LMFDB - Embedded newform 840.2.e.c.491.31

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			491.31
Character	$\chi$	$=$	840.491
Dual form			840.2.e.c.491.32

$q$-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} +(1.91091 - 1.53246i) 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} +(-0.978202 - 3.32312i) 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} +(4.18096 - 0.720796i) 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} +(-4.87283 - 0.505545i) 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} +(1.91091 - 1.53246i) 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} +(1.30313 - 5.85678i) 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} +(-1.53246 - 1.91091i) 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} +(-3.27912 + 6.10306i) 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} +(6.94120 + 2.41240i) 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} +(-0.978202 - 3.32312i) 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} +(-8.33898 - 10.3983i) 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} +(-6.96180 - 4.85112i) 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} +(-9.65567 - 12.0402i) 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} +(-3.32312 + 0.978202i) 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} +(4.18096 - 0.720796i) 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} +(6.22246 + 7.56842i) 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} + 18 q^{6} + 22 q^{8} + 4 q^{9} - 2 q^{10} + 6 q^{12} - 4 q^{14} + 4 q^{15} + 22 q^{16} + 10 q^{18} + 16 q^{19} - 2 q^{20} - 16 q^{23} - 26 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 + 18 * q^6 + 22 * q^8 + 4 * q^9 - 2 * q^10 + 6 * q^12 - 4 * q^14 + 4 * q^15 + 22 * q^16 + 10 * q^18 + 16 * q^19 - 2 * q^20 - 16 * q^23 - 26 * q^24 + 44 * q^25 + 16 * q^26 + 4 * q^27 - 16 * q^29 + 18 * q^30 + 18 * q^32 + 24 * q^33 + 20 * q^34 + 18 * 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 - 38 * q^48 - 44 * q^49 - 2 * q^50 - 20 * q^52 + 32 * q^53 - 18 * q^54 - 8 * q^56 - 4 * q^58 + 6 * q^60 - 32 * q^62 - 50 * q^64 - 44 * q^66 + 24 * q^67 + 28 * q^68 + 8 * q^69 - 4 * q^70 - 8 * q^71 - 82 * q^72 + 8 * q^73 + 48 * q^74 + 4 * q^75 + 12 * q^76 - 8 * q^77 + 16 * q^78 + 22 * q^80 + 20 * q^81 - 8 * q^82 - 16 * q^84 + 4 * q^86 + 16 * q^87 - 28 * q^88 + 10 * q^90 - 16 * q^91 - 76 * q^92 - 16 * q^93 + 16 * q^95 + 18 * 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
$6$	1.91091	−	1.53246i	0.780125	−	0.625624i
$7$		−	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	$-0.306220\pi$
$12$	−0.978202	−	3.32312i	−0.282383	−	0.959302i
$13$		−	6.30076i		−	1.74752i	−0.486360	−	0.873759i	$-0.661676\pi$
$13$		−	6.30076i		−	1.74752i	0.486360	−	0.873759i	$-0.338324\pi$
$14$	−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	$0.773424\pi$
$18$	4.18096	−	0.720796i	0.985462	−	0.169893i
$19$	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	$-0.427237\pi$
$23$	2.17353			0.453213			0.226606	+	0.973986i	$0.427237\pi$
$24$	−4.87283	−	0.505545i	−0.994661	−	0.103194i
$25$	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	$-0.427090\pi$
$29$	2.44547			0.454113			0.227056	+	0.973882i	$0.427090\pi$
$30$	1.91091	−	1.53246i	0.348882	−	0.279788i
$31$		−	7.36749i		−	1.32324i	−0.749839	−	0.661620i	$-0.769869\pi$
$31$		−	7.36749i		−	1.32324i	0.749839	−	0.661620i	$-0.230131\pi$
$32$	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
$36$	1.30313	−	5.85678i	0.217189	−	0.976130i
$37$		−	0.165494i		−	0.0272070i	−0.999907	−	0.0136035i	$-0.995670\pi$
$37$		−	0.165494i		−	0.0272070i	0.999907	−	0.0136035i	$-0.00433027\pi$
$38$	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	$0.951323\pi$
$42$	−1.53246	−	1.91091i	−0.236464	−	0.294859i
$43$	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	$-0.608341\pi$
$47$	−4.57724			−0.667659			−0.333829	+	0.942634i	$0.608341\pi$
$48$	−3.27912	+	6.10306i	−0.473300	+	0.880902i
$49$	−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	$-0.645980\pi$
$53$	−6.44585			−0.885406			−0.442703	+	0.896668i	$0.645980\pi$
$54$	6.94120	+	2.41240i	0.944578	+	0.328286i
