LMFDB - Embedded newform 403.2.e.a.191.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(191,403)]

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([4, 4]))

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

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

chi := DirichletCharacter("403.191");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.e (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:	$70$
Relative dimension:	$35$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			191.11
Character	$\chi$	$=$	403.191
Dual form			403.2.e.a.211.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.770644 + 1.33479i) q^{2} +(-0.329492 - 0.570697i) q^{3} +(-0.187783 - 0.325250i) q^{4} +(-0.614094 - 1.06364i) q^{5} +1.01568 q^{6} +0.583300 q^{7} -2.50372 q^{8} +(1.28287 - 2.22200i) q^{9} +O(q^{10})$	\(q+(-0.770644 + 1.33479i) q^{2} +(-0.329492 - 0.570697i) q^{3} +(-0.187783 - 0.325250i) q^{4} +(-0.614094 - 1.06364i) q^{5} +1.01568 q^{6} +0.583300 q^{7} -2.50372 q^{8} +(1.28287 - 2.22200i) q^{9} +1.89299 q^{10} +2.12773 q^{11} +(-0.123746 + 0.214334i) q^{12} +(-1.53824 - 3.26095i) q^{13} +(-0.449516 + 0.778585i) q^{14} +(-0.404678 + 0.700923i) q^{15} +(2.30504 - 3.99245i) q^{16} -1.62931 q^{17} +(1.97727 + 3.42473i) q^{18} +6.44171 q^{19} +(-0.230633 + 0.399468i) q^{20} +(-0.192193 - 0.332887i) q^{21} +(-1.63972 + 2.84008i) q^{22} +(-0.0727100 + 0.125937i) q^{23} +(0.824956 + 1.42887i) q^{24} +(1.74578 - 3.02377i) q^{25} +(5.53814 + 0.459797i) q^{26} -3.66773 q^{27} +(-0.109534 - 0.189718i) q^{28} +(1.56261 - 2.70652i) q^{29} +(-0.623725 - 1.08032i) q^{30} +(4.19465 - 3.66127i) q^{31} +(1.04901 + 1.81694i) q^{32} +(-0.701069 - 1.21429i) q^{33} +(1.25562 - 2.17480i) q^{34} +(-0.358201 - 0.620422i) q^{35} -0.963605 q^{36} +(5.07722 + 8.79400i) q^{37} +(-4.96427 + 8.59836i) q^{38} +(-1.35418 + 1.95233i) q^{39} +(1.53752 + 2.66306i) q^{40} +0.420077 q^{41} +0.592448 q^{42} -0.227647 q^{43} +(-0.399551 - 0.692043i) q^{44} -3.15121 q^{45} +(-0.112067 - 0.194106i) q^{46} +5.46942 q^{47} -3.03797 q^{48} -6.65976 q^{49} +(2.69074 + 4.66050i) q^{50} +(0.536846 + 0.929844i) q^{51} +(-0.771768 + 1.11266i) q^{52} +(0.615895 + 1.06676i) q^{53} +(2.82652 - 4.89567i) q^{54} +(-1.30662 - 2.26314i) q^{55} -1.46042 q^{56} +(-2.12249 - 3.67627i) q^{57} +(2.40843 + 4.17153i) q^{58} -3.67966 q^{59} +0.303967 q^{60} +(-2.45004 - 4.24359i) q^{61} +(1.65446 + 8.42053i) q^{62} +(0.748298 - 1.29609i) q^{63} +5.98651 q^{64} +(-2.52386 + 3.63867i) q^{65} +2.16110 q^{66} -1.87935 q^{67} +(0.305957 + 0.529934i) q^{68} +0.0958295 q^{69} +1.10418 q^{70} +(-1.32116 + 2.28831i) q^{71} +(-3.21195 + 5.56325i) q^{72} +(-1.40947 - 2.44127i) q^{73} -15.6509 q^{74} -2.30088 q^{75} +(-1.20964 - 2.09517i) q^{76} +1.24110 q^{77} +(-1.56237 - 3.31210i) q^{78} +(2.90930 - 5.03905i) q^{79} -5.66205 q^{80} +(-2.64012 - 4.57282i) q^{81} +(-0.323730 + 0.560717i) q^{82} +(-7.89739 - 13.6787i) q^{83} +(-0.0721810 + 0.125021i) q^{84} +(1.00055 + 1.73301i) q^{85} +(0.175435 - 0.303862i) q^{86} -2.05947 q^{87} -5.32723 q^{88} +(-8.66712 + 15.0119i) q^{89} +(2.42846 - 4.20622i) q^{90} +(-0.897256 - 1.90211i) q^{91} +0.0546148 q^{92} +(-3.47158 - 1.18751i) q^{93} +(-4.21497 + 7.30055i) q^{94} +(-3.95582 - 6.85168i) q^{95} +(0.691282 - 1.19733i) q^{96} +(2.93445 + 5.08262i) q^{97} +(5.13230 - 8.88941i) q^{98} +(2.72960 - 4.72780i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 70 q - 2 q^{2} + 4 q^{3} - 34 q^{4} - 2 q^{5} + 8 q^{7} - 6 q^{8} - 29 q^{9}+O(q^{10}) $ 70 * q - 2 * q^2 + 4 * q^3 - 34 * q^4 - 2 * q^5 + 8 * q^7 - 6 * q^8 - 29 * q^9	\( 70 q - 2 q^{2} + 4 q^{3} - 34 q^{4} - 2 q^{5} + 8 q^{7} - 6 q^{8} - 29 q^{9} - 6 q^{10} - 4 q^{11} + 5 q^{12} + q^{13} - 10 q^{14} + q^{15} - 28 q^{16} - 28 q^{17} - 20 q^{18} + 4 q^{19} + 25 q^{20} - 21 q^{21} + 4 q^{22} + 2 q^{23} + 4 q^{24} - 23 q^{25} - 24 q^{26} - 38 q^{27} - 21 q^{28} + 6 q^{29} + 31 q^{30} + 22 q^{31} + 14 q^{32} + 2 q^{33} - 11 q^{34} + 4 q^{35} + 56 q^{36} - 12 q^{37} - 7 q^{38} + 10 q^{39} - q^{40} + 4 q^{41} - 54 q^{42} + 2 q^{43} + 2 q^{44} + 58 q^{45} + 14 q^{46} - 2 q^{48} + 74 q^{49} + 7 q^{50} - 9 q^{51} + 5 q^{52} - 2 q^{53} + 24 q^{54} + 5 q^{55} + 26 q^{56} - q^{57} + 6 q^{58} - 42 q^{59} + 18 q^{60} - 3 q^{61} + 13 q^{62} - 32 q^{63} - 14 q^{64} + 20 q^{65} - 28 q^{66} + 4 q^{67} + 42 q^{68} - 64 q^{69} - 14 q^{70} + 43 q^{71} - 5 q^{72} + 11 q^{73} + 14 q^{74} - 74 q^{75} - 28 q^{76} - 10 q^{77} - 64 q^{78} + 2 q^{79} - 76 q^{80} - 11 q^{81} - 17 q^{82} + 56 q^{83} - 45 q^{84} - 5 q^{85} + 54 q^{86} + 48 q^{87} - 8 q^{88} + 30 q^{89} - 23 q^{90} - 36 q^{91} + 74 q^{92} + 22 q^{93} + 47 q^{94} - 9 q^{95} + 26 q^{96} + 29 q^{97} + 12 q^{98} + 3 q^{99}+O(q^{100}) \) 70 * q - 2 * q^2 + 4 * q^3 - 34 * q^4 - 2 * q^5 + 8 * q^7 - 6 * q^8 - 29 * q^9 - 6 * q^10 - 4 * q^11 + 5 * q^12 + q^13 - 10 * q^14 + q^15 - 28 * q^16 - 28 * q^17 - 20 * q^18 + 4 * q^19 + 25 * q^20 - 21 * q^21 + 4 * q^22 + 2 * q^23 + 4 * q^24 - 23 * q^25 - 24 * q^26 - 38 * q^27 - 21 * q^28 + 6 * q^29 + 31 * q^30 + 22 * q^31 + 14 * q^32 + 2 * q^33 - 11 * q^34 + 4 * q^35 + 56 * q^36 - 12 * q^37 - 7 * q^38 + 10 * q^39 - q^40 + 4 * q^41 - 54 * q^42 + 2 * q^43 + 2 * q^44 + 58 * q^45 + 14 * q^46 - 2 * q^48 + 74 * q^49 + 7 * q^50 - 9 * q^51 + 5 * q^52 - 2 * q^53 + 24 * q^54 + 5 * q^55 + 26 * q^56 - q^57 + 6 * q^58 - 42 * q^59 + 18 * q^60 - 3 * q^61 + 13 * q^62 - 32 * q^63 - 14 * q^64 + 20 * q^65 - 28 * q^66 + 4 * q^67 + 42 * q^68 - 64 * q^69 - 14 * q^70 + 43 * q^71 - 5 * q^72 + 11 * q^73 + 14 * q^74 - 74 * q^75 - 28 * q^76 - 10 * q^77 - 64 * q^78 + 2 * q^79 - 76 * q^80 - 11 * q^81 - 17 * q^82 + 56 * q^83 - 45 * q^84 - 5 * q^85 + 54 * q^86 + 48 * q^87 - 8 * q^88 + 30 * q^89 - 23 * q^90 - 36 * q^91 + 74 * q^92 + 22 * q^93 + 47 * q^94 - 9 * q^95 + 26 * q^96 + 29 * q^97 + 12 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$249$	$313$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.770644	+	1.33479i	−0.544927	+	0.943842i	0.453684	+	0.891163i	$0.350109\pi$
$2$	−0.770644	+	1.33479i	−0.544927	+	0.943842i	−0.998611	+	0.0526792i	$0.983224\pi$
$3$	−0.329492	−	0.570697i	−0.190232	−	0.329492i	0.755095	−	0.655616i	$-0.227591\pi$
$3$	−0.329492	−	0.570697i	−0.190232	−	0.329492i	−0.945327	+	0.326124i	$0.894257\pi$
$4$	−0.187783	−	0.325250i	−0.0938915	−	0.162625i
$5$	−0.614094	−	1.06364i	−0.274631	−	0.475675i	0.695411	−	0.718612i	$-0.255222\pi$
$5$	−0.614094	−	1.06364i	−0.274631	−	0.475675i	−0.970042	+	0.242937i	$0.921889\pi$
$6$	1.01568			0.414651
$7$	0.583300			0.220467			0.110233	−	0.993906i	$-0.464840\pi$
$7$	0.583300			0.220467			0.110233	+	0.993906i	$0.464840\pi$
$8$	−2.50372			−0.885198
$9$	1.28287	−	2.22200i	0.427623	−	0.740665i
$10$	1.89299			0.598616
$11$	2.12773			0.641534			0.320767	−	0.947158i	$-0.396059\pi$
$11$	2.12773			0.641534			0.320767	+	0.947158i	$0.396059\pi$
$12$	−0.123746	+	0.214334i	−0.0357224	+	0.0618730i
$13$	−1.53824	−	3.26095i	−0.426631	−	0.904426i
$13$	−1.53824	−	3.26095i	−0.426631	−	0.904426i
$14$	−0.449516	+	0.778585i	−0.120138	+	0.208086i
$15$	−0.404678	+	0.700923i	−0.104487	+	0.180978i
$16$	2.30504	−	3.99245i	0.576260	−	0.998112i
$17$	−1.62931			−0.395167			−0.197583	−	0.980286i	$-0.563309\pi$
$17$	−1.62931			−0.395167			−0.197583	+	0.980286i	$0.563309\pi$
$18$	1.97727	+	3.42473i	0.466047	+	0.807217i
$19$	6.44171			1.47783			0.738915	−	0.673798i	$-0.235338\pi$
$19$	6.44171			1.47783			0.738915	+	0.673798i	$0.235338\pi$
$20$	−0.230633	+	0.399468i	−0.0515711	+	0.0893237i
$21$	−0.192193	−	0.332887i	−0.0419399	−	0.0726420i
$22$	−1.63972	+	2.84008i	−0.349589	+	0.605507i
$23$	−0.0727100	+	0.125937i	−0.0151611	+	0.0262598i	−0.873506	−	0.486813i	$-0.838159\pi$
$23$	−0.0727100	+	0.125937i	−0.0151611	+	0.0262598i	0.858345	+	0.513072i	$0.171493\pi$
$24$	0.824956	+	1.42887i	0.168393	+	0.291666i
$25$	1.74578	−	3.02377i	0.349155	−	0.604755i
$26$	5.53814	+	0.459797i	1.08612	+	0.0901736i
$27$	−3.66773			−0.705856
$28$	−0.109534	−	0.189718i	−0.0206999	−	0.0358533i
$29$	1.56261	−	2.70652i	0.290170	−	0.502589i	−0.683680	−	0.729782i	$-0.739622\pi$
$29$	1.56261	−	2.70652i	0.290170	−	0.502589i	0.973850	+	0.227193i	$0.0729549\pi$
$30$	−0.623725	−	1.08032i	−0.113876	−	0.197239i
$31$	4.19465	−	3.66127i	0.753381	−	0.657584i
$31$	4.19465	−	3.66127i	0.753381	−	0.657584i
$32$	1.04901	+	1.81694i	0.185441	+	0.321193i
$33$	−0.701069	−	1.21429i	−0.122041	−	0.211380i
$34$	1.25562	−	2.17480i	0.215337	−	0.372975i
$35$	−0.358201	−	0.620422i	−0.0605470	−	0.104870i
$36$	−0.963605			−0.160601
$37$	5.07722	+	8.79400i	0.834689	+	1.44572i	0.894283	+	0.447502i	$0.147686\pi$
$37$	5.07722	+	8.79400i	0.834689	+	1.44572i	−0.0595938	+	0.998223i	$0.518981\pi$
$38$	−4.96427	+	8.59836i	−0.805310	+	1.39484i
$39$	−1.35418	+	1.95233i	−0.216842	+	0.312623i
$40$	1.53752	+	2.66306i	0.243103	+	0.421067i
$41$	0.420077			0.0656051			0.0328025	−	0.999462i	$-0.489557\pi$
$41$	0.420077			0.0656051			0.0328025	+	0.999462i	$0.489557\pi$
$42$	0.592448			0.0914167
$43$	−0.227647			−0.0347158			−0.0173579	−	0.999849i	$-0.505525\pi$
$43$	−0.227647			−0.0347158			−0.0173579	+	0.999849i	$0.505525\pi$
