LMFDB - Embedded newform 231.2.w.a.13.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(13,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 1]))

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

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

chi := DirichletCharacter("231.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.w (of order $10$, degree $4$, 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:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			13.6
Character	$\chi$	$=$	231.13
Dual form			231.2.w.a.160.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50185 - 0.487979i) q^{2} +(0.587785 + 0.809017i) q^{3} +(0.399382 + 0.290168i) q^{4} +(-2.27762 + 0.740044i) q^{5} +(-0.487979 - 1.50185i) q^{6} +(1.23267 - 2.34105i) q^{7} +(1.39817 + 1.92441i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(-1.50185 - 0.487979i) q^{2} +(0.587785 + 0.809017i) q^{3} +(0.399382 + 0.290168i) q^{4} +(-2.27762 + 0.740044i) q^{5} +(-0.487979 - 1.50185i) q^{6} +(1.23267 - 2.34105i) q^{7} +(1.39817 + 1.92441i) q^{8} +(-0.309017 + 0.951057i) q^{9} +3.78176 q^{10} +(-1.12813 + 3.11886i) q^{11} +0.493663i q^{12} +(-1.34865 + 4.15073i) q^{13} +(-2.99367 + 2.91438i) q^{14} +(-1.93746 - 1.40765i) q^{15} +(-1.46586 - 4.51145i) q^{16} +(1.39659 + 4.29826i) q^{17} +(0.928191 - 1.27755i) q^{18} +(-4.07619 + 2.96153i) q^{19} +(-1.12438 - 0.365332i) q^{20} +(2.61850 - 0.378780i) q^{21} +(3.21622 - 4.13355i) q^{22} -3.78029 q^{23} +(-0.735061 + 2.26229i) q^{24} +(0.594803 - 0.432150i) q^{25} +(4.05094 - 5.57564i) q^{26} +(-0.951057 + 0.309017i) q^{27} +(1.17160 - 0.577290i) q^{28} +(0.149275 - 0.205459i) q^{29} +(2.22286 + 3.05951i) q^{30} +(8.12858 + 2.64114i) q^{31} +2.73340i q^{32} +(-3.18631 + 0.920544i) q^{33} -7.13683i q^{34} +(-1.07508 + 6.24425i) q^{35} +(-0.399382 + 0.290168i) q^{36} +(6.47684 + 4.70570i) q^{37} +(7.56697 - 2.45866i) q^{38} +(-4.15073 + 1.34865i) q^{39} +(-4.60865 - 3.34838i) q^{40} +(-1.59628 + 1.15977i) q^{41} +(-4.11741 - 0.708902i) q^{42} +1.35422i q^{43} +(-1.35555 + 0.918270i) q^{44} -2.39483i q^{45} +(5.67741 + 1.84470i) q^{46} +(-7.89040 - 10.8602i) q^{47} +(2.78823 - 3.83767i) q^{48} +(-3.96103 - 5.77150i) q^{49} +(-1.10418 + 0.358770i) q^{50} +(-2.65647 + 3.65632i) q^{51} +(-1.74304 + 1.26639i) q^{52} +(2.84457 - 8.75470i) q^{53} +1.57913 q^{54} +(0.261362 - 7.93846i) q^{55} +(6.22864 - 0.901007i) q^{56} +(-4.79185 - 1.55697i) q^{57} +(-0.324448 + 0.235725i) q^{58} +(4.41538 - 6.07725i) q^{59} +(-0.365332 - 1.12438i) q^{60} +(1.04478 + 3.21550i) q^{61} +(-10.9191 - 7.93316i) q^{62} +(1.84555 + 1.89577i) q^{63} +(-1.59788 + 4.91776i) q^{64} -10.4518i q^{65} +(5.23456 + 0.172340i) q^{66} -2.58370 q^{67} +(-0.689445 + 2.12189i) q^{68} +(-2.22200 - 3.05832i) q^{69} +(4.66168 - 8.85329i) q^{70} +(2.58274 + 7.94885i) q^{71} +(-2.26229 + 0.735061i) q^{72} +(-7.95082 - 5.77661i) q^{73} +(-7.43092 - 10.2278i) q^{74} +(0.699233 + 0.227194i) q^{75} -2.48730 q^{76} +(5.91080 + 6.48556i) q^{77} +6.89187 q^{78} +(5.10022 + 1.65716i) q^{79} +(6.67734 + 9.19058i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(2.96331 - 0.962837i) q^{82} +(1.64799 + 5.07201i) q^{83} +(1.15569 + 0.608526i) q^{84} +(-6.36180 - 8.75627i) q^{85} +(0.660830 - 2.03383i) q^{86} +0.253962 q^{87} +(-7.57931 + 2.18970i) q^{88} +4.76358i q^{89} +(-1.16863 + 3.59667i) q^{90} +(8.05461 + 8.27376i) q^{91} +(-1.50978 - 1.09692i) q^{92} +(2.64114 + 8.12858i) q^{93} +(6.55061 + 20.1607i) q^{94} +(7.09235 - 9.76179i) q^{95} +(-2.21137 + 1.60665i) q^{96} +(-10.2381 - 3.32658i) q^{97} +(3.13248 + 10.6008i) q^{98} +(-2.61760 - 2.03670i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 12 q^{4} + 10 q^{7} - 20 q^{8} + 16 q^{9}+O(q^{10}) $ 64 * q + 12 * q^4 + 10 * q^7 - 20 * q^8 + 16 * q^9	$ 64 q + 12 q^{4} + 10 q^{7} - 20 q^{8} + 16 q^{9} - 16 q^{11} + 12 q^{14} - 12 q^{15} - 16 q^{16} + 10 q^{18} - 40 q^{22} - 24 q^{23} + 44 q^{25} - 30 q^{28} - 40 q^{29} - 40 q^{35} - 12 q^{36} + 32 q^{37} - 2 q^{42} + 22 q^{44} - 70 q^{46} - 50 q^{49} - 40 q^{51} - 64 q^{53} + 80 q^{56} + 2 q^{58} - 36 q^{60} + 10 q^{63} + 72 q^{64} - 8 q^{67} - 26 q^{70} + 68 q^{71} - 10 q^{72} + 80 q^{74} + 90 q^{77} - 72 q^{78} + 40 q^{79} - 16 q^{81} + 60 q^{84} - 40 q^{85} - 62 q^{86} + 140 q^{88} + 54 q^{91} + 18 q^{92} - 20 q^{93} + 20 q^{95} - 4 q^{99}+O(q^{100}) $ 64 * q + 12 * q^4 + 10 * q^7 - 20 * q^8 + 16 * q^9 - 16 * q^11 + 12 * q^14 - 12 * q^15 - 16 * q^16 + 10 * q^18 - 40 * q^22 - 24 * q^23 + 44 * q^25 - 30 * q^28 - 40 * q^29 - 40 * q^35 - 12 * q^36 + 32 * q^37 - 2 * q^42 + 22 * q^44 - 70 * q^46 - 50 * q^49 - 40 * q^51 - 64 * q^53 + 80 * q^56 + 2 * q^58 - 36 * q^60 + 10 * q^63 + 72 * q^64 - 8 * q^67 - 26 * q^70 + 68 * q^71 - 10 * q^72 + 80 * q^74 + 90 * q^77 - 72 * q^78 + 40 * q^79 - 16 * q^81 + 60 * q^84 - 40 * q^85 - 62 * q^86 + 140 * q^88 + 54 * q^91 + 18 * q^92 - 20 * q^93 + 20 * q^95 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{10}\right)$

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 $

$2$	−1.50185	−	0.487979i	−1.06196	−	0.345053i	−0.274612	−	0.961555i	$-0.588549\pi$
$2$	−1.50185	−	0.487979i	−1.06196	−	0.345053i	−0.787353	+	0.616502i	$0.788549\pi$
$3$	0.587785	+	0.809017i	0.339358	+	0.467086i
$3$	0.587785	+	0.809017i	0.339358	+	0.467086i
$4$	0.399382	+	0.290168i	0.199691	+	0.145084i
$5$	−2.27762	+	0.740044i	−1.01858	+	0.330958i	−0.770267	−	0.637722i	$-0.779877\pi$
$5$	−2.27762	+	0.740044i	−1.01858	+	0.330958i	−0.248316	+	0.968679i	$0.579877\pi$
$6$	−0.487979	−	1.50185i	−0.199217	−	0.613126i
$7$	1.23267	−	2.34105i	0.465907	−	0.884834i
$7$	1.23267	−	2.34105i	0.465907	−	0.884834i
$8$	1.39817	+	1.92441i	0.494327	+	0.680383i
$9$	−0.309017	+	0.951057i	−0.103006	+	0.317019i
$10$	3.78176			1.19590
$11$	−1.12813	+	3.11886i	−0.340145	+	0.940373i
$11$	−1.12813	+	3.11886i	−0.340145	+	0.940373i
$12$			0.493663i			0.142508i
$13$	−1.34865	+	4.15073i	−0.374049	+	1.15120i	0.570069	+	0.821597i	$0.306917\pi$
$13$	−1.34865	+	4.15073i	−0.374049	+	1.15120i	−0.944118	+	0.329608i	$0.893083\pi$
$14$	−2.99367	+	2.91438i	−0.800092	+	0.778900i
$15$	−1.93746	−	1.40765i	−0.500250	−	0.363453i
$16$	−1.46586	−	4.51145i	−0.366465	−	1.12786i
$17$	1.39659	+	4.29826i	0.338723	+	1.04248i	0.964859	+	0.262768i	$0.0846355\pi$
$17$	1.39659	+	4.29826i	0.338723	+	1.04248i	−0.626136	+	0.779714i	$0.715365\pi$
$18$	0.928191	−	1.27755i	0.218777	−	0.301120i
$19$	−4.07619	+	2.96153i	−0.935142	+	0.679421i	−0.947246	−	0.320506i	$-0.896147\pi$
$19$	−4.07619	+	2.96153i	−0.935142	+	0.679421i	0.0121042	+	0.999927i	$0.496147\pi$
$20$	−1.12438	−	0.365332i	−0.251418	−	0.0816907i
$21$	2.61850	−	0.378780i	0.571403	−	0.0826566i
$22$	3.21622	−	4.13355i	0.685701	−	0.881275i
$23$	−3.78029			−0.788245			−0.394123	−	0.919058i	$-0.628952\pi$
$23$	−3.78029			−0.788245			−0.394123	+	0.919058i	$0.628952\pi$
$24$	−0.735061	+	2.26229i	−0.150044	+	0.461787i
$25$	0.594803	−	0.432150i	0.118961	−	0.0864299i
$26$	4.05094	−	5.57564i	0.794454	−	1.09347i
$27$	−0.951057	+	0.309017i	−0.183031	+	0.0594703i
$28$	1.17160	−	0.577290i	0.221412	−	0.109098i
$29$	0.149275	−	0.205459i	0.0277196	−	0.0381528i	−0.794932	−	0.606698i	$-0.792494\pi$
$29$	0.149275	−	0.205459i	0.0277196	−	0.0381528i	0.822652	+	0.568545i	$0.192494\pi$
$30$	2.22286	+	3.05951i	0.405837	+	0.558587i
$31$	8.12858	+	2.64114i	1.45994	+	0.474362i	0.928051	−	0.372454i	$-0.121484\pi$
$31$	8.12858	+	2.64114i	1.45994	+	0.474362i	0.531886	+	0.846816i	$0.321484\pi$
$32$			2.73340i			0.483201i
$33$	−3.18631	+	0.920544i	−0.554666	+	0.160246i
$34$		−	7.13683i		−	1.22396i
$35$	−1.07508	+	6.24425i	−0.181722	+	1.05547i
$36$	−0.399382	+	0.290168i	−0.0665636	+	0.0483613i
$37$	6.47684	+	4.70570i	1.06479	+	0.773612i	0.974968	−	0.222346i	$-0.0713716\pi$
$37$	6.47684	+	4.70570i	1.06479	+	0.773612i	0.0898176	+	0.995958i	$0.471372\pi$
$38$	7.56697	−	2.45866i	1.22752	−	0.398847i
$39$	−4.15073	+	1.34865i	−0.664649	+	0.215957i
$40$	−4.60865	−	3.34838i	−0.728691	−	0.529425i
$41$	−1.59628	+	1.15977i	−0.249297	+	0.181125i	−0.705415	−	0.708794i	$-0.749239\pi$
$41$	−1.59628	+	1.15977i	−0.249297	+	0.181125i	0.456118	+	0.889919i	$0.349239\pi$
$42$	−4.11741	−	0.708902i	−0.635331	−	0.109386i
$43$			1.35422i			0.206516i	0.994655	+	0.103258i	$0.0329268\pi$
$43$			1.35422i			0.206516i	−0.994655	+	0.103258i	$0.967073\pi$
$44$	−1.35555	+	0.918270i	−0.204357	+	0.138434i
$45$		−	2.39483i		−	0.357000i
$46$	5.67741	+	1.84470i	0.837089	+	0.271987i
$47$	−7.89040	−	10.8602i	−1.15093	−	1.58412i	−0.740228	−	0.672356i	$-0.765282\pi$
$47$	−7.89040	−	10.8602i	−1.15093	−	1.58412i	−0.410706	−	0.911768i	$-0.634718\pi$
$48$	2.78823	−	3.83767i	0.402447	−	0.553920i
$49$	−3.96103	−	5.77150i	−0.565861	−	0.824500i
$50$	−1.10418	+	0.358770i	−0.156155	+	0.0507378i
$51$	−2.65647	+	3.65632i	−0.371981	+	0.511987i
$52$	−1.74304	+	1.26639i	−0.241715	+	0.175617i
$53$	2.84457	−	8.75470i	0.390732	−	1.20255i	−0.541503	−	0.840699i	$-0.682145\pi$
$53$	2.84457	−	8.75470i	0.390732	−	1.20255i	0.932236	−	0.361852i	$-0.117855\pi$
$54$	1.57913			0.214893
$55$	0.261362	−	7.93846i	0.0352421	−	1.07042i
$56$	6.22864	−	0.901007i	0.832337	−	0.120402i
$57$	−4.79185	−	1.55697i	−0.634696	−	0.206225i
$58$	−0.324448	+	0.235725i	−0.0426020	+	0.0309522i
$59$	4.41538	−	6.07725i	0.574833	−	0.791190i	−0.418284	−	0.908316i	$-0.637368\pi$
