LMFDB - Embedded newform 560.2.bn.a.13.57

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(13,560)]

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, 3, 2]))

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

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

chi := DirichletCharacter("560.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.bn (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			13.57
Character	$\chi$	$=$	560.13
Dual form			560.2.bn.a.517.57

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.466046 + 1.33522i) q^{2} -0.958223 q^{3} +(-1.56560 + 1.24454i) q^{4} +(2.13454 - 0.666131i) q^{5} +(-0.446576 - 1.27943i) q^{6} +(-0.729292 - 2.54325i) q^{7} +(-2.39138 - 1.51040i) q^{8} -2.08181 q^{9} +(1.88422 + 2.53963i) q^{10} +(3.64406 - 3.64406i) q^{11} +(1.50020 - 1.19255i) q^{12} +5.12086 q^{13} +(3.05591 - 2.15904i) q^{14} +(-2.04537 + 0.638302i) q^{15} +(0.902218 - 3.89692i) q^{16} +(-0.135731 - 0.135731i) q^{17} +(-0.970219 - 2.77966i) q^{18} +(-0.763055 - 0.763055i) q^{19} +(-2.51281 + 3.69943i) q^{20} +(0.698824 + 2.43700i) q^{21} +(6.56390 + 3.16730i) 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} +4.86951 q^{27} +(4.30697 + 3.07408i) q^{28} +(-1.76859 + 1.76859i) q^{29} +(-1.80551 - 2.43353i) q^{30} -6.27749i q^{31} +(5.62371 - 0.611490i) q^{32} +(-3.49182 + 3.49182i) q^{33} +(0.117973 - 0.244487i) q^{34} +(-3.25084 - 4.94288i) q^{35} +(3.25928 - 2.59090i) q^{36} +3.32890i q^{37} +(0.663224 - 1.37446i) q^{38} -4.90692 q^{39} +(-6.11062 - 1.63104i) q^{40} +8.79916 q^{41} +(-2.92824 + 2.06884i) q^{42} -6.58815 q^{43} +(-1.16995 + 10.2403i) q^{44} +(-4.44371 + 1.38676i) q^{45} +(-2.95815 - 1.42741i) q^{46} +(3.60682 + 3.60682i) q^{47} +(-0.864526 + 3.73412i) q^{48} +(-5.93627 + 3.70955i) q^{49} +(5.71368 + 4.16580i) q^{50} +(0.130060 + 0.130060i) q^{51} +(-8.01722 + 6.37314i) q^{52} -1.10982 q^{53} +(2.26941 + 6.50184i) q^{54} +(5.35097 - 10.2058i) q^{55} +(-2.09732 + 7.18340i) q^{56} +(0.731177 + 0.731177i) q^{57} +(-3.18570 - 1.53721i) q^{58} +(10.4667 - 10.4667i) q^{59} +(2.40784 - 3.54488i) q^{60} +(-4.04412 + 4.04412i) q^{61} +(8.38181 - 2.92560i) 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} -2.74917 q^{67} +(0.381424 + 0.0435774i) q^{68} +(1.57366 - 1.57366i) q^{69} +(5.08476 - 6.64419i) q^{70} -0.522556i q^{71} +(4.97839 + 3.14437i) q^{72} +(7.09935 + 7.09935i) q^{73} +(-4.44479 + 1.55142i) q^{74} +(-3.94073 + 2.72497i) q^{75} +(2.14430 + 0.244984i) q^{76} +(-11.9253 - 6.61018i) q^{77} +(-2.28685 - 6.55180i) q^{78} -11.9737i q^{79} +(-0.670039 - 8.91914i) q^{80} +1.57935 q^{81} +(4.10081 + 11.7488i) q^{82} -16.4004 q^{83} +(-4.12704 - 2.94566i) q^{84} +(-0.380138 - 0.199309i) q^{85} +(-3.07038 - 8.79660i) q^{86} +(1.69471 - 1.69471i) q^{87} +(-14.2183 + 3.21033i) q^{88} +8.03500i q^{89} +(-3.92259 - 5.28702i) q^{90} +(-3.73460 - 13.0236i) q^{91} +(0.527262 - 4.61501i) q^{92} +6.01524i 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} +(-7.71962 - 6.19738i) 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} - 24 q^{18} - 4 q^{21} + 4 q^{22} + 12 q^{28} - 4 q^{30} + 16 q^{32} - 40 q^{36} - 48 q^{39} - 36 q^{42} - 8 q^{43} - 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 - 24 * q^18 - 4 * q^21 + 4 * q^22 + 12 * q^28 - 4 * q^30 + 16 * q^32 - 40 * q^36 - 48 * q^39 - 36 * q^42 - 8 * q^43 - 24 * q^44 - 8 * q^46 - 4 * q^50 - 8 * q^51 - 8 * q^53 - 4 * q^56 - 24 * q^57 - 68 * q^58 - 32 * q^63 - 8 * q^65 - 56 * q^67 + 80 * q^70 - 8 * q^72 - 40 * q^74 + 24 * q^77 - 100 * q^78 + 104 * q^81 + 48 * q^84 - 24 * q^85 + 8 * q^86 - 16 * q^88 - 20 * q^91 - 56 * q^92 - 56 * q^95 + 52 * q^98 - 24 * q^99

Character values

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

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

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 $

$2$	0.466046	+	1.33522i	0.329544	+	0.944140i
$2$	0.466046	+	1.33522i	0.329544	+	0.944140i
$3$	−0.958223			−0.553230			−0.276615	−	0.960981i	$-0.589213\pi$
$3$	−0.958223			−0.553230			−0.276615	+	0.960981i	$0.589213\pi$
$4$	−1.56560	+	1.24454i	−0.782801	+	0.622272i
$5$	2.13454	−	0.666131i	0.954596	−	0.297903i
$5$	2.13454	−	0.666131i	0.954596	−	0.297903i
$6$	−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
$8$	−2.39138	−	1.51040i	−0.845480	−	0.534007i
$9$	−2.08181			−0.693936
$10$	1.88422	+	2.53963i	0.595844	+	0.803100i
$11$	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	$-0.0332170\pi$
$12$	1.50020	−	1.19255i	0.433069	−	0.344260i
$13$	5.12086			1.42027			0.710135	−	0.704065i	$-0.248634\pi$
$13$	5.12086			1.42027			0.710135	+	0.704065i	$0.248634\pi$
$14$	3.05591	−	2.15904i	0.816726	−	0.577026i
$15$	−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	0.690455	−	0.723375i	$-0.257410\pi$
$17$	−0.135731	−	0.135731i	−0.0329196	−	0.0329196i	−0.723375	+	0.690455i	$0.757410\pi$
$18$	−0.970219	−	2.77966i	−0.228683	−	0.655173i
$19$	−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	$0.789503\pi$
$20$	−2.51281	+	3.69943i	−0.561882	+	0.827217i
$21$	0.698824	+	2.43700i	0.152496	+	0.531798i
$22$	6.56390	+	3.16730i	1.39943	+	0.675272i
$23$	−1.64227	+	1.64227i	−0.342436	+	0.342436i	−0.857283	−	0.514846i	$-0.827849\pi$
$23$	−1.64227	+	1.64227i	−0.342436	+	0.342436i	0.514846	+	0.857283i	$0.327849\pi$
$24$	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
$27$	4.86951			0.937137
$28$	4.30697	+	3.07408i	0.813941	+	0.580947i
$29$	−1.76859	+	1.76859i	−0.328419	+	0.328419i	−0.851985	−	0.523566i	$-0.824601\pi$
$29$	−1.76859	+	1.76859i	−0.328419	+	0.328419i	0.523566	+	0.851985i	$0.324601\pi$
$30$	−1.80551	−	2.43353i	−0.329639	−	0.444299i
$31$		−	6.27749i		−	1.12747i	−0.825955	−	0.563735i	$-0.809364\pi$
$31$		−	6.27749i		−	1.12747i	0.825955	−	0.563735i	$-0.190636\pi$
$32$	5.62371	−	0.611490i	0.994140	−	0.108097i
$33$	−3.49182	+	3.49182i	−0.607848	+	0.607848i
$34$	0.117973	−	0.244487i	0.0202322	−	0.0419292i
$35$	−3.25084	−	4.94288i	−0.549493	−	0.835498i
$36$	3.25928	−	2.59090i	0.543214	−	0.431817i
$37$			3.32890i			0.547267i	0.961834	+	0.273634i	$0.0882256\pi$
$37$			3.32890i			0.547267i	−0.961834	+	0.273634i	$0.911774\pi$
$38$	0.663224	−	1.37446i	0.107589	−	0.222967i
$39$	−4.90692			−0.785737
$40$	−6.11062	−	1.63104i	−0.966174	−	0.257890i
$41$	8.79916			1.37420			0.687099	−	0.726564i	$-0.258884\pi$
$41$	8.79916			1.37420			0.687099	+	0.726564i	$0.258884\pi$
$42$	−2.92824	+	2.06884i	−0.451837	+	0.319228i
$43$	−6.58815			−1.00468			−0.502342	−	0.864669i	$-0.667528\pi$
$43$	−6.58815			−1.00468			−0.502342	+	0.864669i	$0.667528\pi$
$44$	−1.16995	+	10.2403i	−0.176377	+	1.54379i
$45$	−4.44371	+	1.38676i	−0.662429	+	0.206726i
$46$	−2.95815	−	1.42741i	−0.436156	−	0.210460i
$47$	3.60682	+	3.60682i	0.526109	+	0.526109i	0.919410	−	0.393301i	$-0.128667\pi$
$47$	3.60682	+	3.60682i	0.526109	+	0.526109i	−0.393301	+	0.919410i	$0.628667\pi$
$48$	−0.864526	+	3.73412i	−0.124784	+	0.538974i
$49$	−5.93627	+	3.70955i	−0.848038	+	0.529935i
$50$	5.71368	+	4.16580i	0.808036	+	0.589133i
$51$	0.130060	+	0.130060i	0.0182121	+	0.0182121i
$52$	−8.01722	+	6.37314i	−1.11179	+	0.883795i
$53$	−1.10982			−0.152446			−0.0762229	−	0.997091i	$-0.524286\pi$
$53$	−1.10982			−0.152446			−0.0762229	+	0.997091i	$0.524286\pi$
$54$	2.26941	+	6.50184i	0.308828	+	0.884788i
$55$	5.35097	−	10.2058i	0.721525	−	1.37615i
$56$	−2.09732	+	7.18340i	−0.280266	+	0.959922i
$57$	0.731177	+	0.731177i	0.0968467	+	0.0968467i
$58$	−3.18570	−	1.53721i	−0.418303	−	0.201845i
$59$	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	$-0.163776\pi$
$60$	2.40784	−	3.54488i	0.310850	−	0.457642i
$61$	−4.04412	+	4.04412i	−0.517797	+	0.517797i	−0.916904	−	0.399108i	$-0.869320\pi$
$61$	−4.04412	+	4.04412i	−0.517797	+	0.517797i	0.399108	+	0.916904i	$0.369320\pi$
$62$	8.38181	−	2.92560i	1.06449	−	0.371552i
$63$	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
$67$	−2.74917			−0.335865			−0.167932	−	0.985799i	$-0.553709\pi$
$67$	−2.74917			−0.335865			−0.167932	+	0.985799i	$0.553709\pi$