$44$	−0.399551	−	0.692043i	−0.0602346	−	0.104329i
$45$	−3.15121			−0.469755
$46$	−0.112067	−	0.194106i	−0.0165234	−	0.0286193i
$47$	5.46942			0.797797			0.398898	−	0.916995i	$-0.369393\pi$
$47$	5.46942			0.797797			0.398898	+	0.916995i	$0.369393\pi$
$48$	−3.03797			−0.438493
$49$	−6.65976			−0.951395
$50$	2.69074	+	4.66050i	0.380529	+	0.659095i
$51$	0.536846	+	0.929844i	0.0751735	+	0.130204i
$52$	−0.771768	+	1.11266i	−0.107025	+	0.154299i
$53$	0.615895	+	1.06676i	0.0845997	+	0.146531i	0.905221	−	0.424942i	$-0.139706\pi$
$53$	0.615895	+	1.06676i	0.0845997	+	0.146531i	−0.820621	+	0.571473i	$0.806372\pi$
$54$	2.82652	−	4.89567i	0.384640	−	0.666216i
$55$	−1.30662	−	2.26314i	−0.176185	−	0.305162i
$56$	−1.46042			−0.195157
$57$	−2.12249	−	3.67627i	−0.281131	−	0.486933i
$58$	2.40843	+	4.17153i	0.316243	+	0.547749i
$59$	−3.67966			−0.479050			−0.239525	−	0.970890i	$-0.576992\pi$
$59$	−3.67966			−0.479050			−0.239525	+	0.970890i	$0.576992\pi$
$60$	0.303967			0.0392420
$61$	−2.45004	−	4.24359i	−0.313695	−	0.543336i	0.665464	−	0.746430i	$-0.268234\pi$
$61$	−2.45004	−	4.24359i	−0.313695	−	0.543336i	−0.979159	+	0.203094i	$0.934900\pi$
$62$	1.65446	+	8.42053i	0.210117	+	1.06941i
$63$	0.748298	−	1.29609i	0.0942766	−	0.163292i
$64$	5.98651			0.748314
$65$	−2.52386	+	3.63867i	−0.313047	+	0.451322i
$66$	2.16110			0.266013
$67$	−1.87935			−0.229599			−0.114799	−	0.993389i	$-0.536623\pi$
$67$	−1.87935			−0.229599			−0.114799	+	0.993389i	$0.536623\pi$
$68$	0.305957	+	0.529934i	0.0371028	+	0.0642639i
$69$	0.0958295			0.0115365
$70$	1.10418			0.131975
$71$	−1.32116	+	2.28831i	−0.156793	+	0.271573i	−0.933710	−	0.358029i	$-0.883449\pi$
$71$	−1.32116	+	2.28831i	−0.156793	+	0.271573i	0.776918	+	0.629602i	$0.216782\pi$
$72$	−3.21195	+	5.56325i	−0.378531	+	0.655636i
$73$	−1.40947	−	2.44127i	−0.164966	−	0.285729i	0.771677	−	0.636014i	$-0.219418\pi$
$73$	−1.40947	−	2.44127i	−0.164966	−	0.285729i	−0.936643	+	0.350285i	$0.886085\pi$
$74$	−15.6509			−1.81938
$75$	−2.30088			−0.265683
$76$	−1.20964	−	2.09517i	−0.138756	−	0.240332i
$77$	1.24110			0.141437
$78$	−1.56237	−	3.31210i	−0.176903	−	0.375021i
$79$	2.90930	−	5.03905i	0.327321	−	0.566937i	−0.654658	−	0.755925i	$-0.727187\pi$
$79$	2.90930	−	5.03905i	0.327321	−	0.566937i	0.981979	+	0.188988i	$0.0605207\pi$
$80$	−5.66205			−0.633036
$81$	−2.64012	−	4.57282i	−0.293347	−	0.508091i
$82$	−0.323730	+	0.560717i	−0.0357500	+	0.0619208i
$83$	−7.89739	−	13.6787i	−0.866851	−	1.50143i	−0.865197	−	0.501431i	$-0.832807\pi$
$83$	−7.89739	−	13.6787i	−0.866851	−	1.50143i	−0.00165351	−	0.999999i	$-0.500526\pi$
$84$	−0.0721810	+	0.125021i	−0.00787559	+	0.0136409i
$85$	1.00055	+	1.73301i	0.108525	+	0.187971i
$86$	0.175435	−	0.303862i	0.0189176	−	0.0327663i
$87$	−2.05947			−0.220799
$88$	−5.32723			−0.567885
$89$	−8.66712	+	15.0119i	−0.918713	+	1.59126i	−0.117341	+	0.993092i	$0.537437\pi$
$89$	−8.66712	+	15.0119i	−0.918713	+	1.59126i	−0.801372	+	0.598166i	$0.795896\pi$
$90$	2.42846	−	4.20622i	0.255982	−	0.443374i
$91$	−0.897256	−	1.90211i	−0.0940580	−	0.199396i
$92$	0.0546148			0.00569399
$93$	−3.47158	−	1.18751i	−0.359986	−	0.123139i
$94$	−4.21497	+	7.30055i	−0.434741	+	0.752994i
$95$	−3.95582	−	6.85168i	−0.405858	−	0.702967i
$96$	0.691282	−	1.19733i	0.0705536	−	0.122202i
$97$	2.93445	+	5.08262i	0.297949	+	0.516062i	0.975666	−	0.219260i	$-0.0703643\pi$
$97$	2.93445	+	5.08262i	0.297949	+	0.516062i	−0.677718	+	0.735322i	$0.737031\pi$
$98$	5.13230	−	8.88941i	0.518441	−	0.897966i
$99$	2.72960	−	4.72780i	0.274335	−	0.475162i
$100$	−1.31131			−0.131131
$101$	−0.106315	+	0.184143i	−0.0105787	+	0.0183229i	−0.871266	−	0.490811i	$-0.836701\pi$
$101$	−0.106315	+	0.184143i	−0.0105787	+	0.0183229i	0.860688	+	0.509133i	$0.170034\pi$
$102$	−1.65487			−0.163856
$103$	−6.42073	−	11.1210i	−0.632653	−	1.09579i	−0.987007	−	0.160676i	$-0.948633\pi$
$103$	−6.42073	−	11.1210i	−0.632653	−	1.09579i	0.354354	−	0.935111i	$-0.384701\pi$
$104$	3.85132	+	8.16451i	0.377653	+	0.800596i
$105$	−0.236049	+	0.408848i	−0.0230360	+	0.0398995i
$106$	−1.89854			−0.184403
$107$	−8.25512	−	14.2983i	−0.798053	−	1.38227i	−0.920883	−	0.389840i	$-0.872530\pi$
$107$	−8.25512	−	14.2983i	−0.798053	−	1.38227i	0.122830	−	0.992428i	$-0.460803\pi$
$108$	0.688738	+	1.19293i	0.0662739	+	0.114790i
$109$	18.7165			1.79272			0.896358	−	0.443332i	$-0.146204\pi$
$109$	18.7165			1.79272			0.896358	+	0.443332i	$0.146204\pi$
$110$	4.02777			0.384033
$111$	3.34581	−	5.79511i	0.317570	−	0.550047i
$112$	1.34453	−	2.32879i	0.127046	−	0.220050i
$113$	−2.30676	+	3.99542i	−0.217002	+	0.375858i	−0.953890	−	0.300157i	$-0.902961\pi$
$113$	−2.30676	+	3.99542i	−0.217002	+	0.375858i	0.736888	+	0.676015i	$0.236294\pi$
$114$	6.54274			0.612784
$115$	0.178603			0.0166548
$116$	−1.17373			−0.108978
$117$	−9.21919	−	0.765412i	−0.852314	−	0.0707624i
$118$	2.83570	−	4.91158i	0.261048	−	0.452148i
$119$	−0.950378			−0.0871210
$120$	1.01320	−	1.75492i	0.0924922	−	0.160201i
$121$	−6.47278			−0.588434
$122$	7.55242			0.683764
$123$	−0.138412	−	0.239737i	−0.0124802	−	0.0216164i
$124$	−1.97851	−	0.676784i	−0.177676	−	0.0607770i
$125$	−10.4292			−0.932818
$126$	1.15334	+	1.99765i	0.102748	+	0.177964i
$127$	7.39930	+	12.8160i	0.656582	+	1.13723i	0.981495	+	0.191489i	$0.0613316\pi$
$127$	7.39930	+	12.8160i	0.656582	+	1.13723i	−0.324913	+	0.945744i	$0.605335\pi$
$128$	−6.71149	+	11.6246i	−0.593217	+	1.02748i
$129$	0.0750079	+	0.129917i	0.00660408	+	0.0114386i
$130$	−2.91188	−	6.17295i	−0.255388	−	0.541404i
$131$	−2.89935	+	5.02182i	−0.253317	+	0.438758i	−0.964437	−	0.264312i	$-0.914855\pi$
$131$	−2.89935	+	5.02182i	−0.253317	+	0.438758i	0.711120	+	0.703071i	$0.248188\pi$
$132$	−0.263298	+	0.456045i	−0.0229171	+	0.0396936i
$133$	3.75745			0.325812
$134$	1.44831	−	2.50854i	0.125115	−	0.216705i
$135$	2.25233	+	3.90116i	0.193850	+	0.335758i
$136$	4.07934			0.349801
$137$	−7.67155	+	13.2875i	−0.655424	+	1.13523i	0.326363	+	0.945245i	$0.394177\pi$
$137$	−7.67155	+	13.2875i	−0.655424	+	1.13523i	−0.981787	+	0.189984i	$0.939156\pi$
$138$	−0.0738504	+	0.127913i	−0.00628656	+	0.0108886i
$139$	−1.77751	−	3.07874i	−0.150766	−	0.261135i	0.780743	−	0.624852i	$-0.214841\pi$
$139$	−1.77751	−	3.07874i	−0.150766	−	0.261135i	−0.931509	+	0.363717i	$0.881507\pi$
$140$	−0.134528	+	0.233009i	−0.0113697	+	0.0196929i
$141$	−1.80213	−	3.12138i	−0.151767	−	0.262868i
$142$	−2.03628	−	3.52694i	−0.170881	−	0.295975i
$143$	−3.27296	−	6.93842i	−0.273699	−	0.580220i
$144$	−5.91414	−	10.2436i	−0.492845	−	0.853632i
$145$	−3.83836			−0.318759
$146$	4.34479			0.359578
$147$	2.19434	+	3.80071i	0.180986	+	0.313477i
$148$	1.90683	−	3.30273i	0.156740	−	0.271482i
$149$	−4.15569			−0.340447			−0.170224	−	0.985405i	$-0.554449\pi$
$149$	−4.15569			−0.340447			−0.170224	+	0.985405i	$0.554449\pi$
$150$	1.77316	−	3.07120i	0.144778	−	0.250762i
$151$	−0.226079			−0.0183981			−0.00919904	−	0.999958i	$-0.502928\pi$
$151$	−0.226079			−0.0183981			−0.00919904	+	0.999958i	$0.502928\pi$
$152$	−16.1282			−1.30817
$153$	−2.09020	+	3.62033i	−0.168982	+	0.292686i
$154$	−0.956448	+	1.65662i	−0.0770728	+	0.133494i
$155$	−6.47019	−	2.21324i	−0.519698	−	0.177772i
$156$	0.889286	+	0.0738319i	0.0711998	+	0.00591128i
$157$	17.1033			1.36499			0.682494	−	0.730891i	$-0.260895\pi$
$157$	17.1033			1.36499			0.682494	+	0.730891i	$0.260895\pi$
$158$	4.48406	+	7.76662i	0.356733	+	0.617879i
$159$	0.405865	−	0.702979i	0.0321872	−	0.0557498i
$160$	1.28838	−	2.23154i	0.101856	−	0.176419i
$161$	−0.0424117	+	0.0734593i	−0.00334251	+	0.00578940i
$162$	8.13837			0.639410
$163$	5.05236	+	8.75094i	0.395731	+	0.685427i	0.993194	−	0.116470i	$-0.0371578\pi$
$163$	5.05236	+	8.75094i	0.395731	+	0.685427i	−0.597463	+	0.801897i	$0.703824\pi$
$164$	−0.0788834	−	0.136630i	−0.00615976	−	0.0106690i
$165$	−0.861045	+	1.49137i	−0.0670323	+	0.116103i
$166$	24.3443			1.88948
$167$	10.5755	+	18.3173i	0.818356	+	1.41743i	0.906893	+	0.421361i	$0.138447\pi$
$167$	10.5755	+	18.3173i	0.818356	+	1.41743i	−0.0885375	+	0.996073i	$0.528219\pi$
$168$	0.481196	+	0.833456i	0.0371251	+	0.0643026i
$169$	−8.26763	+	10.0323i	−0.635971	+	0.771713i
$170$	−3.08427			−0.236553
$171$	8.26388	−	14.3135i	0.631955	−	1.09458i
$172$	0.0427482	+	0.0740421i	0.00325952	+	0.00564566i
$173$	1.70370	−	2.95089i	0.129530	−	0.224352i	−0.793965	−	0.607964i	$-0.791987\pi$
$173$	1.70370	−	2.95089i	0.129530	−	0.224352i	0.923494	+	0.383612i	$0.125320\pi$
$174$	1.58712	−	2.74897i	0.120319	−	0.208399i
$175$	1.01831	−	1.76377i	0.0769771	−	0.133328i
$176$	4.90450	−	8.49484i	0.369691	−	0.640323i
$177$	1.21242	+	2.09997i	0.0911309	+	0.157843i
$178$	−13.3585	−	23.1376i	−1.00126	−	1.73424i
$179$	9.83674	+	17.0377i	0.735232	+	1.27346i	0.954621	+	0.297822i	$0.0962602\pi$
$179$	9.83674	+	17.0377i	0.735232	+	1.27346i	−0.219389	+	0.975637i	$0.570406\pi$
$180$	0.591744	+	1.02493i	0.0441060	+	0.0763938i
$181$	9.47092	+	16.4041i	0.703968	+	1.21931i	0.967063	+	0.254539i	$0.0819236\pi$
$181$	9.47092	+	16.4041i	0.703968	+	1.21931i	−0.263094	+	0.964770i	$0.584743\pi$
$182$	3.23039	+	0.268199i	0.239453	+	0.0198803i
$183$	−1.61454	+	2.79646i	−0.119350	+	0.206720i
