LMFDB - Embedded newform 840.2.e.d.491.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [840,2,Mod(491,840)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(840, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1, 0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("840.491"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	840.e (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [44,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$6.70743376979$
Analytic rank:	$0$
Dimension:	$44$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			491.13
Character	$\chi$	$=$	840.491
Dual form			840.2.e.d.491.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.537216 - 1.30820i) q^{2} +(1.51567 + 0.838298i) q^{3} +(-1.42280 + 1.40558i) q^{4} -1.00000 q^{5} +(0.282422 - 2.43315i) q^{6} +1.00000i q^{7} +(2.60313 + 1.10621i) q^{8} +(1.59451 + 2.54117i) q^{9} +(0.537216 + 1.30820i) q^{10} -5.44156i q^{11} +(-3.33478 + 0.937663i) q^{12} +6.30076i q^{13} +(1.30820 - 0.537216i) q^{14} +(-1.51567 - 0.838298i) q^{15} +(0.0487085 - 3.99970i) q^{16} +5.38646i q^{17} +(2.46777 - 3.45111i) q^{18} +0.450936 q^{19} +(1.42280 - 1.40558i) q^{20} +(-0.838298 + 1.51567i) q^{21} +(-7.11868 + 2.92330i) q^{22} -2.17353 q^{23} +(3.01815 + 3.85885i) q^{24} +1.00000 q^{25} +(8.24269 - 3.38487i) q^{26} +(0.286506 + 5.18825i) q^{27} +(-1.40558 - 1.42280i) q^{28} -2.44547 q^{29} +(-0.282422 + 2.43315i) q^{30} +7.36749i q^{31} +(-5.25860 + 2.08498i) q^{32} +(4.56165 - 8.24762i) q^{33} +(7.04659 - 2.89369i) q^{34} -1.00000i q^{35} +(-5.84048 - 1.37435i) q^{36} +0.165494i q^{37} +(-0.242250 - 0.589917i) q^{38} +(-5.28191 + 9.54988i) q^{39} +(-2.60313 - 1.10621i) q^{40} +1.95075i q^{41} +(2.43315 + 0.282422i) q^{42} +11.0522 q^{43} +(7.64854 + 7.74225i) q^{44} +(-1.59451 - 2.54117i) q^{45} +(1.16766 + 2.84342i) q^{46} +4.57724 q^{47} +(3.42677 - 6.02140i) q^{48} -1.00000 q^{49} +(-0.537216 - 1.30820i) q^{50} +(-4.51546 + 8.16410i) q^{51} +(-8.85621 - 8.96471i) q^{52} +6.44585 q^{53} +(6.63337 - 3.16202i) q^{54} +5.44156i q^{55} +(-1.10621 + 2.60313i) q^{56} +(0.683471 + 0.378019i) q^{57} +(1.31375 + 3.19918i) q^{58} +12.1236i q^{59} +(3.33478 - 0.937663i) q^{60} -3.72274i q^{61} +(9.63819 - 3.95793i) q^{62} +(-2.54117 + 1.59451i) q^{63} +(5.55259 + 5.75923i) q^{64} -6.30076i q^{65} +(-13.2402 - 1.53682i) q^{66} +3.23021 q^{67} +(-7.57108 - 7.66385i) q^{68} +(-3.29436 - 1.82207i) q^{69} +(-1.30820 + 0.537216i) q^{70} -1.24334 q^{71} +(1.33966 + 8.37886i) q^{72} -15.6470 q^{73} +(0.216500 - 0.0889060i) q^{74} +(1.51567 + 0.838298i) q^{75} +(-0.641591 + 0.633825i) q^{76} +5.44156 q^{77} +(15.3307 + 1.77948i) q^{78} -5.02829i q^{79} +(-0.0487085 + 3.99970i) q^{80} +(-3.91505 + 8.10385i) q^{81} +(2.55198 - 1.04797i) q^{82} +9.16060i q^{83} +(-0.937663 - 3.33478i) q^{84} -5.38646i q^{85} +(-5.93743 - 14.4586i) q^{86} +(-3.70653 - 2.05003i) q^{87} +(6.01953 - 14.1651i) q^{88} -1.11292i q^{89} +(-2.46777 + 3.45111i) q^{90} -6.30076 q^{91} +(3.09250 - 3.05506i) q^{92} +(-6.17615 + 11.1667i) q^{93} +(-2.45897 - 5.98796i) q^{94} -0.450936 q^{95} +(-9.71814 - 1.24812i) q^{96} +6.10287 q^{97} +(0.537216 + 1.30820i) q^{98} +(13.8279 - 8.67665i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 2 q^{2} + 4 q^{3} - 2 q^{4} - 44 q^{5} - 6 q^{6} - 22 q^{8} + 4 q^{9} - 2 q^{10} + 6 q^{12} + 4 q^{14} - 4 q^{15} + 22 q^{16} + 2 q^{18} + 16 q^{19} + 2 q^{20} + 16 q^{23} + 10 q^{24} + 44 q^{25}+ \cdots - 64 q^{99}+O(q^{100}) $ 44 * q + 2 * q^2 + 4 * q^3 - 2 * q^4 - 44 * q^5 - 6 * q^6 - 22 * q^8 + 4 * q^9 - 2 * q^10 + 6 * q^12 + 4 * q^14 - 4 * q^15 + 22 * q^16 + 2 * q^18 + 16 * q^19 + 2 * q^20 + 16 * q^23 + 10 * q^24 + 44 * q^25 - 16 * q^26 + 4 * q^27 + 16 * q^29 + 6 * q^30 - 18 * q^32 + 24 * q^33 + 20 * q^34 - 46 * q^36 + 8 * q^38 - 16 * q^39 + 22 * q^40 - 4 * q^42 + 24 * q^43 + 32 * q^44 - 4 * q^45 - 24 * q^47 + 18 * q^48 - 44 * q^49 + 2 * q^50 - 20 * q^52 - 32 * q^53 + 2 * q^54 + 8 * q^56 - 4 * q^58 - 6 * q^60 + 32 * q^62 - 50 * q^64 - 8 * q^66 + 24 * q^67 - 28 * q^68 - 8 * q^69 - 4 * q^70 + 8 * q^71 + 2 * q^72 + 8 * q^73 - 48 * q^74 + 4 * q^75 + 12 * q^76 + 8 * q^77 - 84 * q^78 - 22 * q^80 + 20 * q^81 - 8 * q^82 + 4 * q^84 - 4 * q^86 - 16 * q^87 - 28 * q^88 - 2 * q^90 - 16 * q^91 + 76 * q^92 + 16 * q^93 - 16 * q^95 + 38 * q^96 + 24 * q^97 - 2 * q^98 - 64 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$1$	$-1$	$1$	$-1$	$-1$

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 $

$2$	−0.537216	−	1.30820i	−0.379869	−	0.925040i
$2$	−0.537216	−	1.30820i	−0.379869	−	0.925040i
$3$	1.51567	+	0.838298i	0.875073	+	0.483991i
$3$	1.51567	+	0.838298i	0.875073	+	0.483991i
$4$	−1.42280	+	1.40558i	−0.711399	+	0.702788i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	0.282422	−	2.43315i	0.115298	−	0.993331i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	2.60313	+	1.10621i	0.920346	+	0.391105i
$9$	1.59451	+	2.54117i	0.531505	+	0.847055i
$10$	0.537216	+	1.30820i	0.169883	+	0.413691i
$11$		−	5.44156i		−	1.64069i	−0.571867	−	0.820347i	$-0.693780\pi$
$11$		−	5.44156i		−	1.64069i	0.571867	−	0.820347i	$-0.306220\pi$
$12$	−3.33478	+	0.937663i	−0.962669	+	0.270680i
$13$			6.30076i			1.74752i	0.486360	+	0.873759i	$0.338324\pi$
$13$			6.30076i			1.74752i	−0.486360	+	0.873759i	$0.661676\pi$
$14$	1.30820	−	0.537216i	0.349632	−	0.143577i
$15$	−1.51567	−	0.838298i	−0.391344	−	0.216447i
$16$	0.0487085	−	3.99970i	0.0121771	−	0.999926i
$17$			5.38646i			1.30641i	0.757182	+	0.653204i	$0.226576\pi$
$17$			5.38646i			1.30641i	−0.757182	+	0.653204i	$0.773424\pi$
$18$	2.46777	−	3.45111i	0.581658	−	0.813433i
$19$	0.450936			0.103452			0.0517259	−	0.998661i	$-0.483528\pi$
$19$	0.450936			0.103452			0.0517259	+	0.998661i	$0.483528\pi$
$20$	1.42280	−	1.40558i	0.318147	−	0.314296i
$21$	−0.838298	+	1.51567i	−0.182932	+	0.330746i
$22$	−7.11868	+	2.92330i	−1.51771	+	0.623249i
$23$	−2.17353			−0.453213			−0.226606	−	0.973986i	$-0.572763\pi$
$23$	−2.17353			−0.453213			−0.226606	+	0.973986i	$0.572763\pi$
$24$	3.01815	+	3.85885i	0.616078	+	0.787685i
$25$	1.00000			0.200000
$26$	8.24269	−	3.38487i	1.61652	−	0.663828i
$27$	0.286506	+	5.18825i	0.0551381	+	0.998479i
$28$	−1.40558	−	1.42280i	−0.265629	−	0.268884i
$29$	−2.44547			−0.454113			−0.227056	−	0.973882i	$-0.572910\pi$
$29$	−2.44547			−0.454113			−0.227056	+	0.973882i	$0.572910\pi$
$30$	−0.282422	+	2.43315i	−0.0515630	+	0.444231i
$31$			7.36749i			1.32324i	0.749839	+	0.661620i	$0.230131\pi$
$31$			7.36749i			1.32324i	−0.749839	+	0.661620i	$0.769869\pi$
$32$	−5.25860	+	2.08498i	−0.929597	+	0.368577i
$33$	4.56165	−	8.24762i	0.794081	−	1.43573i
$34$	7.04659	−	2.89369i	1.20848	−	0.496264i
$35$		−	1.00000i		−	0.169031i
$36$	−5.84048	−	1.37435i	−0.973413	−	0.229059i
$37$			0.165494i			0.0272070i	0.999907	+	0.0136035i	$0.00433027\pi$
$37$			0.165494i			0.0272070i	−0.999907	+	0.0136035i	$0.995670\pi$
$38$	−0.242250	−	0.589917i	−0.0392981	−	0.0956971i
$39$	−5.28191	+	9.54988i	−0.845783	+	1.52920i
$40$	−2.60313	−	1.10621i	−0.411591	−	0.174908i
$41$			1.95075i			0.304656i	0.988330	+	0.152328i	$0.0486770\pi$
$41$			1.95075i			0.304656i	−0.988330	+	0.152328i	$0.951323\pi$
$42$	2.43315	+	0.282422i	0.375444	+	0.0435787i
$43$	11.0522			1.68545			0.842724	−	0.538346i	$-0.180951\pi$
$43$	11.0522			1.68545			0.842724	+	0.538346i	$0.180951\pi$
$44$	7.64854	+	7.74225i	1.15306	+	1.16719i
$45$	−1.59451	−	2.54117i	−0.237696	−	0.378815i
$46$	1.16766	+	2.84342i	0.172161	+	0.419240i
$47$	4.57724			0.667659			0.333829	−	0.942634i	$-0.391659\pi$
$47$	4.57724			0.667659			0.333829	+	0.942634i	$0.391659\pi$
$48$	3.42677	−	6.02140i	0.494611	−	0.869114i
$49$	−1.00000			−0.142857
$50$	−0.537216	−	1.30820i	−0.0759738	−	0.185008i
$51$	−4.51546	+	8.16410i	−0.632290	+	1.14320i
$52$	−8.85621	−	8.96471i	−1.22813	−	1.24318i
$53$	6.44585			0.885406			0.442703	−	0.896668i	$-0.354020\pi$
$53$	6.44585			0.885406			0.442703	+	0.896668i	$0.354020\pi$
$54$	6.63337	−	3.16202i	0.902688	−	0.430296i
$55$			5.44156i			0.733740i
$56$	−1.10621	+	2.60313i	−0.147824	+	0.347858i
$57$	0.683471	+	0.378019i	0.0905279	+	0.0500698i
$58$	1.31375	+	3.19918i	0.172503	+	0.420072i
$59$			12.1236i			1.57836i	0.614159	+	0.789182i	$0.289495\pi$
$59$			12.1236i			1.57836i	−0.614159	+	0.789182i	$0.710505\pi$
$60$	3.33478	−	0.937663i	0.430519	−	0.121052i
$61$		−	3.72274i		−	0.476648i	−0.971186	−	0.238324i	$-0.923402\pi$
