LMFDB - Embedded newform 76.4.k.a.3.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,4,Mod(3,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 13]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("76.3");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	76.k (of order $18$, degree $6$, 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:	$4.48414516044$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$28$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			3.19
Character	$\chi$	$=$	76.3
Dual form			76.4.k.a.51.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.38498 + 2.46614i) q^{2} +(-2.28426 + 0.831401i) q^{3} +(-4.16368 + 6.83109i) q^{4} +(-1.38264 + 7.84134i) q^{5} +(-5.21399 - 4.48182i) q^{6} +(8.80596 - 5.08413i) q^{7} +(-22.6130 - 0.807318i) q^{8} +(-16.1566 + 13.5570i) q^{9} +O(q^{10})$	\(q+(1.38498 + 2.46614i) q^{2} +(-2.28426 + 0.831401i) q^{3} +(-4.16368 + 6.83109i) q^{4} +(-1.38264 + 7.84134i) q^{5} +(-5.21399 - 4.48182i) q^{6} +(8.80596 - 5.08413i) q^{7} +(-22.6130 - 0.807318i) q^{8} +(-16.1566 + 13.5570i) q^{9} +(-21.2527 + 7.45029i) q^{10} +(-36.8082 - 21.2512i) q^{11} +(3.83154 - 19.0656i) q^{12} +(-12.2465 + 33.6471i) q^{13} +(24.7342 + 14.6753i) q^{14} +(-3.36099 - 19.0611i) q^{15} +(-29.3275 - 56.8849i) q^{16} +(99.7828 + 83.7277i) q^{17} +(-55.8100 - 21.0683i) q^{18} +(80.8816 + 17.8090i) q^{19} +(-47.8080 - 42.0938i) q^{20} +(-15.8881 + 18.9347i) q^{21} +(1.42998 - 120.207i) q^{22} +(-38.6251 + 6.81065i) q^{23} +(52.3251 - 16.9564i) q^{24} +(57.8867 + 21.0690i) q^{25} +(-99.9396 + 16.3988i) q^{26} +(58.4510 - 101.240i) q^{27} +(-1.93511 + 81.3230i) q^{28} +(-37.3435 - 44.5042i) q^{29} +(42.3525 - 34.6879i) q^{30} +(124.321 + 215.330i) q^{31} +(99.6682 - 151.110i) q^{32} +(101.748 + 17.9408i) q^{33} +(-68.2873 + 362.039i) q^{34} +(27.6909 + 76.0800i) q^{35} +(-25.3381 - 166.814i) q^{36} +118.853i q^{37} +(68.0998 + 224.130i) q^{38} -87.0403i q^{39} +(37.5961 - 176.200i) q^{40} +(-65.9833 - 181.288i) q^{41} +(-68.7003 - 12.9582i) q^{42} +(74.8431 + 13.1969i) q^{43} +(298.427 - 162.957i) q^{44} +(-83.9663 - 145.434i) q^{45} +(-70.2909 - 85.8223i) q^{46} +(29.3598 + 34.9897i) q^{47} +(114.286 + 105.557i) q^{48} +(-119.803 + 207.505i) q^{49} +(28.2126 + 171.937i) q^{50} +(-297.541 - 108.296i) q^{51} +(-178.856 - 223.753i) q^{52} +(292.316 - 51.5431i) q^{53} +(330.626 + 3.93312i) q^{54} +(217.530 - 259.243i) q^{55} +(-203.234 + 107.858i) q^{56} +(-199.561 + 26.5648i) q^{57} +(58.0338 - 153.732i) q^{58} +(-521.703 - 437.761i) q^{59} +(144.202 + 56.4053i) q^{60} +(-96.6680 - 548.231i) q^{61} +(-358.851 + 604.818i) q^{62} +(-73.3490 + 201.525i) q^{63} +(510.696 + 36.5118i) q^{64} +(-246.906 - 142.551i) q^{65} +(96.6734 + 275.771i) q^{66} +(-338.848 + 284.327i) q^{67} +(-987.415 + 333.010i) q^{68} +(82.5673 - 47.6702i) q^{69} +(-149.273 + 173.659i) q^{70} +(-85.1841 + 483.103i) q^{71} +(376.294 - 293.521i) q^{72} +(279.894 - 101.873i) q^{73} +(-293.108 + 164.609i) q^{74} -149.745 q^{75} +(-458.420 + 478.359i) q^{76} -432.176 q^{77} +(214.654 - 120.549i) q^{78} +(484.949 - 176.507i) q^{79} +(486.603 - 151.316i) q^{80} +(49.5390 - 280.950i) q^{81} +(355.695 - 413.803i) q^{82} +(-491.945 + 284.025i) q^{83} +(-63.1917 - 187.371i) q^{84} +(-794.500 + 666.665i) q^{85} +(71.1107 + 202.851i) q^{86} +(122.303 + 70.6116i) q^{87} +(815.188 + 510.270i) q^{88} +(-102.114 + 280.555i) q^{89} +(242.369 - 408.495i) q^{90} +(63.2235 + 358.558i) q^{91} +(114.299 - 292.209i) q^{92} +(-463.005 - 388.507i) q^{93} +(-45.6267 + 120.865i) q^{94} +(-251.476 + 609.597i) q^{95} +(-102.035 + 428.038i) q^{96} +(971.884 - 1158.25i) q^{97} +(-677.662 - 8.06147i) q^{98} +(882.798 - 155.661i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q - 6 q^{2} - 24 q^{4} - 12 q^{5} - 24 q^{6} - 9 q^{8} + 18 q^{9}+O(q^{10}) $ 168 * q - 6 * q^2 - 24 * q^4 - 12 * q^5 - 24 * q^6 - 9 * q^8 + 18 * q^9	$ 168 q - 6 q^{2} - 24 q^{4} - 12 q^{5} - 24 q^{6} - 9 q^{8} + 18 q^{9} - 105 q^{10} - 9 q^{12} - 120 q^{13} + 69 q^{14} + 192 q^{16} - 12 q^{17} + 558 q^{20} + 6 q^{21} - 30 q^{22} + 96 q^{24} - 12 q^{25} - 411 q^{26} + 756 q^{28} - 12 q^{29} + 276 q^{30} - 471 q^{32} - 576 q^{33} + 36 q^{34} - 2673 q^{36} - 648 q^{38} - 2298 q^{40} - 606 q^{41} - 321 q^{42} - 1203 q^{44} - 6 q^{45} + 1566 q^{46} + 3237 q^{48} + 2346 q^{49} + 3204 q^{50} + 1077 q^{52} + 576 q^{53} - 627 q^{54} - 12 q^{57} - 4116 q^{58} + 90 q^{60} + 3528 q^{61} - 3300 q^{62} - 381 q^{64} + 1242 q^{65} + 276 q^{66} + 1170 q^{68} - 4770 q^{69} + 1449 q^{70} + 1146 q^{72} - 3468 q^{73} + 3105 q^{74} + 4386 q^{76} - 9396 q^{77} + 6939 q^{78} + 2133 q^{80} + 1980 q^{81} + 7299 q^{82} + 315 q^{84} - 516 q^{85} - 3804 q^{86} - 5841 q^{88} + 3576 q^{89} - 8898 q^{90} - 7668 q^{92} + 5694 q^{93} + 18942 q^{96} + 774 q^{97} + 8745 q^{98}+O(q^{100}) $ 168 * q - 6 * q^2 - 24 * q^4 - 12 * q^5 - 24 * q^6 - 9 * q^8 + 18 * q^9 - 105 * q^10 - 9 * q^12 - 120 * q^13 + 69 * q^14 + 192 * q^16 - 12 * q^17 + 558 * q^20 + 6 * q^21 - 30 * q^22 + 96 * q^24 - 12 * q^25 - 411 * q^26 + 756 * q^28 - 12 * q^29 + 276 * q^30 - 471 * q^32 - 576 * q^33 + 36 * q^34 - 2673 * q^36 - 648 * q^38 - 2298 * q^40 - 606 * q^41 - 321 * q^42 - 1203 * q^44 - 6 * q^45 + 1566 * q^46 + 3237 * q^48 + 2346 * q^49 + 3204 * q^50 + 1077 * q^52 + 576 * q^53 - 627 * q^54 - 12 * q^57 - 4116 * q^58 + 90 * q^60 + 3528 * q^61 - 3300 * q^62 - 381 * q^64 + 1242 * q^65 + 276 * q^66 + 1170 * q^68 - 4770 * q^69 + 1449 * q^70 + 1146 * q^72 - 3468 * q^73 + 3105 * q^74 + 4386 * q^76 - 9396 * q^77 + 6939 * q^78 + 2133 * q^80 + 1980 * q^81 + 7299 * q^82 + 315 * q^84 - 516 * q^85 - 3804 * q^86 - 5841 * q^88 + 3576 * q^89 - 8898 * q^90 - 7668 * q^92 + 5694 * q^93 + 18942 * q^96 + 774 * q^97 + 8745 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$-1$

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 $

$2$	1.38498	+	2.46614i	0.489663	+	0.871912i
$2$	1.38498	+	2.46614i	0.489663	+	0.871912i
$3$	−2.28426	+	0.831401i	−0.439605	+	0.160003i	−0.552335	−	0.833623i	$-0.686263\pi$
$3$	−2.28426	+	0.831401i	−0.439605	+	0.160003i	0.112729	+	0.993626i	$0.464041\pi$
$4$	−4.16368	+	6.83109i	−0.520460	+	0.853886i
$5$	−1.38264	+	7.84134i	−0.123667	+	0.701350i	0.858424	+	0.512941i	$0.171444\pi$
$5$	−1.38264	+	7.84134i	−0.123667	+	0.701350i	−0.982091	+	0.188409i	$0.939667\pi$
$6$	−5.21399	−	4.48182i	−0.354767	−	0.304949i
$7$	8.80596	−	5.08413i	0.475477	−	0.274517i	−0.243052	−	0.970013i	$-0.578149\pi$
$7$	8.80596	−	5.08413i	0.475477	−	0.274517i	0.718530	+	0.695496i	$0.244815\pi$
$8$	−22.6130	−	0.807318i	−0.999363	−	0.0356788i
$9$	−16.1566	+	13.5570i	−0.598393	+	0.502111i
$10$	−21.2527	+	7.45029i	−0.672071	+	0.235599i
$11$	−36.8082	−	21.2512i	−1.00892	−	0.582499i	−0.0980427	−	0.995182i	$-0.531258\pi$
$11$	−36.8082	−	21.2512i	−1.00892	−	0.582499i	−0.910874	+	0.412684i	$0.864592\pi$
$12$	3.83154	−	19.0656i	0.0921724	−	0.458648i
$13$	−12.2465	+	33.6471i	−0.261275	+	0.717848i	0.737807	+	0.675012i	$0.235862\pi$
$13$	−12.2465	+	33.6471i	−0.261275	+	0.717848i	−0.999082	+	0.0428362i	$0.986361\pi$
$14$	24.7342	+	14.6753i	0.472178	+	0.280153i
$15$	−3.36099	−	19.0611i	−0.0578537	−	0.328104i
$16$	−29.3275	−	56.8849i	−0.458243	−	0.888827i
$17$	99.7828	+	83.7277i	1.42358	+	1.19453i	0.949388	+	0.314105i	$0.101704\pi$
$17$	99.7828	+	83.7277i	1.42358	+	1.19453i	0.474193	+	0.880421i	$0.342740\pi$
$18$	−55.8100	−	21.0683i	−0.730808	−	0.275880i
$19$	80.8816	+	17.8090i	0.976606	+	0.215035i
$19$	80.8816	+	17.8090i	0.976606	+	0.215035i
$20$	−47.8080	−	42.0938i	−0.534510	−	0.470622i
$21$	−15.8881	+	18.9347i	−0.165099	+	0.196757i
$22$	1.42998	−	120.207i	0.0138578	−	1.16491i
$23$	−38.6251	+	6.81065i	−0.350169	+	0.0617443i	−0.345967	−	0.938247i	$-0.612449\pi$
$23$	−38.6251	+	6.81065i	−0.350169	+	0.0617443i	−0.00420284	+	0.999991i	$0.501338\pi$
$24$	52.3251	−	16.9564i	0.445034	−	0.144217i
$25$	57.8867	+	21.0690i	0.463094	+	0.168552i
$26$	−99.9396	+	16.3988i	−0.753837	+	0.123695i
$27$	58.4510	−	101.240i	0.416626	−	0.721618i
$28$	−1.93511	+	81.3230i	−0.0130608	+	0.548879i
$29$	−37.3435	−	44.5042i	−0.239121	−	0.284973i	0.633116	−	0.774057i	$-0.281776\pi$
$29$	−37.3435	−	44.5042i	−0.239121	−	0.284973i	−0.872237	+	0.489084i	$0.837331\pi$
$30$	42.3525	−	34.6879i	0.257749	−	0.211104i
$31$	124.321	+	215.330i	0.720278	+	1.24756i	0.960888	+	0.276937i	$0.0893193\pi$
$31$	124.321	+	215.330i	0.720278	+	1.24756i	−0.240610	+	0.970622i	$0.577347\pi$
$32$	99.6682	−	151.110i	0.550594	−	0.834773i
$33$	101.748	+	17.9408i	0.536727	+	0.0946394i
$34$	−68.2873	+	362.039i	−0.344446	+	1.82615i
$35$	27.6909	+	76.0800i	0.133732	+	0.367425i
$36$	−25.3381	−	166.814i	−0.117306	−	0.772288i
$37$			118.853i			0.528090i	0.964510	+	0.264045i	$0.0850567\pi$
$37$			118.853i			0.528090i	−0.964510	+	0.264045i	$0.914943\pi$
$38$	68.0998	+	224.130i	0.290717	+	0.956809i
$39$		−	87.0403i		−	0.357375i
$40$	37.5961	−	176.200i	0.148612	−	0.696492i
$41$	−65.9833	−	181.288i	−0.251338	−	0.690545i	−0.999631	−	0.0271767i	$-0.991348\pi$
$41$	−65.9833	−	181.288i	−0.251338	−	0.690545i	0.748293	−	0.663369i	$-0.230874\pi$
$42$	−68.7003	−	12.9582i	−0.252397	−	0.0476069i
$43$	74.8431	+	13.1969i	0.265429	+	0.0468024i	0.304779	−	0.952423i	$-0.401417\pi$
$43$	74.8431	+	13.1969i	0.265429	+	0.0468024i	−0.0393494	+	0.999226i	$0.512529\pi$
$44$	298.427	−	162.957i	1.02249	−	0.558333i
$45$	−83.9663	−	145.434i	−0.278154	−	0.481778i
$46$	−70.2909	−	85.8223i	−0.225301	−	0.275083i
$47$	29.3598	+	34.9897i	0.0911185	+	0.108591i	0.809677	−	0.586876i	$-0.199642\pi$
$47$	29.3598	+	34.9897i	0.0911185	+	0.108591i	−0.718559	+	0.695466i	$0.755198\pi$
$48$	114.286	+	105.557i	0.343661	+	0.317413i
$49$	−119.803	+	207.505i	−0.349281	+	0.604972i
$50$	28.2126	+	171.937i	0.0797972	+	0.486311i