$184$	0.182045	−	0.315312i	0.0134206	−	0.0232451i
$185$	6.23578	−	10.8007i	0.458464	−	0.794082i
$186$	4.26044	−	3.71869i	0.312390	−	0.272668i
$187$	−3.46673			−0.253513
$188$	−1.02706	−	1.77893i	−0.0749064	−	0.129742i
$189$	−2.13939			−0.155618
$190$	12.1941			0.884653
$191$	5.32043	−	9.21526i	0.384973	−	0.666793i	−0.606793	−	0.794860i	$-0.707544\pi$
$191$	5.32043	−	9.21526i	0.384973	−	0.666793i	0.991765	+	0.128068i	$0.0408774\pi$
$192$	−1.97251	−	3.41648i	−0.142353	−	0.246563i
$193$	8.74567	+	15.1480i	0.629527	+	1.09037i	0.987647	+	0.156698i	$0.0500848\pi$
$193$	8.74567	+	15.1480i	0.629527	+	1.09037i	−0.358119	+	0.933676i	$0.616582\pi$
$194$	−9.04567			−0.649441
$195$	2.90817	+	0.241447i	0.208258	+	0.0172904i
$196$	1.25059	+	2.16609i	0.0893279	+	0.154720i
$197$	19.7287			1.40561			0.702805	−	0.711383i	$-0.251931\pi$
$197$	19.7287			1.40561			0.702805	+	0.711383i	$0.251931\pi$
$198$	4.20709	+	7.28690i	0.298985	+	0.517857i
$199$	−7.02000	+	12.1590i	−0.497635	+	0.861929i	−0.999996	−	0.00272883i	$-0.999131\pi$
$199$	−7.02000	+	12.1590i	−0.497635	+	0.861929i	0.502361	+	0.864658i	$0.332465\pi$
$200$	−4.37094	+	7.57068i	−0.309072	+	0.535328i
$201$	0.619230	+	1.07254i	0.0436771	+	0.0756509i
$202$	−0.163862	−	0.283816i	−0.0115293	−	0.0199693i
$203$	0.911471	−	1.57871i	0.0639727	−	0.110804i
$204$	0.201621	−	0.349218i	0.0141163	−	0.0244501i
$205$	−0.257967	−	0.446812i	−0.0180172	−	0.0312067i
$206$	19.7924			1.37900
$207$	0.186555	+	0.323123i	0.0129665	+	0.0224586i
$208$	−16.5649	−	1.37528i	−1.14857	−	0.0953585i
$209$	13.7062			0.948078
$210$	−0.363819	−	0.630153i	−0.0251059	−	0.0434847i
$211$	−0.977817	−	1.69363i	−0.0673157	−	0.116594i	0.830403	−	0.557163i	$-0.188110\pi$
$211$	−0.977817	−	1.69363i	−0.0673157	−	0.116594i	−0.897719	+	0.440569i	$0.854777\pi$
$212$	0.231309	−	0.400639i	0.0158864	−	0.0275160i
$213$	1.74124			0.119308
$214$	25.4470			1.73952
$215$	0.139797	+	0.242135i	0.00953405	+	0.0165135i
$216$	9.18298			0.624822
$217$	2.44674	−	2.13562i	0.166095	−	0.144975i
$218$	−14.4237	+	24.9827i	−0.976899	+	1.69204i
$219$	−0.928818	+	1.60876i	−0.0627637	+	0.108710i
$220$	−0.490724	+	0.849959i	−0.0330846	+	0.0573042i
$221$	2.50628	+	5.31311i	0.168590	+	0.357399i
$222$	5.15685	+	8.93192i	0.346105	+	0.599471i
$223$	0.320950	+	0.555902i	0.0214924	+	0.0372259i	0.876572	−	0.481272i	$-0.159825\pi$
$223$	0.320950	+	0.555902i	0.0214924	+	0.0372259i	−0.855079	+	0.518497i	$0.826492\pi$
$224$	0.611888	+	1.05982i	0.0408835	+	0.0708122i
$225$	−4.47921	−	7.75822i	−0.298614	−	0.517215i
$226$	−3.55538	−	6.15810i	−0.236500	−	0.409630i
$227$	7.13844	−	12.3641i	0.473795	−	0.820636i	−0.525755	−	0.850636i	$-0.676217\pi$
$227$	7.13844	−	12.3641i	0.473795	−	0.820636i	0.999550	+	0.0299995i	$0.00955057\pi$
$228$	−0.797137	+	1.38068i	−0.0527917	+	0.0914378i
$229$	−2.56212	+	4.43771i	−0.169309	+	0.293252i	−0.938177	−	0.346155i	$-0.887487\pi$
$229$	−2.56212	+	4.43771i	−0.169309	+	0.293252i	0.768868	+	0.639408i	$0.220820\pi$
$230$	−0.137639	+	0.238398i	−0.00907567	+	0.0157195i
$231$	−0.408933	−	0.708294i	−0.0269058	−	0.0466023i
$232$	−3.91234	+	6.77638i	−0.256858	+	0.444891i
$233$	−2.85458			−0.187010			−0.0935050	−	0.995619i	$-0.529807\pi$
$233$	−2.85458			−0.187010			−0.0935050	+	0.995619i	$0.529807\pi$
$234$	8.12637	−	11.7159i	0.531238	−	0.765889i
$235$	−3.35874	−	5.81751i	−0.219100	−	0.379492i
$236$	0.690977	+	1.19681i	0.0449788	+	0.0779055i
$237$	−3.83436			−0.249068
$238$	0.732403	−	1.26856i	0.0474746	−	0.0822284i
$239$	3.03864	+	5.26308i	0.196553	+	0.340440i	0.947409	−	0.320026i	$-0.103692\pi$
$239$	3.03864	+	5.26308i	0.196553	+	0.340440i	−0.750855	+	0.660467i	$0.770358\pi$
$240$	1.86560	+	3.23131i	0.120424	+	0.208580i
$241$	−18.8163			−1.21206			−0.606032	−	0.795440i	$-0.707240\pi$
$241$	−18.8163			−1.21206			−0.606032	+	0.795440i	$0.707240\pi$
$242$	4.98820	−	8.63982i	0.320654	−	0.555389i
$243$	−7.24140	+	12.5425i	−0.464536	+	0.804600i
$244$	−0.920150	+	1.59375i	−0.0589066	+	0.102029i
$245$	4.08972	+	7.08360i	0.261283	+	0.452555i
$246$	0.426666			0.0272032
$247$	−9.90891	−	21.0061i	−0.630489	−	1.33659i
$248$	−10.5022	+	9.16680i	−0.666892	+	0.582092i
$249$	−5.20425	+	9.01403i	−0.329806	+	0.571241i
$250$	8.03722	−	13.9209i	0.508318	−	0.880433i
$251$	12.3495			0.779496			0.389748	−	0.920922i	$-0.372562\pi$
$251$	12.3495			0.779496			0.389748	+	0.920922i	$0.372562\pi$
$252$	−0.562070			−0.0354071
$253$	−0.154707	+	0.267961i	−0.00972635	+	0.0168465i
$254$	−22.8089			−1.43116
$255$	0.659348	−	1.14202i	0.0412900	−	0.0715163i
$256$	−4.35782	−	7.54796i	−0.272364	−	0.471748i
$257$	−9.82490			−0.612860			−0.306430	−	0.951893i	$-0.599135\pi$
$257$	−9.82490			−0.612860			−0.306430	+	0.951893i	$0.599135\pi$
$258$	−0.231217			−0.0143950
$259$	2.96154	+	5.12954i	0.184021	+	0.318734i
$260$	1.65741	+	0.137605i	0.102789	+	0.00853389i
$261$	−4.00926	−	6.94424i	−0.248167	−	0.429838i
$262$	−4.46873	−	7.74007i	−0.276079	−	0.478183i
$263$	−10.9939	+	19.0420i	−0.677912	+	1.17418i	0.297697	+	0.954660i	$0.403782\pi$
$263$	−10.9939	+	19.0420i	−0.677912	+	1.17418i	−0.975609	+	0.219517i	$0.929552\pi$
$264$	1.75528	+	3.04024i	0.108030	+	0.187114i
$265$	0.756435	−	1.31018i	0.0464674	−	0.0804839i
$266$	−2.89565	+	5.01542i	−0.177544	+	0.307515i
$267$	11.4230			0.699076
$268$	0.352909	+	0.611257i	0.0215574	+	0.0373385i
$269$	2.85045	−	4.93713i	0.173795	−	0.301022i	−0.765949	−	0.642902i	$-0.777730\pi$
$269$	2.85045	−	4.93713i	0.173795	−	0.301022i	0.939744	+	0.341880i	$0.111064\pi$
$270$	−6.94299			−0.422537
$271$	7.25778	−	12.5708i	0.440878	−	0.763624i	−0.556876	−	0.830595i	$-0.688000\pi$
$271$	7.25778	−	12.5708i	0.440878	−	0.763624i	0.997755	+	0.0669715i	$0.0213336\pi$
$272$	−3.75563	+	6.50495i	−0.227719	+	0.394420i
$273$	−0.789891	+	1.13879i	−0.0478064	+	0.0689228i
$274$	−11.8241	−	20.4799i	−0.714317	−	1.23723i
$275$	3.71454	−	6.43377i	0.223995	−	0.387971i
$276$	−0.0179952	−	0.0311685i	−0.00108318	−	0.00187612i
$277$	−2.16714	−	3.75360i	−0.130211	−	0.225532i	0.793547	−	0.608509i	$-0.208232\pi$
$277$	−2.16714	−	3.75360i	−0.130211	−	0.225532i	−0.923758	+	0.382977i	$0.874899\pi$
$278$	5.47930			0.328627
$279$	−2.75414	−	14.0174i	−0.164886	−	0.839202i
$280$	0.896834	+	1.55336i	0.0535961	+	0.0928312i
$281$	29.8617			1.78140			0.890700	−	0.454592i	$-0.150215\pi$
$281$	29.8617			1.78140			0.890700	+	0.454592i	$0.150215\pi$
$282$	5.55520			0.330807
$283$	4.34274	−	7.52185i	0.258149	−	0.447127i	−0.707597	−	0.706616i	$-0.750221\pi$
$283$	4.34274	−	7.52185i	0.258149	−	0.447127i	0.965746	+	0.259489i	$0.0835541\pi$
$284$	0.992363			0.0588859
$285$	−2.60682	+	4.51515i	−0.154415	+	0.267454i
$286$	11.7836	+	0.978323i	0.696781	+	0.0578494i
$287$	0.245031			0.0144637
$288$	5.38298			0.317195
$289$	−14.3453			−0.843843
$290$	2.95801	−	5.12343i	0.173700	−	0.300858i
$291$	1.93376	−	3.34937i	0.113359	−	0.196343i
$292$	−0.529349	+	0.916859i	−0.0309778	+	0.0536551i
$293$	6.80242			0.397401			0.198701	−	0.980060i	$-0.436328\pi$
$293$	6.80242			0.397401			0.198701	+	0.980060i	$0.436328\pi$
$294$	−6.76421			−0.394497
$295$	2.25965	+	3.91384i	0.131562	+	0.227872i
$296$	−12.7119	−	22.0177i	−0.738866	−	1.27975i
$297$	−7.80394			−0.452830
$298$	3.20255	−	5.54699i	0.185519	−	0.321328i
$299$	0.522522	+	0.0433817i	0.0302182	+	0.00250883i
$300$	0.432066	+	0.748360i	0.0249453	+	0.0432066i
$301$	−0.132786			−0.00765368
$302$	0.174227	−	0.301769i	0.0100256	−	0.0173649i
$303$	0.140119			0.00804965
$304$	14.8484	−	25.7182i	0.851615	−	1.47504i
$305$	−3.00911	+	5.21192i	−0.172301	+	0.298434i
$306$	−3.22159	−	5.57996i	−0.184166	−	0.318985i
$307$	15.5831	−	26.9907i	0.889374	−	1.54044i	0.0487562	−	0.998811i	$-0.484474\pi$
$307$	15.5831	−	26.9907i	0.889374	−	1.54044i	0.840617	−	0.541629i	$-0.182192\pi$
$308$	−0.233058	−	0.403668i	−0.0132797	−	0.0230011i
$309$	−4.23116	+	7.32858i	−0.240702	+	0.416908i
$310$	7.94043	−	6.93075i	0.450986	−	0.393640i
$311$	1.98236			0.112410			0.0562048	−	0.998419i	$-0.482100\pi$
$311$	1.98236			0.112410			0.0562048	+	0.998419i	$0.482100\pi$
$312$	3.39048	−	4.88808i	0.191948	−	0.276733i
$313$	−5.24119	+	9.07800i	−0.296249	+	0.513119i	−0.975275	−	0.220996i	$-0.929069\pi$
$313$	−5.24119	+	9.07800i	−0.296249	+	0.513119i	0.679025	+	0.734115i	$0.262403\pi$
$314$	−13.1805	+	22.8293i	−0.743820	+	1.28833i
$315$	−1.83810			−0.103565
$316$	−2.18527			−0.122931
$317$	−15.1197	+	26.1881i	−0.849208	+	1.47087i	0.0327089	+	0.999465i	$0.489587\pi$
$317$	−15.1197	+	26.1881i	−0.849208	+	1.47087i	−0.881916	+	0.471406i	$0.843747\pi$
$318$	0.625555	+	1.08349i	0.0350794	+	0.0607592i
$319$	3.32481	−	5.75875i	0.186154	−	0.322428i
$320$	−3.67628	−	6.36750i	−0.205510	−	0.355954i
$321$	−5.43999	+	9.42235i	−0.303631	+	0.525904i
$322$	−0.0653687	−	0.113222i	−0.00364285	−	0.00630961i
$323$	−10.4956			−0.583989
$324$	−0.991539	+	1.71740i	−0.0550855	+	0.0954109i
$325$	−12.5458	−	1.04160i	−0.695916	−	0.0577776i
$326$	−15.5743			−0.862579
$327$	−6.16694	−	10.6814i	−0.341032	−	0.590685i
$328$	−1.05176			−0.0580735
$329$	3.19031			0.175888
$330$	−1.32712	−	2.29864i	−0.0730554	−	0.126536i
$331$	−3.18431	+	5.51539i	−0.175026	+	0.303153i	−0.940170	−	0.340705i	$-0.889334\pi$
