LMFDB - Embedded newform 36.5.f.a.7.1

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			7.1
Character	$\chi$	$=$	36.7
Dual form			36.5.f.a.31.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.96529 + 0.525827i) q^{2} +(-4.76702 + 7.63384i) q^{3} +(15.4470 - 4.17011i) q^{4} +(11.0746 + 19.1817i) q^{5} +(14.8885 - 32.7770i) q^{6} +(-82.7885 - 47.7980i) q^{7} +(-59.0591 + 24.6582i) q^{8} +(-35.5511 - 72.7813i) q^{9} +O(q^{10})$	\(q+(-3.96529 + 0.525827i) q^{2} +(-4.76702 + 7.63384i) q^{3} +(15.4470 - 4.17011i) q^{4} +(11.0746 + 19.1817i) q^{5} +(14.8885 - 32.7770i) q^{6} +(-82.7885 - 47.7980i) q^{7} +(-59.0591 + 24.6582i) q^{8} +(-35.5511 - 72.7813i) q^{9} +(-54.0000 - 70.2376i) q^{10} +(18.9394 + 10.9346i) q^{11} +(-41.8022 + 137.799i) q^{12} +(-63.1124 - 109.314i) q^{13} +(353.414 + 146.000i) q^{14} +(-199.223 - 6.89808i) q^{15} +(221.220 - 128.832i) q^{16} -283.865 q^{17} +(179.241 + 269.905i) q^{18} +323.729i q^{19} +(251.059 + 250.118i) q^{20} +(759.536 - 404.141i) q^{21} +(-80.8497 - 33.4002i) q^{22} +(-198.433 + 114.565i) q^{23} +(93.2993 - 568.394i) q^{24} +(67.2085 - 116.409i) q^{25} +(307.739 + 400.274i) q^{26} +(725.074 + 75.5587i) q^{27} +(-1478.16 - 393.098i) q^{28} +(-604.822 + 1047.58i) q^{29} +(793.602 - 77.4038i) q^{30} +(-718.565 + 414.863i) q^{31} +(-809.459 + 627.178i) q^{32} +(-173.758 + 92.4544i) q^{33} +(1125.61 - 149.264i) q^{34} -2117.36i q^{35} +(-852.664 - 976.002i) q^{36} -318.650 q^{37} +(-170.226 - 1283.68i) q^{38} +(1135.34 + 39.3112i) q^{39} +(-1127.04 - 859.775i) q^{40} +(-164.418 - 284.781i) q^{41} +(-2799.27 + 2001.92i) q^{42} +(179.336 + 103.539i) q^{43} +(338.155 + 89.9283i) q^{44} +(1002.36 - 1487.95i) q^{45} +(726.602 - 558.626i) q^{46} +(1062.42 + 613.390i) q^{47} +(-71.0817 + 2302.90i) q^{48} +(3368.79 + 5834.92i) q^{49} +(-205.290 + 496.933i) q^{50} +(1353.19 - 2166.98i) q^{51} +(-1430.75 - 1425.39i) q^{52} -2834.27 q^{53} +(-2914.86 + 81.6516i) q^{54} +484.385i q^{55} +(6068.02 + 781.492i) q^{56} +(-2471.30 - 1543.22i) q^{57} +(1847.44 - 4471.99i) q^{58} +(-1278.13 + 737.929i) q^{59} +(-3106.16 + 724.226i) q^{60} +(936.180 - 1621.51i) q^{61} +(2631.17 - 2022.89i) q^{62} +(-535.579 + 7724.73i) q^{63} +(2879.95 - 2912.58i) q^{64} +(1397.88 - 2421.20i) q^{65} +(640.384 - 457.975i) q^{66} +(-214.663 + 123.936i) q^{67} +(-4384.87 + 1183.75i) q^{68} +(71.3600 - 2060.94i) q^{69} +(1113.37 + 8395.96i) q^{70} -4308.28i q^{71} +(3894.27 + 3421.77i) q^{72} +3010.75 q^{73} +(1263.54 - 167.555i) q^{74} +(568.260 + 1067.98i) q^{75} +(1349.99 + 5000.65i) q^{76} +(-1045.31 - 1810.52i) q^{77} +(-4522.63 + 441.113i) q^{78} +(-6228.39 - 3595.96i) q^{79} +(4921.12 + 2816.63i) q^{80} +(-4033.24 + 5174.91i) q^{81} +(801.712 + 1042.78i) q^{82} +(-2877.35 - 1661.24i) q^{83} +(10047.3 - 9410.12i) q^{84} +(-3143.68 - 5445.01i) q^{85} +(-765.561 - 316.264i) q^{86} +(-5113.88 - 9610.95i) q^{87} +(-1388.17 - 178.780i) q^{88} -1549.85 q^{89} +(-3192.23 + 6427.22i) q^{90} +12066.6i q^{91} +(-2587.44 + 2597.18i) q^{92} +(258.409 - 7463.07i) q^{93} +(-4535.35 - 1873.62i) q^{94} +(-6209.67 + 3585.16i) q^{95} +(-929.070 - 9169.05i) q^{96} +(-2918.68 + 5055.31i) q^{97} +(-16426.4 - 21365.7i) q^{98} +(122.523 - 1767.17i) 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 $\left(\mathbb{Z}/36\mathbb{Z}\right)^\times$.

