LMFDB - Embedded newform 930.2.s.c.769.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(439,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("930.439");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.s (of order $6$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			769.7
Character	$\chi$	$=$	930.769
Dual form			930.2.s.c.439.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(-0.866025 + 0.500000i) q^{3} -1.00000 q^{4} +(-1.89131 - 1.19288i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(2.10840 - 1.21729i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(-0.866025 + 0.500000i) q^{3} -1.00000 q^{4} +(-1.89131 - 1.19288i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(2.10840 - 1.21729i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(1.19288 - 1.89131i) q^{10} +(-0.345410 + 0.598267i) q^{11} +(0.866025 - 0.500000i) q^{12} +(-1.66153 - 0.959287i) q^{13} +(1.21729 + 2.10840i) q^{14} +(2.23436 + 0.0874091i) q^{15} +1.00000 q^{16} +(-4.39938 + 2.53998i) q^{17} +(0.866025 + 0.500000i) q^{18} +(2.14339 + 3.71246i) q^{19} +(1.89131 + 1.19288i) q^{20} +(-1.21729 + 2.10840i) q^{21} +(-0.598267 - 0.345410i) q^{22} +6.84889i q^{23} +(0.500000 + 0.866025i) q^{24} +(2.15408 + 4.51220i) q^{25} +(0.959287 - 1.66153i) q^{26} +1.00000i q^{27} +(-2.10840 + 1.21729i) q^{28} +6.99184 q^{29} +(-0.0874091 + 2.23436i) q^{30} +(4.90403 - 2.63639i) q^{31} +1.00000i q^{32} -0.690820i q^{33} +(-2.53998 - 4.39938i) q^{34} +(-5.43971 - 0.212804i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(1.27322 - 0.735092i) q^{37} +(-3.71246 + 2.14339i) q^{38} +1.91857 q^{39} +(-1.19288 + 1.89131i) q^{40} +(-5.94045 + 10.2892i) q^{41} +(-2.10840 - 1.21729i) q^{42} +(-9.13197 + 5.27234i) q^{43} +(0.345410 - 0.598267i) q^{44} +(-1.97872 + 1.04148i) q^{45} -6.84889 q^{46} -1.99288i q^{47} +(-0.866025 + 0.500000i) q^{48} +(-0.536422 + 0.929110i) q^{49} +(-4.51220 + 2.15408i) q^{50} +(2.53998 - 4.39938i) q^{51} +(1.66153 + 0.959287i) q^{52} +(-9.46466 - 5.46443i) q^{53} -1.00000 q^{54} +(1.36694 - 0.719476i) q^{55} +(-1.21729 - 2.10840i) q^{56} +(-3.71246 - 2.14339i) q^{57} +6.99184i q^{58} +(1.78710 + 3.09535i) q^{59} +(-2.23436 - 0.0874091i) q^{60} -7.77605 q^{61} +(2.63639 + 4.90403i) q^{62} -2.43458i q^{63} -1.00000 q^{64} +(1.99816 + 3.79631i) q^{65} +0.690820 q^{66} +(12.2861 + 7.09338i) q^{67} +(4.39938 - 2.53998i) q^{68} +(-3.42445 - 5.93131i) q^{69} +(0.212804 - 5.43971i) q^{70} +(-5.66295 + 9.80852i) q^{71} +(-0.866025 - 0.500000i) q^{72} +(5.34755 + 3.08741i) q^{73} +(0.735092 + 1.27322i) q^{74} +(-4.12159 - 2.83063i) q^{75} +(-2.14339 - 3.71246i) q^{76} +1.68185i q^{77} +1.91857i q^{78} +(-7.37533 - 12.7744i) q^{79} +(-1.89131 - 1.19288i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-10.2892 - 5.94045i) q^{82} +(-0.756161 - 0.436570i) q^{83} +(1.21729 - 2.10840i) q^{84} +(11.3505 + 0.444035i) q^{85} +(-5.27234 - 9.13197i) q^{86} +(-6.05511 + 3.49592i) q^{87} +(0.598267 + 0.345410i) q^{88} +7.31445 q^{89} +(-1.04148 - 1.97872i) q^{90} -4.67091 q^{91} -6.84889i q^{92} +(-2.92882 + 4.73519i) q^{93} +1.99288 q^{94} +(0.374704 - 9.57821i) q^{95} +(-0.500000 - 0.866025i) q^{96} +9.79647i q^{97} +(-0.929110 - 0.536422i) q^{98} +(0.345410 + 0.598267i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{4} + 4 q^{5} - 12 q^{6} + 12 q^{9}+O(q^{10}) $ 24 * q - 24 * q^4 + 4 * q^5 - 12 * q^6 + 12 * q^9	$ 24 q - 24 q^{4} + 4 q^{5} - 12 q^{6} + 12 q^{9} - 4 q^{11} + 12 q^{14} + 24 q^{16} - 4 q^{19} - 4 q^{20} - 12 q^{21} + 12 q^{24} - 4 q^{25} + 16 q^{26} + 32 q^{29} - 8 q^{30} + 24 q^{31} - 20 q^{34} + 48 q^{35} - 12 q^{36} + 32 q^{39} - 12 q^{41} + 4 q^{44} - 4 q^{45} + 56 q^{46} + 24 q^{49} - 16 q^{50} + 20 q^{51} - 24 q^{54} + 36 q^{55} - 12 q^{56} - 4 q^{59} - 40 q^{61} - 24 q^{64} - 4 q^{65} + 8 q^{66} + 28 q^{69} - 32 q^{70} - 56 q^{71} + 12 q^{74} + 16 q^{75} + 4 q^{76} - 72 q^{79} + 4 q^{80} - 12 q^{81} + 12 q^{84} + 40 q^{85} - 24 q^{86} + 128 q^{89} - 160 q^{91} + 56 q^{94} - 56 q^{95} - 12 q^{96} + 4 q^{99}+O(q^{100}) $ 24 * q - 24 * q^4 + 4 * q^5 - 12 * q^6 + 12 * q^9 - 4 * q^11 + 12 * q^14 + 24 * q^16 - 4 * q^19 - 4 * q^20 - 12 * q^21 + 12 * q^24 - 4 * q^25 + 16 * q^26 + 32 * q^29 - 8 * q^30 + 24 * q^31 - 20 * q^34 + 48 * q^35 - 12 * q^36 + 32 * q^39 - 12 * q^41 + 4 * q^44 - 4 * q^45 + 56 * q^46 + 24 * q^49 - 16 * q^50 + 20 * q^51 - 24 * q^54 + 36 * q^55 - 12 * q^56 - 4 * q^59 - 40 * q^61 - 24 * q^64 - 4 * q^65 + 8 * q^66 + 28 * q^69 - 32 * q^70 - 56 * q^71 + 12 * q^74 + 16 * q^75 + 4 * q^76 - 72 * q^79 + 4 * q^80 - 12 * q^81 + 12 * q^84 + 40 * q^85 - 24 * q^86 + 128 * q^89 - 160 * q^91 + 56 * q^94 - 56 * q^95 - 12 * q^96 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	−1.00000			−0.500000
$5$	−1.89131	−	1.19288i	−0.845818	−	0.533471i
$5$	−1.89131	−	1.19288i	−0.845818	−	0.533471i
$6$	−0.500000	−	0.866025i	−0.204124	−	0.353553i
$7$	2.10840	−	1.21729i	0.796902	−	0.460091i	−0.0454849	−	0.998965i	$-0.514483\pi$
$7$	2.10840	−	1.21729i	0.796902	−	0.460091i	0.842387	+	0.538874i	$0.181150\pi$
$8$		−	1.00000i		−	0.353553i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	1.19288	−	1.89131i	0.377221	−	0.598084i
$11$	−0.345410	+	0.598267i	−0.104145	+	0.180384i	−0.913389	−	0.407089i	$-0.866544\pi$
$11$	−0.345410	+	0.598267i	−0.104145	+	0.180384i	0.809244	+	0.587473i	$0.199877\pi$
$12$	0.866025	−	0.500000i	0.250000	−	0.144338i
$13$	−1.66153	−	0.959287i	−0.460826	−	0.266058i	0.251565	−	0.967840i	$-0.419055\pi$
$13$	−1.66153	−	0.959287i	−0.460826	−	0.266058i	−0.712392	+	0.701782i	$0.752388\pi$
$14$	1.21729	+	2.10840i	0.325334	+	0.563495i
$15$	2.23436	+	0.0874091i	0.576909	+	0.0225689i
$16$	1.00000			0.250000
$17$	−4.39938	+	2.53998i	−1.06701	+	0.616036i	−0.927362	−	0.374166i	$-0.877929\pi$
$17$	−4.39938	+	2.53998i	−1.06701	+	0.616036i	−0.139644	+	0.990202i	$0.544596\pi$
$18$	0.866025	+	0.500000i	0.204124	+	0.117851i
$19$	2.14339	+	3.71246i	0.491728	+	0.851697i	0.999955	−	0.00952590i	$-0.00303223\pi$
$19$	2.14339	+	3.71246i	0.491728	+	0.851697i	−0.508227	+	0.861223i	$0.669699\pi$
$20$	1.89131	+	1.19288i	0.422909	+	0.266736i
$21$	−1.21729	+	2.10840i	−0.265634	+	0.460091i
$22$	−0.598267	−	0.345410i	−0.127551	−	0.0736416i
$23$			6.84889i			1.42809i	0.700098	+	0.714046i	$0.253139\pi$
$23$			6.84889i			1.42809i	−0.700098	+	0.714046i	$0.746861\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	2.15408	+	4.51220i	0.430817	+	0.902439i
$26$	0.959287	−	1.66153i	0.188132	−	0.325854i
$27$			1.00000i			0.192450i
$28$	−2.10840	+	1.21729i	−0.398451	+	0.230046i
$29$	6.99184			1.29835			0.649176	−	0.760638i	$-0.275114\pi$
$29$	6.99184			1.29835			0.649176	+	0.760638i	$0.275114\pi$
$30$	−0.0874091	+	2.23436i	−0.0159586	+	0.407936i
$31$	4.90403	−	2.63639i	0.880789	−	0.473509i
$31$	4.90403	−	2.63639i	0.880789	−	0.473509i
$32$			1.00000i			0.176777i
$33$		−	0.690820i		−	0.120256i
$34$	−2.53998	−	4.39938i	−0.435603	−	0.754487i
$35$	−5.43971	−	0.212804i	−0.919480	−	0.0359704i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	1.27322	−	0.735092i	0.209315	−	0.120848i	−0.391678	−	0.920102i	$-0.628105\pi$
$37$	1.27322	−	0.735092i	0.209315	−	0.120848i	0.600993	+	0.799254i	$0.294772\pi$
$38$	−3.71246	+	2.14339i	−0.602241	+	0.347704i
$39$	1.91857			0.307218
$40$	−1.19288	+	1.89131i	−0.188611	+	0.299042i
$41$	−5.94045	+	10.2892i	−0.927742	+	1.60690i	−0.140651	+	0.990059i	$0.544920\pi$
$41$	−5.94045	+	10.2892i	−0.927742	+	1.60690i	−0.787091	+	0.616837i	$0.788414\pi$
$42$	−2.10840	−	1.21729i	−0.325334	−	0.187832i
$43$	−9.13197	+	5.27234i	−1.39261	+	0.804025i	−0.993604	−	0.112922i	$-0.963979\pi$
$43$	−9.13197	+	5.27234i	−1.39261	+	0.804025i	−0.399008	+	0.916947i	$0.630646\pi$
$44$	0.345410	−	0.598267i	0.0520725	−	0.0901922i
$45$	−1.97872	+	1.04148i	−0.294970	+	0.155255i
$46$	−6.84889			−1.00981
$47$		−	1.99288i		−	0.290692i	−0.989381	−	0.145346i	$-0.953570\pi$
$47$		−	1.99288i		−	0.290692i	0.989381	−	0.145346i	$-0.0464295\pi$
$48$	−0.866025	+	0.500000i	−0.125000	+	0.0721688i
$49$	−0.536422	+	0.929110i	−0.0766317	+	0.132730i
$50$	−4.51220	+	2.15408i	−0.638121	+	0.304634i
$51$	2.53998	−	4.39938i	0.355668	−	0.616036i
$52$	1.66153	+	0.959287i	0.230413	+	0.133029i
$53$	−9.46466	−	5.46443i	−1.30007	−	0.750597i	−0.319655	−	0.947534i	$-0.603567\pi$
$53$	−9.46466	−	5.46443i	−1.30007	−	0.750597i	−0.980416	+	0.196937i	$0.936901\pi$
$54$	−1.00000			−0.136083
$55$	1.36694	−	0.719476i	0.184318	−	0.0970141i
$56$	−1.21729	−	2.10840i	−0.162667	−	0.281747i
$57$	−3.71246	−	2.14339i	−0.491728	−	0.283899i
$58$			6.99184i			0.918073i
$59$	1.78710	+	3.09535i	0.232661	+	0.402981i	0.958590	−	0.284789i	$-0.0919234\pi$
$59$	1.78710	+	3.09535i	0.232661	+	0.402981i	−0.725929	+	0.687769i	$0.758590\pi$
$60$	−2.23436	−	0.0874091i	−0.288454	−	0.0112845i
$61$	−7.77605			−0.995621			−0.497810	−	0.867286i	$-0.665862\pi$
$61$	−7.77605			−0.995621			−0.497810	+	0.867286i	$0.665862\pi$