$59$	4.41538	−	6.07725i	0.574833	−	0.791190i	0.993117	+	0.117126i	$0.0373683\pi$
$60$	−0.365332	−	1.12438i	−0.0471642	−	0.145156i
$61$	1.04478	+	3.21550i	0.133770	+	0.411702i	0.995397	−	0.0958405i	$-0.0305539\pi$
$61$	1.04478	+	3.21550i	0.133770	+	0.411702i	−0.861626	+	0.507543i	$0.830554\pi$
$62$	−10.9191	−	7.93316i	−1.38672	−	1.00751i
$63$	1.84555	+	1.89577i	0.232518	+	0.238844i
$64$	−1.59788	+	4.91776i	−0.199735	+	0.614721i
$65$		−	10.4518i		−	1.29639i
$66$	5.23456	+	0.172340i	0.644329	+	0.0212136i
$67$	−2.58370			−0.315649			−0.157824	−	0.987467i	$-0.550448\pi$
$67$	−2.58370			−0.315649			−0.157824	+	0.987467i	$0.550448\pi$
$68$	−0.689445	+	2.12189i	−0.0836075	+	0.257317i
$69$	−2.22200	−	3.05832i	−0.267497	−	0.368179i
$70$	4.66168	−	8.85329i	0.557177	−	1.05817i
$71$	2.58274	+	7.94885i	0.306515	+	0.943355i	0.979108	+	0.203342i	$0.0651805\pi$
$71$	2.58274	+	7.94885i	0.306515	+	0.943355i	−0.672593	+	0.740013i	$0.734820\pi$
$72$	−2.26229	+	0.735061i	−0.266613	+	0.0866278i
$73$	−7.95082	−	5.77661i	−0.930573	−	0.676101i	0.0155604	−	0.999879i	$-0.495047\pi$
$73$	−7.95082	−	5.77661i	−0.930573	−	0.676101i	−0.946133	+	0.323778i	$0.895047\pi$
$74$	−7.43092	−	10.2278i	−0.863827	−	1.18896i
$75$	0.699233	+	0.227194i	0.0807404	+	0.0262342i
$76$	−2.48730			−0.285312
$77$	5.91080	+	6.48556i	0.673598	+	0.739098i
$78$	6.89187			0.780350
$79$	5.10022	+	1.65716i	0.573820	+	0.186445i	0.581530	−	0.813525i	$-0.302454\pi$
$79$	5.10022	+	1.65716i	0.573820	+	0.186445i	−0.00771021	+	0.999970i	$0.502454\pi$
$80$	6.67734	+	9.19058i	0.746550	+	1.02754i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	2.96331	−	0.962837i	0.327243	−	0.106328i
$83$	1.64799	+	5.07201i	0.180891	+	0.556725i	0.999853	−	0.0171221i	$-0.00545040\pi$
$83$	1.64799	+	5.07201i	0.180891	+	0.556725i	−0.818963	+	0.573847i	$0.805450\pi$
$84$	1.15569	+	0.608526i	0.126096	+	0.0663956i
$85$	−6.36180	−	8.75627i	−0.690035	−	0.949751i
$86$	0.660830	−	2.03383i	0.0712592	−	0.219313i
$87$	0.253962			0.0272275
$88$	−7.57931	+	2.18970i	−0.807957	+	0.233423i
$89$			4.76358i			0.504938i	0.967605	+	0.252469i	$0.0812426\pi$
$89$			4.76358i			0.504938i	−0.967605	+	0.252469i	$0.918757\pi$
$90$	−1.16863	+	3.59667i	−0.123184	+	0.379122i
$91$	8.05461	+	8.27376i	0.844353	+	0.867326i
$92$	−1.50978	−	1.09692i	−0.157405	−	0.114362i
$93$	2.64114	+	8.12858i	0.273873	+	0.842895i
$94$	6.55061	+	20.1607i	0.675644	+	2.07942i
$95$	7.09235	−	9.76179i	0.727660	−	1.00154i
$96$	−2.21137	+	1.60665i	−0.225697	+	0.163978i
$97$	−10.2381	−	3.32658i	−1.03953	−	0.337763i	−0.260976	−	0.965345i	$-0.584044\pi$
$97$	−10.2381	−	3.32658i	−1.03953	−	0.337763i	−0.778550	+	0.627583i	$0.784044\pi$
$98$	3.13248	+	10.6008i	0.316428	+	1.07084i
$99$	−2.61760	−	2.03670i	−0.263079	−	0.204696i
$100$	0.362949			0.0362949
$101$	−3.02191	+	9.30050i	−0.300692	+	0.925434i	0.680558	+	0.732694i	$0.261737\pi$
$101$	−3.02191	+	9.30050i	−0.300692	+	0.925434i	−0.981250	+	0.192740i	$0.938263\pi$
$102$	5.77382	−	4.19493i	0.571693	−	0.415360i
$103$	4.47540	−	6.15986i	0.440974	−	0.606949i	−0.529454	−	0.848339i	$-0.677603\pi$
$103$	4.47540	−	6.15986i	0.440974	−	0.606949i	0.970428	+	0.241390i	$0.0776032\pi$
$104$	−9.87337	+	3.20805i	−0.968164	+	0.314575i
$105$	−5.68363	+	2.80052i	−0.554665	+	0.273303i
$106$	−8.54422	+	11.7601i	−0.829888	+	1.14224i
$107$	0.109443	+	0.150635i	0.0105802	+	0.0145624i	0.814274	−	0.580480i	$-0.197135\pi$
$107$	0.109443	+	0.150635i	0.0105802	+	0.0145624i	−0.803694	+	0.595043i	$0.797135\pi$
$108$	−0.469501	−	0.152550i	−0.0451778	−	0.0146792i
$109$			19.8999i			1.90606i	0.302869	+	0.953032i	$0.402056\pi$
$109$			19.8999i			1.90606i	−0.302869	+	0.953032i	$0.597944\pi$
$110$	−4.26633	+	11.7948i	−0.406778	+	1.12459i
$111$			8.00581i			0.759878i
$112$	−12.3685	−	2.12950i	−1.16871	−	0.201219i
$113$	1.45833	−	1.05954i	0.137188	−	0.0996727i	−0.517075	−	0.855940i	$-0.672979\pi$
$113$	1.45833	−	1.05954i	0.137188	−	0.0996727i	0.654263	+	0.756267i	$0.272979\pi$
$114$	6.43685	+	4.67664i	0.602866	+	0.438008i
$115$	8.61007	−	2.79758i	0.802893	−	0.260876i
$116$	0.119235	−	0.0387419i	0.0110707	−	0.00359709i
$117$	−3.53082	−	2.56529i	−0.326424	−	0.237161i
$118$	−9.59678	+	6.97247i	−0.883455	+	0.641868i
$119$	11.7840	+	2.02887i	1.08024	+	0.185986i
$120$		−	5.69660i		−	0.520026i
$121$	−8.45463	−	7.03699i	−0.768603	−	0.639726i
$122$		−	5.33901i		−	0.483371i
$123$	−1.87654	−	0.609725i	−0.169202	−	0.0549770i
$124$	2.48003	+	3.41347i	0.222714	+	0.306539i
$125$	6.00331	−	8.26284i	0.536952	−	0.739051i
$126$	−1.84664	−	3.74774i	−0.164512	−	0.333875i
$127$	14.6518	−	4.76067i	1.30014	−	0.422442i	0.424511	−	0.905423i	$-0.360446\pi$
$127$	14.6518	−	4.76067i	1.30014	−	0.422442i	0.875631	+	0.482981i	$0.160446\pi$
$128$	8.01284	−	11.0287i	0.708241	−	0.974811i
$129$	−1.09559	+	0.795990i	−0.0964609	+	0.0700830i
$130$	−5.10028	+	15.6971i	−0.447324	+	1.37672i
$131$	21.6575			1.89223			0.946114	−	0.323834i	$-0.104972\pi$
$131$	21.6575			1.89223			0.946114	+	0.323834i	$0.104972\pi$
$132$	−1.53967	−	0.556917i	−0.134011	−	0.0484734i
$133$	1.90846	+	13.1932i	0.165485	+	1.14399i
$134$	3.88031	+	1.26079i	0.335208	+	0.108916i
$135$	1.93746	−	1.40765i	0.166750	−	0.121151i
$136$	−6.31897	+	8.69732i	−0.541847	+	0.745789i
$137$	0.848396	+	2.61109i	0.0724834	+	0.223081i	0.980735	−	0.195344i	$-0.0625823\pi$
$137$	0.848396	+	2.61109i	0.0724834	+	0.223081i	−0.908251	+	0.418425i	$0.862582\pi$
$138$	1.84470	+	5.67741i	0.157032	+	0.483294i
$139$	−0.0505775	−	0.0367467i	−0.00428993	−	0.00311682i	0.585638	−	0.810573i	$-0.300844\pi$
$139$	−0.0505775	−	0.0367467i	−0.00428993	−	0.00311682i	−0.589928	+	0.807456i	$0.700844\pi$
$140$	−2.24125	+	2.18189i	−0.189420	+	0.184403i
$141$	4.14823	−	12.7669i	0.349344	−	1.07517i
$142$		−	13.1983i		−	1.10757i
$143$	−11.4241	−	8.88884i	−0.955331	−	0.743322i
$144$	4.74362			0.395302
$145$	−0.187943	+	0.578428i	−0.0156078	+	0.0480358i
$146$	9.12203	+	12.5554i	0.754945	+	1.03909i
$147$	2.34101	−	6.59694i	0.193083	−	0.544107i
$148$	1.22129	+	3.75874i	0.100389	+	0.308966i
$149$	−3.05059	+	0.991197i	−0.249914	+	0.0812021i	−0.431295	−	0.902211i	$-0.641943\pi$
$149$	−3.05059	+	0.991197i	−0.249914	+	0.0812021i	0.181381	+	0.983413i	$0.441943\pi$
$150$	−0.939273	−	0.682422i	−0.0766913	−	0.0557195i
$151$	7.53153	+	10.3663i	0.612908	+	0.843595i	0.996813	−	0.0797777i	$-0.0254210\pi$
$151$	7.53153	+	10.3663i	0.612908	+	0.843595i	−0.383905	+	0.923373i	$0.625421\pi$
$152$	−11.3984	−	3.70357i	−0.924533	−	0.300399i
$153$	−4.51946			−0.365377
$154$	−5.71229	−	12.6247i	−0.460309	−	1.01732i
$155$	−20.4684			−1.64406
$156$	−2.04906	−	0.665780i	−0.164056	−	0.0533051i
$157$	−11.7200	−	16.1312i	−0.935361	−	1.28741i	−0.957731	−	0.287664i	$-0.907121\pi$
$157$	−11.7200	−	16.1312i	−0.935361	−	1.28741i	0.0223707	−	0.999750i	$-0.492879\pi$
$158$	−6.85108	−	4.97760i	−0.545043	−	0.395997i
$159$	8.75470	−	2.84457i	0.694293	−	0.225589i
$160$	−2.02283	−	6.22564i	−0.159919	−	0.492180i
$161$	−4.65987	+	8.84985i	−0.367249	+	0.697466i
$162$	0.928191	+	1.27755i	0.0729256	+	0.100373i
$163$	−4.79540	+	14.7587i	−0.375605	+	1.15599i	0.567465	+	0.823397i	$0.307924\pi$
$163$	−4.79540	+	14.7587i	−0.375605	+	1.15599i	−0.943070	+	0.332595i	$0.892076\pi$
$164$	−0.974052			−0.0760607
$165$	6.57597	−	4.45466i	0.511939	−	0.346795i
$166$		−	8.42155i		−	0.653639i
$167$	1.99393	−	6.13668i	0.154295	−	0.474870i	−0.843794	−	0.536667i	$-0.819683\pi$
$167$	1.99393	−	6.13668i	0.154295	−	0.474870i	0.998089	+	0.0617968i	$0.0196831\pi$
$168$	4.39003	+	4.50948i	0.338698	+	0.347914i
$169$	−4.89246	−	3.55458i	−0.376343	−	0.273429i
$170$	5.28157	+	16.2550i	0.405078	+	1.24670i
$171$	−1.55697	−	4.79185i	−0.119064	−	0.366442i
$172$	−0.392951	+	0.540850i	−0.0299622	+	0.0412394i
$173$	−1.55305	+	1.12836i	−0.118076	+	0.0857873i	−0.645256	−	0.763966i	$-0.723249\pi$
$173$	−1.55305	+	1.12836i	−0.118076	+	0.0857873i	0.527180	+	0.849754i	$0.323249\pi$
$174$	−0.381411	−	0.123928i	−0.0289147	−	0.00939495i
$175$	−0.278486	−	1.92516i	−0.0210515	−	0.145529i
$176$	15.7243	+	0.517700i	1.18526	+	0.0390231i
$177$	7.51189			0.564628
$178$	2.32453	−	7.15416i	0.174231	−	0.536227i
$179$	3.93050	−	2.85568i	0.293779	−	0.213443i	−0.431126	−	0.902292i	$-0.641884\pi$
$179$	3.93050	−	2.85568i	0.293779	−	0.213443i	0.724905	+	0.688849i	$0.241884\pi$
$180$	0.694903	−	0.956452i	0.0517950	−	0.0712897i
$181$	5.18535	−	1.68482i	0.385424	−	0.125232i	−0.109894	−	0.993943i	$-0.535051\pi$
$181$	5.18535	−	1.68482i	0.385424	−	0.125232i	0.495319	+	0.868711i	$0.335051\pi$
$182$	−8.05936	−	16.3564i	−0.597399	−	1.21242i
$183$	−1.98729	+	2.73527i	−0.146905	+	0.202197i
$184$	−5.28549	−	7.27485i	−0.389651	−	0.536309i
$185$	−18.2342	−	5.92465i	−1.34060	−	0.435589i
$186$		−	13.4967i		−	0.989626i
$187$	−14.9812	−	0.493236i	−1.09554	−	0.0360690i
$188$		−	6.62691i		−	0.483317i
$189$	−0.448919	+	2.60739i	−0.0326540	+	0.189660i
$190$	−15.4152	+	11.1998i	−1.11833	+	0.812517i
$191$	−6.84435	−	4.97271i	−0.495240	−	0.359813i	0.311956	−	0.950097i	$-0.399016\pi$
$191$	−6.84435	−	4.97271i	−0.495240	−	0.359813i	−0.807196	+	0.590284i	$0.799016\pi$
$192$	−4.91776	+	1.59788i	−0.354909	+	0.115317i
$193$	3.07990	−	1.00072i	0.221696	−	0.0720335i	−0.196063	−	0.980591i	$-0.562816\pi$
$193$	3.07990	−	1.00072i	0.221696	−	0.0720335i	0.417759	+	0.908558i	$0.362816\pi$
$194$	13.7528	+	9.99200i	0.987394	+	0.717384i
$195$	8.45572	−	6.14344i	0.605527	−	0.439941i