$331$	−3.18431	+	5.51539i	−0.175026	+	0.303153i	0.765145	+	0.643858i	$0.222667\pi$
$332$	−2.96599	+	5.13725i	−0.162780	+	0.281943i
$333$	26.0536			1.42773
$334$	−32.5997			−1.78378
$335$	1.15410	+	1.99895i	0.0630550	+	0.109214i
$336$	−1.77205			−0.0966731
$337$	−27.0380			−1.47286			−0.736428	−	0.676516i	$-0.763489\pi$
$337$	−27.0380			−1.47286			−0.736428	+	0.676516i	$0.763489\pi$
$338$	−7.01961	−	18.7669i	−0.381817	−	1.02078i
$339$	3.04024			0.165123
$340$	0.375773	−	0.650858i	0.0203792	−	0.0352977i
$341$	8.92507	−	7.79019i	0.483320	−	0.421862i
$342$	12.7370	+	22.0612i	0.688739	+	1.19293i
$343$	−7.96773			−0.430217
$344$	0.569964			0.0307304
$345$	−0.0588483	−	0.101928i	−0.00316829	−	0.00548764i
$346$	2.62589	+	4.54817i	0.141169	+	0.244511i
$347$	27.0114			1.45005			0.725023	−	0.688725i	$-0.241829\pi$
$347$	27.0114			1.45005			0.725023	+	0.688725i	$0.241829\pi$
$348$	0.386734	+	0.669843i	0.0207311	+	0.0359074i
$349$	−9.56795	+	16.5722i	−0.512161	+	0.887089i	0.487740	+	0.872989i	$0.337822\pi$
$349$	−9.56795	+	16.5722i	−0.512161	+	0.887089i	−0.999901	+	0.0140995i	$0.995512\pi$
$350$	1.56951	+	2.71847i	0.0838938	+	0.145308i
$351$	5.64186	+	11.9603i	0.301140	+	0.638394i
$352$	2.23201	+	3.86595i	0.118967	+	0.206056i
$353$	−12.8852	−	22.3178i	−0.685811	−	1.18786i	−0.973181	−	0.230040i	$-0.926114\pi$
$353$	−12.8852	−	22.3178i	−0.685811	−	1.18786i	0.287370	−	0.957820i	$-0.407219\pi$
$354$	−3.73737			−0.198639
$355$	3.24526			0.172240
$356$	6.51015			0.345037
$357$	0.313142	+	0.542378i	0.0165732	+	0.0287057i
$358$	−30.3225			−1.60259
$359$	−6.50919	−	11.2742i	−0.343542	−	0.595032i	0.641546	−	0.767085i	$-0.278293\pi$
$359$	−6.50919	−	11.2742i	−0.343542	−	0.595032i	−0.985088	+	0.172053i	$0.944960\pi$
$360$	7.88975			0.415826
$361$	22.4957			1.18398
$362$	−29.1948			−1.53445
$363$	2.13273	+	3.69399i	0.111939	+	0.193884i
$364$	−0.450172	+	0.649017i	−0.0235954	+	0.0340177i
$365$	−1.73109	+	2.99834i	−0.0906095	+	0.156940i
$366$	−2.48846	−	4.31014i	−0.130074	−	0.225295i
$367$	−19.2727			−1.00603			−0.503014	−	0.864278i	$-0.667776\pi$
$367$	−19.2727			−1.00603			−0.503014	+	0.864278i	$0.667776\pi$
$368$	0.335199	+	0.580582i	0.0174735	+	0.0302649i
$369$	0.538905	−	0.933410i	0.0280543	−	0.0485914i
$370$	9.61112	+	16.6470i	0.499659	+	0.865434i
$371$	0.359251	+	0.622241i	0.0186514	+	0.0323052i
$372$	0.265665	+	1.35213i	0.0137741	+	0.0701045i
$373$	0.157671	+	0.273094i	0.00816390	+	0.0141403i	0.870078	−	0.492913i	$-0.164068\pi$
$373$	0.157671	+	0.273094i	0.00816390	+	0.0141403i	−0.861915	+	0.507053i	$0.830735\pi$
$374$	2.67162	−	4.62738i	0.138146	−	0.239276i
$375$	3.43635	+	5.95193i	0.177452	+	0.307356i
$376$	−13.6939			−0.706209
$377$	−11.2295	−	0.932318i	−0.578350	−	0.0480168i
$378$	1.64871	−	2.85564i	0.0848003	−	0.146878i
$379$	10.6785	+	18.4957i	0.548518	+	0.950061i	0.998376	+	0.0569611i	$0.0181411\pi$
$379$	10.6785	+	18.4957i	0.548518	+	0.950061i	−0.449858	+	0.893100i	$0.648526\pi$
$380$	−1.48567	+	2.57326i	−0.0762133	+	0.132005i
$381$	4.87602	−	8.44552i	0.249806	−	0.432677i
$382$	8.20031	+	14.2034i	0.419565	+	0.726707i
$383$	7.19604	−	12.4639i	0.367700	−	0.636876i	−0.621505	−	0.783410i	$-0.713479\pi$
$383$	7.19604	−	12.4639i	0.367700	−	0.636876i	0.989206	+	0.146534i	$0.0468119\pi$
$384$	8.84553			0.451396
$385$	−0.762154	−	1.32009i	−0.0388430	−	0.0672780i
$386$	−26.9592			−1.37219
$387$	−0.292041	+	0.505831i	−0.0148453	+	0.0257128i
$388$	1.10208	−	1.90886i	0.0559497	−	0.0969077i
$389$	2.63938	−	4.57153i	0.133822	−	0.231786i	−0.791325	−	0.611396i	$-0.790608\pi$
$389$	2.63938	−	4.57153i	0.133822	−	0.231786i	0.925147	+	0.379610i	$0.123942\pi$
$390$	−2.56345	+	3.69574i	−0.129805	+	0.187141i
$391$	0.118467	−	0.205192i	0.00599115	−	0.0103770i
$392$	16.6742			0.842173
$393$	3.82125			0.192757
$394$	−15.2038	+	26.3337i	−0.765955	+	1.32667i
$395$	−7.14633			−0.359571
$396$	−2.05029			−0.103031
$397$	−16.5938			−0.832817			−0.416409	−	0.909178i	$-0.636711\pi$
$397$	−16.5938			−0.832817			−0.416409	+	0.909178i	$0.636711\pi$
$398$	−10.8198	−	18.7405i	−0.542350	−	0.939377i
$399$	−1.23805	−	2.14437i	−0.0619800	−	0.107353i
$400$	−8.04817	−	13.9398i	−0.402409	−	0.696992i
$401$	16.4834	−	28.5501i	0.823142	−	1.42572i	−0.0801892	−	0.996780i	$-0.525552\pi$
$401$	16.4834	−	28.5501i	0.823142	−	1.42572i	0.903331	−	0.428944i	$-0.141114\pi$
$402$	−1.90882			−0.0952034
$403$	−18.3916	−	8.04664i	−0.916152	−	0.400831i
$404$	0.0798564			0.00397300
$405$	−3.24256	+	5.61629i	−0.161124	+	0.279076i
$406$	1.40484	+	2.43325i	0.0697210	+	0.120760i
$407$	10.8029	+	18.7112i	0.535482	+	0.927481i
$408$	−1.34411	−	2.32807i	−0.0665434	−	0.115257i
$409$	−35.8101			−1.77070			−0.885348	−	0.464929i	$-0.846080\pi$
$409$	−35.8101			−1.77070			−0.885348	+	0.464929i	$0.846080\pi$
$410$	0.795203			0.0392723
$411$	10.1109			0.498732
$412$	−2.41141	+	4.17668i	−0.118802	+	0.205770i
$413$	−2.14634			−0.105615
$414$	−0.575070			−0.0282631
$415$	−9.69948	+	16.8000i	−0.476129	+	0.824679i
$416$	4.31132	−	6.21567i	0.211380	−	0.304748i
$417$	−1.17135	+	2.02884i	−0.0573613	+	0.0993526i
$418$	−10.5626	+	18.2950i	−0.516634	+	0.894836i
$419$	13.6690	−	23.6755i	0.667776	−	1.15662i	−0.310748	−	0.950492i	$-0.600580\pi$
$419$	13.6690	−	23.6755i	0.667776	−	1.15662i	0.978525	−	0.206130i	$-0.0660870\pi$
$420$	0.177304			0.00865154
$421$	2.62912	+	4.55376i	0.128135	+	0.221937i	0.922954	−	0.384910i	$-0.125767\pi$
$421$	2.62912	+	4.55376i	0.128135	+	0.221937i	−0.794819	+	0.606847i	$0.792434\pi$
$422$	3.01419			0.146729
$423$	7.01655	−	12.1530i	0.341157	−	0.590901i
$424$	−1.54203	−	2.67087i	−0.0748875	−	0.129709i
$425$	−2.84442	+	4.92668i	−0.137975	+	0.238979i
$426$	−1.34188	+	2.32420i	−0.0650142	+	0.112608i
$427$	−1.42911	−	2.47528i	−0.0691593	−	0.119787i
$428$	−3.10034	+	5.36995i	−0.149861	+	0.259566i
$429$	−2.88132	+	4.15402i	−0.139111	+	0.200558i
$430$	−0.430934			−0.0207815
$431$	11.5175	+	19.9488i	0.554777	+	0.960902i	0.997921	+	0.0644514i	$0.0205297\pi$
$431$	11.5175	+	19.9488i	0.554777	+	0.960902i	−0.443144	+	0.896451i	$0.646137\pi$
$432$	−8.45428	+	14.6432i	−0.406757	+	0.704523i
$433$	17.7529	+	30.7489i	0.853149	+	1.47770i	0.878351	+	0.478015i	$0.158644\pi$
$433$	17.7529	+	30.7489i	0.853149	+	1.47770i	−0.0252023	+	0.999682i	$0.508023\pi$
$434$	0.965048	+	4.91169i	0.0463238	+	0.235769i
$435$	1.26471	+	2.19054i	0.0606382	+	0.105029i
$436$	−3.51464	−	6.08753i	−0.168321	−	0.291540i
$437$	−0.468377	+	0.811253i	−0.0224055	+	0.0388075i
$438$	−1.43157	−	2.47956i	−0.0684033	−	0.118478i
$439$	20.0085			0.954955			0.477477	−	0.878644i	$-0.341551\pi$
$439$	20.0085			0.954955			0.477477	+	0.878644i	$0.341551\pi$
$440$	3.27142	+	5.66627i	0.155959	+	0.270129i
$441$	−8.54361	+	14.7980i	−0.406838	+	0.704665i
$442$	−9.02336	−	0.749153i	−0.429197	−	0.0356336i
$443$	9.46794	+	16.3990i	0.449835	+	0.779138i	0.998375	−	0.0569869i	$-0.0181493\pi$
$443$	9.46794	+	16.3990i	0.449835	+	0.779138i	−0.548540	+	0.836125i	$0.684816\pi$
$444$	−2.51314			−0.119268
$445$	21.2897			1.00923
$446$	−0.989353			−0.0468472
$447$	1.36927	+	2.37164i	0.0647641	+	0.112175i
$448$	3.49193			0.164978
$449$	7.96551	+	13.7967i	0.375915	+	0.651105i	0.990464	−	0.137775i	$-0.0439950\pi$
$449$	7.96551	+	13.7967i	0.375915	+	0.651105i	−0.614548	+	0.788879i	$0.710662\pi$
$450$	13.8075			0.650892
$451$	0.893810			0.0420879
$452$	1.73268			0.0814984
$453$	0.0744914	+	0.129023i	0.00349991	+	0.00606202i
$454$	11.0024	+	19.0567i	0.516367	+	0.894374i
$455$	−1.47217	+	2.12244i	−0.0690163	+	0.0995013i
$456$	5.31413	+	9.20434i	0.248857	+	0.431033i
$457$	−11.1382	+	19.2919i	−0.521023	+	0.902438i	0.478679	+	0.877990i	$0.341116\pi$
$457$	−11.1382	+	19.2919i	−0.521023	+	0.902438i	−0.999701	+	0.0244474i	$0.992217\pi$
$458$	−3.94896	−	6.83979i	−0.184523	−	0.319602i
$459$	5.97589			0.278931
$460$	−0.0335386	−	0.0580906i	−0.00156375	−	0.00270849i
$461$	9.15862	+	15.8632i	0.426560	+	0.738823i	0.996565	−	0.0828182i	$-0.0263921\pi$
$461$	9.15862	+	15.8632i	0.426560	+	0.738823i	−0.570005	+	0.821641i	$0.693059\pi$
$462$	1.26057			0.0586469
$463$	−24.4104			−1.13445			−0.567224	−	0.823563i	$-0.691983\pi$
$463$	−24.4104			−1.13445			−0.567224	+	0.823563i	$0.691983\pi$
$464$	−7.20377	−	12.4773i	−0.334427	−	0.579244i
$465$	0.868787	+	4.42177i	0.0402890	+	0.205054i
$466$	2.19987	−	3.81028i	0.101907	−	0.176508i
$467$	1.20582			0.0557986			0.0278993	−	0.999611i	$-0.491118\pi$
$467$	1.20582			0.0557986			0.0278993	+	0.999611i	$0.491118\pi$
$468$	1.48226	+	3.14227i	0.0685173	+	0.145251i
$469$	−1.09622			−0.0506188
$470$	10.3536			0.477574
$471$	−5.63539	−	9.76078i	−0.259665	−	0.449753i
$472$	9.21282			0.424055
$473$	−0.484371			−0.0222714
$474$	2.95493	−	5.11808i	0.135724	−	0.235081i
$475$	11.2458	−	19.4783i	0.515992	−	0.893725i
$476$	0.178465	+	0.309110i	0.00817992	+	0.0141680i
$477$	3.16045			0.144707
$478$	−9.36683			−0.428429
$479$	−16.6434	−	28.8272i	−0.760455	−	1.31715i	−0.942616	−	0.333878i	$-0.891643\pi$
$479$	−16.6434	−	28.8272i	−0.760455	−	1.31715i	0.182161	−	0.983269i	$-0.441691\pi$
$480$	−1.69805			−0.0775049
$481$	20.8668	−	30.0839i	0.951445	−	1.37171i
$482$	14.5007	−	25.1159i	0.660487	−	1.14400i