$62$	2.63639	+	4.90403i	0.334821	+	0.622812i
$63$		−	2.43458i		−	0.306728i
$64$	−1.00000			−0.125000
$65$	1.99816	+	3.79631i	0.247841	+	0.470875i
$66$	0.690820			0.0850340
$67$	12.2861	+	7.09338i	1.50099	+	0.866594i	0.999999	+	0.00113891i	$0.000362526\pi$
$67$	12.2861	+	7.09338i	1.50099	+	0.866594i	0.500986	+	0.865455i	$0.332971\pi$
$68$	4.39938	−	2.53998i	0.533503	−	0.308018i
$69$	−3.42445	−	5.93131i	−0.412255	−	0.714046i
$70$	0.212804	−	5.43971i	0.0254349	−	0.650170i
$71$	−5.66295	+	9.80852i	−0.672069	+	1.16406i	0.305248	+	0.952273i	$0.401261\pi$
$71$	−5.66295	+	9.80852i	−0.672069	+	1.16406i	−0.977316	+	0.211784i	$0.932073\pi$
$72$	−0.866025	−	0.500000i	−0.102062	−	0.0589256i
$73$	5.34755	+	3.08741i	0.625883	+	0.361354i	0.779156	−	0.626830i	$-0.215648\pi$
$73$	5.34755	+	3.08741i	0.625883	+	0.361354i	−0.153273	+	0.988184i	$0.548981\pi$
$74$	0.735092	+	1.27322i	0.0854527	+	0.148008i
$75$	−4.12159	−	2.83063i	−0.475920	−	0.326854i
$76$	−2.14339	−	3.71246i	−0.245864	−	0.425849i
$77$			1.68185i			0.191665i
$78$			1.91857i			0.217236i
$79$	−7.37533	−	12.7744i	−0.829789	−	1.43724i	−0.898204	−	0.439580i	$-0.855127\pi$
$79$	−7.37533	−	12.7744i	−0.829789	−	1.43724i	0.0684146	−	0.997657i	$-0.478206\pi$
$80$	−1.89131	−	1.19288i	−0.211455	−	0.133368i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−10.2892	−	5.94045i	−1.13625	−	0.656013i
$83$	−0.756161	−	0.436570i	−0.0829995	−	0.0479198i	0.457926	−	0.888990i	$-0.348593\pi$
$83$	−0.756161	−	0.436570i	−0.0829995	−	0.0479198i	−0.540925	+	0.841071i	$0.681926\pi$
$84$	1.21729	−	2.10840i	0.132817	−	0.230046i
$85$	11.3505	+	0.444035i	1.23113	+	0.0481623i
$86$	−5.27234	−	9.13197i	−0.568532	−	0.984726i
$87$	−6.05511	+	3.49592i	−0.649176	+	0.374802i
$88$	0.598267	+	0.345410i	0.0637755	+	0.0368208i
$89$	7.31445			0.775330			0.387665	−	0.921800i	$-0.373282\pi$
$89$	7.31445			0.775330			0.387665	+	0.921800i	$0.373282\pi$
$90$	−1.04148	−	1.97872i	−0.109782	−	0.208575i
$91$	−4.67091			−0.489645
$92$		−	6.84889i		−	0.714046i
$93$	−2.92882	+	4.73519i	−0.303704	+	0.491016i
$94$	1.99288			0.205550
$95$	0.374704	−	9.57821i	0.0384438	−	0.982704i
$96$	−0.500000	−	0.866025i	−0.0510310	−	0.0883883i
$97$			9.79647i			0.994681i	0.867555	+	0.497340i	$0.165690\pi$
$97$			9.79647i			0.994681i	−0.867555	+	0.497340i	$0.834310\pi$
$98$	−0.929110	−	0.536422i	−0.0938543	−	0.0541868i
$99$	0.345410	+	0.598267i	0.0347150	+	0.0601281i
$100$	−2.15408	−	4.51220i	−0.215408	−	0.451220i
$101$	−10.9050			−1.08508			−0.542542	−	0.840029i	$-0.682538\pi$
$101$	−10.9050			−1.08508			−0.542542	+	0.840029i	$0.682538\pi$
$102$	4.39938	+	2.53998i	0.435603	+	0.251496i
$103$	6.50162	+	3.75371i	0.640623	+	0.369864i	0.784855	−	0.619680i	$-0.212738\pi$
$103$	6.50162	+	3.75371i	0.640623	+	0.369864i	−0.144231	+	0.989544i	$0.546071\pi$
$104$	−0.959287	+	1.66153i	−0.0940658	+	0.162927i
$105$	4.81733	−	2.53556i	0.470124	−	0.247446i
$106$	5.46443	−	9.46466i	0.530752	−	0.919289i
$107$	−3.59914	+	2.07797i	−0.347942	+	0.200885i	−0.663779	−	0.747929i	$-0.731048\pi$
$107$	−3.59914	+	2.07797i	−0.347942	+	0.200885i	0.315836	+	0.948814i	$0.397715\pi$
$108$		−	1.00000i		−	0.0962250i
$109$	18.2124			1.74444			0.872218	−	0.489117i	$-0.162681\pi$
$109$	18.2124			1.74444			0.872218	+	0.489117i	$0.162681\pi$
$110$	0.719476	+	1.36694i	0.0685993	+	0.130332i
$111$	−0.735092	+	1.27322i	−0.0697718	+	0.120848i
$112$	2.10840	−	1.21729i	0.199225	−	0.115023i
$113$	17.0560	+	9.84730i	1.60450	+	0.926356i	0.990572	+	0.136990i	$0.0437429\pi$
$113$	17.0560	+	9.84730i	1.60450	+	0.926356i	0.613923	+	0.789366i	$0.289590\pi$
$114$	2.14339	−	3.71246i	0.200747	−	0.347704i
$115$	8.16989	−	12.9534i	0.761846	−	1.20791i
$116$	−6.99184			−0.649176
$117$	−1.66153	+	0.959287i	−0.153609	+	0.0886861i
$118$	−3.09535	+	1.78710i	−0.284950	+	0.164516i
$119$	−6.18377	+	10.7106i	−0.566866	+	0.981840i
$120$	0.0874091	−	2.23436i	0.00797932	−	0.203968i
$121$	5.26138	+	9.11298i	0.478308	+	0.828453i
$122$		−	7.77605i		−	0.704010i
$123$		−	11.8809i		−	1.07126i
$124$	−4.90403	+	2.63639i	−0.440395	+	0.236754i
$125$	1.30847	−	11.1035i	0.117033	−	0.993128i
$126$	2.43458			0.216889
$127$	14.0922	−	8.13615i	1.25048	−	0.721967i	0.279278	−	0.960210i	$-0.409905\pi$
$127$	14.0922	−	8.13615i	1.25048	−	0.721967i	0.971205	+	0.238244i	$0.0765716\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	5.27234	−	9.13197i	0.464204	−	0.804025i
$130$	−3.79631	+	1.99816i	−0.332959	+	0.175250i
$131$	−10.0338	−	17.3791i	−0.876660	−	1.51842i	−0.854984	−	0.518654i	$-0.826433\pi$
$131$	−10.0338	−	17.3791i	−0.876660	−	1.51842i	−0.0216753	−	0.999765i	$-0.506900\pi$
$132$			0.690820i			0.0601281i
$133$	9.03827	+	5.21825i	0.783717	+	0.452479i
$134$	−7.09338	+	12.2861i	−0.612775	+	1.06136i
$135$	1.19288	−	1.89131i	0.102667	−	0.162778i
$136$	2.53998	+	4.39938i	0.217802	+	0.377243i
$137$	5.58082	+	3.22209i	0.476802	+	0.275282i	0.719083	−	0.694924i	$-0.244562\pi$
$137$	5.58082	+	3.22209i	0.476802	+	0.275282i	−0.242281	+	0.970206i	$0.577896\pi$
$138$	5.93131	−	3.42445i	0.504907	−	0.291508i
$139$	−6.56923			−0.557195			−0.278597	−	0.960408i	$-0.589869\pi$
$139$	−6.56923			−0.557195			−0.278597	+	0.960408i	$0.589869\pi$
$140$	5.43971	+	0.212804i	0.459740	+	0.0179852i
$141$	0.996441	+	1.72589i	0.0839155	+	0.145346i
$142$	−9.80852	−	5.66295i	−0.823113	−	0.475224i
$143$	1.14782	−	0.662694i	0.0959855	−	0.0554173i
$144$	0.500000	−	0.866025i	0.0416667	−	0.0721688i
$145$	−13.2237	−	8.34041i	−1.09817	−	0.692633i
$146$	−3.08741	+	5.34755i	−0.255516	+	0.442566i
$147$		−	1.07284i		−	0.0884866i
$148$	−1.27322	+	0.735092i	−0.104658	+	0.0604242i
$149$	9.09075	+	15.7456i	0.744743	+	1.28993i	0.950315	+	0.311291i	$0.100761\pi$
$149$	9.09075	+	15.7456i	0.744743	+	1.28993i	−0.205572	+	0.978642i	$0.565905\pi$
$150$	2.83063	−	4.12159i	0.231120	−	0.336526i
$151$	−4.42641			−0.360216			−0.180108	−	0.983647i	$-0.557645\pi$
$151$	−4.42641			−0.360216			−0.180108	+	0.983647i	$0.557645\pi$
$152$	3.71246	−	2.14339i	0.301120	−	0.173852i
$153$			5.07996i			0.410691i
$154$	−1.68185			−0.135528
$155$	−12.4199	−	0.863688i	−0.997591	−	0.0693731i
$156$	−1.91857			−0.153609
$157$			5.09193i			0.406380i	0.979139	+	0.203190i	$0.0651309\pi$
$157$			5.09193i			0.406380i	−0.979139	+	0.203190i	$0.934869\pi$
$158$	12.7744	−	7.37533i	1.01628	−	0.586749i
$159$	10.9289			0.866714
$160$	1.19288	−	1.89131i	0.0943053	−	0.149521i
$161$	8.33707	+	14.4402i	0.657053	+	1.13805i
$162$	0.866025	−	0.500000i	0.0680414	−	0.0392837i
$163$		−	2.46160i		−	0.192807i	−0.995342	−	0.0964037i	$-0.969266\pi$
$163$		−	2.46160i		−	0.192807i	0.995342	−	0.0964037i	$-0.0307340\pi$
$164$	5.94045	−	10.2892i	0.463871	−	0.803448i
$165$	−0.824064	+	1.30655i	−0.0641533	+	0.101715i
$166$	0.436570	−	0.756161i	0.0338844	−	0.0586895i
$167$	−0.664645	+	0.383733i	−0.0514317	+	0.0296941i	−0.525495	−	0.850796i	$-0.676120\pi$
$167$	−0.664645	+	0.383733i	−0.0514317	+	0.0296941i	0.474064	+	0.880491i	$0.342787\pi$
$168$	2.10840	+	1.21729i	0.162667	+	0.0939158i
$169$	−4.65954	−	8.07056i	−0.358426	−	0.620812i
$170$	−0.444035	+	11.3505i	−0.0340559	+	0.870540i
$171$	4.28678			0.327818
$172$	9.13197	−	5.27234i	0.696306	−	0.402013i
$173$	−1.83399	−	1.05885i	−0.139436	−	0.0805032i	0.428659	−	0.903466i	$-0.358986\pi$
$173$	−1.83399	−	1.05885i	−0.139436	−	0.0805032i	−0.568095	+	0.822963i	$0.692319\pi$
$174$	−3.49592	−	6.05511i	−0.265025	−	0.459037i
$175$	10.0343	+	6.89139i	0.758523	+	0.520940i
$176$	−0.345410	+	0.598267i	−0.0260362	+	0.0450961i
$177$	−3.09535	−	1.78710i	−0.232661	−	0.134327i
$178$			7.31445i			0.548241i
$179$	2.57977	+	4.46829i	0.192821	+	0.333976i	0.946184	−	0.323629i	$-0.104903\pi$
$179$	2.57977	+	4.46829i	0.192821	+	0.333976i	−0.753363	+	0.657605i	$0.771570\pi$
$180$	1.97872	−	1.04148i	0.147485	−	0.0776274i
$181$	−4.76919	+	8.26048i	−0.354491	+	0.613996i	−0.987031	−	0.160532i	$-0.948679\pi$
$181$	−4.76919	+	8.26048i	−0.354491	+	0.613996i	0.632540	+	0.774528i	$0.282012\pi$
$182$		−	4.67091i		−	0.346231i
$183$	6.73426	−	3.88802i	0.497810	−	0.287411i
$184$	6.84889			0.504907
$185$	−3.28492	−	0.128507i	−0.241512	−	0.00944805i
$186$	−4.73519	−	2.92882i	−0.347201	−	0.214751i
$187$		−	3.50934i		−	0.256628i
$188$			1.99288i			0.145346i
$189$	1.21729	+	2.10840i	0.0885446	+	0.153364i
$190$	9.57821	+	0.374704i	0.694876	+	0.0271839i
$191$	−12.7369	+	22.0610i	−0.921611	+	1.59628i	−0.124688	+	0.992196i	$0.539793\pi$
$191$	−12.7369	+	22.0610i	−0.921611	+	1.59628i	−0.796923	+	0.604081i	$0.793540\pi$
$192$	0.866025	−	0.500000i	0.0625000	−	0.0360844i
$193$	−12.9450	+	7.47378i	−0.931799	+	0.537974i	−0.887380	−	0.461039i	$-0.847477\pi$
$193$	−12.9450	+	7.47378i	−0.931799	+	0.537974i	−0.0444186	+	0.999013i	$0.514144\pi$
$194$	−9.79647			−0.703346
$195$	−3.62861	−	2.28862i	−0.259850	−	0.163892i
$196$	0.536422	−	0.929110i	0.0383158	−	0.0663650i
$197$	−6.79861	−	3.92518i	−0.484381	−	0.279657i	0.237860	−	0.971300i	$-0.423554\pi$
$197$	−6.79861	−	3.92518i	−0.484381	−	0.279657i	−0.722240	+	0.691642i	$0.756888\pi$
