LMFDB - Embedded newform 403.2.c.b.311.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(311,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("403.311");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.c (of order $2$, degree $1$, 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:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			311.6
Character	$\chi$	$=$	403.311
Dual form			403.2.c.b.311.27

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.99449i q^{2} -1.58843 q^{3} -1.97798 q^{4} -2.66789i q^{5} +3.16810i q^{6} +1.73927i q^{7} -0.0439183i q^{8} -0.476895 q^{9} +O(q^{10})$	\(q-1.99449i q^{2} -1.58843 q^{3} -1.97798 q^{4} -2.66789i q^{5} +3.16810i q^{6} +1.73927i q^{7} -0.0439183i q^{8} -0.476895 q^{9} -5.32107 q^{10} -2.93947i q^{11} +3.14188 q^{12} +(-3.42506 + 1.12648i) q^{13} +3.46896 q^{14} +4.23775i q^{15} -4.04355 q^{16} -1.90448 q^{17} +0.951161i q^{18} +4.24721i q^{19} +5.27703i q^{20} -2.76271i q^{21} -5.86273 q^{22} +3.75923 q^{23} +0.0697611i q^{24} -2.11762 q^{25} +(2.24675 + 6.83124i) q^{26} +5.52280 q^{27} -3.44025i q^{28} -4.27051 q^{29} +8.45213 q^{30} -1.00000i q^{31} +7.97698i q^{32} +4.66914i q^{33} +3.79847i q^{34} +4.64018 q^{35} +0.943288 q^{36} -3.05862i q^{37} +8.47100 q^{38} +(5.44046 - 1.78933i) q^{39} -0.117169 q^{40} +5.80663i q^{41} -5.51019 q^{42} -11.6866 q^{43} +5.81421i q^{44} +1.27230i q^{45} -7.49773i q^{46} -10.5119i q^{47} +6.42290 q^{48} +3.97493 q^{49} +4.22356i q^{50} +3.02514 q^{51} +(6.77470 - 2.22816i) q^{52} -13.8094 q^{53} -11.0152i q^{54} -7.84217 q^{55} +0.0763859 q^{56} -6.74639i q^{57} +8.51748i q^{58} -13.7930i q^{59} -8.38218i q^{60} +5.05405 q^{61} -1.99449 q^{62} -0.829450i q^{63} +7.82288 q^{64} +(3.00532 + 9.13767i) q^{65} +9.31253 q^{66} -12.7046i q^{67} +3.76703 q^{68} -5.97127 q^{69} -9.25478i q^{70} -5.83066i q^{71} +0.0209444i q^{72} +4.92019i q^{73} -6.10039 q^{74} +3.36368 q^{75} -8.40089i q^{76} +5.11254 q^{77} +(-3.56881 - 10.8509i) q^{78} +0.743732 q^{79} +10.7877i q^{80} -7.34189 q^{81} +11.5812 q^{82} +0.165627i q^{83} +5.46459i q^{84} +5.08094i q^{85} +23.3087i q^{86} +6.78340 q^{87} -0.129096 q^{88} -1.85214i q^{89} +2.53759 q^{90} +(-1.95926 - 5.95712i) q^{91} -7.43568 q^{92} +1.58843i q^{93} -20.9659 q^{94} +11.3311 q^{95} -12.6709i q^{96} -6.35644i q^{97} -7.92795i q^{98} +1.40182i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{3} - 36 q^{4} + 20 q^{9}+O(q^{10}) $ 32 * q - 4 * q^3 - 36 * q^4 + 20 * q^9	$ 32 q - 4 q^{3} - 36 q^{4} + 20 q^{9} + 4 q^{10} - 16 q^{12} + 10 q^{13} - 16 q^{14} + 28 q^{16} - 8 q^{17} - 16 q^{22} - 8 q^{23} + 4 q^{25} + 18 q^{26} + 20 q^{27} - 16 q^{29} + 40 q^{30} - 4 q^{35} - 44 q^{36} + 12 q^{38} + 4 q^{39} + 28 q^{40} + 28 q^{42} - 32 q^{43} - 64 q^{49} - 64 q^{52} - 12 q^{53} + 44 q^{55} + 8 q^{56} + 16 q^{61} + 8 q^{62} - 76 q^{64} - 66 q^{65} - 68 q^{66} + 64 q^{68} + 20 q^{69} + 16 q^{74} - 32 q^{77} - 20 q^{78} + 64 q^{79} - 16 q^{81} + 12 q^{82} - 72 q^{87} + 80 q^{88} + 68 q^{90} + 22 q^{91} + 28 q^{92} + 88 q^{94} + 4 q^{95}+O(q^{100}) $ 32 * q - 4 * q^3 - 36 * q^4 + 20 * q^9 + 4 * q^10 - 16 * q^12 + 10 * q^13 - 16 * q^14 + 28 * q^16 - 8 * q^17 - 16 * q^22 - 8 * q^23 + 4 * q^25 + 18 * q^26 + 20 * q^27 - 16 * q^29 + 40 * q^30 - 4 * q^35 - 44 * q^36 + 12 * q^38 + 4 * q^39 + 28 * q^40 + 28 * q^42 - 32 * q^43 - 64 * q^49 - 64 * q^52 - 12 * q^53 + 44 * q^55 + 8 * q^56 + 16 * q^61 + 8 * q^62 - 76 * q^64 - 66 * q^65 - 68 * q^66 + 64 * q^68 + 20 * q^69 + 16 * q^74 - 32 * q^77 - 20 * q^78 + 64 * q^79 - 16 * q^81 + 12 * q^82 - 72 * q^87 + 80 * q^88 + 68 * q^90 + 22 * q^91 + 28 * q^92 + 88 * q^94 + 4 * q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$249$	$313$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$		−	1.99449i		−	1.41032i	−0.709050	−	0.705158i	$-0.750876\pi$
$2$		−	1.99449i		−	1.41032i	0.709050	−	0.705158i	$-0.249124\pi$
$3$	−1.58843			−0.917080			−0.458540	−	0.888674i	$-0.651627\pi$
$3$	−1.58843			−0.917080			−0.458540	+	0.888674i	$0.651627\pi$
$4$	−1.97798			−0.988990
$5$		−	2.66789i		−	1.19311i	−0.802570	−	0.596557i	$-0.796535\pi$
$5$		−	2.66789i		−	1.19311i	0.802570	−	0.596557i	$-0.203465\pi$
$6$			3.16810i			1.29337i
$7$			1.73927i			0.657383i	0.944437	+	0.328692i	$0.106608\pi$
$7$			1.73927i			0.657383i	−0.944437	+	0.328692i	$0.893392\pi$
$8$		−	0.0439183i		−	0.0155275i
$9$	−0.476895			−0.158965
$10$	−5.32107			−1.68267
$11$		−	2.93947i		−	0.886283i	−0.896452	−	0.443142i	$-0.853864\pi$
$11$		−	2.93947i		−	0.886283i	0.896452	−	0.443142i	$-0.146136\pi$
$12$	3.14188			0.906983
$13$	−3.42506	+	1.12648i	−0.949941	+	0.312430i
$13$	−3.42506	+	1.12648i	−0.949941	+	0.312430i
$14$	3.46896			0.927118
$15$			4.23775i			1.09418i
$16$	−4.04355			−1.01089
$17$	−1.90448			−0.461905			−0.230952	−	0.972965i	$-0.574184\pi$
$17$	−1.90448			−0.461905			−0.230952	+	0.972965i	$0.574184\pi$
$18$			0.951161i			0.224191i
$19$			4.24721i			0.974376i	0.873297	+	0.487188i	$0.161977\pi$
$19$			4.24721i			0.974376i	−0.873297	+	0.487188i	$0.838023\pi$
$20$			5.27703i			1.17998i
$21$		−	2.76271i		−	0.602873i
$22$	−5.86273			−1.24994
$23$	3.75923			0.783853			0.391927	−	0.919996i	$-0.371809\pi$
$23$	3.75923			0.783853			0.391927	+	0.919996i	$0.371809\pi$
$24$			0.0697611i			0.0142399i
$25$	−2.11762			−0.423523
$26$	2.24675	+	6.83124i	0.440624	+	1.33972i
$27$	5.52280			1.06286
$28$		−	3.44025i		−	0.650146i
$29$	−4.27051			−0.793014			−0.396507	−	0.918032i	$-0.629778\pi$
$29$	−4.27051			−0.793014			−0.396507	+	0.918032i	$0.629778\pi$
$30$	8.45213			1.54314
$31$		−	1.00000i		−	0.179605i
$31$		−	1.00000i		−	0.179605i
$32$			7.97698i			1.41014i
$33$			4.66914i			0.812792i
$34$			3.79847i			0.651432i
$35$	4.64018			0.784334
$36$	0.943288			0.157215
$37$		−	3.05862i		−	0.502835i	−0.967879	−	0.251417i	$-0.919103\pi$
$37$		−	3.05862i		−	0.502835i	0.967879	−	0.251417i	$-0.0808967\pi$
$38$	8.47100			1.37418
$39$	5.44046	−	1.78933i	0.871171	−	0.286523i
$40$	−0.117169			−0.0185260
$41$			5.80663i			0.906843i	0.891296	+	0.453421i	$0.149797\pi$
$41$			5.80663i			0.906843i	−0.891296	+	0.453421i	$0.850203\pi$
$42$	−5.51019			−0.850241
$43$	−11.6866			−1.78218			−0.891092	−	0.453822i	$-0.850060\pi$
$43$	−11.6866			−1.78218			−0.891092	+	0.453822i	$0.850060\pi$
$44$			5.81421i			0.876525i
$45$			1.27230i			0.189663i
$46$		−	7.49773i		−	1.10548i
$47$		−	10.5119i		−	1.53332i	−0.642054	−	0.766659i	$-0.721917\pi$
$47$		−	10.5119i		−	1.53332i	0.642054	−	0.766659i	$-0.278083\pi$
$48$	6.42290			0.927065
$49$	3.97493			0.567847
$50$			4.22356i			0.597301i
$51$	3.02514			0.423604
$52$	6.77470	−	2.22816i	0.939482	−	0.308990i
$53$	−13.8094			−1.89687			−0.948433	−	0.316979i	$-0.897332\pi$
$53$	−13.8094			−1.89687			−0.948433	+	0.316979i	$0.897332\pi$
$54$		−	11.0152i		−	1.49897i
$55$	−7.84217			−1.05744
