LMFDB - Embedded newform 403.2.bl.b.250.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(16,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([10, 6]))

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

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

chi := DirichletCharacter("403.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.bl (of order $15$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$280$
Relative dimension:	$35$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			250.18
Character	$\chi$	$=$	403.250
Dual form			403.2.bl.b.295.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.00532047 + 0.0506209i) q^{2} +(-2.76686 - 1.23189i) q^{3} +(1.95376 + 0.415285i) q^{4} +3.26010 q^{5} +(0.0770802 - 0.133507i) q^{6} +(1.07316 + 0.228106i) q^{7} +(-0.0628748 + 0.193509i) q^{8} +(4.13060 + 4.58749i) q^{9} +O(q^{10})$	\(q+(-0.00532047 + 0.0506209i) q^{2} +(-2.76686 - 1.23189i) q^{3} +(1.95376 + 0.415285i) q^{4} +3.26010 q^{5} +(0.0770802 - 0.133507i) q^{6} +(1.07316 + 0.228106i) q^{7} +(-0.0628748 + 0.193509i) q^{8} +(4.13060 + 4.58749i) q^{9} +(-0.0173453 + 0.165029i) q^{10} +(-3.83962 + 4.26433i) q^{11} +(-4.89421 - 3.55585i) q^{12} +(1.05374 - 3.44814i) q^{13} +(-0.0172566 + 0.0531105i) q^{14} +(-9.02025 - 4.01608i) q^{15} +(3.63999 + 1.62063i) q^{16} +(2.82293 + 3.13518i) q^{17} +(-0.254200 + 0.184687i) q^{18} +(-3.81744 + 1.69963i) q^{19} +(6.36946 + 1.35387i) q^{20} +(-2.68827 - 1.95314i) q^{21} +(-0.195436 - 0.217053i) q^{22} +(8.27173 - 1.75821i) q^{23} +(0.412347 - 0.457957i) q^{24} +5.62825 q^{25} +(0.168941 + 0.0716867i) q^{26} +(-2.96976 - 9.13997i) q^{27} +(2.00196 + 0.891330i) q^{28} +(0.351359 - 3.34296i) q^{29} +(0.251289 - 0.435246i) q^{30} +(2.53302 - 4.95820i) q^{31} +(-0.304871 + 0.528052i) q^{32} +(15.8769 - 7.06884i) q^{33} +(-0.173725 + 0.126219i) q^{34} +(3.49859 + 0.743649i) q^{35} +(6.16508 + 10.6782i) q^{36} +(-1.85882 - 3.21958i) q^{37} +(-0.0657264 - 0.202285i) q^{38} +(-7.16325 + 8.24244i) q^{39} +(-0.204978 + 0.630858i) q^{40} +(-0.202464 + 1.92632i) q^{41} +(0.113173 - 0.125691i) q^{42} +(-6.40155 + 2.85015i) q^{43} +(-9.27261 + 6.73694i) q^{44} +(13.4662 + 14.9557i) q^{45} +(0.0449927 + 0.428077i) q^{46} +(7.25820 - 5.27339i) q^{47} +(-8.07492 - 8.96811i) q^{48} +(-5.29519 - 2.35757i) q^{49} +(-0.0299450 + 0.284907i) q^{50} +(-3.94847 - 12.1521i) q^{51} +(3.49070 - 6.29923i) q^{52} +(-2.65231 + 8.16297i) q^{53} +(0.478474 - 0.101703i) q^{54} +(-12.5175 + 13.9021i) q^{55} +(-0.111615 + 0.193323i) q^{56} +12.6561 q^{57} +(0.167354 + 0.0355722i) q^{58} +(-0.324314 - 3.08564i) q^{59} +(-15.9556 - 11.5924i) q^{60} +(1.39632 - 2.41850i) q^{61} +(0.237512 + 0.154604i) q^{62} +(3.38634 + 5.86530i) q^{63} +(6.42189 + 4.66577i) q^{64} +(3.43528 - 11.2413i) q^{65} +(0.273359 + 0.841311i) q^{66} +(0.0943327 + 0.163389i) q^{67} +(4.21333 + 7.29771i) q^{68} +(-25.0527 - 5.32511i) q^{69} +(-0.0562584 + 0.173145i) q^{70} +(-5.19163 - 5.76589i) q^{71} +(-1.14743 + 0.510869i) q^{72} +(-1.84697 - 5.68439i) q^{73} +(0.172868 - 0.0769657i) q^{74} +(-15.5726 - 6.93337i) q^{75} +(-8.16419 + 1.73535i) q^{76} +(-5.09323 + 3.70045i) q^{77} +(-0.379128 - 0.406464i) q^{78} +(-4.26652 + 13.1310i) q^{79} +(11.8667 + 5.28341i) q^{80} +(-1.10671 + 10.5297i) q^{81} +(-0.0964349 - 0.0204979i) q^{82} +(-3.12374 - 2.26953i) q^{83} +(-4.44113 - 4.93238i) q^{84} +(9.20303 + 10.2210i) q^{85} +(-0.110218 - 0.339216i) q^{86} +(-5.09031 + 8.81667i) q^{87} +(-0.583769 - 1.01112i) q^{88} +(-2.02975 + 2.25426i) q^{89} +(-0.828716 + 0.602098i) q^{90} +(1.91736 - 3.46002i) q^{91} +16.8911 q^{92} +(-13.1165 + 10.5983i) q^{93} +(0.228327 + 0.395474i) q^{94} +(-12.4452 + 5.54097i) q^{95} +(1.49404 - 1.08548i) q^{96} +(-1.27696 - 0.271426i) q^{97} +(0.147515 - 0.255504i) q^{98} -35.4225 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 280 q + q^{2} + 39 q^{4} - 8 q^{5} - 2 q^{7} + 12 q^{8} + 29 q^{9}+O(q^{10}) $ 280 * q + q^2 + 39 * q^4 - 8 * q^5 - 2 * q^7 + 12 * q^8 + 29 * q^9	\( 280 q + q^{2} + 39 q^{4} - 8 q^{5} - 2 q^{7} + 12 q^{8} + 29 q^{9} - 21 q^{10} - q^{11} - 16 q^{12} - 54 q^{14} - 27 q^{15} + 31 q^{16} + 2 q^{17} - 10 q^{18} + 5 q^{19} - 3 q^{20} + 68 q^{21} - 39 q^{22} - 7 q^{23} + 48 q^{24} + 200 q^{25} + 6 q^{26} - 78 q^{27} + 30 q^{28} - 16 q^{29} - 66 q^{30} - 62 q^{31} - 56 q^{32} - 20 q^{33} - 126 q^{34} - 37 q^{35} - 140 q^{36} - 36 q^{37} + 4 q^{38} + 28 q^{39} - 158 q^{40} - 4 q^{41} + 16 q^{42} - 16 q^{43} + 42 q^{44} - 46 q^{45} - 29 q^{46} + 8 q^{47} - 36 q^{48} + 43 q^{49} - 5 q^{50} - 134 q^{51} - q^{52} + 8 q^{53} + 44 q^{54} - 55 q^{55} - 42 q^{56} + 140 q^{57} + 38 q^{58} - 23 q^{59} + 38 q^{60} + 40 q^{61} + 19 q^{62} - 146 q^{63} - 68 q^{64} + 2 q^{65} + 6 q^{66} + 46 q^{67} + 86 q^{68} - 32 q^{69} - 4 q^{70} + 60 q^{71} + 73 q^{72} - 12 q^{73} - 44 q^{74} + 16 q^{75} - 70 q^{76} + 10 q^{77} - 142 q^{78} + 134 q^{79} - 72 q^{80} - 18 q^{81} + 28 q^{82} - 88 q^{83} + 81 q^{84} - 69 q^{85} + 188 q^{86} - 28 q^{87} + 42 q^{88} + 12 q^{89} + 22 q^{90} + 67 q^{91} - 324 q^{92} - 25 q^{93} - 62 q^{94} + 16 q^{95} + 276 q^{96} + 16 q^{97} + 76 q^{98} - 60 q^{99}+O(q^{100}) \) 280 * q + q^2 + 39 * q^4 - 8 * q^5 - 2 * q^7 + 12 * q^8 + 29 * q^9 - 21 * q^10 - q^11 - 16 * q^12 - 54 * q^14 - 27 * q^15 + 31 * q^16 + 2 * q^17 - 10 * q^18 + 5 * q^19 - 3 * q^20 + 68 * q^21 - 39 * q^22 - 7 * q^23 + 48 * q^24 + 200 * q^25 + 6 * q^26 - 78 * q^27 + 30 * q^28 - 16 * q^29 - 66 * q^30 - 62 * q^31 - 56 * q^32 - 20 * q^33 - 126 * q^34 - 37 * q^35 - 140 * q^36 - 36 * q^37 + 4 * q^38 + 28 * q^39 - 158 * q^40 - 4 * q^41 + 16 * q^42 - 16 * q^43 + 42 * q^44 - 46 * q^45 - 29 * q^46 + 8 * q^47 - 36 * q^48 + 43 * q^49 - 5 * q^50 - 134 * q^51 - q^52 + 8 * q^53 + 44 * q^54 - 55 * q^55 - 42 * q^56 + 140 * q^57 + 38 * q^58 - 23 * q^59 + 38 * q^60 + 40 * q^61 + 19 * q^62 - 146 * q^63 - 68 * q^64 + 2 * q^65 + 6 * q^66 + 46 * q^67 + 86 * q^68 - 32 * q^69 - 4 * q^70 + 60 * q^71 + 73 * q^72 - 12 * q^73 - 44 * q^74 + 16 * q^75 - 70 * q^76 + 10 * q^77 - 142 * q^78 + 134 * q^79 - 72 * q^80 - 18 * q^81 + 28 * q^82 - 88 * q^83 + 81 * q^84 - 69 * q^85 + 188 * q^86 - 28 * q^87 + 42 * q^88 + 12 * q^89 + 22 * q^90 + 67 * q^91 - 324 * q^92 - 25 * q^93 - 62 * q^94 + 16 * q^95 + 276 * q^96 + 16 * q^97 + 76 * q^98 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	−0.00532047	+	0.0506209i	−0.00376214	+	0.0357944i	−0.996242	−	0.0866143i	$-0.972395\pi$
$2$	−0.00532047	+	0.0506209i	−0.00376214	+	0.0357944i	0.992480	+	0.122409i	$0.0390619\pi$
$3$	−2.76686	−	1.23189i	−1.59745	−	0.711230i	−0.601310	−	0.799016i	$-0.705354\pi$
$3$	−2.76686	−	1.23189i	−1.59745	−	0.711230i	−0.996139	+	0.0877857i	$0.972021\pi$
$4$	1.95376	+	0.415285i	0.976881	+	0.207642i
$5$	3.26010			1.45796			0.728981	−	0.684534i	$-0.239994\pi$
$5$	3.26010			1.45796			0.728981	+	0.684534i	$0.239994\pi$
$6$	0.0770802	−	0.133507i	0.0314679	−	0.0545040i
$7$	1.07316	+	0.228106i	0.405615	+	0.0862160i	0.406201	−	0.913784i	$-0.366853\pi$
$7$	1.07316	+	0.228106i	0.405615	+	0.0862160i	−0.000586343		1.00000i	$0.500187\pi$
$8$	−0.0628748	+	0.193509i	−0.0222296	+	0.0684157i
$9$	4.13060	+	4.58749i	1.37687	+	1.52916i
$10$	−0.0173453	+	0.165029i	−0.00548506	+	0.0521868i
$11$	−3.83962	+	4.26433i	−1.15769	+	1.28574i	−0.206044	+	0.978543i	$0.566059\pi$
$11$	−3.83962	+	4.26433i	−1.15769	+	1.28574i	−0.951645	+	0.307201i	$0.900608\pi$
$12$	−4.89421	−	3.55585i	−1.41284	−	1.02649i
$13$	1.05374	−	3.44814i	0.292254	−	0.956341i
$13$	1.05374	−	3.44814i	0.292254	−	0.956341i
$14$	−0.0172566	+	0.0531105i	−0.00461203	+	0.0141944i
$15$	−9.02025	−	4.01608i	−2.32902	−	1.03695i
$16$	3.63999	+	1.62063i	0.909997	+	0.405157i
$17$	2.82293	+	3.13518i	0.684661	+	0.760393i	0.980856	−	0.194735i	$-0.0623846\pi$
$17$	2.82293	+	3.13518i	0.684661	+	0.760393i	−0.296195	+	0.955127i	$0.595718\pi$
$18$	−0.254200	+	0.184687i	−0.0599154	+	0.0435311i
$19$	−3.81744	+	1.69963i	−0.875780	+	0.389922i	−0.794856	−	0.606798i	$-0.792454\pi$
$19$	−3.81744	+	1.69963i	−0.875780	+	0.389922i	−0.0809238	+	0.996720i	$0.525787\pi$
$20$	6.36946	+	1.35387i	1.42425	+	0.302735i
$21$	−2.68827	−	1.95314i	−0.586629	−	0.426211i
$22$	−0.195436	−	0.217053i	−0.0416670	−	0.0462759i
$23$	8.27173	−	1.75821i	1.72478	−	0.366612i	0.764275	−	0.644891i	$-0.223097\pi$
$23$	8.27173	−	1.75821i	1.72478	−	0.366612i	0.960500	+	0.278278i	$0.0897638\pi$
$24$	0.412347	−	0.457957i	0.0841699	−	0.0934802i
$25$	5.62825			1.12565
$26$	0.168941	+	0.0716867i	0.0331321	+	0.0140589i
$27$	−2.96976	−	9.13997i	−0.571530	−	1.75899i
$28$	2.00196	+	0.891330i	0.378335	+	0.168446i
$29$	0.351359	−	3.34296i	0.0652457	−	0.620771i	−0.912223	−	0.409693i	$-0.865636\pi$
$29$	0.351359	−	3.34296i	0.0652457	−	0.620771i	0.977469	−	0.211078i	$-0.0676975\pi$
$30$	0.251289	−	0.435246i	0.0458789	−	0.0794647i
$31$	2.53302	−	4.95820i	0.454944	−	0.890520i
$31$	2.53302	−	4.95820i	0.454944	−	0.890520i
$32$	−0.304871	+	0.528052i	−0.0538941	+	0.0933473i
$33$	15.8769	−	7.06884i	2.76381	−	1.23053i
$34$	−0.173725	+	0.126219i	−0.0297936	+	0.0216463i
$35$	3.49859	+	0.743649i	0.591370	+	0.125700i
$36$	6.16508	+	10.6782i	1.02751	+	1.77971i
$37$	−1.85882	−	3.21958i	−0.305589	−	0.529295i	0.671803	−	0.740729i	$-0.265520\pi$
$37$	−1.85882	−	3.21958i	−0.305589	−	0.529295i	−0.977392	+	0.211434i	$0.932187\pi$
$38$	−0.0657264	−	0.202285i	−0.0106622	−	0.0328149i
$39$	−7.16325	+	8.24244i	−1.14704	+	1.31985i
$40$	−0.204978	+	0.630858i	−0.0324099	+	0.0997474i
$41$	−0.202464	+	1.92632i	−0.0316196	+	0.300841i	0.967271	+	0.253746i	$0.0816628\pi$
$41$	−0.202464	+	1.92632i	−0.0316196	+	0.300841i	−0.998890	+	0.0470944i	$0.985004\pi$
$42$	0.113173	−	0.125691i	0.0174629	−	0.0193946i
$43$	−6.40155	+	2.85015i	−0.976227	+	0.434644i	−0.831924	−	0.554889i	$-0.812761\pi$
$43$	−6.40155	+	2.85015i	−0.976227	+	0.434644i	−0.144303	+	0.989534i	$0.546094\pi$
$44$	−9.27261	+	6.73694i	−1.39790	+	1.01563i
$45$	13.4662	+	14.9557i	2.00742	+	2.22946i
$46$	0.0449927	+	0.428077i	0.00663381	+	0.0631165i
