.633182	−	0.774003i	$-0.718252\pi$
$131$	4.04845	−	7.01212i	0.353715	−	0.612652i	0.986897	+	0.161351i	$0.0515850\pi$
$132$	−7.47775	−	8.38235i	−0.650854	−	0.729590i
$133$	−1.48463	−	2.57146i	−0.128734	−	0.222973i
$134$	−2.76755			−0.239079
$135$	0.471556	+	5.17471i	0.0405851	+	0.445368i
$136$	16.1579			1.38553
$137$	−10.2992	−	17.8387i	−0.879917	−	1.52406i	−0.851431	−	0.524466i	$-0.824265\pi$
$137$	−10.2992	−	17.8387i	−0.879917	−	1.52406i	−0.0284854	−	0.999594i	$-0.509068\pi$
$138$	−5.94823	−	6.66780i	−0.506347	−	0.567601i
$139$	−7.80434	+	13.5175i	−0.661956	+	1.14654i	0.318146	+	0.948042i	$0.396940\pi$
$139$	−7.80434	+	13.5175i	−0.661956	+	1.14654i	−0.980101	+	0.198499i	$0.936393\pi$
$140$	−1.43326	+	2.48248i	−0.121133	+	0.209808i
$141$	5.07675	−	15.3827i	0.427539	−	1.29546i
$142$	−0.889348	−	1.54040i	−0.0746324	−	0.129267i
$143$	−4.05578			−0.339162
$144$	4.82947	−	2.09703i	0.402456	−	0.174752i
$145$	1.63302			0.135615
$146$	−1.58465	−	2.74469i	−0.131147	−	0.227153i
$147$	−6.42119	+	1.33393i	−0.529611	+	0.110020i
$148$	0.583120	−	1.00999i	0.0479322	−	0.0830210i
$149$	0.786454	−	1.36218i	0.0644288	−	0.111594i	−0.832012	−	0.554758i	$-0.812811\pi$
$149$	0.786454	−	1.36218i	0.0644288	−	0.111594i	0.896440	+	0.443164i	$0.146144\pi$
$150$	−1.07383	+	0.223075i	−0.0876775	+	0.0182140i
$151$	−5.64265	−	9.77336i	−0.459193	−	0.795345i	0.539726	−	0.841841i	$-0.318528\pi$
$151$	−5.64265	−	9.77336i	−0.459193	−	0.795345i	−0.998918	+	0.0464959i	$0.985195\pi$
$152$	−3.77476			−0.306173
$153$	−2.41848	+	21.1323i	−0.195522	+	1.70844i
$154$	−4.60380			−0.370985
$155$	−2.17278	−	3.76337i	−0.174522	−	0.302281i
$156$	0.868008	−	2.63009i	0.0694962	−	0.210576i
$157$	5.93626	−	10.2819i	0.473765	−	0.820586i	−0.525783	−	0.850618i	$-0.676228\pi$
$157$	5.93626	−	10.2819i	0.473765	−	0.820586i	0.999549	+	0.0300326i	$0.00956112\pi$
$158$	2.16017	−	3.74153i	0.171854	−	0.297660i
$159$	−6.21526	−	6.96713i	−0.492902	−	0.552530i
$160$	2.83460	+	4.90968i	0.224095	+	0.388144i
$161$	14.6049			1.15103
$162$	−1.66072	−	5.45155i	−0.130478	−	0.428314i
$163$	−14.1027			−1.10461			−0.552306	−	0.833642i	$-0.686252\pi$
$163$	−14.1027			−1.10461			−0.552306	+	0.833642i	$0.686252\pi$
$164$	0.702980	+	1.21760i	0.0548935	+	0.0950784i
$165$	4.67638	+	5.24210i	0.364056	+	0.408097i
$166$	2.06280	−	3.57287i	0.160104	−	0.277308i
$167$	6.40109	−	11.0870i	0.495332	−	0.857939i	−0.504654	−	0.863322i	$-0.668380\pi$
$167$	6.40109	−	11.0870i	0.495332	−	0.857939i	0.999986	+	0.00538227i	$0.00171324\pi$
$168$	2.21765	−	6.71955i	0.171095	−	0.518424i
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$	−4.48951			−0.344329
$171$	0.564996	−	4.93685i	0.0432063	−	0.377530i
$172$	−8.85810			−0.675424
$173$	10.0917	+	17.4793i	0.767256	+	1.32893i	0.939046	+	0.343793i	$0.111712\pi$
$173$	10.0917	+	17.4793i	0.767256	+	1.32893i	−0.171790	+	0.985134i	$0.554955\pi$
$174$	−1.75358	+	0.364285i	−0.132938	+	0.0276164i
$175$	0.896323	−	1.55248i	0.0677556	−	0.117356i
$176$	3.55902	−	6.16440i	0.268271	−	0.464659i
$177$	21.8805	−	4.54542i	1.64464	−	0.341655i
$178$	2.40390	+	4.16368i	0.180180	+	0.312081i
$179$	−10.7902			−0.806497			−0.403249	−	0.915090i	$-0.632119\pi$
$179$	−10.7902			−0.806497			−0.403249	+	0.915090i	$0.632119\pi$
$180$	−4.40022	+	1.91064i	−0.327973	+	0.142411i
$181$	−17.0991			−1.27096			−0.635482	−	0.772116i	$-0.719199\pi$
$181$	−17.0991			−1.27096			−0.635482	+	0.772116i	$0.719199\pi$
$182$	−0.567560	−	0.983044i	−0.0420704	−	0.0728680i
$183$	2.76589	−	8.38075i	0.204461	−	0.619523i
$184$	9.28346	−	16.0794i	0.684385	−	1.18539i
$185$	−0.364668	+	0.631623i	−0.0268109	+	0.0464379i
$186$	3.17270	+	3.55651i	0.232634	+	0.260776i
$187$	14.3779	+	24.9033i	1.05142	+	1.82111i
$188$	14.9549			1.09070
$189$	8.45628	+	3.90613i	0.615104	+	0.284129i
$190$	1.04882			0.0760896
$191$	2.89056	+	5.00660i	0.209154	+	0.362265i	0.951448	−	0.307809i	$-0.0995958\pi$
$191$	2.89056	+	5.00660i	0.209154	+	0.362265i	−0.742295	+	0.670074i	$0.766262\pi$
$192$	−0.0919303	−	0.103051i	−0.00663450	−	0.00743709i
$193$	−4.80100	+	8.31557i	−0.345583	+	0.598568i	−0.985460	−	0.169910i	$-0.945652\pi$
$193$	−4.80100	+	8.31557i	−0.345583	+	0.598568i	0.639876	+	0.768478i	$0.278986\pi$
$194$	−3.97158	+	6.87897i	−0.285143	+	0.493882i
$195$	−0.542829	+	1.64479i	−0.0388728	+	0.117786i
$196$	−3.02733	−	5.24349i	−0.216238	−	0.374535i
$197$	−11.8141			−0.841721			−0.420861	−	0.907125i	$-0.638272\pi$
$197$	−11.8141			−0.841721			−0.420861	+	0.907125i	$0.638272\pi$
$198$	−6.19100	−	4.58592i	−0.439975	−	0.325907i
$199$	−16.7437			−1.18693			−0.593465	−	0.804860i	$-0.702241\pi$
$199$	−16.7437			−1.18693			−0.593465	+	0.804860i	$0.702241\pi$
$200$	−1.13948	−	1.97363i	−0.0805731	−	0.139557i
$201$	7.41196	−	1.53975i	0.522799	−	0.108605i
$202$	−1.65643	+	2.86901i	−0.116546	+	0.201863i
$203$	1.46371	−	2.53522i	0.102732	−	0.177938i
$204$	−19.2264	+	3.99406i	−1.34612	+	0.279640i
$205$	−0.439625	−	0.761453i	−0.0307048	−	0.0531822i
$206$	10.8734			0.757583
$207$	19.6401	+	14.5482i	1.36508	+	1.01117i
$208$	1.75503			0.121690
$209$	−3.35891	−	5.81781i	−0.232341	−	0.402426i
$210$	−0.616176	+	1.86704i	−0.0425202	+	0.128838i
$211$	11.3208	−	19.6081i	0.779353	−	1.34988i	−0.152962	−	0.988232i	$-0.548881\pi$
$211$	11.3208	−	19.6081i	0.779353	−	1.34988i	0.932315	−	0.361647i	$-0.117785\pi$
$212$	4.30978	−	7.46475i	0.295997	−	0.512681i
$213$	3.23884	+	3.63065i	0.221922	+	0.248768i
$214$	−1.57806	−	2.73328i	−0.107874	−	0.186843i
$215$	5.53962			0.377799
$216$	9.67564	−	6.82713i	0.658344	−	0.464528i
$217$	−7.79005			−0.528823
$218$	−1.52327	−	2.63838i	−0.103169	−	0.178694i
$219$	5.77100	+	6.46913i	0.389968	+	0.437143i
$220$	−3.24269	+	5.61650i	−0.218622	+	0.378665i
$221$	−3.54504	+	6.14019i	−0.238465	+	0.413034i
$222$	0.250691	−	0.759602i	0.0168253	−	0.0509811i
$223$	−6.77483	−	11.7344i	−0.453676	−	0.785791i	0.544935	−	0.838479i	$-0.316554\pi$
$223$	−6.77483	−	11.7344i	−0.453676	−	0.785791i	−0.998611	+	0.0526879i	$0.983221\pi$
$224$	10.1629			0.679036
$225$	2.75178	−	1.19486i	0.183452	−	0.0796576i
$226$	−5.95853			−0.396356
$227$	−11.8716	−	20.5622i	−0.787946	−	1.36476i	−0.927223	−	0.374510i	$-0.877811\pi$
$227$	−11.8716	−	20.5622i	−0.787946	−	1.36476i	0.139277	−	0.990254i	$-0.455522\pi$
$228$	4.49160	−	0.933077i	0.297463	−	0.0617945i
$229$	3.74054	−	6.47881i	0.247182	−	0.428131i	−0.715561	−	0.698550i	$-0.753829\pi$
$229$	3.74054	−	6.47881i	0.247182	−	0.428131i	0.962743	+	0.270419i	$0.0871622\pi$
$230$	−2.57942	+	4.46769i	−0.170082	+	0.294591i
$231$	12.3298	−	2.56137i	0.811240	−	0.168525i
$232$	−1.86078	−	3.22297i	−0.122166	−	0.211599i
$233$	19.4760			1.27592			0.637959	−	0.770071i	$-0.279779\pi$
$233$	19.4760			1.27592			0.637959	+	0.770071i	$0.279779\pi$
$234$	0.215993	−	1.88731i	0.0141199	−	0.123377i
$235$	−9.35239			−0.610083
$236$	10.3158	+	17.8675i	0.671501	+	1.16307i
$237$	−3.70368	+	11.2223i	−0.240580	+	0.728966i
$238$	−4.02405	+	6.96985i	−0.260840	+	0.451788i
$239$	−4.54451	+	7.87132i	−0.293960	+	0.509153i	−0.974742	−	0.223332i	$-0.928307\pi$
$239$	−4.54451	+	7.87132i	−0.293960	+	0.509153i	0.680783	+	0.732486i	$0.261640\pi$
$240$	−2.02358	−	2.26838i	−0.130622	−	0.146423i
$241$	5.93896	+	10.2866i	0.382562	+	0.662617i	0.991428	−	0.130657i	$-0.0417085\pi$
$241$	5.93896	+	10.2866i	0.382562	+	0.662617i	−0.608866	+	0.793273i	$0.708375\pi$
$242$	−3.45060			−0.221813
$243$	7.48070	+	13.6762i	0.479887	+	0.877330i
$244$	8.14766			0.521600