$56$	0.0763859			0.0102075
$57$		−	6.74639i		−	0.893581i
$58$			8.51748i			1.11840i
$59$		−	13.7930i		−	1.79569i	−0.440308	−	0.897847i	$-0.645131\pi$
$59$		−	13.7930i		−	1.79569i	0.440308	−	0.897847i	$-0.354869\pi$
$60$		−	8.38218i		−	1.08213i
$61$	5.05405			0.647104			0.323552	−	0.946210i	$-0.395123\pi$
$61$	5.05405			0.647104			0.323552	+	0.946210i	$0.395123\pi$
$62$	−1.99449			−0.253300
$63$		−	0.829450i		−	0.104501i
$64$	7.82288			0.977860
$65$	3.00532	+	9.13767i	0.372764	+	1.13339i
$66$	9.31253			1.14629
$67$		−	12.7046i		−	1.55211i	−0.630664	−	0.776056i	$-0.717218\pi$
$67$		−	12.7046i		−	1.55211i	0.630664	−	0.776056i	$-0.282782\pi$
$68$	3.76703			0.456819
$69$	−5.97127			−0.718856
$70$		−	9.25478i		−	1.10616i
$71$		−	5.83066i		−	0.691971i	−0.938240	−	0.345986i	$-0.887545\pi$
$71$		−	5.83066i		−	0.691971i	0.938240	−	0.345986i	$-0.112455\pi$
$72$			0.0209444i			0.00246832i
$73$			4.92019i			0.575865i	0.957651	+	0.287932i	$0.0929678\pi$
$73$			4.92019i			0.575865i	−0.957651	+	0.287932i	$0.907032\pi$
$74$	−6.10039			−0.709156
$75$	3.36368			0.388405
$76$		−	8.40089i		−	0.963648i
$77$	5.11254			0.582628
$78$	−3.56881	−	10.8509i	−0.404088	−	1.22863i
$79$	0.743732			0.0836764			0.0418382	−	0.999124i	$-0.486679\pi$
$79$	0.743732			0.0836764			0.0418382	+	0.999124i	$0.486679\pi$
$80$			10.7877i			1.20611i
$81$	−7.34189			−0.815765
$82$	11.5812			1.27893
$83$			0.165627i			0.0181799i	0.999959	+	0.00908994i	$0.00289346\pi$
$83$			0.165627i			0.0181799i	−0.999959	+	0.00908994i	$0.997107\pi$
$84$			5.46459i			0.596235i
$85$			5.08094i			0.551106i
$86$			23.3087i			2.51344i
$87$	6.78340			0.727257
$88$	−0.129096			−0.0137617
$89$		−	1.85214i		−	0.196326i	−0.995170	−	0.0981631i	$-0.968703\pi$
$89$		−	1.85214i		−	0.196326i	0.995170	−	0.0981631i	$-0.0312967\pi$
$90$	2.53759			0.267485
$91$	−1.95926	−	5.95712i	−0.205386	−	0.624475i
$92$	−7.43568			−0.775223
$93$			1.58843i			0.164712i
$94$	−20.9659			−2.16246
$95$	11.3311			1.16254
$96$		−	12.6709i		−	1.29321i
$97$		−	6.35644i		−	0.645399i	−0.946501	−	0.322699i	$-0.895410\pi$
$97$		−	6.35644i		−	0.645399i	0.946501	−	0.322699i	$-0.104590\pi$
$98$		−	7.92795i		−	0.800844i
$99$			1.40182i			0.140888i
$100$	4.18860			0.418860
$101$	3.11790			0.310243			0.155122	−	0.987895i	$-0.450423\pi$
$101$	3.11790			0.310243			0.155122	+	0.987895i	$0.450423\pi$
$102$		−	6.03359i		−	0.597415i
$103$	2.88258			0.284029			0.142015	−	0.989865i	$-0.454642\pi$
$103$	2.88258			0.284029			0.142015	+	0.989865i	$0.454642\pi$
$104$	0.0494731	+	0.150423i	0.00485124	+	0.0147502i
$105$	−7.37060			−0.719297
$106$			27.5427i			2.67518i
$107$	−7.35117			−0.710664			−0.355332	−	0.934740i	$-0.615632\pi$
$107$	−7.35117			−0.710664			−0.355332	+	0.934740i	$0.615632\pi$
$108$	−10.9240			−1.05116
$109$		−	12.9872i		−	1.24395i	−0.783038	−	0.621974i	$-0.786331\pi$
$109$		−	12.9872i		−	1.24395i	0.783038	−	0.621974i	$-0.213669\pi$
$110$			15.6411i			1.49132i
$111$			4.85841i			0.461140i
$112$		−	7.03285i		−	0.664541i
$113$	−7.63258			−0.718013			−0.359006	−	0.933335i	$-0.616884\pi$
$113$	−7.63258			−0.718013			−0.359006	+	0.933335i	$0.616884\pi$
$114$	−13.4556			−1.26023
$115$		−	10.0292i		−	0.935227i
$116$	8.44698			0.784282
$117$	1.63339	−	0.537213i	0.151007	−	0.0496653i
$118$	−27.5099			−2.53249
$119$		−	3.31242i		−	0.303649i
$120$	0.186115			0.0169899
$121$	2.35952			0.214502
$122$		−	10.0802i		−	0.912621i
$123$		−	9.22341i		−	0.831647i
$124$			1.97798i			0.177628i
$125$		−	7.68987i		−	0.687803i
$126$	−1.65433			−0.147379
$127$	−0.0992933			−0.00881085			−0.00440543	−	0.999990i	$-0.501402\pi$
$127$	−0.0992933			−0.00881085			−0.00440543	+	0.999990i	$0.501402\pi$
$128$			0.351325i			0.0310530i
$129$	18.5633			1.63440
$130$	18.2250	−	5.99408i	1.59844	−	0.525715i
$131$	1.56404			0.136651			0.0683256	−	0.997663i	$-0.478234\pi$
$131$	1.56404			0.136651			0.0683256	+	0.997663i	$0.478234\pi$
$132$		−	9.23546i		−	0.803843i
$133$	−7.38705			−0.640539
$134$	−25.3391			−2.18897
$135$		−	14.7342i		−	1.26812i
$136$			0.0836416i			0.00717221i
$137$		−	7.31021i		−	0.624553i	−0.949991	−	0.312277i	$-0.898908\pi$
$137$		−	7.31021i		−	0.624553i	0.949991	−	0.312277i	$-0.101092\pi$
$138$			11.9096i			1.01381i
$139$	8.35831			0.708943			0.354471	−	0.935067i	$-0.384661\pi$
$139$	8.35831			0.708943			0.354471	+	0.935067i	$0.384661\pi$
$140$	−9.17819			−0.775698
$141$			16.6974i			1.40618i
$142$	−11.6292			−0.975898
$143$	3.31126	+	10.0679i	0.276901	+	0.841917i
$144$	1.92835			0.160696
$145$			11.3932i			0.946156i
$146$	9.81326			0.812151
$147$	−6.31389			−0.520761
$148$			6.04990i			0.497299i
$149$			14.9219i			1.22245i	0.791456	+	0.611226i	$0.209323\pi$
$149$			14.9219i			1.22245i	−0.791456	+	0.611226i	$0.790677\pi$
$150$		−	6.70882i		−	0.547773i
$151$			13.0134i			1.05902i	0.848304	+	0.529509i	$0.177624\pi$
$151$			13.0134i			1.05902i	−0.848304	+	0.529509i	$0.822376\pi$
$152$	0.186530			0.0151296
$153$	0.908238			0.0734267
$154$		−	10.1969i		−	0.821689i
$155$	−2.66789			−0.214290
$156$	−10.7611	+	3.53927i	−0.861580	+	0.283368i
$157$	−18.1118			−1.44548			−0.722738	−	0.691122i	$-0.757117\pi$
$157$	−18.1118			−1.44548			−0.722738	+	0.691122i	$0.757117\pi$
$158$		−	1.48336i		−	0.118010i
$159$	21.9352			1.73958
$160$	21.2817			1.68246
$161$			6.53832i			0.515292i
$162$			14.6433i			1.15049i
$163$			3.67145i			0.287570i	0.989609	+	0.143785i	$0.0459274\pi$
$163$			3.67145i			0.287570i	−0.989609	+	0.143785i	$0.954073\pi$
$164$		−	11.4854i		−	0.896858i
$165$	12.4567			0.969755
$166$	0.330340			0.0256394
$167$			3.59433i			0.278138i	0.990283	+	0.139069i	$0.0444110\pi$
$167$			3.59433i			0.278138i	−0.990283	+	0.139069i	$0.955589\pi$
$168$	−0.121334			−0.00936108
$169$	10.4621	−	7.71653i	0.804776	−	0.593579i
$170$	10.1339			0.777233
$171$		−	2.02547i		−	0.154892i
$172$	23.1158			1.76256
$173$	13.7740			1.04721			0.523607	−	0.851960i	$-0.324586\pi$
$173$	13.7740			1.04721			0.523607	+	0.851960i	$0.324586\pi$
$174$		−	13.5294i		−	1.02566i
$175$		−	3.68311i		−	0.278417i
$176$			11.8859i			0.895934i
$177$			21.9092i			1.64679i
$178$	−3.69407			−0.276882
$179$	13.7364			1.02671			0.513353	−	0.858178i	$-0.328403\pi$
$179$	13.7364			1.02671			0.513353	+	0.858178i	$0.328403\pi$
$180$		−	2.51659i		−	0.187575i
$181$	−8.36084			−0.621457			−0.310728	−	0.950499i	$-0.600573\pi$
$181$	−8.36084			−0.621457			−0.310728	+	0.950499i	$0.600573\pi$
$182$	−11.8814	+	3.90771i	−0.880707	+	0.289659i
$183$	−8.02799			−0.593446
$184$		−	0.165099i		−	0.0121712i
$185$	−8.16006			−0.599940
$186$	3.16810			0.232296
$187$			5.59817i			0.409379i
$188$			20.7923i			1.51644i
$189$			9.60565i			0.698709i
$190$		−	22.5997i		−	1.63955i
$191$	25.1884			1.82257			0.911286	−	0.411774i	$-0.135091\pi$
$191$	25.1884			1.82257			0.911286	+	0.411774i	$0.135091\pi$