$198$	−0.598267	+	0.345410i	−0.0425170	+	0.0245472i
$199$	4.15396	−	7.19486i	0.294466	−	0.510030i	−0.680394	−	0.732846i	$-0.738192\pi$
$199$	4.15396	−	7.19486i	0.294466	−	0.510030i	0.974861	+	0.222816i	$0.0715248\pi$
$200$	4.51220	−	2.15408i	0.319060	−	0.152317i
$201$	−14.1868			−1.00066
$202$		−	10.9050i		−	0.767270i
$203$	14.7416	−	8.51108i	1.03466	−	0.597360i
$204$	−2.53998	+	4.39938i	−0.177834	+	0.308018i
$205$	23.5089	−	12.3737i	1.64193	−	0.864218i
$206$	−3.75371	+	6.50162i	−0.261533	+	0.452989i
$207$	5.93131	+	3.42445i	0.412255	+	0.238015i
$208$	−1.66153	−	0.959287i	−0.115207	−	0.0665146i
$209$	−2.96139			−0.204844
$210$	2.53556	+	4.81733i	0.174971	+	0.332428i
$211$	−3.66651	−	6.35058i	−0.252413	−	0.437192i	0.711777	−	0.702406i	$-0.247891\pi$
$211$	−3.66651	−	6.35058i	−0.252413	−	0.437192i	−0.964190	+	0.265214i	$0.914557\pi$
$212$	9.46466	+	5.46443i	0.650036	+	0.375298i
$213$		−	11.3259i		−	0.776038i
$214$	−2.07797	−	3.59914i	−0.142047	−	0.246032i
$215$	23.5606	+	0.921702i	1.60682	+	0.0628595i
$216$	1.00000			0.0680414
$217$	7.13043	−	11.5282i	0.484045	−	0.782584i
$218$			18.2124i			1.23350i
$219$	−6.17482			−0.417256
$220$	−1.36694	+	0.719476i	−0.0921588	+	0.0485070i
$221$	9.74628			0.655606
$222$	−1.27322	−	0.735092i	−0.0854527	−	0.0493361i
$223$	−1.48728	+	0.858684i	−0.0995959	+	0.0575017i	−0.548971	−	0.835842i	$-0.684980\pi$
$223$	−1.48728	+	0.858684i	−0.0995959	+	0.0575017i	0.449375	+	0.893343i	$0.351647\pi$
$224$	1.21729	+	2.10840i	0.0813334	+	0.140874i
$225$	4.98472	+	0.390607i	0.332315	+	0.0260404i
$226$	−9.84730	+	17.0560i	−0.655033	+	1.13455i
$227$	−15.3472	−	8.86071i	−1.01863	−	0.588106i	−0.104923	−	0.994480i	$-0.533460\pi$
$227$	−15.3472	−	8.86071i	−1.01863	−	0.588106i	−0.913707	+	0.406374i	$0.866793\pi$
$228$	3.71246	+	2.14339i	0.245864	+	0.141950i
$229$	−0.329170	−	0.570139i	−0.0217522	−	0.0376759i	0.854944	−	0.518720i	$-0.173591\pi$
$229$	−0.329170	−	0.570139i	−0.0217522	−	0.0376759i	−0.876697	+	0.481044i	$0.840258\pi$
$230$	12.9534	+	8.16989i	0.854119	+	0.538707i
$231$	−0.840926	−	1.45653i	−0.0553289	−	0.0958324i
$232$		−	6.99184i		−	0.459037i
$233$			14.8471i			0.972668i	0.873773	+	0.486334i	$0.161666\pi$
$233$			14.8471i			0.972668i	−0.873773	+	0.486334i	$0.838334\pi$
$234$	−0.959287	−	1.66153i	−0.0627105	−	0.108618i
$235$	−2.37727	+	3.76915i	−0.155076	+	0.245872i
$236$	−1.78710	−	3.09535i	−0.116330	−	0.201490i
$237$	12.7744	+	7.37533i	0.829789	+	0.479079i
$238$	−10.7106	−	6.18377i	−0.694266	−	0.400835i
$239$	−5.66269	+	9.80807i	−0.366289	+	0.634432i	−0.988982	−	0.148035i	$-0.952705\pi$
$239$	−5.66269	+	9.80807i	−0.366289	+	0.634432i	0.622693	+	0.782466i	$0.286039\pi$
$240$	2.23436	+	0.0874091i	0.144227	+	0.00564223i
$241$	−12.3270	−	21.3510i	−0.794052	−	1.37534i	−0.923439	−	0.383745i	$-0.874634\pi$
$241$	−12.3270	−	21.3510i	−0.794052	−	1.37534i	0.129387	−	0.991594i	$-0.458699\pi$
$242$	−9.11298	+	5.26138i	−0.585805	+	0.338215i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	7.77605			0.497810
$245$	2.12285	−	1.11735i	0.135624	−	0.0713846i
$246$	11.8809			0.757498
$247$		−	8.22451i		−	0.523313i
$248$	−2.63639	−	4.90403i	−0.167411	−	0.311406i
$249$	0.873140			0.0553330
$250$	11.1035	+	1.30847i	0.702248	+	0.0827546i
$251$	−11.4583	−	19.8463i	−0.723241	−	1.25269i	−0.959694	−	0.281047i	$-0.909318\pi$
$251$	−11.4583	−	19.8463i	−0.723241	−	1.25269i	0.236454	−	0.971643i	$-0.424015\pi$
$252$			2.43458i			0.153364i
$253$	−4.09747	−	2.36567i	−0.257606	−	0.148729i
$254$	8.13615	+	14.0922i	0.510508	+	0.884225i
$255$	−10.0518	+	5.29068i	−0.629468	+	0.331315i
$256$	1.00000			0.0625000
$257$	7.37347	+	4.25708i	0.459945	+	0.265549i	0.712021	−	0.702158i	$-0.247780\pi$
$257$	7.37347	+	4.25708i	0.459945	+	0.265549i	−0.252076	+	0.967707i	$0.581113\pi$
$258$	9.13197	+	5.27234i	0.568532	+	0.328242i
$259$	1.78964	−	3.09974i	0.111203	−	0.192608i
$260$	−1.99816	−	3.79631i	−0.123920	−	0.235437i
$261$	3.49592	−	6.05511i	0.216392	−	0.374802i
$262$	17.3791	−	10.0338i	1.07368	−	0.619892i
$263$		−	26.9888i		−	1.66420i	−0.554624	−	0.832101i	$-0.687138\pi$
$263$		−	26.9888i		−	1.66420i	0.554624	−	0.832101i	$-0.312862\pi$
$264$	−0.690820			−0.0425170
$265$	11.3822	+	21.6251i	0.699202	+	1.32842i
$266$	−5.21825	+	9.03827i	−0.319951	+	0.554172i
$267$	−6.33450	+	3.65722i	−0.387665	+	0.223818i
$268$	−12.2861	−	7.09338i	−0.750493	−	0.433297i
$269$	2.87461	−	4.97896i	0.175268	−	0.303573i	−0.764986	−	0.644047i	$-0.777254\pi$
$269$	2.87461	−	4.97896i	0.175268	−	0.303573i	0.940254	+	0.340474i	$0.110588\pi$
$270$	1.89131	+	1.19288i	0.115101	+	0.0725962i
$271$	−3.56495			−0.216555			−0.108278	−	0.994121i	$-0.534534\pi$
$271$	−3.56495			−0.216555			−0.108278	+	0.994121i	$0.534534\pi$
$272$	−4.39938	+	2.53998i	−0.266751	+	0.154009i
$273$	4.04513	−	2.33546i	0.244822	−	0.141348i
$274$	−3.22209	+	5.58082i	−0.194654	+	0.337150i
$275$	−3.44354	−	0.269839i	−0.207653	−	0.0162719i
$276$	3.42445	+	5.93131i	0.206127	+	0.357023i
$277$		−	17.7469i		−	1.06631i	−0.846018	−	0.533154i	$-0.821006\pi$
$277$		−	17.7469i		−	1.06631i	0.846018	−	0.533154i	$-0.178994\pi$
$278$		−	6.56923i		−	0.393996i
$279$	0.168835	−	5.56520i	0.0101079	−	0.333180i
$280$	−0.212804	+	5.43971i	−0.0127175	+	0.325085i
$281$	16.1982			0.966306			0.483153	−	0.875536i	$-0.339492\pi$
$281$	16.1982			0.966306			0.483153	+	0.875536i	$0.339492\pi$
$282$	−1.72589	+	0.996441i	−0.102775	+	0.0593372i
$283$		−	19.8725i		−	1.18130i	−0.806928	−	0.590650i	$-0.798872\pi$
$283$		−	19.8725i		−	1.18130i	0.806928	−	0.590650i	$-0.201128\pi$
$284$	5.66295	−	9.80852i	0.336034	−	0.582029i
$285$	4.46460	+	8.48232i	0.264460	+	0.502450i
$286$	0.662694	+	1.14782i	0.0391859	+	0.0678720i
$287$			28.9249i			1.70738i
$288$	0.866025	+	0.500000i	0.0510310	+	0.0294628i
$289$	4.40300	−	7.62622i	0.259000	−	0.448601i
$290$	8.34041	−	13.2237i	0.489766	−	0.776523i
$291$	−4.89824	−	8.48399i	−0.287140	−	0.497340i
$292$	−5.34755	−	3.08741i	−0.312942	−	0.180677i
$293$	5.33888	−	3.08240i	0.311901	−	0.180076i	−0.335876	−	0.941906i	$-0.609032\pi$
$293$	5.33888	−	3.08240i	0.311901	−	0.180076i	0.647777	+	0.761830i	$0.275699\pi$
$294$	1.07284			0.0625695
$295$	0.312418	−	7.98606i	0.0181897	−	0.464966i
$296$	−0.735092	−	1.27322i	−0.0427263	−	0.0740042i
$297$	−0.598267	−	0.345410i	−0.0347150	−	0.0200427i
$298$	−15.7456	+	9.09075i	−0.912120	+	0.526613i
$299$	6.57005	−	11.3797i	0.379956	−	0.658103i
$300$	4.12159	+	2.83063i	0.237960	+	0.163427i
$301$	−12.8359	+	22.2325i	−0.739850	+	1.28146i
$302$		−	4.42641i		−	0.254711i
$303$	9.44397	−	5.45248i	0.542542	−	0.313237i
$304$	2.14339	+	3.71246i	0.122932	+	0.212924i
$305$	14.7069	+	9.27588i	0.842114	+	0.531135i
$306$	−5.07996			−0.290402
$307$	−14.7387	+	8.50942i	−0.841185	+	0.485658i	−0.857667	−	0.514206i	$-0.828087\pi$
$307$	−14.7387	+	8.50942i	−0.841185	+	0.485658i	0.0164821	+	0.999864i	$0.494753\pi$
$308$		−	1.68185i		−	0.0958324i
$309$	−7.50742			−0.427082
$310$	0.863688	−	12.4199i	0.0490542	−	0.705403i
$311$	15.0411			0.852903			0.426451	−	0.904510i	$-0.359763\pi$
$311$	15.0411			0.852903			0.426451	+	0.904510i	$0.359763\pi$
$312$		−	1.91857i		−	0.108618i
$313$	−10.8842	+	6.28401i	−0.615213	+	0.355193i	−0.775003	−	0.631958i	$-0.782252\pi$
$313$	−10.8842	+	6.28401i	−0.615213	+	0.355193i	0.159790	+	0.987151i	$0.448918\pi$
$314$	−5.09193			−0.287354
$315$	−2.90415	+	4.60453i	−0.163630	+	0.259436i
$316$	7.37533	+	12.7744i	0.414894	+	0.718618i
$317$	14.2524	−	8.22860i	0.800492	−	0.462164i	−0.0431511	−	0.999069i	$-0.513740\pi$
$317$	14.2524	−	8.22860i	0.800492	−	0.462164i	0.843643	+	0.536904i	$0.180406\pi$
$318$			10.9289i			0.612860i
$319$	−2.41505	+	4.18299i	−0.135217	+	0.234202i
$320$	1.89131	+	1.19288i	0.105727	+	0.0666839i
$321$	2.07797	−	3.59914i	0.115981	−	0.200885i
$322$	−14.4402	+	8.33707i	−0.804723	+	0.464607i
$323$	−18.8592	−	10.8883i	−1.04935	−	0.605844i
$324$	0.500000	+	0.866025i	0.0277778	+	0.0481125i
$325$	0.749408	−	9.56355i	0.0415697	−	0.530490i
$326$	2.46160			0.136335
$327$	−15.7724	+	9.10622i	−0.872218	+	0.503575i
$328$	10.2892	+	5.94045i	0.568124	+	0.328006i
$329$	−2.42591	−	4.20180i	−0.133745	−	0.231653i
$330$	−1.30655	−	0.824064i	−0.0719233	−	0.0453632i
$331$	2.92387	−	5.06429i	0.160710	−	0.278359i	−0.774413	−	0.632680i	$-0.781955\pi$
$331$	2.92387	−	5.06429i	0.160710	−	0.278359i	0.935124	+	0.354321i	$0.115288\pi$
$332$	0.756161	+	0.436570i	0.0414997	+	0.0239599i
$333$		−	1.47018i		−	0.0805655i
$334$	−0.383733	−	0.664645i	−0.0209969	−	0.0363677i
$335$	−14.7752	−	28.0716i	−0.807258	−	1.53371i
$336$	−1.21729	+	2.10840i	−0.0664085	+	0.115023i
$337$			31.5048i			1.71618i	0.513503	+	0.858088i	$0.328347\pi$
$337$			31.5048i			1.71618i	−0.513503	+	0.858088i	$0.671653\pi$
$338$	8.07056	−	4.65954i	0.438980	−	0.253445i
$339$	−19.6946			−1.06966
$340$	−11.3505	−	0.444035i	−0.615565	−	0.0240812i
$341$	−0.116635	+	3.84455i	−0.00631613	+	0.208194i
$342$			4.28678i			0.231803i