$245$	1.89321	+	3.27914i	0.120953	+	0.209496i
$246$	0.641942	+	0.719599i	0.0409287	+	0.0458800i
$247$	0.828179	−	1.43445i	0.0526958	−	0.0912717i
$248$	−4.95166	+	8.57653i	−0.314431	+	0.544610i
$249$	−3.53673	+	10.7164i	−0.224131	+	0.679125i
$250$	0.316605	+	0.548376i	0.0200239	+	0.0346823i
$251$	−25.0409			−1.58057			−0.790285	−	0.612740i	$-0.790067\pi$
$251$	−25.0409			−1.58057			−0.790285	+	0.612740i	$0.790067\pi$
$252$	−0.977791	+	8.54379i	−0.0615951	+	0.538208i
$253$	33.0430			2.07739
$254$	−3.01254	−	5.21787i	−0.189024	−	0.327399i
$255$	12.0237	−	2.49778i	0.752951	−	0.156417i
$256$	3.65355	−	6.32813i	0.228347	−	0.395508i
$257$	−8.54277	+	14.7965i	−0.532883	+	0.922981i	0.466379	+	0.884585i	$0.345558\pi$
$257$	−8.54277	+	14.7965i	−0.532883	+	0.922981i	−0.999263	+	0.0383959i	$0.987775\pi$
$258$	−5.94859	+	1.23575i	−0.370343	+	0.0769344i
$259$	0.653720	+	1.13228i	0.0406202	+	0.0703562i
$260$	−1.59905			−0.0991686
$261$	4.49371	−	1.95124i	0.278154	−	0.120778i
$262$	5.12704			0.316750
$263$	8.27935	+	14.3403i	0.510527	+	0.884258i	0.999926	+	0.0121979i	$0.00388281\pi$
$263$	8.27935	+	14.3403i	0.510527	+	0.884258i	−0.489399	+	0.872060i	$0.662784\pi$
$264$	5.01733	−	15.2027i	0.308795	−	0.935661i
$265$	−2.69522	+	4.66826i	−0.165566	+	0.286769i
$266$	0.940083	−	1.62827i	0.0576402	−	0.0998357i
$267$	−8.75457	−	9.81362i	−0.535771	−	0.600584i
$268$	3.49444	+	6.05255i	0.213457	+	0.369718i
$269$	12.7025			0.774487			0.387244	−	0.921977i	$-0.373427\pi$
$269$	12.7025			0.774487			0.387244	+	0.921977i	$0.373427\pi$
$270$	−2.68839	+	1.89693i	−0.163610	+	0.115443i
$271$	−27.7692			−1.68686			−0.843431	−	0.537238i	$-0.819468\pi$
$271$	−27.7692			−1.68686			−0.843431	+	0.537238i	$0.819468\pi$
$272$	−6.22167	−	10.7762i	−0.377244	−	0.653406i
$273$	2.06695	+	2.31699i	0.125097	+	0.140231i
$274$	6.52153	−	11.2956i	0.393980	−	0.682394i
$275$	2.02789	−	3.51241i	0.122286	−	0.211806i
$276$	−7.07177	+	21.4277i	−0.425671	+	1.28980i
$277$	14.2555	+	24.6913i	0.856532	+	1.48356i	0.875217	+	0.483731i	$0.160719\pi$
$277$	14.2555	+	24.6913i	0.856532	+	1.48356i	−0.0186853	+	0.999825i	$0.505948\pi$
$278$	−9.88358			−0.592777
$279$	−10.4757	−	7.75978i	−0.627165	−	0.464566i
$280$	−4.08535			−0.244146
$281$	2.86416	+	4.96088i	0.170862	+	0.295941i	0.938721	−	0.344677i	$-0.112012\pi$
$281$	2.86416	+	4.96088i	0.170862	+	0.295941i	−0.767860	+	0.640618i	$0.778678\pi$
$282$	10.0428	−	2.08628i	0.598042	−	0.124236i
$283$	10.4934	−	18.1752i	0.623770	−	1.08040i	−0.365007	−	0.931005i	$-0.618933\pi$
$283$	10.4934	−	18.1752i	0.623770	−	1.08040i	0.988777	−	0.149397i	$-0.0477332\pi$
$284$	−2.24587	+	3.88996i	−0.133268	+	0.230827i
$285$	−2.80893	+	0.583521i	−0.166386	+	0.0345648i
$286$	−1.28408	−	2.22409i	−0.0759293	−	0.131513i
$287$	−1.57618			−0.0930392
$288$	13.6666	+	10.1234i	0.805313	+	0.596527i
$289$	33.2692			1.95701
$290$	0.517022	+	0.895508i	0.0303606	+	0.0525860i
$291$	6.80939	−	20.6327i	0.399174	−	1.20951i
$292$	−4.00172	+	6.93118i	−0.234183	+	0.405616i
$293$	−15.2303	+	26.3796i	−0.889763	+	1.54111i	−0.0496073	+	0.998769i	$0.515797\pi$
$293$	−15.2303	+	26.3796i	−0.889763	+	1.54111i	−0.840156	+	0.542346i	$0.817536\pi$
$294$	−2.76447	−	3.09890i	−0.161227	−	0.180731i
$295$	−6.45122	−	11.1738i	−0.375604	−	0.650566i
$296$	1.66212			0.0966088
$297$	19.1320	+	8.83745i	1.11015	+	0.512801i
$298$	0.995981			0.0576956
$299$	4.07356	+	7.05562i	0.235580	+	0.408037i
$300$	1.84372	+	2.06676i	0.106447	+	0.119325i
$301$	4.96529	−	8.60013i	0.286194	−	0.495703i
$302$	3.57298	−	6.18859i	0.205602	−	0.356113i
$303$	2.83999	−	8.60528i	0.163153	−	0.494360i
$304$	1.45348	+	2.51751i	0.0833629	+	0.144389i
$305$	−5.09533			−0.291758
$306$	−12.3541	+	5.36435i	−0.706239	+	0.306660i
$307$	−31.0677			−1.77313			−0.886565	−	0.462604i	$-0.846915\pi$
$307$	−31.0677			−1.77313			−0.886565	+	0.462604i	$0.846915\pi$
$308$	5.81299	+	10.0684i	0.331226	+	0.573700i
$309$	−29.1207	+	6.04949i	−1.65662	+	0.344143i
$310$	1.37583	−	2.38300i	0.0781417	−	0.135345i
$311$	−5.37041	+	9.30182i	−0.304528	+	0.527458i	−0.977156	−	0.212523i	$-0.931832\pi$
$311$	−5.37041	+	9.30182i	−0.304528	+	0.527458i	0.672628	+	0.739981i	$0.265165\pi$
$312$	3.86475	−	0.802856i	0.218798	−	0.0454528i
$313$	−9.75160	−	16.8903i	−0.551193	−	0.954694i	−0.998189	−	0.0601580i	$-0.980840\pi$
$313$	−9.75160	−	16.8903i	−0.551193	−	0.954694i	0.446996	−	0.894536i	$-0.352494\pi$
$314$	7.51780			0.424254
$315$	0.611485	−	5.34306i	0.0344533	−	0.301047i
$316$	−10.9102			−0.613745
$317$	−5.34516	−	9.25809i	−0.300214	−	0.519986i	0.675970	−	0.736929i	$-0.263725\pi$
$317$	−5.34516	−	9.25809i	−0.300214	−	0.519986i	−0.976184	+	0.216943i	$0.930391\pi$
$318$	1.85283	−	5.61413i	0.103901	−	0.314825i
$319$	3.31158	−	5.73583i	0.185413	−	0.321145i
$320$	−0.0398652	+	0.0690485i	−0.00222853	+	0.00385993i
$321$	5.74700	+	6.44223i	0.320766	+	0.359570i
$322$	4.62399	+	8.00898i	0.257685	+	0.446323i
$323$	−11.7437			−0.653437
$324$	−9.82549	+	10.5153i	−0.545860	+	0.584185i
$325$	1.00000			0.0554700
$326$	−4.46500	−	7.73360i	−0.247293	−	0.428325i
$327$	5.54746	+	6.21855i	0.306775	+	0.343886i
$328$	−1.00188	+	1.73531i	−0.0553198	+	0.0958167i
$329$	−8.38276	+	14.5194i	−0.462156	+	0.800478i
$330$	−1.39407	+	4.22409i	−0.0767412	+	0.232529i
$331$	−6.33425	−	10.9712i	−0.348162	−	0.603034i	0.637761	−	0.770234i	$-0.279861\pi$
$331$	−6.33425	−	10.9712i	−0.348162	−	0.603034i	−0.985923	+	0.167200i	$0.946527\pi$
$332$	−10.4184			−0.571782
$333$	−0.248782	+	2.17382i	−0.0136332	+	0.119124i
$334$	8.10648			0.443567
$335$	−2.18533	−	3.78510i	−0.119397	−	0.206802i
$336$	−5.33539	+	1.10836i	−0.291069	+	0.0604662i
$337$	16.4922	−	28.5653i	0.898387	−	1.55605i	0.0688313	−	0.997628i	$-0.478073\pi$
$337$	16.4922	−	28.5653i	0.898387	−	1.55605i	0.829556	−	0.558424i	$-0.188594\pi$
$338$	0.316605	−	0.548376i	0.0172210	−	0.0298277i
$339$	15.9580	−	3.31508i	0.866718	−	0.180050i
$340$	5.66868	+	9.81843i	0.307427	+	0.532479i
$341$	−17.6246			−0.954428
$342$	2.88613	−	1.25320i	0.156064	−	0.0677653i
$343$	19.3362			1.04406
$344$	−6.31226	−	10.9332i	−0.340334	−	0.589476i
$345$	4.42250	−	13.4003i	0.238099	−	0.721449i
$346$	−6.39015	+	11.0681i	−0.343537	+	0.595023i
$347$	4.50193	−	7.79757i	0.241676	−	0.418596i	−0.719516	−	0.694476i	$-0.755636\pi$
$347$	4.50193	−	7.79757i	0.241676	−	0.418596i	0.961192	+	0.275881i	$0.0889694\pi$
$348$	3.01084	+	3.37506i	0.161398	+	0.180922i
$349$	10.6147	+	18.3851i	0.568190	+	0.984133i	0.996745	+	0.0806177i	$0.0256893\pi$
$349$	10.6147	+	18.3851i	0.568190	+	0.984133i	−0.428556	+	0.903515i	$0.640977\pi$
$350$	1.13512			0.0606748
$351$	0.471556	+	5.17471i	0.0251698	+	0.276206i
$352$	22.9931			1.22554
$353$	−9.80604	−	16.9846i	−0.521923	−	0.903997i	−0.999675	−	0.0255022i	$-0.991882\pi$
$353$	−9.80604	−	16.9846i	−0.521923	−	0.903997i	0.477752	−	0.878495i	$-0.341452\pi$
$354$	9.42009	+	10.5597i	0.500672	+	0.561239i
$355$	1.40451	−	2.43268i	0.0745435	−	0.129113i
$356$	6.07058	−	10.5145i	0.321740	−	0.557270i
$357$	6.89935	−	20.9053i	0.365152	−	1.10642i
$358$	−3.41623	−	5.91709i	−0.180553	−	0.312728i
$359$	16.8856			0.891187			0.445593	−	0.895235i	$-0.352993\pi$
$359$	16.8856			0.891187			0.445593	+	0.895235i	$0.352993\pi$
$360$	−5.49381	−	4.06948i	−0.289549	−	0.214480i
$361$	−16.2565			−0.855604
$362$	−5.41365	−	9.37672i	−0.284535	−	0.492830i
$363$	9.24129	−	1.91977i	0.485042	−	0.100762i
$364$	−1.43326	+	2.48248i	−0.0751232	+	0.130117i