$47$	7.25820	−	5.27339i	1.05872	−	0.769203i	0.0848669	−	0.996392i	$-0.472954\pi$
$47$	7.25820	−	5.27339i	1.05872	−	0.769203i	0.973851	+	0.227189i	$0.0729535\pi$
$48$	−8.07492	−	8.96811i	−1.16551	−	1.29443i
$49$	−5.29519	−	2.35757i	−0.756455	−	0.336796i
$50$	−0.0299450	+	0.284907i	−0.00423486	+	0.0402920i
$51$	−3.94847	−	12.1521i	−0.552896	−	1.70164i
$52$	3.49070	−	6.29923i	0.484074	−	0.873547i
$53$	−2.65231	+	8.16297i	−0.364323	+	1.12127i	0.586081	+	0.810252i	$0.300670\pi$
$53$	−2.65231	+	8.16297i	−0.364323	+	1.12127i	−0.950404	+	0.311018i	$0.899330\pi$
$54$	0.478474	−	0.101703i	0.0651120	−	0.0138400i
$55$	−12.5175	+	13.9021i	−1.68787	+	1.87456i
$56$	−0.111615	+	0.193323i	−0.0149152	+	0.0258338i
$57$	12.6561			1.67634
$58$	0.167354	+	0.0355722i	0.0219747	+	0.00467086i
$59$	−0.324314	−	3.08564i	−0.0422221	−	0.401717i	−0.995139	−	0.0984839i	$-0.968601\pi$
$59$	−0.324314	−	3.08564i	−0.0422221	−	0.401717i	0.952917	−	0.303233i	$-0.0980660\pi$
$60$	−15.9556	−	11.5924i	−2.05986	−	1.49658i
$61$	1.39632	−	2.41850i	0.178780	−	0.309657i	−0.762683	−	0.646773i	$-0.776118\pi$
$61$	1.39632	−	2.41850i	0.178780	−	0.309657i	0.941463	+	0.337116i	$0.109452\pi$
$62$	0.237512	+	0.154604i	0.0301640	+	0.0196347i
$63$	3.38634	+	5.86530i	0.426638	+	0.738959i
$64$	6.42189	+	4.66577i	0.802736	+	0.583222i
$65$	3.43528	−	11.2413i	0.426094	−	1.39431i
$66$	0.273359	+	0.841311i	0.0336481	+	0.103558i
$67$	0.0943327	+	0.163389i	0.0115246	+	0.0199611i	0.871730	−	0.489986i	$-0.162998\pi$
$67$	0.0943327	+	0.163389i	0.0115246	+	0.0199611i	−0.860206	+	0.509947i	$0.829665\pi$
$68$	4.21333	+	7.29771i	0.510942	+	0.884977i
$69$	−25.0527	−	5.32511i	−3.01599	−	0.641068i
$70$	−0.0562584	+	0.173145i	−0.00672416	+	0.0206948i
$71$	−5.19163	−	5.76589i	−0.616133	−	0.684285i	0.351633	−	0.936138i	$-0.385627\pi$
$71$	−5.19163	−	5.76589i	−0.616133	−	0.684285i	−0.967765	+	0.251853i	$0.918960\pi$
$72$	−1.14743	+	0.510869i	−0.135226	+	0.0602064i
$73$	−1.84697	−	5.68439i	−0.216171	−	0.665307i	−0.999068	−	0.0431557i	$-0.986259\pi$
$73$	−1.84697	−	5.68439i	−0.216171	−	0.665307i	0.782897	−	0.622151i	$-0.213741\pi$
$74$	0.172868	−	0.0769657i	0.0200955	−	0.00894708i
$75$	−15.5726	−	6.93337i	−1.79817	−	0.800597i
$76$	−8.16419	+	1.73535i	−0.936497	+	0.199059i
$77$	−5.09323	+	3.70045i	−0.580427	+	0.421705i
$78$	−0.379128	−	0.406464i	−0.0429278	−	0.0460230i
$79$	−4.26652	+	13.1310i	−0.480021	+	1.47735i	0.359044	+	0.933321i	$0.383103\pi$
$79$	−4.26652	+	13.1310i	−0.480021	+	1.47735i	−0.839065	+	0.544031i	$0.816897\pi$
$80$	11.8667	+	5.28341i	1.32674	+	0.590703i
$81$	−1.10671	+	10.5297i	−0.122968	+	1.16996i
$82$	−0.0964349	−	0.0204979i	−0.0106495	−	0.00226361i
$83$	−3.12374	−	2.26953i	−0.342875	−	0.249113i	0.402999	−	0.915200i	$-0.367968\pi$
$83$	−3.12374	−	2.26953i	−0.342875	−	0.249113i	−0.745874	+	0.666087i	$0.767968\pi$
$84$	−4.44113	−	4.93238i	−0.484567	−	0.538166i
$85$	9.20303	+	10.2210i	0.998209	+	1.10862i
$86$	−0.110218	−	0.339216i	−0.0118851	−	0.0365786i
$87$	−5.09031	+	8.81667i	−0.545738	+	0.945246i
$88$	−0.583769	−	1.01112i	−0.0622300	−	0.107786i
$89$	−2.02975	+	2.25426i	−0.215153	+	0.238952i	−0.841054	−	0.540951i	$-0.818065\pi$
$89$	−2.02975	+	2.25426i	−0.215153	+	0.238952i	0.625901	+	0.779902i	$0.284731\pi$
$90$	−0.828716	+	0.602098i	−0.0873544	+	0.0634667i
$91$	1.91736	−	3.46002i	0.200994	−	0.362709i
$92$	16.8911			1.76102
$93$	−13.1165	+	10.5983i	−1.36012	+	1.09899i
$94$	0.228327	+	0.395474i	0.0235501	+	0.0407900i
$95$	−12.4452	+	5.54097i	−1.27685	+	0.568492i
$96$	1.49404	−	1.08548i	0.152485	−	0.110787i
$97$	−1.27696	−	0.271426i	−0.129656	−	0.0275592i	0.142627	−	0.989777i	$-0.454445\pi$
$97$	−1.27696	−	0.271426i	−0.129656	−	0.0275592i	−0.272282	+	0.962217i	$0.587779\pi$
$98$	0.147515	−	0.255504i	0.0149013	−	0.0258098i
$99$	−35.4225			−3.56009
$100$	10.9963	+	2.33733i	1.09963	+	0.233733i
$101$	6.50323	−	1.38230i	0.647096	−	0.137544i	0.127340	−	0.991859i	$-0.459356\pi$
$101$	6.50323	−	1.38230i	0.647096	−	0.137544i	0.519756	+	0.854315i	$0.326023\pi$
$102$	0.636160	−	0.135220i	0.0629892	−	0.0133888i
$103$	−7.34209	−	5.33434i	−0.723438	−	0.525608i	0.164043	−	0.986453i	$-0.447546\pi$
$103$	−7.34209	−	5.33434i	−0.723438	−	0.525608i	−0.887481	+	0.460845i	$0.847546\pi$
$104$	0.600991	+	0.420708i	0.0589320	+	0.0412538i
$105$	−8.76404	−	6.36745i	−0.855283	−	0.621399i
$106$	−0.399105	−	0.177693i	−0.0387645	−	0.0172591i
$107$	3.52460	−	0.749178i	0.340736	−	0.0724258i	−0.0343655	−	0.999409i	$-0.510941\pi$
$107$	3.52460	−	0.749178i	0.340736	−	0.0724258i	0.375102	+	0.926984i	$0.377608\pi$
$108$	−2.00650	−	19.0906i	−0.193076	−	1.83699i
$109$	−11.1802	+	8.12291i	−1.07087	+	0.778033i	−0.976069	−	0.217463i	$-0.930222\pi$
$109$	−11.1802	+	8.12291i	−1.07087	+	0.778033i	−0.0948025	+	0.995496i	$0.530222\pi$
$110$	−0.637140	−	0.707615i	−0.0607489	−	0.0674685i
$111$	1.17696	+	11.1980i	0.111712	+	1.06287i
$112$	3.53660	+	2.56949i	0.334177	+	0.242794i
$113$	−0.642451	−	0.136557i	−0.0604367	−	0.0128462i	0.177594	−	0.984104i	$-0.443169\pi$
$113$	−0.642451	−	0.136557i	−0.0604367	−	0.0128462i	−0.238031	+	0.971258i	$0.576502\pi$
$114$	−0.0673363	+	0.640662i	−0.00630662	+	0.0600035i
$115$	26.9667	−	5.73194i	2.51466	−	0.534507i
$116$	2.07475	−	6.38542i	0.192636	−	0.592872i
$117$	20.1708	−	9.40885i	1.86480	−	0.869849i
$118$	0.157924			0.0145380
$119$	2.31429	+	4.00846i	0.212150	+	0.367455i
$120$	1.34429	−	1.49299i	0.122716	−	0.136290i
$121$	−2.29201	−	21.8070i	−0.208365	−	1.98246i
$122$	0.114997	+	0.0835504i	0.0104114	+	0.00756430i
$123$	2.93320	−	5.08045i	0.264478	−	0.458089i
$124$	7.00799	−	8.63522i	0.629336	−	0.775466i
$125$	2.04817			0.183194
$126$	−0.314924	+	0.140213i	−0.0280557	+	0.0124912i
$127$	1.58969	+	0.707776i	0.141062	+	0.0628050i	0.476054	−	0.879416i	$-0.342067\pi$
$127$	1.58969	+	0.707776i	0.141062	+	0.0628050i	−0.334991	+	0.942221i	$0.608733\pi$
$128$	−1.08635	+	1.20651i	−0.0960205	+	0.106642i
$129$	21.2233			1.86860
$130$	0.550766	+	0.233706i	0.0483054	+	0.0204974i
$131$	5.62512	+	17.3123i	0.491469	+	1.51258i	0.822389	+	0.568926i	$0.192641\pi$
$131$	5.62512	+	17.3123i	0.491469	+	1.51258i	−0.330920	+	0.943659i	$0.607359\pi$
$132$	33.9552	−	7.21740i	2.95542	−	0.628194i
$133$	−4.48440	+	0.953188i	−0.388847	+	0.0826519i
$134$	−0.00877279	+	0.00390590i	−0.000757854	+	0.000337418i
$135$	−9.68170	−	29.7972i	−0.833268	−	2.56454i
$136$	−0.784175	+	0.349137i	−0.0672425	+	0.0299383i
$137$	−1.00846	−	9.59486i	−0.0861586	−	0.819745i	−0.949213	−	0.314634i	$-0.898118\pi$
$137$	−1.00846	−	9.59486i	−0.0861586	−	0.819745i	0.863055	−	0.505111i	$-0.168548\pi$
$138$	0.402854	−	1.23986i	0.0342932	−	0.105544i
$139$	−0.0318798	−	0.303316i	−0.00270401	−	0.0257269i	0.993087	−	0.117383i	$-0.0374506\pi$
$139$	−0.0318798	−	0.303316i	−0.00270401	−	0.0257269i	−0.995791	+	0.0916562i	$0.970784\pi$
$140$	6.52659	+	2.90583i	0.551598	+	0.245587i
$141$	−26.5787	+	5.64947i	−2.23833	+	0.475771i
$142$	0.319496	−	0.232128i	0.0268115	−	0.0194797i
$143$	10.6580	+	17.7330i	0.891270	+	1.48291i
$144$	7.60070	+	23.3926i	0.633392	+	1.94938i
$145$	1.14547	−	10.8984i	0.0951257	−	0.905061i
$146$	0.297575	−	0.0632516i	0.0246275	−	0.00523474i
$147$	11.7468	+	13.0461i	0.968860	+	1.07603i
$148$	−2.29466	−	7.06223i	−0.188620	−	0.580511i
$149$	−8.77985	+	15.2071i	−0.719273	+	1.24582i	0.242015	+	0.970273i	$0.422192\pi$
$149$	−8.77985	+	15.2071i	−0.719273	+	1.24582i	−0.961288	+	0.275545i	$0.911142\pi$
$150$	0.433827	−	0.751411i	0.0354218	−	0.0613524i
$151$	−0.885346	−	2.72482i	−0.0720485	−	0.221742i	0.908548	−	0.417781i	$-0.137192\pi$
$151$	−0.885346	−	2.72482i	−0.0720485	−	0.221742i	−0.980596	+	0.196039i	$0.937192\pi$
$152$	−0.0888731	−	0.845571i	−0.00720856	−	0.0685849i
$153$	−2.72223	+	25.9003i	−0.220079	+	2.09392i
$154$	−0.160222	−	0.277512i	−0.0129110	−	0.0223625i
$155$	8.25791	−	16.1642i	0.663291	−	1.29834i
$156$	−17.4182	+	13.1290i	−1.39458	+	1.05116i
$157$	−15.5839	−	11.3224i	−1.24373	−	0.903625i	−0.245892	−	0.969297i	$-0.579081\pi$
$157$	−15.5839	−	11.3224i	−1.24373	−	0.903625i	−0.997841	+	0.0656720i	$0.979081\pi$
$158$	−0.642003	−	0.285838i	−0.0510750	−	0.0227401i
$159$	17.3944	−	19.3185i	1.37947	−	1.53205i
$160$	−0.993910	+	1.72150i	−0.0785755	+	0.136097i
$161$	9.27791			0.731202
$162$	−0.527132	−	0.112045i	−0.0414154	−	0.00880312i
$163$	−10.2823	−	11.4196i	−0.805369	−	0.894453i	0.190824	−	0.981624i	$-0.438884\pi$
$163$	−10.2823	−	11.4196i	−0.805369	−	0.894453i	−0.996193	+	0.0871711i	$0.972217\pi$
$164$	−1.19554	+	3.67949i	−0.0933559	+	0.287320i
$165$	51.7602	−	23.0451i	4.02953	−	1.79406i
$166$	0.131505	−	0.146052i	0.0102068	−	0.0113358i
$167$	−0.412977	+	3.92922i	−0.0319571	+	0.304052i	0.966855	+	0.255326i	$0.0821828\pi$
$167$	−0.412977	+	3.92922i	−0.0319571	+	0.304052i	−0.998812	+	0.0487260i	$0.984484\pi$
$168$	0.546975	−	0.397401i	0.0422000	−	0.0306601i
$169$	−10.7793	−	7.26684i	−0.829176	−	0.558988i
$170$	−0.566361	+	0.411485i	−0.0434379	+	0.0315595i
$171$	−23.5653	−	10.4920i	−1.80209	−	0.802340i
$172$	−13.6907	+	2.91005i	−1.04391	+	0.221889i
$173$	2.47581	+	23.5557i	0.188232	+	1.79091i	0.526822	+	0.849976i	$0.323383\pi$
$173$	2.47581	+	23.5557i	0.188232	+	1.79091i	−0.338590	+	0.940934i	$0.609950\pi$
$174$	−0.419225	−	0.304585i	−0.0317814	−	0.0230905i
$175$	6.03999	+	1.28384i	0.456580	+	0.0970492i
$176$	−20.8870	+	9.29951i	−1.57442	+	0.700977i
$177$	−2.90383	+	8.93707i	−0.218265	+	0.671752i
$178$	−0.103314	−	0.114741i	−0.00774369	−	0.00860023i
$179$	−6.88972	+	7.65180i	−0.514962	+	0.571923i	−0.943404	−	0.331646i	$-0.892396\pi$
$179$	−6.88972	+	7.65180i	−0.514962	+	0.571923i	0.428442	+	0.903569i	$0.359063\pi$
$180$	20.0988	+	34.8121i	1.49807	+	2.59474i
$181$	3.75622			0.279198			0.139599	−	0.990208i	$-0.455419\pi$
$181$	3.75622			0.279198			0.139599	+	0.990208i	$0.455419\pi$
$182$	0.164948	+	0.115468i	0.0122268	+	0.00855903i
$183$	−6.84274	+	4.97154i	−0.505830	+	0.367507i
$184$	−0.179854	+	1.71120i	−0.0132590	+	0.126151i
$185$	−6.05995	−	10.4961i	−0.445537	−	0.771692i
$186$	−0.466708	−	0.720356i	−0.0342207	−	0.0528190i
$187$	−24.2084			−1.77029