$192$	−12.4261			−0.896776
$193$		−	8.03820i		−	0.578603i	−0.957238	−	0.289301i	$-0.906577\pi$
$193$		−	8.03820i		−	0.578603i	0.957238	−	0.289301i	$-0.0934229\pi$
$194$	−12.6778			−0.910216
$195$	−4.77374	−	14.5145i	−0.341855	−	1.03941i
$196$	−7.86233			−0.561595
$197$		−	2.79581i		−	0.199193i	−0.995028	−	0.0995964i	$-0.968245\pi$
$197$		−	2.79581i		−	0.199193i	0.995028	−	0.0995964i	$-0.0317552\pi$
$198$	2.79591			0.198696
$199$	16.3408			1.15837			0.579183	−	0.815197i	$-0.303372\pi$
$199$	16.3408			1.15837			0.579183	+	0.815197i	$0.303372\pi$
$200$			0.0930021i			0.00657624i
$201$			20.1803i			1.42341i
$202$		−	6.21862i		−	0.437541i
$203$		−	7.42758i		−	0.521314i
$204$	−5.98366			−0.418940
$205$	15.4914			1.08197
$206$		−	5.74927i		−	0.400571i
$207$	−1.79276			−0.124605
$208$	13.8494	−	4.55499i	0.960285	−	0.315832i
$209$	12.4845			0.863573
$210$			14.7006i			1.01444i
$211$	16.1104			1.10909			0.554544	−	0.832155i	$-0.312893\pi$
$211$	16.1104			1.10909			0.554544	+	0.832155i	$0.312893\pi$
$212$	27.3147			1.87598
$213$			9.26158i			0.634593i
$214$			14.6618i			1.00226i
$215$			31.1784i			2.12635i
$216$		−	0.242552i		−	0.0165036i
$217$	1.73927			0.118070
$218$	−25.9028			−1.75436
$219$		−	7.81537i		−	0.528114i
$220$	15.5117			1.04580
$221$	6.52297	−	2.14536i	0.438782	−	0.144313i
$222$	9.69003			0.650352
$223$		−	10.5250i		−	0.704805i	−0.935849	−	0.352403i	$-0.885365\pi$
$223$		−	10.5250i		−	0.704805i	0.935849	−	0.352403i	$-0.114635\pi$
$224$	−13.8741			−0.927006
$225$	1.00988			0.0673253
$226$			15.2231i			1.01262i
$227$		−	1.53439i		−	0.101841i	−0.998703	−	0.0509204i	$-0.983785\pi$
$227$		−	1.53439i		−	0.101841i	0.998703	−	0.0509204i	$-0.0162155\pi$
$228$			13.3442i			0.883742i
$229$		−	1.33677i		−	0.0883364i	−0.999024	−	0.0441682i	$-0.985936\pi$
$229$		−	1.33677i		−	0.0883364i	0.999024	−	0.0441682i	$-0.0140637\pi$
$230$	−20.0031			−1.31897
$231$	−8.12090			−0.534316
$232$			0.187553i			0.0123135i
$233$	−23.1697			−1.51790			−0.758948	−	0.651151i	$-0.774287\pi$
$233$	−23.1697			−1.51790			−0.758948	+	0.651151i	$0.774287\pi$
$234$	−1.07146	−	3.25778i	−0.0700438	−	0.212968i
$235$	−28.0446			−1.82943
$236$			27.2822i			1.77592i
$237$	−1.18137			−0.0767379
$238$	−6.60657			−0.428240
$239$			5.95278i			0.385053i	0.981292	+	0.192527i	$0.0616682\pi$
$239$			5.95278i			0.385053i	−0.981292	+	0.192527i	$0.938332\pi$
$240$		−	17.1356i		−	1.10610i
$241$			27.2642i			1.75624i	0.478439	+	0.878121i	$0.341203\pi$
$241$			27.2642i			1.75624i	−0.478439	+	0.878121i	$0.658797\pi$
$242$		−	4.70604i		−	0.302516i
$243$	−4.90633			−0.314741
$244$	−9.99680			−0.639980
$245$		−	10.6047i		−	0.677507i
$246$	−18.3960			−1.17288
$247$	−4.78440	−	14.5469i	−0.304424	−	0.925600i
$248$	−0.0439183			−0.00278881
$249$		−	0.263086i		−	0.0166724i
$250$	−15.3374			−0.970019
$251$	−26.2008			−1.65378			−0.826888	−	0.562366i	$-0.809891\pi$
$251$	−26.2008			−1.65378			−0.826888	+	0.562366i	$0.809891\pi$
$252$			1.64064i			0.103350i
$253$		−	11.0501i		−	0.694716i
$254$			0.198039i			0.0124261i
$255$		−	8.07072i		−	0.505408i
$256$	16.3465			1.02165
$257$	19.4518			1.21337			0.606684	−	0.794943i	$-0.292499\pi$
$257$	19.4518			1.21337			0.606684	+	0.794943i	$0.292499\pi$
$258$		−	37.0242i		−	2.30503i
$259$	5.31978			0.330555
$260$	−5.94447	−	18.0741i	−0.368660	−	1.12091i
$261$	2.03658			0.126061
$262$		−	3.11947i		−	0.192721i
$263$	−29.8002			−1.83756			−0.918781	−	0.394768i	$-0.870825\pi$
$263$	−29.8002			−1.83756			−0.918781	+	0.394768i	$0.870825\pi$
$264$	0.205060			0.0126206
$265$			36.8419i			2.26318i
$266$			14.7334i			0.903362i
$267$			2.94199i			0.180047i
$268$			25.1294i			1.53502i
$269$	7.60454			0.463657			0.231829	−	0.972757i	$-0.425529\pi$
$269$	7.60454			0.463657			0.231829	+	0.972757i	$0.425529\pi$
$270$	−29.3872			−1.78845
$271$		−	22.1272i		−	1.34413i	−0.740493	−	0.672065i	$-0.765408\pi$
$271$		−	22.1272i		−	1.34413i	0.740493	−	0.672065i	$-0.234592\pi$
$272$	7.70088			0.466935
$273$	3.11214	+	9.46245i	0.188355	+	0.572694i
$274$	−14.5801			−0.880817
$275$			6.22467i			0.375362i
$276$	11.8110			0.710941
$277$	−9.45363			−0.568013			−0.284007	−	0.958822i	$-0.591664\pi$
$277$	−9.45363			−0.568013			−0.284007	+	0.958822i	$0.591664\pi$
$278$		−	16.6705i		−	0.999833i
$279$			0.476895i			0.0285509i
$280$		−	0.203789i		−	0.0121787i
$281$			12.6507i			0.754676i	0.926076	+	0.377338i	$0.123160\pi$
$281$			12.6507i			0.754676i	−0.926076	+	0.377338i	$0.876840\pi$
$282$	33.3028			1.98315
$283$	17.2687			1.02652			0.513258	−	0.858234i	$-0.328438\pi$
$283$	17.2687			1.02652			0.513258	+	0.858234i	$0.328438\pi$
$284$			11.5329i			0.684353i
$285$	−17.9986			−1.06614
$286$	20.0802	−	6.60426i	1.18737	−	0.390518i
$287$	−10.0993			−0.596143
$288$		−	3.80418i		−	0.224164i
$289$	−13.3729			−0.786644
$290$	22.7237			1.33438
$291$			10.0968i			0.591882i
$292$		−	9.73204i		−	0.569525i
$293$		−	6.27750i		−	0.366736i	−0.983044	−	0.183368i	$-0.941300\pi$
$293$		−	6.27750i		−	0.366736i	0.983044	−	0.183368i	$-0.0586999\pi$
$294$			12.5930i			0.734437i
$295$	−36.7981			−2.14247
$296$	−0.134330			−0.00780775
$297$		−	16.2341i		−	0.941998i
$298$	29.7616			1.72404
$299$	−12.8756	+	4.23470i	−0.744614	+	0.244899i
$300$	−6.65330			−0.384128
$301$		−	20.3261i		−	1.17158i
$302$	25.9551			1.49355
$303$	−4.95257			−0.284518
$304$		−	17.1738i		−	0.984986i
$305$		−	13.4836i		−	0.772070i
$306$		−	1.81147i		−	0.103555i
$307$		−	17.0517i		−	0.973191i	−0.873627	−	0.486595i	$-0.838239\pi$
$307$		−	17.0517i		−	0.973191i	0.873627	−	0.486595i	$-0.161761\pi$
$308$	−10.1125			−0.576213
$309$	−4.57877			−0.260477
$310$			5.32107i			0.302216i
$311$	4.01012			0.227393			0.113697	−	0.993516i	$-0.463731\pi$
$311$	4.01012			0.227393			0.113697	+	0.993516i	$0.463731\pi$
$312$	−0.0785845	−	0.238936i	−0.00444897	−	0.0135271i
$313$	−6.03967			−0.341382			−0.170691	−	0.985325i	$-0.554600\pi$
$313$	−6.03967			−0.341382			−0.170691	+	0.985325i	$0.554600\pi$
$314$			36.1237i			2.03858i
$315$	−2.21288			−0.124682
$316$	−1.47109			−0.0827551
$317$			14.0309i			0.788056i	0.919098	+	0.394028i	$0.128919\pi$
$317$			14.0309i			0.788056i	−0.919098	+	0.394028i	$0.871081\pi$
$318$		−	43.7495i		−	2.45335i
$319$			12.5530i			0.702834i
$320$		−	20.8706i		−	1.16670i
$321$	11.6768			0.651736
$322$	13.0406			0.726724
$323$		−	8.08873i		−	0.450069i
$324$	14.5221			0.806784
$325$	7.25296	−	2.38545i	0.402322	−	0.132321i
$326$	7.32265			0.405564
$327$			20.6292i			1.14080i
$328$	0.255017			0.0140810
$329$	18.2831			1.00798
$330$		−	24.8448i		−	1.36766i
$331$		−	11.1671i		−	0.613802i	−0.951741	−	0.306901i	$-0.900708\pi$
$331$		−	11.1671i		−	0.613802i	0.951741	−	0.306901i	$-0.0992920\pi$
$332$		−	0.327606i		−	0.0179797i
$333$			1.45864i			0.0799331i
$334$	7.16885			0.392262
$335$	−33.8944			−1.85185
$336$			11.1712i			0.609437i
