LMFDB - Embedded newform 930.2.j.h.497.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(497,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("930.497");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.j (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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			497.12
Character	$\chi$	$=$	930.497
Dual form			930.2.j.h.683.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 - 0.707107i) q^{2} +(-1.49353 - 0.877144i) q^{3} -1.00000i q^{4} +(1.98408 + 1.03122i) q^{5} +(-1.67632 + 0.435847i) q^{6} +(2.39520 + 2.39520i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.46124 + 2.62007i) q^{9} +(2.13214 - 0.673776i) q^{10} -0.0383198i q^{11} +(-0.877144 + 1.49353i) q^{12} +(-2.42230 + 2.42230i) q^{13} +3.38733 q^{14} +(-2.05875 - 3.28048i) q^{15} -1.00000 q^{16} +(-3.70534 + 3.70534i) q^{17} +(2.88592 + 0.819423i) q^{18} +7.16937i q^{19} +(1.03122 - 1.98408i) q^{20} +(-1.47636 - 5.67823i) q^{21} +(-0.0270962 - 0.0270962i) q^{22} +(3.94658 + 3.94658i) q^{23} +(0.435847 + 1.67632i) q^{24} +(2.87317 + 4.09205i) q^{25} +3.42565i q^{26} +(0.115791 - 5.19486i) q^{27} +(2.39520 - 2.39520i) q^{28} -3.49394 q^{29} +(-3.77541 - 0.863894i) q^{30} -1.00000 q^{31} +(-0.707107 + 0.707107i) q^{32} +(-0.0336120 + 0.0572316i) q^{33} +5.24015i q^{34} +(2.28230 + 7.22226i) q^{35} +(2.62007 - 1.46124i) q^{36} +(-4.89823 - 4.89823i) q^{37} +(5.06951 + 5.06951i) q^{38} +(5.74247 - 1.49306i) q^{39} +(-0.673776 - 2.13214i) q^{40} -10.1701i q^{41} +(-5.05906 - 2.97117i) q^{42} +(-6.93875 + 6.93875i) q^{43} -0.0383198 q^{44} +(0.197341 + 6.70530i) q^{45} +5.58130 q^{46} +(7.35619 - 7.35619i) q^{47} +(1.49353 + 0.877144i) q^{48} +4.47399i q^{49} +(4.92516 + 0.861878i) q^{50} +(8.78415 - 2.28390i) q^{51} +(2.42230 + 2.42230i) q^{52} +(0.287477 + 0.287477i) q^{53} +(-3.59145 - 3.75520i) q^{54} +(0.0395162 - 0.0760297i) q^{55} -3.38733i q^{56} +(6.28857 - 10.7076i) q^{57} +(-2.47059 + 2.47059i) q^{58} +15.0023 q^{59} +(-3.28048 + 2.05875i) q^{60} +5.16656 q^{61} +(-0.707107 + 0.707107i) q^{62} +(-2.77565 + 9.77556i) q^{63} +1.00000i q^{64} +(-7.30396 + 2.30812i) q^{65} +(0.0167016 + 0.0642362i) q^{66} +(5.80813 + 5.80813i) q^{67} +(3.70534 + 3.70534i) q^{68} +(-2.43259 - 9.35603i) q^{69} +(6.72074 + 3.49308i) q^{70} -9.58222i q^{71} +(0.819423 - 2.88592i) q^{72} +(9.96911 - 9.96911i) q^{73} -6.92715 q^{74} +(-0.701836 - 8.63177i) q^{75} +7.16937 q^{76} +(0.0917837 - 0.0917837i) q^{77} +(3.00479 - 5.11629i) q^{78} -16.7308i q^{79} +(-1.98408 - 1.03122i) q^{80} +(-4.72958 + 7.65709i) q^{81} +(-7.19133 - 7.19133i) q^{82} +(8.18895 + 8.18895i) q^{83} +(-5.67823 + 1.47636i) q^{84} +(-11.1727 + 3.53069i) q^{85} +9.81288i q^{86} +(5.21829 + 3.06469i) q^{87} +(-0.0270962 + 0.0270962i) q^{88} -3.51450 q^{89} +(4.88090 + 4.60182i) q^{90} -11.6038 q^{91} +(3.94658 - 3.94658i) q^{92} +(1.49353 + 0.877144i) q^{93} -10.4032i q^{94} +(-7.39319 + 14.2246i) q^{95} +(1.67632 - 0.435847i) q^{96} +(-2.47587 - 2.47587i) q^{97} +(3.16359 + 3.16359i) q^{98} +(0.100401 - 0.0559943i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{3} + 8 q^{6} - 8 q^{7} + 4 q^{12} + 24 q^{13} - 12 q^{15} - 40 q^{16} - 56 q^{21} + 16 q^{22} - 48 q^{25} + 8 q^{27} - 8 q^{28} + 4 q^{30} - 40 q^{31} - 20 q^{33} - 8 q^{37} - 8 q^{40} + 12 q^{42}+ \cdots + 24 q^{97}+O(q^{100}) $ 40 * q - 4 * q^3 + 8 * q^6 - 8 * q^7 + 4 * q^12 + 24 * q^13 - 12 * q^15 - 40 * q^16 - 56 * q^21 + 16 * q^22 - 48 * q^25 + 8 * q^27 - 8 * q^28 + 4 * q^30 - 40 * q^31 - 20 * q^33 - 8 * q^37 - 8 * q^40 + 12 * q^42 - 16 * q^43 + 76 * q^45 - 8 * q^46 + 4 * q^48 + 16 * q^51 - 24 * q^52 - 48 * q^55 + 56 * q^57 - 56 * q^58 + 12 * q^60 + 128 * q^61 - 24 * q^63 + 16 * q^66 + 8 * q^67 + 32 * q^70 + 248 * q^73 - 8 * q^75 + 56 * q^76 + 8 * q^78 + 40 * q^81 - 8 * q^82 - 48 * q^85 + 12 * q^87 + 16 * q^88 + 16 * q^90 - 192 * q^91 + 4 * q^93 - 8 * q^96 + 24 * q^97

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	−1.49353	−	0.877144i	−0.862287	−	0.506420i
$3$	−1.49353	−	0.877144i	−0.862287	−	0.506420i
$4$		−	1.00000i		−	0.500000i
$5$	1.98408	+	1.03122i	0.887309	+	0.461175i
$5$	1.98408	+	1.03122i	0.887309	+	0.461175i
$6$	−1.67632	+	0.435847i	−0.684353	+	0.177934i
$7$	2.39520	+	2.39520i	0.905301	+	0.905301i	0.995889	−	0.0905872i	$-0.0288744\pi$
$7$	2.39520	+	2.39520i	0.905301	+	0.905301i	−0.0905872	+	0.995889i	$0.528874\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	1.46124	+	2.62007i	0.487079	+	0.873358i
$10$	2.13214	−	0.673776i	0.674242	−	0.213067i
$11$		−	0.0383198i		−	0.0115539i	−0.999983	−	0.00577693i	$-0.998161\pi$
$11$		−	0.0383198i		−	0.0115539i	0.999983	−	0.00577693i	$-0.00183886\pi$
$12$	−0.877144	+	1.49353i	−0.253210	+	0.431144i
$13$	−2.42230	+	2.42230i	−0.671825	+	0.671825i	−0.958136	−	0.286312i	$-0.907571\pi$
$13$	−2.42230	+	2.42230i	−0.671825	+	0.671825i	0.286312	+	0.958136i	$0.407571\pi$
$14$	3.38733			0.905301
$15$	−2.05875	−	3.28048i	−0.531567	−	0.847016i
$16$	−1.00000			−0.250000
$17$	−3.70534	+	3.70534i	−0.898678	+	0.898678i	−0.995319	−	0.0966412i	$-0.969190\pi$
$17$	−3.70534	+	3.70534i	−0.898678	+	0.898678i	0.0966412	+	0.995319i	$0.469190\pi$
$18$	2.88592	+	0.819423i	0.680218	+	0.193140i
$19$			7.16937i			1.64477i	0.568934	+	0.822383i	$0.307356\pi$
$19$			7.16937i			1.64477i	−0.568934	+	0.822383i	$0.692644\pi$
$20$	1.03122	−	1.98408i	0.230588	−	0.443654i
$21$	−1.47636	−	5.67823i	−0.322168	−	1.23909i
$22$	−0.0270962	−	0.0270962i	−0.00577693	−	0.00577693i
$23$	3.94658	+	3.94658i	0.822918	+	0.822918i	0.986525	−	0.163608i	$-0.0523131\pi$
$23$	3.94658	+	3.94658i	0.822918	+	0.822918i	−0.163608	+	0.986525i	$0.552313\pi$
$24$	0.435847	+	1.67632i	0.0889669	+	0.342177i
$25$	2.87317	+	4.09205i	0.574634	+	0.818410i
$26$			3.42565i			0.671825i
$27$	0.115791	−	5.19486i	0.0222840	−	0.999752i
$28$	2.39520	−	2.39520i	0.452651	−	0.452651i
$29$	−3.49394			−0.648809			−0.324404	−	0.945919i	$-0.605164\pi$
$29$	−3.49394			−0.648809			−0.324404	+	0.945919i	$0.605164\pi$
$30$	−3.77541	−	0.863894i	−0.689292	−	0.157725i
$31$	−1.00000			−0.179605
$31$	−1.00000			−0.179605
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	−0.0336120	+	0.0572316i	−0.00585110	+	0.00996275i
$34$			5.24015i			0.898678i
$35$	2.28230	+	7.22226i	0.385779	+	1.22078i
$36$	2.62007	−	1.46124i	0.436679	−	0.243539i
$37$	−4.89823	−	4.89823i	−0.805265	−	0.805265i	0.178648	−	0.983913i	$-0.442828\pi$
$37$	−4.89823	−	4.89823i	−0.805265	−	0.805265i	−0.983913	+	0.178648i	$0.942828\pi$
$38$	5.06951	+	5.06951i	0.822383	+	0.822383i
$39$	5.74247	−	1.49306i	0.919531	−	0.239081i
$40$	−0.673776	−	2.13214i	−0.106533	−	0.337121i
$41$		−	10.1701i		−	1.58830i	−0.607723	−	0.794149i	$-0.707917\pi$
$41$		−	10.1701i		−	1.58830i	0.607723	−	0.794149i	$-0.292083\pi$
$42$	−5.05906	−	2.97117i	−0.780630	−	0.458462i
$43$	−6.93875	+	6.93875i	−1.05815	+	1.05815i	−0.0599483	+	0.998201i	$0.519094\pi$
$43$	−6.93875	+	6.93875i	−1.05815	+	1.05815i	−0.998201	+	0.0599483i	$0.980906\pi$
$44$	−0.0383198			−0.00577693
$45$	0.197341	+	6.70530i	0.0294178	+	0.999567i
$46$	5.58130			0.822918
$47$	7.35619	−	7.35619i	1.07301	−	1.07301i	0.0758955	−	0.997116i	$-0.475818\pi$
$47$	7.35619	−	7.35619i	1.07301	−	1.07301i	0.997116	−	0.0758955i	$-0.0241815\pi$
$48$	1.49353	+	0.877144i	0.215572	+	0.126605i
$49$			4.47399i			0.639141i
$50$	4.92516	+	0.861878i	0.696522	+	0.121888i
$51$	8.78415	−	2.28390i	1.23003	−	0.319811i
$52$	2.42230	+	2.42230i	0.335912	+	0.335912i
$53$	0.287477	+	0.287477i	0.0394880	+	0.0394880i	0.726575	−	0.687087i	$-0.241111\pi$
$53$	0.287477	+	0.287477i	0.0394880	+	0.0394880i	−0.687087	+	0.726575i	$0.741111\pi$
$54$	−3.59145	−	3.75520i	−0.488734	−	0.511018i
$55$	0.0395162	−	0.0760297i	0.00532836	−	0.0102518i
$56$		−	3.38733i		−	0.452651i
$57$	6.28857	−	10.7076i	0.832942	−	1.41826i
$58$	−2.47059	+	2.47059i	−0.324404	+	0.324404i
$59$	15.0023			1.95314			0.976568	−	0.215211i	$-0.0690439\pi$
$59$	15.0023			1.95314			0.976568	+	0.215211i	$0.0690439\pi$
$60$	−3.28048	+	2.05875i	−0.423508	+	0.265783i
$61$	5.16656			0.661511			0.330755	−	0.943717i	$-0.392697\pi$
$61$	5.16656			0.661511			0.330755	+	0.943717i	$0.392697\pi$
$62$	−0.707107	+	0.707107i	−0.0898027	+	0.0898027i
$63$	−2.77565	+	9.77556i	−0.349699	+	1.23161i
$64$			1.00000i			0.125000i
$65$	−7.30396	+	2.30812i	−0.905945	+	0.286287i
$66$	0.0167016	+	0.0642362i	0.00205582	+	0.00790693i
$67$	5.80813	+	5.80813i	0.709576	+	0.709576i	0.966446	−	0.256870i	$-0.0826912\pi$
$67$	5.80813	+	5.80813i	0.709576	+	0.709576i	−0.256870	+	0.966446i	$0.582691\pi$
$68$	3.70534	+	3.70534i	0.449339	+	0.449339i
$69$	−2.43259	−	9.35603i	−0.292850	−	1.12633i
$70$	6.72074	+	3.49308i	0.803282	+	0.417503i