$55$		−	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	$0.710505\pi$
$60$	−0.978202	−	3.32312i	−0.126285	−	0.429013i
$61$			3.72274i			0.476648i	0.971186	+	0.238324i	$0.0765980\pi$
$61$			3.72274i			0.476648i	−0.971186	+	0.238324i	$0.923402\pi$
$62$	−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
$66$	−8.33898	−	10.3983i	−1.02646	−	1.27995i
$67$	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	$-0.476494\pi$
$71$	1.24334			0.147557			0.0737787	+	0.997275i	$0.476494\pi$
$72$	−6.96180	−	4.85112i	−0.820456	−	0.571710i
$73$	−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
$78$	−9.65567	−	12.0402i	−1.09329	−	1.36328i
$79$			5.02829i			0.565726i	0.959160	+	0.282863i	$0.0912842\pi$
$79$			5.02829i			0.565726i	−0.959160	+	0.282863i	$0.908716\pi$
$80$	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	$0.832320\pi$
$84$	−3.32312	+	0.978202i	−0.362582	+	0.106731i
$85$			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	$-0.0187864\pi$
$90$	4.18096	−	0.720796i	0.440712	−	0.0759786i
$91$	−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
$96$	6.22246	+	7.56842i	0.635078	+	0.772448i
$97$	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	$-0.520393\pi$
$101$	−1.28684			−0.128046			−0.0640229	+	0.997948i	$0.520393\pi$
$102$	8.25454	+	10.2930i	0.817321	+	1.01916i
$103$			14.3515i			1.41409i	0.707167	+	0.707046i	$0.249973\pi$
$103$			14.3515i			1.41409i	−0.707167	+	0.707046i	$0.750027\pi$
$104$	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	$-0.262455\pi$
$108$	6.88484	−	7.78453i	0.662494	−	0.749067i
$109$			8.89022i			0.851529i	0.904834	+	0.425764i	$0.139995\pi$
$109$			8.89022i			0.851529i	−0.904834	+	0.425764i	$0.860005\pi$
$110$	−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	$0.872658\pi$
$114$	0.861697	−	0.691042i	0.0807053	−	0.0647220i
$115$	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
$120$	−4.87283	−	0.505545i	−0.444826	−	0.0461497i
$121$	−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
$126$	−0.720796	−	4.18096i	−0.0642136	−	0.372470i
$127$			5.57578i			0.494770i	0.968917	+	0.247385i	$0.0795713\pi$
$127$			5.57578i			0.494770i	−0.968917	+	0.247385i	$0.920429\pi$
$128$	−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	$-0.195390\pi$
$132$	−18.0830	+	5.32295i	−1.57392	+	0.463303i
$133$		−	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	$-0.0247981\pi$
$138$	4.15342	−	3.33085i	0.353562	−	0.283541i
$139$	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
$144$	−10.0862	+	6.50136i	−0.840520	+	0.541780i
$145$	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	$-0.861065\pi$
$149$	−22.1243			−1.81249			−0.906246	+	0.422751i	$0.861065\pi$
$150$	1.91091	−	1.53246i	0.156025	−	0.125125i
$151$		−	5.15119i		−	0.419198i	−0.977787	−	0.209599i	$-0.932784\pi$
$151$		−	5.15119i		−	0.419198i	0.977787	−	0.209599i	$-0.0672159\pi$
$152$	−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
$156$	−20.9382	+	6.16342i	−1.67640	+	0.493468i
$157$			24.1605i			1.92822i	0.265501	+	0.964110i	$0.414463\pi$
$157$			24.1605i			1.92822i	−0.265501	+	0.964110i	$0.585537\pi$
$158$	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
$162$	8.49827	+	9.47520i	0.667687	+	0.744442i
$163$	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	$-0.396834\pi$
$167$	8.23086			0.636923			0.318462	+	0.947936i	$0.396834\pi$
$168$	−0.505545	+	4.87283i	−0.0390036	+	0.375947i
$169$	−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	$-0.261446\pi$
$173$	17.9203			1.36246			0.681229	+	0.732070i	$0.261446\pi$
$174$	4.67307	−	3.74759i	0.354264	−	0.284104i
$175$		−	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	$-0.0409123\pi$
$180$	1.30313	−	5.85678i	0.0971297	−	0.436538i
$181$			20.0077i			1.48716i	0.668646	+	0.743581i	$0.266874\pi$
$181$			20.0077i			1.48716i	−0.668646	+	0.743581i	$0.733126\pi$
$182$	−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
$186$	−11.2904	−	14.0786i	−0.827851	−	1.03229i
$187$	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	$-0.246403\pi$
$191$	19.7644			1.43010			0.715052	+	0.699072i	$0.246403\pi$
$192$	13.2438	−	4.07438i	0.955792	−	0.294043i