$337$	−5.01505			−0.273187			−0.136594	−	0.990627i	$-0.543615\pi$
$337$	−5.01505			−0.273187			−0.136594	+	0.990627i	$0.543615\pi$
$338$	−15.3905	−	20.8665i	−0.837134	−	1.13499i
$339$	12.1238			0.658475
$340$		−	10.0500i		−	0.545038i
$341$	−2.93947			−0.159181
$342$	−4.03978			−0.218446
$343$			19.0884i			1.03068i
$344$			0.513254i			0.0276728i
$345$			15.9307i			0.857678i
$346$		−	27.4720i		−	1.47690i
$347$	−0.923189			−0.0495594			−0.0247797	−	0.999693i	$-0.507888\pi$
$347$	−0.923189			−0.0495594			−0.0247797	+	0.999693i	$0.507888\pi$
$348$	−13.4174			−0.719250
$349$		−	13.5903i		−	0.727473i	−0.931502	−	0.363736i	$-0.881501\pi$
$349$		−	13.5903i		−	0.727473i	0.931502	−	0.363736i	$-0.118499\pi$
$350$	−7.34592			−0.392656
$351$	−18.9159	+	6.22133i	−1.00966	+	0.332070i
$352$	23.4481			1.24979
$353$			23.8408i			1.26892i	0.772957	+	0.634459i	$0.218777\pi$
$353$			23.8408i			1.26892i	−0.772957	+	0.634459i	$0.781223\pi$
$354$	43.6976			2.32250
$355$	−15.5555			−0.825602
$356$			3.66349i			0.194165i
$357$			5.26154i			0.278470i
$358$		−	27.3970i		−	1.44798i
$359$		−	5.95185i		−	0.314127i	−0.987589	−	0.157063i	$-0.949797\pi$
$359$		−	5.95185i		−	0.314127i	0.987589	−	0.157063i	$-0.0502027\pi$
$360$	0.0558773			0.00294499
$361$	0.961228			0.0505910
$362$			16.6756i			0.876450i
$363$	−3.74794			−0.196716
$364$	3.87537	+	11.7831i	0.203125	+	0.617600i
$365$	13.1265			0.687073
$366$			16.0117i			0.836947i
$367$	28.6410			1.49505			0.747523	−	0.664236i	$-0.231243\pi$
$367$	28.6410			1.49505			0.747523	+	0.664236i	$0.231243\pi$
$368$	−15.2006			−0.792388
$369$		−	2.76915i		−	0.144156i
$370$			16.2751i			0.846104i
$371$		−	24.0183i		−	1.24697i
$372$		−	3.14188i		−	0.162899i
$373$	−32.6896			−1.69260			−0.846302	−	0.532704i	$-0.821176\pi$
$373$	−32.6896			−1.69260			−0.846302	+	0.532704i	$0.821176\pi$
$374$	11.1655			0.577353
$375$			12.2148i			0.630770i
$376$	−0.461665			−0.0238085
$377$	14.6268	−	4.81065i	0.753316	−	0.247761i
$378$	19.1584			0.985400
$379$			13.9594i			0.717044i	0.933521	+	0.358522i	$0.116719\pi$
$379$			13.9594i			0.717044i	−0.933521	+	0.358522i	$0.883281\pi$
$380$	−22.4126			−1.14974
$381$	0.157720			0.00808025
$382$		−	50.2380i		−	2.57040i
$383$			4.62452i			0.236302i	0.992996	+	0.118151i	$0.0376967\pi$
$383$			4.62452i			0.236302i	−0.992996	+	0.118151i	$0.962303\pi$
$384$		−	0.558055i		−	0.0284781i
$385$		−	13.6397i		−	0.695142i
$386$	−16.0321			−0.816012
$387$	5.57326			0.283305
$388$			12.5729i			0.638293i
$389$	−28.4539			−1.44267			−0.721336	−	0.692585i	$-0.756472\pi$
$389$	−28.4539			−1.44267			−0.721336	+	0.692585i	$0.756472\pi$
$390$	−28.9491	+	9.52117i	−1.46589	+	0.482123i
$391$	−7.15939			−0.362066
$392$		−	0.174572i		−	0.00881722i
$393$	−2.48437			−0.125320
$394$	−5.57620			−0.280925
$395$		−	1.98419i		−	0.0998356i
$396$		−	2.77277i		−	0.139337i
$397$			4.82894i			0.242358i	0.992631	+	0.121179i	$0.0386674\pi$
$397$			4.82894i			0.242358i	−0.992631	+	0.121179i	$0.961333\pi$
$398$		−	32.5915i		−	1.63366i
$399$	11.7338			0.587425
$400$	8.56270			0.428135
$401$		−	33.7317i		−	1.68448i	−0.539101	−	0.842241i	$-0.681236\pi$
$401$		−	33.7317i		−	1.68448i	0.539101	−	0.842241i	$-0.318764\pi$
$402$	40.2494			2.00746
$403$	1.12648	+	3.42506i	0.0561140	+	0.170614i
$404$	−6.16715			−0.306827
$405$			19.5873i			0.973302i
$406$	−14.8142			−0.735217
$407$	−8.99073			−0.445654
$408$		−	0.132859i		−	0.00657749i
$409$			34.0260i			1.68248i	0.540664	+	0.841239i	$0.318173\pi$
$409$			34.0260i			1.68248i	−0.540664	+	0.841239i	$0.681827\pi$
$410$		−	30.8974i		−	1.52592i
$411$			11.6117i			0.572765i
$412$	−5.70169			−0.280902
$413$	23.9898			1.18046
$414$			3.57563i			0.175733i
$415$	0.441873			0.0216907
$416$	−8.98592	−	27.3216i	−0.440571	−	1.33955i
$417$	−13.2766			−0.650157
$418$		−	24.9002i		−	1.21791i
$419$	19.7565			0.965166			0.482583	−	0.875850i	$-0.339699\pi$
$419$	19.7565			0.965166			0.482583	+	0.875850i	$0.339699\pi$
$420$	14.5789			0.711377
$421$			24.0860i			1.17388i	0.809631	+	0.586940i	$0.199667\pi$
$421$			24.0860i			1.17388i	−0.809631	+	0.586940i	$0.800333\pi$
$422$		−	32.1320i		−	1.56416i
$423$			5.01307i			0.243744i
$424$			0.606485i			0.0294535i
$425$	4.03296			0.195628
$426$	18.4721			0.894976
$427$			8.79037i			0.425396i
$428$	14.5405			0.702840
$429$	−5.25969	−	15.9921i	−0.253940	−	0.772105i
$430$	62.1850			2.99883
$431$		−	34.5870i		−	1.66600i	−0.553276	−	0.832998i	$-0.686623\pi$
$431$		−	34.5870i		−	1.66600i	0.553276	−	0.832998i	$-0.313377\pi$
$432$	−22.3317			−1.07444
$433$	19.9707			0.959731			0.479865	−	0.877342i	$-0.340686\pi$
$433$	19.9707			0.959731			0.479865	+	0.877342i	$0.340686\pi$
$434$		−	3.46896i		−	0.166515i
$435$		−	18.0973i		−	0.867701i
$436$			25.6884i			1.23025i
$437$			15.9662i			0.763768i
$438$	−15.5877			−0.744807
$439$	−16.2325			−0.774733			−0.387366	−	0.921926i	$-0.626615\pi$
$439$	−16.2325			−0.774733			−0.387366	+	0.921926i	$0.626615\pi$
$440$			0.344415i			0.0164193i
$441$	−1.89562			−0.0902678
$442$	−4.27890	−	13.0100i	−0.203527	−	0.618822i
$443$	38.9490			1.85052			0.925261	−	0.379330i	$-0.123846\pi$
$443$	38.9490			1.85052			0.925261	+	0.379330i	$0.123846\pi$
$444$		−	9.60983i		−	0.456062i
$445$	−4.94129			−0.234240
$446$	−20.9919			−0.993997
$447$		−	23.7024i		−	1.12109i
$448$			13.6061i			0.642829i
$449$		−	20.3615i		−	0.960919i	−0.877017	−	0.480459i	$-0.840470\pi$
$449$		−	20.3615i		−	0.960919i	0.877017	−	0.480459i	$-0.159530\pi$
$450$		−	2.01419i		−	0.0949500i
$451$	17.0684			0.803719
$452$	15.0971			0.710108
$453$		−	20.6709i		−	0.971204i
$454$	−3.06032			−0.143628
$455$	−15.8929	+	5.22708i	−0.745071	+	0.245049i
$456$	−0.296290			−0.0138750
$457$		−	14.9242i		−	0.698123i	−0.937100	−	0.349061i	$-0.886500\pi$
$457$		−	14.9242i		−	0.698123i	0.937100	−	0.349061i	$-0.113500\pi$
$458$	−2.66617			−0.124582
$459$	−10.5181			−0.490942
$460$			19.8375i			0.924930i
$461$		−	17.9790i		−	0.837367i	−0.908132	−	0.418683i	$-0.862492\pi$
$461$		−	17.9790i		−	0.837367i	0.908132	−	0.418683i	$-0.137508\pi$
$462$			16.1970i			0.753554i
$463$			40.4466i			1.87971i	0.341571	+	0.939856i	$0.389041\pi$
$463$			40.4466i			1.87971i	−0.341571	+	0.939856i	$0.610959\pi$
$464$	17.2680			0.801648
$465$	4.23775			0.196521
$466$			46.2117i			2.14071i
$467$	37.4781			1.73428			0.867139	−	0.498066i	$-0.165956\pi$
$467$	37.4781			1.73428			0.867139	+	0.498066i	$0.165956\pi$
$468$	−3.23082	+	1.06260i	−0.149345	+	0.0491185i
$469$	22.0967			1.02033
$470$			55.9345i			2.58007i
$471$	28.7692			1.32562
$472$	−0.605764			−0.0278826
$473$			34.3523i			1.57952i
$474$			2.35622i			0.108225i
$475$		−	8.99396i		−	0.412671i
$476$			6.55189i			0.300306i
$477$	6.58562			0.301535
$478$	11.8727			0.543047
$479$		−	4.59305i		−	0.209862i	−0.994480	−	0.104931i	$-0.966538\pi$