$365$	2.50257	−	4.33457i	0.130990	−	0.226882i
$366$	5.47149	−	1.13664i	0.286000	−	0.0594130i
$367$	9.95269	+	17.2386i	0.519526	+	0.899846i	0.999742	+	0.0226955i	$0.00722482\pi$
$367$	9.95269	+	17.2386i	0.519526	+	0.899846i	−0.480216	+	0.877150i	$0.659442\pi$
$368$	−14.2985			−0.745361
$369$	−2.11959	−	1.57006i	−0.110341	−	0.0817340i
$370$	−0.461823			−0.0240090
$371$	4.83157	+	8.36853i	0.250843	+	0.434472i
$372$	3.77198	−	11.4292i	0.195568	−	0.592578i
$373$	−2.99102	+	5.18060i	−0.154869	+	0.268241i	−0.933011	−	0.359847i	$-0.882829\pi$
$373$	−2.99102	+	5.18060i	−0.154869	+	0.268241i	0.778142	+	0.628088i	$0.216162\pi$
$374$	−9.10423	+	15.7690i	−0.470769	+	0.815395i
$375$	−1.15302	−	1.29250i	−0.0595415	−	0.0667444i
$376$	10.6568	+	18.4582i	0.549584	+	0.951907i
$377$	1.63302			0.0841047
$378$	0.535273	+	5.87392i	0.0275315	+	0.302122i
$379$	10.5304			0.540911			0.270456	−	0.962732i	$-0.412826\pi$
$379$	10.5304			0.540911			0.270456	+	0.962732i	$0.412826\pi$
$380$	−1.32430	−	2.29375i	−0.0679349	−	0.117667i
$381$	10.9711	+	12.2983i	0.562067	+	0.630061i
$382$	−1.83033	+	3.17023i	−0.0936480	+	0.162203i
$383$	8.04037	−	13.9263i	0.410844	−	0.711602i	−0.584139	−	0.811654i	$-0.698568\pi$
$383$	8.04037	−	13.9263i	0.410844	−	0.711602i	0.994982	+	0.100052i	$0.0319009\pi$
$384$	−6.12742	+	18.5663i	−0.312688	+	0.947457i
$385$	−3.63529	−	6.29651i	−0.185272	−	0.320900i
$386$	−6.08008			−0.309468
$387$	15.2438	−	6.61909i	0.774887	−	0.336467i
$388$	20.0588			1.01833
$389$	7.59040	+	13.1470i	0.384849	+	0.666577i	0.991748	−	0.128201i	$-0.0409203\pi$
$389$	7.59040	+	13.1470i	0.384849	+	0.666577i	−0.606900	+	0.794779i	$0.707587\pi$
$390$	−1.07383	+	0.223075i	−0.0543753	+	0.0112958i
$391$	28.8819	−	50.0249i	1.46062	−	2.52987i
$392$	4.31454	−	7.47300i	0.217917	−	0.377443i
$393$	−13.7311	+	2.85247i	−0.692642	+	0.143888i
$394$	−3.74041	−	6.47858i	−0.188439	−	0.326386i
$395$	6.82293			0.343299
$396$	−2.21221	+	19.3300i	−0.111168	+	0.971367i
$397$	−3.30120			−0.165683			−0.0828413	−	0.996563i	$-0.526399\pi$
$397$	−3.30120			−0.165683			−0.0828413	+	0.996563i	$0.526399\pi$
$398$	−5.30114	−	9.18185i	−0.265722	−	0.460245i
$399$	−1.61180	+	4.88381i	−0.0806910	+	0.244496i
$400$	−0.877517	+	1.51990i	−0.0438759	+	0.0759952i
$401$	15.6024	−	27.0241i	0.779146	−	1.34952i	−0.153288	−	0.988182i	$-0.548986\pi$
$401$	15.6024	−	27.0241i	0.779146	−	1.34952i	0.932434	−	0.361339i	$-0.117680\pi$
$402$	3.19102	+	3.57705i	0.159154	+	0.178407i
$403$	−2.17278	−	3.76337i	−0.108234	−	0.187467i
$404$	8.36594			0.416221
$405$	6.14460	−	6.57601i	0.305328	−	0.326765i
$406$	1.85367			0.0919962
$407$	1.47901	+	2.56173i	0.0733120	+	0.126980i
$408$	−18.6304	−	20.8841i	−0.922340	−	1.03392i
$409$	5.02681	−	8.70669i	0.248560	−	0.430518i	−0.714567	−	0.699567i	$-0.753376\pi$
$409$	5.02681	−	8.70669i	0.248560	−	0.430518i	0.963126	+	0.269049i	$0.0867094\pi$
$410$	0.278375	−	0.482160i	0.0137480	−	0.0238122i
$411$	−11.1814	+	33.8799i	−0.551536	+	1.67117i
$412$	−13.7292	−	23.7798i	−0.676391	−	1.17154i
$413$	−23.1295			−1.13813
$414$	−1.75972	+	15.3762i	−0.0864855	+	0.755697i
$415$	6.51536			0.319826
$416$	2.83460	+	4.90968i	0.138978	+	0.240717i
$417$	26.4699	−	5.49881i	1.29624	−	0.269278i
$418$	2.12690	−	3.68389i	0.104030	−	0.180185i
$419$	17.3130	−	29.9869i	0.845793	−	1.46496i	−0.0391372	−	0.999234i	$-0.512461\pi$
$419$	17.3130	−	29.9869i	0.845793	−	1.46496i	0.884930	−	0.465723i	$-0.154206\pi$
$420$	4.86117	−	1.00985i	0.237201	−	0.0492757i
$421$	3.31470	+	5.74123i	0.161549	+	0.279811i	0.935424	−	0.353527i	$-0.115018\pi$
$421$	3.31470	+	5.74123i	0.161549	+	0.279811i	−0.773876	+	0.633338i	$0.781684\pi$
$422$	14.3368			0.697906
$423$	−25.7357	+	11.1748i	−1.25131	+	0.543339i
$424$	12.2845			0.596590
$425$	−3.54504	−	6.14019i	−0.171960	−	0.297843i
$426$	−0.965528	+	2.92558i	−0.0467800	+	0.141745i
$427$	−4.56706	+	7.91037i	−0.221015	+	0.382810i
$428$	−3.98508	+	6.90235i	−0.192626	+	0.333638i
$429$	4.67638	+	5.24210i	0.225778	+	0.253091i
$430$	1.75387	+	3.03779i	0.0845792	+	0.146495i
$431$	−37.5004			−1.80633			−0.903165	−	0.429293i	$-0.858763\pi$
$431$	−37.5004			−1.80633			−0.903165	+	0.429293i	$0.858763\pi$
$432$	−8.27887	−	3.82418i	−0.398317	−	0.183991i
$433$	14.1428			0.679662			0.339831	−	0.940487i	$-0.389630\pi$
$433$	14.1428			0.679662			0.339831	+	0.940487i	$0.389630\pi$
$434$	−2.46637	−	4.27187i	−0.118389	−	0.205057i
$435$	−1.88290	−	2.11067i	−0.0902780	−	0.101199i
$436$	−3.84671	+	6.66269i	−0.184224	+	0.319085i
$437$	−6.74728	+	11.6866i	−0.322766	+	0.559047i
$438$	−1.72039	+	5.21284i	−0.0822033	+	0.249079i
$439$	−14.8461	−	25.7142i	−0.708566	−	1.22727i	−0.965389	−	0.260814i	$-0.916009\pi$
$439$	−14.8461	−	25.7142i	−0.708566	−	1.22727i	0.256823	−	0.966458i	$-0.417324\pi$
$440$	−9.24293			−0.440640
$441$	9.12783	+	6.76134i	0.434659	+	0.321969i
$442$	−4.48951			−0.213544
$443$	12.7024	+	22.0013i	0.603511	+	1.04531i	0.992285	+	0.123978i	$0.0395654\pi$
$443$	12.7024	+	22.0013i	0.603511	+	1.04531i	−0.388774	+	0.921333i	$0.627101\pi$
$444$	−1.97776	+	0.410857i	−0.0938605	+	0.0194984i
$445$	−3.79638	+	6.57552i	−0.179965	+	0.311709i
$446$	4.28989	−	7.43031i	0.203132	−	0.351836i
$447$	−2.66741	+	0.554122i	−0.126164	+	0.0262091i
$448$	0.0714641	+	0.123779i	0.00337636	+	0.00584803i
$449$	−24.8926			−1.17475			−0.587376	−	0.809314i	$-0.699839\pi$
$449$	−24.8926			−1.17475			−0.587376	+	0.809314i	$0.699839\pi$
$450$	1.52646	+	1.13071i	0.0719581	+	0.0533022i
$451$	−3.56605			−0.167919
$452$	7.52354	+	13.0311i	0.353877	+	0.612934i
$453$	−6.12599	+	18.5620i	−0.287824	+	0.872117i
$454$	7.51722	−	13.0202i	0.352801	−	0.611069i
$455$	0.896323	−	1.55248i	0.0420203	−	0.0727812i
$456$	4.35236	+	4.87887i	0.203818	+	0.228474i
$457$	−18.1540	−	31.4436i	−0.849207	−	1.47087i	−0.881917	−	0.471404i	$-0.843747\pi$
$457$	−18.1540	−	31.4436i	−0.849207	−	1.47087i	0.0327109	−	0.999465i	$-0.489586\pi$
$458$	4.73710			0.221350
$459$	30.1020	−	21.2400i	1.40504	−	0.991398i
$460$	13.0276			0.607416
$461$	−0.354634	−	0.614244i	−0.0165169	−	0.0286082i	0.857649	−	0.514236i	$-0.171924\pi$
$461$	−0.354634	−	0.614244i	−0.0165169	−	0.0286082i	−0.874166	+	0.485628i	$0.838591\pi$
$462$	5.30826	+	5.95041i	0.246963	+	0.276838i
$463$	20.1443	−	34.8910i	0.936186	−	1.62152i	0.163682	−	0.986513i	$-0.447663\pi$
$463$	20.1443	−	34.8910i	0.936186	−	1.62152i	0.772505	−	0.635009i	$-0.219004\pi$
$464$	−1.43300	+	2.48203i	−0.0665254	+	0.115225i
$465$	−2.35890	+	7.14754i	−0.109391	+	0.331459i
$466$	6.16621	+	10.6802i	0.285644	+	0.494750i
$467$	−13.8688			−0.641773			−0.320887	−	0.947118i	$-0.603981\pi$
$467$	−13.8688			−0.641773			−0.320887	+	0.947118i	$0.603981\pi$
$468$	−4.40022	+	1.91064i	−0.203400	+	0.0883195i
$469$	−7.83504			−0.361789
$470$	−2.96101	−	5.12863i	−0.136581	−	0.236566i
$471$	−20.1340	+	4.18259i	−0.927724	+	0.192724i
$472$	−14.7020	+	25.4646i	−0.676715	+	1.17210i
$473$	11.2337	−	19.4574i	0.516528	−	0.894653i
$474$	−7.32664	+	1.52202i	−0.336524	+	0.0699088i
$475$	0.828179	+	1.43445i	0.0379994	+	0.0658170i
$476$	20.3238			0.931542
$477$	−1.83872	+	16.0664i	−0.0841891	+	0.735632i
$478$	−5.75526			−0.263239
$479$	19.5280	+	33.8234i	0.892255	+	1.54543i	0.837165	+	0.546950i	$0.184211\pi$
$479$	19.5280	+	33.8234i	0.892255	+	1.54543i	0.0550902	+	0.998481i	$0.482455\pi$
$480$	3.07741	−	9.32466i	0.140464	−	0.425611i
$481$	−0.364668	+	0.631623i	−0.0166274	+	0.0287995i
$482$	−3.76061	+	6.51356i	−0.171291	+	0.296685i
