LMFDB - Embedded newform 560.2.r.a.237.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(237,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 1, 2]))

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

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

chi := DirichletCharacter("560.237");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.r (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$184$
Relative dimension:	$92$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			237.11
Character	$\chi$	$=$	560.237
Dual form			560.2.r.a.293.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.33522 + 0.466046i) q^{2} -0.958223i q^{3} +(1.56560 - 1.24454i) q^{4} +(0.666131 - 2.13454i) q^{5} +(0.446576 + 1.27943i) q^{6} +(0.729292 - 2.54325i) q^{7} +(-1.51040 + 2.39138i) q^{8} +2.08181 q^{9} +(0.105366 + 3.16052i) q^{10} +(3.64406 - 3.64406i) q^{11} +(-1.19255 - 1.50020i) q^{12} +5.12086i q^{13} +(0.211511 + 3.73567i) q^{14} +(-2.04537 - 0.638302i) q^{15} +(0.902218 - 3.89692i) q^{16} +(-0.135731 + 0.135731i) q^{17} +(-2.77966 + 0.970219i) q^{18} +(-0.763055 - 0.763055i) q^{19} +(-1.61364 - 4.17087i) q^{20} +(-2.43700 - 0.698824i) q^{21} +(-3.16730 + 6.56390i) q^{22} +(1.64227 + 1.64227i) q^{23} +(2.29147 + 1.44730i) q^{24} +(-4.11254 - 2.84377i) q^{25} +(-2.38656 - 6.83745i) q^{26} -4.86951i q^{27} +(-2.02341 - 4.88936i) q^{28} +(1.76859 - 1.76859i) q^{29} +(3.02848 - 0.100964i) q^{30} +6.27749i q^{31} +(0.611490 + 5.62371i) q^{32} +(-3.49182 - 3.49182i) q^{33} +(0.117973 - 0.244487i) q^{34} +(-4.94288 - 3.25084i) q^{35} +(3.25928 - 2.59090i) q^{36} -3.32890 q^{37} +(1.37446 + 0.663224i) q^{38} +4.90692 q^{39} +(4.09837 + 4.81699i) q^{40} -8.79916 q^{41} +(3.57961 - 0.202675i) q^{42} +6.58815i q^{43} +(1.16995 - 10.2403i) q^{44} +(1.38676 - 4.44371i) q^{45} +(-2.95815 - 1.42741i) q^{46} +(3.60682 - 3.60682i) q^{47} +(-3.73412 - 0.864526i) q^{48} +(-5.93627 - 3.70955i) q^{49} +(6.81645 + 1.88041i) q^{50} +(0.130060 + 0.130060i) q^{51} +(6.37314 + 8.01722i) q^{52} +1.10982i q^{53} +(2.26941 + 6.50184i) q^{54} +(-5.35097 - 10.2058i) q^{55} +(4.98036 + 5.58534i) q^{56} +(-0.731177 + 0.731177i) q^{57} +(-1.53721 + 3.18570i) q^{58} +(10.4667 - 10.4667i) q^{59} +(-3.99663 + 1.54622i) q^{60} +(4.04412 - 4.04412i) q^{61} +(-2.92560 - 8.38181i) q^{62} +(1.51825 - 5.29457i) q^{63} +(-3.43738 - 7.22388i) q^{64} +(10.9307 + 3.41116i) q^{65} +(6.28968 + 3.03498i) q^{66} -2.74917i q^{67} +(-0.0435774 + 0.381424i) q^{68} +(1.57366 - 1.57366i) q^{69} +(8.11485 + 2.03697i) q^{70} -0.522556i q^{71} +(-3.14437 + 4.97839i) q^{72} +(-7.09935 + 7.09935i) q^{73} +(4.44479 - 1.55142i) q^{74} +(-2.72497 + 3.94073i) q^{75} +(-2.14430 - 0.244984i) q^{76} +(-6.61018 - 11.9253i) q^{77} +(-6.55180 + 2.28685i) q^{78} +11.9737i q^{79} +(-7.71715 - 4.52168i) q^{80} +1.57935 q^{81} +(11.7488 - 4.10081i) q^{82} -16.4004i q^{83} +(-4.68509 + 1.93888i) q^{84} +(0.199309 + 0.380138i) q^{85} +(-3.07038 - 8.79660i) q^{86} +(-1.69471 - 1.69471i) q^{87} +(3.21033 + 14.2183i) q^{88} +8.03500i q^{89} +(0.219353 + 6.57960i) q^{90} +(13.0236 + 3.73460i) q^{91} +(4.61501 + 0.527262i) q^{92} +6.01524 q^{93} +(-3.13494 + 6.49683i) q^{94} +(-2.13707 + 1.12048i) q^{95} +(5.38877 - 0.585944i) q^{96} +(-2.65658 + 2.65658i) q^{97} +(9.65502 + 2.18647i) q^{98} +(7.58623 - 7.58623i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 184 q - 4 q^{2} + 8 q^{8} - 168 q^{9} - 8 q^{11} - 8 q^{15} - 8 q^{16} - 4 q^{21} - 12 q^{22} - 32 q^{28} - 44 q^{30} - 24 q^{32} + 20 q^{35} - 40 q^{36} - 8 q^{37} + 48 q^{39} - 32 q^{42} + 24 q^{44} - 8 q^{46}+ \cdots + 24 q^{99}+O(q^{100}) $ 184 * q - 4 * q^2 + 8 * q^8 - 168 * q^9 - 8 * q^11 - 8 * q^15 - 8 * q^16 - 4 * q^21 - 12 * q^22 - 32 * q^28 - 44 * q^30 - 24 * q^32 + 20 * q^35 - 40 * q^36 - 8 * q^37 + 48 * q^39 - 32 * q^42 + 24 * q^44 - 8 * q^46 - 4 * q^50 - 8 * q^51 - 4 * q^56 + 24 * q^57 - 4 * q^58 + 64 * q^60 - 32 * q^63 - 8 * q^65 + 12 * q^70 - 64 * q^72 + 40 * q^74 - 28 * q^78 + 104 * q^81 - 48 * q^84 + 16 * q^85 + 8 * q^86 + 96 * q^88 - 20 * q^91 - 56 * q^92 + 16 * q^93 - 56 * q^95 - 80 * q^98 + 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−1.33522	+	0.466046i	−0.944140	+	0.329544i
$2$	−1.33522	+	0.466046i	−0.944140	+	0.329544i
$3$		−	0.958223i		−	0.553230i	−0.960981	−	0.276615i	$-0.910787\pi$
$3$		−	0.958223i		−	0.553230i	0.960981	−	0.276615i	$-0.0892127\pi$
$4$	1.56560	−	1.24454i	0.782801	−	0.622272i
$5$	0.666131	−	2.13454i	0.297903	−	0.954596i
$5$	0.666131	−	2.13454i	0.297903	−	0.954596i
$6$	0.446576	+	1.27943i	0.182314	+	0.522327i
$7$	0.729292	−	2.54325i	0.275646	−	0.961259i
$7$	0.729292	−	2.54325i	0.275646	−	0.961259i
$8$	−1.51040	+	2.39138i	−0.534007	+	0.845480i
$9$	2.08181			0.693936
$10$	0.105366	+	3.16052i	0.0333198	+	0.999445i
$11$	3.64406	−	3.64406i	1.09873	−	1.09873i	0.104165	−	0.994560i	$-0.466783\pi$
$11$	3.64406	−	3.64406i	1.09873	−	1.09873i	0.994560	−	0.104165i	$-0.0332170\pi$
$12$	−1.19255	−	1.50020i	−0.344260	−	0.433069i
$13$			5.12086i			1.42027i	0.704065	+	0.710135i	$0.251366\pi$
$13$			5.12086i			1.42027i	−0.704065	+	0.710135i	$0.748634\pi$
$14$	0.211511	+	3.73567i	0.0565288	+	0.998401i
$15$	−2.04537	−	0.638302i	−0.528112	−	0.164809i
$16$	0.902218	−	3.89692i	0.225555	−	0.974231i
$17$	−0.135731	+	0.135731i	−0.0329196	+	0.0329196i	−0.723375	−	0.690455i	$-0.757410\pi$
$17$	−0.135731	+	0.135731i	−0.0329196	+	0.0329196i	0.690455	+	0.723375i	$0.257410\pi$
$18$	−2.77966	+	0.970219i	−0.655173	+	0.228683i
$19$	−0.763055	−	0.763055i	−0.175057	−	0.175057i	0.614140	−	0.789197i	$-0.289503\pi$
$19$	−0.763055	−	0.763055i	−0.175057	−	0.175057i	−0.789197	+	0.614140i	$0.789503\pi$
$20$	−1.61364	−	4.17087i	−0.360820	−	0.932635i
$21$	−2.43700	−	0.698824i	−0.531798	−	0.152496i
$22$	−3.16730	+	6.56390i	−0.675272	+	1.39943i
$23$	1.64227	+	1.64227i	0.342436	+	0.342436i	0.857283	−	0.514846i	$-0.172151\pi$
$23$	1.64227	+	1.64227i	0.342436	+	0.342436i	−0.514846	+	0.857283i	$0.672151\pi$
$24$	2.29147	+	1.44730i	0.467745	+	0.295429i
$25$	−4.11254	−	2.84377i	−0.822508	−	0.568754i
$26$	−2.38656	−	6.83745i	−0.468042	−	1.34093i
$27$		−	4.86951i		−	0.937137i
$28$	−2.02341	−	4.88936i	−0.382389	−	0.924002i
$29$	1.76859	−	1.76859i	0.328419	−	0.328419i	−0.523566	−	0.851985i	$-0.675399\pi$
$29$	1.76859	−	1.76859i	0.328419	−	0.328419i	0.851985	+	0.523566i	$0.175399\pi$
$30$	3.02848	−	0.100964i	0.552923	−	0.0184335i
$31$			6.27749i			1.12747i	0.825955	+	0.563735i	$0.190636\pi$
$31$			6.27749i			1.12747i	−0.825955	+	0.563735i	$0.809364\pi$
$32$	0.611490	+	5.62371i	0.108097	+	0.994140i
$33$	−3.49182	−	3.49182i	−0.607848	−	0.607848i
$34$	0.117973	−	0.244487i	0.0202322	−	0.0419292i
$35$	−4.94288	−	3.25084i	−0.835498	−	0.549493i
$36$	3.25928	−	2.59090i	0.543214	−	0.431817i
$37$	−3.32890			−0.547267			−0.273634	−	0.961834i	$-0.588226\pi$
$37$	−3.32890			−0.547267			−0.273634	+	0.961834i	$0.588226\pi$
$38$	1.37446	+	0.663224i	0.222967	+	0.107589i
$39$	4.90692			0.785737
$40$	4.09837	+	4.81699i	0.648009	+	0.761632i
$41$	−8.79916			−1.37420			−0.687099	−	0.726564i	$-0.741116\pi$
$41$	−8.79916			−1.37420			−0.687099	+	0.726564i	$0.741116\pi$
$42$	3.57961	−	0.202675i	0.552346	−	0.0312735i
$43$			6.58815i			1.00468i	0.864669	+	0.502342i	$0.167528\pi$
$43$			6.58815i			1.00468i	−0.864669	+	0.502342i	$0.832472\pi$
$44$	1.16995	−	10.2403i	0.176377	−	1.54379i
$45$	1.38676	−	4.44371i	0.206726	−	0.662429i
$46$	−2.95815	−	1.42741i	−0.436156	−	0.210460i
$47$	3.60682	−	3.60682i	0.526109	−	0.526109i	−0.393301	−	0.919410i	$-0.628667\pi$
$47$	3.60682	−	3.60682i	0.526109	−	0.526109i	0.919410	+	0.393301i	$0.128667\pi$
$48$	−3.73412	−	0.864526i	−0.538974	−	0.124784i
$49$	−5.93627	−	3.70955i	−0.848038	−	0.529935i
$50$	6.81645	+	1.88041i	0.963992	+	0.265931i
$51$	0.130060	+	0.130060i	0.0182121	+	0.0182121i
$52$	6.37314	+	8.01722i	0.883795	+	1.11179i
$53$			1.10982i			0.152446i	0.997091	+	0.0762229i	$0.0242861\pi$
$53$			1.10982i			0.152446i	−0.997091	+	0.0762229i	$0.975714\pi$
$54$	2.26941	+	6.50184i	0.308828	+	0.884788i
$55$	−5.35097	−	10.2058i	−0.721525	−	1.37615i
$56$	4.98036	+	5.58534i	0.665528	+	0.746373i
$57$	−0.731177	+	0.731177i	−0.0968467	+	0.0968467i
$58$	−1.53721	+	3.18570i	−0.201845	+	0.418303i
$59$	10.4667	−	10.4667i	1.36264	−	1.36264i	0.492114	−	0.870531i	$-0.336224\pi$
$59$	10.4667	−	10.4667i	1.36264	−	1.36264i	0.870531	−	0.492114i	$-0.163776\pi$
$60$	−3.99663	+	1.54622i	−0.515962	+	0.199617i
$61$	4.04412	−	4.04412i	0.517797	−	0.517797i	−0.399108	−	0.916904i	$-0.630680\pi$
$61$	4.04412	−	4.04412i	0.517797	−	0.517797i	0.916904	+	0.399108i	$0.130680\pi$
$62$	−2.92560	−	8.38181i	−0.371552	−	1.06449i
$63$	1.51825	−	5.29457i	0.191281	−	0.667053i
$64$	−3.43738	−	7.22388i	−0.429672	−	0.902985i
$65$	10.9307	+	3.41116i	1.35578	+	0.423103i
$66$	6.28968	+	3.03498i	0.774207	+	0.373581i
$67$		−	2.74917i		−	0.335865i	−0.985799	−	0.167932i	$-0.946291\pi$
$67$		−	2.74917i		−	0.335865i	0.985799	−	0.167932i	$-0.0537091\pi$