$479$		−	4.59305i		−	0.209862i	0.994480	−	0.104931i	$-0.0334622\pi$
$480$	−33.8044			−1.54295
$481$	3.44548	+	10.4760i	0.157100	+	0.477663i
$482$	54.3781			2.47685
$483$		−	10.3857i		−	0.472564i
$484$	−4.66709			−0.212141
$485$	−16.9583			−0.770035
$486$			9.78562i			0.443885i
$487$		−	29.6112i		−	1.34181i	−0.741542	−	0.670906i	$-0.765905\pi$
$487$		−	29.6112i		−	1.34181i	0.741542	−	0.670906i	$-0.234095\pi$
$488$		−	0.221965i		−	0.0100479i
$489$		−	5.83183i		−	0.263725i
$490$	−21.1509			−0.955499
$491$	35.0863			1.58342			0.791712	−	0.610894i	$-0.209190\pi$
$491$	35.0863			1.58342			0.791712	+	0.610894i	$0.209190\pi$
$492$			18.2437i			0.822491i
$493$	8.13311			0.366297
$494$	−29.0137	+	9.54242i	−1.30539	+	0.429334i
$495$	3.73989			0.168095
$496$			4.04355i			0.181561i
$497$	10.1411			0.454891
$498$	−0.524722			−0.0235133
$499$			3.07949i			0.137857i	0.997622	+	0.0689284i	$0.0219580\pi$
$499$			3.07949i			0.137857i	−0.997622	+	0.0689284i	$0.978042\pi$
$500$			15.2104i			0.680230i
$501$		−	5.70934i		−	0.255075i
$502$			52.2571i			2.33235i
$503$	10.3434			0.461189			0.230594	−	0.973050i	$-0.425933\pi$
$503$	10.3434			0.461189			0.230594	+	0.973050i	$0.425933\pi$
$504$	−0.0364280			−0.00162263
$505$		−	8.31821i		−	0.370156i
$506$	−22.0394			−0.979769
$507$	−16.6183	+	12.2572i	−0.738043	+	0.544359i
$508$	0.196400			0.00871385
$509$		−	4.96830i		−	0.220216i	−0.993920	−	0.110108i	$-0.964880\pi$
$509$		−	4.96830i		−	0.220216i	0.993920	−	0.110108i	$-0.0351197\pi$
$510$	−16.0969			−0.712785
$511$	−8.55755			−0.378564
$512$		−	31.9002i		−	1.40980i
$513$			23.4565i			1.03563i
$514$		−	38.7963i		−	1.71123i
$515$		−	7.69039i		−	0.338879i
$516$	−36.7178			−1.61641
$517$	−30.8994			−1.35895
$518$		−	10.6102i		−	0.466187i
$519$	−21.8789			−0.960379
$520$	0.401311	−	0.131989i	0.0175986	−	0.00578808i
$521$	−6.67995			−0.292654			−0.146327	−	0.989236i	$-0.546745\pi$
$521$	−6.67995			−0.292654			−0.146327	+	0.989236i	$0.546745\pi$
$522$		−	4.06194i		−	0.177786i
$523$	11.6369			0.508846			0.254423	−	0.967093i	$-0.418114\pi$
$523$	11.6369			0.508846			0.254423	+	0.967093i	$0.418114\pi$
$524$	−3.09365			−0.135147
$525$			5.85036i			0.255331i
$526$			59.4362i			2.59154i
$527$			1.90448i			0.0829606i
$528$		−	18.8799i		−	0.821642i
$529$	−8.86820			−0.385574
$530$	73.4807			3.19180
$531$			6.57780i			0.285452i
$532$	14.6114			0.633486
$533$	−6.54105	−	19.8880i	−0.283324	−	0.861447i
$534$	5.86776			0.253923
$535$			19.6121i			0.847904i
$536$	−0.557963			−0.0241003
$537$	−21.8193			−0.941571
$538$		−	15.1672i		−	0.653903i
$539$		−	11.6842i		−	0.503273i
$540$			29.1440i			1.25416i
$541$		−	8.27417i		−	0.355734i	−0.984054	−	0.177867i	$-0.943080\pi$
$541$		−	8.27417i		−	0.355734i	0.984054	−	0.177867i	$-0.0569198\pi$
$542$	−44.1323			−1.89565
$543$	13.2806			0.569925
$544$		−	15.1920i		−	0.651353i
$545$	−34.6483			−1.48417
$546$	18.8727	−	6.20713i	0.807679	−	0.265640i
$547$	−9.31963			−0.398479			−0.199239	−	0.979951i	$-0.563847\pi$
$547$	−9.31963			−0.398479			−0.199239	+	0.979951i	$0.563847\pi$
$548$			14.4595i			0.617677i
$549$	−2.41025			−0.102867
$550$	12.4150			0.529378
$551$		−	18.1377i		−	0.772694i
$552$			0.262248i			0.0111620i
$553$			1.29355i			0.0550075i
$554$			18.8551i			0.801078i
$555$	12.9617			0.550192
$556$	−16.5326			−0.701137
$557$		−	22.3462i		−	0.946839i	−0.880837	−	0.473419i	$-0.843020\pi$
$557$		−	22.3462i		−	0.946839i	0.880837	−	0.473419i	$-0.156980\pi$
$558$	0.951161			0.0402658
$559$	40.0272	−	13.1647i	1.69297	−	0.556807i
$560$	−18.7628			−0.792874
$561$		−	8.89229i		−	0.375433i
$562$	25.2316			1.06433
$563$	−19.9509			−0.840832			−0.420416	−	0.907332i	$-0.638116\pi$
$563$	−19.9509			−0.840832			−0.420416	+	0.907332i	$0.638116\pi$
$564$		−	33.0271i		−	1.39069i
$565$			20.3629i			0.856672i
$566$		−	34.4422i		−	1.44771i
$567$		−	12.7695i		−	0.536270i
$568$	−0.256072			−0.0107446
$569$	−30.1940			−1.26580			−0.632898	−	0.774235i	$-0.718135\pi$
$569$	−30.1940			−1.26580			−0.632898	+	0.774235i	$0.718135\pi$
$570$			35.8980i			1.50360i
$571$	−35.6144			−1.49042			−0.745208	−	0.666832i	$-0.767650\pi$
$571$	−35.6144			−1.49042			−0.745208	+	0.666832i	$0.767650\pi$
$572$	−6.54960	−	19.9140i	−0.273852	−	0.832647i
$573$	−40.0100			−1.67144
$574$			20.1429i			0.840750i
$575$	−7.96060			−0.331980
$576$	−3.73069			−0.155445
$577$		−	30.0336i		−	1.25032i	−0.780498	−	0.625158i	$-0.785035\pi$
$577$		−	30.0336i		−	1.25032i	0.780498	−	0.625158i	$-0.214965\pi$
$578$			26.6722i			1.10942i
$579$			12.7681i			0.530625i
$580$		−	22.5356i		−	0.935739i
$581$	−0.288070			−0.0119511
$582$	20.1378			0.834741
$583$			40.5923i			1.68116i
$584$	0.216086			0.00894172
$585$	−1.43322	−	4.35771i	−0.0592565	−	0.180169i
$586$	−12.5204			−0.517213
$587$			16.0884i			0.664039i	0.943272	+	0.332020i	$0.107730\pi$
$587$			16.0884i			0.664039i	−0.943272	+	0.332020i	$0.892270\pi$
$588$	12.4888			0.515027
$589$	4.24721			0.175003
$590$			73.3934i			3.02156i
$591$			4.44094i			0.182676i
$592$			12.3677i			0.508310i
$593$			7.42015i			0.304709i	0.988326	+	0.152355i	$0.0486856\pi$
$593$			7.42015i			0.304709i	−0.988326	+	0.152355i	$0.951314\pi$
$594$	−32.3787			−1.32851
$595$	−8.83715			−0.362288
$596$		−	29.5153i		−	1.20899i
$597$	−25.9561			−1.06231
$598$	8.44605	+	25.6802i	0.345385	+	1.05014i
$599$	30.1928			1.23364			0.616822	−	0.787102i	$-0.288420\pi$
$599$	30.1928			1.23364			0.616822	+	0.787102i	$0.288420\pi$
$600$		−	0.147727i		−	0.00603094i
$601$	30.9392			1.26204			0.631019	−	0.775767i	$-0.282637\pi$
$601$	30.9392			1.26204			0.631019	+	0.775767i	$0.282637\pi$
$602$	−40.5402			−1.65230
$603$			6.05875i			0.246731i
$604$		−	25.7403i		−	1.04736i
$605$		−	6.29494i		−	0.255926i
$606$			9.87783i			0.401260i
$607$	−0.0358681			−0.00145584			−0.000727920	−	1.00000i	$-0.500232\pi$
$607$	−0.0358681			−0.00145584			−0.000727920		1.00000i	$0.500232\pi$
$608$	−33.8799			−1.37401
$609$			11.7982i			0.478086i
$610$	−26.8929			−1.08886
$611$	11.8415	+	36.0039i	0.479054	+	1.45656i
$612$	−1.79648			−0.0726183
$613$		−	38.0409i		−	1.53646i	−0.640176	−	0.768228i	$-0.721139\pi$
$613$		−	38.0409i		−	1.53646i	0.640176	−	0.768228i	$-0.278861\pi$
$614$	−34.0094			−1.37251
$615$	−24.6070			−0.992250
$616$		−	0.224534i		−	0.00904673i
$617$			29.8852i			1.20313i	0.798822	+	0.601567i	$0.205457\pi$
$617$			29.8852i			1.20313i	−0.798822	+	0.601567i	$0.794543\pi$
$618$			9.13230i			0.367355i
$619$			10.9872i			0.441612i	0.975318	+	0.220806i	$0.0708687\pi$
$619$			10.9872i			0.441612i	−0.975318	+	0.220806i	$0.929131\pi$
$620$	5.27703			0.211930
$621$	20.7615			0.833129
$622$		−	7.99814i		−	0.320696i
$623$	3.22137			0.129062
$624$	−21.9988	+	7.23527i	−0.880657	+	0.289643i
$625$	−31.1038			−1.24415
$626$			12.0460i			0.481457i
$627$	−19.8308			−0.791965
$628$	35.8247			1.42956