$483$	−16.8397	−	18.8768i	−0.766233	−	0.858926i
$484$	4.35690	+	7.54637i	0.198041	+	0.343017i
$485$	−12.5443			−0.569606
$486$	−5.13129	+	8.43220i	−0.232760	+	0.382492i
$487$	−10.3472			−0.468875			−0.234437	−	0.972131i	$-0.575325\pi$
$487$	−10.3472			−0.468875			−0.234437	+	0.972131i	$0.575325\pi$
$488$	5.80600	+	10.0563i	0.262825	+	0.455227i
$489$	16.2607	+	18.2278i	0.735333	+	0.824288i
$490$	−1.19880	+	2.07638i	−0.0541563	+	0.0938015i
$491$	−0.542644	+	0.939888i	−0.0244892	+	0.0424165i	−0.878010	−	0.478642i	$-0.841129\pi$
$491$	−0.542644	+	0.939888i	−0.0244892	+	0.0424165i	0.853521	+	0.521058i	$0.174463\pi$
$492$	0.763196	−	2.31251i	0.0344075	−	0.104256i
$493$	−5.78911	−	10.0270i	−0.260728	−	0.451595i
$494$	1.04882			0.0471887
$495$	1.38346	−	12.0884i	0.0621818	−	0.543335i
$496$	7.62661			0.342445
$497$	−2.51778	−	4.36093i	−0.112938	−	0.195614i
$498$	−6.99636	+	1.45341i	−0.313515	+	0.0651290i
$499$	21.2100	−	36.7368i	0.949489	−	1.64456i	0.202986	−	0.979182i	$-0.434935\pi$
$499$	21.2100	−	36.7368i	0.949489	−	1.64456i	0.746503	−	0.665382i	$-0.231731\pi$
$500$	0.799523	−	1.38481i	0.0357557	−	0.0619307i
$501$	−21.7105	+	4.51011i	−0.969955	+	0.201497i
$502$	−7.92808	−	13.7318i	−0.353848	−	0.612882i
$503$	7.96629			0.355199			0.177600	−	0.984103i	$-0.443167\pi$
$503$	7.96629			0.355199			0.177600	+	0.984103i	$0.443167\pi$
$504$	−11.2420	+	4.88144i	−0.500758	+	0.217437i
$505$	−5.23184			−0.232814
$506$	10.4616	+	18.1200i	0.465074	+	0.805531i
$507$	−0.542829	+	1.64479i	−0.0241079	+	0.0730477i
$508$	−7.60757	+	13.1767i	−0.337531	+	0.584621i
$509$	6.43669	−	11.1487i	0.285301	−	0.494157i	−0.687381	−	0.726297i	$-0.741240\pi$
$509$	6.43669	−	11.1487i	0.285301	−	0.494157i	0.972682	+	0.232141i	$0.0745730\pi$
$510$	5.17647	+	5.80268i	0.229218	+	0.256947i
$511$	−4.48621	−	7.77035i	−0.198458	−	0.343740i
$512$	−17.9489			−0.793239
$513$	−7.03232	+	4.96201i	−0.310484	+	0.219078i
$514$	−10.8187			−0.477194
$515$	8.58590	+	14.8712i	0.378340	+	0.655304i
$516$	10.2135	+	11.4491i	0.449626	+	0.504018i
$517$	−18.9656	+	32.8494i	−0.834107	+	1.44472i
$518$	−0.413942	+	0.716969i	−0.0181876	+	0.0315018i
$519$	10.9561	−	33.1974i	0.480920	−	1.45720i
$520$	−1.13948	−	1.97363i	−0.0499693	−	0.0865494i
$521$	−7.60942			−0.333375			−0.166687	−	0.986010i	$-0.553307\pi$
$521$	−7.60942			−0.333375			−0.166687	+	0.986010i	$0.553307\pi$
$522$	2.49274	+	1.84647i	0.109104	+	0.0808178i
$523$	−34.6906			−1.51692			−0.758458	−	0.651722i	$-0.774047\pi$
$523$	−34.6906			−1.51692			−0.758458	+	0.651722i	$0.774047\pi$
$524$	−6.47365	−	11.2127i	−0.282803	−	0.489829i
$525$	−3.04005	+	0.631534i	−0.132679	+	0.0275624i
$526$	−5.24257	+	9.08039i	−0.228587	+	0.395924i
$527$	−15.4052	+	26.6825i	−0.671060	+	1.16231i
$528$	−12.0711	+	2.50763i	−0.525327	+	0.109130i
$529$	−21.6879	−	37.5645i	−0.942950	−	1.63324i
$530$	−3.41328			−0.148263
$531$	−31.1036	−	23.0396i	−1.34978	−	0.999834i
$532$	−4.74798			−0.205851
$533$	−0.439625	−	0.761453i	−0.0190423	−	0.0329822i
$534$	2.60982	−	7.90784i	0.112938	−	0.342206i
$535$	2.49216	−	4.31655i	0.107745	−	0.186621i
$536$	−4.98026	+	8.62606i	−0.215114	+	0.372589i
$537$	12.4413	+	13.9463i	0.536881	+	0.601828i
$538$	4.02169	+	6.96576i	0.173387	+	0.300315i
$539$	15.3569			0.661469
$540$	7.54303	+	3.48428i	0.324600	+	0.149940i
$541$	−0.0126565			−0.000544145			−0.000272073	−	1.00000i	$-0.500087\pi$
$541$	−0.0126565			−0.000544145			−0.000272073		1.00000i	$0.500087\pi$
$542$	−8.79188	−	15.2280i	−0.377644	−	0.654098i
$543$	19.7155	+	22.1005i	0.846074	+	0.948425i
$544$	20.0976	−	34.8100i	0.861676	−	1.49247i
$545$	2.40563	−	4.16667i	0.103046	−	0.178481i
$546$	−0.616176	+	1.86704i	−0.0263699	+	0.0799018i
$547$	4.27856	+	7.41069i	0.182938	+	0.316858i	0.942880	−	0.333133i	$-0.108106\pi$
$547$	4.27856	+	7.41069i	0.182938	+	0.316858i	−0.759942	+	0.649991i	$0.774773\pi$
$548$	−32.9376			−1.40703
$549$	−14.0212	+	6.08822i	−0.598411	+	0.259839i
$550$	2.56816			0.109507
$551$	1.35243	+	2.34248i	0.0576155	+	0.0997929i
$552$	−31.4866	+	6.54097i	−1.34016	+	0.278402i
$553$	6.11554	−	10.5924i	0.260059	−	0.450436i
$554$	−9.02674	+	15.6348i	−0.383510	+	0.664258i
$555$	1.23684	−	0.256939i	0.0525009	−	0.0109065i
$556$	12.4795	+	21.6151i	0.529248	+	0.916685i
$557$	−13.3178			−0.564292			−0.282146	−	0.959371i	$-0.591046\pi$
$557$	−13.3178			−0.564292			−0.282146	+	0.959371i	$0.591046\pi$
$558$	0.938609	−	8.20142i	0.0397345	−	0.347194i
$559$	5.53962			0.234301
$560$	1.57308	+	2.72465i	0.0664747	+	0.115137i
$561$	15.6095	−	47.2973i	0.659033	−	1.99689i
$562$	−1.81362	+	3.14128i	−0.0765028	+	0.132507i
$563$	−15.2675	+	26.4441i	−0.643449	+	1.11449i	0.341209	+	0.939988i	$0.389164\pi$
$563$	−15.2675	+	26.4441i	−0.643449	+	1.11449i	−0.984657	+	0.174498i	$0.944170\pi$
$564$	−17.2432	−	19.3292i	−0.726071	−	0.813905i
$565$	−4.70502	−	8.14933i	−0.197942	−	0.342845i
$566$	13.2891			0.558583
$567$	−4.70156	−	15.4336i	−0.197447	−	0.648149i
$568$	−6.40161			−0.268606
$569$	−12.1303	−	21.0103i	−0.508529	−	0.880798i	−0.999951	−	0.00987675i	$-0.996856\pi$
$569$	−12.1303	−	21.0103i	−0.508529	−	0.880798i	0.491422	−	0.870922i	$-0.336477\pi$
$570$	−1.20931	−	1.35560i	−0.0506524	−	0.0567799i
$571$	−13.5254	+	23.4266i	−0.566020	+	0.980375i	0.430934	+	0.902383i	$0.358184\pi$
$571$	−13.5254	+	23.4266i	−0.566020	+	0.980375i	−0.996954	+	0.0779915i	$0.975149\pi$
$572$	−3.24269	+	5.61650i	−0.135584	+	0.234838i
$573$	3.13816	−	9.50874i	0.131099	−	0.397233i
$574$	−0.499028	−	0.864341i	−0.0208290	−	0.0360769i
$575$	−8.14713			−0.339759
$576$	−0.0271966	+	0.237640i	−0.00113319	+	0.00990166i
$577$	21.8806			0.910903			0.455451	−	0.890261i	$-0.349478\pi$
$577$	21.8806			0.910903			0.455451	+	0.890261i	$0.349478\pi$
$578$	10.5332	+	18.2440i	0.438123	+	0.758851i
$579$	16.2835	−	3.38270i	0.676719	−	0.140580i
$580$	1.30563	−	2.26143i	0.0542135	−	0.0939006i
$581$	5.83986	−	10.1149i	0.242278	−	0.419639i
$582$	13.4704	−	2.79831i	0.558364	−	0.115994i
$583$	10.9312	+	18.9334i	0.452725	+	0.784143i
$584$	−11.4065			−0.472002
$585$	2.75178	−	1.19486i	0.113772	−	0.0494016i
$586$	−19.2879			−0.796777
$587$	−13.4602	−	23.3138i	−0.555564	−	0.962265i	−0.997859	−	0.0653955i	$-0.979169\pi$
$587$	−13.4602	−	23.3138i	−0.555564	−	0.962265i	0.442296	−	0.896869i	$-0.354164\pi$
$588$	−3.28665	+	9.95865i	−0.135539	+	0.410688i
$589$	3.59890	−	6.23348i	0.148290	−	0.256846i
$590$	4.08498	−	7.07539i	0.168176	−	0.291289i
$591$	13.6219	+	15.2697i	0.560329	+	0.628113i
$592$	−0.640005	−	1.10852i	−0.0263040	−	0.0455599i
$593$	−13.3259			−0.547231			−0.273616	−	0.961839i	$-0.588220\pi$
$593$	−13.3259			−0.547231			−0.273616	+	0.961839i	$0.588220\pi$
$594$	1.21103	+	13.2895i	0.0496893	+	0.545275i
$595$	−12.7100			−0.521059
$596$	−1.25757	−	2.17818i	−0.0515123	−	0.0892219i
$597$	19.3058	+	21.6412i	0.790133	+	0.885717i
$598$	−2.57942	+	4.46769i	−0.105480	+	0.182697i
$599$	−13.6803	+	23.6949i	−0.558960	+	0.968147i	0.438623	+	0.898671i	$0.355466\pi$
$599$	−13.6803	+	23.6949i	−0.558960	+	0.968147i	−0.997584	+	0.0694765i	$0.977867\pi$
$600$	−1.23708	+	3.74840i	−0.0505036	+	0.153028i
$601$	18.3866	+	31.8465i	0.750003	+	1.29904i	0.947820	+	0.318805i	$0.103281\pi$
$601$	18.3866	+	31.8465i	0.750003	+	1.29904i	−0.197817	+	0.980239i	$0.563385\pi$
$602$	6.28814			0.256285
$603$	−10.5362	−	7.80460i	−0.429069	−	0.317828i
$604$	−18.0457			−0.734270
$605$	−2.72469	−	4.71930i	−0.110774	−	0.191867i
$606$	5.61808	−	1.16709i	0.228219	−	0.0474098i
