LMFDB - Embedded newform 201.3.c.a.68.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [201,3,Mod(68,201)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(201, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("201.68");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 201 = 3 \cdot 67 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	201.c (of order $2$, degree $1$, 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:	$5.47685331364$
Analytic rank:	$0$
Dimension:	$44$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			68.12
Character	$\chi$	$=$	201.68
Dual form			201.3.c.a.68.33

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.26735i q^{2} +(-2.13323 - 2.10934i) q^{3} -1.14089 q^{4} -6.81017i q^{5} +(-4.78262 + 4.83679i) q^{6} -3.54429 q^{7} -6.48261i q^{8} +(0.101366 + 8.99943i) q^{9} +O(q^{10})$	\(q-2.26735i q^{2} +(-2.13323 - 2.10934i) q^{3} -1.14089 q^{4} -6.81017i q^{5} +(-4.78262 + 4.83679i) q^{6} -3.54429 q^{7} -6.48261i q^{8} +(0.101366 + 8.99943i) q^{9} -15.4411 q^{10} -2.44435i q^{11} +(2.43379 + 2.40653i) q^{12} +10.2691 q^{13} +8.03616i q^{14} +(-14.3650 + 14.5277i) q^{15} -19.2619 q^{16} -4.43800i q^{17} +(20.4049 - 0.229833i) q^{18} -0.511441 q^{19} +7.76967i q^{20} +(7.56080 + 7.47612i) q^{21} -5.54222 q^{22} +36.8541i q^{23} +(-13.6740 + 13.8289i) q^{24} -21.3785 q^{25} -23.2837i q^{26} +(18.7666 - 19.4117i) q^{27} +4.04365 q^{28} +2.56708i q^{29} +(32.9394 + 32.5705i) q^{30} -20.9621 q^{31} +17.7432i q^{32} +(-5.15598 + 5.21438i) q^{33} -10.0625 q^{34} +24.1372i q^{35} +(-0.115648 - 10.2674i) q^{36} +40.3368 q^{37} +1.15962i q^{38} +(-21.9064 - 21.6610i) q^{39} -44.1477 q^{40} -80.7723i q^{41} +(16.9510 - 17.1430i) q^{42} +6.29897 q^{43} +2.78874i q^{44} +(61.2877 - 0.690320i) q^{45} +83.5612 q^{46} +1.45283i q^{47} +(41.0902 + 40.6300i) q^{48} -36.4380 q^{49} +48.4725i q^{50} +(-9.36125 + 9.46729i) q^{51} -11.7159 q^{52} -60.2037i q^{53} +(-44.0132 - 42.5506i) q^{54} -16.6465 q^{55} +22.9763i q^{56} +(1.09102 + 1.07880i) q^{57} +5.82047 q^{58} -99.5572i q^{59} +(16.3889 - 16.5745i) q^{60} -30.2420 q^{61} +47.5284i q^{62} +(-0.359271 - 31.8966i) q^{63} -36.8177 q^{64} -69.9343i q^{65} +(11.8228 + 11.6904i) q^{66} +8.18535 q^{67} +5.06328i q^{68} +(77.7378 - 78.6183i) q^{69} +54.7277 q^{70} -43.8958i q^{71} +(58.3398 - 0.657116i) q^{72} +8.71602 q^{73} -91.4577i q^{74} +(45.6052 + 45.0944i) q^{75} +0.583499 q^{76} +8.66351i q^{77} +(-49.1132 + 49.6695i) q^{78} -41.8917 q^{79} +131.177i q^{80} +(-80.9794 + 1.82447i) q^{81} -183.139 q^{82} +16.0339i q^{83} +(-8.62606 - 8.52944i) q^{84} -30.2236 q^{85} -14.2820i q^{86} +(5.41484 - 5.47617i) q^{87} -15.8458 q^{88} +70.2599i q^{89} +(-1.56520 - 138.961i) q^{90} -36.3967 q^{91} -42.0465i q^{92} +(44.7170 + 44.2162i) q^{93} +3.29409 q^{94} +3.48300i q^{95} +(37.4264 - 37.8503i) q^{96} +95.3425 q^{97} +82.6178i q^{98} +(21.9978 - 0.247774i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 92 q^{4} + 6 q^{6} + 8 q^{7} + 4 q^{9}+O(q^{10}) $ 44 * q - 92 * q^4 + 6 * q^6 + 8 * q^7 + 4 * q^9	$ 44 q - 92 q^{4} + 6 q^{6} + 8 q^{7} + 4 q^{9} + 12 q^{10} - 20 q^{12} - 32 q^{13} - 30 q^{15} + 204 q^{16} + 22 q^{18} - 32 q^{19} + 36 q^{21} - 8 q^{22} - 24 q^{24} - 164 q^{25} + 42 q^{27} - 48 q^{28} + 58 q^{30} + 20 q^{31} + 6 q^{33} - 48 q^{34} - 78 q^{36} + 100 q^{37} + 4 q^{39} + 160 q^{40} - 204 q^{42} - 108 q^{43} - 132 q^{45} - 244 q^{46} + 34 q^{48} + 332 q^{49} + 114 q^{51} - 8 q^{52} + 432 q^{54} + 128 q^{55} - 26 q^{57} - 12 q^{58} + 250 q^{60} - 164 q^{61} - 290 q^{63} - 432 q^{64} - 78 q^{66} + 76 q^{69} + 612 q^{70} - 464 q^{72} + 156 q^{73} - 118 q^{75} - 180 q^{76} - 392 q^{79} + 348 q^{81} + 524 q^{82} - 202 q^{84} - 188 q^{85} - 68 q^{87} - 348 q^{88} + 94 q^{90} - 44 q^{91} + 322 q^{93} - 304 q^{94} + 224 q^{96} + 68 q^{97} + 104 q^{99}+O(q^{100}) $ 44 * q - 92 * q^4 + 6 * q^6 + 8 * q^7 + 4 * q^9 + 12 * q^10 - 20 * q^12 - 32 * q^13 - 30 * q^15 + 204 * q^16 + 22 * q^18 - 32 * q^19 + 36 * q^21 - 8 * q^22 - 24 * q^24 - 164 * q^25 + 42 * q^27 - 48 * q^28 + 58 * q^30 + 20 * q^31 + 6 * q^33 - 48 * q^34 - 78 * q^36 + 100 * q^37 + 4 * q^39 + 160 * q^40 - 204 * q^42 - 108 * q^43 - 132 * q^45 - 244 * q^46 + 34 * q^48 + 332 * q^49 + 114 * q^51 - 8 * q^52 + 432 * q^54 + 128 * q^55 - 26 * q^57 - 12 * q^58 + 250 * q^60 - 164 * q^61 - 290 * q^63 - 432 * q^64 - 78 * q^66 + 76 * q^69 + 612 * q^70 - 464 * q^72 + 156 * q^73 - 118 * q^75 - 180 * q^76 - 392 * q^79 + 348 * q^81 + 524 * q^82 - 202 * q^84 - 188 * q^85 - 68 * q^87 - 348 * q^88 + 94 * q^90 - 44 * q^91 + 322 * q^93 - 304 * q^94 + 224 * q^96 + 68 * q^97 + 104 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/201\mathbb{Z}\right)^\times$.

$n$	$68$	$136$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	2.26735i		−	1.13368i	−0.823829	−	0.566838i	$-0.808166\pi$
$2$		−	2.26735i		−	1.13368i	0.823829	−	0.566838i	$-0.191834\pi$
$3$	−2.13323	−	2.10934i	−0.711078	−	0.703113i
$3$	−2.13323	−	2.10934i	−0.711078	−	0.703113i
$4$	−1.14089			−0.285223
$5$		−	6.81017i		−	1.36203i	−0.732267	−	0.681017i	$-0.761538\pi$
$5$		−	6.81017i		−	1.36203i	0.732267	−	0.681017i	$-0.238462\pi$
$6$	−4.78262	+	4.83679i	−0.797103	+	0.806132i
$7$	−3.54429			−0.506327			−0.253164	−	0.967423i	$-0.581471\pi$
$7$	−3.54429			−0.506327			−0.253164	+	0.967423i	$0.581471\pi$
$8$		−	6.48261i		−	0.810326i
$9$	0.101366	+	8.99943i	0.0112629	+	0.999937i
$10$	−15.4411			−1.54411
$11$		−	2.44435i		−	0.222214i	−0.993808	−	0.111107i	$-0.964560\pi$
$11$		−	2.44435i		−	0.222214i	0.993808	−	0.111107i	$-0.0354396\pi$
$12$	2.43379	+	2.40653i	0.202816	+	0.200544i
$13$	10.2691			0.789930			0.394965	−	0.918696i	$-0.370757\pi$
$13$	10.2691			0.789930			0.394965	+	0.918696i	$0.370757\pi$
$14$			8.03616i			0.574012i
$15$	−14.3650	+	14.5277i	−0.957665	+	0.968512i
$16$	−19.2619			−1.20387
$17$		−	4.43800i		−	0.261059i	−0.991444	−	0.130529i	$-0.958332\pi$
$17$		−	4.43800i		−	0.261059i	0.991444	−	0.130529i	$-0.0416677\pi$
$18$	20.4049	−	0.229833i	1.13360	−	0.0127685i
$19$	−0.511441			−0.0269180			−0.0134590	−	0.999909i	$-0.504284\pi$
$19$	−0.511441			−0.0269180			−0.0134590	+	0.999909i	$0.504284\pi$
$20$			7.76967i			0.388483i
$21$	7.56080	+	7.47612i	0.360038	+	0.356006i
$22$	−5.54222			−0.251919
$23$			36.8541i			1.60235i	0.598430	+	0.801175i	$0.295791\pi$
$23$			36.8541i			1.60235i	−0.598430	+	0.801175i	$0.704209\pi$
$24$	−13.6740	+	13.8289i	−0.569751	+	0.576205i
$25$	−21.3785			−0.855138
$26$		−	23.2837i		−	0.895525i
$27$	18.7666	−	19.4117i	0.695060	−	0.718952i
$28$	4.04365			0.144416
$29$			2.56708i			0.0885199i	0.999020	+	0.0442600i	$0.0140930\pi$
$29$			2.56708i			0.0885199i	−0.999020	+	0.0442600i	$0.985907\pi$
$30$	32.9394	+	32.5705i	1.09798	+	1.08568i
$31$	−20.9621			−0.676196			−0.338098	−	0.941111i	$-0.609784\pi$
$31$	−20.9621			−0.676196			−0.338098	+	0.941111i	$0.609784\pi$
$32$			17.7432i			0.554474i
$33$	−5.15598	+	5.21438i	−0.156242	+	0.158011i
$34$	−10.0625			−0.295956
$35$			24.1372i			0.689636i
$36$	−0.115648	−	10.2674i	−0.00321243	−	0.285205i
$37$	40.3368			1.09018			0.545092	−	0.838376i	$-0.316495\pi$
$37$	40.3368			1.09018			0.545092	+	0.838376i	$0.316495\pi$
$38$			1.15962i			0.0305163i
$39$	−21.9064	−	21.6610i	−0.561702	−	0.555411i
$40$	−44.1477			−1.10369
$41$		−	80.7723i		−	1.97006i	−0.172394	−	0.985028i	$-0.555150\pi$
$41$		−	80.7723i		−	1.97006i	0.172394	−	0.985028i	$-0.444850\pi$
$42$	16.9510	−	17.1430i	0.403595	−	0.408167i
$43$	6.29897			0.146488			0.0732438	−	0.997314i	$-0.476665\pi$
$43$	6.29897			0.146488			0.0732438	+	0.997314i	$0.476665\pi$
$44$			2.78874i			0.0633805i
$45$	61.2877	−	0.690320i	1.36195	−	0.0153404i
