LMFDB - Embedded newform 36.5.f.a.31.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [36,5,Mod(7,36)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(36, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("36.7");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 36 = 2^{2} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	36.f (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.72131867102$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.21
Character	$\chi$	$=$	36.31
Dual form			36.5.f.a.7.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.89672 - 0.903087i) q^{2} +(-8.98168 - 0.573987i) q^{3} +(14.3689 - 7.03816i) q^{4} +(19.5394 - 33.8433i) q^{5} +(-35.5175 + 5.87457i) q^{6} +(10.5700 - 6.10260i) q^{7} +(49.6354 - 40.4021i) q^{8} +(80.3411 + 10.3107i) q^{9} +O(q^{10})$	\(q+(3.89672 - 0.903087i) q^{2} +(-8.98168 - 0.573987i) q^{3} +(14.3689 - 7.03816i) q^{4} +(19.5394 - 33.8433i) q^{5} +(-35.5175 + 5.87457i) q^{6} +(10.5700 - 6.10260i) q^{7} +(49.6354 - 40.4021i) q^{8} +(80.3411 + 10.3107i) q^{9} +(45.5763 - 149.524i) q^{10} +(-96.1446 + 55.5091i) q^{11} +(-133.096 + 54.9669i) q^{12} +(-104.491 + 180.984i) q^{13} +(35.6772 - 33.3258i) q^{14} +(-194.923 + 292.754i) q^{15} +(156.929 - 202.261i) q^{16} +93.3790 q^{17} +(322.378 - 32.3769i) q^{18} +26.8894i q^{19} +(42.5651 - 623.812i) q^{20} +(-98.4393 + 48.7446i) q^{21} +(-324.519 + 303.130i) q^{22} +(757.577 + 437.387i) q^{23} +(-468.999 + 334.388i) q^{24} +(-451.080 - 781.293i) q^{25} +(-243.728 + 799.608i) q^{26} +(-715.679 - 138.723i) q^{27} +(108.928 - 162.081i) q^{28} +(650.809 + 1127.23i) q^{29} +(-495.176 + 1316.81i) q^{30} +(-593.492 - 342.653i) q^{31} +(428.848 - 929.874i) q^{32} +(895.401 - 443.379i) q^{33} +(363.872 - 84.3293i) q^{34} -476.966i q^{35} +(1226.98 - 417.299i) q^{36} -1760.25 q^{37} +(24.2835 + 104.780i) q^{38} +(1042.39 - 1565.56i) q^{39} +(-397.492 - 2469.26i) q^{40} +(-39.0421 + 67.6229i) q^{41} +(-339.570 + 278.843i) q^{42} +(1405.46 - 811.442i) q^{43} +(-990.807 + 1474.28i) q^{44} +(1918.77 - 2517.54i) q^{45} +(3347.06 + 1020.22i) q^{46} +(1999.54 - 1154.43i) q^{47} +(-1525.58 + 1726.57i) q^{48} +(-1126.02 + 1950.32i) q^{49} +(-2463.31 - 2637.12i) q^{50} +(-838.700 - 53.5984i) q^{51} +(-227.626 + 3335.96i) q^{52} -1313.48 q^{53} +(-2914.08 + 105.758i) q^{54} +4338.47i q^{55} +(278.089 - 729.956i) q^{56} +(15.4342 - 241.512i) q^{57} +(3554.01 + 3804.78i) q^{58} +(-4818.38 - 2781.89i) q^{59} +(-740.367 + 5578.44i) q^{60} +(-1090.13 - 1888.16i) q^{61} +(-2622.12 - 799.247i) q^{62} +(912.129 - 381.305i) q^{63} +(831.345 - 4010.75i) q^{64} +(4083.39 + 7072.65i) q^{65} +(3088.72 - 2536.35i) q^{66} +(213.077 + 123.020i) q^{67} +(1341.75 - 657.216i) q^{68} +(-6553.25 - 4363.31i) q^{69} +(-430.742 - 1858.60i) q^{70} +4608.15i q^{71} +(4404.34 - 2734.17i) q^{72} +2564.79 q^{73} +(-6859.21 + 1589.66i) q^{74} +(3603.00 + 7276.24i) q^{75} +(189.252 + 386.370i) q^{76} +(-677.500 + 1173.46i) q^{77} +(2648.05 - 7041.92i) q^{78} +(-4486.29 + 2590.16i) q^{79} +(-3778.87 - 9263.05i) q^{80} +(6348.38 + 1656.75i) q^{81} +(-91.0669 + 298.766i) q^{82} +(1622.37 - 936.677i) q^{83} +(-1071.39 + 1393.24i) q^{84} +(1824.57 - 3160.25i) q^{85} +(4743.88 - 4431.22i) q^{86} +(-5198.34 - 10498.0i) q^{87} +(-2529.49 + 6639.66i) q^{88} -1167.17 q^{89} +(5203.35 - 11543.0i) q^{90} +2550.67i q^{91} +(13963.9 + 952.813i) q^{92} +(5133.87 + 3418.25i) q^{93} +(6749.08 - 6304.26i) q^{94} +(910.026 + 525.404i) q^{95} +(-4385.51 + 8105.67i) q^{96} +(2869.58 + 4970.26i) q^{97} +(-2626.47 + 8616.73i) q^{98} +(-8296.70 + 3468.34i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - q^{2} - q^{4} - 2 q^{5} + 15 q^{6} + 122 q^{8} - 60 q^{9}+O(q^{10}) $ 44 * q - q^2 - q^4 - 2 * q^5 + 15 * q^6 + 122 * q^8 - 60 * q^9	$ 44 q - q^{2} - q^{4} - 2 q^{5} + 15 q^{6} + 122 q^{8} - 60 q^{9} + 28 q^{10} - 228 q^{12} - 2 q^{13} + 252 q^{14} - q^{16} - 56 q^{17} + 72 q^{18} - 140 q^{20} + 138 q^{21} - 33 q^{22} - 951 q^{24} - 1752 q^{25} + 1096 q^{26} - 516 q^{28} + 526 q^{29} - 1980 q^{30} - 121 q^{32} + 2994 q^{33} + 385 q^{34} - 1005 q^{36} - 8 q^{37} + 1395 q^{38} - 2276 q^{40} - 2762 q^{41} + 3330 q^{42} + 6714 q^{44} + 4110 q^{45} + 3576 q^{46} + 2163 q^{48} + 3428 q^{49} + 6375 q^{50} + 1438 q^{52} - 10088 q^{53} - 4983 q^{54} - 7506 q^{56} + 1752 q^{57} - 4064 q^{58} - 16392 q^{60} - 2 q^{61} - 18324 q^{62} + 9026 q^{64} - 2014 q^{65} - 17358 q^{66} - 11405 q^{68} + 3354 q^{69} + 3666 q^{70} + 4083 q^{72} - 3416 q^{73} + 14620 q^{74} + 1581 q^{76} - 3942 q^{77} + 34566 q^{78} + 45520 q^{80} - 1164 q^{81} - 8486 q^{82} + 51078 q^{84} - 1252 q^{85} + 22113 q^{86} + 1995 q^{88} + 13048 q^{89} - 4692 q^{90} - 30294 q^{92} + 12090 q^{93} + 7524 q^{94} - 76164 q^{96} + 5638 q^{97} - 92938 q^{98}+O(q^{100}) $ 44 * q - q^2 - q^4 - 2 * q^5 + 15 * q^6 + 122 * q^8 - 60 * q^9 + 28 * q^10 - 228 * q^12 - 2 * q^13 + 252 * q^14 - q^16 - 56 * q^17 + 72 * q^18 - 140 * q^20 + 138 * q^21 - 33 * q^22 - 951 * q^24 - 1752 * q^25 + 1096 * q^26 - 516 * q^28 + 526 * q^29 - 1980 * q^30 - 121 * q^32 + 2994 * q^33 + 385 * q^34 - 1005 * q^36 - 8 * q^37 + 1395 * q^38 - 2276 * q^40 - 2762 * q^41 + 3330 * q^42 + 6714 * q^44 + 4110 * q^45 + 3576 * q^46 + 2163 * q^48 + 3428 * q^49 + 6375 * q^50 + 1438 * q^52 - 10088 * q^53 - 4983 * q^54 - 7506 * q^56 + 1752 * q^57 - 4064 * q^58 - 16392 * q^60 - 2 * q^61 - 18324 * q^62 + 9026 * q^64 - 2014 * q^65 - 17358 * q^66 - 11405 * q^68 + 3354 * q^69 + 3666 * q^70 + 4083 * q^72 - 3416 * q^73 + 14620 * q^74 + 1581 * q^76 - 3942 * q^77 + 34566 * q^78 + 45520 * q^80 - 1164 * q^81 - 8486 * q^82 + 51078 * q^84 - 1252 * q^85 + 22113 * q^86 + 1995 * q^88 + 13048 * q^89 - 4692 * q^90 - 30294 * q^92 + 12090 * q^93 + 7524 * q^94 - 76164 * q^96 + 5638 * q^97 - 92938 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/36\mathbb{Z}\right)^\times$.

$n$	$19$	$29$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	3.89672	−	0.903087i	0.974180	−	0.225772i
$2$	3.89672	−	0.903087i	0.974180	−	0.225772i
$3$	−8.98168	−	0.573987i	−0.997964	−	0.0637764i
$3$	−8.98168	−	0.573987i	−0.997964	−	0.0637764i
$4$	14.3689	−	7.03816i	0.898054	−	0.439885i
$5$	19.5394	−	33.8433i	0.781578	−	1.35373i	−0.149444	−	0.988770i	$-0.547749\pi$
$5$	19.5394	−	33.8433i	0.781578	−	1.35373i	0.931022	−	0.364962i	$-0.118918\pi$
$6$	−35.5175	+	5.87457i	−0.986596	+	0.163182i
$7$	10.5700	−	6.10260i	0.215715	−	0.124543i	−0.388250	−	0.921554i	$-0.626920\pi$
$7$	10.5700	−	6.10260i	0.215715	−	0.124543i	0.603964	+	0.797011i	$0.293587\pi$
$8$	49.6354	−	40.4021i	0.775553	−	0.631282i
$9$	80.3411	+	10.3107i	0.991865	+	0.127293i
$10$	45.5763	−	149.524i	0.455763	−	1.49524i
$11$	−96.1446	+	55.5091i	−0.794583	+	0.458753i	−0.841574	−	0.540142i	$-0.818370\pi$
$11$	−96.1446	+	55.5091i	−0.794583	+	0.458753i	0.0469902	+	0.998895i	$0.485037\pi$
$12$	−133.096	+	54.9669i	−0.924280	+	0.381715i
$13$	−104.491	+	180.984i	−0.618290	+	1.07091i	0.371507	+	0.928430i	$0.378841\pi$
$13$	−104.491	+	180.984i	−0.618290	+	1.07091i	−0.989798	+	0.142480i	$0.954492\pi$
$14$	35.6772	−	33.3258i	0.182027	−	0.170030i
$15$	−194.923	+	292.754i	−0.866323	+	1.30113i
$16$	156.929	−	202.261i	0.613003	−	0.790081i
$17$	93.3790			0.323111			0.161555	−	0.986864i	$-0.448349\pi$
$17$	93.3790			0.323111			0.161555	+	0.986864i	$0.448349\pi$
$18$	322.378	−	32.3769i	0.994995	−	0.0999288i
$19$			26.8894i			0.0744859i	0.999306	+	0.0372429i	$0.0118575\pi$
$19$			26.8894i			0.0744859i	−0.999306	+	0.0372429i	$0.988142\pi$
$20$	42.5651	−	623.812i	0.106413	−	1.55953i
$21$	−98.4393	+	48.7446i	−0.223218	+	0.110532i
$22$	−324.519	+	303.130i	−0.670494	+	0.626303i
$23$	757.577	+	437.387i	1.43209	+	0.826819i	0.997280	−	0.0737029i	$-0.0234816\pi$
$23$	757.577	+	437.387i	1.43209	+	0.826819i	0.434812	+	0.900521i	$0.356815\pi$
$24$	−468.999	+	334.388i	−0.814235	+	0.580535i
$25$	−451.080	−	781.293i	−0.721728	−	1.25007i
$26$	−243.728	+	799.608i	−0.360545	+	1.18285i
$27$	−715.679	−	138.723i	−0.981728	−	0.190292i
$28$	108.928	−	162.081i	0.138939	−	0.206736i
$29$	650.809	+	1127.23i	0.773851	+	1.34035i	0.935438	+	0.353491i	$0.115005\pi$
$29$	650.809	+	1127.23i	0.773851	+	1.34035i	−0.161587	+	0.986858i	$0.551661\pi$
$30$	−495.176	+	1316.81i	−0.550196	+	1.46313i
$31$	−593.492	−	342.653i	−0.617577	−	0.356558i	0.158348	−	0.987383i	$-0.449383\pi$
$31$	−593.492	−	342.653i	−0.617577	−	0.356558i	−0.775925	+	0.630825i	$0.782717\pi$
$32$	428.848	−	929.874i	0.418797	−	0.908080i
$33$	895.401	−	443.379i	0.822223	−	0.407143i
$34$	363.872	−	84.3293i	0.314768	−	0.0729493i
$35$		−	476.966i		−	0.389360i
$36$	1226.98	−	417.299i	0.946743	−	0.321990i
$37$	−1760.25			−1.28579			−0.642897	−	0.765953i	$-0.722268\pi$
$37$	−1760.25			−1.28579			−0.642897	+	0.765953i	$0.722268\pi$
$38$	24.2835	+	104.780i	0.0168168	+	0.0725626i
$39$	1042.39	−	1565.56i	0.685330	−	1.02930i
$40$	−397.492	−	2469.26i	−0.248432	−	1.54329i
$41$	−39.0421	+	67.6229i	−0.0232255	+	0.0402278i	−0.877405	−	0.479751i	$-0.840727\pi$
$41$	−39.0421	+	67.6229i	−0.0232255	+	0.0402278i	0.854179	+	0.519979i	$0.174060\pi$
$42$	−339.570	+	278.843i	−0.192500	+	0.158074i
$43$	1405.46	−	811.442i	0.760118	−	0.438855i	−0.0692198	−	0.997601i	$-0.522051\pi$
$43$	1405.46	−	811.442i	0.760118	−	0.438855i	0.829338	+	0.558747i	$0.188718\pi$
$44$	−990.807	+	1474.28i	−0.511780	+	0.761510i
$45$	1918.77	−	2517.54i	0.947541	−	1.24323i
$46$	3347.06	+	1020.22i	1.58179	+	0.482144i
$47$	1999.54	−	1154.43i	0.905177	−	0.522604i	0.0263007	−	0.999654i	$-0.491627\pi$
$47$	1999.54	−	1154.43i	0.905177	−	0.522604i	0.878876	+	0.477050i	$0.158294\pi$
$48$	−1525.58	+	1726.57i	−0.662143	+	0.749377i