$71$		−	9.58222i		−	1.13720i	−0.822614	−	0.568600i	$-0.807485\pi$
$71$		−	9.58222i		−	1.13720i	0.822614	−	0.568600i	$-0.192515\pi$
$72$	0.819423	−	2.88592i	0.0965699	−	0.340109i
$73$	9.96911	−	9.96911i	1.16680	−	1.16680i	0.183840	−	0.982956i	$-0.441147\pi$
$73$	9.96911	−	9.96911i	1.16680	−	1.16680i	0.982956	−	0.183840i	$-0.0588529\pi$
$74$	−6.92715			−0.805265
$75$	−0.701836	−	8.63177i	−0.0810410	−	0.996711i
$76$	7.16937			0.822383
$77$	0.0917837	−	0.0917837i	0.0104597	−	0.0104597i
$78$	3.00479	−	5.11629i	0.340225	−	0.579306i
$79$		−	16.7308i		−	1.88236i	−0.337908	−	0.941179i	$-0.609719\pi$
$79$		−	16.7308i		−	1.88236i	0.337908	−	0.941179i	$-0.390281\pi$
$80$	−1.98408	−	1.03122i	−0.221827	−	0.115294i
$81$	−4.72958	+	7.65709i	−0.525509	+	0.850788i
$82$	−7.19133	−	7.19133i	−0.794149	−	0.794149i
$83$	8.18895	+	8.18895i	0.898855	+	0.898855i	0.995335	−	0.0964803i	$-0.0307585\pi$
$83$	8.18895	+	8.18895i	0.898855	+	0.898855i	−0.0964803	+	0.995335i	$0.530758\pi$
$84$	−5.67823	+	1.47636i	−0.619546	+	0.161084i
$85$	−11.1727	+	3.53069i	−1.21185	+	0.382957i
$86$			9.81288i			1.05815i
$87$	5.21829	+	3.06469i	0.559459	+	0.328569i
$88$	−0.0270962	+	0.0270962i	−0.00288847	+	0.00288847i
$89$	−3.51450			−0.372536			−0.186268	−	0.982499i	$-0.559639\pi$
$89$	−3.51450			−0.372536			−0.186268	+	0.982499i	$0.559639\pi$
$90$	4.88090	+	4.60182i	0.514493	+	0.485075i
$91$	−11.6038			−1.21641
$92$	3.94658	−	3.94658i	0.411459	−	0.411459i
$93$	1.49353	+	0.877144i	0.154871	+	0.0909556i
$94$		−	10.4032i		−	1.07301i
$95$	−7.39319	+	14.2246i	−0.758526	+	1.45942i
$96$	1.67632	−	0.435847i	0.171088	−	0.0444835i
$97$	−2.47587	−	2.47587i	−0.251386	−	0.251386i	0.570153	−	0.821539i	$-0.306884\pi$
$97$	−2.47587	−	2.47587i	−0.251386	−	0.251386i	−0.821539	+	0.570153i	$0.806884\pi$
$98$	3.16359	+	3.16359i	0.319570	+	0.319570i
$99$	0.100401	−	0.0559943i	0.0100907	−	0.00562764i
$100$	4.09205	−	2.87317i	0.409205	−	0.287317i
$101$		−	7.43842i		−	0.740150i	−0.929002	−	0.370075i	$-0.879332\pi$
$101$		−	7.43842i		−	0.740150i	0.929002	−	0.370075i	$-0.120668\pi$
$102$	4.59637	−	7.82630i	0.455108	−	0.774919i
$103$	−3.85645	+	3.85645i	−0.379987	+	0.379987i	−0.871097	−	0.491110i	$-0.836591\pi$
$103$	−3.85645	+	3.85645i	−0.379987	+	0.379987i	0.491110	+	0.871097i	$0.336591\pi$
$104$	3.42565			0.335912
$105$	2.92629	−	12.7885i	0.285577	−	1.24803i
$106$	0.406553			0.0394880
$107$	−12.8902	+	12.8902i	−1.24614	+	1.24614i	−0.288732	+	0.957410i	$0.593234\pi$
$107$	−12.8902	+	12.8902i	−1.24614	+	1.24614i	−0.957410	+	0.288732i	$0.906766\pi$
$108$	−5.19486	−	0.115791i	−0.499876	−	0.0111420i
$109$			0.836888i			0.0801593i	0.999196	+	0.0400796i	$0.0127612\pi$
$109$			0.836888i			0.0801593i	−0.999196	+	0.0400796i	$0.987239\pi$
$110$	−0.0258190	−	0.0817033i	−0.00246174	−	0.00779010i
$111$	3.01918	+	11.6121i	0.286568	+	1.10217i
$112$	−2.39520	−	2.39520i	−0.226325	−	0.226325i
$113$	−12.2848	−	12.2848i	−1.15566	−	1.15566i	−0.985400	−	0.170256i	$-0.945540\pi$
$113$	−12.2848	−	12.2848i	−1.15566	−	1.15566i	−0.170256	−	0.985400i	$-0.554460\pi$
$114$	−3.12475	−	12.0181i	−0.292660	−	1.12560i
$115$	3.76055	+	11.9001i	0.350673	+	1.10969i
$116$			3.49394i			0.324404i
$117$	−9.88615	−	2.80705i	−0.913975	−	0.259512i
$118$	10.6082	−	10.6082i	0.976568	−	0.976568i
$119$	−17.7501			−1.62715
$120$	−0.863894	+	3.77541i	−0.0788623	+	0.344646i
$121$	10.9985			0.999867
$122$	3.65331	−	3.65331i	0.330755	−	0.330755i
$123$	−8.92062	+	15.1893i	−0.804345	+	1.36957i
$124$			1.00000i			0.0898027i
$125$	1.48081	+	11.0818i	0.132448	+	0.991190i
$126$	4.94968	+	8.87505i	0.440953	+	0.790652i
$127$	7.40826	+	7.40826i	0.657377	+	0.657377i	0.954759	−	0.297382i	$-0.0961135\pi$
$127$	7.40826	+	7.40826i	0.657377	+	0.657377i	−0.297382	+	0.954759i	$0.596113\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	16.4495	−	4.27691i	1.44830	−	0.376561i
$130$	−3.53259	+	6.79677i	−0.309829	+	0.596116i
$131$		−	16.8454i		−	1.47179i	−0.677098	−	0.735893i	$-0.736763\pi$
$131$		−	16.8454i		−	1.47179i	0.677098	−	0.735893i	$-0.263237\pi$
$132$	0.0572316	+	0.0336120i	0.00498137	+	0.00292555i
$133$	−17.1721	+	17.1721i	−1.48901	+	1.48901i
$134$	8.21393			0.709576
$135$	5.58678	−	10.1876i	0.480834	−	0.876812i
$136$	5.24015			0.449339
$137$	−2.39174	+	2.39174i	−0.204340	+	0.204340i	−0.801856	−	0.597517i	$-0.796154\pi$
$137$	−2.39174	+	2.39174i	−0.204340	+	0.204340i	0.597517	+	0.801856i	$0.296154\pi$
$138$	−8.33581	−	4.89561i	−0.709592	−	0.416742i
$139$			4.41411i			0.374400i	0.982322	+	0.187200i	$0.0599412\pi$
$139$			4.41411i			0.374400i	−0.982322	+	0.187200i	$0.940059\pi$
$140$	7.22226	−	2.28230i	0.610392	−	0.192890i
$141$	−17.4391	+	4.53422i	−1.46864	+	0.381850i
$142$	−6.77566	−	6.77566i	−0.568600	−	0.568600i
$143$	0.0928221	+	0.0928221i	0.00776217	+	0.00776217i
$144$	−1.46124	−	2.62007i	−0.121770	−	0.218340i
$145$	−6.93227	−	3.60302i	−0.575694	−	0.299215i
$146$		−	14.0985i		−	1.16680i
$147$	3.92433	−	6.68201i	0.323673	−	0.551123i
$148$	−4.89823	+	4.89823i	−0.402632	+	0.402632i
$149$	−5.68468			−0.465707			−0.232853	−	0.972512i	$-0.574806\pi$
$149$	−5.68468			−0.465707			−0.232853	+	0.972512i	$0.574806\pi$
$150$	−6.59985	−	5.60731i	−0.538876	−	0.457835i
$151$	6.13286			0.499085			0.249542	−	0.968364i	$-0.419720\pi$
$151$	6.13286			0.499085			0.249542	+	0.968364i	$0.419720\pi$
$152$	5.06951	−	5.06951i	0.411191	−	0.411191i
$153$	−15.1227	−	4.29390i	−1.22259	−	0.347141i
$154$		−	0.129802i		−	0.0104597i
$155$	−1.98408	−	1.03122i	−0.159365	−	0.0828296i
$156$	−1.49306	−	5.74247i	−0.119540	−	0.459765i
$157$	−1.92479	−	1.92479i	−0.153615	−	0.153615i	0.626116	−	0.779730i	$-0.284644\pi$
$157$	−1.92479	−	1.92479i	−0.153615	−	0.153615i	−0.779730	+	0.626116i	$0.784644\pi$
$158$	−11.8304	−	11.8304i	−0.941179	−	0.941179i
$159$	−0.177195	−	0.681512i	−0.0140525	−	0.0540474i
$160$	−2.13214	+	0.673776i	−0.168561	+	0.0532667i
$161$			18.9057i			1.48998i
$162$	2.07006	+	8.75870i	0.162640	+	0.688149i
$163$	−8.59083	+	8.59083i	−0.672886	+	0.672886i	−0.958380	−	0.285494i	$-0.907842\pi$
$163$	−8.59083	+	8.59083i	−0.672886	+	0.672886i	0.285494	+	0.958380i	$0.407842\pi$
$164$	−10.1701			−0.794149
$165$	−0.125707	+	0.0788910i	−0.00978631	+	0.00614165i
$166$	11.5809			0.898855
$167$	−1.68138	+	1.68138i	−0.130109	+	0.130109i	−0.769163	−	0.639053i	$-0.779326\pi$
$167$	−1.68138	+	1.68138i	−0.130109	+	0.130109i	0.639053	+	0.769163i	$0.279326\pi$
$168$	−2.97117	+	5.05906i	−0.229231	+	0.390315i
$169$			1.26494i			0.0973032i
$170$	−5.40374	+	10.3969i	−0.414448	+	0.797405i
$171$	−18.7843	+	10.4761i	−1.43647	+	0.801130i
$172$	6.93875	+	6.93875i	0.529075	+	0.529075i
$173$	0.350482	+	0.350482i	0.0266466	+	0.0266466i	0.720305	−	0.693658i	$-0.244002\pi$
$173$	0.350482	+	0.350482i	0.0266466	+	0.0266466i	−0.693658	+	0.720305i	$0.744002\pi$
$174$	5.85695	−	1.52282i	0.444014	−	0.115445i
$175$	−2.91946	+	16.6831i	−0.220691	+	1.26113i
$176$			0.0383198i			0.00288847i
$177$	−22.4063	−	13.1592i	−1.68416	−	0.989106i
$178$	−2.48513	+	2.48513i	−0.186268	+	0.186268i
$179$	1.82086			0.136097			0.0680486	−	0.997682i	$-0.478323\pi$
$179$	1.82086			0.136097			0.0680486	+	0.997682i	$0.478323\pi$
$180$	6.70530	−	0.197341i	0.499784	−	0.0147089i
$181$	18.7741			1.39547			0.697733	−	0.716358i	$-0.254192\pi$
$181$	18.7741			1.39547			0.697733	+	0.716358i	$0.254192\pi$
$182$	−8.20512	+	8.20512i	−0.608204	+	0.608204i
$183$	−7.71639	−	4.53182i	−0.570412	−	0.335002i
$184$		−	5.58130i		−	0.411459i
$185$	−4.66735	−	14.7697i	−0.343150	−	1.08589i
$186$	1.67632	−	0.435847i	0.122913	−	0.0319579i
$187$	0.141988	+	0.141988i	0.0103832	+	0.0103832i
$188$	−7.35619	−	7.35619i	−0.536506	−	0.536506i
$189$	12.7201	−	12.1654i	0.925250	−	0.884903i
$190$	4.83055	+	15.2861i	0.350445	+	1.10897i
$191$		−	5.71872i		−	0.413792i	−0.978363	−	0.206896i	$-0.933664\pi$
$191$		−	5.71872i		−	0.413792i	0.978363	−	0.206896i	$-0.0663362\pi$
$192$	0.877144	−	1.49353i	0.0633024	−	0.107786i
$193$	2.43627	−	2.43627i	0.175366	−	0.175366i	−0.613966	−	0.789332i	$-0.710427\pi$
$193$	2.43627	−	2.43627i	0.175366	−	0.175366i	0.789332	+	0.613966i	$0.210427\pi$
$194$	−3.50140			−0.251386
$195$	12.9332	+	2.95939i	0.926166	+	0.211927i
$196$	4.47399			0.319570
$197$	1.37187	−	1.37187i	0.0977414	−	0.0977414i	−0.656545	−	0.754287i	$-0.727983\pi$
$197$	1.37187	−	1.37187i	0.0977414	−	0.0977414i	0.754287	+	0.656545i	$0.227983\pi$
$198$	0.0314001	−	0.110588i	0.00223151	−	0.00785915i
$199$		−	5.04179i		−	0.357403i	−0.983903	−	0.178701i	$-0.942810\pi$
$199$		−	5.04179i		−	0.357403i	0.983903	−	0.178701i	$-0.0571896\pi$
$200$	0.861878	−	4.92516i	0.0609440	−	0.348261i
$201$	−3.58002	−	13.7692i	−0.252515	−	0.971201i
$202$	−5.25975	−	5.25975i	−0.370075	−	0.370075i