$51$	−297.541	−	108.296i	−0.816941	−	0.297342i
$52$	−178.856	−	223.753i	−0.476977	−	0.596711i
$53$	292.316	−	51.5431i	0.757597	−	0.133585i	0.218510	−	0.975835i	$-0.429880\pi$
$53$	292.316	−	51.5431i	0.757597	−	0.133585i	0.539087	+	0.842250i	$0.318769\pi$
$54$	330.626	+	3.93312i	0.833193	+	0.00991167i
$55$	217.530	−	259.243i	0.533305	−	0.635569i
$56$	−203.234	+	107.858i	−0.484969	+	0.257378i
$57$	−199.561	+	26.5648i	−0.463727	+	0.0617298i
$58$	58.0338	−	153.732i	0.131383	−	0.348034i
$59$	−521.703	−	437.761i	−1.15119	−	0.965959i	−0.151439	−	0.988467i	$-0.548391\pi$
$59$	−521.703	−	437.761i	−1.15119	−	0.965959i	−0.999747	+	0.0225074i	$0.992835\pi$
$60$	144.202	+	56.4053i	0.310274	+	0.121365i
$61$	−96.6680	−	548.231i	−0.202903	−	1.15072i	−0.900706	−	0.434429i	$-0.856950\pi$
$61$	−96.6680	−	548.231i	−0.202903	−	1.15072i	0.697803	−	0.716289i	$-0.254161\pi$
$62$	−358.851	+	604.818i	−0.735067	+	1.23890i
$63$	−73.3490	+	201.525i	−0.146684	+	0.403011i
$64$	510.696	+	36.5118i	0.997454	+	0.0713121i
$65$	−246.906	−	142.551i	−0.471152	−	0.272020i
$66$	96.6734	+	275.771i	0.180298	+	0.514320i
$67$	−338.848	+	284.327i	−0.617863	+	0.518449i	−0.897131	−	0.441764i	$-0.854353\pi$
$67$	−338.848	+	284.327i	−0.617863	+	0.518449i	0.279268	+	0.960213i	$0.409908\pi$
$68$	−987.415	+	333.010i	−1.76091	+	0.593873i
$69$	82.5673	−	47.6702i	0.144057	−	0.0831713i
$70$	−149.273	+	173.659i	−0.254879	+	0.296517i
$71$	−85.1841	+	483.103i	−0.142387	+	0.807518i	0.827041	+	0.562142i	$0.190023\pi$
$71$	−85.1841	+	483.103i	−0.142387	+	0.807518i	−0.969428	+	0.245376i	$0.921089\pi$
$72$	376.294	−	293.521i	0.615927	−	0.480442i
$73$	279.894	−	101.873i	0.448754	−	0.163333i	−0.107750	−	0.994178i	$-0.534365\pi$
$73$	279.894	−	101.873i	0.448754	−	0.163333i	0.556504	+	0.830845i	$0.312142\pi$
$74$	−293.108	+	164.609i	−0.460448	+	0.258586i
$75$	−149.745			−0.230547
$76$	−458.420	+	478.359i	−0.691900	+	0.721994i
$77$	−432.176			−0.639623
$78$	214.654	−	120.549i	0.311599	−	0.174993i
$79$	484.949	−	176.507i	0.690646	−	0.251375i	0.0272344	−	0.999629i	$-0.491330\pi$
$79$	484.949	−	176.507i	0.690646	−	0.251375i	0.663412	+	0.748254i	$0.269108\pi$
$80$	486.603	−	151.316i	0.680049	−	0.211470i
$81$	49.5390	−	280.950i	0.0679548	−	0.385391i
$82$	355.695	−	413.803i	0.479024	−	0.557279i
$83$	−491.945	+	284.025i	−0.650578	+	0.375612i	−0.788678	−	0.614807i	$-0.789234\pi$
$83$	−491.945	+	284.025i	−0.650578	+	0.375612i	0.138099	+	0.990418i	$0.455901\pi$
$84$	−63.1917	−	187.371i	−0.0820807	−	0.243380i
$85$	−794.500	+	666.665i	−1.01383	+	0.850706i
$86$	71.1107	+	202.851i	0.0891635	+	0.254348i
$87$	122.303	+	70.6116i	0.150716	+	0.0870157i
$88$	815.188	+	510.270i	0.987492	+	0.618125i
$89$	−102.114	+	280.555i	−0.121618	+	0.334144i	−0.985530	−	0.169499i	$-0.945785\pi$
$89$	−102.114	+	280.555i	−0.121618	+	0.334144i	0.863912	+	0.503643i	$0.168007\pi$
$90$	242.369	−	408.495i	0.283866	−	0.478435i
$91$	63.2235	+	358.558i	0.0728310	+	0.413045i
$92$	114.299	−	292.209i	0.129527	−	0.331140i
$93$	−463.005	−	388.507i	−0.516251	−	0.433186i
$94$	−45.6267	+	120.865i	−0.0500642	+	0.132620i
$95$	−251.476	+	609.597i	−0.271589	+	0.658351i
$96$	−102.035	+	428.038i	−0.108478	+	0.455067i
$97$	971.884	−	1158.25i	1.01732	−	1.21239i	0.0403113	−	0.999187i	$-0.487165\pi$
$97$	971.884	−	1158.25i	1.01732	−	1.21239i	0.977007	−	0.213206i	$-0.0683905\pi$
$98$	−677.662	−	8.06147i	−0.698512	−	0.00830951i
$99$	882.798	−	155.661i	0.896208	−	0.158026i
$100$	−384.946	+	307.704i	−0.384946	+	0.307704i
$101$	22.6357	+	8.23873i	0.0223004	+	0.00811667i	0.353146	−	0.935568i	$-0.385112\pi$
$101$	22.6357	+	8.23873i	0.0223004	+	0.00811667i	−0.330846	+	0.943685i	$0.607334\pi$
$102$	−145.014	−	883.764i	−0.140770	−	0.857898i
$103$	837.724	−	1450.98i	0.801392	−	1.38805i	−0.117308	−	0.993096i	$-0.537426\pi$
$103$	837.724	−	1450.98i	0.801392	−	1.38805i	0.918700	−	0.394956i	$-0.129240\pi$
$104$	304.095	−	750.975i	0.286721	−	0.708069i
$105$	−126.506	−	150.764i	−0.117578	−	0.140124i
$106$	531.963	+	649.505i	0.487441	+	0.595146i
$107$	−374.824	−	649.214i	−0.338650	−	0.586559i	0.645529	−	0.763736i	$-0.276637\pi$
$107$	−374.824	−	649.214i	−0.338650	−	0.586559i	−0.984179	+	0.177176i	$0.943304\pi$
$108$	448.209	+	820.816i	0.399342	+	0.731324i
$109$	2209.45	+	389.586i	1.94153	+	0.342344i	0.999985	+	0.00545945i	$0.00173781\pi$
$109$	2209.45	+	389.586i	1.94153	+	0.342344i	0.941546	+	0.336885i	$0.109373\pi$
$110$	940.603	+	177.415i	0.815300	+	0.153781i
$111$	−98.8145	−	271.491i	−0.0844960	−	0.232151i
$112$	−547.467	−	351.822i	−0.461882	−	0.296822i
$113$			911.973i			0.759215i	0.925148	+	0.379607i	$0.123941\pi$
$113$			911.973i			0.759215i	−0.925148	+	0.379607i	$0.876059\pi$
$114$	−341.899	−	455.353i	−0.280893	−	0.374103i
$115$		−	312.289i		−	0.253227i
$116$	459.499	−	69.7953i	0.367788	−	0.0558649i
$117$	−258.291	−	709.649i	−0.204094	−	0.560744i
$118$	357.032	−	1892.88i	0.278538	−	1.47673i
$119$	1304.37	+	229.995i	1.00480	+	0.177173i
$120$	60.6138	+	433.743i	0.0461105	+	0.329960i
$121$	237.729	+	411.759i	0.178609	+	0.309360i
$122$	1218.13	−	997.684i	0.903971	−	0.740378i
$123$	301.445	+	359.249i	0.220979	+	0.263352i
$124$	−1988.57	−	47.3187i	−1.44015	−	0.0342689i
$125$	−742.890	+	1286.72i	−0.531569	+	0.920704i
$126$	−598.574	+	98.2182i	−0.423216	+	0.0694442i
$127$	−853.218	−	310.546i	−0.596148	−	0.216980i	0.0262832	−	0.999655i	$-0.491633\pi$
$127$	−853.218	−	310.546i	−0.596148	−	0.216980i	−0.622431	+	0.782674i	$0.713855\pi$
$128$	617.259	+	1310.02i	0.426239	+	0.904611i
$129$	−181.933	+	32.0796i	−0.124173	+	0.0218950i
$130$	9.59215	−	806.334i	0.00647144	−	0.544001i
$131$	−1041.85	+	1241.62i	−0.694859	+	0.828100i	−0.991934	−	0.126754i	$-0.959544\pi$
$131$	−1041.85	+	1241.62i	−0.694859	+	0.828100i	0.297076	+	0.954854i	$0.403989\pi$
$132$	−546.200	+	620.347i	−0.360156	+	0.409047i
$133$	802.784	−	254.387i	0.523385	−	0.165851i
$134$	−1170.49	−	441.859i	−0.754587	−	0.284857i
$135$	713.041	+	598.313i	0.454584	+	0.381441i
$136$	−2188.79	−	1973.89i	−1.38006	−	1.24456i
$137$	374.504	+	2123.92i	0.233548	+	1.32451i	0.845651	+	0.533736i	$0.179212\pi$
$137$	374.504	+	2123.92i	0.233548	+	1.32451i	−0.612104	+	0.790778i	$0.709676\pi$
$138$	231.915	+	137.600i	0.143057	+	0.0848790i
$139$	−445.840	+	1224.94i	−0.272055	+	0.747466i	0.726147	+	0.687539i	$0.241309\pi$
$139$	−445.840	+	1224.94i	−0.272055	+	0.747466i	−0.998203	+	0.0599269i	$0.980913\pi$
$140$	−635.005	−	127.614i	−0.383341	−	0.0770384i
$141$	−96.1557	−	55.5155i	−0.0574310	−	0.0331578i
$142$	−1309.38	+	459.011i	−0.773806	+	0.271263i
$143$	1165.82	−	978.235i	0.681751	−	0.572057i
$144$	1245.02	+	521.474i	0.720499	+	0.301779i
$145$	400.605	−	231.290i	0.229438	−	0.132466i
$146$	638.879	+	549.165i	0.362151	+	0.311296i
$147$	101.141	−	573.600i	0.0567482	−	0.321835i
$148$	−811.896	−	494.866i	−0.450928	−	0.274850i
$149$	484.435	−	176.320i	0.266352	−	0.0969442i	−0.205392	−	0.978680i	$-0.565847\pi$
$149$	484.435	−	176.320i	0.266352	−	0.0969442i	0.471744	+	0.881736i	$0.343625\pi$
$150$	−207.393	−	369.292i	−0.112890	−	0.201017i
$151$	2835.70			1.52825			0.764125	−	0.645069i	$-0.223171\pi$
$151$	2835.70			1.52825			0.764125	+	0.645069i	$0.223171\pi$
$152$	−1814.60	−	468.012i	−0.968312	−	0.249742i
$153$	−2747.25			−1.45165
$154$	−598.553	−	1065.80i	−0.313200	−	0.557695i
$155$	−1860.36	+	677.116i	−0.964051	+	0.350886i
$156$	594.580	+	362.408i	0.305157	+	0.185999i
$157$	−554.680	+	3145.74i	−0.281963	+	1.59909i	0.433971	+	0.900927i	$0.357112\pi$
$157$	−554.680	+	3145.74i	−0.281963	+	1.59909i	−0.715935	+	0.698167i	$0.753999\pi$
$158$	1106.93	+	951.494i	0.557361	+	0.479094i
$159$	−624.870	+	360.769i	−0.311670	+	0.179942i
$160$	1047.10	+	990.463i	0.517378	+	0.489393i
$161$	−305.505	+	256.349i	−0.149548	+	0.125485i
$162$	761.472	−	266.939i	0.369302	−	0.129461i
$163$	−2298.66	−	1327.13i	−1.10457	−	0.637723i	−0.167152	−	0.985931i	$-0.553457\pi$
$163$	−2298.66	−	1327.13i	−1.10457	−	0.637723i	−0.937417	+	0.348208i	$0.886790\pi$
$164$	1513.12	+	304.086i	0.720458	+	0.144787i
$165$	−281.360	+	773.031i	−0.132751	+	0.364730i
$166$	−1381.78	−	819.838i	−0.646064	−	0.383324i
$167$	−274.172	−	1554.91i	−0.127042	−	0.720493i	−0.980074	−	0.198633i	$-0.936350\pi$
$167$	−274.172	−	1554.91i	−0.127042	−	0.720493i	0.853032	−	0.521859i	$-0.174761\pi$
$168$	374.565	−	415.344i	0.172014	−	0.190741i
$169$	700.850	+	588.083i	0.319003	+	0.267676i
$170$	−2744.45	−	1036.03i	−1.23818	−	0.467412i
$171$	−1548.21	+	808.780i	−0.692366	+	0.361690i
$172$	−401.772	+	456.312i	−0.178109	+	0.202288i
$173$	1880.13	−	2240.65i	0.826263	−	0.984702i	−0.173737	−	0.984792i	$-0.555584\pi$
$173$	1880.13	−	2240.65i	0.826263	−	0.984702i	1.00000		8.97974e-5i	$2.85834e-5\pi$
$174$	−4.75140	+	399.412i	−0.00207013	+	0.174019i
$175$	616.866	−	108.770i	0.266461	−	0.0469843i
$176$	−129.381	+	2717.08i	−0.0554117	+	1.16368i
$177$	1555.66	+	566.213i	0.660624	+	0.240447i
$178$	−833.314	+	136.736i	−0.350896	+	0.0575774i
$179$	700.782	−	1213.79i	0.292619	−	0.506832i	−0.681809	−	0.731530i	$-0.738806\pi$
$179$	700.782	−	1213.79i	0.292619	−	0.506832i	0.974428	+	0.224699i	$0.0721398\pi$
$180$	1343.08	+	31.9591i	0.556151	+	0.0132338i
$181$	235.151	+	280.242i	0.0965672	+	0.115084i	0.812164	−	0.583429i	$-0.198290\pi$
$181$	235.151	+	280.242i	0.0965672	+	0.115084i	−0.715597	+	0.698514i	$0.753845\pi$
$182$	−796.691	+	652.512i	−0.324476	+	0.265755i
$183$	676.614	+	1171.93i	0.273316	+	0.473397i
$184$	878.929	−	122.827i	0.352149	−	0.0492114i
$185$	−931.967	−	164.331i	−0.370376	−	0.0653073i
$186$	316.862	−	1679.91i	0.124911	−	0.662241i
$187$	−1893.51	−	5202.37i	−0.740465	−	2.03441i
$188$	−361.262	+	54.8737i	−0.140148	+	0.0212876i
$189$		−	1188.69i		−	0.457484i
$190$	−1851.64	+	224.102i	−0.707011	+	0.0855687i
$191$			3796.23i			1.43814i	0.694936	+	0.719071i	$0.255433\pi$