$343$			19.6539i			1.06121i
$344$	5.27234	+	9.13197i	0.284266	+	0.492363i
$345$	−0.598655	+	15.3029i	−0.0322305	+	0.823879i
$346$	1.05885	−	1.83399i	0.0569244	−	0.0985959i
$347$	12.4613	−	7.19454i	0.668958	−	0.386223i	−0.126724	−	0.991938i	$-0.540446\pi$
$347$	12.4613	−	7.19454i	0.668958	−	0.386223i	0.795682	+	0.605715i	$0.207113\pi$
$348$	6.05511	−	3.49592i	0.324588	−	0.187401i
$349$	−19.6230			−1.05039			−0.525197	−	0.850981i	$-0.676008\pi$
$349$	−19.6230			−1.05039			−0.525197	+	0.850981i	$0.676008\pi$
$350$	−6.89139	+	10.0343i	−0.368360	+	0.536357i
$351$	0.959287	−	1.66153i	0.0512029	−	0.0886861i
$352$	−0.598267	−	0.345410i	−0.0318878	−	0.0184104i
$353$	5.94740	−	3.43373i	0.316548	−	0.182759i	−0.333305	−	0.942819i	$-0.608164\pi$
$353$	5.94740	−	3.43373i	0.316548	−	0.182759i	0.649853	+	0.760060i	$0.274830\pi$
$354$	1.78710	−	3.09535i	0.0949834	−	0.164516i
$355$	22.4107	−	11.7957i	1.18944	−	0.626051i
$356$	−7.31445			−0.387665
$357$		−	12.3675i		−	0.654560i
$358$	−4.46829	+	2.57977i	−0.236156	+	0.136345i
$359$	3.46814	−	6.00700i	0.183042	−	0.317037i	−0.759873	−	0.650071i	$-0.774739\pi$
$359$	3.46814	−	6.00700i	0.183042	−	0.317037i	0.942915	+	0.333034i	$0.108072\pi$
$360$	1.04148	+	1.97872i	0.0548909	+	0.104287i
$361$	0.311749	−	0.539966i	0.0164079	−	0.0284192i
$362$	−8.26048	−	4.76919i	−0.434161	−	0.250663i
$363$	−9.11298	−	5.26138i	−0.478308	−	0.276151i
$364$	4.67091			0.244822
$365$	−6.43096	−	12.2182i	−0.336612	−	0.639530i
$366$	3.88802	+	6.73426i	0.203230	+	0.352005i
$367$	28.2604	+	16.3161i	1.47518	+	0.851696i	0.999608	−	0.0279810i	$-0.00890780\pi$
$367$	28.2604	+	16.3161i	1.47518	+	0.851696i	0.475572	+	0.879677i	$0.342241\pi$
$368$			6.84889i			0.357023i
$369$	5.94045	+	10.2892i	0.309247	+	0.535632i
$370$	0.128507	−	3.28492i	0.00668078	−	0.170775i
$371$	−26.6071			−1.38137
$372$	2.92882	−	4.73519i	0.151852	−	0.245508i
$373$		−	12.7573i		−	0.660546i	−0.943886	−	0.330273i	$-0.892859\pi$
$373$		−	12.7573i		−	0.660546i	0.943886	−	0.330273i	$-0.107141\pi$
$374$	3.50934			0.181464
$375$	4.41859	+	10.2702i	0.228175	+	0.530348i
$376$	−1.99288			−0.102775
$377$	−11.6172	−	6.70718i	−0.598315	−	0.345437i
$378$	−2.10840	+	1.21729i	−0.108445	+	0.0626105i
$379$	−4.42316	−	7.66113i	−0.227202	−	0.393526i	0.729776	−	0.683687i	$-0.239625\pi$
$379$	−4.42316	−	7.66113i	−0.227202	−	0.393526i	−0.956978	+	0.290161i	$0.906291\pi$
$380$	−0.374704	+	9.57821i	−0.0192219	+	0.491352i
$381$	−8.13615	+	14.0922i	−0.416828	+	0.721967i
$382$	−22.0610	−	12.7369i	−1.12874	−	0.651677i
$383$	−0.629849	−	0.363643i	−0.0321838	−	0.0185813i	0.483822	−	0.875167i	$-0.339248\pi$
$383$	−0.629849	−	0.363643i	−0.0321838	−	0.0185813i	−0.516006	+	0.856585i	$0.672582\pi$
$384$	0.500000	+	0.866025i	0.0255155	+	0.0441942i
$385$	2.00624	−	3.18090i	0.102248	−	0.162114i
$386$	−7.47378	−	12.9450i	−0.380405	−	0.658881i
$387$			10.5447i			0.536017i
$388$		−	9.79647i		−	0.497340i
$389$	−4.37234	−	7.57312i	−0.221687	−	0.383972i	0.733634	−	0.679545i	$-0.237823\pi$
$389$	−4.37234	−	7.57312i	−0.221687	−	0.383972i	−0.955320	+	0.295573i	$0.904489\pi$
$390$	2.28862	−	3.62861i	0.115889	−	0.183742i
$391$	−17.3961	−	30.1308i	−0.879756	−	1.52378i
$392$	0.929110	+	0.536422i	0.0469271	+	0.0270934i
$393$	17.3791	+	10.0338i	0.876660	+	0.506140i
$394$	3.92518	−	6.79861i	0.197748	−	0.342509i
$395$	−1.28934	+	32.9582i	−0.0648738	+	1.65831i
$396$	−0.345410	−	0.598267i	−0.0173575	−	0.0300641i
$397$	−10.1115	+	5.83790i	−0.507483	+	0.292996i	−0.731799	−	0.681521i	$-0.761319\pi$
$397$	−10.1115	+	5.83790i	−0.507483	+	0.292996i	0.224315	+	0.974517i	$0.427985\pi$
$398$	7.19486	+	4.15396i	0.360646	+	0.208219i
$399$	−10.4365			−0.522478
$400$	2.15408	+	4.51220i	0.107704	+	0.225610i
$401$	15.2311			0.760604			0.380302	−	0.924862i	$-0.375820\pi$
$401$	15.2311			0.760604			0.380302	+	0.924862i	$0.375820\pi$
$402$		−	14.1868i		−	0.707571i
$403$	−10.6773	−	0.323923i	−0.531872	−	0.0161358i
$404$	10.9050			0.542542
$405$	−0.0874091	+	2.23436i	−0.00434339	+	0.111026i
$406$	8.51108	+	14.7416i	0.422398	+	0.731614i
$407$			1.01563i			0.0503430i
$408$	−4.39938	−	2.53998i	−0.217802	−	0.125748i
$409$	16.8737	+	29.2261i	0.834349	+	1.44514i	0.894559	+	0.446950i	$0.147490\pi$
$409$	16.8737	+	29.2261i	0.834349	+	1.44514i	−0.0602095	+	0.998186i	$0.519177\pi$
$410$	12.3737	+	23.5089i	0.611095	+	1.16102i
$411$	−6.44418			−0.317868
$412$	−6.50162	−	3.75371i	−0.320312	−	0.184932i
$413$	7.53587	+	4.35084i	0.370816	+	0.214091i
$414$	−3.42445	+	5.93131i	−0.168302	+	0.291508i
$415$	0.909358	+	1.72770i	0.0446386	+	0.0848092i
$416$	0.959287	−	1.66153i	0.0470329	−	0.0814634i
$417$	5.68912	−	3.28461i	0.278597	−	0.160848i
$418$		−	2.96139i		−	0.144846i
$419$	−6.74959			−0.329739			−0.164870	−	0.986315i	$-0.552720\pi$
$419$	−6.74959			−0.329739			−0.164870	+	0.986315i	$0.552720\pi$
$420$	−4.81733	+	2.53556i	−0.235062	+	0.123723i
$421$	−1.66512	+	2.88407i	−0.0811529	+	0.140561i	−0.903745	−	0.428070i	$-0.859194\pi$
$421$	−1.66512	+	2.88407i	−0.0811529	+	0.140561i	0.822593	+	0.568631i	$0.192527\pi$
$422$	6.35058	−	3.66651i	0.309141	−	0.178483i
$423$	−1.72589	−	0.996441i	−0.0839155	−	0.0484486i
$424$	−5.46443	+	9.46466i	−0.265376	+	0.459645i
$425$	−20.9375	−	14.3795i	−1.01562	−	0.697509i
$426$	11.3259			0.548742
$427$	−16.3951	+	9.46569i	−0.793412	+	0.458077i
$428$	3.59914	−	2.07797i	0.173971	−	0.100442i
$429$	−0.662694	+	1.14782i	−0.0319952	+	0.0554173i
$430$	−0.921702	+	23.5606i	−0.0444484	+	1.13619i
$431$	−14.7762	−	25.5931i	−0.711743	−	1.23277i	−0.964202	−	0.265167i	$-0.914573\pi$
$431$	−14.7762	−	25.5931i	−0.711743	−	1.23277i	0.252460	−	0.967607i	$-0.418760\pi$
$432$			1.00000i			0.0481125i
$433$			6.33397i			0.304391i	0.988350	+	0.152196i	$0.0486344\pi$
$433$			6.33397i			0.304391i	−0.988350	+	0.152196i	$0.951366\pi$
$434$	11.5282	+	7.13043i	0.553370	+	0.342271i
$435$	15.6223	+	0.611150i	0.749031	+	0.0293024i
$436$	−18.2124			−0.872218
$437$	−25.4263	+	14.6799i	−1.21630	+	0.702233i
$438$		−	6.17482i		−	0.295044i
$439$	−3.26078	+	5.64784i	−0.155629	+	0.269556i	−0.933288	−	0.359130i	$-0.883074\pi$
$439$	−3.26078	+	5.64784i	−0.155629	+	0.269556i	0.777659	+	0.628686i	$0.216407\pi$
$440$	−0.719476	−	1.36694i	−0.0342997	−	0.0651661i
$441$	0.536422	+	0.929110i	0.0255439	+	0.0442433i
$442$			9.74628i			0.463583i
$443$	−13.2623	−	7.65698i	−0.630110	−	0.363794i	0.150685	−	0.988582i	$-0.451852\pi$
$443$	−13.2623	−	7.65698i	−0.630110	−	0.363794i	−0.780795	+	0.624788i	$0.785186\pi$
$444$	0.735092	−	1.27322i	0.0348859	−	0.0604242i
$445$	−13.8339	−	8.72524i	−0.655788	−	0.413616i
$446$	−0.858684	−	1.48728i	−0.0406599	−	0.0704250i
$447$	−15.7456	−	9.09075i	−0.744743	−	0.429978i
$448$	−2.10840	+	1.21729i	−0.0996127	+	0.0575114i
$449$	−12.4145			−0.585875			−0.292938	−	0.956132i	$-0.594633\pi$
$449$	−12.4145			−0.585875			−0.292938	+	0.956132i	$0.594633\pi$
$450$	−0.390607	+	4.98472i	−0.0184134	+	0.234982i
$451$	−4.10378	−	7.10795i	−0.193239	−	0.334700i
$452$	−17.0560	−	9.84730i	−0.802248	−	0.463178i
$453$	3.83339	−	2.21321i	0.180108	−	0.103985i
$454$	8.86071	−	15.3472i	0.415854	−	0.720280i
$455$	8.83413	+	5.57183i	0.414150	+	0.261211i
$456$	−2.14339	+	3.71246i	−0.100373	+	0.173852i
$457$			6.38963i			0.298894i	0.988770	+	0.149447i	$0.0477494\pi$
$457$			6.38963i			0.298894i	−0.988770	+	0.149447i	$0.952251\pi$
$458$	0.570139	−	0.329170i	0.0266408	−	0.0153811i
$459$	−2.53998	−	4.39938i	−0.118556	−	0.205345i
$460$	−8.16989	+	12.9534i	−0.380923	+	0.603953i
$461$	2.58745			0.120509			0.0602547	−	0.998183i	$-0.480809\pi$
$461$	2.58745			0.120509			0.0602547	+	0.998183i	$0.480809\pi$
$462$	1.45653	−	0.840926i	0.0677638	−	0.0391234i
$463$			18.0339i			0.838106i	0.907962	+	0.419053i	$0.137638\pi$
$463$			18.0339i			0.838106i	−0.907962	+	0.419053i	$0.862362\pi$
$464$	6.99184			0.324588
$465$	11.1878	−	5.46198i	0.518822	−	0.253293i
$466$	−14.8471			−0.687780
$467$		−	9.09546i		−	0.420888i	−0.977606	−	0.210444i	$-0.932509\pi$
$467$		−	9.09546i		−	0.420888i	0.977606	−	0.210444i	$-0.0674909\pi$
$468$	1.66153	−	0.959287i	0.0768044	−	0.0443431i
$469$	34.5387			1.59485
$470$	−3.76915	−	2.37727i	−0.173858	−	0.109655i
$471$	−2.54596	−	4.40974i	−0.117312	−	0.203190i
$472$	3.09535	−	1.78710i	0.142475	−	0.0822581i
$473$		−	7.28448i		−	0.334941i
$474$	−7.37533	+	12.7744i	−0.338760	+	0.586749i
$475$	−12.1343	+	17.6684i	−0.556761	+	0.810680i
$476$	6.18377	−	10.7106i	0.283433	−	0.490920i
$477$	−9.46466	+	5.46443i	−0.433357	+	0.250199i
$478$	−9.80807	−	5.66269i	−0.448611	−	0.259006i
$479$	−3.98541	−	6.90292i	−0.182098	−	0.315403i	0.760497	−	0.649342i	$-0.224955\pi$
$479$	−3.98541	−	6.90292i	−0.182098	−	0.315403i	−0.942595	+	0.333939i	$0.891622\pi$
$480$	−0.0874091	+	2.23436i	−0.00398966	+	0.101984i
$481$	−2.82065			−0.128611
$482$	21.3510	−	12.3270i	0.972511	−	0.561480i
$483$	−14.4402	−	8.33707i	−0.657053	−	0.379350i
$484$	−5.26138	−	9.11298i	−0.239154	−	0.414227i