$483$	0.0558973			0.00254342
$484$	1.21548	+	2.10527i	0.0552490	+	0.0956940i
$485$	3.60406	−	6.24242i	0.163652	−	0.283454i
$486$	−11.1611	−	19.3315i	−0.506277	−	0.876897i
$487$	−8.55724	+	14.8216i	−0.387765	+	0.671629i	−0.992149	−	0.125064i	$-0.960086\pi$
$487$	−8.55724	+	14.8216i	−0.387765	+	0.671629i	0.604383	+	0.796694i	$0.293420\pi$
$488$	6.13420	+	10.6248i	0.277682	+	0.480960i
$489$	3.32943	−	5.76673i	0.150562	−	0.260781i
$490$	−12.6069			−0.569520
$491$	12.8393			0.579431			0.289716	−	0.957113i	$-0.406439\pi$
$491$	12.8393			0.579431			0.289716	+	0.957113i	$0.406439\pi$
$492$	−0.0519829	+	0.0900370i	−0.00234357	+	0.00405918i
$493$	−2.54599	+	4.40978i	−0.114665	+	0.198606i
$494$	35.6751	+	2.96188i	1.60510	+	0.133261i
$495$	−6.70492			−0.301364
$496$	−4.94860	−	25.1863i	−0.222199	−	1.13090i
$497$	−0.770630	+	1.33477i	−0.0345675	+	0.0598727i
$498$	−8.02125	−	13.8932i	−0.359441	−	0.622570i
$499$	−9.33960	+	16.1767i	−0.418098	+	0.724167i	−0.995748	−	0.0921174i	$-0.970636\pi$
$499$	−9.33960	+	16.1767i	−0.418098	+	0.724167i	0.577650	+	0.816284i	$0.303970\pi$
$500$	1.95843	+	3.39210i	0.0875837	+	0.151699i
$501$	6.96908	−	12.0708i	0.311355	−	0.539283i
$502$	−9.51709	+	16.4841i	−0.424768	+	0.735720i
$503$	31.9887			1.42631			0.713153	−	0.701009i	$-0.247267\pi$
$503$	31.9887			1.42631			0.713153	+	0.701009i	$0.247267\pi$
$504$	−1.87353	+	3.24504i	−0.0834535	+	0.144546i
$505$	0.261149			0.0116210
$506$	−0.238448	−	0.413004i	−0.0106003	−	0.0183603i
$507$	8.44950	+	1.41276i	0.375256	+	0.0627428i
$508$	2.77893	−	4.81324i	0.123295	−	0.213553i
$509$	3.71554			0.164688			0.0823442	−	0.996604i	$-0.473759\pi$
$509$	3.71554			0.164688			0.0823442	+	0.996604i	$0.473759\pi$
$510$	1.01624	+	1.76019i	0.0450000	+	0.0779424i
$511$	−0.822143	−	1.42399i	−0.0363694	−	0.0629937i
$512$	−13.4126			−0.592761
$513$	−23.6265			−1.04314
$514$	7.57149	−	13.1142i	0.333964	−	0.578443i
$515$	−7.88586	+	13.6587i	−0.347493	+	0.601875i
$516$	0.0281704	−	0.0487926i	0.00124013	−	0.00214797i
$517$	11.6374			0.511814
$518$	−9.12916			−0.401112
$519$	−2.24542			−0.0985630
$520$	6.31904	−	9.11021i	0.277108	−	0.399509i
$521$	6.63403	−	11.4905i	0.290642	−	0.503407i	−0.683320	−	0.730119i	$-0.739464\pi$
$521$	6.63403	−	11.4905i	0.290642	−	0.503407i	0.973962	+	0.226712i	$0.0727977\pi$
$522$	12.3588			0.540931
$523$	4.55031	−	7.88136i	0.198971	−	0.344628i	−0.749224	−	0.662317i	$-0.769573\pi$
$523$	4.55031	−	7.88136i	0.198971	−	0.344628i	0.948195	+	0.317689i	$0.102907\pi$
$524$	2.17779			0.0951374
$525$	−1.34210			−0.0585741
$526$	−16.9447	−	29.3491i	−0.738825	−	1.27968i
$527$	−6.83440	+	5.96536i	−0.297711	+	0.259855i
$528$	−6.46397			−0.281308
$529$	11.4894	+	19.9003i	0.499540	+	0.865229i
$530$	1.16588	+	2.01937i	0.0506427	+	0.0877158i
$531$	−4.72052	+	8.17618i	−0.204853	+	0.354816i
$532$	−0.705585	−	1.22211i	−0.0305910	−	0.0529852i
$533$	−0.646180	−	1.36985i	−0.0279892	−	0.0593349i
$534$	−8.80305	+	15.2473i	−0.380945	+	0.659817i
$535$	−10.1388	+	17.5610i	−0.438340	+	0.759228i
$536$	4.70536			0.203240
$537$	6.48225	−	11.2276i	0.279730	−	0.484506i
$538$	4.39336	+	7.60953i	0.189411	+	0.328070i
$539$	−14.1702			−0.610352
$540$	0.845900	−	1.46514i	0.0364017	−	0.0630497i
$541$	0.704181	−	1.21968i	0.0302751	−	0.0524380i	−0.850491	−	0.525990i	$-0.823695\pi$
$541$	0.704181	−	1.21968i	0.0302751	−	0.0524380i	0.880766	+	0.473552i	$0.157028\pi$
$542$	11.1863	+	19.3753i	0.480493	+	0.832239i
$543$	6.24119	−	10.8101i	0.267835	−	0.463904i
$544$	−1.70917	−	2.96037i	−0.0732800	−	0.126925i
$545$	−11.4937	−	19.9077i	−0.492336	−	0.852750i
$546$	−0.911328	−	1.93194i	−0.0390012	−	0.0826796i
$547$	−6.96659	−	12.0665i	−0.297870	−	0.515926i	0.677778	−	0.735266i	$-0.262943\pi$
$547$	−6.96659	−	12.0665i	−0.297870	−	0.515926i	−0.975648	+	0.219340i	$0.929610\pi$
$548$	5.76234			0.246155
$549$	−12.5723			−0.536573
$550$	5.72517	+	9.91628i	0.244122	+	0.422832i
$551$	10.0659	−	17.4347i	0.428822	−	0.742741i
$552$	−0.239930			−0.0102121
$553$	1.69699	−	2.93928i	0.0721634	−	0.124991i
$554$	6.68038			0.283822
$555$	−8.21856			−0.348858
$556$	−0.667572	+	1.15627i	−0.0283114	+	0.0490367i
$557$	8.29630	−	14.3696i	0.351526	−	0.608860i	−0.634991	−	0.772519i	$-0.718996\pi$
$557$	8.29630	−	14.3696i	0.351526	−	0.608860i	0.986517	+	0.163659i	$0.0523297\pi$
$558$	20.8328	+	7.12623i	0.881924	+	0.301678i
$559$	0.350176	+	0.742346i	0.0148109	+	0.0313979i
$560$	−3.30267			−0.139563
$561$	1.14226	+	1.97846i	0.0482263	+	0.0835304i
$562$	−23.0127	+	39.8592i	−0.970733	+	1.68136i
$563$	4.65672	−	8.06567i	0.196257	−	0.339928i	−0.751055	−	0.660240i	$-0.770455\pi$
$563$	4.65672	−	8.06567i	0.196257	−	0.339928i	0.947312	+	0.320312i	$0.103788\pi$
$564$	−0.676819	+	1.17229i	−0.0284992	+	0.0493621i
$565$	5.66627			0.238382
$566$	6.69341	+	11.5933i	0.281345	+	0.487304i
$567$	−1.53998	−	2.66733i	−0.0646731	−	0.112017i
$568$	3.30781	−	5.72929i	0.138792	−	0.240396i
$569$	−18.9103			−0.792760			−0.396380	−	0.918087i	$-0.629734\pi$
$569$	−18.9103			−0.792760			−0.396380	+	0.918087i	$0.629734\pi$
$570$	−4.01786	−	6.95914i	−0.168290	−	0.291486i
$571$	3.26736	+	5.65923i	0.136735	+	0.236831i	0.926259	−	0.376888i	$-0.123006\pi$
$571$	3.26736	+	5.65923i	0.136735	+	0.236831i	−0.789524	+	0.613720i	$0.789673\pi$
$572$	−1.64211	+	2.36745i	−0.0686602	+	0.0989879i
$573$	−7.01216			−0.292937
$574$	−0.188832	+	0.327066i	−0.00788168	+	0.0136515i
$575$	0.253871	+	0.439717i	0.0105872	+	0.0183375i
$576$	7.67991	−	13.3020i	0.319996	−	0.554250i
$577$	2.89030	−	5.00615i	0.120325	−	0.208409i	−0.799571	−	0.600572i	$-0.794940\pi$
$577$	2.89030	−	5.00615i	0.120325	−	0.208409i	0.919896	+	0.392163i	$0.128273\pi$
$578$	11.0551	−	19.1481i	0.459833	−	0.796455i
$579$	5.76326	−	9.98226i	0.239513	−	0.414849i
$580$	0.720780	+	1.24843i	0.0299287	+	0.0518381i
$581$	−4.60654	−	7.97877i	−0.191112	−	0.331015i
$582$	2.98048	+	5.16234i	0.123545	+	0.213986i
$583$	1.31046	+	2.26978i	0.0542736	+	0.0940046i
$584$	3.52891	+	6.11226i	0.146027	+	0.252927i
$585$	4.84732	+	10.2760i	0.200412	+	0.424858i
$586$	−5.24224	+	9.07982i	−0.216555	+	0.375084i
$587$	3.15636	−	5.46697i	0.130277	−	0.225646i	−0.793506	−	0.608562i	$-0.791747\pi$
$587$	3.15636	−	5.46697i	0.130277	−	0.225646i	0.923783	+	0.382916i	$0.125080\pi$
$588$	0.824119	−	1.42742i	0.0339861	−	0.0588656i
$589$	27.0207	−	23.5849i	1.11337	−	0.971797i
$590$	−6.96555			−0.286767
$591$	−6.50044	−	11.2591i	−0.267392	−	0.463137i
$592$	46.8128			1.92399
$593$	25.8994			1.06356			0.531780	−	0.846882i	$-0.321523\pi$
$593$	25.8994			1.06356			0.531780	+	0.846882i	$0.321523\pi$
$594$	6.01406	−	10.4166i	0.246760	−	0.427400i
$595$	0.583621	+	1.01086i	0.0239261	+	0.0414413i
$596$	0.780368	+	1.35164i	0.0319651	+	0.0553652i
$597$	9.25214			0.378665
$598$	−0.460584	+	0.664027i	−0.0188347	+	0.0271541i
$599$	−5.60704	−	9.71167i	−0.229097	−	0.396808i	0.728444	−	0.685106i	$-0.240244\pi$
$599$	−5.60704	−	9.71167i	−0.229097	−	0.396808i	−0.957541	+	0.288298i	$0.906911\pi$
$600$	5.76075			0.235182
$601$	−2.88351	−	4.99439i	−0.117621	−	0.203726i	0.801203	−	0.598392i	$-0.204193\pi$
$601$	−2.88351	−	4.99439i	−0.117621	−	0.203726i	−0.918824	+	0.394666i	$0.870860\pi$
$602$	0.102331	−	0.177242i	0.00417070	−	0.00722386i
$603$	−2.41096	+	4.17590i	−0.0981817	+	0.170056i
$604$	0.0424539	+	0.0735322i	0.00172742	+	0.00299198i
$605$	3.97489	+	6.88472i	0.161602	+	0.279904i
$606$	−0.107982	+	0.187031i	−0.00438648	+	0.00759760i
$607$	−1.74270	+	3.01844i	−0.0707340	+	0.122515i	−0.899223	−	0.437490i	$-0.855867\pi$
$607$	−1.74270	+	3.01844i	−0.0707340	+	0.122515i	0.828489	+	0.560005i	$0.189201\pi$
$608$	6.75743	+	11.7042i	0.274050	+	0.474668i
$609$	−1.20129			−0.0486787
$610$	−4.63790	−	8.03307i	−0.187783	−	0.325250i
$611$	−8.41329	−	17.8355i	−0.340365	−	0.721548i
$612$	1.57001			0.0634641
$613$	−3.66863	−	6.35425i	−0.148174	−	0.256646i	0.782378	−	0.622803i	$-0.214006\pi$
$613$	−3.66863	−	6.35425i	−0.148174	−	0.256646i	−0.930553	+	0.366158i	$0.880673\pi$
$614$	24.0180	+	41.6004i	0.969288	+	1.67886i
$615$	−0.169996	+	0.294442i	−0.00685491	+	0.0118730i
$616$	−3.10737			−0.125200
$617$	−43.5762			−1.75431			−0.877156	−	0.480205i	$-0.840562\pi$
$617$	−43.5762			−1.75431			−0.877156	+	0.480205i	$0.840562\pi$
$618$	−6.52143	−	11.2954i	−0.262330	−	0.454370i
$619$	5.90577			0.237373			0.118687	−	0.992932i	$-0.462132\pi$
$619$	5.90577			0.237373			0.118687	+	0.992932i	$0.462132\pi$
$620$	0.495136	+	2.52004i	0.0198851	+	0.101207i
$621$	0.266681	−	0.461905i	0.0107015	−	0.0185356i
$622$	−1.52770	+	2.64605i	−0.0612550	+	0.106097i
$623$	−5.05553	+	8.75643i	−0.202545	+	0.350819i
$624$	4.67313	+	9.90668i	0.187075	+	0.396585i
$625$	−2.32436	−	4.02591i	−0.0929743	−	0.161036i
$626$	−8.07817	−	13.9918i	−0.322869	−	0.559225i
$627$	−4.51609	−	7.82209i	−0.180355	−	0.312384i
$628$	−3.21170	−	5.56283i	−0.128161	−	0.221981i
$629$	−8.27238	−	14.3282i	−0.329841	−	0.571302i
$630$	1.41652	−	2.45349i	0.0564355	−	0.0977492i
$631$	6.98897	−	12.1053i	0.278227	−	0.481903i	−0.692717	−	0.721209i	$-0.743587\pi$
$631$	6.98897	−	12.1053i	0.278227	−	0.481903i	0.970944	+	0.239306i	$0.0769200\pi$
$632$	−7.28406	+	12.6164i	−0.289744	+	0.501852i