$61$		−	3.72274i		−	0.476648i	0.971186	−	0.238324i	$-0.0765980\pi$
$62$	9.63819	−	3.95793i	1.22405	−	0.502658i
$63$	−2.54117	+	1.59451i	−0.320157	+	0.200890i
$64$	5.55259	+	5.75923i	0.694073	+	0.719904i
$65$		−	6.30076i		−	0.781514i
$66$	−13.2402	−	1.53682i	−1.62975	−	0.189169i
$67$	3.23021			0.394633			0.197317	−	0.980340i	$-0.436777\pi$
$67$	3.23021			0.394633			0.197317	+	0.980340i	$0.436777\pi$
$68$	−7.57108	−	7.66385i	−0.918129	−	0.929378i
$69$	−3.29436	−	1.82207i	−0.396594	−	0.219351i
$70$	−1.30820	+	0.537216i	−0.156360	+	0.0642096i
$71$	−1.24334			−0.147557			−0.0737787	−	0.997275i	$-0.523506\pi$
$71$	−1.24334			−0.147557			−0.0737787	+	0.997275i	$0.523506\pi$
$72$	1.33966	+	8.37886i	0.157881	+	0.987458i
$73$	−15.6470			−1.83134			−0.915669	−	0.401933i	$-0.868338\pi$
$73$	−15.6470			−1.83134			−0.915669	+	0.401933i	$0.868338\pi$
$74$	0.216500	−	0.0889060i	0.0251676	−	0.0103351i
$75$	1.51567	+	0.838298i	0.175015	+	0.0967983i
$76$	−0.641591	+	0.633825i	−0.0735955	+	0.0727047i
$77$	5.44156			0.620124
$78$	15.3307	+	1.77948i	1.73586	+	0.201486i
$79$		−	5.02829i		−	0.565726i	−0.959160	−	0.282863i	$-0.908716\pi$
$79$		−	5.02829i		−	0.565726i	0.959160	−	0.282863i	$-0.0912842\pi$
$80$	−0.0487085	+	3.99970i	−0.00544577	+	0.447180i
$81$	−3.91505	+	8.10385i	−0.435005	+	0.900428i
$82$	2.55198	−	1.04797i	0.281819	−	0.115729i
$83$			9.16060i			1.00551i	0.864430	+	0.502753i	$0.167680\pi$
$83$			9.16060i			1.00551i	−0.864430	+	0.502753i	$0.832320\pi$
$84$	−0.937663	−	3.33478i	−0.102307	−	0.363855i
$85$		−	5.38646i		−	0.584244i
$86$	−5.93743	−	14.4586i	−0.640249	−	1.55911i
$87$	−3.70653	−	2.05003i	−0.397382	−	0.219786i
$88$	6.01953	−	14.1651i	0.641684	−	1.51001i
$89$		−	1.11292i		−	0.117970i	−0.998259	−	0.0589848i	$-0.981214\pi$
$89$		−	1.11292i		−	0.117970i	0.998259	−	0.0589848i	$-0.0187864\pi$
$90$	−2.46777	+	3.45111i	−0.260125	+	0.363779i
$91$	−6.30076			−0.660499
$92$	3.09250	−	3.05506i	0.322415	−	0.318512i
$93$	−6.17615	+	11.1667i	−0.640437	+	1.15793i
$94$	−2.45897	−	5.98796i	−0.253623	−	0.617611i
$95$	−0.450936			−0.0462651
$96$	−9.71814	−	1.24812i	−0.991853	−	0.127386i
$97$	6.10287			0.619653			0.309827	−	0.950793i	$-0.399729\pi$
$97$	6.10287			0.619653			0.309827	+	0.950793i	$0.399729\pi$
$98$	0.537216	+	1.30820i	0.0542670	+	0.132149i
$99$	13.8279	−	8.67665i	1.38976	−	0.872036i
$100$	−1.42280	+	1.40558i	−0.142280	+	0.140558i
$101$	1.28684			0.128046			0.0640229	−	0.997948i	$-0.479607\pi$
$101$	1.28684			0.128046			0.0640229	+	0.997948i	$0.479607\pi$
$102$	13.1061	+	1.52126i	1.29770	+	0.150627i
$103$		−	14.3515i		−	1.41409i	−0.707167	−	0.707046i	$-0.750027\pi$
$103$		−	14.3515i		−	1.41409i	0.707167	−	0.707046i	$-0.249973\pi$
$104$	−6.96998	+	16.4017i	−0.683463	+	1.60832i
$105$	0.838298	−	1.51567i	0.0818095	−	0.147914i
$106$	−3.46281	−	8.43249i	−0.336338	−	0.819036i
$107$		−	15.1898i		−	1.46845i	−0.678906	−	0.734225i	$-0.737545\pi$
$107$		−	15.1898i		−	1.46845i	0.678906	−	0.734225i	$-0.262455\pi$
$108$	−7.70012	−	6.97912i	−0.740944	−	0.671566i
$109$		−	8.89022i		−	0.851529i	−0.904834	−	0.425764i	$-0.860005\pi$
$109$		−	8.89022i		−	0.851529i	0.904834	−	0.425764i	$-0.139995\pi$
$110$	7.11868	−	2.92330i	0.678739	−	0.278725i
$111$	−0.138733	+	0.250834i	−0.0131680	+	0.0238081i
$112$	3.99970	+	0.0487085i	0.377936	+	0.00460252i
$113$			8.28028i			0.778943i	0.921039	+	0.389472i	$0.127342\pi$
$113$			8.28028i			0.778943i	−0.921039	+	0.389472i	$0.872658\pi$
$114$	0.127354	−	1.09720i	0.0119278	−	0.102762i
$115$	2.17353			0.202683
$116$	3.47941	−	3.43730i	0.323055	−	0.319145i
$117$	−16.0113	+	10.0467i	−1.48024	+	0.928814i
$118$	15.8602	−	6.51302i	1.46005	−	0.599572i
$119$	−5.38646			−0.493776
$120$	−3.01815	−	3.85885i	−0.275519	−	0.352263i
$121$	−18.6106			−1.69187
$122$	−4.87010	+	1.99991i	−0.440918	+	0.181064i
$123$	−1.63531	+	2.95669i	−0.147451	+	0.266596i
$124$	−10.3556	−	10.4825i	−0.929958	−	0.941352i
$125$	−1.00000			−0.0894427
$126$	3.45111	+	2.46777i	0.307449	+	0.219846i
$127$		−	5.57578i		−	0.494770i	−0.968917	−	0.247385i	$-0.920429\pi$
$127$		−	5.57578i		−	0.494770i	0.968917	−	0.247385i	$-0.0795713\pi$
$128$	4.55132	−	10.3579i	0.402283	−	0.915515i
$129$	16.7515	+	9.26505i	1.47489	+	0.815742i
$130$	−8.24269	+	3.38487i	−0.722931	+	0.296873i
$131$		−	13.1854i		−	1.15201i	−0.817445	−	0.576007i	$-0.804610\pi$
$131$		−	13.1854i		−	1.15201i	0.817445	−	0.576007i	$-0.195390\pi$
$132$	5.10235	+	18.1464i	0.444103	+	1.57945i
$133$			0.450936i			0.0391011i
$134$	−1.73532	−	4.22578i	−0.149909	−	0.365052i
$135$	−0.286506	−	5.18825i	−0.0246585	−	0.446533i
$136$	−5.95857	+	14.0217i	−0.510943	+	1.20235i
$137$		−	1.82188i		−	0.155654i	−0.996967	−	0.0778269i	$-0.975202\pi$
$137$		−	1.82188i		−	0.155654i	0.996967	−	0.0778269i	$-0.0247981\pi$
$138$	−0.613853	+	5.28854i	−0.0522547	+	0.450190i
$139$	2.81981			0.239173			0.119586	−	0.992824i	$-0.461843\pi$
$139$	2.81981			0.239173			0.119586	+	0.992824i	$0.461843\pi$
$140$	1.40558	+	1.42280i	0.118793	+	0.120248i
$141$	6.93759	+	3.83709i	0.584250	+	0.323141i
$142$	0.667942	+	1.62654i	0.0560525	+	0.136496i
$143$	34.2860			2.86714
$144$	10.2416	−	6.25381i	0.853465	−	0.521151i
$145$	2.44547			0.203085
$146$	8.40580	+	20.4694i	0.695669	+	1.69406i
$147$	−1.51567	−	0.838298i	−0.125010	−	0.0691416i
$148$	−0.232614	−	0.235464i	−0.0191208	−	0.0193551i
$149$	22.1243			1.81249			0.906246	−	0.422751i	$-0.138935\pi$
$149$	22.1243			1.81249			0.906246	+	0.422751i	$0.138935\pi$
$150$	0.282422	−	2.43315i	0.0230597	−	0.198666i
$151$			5.15119i			0.419198i	0.977787	+	0.209599i	$0.0672159\pi$
$151$			5.15119i			0.419198i	−0.977787	+	0.209599i	$0.932784\pi$
$152$	1.17385	+	0.498831i	0.0952115	+	0.0404605i
$153$	−13.6879	+	8.58879i	−1.10660	+	0.694363i
$154$	−2.92330	−	7.11868i	−0.235566	−	0.573639i
$155$		−	7.36749i		−	0.591771i
$156$	−5.90799	−	21.0117i	−0.473018	−	1.68228i
$157$		−	24.1605i		−	1.92822i	−0.265501	−	0.964110i	$-0.585537\pi$
$157$		−	24.1605i		−	1.92822i	0.265501	−	0.964110i	$-0.414463\pi$
$158$	−6.57803	+	2.70128i	−0.523320	+	0.214902i
$159$	9.76979	+	5.40354i	0.774795	+	0.428529i
$160$	5.25860	−	2.08498i	0.415729	−	0.164832i
$161$		−	2.17353i		−	0.171298i
$162$	12.7047	+	0.768163i	0.998177	+	0.0603526i
$163$	11.6705			0.914107			0.457054	−	0.889439i	$-0.348905\pi$
$163$	11.6705			0.914107			0.457054	+	0.889439i	$0.348905\pi$
$164$	−2.74193	−	2.77552i	−0.214109	−	0.216732i
$165$	−4.56165	+	8.24762i	−0.355124	+	0.642076i
$166$	11.9839	−	4.92122i	0.930134	−	0.381961i
$167$	−8.23086			−0.636923			−0.318462	−	0.947936i	$-0.603166\pi$
$167$	−8.23086			−0.636923			−0.318462	+	0.947936i	$0.603166\pi$
$168$	−3.85885	+	3.01815i	−0.297717	+	0.232856i
$169$	−26.6996			−2.05382
$170$	−7.04659	+	2.89369i	−0.540449	+	0.221936i
$171$	0.719024	+	1.14590i	0.0549851	+	0.0876294i
$172$	−15.7251	+	15.5347i	−1.19903	+	1.18451i
$173$	−17.9203			−1.36246			−0.681229	−	0.732070i	$-0.738554\pi$
$173$	−17.9203			−1.36246			−0.681229	+	0.732070i	$0.738554\pi$
$174$	−0.690655	+	5.95021i	−0.0523584	+	0.451084i
$175$			1.00000i			0.0755929i
$176$	−21.7646	−	0.265050i	−1.64057	−	0.0199789i
$177$	−10.1632	+	18.3755i	−0.763914	+	1.38118i
$178$	−1.45593	+	0.597880i	−0.109127	+	0.0448130i
$179$		−	3.42976i		−	0.256352i	−0.991751	−	0.128176i	$-0.959088\pi$
$179$		−	3.42976i		−	0.256352i	0.991751	−	0.128176i	$-0.0409123\pi$
$180$	5.84048	+	1.37435i	0.435323	+	0.102438i
$181$		−	20.0077i		−	1.48716i	−0.668646	−	0.743581i	$-0.733126\pi$
$181$		−	20.0077i		−	1.48716i	0.668646	−	0.743581i	$-0.266874\pi$
$182$	3.38487	+	8.24269i	0.250903	+	0.610989i
$183$	3.12076	−	5.64244i	0.230693	−	0.417101i
$184$	−5.65799	−	2.40439i	−0.417112	−	0.177254i
$185$		−	0.165494i		−	0.0121674i
$186$	17.9262	+	2.08074i	1.31442	+	0.152567i
$187$	29.3108			2.14342
$188$	−6.51249	+	6.43366i	−0.474972	+	0.469223i
$189$	−5.18825	+	0.286506i	−0.377389	+	0.0208402i
$190$	0.242250	+	0.589917i	0.0175747	+	0.0427970i
$191$	−19.7644			−1.43010			−0.715052	−	0.699072i	$-0.753597\pi$
$191$	−19.7644			−1.43010			−0.715052	+	0.699072i	$0.753597\pi$
$192$	3.58794	+	13.3838i	0.258937	+	0.965894i
$193$	8.55215			0.615597			0.307798	−	0.951452i	$-0.400408\pi$
$193$	8.55215			0.615597			0.307798	+	0.951452i	$0.400408\pi$
$194$	−3.27856	−	7.98381i	−0.235387	−	0.573204i
$195$	5.28191	−	9.54988i	0.378246	−	0.683881i
$196$	1.42280	−	1.40558i	0.101628	−	0.100398i
$197$	−7.82139			−0.557251			−0.278625	−	0.960400i	$-0.589879\pi$