$203$	−8.36870	−	8.36870i	−0.587367	−	0.587367i
$204$	−2.28390	−	8.78415i	−0.159905	−	0.615013i
$205$	10.4876	−	20.1783i	0.732484	−	1.40931i
$206$			5.45384i			0.379987i
$207$	−4.57344	+	16.1072i	−0.317876	+	1.11953i
$208$	2.42230	−	2.42230i	0.167956	−	0.167956i
$209$	0.274729			0.0190034
$210$	−6.97366	−	11.1121i	−0.481228	−	0.766805i
$211$	25.9870			1.78902			0.894510	−	0.447049i	$-0.147525\pi$
$211$	25.9870			1.78902			0.894510	+	0.447049i	$0.147525\pi$
$212$	0.287477	−	0.287477i	0.0197440	−	0.0197440i
$213$	−8.40499	+	14.3113i	−0.575901	+	0.980594i
$214$			18.2295i			1.24614i
$215$	−20.9224	+	6.61168i	−1.42690	+	0.450913i
$216$	−3.75520	+	3.59145i	−0.255509	+	0.244367i
$217$	−2.39520	−	2.39520i	−0.162597	−	0.162597i
$218$	0.591769	+	0.591769i	0.0400796	+	0.0400796i
$219$	−23.6335	+	6.14477i	−1.59700	+	0.415225i
$220$	−0.0760297	−	0.0395162i	−0.00512592	−	0.00266418i
$221$		−	17.9509i		−	1.20751i
$222$	10.3459	+	6.07611i	0.694369	+	0.407802i
$223$	−4.78005	+	4.78005i	−0.320096	+	0.320096i	−0.848804	−	0.528708i	$-0.822677\pi$
$223$	−4.78005	+	4.78005i	−0.320096	+	0.320096i	0.528708	+	0.848804i	$0.322677\pi$
$224$	−3.38733			−0.226325
$225$	−6.52310	+	13.5074i	−0.434873	+	0.900492i
$226$	−17.3733			−1.15566
$227$	7.48071	−	7.48071i	0.496512	−	0.496512i	−0.413838	−	0.910350i	$-0.635812\pi$
$227$	7.48071	−	7.48071i	0.496512	−	0.496512i	0.910350	+	0.413838i	$0.135812\pi$
$228$	−10.7076	−	6.28857i	−0.709130	−	0.416471i
$229$			1.28796i			0.0851107i	0.999094	+	0.0425553i	$0.0135499\pi$
$229$			1.28796i			0.0851107i	−0.999094	+	0.0425553i	$0.986450\pi$
$230$	11.0738	+	5.75555i	0.730182	+	0.379510i
$231$	−0.217589	+	0.0565738i	−0.0143163	+	0.00372228i
$232$	2.47059	+	2.47059i	0.162202	+	0.162202i
$233$	−2.55890	−	2.55890i	−0.167639	−	0.167639i	0.618302	−	0.785941i	$-0.287821\pi$
$233$	−2.55890	−	2.55890i	−0.167639	−	0.167639i	−0.785941	+	0.618302i	$0.787821\pi$
$234$	−8.97545	+	5.00568i	−0.586744	+	0.327231i
$235$	22.1812	−	7.00945i	1.44694	−	0.457246i
$236$		−	15.0023i		−	0.976568i
$237$	−14.6753	+	24.9878i	−0.953263	+	1.62313i
$238$	−12.5512	+	12.5512i	−0.813574	+	0.813574i
$239$	−11.0066			−0.711956			−0.355978	−	0.934494i	$-0.615852\pi$
$239$	−11.0066			−0.711956			−0.355978	+	0.934494i	$0.615852\pi$
$240$	2.05875	+	3.28048i	0.132892	+	0.211754i
$241$	5.18138			0.333762			0.166881	−	0.985977i	$-0.446630\pi$
$241$	5.18138			0.333762			0.166881	+	0.985977i	$0.446630\pi$
$242$	7.77714	−	7.77714i	0.499933	−	0.499933i
$243$	13.7801	−	7.28754i	0.883995	−	0.467496i
$244$		−	5.16656i		−	0.330755i
$245$	−4.61366	+	8.87676i	−0.294756	+	0.567115i
$246$	4.43260	+	17.0483i	0.282612	+	1.08696i
$247$	−17.3663	−	17.3663i	−1.10499	−	1.10499i
$248$	0.707107	+	0.707107i	0.0449013	+	0.0449013i
$249$	−5.04752	−	19.4133i	−0.319873	−	1.23027i
$250$	8.88313	+	6.78896i	0.561819	+	0.429371i
$251$		−	10.9548i		−	0.691460i	−0.938334	−	0.345730i	$-0.887631\pi$
$251$		−	10.9548i		−	0.691460i	0.938334	−	0.345730i	$-0.112369\pi$
$252$	9.77556	+	2.77565i	0.615803	+	0.174850i
$253$	0.151232	−	0.151232i	0.00950788	−	0.00950788i
$254$	10.4769			0.657377
$255$	19.7837	+	4.52693i	1.23890	+	0.283487i
$256$	1.00000			0.0625000
$257$	−2.60182	+	2.60182i	−0.162297	+	0.162297i	−0.783583	−	0.621286i	$-0.786610\pi$
$257$	−2.60182	+	2.60182i	−0.162297	+	0.162297i	0.621286	+	0.783583i	$0.286610\pi$
$258$	8.60731	−	14.6558i	0.535868	−	0.912429i
$259$		−	23.4645i		−	1.45801i
$260$	2.30812	+	7.30396i	0.143144	+	0.452973i
$261$	−5.10547	−	9.15439i	−0.316021	−	0.566642i
$262$	−11.9115	−	11.9115i	−0.735893	−	0.735893i
$263$	12.9412	+	12.9412i	0.797990	+	0.797990i	0.982778	−	0.184788i	$-0.0591599\pi$
$263$	12.9412	+	12.9412i	0.797990	+	0.797990i	−0.184788	+	0.982778i	$0.559160\pi$
$264$	0.0642362	−	0.0167016i	0.00395346	−	0.00102791i
$265$	0.273926	+	0.866829i	0.0168271	+	0.0532489i
$266$			24.2850i			1.48901i
$267$	5.24899	+	3.08272i	0.321233	+	0.188660i
$268$	5.80813	−	5.80813i	0.354788	−	0.354788i
$269$	−9.27758			−0.565664			−0.282832	−	0.959169i	$-0.591274\pi$
$269$	−9.27758			−0.565664			−0.282832	+	0.959169i	$0.591274\pi$
$270$	−3.25329	−	11.1542i	−0.197989	−	0.678823i
$271$	30.1199			1.82965			0.914826	−	0.403847i	$-0.132327\pi$
$271$	30.1199			1.82965			0.914826	+	0.403847i	$0.132327\pi$
$272$	3.70534	−	3.70534i	0.224670	−	0.224670i
$273$	17.3306	+	10.1782i	1.04889	+	0.616012i
$274$			3.38243i			0.204340i
$275$	0.156807	−	0.110099i	0.00945580	−	0.00663925i
$276$	−9.35603	+	2.43259i	−0.563167	+	0.146425i
$277$	13.4595	+	13.4595i	0.808703	+	0.808703i	0.984438	−	0.175735i	$-0.0562302\pi$
$277$	13.4595	+	13.4595i	0.808703	+	0.808703i	−0.175735	+	0.984438i	$0.556230\pi$
$278$	3.12125	+	3.12125i	0.187200	+	0.187200i
$279$	−1.46124	−	2.62007i	−0.0874819	−	0.156860i
$280$	3.49308	−	6.72074i	0.208751	−	0.401641i
$281$		−	0.798668i		−	0.0476445i	−0.999716	−	0.0238223i	$-0.992416\pi$
$281$		−	0.798668i		−	0.0476445i	0.999716	−	0.0238223i	$-0.00758358\pi$
$282$	−9.12513	+	15.5375i	−0.543394	+	0.925244i
$283$	7.42997	−	7.42997i	0.441666	−	0.441666i	−0.450906	−	0.892572i	$-0.648899\pi$
$283$	7.42997	−	7.42997i	0.441666	−	0.441666i	0.892572	+	0.450906i	$0.148899\pi$
$284$	−9.58222			−0.568600
$285$	23.5190	−	14.7599i	1.39314	−	0.874303i
$286$	0.131270			0.00776217
$287$	24.3594	−	24.3594i	1.43789	−	1.43789i
$288$	−2.88592	−	0.819423i	−0.170055	−	0.0482850i
$289$		−	10.4592i		−	0.615245i
$290$	−7.44958	+	2.35413i	−0.437454	+	0.138240i
$291$	1.52608	+	5.86946i	0.0894602	+	0.344074i
$292$	−9.96911	−	9.96911i	−0.583398	−	0.583398i
$293$	9.23580	+	9.23580i	0.539561	+	0.539561i	0.923400	−	0.383839i	$-0.125398\pi$
$293$	9.23580	+	9.23580i	0.539561	+	0.539561i	−0.383839	+	0.923400i	$0.625398\pi$
$294$	−1.94997	−	7.49982i	−0.113725	−	0.437398i
$295$	29.7658	+	15.4707i	1.73303	+	0.900738i
$296$			6.92715i			0.402632i
$297$	−0.199066	−	0.00443709i	−0.0115510	−	0.000257466i
$298$	−4.01967	+	4.01967i	−0.232853	+	0.232853i
$299$	−19.1196			−1.10571
$300$	−8.63177	+	0.701836i	−0.498355	+	0.0405205i
$301$	−33.2394			−1.91589
$302$	4.33659	−	4.33659i	0.249542	−	0.249542i
$303$	−6.52456	+	11.1095i	−0.374826	+	0.638222i
$304$		−	7.16937i		−	0.411191i
$305$	10.2509	+	5.32786i	0.586964	+	0.305072i
$306$	−13.7296	+	7.65709i	−0.784868	+	0.437727i
$307$	12.8688	+	12.8688i	0.734461	+	0.734461i	0.971500	−	0.237039i	$-0.0761769\pi$
$307$	12.8688	+	12.8688i	0.734461	+	0.734461i	−0.237039	+	0.971500i	$0.576177\pi$
$308$	−0.0917837	−	0.0917837i	−0.00522986	−	0.00522986i
$309$	9.14236	−	2.37704i	0.520091	−	0.135225i
$310$	−2.13214	+	0.673776i	−0.121097	+	0.0382679i
$311$			23.7802i			1.34845i	0.738526	+	0.674226i	$0.235522\pi$
$311$			23.7802i			1.34845i	−0.738526	+	0.674226i	$0.764478\pi$
$312$	−5.11629	−	3.00479i	−0.289653	−	0.170113i
$313$	2.99407	−	2.99407i	0.169235	−	0.169235i	−0.617408	−	0.786643i	$-0.711817\pi$
$313$	2.99407	−	2.99407i	0.169235	−	0.169235i	0.786643	+	0.617408i	$0.211817\pi$
$314$	−2.72206			−0.153615
$315$	−15.5879	+	16.5332i	−0.878277	+	0.931541i
$316$	−16.7308			−0.941179
$317$	−18.9997	+	18.9997i	−1.06713	+	1.06713i	−0.0695500	+	0.997578i	$0.522156\pi$
$317$	−18.9997	+	18.9997i	−1.06713	+	1.06713i	−0.997578	+	0.0695500i	$0.977844\pi$
$318$	−0.607198	−	0.356606i	−0.0340500	−	0.0199975i
$319$			0.133887i			0.00749625i
$320$	−1.03122	+	1.98408i	−0.0576469	+	0.110914i
$321$	30.5584	−	7.94527i	1.70560	−	0.443462i
$322$	13.3683	+	13.3683i	0.744989	+	0.744989i
$323$	−26.5650	−	26.5650i	−1.47812	−	1.47812i
$324$	7.65709	+	4.72958i	0.425394	+	0.262754i
$325$	−16.8718	−	2.95249i	−0.935882	−	0.163775i
$326$			12.1493i			0.672886i
$327$	0.734071	−	1.24991i	0.0405942	−	0.0691203i
$328$	−7.19133	+	7.19133i	−0.397075	+	0.397075i
$329$	35.2391			1.94280
$330$	−0.0331043	+	0.144673i	−0.00182233	+	0.00796398i
$331$	−3.70761			−0.203789			−0.101894	−	0.994795i	$-0.532490\pi$
$331$	−3.70761			−0.203789			−0.101894	+	0.994795i	$0.532490\pi$
$332$	8.18895	−	8.18895i	0.449427	−	0.449427i
$333$	5.67626	−	19.9912i	0.311057	−	1.09551i
$334$			2.37783i			0.130109i
$335$	5.53435	+	17.5133i	0.302374	+	0.956852i
$336$	1.47636	+	5.67823i	0.0805419	+	0.309773i
$337$	−6.75125	−	6.75125i	−0.367764	−	0.367764i	0.498897	−	0.866661i	$-0.333738\pi$
$337$	−6.75125	−	6.75125i	−0.367764	−	0.367764i	−0.866661	+	0.498897i	$0.833738\pi$
$338$	0.894449	+	0.894449i	0.0486516	+	0.0486516i
$339$	7.57211	+	29.1232i	0.411261	+	1.58175i
$340$	3.53069	+	11.1727i	0.191478	+	0.605927i
$341$			0.0383198i			0.00207514i
$342$	−5.87474	+	20.6902i	−0.317670	+	1.11880i
$343$	6.05031	−	6.05031i	0.326686	−	0.326686i
$344$	9.81288			0.529075
$345$	4.82165	−	21.0717i	0.259589	−	1.13446i
$346$	0.495656			0.0266466