$68$	0.381424	+	0.0435774i	0.0462544	+	0.00528454i
$69$	1.57366	−	1.57366i	0.189446	−	0.189446i
$70$	5.08476	−	6.64419i	0.607745	−	0.794132i
$71$		−	0.522556i		−	0.0620160i	−0.999519	−	0.0310080i	$-0.990128\pi$
$71$		−	0.522556i		−	0.0620160i	0.999519	−	0.0310080i	$-0.00987174\pi$
$72$	4.97839	+	3.14437i	0.586709	+	0.370567i
$73$	7.09935	+	7.09935i	0.830916	+	0.830916i	0.987642	−	0.156726i	$-0.0500940\pi$
$73$	7.09935	+	7.09935i	0.830916	+	0.830916i	−0.156726	+	0.987642i	$0.550094\pi$
$74$	−4.44479	+	1.55142i	−0.516697	+	0.180349i
$75$	−3.94073	+	2.72497i	−0.455036	+	0.314652i
$76$	2.14430	+	0.244984i	0.245968	+	0.0281016i
$77$	−11.9253	−	6.61018i	−1.35902	−	0.753300i
$78$	−2.28685	−	6.55180i	−0.258935	−	0.741845i
$79$		−	11.9737i		−	1.34715i	−0.739120	−	0.673574i	$-0.764758\pi$
$79$		−	11.9737i		−	1.34715i	0.739120	−	0.673574i	$-0.235242\pi$
$80$	−0.670039	−	8.91914i	−0.0749126	−	0.997190i
$81$	1.57935			0.175484
$82$	4.10081	+	11.7488i	0.452859	+	1.29743i
$83$	−16.4004			−1.80018			−0.900089	−	0.435707i	$-0.856498\pi$
$83$	−16.4004			−1.80018			−0.900089	+	0.435707i	$0.856498\pi$
$84$	−4.12704	−	2.94566i	−0.450297	−	0.321398i
$85$	−0.380138	−	0.199309i	−0.0412317	−	0.0216181i
$86$	−3.07038	−	8.79660i	−0.331088	−	0.948562i
$87$	1.69471	−	1.69471i	0.181692	−	0.181692i
$88$	−14.2183	+	3.21033i	−1.51568	+	0.342223i
$89$			8.03500i			0.851709i	0.904792	+	0.425854i	$0.140026\pi$
$89$			8.03500i			0.851709i	−0.904792	+	0.425854i	$0.859974\pi$
$90$	−3.92259	−	5.28702i	−0.413478	−	0.557300i
$91$	−3.73460	−	13.0236i	−0.391492	−	1.36525i
$92$	0.527262	−	4.61501i	0.0549709	−	0.481148i
$93$			6.01524i			0.623751i
$94$	−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	0.559258	−	0.828993i	$-0.311086\pi$
$97$	−2.65658	−	2.65658i	−0.269735	−	0.269735i	−0.828993	+	0.559258i	$0.811086\pi$
$98$	−7.71962	−	6.19738i	−0.779799	−	0.626030i
$99$	−7.58623	+	7.58623i	−0.762445	+	0.762445i
$100$	−2.89940	+	9.57045i	−0.289940	+	0.957045i
$101$	−12.9993	−	12.9993i	−1.29348	−	1.29348i	−0.932620	−	0.360859i	$-0.882484\pi$
$101$	−12.9993	−	12.9993i	−1.29348	−	1.29348i	−0.360859	−	0.932620i	$-0.617516\pi$
$102$	−0.113045	+	0.234273i	−0.0111931	+	0.0231965i
$103$	3.46620	+	3.46620i	0.341535	+	0.341535i	0.856944	−	0.515409i	$-0.172360\pi$
$103$	3.46620	+	3.46620i	0.341535	+	0.341535i	−0.515409	+	0.856944i	$0.672360\pi$
$104$	−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
$107$			13.6452i			1.31913i	0.751647	+	0.659566i	$0.229260\pi$
$107$			13.6452i			1.31913i	−0.751647	+	0.659566i	$0.770740\pi$
$108$	−7.62371	+	6.06032i	−0.733592	+	0.583154i
$109$	12.3259	−	12.3259i	1.18061	−	1.18061i	0.201018	−	0.979587i	$-0.435575\pi$
$109$	12.3259	−	12.3259i	1.18061	−	1.18061i	0.979587	−	0.201018i	$-0.0644251\pi$
$110$	16.1208	+	2.38832i	1.53706	+	0.227718i
$111$		−	3.18982i		−	0.302765i
$112$	−10.5688	+	0.547424i	−0.998661	+	0.0517267i
$113$	−7.09863	−	7.09863i	−0.667783	−	0.667783i	0.289419	−	0.957202i	$-0.406538\pi$
$113$	−7.09863	−	7.09863i	−0.667783	−	0.667783i	−0.957202	+	0.289419i	$0.906538\pi$
$114$	−0.635516	+	1.31704i	−0.0595216	+	0.123352i
$115$	−2.41152	+	4.59945i	−0.224876	+	0.428901i
$116$	0.567820	−	4.97000i	0.0527207	−	0.461453i
$117$	−10.6606			−0.985577
$118$	18.8532	+	9.09731i	1.73558	+	0.837475i
$119$	−0.246210	+	0.444185i	−0.0225701	+	0.0407184i
$120$	5.85534	+	1.56290i	0.534517	+	0.142673i
$121$		−	15.5583i		−	1.41439i
$122$	−7.28452	−	3.51503i	−0.659509	−	0.318235i
$123$	−8.43155			−0.760248
$124$	7.81262	+	9.82805i	0.701594	+	0.882585i
$125$	6.88406	−	8.80964i	0.615729	−	0.787958i
$126$	−6.36181	+	4.49470i	−0.566755	+	0.400420i
$127$	−5.95490	+	5.95490i	−0.528412	+	0.528412i	−0.920099	−	0.391687i	$-0.871892\pi$
$127$	−5.95490	+	5.95490i	−0.528412	+	0.528412i	0.391687	+	0.920099i	$0.371892\pi$
$128$	−8.04346	+	7.95630i	−0.710948	+	0.703244i
$129$	6.31292			0.555821
$130$	9.64884	+	13.0051i	0.846260	+	1.14062i
$131$	1.12696	−	1.12696i	0.0984632	−	0.0984632i	−0.656159	−	0.754622i	$-0.727820\pi$
$131$	1.12696	−	1.12696i	0.0984632	−	0.0984632i	0.754622	+	0.656159i	$0.227820\pi$
$132$	1.12107	−	9.81253i	0.0975770	−	0.854071i
$133$	−1.38415	+	2.49713i	−0.120021	+	0.216529i
$134$	−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	$-0.263235\pi$
$137$	−0.688069	−	0.688069i	−0.0587857	−	0.0587857i	−0.735888	+	0.677103i	$0.763235\pi$
$138$	2.83457	+	1.36778i	0.241295	+	0.116433i
$139$	−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	$0.321112\pi$
$140$	11.2412	+	3.69275i	0.950051	+	0.312095i
$141$	−3.45614	−	3.45614i	−0.291059	−	0.291059i
$142$	0.697726	−	0.243535i	0.0585518	−	0.0204370i
$143$	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
$147$	5.68827	−	3.55457i	0.469160	−	0.293176i
$148$	−4.14296	−	5.21173i	−0.340549	−	0.428401i
$149$	0.997064	+	0.997064i	0.0816827	+	0.0816827i	0.746768	−	0.665085i	$-0.231605\pi$
$149$	0.997064	+	0.997064i	0.0816827	+	0.0816827i	−0.665085	+	0.746768i	$0.731605\pi$
$150$	−5.47498	−	3.99176i	−0.447030	−	0.325926i
$151$			8.68507i			0.706781i	0.935476	+	0.353390i	$0.114971\pi$
$151$			8.68507i			0.706781i	−0.935476	+	0.353390i	$0.885029\pi$
$152$	0.672234	+	2.97727i	0.0545254	+	0.241489i
$153$	0.282566	+	0.282566i	0.0228441	+	0.0228441i
$154$	3.26825	−	19.0036i	0.263363	−	1.53135i
$155$	−4.18163	−	13.3996i	−0.335877	−	1.07628i
$156$	7.68229	−	6.10688i	0.615075	−	0.488942i
$157$			20.9748i			1.67397i	0.547227	+	0.836984i	$0.315683\pi$
$157$			20.9748i			1.67397i	−0.547227	+	0.836984i	$0.684317\pi$
$158$	15.9875	−	5.58030i	1.27190	−	0.443945i
$159$	1.06346			0.0843377
$160$	11.5967	−	5.05138i	0.916800	−	0.399346i
$161$	5.37439	+	2.97901i	0.423561	+	0.234779i
$162$	0.736052	+	2.10878i	0.0578297	+	0.165681i
$163$			16.5131i			1.29340i	0.762743	+	0.646701i	$0.223852\pi$
$163$			16.5131i			1.29340i	−0.762743	+	0.646701i	$0.776148\pi$
$164$	−13.7760	+	10.9509i	−1.07572	+	0.855125i
$165$	−5.12743	+	9.77945i	−0.399170	+	0.761329i
$166$	−7.64334	−	21.8981i	−0.593238	−	1.69962i
$167$	5.27346	−	5.27346i	0.408073	−	0.408073i	−0.472993	−	0.881066i	$-0.656827\pi$
$167$	5.27346	−	5.27346i	0.408073	−	0.408073i	0.881066	+	0.472993i	$0.156827\pi$
$168$	2.00970	−	6.88330i	0.155052	−	0.531058i
$169$	13.2232			1.01717
$170$	0.0889583	−	0.600453i	0.00682279	−	0.0460526i
$171$	1.58853	+	1.58853i	0.121478	+	0.121478i
$172$	10.3144	−	8.19925i	0.786467	−	0.625187i
$173$	12.0157			0.913537			0.456768	−	0.889586i	$-0.349007\pi$
$173$	12.0157			0.913537			0.456768	+	0.889586i	$0.349007\pi$
$174$	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
$178$	−10.7285	+	3.74468i	−0.804132	+	0.280676i
$179$	−12.8989	+	12.8989i	−0.964110	+	0.964110i	−0.999378	−	0.0352677i	$-0.988772\pi$
$179$	−12.8989	+	12.8989i	−0.964110	+	0.964110i	0.0352677	+	0.999378i	$0.488772\pi$
$180$	5.23120	−	7.70150i	0.389910	−	0.574036i
$181$	0.0690244	+	0.0690244i	0.00513054	+	0.00513054i	0.709667	−	0.704537i	$-0.248845\pi$
$181$	0.0690244	+	0.0690244i	0.00513054	+	0.00513054i	−0.704537	+	0.709667i	$0.748845\pi$
$182$	15.6489	−	11.0561i	1.15997	−	0.819534i
$183$	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
$187$	−0.989223			−0.0723391
$188$	−10.1357	−	1.15800i	−0.739221	−	0.0844556i
$189$	−3.55129	−	12.3844i	−0.258318	−	0.900831i
$190$	0.500108	−	3.37564i	0.0362816	−	0.244895i
$191$	−8.58978			−0.621535			−0.310767	−	0.950486i	$-0.600586\pi$
$191$	−8.58978			−0.621535			−0.310767	+	0.950486i	$0.600586\pi$
$192$	−3.29378	−	6.92209i	−0.237708	−	0.499559i
$193$	13.6481	+	13.6481i	0.982413	+	0.982413i	0.999848	−	0.0174354i	$-0.00555013\pi$
$193$	13.6481	+	13.6481i	0.982413	+	0.982413i	−0.0174354	+	0.999848i	$0.505550\pi$
$194$	2.30902	−	4.78520i	0.165778	−	0.343557i
$195$	−10.4740	+	3.26866i	−0.750061	+	0.234073i
$196$	4.67714	−	13.1956i	0.334081	−	0.942544i
$197$			5.59110i			0.398350i	0.979964	+	0.199175i	$0.0638262\pi$
$197$			5.59110i			0.398350i	−0.979964	+	0.199175i	$0.936174\pi$
$198$	−13.6648	−	6.59372i	−0.971115	−	0.468595i