$193$	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	$-0.410121\pi$
$197$	7.82139			0.557251			0.278625	+	0.960400i	$0.410121\pi$
$198$	−3.92226	−	22.7510i	−0.278743	−	1.61684i
$199$		−	9.39557i		−	0.666035i	−0.942921	−	0.333017i	$-0.891933\pi$
$199$		−	9.39557i		−	0.666035i	0.942921	−	0.333017i	$-0.108067\pi$
$200$	−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
$204$	17.8999	−	5.26905i	1.25324	−	0.368907i
$205$			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
$210$	−1.53246	−	1.91091i	−0.105750	−	0.131865i
$211$	−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
$216$	−6.48512	−	13.1888i	−0.441256	−	0.897381i
$217$	−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
$222$	−0.253613	−	0.316244i	−0.0170214	−	0.0212249i
$223$		−	7.37577i		−	0.493918i	−0.969026	−	0.246959i	$-0.920569\pi$
$223$		−	7.37577i		−	0.493918i	0.969026	−	0.246959i	$-0.0794313\pi$
$224$	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	$0.869326\pi$
$228$	−0.441106	−	1.49851i	−0.0292130	−	0.0992415i
$229$			1.33389i			0.0881456i	0.999028	+	0.0440728i	$0.0140334\pi$
$229$			1.33389i			0.0881456i	−0.999028	+	0.0440728i	$0.985967\pi$
$230$	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	$0.820509\pi$
$234$	−4.54157	−	26.3433i	−0.296892	−	1.72211i
$235$	−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	$-0.443577\pi$
$239$	5.45208			0.352665			0.176333	+	0.984331i	$0.443577\pi$
$240$	−3.27912	+	6.10306i	−0.211666	+	0.393951i
$241$	−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
$246$	2.98945	+	3.72770i	0.190600	+	0.237670i
$247$		−	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	$-0.166222\pi$
$252$	−5.85678	−	1.30313i	−0.368942	−	0.0820895i
$253$		−	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	$-0.0310010\pi$
$258$	21.1198	−	16.9371i	1.31486	−	1.05446i
$259$	−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	$-0.706191\pi$
$263$	−19.5713			−1.20682			−0.603408	+	0.797433i	$0.706191\pi$
$264$	−2.75095	+	26.5158i	−0.169310	+	1.63193i
$265$	−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	$-0.517508\pi$
$269$	−1.80334			−0.109951			−0.0549757	+	0.998488i	$0.517508\pi$
$270$	6.94120	+	2.41240i	0.422428	+	0.146814i
$271$		−	31.2148i		−	1.89616i	−0.318029	−	0.948081i	$-0.603021\pi$
$271$		−	31.2148i		−	1.89616i	0.318029	−	0.948081i	$-0.396979\pi$
$272$	−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
$276$	−2.12615	−	7.22290i	−0.127979	−	0.434768i
$277$			16.5075i			0.991839i	0.868369	+	0.495919i	$0.165169\pi$
$277$			16.5075i			0.991839i	−0.868369	+	0.495919i	$0.834831\pi$
$278$	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	$-0.298307\pi$
$282$	−8.74668	+	7.01444i	−0.520857	+	0.417704i
$283$	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
$288$	3.08662	+	16.6875i	0.181881	+	0.983321i
$289$	−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	$-0.347270\pi$
$293$	15.8032			0.923233			0.461617	+	0.887079i	$0.347270\pi$
$294$	−1.91091	+	1.53246i	−0.111446	+	0.0893749i
$295$			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
$300$	−0.978202	−	3.32312i	−0.0564765	−	0.191860i
$301$		−	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
$306$	3.88254	+	22.5206i	0.221950	+	1.28742i
$307$	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	$-0.894732\pi$
$311$	−33.3592			−1.89162			−0.945812	+	0.324714i	$0.894732\pi$
$312$	−3.18532	+	30.7025i	−0.180333	+	1.73819i
$313$	−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	$-0.836474\pi$
$317$	−31.0124			−1.74183			−0.870916	+	0.491432i	$0.836474\pi$
$318$	−12.3174	+	9.87801i	−0.690727	+	0.553931i
$319$		−	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
$324$	16.9609	−	6.02725i	0.942273	−	0.334847i
$325$		−	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
$330$	−8.33898	−	10.3983i	−0.459046	−	0.572409i
$331$	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
$336$	6.10306	+	3.27912i	0.332949	+	0.178890i
$337$	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
$342$	1.88535	−	0.325033i	0.101948	−	0.0175758i
$343$			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	$-0.0828342\pi$
$348$	−2.39216	−	8.12659i	−0.128233	−	0.435631i