$n$	$19$	$29$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−3.96529	+	0.525827i	−0.991322	+	0.131457i
$2$	−3.96529	+	0.525827i	−0.991322	+	0.131457i
$3$	−4.76702	+	7.63384i	−0.529669	+	0.848205i
$3$	−4.76702	+	7.63384i	−0.529669	+	0.848205i
$4$	15.4470	−	4.17011i	0.965438	−	0.260632i
$5$	11.0746	+	19.1817i	0.442982	+	0.767268i	0.997909	−	0.0646314i	$-0.0205872\pi$
$5$	11.0746	+	19.1817i	0.442982	+	0.767268i	−0.554927	+	0.831899i	$0.687254\pi$
$6$	14.8885	−	32.7770i	0.413570	−	0.910472i
$7$	−82.7885	−	47.7980i	−1.68956	−	0.975469i	−0.954850	−	0.297089i	$-0.903984\pi$
$7$	−82.7885	−	47.7980i	−1.68956	−	0.975469i	−0.734711	−	0.678380i	$-0.762682\pi$
$8$	−59.0591	+	24.6582i	−0.922798	+	0.385284i
$9$	−35.5511	−	72.7813i	−0.438902	−	0.898535i
$10$	−54.0000	−	70.2376i	−0.540000	−	0.702376i
$11$	18.9394	+	10.9346i	0.156524	+	0.0903689i	0.576216	−	0.817297i	$-0.304529\pi$
$11$	18.9394	+	10.9346i	0.156524	+	0.0903689i	−0.419692	+	0.907666i	$0.637862\pi$
$12$	−41.8022	+	137.799i	−0.290293	+	0.956938i
$13$	−63.1124	−	109.314i	−0.373446	−	0.646827i	0.616647	−	0.787240i	$-0.288491\pi$
$13$	−63.1124	−	109.314i	−0.373446	−	0.646827i	−0.990093	+	0.140412i	$0.955157\pi$
$14$	353.414	+	146.000i	1.80313	+	0.744899i
$15$	−199.223	−	6.89808i	−0.885434	−	0.0306581i
$16$	221.220	−	128.832i	0.864142	−	0.503248i
$17$	−283.865			−0.982232			−0.491116	−	0.871094i	$-0.663411\pi$
$17$	−283.865			−0.982232			−0.491116	+	0.871094i	$0.663411\pi$
$18$	179.241	+	269.905i	0.553212	+	0.833041i
$19$			323.729i			0.896756i	0.893844	+	0.448378i	$0.147998\pi$
$19$			323.729i			0.896756i	−0.893844	+	0.448378i	$0.852002\pi$
$20$	251.059	+	250.118i	0.627646	+	0.625294i
$21$	759.536	−	404.141i	1.72230	−	0.916418i
$22$	−80.8497	−	33.4002i	−0.167045	−	0.0690086i
$23$	−198.433	+	114.565i	−0.375109	+	0.216570i	−0.675688	−	0.737187i	$-0.736153\pi$
$23$	−198.433	+	114.565i	−0.375109	+	0.216570i	0.300579	+	0.953757i	$0.402820\pi$
$24$	93.2993	−	568.394i	0.161978	−	0.986794i
$25$	67.2085	−	116.409i	0.107534	−	0.186254i
$26$	307.739	+	400.274i	0.455235	+	0.592122i
$27$	725.074	+	75.5587i	0.994614	+	0.103647i
$28$	−1478.16	−	393.098i	−1.88541	−	0.501401i
$29$	−604.822	+	1047.58i	−0.719170	+	1.24564i	0.242160	+	0.970236i	$0.422144\pi$
$29$	−604.822	+	1047.58i	−0.719170	+	1.24564i	−0.961329	+	0.275402i	$0.911189\pi$
$30$	793.602	−	77.4038i	0.881780	−	0.0860042i
$31$	−718.565	+	414.863i	−0.747726	+	0.431700i	−0.824872	−	0.565320i	$-0.808753\pi$
