LMFDB - Embedded newform 403.2.h.a.118.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(118,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("403.118");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.h (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:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			118.13
Character	$\chi$	$=$	403.118
Dual form			403.2.h.a.222.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.58004 q^{2} +(1.43561 + 2.48655i) q^{3} +0.496524 q^{4} +(1.71834 - 2.97625i) q^{5} +(2.26832 + 3.92885i) q^{6} +(0.908007 + 1.57271i) q^{7} -2.37555 q^{8} +(-2.62196 + 4.54137i) q^{9} +O(q^{10})$	\(q+1.58004 q^{2} +(1.43561 + 2.48655i) q^{3} +0.496524 q^{4} +(1.71834 - 2.97625i) q^{5} +(2.26832 + 3.92885i) q^{6} +(0.908007 + 1.57271i) q^{7} -2.37555 q^{8} +(-2.62196 + 4.54137i) q^{9} +(2.71504 - 4.70259i) q^{10} +(0.701394 - 1.21485i) q^{11} +(0.712816 + 1.23463i) q^{12} +(0.500000 - 0.866025i) q^{13} +(1.43469 + 2.48495i) q^{14} +9.86746 q^{15} -4.74651 q^{16} +(0.332988 + 0.576751i) q^{17} +(-4.14280 + 7.17554i) q^{18} +(0.934963 + 1.61940i) q^{19} +(0.853196 - 1.47778i) q^{20} +(-2.60709 + 4.51561i) q^{21} +(1.10823 - 1.91951i) q^{22} -6.53846 q^{23} +(-3.41037 - 5.90693i) q^{24} +(-3.40537 - 5.89827i) q^{25} +(0.790020 - 1.36835i) q^{26} -6.44279 q^{27} +(0.450848 + 0.780891i) q^{28} -5.25726 q^{29} +15.5910 q^{30} +(0.769283 - 5.51436i) q^{31} -2.74857 q^{32} +4.02771 q^{33} +(0.526133 + 0.911290i) q^{34} +6.24105 q^{35} +(-1.30187 + 2.25490i) q^{36} +(-4.05131 - 7.01707i) q^{37} +(1.47728 + 2.55872i) q^{38} +2.87122 q^{39} +(-4.08200 + 7.07023i) q^{40} +(-1.91003 + 3.30827i) q^{41} +(-4.11931 + 7.13485i) q^{42} +(0.255056 + 0.441770i) q^{43} +(0.348259 - 0.603202i) q^{44} +(9.01082 + 15.6072i) q^{45} -10.3310 q^{46} +9.00962 q^{47} +(-6.81415 - 11.8024i) q^{48} +(1.85105 - 3.20611i) q^{49} +(-5.38062 - 9.31950i) q^{50} +(-0.956081 + 1.65598i) q^{51} +(0.248262 - 0.430003i) q^{52} +(-3.50488 + 6.07063i) q^{53} -10.1799 q^{54} +(-2.41046 - 4.17504i) q^{55} +(-2.15702 - 3.73606i) q^{56} +(-2.68449 + 4.64967i) q^{57} -8.30668 q^{58} +(5.41024 + 9.37080i) q^{59} +4.89943 q^{60} +7.62328 q^{61} +(1.21550 - 8.71291i) q^{62} -9.52303 q^{63} +5.15017 q^{64} +(-1.71834 - 2.97625i) q^{65} +6.36395 q^{66} +(7.31479 - 12.6696i) q^{67} +(0.165336 + 0.286371i) q^{68} +(-9.38668 - 16.2582i) q^{69} +9.86111 q^{70} +(-1.40295 + 2.42998i) q^{71} +(6.22860 - 10.7882i) q^{72} +(-7.03071 + 12.1775i) q^{73} +(-6.40123 - 11.0873i) q^{74} +(9.77757 - 16.9352i) q^{75} +(0.464232 + 0.804073i) q^{76} +2.54748 q^{77} +4.53664 q^{78} +(-6.28626 - 10.8881i) q^{79} +(-8.15611 + 14.1268i) q^{80} +(-1.38346 - 2.39623i) q^{81} +(-3.01792 + 5.22719i) q^{82} +(-0.888910 + 1.53964i) q^{83} +(-1.29448 + 2.24211i) q^{84} +2.28874 q^{85} +(0.402999 + 0.698015i) q^{86} +(-7.54739 - 13.0725i) q^{87} +(-1.66620 + 2.88594i) q^{88} +9.70425 q^{89} +(14.2375 + 24.6600i) q^{90} +1.81601 q^{91} -3.24650 q^{92} +(14.8161 - 6.00362i) q^{93} +14.2356 q^{94} +6.42633 q^{95} +(-3.94588 - 6.83447i) q^{96} -9.81304 q^{97} +(2.92473 - 5.06577i) q^{98} +(3.67805 + 6.37057i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 6 q^{2} - 2 q^{3} + 22 q^{4} + 7 q^{5} + 6 q^{7} - 24 q^{8} - 13 q^{9}+O(q^{10}) $ 30 * q - 6 * q^2 - 2 * q^3 + 22 * q^4 + 7 * q^5 + 6 * q^7 - 24 * q^8 - 13 * q^9	\( 30 q - 6 q^{2} - 2 q^{3} + 22 q^{4} + 7 q^{5} + 6 q^{7} - 24 q^{8} - 13 q^{9} - 3 q^{10} - 3 q^{11} + 12 q^{12} + 15 q^{13} + 3 q^{14} + 4 q^{15} + 22 q^{16} + 4 q^{17} - 6 q^{18} + 5 q^{19} + 10 q^{20} - 15 q^{21} + 2 q^{22} - 6 q^{23} - 6 q^{24} - 20 q^{25} - 3 q^{26} + 4 q^{27} + 13 q^{28} + 26 q^{29} + 28 q^{30} + 19 q^{31} - 74 q^{32} + 2 q^{33} - 21 q^{34} - 30 q^{35} + 37 q^{36} - 4 q^{37} - 4 q^{38} - 4 q^{39} - 17 q^{40} + 7 q^{41} + 44 q^{42} + 15 q^{43} - 70 q^{44} + 15 q^{45} - 58 q^{46} - 24 q^{47} + 31 q^{48} - 29 q^{49} + 2 q^{50} + 25 q^{51} + 11 q^{52} + 4 q^{53} + 34 q^{54} + 13 q^{55} - 41 q^{56} + 8 q^{57} - 46 q^{58} + 27 q^{59} + 78 q^{60} + 8 q^{61} + 20 q^{62} - 112 q^{63} + 60 q^{64} - 7 q^{65} + 60 q^{66} + 29 q^{67} + 41 q^{68} - 23 q^{69} - 112 q^{70} + 29 q^{71} + 14 q^{72} - 10 q^{73} + 25 q^{74} - 18 q^{75} + 24 q^{76} - 72 q^{77} + 9 q^{79} - 11 q^{81} - 38 q^{82} - 13 q^{83} - 62 q^{84} + 108 q^{85} - 38 q^{86} - 18 q^{87} + 32 q^{88} + 6 q^{89} + 7 q^{90} + 12 q^{91} + 2 q^{92} + 37 q^{93} - 154 q^{94} - 28 q^{95} - 105 q^{96} - 84 q^{97} + 50 q^{98} + 10 q^{99}+O(q^{100}) \) 30 * q - 6 * q^2 - 2 * q^3 + 22 * q^4 + 7 * q^5 + 6 * q^7 - 24 * q^8 - 13 * q^9 - 3 * q^10 - 3 * q^11 + 12 * q^12 + 15 * q^13 + 3 * q^14 + 4 * q^15 + 22 * q^16 + 4 * q^17 - 6 * q^18 + 5 * q^19 + 10 * q^20 - 15 * q^21 + 2 * q^22 - 6 * q^23 - 6 * q^24 - 20 * q^25 - 3 * q^26 + 4 * q^27 + 13 * q^28 + 26 * q^29 + 28 * q^30 + 19 * q^31 - 74 * q^32 + 2 * q^33 - 21 * q^34 - 30 * q^35 + 37 * q^36 - 4 * q^37 - 4 * q^38 - 4 * q^39 - 17 * q^40 + 7 * q^41 + 44 * q^42 + 15 * q^43 - 70 * q^44 + 15 * q^45 - 58 * q^46 - 24 * q^47 + 31 * q^48 - 29 * q^49 + 2 * q^50 + 25 * q^51 + 11 * q^52 + 4 * q^53 + 34 * q^54 + 13 * q^55 - 41 * q^56 + 8 * q^57 - 46 * q^58 + 27 * q^59 + 78 * q^60 + 8 * q^61 + 20 * q^62 - 112 * q^63 + 60 * q^64 - 7 * q^65 + 60 * q^66 + 29 * q^67 + 41 * q^68 - 23 * q^69 - 112 * q^70 + 29 * q^71 + 14 * q^72 - 10 * q^73 + 25 * q^74 - 18 * q^75 + 24 * q^76 - 72 * q^77 + 9 * q^79 - 11 * q^81 - 38 * q^82 - 13 * q^83 - 62 * q^84 + 108 * q^85 - 38 * q^86 - 18 * q^87 + 32 * q^88 + 6 * q^89 + 7 * q^90 + 12 * q^91 + 2 * q^92 + 37 * q^93 - 154 * q^94 - 28 * q^95 - 105 * q^96 - 84 * q^97 + 50 * q^98 + 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.58004			1.11726			0.558628	−	0.829418i	$-0.311328\pi$
$2$	1.58004			1.11726			0.558628	+	0.829418i	$0.311328\pi$
$3$	1.43561	+	2.48655i	0.828851	+	1.43561i	0.898941	+	0.438071i	$0.144338\pi$
$3$	1.43561	+	2.48655i	0.828851	+	1.43561i	−0.0700901	+	0.997541i	$0.522329\pi$
$4$	0.496524			0.248262
$5$	1.71834	−	2.97625i	0.768464	−	1.33102i	−0.169932	−	0.985456i	$-0.554355\pi$
$5$	1.71834	−	2.97625i	0.768464	−	1.33102i	0.938396	−	0.345563i	$-0.112312\pi$
$6$	2.26832	+	3.92885i	0.926039	+	1.60395i
$7$	0.908007	+	1.57271i	0.343194	+	0.594430i	0.985024	−	0.172417i	$-0.0551577\pi$
$7$	0.908007	+	1.57271i	0.343194	+	0.594430i	−0.641830	+	0.766847i	$0.721824\pi$
$8$	−2.37555			−0.839884
$9$	−2.62196	+	4.54137i	−0.873986	+	1.51379i
$10$	2.71504	−	4.70259i	0.858571	−	1.48709i
$11$	0.701394	−	1.21485i	0.211478	−	0.366291i	−0.740699	−	0.671837i	$-0.765506\pi$
$11$	0.701394	−	1.21485i	0.211478	−	0.366291i	0.952177	+	0.305546i	$0.0988389\pi$
$12$	0.712816	+	1.23463i	0.205772	+	0.356408i
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i
$14$	1.43469	+	2.48495i	0.383436	+	0.664131i
$15$	9.86746			2.54777
$16$	−4.74651			−1.18663
$17$	0.332988	+	0.576751i	0.0807613	+	0.139883i	0.903577	−	0.428425i	$-0.140932\pi$
$17$	0.332988	+	0.576751i	0.0807613	+	0.139883i	−0.822816	+	0.568308i	$0.807598\pi$
$18$	−4.14280	+	7.17554i	−0.976467	+	1.69129i
$19$	0.934963	+	1.61940i	0.214495	+	0.371517i	0.953116	−	0.302604i	$-0.0978560\pi$
$19$	0.934963	+	1.61940i	0.214495	+	0.371517i	−0.738621	+	0.674121i	$0.764523\pi$
$20$	0.853196	−	1.47778i	0.190781	−	0.330442i
$21$	−2.60709	+	4.51561i	−0.568914	+	0.985387i
$22$	1.10823	−	1.91951i	0.236275	−	0.409241i
$23$	−6.53846			−1.36336			−0.681681	−	0.731649i	$-0.738751\pi$
$23$	−6.53846			−1.36336			−0.681681	+	0.731649i	$0.738751\pi$
$24$	−3.41037	−	5.90693i	−0.696138	−	1.20575i
$25$	−3.40537	−	5.89827i	−0.681074	−	1.17965i
$26$	0.790020	−	1.36835i	0.154936	−	0.268356i
$27$	−6.44279			−1.23992
$28$	0.450848	+	0.780891i	0.0852022	+	0.147575i
$29$	−5.25726			−0.976249			−0.488125	−	0.872774i	$-0.662319\pi$
$29$	−5.25726			−0.976249			−0.488125	+	0.872774i	$0.662319\pi$
$30$	15.5910			2.84651
$31$	0.769283	−	5.51436i	0.138167	−	0.990409i
$31$	0.769283	−	5.51436i	0.138167	−	0.990409i
$32$	−2.74857			−0.485884
$33$	4.02771			0.701135
$34$	0.526133	+	0.911290i	0.0902311	+	0.156285i
$35$	6.24105			1.05493
$36$	−1.30187	+	2.25490i	−0.216978	+	0.375817i
$37$	−4.05131	−	7.01707i	−0.666031	−	1.15360i	−0.979005	−	0.203838i	$-0.934658\pi$
$37$	−4.05131	−	7.01707i	−0.666031	−	1.15360i	0.312973	−	0.949762i	$-0.398675\pi$
$38$	1.47728	+	2.55872i	0.239646	+	0.415080i
$39$	2.87122			0.459764
$40$	−4.08200	+	7.07023i	−0.645421	+	1.11790i
$41$	−1.91003	+	3.30827i	−0.298297	+	0.516665i	−0.975746	−	0.218904i	$-0.929752\pi$
$41$	−1.91003	+	3.30827i	−0.298297	+	0.516665i	0.677450	+	0.735569i	$0.263085\pi$
$42$	−4.11931	+	7.13485i	−0.635623	+	1.10093i
$43$	0.255056	+	0.441770i	0.0388957	+	0.0673694i	0.884818	−	0.465937i	$-0.154283\pi$
$43$	0.255056	+	0.441770i	0.0388957	+	0.0673694i	−0.845922	+	0.533306i	$0.820949\pi$
$44$	0.348259	−	0.603202i	0.0525020	−	0.0909362i