$607$	−14.8270	+	25.6812i	−0.601811	+	1.04237i	0.390736	+	0.920503i	$0.372220\pi$
$607$	−14.8270	+	25.6812i	−0.601811	+	1.04237i	−0.992547	+	0.121864i	$0.961113\pi$
$608$	−4.69512	+	8.13218i	−0.190412	+	0.329804i
$609$	−4.96445	+	1.03131i	−0.201170	+	0.0417906i
$610$	−1.61321	−	2.79415i	−0.0653168	−	0.113132i
$611$	−9.35239			−0.378357
$612$	27.3306	+	20.2449i	1.10478	+	0.818351i
$613$	−9.69185			−0.391450			−0.195725	−	0.980659i	$-0.562706\pi$
$613$	−9.69185			−0.391450			−0.195725	+	0.980659i	$0.562706\pi$
$614$	−9.83621	−	17.0368i	−0.396957	−	0.687550i
$615$	−0.477282	+	1.44618i	−0.0192459	+	0.0583157i
$616$	−8.28465	+	14.3494i	−0.333798	+	0.578155i
$617$	11.3459	−	19.6517i	0.456770	−	0.791150i	−0.542018	−	0.840367i	$-0.682339\pi$
$617$	11.3459	−	19.6517i	0.456770	−	0.791150i	0.998788	+	0.0492175i	$0.0156727\pi$
$618$	−12.5372	−	14.0538i	−0.504319	−	0.565327i
$619$	−20.8506	−	36.1142i	−0.838055	−	1.45155i	−0.891519	−	0.452984i	$-0.850359\pi$
$619$	−20.8506	−	36.1142i	−0.838055	−	1.45155i	0.0534637	−	0.998570i	$-0.482974\pi$
$620$	−6.94875			−0.279068
$621$	−3.84183	−	42.1590i	−0.154167	−	1.69178i
$622$	−6.80119			−0.272703
$623$	6.80555	+	11.7876i	0.272659	+	0.472259i
$624$	−2.02358	−	2.26838i	−0.0810082	−	0.0908079i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	6.17481	−	10.6951i	0.246795	−	0.427461i
$627$	−3.64663	+	11.0494i	−0.145632	+	0.441271i
$628$	−9.49235	−	16.4412i	−0.378786	−	0.656077i
$629$	5.17105			0.206183
$630$	3.12360	−	1.35632i	0.124447	−	0.0540369i
$631$	8.75145			0.348390			0.174195	−	0.984711i	$-0.444268\pi$
$631$	8.75145			0.348390			0.174195	+	0.984711i	$0.444268\pi$
$632$	−7.77456	−	13.4659i	−0.309255	−	0.535646i
$633$	−38.3965	+	7.97642i	−1.52612	+	0.317034i
$634$	3.38461	−	5.86232i	0.134420	−	0.232822i
$635$	4.75757	−	8.24035i	0.188798	−	0.327008i
$636$	−14.6174	+	3.03660i	−0.579619	+	0.120409i
$637$	1.89321	+	3.27914i	0.0750118	+	0.129924i
$638$	4.19386			0.166036
$639$	0.958176	−	8.37239i	0.0379049	−	0.331207i
$640$	11.2879			0.446195
$641$	−1.05265	−	1.82324i	−0.0415770	−	0.0720135i	0.844488	−	0.535574i	$-0.179905\pi$
$641$	−1.05265	−	1.82324i	−0.0415770	−	0.0720135i	−0.886065	+	0.463561i	$0.846572\pi$
$642$	−1.71323	+	5.19116i	−0.0676160	+	0.204879i
$643$	−10.8108	+	18.7248i	−0.426335	+	0.738434i	−0.996544	−	0.0830654i	$-0.973529\pi$
$643$	−10.8108	+	18.7248i	−0.426335	+	0.738434i	0.570209	+	0.821500i	$0.306862\pi$
$644$	11.6770	−	20.2251i	0.460137	−	0.796980i
$645$	−6.38727	−	7.15995i	−0.251498	−	0.281923i
$646$	−3.71811	−	6.43996i	−0.146287	−	0.253377i
$647$	42.5198			1.67163			0.835814	−	0.549013i	$-0.184996\pi$
$647$	42.5198			1.67163			0.835814	+	0.549013i	$0.184996\pi$
$648$	−19.9802	−	4.63396i	−0.784898	−	0.182039i
$649$	−52.3295			−2.05411
$650$	0.316605	+	0.548376i	0.0124183	+	0.0215091i
$651$	8.98205	+	10.0686i	0.352034	+	0.394621i
$652$	−11.2755	+	19.5297i	−0.441581	+	0.764840i
$653$	3.45757	−	5.98869i	0.135305	−	0.234356i	−0.790409	−	0.612580i	$-0.790132\pi$
$653$	3.45757	−	5.98869i	0.135305	−	0.234356i	0.925714	+	0.378224i	$0.123465\pi$
$654$	−1.65375	+	5.01092i	−0.0646667	+	0.195942i
$655$	4.04845	+	7.01212i	0.158186	+	0.273986i
$656$	1.54311			0.0602485
$657$	1.70729	−	14.9180i	0.0666077	−	0.582007i
$658$	−10.6161			−0.413858
$659$	16.0766	+	27.8454i	0.626254	+	1.08470i	0.988297	+	0.152543i	$0.0487462\pi$
$659$	16.0766	+	27.8454i	0.626254	+	1.08470i	−0.362043	+	0.932162i	$0.617921\pi$
$660$	10.9982	−	2.28475i	0.428104	−	0.0889336i
$661$	0.888579	−	1.53906i	0.0345617	−	0.0598627i	−0.848227	−	0.529633i	$-0.822330\pi$
$661$	0.888579	−	1.53906i	0.0345617	−	0.0598627i	0.882789	+	0.469770i	$0.155663\pi$
$662$	4.01091	−	6.94710i	0.155888	−	0.270007i
$663$	12.0237	−	2.49778i	0.466961	−	0.0970056i
$664$	−7.42410	−	12.8589i	−0.288111	−	0.499023i
$665$	2.96926			0.115143
$666$	−1.27083	+	0.551816i	−0.0492439	+	0.0213824i
$667$	−13.3044			−0.515149
$668$	−10.2356	−	17.7286i	−0.396029	−	0.685942i
$669$	−7.35515	+	22.2864i	−0.284367	+	0.861641i
$670$	1.38377	−	2.39676i	0.0534598	−	0.0925951i
$671$	−10.3328	+	17.8969i	−0.398892	+	0.690901i
$672$	−11.7180	−	13.1355i	−0.452030	−	0.506713i
$673$	10.1709	+	17.6165i	0.392060	+	0.679068i	0.992721	−	0.120436i	$-0.0384292\pi$
$673$	10.1709	+	17.6165i	0.392060	+	0.679068i	−0.600661	+	0.799504i	$0.705096\pi$
$674$	20.8860			0.804501
$675$	−4.71721	−	2.17898i	−0.181565	−	0.0838688i
$676$	−1.59905			−0.0615017
$677$	7.37126	+	12.7674i	0.283300	+	0.490691i	0.972196	−	0.234170i	$-0.0752373\pi$
$677$	7.37126	+	12.7674i	0.283300	+	0.490691i	−0.688895	+	0.724861i	$0.741904\pi$
$678$	6.87028	+	7.70140i	0.263852	+	0.295770i
$679$	−11.2437	+	19.4747i	−0.431494	+	0.747369i
$680$	−8.07897	+	13.9932i	−0.309814	+	0.536614i
$681$	−12.8885	+	39.0526i	−0.493889	+	1.49650i
$682$	−5.58005	−	9.66493i	−0.213671	−	0.370089i
$683$	15.1539			0.579847			0.289923	−	0.957050i	$-0.406370\pi$
$683$	15.1539			0.579847			0.289923	+	0.957050i	$0.406370\pi$
$684$	−6.38489	−	4.72953i	−0.244132	−	0.180838i
$685$	20.5983			0.787021
$686$	6.12195	+	10.6035i	0.233737	+	0.404844i
$687$	−12.6868	+	2.63552i	−0.484030	+	0.100551i
$688$	−4.86111	+	8.41969i	−0.185328	+	0.320998i
$689$	−2.69522	+	4.66826i	−0.102680	+	0.177846i
$690$	8.74860	−	1.81742i	0.333054	−	0.0691879i
$691$	7.81607	+	13.5378i	0.297337	+	0.515003i	0.975526	−	0.219885i	$-0.0705681\pi$
$691$	7.81607	+	13.5378i	0.297337	+	0.515003i	−0.678189	+	0.734888i	$0.737235\pi$
$692$	32.2741			1.22688
$693$	−17.5270	−	12.9829i	−0.665795	−	0.493181i
$694$	5.70134			0.216420
$695$	−7.80434	−	13.5175i	−0.296036	−	0.512749i
$696$	−2.02018	+	6.12120i	−0.0765745	+	0.232024i
$697$	−3.11698	+	5.39876i	−0.118064	+	0.204493i
$698$	−6.72131	+	11.6416i	−0.254405	+	0.440643i
$699$	−22.4562	−	25.1728i	−0.849371	−	0.952121i
$700$	−1.43326	−	2.48248i	−0.0541721	−	0.0938289i
$701$	−8.91657			−0.336774			−0.168387	−	0.985721i	$-0.553856\pi$
$701$	−8.91657			−0.336774			−0.168387	+	0.985721i	$0.553856\pi$
$702$	−2.68839	+	1.89693i	−0.101467	+	0.0715950i
$703$	−1.20804			−0.0455621
$704$	0.161684	+	0.280046i	0.00609371	+	0.0105546i
$705$	10.7835	+	12.0880i	0.406128	+	0.455259i
$706$	6.20928	−	10.7548i	0.233689	−	0.404762i
$707$	−4.68941	+	8.12230i	−0.176364	+	0.305471i
$708$	11.1994	−	33.9346i	0.420900	−	1.27534i
$709$	19.9555	+	34.5639i	0.749444	+	1.29808i	0.948089	+	0.318004i	$0.103012\pi$
$709$	19.9555	+	34.5639i	0.749444	+	1.29808i	−0.198645	+	0.980071i	$0.563654\pi$
$710$	1.77870			0.0667533
$711$	18.7752	−	8.15247i	0.704125	−	0.305742i
$712$	17.3035			0.648477
$713$	17.7019	+	30.6606i	0.662942	+	1.14825i
$714$	13.6483	−	2.83528i	0.510776	−	0.106108i
$715$	2.02789	−	3.51241i	0.0758388	−	0.131357i
$716$	−8.62701	+	14.9424i	−0.322406	+	0.558424i
$717$	15.4136	−	3.20199i	0.575630	−	0.119580i
$718$	5.34606	+	9.25965i	0.199513	+	0.345567i
$719$	34.4119			1.28335			0.641673	−	0.766978i	$-0.278241\pi$
$719$	34.4119			1.28335			0.641673	+	0.766978i	$0.278241\pi$
$720$	−0.598656	+	5.23096i	−0.0223106	+	0.194946i
$721$	30.7830			1.14642
$722$	−5.14688	−	8.91466i	−0.191547	−	0.331769i
$723$	6.44768	−	19.5367i	0.239792	−	0.726577i
$724$	−13.6711	+	23.6790i	−0.508082	+	0.880024i
$725$	−0.816509	+	1.41423i	−0.0303244	+	0.0525234i
$726$	3.97860	+	4.45989i	0.147660	+	0.165522i
$727$	3.48081	+	6.02894i	0.129096	+	0.223601i	0.923327	−	0.384016i	$-0.125459\pi$
$727$	3.48081	+	6.02894i	0.129096	+	0.223601i	−0.794231	+	0.607617i	$0.792126\pi$