$49$	−1126.02	+	1950.32i	−0.468978	+	0.812294i
$50$	−2463.31	−	2637.12i	−0.985323	−	1.05485i
$51$	−838.700	−	53.5984i	−0.322453	−	0.0206068i
$52$	−227.626	+	3335.96i	−0.0841811	+	1.23371i
$53$	−1313.48			−0.467598			−0.233799	−	0.972285i	$-0.575116\pi$
$53$	−1313.48			−0.467598			−0.233799	+	0.972285i	$0.575116\pi$
$54$	−2914.08	+	105.758i	−0.999342	+	0.0362682i
$55$			4338.47i			1.43420i
$56$	278.089	−	729.956i	0.0886764	−	0.232767i
$57$	15.4342	−	241.512i	0.00475044	−	0.0743342i
$58$	3554.01	+	3804.78i	1.05648	+	1.13103i
$59$	−4818.38	−	2781.89i	−1.38419	−	0.799164i	−0.391540	−	0.920161i	$-0.628058\pi$
$59$	−4818.38	−	2781.89i	−1.38419	−	0.799164i	−0.992653	+	0.120997i	$0.961391\pi$
$60$	−740.367	+	5578.44i	−0.205657	+	1.54957i
$61$	−1090.13	−	1888.16i	−0.292967	−	0.507433i	0.681543	−	0.731778i	$-0.261309\pi$
$61$	−1090.13	−	1888.16i	−0.292967	−	0.507433i	−0.974510	+	0.224345i	$0.927976\pi$
$62$	−2622.12	−	799.247i	−0.682132	−	0.207921i
$63$	912.129	−	381.305i	0.229813	−	0.0960708i
$64$	831.345	−	4010.75i	0.202965	−	0.979186i
$65$	4083.39	+	7072.65i	0.966484	+	1.67400i
$66$	3088.72	−	2536.35i	0.709072	−	0.582266i
$67$	213.077	+	123.020i	0.0474665	+	0.0274048i	0.523545	−	0.851998i	$-0.324609\pi$
$67$	213.077	+	123.020i	0.0474665	+	0.0274048i	−0.476079	+	0.879403i	$0.657942\pi$
$68$	1341.75	−	657.216i	0.290171	−	0.142131i
$69$	−6553.25	−	4363.31i	−1.37644	−	0.916469i
$70$	−430.742	−	1858.60i	−0.0879065	−	0.379307i
$71$			4608.15i			0.914134i	0.889432	+	0.457067i	$0.151100\pi$
$71$			4608.15i			0.914134i	−0.889432	+	0.457067i	$0.848900\pi$
$72$	4404.34	−	2734.17i	0.849602	−	0.527424i
$73$	2564.79			0.481290			0.240645	−	0.970613i	$-0.422641\pi$
$73$	2564.79			0.481290			0.240645	+	0.970613i	$0.422641\pi$
$74$	−6859.21	+	1589.66i	−1.25259	+	0.290296i
$75$	3603.00	+	7276.24i	0.640534	+	1.29355i
$76$	189.252	+	386.370i	0.0327652	+	0.0668923i
$77$	−677.500	+	1173.46i	−0.114269	+	0.197919i
$78$	2648.05	−	7041.92i	0.435249	−	1.15745i
$79$	−4486.29	+	2590.16i	−0.718842	+	0.415023i	−0.814326	−	0.580408i	$-0.802893\pi$
$79$	−4486.29	+	2590.16i	−0.718842	+	0.415023i	0.0954846	+	0.995431i	$0.469560\pi$
$80$	−3778.87	−	9263.05i	−0.590449	−	1.44735i
$81$	6348.38	+	1656.75i	0.967593	+	0.252515i
$82$	−91.0669	+	298.766i	−0.0135436	+	0.0444328i
$83$	1622.37	−	936.677i	0.235502	−	0.135967i	−0.377606	−	0.925966i	$-0.623253\pi$
$83$	1622.37	−	936.677i	0.235502	−	0.135967i	0.613108	+	0.789999i	$0.289919\pi$
$84$	−1071.39	+	1393.24i	−0.151841	+	0.197454i
$85$	1824.57	−	3160.25i	0.252536	−	0.437405i
$86$	4743.88	−	4431.22i	0.641411	−	0.599137i
$87$	−5198.34	−	10498.0i	−0.686793	−	1.38697i
$88$	−2529.49	+	6639.66i	−0.326639	+	0.857394i
$89$	−1167.17			−0.147352			−0.0736759	−	0.997282i	$-0.523473\pi$
$89$	−1167.17			−0.147352			−0.0736759	+	0.997282i	$0.523473\pi$
$90$	5203.35	−	11543.0i	0.642389	−	1.42506i
$91$			2550.67i			0.308015i
$92$	13963.9	+	952.813i	1.64980	+	0.112572i
$93$	5133.87	+	3418.25i	0.593580	+	0.395219i
$94$	6749.08	−	6304.26i	0.763816	−	0.713474i
$95$	910.026	+	525.404i	0.100834	+	0.0582165i
$96$	−4385.51	+	8105.67i	−0.475859	+	0.879522i
$97$	2869.58	+	4970.26i	0.304983	+	0.528245i	0.977257	−	0.212056i	$-0.0680160\pi$
$97$	2869.58	+	4970.26i	0.304983	+	0.528245i	−0.672275	+	0.740302i	$0.734683\pi$
$98$	−2626.47	+	8616.73i	−0.273476	+	0.897203i
$99$	−8296.70	+	3468.34i	−0.846516	+	0.353876i
$100$	−11980.4	−	8051.53i	−1.19804	−	0.805153i
$101$	−7793.37	−	13498.5i	−0.763981	−	1.32325i	−0.940783	−	0.339008i	$-0.889909\pi$
$101$	−7793.37	−	13498.5i	−0.763981	−	1.32325i	0.176802	−	0.984246i	$-0.443425\pi$
$102$	−3316.58	+	548.561i	−0.318780	+	0.0527260i
$103$	−9636.52	−	5563.65i	−0.908334	−	0.524427i	−0.0284395	−	0.999596i	$-0.509054\pi$
$103$	−9636.52	−	5563.65i	−0.908334	−	0.524427i	−0.879895	+	0.475168i	$0.842387\pi$
$104$	2125.67	+	13204.9i	0.196530	+	1.22086i
$105$	−273.772	+	4283.95i	−0.0248320	+	0.388567i
$106$	−5118.28	+	1186.19i	−0.455525	+	0.105570i
$107$			4464.91i			0.389983i	0.980805	+	0.194991i	$0.0624679\pi$
$107$			4464.91i			0.389983i	−0.980805	+	0.194991i	$0.937532\pi$
$108$	−11259.9	+	3043.78i	−0.965351	+	0.260955i
$109$	−4736.05			−0.398624			−0.199312	−	0.979936i	$-0.563871\pi$
$109$	−4736.05			−0.398624			−0.199312	+	0.979936i	$0.563871\pi$
$110$	3918.02	+	16905.8i	0.323803	+	1.39717i
$111$	15810.0	+	1010.36i	1.28318	+	0.0820033i
$112$	424.422	−	3095.57i	0.0338347	−	0.246777i
$113$	9173.06	−	15888.2i	0.718385	−	1.24428i	−0.243254	−	0.969963i	$-0.578215\pi$
$113$	9173.06	−	15888.2i	0.718385	−	1.24428i	0.961639	−	0.274317i	$-0.0884519\pi$
$114$	−157.964	−	955.043i	−0.0121548	−	0.0734874i
$115$	29605.3	−	17092.6i	2.23858	−	1.29245i
$116$	17285.0	+	11616.6i	1.28456	+	0.863301i
$117$	−10261.0	+	13463.1i	−0.749580	+	0.983494i
$118$	−21288.2	−	6488.84i	−1.52888	−	0.466018i
$119$	987.017	−	569.855i	0.0696997	−	0.0402411i
$120$	2152.82	+	22406.3i	0.149501	+	1.55599i
$121$	−1157.98	+	2005.68i	−0.0790915	+	0.136990i
$122$	−5953.10	−	6373.14i	−0.399966	−	0.428188i
$123$	389.479	−	584.958i	0.0257438	−	0.0386647i
$124$	−10939.4	−	746.442i	−0.711462	−	0.0485459i
$125$	−10831.1			−0.693190
$126$	3209.96	−	2309.57i	0.202189	−	0.145476i
$127$		−	8169.42i		−	0.506505i	−0.967400	−	0.253252i	$-0.918500\pi$
$127$		−	8169.42i		−	0.506505i	0.967400	−	0.253252i	$-0.0815003\pi$
$128$	−382.534	−	16379.5i	−0.0233480	−	0.999727i
$129$	−13089.1	+	6481.40i	−0.786560	+	0.389484i
$130$	22299.1	+	23872.5i	1.31947	+	1.41257i
$131$	9131.01	+	5271.79i	0.532079	+	0.307196i	0.741863	−	0.670552i	$-0.233943\pi$
$131$	9131.01	+	5271.79i	0.532079	+	0.307196i	−0.209784	+	0.977748i	$0.567276\pi$
$132$	9745.33	−	12672.8i	0.559305	−	0.727320i
$133$	164.095	+	284.221i	0.00927669	+	0.0160677i
$134$	941.399	+	286.948i	0.0524281	+	0.0159806i
$135$	−18678.8	+	21510.4i	−1.02490	+	1.18027i
$136$	4634.90	−	3772.70i	0.250589	−	0.203974i
$137$	−1612.85	−	2793.54i	−0.0859318	−	0.148838i	0.819856	−	0.572570i	$-0.194053\pi$
$137$	−1612.85	−	2793.54i	−0.0859318	−	0.148838i	−0.905788	+	0.423731i	$0.860720\pi$
$138$	−29476.7	−	11084.4i	−1.54782	−	0.582044i
$139$	−16276.4	−	9397.17i	−0.842419	−	0.486371i	0.0156666	−	0.999877i	$-0.495013\pi$
$139$	−16276.4	−	9397.17i	−0.842419	−	0.486371i	−0.858086	+	0.513506i	$0.828346\pi$
$140$	−3356.96	−	6853.46i	−0.171274	−	0.349666i
$141$	−18621.8	+	9221.03i	−0.936664	+	0.463811i
$142$	4161.56	+	17956.7i	0.206386	+	0.890531i
$143$		−	23200.8i		−	1.13457i
$144$	14693.3	−	14631.8i	0.708588	−	0.705623i
$145$	50865.8			2.41930
$146$	9994.28	−	2316.23i	0.468863	−	0.108662i
$147$	11233.0	−	16870.8i	0.519829	−	0.780731i
$148$	−25292.8	+	12388.9i	−1.15471	+	0.565601i
$149$	3825.13	−	6625.31i	0.172295	−	0.298424i	−0.766927	−	0.641735i	$-0.778215\pi$
$149$	3825.13	−	6625.31i	0.172295	−	0.298424i	0.939222	+	0.343311i	$0.111548\pi$
$150$	20611.0	+	25099.6i	0.916043	+	1.11554i
$151$	974.974	−	562.901i	0.0427601	−	0.0246876i	−0.478468	−	0.878105i	$-0.658808\pi$
$151$	974.974	−	562.901i	0.0427601	−	0.0246876i	0.521228	+	0.853418i	$0.325474\pi$
$152$	1086.39	+	1334.67i	0.0470216	+	0.0577677i
$153$	7502.17	+	962.806i	0.320482	+	0.0411297i
$154$	−1580.29	+	5184.51i	−0.0666338	+	0.218608i
$155$	−23193.0	+	13390.5i	−0.965369	+	0.557356i
$156$	3959.26	−	29831.8i	0.162691	−	1.22583i
$157$	1755.81	−	3041.15i	0.0712326	−	0.123378i	−0.828209	−	0.560419i	$-0.810640\pi$
$157$	1755.81	−	3041.15i	0.0712326	−	0.123378i	0.899442	+	0.437041i	$0.143973\pi$
$158$	−15142.7	+	14144.6i	−0.606581	+	0.566602i
$159$	11797.3	+	753.923i	0.466646	+	0.0298217i
$160$	−23090.6	−	32682.9i	−0.901975	−	1.27667i
$161$	10676.8			0.411898
$162$	26234.0	+	722.762i	0.999621	+	0.0275401i
$163$			41947.9i			1.57883i	0.613861	+	0.789414i	$0.289615\pi$
$163$			41947.9i			1.57883i	−0.613861	+	0.789414i	$0.710385\pi$
$164$	−85.0502	+	1246.45i	−0.00316219	+	0.0463433i
$165$	2490.23	−	38966.7i	0.0914684	−	1.43128i
$166$	5476.03	−	5115.11i	0.198724	−	0.185626i
$167$	−5900.58	−	3406.70i	−0.211574	−	0.122152i	0.390469	−	0.920616i	$-0.372313\pi$
$167$	−5900.58	−	3406.70i	−0.211574	−	0.122152i	−0.602043	+	0.798464i	$0.705646\pi$
$168$	−2916.69	+	6396.61i	−0.103341	+	0.226637i
$169$	−7556.26	−	13087.8i	−0.264566	−	0.458241i
$170$	4255.87	−	13962.4i	0.147262	−	0.483127i
$171$	−277.250	+	2160.32i	−0.00948153	+	0.0738799i
$172$	14483.8	−	21551.3i	0.489582	−	0.728480i
$173$	−7874.16	−	13638.4i	−0.263095	−	0.455693i	0.703968	−	0.710232i	$-0.251410\pi$
$173$	−7874.16	−	13638.4i	−0.263095	−	0.455693i	−0.967063	+	0.254539i	$0.918076\pi$
$174$	−29737.1	−	36213.3i	−0.982200	−	1.19610i
$175$	−9535.85	−	5505.52i	−0.311375	−	0.179772i
$176$	−3860.53	+	28157.2i	−0.124630	+	0.909002i
$177$	41680.3	+	27751.7i	1.33041	+	0.885816i
$178$	−4548.15	+	1054.06i	−0.143547	+	0.0332679i
$179$			22497.6i			0.702151i	0.936347	+	0.351075i	$0.114184\pi$
$179$			22497.6i			0.702151i	−0.936347	+	0.351075i	$0.885816\pi$
$180$	9851.69	−	49678.8i	0.304065	−	1.53330i
$181$	−21847.2			−0.666867			−0.333434	−	0.942774i	$-0.608207\pi$
$181$	−21847.2			−0.666867			−0.333434	+	0.942774i	$0.608207\pi$
$182$	2303.48	+	9939.25i	0.0695410	+	0.300062i
$183$	8707.40	+	17584.5i	0.260008	+	0.525084i
$184$	55274.0	−	8897.79i	1.63262	−	0.262813i
$185$	−34394.3	+	59572.7i	−1.00495	+	1.74062i
$186$	23092.2	+	8683.64i	0.667483	+	0.251001i
$187$	−8977.88	+	5183.38i	−0.256738	+	0.148228i
$188$	20606.0	−	30660.9i	0.583012	−	0.867500i
$189$	−8411.31	+	2901.21i	−0.235473	+	0.0812186i
$190$	4020.60	+	1225.52i	0.111374	+	0.0339479i
$191$	−16182.1	+	9342.76i	−0.443577	+	0.256099i	−0.705114	−	0.709094i	$-0.749104\pi$