$196$	0.0927419	−	3.45440i	0.00662442	−	0.246743i
$197$			23.4951i			1.67396i	0.547235	+	0.836979i	$0.315680\pi$
$197$			23.4951i			1.67396i	−0.547235	+	0.836979i	$0.684320\pi$
$198$	2.93737	+	4.33614i	0.208750	+	0.308156i
$199$		−	8.42309i		−	0.597097i	−0.954394	−	0.298549i	$-0.903497\pi$
$199$		−	8.42309i		−	0.597097i	0.954394	−	0.298549i	$-0.0965025\pi$
$200$	1.66327	+	0.540429i	0.117611	+	0.0382141i
$201$	−1.51866	−	2.09025i	−0.107118	−	0.147435i
$202$	9.07690	−	12.4933i	0.638648	−	0.879024i
$203$	−0.296983	−	0.602724i	−0.0208441	−	0.0423029i
$204$	−2.12189	+	0.689445i	−0.148562	+	0.0482708i
$205$	2.77744	−	3.82282i	0.193985	−	0.266997i
$206$	−9.72724	+	7.06725i	−0.677729	+	0.492399i
$207$	1.16817	−	3.59527i	0.0811937	−	0.249889i
$208$	20.7028			1.43548
$209$	−4.63811	−	16.0541i	−0.320825	−	1.11048i
$210$	9.90252	−	1.43246i	0.683339	−	0.0988488i
$211$	3.44551	+	1.11951i	0.237198	+	0.0770705i	0.425204	−	0.905097i	$-0.360202\pi$
$211$	3.44551	+	1.11951i	0.237198	+	0.0770705i	−0.188006	+	0.982168i	$0.560202\pi$
$212$	3.67640	−	2.67106i	0.252496	−	0.183449i
$213$	−4.91266	+	6.76170i	−0.336610	+	0.463304i
$214$	−0.0908591	−	0.279636i	−0.00621100	−	0.0191155i
$215$	−1.00218	−	3.08439i	−0.0683482	−	0.210354i
$216$	−1.92441	−	1.39817i	−0.130940	−	0.0951334i
$217$	16.2029	−	15.7738i	1.09993	−	1.07079i
$218$	9.71074	−	29.8866i	0.657694	−	2.02417i
$219$		−	9.82775i		−	0.664098i
$220$	2.40787	−	3.09463i	0.162338	−	0.208640i
$221$	−19.7244			−1.32681
$222$	3.90667	−	12.0235i	0.262198	−	0.806964i
$223$	14.6952	+	20.2262i	0.984065	+	1.35445i	0.934611	+	0.355673i	$0.115748\pi$
$223$	14.6952	+	20.2262i	0.984065	+	1.35445i	0.0494541	+	0.998776i	$0.484252\pi$
$224$	6.39902	+	3.36939i	0.427553	+	0.225127i
$225$	0.227194	+	0.699233i	0.0151463	+	0.0466155i
$226$	−2.70721	+	0.879626i	−0.180081	+	0.0585118i
$227$	−6.13203	−	4.45518i	−0.406997	−	0.295701i	0.365388	−	0.930855i	$-0.380936\pi$
$227$	−6.13203	−	4.45518i	−0.406997	−	0.295701i	−0.772385	+	0.635155i	$0.780936\pi$
$228$	−1.46200	−	2.01226i	−0.0968230	−	0.133265i
$229$	4.03037	+	1.30955i	0.266334	+	0.0865373i	0.439140	−	0.898419i	$-0.355283\pi$
$229$	4.03037	+	1.30955i	0.266334	+	0.0865373i	−0.172806	+	0.984956i	$0.555283\pi$
$230$	−14.2962			−0.942660
$231$	−1.77265	+	8.59405i	−0.116632	+	0.565447i
$232$	0.604100			0.0396611
$233$	1.90879	+	0.620203i	0.125049	+	0.0406309i	0.370873	−	0.928684i	$-0.379059\pi$
$233$	1.90879	+	0.620203i	0.125049	+	0.0406309i	−0.245824	+	0.969314i	$0.579059\pi$
$234$	4.05094	+	5.57564i	0.264818	+	0.364491i
$235$	26.0084	+	18.8962i	1.69660	+	1.23265i
$236$	3.52684	−	1.14594i	0.229578	−	0.0745944i
$237$	1.65716	+	5.10022i	0.107644	+	0.331295i
$238$	−16.7077	−	8.79739i	−1.08300	−	0.570250i
$239$	13.0606	+	17.9763i	0.844818	+	1.16279i	0.984981	+	0.172664i	$0.0552374\pi$
$239$	13.0606	+	17.9763i	0.844818	+	1.16279i	−0.140163	+	0.990128i	$0.544763\pi$
$240$	−3.51049	+	10.8042i	−0.226601	+	0.697406i
$241$	−14.4971			−0.933841			−0.466921	−	0.884299i	$-0.654637\pi$
$241$	−14.4971			−0.933841			−0.466921	+	0.884299i	$0.654637\pi$
$242$	9.26365	+	14.6942i	0.595490	+	0.944576i
$243$		−	1.00000i		−	0.0641500i
$244$	−0.515769	+	1.58737i	−0.0330187	+	0.101621i
$245$	13.2929	+	10.2140i	0.849251	+	0.652546i
$246$	2.52074	+	1.83142i	0.160717	+	0.116767i
$247$	−6.79512	−	20.9132i	−0.432363	−	1.33068i
$248$	6.28249	+	19.3355i	0.398939	+	1.22781i
$249$	−3.13467	+	4.31451i	−0.198652	+	0.273421i
$250$	−13.0481	+	9.48002i	−0.825236	+	0.599569i
$251$	6.15040	+	1.99839i	0.388210	+	0.126137i	0.496618	−	0.867969i	$-0.334575\pi$
$251$	6.15040	+	1.99839i	0.388210	+	0.126137i	−0.108408	+	0.994107i	$0.534575\pi$
$252$	0.186990	+	1.29265i	0.0117792	+	0.0814296i
$253$	4.26467	−	11.7902i	0.268118	−	0.741245i
$254$	−24.3279			−1.52647
$255$	3.34460	−	10.2936i	0.209447	−	0.644611i
$256$	−9.04923	+	6.57465i	−0.565577	+	0.410915i
$257$	−13.7146	+	18.8765i	−0.855492	+	1.17748i	0.127134	+	0.991886i	$0.459422\pi$
$257$	−13.7146	+	18.8765i	−0.855492	+	1.17748i	−0.982626	+	0.185598i	$0.940578\pi$
$258$	2.03383	−	0.660830i	0.126621	−	0.0411415i
$259$	19.0001	−	9.36201i	1.18061	−	0.581727i
$260$	3.03279	−	4.17428i	0.188086	−	0.258878i
$261$	0.149275	+	0.205459i	0.00923988	+	0.0127176i
$262$	−32.5263	−	10.5684i	−2.00948	−	0.652920i
$263$		−	25.7659i		−	1.58879i	−0.607399	−	0.794397i	$-0.707787\pi$
$263$		−	25.7659i		−	1.58879i	0.607399	−	0.794397i	$-0.292213\pi$
$264$	−6.22651	−	4.84471i	−0.383215	−	0.298172i
$265$			22.0450i			1.35421i
$266$	3.57177	−	20.7454i	0.218999	−	1.27198i
$267$	−3.85382	+	2.79996i	−0.235850	+	0.171355i
$268$	−1.03188	−	0.749706i	−0.0630322	−	0.0457956i
$269$	17.9003	−	5.81616i	1.09140	−	0.354618i	0.292613	−	0.956231i	$-0.405475\pi$
$269$	17.9003	−	5.81616i	1.09140	−	0.354618i	0.798788	+	0.601613i	$0.205475\pi$
$270$	−3.59667	+	1.16863i	−0.218886	+	0.0711204i
$271$	11.8757	+	8.62818i	0.721395	+	0.524124i	0.886830	−	0.462096i	$-0.152903\pi$
$271$	11.8757	+	8.62818i	0.721395	+	0.524124i	−0.165434	+	0.986221i	$0.552903\pi$
$272$	17.3442	−	12.6013i	1.05165	−	0.764066i
$273$	−1.95923	+	11.3795i	−0.118578	+	0.688719i
$274$		−	4.33546i		−	0.261915i
$275$	0.676799	+	2.34263i	0.0408125	+	0.141266i
$276$		−	1.86619i		−	0.112331i
$277$	−24.3295	−	7.90512i	−1.46182	−	0.474973i	−0.533192	−	0.845994i	$-0.679008\pi$
$277$	−24.3295	−	7.90512i	−1.46182	−	0.474973i	−0.928624	+	0.371022i	$0.879008\pi$
$278$	0.0580280	+	0.0798687i	0.00348029	+	0.00479021i
$279$	−5.02374	+	6.91459i	−0.300763	+	0.413965i
$280$	−13.5197	+	6.66162i	−0.807956	+	0.398108i
$281$	−0.849968	+	0.276171i	−0.0507048	+	0.0164750i	−0.334260	−	0.942481i	$-0.608486\pi$
$281$	−0.849968	+	0.276171i	−0.0507048	+	0.0164750i	0.283555	+	0.958956i	$0.408486\pi$
$282$	−12.4600	+	17.1497i	−0.741982	+	1.02125i
$283$	17.2204	−	12.5114i	1.02365	−	0.743724i	0.0566210	−	0.998396i	$-0.481967\pi$
$283$	17.2204	−	12.5114i	1.02365	−	0.743724i	0.967028	+	0.254671i	$0.0819673\pi$
$284$	−1.27500	+	3.92405i	−0.0756574	+	0.232850i
$285$	12.0662			0.714742
$286$	12.8197	+	18.9244i	0.758043	+	1.11902i
$287$	0.747376	+	5.16659i	0.0441162	+	0.304974i
$288$	−2.59962	−	0.844667i	−0.153184	−	0.0497725i
$289$	−2.77132	+	2.01348i	−0.163019	+	0.118440i
$290$	0.564521	−	0.776997i	0.0331498	−	0.0456268i
$291$	−3.32658	−	10.2381i	−0.195007	−	0.600171i
$292$	−1.49923	−	4.61414i	−0.0877355	−	0.270022i
$293$	10.2442	+	7.44284i	0.598472	+	0.434815i	0.845336	−	0.534235i	$-0.179400\pi$
$293$	10.2442	+	7.44284i	0.598472	+	0.434815i	−0.246864	+	0.969050i	$0.579400\pi$
$294$	−6.73501	+	8.76523i	−0.392794	+	0.511198i
$295$	−5.55912	+	17.1092i	−0.323665	+	0.996138i
$296$			19.0435i			1.10688i
$297$	0.109136	−	3.31483i	0.00633271	−	0.192346i
$298$	5.06520			0.293419
$299$	5.09830	−	15.6910i	0.294843	−	0.907432i
$300$	0.213336	+	0.293632i	0.0123170	+	0.0169529i
$301$	3.17029	+	1.66931i	0.182733	+	0.0962174i
$302$	−6.25268	−	19.2438i	−0.359801	−	1.10735i
$303$	−9.30050	+	3.02191i	−0.534300	+	0.173604i
$304$	19.3359	+	14.0484i	1.10899	+	0.805729i
$305$	−4.75922	−	6.55050i	−0.272512	−	0.375081i
$306$	6.78753	+	2.20540i	0.388017	+	0.126075i
$307$	−16.8071			−0.959233			−0.479617	−	0.877478i	$-0.659224\pi$
$307$	−16.8071			−0.959233			−0.479617	+	0.877478i	$0.659224\pi$
$308$	0.478764	+	4.30534i	0.0272801	+	0.245319i
$309$	7.61400			0.433145
$310$	30.7403	+	9.98814i	1.74593	+	0.567288i
$311$	−8.66130	−	11.9213i	−0.491137	−	0.675993i	0.489460	−	0.872026i	$-0.337194\pi$
$311$	−8.66130	−	11.9213i	−0.491137	−	0.675993i	−0.980597	+	0.196033i	$0.937194\pi$
$312$	−8.39879	−	6.10208i	−0.475488	−	0.345462i
$313$	8.07108	−	2.62245i	0.456204	−	0.148230i	−0.0718953	−	0.997412i	$-0.522905\pi$
$313$	8.07108	−	2.62245i	0.456204	−	0.148230i	0.528100	+	0.849182i	$0.322905\pi$
$314$	9.72997	+	29.9458i	0.549094	+	1.68994i
$315$	−5.60642	−	2.95205i	−0.315886	−	0.166329i
$316$	1.55608	+	2.14176i	0.0875364	+	0.120483i
$317$	0.970572	−	2.98711i	0.0545127	−	0.167773i	−0.920093	−	0.391699i	$-0.871887\pi$
$317$	0.970572	−	2.98711i	0.0545127	−	0.167773i	0.974606	+	0.223926i	$0.0718874\pi$
$318$	−14.5363			−0.815155
$319$	0.472398	+	0.697353i	0.0264492	+	0.0390443i
$320$		−	12.3833i		−	0.692247i
$321$	−0.0575373	+	0.177082i	−0.00321142	+	0.00988374i
$322$	11.3169	−	11.0172i	0.630669	−	0.613964i
$323$	−18.4222	−	13.3845i	−1.02504	−	0.744734i
$324$	−0.152550	−	0.469501i	−0.00847501	−	0.0260834i
$325$	0.991553	+	3.05169i	0.0550014	+	0.169277i
$326$	14.4039	−	19.8253i	0.797758	−	1.09802i
$327$	−16.0994	+	11.6969i	−0.890296	+	0.646838i
$328$	−4.46374	−	1.45036i	−0.246469	−	0.0800826i
$329$	−35.1506	+	5.08473i	−1.93791	+	0.280330i
$330$	−12.0499	+	3.48127i	−0.663324	+	0.191638i
$331$	13.4883			0.741382			0.370691	−	0.928756i	$-0.379121\pi$
$331$	13.4883			0.741382			0.370691	+	0.928756i	$0.379121\pi$
$332$	−0.813554	+	2.50386i	−0.0446496	+	0.137417i
$333$	−6.47684	+	4.70570i	−0.354928	+	0.257871i
$334$	−5.98914	+	8.24335i	−0.327711	+	0.451056i
$335$	5.88468	−	1.91205i	0.321514	−	0.104466i
$336$	−5.54720	−	11.2580i	−0.302625	−	0.614174i
$337$	15.1400	−	20.8385i	0.824730	−	1.13514i	−0.164151	−	0.986435i	$-0.552489\pi$
$337$	15.1400	−	20.8385i	0.824730	−	1.13514i	0.988881	−	0.148708i	$-0.0475115\pi$
$338$	5.61316	+	7.72585i	0.305316	+	0.420231i
$339$	1.71436	+	0.557031i	0.0931115	+	0.0302538i
$340$		−	5.34309i		−	0.289770i