$45$	9.01082	+	15.6072i	1.34325	+	2.32658i
$46$	−10.3310			−1.52323
$47$	9.00962			1.31419			0.657094	−	0.753809i	$-0.271785\pi$
$47$	9.00962			1.31419			0.657094	+	0.753809i	$0.271785\pi$
$48$	−6.81415	−	11.8024i	−0.983537	−	1.70354i
$49$	1.85105	−	3.20611i	0.264435	−	0.458015i
$50$	−5.38062	−	9.31950i	−0.760934	−	1.31798i
$51$	−0.956081	+	1.65598i	−0.133878	+	0.231884i
$52$	0.248262	−	0.430003i	0.0344278	−	0.0596306i
$53$	−3.50488	+	6.07063i	−0.481432	+	0.833865i	−0.999773	−	0.0213093i	$-0.993217\pi$
$53$	−3.50488	+	6.07063i	−0.481432	+	0.833865i	0.518341	+	0.855174i	$0.326550\pi$
$54$	−10.1799			−1.38530
$55$	−2.41046	−	4.17504i	−0.325027	−	0.562963i
$56$	−2.15702	−	3.73606i	−0.288243	−	0.499252i
$57$	−2.68449	+	4.64967i	−0.355569	+	0.615864i
$58$	−8.30668			−1.09072
$59$	5.41024	+	9.37080i	0.704353	+	1.21997i	0.966925	+	0.255062i	$0.0820960\pi$
$59$	5.41024	+	9.37080i	0.704353	+	1.21997i	−0.262572	+	0.964912i	$0.584571\pi$
$60$	4.89943			0.632514
$61$	7.62328			0.976061			0.488031	−	0.872826i	$-0.337715\pi$
$61$	7.62328			0.976061			0.488031	+	0.872826i	$0.337715\pi$
$62$	1.21550	−	8.71291i	0.154368	−	1.10654i
$63$	−9.52303			−1.19979
$64$	5.15017			0.643771
$65$	−1.71834	−	2.97625i	−0.213134	−	0.369158i
$66$	6.36395			0.783348
$67$	7.31479	−	12.6696i	0.893644	−	1.54784i	0.0581691	−	0.998307i	$-0.481474\pi$
$67$	7.31479	−	12.6696i	0.893644	−	1.54784i	0.835474	−	0.549529i	$-0.185193\pi$
$68$	0.165336	+	0.286371i	0.0200500	+	0.0347276i
$69$	−9.38668	−	16.2582i	−1.13002	−	1.95726i
$70$	9.86111			1.17863
$71$	−1.40295	+	2.42998i	−0.166500	+	0.288386i	−0.937187	−	0.348828i	$-0.886580\pi$
$71$	−1.40295	+	2.42998i	−0.166500	+	0.288386i	0.770687	+	0.637214i	$0.219913\pi$
$72$	6.22860	−	10.7882i	0.734047	−	1.27141i
$73$	−7.03071	+	12.1775i	−0.822882	+	1.42527i	0.0806454	+	0.996743i	$0.474302\pi$
$73$	−7.03071	+	12.1775i	−0.822882	+	1.42527i	−0.903527	+	0.428530i	$0.859031\pi$
$74$	−6.40123	−	11.0873i	−0.744128	−	1.28887i
$75$	9.77757	−	16.9352i	1.12902	−	1.95551i
$76$	0.464232	+	0.804073i	0.0532511	+	0.0922336i
$77$	2.54748			0.290312
$78$	4.53664			0.513674
$79$	−6.28626	−	10.8881i	−0.707260	−	1.22501i	−0.965870	−	0.259028i	$-0.916598\pi$
$79$	−6.28626	−	10.8881i	−0.707260	−	1.22501i	0.258610	−	0.965982i	$-0.416735\pi$
$80$	−8.15611	+	14.1268i	−0.911881	+	1.57942i
$81$	−1.38346	−	2.39623i	−0.153718	−	0.266248i
$82$	−3.01792	+	5.22719i	−0.333274	+	0.577247i
$83$	−0.888910	+	1.53964i	−0.0975705	+	0.168997i	−0.910679	−	0.413116i	$-0.864440\pi$
$83$	−0.888910	+	1.53964i	−0.0975705	+	0.168997i	0.813108	+	0.582113i	$0.197774\pi$
$84$	−1.29448	+	2.24211i	−0.141240	+	0.244634i
$85$	2.28874			0.248249
$86$	0.402999	+	0.698015i	0.0434565	+	0.0752689i
$87$	−7.54739	−	13.0725i	−0.809165	−	1.40151i
$88$	−1.66620	+	2.88594i	−0.177617	+	0.307642i
$89$	9.70425			1.02865			0.514324	−	0.857596i	$-0.328043\pi$
$89$	9.70425			1.02865			0.514324	+	0.857596i	$0.328043\pi$
$90$	14.2375	+	24.6600i	1.50076	+	2.59939i
$91$	1.81601			0.190370
$92$	−3.24650			−0.338471
$93$	14.8161	−	6.00362i	1.53636	−	0.622546i
$94$	14.2356			1.46829
$95$	6.42633			0.659328
$96$	−3.94588	−	6.83447i	−0.402725	−	0.697540i
$97$	−9.81304			−0.996363			−0.498182	−	0.867073i	$-0.665999\pi$
$97$	−9.81304			−0.996363			−0.498182	+	0.867073i	$0.665999\pi$
$98$	2.92473	−	5.06577i	0.295442	−	0.511721i
$99$	3.67805	+	6.37057i	0.369658	+	0.640267i
$100$	−1.69085	−	2.92864i	−0.169085	−	0.292864i
$101$	2.13475			0.212416			0.106208	−	0.994344i	$-0.466129\pi$
$101$	2.13475			0.212416			0.106208	+	0.994344i	$0.466129\pi$
$102$	−1.51065	+	2.61652i	−0.149576	+	0.259074i
$103$	3.70863	−	6.42353i	0.365422	−	0.632930i	−0.623422	−	0.781886i	$-0.714258\pi$
$103$	3.70863	−	6.42353i	0.365422	−	0.632930i	0.988844	+	0.148956i	$0.0475913\pi$
$104$	−1.18778	+	2.05729i	−0.116471	+	0.201734i
$105$	8.95972	+	15.5187i	0.874379	+	1.51447i
$106$	−5.53785	+	9.59183i	−0.537883	+	0.931641i
$107$	−3.40551	−	5.89852i	−0.329224	−	0.570232i	0.653134	−	0.757242i	$-0.273454\pi$
$107$	−3.40551	−	5.89852i	−0.329224	−	0.570232i	−0.982358	+	0.187010i	$0.940120\pi$
$108$	−3.19900			−0.307824
$109$	−20.4051			−1.95446			−0.977228	−	0.212193i	$-0.931939\pi$
$109$	−20.4051			−1.95446			−0.977228	+	0.212193i	$0.931939\pi$
$110$	−3.80863	−	6.59673i	−0.363138	−	0.628974i
$111$	11.6322	−	20.1476i	1.10408	−	1.91232i
$112$	−4.30987	−	7.46491i	−0.407244	−	0.705367i
$113$	−9.65871	+	16.7294i	−0.908615	+	1.57377i	−0.0926244	+	0.995701i	$0.529526\pi$
$113$	−9.65871	+	16.7294i	−0.908615	+	1.57377i	−0.815990	+	0.578066i	$0.803808\pi$
$114$	−4.24160	+	7.34666i	−0.397262	+	0.688078i
$115$	−11.2353	+	19.4601i	−1.04769	+	1.81466i
$116$	−2.61036			−0.242366
$117$	2.62196	+	4.54137i	0.242400	+	0.419849i
$118$	8.54839	+	14.8062i	0.786943	+	1.36302i
$119$	−0.604710	+	1.04739i	−0.0554337	+	0.0960139i
$120$	−23.4406			−2.13983
$121$	4.51609	+	7.82210i	0.410554	+	0.711100i
$122$	12.0451			1.09051
$123$	−10.9682			−0.988973
$124$	0.381968	−	2.73802i	0.0343017	−	0.245881i
$125$	−6.22291			−0.556594
$126$	−15.0468			−1.34047
$127$	1.93835	+	3.35731i	0.172000	+	0.297913i	0.939119	−	0.343592i	$-0.111644\pi$
$127$	1.93835	+	3.35731i	0.172000	+	0.297913i	−0.767119	+	0.641505i	$0.778310\pi$
$128$	13.6346			1.20514
$129$	−0.732323	+	1.26842i	−0.0644775	+	0.111678i
$130$	−2.71504	−	4.70259i	−0.238125	−	0.412444i
$131$	−1.81715	−	3.14740i	−0.158765	−	0.274990i	0.775658	−	0.631153i	$-0.217418\pi$
$131$	−1.81715	−	3.14740i	−0.158765	−	0.274990i	−0.934424	+	0.356163i	$0.884085\pi$
$132$	1.99986			0.174065
$133$	−1.69791	+	2.94086i	−0.147227	+	0.255005i
$134$	11.5577	−	20.0184i	0.998429	−	1.72933i
$135$	−11.0709	+	19.1753i	−0.952830	+	1.65035i
$136$	−0.791029	−	1.37010i	−0.0678302	−	0.117485i
$137$	−10.7421	+	18.6058i	−0.917757	+	1.58960i	−0.114943	+	0.993372i	$0.536668\pi$
$137$	−10.7421	+	18.6058i	−0.917757	+	1.58960i	−0.802814	+	0.596229i	$0.796665\pi$
$138$	−14.8313	−	25.6886i	−1.26253	−	2.18676i
$139$	−3.64655			−0.309296			−0.154648	−	0.987970i	$-0.549424\pi$
$139$	−3.64655			−0.309296			−0.154648	+	0.987970i	$0.549424\pi$
$140$	3.09883			0.261899
$141$	12.9343	+	22.4029i	1.08927	+	1.88666i
$142$	−2.21672	+	3.83947i	−0.186023	+	0.322201i
$143$	−0.701394	−	1.21485i	−0.0586535	−	0.101591i
$144$	12.4452	−	21.5557i	1.03710	−	1.79630i
$145$	−9.03375	+	15.6469i	−0.750213	+	1.29941i
$146$	−11.1088	+	19.2410i	−0.919370	+	1.59240i
$147$	10.6295			0.876709
$148$	−2.01157	−	3.48415i	−0.165350	−	0.286395i
$149$	0.285874	+	0.495148i	0.0234197	+	0.0405641i	0.877498	−	0.479581i	$-0.159211\pi$
$149$	0.285874	+	0.495148i	0.0234197	+	0.0405641i	−0.854078	+	0.520145i	$0.825878\pi$
$150$	15.4489	−	26.7584i	1.26140	−	2.18481i
$151$	7.77620			0.632818			0.316409	−	0.948623i	$-0.397523\pi$
$151$	7.77620			0.632818			0.316409	+	0.948623i	$0.397523\pi$
$152$	−2.22105	−	3.84698i	−0.180151	−	0.312031i
$153$	−3.49232			−0.282337
$154$	4.02512			0.324354
$155$	−15.0902	−	11.7651i	−1.21208	−	0.944997i
$156$	1.42563			0.114142
$157$	19.1866			1.53125			0.765627	−	0.643284i	$-0.222429\pi$
$157$	19.1866			1.53125			0.765627	+	0.643284i	$0.222429\pi$
$158$	−9.93254	−	17.2037i	−0.790190	−	1.36865i
$159$	−20.1266			−1.59614
$160$	−4.72298	+	8.18044i	−0.373384	+	0.646721i
$161$	−5.93696	−	10.2831i	−0.467898	−	0.810424i
$162$	−2.18593	−	3.78613i	−0.171743	−	0.297467i
$163$	16.0599			1.25791			0.628955	−	0.777441i	$-0.283483\pi$
$163$	16.0599			1.25791			0.628955	+	0.777441i	$0.283483\pi$
$164$	−0.948376	+	1.64264i	−0.0740557	+	0.128268i
$165$	6.92097	−	11.9875i	0.538797	−	0.933224i
$166$	−1.40451	+	2.43269i	−0.109011	+	0.188813i
$167$	8.09902	+	14.0279i	0.626721	+	1.08551i	0.988205	+	0.153134i	$0.0489367\pi$
$167$	8.09902	+	14.0279i	0.626721	+	1.08551i	−0.361485	+	0.932378i	$0.617730\pi$
$168$	6.19327	−	10.7271i	0.477822	−	0.827611i
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$	3.61630			0.277357
$171$	−9.80574			−0.749864
$172$	0.126642	+	0.219350i	0.00965633	+	0.0167253i
$173$	7.63156	−	13.2183i	0.580217	−	1.00497i	−0.415236	−	0.909714i	$-0.636301\pi$
$173$	7.63156	−	13.2183i	0.580217	−	1.00497i	0.995453	−	0.0952516i	$-0.0303655\pi$
$174$	−11.9252	−	20.6550i	−0.904045	−	1.56585i
$175$	6.18420	−	10.7113i	0.467481	−	0.809701i
$176$	−3.32917	+	5.76630i	−0.250946	+	0.434651i
$177$	−15.5340	+	26.9057i	−1.16761	+	2.02235i
$178$	15.3331			1.14926
$179$	2.35215	+	4.07405i	0.175808	+	0.304508i	0.940441	−	0.339958i	$-0.110413\pi$
$179$	2.35215	+	4.07405i	0.175808	+	0.304508i	−0.764633	+	0.644466i	$0.777080\pi$
$180$	4.47409	+	7.74936i	0.333479	+	0.577603i
$181$	−1.02888	+	1.78207i	−0.0764758	+	0.132460i	−0.901727	−	0.432306i	$-0.857700\pi$
$181$	−1.02888	+	1.78207i	−0.0764758	+	0.132460i	0.825251	+	0.564766i	$0.191033\pi$
$182$	2.86937			0.212692
$183$	10.9441	+	18.9557i	0.809009	+	1.40124i
$184$	15.5324			1.14507
$185$	−27.8461			−2.04728
$186$	23.4101	−	9.48596i	1.71651	−	0.695544i