$191$			3796.23i			1.43814i	−0.694936	+	0.719071i	$0.744567\pi$
$192$	−1196.92	+	341.191i	−0.449896	+	0.128247i
$193$	−1186.20	−	3259.05i	−0.442406	−	1.21550i	−0.937905	−	0.346891i	$-0.887237\pi$
$193$	−1186.20	−	3259.05i	−0.442406	−	1.21550i	0.495500	−	0.868608i	$-0.334985\pi$
$194$	4202.43	+	792.657i	1.55524	+	0.293348i
$195$	682.513	+	120.345i	0.250645	+	0.0441955i
$196$	−918.665	−	1682.37i	−0.334791	−	0.613110i
$197$	−1914.48	−	3315.97i	−0.692391	−	1.19926i	−0.971052	−	0.238867i	$-0.923224\pi$
$197$	−1914.48	−	3315.97i	−0.692391	−	1.19926i	0.278662	−	0.960389i	$-0.410109\pi$
$198$	1606.54	+	1961.52i	0.576624	+	0.704035i
$199$	1402.90	+	1671.91i	0.499744	+	0.595572i	0.955668	−	0.294447i	$-0.0951355\pi$
$199$	1402.90	+	1671.91i	0.499744	+	0.595572i	−0.455924	+	0.890019i	$0.650691\pi$
$200$	−1291.98	−	523.167i	−0.456785	−	0.184968i
$201$	537.625	−	931.194i	0.188662	−	0.326773i
$202$	11.0321	+	67.2332i	0.00384265	+	0.0234184i
$203$	−555.111	−	202.044i	−0.191927	−	0.0698556i
$204$	1978.64	−	1581.62i	0.679082	−	0.542820i
$205$	1512.77	−	266.742i	0.515397	−	0.0908783i
$206$	4738.55	+	56.3698i	1.60267	+	0.0190654i
$207$	531.719	−	633.678i	0.178536	−	0.212771i
$208$	2273.17	−	290.142i	0.757770	−	0.0967200i
$209$	−2598.65	−	2374.35i	−0.860058	−	0.785824i
$210$	196.597	−	520.786i	0.0646023	−	0.171132i
$211$	−1142.77	−	958.895i	−0.372850	−	0.312858i	0.437038	−	0.899443i	$-0.356028\pi$
$211$	−1142.77	−	958.895i	−0.372850	−	0.312858i	−0.809888	+	0.586585i	$0.800472\pi$
$212$	−865.013	+	2211.44i	−0.280233	+	0.716427i
$213$	−207.070	−	1174.35i	−0.0666113	−	0.377772i
$214$	1081.93	−	1823.51i	0.345603	−	0.582490i
$215$	−206.962	+	568.624i	−0.0656497	+	0.180371i
$216$	−1403.49	+	2242.16i	−0.442107	+	0.706294i
$217$	2189.52	+	1264.12i	0.684952	+	0.395457i
$218$	2099.26	+	5988.38i	0.652202	+	1.86048i
$219$	−554.651	+	465.408i	−0.171141	+	0.143604i
$220$	865.182	+	2565.37i	0.265139	+	0.786170i
$221$	−4039.19	+	2332.03i	−1.22944	+	0.709815i
$222$	532.678	−	619.698i	0.161041	−	0.187349i
$223$	−337.857	+	1916.08i	−0.101455	+	0.575383i	0.891121	+	0.453765i	$0.149919\pi$
$223$	−337.857	+	1916.08i	−0.101455	+	0.575383i	−0.992577	+	0.121618i	$0.961192\pi$
$224$	109.412	−	1837.40i	0.0326358	−	0.548063i
$225$	−1220.89	+	444.366i	−0.361744	+	0.131664i
$226$	−2249.05	+	1263.06i	−0.661968	+	0.371759i
$227$	1911.50			0.558902			0.279451	−	0.960160i	$-0.409848\pi$
$227$	1911.50			0.558902			0.279451	+	0.960160i	$0.409848\pi$
$228$	649.440	−	1473.82i	0.188641	−	0.428098i
$229$	3101.42			0.894969			0.447484	−	0.894292i	$-0.352320\pi$
$229$	3101.42			0.894969			0.447484	+	0.894292i	$0.352320\pi$
$230$	770.149	−	432.513i	0.220792	−	0.123996i
$231$	987.199	−	359.311i	0.281182	−	0.102342i
$232$	808.520	+	1036.52i	0.228801	+	0.293324i
$233$	662.223	−	3755.65i	0.186196	−	1.05597i	−0.738213	−	0.674567i	$-0.764330\pi$
$233$	662.223	−	3755.65i	0.186196	−	1.05597i	0.924409	−	0.381402i	$-0.124559\pi$
$234$	1392.37	−	1619.83i	0.388982	−	0.452528i
$235$	−314.960	+	181.842i	−0.0874285	+	0.0504769i
$236$	5162.59	−	1741.10i	1.42397	−	0.480238i
$237$	−961.000	+	806.375i	−0.263391	+	0.221011i
$238$	1239.32	+	3535.28i	0.337533	+	0.962850i
$239$	6030.47	+	3481.69i	1.63213	+	0.942310i	0.983435	+	0.181259i	$0.0580172\pi$
$239$	6030.47	+	3481.69i	1.63213	+	0.942310i	0.648693	+	0.761051i	$0.275316\pi$
$240$	−985.722	+	750.206i	−0.265117	+	0.201773i
$241$	459.509	−	1262.49i	0.122820	−	0.337445i	−0.863011	−	0.505184i	$-0.831424\pi$
$241$	459.509	−	1262.49i	0.122820	−	0.337445i	0.985831	+	0.167739i	$0.0536467\pi$
$242$	−686.205	+	1156.55i	−0.182276	+	0.307214i
$243$	668.518	+	3791.35i	0.176483	+	1.00089i
$244$	4147.51	+	1622.31i	1.08819	+	0.425647i
$245$	−1461.48	−	1226.32i	−0.381103	−	0.319783i
$246$	−468.462	+	1240.96i	−0.121415	+	0.321628i
$247$	−1589.74	+	2503.33i	−0.409525	+	0.644872i
$248$	−2637.42	−	4969.61i	−0.675308	−	1.27246i
$249$	887.590	−	1057.79i	0.225899	−	0.269215i
$250$	−4202.12	−	49.9885i	−1.06306	−	0.0126462i
$251$	−7197.38	+	1269.09i	−1.80994	+	0.319141i	−0.973460	−	0.228858i	$-0.926501\pi$
$251$	−7197.38	+	1269.09i	−1.80994	+	0.319141i	−0.836479	+	0.547999i	$0.815390\pi$
$252$	−1071.23	−	1340.14i	−0.267783	−	0.335003i
$253$	1566.46	+	570.143i	0.389258	+	0.141678i
$254$	−415.837	−	2534.25i	−0.102724	−	0.626036i
$255$	1260.58	−	2183.38i	0.309570	−	0.536191i
$256$	−2375.79	+	3336.59i	−0.580027	+	0.814597i
$257$	−2329.70	−	2776.43i	−0.565458	−	0.673887i	0.405234	−	0.914213i	$-0.367190\pi$
$257$	−2329.70	−	2776.43i	−0.565458	−	0.673887i	−0.970692	+	0.240326i	$0.922746\pi$
$258$	−331.085	−	404.242i	−0.0798933	−	0.0975465i
$259$	604.264	+	1046.62i	0.144970	+	0.251095i
$260$	2001.82	−	1093.10i	0.477490	−	0.260735i
$261$	1206.69	+	212.772i	0.286177	+	0.0504607i
$262$	−4504.95	−	849.717i	−1.06228	−	0.200365i
$263$	−2779.37	−	7636.26i	−0.651648	−	1.79039i	−0.611569	−	0.791191i	$-0.709461\pi$
$263$	−2779.37	−	7636.26i	−0.651648	−	1.79039i	−0.0400787	−	0.999197i	$-0.512761\pi$
$264$	−2286.34	−	487.839i	−0.533008	−	0.113729i
$265$			2363.41i			0.547861i
$266$	1739.19	+	1627.46i	0.400890	+	0.375134i
$267$		−	725.758i		−	0.166351i
$268$	−531.409	−	3498.55i	−0.121123	−	0.797417i
$269$	256.013	+	703.391i	0.0580276	+	0.159429i	0.965319	−	0.261073i	$-0.0840762\pi$
$269$	256.013	+	703.391i	0.0580276	+	0.159429i	−0.907292	+	0.420502i	$0.861854\pi$
$270$	−487.977	+	2587.11i	−0.109990	+	0.583135i
$271$	2200.45	+	387.999i	0.493240	+	0.0869715i	0.414735	−	0.909942i	$-0.363874\pi$
$271$	2200.45	+	387.999i	0.493240	+	0.0869715i	0.0785048	+	0.996914i	$0.474985\pi$
$272$	1836.46	−	8131.66i	0.409382	−	1.81270i
$273$	−442.524	−	766.474i	−0.0981054	−	0.169924i
$274$	−4719.19	+	3865.15i	−1.04050	+	0.852198i
$275$	−1682.96	−	2005.68i	−0.369042	−	0.439807i
$276$	−18.1442	+	762.508i	−0.00395707	+	0.166296i
$277$	−577.536	+	1000.32i	−0.125274	+	0.216980i	−0.921840	−	0.387571i	$-0.873314\pi$
$277$	−577.536	+	1000.32i	−0.125274	+	0.216980i	0.796566	+	0.604551i	$0.206648\pi$
$278$	−3638.34	+	597.004i	−0.784940	+	0.128798i
$279$	−4927.82	−	1793.58i	−1.05742	−	0.384870i
$280$	−564.753	−	1742.75i	−0.120537	−	0.371962i
$281$	1451.38	−	255.918i	0.308122	−	0.0543302i	−0.0174492	−	0.999848i	$-0.505555\pi$
$281$	1451.38	−	255.918i	0.308122	−	0.0543302i	0.325571	+	0.945518i	$0.394443\pi$
$282$	3.73560	−	314.021i	0.000788835	−	0.0663109i
$283$	2802.33	−	3339.68i	0.588626	−	0.701497i	−0.386715	−	0.922199i	$-0.626390\pi$
$283$	2802.33	−	3339.68i	0.588626	−	0.701497i	0.975341	+	0.220702i	$0.0708349\pi$
$284$	−2945.44	−	2593.39i	−0.615422	−	0.541863i
$285$	67.6166	−	1601.55i	0.0140536	−	0.332869i
$286$	4027.09	+	1520.23i	0.832611	+	0.314311i
$287$	−1502.74	−	1260.94i	−0.309072	−	0.259342i
$288$	438.299	+	3792.63i	0.0896772	+	0.775982i
$289$	2093.14	+	11870.8i	0.426041	+	2.41620i
$290$	1125.22	+	667.618i	0.227846	+	0.135186i
$291$	−1257.06	+	3453.76i	−0.253232	+	0.695748i
$292$	−469.485	+	2336.14i	−0.0940908	+	0.468194i
$293$	2966.85	+	1712.91i	0.591554	+	0.341534i	0.765712	−	0.643184i	$-0.222387\pi$
$293$	2966.85	+	1712.91i	0.591554	+	0.341534i	−0.174158	+	0.984718i	$0.555720\pi$
$294$	1554.66	−	544.994i	0.308399	−	0.108111i
$295$	4153.96	−	3485.58i	0.819840	−	0.687927i
$296$	95.9522	−	2687.62i	0.0188416	−	0.527753i
$297$	−4302.95	+	2484.31i	−0.840683	+	0.485368i
$298$	1105.76	+	950.484i	0.214949	+	0.184765i
$299$	243.866	−	1383.03i	0.0471676	−	0.267501i
$300$	623.490	−	1022.92i	0.119991	−	0.196861i
$301$	726.160	−	264.301i	0.139054	−	0.0506114i
$302$	3927.37	+	6993.22i	0.748327	+	1.33250i
$303$	−58.5554			−0.0111021
$304$	−1359.00	−	5123.24i	−0.256394	−	0.966572i
$305$	4432.52			0.832149
$306$	−3804.87	−	6775.09i	−0.710817	−	1.26571i
$307$	−4516.42	+	1643.84i	−0.839627	+	0.305599i	−0.725804	−	0.687902i	$-0.758532\pi$
$307$	−4516.42	+	1643.84i	−0.839627	+	0.305599i	−0.113823	+	0.993501i	$0.536310\pi$
$308$	1799.44	−	2952.23i	0.332898	−	0.546165i
$309$	−707.229	+	4010.89i	−0.130203	+	0.738420i
$310$	−4246.42	−	3650.12i	−0.778001	−	0.668751i
$311$	6713.39	−	3875.98i	1.22406	−	0.706710i	0.258277	−	0.966071i	$-0.416845\pi$
$311$	6713.39	−	3875.98i	1.22406	−	0.706710i	0.965780	+	0.259361i	$0.0835121\pi$
$312$	−70.2692	+	1968.24i	−0.0127507	+	0.357147i
$313$	−2987.32	+	2506.66i	−0.539468	+	0.452667i	−0.871356	−	0.490651i	$-0.836759\pi$
$313$	−2987.32	+	2506.66i	−0.539468	+	0.452667i	0.331888	+	0.943319i	$0.392314\pi$
$314$	−8526.06	+	2988.86i	−1.53234	+	0.537170i
$315$	−1478.81	−	853.790i	−0.264512	−	0.152716i
$316$	−813.439	+	4047.65i	−0.144809	+	0.720564i
$317$	−1892.28	+	5198.99i	−0.335271	+	0.921149i	0.651445	+	0.758696i	$0.274163\pi$
$317$	−1892.28	+	5198.99i	−0.335271	+	0.921149i	−0.986716	+	0.162454i	$0.948059\pi$
$318$	−1755.14	−	1041.36i	−0.309507	−	0.183637i
$319$	428.777	+	2431.72i	0.0752568	+	0.426802i
$320$	−992.410	+	3954.06i	−0.173367	+	0.690746i
$321$	1395.95	+	1171.34i	0.242724	+	0.203669i
$322$	−1055.31	−	398.381i	−0.182640	−	0.0689468i
$323$	6579.49	+	8549.06i	1.13341	+	1.47270i
$324$	1712.93	+	1508.19i	0.293712	+	0.258606i
$325$	−1417.82	+	1689.70i	−0.241990	+	0.288392i
$326$	89.3016	−	7506.86i	0.0151716	−	1.27536i
$327$	−5370.85	+	947.025i	−0.908283	+	0.160155i
$328$	1345.72	+	4152.73i	0.226540	+	0.699073i
$329$	436.433	+	158.849i	0.0731348	+	0.0266189i
$330$	−2296.08	+	376.756i	−0.383015	+	0.0628478i
$331$	2827.54	−	4897.44i	0.469534	−	0.813256i	−0.529859	−	0.848085i	$-0.677755\pi$
$331$	2827.54	−	4897.44i	0.469534	−	0.813256i	0.999393	+	0.0348290i	$0.0110887\pi$
$332$	108.105	−	4543.11i	0.0178706	−	0.751011i
$333$	−1611.29	−	1920.26i	−0.265160	−	0.316005i
$334$	3454.89	−	2829.65i	0.565998	−	0.463568i
$335$	−1761.00	−	3050.14i	−0.287205	−	0.497454i
$336$	1543.06	+	348.486i	0.250538	+	0.0565818i