$341$	−17.4075	+	22.3724i	−0.942667	+	1.21153i
$342$			7.95638i			0.430232i
$343$	−18.3940	+	2.15858i	−0.993185	+	0.116553i
$344$	−2.60608	+	1.89343i	−0.140510	+	0.102087i
$345$	7.32416	+	5.32132i	0.394320	+	0.286490i
$346$	2.88305	−	0.936760i	0.154994	−	0.0503606i
$347$	1.54622	−	0.502397i	0.0830054	−	0.0269701i	−0.267220	−	0.963636i	$-0.586105\pi$
$347$	1.54622	−	0.502397i	0.0830054	−	0.0269701i	0.350225	+	0.936665i	$0.386105\pi$
$348$	0.101428	+	0.0736915i	0.00543709	+	0.00395028i
$349$	14.0021	−	10.1731i	0.749514	−	0.544554i	−0.146162	−	0.989261i	$-0.546692\pi$
$349$	14.0021	−	10.1731i	0.749514	−	0.544554i	0.895676	+	0.444707i	$0.146692\pi$
$350$	−0.521197	+	3.02719i	−0.0278591	+	0.161810i
$351$		−	4.36433i		−	0.232951i
$352$	−8.52510	−	3.08364i	−0.454389	−	0.164358i
$353$		−	13.0368i		−	0.693878i	−0.937888	−	0.346939i	$-0.887221\pi$
$353$		−	13.0368i		−	0.693878i	0.937888	−	0.346939i	$-0.112779\pi$
$354$	−11.2817	−	3.66564i	−0.599615	−	0.194827i
$355$	−11.7650	−	16.1931i	−0.624421	−	0.859442i
$356$	−1.38224	+	1.90249i	−0.0732584	+	0.100832i
$357$	5.28507	+	10.7260i	0.279715	+	0.567680i
$358$	−7.29651	+	2.37078i	−0.385633	+	0.125300i
$359$	0.856127	−	1.17836i	0.0451847	−	0.0621914i	−0.785827	−	0.618447i	$-0.787762\pi$
$359$	0.856127	−	1.17836i	0.0451847	−	0.0621914i	0.831012	+	0.556255i	$0.187762\pi$
$360$	4.60865	−	3.34838i	0.242897	−	0.176475i
$361$	1.97337	−	6.07341i	0.103862	−	0.319653i
$362$	−8.60976			−0.452519
$363$	0.723534	−	10.9762i	0.0379757	−	0.576100i
$364$	0.816086	+	5.64158i	0.0427745	+	0.295699i
$365$	22.3839	+	7.27296i	1.17163	+	0.380684i
$366$	4.31935	−	3.13819i	0.225776	−	0.164036i
$367$	−13.8063	+	19.0027i	−0.720683	+	0.991935i	0.278818	+	0.960344i	$0.410057\pi$
$367$	−13.8063	+	19.0027i	−0.720683	+	0.991935i	−0.999501	+	0.0315913i	$0.989943\pi$
$368$	5.54138	+	17.0546i	0.288864	+	0.889033i
$369$	−0.609725	−	1.87654i	−0.0317410	−	0.0976888i
$370$	24.4938	+	17.7958i	1.27337	+	0.925160i
$371$	−16.9888	−	17.4510i	−0.882012	−	0.906010i
$372$	−1.30383	+	4.01278i	−0.0676005	+	0.208053i
$373$		−	5.16926i		−	0.267654i	−0.991005	−	0.133827i	$-0.957273\pi$
$373$		−	5.16926i		−	0.267654i	0.991005	−	0.133827i	$-0.0427267\pi$
$374$	22.2588	+	8.05130i	1.15098	+	0.416323i
$375$	10.2134			0.527420
$376$	9.86743	−	30.3688i	0.508874	−	1.56615i
$377$	0.651485	+	0.896693i	0.0335532	+	0.0461820i
$378$	1.94656	−	3.69683i	0.100120	−	0.190144i
$379$	1.53614	+	4.72776i	0.0789064	+	0.242849i	0.982727	−	0.185064i	$-0.0592491\pi$
$379$	1.53614	+	4.72776i	0.0789064	+	0.242849i	−0.903820	+	0.427913i	$0.859249\pi$
$380$	5.66511	−	1.84071i	0.290614	−	0.0944263i
$381$	12.4636	+	9.05534i	0.638530	+	0.463919i
$382$	7.85258	+	10.8082i	0.401773	+	0.552993i
$383$	32.0321	+	10.4078i	1.63676	+	0.531816i	0.975811	−	0.218614i	$-0.0701535\pi$
$383$	32.0321	+	10.4078i	1.63676	+	0.531816i	0.660950	+	0.750430i	$0.270154\pi$
$384$	13.6323			0.695668
$385$	−18.2621	−	10.3974i	−0.930725	−	0.529900i
$386$	−5.11387			−0.260289
$387$	−1.28794	−	0.418477i	−0.0654696	−	0.0212724i
$388$	−3.12366	−	4.29935i	−0.158580	−	0.218267i
$389$	0.0908884	+	0.0660343i	0.00460823	+	0.00334807i	0.590087	−	0.807340i	$-0.299093\pi$
$389$	0.0908884	+	0.0660343i	0.00460823	+	0.00334807i	−0.585479	+	0.810688i	$0.699093\pi$
$390$	−15.6971	+	5.10028i	−0.794851	+	0.258263i
$391$	−5.27952	−	16.2487i	−0.266997	−	0.821732i
$392$	5.56858	−	15.6922i	0.281256	−	0.792576i
$393$	12.7300	+	17.5213i	0.642143	+	0.883834i
$394$	11.4651	−	35.2860i	0.577605	−	1.77768i
$395$	−12.8427			−0.646188
$396$	−0.454438	−	1.57297i	−0.0228364	−	0.0790445i
$397$			14.7372i			0.739637i	0.929104	+	0.369818i	$0.120580\pi$
$397$			14.7372i			0.739637i	−0.929104	+	0.369818i	$0.879420\pi$
$398$	−4.11029	+	12.6502i	−0.206030	+	0.634096i
$399$	−9.55172	+	9.29873i	−0.478184	+	0.465519i
$400$	−2.82152	−	2.04995i	−0.141076	−	0.102498i
$401$	9.85223	+	30.3220i	0.491997	+	1.51421i	0.821585	+	0.570086i	$0.193090\pi$
$401$	9.85223	+	30.3220i	0.491997	+	1.51421i	−0.329589	+	0.944125i	$0.606910\pi$
$402$	1.26079	+	3.88031i	0.0628825	+	0.193532i
$403$	−21.9253	+	30.1776i	−1.09218	+	1.50325i
$404$	−3.90560	+	2.83759i	−0.194311	+	0.141175i
$405$	2.27762	+	0.740044i	0.113176	+	0.0367731i
$406$	0.151906	+	1.05012i	0.00753895	+	0.0521166i
$407$	−21.9832	+	14.8917i	−1.08966	+	0.738155i
$408$	−10.7505			−0.532228
$409$	−4.07043	+	12.5275i	−0.201270	+	0.619445i	0.798576	+	0.601894i	$0.205587\pi$
$409$	−4.07043	+	12.5275i	−0.201270	+	0.619445i	−0.999846	+	0.0175509i	$0.994413\pi$
$410$	−6.03675	+	4.38595i	−0.298134	+	0.216607i
$411$	−1.61375	+	2.22113i	−0.0796002	+	0.109560i
$412$	3.57478	−	1.16152i	0.176117	−	0.0572239i
$413$	−8.78441	−	17.8279i	−0.432253	−	0.877253i
$414$	−3.50884	+	4.82950i	−0.172450	+	0.237357i
$415$	−7.50701	−	10.3325i	−0.368505	−	0.507203i
$416$	−11.3456	−	3.68641i	−0.556264	−	0.180741i
$417$		−	0.0625173i		−	0.00306148i
$418$	−0.868328	+	26.3740i	−0.0424713	+	1.29000i
$419$			33.5231i			1.63771i	0.574001	+	0.818854i	$0.305390\pi$
$419$			33.5231i			1.63771i	−0.574001	+	0.818854i	$0.694610\pi$
$420$	−3.08256	−	0.530729i	−0.150413	−	0.0258969i
$421$	−6.13706	+	4.45883i	−0.299102	+	0.217310i	−0.727206	−	0.686419i	$-0.759182\pi$
$421$	−6.13706	+	4.45883i	−0.299102	+	0.217310i	0.428104	+	0.903729i	$0.359182\pi$
$422$	−4.62832	−	3.36267i	−0.225303	−	0.163692i
$423$	12.7669	−	4.14823i	0.620750	−	0.201694i
$424$	20.8249	−	6.76641i	1.01135	−	0.328606i
$425$	2.68819	+	1.95308i	0.130396	+	0.0947385i
$426$	10.6776	−	7.75775i	0.517332	−	0.375864i
$427$	8.81552	+	1.51778i	0.426613	+	0.0734507i
$428$			0.0919174i			0.00444300i
$429$	0.476306	−	14.4670i	0.0229963	−	0.698474i
$430$			5.12133i			0.246972i
$431$	7.62478	+	2.47744i	0.367273	+	0.119334i	0.486838	−	0.873492i	$-0.338150\pi$
$431$	7.62478	+	2.47744i	0.367273	+	0.119334i	−0.119565	+	0.992826i	$0.538150\pi$
$432$	2.78823	+	3.83767i	0.134149	+	0.184640i
$433$	0.703068	−	0.967690i	0.0337873	−	0.0465042i	−0.791789	−	0.610795i	$-0.790850\pi$
$433$	0.703068	−	0.967690i	0.0337873	−	0.0465042i	0.825576	+	0.564290i	$0.190850\pi$
$434$	−32.0316	+	15.7831i	−1.53756	+	0.757611i
$435$	−0.578428	+	0.187943i	−0.0277335	+	0.00901116i
$436$	−5.77431	+	7.94766i	−0.276539	+	0.380624i
$437$	15.4092	−	11.1954i	0.737122	−	0.535550i
$438$	−4.79574	+	14.7598i	−0.229149	+	0.705248i
$439$	15.4607			0.737897			0.368948	−	0.929450i	$-0.379718\pi$
$439$	15.4607			0.737897			0.368948	+	0.929450i	$0.379718\pi$
$440$	15.6423	−	10.5963i	0.745718	−	0.505160i
$441$	6.71305	−	1.98367i	0.319669	−	0.0944605i
$442$	29.6231	+	9.62512i	1.40903	+	0.457820i
$443$	−7.54062	+	5.47858i	−0.358266	+	0.260295i	−0.752328	−	0.658788i	$-0.771069\pi$
$443$	−7.54062	+	5.47858i	−0.358266	+	0.260295i	0.394063	+	0.919084i	$0.371069\pi$
$444$	−2.32303	+	3.19737i	−0.110246	+	0.151741i
$445$	−3.52526	−	10.8496i	−0.167113	−	0.514322i
$446$	−12.2000	−	37.5476i	−0.577685	−	1.77793i
$447$	−2.59499	−	1.88537i	−0.122739	−	0.0891749i
$448$	9.54307	+	9.80271i	0.450868	+	0.463135i
$449$	6.04832	−	18.6148i	0.285438	−	0.878488i	−0.700829	−	0.713329i	$-0.747186\pi$
$449$	6.04832	−	18.6148i	0.285438	−	0.878488i	0.986267	−	0.165159i	$-0.0528136\pi$
$450$		−	1.16101i		−	0.0547303i
$451$	−1.81634	−	6.28695i	−0.0855279	−	0.296041i
$452$	0.889871			0.0418560
$453$	−3.95956	+	12.1863i	−0.186036	+	0.572561i
$454$	7.03532	+	9.68329i	0.330184	+	0.454459i
$455$	−24.4683	−	12.8837i	−1.14709	−	0.603998i
$456$	−3.70357	−	11.3984i	−0.173435	−	0.533779i
$457$	−21.6525	+	7.03532i	−1.01286	+	0.329098i	−0.767993	−	0.640458i	$-0.778744\pi$
$457$	−21.6525	+	7.03532i	−1.01286	+	0.329098i	−0.244868	+	0.969557i	$0.578744\pi$
$458$	−5.41396	−	3.93347i	−0.252978	−	0.183799i
$459$	−2.65647	−	3.65632i	−0.123994	−	0.170662i
$460$	4.25047	+	1.38106i	0.198179	+	0.0643923i
$461$	5.86169			0.273006			0.136503	−	0.990640i	$-0.456414\pi$
$461$	5.86169			0.273006			0.136503	+	0.990640i	$0.456414\pi$
$462$	6.85596	−	12.0419i	0.318968	−	0.560241i
$463$	39.6844			1.84429			0.922146	−	0.386842i	$-0.126434\pi$
$463$	39.6844			1.84429			0.922146	+	0.386842i	$0.126434\pi$
$464$	−1.14574	−	0.372272i	−0.0531894	−	0.0172823i
$465$	−12.0310	−	16.5593i	−0.557925	−	0.767918i
$466$	−2.56406	−	1.86290i	−0.118778	−	0.0862971i
$467$	2.72149	−	0.884266i	0.125936	−	0.0409190i	−0.245371	−	0.969429i	$-0.578910\pi$
$467$	2.72149	−	0.884266i	0.125936	−	0.0409190i	0.371307	+	0.928510i	$0.378910\pi$
$468$	−0.665780	−	2.04906i	−0.0307757	−	0.0947179i
$469$	−3.18486	+	6.04856i	−0.147063	+	0.279297i
$470$	−29.8396	−	41.0707i	−1.37640	−	1.89445i
$471$	6.16159	−	18.9634i	0.283911	−	0.873788i
$472$	17.8686			0.822468
$473$	−4.22362	−	1.52774i	−0.194202	−	0.0702455i
$474$		−	8.46841i		−	0.388967i
$475$	−1.14471	+	3.52305i	−0.0525228	+	0.161649i
$476$	4.11760	+	4.22963i	0.188730	+	0.193865i
$477$	7.44719	+	5.41070i	0.340983	+	0.247739i
$478$	−10.8429	−	33.3710i	−0.495942	−	1.52635i
$479$	4.19338	+	12.9059i	0.191601	+	0.589686i	0.999999	+	0.00105098i	$0.000334536\pi$
$479$	4.19338	+	12.9059i	0.191601	+	0.589686i	−0.808399	+	0.588635i	$0.799665\pi$
$480$	3.84766	−	5.29585i	0.175621	−	0.241721i
$481$	−28.2671	+	20.5372i	−1.28887	+	0.936417i
$482$	21.7724	+	7.07429i	0.991707	+	0.322225i
$483$	−9.89868	+	1.43190i	−0.450406	+	0.0651537i
$484$	−1.33472	−	5.26371i	−0.0606690	−	0.239259i
$485$	25.7804			1.17063
$486$	−0.487979	+	1.50185i	−0.0221352	+	0.0681251i