$188$	16.3708	−	7.28873i	1.19396	−	0.531585i
$189$	−1.10213	−	10.4860i	−0.0801678	−	0.762746i
$190$	−0.214275	−	0.659469i	−0.0155451	−	0.0478429i
$191$	−0.600344	+	1.03983i	−0.0434394	+	0.0752392i	−0.886928	−	0.461908i	$-0.847165\pi$
$191$	−0.600344	+	1.03983i	−0.0434394	+	0.0752392i	0.843488	+	0.537148i	$0.180498\pi$
$192$	−12.0208	−	20.8206i	−0.867525	−	1.50260i
$193$	2.49101	−	2.76655i	0.179307	−	0.199140i	−0.646791	−	0.762668i	$-0.723889\pi$
$193$	2.49101	−	2.76655i	0.179307	−	0.199140i	0.826098	+	0.563527i	$0.190556\pi$
$194$	0.0205339	−	0.0631968i	0.00147425	−	0.00453727i
$195$	−23.3529	+	26.8712i	−1.67234	+	1.92429i
$196$	−9.36647	−	6.80514i	−0.669034	−	0.486081i
$197$	3.04806	−	3.38522i	0.217165	−	0.241187i	−0.624712	−	0.780855i	$-0.714784\pi$
$197$	3.04806	−	3.38522i	0.217165	−	0.241187i	0.841878	+	0.539668i	$0.181450\pi$
$198$	0.188464	−	1.79312i	0.0133936	−	0.127431i
$199$	−0.243746	−	2.31909i	−0.0172787	−	0.164396i	0.982480	−	0.186369i	$-0.0596719\pi$
$199$	−0.243746	−	2.31909i	−0.0172787	−	0.164396i	−0.999759	+	0.0219730i	$0.993005\pi$
$200$	−0.353875	+	1.08912i	−0.0250228	+	0.0770121i
$201$	−0.0597289	−	0.568282i	−0.00421295	−	0.0400835i
$202$	0.0353732	+	0.336554i	0.00248885	+	0.0236798i
$203$	1.13961	−	3.50736i	0.0799851	−	0.246169i
$204$	−2.66777	−	25.3821i	−0.186781	−	1.77710i
$205$	−0.660054	+	6.28000i	−0.0461002	+	0.438614i
$206$	0.309093	−	0.343282i	0.0215355	−	0.0239176i
$207$	42.2330	+	30.6840i	2.93539	+	2.13269i
$208$	9.42372	−	10.8435i	0.653418	−	0.751859i
$209$	7.40971	−	22.8047i	0.512540	−	1.57744i
$210$	0.368955	−	0.409766i	0.0254603	−	0.0282765i
$211$	−6.74960	−	11.6907i	−0.464662	−	0.804818i	0.534524	−	0.845153i	$-0.320491\pi$
$211$	−6.74960	−	11.6907i	−0.464662	−	0.804818i	−0.999186	+	0.0403352i	$0.987157\pi$
$212$	−8.57194	+	14.8470i	−0.588723	+	1.01970i
$213$	7.26160	+	22.3489i	0.497557	+	1.53132i
$214$	0.0191715	+	0.182405i	0.00131054	+	0.0124689i
$215$	−20.8697	+	9.29178i	−1.42330	+	0.633694i
$216$	1.95539			0.133047
$217$	3.84932	−	4.74313i	0.261309	−	0.321984i
$218$	−0.351705	−	0.609171i	−0.0238205	−	0.0412582i
$219$	−1.89221	+	18.0032i	−0.127864	+	1.21654i
$220$	−30.2296	+	21.9631i	−2.03808	+	1.48075i
$221$	13.7851	−	6.43019i	0.927289	−	0.432541i
$222$	−0.573114			−0.0384649
$223$	−12.3280	−	21.3528i	−0.825547	−	1.42989i	−0.901500	−	0.432778i	$-0.857533\pi$
$223$	−12.3280	−	21.3528i	−0.825547	−	1.42989i	0.0759532	−	0.997111i	$-0.475800\pi$
$224$	−0.447626	+	0.497139i	−0.0299083	+	0.0332165i
$225$	23.2480	+	25.8196i	1.54987	+	1.72130i
$226$	0.0103308	−	0.0317949i	0.000687193	−	0.00211496i
$227$	−0.223339	+	0.0994369i	−0.0148235	+	0.00659986i	−0.414135	−	0.910215i	$-0.635916\pi$
$227$	−0.223339	+	0.0994369i	−0.0148235	+	0.00659986i	0.399311	+	0.916815i	$0.369249\pi$
$228$	24.7270	+	5.25588i	1.63758	+	0.348079i
$229$	20.5331	+	14.9182i	1.35686	+	0.985820i	0.998637	+	0.0521854i	$0.0166187\pi$
$229$	20.5331	+	14.9182i	1.35686	+	0.985820i	0.358227	+	0.933634i	$0.383381\pi$
$230$	0.146681	+	1.39557i	0.00967184	+	0.0920214i
$231$	18.6508	−	3.96435i	1.22713	−	0.260835i
$232$	0.624799	+	0.278179i	0.0410201	+	0.0182633i
$233$	−13.9088	+	10.1053i	−0.911196	+	0.662022i	−0.941317	−	0.337524i	$-0.890411\pi$
$233$	−13.9088	+	10.1053i	−0.911196	+	0.662022i	0.0301213	+	0.999546i	$0.490411\pi$
$234$	0.368966	+	1.07113i	0.0241201	+	0.0700217i
$235$	23.6625	−	17.1918i	1.54357	−	1.12147i
$236$	0.647788	−	6.16329i	0.0421674	−	0.401196i
$237$	27.9808	−	31.0758i	1.81755	−	2.01859i
$238$	−0.215225	+	0.0958243i	−0.0139510	+	0.00621137i
$239$	7.43542	−	22.8839i	0.480958	−	1.48024i	−0.356794	−	0.934183i	$-0.616130\pi$
$239$	7.43542	−	22.8839i	0.480958	−	1.48024i	0.837751	−	0.546052i	$-0.183870\pi$
$240$	−26.3250	−	29.2369i	−1.69927	−	1.88724i
$241$	9.61961	+	2.04471i	0.619654	+	0.131711i	0.507033	−	0.861927i	$-0.330742\pi$
$241$	9.61961	+	2.04471i	0.619654	+	0.131711i	0.112621	+	0.993638i	$0.464075\pi$
$242$	1.11609			0.0717448
$243$	1.61797	−	2.80241i	0.103793	−	0.179775i
$244$	3.73244	−	4.14529i	0.238945	−	0.265375i
$245$	−17.2628	−	7.68591i	−1.10288	−	0.491035i
$246$	0.241571	+	0.175512i	0.0154020	+	0.0111902i
$247$	1.83800	+	14.9540i	0.116949	+	0.951500i
$248$	0.800192	+	0.801908i	0.0508123	+	0.0509212i
$249$	5.84716	+	10.1276i	0.370548	+	0.641809i
$250$	−0.0108972	+	0.103680i	−0.000689203	+	0.00655732i
$251$	0.551610	+	5.24822i	0.0348173	+	0.331265i	0.998041	+	0.0625637i	$0.0199277\pi$
$251$	0.551610	+	5.24822i	0.0348173	+	0.331265i	−0.963224	+	0.268701i	$0.913406\pi$
$252$	4.18032	+	12.8657i	0.263335	+	0.810463i
$253$	−24.2627	+	42.0242i	−1.52538	+	2.64204i
$254$	−0.0442862	+	0.0767059i	−0.00277876	+	0.00481296i
$255$	−12.8724	−	39.6172i	−0.806101	−	2.48092i
$256$	10.5677	+	11.7366i	0.660480	+	0.733537i
$257$	2.20287	−	0.468235i	0.137411	−	0.0292077i	−0.138692	−	0.990336i	$-0.544290\pi$
$257$	2.20287	−	0.468235i	0.137411	−	0.0292077i	0.276104	+	0.961128i	$0.410957\pi$
$258$	−0.112918	+	1.07434i	−0.00702996	+	0.0668856i
$259$	−1.26040	−	3.87912i	−0.0783175	−	0.241037i
$260$	11.3800	−	20.5361i	0.705761	−	1.27360i
$261$	16.7871	−	12.1965i	1.03910	−	0.754947i
$262$	−0.906294	+	0.192639i	−0.0559910	+	0.0119013i
$263$	8.33572	+	3.71130i	0.514003	+	0.228849i	0.647311	−	0.762226i	$-0.275893\pi$
$263$	8.33572	+	3.71130i	0.514003	+	0.228849i	−0.133308	+	0.991075i	$0.542560\pi$
$264$	0.369627	+	3.51676i	0.0227490	+	0.216442i
$265$	−8.64680	+	26.6121i	−0.531168	+	1.63477i
$266$	−0.0243921	−	0.232076i	−0.00149558	−	0.0142295i
$267$	8.39304	−	3.73682i	0.513645	−	0.228690i
$268$	0.116451	+	0.358398i	0.00711335	+	0.0218926i
$269$	−6.07983	+	2.70691i	−0.370694	+	0.165043i	−0.583624	−	0.812024i	$-0.698366\pi$
$269$	−6.07983	+	2.70691i	−0.370694	+	0.165043i	0.212931	+	0.977067i	$0.431699\pi$
$270$	1.55987	−	0.331561i	0.0949308	−	0.0201782i
$271$	−4.61817	+	0.981623i	−0.280534	+	0.0596293i	−0.346030	−	0.938224i	$-0.612470\pi$
$271$	−4.61817	+	0.981623i	−0.280534	+	0.0596293i	0.0654959	+	0.997853i	$0.479137\pi$
$272$	5.19447	+	15.9869i	0.314961	+	0.969350i
$273$	−9.56744	+	7.21143i	−0.579048	+	0.436456i
$274$	0.491066			0.0296664
$275$	−21.6104	+	24.0007i	−1.30315	+	1.44730i
$276$	−46.7355	−	20.8080i	−2.81315	−	1.25249i
$277$	8.68794	−	3.86812i	0.522008	−	0.232413i	−0.128779	−	0.991673i	$-0.541106\pi$
$277$	8.68794	−	3.86812i	0.522008	−	0.232413i	0.650787	+	0.759261i	$0.274439\pi$
$278$	0.0155238			0.000931053
$279$	33.2086	−	8.86011i	1.98815	−	0.530441i
$280$	−0.363876	+	0.630252i	−0.0217457	+	0.0376647i
$281$	−16.5410	−	12.0178i	−0.986755	−	0.716919i	−0.0275467	−	0.999621i	$-0.508769\pi$
$281$	−16.5410	−	12.0178i	−0.986755	−	0.716919i	−0.959208	+	0.282701i	$0.908769\pi$
$282$	−0.144570	−	1.37549i	−0.00860903	−	0.0819095i
$283$	9.75936	−	10.8389i	0.580134	−	0.644304i	−0.379622	−	0.925142i	$-0.623946\pi$
$283$	9.75936	−	10.8389i	0.580134	−	0.644304i	0.959755	+	0.280838i	$0.0906125\pi$
$284$	−7.74871	−	13.4212i	−0.459802	−	0.796400i
$285$	41.2601			2.44404
$286$	−0.954366	+	0.445172i	−0.0564329	+	0.0263236i
$287$	−0.656681	+	2.02106i	−0.0387627	+	0.119299i
$288$	−3.68173	+	0.782577i	−0.216948	+	0.0461138i
$289$	−0.0834418	+	0.793895i	−0.00490834	+	0.0466997i
$290$	0.545591	+	0.115969i	0.0320382	+	0.00680993i
$291$	3.19881	+	2.32407i	0.187518	+	0.136239i
$292$	−1.24790	−	11.8729i	−0.0730277	−	0.694812i
$293$	−7.03378	−	7.81180i	−0.410918	−	0.456370i	0.501786	−	0.864992i	$-0.332676\pi$
$293$	−7.03378	−	7.81180i	−0.410918	−	0.456370i	−0.912704	+	0.408621i	$0.866010\pi$
$294$	−0.722906	+	0.525222i	−0.0421607	+	0.0306316i
$295$	−1.05730	−	10.0595i	−0.0615582	−	0.585687i
$296$	0.739889	−	0.157268i	0.0430052	−	0.00914104i
$297$	50.3785	+	22.4300i	2.92326	+	1.30152i
$298$	−0.723086	−	0.525353i	−0.0418873	−	0.0304329i
$299$	2.65366	−	30.3747i	0.153465	−	1.75662i
$300$	−27.5458	−	20.0132i	−1.59036	−	1.15546i
$301$	−7.51999	+	1.59842i	−0.433445	+	0.0921316i
$302$	0.142643	−	0.0303197i	0.00820819	−	0.00174470i
$303$	−19.6964	−	4.18660i	−1.13153	−	0.240514i
$304$	−16.6499			−0.954937
$305$	4.55214	−	7.88454i	0.260655	−	0.451467i
$306$	−1.29661	−	0.275604i	−0.0741225	−	0.0157552i
$307$	20.1731	−	14.6566i	1.15134	−	0.836497i	0.162681	−	0.986679i	$-0.447986\pi$
$307$	20.1731	−	14.6566i	1.15134	−	0.836497i	0.988658	+	0.150182i	$0.0479860\pi$
$308$	−11.4877	+	5.11465i	−0.654572	+	0.291434i
$309$	13.7433	+	23.8040i	0.781827	+	1.35416i
$310$	0.774313	+	0.504024i	0.0439780	+	0.0286267i
$311$	15.7595			0.893638			0.446819	−	0.894624i	$-0.352557\pi$
$311$	15.7595			0.893638			0.446819	+	0.894624i	$0.352557\pi$
$312$	−1.14460	−	1.90439i	−0.0648000	−	0.107815i
$313$	−0.555676	+	0.403722i	−0.0314087	+	0.0228197i	−0.603379	−	0.797455i	$-0.706179\pi$
$313$	−0.555676	+	0.403722i	−0.0314087	+	0.0228197i	0.571970	+	0.820274i	$0.306179\pi$
$314$	0.656064	−	0.728632i	0.0370238	−	0.0411191i
$315$	11.0398	+	19.1215i	0.622022	+	1.07737i
$316$	−13.7889	+	23.8830i	−0.775684	+	1.34352i
$317$	−7.32215	−	22.5353i	−0.411253	−	1.26571i	−0.915560	−	0.402182i	$-0.868252\pi$
$317$	−7.32215	−	22.5353i	−0.411253	−	1.26571i	0.504307	−	0.863525i	$-0.331748\pi$
$318$	0.885372	+	0.983305i	0.0496492	+	0.0551410i
$319$	12.9064	+	14.3340i	0.722619	+	0.802549i
$320$	20.9360	+	15.2109i	1.17036	+	0.850315i
$321$	−10.6750	−	2.26904i	−0.595820	−	0.126646i
$322$	−0.0493629	+	0.469656i	−0.00275088	+	0.0261729i
$323$	−16.1050	−	7.17041i	−0.896106	−	0.398972i
$324$	−6.53506	+	20.1128i	−0.363059	+	1.11738i
$325$	5.93069	−	19.4070i	0.328975	−	1.07651i
$326$	0.632778	−	0.459740i	0.0350463	−	0.0254626i
$327$	40.9407	−	8.70220i	2.26402	−	0.481233i
$328$	−0.360030	−	0.160296i	−0.0198793	−	0.00885084i
$329$	8.99207	−	4.00353i	0.495749	−	0.220722i
$330$	0.891176	+	2.74276i	0.0490576	+	0.150984i
$331$	8.61773	−	3.83686i	0.473673	−	0.210893i	−0.155994	−	0.987758i	$-0.549858\pi$
$331$	8.61773	−	3.83686i	0.473673	−	0.210893i	0.629667	+	0.776865i	$0.283191\pi$
$332$	−5.16054	−	5.73136i	−0.283221	−	0.314549i
$333$	7.09173	−	21.8261i	0.388625	−	1.19606i