$199$			9.69405i			0.687193i	0.939117	+	0.343597i	$0.111645\pi$
$199$			9.69405i			0.687193i	−0.939117	+	0.343597i	$0.888355\pi$
$200$	−14.1299	+	0.588948i	−0.999132	+	0.0416449i
$201$	2.63432			0.185811
$202$	11.2986	−	23.4152i	0.794967	−	1.64748i
$203$	5.78780	+	3.20816i	0.406224	+	0.225169i
$204$	−0.365489	−	0.0417569i	−0.0255893	−	0.00292357i
$205$	18.7822	−	5.86139i	1.31180	−	0.409377i
$206$	−3.01272	+	6.24354i	−0.209906	+	0.435008i
$207$	3.41889	−	3.41889i	0.237629	−	0.237629i
$208$	4.62013	−	19.9556i	0.320348	−	1.38367i
$209$	−5.56123			−0.384679
$210$	−4.87233	+	6.36661i	−0.336223	+	0.439338i
$211$	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	$0.399324\pi$
$212$	1.73754	−	1.38122i	0.119335	−	0.0948628i
$213$			0.500726i			0.0343092i
$214$	−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
$218$	22.2021	+	10.7133i	1.50372	+	0.725595i
$219$	−6.80276	−	6.80276i	−0.459688	−	0.459688i
$220$	4.32410	+	22.6378i	0.291531	+	1.52624i
$221$	−0.695059	−	0.695059i	−0.0467547	−	0.0467547i
$222$	4.25910	−	1.48661i	0.285852	−	0.0997744i
$223$	5.09759	−	5.09759i	0.341360	−	0.341360i	−0.515519	−	0.856878i	$-0.672401\pi$
$223$	5.09759	−	5.09759i	0.341360	−	0.341360i	0.856878	+	0.515519i	$0.172401\pi$
$224$	−5.65650	−	13.8566i	−0.377941	−	0.925830i
$225$	−8.56152	+	5.92019i	−0.570768	+	0.394679i
$226$	6.16991	−	12.7865i	0.410416	−	0.850545i
$227$			11.8688i			0.787757i	0.919163	+	0.393879i	$0.128867\pi$
$227$			11.8688i			0.787757i	−0.919163	+	0.393879i	$0.871133\pi$
$228$	−2.05471	−	0.234750i	−0.136077	−	0.0155467i
$229$	−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	$0.317181\pi$
$230$	−7.26514	−	1.07634i	−0.479049	−	0.0709721i
$231$	11.4271	+	6.33403i	0.751851	+	0.416748i
$232$	6.90066	−	1.55809i	0.453050	−	0.102294i
$233$	−11.1266	+	11.1266i	−0.728926	+	0.728926i	−0.970406	−	0.241480i	$-0.922367\pi$
$233$	−11.1266	+	11.1266i	−0.728926	+	0.728926i	0.241480	+	0.970406i	$0.422367\pi$
$234$	−4.96835	−	14.2343i	−0.324791	−	0.930523i
$235$	10.1015	+	5.29629i	0.658951	+	0.345492i
$236$	−3.36040	+	29.4129i	−0.218744	+	1.91462i
$237$			11.4735i			0.745283i
$238$	−0.707829	−	0.121733i	−0.0458817	−	0.00789079i
$239$		−	14.1701i		−	0.916586i	−0.888801	−	0.458293i	$-0.848461\pi$
$239$		−	14.1701i		−	0.916586i	0.888801	−	0.458293i	$-0.151539\pi$
$240$	0.642047	+	8.54652i	0.0414439	+	0.551676i
$241$			25.0401i			1.61298i	0.591251	+	0.806488i	$0.298634\pi$
$241$			25.0401i			1.61298i	−0.591251	+	0.806488i	$0.701366\pi$
$242$	20.7737	−	7.25090i	1.33539	−	0.466106i
$243$	−16.1219			−1.03422
$244$	1.29839	−	11.3646i	0.0831212	−	0.727542i
$245$	−10.2002	+	11.8725i	−0.651665	+	0.758507i
$246$	−3.92949	−	11.2579i	−0.250535	−	0.717780i
$247$	−3.90750	−	3.90750i	−0.248628	−	0.248628i
$248$	−9.48153	+	15.0119i	−0.602078	+	0.953254i
$249$	15.7152			0.995913
$250$	14.9711	+	5.08601i	0.946853	+	0.321667i
$251$	4.38367	+	4.38367i	0.276695	+	0.276695i	0.831788	−	0.555093i	$-0.187317\pi$
$251$	4.38367	+	4.38367i	0.276695	+	0.276695i	−0.555093	+	0.831788i	$0.687317\pi$
$252$	−8.96629	−	6.39966i	−0.564823	−	0.403140i
$253$			11.9690i			0.752487i
$254$	−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	0.975168	−	0.221468i	$-0.0710849\pi$
$257$	12.0827	+	12.0827i	0.753700	+	0.753700i	−0.221468	+	0.975168i	$0.571085\pi$
$258$	2.94211	+	8.42911i	0.183168	+	0.524773i
$259$	8.46622	−	2.42774i	0.526066	−	0.150852i
$260$	−12.8678	+	18.9442i	−0.798024	+	1.17487i
$261$	3.68187	−	3.68187i	0.227902	−	0.227902i
$262$	2.02996	+	0.979522i	0.125411	+	0.0605151i
$263$	6.50590	−	6.50590i	0.401171	−	0.401171i	−0.477475	−	0.878645i	$-0.658448\pi$
$263$	6.50590	−	6.50590i	0.401171	−	0.401171i	0.878645	+	0.477475i	$0.158448\pi$
$264$	13.6243	−	3.07621i	0.838519	−	0.189328i
$265$	−2.36896	+	0.739287i	−0.145524	+	0.0454141i
$266$	−3.97929	−	0.684363i	−0.243986	−	0.0419610i
$267$		−	7.69933i		−	0.471191i
$268$	4.30411	−	3.42147i	0.262915	−	0.208999i
$269$	−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	$0.814348\pi$
$270$	9.17524	+	12.3667i	0.558387	+	0.752615i
$271$			17.5711i			1.06737i	0.845684	+	0.533684i	$0.179193\pi$
$271$			17.5711i			1.06737i	−0.845684	+	0.533684i	$0.820807\pi$
$272$	−0.651392	+	0.406474i	−0.0394964	+	0.0246461i
$273$	3.57858	+	12.4795i	0.216585	+	0.755297i
$274$	0.598048	−	1.23939i	0.0361294	−	0.0748744i
$275$	4.62347	−	25.3492i	0.278805	−	1.52861i
$276$	−0.505234	+	4.42221i	−0.0304115	+	0.266186i
$277$		−	23.7488i		−	1.42693i	−0.700692	−	0.713464i	$-0.747125\pi$
$277$		−	23.7488i		−	1.42693i	0.700692	−	0.713464i	$-0.252875\pi$
$278$	−6.65387	−	3.21072i	−0.399072	−	0.192566i
$279$			13.0685i			0.782393i
$280$	0.308274	+	16.7304i	0.0184229	+	0.999830i
$281$			7.74368i			0.461949i	0.972960	+	0.230975i	$0.0741914\pi$
$281$			7.74368i			0.461949i	−0.972960	+	0.230975i	$0.925809\pi$
$282$	3.00397	−	6.22541i	0.178884	−	0.370718i
$283$			1.67333i			0.0994694i	0.998762	+	0.0497347i	$0.0158376\pi$
$283$			1.67333i			0.0994694i	−0.998762	+	0.0497347i	$0.984162\pi$
$284$	0.650345	+	0.818115i	0.0385909	+	0.0485462i
$285$	2.04779	+	1.07367i	0.121300	+	0.0635986i
$286$	33.6128	+	16.2193i	1.98757	+	0.959068i
$287$	−6.41715	−	22.3785i	−0.378793	−	1.32096i
$288$	−11.7075	+	1.27301i	−0.689870	+	0.0750125i
$289$		−	16.9632i		−	0.997833i
$290$	−7.82399	−	1.15914i	−0.459440	−	0.0680670i
$291$	2.54560	+	2.54560i	0.149226	+	0.149226i
$292$	−19.9502	−	2.27930i	−1.16750	−	0.133386i
$293$		−	30.8617i		−	1.80296i	−0.432823	−	0.901479i	$-0.642482\pi$
$293$		−	30.8617i		−	1.80296i	0.432823	−	0.901479i	$-0.357518\pi$
$294$	7.39712	+	5.93847i	0.431409	+	0.346339i
$295$	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
$298$	−0.866618	+	1.79597i	−0.0502018	+	0.104038i
$299$	−8.40982	+	8.40982i	−0.486352	+	0.486352i
$300$	2.77827	−	9.17062i	0.160404	−	0.529466i
$301$	4.80468	+	16.7553i	0.276937	+	0.965761i
$302$	−11.5964	+	4.04764i	−0.667300	+	0.232916i
$303$	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
$307$			15.9242i			0.908845i	0.890786	+	0.454422i	$0.150154\pi$
$307$			15.9242i			0.908845i	−0.890786	+	0.454422i	$0.849846\pi$
$308$	26.8970	−	4.49271i	1.53260	−	0.255996i
$309$	−3.32140	−	3.32140i	−0.188948	−	0.188948i
$310$	15.9425	−	11.8282i	0.905472	−	0.671797i
$311$	5.40593			0.306542			0.153271	−	0.988184i	$-0.451019\pi$
$311$	5.40593			0.306542			0.153271	+	0.988184i	$0.451019\pi$
$312$	11.7343	+	7.41142i	0.664324	+	0.419589i
$313$	20.5975	+	20.5975i	1.16424	+	1.16424i	0.983538	+	0.180699i	$0.0578360\pi$
$313$	20.5975	+	20.5975i	1.16424	+	1.16424i	0.180699	+	0.983538i	$0.442164\pi$
$314$	−28.0058	+	9.77521i	−1.58046	+	0.551647i
$315$	6.76763	+	10.2901i	0.381313	+	0.579783i
$316$	14.9018	+	18.7461i	0.838293	+	1.05455i
$317$	−32.3130			−1.81488			−0.907439	−	0.420184i	$-0.861965\pi$
$317$	−32.3130			−1.81488			−0.907439	+	0.420184i	$0.861965\pi$
$318$	0.495620	+	1.41994i	0.0277930	+	0.0796266i
$319$			12.8897i			0.721685i
$320$	12.1493	+	13.1299i	0.679165	+	0.733985i
$321$		−	13.0752i		−	0.729784i
$322$	−1.47290	+	8.56433i	−0.0820817	+	0.477271i
$323$			0.207140i			0.0115256i
$324$	−2.47264	+	1.96558i	−0.137369	+	0.109199i
$325$	21.0597	−	14.5625i	1.16818	−	0.807785i
$326$	−22.0485	+	7.69585i	−1.22115	+	0.426234i
$327$	−11.8109	+	11.8109i	−0.653147	+	0.653147i
$328$	−21.0421	−	13.2903i	−1.16186	−	0.733832i
$329$	6.54263	−	11.8035i	0.360707	−	0.650747i
$330$	−15.4473	−	2.28855i	−0.850345	−	0.125980i
$331$	−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	$0.398486\pi$
$332$	25.6765	−	20.4110i	1.40918	−	1.12020i
$333$		−	6.93012i		−	0.379768i
$334$	9.49889	+	4.58353i	0.519756	+	0.250800i
$335$	−5.86823	+	1.83131i	−0.320615	+	0.100055i
$336$	10.1273	−	0.524555i	0.552490	−	0.0286168i
$337$	−7.63386	+	7.63386i	−0.415843	+	0.415843i	−0.883768	−	0.467925i	$-0.845002\pi$
$337$	−7.63386	+	7.63386i	−0.415843	+	0.415843i	0.467925	+	0.883768i	$0.345002\pi$
$338$	6.16262	+	17.6558i	0.335202	+	0.960349i
$339$	6.80207	+	6.80207i	0.369438	+	0.369438i