$31$	−718.565	+	414.863i	−0.747726	+	0.431700i	0.0771458	+	0.997020i	$0.475419\pi$
$32$	−809.459	+	627.178i	−0.790487	+	0.612478i
$33$	−173.758	+	92.4544i	−0.159557	+	0.0848984i
$34$	1125.61	−	149.264i	0.973708	−	0.129121i
$35$		−	2117.36i		−	1.72846i
$36$	−852.664	−	976.002i	−0.657920	−	0.753088i
$37$	−318.650			−0.232761			−0.116380	−	0.993205i	$-0.537129\pi$
$37$	−318.650			−0.232761			−0.116380	+	0.993205i	$0.537129\pi$
$38$	−170.226	−	1283.68i	−0.117885	−	0.888974i
$39$	1135.34	+	39.3112i	0.746444	+	0.0258456i
$40$	−1127.04	−	859.775i	−0.704399	−	0.537359i
$41$	−164.418	−	284.781i	−0.0978099	−	0.169412i	0.812968	−	0.582308i	$-0.197850\pi$
$41$	−164.418	−	284.781i	−0.0978099	−	0.169412i	−0.910778	+	0.412897i	$0.864517\pi$
$42$	−2799.27	+	2001.92i	−1.58689	+	1.13487i
$43$	179.336	+	103.539i	0.0969906	+	0.0559976i	0.547711	−	0.836668i	$-0.315499\pi$
$43$	179.336	+	103.539i	0.0969906	+	0.0559976i	−0.450720	+	0.892665i	$0.648833\pi$
$44$	338.155	+	89.9283i	0.174667	+	0.0464506i
$45$	1002.36	−	1487.95i	0.494991	−	0.734790i
$46$	726.602	−	558.626i	0.343385	−	0.264001i
$47$	1062.42	+	613.390i	0.480952	+	0.277678i	0.720813	−	0.693129i	$-0.243769\pi$
$47$	1062.42	+	613.390i	0.480952	+	0.277678i	−0.239861	+	0.970807i	$0.577102\pi$
$48$	−71.0817	+	2302.90i	−0.0308514	+	0.999524i
$49$	3368.79	+	5834.92i	1.40308	+	2.43020i
$50$	−205.290	+	496.933i	−0.0821161	+	0.198773i
$51$	1353.19	−	2166.98i	0.520258	−	0.833134i
$52$	−1430.75	−	1425.39i	−0.529123	−	0.527140i
$53$	−2834.27			−1.00900			−0.504499	−	0.863412i	$-0.668323\pi$
$53$	−2834.27			−1.00900			−0.504499	+	0.863412i	$0.668323\pi$
$54$	−2914.86	+	81.6516i	−0.999608	+	0.0280012i
$55$			484.385i			0.160127i
$56$	6068.02	+	781.492i	1.93496	+	0.249200i
$57$	−2471.30	−	1543.22i	−0.760633	−	0.474984i
$58$	1847.44	−	4471.99i	0.549181	−	1.32937i
$59$	−1278.13	+	737.929i	−0.367173	+	0.211988i	−0.672223	−	0.740349i	$-0.734660\pi$
$59$	−1278.13	+	737.929i	−0.367173	+	0.211988i	0.305049	+	0.952337i	$0.401327\pi$
$60$	−3106.16	+	724.226i	−0.862822	+	0.201174i
$61$	936.180	−	1621.51i	0.251594	−	0.435773i	−0.712371	−	0.701803i	$-0.752379\pi$
$61$	936.180	−	1621.51i	0.251594	−	0.435773i	0.963965	+	0.266030i	$0.0857120\pi$
$62$	2631.17	−	2022.89i	0.684487	−	0.526247i
$63$	−535.579	+	7724.73i	−0.134941	+	1.94627i
$64$	2879.95	−	2912.58i	0.703113	−	0.711078i
$65$	1397.88	−	2421.20i	0.330860	−	0.573066i
$66$	640.384	−	457.975i	0.147012	−	0.105137i