$337$	−1453.68	−	256.323i	−0.234976	−	0.0414327i	0.0549199	−	0.998491i	$-0.482510\pi$
$337$	−1453.68	−	256.323i	−0.234976	−	0.0414327i	−0.289896	+	0.957058i	$0.593621\pi$
$338$	−479.634	+	2542.87i	−0.0771853	+	0.409213i
$339$	−758.216	−	2083.18i	−0.121477	−	0.333755i
$340$	−1246.00	−	8203.08i	−0.198747	−	1.30845i
$341$		−	10567.9i		−	1.67824i
$342$	−4138.80	−	2697.96i	−0.654387	−	0.426575i
$343$			5924.09i			0.932568i
$344$	−1681.77	−	358.843i	−0.263591	−	0.0562428i
$345$	259.638	+	713.348i	0.0405172	+	0.111320i
$346$	8129.69	+	1533.41i	1.26316	+	0.238256i
$347$	7809.36	+	1377.00i	1.20815	+	0.213030i	0.741219	−	0.671264i	$-0.234248\pi$
$347$	7809.36	+	1377.00i	1.20815	+	0.213030i	0.466932	+	0.884293i	$0.345359\pi$
$348$	−991.585	+	541.458i	−0.152743	+	0.0834057i
$349$	936.146	+	1621.45i	0.143584	+	0.248694i	0.928844	−	0.370472i	$-0.120804\pi$
$349$	936.146	+	1621.45i	0.143584	+	0.248694i	−0.785260	+	0.619166i	$0.787471\pi$
$350$	1122.59	+	1370.63i	0.171442	+	0.209324i
$351$	2690.61	+	3206.55i	0.409158	+	0.487615i
$352$	−6879.88	+	3444.02i	−1.04176	+	0.521496i
$353$	1768.57	−	3063.25i	0.266661	−	0.461871i	−0.701336	−	0.712830i	$-0.747413\pi$
$353$	1768.57	−	3063.25i	0.266661	−	0.461871i	0.967997	+	0.250960i	$0.0807462\pi$
$354$	758.189	+	4620.66i	0.113834	+	0.693744i
$355$	−3670.40	−	1335.91i	−0.548745	−	0.199727i
$356$	−1491.33	−	1865.69i	−0.222023	−	0.277757i
$357$	−3170.72	+	559.084i	−0.470063	+	0.0828847i
$358$	3963.94	+	47.1550i	0.585197	+	0.00696151i
$359$	−4546.22	+	5417.98i	−0.668358	+	0.796518i	−0.988559	−	0.150831i	$-0.951805\pi$
$359$	−4546.22	+	5417.98i	−0.668358	+	0.796518i	0.320202	+	0.947349i	$0.396249\pi$
$360$	1781.32	+	3356.48i	0.260788	+	0.491395i
$361$	6224.68	+	2880.84i	0.907520	+	0.420008i
$362$	−365.438	+	968.045i	−0.0530579	+	0.140551i
$363$	−885.370	−	742.914i	−0.128016	−	0.107418i
$364$	−2712.58	−	1061.04i	−0.390599	−	0.152784i
$365$	411.828	+	2335.59i	0.0590577	+	0.334933i
$366$	−1953.05	+	3291.72i	−0.278928	+	0.470112i
$367$	−1409.31	+	3872.05i	−0.200451	+	0.550734i	−0.998666	−	0.0516385i	$-0.983556\pi$
$367$	−1409.31	+	3872.05i	−0.200451	+	0.550734i	0.798215	+	0.602373i	$0.205778\pi$
$368$	1520.20	+	1997.45i	0.215343	+	0.282946i
$369$	3523.78	+	2034.46i	0.497129	+	0.287018i
$370$	−885.489	−	2525.95i	−0.124417	−	0.354914i
$371$	2312.07	−	1940.06i	0.323549	−	0.271490i
$372$	4581.73	−	1545.21i	0.638580	−	0.215364i
$373$	8093.20	−	4672.61i	1.12346	−	0.648629i	0.181177	−	0.983450i	$-0.442009\pi$
$373$	8093.20	−	4672.61i	1.12346	−	0.648629i	0.942282	+	0.334821i	$0.108676\pi$
$374$	10207.3	−	11874.8i	1.41125	−	1.64180i
$375$	627.167	−	3556.84i	0.0863647	−	0.489799i
$376$	−635.666	−	814.924i	−0.0871861	−	0.111773i
$377$	1954.77	−	711.477i	0.267044	−	0.0971961i
$378$	2931.47	−	1646.31i	0.398885	−	0.224013i
$379$	11510.7			1.56007			0.780036	−	0.625735i	$-0.215201\pi$
$379$	11510.7			1.56007			0.780036	+	0.625735i	$0.215201\pi$
$380$	−3117.14	−	4256.02i	−0.420805	−	0.574551i
$381$	2207.16			0.296787
$382$	−9362.02	+	5257.68i	−1.25393	+	0.704206i
$383$	6848.24	−	2492.55i	0.913652	−	0.332542i	0.157942	−	0.987448i	$-0.449514\pi$
$383$	6848.24	−	2492.55i	0.913652	−	0.332542i	0.755710	+	0.654906i	$0.227292\pi$
$384$	−2499.13	−	2479.22i	−0.332117	−	0.329472i
$385$	597.543	−	3388.83i	0.0791003	−	0.448600i
$386$	6394.41	−	7439.03i	0.843179	−	0.980924i
$387$	−1388.12	+	801.432i	−0.182331	+	0.105269i
$388$	3865.47	+	11461.6i	0.505772	+	1.49968i
$389$	−2445.84	+	2052.30i	−0.318789	+	0.267496i	−0.788113	−	0.615530i	$-0.788942\pi$
$389$	−2445.84	+	2052.30i	−0.318789	+	0.267496i	0.469324	+	0.883026i	$0.344497\pi$
$390$	648.476	+	1849.85i	0.0841970	+	0.240181i
$391$	−4424.36	−	2554.41i	−0.572250	−	0.330388i
$392$	2876.64	−	4595.60i	0.370643	−	0.592125i
$393$	1347.55	−	3702.38i	0.172965	−	0.475217i
$394$	5526.15	−	9313.92i	0.706607	−	1.19094i
$395$	713.542	+	4046.70i	0.0908916	+	0.515472i
$396$	−2612.36	+	6678.60i	−0.331505	+	0.847505i
$397$	−4838.54	−	4060.02i	−0.611686	−	0.513265i	0.283492	−	0.958975i	$-0.408507\pi$
$397$	−4838.54	−	4060.02i	−0.611686	−	0.513265i	−0.895178	+	0.445709i	$0.852952\pi$
$398$	−2180.18	+	5775.31i	−0.274580	+	0.727362i
$399$	−1622.27	+	1248.52i	−0.203546	+	0.156652i
$400$	−499.163	−	3910.78i	−0.0623954	−	0.488848i
$401$	−1636.88	+	1950.75i	−0.203845	+	0.242933i	−0.858275	−	0.513189i	$-0.828464\pi$
$401$	−1636.88	+	1950.75i	−0.203845	+	0.242933i	0.654431	+	0.756122i	$0.272908\pi$
$402$	3041.05	+	36.1764i	0.377298	+	0.00448834i
$403$	−8767.71	+	1545.98i	−1.08375	+	0.191094i
$404$	−150.527	+	120.323i	−0.0185372	+	0.0148176i
$405$	2134.53	+	776.904i	0.261890	+	0.0953202i
$406$	−270.547	−	1648.81i	−0.0330715	−	0.201549i
$407$	2525.77	−	4374.77i	0.307612	−	0.532799i
$408$	6640.86	+	2689.11i	0.805812	+	0.326300i
$409$	−7750.81	−	9237.05i	−0.937048	−	1.11673i	−0.992978	−	0.118296i	$-0.962257\pi$
$409$	−7750.81	−	9237.05i	−0.937048	−	1.11673i	0.0559300	−	0.998435i	$-0.482188\pi$
$410$	2752.97	+	3361.26i	0.331609	+	0.404881i
$411$	−2621.29	−	4540.20i	−0.314595	−	0.544895i
$412$	6423.76	+	11764.0i	0.768145	+	1.40672i
$413$	−6819.73	−	1202.50i	−0.812535	−	0.143272i
$414$	2299.16	+	433.664i	0.272940	+	0.0514816i
$415$	−1546.95	−	4250.21i	−0.182980	−	0.502734i
$416$	3863.82	+	5204.12i	0.455384	+	0.613349i
$417$		−	3168.74i		−	0.372120i
$418$	2256.41	−	9697.04i	0.264031	−	1.13468i
$419$			3268.39i			0.381078i	0.981680	+	0.190539i	$0.0610235\pi$
$419$			3268.39i			0.381078i	−0.981680	+	0.190539i	$0.938977\pi$
$420$	1556.61	−	236.441i	0.180845	−	0.0274693i
$421$	−2380.85	−	6541.32i	−0.275618	−	0.757255i	−0.997846	−	0.0655999i	$-0.979104\pi$
$421$	−2380.85	−	6541.32i	−0.275618	−	0.757255i	0.722228	−	0.691655i	$-0.243118\pi$
$422$	782.064	−	4146.27i	0.0902139	−	0.478287i
$423$	−948.710	−	167.283i	−0.109049	−	0.0192283i
$424$	−6651.75	+	929.554i	−0.761881	+	0.106470i
$425$	4012.03	+	6949.05i	0.457911	+	0.793125i
$426$	2609.33	−	2137.11i	0.296766	−	0.243060i
$427$	−3638.53	−	4336.23i	−0.412367	−	0.491440i
$428$	5995.48	+	142.665i	0.677109	+	0.0161121i
$429$	−1849.71	+	3203.80i	−0.208170	+	0.360561i
$430$	−1688.94	+	277.133i	−0.189414	+	0.0310803i
$431$	−6510.40	−	2369.59i	−0.727598	−	0.264824i	−0.0484504	−	0.998826i	$-0.515428\pi$
$431$	−6510.40	−	2369.59i	−0.727598	−	0.264824i	−0.679148	+	0.734001i	$0.737651\pi$
$432$	−7473.26	−	355.860i	−0.832309	−	0.0396327i
$433$	−1528.81	+	269.570i	−0.169676	+	0.0299185i	−0.257841	−	0.966187i	$-0.583011\pi$
$433$	−1528.81	+	269.570i	−0.169676	+	0.0299185i	0.0881645	+	0.996106i	$0.471900\pi$
$434$	−85.0618	+	7150.45i	−0.00940806	+	0.790859i
$435$	−722.790	+	861.388i	−0.0796670	+	0.0949435i
$436$	−11860.7	+	13470.8i	−1.30281	+	1.47967i
$437$	−3245.35	−	137.017i	−0.355255	−	0.0149987i
$438$	−1915.94	−	723.268i	−0.209012	−	0.0789020i
$439$	5027.39	+	4218.48i	0.546570	+	0.458626i	0.873777	−	0.486326i	$-0.161663\pi$
$439$	5027.39	+	4218.48i	0.546570	+	0.458626i	−0.327208	+	0.944952i	$0.606108\pi$
$440$	−5128.31	+	5686.64i	−0.555642	+	0.616136i
$441$	−877.537	−	4976.76i	−0.0947562	−	0.537389i
$442$	−11345.3	−	6731.40i	−1.22090	−	0.724389i
$443$	−2907.59	+	7988.54i	−0.311837	+	0.856765i	0.680449	+	0.732795i	$0.261785\pi$
$443$	−2907.59	+	7988.54i	−0.311837	+	0.856765i	−0.992286	+	0.123970i	$0.960437\pi$
$444$	2266.01	+	455.390i	0.242207	+	0.0486753i
$445$	−2058.74	−	1188.62i	−0.219312	−	0.126620i
$446$	−5193.25	+	1820.53i	−0.551362	+	0.193283i
$447$	−959.980	+	805.519i	−0.101578	+	0.0852343i
$448$	4682.81	−	2274.92i	0.493843	−	0.239911i
$449$	−3012.30	+	1739.15i	−0.316613	+	0.182797i	−0.649882	−	0.760035i	$-0.725182\pi$
$449$	−3012.30	+	1739.15i	−0.316613	+	0.182797i	0.333269	+	0.942832i	$0.391848\pi$
$450$	−2786.77	−	2395.44i	−0.291932	−	0.250938i
$451$	−1423.86	+	8075.09i	−0.148663	+	0.843107i
$452$	−6229.77	−	3797.17i	−0.648283	−	0.395141i
$453$	−6477.45	+	2357.60i	−0.671826	+	0.244525i
$454$	2647.38	+	4714.02i	0.273674	+	0.487313i
$455$	−2898.99			−0.298696
$456$	4534.11	−	439.602i	0.465635	−	0.0451453i
$457$	−2041.07			−0.208922			−0.104461	−	0.994529i	$-0.533312\pi$
$457$	−2041.07			−0.208922			−0.104461	+	0.994529i	$0.533312\pi$
$458$	4295.40	+	7648.54i	0.438233	+	0.780334i
$459$	14309.0	−	5208.05i	1.45509	−	0.529610i
$460$	2133.28	+	1300.27i	0.216227	+	0.131795i
$461$	1732.51	−	9825.54i	0.175035	−	0.992670i	−0.763069	−	0.646316i	$-0.776309\pi$
$461$	1732.51	−	9825.54i	0.175035	−	0.992670i	0.938104	−	0.346354i	$-0.112580\pi$
$462$	2253.36	+	1936.93i	0.226917	+	0.195053i
$463$	−16562.7	+	9562.48i	−1.66249	+	0.959841i	−0.690974	+	0.722880i	$0.742818\pi$
$463$	−16562.7	+	9562.48i	−1.66249	+	0.959841i	−0.971519	+	0.236961i	$0.923849\pi$
$464$	−1436.43	+	3429.48i	−0.143717	+	0.343124i
$465$	3686.59	−	3093.41i	0.367659	−	0.308502i
$466$	10179.1	−	3568.36i	1.01189	−	0.354723i
$467$	−2083.97	−	1203.18i	−0.206499	−	0.119222i	0.393185	−	0.919460i	$-0.371373\pi$
$467$	−2083.97	−	1203.18i	−0.206499	−	0.119222i	−0.599683	+	0.800238i	$0.704707\pi$
$468$	5923.12	+	1190.34i	0.585035	+	0.117572i
$469$	−1538.33	+	4226.52i	−0.151457	+	0.416125i
$470$	−884.660	−	524.887i	−0.0868219	−	0.0515133i
$471$	−1348.34	−	7646.84i	−0.131908	−	0.748085i
$472$	11443.9	+	10320.3i	1.11599	+	1.00642i
$473$	−2474.39	−	2076.26i	−0.240534	−	0.201832i
$474$	−3319.59	−	1253.15i	−0.321675	−	0.121433i
$475$	4306.75	+	2735.00i	0.416016	+	0.264190i
$476$	−7002.08	+	7952.61i	−0.674243	+	0.765772i
$477$	−4024.06	+	4795.69i	−0.386266	+	0.460334i
$478$	−234.280	+	19694.0i	−0.0224178	+	1.88449i
$479$	−2131.97	+	375.924i	−0.203366	+	0.0358589i	−0.274403	−	0.961615i	$-0.588480\pi$
$479$	−2131.97	+	375.924i	−0.203366	+	0.0358589i	0.0710370	+	0.997474i	$0.477369\pi$
$480$	−3215.31	−	1391.91i	−0.305747	−	0.132358i
$481$	−3999.06	−	1455.54i	−0.379088	−	0.137977i
$482$	3749.89	−	615.307i	0.354363	−	0.0581462i