$46$	83.5612			1.81655
$47$			1.45283i			0.0309114i	0.999881	+	0.0154557i	$0.00491989\pi$
$47$			1.45283i			0.0309114i	−0.999881	+	0.0154557i	$0.995080\pi$
$48$	41.0902	+	40.6300i	0.856046	+	0.846458i
$49$	−36.4380			−0.743632
$50$			48.4725i			0.969450i
$51$	−9.36125	+	9.46729i	−0.183554	+	0.185633i
$52$	−11.7159			−0.225306
$53$		−	60.2037i		−	1.13592i	−0.823057	−	0.567959i	$-0.807733\pi$
$53$		−	60.2037i		−	1.13592i	0.823057	−	0.567959i	$-0.192267\pi$
$54$	−44.0132	−	42.5506i	−0.815059	−	0.787973i
$55$	−16.6465			−0.302663
$56$			22.9763i			0.410290i
$57$	1.09102	+	1.07880i	0.0191408	+	0.0189264i
$58$	5.82047			0.100353
$59$		−	99.5572i		−	1.68741i	−0.536807	−	0.843705i	$-0.680370\pi$
$59$		−	99.5572i		−	1.68741i	0.536807	−	0.843705i	$-0.319630\pi$
$60$	16.3889	−	16.5745i	0.273148	−	0.276242i
$61$	−30.2420			−0.495770			−0.247885	−	0.968789i	$-0.579735\pi$
$61$	−30.2420			−0.495770			−0.247885	+	0.968789i	$0.579735\pi$
$62$			47.5284i			0.766588i
$63$	−0.359271	−	31.8966i	−0.00570271	−	0.506295i
$64$	−36.8177			−0.575276
$65$		−	69.9343i		−	1.07591i
$66$	11.8228	+	11.6904i	0.179134	+	0.177128i
$67$	8.18535			0.122169
$67$	8.18535			0.122169
$68$			5.06328i			0.0744600i
$69$	77.7378	−	78.6183i	1.12663	−	1.13940i
$70$	54.7277			0.781824
$71$		−	43.8958i		−	0.618251i	−0.951021	−	0.309126i	$-0.899964\pi$
$71$		−	43.8958i		−	0.618251i	0.951021	−	0.309126i	$-0.100036\pi$
$72$	58.3398	−	0.657116i	0.810275	−	0.00912661i
$73$	8.71602			0.119398			0.0596988	−	0.998216i	$-0.480986\pi$
$73$	8.71602			0.119398			0.0596988	+	0.998216i	$0.480986\pi$
$74$		−	91.4577i		−	1.23592i
$75$	45.6052	+	45.0944i	0.608070	+	0.601259i
$76$	0.583499			0.00767762
$77$			8.66351i			0.112513i
$78$	−49.1132	+	49.6695i	−0.629656	+	0.636788i
$79$	−41.8917			−0.530275			−0.265137	−	0.964211i	$-0.585417\pi$
$79$	−41.8917			−0.530275			−0.265137	+	0.964211i	$0.585417\pi$
$80$			131.177i			1.63971i
$81$	−80.9794	+	1.82447i	−0.999746	+	0.0225244i
$82$	−183.139			−2.23341
$83$			16.0339i			0.193180i	0.995324	+	0.0965899i	$0.0307935\pi$
$83$			16.0339i			0.193180i	−0.995324	+	0.0965899i	$0.969206\pi$
$84$	−8.62606	−	8.52944i	−0.102691	−	0.101541i
$85$	−30.2236			−0.355571
$86$		−	14.2820i		−	0.166070i
$87$	5.41484	−	5.47617i	0.0622395	−	0.0629445i
$88$	−15.8458			−0.180066
$89$			70.2599i			0.789437i	0.918802	+	0.394718i	$0.129158\pi$
$89$			70.2599i			0.789437i	−0.918802	+	0.394718i	$0.870842\pi$
$90$	−1.56520	−	138.961i	−0.0173911	−	1.54401i
$91$	−36.3967			−0.399963
$92$		−	42.0465i		−	0.457027i
$93$	44.7170	+	44.2162i	0.480828	+	0.475443i
$94$	3.29409			0.0350435
$95$			3.48300i			0.0366632i
$96$	37.4264	−	37.8503i	0.389858	−	0.394274i
$97$	95.3425			0.982912			0.491456	−	0.870902i	$-0.336465\pi$
$97$	95.3425			0.982912			0.491456	+	0.870902i	$0.336465\pi$
$98$			82.6178i			0.843039i
$99$	21.9978	−	0.247774i	0.222200	−	0.00250277i
$100$	24.3905			0.243905
$101$			118.385i			1.17213i	0.810263	+	0.586066i	$0.199324\pi$
$101$			118.385i			1.17213i	−0.810263	+	0.586066i	$0.800676\pi$
$102$	21.4657	+	21.2253i	0.210448	+	0.208091i
$103$	202.302			1.96409			0.982047	−	0.188636i	$-0.0604065\pi$
$103$	202.302			1.96409			0.982047	+	0.188636i	$0.0604065\pi$
$104$		−	66.5705i		−	0.640101i
$105$	50.9137	−	51.4904i	0.484892	−	0.490384i
$106$	−136.503			−1.28776
$107$			112.038i			1.04709i	0.851999	+	0.523543i	$0.175390\pi$
$107$			112.038i			1.04709i	−0.851999	+	0.523543i	$0.824610\pi$
$108$	−21.4107	+	22.1466i	−0.198247	+	0.205061i
$109$	177.807			1.63126			0.815629	−	0.578576i	$-0.196391\pi$
$109$	177.807			1.63126			0.815629	+	0.578576i	$0.196391\pi$
$110$			37.7434i			0.343122i
$111$	−86.0477	−	85.0840i	−0.775205	−	0.766522i
$112$	68.2699			0.609553
$113$		−	159.820i		−	1.41433i	−0.707047	−	0.707167i	$-0.749973\pi$
$113$		−	159.820i		−	1.41433i	0.707047	−	0.707167i	$-0.250027\pi$
$114$	2.44603	−	2.47374i	0.0214564	−	0.0216994i
$115$	250.983			2.18246
$116$		−	2.92876i		−	0.0252479i
$117$	1.04094	+	92.4160i	0.00889690	+	0.789880i
$118$	−225.731			−1.91298
$119$			15.7296i			0.132181i
$120$	94.1773	+	93.1225i	0.784811	+	0.776021i
$121$	115.025			0.950621
$122$			68.5692i			0.562043i
$123$	−170.376	+	172.306i	−1.38517	+	1.40086i
$124$	23.9155			0.192867
$125$		−	24.6633i		−	0.197307i
$126$	−72.3209	+	0.814594i	−0.573975	+	0.00646503i
$127$	−151.306			−1.19138			−0.595692	−	0.803213i	$-0.703122\pi$
$127$	−151.306			−1.19138			−0.595692	+	0.803213i	$0.703122\pi$
$128$			154.451i			1.20665i
$129$	−13.4372	−	13.2867i	−0.104164	−	0.102997i
$130$	−158.566			−1.21974
$131$			151.141i			1.15374i	0.816834	+	0.576872i	$0.195727\pi$
$131$			151.141i			1.15374i	−0.816834	+	0.576872i	$0.804273\pi$
$132$	5.88241	−	5.94904i	0.0445637	−	0.0450685i
$133$	1.81270			0.0136293
$134$		−	18.5591i		−	0.138501i
$135$	−132.197	−	127.804i	−0.979237	−	0.946696i
$136$	−28.7698			−0.211543
$137$			93.1071i			0.679614i	0.940495	+	0.339807i	$0.110362\pi$
$137$			93.1071i			0.679614i	−0.940495	+	0.339807i	$0.889638\pi$
$138$	−178.255	−	176.259i	−1.29171	−	1.27724i
$139$	−24.9387			−0.179415			−0.0897076	−	0.995968i	$-0.528593\pi$
$139$	−24.9387			−0.179415			−0.0897076	+	0.995968i	$0.528593\pi$
$140$		−	27.5380i		−	0.196700i
$141$	3.06452	−	3.09923i	0.0217342	−	0.0219804i
$142$	−99.5274			−0.700897
$143$		−	25.1013i		−	0.175534i
$144$	−1.95251	−	173.346i	−0.0135591	−	1.20379i
$145$	17.4822			0.120567
$146$		−	19.7623i		−	0.135358i
$147$	77.7307	+	76.8601i	0.528780	+	0.522858i
$148$	−46.0199			−0.310945
$149$		−	75.1798i		−	0.504562i	−0.967654	−	0.252281i	$-0.918819\pi$
$149$		−	75.1798i		−	0.504562i	0.967654	−	0.252281i	$-0.0811808\pi$
$150$	102.245	−	103.403i	0.681634	−	0.689354i
$151$	−254.687			−1.68667			−0.843333	−	0.537392i	$-0.819410\pi$
$151$	−254.687			−1.68667			−0.843333	+	0.537392i	$0.819410\pi$
$152$			3.31547i			0.0218123i
$153$	39.9395	−	0.449862i	0.261042	−	0.00294028i
$154$	19.6432			0.127553
$155$			142.755i			0.921003i
$156$	24.9928	+	24.7129i	0.160210	+	0.158416i
$157$	136.009			0.866302			0.433151	−	0.901321i	$-0.357402\pi$
$157$	136.009			0.866302			0.433151	+	0.901321i	$0.357402\pi$
$158$			94.9833i			0.601160i
$159$	−126.990	+	128.428i	−0.798679	+	0.807726i
$160$	120.834			0.755213
$161$		−	130.622i		−	0.811314i
$162$	4.13672	+	183.609i	0.0255353	+	1.13339i
$163$	−14.4366			−0.0885682			−0.0442841	−	0.999019i	$-0.514101\pi$
$163$	−14.4366			−0.0885682			−0.0442841	+	0.999019i	$0.514101\pi$
$164$			92.1524i			0.561905i
$165$	35.5108	+	35.1131i	0.215217	+	0.212807i
$166$	36.3546			0.219003
$167$			54.7010i			0.327551i	0.986498	+	0.163775i	$0.0523673\pi$
$167$			54.7010i			0.327551i	−0.986498	+	0.163775i	$0.947633\pi$
$168$	48.4648	−	49.0137i	0.288481	−	0.291748i
$169$	−63.5457			−0.376010
$170$			68.5275i			0.403103i
$171$	−0.0518428	−	4.60268i	−0.000303174	−	0.0269163i
$172$	−7.18644			−0.0417816
$173$		−	304.280i		−	1.75884i	−0.476045	−	0.879421i	$-0.657930\pi$
$173$		−	304.280i		−	1.75884i	0.476045	−	0.879421i	$-0.342070\pi$
$174$	−12.4164	−	12.2774i	−0.0713587	−	0.0705595i
$175$	75.7715			0.432980
$176$			47.0830i			0.267517i
$177$	−210.000	+	212.379i	−1.18644	+	1.19988i
$178$	159.304			0.894966
$179$			134.868i			0.753452i	0.926325	+	0.376726i	$0.122950\pi$
$179$			134.868i			0.753452i	−0.926325	+	0.376726i	$0.877050\pi$
$180$	−69.9226	+	0.787580i	−0.388459	+	0.00437545i
$181$	−250.429			−1.38359			−0.691793	−	0.722096i	$-0.743179\pi$
$181$	−250.429			−1.38359			−0.691793	+	0.722096i	$0.743179\pi$
$182$			82.5241i			0.453429i
$183$	64.5132	+	63.7906i	0.352531	+	0.348582i
$184$	238.910			1.29843
$185$		−	274.700i		−	1.48487i
$186$	100.254	−	101.389i	0.538998	−	0.545104i