$191$	−16182.1	+	9342.76i	−0.443577	+	0.256099i	0.261537	+	0.965194i	$0.415771\pi$
$192$	−9768.99	+	35546.0i	−0.265001	+	0.964248i
$193$	−23049.7	+	39923.2i	−0.618800	+	1.07179i	0.370905	+	0.928671i	$0.379048\pi$
$193$	−23049.7	+	39923.2i	−0.618800	+	1.07179i	−0.989705	+	0.143123i	$0.954286\pi$
$194$	15670.5	+	16776.2i	0.416371	+	0.445750i
$195$	−32616.1	−	65868.1i	−0.857755	−	1.73223i
$196$	−2452.94	+	35948.9i	−0.0638520	+	0.935780i
$197$	15934.7			0.410592			0.205296	−	0.978700i	$-0.434184\pi$
$197$	15934.7			0.410592			0.205296	+	0.978700i	$0.434184\pi$
$198$	−29197.7	+	21007.8i	−0.744764	+	0.535858i
$199$			73733.8i			1.86192i	0.365124	+	0.930959i	$0.381026\pi$
$199$			73733.8i			1.86192i	−0.365124	+	0.930959i	$0.618974\pi$
$200$	−53955.4	−	20555.2i	−1.34888	−	0.513881i
$201$	−1843.18	−	1227.23i	−0.0456221	−	0.0303762i
$202$	−42558.9	−	45561.9i	−1.04301	−	1.11660i
$203$	13758.1	+	7943.25i	0.333862	+	0.192755i
$204$	−12428.4	+	5132.75i	−0.298645	+	0.123336i
$205$	1525.72	+	2642.63i	0.0363051	+	0.0628823i
$206$	−42575.3	−	12977.4i	−1.00328	−	0.305810i
$207$	56354.7	+	42951.3i	1.31519	+	1.00239i
$208$	20208.3	+	49536.0i	0.467092	+	1.14497i
$209$	−1492.61	−	2585.27i	−0.0341706	−	0.0591852i
$210$	2801.97	+	16940.6i	0.0635367	+	0.384141i
$211$	−15431.2	−	8909.20i	−0.346605	−	0.200112i	0.316584	−	0.948564i	$-0.397464\pi$
$211$	−15431.2	−	8909.20i	−0.346605	−	0.200112i	−0.663189	+	0.748452i	$0.730797\pi$
$212$	−18873.3	+	9244.50i	−0.419929	+	0.205689i
$213$	2645.02	−	41388.9i	0.0583001	−	0.912273i
$214$	4032.20	+	17398.5i	0.0880471	+	0.379913i
$215$		−	63420.5i		−	1.37200i
$216$	−41127.7	+	22029.4i	−0.881510	+	0.472166i
$217$	−8364.29			−0.177627
$218$	−18455.1	+	4277.07i	−0.388332	+	0.0899980i
$219$	−23036.1	−	1472.16i	−0.480310	−	0.0306949i
$220$	30534.8	+	62338.9i	0.630885	+	1.28799i
$221$	−9757.27	+	16900.1i	−0.199776	+	0.346022i
$222$	62519.6	−	10340.7i	1.26856	−	0.209819i
$223$	58353.8	−	33690.6i	1.17344	−	0.677483i	0.218949	−	0.975736i	$-0.429737\pi$
$223$	58353.8	−	33690.6i	1.17344	−	0.677483i	0.954487	+	0.298253i	$0.0964039\pi$
$224$	−1141.72	−	12445.9i	−0.0227542	−	0.248044i
$225$	−28184.5	−	67420.9i	−0.556732	−	1.33177i
$226$	21396.4	−	70196.0i	0.418914	−	1.37434i
$227$	54381.5	−	31397.2i	1.05536	−	0.609310i	0.131212	−	0.991354i	$-0.458113\pi$
$227$	54381.5	−	31397.2i	1.05536	−	0.609310i	0.924144	+	0.382044i	$0.124780\pi$
$228$	−1478.03	−	3578.88i	−0.0284323	−	0.0688458i
$229$	20463.2	−	35443.2i	0.390213	−	0.675868i	−0.602265	−	0.798297i	$-0.705735\pi$
$229$	20463.2	−	35443.2i	0.390213	−	0.675868i	0.992477	+	0.122428i	$0.0390681\pi$
$230$	99927.3	−	93341.2i	1.88898	−	1.76448i
$231$	6758.64	−	10150.8i	0.126659	−	0.190229i
$232$	77845.7	+	29656.7i	1.44630	+	0.550993i
$233$	79254.5			1.45986			0.729932	−	0.683520i	$-0.239552\pi$
$233$	79254.5			1.45986			0.729932	+	0.683520i	$0.239552\pi$
$234$	−27825.9	+	61728.3i	−0.508181	+	1.12733i
$235$		−	90227.9i		−	1.63382i
$236$	−88814.0	−	6060.13i	−1.59462	−	0.108807i
$237$	41781.1	−	20688.9i	0.743847	−	0.368333i
$238$	3331.50	−	3111.93i	0.0588148	−	0.0549383i
$239$	−39084.7	−	22565.5i	−0.684243	−	0.395048i	0.117209	−	0.993107i	$-0.462605\pi$
$239$	−39084.7	−	22565.5i	−0.684243	−	0.395048i	−0.801452	+	0.598059i	$0.795939\pi$
$240$	28623.7	+	85366.7i	0.496940	+	1.48206i
$241$	−37826.8	−	65517.9i	−0.651276	−	1.12804i	−0.982814	−	0.184601i	$-0.940901\pi$
$241$	−37826.8	−	65517.9i	−0.651276	−	1.12804i	0.331537	−	0.943442i	$-0.392433\pi$
$242$	−2701.02	+	8861.32i	−0.0461208	+	0.151310i
$243$	−56068.1	−	18524.3i	−0.949519	−	0.313711i
$244$	−28953.1	−	19458.2i	−0.486312	−	0.326831i
$245$	44003.5	+	76216.3i	0.733086	+	1.26974i
$246$	989.421	−	2631.15i	0.0163497	−	0.0434786i
$247$	−4866.55	−	2809.70i	−0.0797677	−	0.0460539i
$248$	−43302.1	+	6970.60i	−0.704053	+	0.113336i
$249$	−15109.3	+	7481.71i	−0.243694	+	0.120671i
$250$	−42205.8	+	9781.43i	−0.675292	+	0.156503i
$251$			78270.9i			1.24238i	0.783662	+	0.621188i	$0.213350\pi$
$251$			78270.9i			1.24238i	−0.783662	+	0.621188i	$0.786650\pi$
$252$	10422.6	−	11898.6i	0.164125	−	0.187368i
$253$	−97115.9			−1.51722
$254$	−7377.70	−	31833.9i	−0.114355	−	0.493427i
$255$	−18201.7	+	27337.1i	−0.279918	+	0.420409i
$256$	−16282.8	−	63481.0i	−0.248455	−	0.968643i
$257$	11506.3	−	19929.5i	0.174209	−	0.301739i	−0.765678	−	0.643224i	$-0.777597\pi$
$257$	11506.3	−	19929.5i	0.174209	−	0.301739i	0.939887	+	0.341485i	$0.110930\pi$
$258$	−45151.5	+	37076.8i	−0.678316	+	0.557010i
$259$	−18605.9	+	10742.1i	−0.277365	+	0.160136i
$260$	108452.	+	72886.4i	1.60432	+	1.07820i
$261$	40664.1	+	97273.5i	0.596939	+	1.42795i
$262$	40341.9	+	12296.6i	0.587697	+	0.179136i
$263$	75237.8	−	43438.5i	1.08774	−	0.628006i	0.154765	−	0.987951i	$-0.450538\pi$
$263$	75237.8	−	43438.5i	1.08774	−	0.628006i	0.932973	+	0.359945i	$0.117205\pi$
$264$	26530.2	−	58183.4i	0.380655	−	0.834816i
$265$	−25664.7	+	44452.6i	−0.365464	+	0.633003i
$266$	896.110	+	959.339i	0.0126648	+	0.0135584i
$267$	10483.2	+	669.943i	0.147052	+	0.00939757i
$268$	3927.51	+	267.990i	0.0546824	+	0.00373120i
$269$	−54083.3			−0.747409			−0.373705	−	0.927548i	$-0.621913\pi$
$269$	−54083.3			−0.747409			−0.373705	+	0.927548i	$0.621913\pi$
$270$	−53360.3	+	100689.i	−0.731966	+	1.38119i
$271$		−	47957.3i		−	0.653004i	−0.945197	−	0.326502i	$-0.894130\pi$
$271$		−	47957.3i		−	0.653004i	0.945197	−	0.326502i	$-0.105870\pi$
$272$	14653.8	−	18886.9i	0.198068	−	0.255284i
$273$	1464.05	−	22909.3i	0.0196441	−	0.307388i
$274$	−8807.65	−	9429.11i	−0.117316	−	0.125594i
$275$	86737.8	+	50078.1i	1.14695	+	0.662190i
$276$	−124872.	−	16573.0i	−1.63926	−	0.217562i
$277$	36861.8	+	63846.5i	0.480415	+	0.832103i	0.999748	−	0.0224689i	$-0.00715269\pi$
$277$	36861.8	+	63846.5i	0.480415	+	0.832103i	−0.519332	+	0.854572i	$0.673819\pi$
$278$	−71911.0	−	21919.2i	−0.930477	−	0.283618i
$279$	−44148.8	−	33648.4i	−0.567166	−	0.432271i
$280$	−19270.4	−	23674.4i	−0.245796	−	0.301969i
$281$	−28062.0	−	48604.7i	−0.355390	−	0.615554i	0.631795	−	0.775136i	$-0.282319\pi$
$281$	−28062.0	−	48604.7i	−0.355390	−	0.615554i	−0.987185	+	0.159582i	$0.948985\pi$
$282$	−64236.6	+	52748.9i	−0.807764	+	0.663308i
$283$	132300.	+	76383.2i	1.65191	+	0.953730i	0.976287	+	0.216481i	$0.0694578\pi$
$283$	132300.	+	76383.2i	1.65191	+	0.953730i	0.675621	+	0.737249i	$0.263876\pi$
$284$	32432.9	+	66213.9i	0.402114	+	0.820942i
$285$	−7871.99	−	5241.35i	−0.0969158	−	0.0645288i
$286$	−20952.4	−	90407.1i	−0.256154	−	1.10528i
$287$			953.034i			0.0115703i
$288$	44041.8	−	70285.3i	0.530983	−	0.847383i
$289$	−74801.4			−0.895600
$290$	198210.	−	45936.2i	2.35683	−	0.546210i
$291$	−22920.8	−	46288.4i	−0.270672	−	0.546620i
$292$	36853.2	−	18051.4i	0.432224	−	0.211712i
$293$	19420.1	−	33636.7i	0.226213	−	0.391812i	−0.730470	−	0.682945i	$-0.760699\pi$
$293$	19420.1	−	33636.7i	0.226213	−	0.391812i	0.956683	+	0.291133i	$0.0940322\pi$
$294$	28536.0	−	75885.2i	0.330140	−	0.877935i
$295$	−188297.	+	108713.i	−2.16371	+	1.24922i
$296$	−87370.8	+	71117.8i	−0.997201	+	0.811699i
$297$	76509.1	−	26389.3i	0.867361	−	0.299168i
$298$	8922.21	−	29271.4i	0.100471	−	0.329618i
$299$	−158320.	+	91406.1i	−1.77090	+	1.02243i
$300$	102982.	+	79192.8i	1.14425	+	0.879920i
$301$	9903.82	−	17153.9i	0.109312	−	0.189335i
$302$	3290.85	−	3073.96i	0.0360823	−	0.0337042i
$303$	62249.6	+	125713.i	0.678034	+	1.36928i
$304$	5438.67	+	4219.72i	0.0588498	+	0.0456600i
$305$	−85202.0			−0.915905
$306$	30103.3	−	3023.32i	0.321493	−	0.0322880i
$307$		−	457.528i		−	0.00485446i	−0.999997	−	0.00242723i	$-0.999227\pi$
$307$		−	457.528i		−	0.00485446i	0.999997	−	0.00242723i	$-0.000772612\pi$
$308$	−1475.88	+	21629.7i	−0.0155579	+	0.228008i
$309$	83358.6	+	55502.1i	0.873039	+	0.581290i
$310$	−78283.9	+	73124.3i	−0.814608	+	0.760919i
$311$	9285.82	+	5361.17i	0.0960062	+	0.0554292i	0.547234	−	0.836979i	$-0.315681\pi$
$311$	9285.82	+	5361.17i	0.0960062	+	0.0554292i	−0.451228	+	0.892409i	$0.649014\pi$
$312$	−11512.6	−	119822.i	−0.118267	−	1.23091i
$313$	−8976.10	−	15547.1i	−0.0916218	−	0.158694i	0.816572	−	0.577244i	$-0.195872\pi$
$313$	−8976.10	−	15547.1i	−0.0916218	−	0.158694i	−0.908194	+	0.418550i	$0.862538\pi$
$314$	4095.48	−	13436.2i	0.0415380	−	0.136275i
$315$	4917.87	−	38320.0i	0.0495628	−	0.386193i
$316$	−46232.9	+	68792.9i	−0.462996	+	0.688921i
$317$	30685.9	+	53149.6i	0.305366	+	0.528909i	0.977343	−	0.211663i	$-0.0678879\pi$
$317$	30685.9	+	53149.6i	0.305366	+	0.528909i	−0.671977	+	0.740572i	$0.734555\pi$
$318$	46651.6	−	7716.15i	0.461330	−	0.0763038i
$319$	−125143.	−	72251.6i	−1.22978	−	0.710013i
$320$	−119493.	−	106503.i	−1.16692	−	1.04007i
$321$	2562.80	−	40102.4i	0.0248717	−	0.389189i
$322$	41604.5	−	9642.08i	0.401262	−	0.0929949i
$323$			2510.90i			0.0240672i
$324$	102879.	−	20875.2i	0.980028	−	0.198857i
$325$	188535.			1.78495
$326$	37882.6	+	163459.i	0.356455	+	1.53806i
$327$	42537.7	+	2718.43i	0.397812	+	0.0254228i
$328$	794.236	+	4933.87i	0.00738247	+	0.0458607i
$329$	14090.1	−	24404.7i	0.130173	−	0.225467i
$330$	−25486.6	−	154091.i	−0.234037	−	1.41498i
$331$	160993.	−	92949.3i	1.46944	−	0.848379i	0.470023	−	0.882654i	$-0.344245\pi$
$331$	160993.	−	92949.3i	1.46944	−	0.848379i	0.999412	+	0.0342747i	$0.0109121\pi$
$332$	16719.2	−	24877.5i	0.151684	−	0.225700i
$333$	−141420.	−	18149.5i	−1.27533	−	0.163673i
$334$	−26069.4	−	7946.22i	−0.233689	−	0.0712308i
$335$	8326.81	−	4807.49i	0.0741975	−	0.0428379i
$336$	−5588.85	+	27559.8i	−0.0495044	+	0.244117i
$337$	73998.8	−	128170.i	0.651576	−	1.12856i	−0.331165	−	0.943573i	$-0.607442\pi$
$337$	73998.8	−	128170.i	0.651576	−	1.12856i	0.982741	−	0.184989i	$-0.0592251\pi$
$338$	−41264.1	−	44175.7i	−0.361193	−	0.386678i