$728$	−4.08535			−0.151413
$729$	9.05114	−	25.4377i	0.335228	−	0.942137i
$730$	3.16930			0.117301
$731$	−19.6382	−	34.0143i	−0.726343	−	1.25806i
$732$	−9.39438	−	10.5308i	−0.347226	−	0.389231i
$733$	−12.6573	+	21.9231i	−0.467508	+	0.809748i	−0.999311	−	0.0371207i	$-0.988181\pi$
$733$	−12.6573	+	21.9231i	−0.467508	+	0.809748i	0.531803	+	0.846868i	$0.321515\pi$
$734$	−6.30214	+	10.9156i	−0.232616	+	0.402903i
$735$	2.05538	−	6.22787i	0.0758138	−	0.229719i
$736$	−23.0939	−	39.9998i	−0.851252	−	1.47441i
$737$	−17.7264			−0.652962
$738$	0.189912	−	1.65942i	0.00699074	−	0.0610840i
$739$	45.7042			1.68126			0.840628	−	0.541613i	$-0.182186\pi$
$739$	45.7042			1.68126			0.840628	+	0.541613i	$0.182186\pi$
$740$	0.583120	+	1.00999i	0.0214359	+	0.0371281i
$741$	−2.80893	+	0.583521i	−0.103188	+	0.0214362i
$742$	−3.05940	+	5.29903i	−0.112314	+	0.194534i
$743$	7.83871	−	13.5771i	0.287575	−	0.498094i	−0.685656	−	0.727926i	$-0.740484\pi$
$743$	7.83871	−	13.5771i	0.287575	−	0.498094i	0.973230	+	0.229832i	$0.0738178\pi$
$744$	16.7945	−	3.48886i	0.615716	−	0.127908i
$745$	0.786454	+	1.36218i	0.0288134	+	0.0499063i
$746$	−3.78789			−0.138685
$747$	17.9288	−	7.78497i	0.655982	−	0.284837i
$748$	45.9818			1.68126
$749$	−4.46756	−	7.73804i	−0.163241	−	0.282742i
$750$	0.343725	−	1.04150i	0.0125511	−	0.0380301i
$751$	−0.302484	+	0.523918i	−0.0110378	+	0.0191181i	−0.871492	−	0.490411i	$-0.836847\pi$
$751$	−0.302484	+	0.523918i	−0.0110378	+	0.0191181i	0.860454	+	0.509529i	$0.170180\pi$
$752$	8.20688	−	14.2147i	0.299274	−	0.518358i
$753$	28.8726	+	32.3654i	1.05218	+	1.17946i
$754$	0.517022	+	0.895508i	0.0188288	+	0.0326125i
$755$	11.2853			0.410714
$756$	12.1703	−	8.58733i	0.442628	−	0.312318i
$757$	35.7570			1.29961			0.649806	−	0.760100i	$-0.274850\pi$
$757$	35.7570			1.29961			0.649806	+	0.760100i	$0.274850\pi$
$758$	3.33398	+	5.77463i	0.121096	+	0.209744i
$759$	−38.0991	−	42.7080i	−1.38291	−	1.55020i
$760$	1.88738	−	3.26904i	0.0684624	−	0.118580i
$761$	3.84117	−	6.65311i	0.139242	−	0.241175i	−0.787968	−	0.615717i	$-0.788867\pi$
$761$	3.84117	−	6.65311i	0.139242	−	0.241175i	0.927210	+	0.374542i	$0.122200\pi$
$762$	−3.27059	+	9.91000i	−0.118481	+	0.359001i
$763$	−4.31244	−	7.46936i	−0.156121	−	0.270409i
$764$	9.24427			0.334446
$765$	−17.0919	−	12.6606i	−0.617957	−	0.457745i
$766$	10.1825			0.367908
$767$	−6.45122	−	11.1738i	−0.232940	−	0.403464i
$768$	−12.3917	+	2.57423i	−0.447147	+	0.0928895i
$769$	1.76479	−	3.05670i	0.0636398	−	0.110227i	−0.832450	−	0.554100i	$-0.813062\pi$
$769$	1.76479	−	3.05670i	0.0636398	−	0.110227i	0.896090	+	0.443873i	$0.146396\pi$
$770$	2.30190	−	3.98701i	0.0829548	−	0.143682i
$771$	28.9744	−	6.01909i	1.04349	−	0.216772i
$772$	7.67701	+	13.2970i	0.276302	+	0.478568i
$773$	37.6062			1.35260			0.676300	−	0.736626i	$-0.263582\pi$
$773$	37.6062			1.35260			0.676300	+	0.736626i	$0.263582\pi$
$774$	8.45602	+	6.26371i	0.303945	+	0.225144i
$775$	4.34556			0.156097
$776$	14.2939	+	24.7577i	0.513121	+	0.888751i
$777$	0.709716	−	2.15047i	0.0254609	−	0.0771475i
$778$	−4.80632	+	8.32479i	−0.172315	+	0.298458i
$779$	0.728176	−	1.26124i	0.0260896	−	0.0451886i
$780$	1.84372	+	2.06676i	0.0660159	+	0.0740020i
$781$	−5.69638	−	9.86641i	−0.203832	−	0.353048i
$782$	36.5766			1.30798
$783$	−7.70329	−	3.55831i	−0.275293	−	0.127164i
$784$	−6.64531			−0.237332
$785$	5.93626	+	10.2819i	0.211874	+	0.366977i
$786$	−5.91156	−	6.62669i	−0.210858	−	0.236366i
$787$	−5.85018	+	10.1328i	−0.208536	+	0.361196i	−0.951254	−	0.308409i	$-0.900203\pi$
$787$	−5.85018	+	10.1328i	−0.208536	+	0.361196i	0.742717	+	0.669605i	$0.233537\pi$
$788$	−9.44566	+	16.3604i	−0.336488	+	0.582814i
$789$	8.98854	−	27.2356i	0.320000	−	0.969613i
$790$	2.16017	+	3.74153i	0.0768555	+	0.133118i
$791$	−16.8689			−0.599788
$792$	−25.4345	+	11.0441i	−0.903777	+	0.392433i
$793$	−5.09533			−0.180940
$794$	−1.04518	−	1.81030i	−0.0370919	−	0.0642451i
$795$	9.14135	−	1.89901i	0.324210	−	0.0673508i
$796$	−13.3870	+	23.1869i	−0.474489	+	0.821839i
$797$	−25.2728	+	43.7737i	−0.895208	+	1.55055i	−0.0616602	+	0.998097i	$0.519640\pi$
$797$	−25.2728	+	43.7737i	−0.895208	+	1.55055i	−0.833547	+	0.552448i	$0.813694\pi$
$798$	−3.18847	+	0.662367i	−0.112871	+	0.0234475i
$799$	33.1546	+	57.4254i	1.17292	+	2.03156i
$800$	−5.66921			−0.200437
$801$	−2.58994	+	22.6305i	−0.0915112	+	0.799611i
$802$	19.7592			0.697721
$803$	−10.1499	−	17.5801i	−0.358181	−	0.620388i
$804$	3.79377	−	11.4952i	0.133796	−	0.405406i
$805$	−7.30246	+	12.6482i	−0.257378	+	0.445791i
$806$	1.37583	−	2.38300i	0.0484614	−	0.0839376i
$807$	−14.6462	−	16.4180i	−0.515571	−	0.577941i
$808$	5.96155	+	10.3257i	0.209727	+	0.363257i
$809$	35.0243			1.23139			0.615695	−	0.787985i	$-0.288875\pi$
$809$	35.0243			1.23139			0.615695	+	0.787985i	$0.288875\pi$
$810$	5.55154	+	1.28755i	0.195061	+	0.0452400i
$811$	−14.0250			−0.492483			−0.246242	−	0.969208i	$-0.579196\pi$
$811$	−14.0250			−0.492483			−0.246242	+	0.969208i	$0.579196\pi$
$812$	−2.34054	−	4.05393i	−0.0821368	−	0.142265i
$813$	32.0184	+	35.8917i	1.12293	+	1.25878i
$814$	−0.936526	+	1.62211i	−0.0328252	+	0.0568550i
$815$	7.05137	−	12.2133i	0.246999	−	0.427814i
$816$	−6.75460	+	20.4667i	−0.236458	+	0.716477i
$817$	4.58779	+	7.94629i	0.160507	+	0.278006i
$818$	6.36606			0.222584
$819$	0.611485	−	5.34306i	0.0213670	−	0.186702i
$820$	−1.40596			−0.0490983
$821$	−11.2771	−	19.5326i	−0.393575	−	0.681691i	0.599343	−	0.800492i	$-0.295428\pi$
$821$	−11.2771	−	19.5326i	−0.393575	−	0.681691i	−0.992918	+	0.118801i	$0.962095\pi$
$822$	−22.1190	+	4.59496i	−0.771489	+	0.160268i
$823$	7.67465	−	13.2929i	0.267521	−	0.463361i	−0.700700	−	0.713456i	$-0.747129\pi$
$823$	7.67465	−	13.2929i	0.267521	−	0.463361i	0.968221	+	0.250096i	$0.0804621\pi$
$824$	19.5669	−	33.8908i	0.681644	−	1.18064i
$825$	−6.87798	+	1.42882i	−0.239460	+	0.0497451i
$826$	−7.32291	−	12.6837i	−0.254797	−	0.441321i
$827$	6.03698			0.209926			0.104963	−	0.994476i	$-0.466528\pi$
$827$	6.03698			0.209926			0.104963	+	0.994476i	$0.466528\pi$
$828$	35.8492	−	15.5662i	1.24584	−	0.540965i
$829$	−8.49351			−0.294992			−0.147496	−	0.989063i	$-0.547121\pi$
$829$	−8.49351			−0.294992			−0.147496	+	0.989063i	$0.547121\pi$
$830$	2.06280	+	3.57287i	0.0716007	+	0.124016i
$831$	15.4766	−	46.8947i	0.536878	−	1.62676i
$832$	−0.0398652	+	0.0690485i	−0.00138208	+	0.00239383i
$833$	13.4230	−	23.2493i	0.465080	−	0.805542i
$834$	11.3959	+	12.7745i	0.394609	+	0.442345i
$835$	6.40109	+	11.0870i	0.221519	+	0.383682i
$836$	−10.7421			−0.371524
$837$	2.04917	+	22.4870i	0.0708298	+	0.777265i
$838$	21.9255			0.757403
$839$	2.12770	+	3.68528i	0.0734563	+	0.127230i	0.900414	−	0.435034i	$-0.143264\pi$
$839$	2.12770	+	3.68528i	0.0734563	+	0.127230i	−0.826958	+	0.562264i	$0.809930\pi$
$840$	4.71048	+	5.28031i	0.162527	+	0.182188i
$841$	13.1666	−	22.8053i	0.454022	−	0.786388i
$842$	−2.09890	+	3.63541i	−0.0723330	+	0.125284i
$843$	3.10950	−	9.42190i	0.107097	−	0.324507i
$844$	−18.1024	−	31.3543i	−0.623110	−	1.07926i
$845$	1.00000			0.0344010
$846$	−14.2761	−	10.5748i	−0.490821	−	0.363571i
$847$	−9.76879			−0.335660
$848$	−4.73020	−	8.19295i	−0.162436	−	0.281347i
$849$	−35.5905	+	7.39350i	−1.22146	+	0.253744i
$850$	2.24475	−	3.88803i	0.0769944	−	0.133358i
$851$	2.97100	−	5.14592i	0.101844	−	0.176400i
$852$	7.61730	−	1.58240i	0.260964	−	0.0542122i
$853$	−3.63511	−	6.29619i	−0.124464	−	0.215577i	0.797060	−	0.603901i	$-0.206388\pi$