$68$	−0.0435774	+	0.381424i	−0.00528454	+	0.0462544i
$69$	1.57366	−	1.57366i	0.189446	−	0.189446i
$70$	8.11485	+	2.03697i	0.969910	+	0.243464i
$71$		−	0.522556i		−	0.0620160i	−0.999519	−	0.0310080i	$-0.990128\pi$
$71$		−	0.522556i		−	0.0620160i	0.999519	−	0.0310080i	$-0.00987174\pi$
$72$	−3.14437	+	4.97839i	−0.370567	+	0.586709i
$73$	−7.09935	+	7.09935i	−0.830916	+	0.830916i	−0.987642	−	0.156726i	$-0.949906\pi$
$73$	−7.09935	+	7.09935i	−0.830916	+	0.830916i	0.156726	+	0.987642i	$0.449906\pi$
$74$	4.44479	−	1.55142i	0.516697	−	0.180349i
$75$	−2.72497	+	3.94073i	−0.314652	+	0.455036i
$76$	−2.14430	−	0.244984i	−0.245968	−	0.0281016i
$77$	−6.61018	−	11.9253i	−0.753300	−	1.35902i
$78$	−6.55180	+	2.28685i	−0.741845	+	0.258935i
$79$			11.9737i			1.34715i	0.739120	+	0.673574i	$0.235242\pi$
$79$			11.9737i			1.34715i	−0.739120	+	0.673574i	$0.764758\pi$
$80$	−7.71715	−	4.52168i	−0.862803	−	0.505540i
$81$	1.57935			0.175484
$82$	11.7488	−	4.10081i	1.29743	−	0.452859i
$83$		−	16.4004i		−	1.80018i	−0.435707	−	0.900089i	$-0.643502\pi$
$83$		−	16.4004i		−	1.80018i	0.435707	−	0.900089i	$-0.356498\pi$
$84$	−4.68509	+	1.93888i	−0.511186	+	0.211549i
$85$	0.199309	+	0.380138i	0.0216181	+	0.0412317i
$86$	−3.07038	−	8.79660i	−0.331088	−	0.948562i
$87$	−1.69471	−	1.69471i	−0.181692	−	0.181692i
$88$	3.21033	+	14.2183i	0.342223	+	1.51568i
$89$			8.03500i			0.851709i	0.904792	+	0.425854i	$0.140026\pi$
$89$			8.03500i			0.851709i	−0.904792	+	0.425854i	$0.859974\pi$
$90$	0.219353	+	6.57960i	0.0231218	+	0.693551i
$91$	13.0236	+	3.73460i	1.36525	+	0.391492i
$92$	4.61501	+	0.527262i	0.481148	+	0.0549709i
$93$	6.01524			0.623751
$94$	−3.13494	+	6.49683i	−0.323344	+	0.670097i
$95$	−2.13707	+	1.12048i	−0.219258	+	0.114959i
$96$	5.38877	−	0.585944i	0.549989	−	0.0598026i
$97$	−2.65658	+	2.65658i	−0.269735	+	0.269735i	−0.828993	−	0.559258i	$-0.811086\pi$
$97$	−2.65658	+	2.65658i	−0.269735	+	0.269735i	0.559258	+	0.828993i	$0.311086\pi$
$98$	9.65502	+	2.18647i	0.975304	+	0.220867i
$99$	7.58623	−	7.58623i	0.762445	−	0.762445i
$100$	−9.97780	+	0.666025i	−0.997780	+	0.0666025i
$101$	12.9993	+	12.9993i	1.29348	+	1.29348i	0.932620	+	0.360859i	$0.117516\pi$
$101$	12.9993	+	12.9993i	1.29348	+	1.29348i	0.360859	+	0.932620i	$0.382484\pi$
$102$	−0.234273	−	0.113045i	−0.0231965	−	0.0111931i
$103$	−3.46620	+	3.46620i	−0.341535	+	0.341535i	−0.856944	−	0.515409i	$-0.827640\pi$
$103$	−3.46620	+	3.46620i	−0.341535	+	0.341535i	0.515409	+	0.856944i	$0.327640\pi$
$104$	−12.2459	−	7.73455i	−1.20081	−	0.758435i
$105$	−3.11503	+	4.73638i	−0.303996	+	0.462223i
$106$	−0.517229	−	1.48185i	−0.0502377	−	0.143930i
$107$	−13.6452			−1.31913			−0.659566	−	0.751647i	$-0.729260\pi$
$107$	−13.6452			−1.31913			−0.659566	+	0.751647i	$0.729260\pi$
$108$	−6.06032	−	7.62371i	−0.583154	−	0.733592i
$109$	−12.3259	+	12.3259i	−1.18061	+	1.18061i	−0.201018	+	0.979587i	$0.564425\pi$
$109$	−12.3259	+	12.3259i	−1.18061	+	1.18061i	−0.979587	+	0.201018i	$0.935575\pi$
$110$	11.9011	+	11.1332i	1.13472	+	1.06151i
$111$			3.18982i			0.302765i
$112$	−9.25288	−	5.13656i	−0.874315	−	0.485359i
$113$	−7.09863	+	7.09863i	−0.667783	+	0.667783i	−0.957202	−	0.289419i	$-0.906538\pi$
$113$	−7.09863	+	7.09863i	−0.667783	+	0.667783i	0.289419	+	0.957202i	$0.406538\pi$
$114$	0.635516	−	1.31704i	0.0595216	−	0.123352i
$115$	4.59945	−	2.41152i	0.428901	−	0.224876i
$116$	0.567820	−	4.97000i	0.0527207	−	0.461453i
$117$			10.6606i			0.985577i
$118$	−9.09731	+	18.8532i	−0.837475	+	1.73558i
$119$	0.246210	+	0.444185i	0.0225701	+	0.0407184i
$120$	4.61575	−	3.92715i	0.421358	−	0.358498i
$121$		−	15.5583i		−	1.41439i
$122$	−3.51503	+	7.28452i	−0.318235	+	0.659509i
$123$			8.43155i			0.760248i
$124$	7.81262	+	9.82805i	0.701594	+	0.882585i
$125$	−8.80964	+	6.88406i	−0.787958	+	0.615729i
$126$	0.440326	+	7.77696i	0.0392274	+	0.692827i
$127$	−5.95490	−	5.95490i	−0.528412	−	0.528412i	0.391687	−	0.920099i	$-0.371892\pi$
$127$	−5.95490	−	5.95490i	−0.528412	−	0.528412i	−0.920099	+	0.391687i	$0.871892\pi$
$128$	7.95630	+	8.04346i	0.703244	+	0.710948i
$129$	6.31292			0.555821
$130$	−16.1846	+	0.539566i	−1.41948	+	0.0473231i
$131$	−1.12696	+	1.12696i	−0.0984632	+	0.0984632i	−0.754622	−	0.656159i	$-0.772180\pi$
$131$	−1.12696	+	1.12696i	−0.0984632	+	0.0984632i	0.656159	+	0.754622i	$0.272180\pi$
$132$	−9.81253	−	1.12107i	−0.854071	−	0.0975770i
$133$	−2.49713	+	1.38415i	−0.216529	+	0.120021i
$134$	1.28124	+	3.67074i	0.110682	+	0.317104i
$135$	−10.3942	−	3.24373i	−0.894587	−	0.279176i
$136$	−0.119576	−	0.529592i	−0.0102535	−	0.0454121i
$137$	0.688069	−	0.688069i	0.0587857	−	0.0587857i	−0.677103	−	0.735888i	$-0.736765\pi$
$137$	0.688069	−	0.688069i	0.0587857	−	0.0587857i	0.735888	+	0.677103i	$0.236765\pi$
$138$	−1.36778	+	2.83457i	−0.116433	+	0.241295i
$139$	−3.69400	+	3.69400i	−0.313321	+	0.313321i	−0.846195	−	0.532874i	$-0.821112\pi$
$139$	−3.69400	+	3.69400i	−0.313321	+	0.313321i	0.532874	+	0.846195i	$0.321112\pi$
$140$	−11.7844	+	1.06210i	−0.995963	+	0.0897639i
$141$	−3.45614	−	3.45614i	−0.291059	−	0.291059i
$142$	0.243535	+	0.697726i	0.0204370	+	0.0585518i
$143$	18.6607	+	18.6607i	1.56049	+	1.56049i
$144$	1.87825	−	8.11265i	0.156520	−	0.676054i
$145$	−2.59702	−	4.95325i	−0.215671	−	0.411345i
$146$	6.17054	−	12.7878i	0.510677	−	1.05832i
$147$	−3.55457	+	5.68827i	−0.293176	+	0.469160i
$148$	−5.21173	+	4.14296i	−0.428401	+	0.340549i
$149$	−0.997064	−	0.997064i	−0.0816827	−	0.0816827i	0.665085	−	0.746768i	$-0.268395\pi$
$149$	−0.997064	−	0.997064i	−0.0816827	−	0.0816827i	−0.746768	+	0.665085i	$0.768395\pi$
$150$	1.80186	−	6.53168i	0.147121	−	0.533310i
$151$			8.68507i			0.706781i	0.935476	+	0.353390i	$0.114971\pi$
$151$			8.68507i			0.706781i	−0.935476	+	0.353390i	$0.885029\pi$
$152$	2.97727	−	0.672234i	0.241489	−	0.0545254i
$153$	−0.282566	+	0.282566i	−0.0228441	+	0.0228441i
$154$	14.3838	+	12.8423i	1.15908	+	1.03486i
$155$	13.3996	+	4.18163i	1.07628	+	0.335877i
$156$	7.68229	−	6.10688i	0.615075	−	0.488942i
$157$	20.9748			1.67397			0.836984	−	0.547227i	$-0.184317\pi$
$157$	20.9748			1.67397			0.836984	+	0.547227i	$0.184317\pi$
$158$	−5.58030	−	15.9875i	−0.443945	−	1.27190i
$159$	1.06346			0.0843377
$160$	12.4114	+	2.44088i	0.981205	+	0.192968i
$161$	5.37439	−	2.97901i	0.423561	−	0.234779i
$162$	−2.10878	+	0.736052i	−0.165681	+	0.0578297i
$163$	16.5131			1.29340			0.646701	−	0.762743i	$-0.276148\pi$
$163$	16.5131			1.29340			0.646701	+	0.762743i	$0.276148\pi$
$164$	−13.7760	+	10.9509i	−1.07572	+	0.855125i
$165$	−9.77945	+	5.12743i	−0.761329	+	0.399170i
$166$	7.64334	+	21.8981i	0.593238	+	1.69962i
$167$	−5.27346	−	5.27346i	−0.408073	−	0.408073i	0.472993	−	0.881066i	$-0.343173\pi$
$167$	−5.27346	−	5.27346i	−0.408073	−	0.408073i	−0.881066	+	0.472993i	$0.843173\pi$
$168$	5.35200	−	4.77229i	0.412916	−	0.368190i
$169$	−13.2232			−1.01717
$170$	−0.443282	−	0.414679i	−0.0339982	−	0.0318044i
$171$	−1.58853	−	1.58853i	−0.121478	−	0.121478i
$172$	8.19925	+	10.3144i	0.625187	+	0.786467i
$173$			12.0157i			0.913537i	0.889586	+	0.456768i	$0.150993\pi$
$173$			12.0157i			0.913537i	−0.889586	+	0.456768i	$0.849007\pi$
$174$	3.05261	+	1.47299i	0.231418	+	0.111667i
$175$	−10.2317	+	8.38529i	−0.773441	+	0.633868i
$176$	−10.9129	−	17.4883i	−0.822589	−	1.31823i
$177$	−10.0294	−	10.0294i	−0.753856	−	0.753856i
$178$	−3.74468	−	10.7285i	−0.280676	−	0.804132i
$179$	12.8989	−	12.8989i	0.964110	−	0.964110i	−0.0352677	−	0.999378i	$-0.511228\pi$
$179$	12.8989	−	12.8989i	0.964110	−	0.964110i	0.999378	+	0.0352677i	$0.0112284\pi$
$180$	−3.35928	−	8.68296i	−0.250386	−	0.647190i
$181$	−0.0690244	−	0.0690244i	−0.00513054	−	0.00513054i	0.704537	−	0.709667i	$-0.251155\pi$
$181$	−0.0690244	−	0.0690244i	−0.00513054	−	0.00513054i	−0.709667	+	0.704537i	$0.751155\pi$
$182$	−19.1299	+	1.08312i	−1.41800	+	0.0802862i
$183$	−3.87517	−	3.87517i	−0.286461	−	0.286461i
$184$	−6.40776	+	1.44680i	−0.472387	+	0.106659i
$185$	−2.21748	+	7.10567i	−0.163032	+	0.522419i
$186$	−8.03164	+	2.80338i	−0.588908	+	0.205554i
$187$			0.989223i			0.0723391i
$188$	1.15800	−	10.1357i	0.0844556	−	0.739221i
$189$	−12.3844	−	3.55129i	−0.900831	−	0.258318i
$190$	2.33125	−	2.49205i	0.169127	−	0.180792i
$191$	−8.58978			−0.621535			−0.310767	−	0.950486i	$-0.600586\pi$
$191$	−8.58978			−0.621535			−0.310767	+	0.950486i	$0.600586\pi$
$192$	−6.92209	+	3.29378i	−0.499559	+	0.237708i
$193$	13.6481	−	13.6481i	0.982413	−	0.982413i	−0.0174354	−	0.999848i	$-0.505550\pi$
$193$	13.6481	−	13.6481i	0.982413	−	0.982413i	0.999848	+	0.0174354i	$0.00555013\pi$
$194$	2.30902	−	4.78520i	0.165778	−	0.343557i
$195$	3.26866	−	10.4740i	0.234073	−	0.750061i
$196$	−13.9105	+	1.58028i	−0.993609	+	0.112877i
$197$	−5.59110			−0.398350			−0.199175	−	0.979964i	$-0.563826\pi$
$197$	−5.59110			−0.398350			−0.199175	+	0.979964i	$0.563826\pi$
$198$	−6.59372	+	13.6648i	−0.468595	+	0.971115i
$199$			9.69405i			0.687193i	0.939117	+	0.343597i	$0.111645\pi$
$199$			9.69405i			0.687193i	−0.939117	+	0.343597i	$0.888355\pi$