$349$		−	19.2627i		−	1.03111i	−0.856858	−	0.515553i	$-0.827586\pi$
$349$		−	19.2627i		−	1.03111i	0.856858	−	0.515553i	$-0.172414\pi$
$350$	−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	$0.907605\pi$
$354$	18.5790	+	23.1672i	0.987463	+	1.23132i
$355$	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	$-0.525636\pi$
$359$	−3.04868			−0.160903			−0.0804515	+	0.996759i	$0.525636\pi$
$360$	−6.96180	−	4.85112i	−0.366919	−	0.255676i
$361$	−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
$366$	5.70495	+	7.11381i	0.298202	+	0.371845i
$367$			26.3146i			1.37361i	0.726841	+	0.686806i	$0.240988\pi$
$367$			26.3146i			1.37361i	−0.726841	+	0.686806i	$0.759012\pi$
$368$	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
$372$	−24.4831	+	7.20689i	−1.26939	+	0.373660i
$373$		−	28.4560i		−	1.47340i	−0.676221	−	0.736698i	$-0.736384\pi$
$373$		−	28.4560i		−	1.47340i	0.676221	−	0.736698i	$-0.263616\pi$
$374$	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
$378$	2.41240	−	6.94120i	0.124081	−	0.357017i
$379$	−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	$-0.629499\pi$
$383$	−15.4881			−0.791403			−0.395702	+	0.918379i	$0.629499\pi$
$384$	1.78468	−	19.5145i	0.0910741	−	0.995844i
$385$	−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	$-0.627567\pi$
$389$	−15.3888			−0.780243			−0.390122	+	0.920763i	$0.627567\pi$
$390$	−9.65567	−	12.0402i	−0.488934	−	0.609678i
$391$			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
$396$	−31.8700	−	7.09107i	−1.60153	−	0.356340i
$397$			29.1797i			1.46449i	0.681042	+	0.732245i	$0.261527\pi$
$397$			29.1797i			1.46449i	−0.681042	+	0.732245i	$0.738473\pi$
$398$	−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	$0.940094\pi$
$402$	6.17264	−	4.95017i	0.307863	−	0.246892i
$403$	−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
$408$	2.72310	−	26.2473i	0.134813	−	1.29943i
$409$	−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
$414$	9.08745	−	1.56667i	0.446624	−	0.0769978i
$415$			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	$-0.102450\pi$
$420$	−3.32312	+	0.978202i	−0.162152	+	0.0477314i
$421$		−	33.0234i		−	1.60946i	−0.593639	−	0.804731i	$-0.702309\pi$
$421$		−	33.0234i		−	1.60946i	0.593639	−	0.804731i	$-0.297691\pi$
$422$	−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
$426$	2.37591	−	1.90537i	0.115113	−	0.0923154i
$427$	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	$-0.696679\pi$
$431$	−24.0536			−1.15862			−0.579312	+	0.815106i	$0.696679\pi$
$432$	−20.7375	+	1.39865i	−0.997733	+	0.0672926i
$433$	−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
$438$	−29.8999	+	23.9783i	−1.42867	+	1.14573i
$439$			15.3749i			0.733806i	0.930259	+	0.366903i	$0.119582\pi$
$439$			15.3749i			0.733806i	−0.930259	+	0.366903i	$0.880418\pi$
$440$	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	$-0.0573034\pi$
$444$	−0.549956	+	0.161886i	−0.0260998	+	0.00768279i
$445$		−	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	$0.924584\pi$
$450$	4.18096	−	0.720796i	0.197092	−	0.0339787i
$451$	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
$456$	−2.19733	−	0.227968i	−0.102900	−	0.0106756i
$457$	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	$-0.507854\pi$
$461$	−1.05944			−0.0493431			−0.0246715	+	0.999696i	$0.507854\pi$
$462$	−10.3983	+	8.33898i	−0.483774	+	0.387965i
$463$			5.56498i			0.258626i	0.991604	+	0.129313i	$0.0412773\pi$
$463$			5.56498i			0.258626i	−0.991604	+	0.129313i	$0.958723\pi$
$464$	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	$-0.107653\pi$
$468$	−36.9022	−	8.21072i	−1.70580	−	0.379541i
$469$		−	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
$474$	7.70565	+	9.60859i	0.353932	+	0.441337i
$475$	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	$-0.349520\pi$
$479$	19.9309			0.910665			0.455332	+	0.890321i	$0.349520\pi$
$480$	6.22246	+	7.56842i	0.284015	+	0.345449i
$481$	−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
$486$	4.93754	+	21.4854i	0.223971	+	0.974596i
$487$		−	44.0236i		−	1.99490i	−0.0713704	−	0.997450i	$-0.522737\pi$
$487$		−	44.0236i		−	1.99490i	0.0713704	−	0.997450i	$-0.477263\pi$