$197$	−7.82139			−0.557251			−0.278625	+	0.960400i	$0.589879\pi$
$198$	−18.7794	−	13.4285i	−1.33459	−	0.954322i
$199$			9.39557i			0.666035i	0.942921	+	0.333017i	$0.108067\pi$
$199$			9.39557i			0.666035i	−0.942921	+	0.333017i	$0.891933\pi$
$200$	2.60313	+	1.10621i	0.184069	+	0.0782210i
$201$	4.89594	+	2.70788i	0.345333	+	0.190999i
$202$	−0.691313	−	1.68345i	−0.0486406	−	0.118447i
$203$		−	2.44547i		−	0.171638i
$204$	−5.05069	−	17.9627i	−0.353619	−	1.25764i
$205$		−	1.95075i		−	0.136246i
$206$	−18.7747	+	7.70984i	−1.30809	+	0.537170i
$207$	−3.46573	−	5.52330i	−0.240885	−	0.383896i
$208$	25.2012	+	0.306901i	1.74739	+	0.0212797i
$209$		−	2.45380i		−	0.169733i
$210$	−2.43315	−	0.282422i	−0.167904	−	0.0194890i
$211$	−9.09833			−0.626355			−0.313178	−	0.949695i	$-0.601393\pi$
$211$	−9.09833			−0.626355			−0.313178	+	0.949695i	$0.601393\pi$
$212$	−9.17115	+	9.06014i	−0.629877	+	0.622253i
$213$	−1.88449	−	1.04229i	−0.129123	−	0.0714165i
$214$	−19.8713	+	8.16019i	−1.35838	+	0.557819i
$215$	−11.0522			−0.753755
$216$	−4.99349	+	13.8226i	−0.339764	+	0.940511i
$217$	−7.36749			−0.500138
$218$	−11.6302	+	4.77597i	−0.787699	+	0.323469i
$219$	−23.7156	−	13.1168i	−1.60255	−	0.886352i
$220$	−7.64854	−	7.74225i	−0.515664	−	0.521982i
$221$	−33.9388			−2.28297
$222$	0.402672	+	0.0467392i	0.0270256	+	0.00313693i
$223$			7.37577i			0.493918i	0.969026	+	0.246959i	$0.0794313\pi$
$223$			7.37577i			0.493918i	−0.969026	+	0.246959i	$0.920569\pi$
$224$	−2.08498	−	5.25860i	−0.139309	−	0.351355i
$225$	1.59451	+	2.54117i	0.106301	+	0.169411i
$226$	10.8323	−	4.44830i	0.720554	−	0.295896i
$227$			12.0258i			0.798180i	0.916912	+	0.399090i	$0.130674\pi$
$227$			12.0258i			0.798180i	−0.916912	+	0.399090i	$0.869326\pi$
$228$	−1.50377	+	0.422826i	−0.0995899	+	0.0280023i
$229$		−	1.33389i		−	0.0881456i	−0.999028	−	0.0440728i	$-0.985967\pi$
$229$		−	1.33389i		−	0.0881456i	0.999028	−	0.0440728i	$-0.0140334\pi$
$230$	−1.16766	−	2.84342i	−0.0769929	−	0.187490i
$231$	8.24762	+	4.56165i	0.542653	+	0.300135i
$232$	−6.36588	−	2.70521i	−0.417941	−	0.177606i
$233$			16.3168i			1.06895i	0.845184	+	0.534475i	$0.179491\pi$
$233$			16.3168i			1.06895i	−0.845184	+	0.534475i	$0.820509\pi$
$234$	21.7446	+	15.5488i	1.42149	+	1.01646i
$235$	−4.57724			−0.298586
$236$	−17.0407	−	17.2495i	−1.10926	−	1.12285i
$237$	4.21520	−	7.62123i	0.273807	−	0.495052i
$238$	2.89369	+	7.04659i	0.187570	+	0.456763i
$239$	−5.45208			−0.352665			−0.176333	−	0.984331i	$-0.556423\pi$
$239$	−5.45208			−0.352665			−0.176333	+	0.984331i	$0.556423\pi$
$240$	−3.42677	+	6.02140i	−0.221197	+	0.388680i
$241$	−7.02214			−0.452336			−0.226168	−	0.974088i	$-0.572620\pi$
$241$	−7.02214			−0.452336			−0.226168	+	0.974088i	$0.572620\pi$
$242$	9.99792	+	24.3465i	0.642691	+	1.56505i
$243$	−12.7274	+	9.00080i	−0.816460	+	0.577401i
$244$	5.23259	+	5.29670i	0.334982	+	0.339087i
$245$	1.00000			0.0638877
$246$	4.74647	+	0.550935i	0.302624	+	0.0351263i
$247$			2.84124i			0.180784i
$248$	−8.15001	+	19.1786i	−0.517526	+	1.21784i
$249$	−7.67931	+	13.8845i	−0.486656	+	0.879891i
$250$	0.537216	+	1.30820i	0.0339765	+	0.0827381i
$251$		−	15.8047i		−	0.997581i	−0.866723	−	0.498791i	$-0.833778\pi$
$251$		−	15.8047i		−	0.997581i	0.866723	−	0.498791i	$-0.166222\pi$
$252$	1.37435	−	5.84048i	0.0865761	−	0.367915i
$253$			11.8274i			0.743583i
$254$	−7.29426	+	2.99540i	−0.457682	+	0.187948i
$255$	4.51546	−	8.16410i	0.282769	−	0.511256i
$256$	−15.9953	−	0.389639i	−0.999703	−	0.0243524i
$257$		−	3.11771i		−	0.194477i	−0.995261	−	0.0972386i	$-0.968999\pi$
$257$		−	3.11771i		−	0.194477i	0.995261	−	0.0972386i	$-0.0310010\pi$
$258$	3.12139	−	26.8917i	0.194329	−	1.67421i
$259$	−0.165494			−0.0102833
$260$	8.85621	+	8.96471i	0.549239	+	0.555968i
$261$	−3.89934	−	6.21435i	−0.241363	−	0.384658i
$262$	−17.2492	+	7.08341i	−1.06566	+	0.437615i
$263$	19.5713			1.20682			0.603408	−	0.797433i	$-0.293809\pi$
$263$	19.5713			1.20682			0.603408	+	0.797433i	$0.293809\pi$
$264$	20.9982	−	16.4235i	1.29235	−	1.01080i
$265$	−6.44585			−0.395966
$266$	0.589917	−	0.242250i	0.0361701	−	0.0148533i
$267$	0.932961	−	1.68683i	0.0570963	−	0.103232i
$268$	−4.59594	+	4.54031i	−0.280742	+	0.277344i
$269$	1.80334			0.109951			0.0549757	−	0.998488i	$-0.482492\pi$
$269$	1.80334			0.109951			0.0549757	+	0.998488i	$0.482492\pi$
$270$	−6.63337	+	3.16202i	−0.403694	+	0.192434i
$271$			31.2148i			1.89616i	0.318029	+	0.948081i	$0.396979\pi$
$271$			31.2148i			1.89616i	−0.318029	+	0.948081i	$0.603021\pi$
$272$	21.5442	+	0.262366i	1.30631	+	0.0159083i
$273$	−9.54988	−	5.28191i	−0.577985	−	0.319676i
$274$	−2.38339	+	0.978743i	−0.143986	+	0.0591280i
$275$		−	5.44156i		−	0.328139i
$276$	7.24826	−	2.03804i	0.436294	−	0.122676i
$277$		−	16.5075i		−	0.991839i	−0.868369	−	0.495919i	$-0.834831\pi$
$277$		−	16.5075i		−	0.991839i	0.868369	−	0.495919i	$-0.165169\pi$
$278$	−1.51484	−	3.68888i	−0.0908544	−	0.221244i
$279$	−18.7220	+	11.7476i	−1.12086	+	0.703309i
$280$	1.10621	−	2.60313i	0.0661088	−	0.155567i
$281$		−	27.0180i		−	1.61176i	−0.592080	−	0.805879i	$-0.701693\pi$
$281$		−	27.0180i		−	1.61176i	0.592080	−	0.805879i	$-0.298307\pi$
$282$	1.29271	−	11.1371i	0.0769800	−	0.663206i
$283$	30.7294			1.82667			0.913337	−	0.407204i	$-0.133496\pi$
$283$	30.7294			1.82667			0.913337	+	0.407204i	$0.133496\pi$
$284$	1.76902	−	1.74761i	0.104972	−	0.103702i
$285$	−0.683471	−	0.378019i	−0.0404853	−	0.0223919i
$286$	−18.4190	−	44.8531i	−1.08914	−	2.65222i
$287$	−1.95075			−0.115149
$288$	−13.6832	−	10.0384i	−0.806290	−	0.591520i
$289$	−12.0140			−0.706704
$290$	−1.31375	−	3.19918i	−0.0771458	−	0.187862i
$291$	9.24995	+	5.11602i	0.542242	+	0.299907i
$292$	22.2625	−	21.9930i	1.30281	−	1.28704i
$293$	−15.8032			−0.923233			−0.461617	−	0.887079i	$-0.652730\pi$
$293$	−15.8032			−0.923233			−0.461617	+	0.887079i	$0.652730\pi$
$294$	−0.282422	+	2.43315i	−0.0164712	+	0.141904i
$295$		−	12.1236i		−	0.705866i
$296$	−0.183071	+	0.430803i	−0.0106408	+	0.0250399i
$297$	28.2322	−	1.55904i	1.63820	−	0.0904647i
$298$	−11.8855	−	28.9431i	−0.688510	−	1.67663i
$299$		−	13.6949i		−	0.791997i
$300$	−3.33478	+	0.937663i	−0.192534	+	0.0541360i
$301$			11.0522i			0.637039i
$302$	6.73881	−	2.76730i	0.387775	−	0.159240i
$303$	1.95043	+	1.07876i	0.112049	+	0.0619730i
$304$	0.0219644	−	1.80361i	0.00125975	−	0.103444i
$305$			3.72274i			0.213163i
$306$	18.5892	+	13.2925i	1.06268	+	0.759883i
$307$	14.2385			0.812634			0.406317	−	0.913732i	$-0.366813\pi$
$307$	14.2385			0.812634			0.406317	+	0.913732i	$0.366813\pi$
$308$	−7.74225	+	7.64854i	−0.441155	+	0.435816i
$309$	12.0308	−	21.7521i	0.684409	−	1.23743i
$310$	−9.63819	+	3.95793i	−0.547412	+	0.224796i
$311$	33.3592			1.89162			0.945812	−	0.324714i	$-0.105268\pi$
$311$	33.3592			1.89162			0.945812	+	0.324714i	$0.105268\pi$
$312$	−24.3137	+	19.0167i	−1.37649	+	1.07661i
$313$	−11.5901			−0.655113			−0.327556	−	0.944832i	$-0.606225\pi$
$313$	−11.5901			−0.655113			−0.327556	+	0.944832i	$0.606225\pi$
$314$	−31.6069	+	12.9794i	−1.78368	+	0.732471i
$315$	2.54117	−	1.59451i	0.143178	−	0.0898407i
$316$	7.06764	+	7.15424i	0.397586	+	0.402457i
$317$	31.0124			1.74183			0.870916	−	0.491432i	$-0.163526\pi$
$317$	31.0124			1.74183			0.870916	+	0.491432i	$0.163526\pi$
$318$	1.82045	−	15.6838i	0.102086	−	0.879501i
$319$			13.3072i			0.745059i
$320$	−5.55259	−	5.75923i	−0.310399	−	0.321951i
$321$	12.7336	−	23.0227i	0.710717	−	1.28500i
$322$	−2.84342	+	1.16766i	−0.158458	+	0.0650709i
$323$			2.42895i			0.135150i
$324$	−5.82026	−	17.0330i	−0.323348	−	0.946280i
$325$			6.30076i			0.349503i
$326$	−6.26960	−	15.2675i	−0.347241	−	0.845586i
$327$	7.45265	−	13.4746i	0.412133	−	0.745150i
$328$	−2.15794	+	5.07806i	−0.119153	+	0.280389i
$329$			4.57724i			0.252351i
$330$	13.2402	+	1.53682i	0.728847	+	0.0845991i
$331$	24.0577			1.32233			0.661165	−	0.750241i	$-0.270062\pi$
$331$	24.0577			1.32233			0.661165	+	0.750241i	$0.270062\pi$
$332$	−12.8759	−	13.0337i	−0.706658	−	0.715316i
$333$	−0.420548	+	0.263883i	−0.0230459	+	0.0144607i
$334$	4.42175	+	10.7677i	0.241947	+	0.589180i
$335$	−3.23021			−0.176485
$336$	6.02140	+	3.42677i	0.328494	+	0.186945i
$337$	20.1078			1.09534			0.547670	−	0.836694i	$-0.315515\pi$
$337$	20.1078			1.09534			0.547670	+	0.836694i	$0.315515\pi$
$338$	14.3435	+	34.9286i	0.780181	+	1.89986i
$339$	−6.94134	+	12.5502i	−0.377002	+	0.681632i
$340$	7.57108	+	7.66385i	0.410600	+	0.415630i
$341$	40.0907			2.17103