$187$	−10.8480			−0.0580110
$188$		−	1.65753i		−	0.00881663i
$189$	−66.5144	+	68.8007i	−0.351928	+	0.364025i
$190$	7.89720			0.0415642
$191$			37.2439i			0.194994i	0.995236	+	0.0974971i	$0.0310837\pi$
$191$			37.2439i			0.194994i	−0.995236	+	0.0974971i	$0.968916\pi$
$192$	78.5407	+	77.6610i	0.409066	+	0.404485i
$193$	181.439			0.940098			0.470049	−	0.882640i	$-0.344236\pi$
$193$	181.439			0.940098			0.470049	+	0.882640i	$0.344236\pi$
$194$		−	216.175i		−	1.11430i
$195$	−147.515	+	149.186i	−0.756488	+	0.765057i
$196$	41.5718			0.212101
$197$		−	212.954i		−	1.08098i	−0.841349	−	0.540492i	$-0.818238\pi$
$197$		−	212.954i		−	1.08098i	0.841349	−	0.540492i	$-0.181762\pi$
$198$	−0.561792	−	49.8768i	−0.00283733	−	0.251903i
$199$	311.637			1.56602			0.783009	−	0.622011i	$-0.213684\pi$
$199$	311.637			1.56602			0.783009	+	0.622011i	$0.213684\pi$
$200$			138.588i			0.692941i
$201$	−17.4613	−	17.2657i	−0.0868720	−	0.0858990i
$202$	268.421			1.32882
$203$		−	9.09847i		−	0.0448201i
$204$	10.6802	−	10.8012i	0.0523538	−	0.0529468i
$205$	−550.073			−2.68328
$206$		−	458.689i		−	2.22665i
$207$	−331.665	+	3.73575i	−1.60225	+	0.0180471i
$208$	−197.803			−0.950974
$209$			1.25014i			0.00598155i
$210$	−116.747	−	115.439i	−0.555937	−	0.549711i
$211$	120.422			0.570722			0.285361	−	0.958420i	$-0.407886\pi$
$211$	120.422			0.570722			0.285361	+	0.958420i	$0.407886\pi$
$212$			68.6859i			0.323990i
$213$	−92.5912	+	93.6400i	−0.434701	+	0.439625i
$214$	254.030			1.18706
$215$		−	42.8971i		−	0.199521i
$216$	−125.838	−	121.657i	−0.582585	−	0.563225i
$217$	74.2957			0.342377
$218$		−	403.151i		−	1.84932i
$219$	−18.5933	−	18.3851i	−0.0849010	−	0.0839501i
$220$	18.9918			0.0863265
$221$		−	45.5742i		−	0.206218i
$222$	−192.915	+	195.101i	−0.868989	+	0.878832i
$223$	260.613			1.16867			0.584335	−	0.811513i	$-0.301355\pi$
$223$	260.613			1.16867			0.584335	+	0.811513i	$0.301355\pi$
$224$		−	62.8870i		−	0.280746i
$225$	−2.16705	−	192.394i	−0.00963133	−	0.855084i
$226$	−362.368			−1.60340
$227$		−	1.04089i		−	0.00458544i	−0.999997	−	0.00229272i	$-0.999270\pi$
$227$		−	1.04089i		−	0.00458544i	0.999997	−	0.00229272i	$-0.000729796\pi$
$228$	−1.24474	−	1.23080i	−0.00545938	−	0.00539824i
$229$	164.192			0.716997			0.358498	−	0.933530i	$-0.383289\pi$
$229$	164.192			0.716997			0.358498	+	0.933530i	$0.383289\pi$
$230$		−	569.066i		−	2.47420i
$231$	18.2743	−	18.4813i	0.0791095	−	0.0800055i
$232$	16.6414			0.0717300
$233$			203.876i			0.875003i	0.899218	+	0.437502i	$0.144137\pi$
$233$			203.876i			0.875003i	−0.899218	+	0.437502i	$0.855863\pi$
$234$	209.540	−	2.36017i	0.895469	−	0.0100862i
$235$	9.89405			0.0421023
$236$			113.584i			0.481288i
$237$	89.3648	+	88.3639i	0.377066	+	0.372843i
$238$	35.6645			0.149851
$239$		−	207.877i		−	0.869780i	−0.900484	−	0.434890i	$-0.856787\pi$
$239$		−	207.877i		−	0.869780i	0.900484	−	0.434890i	$-0.143213\pi$
$240$	276.697	−	279.831i	1.15290	−	1.16596i
$241$	297.368			1.23389			0.616946	−	0.787005i	$-0.288370\pi$
$241$	297.368			1.23389			0.616946	+	0.787005i	$0.288370\pi$
$242$		−	260.803i		−	1.07770i
$243$	176.596	+	166.921i	0.726734	+	0.686919i
$244$	34.5028			0.141405
$245$			248.149i			1.01285i
$246$	390.679	+	386.303i	1.58813	+	1.57034i
$247$	−5.25204			−0.0212633
$248$			135.889i			0.547939i
$249$	33.8210	−	34.2041i	0.135827	−	0.137366i
$250$	−55.9205			−0.223682
$251$			259.249i			1.03286i	0.856328	+	0.516432i	$0.172740\pi$
$251$			259.249i			1.03286i	−0.856328	+	0.516432i	$0.827260\pi$
$252$	0.409889	+	36.3906i	0.00162654	+	0.144407i
$253$	90.0844			0.356065
$254$			343.064i			1.35065i
$255$	64.4739	+	63.7518i	0.252839	+	0.250007i
$256$	202.925			0.792676
$257$		−	357.431i		−	1.39078i	−0.718631	−	0.695391i	$-0.755231\pi$
$257$		−	357.431i		−	1.39078i	0.718631	−	0.695391i	$-0.244769\pi$
$258$	−30.1256	+	30.4668i	−0.116766	+	0.118088i
$259$	−142.965			−0.551990
$260$			79.7875i			0.306875i
$261$	−23.1022	+	0.260214i	−0.0885143	+	0.000996990i
$262$	342.689			1.30797
$263$			157.813i			0.600051i	0.953931	+	0.300026i	$0.0969952\pi$
$263$			157.813i			0.600051i	−0.953931	+	0.300026i	$0.903005\pi$
$264$	33.8028	+	33.4242i	0.128041	+	0.126607i
$265$	−409.997			−1.54716
$266$		−	4.11003i		−	0.0154512i
$267$	148.202	−	149.881i	0.555064	−	0.561351i
$268$	−9.33860			−0.0348455
$269$		−	97.7773i		−	0.363485i	−0.983346	−	0.181742i	$-0.941826\pi$
$269$		−	97.7773i		−	0.363485i	0.983346	−	0.181742i	$-0.0581737\pi$
$270$	−289.777	+	299.737i	−1.07325	+	1.11014i
$271$	−151.126			−0.557662			−0.278831	−	0.960340i	$-0.589947\pi$
$271$	−151.126			−0.557662			−0.278831	+	0.960340i	$0.589947\pi$
$272$			85.4845i			0.314281i
$273$	77.6426	+	76.7730i	0.284405	+	0.281220i
$274$	211.107			0.770462
$275$			52.2565i			0.190024i
$276$	−88.6903	+	89.6949i	−0.321342	+	0.324982i
$277$	319.777			1.15443			0.577215	−	0.816592i	$-0.304140\pi$
$277$	319.777			1.15443			0.577215	+	0.816592i	$0.304140\pi$
$278$			56.5449i			0.203399i
$279$	−2.12484	−	188.647i	−0.00761592	−	0.676153i
$280$	156.472			0.558830
$281$			79.8125i			0.284030i	0.989864	+	0.142015i	$0.0453582\pi$
$281$			79.8125i			0.284030i	−0.989864	+	0.142015i	$0.954642\pi$
$282$	−7.02706	−	6.94835i	−0.0249186	−	0.0246395i
$283$	456.758			1.61399			0.806993	−	0.590561i	$-0.201093\pi$
$283$	456.758			1.61399			0.806993	+	0.590561i	$0.201093\pi$
$284$			50.0804i			0.176339i
$285$	7.34684	−	7.43006i	0.0257784	−	0.0260704i
$286$	−56.9135			−0.198998
$287$			286.281i			0.997494i
$288$	−159.678	+	1.79855i	−0.554439	+	0.00624498i
$289$	269.304			0.931848
$290$		−	39.6384i		−	0.136684i
$291$	−203.388	−	201.110i	−0.698927	−	0.691099i
$292$	−9.94404			−0.0340549
$293$		−	377.983i		−	1.29004i	−0.764164	−	0.645022i	$-0.776848\pi$
$293$		−	377.983i		−	1.29004i	0.764164	−	0.645022i	$-0.223152\pi$
$294$	174.269	−	176.243i	0.592752	−	0.599466i
$295$	−678.002			−2.29831
$296$		−	261.488i		−	0.883404i
$297$	−47.4491	−	45.8723i	−0.159761	−	0.154452i
$298$	−170.459			−0.572011
$299$			378.458i			1.26574i
$300$	−52.0306	−	51.4479i	−0.173435	−	0.171493i
$301$	−22.3254			−0.0741707
$302$			577.464i			1.91213i
$303$	249.715	−	252.543i	0.824142	−	0.833477i
$304$	9.85135			0.0324058
$305$			205.953i			0.675256i
$306$	−1.02000	−	90.5569i	−0.00333332	−	0.295938i
$307$	−340.808			−1.11012			−0.555062	−	0.831809i	$-0.687305\pi$
$307$	−340.808			−1.11012			−0.555062	+	0.831809i	$0.687305\pi$
$308$		−	9.88412i		−	0.0320913i
$309$	−431.557	−	426.723i	−1.39662	−	1.38098i
$310$	323.677			1.04412
$311$		−	49.9057i		−	0.160468i	−0.996776	−	0.0802342i	$-0.974433\pi$
$311$		−	49.9057i		−	0.160468i	0.996776	−	0.0802342i	$-0.0255668\pi$
$312$	−140.420	+	142.010i	−0.450064	+	0.455162i
$313$	59.0956			0.188804			0.0944020	−	0.995534i	$-0.469906\pi$
$313$	59.0956			0.188804			0.0944020	+	0.995534i	$0.469906\pi$
$314$		−	308.381i		−	0.982106i
$315$	−217.221	+	2.44670i	−0.689592	+	0.00776729i
$316$	47.7939			0.151246
$317$			473.151i			1.49259i	0.665615	+	0.746295i	$0.268169\pi$
$317$			473.151i			1.49259i	−0.665615	+	0.746295i	$0.731831\pi$
$318$	291.193	+	287.931i	0.915700	+	0.905444i
$319$	6.27485			0.0196704
$320$			250.735i			0.783546i
$321$	236.327	−	239.004i	0.736220	−	0.744560i
$322$	−296.165			−0.919768
$323$			2.26978i			0.00702717i
$324$	92.3888	−	2.08153i	0.285151	−	0.00642446i
$325$	−219.537			−0.675499
$326$			32.7329i			0.100408i
$327$	−379.304	−	375.056i	−1.15995	−	1.14696i
$328$	−523.615			−1.59639
$329$		−	5.14927i		−	0.0156513i
$330$	79.6138	−	80.5156i	0.241254	−	0.243987i
$331$	−227.397			−0.686999			−0.343500	−	0.939153i	$-0.611612\pi$
$331$	−227.397			−0.686999			−0.343500	+	0.939153i	$0.611612\pi$