$187$	0.934221			0.0683170
$188$	4.47349			0.326263
$189$	−5.85010	−	10.1327i	−0.425532	−	0.737043i
$190$	10.1539			0.736638
$191$	−5.86883	+	10.1651i	−0.424654	+	0.735522i	−0.996388	−	0.0849168i	$-0.972938\pi$
$191$	−5.86883	+	10.1651i	−0.424654	+	0.735522i	0.571734	+	0.820439i	$0.306271\pi$
$192$	7.39364	+	12.8062i	0.533590	+	0.924205i
$193$	6.87461	+	11.9072i	0.494845	+	0.857097i	0.999982	−	0.00594178i	$-0.00189134\pi$
$193$	6.87461	+	11.9072i	0.494845	+	0.857097i	−0.505137	+	0.863039i	$0.668558\pi$
$194$	−15.5050			−1.11319
$195$	4.93373	−	8.54547i	0.353312	−	0.611954i
$196$	0.919090	−	1.59191i	0.0656493	−	0.113708i
$197$	7.94409	−	13.7596i	0.565993	−	0.980329i	−0.430963	−	0.902369i	$-0.641826\pi$
$197$	7.94409	−	13.7596i	0.565993	−	0.980329i	0.996957	−	0.0779596i	$-0.0248405\pi$
$198$	5.81147	+	10.0658i	0.413003	+	0.715342i
$199$	−0.472127	+	0.817749i	−0.0334682	+	0.0579687i	−0.882274	−	0.470736i	$-0.843989\pi$
$199$	−0.472127	+	0.817749i	−0.0334682	+	0.0579687i	0.848806	+	0.528704i	$0.177322\pi$
$200$	8.08963	+	14.0116i	0.572023	+	0.990773i
$201$	42.0048			2.96279
$202$	3.37299			0.237323
$203$	−4.77363	−	8.26817i	−0.335043	−	0.580312i
$204$	−0.474718	+	0.822235i	−0.0332369	+	0.0575680i
$205$	6.56415	+	11.3694i	0.458460	+	0.794077i
$206$	5.85978	−	10.1494i	0.408270	−	0.707145i
$207$	17.1436	−	29.6935i	1.19156	−	2.06384i
$208$	−2.37326	+	4.11060i	−0.164556	+	0.285019i
$209$	2.62311			0.181444
$210$	14.1567	+	24.5201i	0.976906	+	1.69205i
$211$	2.70882	+	4.69181i	0.186483	+	0.322997i	0.944075	−	0.329730i	$-0.106958\pi$
$211$	2.70882	+	4.69181i	0.186483	+	0.322997i	−0.757593	+	0.652728i	$0.773625\pi$
$212$	−1.74026	+	3.01421i	−0.119521	+	0.207017i
$213$	−8.05637			−0.552013
$214$	−5.38085	−	9.31990i	−0.367827	−	0.637095i
$215$	1.75309			0.119560
$216$	15.3052			1.04139
$217$	9.37103	−	3.79722i	0.636147	−	0.257772i
$218$	−32.2409			−2.18363
$219$	−40.3734			−2.72818
$220$	−1.19685	−	2.07301i	−0.0806918	−	0.139762i
$221$	0.665975			0.0447983
$222$	18.3794	−	31.8340i	1.23354	−	2.13656i
$223$	6.13231	+	10.6215i	0.410650	+	0.711266i	0.994961	−	0.100263i	$-0.0319686\pi$
$223$	6.13231	+	10.6215i	0.410650	+	0.711266i	−0.584311	+	0.811530i	$0.698635\pi$
$224$	−2.49573	−	4.32272i	−0.166753	−	0.288824i
$225$	35.7149			2.38100
$226$	−15.2611	+	26.4331i	−1.01516	+	1.75830i
$227$	−2.93751	+	5.08792i	−0.194970	+	0.337697i	−0.946891	−	0.321556i	$-0.895794\pi$
$227$	−2.93751	+	5.08792i	−0.194970	+	0.337697i	0.751921	+	0.659253i	$0.229127\pi$
$228$	−1.33291	+	2.30867i	−0.0882744	+	0.152896i
$229$	−11.6176	−	20.1222i	−0.767712	−	1.32972i	−0.938801	−	0.344460i	$-0.888062\pi$
$229$	−11.6176	−	20.1222i	−0.767712	−	1.32972i	0.171089	−	0.985256i	$-0.445271\pi$
$230$	−17.7522	+	30.7477i	−1.17054	+	2.02744i
$231$	3.65719	+	6.33444i	0.240626	+	0.416776i
$232$	12.4889			0.819936
$233$	−9.20974			−0.603350			−0.301675	−	0.953411i	$-0.597546\pi$
$233$	−9.20974			−0.603350			−0.301675	+	0.953411i	$0.597546\pi$
$234$	4.14280	+	7.17554i	0.270823	+	0.469080i
$235$	15.4816	−	26.8149i	1.00991	−	1.74921i
$236$	2.68631	+	4.65283i	0.174864	+	0.302874i
$237$	18.0493	−	31.2622i	1.17243	−	2.03070i
$238$	−0.955466	+	1.65491i	−0.0619336	+	0.107272i
$239$	−8.81584	+	15.2695i	−0.570249	+	0.987701i	0.426291	+	0.904586i	$0.359820\pi$
$239$	−8.81584	+	15.2695i	−0.570249	+	0.987701i	−0.996540	+	0.0831147i	$0.973513\pi$
$240$	−46.8360			−3.02325
$241$	−12.1015	−	20.9604i	−0.779525	−	1.35018i	−0.932216	−	0.361903i	$-0.882127\pi$
$241$	−12.1015	−	20.9604i	−0.779525	−	1.35018i	0.152690	−	0.988274i	$-0.451206\pi$
$242$	7.13561	+	12.3592i	0.458694	+	0.794481i
$243$	−5.69195	+	9.85875i	−0.365139	+	0.632439i
$244$	3.78515			0.242319
$245$	−6.36145	−	11.0183i	−0.406418	−	0.703936i
$246$	−17.3303			−1.10494
$247$	1.86993			0.118981
$248$	−1.82747	+	13.0996i	−0.116045	+	0.831829i
$249$	−5.10451			−0.323485
$250$	−9.83245			−0.621859
$251$	1.30238	+	2.25579i	0.0822056	+	0.142384i	0.904197	−	0.427116i	$-0.140470\pi$
$251$	1.30238	+	2.25579i	0.0822056	+	0.142384i	−0.821991	+	0.569500i	$0.807137\pi$
$252$	−4.72842			−0.297862
$253$	−4.58603	+	7.94324i	−0.288321	+	0.499387i
$254$	3.06266	+	5.30469i	0.192168	+	0.332846i
$255$	3.28574	+	5.69107i	0.205761	+	0.356389i
$256$	11.2429			0.702681
$257$	4.40759	−	7.63418i	0.274938	−	0.476207i	−0.695181	−	0.718834i	$-0.744676\pi$
$257$	4.40759	−	7.63418i	0.274938	−	0.476207i	0.970120	+	0.242627i	$0.0780093\pi$
$258$	−1.15710	+	2.00416i	−0.0720379	+	0.124773i
$259$	7.35724	−	12.7431i	0.457156	−	0.791818i
$260$	−0.853196	−	1.47778i	−0.0529130	−	0.0916480i
$261$	13.7843	−	23.8752i	0.853229	−	1.47784i
$262$	−2.87117	−	4.97302i	−0.177382	−	0.307234i
$263$	0.842062			0.0519238			0.0259619	−	0.999663i	$-0.491735\pi$
$263$	0.842062			0.0519238			0.0259619	+	0.999663i	$0.491735\pi$
$264$	−9.56804			−0.588872
$265$	12.0451	+	20.8628i	0.739926	+	1.28159i
$266$	−2.68276	+	4.64668i	−0.164491	+	0.284906i
$267$	13.9315	+	24.1301i	0.852596	+	1.47674i
$268$	3.63197	−	6.29076i	0.221858	−	0.384269i
$269$	−1.24134	+	2.15006i	−0.0756858	+	0.131092i	−0.901384	−	0.433020i	$-0.857448\pi$
$269$	−1.24134	+	2.15006i	−0.0756858	+	0.131092i	0.825698	+	0.564112i	$0.190781\pi$
$270$	−17.4924	+	30.2978i	−1.06456	+	1.84386i
$271$	−21.9915			−1.33589			−0.667943	−	0.744212i	$-0.732825\pi$
$271$	−21.9915			−1.33589			−0.667943	+	0.744212i	$0.732825\pi$
$272$	−1.58053	−	2.73756i	−0.0958337	−	0.165989i
$273$	2.60709	+	4.51561i	0.157788	+	0.273297i
$274$	−16.9729	+	29.3979i	−1.02537	+	1.77599i
$275$	−9.55402			−0.576129
$276$	−4.66071	−	8.07259i	−0.280542	−	0.485913i
$277$	−18.5018			−1.11166			−0.555832	−	0.831294i	$-0.687600\pi$
$277$	−18.5018			−1.11166			−0.555832	+	0.831294i	$0.687600\pi$
$278$	−5.76169			−0.345563
$279$	23.0257	+	17.9520i	1.37851	+	1.07476i
$280$	−14.8259			−0.886019
$281$	−17.2395			−1.02842			−0.514212	−	0.857663i	$-0.671915\pi$
$281$	−17.2395			−1.02842			−0.514212	+	0.857663i	$0.671915\pi$
$282$	20.4367	+	35.3974i	1.21699	+	2.10789i
$283$	9.89244			0.588045			0.294022	−	0.955799i	$-0.405006\pi$
$283$	9.89244			0.588045			0.294022	+	0.955799i	$0.405006\pi$
$284$	−0.696599	+	1.20655i	−0.0413356	+	0.0715953i
$285$	9.22571	+	15.9794i	0.546484	+	0.946538i
$286$	−1.10823	−	1.91951i	−0.0655310	−	0.113503i
$287$	−6.93728			−0.409495
$288$	7.20665	−	12.4823i	0.424656	−	0.735526i
$289$	8.27824	−	14.3383i	0.486955	−	0.843431i
$290$	−14.2737	+	24.7228i	−0.838180	+	1.45177i
$291$	−14.0877	−	24.4006i	−0.825836	−	1.43039i
$292$	−3.49092	+	6.04645i	−0.204290	+	0.353841i
$293$	4.78429	+	8.28663i	0.279501	+	0.484110i	0.971261	−	0.238018i	$-0.0764976\pi$
$293$	4.78429	+	8.28663i	0.279501	+	0.484110i	−0.691760	+	0.722128i	$0.743164\pi$
$294$	16.7951			0.979509
$295$	37.1864			2.16508
$296$	9.62409	+	16.6694i	0.559389	+	0.968890i
$297$	−4.51893	+	7.82702i	−0.262215	+	0.454170i
$298$	0.451692	+	0.782353i	0.0261658	+	0.0453205i
$299$	−3.26923	+	5.66247i	−0.189064	+	0.327469i
$300$	4.85480	−	8.40876i	0.280292	−	0.485480i
$301$	−0.463186	+	0.802261i	−0.0266976	+	0.0462416i
$302$	12.2867			0.707021
$303$	3.06467	+	5.30817i	0.176061	+	0.304946i
$304$	−4.43781	−	7.68652i	−0.254526	−	0.440852i
$305$	13.0994	−	22.6888i	0.750068	−	1.29916i
$306$	−5.51800			−0.315443
$307$	3.44814	+	5.97236i	0.196796	+	0.340861i	0.947488	−	0.319792i	$-0.103613\pi$
$307$	3.44814	+	5.97236i	0.196796	+	0.340861i	−0.750692	+	0.660653i	$0.770280\pi$
$308$	1.26489			0.0720736
$309$	21.2966			1.21152
$310$	−23.8432	−	18.5893i	−1.35420	−	1.05580i
$311$	−7.61219			−0.431648			−0.215824	−	0.976432i	$-0.569244\pi$
$311$	−7.61219			−0.431648			−0.215824	+	0.976432i	$0.569244\pi$
$312$	−6.82073			−0.386148
$313$	−13.0657	−	22.6305i	−0.738518	−	1.27915i	−0.953162	−	0.302459i	$-0.902193\pi$
$313$	−13.0657	−	22.6305i	−0.738518	−	1.27915i	0.214644	−	0.976692i	$-0.431141\pi$
$314$	30.3155			1.71080
$315$	−16.3638	+	28.3429i	−0.921995	+	1.59694i
$316$	−3.12128	−	5.40622i	−0.175586	−	0.304124i
$317$	−0.0428837	−	0.0742768i	−0.00240859	−	0.00417180i	0.864819	−	0.502084i	$-0.167433\pi$
$317$	−0.0428837	−	0.0742768i	−0.00240859	−	0.00417180i	−0.867227	+	0.497913i	$0.834100\pi$
$318$	−31.8008			−1.78330
$319$	−3.68741	+	6.38679i	−0.206455	+	0.357591i
$320$	8.84973	−	15.3282i	0.494715	−	0.856871i
$321$	9.77799	−	16.9360i	0.545754	−	0.945274i
$322$	−9.38064	−	16.2477i	−0.522762	−	0.905451i
$323$	−0.622662	+	1.07848i	−0.0346459	+	0.0600084i
$324$	−0.686923	−	1.18979i	−0.0381624	−	0.0660992i
$325$	−6.81074			−0.377792
$326$	25.3753			1.40541
$327$	−29.2938	−	50.7384i	−1.61995	−	2.80584i
$328$	4.53737	−	7.85896i	0.250535	−	0.433938i
$329$	8.18080	+	14.1696i	0.451022	+	0.781193i
$330$	10.9354	−	18.9407i	0.601975	−	1.04265i
$331$	10.7268	−	18.5794i	0.589598	−	1.02121i	−0.404686	−	0.914455i	$-0.632619\pi$
$331$	10.7268	−	18.5794i	0.589598	−	1.02121i	0.994285	−	0.106759i	$-0.0340473\pi$