$339$	−91509.1	+	137438.i	−0.796279	+	1.19593i
$340$	3974.69	−	58250.9i	0.0343831	−	0.503901i
$341$	76081.3			0.654289
$342$	870.596	+	8668.56i	0.00744328	+	0.0741130i
$343$			56791.2i			0.482717i
$344$	36976.6	−	97059.7i	0.312471	−	0.820204i
$345$	−275716.	+	136527.i	−2.31645	+	1.14705i
$346$	−43000.1	−	46034.1i	−0.359184	−	0.384528i
$347$	−125556.	−	72490.0i	−1.04275	−	0.602031i	−0.122138	−	0.992513i	$-0.538975\pi$
$347$	−125556.	−	72490.0i	−1.04275	−	0.602031i	−0.920611	+	0.390482i	$0.872308\pi$
$348$	−148581.	−	114258.i	−1.22689	−	0.943468i
$349$	89475.8	+	154977.i	0.734606	+	1.27238i	0.954896	+	0.296941i	$0.0959664\pi$
$349$	89475.8	+	154977.i	0.734606	+	1.27238i	−0.220290	+	0.975435i	$0.570700\pi$
$350$	−42130.5	−	12841.8i	−0.343922	−	0.104831i
$351$	99888.6	−	115031.i	0.810778	−	0.933687i
$352$	10385.0	+	113207.i	0.0838150	+	0.913670i
$353$	−13197.7	−	22859.1i	−0.105913	−	0.183446i	0.808198	−	0.588911i	$-0.200443\pi$
$353$	−13197.7	−	22859.1i	−0.105913	−	0.183446i	−0.914111	+	0.405465i	$0.867110\pi$
$354$	187479.	+	70499.8i	1.49605	+	0.562576i
$355$	155955.	+	90040.7i	1.23749	+	0.714467i
$356$	−16771.0	+	8214.76i	−0.132330	+	0.0648179i
$357$	−9192.16	+	4551.72i	−0.0721242	+	0.0357140i
$358$	20317.3	+	87666.9i	0.158526	+	0.684022i
$359$		−	181364.i		−	1.40722i	−0.710587	−	0.703609i	$-0.751571\pi$
$359$		−	181364.i		−	1.40722i	0.710587	−	0.703609i	$-0.248429\pi$
$360$	−6475.02	−	202481.i	−0.0499616	−	1.56236i
$361$	129598.			0.994452
$362$	−85132.6	+	19730.0i	−0.649649	+	0.150560i
$363$	11551.8	−	17349.7i	0.0876672	−	0.131667i
$364$	17952.0	+	36650.2i	0.135491	+	0.276614i
$365$	50114.6	−	86801.1i	0.376165	−	0.651537i
$366$	49810.7	+	60658.5i	0.371844	+	0.452824i
$367$	−181000.	+	104500.i	−1.34383	+	0.775863i	−0.987368	−	0.158445i	$-0.949352\pi$
$367$	−181000.	+	104500.i	−1.34383	+	0.775863i	−0.356467	+	0.934308i	$0.616019\pi$
$368$	207352.	−	84589.4i	1.53113	−	0.624626i
$369$	−3833.93	+	5030.35i	−0.0281573	+	0.0369441i
$370$	−80225.8	+	263199.i	−0.586017	+	1.92257i
$371$	−13883.5	+	8015.67i	−0.100868	+	0.0582360i
$372$	97826.1	+	12983.4i	0.706918	+	0.0938216i
$373$	38298.0	−	66334.0i	0.275269	−	0.476781i	−0.694934	−	0.719074i	$-0.744566\pi$
$373$	38298.0	−	66334.0i	0.275269	−	0.476781i	0.970203	+	0.242293i	$0.0778996\pi$
$374$	−30303.3	+	28306.0i	−0.216644	+	0.202365i
$375$	97281.4	+	6216.91i	0.691779	+	0.0442092i
$376$	52606.3	−	138086.i	0.372102	−	0.976729i
$377$	−272015.			−1.91386
$378$	−30156.5	+	18901.3i	−0.211056	+	0.132285i
$379$		−	232118.i		−	1.61596i	−0.589211	−	0.807979i	$-0.700561\pi$
$379$		−	232118.i		−	1.61596i	0.589211	−	0.807979i	$-0.299439\pi$
$380$	16773.9	+	1144.55i	0.116163	+	0.00792625i
$381$	−4689.14	+	73375.1i	−0.0323030	+	0.505474i
$382$	−54620.0	+	51020.0i	−0.374304	+	0.349634i
$383$	−74119.1	−	42792.7i	−0.505280	−	0.291724i	0.225611	−	0.974217i	$-0.427562\pi$
$383$	−74119.1	−	42792.7i	−0.505280	−	0.291724i	−0.730891	+	0.682494i	$0.760895\pi$
$384$	−5965.85	+	147335.i	−0.0404585	+	0.999181i
$385$	26476.0	+	45857.7i	0.178620	+	0.309379i
$386$	−53764.1	+	176386.i	−0.360842	+	1.18383i
$387$	121283.	−	50700.8i	0.809798	−	0.338527i
$388$	76214.1	+	51220.4i	0.506258	+	0.340236i
$389$	−60869.2	−	105429.i	−0.402252	−	0.696721i	0.591745	−	0.806125i	$-0.298439\pi$
$389$	−60869.2	−	105429.i	−0.402252	−	0.696721i	−0.993997	+	0.109404i	$0.965106\pi$
$390$	−186581.	−	227214.i	−1.22670	−	1.49385i
$391$	70741.7	+	40842.8i	0.462724	+	0.267154i
$392$	22906.6	+	142298.i	0.149069	+	0.926035i
$393$	−78985.8	−	52590.6i	−0.511404	−	0.340505i
$394$	62092.9	−	14390.4i	0.399990	−	0.0927001i
$395$			202441.i			1.29749i
$396$	−94803.5	+	108230.i	−0.604552	+	0.690169i
$397$	−71690.8			−0.454865			−0.227432	−	0.973794i	$-0.573033\pi$
$397$	−71690.8			−0.454865			−0.227432	+	0.973794i	$0.573033\pi$
$398$	66588.0	+	287320.i	0.420368	+	1.81384i
$399$	−1310.71	−	2646.97i	−0.00823306	−	0.0166266i
$400$	−228812.	−	31371.6i	−1.43008	−	0.196073i
$401$	43140.3	−	74721.1i	0.268283	−	0.464681i	−0.700135	−	0.714010i	$-0.746877\pi$
$401$	43140.3	−	74721.1i	0.268283	−	0.464681i	0.968419	+	0.249330i	$0.0802103\pi$
$402$	−8290.64	−	3117.62i	−0.0513022	−	0.0192917i
$403$	124029.	−	71608.3i	0.763684	−	0.440913i
$404$	−206987.	−	139107.i	−1.26818	−	0.852291i
$405$	180114.	−	182478.i	1.09809	−	1.11250i
$406$	60785.0	+	18527.9i	0.368761	+	0.112402i
$407$	169239.	−	97710.0i	1.02167	−	0.589862i
$408$	−43794.7	+	31224.8i	−0.263088	+	0.187577i
$409$	−115231.	+	199585.i	−0.688844	+	1.19311i	0.283368	+	0.959011i	$0.408548\pi$
$409$	−115231.	+	199585.i	−0.688844	+	1.19311i	−0.972212	+	0.234102i	$0.924785\pi$
$410$	8331.84	+	8919.73i	0.0495648	+	0.0530620i
$411$	12882.7	+	26016.5i	0.0762645	+	0.154016i
$412$	−177624.	−	12120.0i	−1.04642	−	0.0714015i
$413$	−67907.1			−0.398121
$414$	258387.	+	116476.i	1.50755	+	0.679573i
$415$		−	73208.6i		−	0.425075i
$416$	123481.	+	174778.i	0.713534	+	1.00995i
$417$	140795.	+	93744.8i	0.809685	+	0.539107i
$418$	−8150.99	−	8726.12i	−0.0466507	−	0.0499423i
$419$	−48172.3	−	27812.3i	−0.274391	−	0.158420i	0.356491	−	0.934299i	$-0.383973\pi$
$419$	−48172.3	−	27812.3i	−0.274391	−	0.158420i	−0.630881	+	0.775879i	$0.717307\pi$
$420$	26217.3	+	63482.4i	0.148624	+	0.359878i
$421$	−70485.7	−	122085.i	−0.397683	−	0.688807i	0.595757	−	0.803165i	$-0.296852\pi$
$421$	−70485.7	−	122085.i	−0.397683	−	0.688807i	−0.993440	+	0.114358i	$0.963519\pi$
$422$	−68176.8	−	20781.0i	−0.382835	−	0.116692i
$423$	172548.	−	72131.7i	0.964337	−	0.403130i
$424$	−65195.3	+	53067.4i	−0.362647	+	0.295186i
$425$	−42121.4	−	72956.4i	−0.233198	−	0.403911i
$426$	−27070.9	−	163670.i	−0.149171	−	0.901881i
$427$	−23045.4	−	13305.2i	−0.126394	−	0.0729738i
$428$	31424.7	+	64155.7i	0.171547	+	0.350225i
$429$	−13317.0	+	208382.i	−0.0723588	+	1.13226i
$430$	−57274.3	−	247132.i	−0.309758	−	1.33657i
$431$			191015.i			1.02828i	0.857705	+	0.514142i	$0.171889\pi$
$431$			191015.i			1.02828i	−0.857705	+	0.514142i	$0.828111\pi$
$432$	−140369.	+	122984.i	−0.752147	+	0.658995i
$433$	48243.4			0.257313			0.128657	−	0.991689i	$-0.458933\pi$
$433$	48243.4			0.257313			0.128657	+	0.991689i	$0.458933\pi$
$434$	−32593.3	+	7553.68i	−0.173041	+	0.0401032i
$435$	−456860.	−	29196.3i	−2.41437	−	0.154294i
$436$	−68051.7	+	33333.1i	−0.357986	+	0.175349i
$437$	−11761.1	+	20370.8i	−0.0615863	+	0.106671i
$438$	−91094.9	+	15067.0i	−0.474838	+	0.0785380i
$439$	−227081.	+	131105.i	−1.17829	+	0.680285i	−0.955618	−	0.294609i	$-0.904811\pi$
$439$	−227081.	+	131105.i	−1.17829	+	0.680285i	−0.222670	+	0.974894i	$0.571477\pi$
$440$	175283.	+	215342.i	0.905388	+	1.11230i
$441$	−110575.	+	145081.i	−0.568562	+	0.745988i
$442$	−22759.1	+	74666.6i	−0.116496	+	0.382192i
$443$	78793.6	−	45491.5i	0.401498	−	0.231805i	−0.285632	−	0.958339i	$-0.592204\pi$
$443$	78793.6	−	45491.5i	0.401498	−	0.231805i	0.687130	+	0.726534i	$0.258870\pi$
$444$	234283.	−	96755.6i	1.18843	−	0.490806i
$445$	−22805.9	+	39501.0i	−0.115167	+	0.199475i
$446$	196963.	−	183981.i	0.990181	−	0.924920i
$447$	−38158.9	+	57310.8i	−0.190977	+	0.286828i
$448$	−15688.7	−	47467.0i	−0.0781681	−	0.236503i
$449$	283350.			1.40550			0.702748	−	0.711438i	$-0.251956\pi$
$449$	283350.			1.40550			0.702748	+	0.711438i	$0.251956\pi$
$450$	−170714.	−	237267.i	−0.843033	−	1.17169i
$451$		−	8668.77i		−	0.0426191i
$452$	19982.8	−	292857.i	0.0978091	−	1.43344i
$453$	−9080.00	+	4496.18i	−0.0442476	+	0.0219102i
$454$	183555.	−	171457.i	0.890542	−	0.831848i
$455$	86323.1	+	49838.7i	0.416970	+	0.240737i
$456$	−8991.50	−	12611.1i	−0.0432417	−	0.0606490i
$457$	−99226.7	−	171866.i	−0.475112	−	0.822918i	0.524482	−	0.851422i	$-0.324259\pi$
$457$	−99226.7	−	171866.i	−0.475112	−	0.822918i	−0.999594	+	0.0285035i	$0.990926\pi$
$458$	47730.9	−	156592.i	0.227546	−	0.746517i
$459$	−66829.4	−	12953.8i	−0.317207	−	0.0614852i
$460$	305094.	−	453968.i	1.44184	−	2.14541i
$461$	104347.	+	180735.i	0.490998	+	0.850433i	0.999946	−	0.0103639i	$-0.00329898\pi$
$461$	104347.	+	180735.i	0.490998	+	0.850433i	−0.508949	+	0.860797i	$0.669966\pi$
$462$	17169.5	−	45658.5i	0.0804402	−	0.213913i
$463$	22687.9	+	13098.9i	0.105836	+	0.0611044i	0.551984	−	0.833855i	$-0.313871\pi$
$463$	22687.9	+	13098.9i	0.105836	+	0.0611044i	−0.446148	+	0.894959i	$0.647204\pi$
$464$	330126.	+	45262.3i	1.53336	+	0.210233i
$465$	215998.	−	106957.i	0.998950	−	0.494654i
$466$	308833.	−	71573.7i	1.42217	−	0.329596i
$467$			96607.8i			0.442974i	0.975163	+	0.221487i	$0.0710911\pi$
$467$			96607.8i			0.442974i	−0.975163	+	0.221487i	$0.928909\pi$
$468$	−52683.9	+	265667.i	−0.240539	+	1.21296i
$469$	3002.97			0.0136523
$470$	−81483.6	−	351593.i	−0.368871	−	1.59164i
$471$	−17515.7	+	26306.9i	−0.0789562	+	0.118584i
$472$	−351556.	+	56592.1i	−1.57801	+	0.254022i
$473$	−90084.9	+	156032.i	−0.402652	+	0.697413i
$474$	144126.	−	118351.i	0.641482	−	0.526763i
$475$	21008.5	−	12129.3i	0.0931125	−	0.0537585i
$476$	10171.6	−	15135.0i	0.0448926	−	0.0667986i
$477$	−105527.	−	13543.0i	−0.463794	−	0.0595220i
$478$	−172681.	−	52634.7i	−0.755767	−	0.230365i
$479$	29664.3	−	17126.7i	0.129289	−	0.0746453i	−0.433960	−	0.900932i	$-0.642884\pi$
$479$	29664.3	−	17126.7i	0.129289	−	0.0746453i	0.563250	+	0.826287i	$0.309551\pi$
$480$	188632.	+	306801.i	0.818717	+	1.33160i
$481$	183931.	−	318577.i	0.794994	−	1.37697i
$482$	−206569.	−	221144.i	−0.889141	−	0.951878i
$483$	−95895.6	−	6128.35i	−0.411059	−	0.0262693i
$484$	−2522.57	+	36969.4i	−0.0107684	+	0.157816i
$485$	224280.			0.953470
$486$	−235211.	−	21549.6i	−0.995829	−	0.0912362i
$487$		−	69521.4i		−	0.293130i	−0.989201	−	0.146565i	$-0.953178\pi$