$347$	6.23364	−	6.23364i	0.334640	−	0.334640i	−0.519706	−	0.854345i	$-0.673958\pi$
$347$	6.23364	−	6.23364i	0.334640	−	0.334640i	0.854345	+	0.519706i	$0.173958\pi$
$348$	3.06469	−	5.21829i	0.164285	−	0.279730i
$349$			21.2431i			1.13712i	0.822643	+	0.568558i	$0.192498\pi$
$349$			21.2431i			1.13712i	−0.822643	+	0.568558i	$0.807502\pi$
$350$	9.73237	+	13.8611i	0.520217	+	0.740908i
$351$	12.3030	+	12.8640i	0.656687	+	0.686629i
$352$	0.0270962	+	0.0270962i	0.00144423	+	0.00144423i
$353$	−17.2207	−	17.2207i	−0.916566	−	0.916566i	0.0802115	−	0.996778i	$-0.474440\pi$
$353$	−17.2207	−	17.2207i	−0.916566	−	0.916566i	−0.996778	+	0.0802115i	$0.974440\pi$
$354$	−25.1486	+	6.53872i	−1.33663	+	0.347529i
$355$	9.88138	−	19.0119i	0.524449	−	1.00905i
$356$			3.51450i			0.186268i
$357$	26.5102	+	15.5694i	1.40307	+	0.824020i
$358$	1.28754	−	1.28754i	0.0680486	−	0.0680486i
$359$	9.65176			0.509400			0.254700	−	0.967020i	$-0.418023\pi$
$359$	9.65176			0.509400			0.254700	+	0.967020i	$0.418023\pi$
$360$	4.60182	−	4.88090i	0.242537	−	0.257246i
$361$	−32.3998			−1.70526
$362$	13.2753	−	13.2753i	0.697733	−	0.697733i
$363$	−16.4266	−	9.64730i	−0.862172	−	0.506352i
$364$			11.6038i			0.608204i
$365$	30.0599	−	9.49920i	1.57341	−	0.497211i
$366$	−8.66080	+	2.25183i	−0.452707	+	0.117705i
$367$	−8.60226	−	8.60226i	−0.449034	−	0.449034i	0.445999	−	0.895033i	$-0.352848\pi$
$367$	−8.60226	−	8.60226i	−0.449034	−	0.449034i	−0.895033	+	0.445999i	$0.852848\pi$
$368$	−3.94658	−	3.94658i	−0.205729	−	0.205729i
$369$	26.6464	−	14.8609i	1.38715	−	0.773626i
$370$	−13.7440	−	7.14341i	−0.714519	−	0.371368i
$371$			1.37713i			0.0714970i
$372$	0.877144	−	1.49353i	0.0454778	−	0.0774357i
$373$	−4.18624	+	4.18624i	−0.216756	+	0.216756i	−0.807130	−	0.590374i	$-0.798980\pi$
$373$	−4.18624	+	4.18624i	−0.216756	+	0.216756i	0.590374	+	0.807130i	$0.298980\pi$
$374$	0.200802			0.0103832
$375$	7.50875	−	17.8499i	0.387750	−	0.921765i
$376$	−10.4032			−0.536506
$377$	8.46337	−	8.46337i	0.435886	−	0.435886i
$378$	0.392222	−	17.5967i	0.0201737	−	0.905076i
$379$		−	16.0997i		−	0.826988i	−0.910507	−	0.413494i	$-0.864308\pi$
$379$		−	16.0997i		−	0.826988i	0.910507	−	0.413494i	$-0.135692\pi$
$380$	14.2246	+	7.39319i	0.729708	+	0.379263i
$381$	−4.56631	−	17.5625i	−0.233939	−	0.899756i
$382$	−4.04375	−	4.04375i	−0.206896	−	0.206896i
$383$	3.06182	+	3.06182i	0.156452	+	0.156452i	0.780992	−	0.624541i	$-0.214714\pi$
$383$	3.06182	+	3.06182i	0.156452	+	0.156452i	−0.624541	+	0.780992i	$0.714714\pi$
$384$	−0.435847	−	1.67632i	−0.0222417	−	0.0855442i
$385$	0.276756	−	0.0874574i	0.0141048	−	0.00445724i
$386$		−	3.44540i		−	0.175366i
$387$	−28.3192	−	8.04090i	−1.43955	−	0.408742i
$388$	−2.47587	+	2.47587i	−0.125693	+	0.125693i
$389$	−3.48655			−0.176775			−0.0883874	−	0.996086i	$-0.528171\pi$
$389$	−3.48655			−0.176775			−0.0883874	+	0.996086i	$0.528171\pi$
$390$	11.2378	−	7.05255i	0.569046	−	0.357120i
$391$	−29.2468			−1.47908
$392$	3.16359	−	3.16359i	0.159785	−	0.159785i
$393$	−14.7758	+	25.1590i	−0.745341	+	1.26910i
$394$		−	1.94011i		−	0.0977414i
$395$	17.2531	−	33.1952i	0.868097	−	1.67023i
$396$	−0.0559943	−	0.100401i	−0.00281382	−	0.00504533i
$397$	−19.3189	−	19.3189i	−0.969587	−	0.969587i	0.0299644	−	0.999551i	$-0.490461\pi$
$397$	−19.3189	−	19.3189i	−0.969587	−	0.969587i	−0.999551	+	0.0299644i	$0.990461\pi$
$398$	−3.56508	−	3.56508i	−0.178701	−	0.178701i
$399$	40.7093	−	10.5845i	2.03802	−	0.529890i
$400$	−2.87317	−	4.09205i	−0.143659	−	0.204603i
$401$		−	9.08809i		−	0.453837i	−0.973914	−	0.226919i	$-0.927135\pi$
$401$		−	9.08809i		−	0.453837i	0.973914	−	0.226919i	$-0.0728652\pi$
$402$	−12.2677	−	7.20481i	−0.611858	−	0.359343i
$403$	2.42230	−	2.42230i	0.120663	−	0.120663i
$404$	−7.43842			−0.370075
$405$	−17.2800	+	10.3151i	−0.858651	+	0.512560i
$406$	−11.8351			−0.587367
$407$	−0.187699	+	0.187699i	−0.00930392	+	0.00930392i
$408$	−7.82630	−	4.59637i	−0.387459	−	0.227554i
$409$			15.9929i			0.790800i	0.918509	+	0.395400i	$0.129394\pi$
$409$			15.9929i			0.790800i	−0.918509	+	0.395400i	$0.870606\pi$
$410$	−6.85235	−	21.6840i	−0.338414	−	1.07090i
$411$	5.67002	−	1.47422i	0.279681	−	0.0727179i
$412$	3.85645	+	3.85645i	0.189994	+	0.189994i
$413$	35.9336	+	35.9336i	1.76818	+	1.76818i
$414$	8.15560	+	14.6234i	0.400826	+	0.718702i
$415$	7.80296	+	24.6922i	0.383032	+	1.21209i
$416$		−	3.42565i		−	0.167956i
$417$	3.87181	−	6.59258i	0.189603	−	0.322840i
$418$	0.194263	−	0.194263i	0.00950170	−	0.00950170i
$419$	−22.1030			−1.07980			−0.539900	−	0.841729i	$-0.681538\pi$
$419$	−22.1030			−1.07980			−0.539900	+	0.841729i	$0.681538\pi$
$420$	−12.7885	−	2.92629i	−0.624017	−	0.142788i
$421$	−23.3654			−1.13876			−0.569381	−	0.822074i	$-0.692817\pi$
$421$	−23.3654			−1.13876			−0.569381	+	0.822074i	$0.692817\pi$
$422$	18.3756	−	18.3756i	0.894510	−	0.894510i
$423$	30.0229	+	8.52464i	1.45976	+	0.414482i
$424$		−	0.406553i		−	0.0197440i
$425$	−25.8086	−	4.51637i	−1.25190	−	0.219076i
$426$	4.17639	+	16.0628i	0.202347	+	0.778247i
$427$	12.3750	+	12.3750i	0.598866	+	0.598866i
$428$	12.8902	+	12.8902i	0.623071	+	0.623071i
$429$	−0.0572138	−	0.220050i	−0.00276231	−	0.0106241i
$430$	−10.1192	+	19.4696i	−0.487993	+	0.938906i
$431$			5.05677i			0.243576i	0.992556	+	0.121788i	$0.0388628\pi$
$431$			5.05677i			0.243576i	−0.992556	+	0.121788i	$0.961137\pi$
$432$	−0.115791	+	5.19486i	−0.00557100	+	0.249938i
$433$	14.4819	−	14.4819i	0.695955	−	0.695955i	−0.267581	−	0.963535i	$-0.586224\pi$
$433$	14.4819	−	14.4819i	0.695955	−	0.695955i	0.963535	+	0.267581i	$0.0862242\pi$
$434$	−3.38733			−0.162597
$435$	7.19315	+	11.4618i	0.344885	+	0.549551i
$436$	0.836888			0.0400796
$437$	−28.2945	+	28.2945i	−1.35351	+	1.35351i
$438$	−12.3664	+	21.0564i	−0.590888	+	1.00611i
$439$		−	29.8494i		−	1.42463i	−0.701858	−	0.712317i	$-0.747646\pi$
$439$		−	29.8494i		−	1.42463i	0.701858	−	0.712317i	$-0.252354\pi$
$440$	−0.0817033	+	0.0258190i	−0.00389505	+	0.00123087i
$441$	−11.7222	+	6.53755i	−0.558199	+	0.311312i
$442$	−12.6932	−	12.6932i	−0.603754	−	0.603754i
$443$	6.49714	+	6.49714i	0.308688	+	0.308688i	0.844401	−	0.535712i	$-0.179957\pi$
$443$	6.49714	+	6.49714i	0.308688	+	0.308688i	−0.535712	+	0.844401i	$0.679957\pi$
$444$	11.6121	−	3.01918i	0.551086	−	0.143284i
$445$	−6.97306	−	3.62422i	−0.330555	−	0.171805i
$446$			6.76001i			0.320096i
$447$	8.49021	+	4.98628i	0.401573	+	0.235843i
$448$	−2.39520	+	2.39520i	−0.113163	+	0.113163i
$449$	15.1932			0.717012			0.358506	−	0.933527i	$-0.383286\pi$
$449$	15.1932			0.717012			0.358506	+	0.933527i	$0.383286\pi$
$450$	4.93863	+	14.1637i	0.232809	+	0.667682i
$451$	−0.389716			−0.0183510
$452$	−12.2848	+	12.2848i	−0.577828	+	0.577828i
$453$	−9.15958	−	5.37940i	−0.430355	−	0.252746i
$454$		−	10.5793i		−	0.496512i
$455$	−23.0229	−	11.9661i	−1.07933	−	0.560977i
$456$	−12.0181	+	3.12475i	−0.562801	+	0.146330i
$457$	−8.92437	−	8.92437i	−0.417464	−	0.417464i	0.466864	−	0.884329i	$-0.345384\pi$
$457$	−8.92437	−	8.92437i	−0.417464	−	0.417464i	−0.884329	+	0.466864i	$0.845384\pi$
$458$	0.910724	+	0.910724i	0.0425553	+	0.0425553i
$459$	18.8197	+	19.6778i	0.878429	+	0.918481i
$460$	11.9001	−	3.76055i	0.554846	−	0.175336i
$461$		−	9.87377i		−	0.459867i	−0.973206	−	0.229934i	$-0.926149\pi$
$461$		−	9.87377i		−	0.459867i	0.973206	−	0.229934i	$-0.0738509\pi$
$462$	−0.113855	+	0.193862i	−0.00529701	+	0.00901929i
$463$	−10.7503	+	10.7503i	−0.499609	+	0.499609i	−0.911316	−	0.411707i	$-0.864933\pi$
$463$	−10.7503	+	10.7503i	−0.499609	+	0.499609i	0.411707	+	0.911316i	$0.364933\pi$
$464$	3.49394			0.162202
$465$	2.05875	+	3.28048i	0.0954722	+	0.152129i
$466$	−3.61884			−0.167639
$467$	7.08525	−	7.08525i	0.327866	−	0.327866i	−0.523908	−	0.851775i	$-0.675527\pi$
$467$	7.08525	−	7.08525i	0.327866	−	0.327866i	0.851775	+	0.523908i	$0.175527\pi$
$468$	−2.80705	+	9.88615i	−0.129756	+	0.456987i
$469$			27.8233i			1.28476i
$470$	10.7280	−	20.6409i	0.494846	−	0.952093i
$471$	1.18640	+	4.56303i	0.0546665	+	0.210253i
$472$	−10.6082	−	10.6082i	−0.488284	−	0.488284i
$473$	0.265892	+	0.265892i	0.0122257	+	0.0122257i
$474$	7.29206	+	28.0461i	0.334935	+	1.28820i
$475$	−29.3374	+	20.5988i	−1.34609	+	0.945139i
$476$			17.7501i			0.813574i
$477$	−0.333139	+	1.17328i	−0.0152534	+	0.0537209i
$478$	−7.78283	+	7.78283i	−0.355978	+	0.355978i
$479$	−39.1461			−1.78863			−0.894316	−	0.447436i	$-0.852337\pi$
$479$	−39.1461			−1.78863			−0.894316	+	0.447436i	$0.852337\pi$
$480$	3.77541	+	0.863894i	0.172323	+	0.0394312i
$481$	23.7300			1.08199
$482$	3.66379	−	3.66379i	0.166881	−	0.166881i
$483$	16.5830	−	28.2361i	0.754554	−	1.28479i
$484$		−	10.9985i		−	0.499933i
$485$	−2.35916	−	7.46548i	−0.107124	−	0.338990i
$486$	4.59095	−	14.8971i	0.208250	−	0.675746i