$67$	−214.663	+	123.936i	−0.0478197	+	0.0276087i	−0.523719	−	0.851891i	$-0.675456\pi$
$67$	−214.663	+	123.936i	−0.0478197	+	0.0276087i	0.475900	+	0.879500i	$0.342123\pi$
$68$	−4384.87	+	1183.75i	−0.948284	+	0.256001i
$69$	71.3600	−	2060.94i	0.0149885	−	0.432880i
$70$	1113.37	+	8395.96i	0.227218	+	1.71346i
$71$		−	4308.28i		−	0.854648i	−0.904099	−	0.427324i	$-0.859456\pi$
$71$		−	4308.28i		−	0.854648i	0.904099	−	0.427324i	$-0.140544\pi$
$72$	3894.27	+	3421.77i	0.751209	+	0.660065i
$73$	3010.75			0.564974			0.282487	−	0.959271i	$-0.408841\pi$
$73$	3010.75			0.564974			0.282487	+	0.959271i	$0.408841\pi$
$74$	1263.54	−	167.555i	0.230741	−	0.0305980i
$75$	568.260	+	1067.98i	0.101024	+	0.189863i
$76$	1349.99	+	5000.65i	0.233723	+	0.865763i
$77$	−1045.31	−	1810.52i	−0.176304	−	0.305368i
$78$	−4522.63	+	441.113i	−0.743364	+	0.0725039i
$79$	−6228.39	−	3595.96i	−0.997980	−	0.576184i	−0.0903300	−	0.995912i	$-0.528792\pi$
$79$	−6228.39	−	3595.96i	−0.997980	−	0.576184i	−0.907650	+	0.419728i	$0.862126\pi$
$80$	4921.12	+	2816.63i	0.768926	+	0.440098i
$81$	−4033.24	+	5174.91i	−0.614730	+	0.788738i
$82$	801.712	+	1042.78i	0.119231	+	0.155084i
$83$	−2877.35	−	1661.24i	−0.417673	−	0.241144i	0.276408	−	0.961040i	$-0.410856\pi$
$83$	−2877.35	−	1661.24i	−0.417673	−	0.241144i	−0.694081	+	0.719897i	$0.744189\pi$
$84$	10047.3	−	9410.12i	1.42393	−	1.33363i
$85$	−3143.68	−	5445.01i	−0.435111	−	0.753635i
$86$	−765.561	−	316.264i	−0.103510	−	0.0427615i
$87$	−5113.88	−	9610.95i	−0.675634	−	1.26978i
$88$	−1388.17	−	178.780i	−0.179257	−	0.0230863i
$89$	−1549.85			−0.195664			−0.0978318	−	0.995203i	$-0.531191\pi$
$89$	−1549.85			−0.195664			−0.0978318	+	0.995203i	$0.531191\pi$
$90$	−3192.23	+	6427.22i	−0.394102	+	0.793484i
$91$			12066.6i			1.45714i
$92$	−2587.44	+	2597.18i	−0.305700	+	0.306850i
$93$	258.409	−	7463.07i	0.0298773	−	0.862882i
$94$	−4535.35	−	1873.62i	−0.513281	−	0.212044i
$95$	−6209.67	+	3585.16i	−0.688052	+	0.397247i
$96$	−929.070	−	9169.05i	−0.100811	−	0.994906i
$97$	−2918.68	+	5055.31i	−0.310201	+	0.537285i	−0.978406	−	0.206693i	$-0.933730\pi$
$97$	−2918.68	+	5055.31i	−0.310201	+	0.537285i	0.668204	+	0.743978i	$0.267063\pi$
$98$	−16426.4	−	21365.7i	−1.71037	−	2.22467i
$99$	122.523	−	1767.17i	0.0125011	−	0.180305i
$100$	552.734	−	2078.43i	0.0552734	−	0.207843i
$101$	2749.50	−	4762.27i	0.269532	−	0.466844i	−0.699209	−	0.714918i	$-0.746464\pi$
$101$	2749.50	−	4762.27i	0.269532	−	0.466844i	0.968741	+	0.248074i	$0.0797976\pi$