$485$	11.6860	−	18.5281i	0.530634	−	0.841319i
$486$	−0.500000	+	0.866025i	−0.0226805	+	0.0392837i
$487$	−17.4128	−	10.0533i	−0.789047	−	0.455557i	0.0505797	−	0.998720i	$-0.483893\pi$
$487$	−17.4128	−	10.0533i	−0.789047	−	0.455557i	−0.839627	+	0.543163i	$0.817226\pi$
$488$			7.77605i			0.352005i
$489$	1.23080	+	2.13181i	0.0556587	+	0.0964037i
$490$	1.11735	+	2.12285i	0.0504766	+	0.0959007i
$491$	7.90372	−	13.6896i	0.356690	−	0.617805i	−0.630716	−	0.776014i	$-0.717239\pi$
$491$	7.90372	−	13.6896i	0.356690	−	0.617805i	0.987406	+	0.158209i	$0.0505720\pi$
$492$			11.8809i			0.535632i
$493$	−30.7597	+	17.7591i	−1.38535	+	0.799831i
$494$	8.22451			0.370038
$495$	0.0603839	−	1.54354i	0.00271406	−	0.0693769i
$496$	4.90403	−	2.63639i	0.220197	−	0.118377i
$497$			27.5738i			1.23685i
$498$			0.873140i			0.0391263i
$499$	−5.91086	−	10.2379i	−0.264606	−	0.458312i	0.702854	−	0.711334i	$-0.251909\pi$
$499$	−5.91086	−	10.2379i	−0.264606	−	0.458312i	−0.967460	+	0.253023i	$0.918575\pi$
$500$	−1.30847	+	11.1035i	−0.0585163	+	0.496564i
$501$	0.383733	−	0.664645i	0.0171439	−	0.0296941i
$502$	19.8463	−	11.4583i	0.885785	−	0.511408i
$503$	−16.9547	+	9.78878i	−0.755971	+	0.436460i	−0.827847	−	0.560954i	$-0.810435\pi$
$503$	−16.9547	+	9.78878i	−0.755971	+	0.436460i	0.0718764	+	0.997414i	$0.477101\pi$
$504$	−2.43458			−0.108445
$505$	20.6246	+	13.0083i	0.917784	+	0.578861i
$506$	2.36567	−	4.09747i	0.105167	−	0.182155i
$507$	8.07056	+	4.65954i	0.358426	+	0.206937i
$508$	−14.0922	+	8.13615i	−0.625242	+	0.360983i
$509$	12.2510	−	21.2194i	0.543016	−	0.940531i	−0.455713	−	0.890127i	$-0.650616\pi$
$509$	12.2510	−	21.2194i	0.543016	−	0.940531i	0.998729	−	0.0504044i	$-0.0160510\pi$
$510$	−5.29068	−	10.0518i	−0.234275	−	0.445101i
$511$	15.0331			0.665023
$512$			1.00000i			0.0441942i
$513$	−3.71246	+	2.14339i	−0.163909	+	0.0946330i
$514$	−4.25708	+	7.37347i	−0.187772	+	0.325230i
$515$	−7.81883	−	14.8551i	−0.344539	−	0.654592i
$516$	−5.27234	+	9.13197i	−0.232102	+	0.402013i
$517$	1.19228	+	0.688361i	0.0524363	+	0.0302741i
$518$	3.09974	+	1.78964i	0.136195	+	0.0786321i
$519$	2.11771			0.0929571
$520$	3.79631	−	1.99816i	0.166479	−	0.0876250i
$521$	−6.10042	−	10.5662i	−0.267264	−	0.462915i	0.700890	−	0.713269i	$-0.252786\pi$
$521$	−6.10042	−	10.5662i	−0.267264	−	0.462915i	−0.968154	+	0.250354i	$0.919453\pi$
$522$	6.05511	+	3.49592i	0.265025	+	0.153012i
$523$			11.9913i			0.524342i	0.965021	+	0.262171i	$0.0844385\pi$
$523$			11.9913i			0.524342i	−0.965021	+	0.262171i	$0.915561\pi$
$524$	10.0338	+	17.3791i	0.438330	+	0.759209i
$525$	−12.1357	−	0.950961i	−0.529644	−	0.0415033i
$526$	26.9888			1.17677
$527$	−14.8783	+	24.0546i	−0.648108	+	1.04783i
$528$		−	0.690820i		−	0.0300641i
$529$	−23.9073			−1.03945
$530$	−21.6251	+	11.3822i	−0.939334	+	0.494411i
$531$	3.57420			0.155107
$532$	−9.03827	−	5.21825i	−0.391859	−	0.226240i
$533$	19.7405	−	11.3972i	0.855056	−	0.493667i
$534$	−3.65722	−	6.33450i	−0.158264	−	0.274121i
$535$	9.28584	+	0.363266i	0.401462	+	0.0157054i
$536$	7.09338	−	12.2861i	0.306387	−	0.530678i
$537$	−4.46829	−	2.57977i	−0.192821	−	0.111325i
$538$	4.97896	+	2.87461i	0.214658	+	0.123933i
$539$	−0.370571	−	0.641847i	−0.0159616	−	0.0276463i
$540$	−1.19288	+	1.89131i	−0.0513333	+	0.0813889i
$541$	8.12723	+	14.0768i	0.349417	+	0.605208i	0.986146	−	0.165880i	$-0.0530463\pi$
$541$	8.12723	+	14.0768i	0.349417	+	0.605208i	−0.636729	+	0.771088i	$0.719713\pi$
$542$		−	3.56495i		−	0.153128i
$543$		−	9.53838i		−	0.409331i
$544$	−2.53998	−	4.39938i	−0.108901	−	0.188622i
$545$	−34.4453	−	21.7252i	−1.47548	−	0.930607i
$546$	2.33546	+	4.04513i	0.0999483	+	0.173116i
$547$	21.5351	+	12.4333i	0.920773	+	0.531608i	0.883881	−	0.467711i	$-0.154921\pi$
$547$	21.5351	+	12.4333i	0.920773	+	0.531608i	0.0368912	+	0.999319i	$0.488255\pi$
$548$	−5.58082	−	3.22209i	−0.238401	−	0.137641i
$549$	−3.88802	+	6.73426i	−0.165937	+	0.287411i
$550$	0.269839	−	3.44354i	0.0115060	−	0.146833i
$551$	14.9862	+	25.9569i	0.638435	+	1.10580i
$552$	−5.93131	+	3.42445i	−0.252454	+	0.145754i
$553$	−31.1003	−	17.9558i	−1.32252	−	0.763558i
$554$	17.7469			0.753994
$555$	2.90908	−	1.53117i	0.123483	−	0.0649945i
$556$	6.56923			0.278597
$557$			23.7472i			1.00620i	0.864228	+	0.503101i	$0.167808\pi$
$557$			23.7472i			1.00620i	−0.864228	+	0.503101i	$0.832192\pi$
$558$	5.56520	+	0.168835i	0.235594	+	0.00714737i
$559$	20.2308			0.855670
$560$	−5.43971	−	0.212804i	−0.229870	−	0.00899261i
$561$	1.75467	+	3.03918i	0.0740822	+	0.128314i
$562$			16.1982i			0.683281i
$563$	−10.1675	−	5.87021i	−0.428509	−	0.247400i	0.270202	−	0.962804i	$-0.412909\pi$
$563$	−10.1675	−	5.87021i	−0.428509	−	0.247400i	−0.698711	+	0.715404i	$0.746243\pi$
$564$	−0.996441	−	1.72589i	−0.0419577	−	0.0726730i
$565$	−20.5115	−	38.9700i	−0.862927	−	1.63948i
$566$	19.8725			0.835305
$567$	−2.10840	−	1.21729i	−0.0885446	−	0.0511213i
$568$	9.80852	+	5.66295i	0.411556	+	0.237612i
$569$	−0.658270	+	1.14016i	−0.0275961	+	0.0477979i	−0.879494	−	0.475911i	$-0.842119\pi$
$569$	−0.658270	+	1.14016i	−0.0275961	+	0.0477979i	0.851898	+	0.523709i	$0.175452\pi$
$570$	−8.48232	+	4.46460i	−0.355285	+	0.187002i
$571$	9.37311	−	16.2347i	0.392252	−	0.679401i	−0.600494	−	0.799629i	$-0.705029\pi$
$571$	9.37311	−	16.2347i	0.392252	−	0.679401i	0.992746	+	0.120228i	$0.0383626\pi$
$572$	−1.14782	+	0.662694i	−0.0479928	+	0.0277086i
$573$		−	25.4738i		−	1.06418i
$574$	−28.9249			−1.20730
$575$	−30.9035	+	14.7531i	−1.28877	+	0.615246i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	19.1757	−	11.0711i	0.798294	−	0.460895i	−0.0445803	−	0.999006i	$-0.514195\pi$
$577$	19.1757	−	11.0711i	0.798294	−	0.460895i	0.842874	+	0.538111i	$0.180862\pi$
$578$	7.62622	+	4.40300i	0.317209	+	0.183141i
$579$	7.47378	−	12.9450i	0.310600	−	0.537974i
$580$	13.2237	+	8.34041i	0.549085	+	0.346317i
$581$	−2.12572			−0.0881899
$582$	8.48399	−	4.89824i	0.351673	−	0.203038i
$583$	6.53838	−	3.77493i	0.270792	−	0.156342i
$584$	3.08741	−	5.34755i	0.127758	−	0.221283i
$585$	4.28678	+	0.167701i	0.177237	+	0.00693357i
$586$	3.08240	+	5.33888i	0.127333	+	0.220547i
$587$			35.5097i			1.46564i	0.680422	+	0.732821i	$0.261797\pi$
$587$			35.5097i			1.46564i	−0.680422	+	0.732821i	$0.738203\pi$
$588$			1.07284i			0.0442433i
$589$	20.2987	+	12.5552i	0.836395	+	0.517328i
$590$	7.98606	+	0.312418i	0.328781	+	0.0128620i
$591$	7.85036			0.322921
$592$	1.27322	−	0.735092i	0.0523289	−	0.0302121i
$593$		−	33.3732i		−	1.37047i	−0.728321	−	0.685236i	$-0.759699\pi$
$593$		−	33.3732i		−	1.37047i	0.728321	−	0.685236i	$-0.240301\pi$
$594$	0.345410	−	0.598267i	0.0141723	−	0.0245472i
$595$	24.4719	−	12.8806i	1.00325	−	0.528052i
$596$	−9.09075	−	15.7456i	−0.372371	−	0.644966i
$597$			8.30791i			0.340020i
$598$	11.3797	+	6.57005i	0.465349	+	0.268669i
$599$	13.2395	−	22.9315i	0.540951	−	0.936955i	−0.457898	−	0.889004i	$-0.651398\pi$
$599$	13.2395	−	22.9315i	0.540951	−	0.936955i	0.998850	−	0.0479505i	$-0.0152690\pi$
$600$	−2.83063	+	4.12159i	−0.115560	+	0.168263i
$601$	−6.21030	−	10.7566i	−0.253323	−	0.438769i	0.711115	−	0.703075i	$-0.248190\pi$
$601$	−6.21030	−	10.7566i	−0.253323	−	0.438769i	−0.964439	+	0.264306i	$0.914857\pi$
$602$	−22.2325	−	12.8359i	−0.906128	−	0.523153i
$603$	12.2861	−	7.09338i	0.500328	−	0.288865i
$604$	4.42641			0.180108
$605$	0.919786	−	23.5116i	0.0373946	−	0.955884i
$606$	5.45248	+	9.44397i	0.221492	+	0.383635i
$607$	11.8505	+	6.84190i	0.480998	+	0.277704i	0.720832	−	0.693110i	$-0.243760\pi$
$607$	11.8505	+	6.84190i	0.480998	+	0.277704i	−0.239834	+	0.970814i	$0.577093\pi$
$608$	−3.71246	+	2.14339i	−0.150560	+	0.0869260i
$609$	−8.51108	+	14.7416i	−0.344886	+	0.597360i
$610$	−9.27588	+	14.7069i	−0.375569	+	0.595465i
$611$	−1.91175	+	3.31124i	−0.0773410	+	0.133958i
$612$		−	5.07996i		−	0.205345i
$613$	−7.33980	+	4.23763i	−0.296452	+	0.171156i	−0.640848	−	0.767668i	$-0.721417\pi$
$613$	−7.33980	+	4.23763i	−0.296452	+	0.171156i	0.344396	+	0.938824i	$0.388084\pi$
$614$	−8.50942	−	14.7387i	−0.343412	−	0.594807i
$615$	−14.1725	+	22.4704i	−0.571489	+	0.906095i
$616$	1.68185			0.0677638
$617$	22.0069	−	12.7057i	0.885963	−	0.511511i	0.0133429	−	0.999911i	$-0.495753\pi$
$617$	22.0069	−	12.7057i	0.885963	−	0.511511i	0.872620	+	0.488400i	$0.162419\pi$
$618$		−	7.50742i		−	0.301993i
$619$	−19.6236			−0.788738			−0.394369	−	0.918952i	$-0.629037\pi$
$619$	−19.6236			−0.788738			−0.394369	+	0.918952i	$0.629037\pi$
$620$	12.4199	+	0.863688i	0.498795	+	0.0346866i
$621$	−6.84889			−0.274837
$622$			15.0411i			0.603093i
$623$	15.4218	−	8.90379i	0.617862	−	0.356723i
$624$	1.91857			0.0768044
$625$	−15.7198	+	19.4393i	−0.628794	+	0.777572i
$626$	−6.28401	−	10.8842i	−0.251159	−	0.435021i
$627$	2.56464	−	1.48070i	0.102422	−	0.0591333i
$628$		−	5.09193i		−	0.203190i
$629$	−3.73424	+	6.46789i	−0.148894	+	0.257892i
$630$	−4.60453	−	2.90415i	−0.183449	−	0.115704i
$631$	−19.5977	+	33.9442i	−0.780171	+	1.35130i	0.151671	+	0.988431i	$0.451535\pi$