$487$		−	69521.4i		−	0.293130i	0.989201	−	0.146565i	$-0.0468218\pi$
$488$	−130394.	−	49676.0i	−0.547545	−	0.208597i
$489$	24077.6	−	376762.i	0.100692	−	1.57561i
$490$	240299.	+	257255.i	1.00083	+	1.07145i
$491$	174305.	+	100635.i	0.723016	+	0.417433i	0.815862	−	0.578247i	$-0.196263\pi$
$491$	174305.	+	100635.i	0.723016	+	0.417433i	−0.0928458	+	0.995681i	$0.529596\pi$
$492$	1479.34	−	11146.4i	0.00611136	−	0.0460473i
$493$	60771.9	+	105260.i	0.250040	+	0.433081i
$494$	−21501.0	−	6553.71i	−0.0881057	−	0.0268555i
$495$	−44732.8	+	348557.i	−0.182564	+	1.42254i
$496$	−162441.	+	66268.0i	−0.660286	+	0.269365i
$497$	28121.7	+	48708.2i	0.113849	+	0.197192i
$498$	−52120.0	+	42799.1i	−0.210158	+	0.172574i
$499$	−46850.8	−	27049.3i	−0.188155	−	0.108631i	0.402964	−	0.915216i	$-0.367980\pi$
$499$	−46850.8	−	27049.3i	−0.188155	−	0.108631i	−0.591119	+	0.806585i	$0.701313\pi$
$500$	−155631.	+	76231.0i	−0.622522	+	0.304924i
$501$	51041.7	+	33984.7i	0.203352	+	0.135397i
$502$	70685.5	+	305000.i	0.280493	+	1.21030i
$503$		−	239548.i		−	0.946795i	−0.880849	−	0.473397i	$-0.843027\pi$
$503$		−	239548.i		−	0.946795i	0.880849	−	0.473397i	$-0.156973\pi$
$504$	29868.4	−	55778.1i	0.117585	−	0.219585i
$505$	−609113.			−2.38844
$506$	−378433.	+	87704.1i	−1.47805	+	0.342546i
$507$	60355.7	+	121888.i	0.234802	+	0.474181i
$508$	−57497.6	−	117385.i	−0.222804	−	0.454869i
$509$	−57738.0	+	100005.i	−0.222857	+	0.386000i	−0.955674	−	0.294426i	$-0.904872\pi$
$509$	−57738.0	+	100005.i	−0.222857	+	0.386000i	0.732817	+	0.680425i	$0.238205\pi$
$510$	−46239.1	+	122963.i	−0.177774	+	0.472752i
$511$	27109.9	−	15651.9i	0.103821	−	0.0599412i
$512$	−120778.	−	232663.i	−0.460733	−	0.887539i
$513$	3730.16	−	19244.2i	0.0141740	−	0.0731248i
$514$	26838.8	−	88051.1i	0.101587	−	0.333279i
$515$	−376584.	+	217421.i	−1.41987	+	0.819761i
$516$	−142459.	+	185254.i	−0.535045	+	0.695773i
$517$	−128163.	+	221985.i	−0.479492	+	0.830505i
$518$	−62800.9	+	58661.8i	−0.234049	+	0.218623i
$519$	62894.8	+	127016.i	0.233496	+	0.471545i
$520$	488431.	+	186076.i	1.80633	+	0.688151i
$521$	217267.			0.800420			0.400210	−	0.916424i	$-0.368937\pi$
$521$	217267.			0.800420			0.400210	+	0.916424i	$0.368937\pi$
$522$	246303.	+	342324.i	0.903917	+	1.25631i
$523$			39683.4i			0.145079i	0.997366	+	0.0725397i	$0.0231104\pi$
$523$			39683.4i			0.145079i	−0.997366	+	0.0725397i	$0.976890\pi$
$524$	168306.	+	11484.2i	0.612967	+	0.0418251i
$525$	82487.8	+	54922.3i	0.299275	+	0.199265i
$526$	253952.	−	237214.i	0.917867	−	0.857372i
$527$	−55419.6	−	31996.5i	−0.199546	−	0.115208i
$528$	50836.0	−	250683.i	0.182349	−	0.899203i
$529$	242694.	+	420359.i	0.867258	+	1.50213i
$530$	−59863.7	+	196397.i	−0.213114	+	0.699170i
$531$	−358430.	−	273181.i	−1.27120	−	0.968861i
$532$	4358.26	+	2929.01i	0.0153989	+	0.0103490i
$533$	−8159.11	−	14132.0i	−0.0287202	−	0.0497449i
$534$	41455.1	−	6856.65i	0.145377	−	0.0240452i
$535$	151107.	+	87241.9i	0.527932	+	0.304802i
$536$	15546.4	−	2502.60i	0.0541129	−	0.00871089i
$537$	12913.3	−	202066.i	0.0447806	−	0.700721i
$538$	−210747.	+	48841.9i	−0.728111	+	0.168744i
$539$		−	250017.i		−	0.860580i
$540$	−117000.	+	440545.i	−0.401234	+	1.51078i
$541$	−194992.			−0.666228			−0.333114	−	0.942887i	$-0.608099\pi$
$541$	−194992.			−0.666228			−0.333114	+	0.942887i	$0.608099\pi$
$542$	−43309.6	−	186876.i	−0.147430	−	0.636143i
$543$	196225.	+	12540.0i	0.665510	+	0.0425304i
$544$	40045.4	−	86830.7i	0.135318	−	0.293410i
$545$	−92539.8	+	160284.i	−0.311556	+	0.539630i
$546$	−14984.1	−	90593.3i	−0.0502626	−	0.303886i
$547$	−81637.9	+	47133.6i	−0.272846	+	0.157527i	−0.630180	−	0.776449i	$-0.717019\pi$
$547$	−81637.9	+	47133.6i	−0.272846	+	0.157527i	0.357335	+	0.933976i	$0.383686\pi$
$548$	−42836.3	−	28788.5i	−0.142643	−	0.0958647i
$549$	−68113.8	−	162937.i	−0.225991	−	0.540598i
$550$	383218.	+	116809.i	1.26684	+	0.386144i
$551$	−30310.6	+	17499.9i	−0.0998371	+	0.0576410i
$552$	−501560.	+	48190.5i	−1.64606	+	0.158155i
$553$	−31613.4	+	54756.1i	−0.103376	+	0.179053i
$554$	201299.	+	215502.i	0.655876	+	0.702154i
$555$	343113.	−	515321.i	1.11391	−	1.67299i
$556$	−300012.	−	20471.0i	−0.970485	−	0.0662201i
$557$	−563587.			−1.81656			−0.908282	−	0.418358i	$-0.862606\pi$
$557$	−563587.			−1.81656			−0.908282	+	0.418358i	$0.862606\pi$
$558$	−202423.	−	91248.3i	−0.650116	−	0.293060i
$559$			339154.i			1.08536i
$560$	−96471.5	−	74849.6i	−0.307626	−	0.238679i
$561$	83611.6	−	41402.3i	0.265669	−	0.131552i
$562$	−153244.	−	164057.i	−0.485189	−	0.519423i
$563$	543509.	+	313795.i	1.71471	+	0.989986i	0.927935	+	0.372741i	$0.121582\pi$
$563$	543509.	+	313795.i	1.71471	+	0.989986i	0.786771	+	0.617245i	$0.211751\pi$
$564$	−202675.	+	263559.i	−0.637151	+	0.828552i
$565$	−358473.	−	620894.i	−1.12295	−	1.94500i
$566$	584516.	+	178166.i	1.82458	+	0.556150i
$567$	77213.0	−	21229.7i	0.240173	−	0.0660356i
$568$	186179.	+	228727.i	0.577077	+	0.708959i
$569$	38859.9	+	67307.3i	0.120026	+	0.207892i	0.919778	−	0.392439i	$-0.128369\pi$
$569$	38859.9	+	67307.3i	0.120026	+	0.207892i	−0.799751	+	0.600331i	$0.795035\pi$
$570$	−35408.3	−	13315.0i	−0.108982	−	0.0409818i
$571$	276094.	+	159403.i	0.846809	+	0.488905i	0.859573	−	0.511013i	$-0.170730\pi$
$571$	276094.	+	159403.i	0.846809	+	0.488905i	−0.0127640	+	0.999919i	$0.504063\pi$
$572$	−163291.	−	333370.i	−0.499080	−	1.01891i
$573$	150705.	−	74625.4i	0.459007	−	0.227288i
$574$	860.673	+	3713.71i	0.00261225	+	0.0112716i
$575$		−	789186.i		−	2.38695i
$576$	108145.	−	313656.i	0.325958	−	0.945384i
$577$	40053.7			0.120307			0.0601534	−	0.998189i	$-0.480841\pi$
$577$	40053.7			0.120307			0.0601534	+	0.998189i	$0.480841\pi$
$578$	−291480.	+	67552.2i	−0.872475	+	0.202201i
$579$	229940.	−	345348.i	0.685896	−	1.03015i
$580$	730883.	−	358001.i	2.17266	−	1.06421i
$581$	11432.3	−	19801.4i	0.0338675	−	0.0586602i
$582$	−131118.	−	159673.i	−0.387095	−	0.471397i
$583$	126284.	−	72910.3i	0.371546	−	0.214512i
$584$	127304.	−	103623.i	0.373266	−	0.303830i
$585$	255140.	+	610327.i	0.745533	+	1.78341i
$586$	45298.0	−	148611.i	0.131912	−	0.432768i
$587$	11894.5	−	6867.28i	0.0345199	−	0.0199301i	−0.482641	−	0.875818i	$-0.660322\pi$
$587$	11894.5	−	6867.28i	0.0345199	−	0.0199301i	0.517161	+	0.855888i	$0.326989\pi$
$588$	42665.7	−	321474.i	0.123403	−	0.929803i
$589$	9213.72	−	15958.6i	0.0265586	−	0.0460008i
$590$	−635563.	+	593673.i	−1.82580	+	1.70547i
$591$	−143120.	−	9146.29i	−0.409756	−	0.0261861i
$592$	−276234.	+	356030.i	−0.788195	+	1.01588i
$593$	537582.			1.52875			0.764373	−	0.644775i	$-0.223049\pi$
$593$	537582.			1.52875			0.764373	+	0.644775i	$0.223049\pi$
$594$	274303.	−	171926.i	0.777422	−	0.487269i
$595$		−	44538.6i		−	0.125806i
$596$	8332.74	−	122120.i	0.0234582	−	0.343791i
$597$	42322.3	−	662253.i	0.118746	−	1.85813i
$598$	−534381.	+	499161.i	−1.49434	+	1.39585i
$599$	−394401.	−	227708.i	−1.09922	−	0.634635i	−0.163204	−	0.986592i	$-0.552183\pi$
$599$	−394401.	−	227708.i	−1.09922	−	0.634635i	−0.936016	+	0.351958i	$0.885516\pi$
$600$	472812.	+	215590.i	1.31337	+	0.598862i
$601$	118996.	+	206108.i	0.329446	+	0.570618i	0.982402	−	0.186778i	$-0.0598046\pi$
$601$	118996.	+	206108.i	0.329446	+	0.570618i	−0.652956	+	0.757396i	$0.726471\pi$
$602$	23100.9	−	75788.0i	0.0637436	−	0.209126i
$603$	15850.4	+	12080.5i	0.0435919	+	0.0332240i
$604$	10047.5	−	14950.3i	0.0275412	−	0.0409803i
$605$	45252.5	+	78379.7i	0.123632	+	0.214137i
$606$	356099.	+	433650.i	0.969673	+	1.18085i
$607$	−516142.	−	297995.i	−1.40085	−	0.808781i	−0.406371	−	0.913708i	$-0.633206\pi$
$607$	−516142.	−	297995.i	−1.40085	−	0.808781i	−0.994480	+	0.104927i	$0.966539\pi$
$608$	25003.7	+	11531.5i	0.0676391	+	0.0311945i
$609$	−119012.	−	79240.7i	−0.320889	−	0.213655i
$610$	−332008.	+	76944.8i	−0.892256	+	0.206785i
$611$			482511.i			1.29248i
$612$	114574.	−	38967.0i	0.305903	−	0.104038i
$613$	547275.			1.45641			0.728206	−	0.685358i	$-0.240354\pi$
$613$	547275.			1.45641			0.728206	+	0.685358i	$0.240354\pi$
$614$	−413.188	−	1782.86i	−0.00109600	−	0.00472912i
$615$	−12186.7	−	24611.0i	−0.0322208	−	0.0650697i
$616$	13782.4	+	85617.8i	0.0363215	+	0.225633i
$617$	−259077.	+	448735.i	−0.680549	+	1.17874i	0.294265	+	0.955724i	$0.404925\pi$
$617$	−259077.	+	448735.i	−0.680549	+	1.17874i	−0.974814	+	0.223021i	$0.928408\pi$
$618$	374949.	+	140996.i	0.981736	+	0.369173i
$619$	−176869.	+	102115.i	−0.461605	+	0.266508i	−0.712719	−	0.701450i	$-0.752537\pi$
$619$	−176869.	+	102115.i	−0.461605	+	0.266508i	0.251114	+	0.967958i	$0.419203\pi$
$620$	−239013.	+	355642.i	−0.621781	+	0.925187i
$621$	−481507.	−	418122.i	−1.24859	−	1.08423i
$622$	41025.8	+	12505.1i	0.106042	+	0.0323226i
$623$	−12337.1	+	7122.80i	−0.0317860	+	0.0183516i
$624$	−153071.	−	456516.i	−0.393119	−	1.17243i
$625$	70291.3	−	121748.i	0.179946	−	0.311675i
$626$	−49017.7	−	52476.4i	−0.125085	−	0.133911i
$627$	11922.2	+	24076.8i	0.0303264	+	0.0612440i
$628$	3824.90	−	56055.6i	0.00969841	−	0.142135i
$629$	−164370.			−0.415454
$630$	−15442.7	−	153763.i	−0.0389083	−	0.387411i
$631$		−	177036.i		−	0.444633i	−0.974975	−	0.222317i	$-0.928638\pi$
$631$		−	177036.i		−	0.444633i	0.974975	−	0.222317i	$-0.0713618\pi$
$632$	−118031.	+	309819.i	−0.295503	+	0.775665i
$633$	133484.	+	88876.8i	0.333137	+	0.221810i
$634$	167573.	+	179397.i	0.416894	+	0.446310i
$635$	−276480.	−	159626.i	−0.685672	−	0.395873i
$636$	174820.	−	72198.1i	0.432192	−	0.178489i
$637$	−235317.	−	407582.i	−0.579929	−	1.00447i
$638$	−552899.	−	168529.i	−1.35833	−	0.414031i
$639$	−47513.4	+	370224.i	−0.116363	+	0.906698i
$640$	−561812.	−	307101.i	−1.37161	−	0.749758i
$641$	−109444.	−	189562.i	−0.266364	−	0.461356i	0.701556	−	0.712614i	$-0.252489\pi$