$334$	−0.196703	−	0.0418106i	−0.0107631	−	0.00228777i
$335$	0.307534	+	0.532665i	0.0168024	+	0.0291026i
$336$	−6.61996	−	11.4661i	−0.361148	−	0.625527i
$337$	5.29503	+	16.2964i	0.288439	+	0.887722i	0.985347	+	0.170562i	$0.0545584\pi$
$337$	5.29503	+	16.2964i	0.288439	+	0.887722i	−0.696908	+	0.717160i	$0.745442\pi$
$338$	0.425205	−	0.506994i	0.0231281	−	0.0275768i
$339$	1.60935	+	1.16926i	0.0874079	+	0.0635055i
$340$	13.7359	+	23.7913i	0.744933	+	1.29026i
$341$	11.4176	+	29.8393i	0.618296	+	1.61589i
$342$	0.656491	−	1.13708i	0.0354990	−	0.0614860i
$343$	−11.3580	−	8.25204i	−0.613272	−	0.445568i
$344$	−0.149033	−	1.41796i	−0.00803534	−	0.0764512i
$345$	−81.6742	−	17.3604i	−4.39719	−	0.934652i
$346$	−1.20559			−0.0648127
$347$	7.42809	−	12.8658i	0.398761	−	0.690674i	−0.594812	−	0.803865i	$-0.702774\pi$
$347$	7.42809	−	12.8658i	0.398761	−	0.690674i	0.993573	+	0.113190i	$0.0361070\pi$
$348$	−13.6067	+	15.1117i	−0.729394	+	0.810074i
$349$	1.63898	−	0.348376i	0.0877326	−	0.0186481i	−0.163836	−	0.986488i	$-0.552387\pi$
$349$	1.63898	−	0.348376i	0.0877326	−	0.0186481i	0.251569	+	0.967839i	$0.419054\pi$
$350$	−0.0971247	+	0.298919i	−0.00519154	+	0.0159779i
$351$	−34.6452	+	0.609017i	−1.84922	+	0.0325069i
$352$	−1.08120	−	3.32759i	−0.0576281	−	0.177361i
$353$	−0.238427	+	2.26848i	−0.0126902	+	0.120739i	−0.999033	−	0.0439663i	$-0.986001\pi$
$353$	−0.238427	+	2.26848i	−0.0126902	+	0.120739i	0.986343	+	0.164705i	$0.0526673\pi$
$354$	−0.436953	−	0.194544i	−0.0232238	−	0.0103399i
$355$	−16.9252	−	18.7974i	−0.898298	−	0.997661i
$356$	−4.90181	+	3.56137i	−0.259795	+	0.188752i
$357$	−1.46534	−	13.9418i	−0.0775542	−	0.737878i
$358$	−0.350685	−	0.389475i	−0.0185343	−	0.0205844i
$359$	−17.6180	+	12.8003i	−0.929845	+	0.675572i	−0.945955	−	0.324299i	$-0.894872\pi$
$359$	−17.6180	+	12.8003i	−0.929845	+	0.675572i	0.0161102	+	0.999870i	$0.494872\pi$
$360$	−3.74074	+	1.66548i	−0.197154	+	0.0877787i
$361$	−1.02941	+	1.14328i	−0.0541795	+	0.0601724i
$362$	−0.0199849	+	0.190143i	−0.00105038	+	0.00999371i
$363$	−20.5221	+	63.1606i	−1.07713	+	3.31507i
$364$	5.18296	−	5.96380i	0.271661	−	0.312588i
$365$	−6.02130	−	18.5317i	−0.315169	−	0.969992i
$366$	−0.215257	−	0.372836i	−0.0112517	−	0.0194885i
$367$	−10.8756	−	18.8370i	−0.567699	−	0.983284i	−0.996793	−	0.0800241i	$-0.974500\pi$
$367$	−10.8756	−	18.8370i	−0.567699	−	0.983284i	0.429094	−	0.903260i	$-0.358833\pi$
$368$	32.9584	+	7.00552i	1.71808	+	0.365188i
$369$	−9.67328	+	7.02805i	−0.503571	+	0.365866i
$370$	0.563566	−	0.250916i	0.0292984	−	0.0130445i
$371$	−4.70836	+	8.15513i	−0.244446	+	0.423393i
$372$	−30.0278	+	15.2594i	−1.55687	+	0.791164i
$373$	5.36365	−	9.29011i	0.277719	−	0.481024i	−0.693098	−	0.720843i	$-0.743755\pi$
$373$	5.36365	−	9.29011i	0.277719	−	0.481024i	0.970818	+	0.239819i	$0.0770882\pi$
$374$	0.128800	−	1.22545i	0.00666009	−	0.0633666i
$375$	−5.66702	−	2.52312i	−0.292643	−	0.130293i
$376$	0.564089	+	1.73609i	0.0290907	+	0.0895319i
$377$	−11.1567	−	4.73412i	−0.574601	−	0.243820i
$378$	0.536676			0.0276036
$379$	−8.96830	+	9.96030i	−0.460670	+	0.511626i	−0.928063	−	0.372424i	$-0.878527\pi$
$379$	−8.96830	+	9.96030i	−0.460670	+	0.511626i	0.467392	+	0.884050i	$0.345194\pi$
$380$	−26.6161	+	5.65742i	−1.36538	+	0.290220i
$381$	−3.52656	−	3.91664i	−0.180671	−	0.200656i
$382$	−0.0494428	−	0.0359223i	−0.00252971	−	0.00183795i
$383$	8.47793	+	1.80204i	0.433202	+	0.0920800i	0.419351	−	0.907824i	$-0.362258\pi$
$383$	8.47793	+	1.80204i	0.433202	+	0.0920800i	0.0138510	+	0.999904i	$0.495591\pi$
$384$	4.49206	−	1.99999i	0.229234	−	0.102062i
$385$	−16.6044	+	12.0638i	−0.846240	+	0.614829i
$386$	0.126792	+	0.140817i	0.00645353	+	0.00716737i
$387$	−39.5172	−	17.5942i	−2.00877	−	0.894364i
$388$	−2.38216	−	1.06060i	−0.120936	−	0.0538441i
$389$	4.45100	−	13.6988i	0.225674	−	0.694555i	−0.772548	−	0.634956i	$-0.781018\pi$
$389$	4.45100	−	13.6988i	0.225674	−	0.694555i	0.998222	−	0.0595982i	$-0.0189819\pi$
$390$	−1.23599	−	1.32511i	−0.0625870	−	0.0670997i
$391$	28.8628	+	20.9701i	1.45965	+	1.06050i
$392$	0.789144	−	0.876433i	0.0398578	−	0.0442666i
$393$	5.76290	−	54.8303i	0.290700	−	2.76582i
$394$	0.155146	+	0.172307i	0.00781612	+	0.00868068i
$395$	−13.9093	+	42.8084i	−0.699852	+	2.15392i
$396$	−69.2071	−	14.7104i	−3.47779	−	0.739226i
$397$	−6.35772	+	11.0119i	−0.319085	+	0.552671i	−0.980297	−	0.197528i	$-0.936709\pi$
$397$	−6.35772	+	11.0119i	−0.319085	+	0.552671i	0.661213	+	0.750199i	$0.270042\pi$
$398$	0.118691			0.00594945
$399$	13.5819	+	2.88693i	0.679947	+	0.144527i
$400$	20.4868	+	9.12130i	1.02434	+	0.456065i
$401$	−3.07416	+	29.2487i	−0.153516	+	1.46061i	0.598319	+	0.801258i	$0.295836\pi$
$401$	−3.07416	+	29.2487i	−0.153516	+	1.46061i	−0.751835	+	0.659351i	$0.770831\pi$
$402$	0.0290847			0.00145062
$403$	−14.4274	−	13.9588i	−0.718681	−	0.695340i
$404$	13.2798			0.660695
$405$	−3.60799	+	34.3277i	−0.179282	+	1.70576i
$406$	0.171483	+	0.0763490i	0.00851054	+	0.00378914i
$407$	20.8665	+	4.43531i	1.03431	+	0.219850i
$408$	2.59980			0.128709
$409$	−5.14618	+	8.91344i	−0.254462	+	0.440741i	−0.964749	−	0.263171i	$-0.915232\pi$
$409$	−5.14618	+	8.91344i	−0.254462	+	0.440741i	0.710287	+	0.703912i	$0.248565\pi$
$410$	−0.314387	−	0.0668251i	−0.0155265	−	0.00330026i
$411$	−9.02951	+	27.7900i	−0.445393	+	1.37078i
$412$	−12.1294	−	13.4711i	−0.597574	−	0.663673i
$413$	0.355815	−	3.38535i	0.0175085	−	0.166582i
$414$	−1.77795	+	1.97462i	−0.0873816	+	0.0970471i
$415$	−10.1837	−	7.39889i	−0.499898	−	0.363197i
$416$	1.49954	+	1.60766i	0.0735211	+	0.0788222i
$417$	−0.285444	+	0.878507i	−0.0139783	+	0.0430207i
$418$	1.11497	+	0.496418i	0.0545351	+	0.0242806i
$419$	26.0394	+	11.5935i	1.27211	+	0.566378i	0.928010	−	0.372556i	$-0.121518\pi$
$419$	26.0394	+	11.5935i	1.27211	+	0.566378i	0.344097	+	0.938934i	$0.388185\pi$
$420$	−14.4785	−	16.0800i	−0.706480	−	0.784626i
$421$	3.47752	−	2.52657i	0.169484	−	0.123137i	−0.499810	−	0.866135i	$-0.666597\pi$
$421$	3.47752	−	2.52657i	0.169484	−	0.123137i	0.669294	+	0.742998i	$0.266597\pi$
$422$	0.627703	−	0.279471i	0.0305561	−	0.0136044i
$423$	54.1723	+	11.5147i	2.63395	+	0.559863i
$424$	−1.41284	−	1.02649i	−0.0686137	−	0.0498508i
$425$	15.8882	+	17.6456i	0.770689	+	0.855937i
$426$	−1.16996	+	0.248682i	−0.0566846	+	0.0120487i
$427$	2.05014	−	2.27691i	0.0992133	−	0.110187i
$428$	7.19736			0.347897
$429$	−7.64430	−	62.1943i	−0.369070	−	3.00277i
$430$	−0.359322	−	1.10588i	−0.0173280	−	0.0533302i
$431$	16.8327	+	7.49438i	0.810800	+	0.360992i	0.769894	−	0.638171i	$-0.220309\pi$
$431$	16.8327	+	7.49438i	0.810800	+	0.360992i	0.0409061	+	0.999163i	$0.486976\pi$
$432$	4.00260	−	38.0822i	0.192575	−	1.83223i
$433$	6.29779	−	10.9081i	0.302653	−	0.524210i	−0.674083	−	0.738655i	$-0.735461\pi$
$433$	6.29779	−	10.9081i	0.302653	−	0.524210i	0.976736	+	0.214446i	$0.0687945\pi$
$434$	0.219621	+	0.220092i	0.0105421	+	0.0105648i
$435$	−16.5949	+	28.7432i	−0.795665	+	1.37813i
$436$	−25.2168	+	11.2272i	−1.20767	+	0.537687i
$437$	−28.5885	+	20.7708i	−1.36757	+	0.993600i
$438$	−0.901270	−	0.191571i	−0.0430643	−	0.00915360i
$439$	18.2127	+	31.5453i	0.869244	+	1.50557i	0.862771	+	0.505595i	$0.168727\pi$
$439$	18.2127	+	31.5453i	0.869244	+	1.50557i	0.00647275	+	0.999979i	$0.497940\pi$
$440$	−1.90315	−	3.29635i	−0.0907290	−	0.157147i
$441$	−11.0570	−	34.0298i	−0.526521	−	1.62047i
$442$	0.252159	+	0.732028i	0.0119940	+	0.0348190i
$443$	4.35393	−	13.4000i	0.206861	−	0.636654i	−0.792770	−	0.609520i	$-0.791362\pi$
$443$	4.35393	−	13.4000i	0.206861	−	0.636654i	0.999632	−	0.0271337i	$-0.00863799\pi$
$444$	−2.35086	+	22.3670i	−0.111567	+	1.06149i
$445$	−6.61718	+	7.34913i	−0.313685	+	0.348382i
$446$	1.14649	−	0.510450i	0.0542878	−	0.0241705i
$447$	43.0261	−	31.2603i	2.03507	−	1.47856i
$448$	5.82739	+	6.47197i	0.275318	+	0.305772i
$449$	1.56679	+	14.9070i	0.0739413	+	0.703504i	0.967209	+	0.253980i	$0.0817398\pi$
$449$	1.56679	+	14.9070i	0.0739413	+	0.703504i	−0.893268	+	0.449524i	$0.851594\pi$
$450$	−1.43070	+	1.03946i	−0.0674439	+	0.0490008i
$451$	−7.43708	−	8.25971i	−0.350198	−	0.388935i
$452$	−1.19848	−	0.533600i	−0.0563720	−	0.0250984i
$453$	−0.907033	+	8.62984i	−0.0426161	+	0.405465i
$454$	−0.00384532	−	0.0118347i	−0.000180470	−	0.000555429i
$455$	6.25079	−	11.2800i	0.293042	−	0.528815i
$456$	−0.795748	+	2.44906i	−0.0372643	+	0.114688i
$457$	−6.23711	+	1.32574i	−0.291759	+	0.0620154i	−0.351466	−	0.936201i	$-0.614317\pi$
$457$	−6.23711	+	1.32574i	−0.291759	+	0.0620154i	0.0597067	+	0.998216i	$0.480983\pi$
$458$	−0.864416	+	0.960032i	−0.0403915	+	0.0448593i
$459$	20.2720	−	35.1122i	0.946217	−	1.63890i
$460$	55.0668			2.56750
$461$	−30.4896	−	6.48076i	−1.42004	−	0.301839i	−0.567015	−	0.823708i	$-0.691902\pi$
$461$	−30.4896	−	6.48076i	−1.42004	−	0.301839i	−0.853026	+	0.521869i	$0.825235\pi$
$462$	0.101448	+	0.965212i	0.00471978	+	0.0449057i
$463$	11.3857	+	8.27217i	0.529136	+	0.384440i	0.820035	−	0.572314i	$-0.193954\pi$
$463$	11.3857	+	8.27217i	0.529136	+	0.384440i	−0.290898	+	0.956754i	$0.593954\pi$
$464$	6.69663	−	11.5989i	0.310883	−	0.538465i
$465$	−42.7610	+	34.5514i	−1.98300	+	1.60228i
$466$	−0.437540	−	0.757841i	−0.0202686	−	0.0351063i
$467$	−16.8620	−	12.2510i	−0.780282	−	0.566908i	0.124782	−	0.992184i	$-0.460177\pi$
$467$	−16.8620	−	12.2510i	−0.780282	−	0.566908i	−0.905064	+	0.425276i	$0.860177\pi$
$468$	43.3164	−	10.0060i	2.00230	−	0.462528i
$469$	0.0639636	+	0.196860i	0.00295356	+	0.00909013i
$470$	0.744368	+	1.28928i	0.0343352	+	0.0594702i
$471$	29.1707	+	50.5252i	1.34412	+	2.32808i
$472$	0.617490	+	0.131252i	0.0284223	+	0.00604134i
$473$	12.4255	−	38.2418i	0.571326	−	1.75836i
$474$	1.42421	+	1.58175i	0.0654163	+	0.0726522i
$475$	−21.4855	+	9.56596i	−0.985823	+	0.438916i
$476$	2.85691	+	8.79266i	0.130946	+	0.403011i
$477$	−48.4032	+	21.5505i	−2.21623	+	0.986729i
$478$	1.11884	+	0.498141i	0.0511747	+	0.0227844i
$479$	26.2267	−	5.57467i	1.19833	−	0.254713i	0.434825	−	0.900515i	$-0.356810\pi$
$479$	26.2267	−	5.57467i	1.19833	−	0.254713i	0.763505	+	0.645802i	$0.223477\pi$
$480$	4.87071	−	3.53878i	0.222317	−	0.161522i