$332$	−0.441365	+	0.764467i	−0.0242231	+	0.0419556i
$333$	42.4895			2.32841
$334$	12.7968	+	22.1647i	0.700208	+	1.21280i
$335$	−25.1386	−	43.5412i	−1.37347	−	2.37891i
$336$	12.3746	−	21.4334i	0.675089	−	1.16929i
$337$	32.8905			1.79166			0.895830	−	0.444396i	$-0.146582\pi$
$337$	32.8905			1.79166			0.895830	+	0.444396i	$0.146582\pi$
$338$	−0.790020	−	1.36835i	−0.0429714	−	0.0744287i
$339$	−55.4646			−3.01242
$340$	1.13642			0.0616308
$341$	−6.15955	−	4.80230i	−0.333558	−	0.260059i
$342$	−15.4935			−0.837790
$343$	19.4352			1.04940
$344$	−0.605899	−	1.04945i	−0.0326679	−	0.0565824i
$345$	−64.5179			−3.47353
$346$	12.0582	−	20.8854i	0.648251	−	1.12280i
$347$	16.2205	+	28.0948i	0.870765	+	1.50821i	0.861207	+	0.508254i	$0.169709\pi$
$347$	16.2205	+	28.0948i	0.870765	+	1.50821i	0.00955754	+	0.999954i	$0.496958\pi$
$348$	−3.74746	−	6.49079i	−0.200885	−	0.347943i
$349$	34.1557			1.82831			0.914156	−	0.405362i	$-0.132854\pi$
$349$	34.1557			1.82831			0.914156	+	0.405362i	$0.132854\pi$
$350$	9.77127	−	16.9243i	0.522297	−	0.904644i
$351$	−3.22139	+	5.57962i	−0.171945	+	0.297818i
$352$	−1.92783	+	3.33910i	−0.102754	+	0.177975i
$353$	5.27056	+	9.12887i	0.280523	+	0.485881i	0.971514	−	0.236983i	$-0.0761586\pi$
$353$	5.27056	+	9.12887i	0.280523	+	0.485881i	−0.690990	+	0.722864i	$0.742825\pi$
$354$	−24.5443	+	42.5120i	−1.30452	+	2.25949i
$355$	4.82149	+	8.35106i	0.255898	+	0.443228i
$356$	4.81840			0.255374
$357$	−3.47251			−0.183785
$358$	3.71649	+	6.43715i	0.196423	+	0.340214i
$359$	13.4089	−	23.2249i	0.707696	−	1.22577i	−0.258014	−	0.966141i	$-0.583068\pi$
$359$	13.4089	−	23.2249i	0.707696	−	1.22577i	0.965710	−	0.259624i	$-0.0835988\pi$
$360$	−21.4057	−	37.0757i	−1.12818	−	1.95406i
$361$	7.75169	−	13.4263i	0.407984	−	0.706648i
$362$	−1.62567	+	2.81573i	−0.0854431	+	0.147992i
$363$	−12.9667	+	22.4590i	−0.680576	+	1.17879i
$364$	0.901695			0.0472617
$365$	24.1623	+	41.8503i	1.26471	+	2.19054i
$366$	17.2921	+	29.9507i	0.903871	+	1.56555i
$367$	−6.68489	+	11.5786i	−0.348949	+	0.604397i	−0.986063	−	0.166373i	$-0.946795\pi$
$367$	−6.68489	+	11.5786i	−0.348949	+	0.604397i	0.637114	+	0.770769i	$0.280128\pi$
$368$	31.0349			1.61780
$369$	−10.0160	−	17.3483i	−0.521414	−	0.903116i
$370$	−43.9979			−2.28734
$371$	−12.7298			−0.660899
$372$	7.35657	−	2.98094i	0.381421	−	0.154555i
$373$	−2.52488			−0.130734			−0.0653668	−	0.997861i	$-0.520822\pi$
$373$	−2.52488			−0.130734			−0.0653668	+	0.997861i	$0.520822\pi$
$374$	1.47611			0.0763277
$375$	−8.93369	−	15.4736i	−0.461334	−	0.799053i
$376$	−21.4028			−1.10377
$377$	−2.62863	+	4.55292i	−0.135381	+	0.234488i
$378$	−9.24338	−	16.0100i	−0.475428	−	0.823466i
$379$	−11.7850	−	20.4122i	−0.605353	−	1.04850i	−0.991996	−	0.126272i	$-0.959699\pi$
$379$	−11.7850	−	20.4122i	−0.605353	−	1.04850i	0.386643	−	0.922230i	$-0.373635\pi$
$380$	3.19083			0.163686
$381$	−5.56542	+	9.63959i	−0.285125	+	0.493851i
$382$	−9.27299	+	16.0613i	−0.474447	+	0.821767i
$383$	13.8930	−	24.0633i	0.709898	−	1.22958i	−0.254997	−	0.966942i	$-0.582074\pi$
$383$	13.8930	−	24.0633i	0.709898	−	1.22958i	0.964895	−	0.262637i	$-0.0845922\pi$
$384$	19.5740	+	33.9032i	0.998882	+	1.73011i
$385$	4.37743	−	7.58194i	0.223095	−	0.386411i
$386$	10.8622	+	18.8138i	0.552869	+	0.957598i
$387$	−2.67499			−0.135977
$388$	−4.87241			−0.247359
$389$	−9.61882	−	16.6603i	−0.487694	−	0.844710i	0.512206	−	0.858862i	$-0.328828\pi$
$389$	−9.61882	−	16.6603i	−0.487694	−	0.844710i	−0.999900	+	0.0141524i	$0.995495\pi$
$390$	7.79549	−	13.5022i	0.394740	−	0.683709i
$391$	−2.17722	−	3.77106i	−0.110107	−	0.190711i
$392$	−4.39725	+	7.61627i	−0.222095	+	0.384680i
$393$	5.21745	−	9.03689i	0.263186	−	0.455851i
$394$	12.5520	−	21.7407i	0.632360	−	1.09528i
$395$	−43.2077			−2.17401
$396$	1.82624	+	3.16314i	0.0917721	+	0.158954i
$397$	−2.39093	−	4.14121i	−0.119997	−	0.207841i	0.799769	−	0.600308i	$-0.204955\pi$
$397$	−2.39093	−	4.14121i	−0.119997	−	0.207841i	−0.919766	+	0.392466i	$0.871622\pi$
$398$	−0.745980	+	1.29208i	−0.0373926	+	0.0647659i
$399$	−9.75013			−0.488117
$400$	16.1636	+	27.9962i	0.808181	+	1.39981i
$401$	−7.82570			−0.390797			−0.195398	−	0.980724i	$-0.562600\pi$
$401$	−7.82570			−0.390797			−0.195398	+	0.980724i	$0.562600\pi$
$402$	66.3692			3.31019
$403$	−4.39094	−	3.42340i	−0.218728	−	0.170532i
$404$	1.05996			0.0527348
$405$	−9.50903			−0.472507
$406$	−7.54253	−	13.0640i	−0.374329	−	0.648357i
$407$	−11.3663			−0.563404
$408$	2.27122	−	3.93387i	0.112442	−	0.194755i
$409$	0.448009	+	0.775974i	0.0221526	+	0.0383694i	0.876889	−	0.480693i	$-0.159615\pi$
$409$	0.448009	+	0.775974i	0.0221526	+	0.0383694i	−0.854737	+	0.519062i	$0.826281\pi$
$410$	10.3716	+	17.9642i	0.512218	+	0.887187i
$411$	−61.6857			−3.04273
$412$	1.84142	−	3.18944i	0.0907205	−	0.157132i
$413$	−9.82506	+	17.0175i	−0.483460	+	0.837377i
$414$	27.0875	−	46.9169i	1.33128	−	2.30584i
$415$	3.05489	+	5.29123i	0.149959	+	0.259736i
$416$	−1.37429	+	2.38034i	−0.0673800	+	0.116706i
$417$	−5.23503	−	9.06733i	−0.256360	−	0.444029i
$418$	4.14462			0.202720
$419$	−26.8423			−1.31133			−0.655667	−	0.755050i	$-0.727612\pi$
$419$	−26.8423			−1.31133			−0.655667	+	0.755050i	$0.727612\pi$
$420$	4.44872	+	7.70541i	0.217075	+	0.375985i
$421$	3.00241	−	5.20033i	0.146329	−	0.253449i	−0.783539	−	0.621342i	$-0.786588\pi$
$421$	3.00241	−	5.20033i	0.146329	−	0.253449i	0.929868	+	0.367894i	$0.119921\pi$
$422$	4.28004	+	7.41324i	0.208349	+	0.360871i
$423$	−23.6229	+	40.9160i	−1.14858	+	1.98940i
$424$	8.32602	−	14.4211i	0.404347	−	0.700350i
$425$	2.26789	−	3.92810i	0.110009	−	0.190541i
$426$	−12.7294			−0.616740
$427$	6.92199	+	11.9892i	0.334979	+	0.580200i
$428$	−1.69092	−	2.92876i	−0.0817338	−	0.141567i
$429$	2.01386	−	3.48810i	0.0972300	−	0.168407i
$430$	2.76995			0.133579
$431$	−15.1228	−	26.1935i	−0.728441	−	1.26170i	−0.957542	−	0.288294i	$-0.906912\pi$
$431$	−15.1228	−	26.1935i	−0.728441	−	1.26170i	0.229101	−	0.973403i	$-0.426421\pi$
$432$	30.5808			1.47132
$433$	−26.4402			−1.27063			−0.635317	−	0.772252i	$-0.719130\pi$
$433$	−26.4402			−1.27063			−0.635317	+	0.772252i	$0.719130\pi$
$434$	14.8066	−	5.99975i	0.710740	−	0.287997i
$435$	−51.8758			−2.48726
$436$	−10.1316			−0.485217
$437$	−6.11322	−	10.5884i	−0.292435	−	0.506512i
$438$	−63.7916			−3.04808
$439$	−16.9965	+	29.4387i	−0.811197	+	1.40503i	0.100829	+	0.994904i	$0.467850\pi$
$439$	−16.9965	+	29.4387i	−0.811197	+	1.40503i	−0.912027	+	0.410131i	$0.865483\pi$
$440$	5.72618	+	9.91803i	0.272985	+	0.472823i
$441$	9.70674	+	16.8126i	0.462226	+	0.800598i
$442$	1.05227			0.0500512
$443$	14.8227	−	25.6736i	0.704245	−	1.21979i	−0.262718	−	0.964873i	$-0.584619\pi$
$443$	14.8227	−	25.6736i	0.704245	−	1.21979i	0.966963	−	0.254916i	$-0.0820478\pi$
$444$	5.77568	−	10.0038i	0.274101	−	0.474758i
$445$	16.6752	−	28.8822i	0.790479	−	1.36915i
$446$	9.68929	+	16.7823i	0.458801	+	0.794667i
$447$	−0.820807	+	1.42168i	−0.0388229	+	0.0672432i
$448$	4.67639	+	8.09974i	0.220939	+	0.382677i
$449$	6.36099			0.300194			0.150097	−	0.988671i	$-0.452041\pi$
$449$	6.36099			0.300194			0.150097	+	0.988671i	$0.452041\pi$
$450$	56.4310			2.66018
$451$	2.67937	+	4.64080i	0.126166	+	0.218527i
$452$	−4.79578	+	8.30654i	−0.225575	+	0.390707i
$453$	11.1636	+	19.3359i	0.524512	+	0.908481i
$454$	−4.64139	+	8.03912i	−0.217831	+	0.377294i
$455$	3.12053	−	5.40491i	0.146292	−	0.253386i
$456$	6.37714	−	11.0455i	0.298637	−	0.517254i
$457$	−16.2978			−0.762380			−0.381190	−	0.924497i	$-0.624486\pi$
$457$	−16.2978			−0.762380			−0.381190	+	0.924497i	$0.624486\pi$
$458$	−18.3562	−	31.7939i	−0.857731	−	1.48563i
$459$	−2.14537	−	3.71589i	−0.100137	−	0.173443i
$460$	−5.57859	+	9.66240i	−0.260103	+	0.450512i
$461$	−11.0286			−0.513655			−0.256827	−	0.966457i	$-0.582677\pi$
$461$	−11.0286			−0.513655			−0.256827	+	0.966457i	$0.582677\pi$
$462$	5.77851	+	10.0087i	0.268841	+	0.465646i
$463$	13.7713			0.640008			0.320004	−	0.947416i	$-0.396316\pi$
$463$	13.7713			0.640008			0.320004	+	0.947416i	$0.396316\pi$
$464$	24.9537			1.15844
$465$	7.59087	−	54.4128i	0.352018	−	2.52333i
$466$	−14.5518			−0.674097
$467$	2.44977			0.113362			0.0566808	−	0.998392i	$-0.481948\pi$
$467$	2.44977			0.113362			0.0566808	+	0.998392i	$0.481948\pi$
$468$	1.30187	+	2.25490i	0.0601788	+	0.104233i
$469$	26.5675			1.22677
$470$	24.4615	−	42.3685i	1.12832	−	1.95431i
$471$	27.5444	+	47.7084i	1.26918	+	2.19829i
$472$	−12.8523	−	22.2608i	−0.591575	−	1.02464i
$473$	0.715579			0.0329024
$474$	28.5185	−	49.3955i	1.30990	−	2.26881i
$475$	6.36779	−	11.0293i	0.292174	−	0.506061i
$476$	−0.300253	+	0.520054i	−0.0137621	+	0.0238366i
$477$	−18.3793	−	31.8339i	−0.841530	−	1.45757i
$478$	−13.9294	+	24.1264i	−0.637115	+	1.10352i
$479$	−6.59319	−	11.4197i	−0.301251	−	0.521781i	0.675169	−	0.737663i	$-0.264071\pi$
$479$	−6.59319	−	11.4197i	−0.301251	−	0.521781i	−0.976420	+	0.215882i	$0.930737\pi$
$480$	−27.1214			−1.23792