$633$	−0.644366	+	1.11607i	−0.0256113	+	0.0443600i
$634$	−23.3038	−	40.3634i	−0.925513	−	1.60304i
$635$	9.08773	−	15.7404i	0.360636	−	0.624639i
$636$	−0.304858			−0.0120884
$637$	10.2443	+	21.7172i	0.405895	+	0.860466i
$638$	5.12449	+	8.87588i	0.202881	+	0.351399i
$639$	3.38975	+	5.87121i	0.134096	+	0.232262i
$640$	16.4859			0.651664
$641$	−5.60628	+	9.71036i	−0.221435	+	0.383536i	−0.955244	−	0.295820i	$-0.904407\pi$
$641$	−5.60628	+	9.71036i	−0.221435	+	0.383536i	0.733809	+	0.679356i	$0.237741\pi$
$642$	−8.38459	−	14.5225i	−0.330913	−	0.573159i
$643$	−6.39985	−	11.0849i	−0.252386	−	0.437145i	0.711797	−	0.702386i	$-0.247882\pi$
$643$	−6.39985	−	11.0849i	−0.252386	−	0.437145i	−0.964182	+	0.265241i	$0.914548\pi$
$644$	0.0318568			0.00125533
$645$	0.0921238	−	0.159563i	0.00362737	−	0.00628279i
$646$	8.08834	−	14.0094i	0.318232	−	0.551193i
$647$	−19.6628	+	34.0571i	−0.773026	+	1.33892i	0.162871	+	0.986647i	$0.447925\pi$
$647$	−19.6628	+	34.0571i	−0.773026	+	1.33892i	−0.935897	+	0.352273i	$0.885409\pi$
$648$	6.61012	+	11.4491i	0.259670	+	0.449762i
$649$	−7.82930			−0.307327
$650$	11.0587	−	15.9434i	0.433757	−	0.625350i
$651$	−2.02497	−	0.692677i	−0.0793649	−	0.0271481i
$652$	1.89749	−	3.28656i	0.0743116	−	0.128712i
$653$	10.7462	−	18.6130i	0.420533	−	0.728385i	−0.575459	−	0.817831i	$-0.695176\pi$
$653$	10.7462	−	18.6130i	0.420533	−	0.728385i	0.995992	+	0.0894463i	$0.0285097\pi$
$654$	19.0100			0.743351
$655$	7.12189			0.278275
$656$	0.968296	−	1.67714i	0.0378056	−	0.0654812i
$657$	−7.23266			−0.282173
$658$	−2.45859	+	4.25841i	−0.0958459	+	0.166010i
$659$	16.9789	+	29.4083i	0.661403	+	1.14558i	0.980247	+	0.197777i	$0.0633721\pi$
$659$	16.9789	+	29.4083i	0.661403	+	1.14558i	−0.318844	+	0.947807i	$0.603295\pi$
$660$	0.646759			0.0251750
$661$	10.4041			0.404671			0.202336	−	0.979316i	$-0.435147\pi$
$661$	10.4041			0.404671			0.202336	+	0.979316i	$0.435147\pi$
$662$	−4.90794	−	8.50080i	−0.190752	−	0.330393i
$663$	2.20638	−	3.18095i	0.0856887	−	0.123538i
$664$	19.7728	+	34.2476i	0.767335	+	1.32906i
$665$	−2.30743	−	3.99658i	−0.0894782	−	0.154981i
$666$	−20.0781	+	34.7762i	−0.778009	+	1.34755i
$667$	0.227235	+	0.393583i	0.00879858	+	0.0152396i
$668$	3.97179	−	6.87935i	0.153673	−	0.266170i
$669$	0.211501	−	0.366331i	0.00817710	−	0.0141632i
$670$	−3.55758			−0.137441
$671$	−5.21301	−	9.02920i	−0.201246	−	0.348568i
$672$	0.403224	−	0.698405i	0.0155547	−	0.0269416i
$673$	−11.1348			−0.429214			−0.214607	−	0.976700i	$-0.568847\pi$
$673$	−11.1348			−0.429214			−0.214607	+	0.976700i	$0.568847\pi$
$674$	20.8367	−	36.0902i	0.802599	−	1.39014i
$675$	−6.40305	+	11.0904i	−0.246453	+	0.426870i
$676$	4.81551	+	0.805154i	0.185212	+	0.0309675i
$677$	−9.57405	−	16.5827i	−0.367961	−	0.637327i	0.621286	−	0.783584i	$-0.286611\pi$
$677$	−9.57405	−	16.5827i	−0.367961	−	0.637327i	−0.989247	+	0.146257i	$0.953277\pi$
$678$	−2.34294	+	4.05809i	−0.0899800	+	0.155850i
$679$	1.71167	+	2.96469i	0.0656877	+	0.113774i
$680$	−2.50510	−	4.33896i	−0.0960662	−	0.166392i
$681$	−9.40823			−0.360524
$682$	3.52025	+	17.9166i	0.134797	+	0.686062i
$683$	16.5140	+	28.6030i	0.631889	+	1.09446i	0.987165	+	0.159703i	$0.0510537\pi$
$683$	16.5140	+	28.6030i	0.631889	+	1.09446i	−0.355276	+	0.934762i	$0.615613\pi$
$684$	−6.20727			−0.237341
$685$	18.8442			0.720000
$686$	6.14028	−	10.6353i	0.234437	−	0.406057i
$687$	3.37679			0.128832
$688$	−0.524736	+	0.908869i	−0.0200054	+	0.0346503i
$689$	2.53126	−	3.64934i	0.0964334	−	0.139029i
$690$	0.181404			0.00690595
$691$	−38.6201			−1.46918			−0.734589	−	0.678513i	$-0.762625\pi$
$691$	−38.6201			−1.46918			−0.734589	+	0.678513i	$0.762625\pi$
$692$	−1.27970			−0.0486470
$693$	1.59217	−	2.75772i	0.0604817	−	0.104757i
$694$	−20.8161	+	36.0546i	−0.790170	+	1.36861i
$695$	−2.18312	+	3.78127i	−0.0828103	+	0.143432i
$696$	5.15634			0.195451
$697$	−0.684438			−0.0259249
$698$	−14.7470	−	25.5425i	−0.558181	−	0.966798i
$699$	0.940563	+	1.62910i	0.0355754	+	0.0616183i
$700$	−0.764886			−0.0289100
$701$	−13.9037	+	24.0819i	−0.525134	+	0.909560i	0.474437	+	0.880289i	$0.342652\pi$
$701$	−13.9037	+	24.0819i	−0.525134	+	0.909560i	−0.999572	+	0.0292702i	$0.990682\pi$
$702$	−20.3124	−	1.68641i	−0.766643	−	0.0636496i
$703$	32.7060	+	56.6484i	1.23353	+	2.13654i
$704$	12.7377			0.480069
$705$	−2.21336	+	3.83364i	−0.0833598	+	0.144383i
$706$	39.7196			1.49487
$707$	−0.0620133	+	0.107410i	−0.00233225	+	0.00403958i
$708$	0.455343	−	0.788677i	0.0171128	−	0.0296403i
$709$	−13.4659	−	23.3237i	−0.505724	−	0.875940i	−0.999978	−	0.00662256i	$-0.997892\pi$
$709$	−13.4659	−	23.3237i	−0.505724	−	0.875940i	0.494254	−	0.869318i	$-0.335441\pi$
$710$	−2.50094	+	4.33175i	−0.0938585	+	0.162568i
$711$	−7.46450	−	12.9289i	−0.279941	−	0.484871i
$712$	21.7000	−	37.5856i	0.813243	−	1.40858i
$713$	0.156098	+	0.794475i	0.00584592	+	0.0297533i
$714$	−0.965283			−0.0361248
$715$	−5.37009	+	7.74210i	−0.200830	+	0.289538i
$716$	3.69434	−	6.39879i	0.138064	−	0.239134i
$717$	2.00242	−	3.46829i	0.0747816	−	0.129526i
$718$	20.0651			0.748821
$719$	27.7258			1.03400			0.516998	−	0.855987i	$-0.327049\pi$
$719$	27.7258			1.03400			0.516998	+	0.855987i	$0.327049\pi$
$720$	−7.26367	+	12.5810i	−0.270701	+	0.468868i
$721$	−3.74521	−	6.48689i	−0.139479	−	0.241584i
$722$	−17.3361	+	30.0271i	−0.645185	+	1.11749i
$723$	6.19982	+	10.7384i	0.230574	+	0.399365i
$724$	3.55696	−	6.16083i	0.132193	−	0.228965i
$725$	−5.45595	−	9.44998i	−0.202629	−	0.350963i
$726$	−6.57429			−0.243995
$727$	25.4822	−	44.1365i	0.945082	−	1.63693i	0.189496	−	0.981882i	$-0.439315\pi$
$727$	25.4822	−	44.1365i	0.945082	−	1.63693i	0.755586	−	0.655049i	$-0.227352\pi$
$728$	2.24648	+	4.76236i	0.0832599	+	0.176505i
$729$	−6.29679			−0.233214
$730$	−2.66811	−	4.62130i	−0.0987512	−	0.171042i
$731$	0.370908			0.0137185
$732$	1.21273			0.0448238
$733$	4.72905	+	8.19095i	0.174671	+	0.302540i	0.940048	−	0.341044i	$-0.110780\pi$
$733$	4.72905	+	8.19095i	0.174671	+	0.302540i	−0.765376	+	0.643583i	$0.777447\pi$
$734$	14.8524	−	25.7251i	0.548212	−	0.949532i
$735$	2.69506	−	4.66798i	0.0994088	−	0.172181i
$736$	−0.305094			−0.0112459
$737$	−3.99874			−0.147295
$738$	0.830607	+	1.43865i	0.0305751	+	0.0529576i
$739$	−34.5040			−1.26925			−0.634625	−	0.772820i	$-0.718846\pi$
$739$	−34.5040			−1.26925			−0.634625	+	0.772820i	$0.718846\pi$
$740$	−4.68389			−0.172183
$741$	−8.72323	+	12.5763i	−0.320456	+	0.462003i
$742$	−1.10742			−0.0406546
$743$	5.40465	−	9.36112i	0.198277	−	0.343426i	−0.749693	−	0.661786i	$-0.769799\pi$
$743$	5.40465	−	9.36112i	0.198277	−	0.343426i	0.947970	+	0.318360i	$0.103132\pi$
$744$	8.69186	+	2.97320i	0.318659	+	0.109003i
$745$	2.55198	+	4.42016i	0.0934974	+	0.161942i
$746$	−0.486033			−0.0177949
$747$	−40.5253			−1.48274
$748$	0.650994	+	1.12755i	0.0238027	+	0.0412275i
$749$	−4.81521	−	8.34019i	−0.175944	−	0.304744i
$750$	−10.5928			−0.386794
$751$	6.41880	+	11.1177i	0.234225	+	0.405690i	0.959047	−	0.283246i	$-0.0914113\pi$
$751$	6.41880	+	11.1177i	0.234225	+	0.405690i	−0.724822	+	0.688936i	$0.758078\pi$
$752$	12.6072	−	21.8364i	0.459739	−	0.796291i
$753$	−4.06907	−	7.04784i	−0.148285	−	0.256838i
$754$	9.89841	−	14.2706i	0.360479	−	0.519705i
$755$	0.138834	+	0.240468i	0.00505269	+	0.00875151i
$756$	0.401741	+	0.695835i	0.0146112	+	0.0253073i
$757$	−15.2458			−0.554116			−0.277058	−	0.960853i	$-0.589359\pi$
$757$	−15.2458			−0.554116			−0.277058	+	0.960853i	$0.589359\pi$
$758$	−32.9173			−1.19561
$759$	0.203899			0.00740107
$760$	9.90426	+	17.1547i	0.359265	+	0.622266i
$761$	−25.6961			−0.931482			−0.465741	−	0.884921i	$-0.654212\pi$
$761$	−25.6961			−0.931482			−0.465741	+	0.884921i	$0.654212\pi$
$762$	7.51535	+	13.0170i	0.272252	+	0.471555i
$763$	10.9173			0.395234
$764$	−3.99635			−0.144583
$765$	5.13431			0.185631
$766$	11.0912	+	19.2105i	0.400740	+	0.694102i
$767$	5.66020	+	11.9992i	0.204378	+	0.433265i
$768$	−2.87173	+	4.97399i	−0.103625	+	0.179483i
$769$	20.8204	+	36.0620i	0.750802	+	1.30043i	0.947434	+	0.319950i	$0.103666\pi$
$769$	20.8204	+	36.0620i	0.750802	+	1.30043i	−0.196632	+	0.980477i	$0.563001\pi$
$770$	2.34940			0.0846663
$771$	3.23723	+	5.60704i	0.116586	+	0.201933i
$772$	3.28458	−	5.68906i	0.118215	−	0.204754i
$773$	−2.54959	−	4.41603i	−0.0917025	−	0.158833i	0.816525	−	0.577310i	$-0.195898\pi$
$773$	−2.54959	−	4.41603i	−0.0917025	−	0.158833i	−0.908228	+	0.418477i	$0.862564\pi$
$774$	−0.450120	−	0.779630i	−0.0161792	−	0.0280232i
$775$	−3.74794	−	19.0754i	−0.134630	−	0.685210i
$776$	−7.34705	−	12.7255i	−0.263744	−	0.456817i
$777$	1.95161	−	3.38028i	0.0700135	−	0.121267i
$778$	4.06804	+	7.04604i	0.145846	+	0.252613i
$779$	2.70602			0.0969532
$780$	−0.467574	−	0.991222i	−0.0167418	−	0.0354914i
$781$	−2.81106	+	4.86890i	−0.100588	+	0.174223i
$782$	0.182592	+	0.316259i	0.00652949	+	0.0113094i
$783$	−5.73125	+	9.92681i	−0.204818	+	0.354755i
$784$	−15.3510	+	26.5888i	−0.548251	+	0.949598i
$785$	−10.5030	−	18.1917i	−0.374868	−	0.649291i
$786$	−2.94482	+	5.10058i	−0.105038	+	0.181932i
$787$	−32.2535			−1.14971			−0.574857	−	0.818254i	$-0.694942\pi$
$787$	−32.2535			−1.14971			−0.574857	+	0.818254i	$0.694942\pi$