$488$	−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	$-0.330403\pi$
$492$	6.48257	−	1.90823i	0.292257	−	0.0860295i
$493$			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
$498$	14.0383	+	17.5051i	0.629069	+	0.784420i
$499$	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	$-0.610562\pi$
$503$	−15.2687			−0.680796			−0.340398	+	0.940281i	$0.610562\pi$
$504$	−4.85112	+	6.96180i	−0.216086	+	0.310103i
$505$	−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	$-0.655907\pi$
$509$	−21.2276			−0.940895			−0.470447	+	0.882428i	$0.655907\pi$
$510$	8.25454	+	10.2930i	0.365517	+	0.455783i
$511$			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
$516$	−10.8113	−	36.7278i	−0.475941	−	1.61685i
$517$			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	$-0.123213\pi$
$522$	10.2244	−	1.76269i	0.447511	−	0.0771507i
$523$	−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
$528$	33.2102	+	17.8435i	1.44529	+	0.776539i
$529$	−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
$534$	−1.70551	−	2.12669i	−0.0738047	−	0.0920311i
$535$		−	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
$540$	6.88484	−	7.78453i	0.296276	−	0.334993i
$541$		−	4.48368i		−	0.192768i	−0.995344	−	0.0963841i	$-0.969272\pi$
$541$		−	4.48368i		−	0.192768i	0.995344	−	0.0963841i	$-0.0307277\pi$
$542$	−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
$546$	−12.0402	+	9.65567i	−0.515272	+	0.413225i
$547$	−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
$552$	−10.5912	−	1.09882i	−0.450793	−	0.0467688i
$553$	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	$-0.292282\pi$
$557$	28.6621			1.21445			0.607226	+	0.794529i	$0.292282\pi$
$558$	−5.31046	−	30.8032i	−0.224810	−	1.30400i
$559$		−	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	$0.759067\pi$
$564$	4.47746	+	15.2107i	0.188535	+	0.640486i
$565$			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	$-0.0283234\pi$
$570$	0.861697	−	0.691042i	0.0360925	−	0.0289445i
$571$	−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
$576$	23.4888	+	4.92686i	0.978702	+	0.205286i
$577$	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
$582$	11.6620	−	9.35241i	0.483407	−	0.387670i
$583$			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	$-0.0181798\pi$
$588$	0.978202	+	3.32312i	0.0403404	+	0.137043i
$589$		−	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	$0.930271\pi$
$594$	13.1272	−	37.7710i	0.538617	−	1.54976i
$595$	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	$-0.638663\pi$
$599$	−20.6552			−0.843950			−0.421975	+	0.906607i	$0.638663\pi$
$600$	−4.87283	−	0.505545i	−0.198932	−	0.0206388i
$601$	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
$606$	−2.45904	+	1.97204i	−0.0998916	+	0.0801085i
$607$			22.3226i			0.906046i	0.891499	+	0.453023i	$0.149654\pi$
$607$			22.3226i			0.906046i	−0.891499	+	0.453023i	$0.850346\pi$
$608$	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
$612$	31.5473	+	7.01927i	1.27522	+	0.283737i
$613$		−	29.6525i		−	1.19765i	−0.800879	−	0.598826i	$-0.795634\pi$
$613$		−	29.6525i		−	1.19765i	0.800879	−	0.598826i	$-0.204366\pi$
$614$	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	$-0.394600\pi$
$618$	21.9931	+	27.4243i	0.884691	+	1.10317i
$619$	−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
$624$	38.4540	+	20.6609i	1.53939	+	0.827099i
$625$	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
$630$	−0.720796	−	4.18096i	−0.0287172	−	0.166574i
$631$		−	8.13744i		−	0.323946i	−0.986795	−	0.161973i	$-0.948214\pi$
$631$		−	8.13744i		−	0.323946i	0.986795	−	0.161973i	$-0.0517858\pi$
$632$	−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
$636$	6.30534	+	21.4203i	0.250023	+	0.849372i
$637$			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	$0.986094\pi$
$642$	−23.2777	−	29.0262i	−0.918699	−	1.14557i
$643$	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	$-0.628856\pi$
$647$	−20.0359			−0.787693			−0.393846	+	0.919176i	$0.628856\pi$
$648$	1.22680	−	25.4263i	0.0481932	−	0.998838i
$649$	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	$-0.512104\pi$
$653$	−1.94296			−0.0760340			−0.0380170	+	0.999277i	$0.512104\pi$