$631$	−19.5977	+	33.9442i	−0.780171	+	1.35130i	−0.931842	+	0.362865i	$0.881799\pi$
$632$	−12.7744	+	7.37533i	−0.508140	+	0.293375i
$633$	6.35058	+	3.66651i	0.252413	+	0.145731i
$634$	8.22860	+	14.2524i	0.326800	+	0.566033i
$635$	−36.3582	−	1.42235i	−1.44283	−	0.0564441i
$636$	−10.9289			−0.433357
$637$	1.78257	−	1.02916i	0.0706278	−	0.0407770i
$638$	−4.18299	−	2.41505i	−0.165606	−	0.0956127i
$639$	5.66295	+	9.80852i	0.224023	+	0.388019i
$640$	−1.19288	+	1.89131i	−0.0471526	+	0.0747605i
$641$	−6.98552	+	12.0993i	−0.275911	+	0.477892i	−0.970365	−	0.241645i	$-0.922313\pi$
$641$	−6.98552	+	12.0993i	−0.275911	+	0.477892i	0.694453	+	0.719538i	$0.255646\pi$
$642$	3.59914	+	2.07797i	0.142047	+	0.0820108i
$643$			41.1320i			1.62209i	0.584987	+	0.811043i	$0.301100\pi$
$643$			41.1320i			1.62209i	−0.584987	+	0.811043i	$0.698900\pi$
$644$	−8.33707	−	14.4402i	−0.328527	−	0.569025i
$645$	−20.8649	+	10.9821i	−0.821556	+	0.432419i
$646$	10.8883	−	18.8592i	0.428396	−	0.742004i
$647$		−	31.8054i		−	1.25040i	−0.780465	−	0.625199i	$-0.785018\pi$
$647$		−	31.8054i		−	1.25040i	0.780465	−	0.625199i	$-0.214982\pi$
$648$	−0.866025	+	0.500000i	−0.0340207	+	0.0196419i
$649$	−2.46913			−0.0969219
$650$	9.56355	+	0.749408i	0.375113	+	0.0293942i
$651$	−0.411042	+	13.5489i	−0.0161100	+	0.531024i
$652$			2.46160i			0.0964037i
$653$			27.3114i			1.06878i	0.845239	+	0.534388i	$0.179458\pi$
$653$			27.3114i			1.06878i	−0.845239	+	0.534388i	$0.820542\pi$
$654$	−9.10622	−	15.7724i	−0.356082	−	0.616751i
$655$	−1.75410	+	44.8383i	−0.0685382	+	1.75198i
$656$	−5.94045	+	10.2892i	−0.231936	+	0.401724i
$657$	5.34755	−	3.08741i	0.208628	−	0.120451i
$658$	4.20180	−	2.42591i	0.163803	−	0.0945719i
$659$	19.1290			0.745159			0.372580	−	0.928000i	$-0.378473\pi$
$659$	19.1290			0.745159			0.372580	+	0.928000i	$0.378473\pi$
$660$	0.824064	−	1.30655i	0.0320766	−	0.0508575i
$661$	−14.5648	+	25.2270i	−0.566505	+	0.981215i	0.430403	+	0.902637i	$0.358371\pi$
$661$	−14.5648	+	25.2270i	−0.566505	+	0.981215i	−0.996908	+	0.0785782i	$0.974962\pi$
$662$	5.06429	+	2.92387i	0.196829	+	0.113639i
$663$	−8.44053	+	4.87314i	−0.327803	+	0.189257i
$664$	−0.436570	+	0.756161i	−0.0169422	+	0.0293447i
$665$	−10.8694	−	20.6509i	−0.421498	−	0.800806i
$666$	1.47018			0.0569684
$667$			47.8863i			1.85417i
$668$	0.664645	−	0.383733i	0.0257159	−	0.0148471i
$669$	0.858684	−	1.48728i	0.0331986	−	0.0575017i
$670$	28.0716	−	14.7752i	1.08450	−	0.570817i
$671$	2.68592	−	4.65216i	0.103689	−	0.179595i
$672$	−2.10840	−	1.21729i	−0.0813334	−	0.0469579i
$673$	−25.0845	−	14.4825i	−0.966935	−	0.558260i	−0.0686345	−	0.997642i	$-0.521864\pi$
$673$	−25.0845	−	14.4825i	−0.966935	−	0.558260i	−0.898300	+	0.439382i	$0.855198\pi$
$674$	−31.5048			−1.21352
$675$	−4.51220	+	2.15408i	−0.173675	+	0.0829107i
$676$	4.65954	+	8.07056i	0.179213	+	0.310406i
$677$	10.6112	+	6.12637i	0.407821	+	0.235456i	0.689853	−	0.723949i	$-0.257675\pi$
$677$	10.6112	+	6.12637i	0.407821	+	0.235456i	−0.282032	+	0.959405i	$0.591008\pi$
$678$		−	19.6946i		−	0.756366i
$679$	11.9251	+	20.6549i	0.457644	+	0.792663i
$680$	0.444035	−	11.3505i	0.0170280	−	0.435270i
$681$	17.7214			0.679086
$682$	−3.84455	−	0.116635i	−0.147216	−	0.00446618i
$683$		−	25.1914i		−	0.963924i	−0.876192	−	0.481962i	$-0.839924\pi$
$683$		−	25.1914i		−	0.963924i	0.876192	−	0.481962i	$-0.160076\pi$
$684$	−4.28678			−0.163909
$685$	−6.71149	−	12.7512i	−0.256433	−	0.487198i
$686$	−19.6539			−0.750391
$687$	0.570139	+	0.329170i	0.0217522	+	0.0125586i
$688$	−9.13197	+	5.27234i	−0.348153	+	0.201006i
$689$	10.4839	+	18.1587i	0.399405	+	0.691790i
$690$	−15.3029	−	0.598655i	−0.582571	−	0.0227904i
$691$	−4.46066	+	7.72609i	−0.169691	+	0.293914i	−0.938311	−	0.345791i	$-0.887610\pi$
$691$	−4.46066	+	7.72609i	−0.169691	+	0.293914i	0.768620	+	0.639706i	$0.220944\pi$
$692$	1.83399	+	1.05885i	0.0697178	+	0.0402516i
$693$	1.45653	+	0.840926i	0.0553289	+	0.0319441i
$694$	7.19454	+	12.4613i	0.273101	+	0.473025i
$695$	12.4244	+	7.83629i	0.471285	+	0.297247i
$696$	3.49592	+	6.05511i	0.132512	+	0.229518i
$697$		−	60.3545i		−	2.28609i
$698$		−	19.6230i		−	0.742740i
$699$	−7.42357	−	12.8580i	−0.280785	−	0.486334i
$700$	−10.0343	−	6.89139i	−0.379262	−	0.260470i
$701$	25.2498	+	43.7339i	0.953670	+	1.65181i	0.737382	+	0.675476i	$0.236062\pi$
$701$	25.2498	+	43.7339i	0.953670	+	1.65181i	0.216289	+	0.976329i	$0.430605\pi$
$702$	1.66153	+	0.959287i	0.0627105	+	0.0362059i
$703$	5.45800	+	3.15118i	0.205852	+	0.118849i
$704$	0.345410	−	0.598267i	0.0130181	−	0.0225481i
$705$	0.174196	−	4.45281i	0.00656060	−	0.167703i
$706$	3.43373	+	5.94740i	0.129230	+	0.223833i
$707$	−22.9921	+	13.2745i	−0.864705	+	0.499238i
$708$	3.09535	+	1.78710i	0.116330	+	0.0671634i
$709$	−7.69872			−0.289131			−0.144566	−	0.989495i	$-0.546178\pi$
$709$	−7.69872			−0.289131			−0.144566	+	0.989495i	$0.546178\pi$
$710$	11.7957	+	22.4107i	0.442685	+	0.841060i
$711$	−14.7507			−0.553193
$712$		−	7.31445i		−	0.274121i
$713$	18.0563	+	33.5871i	0.676215	+	1.25785i
$714$	12.3675			0.462844
$715$	−2.96139	−	0.115851i	−0.110750	−	0.00433258i
$716$	−2.57977	−	4.46829i	−0.0964105	−	0.166988i
$717$		−	11.3254i		−	0.422954i
$718$	6.00700	+	3.46814i	0.224179	+	0.129430i
$719$	12.6926	+	21.9842i	0.473353	+	0.819872i	0.999535	−	0.0305002i	$-0.00971002\pi$
$719$	12.6926	+	21.9842i	0.473353	+	0.819872i	−0.526181	+	0.850372i	$0.676377\pi$
$720$	−1.97872	+	1.04148i	−0.0737424	+	0.0388137i
$721$	18.2774			0.680685
$722$	0.539966	+	0.311749i	0.0200954	+	0.0116021i
$723$	21.3510	+	12.3270i	0.794052	+	0.458446i
$724$	4.76919	−	8.26048i	0.177245	−	0.306998i
$725$	15.0610	+	31.5485i	0.559352	+	1.17168i
$726$	5.26138	−	9.11298i	0.195268	−	0.338215i
$727$	26.3923	−	15.2376i	0.978837	−	0.565132i	0.0769182	−	0.997037i	$-0.475492\pi$
$727$	26.3923	−	15.2376i	0.978837	−	0.565132i	0.901919	+	0.431906i	$0.142159\pi$
$728$			4.67091i			0.173116i
$729$	−1.00000			−0.0370370
$730$	12.2182	−	6.43096i	0.452216	−	0.238020i
$731$	26.7833	−	46.3900i	0.990616	−	1.71580i
$732$	−6.73426	+	3.88802i	−0.248905	+	0.143706i
$733$	2.90532	+	1.67739i	0.107311	+	0.0619558i	0.552695	−	0.833384i	$-0.313600\pi$
$733$	2.90532	+	1.67739i	0.107311	+	0.0619558i	−0.445384	+	0.895340i	$0.646933\pi$
$734$	−16.3161	+	28.2604i	−0.602240	+	1.04311i
$735$	−1.27977	+	2.02908i	−0.0472051	+	0.0748436i
$736$	−6.84889			−0.252454
$737$	−8.48748	+	4.90025i	−0.312640	+	0.180503i
$738$	−10.2892	+	5.94045i	−0.378749	+	0.218671i
$739$	−2.15223	+	3.72777i	−0.0791711	+	0.137128i	−0.902893	−	0.429866i	$-0.858561\pi$
$739$	−2.15223	+	3.72777i	−0.0791711	+	0.137128i	0.823721	+	0.566995i	$0.191894\pi$
$740$	3.28492	+	0.128507i	0.120756	+	0.00472403i
$741$	4.11225	+	7.12263i	0.151067	+	0.261656i
$742$		−	26.6071i		−	0.976778i
$743$		−	42.6403i		−	1.56432i	−0.623077	−	0.782161i	$-0.714118\pi$
$743$		−	42.6403i		−	1.56432i	0.623077	−	0.782161i	$-0.285882\pi$
$744$	4.73519	+	2.92882i	0.173600	+	0.107376i
$745$	1.58923	−	40.6240i	0.0582248	−	1.48835i
$746$	12.7573			0.467076
$747$	−0.756161	+	0.436570i	−0.0276665	+	0.0159733i
$748$			3.50934i			0.128314i
$749$	−5.05897	+	8.76238i	−0.184851	+	0.320171i
$750$	−10.2702	+	4.41859i	−0.375013	+	0.161344i
$751$	14.5357	+	25.1766i	0.530415	+	0.918706i	0.999370	+	0.0354843i	$0.0112974\pi$
$751$	14.5357	+	25.1766i	0.530415	+	0.918706i	−0.468955	+	0.883222i	$0.655369\pi$
$752$		−	1.99288i		−	0.0726730i
$753$	19.8463	+	11.4583i	0.723241	+	0.417563i
$754$	6.70718	−	11.6172i	0.244261	−	0.423072i
$755$	8.37170	+	5.28017i	0.304677	+	0.192165i
$756$	−1.21729	−	2.10840i	−0.0442723	−	0.0766819i
$757$	−7.88304	−	4.55128i	−0.286514	−	0.165419i	0.349855	−	0.936804i	$-0.386231\pi$
$757$	−7.88304	−	4.55128i	−0.286514	−	0.165419i	−0.636369	+	0.771385i	$0.719564\pi$
$758$	7.66113	−	4.42316i	0.278265	−	0.160656i
$759$	4.73135			0.171737
$760$	−9.57821	−	0.374704i	−0.347438	−	0.0135919i
$761$	−10.8502	−	18.7931i	−0.393319	−	0.681248i	0.599566	−	0.800325i	$-0.295340\pi$
$761$	−10.8502	−	18.7931i	−0.393319	−	0.681248i	−0.992885	+	0.119077i	$0.962006\pi$
$762$	−14.0922	−	8.13615i	−0.510508	−	0.294742i
$763$	38.3992	−	22.1698i	1.39014	−	0.802600i
$764$	12.7369	−	22.0610i	0.460805	−	0.798138i
$765$	6.05977	−	9.60777i	0.219092	−	0.347370i
$766$	0.363643	−	0.629849i	0.0131390	−	0.0227574i
$767$		−	6.85738i		−	0.247605i
$768$	−0.866025	+	0.500000i	−0.0312500	+	0.0180422i
$769$	−20.5788	−	35.6435i	−0.742090	−	1.28534i	−0.951542	−	0.307519i	$-0.900501\pi$
$769$	−20.5788	−	35.6435i	−0.742090	−	1.28534i	0.209452	−	0.977819i	$-0.432832\pi$
$770$	3.18090	+	2.00624i	0.114632	+	0.0723000i
$771$	−8.51415			−0.306630
$772$	12.9450	−	7.47378i	0.465899	−	0.268987i
$773$		−	36.6320i		−	1.31756i	−0.752336	−	0.658780i	$-0.771073\pi$
$773$		−	36.6320i		−	1.31756i	0.752336	−	0.658780i	$-0.228927\pi$
$774$	−10.5447			−0.379021
$775$	22.4596	+	16.4489i	0.806772	+	0.590863i
$776$	9.79647			0.351673
$777$			3.57927i			0.128406i
$778$	7.57312	−	4.37234i	0.271509	−	0.156756i