$332$		−	18.2930i		−	0.0550993i
$333$	4.08878	+	363.008i	0.0122786	+	1.09011i
$334$	124.027			0.371337
$335$		−	55.7437i		−	0.166399i
$336$	−145.636	−	144.005i	−0.433439	−	0.428585i
$337$	−465.156			−1.38029			−0.690143	−	0.723673i	$-0.742452\pi$
$337$	−465.156			−1.38029			−0.690143	+	0.723673i	$0.742452\pi$
$338$			144.081i			0.426274i
$339$	−337.114	+	340.933i	−0.994437	+	1.00570i
$340$	34.4818			0.101417
$341$			51.2388i			0.150260i
$342$	−10.4359	+	0.117546i	−0.0305143	+	0.000343701i
$343$	302.817			0.882849
$344$		−	40.8338i		−	0.118703i
$345$	−535.404	−	529.408i	−1.55190	−	1.53451i
$346$	−689.909			−1.99396
$347$			158.901i			0.457928i	0.973435	+	0.228964i	$0.0735337\pi$
$347$			158.901i			0.457928i	−0.973435	+	0.228964i	$0.926466\pi$
$348$	−6.17775	+	6.24772i	−0.0177521	+	0.0179532i
$349$	546.405			1.56563			0.782815	−	0.622255i	$-0.213783\pi$
$349$	546.405			1.56563			0.782815	+	0.622255i	$0.213783\pi$
$350$		−	171.801i		−	0.490859i
$351$	192.716	−	199.340i	0.549049	−	0.567922i
$352$	43.3706			0.123212
$353$			363.457i			1.02962i	0.857303	+	0.514812i	$0.172138\pi$
$353$			363.457i			1.02962i	−0.857303	+	0.514812i	$0.827862\pi$
$354$	481.538	+	476.144i	1.36028	+	1.34504i
$355$	−298.938			−0.842079
$356$		−	80.1589i		−	0.225165i
$357$	33.1790	−	33.5548i	0.0929384	−	0.0939912i
$358$	305.793			0.854171
$359$		−	608.223i		−	1.69421i	−0.531422	−	0.847107i	$-0.678342\pi$
$359$		−	608.223i		−	1.69421i	0.531422	−	0.847107i	$-0.321658\pi$
$360$	−4.47508	−	397.304i	−0.0124308	−	1.10362i
$361$	−360.738			−0.999275
$362$			567.811i			1.56854i
$363$	−245.375	−	242.627i	−0.675965	−	0.668394i
$364$	41.5247			0.114079
$365$		−	59.3576i		−	0.162624i
$366$	144.636	−	146.274i	0.395180	−	0.399656i
$367$	−674.819			−1.83874			−0.919371	−	0.393390i	$-0.871302\pi$
$367$	−674.819			−1.83874			−0.919371	+	0.393390i	$0.871302\pi$
$368$		−	709.880i		−	1.92902i
$369$	726.905	−	8.18757i	1.96993	−	0.0221885i
$370$	−622.843			−1.68336
$371$			213.379i			0.575147i
$372$	−51.0173	−	50.4459i	−0.137143	−	0.135607i
$373$	6.95096			0.0186353			0.00931764	−	0.999957i	$-0.497034\pi$
$373$	6.95096			0.0186353			0.00931764	+	0.999957i	$0.497034\pi$
$374$			24.5964i			0.0657657i
$375$	−52.0234	+	52.6127i	−0.138729	+	0.140300i
$376$	9.41815			0.0250483
$377$			26.3616i			0.0699245i
$378$	155.996	+	150.812i	0.412687	+	0.398973i
$379$	−174.412			−0.460190			−0.230095	−	0.973168i	$-0.573904\pi$
$379$	−174.412			−0.460190			−0.230095	+	0.973168i	$0.573904\pi$
$380$		−	3.97373i		−	0.0104572i
$381$	322.771	+	319.156i	0.847167	+	0.837679i
$382$	84.4450			0.221060
$383$			545.256i			1.42365i	0.702359	+	0.711823i	$0.252130\pi$
$383$			545.256i			1.42365i	−0.702359	+	0.711823i	$0.747870\pi$
$384$	325.791	−	329.481i	0.848413	−	0.858023i
$385$	59.0000			0.153247
$386$		−	411.386i		−	1.06577i
$387$	0.638502	+	56.6871i	0.00164987	+	0.146478i
$388$	−108.775			−0.280349
$389$			425.355i			1.09346i	0.837310	+	0.546729i	$0.184127\pi$
$389$			425.355i			1.09346i	−0.837310	+	0.546729i	$0.815873\pi$
$390$	338.258	+	334.469i	0.867327	+	0.857613i
$391$	163.558			0.418308
$392$			236.213i			0.602585i
$393$	318.807	−	322.418i	0.811213	−	0.820402i
$394$	−482.842			−1.22549
$395$			285.290i			0.722252i
$396$	−25.0971	+	0.282684i	−0.0633765	+	0.000713848i
$397$	274.032			0.690256			0.345128	−	0.938556i	$-0.387836\pi$
$397$	274.032			0.690256			0.345128	+	0.938556i	$0.387836\pi$
$398$		−	706.592i		−	1.77536i
$399$	−3.86691	−	3.82360i	−0.00969150	−	0.00958295i
$400$	411.790			1.02948
$401$		−	374.951i		−	0.935041i	−0.883982	−	0.467520i	$-0.845147\pi$
$401$		−	374.951i		−	0.935041i	0.883982	−	0.467520i	$-0.154853\pi$
$402$	−39.1474	+	39.5909i	−0.0973817	+	0.0984847i
$403$	−215.262			−0.534148
$404$		−	135.065i		−	0.334319i
$405$	12.4250	+	551.484i	0.0306789	+	1.36169i
$406$	−20.6295			−0.0508115
$407$		−	98.5974i		−	0.242254i
$408$	61.3727	+	60.6854i	0.150423	+	0.148739i
$409$	365.273			0.893088			0.446544	−	0.894762i	$-0.352655\pi$
$409$	365.273			0.893088			0.446544	+	0.894762i	$0.352655\pi$
$410$			1247.21i			3.04198i
$411$	196.395	−	198.619i	0.477846	−	0.483258i
$412$	−230.804			−0.560205
$413$			352.860i			0.854382i
$414$	8.47026	+	752.003i	0.0204596	+	1.81643i
$415$	109.194			0.263117
$416$			182.206i			0.437996i
$417$	53.2001	+	52.6042i	0.127578	+	0.126149i
$418$	2.83452			0.00678114
$419$		−	772.290i		−	1.84317i	−0.388172	−	0.921587i	$-0.626893\pi$
$419$		−	772.290i		−	1.84317i	0.388172	−	0.921587i	$-0.373107\pi$
$420$	−58.0870	+	58.7449i	−0.138302	+	0.139869i
$421$	−217.533			−0.516706			−0.258353	−	0.966051i	$-0.583180\pi$
$421$	−217.533			−0.516706			−0.258353	+	0.966051i	$0.583180\pi$
$422$		−	273.040i		−	0.647015i
$423$	−13.0747	+	0.147268i	−0.0309094	+	0.000348151i
$424$	−390.277			−0.920464
$425$			94.8776i			0.223241i
$426$	212.315	+	209.937i	0.498392	+	0.492810i
$427$	107.186			0.251022
$428$		−	127.823i		−	0.298653i
$429$	−52.9472	+	53.5469i	−0.123420	+	0.124818i
$430$	−97.2628			−0.226193
$431$			53.1247i			0.123259i	0.998099	+	0.0616295i	$0.0196297\pi$
$431$			53.1247i			0.123259i	−0.998099	+	0.0616295i	$0.980370\pi$
$432$	−361.481	+	373.907i	−0.836763	+	0.865525i
$433$	−142.578			−0.329280			−0.164640	−	0.986354i	$-0.552646\pi$
$433$	−142.578			−0.329280			−0.164640	+	0.986354i	$0.552646\pi$
$434$		−	168.455i		−	0.388145i
$435$	−37.2937	−	36.8760i	−0.0857326	−	0.0847724i
$436$	−202.859			−0.465272
$437$		−	18.8487i		−	0.0431320i
$438$	−41.6854	+	42.1576i	−0.0951722	+	0.0962503i
$439$	672.192			1.53119			0.765595	−	0.643323i	$-0.222445\pi$
$439$	672.192			1.53119			0.765595	+	0.643323i	$0.222445\pi$
$440$			107.913i			0.245256i
$441$	−3.69357	−	327.921i	−0.00837545	−	0.743585i
$442$	−103.333			−0.233785
$443$		−	474.604i		−	1.07134i	−0.844427	−	0.535670i	$-0.820059\pi$
$443$		−	474.604i		−	1.07134i	0.844427	−	0.535670i	$-0.179941\pi$
$444$	98.1712	+	97.0716i	0.221106	+	0.218630i
$445$	478.482			1.07524
$446$		−	590.903i		−	1.32489i
$447$	−158.580	+	160.376i	−0.354765	+	0.358783i
$448$	130.493			0.291278
$449$			67.7639i			0.150922i	0.997149	+	0.0754609i	$0.0240428\pi$
$449$			67.7639i			0.150922i	−0.997149	+	0.0754609i	$0.975957\pi$
$450$	−436.225	+	4.91347i	−0.969389	+	0.0109188i
$451$	−197.436			−0.437774
$452$			182.337i			0.403400i
$453$	543.306	+	537.221i	1.19935	+	1.18592i
$454$	−2.36008			−0.00519841
$455$			247.868i			0.544764i
$456$	6.99346	−	7.07268i	0.0153365	−	0.0155103i
$457$	−95.2205			−0.208360			−0.104180	−	0.994558i	$-0.533222\pi$
$457$	−95.2205			−0.208360			−0.104180	+	0.994558i	$0.533222\pi$
$458$		−	372.282i		−	0.812842i
$459$	−86.1491	−	83.2863i	−0.187689	−	0.181452i
$460$	−286.344			−0.622487
$461$			861.998i			1.86984i	0.354854	+	0.934922i	$0.384531\pi$
$461$			861.998i			1.86984i	−0.354854	+	0.934922i	$0.615469\pi$
$462$	−41.9036	−	41.4343i	−0.0907004	−	0.0896846i
$463$	270.031			0.583221			0.291610	−	0.956537i	$-0.405809\pi$
$463$	270.031			0.583221			0.291610	+	0.956537i	$0.405809\pi$
$464$		−	49.4469i		−	0.106567i
$465$	301.120	−	304.531i	0.647569	−	0.654904i
$466$	462.258			0.991971
$467$			842.340i			1.80373i	0.432023	+	0.901863i	$0.357800\pi$
$467$			842.340i			1.80373i	−0.432023	+	0.901863i	$0.642200\pi$
$468$	−1.18760	−	105.437i	−0.00253760	−	0.225292i
$469$	−29.0113			−0.0618577
$470$		−	22.4333i		−	0.0477304i
$471$	−290.140	−	286.890i	−0.616008	−	0.609109i
$472$	−645.391			−1.36735
$473$		−	15.3969i		−	0.0325516i
$474$	200.352	−	202.621i	0.422684	−	0.427472i
$475$	10.9338			0.0230186
$476$		−	17.9457i		−	0.0377011i
$477$	541.799	−	6.10261i	1.13585	−	0.0127937i
$478$	−471.332			−0.986050
$479$		−	552.842i		−	1.15416i	−0.816688	−	0.577079i	$-0.804192\pi$