$483$	484.723	−	839.565i	0.0456639	−	0.0790922i
$484$	−3802.59	−	90.4840i	−0.357117	−	0.00849774i
$485$	7738.44	+	9222.31i	0.724504	+	0.863430i
$486$	−8424.12	+	6899.59i	−0.786267	+	0.643975i
$487$	−5812.55	−	10067.6i	−0.540846	−	0.936773i	−0.998856	−	0.0478255i	$-0.984771\pi$
$487$	−5812.55	−	10067.6i	−0.540846	−	0.936773i	0.458010	−	0.888947i	$-0.348562\pi$
$488$	1743.36	+	12475.2i	0.161717	+	1.15723i
$489$	6354.10	+	1120.40i	0.587612	+	0.103612i
$490$	1000.17	−	5302.63i	0.0922108	−	0.488874i
$491$	−5079.84	−	13956.7i	−0.466904	−	1.28281i	−0.920200	−	0.391448i	$-0.871974\pi$
$491$	−5079.84	−	13956.7i	−0.466904	−	1.28281i	0.453296	−	0.891360i	$-0.350248\pi$
$492$	−3709.18	+	563.403i	−0.339884	+	0.0516264i
$493$		−	7567.44i		−	0.691319i
$494$	−8375.32	−	453.462i	−0.762801	−	0.0413001i
$495$			7137.54i			0.648098i
$496$	8602.99	−	13387.0i	0.778802	−	1.21189i
$497$	1706.03	+	4687.28i	0.153976	+	0.423044i
$498$	3837.95	+	723.908i	0.345346	+	0.0651387i
$499$	8574.52	+	1511.92i	0.769235	+	0.135637i	0.544475	−	0.838777i	$-0.316729\pi$
$499$	8574.52	+	1511.92i	0.769235	+	0.135637i	0.224760	+	0.974414i	$0.427840\pi$
$500$	−5696.56	−	10432.2i	−0.509516	−	0.933089i
$501$	1919.03	+	3323.86i	0.171130	+	0.296405i
$502$	−13098.0	−	15992.1i	−1.16452	−	1.42184i
$503$	−12969.2	−	15456.1i	−1.14964	−	1.37009i	−0.917659	−	0.397369i	$-0.869923\pi$
$503$	−12969.2	−	15456.1i	−1.14964	−	1.37009i	−0.231983	−	0.972720i	$-0.574521\pi$
$504$	1821.34	−	4497.86i	0.160970	−	0.397521i
$505$	−95.8996	+	166.103i	−0.00845045	+	0.0146366i
$506$	763.452	+	4652.73i	0.0670743	+	0.408773i
$507$	−2089.85	−	760.644i	−0.183064	−	0.0666300i
$508$	5673.89	−	4535.39i	0.495548	−	0.396113i
$509$	10267.4	−	1810.42i	0.894094	−	0.157653i	0.292321	−	0.956320i	$-0.405572\pi$
$509$	10267.4	−	1810.42i	0.894094	−	0.157653i	0.601773	+	0.798667i	$0.294461\pi$
$510$	7130.39	+	84.8231i	0.619096	+	0.00736477i
$511$	1946.80	−	2320.10i	0.168535	−	0.200852i
$512$	−11518.9	−	1237.94i	−0.994275	−	0.106855i
$513$	6530.60	−	7147.52i	0.562053	−	0.615147i
$514$	3620.48	−	9590.65i	0.310686	−	0.823007i
$515$	10219.4	+	8575.06i	0.874405	+	0.733713i
$516$	538.371	−	1376.37i	0.0459311	−	0.117425i
$517$	−337.109	−	1911.84i	−0.0286770	−	0.162635i
$518$	−1744.21	+	2939.74i	−0.147946	+	0.249352i
$519$	−2431.82	+	6681.36i	−0.205674	+	0.565085i
$520$	5468.20	+	3422.84i	0.461147	+	0.288657i
$521$	−17277.9	−	9975.42i	−1.45290	−	0.838831i	−0.454254	−	0.890872i	$-0.650094\pi$
$521$	−17277.9	−	9975.42i	−1.45290	−	0.838831i	−0.998645	+	0.0520411i	$0.983427\pi$
$522$	1146.51	+	3270.54i	0.0961329	+	0.274230i
$523$	10066.5	−	8446.79i	0.841639	−	0.706219i	−0.116293	−	0.993215i	$-0.537101\pi$
$523$	10066.5	−	8446.79i	0.841639	−	0.706219i	0.957932	+	0.286996i	$0.0926567\pi$
$524$	−4143.73	−	12286.7i	−0.345457	−	1.02432i
$525$	−1318.65	+	761.322i	−0.109620	+	0.0632891i
$526$	14982.7	−	17430.4i	1.24197	−	1.44487i
$527$	−5623.99	+	31895.2i	−0.464867	+	2.63639i
$528$	−1963.44	−	6314.07i	−0.161833	−	0.520425i
$529$	−9987.72	+	3635.23i	−0.820886	+	0.298778i
$530$	−5828.50	+	3273.27i	−0.477686	+	0.268267i
$531$	14363.7			1.17388
$532$	−1604.79	+	6543.07i	−0.130783	+	0.533230i
$533$	6907.87			0.561375
$534$	1789.82	−	1005.16i	0.145043	−	0.0814558i
$535$	5608.95	−	2041.49i	0.453264	−	0.164974i
$536$	7891.91	−	6155.93i	0.635968	−	0.496074i
$537$	−591.618	+	3355.23i	−0.0475423	+	0.269626i
$538$	−1380.09	+	1605.54i	−0.110594	+	0.128662i
$539$	8819.49	−	5091.93i	0.704791	−	0.406911i
$540$	−7056.00	+	2379.67i	−0.562300	+	0.189638i
$541$	8538.01	−	7164.24i	0.678517	−	0.569343i	−0.237056	−	0.971496i	$-0.576182\pi$
$541$	8538.01	−	7164.24i	0.678517	−	0.569343i	0.915572	+	0.402153i	$0.131738\pi$
$542$	2090.72	+	5963.99i	0.165690	+	0.472648i
$543$	−770.139	−	444.640i	−0.0608653	−	0.0351406i
$544$	22597.3	−	6733.19i	1.78097	−	0.530668i
$545$	−6109.74	+	16786.4i	−0.480207	+	1.31936i
$546$	1277.35	−	2152.87i	0.100120	−	0.168745i
$547$	919.596	+	5215.29i	0.0718813	+	0.407659i	0.999424	+	0.0339416i	$0.0108060\pi$
$547$	919.596	+	5215.29i	0.0718813	+	0.407659i	−0.927542	+	0.373718i	$0.878083\pi$
$548$	−16068.0	−	6285.04i	−1.25254	−	0.489934i
$549$	8994.20	+	7547.03i	0.699204	+	0.586702i
$550$	2615.41	−	6928.23i	0.202767	−	0.537129i
$551$	−2227.83	−	4264.63i	−0.172248	−	0.329726i
$552$	−1905.58	+	1011.31i	−0.146933	+	0.0779786i
$553$	3373.06	−	4019.86i	0.259380	−	0.309117i
$554$	−3266.81	−	38.8619i	−0.250529	−	0.00298030i
$555$	2265.47	−	399.464i	0.173269	−	0.0305519i
$556$	−6511.31	−	8145.82i	−0.496657	−	0.621330i
$557$	22047.8	+	8024.76i	1.67719	+	0.610449i	0.992921	−	0.118777i	$-0.0378975\pi$
$557$	22047.8	+	8024.76i	1.67719	+	0.610449i	0.684273	+	0.729226i	$0.260120\pi$
$558$	−2401.70	−	14636.8i	−0.182208	−	1.11044i
$559$	−1360.61	+	2356.64i	−0.102947	+	0.178310i
$560$	3515.70	−	3806.43i	0.265296	−	0.287234i
$561$	8650.51	+	10309.3i	0.651025	+	0.775861i
$562$	2641.26	+	3224.87i	0.198247	+	0.242052i
$563$	3034.45	+	5255.82i	0.227152	+	0.393440i	0.956963	−	0.290210i	$-0.0937251\pi$
$563$	3034.45	+	5255.82i	0.227152	+	0.393440i	−0.729811	+	0.683649i	$0.760392\pi$
$564$	779.593	−	425.699i	0.0582035	−	0.0317822i
$565$	−7151.09	−	1260.93i	−0.532475	−	0.0938898i
$566$	12117.3	+	2285.55i	0.899872	+	0.169733i
$567$	−992.145	−	2725.90i	−0.0734853	−	0.201899i
$568$	2316.29	−	10855.6i	0.171108	−	0.801924i
$569$			14380.5i			1.05951i	0.848150	+	0.529756i	$0.177717\pi$
$569$			14380.5i			1.05951i	−0.848150	+	0.529756i	$0.822283\pi$
$570$	4043.30	−	2051.36i	0.297114	−	0.150740i
$571$		−	9515.51i		−	0.697393i	−0.937236	−	0.348697i	$-0.886624\pi$
$571$		−	9515.51i		−	0.697393i	0.937236	−	0.348697i	$-0.113376\pi$
$572$	1828.33	+	12036.8i	0.133647	+	0.879870i
$573$	−3156.19	−	8671.55i	−0.230107	−	0.632215i
$574$	1028.41	−	5452.33i	0.0747823	−	0.396474i
$575$	−2379.38	−	419.548i	−0.172568	−	0.0304285i
$576$	−8746.11	+	6333.61i	−0.632676	+	0.458160i
$577$	−7326.86	−	12690.5i	−0.528633	−	0.915619i	−0.999443	−	0.0333845i	$-0.989371\pi$
$577$	−7326.86	−	12690.5i	−0.528633	−	0.915619i	0.470809	−	0.882235i	$-0.343962\pi$
$578$	−26376.1	+	21602.8i	−1.89810	+	1.55460i
$579$	5419.15	+	6458.29i	0.388968	+	0.463554i
$580$	−88.0331	+	3699.59i	−0.00630237	+	0.264857i
$581$	−2888.03	+	5002.22i	−0.206224	+	0.357190i
$582$	−10258.4	+	1683.28i	−0.730629	+	0.119887i
$583$	−11855.0	−	4314.85i	−0.842166	−	0.306523i
$584$	−6411.48	+	2077.69i	−0.454296	+	0.147218i
$585$	5921.72	−	1044.16i	0.418518	−	0.0737960i
$586$	−115.260	+	9689.00i	−0.00812520	+	0.683019i
$587$	3511.11	−	4184.37i	0.246880	−	0.294221i	−0.628346	−	0.777934i	$-0.716268\pi$
$587$	3511.11	−	4184.37i	0.246880	−	0.294221i	0.875227	+	0.483713i	$0.160712\pi$
$588$	3497.19	+	3079.19i	0.245275	+	0.215959i
$589$	6220.45	+	19630.2i	0.435160	+	1.37326i
$590$	14349.1	+	5416.78i	1.00126	+	0.377975i
$591$	7130.06	+	5982.83i	0.496263	+	0.416414i
$592$	6760.95	−	3485.67i	0.469380	−	0.241993i
$593$	−2479.29	−	14060.8i	−0.171690	−	0.973704i	−0.941895	−	0.335907i	$-0.890957\pi$
$593$	−2479.29	−	14060.8i	−0.171690	−	0.973704i	0.770205	−	0.637797i	$-0.220154\pi$
$594$	−12086.1	−	7170.97i	−0.834850	−	0.495334i
$595$	−3606.93	+	9909.97i	−0.248521	+	0.682805i
$596$	−812.575	+	4043.35i	−0.0558463	+	0.277890i
$597$	−4594.61	−	2652.70i	−0.314983	−	0.181856i
$598$	3748.49	−	1314.06i	0.256333	−	0.0898592i
$599$	12529.7	−	10513.7i	0.854677	−	0.717159i	−0.106137	−	0.994351i	$-0.533848\pi$
$599$	12529.7	−	10513.7i	0.854677	−	0.717159i	0.960815	+	0.277192i	$0.0894038\pi$
$600$	3386.18	+	120.892i	0.230400	+	0.00822564i
$601$	−8067.59	+	4657.83i	−0.547561	+	0.316134i	−0.748138	−	0.663544i	$-0.769052\pi$
$601$	−8067.59	+	4657.83i	−0.547561	+	0.316134i	0.200577	+	0.979678i	$0.435718\pi$
$602$	1657.52	+	1424.76i	0.112218	+	0.0964601i
$603$	1620.01	−	9187.52i	0.109406	−	0.620472i
$604$	−11806.9	+	19370.9i	−0.795393	+	1.30495i
$605$	−3557.43	+	1294.80i	−0.239058	+	0.0870100i
$606$	−81.0979	−	144.406i	−0.00543626	−	0.00968001i
$607$	18783.9			1.25604			0.628019	−	0.778198i	$-0.283866\pi$
$607$	18783.9			1.25604			0.628019	+	0.778198i	$0.283866\pi$
$608$	10752.4	−	10447.0i	0.717219	−	0.696848i
$609$	1435.99			0.0955491
$610$	6138.94	+	10931.2i	0.407473	+	0.725561i
$611$	−1536.86	+	559.370i	−0.101759	+	0.0370371i
$612$	11438.7	−	18766.7i	0.755523	−	1.23954i
$613$	462.213	−	2621.34i	0.0304545	−	0.172716i	−0.965787	−	0.259337i	$-0.916496\pi$
$613$	462.213	−	2621.34i	0.0304545	−	0.172716i	0.996241	+	0.0866212i	$0.0276070\pi$
$614$	−10309.1	−	8861.43i	−0.677590	−	0.582440i
$615$	−3233.78	+	1867.02i	−0.212030	+	0.122416i
$616$	9772.79	+	348.903i	0.639216	+	0.0228210i
$617$	9321.16	−	7821.39i	0.608194	−	0.510336i	−0.285873	−	0.958267i	$-0.592284\pi$
$617$	9321.16	−	7821.39i	0.608194	−	0.510336i	0.894068	+	0.447932i	$0.147839\pi$
$618$	−10870.9	+	3810.87i	−0.707593	+	0.248051i
$619$	−8687.89	−	5015.96i	−0.564129	−	0.325700i	0.190672	−	0.981654i	$-0.438933\pi$
$619$	−8687.89	−	5015.96i	−0.564129	−	0.325700i	−0.754801	+	0.655954i	$0.772267\pi$
$620$	3120.51	−	15527.6i	0.202133	−	1.00581i
$621$	−1568.17	+	4308.50i	−0.101334	+	0.278413i
$622$	18856.6	+	11188.0i	1.21556	+	0.721220i
$623$	527.169	+	2989.72i	0.0339014	+	0.192264i
$624$	−4951.28	+	2552.68i	−0.317644	+	0.163764i
$625$	−3163.77	−	2654.72i	−0.202481	−	0.169902i
$626$	−10319.1	−	3895.49i	−0.658844	−	0.248714i
$627$	7910.01	+	3263.11i	0.503820	+	0.207840i
$628$	−19179.3	−	16886.9i	−1.21869	−	1.07303i
$629$	−9951.29	+	11859.5i	−0.630817	+	0.751778i
$630$	57.4508	−	4829.42i	0.00363317	−	0.305411i
$631$	−20212.4	+	3563.99i	−1.27519	+	0.224850i	−0.769934	−	0.638123i	$-0.779711\pi$
$631$	−20212.4	+	3563.99i	−1.27519	+	0.224850i	−0.505251	+	0.862973i	$0.668600\pi$
$632$	−11108.7	+	3599.85i	−0.699175	+	0.226573i