$200$	13.0121	−	5.53940i	0.920095	−	0.391695i
$201$	−2.63432			−0.185811
$202$	−23.4152	−	11.2986i	−1.64748	−	0.794967i
$203$	−3.20816	−	5.78780i	−0.225169	−	0.406224i
$204$	0.365489	+	0.0417569i	0.0255893	+	0.00292357i
$205$	−5.86139	+	18.7822i	−0.409377	+	1.31180i
$206$	3.01272	−	6.24354i	0.209906	−	0.435008i
$207$	3.41889	+	3.41889i	0.237629	+	0.237629i
$208$	19.9556	+	4.62013i	1.38367	+	0.320348i
$209$	−5.56123			−0.384679
$210$	1.95187	−	7.77583i	0.134692	−	0.536584i
$211$	18.3234	+	18.3234i	1.26143	+	1.26143i	0.950398	+	0.311035i	$0.100676\pi$
$211$	18.3234	+	18.3234i	1.26143	+	1.26143i	0.311035	+	0.950398i	$0.399324\pi$
$212$	1.38122	+	1.73754i	0.0948628	+	0.119335i
$213$	−0.500726			−0.0343092
$214$	18.2193	−	6.35930i	1.24545	−	0.434713i
$215$	14.0627	+	4.38857i	0.959067	+	0.299298i
$216$	11.6448	+	7.35491i	0.792330	+	0.500438i
$217$	15.9652	+	4.57812i	1.08379	+	0.310783i
$218$	10.7133	−	22.2021i	0.725595	−	1.50372i
$219$	6.80276	+	6.80276i	0.459688	+	0.459688i
$220$	−21.0791	−	9.31872i	−1.42115	−	0.628268i
$221$	−0.695059	−	0.695059i	−0.0467547	−	0.0467547i
$222$	−1.48661	−	4.25910i	−0.0997744	−	0.285852i
$223$	5.09759	+	5.09759i	0.341360	+	0.341360i	0.856878	−	0.515519i	$-0.172401\pi$
$223$	5.09759	+	5.09759i	0.341360	+	0.341360i	−0.515519	+	0.856878i	$0.672401\pi$
$224$	14.7485	+	2.54615i	0.985423	+	0.170122i
$225$	−8.56152	−	5.92019i	−0.570768	−	0.394679i
$226$	6.16991	−	12.7865i	0.410416	−	0.850545i
$227$	11.8688			0.787757			0.393879	−	0.919163i	$-0.371133\pi$
$227$	11.8688			0.787757			0.393879	+	0.919163i	$0.371133\pi$
$228$	−0.234750	+	2.05471i	−0.0155467	+	0.136077i
$229$	−4.48332	+	4.48332i	−0.296266	+	0.296266i	−0.839550	−	0.543283i	$-0.817181\pi$
$229$	−4.48332	+	4.48332i	−0.296266	+	0.296266i	0.543283	+	0.839550i	$0.317181\pi$
$230$	−5.01738	+	5.36346i	−0.330836	+	0.353656i
$231$	−11.4271	+	6.33403i	−0.751851	+	0.416748i
$232$	1.55809	+	6.90066i	0.102294	+	0.453050i
$233$	11.1266	+	11.1266i	0.728926	+	0.728926i	0.970406	−	0.241480i	$-0.0776328\pi$
$233$	11.1266	+	11.1266i	0.728926	+	0.728926i	−0.241480	+	0.970406i	$0.577633\pi$
$234$	−4.96835	−	14.2343i	−0.324791	−	0.930523i
$235$	−5.29629	−	10.1015i	−0.345492	−	0.658951i
$236$	3.36040	−	29.4129i	0.218744	−	1.91462i
$237$	11.4735			0.745283
$238$	−0.535755	−	0.478338i	−0.0347278	−	0.0310060i
$239$			14.1701i			0.916586i	0.888801	+	0.458293i	$0.151539\pi$
$239$			14.1701i			0.916586i	−0.888801	+	0.458293i	$0.848461\pi$
$240$	−4.33278	+	7.39475i	−0.279680	+	0.477329i
$241$		−	25.0401i		−	1.61298i	−0.591251	−	0.806488i	$-0.701366\pi$
$241$		−	25.0401i		−	1.61298i	0.591251	−	0.806488i	$-0.298634\pi$
$242$	7.25090	+	20.7737i	0.466106	+	1.33539i
$243$		−	16.1219i		−	1.03422i
$244$	1.29839	−	11.3646i	0.0831212	−	0.727542i
$245$	−11.8725	+	10.2002i	−0.758507	+	0.651665i
$246$	−3.92949	−	11.2579i	−0.250535	−	0.717780i
$247$	3.90750	−	3.90750i	0.248628	−	0.248628i
$248$	−15.0119	−	9.48153i	−0.953254	−	0.602078i
$249$	−15.7152			−0.995913
$250$	8.55447	−	13.2974i	0.541032	−	0.841002i
$251$	−4.38367	−	4.38367i	−0.276695	−	0.276695i	0.555093	−	0.831788i	$-0.312683\pi$
$251$	−4.38367	−	4.38367i	−0.276695	−	0.276695i	−0.831788	+	0.555093i	$0.812683\pi$
$252$	−4.21235	−	10.1787i	−0.265353	−	0.641198i
$253$	11.9690			0.752487
$254$	10.7263	+	5.17582i	0.673030	+	0.324760i
$255$	0.364257	−	0.190982i	0.0228106	−	0.0119598i
$256$	−14.3720	−	7.03175i	−0.898250	−	0.439484i
$257$	12.0827	−	12.0827i	0.753700	−	0.753700i	−0.221468	−	0.975168i	$-0.571085\pi$
$257$	12.0827	−	12.0827i	0.753700	−	0.753700i	0.975168	+	0.221468i	$0.0710849\pi$
$258$	−8.42911	+	2.94211i	−0.524773	+	0.183168i
$259$	−2.42774	+	8.46622i	−0.150852	+	0.526066i
$260$	21.3584	−	8.26320i	1.32459	−	0.512462i
$261$	3.68187	−	3.68187i	0.227902	−	0.227902i
$262$	0.979522	−	2.02996i	0.0605151	−	0.125411i
$263$	−6.50590	−	6.50590i	−0.401171	−	0.401171i	0.477475	−	0.878645i	$-0.341552\pi$
$263$	−6.50590	−	6.50590i	−0.401171	−	0.401171i	−0.878645	+	0.477475i	$0.841552\pi$
$264$	13.6243	−	3.07621i	0.838519	−	0.189328i
$265$	2.36896	+	0.739287i	0.145524	+	0.0454141i
$266$	2.68913	−	3.01192i	0.164881	−	0.184673i
$267$	7.69933			0.471191
$268$	−3.42147	−	4.30411i	−0.208999	−	0.262915i
$269$	−4.65709	−	4.65709i	−0.283948	−	0.283948i	0.550733	−	0.834681i	$-0.314348\pi$
$269$	−4.65709	−	4.65709i	−0.283948	−	0.283948i	−0.834681	+	0.550733i	$0.814348\pi$
$270$	15.3902	−	0.513082i	0.936617	−	0.0312252i
$271$		−	17.5711i		−	1.06737i	−0.845684	−	0.533684i	$-0.820807\pi$
$271$		−	17.5711i		−	1.06737i	0.845684	−	0.533684i	$-0.179193\pi$
$272$	0.406474	+	0.651392i	0.0246461	+	0.0394964i
$273$	3.57858	−	12.4795i	0.216585	−	0.755297i
$274$	−0.598048	+	1.23939i	−0.0361294	+	0.0748744i
$275$	−25.3492	+	4.62347i	−1.52861	+	0.278805i
$276$	0.505234	−	4.42221i	0.0304115	−	0.266186i
$277$	23.7488			1.42693			0.713464	−	0.700692i	$-0.247125\pi$
$277$	23.7488			1.42693			0.713464	+	0.700692i	$0.247125\pi$
$278$	3.21072	−	6.65387i	0.192566	−	0.399072i
$279$			13.0685i			0.782393i
$280$	15.2397	−	6.91021i	0.910747	−	0.412964i
$281$			7.74368i			0.461949i	0.972960	+	0.230975i	$0.0741914\pi$
$281$			7.74368i			0.461949i	−0.972960	+	0.230975i	$0.925809\pi$
$282$	6.22541	+	3.00397i	0.370718	+	0.178884i
$283$	−1.67333			−0.0994694			−0.0497347	−	0.998762i	$-0.515838\pi$
$283$	−1.67333			−0.0994694			−0.0497347	+	0.998762i	$0.515838\pi$
$284$	−0.650345	−	0.818115i	−0.0385909	−	0.0485462i
$285$	1.07367	+	2.04779i	0.0635986	+	0.121300i
$286$	−33.6128	−	16.2193i	−1.98757	−	0.959068i
$287$	−6.41715	+	22.3785i	−0.378793	+	1.32096i
$288$	1.27301	+	11.7075i	0.0750125	+	0.689870i
$289$			16.9632i			0.997833i
$290$	5.77603	+	5.40333i	0.339180	+	0.317294i
$291$	2.54560	+	2.54560i	0.149226	+	0.149226i
$292$	−2.27930	+	19.9502i	−0.133386	+	1.16750i
$293$	30.8617			1.80296			0.901479	−	0.432823i	$-0.142482\pi$
$293$	30.8617			1.80296			0.901479	+	0.432823i	$0.142482\pi$
$294$	2.09513	−	9.25166i	0.122190	−	0.539568i
$295$	−15.3694	−	29.3137i	−0.894840	−	1.70671i
$296$	5.02797	−	7.96065i	0.292245	−	0.462703i
$297$	−17.7448	−	17.7448i	−1.02966	−	1.02966i
$298$	1.79597	+	0.866618i	0.104038	+	0.0502018i
$299$	−8.40982	+	8.40982i	−0.486352	+	0.486352i
$300$	0.638201	+	9.56095i	0.0368465	+	0.552002i
$301$	16.7553	+	4.80468i	0.965761	+	0.276937i
$302$	−4.04764	−	11.5964i	−0.232916	−	0.667300i
$303$	12.4562	−	12.4562i	0.715592	−	0.715592i
$304$	−3.66201	+	2.28512i	−0.210031	+	0.131061i
$305$	−5.93843	−	11.3263i	−0.340033	−	0.648540i
$306$	0.245597	−	0.508975i	0.0140399	−	0.0290962i
$307$	15.9242			0.908845			0.454422	−	0.890786i	$-0.349846\pi$
$307$	15.9242			0.908845			0.454422	+	0.890786i	$0.349846\pi$
$308$	−25.1905	−	10.4437i	−1.43536	−	0.595084i
$309$	3.32140	+	3.32140i	0.188948	+	0.188948i
$310$	−19.8401	+	0.661436i	−1.12684	+	0.0375671i
$311$	−5.40593			−0.306542			−0.153271	−	0.988184i	$-0.548981\pi$
$311$	−5.40593			−0.306542			−0.153271	+	0.988184i	$0.548981\pi$
$312$	−7.41142	+	11.7343i	−0.419589	+	0.664324i
$313$	−20.5975	+	20.5975i	−1.16424	+	1.16424i	−0.180699	+	0.983538i	$0.557836\pi$
$313$	−20.5975	+	20.5975i	−1.16424	+	1.16424i	−0.983538	+	0.180699i	$0.942164\pi$
$314$	−28.0058	+	9.77521i	−1.58046	+	0.551647i
$315$	−10.2901	−	6.76763i	−0.579783	−	0.381313i
$316$	14.9018	+	18.7461i	0.838293	+	1.05455i
$317$		−	32.3130i		−	1.81488i	−0.420184	−	0.907439i	$-0.638035\pi$
$317$		−	32.3130i		−	1.81488i	0.420184	−	0.907439i	$-0.361965\pi$
$318$	−1.41994	+	0.495620i	−0.0796266	+	0.0277930i
$319$		−	12.8897i		−	0.721685i
$320$	−17.7094	+	2.52518i	−0.989987	+	0.141162i
$321$			13.0752i			0.729784i
$322$	−5.78762	+	6.48233i	−0.322531	+	0.361246i
$323$	0.207140			0.0115256
$324$	2.47264	−	1.96558i	0.137369	−	0.109199i
$325$	14.5625	−	21.0597i	0.807785	−	1.16818i
$326$	−22.0485	+	7.69585i	−1.22115	+	0.426234i
$327$	11.8109	+	11.8109i	0.653147	+	0.653147i
$328$	13.2903	−	21.0421i	0.733832	−	1.16186i
$329$	−6.54263	−	11.8035i	−0.360707	−	0.650747i
$330$	10.6681	−	11.4039i	0.587257	−	0.627764i
$331$	−11.5717	+	11.5717i	−0.636040	+	0.636040i	−0.949576	−	0.313536i	$-0.898486\pi$
$331$	−11.5717	+	11.5717i	−0.636040	+	0.636040i	0.313536	+	0.949576i	$0.398486\pi$
$332$	−20.4110	−	25.6765i	−1.12020	−	1.40918i
$333$	−6.93012			−0.379768
$334$	9.49889	+	4.58353i	0.519756	+	0.250800i
$335$	−5.86823	−	1.83131i	−0.320615	−	0.100055i
$336$	−4.92197	+	8.86632i	−0.268516	+	0.483697i
$337$	−7.63386	−	7.63386i	−0.415843	−	0.415843i	0.467925	−	0.883768i	$-0.345002\pi$
$337$	−7.63386	−	7.63386i	−0.415843	−	0.415843i	−0.883768	+	0.467925i	$0.845002\pi$
$338$	17.6558	−	6.16262i	0.960349	−	0.335202i
$339$	6.80207	+	6.80207i	0.369438	+	0.369438i
$340$	0.785136	+	0.347096i	0.0425800	+	0.0188239i
$341$	22.8755	+	22.8755i	1.23878	+	1.23878i
$342$	2.86137	+	1.38071i	0.154725	+	0.0746600i
$343$	−13.7636	+	12.3921i	−0.743164	+	0.669110i
$344$	−15.7548	−	9.95075i	−0.849440	−	0.536508i
$345$	−2.31078	−	4.40730i	−0.124408	−	0.237281i