$481$	−8.10262			−0.369448
$482$	−19.1208	−	33.1182i	−0.870930	−	1.50849i
$483$	17.0463	−	29.5251i	0.775635	−	1.34344i
$484$	2.24235	+	3.88386i	0.101925	+	0.176539i
$485$	−16.8621	+	29.2060i	−0.765669	+	1.32618i
$486$	−8.99351	+	15.5772i	−0.407954	+	0.706597i
$487$	12.3937	−	21.4665i	0.561611	−	0.972739i	−0.435745	−	0.900070i	$-0.643515\pi$
$487$	12.3937	−	21.4665i	0.561611	−	0.972739i	0.997356	−	0.0726689i	$-0.0231516\pi$
$488$	−18.1095			−0.819778
$489$	23.0558	+	39.9338i	1.04262	+	1.80587i
$490$	−10.0513	−	17.4094i	−0.454073	−	0.786478i
$491$	11.6756	−	20.2228i	0.526913	−	0.912640i	−0.472595	−	0.881280i	$-0.656683\pi$
$491$	11.6756	−	20.2228i	0.526913	−	0.912640i	0.999508	−	0.0313607i	$-0.00998405\pi$
$492$	−5.44600			−0.245525
$493$	−1.75060	−	3.03213i	−0.0788432	−	0.136560i
$494$	2.95456			0.132932
$495$	25.2805			1.13628
$496$	−3.65141	+	26.1740i	−0.163953	+	1.17525i
$497$	−5.09556			−0.228567
$498$	−8.06533			−0.361416
$499$	2.13024	+	3.68968i	0.0953626	+	0.165173i	0.909760	−	0.415135i	$-0.136266\pi$
$499$	2.13024	+	3.68968i	0.0953626	+	0.165173i	−0.814397	+	0.580308i	$0.802932\pi$
$500$	−3.08983			−0.138181
$501$	−23.2541	+	40.2773i	−1.03892	+	1.79946i
$502$	2.05781	+	3.56424i	0.0918447	+	0.159080i
$503$	16.2988	+	28.2304i	0.726728	+	1.25873i	0.958259	+	0.285903i	$0.0922935\pi$
$503$	16.2988	+	28.2304i	0.726728	+	1.25873i	−0.231530	+	0.972828i	$0.574373\pi$
$504$	22.6224			1.00768
$505$	3.66822	−	6.35355i	0.163234	−	0.282729i
$506$	−7.24611	+	12.5506i	−0.322129	+	0.557944i
$507$	1.43561	−	2.48655i	0.0637577	−	0.110432i
$508$	0.962436	+	1.66699i	0.0427012	+	0.0739606i
$509$	−3.16636	+	5.48430i	−0.140347	+	0.243087i	−0.927627	−	0.373508i	$-0.878155\pi$
$509$	−3.16636	+	5.48430i	−0.140347	+	0.243087i	0.787281	+	0.616595i	$0.211488\pi$
$510$	5.19160	+	8.99211i	0.229888	+	0.398178i
$511$	−25.5357			−1.12963
$512$	−9.50502			−0.420066
$513$	−6.02377	−	10.4335i	−0.265956	−	0.460649i
$514$	6.96417	−	12.0623i	0.307177	−	0.532045i
$515$	−12.7454	−	22.0756i	−0.561627	−	0.972767i
$516$	−0.363616	+	0.629802i	−0.0160073	+	0.0277255i
$517$	6.31929	−	10.9453i	0.277922	−	0.481375i
$518$	11.6247	−	20.1346i	0.510761	−	0.884664i
$519$	43.8238			1.92365
$520$	4.08200	+	7.07023i	0.179007	+	0.310050i
$521$	−6.33762	−	10.9771i	−0.277656	−	0.480914i	0.693146	−	0.720797i	$-0.256224\pi$
$521$	−6.33762	−	10.9771i	−0.277656	−	0.480914i	−0.970802	+	0.239883i	$0.922891\pi$
$522$	21.7798	−	37.7237i	0.953275	−	1.65112i
$523$	23.0180			1.00651			0.503253	−	0.864139i	$-0.332136\pi$
$523$	23.0180			1.00651			0.503253	+	0.864139i	$0.332136\pi$
$524$	−0.902261	−	1.56276i	−0.0394155	−	0.0682696i
$525$	35.5124			1.54989
$526$	1.33049			0.0580122
$527$	3.43658	−	1.39253i	0.149700	−	0.0606595i
$528$	−19.1176			−0.831987
$529$	19.7514			0.858756
$530$	19.0318	+	32.9640i	0.826688	+	1.43186i
$531$	−56.7417			−2.46238
$532$	−0.843052	+	1.46021i	−0.0365509	+	0.0633081i
$533$	1.91003	+	3.30827i	0.0827326	+	0.143297i
$534$	22.0124	+	38.1265i	0.952568	+	1.64990i
$535$	−23.4073			−1.01199
$536$	−17.3766	+	30.0972i	−0.750557	+	1.30000i
$537$	−6.75355	+	11.6975i	−0.291437	+	0.504784i
$538$	−1.96137	+	3.39719i	−0.0845605	+	0.146463i
$539$	−2.59662	−	4.49749i	−0.111845	−	0.193720i
$540$	−5.49696	+	9.52102i	−0.236552	+	0.409720i
$541$	10.8439	+	18.7822i	0.466215	+	0.807508i	0.999255	−	0.0385817i	$-0.0122840\pi$
$541$	10.8439	+	18.7822i	0.466215	+	0.807508i	−0.533040	+	0.846090i	$0.678951\pi$
$542$	−34.7474			−1.49253
$543$	−5.90827			−0.253548
$544$	−0.915241	−	1.58524i	−0.0392406	−	0.0679668i
$545$	−35.0629	+	60.7307i	−1.50193	+	2.60142i
$546$	4.11931	+	7.13485i	0.176290	+	0.305343i
$547$	−3.25830	+	5.64353i	−0.139315	+	0.241300i	−0.927237	−	0.374474i	$-0.877823\pi$
$547$	−3.25830	+	5.64353i	−0.139315	+	0.241300i	0.787923	+	0.615774i	$0.211157\pi$
$548$	−5.33370	+	9.23824i	−0.227844	+	0.394638i
$549$	−19.9879	+	34.6201i	−0.853064	+	1.47755i
$550$	−15.0957			−0.643684
$551$	−4.91535	−	8.51363i	−0.209401	−	0.362693i
$552$	22.2985	+	38.6222i	0.949089	+	1.64387i
$553$	11.4159	−	19.7730i	0.485455	−	0.840833i
$554$	−29.2336			−1.24201
$555$	−39.9761	−	69.2407i	−1.69689	−	2.93910i
$556$	−1.81060			−0.0767865
$557$	−30.9991			−1.31347			−0.656737	−	0.754119i	$-0.728064\pi$
$557$	−30.9991			−1.31347			−0.656737	+	0.754119i	$0.728064\pi$
$558$	36.3815	+	28.3649i	1.54015	+	1.20078i
$559$	0.510113			0.0215755
$560$	−29.6232			−1.25181
$561$	1.34118	+	2.32299i	0.0566246	+	0.0980767i
$562$	−27.2391			−1.14901
$563$	9.67786	−	16.7625i	0.407873	−	0.706457i	−0.586778	−	0.809748i	$-0.699604\pi$
$563$	9.67786	−	16.7625i	0.407873	−	0.706457i	0.994651	+	0.103291i	$0.0329372\pi$
$564$	6.42220	+	11.1236i	0.270423	+	0.468387i
$565$	33.1938	+	57.4934i	1.39648	+	2.41877i
$566$	15.6304			0.656997
$567$	2.51239	−	4.35158i	0.105510	−	0.182749i
$568$	3.33278	−	5.77254i	0.139840	−	0.242211i
$569$	2.25142	−	3.89958i	0.0943846	−	0.163479i	−0.814967	−	0.579507i	$-0.803245\pi$
$569$	2.25142	−	3.89958i	0.0943846	−	0.163479i	0.909352	+	0.416028i	$0.136578\pi$
$570$	14.5770	+	25.2481i	0.610563	+	1.05753i
$571$	−12.5273	+	21.6979i	−0.524250	+	0.908028i	0.475351	+	0.879796i	$0.342321\pi$
$571$	−12.5273	+	21.6979i	−0.524250	+	0.908028i	−0.999601	+	0.0282318i	$0.991012\pi$
$572$	−0.348259	−	0.603202i	−0.0145614	−	0.0252212i
$573$	−33.7015			−1.40790
$574$	−10.9612			−0.457511
$575$	22.2658	+	38.5656i	0.928550	+	1.60830i
$576$	−13.5035	+	23.3888i	−0.562647	+	0.974533i
$577$	−20.7234	−	35.8940i	−0.862726	−	1.49429i	−0.869287	−	0.494307i	$-0.835422\pi$
$577$	−20.7234	−	35.8940i	−0.862726	−	1.49429i	0.00656136	−	0.999978i	$-0.497911\pi$
$578$	13.0799	−	22.6551i	0.544054	−	0.942329i
$579$	−19.7385	+	34.1882i	−0.820306	+	1.42081i
$580$	−4.48548	+	7.76908i	−0.186249	+	0.322593i
$581$	−3.22854			−0.133943
$582$	−22.2591	−	38.5540i	−0.922671	−	1.59811i
$583$	4.91660	+	8.51580i	0.203625	+	0.352688i
$584$	16.7018	−	28.9284i	0.691125	−	1.19706i
$585$	18.0216			0.745103
$586$	7.55936	+	13.0932i	0.312274	+	0.540875i
$587$	6.38120			0.263380			0.131690	−	0.991291i	$-0.457960\pi$
$587$	6.38120			0.263380			0.131690	+	0.991291i	$0.457960\pi$
$588$	5.27782			0.217654
$589$	9.64923	−	3.90995i	0.397590	−	0.161107i
$590$	58.7560			2.41895
$591$	45.6185			1.87650
$592$	19.2296	+	33.3066i	0.790331	+	1.36889i
$593$	25.1362			1.03222			0.516109	−	0.856523i	$-0.327380\pi$
$593$	25.1362			1.03222			0.516109	+	0.856523i	$0.327380\pi$
$594$	−7.14009	+	12.3670i	−0.292961	+	0.507424i
$595$	2.07819	+	3.59953i	0.0851976	+	0.147567i
$596$	0.141943	+	0.245853i	0.00581423	+	0.0100705i
$597$	−2.71117			−0.110961
$598$	−5.16551	+	8.94692i	−0.211233	+	0.365867i
$599$	12.0839	−	20.9299i	0.493734	−	0.855172i	−0.506240	−	0.862392i	$-0.668965\pi$
$599$	12.0839	−	20.9299i	0.493734	−	0.855172i	0.999974	+	0.00722073i	$0.00229845\pi$
$600$	−23.2271	+	40.2305i	−0.948243	+	1.64241i
$601$	−16.5001	−	28.5790i	−0.673053	−	1.16576i	−0.977034	−	0.213083i	$-0.931649\pi$
$601$	−16.5001	−	28.5790i	−0.673053	−	1.16576i	0.303981	−	0.952678i	$-0.401684\pi$
$602$	−0.731852	+	1.26760i	−0.0298280	+	0.0516637i
$603$	38.3582	+	66.4383i	1.56206	+	2.70558i
$604$	3.86107			0.157105
$605$	31.0407			1.26198
$606$	4.84231	+	8.38712i	0.196705	+	0.340703i
$607$	15.0929	−	26.1417i	0.612602	−	1.06106i	−0.378198	−	0.925725i	$-0.623456\pi$
$607$	15.0929	−	26.1417i	0.612602	−	1.06106i	0.990800	−	0.135333i	$-0.0432105\pi$
$608$	−2.56982	−	4.45105i	−0.104220	−	0.180514i
$609$	13.7062	−	23.7398i	0.555402	−	0.961984i
$610$	20.6975	−	35.8492i	0.838018	−	1.45149i
$611$	4.50481	−	7.80256i	0.182245	−	0.315658i
$612$	−1.73402			−0.0700937
$613$	23.2056	+	40.1932i	0.937264	+	1.62339i	0.770546	+	0.637385i	$0.219984\pi$
$613$	23.2056	+	40.1932i	0.937264	+	1.62339i	0.166718	+	0.986005i	$0.446683\pi$
$614$	5.44820	+	9.43656i	0.219872	+	0.380829i
$615$	−18.8471	+	32.6442i	−0.759990	+	1.31634i
$616$	−6.05167			−0.243829
$617$	−3.85247	−	6.67267i	−0.155095	−	0.268632i	0.777999	−	0.628266i	$-0.216235\pi$
$617$	−3.85247	−	6.67267i	−0.155095	−	0.268632i	−0.933093	+	0.359634i	$0.882902\pi$
$618$	33.6495			1.35358
$619$	40.3830			1.62313			0.811565	−	0.584262i	$-0.198616\pi$
$619$	40.3830			1.62313			0.811565	+	0.584262i	$0.198616\pi$
$620$	−7.49266	−	5.84167i	−0.300913	−	0.234607i
$621$	42.1259			1.69045
$622$	−12.0276			−0.482261
$623$	8.81152	+	15.2620i	0.353026	+	0.611459i
$624$	−13.6283			−0.545568
$625$	6.33377	−	10.9704i	0.253351	−	0.438817i
$626$	−20.6444	−	35.7571i	−0.825114	−	1.42914i
$627$	3.76577	+	6.52250i	0.150390	+	0.260483i
$628$	9.52660			0.380153
$629$	2.69807	−	4.67320i	0.107579	−	0.186333i
$630$	−25.8554	+	44.7829i	−1.03010	+	1.78419i
$631$	−3.40620	+	5.89971i	−0.135599	+	0.234864i	−0.925826	−	0.377950i	$-0.876629\pi$
$631$	−3.40620	+	5.89971i	−0.135599	+	0.234864i	0.790227	+	0.612814i	$0.209962\pi$
$632$	14.9333	+	25.8653i	0.594016	+	1.02887i