$633$	3407.60	+	1240.26i	0.213965	+	0.0778769i
$634$	−15442.2	+	2533.86i	−0.967330	+	0.158726i
$635$	3614.79	−	6261.00i	0.225903	−	0.391276i
$636$	137.315	−	5770.67i	0.00856117	−	0.359783i
$637$	−5514.78	−	6572.26i	−0.343020	−	0.408795i
$638$	−5403.10	+	4425.29i	−0.335284	+	0.274607i
$639$	−5173.14	−	8960.15i	−0.320260	−	0.554707i
$640$	−11125.7	+	3028.86i	−0.687161	+	0.187072i
$641$	28656.9	+	5052.99i	1.76580	+	0.311359i	0.959828	−	0.280590i	$-0.0905301\pi$
$641$	28656.9	+	5052.99i	1.76580	+	0.311359i	0.805976	+	0.591949i	$0.201641\pi$
$642$	−955.332	+	5064.89i	−0.0587289	+	0.311363i
$643$	10888.9	+	29916.9i	0.667831	+	1.83485i	0.537273	+	0.843409i	$0.319455\pi$
$643$	10888.9	+	29916.9i	0.667831	+	1.83485i	0.130558	+	0.991441i	$0.458323\pi$
$644$	−479.119	−	3154.29i	−0.0293166	−	0.193007i
$645$		−	1470.95i		−	0.0897963i
$646$	−11970.7	+	28066.2i	−0.729074	+	1.70936i
$647$		−	15686.2i		−	0.953150i	−0.879134	−	0.476575i	$-0.841878\pi$
$647$		−	15686.2i		−	0.953150i	0.879134	−	0.476575i	$-0.158122\pi$
$648$	−1347.04	+	6313.13i	−0.0816618	+	0.382721i
$649$	9899.99	+	27200.0i	0.598781	+	1.64514i
$650$	−6130.68	−	1156.36i	−0.369946	−	0.0697788i
$651$	−6052.43	−	1067.21i	−0.364383	−	0.0642505i
$652$	18636.6	−	10176.6i	1.11943	−	0.611267i
$653$	4361.04	+	7553.54i	0.261348	+	0.452669i	0.966601	−	0.256288i	$-0.0824995\pi$
$653$	4361.04	+	7553.54i	0.261348	+	0.452669i	−0.705252	+	0.708957i	$0.749166\pi$
$654$	−9773.99	−	11933.6i	−0.584394	−	0.713521i
$655$	−8295.49	−	9886.18i	−0.494857	−	0.589748i
$656$	−8377.41	+	9070.17i	−0.498602	+	0.539833i
$657$	−3141.04	+	5440.44i	−0.186520	+	0.323062i
$658$	212.707	+	1296.31i	0.0126021	+	0.0768014i
$659$	−22174.2	−	8070.73i	−1.31075	−	0.477073i	−0.410265	−	0.911966i	$-0.634564\pi$
$659$	−22174.2	−	8070.73i	−1.31075	−	0.477073i	−0.900482	+	0.434893i	$0.856786\pi$
$660$	−4109.15	−	5140.65i	−0.242346	−	0.303181i
$661$	−25789.0	+	4547.30i	−1.51751	+	0.267578i	−0.869455	−	0.494013i	$-0.835530\pi$
$661$	−25789.0	+	4547.30i	−1.51751	+	0.267578i	−0.648058	+	0.761591i	$0.724419\pi$
$662$	15993.9	+	190.263i	0.939001	+	0.0111704i
$663$	7287.69	−	8685.13i	0.426893	−	0.508752i
$664$	11353.7	−	6025.50i	0.663566	−	0.352161i
$665$	884.776	+	6646.62i	0.0515942	+	0.387587i
$666$	2504.03	−	6633.18i	0.145690	−	0.385932i
$667$	1745.50	+	1464.65i	0.101328	+	0.0850246i
$668$	11763.3	+	4601.24i	0.681339	+	0.266508i
$669$	−821.281	−	4657.72i	−0.0474627	−	0.269174i
$670$	5083.13	−	8567.24i	0.293102	−	0.494002i
$671$	−8092.41	+	22233.7i	−0.465580	+	1.27917i
$672$	1277.69	+	4288.05i	0.0733450	+	0.246153i
$673$	−26839.3	−	15495.7i	−1.53727	−	0.887541i	−0.998997	−	0.0447674i	$-0.985745\pi$
$673$	−26839.3	−	15495.7i	−1.53727	−	0.887541i	−0.538268	−	0.842773i	$-0.680921\pi$
$674$	−1381.18	−	3939.98i	−0.0789336	−	0.225167i
$675$	5516.57	−	4628.95i	0.314567	−	0.263953i
$676$	−6935.36	+	2338.98i	−0.394593	+	0.133078i
$677$	21970.4	−	12684.6i	1.24726	−	0.720103i	0.276694	−	0.960958i	$-0.410761\pi$
$677$	21970.4	−	12684.6i	1.24726	−	0.720103i	0.970561	+	0.240855i	$0.0774277\pi$
$678$	4087.30	−	4755.02i	0.231522	−	0.269344i
$679$	2669.71	−	15140.7i	0.150889	−	0.855737i
$680$	18504.3	−	14433.9i	1.04354	−	0.813992i
$681$	−4366.35	+	1589.22i	−0.245696	+	0.0894260i
$682$	26061.8	−	14636.2i	1.46328	−	0.821775i
$683$	−29066.5			−1.62840			−0.814201	−	0.580583i	$-0.802825\pi$
$683$	−29066.5			−1.62840			−0.814201	+	0.580583i	$0.802825\pi$
$684$	921.400	−	13943.5i	0.0515068	−	0.779446i
$685$	−17172.1			−0.957830
$686$	−14609.6	+	8204.73i	−0.813117	+	0.456644i
$687$	−7084.44	+	2578.53i	−0.393433	+	0.143198i
$688$	−1444.26	−	4644.48i	−0.0800319	−	0.257368i
$689$	−1845.58	+	10466.8i	−0.102048	+	0.578742i
$690$	−1399.62	+	1628.27i	−0.0772214	+	0.0898367i
$691$	24449.0	−	14115.6i	1.34600	−	0.777111i	0.358316	−	0.933600i	$-0.383351\pi$
$691$	24449.0	−	14115.6i	1.34600	−	0.777111i	0.987680	+	0.156489i	$0.0500176\pi$
$692$	7477.82	+	22172.7i	0.410786	+	1.21803i
$693$	6982.49	−	5859.00i	0.382746	−	0.321162i
$694$	7419.90	+	21166.1i	0.405844	+	1.15771i
$695$	−8988.70	−	5189.63i	−0.490591	−	0.283243i
$696$	−2708.63	−	1695.48i	−0.147515	−	0.0923376i
$697$	8594.79	−	23614.0i	0.467075	−	1.28328i
$698$	−2702.19	+	4554.34i	−0.146532	+	0.246969i
$699$	1609.77	+	9129.44i	0.0871058	+	0.494002i
$700$	−1825.41	+	4666.75i	−0.0985631	+	0.251981i
$701$	8030.69	+	6738.55i	0.432689	+	0.363069i	0.832965	−	0.553325i	$-0.186641\pi$
$701$	8030.69	+	6738.55i	0.432689	+	0.363069i	−0.400276	+	0.916394i	$0.631086\pi$
$702$	−4181.36	+	11076.4i	−0.224808	+	0.595517i
$703$	−2116.65	+	9613.03i	−0.113558	+	0.515736i
$704$	−18021.9	−	12196.9i	−0.964809	−	0.652964i
$705$	568.265	−	677.232i	0.0303576	−	0.0361787i
$706$	10003.8	+	119.006i	0.533284	+	0.00634395i
$707$	241.216	−	42.5329i	0.0128315	−	0.00226254i
$708$	−10345.1	+	8269.30i	−0.549143	+	0.438954i
$709$	−9157.68	−	3333.12i	−0.485083	−	0.176556i	0.0878898	−	0.996130i	$-0.471988\pi$
$709$	−9157.68	−	3333.12i	−0.485083	−	0.176556i	−0.572973	+	0.819574i	$0.694210\pi$
$710$	−1788.86	−	10901.9i	−0.0945559	−	0.576256i
$711$	−5442.23	+	9426.22i	−0.287060	+	0.497202i
$712$	2535.60	−	6261.77i	0.133463	−	0.329592i
$713$	−6268.43	−	7470.43i	−0.329249	−	0.392384i
$714$	−5770.15	−	7045.12i	−0.302441	−	0.369268i
$715$	6058.77	+	10494.1i	0.316902	+	0.548891i
$716$	5373.67	+	9840.93i	0.280480	+	0.513649i
$717$	−16669.8	−	2939.34i	−0.868264	−	0.153098i
$718$	−19657.9	−	3707.85i	−1.02176	−	0.192724i
$719$	−4544.29	−	12485.3i	−0.235707	−	0.647600i	−0.999996	−	0.00272616i	$-0.999132\pi$
$719$	−4544.29	−	12485.3i	−0.235707	−	0.647600i	0.764289	−	0.644874i	$-0.223090\pi$
$720$	−5810.47	+	9041.63i	−0.300755	+	0.468002i
$721$		−	17036.4i		−	0.879983i
$722$	1516.49	+	19340.8i	0.0781689	+	0.996940i
$723$			3265.89i			0.167994i
$724$	−2893.46	+	439.499i	−0.148528	+	0.0225606i
$725$	−1224.03	−	3363.00i	−0.0627026	−	0.172274i
$726$	605.911	−	3212.36i	0.0309745	−	0.164218i
$727$	−173.644	−	30.6180i	−0.00885844	−	0.00156198i	0.169217	−	0.985579i	$-0.445876\pi$
$727$	−173.644	−	30.6180i	−0.00885844	−	0.00156198i	−0.178076	+	0.984017i	$0.556987\pi$
$728$	−1140.20	−	8159.12i	−0.0580477	−	0.415381i
$729$	−827.865	−	1433.90i	−0.0420599	−	0.0728499i
$730$	−5189.53	+	4250.37i	−0.263114	+	0.215497i
$731$	6363.11	+	7583.26i	0.321954	+	0.383689i
$732$	−10822.8	−	257.532i	−0.546477	−	0.0130036i
$733$	7973.12	−	13809.9i	0.401765	−	0.695878i	−0.592174	−	0.805810i	$-0.701730\pi$
$733$	7973.12	−	13809.9i	0.401765	−	0.695878i	0.993939	+	0.109932i	$0.0350634\pi$
$734$	−11500.9	+	1887.14i	−0.578345	+	0.0948988i
$735$	4357.95	+	1586.16i	0.218701	+	0.0796007i
$736$	−2820.54	+	6515.45i	−0.141259	+	0.326308i
$737$	18514.7	−	3264.64i	0.925369	−	0.163167i
$738$	−136.897	+	11507.8i	−0.00682825	+	0.573995i
$739$	−6077.32	+	7242.67i	−0.302514	+	0.360522i	−0.895790	−	0.444477i	$-0.853390\pi$
$739$	−6077.32	+	7242.67i	−0.302514	+	0.360522i	0.593276	+	0.804999i	$0.297834\pi$
$740$	5002.97	−	5682.13i	0.248531	−	0.282269i
$741$	1550.10	−	7039.97i	0.0768479	−	0.349014i
$742$	7986.61	+	3014.95i	0.395145	+	0.149168i
$743$	−96.2601	−	80.7719i	−0.00475295	−	0.00398820i	0.640408	−	0.768035i	$-0.278765\pi$
$743$	−96.2601	−	80.7719i	−0.00475295	−	0.00398820i	−0.645161	+	0.764047i	$0.723210\pi$
$744$	10156.3	+	9159.11i	0.500467	+	0.451330i
$745$	712.784	+	4042.40i	0.0350529	+	0.198795i
$746$	22732.2	+	13487.5i	1.11566	+	0.661947i
$747$	4097.64	−	11258.2i	0.200703	−	0.551426i
$748$	43421.8	+	8726.29i	2.12254	+	0.426557i
$749$	−6601.37	−	3811.30i	−0.322041	−	0.185930i
$750$	9640.28	−	3379.46i	0.469351	−	0.164534i
$751$	−17257.2	+	14480.5i	−0.838514	+	0.703596i	−0.957229	−	0.289332i	$-0.906567\pi$
$751$	−17257.2	+	14480.5i	−0.838514	+	0.703596i	0.118715	+	0.992928i	$0.462122\pi$
$752$	1129.33	−	2696.29i	0.0547641	−	0.130750i
$753$	15385.5	−	8882.84i	0.744595	−	0.429892i
$754$	4461.91	+	3835.35i	0.215508	+	0.185246i
$755$	−3920.74	+	22235.6i	−0.188994	+	1.07184i
$756$	8120.04	+	4949.32i	0.390639	+	0.238102i
$757$	−6864.93	+	2498.63i	−0.329604	+	0.119966i	−0.501521	−	0.865145i	$-0.667226\pi$
$757$	−6864.93	+	2498.63i	−0.329604	+	0.119966i	0.171917	+	0.985111i	$0.445004\pi$
$758$	15942.1	+	28387.1i	0.763909	+	1.36024i
$759$	−4052.20			−0.193789
$760$	6178.77	−	13581.8i	0.294905	−	0.648242i
$761$	−23827.1			−1.13500			−0.567499	−	0.823374i	$-0.692089\pi$
$761$	−23827.1			−1.13500			−0.567499	+	0.823374i	$0.692089\pi$
$762$	3056.86	+	5443.15i	0.145326	+	0.258772i
$763$	21437.0	−	7802.44i	1.01713	−	0.370206i
$764$	−25932.4	−	15806.3i	−1.22801	−	0.748496i
$765$	3798.45	−	21542.1i	0.179521	−	1.01811i
$766$	15631.6	+	13436.6i	0.737329	+	0.633790i
$767$	21118.4	−	12192.7i	0.994188	−	0.573995i
$768$	2652.87	−	9596.86i	0.124645	−	0.450907i
$769$	−17215.8	+	14445.8i	−0.807307	+	0.677411i	−0.949963	−	0.312361i	$-0.898880\pi$
$769$	−17215.8	+	14445.8i	−0.807307	+	0.677411i	0.142656	+	0.989772i	$0.454436\pi$
$770$	9184.92	−	3219.83i	0.429872	−	0.150694i
$771$	7629.96	+	4405.16i	0.356402	+	0.205769i
$772$	27201.8	+	5466.62i	1.26815	+	0.254855i
$773$	723.750	−	1988.49i	0.0336759	−	0.0925238i	−0.921715	−	0.387867i	$-0.873212\pi$
$773$	723.750	−	1988.49i	0.0336759	−	0.0925238i	0.955391	+	0.295344i	$0.0954341\pi$
$774$	−3898.96	−	2313.33i	−0.181066	−	0.107430i
$775$	2659.72	+	15084.0i	0.123277	+	0.699141i
$776$	−22912.3	+	25406.8i	−1.05993	+	1.17532i
$777$	−2250.45	−	1888.35i	−0.103905	−	0.0871869i
$778$	−8448.68	−	3189.38i	−0.389332	−	0.146973i
$779$	−2108.29	−	15837.9i	−0.0969671	−	0.728437i
$780$	−3663.85	+	4161.22i	−0.168189	+	0.191020i
$781$	13402.0	−	15971.9i	0.614035	−	0.731779i
$782$	171.884	−	14448.9i	0.00786005	−	0.660730i
$783$	−6688.38	+	1179.34i	−0.305266	+	0.0538266i
$784$	15317.5	+	729.383i	0.697771	+	0.0332263i
$785$	−23899.9	−	8698.86i	−1.08666	−	0.395510i