$340$	0.843193	−	0.161060i	0.0457286	−	0.00873473i
$341$	−22.8755	−	22.8755i	−1.23878	−	1.23878i
$342$	−1.38071	+	2.86137i	−0.0746600	+	0.154725i
$343$	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
$347$		−	2.37523i		−	0.127509i	−0.997966	−	0.0637545i	$-0.979693\pi$
$347$		−	2.37523i		−	0.127509i	0.997966	−	0.0637545i	$-0.0203075\pi$
$348$	−0.544098	+	4.76237i	−0.0291667	+	0.255290i
$349$	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	$0.715518\pi$
$350$	6.42774	−	17.5694i	0.343577	−	0.939125i
$351$	24.9360			1.33099
$352$	18.2648	−	22.7214i	0.973518	−	1.21106i
$353$	8.80022	−	8.80022i	0.468389	−	0.468389i	−0.433004	−	0.901392i	$-0.642546\pi$
$353$	8.80022	−	8.80022i	0.468389	−	0.468389i	0.901392	+	0.433004i	$0.142546\pi$
$354$	−18.0656	−	8.71725i	−0.960175	−	0.463317i
$355$	−0.348091	−	1.11542i	−0.0184748	−	0.0592003i
$356$	−9.99992	−	12.5796i	−0.529995	−	0.666718i
$357$	0.235925	−	0.425629i	0.0124865	−	0.0225267i
$358$	−23.2343	−	11.2113i	−1.22797	−	0.592538i
$359$	−8.43216			−0.445032			−0.222516	−	0.974929i	$-0.571427\pi$
$359$	−8.43216			−0.445032			−0.222516	+	0.974929i	$0.571427\pi$
$360$	12.7211	+	3.39552i	0.670463	+	0.178960i
$361$		−	17.8355i		−	0.938710i
$362$	−0.0599939	+	0.124331i	−0.00315321	+	0.00653469i
$363$			14.9083i			0.782485i
$364$	22.0554	+	15.7420i	1.15602	+	0.825102i
$365$	19.8830	+	10.4248i	1.04072	+	0.545657i
$366$	6.98019	+	3.36818i	0.364861	+	0.176058i
$367$	5.12716	+	5.12716i	0.267635	+	0.267635i	0.828147	−	0.560511i	$-0.189395\pi$
$367$	5.12716	+	5.12716i	0.267635	+	0.267635i	−0.560511	+	0.828147i	$0.689395\pi$
$368$	4.91810	+	7.88147i	0.256374	+	0.410850i
$369$	−18.3182			−0.953605
$370$	−8.45415	+	6.27239i	−0.439510	+	0.326086i
$371$	0.809384	+	2.82256i	0.0420211	+	0.146540i
$372$	−7.48623	−	9.41747i	−0.388143	−	0.488273i
$373$	−0.691599			−0.0358096			−0.0179048	−	0.999840i	$-0.505700\pi$
$373$	−0.691599			−0.0358096			−0.0179048	+	0.999840i	$0.505700\pi$
$374$	−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
$378$	14.8808	−	10.5134i	0.765384	−	0.540753i
$379$	15.5592	+	15.5592i	0.799222	+	0.799222i	0.982973	−	0.183751i	$-0.0588239\pi$
$379$	15.5592	+	15.5592i	0.799222	+	0.799222i	−0.183751	+	0.982973i	$0.558824\pi$
$380$	4.74028	−	0.905453i	0.243171	−	0.0464488i
$381$	5.70612	−	5.70612i	0.292334	−	0.292334i
$382$	−4.00324	−	11.4692i	−0.204823	−	0.586816i
$383$	−7.48417	+	7.48417i	−0.382423	+	0.382423i	−0.871974	−	0.489551i	$-0.837161\pi$
$383$	−7.48417	+	7.48417i	−0.382423	+	0.382423i	0.489551	+	0.871974i	$0.337161\pi$
$384$	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
$387$	13.7153			0.697186
$388$	7.46538	+	0.852915i	0.378997	+	0.0433002i
$389$	−11.9071	−	11.9071i	−0.603715	−	0.603715i	0.337581	−	0.941296i	$-0.390391\pi$
$389$	−11.9071	−	11.9071i	−0.603715	−	0.603715i	−0.941296	+	0.337581i	$0.890391\pi$
$390$	−9.24574	−	12.4618i	−0.468176	−	0.631025i
$391$	0.445813			0.0225457
$392$	19.7988	+	0.0952157i	0.999988	+	0.00480912i
$393$	−1.07988	+	1.07988i	−0.0544728	+	0.0544728i
$394$	−7.46533	+	2.60571i	−0.376098	+	0.131274i
$395$	−7.97607	−	25.5584i	−0.401319	−	1.28598i
$396$	2.43562	−	21.3184i	0.122394	−	1.07129i
$397$		−	6.97405i		−	0.350018i	−0.984567	−	0.175009i	$-0.944005\pi$
$397$		−	6.97405i		−	0.350018i	0.984567	−	0.175009i	$-0.0559954\pi$
$398$	−12.9437	+	4.51788i	−0.648807	+	0.226461i
$399$	1.32633	−	2.39281i	0.0663993	−	0.119790i
$400$	−7.37154	−	18.5919i	−0.368577	−	0.929597i
$401$	16.0305			0.800524			0.400262	−	0.916401i	$-0.368919\pi$
$401$	16.0305			0.800524			0.400262	+	0.916401i	$0.368919\pi$
$402$	1.22772	+	3.51739i	0.0612329	+	0.175431i
$403$		−	32.1461i		−	1.60131i
$404$	36.5299	+	4.17352i	1.81743	+	0.207641i
$405$	3.37120	−	1.05206i	0.167516	−	0.0522771i
$406$	−1.58620	+	9.22311i	−0.0787219	+	0.457735i
$407$	12.1307	+	12.1307i	0.601296	+	0.601296i
$408$	−0.114580	−	0.507467i	−0.00567257	−	0.0251234i
$409$		−	10.9742i		−	0.542641i	−0.962489	−	0.271320i	$-0.912540\pi$
$409$		−	10.9742i		−	0.542641i	0.962489	−	0.271320i	$-0.0874603\pi$
$410$	16.5796	+	22.3466i	0.818807	+	1.10362i
$411$	0.659323	+	0.659323i	0.0325220	+	0.0325220i
$412$	−9.74054	−	1.11285i	−0.479882	−	0.0548262i
$413$	−34.2527	−	18.9861i	−1.68546	−	0.934247i
$414$	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
$418$	−2.59179	−	7.42545i	−0.126769	−	0.363190i
$419$	−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	$0.761673\pi$
$420$	−10.7715	−	3.53848i	−0.525597	−	0.172660i
$421$	−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	$0.378890\pi$
$422$	−15.9261	+	33.0052i	−0.775272	+	1.60667i
$423$	−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
$427$	13.2346	+	7.33588i	0.640465	+	0.355008i
$428$	−16.9821	−	21.3630i	−0.820859	−	1.03262i
$429$	−17.8811	+	17.8811i	−0.863309	+	0.863309i
$430$	−12.4136	−	16.7314i	−0.598635	−	0.806861i
$431$	−22.2366			−1.07110			−0.535549	−	0.844504i	$-0.679895\pi$
$431$	−22.2366			−1.07110			−0.535549	+	0.844504i	$0.679895\pi$
$432$	4.39336	−	18.9761i	0.211375	−	0.912987i
$433$	22.1069	−	22.1069i	1.06239	−	1.06239i	0.0644701	−	0.997920i	$-0.479464\pi$
$433$	22.1069	−	22.1069i	1.06239	−	1.06239i	0.997920	−	0.0644701i	$-0.0205357\pi$
$434$	−13.5533	−	19.1834i	−0.650580	−	0.920834i
$435$	2.48852	−	4.74632i	0.119316	−	0.227569i
$436$	−3.95732	+	34.6375i	−0.189521	+	1.65884i
$437$	2.50628			0.119892
$438$	5.91275	−	12.2536i	0.282522	−	0.585497i
$439$			3.16955i			0.151274i	0.997135	+	0.0756371i	$0.0240991\pi$
$439$			3.16955i			0.151274i	−0.997135	+	0.0756371i	$0.975901\pi$
$440$	−28.2111	+	16.3239i	−1.34491	+	0.778209i
$441$	12.3582	−	7.72257i	0.588484	−	0.367741i
$442$	0.604124	−	1.25198i	0.0287352	−	0.0595507i
$443$	23.1079			1.09789			0.548945	−	0.835859i	$-0.315030\pi$
$443$	23.1079			1.09789			0.548945	+	0.835859i	$0.315030\pi$
$444$	3.96988	+	4.99400i	0.188402	+	0.237005i
$445$	5.35237	+	17.1511i	0.253727	+	0.813038i
$446$	9.18209	+	4.43067i	0.434785	+	0.209798i
$447$	−0.955410	−	0.955410i	−0.0451893	−	0.0451893i
$448$	15.8653	−	14.0104i	0.749565	−	0.661931i
$449$		−	36.3575i		−	1.71582i	−0.513802	−	0.857909i	$-0.671764\pi$
$449$		−	36.3575i		−	1.71582i	0.513802	−	0.857909i	$-0.328236\pi$
$450$	−11.8948	−	8.67239i	−0.560726	−	0.408821i
$451$	32.0646	−	32.0646i	1.50987	−	1.50987i
$452$	19.9482	+	2.27907i	0.938284	+	0.107198i
$453$		−	8.32223i		−	0.391013i
$454$	−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	$-0.159619\pi$
$457$	8.46932	+	8.46932i	0.396178	+	0.396178i	−0.480704	+	0.876883i	$0.659619\pi$
$458$	−8.07564	−	3.89677i	−0.377350	−	0.182084i
$459$	−0.660942	−	0.660942i	−0.0308501	−	0.0308501i
$460$	−1.94874	−	10.2022i	−0.0908605	−	0.475678i
$461$	23.0573	−	23.0573i	1.07388	−	1.07388i	0.0768407	−	0.997043i	$-0.475517\pi$
$461$	23.0573	−	23.0573i	1.07388	−	1.07388i	0.997043	−	0.0768407i	$-0.0244833\pi$
$462$	−3.13172	+	18.2096i	−0.145701	+	0.847189i
$463$	−7.97699	−	7.97699i	−0.370722	−	0.370722i	0.497018	−	0.867740i	$-0.334428\pi$
$463$	−7.97699	−	7.97699i	−0.370722	−	0.370722i	−0.867740	+	0.497018i	$0.834428\pi$
$464$	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
$467$		−	18.6510i		−	0.863066i	−0.902097	−	0.431533i	$-0.857973\pi$
$467$		−	18.6510i		−	0.863066i	0.902097	−	0.431533i	$-0.142027\pi$
$468$	16.6903	−	13.2676i	0.771511	−	0.613297i
$469$	2.00495	+	6.99184i	0.0925800	+	0.322853i
$470$	−2.36392	+	15.9560i	−0.109039	+	0.735997i
$471$		−	20.0985i		−	0.926090i
$472$	−40.8386	+	9.22090i	−1.87975	+	0.424426i
$473$	−24.0076	+	24.0076i	−1.10387	+	1.10387i
$474$	−15.3196	+	5.34718i	−0.703652	+	0.245604i
$475$	−5.30804	−	0.968140i	−0.243550	−	0.0444213i
$476$	−0.167341	−	1.00184i	−0.00767005	−	0.0459191i
$477$	2.31044			0.105788
$478$	18.9201	−	6.60391i	0.865386	−	0.302056i
$479$	34.7955			1.58985			0.794923	−	0.606710i	$-0.207511\pi$
$479$	34.7955			1.58985			0.794923	+	0.606710i	$0.207511\pi$
$480$	−11.1122	+	4.84035i	−0.507202	+	0.220931i
$481$			17.0468i			0.777267i
$482$	−33.4340	+	11.6698i	−1.52287	+	0.531547i
$483$	−5.14987	−	2.85455i	−0.234327	−	0.129887i