$342$	1.11280	−	1.55623i	0.0601736	−	0.0841512i
$343$		−	1.00000i		−	0.0539949i
$344$	28.7704	+	12.2261i	1.55119	+	0.659187i
$345$	3.29436	+	1.82207i	0.177362	+	0.0980967i
$346$	9.62709	+	23.4435i	0.517556	+	1.26033i
$347$		−	9.58609i		−	0.514608i	−0.966330	−	0.257304i	$-0.917166\pi$
$347$		−	9.58609i		−	0.514608i	0.966330	−	0.257304i	$-0.0828342\pi$
$348$	8.15512	−	2.29303i	0.437160	−	0.122919i
$349$			19.2627i			1.03111i	0.856858	+	0.515553i	$0.172414\pi$
$349$			19.2627i			1.03111i	−0.856858	+	0.515553i	$0.827586\pi$
$350$	1.30820	−	0.537216i	0.0699265	−	0.0287154i
$351$	−32.6899	+	1.80521i	−1.74486	+	0.0963548i
$352$	11.3456	+	28.6150i	0.604721	+	1.52518i
$353$			10.7547i			0.572417i	0.958167	+	0.286209i	$0.0923950\pi$
$353$			10.7547i			0.572417i	−0.958167	+	0.286209i	$0.907605\pi$
$354$	29.4987	+	3.42399i	1.56784	+	0.181983i
$355$	1.24334			0.0659896
$356$	1.56430	+	1.58347i	0.0829077	+	0.0839235i
$357$	−8.16410	−	4.51546i	−0.432090	−	0.238983i
$358$	−4.48683	+	1.84252i	−0.237136	+	0.0973803i
$359$	3.04868			0.160903			0.0804515	−	0.996759i	$-0.474364\pi$
$359$	3.04868			0.160903			0.0804515	+	0.996759i	$0.474364\pi$
$360$	−1.33966	−	8.37886i	−0.0706064	−	0.441605i
$361$	−18.7967			−0.989298
$362$	−26.1742	+	10.7485i	−1.37568	+	0.564927i
$363$	−28.2076	−	15.6012i	−1.48051	−	0.818853i
$364$	8.96471	−	8.85621i	0.469879	−	0.464191i
$365$	15.6470			0.818999
$366$	−9.05799	−	1.05138i	−0.473469	−	0.0549567i
$367$		−	26.3146i		−	1.37361i	−0.726841	−	0.686806i	$-0.759012\pi$
$367$		−	26.3146i		−	1.37361i	0.726841	−	0.686806i	$-0.240988\pi$
$368$	−0.105869	+	8.69348i	−0.00551882	+	0.453179i
$369$	−4.95718	+	3.11050i	−0.258060	+	0.161926i
$370$	−0.216500	+	0.0889060i	−0.0112553	+	0.00462200i
$371$			6.44585i			0.334652i
$372$	−6.90823	−	24.5690i	−0.358175	−	1.27384i
$373$			28.4560i			1.47340i	0.676221	+	0.736698i	$0.263616\pi$
$373$			28.4560i			1.47340i	−0.676221	+	0.736698i	$0.736384\pi$
$374$	−15.7462	−	38.3445i	−0.814217	−	1.98275i
$375$	−1.51567	−	0.838298i	−0.0782689	−	0.0432895i
$376$	11.9152	+	5.06340i	0.614477	+	0.261125i
$377$		−	15.4083i		−	0.793569i
$378$	3.16202	+	6.63337i	0.162637	+	0.341184i
$379$	−10.6033			−0.544656			−0.272328	−	0.962204i	$-0.587794\pi$
$379$	−10.6033			−0.544656			−0.272328	+	0.962204i	$0.587794\pi$
$380$	0.641591	−	0.633825i	0.0329129	−	0.0325145i
$381$	4.67416	−	8.45104i	0.239464	−	0.432960i
$382$	10.6178	+	25.8559i	0.543252	+	1.32290i
$383$	15.4881			0.791403			0.395702	−	0.918379i	$-0.370501\pi$
$383$	15.4881			0.791403			0.395702	+	0.918379i	$0.370501\pi$
$384$	15.5813	−	11.8838i	0.795129	−	0.606441i
$385$	−5.44156			−0.277328
$386$	−4.59435	−	11.1880i	−0.233846	−	0.569452i
$387$	17.6229	+	28.0855i	0.895823	+	1.42767i
$388$	−8.68316	+	8.57806i	−0.440821	+	0.435485i
$389$	15.3888			0.780243			0.390122	−	0.920763i	$-0.372433\pi$
$389$	15.3888			0.780243			0.390122	+	0.920763i	$0.372433\pi$
$390$	−15.3307	−	1.77948i	−0.776302	−	0.0901072i
$391$		−	11.7076i		−	0.592081i
$392$	−2.60313	−	1.10621i	−0.131478	−	0.0558722i
$393$	11.0533	−	19.9847i	0.557565	−	1.00810i
$394$	4.20177	+	10.2320i	0.211682	+	0.515479i
$395$			5.02829i			0.253001i
$396$	−7.47863	+	31.7813i	−0.375815	+	1.59707i
$397$		−	29.1797i		−	1.46449i	−0.681042	−	0.732245i	$-0.738473\pi$
$397$		−	29.1797i		−	1.46449i	0.681042	−	0.732245i	$-0.261527\pi$
$398$	12.2913	−	5.04745i	0.616109	−	0.253006i
$399$	−0.378019	+	0.683471i	−0.0189246	+	0.0342163i
$400$	0.0487085	−	3.99970i	0.00243542	−	0.199985i
$401$			7.49305i			0.374185i	0.982342	+	0.187093i	$0.0599065\pi$
$401$			7.49305i			0.374185i	−0.982342	+	0.187093i	$0.940094\pi$
$402$	0.912284	−	7.85960i	0.0455006	−	0.392001i
$403$	−46.4208			−2.31239
$404$	−1.83092	+	1.80876i	−0.0910916	+	0.0899890i
$405$	3.91505	−	8.10385i	0.194540	−	0.402684i
$406$	−3.19918	+	1.31375i	−0.158772	+	0.0652001i
$407$	0.900546			0.0446384
$408$	−20.7856	+	16.2572i	−1.02904	+	0.804850i
$409$	−5.43009			−0.268501			−0.134250	−	0.990947i	$-0.542863\pi$
$409$	−5.43009			−0.268501			−0.134250	+	0.990947i	$0.542863\pi$
$410$	−2.55198	+	1.04797i	−0.126033	+	0.0517557i
$411$	1.52728	−	2.76137i	0.0753350	−	0.136208i
$412$	20.1721	+	20.4193i	0.993808	+	1.00598i
$413$	−12.1236			−0.596566
$414$	−5.36377	+	7.50109i	−0.263615	+	0.368658i
$415$		−	9.16060i		−	0.449676i
$416$	−13.1370	−	33.1332i	−0.644094	−	1.62449i
$417$	4.27390	+	2.36384i	0.209294	+	0.115758i
$418$	−3.21007	+	1.31822i	−0.157010	+	0.0644762i
$419$		−	12.9501i		−	0.632655i	−0.948650	−	0.316328i	$-0.897550\pi$
$419$		−	12.9501i		−	0.632655i	0.948650	−	0.316328i	$-0.102450\pi$
$420$	0.937663	+	3.33478i	0.0457533	+	0.162721i
$421$			33.0234i			1.60946i	0.593639	+	0.804731i	$0.297691\pi$
$421$			33.0234i			1.60946i	−0.593639	+	0.804731i	$0.702309\pi$
$422$	4.88777	+	11.9025i	0.237933	+	0.579404i
$423$	7.29847	+	11.6315i	0.354864	+	0.565544i
$424$	16.7794	+	7.13048i	0.814880	+	0.346287i
$425$			5.38646i			0.261282i
$426$	−0.351147	+	3.02524i	−0.0170131	+	0.146573i
$427$	3.72274			0.180156
$428$	21.3504	+	21.6120i	1.03201	+	1.04465i
$429$	51.9663	+	28.7419i	2.50896	+	1.38767i
$430$	5.93743	+	14.4586i	0.286328	+	0.697254i
$431$	24.0536			1.15862			0.579312	−	0.815106i	$-0.303321\pi$
$431$	24.0536			1.15862			0.579312	+	0.815106i	$0.303321\pi$
$432$	20.7654	−	0.893227i	0.999076	−	0.0429754i
$433$	−11.0992			−0.533395			−0.266698	−	0.963780i	$-0.585933\pi$
$433$	−11.0992			−0.533395			−0.266698	+	0.963780i	$0.585933\pi$
$434$	3.95793	+	9.63819i	0.189987	+	0.462648i
$435$	3.70653	+	2.05003i	0.177714	+	0.0982915i
$436$	12.4959	+	12.6490i	0.598445	+	0.605777i
$437$	−0.980123			−0.0468857
$438$	−4.41905	+	38.0715i	−0.211150	+	1.81912i
$439$		−	15.3749i		−	0.733806i	−0.930259	−	0.366903i	$-0.880418\pi$
$439$		−	15.3749i		−	0.733806i	0.930259	−	0.366903i	$-0.119582\pi$
$440$	−6.01953	+	14.1651i	−0.286970	+	0.675295i
$441$	−1.59451	−	2.54117i	−0.0759293	−	0.121008i
$442$	18.2325	+	44.3989i	0.867230	+	2.11184i
$443$		−	7.53726i		−	0.358106i	−0.983839	−	0.179053i	$-0.942697\pi$
$443$		−	7.53726i		−	0.358106i	0.983839	−	0.179053i	$-0.0573034\pi$
$444$	−0.155178	−	0.551887i	−0.00736440	−	0.0261914i
$445$			1.11292i			0.0527577i
$446$	9.64901	−	3.96238i	0.456894	−	0.187624i
$447$	33.5331	+	18.5467i	1.58606	+	0.877230i
$448$	−5.75923	+	5.55259i	−0.272098	+	0.262335i
$449$			9.94711i			0.469433i	0.972064	+	0.234716i	$0.0754162\pi$
$449$			9.94711i			0.469433i	−0.972064	+	0.234716i	$0.924584\pi$
$450$	2.46777	−	3.45111i	0.116332	−	0.162687i
$451$	10.6151			0.499847
$452$	−11.6386	−	11.7812i	−0.547432	−	0.554139i
$453$	−4.31823	+	7.80751i	−0.202888	+	0.366829i
$454$	15.7322	−	6.46045i	0.738349	−	0.303204i
$455$	6.30076			0.295384
$456$	1.36099	+	1.74010i	0.0637344	+	0.0814874i
$457$	14.8038			0.692493			0.346246	−	0.938144i	$-0.387456\pi$
$457$	14.8038			0.692493			0.346246	+	0.938144i	$0.387456\pi$
$458$	−1.74500	+	0.716585i	−0.0815383	+	0.0334838i
$459$	−27.9463	+	1.54325i	−1.30442	+	0.0720329i
$460$	−3.09250	+	3.05506i	−0.144188	+	0.142443i
$461$	1.05944			0.0493431			0.0246715	−	0.999696i	$-0.492146\pi$
$461$	1.05944			0.0493431			0.0246715	+	0.999696i	$0.492146\pi$
$462$	1.53682	−	13.2402i	0.0714993	−	0.615988i
$463$		−	5.56498i		−	0.258626i	−0.991604	−	0.129313i	$-0.958723\pi$
$463$		−	5.56498i		−	0.258626i	0.991604	−	0.129313i	$-0.0412773\pi$
$464$	−0.119115	+	9.78116i	−0.00552978	+	0.454079i
$465$	6.17615	−	11.1667i	0.286412	−	0.517843i
$466$	21.3457	−	8.76565i	0.988821	−	0.406061i
$467$		−	14.3401i		−	0.663582i	−0.943353	−	0.331791i	$-0.892347\pi$
$467$		−	14.3401i		−	0.663582i	0.943353	−	0.331791i	$-0.107653\pi$
$468$	8.65947	−	36.7995i	0.400284	−	1.70106i
$469$			3.23021i			0.149157i
$470$	2.45897	+	5.98796i	0.113424	+	0.276204i
$471$	20.2537	−	36.6194i	0.933242	−	1.68733i
$472$	−13.4113	+	31.5594i	−0.617306	+	1.45264i
$473$		−	60.1414i		−	2.76530i
$474$	−12.2346	−	1.42010i	−0.561953	−	0.0652273i
$475$	0.450936			0.0206904
$476$	7.66385	−	7.57108i	0.351272	−	0.347020i
$477$	10.2780	+	16.3800i	0.470598	+	0.749988i
$478$	2.92894	+	7.13243i	0.133967	+	0.326230i
$479$	−19.9309			−0.910665			−0.455332	−	0.890321i	$-0.650480\pi$
$479$	−19.9309			−0.910665			−0.455332	+	0.890321i	$0.650480\pi$
$480$	9.71814	+	1.24812i	0.443570	+	0.0569686i
$481$	−1.04274			−0.0475448
$482$	3.77240	+	9.18639i	0.171828	+	0.418429i
$483$	1.82207	−	3.29436i	0.0829069	−	0.149898i
$484$	26.4792	−	26.1587i	1.20360	−	1.18903i