$487$	−8.33574	−	8.33574i	−0.377729	−	0.377729i	0.492554	−	0.870282i	$-0.336064\pi$
$487$	−8.33574	−	8.33574i	−0.377729	−	0.377729i	−0.870282	+	0.492554i	$0.836064\pi$
$488$	−3.65331	−	3.65331i	−0.165378	−	0.165378i
$489$	20.3660	−	5.29523i	0.920984	−	0.239458i
$490$	3.01447	+	9.53917i	0.136180	+	0.430936i
$491$		−	18.7400i		−	0.845722i	−0.906195	−	0.422861i	$-0.861026\pi$
$491$		−	18.7400i		−	0.845722i	0.906195	−	0.422861i	$-0.138974\pi$
$492$	15.1893	+	8.92062i	0.684785	+	0.402173i
$493$	12.9463	−	12.9463i	0.583070	−	0.583070i
$494$	−24.5597			−1.10499
$495$	0.256946	−	0.00756206i	0.0115489	−	0.000339890i
$496$	1.00000			0.0449013
$497$	22.9514	−	22.9514i	1.02951	−	1.02951i
$498$	−17.2964	−	10.1581i	−0.775071	−	0.455197i
$499$			26.7204i			1.19617i	0.801433	+	0.598084i	$0.204071\pi$
$499$			26.7204i			1.19617i	−0.801433	+	0.598084i	$0.795929\pi$
$500$	11.0818	−	1.48081i	0.495595	−	0.0662238i
$501$	3.98600	−	1.03637i	0.178081	−	0.0463017i
$502$	−7.74621	−	7.74621i	−0.345730	−	0.345730i
$503$	2.30936	+	2.30936i	0.102969	+	0.102969i	0.756715	−	0.653745i	$-0.226803\pi$
$503$	2.30936	+	2.30936i	0.102969	+	0.102969i	−0.653745	+	0.756715i	$0.726803\pi$
$504$	8.87505	−	4.94968i	0.395326	−	0.220476i
$505$	7.67064	−	14.7584i	0.341339	−	0.656742i
$506$		−	0.213874i		−	0.00950788i
$507$	1.10954	−	1.88922i	0.0492763	−	0.0839033i
$508$	7.40826	−	7.40826i	0.328688	−	0.328688i
$509$	−8.19351			−0.363171			−0.181586	−	0.983375i	$-0.558123\pi$
$509$	−8.19351			−0.363171			−0.181586	+	0.983375i	$0.558123\pi$
$510$	17.1902	−	10.7882i	0.761195	−	0.477708i
$511$	47.7561			2.11260
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	37.2439	+	0.830149i	1.64436	+	0.0366520i
$514$			3.67953i			0.162297i
$515$	−11.6284	+	3.67467i	−0.512407	+	0.161925i
$516$	−4.27691	−	16.4495i	−0.188281	−	0.724148i
$517$	−0.281888	−	0.281888i	−0.0123974	−	0.0123974i
$518$	−16.5919	−	16.5919i	−0.729007	−	0.729007i
$519$	−0.216030	−	0.830877i	−0.00948268	−	0.0364714i
$520$	6.79677	+	3.53259i	0.298058	+	0.154915i
$521$			8.17200i			0.358022i	0.983847	+	0.179011i	$0.0572897\pi$
$521$			8.17200i			0.358022i	−0.983847	+	0.179011i	$0.942710\pi$
$522$	−10.0832	−	2.86302i	−0.441332	−	0.125311i
$523$	−15.3859	+	15.3859i	−0.672777	+	0.672777i	−0.958355	−	0.285578i	$-0.907814\pi$
$523$	−15.3859	+	15.3859i	−0.672777	+	0.672777i	0.285578	+	0.958355i	$0.407814\pi$
$524$	−16.8454			−0.735893
$525$	18.9938	−	22.3559i	0.828957	−	0.975690i
$526$	18.3017			0.797990
$527$	3.70534	−	3.70534i	0.161407	−	0.161407i
$528$	0.0336120	−	0.0572316i	0.00146278	−	0.00249069i
$529$			8.15092i			0.354388i
$530$	0.806636	+	0.419246i	0.0350380	+	0.0182109i
$531$	21.9219	+	39.3072i	0.951330	+	1.70579i
$532$	17.1721	+	17.1721i	0.744504	+	0.744504i
$533$	24.6350	+	24.6350i	1.06706	+	1.06706i
$534$	5.89141	−	1.53178i	0.254946	−	0.0662868i
$535$	−38.8678	+	12.2826i	−1.68040	+	0.531023i
$536$		−	8.21393i		−	0.354788i
$537$	−2.71949	−	1.59715i	−0.117355	−	0.0689222i
$538$	−6.56024	+	6.56024i	−0.282832	+	0.282832i
$539$	0.171442			0.00738455
$540$	−10.1876	−	5.58678i	−0.438406	−	0.240417i
$541$	21.4116			0.920558			0.460279	−	0.887774i	$-0.347749\pi$
$541$	21.4116			0.920558			0.460279	+	0.887774i	$0.347749\pi$
$542$	21.2980	−	21.2980i	0.914826	−	0.914826i
$543$	−28.0396	−	16.4676i	−1.20329	−	0.706691i
$544$		−	5.24015i		−	0.224670i
$545$	−0.863015	+	1.66045i	−0.0369675	+	0.0711261i
$546$	19.4516	−	5.05748i	0.832453	−	0.216440i
$547$	−21.2857	−	21.2857i	−0.910110	−	0.910110i	0.0861708	−	0.996280i	$-0.472537\pi$
$547$	−21.2857	−	21.2857i	−0.910110	−	0.910110i	−0.996280	+	0.0861708i	$0.972537\pi$
$548$	2.39174	+	2.39174i	0.102170	+	0.102170i
$549$	7.54957	+	13.5368i	0.322208	+	0.577736i
$550$	0.0330270	−	0.188731i	0.00140828	−	0.00804752i
$551$		−	25.0494i		−	1.06714i
$552$	−4.89561	+	8.33581i	−0.208371	+	0.354796i
$553$	40.0736	−	40.0736i	1.70410	−	1.70410i
$554$	19.0346			0.808703
$555$	−5.98432	+	26.1528i	−0.254020	+	1.11012i
$556$	4.41411			0.187200
$557$	−5.01845	+	5.01845i	−0.212639	+	0.212639i	−0.805387	−	0.592749i	$-0.798043\pi$
$557$	−5.01845	+	5.01845i	−0.212639	+	0.212639i	0.592749	+	0.805387i	$0.298043\pi$
$558$	−2.88592	−	0.819423i	−0.122171	−	0.0346889i
$559$		−	33.6155i		−	1.42178i
$560$	−2.28230	−	7.22226i	−0.0964448	−	0.305196i
$561$	−0.0875188	−	0.336607i	−0.00369505	−	0.0142116i
$562$	−0.564744	−	0.564744i	−0.0238223	−	0.0238223i
$563$	15.0576	+	15.0576i	0.634603	+	0.634603i	0.949219	−	0.314616i	$-0.101876\pi$
$563$	15.0576	+	15.0576i	0.634603	+	0.634603i	−0.314616	+	0.949219i	$0.601876\pi$
$564$	4.53422	+	17.4391i	0.190925	+	0.734319i
$565$	−11.7057	−	37.0424i	−0.492464	−	1.55838i
$566$		−	10.5076i		−	0.441666i
$567$	−29.6686	+	7.01198i	−1.24596	+	0.294476i
$568$	−6.77566	+	6.77566i	−0.284300	+	0.284300i
$569$	28.8741			1.21046			0.605232	−	0.796049i	$-0.293080\pi$
$569$	28.8741			1.21046			0.605232	+	0.796049i	$0.293080\pi$
$570$	6.19357	−	27.0673i	0.259420	−	1.13372i
$571$	−32.0685			−1.34203			−0.671013	−	0.741445i	$-0.734141\pi$
$571$	−32.0685			−1.34203			−0.671013	+	0.741445i	$0.734141\pi$
$572$	0.0928221	−	0.0928221i	0.00388109	−	0.00388109i
$573$	−5.01615	+	8.54106i	−0.209552	+	0.356808i
$574$		−	34.4494i		−	1.43789i
$575$	−4.81040	+	27.4888i	−0.200607	+	1.14636i
$576$	−2.62007	+	1.46124i	−0.109170	+	0.0608848i
$577$	−17.0551	−	17.0551i	−0.710014	−	0.710014i	0.256524	−	0.966538i	$-0.417423\pi$
$577$	−17.0551	−	17.0551i	−0.710014	−	0.710014i	−0.966538	+	0.256524i	$0.917423\pi$
$578$	−7.39574	−	7.39574i	−0.307622	−	0.307622i
$579$	−5.77559	+	1.50167i	−0.240025	+	0.0624073i
$580$	−3.60302	+	6.93227i	−0.149607	+	0.287847i
$581$			39.2284i			1.62747i
$582$	5.22943	+	3.07124i	0.216767	+	0.127307i
$583$	0.0110161	−	0.0110161i	0.000456238	−	0.000456238i
$584$	−14.0985			−0.583398
$585$	−16.7203	−	15.7642i	−0.691298	−	0.651770i
$586$	13.0614			0.539561
$587$	13.9394	−	13.9394i	0.575340	−	0.575340i	−0.358275	−	0.933616i	$-0.616635\pi$
$587$	13.9394	−	13.9394i	0.575340	−	0.575340i	0.933616	+	0.358275i	$0.116635\pi$
$588$	−6.68201	−	3.92433i	−0.275562	−	0.161837i
$589$		−	7.16937i		−	0.295409i
$590$	31.9871	−	10.1082i	1.31689	−	0.416148i
$591$	−3.25224	+	0.845592i	−0.133779	+	0.0347830i
$592$	4.89823	+	4.89823i	0.201316	+	0.201316i
$593$	4.85911	+	4.85911i	0.199540	+	0.199540i	0.799803	−	0.600263i	$-0.204937\pi$
$593$	4.85911	+	4.85911i	0.199540	+	0.199540i	−0.600263	+	0.799803i	$0.704937\pi$
$594$	−0.143899	+	0.137624i	−0.00590423	+	0.00564676i
$595$	−35.2177	−	18.3043i	−1.44378	−	0.750401i
$596$			5.68468i			0.232853i
$597$	−4.42238	+	7.53004i	−0.180996	+	0.308184i
$598$	−13.5196	+	13.5196i	−0.552857	+	0.552857i
$599$	1.68745			0.0689475			0.0344738	−	0.999406i	$-0.489024\pi$
$599$	1.68745			0.0689475			0.0344738	+	0.999406i	$0.489024\pi$
$600$	−5.60731	+	6.59985i	−0.228917	+	0.269438i
$601$	34.0778			1.39006			0.695032	−	0.718979i	$-0.255390\pi$
$601$	34.0778			1.39006			0.695032	+	0.718979i	$0.255390\pi$
$602$	−23.5038	+	23.5038i	−0.957944	+	0.957944i
$603$	−6.73069	+	23.7048i	−0.274095	+	0.965333i
$604$		−	6.13286i		−	0.249542i
$605$	21.8220	+	11.3419i	0.887191	+	0.461114i
$606$	3.24201	+	12.4691i	0.131698	+	0.506524i
$607$	28.6914	+	28.6914i	1.16455	+	1.16455i	0.983469	+	0.181079i	$0.0579589\pi$
$607$	28.6914	+	28.6914i	1.16455	+	1.16455i	0.181079	+	0.983469i	$0.442041\pi$
$608$	−5.06951	−	5.06951i	−0.205596	−	0.205596i
$609$	5.15830	+	19.8394i	0.209025	+	0.803934i
$610$	11.0158	−	3.48111i	0.446018	−	0.140946i
$611$			35.6378i			1.44175i
$612$	−4.29390	+	15.1227i	−0.173571	+	0.611297i
$613$	13.7211	−	13.7211i	0.554190	−	0.554190i	−0.373458	−	0.927647i	$-0.621828\pi$
$613$	13.7211	−	13.7211i	0.554190	−	0.554190i	0.927647	+	0.373458i	$0.121828\pi$
$614$	18.1992			0.734461
$615$	−33.3627	+	20.9376i	−1.34531	+	0.844287i
$616$	−0.129802			−0.00522986
$617$	−25.0384	+	25.0384i	−1.00801	+	1.00801i	−0.00804029	+	0.999968i	$0.502559\pi$
$617$	−25.0384	+	25.0384i	−1.00801	+	1.00801i	−0.999968	+	0.00804029i	$0.997441\pi$
$618$	4.78381	−	8.14545i	0.192433	−	0.327658i
$619$			31.7434i			1.27587i	0.770088	+	0.637937i	$0.220212\pi$
$619$			31.7434i			1.27587i	−0.770088	+	0.637937i	$0.779788\pi$
$620$	−1.03122	+	1.98408i	−0.0414148	+	0.0796827i
$621$	20.9589	−	20.0449i	0.841051	−	0.804376i
$622$	16.8151	+	16.8151i	0.674226	+	0.674226i
$623$	−8.41794	−	8.41794i	−0.337257	−	0.337257i
$624$	−5.74247	+	1.49306i	−0.229883	+	0.0597702i
$625$	−8.48977	+	23.5143i	−0.339591	+	0.940573i
$626$		−	4.23426i		−	0.169235i
$627$	−0.410315	−	0.240977i	−0.0163864	−	0.00962369i
$628$	−1.92479	+	1.92479i	−0.0768073	+	0.0768073i
$629$	36.2993			1.44735
$630$	0.668458	+	22.7130i	0.0266320	+	0.904909i