$479$		−	552.842i		−	1.15416i	0.816688	−	0.577079i	$-0.195808\pi$
$480$	−257.767	−	254.880i	−0.537015	−	0.531000i
$481$	414.222			0.861169
$482$		−	674.239i		−	1.39884i
$483$	−275.525	+	278.646i	−0.570446	+	0.576907i
$484$	−131.231			−0.271139
$485$		−	649.299i		−	1.33876i
$486$	378.469	−	400.407i	0.778744	−	0.823882i
$487$	671.422			1.37869			0.689345	−	0.724433i	$-0.257898\pi$
$487$	671.422			1.37869			0.689345	+	0.724433i	$0.257898\pi$
$488$			196.047i			0.401735i
$489$	30.7967	+	30.4517i	0.0629788	+	0.0622735i
$490$	562.642			1.14825
$491$			525.860i			1.07100i	0.844536	+	0.535499i	$0.179877\pi$
$491$			525.860i			1.07100i	−0.844536	+	0.535499i	$0.820123\pi$
$492$	194.381	−	196.583i	0.395083	−	0.399558i
$493$	11.3927			0.0231089
$494$			11.9082i			0.0241057i
$495$	−1.68739	−	149.809i	−0.00340886	−	0.302644i
$496$	403.770			0.814053
$497$			155.580i			0.313038i
$498$	−77.5527	−	76.6841i	−0.155728	−	0.153984i
$499$	−205.220			−0.411262			−0.205631	−	0.978630i	$-0.565925\pi$
$499$	−205.220			−0.411262			−0.205631	+	0.978630i	$0.565925\pi$
$500$			28.1382i			0.0562764i
$501$	115.383	−	116.690i	0.230305	−	0.232914i
$502$	587.809			1.17093
$503$		−	473.536i		−	0.941424i	−0.882287	−	0.470712i	$-0.843997\pi$
$503$		−	473.536i		−	0.941424i	0.882287	−	0.470712i	$-0.156003\pi$
$504$	−206.773	+	2.32901i	−0.410264	+	0.00462106i
$505$	806.225			1.59648
$506$		−	204.253i		−	0.403662i
$507$	135.558	+	134.040i	0.267373	+	0.264378i
$508$	172.624			0.339810
$509$			621.410i			1.22085i	0.792076	+	0.610423i	$0.209000\pi$
$509$			621.410i			1.22085i	−0.792076	+	0.610423i	$0.791000\pi$
$510$	144.548	−	146.185i	0.283427	−	0.286637i
$511$	−30.8921			−0.0604543
$512$			157.703i			0.308013i
$513$	−9.59803	+	9.92794i	−0.0187096	+	0.0193527i
$514$	−810.423			−1.57670
$515$		−	1377.71i		−	2.67516i
$516$	15.3304	+	15.1587i	0.0297100	+	0.0293772i
$517$	3.55124			0.00686894
$518$			324.153i			0.625778i
$519$	−641.829	+	649.099i	−1.23667	+	1.25067i
$520$	−453.357			−0.871840
$521$			696.094i			1.33607i	0.744128	+	0.668037i	$0.232865\pi$
$521$			696.094i			1.33607i	−0.744128	+	0.668037i	$0.767135\pi$
$522$	0.589998	+	52.3809i	0.00113026	+	0.100347i
$523$	−229.771			−0.439334			−0.219667	−	0.975575i	$-0.570497\pi$
$523$	−229.771			−0.439334			−0.219667	+	0.975575i	$0.570497\pi$
$524$		−	172.435i		−	0.329074i
$525$	−161.638	−	159.828i	−0.307882	−	0.304434i
$526$	357.819			0.680264
$527$			93.0297i			0.176527i
$528$	99.3141	−	100.439i	0.188095	−	0.190225i
$529$	−829.222			−1.56753
$530$			929.609i			1.75398i
$531$	895.958	−	10.0917i	1.68730	−	0.0190051i
$532$	−2.06809			−0.00388739
$533$		−	829.458i		−	1.55621i
$534$	−339.832	−	336.026i	−0.636390	−	0.629263i
$535$	763.000			1.42617
$536$		−	53.0624i		−	0.0989971i
$537$	284.482	−	287.705i	0.529762	−	0.535763i
$538$	−221.696			−0.412074
$539$			89.0674i			0.165246i
$540$	150.822	+	145.810i	0.279301	+	0.270019i
$541$	−54.4880			−0.100717			−0.0503586	−	0.998731i	$-0.516036\pi$
$541$	−54.4880			−0.100717			−0.0503586	+	0.998731i	$0.516036\pi$
$542$			342.657i			0.632208i
$543$	534.223	+	528.240i	0.983836	+	0.972817i
$544$	78.7442			0.144750
$545$		−	1210.90i		−	2.22183i
$546$	174.071	−	176.043i	0.318812	−	0.322423i
$547$	353.825			0.646846			0.323423	−	0.946254i	$-0.395166\pi$
$547$	353.825			0.646846			0.323423	+	0.946254i	$0.395166\pi$
$548$		−	106.225i		−	0.193841i
$549$	−3.06551	−	272.160i	−0.00558380	−	0.495738i
$550$	118.484			0.215425
$551$		−	1.31291i		−	0.00238278i
$552$	−509.652	−	503.943i	−0.923282	−	0.912941i
$553$	148.476			0.268493
$554$		−	725.047i		−	1.30875i
$555$	−579.437	+	586.000i	−1.04403	+	1.05586i
$556$	28.4524			0.0511733
$557$			96.5468i			0.173334i	0.996237	+	0.0866668i	$0.0276216\pi$
$557$			96.5468i			0.173334i	−0.996237	+	0.0866668i	$0.972378\pi$
$558$	−427.729	+	4.81777i	−0.766539	+	0.00863400i
$559$	64.6847			0.115715
$560$		−	464.930i		−	0.830232i
$561$	23.1414	+	22.8822i	0.0412503	+	0.0407883i
$562$	180.963			0.321999
$563$		−	1064.69i		−	1.89110i	−0.325475	−	0.945551i	$-0.605524\pi$
$563$		−	1064.69i		−	1.89110i	0.325475	−	0.945551i	$-0.394476\pi$
$564$	−3.49629	+	3.53589i	−0.00619909	+	0.00626931i
$565$	−1088.40			−1.92637
$566$		−	1035.63i		−	1.82974i
$567$	287.015	−	6.46646i	0.506199	−	0.0114047i
$568$	−284.560			−0.500985
$569$			328.633i			0.577562i	0.957395	+	0.288781i	$0.0932500\pi$
$569$			328.633i			0.577562i	−0.957395	+	0.288781i	$0.906750\pi$
$570$	−16.8466	−	16.6579i	−0.0295554	−	0.0292244i
$571$	−139.054			−0.243527			−0.121764	−	0.992559i	$-0.538855\pi$
$571$	−139.054			−0.243527			−0.121764	+	0.992559i	$0.538855\pi$
$572$			28.6379i			0.0500662i
$573$	78.5600	−	79.4499i	0.137103	−	0.138656i
$574$	649.099			1.13084
$575$		−	787.883i		−	1.37023i
$576$	−3.73206	−	331.338i	−0.00647927	−	0.575240i
$577$	−241.620			−0.418752			−0.209376	−	0.977835i	$-0.567143\pi$
$577$	−241.620			−0.418752			−0.209376	+	0.977835i	$0.567143\pi$
$578$		−	610.608i		−	1.05641i
$579$	−387.051	−	382.716i	−0.668482	−	0.660995i
$580$	−19.9453			−0.0343885
$581$		−	56.8289i		−	0.0978122i
$582$	−455.987	+	461.152i	−0.783482	+	0.792357i
$583$	−147.159			−0.252417
$584$		−	56.5026i		−	0.0967510i
$585$	629.369	−	7.08896i	1.07584	−	0.0121179i
$586$	−857.021			−1.46249
$587$		−	30.7111i		−	0.0523187i	−0.999658	−	0.0261593i	$-0.991672\pi$
$587$		−	30.7111i		−	0.0523187i	0.999658	−	0.0261593i	$-0.00832773\pi$
$588$	−88.6823	−	87.6891i	−0.150820	−	0.149131i
$589$	10.7209			0.0182018
$590$			1537.27i			2.60554i
$591$	−449.193	+	454.281i	−0.760055	+	0.768664i
$592$	−776.964			−1.31244
$593$		−	55.4209i		−	0.0934585i	−0.998908	−	0.0467292i	$-0.985120\pi$
$593$		−	55.4209i		−	0.0934585i	0.998908	−	0.0467292i	$-0.0148798\pi$
$594$	−104.009	+	107.584i	−0.175099	+	0.181118i
$595$	107.121			0.180035
$596$			85.7720i			0.143913i
$597$	−664.795	−	657.349i	−1.11356	−	1.10109i
$598$	858.097			1.43495
$599$			613.371i			1.02399i	0.858988	+	0.511996i	$0.171094\pi$
$599$			613.371i			1.02399i	−0.858988	+	0.511996i	$0.828906\pi$
$600$	292.330	−	295.641i	0.487216	−	0.492735i
$601$	−557.815			−0.928144			−0.464072	−	0.885797i	$-0.653612\pi$
$601$	−557.815			−0.928144			−0.464072	+	0.885797i	$0.653612\pi$
$602$			50.6196i			0.0840857i
$603$	0.829717	+	73.6635i	0.00137598	+	0.122162i
$604$	290.570			0.481076
$605$		−	783.341i		−	1.29478i
$606$	−572.605	−	566.192i	−0.944893	−	0.934310i
$607$	874.423			1.44057			0.720283	−	0.693681i	$-0.244012\pi$
$607$	874.423			1.44057			0.720283	+	0.693681i	$0.244012\pi$
$608$		−	9.07459i		−	0.0149253i
$609$	−19.1918	+	19.4092i	−0.0315136	+	0.0318705i
$610$	466.968			0.765522
$611$			14.9193i			0.0244178i
$612$	−45.5666	+	0.513244i	−0.0744552	+	0.000838635i
$613$	−1025.24			−1.67250			−0.836249	−	0.548349i	$-0.815256\pi$
$613$	−1025.24			−1.67250			−0.836249	+	0.548349i	$0.815256\pi$
$614$			772.732i			1.25852i
$615$	1173.43	+	1160.29i	1.90802	+	1.88665i
$616$	56.1621			0.0911723
$617$			240.920i			0.390470i	0.980756	+	0.195235i	$0.0625470\pi$
$617$			240.920i			0.390470i	−0.980756	+	0.195235i	$0.937453\pi$
$618$	−967.532	+	978.492i	−1.56559	+	1.58332i
$619$	−632.006			−1.02101			−0.510506	−	0.859874i	$-0.670542\pi$
$619$	−632.006			−1.02101			−0.510506	+	0.859874i	$0.670542\pi$
$620$		−	162.868i		−	0.262691i
$621$	715.400	+	691.626i	1.15201	+	1.11373i
$622$	−113.154			−0.181919
$623$		−	249.022i		−	0.399714i
$624$	421.959	+	417.233i	0.676216	+	0.668643i
$625$	−702.423			−1.12388
$626$		−	133.991i		−	0.214043i
$627$	2.63698	−	2.66685i	0.00420571	−	0.00425335i
$628$	−155.172			−0.247089
$629$		−	179.015i		−	0.284602i
$630$	5.54753	+	492.518i	0.00880560	+	0.781774i