$485$	−6.10287			−0.277117
$486$	18.6122	+	11.8146i	0.844268	+	0.535922i
$487$			44.0236i			1.99490i	0.0713704	+	0.997450i	$0.477263\pi$
$487$			44.0236i			1.99490i	−0.0713704	+	0.997450i	$0.522737\pi$
$488$	4.11814	−	9.69078i	0.186419	−	0.438681i
$489$	17.6887	+	9.78339i	0.799910	+	0.442420i
$490$	−0.537216	−	1.30820i	−0.0242689	−	0.0590987i
$491$		−	38.1740i		−	1.72277i	−0.507953	−	0.861385i	$-0.669597\pi$
$491$		−	38.1740i		−	1.72277i	0.507953	−	0.861385i	$-0.330403\pi$
$492$	−1.82915	−	6.50533i	−0.0824643	−	0.293283i
$493$		−	13.1724i		−	0.593257i
$494$	3.71692	−	1.52636i	0.167232	−	0.0686742i
$495$	−13.8279	+	8.67665i	−0.621519	+	0.389987i
$496$	29.4678	+	0.358859i	1.32314	+	0.0161133i
$497$		−	1.24334i		−	0.0557714i
$498$	22.2891	+	2.58716i	0.998801	+	0.115933i
$499$	10.5612			0.472783			0.236391	−	0.971658i	$-0.424035\pi$
$499$	10.5612			0.472783			0.236391	+	0.971658i	$0.424035\pi$
$500$	1.42280	−	1.40558i	0.0636295	−	0.0628593i
$501$	−12.4753	−	6.89991i	−0.557354	−	0.308265i
$502$	−20.6757	+	8.49051i	−0.922803	+	0.378950i
$503$	15.2687			0.680796			0.340398	−	0.940281i	$-0.389438\pi$
$503$	15.2687			0.680796			0.340398	+	0.940281i	$0.389438\pi$
$504$	−8.37886	+	1.33966i	−0.373224	+	0.0596733i
$505$	−1.28684			−0.0572638
$506$	15.4727	−	6.35387i	0.687844	−	0.282464i
$507$	−40.4678	−	22.3822i	−1.79724	−	0.994029i
$508$	7.83718	+	7.93320i	0.347719	+	0.351979i
$509$	21.2276			0.940895			0.470447	−	0.882428i	$-0.344093\pi$
$509$	21.2276			0.940895			0.470447	+	0.882428i	$0.344093\pi$
$510$	−13.1061	−	1.52126i	−0.580347	−	0.0673624i
$511$		−	15.6470i		−	0.692181i
$512$	8.08318	+	21.1344i	0.357229	+	0.934017i
$513$	0.129196	+	2.33957i	0.00570414	+	0.103294i
$514$	−4.07860	+	1.67488i	−0.179899	+	0.0738759i
$515$			14.3515i			0.632402i
$516$	−36.8568	+	10.3633i	−1.62253	+	0.456217i
$517$		−	24.9073i		−	1.09542i
$518$	0.0889060	+	0.216500i	0.00390630	+	0.00951246i
$519$	−27.1613	−	15.0226i	−1.19225	−	0.659418i
$520$	6.96998	−	16.4017i	0.305654	−	0.719263i
$521$		−	17.2328i		−	0.754983i	−0.926013	−	0.377492i	$-0.876787\pi$
$521$		−	17.2328i		−	0.754983i	0.926013	−	0.377492i	$-0.123213\pi$
$522$	−6.03485	+	8.43958i	−0.264138	+	0.369390i
$523$	−1.39211			−0.0608725			−0.0304363	−	0.999537i	$-0.509690\pi$
$523$	−1.39211			−0.0608725			−0.0304363	+	0.999537i	$0.509690\pi$
$524$	18.5331	+	18.7602i	0.809622	+	0.819542i
$525$	−0.838298	+	1.51567i	−0.0365863	+	0.0661493i
$526$	−10.5140	−	25.6032i	−0.458432	−	1.11635i
$527$	−39.6847			−1.72869
$528$	−32.7658	−	18.6470i	−1.42595	−	0.811505i
$529$	−18.2758			−0.794598
$530$	3.46281	+	8.43249i	0.150415	+	0.366284i
$531$	−30.8082	+	19.3313i	−1.33696	+	0.838908i
$532$	−0.633825	−	0.641591i	−0.0274798	−	0.0278165i
$533$	−12.2912			−0.532392
$534$	−2.70792	−	0.314314i	−0.117183	−	0.0136017i
$535$			15.1898i			0.656711i
$536$	8.40867	+	3.57330i	0.363199	+	0.154343i
$537$	2.87516	−	5.19839i	0.124072	−	0.224327i
$538$	−0.968781	−	2.35913i	−0.0417671	−	0.101709i
$539$			5.44156i			0.234385i
$540$	7.70012	+	6.97912i	0.331360	+	0.300334i
$541$			4.48368i			0.192768i	0.995344	+	0.0963841i	$0.0307277\pi$
$541$			4.48368i			0.192768i	−0.995344	+	0.0963841i	$0.969272\pi$
$542$	40.8353	−	16.7691i	1.75403	−	0.720293i
$543$	16.7724	−	30.3251i	0.719773	−	1.30138i
$544$	−11.2307	−	28.3252i	−0.481512	−	1.21443i
$545$			8.89022i			0.380815i
$546$	−1.77948	+	15.3307i	−0.0761545	+	0.656095i
$547$	−1.74728			−0.0747084			−0.0373542	−	0.999302i	$-0.511893\pi$
$547$	−1.74728			−0.0747084			−0.0373542	+	0.999302i	$0.511893\pi$
$548$	2.56079	+	2.59217i	0.109392	+	0.110732i
$549$	9.46009	−	5.93596i	0.403747	−	0.253341i
$550$	−7.11868	+	2.92330i	−0.303541	+	0.124650i
$551$	−1.10275			−0.0469788
$552$	−6.56005	−	8.38734i	−0.279214	−	0.356989i
$553$	5.02829			0.213824
$554$	−21.5952	+	8.86808i	−0.917491	+	0.376769i
$555$	0.138733	−	0.250834i	0.00588889	−	0.0106473i
$556$	−4.01201	+	3.96345i	−0.170147	+	0.168088i
$557$	−28.6621			−1.21445			−0.607226	−	0.794529i	$-0.707718\pi$
$557$	−28.6621			−1.21445			−0.607226	+	0.794529i	$0.707718\pi$
$558$	25.4260	+	18.1812i	1.07637	+	0.769673i
$559$			69.6374i			2.94535i
$560$	−3.99970	−	0.0487085i	−0.169018	−	0.00205831i
$561$	44.4255	+	24.5712i	1.87565	+	1.03739i
$562$	−35.3451	+	14.5145i	−1.49094	+	0.612257i
$563$			32.5866i			1.37336i	0.726960	+	0.686680i	$0.240933\pi$
$563$			32.5866i			1.37336i	−0.726960	+	0.686680i	$0.759067\pi$
$564$	−15.2641	+	4.29191i	−0.642735	+	0.180722i
$565$		−	8.28028i		−	0.348354i
$566$	−16.5083	−	40.2004i	−0.693897	−	1.68975i
$567$	−8.10385	−	3.91505i	−0.340330	−	0.164417i
$568$	−3.23658	−	1.37540i	−0.135804	−	0.0577104i
$569$		−	4.23943i		−	0.177726i	−0.996044	−	0.0888632i	$-0.971677\pi$
$569$		−	4.23943i		−	0.177726i	0.996044	−	0.0888632i	$-0.0283234\pi$
$570$	−0.127354	+	1.09720i	−0.00533429	+	0.0459565i
$571$	−29.0004			−1.21363			−0.606814	−	0.794844i	$-0.707553\pi$
$571$	−29.0004			−1.21363			−0.606814	+	0.794844i	$0.707553\pi$
$572$	−48.7821	+	48.1916i	−2.03968	+	2.01499i
$573$	−29.9564	−	16.5685i	−1.25144	−	0.692158i
$574$	1.04797	+	2.55198i	0.0437416	+	0.106518i
$575$	−2.17353			−0.0906425
$576$	−5.78149	+	23.2932i	−0.240895	+	0.970551i
$577$	25.8553			1.07637			0.538186	−	0.842826i	$-0.319110\pi$
$577$	25.8553			1.07637			0.538186	+	0.842826i	$0.319110\pi$
$578$	6.45409	+	15.7167i	0.268455	+	0.653730i
$579$	12.9622	+	7.16924i	0.538692	+	0.297944i
$580$	−3.47941	+	3.43730i	−0.144475	+	0.142726i
$581$	−9.16060			−0.380046
$582$	1.72359	−	14.8492i	0.0714450	−	0.615521i
$583$		−	35.0755i		−	1.45268i
$584$	−40.7311	−	17.3089i	−1.68546	−	0.716246i
$585$	16.0113	−	10.0467i	0.661985	−	0.415378i
$586$	8.48974	+	20.6738i	0.350708	+	0.854028i
$587$		−	2.76600i		−	0.114165i	−0.998369	−	0.0570826i	$-0.981820\pi$
$587$		−	2.76600i		−	0.114165i	0.998369	−	0.0570826i	$-0.0181798\pi$
$588$	3.33478	−	0.937663i	0.137524	−	0.0386686i
$589$			3.32227i			0.136892i
$590$	−15.8602	+	6.51302i	−0.652954	+	0.268137i
$591$	−11.8546	−	6.55665i	−0.487635	−	0.269705i
$592$	0.661927	+	0.00806096i	0.0272050	+	0.000331303i
$593$			10.5837i			0.434622i	0.976102	+	0.217311i	$0.0697286\pi$
$593$			10.5837i			0.434622i	−0.976102	+	0.217311i	$0.930271\pi$
$594$	−17.2063	−	36.0959i	−0.705984	−	1.48103i
$595$	5.38646			0.220823
$596$	−31.4784	+	31.0974i	−1.28940	+	1.27380i
$597$	−7.87629	+	14.2406i	−0.322355	+	0.582829i
$598$	−17.9157	+	7.35712i	−0.732629	+	0.300855i
$599$	20.6552			0.843950			0.421975	−	0.906607i	$-0.361337\pi$
$599$	20.6552			0.843950			0.421975	+	0.906607i	$0.361337\pi$
$600$	3.01815	+	3.85885i	0.123216	+	0.157537i
$601$	30.1511			1.22989			0.614945	−	0.788570i	$-0.289178\pi$
$601$	30.1511			1.22989			0.614945	+	0.788570i	$0.289178\pi$
$602$	14.4586	−	5.93743i	0.589287	−	0.241991i
$603$	5.15062	+	8.20850i	0.209749	+	0.334276i
$604$	−7.24040	−	7.32911i	−0.294608	−	0.298217i
$605$	18.6106			0.756629
$606$	0.363433	−	3.13109i	0.0147635	−	0.127192i
$607$		−	22.3226i		−	0.906046i	−0.891499	−	0.453023i	$-0.850346\pi$
$607$		−	22.3226i		−	0.906046i	0.891499	−	0.453023i	$-0.149654\pi$
$608$	−2.37129	+	0.940194i	−0.0961685	+	0.0381299i
$609$	2.05003	−	3.70653i	0.0830715	−	0.150196i
$610$	4.87010	−	1.99991i	0.197185	−	0.0809742i
$611$			28.8401i			1.16675i
$612$	7.40290	−	31.4595i	0.299245	−	1.27167i
$613$			29.6525i			1.19765i	0.800879	+	0.598826i	$0.204366\pi$
$613$			29.6525i			1.19765i	−0.800879	+	0.598826i	$0.795634\pi$
$614$	−7.64915	−	18.6269i	−0.308695	−	0.751719i
$615$	1.63531	−	2.95669i	0.0659420	−	0.119225i
$616$	14.1651	+	6.01953i	0.570728	+	0.242534i
$617$		−	46.9803i		−	1.89136i	−0.325105	−	0.945678i	$-0.605400\pi$
$617$		−	46.9803i		−	1.89136i	0.325105	−	0.945678i	$-0.394600\pi$
$618$	−34.9193	−	4.05317i	−1.40466	−	0.163043i
$619$	−44.3264			−1.78163			−0.890814	−	0.454368i	$-0.849865\pi$
$619$	−44.3264			−1.78163			−0.890814	+	0.454368i	$0.849865\pi$
$620$	10.3556	+	10.4825i	0.415890	+	0.420985i
$621$	−0.622729	−	11.2768i	−0.0249893	−	0.452523i
$622$	−17.9211	−	43.6406i	−0.718569	−	1.74983i
$623$	1.11292			0.0445884
$624$	37.9394	+	21.5913i	1.51879	+	0.864342i
$625$	1.00000			0.0400000
$626$	6.22640	+	15.1623i	0.248857	+	0.606006i
$627$	2.05701	−	3.71915i	0.0821492	−	0.148528i
$628$	33.9595	+	34.3756i	1.35513	+	1.37173i
$629$	−0.891427			−0.0355435
$630$	−3.45111	−	2.46777i	−0.137495	−	0.0983181i
$631$			8.13744i			0.323946i	0.986795	+	0.161973i	$0.0517858\pi$