$346$	−5.59987	−	16.0436i	−0.301051	−	0.862507i
$347$	2.37523			0.127509			0.0637545	−	0.997966i	$-0.479693\pi$
$347$	2.37523			0.127509			0.0637545	+	0.997966i	$0.479693\pi$
$348$	−4.76237	−	0.544098i	−0.255290	−	0.0291667i
$349$	2.85639	+	2.85639i	0.152899	+	0.152899i	0.779411	−	0.626513i	$-0.215518\pi$
$349$	2.85639	+	2.85639i	0.152899	+	0.152899i	−0.626513	+	0.779411i	$0.715518\pi$
$350$	9.75355	−	15.9646i	0.521349	−	0.853343i
$351$	24.9360			1.33099
$352$	22.7214	+	18.2648i	1.21106	+	0.973518i
$353$	8.80022	+	8.80022i	0.468389	+	0.468389i	0.901392	−	0.433004i	$-0.142546\pi$
$353$	8.80022	+	8.80022i	0.468389	+	0.468389i	−0.433004	+	0.901392i	$0.642546\pi$
$354$	18.0656	+	8.71725i	0.960175	+	0.463317i
$355$	−1.11542	−	0.348091i	−0.0592003	−	0.0184748i
$356$	9.99992	+	12.5796i	0.529995	+	0.666718i
$357$	0.425629	−	0.235925i	0.0225267	−	0.0124865i
$358$	−11.2113	+	23.2343i	−0.592538	+	1.22797i
$359$	8.43216			0.445032			0.222516	−	0.974929i	$-0.428573\pi$
$359$	8.43216			0.445032			0.222516	+	0.974929i	$0.428573\pi$
$360$	8.53203	+	10.0280i	0.449677	+	0.528524i
$361$		−	17.8355i		−	0.938710i
$362$	0.124331	+	0.0599939i	0.00653469	+	0.00315321i
$363$	−14.9083			−0.782485
$364$	25.0377	−	10.3616i	1.31233	−	0.543095i
$365$	10.4248	+	19.8830i	0.545657	+	1.04072i
$366$	6.98019	+	3.36818i	0.364861	+	0.176058i
$367$	5.12716	−	5.12716i	0.267635	−	0.267635i	−0.560511	−	0.828147i	$-0.689395\pi$
$367$	5.12716	−	5.12716i	0.267635	−	0.267635i	0.828147	+	0.560511i	$0.189395\pi$
$368$	7.88147	−	4.91810i	0.410850	−	0.256374i
$369$	−18.3182			−0.953605
$370$	−0.350754	−	10.5210i	−0.0182348	−	0.546963i
$371$	2.82256	+	0.809384i	0.146540	+	0.0420211i
$372$	9.41747	−	7.48623i	0.488273	−	0.388143i
$373$			0.691599i			0.0358096i	0.999840	+	0.0179048i	$0.00569958\pi$
$373$			0.691599i			0.0358096i	−0.999840	+	0.0179048i	$0.994300\pi$
$374$	−0.461023	−	1.32083i	−0.0238390	−	0.0682983i
$375$	6.59647	+	8.44160i	0.340640	+	0.435922i
$376$	3.17753	+	14.0730i	0.163868	+	0.725760i
$377$	9.05671	+	9.05671i	0.466444	+	0.466444i
$378$	18.1909	−	1.02996i	0.935638	−	0.0529752i
$379$	−15.5592	−	15.5592i	−0.799222	−	0.799222i	0.183751	−	0.982973i	$-0.441176\pi$
$379$	−15.5592	−	15.5592i	−0.799222	−	0.799222i	−0.982973	+	0.183751i	$0.941176\pi$
$380$	−1.95131	+	4.41390i	−0.100100	+	0.226428i
$381$	−5.70612	+	5.70612i	−0.292334	+	0.292334i
$382$	11.4692	−	4.00324i	0.586816	−	0.204823i
$383$	−7.48417	−	7.48417i	−0.382423	−	0.382423i	0.489551	−	0.871974i	$-0.337161\pi$
$383$	−7.48417	−	7.48417i	−0.382423	−	0.382423i	−0.871974	+	0.489551i	$0.837161\pi$
$384$	7.70743	−	7.62391i	0.393318	−	0.389056i
$385$	−29.8584	+	6.16586i	−1.52172	+	0.314241i
$386$	−11.8625	+	24.5838i	−0.603786	+	1.25128i
$387$			13.7153i			0.697186i
$388$	−0.852915	+	7.46538i	−0.0433002	+	0.378997i
$389$	11.9071	+	11.9071i	0.603715	+	0.603715i	0.941296	−	0.337581i	$-0.109609\pi$
$389$	11.9071	+	11.9071i	0.603715	+	0.603715i	−0.337581	+	0.941296i	$0.609609\pi$
$390$	0.517025	+	15.5084i	0.0261806	+	0.785300i
$391$	−0.445813			−0.0225457
$392$	17.8371	−	8.59296i	0.900908	−	0.434010i
$393$	1.07988	+	1.07988i	0.0544728	+	0.0544728i
$394$	7.46533	−	2.60571i	0.376098	−	0.131274i
$395$	25.5584	+	7.97607i	1.28598	+	0.401319i
$396$	2.43562	−	21.3184i	0.122394	−	1.07129i
$397$	−6.97405			−0.350018			−0.175009	−	0.984567i	$-0.555995\pi$
$397$	−6.97405			−0.350018			−0.175009	+	0.984567i	$0.555995\pi$
$398$	−4.51788	−	12.9437i	−0.226461	−	0.648807i
$399$	1.32633	+	2.39281i	0.0663993	+	0.119790i
$400$	−14.7924	+	13.4605i	−0.739618	+	0.673027i
$401$	16.0305			0.800524			0.400262	−	0.916401i	$-0.368919\pi$
$401$	16.0305			0.800524			0.400262	+	0.916401i	$0.368919\pi$
$402$	3.51739	−	1.22772i	0.175431	−	0.0612329i
$403$	−32.1461			−1.60131
$404$	36.5299	+	4.17352i	1.81743	+	0.207641i
$405$	1.05206	−	3.37120i	0.0522771	−	0.167516i
$406$	6.98096	+	6.23281i	0.346459	+	0.309329i
$407$	−12.1307	+	12.1307i	−0.601296	+	0.601296i
$408$	−0.507467	+	0.114580i	−0.0251234	+	0.00567257i
$409$		−	10.9742i		−	0.542641i	−0.962489	−	0.271320i	$-0.912540\pi$
$409$		−	10.9742i		−	0.542641i	0.962489	−	0.271320i	$-0.0874603\pi$
$410$	−0.927135	−	27.8099i	−0.0457879	−	1.37343i
$411$	−0.659323	−	0.659323i	−0.0325220	−	0.0325220i
$412$	−1.11285	+	9.74054i	−0.0548262	+	0.479882i
$413$	−18.9861	−	34.2527i	−0.934247	−	1.68546i
$414$	−6.15831	−	2.97159i	−0.302664	−	0.146046i
$415$	−35.0073	−	10.9248i	−1.71844	−	0.536278i
$416$	−28.7982	+	3.13135i	−1.41195	+	0.153527i
$417$	3.53968	+	3.53968i	0.173339	+	0.173339i
$418$	7.42545	−	2.59179i	0.363190	−	0.126769i
$419$	−1.06132	−	1.06132i	−0.0518491	−	0.0518491i	0.680707	−	0.732556i	$-0.261673\pi$
$419$	−1.06132	−	1.06132i	−0.0518491	−	0.0518491i	−0.732556	+	0.680707i	$0.761673\pi$
$420$	1.01773	+	11.2921i	0.0496601	+	0.550997i
$421$	−11.4312	+	11.4312i	−0.557123	+	0.557123i	−0.928487	−	0.371364i	$-0.878890\pi$
$421$	−11.4312	+	11.4312i	−0.557123	+	0.557123i	0.371364	+	0.928487i	$0.378890\pi$
$422$	−33.0052	−	15.9261i	−1.60667	−	0.775272i
$423$	7.50871	−	7.50871i	0.365086	−	0.365086i
$424$	−2.65400	−	1.67628i	−0.128890	−	0.0814072i
$425$	0.944186	−	0.172211i	0.0457997	−	0.00835346i
$426$	0.668577	−	0.233361i	0.0323926	−	0.0113064i
$427$	−7.33588	−	13.2346i	−0.355008	−	0.640465i
$428$	−21.3630	+	16.9821i	−1.03262	+	0.820859i
$429$	17.8811	−	17.8811i	0.863309	−	0.863309i
$430$	−20.8220	+	0.694169i	−1.00413	+	0.0334758i
$431$	−22.2366			−1.07110			−0.535549	−	0.844504i	$-0.679895\pi$
$431$	−22.2366			−1.07110			−0.535549	+	0.844504i	$0.679895\pi$
$432$	−18.9761	−	4.39336i	−0.912987	−	0.211375i
$433$	22.1069	+	22.1069i	1.06239	+	1.06239i	0.997920	+	0.0644701i	$0.0205357\pi$
$433$	22.1069	+	22.1069i	1.06239	+	1.06239i	0.0644701	+	0.997920i	$0.479464\pi$
$434$	−23.4507	+	1.32776i	−1.12567	+	0.0637346i
$435$	−4.74632	+	2.48852i	−0.227569	+	0.119316i
$436$	−3.95732	+	34.6375i	−0.189521	+	1.65884i
$437$		−	2.50628i		−	0.119892i
$438$	−12.2536	−	5.91275i	−0.585497	−	0.282522i
$439$			3.16955i			0.151274i	0.997135	+	0.0756371i	$0.0240991\pi$
$439$			3.16955i			0.151274i	−0.997135	+	0.0756371i	$0.975901\pi$
$440$	32.4881	+	2.61867i	1.54881	+	0.124840i
$441$	−12.3582	−	7.72257i	−0.588484	−	0.367741i
$442$	1.25198	+	0.604124i	0.0595507	+	0.0287352i
$443$		−	23.1079i		−	1.09789i	−0.835859	−	0.548945i	$-0.815030\pi$
$443$		−	23.1079i		−	1.09789i	0.835859	−	0.548945i	$-0.184970\pi$
$444$	3.96988	+	4.99400i	0.188402	+	0.237005i
$445$	17.1511	+	5.35237i	0.813038	+	0.253727i
$446$	−9.18209	−	4.43067i	−0.434785	−	0.209798i
$447$	−0.955410	+	0.955410i	−0.0451893	+	0.0451893i
$448$	−20.8790	+	3.47381i	−0.986440	+	0.164122i
$449$			36.3575i			1.71582i	0.513802	+	0.857909i	$0.328236\pi$
$449$			36.3575i			1.71582i	−0.513802	+	0.857909i	$0.671764\pi$
$450$	14.1906	+	3.91466i	0.668949	+	0.184539i
$451$	−32.0646	+	32.0646i	−1.50987	+	1.50987i
$452$	−2.27907	+	19.9482i	−0.107198	+	0.938284i
$453$	8.32223			0.391013
$454$	−15.8474	+	5.53139i	−0.743753	+	0.259601i
$455$	16.6471	−	25.3118i	0.780428	−	1.18663i
$456$	−0.644150	−	2.85289i	−0.0301651	−	0.133599i
$457$	−8.46932	+	8.46932i	−0.396178	+	0.396178i	−0.876883	−	0.480704i	$-0.840381\pi$
$457$	−8.46932	+	8.46932i	−0.396178	+	0.396178i	0.480704	+	0.876883i	$0.340381\pi$
$458$	3.89677	−	8.07564i	0.182084	−	0.377350i
$459$	0.660942	+	0.660942i	0.0308501	+	0.0308501i
$460$	4.19966	−	9.49971i	0.195810	−	0.442926i
$461$	−23.0573	+	23.0573i	−1.07388	+	1.07388i	−0.0768407	+	0.997043i	$0.524483\pi$
$461$	−23.0573	+	23.0573i	−1.07388	+	1.07388i	−0.997043	+	0.0768407i	$0.975517\pi$
$462$	12.3057	−	13.7829i	0.572515	−	0.641237i
$463$	−7.97699	+	7.97699i	−0.370722	+	0.370722i	−0.867740	−	0.497018i	$-0.834428\pi$
$463$	−7.97699	+	7.97699i	−0.370722	+	0.370722i	0.497018	+	0.867740i	$0.334428\pi$
$464$	−5.29641	−	8.48772i	−0.245880	−	0.394033i
$465$	4.00694	−	12.8398i	0.185817	−	0.595430i
$466$	−20.0419	−	9.67088i	−0.928422	−	0.447995i
$467$	−18.6510			−0.863066			−0.431533	−	0.902097i	$-0.642027\pi$
$467$	−18.6510			−0.863066			−0.431533	+	0.902097i	$0.642027\pi$
$468$	13.2676	+	16.6903i	0.613297	+	0.771511i
$469$	−6.99184	−	2.00495i	−0.322853	−	0.0925800i
$470$	11.7795	+	11.0194i	0.543347	+	0.508287i
$471$		−	20.0985i		−	0.926090i
$472$	9.22090	+	40.8386i	0.424426	+	1.87975i
$473$	24.0076	+	24.0076i	1.10387	+	1.10387i
$474$	−15.3196	+	5.34718i	−0.703652	+	0.245604i
$475$	0.968140	+	5.30804i	0.0444213	+	0.243550i
$476$	0.938276	+	0.388997i	0.0430058	+	0.0178297i
$477$			2.31044i			0.105788i
$478$	−6.60391	−	18.9201i	−0.302056	−	0.865386i
$479$	34.7955			1.58985			0.794923	−	0.606710i	$-0.207511\pi$
$479$	34.7955			1.58985			0.794923	+	0.606710i	$0.207511\pi$
$480$	2.33890	−	11.8929i	0.106756	−	0.542832i
$481$		−	17.0468i		−	0.777267i
$482$	11.6698	+	33.4340i	0.531547	+	1.52287i
$483$	−2.85455	−	5.14987i	−0.129887	−	0.234327i
$484$	−19.3630	−	24.3581i	−0.880138	−	1.10719i
$485$	3.90095	+	7.44022i	0.177133	+	0.337843i
$486$	7.51355	+	21.5262i	0.340821	+	0.976448i