$654$	13.6239	+	16.9884i	0.532737	+	0.664299i
$655$		−	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	$0.799853\pi$
$660$	−18.0830	+	5.32295i	−0.703879	+	0.207195i
$661$		−	18.1561i		−	0.706192i	−0.935587	−	0.353096i	$-0.885129\pi$
$661$		−	18.1561i		−	0.706192i	0.935587	−	0.353096i	$-0.114871\pi$
$662$	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
$666$	−0.119287	−	0.691924i	−0.00462229	−	0.0268115i
$667$	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
$672$	7.56842	−	6.22246i	0.291958	−	0.240037i
$673$	−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	$-0.441638\pi$
$677$	9.48786			0.364648			0.182324	+	0.983239i	$0.441638\pi$
$678$	12.6892	+	15.8228i	0.487326	+	0.607673i
$679$		−	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	$0.835697\pi$
$684$	0.587629	−	2.64103i	0.0224685	−	0.100982i
$685$		−	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
$690$	4.15342	−	3.33085i	0.158118	−	0.126803i
$691$	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
$696$	−11.9164	−	1.23630i	−0.451688	−	0.0468616i
$697$	−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	$-0.381896\pi$
$701$	19.1996			0.725157			0.362579	+	0.931953i	$0.381896\pi$
$702$	15.2000	−	43.7349i	0.573686	−	1.65067i
$703$		−	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
$708$	40.2883	−	11.8594i	1.51413	−	0.445702i
$709$			20.0482i			0.752925i	0.926432	+	0.376463i	$0.122860\pi$
$709$			20.0482i			0.752925i	−0.926432	+	0.376463i	$0.877140\pi$
$710$	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
$714$	10.2930	−	8.25454i	0.385207	−	0.308918i
$715$	−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	$-0.562291\pi$
$719$	−10.4278			−0.388891			−0.194445	+	0.980913i	$0.562291\pi$
$720$	−10.0862	+	6.50136i	−0.375892	+	0.242291i
$721$	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
$726$	−35.5632	+	28.5200i	−1.31987	+	1.05848i
$727$			24.1849i			0.896970i	0.893790	+	0.448485i	$0.148036\pi$
$727$			24.1849i			0.896970i	−0.893790	+	0.448485i	$0.851964\pi$
$728$	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
$732$	12.3711	−	3.64159i	0.457249	−	0.134597i
$733$			3.88553i			0.143515i	0.997422	+	0.0717576i	$0.0228608\pi$
$733$			3.88553i			0.143515i	−0.997422	+	0.0717576i	$0.977139\pi$
$734$	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
$738$	1.40609	+	8.15601i	0.0517590	+	0.300227i
$739$	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	$-0.318992\pi$
$743$	29.3568			1.07700			0.538498	+	0.842627i	$0.318992\pi$
$744$	−3.72460	+	35.9005i	−0.136550	+	1.31618i
$745$	−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
$750$	1.91091	−	1.53246i	0.0697765	−	0.0559575i
$751$			33.5351i			1.22371i	0.790969	+	0.611857i	$0.209577\pi$
$751$			33.5351i			1.22371i	−0.790969	+	0.611857i	$0.790423\pi$
$752$	−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
$756$	−7.78453	−	6.88484i	−0.283121	−	0.250399i
$757$		−	43.8155i		−	1.59250i	−0.604967	−	0.796250i	$-0.706814\pi$
$757$		−	43.8155i		−	1.59250i	0.604967	−	0.796250i	$-0.293186\pi$
$758$	−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	$0.865835\pi$
$762$	8.54466	+	10.6548i	0.309540	+	0.385982i
$763$	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
$768$	−24.5702	−	12.8182i	−0.886600	−	0.462538i
$769$	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	$-0.767099\pi$
$773$	−41.3736			−1.48811			−0.744053	+	0.668121i	$0.767099\pi$
$774$	46.2089	−	7.96640i	1.66095	−	0.286346i
$775$		−	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
$780$	−20.9382	+	6.16342i	−0.749707	+	0.220686i
$781$		−	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
$786$	−20.2061	−	25.1961i	−0.720728	−	0.898714i
$787$	−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
$792$	−26.3977	+	37.8831i	−0.938000	+	1.34612i
$793$	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	$-0.461520\pi$
$797$	6.80905			0.241189			0.120595	+	0.992702i	$0.461520\pi$
$798$	−0.691042	−	0.861697i	−0.0244626	−	0.0305037i
$799$		−	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
$804$	−3.15980	−	10.7344i	−0.111438	−	0.378572i
$805$		−	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	$-0.117609\pi$