$633$	−7.77761	+	13.4712i	−0.309132	+	0.535433i
$634$	−0.0677580	−	0.117360i	−0.00269101	−	0.00466097i
$635$	13.3229			0.528704
$636$	−9.99333			−0.396261
$637$	−1.85105	−	3.20611i	−0.0733411	−	0.127031i
$638$	−5.82626	+	10.0914i	−0.230664	+	0.399521i
$639$	−7.35696	−	12.7426i	−0.291037	−	0.504091i
$640$	23.4289	−	40.5800i	0.926108	−	1.60407i
$641$	9.55042	−	16.5418i	0.377219	−	0.653362i	−0.613438	−	0.789743i	$-0.710214\pi$
$641$	9.55042	−	16.5418i	0.377219	−	0.653362i	0.990656	+	0.136381i	$0.0435472\pi$
$642$	15.4496	−	26.7595i	0.609747	−	1.05611i
$643$	−25.1342			−0.991197			−0.495599	−	0.868552i	$-0.665051\pi$
$643$	−25.1342			−0.991197			−0.495599	+	0.868552i	$0.665051\pi$
$644$	−2.94785	−	5.10582i	−0.116161	−	0.201198i
$645$	2.51676	+	4.35915i	0.0990972	+	0.171641i
$646$	−0.983831	+	1.70405i	−0.0387083	+	0.0670448i
$647$	−5.78461			−0.227416			−0.113708	−	0.993514i	$-0.536273\pi$
$647$	−5.78461			−0.227416			−0.113708	+	0.993514i	$0.536273\pi$
$648$	3.28649	+	5.69236i	0.129105	+	0.223617i
$649$	15.1788			0.595821
$650$	−10.7612			−0.422090
$651$	22.8951	+	17.8502i	0.897331	+	0.699606i
$652$	7.97414			0.312292
$653$	−4.89443			−0.191534			−0.0957669	−	0.995404i	$-0.530530\pi$
$653$	−4.89443			−0.191534			−0.0957669	+	0.995404i	$0.530530\pi$
$654$	−46.2854	−	80.1686i	−1.80990	−	3.13484i
$655$	−12.4899			−0.488022
$656$	9.06598	−	15.7027i	0.353967	−	0.613089i
$657$	−36.8685	−	63.8580i	−1.43838	−	2.49134i
$658$	12.9260	+	22.3885i	0.503907	+	0.872793i
$659$	6.61786			0.257795			0.128898	−	0.991658i	$-0.458856\pi$
$659$	6.61786			0.257795			0.128898	+	0.991658i	$0.458856\pi$
$660$	3.43643	−	5.95207i	0.133763	−	0.231684i
$661$	−17.0321	+	29.5004i	−0.662470	+	1.14743i	0.317494	+	0.948260i	$0.397159\pi$
$661$	−17.0321	+	29.5004i	−0.662470	+	1.14743i	−0.979964	+	0.199172i	$0.936175\pi$
$662$	16.9488	−	29.3561i	0.658733	−	1.14096i
$663$	0.956081	+	1.65598i	0.0371311	+	0.0643130i
$664$	2.11165	−	3.65748i	0.0819479	−	0.141938i
$665$	5.83515	+	10.1068i	0.226278	+	0.391924i
$666$	67.1350			2.60143
$667$	34.3744			1.33098
$668$	4.02136	+	6.96520i	0.155591	+	0.269492i
$669$	−17.6072	+	30.4966i	−0.680735	+	1.17907i
$670$	−39.7199	−	68.7969i	−1.53451	−	2.65786i
$671$	5.34692	−	9.26114i	0.206416	−	0.357522i
$672$	7.16578	−	12.4115i	0.276426	−	0.478784i
$673$	−13.9016	+	24.0783i	−0.535867	+	0.928148i	0.463254	+	0.886225i	$0.346682\pi$
$673$	−13.9016	+	24.0783i	−0.535867	+	0.928148i	−0.999121	+	0.0419229i	$0.986652\pi$
$674$	51.9683			2.00174
$675$	21.9401	+	38.0013i	0.844474	+	1.46267i
$676$	−0.248262	−	0.430003i	−0.00954854	−	0.0165386i
$677$	9.07318	−	15.7152i	0.348711	−	0.603985i	−0.637310	−	0.770608i	$-0.719953\pi$
$677$	9.07318	−	15.7152i	0.348711	−	0.603985i	0.986021	+	0.166623i	$0.0532863\pi$
$678$	−87.6362			−3.36565
$679$	−8.91031	−	15.4331i	−0.341946	−	0.592268i
$680$	−5.43702			−0.208500
$681$	−16.8685			−0.646403
$682$	−9.73233	−	7.58783i	−0.372670	−	0.290553i
$683$	−18.0767			−0.691685			−0.345843	−	0.938293i	$-0.612407\pi$
$683$	−18.0767			−0.691685			−0.345843	+	0.938293i	$0.612407\pi$
$684$	−4.86879			−0.186163
$685$	36.9170	+	63.9421i	1.41053	+	2.44310i
$686$	30.7083			1.17245
$687$	33.3567	−	57.7755i	1.27264	−	2.20427i
$688$	−1.21063	−	2.09687i	−0.0461547	−	0.0799424i
$689$	3.50488	+	6.07063i	0.133525	+	0.231272i
$690$	−101.941			−3.88082
$691$	−25.9938	+	45.0226i	−0.988850	+	1.71274i	−0.365462	+	0.930826i	$0.619089\pi$
$691$	−25.9938	+	45.0226i	−0.988850	+	1.71274i	−0.623388	+	0.781913i	$0.714244\pi$
$692$	3.78926	−	6.56318i	0.144046	−	0.249495i
$693$	−6.67939	+	11.5690i	−0.253729	+	0.439472i
$694$	25.6291	+	44.3909i	0.972867	+	1.68506i
$695$	−6.26600	+	10.8530i	−0.237683	+	0.411679i
$696$	17.9292	+	31.0543i	0.679605	+	1.17711i
$697$	−2.54406			−0.0963633
$698$	53.9674			2.04269
$699$	−13.2216	−	22.9005i	−0.500087	−	0.866176i
$700$	3.07060	−	5.31844i	0.116058	−	0.201018i
$701$	−2.14821	−	3.72081i	−0.0811367	−	0.140533i	0.822602	−	0.568618i	$-0.192522\pi$
$701$	−2.14821	−	3.72081i	−0.0811367	−	0.140533i	−0.903738	+	0.428085i	$0.859188\pi$
$702$	−5.08993	+	8.81602i	−0.192107	+	0.332739i
$703$	7.57565	−	13.1214i	0.285721	−	0.494884i
$704$	3.61230	−	6.25668i	0.136144	−	0.235807i
$705$	88.9020			3.34824
$706$	8.32768	+	14.4240i	0.313417	+	0.542853i
$707$	1.93837	+	3.35736i	0.0728999	+	0.126266i
$708$	−7.71300	+	13.3593i	−0.289872	+	0.502074i
$709$	0.757459			0.0284470			0.0142235	−	0.999899i	$-0.495472\pi$
$709$	0.757459			0.0284470			0.0142235	+	0.999899i	$0.495472\pi$
$710$	7.61814	+	13.1950i	0.285904	+	0.495200i
$711$	65.9293			2.47254
$712$	−23.0529			−0.863945
$713$	−5.02992	+	36.0554i	−0.188372	+	1.35029i
$714$	−5.48671			−0.205335
$715$	−4.82092			−0.180292
$716$	1.16790	+	2.02286i	0.0436465	+	0.0755979i
$717$	−50.6245			−1.89061
$718$	21.1866	−	36.6963i	0.790678	−	1.36949i
$719$	−1.26370	−	2.18879i	−0.0471279	−	0.0816280i	0.841499	−	0.540258i	$-0.181674\pi$
$719$	−1.26370	−	2.18879i	−0.0471279	−	0.0816280i	−0.888627	+	0.458630i	$0.848340\pi$
$720$	−42.7700	−	74.0798i	−1.59394	−	2.76079i
$721$	13.4698			0.501643
$722$	12.2480	−	21.2141i	0.455822	−	0.789507i
$723$	34.7461	−	60.1820i	1.29222	−	2.23819i
$724$	−0.510862	+	0.884839i	−0.0189860	+	0.0328848i
$725$	17.9029	+	31.0088i	0.664898	+	1.15164i
$726$	−20.4879	+	35.4861i	−0.760378	+	1.31701i
$727$	−24.4908	−	42.4194i	−0.908315	−	1.57325i	−0.816404	−	0.577481i	$-0.804036\pi$
$727$	−24.4908	−	42.4194i	−0.908315	−	1.57325i	−0.0919109	−	0.995767i	$-0.529298\pi$
$728$	−4.31403			−0.159889
$729$	−40.9865			−1.51802
$730$	38.1773	+	66.1250i	1.41301	+	2.44740i
$731$	−0.169861	+	0.294208i	−0.00628254	+	0.0108817i
$732$	5.43400	+	9.41196i	0.200846	+	0.347876i
$733$	7.39076	−	12.8012i	0.272984	−	0.472822i	−0.696641	−	0.717420i	$-0.745323\pi$
$733$	7.39076	−	12.8012i	0.272984	−	0.472822i	0.969625	+	0.244598i	$0.0786561\pi$
$734$	−10.5624	+	18.2946i	−0.389865	+	0.675266i
$735$	18.2651	−	31.6361i	0.673719	−	1.16692i
$736$	17.9714			0.662436
$737$	−10.2611	−	17.7727i	−0.377972	−	0.654667i
$738$	−15.8257	−	27.4110i	−0.582554	−	1.00901i
$739$	−15.4339	+	26.7323i	−0.567745	+	0.983364i	0.429043	+	0.903284i	$0.358851\pi$
$739$	−15.4339	+	26.7323i	−0.567745	+	0.983364i	−0.996788	+	0.0800799i	$0.974482\pi$
$740$	−13.8263			−0.508263
$741$	2.68449	+	4.64967i	0.0986171	+	0.170810i
$742$	−20.1136			−0.738394
$743$	39.2436			1.43971			0.719853	−	0.694126i	$-0.244209\pi$
$743$	39.2436			1.43971			0.719853	+	0.694126i	$0.244209\pi$
$744$	−35.1965	+	14.2619i	−1.29037	+	0.522867i
$745$	1.96491			0.0719888
$746$	−3.98941			−0.146063
$747$	−4.66137	−	8.07373i	−0.170551	−	0.295402i
$748$	0.463864			0.0169605
$749$	6.18446	−	10.7118i	0.225975	−	0.391401i
$750$	−14.1156	−	24.4489i	−0.515428	−	0.892747i
$751$	−9.70766	−	16.8142i	−0.354238	−	0.613558i	0.632750	−	0.774357i	$-0.281926\pi$
$751$	−9.70766	−	16.8142i	−0.354238	−	0.613558i	−0.986987	+	0.160799i	$0.948593\pi$
$752$	−42.7643			−1.55945
$753$	−3.73943	+	6.47688i	−0.136272	+	0.236030i
$754$	−4.15334	+	7.19380i	−0.151256	+	0.261983i
$755$	13.3621	−	23.1439i	0.486298	−	0.842293i
$756$	−2.90472	−	5.03112i	−0.105643	−	0.182980i
$757$	4.03503	−	6.98887i	0.146656	−	0.254015i	−0.783334	−	0.621601i	$-0.786482\pi$
$757$	4.03503	−	6.98887i	0.146656	−	0.254015i	0.929989	+	0.367586i	$0.119816\pi$
$758$	−18.6207	−	32.2520i	−0.676335	−	1.17145i
$759$	−26.3350			−0.955901
$760$	−15.2661			−0.553759
$761$	−3.49351	−	6.05094i	−0.126640	−	0.219346i	0.795733	−	0.605648i	$-0.207086\pi$
$761$	−3.49351	−	6.05094i	−0.126640	−	0.219346i	−0.922373	+	0.386301i	$0.873753\pi$
$762$	−8.79358	+	15.2309i	−0.318558	+	0.551759i
$763$	−18.5280	−	32.0914i	−0.670758	−	1.16179i
$764$	−2.91402	+	5.04723i	−0.105425	+	0.182602i
$765$	−6.00098	+	10.3940i	−0.216966	+	0.375796i
$766$	21.9514	−	38.0210i	0.793138	−	1.37376i
$767$	10.8205			0.390705
$768$	16.1404	+	27.9560i	0.582418	+	1.00878i
$769$	25.6188	+	44.3731i	0.923839	+	1.60014i	0.793419	+	0.608676i	$0.208299\pi$
$769$	25.6188	+	44.3731i	0.923839	+	1.60014i	0.130420	+	0.991459i	$0.458367\pi$
$770$	6.91652	−	11.9798i	0.249254	−	0.431721i
$771$	25.3104			0.911531
$772$	3.41341	+	5.91220i	0.122851	+	0.212785i
$773$	−23.4520			−0.843510			−0.421755	−	0.906710i	$-0.638586\pi$
$773$	−23.4520			−0.843510			−0.421755	+	0.906710i	$0.638586\pi$
$774$	−4.22659			−0.151922
$775$	−35.1449	+	14.2410i	−1.26244	+	0.511552i
$776$	23.3114			0.836829
$777$	42.2485			1.51566
$778$	−15.1981	−	26.3239i	−0.544879	−	0.943758i
$779$	−7.14323			−0.255933
$780$	2.44972	−	4.24303i	0.0877139	−	0.151925i
$781$	1.96804	+	3.40875i	0.0704221	+	0.121975i
$782$	−3.44010	−	5.95843i	−0.123018	−	0.213073i
$783$	33.8714			1.21047
$784$	−8.78601	+	15.2178i	−0.313786	+	0.543494i
$785$	32.9690	−	57.1040i	1.17671	−	2.03813i
$786$	8.24378	−	14.2786i	0.294046	−	0.509302i
$787$	−15.7704	−	27.3152i	−0.562154	−	0.973680i	−0.997308	−	0.0733238i	$-0.976639\pi$