$487$	−6.89855	+	6.89855i	−0.312603	+	0.312603i	−0.845917	−	0.533314i	$-0.820946\pi$
$487$	−6.89855	+	6.89855i	−0.312603	+	0.312603i	0.533314	+	0.845917i	$0.320946\pi$
$488$	3.56278	+	15.7793i	0.161279	+	0.714294i
$489$		−	15.8232i		−	0.715549i
$490$	11.0986	−	19.1526i	0.501384	−	0.865225i
$491$	−24.4672	+	24.4672i	−1.10419	+	1.10419i	−0.110291	+	0.993899i	$0.535178\pi$
$491$	−24.4672	+	24.4672i	−1.10419	+	1.10419i	−0.993899	+	0.110291i	$0.964822\pi$
$492$	10.4934	+	13.2005i	0.473081	+	0.595123i
$493$			0.480105i			0.0216229i
$494$	−3.39628	+	7.03842i	−0.152806	+	0.316674i
$495$	−11.1397	−	21.2466i	−0.500693	−	0.954962i
$496$	24.4629	+	5.66367i	1.09842	+	0.254306i
$497$	−1.32899	−	0.381096i	−0.0596135	−	0.0170945i
$498$	20.9832	−	7.32403i	0.940281	−	0.328197i
$499$	17.9727	−	17.9727i	0.804570	−	0.804570i	−0.179236	−	0.983806i	$-0.557363\pi$
$499$	17.9727	−	17.9727i	0.804570	−	0.804570i	0.983806	+	0.179236i	$0.0573626\pi$
$500$	−5.22486	+	21.7417i	−0.233663	+	0.972318i
$501$	−5.05315	+	5.05315i	−0.225758	+	0.225758i
$502$	7.89614	+	3.81016i	0.352422	+	0.170056i
$503$	−2.45163	+	2.45163i	−0.109313	+	0.109313i	−0.759648	−	0.650335i	$-0.774629\pi$
$503$	−2.45163	+	2.45163i	−0.109313	+	0.109313i	0.650335	+	0.759648i	$0.274629\pi$
$504$	10.3681	+	11.6276i	0.461834	+	0.517935i
$505$	36.4068	−	19.0883i	1.62008	−	0.849419i
$506$	−15.9812	+	5.57812i	−0.710453	+	0.247978i
$507$			12.6708i			0.562728i
$508$	−16.7341	−	1.91187i	−0.742458	−	0.0848253i
$509$	−7.36872	−	7.36872i	−0.326613	−	0.326613i	0.524684	−	0.851297i	$-0.324183\pi$
$509$	−7.36872	−	7.36872i	−0.326613	−	0.326613i	−0.851297	+	0.524684i	$0.824183\pi$
$510$	−0.397355	+	0.424763i	−0.0175952	+	0.0188088i
$511$	12.8779	+	23.2329i	0.569687	+	1.02776i
$512$	22.4668	+	2.69088i	0.992904	+	0.118921i
$513$	−3.71570	+	3.71570i	−0.164052	+	0.164052i
$514$	−10.5019	+	21.7641i	−0.463220	+	0.959975i
$515$	5.08981	+	9.70771i	0.224284	+	0.427773i
$516$	9.88351	−	7.85671i	0.435097	−	0.345872i
$517$		−	26.2869i		−	1.15610i
$518$	−0.704100	−	12.4357i	−0.0309364	−	0.546392i
$519$	11.5137			0.505396
$520$	−24.6671	+	20.9872i	−1.08172	+	0.920349i
$521$	37.0562			1.62346			0.811730	−	0.584033i	$-0.198526\pi$
$521$	37.0562			1.62346			0.811730	+	0.584033i	$0.198526\pi$
$522$	−3.20017	+	6.63202i	−0.140068	+	0.290275i
$523$	−9.08448			−0.397237			−0.198618	−	0.980077i	$-0.563645\pi$
$523$	−9.08448			−0.397237			−0.198618	+	0.980077i	$0.563645\pi$
$524$	−0.361820	+	3.16693i	−0.0158062	+	0.138348i
$525$	8.03497	+	9.80422i	0.350675	+	0.427891i
$526$	11.7188	+	5.65473i	0.510965	+	0.246558i
$527$	−0.852049	−	0.852049i	−0.0371159	−	0.0371159i
$528$	−16.7577	+	10.4570i	−0.729287	+	0.455081i
$529$		−	17.6059i		−	0.765475i
$530$	−3.50762	+	0.116938i	−0.152361	+	0.00507946i
$531$	21.7896	−	21.7896i	0.945589	−	0.945589i
$532$	−2.18687	+	5.27482i	−0.0948130	+	0.228692i
$533$		−	45.0592i		−	1.95173i
$534$	−10.2803	+	3.58824i	−0.444870	+	0.155278i
$535$	−9.08950	+	29.1263i	−0.392973	+	1.25924i
$536$	6.57431	+	4.15235i	0.283967	+	0.179354i
$537$	−12.3600	−	12.3600i	−0.533375	−	0.533375i
$538$	8.38865	+	4.04780i	0.361660	+	0.174513i
$539$	−35.1499	+	8.11430i	−1.51401	+	0.349508i
$540$	−20.3101	+	7.85761i	−0.874007	+	0.338138i
$541$	7.86672	+	7.86672i	0.338217	+	0.338217i	0.855696	−	0.517479i	$-0.173130\pi$
$541$	7.86672	+	7.86672i	0.338217	+	0.338217i	−0.517479	+	0.855696i	$0.673130\pi$
$542$	8.18894	+	23.4612i	0.351745	+	1.00775i
$543$	−0.0661407	+	0.0661407i	−0.00283837	+	0.00283837i
$544$	−0.846309	−	0.680313i	−0.0362852	−	0.0291682i
$545$	18.0995	+	34.5208i	0.775296	+	1.47871i
$546$	1.03787	+	18.3307i	0.0444168	+	0.784480i
$547$		−	29.4501i		−	1.25919i	−0.776922	−	0.629597i	$-0.783220\pi$
$547$		−	29.4501i		−	1.25919i	0.776922	−	0.629597i	$-0.216780\pi$
$548$	0.220910	−	1.93357i	0.00943679	−	0.0825982i
$549$	8.41908	−	8.41908i	0.359318	−	0.359318i
$550$	31.6919	−	17.9872i	1.35135	−	0.766978i
$551$	−2.69907			−0.114984
$552$	1.38636	+	6.14007i	0.0590073	+	0.261339i
$553$	30.4522	+	8.73233i	1.29496	+	0.371337i
$554$	−31.7098	+	11.0680i	−1.34722	+	0.470236i
$555$	6.80881	+	2.12484i	0.289018	+	0.0901945i
$556$	−1.18599	+	10.3807i	−0.0502971	+	0.440239i
$557$		−	10.4320i		−	0.442017i	−0.975272	−	0.221008i	$-0.929065\pi$
$557$		−	10.4320i		−	0.442017i	0.975272	−	0.221008i	$-0.0709348\pi$
$558$	−6.09054	−	17.4493i	−0.257833	−	0.738688i
$559$	−33.7370			−1.42692
$560$	−17.1278	+	16.3290i	−0.723783	+	0.690027i
$561$	0.947896			0.0400202
$562$	−3.60891	−	10.3395i	−0.152233	−	0.436145i
$563$			26.6324i			1.12242i	0.827673	+	0.561210i	$0.189664\pi$
$563$			26.6324i			1.12242i	−0.827673	+	0.561210i	$0.810336\pi$
$564$	−9.71226	−	1.10962i	−0.408960	−	0.0467234i
$565$	10.4237	+	19.8809i	0.438529	+	0.836398i
$566$	2.23426	−	0.779851i	0.0939130	−	0.0327796i
$567$	1.15181	−	4.01669i	0.0483714	−	0.168685i
$568$	1.24963	+	0.789270i	0.0524333	+	0.0331170i
$569$	−31.2336			−1.30938			−0.654690	−	0.755897i	$-0.727201\pi$
$569$	−31.2336			−1.30938			−0.654690	+	0.755897i	$0.727201\pi$
$570$	−2.38794	−	2.23386i	−0.100020	−	0.0935660i
$571$	25.0247	−	25.0247i	1.04725	−	1.04725i	0.0484258	−	0.998827i	$-0.484580\pi$
$571$	25.0247	−	25.0247i	1.04725	−	1.04725i	0.998827	−	0.0484258i	$-0.0154204\pi$
$572$	52.4393	+	5.99116i	2.19260	+	0.250503i
$573$			8.23093i			0.343852i
$574$	−1.86112	−	32.8708i	−0.0776818	−	1.37200i
$575$	−2.08366	−	11.4241i	−0.0868945	−	0.476419i
$576$	−7.15596	−	15.0387i	−0.298165	−	0.626614i
$577$	7.84300	−	7.84300i	0.326508	−	0.326508i	−0.524749	−	0.851257i	$-0.675841\pi$
$577$	7.84300	−	7.84300i	0.326508	−	0.326508i	0.851257	+	0.524749i	$0.175841\pi$
$578$	−7.90561	−	22.6495i	−0.328830	−	0.942094i
$579$	−13.0779	−	13.0779i	−0.543500	−	0.543500i
$580$	−10.2304	−	4.52271i	−0.424796	−	0.187795i
$581$	−41.7103	−	11.9607i	−1.73044	−	0.496212i
$582$	−4.58529	−	2.21256i	−0.190066	−	0.0917134i
$583$	4.04426	+	4.04426i	0.167496	+	0.167496i
$584$	−6.25437	−	27.7001i	−0.258808	−	1.14624i
$585$	22.7556	+	7.10139i	0.940828	+	0.293606i
$586$	−41.2070	+	14.3830i	−1.70224	+	0.594155i
$587$			7.10175i			0.293121i	0.989202	+	0.146560i	$0.0468203\pi$
$587$			7.10175i			0.293121i	−0.989202	+	0.146560i	$0.953180\pi$
$588$	1.51426	+	13.3294i	0.0624469	+	0.549695i
$589$	4.79007	−	4.79007i	0.197371	−	0.197371i
$590$	34.1830	+	31.9773i	1.40729	+	1.31649i
$591$			5.35752i			0.220379i
$592$	−3.00339	+	12.9724i	−0.123439	+	0.533164i
$593$	4.12969	+	4.12969i	0.169586	+	0.169586i	0.786797	−	0.617211i	$-0.211738\pi$
$593$	4.12969	+	4.12969i	0.169586	+	0.169586i	−0.617211	+	0.786797i	$0.711738\pi$
$594$	31.9630	+	15.4232i	1.31146	+	0.632822i
$595$	1.11214	−	0.229661i	0.0455933	−	0.00941518i
$596$	−2.80190	−	0.320115i	−0.114770	−	0.0131124i
$597$	9.28906			0.380176
$598$	7.30955	−	15.1483i	0.298910	−	0.619459i
$599$	−26.3704			−1.07746			−0.538732	−	0.842477i	$-0.681096\pi$
$599$	−26.3704			−1.07746			−0.538732	+	0.842477i	$0.681096\pi$
$600$	−5.30798	−	12.4685i	−0.216697	−	0.509025i
$601$	27.5868			1.12529			0.562644	−	0.826699i	$-0.309784\pi$
$601$	27.5868			1.12529			0.562644	+	0.826699i	$0.309784\pi$
$602$	−24.6112	+	1.39347i	−1.00308	+	0.0567936i
$603$		−	5.72325i		−	0.233069i
$604$	10.8090	+	13.5974i	0.439810	+	0.553269i
$605$	−33.2099	−	10.3639i	−1.35017	−	0.421352i
$606$	−10.8266	+	22.4369i	−0.439800	+	0.911438i
$607$	−14.3333	+	14.3333i	−0.581771	+	0.581771i	−0.935390	−	0.353619i	$-0.884951\pi$
$607$	−14.3333	+	14.3333i	−0.581771	+	0.581771i	0.353619	+	0.935390i	$0.384951\pi$
$608$	3.82460	−	4.75780i	0.155108	−	0.192954i
$609$	−5.54600	+	3.07413i	−0.224735	+	0.124570i
$610$	13.2076	+	12.3554i	0.534762	+	0.500256i
$611$	18.4700	+	18.4700i	0.747217	+	0.747217i
$612$	−0.0907198	+	0.794051i	−0.00366713	+	0.0320976i
$613$			17.1490i			0.692640i	0.938116	+	0.346320i	$0.112569\pi$
$613$			17.1490i			0.692640i	−0.938116	+	0.346320i	$0.887431\pi$
$614$	−21.2623	+	7.42144i	−0.858077	+	0.299505i
$615$	17.9975	+	5.61652i	0.725729	+	0.226480i
$616$	38.5020	+	2.20461i	1.55129	+	0.0888263i
$617$	9.39842	−	9.39842i	0.378366	−	0.378366i	−0.492146	−	0.870513i	$-0.663787\pi$
$617$	9.39842	−	9.39842i	0.378366	−	0.378366i	0.870513	+	0.492146i	$0.163787\pi$
$618$	−5.98271	−	2.88686i	−0.240660	−	0.116126i
$619$	10.2187	−	10.2187i	0.410726	−	0.410726i	−0.471265	−	0.881991i	$-0.656203\pi$
$619$	10.2187	−	10.2187i	0.410726	−	0.410726i	0.881991	+	0.471265i	$0.156203\pi$
$620$	26.1826	−	10.1296i	1.05152	−	0.406814i
$621$	7.99703	−	7.99703i	0.320910	−	0.320910i
$622$	7.21808	−	2.51941i	0.289419	−	0.101019i
$623$	20.4350	+	5.85986i	0.818713	+	0.234770i
$624$	4.42712	−	19.1219i	0.177226	−	0.765489i
$625$	8.82594	+	23.3902i	0.353038	+	0.935609i
$626$	17.9027	−	37.1014i	0.715535	−	1.48287i
$627$			5.32890i			0.212816i
$628$	32.8381	−	26.1040i	1.31038	−	1.04166i
$629$	0.451834	−	0.451834i	0.0180158	−	0.0180158i
$630$	16.8936	+	4.24058i	0.673056	+	0.168949i
$631$			16.0215i			0.637807i	0.947787	+	0.318903i	$0.103315\pi$