$810$	8.49827	+	9.47520i	0.298599	+	0.332925i
$811$	−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
$816$	−32.8739	−	17.6628i	−1.15082	−	0.618323i
$817$	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	$-0.310678\pi$
$821$	32.1099			1.12064			0.560322	+	0.828275i	$0.310678\pi$
$822$	−2.79196	−	3.48144i	−0.0973807	−	0.121429i
$823$		−	44.6648i		−	1.55692i	−0.627697	−	0.778458i	$-0.716002\pi$
$823$		−	44.6648i		−	1.55692i	0.627697	−	0.778458i	$-0.283998\pi$
$824$	−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	$-0.0732072\pi$
$828$	2.83240	−	12.7299i	0.0984326	−	0.442394i
$829$			32.9548i			1.14457i	0.820056	+	0.572283i	$0.193942\pi$
$829$			32.9548i			1.14457i	−0.820056	+	0.572283i	$0.806058\pi$
$830$	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
$834$	5.38839	−	4.32124i	0.186585	−	0.149632i
$835$	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	$-0.553266\pi$
$839$	−9.64905			−0.333122			−0.166561	+	0.986031i	$0.553266\pi$
$840$	−0.505545	+	4.87283i	−0.0174430	+	0.168128i
$841$	−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
$846$	−19.1373	+	3.29926i	−0.657953	+	0.113431i
$847$			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
$852$	−1.21624	−	4.13177i	−0.0416676	−	0.141552i
$853$			56.9045i			1.94837i	0.225746	+	0.974186i	$0.427518\pi$
$853$			56.9045i			1.94837i	−0.225746	+	0.974186i	$0.572482\pi$
$854$	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	$0.700294\pi$
$858$	−65.5174	+	52.5419i	−2.23673	+	1.79375i
$859$	−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	$-0.660790\pi$
$863$	−28.4324			−0.967852			−0.483926	+	0.875109i	$0.660790\pi$
$864$	−9.31079	+	27.8803i	−0.316760	+	0.948506i
$865$	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
$870$	4.67307	−	3.74759i	0.158432	−	0.127055i
$871$		−	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
$876$	15.3059	+	51.9967i	0.517138	+	1.75681i
$877$		−	44.7606i		−	1.51146i	−0.654883	−	0.755730i	$-0.727282\pi$
$877$		−	44.7606i		−	1.51146i	0.654883	−	0.755730i	$-0.272718\pi$
$878$	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	$-0.183360\pi$
$882$	−4.18096	+	0.720796i	−0.140780	+	0.0242705i
$883$	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	$-0.471858\pi$
$887$	5.25939			0.176593			0.0882965	+	0.996094i	$0.471858\pi$
$888$	−0.0836646	+	0.806423i	−0.00280760	+	0.0270618i
$889$	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
$894$	−42.2774	+	33.9046i	−1.41397	+	1.13394i
$895$		−	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
$900$	1.30313	−	5.85678i	0.0434377	−	0.195226i
$901$		−	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
$906$	−7.89400	−	9.84345i	−0.262261	−	0.327027i
$907$	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	$-0.627138\pi$
$911$	−23.4750			−0.777760			−0.388880	+	0.921288i	$0.627138\pi$
$912$	−1.47867	+	2.75209i	−0.0489637	+	0.0911309i
$913$	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
$918$	−12.9943	+	37.3885i	−0.428876	+	1.23401i
$919$		−	7.89412i		−	0.260403i	−0.991488	−	0.130201i	$-0.958438\pi$
$919$		−	7.89412i		−	0.260403i	0.991488	−	0.130201i	$-0.0415624\pi$
$920$	−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
$924$	5.32295	+	18.0830i	0.175112	+	0.594886i
$925$		−	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	$0.974751\pi$
$930$	−11.2904	−	14.0786i	−0.370226	−	0.461655i
$931$	−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
$936$	−30.5657	+	43.8647i	−0.999072	+	1.43376i
$937$	−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	$-0.385968\pi$
$941$	21.5116			0.701258			0.350629	+	0.936514i	$0.385968\pi$
$942$	37.0251	+	46.1685i	1.20634	+	1.50425i
$943$			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	$-0.0132481\pi$
$948$	16.7096	−	4.91868i	0.542702	−	0.159751i
$949$			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	$0.790499\pi$
$954$	−26.9499	+	4.64615i	−0.872534	+	0.150425i
$955$	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
$960$	13.2438	−	4.07438i	0.427443	−	0.131500i
$961$	−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
$966$	−3.33085	−	4.15342i	−0.107168	−	0.133634i