$853$	−3.63511	−	6.29619i	−0.124464	−	0.215577i	−0.921523	+	0.388323i	$0.873054\pi$
$854$	−5.78381			−0.197918
$855$	3.99294	+	2.95772i	0.136556	+	0.101152i
$856$	−11.3590			−0.388243
$857$	−1.09806	−	1.90190i	−0.0375092	−	0.0649678i	0.846661	−	0.532132i	$-0.178609\pi$
$857$	−1.09806	−	1.90190i	−0.0375092	−	0.0649678i	−0.884171	+	0.467164i	$0.845276\pi$
$858$	−1.39407	+	4.22409i	−0.0475929	+	0.144208i
$859$	−11.2088	+	19.4143i	−0.382441	+	0.662407i	−0.991411	−	0.130787i	$-0.958250\pi$
$859$	−11.2088	+	19.4143i	−0.382441	+	0.662407i	0.608970	+	0.793193i	$0.291583\pi$
$860$	4.42905	−	7.67134i	0.151029	−	0.261590i
$861$	1.81737	+	2.03722i	0.0619356	+	0.0694281i
$862$	−11.8728	−	20.5643i	−0.404390	−	0.700423i
$863$	20.7310			0.705690			0.352845	−	0.935682i	$-0.385214\pi$
$863$	20.7310			0.705690			0.352845	+	0.935682i	$0.385214\pi$
$864$	−2.67335	−	29.3365i	−0.0909492	−	0.998049i
$865$	−20.1834			−0.686255
$866$	4.47770	+	7.75560i	0.152158	+	0.263546i
$867$	−38.3599	−	43.0004i	−1.30277	−	1.46037i
$868$	−6.22832	+	10.7878i	−0.211403	+	0.366161i
$869$	13.8362	−	23.9649i	0.469359	−	0.812954i
$870$	0.561309	−	1.70079i	0.0190301	−	0.0576620i
$871$	−2.18533	−	3.78510i	−0.0740471	−	0.128253i
$872$	−10.9646			−0.371309
$873$	−34.5191	+	14.9887i	−1.16829	+	0.507291i
$874$	−8.54489			−0.289035
$875$	0.896323	+	1.55248i	0.0303012	+	0.0524833i
$876$	13.5726	−	2.81954i	0.458575	−	0.0952635i
$877$	−1.64821	+	2.85478i	−0.0556561	+	0.0963992i	−0.892511	−	0.451025i	$-0.851058\pi$
$877$	−1.64821	+	2.85478i	−0.0556561	+	0.0963992i	0.836855	+	0.547425i	$0.184392\pi$
$878$	9.40070	−	16.2825i	0.317258	−	0.549508i
$879$	51.6564	−	10.7310i	1.74233	−	0.361948i
$880$	3.55902	+	6.16440i	0.119975	+	0.207802i
$881$	−28.3286			−0.954415			−0.477207	−	0.878791i	$-0.658351\pi$
$881$	−28.3286			−0.954415			−0.477207	+	0.878791i	$0.658351\pi$
$882$	−0.817840	+	7.14616i	−0.0275381	+	0.240624i
$883$	−36.8595			−1.24042			−0.620210	−	0.784436i	$-0.712952\pi$
$883$	−36.8595			−1.24042			−0.620210	+	0.784436i	$0.712952\pi$
$884$	5.66868	+	9.81843i	0.190658	+	0.330230i
$885$	−7.00382	+	21.2218i	−0.235431	+	0.713363i
$886$	−8.04331	+	13.9314i	−0.270220	+	0.468035i
$887$	19.9698	−	34.5888i	0.670521	−	1.16138i	−0.307235	−	0.951634i	$-0.599404\pi$
$887$	19.9698	−	34.5888i	0.670521	−	1.16138i	0.977756	−	0.209743i	$-0.0672628\pi$
$888$	−1.91645	−	2.14829i	−0.0643119	−	0.0720919i
$889$	−8.52863	−	14.7720i	−0.286041	−	0.495438i
$890$	−4.80781			−0.161158
$891$	−10.6371	−	34.9178i	−0.356355	−	1.16979i
$892$	−21.6665			−0.725449
$893$	−7.74545	−	13.4155i	−0.259192	−	0.448933i
$894$	−1.14838	−	1.28730i	−0.0384076	−	0.0430539i
$895$	5.39510	−	9.34459i	0.180338	−	0.312355i
$896$	10.1176	−	17.5242i	0.338006	−	0.585444i
$897$	4.42250	−	13.4003i	0.147663	−	0.447424i
$898$	−7.88111	−	13.6505i	−0.262996	−	0.455522i
$899$	7.09638			0.236677
$900$	0.545446	−	4.76602i	0.0181815	−	0.158867i
$901$	38.2186			1.27325
$902$	−1.12903	−	1.95554i	−0.0375925	−	0.0651122i
$903$	−16.8407	+	3.49846i	−0.560424	+	0.116421i
$904$	−10.7225	+	18.5719i	−0.356625	+	0.617693i
$905$	8.54954	−	14.8082i	0.284196	−	0.492242i
$906$	−12.1185	+	2.51747i	−0.402609	+	0.0836372i
$907$	1.20039	+	2.07915i	0.0398585	+	0.0690369i	0.885266	−	0.465084i	$-0.153976\pi$
$907$	1.20039	+	2.07915i	0.0398585	+	0.0690369i	−0.845408	+	0.534121i	$0.820643\pi$
$908$	−37.9665			−1.25996
$909$	−14.3969	+	6.25134i	−0.477514	+	0.207344i
$910$	1.13512			0.0376289
$911$	27.1185	+	46.9706i	0.898476	+	1.55621i	0.829443	+	0.558591i	$0.188658\pi$
$911$	27.1185	+	46.9706i	0.898476	+	1.55621i	0.0690329	+	0.997614i	$0.478009\pi$
$912$	1.57798	−	4.78135i	0.0522523	−	0.158326i
$913$	13.2124	−	22.8846i	0.437268	−	0.757370i
$914$	11.4953	−	19.9104i	0.380230	−	0.658577i
$915$	5.87499	+	6.58570i	0.194221	+	0.217717i
$916$	−5.98129	−	10.3599i	−0.197627	−	0.342301i
$917$	14.5149			0.479323
$918$	21.1779	+	9.78253i	0.698976	+	0.322872i
$919$	13.8459			0.456733			0.228367	−	0.973575i	$-0.426662\pi$
$919$	13.8459			0.456733			0.228367	+	0.973575i	$0.426662\pi$
$920$	9.28346	+	16.0794i	0.306066	+	0.530123i
$921$	35.8216	+	40.1550i	1.18036	+	1.32315i
$922$	0.224558	−	0.388945i	0.00739541	−	0.0128092i
$923$	1.40451	−	2.43268i	0.0462299	−	0.0800726i
$924$	6.31092	−	19.1223i	0.207614	−	0.629078i
$925$	−0.364668	−	0.631623i	−0.0119902	−	0.0207676i
$926$	25.5112			0.838350
$927$	41.3956	+	30.6634i	1.35961	+	1.00712i
$928$	−9.25792			−0.303906
$929$	−1.28662	−	2.22849i	−0.0422127	−	0.0731145i	0.844147	−	0.536112i	$-0.180107\pi$
$929$	−1.28662	−	2.22849i	−0.0422127	−	0.0731145i	−0.886360	+	0.462997i	$0.846774\pi$
$930$	−4.66638	+	0.969384i	−0.153016	+	0.0317874i
$931$	−3.13584	+	5.43143i	−0.102773	+	0.178008i
$932$	15.5715	−	26.9707i	0.510062	−	0.883454i
$933$	18.2148	−	3.78390i	0.596324	−	0.123879i
$934$	−4.39094	−	7.60534i	−0.143676	−	0.248854i
$935$	−28.7558			−0.940415
$936$	−5.49381	−	4.06948i	−0.179571	−	0.133015i
$937$	4.68434			0.153031			0.0765154	−	0.997068i	$-0.475621\pi$
$937$	4.68434			0.153031			0.0765154	+	0.997068i	$0.475621\pi$
$938$	−2.48061	−	4.29655i	−0.0809949	−	0.140287i
$939$	−10.5869	+	32.0787i	−0.345490	+	1.04685i
$940$	−7.47744	+	12.9513i	−0.243887	+	0.422425i
$941$	28.2403	−	48.9137i	0.920608	−	1.59454i	0.122131	−	0.992514i	$-0.461027\pi$
$941$	28.2403	−	48.9137i	0.920608	−	1.59454i	0.798477	−	0.602026i	$-0.205640\pi$
$942$	−8.66815	−	9.71675i	−0.282424	−	0.316589i
$943$	3.58168	+	6.20366i	0.116636	+	0.202019i
$944$	22.6442			0.737007
$945$	−7.61095	+	5.37029i	−0.247584	+	0.174696i
$946$	14.2266			0.462548
$947$	−13.0153	−	22.5431i	−0.422940	−	0.732553i	0.573286	−	0.819356i	$-0.305669\pi$
$947$	−13.0153	−	22.5431i	−0.422940	−	0.732553i	−0.996226	+	0.0868022i	$0.972335\pi$
$948$	12.5796	+	14.1014i	0.408566	+	0.457992i
$949$	2.50257	−	4.33457i	0.0812367	−	0.140706i
$950$	−0.524411	+	0.908307i	−0.0170141	+	0.0294694i
$951$	−5.80302	+	17.5833i	−0.188176	+	0.570179i
$952$	14.4827	+	25.0848i	0.469388	+	0.813004i
$953$	−17.8899			−0.579512			−0.289756	−	0.957101i	$-0.593574\pi$
$953$	−17.8899			−0.579512			−0.289756	+	0.957101i	$0.593574\pi$
$954$	−9.39260	+	4.07841i	−0.304097	+	0.132043i
$955$	−5.78112			−0.187073
$956$	7.26687	+	12.5866i	0.235027	+	0.407079i
$957$	−11.2319	+	2.33329i	−0.363075	+	0.0754245i
$958$	−12.3653	+	21.4173i	−0.399505	+	0.691963i
$959$	18.4627	−	31.9784i	0.596193	−	1.03264i
$960$	0.135210	−	0.0280883i	0.00436389	−	0.000906547i
$961$	6.05806	+	10.4929i	0.195421	+	0.338479i
$962$	−0.461823			−0.0148898
$963$	1.70019	−	14.8560i	0.0547878	−	0.478727i
$964$	18.9933			0.611734
$965$	−4.80100	−	8.31557i	−0.154550	−	0.267688i
$966$	5.02007	−	15.2110i	0.161518	−	0.489406i
$967$	−17.2588	+	29.8931i	−0.555006	+	0.961298i	0.442898	+	0.896572i	$0.353951\pi$
$967$	−17.2588	+	29.8931i	−0.555006	+	0.961298i	−0.997903	+	0.0647256i	$0.979383\pi$
$968$	−6.20943	+	10.7550i	−0.199579	+	0.345680i
$969$	13.5407	+	15.1787i	0.434989	+	0.487611i
$970$	−3.97158	−	6.87897i	−0.127520	−	0.220871i
$971$	14.6900			0.471423			0.235712	−	0.971823i	$-0.424258\pi$
$971$	14.6900			0.471423			0.235712	+	0.971823i	$0.424258\pi$
$972$	24.9200	+	0.575079i	0.799310	+	0.0184457i
$973$	−27.9808			−0.897024
$974$	−3.27596	−	5.67414i	−0.104969	−	0.181811i
$975$	−1.15302	−	1.29250i	−0.0369261	−	0.0413931i
$976$	4.47124	−	7.74441i	0.143121	−	0.247893i
$977$	−18.5847	+	32.1896i	−0.594576	+	1.02984i	0.399031	+	0.916937i	$0.369347\pi$