$631$	15.1458			0.602945			0.301472	−	0.953475i	$-0.402522\pi$
$631$	15.1458			0.602945			0.301472	+	0.953475i	$0.402522\pi$
$632$	−11.8304	+	11.8304i	−0.470590	+	0.470590i
$633$	−38.8122	−	22.7944i	−1.54265	−	0.905994i
$634$			26.8696i			1.06713i
$635$	7.05906	+	22.3381i	0.280130	+	0.886462i
$636$	−0.681512	+	0.177195i	−0.0270237	+	0.00702624i
$637$	−10.8373	−	10.8373i	−0.429391	−	0.429391i
$638$	0.0946726	+	0.0946726i	0.00374812	+	0.00374812i
$639$	25.1061	−	14.0019i	0.993184	−	0.553906i
$640$	0.673776	+	2.13214i	0.0266333	+	0.0842803i
$641$			9.65606i			0.381392i	0.981649	+	0.190696i	$0.0610744\pi$
$641$			9.65606i			0.381392i	−0.981649	+	0.190696i	$0.938926\pi$
$642$	15.9899	−	27.2262i	0.631071	−	1.07453i
$643$	−9.67454	+	9.67454i	−0.381526	+	0.381526i	−0.871652	−	0.490125i	$-0.836951\pi$
$643$	−9.67454	+	9.67454i	−0.381526	+	0.381526i	0.490125	+	0.871652i	$0.336951\pi$
$644$	18.9057			0.744989
$645$	37.0476	+	8.47728i	1.45875	+	0.333793i
$646$	−37.5686			−1.47812
$647$	27.1946	−	27.1946i	1.06913	−	1.06913i	0.0717042	−	0.997426i	$-0.477156\pi$
$647$	27.1946	−	27.1946i	1.06913	−	1.06913i	0.997426	−	0.0717042i	$-0.0228438\pi$
$648$	8.75870	−	2.07006i	0.344074	−	0.0813198i
$649$		−	0.574886i		−	0.0225663i
$650$	−14.0179	+	9.84247i	−0.549828	+	0.386054i
$651$	1.47636	+	5.67823i	0.0578630	+	0.222547i
$652$	8.59083	+	8.59083i	0.336443	+	0.336443i
$653$	21.3008	+	21.3008i	0.833566	+	0.833566i	0.988003	−	0.154437i	$-0.0493562\pi$
$653$	21.3008	+	21.3008i	0.833566	+	0.833566i	−0.154437	+	0.988003i	$0.549356\pi$
$654$	−0.364755	−	1.40289i	−0.0142631	−	0.0548573i
$655$	17.3713	−	33.4226i	0.678752	−	1.30593i
$656$			10.1701i			0.397075i
$657$	40.6870	+	11.5526i	1.58735	+	0.450710i
$658$	24.9178	−	24.9178i	0.971398	−	0.971398i
$659$	−30.2780			−1.17946			−0.589731	−	0.807600i	$-0.700766\pi$
$659$	−30.2780			−1.17946			−0.589731	+	0.807600i	$0.700766\pi$
$660$	0.0788910	+	0.125707i	0.00307083	+	0.00489316i
$661$	−12.9343			−0.503087			−0.251544	−	0.967846i	$-0.580938\pi$
$661$	−12.9343			−0.503087			−0.251544	+	0.967846i	$0.580938\pi$
$662$	−2.62168	+	2.62168i	−0.101894	+	0.101894i
$663$	−15.7455	+	26.8101i	−0.611506	+	1.04122i
$664$		−	11.5809i		−	0.449427i
$665$	−51.7790	+	16.3627i	−2.00791	+	0.634517i
$666$	−10.1222	−	18.1496i	−0.392227	−	0.703284i
$667$	−13.7891	−	13.7891i	−0.533916	−	0.533916i
$668$	1.68138	+	1.68138i	0.0650546	+	0.0650546i
$669$	11.3319	−	2.94633i	0.438117	−	0.113912i
$670$	16.2971	+	8.47037i	0.629613	+	0.327239i
$671$		−	0.197982i		−	0.00764300i
$672$	5.05906	+	2.97117i	0.195157	+	0.114616i
$673$	3.82947	−	3.82947i	0.147615	−	0.147615i	−0.629437	−	0.777052i	$-0.716714\pi$
$673$	3.82947	−	3.82947i	0.147615	−	0.147615i	0.777052	+	0.629437i	$0.216714\pi$
$674$	−9.54770			−0.367764
$675$	21.5903	−	14.4519i	0.831012	−	0.556254i
$676$	1.26494			0.0486516
$677$	2.79395	−	2.79395i	0.107380	−	0.107380i	−0.651375	−	0.758756i	$-0.725808\pi$
$677$	2.79395	−	2.79395i	0.107380	−	0.107380i	0.758756	+	0.651375i	$0.225808\pi$
$678$	25.9475	+	15.2389i	0.996507	+	0.585247i
$679$		−	11.8604i		−	0.455160i
$680$	10.3969	+	5.40374i	0.398703	+	0.207224i
$681$	−17.7343	+	4.61097i	−0.679580	+	0.176693i
$682$	0.0270962	+	0.0270962i	0.00103757	+	0.00103757i
$683$	−17.3883	−	17.3883i	−0.665345	−	0.665345i	0.291290	−	0.956635i	$-0.405916\pi$
$683$	−17.3883	−	17.3883i	−0.665345	−	0.665345i	−0.956635	+	0.291290i	$0.905916\pi$
$684$	10.4761	+	18.7843i	0.400565	+	0.718235i
$685$	−7.21181	+	2.27900i	−0.275549	+	0.0870760i
$686$		−	8.55644i		−	0.326686i
$687$	1.12973	−	1.92360i	0.0431017	−	0.0733899i
$688$	6.93875	−	6.93875i	0.264537	−	0.264537i
$689$	−1.39271			−0.0530580
$690$	−11.4905	−	18.3093i	−0.437436	−	0.697025i
$691$	6.95698			0.264656			0.132328	−	0.991206i	$-0.457755\pi$
$691$	6.95698			0.264656			0.132328	+	0.991206i	$0.457755\pi$
$692$	0.350482	−	0.350482i	0.0133233	−	0.0133233i
$693$	0.374598	+	0.106363i	0.0142298	+	0.00404038i
$694$		−	8.81570i		−	0.334640i
$695$	−4.55192	+	8.75796i	−0.172664	+	0.332208i
$696$	−1.52282	−	5.85695i	−0.0577225	−	0.222007i
$697$	37.6836	+	37.6836i	1.42737	+	1.42737i
$698$	15.0211	+	15.0211i	0.568558	+	0.568558i
$699$	1.57726	+	6.06631i	0.0596574	+	0.229449i
$700$	16.6831	+	2.91946i	0.630563	+	0.110345i
$701$			30.4250i			1.14914i	0.818456	+	0.574569i	$0.194830\pi$
$701$			30.4250i			1.14914i	−0.818456	+	0.574569i	$0.805170\pi$
$702$	17.7958	+	0.396659i	0.671658	+	0.0149709i
$703$	35.1172	−	35.1172i	1.32447	−	1.32447i
$704$	0.0383198			0.00144423
$705$	−39.2764	−	8.98728i	−1.47924	−	0.338481i
$706$	−24.3538			−0.916566
$707$	17.8165	−	17.8165i	0.670059	−	0.670059i
$708$	−13.1592	+	22.4063i	−0.494553	+	0.842082i
$709$		−	43.7876i		−	1.64448i	−0.569143	−	0.822238i	$-0.692725\pi$
$709$		−	43.7876i		−	1.64448i	0.569143	−	0.822238i	$-0.307275\pi$
$710$	−6.45627	−	20.4307i	−0.242300	−	0.766749i
$711$	43.8359	−	24.4476i	1.64397	−	0.916856i
$712$	2.48513	+	2.48513i	0.0931340	+	0.0931340i
$713$	−3.94658	−	3.94658i	−0.147800	−	0.147800i
$714$	29.7548	−	7.73633i	1.11354	−	0.289525i
$715$	0.0884468	+	0.279887i	0.00330772	+	0.0104672i
$716$		−	1.82086i		−	0.0680486i
$717$	16.4386	+	9.65436i	0.613911	+	0.360549i
$718$	6.82483	−	6.82483i	0.254700	−	0.254700i
$719$	15.8238			0.590130			0.295065	−	0.955477i	$-0.404659\pi$
$719$	15.8238			0.590130			0.295065	+	0.955477i	$0.404659\pi$
$720$	−0.197341	−	6.70530i	−0.00735446	−	0.249892i
$721$	−18.4739			−0.688006
$722$	−22.9102	+	22.9102i	−0.852628	+	0.852628i
$723$	−7.73852	−	4.54482i	−0.287799	−	0.169024i
$724$		−	18.7741i		−	0.697733i
$725$	−10.0387	−	14.2974i	−0.372828	−	0.530992i
$726$	−18.4370	+	4.79368i	−0.684262	+	0.177910i
$727$	−6.35959	−	6.35959i	−0.235864	−	0.235864i	0.579271	−	0.815135i	$-0.303337\pi$
$727$	−6.35959	−	6.35959i	−0.235864	−	0.235864i	−0.815135	+	0.579271i	$0.803337\pi$
$728$	8.20512	+	8.20512i	0.304102	+	0.304102i
$729$	−26.9732	−	1.20304i	−0.999007	−	0.0445569i
$730$	14.5386	−	27.9725i	0.538098	−	1.03531i
$731$		−	51.4209i		−	1.90187i
$732$	−4.53182	+	7.71639i	−0.167501	+	0.285206i
$733$	−16.6044	+	16.6044i	−0.613299	+	0.613299i	−0.943804	−	0.330505i	$-0.892781\pi$
$733$	−16.6044	+	16.6044i	−0.613299	+	0.613299i	0.330505	+	0.943804i	$0.392781\pi$
$734$	−12.1654			−0.449034
$735$	14.6768	−	9.21082i	0.541363	−	0.339746i
$736$	−5.58130			−0.205729
$737$	0.222567	−	0.222567i	0.00819834	−	0.00819834i
$738$	8.33359	−	29.3500i	0.306764	−	1.08039i
$739$			46.2648i			1.70188i	0.525265	+	0.850939i	$0.323966\pi$
$739$			46.2648i			1.70188i	−0.525265	+	0.850939i	$0.676034\pi$
$740$	−14.7697	+	4.66735i	−0.542943	+	0.171575i
$741$	10.7043	+	41.1699i	0.393232	+	1.51241i
$742$	0.973778	+	0.973778i	0.0357485	+	0.0357485i
$743$	21.0299	+	21.0299i	0.771513	+	0.771513i	0.978371	−	0.206858i	$-0.0663237\pi$
$743$	21.0299	+	21.0299i	0.771513	+	0.771513i	−0.206858	+	0.978371i	$0.566324\pi$
$744$	−0.435847	−	1.67632i	−0.0159789	−	0.0614567i
$745$	−11.2789	−	5.86215i	−0.413226	−	0.214773i
$746$			5.92024i			0.216756i
$747$	−9.48968	+	33.4217i	−0.347209	+	1.22283i
$748$	0.141988	−	0.141988i	0.00519160	−	0.00519160i
$749$	−61.7492			−2.25627
$750$	−7.31229	−	17.9313i	−0.267007	−	0.654757i
$751$	−15.8787			−0.579421			−0.289710	−	0.957114i	$-0.593559\pi$
$751$	−15.8787			−0.579421			−0.289710	+	0.957114i	$0.593559\pi$
$752$	−7.35619	+	7.35619i	−0.268253	+	0.268253i
$753$	−9.60893	+	16.3613i	−0.350169	+	0.596237i
$754$		−	11.9690i		−	0.435886i
$755$	12.1681	+	6.32432i	0.442843	+	0.230166i
$756$	−12.1654	−	12.7201i	−0.442451	−	0.462625i
$757$	−9.22666	−	9.22666i	−0.335349	−	0.335349i	0.519265	−	0.854613i	$-0.326206\pi$
$757$	−9.22666	−	9.22666i	−0.335349	−	0.335349i	−0.854613	+	0.519265i	$0.826206\pi$
$758$	−11.3842	−	11.3842i	−0.413494	−	0.413494i
$759$	−0.358521	+	0.0932166i	−0.0130135	+	0.00338355i
$760$	15.2861	−	4.83055i	0.554485	−	0.175222i
$761$		−	29.4202i		−	1.06648i	−0.845963	−	0.533242i	$-0.820974\pi$
$761$		−	29.4202i		−	1.06648i	0.845963	−	0.533242i	$-0.179026\pi$
$762$	−15.6475	−	9.18972i	−0.566847	−	0.332908i
$763$	−2.00451	+	2.00451i	−0.0725683	+	0.0725683i
$764$	−5.71872			−0.206896
$765$	−25.5767	−	24.1142i	−0.924726	−	0.871852i
$766$	4.33007			0.156452
$767$	−36.3401	+	36.3401i	−1.31216	+	1.31216i
$768$	−1.49353	−	0.877144i	−0.0538930	−	0.0316512i
$769$			42.6183i			1.53686i	0.639937	+	0.768428i	$0.278961\pi$
$769$			42.6183i			1.53686i	−0.639937	+	0.768428i	$0.721039\pi$
$770$	0.133854	−	0.257538i	0.00482377	−	0.00928101i
$771$	6.16805	−	1.60371i	0.222137	−	0.0577563i
$772$	−2.43627	−	2.43627i	−0.0876832	−	0.0876832i
$773$	−7.38044	−	7.38044i	−0.265456	−	0.265456i	0.561810	−	0.827266i	$-0.310105\pi$