$487$	22.4241	−	16.2921i	1.01613	−	0.738264i	0.0506467	−	0.998717i	$-0.483872\pi$
$487$	22.4241	−	16.2921i	1.01613	−	0.738264i	0.965487	+	0.260453i	$0.0838718\pi$
$488$	−4.72718	+	6.50640i	−0.213989	+	0.294531i
$489$	−14.7587	+	4.79540i	−0.667412	+	0.216855i
$490$	−14.9797	−	21.8264i	−0.676712	−	0.986018i
$491$	−13.5446	+	18.6426i	−0.611260	+	0.841327i	−0.996680	−	0.0814142i	$-0.974056\pi$
$491$	−13.5446	+	18.6426i	−0.611260	+	0.841327i	0.385421	+	0.922741i	$0.374056\pi$
$492$	−0.572533	−	0.788024i	−0.0258118	−	0.0355269i
$493$	1.09159	+	0.354680i	0.0491629	+	0.0159740i
$494$			34.7243i			1.56232i
$495$	7.46915	+	2.70169i	0.335714	+	0.121432i
$496$		−	40.5433i		−	1.82045i
$497$	21.7923	+	3.75202i	0.977520	+	0.168301i
$498$	6.81318	−	4.95007i	0.305306	−	0.221818i
$499$	0.314460	+	0.228469i	0.0140772	+	0.0102277i	0.594802	−	0.803873i	$-0.297231\pi$
$499$	0.314460	+	0.228469i	0.0140772	+	0.0102277i	−0.580724	+	0.814100i	$0.697231\pi$
$500$	4.79522	−	1.55806i	0.214449	−	0.0696787i
$501$	6.13668	−	1.99393i	0.274167	−	0.0890821i
$502$	−8.26178	−	6.00254i	−0.368741	−	0.267906i
$503$	7.12432	−	5.17612i	0.317658	−	0.230792i	−0.417518	−	0.908669i	$-0.637100\pi$
$503$	7.12432	−	5.17612i	0.317658	−	0.230792i	0.735175	+	0.677877i	$0.237100\pi$
$504$	−1.06785	+	6.20221i	−0.0475656	+	0.276269i
$505$		−	23.4193i		−	1.04215i
$506$	−12.1583	+	15.6260i	−0.540501	+	0.694661i
$507$		−	6.04741i		−	0.268575i
$508$	7.23307	+	2.35017i	0.320916	+	0.104272i
$509$	−19.1615	−	26.3735i	−0.849317	−	1.16898i	−0.984013	−	0.178098i	$-0.943006\pi$
$509$	−19.1615	−	26.3735i	−0.849317	−	1.16898i	0.134696	−	0.990887i	$-0.456994\pi$
$510$	−10.0461	+	13.8273i	−0.444851	+	0.612284i
$511$	−23.3241	+	11.4926i	−1.03180	+	0.508402i
$512$	−9.13125	+	2.96692i	−0.403548	+	0.131121i
$513$	2.96153	−	4.07619i	0.130755	−	0.179968i
$514$	29.8085	−	21.6572i	1.31480	−	0.955256i
$515$	−5.63469	+	17.3418i	−0.248294	+	0.764171i
$516$	−0.668527			−0.0294303
$517$	42.7729	−	12.3573i	1.88115	−	0.543475i
$518$	−33.1037	+	4.78863i	−1.45449	+	0.210400i
$519$	−1.82572	−	0.593212i	−0.0801401	−	0.0260391i
$520$	20.1137	−	14.6134i	0.882043	−	0.640842i
$521$	2.92396	−	4.02449i	0.128101	−	0.176316i	−0.740149	−	0.672443i	$-0.765245\pi$
$521$	2.92396	−	4.02449i	0.128101	−	0.176316i	0.868250	+	0.496127i	$0.165245\pi$
$522$	−0.123928	−	0.381411i	−0.00542418	−	0.0166939i
$523$	−5.78854	−	17.8153i	−0.253115	−	0.779008i	−0.994195	−	0.107592i	$-0.965686\pi$
$523$	−5.78854	−	17.8153i	−0.253115	−	0.779008i	0.741080	−	0.671417i	$-0.234314\pi$
$524$	8.64962	+	6.28432i	0.377861	+	0.274532i
$525$	1.39380	−	1.35688i	0.0608304	−	0.0592192i
$526$	−12.5732	+	38.6964i	−0.548219	+	1.68724i
$527$			38.6274i			1.68264i
$528$	8.82368	+	13.0255i	0.384001	+	0.566863i
$529$	−8.70939			−0.378669
$530$	10.7575	−	33.1082i	0.467276	−	1.43813i
$531$	4.41538	+	6.07725i	0.191611	+	0.263730i
$532$	−3.06602	+	5.82288i	−0.132929	+	0.252454i
$533$	−2.66104	−	8.18985i	−0.115263	−	0.354742i
$534$	7.15416	−	2.32453i	0.309591	−	0.100592i
$535$	−0.360745	−	0.262096i	−0.0155964	−	0.0113314i
$536$	−3.61245	−	4.97210i	−0.156034	−	0.214762i
$537$	4.62058	+	1.50132i	0.199393	+	0.0647866i
$538$	−29.7217			−1.28139
$539$	22.4691	−	5.84289i	0.967813	−	0.251671i
$540$	1.18224			0.0508755
$541$	−36.6043	−	11.8935i	−1.57374	−	0.511340i	−0.613307	−	0.789845i	$-0.710161\pi$
$541$	−36.6043	−	11.8935i	−1.57374	−	0.511340i	−0.960435	+	0.278505i	$0.910161\pi$
$542$	−13.6250	−	18.7533i	−0.585246	−	0.805522i
$543$	4.41092	+	3.20472i	0.189291	+	0.137528i
$544$	−11.7489	+	3.81744i	−0.503729	+	0.163671i
$545$	−14.7268	−	45.3244i	−0.630826	−	1.94148i
$546$	8.49543	−	16.1342i	0.363571	−	0.690480i
$547$	3.77889	+	5.20119i	0.161574	+	0.222387i	0.882126	−	0.471014i	$-0.156112\pi$
$547$	3.77889	+	5.20119i	0.161574	+	0.222387i	−0.720552	+	0.693400i	$0.756112\pi$
$548$	−0.418822	+	1.28900i	−0.0178912	+	0.0550634i
$549$	−3.38098			−0.144297
$550$	0.126707	−	3.84853i	0.00540283	−	0.164102i
$551$			1.27957i			0.0545116i
$552$	2.77875	−	8.55210i	0.118271	−	0.364002i
$553$	10.1664	−	9.89713i	0.432320	−	0.420869i
$554$	32.6816	+	23.7445i	1.38851	+	1.00881i
$555$	−5.92465	−	18.2342i	−0.251487	−	0.773998i
$556$	−0.00953702	−	0.0293519i	−0.000404460	−	0.00124480i
$557$	3.27715	−	4.51061i	0.138857	−	0.191121i	−0.733925	−	0.679231i	$-0.762314\pi$
$557$	3.27715	−	4.51061i	0.138857	−	0.191121i	0.872782	+	0.488110i	$0.162314\pi$
$558$	10.9191	−	7.93316i	0.462240	−	0.335837i
$559$	−5.62099	−	1.82637i	−0.237743	−	0.0772473i
$560$	29.7466	−	4.30301i	1.25702	−	0.181835i
$561$	−8.40672	−	12.4100i	−0.354932	−	0.523950i
$562$	1.41129			0.0595315
$563$	−6.51811	+	20.0607i	−0.274706	+	0.845457i	0.714591	+	0.699542i	$0.246613\pi$
$563$	−6.51811	+	20.0607i	−0.274706	+	0.845457i	−0.989297	+	0.145915i	$0.953387\pi$
$564$	5.36128	−	3.89520i	0.225751	−	0.164017i
$565$	−2.53741	+	3.49244i	−0.106750	+	0.146928i
$566$	−31.9677	+	10.3869i	−1.34370	+	0.436596i
$567$	−2.37329	+	1.16940i	−0.0996688	+	0.0491102i
$568$	−11.6858	+	16.0841i	−0.490324	+	0.674874i
$569$	8.54243	+	11.7577i	0.358117	+	0.492906i	0.949623	−	0.313394i	$-0.101466\pi$
$569$	8.54243	+	11.7577i	0.358117	+	0.492906i	−0.591506	+	0.806301i	$0.701466\pi$
$570$	−18.1216	−	5.88807i	−0.759031	−	0.246624i
$571$			13.4953i			0.564762i	0.959302	+	0.282381i	$0.0911242\pi$
$571$			13.4953i			0.564762i	−0.959302	+	0.282381i	$0.908876\pi$
$572$	−1.98332	−	6.86495i	−0.0829268	−	0.287038i
$573$		−	8.46009i		−	0.353425i
$574$	1.39874	−	8.12412i	0.0583824	−	0.339094i
$575$	−2.24853	+	1.63365i	−0.0937701	+	0.0681280i
$576$	−4.18330	−	3.03935i	−0.174304	−	0.126639i
$577$	12.0202	−	3.90559i	0.500406	−	0.162592i	−0.0479288	−	0.998851i	$-0.515262\pi$
$577$	12.0202	−	3.90559i	0.500406	−	0.162592i	0.548335	+	0.836259i	$0.315262\pi$
$578$	5.14463	−	1.67159i	0.213988	−	0.0695290i
$579$	2.61992	+	1.90349i	0.108880	+	0.0791062i
$580$	−0.242902	+	0.176479i	−0.0100860	+	0.00732787i
$581$	13.9053	+	2.39409i	0.576887	+	0.0993237i
$582$			16.9994i			0.704648i
$583$	24.0957	+	18.7483i	0.997940	+	0.776475i
$584$		−	23.3773i		−	0.967361i
$585$	9.94029	+	3.22980i	0.410981	+	0.133536i
$586$	−11.7532	−	16.1769i	−0.485522	−	0.668263i
$587$	−19.1271	+	26.3262i	−0.789459	+	1.08660i	0.204717	+	0.978821i	$0.434373\pi$
$587$	−19.1271	+	26.3262i	−0.789459	+	1.08660i	−0.994175	+	0.107775i	$0.965627\pi$
$588$	2.84918	−	1.95541i	0.117498	−	0.0806399i
$589$	−40.9554	+	13.3072i	−1.68754	+	0.548315i
$590$	16.6979	−	22.9827i	0.687441	−	0.946182i
$591$	−19.0079	+	13.8101i	−0.781882	+	0.568071i
$592$	11.7354	−	36.1178i	0.482322	−	1.48443i
$593$	24.7966			1.01827			0.509136	−	0.860686i	$-0.329965\pi$
$593$	24.7966			1.01827			0.509136	+	0.860686i	$0.329965\pi$
$594$	−1.78147	+	4.92510i	−0.0730947	+	0.202079i
$595$	−28.3409	+	4.09967i	−1.16186	+	0.168070i
$596$	−1.50596	−	0.489317i	−0.0616867	−	0.0200432i
$597$	6.81443	−	4.95097i	0.278896	−	0.202630i
$598$	−15.3137	+	21.0775i	−0.626225	+	0.861925i
$599$	−1.70273	−	5.24047i	−0.0695718	−	0.214120i	0.910226	−	0.414113i	$-0.135908\pi$
$599$	−1.70273	−	5.24047i	−0.0695718	−	0.214120i	−0.979797	+	0.199993i	$0.935908\pi$
$600$	0.540429	+	1.66327i	0.0220629	+	0.0679027i
$601$	−20.7594	−	15.0826i	−0.846793	−	0.615231i	0.0774672	−	0.996995i	$-0.475317\pi$
$601$	−20.7594	−	15.0826i	−0.846793	−	0.615231i	−0.924260	+	0.381764i	$0.875317\pi$
$602$	−3.94670	−	4.05408i	−0.160856	−	0.165232i
$603$	0.798406	−	2.45724i	0.0325136	−	0.100067i
$604$			6.32551i			0.257381i
$605$	24.4641	+	9.77079i	0.994608	+	0.397239i
$606$	15.4425			0.627310
$607$	−2.18909	+	6.73732i	−0.0888524	+	0.273459i	−0.985603	−	0.169077i	$-0.945921\pi$
$607$	−2.18909	+	6.73732i	−0.0888524	+	0.273459i	0.896750	+	0.442537i	$0.145921\pi$
$608$	−8.09503	−	11.1419i	−0.328297	−	0.451862i
$609$	0.313052	−	0.594537i	0.0126855	−	0.0240918i
$610$	3.95110	+	12.1602i	0.159975	+	0.492354i
$611$	55.7192	−	18.1043i	2.25416	−	0.732420i
$612$	−1.80499	−	1.31140i	−0.0729624	−	0.0530103i
$613$	−0.479532	−	0.660019i	−0.0193681	−	0.0266579i	0.799223	−	0.601034i	$-0.205245\pi$
$613$	−0.479532	−	0.660019i	−0.0193681	−	0.0266579i	−0.818591	+	0.574377i	$0.805245\pi$
$614$	25.2417	+	8.20153i	1.01867	+	0.330987i
$615$	4.72527			0.190541
$616$	−4.21661	+	20.4427i	−0.169892	+	0.823661i
$617$	−10.1669			−0.409303			−0.204651	−	0.978835i	$-0.565606\pi$
$617$	−10.1669			−0.409303			−0.204651	+	0.978835i	$0.565606\pi$
$618$	−11.4351	−	3.71547i	−0.459985	−	0.149458i
$619$	−16.9771	−	23.3670i	−0.682367	−	0.939198i	0.317592	−	0.948227i	$-0.397126\pi$
$619$	−16.9771	−	23.3670i	−0.682367	−	0.939198i	−0.999959	+	0.00902970i	$0.997126\pi$
$620$	−8.17470	−	5.93926i	−0.328304	−	0.238527i
$621$	3.59527	−	1.16817i	0.144273	−	0.0468772i
$622$	7.19061	+	22.1304i	0.288317	+	0.887349i
$623$	11.1518	+	5.87194i	0.446787	+	0.235254i
$624$	12.1688	+	16.7489i	0.487141	+	0.670492i
$625$	−8.69436	+	26.7585i	−0.347774	+	1.07034i
$626$	−13.4012			−0.535620
$627$	10.2618	−	13.1887i	0.409817	−	0.526704i
$628$		−	9.84330i		−	0.392790i
$629$	−11.1808	+	34.4111i	−0.445809	+	1.37206i
$630$	6.97944	+	7.16933i	0.278067	+	0.285633i
$631$	−28.4139	−	20.6439i	−1.13114	−	0.821821i	−0.145279	−	0.989391i	$-0.546408\pi$
$631$	−28.4139	−	20.6439i	−1.13114	−	0.821821i	−0.985860	+	0.167570i	$0.946408\pi$
$632$	3.94191	+	12.1319i	0.156801	+	0.482583i
$633$	1.11951	+	3.44551i	0.0444967	+	0.136947i