$484$	19.3630	+	24.3581i	0.880138	+	1.10719i
$485$	−7.44022	−	3.90095i	−0.337843	−	0.177133i
$486$	−7.51355	−	21.5262i	−0.340821	−	0.976448i
$487$	6.89855	+	6.89855i	0.312603	+	0.312603i	0.845917	−	0.533314i	$-0.179054\pi$
$487$	6.89855	+	6.89855i	0.312603	+	0.312603i	−0.533314	+	0.845917i	$0.679054\pi$
$488$	15.7793	−	3.56278i	0.714294	−	0.161279i
$489$		−	15.8232i		−	0.715549i
$490$	−20.6061	−	8.08628i	−0.930889	−	0.365301i
$491$	−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	$0.964822\pi$
$492$	13.2005	−	10.4934i	0.595123	−	0.473081i
$493$	0.480105			0.0216229
$494$	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
$498$	7.32403	+	20.9832i	0.328197	+	0.940281i
$499$	−17.9727	+	17.9727i	−0.804570	+	0.804570i	−0.983806	−	0.179236i	$-0.942637\pi$
$499$	−17.9727	+	17.9727i	−0.804570	+	0.804570i	0.179236	+	0.983806i	$0.442637\pi$
$500$	0.186285	+	22.3599i	0.00833094	+	0.999965i
$501$	−5.05315	+	5.05315i	−0.225758	+	0.225758i
$502$	−3.81016	+	7.89614i	−0.170056	+	0.352422i
$503$	2.45163	+	2.45163i	0.109313	+	0.109313i	0.759648	−	0.650335i	$-0.225371\pi$
$503$	2.45163	+	2.45163i	0.109313	+	0.109313i	−0.650335	+	0.759648i	$0.725371\pi$
$504$	4.36622	−	14.9545i	0.194487	−	0.666125i
$505$	−36.4068	−	19.0883i	−1.62008	−	0.849419i
$506$	−15.9812	+	5.57812i	−0.710453	+	0.247978i
$507$	−12.6708			−0.562728
$508$	1.91187	−	16.7341i	0.0848253	−	0.742458i
$509$	−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	$0.824183\pi$
$510$	−0.0852419	+	0.575368i	−0.00377457	+	0.0254777i
$511$	12.8779	−	23.2329i	0.569687	−	1.02776i
$512$	2.69088	−	22.4668i	0.118921	−	0.992904i
$513$	−3.71570	−	3.71570i	−0.164052	−	0.164052i
$514$	−10.5019	+	21.7641i	−0.463220	+	0.959975i
$515$	9.70771	+	5.08981i	0.427773	+	0.224284i
$516$	−9.88351	+	7.85671i	−0.435097	+	0.345872i
$517$	26.2869			1.15610
$518$	7.18720	+	10.1728i	0.315788	+	0.446967i
$519$	−11.5137			−0.505396
$520$	−31.2916	−	8.35234i	−1.37223	−	0.366274i
$521$	−37.0562			−1.62346			−0.811730	−	0.584033i	$-0.801474\pi$
$521$	−37.0562			−1.62346			−0.811730	+	0.584033i	$0.801474\pi$
$522$	6.63202	+	3.20017i	0.290275	+	0.140068i
$523$			9.08448i			0.397237i	0.980077	+	0.198618i	$0.0636454\pi$
$523$			9.08448i			0.397237i	−0.980077	+	0.198618i	$0.936355\pi$
$524$	−0.361820	+	3.16693i	−0.0158062	+	0.138348i
$525$	9.80422	+	8.03497i	0.427891	+	0.350675i
$526$	11.7188	+	5.65473i	0.510965	+	0.246558i
$527$	−0.852049	+	0.852049i	−0.0371159	+	0.0371159i
$528$	10.4570	+	16.7577i	0.455081	+	0.729287i
$529$			17.6059i			0.765475i
$530$	−2.09115	−	2.81853i	−0.0908339	−	0.122429i
$531$	−21.7896	+	21.7896i	−0.945589	+	0.945589i
$532$	−0.940760	−	5.63215i	−0.0407871	−	0.244185i
$533$	45.0592			1.95173
$534$	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
$538$	4.04780	−	8.38865i	0.174513	−	0.361660i
$539$	−8.11430	+	35.1499i	−0.349508	+	1.51401i
$540$	−12.2362	+	18.0144i	−0.526560	+	0.775216i
$541$	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	$0.673130\pi$
$542$	−23.4612	+	8.18894i	−1.00775	+	0.351745i
$543$	−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
$546$	−14.9951	+	10.5942i	−0.641731	+	0.453391i
$547$	−29.4501			−1.25919			−0.629597	−	0.776922i	$-0.716780\pi$
$547$	−29.4501			−1.25919			−0.629597	+	0.776922i	$0.716780\pi$
$548$	1.93357	+	0.220910i	0.0825982	+	0.00943679i
$549$	8.41908	−	8.41908i	0.359318	−	0.359318i
$550$	36.0014	−	5.64057i	1.53510	−	0.240515i
$551$	2.69907			0.114984
$552$	−6.14007	+	1.38636i	−0.261339	+	0.0590073i
$553$	−30.4522	+	8.73233i	−1.29496	+	0.371337i
$554$	31.7098	−	11.0680i	1.34722	−	0.470236i
$555$	−2.12484	−	6.80881i	−0.0901945	−	0.289018i
$556$	1.18599	−	10.3807i	0.0502971	−	0.440239i
$557$	−10.4320			−0.442017			−0.221008	−	0.975272i	$-0.570935\pi$
$557$	−10.4320			−0.442017			−0.221008	+	0.975272i	$0.570935\pi$
$558$	−17.4493	+	6.09054i	−0.738688	+	0.257833i
$559$	−33.7370			−1.42692
$560$	−22.1950	+	8.20873i	−0.937909	+	0.346882i
$561$	0.947896			0.0400202
$562$	−10.3395	+	3.60891i	−0.436145	+	0.152233i
$563$	26.6324			1.12242			0.561210	−	0.827673i	$-0.310336\pi$
$563$	26.6324			1.12242			0.561210	+	0.827673i	$0.310336\pi$
$564$	9.71226	+	1.10962i	0.408960	+	0.0467234i
$565$	−19.8809	−	10.4237i	−0.836398	−	0.438529i
$566$	−2.23426	+	0.779851i	−0.0939130	+	0.0327796i
$567$	−1.15181	−	4.01669i	−0.0483714	−	0.168685i
$568$	−0.789270	+	1.24963i	−0.0331170	+	0.0524333i
$569$	31.2336			1.30938			0.654690	−	0.755897i	$-0.272799\pi$
$569$	31.2336			1.30938			0.654690	+	0.755897i	$0.272799\pi$
$570$	−0.479215	+	3.23462i	−0.0200721	+	0.135483i
$571$	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	$-0.0154204\pi$
$572$	−5.99116	+	52.4393i	−0.250503	+	2.19260i
$573$	8.23093			0.343852
$574$	26.8894	−	18.9977i	1.12234	−	0.792948i
$575$	−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	0.851257	−	0.524749i	$-0.175841\pi$
$577$	7.84300	+	7.84300i	0.326508	+	0.326508i	−0.524749	+	0.851257i	$0.675841\pi$
$578$	22.6495	−	7.90561i	0.942094	−	0.328830i
$579$	−13.0779	−	13.0779i	−0.543500	−	0.543500i
$580$	−2.09864	−	10.9869i	−0.0871413	−	0.456207i
$581$	11.9607	+	41.7103i	0.496212	+	1.73044i
$582$	−2.21256	+	4.58529i	−0.0917134	+	0.190066i
$583$	−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
$587$	−7.10175			−0.293121			−0.146560	−	0.989202i	$-0.546820\pi$
$587$	−7.10175			−0.293121			−0.146560	+	0.989202i	$0.546820\pi$
$588$	−4.48174	+	12.6443i	−0.184824	+	0.521444i
$589$	−4.79007	+	4.79007i	−0.197371	+	0.197371i
$590$	46.3030	+	6.85988i	1.90626	+	0.282417i
$591$		−	5.35752i		−	0.220379i
$592$	12.9724	+	3.00339i	0.533164	+	0.123439i
$593$	4.12969	−	4.12969i	0.169586	−	0.169586i	−0.617211	−	0.786797i	$-0.711738\pi$
$593$	4.12969	−	4.12969i	0.169586	−	0.169586i	0.786797	+	0.617211i	$0.211738\pi$
$594$	31.9630	+	15.4232i	1.31146	+	0.632822i
$595$	−0.229661	+	1.11214i	−0.00941518	+	0.0455933i
$596$	−2.80190	−	0.320115i	−0.114770	−	0.0131124i
$597$		−	9.28906i		−	0.380176i
$598$	−15.1483	−	7.30955i	−0.619459	−	0.298910i
$599$	26.3704			1.07746			0.538732	−	0.842477i	$-0.318904\pi$
$599$	26.3704			1.07746			0.538732	+	0.842477i	$0.318904\pi$
$600$	13.5396	−	0.564344i	0.552750	−	0.0230392i
$601$	−27.5868			−1.12529			−0.562644	−	0.826699i	$-0.690216\pi$
$601$	−27.5868			−1.12529			−0.562644	+	0.826699i	$0.690216\pi$
$602$	−20.1328	+	14.2240i	−0.820551	+	0.579729i
$603$	5.72325			0.233069
$604$	−10.8090	−	13.5974i	−0.439810	−	0.553269i
$605$	−10.3639	−	33.2099i	−0.421352	−	1.35017i
$606$	−10.8266	+	22.4369i	−0.439800	+	0.911438i
$607$	−14.3333	−	14.3333i	−0.581771	−	0.581771i	0.353619	−	0.935390i	$-0.384951\pi$
$607$	−14.3333	−	14.3333i	−0.581771	−	0.581771i	−0.935390	+	0.353619i	$0.884951\pi$
$608$	−4.75780	−	3.82460i	−0.192954	−	0.155108i
$609$	−5.54600	−	3.07413i	−0.224735	−	0.124570i
$610$	−17.8906	−	2.65052i	−0.724368	−	0.107317i
$611$	18.4700	+	18.4700i	0.747217	+	0.747217i
$612$	−0.794051	−	0.0907198i	−0.0320976	−	0.00366713i
$613$	−17.1490			−0.692640			−0.346320	−	0.938116i	$-0.612569\pi$
$613$	−17.1490			−0.692640			−0.346320	+	0.938116i	$0.612569\pi$
$614$	−21.2623	+	7.42144i	−0.858077	+	0.299505i
$615$	−17.9975	+	5.61652i	−0.725729	+	0.226480i
$616$	18.5340	+	33.8195i	0.746756	+	1.36263i
$617$	−9.39842	−	9.39842i	−0.378366	−	0.378366i	0.492146	−	0.870513i	$-0.336213\pi$
$617$	−9.39842	−	9.39842i	−0.378366	−	0.378366i	−0.870513	+	0.492146i	$0.836213\pi$
$618$	2.88686	−	5.98271i	0.116126	−	0.240660i
$619$	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	$0.156203\pi$
$620$	23.2231	+	15.7742i	0.932663	+	0.633506i
$621$	−7.99703	+	7.99703i	−0.320910	+	0.320910i
$622$	2.51941	+	7.21808i	0.101019	+	0.289419i
$623$	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
$627$	5.32890			0.212816
$628$	−26.1040	−	32.8381i	−1.04166	−	1.31038i
$629$	0.451834	−	0.451834i	0.0180158	−	0.0180158i
$630$	−10.5855	+	13.8319i	−0.421736	+	0.551077i
$631$			16.0215i			0.637807i	0.947787	+	0.318903i	$0.103315\pi$