$631$			16.0215i			0.637807i	−0.947787	+	0.318903i	$0.896685\pi$
$632$	−28.6337	−	18.0851i	−1.13899	−	0.719387i
$633$	17.5579	−	17.5579i	0.697863	−	0.697863i
$634$	15.0593	+	43.1448i	0.598083	+	1.71350i
$635$	−16.6777	+	8.74424i	−0.661836	+	0.347005i
$636$	1.66495	−	1.32352i	0.0660196	−	0.0524810i
$637$	18.9961	−	30.3988i	0.752651	−	1.20444i
$638$	6.00720	+	17.2105i	0.237827	+	0.681372i
$639$		−	1.08786i		−	0.0430352i
$640$	22.4690	−	11.6251i	0.888167	−	0.459521i
$641$	−47.0254			−1.85739			−0.928695	−	0.370845i	$-0.879068\pi$
$641$	−47.0254			−1.85739			−0.928695	+	0.370845i	$0.879068\pi$
$642$	−6.09363	−	17.4581i	−0.240496	−	0.689018i
$643$		−	39.8145i		−	1.57013i	−0.619413	−	0.785066i	$-0.712629\pi$
$643$		−	39.8145i		−	1.57013i	0.619413	−	0.785066i	$-0.287371\pi$
$644$	4.70665	−	11.3526i	0.185468	−	0.447355i
$645$	4.20523	−	13.4752i	0.165581	−	0.530585i
$646$	−0.276577	+	0.0965369i	−0.0108818	+	0.00379819i
$647$	−12.0251	−	12.0251i	−0.472757	−	0.472757i	0.430049	−	0.902806i	$-0.358496\pi$
$647$	−12.0251	−	12.0251i	−0.472757	−	0.472757i	−0.902806	+	0.430049i	$0.858496\pi$
$648$	−2.38546	+	3.77683i	−0.0937096	+	0.148368i
$649$		−	76.2823i		−	2.99434i
$650$	−9.62933	+	34.9061i	−0.377693	+	1.36913i
$651$	4.38686	−	15.2983i	0.171935	−	0.599586i
$652$	25.8529	−	20.5512i	1.01248	−	0.804848i
$653$	−23.2407			−0.909477			−0.454738	−	0.890625i	$-0.650267\pi$
$653$	−23.2407			−0.909477			−0.454738	+	0.890625i	$0.650267\pi$
$654$	−21.2746	−	10.2657i	−0.831903	−	0.401421i
$655$	1.65484	+	3.15625i	0.0646601	+	0.123325i
$656$	−7.93876	+	34.2896i	−0.309956	+	1.33879i
$657$	−14.7795	+	14.7795i	−0.576603	+	0.576603i
$658$	14.2368	+	12.7110i	0.555008	+	0.495527i
$659$	2.20822	−	2.20822i	0.0860202	−	0.0860202i	−0.662787	−	0.748808i	$-0.730627\pi$
$659$	2.20822	−	2.20822i	0.0860202	−	0.0860202i	0.748808	+	0.662787i	$0.230627\pi$
$660$	−8.92941	+	20.1985i	−0.347577	+	0.786224i
$661$	−24.8842	−	24.8842i	−0.967882	−	0.967882i	0.0316181	−	0.999500i	$-0.489934\pi$
$661$	−24.8842	−	24.8842i	−0.967882	−	0.967882i	−0.999500	+	0.0316181i	$0.989934\pi$
$662$	10.0578	−	20.8437i	0.390907	−	0.810114i
$663$	−0.666021	+	0.666021i	−0.0258661	+	0.0258661i
$664$	39.2195	+	24.7712i	1.52201	+	0.961308i
$665$	1.29111	+	6.25226i	0.0500672	+	0.242452i
$666$	9.25321	−	3.22976i	0.358555	−	0.125151i
$667$	5.80900			0.224925
$668$	−14.8192	−	1.69308i	−0.573372	−	0.0655074i
$669$	4.88463	−	4.88463i	0.188851	−	0.188851i
$670$	8.68882	−	0.289670i	0.335678	−	0.0111909i
$671$		−	29.4740i		−	1.13783i
$672$	2.43978	−	14.1323i	0.0941165	−	0.545166i
$673$	7.59933	−	7.59933i	0.292933	−	0.292933i	−0.545305	−	0.838238i	$-0.683586\pi$
$673$	7.59933	−	7.59933i	0.292933	−	0.292933i	0.838238	+	0.545305i	$0.183586\pi$
$674$	13.7506	+	6.63511i	0.529652	+	0.255575i
$675$	−13.8478	+	20.0260i	−0.533000	+	0.770802i
$676$	−20.7022	+	16.4568i	−0.796240	+	0.632955i
$677$			19.7429i			0.758780i	0.925237	+	0.379390i	$0.123866\pi$
$677$			19.7429i			0.758780i	−0.925237	+	0.379390i	$0.876134\pi$
$678$	−12.2523	−	5.91215i	−0.470547	−	0.227055i
$679$	4.81893	+	8.69378i	0.184934	+	0.333637i
$680$	−1.21009	−	0.0975381i	−0.0464048	−	0.00374042i
$681$		−	11.3729i		−	0.435811i
$682$	−41.2049	−	19.8827i	−1.57782	−	0.761349i
$683$			35.4694i			1.35720i	0.734509	+	0.678599i	$0.237413\pi$
$683$			35.4694i			1.35720i	−0.734509	+	0.678599i	$0.762587\pi$
$684$	−4.46401	−	0.510011i	−0.170686	−	0.0195007i
$685$	−1.01037	−	1.92706i	−0.0386042	−	0.0736290i
$686$	12.6021	−	22.9606i	0.481149	−	0.876639i
$687$	4.29602	+	4.29602i	0.163904	+	0.163904i
$688$	25.6735	+	5.94395i	0.978793	+	0.226611i
$689$	−5.68324			−0.216514
$690$	5.13939	+	4.80777i	0.195653	+	0.183029i
$691$	−30.5813	+	30.5813i	−1.16337	+	1.16337i	−0.179636	+	0.983733i	$0.557492\pi$
$691$	−30.5813	+	30.5813i	−1.16337	+	1.16337i	−0.983733	+	0.179636i	$0.942508\pi$
$692$	14.9541	+	18.8118i	0.568469	+	0.715117i
$693$	−13.7611	−	24.8263i	−0.522742	−	0.943073i
$694$	−3.17145	+	1.10697i	−0.120386	+	0.0420199i
$695$	5.42431	+	10.3457i	0.205756	+	0.392435i
$696$	6.61237	−	1.49300i	0.250641	−	0.0565919i
$697$	1.19432	−	1.19432i	0.0452380	−	0.0452380i
$698$	−5.14510	−	2.48268i	−0.194745	−	0.0939710i
$699$	10.6617	−	10.6617i	0.403264	−	0.403264i
$700$	−5.58285	+	25.8618i	−0.211012	+	0.977483i
$701$	−22.2507	−	22.2507i	−0.840397	−	0.840397i	0.148513	−	0.988910i	$-0.452551\pi$
$701$	−22.2507	−	22.2507i	−0.840397	−	0.840397i	−0.988910	+	0.148513i	$0.952551\pi$
$702$	−33.2950	+	11.6214i	−1.25664	+	0.438620i
$703$	2.54013	+	2.54013i	0.0958028	+	0.0958028i
$704$	−38.8502	−	13.7982i	−1.46422	−	0.520040i
$705$	−9.67951	+	5.07503i	−0.364552	+	0.191137i
$706$	−15.8515	−	7.64888i	−0.596579	−	0.287870i
$707$	42.5408	−	23.5802i	1.59991	−	0.886826i
$708$	−28.1841	−	3.22002i	−1.05922	−	0.121016i
$709$	−17.7163	−	17.7163i	−0.665351	−	0.665351i	0.291285	−	0.956636i	$-0.405917\pi$
$709$	−17.7163	−	17.7163i	−0.665351	−	0.665351i	−0.956636	+	0.291285i	$0.905917\pi$
$710$	1.65155	−	0.0550599i	0.0619816	−	0.00206636i
$711$			24.9270i			0.934835i
$712$	−19.2147	−	12.1361i	−0.720102	−	0.454819i
$713$	−10.3093	+	10.3093i	−0.386087	+	0.386087i
$714$	−0.458354	+	0.513373i	−0.0171535	+	0.0192125i
$715$	52.2625	−	27.4016i	1.95451	−	1.02476i
$716$	4.14129	−	36.2478i	0.154767	−	1.35465i
$717$	13.5781			0.507083
$718$	−11.2587	+	3.92977i	−0.420173	+	0.146658i
$719$	−11.2953			−0.421243			−0.210621	−	0.977568i	$-0.567549\pi$
$719$	−11.2953			−0.421243			−0.210621	+	0.977568i	$0.567549\pi$
$720$	−16.0656	−	9.41328i	−0.598731	−	0.350812i
$721$	6.28756	+	11.3433i	0.234161	+	0.422447i
$722$	8.31216	+	23.8142i	0.309347	+	0.886274i
$723$	−23.9940			−0.892347
$724$	−0.193969	−	0.0221608i	−0.00720878	−	0.000823599i
$725$	−12.3029	+	2.24393i	−0.456917	+	0.0833376i
$726$	19.9059	−	6.94798i	0.738776	−	0.257864i
$727$	−7.54399	−	7.54399i	−0.279791	−	0.279791i	0.553235	−	0.833026i	$-0.313393\pi$
$727$	−7.54399	−	7.54399i	−0.279791	−	0.279791i	−0.833026	+	0.553235i	$0.813393\pi$
$728$	−28.6017	+	25.5037i	−1.06005	+	0.945230i
$729$	−10.7103			−0.396678
$730$	−23.1857	−	21.6896i	−0.858141	−	0.802769i
$731$	−0.894215	−	0.894215i	−0.0330737	−	0.0330737i
$732$	−10.8898	−	1.24415i	−0.402498	−	0.0459852i
$733$		−	47.4634i		−	1.75310i	−0.481309	−	0.876551i	$-0.659839\pi$
$733$		−	47.4634i		−	1.75310i	0.481309	−	0.876551i	$-0.340161\pi$
$734$	−4.45637	+	9.23535i	−0.164488	+	0.340883i
$735$	9.77403	+	11.3765i	0.360521	+	0.419629i
$736$	−8.23140	+	10.2399i	−0.303413	+	0.377446i
$737$	−10.0181	−	10.0181i	−0.369023	−	0.369023i
$738$	24.4587	−	8.53711i	0.900337	−	0.314255i
$739$	5.14980	−	5.14980i	0.189439	−	0.189439i	−0.606015	−	0.795453i	$-0.707233\pi$
$739$	5.14980	−	5.14980i	0.189439	−	0.189439i	0.795453	+	0.606015i	$0.207233\pi$
$740$	5.37163	+	13.8844i	0.197465	+	0.510401i
$741$	−3.74425	−	3.74425i	−0.137549	−	0.137549i
$742$	−4.14593	+	0.234740i	−0.152202	+	0.00861758i
$743$	−10.7389	−	10.7389i	−0.393973	−	0.393973i	0.482128	−	0.876101i	$-0.339864\pi$
$743$	−10.7389	−	10.7389i	−0.393973	−	0.393973i	−0.876101	+	0.482128i	$0.839864\pi$
$744$	−9.08542	+	14.3847i	−0.333088	+	0.527369i
$745$	−2.79245	+	1.46410i	−0.102308	+	0.0536405i
$746$	−0.322317	−	0.923434i	−0.0118009	−	0.0338093i
$747$		−	34.1425i		−	1.24921i
$748$	1.23113	+	1.54873i	0.0450146	+	0.0566271i
$749$	−9.95134	+	34.7032i	−0.363614	+	1.26803i
$750$	−12.7419	−	8.19709i	−0.465268	−	0.299316i
$751$	34.3640			1.25396			0.626981	−	0.779035i	$-0.284290\pi$
$751$	34.3640			1.25396			0.626981	+	0.779035i	$0.284290\pi$
$752$	−10.8014	−	17.3096i	−0.393885	−	0.631218i
$753$	−4.20054	+	4.20054i	−0.153076	+	0.153076i
$754$	−16.3135	−	7.87182i	−0.594103	−	0.286675i
$755$	18.5386	+	5.78540i	0.674690	+	0.210552i
$756$	−23.8088	+	9.85301i	−0.865916	+	0.358350i
$757$	16.0542			0.583499			0.291749	−	0.956495i	$-0.405763\pi$
$757$	16.0542			0.583499			0.291749	+	0.956495i	$0.405763\pi$
$758$	28.0262	+	13.5236i	1.01796	+	0.491198i
$759$		−	11.4690i		−	0.416298i
$760$	0.548342	−	6.80291i	0.0198905	−	0.246767i
$761$	−52.0169			−1.88561			−0.942805	−	0.333344i	$-0.891823\pi$
$761$	−52.0169			−1.88561			−0.942805	+	0.333344i	$0.891823\pi$
$762$	4.95959	−	10.2782i	0.179667	−	0.372341i
$763$	22.3587	+	40.3370i	0.809438	+	1.46030i
$764$	−13.4482	+	10.6904i	−0.486538	+	0.386764i
$765$	0.414923	+	0.791374i	0.0150016	+	0.0286122i
$766$	13.4809	+	6.50501i	0.487086	+	0.235036i
$767$	53.5983	+	53.5983i	1.93532	+	1.93532i
$768$	−6.73798	+	13.7716i	−0.243136	+	0.496939i
$769$	48.9150			1.76392			0.881961	−	0.471323i	$-0.156223\pi$
$769$	48.9150			1.76392			0.881961	+	0.471323i	$0.156223\pi$
$770$	36.9938	−	22.1481i	1.33316	−	0.798164i
$771$	−11.5779	−	11.5779i	−0.416969	−	0.416969i
$772$	4.38183	−	38.3532i	0.157705	−	1.38036i
$773$	−0.508648			−0.0182948			−0.00914739	−	0.999958i	$-0.502912\pi$
$773$	−0.508648			−0.0182948			−0.00914739	+	0.999958i	$0.502912\pi$
$774$	−6.39195	−	18.3128i	−0.229754	−	0.658241i
$775$	17.8517	−	25.8164i	0.641254	−	0.927353i