$631$			8.13744i			0.323946i	−0.986795	+	0.161973i	$0.948214\pi$
$632$	5.56235	−	13.0893i	0.221259	−	0.520664i
$633$	−13.7901	−	7.62711i	−0.548106	−	0.303150i
$634$	−16.6604	−	40.5706i	−0.661668	−	1.61127i
$635$			5.57578i			0.221268i
$636$	−21.4955	+	6.04404i	−0.852353	+	0.239662i
$637$		−	6.30076i		−	0.249645i
$638$	17.4085	−	7.14883i	0.689210	−	0.283025i
$639$	−1.98252	−	3.15953i	−0.0784274	−	0.124989i
$640$	−4.55132	+	10.3579i	−0.179907	+	0.409431i
$641$			2.21141i			0.0873455i	0.999046	+	0.0436727i	$0.0139059\pi$
$641$			2.21141i			0.0873455i	−0.999046	+	0.0436727i	$0.986094\pi$
$642$	−36.9591	−	4.28993i	−1.45866	−	0.169310i
$643$	23.2844			0.918248			0.459124	−	0.888372i	$-0.348163\pi$
$643$	23.2844			0.918248			0.459124	+	0.888372i	$0.348163\pi$
$644$	3.05506	+	3.09250i	0.120386	+	0.121861i
$645$	−16.7515	−	9.26505i	−0.659590	−	0.364811i
$646$	3.17756	−	1.30487i	0.125020	−	0.0513394i
$647$	20.0359			0.787693			0.393846	−	0.919176i	$-0.371144\pi$
$647$	20.0359			0.787693			0.393846	+	0.919176i	$0.371144\pi$
$648$	−19.1560	+	16.7645i	−0.752517	+	0.658572i
$649$	65.9716			2.58961
$650$	8.24269	−	3.38487i	0.323305	−	0.132766i
$651$	−11.1667	−	6.17615i	−0.437657	−	0.242062i
$652$	−16.6048	+	16.4038i	−0.650295	+	0.642424i
$653$	1.94296			0.0760340			0.0380170	−	0.999277i	$-0.487896\pi$
$653$	1.94296			0.0760340			0.0380170	+	0.999277i	$0.487896\pi$
$654$	−21.6313	−	2.51080i	−0.845850	−	0.0981799i
$655$			13.1854i			0.515196i
$656$	7.80242	+	0.0950181i	0.304633	+	0.00370983i
$657$	−24.9493	−	39.7615i	−0.973365	−	1.55124i
$658$	5.98796	−	2.45897i	0.233435	−	0.0958605i
$659$			30.1972i			1.17632i	0.808746	+	0.588158i	$0.200147\pi$
$659$			30.1972i			1.17632i	−0.808746	+	0.588158i	$0.799853\pi$
$660$	−5.10235	−	18.1464i	−0.198609	−	0.706349i
$661$			18.1561i			0.706192i	0.935587	+	0.353096i	$0.114871\pi$
$661$			18.1561i			0.706192i	−0.935587	+	0.353096i	$0.885129\pi$
$662$	−12.9242	−	31.4724i	−0.502312	−	1.22321i
$663$	−51.4401	−	28.4508i	−1.99777	−	1.10494i
$664$	−10.1336	+	23.8462i	−0.393259	+	0.925414i
$665$		−	0.450936i		−	0.0174866i
$666$	0.571137	+	0.408400i	0.0221311	+	0.0158252i
$667$	5.31531			0.205809
$668$	11.7109	−	11.5691i	0.453107	−	0.447622i
$669$	−6.18309	+	11.1792i	−0.239052	+	0.432214i
$670$	1.73532	+	4.22578i	0.0670413	+	0.163256i
$671$	−20.2575			−0.782033
$672$	1.24812	−	9.71814i	0.0481473	−	0.374885i
$673$	−39.6558			−1.52862			−0.764309	−	0.644850i	$-0.776920\pi$
$673$	−39.6558			−1.52862			−0.764309	+	0.644850i	$0.776920\pi$
$674$	−10.8022	−	26.3051i	−0.416086	−	1.01323i
$675$	0.286506	+	5.18825i	0.0110276	+	0.199696i
$676$	37.9882	−	37.5284i	1.46108	−	1.44340i
$677$	−9.48786			−0.364648			−0.182324	−	0.983239i	$-0.558362\pi$
$677$	−9.48786			−0.364648			−0.182324	+	0.983239i	$0.558362\pi$
$678$	20.1472	+	2.33853i	0.773748	+	0.0898109i
$679$			6.10287i			0.234207i
$680$	5.95857	−	14.0217i	0.228501	−	0.537706i
$681$	−10.0812	+	18.2272i	−0.386312	+	0.698466i
$682$	−21.5374	−	52.4468i	−0.824708	−	2.00829i
$683$			25.7975i			0.987113i	0.869714	+	0.493556i	$0.164303\pi$
$683$			25.7975i			0.987113i	−0.869714	+	0.493556i	$0.835697\pi$
$684$	−2.63368	−	0.619745i	−0.100701	−	0.0236966i
$685$			1.82188i			0.0696105i
$686$	−1.30820	+	0.537216i	−0.0499475	+	0.0205110i
$687$	1.11819	−	2.02173i	0.0426617	−	0.0771339i
$688$	0.538337	−	44.2056i	0.0205239	−	1.68532i
$689$			40.6138i			1.54726i
$690$	0.613853	−	5.28854i	0.0233690	−	0.201331i
$691$	34.5618			1.31479			0.657395	−	0.753546i	$-0.271658\pi$
$691$	34.5618			1.31479			0.657395	+	0.753546i	$0.271658\pi$
$692$	25.4970	−	25.1884i	0.969251	−	0.957520i
$693$	8.67665	+	13.8279i	0.329599	+	0.525279i
$694$	−12.5406	+	5.14980i	−0.476033	+	0.195484i
$695$	−2.81981			−0.106961
$696$	−7.38081	−	9.43671i	−0.279769	−	0.357698i
$697$	−10.5076			−0.398005
$698$	25.1995	−	10.3482i	0.953815	−	0.391685i
$699$	−13.6783	+	24.7309i	−0.517362	+	0.935409i
$700$	−1.40558	−	1.42280i	−0.0531258	−	0.0537767i
$701$	−19.1996			−0.725157			−0.362579	−	0.931953i	$-0.618104\pi$
$701$	−19.1996			−0.725157			−0.362579	+	0.931953i	$0.618104\pi$
$702$	19.9231	+	41.7953i	0.751950	+	1.57746i
$703$			0.0746272i			0.00281462i
$704$	31.3392	−	30.2148i	1.18114	−	1.13876i
$705$	−6.93759	−	3.83709i	−0.261285	−	0.144513i
$706$	14.0694	−	5.77762i	0.529509	−	0.217444i
$707$			1.28684i			0.0483967i
$708$	−11.3679	−	40.4297i	−0.427232	−	1.51944i
$709$		−	20.0482i		−	0.752925i	−0.926432	−	0.376463i	$-0.877140\pi$
$709$		−	20.0482i		−	0.752925i	0.926432	−	0.376463i	$-0.122860\pi$
$710$	−0.667942	−	1.62654i	−0.0250674	−	0.0610431i
$711$	12.7777	−	8.01768i	0.479201	−	0.300686i
$712$	1.23113	−	2.89709i	0.0461386	−	0.108573i
$713$		−	16.0135i		−	0.599709i
$714$	−1.52126	+	13.1061i	−0.0569316	+	0.490483i
$715$	−34.2860			−1.28222
$716$	4.82079	+	4.87986i	0.180161	+	0.182369i
$717$	−8.26355	−	4.57046i	−0.308608	−	0.170687i
$718$	−1.63780	−	3.98829i	−0.0611221	−	0.148842i
$719$	10.4278			0.388891			0.194445	−	0.980913i	$-0.437709\pi$
$719$	10.4278			0.388891			0.194445	+	0.980913i	$0.437709\pi$
$720$	−10.2416	+	6.25381i	−0.381681	+	0.233066i
$721$	14.3515			0.534477
$722$	10.0979	+	24.5899i	0.375804	+	0.915140i
$723$	−10.6432	−	5.88664i	−0.395827	−	0.218926i
$724$	28.1224	+	28.4669i	1.04516	+	1.05797i
$725$	−2.44547			−0.0908225
$726$	−5.25605	+	45.2825i	−0.195070	+	1.68059i
$727$		−	24.1849i		−	0.896970i	−0.893790	−	0.448485i	$-0.851964\pi$
$727$		−	24.1849i		−	0.896970i	0.893790	−	0.448485i	$-0.148036\pi$
$728$	−16.4017	−	6.96998i	−0.607888	−	0.258325i
$729$	−26.8358	+	2.97293i	−0.993920	+	0.110108i
$730$	−8.40580	−	20.4694i	−0.311112	−	0.757607i
$731$			59.5323i			2.20188i
$732$	3.49067	+	12.4145i	0.129019	+	0.458854i
$733$		−	3.88553i		−	0.143515i	−0.997422	−	0.0717576i	$-0.977139\pi$
$733$		−	3.88553i		−	0.143515i	0.997422	−	0.0717576i	$-0.0228608\pi$
$734$	−34.4249	+	14.1366i	−1.27065	+	0.521793i
$735$	1.51567	+	0.838298i	0.0559064	+	0.0309211i
$736$	11.4297	−	4.53178i	0.421305	−	0.167044i
$737$		−	17.5774i		−	0.647472i
$738$	6.73224	+	4.81399i	0.247817	+	0.177206i
$739$	34.9865			1.28700			0.643500	−	0.765446i	$-0.277482\pi$
$739$	34.9865			1.28700			0.643500	+	0.765446i	$0.277482\pi$
$740$	0.232614	+	0.235464i	0.00855108	+	0.00865585i
$741$	−2.38181	+	4.30639i	−0.0874978	+	0.158199i
$742$	8.43249	−	3.46281i	0.309567	−	0.127124i
$743$	−29.3568			−1.07700			−0.538498	−	0.842627i	$-0.681008\pi$
$743$	−29.3568			−1.07700			−0.538498	+	0.842627i	$0.681008\pi$
$744$	−28.4301	+	22.2362i	−1.04230	+	0.815220i
$745$	−22.1243			−0.810571
$746$	37.2263	−	15.2870i	1.36295	−	0.559698i
$747$	−23.2786	+	14.6067i	−0.851719	+	0.534432i
$748$	−41.7033	+	41.1985i	−1.52482	+	1.50637i
$749$	15.1898			0.555022
$750$	−0.282422	+	2.43315i	−0.0103126	+	0.0888462i
$751$		−	33.5351i		−	1.22371i	−0.790969	−	0.611857i	$-0.790423\pi$
$751$		−	33.5351i		−	1.22371i	0.790969	−	0.611857i	$-0.209577\pi$
$752$	0.222950	−	18.3076i	0.00813016	−	0.667609i
$753$	13.2490	−	23.9547i	0.482821	−	0.872956i
$754$	−20.1572	+	8.27760i	−0.734084	+	0.301452i
$755$		−	5.15119i		−	0.187471i
$756$	6.97912	−	7.70012i	0.253828	−	0.280051i
$757$			43.8155i			1.59250i	0.604967	+	0.796250i	$0.293186\pi$
$757$			43.8155i			1.59250i	−0.604967	+	0.796250i	$0.706814\pi$
$758$	5.69628	+	13.8713i	0.206898	+	0.503829i
$759$	−9.91489	+	17.9265i	−0.359888	+	0.650689i
$760$	−1.17385	−	0.498831i	−0.0425799	−	0.0180945i
$761$			22.5723i			0.818246i	0.912479	+	0.409123i	$0.134165\pi$
$761$			22.5723i			0.818246i	−0.912479	+	0.409123i	$0.865835\pi$
$762$	−13.5667	−	1.57472i	−0.491470	−	0.0570462i
$763$	8.89022			0.321848
$764$	28.1208	−	27.7804i	1.01737	−	1.00506i
$765$	13.6879	−	8.58879i	0.494887	−	0.310528i
$766$	−8.32044	−	20.2616i	−0.300630	−	0.732080i
$767$	−76.3882			−2.75822
$768$	−23.9169	−	13.9993i	−0.863027	−	0.505158i
$769$	28.6178			1.03199			0.515993	−	0.856593i	$-0.327423\pi$
$769$	28.6178			1.03199			0.515993	+	0.856593i	$0.327423\pi$
$770$	2.92330	+	7.11868i	0.105348	+	0.256539i
$771$	2.61357	−	4.72542i	0.0941253	−	0.170182i
$772$	−12.1680	+	12.0207i	−0.437935	+	0.432634i
$773$	41.3736			1.48811			0.744053	−	0.668121i	$-0.232901\pi$
$773$	41.3736			1.48811			0.744053	+	0.668121i	$0.232901\pi$
$774$	27.2743	−	38.1424i	0.980354	−	1.37100i
$775$			7.36749i			0.264648i
$776$	15.8866	+	6.75108i	0.570295	+	0.242350i
$777$	−0.250834	−	0.138733i	−0.00899863	−	0.00497702i
$778$	−8.26711	−	20.1317i	−0.296390	−	0.721756i