$631$	−421.377			−0.667793			−0.333896	−	0.942610i	$-0.608364\pi$
$631$	−421.377			−0.667793			−0.333896	+	0.942610i	$0.608364\pi$
$632$			271.568i			0.429695i
$633$	−256.889	−	254.012i	−0.405828	−	0.401283i
$634$	1072.80			1.69212
$635$			1030.42i			1.62271i
$636$	144.882	−	146.523i	0.227802	−	0.230382i
$637$	−374.185			−0.587418
$638$		−	14.2273i		−	0.0222998i
$639$	395.037	−	4.44955i	0.618212	−	0.00696329i
$640$	1051.84			1.64350
$641$			693.287i			1.08157i	0.841161	+	0.540785i	$0.181873\pi$
$641$			693.287i			1.08157i	−0.841161	+	0.540785i	$0.818127\pi$
$642$	−541.906	−	535.836i	−0.844090	−	0.834636i
$643$	802.276			1.24771			0.623854	−	0.781541i	$-0.285566\pi$
$643$	802.276			1.24771			0.623854	+	0.781541i	$0.285566\pi$
$644$			149.025i			0.231405i
$645$	−90.4845	+	91.5095i	−0.140286	+	0.141875i
$646$	5.14639			0.00796654
$647$		−	137.166i		−	0.212003i	−0.994366	−	0.106001i	$-0.966195\pi$
$647$		−	137.166i		−	0.212003i	0.994366	−	0.106001i	$-0.0338048\pi$
$648$	11.8273	+	524.958i	0.0182521	+	0.810121i
$649$	−243.353			−0.374966
$650$			497.769i			0.765798i
$651$	−158.490	−	156.715i	−0.243456	−	0.240730i
$652$	16.4706			0.0252617
$653$			181.773i			0.278366i	0.990267	+	0.139183i	$0.0444476\pi$
$653$			181.773i			0.278366i	−0.990267	+	0.139183i	$0.955552\pi$
$654$	−850.384	+	860.016i	−1.30028	+	1.31501i
$655$	1029.29			1.57144
$656$			1555.83i			2.37169i
$657$	0.883509	+	78.4392i	0.00134476	+	0.119390i
$658$	−11.6752			−0.0177435
$659$		−	435.347i		−	0.660618i	−0.943873	−	0.330309i	$-0.892847\pi$
$659$		−	435.347i		−	0.660618i	0.943873	−	0.330309i	$-0.107153\pi$
$660$	−40.5140	−	40.0602i	−0.0613848	−	0.0606973i
$661$	930.786			1.40815			0.704074	−	0.710126i	$-0.251362\pi$
$661$	930.786			1.40815			0.704074	+	0.710126i	$0.251362\pi$
$662$			515.589i			0.778835i
$663$	−96.1316	+	97.2205i	−0.144995	+	0.146637i
$664$	103.942			0.156539
$665$		−	12.3448i		−	0.0185636i
$666$	823.067	−	9.27071i	1.23584	−	0.0139200i
$667$	−94.6072			−0.141840
$668$		−	62.4079i		−	0.0934250i
$669$	−555.949	−	549.722i	−0.831015	−	0.821708i
$670$	−126.391			−0.188643
$671$			73.9221i			0.110167i
$672$	−132.650	+	134.153i	−0.197396	+	0.199632i
$673$	717.807			1.06658			0.533289	−	0.845933i	$-0.320956\pi$
$673$	717.807			1.06658			0.533289	+	0.845933i	$0.320956\pi$
$674$			1054.67i			1.56480i
$675$	−401.201	+	414.992i	−0.594372	+	0.614803i
$676$	72.4988			0.107247
$677$		−	848.556i		−	1.25341i	−0.779258	−	0.626703i	$-0.784404\pi$
$677$		−	848.556i		−	1.25341i	0.779258	−	0.626703i	$-0.215596\pi$
$678$	773.015	+	764.357i	1.14014	+	1.12737i
$679$	−337.922			−0.497675
$680$			195.927i			0.288129i
$681$	−2.19560	+	2.22047i	−0.00322408	+	0.00326060i
$682$	116.176			0.170347
$683$			432.835i			0.633727i	0.948471	+	0.316863i	$0.102630\pi$
$683$			432.835i			0.633727i	−0.948471	+	0.316863i	$0.897370\pi$
$684$	0.0591470	+	5.25116i	8.64722e−5	+	0.00767713i
$685$	634.075			0.925657
$686$		−	686.594i		−	1.00087i
$687$	−350.260	−	346.337i	−0.509840	−	0.504130i
$688$	−121.330			−0.176352
$689$		−	618.237i		−	0.897296i
$690$	−1200.35	+	1213.95i	−1.73964	+	1.75935i
$691$	−402.674			−0.582741			−0.291371	−	0.956610i	$-0.594111\pi$
$691$	−402.674			−0.582741			−0.291371	+	0.956610i	$0.594111\pi$
$692$			347.150i			0.501662i
$693$	−77.9666	+	0.878185i	−0.112506	+	0.00126722i
$694$	360.284			0.519142
$695$			169.837i			0.244370i
$696$	−35.4999	−	35.1023i	−0.0510056	−	0.0504343i
$697$	−358.468			−0.514301
$698$		−	1238.89i		−	1.77492i
$699$	430.043	−	434.914i	0.615226	−	0.622195i
$700$	−86.4471			−0.123496
$701$			829.546i			1.18337i	0.806168	+	0.591687i	$0.201538\pi$
$701$			829.546i			1.18337i	−0.806168	+	0.591687i	$0.798462\pi$
$702$	−451.975	−	436.956i	−0.643840	−	0.622444i
$703$	−20.6299			−0.0293455
$704$			89.9955i			0.127834i
$705$	−21.1063	−	20.8699i	−0.0299380	−	0.0296027i
$706$	824.086			1.16726
$707$		−	419.592i		−	0.593483i
$708$	239.587	−	242.301i	0.338400	−	0.342233i
$709$	855.194			1.20620			0.603099	−	0.797666i	$-0.293932\pi$
$709$	855.194			1.20620			0.603099	+	0.797666i	$0.293932\pi$
$710$			677.799i			0.954646i
$711$	−4.24639	−	377.001i	−0.00597243	−	0.530241i
$712$	455.467			0.639701
$713$		−	772.538i		−	1.08350i
$714$	−76.0807	−	75.2286i	−0.106556	−	0.105362i
$715$	−170.944			−0.239083
$716$		−	153.870i		−	0.214902i
$717$	−438.484	+	443.451i	−0.611554	+	0.618481i
$718$	−1379.06			−1.92069
$719$			269.870i			0.375340i	0.982232	+	0.187670i	$0.0600936\pi$
$719$			269.870i			0.375340i	−0.982232	+	0.187670i	$0.939906\pi$
$720$	−1180.52	+	13.2969i	−1.63961	+	0.0184679i
$721$	−717.016			−0.994475
$722$			817.922i			1.13286i
$723$	−634.356	−	627.251i	−0.877394	−	0.867567i
$724$	285.712			0.394630
$725$		−	54.8801i		−	0.0756968i
$726$	−550.122	+	556.353i	−0.757743	+	0.766326i
$727$	292.808			0.402762			0.201381	−	0.979513i	$-0.435457\pi$
$727$	292.808			0.402762			0.201381	+	0.979513i	$0.435457\pi$
$728$			235.945i			0.324101i
$729$	−24.6278	−	728.584i	−0.0337830	−	0.999429i
$730$	−134.585			−0.184363
$731$		−	27.9548i		−	0.0382419i
$732$	−73.6025	−	72.7782i	−0.100550	−	0.0994237i
$733$	−558.631			−0.762115			−0.381058	−	0.924551i	$-0.624440\pi$
$733$	−558.631			−0.762115			−0.381058	+	0.924551i	$0.624440\pi$
$734$			1530.05i			2.08454i
$735$	523.431	−	529.360i	0.712151	−	0.720217i
$736$	−653.908			−0.888462
$737$		−	20.0079i		−	0.0271478i
$738$	−18.5641	−	1648.15i	−0.0251546	−	2.23327i
$739$	−495.175			−0.670061			−0.335030	−	0.942207i	$-0.608747\pi$
$739$	−495.175			−0.670061			−0.335030	+	0.942207i	$0.608747\pi$
$740$			313.403i			0.423518i
$741$	11.2038	+	11.0783i	0.0151199	+	0.0149505i
$742$	483.807			0.652030
$743$		−	1330.41i		−	1.79060i	−0.445467	−	0.895298i	$-0.646962\pi$
$743$		−	1330.41i		−	1.79060i	0.445467	−	0.895298i	$-0.353038\pi$
$744$	286.636	−	289.883i	0.385264	−	0.389628i
$745$	−511.987			−0.687231
$746$		−	15.7603i		−	0.0211264i
$747$	−144.296	+	1.62529i	−0.193167	+	0.00217576i
$748$	12.3764			0.0165461
$749$		−	397.096i		−	0.530169i
$750$	119.292	+	117.955i	0.159055	+	0.157274i
$751$	568.470			0.756951			0.378475	−	0.925611i	$-0.376449\pi$
$751$	568.470			0.756951			0.378475	+	0.925611i	$0.376449\pi$
$752$		−	27.9844i		−	0.0372133i
$753$	546.844	−	553.038i	0.726221	−	0.734447i
$754$	59.7710			0.0792718
$755$			1734.46i			2.29730i
$756$	75.8857	−	78.4942i	0.100378	−	0.103828i
$757$	−1445.64			−1.90970			−0.954849	−	0.297090i	$-0.903984\pi$
$757$	−1445.64			−1.90970			−0.954849	+	0.297090i	$0.903984\pi$
$758$			395.454i			0.521707i
$759$	−192.171	−	190.019i	−0.253190	−	0.250354i
$760$	22.5790			0.0297092
$761$			1010.06i			1.32728i	0.748053	+	0.663639i	$0.230989\pi$
$761$			1010.06i			1.32728i	−0.748053	+	0.663639i	$0.769011\pi$
$762$	723.638	−	731.835i	0.949657	−	0.960414i
$763$	−630.200			−0.825950
$764$		−	42.4912i		−	0.0556168i
$765$	−3.06364	−	271.995i	−0.00400476	−	0.355549i
$766$	1236.29			1.61395
$767$		−	1022.36i		−	1.33294i
$768$	−432.887	−	428.038i	−0.563654	−	0.557341i
$769$	409.462			0.532460			0.266230	−	0.963910i	$-0.414222\pi$
$769$	409.462			0.532460			0.266230	+	0.963910i	$0.414222\pi$
$770$		−	133.774i		−	0.173732i
$771$	−753.944	+	762.484i	−0.977878	+	0.988954i
$772$	−207.002			−0.268137
$773$			170.515i			0.220589i	0.993899	+	0.110294i	$0.0351794\pi$
$773$			170.515i			0.220589i	−0.993899	+	0.110294i	$0.964821\pi$
$774$	128.530	−	1.44771i	0.166059	−	0.00187042i
$775$	448.137			0.578241
$776$		−	618.068i		−	0.796479i
$777$	304.978	+	301.563i	0.392508	+	0.388111i
$778$	964.431			1.23963
$779$			41.3103i			0.0530299i
$780$	168.299	−	170.205i	0.215768	−	0.218212i
$781$	−107.297			−0.137384