$631$			16.0215i			0.637807i	−0.947787	+	0.318903i	$0.896685\pi$
$632$	−18.0851	+	28.6337i	−0.719387	+	1.13899i
$633$	−17.5579	−	17.5579i	−0.697863	−	0.697863i
$634$	−15.0593	−	43.1448i	−0.598083	−	1.71350i
$635$	−8.74424	+	16.6777i	−0.347005	+	0.661836i
$636$	−1.66495	+	1.32352i	−0.0660196	+	0.0524810i
$637$	−30.3988	+	18.9961i	−1.20444	+	0.752651i
$638$	−17.2105	+	6.00720i	−0.681372	+	0.237827i
$639$			1.08786i			0.0430352i
$640$	−11.8692	+	22.3411i	−0.469170	+	0.883108i
$641$	−47.0254			−1.85739			−0.928695	−	0.370845i	$-0.879068\pi$
$641$	−47.0254			−1.85739			−0.928695	+	0.370845i	$0.879068\pi$
$642$	17.4581	−	6.09363i	0.689018	−	0.240496i
$643$	−39.8145			−1.57013			−0.785066	−	0.619413i	$-0.787371\pi$
$643$	−39.8145			−1.57013			−0.785066	+	0.619413i	$0.787371\pi$
$644$	−12.1217	+	2.02473i	−0.477660	+	0.0797855i
$645$	13.4752	−	4.20523i	0.530585	−	0.165581i
$646$	−0.276577	+	0.0965369i	−0.0108818	+	0.00379819i
$647$	12.0251	−	12.0251i	0.472757	−	0.472757i	−0.430049	−	0.902806i	$-0.641504\pi$
$647$	12.0251	−	12.0251i	0.472757	−	0.472757i	0.902806	+	0.430049i	$0.141504\pi$
$648$	−3.77683	−	2.38546i	−0.148368	−	0.0937096i
$649$		−	76.2823i		−	2.99434i
$650$	29.2589	+	21.3325i	1.14763	+	0.836728i
$651$	15.2983	−	4.38686i	0.599586	−	0.171935i
$652$	−20.5512	−	25.8529i	−0.804848	−	1.01248i
$653$		−	23.2407i		−	0.909477i	−0.890625	−	0.454738i	$-0.849733\pi$
$653$		−	23.2407i		−	0.909477i	0.890625	−	0.454738i	$-0.150267\pi$
$654$	−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
$658$	18.8094	+	3.23486i	0.733265	+	0.126108i
$659$	−2.20822	+	2.20822i	−0.0860202	+	0.0860202i	−0.748808	−	0.662787i	$-0.769373\pi$
$659$	−2.20822	+	2.20822i	−0.0860202	+	0.0860202i	0.662787	+	0.748808i	$0.269373\pi$
$660$	−4.14345	−	21.6920i	−0.161284	−	0.844361i
$661$	24.8842	+	24.8842i	0.967882	+	0.967882i	0.999500	−	0.0316181i	$-0.0100660\pi$
$661$	24.8842	+	24.8842i	0.967882	+	0.967882i	−0.0316181	+	0.999500i	$0.510066\pi$
$662$	−20.8437	−	10.0578i	−0.810114	−	0.390907i
$663$	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
$667$		−	5.80900i		−	0.224925i
$668$	−1.69308	+	14.8192i	−0.0655074	+	0.573372i
$669$	−4.88463	+	4.88463i	−0.188851	+	0.188851i
$670$	−5.18006	−	6.98187i	−0.200123	−	0.269733i
$671$			29.4740i			1.13783i
$672$	5.42019	+	13.2777i	0.209088	+	0.512197i
$673$	7.59933	+	7.59933i	0.292933	+	0.292933i	0.838238	−	0.545305i	$-0.183586\pi$
$673$	7.59933	+	7.59933i	0.292933	+	0.292933i	−0.545305	+	0.838238i	$0.683586\pi$
$674$	−13.7506	−	6.63511i	−0.529652	−	0.255575i
$675$	20.0260	−	13.8478i	0.770802	−	0.533000i
$676$	−20.7022	+	16.4568i	−0.796240	+	0.632955i
$677$	−19.7429			−0.758780			−0.379390	−	0.925237i	$-0.623866\pi$
$677$	−19.7429			−0.758780			−0.379390	+	0.925237i	$0.623866\pi$
$678$	−5.91215	+	12.2523i	−0.227055	+	0.470547i
$679$	−4.81893	+	8.69378i	−0.184934	+	0.333637i
$680$	0.608017	+	1.05078i	0.0233164	+	0.0402957i
$681$		−	11.3729i		−	0.435811i
$682$	19.8827	−	41.2049i	0.761349	−	1.57782i
$683$	−35.4694			−1.35720			−0.678599	−	0.734509i	$-0.737413\pi$
$683$	−35.4694			−1.35720			−0.678599	+	0.734509i	$0.737413\pi$
$684$	−4.46401	−	0.510011i	−0.170686	−	0.0195007i
$685$	−1.92706	−	1.01037i	−0.0736290	−	0.0386042i
$686$	−10.1316	+	24.1526i	−0.386828	+	0.922152i
$687$	4.29602	−	4.29602i	0.163904	−	0.163904i
$688$	−5.94395	+	25.6735i	−0.226611	+	0.978793i
$689$	−5.68324			−0.216514
$690$	6.96163	+	1.03138i	0.265025	+	0.0392639i
$691$	30.5813	−	30.5813i	1.16337	−	1.16337i	0.179636	−	0.983733i	$-0.442508\pi$
$691$	30.5813	−	30.5813i	1.16337	−	1.16337i	0.983733	−	0.179636i	$-0.0574919\pi$
$692$	−18.8118	+	14.9541i	−0.715117	+	0.568469i
$693$	24.8263	+	13.7611i	0.943073	+	0.522742i
$694$	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
$698$	−2.48268	+	5.14510i	−0.0939710	+	0.194745i
$699$	10.6617	−	10.6617i	0.403264	−	0.403264i
$700$	26.4546	+	0.394256i	0.999889	+	0.0149015i
$701$	−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	$0.952551\pi$
$702$	11.6214	+	33.2950i	0.438620	+	1.25664i
$703$	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
$707$	−23.5802	+	42.5408i	−0.886826	+	1.59991i
$708$	3.22002	−	28.1841i	0.121016	−	1.05922i
$709$	17.7163	+	17.7163i	0.665351	+	0.665351i	0.956636	−	0.291285i	$-0.0940829\pi$
$709$	17.7163	+	17.7163i	0.665351	+	0.665351i	−0.291285	+	0.956636i	$0.594083\pi$
$710$	1.32710	−	0.984613i	0.0498051	−	0.0369519i
$711$			24.9270i			0.934835i
$712$	12.1361	−	19.2147i	0.454819	−	0.720102i
$713$	10.3093	+	10.3093i	0.386087	+	0.386087i
$714$	0.678258	+	0.116648i	0.0253832	+	0.00436543i
$715$	27.4016	−	52.2625i	1.02476	−	1.95451i
$716$	4.14129	−	36.2478i	0.154767	−	1.35465i
$717$			13.5781i			0.507083i
$718$	−3.92977	−	11.2587i	−0.146658	−	0.420173i
$719$	−11.2953			−0.421243			−0.210621	−	0.977568i	$-0.567549\pi$
$719$	−11.2953			−0.421243			−0.210621	+	0.977568i	$0.567549\pi$
$720$	1.39489	+	18.5679i	0.0519846	+	0.691986i
$721$	6.28756	−	11.3433i	0.234161	−	0.422447i
$722$	23.8142	−	8.31216i	0.886274	−	0.309347i
$723$		−	23.9940i		−	0.892347i
$724$	−0.193969	−	0.0221608i	−0.00720878	−	0.000823599i
$725$	−2.24393	+	12.3029i	−0.0833376	+	0.456917i
$726$	−19.9059	+	6.94798i	−0.738776	+	0.257864i
$727$	7.54399	−	7.54399i	0.279791	−	0.279791i	−0.553235	−	0.833026i	$-0.686607\pi$
$727$	7.54399	−	7.54399i	0.279791	−	0.279791i	0.833026	+	0.553235i	$0.186607\pi$
$728$	−10.7401	+	36.7852i	−0.398053	+	1.36335i
$729$	10.7103			0.396678
$730$	−4.65293	+	31.4065i	−0.172213	+	1.16241i
$731$	0.894215	+	0.894215i	0.0330737	+	0.0330737i
$732$	−1.24415	+	10.8898i	−0.0459852	+	0.402498i
$733$	−47.4634			−1.75310			−0.876551	−	0.481309i	$-0.840161\pi$
$733$	−47.4634			−1.75310			−0.876551	+	0.481309i	$0.840161\pi$
$734$	−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
$738$	−8.53711	−	24.4587i	−0.314255	−	0.900337i
$739$	−5.14980	+	5.14980i	−0.189439	+	0.189439i	−0.795453	−	0.606015i	$-0.792767\pi$
$739$	−5.14980	+	5.14980i	−0.189439	+	0.189439i	0.606015	+	0.795453i	$0.292767\pi$
$740$	−12.3150	−	8.36489i	−0.452709	−	0.307500i
$741$	3.74425	+	3.74425i	0.137549	+	0.137549i
$742$	−3.39151	+	2.39615i	−0.124506	+	0.0879653i
$743$	10.7389	−	10.7389i	0.393973	−	0.393973i	−0.482128	−	0.876101i	$-0.660136\pi$
$743$	10.7389	−	10.7389i	0.393973	−	0.393973i	0.876101	+	0.482128i	$0.160136\pi$
$744$	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
$747$	34.1425			1.24921
$748$	1.54873	−	1.23113i	0.0566271	−	0.0450146i
$749$	34.7032	−	9.95134i	1.26803	−	0.363614i
$750$	−14.3456	−	4.87353i	−0.523828	−	0.177956i
$751$	34.3640			1.25396			0.626981	−	0.779035i	$-0.284290\pi$
$751$	34.3640			1.25396			0.626981	+	0.779035i	$0.284290\pi$
$752$	17.3096	−	10.8014i	0.631218	−	0.393885i
$753$	−4.20054	−	4.20054i	−0.153076	−	0.153076i
$754$	−16.3135	−	7.87182i	−0.594103	−	0.286675i
$755$	5.78540	+	18.5386i	0.210552	+	0.674690i
$756$	20.9728	+	14.9693i	0.762774	+	0.544427i
$757$		−	16.0542i		−	0.583499i	−0.956495	−	0.291749i	$-0.905763\pi$
$757$		−	16.0542i		−	0.583499i	0.956495	−	0.291749i	$-0.0942373\pi$
$758$	−13.5236	+	28.0262i	−0.491198	+	1.01796i
$759$		−	11.4690i		−	0.416298i
$760$	3.41816	+	5.90731i	0.123990	+	0.214281i
$761$	52.0169			1.88561			0.942805	−	0.333344i	$-0.108177\pi$
$761$	52.0169			1.88561			0.942805	+	0.333344i	$0.108177\pi$
$762$	10.2782	+	4.95959i	0.372341	+	0.179667i
$763$	−40.3370	−	22.3587i	−1.46030	−	0.809438i
$764$	13.4482	−	10.6904i	0.486538	−	0.386764i
$765$	0.791374	+	0.414923i	0.0286122	+	0.0150016i
$766$	−13.4809	−	6.50501i	−0.487086	−	0.235036i
$767$	53.5983	−	53.5983i	1.93532	−	1.93532i
$768$	13.7716	+	6.73798i	0.496939	+	0.243136i
$769$	48.9150			1.76392			0.881961	−	0.471323i	$-0.156223\pi$
$769$	48.9150			1.76392			0.881961	+	0.471323i	$0.156223\pi$
$770$	−5.68264	−	42.7410i	−0.204788	−	1.54028i
$771$	−11.5779	−	11.5779i	−0.416969	−	0.416969i
$772$	−38.3532	−	4.38183i	−1.38036	−	0.157705i
$773$			0.508648i			0.0182948i	0.999958	+	0.00914739i	$0.00291175\pi$
$773$			0.508648i			0.0182948i	−0.999958	+	0.00914739i	$0.997088\pi$