$481$	−13.0603	+	3.01690i	−0.595496	+	0.137559i
$482$	−0.154686	+	0.476075i	−0.00704576	+	0.0216846i
$483$	−25.6707	−	11.4293i	−1.16806	−	0.520053i
$484$	4.57809	−	43.5576i	0.208095	−	1.97989i
$485$	−4.16302	−	0.884877i	−0.189033	−	0.0401802i
$486$	0.133252	+	0.0968133i	0.00604444	+	0.00439154i
$487$	−3.75921	−	4.17502i	−0.170346	−	0.189188i	0.651927	−	0.758282i	$-0.273961\pi$
$487$	−3.75921	−	4.17502i	−0.170346	−	0.189188i	−0.822273	+	0.569094i	$0.807294\pi$
$488$	0.380207	+	0.422262i	0.0172111	+	0.0191149i
$489$	14.3820	+	44.2631i	0.650374	+	2.00165i
$490$	0.480914	−	0.832968i	0.0217255	−	0.0376297i
$491$	−9.89457	−	17.1379i	−0.446536	−	0.773422i	0.551622	−	0.834094i	$-0.314009\pi$
$491$	−9.89457	−	17.1379i	−0.446536	−	0.773422i	−0.998158	+	0.0606718i	$0.980676\pi$
$492$	7.84061	−	8.70788i	0.353482	−	0.392581i
$493$	11.4726	−	8.33535i	0.516701	−	0.375405i
$494$	−0.766764	+	0.0134787i	−0.0344983	+	0.000606436i
$495$	−115.481			−5.19048
$496$	17.2556	−	13.9427i	0.774798	−	0.626046i
$497$	−4.25619	−	7.37193i	−0.190916	−	0.330676i
$498$	−0.543776	+	0.242105i	−0.0243672	+	0.0108490i
$499$	−1.44079	+	1.04679i	−0.0644985	+	0.0468609i	−0.619567	−	0.784944i	$-0.712692\pi$
$499$	−1.44079	+	1.04679i	−0.0644985	+	0.0468609i	0.555069	+	0.831804i	$0.312692\pi$
$500$	4.00164	+	0.850575i	0.178959	+	0.0380389i
$501$	5.98300	−	10.3629i	0.267301	−	0.462979i
$502$	−0.268604			−0.0119884
$503$	−37.0307	−	7.87112i	−1.65112	−	0.350956i	−0.714047	−	0.700098i	$-0.753140\pi$
$503$	−37.0307	−	7.87112i	−1.65112	−	0.350956i	−0.937070	+	0.349142i	$0.886473\pi$
$504$	−1.34790	+	0.286506i	−0.0600403	+	0.0127620i
$505$	21.2012	−	4.50645i	0.943440	−	0.200534i
$506$	−1.99822	−	1.45179i	−0.0888315	−	0.0645399i
$507$	20.8729	+	33.3852i	0.926997	+	1.48269i
$508$	2.81195	+	2.04300i	0.124760	+	0.0906435i
$509$	−37.6194	−	16.7492i	−1.66745	−	0.742397i	−0.667454	−	0.744651i	$-0.732616\pi$
$509$	−37.6194	−	16.7492i	−1.66745	−	0.742397i	−0.999997	+	0.00225434i	$0.999282\pi$
$510$	2.07395	−	0.440831i	0.0918358	−	0.0195203i
$511$	−0.685441	−	6.52153i	−0.0303221	−	0.288496i
$512$	−3.27725	+	2.38106i	−0.144836	+	0.105229i
$513$	26.8714	+	29.8437i	1.18640	+	1.31763i
$514$	0.0119822	+	0.114003i	0.000528511	+	0.00502844i
$515$	−23.9360	−	17.3905i	−1.05474	−	0.766316i
$516$	41.4652	+	8.81370i	1.82540	+	0.388002i
$517$	−5.38125	+	51.1992i	−0.236667	+	2.25174i
$518$	0.203070	−	0.0431639i	0.00892240	−	0.00189651i
$519$	22.1678	−	68.2254i	0.973058	−	2.99476i
$520$	1.95929	+	1.37155i	0.0859206	+	0.0601464i
$521$	14.2425			0.623974			0.311987	−	0.950086i	$-0.399005\pi$
$521$	14.2425			0.623974			0.311987	+	0.950086i	$0.399005\pi$
$522$	0.528085	+	0.914670i	0.0231136	+	0.0400340i
$523$	23.6226	−	26.2356i	1.03295	−	1.14720i	0.0439843	−	0.999032i	$-0.485995\pi$
$523$	23.6226	−	26.2356i	1.03295	−	1.14720i	0.988962	−	0.148171i	$-0.0473385\pi$
$524$	3.80059	+	36.1602i	0.166029	+	1.57966i
$525$	−15.1303	−	10.9928i	−0.660340	−	0.479765i
$526$	−0.232220	+	0.402216i	−0.0101253	+	0.0175375i
$527$	22.6954	−	6.05517i	0.988627	−	0.263767i
$528$	69.2475			3.01361
$529$	44.3187	−	19.7320i	1.92690	−	0.857911i
$530$	−1.30112	−	0.579297i	−0.0565172	−	0.0251631i
$531$	12.8158	−	14.2333i	0.556156	−	0.617674i
$532$	−9.15729			−0.397019
$533$	6.42887	+	2.72796i	0.278465	+	0.118161i
$534$	0.144506	+	0.444745i	0.00625340	+	0.0192460i
$535$	11.4906	−	2.44239i	0.496780	−	0.105594i
$536$	−0.0375483	+	0.00798114i	−0.00162184	+	0.000344733i
$537$	28.4891	−	12.6841i	1.22939	−	0.547361i
$538$	−0.104679	−	0.322168i	−0.00451302	−	0.0138897i
$539$	30.3850	−	13.5283i	1.30877	−	0.582703i
$540$	−6.54140	−	62.2373i	−0.281497	−	2.67827i
$541$	10.1420	−	31.2138i	0.436038	−	1.34199i	−0.455981	−	0.889990i	$-0.650711\pi$
$541$	10.1420	−	31.2138i	0.436038	−	1.34199i	0.892019	−	0.451998i	$-0.149289\pi$
$542$	−0.0251198	−	0.238999i	−0.00107899	−	0.0102659i
$543$	−10.3929	−	4.62724i	−0.446004	−	0.198574i
$544$	−2.51617	+	0.534828i	−0.107880	+	0.0229306i
$545$	−36.4487	+	26.4815i	−1.56129	+	1.13434i
$546$	−0.314146	−	0.522680i	−0.0134442	−	0.0223687i
$547$	7.16702	+	22.0578i	0.306439	+	0.943124i	0.979136	+	0.203205i	$0.0651359\pi$
$547$	7.16702	+	22.0578i	0.306439	+	0.943124i	−0.672697	+	0.739918i	$0.734864\pi$
$548$	2.01431	−	19.1649i	0.0860470	−	0.818683i
$549$	16.8625	−	3.58422i	0.719672	−	0.152971i
$550$	−1.09996	−	1.22163i	−0.0469025	−	0.0520905i
$551$	4.34051	+	13.3587i	0.184912	+	0.569100i
$552$	2.60564	−	4.51309i	0.110903	−	0.192090i
$553$	−7.57390	+	13.1184i	−0.322075	+	0.557850i
$554$	0.149584	+	0.460372i	0.00635521	+	0.0195593i
$555$	3.83700	+	36.5066i	0.162871	+	1.54962i
$556$	0.0636771	−	0.605847i	0.00270051	−	0.0256936i
$557$	−3.51963	−	6.09618i	−0.149131	−	0.258303i	0.781775	−	0.623560i	$-0.214314\pi$
$557$	−3.51963	−	6.09618i	−0.149131	−	0.258303i	−0.930907	+	0.365257i	$0.880981\pi$
$558$	0.271822	+	1.72819i	0.0115071	+	0.0731601i
$559$	3.08218	+	25.0767i	0.130362	+	1.06063i
$560$	11.5297	+	8.37679i	0.487217	+	0.353984i
$561$	66.9813	+	29.8220i	2.82795	+	1.25909i
$562$	0.696356	−	0.773381i	0.0293740	−	0.0326231i
$563$	17.5453	−	30.3894i	0.739447	−	1.28076i	−0.213298	−	0.976987i	$-0.568421\pi$
$563$	17.5453	−	30.3894i	0.739447	−	1.28076i	0.952745	−	0.303772i	$-0.0982461\pi$
$564$	−54.2745			−2.28537
$565$	−2.09445	−	0.445190i	−0.0881143	−	0.0187293i
$566$	0.496749	+	0.551695i	0.0208799	+	0.0231895i
$567$	−3.58955	+	11.0475i	−0.150747	+	0.463952i
$568$	1.44217	−	0.642096i	0.0605122	−	0.0269418i
$569$	−22.5888	+	25.0874i	−0.946970	+	1.05172i	0.0516219	+	0.998667i	$0.483561\pi$
$569$	−22.5888	+	25.0874i	−0.946970	+	1.05172i	−0.998592	+	0.0530500i	$0.983106\pi$
$570$	−0.219523	+	2.08862i	−0.00919481	+	0.0874828i
$571$	−16.2769	+	11.8259i	−0.681168	+	0.494897i	−0.873745	−	0.486384i	$-0.838315\pi$
$571$	−16.2769	+	11.8259i	−0.681168	+	0.494897i	0.192577	+	0.981282i	$0.438315\pi$
$572$	13.4590	+	39.0722i	0.562750	+	1.63369i
$573$	2.94202	−	2.13750i	0.122905	−	0.0892954i
$574$	−0.0988139	−	0.0439948i	−0.00412441	−	0.00183631i
$575$	46.5554	−	9.89566i	1.94149	−	0.412677i
$576$	5.12202	+	48.7328i	0.213418	+	2.03053i
$577$	−2.40149	−	1.74478i	−0.0999753	−	0.0726363i	0.536674	−	0.843789i	$-0.319680\pi$
$577$	−2.40149	−	1.74478i	−0.0999753	−	0.0726363i	−0.636650	+	0.771153i	$0.719680\pi$
$578$	−0.0397437	−	0.00844779i	−0.00165312	−	0.000351382i
$579$	−10.3004	+	4.58602i	−0.428068	+	0.190588i
$580$	6.76389	−	20.8171i	0.280855	−	0.864384i
$581$	−2.83456	−	3.14810i	−0.117597	−	0.130605i
$582$	−0.134666	+	0.149561i	−0.00558208	+	0.00619952i
$583$	−24.6257	−	42.6530i	−1.01989	−	1.76651i
$584$	1.21611			0.0503228
$585$	65.7590	−	30.6738i	2.71880	−	1.26821i
$586$	0.432863	−	0.314494i	0.0178814	−	0.0129916i
$587$	1.23768	−	11.7757i	0.0510844	−	0.486036i	−0.938831	−	0.344378i	$-0.888090\pi$
$587$	1.23768	−	11.7757i	0.0510844	−	0.486036i	0.989916	−	0.141658i	$-0.0452434\pi$
$588$	17.5326	+	30.3673i	0.723031	+	1.25233i
$589$	−1.24253	+	23.2328i	−0.0511976	+	0.957292i
$590$	0.514847			0.0211959
$591$	−12.6038	+	5.61156i	−0.518450	+	0.230829i
$592$	−1.54836	−	14.7317i	−0.0636373	−	0.605468i
$593$	2.22196	+	6.83850i	0.0912451	+	0.280823i	0.986257	−	0.165219i	$-0.0528331\pi$
$593$	2.22196	+	6.83850i	0.0912451	+	0.280823i	−0.895012	+	0.446042i	$0.852833\pi$
$594$	−1.40346	+	2.43087i	−0.0575848	+	0.0997398i
$595$	7.54481	+	13.0680i	0.309307	+	0.535735i
$596$	−23.4690	+	26.0650i	−0.961328	+	1.06766i
$597$	−2.18244	+	6.71686i	−0.0893214	+	0.274903i
$598$	1.52348	+	0.295939i	0.0622997	+	0.0121018i
$599$	0.448868	+	0.326122i	0.0183403	+	0.0133250i	0.596918	−	0.802303i	$-0.296392\pi$
$599$	0.448868	+	0.326122i	0.0183403	+	0.0133250i	−0.578577	+	0.815628i	$0.696392\pi$
$600$	2.32079	−	2.57750i	0.0947460	−	0.105226i
$601$	−0.327847	+	3.11926i	−0.0133732	+	0.127237i	−0.999172	−	0.0406958i	$-0.987043\pi$
$601$	−0.327847	+	3.11926i	−0.0133732	+	0.127237i	0.985798	+	0.167933i	$0.0537092\pi$
$602$	−0.0409037	−	0.389173i	−0.00166711	−	0.0158615i
$603$	−0.359895	+	1.10764i	−0.0146561	+	0.0451068i
$604$	−0.598181	−	5.69131i	−0.0243396	−	0.231576i
$605$	−7.47219	−	71.0932i	−0.303788	−	2.89035i
$606$	0.316723	−	0.974774i	0.0128660	−	0.0395975i
$607$	2.10550	+	20.0325i	0.0854598	+	0.813096i	0.950360	+	0.311152i	$0.100715\pi$
$607$	2.10550	+	20.0325i	0.0854598	+	0.813096i	−0.864900	+	0.501944i	$0.832618\pi$
$608$	0.266331	−	2.53397i	0.0108012	−	0.102766i
$609$	−7.47383	+	8.30053i	−0.302855	+	0.336354i
$610$	0.374903	+	0.272383i	0.0151794	+	0.0110285i
$611$	−10.5352	−	30.5840i	−0.426207	−	1.23730i
$612$	−16.0746	+	49.4725i	−0.649777	+	1.99981i
$613$	−16.3753	+	18.1867i	−0.661393	+	0.734552i	−0.976741	−	0.214425i	$-0.931212\pi$
$613$	−16.3753	+	18.1867i	−0.661393	+	0.734552i	0.315347	+	0.948976i	$0.397879\pi$
$614$	0.634600	+	1.09916i	0.0256104	+	0.0443585i
$615$	9.56253	−	16.5628i	0.385598	−	0.667876i
$616$	−0.395833	−	1.21825i	−0.0159486	−	0.0490846i
$617$	−0.909974	−	8.65783i	−0.0366342	−	0.348551i	−0.997450	−	0.0713644i	$-0.977265\pi$
$617$	−0.909974	−	8.65783i	−0.0366342	−	0.348551i	0.960816	−	0.277187i	$-0.0894020\pi$
$618$	−1.27810	+	0.569047i	−0.0514128	+	0.0228904i
$619$	−19.8342			−0.797204			−0.398602	−	0.917124i	$-0.630504\pi$
$619$	−19.8342			−0.797204			−0.398602	+	0.917124i	$0.630504\pi$
$620$	22.8467	−	28.1517i	0.917547	−	1.13060i
$621$	−40.6350	−	70.3819i	−1.63063	−	2.82433i
$622$	−0.0838478	+	0.797759i	−0.00336199	+	0.0319872i
$623$	−2.69245	+	1.95618i	−0.107871	+	0.0783726i
$624$	−39.4321	+	18.3934i	−1.57855	+	0.736326i
$625$	−21.4640			−0.858561
$626$	−0.0174803	−	0.0302768i	−0.000698654	−	0.00121010i
$627$	−48.5945	+	53.9697i	−1.94068	+	2.15534i
$628$	−25.7453	−	28.5930i	−1.02735	−	1.14099i
$629$	4.84663	−	14.9164i	0.193248	−	0.594755i
$630$	−1.02668	+	0.457109i	−0.0409041	+	0.0182117i
$631$	40.3873	+	8.58459i	1.60779	+	0.341747i	0.922343	−	0.386372i	$-0.126272\pi$
$631$	40.3873	+	8.58459i	1.60779	+	0.341747i	0.685451	+	0.728119i	$0.259605\pi$
$632$	−2.27270	−	1.65122i	−0.0904033	−	0.0656819i
$633$	4.27366	+	40.6612i	0.169863	+	1.61614i