$634$	−2.91530	+	4.01256i	−0.115781	+	0.159359i
$635$	−29.8482	+	21.6860i	−1.18449	+	0.860583i
$636$	4.32187	+	1.40426i	0.171373	+	0.0556826i
$637$	29.2980	−	8.65740i	1.16083	−	0.343019i
$638$	−0.369174	−	1.27784i	−0.0146157	−	0.0505900i
$639$	−8.35792			−0.330634
$640$	−10.0885	+	31.0491i	−0.398781	+	1.22732i
$641$	25.2362	−	18.3351i	0.996769	−	0.724195i	0.0353757	−	0.999374i	$-0.488737\pi$
$641$	25.2362	−	18.3351i	0.996769	−	0.724195i	0.961393	+	0.275179i	$0.0887372\pi$
$642$	0.172824	−	0.237872i	0.00682083	−	0.00938807i
$643$	−5.77756	+	1.87724i	−0.227845	+	0.0740312i	−0.420714	−	0.907193i	$-0.638221\pi$
$643$	−5.77756	+	1.87724i	−0.227845	+	0.0740312i	0.192870	+	0.981224i	$0.438221\pi$
$644$	−4.42901	+	2.18233i	−0.174527	+	0.0859957i
$645$	1.90626	−	2.62374i	0.0750590	−	0.103310i
$646$	21.1359	+	29.0911i	0.831582	+	1.14457i
$647$	−12.8756	−	4.18354i	−0.506193	−	0.164472i	0.0447774	−	0.998997i	$-0.485742\pi$
$647$	−12.8756	−	4.18354i	−0.506193	−	0.164472i	−0.550970	+	0.834525i	$0.685742\pi$
$648$		−	2.37871i		−	0.0934445i
$649$	13.9730	+	20.6269i	0.548487	+	0.809677i
$650$		−	5.06702i		−	0.198745i
$651$	22.2851	+	3.83686i	0.873421	+	0.150378i
$652$	−6.19770	+	4.50289i	−0.242721	+	0.176347i
$653$	−20.7309	−	15.0619i	−0.811262	−	0.589416i	0.102934	−	0.994688i	$-0.467177\pi$
$653$	−20.7309	−	15.0619i	−0.811262	−	0.589416i	−0.914196	+	0.405272i	$0.867177\pi$
$654$	29.8866	−	9.71074i	1.16866	−	0.379720i
$655$	−49.3276	+	16.0275i	−1.92739	+	0.626247i
$656$	7.57215	+	5.50149i	0.295643	+	0.214797i
$657$	7.95082	−	5.77661i	0.310191	−	0.225367i
$658$	55.2720	+	9.51627i	2.15473	+	0.370983i
$659$		−	45.8130i		−	1.78462i	−0.451423	−	0.892310i	$-0.649083\pi$
$659$		−	45.8130i		−	1.78462i	0.451423	−	0.892310i	$-0.350917\pi$
$660$	3.91892	+	0.129025i	0.152544	+	0.00502229i
$661$			9.74337i			0.378973i	0.981883	+	0.189487i	$0.0606823\pi$
$661$			9.74337i			0.378973i	−0.981883	+	0.189487i	$0.939318\pi$
$662$	−20.2573	−	6.58199i	−0.787321	−	0.255816i
$663$	−11.5937	−	15.9574i	−0.450263	−	0.619734i
$664$	−7.45647	+	10.2629i	−0.289367	+	0.398280i
$665$	−14.1103	−	28.6367i	−0.547173	−	1.11048i
$666$	12.0235	−	3.90667i	0.465901	−	0.151380i
$667$	−0.564303	+	0.776696i	−0.0218499	+	0.0300738i
$668$	2.57700	−	1.87230i	0.0997073	−	0.0724416i
$669$	−7.72573	+	23.7774i	−0.298694	+	0.919286i
$670$	−9.77092			−0.377483
$671$	−11.2074	−	0.368986i	−0.432655	−	0.0142446i
$672$	1.03536	+	7.15740i	0.0399398	+	0.276103i
$673$	−18.6090	−	6.04645i	−0.717326	−	0.233073i	−0.0724626	−	0.997371i	$-0.523086\pi$
$673$	−18.6090	−	6.04645i	−0.717326	−	0.233073i	−0.644863	+	0.764298i	$0.723086\pi$
$674$	−32.9067	+	23.9081i	−1.26752	+	0.920907i
$675$	−0.432150	+	0.594803i	−0.0166334	+	0.0228940i
$676$	−0.922534	−	2.83927i	−0.0354821	−	0.109203i
$677$	7.80996	+	24.0366i	0.300161	+	0.923801i	0.981439	+	0.191776i	$0.0614246\pi$
$677$	7.80996	+	24.0366i	0.300161	+	0.923801i	−0.681278	+	0.732025i	$0.738575\pi$
$678$	−2.30289	−	1.67315i	−0.0884420	−	0.0642569i
$679$	−20.4080	+	19.8674i	−0.783186	+	0.762442i
$680$	7.95582	−	24.4855i	0.305092	−	0.938976i
$681$		−	7.57961i		−	0.290451i
$682$	37.0606	−	25.1054i	1.41912	−	0.961335i
$683$	−0.850645			−0.0325490			−0.0162745	−	0.999868i	$-0.505181\pi$
$683$	−0.850645			−0.0325490			−0.0162745	+	0.999868i	$0.505181\pi$
$684$	0.768616	−	2.36556i	0.0293888	−	0.0904494i
$685$	−3.86465	−	5.31923i	−0.147661	−	0.203237i
$686$	28.6783	+	5.73405i	1.09494	+	0.218927i
$687$	1.30955	+	4.03037i	0.0499623	+	0.153768i
$688$	6.10949	−	1.98509i	0.232922	−	0.0756810i
$689$	32.5020	+	23.6141i	1.23823	+	0.899626i
$690$	−8.40307	−	11.5658i	−0.319899	−	0.440304i
$691$	37.3080	+	12.1221i	1.41926	+	0.461146i	0.915368	−	0.402619i	$-0.131900\pi$
$691$	37.3080	+	12.1221i	1.41926	+	0.461146i	0.503895	+	0.863765i	$0.331900\pi$
$692$	−0.947671			−0.0360251
$693$	−7.99467	+	3.61735i	−0.303692	+	0.137412i
$694$	−2.56734			−0.0974549
$695$	0.142391	+	0.0462655i	0.00540118	+	0.00175495i
$696$	0.355081	+	0.488727i	0.0134593	+	0.0185252i
$697$	−7.21433	−	5.24152i	−0.273262	−	0.198537i
$698$	−25.9932	+	8.44571i	−0.983858	+	0.319675i
$699$	0.620203	+	1.90879i	0.0234582	+	0.0721970i
$700$	0.447398	−	0.849682i	0.0169101	−	0.0321150i
$701$	−2.94930	−	4.05936i	−0.111394	−	0.153320i	0.749680	−	0.661800i	$-0.230207\pi$
$701$	−2.94930	−	4.05936i	−0.111394	−	0.153320i	−0.861074	+	0.508480i	$0.830207\pi$
$702$	−2.12970	+	6.55455i	−0.0803805	+	0.247386i
$703$	−40.3369			−1.52133
$704$	−13.5352	−	10.5315i	−0.510128	−	0.396919i
$705$			32.1481i			1.21077i
$706$	−6.36168	+	19.5792i	−0.239425	+	0.736874i
$707$	18.0479	+	18.5389i	0.678761	+	0.697228i
$708$	3.00011	+	2.17971i	0.112751	+	0.0819184i
$709$	11.4264	+	35.1668i	0.429127	+	1.32072i	0.898987	+	0.437975i	$0.144304\pi$
$709$	11.4264	+	35.1668i	0.429127	+	1.32072i	−0.469861	+	0.882741i	$0.655696\pi$
$710$	9.76729	+	30.0606i	0.366560	+	1.12816i
$711$	−3.15211	+	4.33851i	−0.118213	+	0.162707i
$712$	−9.16710	+	6.66029i	−0.343552	+	0.249605i
$713$	−30.7284	−	9.98427i	−1.15079	−	0.373914i
$714$	−2.70329	−	18.6878i	−0.101168	−	0.699372i
$715$	32.5979	+	11.7911i	1.21909	+	0.440961i
$716$	2.39840			0.0896322
$717$	−6.86635	+	21.1324i	−0.256428	+	0.789206i
$718$	−1.86079	+	1.35194i	−0.0694439	+	0.0504539i
$719$	9.36131	−	12.8847i	0.349118	−	0.480520i	−0.597959	−	0.801527i	$-0.704021\pi$
$719$	9.36131	−	12.8847i	0.349118	−	0.480520i	0.947077	+	0.321007i	$0.104021\pi$
$720$	−10.8042	+	3.51049i	−0.402648	+	0.130828i
$721$	−8.90382	−	18.0702i	−0.331596	−	0.672970i
$722$	−5.92739	+	8.15836i	−0.220595	+	0.303623i
$723$	−8.52119	−	11.7284i	−0.316907	−	0.436184i
$724$	2.55982	+	0.831735i	0.0951348	+	0.0309112i
$725$		−	0.186717i		−	0.00693449i
$726$	−6.44278	+	16.1315i	−0.239114	+	0.598694i
$727$			0.825903i			0.0306310i	0.999883	+	0.0153155i	$0.00487527\pi$
$727$			0.825903i			0.0306310i	−0.999883	+	0.0153155i	$0.995125\pi$
$728$	−4.66044	+	27.0685i	−0.172727	+	1.00323i
$729$	0.809017	−	0.587785i	0.0299636	−	0.0217698i
$730$	−30.0681	−	21.8457i	−1.11287	−	0.808547i
$731$	−5.82079	+	1.89129i	−0.215290	+	0.0699518i
$732$	−1.58737	+	0.515769i	−0.0586710	+	0.0190634i
$733$	31.4653	+	22.8609i	1.16220	+	0.844386i	0.990054	−	0.140686i	$-0.0449307\pi$
$733$	31.4653	+	22.8609i	1.16220	+	0.844386i	0.172144	+	0.985072i	$0.444931\pi$
$734$	30.0079	−	21.8020i	1.10761	−	0.804726i
$735$	−0.449904	+	16.7578i	−0.0165950	+	0.618120i
$736$		−	10.3330i		−	0.380881i
$737$	2.91475	−	8.05820i	0.107366	−	0.296828i
$738$			3.11581i			0.114694i
$739$	−28.1130	−	9.13447i	−1.03415	−	0.336017i	−0.257722	−	0.966219i	$-0.582972\pi$
$739$	−28.1130	−	9.13447i	−1.03415	−	0.336017i	−0.776431	+	0.630202i	$0.782972\pi$
$740$	−5.56326	−	7.65717i	−0.204510	−	0.281483i
$741$	12.9251	−	17.7899i	0.474815	−	0.653527i
$742$	16.9988	+	34.4988i	0.624044	+	1.26649i
$743$	45.9205	−	14.9205i	1.68466	−	0.547379i	0.698854	−	0.715265i	$-0.253694\pi$
$743$	45.9205	−	14.9205i	1.68466	−	0.547379i	0.985806	+	0.167886i	$0.0536939\pi$
$744$	−11.9500	+	16.4478i	−0.438109	+	0.603005i
$745$	6.21456	−	4.51514i	0.227684	−	0.165422i
$746$	−2.52249	+	7.76343i	−0.0923550	+	0.284240i
$747$	−5.33302			−0.195125
$748$	−5.84011	−	4.54406i	−0.213536	−	0.166147i
$749$	0.487550	−	0.0705269i	0.0178147	−	0.00257700i
$750$	−15.3390	−	4.98394i	−0.560101	−	0.181988i
$751$	−43.9820	+	31.9548i	−1.60493	+	1.16605i	−0.727798	+	0.685792i	$0.759456\pi$
$751$	−43.9820	+	31.9548i	−1.60493	+	1.16605i	−0.877129	+	0.480256i	$0.840544\pi$
$752$	−37.4291	+	51.5167i	−1.36490	+	1.87862i
$753$	1.99839	+	6.15040i	0.0728253	+	0.224133i
$754$	−0.540863	−	1.66460i	−0.0196971	−	0.0606213i
$755$	−24.8255	−	18.0368i	−0.903491	−	0.656425i
$756$	−0.935870	+	0.911081i	−0.0340373	+	0.0331357i
$757$	−9.38058	+	28.8705i	−0.340943	+	1.04931i	0.622777	+	0.782399i	$0.286004\pi$
$757$	−9.38058	+	28.8705i	−0.340943	+	1.04931i	−0.963720	+	0.266915i	$0.913996\pi$
$758$		−	7.84998i		−	0.285124i
$759$	12.0452	−	3.47993i	0.437213	−	0.126313i
$760$	28.7020			1.04113
$761$	−7.21164	+	22.1951i	−0.261422	+	0.804573i	0.731074	+	0.682298i	$0.239019\pi$
$761$	−7.21164	+	22.1951i	−0.261422	+	0.804573i	−0.992496	+	0.122276i	$0.960981\pi$
$762$	−14.2996	−	19.6817i	−0.518020	−	0.712993i
$763$	46.5867	+	24.5301i	1.68655	+	0.888049i
$764$	−1.29059	−	3.97202i	−0.0466918	−	0.143703i
$765$	10.2936	−	3.34460i	0.372166	−	0.120924i
$766$	−43.0284	−	31.2619i	−1.55468	−	1.12954i
$767$	19.2702	+	26.5231i	0.695806	+	0.957695i
$768$	−10.6380	−	3.45650i	−0.383866	−	0.124726i
$769$	−16.9136			−0.609919			−0.304960	−	0.952365i	$-0.598643\pi$
$769$	−16.9136			−0.609919			−0.304960	+	0.952365i	$0.598643\pi$
$770$	22.3532	+	24.5268i	0.805554	+	0.883885i
$771$	−23.3326			−0.840304
$772$	1.52043	+	0.494019i	0.0547216	+	0.0177801i
$773$	−4.80733	−	6.61672i	−0.172907	−	0.237987i	0.713764	−	0.700386i	$-0.246989\pi$
$773$	−4.80733	−	6.61672i	−0.172907	−	0.237987i	−0.886672	+	0.462399i	$0.846989\pi$
$774$	1.73008	+	1.25697i	0.0621863	+	0.0451810i
$775$	5.97627	−	1.94181i	0.214674	−	0.0697518i
$776$	−7.91295	−	24.3536i	−0.284058	−	0.874242i
$777$	18.7420	+	9.86855i	0.672366	+	0.354032i
$778$	−0.104277	−	0.143525i	−0.00373851	−	0.00514562i
$779$	3.07207	−	9.45485i	0.110068	−	0.338755i
$780$	5.15969			0.184746
$781$	−27.7051	−	0.912149i	−0.991365	−	0.0326393i
$782$			26.9793i			0.964779i