$787$	−15.7704	−	27.3152i	−0.562154	−	0.973680i	0.435154	−	0.900356i	$-0.356694\pi$
$788$	3.94444	−	6.83196i	0.140515	−	0.243379i
$789$	1.20887	+	2.09383i	0.0430370	+	0.0745423i
$790$	−68.2698			−2.42893
$791$	−35.0807			−1.24733
$792$	−8.73740	−	15.1336i	−0.310470	−	0.537750i
$793$	3.81164	−	6.60196i	0.135355	−	0.234442i
$794$	−3.77776	−	6.54328i	−0.134068	−	0.232212i
$795$	−34.5842	+	59.9017i	−1.22658	+	2.12449i
$796$	−0.234423	+	0.406032i	−0.00830889	+	0.0143914i
$797$	−21.8433	+	37.8337i	−0.773729	+	1.34014i	0.161778	+	0.986827i	$0.448277\pi$
$797$	−21.8433	+	37.8337i	−0.773729	+	1.34014i	−0.935506	+	0.353310i	$0.885056\pi$
$798$	−15.4056			−0.545352
$799$	3.00009	+	5.19631i	0.106136	+	0.183832i
$800$	9.35991	+	16.2118i	0.330923	+	0.573175i
$801$	−25.4441	+	44.0705i	−0.899025	+	1.55716i
$802$	−12.3649			−0.436620
$803$	9.86259	+	17.0825i	0.348043	+	0.602828i
$804$	20.8564			0.735548
$805$	−40.8068			−1.43825
$806$	−6.93785	−	5.40911i	−0.244375	−	0.190528i
$807$	−7.12833			−0.250929
$808$	−5.07121			−0.178405
$809$	−15.1691	−	26.2737i	−0.533319	−	0.923735i	−0.999243	−	0.0389104i	$-0.987611\pi$
$809$	−15.1691	−	26.2737i	−0.533319	−	0.923735i	0.465924	−	0.884825i	$-0.345722\pi$
$810$	−15.0246			−0.527912
$811$	−1.46614	+	2.53943i	−0.0514831	+	0.0891713i	−0.890618	−	0.454751i	$-0.849728\pi$
$811$	−1.46614	+	2.53943i	−0.0514831	+	0.0891713i	0.839135	+	0.543923i	$0.183061\pi$
$812$	−2.37022	−	4.10535i	−0.0831786	−	0.144070i
$813$	−31.5712	−	54.6829i	−1.10725	−	1.91781i
$814$	−17.9591			−0.629467
$815$	27.5964	−	47.7983i	0.966659	−	1.67430i
$816$	4.53805	−	7.86014i	0.158864	−	0.275160i
$817$	−0.476937	+	0.826078i	−0.0166859	+	0.0289008i
$818$	0.707871	+	1.22607i	0.0247501	+	0.0428685i
$819$	−4.76151	+	8.24719i	−0.166381	+	0.288180i
$820$	3.25926	+	5.64521i	0.113818	+	0.197139i
$821$	6.15154			0.214690			0.107345	−	0.994222i	$-0.465765\pi$
$821$	6.15154			0.214690			0.107345	+	0.994222i	$0.465765\pi$
$822$	−97.4659			−3.39951
$823$	−6.77109	−	11.7279i	−0.236025	−	0.408808i	0.723545	−	0.690277i	$-0.242511\pi$
$823$	−6.77109	−	11.7279i	−0.236025	−	0.408808i	−0.959570	+	0.281470i	$0.909178\pi$
$824$	−8.81004	+	15.2594i	−0.306912	+	0.531588i
$825$	−13.7159	−	23.7566i	−0.477525	−	0.827097i
$826$	−15.5240	+	26.8883i	−0.540149	+	0.935565i
$827$	−15.3699	+	26.6215i	−0.534464	+	0.925719i	0.464725	+	0.885455i	$0.346153\pi$
$827$	−15.3699	+	26.6215i	−0.534464	+	0.925719i	−0.999189	+	0.0402641i	$0.987180\pi$
$828$	8.51220	−	14.7436i	0.295819	−	0.512374i
$829$	31.4619			1.09272			0.546359	−	0.837551i	$-0.316013\pi$
$829$	31.4619			1.09272			0.546359	+	0.837551i	$0.316013\pi$
$830$	4.82685	+	8.36035i	0.167542	+	0.290192i
$831$	−26.5614	−	46.0057i	−0.921404	−	1.59592i
$832$	2.57508	−	4.46018i	0.0892750	−	0.154629i
$833$	2.46550			0.0854246
$834$	−8.27155	−	14.3267i	−0.286420	−	0.496094i
$835$	55.6674			1.92645
$836$	1.30244			0.0450458
$837$	−4.95633	+	35.5279i	−0.171316	+	1.22802i
$838$	−42.4119			−1.46510
$839$	17.3819			0.600091			0.300045	−	0.953925i	$-0.402998\pi$
$839$	17.3819			0.600091			0.300045	+	0.953925i	$0.402998\pi$
$840$	−21.2843	−	36.8654i	−0.734377	−	1.27198i
$841$	−1.36117			−0.0469370
$842$	4.74393	−	8.21673i	0.163487	−	0.283167i
$843$	−24.7492	−	42.8669i	−0.852409	−	1.47642i
$844$	1.34499	+	2.32960i	0.0462966	+	0.0801880i
$845$	−3.43668			−0.118225
$846$	−37.3250	+	64.6489i	−1.28326	+	2.22267i
$847$	−8.20129	+	14.2051i	−0.281800	+	0.488091i
$848$	16.6359	−	28.8143i	0.571281	−	0.989487i
$849$	14.2017	+	24.5981i	0.487401	+	0.844203i
$850$	3.58336	−	6.20655i	0.122908	−	0.212883i
$851$	26.4893	+	45.8808i	0.908042	+	1.57277i
$852$	−4.00018			−0.137044
$853$	−29.5772			−1.01271			−0.506353	−	0.862327i	$-0.669007\pi$
$853$	−29.5772			−1.01271			−0.506353	+	0.862327i	$0.669007\pi$
$854$	10.9370	+	18.9435i	0.374257	+	0.648233i
$855$	−16.8496	+	29.1843i	−0.576243	+	0.998083i
$856$	8.08997	+	14.0122i	0.276510	+	0.478929i
$857$	17.6884	−	30.6373i	0.604226	−	1.04655i	−0.387948	−	0.921681i	$-0.626816\pi$
$857$	17.6884	−	30.6373i	0.604226	−	1.04655i	0.992173	−	0.124868i	$-0.0398508\pi$
$858$	3.18197	−	5.51134i	0.108631	−	0.188154i
$859$	−13.9684	+	24.1941i	−0.476597	+	0.825491i	−0.999640	−	0.0268155i	$-0.991463\pi$
$859$	−13.9684	+	24.1941i	−0.476597	+	0.825491i	0.523043	+	0.852306i	$0.324797\pi$
$860$	0.870452			0.0296822
$861$	−9.95924	−	17.2499i	−0.339410	−	0.587875i
$862$	−23.8947	−	41.3868i	−0.813855	−	1.40964i
$863$	−9.76241	+	16.9090i	−0.332316	+	0.575589i	−0.982966	−	0.183790i	$-0.941163\pi$
$863$	−9.76241	+	16.9090i	−0.332316	+	0.575589i	0.650649	+	0.759378i	$0.274497\pi$
$864$	17.7085			0.602455
$865$	−26.2272	−	45.4268i	−0.891752	−	1.54456i
$866$	−41.7765			−1.41962
$867$	47.5373			1.61445
$868$	4.65295	−	1.88541i	0.157931	−	0.0639950i
$869$	−17.6366			−0.598280
$870$	−81.9659			−2.77890
$871$	−7.31479	−	12.6696i	−0.247852	−	0.429292i
$872$	48.4734			1.64152
$873$	25.7294	−	44.5646i	0.870808	−	1.50828i
$874$	−9.65912	−	16.7301i	−0.326725	−	0.565904i
$875$	−5.65045	−	9.78687i	−0.191020	−	0.330856i
$876$	−20.0464			−0.677305
$877$	7.69397	−	13.3264i	0.259807	−	0.449999i	−0.706383	−	0.707830i	$-0.749674\pi$
$877$	7.69397	−	13.3264i	0.259807	−	0.449999i	0.966190	+	0.257831i	$0.0830077\pi$
$878$	−26.8551	+	46.5144i	−0.906315	+	1.56978i
$879$	−13.7368	+	23.7927i	−0.463329	+	0.802510i
$880$	11.4413	+	19.8169i	0.385686	+	0.668027i
$881$	−5.76081	+	9.97802i	−0.194087	+	0.336168i	−0.946601	−	0.322408i	$-0.895508\pi$
$881$	−5.76081	+	9.97802i	−0.194087	+	0.336168i	0.752514	+	0.658576i	$0.228841\pi$
$882$	15.3370	+	26.5645i	0.516425	+	0.894474i
$883$	−49.0959			−1.65221			−0.826104	−	0.563517i	$-0.809448\pi$
$883$	−49.0959			−1.65221			−0.826104	+	0.563517i	$0.809448\pi$
$884$	0.330673			0.0111217
$885$	53.3853	+	92.4660i	1.79453	+	3.10821i
$886$	23.4204	−	40.5653i	0.786823	−	1.36282i
$887$	−8.89724	−	15.4105i	−0.298740	−	0.517433i	0.677108	−	0.735884i	$-0.263233\pi$
$887$	−8.89724	−	15.4105i	−0.298740	−	0.517433i	−0.975848	+	0.218451i	$0.929900\pi$
$888$	−27.6329	+	47.8616i	−0.927300	+	1.60613i
$889$	−3.52006	+	6.09693i	−0.118059	+	0.204484i
$890$	26.3474	−	45.6351i	0.883168	−	1.52969i
$891$	−3.88141			−0.130032
$892$	3.04484	+	5.27382i	0.101949	+	0.176580i
$893$	8.42366	+	14.5902i	0.281887	+	0.488243i
$894$	−1.29691	+	2.24631i	−0.0433751	+	0.0751279i
$895$	16.1672			0.540409
$896$	12.3803	+	21.4434i	0.413598	+	0.716372i
$897$	−18.7734			−0.626824
$898$	10.0506			0.335394
$899$	−4.04432	+	28.9905i	−0.134886	+	0.966886i
$900$	17.7333			0.591111
$901$	−4.66832			−0.155524
$902$	4.23350	+	7.33264i	0.140960	+	0.244150i
$903$	−2.65982			−0.0885132
$904$	22.9447	−	39.7415i	0.763131	−	1.32178i
$905$	3.53591	+	6.12438i	0.117538	+	0.203581i
$906$	17.6389	+	30.5515i	0.586014	+	1.01501i
$907$	19.4499			0.645823			0.322911	−	0.946429i	$-0.395338\pi$
$907$	19.4499			0.645823			0.322911	+	0.946429i	$0.395338\pi$
$908$	−1.45855	+	2.52628i	−0.0484036	+	0.0838374i
$909$	−5.59723	+	9.69469i	−0.185648	+	0.321553i
$910$	4.93055	−	8.53997i	0.163446	−	0.283097i
$911$	8.79004	+	15.2248i	0.291227	+	0.504420i	0.974100	−	0.226117i	$-0.0726032\pi$
$911$	8.79004	+	15.2248i	0.291227	+	0.504420i	−0.682873	+	0.730537i	$0.739270\pi$
$912$	12.7420	−	22.0697i	0.421928	−	0.730801i
$913$	1.24695	+	2.15978i	0.0412681	+	0.0714784i
$914$	−25.7512			−0.851774
$915$	75.2224			2.48678
$916$	−5.76841	−	9.99119i	−0.190594	−	0.330118i
$917$	3.29998	−	5.71573i	0.108975	−	0.188750i
$918$	−3.38977	−	5.87125i	−0.111879	−	0.193780i
$919$	−24.2220	+	41.9538i	−0.799011	+	1.38393i	0.121250	+	0.992622i	$0.461310\pi$
$919$	−24.2220	+	41.9538i	−0.799011	+	1.38393i	−0.920261	+	0.391306i	$0.872023\pi$
$920$	26.6900	−	46.2284i	0.879942	−	1.52410i
$921$	−9.90039	+	17.1480i	−0.326229	+	0.565045i
$922$	−17.4257			−0.573884
$923$	1.40295	+	2.42998i	0.0461787	+	0.0799838i
$924$	1.81589	+	3.14521i	0.0597382	+	0.103470i
$925$	−27.5924	+	47.7914i	−0.907233	+	1.57137i
$926$	21.7592			0.715053
$927$	19.4478	+	33.6845i	0.638748	+	1.10634i
$928$	14.4500			0.474344
$929$	16.2643			0.533614			0.266807	−	0.963750i	$-0.414031\pi$
$929$	16.2643			0.533614			0.266807	+	0.963750i	$0.414031\pi$
$930$	11.9939	−	85.9743i	0.393295	−	2.81921i
$931$	6.92264			0.226880
$932$	−4.57286			−0.149789
$933$	−10.9282	−	18.9281i	−0.357772	−	0.619679i
$934$	3.87073			0.126654
$935$	1.60531	−	2.78047i	0.0524992	−	0.0909312i
$936$	−6.22860	−	10.7882i	−0.203588	−	0.352625i
$937$	−28.2294	−	48.8947i	−0.922213	−	1.59732i	−0.795983	−	0.605319i	$-0.793045\pi$
$937$	−28.2294	−	48.8947i	−0.922213	−	1.59732i	−0.126230	−	0.992001i	$-0.540288\pi$
$938$	41.9777			1.37062
$939$	37.5146	−	64.9772i	1.22424	−	2.12045i
$940$	7.68697	−	13.3142i	0.250721	−	0.434262i
$941$	−26.3763	+	45.6852i	−0.859844	+	1.48929i	0.0122327	+	0.999925i	$0.496106\pi$
$941$	−26.3763	+	45.6852i	−0.859844	+	1.48929i	−0.872077	+	0.489369i	$0.837227\pi$