$779$	−50.9308			−1.82479
$780$	3.62861	+	2.28862i	0.129925	+	0.0819459i
$781$	−3.91208	−	6.77592i	−0.139985	−	0.242461i
$782$	30.1308	−	17.3961i	1.07748	−	0.622082i
$783$			6.99184i			0.249868i
$784$	−0.536422	+	0.929110i	−0.0191579	+	0.0331825i
$785$	6.07405	−	9.63040i	0.216792	−	0.343724i
$786$	−10.0338	+	17.3791i	−0.357895	+	0.619892i
$787$	21.4117	−	12.3620i	0.763245	−	0.440659i	−0.0672149	−	0.997739i	$-0.521411\pi$
$787$	21.4117	−	12.3620i	0.763245	−	0.440659i	0.830459	+	0.557079i	$0.188078\pi$
$788$	6.79861	+	3.92518i	0.242190	+	0.139829i
$789$	13.4944	+	23.3730i	0.480414	+	0.832101i
$790$	−32.9582	−	1.28934i	−1.17260	−	0.0458727i
$791$	47.9480			1.70483
$792$	0.598267	−	0.345410i	0.0212585	−	0.0122736i
$793$	12.9202	+	7.45946i	0.458809	+	0.264893i
$794$	−5.83790	−	10.1115i	−0.207179	−	0.358845i
$795$	−20.6698	−	13.0368i	−0.733083	−	0.462367i
$796$	−4.15396	+	7.19486i	−0.147233	+	0.255015i
$797$	17.2891	+	9.98189i	0.612413	+	0.353577i	0.773909	−	0.633297i	$-0.218299\pi$
$797$	17.2891	+	9.98189i	0.612413	+	0.353577i	−0.161496	+	0.986873i	$0.551632\pi$
$798$		−	10.4365i		−	0.369448i
$799$	5.06188	+	8.76744i	0.179077	+	0.310170i
$800$	−4.51220	+	2.15408i	−0.159530	+	0.0761584i
$801$	3.65722	−	6.33450i	0.129222	−	0.223818i
$802$			15.2311i			0.537828i
$803$	−3.69419	+	2.13284i	−0.130365	+	0.0752664i
$804$	14.1868			0.500328
$805$	1.45747	−	37.2560i	0.0513691	−	1.31310i
$806$	0.323923	−	10.6773i	0.0114097	−	0.376090i
$807$			5.74921i			0.202382i
$808$			10.9050i			0.383635i
$809$	−4.02229	−	6.96682i	−0.141416	−	0.244940i	0.786614	−	0.617445i	$-0.211832\pi$
$809$	−4.02229	−	6.96682i	−0.141416	−	0.244940i	−0.928030	+	0.372505i	$0.878499\pi$
$810$	−2.23436	−	0.0874091i	−0.0785074	−	0.00307124i
$811$	15.1758	−	26.2853i	0.532896	−	0.923002i	−0.466366	−	0.884592i	$-0.654437\pi$
$811$	15.1758	−	26.2853i	0.532896	−	0.923002i	0.999262	−	0.0384107i	$-0.0122295\pi$
$812$	−14.7416	+	8.51108i	−0.517329	+	0.298680i
$813$	3.08734	−	1.78247i	0.108278	−	0.0625141i
$814$	−1.01563			−0.0355979
$815$	−2.93639	+	4.65564i	−0.102857	+	0.163080i
$816$	2.53998	−	4.39938i	0.0889171	−	0.154009i
$817$	−39.1468	−	22.6014i	−1.36957	−	0.790723i
$818$	−29.2261	+	16.8737i	−1.02187	+	0.589974i
$819$	−2.33546	+	4.04513i	−0.0816074	+	0.141348i
$820$	−23.5089	+	12.3737i	−0.820967	+	0.432109i
$821$	28.1161			0.981258			0.490629	−	0.871368i	$-0.336767\pi$
$821$	28.1161			0.981258			0.490629	+	0.871368i	$0.336767\pi$
$822$		−	6.44418i		−	0.224767i
$823$	28.6774	−	16.5569i	0.999632	−	0.577138i	0.0914925	−	0.995806i	$-0.470836\pi$
$823$	28.6774	−	16.5569i	0.999632	−	0.577138i	0.908139	+	0.418668i	$0.137503\pi$
$824$	3.75371	−	6.50162i	0.130767	−	0.226495i
$825$	3.11711	−	1.48808i	0.108524	−	0.0518084i
$826$	−4.35084	+	7.53587i	−0.151385	+	0.262206i
$827$	−2.15353	−	1.24334i	−0.0748856	−	0.0432352i	0.462090	−	0.886833i	$-0.347100\pi$
$827$	−2.15353	−	1.24334i	−0.0748856	−	0.0432352i	−0.536975	+	0.843598i	$0.680433\pi$
$828$	−5.93131	−	3.42445i	−0.206127	−	0.119008i
$829$	−17.9231			−0.622495			−0.311247	−	0.950329i	$-0.600747\pi$
$829$	−17.9231			−0.622495			−0.311247	+	0.950329i	$0.600747\pi$
$830$	−1.72770	+	0.909358i	−0.0599692	+	0.0315643i
$831$	8.87346	+	15.3693i	0.307817	+	0.533154i
$832$	1.66153	+	0.959287i	0.0576033	+	0.0332573i
$833$		−	5.45000i		−	0.188831i
$834$	3.28461	+	5.68912i	0.113737	+	0.196998i
$835$	1.71479	+	0.0670835i	0.0593429	+	0.00232152i
$836$	2.96139			0.102422
$837$	2.63639	+	4.90403i	0.0911268	+	0.169508i
$838$		−	6.74959i		−	0.233161i
$839$	−5.75215			−0.198586			−0.0992931	−	0.995058i	$-0.531658\pi$
$839$	−5.75215			−0.198586			−0.0992931	+	0.995058i	$0.531658\pi$
$840$	−2.53556	−	4.81733i	−0.0874853	−	0.166214i
$841$	19.8858			0.685717
$842$	−2.88407	−	1.66512i	−0.0993916	−	0.0573838i
$843$	−14.0281	+	8.09912i	−0.483153	+	0.278948i
$844$	3.66651	+	6.35058i	0.126206	+	0.218596i
$845$	−0.814572	+	20.8222i	−0.0280221	+	0.716304i
$846$	0.996441	−	1.72589i	0.0342584	−	0.0593372i
$847$	22.1862	+	12.8092i	0.762328	+	0.440131i
$848$	−9.46466	−	5.46443i	−0.325018	−	0.187649i
$849$	9.93627	+	17.2101i	0.341012	+	0.590650i
$850$	14.3795	−	20.9375i	0.493213	−	0.718151i
$851$	5.03456	+	8.72012i	0.172583	+	0.298922i
$852$			11.3259i			0.388019i
$853$			47.3436i			1.62101i	0.585729	+	0.810507i	$0.300808\pi$
$853$			47.3436i			1.62101i	−0.585729	+	0.810507i	$0.699192\pi$
$854$	−9.46569	−	16.3951i	−0.323909	−	0.561027i
$855$	−8.10762	−	5.11361i	−0.277275	−	0.174882i
$856$	2.07797	+	3.59914i	0.0710234	+	0.123016i
$857$	36.0467	+	20.8116i	1.23133	+	0.710911i	0.967308	−	0.253605i	$-0.0816164\pi$
$857$	36.0467	+	20.8116i	1.23133	+	0.710911i	0.264025	+	0.964516i	$0.414950\pi$
$858$	−1.14782	−	0.662694i	−0.0391859	−	0.0226240i
$859$	−21.6316	+	37.4670i	−0.738060	+	1.27836i	0.215307	+	0.976546i	$0.430925\pi$
$859$	−21.6316	+	37.4670i	−0.738060	+	1.27836i	−0.953368	+	0.301812i	$0.902409\pi$
$860$	−23.5606	−	0.921702i	−0.803410	−	0.0314298i
$861$	−14.4625	−	25.0497i	−0.492880	−	0.853692i
$862$	25.5931	−	14.7762i	0.871703	−	0.503278i
$863$	34.3238	+	19.8169i	1.16840	+	0.674574i	0.953302	−	0.302019i	$-0.0976607\pi$
$863$	34.3238	+	19.8169i	1.16840	+	0.674574i	0.215095	+	0.976593i	$0.430994\pi$
$864$	−1.00000			−0.0340207
$865$	2.20555	+	4.19034i	0.0749911	+	0.142476i
$866$	−6.33397			−0.215237
$867$			8.80600i			0.299068i
$868$	−7.13043	+	11.5282i	−0.242022	+	0.391292i
$869$	10.1900			0.345673
$870$	−0.611150	+	15.6223i	−0.0207199	+	0.529645i
$871$	−13.6092	−	23.5718i	−0.461129	−	0.798699i
$872$		−	18.2124i		−	0.616751i
$873$	8.48399	+	4.89824i	0.287140	+	0.165780i
$874$	−14.6799	−	25.4263i	−0.496553	−	0.860056i
$875$	−10.7574	−	25.0035i	−0.363666	−	0.845271i
$876$	6.17482			0.208628
$877$	31.7423	+	18.3264i	1.07186	+	0.618840i	0.928690	−	0.370858i	$-0.120936\pi$
$877$	31.7423	+	18.3264i	1.07186	+	0.618840i	0.143172	+	0.989698i	$0.454270\pi$
$878$	−5.64784	−	3.26078i	−0.190605	−	0.110046i
$879$	−3.08240	+	5.33888i	−0.103967	+	0.180076i
$880$	1.36694	−	0.719476i	0.0460794	−	0.0242535i
$881$	−20.6066	+	35.6917i	−0.694254	+	1.20248i	0.276177	+	0.961107i	$0.410932\pi$
$881$	−20.6066	+	35.6917i	−0.694254	+	1.20248i	−0.970431	+	0.241377i	$0.922401\pi$
$882$	−0.929110	+	0.536422i	−0.0312848	+	0.0180623i
$883$		−	32.0955i		−	1.08010i	−0.841633	−	0.540050i	$-0.818405\pi$
$883$		−	32.0955i		−	1.08010i	0.841633	−	0.540050i	$-0.181595\pi$
$884$	−9.74628			−0.327803
$885$	3.72247	+	7.07234i	0.125129	+	0.237734i
$886$	7.65698	−	13.2623i	0.257241	−	0.445555i
$887$	23.1979	−	13.3933i	0.778909	−	0.449703i	−0.0571345	−	0.998366i	$-0.518196\pi$
$887$	23.1979	−	13.3933i	0.778909	−	0.449703i	0.836043	+	0.548663i	$0.184863\pi$
$888$	1.27322	+	0.735092i	0.0427263	+	0.0246681i
$889$	19.8081	−	34.3086i	0.664342	−	1.15067i
$890$	8.72524	−	13.8339i	0.292471	−	0.463712i
$891$	0.690820			0.0231433
$892$	1.48728	−	0.858684i	0.0497980	−	0.0287509i
$893$	7.39850	−	4.27153i	0.247581	−	0.142941i
$894$	9.09075	−	15.7456i	0.304040	−	0.526613i
$895$	0.450991	−	11.5283i	0.0150750	−	0.385347i
$896$	−1.21729	−	2.10840i	−0.0406667	−	0.0704368i
$897$			13.1401i			0.438735i
$898$		−	12.4145i		−	0.414276i
$899$	34.2881	−	18.4332i	1.14357	−	0.614781i
$900$	−4.98472	−	0.390607i	−0.166157	−	0.0130202i
$901$	55.5181			1.84958
$902$	7.10795	−	4.10378i	0.236669	−	0.136641i
$903$		−	25.6718i		−	0.854305i
$904$	9.84730	−	17.0560i	0.327516	−	0.567275i
$905$	18.8737	−	9.93404i	0.627384	−	0.330219i
$906$	2.21321	+	3.83339i	0.0735288	+	0.127356i
$907$			0.973128i			0.0323122i	0.999869	+	0.0161561i	$0.00514287\pi$
$907$			0.973128i			0.0323122i	−0.999869	+	0.0161561i	$0.994857\pi$
$908$	15.3472	+	8.86071i	0.509315	+	0.294053i
$909$	−5.45248	+	9.44397i	−0.180847	+	0.313237i
$910$	−5.57183	+	8.83413i	−0.184704	+	0.292849i
$911$	4.41941	+	7.65464i	0.146422	+	0.253610i	0.929902	−	0.367806i	$-0.119891\pi$
$911$	4.41941	+	7.65464i	0.146422	+	0.253610i	−0.783481	+	0.621416i	$0.786558\pi$
$912$	−3.71246	−	2.14339i	−0.122932	−	0.0709748i
$913$	0.522371	−	0.301591i	0.0172880	−	0.00998121i
$914$	−6.38963			−0.211350
$915$	−17.3745	−	0.679697i	−0.574383	−	0.0224701i
$916$	0.329170	+	0.570139i	0.0108761	+	0.0188379i
$917$	−42.3107	−	24.4281i	−1.39722	−	0.806687i
$918$	4.39938	−	2.53998i	0.145201	−	0.0838318i
$919$	−12.7782	+	22.1325i	−0.421514	+	0.730083i	−0.996088	−	0.0883696i	$-0.971834\pi$
$919$	−12.7782	+	22.1325i	−0.421514	+	0.730083i	0.574574	+	0.818452i	$0.305168\pi$
$920$	−12.9534	−	8.16989i	−0.427060	−	0.269353i
$921$	8.50942	−	14.7387i	0.280395	−	0.485658i
$922$			2.58745i			0.0852131i
$923$	18.8184	−	10.8648i	0.619414	−	0.357619i
$924$	0.840926	+	1.45653i	0.0276644	+	0.0479162i
$925$	6.05949	+	4.16155i	0.199235	+	0.136831i
$926$	−18.0339			−0.592630
$927$	6.50162	−	3.75371i	0.213541	−	0.123288i
$928$			6.99184i			0.229518i
$929$	−58.7191			−1.92651			−0.963255	−	0.268588i	$-0.913443\pi$
$929$	−58.7191			−1.92651			−0.963255	+	0.268588i	$0.913443\pi$