$634$	1.17971	−	0.250756i	0.0468524	−	0.00995878i
$635$	5.18255	+	2.30742i	0.205663	+	0.0915672i
$636$	42.0072	−	30.5200i	1.66570	−	1.21020i
$637$	−13.7089	+	15.7743i	−0.543168	+	0.625000i
$638$	−0.794267	+	0.577069i	−0.0314453	+	0.0228464i
$639$	5.00644	−	47.6331i	0.198052	−	1.88434i
$640$	−3.54160	+	3.93335i	−0.139994	+	0.155479i
$641$	−7.18605	+	3.19944i	−0.283832	+	0.126370i	−0.543715	−	0.839270i	$-0.682983\pi$
$641$	−7.18605	+	3.19944i	−0.283832	+	0.126370i	0.259883	+	0.965640i	$0.416316\pi$
$642$	0.171657	−	0.528306i	0.00677476	−	0.0208506i
$643$	1.00049	+	1.11116i	0.0394556	+	0.0438199i	0.762550	−	0.646930i	$-0.223947\pi$
$643$	1.00049	+	1.11116i	0.0394556	+	0.0438199i	−0.723094	+	0.690750i	$0.757281\pi$
$644$	18.1268	+	3.85297i	0.714297	+	0.151828i
$645$	69.1900			2.72435
$646$	0.448659	−	0.777100i	0.0176522	−	0.0305746i
$647$	−20.7427	+	23.0371i	−0.815479	+	0.905681i	−0.996976	−	0.0777107i	$-0.975239\pi$
$647$	−20.7427	+	23.0371i	−0.815479	+	0.905681i	0.181497	+	0.983391i	$0.441906\pi$
$648$	−1.96800	−	0.876208i	−0.0773102	−	0.0344207i
$649$	14.4034	+	10.4647i	0.565385	+	0.410776i
$650$	0.950845	+	0.403471i	0.0372952	+	0.0158254i
$651$	−16.4935	+	8.38165i	−0.646433	+	0.328503i
$652$	−15.3467	−	26.5813i	−0.601023	−	1.04100i
$653$	2.69030	−	25.5965i	0.105280	−	1.00167i	−0.806569	−	0.591140i	$-0.798678\pi$
$653$	2.69030	−	25.5965i	0.105280	−	1.00167i	0.911848	−	0.410528i	$-0.134655\pi$
$654$	0.222690	+	2.11875i	0.00870786	+	0.0828498i
$655$	18.3384	+	56.4399i	0.716542	+	2.20529i
$656$	−3.85881	+	6.68366i	−0.150661	+	0.260953i
$657$	18.4480	−	31.9529i	0.719725	−	1.24660i
$658$	0.154820	+	0.476487i	0.00603552	+	0.0185754i
$659$	14.8206	+	16.4600i	0.577330	+	0.641190i	0.959100	−	0.283067i	$-0.0913520\pi$
$659$	14.8206	+	16.4600i	0.577330	+	0.641190i	−0.381770	+	0.924257i	$0.624685\pi$
$660$	110.697	−	23.5294i	4.30889	−	0.915882i
$661$	1.33415	−	12.6936i	0.0518926	−	0.493725i	−0.937450	−	0.348119i	$-0.886820\pi$
$661$	1.33415	−	12.6936i	0.0518926	−	0.493725i	0.989343	−	0.145605i	$-0.0465130\pi$
$662$	0.148375	+	0.456651i	0.00576675	+	0.0177482i
$663$	−46.0629	+	0.809725i	−1.78893	+	0.0314471i
$664$	0.635578	−	0.461774i	0.0246652	−	0.0179203i
$665$	−14.6196	+	3.10749i	−0.566923	+	0.120503i
$666$	1.06713	+	0.475115i	0.0413503	+	0.0184103i
$667$	−2.97128	−	28.2698i	−0.115048	−	1.09461i
$668$	−2.43860	+	7.50525i	−0.0943524	+	0.290387i
$669$	7.80578	+	74.2671i	0.301789	+	2.87133i
$670$	−0.0286002	+	0.0127336i	−0.00110492	+	0.000491943i
$671$	4.95193	+	15.2405i	0.191167	+	0.588351i
$672$	1.85094	−	0.824091i	0.0714015	−	0.0317900i
$673$	8.56111	−	1.81972i	0.330007	−	0.0701451i	−0.0399289	−	0.999203i	$-0.512713\pi$
$673$	8.56111	−	1.81972i	0.330007	−	0.0701451i	0.369935	+	0.929057i	$0.379380\pi$
$674$	−0.853111	+	0.181334i	−0.0328606	+	0.00698474i
$675$	−16.7145	−	51.4421i	−0.643343	−	1.98001i
$676$	−18.0423	−	18.6741i	−0.693936	−	0.718236i
$677$	42.7893			1.64452			0.822262	−	0.569108i	$-0.192712\pi$
$677$	42.7893			1.64452			0.822262	+	0.569108i	$0.192712\pi$
$678$	−0.0677516	+	0.0752457i	−0.00260198	+	0.00288979i
$679$	−1.30846	−	0.582565i	−0.0502142	−	0.0223568i
$680$	−2.55649	+	1.13822i	−0.0980369	+	0.0436489i
$681$	0.740443			0.0283739
$682$	−1.57124	+	0.419209i	−0.0601658	+	0.0160523i
$683$	−22.3941	+	38.7877i	−0.856887	+	1.48417i	0.0179970	+	0.999838i	$0.494271\pi$
$683$	−22.3941	+	38.7877i	−0.856887	+	1.48417i	−0.874884	+	0.484333i	$0.839062\pi$
$684$	−41.6839	−	30.2851i	−1.59382	−	1.15798i
$685$	−3.28768	−	31.2802i	−0.125616	−	1.19516i
$686$	0.478156	−	0.531046i	0.0182561	−	0.0202754i
$687$	−38.4348	−	66.5710i	−1.46638	−	2.53984i
$688$	−27.9206			−1.06446
$689$	25.3522	+	17.7471i	0.965842	+	0.676112i
$690$	1.31334	−	4.04206i	0.0499981	−	0.153878i
$691$	−28.9652	+	6.15675i	−1.10189	+	0.234214i	−0.722739	−	0.691121i	$-0.757117\pi$
$691$	−28.9652	+	6.15675i	−1.10189	+	0.234214i	−0.379150	+	0.925335i	$0.623784\pi$
$692$	−4.94520	+	47.0504i	−0.187988	+	1.78859i
$693$	−38.0138	−	8.08009i	−1.44403	−	0.306937i
$694$	0.611759	+	0.444469i	0.0232221	+	0.0168718i
$695$	−0.103931	−	0.988841i	−0.00394234	−	0.0375089i
$696$	−1.38605	−	1.53936i	−0.0525381	−	0.0583495i
$697$	−6.61090	+	4.80310i	−0.250406	+	0.181930i
$698$	0.00891496	+	0.0848202i	0.000337436	+	0.00321049i
$699$	50.9324	−	10.8260i	1.92644	−	0.409477i
$700$	11.2675	+	5.01663i	0.425873	+	0.189611i
$701$	14.5241	+	10.5524i	0.548568	+	0.398558i	0.827257	−	0.561824i	$-0.189900\pi$
$701$	14.5241	+	10.5524i	0.548568	+	0.398558i	−0.278690	+	0.960381i	$0.589900\pi$
$702$	0.153500	−	1.75701i	0.00579347	−	0.0663141i
$703$	12.5680	+	9.13122i	0.474013	+	0.344390i
$704$	−44.5540	+	9.47024i	−1.67919	+	0.356923i
$705$	−86.6492	+	18.4178i	−3.26340	+	0.693656i
$706$	−0.113564	−	0.0241387i	−0.00427403	−	0.000908473i
$707$	7.29429			0.274330
$708$	−9.38482	+	16.2550i	−0.352703	+	0.610900i
$709$	32.7630	+	6.96399i	1.23044	+	0.261538i	0.776858	−	0.629676i	$-0.216812\pi$
$709$	32.7630	+	6.96399i	1.23044	+	0.261538i	0.453582	+	0.891214i	$0.350146\pi$
$710$	1.04159	−	0.756759i	0.0390902	−	0.0284007i
$711$	−77.8616	+	34.6662i	−2.92004	+	1.30008i
$712$	−0.308600	−	0.534510i	−0.0115653	−	0.0200316i
$713$	12.2349	−	45.4665i	0.458201	−	1.70273i
$714$	0.713543			0.0267037
$715$	34.7463	+	57.8114i	1.29944	+	2.16202i
$716$	−16.6385	+	12.0886i	−0.621811	+	0.451772i
$717$	−48.7632	+	54.1570i	−1.82109	+	2.02253i
$718$	−0.554224	−	0.959944i	−0.0206835	−	0.0358248i
$719$	−4.93473	+	8.54720i	−0.184034	+	0.318757i	−0.943251	−	0.332081i	$-0.892249\pi$
$719$	−4.93473	+	8.54720i	−0.184034	+	0.318757i	0.759216	+	0.650838i	$0.225582\pi$
$720$	24.7791	+	76.2621i	0.923461	+	2.84212i
$721$	−6.66241	−	7.39935i	−0.248121	−	0.275566i
$722$	−0.0523967	−	0.0581924i	−0.00195000	−	0.00216570i
$723$	−24.0973	−	17.5077i	−0.896188	−	0.651119i
$724$	7.33876	+	1.55990i	0.272743	+	0.0579733i
$725$	1.97754	−	18.8150i	0.0734439	−	0.698772i
$726$	−3.08806	−	1.37489i	−0.114609	−	0.0510271i
$727$	−6.33078	+	19.4842i	−0.234796	+	0.722627i	0.762353	+	0.647162i	$0.224044\pi$
$727$	−6.33078	+	19.4842i	−0.234796	+	0.722627i	−0.997148	+	0.0754653i	$0.975956\pi$
$728$	0.548991	+	0.588574i	0.0203469	+	0.0218140i
$729$	17.7678	−	12.9091i	0.658068	−	0.478114i
$730$	0.970126	−	0.206207i	0.0359060	−	0.00763205i
$731$	−27.0068	−	12.0242i	−0.998884	−	0.444732i
$732$	−15.4337	+	6.87151i	−0.570445	+	0.253978i
$733$	7.82691	+	24.0888i	0.289094	+	0.889739i	0.985142	+	0.171744i	$0.0549401\pi$
$733$	7.82691	+	24.0888i	0.289094	+	0.889739i	−0.696048	+	0.717995i	$0.745060\pi$
$734$	1.01141	−	0.450309i	0.0373318	−	0.0166212i
$735$	38.2958	+	42.5317i	1.41256	+	1.56881i
$736$	−1.59338	+	4.90393i	−0.0587329	+	0.180761i
$737$	−1.05895	−	0.225086i	−0.0390068	−	0.00829114i
$738$	−0.304300	−	0.527062i	−0.0112014	−	0.0194014i
$739$	15.2430	+	26.4017i	0.560725	+	0.971203i	0.997433	+	0.0716004i	$0.0228106\pi$
$739$	15.2430	+	26.4017i	0.560725	+	0.971203i	−0.436709	+	0.899603i	$0.643856\pi$
$740$	−7.48081	−	23.0236i	−0.275000	−	0.846363i
$741$	13.3362	−	43.6399i	0.489916	−	1.60315i
$742$	−0.387769	−	0.281731i	−0.0142355	−	0.0103427i
$743$	2.65034	+	4.59052i	0.0972315	+	0.168410i	0.910538	−	0.413426i	$-0.135668\pi$
$743$	2.65034	+	4.59052i	0.0972315	+	0.168410i	−0.813306	+	0.581836i	$0.802335\pi$
$744$	−1.22616	−	3.20452i	−0.0449533	−	0.117483i
$745$	−28.6232	+	49.5768i	−1.04867	+	1.81635i
$746$	0.441737	+	0.320941i	0.0161731	+	0.0117505i
$747$	−2.49146	−	23.7046i	−0.0911576	−	0.867307i
$748$	−47.2974	−	10.0534i	−1.72937	−	0.367588i
$749$	3.95334			0.144452
$750$	0.157874	−	0.273445i	0.00576473	−	0.00998481i
$751$	17.6481	−	19.6002i	0.643988	−	0.715221i	−0.329450	−	0.944173i	$-0.606863\pi$
$751$	17.6481	−	19.6002i	0.643988	−	0.715221i	0.973438	+	0.228952i	$0.0735298\pi$
$752$	34.9660	−	7.43224i	1.27508	−	0.271026i
$753$	4.93898	−	15.2006i	0.179987	−	0.553942i
$754$	0.299005	−	0.539576i	0.0108891	−	0.0196502i
$755$	−2.88632	−	8.88317i	−0.105044	−	0.323292i
$756$	2.20140	−	20.9449i	0.0800640	−	0.761758i
$757$	16.4463	+	7.32234i	0.597749	+	0.266135i	0.683228	−	0.730205i	$-0.260575\pi$
$757$	16.4463	+	7.32234i	0.597749	+	0.266135i	−0.0854790	+	0.996340i	$0.527242\pi$
$758$	−0.456484	−	0.506977i	−0.0165802	−	0.0184142i
$759$	118.901	−	86.3864i	4.31582	−	3.13563i
$760$	−0.289735	−	2.75665i	−0.0105098	−	0.0999941i
$761$	0.390570	+	0.433772i	0.0141581	+	0.0157242i	0.750182	−	0.661231i	$-0.229966\pi$
$761$	0.390570	+	0.433772i	0.0141581	+	0.0157242i	−0.736024	+	0.676955i	$0.763299\pi$
$762$	0.217027	−	0.157679i	0.00786205	−	0.00571211i
$763$	−13.8510	+	6.16686i	−0.501440	+	0.223255i
$764$	−1.60475	+	1.78226i	−0.0580579	+	0.0644798i
$765$	−8.87475	+	84.4376i	−0.320867	+	3.05285i
$766$	−0.136328	+	0.419573i	−0.00492571	+	0.0151598i
$767$	−10.9815	−	2.13317i	−0.396518	−	0.0770244i
$768$	−14.7812	−	45.4917i	−0.533369	−	1.64154i
$769$	−14.4255	−	24.9857i	−0.520198	−	0.901009i	−0.999724	−	0.0234815i	$-0.992525\pi$
$769$	−14.4255	−	24.9857i	−0.520198	−	0.901009i	0.479527	−	0.877527i	$-0.340808\pi$
$770$	−0.522338	−	0.904716i	−0.0188238	−	0.0326037i
$771$	−6.67186	−	1.41815i	−0.240281	−	0.0510734i
$772$	6.01574	−	4.37069i	0.216511	−	0.157305i
$773$	18.5118	−	8.24200i	0.665825	−	0.296444i	−0.0458554	−	0.998948i	$-0.514601\pi$
$773$	18.5118	−	8.24200i	0.665825	−	0.296444i	0.711680	+	0.702504i	$0.247935\pi$
$774$	1.10089	−	1.90679i	0.0395705	−	0.0685381i
$775$	14.2565	−	27.9060i	0.512109	−	1.00241i
$776$	0.132812	−	0.230037i	0.00476767	−	0.00825785i
$777$	−1.29127	+	12.2857i	−0.0463242	+	0.440745i
$778$	0.669762	+	0.298197i	0.0240121	+	0.0106909i
$779$	−2.50114	−	7.69772i	−0.0896127	−	0.275799i
$780$	−56.7852	+	42.8017i	−2.03324	+	1.53255i
$781$	44.5215			1.59310
$782$	−1.21509	+	1.34949i	−0.0434514	+	0.0482577i
$783$	−31.5980	+	6.71635i	−1.12922	+	0.240023i
$784$	−15.4537	−	17.1630i	−0.551917	−	0.612966i
$785$	−50.8052	−	36.9121i	−1.81332	−	1.31745i
$786$	2.74490	+	0.583447i	0.0979073	+	0.0208108i
$787$	37.1308	−	16.5317i	1.32357	−	0.589292i	0.381396	−	0.924412i	$-0.375443\pi$