$783$	−0.0784784	+	0.241532i	−0.00280459	+	0.00863164i
$784$	−20.2316	+	26.3302i	−0.722555	+	0.940365i
$785$	38.6316	+	28.0675i	1.37882	+	1.00177i
$786$	−10.5684	−	32.5263i	−0.376963	−	1.16017i
$787$	15.6117	+	48.0479i	0.556498	+	1.71272i	0.691955	+	0.721941i	$0.256750\pi$
$787$	15.6117	+	48.0479i	0.556498	+	1.71272i	−0.135457	+	0.990783i	$0.543250\pi$
$788$	−6.81753	+	9.38352i	−0.242864	+	0.334274i
$789$	20.8451	−	15.1448i	0.742104	−	0.539170i
$790$	19.2878	+	6.26699i	0.686229	+	0.222969i
$791$	−0.682785	−	4.72007i	−0.0242770	−	0.167827i
$792$	0.259603	−	7.88501i	0.00922458	−	0.280182i
$793$	−14.7557			−0.523991
$794$	7.19143	−	22.1329i	0.255214	−	0.785468i
$795$	−17.8348	+	12.9577i	−0.632534	+	0.459563i
$796$	2.44411	−	3.36403i	0.0866292	−	0.119235i
$797$	49.7877	−	16.1770i	1.76357	−	0.573019i	0.766011	−	0.642827i	$-0.222239\pi$
$797$	49.7877	−	16.1770i	1.76357	−	0.573019i	0.997560	+	0.0698082i	$0.0222387\pi$
$798$	18.8828	−	9.30421i	0.668444	−	0.329365i
$799$	35.6604	−	49.0823i	1.26157	−	1.73641i
$800$	1.18124	+	1.62583i	0.0417630	+	0.0574819i
$801$	−4.53043	−	1.47203i	−0.160075	−	0.0520115i
$802$		−	50.3467i		−	1.77780i
$803$	26.9860	−	18.2807i	0.952316	−	0.645113i
$804$		−	1.27548i		−	0.0449825i
$805$	4.06413	−	23.6051i	0.143242	−	0.831971i
$806$	47.6544	−	34.6230i	1.67855	−	1.21954i
$807$	15.2269	+	11.0630i	0.536013	+	0.389436i
$808$	−22.1232	+	7.18825i	−0.778290	+	0.252882i
$809$	7.10474	−	2.30847i	0.249789	−	0.0811615i	−0.181446	−	0.983401i	$-0.558078\pi$
$809$	7.10474	−	2.30847i	0.249789	−	0.0811615i	0.431235	+	0.902239i	$0.358078\pi$
$810$	−3.05951	−	2.22286i	−0.107500	−	0.0781034i
$811$	−35.4551	+	25.7596i	−1.24500	+	0.904543i	−0.997921	−	0.0644528i	$-0.979470\pi$
$811$	−35.4551	+	25.7596i	−1.24500	+	0.904543i	−0.247076	+	0.968996i	$0.579470\pi$
$812$	0.0562815	−	0.326892i	0.00197510	−	0.0114717i
$813$			14.6791i			0.514820i
$814$	40.2822	−	11.6377i	1.41189	−	0.407903i
$815$		−	37.1636i		−	1.30178i
$816$	20.3893	+	6.62490i	0.713770	+	0.231918i
$817$	−4.01055	−	5.52005i	−0.140311	−	0.193122i
$818$	12.2263	−	16.8281i	0.427483	−	0.588380i
$819$	−10.3578	+	5.10366i	−0.361932	+	0.178336i
$820$	2.21852	−	0.720841i	0.0774741	−	0.0251729i
$821$	10.0757	−	13.8680i	0.351644	−	0.483996i	−0.596153	−	0.802871i	$-0.703305\pi$
$821$	10.0757	−	13.8680i	0.351644	−	0.483996i	0.947797	+	0.318875i	$0.103305\pi$
$822$	3.50746	−	2.54832i	0.122337	−	0.0888829i
$823$	9.44517	−	29.0692i	0.329238	−	1.01329i	−0.640253	−	0.768164i	$-0.721171\pi$
$823$	9.44517	−	29.0692i	0.329238	−	1.01329i	0.969491	−	0.245126i	$-0.0788294\pi$
$824$	18.1115			0.630943
$825$	−1.49742	+	1.92451i	−0.0521333	+	0.0670027i
$826$	4.49320	+	31.0613i	0.156338	+	1.08076i
$827$	−25.4324	−	8.26348i	−0.884371	−	0.287349i	−0.168600	−	0.985685i	$-0.553925\pi$
$827$	−25.4324	−	8.26348i	−0.884371	−	0.287349i	−0.715771	+	0.698335i	$0.753925\pi$
$828$	1.50978	−	1.09692i	0.0524685	−	0.0381206i
$829$	21.3891	−	29.4396i	0.742876	−	1.02248i	−0.255573	−	0.966790i	$-0.582264\pi$
$829$	21.3891	−	29.4396i	0.742876	−	1.02248i	0.998448	−	0.0556906i	$-0.0177360\pi$
$830$	6.23232	+	19.1811i	0.216327	+	0.665786i
$831$	−7.90512	−	24.3295i	−0.274226	−	0.843980i
$832$	−18.2573	−	13.2647i	−0.632959	−	0.459871i
$833$	19.2755	−	25.0860i	0.667857	−	0.869177i
$834$	−0.0305071	+	0.0938913i	−0.00105638	+	0.00325119i
$835$			15.4526i			0.534760i
$836$	2.80600	−	7.75754i	0.0970475	−	0.268300i
$837$	−8.54690			−0.295424
$838$	16.3586	−	50.3465i	0.565097	−	1.73919i
$839$	−17.8301	−	24.5410i	−0.615562	−	0.847248i	0.381458	−	0.924386i	$-0.375422\pi$
$839$	−17.8301	−	24.5410i	−0.615562	−	0.847248i	−0.997020	+	0.0771375i	$0.975422\pi$
$840$	−13.3360	−	7.02206i	−0.460137	−	0.242284i
$841$	8.94156	+	27.5193i	0.308330	+	0.948941i
$842$	11.3927	−	3.70172i	0.392619	−	0.127570i
$843$	−0.723026	−	0.525309i	−0.0249023	−	0.0180926i
$844$	1.05123	+	1.44689i	0.0361847	+	0.0498039i
$845$	13.7737	+	4.47535i	0.473830	+	0.153957i
$846$	−21.1982			−0.728810
$847$	−26.8957	+	11.1184i	−0.924149	+	0.382033i
$848$	−43.6662			−1.49950
$849$	20.2438	+	6.57762i	0.694767	+	0.225743i
$850$	−3.08418	−	4.24501i	−0.105786	−	0.145603i
$851$	−24.4843	−	17.7889i	−0.839312	−	0.609796i
$852$	−3.92405	+	1.27500i	−0.134436	+	0.0436808i
$853$	−13.3518	−	41.0925i	−0.457156	−	1.40698i	−0.868585	−	0.495540i	$-0.834970\pi$
$853$	−13.3518	−	41.0925i	−0.457156	−	1.40698i	0.411429	−	0.911442i	$-0.365030\pi$
$854$	−12.4989	−	6.58126i	−0.427703	−	0.225206i
$855$	7.09235	+	9.76179i	0.242553	+	0.333846i
$856$	−0.136864	+	0.421226i	−0.00467793	+	0.0143972i
$857$	−6.42231			−0.219382			−0.109691	−	0.993966i	$-0.534986\pi$
$857$	−6.42231			−0.219382			−0.109691	+	0.993966i	$0.534986\pi$
$858$	−7.77494	+	21.4948i	−0.265432	+	0.733820i
$859$		−	48.3512i		−	1.64972i	−0.565337	−	0.824860i	$-0.691254\pi$
$859$		−	48.3512i		−	1.64972i	0.565337	−	0.824860i	$-0.308746\pi$
$860$	0.494739	−	1.52265i	0.0168705	−	0.0519220i
$861$	−3.74056	+	3.64148i	−0.127478	+	0.124101i
$862$	−10.2423	−	7.44147i	−0.348854	−	0.253457i
$863$	−5.40168	−	16.6247i	−0.183875	−	0.565910i	0.816052	−	0.577979i	$-0.196158\pi$
$863$	−5.40168	−	16.6247i	−0.183875	−	0.565910i	−0.999927	+	0.0120688i	$0.996158\pi$
$864$	−0.844667	−	2.59962i	−0.0287361	−	0.0884408i
$865$	2.70222	−	3.71929i	0.0918783	−	0.126460i
$866$	−1.52811	+	1.11024i	−0.0519274	+	0.0377274i
$867$	−3.25788	−	1.05855i	−0.110643	−	0.0359502i
$868$	11.0482	−	1.59818i	0.375000	−	0.0542458i
$869$	−10.9222	+	14.0374i	−0.370510	+	0.476186i
$870$	0.960421			0.0325613
$871$	3.48451	−	10.7242i	0.118068	−	0.363376i
$872$	−38.2957	+	27.8234i	−1.29685	+	0.942220i
$873$	6.32752	−	8.70909i	0.214154	−	0.294758i
$874$	−28.6054	+	9.29444i	−0.967591	+	0.314389i
$875$	−11.9436	−	24.2394i	−0.403768	−	0.819442i
$876$	2.85170	−	3.92502i	0.0963499	−	0.132614i
$877$	−24.4767	−	33.6893i	−0.826520	−	1.13761i	−0.988561	−	0.150823i	$-0.951808\pi$
$877$	−24.4767	−	33.6893i	−0.826520	−	1.13761i	0.162041	−	0.986784i	$-0.448192\pi$
$878$	−23.2195	−	7.54448i	−0.783621	−	0.254614i
$879$			12.6625i			0.427096i
$880$	−36.1971	+	10.4575i	−1.22020	+	0.352524i
$881$		−	10.2536i		−	0.345452i	−0.984970	−	0.172726i	$-0.944743\pi$
$881$		−	10.2536i		−	0.345452i	0.984970	−	0.172726i	$-0.0552575\pi$
$882$	−11.0500	−	0.296664i	−0.372071	−	0.00998918i
$883$	30.2675	−	21.9906i	1.01858	−	0.740044i	0.0525915	−	0.998616i	$-0.483252\pi$
$883$	30.2675	−	21.9906i	1.01858	−	0.740044i	0.965992	+	0.258572i	$0.0832519\pi$
$884$	−7.87758	−	5.72340i	−0.264952	−	0.192499i
$885$	−17.1092	+	5.55912i	−0.575120	+	0.186868i
$886$	13.9983	−	4.54832i	0.470281	−	0.152804i
$887$	−38.8634	−	28.2359i	−1.30490	−	0.948069i	−0.304914	−	0.952380i	$-0.598628\pi$
$887$	−38.8634	−	28.2359i	−1.30490	−	0.948069i	−0.999991	+	0.00431082i	$0.998628\pi$
$888$	−15.4065	+	11.1935i	−0.517008	+	0.375628i
$889$	6.91598	−	40.1691i	0.231955	−	1.34723i
$890$			18.0147i			0.603854i
$891$	2.74590	−	1.86011i	0.0919912	−	0.0623162i
$892$			12.3421i			0.413243i
$893$	64.3256	+	20.9006i	2.15257	+	0.699413i
$894$	2.97725	+	4.09783i	0.0995741	+	0.137052i
$895$	−6.83886	+	9.41289i	−0.228598	+	0.314638i
$896$	−15.9416	−	32.3533i	−0.532571	−	1.08085i
$897$	15.6910	−	5.09830i	0.523906	−	0.170227i
$898$	−18.1673	+	25.0051i	−0.606250	+	0.834432i
$899$	1.75604	−	1.27584i	0.0585672	−	0.0425515i
$900$	−0.112157	+	0.345185i	−0.00373858	+	0.0115062i
$901$	41.6027			1.38599
$902$	−0.340047	+	10.3284i	−0.0113223	+	0.343897i
$903$	0.512951	+	3.54602i	0.0170699	+	0.118004i
$904$	4.07797	+	1.32501i	0.135631	+	0.0440693i
$905$	−10.5634	+	7.67477i	−0.351140	+	0.255118i
$906$	11.8933	−	16.3697i	0.395128	−	0.543848i
$907$	−1.41974	−	4.36952i	−0.0471418	−	0.145088i	0.924715	−	0.380661i	$-0.124303\pi$
$907$	−1.41974	−	4.36952i	−0.0471418	−	0.145088i	−0.971857	+	0.235573i	$0.924303\pi$
$908$	−1.15627	−	3.55863i	−0.0383722	−	0.118097i
$909$	−7.91148	−	5.74802i	−0.262407	−	0.190650i
$910$	30.4606	+	31.2894i	1.00976	+	1.03723i
$911$	−13.1126	+	40.3564i	−0.434439	+	1.33707i	0.459220	+	0.888322i	$0.348129\pi$
$911$	−13.1126	+	40.3564i	−0.434439	+	1.33707i	−0.893660	+	0.448745i	$0.851871\pi$
$912$			23.9005i			0.791425i
$913$	−17.6781	−	0.582025i	−0.585058	−	0.0192622i
$914$	35.9518			1.18918
$915$	2.50207	−	7.70058i	0.0827159	−	0.254573i
$916$	1.22967	+	1.69249i	0.0406294	+	0.0559215i
$917$	26.6967	−	50.7014i	0.881602	−	1.67431i
$918$	2.20540	+	6.78753i	0.0727891	+	0.224022i
$919$	−31.7859	+	10.3279i	−1.04852	+	0.340685i	−0.782087	−	0.623169i	$-0.785845\pi$
$919$	−31.7859	+	10.3279i	−1.04852	+	0.340685i	−0.266433	+	0.963854i	$0.585845\pi$
$920$	17.4220	+	12.6579i	0.574388	+	0.417317i
$921$	−9.87898	−	13.5973i	−0.325524	−	0.448045i
$922$	−8.80335	−	2.86038i	−0.289923	−	0.0942017i
$923$	−36.4767			−1.20065
$924$	−3.20168	+	2.91794i	−0.105328	+	0.0959932i
$925$	5.88601			0.193531
$926$	−59.5999	−	19.3652i	−1.95857	−	0.636379i
$927$	4.47540	+	6.15986i	0.146991	+	0.202316i
$928$	0.561602	+	0.408028i	0.0184355	+	0.0133942i
$929$	−6.88772	+	2.23796i	−0.225979	+	0.0734249i	−0.419818	−	0.907608i	$-0.637906\pi$
$929$	−6.88772	+	2.23796i	−0.225979	+	0.0734249i	0.193839	+	0.981033i	$0.437906\pi$
$930$	9.98814	+	30.7403i	0.327524	+	1.00802i
$931$	33.2384	+	11.7951i	1.08934	+	0.386567i
$932$	0.582372	+	0.801567i	0.0190762	+	0.0262562i
$933$	4.55352	−	14.0143i	0.149075	−	0.458807i
$934$	−4.51876			−0.147858