$930$	5.46198	+	11.1878i	0.179105	+	0.366862i
$931$	−4.59905			−0.150728
$932$		−	14.8471i		−	0.486334i
$933$	−13.0260	+	7.52055i	−0.426451	+	0.246212i
$934$	9.09546			0.297613
$935$	−4.18621	+	6.63723i	−0.136904	+	0.217061i
$936$	0.959287	+	1.66153i	0.0313553	+	0.0543089i
$937$	−46.3763	+	26.7754i	−1.51505	+	0.874713i	−0.515203	+	0.857068i	$0.672284\pi$
$937$	−46.3763	+	26.7754i	−1.51505	+	0.874713i	−0.999844	+	0.0176451i	$0.994383\pi$
$938$			34.5387i			1.12773i
$939$	6.28401	−	10.8842i	0.205071	−	0.355193i
$940$	2.37727	−	3.76915i	0.0775379	−	0.122936i
$941$	15.6210	−	27.0563i	0.509229	−	0.882011i	−0.490713	−	0.871321i	$-0.663264\pi$
$941$	15.6210	−	27.0563i	0.509229	−	0.882011i	0.999943	−	0.0106903i	$-0.00340288\pi$
$942$	4.40974	−	2.54596i	0.143677	−	0.0829520i
$943$	−70.4693	−	40.6855i	−2.29480	−	1.32490i
$944$	1.78710	+	3.09535i	0.0581652	+	0.100745i
$945$	0.212804	−	5.43971i	0.00692252	−	0.176954i
$946$	7.28448			0.236839
$947$	31.5133	−	18.1942i	1.02404	−	0.591232i	0.108771	−	0.994067i	$-0.465308\pi$
$947$	31.5133	−	18.1942i	1.02404	−	0.591232i	0.915273	+	0.402835i	$0.131975\pi$
$948$	−12.7744	−	7.37533i	−0.414894	−	0.239539i
$949$	−5.92342	−	10.2597i	−0.192282	−	0.333043i
$950$	−17.6684	−	12.1343i	−0.573237	−	0.393689i
$951$	−8.22860	+	14.2524i	−0.266831	+	0.462164i
$952$	10.7106	+	6.18377i	0.347133	+	0.200417i
$953$			55.7665i			1.80645i	0.429162	+	0.903227i	$0.358809\pi$
$953$			55.7665i			1.80645i	−0.429162	+	0.903227i	$0.641191\pi$
$954$	−5.46443	−	9.46466i	−0.176917	−	0.306430i
$955$	50.4055	−	26.5305i	1.63108	−	0.858507i
$956$	5.66269	−	9.80807i	0.183145	−	0.317216i
$957$		−	4.83010i		−	0.156135i
$958$	6.90292	−	3.98541i	0.223023	−	0.128763i
$959$	15.6888			0.506619
$960$	−2.23436	−	0.0874091i	−0.0721136	−	0.00282112i
$961$	17.0989	−	25.8578i	0.551579	−	0.834123i
$962$		−	2.82065i		−	0.0909416i
$963$			4.15593i			0.133923i
$964$	12.3270	+	21.3510i	0.397026	+	0.687669i
$965$	33.3982	+	1.30655i	1.07513	+	0.0420594i
$966$	8.33707	−	14.4402i	0.268241	−	0.464607i
$967$	2.37611	−	1.37185i	0.0764106	−	0.0441157i	−0.461308	−	0.887240i	$-0.652620\pi$
$967$	2.37611	−	1.37185i	0.0764106	−	0.0441157i	0.537719	+	0.843124i	$0.319286\pi$
$968$	9.11298	−	5.26138i	0.292902	−	0.169107i
$969$	21.7767			0.699568
$970$	18.5281	+	11.6860i	0.594902	+	0.375215i
$971$	1.47808	−	2.56012i	0.0474340	−	0.0821580i	−0.841334	−	0.540516i	$-0.818229\pi$
$971$	1.47808	−	2.56012i	0.0474340	−	0.0821580i	0.888768	+	0.458358i	$0.151562\pi$
$972$	−0.866025	−	0.500000i	−0.0277778	−	0.0160375i
$973$	−13.8506	+	7.99664i	−0.444029	+	0.256360i
$974$	10.0533	−	17.4128i	0.322127	−	0.557941i
$975$	4.13277	+	8.65698i	0.132355	+	0.277245i
$976$	−7.77605			−0.248905
$977$		−	14.0319i		−	0.448922i	−0.974483	−	0.224461i	$-0.927938\pi$
$977$		−	14.0319i		−	0.448922i	0.974483	−	0.224461i	$-0.0720621\pi$
$978$	−2.13181	+	1.23080i	−0.0681677	+	0.0393567i
$979$	−2.52648	+	4.37600i	−0.0807467	+	0.139857i
$980$	−2.12285	+	1.11735i	−0.0678120	+	0.0356923i
$981$	9.10622	−	15.7724i	0.290739	−	0.503575i
$982$	13.6896	+	7.90372i	0.436854	+	0.252218i
$983$	−24.4809	−	14.1341i	−0.780820	−	0.450807i	0.0559008	−	0.998436i	$-0.482197\pi$
$983$	−24.4809	−	14.1341i	−0.780820	−	0.450807i	−0.836721	+	0.547630i	$0.815530\pi$
$984$	−11.8809			−0.378749
$985$	8.17600	+	15.5336i	0.260509	+	0.494943i
$986$	−17.7591	−	30.7597i	−0.565566	−	0.979589i
$987$	4.20180	+	2.42591i	0.133745	+	0.0772176i
$988$			8.22451i			0.261656i
$989$	−36.1097	−	62.5439i	−1.14822	−	1.98878i
$990$	1.54354	+	0.0603839i	0.0490569	+	0.00191913i
$991$	35.7118			1.13442			0.567212	−	0.823572i	$-0.308022\pi$
$991$	35.7118			1.13442			0.567212	+	0.823572i	$0.308022\pi$
$992$	2.63639	+	4.90403i	0.0837053	+	0.155703i
$993$			5.84774i			0.185572i
$994$	−27.5738			−0.874587
$995$	−16.4390	+	8.65253i	−0.521151	+	0.274304i
$996$	−0.873140			−0.0276665
$997$	−21.1645	−	12.2194i	−0.670288	−	0.386991i	0.125898	−	0.992043i	$-0.459819\pi$
$997$	−21.1645	−	12.2194i	−0.670288	−	0.386991i	−0.796186	+	0.605052i	$0.793152\pi$
$998$	10.2379	−	5.91086i	0.324075	−	0.187105i
$999$	0.735092	+	1.27322i	0.0232573	+	0.0402828i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.s.c.769.7	yes	24
5.4	even	2	inner	930.2.s.c.769.5	yes	24
31.5	even	3	inner	930.2.s.c.439.11	yes	24
155.129	even	6	inner	930.2.s.c.439.1	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.s.c.439.1	✓	24	155.129	even	6	inner
930.2.s.c.439.11	yes	24	31.5	even	3	inner
930.2.s.c.769.5	yes	24	5.4	even	2	inner
930.2.s.c.769.7	yes	24	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-0.866025 + 0.500000i) q^{3} -1.00000 q^{4} +(-1.89131 - 1.19288i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(2.10840 - 1.21729i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(-0.866025 + 0.500000i) q^{3} -1.00000 q^{4} +(-1.89131 - 1.19288i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(2.10840 - 1.21729i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(1.19288 - 1.89131i) q^{10} +(-0.345410 + 0.598267i) q^{11} +(0.866025 - 0.500000i) q^{12} +(-1.66153 - 0.959287i) q^{13} +(1.21729 + 2.10840i) q^{14} +(2.23436 + 0.0874091i) q^{15} +1.00000 q^{16} +(-4.39938 + 2.53998i) q^{17} +(0.866025 + 0.500000i) q^{18} +(2.14339 + 3.71246i) q^{19} +(1.89131 + 1.19288i) q^{20} +(-1.21729 + 2.10840i) q^{21} +(-0.598267 - 0.345410i) q^{22} +6.84889i q^{23} +(0.500000 + 0.866025i) q^{24} +(2.15408 + 4.51220i) q^{25} +(0.959287 - 1.66153i) q^{26} +1.00000i q^{27} +(-2.10840 + 1.21729i) q^{28} +6.99184 q^{29} +(-0.0874091 + 2.23436i) q^{30} +(4.90403 - 2.63639i) q^{31} +1.00000i q^{32} -0.690820i q^{33} +(-2.53998 - 4.39938i) q^{34} +(-5.43971 - 0.212804i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(1.27322 - 0.735092i) q^{37} +(-3.71246 + 2.14339i) q^{38} +1.91857 q^{39} +(-1.19288 + 1.89131i) q^{40} +(-5.94045 + 10.2892i) q^{41} +(-2.10840 - 1.21729i) q^{42} +(-9.13197 + 5.27234i) q^{43} +(0.345410 - 0.598267i) q^{44} +(-1.97872 + 1.04148i) q^{45} -6.84889 q^{46} -1.99288i q^{47} +(-0.866025 + 0.500000i) q^{48} +(-0.536422 + 0.929110i) q^{49} +(-4.51220 + 2.15408i) q^{50} +(2.53998 - 4.39938i) q^{51} +(1.66153 + 0.959287i) q^{52} +(-9.46466 - 5.46443i) q^{53} -1.00000 q^{54} +(1.36694 - 0.719476i) q^{55} +(-1.21729 - 2.10840i) q^{56} +(-3.71246 - 2.14339i) q^{57} +6.99184i q^{58} +(1.78710 + 3.09535i) q^{59} +(-2.23436 - 0.0874091i) q^{60} -7.77605 q^{61} +(2.63639 + 4.90403i) q^{62} -2.43458i q^{63} -1.00000 q^{64} +(1.99816 + 3.79631i) q^{65} +0.690820 q^{66} +(12.2861 + 7.09338i) q^{67} +(4.39938 - 2.53998i) q^{68} +(-3.42445 - 5.93131i) q^{69} +(0.212804 - 5.43971i) q^{70} +(-5.66295 + 9.80852i) q^{71} +(-0.866025 - 0.500000i) q^{72} +(5.34755 + 3.08741i) q^{73} +(0.735092 + 1.27322i) q^{74} +(-4.12159 - 2.83063i) q^{75} +(-2.14339 - 3.71246i) q^{76} +1.68185i q^{77} +1.91857i q^{78} +(-7.37533 - 12.7744i) q^{79} +(-1.89131 - 1.19288i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-10.2892 - 5.94045i) q^{82} +(-0.756161 - 0.436570i) q^{83} +(1.21729 - 2.10840i) q^{84} +(11.3505 + 0.444035i) q^{85} +(-5.27234 - 9.13197i) q^{86} +(-6.05511 + 3.49592i) q^{87} +(0.598267 + 0.345410i) q^{88} +7.31445 q^{89} +(-1.04148 - 1.97872i) q^{90} -4.67091 q^{91} -6.84889i q^{92} +(-2.92882 + 4.73519i) q^{93} +1.99288 q^{94} +(0.374704 - 9.57821i) q^{95} +(-0.500000 - 0.866025i) q^{96} +9.79647i q^{97} +(-0.929110 - 0.536422i) q^{98} +(0.345410 + 0.598267i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{4} + 4 q^{5} - 12 q^{6} + 12 q^{9}+O(q^{10}) \) 24 * q - 24 * q^4 + 4 * q^5 - 12 * q^6 + 12 * q^9	\( 24 q - 24 q^{4} + 4 q^{5} - 12 q^{6} + 12 q^{9} - 4 q^{11} + 12 q^{14} + 24 q^{16} - 4 q^{19} - 4 q^{20} - 12 q^{21} + 12 q^{24} - 4 q^{25} + 16 q^{26} + 32 q^{29} - 8 q^{30} + 24 q^{31} - 20 q^{34} + 48 q^{35} - 12 q^{36} + 32 q^{39} - 12 q^{41} + 4 q^{44} - 4 q^{45} + 56 q^{46} + 24 q^{49} - 16 q^{50} + 20 q^{51} - 24 q^{54} + 36 q^{55} - 12 q^{56} - 4 q^{59} - 40 q^{61} - 24 q^{64} - 4 q^{65} + 8 q^{66} + 28 q^{69} - 32 q^{70} - 56 q^{71} + 12 q^{74} + 16 q^{75} + 4 q^{76} - 72 q^{79} + 4 q^{80} - 12 q^{81} + 12 q^{84} + 40 q^{85} - 24 q^{86} + 128 q^{89} - 160 q^{91} + 56 q^{94} - 56 q^{95} - 12 q^{96} + 4 q^{99}+O(q^{100}) \) 24 * q - 24 * q^4 + 4 * q^5 - 12 * q^6 + 12 * q^9 - 4 * q^11 + 12 * q^14 + 24 * q^16 - 4 * q^19 - 4 * q^20 - 12 * q^21 + 12 * q^24 - 4 * q^25 + 16 * q^26 + 32 * q^29 - 8 * q^30 + 24 * q^31 - 20 * q^34 + 48 * q^35 - 12 * q^36 + 32 * q^39 - 12 * q^41 + 4 * q^44 - 4 * q^45 + 56 * q^46 + 24 * q^49 - 16 * q^50 + 20 * q^51 - 24 * q^54 + 36 * q^55 - 12 * q^56 - 4 * q^59 - 40 * q^61 - 24 * q^64 - 4 * q^65 + 8 * q^66 + 28 * q^69 - 32 * q^70 - 56 * q^71 + 12 * q^74 + 16 * q^75 + 4 * q^76 - 72 * q^79 + 4 * q^80 - 12 * q^81 + 12 * q^84 + 40 * q^85 - 24 * q^86 + 128 * q^89 - 160 * q^91 + 56 * q^94 - 56 * q^95 - 12 * q^96 + 4 * q^99

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