$773$	−7.38044	−	7.38044i	−0.265456	−	0.265456i	−0.827266	+	0.561810i	$0.810105\pi$
$774$	−25.7105	+	14.3389i	−0.924144	+	0.515402i
$775$	−2.87317	−	4.09205i	−0.103207	−	0.146991i
$776$			3.50140i			0.125693i
$777$	−20.5818	+	35.0449i	−0.738367	+	1.25723i
$778$	−2.46536	+	2.46536i	−0.0883874	+	0.0883874i
$779$	72.9130			2.61238
$780$	2.95939	−	12.9332i	0.105963	−	0.463083i
$781$	−0.367189			−0.0131391
$782$	−20.6806	+	20.6806i	−0.739538	+	0.739538i
$783$	−0.404567	+	18.1505i	−0.0144580	+	0.648647i
$784$		−	4.47399i		−	0.159785i
$785$	−1.83406	−	5.80381i	−0.0654604	−	0.207147i
$786$	7.34200	+	28.2382i	0.261881	+	1.00722i
$787$	10.3895	+	10.3895i	0.370347	+	0.370347i	0.867603	−	0.497257i	$-0.165659\pi$
$787$	10.3895	+	10.3895i	0.370347	+	0.370347i	−0.497257	+	0.867603i	$0.665659\pi$
$788$	−1.37187	−	1.37187i	−0.0488707	−	0.0488707i
$789$	−7.97672	−	30.6794i	−0.283979	−	1.09221i
$790$	−11.2728	−	35.6724i	−0.401068	−	1.26917i
$791$		−	58.8491i		−	2.09243i
$792$	−0.110588	−	0.0314001i	−0.00392958	−	0.00111576i
$793$	−12.5150	+	12.5150i	−0.444419	+	0.444419i
$794$	−27.3210			−0.969587
$795$	0.351219	−	1.53490i	0.0124565	−	0.0544374i
$796$	−5.04179			−0.178701
$797$	−0.920813	+	0.920813i	−0.0326169	+	0.0326169i	−0.723227	−	0.690610i	$-0.757342\pi$
$797$	−0.920813	+	0.920813i	−0.0326169	+	0.0326169i	0.690610	+	0.723227i	$0.257342\pi$
$798$	21.3014	−	36.2703i	0.754063	−	1.28395i
$799$			54.5145i			1.92858i
$800$	−4.92516	−	0.861878i	−0.174131	−	0.0304720i
$801$	−5.13551	−	9.20825i	−0.181454	−	0.325358i
$802$	−6.42625	−	6.42625i	−0.226919	−	0.226919i
$803$	−0.382015	−	0.382015i	−0.0134810	−	0.0134810i
$804$	−13.7692	+	3.58002i	−0.485601	+	0.126258i
$805$	−19.4959	+	37.5105i	−0.687141	+	1.32207i
$806$		−	3.42565i		−	0.120663i
$807$	13.8563	+	8.13778i	0.487765	+	0.286463i
$808$	−5.25975	+	5.25975i	−0.185038	+	0.185038i
$809$	0.728913			0.0256272			0.0128136	−	0.999918i	$-0.495921\pi$
$809$	0.728913			0.0256272			0.0128136	+	0.999918i	$0.495921\pi$
$810$	−4.92497	+	19.5127i	−0.173046	+	0.685606i
$811$	−3.76569			−0.132231			−0.0661155	−	0.997812i	$-0.521061\pi$
$811$	−3.76569			−0.132231			−0.0661155	+	0.997812i	$0.521061\pi$
$812$	−8.36870	+	8.36870i	−0.293684	+	0.293684i
$813$	−44.9848	−	26.4195i	−1.57769	−	0.926572i
$814$			0.265447i			0.00930392i
$815$	−25.9040	+	8.18589i	−0.907376	+	0.286739i
$816$	−8.78415	+	2.28390i	−0.307507	+	0.0799526i
$817$	−49.7465	−	49.7465i	−1.74041	−	1.74041i
$818$	11.3087	+	11.3087i	0.395400	+	0.395400i
$819$	−16.9559	−	30.4028i	−0.592486	−	1.06236i
$820$	−20.1783	−	10.4876i	−0.704656	−	0.366242i
$821$			6.66388i			0.232571i	0.993216	+	0.116285i	$0.0370987\pi$
$821$			6.66388i			0.232571i	−0.993216	+	0.116285i	$0.962901\pi$
$822$	2.96688	−	5.05174i	0.103482	−	0.176200i
$823$	4.33761	−	4.33761i	0.151200	−	0.151200i	−0.627454	−	0.778654i	$-0.715903\pi$
$823$	4.33761	−	4.33761i	0.151200	−	0.151200i	0.778654	+	0.627454i	$0.215903\pi$
$824$	5.45384			0.189994
$825$	−0.330768	+	0.0268942i	−0.0115159	+	0.000936337i
$826$	50.8178			1.76818
$827$	17.7402	−	17.7402i	0.616886	−	0.616886i	−0.327845	−	0.944731i	$-0.606322\pi$
$827$	17.7402	−	17.7402i	0.616886	−	0.616886i	0.944731	+	0.327845i	$0.106322\pi$
$828$	16.1072	+	4.57344i	0.559764	+	0.158938i
$829$		−	18.4718i		−	0.641554i	−0.947155	−	0.320777i	$-0.896056\pi$
$829$		−	18.4718i		−	0.641554i	0.947155	−	0.320777i	$-0.103944\pi$
$830$	22.9775	+	11.9425i	0.797562	+	0.414530i
$831$	−8.29618	−	31.9080i	−0.287791	−	1.10688i
$832$	−2.42230	−	2.42230i	−0.0839781	−	0.0839781i
$833$	−16.5777	−	16.5777i	−0.574382	−	0.574382i
$834$	−1.92388	−	7.39944i	−0.0666184	−	0.256222i
$835$	−5.06988	+	1.60213i	−0.175450	+	0.0554439i
$836$		−	0.274729i		−	0.00950170i
$837$	−0.115791	+	5.19486i	−0.00400232	+	0.179561i
$838$	−15.6292	+	15.6292i	−0.539900	+	0.539900i
$839$	−37.1676			−1.28317			−0.641583	−	0.767053i	$-0.721722\pi$
$839$	−37.1676			−1.28317			−0.641583	+	0.767053i	$0.721722\pi$
$840$	−11.1121	+	6.97366i	−0.383402	+	0.240614i
$841$	−16.7924			−0.579047
$842$	−16.5218	+	16.5218i	−0.569381	+	0.569381i
$843$	−0.700547	+	1.19283i	−0.0241281	+	0.0410833i
$844$		−	25.9870i		−	0.894510i
$845$	−1.30443	+	2.50975i	−0.0448739	+	0.0863380i
$846$	27.2572	−	15.2016i	0.937123	−	0.522641i
$847$	26.3437	+	26.3437i	0.905180	+	0.905180i
$848$	−0.287477	−	0.287477i	−0.00987199	−	0.00987199i
$849$	−17.6140	+	4.57969i	−0.604511	+	0.157175i
$850$	−21.4430	+	15.0558i	−0.735487	+	0.516411i
$851$		−	38.6625i		−	1.32533i
$852$	14.3113	+	8.40499i	0.490297	+	0.287950i
$853$	7.20464	−	7.20464i	0.246682	−	0.246682i	−0.572925	−	0.819608i	$-0.694192\pi$
$853$	7.20464	−	7.20464i	0.246682	−	0.246682i	0.819608	+	0.572925i	$0.194192\pi$
$854$	17.5008			0.598866
$855$	−48.0728	+	1.41481i	−1.64405	+	0.0483854i
$856$	18.2295			0.623071
$857$	0.0169638	−	0.0169638i	0.000579472	−	0.000579472i	−0.706817	−	0.707396i	$-0.749870\pi$
$857$	0.0169638	−	0.0169638i	0.000579472	−	0.000579472i	0.707396	+	0.706817i	$0.249870\pi$
$858$	−0.196055	−	0.115143i	−0.00669322	−	0.00393091i
$859$		−	1.75493i		−	0.0598775i	−0.999552	−	0.0299387i	$-0.990469\pi$
$859$		−	1.75493i		−	0.0598775i	0.999552	−	0.0299387i	$-0.00953122\pi$
$860$	6.61168	+	20.9224i	0.225457	+	0.713449i
$861$	−57.7481	+	15.0147i	−1.96805	+	0.511698i
$862$	3.57568	+	3.57568i	0.121788	+	0.121788i
$863$	−18.3540	−	18.3540i	−0.624777	−	0.624777i	0.321972	−	0.946749i	$-0.395654\pi$
$863$	−18.3540	−	18.3540i	−0.624777	−	0.624777i	−0.946749	+	0.321972i	$0.895654\pi$
$864$	3.59145	+	3.75520i	0.122183	+	0.127754i
$865$	0.333961	+	1.05681i	0.0113550	+	0.0359326i
$866$		−	20.4805i		−	0.695955i
$867$	−9.17419	+	15.6210i	−0.311572	+	0.530518i
$868$	−2.39520	+	2.39520i	−0.0812985	+	0.0812985i
$869$	−0.641120			−0.0217485
$870$	13.1910	+	3.01839i	0.447218	+	0.102333i
$871$	−28.1380			−0.953421
$872$	0.591769	−	0.591769i	0.0200398	−	0.0200398i
$873$	2.86913	−	10.1048i	0.0971053	−	0.341995i
$874$			40.0144i			1.35351i
$875$	−22.9964	+	30.0901i	−0.777421	+	1.01723i
$876$	6.14477	+	23.6335i	0.207613	+	0.798501i
$877$	−18.5647	−	18.5647i	−0.626886	−	0.626886i	0.320397	−	0.947283i	$-0.396184\pi$
$877$	−18.5647	−	18.5647i	−0.626886	−	0.626886i	−0.947283	+	0.320397i	$0.896184\pi$
$878$	−21.1067	−	21.1067i	−0.712317	−	0.712317i
$879$	−5.69277	−	21.8950i	−0.192012	−	0.738501i
$880$	−0.0395162	+	0.0760297i	−0.00133209	+	0.00256296i
$881$		−	6.58057i		−	0.221705i	−0.993837	−	0.110853i	$-0.964642\pi$
$881$		−	6.58057i		−	0.221705i	0.993837	−	0.110853i	$-0.0353581\pi$
$882$	−3.66609	+	12.9116i	−0.123444	+	0.434755i
$883$	24.4430	−	24.4430i	0.822571	−	0.822571i	−0.163905	−	0.986476i	$-0.552409\pi$
$883$	24.4430	−	24.4430i	0.822571	−	0.822571i	0.986476	+	0.163905i	$0.0524091\pi$
$884$	−17.9509			−0.603754
$885$	−30.8860	−	49.2148i	−1.03822	−	1.65434i
$886$	9.18835			0.308688
$887$	4.64793	−	4.64793i	0.156062	−	0.156062i	−0.624757	−	0.780819i	$-0.714802\pi$
$887$	4.64793	−	4.64793i	0.156062	−	0.156062i	0.780819	+	0.624757i	$0.214802\pi$
$888$	6.07611	−	10.3459i	0.203901	−	0.347185i
$889$			35.4886i			1.19025i
$890$	−7.49341	+	2.36799i	−0.251180	+	0.0793751i
$891$	0.293418	+	0.181237i	0.00982989	+	0.00607166i
$892$	4.78005	+	4.78005i	0.160048	+	0.160048i
$893$	52.7393	+	52.7393i	1.76485	+	1.76485i
$894$	9.52932	−	2.47765i	0.318708	−	0.0828650i
$895$	3.61273	+	1.87770i	0.120760	+	0.0627646i
$896$			3.38733i			0.113163i
$897$	28.5556	+	16.7706i	0.953442	+	0.559955i
$898$	10.7432	−	10.7432i	0.358506	−	0.358506i
$899$	3.49394			0.116529
$900$	13.5074	+	6.52310i	0.450246	+	0.217437i
$901$	−2.13040			−0.0709739
$902$	−0.275570	+	0.275570i	−0.00917549	+	0.00917549i
$903$	49.6439	+	29.1558i	1.65205	+	0.970243i
$904$			17.3733i			0.577828i
$905$	37.2493	+	19.3602i	1.23821	+	0.643555i
$906$	−10.2806	+	2.67299i	−0.341550	+	0.0888041i
$907$	−25.1449	−	25.1449i	−0.834923	−	0.834923i	0.153263	−	0.988186i	$-0.451022\pi$
$907$	−25.1449	−	25.1449i	−0.834923	−	0.834923i	−0.988186	+	0.153263i	$0.951022\pi$
$908$	−7.48071	−	7.48071i	−0.248256	−	0.248256i
$909$	19.4892	−	10.8693i	0.646416	−	0.360511i
$910$	−24.7409	+	7.81836i	−0.820153	+	0.259176i
$911$			15.4101i			0.510561i	0.966867	+	0.255280i	$0.0821678\pi$
$911$			15.4101i			0.510561i	−0.966867	+	0.255280i	$0.917832\pi$
$912$	−6.28857	+	10.7076i	−0.208235	+	0.354565i
$913$	0.313799	−	0.313799i	0.0103852	−	0.0103852i
$914$	−12.6210			−0.417464
$915$	−10.6367	−	16.9488i	−0.351637	−	0.560310i
$916$	1.28796			0.0425553
$917$	40.3480	−	40.3480i	1.33241	−	1.33241i
$918$	27.2219	+	0.606762i	0.898455	+	0.0200261i
$919$		−	4.10799i		−	0.135510i	−0.997702	−	0.0677550i	$-0.978416\pi$
$919$		−	4.10799i		−	0.135510i	0.997702	−	0.0677550i	$-0.0215836\pi$
$920$	5.75555	−	11.0738i	0.189755	−	0.365091i