$641$	−109444.	−	189562.i	−0.266364	−	0.461356i	−0.967920	+	0.251258i	$0.919156\pi$
$642$	−26229.4	−	158582.i	−0.0636383	−	0.384755i
$643$	−298938.	−	172592.i	−0.723035	−	0.417445i	0.0928336	−	0.995682i	$-0.470408\pi$
$643$	−298938.	−	172592.i	−0.723035	−	0.417445i	−0.815869	+	0.578237i	$0.803741\pi$
$644$	153413.	−	75145.0i	0.369906	−	0.181187i
$645$	−36402.6	+	569623.i	−0.0875009	+	1.36920i
$646$	2267.56	+	9784.29i	0.00543369	+	0.0234458i
$647$			398251.i			0.951366i	0.879617	+	0.475683i	$0.157799\pi$
$647$			398251.i			0.951366i	−0.879617	+	0.475683i	$0.842201\pi$
$648$	382040.	−	174254.i	0.909828	−	0.414985i
$649$	617681.			1.46648
$650$	734669.	−	170264.i	1.73886	−	0.402991i
$651$	75125.4	+	4801.00i	0.177266	+	0.0113284i
$652$	295236.	+	602744.i	0.694502	+	1.41787i
$653$	171144.	−	296430.i	0.401361	−	0.695178i	−0.592529	−	0.805549i	$-0.701871\pi$
$653$	171144.	−	296430.i	0.401361	−	0.695178i	0.993890	+	0.110371i	$0.0352040\pi$
$654$	168212.	−	27822.3i	0.393281	−	0.0650484i
$655$	356830.	−	206016.i	0.831722	−	0.480195i
$656$	7550.63	+	18508.7i	0.0175459	+	0.0430098i
$657$	206058.	+	26444.9i	0.477374	+	0.0612648i
$658$	32865.5	−	107823.i	0.0759082	−	0.249035i
$659$	452868.	−	261464.i	1.04280	−	0.602061i	0.122175	−	0.992509i	$-0.461013\pi$
$659$	452868.	−	261464.i	1.04280	−	0.602061i	0.920625	+	0.390447i	$0.127680\pi$
$660$	−238472.	−	577434.i	−0.547457	−	1.32561i
$661$	−154294.	+	267245.i	−0.353140	+	0.611656i	−0.986798	−	0.161957i	$-0.948219\pi$
$661$	−154294.	+	267245.i	−0.353140	+	0.611656i	0.633658	+	0.773613i	$0.281553\pi$
$662$	543403.	−	507588.i	1.23996	−	1.15823i
$663$	97337.1	−	146191.i	0.221438	−	0.332577i
$664$	42683.4	−	112040.i	0.0968106	−	0.254118i
$665$	12825.3			0.0290018
$666$	−567467.	+	56991.5i	−1.27936	+	0.128488i
$667$			1.13862e6i			2.55934i
$668$	−108761.	−	7421.23i	−0.243737	−	0.0166312i
$669$	−543453.	+	269104.i	−1.21425	+	0.601267i
$670$	28105.7	−	26253.3i	0.0626101	−	0.0584836i
$671$	209620.	+	121024.i	0.465573	+	0.268798i
$672$	3110.75	+	112440.i	0.00688853	+	0.248991i
$673$	124260.	+	215225.i	0.274348	+	0.475184i	0.969970	−	0.243223i	$-0.0782047\pi$
$673$	124260.	+	215225.i	0.274348	+	0.475184i	−0.695623	+	0.718407i	$0.744871\pi$
$674$	172604.	−	566269.i	0.379955	−	1.24653i
$675$	214446.	+	621730.i	0.470663	+	1.36457i
$676$	−200689.	−	134875.i	−0.439168	−	0.295147i
$677$	−134761.	−	233413.i	−0.294027	−	0.509270i	0.680731	−	0.732533i	$-0.261662\pi$
$677$	−134761.	−	233413.i	−0.294027	−	0.509270i	−0.974758	+	0.223264i	$0.928329\pi$
$678$	−232467.	+	618197.i	−0.505711	+	1.34483i
$679$	60663.0	+	35023.8i	0.131578	+	0.0759668i
$680$	−37117.4	−	230577.i	−0.0802712	−	0.498653i
$681$	−506458.	+	250785.i	−1.09207	+	0.540763i
$682$	296468.	−	68708.1i	0.637395	−	0.147720i
$683$			124482.i			0.266848i	0.991059	+	0.133424i	$0.0425972\pi$
$683$			124482.i			0.266848i	−0.991059	+	0.133424i	$0.957403\pi$
$684$	11220.9	+	32992.7i	0.0239837	+	0.0705190i
$685$	−126057.			−0.268649
$686$	51287.4	+	221300.i	0.108984	+	0.470254i
$687$	−204137.	+	306594.i	−0.432523	+	0.649606i
$688$	56434.0	−	411608.i	0.119224	−	0.869574i
$689$	137247.	−	237719.i	0.289111	−	0.500756i
$690$	−951091.	+	781004.i	−1.99767	+	1.64042i
$691$	771402.	−	445369.i	1.61557	−	0.932747i	0.627518	−	0.778602i	$-0.284071\pi$
$691$	771402.	−	445369.i	1.61557	−	0.932747i	0.988048	−	0.154145i	$-0.0492623\pi$
$692$	−209132.	−	140549.i	−0.436726	−	0.293506i
$693$	−66530.4	+	87291.9i	−0.138533	+	0.181764i
$694$	−554723.	−	169085.i	−1.15175	−	0.351064i
$695$	−636063.	+	367231.i	−1.31683	+	0.760274i
$696$	−682163.	−	311049.i	−1.40822	−	0.642112i
$697$	−3645.71	+	6314.56i	−0.00750442	+	0.0129980i
$698$	488619.	+	523096.i	1.00291	+	1.07367i
$699$	−711839.	−	45491.1i	−1.45689	−	0.0931048i
$700$	−175768.	−	11993.3i	−0.358710	−	0.0244762i
$701$	−170934.			−0.347851			−0.173925	−	0.984759i	$-0.555645\pi$
$701$	−170934.			−0.347851			−0.173925	+	0.984759i	$0.555645\pi$
$702$	285355.	−	538452.i	0.579044	−	1.09263i
$703$		−	47332.1i		−	0.0957734i
$704$	142704.	+	431759.i	0.287932	+	0.871156i
$705$	−51789.7	+	810398.i	−0.104199	+	1.63050i
$706$	−72071.4	−	77156.7i	−0.144595	−	0.154798i
$707$	−164752.	−	95119.7i	−0.329604	−	0.190297i
$708$	794220.	+	105408.i	1.58443	+	0.210285i
$709$	350963.	+	607886.i	0.698183	+	1.20929i	0.969096	+	0.246684i	$0.0793410\pi$
$709$	350963.	+	607886.i	0.698183	+	1.20929i	−0.270913	+	0.962604i	$0.587326\pi$
$710$	689028.	+	210022.i	1.36685	+	0.416628i
$711$	−387140.	+	161839.i	−0.765823	+	0.320144i
$712$	−57933.2	+	47156.3i	−0.114279	+	0.0930206i
$713$	−299744.	−	519171.i	−0.589618	−	1.02125i
$714$	−31708.7	+	26038.1i	−0.0621988	+	0.0510755i
$715$	−785193.	−	453331.i	−1.53590	−	0.886755i
$716$	158342.	+	323265.i	0.308866	+	0.630570i
$717$	338093.	+	225110.i	0.657655	+	0.437882i
$718$	−163787.	−	706724.i	−0.317710	−	1.37088i
$719$			768366.i			1.48631i	0.669117	+	0.743157i	$0.266672\pi$
$719$			768366.i			1.48631i	−0.669117	+	0.743157i	$0.733328\pi$
$720$	−208090.	−	783166.i	−0.401408	−	1.51074i
$721$	−135811.			−0.261255
$722$	505007.	−	117038.i	0.968775	−	0.224519i
$723$	302141.	+	610173.i	0.578008	+	1.16728i
$724$	−313920.	+	153764.i	−0.598883	+	0.293345i
$725$	587133.	−	1.01695e6i	1.11702	−	1.93473i
$726$	29346.0	−	78039.2i	0.0556769	−	0.148061i
$727$	221493.	−	127879.i	0.419074	−	0.241952i	−0.275607	−	0.961270i	$-0.588879\pi$
$727$	221493.	−	127879.i	0.419074	−	0.241952i	0.694681	+	0.719318i	$0.255546\pi$
$728$	103052.	+	126604.i	0.194444	+	0.238882i
$729$	492953.	+	198562.i	0.927578	+	0.373629i
$730$	116894.	−	383497.i	0.219354	−	0.719642i
$731$	131240.	−	75771.6i	0.245602	−	0.141799i
$732$	248878.	+	191386.i	0.464478	+	0.357181i
$733$	−184829.	+	320133.i	−0.344003	+	0.595831i	−0.985172	−	0.171569i	$-0.945116\pi$
$733$	−184829.	+	320133.i	−0.344003	+	0.595831i	0.641169	+	0.767400i	$0.278450\pi$
$734$	−610932.	+	570667.i	−1.13397	+	1.05923i
$735$	−351478.	−	709807.i	−0.650614	−	1.31391i
$736$	731600.	−	516878.i	1.35057	−	0.954184i
$737$	−27314.9			−0.0502881
$738$	−10396.9	+	23064.2i	−0.0190894	+	0.0423474i
$739$		−	1.03557e6i		−	1.89623i	−0.317932	−	0.948114i	$-0.602988\pi$
$739$		−	1.03557e6i		−	1.89623i	0.317932	−	0.948114i	$-0.397012\pi$
$740$	−74925.4	+	1.09807e6i	−0.136825	+	2.00523i
$741$	42097.0	+	28029.2i	0.0766681	+	0.0510474i
$742$	−46861.4	+	43772.9i	−0.0851153	+	0.0795055i
$743$	−486002.	−	280593.i	−0.880360	−	0.508276i	−0.00958322	−	0.999954i	$-0.503050\pi$
$743$	−486002.	−	280593.i	−0.880360	−	0.508276i	−0.870777	+	0.491678i	$0.836384\pi$
$744$	392926.	−	37752.8i	0.709848	−	0.0682030i
$745$	−149482.	−	258910.i	−0.269324	−	0.466483i
$746$	89331.1	−	293072.i	0.160518	−	0.526618i
$747$	140001.	−	58525.8i	0.250894	−	0.104883i
$748$	−92520.5	+	137667.i	−0.165362	+	0.246052i
$749$	27247.6	+	47194.2i	0.0485696	+	0.0841250i
$750$	384693.	−	63628.0i	0.683899	−	0.113117i
$751$	164898.	+	95204.1i	0.292372	+	0.168801i	0.639011	−	0.769197i	$-0.279344\pi$
$751$	164898.	+	95204.1i	0.292372	+	0.168801i	−0.346639	+	0.937999i	$0.612677\pi$
$752$	80288.2	−	585591.i	0.141976	−	1.03552i
$753$	44926.5	−	703004.i	0.0792342	−	1.23985i
$754$	−1.05997e6	+	245653.i	−1.86444	+	0.432095i
$755$		−	43995.1i		−	0.0771810i
$756$	−100442.	+	100887.i	−0.175740	+	0.176519i
$757$	523077.			0.912797			0.456398	−	0.889776i	$-0.349139\pi$
$757$	523077.			0.912797			0.456398	+	0.889776i	$0.349139\pi$
$758$	−209623.	−	904499.i	−0.364838	−	1.57424i
$759$	872263.	+	55743.3i	1.51413	+	0.0967629i
$760$	66396.9	−	10688.3i	0.114953	−	0.0185047i
$761$	80448.7	−	139341.i	0.138915	−	0.240608i	−0.788171	−	0.615456i	$-0.788972\pi$
$761$	80448.7	−	139341.i	0.138915	−	0.240608i	0.927086	+	0.374848i	$0.122305\pi$
$762$	47991.8	+	290157.i	0.0826527	+	0.499716i
$763$	−50060.1	+	28902.2i	−0.0859890	+	0.0496458i
$764$	−166763.	+	248137.i	−0.285702	+	0.425114i
$765$	179173.	−	235085.i	0.306160	−	0.401701i
$766$	−327467.	−	99815.1i	−0.558097	−	0.170113i
$767$	1.00695e6	−	581365.i	1.71167	−	0.988231i
$768$	109809.	+	579512.i	0.186173	+	0.982517i
$769$	297804.	−	515812.i	0.503591	−	0.872246i	−0.496400	−	0.868094i	$-0.665345\pi$
$769$	297804.	−	515812.i	0.503591	−	0.872246i	0.999991	−	0.00415186i	$-0.00132158\pi$
$770$	144583.	+	154785.i	0.243857	+	0.261063i
$771$	−114785.	+	172396.i	−0.193098	+	0.290014i
$772$	−50212.0	+	735879.i	−0.0842505	+	1.23473i
$773$	−583394.			−0.976345			−0.488172	−	0.872747i	$-0.662336\pi$
$773$	−583394.			−0.976345			−0.488172	+	0.872747i	$0.662336\pi$
$774$	426817.	−	307096.i	0.712460	−	0.512616i
$775$			618255.i			1.02935i
$776$	343242.	+	130764.i	0.570002	+	0.217152i
$777$	173278.	−	85802.7i	0.287013	−	0.142121i
$778$	−332401.	−	355855.i	−0.549166	−	0.587915i
$779$	−1818.34	−	1049.82i	−0.00299640	−	0.00172997i
$780$	−932247.	−	716892.i	−1.53229	−	1.17832i
$781$	−255794.	−	443049.i	−0.419362	−	0.726356i
$782$	312545.	+	95266.9i	0.511092	+	0.155786i
$783$	−309398.	−	897020.i	−0.504654	−	1.46312i
$784$	217768.	+	533810.i	0.354293	+	0.868469i
$785$	−68615.2	−	118845.i	−0.111348	−	0.192860i
$786$	−355280.	−	133600.i	−0.575076	−	0.216252i
$787$	−151046.	−	87206.2i	−0.243870	−	0.140798i	0.373084	−	0.927798i	$-0.378300\pi$
$787$	−151046.	−	87206.2i	−0.243870	−	0.140798i	−0.616954	+	0.786999i	$0.711634\pi$
$788$	228963.	−	112151.i	0.368734	−	0.180613i
$789$	−700695.	+	346966.i	−1.12558	+	0.557355i
$790$	182822.	+	788857.i	0.292937	+	1.26399i
$791$		−	223918.i		−	0.357879i
$792$	−271682.	+	507356.i	−0.433122	+	0.808840i
$793$	455635.			0.724553
$794$	−279359.	+	64743.0i	−0.443120	+	0.102696i
$795$	256028.	−	384528.i	0.405091	−	0.608406i