$782$		−	370.845i		−	0.474226i
$783$	49.8313	+	48.1754i	0.0636415	+	0.0615267i
$784$	701.866			0.895237
$785$		−	926.248i		−	1.17993i
$786$	−731.036	−	722.848i	−0.930071	−	0.919654i
$787$	−534.083			−0.678632			−0.339316	−	0.940672i	$-0.610196\pi$
$787$	−534.083			−0.678632			−0.339316	+	0.940672i	$0.610196\pi$
$788$			242.957i			0.308322i
$789$	332.882	−	336.653i	0.421904	−	0.426683i
$790$	646.853			0.818801
$791$			566.448i			0.716116i
$792$	−1.60623	−	142.603i	−0.00202806	−	0.180054i
$793$	−310.558			−0.391624
$794$		−	621.326i		−	0.782527i
$795$	874.620	+	864.824i	1.10015	+	1.08783i
$796$	−355.545			−0.446664
$797$			29.8799i			0.0374905i	0.999824	+	0.0187453i	$0.00596715\pi$
$797$			29.8799i			0.0374905i	−0.999824	+	0.0187453i	$0.994033\pi$
$798$	−8.66945	+	8.76764i	−0.0108640	+	0.0109870i
$799$	6.44768			0.00806968
$800$		−	379.322i		−	0.474152i
$801$	−632.299	+	7.12196i	−0.789387	+	0.00889134i
$802$	−850.147			−1.06003
$803$		−	21.3051i		−	0.0265318i
$804$	19.9214	+	19.6983i	0.0247779	+	0.0245004i
$805$	−889.555			−1.10504
$806$			488.074i			0.605551i
$807$	−206.246	+	208.582i	−0.255571	+	0.258466i
$808$	767.446			0.949809
$809$		−	1097.81i		−	1.35700i	−0.734601	−	0.678499i	$-0.762631\pi$
$809$		−	1097.81i		−	1.35700i	0.734601	−	0.678499i	$-0.237369\pi$
$810$	1250.41	−	28.1718i	1.54372	−	0.0347800i
$811$	1195.40			1.47398			0.736992	−	0.675902i	$-0.236246\pi$
$811$	1195.40			1.47398			0.736992	+	0.675902i	$0.236246\pi$
$812$			10.3804i			0.0127837i
$813$	322.388	+	318.777i	0.396541	+	0.392100i
$814$	−223.555			−0.274638
$815$			98.3158i			0.120633i
$816$	180.316	−	182.358i	0.220975	−	0.223478i
$817$	−3.22155			−0.00394315
$818$		−	828.203i		−	1.01247i
$819$	−3.68939	−	327.549i	−0.00450474	−	0.399938i
$820$	627.574			0.765334
$821$		−	486.106i		−	0.592090i	−0.955174	−	0.296045i	$-0.904332\pi$
$821$		−	486.106i		−	0.592090i	0.955174	−	0.296045i	$-0.0956678\pi$
$822$	−450.340	−	445.296i	−0.547858	−	0.541722i
$823$	−777.701			−0.944959			−0.472479	−	0.881342i	$-0.656641\pi$
$823$	−777.701			−0.944959			−0.472479	+	0.881342i	$0.656641\pi$
$824$		−	1311.44i		−	1.59156i
$825$	110.227	−	111.475i	0.133608	−	0.135122i
$826$	800.058			0.968593
$827$			783.654i			0.947586i	0.880636	+	0.473793i	$0.157116\pi$
$827$			783.654i			0.947586i	−0.880636	+	0.473793i	$0.842884\pi$
$828$	378.394	−	4.26208i	0.456998	−	0.00514745i
$829$	641.762			0.774140			0.387070	−	0.922050i	$-0.373487\pi$
$829$	641.762			0.774140			0.387070	+	0.922050i	$0.373487\pi$
$830$		−	247.581i		−	0.298290i
$831$	−682.159	−	674.518i	−0.820889	−	0.811695i
$832$	−378.084			−0.454428
$833$			161.712i			0.194132i
$834$	119.272	−	120.623i	0.143012	−	0.144632i
$835$	372.523			0.446136
$836$		−	1.42628i		−	0.00170608i
$837$	−393.387	+	406.910i	−0.469997	+	0.486152i
$838$	−1751.05			−2.08956
$839$			210.616i			0.251032i	0.992092	+	0.125516i	$0.0400586\pi$
$839$			210.616i			0.251032i	−0.992092	+	0.125516i	$0.959941\pi$
$840$	−333.792	−	330.053i	−0.397371	−	0.392921i
$841$	834.410			0.992164
$842$			493.224i			0.585777i
$843$	168.352	−	170.259i	0.199706	−	0.201968i
$844$	−137.389			−0.162783
$845$			432.757i			0.512139i
$846$	0.333909	+	29.6449i	0.000394691	+	0.0350413i
$847$	−407.683			−0.481326
$848$			1159.64i			1.36750i
$849$	−974.372	−	963.458i	−1.14767	−	1.13482i
$850$	215.121			0.253084
$851$			1486.57i			1.74686i
$852$	105.637	−	106.833i	0.123987	−	0.125391i
$853$	1339.93			1.57084			0.785421	−	0.618962i	$-0.212447\pi$
$853$	1339.93			1.57084			0.785421	+	0.618962i	$0.212447\pi$
$854$		−	243.029i		−	0.284578i
$855$	−31.3450	+	0.353058i	−0.0366609	+	0.000412934i
$856$	726.300			0.848481
$857$			857.797i			1.00093i	0.865757	+	0.500465i	$0.166838\pi$
$857$			857.797i			1.00093i	−0.865757	+	0.500465i	$0.833162\pi$
$858$	121.410	+	120.050i	0.141503	+	0.139918i
$859$	−887.213			−1.03284			−0.516422	−	0.856334i	$-0.672736\pi$
$859$	−887.213			−1.03284			−0.516422	+	0.856334i	$0.672736\pi$
$860$			48.9409i			0.0569080i
$861$	603.863	−	610.703i	0.701351	−	0.709295i
$862$	120.452			0.139736
$863$			340.990i			0.395121i	0.980291	+	0.197561i	$0.0633020\pi$
$863$			340.990i			0.395121i	−0.980291	+	0.197561i	$0.936698\pi$
$864$	344.425	+	332.979i	0.398640	+	0.385393i
$865$	−2072.20			−2.39560
$866$			323.275i			0.373297i
$867$	−574.488	−	568.054i	−0.662616	−	0.655195i
$868$	−84.7634			−0.0976537
$869$			102.398i			0.117834i
$870$	−83.6109	+	84.5580i	−0.0961045	+	0.0971931i
$871$	84.0561			0.0965053
$872$		−	1152.65i		−	1.32185i
$873$	9.66448	+	858.028i	0.0110704	+	0.982850i
$874$	−42.7366			−0.0488978
$875$			87.4141i			0.0999018i
$876$	21.2130	+	20.9754i	0.0242157	+	0.0239445i
$877$	40.0156			0.0456278			0.0228139	−	0.999740i	$-0.492737\pi$
$877$	40.0156			0.0456278			0.0228139	+	0.999740i	$0.492737\pi$
$878$		−	1524.10i		−	1.73587i
$879$	−797.295	+	806.326i	−0.907048	+	0.917322i
$880$	320.643			0.364367
$881$			993.378i			1.12756i	0.825926	+	0.563778i	$0.190653\pi$
$881$			993.378i			1.12756i	−0.825926	+	0.563778i	$0.809347\pi$
$882$	−743.513	+	8.37464i	−0.842985	+	0.00949505i
$883$	1536.34			1.73991			0.869956	−	0.493130i	$-0.164147\pi$
$883$	1536.34			1.73991			0.869956	+	0.493130i	$0.164147\pi$
$884$			51.9953i			0.0588182i
$885$	1446.34	+	1430.14i	1.63428	+	1.61597i
$886$	−1076.09			−1.21455
$887$		−	547.879i		−	0.617676i	−0.951115	−	0.308838i	$-0.900060\pi$
$887$		−	547.879i		−	0.617676i	0.951115	−	0.308838i	$-0.0999401\pi$
$888$	−551.566	+	557.814i	−0.621133	+	0.628169i
$889$	536.272			0.603231
$890$		−	1084.89i		−	1.21897i
$891$	4.45966	+	197.942i	0.00500523	+	0.222158i
$892$	−297.332			−0.333331
$893$		−	0.743039i		−	0.000832071i
$894$	363.629	+	359.556i	0.406744	+	0.402188i
$895$	918.474			1.02623
$896$		−	547.421i		−	0.610961i
$897$	798.296	−	807.339i	0.889962	−	0.900043i
$898$	153.645			0.171097
$899$		−	53.8113i		−	0.0598568i
$900$	2.47237	+	219.501i	0.00274708	+	0.243890i
$901$	−267.184			−0.296542
$902$			447.658i			0.496294i
$903$	47.6253	+	47.0919i	0.0527412	+	0.0521505i
$904$	−1036.05			−1.14607
$905$			1705.46i			1.88449i
$906$	1218.07	−	1231.87i	1.34445	−	1.35968i
$907$	−232.144			−0.255947			−0.127974	−	0.991778i	$-0.540847\pi$
$907$	−232.144			−0.255947			−0.127974	+	0.991778i	$0.540847\pi$
$908$			1.18755i			0.00130787i
$909$	−1065.40	+	12.0002i	−1.17206	+	0.0132016i
$910$	562.003			0.617586
$911$			193.054i			0.211915i	0.994371	+	0.105957i	$0.0337907\pi$
$911$			193.054i			0.211915i	−0.994371	+	0.105957i	$0.966209\pi$
$912$	−21.0152	−	20.7798i	−0.0230430	−	0.0227849i
$913$	39.1926			0.0429272
$914$			215.899i			0.236213i
$915$	434.425	−	439.346i	0.474781	−	0.480159i
$916$	−187.326			−0.204504
$917$		−	535.686i		−	0.584173i
$918$	−188.839	+	195.331i	−0.205707	+	0.212778i
$919$	787.336			0.856731			0.428366	−	0.903606i	$-0.359090\pi$
$919$	787.336			0.856731			0.428366	+	0.903606i	$0.359090\pi$
$920$		−	1627.02i		−	1.76850i
$921$	727.023	+	718.880i	0.789384	+	0.780543i
$922$	1954.45			2.11980
$923$		−	450.770i		−	0.488375i
$924$	−20.8490	+	21.0851i	−0.0225638	+	0.0228194i
$925$	−862.338			−0.932257
$926$		−	612.256i		−	0.661184i
$927$	20.5065	+	1820.60i	0.0221214	+	1.96397i
$928$	−45.5481			−0.0490820
$929$		−	879.887i		−	0.947133i	−0.880758	−	0.473567i	$-0.842966\pi$
$929$		−	879.887i		−	0.947133i	0.880758	−	0.473567i	$-0.157034\pi$
$930$	−690.478	−	682.745i	−0.742450	−	0.734134i
$931$	18.6359			0.0200171
$932$		−	232.600i		−	0.249571i
$933$	−105.268	+	106.460i	−0.112828	+	0.114106i
$934$	1909.88			2.04484
$935$			73.8771i			0.0790129i
$936$	599.097	−	6.74799i	0.640060	−	0.00720939i
$937$	−893.592			−0.953674			−0.476837	−	0.878992i	$-0.658217\pi$