$921$	−7.93208	−	30.5077i	−0.261371	−	1.00526i
$922$	−6.98181	−	6.98181i	−0.229934	−	0.229934i
$923$	23.2110	+	23.2110i	0.763999	+	0.763999i
$924$	0.0565738	+	0.217589i	0.00186114	+	0.00715815i
$925$	5.97036	−	34.1173i	0.196304	−	1.12177i
$926$			15.2032i			0.499609i
$927$	−15.7394	−	4.46900i	−0.516948	−	0.146781i
$928$	2.47059	−	2.47059i	0.0811011	−	0.0811011i
$929$	1.62724			0.0533879			0.0266939	−	0.999644i	$-0.491502\pi$
$929$	1.62724			0.0533879			0.0266939	+	0.999644i	$0.491502\pi$
$930$	3.77541	+	0.863894i	0.123800	+	0.0283282i
$931$	−32.0757			−1.05124
$932$	−2.55890	+	2.55890i	−0.0838197	+	0.0838197i
$933$	20.8587	−	35.5163i	0.682882	−	1.16275i
$934$		−	10.0201i		−	0.327866i
$935$	0.135295	+	0.428137i	0.00442463	+	0.0140016i
$936$	5.00568	+	8.97545i	0.163616	+	0.293372i
$937$	19.6327	+	19.6327i	0.641372	+	0.641372i	0.950893	−	0.309521i	$-0.100169\pi$
$937$	19.6327	+	19.6327i	0.641372	+	0.641372i	−0.309521	+	0.950893i	$0.600169\pi$
$938$	19.6740	+	19.6740i	0.642380	+	0.642380i
$939$	−7.09796	+	1.84549i	−0.231633	+	0.0602253i
$940$	−7.00945	−	22.1812i	−0.228623	−	0.723469i
$941$		−	24.6253i		−	0.802763i	−0.915911	−	0.401381i	$-0.868530\pi$
$941$		−	24.6253i		−	0.802763i	0.915911	−	0.401381i	$-0.131470\pi$
$942$	4.06546	+	2.38764i	0.132460	+	0.0777935i
$943$	40.1370	−	40.1370i	1.30704	−	1.30704i
$944$	−15.0023			−0.488284
$945$	37.7829	−	11.0200i	1.22908	−	0.358479i
$946$	0.376028			0.0122257
$947$	−30.8926	+	30.8926i	−1.00388	+	1.00388i	−0.00388328	+	0.999992i	$0.501236\pi$
$947$	−30.8926	+	30.8926i	−1.00388	+	1.00388i	−0.999992	+	0.00388328i	$0.998764\pi$
$948$	24.9878	+	14.6753i	0.811567	+	0.476631i
$949$			48.2963i			1.56777i
$950$	−6.17912	+	35.3103i	−0.200477	+	1.14562i
$951$	45.0420	−	11.7110i	1.46059	−	0.379757i
$952$	12.5512	+	12.5512i	0.406787	+	0.406787i
$953$	−37.6776	−	37.6776i	−1.22050	−	1.22050i	−0.967455	−	0.253044i	$-0.918568\pi$
$953$	−37.6776	−	37.6776i	−1.22050	−	1.22050i	−0.253044	−	0.967455i	$-0.581432\pi$
$954$	0.594070	+	1.06520i	0.0192337	+	0.0344871i
$955$	5.89726	−	11.3464i	0.190831	−	0.367162i
$956$			11.0066i			0.355978i
$957$	0.117438	−	0.199964i	0.00379625	−	0.00646392i
$958$	−27.6805	+	27.6805i	−0.894316	+	0.894316i
$959$	−11.4574			−0.369978
$960$	3.28048	−	2.05875i	0.105877	−	0.0664459i
$961$	1.00000			0.0322581
$962$	16.7796	−	16.7796i	0.540997	−	0.540997i
$963$	−52.6089	−	14.9377i	−1.69530	−	0.481359i
$964$		−	5.18138i		−	0.166881i
$965$	7.34609	−	2.32143i	0.236479	−	0.0747295i
$966$	−8.23999	−	31.6919i	−0.265117	−	1.01967i
$967$	−25.0874	−	25.0874i	−0.806757	−	0.806757i	0.177384	−	0.984142i	$-0.443236\pi$
$967$	−25.0874	−	25.0874i	−0.806757	−	0.806757i	−0.984142	+	0.177384i	$0.943236\pi$
$968$	−7.77714	−	7.77714i	−0.249967	−	0.249967i
$969$	16.3742	+	62.9768i	0.526014	+	2.02311i
$970$	−6.94707	−	3.61072i	−0.223057	−	0.115933i
$971$		−	30.9651i		−	0.993718i	−0.867831	−	0.496859i	$-0.834487\pi$
$971$		−	30.9651i		−	0.993718i	0.867831	−	0.496859i	$-0.165513\pi$
$972$	−7.28754	−	13.7801i	−0.233748	−	0.441998i
$973$	−10.5727	+	10.5727i	−0.338945	+	0.338945i
$974$	−11.7885			−0.377729
$975$	22.6088	+	19.2087i	0.724060	+	0.615170i
$976$	−5.16656			−0.165378
$977$	−19.3792	+	19.3792i	−0.619994	+	0.619994i	−0.945530	−	0.325536i	$-0.894455\pi$
$977$	−19.3792	+	19.3792i	−0.619994	+	0.619994i	0.325536	+	0.945530i	$0.394455\pi$
$978$	10.6567	−	18.1452i	0.340763	−	0.580221i
$979$			0.134675i			0.00430423i
$980$	8.87676	+	4.61366i	0.283558	+	0.147378i
$981$	−2.19271	+	1.22289i	−0.0700078	+	0.0390439i
$982$	−13.2511	−	13.2511i	−0.422861	−	0.422861i
$983$	−3.06898	−	3.06898i	−0.0978851	−	0.0978851i	0.656468	−	0.754354i	$-0.272050\pi$
$983$	−3.06898	−	3.06898i	−0.0978851	−	0.0978851i	−0.754354	+	0.656468i	$0.772050\pi$
$984$	17.0483	−	4.43260i	0.543479	−	0.141306i
$985$	4.13659	−	1.30720i	0.131803	−	0.0416509i
$986$		−	18.3088i		−	0.583070i
$987$	−52.6306	−	30.9098i	−1.67525	−	0.983870i
$988$	−17.3663	+	17.3663i	−0.552497	+	0.552497i
$989$	−54.7686			−1.74154
$990$	0.176341	−	0.187035i	0.00560449	−	0.00594438i
$991$	11.3175			0.359513			0.179756	−	0.983711i	$-0.442469\pi$
$991$	11.3175			0.359513			0.179756	+	0.983711i	$0.442469\pi$
$992$	0.707107	−	0.707107i	0.0224507	−	0.0224507i
$993$	5.53741	+	3.25211i	0.175724	+	0.103203i
$994$		−	32.4581i		−	1.02951i
$995$	5.19919	−	10.0033i	0.164825	−	0.317127i
$996$	−19.4133	+	5.04752i	−0.615134	+	0.159937i
$997$	6.77107	+	6.77107i	0.214442	+	0.214442i	0.806151	−	0.591709i	$-0.201547\pi$
$997$	6.77107	+	6.77107i	0.214442	+	0.214442i	−0.591709	+	0.806151i	$0.701547\pi$
$998$	18.8942	+	18.8942i	0.598084	+	0.598084i
$999$	−26.0128	+	24.8785i	−0.823009	+	0.787120i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.j.h.497.12	yes	40
3.2	odd	2	inner	930.2.j.h.497.8	✓	40
5.3	odd	4	inner	930.2.j.h.683.8	yes	40
15.8	even	4	inner	930.2.j.h.683.12	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.j.h.497.8	✓	40	3.2	odd	2	inner
930.2.j.h.497.12	yes	40	1.1	even	1	trivial
930.2.j.h.683.8	yes	40	5.3	odd	4	inner
930.2.j.h.683.12	yes	40	15.8	even	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(-1.49353 - 0.877144i) q^{3} -1.00000i q^{4} +(1.98408 + 1.03122i) q^{5} +(-1.67632 + 0.435847i) q^{6} +(2.39520 + 2.39520i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.46124 + 2.62007i) q^{9} +(2.13214 - 0.673776i) q^{10} -0.0383198i q^{11} +(-0.877144 + 1.49353i) q^{12} +(-2.42230 + 2.42230i) q^{13} +3.38733 q^{14} +(-2.05875 - 3.28048i) q^{15} -1.00000 q^{16} +(-3.70534 + 3.70534i) q^{17} +(2.88592 + 0.819423i) q^{18} +7.16937i q^{19} +(1.03122 - 1.98408i) q^{20} +(-1.47636 - 5.67823i) q^{21} +(-0.0270962 - 0.0270962i) q^{22} +(3.94658 + 3.94658i) q^{23} +(0.435847 + 1.67632i) q^{24} +(2.87317 + 4.09205i) q^{25} +3.42565i q^{26} +(0.115791 - 5.19486i) q^{27} +(2.39520 - 2.39520i) q^{28} -3.49394 q^{29} +(-3.77541 - 0.863894i) q^{30} -1.00000 q^{31} +(-0.707107 + 0.707107i) q^{32} +(-0.0336120 + 0.0572316i) q^{33} +5.24015i q^{34} +(2.28230 + 7.22226i) q^{35} +(2.62007 - 1.46124i) q^{36} +(-4.89823 - 4.89823i) q^{37} +(5.06951 + 5.06951i) q^{38} +(5.74247 - 1.49306i) q^{39} +(-0.673776 - 2.13214i) q^{40} -10.1701i q^{41} +(-5.05906 - 2.97117i) q^{42} +(-6.93875 + 6.93875i) q^{43} -0.0383198 q^{44} +(0.197341 + 6.70530i) q^{45} +5.58130 q^{46} +(7.35619 - 7.35619i) q^{47} +(1.49353 + 0.877144i) q^{48} +4.47399i q^{49} +(4.92516 + 0.861878i) q^{50} +(8.78415 - 2.28390i) q^{51} +(2.42230 + 2.42230i) q^{52} +(0.287477 + 0.287477i) q^{53} +(-3.59145 - 3.75520i) q^{54} +(0.0395162 - 0.0760297i) q^{55} -3.38733i q^{56} +(6.28857 - 10.7076i) q^{57} +(-2.47059 + 2.47059i) q^{58} +15.0023 q^{59} +(-3.28048 + 2.05875i) q^{60} +5.16656 q^{61} +(-0.707107 + 0.707107i) q^{62} +(-2.77565 + 9.77556i) q^{63} +1.00000i q^{64} +(-7.30396 + 2.30812i) q^{65} +(0.0167016 + 0.0642362i) q^{66} +(5.80813 + 5.80813i) q^{67} +(3.70534 + 3.70534i) q^{68} +(-2.43259 - 9.35603i) q^{69} +(6.72074 + 3.49308i) q^{70} -9.58222i q^{71} +(0.819423 - 2.88592i) q^{72} +(9.96911 - 9.96911i) q^{73} -6.92715 q^{74} +(-0.701836 - 8.63177i) q^{75} +7.16937 q^{76} +(0.0917837 - 0.0917837i) q^{77} +(3.00479 - 5.11629i) q^{78} -16.7308i q^{79} +(-1.98408 - 1.03122i) q^{80} +(-4.72958 + 7.65709i) q^{81} +(-7.19133 - 7.19133i) q^{82} +(8.18895 + 8.18895i) q^{83} +(-5.67823 + 1.47636i) q^{84} +(-11.1727 + 3.53069i) q^{85} +9.81288i q^{86} +(5.21829 + 3.06469i) q^{87} +(-0.0270962 + 0.0270962i) q^{88} -3.51450 q^{89} +(4.88090 + 4.60182i) q^{90} -11.6038 q^{91} +(3.94658 - 3.94658i) q^{92} +(1.49353 + 0.877144i) q^{93} -10.4032i q^{94} +(-7.39319 + 14.2246i) q^{95} +(1.67632 - 0.435847i) q^{96} +(-2.47587 - 2.47587i) q^{97} +(3.16359 + 3.16359i) q^{98} +(0.100401 - 0.0559943i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{3} + 8 q^{6} - 8 q^{7} + 4 q^{12} + 24 q^{13} - 12 q^{15} - 40 q^{16} - 56 q^{21} + 16 q^{22} - 48 q^{25} + 8 q^{27} - 8 q^{28} + 4 q^{30} - 40 q^{31} - 20 q^{33} - 8 q^{37} - 8 q^{40} + 12 q^{42}+ \cdots + 24 q^{97}+O(q^{100}) \) 40 * q - 4 * q^3 + 8 * q^6 - 8 * q^7 + 4 * q^12 + 24 * q^13 - 12 * q^15 - 40 * q^16 - 56 * q^21 + 16 * q^22 - 48 * q^25 + 8 * q^27 - 8 * q^28 + 4 * q^30 - 40 * q^31 - 20 * q^33 - 8 * q^37 - 8 * q^40 + 12 * q^42 - 16 * q^43 + 76 * q^45 - 8 * q^46 + 4 * q^48 + 16 * q^51 - 24 * q^52 - 48 * q^55 + 56 * q^57 - 56 * q^58 + 12 * q^60 + 128 * q^61 - 24 * q^63 + 16 * q^66 + 8 * q^67 + 32 * q^70 + 248 * q^73 - 8 * q^75 + 56 * q^76 + 8 * q^78 + 40 * q^81 - 8 * q^82 - 48 * q^85 + 12 * q^87 + 16 * q^88 + 16 * q^90 - 192 * q^91 + 4 * q^93 - 8 * q^96 + 24 * q^97

Introduction

L-functions

Modular forms

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