$629$			5.82510i			0.232262i
$630$			4.41356i			0.175840i
$631$			7.51654i			0.299229i	0.988744	+	0.149614i	$0.0478032\pi$
$631$			7.51654i			0.299229i	−0.988744	+	0.149614i	$0.952197\pi$
$632$		−	0.0326634i		−	0.00129928i
$633$	−25.5903			−1.01712
$634$	27.9845			1.11141
$635$			0.264903i			0.0105124i
$636$	−43.3874			−1.72042
$637$	−13.6144	+	4.47768i	−0.539421	+	0.177412i
$638$	25.0369			0.991218
$639$			2.78061i			0.109999i
$640$	0.937295			0.0370498
$641$	−19.8746			−0.785001			−0.392501	−	0.919752i	$-0.628390\pi$
$641$	−19.8746			−0.785001			−0.392501	+	0.919752i	$0.628390\pi$
$642$		−	23.2892i		−	0.919153i
$643$			33.0105i			1.30181i	0.759160	+	0.650904i	$0.225610\pi$
$643$			33.0105i			1.30181i	−0.759160	+	0.650904i	$0.774390\pi$
$644$		−	12.9327i		−	0.509619i
$645$		−	49.5247i		−	1.95003i
$646$	−16.1329			−0.634740
$647$	−11.6044			−0.456215			−0.228107	−	0.973636i	$-0.573254\pi$
$647$	−11.6044			−0.456215			−0.228107	+	0.973636i	$0.573254\pi$
$648$			0.322443i			0.0126668i
$649$	−40.5440			−1.59149
$650$	−4.75776	−	14.4659i	−0.186615	−	0.567401i
$651$	−2.76271			−0.108279
$652$		−	7.26205i		−	0.284404i
$653$	43.0663			1.68531			0.842656	−	0.538452i	$-0.180991\pi$
$653$	43.0663			1.68531			0.842656	+	0.538452i	$0.180991\pi$
$654$	41.1447			1.60889
$655$		−	4.17269i		−	0.163041i
$656$		−	23.4794i		−	0.916717i
$657$		−	2.34641i		−	0.0915423i
$658$		−	36.4654i		−	1.42157i
$659$	22.3540			0.870787			0.435393	−	0.900240i	$-0.356609\pi$
$659$	22.3540			0.870787			0.435393	+	0.900240i	$0.356609\pi$
$660$	−24.6391			−0.959078
$661$			39.9481i			1.55380i	0.629624	+	0.776900i	$0.283209\pi$
$661$			39.9481i			1.55380i	−0.629624	+	0.776900i	$0.716791\pi$
$662$	−22.2727			−0.865654
$663$	−10.3613	+	3.40776i	−0.402398	+	0.132346i
$664$	0.00727403			0.000282287
$665$			19.7078i			0.764236i
$666$	2.90924			0.112731
$667$	−16.0538			−0.621606
$668$		−	7.10952i		−	0.275076i
$669$			16.7182i			0.646362i
$670$			67.6019i			2.61169i
$671$		−	14.8562i		−	0.573518i
$672$	22.0381			0.850138
$673$	−4.24478			−0.163624			−0.0818121	−	0.996648i	$-0.526071\pi$
$673$	−4.24478			−0.163624			−0.0818121	+	0.996648i	$0.526071\pi$
$674$			10.0025i			0.385280i
$675$	−11.6952			−0.450147
$676$	−20.6938	+	15.2631i	−0.795915	+	0.587044i
$677$	49.0530			1.88526			0.942629	−	0.333842i	$-0.108345\pi$
$677$	49.0530			1.88526			0.942629	+	0.333842i	$0.108345\pi$
$678$		−	24.1808i		−	0.928658i
$679$	11.0556			0.424274
$680$	0.223146			0.00855727
$681$			2.43726i			0.0933962i
$682$			5.86273i			0.224496i
$683$		−	45.4851i		−	1.74044i	−0.492666	−	0.870219i	$-0.663977\pi$
$683$		−	45.4851i		−	1.74044i	0.492666	−	0.870219i	$-0.336023\pi$
$684$			4.00634i			0.153186i
$685$	−19.5028			−0.745164
$686$	38.0716			1.45358
$687$			2.12337i			0.0810115i
$688$	47.2553			1.80159
$689$	47.2980	−	15.5560i	1.80191	−	0.592637i
$690$	31.7735			1.20960
$691$			1.63712i			0.0622791i	0.999515	+	0.0311395i	$0.00991363\pi$
$691$			1.63712i			0.0622791i	−0.999515	+	0.0311395i	$0.990086\pi$
$692$	−27.2446			−1.03568
$693$	−2.43814			−0.0926174
$694$			1.84129i			0.0698944i
$695$		−	22.2990i		−	0.845850i
$696$		−	0.297915i		−	0.0112924i
$697$		−	11.0586i		−	0.418875i
$698$	−27.1057			−1.02597
$699$	36.8034			1.39203
$700$			7.28512i			0.275352i
$701$	−1.61823			−0.0611197			−0.0305599	−	0.999533i	$-0.509729\pi$
$701$	−1.61823			−0.0611197			−0.0305599	+	0.999533i	$0.509729\pi$
$702$	12.4084	+	37.7276i	0.468323	+	1.42394i
$703$	12.9906			0.489950
$704$		−	22.9951i		−	0.866661i
$705$	44.5468			1.67773
$706$	47.5502			1.78957
$707$			5.42289i			0.203949i
$708$		−	43.3359i		−	1.62866i
$709$		−	21.6641i		−	0.813614i	−0.913514	−	0.406807i	$-0.866642\pi$
$709$		−	21.6641i		−	0.813614i	0.913514	−	0.406807i	$-0.133358\pi$
$710$			31.0253i			1.16436i
$711$	−0.354682			−0.0133016
$712$	−0.0813427			−0.00304845
$713$		−	3.75923i		−	0.140784i
$714$	10.4941			0.392731
$715$	26.8599	−	8.83405i	1.00450	−	0.330375i
$716$	−27.1703			−1.01540
$717$		−	9.45556i		−	0.353125i
$718$	−11.8709			−0.443018
$719$	−11.6958			−0.436178			−0.218089	−	0.975929i	$-0.569982\pi$
$719$	−11.6958			−0.436178			−0.218089	+	0.975929i	$0.569982\pi$
$720$		−	5.14462i		−	0.191729i
$721$			5.01359i			0.186716i
$722$		−	1.91716i		−	0.0713492i
$723$		−	43.3072i		−	1.61061i
$724$	16.5376			0.614614
$725$	9.04330			0.335860
$726$			7.47521i			0.277431i
$727$	−10.7050			−0.397026			−0.198513	−	0.980098i	$-0.563611\pi$
$727$	−10.7050			−0.397026			−0.198513	+	0.980098i	$0.563611\pi$
$728$	−0.261626	+	0.0860472i	−0.00969652	+	0.00318912i
$729$	29.8190			1.10441
$730$		−	26.1807i		−	0.968990i
$731$	22.2569			0.823200
$732$	15.8792			0.586912
$733$		−	37.8613i		−	1.39844i	−0.714907	−	0.699220i	$-0.753531\pi$
$733$		−	37.8613i		−	1.39844i	0.714907	−	0.699220i	$-0.246469\pi$
$734$		−	57.1240i		−	2.10849i
$735$			16.8447i			0.621328i
$736$			29.9873i			1.10535i
$737$	−37.3447			−1.37561
$738$	−5.52303			−0.203306
$739$			8.15442i			0.299965i	0.988689	+	0.149983i	$0.0479218\pi$
$739$			8.15442i			0.299965i	−0.988689	+	0.149983i	$0.952078\pi$
$740$	16.1404			0.593334
$741$	7.59967	+	23.1068i	0.279181	+	0.848849i
$742$	−47.9042			−1.75862
$743$		−	32.4382i		−	1.19004i	−0.803711	−	0.595020i	$-0.797144\pi$
$743$		−	32.4382i		−	1.19004i	0.803711	−	0.595020i	$-0.202856\pi$
$744$	0.0697611			0.00255756
$745$	39.8100			1.45853
$746$			65.1990i			2.38711i
$747$		−	0.0789864i		−	0.00288996i
$748$		−	11.0731i		−	0.404871i
$749$		−	12.7857i		−	0.467179i
$750$	24.3623			0.889585
$751$	−18.4928			−0.674811			−0.337405	−	0.941359i	$-0.609549\pi$
$751$	−18.4928			−0.674811			−0.337405	+	0.941359i	$0.609549\pi$
$752$			42.5055i			1.55001i
$753$	41.6180			1.51665
$754$	−9.59477	−	29.1729i	−0.349421	−	1.06241i
$755$	34.7184			1.26353
$756$		−	18.9998i		−	0.691016i
$757$	36.0911			1.31175			0.655877	−	0.754868i	$-0.272299\pi$
$757$	36.0911			1.31175			0.655877	+	0.754868i	$0.272299\pi$
$758$	27.8417			1.01126
$759$			17.5523i			0.637110i
$760$		−	0.497641i		−	0.0180513i
$761$			6.79105i			0.246175i	0.992396	+	0.123088i	$0.0392797\pi$
$761$			6.79105i			0.246175i	−0.992396	+	0.123088i	$0.960720\pi$
$762$		−	0.314571i		−	0.0113957i
$763$	22.5883			0.817750
$764$	−49.8222			−1.80251
$765$		−	2.42308i		−	0.0876065i
$766$	9.22356			0.333261
$767$	15.5375	+	47.2418i	0.561028	+	1.70580i
$768$	−25.9652			−0.936939
$769$			8.83997i			0.318777i	0.987216	+	0.159389i	$0.0509523\pi$
$769$			8.83997i			0.318777i	−0.987216	+	0.159389i	$0.949048\pi$
$770$	−27.2041			−0.980369
$771$	−30.8978			−1.11276
$772$			15.8994i			0.572232i
$773$		−	40.7935i		−	1.46724i	−0.679559	−	0.733620i	$-0.737829\pi$
$773$		−	40.7935i		−	1.46724i	0.679559	−	0.733620i	$-0.262171\pi$
$774$		−	11.1158i		−	0.399549i
$775$			2.11762i			0.0760670i
$776$	−0.279164			−0.0100214