$796$	518950.	+	1.05947e6i	0.819029	+	1.67210i
$797$	−423576.	+	733655.i	−0.666829	+	1.15498i	0.311957	+	0.950096i	$0.399016\pi$
$797$	−423576.	+	733655.i	−0.666829	+	1.15498i	−0.978786	+	0.204886i	$0.934318\pi$
$798$	−7497.92	−	9130.83i	−0.0117743	−	0.0143385i
$799$	186715.	−	107800.i	0.292472	−	0.168859i
$800$	−919949.	+	84391.1i	−1.43742	+	0.131861i
$801$	−93772.0	−	12034.4i	−0.146153	−	0.0187569i
$802$	100626.	−	330127.i	0.156445	−	0.513254i
$803$	−246591.	+	142369.i	−0.382425	+	0.220793i
$804$	−35121.8	−	4661.34i	−0.0543331	−	0.00721105i
$805$	208619.	−	361338.i	0.321930	−	0.557599i
$806$	418638.	−	391047.i	0.644420	−	0.601947i
$807$	485759.	+	31043.1i	0.745888	+	0.0476671i
$808$	−932195.	−	355136.i	−1.42786	−	0.543966i
$809$	43118.8			0.0658824			0.0329412	−	0.999457i	$-0.489513\pi$
$809$	43118.8			0.0658824			0.0329412	+	0.999457i	$0.489513\pi$
$810$	537059.	−	873725.i	0.818563	−	1.33169i
$811$			372984.i			0.567085i	0.958960	+	0.283543i	$0.0915097\pi$
$811$			372984.i			0.567085i	−0.958960	+	0.283543i	$0.908490\pi$
$812$	253594.	+	17303.8i	0.384616	+	0.0262439i
$813$	−27526.9	+	430737.i	−0.0416462	+	0.651674i
$814$	571235.	−	533586.i	0.862117	−	0.805296i
$815$	1.41966e6	+	819638.i	2.13731	+	1.23398i
$816$	−142457.	+	161225.i	−0.213946	+	0.242132i
$817$	21819.2	+	37791.9i	0.0326885	+	0.0566181i
$818$	−268778.	+	881791.i	−0.401687	+	1.31783i
$819$	−26299.3	+	204924.i	−0.0392081	+	0.305509i
$820$	40522.2	+	27233.3i	0.0602650	+	0.0405017i
$821$	665022.	+	1.15185e6i	0.986620	+	1.70888i	0.634504	+	0.772920i	$0.281204\pi$
$821$	665022.	+	1.15185e6i	0.986620	+	1.70888i	0.352116	+	0.935956i	$0.385462\pi$
$822$	73695.3	+	89744.7i	0.109068	+	0.132821i
$823$	−636230.	−	367328.i	−0.939322	−	0.542318i	−0.0495745	−	0.998770i	$-0.515787\pi$
$823$	−636230.	−	367328.i	−0.939322	−	0.542318i	−0.889748	+	0.456452i	$0.849120\pi$
$824$	−703095.	+	113182.i	−1.03552	+	0.166694i
$825$	−750307.	−	499572.i	−1.10238	−	0.733990i
$826$	−264615.	+	61326.0i	−0.387842	+	0.0898845i
$827$		−	1.27112e6i		−	1.85856i	−0.369375	−	0.929281i	$-0.620428\pi$
$827$		−	1.27112e6i		−	1.85856i	0.369375	−	0.929281i	$-0.379572\pi$
$828$	1.11205e6	+	220528.i	1.62205	+	0.321665i
$829$	−427267.			−0.621714			−0.310857	−	0.950457i	$-0.600616\pi$
$829$	−427267.			−0.621714			−0.310857	+	0.950457i	$0.600616\pi$
$830$	−66113.8	−	285274.i	−0.0959700	−	0.414100i
$831$	−294433.	−	594607.i	−0.426369	−	0.861049i
$832$	639012.	+	569547.i	0.923129	+	0.822779i
$833$	−105146.	+	182119.i	−0.151532	+	0.262461i
$834$	633300.	+	238147.i	0.910495	+	0.342384i
$835$	−230588.	+	133130.i	−0.330723	+	0.190943i
$836$	−39642.6	−	26642.2i	−0.0567217	−	0.0381204i
$837$	377216.	+	327560.i	0.538443	+	0.467563i
$838$	−212831.	−	64873.0i	−0.303073	−	0.0923796i
$839$	−601815.	+	347458.i	−0.854947	+	0.493604i	−0.862317	−	0.506369i	$-0.830987\pi$
$839$	−601815.	+	347458.i	−0.854947	+	0.493604i	0.00737025	+	0.999973i	$0.497654\pi$
$840$	159492.	+	223697.i	0.226037	+	0.317031i
$841$	−493464.	+	854704.i	−0.697691	+	1.20844i
$842$	−384917.	−	412076.i	−0.542928	−	0.581237i
$843$	224145.	+	452659.i	0.315409	+	0.636966i
$844$	−284433.	−	19408.0i	−0.399296	−	0.0272456i
$845$	−590581.			−0.827115
$846$	607230.	−	436903.i	0.848423	−	0.610441i
$847$			28266.7i			0.0394011i
$848$	−206123.	+	265666.i	−0.286639	+	0.369440i
$849$	−1.14443e6	−	761988.i	−1.58772	−	1.05714i
$850$	−230021.	−	246251.i	−0.318368	−	0.340832i
$851$	−1.33353e6	−	769911.i	−1.84137	−	1.06312i
$852$	−253296.	−	613328.i	−0.348938	−	0.844916i
$853$	−72314.7	−	125253.i	−0.0993867	−	0.172143i	0.812044	−	0.583596i	$-0.198355\pi$
$853$	−72314.7	−	125253.i	−0.0993867	−	0.172143i	−0.911431	+	0.411453i	$0.865021\pi$
$854$	−101817.	−	31034.8i	−0.139606	−	0.0425534i
$855$	67695.2	+	51594.6i	0.0926031	+	0.0705784i
$856$	180392.	+	221618.i	0.246189	+	0.302452i
$857$	318005.	+	550800.i	0.432984	+	0.749951i	0.997129	−	0.0757255i	$-0.0241273\pi$
$857$	318005.	+	550800.i	0.432984	+	0.749951i	−0.564145	+	0.825676i	$0.690794\pi$
$858$	136295.	+	824034.i	0.185142	+	1.11936i
$859$	1.16908e6	+	674970.i	1.58438	+	0.914741i	0.994209	+	0.107460i	$0.0342718\pi$
$859$	1.16908e6	+	674970.i	1.58438	+	0.914741i	0.590168	+	0.807281i	$0.299062\pi$
$860$	−446364.	−	911281.i	−0.603520	−	1.23213i
$861$	547.030	−	8559.85i	0.000737912	−	0.0115467i
$862$	172503.	+	744332.i	0.232157	+	1.00173i
$863$			916363.i			1.23040i	0.788372	+	0.615199i	$0.210924\pi$
$863$			916363.i			1.23040i	−0.788372	+	0.615199i	$0.789076\pi$
$864$	−435912.	+	606001.i	−0.583945	+	0.811794i
$865$	−615427.			−0.822515
$866$	187991.	−	43568.0i	0.250670	−	0.0580941i
$867$	671842.	+	42935.0i	0.893776	+	0.0571181i
$868$	−120185.	+	58869.2i	−0.159519	+	0.0781355i
$869$	287555.	−	498060.i	0.380786	−	0.659541i
$870$	−1.80662e6	+	298814.i	−2.38687	+	0.394787i
$871$	−44529.3	+	25709.0i	−0.0586961	+	0.0338882i
$872$	−235076.	+	191346.i	−0.309154	+	0.251644i
$873$	179298.	+	428903.i	0.235260	+	0.562770i
$874$	−27433.0	+	90000.5i	−0.0359129	+	0.117821i
$875$	−114485.	+	66097.9i	−0.149531	+	0.0863319i
$876$	−341364.	+	140979.i	−0.444846	+	0.183715i
$877$	273128.	−	473071.i	0.355113	−	0.615074i	−0.632024	−	0.774949i	$-0.717776\pi$
$877$	273128.	−	473071.i	0.355113	−	0.615074i	0.987137	+	0.159875i	$0.0511090\pi$
$878$	−766471.	+	715954.i	−0.994276	+	0.928744i
$879$	−193732.	+	290967.i	−0.250741	+	0.376587i
$880$	877502.	+	680830.i	1.13314	+	0.879171i
$881$	446863.			0.575735			0.287867	−	0.957670i	$-0.407054\pi$
$881$	446863.			0.575735			0.287867	+	0.957670i	$0.407054\pi$
$882$	−299858.	+	665197.i	−0.385459	+	0.855092i
$883$		−	140436.i		−	0.180119i	−0.995936	−	0.0900593i	$-0.971294\pi$
$883$		−	140436.i		−	0.180119i	0.995936	−	0.0900593i	$-0.0287056\pi$
$884$	−21255.4	+	311508.i	−0.0271998	+	0.398625i
$885$	1.75362e6	−	868347.i	2.23897	−	1.10868i
$886$	265954.	−	248425.i	0.338796	−	0.316467i
$887$	307169.	+	177344.i	0.390418	+	0.225408i	0.682341	−	0.731034i	$-0.260962\pi$
$887$	307169.	+	177344.i	0.390418	+	0.225408i	−0.291923	+	0.956442i	$0.594295\pi$
$888$	825557.	−	588608.i	1.04694	−	0.746449i
$889$	−49854.7	−	86350.9i	−0.0630816	−	0.109261i
$890$	−53195.5	+	174520.i	−0.0671575	+	0.220326i
$891$	−702327.	+	193105.i	−0.884675	+	0.243242i
$892$	601358.	−	894798.i	0.755794	−	1.12459i
$893$	31042.0	+	53766.3i	0.0389266	+	0.0674229i
$894$	−96937.9	+	257785.i	−0.121288	+	0.322539i
$895$	761394.	+	439591.i	0.950525	+	0.548786i
$896$	−104001.	−	170798.i	−0.129545	−	0.212748i
$897$	1.47444e6	−	730106.i	1.83250	−	0.907405i
$898$	1.10413e6	−	255889.i	1.36921	−	0.317322i
$899$		−	892005.i		−	1.10369i
$900$	−879499.	−	770395.i	−1.08580	−	0.951105i
$901$	−122652.			−0.151086
$902$	−7828.66	−	33779.8i	−0.00962220	−	0.0415187i
$903$	−98799.0	+	148386.i	−0.121165	+	0.181978i
$904$	−186608.	−	1.15923e6i	−0.228346	−	1.41851i
$905$	−426883.	+	739383.i	−0.521209	+	0.902760i
$906$	−31321.8	+	25720.4i	−0.0381584	+	0.0313344i
$907$	−1.27955e6	+	738746.i	−1.55540	+	0.898008i	−0.557709	+	0.830037i	$0.688319\pi$
$907$	−1.27955e6	+	738746.i	−1.55540	+	0.898008i	−0.997687	+	0.0679717i	$0.978347\pi$
$908$	560422.	−	833887.i	0.679741	−	1.01143i
$909$	−486948.	−	1.16484e6i	−0.589325	−	1.40974i
$910$	381386.	+	116250.i	0.460555	+	0.140382i
$911$	−41701.0	+	24076.1i	−0.0502470	+	0.0290101i	−0.524913	−	0.851156i	$-0.675902\pi$
$911$	−41701.0	+	24076.1i	−0.0502470	+	0.0290101i	0.474666	+	0.880166i	$0.342569\pi$
$912$	−46426.3	−	41021.9i	−0.0558180	−	0.0493203i
$913$	−103988.	+	180113.i	−0.124751	+	0.216074i
$914$	−541868.	−	580102.i	−0.648637	−	0.694404i
$915$	765257.	+	48904.9i	0.914040	+	0.0584131i
$916$	44577.4	−	653302.i	0.0531280	−	0.778615i
$917$	128687.			0.153036
$918$	−272114.	+	9875.57i	−0.322898	+	0.0117186i
$919$			346372.i			0.410120i	0.978749	+	0.205060i	$0.0657390\pi$
$919$			346372.i			0.410120i	−0.978749	+	0.205060i	$0.934261\pi$
$920$	778892.	−	2.04451e6i	0.920241	−	2.41554i
$921$	−262.615	+	4109.37i	−0.000309600	+	0.00484458i
$922$	569832.	+	610039.i	0.670324	+	0.717622i
$923$	−834000.	−	481510.i	−0.978955	−	0.565200i
$924$	25671.1	−	193424.i	0.0300677	−	0.226551i
$925$	794014.	+	1.37527e6i	0.927993	+	1.60733i
$926$	100238.	+	30553.5i	0.116899	+	0.0356319i
$927$	−716843.	−	546349.i	−0.834189	−	0.635786i
$928$	1.32728e6	−	121758.i	1.54123	−	0.141384i
$929$	−435392.	−	754120.i	−0.504485	−	0.873794i	−0.999987	−	0.00518706i	$-0.998349\pi$
$929$	−435392.	−	754120.i	−0.504485	−	0.873794i	0.495501	−	0.868607i	$-0.334984\pi$
$930$	745093.	−	611845.i	0.861479	−	0.707417i
$931$	−52442.9	−	30277.9i	−0.0605044	−	0.0349322i
$932$	1.13880e6	−	557806.i	1.31104	−	0.642172i
$933$	−80325.0	−	53482.2i	−0.0922757	−	0.0614393i
$934$	87245.3	+	376454.i	0.100011	+	0.431537i
$935$			405122.i			0.463407i
$936$	34626.5	+	1.08281e6i	0.0395236	+	1.23595i
$937$	−1.00280e6			−1.14219			−0.571094	−	0.820885i	$-0.693481\pi$
$937$	−1.00280e6			−1.14219			−0.571094	+	0.820885i	$0.693481\pi$
$938$	11701.7	−	2711.94i	0.0132998	−	0.00308230i
$939$	71696.6	+	144791.i	0.0813144	+	0.164214i
$940$	−635038.	−	1.29647e6i	−0.718694	−	1.46726i
$941$	630949.	−	1.09284e6i	0.712550	−	1.23417i	−0.251348	−	0.967897i	$-0.580874\pi$
$941$	630949.	−	1.09284e6i	0.712550	−	1.23417i	0.963897	−	0.266275i	$-0.0857930\pi$
$942$	−44496.5	+	118329.i	−0.0501446	+	0.133349i
$943$	−59154.8	+	34153.0i	−0.0665222	+	0.0384066i
$944$	−1.31881e6	+	538010.i	−1.47992	+	0.603735i
$945$	−66165.9	+	341355.i	−0.0740919	+	0.382245i
$946$	−210125.	+	689366.i	−0.234799	+	0.770314i
$947$	162072.	−	93572.3i	0.180721	−	0.104339i	−0.406910	−	0.913468i	$-0.633394\pi$
$947$	162072.	−	93572.3i	0.180721	−	0.104339i	0.587631	+	0.809129i	$0.300061\pi$