$788$	−3.70471	−	6.41675i	−0.131975	−	0.228587i
$789$	14.4896			0.515843
$790$	5.50727	−	9.53887i	0.195940	−	0.339378i
$791$	−1.34553	+	2.33053i	−0.0478416	+	0.0828641i
$792$	−6.83415	+	11.8371i	−0.242841	+	0.420613i
$793$	−10.0694	+	14.5171i	−0.357575	+	0.515518i
$794$	12.7879	−	22.1493i	0.453825	−	0.786048i
$795$	−0.996957			−0.0353584
$796$	5.27295			0.186895
$797$	−8.00881	+	13.8717i	−0.283687	+	0.491360i	−0.972290	−	0.233779i	$-0.924891\pi$
$797$	−8.00881	+	13.8717i	−0.283687	+	0.491360i	0.688603	+	0.725138i	$0.258224\pi$
$798$	3.81638			0.135098
$799$	−8.91140			−0.315263
$800$	7.32536			0.258990
$801$	22.2376	+	38.5166i	0.785726	+	1.36092i
$802$	25.4057	+	44.0039i	0.897105	+	1.55383i
$803$	−2.99896	−	5.19436i	−0.105831	−	0.183305i
$804$	0.232562	−	0.402809i	0.00820182	−	0.0142060i
$805$	0.104179			0.00367183
$806$	24.9140	−	18.3479i	0.877558	−	0.646278i
$807$	−3.75680			−0.132246
$808$	0.266182	−	0.461041i	0.00936426	−	0.0162194i
$809$	8.08592	+	14.0052i	0.284286	+	0.492398i	0.972436	−	0.233171i	$-0.0749102\pi$
$809$	8.08592	+	14.0052i	0.284286	+	0.492398i	−0.688150	+	0.725569i	$0.741577\pi$
$810$	−4.99772	−	8.65631i	−0.175602	−	0.304152i
$811$	16.3526	+	28.3235i	0.574216	+	0.994572i	0.996126	+	0.0879339i	$0.0280264\pi$
$811$	16.3526	+	28.3235i	0.574216	+	0.994572i	−0.421910	+	0.906638i	$0.638640\pi$
$812$	−0.684635			−0.0240260
$813$	−9.56552			−0.335477
$814$	−33.3008			−1.16719
$815$	6.20525	−	10.7478i	0.217360	−	0.376479i
$816$	4.94981			0.173278
$817$	−1.46644			−0.0513041
$818$	27.5968	−	47.7991i	0.964900	−	1.67126i
$819$	−5.37755	−	0.446464i	−0.187907	−	0.0156007i
$820$	−0.0968837	+	0.167807i	−0.00338332	+	0.00586009i
$821$	−7.78245	+	13.4796i	−0.271609	+	0.470441i	−0.969274	−	0.245983i	$-0.920889\pi$
$821$	−7.78245	+	13.4796i	−0.271609	+	0.470441i	0.697665	+	0.716424i	$0.254222\pi$
$822$	−7.79186	+	13.4959i	−0.271772	+	0.470724i
$823$	−7.70000			−0.268405			−0.134202	−	0.990954i	$-0.542847\pi$
$823$	−7.70000			−0.268405			−0.134202	+	0.990954i	$0.542847\pi$
$824$	16.0757	+	27.8439i	0.560024	+	0.969989i
$825$	−4.89564			−0.170444
$826$	1.65406	−	2.86492i	0.0575523	−	0.0996834i
$827$	5.34883	+	9.26444i	0.185997	+	0.322156i	0.943912	−	0.330197i	$-0.107115\pi$
$827$	5.34883	+	9.26444i	0.185997	+	0.322156i	−0.757915	+	0.652353i	$0.773782\pi$
$828$	0.0700637	−	0.121354i	0.00243488	−	0.00421734i
$829$	−2.53419	+	4.38935i	−0.0880162	+	0.152449i	−0.906672	−	0.421835i	$-0.861386\pi$
$829$	−2.53419	+	4.38935i	−0.0880162	+	0.152449i	0.818656	+	0.574284i	$0.194719\pi$
$830$	−14.9497	−	25.8936i	−0.518911	−	0.898780i
$831$	−1.42811	+	2.47356i	−0.0495407	+	0.0858070i
$832$	−9.20870	−	19.5217i	−0.319254	−	0.676794i
$833$	10.8508			0.375959
$834$	−1.80539	−	3.12702i	−0.0625154	−	0.108280i
$835$	12.9887	−	22.4971i	0.449492	−	0.778543i
$836$	−2.57379	−	4.45794i	−0.0890165	−	0.154181i
$837$	−15.3849	+	13.4286i	−0.531779	+	0.464159i
$838$	21.0679	+	36.4907i	0.727779	+	1.26055i
$839$	25.3020	+	43.8243i	0.873521	+	1.51298i	0.858330	+	0.513099i	$0.171503\pi$
$839$	25.3020	+	43.8243i	0.873521	+	1.51298i	0.0151917	+	0.999885i	$0.495164\pi$
$840$	0.591000	−	1.02364i	0.0203914	−	0.0353190i
$841$	9.61648	+	16.6562i	0.331603	+	0.574353i
$842$	−8.10445			−0.279298
$843$	−9.83919	−	17.0420i	−0.338880	−	0.586957i
$844$	−0.367235	+	0.636070i	−0.0126407	+	0.0218944i
$845$	15.7478	+	2.63304i	0.541742	+	0.0905793i
$846$	10.8145	+	18.7313i	0.371811	+	0.643996i
$847$	−3.77557			−0.129730
$848$	5.67865			0.195006
$849$	−5.72359			−0.196433
$850$	−4.38406	−	7.59342i	−0.150372	−	0.260452i
$851$	−1.47666			−0.0506192
$852$	−0.326976	−	0.566339i	−0.0112020	−	0.0194025i
$853$	−11.5041			−0.393891			−0.196946	−	0.980414i	$-0.563102\pi$
$853$	−11.5041			−0.393891			−0.196946	+	0.980414i	$0.563102\pi$
$854$	4.40532			0.150747
$855$	−20.2992			−0.694218
$856$	20.6685	+	35.7989i	0.706435	+	1.22358i
$857$	−14.5877	−	25.2667i	−0.498307	−	0.863093i	0.501691	−	0.865047i	$-0.332711\pi$
$857$	−14.5877	−	25.2667i	−0.498307	−	0.863093i	−0.999998	+	0.00195414i	$0.999378\pi$
$858$	−3.32429	−	7.04724i	−0.113489	−	0.240589i
$859$	−25.1594	−	43.5773i	−0.858427	−	1.48684i	−0.873429	−	0.486951i	$-0.838109\pi$
$859$	−25.1594	−	43.5773i	−0.858427	−	1.48684i	0.0150023	−	0.999887i	$-0.495224\pi$
$860$	0.0525029	−	0.0909377i	0.00179033	−	0.00310095i
$861$	−0.0807358	−	0.139838i	−0.00275147	−	0.00476568i
$862$	−35.5035			−1.20925
$863$	13.0118	+	22.5371i	0.442926	+	0.767171i	0.997905	−	0.0646934i	$-0.0206069\pi$
$863$	13.0118	+	22.5371i	0.442926	+	0.767171i	−0.554979	+	0.831865i	$0.687274\pi$
$864$	−3.84749	−	6.66405i	−0.130894	−	0.226716i
$865$	−4.18492			−0.142292
$866$	−54.7246			−1.85962
$867$	4.72668	+	8.18684i	0.160526	+	0.278040i
$868$	−1.15407	−	0.394768i	−0.0391715	−	0.0133993i
$869$	6.19019	−	10.7217i	0.209988	−	0.363709i
$870$	−3.89856			−0.132174
$871$	2.89089	+	6.12846i	0.0979540	+	0.207655i
$872$	−46.8608			−1.58691
$873$	15.0581			0.509639
$874$	−0.721904	−	1.25037i	−0.0244188	−	0.0422945i
$875$	−6.08336			−0.205655
$876$	0.697665			0.0235719
$877$	22.3774	−	38.7587i	0.755630	−	1.30879i	−0.189430	−	0.981894i	$-0.560664\pi$
$877$	22.3774	−	38.7587i	0.755630	−	1.30879i	0.945060	−	0.326896i	$-0.106003\pi$
$878$	−15.4194	+	26.7073i	−0.520381	+	0.901326i
$879$	−2.24134	−	3.88212i	−0.0755986	−	0.130941i
$880$	−12.0473			−0.406114
$881$	−52.4689			−1.76772			−0.883862	−	0.467748i	$-0.845065\pi$
$881$	−52.4689			−1.76772			−0.883862	+	0.467748i	$0.845065\pi$
$882$	−13.1682	−	22.8079i	−0.443395	−	0.767982i
$883$	33.1798			1.11659			0.558294	−	0.829643i	$-0.311456\pi$
$883$	33.1798			1.11659			0.558294	+	0.829643i	$0.311456\pi$
$884$	1.25745	−	1.81288i	0.0422927	−	0.0609737i
$885$	1.48908	−	2.57916i	0.0500548	−	0.0866974i
$886$	−29.1856			−0.980510
$887$	−16.8206	−	29.1341i	−0.564779	−	0.978226i	−0.997070	−	0.0764922i	$-0.975628\pi$
$887$	−16.8206	−	29.1341i	−0.564779	−	0.978226i	0.432291	−	0.901734i	$-0.357705\pi$
$888$	−8.37696	+	14.5093i	−0.281112	+	0.486901i
$889$	4.31601	+	7.47555i	0.144754	+	0.250722i
$890$	−16.4068	+	28.4174i	−0.549956	+	0.952553i
$891$	−5.61746	−	9.72972i	−0.188192	−	0.325958i
$892$	0.120538	−	0.208778i	0.00403591	−	0.00699040i
$893$	35.2324			1.17901
$894$	−4.22086			−0.141167
$895$	12.0814	−	20.9255i	0.403835	−	0.699464i
$896$	−3.91481	+	6.78065i	−0.130785	+	0.226525i
$897$	−0.147409	−	0.312496i	−0.00492184	−	0.0104339i
$898$	−24.5543			−0.819386
$899$	−3.35471	−	17.0741i	−0.111886	−	0.569452i
$900$	−1.68224	+	2.91372i	−0.0560746	+	0.0971241i
$901$	−1.00349	−	1.73809i	−0.0334310	−	0.0579041i
$902$	−0.688809	+	1.19305i	−0.0229348	+	0.0397243i
$903$	0.0437521	+	0.0757808i	0.00145598	+	0.00252183i
$904$	5.77548	−	10.0034i	0.192089	−	0.332709i
$905$	11.6321	−	20.1473i	0.386663	−	0.669721i
$906$	−0.229625			−0.00762878
$907$	2.59313	−	4.49144i	0.0861036	−	0.149136i	−0.819757	−	0.572711i	$-0.805892\pi$
$907$	2.59313	−	4.49144i	0.0861036	−	0.149136i	0.905861	+	0.423575i	$0.139225\pi$
$908$	−5.36191			−0.177941
$909$	0.272776	+	0.472462i	0.00904741	+	0.0156706i
$910$	−1.69850	−	3.60068i	−0.0563046	−	0.119361i
$911$	19.9285	−	34.5172i	0.660261	−	1.14361i	−0.320286	−	0.947321i	$-0.603779\pi$
$911$	19.9285	−	34.5172i	0.660261	−	1.14361i	0.980547	−	0.196285i	$-0.0628878\pi$
$912$	−19.5697			−0.648019
$913$	−16.8035	−	29.1045i	−0.556114	−	0.963218i
$914$	−17.1672	−	29.7344i	−0.567839	−	0.983526i
$915$	3.96591			0.131109
$916$	1.92449			0.0635868
$917$	−1.69119	+	2.92923i	−0.0558480	+	0.0967315i
$918$	−4.60528	+	7.97658i	−0.151997	+	0.263266i
$919$	−27.7899	+	48.1334i	−0.916703	+	1.58778i	−0.112314	+	0.993673i	$0.535826\pi$
$919$	−27.7899	+	48.1334i	−0.916703	+	1.58778i	−0.804389	+	0.594103i	$0.797507\pi$
$920$	−0.447172			−0.0147428
$921$	−20.5380			−0.676750
$922$	−28.2321			−0.929776
$923$	9.49433	+	0.788256i	0.312510	+	0.0259457i
$924$	−0.153582	+	0.266011i	−0.00505246	+	0.00875112i
$925$	35.4548			1.16575
$926$	18.8117	−	32.5829i	0.618192	−	1.07074i
$927$	−32.9478			−1.08215
$928$	6.55679			0.215237
$929$	4.56660	+	7.90958i	0.149825	+	0.259505i	0.931163	−	0.364604i	$-0.118796\pi$
$929$	4.56660	+	7.90958i	0.149825	+	0.259505i	−0.781338	+	0.624109i	$0.785462\pi$
$930$	−6.57167	−	2.24795i	−0.215494	−	0.0737133i
$931$	−42.9003			−1.40600
$932$	0.536042	+	0.928453i	0.0175587	+	0.0304125i
$933$	−0.653173	−	1.13133i	−0.0213839	−	0.0370381i
$934$	−0.929255	+	1.60952i	−0.0304062	+	0.0526650i
$935$	2.12890	+	3.68737i	0.0696225	+	0.120590i
$936$	23.0823	+	1.91638i	0.754467	+	0.0626387i
$937$	24.5211	−	42.4718i	0.801070	−	1.38749i	−0.117843	−	0.993032i	$-0.537598\pi$
$937$	24.5211	−	42.4718i	0.801070	−	1.38749i	0.918913	−	0.394461i	$-0.129069\pi$
$938$	0.844796	−	1.46323i	0.0275836	−	0.0477762i
$939$	6.90772			0.225425
$940$	−1.26143	+	2.18486i	−0.0411433	+	0.0712622i
$941$	−14.1161	−	24.4498i	−0.460172	−	0.797041i	0.538797	−	0.842435i	$-0.318879\pi$
$941$	−14.1161	−	24.4498i	−0.460172	−	0.797041i	−0.998969	+	0.0453944i	$0.985546\pi$
$942$	17.3715			0.565994
$943$	−0.0305438	+	0.0529035i	−0.000994644	+	0.00172277i
$944$	−8.48176	+	14.6908i	−0.276058	+	0.478146i
$945$	1.31379	+	2.27554i	0.0427374	+	0.0740234i