$777$	−8.45009			−0.303145
$778$			56.7510i			2.03462i
$779$	−24.6619			−0.883606
$780$	9.44236	+	28.7095i	0.338091	+	1.02796i
$781$	−17.1390			−0.613283
$782$			14.2793i			0.510627i
$783$	−23.5852			−0.842865
$784$	−16.0728			−0.574030
$785$			48.3201i			1.72462i
$786$			4.95505i			0.176741i
$787$			42.3875i			1.51095i	0.655176	+	0.755476i	$0.272594\pi$
$787$			42.3875i			1.51095i	−0.655176	+	0.755476i	$0.727406\pi$
$788$			5.53005i			0.197000i
$789$	47.3356			1.68519
$790$	−3.95745			−0.140800
$791$		−	13.2751i		−	0.472010i
$792$	0.0615654			0.00218763
$793$	−17.3104	+	5.69329i	−0.614711	+	0.202175i
$794$	9.63126			0.341801
$795$		−	58.5207i		−	2.07551i
$796$	−32.3217			−1.14561
$797$	40.5744			1.43722			0.718610	−	0.695413i	$-0.244779\pi$
$797$	40.5744			1.43722			0.718610	+	0.695413i	$0.244779\pi$
$798$		−	23.4029i		−	0.828455i
$799$			20.0197i			0.708248i
$800$		−	16.8922i		−	0.597229i
$801$			0.883275i			0.0312090i
$802$	−67.2775			−2.37565
$803$	14.4627			0.510379
$804$		−	39.9163i		−	1.40774i
$805$	17.4435			0.614803
$806$	6.83124	−	2.24675i	0.240620	−	0.0791385i
$807$	−12.0793			−0.425211
$808$		−	0.136933i		−	0.00481729i
$809$	−32.9403			−1.15812			−0.579060	−	0.815285i	$-0.696580\pi$
$809$	−32.9403			−1.15812			−0.579060	+	0.815285i	$0.696580\pi$
$810$	39.0667			1.37266
$811$		−	4.85286i		−	0.170407i	−0.996364	−	0.0852034i	$-0.972846\pi$
$811$		−	4.85286i		−	0.170407i	0.996364	−	0.0852034i	$-0.0271540\pi$
$812$			14.6916i			0.515574i
$813$			35.1474i			1.23267i
$814$			17.9319i			0.628513i
$815$	9.79500			0.343104
$816$	−12.2323			−0.428216
$817$		−	49.6353i		−	1.73652i
$818$	67.8644			2.37282
$819$	0.934360	+	2.84092i	0.0326492	+	0.0992697i
$820$	−30.6417			−1.07006
$821$			19.3648i			0.675836i	0.941176	+	0.337918i	$0.109723\pi$
$821$			19.3648i			0.675836i	−0.941176	+	0.337918i	$0.890277\pi$
$822$	23.1595			0.807780
$823$	16.5691			0.577562			0.288781	−	0.957395i	$-0.406750\pi$
$823$	16.5691			0.577562			0.288781	+	0.957395i	$0.406750\pi$
$824$		−	0.126598i		−	0.00441025i
$825$		−	9.88744i		−	0.344236i
$826$		−	47.8473i		−	1.66482i
$827$		−	26.9392i		−	0.936769i	−0.883525	−	0.468385i	$-0.844836\pi$
$827$		−	26.9392i		−	0.936769i	0.883525	−	0.468385i	$-0.155164\pi$
$828$	3.54604			0.123233
$829$	−8.76091			−0.304279			−0.152140	−	0.988359i	$-0.548616\pi$
$829$	−8.76091			−0.304279			−0.152140	+	0.988359i	$0.548616\pi$
$830$		−	0.881310i		−	0.0305907i
$831$	15.0164			0.520914
$832$	−26.7938	+	8.81233i	−0.928909	+	0.305512i
$833$	−7.57019			−0.262291
$834$			26.4800i			0.916927i
$835$	9.58927			0.331850
$836$	−24.6942			−0.854065
$837$		−	5.52280i		−	0.190896i
$838$		−	39.4040i		−	1.36119i
$839$		−	41.9803i		−	1.44932i	−0.689107	−	0.724660i	$-0.741997\pi$
$839$		−	41.9803i		−	1.44932i	0.689107	−	0.724660i	$-0.258003\pi$
$840$			0.323704i			0.0111689i
$841$	−10.7628			−0.371130
$842$	48.0392			1.65554
$843$		−	20.0947i		−	0.692098i
$844$	−31.8661			−1.09688
$845$	−20.5868	−	27.9116i	−0.708208	−	0.960190i
$846$	9.99851			0.343756
$847$			4.10386i			0.141010i
$848$	55.8390			1.91752
$849$	−27.4301			−0.941398
$850$		−	8.04370i		−	0.275897i
$851$		−	11.4981i		−	0.394149i
$852$		−	18.3192i		−	0.627606i
$853$			6.25658i			0.214221i	0.994247	+	0.107111i	$0.0341599\pi$
$853$			6.25658i			0.214221i	−0.994247	+	0.107111i	$0.965840\pi$
$854$	17.5323			0.599942
$855$	−5.40373			−0.184804
$856$			0.322851i			0.0110348i
$857$	−43.5856			−1.48886			−0.744429	−	0.667702i	$-0.767278\pi$
$857$	−43.5856			−1.48886			−0.744429	+	0.667702i	$0.767278\pi$
$858$	−31.8960	+	10.4904i	−1.08891	+	0.358136i
$859$	−1.98766			−0.0678180			−0.0339090	−	0.999425i	$-0.510796\pi$
$859$	−1.98766			−0.0678180			−0.0339090	+	0.999425i	$0.510796\pi$
$860$		−	61.6703i		−	2.10294i
$861$	16.0420			0.546711
$862$	−68.9833			−2.34958
$863$			44.2665i			1.50685i	0.657535	+	0.753424i	$0.271599\pi$
$863$			44.2665i			1.50685i	−0.657535	+	0.753424i	$0.728401\pi$
$864$			44.0553i			1.49879i
$865$		−	36.7473i		−	1.24945i
$866$		−	39.8313i		−	1.35352i
$867$	21.2420			0.721415
$868$	−3.44025			−0.116770
$869$		−	2.18618i		−	0.0741610i
$870$	−36.0949			−1.22373
$871$	14.3115	+	43.5140i	0.484925	+	1.47441i
$872$	−0.570375			−0.0193153
$873$			3.03135i			0.102596i
$874$	31.8444			1.07715
$875$	13.3748			0.452150
$876$			15.4586i			0.522299i
$877$			14.4318i			0.487327i	0.969860	+	0.243664i	$0.0783493\pi$
$877$			14.4318i			0.487327i	−0.969860	+	0.243664i	$0.921651\pi$
$878$			32.3754i			1.09262i
$879$			9.97137i			0.336326i
$880$	31.7102			1.06895
$881$	−12.7791			−0.430539			−0.215269	−	0.976555i	$-0.569063\pi$
$881$	−12.7791			−0.430539			−0.215269	+	0.976555i	$0.569063\pi$
$882$			3.78080i			0.127306i
$883$	40.3665			1.35844			0.679221	−	0.733934i	$-0.262318\pi$
$883$	40.3665			1.35844			0.679221	+	0.733934i	$0.262318\pi$
$884$	−12.9023	+	4.24349i	−0.433951	+	0.142724i
$885$	58.4512			1.96481
$886$		−	77.6833i		−	2.60982i
$887$	−26.7184			−0.897115			−0.448558	−	0.893754i	$-0.648062\pi$
$887$	−26.7184			−0.897115			−0.448558	+	0.893754i	$0.648062\pi$
$888$	0.213373			0.00716033
$889$		−	0.172698i		−	0.00579211i
$890$			9.85535i			0.330352i
$891$			21.5812i			0.722999i
$892$			20.8182i			0.697045i
$893$	44.6462			1.49403
$894$	−47.2742			−1.58109
$895$		−	36.6471i		−	1.22498i
$896$	−0.611050			−0.0204137
$897$	20.4519	−	6.72652i	0.682871	−	0.224592i
$898$	−40.6108			−1.35520
$899$			4.27051i			0.142429i
$900$	−1.99752			−0.0665841
$901$	26.2997			0.876172
$902$		−	34.0427i		−	1.13350i
$903$			32.2866i			1.07443i
$904$			0.335210i			0.0111489i
$905$			22.3058i			0.741469i
$906$	−41.2279			−1.36970
$907$	−43.7286			−1.45199			−0.725993	−	0.687702i	$-0.758619\pi$
$907$	−43.7286			−1.45199			−0.725993	+	0.687702i	$0.758619\pi$
$908$			3.03499i			0.100720i
$909$	−1.48691			−0.0493178
$910$	10.4253	+	31.6982i	0.345597	+	1.05079i
$911$	−24.8683			−0.823925			−0.411962	−	0.911201i	$-0.635157\pi$
$911$	−24.8683			−0.823925			−0.411962	+	0.911201i	$0.635157\pi$
$912$			27.2794i			0.903311i
$913$	0.486854			0.0161125
$914$	−29.7661			−0.984574
$915$			21.4178i			0.708050i
$916$			2.64411i			0.0873638i
$917$			2.72030i			0.0898322i
$918$			20.9782i			0.692383i
$919$	−9.82945			−0.324244			−0.162122	−	0.986771i	$-0.551834\pi$
$919$	−9.82945			−0.324244			−0.162122	+	0.986771i	$0.551834\pi$
$920$	−0.440465			−0.0145217
$921$			27.0854i			0.892493i
$922$	−35.8589			−1.18095
$923$	6.56812	+	19.9703i	0.216192	+	0.657332i
$924$	16.0630			0.528433
$925$			6.47699i			0.212962i
$926$	80.6702			2.65099
$927$	−1.37469			−0.0451507
$928$		−	34.0658i		−	1.11826i
$929$			36.8412i			1.20872i	0.796711	+	0.604360i	$0.206571\pi$
$929$			36.8412i			1.20872i	−0.796711	+	0.604360i	$0.793429\pi$
$930$		−	8.45213i		−	0.277156i
$931$			16.8824i			0.553297i
$932$	45.8292			1.50119