$787$	37.1308	−	16.5317i	1.32357	−	0.589292i	0.942176	+	0.335120i	$0.108777\pi$
$788$	7.36101	−	5.34809i	0.262225	−	0.190518i
$789$	−18.4919	−	20.5373i	−0.658329	−	0.731149i
$790$	−2.09299	−	0.931861i	−0.0744654	−	0.0331541i
$791$	−0.658300	−	0.293094i	−0.0234064	−	0.0104212i
$792$	2.22718	−	6.85456i	0.0791394	−	0.243566i
$793$	−6.86795	−	7.36315i	−0.243888	−	0.261473i
$794$	−0.523606	−	0.380422i	−0.0185821	−	0.0135007i
$795$	56.7076	−	62.9802i	2.01121	−	2.23368i
$796$	0.486860	−	4.63217i	0.0172563	−	0.164183i
$797$	25.7419	+	28.5893i	0.911824	+	1.01268i	0.999863	+	0.0165663i	$0.00527345\pi$
$797$	25.7419	+	28.5893i	0.911824	+	1.01268i	−0.0880386	+	0.996117i	$0.528060\pi$
$798$	−0.218401	+	0.672170i	−0.00773132	+	0.0237946i
$799$	37.0224	+	7.86936i	1.30976	+	0.278398i
$800$	−1.71589	+	2.97201i	−0.0606660	+	0.105077i
$801$	−18.7255			−0.661633
$802$	−1.46424	−	0.311233i	−0.0517040	−	0.0109900i
$803$	31.3317	+	13.9498i	1.10567	+	0.492277i
$804$	0.119303	−	1.13509i	0.00420749	−	0.0400316i
$805$	30.2469			1.06606
$806$	0.783370	−	0.656062i	0.0275930	−	0.0231088i
$807$	20.1567			0.709548
$808$	−0.141401	+	1.34534i	−0.00497448	+	0.0473290i
$809$	44.9143	+	19.9972i	1.57910	+	0.703062i	0.994150	−	0.108004i	$-0.0344461\pi$
$809$	44.9143	+	19.9972i	1.57910	+	0.703062i	0.584953	+	0.811067i	$0.301113\pi$
$810$	−1.71850	−	0.365279i	−0.0603821	−	0.0128346i
$811$	10.9484			0.384451			0.192225	−	0.981351i	$-0.438430\pi$
$811$	10.9484			0.384451			0.192225	+	0.981351i	$0.438430\pi$
$812$	3.68308	−	6.37929i	0.129251	−	0.223869i
$813$	13.9871	+	2.97305i	0.490549	+	0.104269i
$814$	−0.335539	+	1.03268i	−0.0117606	+	0.0361955i
$815$	−33.5212	−	37.2291i	−1.17420	−	1.30408i
$816$	5.32170	−	50.6326i	0.186297	−	1.77250i
$817$	19.5933	−	21.7606i	0.685482	−	0.761305i
$818$	−0.423826	−	0.307928i	−0.0148187	−	0.0107664i
$819$	23.7927	−	5.49607i	0.831383	−	0.192048i
$820$	−3.89758	+	11.9955i	−0.136109	+	0.418901i
$821$	9.68892	+	4.31378i	0.338146	+	0.150552i	0.568783	−	0.822488i	$-0.307414\pi$
$821$	9.68892	+	4.31378i	0.338146	+	0.150552i	−0.230637	+	0.973040i	$0.574081\pi$
$822$	−1.35871	−	0.604938i	−0.0473906	−	0.0210996i
$823$	−0.244919	−	0.272010i	−0.00853733	−	0.00948166i	0.738861	−	0.673858i	$-0.235364\pi$
$823$	−0.244919	−	0.272010i	−0.00853733	−	0.00948166i	−0.747398	+	0.664376i	$0.768697\pi$
$824$	1.49387	−	1.08536i	0.0520416	−	0.0378104i
$825$	89.3591	−	39.7852i	3.11108	−	1.38514i
$826$	0.169477	+	0.0360233i	0.00589684	+	0.00125341i
$827$	−25.1284	−	18.2568i	−0.873799	−	0.634852i	0.0578046	−	0.998328i	$-0.481590\pi$
$827$	−25.1284	−	18.2568i	−0.873799	−	0.634852i	−0.931604	+	0.363476i	$0.881590\pi$
$828$	69.7705	+	77.4880i	2.42469	+	2.69289i
$829$	−20.5160	+	4.36081i	−0.712551	+	0.151457i	−0.549905	−	0.835227i	$-0.685336\pi$
$829$	−20.5160	+	4.36081i	−0.712551	+	0.151457i	−0.162646	+	0.986685i	$0.552003\pi$
$830$	0.428721	−	0.476143i	0.0148811	−	0.0165272i
$831$	−28.8034			−0.999180
$832$	22.8552	−	17.2270i	0.792361	−	0.597240i
$833$	−7.55653	−	23.2566i	−0.261818	−	0.805794i
$834$	−0.0429521	−	0.0191235i	−0.00148731	−	0.000662193i
$835$	−1.34635	+	12.8096i	−0.0465923	+	0.443296i
$836$	23.9473	−	41.4779i	0.828233	−	1.43454i
$837$	−52.8403	−	8.42710i	−1.82643	−	0.291283i
$838$	−0.725414	+	1.25645i	−0.0250590	+	0.0434035i
$839$	−6.07816	+	2.70617i	−0.209841	+	0.0934274i	−0.508966	−	0.860787i	$-0.669972\pi$
$839$	−6.07816	+	2.70617i	−0.209841	+	0.0934274i	0.299125	+	0.954214i	$0.403305\pi$
$840$	1.78319	−	1.29557i	0.0615260	−	0.0447013i
$841$	17.3144	+	3.68028i	0.597047	+	0.126906i
$842$	0.109395	+	0.189478i	0.00377000	+	0.00652984i
$843$	30.9622	+	53.6282i	1.06640	+	1.84705i
$844$	−8.33216	−	25.6438i	−0.286805	−	0.882694i
$845$	−35.1416	−	23.6906i	−1.20891	−	0.814983i
$846$	−0.871106	+	2.68099i	−0.0299492	+	0.0921743i
$847$	2.51464	−	23.9252i	0.0864039	−	0.822079i
$848$	−22.8835	+	25.4147i	−0.785823	+	0.872744i
$849$	−40.3551	+	17.9672i	−1.38498	+	0.616634i
$850$	−0.977768	+	0.710390i	−0.0335372	+	0.0243662i
$851$	−21.0364	−	23.3633i	−0.721118	−	0.800883i
$852$	4.90627	+	46.6801i	0.168086	+	1.59923i
$853$	1.11225	−	0.808097i	0.0380827	−	0.0276687i	−0.568581	−	0.822627i	$-0.692507\pi$
$853$	1.11225	−	0.808097i	0.0380827	−	0.0276687i	0.606664	+	0.794959i	$0.292507\pi$
$854$	0.104352	+	0.115894i	0.00357084	+	0.00396582i
$855$	−76.8253	−	34.2048i	−2.62737	−	1.16978i
$856$	−0.0766363	+	0.729146i	−0.00261938	+	0.0249217i
$857$	11.9573	+	36.8009i	0.408454	+	1.25709i	0.917976	+	0.396635i	$0.129822\pi$
$857$	11.9573	+	36.8009i	0.408454	+	1.25709i	−0.509522	+	0.860458i	$0.670178\pi$
$858$	3.18900	−	0.0560585i	0.108871	−	0.00191380i
$859$	11.1763	−	34.3972i	0.381332	−	1.17362i	−0.557775	−	0.829992i	$-0.688345\pi$
$859$	11.1763	−	34.3972i	0.381332	−	1.17362i	0.939107	−	0.343626i	$-0.111655\pi$
$860$	−44.6331	+	9.48706i	−1.52198	+	0.323506i
$861$	4.30666	−	4.78303i	0.146771	−	0.163005i
$862$	−0.468930	+	0.812210i	−0.0159718	+	0.0276640i
$863$	−46.1243			−1.57009			−0.785044	−	0.619439i	$-0.787360\pi$
$863$	−46.1243			−1.57009			−0.785044	+	0.619439i	$0.787360\pi$
$864$	5.73177	+	1.21833i	0.194999	+	0.0414483i
$865$	8.07138	+	76.7941i	0.274435	+	2.61108i
$866$	0.518670	+	0.376836i	0.0176251	+	0.0128054i
$867$	1.20886	−	2.09381i	0.0410551	−	0.0711095i
$868$	9.49041	−	7.66837i	0.322125	−	0.260281i
$869$	−39.6131	−	68.6118i	−1.34378	−	2.32750i
$870$	−1.36672	−	0.992977i	−0.0463360	−	0.0336651i
$871$	0.662789	−	0.153103i	0.0224578	−	0.00518770i
$872$	−0.868899	−	2.67420i	−0.0294246	−	0.0905597i
$873$	−4.02944	−	6.97920i	−0.136376	−	0.236210i
$874$	−0.899330	−	1.55769i	−0.0304203	−	0.0526895i
$875$	2.19801	+	0.467201i	0.0743062	+	0.0157943i
$876$	−11.1734	+	34.3881i	−0.377513	+	1.16187i
$877$	18.5604	+	20.6134i	0.626740	+	0.696065i	0.969981	−	0.243183i	$-0.0781914\pi$
$877$	18.5604	+	20.6134i	0.626740	+	0.696065i	−0.343241	+	0.939247i	$0.611525\pi$
$878$	−1.69375	+	0.754106i	−0.0571613	+	0.0254499i
$879$	9.83825	+	30.2790i	0.331836	+	1.02129i
$880$	−68.0939	+	30.3173i	−2.29544	+	1.02200i
$881$	−10.5749	−	4.70824i	−0.356276	−	0.158624i	0.220791	−	0.975321i	$-0.429136\pi$
$881$	−10.5749	−	4.70824i	−0.356276	−	0.158624i	−0.577067	+	0.816697i	$0.695803\pi$
$882$	1.78145	−	0.378658i	0.0599844	−	0.0127501i
$883$	−32.4800	+	23.5981i	−1.09304	+	0.794140i	−0.979910	−	0.199441i	$-0.936087\pi$
$883$	−32.4800	+	23.5981i	−1.09304	+	0.794140i	−0.113129	+	0.993580i	$0.536087\pi$
$884$	29.6032	−	6.83830i	0.995664	−	0.229997i
$885$	−9.46678	+	29.1358i	−0.318222	+	0.979388i
$886$	0.655156	+	0.291694i	0.0220104	+	0.00979966i
$887$	−0.600265	+	5.71114i	−0.0201549	+	0.191761i	−0.999967	−	0.00816089i	$-0.997402\pi$
$887$	−0.600265	+	5.71114i	−0.0201549	+	0.191761i	0.979812	+	0.199922i	$0.0640689\pi$
$888$	−2.24091	−	0.476320i	−0.0752000	−	0.0159843i
$889$	1.54454	+	1.12217i	0.0518021	+	0.0376364i
$890$	−0.336813	−	0.374069i	−0.0112900	−	0.0125388i
$891$	−40.6526	−	45.1492i	−1.36191	−	1.51256i
$892$	−15.2186	−	46.8379i	−0.509555	−	1.56825i
$893$	−18.7449	+	32.4671i	−0.627274	+	1.08647i
$894$	1.35351	+	2.34434i	0.0452680	+	0.0784065i
$895$	−22.4612	+	24.9457i	−0.750794	+	0.833841i
$896$	−1.44103	+	1.04697i	−0.0481415	+	0.0349769i
$897$	−44.7606	+	80.7738i	−1.49451	+	2.69696i
$898$	−0.762941			−0.0254597
$899$	−15.6851	−	10.2099i	−0.523126	−	0.340519i
$900$	34.6986	+	60.0998i	1.15662	+	2.00333i
$901$	−33.0796	+	14.7280i	−1.10204	+	0.490661i
$902$	0.457683	−	0.332526i	0.0152392	−	0.0110719i
$903$	22.7759	+	4.84116i	0.757933	+	0.161104i
$904$	0.0668189	−	0.115734i	0.00222236	−	0.00384925i
$905$	12.2457			0.407059
$906$	−0.432024	−	0.0918296i	−0.0143531	−	0.00305084i
$907$	43.1042	−	9.16208i	1.43125	−	0.304222i	0.573888	−	0.818934i	$-0.305435\pi$
$907$	43.1042	−	9.16208i	1.43125	−	0.304222i	0.857363	+	0.514712i	$0.172101\pi$
$908$	−0.477646	+	0.101527i	−0.0158512	+	0.00336928i
$909$	33.2035	+	24.1238i	1.10129	+	0.800135i
$910$	0.537748	+	0.376436i	0.0178262	+	0.0124787i
$911$	24.3202	+	17.6697i	0.805764	+	0.585422i	0.912599	−	0.408855i	$-0.134072\pi$
$911$	24.3202	+	17.6697i	0.805764	+	0.585422i	−0.106835	+	0.994277i	$0.534072\pi$
$912$	46.0680	+	20.5108i	1.52546	+	0.679180i
$913$	21.6720	−	4.60652i	0.717238	−	0.152454i
$914$	−0.0339257	−	0.322781i	−0.00112216	−	0.0106767i
$915$	−22.3080	+	16.2077i	−0.737480	+	0.535810i
$916$	33.9215	+	37.6736i	1.12080	+	1.24477i
$917$	2.08757	+	19.8619i	0.0689378	+	0.655899i
$918$	1.66955	+	1.21300i	0.0551035	+	0.0400350i
$919$	−58.6514	−	12.4667i	−1.93473	−	0.411240i	−0.998151	−	0.0607828i	$-0.980640\pi$
$919$	−58.6514	−	12.4667i	−1.93473	−	0.411240i	−0.936579	−	0.350457i	$-0.886026\pi$
$920$	−0.586343	+	5.57868i	−0.0193312	+	0.183924i
$921$	−73.8715	+	15.7019i	−2.43415	+	0.517394i
$922$	0.490281	−	1.50893i	0.0161465	−	0.0496939i
$923$	−25.3522	+	11.8257i	−0.834477	+	0.389248i
$924$	38.0855			1.25292
$925$	−10.4619	−	18.1206i	−0.343986	−	0.595802i
$926$	−0.479322	+	0.532340i	−0.0157515	+	0.0174938i
$927$	−5.85596	−	55.7158i	−0.192335	−	1.82995i
$928$	1.65814	+	1.20471i	0.0544310	+	0.0395464i
$929$	−9.14001	+	15.8310i	−0.299874	+	0.519397i	−0.976107	−	0.217291i	$-0.930278\pi$
$929$	−9.14001	+	15.8310i	−0.299874	+	0.519397i	0.676233	+	0.736688i	$0.263611\pi$
$930$	−1.52152	−	2.34843i	−0.0498925	−	0.0770081i
$931$	24.2210			0.793813
$932$	−31.3711	+	13.9673i	−1.02759	+	0.457514i
$933$	−43.6043	−	19.4139i	−1.42754	−	0.635582i
$934$	0.709870	−	0.788390i	0.0232277	−	0.0257969i
$935$	−78.9218			−2.58102
$936$	0.552458	+	4.49481i	0.0180576	+	0.146918i
$937$	−11.2087	−	34.4970i	−0.366174	−	1.12697i	−0.949243	−	0.314544i	$-0.898148\pi$
$937$	−11.2087	−	34.4970i	−0.366174	−	1.12697i	0.583069	−	0.812422i	$-0.301852\pi$
$938$	−0.0103055	+	0.00219051i	−0.000336487	+	7.15226e-5i
$939$	2.03482	−	0.432514i	0.0664038	−	0.0141146i
$940$	53.3703	−	23.7620i	1.74075	−	0.775031i
$941$	−12.3546	−	38.0237i	−0.402750	−	1.23954i	−0.922759	−	0.385376i	$-0.874072\pi$
$941$	−12.3546	−	38.0237i	−0.402750	−	1.23954i	0.520010	−	0.854160i	$-0.325928\pi$