$779$			0.879663i			0.0315172i
$780$	5.90799	+	21.0117i	0.211540	+	0.752339i
$781$			6.76572i			0.242096i
$782$	−15.3160	+	6.28953i	−0.547699	+	0.224913i
$783$	−0.700642	−	12.6877i	−0.0250389	−	0.453422i
$784$	−0.0487085	+	3.99970i	−0.00173959	+	0.142847i
$785$			24.1605i			0.862327i
$786$	−32.0821	−	3.72385i	−1.14433	−	0.132825i
$787$	−8.87622			−0.316403			−0.158202	−	0.987407i	$-0.550570\pi$
$787$	−8.87622			−0.316403			−0.158202	+	0.987407i	$0.550570\pi$
$788$	11.1283	−	10.9936i	0.396428	−	0.391629i
$789$	29.6636	+	16.4065i	1.05605	+	0.584088i
$790$	6.57803	−	2.70128i	0.234036	−	0.0961071i
$791$	−8.28028			−0.294413
$792$	45.5941	−	7.28985i	1.62012	−	0.259034i
$793$	23.4561			0.832950
$794$	−38.1731	+	15.6758i	−1.35471	+	0.556314i
$795$	−9.76979	−	5.40354i	−0.346499	−	0.191644i
$796$	−13.2062	−	13.3680i	−0.468081	−	0.473816i
$797$	−6.80905			−0.241189			−0.120595	−	0.992702i	$-0.538480\pi$
$797$	−6.80905			−0.241189			−0.120595	+	0.992702i	$0.538480\pi$
$798$	1.09720	+	0.127354i	0.0388403	+	0.00450829i
$799$			24.6551i			0.872235i
$800$	−5.25860	+	2.08498i	−0.185919	+	0.0737153i
$801$	2.82812	−	1.77457i	0.0999269	−	0.0627015i
$802$	9.80245	−	4.02539i	0.346136	−	0.142141i
$803$			85.1439i			3.00466i
$804$	−10.7721	+	3.02885i	−0.379901	+	0.106819i
$805$			2.17353i			0.0766069i
$806$	24.9380	+	60.7279i	0.878404	+	2.13905i
$807$	2.73326	+	1.51173i	0.0962154	+	0.0532155i
$808$	3.34982	+	1.42352i	0.117846	+	0.0500793i
$809$		−	20.5432i		−	0.722261i	−0.932515	−	0.361130i	$-0.882391\pi$
$809$		−	20.5432i		−	0.722261i	0.932515	−	0.361130i	$-0.117609\pi$
$810$	−12.7047	−	0.768163i	−0.446398	−	0.0269905i
$811$	−39.6773			−1.39326			−0.696630	−	0.717430i	$-0.745318\pi$
$811$	−39.6773			−1.39326			−0.696630	+	0.717430i	$0.745318\pi$
$812$	3.43730	+	3.47941i	0.120625	+	0.122103i
$813$	−26.1673	+	47.3113i	−0.917726	+	1.65928i
$814$	−0.483788	−	1.17810i	−0.0169567	−	0.0412923i
$815$	−11.6705			−0.408801
$816$	32.4340	+	18.4582i	1.13542	+	0.646165i
$817$	4.98384			0.174363
$818$	2.91713	+	7.10367i	0.101995	+	0.248374i
$819$	−10.0467	−	16.0113i	−0.351059	−	0.559480i
$820$	2.74193	+	2.77552i	0.0957523	+	0.0969255i
$821$	−32.1099			−1.12064			−0.560322	−	0.828275i	$-0.689322\pi$
$821$	−32.1099			−1.12064			−0.560322	+	0.828275i	$0.689322\pi$
$822$	−4.43291	−	0.514539i	−0.154616	−	0.0179466i
$823$			44.6648i			1.55692i	0.627697	+	0.778458i	$0.283998\pi$
$823$			44.6648i			1.55692i	−0.627697	+	0.778458i	$0.716002\pi$
$824$	15.8758	−	37.3588i	0.553059	−	1.30145i
$825$	4.56165	−	8.24762i	0.158816	−	0.287145i
$826$	6.51302	+	15.8602i	0.226617	+	0.551847i
$827$		−	13.1115i		−	0.455930i	−0.973669	−	0.227965i	$-0.926793\pi$
$827$		−	13.1115i		−	0.455930i	0.973669	−	0.227965i	$-0.0732072\pi$
$828$	12.6945	+	2.98720i	0.441163	+	0.103812i
$829$		−	32.9548i		−	1.14457i	−0.820056	−	0.572283i	$-0.806058\pi$
$829$		−	32.9548i		−	1.14457i	0.820056	−	0.572283i	$-0.193942\pi$
$830$	−11.9839	+	4.92122i	−0.415969	+	0.170818i
$831$	13.8382	−	25.0199i	0.480041	−	0.867931i
$832$	−36.2876	+	34.9855i	−1.25805	+	1.21291i
$833$		−	5.38646i		−	0.186630i
$834$	0.796376	−	6.86102i	0.0275762	−	0.237578i
$835$	8.23086			0.284841
$836$	3.44900	+	3.49126i	0.119286	+	0.120748i
$837$	−38.2244	+	2.11083i	−1.32123	+	0.0729610i
$838$	−16.9414	+	6.95702i	−0.585232	+	0.240326i
$839$	9.64905			0.333122			0.166561	−	0.986031i	$-0.446734\pi$
$839$	9.64905			0.333122			0.166561	+	0.986031i	$0.446734\pi$
$840$	3.85885	−	3.01815i	0.133143	−	0.104136i
$841$	−23.0197			−0.793782
$842$	43.2014	−	17.7407i	1.48882	−	0.611385i
$843$	22.6491	−	40.9504i	0.780077	−	1.41041i
$844$	12.9451	−	12.7884i	0.445588	−	0.440195i
$845$	26.6996			0.918495
$846$	11.2956	−	15.7965i	0.388349	−	0.543096i
$847$		−	18.6106i		−	0.639469i
$848$	0.313968	−	25.7815i	0.0107817	−	0.885340i
$849$	46.5757	+	25.7604i	1.59847	+	0.884095i
$850$	7.04659	−	2.89369i	0.241696	−	0.0992529i
$851$		−	0.359706i		−	0.0123306i
$852$	4.14627	−	1.16583i	0.142049	−	0.0399408i
$853$		−	56.9045i		−	1.94837i	−0.225746	−	0.974186i	$-0.572482\pi$
$853$		−	56.9045i		−	1.94837i	0.225746	−	0.974186i	$-0.427518\pi$
$854$	−1.99991	−	4.87010i	−0.0684356	−	0.166651i
$855$	−0.719024	−	1.14590i	−0.0245901	−	0.0391891i
$856$	16.8031	−	39.5410i	0.574319	−	1.35148i
$857$			47.3354i			1.61695i	0.588533	+	0.808473i	$0.299706\pi$
$857$			47.3354i			1.61695i	−0.588533	+	0.808473i	$0.700294\pi$
$858$	9.68313	−	83.4231i	0.330577	−	2.84802i
$859$	−50.9077			−1.73695			−0.868474	−	0.495735i	$-0.834899\pi$
$859$	−50.9077			−1.73695			−0.868474	+	0.495735i	$0.834899\pi$
$860$	15.7251	−	15.5347i	0.536221	−	0.529730i
$861$	−2.95669	−	1.63531i	−0.100764	−	0.0557312i
$862$	−12.9220	−	31.4671i	−0.440125	−	1.07177i
$863$	28.4324			0.967852			0.483926	−	0.875109i	$-0.339210\pi$
$863$	28.4324			0.967852			0.483926	+	0.875109i	$0.339210\pi$
$864$	−12.3240	−	26.6855i	−0.419272	−	0.907861i
$865$	17.9203			0.609310
$866$	5.96269	+	14.5201i	0.202620	+	0.493412i
$867$	−18.2092	−	10.0713i	−0.618417	−	0.342039i
$868$	10.4825	−	10.3556i	0.355798	−	0.351491i
$869$	−27.3617			−0.928183
$870$	0.690655	−	5.95021i	0.0234154	−	0.201731i
$871$			20.3528i			0.689628i
$872$	9.83448	−	23.1424i	0.333037	−	0.783701i
$873$	9.73112	+	15.5084i	0.329349	+	0.524880i
$874$	0.526538	+	1.28220i	0.0178104	+	0.0433711i
$875$		−	1.00000i		−	0.0338062i
$876$	52.1792	−	14.6716i	1.76297	−	0.495707i
$877$			44.7606i			1.51146i	0.654883	+	0.755730i	$0.272718\pi$
$877$			44.7606i			1.51146i	−0.654883	+	0.755730i	$0.727282\pi$
$878$	−20.1136	+	8.25966i	−0.678800	+	0.278750i
$879$	−23.9525	−	13.2478i	−0.807897	−	0.446837i
$880$	21.7646	+	0.265050i	0.733686	+	0.00893484i
$881$		−	32.3358i		−	1.08942i	−0.838625	−	0.544710i	$-0.816640\pi$
$881$		−	32.3358i		−	1.08942i	0.838625	−	0.544710i	$-0.183360\pi$
$882$	−2.46777	+	3.45111i	−0.0830940	+	0.116205i
$883$	38.2272			1.28645			0.643223	−	0.765679i	$-0.277597\pi$
$883$	38.2272			1.28645			0.643223	+	0.765679i	$0.277597\pi$
$884$	48.2881	−	47.7036i	1.62410	−	1.60445i
$885$	10.1632	−	18.3755i	0.341633	−	0.617684i
$886$	−9.86028	+	4.04914i	−0.331263	+	0.136033i
$887$	−5.25939			−0.176593			−0.0882965	−	0.996094i	$-0.528142\pi$
$887$	−5.25939			−0.176593			−0.0882965	+	0.996094i	$0.528142\pi$
$888$	−0.638617	+	0.499486i	−0.0214306	+	0.0167617i
$889$	5.57578			0.187006
$890$	1.45593	−	0.597880i	0.0488030	−	0.0200410i
$891$	44.0976	+	21.3040i	1.47733	+	0.713710i
$892$	−10.3672	−	10.4942i	−0.347120	−	0.351373i
$893$	2.06404			0.0690705
$894$	6.24839	−	53.8318i	0.208977	−	1.80040i
$895$			3.42976i			0.114644i
$896$	10.3579	+	4.55132i	0.346032	+	0.152049i
$897$	11.4804	−	20.7570i	0.383320	−	0.693055i
$898$	13.0128	−	5.34374i	0.434244	−	0.178323i
$899$		−	18.0170i		−	0.600900i
$900$	−5.84048	−	1.37435i	−0.194683	−	0.0458118i
$901$			34.7203i			1.15670i
$902$	−5.70262	−	13.8868i	−0.189876	−	0.462379i
$903$	−9.26505	+	16.7515i	−0.308321	+	0.557456i
$904$	−9.15975	+	21.5547i	−0.304649	+	0.716897i
$905$			20.0077i			0.665079i
$906$	12.5336	+	1.45481i	0.416403	+	0.0483329i
$907$	5.86289			0.194674			0.0973370	−	0.995251i	$-0.468968\pi$
$907$	5.86289			0.194674			0.0973370	+	0.995251i	$0.468968\pi$
$908$	−16.9032	−	17.1103i	−0.560952	−	0.567825i
$909$	2.05189	+	3.27008i	0.0680569	+	0.108462i
$910$	−3.38487	−	8.24269i	−0.112207	−	0.273242i
$911$	23.4750			0.777760			0.388880	−	0.921288i	$-0.372862\pi$
$911$	23.4750			0.777760			0.388880	+	0.921288i	$0.372862\pi$
$912$	1.54525	−	2.71527i	0.0511684	−	0.0899115i
$913$	49.8480			1.64973
$914$	−7.95284	−	19.3664i	−0.263057	−	0.640584i
$915$	−3.12076	+	5.64244i	−0.103169	+	0.186533i
$916$	1.87488	+	1.89785i	0.0619477	+	0.0627067i
$917$	13.1854			0.435420
$918$	17.0321	+	35.7304i	0.562143	+	1.17928i
$919$			7.89412i			0.260403i	0.991488	+	0.130201i	$0.0415624\pi$
$919$			7.89412i			0.260403i	−0.991488	+	0.130201i	$0.958438\pi$
$920$	5.65799	+	2.40439i	0.186538	+	0.0792703i
$921$	21.5809	+	11.9361i	0.711114	+	0.393308i
$922$	−0.569149	−	1.38597i	−0.0187439	−	0.0456443i
$923$		−	7.83399i		−	0.257859i
$924$	−18.1464	+	5.10235i	−0.596974	+	0.167855i
$925$			0.165494i			0.00544141i
$926$	−7.28013	+	2.98959i	−0.239240	+	0.0982442i
$927$	36.4695	−	22.8836i	1.19781	−	0.751597i
$928$	12.8597	−	5.09877i	0.422142	−	0.167375i
$929$			4.83035i			0.158479i	0.996856	+	0.0792393i	$0.0252491\pi$
$929$			4.83035i			0.158479i	−0.996856	+	0.0792393i	$0.974751\pi$
$930$	−17.9262	−	2.08074i	−0.587825	−	0.0682303i