$933$	−6.36980			−0.208538
$934$		−	74.7495i		−	2.44588i
$935$	14.9353			0.488436
$936$	−0.0235935	−	0.0717358i	−0.000771177	−	0.00234476i
$937$	−27.3075			−0.892099			−0.446049	−	0.895008i	$-0.647169\pi$
$937$	−27.3075			−0.892099			−0.446049	+	0.895008i	$0.647169\pi$
$938$		−	44.0716i		−	1.43899i
$939$	9.59358			0.313075
$940$	55.4716			1.80928
$941$		−	55.6611i		−	1.81450i	−0.420593	−	0.907249i	$-0.638178\pi$
$941$		−	55.6611i		−	1.81450i	0.420593	−	0.907249i	$-0.361822\pi$
$942$		−	57.3799i		−	1.86954i
$943$			21.8284i			0.710832i
$944$			55.7727i			1.81525i
$945$	25.6268			0.833640
$946$	68.5152			2.22762
$947$			30.9641i			1.00620i	0.864228	+	0.503100i	$0.167807\pi$
$947$			30.9641i			1.00620i	−0.864228	+	0.503100i	$0.832193\pi$
$948$	2.33672			0.0758930
$949$	−5.54250	−	16.8520i	−0.179917	−	0.547038i
$950$	−17.9383			−0.581996
$951$		−	22.2871i		−	0.722710i
$952$	−0.145476			−0.00471489
$953$	16.9362			0.548618			0.274309	−	0.961642i	$-0.411551\pi$
$953$	16.9362			0.548618			0.274309	+	0.961642i	$0.411551\pi$
$954$		−	13.1349i		−	0.425260i
$955$		−	67.1999i		−	2.17454i
$956$		−	11.7745i		−	0.380814i
$957$		−	19.9396i		−	0.644555i
$958$	−9.16079			−0.295972
$959$	12.7145			0.410571
$960$			33.1514i			1.06996i
$961$	−1.00000			−0.0322581
$962$	20.8942	−	6.87197i	0.673656	−	0.221561i
$963$	3.50573			0.112971
$964$		−	53.9280i		−	1.73691i
$965$	−21.4450			−0.690339
$966$	−20.7141			−0.666464
$967$		−	10.2460i		−	0.329488i	−0.986336	−	0.164744i	$-0.947320\pi$
$967$		−	10.2460i		−	0.329488i	0.986336	−	0.164744i	$-0.0526797\pi$
$968$		−	0.103626i		−	0.00333068i
$969$			12.8484i			0.412749i
$970$			33.8230i			1.08599i
$971$	−41.0649			−1.31784			−0.658918	−	0.752214i	$-0.728986\pi$
$971$	−41.0649			−1.31784			−0.658918	+	0.752214i	$0.728986\pi$
$972$	9.70463			0.311276
$973$			14.5374i			0.466047i
$974$	−59.0592			−1.89238
$975$	−11.5208	+	3.78912i	−0.368961	+	0.121349i
$976$	−20.4363			−0.654151
$977$			15.4726i			0.495013i	0.968886	+	0.247507i	$0.0796112\pi$
$977$			15.4726i			0.495013i	−0.968886	+	0.247507i	$0.920389\pi$
$978$	−11.6315			−0.371935
$979$	−5.44430			−0.174001
$980$			20.9758i			0.670048i
$981$			6.19352i			0.197744i
$982$		−	69.9793i		−	2.23313i
$983$		−	14.4229i		−	0.460020i	−0.973188	−	0.230010i	$-0.926124\pi$
$983$		−	14.4229i		−	0.460020i	0.973188	−	0.230010i	$-0.0738759\pi$
$984$	−0.405076			−0.0129134
$985$	−7.45889			−0.237660
$986$		−	16.2214i		−	0.516594i
$987$	−29.0414			−0.924396
$988$	9.46344	+	28.7736i	0.301072	+	0.915409i
$989$	−43.9325			−1.39697
$990$		−	7.45916i		−	0.237068i
$991$	−55.8859			−1.77527			−0.887637	−	0.460543i	$-0.847655\pi$
$991$	−55.8859			−1.77527			−0.887637	+	0.460543i	$0.847655\pi$
$992$	7.97698			0.253269
$993$			17.7382i			0.562905i
$994$		−	20.2263i		−	0.641539i
$995$		−	43.5953i		−	1.38206i
$996$			0.520379i			0.0164888i
$997$	−21.4634			−0.679753			−0.339877	−	0.940470i	$-0.610385\pi$
$997$	−21.4634			−0.679753			−0.339877	+	0.940470i	$0.610385\pi$
$998$	6.14200			0.194421
$999$		−	16.8922i		−	0.534445i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.c.b.311.6	✓	32
13.5	odd	4		5239.2.a.l.1.3		16
13.8	odd	4		5239.2.a.k.1.14		16
13.12	even	2	inner	403.2.c.b.311.27	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.c.b.311.6	✓	32	1.1	even	1	trivial
403.2.c.b.311.27	yes	32	13.12	even	2	inner
5239.2.a.k.1.14		16	13.8	odd	4
5239.2.a.l.1.3		16	13.5	odd	4

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.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.99449i q^{2} -1.58843 q^{3} -1.97798 q^{4} -2.66789i q^{5} +3.16810i q^{6} +1.73927i q^{7} -0.0439183i q^{8} -0.476895 q^{9} +O(q^{10})\)	\(q-1.99449i q^{2} -1.58843 q^{3} -1.97798 q^{4} -2.66789i q^{5} +3.16810i q^{6} +1.73927i q^{7} -0.0439183i q^{8} -0.476895 q^{9} -5.32107 q^{10} -2.93947i q^{11} +3.14188 q^{12} +(-3.42506 + 1.12648i) q^{13} +3.46896 q^{14} +4.23775i q^{15} -4.04355 q^{16} -1.90448 q^{17} +0.951161i q^{18} +4.24721i q^{19} +5.27703i q^{20} -2.76271i q^{21} -5.86273 q^{22} +3.75923 q^{23} +0.0697611i q^{24} -2.11762 q^{25} +(2.24675 + 6.83124i) q^{26} +5.52280 q^{27} -3.44025i q^{28} -4.27051 q^{29} +8.45213 q^{30} -1.00000i q^{31} +7.97698i q^{32} +4.66914i q^{33} +3.79847i q^{34} +4.64018 q^{35} +0.943288 q^{36} -3.05862i q^{37} +8.47100 q^{38} +(5.44046 - 1.78933i) q^{39} -0.117169 q^{40} +5.80663i q^{41} -5.51019 q^{42} -11.6866 q^{43} +5.81421i q^{44} +1.27230i q^{45} -7.49773i q^{46} -10.5119i q^{47} +6.42290 q^{48} +3.97493 q^{49} +4.22356i q^{50} +3.02514 q^{51} +(6.77470 - 2.22816i) q^{52} -13.8094 q^{53} -11.0152i q^{54} -7.84217 q^{55} +0.0763859 q^{56} -6.74639i q^{57} +8.51748i q^{58} -13.7930i q^{59} -8.38218i q^{60} +5.05405 q^{61} -1.99449 q^{62} -0.829450i q^{63} +7.82288 q^{64} +(3.00532 + 9.13767i) q^{65} +9.31253 q^{66} -12.7046i q^{67} +3.76703 q^{68} -5.97127 q^{69} -9.25478i q^{70} -5.83066i q^{71} +0.0209444i q^{72} +4.92019i q^{73} -6.10039 q^{74} +3.36368 q^{75} -8.40089i q^{76} +5.11254 q^{77} +(-3.56881 - 10.8509i) q^{78} +0.743732 q^{79} +10.7877i q^{80} -7.34189 q^{81} +11.5812 q^{82} +0.165627i q^{83} +5.46459i q^{84} +5.08094i q^{85} +23.3087i q^{86} +6.78340 q^{87} -0.129096 q^{88} -1.85214i q^{89} +2.53759 q^{90} +(-1.95926 - 5.95712i) q^{91} -7.43568 q^{92} +1.58843i q^{93} -20.9659 q^{94} +11.3311 q^{95} -12.6709i q^{96} -6.35644i q^{97} -7.92795i q^{98} +1.40182i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{3} - 36 q^{4} + 20 q^{9}+O(q^{10}) \) 32 * q - 4 * q^3 - 36 * q^4 + 20 * q^9	\( 32 q - 4 q^{3} - 36 q^{4} + 20 q^{9} + 4 q^{10} - 16 q^{12} + 10 q^{13} - 16 q^{14} + 28 q^{16} - 8 q^{17} - 16 q^{22} - 8 q^{23} + 4 q^{25} + 18 q^{26} + 20 q^{27} - 16 q^{29} + 40 q^{30} - 4 q^{35} - 44 q^{36} + 12 q^{38} + 4 q^{39} + 28 q^{40} + 28 q^{42} - 32 q^{43} - 64 q^{49} - 64 q^{52} - 12 q^{53} + 44 q^{55} + 8 q^{56} + 16 q^{61} + 8 q^{62} - 76 q^{64} - 66 q^{65} - 68 q^{66} + 64 q^{68} + 20 q^{69} + 16 q^{74} - 32 q^{77} - 20 q^{78} + 64 q^{79} - 16 q^{81} + 12 q^{82} - 72 q^{87} + 80 q^{88} + 68 q^{90} + 22 q^{91} + 28 q^{92} + 88 q^{94} + 4 q^{95}+O(q^{100}) \) 32 * q - 4 * q^3 - 36 * q^4 + 20 * q^9 + 4 * q^10 - 16 * q^12 + 10 * q^13 - 16 * q^14 + 28 * q^16 - 8 * q^17 - 16 * q^22 - 8 * q^23 + 4 * q^25 + 18 * q^26 + 20 * q^27 - 16 * q^29 + 40 * q^30 - 4 * q^35 - 44 * q^36 + 12 * q^38 + 4 * q^39 + 28 * q^40 + 28 * q^42 - 32 * q^43 - 64 * q^49 - 64 * q^52 - 12 * q^53 + 44 * q^55 + 8 * q^56 + 16 * q^61 + 8 * q^62 - 76 * q^64 - 66 * q^65 - 68 * q^66 + 64 * q^68 + 20 * q^69 + 16 * q^74 - 32 * q^77 - 20 * q^78 + 64 * q^79 - 16 * q^81 + 12 * q^82 - 72 * q^87 + 80 * q^88 + 68 * q^90 + 22 * q^91 + 28 * q^92 + 88 * q^94 + 4 * q^95

Introduction

L-functions

Modular forms

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