$942$	43.5213	+	75.3811i	1.41800	+	2.45605i
$943$	12.4886	−	21.6310i	0.406686	−	0.704401i
$944$	−25.6797	−	44.4786i	−0.835805	−	1.44766i
$945$	−40.2098			−1.30802
$946$	1.13064			0.0367604
$947$	−10.5396	−	18.2551i	−0.342491	−	0.593211i	0.642404	−	0.766366i	$-0.277937\pi$
$947$	−10.5396	−	18.2551i	−0.342491	−	0.593211i	−0.984895	+	0.173155i	$0.944604\pi$
$948$	8.96189	−	15.5225i	0.291069	−	0.504146i
$949$	7.03071	+	12.1775i	0.228226	+	0.395300i
$950$	10.0614	−	17.4268i	0.326434	−	0.565399i
$951$	0.123129	−	0.213265i	0.00399272	−	0.00691560i
$952$	1.43652	−	2.48812i	0.0465579	−	0.0806406i
$953$	−7.38603			−0.239257			−0.119629	−	0.992819i	$-0.538170\pi$
$953$	−7.38603			−0.239257			−0.119629	+	0.992819i	$0.538170\pi$
$954$	−29.0400	−	50.2988i	−0.940205	−	1.62848i
$955$	20.1693	+	34.9342i	0.652662	+	1.13044i
$956$	−4.37728	+	7.58167i	−0.141571	+	0.245209i
$957$	−21.1748			−0.684483
$958$	−10.4175	−	18.0436i	−0.336574	−	0.582964i
$959$	−39.0155			−1.25988
$960$	50.8191			1.64018
$961$	−29.8164	−	8.48421i	−0.961820	−	0.273684i
$962$	−12.8025			−0.412768
$963$	35.7165			1.15095
$964$	−6.00868	−	10.4073i	−0.193527	−	0.335198i
$965$	47.2516			1.52108
$966$	26.9339	−	46.6509i	0.866584	−	1.50097i
$967$	2.92773	+	5.07097i	0.0941494	+	0.163071i	0.909253	−	0.416243i	$-0.136654\pi$
$967$	2.92773	+	5.07097i	0.0941494	+	0.163071i	−0.815104	+	0.579315i	$0.803320\pi$
$968$	−10.7282	−	18.5818i	−0.344818	−	0.597242i
$969$	−3.57560			−0.114865
$970$	−26.6428	+	46.1467i	−0.855449	+	1.48168i
$971$	−5.41451	+	9.37821i	−0.173760	+	0.300961i	−0.939731	−	0.341914i	$-0.888925\pi$
$971$	−5.41451	+	9.37821i	−0.173760	+	0.300961i	0.765972	+	0.642875i	$0.222258\pi$
$972$	−2.82619	+	4.89511i	−0.0906502	+	0.157011i
$973$	−3.31109	−	5.73498i	−0.106149	−	0.183855i
$974$	19.5825	−	33.9179i	0.627464	−	1.08680i
$975$	−9.77757	−	16.9352i	−0.313133	−	0.542362i
$976$	−36.1840			−1.15822
$977$	53.3456			1.70668			0.853338	−	0.521358i	$-0.174574\pi$
$977$	53.3456			1.70668			0.853338	+	0.521358i	$0.174574\pi$
$978$	36.4291	+	63.0970i	1.16487	+	2.01762i
$979$	6.80650	−	11.7892i	0.217537	−	0.376785i
$980$	−3.15861	−	5.47088i	−0.100898	−	0.174761i
$981$	53.5014	−	92.6671i	1.70817	−	2.95863i
$982$	18.4479	−	31.9528i	0.588697	−	1.01965i
$983$	2.23918	−	3.87837i	0.0714187	−	0.123701i	−0.828105	−	0.560574i	$-0.810581\pi$
$983$	2.23918	−	3.87837i	0.0714187	−	0.123701i	0.899523	+	0.436873i	$0.143914\pi$
$984$	26.0556			0.830623
$985$	−27.3013	−	47.2872i	−0.869891	−	1.50670i
$986$	−2.76602	−	4.79089i	−0.0880881	−	0.152573i
$987$	−23.4889	+	40.6839i	−0.747660	+	1.29498i
$988$	0.928464			0.0295384
$989$	−1.66767	−	2.88850i	−0.0530289	−	0.0918488i
$990$	39.9442			1.26951
$991$	−8.43787			−0.268038			−0.134019	−	0.990979i	$-0.542788\pi$
$991$	−8.43787			−0.268038			−0.134019	+	0.990979i	$0.542788\pi$
$992$	−2.11443	+	15.1566i	−0.0671333	+	0.481224i
$993$	61.5981			1.95476
$994$	−8.05118			−0.255368
$995$	1.62255	+	2.81034i	0.0514382	+	0.0890937i
$996$	−2.53452			−0.0803092
$997$	−5.13043	+	8.88616i	−0.162482	+	0.281427i	−0.935758	−	0.352642i	$-0.885283\pi$
$997$	−5.13043	+	8.88616i	−0.162482	+	0.281427i	0.773276	+	0.634069i	$0.218617\pi$
$998$	3.36586	+	5.82984i	0.106544	+	0.184540i
$999$	26.1017	+	45.2095i	0.825822	+	1.43037i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.h.a.118.13	✓	30
31.5	even	3	inner	403.2.h.a.222.13	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.h.a.118.13	✓	30	1.1	even	1	trivial
403.2.h.a.222.13	yes	30	31.5	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.58004 q^{2} +(1.43561 + 2.48655i) q^{3} +0.496524 q^{4} +(1.71834 - 2.97625i) q^{5} +(2.26832 + 3.92885i) q^{6} +(0.908007 + 1.57271i) q^{7} -2.37555 q^{8} +(-2.62196 + 4.54137i) q^{9} +O(q^{10})\)	\(q+1.58004 q^{2} +(1.43561 + 2.48655i) q^{3} +0.496524 q^{4} +(1.71834 - 2.97625i) q^{5} +(2.26832 + 3.92885i) q^{6} +(0.908007 + 1.57271i) q^{7} -2.37555 q^{8} +(-2.62196 + 4.54137i) q^{9} +(2.71504 - 4.70259i) q^{10} +(0.701394 - 1.21485i) q^{11} +(0.712816 + 1.23463i) q^{12} +(0.500000 - 0.866025i) q^{13} +(1.43469 + 2.48495i) q^{14} +9.86746 q^{15} -4.74651 q^{16} +(0.332988 + 0.576751i) q^{17} +(-4.14280 + 7.17554i) q^{18} +(0.934963 + 1.61940i) q^{19} +(0.853196 - 1.47778i) q^{20} +(-2.60709 + 4.51561i) q^{21} +(1.10823 - 1.91951i) q^{22} -6.53846 q^{23} +(-3.41037 - 5.90693i) q^{24} +(-3.40537 - 5.89827i) q^{25} +(0.790020 - 1.36835i) q^{26} -6.44279 q^{27} +(0.450848 + 0.780891i) q^{28} -5.25726 q^{29} +15.5910 q^{30} +(0.769283 - 5.51436i) q^{31} -2.74857 q^{32} +4.02771 q^{33} +(0.526133 + 0.911290i) q^{34} +6.24105 q^{35} +(-1.30187 + 2.25490i) q^{36} +(-4.05131 - 7.01707i) q^{37} +(1.47728 + 2.55872i) q^{38} +2.87122 q^{39} +(-4.08200 + 7.07023i) q^{40} +(-1.91003 + 3.30827i) q^{41} +(-4.11931 + 7.13485i) q^{42} +(0.255056 + 0.441770i) q^{43} +(0.348259 - 0.603202i) q^{44} +(9.01082 + 15.6072i) q^{45} -10.3310 q^{46} +9.00962 q^{47} +(-6.81415 - 11.8024i) q^{48} +(1.85105 - 3.20611i) q^{49} +(-5.38062 - 9.31950i) q^{50} +(-0.956081 + 1.65598i) q^{51} +(0.248262 - 0.430003i) q^{52} +(-3.50488 + 6.07063i) q^{53} -10.1799 q^{54} +(-2.41046 - 4.17504i) q^{55} +(-2.15702 - 3.73606i) q^{56} +(-2.68449 + 4.64967i) q^{57} -8.30668 q^{58} +(5.41024 + 9.37080i) q^{59} +4.89943 q^{60} +7.62328 q^{61} +(1.21550 - 8.71291i) q^{62} -9.52303 q^{63} +5.15017 q^{64} +(-1.71834 - 2.97625i) q^{65} +6.36395 q^{66} +(7.31479 - 12.6696i) q^{67} +(0.165336 + 0.286371i) q^{68} +(-9.38668 - 16.2582i) q^{69} +9.86111 q^{70} +(-1.40295 + 2.42998i) q^{71} +(6.22860 - 10.7882i) q^{72} +(-7.03071 + 12.1775i) q^{73} +(-6.40123 - 11.0873i) q^{74} +(9.77757 - 16.9352i) q^{75} +(0.464232 + 0.804073i) q^{76} +2.54748 q^{77} +4.53664 q^{78} +(-6.28626 - 10.8881i) q^{79} +(-8.15611 + 14.1268i) q^{80} +(-1.38346 - 2.39623i) q^{81} +(-3.01792 + 5.22719i) q^{82} +(-0.888910 + 1.53964i) q^{83} +(-1.29448 + 2.24211i) q^{84} +2.28874 q^{85} +(0.402999 + 0.698015i) q^{86} +(-7.54739 - 13.0725i) q^{87} +(-1.66620 + 2.88594i) q^{88} +9.70425 q^{89} +(14.2375 + 24.6600i) q^{90} +1.81601 q^{91} -3.24650 q^{92} +(14.8161 - 6.00362i) q^{93} +14.2356 q^{94} +6.42633 q^{95} +(-3.94588 - 6.83447i) q^{96} -9.81304 q^{97} +(2.92473 - 5.06577i) q^{98} +(3.67805 + 6.37057i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 6 q^{2} - 2 q^{3} + 22 q^{4} + 7 q^{5} + 6 q^{7} - 24 q^{8} - 13 q^{9}+O(q^{10}) \) 30 * q - 6 * q^2 - 2 * q^3 + 22 * q^4 + 7 * q^5 + 6 * q^7 - 24 * q^8 - 13 * q^9	\( 30 q - 6 q^{2} - 2 q^{3} + 22 q^{4} + 7 q^{5} + 6 q^{7} - 24 q^{8} - 13 q^{9} - 3 q^{10} - 3 q^{11} + 12 q^{12} + 15 q^{13} + 3 q^{14} + 4 q^{15} + 22 q^{16} + 4 q^{17} - 6 q^{18} + 5 q^{19} + 10 q^{20} - 15 q^{21} + 2 q^{22} - 6 q^{23} - 6 q^{24} - 20 q^{25} - 3 q^{26} + 4 q^{27} + 13 q^{28} + 26 q^{29} + 28 q^{30} + 19 q^{31} - 74 q^{32} + 2 q^{33} - 21 q^{34} - 30 q^{35} + 37 q^{36} - 4 q^{37} - 4 q^{38} - 4 q^{39} - 17 q^{40} + 7 q^{41} + 44 q^{42} + 15 q^{43} - 70 q^{44} + 15 q^{45} - 58 q^{46} - 24 q^{47} + 31 q^{48} - 29 q^{49} + 2 q^{50} + 25 q^{51} + 11 q^{52} + 4 q^{53} + 34 q^{54} + 13 q^{55} - 41 q^{56} + 8 q^{57} - 46 q^{58} + 27 q^{59} + 78 q^{60} + 8 q^{61} + 20 q^{62} - 112 q^{63} + 60 q^{64} - 7 q^{65} + 60 q^{66} + 29 q^{67} + 41 q^{68} - 23 q^{69} - 112 q^{70} + 29 q^{71} + 14 q^{72} - 10 q^{73} + 25 q^{74} - 18 q^{75} + 24 q^{76} - 72 q^{77} + 9 q^{79} - 11 q^{81} - 38 q^{82} - 13 q^{83} - 62 q^{84} + 108 q^{85} - 38 q^{86} - 18 q^{87} + 32 q^{88} + 6 q^{89} + 7 q^{90} + 12 q^{91} + 2 q^{92} + 37 q^{93} - 154 q^{94} - 28 q^{95} - 105 q^{96} - 84 q^{97} + 50 q^{98} + 10 q^{99}+O(q^{100}) \) 30 * q - 6 * q^2 - 2 * q^3 + 22 * q^4 + 7 * q^5 + 6 * q^7 - 24 * q^8 - 13 * q^9 - 3 * q^10 - 3 * q^11 + 12 * q^12 + 15 * q^13 + 3 * q^14 + 4 * q^15 + 22 * q^16 + 4 * q^17 - 6 * q^18 + 5 * q^19 + 10 * q^20 - 15 * q^21 + 2 * q^22 - 6 * q^23 - 6 * q^24 - 20 * q^25 - 3 * q^26 + 4 * q^27 + 13 * q^28 + 26 * q^29 + 28 * q^30 + 19 * q^31 - 74 * q^32 + 2 * q^33 - 21 * q^34 - 30 * q^35 + 37 * q^36 - 4 * q^37 - 4 * q^38 - 4 * q^39 - 17 * q^40 + 7 * q^41 + 44 * q^42 + 15 * q^43 - 70 * q^44 + 15 * q^45 - 58 * q^46 - 24 * q^47 + 31 * q^48 - 29 * q^49 + 2 * q^50 + 25 * q^51 + 11 * q^52 + 4 * q^53 + 34 * q^54 + 13 * q^55 - 41 * q^56 + 8 * q^57 - 46 * q^58 + 27 * q^59 + 78 * q^60 + 8 * q^61 + 20 * q^62 - 112 * q^63 + 60 * q^64 - 7 * q^65 + 60 * q^66 + 29 * q^67 + 41 * q^68 - 23 * q^69 - 112 * q^70 + 29 * q^71 + 14 * q^72 - 10 * q^73 + 25 * q^74 - 18 * q^75 + 24 * q^76 - 72 * q^77 + 9 * q^79 - 11 * q^81 - 38 * q^82 - 13 * q^83 - 62 * q^84 + 108 * q^85 - 38 * q^86 - 18 * q^87 + 32 * q^88 + 6 * q^89 + 7 * q^90 + 12 * q^91 + 2 * q^92 + 37 * q^93 - 154 * q^94 - 28 * q^95 - 105 * q^96 - 84 * q^97 + 50 * q^98 + 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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