$776$	−2.34039	−	10.3654i	−0.0840150	−	0.372096i
$777$	8.11253	+	2.32631i	0.291035	+	0.0834560i
$778$	−21.4478	−	10.3493i	−0.768943	−	0.371041i
$779$	6.71424	+	6.71424i	0.240563	+	0.240563i
$780$	−7.91799	−	20.4662i	−0.283509	−	0.732806i
$781$	−1.90423	−	1.90423i	−0.0681386	−	0.0681386i
$782$	0.595256	−	0.207769i	0.0212863	−	0.00742982i
$783$	−8.61217	−	8.61217i	−0.307774	−	0.307774i
$784$	−19.8116	+	19.7864i	−0.707558	+	0.706655i
$785$	13.9719	−	44.7715i	0.498680	−	1.59796i
$786$	−1.94515	−	0.938600i	−0.0693812	−	0.0334788i
$787$	−35.5784			−1.26823			−0.634116	−	0.773238i	$-0.718636\pi$
$787$	−35.5784			−1.26823			−0.634116	+	0.773238i	$0.718636\pi$
$788$	−8.75344	+	6.95838i	−0.311828	+	0.247882i
$789$	−6.23410	+	6.23410i	−0.221940	+	0.221940i
$790$	−37.8432	+	1.26163i	−1.34640	+	0.0448867i
$791$	12.8766	+	23.2306i	0.457841	+	0.825984i
$792$	6.68330	+	29.5998i	0.237481	+	1.05178i
$793$	20.7094	+	20.7094i	0.735411	+	0.735411i
$794$	9.31186	−	3.25023i	0.330466	−	0.115346i
$795$	0.708402	−	2.26999i	0.0251244	−	0.0805084i
$796$	12.0647	+	15.1770i	0.427621	+	0.537935i
$797$	−20.7887			−0.736373			−0.368187	−	0.929752i	$-0.620021\pi$
$797$	−20.7887			−0.736373			−0.368187	+	0.929752i	$0.620021\pi$
$798$	−2.88609	−	2.57679i	−0.102166	−	0.0912172i
$799$			0.979114i			0.0346386i
$800$	13.4778	−	24.8666i	0.476511	−	0.879169i
$801$			16.7273i			0.591031i
$802$	−21.4041	+	7.47094i	−0.755806	+	0.263808i
$803$			51.7409i			1.82590i
$804$	−4.12430	+	3.27853i	−0.145453	+	0.115625i
$805$	−2.77877	−	13.4563i	−0.0979387	−	0.474271i
$806$	42.9220	−	14.9816i	1.51186	−	0.527704i
$807$	−4.46253	+	4.46253i	−0.157089	+	0.157089i
$808$	−50.7204	+	11.4521i	−1.78434	+	0.402883i
$809$	−30.4688			−1.07123			−0.535613	−	0.844463i	$-0.679920\pi$
$809$	−30.4688			−1.07123			−0.535613	+	0.844463i	$0.679920\pi$
$810$	0.166411	+	4.99158i	0.00584707	+	0.175386i
$811$	−14.9456	−	14.9456i	−0.524810	−	0.524810i	0.394210	−	0.919020i	$-0.371018\pi$
$811$	−14.9456	−	14.9456i	−0.524810	−	0.524810i	−0.919020	+	0.394210i	$0.871018\pi$
$812$	−12.2259	−	5.06869i	−0.429044	−	0.177876i
$813$	−16.8370			−0.590500
$814$	10.5436	−	21.8506i	0.369554	−	0.765862i
$815$	10.9999	−	35.2478i	0.385308	−	1.23468i
$816$	0.624178	−	0.389493i	0.0218506	−	0.0136350i
$817$	5.02712	−	5.02712i	0.175877	−	0.175877i
$818$	5.11450	+	14.6530i	0.178824	+	0.512329i
$819$	27.1127	+	7.77472i	0.947395	+	0.271671i
$820$	14.1986	+	36.7002i	0.495838	+	1.28163i
$821$	4.32224	−	4.32224i	0.150847	−	0.150847i	−0.627649	−	0.778496i	$-0.715983\pi$
$821$	4.32224	−	4.32224i	0.150847	−	0.150847i	0.778496	+	0.627649i	$0.215983\pi$
$822$	1.18761	+	0.573064i	0.0414228	+	0.0199879i
$823$	−11.6315	−	11.6315i	−0.405447	−	0.405447i	0.474700	−	0.880148i	$-0.342556\pi$
$823$	−11.6315	−	11.6315i	−0.405447	−	0.405447i	−0.880148	+	0.474700i	$0.842556\pi$
$824$	−3.05365	−	13.5244i	−0.106379	−	0.471144i
$825$	4.43031	+	24.2902i	0.154244	+	0.845676i
$826$	41.3139	+	36.8863i	1.43749	+	1.28344i
$827$	−48.0898			−1.67225			−0.836123	−	0.548542i	$-0.815183\pi$
$827$	−48.0898			−1.67225			−0.836123	+	0.548542i	$0.815183\pi$
$828$	9.60757	+	1.09766i	0.333886	+	0.0381463i
$829$	1.76645	+	1.76645i	0.0613514	+	0.0613514i	0.737117	−	0.675765i	$-0.236187\pi$
$829$	1.76645	+	1.76645i	0.0613514	+	0.0613514i	−0.675765	+	0.737117i	$0.736187\pi$
$830$	51.8338	−	1.72805i	1.79918	−	0.0599815i
$831$		−	22.7566i		−	0.789419i
$832$	36.9925	−	17.6023i	1.28248	−	0.610251i
$833$	1.30923	−	0.302235i	0.0453623	−	0.0104718i
$834$	−6.37589	−	3.07658i	−0.220779	−	0.106533i
$835$	−14.7692	+	7.74361i	−0.511111	+	0.267979i
$836$	−8.70668	+	6.92120i	−0.301127	+	0.239375i
$837$	30.5683			1.05659
$838$	1.91172	+	0.922471i	0.0660394	+	0.0318662i
$839$		−	16.3187i		−	0.563384i	−0.959505	−	0.281692i	$-0.909104\pi$
$839$		−	16.3187i		−	0.563384i	0.959505	−	0.281692i	$-0.0908957\pi$
$840$	−6.62152	−	14.6030i	−0.228464	−	0.503853i
$841$			22.7442i			0.784281i
$842$	9.93565	−	20.5906i	0.342405	−	0.709599i
$843$	7.42017			0.255564
$844$	51.4914	+	5.88286i	1.77241	+	0.202496i
$845$	−8.80838	+	28.2254i	−0.303017	+	0.970985i
$846$	−6.52634	+	13.5252i	−0.224380	+	0.465004i
$847$	−39.5688	−	11.3466i	−1.35960	−	0.389872i
$848$	4.32489	+	1.00130i	0.148517	+	0.0343848i
$849$			1.60343i			0.0550295i
$850$	−1.18043	+	0.669973i	−0.0404885	+	0.0229799i
$851$	−5.46694	−	5.46694i	−0.187404	−	0.187404i
$852$	−0.783937	+	0.623175i	−0.0268572	+	0.0213496i
$853$	−52.6306			−1.80204			−0.901019	−	0.433779i	$-0.857180\pi$
$853$	−52.6306			−1.80204			−0.901019	+	0.433779i	$0.857180\pi$
$854$	15.9629	+	14.2521i	0.546239	+	0.487698i
$855$	−4.44896	+	2.33262i	−0.152151	+	0.0797739i
$856$	20.6097	−	32.6309i	0.704426	−	1.11530i
$857$	15.1026	+	15.1026i	0.515894	+	0.515894i	0.916326	−	0.400432i	$-0.131140\pi$
$857$	15.1026	+	15.1026i	0.515894	+	0.515894i	−0.400432	+	0.916326i	$0.631140\pi$
$858$	−15.5417	+	32.2086i	−0.530586	+	1.09958i
$859$	3.06732	−	3.06732i	0.104655	−	0.104655i	−0.652840	−	0.757496i	$-0.726423\pi$
$859$	3.06732	−	3.06732i	0.104655	−	0.104655i	0.757496	+	0.652840i	$0.226423\pi$
$860$	27.4783	−	10.6309i	0.937003	−	0.362510i
$861$	21.4436	+	6.14906i	0.730795	+	0.209560i
$862$	29.6906	−	10.3633i	1.01127	−	0.352975i
$863$	24.2963	−	24.2963i	0.827057	−	0.827057i	−0.160051	−	0.987109i	$-0.551166\pi$
$863$	24.2963	−	24.2963i	0.827057	−	0.827057i	0.987109	+	0.160051i	$0.0511660\pi$
$864$	27.3847	−	2.97765i	0.931646	−	0.101302i
$865$	25.6480	+	8.00403i	0.872059	+	0.272145i
$866$	−39.8203	−	19.2146i	−1.35315	−	0.652940i
$867$	16.2545			0.552031
$868$	30.6929	−	12.7019i	1.04178	−	0.431132i
$869$	43.6329	+	43.6329i	1.48015	+	1.48015i
$870$	5.17759	−	5.53472i	0.175537	−	0.187645i
$871$	14.0781			0.477019
$872$	−10.8588	−	48.0929i	−0.367726	−	1.62863i
$873$	−5.53049	+	5.53049i	−0.187179	+	0.187179i
$874$	1.16804	+	3.34642i	0.0395096	+	0.113194i
$875$	11.0831	+	27.4256i	0.374678	+	0.927155i
$876$	19.1168	+	2.18408i	0.645895	+	0.0737931i
$877$			30.6239i			1.03409i	0.855957	+	0.517047i	$0.172969\pi$
$877$			30.6239i			1.03409i	−0.855957	+	0.517047i	$0.827031\pi$
$878$	−1.47716	−	4.23203i	−0.0498516	−	0.142824i
$879$		−	29.5724i		−	0.997451i
$880$	−44.5990	+	11.6445i	−1.50343	+	0.392535i
$881$			32.5310i			1.09600i	0.836480	+	0.547998i	$0.184610\pi$
$881$			32.5310i			1.09600i	−0.836480	+	0.547998i	$0.815390\pi$
$882$	20.0999	+	4.55181i	0.676799	+	0.153267i
$883$	−48.1773			−1.62130			−0.810648	−	0.585534i	$-0.800885\pi$
$883$	−48.1773			−1.62130			−0.810648	+	0.585534i	$0.800885\pi$
$884$	−1.95322	−	0.223154i	−0.0656938	−	0.00750547i
$885$	−28.0891	+	14.7273i	−0.944204	+	0.495052i
$886$	10.7694	+	30.8540i	0.361803	+	1.03656i
$887$	−7.44138	−	7.44138i	−0.249857	−	0.249857i	0.571055	−	0.820912i	$-0.306534\pi$
$887$	−7.44138	−	7.44138i	−0.249857	−	0.249857i	−0.820912	+	0.571055i	$0.806534\pi$
$888$	−7.62808	−	4.81791i	−0.255982	−	0.161679i
$889$	−19.4877	+	10.8020i	−0.653596	+	0.362286i
$890$	−25.3948	+	0.846619i	−0.851236	+	0.0283787i
$891$	5.75526	−	5.75526i	0.192808	−	0.192808i
$892$	14.3250	+	1.63662i	0.479635	+	0.0547980i
$893$	−5.50440			−0.184198
$894$	0.830413	−	1.72094i	0.0277732	−	0.0575570i
$895$	−18.9409	−	36.1256i	−0.633125	−	1.20755i
$896$	26.2590	−	14.3689i	0.877252	−	0.480030i
$897$	8.05848	+	8.05848i	0.269065	+	0.269065i
$898$	−16.9443	−	48.5451i	−0.565438	−	1.61997i
$899$	11.1023	+	11.1023i	0.370283	+	0.370283i
$900$	−20.7719	+	1.38654i	−0.692395	+	0.0462179i
$901$	−0.150637	−	0.150637i	−0.00501845	−	0.00501845i
$902$	27.8696	−	57.7568i	0.927956	−	1.92309i
$903$	4.60396	−	16.0553i	0.153210	−	0.534288i
$904$	−6.25373	−	27.6973i	−0.207996	−	0.921198i
$905$	−0.193315	+	0.101356i	−0.00642600	+	0.00336919i
$906$	−11.1120	+	3.87855i	−0.369171	+	0.128856i
$907$	−13.9568			−0.463428			−0.231714	−	0.972784i	$-0.574433\pi$
$907$	−13.9568			−0.463428			−0.231714	+	0.972784i	$0.574433\pi$
$908$	18.5817	−	14.7712i	0.616657	−	0.490199i
$909$	27.0621	+	27.0621i	0.897592	+	0.897592i
$910$	−10.4310	+	41.5550i	−0.345785	+	1.37753i
$911$	−33.4838			−1.10937			−0.554683	−	0.832062i	$-0.687161\pi$
$911$	−33.4838			−1.10937			−0.554683	+	0.832062i	$0.687161\pi$
$912$	2.18966	+	3.50902i	0.0725068	+	0.116195i
$913$	−59.7640	−	59.7640i	−1.97790	−	1.97790i
$914$	7.36128	−	15.2555i	0.243489	−	0.504606i
$915$	−10.8531	+	5.69034i	−0.358792	+	0.188117i
$916$	−1.43940	+	12.5988i	−0.0475592	+	0.416276i
$917$	2.04427	+	3.68804i	0.0675076	+	0.121790i
$918$	−1.19053	−	0.574471i	−0.0392934	−	0.0189604i
$919$	29.4411			0.971174			0.485587	−	0.874188i	$-0.338606\pi$
$919$	29.4411			0.971174			0.485587	+	0.874188i	$0.338606\pi$
$920$	−1.18016	+	14.6414i	−0.0389086	+	0.482713i
$921$		−	15.2590i		−	0.502801i
$922$	20.0407	−	41.5322i	0.660004	−	1.36779i
$923$	2.67594			0.0880795
$924$	−10.0074	+	24.1381i	−0.329218	+	0.794087i
$925$	13.6902	+	9.46661i	0.450131	+	0.311260i
$926$	6.93335	−	14.3686i	0.227844	−	0.472183i
$927$	−7.21598	+	7.21598i	−0.237004	+	0.237004i