$774$	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
$778$	10.3493	−	21.4478i	0.371041	−	0.768943i
$779$	−6.71424	−	6.71424i	−0.240563	−	0.240563i
$780$	12.3302	−	18.1528i	0.441491	−	0.649975i
$781$	−1.90423	−	1.90423i	−0.0681386	−	0.0681386i
$782$	0.207769	+	0.595256i	0.00742982	+	0.0212863i
$783$	−8.61217	+	8.61217i	−0.307774	+	0.307774i
$784$	9.10000	+	26.4800i	0.325000	+	0.945714i
$785$	13.9719	+	44.7715i	0.498680	+	1.59796i
$786$	−1.94515	−	0.938600i	−0.0693812	−	0.0334788i
$787$		−	35.5784i		−	1.26823i	−0.773238	−	0.634116i	$-0.781364\pi$
$787$		−	35.5784i		−	1.26823i	0.773238	−	0.634116i	$-0.218636\pi$
$788$	−6.95838	−	8.75344i	−0.247882	−	0.311828i
$789$	−6.23410	+	6.23410i	−0.221940	+	0.221940i
$790$	30.4088	−	22.5612i	1.08190	−	0.802690i
$791$	−12.8766	+	23.2306i	−0.457841	+	0.825984i
$792$	29.5998	−	6.68330i	1.05178	−	0.237481i
$793$	−20.7094	+	20.7094i	−0.735411	+	0.735411i
$794$	9.31186	−	3.25023i	0.330466	−	0.115346i
$795$	2.26999	−	0.708402i	0.0805084	−	0.0251244i
$796$	−12.0647	−	15.1770i	−0.427621	−	0.537935i
$797$		−	20.7887i		−	0.736373i	−0.929752	−	0.368187i	$-0.879979\pi$
$797$		−	20.7887i		−	0.736373i	0.929752	−	0.368187i	$-0.120021\pi$
$798$	3.81304	+	0.655772i	0.134980	+	0.0232141i
$799$		−	0.979114i		−	0.0346386i
$800$	21.3888	−	18.5073i	0.756207	−	0.654332i
$801$		−	16.7273i		−	0.591031i
$802$	7.47094	+	21.4041i	0.263808	+	0.755806i
$803$	51.7409			1.82590
$804$	−4.12430	+	3.27853i	−0.145453	+	0.115625i
$805$	13.4563	+	2.77877i	0.474271	+	0.0979387i
$806$	42.9220	−	14.9816i	1.51186	−	0.527704i
$807$	4.46253	+	4.46253i	0.157089	+	0.157089i
$808$	11.4521	+	50.7204i	0.402883	+	1.78434i
$809$	30.4688			1.07123			0.535613	−	0.844463i	$-0.320080\pi$
$809$	30.4688			1.07123			0.535613	+	0.844463i	$0.320080\pi$
$810$	2.97586	+	4.01097i	0.104561	+	0.140931i
$811$	14.9456	+	14.9456i	0.524810	+	0.524810i	0.919020	−	0.394210i	$-0.128982\pi$
$811$	14.9456	+	14.9456i	0.524810	+	0.524810i	−0.394210	+	0.919020i	$0.628982\pi$
$812$	−13.0541	+	2.18047i	−0.458108	+	0.0765196i
$813$		−	16.8370i		−	0.590500i
$814$	−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
$818$	14.6530	−	5.11450i	0.512329	−	0.178824i
$819$	7.77472	+	27.1127i	0.271671	+	0.947395i
$820$	−22.1106	+	32.5519i	−0.772137	+	1.13676i
$821$	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	$0.215983\pi$
$822$	−0.573064	+	1.18761i	−0.0199879	+	0.0414228i
$823$	11.6315	−	11.6315i	0.405447	−	0.405447i	−0.474700	−	0.880148i	$-0.657444\pi$
$823$	11.6315	−	11.6315i	0.405447	−	0.405447i	0.880148	+	0.474700i	$0.157444\pi$
$824$	−3.05365	−	13.5244i	−0.106379	−	0.471144i
$825$	−4.43031	+	24.2902i	−0.154244	+	0.845676i
$826$	9.38727	−	54.5831i	0.326625	−	1.89919i
$827$			48.0898i			1.67225i	0.548542	+	0.836123i	$0.315183\pi$
$827$			48.0898i			1.67225i	−0.548542	+	0.836123i	$0.684817\pi$
$828$	−1.09766	+	9.60757i	−0.0381463	+	0.333886i
$829$	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	$0.736187\pi$
$830$	−30.9020	−	41.6509i	−1.07262	−	1.44572i
$831$			22.7566i			0.789419i
$832$	17.6023	+	36.9925i	0.610251	+	1.28248i
$833$	1.30923	+	0.302235i	0.0453623	+	0.0104718i
$834$	6.37589	+	3.07658i	0.220779	+	0.106533i
$835$	7.74361	−	14.7692i	0.267979	−	0.511111i
$836$	8.70668	−	6.92120i	0.301127	−	0.239375i
$837$		−	30.5683i		−	1.05659i
$838$	0.922471	−	1.91172i	0.0318662	−	0.0660394i
$839$		−	16.3187i		−	0.563384i	−0.959505	−	0.281692i	$-0.909104\pi$
$839$		−	16.3187i		−	0.563384i	0.959505	−	0.281692i	$-0.0908957\pi$
$840$	−0.295395	−	16.0314i	−0.0101921	−	0.553136i
$841$			22.7442i			0.784281i
$842$	−20.5906	−	9.93565i	−0.709599	−	0.342405i
$843$		−	7.42017i		−	0.255564i
$844$	−51.4914	−	5.88286i	−1.77241	−	0.202496i
$845$	28.2254	−	8.80838i	0.970985	−	0.303017i
$846$	6.52634	−	13.5252i	0.224380	−	0.465004i
$847$	−39.5688	+	11.3466i	−1.35960	+	0.389872i
$848$	−1.00130	+	4.32489i	−0.0343848	+	0.148517i
$849$		−	1.60343i		−	0.0550295i
$850$	−0.210095	−	1.34095i	−0.00720621	−	0.0459942i
$851$	−5.46694	−	5.46694i	−0.187404	−	0.187404i
$852$	−0.623175	−	0.783937i	−0.0213496	−	0.0268572i
$853$			52.6306i			1.80204i	0.433779	+	0.901019i	$0.357180\pi$
$853$			52.6306i			1.80204i	−0.433779	+	0.901019i	$0.642820\pi$
$854$	−3.62706	+	21.0899i	−0.124115	+	0.721680i
$855$	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	$-0.868860\pi$
$857$	−15.1026	+	15.1026i	−0.515894	+	0.515894i	0.400432	+	0.916326i	$0.368860\pi$
$858$	−32.2086	−	15.5417i	−1.09958	−	0.530586i
$859$	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	$0.226423\pi$
$860$	16.5548	−	24.3724i	0.564514	−	0.831092i
$861$	6.14906	+	21.4436i	0.209560	+	0.730795i
$862$	−10.3633	−	29.6906i	−0.352975	−	1.01127i
$863$	24.2963	+	24.2963i	0.827057	+	0.827057i	0.987109	−	0.160051i	$-0.0511660\pi$
$863$	24.2963	+	24.2963i	0.827057	+	0.827057i	−0.160051	+	0.987109i	$0.551166\pi$
$864$	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
$867$			16.2545i			0.552031i
$868$	19.2975	−	27.0370i	0.655001	−	0.917695i
$869$	−43.6329	−	43.6329i	−1.48015	−	1.48015i
$870$	7.49713	+	1.11071i	0.254176	+	0.0376567i
$871$	−14.0781			−0.477019
$872$	−48.0929	+	10.8588i	−1.62863	+	0.367726i
$873$	5.53049	+	5.53049i	0.187179	+	0.187179i
$874$	1.16804	+	3.34642i	0.0395096	+	0.113194i
$875$	−27.4256	−	11.0831i	−0.927155	−	0.374678i
$876$	19.1168	+	2.18408i	0.645895	+	0.0737931i
$877$	30.6239			1.03409			0.517047	−	0.855957i	$-0.327031\pi$
$877$	30.6239			1.03409			0.517047	+	0.855957i	$0.327031\pi$
$878$	−4.23203	+	1.47716i	−0.142824	+	0.0498516i
$879$			29.5724i			0.997451i
$880$	−34.9435	−	30.0602i	−1.17795	−	1.01333i
$881$		−	32.5310i		−	1.09600i	−0.836480	−	0.547998i	$-0.815390\pi$
$881$		−	32.5310i		−	1.09600i	0.836480	−	0.547998i	$-0.184610\pi$
$882$	16.0708	+	12.9018i	0.541131	+	0.434425i
$883$		−	48.1773i		−	1.62130i	−0.585534	−	0.810648i	$-0.699115\pi$
$883$		−	48.1773i		−	1.62130i	0.585534	−	0.810648i	$-0.300885\pi$
$884$	1.95322	+	0.223154i	0.0656938	+	0.00750547i
$885$	−14.7273	+	28.0891i	−0.495052	+	0.944204i
$886$	10.7694	+	30.8540i	0.361803	+	1.03656i
$887$	7.44138	−	7.44138i	0.249857	−	0.249857i	−0.571055	−	0.820912i	$-0.693466\pi$
$887$	7.44138	−	7.44138i	0.249857	−	0.249857i	0.820912	+	0.571055i	$0.193466\pi$
$888$	−4.81791	+	7.62808i	−0.161679	+	0.255982i
$889$	19.4877	+	10.8020i	0.653596	+	0.362286i
$890$	−20.4059	+	15.1397i	−0.684007	+	0.507485i
$891$	5.75526	−	5.75526i	0.192808	−	0.192808i
$892$	−1.63662	+	14.3250i	−0.0547980	+	0.479635i
$893$		−	5.50440i		−	0.184198i
$894$	0.830413	−	1.72094i	0.0277732	−	0.0575570i
$895$	−18.9409	+	36.1256i	−0.633125	+	1.20755i
$896$	26.1009	+	14.6541i	0.871970	+	0.489559i
$897$	8.05848	−	8.05848i	0.269065	−	0.269065i
$898$	48.5451	−	16.9443i	1.61997	−	0.565438i
$899$	11.1023	+	11.1023i	0.370283	+	0.370283i
$900$	6.03599	−	19.9238i	0.201200	−	0.664128i
$901$	0.150637	+	0.150637i	0.00501845	+	0.00501845i
$902$	57.7568	+	27.8696i	1.92309	+	0.927956i
$903$	−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
$907$			13.9568i			0.463428i	0.972784	+	0.231714i	$0.0744334\pi$
$907$			13.9568i			0.463428i	−0.972784	+	0.231714i	$0.925567\pi$
$908$	−14.7712	−	18.5817i	−0.490199	−	0.616657i
$909$	27.0621	+	27.0621i	0.897592	+	0.897592i
$910$	26.0383	−	34.0239i	0.863163	−	1.12788i
$911$	−33.4838			−1.10937			−0.554683	−	0.832062i	$-0.687161\pi$
$911$	−33.4838			−1.10937			−0.554683	+	0.832062i	$0.687161\pi$
$912$	3.50902	−	2.18966i	0.116195	−	0.0725068i
$913$	−59.7640	+	59.7640i	−1.97790	+	1.97790i
$914$	−7.36128	+	15.2555i	−0.243489	+	0.504606i
$915$	5.69034	−	10.8531i	0.188117	−	0.358792i
$916$	1.43940	−	12.5988i	0.0475592	−	0.416276i
$917$	−3.68804	−	2.04427i	−0.121790	−	0.0675076i
$918$	0.574471	−	1.19053i	0.0189604	−	0.0392934i
$919$	−29.4411			−0.971174			−0.485587	−	0.874188i	$-0.661394\pi$
$919$	−29.4411			−0.971174			−0.485587	+	0.874188i	$0.661394\pi$
$920$	12.7139	−	7.35667i	0.419164	−	0.242542i
$921$		−	15.2590i		−	0.502801i
$922$	41.5322	+	20.0407i	1.36779	+	0.660004i