$948$	454736.	−	591338.i	0.505991	−	0.657990i
$949$	−267998.	+	464186.i	−0.297577	+	0.515418i
$950$	70910.5	−	66236.9i	0.0785712	−	0.0733927i
$951$	−245104.	−	494986.i	−0.271012	−	0.547308i
$952$	25967.7	−	68162.5i	0.0286523	−	0.0752093i
$953$	194925.			0.214626			0.107313	−	0.994225i	$-0.465775\pi$
$953$	194925.			0.214626			0.107313	+	0.994225i	$0.465775\pi$
$954$	−423438.	+	42526.5i	−0.465258	+	0.0467265i
$955$			730210.i			0.800647i
$956$	−720422.	−	49157.2i	−0.788263	−	0.0537863i
$957$	1.08253e6	+	720772.i	1.18199	+	0.786998i
$958$	100127.	−	93527.4i	0.109098	−	0.101908i
$959$	−34095.8	−	19685.2i	−0.0370735	−	0.0214044i
$960$	1.01212e6	+	1.02517e6i	1.09822	+	1.11238i
$961$	−226939.	−	393070.i	−0.245732	−	0.425621i
$962$	429023.	−	1.40751e6i	0.463586	−	1.52090i
$963$	−46036.5	+	358716.i	−0.0496421	+	0.386810i
$964$	−1.00465e6	−	675187.i	−1.08109	−	0.726557i
$965$	900757.	+	1.56016e6i	0.967281	+	1.67538i
$966$	−379213.	+	62721.6i	−0.406376	+	0.0672145i
$967$	−374342.	−	216127.i	−0.400328	−	0.231129i	0.286298	−	0.958141i	$-0.407575\pi$
$967$	−374342.	−	216127.i	−0.400328	−	0.231129i	−0.686625	+	0.727011i	$0.740909\pi$
$968$	23556.8	+	146337.i	0.0251400	+	0.156172i
$969$	1441.23	−	22552.1i	0.00153492	−	0.0240182i
$970$	873957.	−	202544.i	0.928852	−	0.215267i
$971$			756598.i			0.802467i	0.915976	+	0.401233i	$0.131418\pi$
$971$			756598.i			0.802467i	−0.915976	+	0.401233i	$0.868582\pi$
$972$	−936012.	+	128443.i	−0.990716	+	0.135950i
$973$	−229389.			−0.242296
$974$	−62783.9	−	270906.i	−0.0661806	−	0.285562i
$975$	−1.69336e6	−	108217.i	−1.78132	−	0.113838i
$976$	−552973.	−	75816.0i	−0.580502	−	0.0795905i
$977$	−903593.	+	1.56507e6i	−0.946638	+	1.63962i	−0.194200	+	0.980962i	$0.562211\pi$
$977$	−903593.	+	1.56507e6i	−0.946638	+	1.63962i	−0.752438	+	0.658663i	$0.771122\pi$
$978$	−246426.	−	1.48988e6i	−0.257637	−	1.55767i
$979$	112217.	−	64788.8i	0.117083	−	0.0675981i
$980$	1.16870e6	+	785438.i	1.21689	+	0.817824i
$981$	−380499.	−	48832.2i	−0.395381	−	0.0507421i
$982$	770102.	+	234735.i	0.798593	+	0.243419i
$983$	−181852.	+	104992.i	−0.188196	+	0.108655i	−0.591138	−	0.806570i	$-0.701321\pi$
$983$	−181852.	+	104992.i	−0.188196	+	0.108655i	0.402942	+	0.915226i	$0.367988\pi$
$984$	−4301.59	−	44770.4i	−0.00444262	−	0.0462381i
$985$	311354.	−	539282.i	0.320910	−	0.555832i
$986$	331870.	+	355286.i	0.341361	+	0.365447i
$987$	−140561.	+	211108.i	−0.144288	+	0.216706i
$988$	−89701.9	−	6120.71i	−0.0918941	−	0.00627030i
$989$	1.41966e6			1.45141
$990$	140466.	+	1.39863e6i	0.143318	+	1.42703i
$991$		−	1.66713e6i		−	1.69755i	−0.528754	−	0.848775i	$-0.677341\pi$
$991$		−	1.66713e6i		−	1.69755i	0.528754	−	0.848775i	$-0.322659\pi$
$992$	−573141.	+	404926.i	−0.582423	+	0.411484i
$993$	−1.49934e6	+	742433.i	−1.52055	+	0.752937i
$994$	153570.	+	164406.i	0.155430	+	0.166397i
$995$	2.49540e6	+	1.44072e6i	2.52054	+	1.45523i
$996$	−164446.	+	213845.i	−0.165769	+	0.215566i
$997$	−671417.	−	1.16293e6i	−0.675464	−	1.16994i	−0.976333	−	0.216273i	$-0.930610\pi$
$997$	−671417.	−	1.16293e6i	−0.675464	−	1.16994i	0.300869	−	0.953666i	$-0.402723\pi$
$998$	−206992.	−	63093.3i	−0.207823	−	0.0633464i
$999$	1.25978e6	+	244187.i	1.26230	+	0.244676i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	36.5.f.a.31.21	yes	44
3.2	odd	2		108.5.f.a.91.2		44
4.3	odd	2	inner	36.5.f.a.31.6	yes	44
9.2	odd	6		108.5.f.a.19.17		44
9.4	even	3		324.5.d.f.163.10		22
9.5	odd	6		324.5.d.e.163.13		22
9.7	even	3	inner	36.5.f.a.7.6	✓	44
12.11	even	2		108.5.f.a.91.17		44
36.7	odd	6	inner	36.5.f.a.7.21	yes	44
36.11	even	6		108.5.f.a.19.2		44
36.23	even	6		324.5.d.e.163.14		22
36.31	odd	6		324.5.d.f.163.9		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.5.f.a.7.6	✓	44	9.7	even	3	inner
36.5.f.a.7.21	yes	44	36.7	odd	6	inner
36.5.f.a.31.6	yes	44	4.3	odd	2	inner
36.5.f.a.31.21	yes	44	1.1	even	1	trivial
108.5.f.a.19.2		44	36.11	even	6
108.5.f.a.19.17		44	9.2	odd	6
108.5.f.a.91.2		44	3.2	odd	2
108.5.f.a.91.17		44	12.11	even	2
324.5.d.e.163.13		22	9.5	odd	6
324.5.d.e.163.14		22	36.23	even	6
324.5.d.f.163.9		22	36.31	odd	6
324.5.d.f.163.10		22	9.4	even	3

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:	\( N \)	\(=\)	\( 36 = 2^{2} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	36.f (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(3.89672 - 0.903087i) q^{2} +(-8.98168 - 0.573987i) q^{3} +(14.3689 - 7.03816i) q^{4} +(19.5394 - 33.8433i) q^{5} +(-35.5175 + 5.87457i) q^{6} +(10.5700 - 6.10260i) q^{7} +(49.6354 - 40.4021i) q^{8} +(80.3411 + 10.3107i) q^{9} +O(q^{10})\)	\(q+(3.89672 - 0.903087i) q^{2} +(-8.98168 - 0.573987i) q^{3} +(14.3689 - 7.03816i) q^{4} +(19.5394 - 33.8433i) q^{5} +(-35.5175 + 5.87457i) q^{6} +(10.5700 - 6.10260i) q^{7} +(49.6354 - 40.4021i) q^{8} +(80.3411 + 10.3107i) q^{9} +(45.5763 - 149.524i) q^{10} +(-96.1446 + 55.5091i) q^{11} +(-133.096 + 54.9669i) q^{12} +(-104.491 + 180.984i) q^{13} +(35.6772 - 33.3258i) q^{14} +(-194.923 + 292.754i) q^{15} +(156.929 - 202.261i) q^{16} +93.3790 q^{17} +(322.378 - 32.3769i) q^{18} +26.8894i q^{19} +(42.5651 - 623.812i) q^{20} +(-98.4393 + 48.7446i) q^{21} +(-324.519 + 303.130i) q^{22} +(757.577 + 437.387i) q^{23} +(-468.999 + 334.388i) q^{24} +(-451.080 - 781.293i) q^{25} +(-243.728 + 799.608i) q^{26} +(-715.679 - 138.723i) q^{27} +(108.928 - 162.081i) q^{28} +(650.809 + 1127.23i) q^{29} +(-495.176 + 1316.81i) q^{30} +(-593.492 - 342.653i) q^{31} +(428.848 - 929.874i) q^{32} +(895.401 - 443.379i) q^{33} +(363.872 - 84.3293i) q^{34} -476.966i q^{35} +(1226.98 - 417.299i) q^{36} -1760.25 q^{37} +(24.2835 + 104.780i) q^{38} +(1042.39 - 1565.56i) q^{39} +(-397.492 - 2469.26i) q^{40} +(-39.0421 + 67.6229i) q^{41} +(-339.570 + 278.843i) q^{42} +(1405.46 - 811.442i) q^{43} +(-990.807 + 1474.28i) q^{44} +(1918.77 - 2517.54i) q^{45} +(3347.06 + 1020.22i) q^{46} +(1999.54 - 1154.43i) q^{47} +(-1525.58 + 1726.57i) q^{48} +(-1126.02 + 1950.32i) q^{49} +(-2463.31 - 2637.12i) q^{50} +(-838.700 - 53.5984i) q^{51} +(-227.626 + 3335.96i) q^{52} -1313.48 q^{53} +(-2914.08 + 105.758i) q^{54} +4338.47i q^{55} +(278.089 - 729.956i) q^{56} +(15.4342 - 241.512i) q^{57} +(3554.01 + 3804.78i) q^{58} +(-4818.38 - 2781.89i) q^{59} +(-740.367 + 5578.44i) q^{60} +(-1090.13 - 1888.16i) q^{61} +(-2622.12 - 799.247i) q^{62} +(912.129 - 381.305i) q^{63} +(831.345 - 4010.75i) q^{64} +(4083.39 + 7072.65i) q^{65} +(3088.72 - 2536.35i) q^{66} +(213.077 + 123.020i) q^{67} +(1341.75 - 657.216i) q^{68} +(-6553.25 - 4363.31i) q^{69} +(-430.742 - 1858.60i) q^{70} +4608.15i q^{71} +(4404.34 - 2734.17i) q^{72} +2564.79 q^{73} +(-6859.21 + 1589.66i) q^{74} +(3603.00 + 7276.24i) q^{75} +(189.252 + 386.370i) q^{76} +(-677.500 + 1173.46i) q^{77} +(2648.05 - 7041.92i) q^{78} +(-4486.29 + 2590.16i) q^{79} +(-3778.87 - 9263.05i) q^{80} +(6348.38 + 1656.75i) q^{81} +(-91.0669 + 298.766i) q^{82} +(1622.37 - 936.677i) q^{83} +(-1071.39 + 1393.24i) q^{84} +(1824.57 - 3160.25i) q^{85} +(4743.88 - 4431.22i) q^{86} +(-5198.34 - 10498.0i) q^{87} +(-2529.49 + 6639.66i) q^{88} -1167.17 q^{89} +(5203.35 - 11543.0i) q^{90} +2550.67i q^{91} +(13963.9 + 952.813i) q^{92} +(5133.87 + 3418.25i) q^{93} +(6749.08 - 6304.26i) q^{94} +(910.026 + 525.404i) q^{95} +(-4385.51 + 8105.67i) q^{96} +(2869.58 + 4970.26i) q^{97} +(-2626.47 + 8616.73i) q^{98} +(-8296.70 + 3468.34i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - q^{2} - q^{4} - 2 q^{5} + 15 q^{6} + 122 q^{8} - 60 q^{9}+O(q^{10}) \) 44 * q - q^2 - q^4 - 2 * q^5 + 15 * q^6 + 122 * q^8 - 60 * q^9	\( 44 q - q^{2} - q^{4} - 2 q^{5} + 15 q^{6} + 122 q^{8} - 60 q^{9} + 28 q^{10} - 228 q^{12} - 2 q^{13} + 252 q^{14} - q^{16} - 56 q^{17} + 72 q^{18} - 140 q^{20} + 138 q^{21} - 33 q^{22} - 951 q^{24} - 1752 q^{25} + 1096 q^{26} - 516 q^{28} + 526 q^{29} - 1980 q^{30} - 121 q^{32} + 2994 q^{33} + 385 q^{34} - 1005 q^{36} - 8 q^{37} + 1395 q^{38} - 2276 q^{40} - 2762 q^{41} + 3330 q^{42} + 6714 q^{44} + 4110 q^{45} + 3576 q^{46} + 2163 q^{48} + 3428 q^{49} + 6375 q^{50} + 1438 q^{52} - 10088 q^{53} - 4983 q^{54} - 7506 q^{56} + 1752 q^{57} - 4064 q^{58} - 16392 q^{60} - 2 q^{61} - 18324 q^{62} + 9026 q^{64} - 2014 q^{65} - 17358 q^{66} - 11405 q^{68} + 3354 q^{69} + 3666 q^{70} + 4083 q^{72} - 3416 q^{73} + 14620 q^{74} + 1581 q^{76} - 3942 q^{77} + 34566 q^{78} + 45520 q^{80} - 1164 q^{81} - 8486 q^{82} + 51078 q^{84} - 1252 q^{85} + 22113 q^{86} + 1995 q^{88} + 13048 q^{89} - 4692 q^{90} - 30294 q^{92} + 12090 q^{93} + 7524 q^{94} - 76164 q^{96} + 5638 q^{97} - 92938 q^{98}+O(q^{100}) \) 44 * q - q^2 - q^4 - 2 * q^5 + 15 * q^6 + 122 * q^8 - 60 * q^9 + 28 * q^10 - 228 * q^12 - 2 * q^13 + 252 * q^14 - q^16 - 56 * q^17 + 72 * q^18 - 140 * q^20 + 138 * q^21 - 33 * q^22 - 951 * q^24 - 1752 * q^25 + 1096 * q^26 - 516 * q^28 + 526 * q^29 - 1980 * q^30 - 121 * q^32 + 2994 * q^33 + 385 * q^34 - 1005 * q^36 - 8 * q^37 + 1395 * q^38 - 2276 * q^40 - 2762 * q^41 + 3330 * q^42 + 6714 * q^44 + 4110 * q^45 + 3576 * q^46 + 2163 * q^48 + 3428 * q^49 + 6375 * q^50 + 1438 * q^52 - 10088 * q^53 - 4983 * q^54 - 7506 * q^56 + 1752 * q^57 - 4064 * q^58 - 16392 * q^60 - 2 * q^61 - 18324 * q^62 + 9026 * q^64 - 2014 * q^65 - 17358 * q^66 - 11405 * q^68 + 3354 * q^69 + 3666 * q^70 + 4083 * q^72 - 3416 * q^73 + 14620 * q^74 + 1581 * q^76 - 3942 * q^77 + 34566 * q^78 + 45520 * q^80 - 1164 * q^81 - 8486 * q^82 + 51078 * q^84 - 1252 * q^85 + 22113 * q^86 + 1995 * q^88 + 13048 * q^89 - 4692 * q^90 - 30294 * q^92 + 12090 * q^93 + 7524 * q^94 - 76164 * q^96 + 5638 * q^97 - 92938 * q^98

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