$937$	−893.592			−0.953674			−0.476837	+	0.878992i	$0.658217\pi$
$938$			65.7788i			0.0701267i
$939$	−126.065	−	124.653i	−0.134254	−	0.132751i
$940$	−11.2880			−0.0120086
$941$			14.0022i			0.0148801i	0.999972	+	0.00744004i	$0.00236826\pi$
$941$			14.0022i			0.0148801i	−0.999972	+	0.00744004i	$0.997632\pi$
$942$	−650.481	+	657.849i	−0.690532	+	0.698354i
$943$	2976.79			3.15672
$944$			1917.66i			2.03142i
$945$	468.545	+	452.975i	0.495815	+	0.479338i
$946$	−34.9103			−0.0369030
$947$		−	625.521i		−	0.660529i	−0.943888	−	0.330264i	$-0.892862\pi$
$947$		−	625.521i		−	0.660529i	0.943888	−	0.330264i	$-0.107138\pi$
$948$	−101.956	−	100.814i	−0.107548	−	0.106343i
$949$	89.5057			0.0943158
$950$		−	24.7908i		−	0.0260956i
$951$	998.037	−	1009.34i	1.04946	−	1.06135i
$952$	101.969			0.107110
$953$			955.211i			1.00232i	0.865355	+	0.501160i	$0.167093\pi$
$953$			955.211i			1.00232i	−0.865355	+	0.501160i	$0.832907\pi$
$954$	−13.8368	−	1228.45i	−0.0145039	−	1.28768i
$955$	253.637			0.265589
$956$			237.166i			0.248081i
$957$	−13.3857	−	13.2358i	−0.0139872	−	0.0138305i
$958$	−1253.49			−1.30844
$959$		−	329.999i		−	0.344107i
$960$	528.885	−	534.876i	0.550922	−	0.557162i
$961$	−521.591			−0.542759
$962$		−	939.188i		−	0.976287i
$963$	−1008.28	+	11.3569i	−1.04702	+	0.0117932i
$964$	−339.265			−0.351934
$965$		−	1235.63i		−	1.28045i
$966$	631.789	+	624.713i	0.654026	+	0.646701i
$967$	248.907			0.257402			0.128701	−	0.991683i	$-0.458919\pi$
$967$	248.907			0.257402			0.128701	+	0.991683i	$0.458919\pi$
$968$		−	745.663i		−	0.770313i
$969$	4.78773	−	4.84196i	0.00494090	−	0.00499687i
$970$	−1472.19			−1.51772
$971$			186.226i			0.191788i	0.995392	+	0.0958940i	$0.0305710\pi$
$971$			186.226i			0.191788i	−0.995392	+	0.0958940i	$0.969429\pi$
$972$	−201.477	−	190.439i	−0.207281	−	0.195925i
$973$	88.3901			0.0908428
$974$		−	1522.35i		−	1.56299i
$975$	468.324	+	463.079i	0.480333	+	0.474953i
$976$	582.519			0.596843
$977$		−	735.353i		−	0.752664i	−0.926485	−	0.376332i	$-0.877185\pi$
$977$		−	735.353i		−	0.752664i	0.926485	−	0.376332i	$-0.122815\pi$
$978$	69.0448	−	69.8269i	0.0705980	−	0.0713976i
$979$	171.740			0.175424
$980$		−	283.111i		−	0.288889i
$981$	18.0236	+	1600.16i	0.0183727	+	1.63115i
$982$	1192.31			1.21417
$983$		−	87.7260i		−	0.0892431i	−0.999004	−	0.0446216i	$-0.985792\pi$
$983$		−	87.7260i		−	0.0892431i	0.999004	−	0.0446216i	$-0.0142082\pi$
$984$	1116.99	+	1104.48i	1.13516	+	1.12244i
$985$	−1450.25			−1.47234
$986$		−	25.8313i		−	0.0261980i
$987$	−10.8616	+	10.9846i	−0.0110046	+	0.0111293i
$988$	5.99201			0.00606478
$989$			232.143i			0.234725i
$990$	−339.669	+	3.82590i	−0.343100	+	0.00386455i
$991$	−1311.63			−1.32354			−0.661770	−	0.749707i	$-0.730194\pi$
$991$	−1311.63			−1.32354			−0.661770	+	0.749707i	$0.730194\pi$
$992$		−	371.934i		−	0.374933i
$993$	485.090	+	479.657i	0.488510	+	0.483039i
$994$	352.754			0.354883
$995$		−	2122.30i		−	2.13297i
$996$	−38.5861	+	39.0231i	−0.0387410	+	0.0391799i
$997$	−1038.28			−1.04141			−0.520704	−	0.853738i	$-0.674330\pi$
$997$	−1038.28			−1.04141			−0.520704	+	0.853738i	$0.674330\pi$
$998$			465.306i			0.466238i
$999$	756.985	−	783.005i	0.757743	−	0.783789i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.3.c.a.68.12	✓	44
3.2	odd	2	inner	201.3.c.a.68.33	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.3.c.a.68.12	✓	44	1.1	even	1	trivial
201.3.c.a.68.33	yes	44	3.2	odd	2	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:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	201.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.26735i q^{2} +(-2.13323 - 2.10934i) q^{3} -1.14089 q^{4} -6.81017i q^{5} +(-4.78262 + 4.83679i) q^{6} -3.54429 q^{7} -6.48261i q^{8} +(0.101366 + 8.99943i) q^{9} +O(q^{10})\)	\(q-2.26735i q^{2} +(-2.13323 - 2.10934i) q^{3} -1.14089 q^{4} -6.81017i q^{5} +(-4.78262 + 4.83679i) q^{6} -3.54429 q^{7} -6.48261i q^{8} +(0.101366 + 8.99943i) q^{9} -15.4411 q^{10} -2.44435i q^{11} +(2.43379 + 2.40653i) q^{12} +10.2691 q^{13} +8.03616i q^{14} +(-14.3650 + 14.5277i) q^{15} -19.2619 q^{16} -4.43800i q^{17} +(20.4049 - 0.229833i) q^{18} -0.511441 q^{19} +7.76967i q^{20} +(7.56080 + 7.47612i) q^{21} -5.54222 q^{22} +36.8541i q^{23} +(-13.6740 + 13.8289i) q^{24} -21.3785 q^{25} -23.2837i q^{26} +(18.7666 - 19.4117i) q^{27} +4.04365 q^{28} +2.56708i q^{29} +(32.9394 + 32.5705i) q^{30} -20.9621 q^{31} +17.7432i q^{32} +(-5.15598 + 5.21438i) q^{33} -10.0625 q^{34} +24.1372i q^{35} +(-0.115648 - 10.2674i) q^{36} +40.3368 q^{37} +1.15962i q^{38} +(-21.9064 - 21.6610i) q^{39} -44.1477 q^{40} -80.7723i q^{41} +(16.9510 - 17.1430i) q^{42} +6.29897 q^{43} +2.78874i q^{44} +(61.2877 - 0.690320i) q^{45} +83.5612 q^{46} +1.45283i q^{47} +(41.0902 + 40.6300i) q^{48} -36.4380 q^{49} +48.4725i q^{50} +(-9.36125 + 9.46729i) q^{51} -11.7159 q^{52} -60.2037i q^{53} +(-44.0132 - 42.5506i) q^{54} -16.6465 q^{55} +22.9763i q^{56} +(1.09102 + 1.07880i) q^{57} +5.82047 q^{58} -99.5572i q^{59} +(16.3889 - 16.5745i) q^{60} -30.2420 q^{61} +47.5284i q^{62} +(-0.359271 - 31.8966i) q^{63} -36.8177 q^{64} -69.9343i q^{65} +(11.8228 + 11.6904i) q^{66} +8.18535 q^{67} +5.06328i q^{68} +(77.7378 - 78.6183i) q^{69} +54.7277 q^{70} -43.8958i q^{71} +(58.3398 - 0.657116i) q^{72} +8.71602 q^{73} -91.4577i q^{74} +(45.6052 + 45.0944i) q^{75} +0.583499 q^{76} +8.66351i q^{77} +(-49.1132 + 49.6695i) q^{78} -41.8917 q^{79} +131.177i q^{80} +(-80.9794 + 1.82447i) q^{81} -183.139 q^{82} +16.0339i q^{83} +(-8.62606 - 8.52944i) q^{84} -30.2236 q^{85} -14.2820i q^{86} +(5.41484 - 5.47617i) q^{87} -15.8458 q^{88} +70.2599i q^{89} +(-1.56520 - 138.961i) q^{90} -36.3967 q^{91} -42.0465i q^{92} +(44.7170 + 44.2162i) q^{93} +3.29409 q^{94} +3.48300i q^{95} +(37.4264 - 37.8503i) q^{96} +95.3425 q^{97} +82.6178i q^{98} +(21.9978 - 0.247774i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 92 q^{4} + 6 q^{6} + 8 q^{7} + 4 q^{9}+O(q^{10}) \) 44 * q - 92 * q^4 + 6 * q^6 + 8 * q^7 + 4 * q^9	\( 44 q - 92 q^{4} + 6 q^{6} + 8 q^{7} + 4 q^{9} + 12 q^{10} - 20 q^{12} - 32 q^{13} - 30 q^{15} + 204 q^{16} + 22 q^{18} - 32 q^{19} + 36 q^{21} - 8 q^{22} - 24 q^{24} - 164 q^{25} + 42 q^{27} - 48 q^{28} + 58 q^{30} + 20 q^{31} + 6 q^{33} - 48 q^{34} - 78 q^{36} + 100 q^{37} + 4 q^{39} + 160 q^{40} - 204 q^{42} - 108 q^{43} - 132 q^{45} - 244 q^{46} + 34 q^{48} + 332 q^{49} + 114 q^{51} - 8 q^{52} + 432 q^{54} + 128 q^{55} - 26 q^{57} - 12 q^{58} + 250 q^{60} - 164 q^{61} - 290 q^{63} - 432 q^{64} - 78 q^{66} + 76 q^{69} + 612 q^{70} - 464 q^{72} + 156 q^{73} - 118 q^{75} - 180 q^{76} - 392 q^{79} + 348 q^{81} + 524 q^{82} - 202 q^{84} - 188 q^{85} - 68 q^{87} - 348 q^{88} + 94 q^{90} - 44 q^{91} + 322 q^{93} - 304 q^{94} + 224 q^{96} + 68 q^{97} + 104 q^{99}+O(q^{100}) \) 44 * q - 92 * q^4 + 6 * q^6 + 8 * q^7 + 4 * q^9 + 12 * q^10 - 20 * q^12 - 32 * q^13 - 30 * q^15 + 204 * q^16 + 22 * q^18 - 32 * q^19 + 36 * q^21 - 8 * q^22 - 24 * q^24 - 164 * q^25 + 42 * q^27 - 48 * q^28 + 58 * q^30 + 20 * q^31 + 6 * q^33 - 48 * q^34 - 78 * q^36 + 100 * q^37 + 4 * q^39 + 160 * q^40 - 204 * q^42 - 108 * q^43 - 132 * q^45 - 244 * q^46 + 34 * q^48 + 332 * q^49 + 114 * q^51 - 8 * q^52 + 432 * q^54 + 128 * q^55 - 26 * q^57 - 12 * q^58 + 250 * q^60 - 164 * q^61 - 290 * q^63 - 432 * q^64 - 78 * q^66 + 76 * q^69 + 612 * q^70 - 464 * q^72 + 156 * q^73 - 118 * q^75 - 180 * q^76 - 392 * q^79 + 348 * q^81 + 524 * q^82 - 202 * q^84 - 188 * q^85 - 68 * q^87 - 348 * q^88 + 94 * q^90 - 44 * q^91 + 322 * q^93 - 304 * q^94 + 224 * q^96 + 68 * q^97 + 104 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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