$923$		−	2.67594i		−	0.0880795i
$924$	−25.7733	+	4.30502i	−0.847880	+	0.141625i
$925$	9.46661	+	13.6902i	0.311260	+	0.450131i
$926$	6.93335	−	14.3686i	0.227844	−	0.472183i
$927$	−7.21598	−	7.21598i	−0.237004	−	0.237004i
$928$	−8.86457	+	11.0275i	−0.290994	+	0.361996i
$929$	28.7552			0.943426			0.471713	−	0.881752i	$-0.343636\pi$
$929$	28.7552			0.943426			0.471713	+	0.881752i	$0.343636\pi$
$930$	−15.2765	+	11.3341i	−0.500935	+	0.371658i
$931$	7.36028	+	1.69911i	0.241224	+	0.0556861i
$932$	3.57227	−	31.2673i	0.117014	−	1.02419i
$933$	−5.18009			−0.169588
$934$	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	$-0.909089\pi$
$937$	−20.7464	+	20.7464i	−0.677755	+	0.677755i	0.281737	+	0.959492i	$0.409089\pi$
$938$	−8.40122	+	5.93556i	−0.274309	+	0.193803i
$939$	−19.7370	−	19.7370i	−0.644091	−	0.644091i
$940$	−22.4064	+	4.27991i	−0.730818	+	0.139595i
$941$	−23.4129	+	23.4129i	−0.763240	+	0.763240i	−0.976907	−	0.213667i	$-0.931459\pi$
$941$	−23.4129	+	23.4129i	−0.763240	+	0.763240i	0.213667	+	0.976907i	$0.431459\pi$
$942$	26.8358	−	9.36683i	0.874358	−	0.305188i
$943$	−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
$947$	−10.5391			−0.342476			−0.171238	−	0.985230i	$-0.554777\pi$
$947$	−10.5391			−0.342476			−0.171238	+	0.985230i	$0.554777\pi$
$948$	−14.2793	−	17.9629i	−0.463769	−	0.583408i
$949$	36.3548	+	36.3548i	1.18013	+	1.18013i
$950$	−1.18112	−	7.53858i	−0.0383206	−	0.244584i
$951$	30.9630			1.00405
$952$	1.25968	−	0.690338i	0.0408265	−	0.0223740i
$953$	21.2956	−	21.2956i	0.689832	−	0.689832i	−0.272362	−	0.962195i	$-0.587805\pi$
$953$	21.2956	−	21.2956i	0.689832	−	0.689832i	0.962195	+	0.272362i	$0.0878049\pi$
$954$	1.07677	+	3.08493i	0.0348617	+	0.0998784i
$955$	−18.3353	+	5.72192i	−0.593315	+	0.185157i
$956$	17.6353	+	22.1847i	0.570366	+	0.717504i
$957$		−	12.3512i		−	0.399258i
$958$	16.2163	+	46.4595i	0.523925	+	1.50104i
$959$	−1.24813	+	2.25174i	−0.0403042	+	0.0727123i
$960$	−11.6417	−	12.5814i	−0.375735	−	0.406063i
$961$	−8.40690			−0.271190
$962$	−22.7612	+	7.94460i	−0.733849	+	0.256144i
$963$		−	28.4067i		−	0.915393i
$964$	−31.1635	−	39.2028i	−1.00371	−	1.26264i
$965$	38.2239	+	20.0410i	1.23047	+	0.645144i
$966$	1.41137	−	8.20653i	0.0454101	−	0.264041i
$967$	25.7453	+	25.7453i	0.827912	+	0.827912i	0.987228	−	0.159316i	$-0.0509288\pi$
$967$	25.7453	+	25.7453i	0.827912	+	0.827912i	−0.159316	+	0.987228i	$0.550929\pi$
$968$	−23.4993	+	37.2058i	−0.755297	+	1.19584i
$969$		−	0.198487i		−	0.00637631i
$970$	1.74113	−	11.7523i	0.0559043	−	0.377344i
$971$	−22.3570	−	22.3570i	−0.717470	−	0.717470i	0.250616	−	0.968087i	$-0.419367\pi$
$971$	−22.3570	−	22.3570i	−0.717470	−	0.717470i	−0.968087	+	0.250616i	$0.919367\pi$
$972$	25.2405	−	20.0644i	0.809588	−	0.643566i
$973$	12.0888	+	6.70078i	0.387549	+	0.214817i
$974$	−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	−0.366575	−	0.930389i	$-0.619470\pi$
$977$	17.6231	−	17.6231i	0.563814	−	0.563814i	0.930389	+	0.366575i	$0.119470\pi$
$978$	21.1274	−	7.37434i	0.675579	−	0.235805i
$979$	29.2800	+	29.2800i	0.935794	+	0.935794i
$980$	1.19353	−	31.2822i	0.0381258	−	0.999273i
$981$	−25.6601	+	25.6601i	−0.819265	+	0.819265i
$982$	−44.0719	−	21.2662i	−1.40639	−	0.678631i
$983$	−34.8611	−	34.8611i	−1.11190	−	1.11190i	−0.992894	−	0.119004i	$-0.962030\pi$
$983$	−34.8611	−	34.8611i	−1.11190	−	1.11190i	−0.119004	−	0.992894i	$-0.537970\pi$
$984$	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
$987$	−6.26930	+	11.3104i	−0.199554	+	0.360013i
$988$	10.9806	+	1.25453i	0.349340	+	0.0399119i
$989$	10.8195	−	10.8195i	0.344040	−	0.344040i
$990$	−33.5604	−	4.97203i	−1.06662	−	0.158022i
$991$	−44.5557			−1.41536			−0.707679	−	0.706534i	$-0.750258\pi$
$991$	−44.5557			−1.41536			−0.707679	+	0.706534i	$0.750258\pi$
$992$	−3.83862	−	35.3028i	−0.121876	−	1.12086i
$993$	11.0883	−	11.0883i	0.351877	−	0.351877i
$994$	−1.12822	−	1.59688i	−0.0357849	−	0.0506501i
$995$	6.45751	+	20.6924i	0.204717	+	0.655992i
$996$	−24.6038	+	19.5583i	−0.779601	+	0.619729i
$997$	−23.3077			−0.738163			−0.369082	−	0.929397i	$-0.620328\pi$
$997$	−23.3077			−0.738163			−0.369082	+	0.929397i	$0.620328\pi$
$998$	−32.3736	−	15.6214i	−1.02477	−	0.494485i
$999$			16.2101i			0.512864i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.r.a.237.11	✓	184	35.27	even	4
560.2.r.a.237.12	yes	184	5.2	odd	4
560.2.r.a.293.11	yes	184	112.69	odd	4
560.2.r.a.293.12	yes	184	16.5	even	4
560.2.bn.a.13.57	yes	184	1.1	even	1	trivial
560.2.bn.a.13.58	yes	184	7.6	odd	2	inner
560.2.bn.a.517.57	yes	184	560.517	even	4	inner
560.2.bn.a.517.58	yes	184	80.37	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.466046 + 1.33522i) q^{2} -0.958223 q^{3} +(-1.56560 + 1.24454i) q^{4} +(2.13454 - 0.666131i) q^{5} +(-0.446576 - 1.27943i) q^{6} +(-0.729292 - 2.54325i) q^{7} +(-2.39138 - 1.51040i) q^{8} -2.08181 q^{9} +(1.88422 + 2.53963i) q^{10} +(3.64406 - 3.64406i) q^{11} +(1.50020 - 1.19255i) q^{12} +5.12086 q^{13} +(3.05591 - 2.15904i) q^{14} +(-2.04537 + 0.638302i) q^{15} +(0.902218 - 3.89692i) q^{16} +(-0.135731 - 0.135731i) q^{17} +(-0.970219 - 2.77966i) q^{18} +(-0.763055 - 0.763055i) q^{19} +(-2.51281 + 3.69943i) q^{20} +(0.698824 + 2.43700i) q^{21} +(6.56390 + 3.16730i) 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} +4.86951 q^{27} +(4.30697 + 3.07408i) q^{28} +(-1.76859 + 1.76859i) q^{29} +(-1.80551 - 2.43353i) q^{30} -6.27749i q^{31} +(5.62371 - 0.611490i) q^{32} +(-3.49182 + 3.49182i) q^{33} +(0.117973 - 0.244487i) q^{34} +(-3.25084 - 4.94288i) q^{35} +(3.25928 - 2.59090i) q^{36} +3.32890i q^{37} +(0.663224 - 1.37446i) q^{38} -4.90692 q^{39} +(-6.11062 - 1.63104i) q^{40} +8.79916 q^{41} +(-2.92824 + 2.06884i) q^{42} -6.58815 q^{43} +(-1.16995 + 10.2403i) q^{44} +(-4.44371 + 1.38676i) q^{45} +(-2.95815 - 1.42741i) q^{46} +(3.60682 + 3.60682i) q^{47} +(-0.864526 + 3.73412i) q^{48} +(-5.93627 + 3.70955i) q^{49} +(5.71368 + 4.16580i) q^{50} +(0.130060 + 0.130060i) q^{51} +(-8.01722 + 6.37314i) q^{52} -1.10982 q^{53} +(2.26941 + 6.50184i) q^{54} +(5.35097 - 10.2058i) q^{55} +(-2.09732 + 7.18340i) q^{56} +(0.731177 + 0.731177i) q^{57} +(-3.18570 - 1.53721i) q^{58} +(10.4667 - 10.4667i) q^{59} +(2.40784 - 3.54488i) q^{60} +(-4.04412 + 4.04412i) q^{61} +(8.38181 - 2.92560i) 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} -2.74917 q^{67} +(0.381424 + 0.0435774i) q^{68} +(1.57366 - 1.57366i) q^{69} +(5.08476 - 6.64419i) q^{70} -0.522556i q^{71} +(4.97839 + 3.14437i) q^{72} +(7.09935 + 7.09935i) q^{73} +(-4.44479 + 1.55142i) q^{74} +(-3.94073 + 2.72497i) q^{75} +(2.14430 + 0.244984i) q^{76} +(-11.9253 - 6.61018i) q^{77} +(-2.28685 - 6.55180i) q^{78} -11.9737i q^{79} +(-0.670039 - 8.91914i) q^{80} +1.57935 q^{81} +(4.10081 + 11.7488i) q^{82} -16.4004 q^{83} +(-4.12704 - 2.94566i) q^{84} +(-0.380138 - 0.199309i) q^{85} +(-3.07038 - 8.79660i) q^{86} +(1.69471 - 1.69471i) q^{87} +(-14.2183 + 3.21033i) q^{88} +8.03500i q^{89} +(-3.92259 - 5.28702i) q^{90} +(-3.73460 - 13.0236i) q^{91} +(0.527262 - 4.61501i) q^{92} +6.01524i 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} +(-7.71962 - 6.19738i) q^{98} +(-7.58623 + 7.58623i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q - 4 q^{2} + 8 q^{8} + 168 q^{9} - 8 q^{11} - 8 q^{15} - 8 q^{16} - 24 q^{18} - 4 q^{21} + 4 q^{22} + 12 q^{28} - 4 q^{30} + 16 q^{32} - 40 q^{36} - 48 q^{39} - 36 q^{42} - 8 q^{43} - 24 q^{44} - 8 q^{46}+ \cdots - 24 q^{99}+O(q^{100}) \) 184 * q - 4 * q^2 + 8 * q^8 + 168 * q^9 - 8 * q^11 - 8 * q^15 - 8 * q^16 - 24 * q^18 - 4 * q^21 + 4 * q^22 + 12 * q^28 - 4 * q^30 + 16 * q^32 - 40 * q^36 - 48 * q^39 - 36 * q^42 - 8 * q^43 - 24 * q^44 - 8 * q^46 - 4 * q^50 - 8 * q^51 - 8 * q^53 - 4 * q^56 - 24 * q^57 - 68 * q^58 - 32 * q^63 - 8 * q^65 - 56 * q^67 + 80 * q^70 - 8 * q^72 - 40 * q^74 + 24 * q^77 - 100 * q^78 + 104 * q^81 + 48 * q^84 - 24 * q^85 + 8 * q^86 - 16 * q^88 - 20 * q^91 - 56 * q^92 - 56 * q^95 + 52 * q^98 - 24 * q^99

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