$931$	−0.450936			−0.0147788
$932$	−22.9345	−	23.2155i	−0.751245	−	0.760450i
$933$	50.5615	+	27.9649i	1.65531	+	0.915530i
$934$	−18.7598	+	7.70374i	−0.613840	+	0.252074i
$935$	−29.3108			−0.958565
$936$	−52.7932	+	8.44089i	−1.72560	+	0.275899i
$937$	−15.8234			−0.516927			−0.258463	−	0.966021i	$-0.583216\pi$
$937$	−15.8234			−0.516927			−0.258463	+	0.966021i	$0.583216\pi$
$938$	4.22578	−	1.73532i	0.137977	−	0.0566603i
$939$	−17.5668	−	9.71598i	−0.573271	−	0.317069i
$940$	6.51249	−	6.43366i	0.212414	−	0.209843i
$941$	−21.5116			−0.701258			−0.350629	−	0.936514i	$-0.614032\pi$
$941$	−21.5116			−0.701258			−0.350629	+	0.936514i	$0.614032\pi$
$942$	−58.7863	−	6.82347i	−1.91536	−	0.222321i
$943$		−	4.24002i		−	0.138074i
$944$	48.4910	+	0.590524i	1.57825	+	0.0192199i
$945$	5.18825	−	0.286506i	0.168774	−	0.00932004i
$946$	−78.6772	+	32.3089i	−2.55802	+	1.05045i
$947$		−	2.56085i		−	0.0832165i	−0.999134	−	0.0416083i	$-0.986752\pi$
$947$		−	2.56085i		−	0.0832165i	0.999134	−	0.0416083i	$-0.0132481\pi$
$948$	4.71484	+	16.7683i	0.153131	+	0.544607i
$949$		−	98.5878i		−	3.20030i
$950$	−0.242250	−	0.589917i	−0.00785963	−	0.0191394i
$951$	47.0046	+	25.9977i	1.52423	+	0.843032i
$952$	−14.0217	−	5.95857i	−0.454445	−	0.193118i
$953$			37.7653i			1.22334i	0.791114	+	0.611669i	$0.209501\pi$
$953$			37.7653i			1.22334i	−0.791114	+	0.611669i	$0.790499\pi$
$954$	15.9069	−	22.2453i	0.515003	−	0.720219i
$955$	19.7644			0.639562
$956$	7.75720	−	7.66331i	0.250886	−	0.247849i
$957$	−11.1554	+	20.1693i	−0.360602	+	0.651981i
$958$	10.7072	+	26.0737i	0.345933	+	0.842402i
$959$	1.82188			0.0588316
$960$	−3.58794	−	13.3838i	−0.115800	−	0.431961i
$961$	−23.2799			−0.750966
$962$	0.560176	+	1.36411i	0.0180608	+	0.0439808i
$963$	38.5997	−	24.2203i	1.24386	−	0.780489i
$964$	9.99108	−	9.87015i	0.321791	−	0.317896i
$965$	−8.55215			−0.275303
$966$	−5.28854	−	0.613853i	−0.170156	−	0.0197504i
$967$		−	35.3522i		−	1.13685i	−0.822735	−	0.568425i	$-0.807553\pi$
$967$		−	35.3522i		−	1.13685i	0.822735	−	0.568425i	$-0.192447\pi$
$968$	−48.4459	−	20.5873i	−1.55711	−	0.661701i
$969$	−2.03618	+	3.68149i	−0.0654116	+	0.118266i
$970$	3.27856	+	7.98381i	0.105268	+	0.256345i
$971$		−	14.4815i		−	0.464734i	−0.972628	−	0.232367i	$-0.925353\pi$
$971$		−	14.4815i		−	0.464734i	0.972628	−	0.232367i	$-0.0746470\pi$
$972$	5.45715	−	30.6956i	0.175038	−	0.984562i
$973$			2.81981i			0.0903988i
$974$	57.5919	−	23.6502i	1.84536	−	0.757801i
$975$	−5.28191	+	9.54988i	−0.169157	+	0.305841i
$976$	−14.8898	−	0.181329i	−0.476612	−	0.00580420i
$977$			29.2774i			0.936667i	0.883552	+	0.468333i	$0.155145\pi$
$977$			29.2774i			0.936667i	−0.883552	+	0.468333i	$0.844855\pi$
$978$	3.29602	−	28.3962i	0.105395	−	0.908011i
$979$	−6.05605			−0.193552
$980$	−1.42280	+	1.40558i	−0.0454496	+	0.0448995i
$981$	22.5915	−	14.1756i	0.721292	−	0.452592i
$982$	−49.9394	+	20.5077i	−1.59363	+	0.654427i
$983$	−24.6216			−0.785307			−0.392653	−	0.919687i	$-0.628443\pi$
$983$	−24.6216			−0.785307			−0.392653	+	0.919687i	$0.628443\pi$
$984$	−7.52766	+	5.88766i	−0.239973	+	0.187692i
$985$	7.82139			0.249210
$986$	−17.2322	+	7.07644i	−0.548786	+	0.225360i
$987$	−3.83709	+	6.93759i	−0.122136	+	0.220826i
$988$	−3.99358	−	4.04251i	−0.127053	−	0.128609i
$989$	−24.0223			−0.763866
$990$	18.7794	+	13.4285i	0.596849	+	0.426786i
$991$			29.1715i			0.926663i	0.886185	+	0.463331i	$0.153346\pi$
$991$			29.1715i			0.926663i	−0.886185	+	0.463331i	$0.846654\pi$
$992$	−15.3611	−	38.7427i	−0.487715	−	1.23008i
$993$	36.4635	+	20.1675i	1.15713	+	0.639996i
$994$	−1.62654	+	0.667942i	−0.0515908	+	0.0211858i
$995$		−	9.39557i		−	0.297860i
$996$	−8.58956	−	30.5486i	−0.272171	−	0.967970i
$997$			36.6193i			1.15975i	0.814707	+	0.579873i	$0.196898\pi$
$997$			36.6193i			1.15975i	−0.814707	+	0.579873i	$0.803102\pi$
$998$	−5.67363	−	13.8162i	−0.179596	−	0.437343i
$999$	−0.858624	+	0.0474150i	−0.0271656	+	0.00150014i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.e.d.491.13	yes	44
3.2	odd	2		840.2.e.c.491.32	yes	44
4.3	odd	2		3360.2.e.c.911.9		44
8.3	odd	2		840.2.e.c.491.31	✓	44
8.5	even	2		3360.2.e.d.911.9		44
12.11	even	2		3360.2.e.d.911.10		44
24.5	odd	2		3360.2.e.c.911.10		44
24.11	even	2	inner	840.2.e.d.491.14	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.e.c.491.31	✓	44	8.3	odd	2
840.2.e.c.491.32	yes	44	3.2	odd	2
840.2.e.d.491.13	yes	44	1.1	even	1	trivial
840.2.e.d.491.14	yes	44	24.11	even	2	inner
3360.2.e.c.911.9		44	4.3	odd	2
3360.2.e.c.911.10		44	24.5	odd	2
3360.2.e.d.911.9		44	8.5	even	2
3360.2.e.d.911.10		44	12.11	even	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	840.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.537216 - 1.30820i) q^{2} +(1.51567 + 0.838298i) q^{3} +(-1.42280 + 1.40558i) q^{4} -1.00000 q^{5} +(0.282422 - 2.43315i) q^{6} +1.00000i q^{7} +(2.60313 + 1.10621i) q^{8} +(1.59451 + 2.54117i) q^{9} +(0.537216 + 1.30820i) q^{10} -5.44156i q^{11} +(-3.33478 + 0.937663i) q^{12} +6.30076i q^{13} +(1.30820 - 0.537216i) q^{14} +(-1.51567 - 0.838298i) q^{15} +(0.0487085 - 3.99970i) q^{16} +5.38646i q^{17} +(2.46777 - 3.45111i) q^{18} +0.450936 q^{19} +(1.42280 - 1.40558i) q^{20} +(-0.838298 + 1.51567i) q^{21} +(-7.11868 + 2.92330i) q^{22} -2.17353 q^{23} +(3.01815 + 3.85885i) q^{24} +1.00000 q^{25} +(8.24269 - 3.38487i) q^{26} +(0.286506 + 5.18825i) q^{27} +(-1.40558 - 1.42280i) q^{28} -2.44547 q^{29} +(-0.282422 + 2.43315i) q^{30} +7.36749i q^{31} +(-5.25860 + 2.08498i) q^{32} +(4.56165 - 8.24762i) q^{33} +(7.04659 - 2.89369i) q^{34} -1.00000i q^{35} +(-5.84048 - 1.37435i) q^{36} +0.165494i q^{37} +(-0.242250 - 0.589917i) q^{38} +(-5.28191 + 9.54988i) q^{39} +(-2.60313 - 1.10621i) q^{40} +1.95075i q^{41} +(2.43315 + 0.282422i) q^{42} +11.0522 q^{43} +(7.64854 + 7.74225i) q^{44} +(-1.59451 - 2.54117i) q^{45} +(1.16766 + 2.84342i) q^{46} +4.57724 q^{47} +(3.42677 - 6.02140i) q^{48} -1.00000 q^{49} +(-0.537216 - 1.30820i) q^{50} +(-4.51546 + 8.16410i) q^{51} +(-8.85621 - 8.96471i) q^{52} +6.44585 q^{53} +(6.63337 - 3.16202i) q^{54} +5.44156i q^{55} +(-1.10621 + 2.60313i) q^{56} +(0.683471 + 0.378019i) q^{57} +(1.31375 + 3.19918i) q^{58} +12.1236i q^{59} +(3.33478 - 0.937663i) q^{60} -3.72274i q^{61} +(9.63819 - 3.95793i) q^{62} +(-2.54117 + 1.59451i) q^{63} +(5.55259 + 5.75923i) q^{64} -6.30076i q^{65} +(-13.2402 - 1.53682i) q^{66} +3.23021 q^{67} +(-7.57108 - 7.66385i) q^{68} +(-3.29436 - 1.82207i) q^{69} +(-1.30820 + 0.537216i) q^{70} -1.24334 q^{71} +(1.33966 + 8.37886i) q^{72} -15.6470 q^{73} +(0.216500 - 0.0889060i) q^{74} +(1.51567 + 0.838298i) q^{75} +(-0.641591 + 0.633825i) q^{76} +5.44156 q^{77} +(15.3307 + 1.77948i) q^{78} -5.02829i q^{79} +(-0.0487085 + 3.99970i) q^{80} +(-3.91505 + 8.10385i) q^{81} +(2.55198 - 1.04797i) q^{82} +9.16060i q^{83} +(-0.937663 - 3.33478i) q^{84} -5.38646i q^{85} +(-5.93743 - 14.4586i) q^{86} +(-3.70653 - 2.05003i) q^{87} +(6.01953 - 14.1651i) q^{88} -1.11292i q^{89} +(-2.46777 + 3.45111i) q^{90} -6.30076 q^{91} +(3.09250 - 3.05506i) q^{92} +(-6.17615 + 11.1667i) q^{93} +(-2.45897 - 5.98796i) q^{94} -0.450936 q^{95} +(-9.71814 - 1.24812i) q^{96} +6.10287 q^{97} +(0.537216 + 1.30820i) q^{98} +(13.8279 - 8.67665i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 2 q^{2} + 4 q^{3} - 2 q^{4} - 44 q^{5} - 6 q^{6} - 22 q^{8} + 4 q^{9} - 2 q^{10} + 6 q^{12} + 4 q^{14} - 4 q^{15} + 22 q^{16} + 2 q^{18} + 16 q^{19} + 2 q^{20} + 16 q^{23} + 10 q^{24} + 44 q^{25}+ \cdots - 64 q^{99}+O(q^{100}) \) 44 * q + 2 * q^2 + 4 * q^3 - 2 * q^4 - 44 * q^5 - 6 * q^6 - 22 * q^8 + 4 * q^9 - 2 * q^10 + 6 * q^12 + 4 * q^14 - 4 * q^15 + 22 * q^16 + 2 * q^18 + 16 * q^19 + 2 * q^20 + 16 * q^23 + 10 * q^24 + 44 * q^25 - 16 * q^26 + 4 * q^27 + 16 * q^29 + 6 * q^30 - 18 * q^32 + 24 * q^33 + 20 * q^34 - 46 * q^36 + 8 * q^38 - 16 * q^39 + 22 * q^40 - 4 * q^42 + 24 * q^43 + 32 * q^44 - 4 * q^45 - 24 * q^47 + 18 * q^48 - 44 * q^49 + 2 * q^50 - 20 * q^52 - 32 * q^53 + 2 * q^54 + 8 * q^56 - 4 * q^58 - 6 * q^60 + 32 * q^62 - 50 * q^64 - 8 * q^66 + 24 * q^67 - 28 * q^68 - 8 * q^69 - 4 * q^70 + 8 * q^71 + 2 * q^72 + 8 * q^73 - 48 * q^74 + 4 * q^75 + 12 * q^76 + 8 * q^77 - 84 * q^78 - 22 * q^80 + 20 * q^81 - 8 * q^82 + 4 * q^84 - 4 * q^86 - 16 * q^87 - 28 * q^88 - 2 * q^90 - 16 * q^91 + 76 * q^92 + 16 * q^93 - 16 * q^95 + 38 * q^96 + 24 * q^97 - 2 * q^98 - 64 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more