$967$			35.3522i			1.13685i	0.822735	+	0.568425i	$0.192447\pi$
$967$			35.3522i			1.13685i	−0.822735	+	0.568425i	$0.807553\pi$
$968$	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	$-0.0746470\pi$
$972$	30.7598	+	5.08297i	0.986620	+	0.163036i
$973$		−	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	$0.844855\pi$
$978$	22.3013	−	17.8846i	0.713118	−	0.571888i
$979$	−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	$-0.371557\pi$
$983$	24.6216			0.785307			0.392653	+	0.919687i	$0.371557\pi$
$984$	0.986192	−	9.50566i	0.0314386	−	0.303029i
$985$	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
$990$	−3.92226	−	22.7510i	−0.124658	−	0.723074i
$991$		−	29.1715i		−	0.926663i	−0.886185	−	0.463331i	$-0.846654\pi$
$991$		−	29.1715i		−	0.926663i	0.886185	−	0.463331i	$-0.153346\pi$
$992$	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
$996$	30.4418	−	8.96091i	0.964584	−	0.283937i
$997$		−	36.6193i		−	1.15975i	−0.814707	−	0.579873i	$-0.803102\pi$
$997$		−	36.6193i		−	1.15975i	0.814707	−	0.579873i	$-0.196898\pi$
$998$	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.c.491.31	✓	44
3.2	odd	2		840.2.e.d.491.14	yes	44
4.3	odd	2		3360.2.e.d.911.9		44
8.3	odd	2		840.2.e.d.491.13	yes	44
8.5	even	2		3360.2.e.c.911.9		44
12.11	even	2		3360.2.e.c.911.10		44
24.5	odd	2		3360.2.e.d.911.10		44
24.11	even	2	inner	840.2.e.c.491.32	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.e.c.491.31	✓	44	1.1	even	1	trivial
840.2.e.c.491.32	yes	44	24.11	even	2	inner
840.2.e.d.491.13	yes	44	8.3	odd	2
840.2.e.d.491.14	yes	44	3.2	odd	2
3360.2.e.c.911.9		44	8.5	even	2
3360.2.e.c.911.10		44	12.11	even	2
3360.2.e.d.911.9		44	4.3	odd	2
3360.2.e.d.911.10		44	24.5	odd	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} +(1.91091 - 1.53246i) 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} +(-0.978202 - 3.32312i) 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} +(4.18096 - 0.720796i) 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} +(-4.87283 - 0.505545i) 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} +(1.91091 - 1.53246i) 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} +(1.30313 - 5.85678i) 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} +(-1.53246 - 1.91091i) 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} +(-3.27912 + 6.10306i) 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} +(6.94120 + 2.41240i) 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} +(-0.978202 - 3.32312i) 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} +(-8.33898 - 10.3983i) 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} +(-6.96180 - 4.85112i) 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} +(-9.65567 - 12.0402i) 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} +(-3.32312 + 0.978202i) 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} +(4.18096 - 0.720796i) 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} +(6.22246 + 7.56842i) q^{96} +6.10287 q^{97} +(-0.537216 + 1.30820i) q^{98} +(13.8279 - 8.67665i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 2 q^{2} + 4 q^{3} - 2 q^{4} + 44 q^{5} + 18 q^{6} + 22 q^{8} + 4 q^{9} - 2 q^{10} + 6 q^{12} - 4 q^{14} + 4 q^{15} + 22 q^{16} + 10 q^{18} + 16 q^{19} - 2 q^{20} - 16 q^{23} - 26 q^{24} + 44 q^{25}+ \cdots - 64 q^{99}+O(q^{100}) \) 44 * q - 2 * q^2 + 4 * q^3 - 2 * q^4 + 44 * q^5 + 18 * q^6 + 22 * q^8 + 4 * q^9 - 2 * q^10 + 6 * q^12 - 4 * q^14 + 4 * q^15 + 22 * q^16 + 10 * q^18 + 16 * q^19 - 2 * q^20 - 16 * q^23 - 26 * q^24 + 44 * q^25 + 16 * q^26 + 4 * q^27 - 16 * q^29 + 18 * q^30 + 18 * q^32 + 24 * q^33 + 20 * q^34 + 18 * 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 - 38 * q^48 - 44 * q^49 - 2 * q^50 - 20 * q^52 + 32 * q^53 - 18 * q^54 - 8 * q^56 - 4 * q^58 + 6 * q^60 - 32 * q^62 - 50 * q^64 - 44 * q^66 + 24 * q^67 + 28 * q^68 + 8 * q^69 - 4 * q^70 - 8 * q^71 - 82 * q^72 + 8 * q^73 + 48 * q^74 + 4 * q^75 + 12 * q^76 - 8 * q^77 + 16 * q^78 + 22 * q^80 + 20 * q^81 - 8 * q^82 - 16 * q^84 + 4 * q^86 + 16 * q^87 - 28 * q^88 + 10 * q^90 - 16 * q^91 - 76 * q^92 - 16 * q^93 + 16 * q^95 + 18 * 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