$928$	11.0275	+	8.86457i	0.361996	+	0.290994i
$929$	28.7552			0.943426			0.471713	−	0.881752i	$-0.343636\pi$
$929$	28.7552			0.943426			0.471713	+	0.881752i	$0.343636\pi$
$930$	0.633803	+	19.0113i	0.0207832	+	0.623405i
$931$	1.69911	+	7.36028i	0.0556861	+	0.241224i
$932$	31.2673	+	3.57227i	1.02419	+	0.117014i
$933$			5.18009i			0.169588i
$934$	24.9031	−	8.69224i	0.814855	−	0.284419i
$935$	2.11154	+	0.658952i	0.0690546	+	0.0215500i
$936$	−25.4936	−	16.1018i	−0.833286	−	0.526305i
$937$	20.7464	+	20.7464i	0.677755	+	0.677755i	0.959492	−	0.281737i	$-0.0909105\pi$
$937$	20.7464	+	20.7464i	0.677755	+	0.677755i	−0.281737	+	0.959492i	$0.590911\pi$
$938$	10.2700	−	0.581482i	0.335328	−	0.0189861i
$939$	19.7370	+	19.7370i	0.644091	+	0.644091i
$940$	−20.8637	−	9.22349i	−0.680498	−	0.300837i
$941$	23.4129	−	23.4129i	0.763240	−	0.763240i	−0.213667	−	0.976907i	$-0.568541\pi$
$941$	23.4129	−	23.4129i	0.763240	−	0.763240i	0.976907	+	0.213667i	$0.0685407\pi$
$942$	9.36683	+	26.8358i	0.305188	+	0.874358i
$943$	−14.4506	−	14.4506i	−0.470575	−	0.470575i
$944$	−31.3446	−	50.2310i	−1.02018	−	1.63488i
$945$	−15.8300	+	24.0694i	−0.514950	+	0.782976i
$946$	−43.2440	−	20.8667i	−1.40598	−	0.678434i
$947$		−	10.5391i		−	0.342476i	−0.985230	−	0.171238i	$-0.945223\pi$
$947$		−	10.5391i		−	0.342476i	0.985230	−	0.171238i	$-0.0547767\pi$
$948$	17.9629	−	14.2793i	0.583408	−	0.463769i
$949$	−36.3548	−	36.3548i	−1.18013	−	1.18013i
$950$	−3.76647	−	6.63619i	−0.122200	−	0.215306i
$951$	−30.9630			−1.00405
$952$	−1.43409	−	0.0821155i	−0.0464792	−	0.00266138i
$953$	−21.2956	−	21.2956i	−0.689832	−	0.689832i	0.272362	−	0.962195i	$-0.412195\pi$
$953$	−21.2956	−	21.2956i	−0.689832	−	0.689832i	−0.962195	+	0.272362i	$0.912195\pi$
$954$	−1.07677	−	3.08493i	−0.0348617	−	0.0998784i
$955$	−5.72192	+	18.3353i	−0.185157	+	0.593315i
$956$	17.6353	+	22.1847i	0.570366	+	0.717504i
$957$	−12.3512			−0.399258
$958$	−46.4595	+	16.2163i	−1.50104	+	0.523925i
$959$	−1.24813	−	2.25174i	−0.0403042	−	0.0727123i
$960$	2.41968	+	16.9696i	0.0780949	+	0.547691i
$961$	−8.40690			−0.271190
$962$	7.94460	+	22.7612i	0.256144	+	0.733849i
$963$	−28.4067			−0.915393
$964$	−31.1635	−	39.2028i	−1.00371	−	1.26264i
$965$	−20.0410	−	38.2239i	−0.645144	−	1.23047i
$966$	6.21152	+	5.54583i	0.199852	+	0.178434i
$967$	−25.7453	+	25.7453i	−0.827912	+	0.827912i	−0.987228	−	0.159316i	$-0.949071\pi$
$967$	−25.7453	+	25.7453i	−0.827912	+	0.827912i	0.159316	+	0.987228i	$0.449071\pi$
$968$	37.2058	+	23.4993i	1.19584	+	0.755297i
$969$		−	0.198487i		−	0.00637631i
$970$	−8.67610	−	8.11627i	−0.278573	−	0.260598i
$971$	22.3570	+	22.3570i	0.717470	+	0.717470i	0.968087	−	0.250616i	$-0.0806332\pi$
$971$	22.3570	+	22.3570i	0.717470	+	0.717470i	−0.250616	+	0.968087i	$0.580633\pi$
$972$	−20.0644	−	25.2405i	−0.643566	−	0.809588i
$973$	6.70078	+	12.0888i	0.214817	+	0.387549i
$974$	5.99601	−	12.4261i	0.192125	−	0.398158i
$975$	−20.1799	−	13.9542i	−0.646274	−	0.446891i
$976$	−12.1109	−	19.4083i	−0.387662	−	0.621245i
$977$	17.6231	+	17.6231i	0.563814	+	0.563814i	0.930389	−	0.366575i	$-0.119470\pi$
$977$	17.6231	+	17.6231i	0.563814	+	0.563814i	−0.366575	+	0.930389i	$0.619470\pi$
$978$	7.37434	+	21.1274i	0.235805	+	0.675579i
$979$	29.2800	+	29.2800i	0.935794	+	0.935794i
$980$	−5.89307	+	30.7453i	−0.188247	+	0.982122i
$981$	−25.6601	+	25.6601i	−0.819265	+	0.819265i
$982$	21.2662	−	44.0719i	0.678631	−	1.40639i
$983$	34.8611	−	34.8611i	1.11190	−	1.11190i	0.119004	−	0.992894i	$-0.462030\pi$
$983$	34.8611	−	34.8611i	1.11190	−	1.11190i	0.992894	−	0.119004i	$-0.0379701\pi$
$984$	−20.1630	−	12.7350i	−0.642774	−	0.405978i
$985$	−3.72441	+	11.9344i	−0.118670	+	0.380263i
$986$	−0.223751	−	0.641044i	−0.00712569	−	0.0204150i
$987$	−11.3104	+	6.26930i	−0.360013	+	0.199554i
$988$	1.25453	−	10.9806i	0.0399119	−	0.349340i
$989$	−10.8195	+	10.8195i	−0.344040	+	0.344040i
$990$	24.7758	+	23.1771i	0.787426	+	0.736617i
$991$	−44.5557			−1.41536			−0.707679	−	0.706534i	$-0.750258\pi$
$991$	−44.5557			−1.41536			−0.707679	+	0.706534i	$0.750258\pi$
$992$	−35.3028	+	3.83862i	−1.12086	+	0.121876i
$993$	11.0883	+	11.0883i	0.351877	+	0.351877i
$994$	1.95210	−	0.110527i	0.0619169	−	0.00350569i
$995$	20.6924	+	6.45751i	0.655992	+	0.204717i
$996$	−24.6038	+	19.5583i	−0.779601	+	0.619729i
$997$			23.3077i			0.738163i	0.929397	+	0.369082i	$0.120328\pi$
$997$			23.3077i			0.738163i	−0.929397	+	0.369082i	$0.879672\pi$
$998$	−15.6214	+	32.3736i	−0.494485	+	1.02477i
$999$			16.2101i			0.512864i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.r.a.237.11	✓	184
5.3	odd	4		560.2.bn.a.13.58	yes	184
7.6	odd	2	inner	560.2.r.a.237.12	yes	184
16.5	even	4		560.2.bn.a.517.57	yes	184
35.13	even	4		560.2.bn.a.13.57	yes	184
80.53	odd	4	inner	560.2.r.a.293.11	yes	184
112.69	odd	4		560.2.bn.a.517.58	yes	184
560.293	even	4	inner	560.2.r.a.293.12	yes	184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.r.a.237.11	✓	184	1.1	even	1	trivial
560.2.r.a.237.12	yes	184	7.6	odd	2	inner
560.2.r.a.293.11	yes	184	80.53	odd	4	inner
560.2.r.a.293.12	yes	184	560.293	even	4	inner
560.2.bn.a.13.57	yes	184	35.13	even	4
560.2.bn.a.13.58	yes	184	5.3	odd	4
560.2.bn.a.517.57	yes	184	16.5	even	4
560.2.bn.a.517.58	yes	184	112.69	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:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.r (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.33522 + 0.466046i) q^{2} -0.958223i q^{3} +(1.56560 - 1.24454i) q^{4} +(0.666131 - 2.13454i) q^{5} +(0.446576 + 1.27943i) q^{6} +(0.729292 - 2.54325i) q^{7} +(-1.51040 + 2.39138i) q^{8} +2.08181 q^{9} +(0.105366 + 3.16052i) q^{10} +(3.64406 - 3.64406i) q^{11} +(-1.19255 - 1.50020i) q^{12} +5.12086i q^{13} +(0.211511 + 3.73567i) q^{14} +(-2.04537 - 0.638302i) q^{15} +(0.902218 - 3.89692i) q^{16} +(-0.135731 + 0.135731i) q^{17} +(-2.77966 + 0.970219i) q^{18} +(-0.763055 - 0.763055i) q^{19} +(-1.61364 - 4.17087i) q^{20} +(-2.43700 - 0.698824i) q^{21} +(-3.16730 + 6.56390i) q^{22} +(1.64227 + 1.64227i) q^{23} +(2.29147 + 1.44730i) q^{24} +(-4.11254 - 2.84377i) q^{25} +(-2.38656 - 6.83745i) q^{26} -4.86951i q^{27} +(-2.02341 - 4.88936i) q^{28} +(1.76859 - 1.76859i) q^{29} +(3.02848 - 0.100964i) q^{30} +6.27749i q^{31} +(0.611490 + 5.62371i) q^{32} +(-3.49182 - 3.49182i) q^{33} +(0.117973 - 0.244487i) q^{34} +(-4.94288 - 3.25084i) q^{35} +(3.25928 - 2.59090i) q^{36} -3.32890 q^{37} +(1.37446 + 0.663224i) q^{38} +4.90692 q^{39} +(4.09837 + 4.81699i) q^{40} -8.79916 q^{41} +(3.57961 - 0.202675i) q^{42} +6.58815i q^{43} +(1.16995 - 10.2403i) q^{44} +(1.38676 - 4.44371i) q^{45} +(-2.95815 - 1.42741i) q^{46} +(3.60682 - 3.60682i) q^{47} +(-3.73412 - 0.864526i) q^{48} +(-5.93627 - 3.70955i) q^{49} +(6.81645 + 1.88041i) q^{50} +(0.130060 + 0.130060i) q^{51} +(6.37314 + 8.01722i) q^{52} +1.10982i q^{53} +(2.26941 + 6.50184i) q^{54} +(-5.35097 - 10.2058i) q^{55} +(4.98036 + 5.58534i) q^{56} +(-0.731177 + 0.731177i) q^{57} +(-1.53721 + 3.18570i) q^{58} +(10.4667 - 10.4667i) q^{59} +(-3.99663 + 1.54622i) q^{60} +(4.04412 - 4.04412i) q^{61} +(-2.92560 - 8.38181i) q^{62} +(1.51825 - 5.29457i) q^{63} +(-3.43738 - 7.22388i) q^{64} +(10.9307 + 3.41116i) q^{65} +(6.28968 + 3.03498i) q^{66} -2.74917i q^{67} +(-0.0435774 + 0.381424i) q^{68} +(1.57366 - 1.57366i) q^{69} +(8.11485 + 2.03697i) q^{70} -0.522556i q^{71} +(-3.14437 + 4.97839i) q^{72} +(-7.09935 + 7.09935i) q^{73} +(4.44479 - 1.55142i) q^{74} +(-2.72497 + 3.94073i) q^{75} +(-2.14430 - 0.244984i) q^{76} +(-6.61018 - 11.9253i) q^{77} +(-6.55180 + 2.28685i) q^{78} +11.9737i q^{79} +(-7.71715 - 4.52168i) q^{80} +1.57935 q^{81} +(11.7488 - 4.10081i) q^{82} -16.4004i q^{83} +(-4.68509 + 1.93888i) q^{84} +(0.199309 + 0.380138i) q^{85} +(-3.07038 - 8.79660i) q^{86} +(-1.69471 - 1.69471i) q^{87} +(3.21033 + 14.2183i) q^{88} +8.03500i q^{89} +(0.219353 + 6.57960i) q^{90} +(13.0236 + 3.73460i) q^{91} +(4.61501 + 0.527262i) q^{92} +6.01524 q^{93} +(-3.13494 + 6.49683i) q^{94} +(-2.13707 + 1.12048i) q^{95} +(5.38877 - 0.585944i) q^{96} +(-2.65658 + 2.65658i) q^{97} +(9.65502 + 2.18647i) q^{98} +(7.58623 - 7.58623i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q - 4 q^{2} + 8 q^{8} - 168 q^{9} - 8 q^{11} - 8 q^{15} - 8 q^{16} - 4 q^{21} - 12 q^{22} - 32 q^{28} - 44 q^{30} - 24 q^{32} + 20 q^{35} - 40 q^{36} - 8 q^{37} + 48 q^{39} - 32 q^{42} + 24 q^{44} - 8 q^{46}+ \cdots + 24 q^{99}+O(q^{100}) \) 184 * q - 4 * q^2 + 8 * q^8 - 168 * q^9 - 8 * q^11 - 8 * q^15 - 8 * q^16 - 4 * q^21 - 12 * q^22 - 32 * q^28 - 44 * q^30 - 24 * q^32 + 20 * q^35 - 40 * q^36 - 8 * q^37 + 48 * q^39 - 32 * q^42 + 24 * q^44 - 8 * q^46 - 4 * q^50 - 8 * q^51 - 4 * q^56 + 24 * q^57 - 4 * q^58 + 64 * q^60 - 32 * q^63 - 8 * q^65 + 12 * q^70 - 64 * q^72 + 40 * q^74 - 28 * q^78 + 104 * q^81 - 48 * q^84 + 16 * q^85 + 8 * q^86 + 96 * q^88 - 20 * q^91 - 56 * q^92 + 16 * q^93 - 56 * q^95 - 80 * q^98 + 24 * q^99

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