$942$	−2.71283	+	1.20783i	−0.0883888	+	0.0393532i
$943$	1.71215	+	16.2900i	0.0557551	+	0.530475i
$944$	3.82018	−	11.7573i	0.124336	−	0.382667i
$945$	−3.59304	−	34.1855i	−0.116882	−	1.11205i
$946$	1.86972	+	0.832455i	0.0607900	+	0.0270654i
$947$	−18.9862	+	4.03563i	−0.616967	+	0.131140i	−0.505785	−	0.862660i	$-0.668797\pi$
$947$	−18.9862	+	4.03563i	−0.616967	+	0.131140i	−0.111182	+	0.993800i	$0.535464\pi$
$948$	67.5730	−	49.0947i	2.19467	−	1.59452i
$949$	−21.5468	+	0.378764i	−0.699437	+	0.0122952i
$950$	−0.369925	−	1.13851i	−0.0120019	−	0.0369382i
$951$	−7.50151	+	71.3721i	−0.243253	+	2.31440i
$952$	−0.921182	+	0.195803i	−0.0298557	+	0.00634602i
$953$	−10.4981	−	11.6594i	−0.340068	−	0.377684i	0.548717	−	0.836008i	$-0.315116\pi$
$953$	−10.4981	−	11.6594i	−0.340068	−	0.377684i	−0.888785	+	0.458324i	$0.848450\pi$
$954$	−0.833377	−	2.56487i	−0.0269816	−	0.0830407i
$955$	−1.95718	+	3.38994i	−0.0633329	+	0.109696i
$956$	24.0304	−	41.6218i	0.777198	−	1.34615i
$957$	−18.0523	−	55.5594i	−0.583549	−	1.79598i
$958$	0.142656	+	1.35728i	0.00460901	+	0.0438518i
$959$	1.10641	−	10.5268i	0.0357279	−	0.339929i
$960$	−39.1889	−	67.8772i	−1.26482	−	2.19073i
$961$	−18.1676	−	25.1185i	−0.586051	−	0.810274i
$962$	−0.0832313	−	0.677173i	−0.00268349	−	0.0218329i
$963$	17.9956	+	13.0745i	0.579899	+	0.421321i
$964$	17.9453	+	7.98976i	0.577979	+	0.257333i
$965$	8.12094	−	9.01922i	0.261422	−	0.290339i
$966$	0.715144	−	1.23867i	0.0230094	−	0.0398534i
$967$	−18.0794			−0.581394			−0.290697	−	0.956815i	$-0.593887\pi$
$967$	−18.0794			−0.581394			−0.290697	+	0.956815i	$0.593887\pi$
$968$	4.36396	+	0.927589i	0.140263	+	0.0298138i
$969$	35.7272	+	39.6791i	1.14772	+	1.27468i
$970$	0.0669425	−	0.206028i	0.00214940	−	0.00661516i
$971$	39.9084	−	17.7683i	1.28072	−	0.570213i	0.350276	−	0.936647i	$-0.386088\pi$
$971$	39.9084	−	17.7683i	1.28072	−	0.570213i	0.930444	+	0.366433i	$0.119421\pi$
$972$	4.32493	−	4.80332i	0.138722	−	0.154066i
$973$	0.0349763	−	0.332777i	0.00112129	−	0.0106684i
$974$	0.231344	−	0.168081i	0.00741274	−	0.00538567i
$975$	−40.3166	+	46.3905i	−1.29117	+	1.48569i
$976$	9.00206	−	6.54038i	0.288149	−	0.209352i
$977$	16.2567	+	7.23797i	0.520099	+	0.231563i	0.649959	−	0.759969i	$-0.274786\pi$
$977$	16.2567	+	7.23797i	0.520099	+	0.231563i	−0.129860	+	0.991532i	$0.541453\pi$
$978$	−2.31716	+	0.492527i	−0.0740945	+	0.0157493i
$979$	−1.81946	−	17.3110i	−0.0581503	−	0.553263i
$980$	−30.5356	−	22.1854i	−0.975425	−	0.708688i
$981$	−83.4447	−	17.7367i	−2.66419	−	0.566290i
$982$	0.920179	−	0.409690i	0.0293641	−	0.0130737i
$983$	−17.6154	+	54.2147i	−0.561845	+	1.72918i	0.115299	+	0.993331i	$0.463218\pi$
$983$	−17.6154	+	54.2147i	−0.561845	+	1.72918i	−0.677144	+	0.735851i	$0.736782\pi$
$984$	0.798687	+	0.887032i	0.0254612	+	0.0282776i
$985$	9.93699	−	11.0361i	0.316619	−	0.351641i
$986$	0.360903	+	0.625103i	0.0114935	+	0.0199073i
$987$	−29.8117			−0.948918
$988$	−2.61916	+	29.9798i	−0.0833267	+	0.953786i
$989$	−47.9407	+	34.8310i	−1.52443	+	1.10756i
$990$	0.614412	−	5.84574i	0.0195273	−	0.185790i
$991$	28.9126	+	50.0782i	0.918440	+	1.59079i	0.801785	+	0.597613i	$0.203884\pi$
$991$	28.9126	+	50.0782i	0.918440	+	1.59079i	0.116656	+	0.993172i	$0.462783\pi$
$992$	1.84595	+	2.84918i	0.0586088	+	0.0904616i
$993$	−28.5706			−0.906662
$994$	0.395819	−	0.176230i	0.0125546	−	0.00558967i
$995$	−0.794636	−	7.56046i	−0.0251917	−	0.239683i
$996$	7.21812	+	22.2151i	0.228715	+	0.703912i
$997$	0.700143	−	1.21268i	0.0221738	−	0.0384061i	−0.854726	−	0.519080i	$-0.826275\pi$
$997$	0.700143	−	1.21268i	0.0221738	−	0.0384061i	0.876899	+	0.480674i	$0.159608\pi$
$998$	−0.0453239	−	0.0785034i	−0.00143470	−	0.00248498i
$999$	−23.9066	+	26.5509i	−0.756371	+	0.840035i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.bl.b.250.18	yes	280
13.9	even	3	inner	403.2.bl.b.126.18	yes	280
31.16	even	5	inner	403.2.bl.b.16.18	✓	280
403.295	even	15	inner	403.2.bl.b.295.18	yes	280

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.bl.b.16.18	✓	280	31.16	even	5	inner
403.2.bl.b.126.18	yes	280	13.9	even	3	inner
403.2.bl.b.250.18	yes	280	1.1	even	1	trivial
403.2.bl.b.295.18	yes	280	403.295	even	15	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.bl (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.00532047 + 0.0506209i) q^{2} +(-2.76686 - 1.23189i) q^{3} +(1.95376 + 0.415285i) q^{4} +3.26010 q^{5} +(0.0770802 - 0.133507i) q^{6} +(1.07316 + 0.228106i) q^{7} +(-0.0628748 + 0.193509i) q^{8} +(4.13060 + 4.58749i) q^{9} +O(q^{10})\)	\(q+(-0.00532047 + 0.0506209i) q^{2} +(-2.76686 - 1.23189i) q^{3} +(1.95376 + 0.415285i) q^{4} +3.26010 q^{5} +(0.0770802 - 0.133507i) q^{6} +(1.07316 + 0.228106i) q^{7} +(-0.0628748 + 0.193509i) q^{8} +(4.13060 + 4.58749i) q^{9} +(-0.0173453 + 0.165029i) q^{10} +(-3.83962 + 4.26433i) q^{11} +(-4.89421 - 3.55585i) q^{12} +(1.05374 - 3.44814i) q^{13} +(-0.0172566 + 0.0531105i) q^{14} +(-9.02025 - 4.01608i) q^{15} +(3.63999 + 1.62063i) q^{16} +(2.82293 + 3.13518i) q^{17} +(-0.254200 + 0.184687i) q^{18} +(-3.81744 + 1.69963i) q^{19} +(6.36946 + 1.35387i) q^{20} +(-2.68827 - 1.95314i) q^{21} +(-0.195436 - 0.217053i) q^{22} +(8.27173 - 1.75821i) q^{23} +(0.412347 - 0.457957i) q^{24} +5.62825 q^{25} +(0.168941 + 0.0716867i) q^{26} +(-2.96976 - 9.13997i) q^{27} +(2.00196 + 0.891330i) q^{28} +(0.351359 - 3.34296i) q^{29} +(0.251289 - 0.435246i) q^{30} +(2.53302 - 4.95820i) q^{31} +(-0.304871 + 0.528052i) q^{32} +(15.8769 - 7.06884i) q^{33} +(-0.173725 + 0.126219i) q^{34} +(3.49859 + 0.743649i) q^{35} +(6.16508 + 10.6782i) q^{36} +(-1.85882 - 3.21958i) q^{37} +(-0.0657264 - 0.202285i) q^{38} +(-7.16325 + 8.24244i) q^{39} +(-0.204978 + 0.630858i) q^{40} +(-0.202464 + 1.92632i) q^{41} +(0.113173 - 0.125691i) q^{42} +(-6.40155 + 2.85015i) q^{43} +(-9.27261 + 6.73694i) q^{44} +(13.4662 + 14.9557i) q^{45} +(0.0449927 + 0.428077i) q^{46} +(7.25820 - 5.27339i) q^{47} +(-8.07492 - 8.96811i) q^{48} +(-5.29519 - 2.35757i) q^{49} +(-0.0299450 + 0.284907i) q^{50} +(-3.94847 - 12.1521i) q^{51} +(3.49070 - 6.29923i) q^{52} +(-2.65231 + 8.16297i) q^{53} +(0.478474 - 0.101703i) q^{54} +(-12.5175 + 13.9021i) q^{55} +(-0.111615 + 0.193323i) q^{56} +12.6561 q^{57} +(0.167354 + 0.0355722i) q^{58} +(-0.324314 - 3.08564i) q^{59} +(-15.9556 - 11.5924i) q^{60} +(1.39632 - 2.41850i) q^{61} +(0.237512 + 0.154604i) q^{62} +(3.38634 + 5.86530i) q^{63} +(6.42189 + 4.66577i) q^{64} +(3.43528 - 11.2413i) q^{65} +(0.273359 + 0.841311i) q^{66} +(0.0943327 + 0.163389i) q^{67} +(4.21333 + 7.29771i) q^{68} +(-25.0527 - 5.32511i) q^{69} +(-0.0562584 + 0.173145i) q^{70} +(-5.19163 - 5.76589i) q^{71} +(-1.14743 + 0.510869i) q^{72} +(-1.84697 - 5.68439i) q^{73} +(0.172868 - 0.0769657i) q^{74} +(-15.5726 - 6.93337i) q^{75} +(-8.16419 + 1.73535i) q^{76} +(-5.09323 + 3.70045i) q^{77} +(-0.379128 - 0.406464i) q^{78} +(-4.26652 + 13.1310i) q^{79} +(11.8667 + 5.28341i) q^{80} +(-1.10671 + 10.5297i) q^{81} +(-0.0964349 - 0.0204979i) q^{82} +(-3.12374 - 2.26953i) q^{83} +(-4.44113 - 4.93238i) q^{84} +(9.20303 + 10.2210i) q^{85} +(-0.110218 - 0.339216i) q^{86} +(-5.09031 + 8.81667i) q^{87} +(-0.583769 - 1.01112i) q^{88} +(-2.02975 + 2.25426i) q^{89} +(-0.828716 + 0.602098i) q^{90} +(1.91736 - 3.46002i) q^{91} +16.8911 q^{92} +(-13.1165 + 10.5983i) q^{93} +(0.228327 + 0.395474i) q^{94} +(-12.4452 + 5.54097i) q^{95} +(1.49404 - 1.08548i) q^{96} +(-1.27696 - 0.271426i) q^{97} +(0.147515 - 0.255504i) q^{98} -35.4225 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 280 q + q^{2} + 39 q^{4} - 8 q^{5} - 2 q^{7} + 12 q^{8} + 29 q^{9}+O(q^{10}) \) 280 * q + q^2 + 39 * q^4 - 8 * q^5 - 2 * q^7 + 12 * q^8 + 29 * q^9	\( 280 q + q^{2} + 39 q^{4} - 8 q^{5} - 2 q^{7} + 12 q^{8} + 29 q^{9} - 21 q^{10} - q^{11} - 16 q^{12} - 54 q^{14} - 27 q^{15} + 31 q^{16} + 2 q^{17} - 10 q^{18} + 5 q^{19} - 3 q^{20} + 68 q^{21} - 39 q^{22} - 7 q^{23} + 48 q^{24} + 200 q^{25} + 6 q^{26} - 78 q^{27} + 30 q^{28} - 16 q^{29} - 66 q^{30} - 62 q^{31} - 56 q^{32} - 20 q^{33} - 126 q^{34} - 37 q^{35} - 140 q^{36} - 36 q^{37} + 4 q^{38} + 28 q^{39} - 158 q^{40} - 4 q^{41} + 16 q^{42} - 16 q^{43} + 42 q^{44} - 46 q^{45} - 29 q^{46} + 8 q^{47} - 36 q^{48} + 43 q^{49} - 5 q^{50} - 134 q^{51} - q^{52} + 8 q^{53} + 44 q^{54} - 55 q^{55} - 42 q^{56} + 140 q^{57} + 38 q^{58} - 23 q^{59} + 38 q^{60} + 40 q^{61} + 19 q^{62} - 146 q^{63} - 68 q^{64} + 2 q^{65} + 6 q^{66} + 46 q^{67} + 86 q^{68} - 32 q^{69} - 4 q^{70} + 60 q^{71} + 73 q^{72} - 12 q^{73} - 44 q^{74} + 16 q^{75} - 70 q^{76} + 10 q^{77} - 142 q^{78} + 134 q^{79} - 72 q^{80} - 18 q^{81} + 28 q^{82} - 88 q^{83} + 81 q^{84} - 69 q^{85} + 188 q^{86} - 28 q^{87} + 42 q^{88} + 12 q^{89} + 22 q^{90} + 67 q^{91} - 324 q^{92} - 25 q^{93} - 62 q^{94} + 16 q^{95} + 276 q^{96} + 16 q^{97} + 76 q^{98} - 60 q^{99}+O(q^{100}) \) 280 * q + q^2 + 39 * q^4 - 8 * q^5 - 2 * q^7 + 12 * q^8 + 29 * q^9 - 21 * q^10 - q^11 - 16 * q^12 - 54 * q^14 - 27 * q^15 + 31 * q^16 + 2 * q^17 - 10 * q^18 + 5 * q^19 - 3 * q^20 + 68 * q^21 - 39 * q^22 - 7 * q^23 + 48 * q^24 + 200 * q^25 + 6 * q^26 - 78 * q^27 + 30 * q^28 - 16 * q^29 - 66 * q^30 - 62 * q^31 - 56 * q^32 - 20 * q^33 - 126 * q^34 - 37 * q^35 - 140 * q^36 - 36 * q^37 + 4 * q^38 + 28 * q^39 - 158 * q^40 - 4 * q^41 + 16 * q^42 - 16 * q^43 + 42 * q^44 - 46 * q^45 - 29 * q^46 + 8 * q^47 - 36 * q^48 + 43 * q^49 - 5 * q^50 - 134 * q^51 - q^52 + 8 * q^53 + 44 * q^54 - 55 * q^55 - 42 * q^56 + 140 * q^57 + 38 * q^58 - 23 * q^59 + 38 * q^60 + 40 * q^61 + 19 * q^62 - 146 * q^63 - 68 * q^64 + 2 * q^65 + 6 * q^66 + 46 * q^67 + 86 * q^68 - 32 * q^69 - 4 * q^70 + 60 * q^71 + 73 * q^72 - 12 * q^73 - 44 * q^74 + 16 * q^75 - 70 * q^76 + 10 * q^77 - 142 * q^78 + 134 * q^79 - 72 * q^80 - 18 * q^81 + 28 * q^82 - 88 * q^83 + 81 * q^84 - 69 * q^85 + 188 * q^86 - 28 * q^87 + 42 * q^88 + 12 * q^89 + 22 * q^90 + 67 * q^91 - 324 * q^92 - 25 * q^93 - 62 * q^94 + 16 * q^95 + 276 * q^96 + 16 * q^97 + 76 * q^98 - 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more