$786$	10996.9	−	1804.45i	0.499041	−	0.0818861i
$787$	−5813.93	+	10070.0i	−0.263335	+	0.456109i	−0.967126	−	0.254298i	$-0.918156\pi$
$787$	−5813.93	+	10070.0i	−0.263335	+	0.456109i	0.703791	+	0.710407i	$0.251489\pi$
$788$	30623.0	+	728.686i	1.38439	+	0.0329421i
$789$	12697.6	+	15132.4i	0.572935	+	0.682798i
$790$	−8991.48	+	7364.27i	−0.404940	+	0.331657i
$791$	4636.59	+	8030.81i	0.208417	+	0.360989i
$792$	−20088.4	+	2807.27i	−0.901275	+	0.125949i
$793$	19630.2	+	3461.34i	0.879055	+	0.155001i
$794$	3311.30	−	17555.5i	0.148002	−	0.784663i
$795$	−1964.94	−	5398.63i	−0.0876595	−	0.240842i
$796$	−17262.2	+	2622.03i	−0.768647	+	0.116753i
$797$			3355.49i			0.149131i	0.997216	+	0.0745657i	$0.0237570\pi$
$797$			3355.49i			0.149131i	−0.997216	+	0.0745657i	$0.976243\pi$
$798$	−5325.82	−	2271.56i	−0.236256	−	0.100767i
$799$			5949.59i			0.263431i
$800$	8953.21	−	6647.35i	0.395680	−	0.293774i
$801$	−2153.68	−	5917.18i	−0.0950018	−	0.261015i
$802$	−7077.86	−	1335.02i	−0.311631	−	0.0587794i
$803$	−12467.3	−	2198.32i	−0.547897	−	0.0966091i
$804$	4122.57	+	7549.76i	0.180836	+	0.331168i
$805$	−1587.72	−	2750.01i	−0.0695152	−	0.120404i
$806$	−15955.7	−	19481.2i	−0.697289	−	0.851362i
$807$	−1169.60	−	1393.87i	−0.0510184	−	0.0608014i
$808$	−505.210	−	204.577i	−0.0219966	−	0.00890715i
$809$	9527.88	−	16502.8i	0.414070	−	0.717190i	−0.581260	−	0.813718i	$-0.697440\pi$
$809$	9527.88	−	16502.8i	0.414070	−	0.717190i	0.995330	+	0.0965275i	$0.0307736\pi$
$810$	1040.32	+	6340.03i	0.0451271	+	0.275020i
$811$	7353.77	+	2676.55i	0.318404	+	0.115890i	0.496278	−	0.868164i	$-0.334700\pi$
$811$	7353.77	+	2676.55i	0.318404	+	0.115890i	−0.177874	+	0.984053i	$0.556922\pi$
$812$	3691.48	−	2950.76i	0.159539	−	0.127527i
$813$	−5348.98	+	943.169i	−0.230746	+	0.0406868i
$814$	14286.9	+	169.957i	0.615179	+	0.00731818i
$815$	13584.7	−	16189.6i	0.583866	−	0.695825i
$816$	2565.72	+	20101.6i	0.110071	+	0.862375i
$817$	5818.41	+	2400.26i	0.249156	+	0.102784i
$818$	12045.2	−	31907.7i	0.514853	−	1.36385i
$819$	−5882.45	−	4935.96i	−0.250976	−	0.210594i
$820$	−4476.55	+	11444.5i	−0.190644	+	0.487388i
$821$	333.754	+	1892.81i	0.0141877	+	0.0804624i	0.991079	−	0.133272i	$-0.0425484\pi$
$821$	333.754	+	1892.81i	0.0141877	+	0.0804624i	−0.976892	+	0.213734i	$0.931437\pi$
$822$	7566.35	−	12752.5i	0.321054	−	0.541114i
$823$	2957.23	−	8124.93i	0.125252	−	0.344128i	−0.861179	−	0.508302i	$-0.830274\pi$
$823$	2957.23	−	8124.93i	0.125252	−	0.344128i	0.986431	+	0.164174i	$0.0524958\pi$
$824$	−20114.9	+	32134.7i	−0.850406	+	1.35858i
$825$	5511.84	+	3182.26i	0.232603	+	0.134293i
$826$	−6479.63	−	18483.8i	−0.272948	−	0.778614i
$827$	−9202.08	+	7721.46i	−0.386926	+	0.324669i	−0.815414	−	0.578878i	$-0.803491\pi$
$827$	−9202.08	+	7721.46i	−0.386926	+	0.324669i	0.428488	+	0.903547i	$0.359046\pi$
$828$	2114.80	+	6270.65i	0.0887614	+	0.263189i
$829$	−1194.93	+	689.892i	−0.0500622	+	0.0289034i	−0.524822	−	0.851212i	$-0.675868\pi$
$829$	−1194.93	+	689.892i	−0.0500622	+	0.0289034i	0.474760	+	0.880115i	$0.342535\pi$
$830$	8339.12	−	9701.44i	0.348741	−	0.405713i
$831$	487.571	−	2765.15i	0.0203534	−	0.115430i
$832$	−7482.78	+	16736.3i	−0.311801	+	0.697388i
$833$	−29328.3	+	10674.6i	−1.21988	+	0.444002i
$834$	7814.55	−	4388.63i	0.324455	−	0.182213i
$835$	12571.6			0.521029
$836$	27039.3	−	7865.54i	1.11863	−	0.325401i
$837$	29066.7			1.20035
$838$	−8060.31	+	4526.65i	−0.332266	+	0.186600i
$839$	26592.9	−	9679.03i	1.09427	−	0.398280i	0.269067	−	0.963122i	$-0.413285\pi$
$839$	26592.9	−	9679.03i	1.09427	−	0.398280i	0.825200	+	0.564841i	$0.191063\pi$
$840$	2738.97	+	3511.36i	0.112504	+	0.144230i
$841$	3649.01	−	20694.6i	0.149617	−	0.848521i
$842$	12834.4	−	14931.1i	0.525300	−	0.611115i
$843$	−3102.56	+	1791.26i	−0.126759	+	0.0731843i
$844$	11308.4	−	3813.81i	0.461199	−	0.155541i
$845$	−5580.38	+	4682.50i	−0.227185	+	0.190630i
$846$	−901.397	−	2571.33i	−0.0366320	−	0.104497i
$847$	4186.86	+	2417.29i	0.169849	+	0.0980625i
$848$	−11504.9	−	15116.7i	−0.465897	−	0.612158i
$849$	−3624.62	+	9958.55i	−0.146521	+	0.402564i
$850$	−11580.7	+	19518.5i	−0.467313	+	0.787622i
$851$	−809.467	−	4590.71i	−0.0326065	−	0.184921i
$852$	8884.28	+	3475.12i	0.357242	+	0.139737i
$853$	−19769.3	−	16588.4i	−0.793540	−	0.665859i	0.153079	−	0.988214i	$-0.451081\pi$
$853$	−19769.3	−	16588.4i	−0.793540	−	0.665859i	−0.946619	+	0.322355i	$0.895526\pi$
$854$	5654.47	−	14978.7i	0.226571	−	0.600188i
$855$	−4201.30	−	13258.3i	−0.168049	−	0.530320i
$856$	7951.77	+	14983.3i	0.317507	+	0.598269i
$857$	4342.36	−	5175.02i	0.173083	−	0.206272i	−0.672528	−	0.740071i	$-0.734792\pi$
$857$	4342.36	−	5175.02i	0.173083	−	0.206272i	0.845611	+	0.533799i	$0.179236\pi$
$858$	−10462.8	−	124.466i	−0.416311	−	0.00495244i
$859$	−23284.1	+	4105.62i	−0.924848	+	0.163076i	−0.615738	−	0.787951i	$-0.711142\pi$
$859$	−23284.1	+	4105.62i	−0.924848	+	0.163076i	−0.309110	+	0.951026i	$0.600031\pi$
$860$	−3022.59	−	3781.34i	−0.119848	−	0.149933i
$861$	4480.98	+	1630.94i	0.177365	+	0.0645556i
$862$	−3173.01	−	19337.4i	−0.125375	−	0.764076i
$863$	−8228.27	+	14251.8i	−0.324558	+	0.562151i	−0.981423	−	0.191857i	$-0.938549\pi$
$863$	−8228.27	+	14251.8i	−0.324558	+	0.562151i	0.656865	+	0.754008i	$0.271882\pi$
$864$	−9472.70	−	18923.0i	−0.372995	−	0.745107i
$865$	14970.2	+	17840.7i	0.588440	+	0.701275i
$866$	−2782.16	−	3396.91i	−0.109171	−	0.133293i
$867$	−14650.7	−	25375.7i	−0.573890	−	0.994006i
$868$	−17751.8	+	9693.43i	−0.694166	+	0.379051i
$869$	−21601.1	−	3808.86i	−0.843230	−	0.148684i
$870$	−3125.35	−	589.499i	−0.121792	−	0.0229723i
$871$	−5417.07	−	14883.3i	−0.210735	−	0.578990i
$872$	−49647.8	−	10593.4i	−1.92808	−	0.411398i
$873$			31889.2i			1.23629i
$874$	−4156.84	−	8193.26i	−0.160878	−	0.317095i
$875$			15107.8i			0.583698i
$876$	−869.850	−	5726.68i	−0.0335497	−	0.220875i
$877$	13627.8	+	37442.2i	0.524720	+	1.44166i	0.865211	+	0.501409i	$0.167185\pi$
$877$	13627.8	+	37442.2i	0.524720	+	1.44166i	−0.340490	+	0.940248i	$0.610593\pi$
$878$	−3440.54	+	18240.7i	−0.132247	+	0.701133i
$879$	−8201.16	−	1446.09i	−0.314696	−	0.0554895i
$880$	−21126.6	−	4771.26i	−0.809294	−	0.182772i
$881$	6589.24	+	11412.9i	0.251983	+	0.436448i	0.964072	−	0.265642i	$-0.0855839\pi$
$881$	6589.24	+	11412.9i	0.251983	+	0.436448i	−0.712089	+	0.702090i	$0.752251\pi$
$882$	11058.0	−	9056.82i	0.422157	−	0.345758i
$883$	−5316.44	−	6335.89i	−0.202619	−	0.241472i	0.655161	−	0.755490i	$-0.272601\pi$
$883$	−5316.44	−	6335.89i	−0.202619	−	0.241472i	−0.857779	+	0.514018i	$0.828156\pi$
$884$	887.612	−	37301.9i	0.0337711	−	1.41923i
$885$	−6590.78	+	11415.6i	−0.250335	+	0.433593i
$886$	−23727.8	+	3893.42i	−0.899719	+	0.147632i
$887$	36367.2	+	13236.6i	1.37665	+	0.501061i	0.921162	−	0.389179i	$-0.127241\pi$
$887$	36367.2	+	13236.6i	1.37665	+	0.501061i	0.455492	+	0.890240i	$0.349463\pi$
$888$	2015.31	+	6219.00i	0.0761594	+	0.235018i
$889$	−9092.26	+	1603.21i	−0.343020	+	0.0604836i
$890$	79.9810	−	6723.35i	0.00301233	−	0.253222i
$891$	−7793.97	+	9288.49i	−0.293050	+	0.349244i
$892$	−11682.2	−	10285.9i	−0.438508	−	0.386095i
$893$	1751.54	+	3352.89i	0.0656361	+	0.125644i
$894$	−3316.07	−	1251.82i	−0.124056	−	0.0468312i
$895$	8548.80	+	7173.30i	0.319279	+	0.267907i
$896$	12095.9	+	8397.73i	0.450998	+	0.313112i
$897$	592.801	+	3361.94i	0.0220658	+	0.125142i
$898$	−8460.96	−	5020.07i	−0.314416	−	0.186550i
$899$	4940.51	−	13574.0i	0.183287	−	0.503578i
$900$	2047.87	−	10190.2i	0.0758472	−	0.377414i
$901$	33483.6	+	19331.8i	1.23807	+	0.714801i
$902$	−21886.3	+	7672.39i	−0.807910	+	0.283218i
$903$	−1439.00	+	1207.46i	−0.0530308	+	0.0444981i
$904$	736.253	−	20622.5i	0.0270878	−	0.758731i
$905$	−2522.60	+	1456.43i	−0.0926566	+	0.0534953i
$906$	−14785.3	−	12709.1i	−0.542172	−	0.466038i
$907$	6200.98	−	35167.5i	0.227012	−	1.28745i	−0.631788	−	0.775141i	$-0.717679\pi$
$907$	6200.98	−	35167.5i	0.227012	−	1.28745i	0.858801	−	0.512310i	$-0.171210\pi$
$908$	−7958.87	+	13057.6i	−0.290886	+	0.477238i
$909$	−477.409	+	173.763i	−0.0174199	+	0.00634031i
$910$	−4015.03	−	7149.31i	−0.146260	−	0.260437i
$911$	92.0822			0.00334887			0.00167443	−	0.999999i	$-0.499467\pi$
$911$	92.0822			0.00334887			0.00167443	+	0.999999i	$0.499467\pi$
$912$	7363.76	+	10572.9i	0.267367	+	0.383886i
$913$	24143.5			0.875173
$914$	−2826.84	−	5033.57i	−0.102301	−	0.182162i
$915$	−10125.0	+	3685.20i	−0.365817	+	0.133147i
$916$	−12913.3	+	21186.1i	−0.465796	+	0.764201i
$917$	−2861.89	+	16230.6i	−0.103062	+	0.584493i
$918$	32661.4	+	28075.0i	1.17428	+	1.00938i
$919$	−21834.2	+	12606.0i	−0.783727	+	0.452485i	−0.837749	−	0.546055i	$-0.816129\pi$
$919$	−21834.2	+	12606.0i	−0.783727	+	0.452485i	0.0540227	+	0.998540i	$0.482796\pi$
$920$	−252.117	+	7061.80i	−0.00903483	+	0.253066i
$921$	8949.96	−	7509.91i	0.320208	−	0.268686i
$922$	26630.6	−	9335.53i	0.951229	−	0.333459i
$923$	−15211.8	−	8782.54i	−0.542473	−	0.313197i
$924$	−1655.90	+	8239.70i	−0.0589556	+	0.293362i
$925$	−2504.12	+	6880.01i	−0.0890107	+	0.244555i
$926$	−46521.4	−	27602.1i	−1.65096	−	0.979549i
$927$	6136.17	+	34799.9i	0.217409	+	1.23299i
$928$	−10447.0	+	1207.32i	−0.369547	+	0.0427071i
$929$	41077.7	+	34468.3i	1.45072	+	1.21730i	0.932054	+	0.362318i	$0.118015\pi$
$929$	41077.7	+	34468.3i	1.45072	+	1.21730i	0.518664	+	0.854978i	$0.326430\pi$
$930$	12734.6	+	4807.33i	0.449016	+	0.169504i
$931$	−13385.3	+	14649.8i	−0.471200	+	0.515712i
$932$	22897.9	+	20161.0i	0.804770	+	0.708580i
$933$	−12112.6	+	14435.3i	−0.425026	+	0.506526i
$934$	80.9612	−	6805.75i	0.00283633	−	0.238427i
$935$	43411.6	−	7654.63i	1.51841	−	0.267736i
$936$	5267.83	+	16255.8i	0.183958	+	0.567669i
$937$	−16665.4	−	6065.71i	−0.581041	−	0.211482i	0.0347437	−	0.999396i	$-0.488939\pi$
$937$	−16665.4	−	6065.71i	−0.581041	−	0.211482i	−0.615784	+	0.787915i	$0.711161\pi$