$946$	0.373277	−	0.646535i	0.0121363	−	0.0210207i
$947$	−0.552811	−	0.957497i	−0.0179640	−	0.0311145i	0.856904	−	0.515477i	$-0.172385\pi$
$947$	−0.552811	−	0.957497i	−0.0179640	−	0.0311145i	−0.874868	+	0.484362i	$0.839052\pi$
$948$	0.720028	+	1.24712i	0.0233854	+	0.0405047i
$949$	−5.79277	+	8.35148i	−0.188041	+	0.271100i
$950$	17.3330	+	30.0216i	0.562357	+	0.974030i
$951$	19.9273			0.646187
$952$	2.37948			0.0771194
$953$	−13.2934	−	23.0248i	−0.430615	−	0.745847i	0.566312	−	0.824191i	$-0.308370\pi$
$953$	−13.2934	−	23.0248i	−0.430615	−	0.745847i	−0.996926	+	0.0783446i	$0.975037\pi$
$954$	−2.43558	+	4.21855i	−0.0788549	+	0.136581i
$955$	−13.0690			−0.422902
$956$	1.14121	−	1.97663i	0.0369094	−	0.0639289i
$957$	−4.38200			−0.141650
$958$	51.3044			1.65757
$959$	−4.47481	+	7.75060i	−0.144499	+	0.250280i
$960$	−2.42261	+	4.19608i	−0.0781894	+	0.135428i
$961$	4.19018	−	30.7155i	0.135167	−	0.990823i
$962$	24.0749	+	51.0368i	0.776205	+	1.64549i
$963$	−42.3610			−1.36506
$964$	3.53338	+	6.11999i	0.113802	+	0.197112i
$965$	10.7413	−	18.6045i	0.345776	−	0.598901i
$966$	−0.0430769	+	0.0746114i	−0.00138598	+	0.00240058i
$967$	5.64972	−	9.78561i	0.181683	−	0.314684i	−0.760771	−	0.649021i	$-0.775179\pi$
$967$	5.64972	−	9.78561i	0.181683	−	0.314684i	0.942454	+	0.334337i	$0.108512\pi$
$968$	16.2060			0.520881
$969$	3.45821	+	5.98979i	0.111094	+	0.192420i
$970$	5.55489	+	9.62136i	0.178357	+	0.308923i
$971$	−3.32289	+	5.75541i	−0.106636	+	0.184700i	−0.914406	−	0.404799i	$-0.867341\pi$
$971$	−3.32289	+	5.75541i	−0.106636	+	0.184700i	0.807769	+	0.589499i	$0.200675\pi$
$972$	5.43925			0.174464
$973$	−1.03682	−	1.79583i	−0.0332389	−	0.0575715i
$974$	−13.1892	−	22.8443i	−0.422608	−	0.731978i
$975$	3.53931	+	7.50306i	0.113349	+	0.240290i
$976$	−22.5897			−0.723080
$977$	−9.08273	+	15.7317i	−0.290582	+	0.503303i	−0.973948	−	0.226774i	$-0.927182\pi$
$977$	−9.08273	+	15.7317i	−0.290582	+	0.503303i	0.683365	+	0.730077i	$0.260516\pi$
$978$	5.13160	+	8.88819i	0.164090	+	0.284213i
$979$	−18.4413	+	31.9412i	−0.589386	+	1.02085i
$980$	1.53596	−	2.66036i	0.0490644	−	0.0849821i
$981$	24.0108	−	41.5880i	0.766607	−	1.32780i
$982$	−9.89455	+	17.1379i	−0.315748	+	0.546891i
$983$	7.90826	+	13.6975i	0.252234	+	0.436883i	0.964141	−	0.265392i	$-0.0855013\pi$
$983$	7.90826	+	13.6975i	0.252234	+	0.436883i	−0.711906	+	0.702274i	$0.752168\pi$
$984$	0.346545	+	0.600234i	0.0110475	+	0.0191348i
$985$	−12.1153	−	20.9843i	−0.386024	−	0.668614i
$986$	−3.92409	−	6.79673i	−0.124969	−	0.216452i
$987$	−1.05118	−	1.82070i	−0.0334595	−	0.0579535i
$988$	−4.97151	+	7.16746i	−0.158165	+	0.228027i
$989$	0.0165522	−	0.0286693i	0.000526330	−	0.000911630i
$990$	5.16710	−	8.94968i	0.164221	−	0.284440i
$991$	−21.8499	+	37.8451i	−0.694084	+	1.20219i	0.276404	+	0.961042i	$0.410857\pi$
$991$	−21.8499	+	37.8451i	−0.694084	+	1.20219i	−0.970488	+	0.241148i	$0.922476\pi$
$992$	11.0525	+	3.78071i	0.350919	+	0.120038i
$993$	4.19682			0.133182
$994$	−1.18776	−	2.05727i	−0.0376735	−	0.0652525i
$995$	17.2438			0.546664
$996$	3.90908			0.123864
$997$	26.4761	−	45.8580i	0.838507	−	1.45234i	−0.0526350	−	0.998614i	$-0.516762\pi$
$997$	26.4761	−	45.8580i	0.838507	−	1.45234i	0.891142	−	0.453724i	$-0.149905\pi$
$998$	−14.3950	−	24.9329i	−0.455666	−	0.789237i
$999$	−18.6219	−	32.2540i	−0.589170	−	1.02047i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.e.a.191.11	✓	70
13.3	even	3		403.2.g.a.315.11	yes	70
31.25	even	3		403.2.g.a.87.11	yes	70
403.211	even	3	inner	403.2.e.a.211.11	yes	70

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.e.a.191.11	✓	70	1.1	even	1	trivial
403.2.e.a.211.11	yes	70	403.211	even	3	inner
403.2.g.a.87.11	yes	70	31.25	even	3
403.2.g.a.315.11	yes	70	13.3	even	3

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.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.770644 + 1.33479i) q^{2} +(-0.329492 - 0.570697i) q^{3} +(-0.187783 - 0.325250i) q^{4} +(-0.614094 - 1.06364i) q^{5} +1.01568 q^{6} +0.583300 q^{7} -2.50372 q^{8} +(1.28287 - 2.22200i) q^{9} +O(q^{10})\)	\(q+(-0.770644 + 1.33479i) q^{2} +(-0.329492 - 0.570697i) q^{3} +(-0.187783 - 0.325250i) q^{4} +(-0.614094 - 1.06364i) q^{5} +1.01568 q^{6} +0.583300 q^{7} -2.50372 q^{8} +(1.28287 - 2.22200i) q^{9} +1.89299 q^{10} +2.12773 q^{11} +(-0.123746 + 0.214334i) q^{12} +(-1.53824 - 3.26095i) q^{13} +(-0.449516 + 0.778585i) q^{14} +(-0.404678 + 0.700923i) q^{15} +(2.30504 - 3.99245i) q^{16} -1.62931 q^{17} +(1.97727 + 3.42473i) q^{18} +6.44171 q^{19} +(-0.230633 + 0.399468i) q^{20} +(-0.192193 - 0.332887i) q^{21} +(-1.63972 + 2.84008i) q^{22} +(-0.0727100 + 0.125937i) q^{23} +(0.824956 + 1.42887i) q^{24} +(1.74578 - 3.02377i) q^{25} +(5.53814 + 0.459797i) q^{26} -3.66773 q^{27} +(-0.109534 - 0.189718i) q^{28} +(1.56261 - 2.70652i) q^{29} +(-0.623725 - 1.08032i) q^{30} +(4.19465 - 3.66127i) q^{31} +(1.04901 + 1.81694i) q^{32} +(-0.701069 - 1.21429i) q^{33} +(1.25562 - 2.17480i) q^{34} +(-0.358201 - 0.620422i) q^{35} -0.963605 q^{36} +(5.07722 + 8.79400i) q^{37} +(-4.96427 + 8.59836i) q^{38} +(-1.35418 + 1.95233i) q^{39} +(1.53752 + 2.66306i) q^{40} +0.420077 q^{41} +0.592448 q^{42} -0.227647 q^{43} +(-0.399551 - 0.692043i) q^{44} -3.15121 q^{45} +(-0.112067 - 0.194106i) q^{46} +5.46942 q^{47} -3.03797 q^{48} -6.65976 q^{49} +(2.69074 + 4.66050i) q^{50} +(0.536846 + 0.929844i) q^{51} +(-0.771768 + 1.11266i) q^{52} +(0.615895 + 1.06676i) q^{53} +(2.82652 - 4.89567i) q^{54} +(-1.30662 - 2.26314i) q^{55} -1.46042 q^{56} +(-2.12249 - 3.67627i) q^{57} +(2.40843 + 4.17153i) q^{58} -3.67966 q^{59} +0.303967 q^{60} +(-2.45004 - 4.24359i) q^{61} +(1.65446 + 8.42053i) q^{62} +(0.748298 - 1.29609i) q^{63} +5.98651 q^{64} +(-2.52386 + 3.63867i) q^{65} +2.16110 q^{66} -1.87935 q^{67} +(0.305957 + 0.529934i) q^{68} +0.0958295 q^{69} +1.10418 q^{70} +(-1.32116 + 2.28831i) q^{71} +(-3.21195 + 5.56325i) q^{72} +(-1.40947 - 2.44127i) q^{73} -15.6509 q^{74} -2.30088 q^{75} +(-1.20964 - 2.09517i) q^{76} +1.24110 q^{77} +(-1.56237 - 3.31210i) q^{78} +(2.90930 - 5.03905i) q^{79} -5.66205 q^{80} +(-2.64012 - 4.57282i) q^{81} +(-0.323730 + 0.560717i) q^{82} +(-7.89739 - 13.6787i) q^{83} +(-0.0721810 + 0.125021i) q^{84} +(1.00055 + 1.73301i) q^{85} +(0.175435 - 0.303862i) q^{86} -2.05947 q^{87} -5.32723 q^{88} +(-8.66712 + 15.0119i) q^{89} +(2.42846 - 4.20622i) q^{90} +(-0.897256 - 1.90211i) q^{91} +0.0546148 q^{92} +(-3.47158 - 1.18751i) q^{93} +(-4.21497 + 7.30055i) q^{94} +(-3.95582 - 6.85168i) q^{95} +(0.691282 - 1.19733i) q^{96} +(2.93445 + 5.08262i) q^{97} +(5.13230 - 8.88941i) q^{98} +(2.72960 - 4.72780i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 70 q - 2 q^{2} + 4 q^{3} - 34 q^{4} - 2 q^{5} + 8 q^{7} - 6 q^{8} - 29 q^{9}+O(q^{10}) \) 70 * q - 2 * q^2 + 4 * q^3 - 34 * q^4 - 2 * q^5 + 8 * q^7 - 6 * q^8 - 29 * q^9	\( 70 q - 2 q^{2} + 4 q^{3} - 34 q^{4} - 2 q^{5} + 8 q^{7} - 6 q^{8} - 29 q^{9} - 6 q^{10} - 4 q^{11} + 5 q^{12} + q^{13} - 10 q^{14} + q^{15} - 28 q^{16} - 28 q^{17} - 20 q^{18} + 4 q^{19} + 25 q^{20} - 21 q^{21} + 4 q^{22} + 2 q^{23} + 4 q^{24} - 23 q^{25} - 24 q^{26} - 38 q^{27} - 21 q^{28} + 6 q^{29} + 31 q^{30} + 22 q^{31} + 14 q^{32} + 2 q^{33} - 11 q^{34} + 4 q^{35} + 56 q^{36} - 12 q^{37} - 7 q^{38} + 10 q^{39} - q^{40} + 4 q^{41} - 54 q^{42} + 2 q^{43} + 2 q^{44} + 58 q^{45} + 14 q^{46} - 2 q^{48} + 74 q^{49} + 7 q^{50} - 9 q^{51} + 5 q^{52} - 2 q^{53} + 24 q^{54} + 5 q^{55} + 26 q^{56} - q^{57} + 6 q^{58} - 42 q^{59} + 18 q^{60} - 3 q^{61} + 13 q^{62} - 32 q^{63} - 14 q^{64} + 20 q^{65} - 28 q^{66} + 4 q^{67} + 42 q^{68} - 64 q^{69} - 14 q^{70} + 43 q^{71} - 5 q^{72} + 11 q^{73} + 14 q^{74} - 74 q^{75} - 28 q^{76} - 10 q^{77} - 64 q^{78} + 2 q^{79} - 76 q^{80} - 11 q^{81} - 17 q^{82} + 56 q^{83} - 45 q^{84} - 5 q^{85} + 54 q^{86} + 48 q^{87} - 8 q^{88} + 30 q^{89} - 23 q^{90} - 36 q^{91} + 74 q^{92} + 22 q^{93} + 47 q^{94} - 9 q^{95} + 26 q^{96} + 29 q^{97} + 12 q^{98} + 3 q^{99}+O(q^{100}) \) 70 * q - 2 * q^2 + 4 * q^3 - 34 * q^4 - 2 * q^5 + 8 * q^7 - 6 * q^8 - 29 * q^9 - 6 * q^10 - 4 * q^11 + 5 * q^12 + q^13 - 10 * q^14 + q^15 - 28 * q^16 - 28 * q^17 - 20 * q^18 + 4 * q^19 + 25 * q^20 - 21 * q^21 + 4 * q^22 + 2 * q^23 + 4 * q^24 - 23 * q^25 - 24 * q^26 - 38 * q^27 - 21 * q^28 + 6 * q^29 + 31 * q^30 + 22 * q^31 + 14 * q^32 + 2 * q^33 - 11 * q^34 + 4 * q^35 + 56 * q^36 - 12 * q^37 - 7 * q^38 + 10 * q^39 - q^40 + 4 * q^41 - 54 * q^42 + 2 * q^43 + 2 * q^44 + 58 * q^45 + 14 * q^46 - 2 * q^48 + 74 * q^49 + 7 * q^50 - 9 * q^51 + 5 * q^52 - 2 * q^53 + 24 * q^54 + 5 * q^55 + 26 * q^56 - q^57 + 6 * q^58 - 42 * q^59 + 18 * q^60 - 3 * q^61 + 13 * q^62 - 32 * q^63 - 14 * q^64 + 20 * q^65 - 28 * q^66 + 4 * q^67 + 42 * q^68 - 64 * q^69 - 14 * q^70 + 43 * q^71 - 5 * q^72 + 11 * q^73 + 14 * q^74 - 74 * q^75 - 28 * q^76 - 10 * q^77 - 64 * q^78 + 2 * q^79 - 76 * q^80 - 11 * q^81 - 17 * q^82 + 56 * q^83 - 45 * q^84 - 5 * q^85 + 54 * q^86 + 48 * q^87 - 8 * q^88 + 30 * q^89 - 23 * q^90 - 36 * q^91 + 74 * q^92 + 22 * q^93 + 47 * q^94 - 9 * q^95 + 26 * q^96 + 29 * q^97 + 12 * q^98 + 3 * q^99

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