$935$	34.4866	−	9.96337i	1.12783	−	0.325837i
$936$		−	10.3815i		−	0.339329i
$937$	14.7206	−	45.3054i	0.480902	−	1.48006i	−0.356928	−	0.934132i	$-0.616176\pi$
$937$	14.7206	−	45.3054i	0.480902	−	1.48006i	0.837830	−	0.545932i	$-0.183824\pi$
$938$	7.73473	−	7.52986i	0.252548	−	0.245859i
$939$	6.86567	+	4.98820i	0.224053	+	0.162784i
$940$	4.90420	+	15.0936i	0.159957	+	0.492298i
$941$	3.07182	+	9.45410i	0.100139	+	0.308195i	0.988559	−	0.150836i	$-0.0481966\pi$
$941$	3.07182	+	9.45410i	0.100139	+	0.308195i	−0.888420	+	0.459031i	$0.848197\pi$
$942$	−18.5075	+	25.4734i	−0.603007	+	0.829968i
$943$	6.03441	−	4.38425i	0.196507	−	0.142771i
$944$	−33.8895	−	11.0114i	−1.10301	−	0.358390i
$945$	−0.907115	−	6.27086i	−0.0295084	−	0.203991i
$946$	5.59773	+	4.35547i	0.181998	+	0.141608i
$947$	−10.9512			−0.355866			−0.177933	−	0.984043i	$-0.556941\pi$
$947$	−10.9512			−0.355866			−0.177933	+	0.984043i	$0.556941\pi$
$948$	−0.818080	+	2.51779i	−0.0265700	+	0.0817740i
$949$	34.7000	−	25.2110i	1.12641	−	0.818385i
$950$	3.43835	−	4.73248i	0.111555	−	0.153542i
$951$	2.98711	−	0.970572i	0.0968638	−	0.0314729i
$952$	12.5716	+	25.5140i	0.407449	+	0.826913i
$953$	−22.4087	+	30.8429i	−0.725889	+	0.999100i	0.273419	+	0.961895i	$0.411846\pi$
$953$	−22.4087	+	30.8429i	−0.725889	+	0.999100i	−0.999308	+	0.0372052i	$0.988154\pi$
$954$	−8.54422	−	11.7601i	−0.276629	−	0.380748i
$955$	19.2689	+	6.26083i	0.623526	+	0.202596i
$956$			10.9692i			0.354768i
$957$	−0.286502	+	0.792072i	−0.00926131	+	0.0256040i
$958$		−	21.4290i		−	0.692339i
$959$	7.15850	+	1.23249i	0.231160	+	0.0397992i
$960$	10.0183	−	7.27872i	0.323339	−	0.234920i
$961$	34.0187	+	24.7161i	1.09738	+	0.797292i
$962$	52.4745	−	17.0500i	1.69185	−	0.549714i
$963$	−0.177082	+	0.0575373i	−0.00570638	+	0.00185411i
$964$	−5.78988	−	4.20660i	−0.186480	−	0.135485i
$965$	−6.27427	+	4.55853i	−0.201976	+	0.146744i
$966$	15.5650	+	2.67986i	0.500797	+	0.0862230i
$967$		−	41.1836i		−	1.32438i	−0.749338	−	0.662188i	$-0.769628\pi$
$967$		−	41.1836i		−	1.32438i	0.749338	−	0.662188i	$-0.230372\pi$
$968$	1.72108	−	26.1091i	0.0553175	−	0.839179i
$969$		−	22.7711i		−	0.731512i
$970$	−38.7182	−	12.5803i	−1.24317	−	0.403929i
$971$	27.8846	+	38.3799i	0.894861	+	1.23167i	0.972078	+	0.234656i	$0.0753963\pi$
$971$	27.8846	+	38.3799i	0.894861	+	1.23167i	−0.0772177	+	0.997014i	$0.524604\pi$
$972$	0.290168	−	0.399382i	0.00930714	−	0.0128102i
$973$	−0.148372	+	0.0731078i	−0.00475657	+	0.00234373i
$974$	−41.6277	+	13.5257i	−1.33384	+	0.433390i
$975$	−1.88605	+	2.59592i	−0.0604018	+	0.0831359i
$976$	12.9751	−	9.42694i	0.415322	−	0.301749i
$977$	−14.2428	+	43.8347i	−0.455666	+	1.40240i	0.414685	+	0.909965i	$0.363892\pi$
$977$	−14.2428	+	43.8347i	−0.455666	+	1.40240i	−0.870351	+	0.492432i	$0.836108\pi$
$978$	24.5054			0.783595
$979$	−14.8570	−	5.37395i	−0.474831	−	0.171752i
$980$	2.34517	+	7.93643i	0.0749138	+	0.253520i
$981$	−18.9259	−	6.14941i	−0.604258	−	0.196335i
$982$	29.4391	−	21.3887i	0.939439	−	0.682542i
$983$	−15.6553	+	21.5477i	−0.499327	+	0.687265i	−0.982074	−	0.188495i	$-0.939639\pi$
$983$	−15.6553	+	21.5477i	−0.499327	+	0.687265i	0.482747	+	0.875760i	$0.339639\pi$
$984$	−1.45036	−	4.46374i	−0.0462357	−	0.142299i
$985$	−17.3874	−	53.5129i	−0.554009	−	1.70506i
$986$	−1.46633	−	1.06535i	−0.0466974	−	0.0339276i
$987$	−24.7746	−	25.4487i	−0.788585	−	0.810041i
$988$	3.35450	−	10.3241i	0.106721	−	0.328453i
$989$		−	5.11934i		−	0.162786i
$990$	−9.89915	−	7.70231i	−0.314616	−	0.244795i
$991$	28.7689			0.913873			0.456937	−	0.889499i	$-0.348947\pi$
$991$	28.7689			0.913873			0.456937	+	0.889499i	$0.348947\pi$
$992$	−7.21928	+	22.2187i	−0.229212	+	0.705443i
$993$	7.92820	+	10.9122i	0.251594	+	0.346289i
$994$	−30.8978	−	16.2692i	−0.980019	−	0.516026i
$995$	6.23346	+	19.1846i	0.197614	+	0.608193i
$996$	−2.50386	+	0.813554i	−0.0793379	+	0.0257784i
$997$	35.2553	+	25.6145i	1.11655	+	0.811218i	0.983682	−	0.179916i	$-0.0575825\pi$
$997$	35.2553	+	25.6145i	1.11655	+	0.811218i	0.132864	+	0.991134i	$0.457583\pi$
$998$	−0.360782	−	0.496574i	−0.0114204	−	0.0157188i
$999$	−7.61398	−	2.47393i	−0.240896	−	0.0782717i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.w.a.13.6	yes	64
3.2	odd	2		693.2.bu.f.244.12		64
7.6	odd	2	inner	231.2.w.a.13.5	✓	64
11.6	odd	10	inner	231.2.w.a.160.5	yes	64
21.20	even	2		693.2.bu.f.244.11		64
33.17	even	10		693.2.bu.f.622.11		64
77.6	even	10	inner	231.2.w.a.160.6	yes	64
231.83	odd	10		693.2.bu.f.622.12		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.w.a.13.5	✓	64	7.6	odd	2	inner
231.2.w.a.13.6	yes	64	1.1	even	1	trivial
231.2.w.a.160.5	yes	64	11.6	odd	10	inner
231.2.w.a.160.6	yes	64	77.6	even	10	inner
693.2.bu.f.244.11		64	21.20	even	2
693.2.bu.f.244.12		64	3.2	odd	2
693.2.bu.f.622.11		64	33.17	even	10
693.2.bu.f.622.12		64	231.83	odd	10

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:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.w (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.50185 - 0.487979i) q^{2} +(0.587785 + 0.809017i) q^{3} +(0.399382 + 0.290168i) q^{4} +(-2.27762 + 0.740044i) q^{5} +(-0.487979 - 1.50185i) q^{6} +(1.23267 - 2.34105i) q^{7} +(1.39817 + 1.92441i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(-1.50185 - 0.487979i) q^{2} +(0.587785 + 0.809017i) q^{3} +(0.399382 + 0.290168i) q^{4} +(-2.27762 + 0.740044i) q^{5} +(-0.487979 - 1.50185i) q^{6} +(1.23267 - 2.34105i) q^{7} +(1.39817 + 1.92441i) q^{8} +(-0.309017 + 0.951057i) q^{9} +3.78176 q^{10} +(-1.12813 + 3.11886i) q^{11} +0.493663i q^{12} +(-1.34865 + 4.15073i) q^{13} +(-2.99367 + 2.91438i) q^{14} +(-1.93746 - 1.40765i) q^{15} +(-1.46586 - 4.51145i) q^{16} +(1.39659 + 4.29826i) q^{17} +(0.928191 - 1.27755i) q^{18} +(-4.07619 + 2.96153i) q^{19} +(-1.12438 - 0.365332i) q^{20} +(2.61850 - 0.378780i) q^{21} +(3.21622 - 4.13355i) q^{22} -3.78029 q^{23} +(-0.735061 + 2.26229i) q^{24} +(0.594803 - 0.432150i) q^{25} +(4.05094 - 5.57564i) q^{26} +(-0.951057 + 0.309017i) q^{27} +(1.17160 - 0.577290i) q^{28} +(0.149275 - 0.205459i) q^{29} +(2.22286 + 3.05951i) q^{30} +(8.12858 + 2.64114i) q^{31} +2.73340i q^{32} +(-3.18631 + 0.920544i) q^{33} -7.13683i q^{34} +(-1.07508 + 6.24425i) q^{35} +(-0.399382 + 0.290168i) q^{36} +(6.47684 + 4.70570i) q^{37} +(7.56697 - 2.45866i) q^{38} +(-4.15073 + 1.34865i) q^{39} +(-4.60865 - 3.34838i) q^{40} +(-1.59628 + 1.15977i) q^{41} +(-4.11741 - 0.708902i) q^{42} +1.35422i q^{43} +(-1.35555 + 0.918270i) q^{44} -2.39483i q^{45} +(5.67741 + 1.84470i) q^{46} +(-7.89040 - 10.8602i) q^{47} +(2.78823 - 3.83767i) q^{48} +(-3.96103 - 5.77150i) q^{49} +(-1.10418 + 0.358770i) q^{50} +(-2.65647 + 3.65632i) q^{51} +(-1.74304 + 1.26639i) q^{52} +(2.84457 - 8.75470i) q^{53} +1.57913 q^{54} +(0.261362 - 7.93846i) q^{55} +(6.22864 - 0.901007i) q^{56} +(-4.79185 - 1.55697i) q^{57} +(-0.324448 + 0.235725i) q^{58} +(4.41538 - 6.07725i) q^{59} +(-0.365332 - 1.12438i) q^{60} +(1.04478 + 3.21550i) q^{61} +(-10.9191 - 7.93316i) q^{62} +(1.84555 + 1.89577i) q^{63} +(-1.59788 + 4.91776i) q^{64} -10.4518i q^{65} +(5.23456 + 0.172340i) q^{66} -2.58370 q^{67} +(-0.689445 + 2.12189i) q^{68} +(-2.22200 - 3.05832i) q^{69} +(4.66168 - 8.85329i) q^{70} +(2.58274 + 7.94885i) q^{71} +(-2.26229 + 0.735061i) q^{72} +(-7.95082 - 5.77661i) q^{73} +(-7.43092 - 10.2278i) q^{74} +(0.699233 + 0.227194i) q^{75} -2.48730 q^{76} +(5.91080 + 6.48556i) q^{77} +6.89187 q^{78} +(5.10022 + 1.65716i) q^{79} +(6.67734 + 9.19058i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(2.96331 - 0.962837i) q^{82} +(1.64799 + 5.07201i) q^{83} +(1.15569 + 0.608526i) q^{84} +(-6.36180 - 8.75627i) q^{85} +(0.660830 - 2.03383i) q^{86} +0.253962 q^{87} +(-7.57931 + 2.18970i) q^{88} +4.76358i q^{89} +(-1.16863 + 3.59667i) q^{90} +(8.05461 + 8.27376i) q^{91} +(-1.50978 - 1.09692i) q^{92} +(2.64114 + 8.12858i) q^{93} +(6.55061 + 20.1607i) q^{94} +(7.09235 - 9.76179i) q^{95} +(-2.21137 + 1.60665i) q^{96} +(-10.2381 - 3.32658i) q^{97} +(3.13248 + 10.6008i) q^{98} +(-2.61760 - 2.03670i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 12 q^{4} + 10 q^{7} - 20 q^{8} + 16 q^{9}+O(q^{10}) \) 64 * q + 12 * q^4 + 10 * q^7 - 20 * q^8 + 16 * q^9	\( 64 q + 12 q^{4} + 10 q^{7} - 20 q^{8} + 16 q^{9} - 16 q^{11} + 12 q^{14} - 12 q^{15} - 16 q^{16} + 10 q^{18} - 40 q^{22} - 24 q^{23} + 44 q^{25} - 30 q^{28} - 40 q^{29} - 40 q^{35} - 12 q^{36} + 32 q^{37} - 2 q^{42} + 22 q^{44} - 70 q^{46} - 50 q^{49} - 40 q^{51} - 64 q^{53} + 80 q^{56} + 2 q^{58} - 36 q^{60} + 10 q^{63} + 72 q^{64} - 8 q^{67} - 26 q^{70} + 68 q^{71} - 10 q^{72} + 80 q^{74} + 90 q^{77} - 72 q^{78} + 40 q^{79} - 16 q^{81} + 60 q^{84} - 40 q^{85} - 62 q^{86} + 140 q^{88} + 54 q^{91} + 18 q^{92} - 20 q^{93} + 20 q^{95} - 4 q^{99}+O(q^{100}) \) 64 * q + 12 * q^4 + 10 * q^7 - 20 * q^8 + 16 * q^9 - 16 * q^11 + 12 * q^14 - 12 * q^15 - 16 * q^16 + 10 * q^18 - 40 * q^22 - 24 * q^23 + 44 * q^25 - 30 * q^28 - 40 * q^29 - 40 * q^35 - 12 * q^36 + 32 * q^37 - 2 * q^42 + 22 * q^44 - 70 * q^46 - 50 * q^49 - 40 * q^51 - 64 * q^53 + 80 * q^56 + 2 * q^58 - 36 * q^60 + 10 * q^63 + 72 * q^64 - 8 * q^67 - 26 * q^70 + 68 * q^71 - 10 * q^72 + 80 * q^74 + 90 * q^77 - 72 * q^78 + 40 * q^79 - 16 * q^81 + 60 * q^84 - 40 * q^85 - 62 * q^86 + 140 * q^88 + 54 * q^91 + 18 * q^92 - 20 * q^93 + 20 * q^95 - 4 * q^99

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