$938$	−12553.7	+	2059.90i	−0.436987	+	0.0717038i
$939$	4739.77	−	8209.52i	0.164725	−	0.285312i
$940$	69.2124	−	2908.65i	0.00240155	−	0.100925i
$941$	−29254.6	−	34864.3i	−1.01347	−	1.20780i	−0.978037	−	0.208432i	$-0.933164\pi$
$941$	−29254.6	−	34864.3i	−1.01347	−	1.20780i	−0.0354310	−	0.999372i	$-0.511280\pi$
$942$	16990.8	−	13915.9i	0.587674	−	0.481321i
$943$	3783.30	+	6552.87i	0.130648	+	0.226289i
$944$	−9601.74	+	42515.5i	−0.331049	+	1.46585i
$945$	9320.91	+	1643.53i	0.320856	+	0.0565757i
$946$	1693.37	−	8977.76i	0.0581991	−	0.308554i
$947$	11113.4	+	30533.7i	0.381347	+	1.04774i	0.970790	+	0.239932i	$0.0771251\pi$
$947$	11113.4	+	30533.7i	0.381347	+	1.04774i	−0.589443	+	0.807810i	$0.700653\pi$
$948$	−1507.12	−	9922.16i	−0.0516339	−	0.339933i
$949$			10665.2i			0.364812i
$950$	−780.139	+	14409.0i	−0.0266432	+	0.492093i
$951$		−	13449.1i		−	0.458586i
$952$	−29309.9	−	6253.91i	−0.997837	−	0.212910i
$953$	−4882.80	−	13415.4i	−0.165970	−	0.455999i	0.828628	−	0.559799i	$-0.189122\pi$
$953$	−4882.80	−	13415.4i	−0.165970	−	0.455999i	−0.994598	+	0.103801i	$0.966900\pi$
$954$	−17400.1	−	3281.97i	−0.590511	−	0.111381i
$955$	−29767.5	−	5248.81i	−1.00864	−	0.177851i
$956$	−48892.7	+	26698.0i	−1.65408	+	0.903217i
$957$	−3001.17	−	5198.17i	−0.101373	−	0.175583i
$958$	−3879.81	−	4737.10i	−0.130847	−	0.159758i
$959$	14096.1	+	16799.1i	0.474648	+	0.565664i
$960$	−1020.49	−	9857.17i	−0.0343086	−	0.331395i
$961$	−16015.7	+	27740.0i	−0.537602	+	0.931154i
$962$	−1949.04	−	11878.1i	−0.0653219	−	0.398094i
$963$	14857.3	+	5407.60i	0.497164	+	0.180953i
$964$	6710.94	+	8395.56i	0.224217	+	0.280501i
$965$	27195.4	−	4795.28i	0.907202	−	0.159964i
$966$	2741.81	+	32.6166i	0.0913213	+	0.00108636i
$967$	−2582.98	+	3078.28i	−0.0858978	+	0.102369i	−0.807281	−	0.590167i	$-0.799062\pi$
$967$	−2582.98	+	3078.28i	−0.0858978	+	0.102369i	0.721384	+	0.692536i	$0.243506\pi$
$968$	−5043.35	−	9503.02i	−0.167458	−	0.315536i
$969$	−22136.9	−	14058.0i	−0.733891	−	0.466057i
$970$	−12025.9	+	31856.7i	−0.398072	+	1.05449i
$971$	−10424.0	−	8746.75i	−0.344512	−	0.289080i	0.454070	−	0.890966i	$-0.349972\pi$
$971$	−10424.0	−	8746.75i	−0.344512	−	0.289080i	−0.798582	+	0.601886i	$0.794416\pi$
$972$	−28682.5	−	11219.3i	−0.946495	−	0.370225i
$973$	2301.68	+	13053.5i	0.0758359	+	0.430087i
$974$	16777.9	−	28278.0i	0.551951	−	0.930273i
$975$	1833.86	−	5038.48i	0.0602363	−	0.165498i
$976$	−28351.1	+	21577.2i	−0.929811	+	0.707654i
$977$	8323.78	+	4805.74i	0.272570	+	0.157369i	0.630055	−	0.776550i	$-0.283032\pi$
$977$	8323.78	+	4805.74i	0.272570	+	0.157369i	−0.357485	+	0.933919i	$0.616366\pi$
$978$	6037.22	+	17221.8i	0.197392	+	0.563081i
$979$	9720.77	−	8156.70i	0.317341	−	0.266281i
$980$	14462.2	−	4877.45i	0.471407	−	0.158984i
$981$	−40978.8	+	23659.1i	−1.33369	+	0.770008i
$982$	27383.8	−	31857.3i	0.889870	−	1.03524i
$983$	6582.72	−	37332.5i	0.213587	−	1.21131i	−0.669754	−	0.742583i	$-0.733600\pi$
$983$	6582.72	−	37332.5i	0.213587	−	1.21131i	0.883341	−	0.468730i	$-0.155288\pi$
$984$	−6526.56	−	8367.05i	−0.211442	−	0.271069i
$985$	28648.7	−	10427.3i	0.926725	−	0.337300i
$986$	18662.4	−	10480.7i	0.602769	−	0.338514i
$987$	−1128.99			−0.0364095
$988$	−10481.3	−	21282.7i	−0.337505	−	0.685318i
$989$	−2980.70			−0.0958350
$990$	−17602.2	+	9885.33i	−0.565085	+	0.317350i
$991$	−45104.2	+	16416.6i	−1.44579	+	0.526226i	−0.941413	−	0.337255i	$-0.890501\pi$
$991$	−45104.2	+	16416.6i	−1.44579	+	0.526226i	−0.504381	+	0.863481i	$0.668279\pi$
$992$	44929.3	+	2675.42i	1.43801	+	0.0856298i
$993$	−2387.09	+	13537.8i	−0.0762859	+	0.432639i
$994$	−9196.66	+	10699.1i	−0.293461	+	0.341402i
$995$	−15049.7	+	8688.97i	−0.479506	+	0.276843i
$996$	3530.21	+	10467.5i	0.112308	+	0.333007i
$997$	−8783.33	+	7370.09i	−0.279008	+	0.234115i	−0.771543	−	0.636177i	$-0.780515\pi$
$997$	−8783.33	+	7370.09i	−0.279008	+	0.234115i	0.492535	+	0.870293i	$0.336070\pi$
$998$	8146.90	+	23239.9i	0.258402	+	0.737121i
$999$	12032.7	+	6947.08i	0.381079	+	0.220016i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.4.k.a.3.19	yes	168
4.3	odd	2	inner	76.4.k.a.3.4	✓	168
19.13	odd	18	inner	76.4.k.a.51.4	yes	168
76.51	even	18	inner	76.4.k.a.51.19	yes	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.4.k.a.3.4	✓	168	4.3	odd	2	inner
76.4.k.a.3.19	yes	168	1.1	even	1	trivial
76.4.k.a.51.4	yes	168	19.13	odd	18	inner
76.4.k.a.51.19	yes	168	76.51	even	18	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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	76.k (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.38498 + 2.46614i) q^{2} +(-2.28426 + 0.831401i) q^{3} +(-4.16368 + 6.83109i) q^{4} +(-1.38264 + 7.84134i) q^{5} +(-5.21399 - 4.48182i) q^{6} +(8.80596 - 5.08413i) q^{7} +(-22.6130 - 0.807318i) q^{8} +(-16.1566 + 13.5570i) q^{9} +O(q^{10})\)	\(q+(1.38498 + 2.46614i) q^{2} +(-2.28426 + 0.831401i) q^{3} +(-4.16368 + 6.83109i) q^{4} +(-1.38264 + 7.84134i) q^{5} +(-5.21399 - 4.48182i) q^{6} +(8.80596 - 5.08413i) q^{7} +(-22.6130 - 0.807318i) q^{8} +(-16.1566 + 13.5570i) q^{9} +(-21.2527 + 7.45029i) q^{10} +(-36.8082 - 21.2512i) q^{11} +(3.83154 - 19.0656i) q^{12} +(-12.2465 + 33.6471i) q^{13} +(24.7342 + 14.6753i) q^{14} +(-3.36099 - 19.0611i) q^{15} +(-29.3275 - 56.8849i) q^{16} +(99.7828 + 83.7277i) q^{17} +(-55.8100 - 21.0683i) q^{18} +(80.8816 + 17.8090i) q^{19} +(-47.8080 - 42.0938i) q^{20} +(-15.8881 + 18.9347i) q^{21} +(1.42998 - 120.207i) q^{22} +(-38.6251 + 6.81065i) q^{23} +(52.3251 - 16.9564i) q^{24} +(57.8867 + 21.0690i) q^{25} +(-99.9396 + 16.3988i) q^{26} +(58.4510 - 101.240i) q^{27} +(-1.93511 + 81.3230i) q^{28} +(-37.3435 - 44.5042i) q^{29} +(42.3525 - 34.6879i) q^{30} +(124.321 + 215.330i) q^{31} +(99.6682 - 151.110i) q^{32} +(101.748 + 17.9408i) q^{33} +(-68.2873 + 362.039i) q^{34} +(27.6909 + 76.0800i) q^{35} +(-25.3381 - 166.814i) q^{36} +118.853i q^{37} +(68.0998 + 224.130i) q^{38} -87.0403i q^{39} +(37.5961 - 176.200i) q^{40} +(-65.9833 - 181.288i) q^{41} +(-68.7003 - 12.9582i) q^{42} +(74.8431 + 13.1969i) q^{43} +(298.427 - 162.957i) q^{44} +(-83.9663 - 145.434i) q^{45} +(-70.2909 - 85.8223i) q^{46} +(29.3598 + 34.9897i) q^{47} +(114.286 + 105.557i) q^{48} +(-119.803 + 207.505i) q^{49} +(28.2126 + 171.937i) q^{50} +(-297.541 - 108.296i) q^{51} +(-178.856 - 223.753i) q^{52} +(292.316 - 51.5431i) q^{53} +(330.626 + 3.93312i) q^{54} +(217.530 - 259.243i) q^{55} +(-203.234 + 107.858i) q^{56} +(-199.561 + 26.5648i) q^{57} +(58.0338 - 153.732i) q^{58} +(-521.703 - 437.761i) q^{59} +(144.202 + 56.4053i) q^{60} +(-96.6680 - 548.231i) q^{61} +(-358.851 + 604.818i) q^{62} +(-73.3490 + 201.525i) q^{63} +(510.696 + 36.5118i) q^{64} +(-246.906 - 142.551i) q^{65} +(96.6734 + 275.771i) q^{66} +(-338.848 + 284.327i) q^{67} +(-987.415 + 333.010i) q^{68} +(82.5673 - 47.6702i) q^{69} +(-149.273 + 173.659i) q^{70} +(-85.1841 + 483.103i) q^{71} +(376.294 - 293.521i) q^{72} +(279.894 - 101.873i) q^{73} +(-293.108 + 164.609i) q^{74} -149.745 q^{75} +(-458.420 + 478.359i) q^{76} -432.176 q^{77} +(214.654 - 120.549i) q^{78} +(484.949 - 176.507i) q^{79} +(486.603 - 151.316i) q^{80} +(49.5390 - 280.950i) q^{81} +(355.695 - 413.803i) q^{82} +(-491.945 + 284.025i) q^{83} +(-63.1917 - 187.371i) q^{84} +(-794.500 + 666.665i) q^{85} +(71.1107 + 202.851i) q^{86} +(122.303 + 70.6116i) q^{87} +(815.188 + 510.270i) q^{88} +(-102.114 + 280.555i) q^{89} +(242.369 - 408.495i) q^{90} +(63.2235 + 358.558i) q^{91} +(114.299 - 292.209i) q^{92} +(-463.005 - 388.507i) q^{93} +(-45.6267 + 120.865i) q^{94} +(-251.476 + 609.597i) q^{95} +(-102.035 + 428.038i) q^{96} +(971.884 - 1158.25i) q^{97} +(-677.662 - 8.06147i) q^{98} +(882.798 - 155.661i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q - 6 q^{2} - 24 q^{4} - 12 q^{5} - 24 q^{6} - 9 q^{8} + 18 q^{9}+O(q^{10}) \) 168 * q - 6 * q^2 - 24 * q^4 - 12 * q^5 - 24 * q^6 - 9 * q^8 + 18 * q^9	\( 168 q - 6 q^{2} - 24 q^{4} - 12 q^{5} - 24 q^{6} - 9 q^{8} + 18 q^{9} - 105 q^{10} - 9 q^{12} - 120 q^{13} + 69 q^{14} + 192 q^{16} - 12 q^{17} + 558 q^{20} + 6 q^{21} - 30 q^{22} + 96 q^{24} - 12 q^{25} - 411 q^{26} + 756 q^{28} - 12 q^{29} + 276 q^{30} - 471 q^{32} - 576 q^{33} + 36 q^{34} - 2673 q^{36} - 648 q^{38} - 2298 q^{40} - 606 q^{41} - 321 q^{42} - 1203 q^{44} - 6 q^{45} + 1566 q^{46} + 3237 q^{48} + 2346 q^{49} + 3204 q^{50} + 1077 q^{52} + 576 q^{53} - 627 q^{54} - 12 q^{57} - 4116 q^{58} + 90 q^{60} + 3528 q^{61} - 3300 q^{62} - 381 q^{64} + 1242 q^{65} + 276 q^{66} + 1170 q^{68} - 4770 q^{69} + 1449 q^{70} + 1146 q^{72} - 3468 q^{73} + 3105 q^{74} + 4386 q^{76} - 9396 q^{77} + 6939 q^{78} + 2133 q^{80} + 1980 q^{81} + 7299 q^{82} + 315 q^{84} - 516 q^{85} - 3804 q^{86} - 5841 q^{88} + 3576 q^{89} - 8898 q^{90} - 7668 q^{92} + 5694 q^{93} + 18942 q^{96} + 774 q^{97} + 8745 q^{98}+O(q^{100}) \) 168 * q - 6 * q^2 - 24 * q^4 - 12 * q^5 - 24 * q^6 - 9 * q^8 + 18 * q^9 - 105 * q^10 - 9 * q^12 - 120 * q^13 + 69 * q^14 + 192 * q^16 - 12 * q^17 + 558 * q^20 + 6 * q^21 - 30 * q^22 + 96 * q^24 - 12 * q^25 - 411 * q^26 + 756 * q^28 - 12 * q^29 + 276 * q^30 - 471 * q^32 - 576 * q^33 + 36 * q^34 - 2673 * q^36 - 648 * q^38 - 2298 * q^40 - 606 * q^41 - 321 * q^42 - 1203 * q^44 - 6 * q^45 + 1566 * q^46 + 3237 * q^48 + 2346 * q^49 + 3204 * q^50 + 1077 * q^52 + 576 * q^53 - 627 * q^54 - 12 * q^57 - 4116 * q^58 + 90 * q^60 + 3528 * q^61 - 3300 * q^62 - 381 * q^64 + 1242 * q^65 + 276 * q^66 + 1170 * q^68 - 4770 * q^69 + 1449 * q^70 + 1146 * q^72 - 3468 * q^73 + 3105 * q^74 + 4386 * q^76 - 9396 * q^77 + 6939 * q^78 + 2133 * q^80 + 1980 * q^81 + 7299 * q^82 + 315 * q^84 - 516 * q^85 - 3804 * q^86 - 5841 * q^88 + 3576 * q^89 - 8898 * q^90 - 7668 * q^92 + 5694 * q^93 + 18942 * q^96 + 774 * q^97 + 8745 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more