$977$	−18.5847	+	32.1896i	−0.594576	+	1.02984i	−0.993607	+	0.112898i	$0.963987\pi$
$978$	−4.84746	+	14.6880i	−0.155005	+	0.469670i
$979$	15.3973	+	26.6689i	0.492099	+	0.852341i
$980$	6.05466			0.193409
$981$	1.64116	−	14.3402i	0.0523981	−	0.457846i
$982$	−0.687216			−0.0219299
$983$	20.7022	+	35.8573i	0.660298	+	1.14367i	0.980537	+	0.196333i	$0.0629032\pi$
$983$	20.7022	+	35.8573i	0.660298	+	1.14367i	−0.320240	+	0.947337i	$0.603763\pi$
$984$	3.39808	−	0.705911i	0.108327	−	0.0225036i
$985$	5.90706	−	10.2313i	0.188215	−	0.325997i
$986$	3.66572	−	6.34922i	0.116740	−	0.202200i
$987$	28.4317	−	5.90635i	0.904991	−	0.188001i
$988$	−1.32430	−	2.29375i	−0.0421314	−	0.0729738i
$989$	−45.1320			−1.43511
$990$	7.06702	−	3.06861i	0.224605	−	0.0975267i
$991$	8.06215			0.256102			0.128051	−	0.991768i	$-0.459128\pi$
$991$	8.06215			0.256102			0.128051	+	0.991768i	$0.459128\pi$
$992$	12.3179	+	21.3353i	0.391095	+	0.677397i
$993$	−6.87683	+	20.8370i	−0.218230	+	0.661243i
$994$	1.59429	−	2.76138i	0.0505677	−	0.0875858i
$995$	8.37186	−	14.5005i	0.265406	−	0.459696i
$996$	12.0125	+	13.4657i	0.380632	+	0.426677i
$997$	−15.0976	−	26.1499i	−0.478147	−	0.828174i	0.521540	−	0.853227i	$-0.325358\pi$
$997$	−15.0976	−	26.1499i	−0.478147	−	0.828174i	−0.999686	+	0.0250530i	$0.992025\pi$
$998$	26.8607			0.850262
$999$	3.09651	−	2.18490i	0.0979691	−	0.0691271i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.i.f.391.5	yes	16
3.2	odd	2		1755.2.i.e.1171.4		16
9.2	odd	6		1755.2.i.e.586.4		16
9.4	even	3		5265.2.a.bb.1.4		8
9.5	odd	6		5265.2.a.be.1.5		8
9.7	even	3	inner	585.2.i.f.196.5	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.i.f.196.5	✓	16	9.7	even	3	inner
585.2.i.f.391.5	yes	16	1.1	even	1	trivial
1755.2.i.e.586.4		16	9.2	odd	6
1755.2.i.e.1171.4		16	3.2	odd	2
5265.2.a.bb.1.4		8	9.4	even	3
5265.2.a.be.1.5		8	9.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.316605 + 0.548376i) q^{2} +(-1.15302 - 1.29250i) q^{3} +(0.799523 - 1.38481i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.343725 - 1.04150i) q^{6} +(0.896323 + 1.55248i) q^{7} +2.27895 q^{8} +(-0.341107 + 2.98054i) q^{9} +O(q^{10})\)	\(q+(0.316605 + 0.548376i) q^{2} +(-1.15302 - 1.29250i) q^{3} +(0.799523 - 1.38481i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.343725 - 1.04150i) q^{6} +(0.896323 + 1.55248i) q^{7} +2.27895 q^{8} +(-0.341107 + 2.98054i) q^{9} -0.633210 q^{10} +(2.02789 + 3.51241i) q^{11} +(-2.71173 + 0.563330i) q^{12} +(-0.500000 + 0.866025i) q^{13} +(-0.567560 + 0.983044i) q^{14} +(1.69585 - 0.352292i) q^{15} +(-0.877517 - 1.51990i) q^{16} +7.09008 q^{17} +(-1.74246 + 0.756600i) q^{18} -1.65636 q^{19} +(0.799523 + 1.38481i) q^{20} +(0.973100 - 2.94853i) q^{21} +(-1.28408 + 2.22409i) q^{22} +(4.07356 - 7.05562i) q^{23} +(-2.62767 - 2.94554i) q^{24} +(-0.500000 - 0.866025i) q^{25} -0.633210 q^{26} +(4.24565 - 2.99573i) q^{27} +2.86652 q^{28} +(-0.816509 - 1.41423i) q^{29} +(0.730101 + 0.818423i) q^{30} +(-2.17278 + 3.76337i) q^{31} +(2.83460 - 4.90968i) q^{32} +(2.20160 - 6.67091i) q^{33} +(2.24475 + 3.88803i) q^{34} -1.79265 q^{35} +(3.85478 + 2.85538i) q^{36} +0.729336 q^{37} +(-0.524411 - 0.908307i) q^{38} +(1.69585 - 0.352292i) q^{39} +(-1.13948 + 1.97363i) q^{40} +(-0.439625 + 0.761453i) q^{41} +(1.92499 - 0.399894i) q^{42} +(-2.76981 - 4.79745i) q^{43} +6.48538 q^{44} +(-2.41067 - 1.78568i) q^{45} +5.15884 q^{46} +(4.67619 + 8.09941i) q^{47} +(-0.952684 + 2.88667i) q^{48} +(1.89321 - 3.27914i) q^{49} +(0.316605 - 0.548376i) q^{50} +(-8.17497 - 9.16392i) q^{51} +(0.799523 + 1.38481i) q^{52} +5.39044 q^{53} +(2.98698 + 1.37975i) q^{54} -4.05578 q^{55} +(2.04268 + 3.53802i) q^{56} +(1.90981 + 2.14084i) q^{57} +(0.517022 - 0.895508i) q^{58} +(-6.45122 + 11.1738i) q^{59} +(0.868008 - 2.63009i) q^{60} +(2.54766 + 4.41268i) q^{61} -2.75165 q^{62} +(-4.93297 + 2.14197i) q^{63} +0.0797303 q^{64} +(-0.500000 - 0.866025i) q^{65} +(4.35521 - 0.904743i) q^{66} +(-2.18533 + 3.78510i) q^{67} +(5.66868 - 9.81843i) q^{68} +(-13.8163 + 2.87017i) q^{69} +(-0.567560 - 0.983044i) q^{70} -2.80901 q^{71} +(-0.777367 + 6.79252i) q^{72} -5.00513 q^{73} +(0.230911 + 0.399950i) q^{74} +(-0.542829 + 1.64479i) q^{75} +(-1.32430 + 2.29375i) q^{76} +(-3.63529 + 6.29651i) q^{77} +(0.730101 + 0.818423i) q^{78} +(-3.41146 - 5.90883i) q^{79} +1.75503 q^{80} +(-8.76729 - 2.03337i) q^{81} -0.556750 q^{82} +(-3.25768 - 5.64247i) q^{83} +(-3.30514 - 3.70497i) q^{84} +(-3.54504 + 6.14019i) q^{85} +(1.75387 - 3.03779i) q^{86} +(-0.886449 + 2.68597i) q^{87} +(4.62147 + 8.00461i) q^{88} +7.59275 q^{89} +(0.215993 - 1.88731i) q^{90} -1.79265 q^{91} +(-6.51381 - 11.2823i) q^{92} +(7.36940 - 1.53090i) q^{93} +(-2.96101 + 5.12863i) q^{94} +(0.828179 - 1.43445i) q^{95} +(-9.61410 + 1.99722i) q^{96} +(6.27213 + 10.8637i) q^{97} +2.39760 q^{98} +(-11.1606 + 4.84611i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + q^{2} - 2 q^{3} - 5 q^{4} - 8 q^{5} - 13 q^{6} + 6 q^{7} - 12 q^{8} + 4 q^{9}+O(q^{10}) \) 16 * q + q^2 - 2 * q^3 - 5 * q^4 - 8 * q^5 - 13 * q^6 + 6 * q^7 - 12 * q^8 + 4 * q^9	\( 16 q + q^{2} - 2 q^{3} - 5 q^{4} - 8 q^{5} - 13 q^{6} + 6 q^{7} - 12 q^{8} + 4 q^{9} - 2 q^{10} + 9 q^{11} - 16 q^{12} - 8 q^{13} - 3 q^{14} + q^{15} + 13 q^{16} + 12 q^{17} + 23 q^{18} - 22 q^{19} - 5 q^{20} + 15 q^{21} + 4 q^{22} + 3 q^{23} - 12 q^{24} - 8 q^{25} - 2 q^{26} + 22 q^{27} - 26 q^{28} + 8 q^{29} + 8 q^{30} + 18 q^{31} + 3 q^{32} - 26 q^{33} + 9 q^{34} - 12 q^{35} + 5 q^{36} - 36 q^{37} - 8 q^{38} + q^{39} + 6 q^{40} - 17 q^{41} - 45 q^{42} + 17 q^{43} + 10 q^{44} + q^{45} + 6 q^{46} + 11 q^{47} + 35 q^{48} + 16 q^{49} + q^{50} - 16 q^{51} - 5 q^{52} + 20 q^{53} + 44 q^{54} - 18 q^{55} - q^{56} - 25 q^{57} + 10 q^{58} + 7 q^{59} + 5 q^{60} + 21 q^{61} - 58 q^{62} - 30 q^{63} - 20 q^{64} - 8 q^{65} + 68 q^{66} + 13 q^{67} - 16 q^{68} - 13 q^{69} - 3 q^{70} - 68 q^{71} + 36 q^{72} - 32 q^{73} - 4 q^{74} + q^{75} + 2 q^{76} + 18 q^{77} + 8 q^{78} + 37 q^{79} - 26 q^{80} - 32 q^{81} + 2 q^{82} + 3 q^{83} + 27 q^{84} - 6 q^{85} - 2 q^{86} - 20 q^{87} + 19 q^{88} + 28 q^{89} - 16 q^{90} - 12 q^{91} - 14 q^{92} + 19 q^{93} + 44 q^{94} + 11 q^{95} - 35 q^{96} + 17 q^{97} + 90 q^{98} - 44 q^{99}+O(q^{100}) \) 16 * q + q^2 - 2 * q^3 - 5 * q^4 - 8 * q^5 - 13 * q^6 + 6 * q^7 - 12 * q^8 + 4 * q^9 - 2 * q^10 + 9 * q^11 - 16 * q^12 - 8 * q^13 - 3 * q^14 + q^15 + 13 * q^16 + 12 * q^17 + 23 * q^18 - 22 * q^19 - 5 * q^20 + 15 * q^21 + 4 * q^22 + 3 * q^23 - 12 * q^24 - 8 * q^25 - 2 * q^26 + 22 * q^27 - 26 * q^28 + 8 * q^29 + 8 * q^30 + 18 * q^31 + 3 * q^32 - 26 * q^33 + 9 * q^34 - 12 * q^35 + 5 * q^36 - 36 * q^37 - 8 * q^38 + q^39 + 6 * q^40 - 17 * q^41 - 45 * q^42 + 17 * q^43 + 10 * q^44 + q^45 + 6 * q^46 + 11 * q^47 + 35 * q^48 + 16 * q^49 + q^50 - 16 * q^51 - 5 * q^52 + 20 * q^53 + 44 * q^54 - 18 * q^55 - q^56 - 25 * q^57 + 10 * q^58 + 7 * q^59 + 5 * q^60 + 21 * q^61 - 58 * q^62 - 30 * q^63 - 20 * q^64 - 8 * q^65 + 68 * q^66 + 13 * q^67 - 16 * q^68 - 13 * q^69 - 3 * q^70 - 68 * q^71 + 36 * q^72 - 32 * q^73 - 4 * q^74 + q^75 + 2 * q^76 + 18 * q^77 + 8 * q^78 + 37 * q^79 - 26 * q^80 - 32 * q^81 + 2 * q^82 + 3 * q^83 + 27 * q^84 - 6 * q^85 - 2 * q^86 - 20 * q^87 + 19 * q^88 + 28 * q^89 - 16 * q^90 - 12 * q^91 - 14 * q^92 + 19 * q^93 + 44 * q^94 + 11 * q^95 - 35 * q^96 + 17 * q^97 + 90 * q^98 - 44 * q^99

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