$102$	−4226.33	+	9304.25i	−0.406222	+	0.894295i
$103$	15530.7	−	8966.63i	1.46391	−	0.845191i	0.464725	−	0.885455i	$-0.346153\pi$
$103$	15530.7	−	8966.63i	1.46391	−	0.845191i	0.999189	+	0.0402641i	$0.0128199\pi$
$104$	6422.83	+	4899.74i	0.593827	+	0.453008i
$105$	16163.6	+	10093.5i	1.46609	+	0.915512i
$106$	11238.7	−	1490.34i	1.00024	−	0.132640i
$107$			8715.17i			0.761217i	0.924736	+	0.380608i	$0.124285\pi$
$107$			8715.17i			0.761217i	−0.924736	+	0.380608i	$0.875715\pi$
$108$	11515.3	−	1856.48i	0.987252	−	0.159164i
$109$	−12162.1			−1.02366			−0.511830	−	0.859087i	$-0.671032\pi$
$109$	−12162.1			−1.02366			−0.511830	+	0.859087i	$0.671032\pi$
$110$	−254.703	−	1920.73i	−0.0210498	−	0.158738i
$111$	1519.01	−	2432.52i	0.123286	−	0.197429i
$112$	−24472.4	+	91.8909i	−1.95092	+	0.00732549i
$113$	10236.7	+	17730.5i	0.801684	+	1.38856i	0.918507	+	0.395404i	$0.129396\pi$
$113$	10236.7	+	17730.5i	0.801684	+	1.38856i	−0.116823	+	0.993153i	$0.537271\pi$
$114$	10610.9	+	4819.85i	0.816472	+	0.370871i
$115$	−4395.11	−	2537.52i	−0.332334	−	0.191873i
$116$	−4974.15	+	18704.2i	−0.369661	+	1.39003i
$117$	−5712.29	+	8479.62i	−0.417291	+	0.619448i
$118$	4680.13	−	3598.18i	0.336120	−	0.258415i
$119$	23500.8	+	13568.2i	1.65954	+	0.958136i
$120$	11936.0	−	4505.07i	0.828889	−	0.312852i
$121$	−7081.37	−	12265.3i	−0.483667	−	0.837736i
$122$	−2859.59	+	6922.03i	−0.192125	+	0.465065i
$123$	2957.76	+	102.412i	0.195503	+	0.00676928i
$124$	−9369.65	+	9404.89i	−0.609368	+	0.611661i
$125$	16820.4			1.07651
$126$	−1938.15	−	30912.4i	−0.122080	−	1.94711i
$127$		−	8130.42i		−	0.504087i	−0.967716	−	0.252044i	$-0.918897\pi$
$127$		−	8130.42i		−	0.504087i	0.967716	−	0.252044i	$-0.0811026\pi$
$128$	−9888.32	+	13063.6i	−0.603535	+	0.797336i
$129$	−1645.30	+	875.445i	−0.0988703	+	0.0526077i
$130$	−4269.87	+	10335.8i	−0.252655	+	0.611586i
$131$	14095.1	−	8137.79i	0.821343	−	0.474203i	−0.0295362	−	0.999564i	$-0.509403\pi$
$131$	14095.1	−	8137.79i	0.821343	−	0.474203i	0.850879	+	0.525361i	$0.176070\pi$
$132$	−2298.49	+	2152.73i	−0.131915	+	0.123550i
$133$	15473.6	−	26801.0i	0.874758	−	1.51512i
$134$	786.030	−	604.315i	0.0437754	−	0.0336554i
$135$	6580.52	+	14744.9i	0.361071	+	0.809049i
$136$	16764.8	−	6999.59i	0.906402	−	0.378438i
$137$	−12331.4	+	21358.7i	−0.657011	+	1.13798i	0.324375	+	0.945929i	$0.394846\pi$
$137$	−12331.4	+	21358.7i	−0.657011	+	1.13798i	−0.981386	+	0.192047i	$0.938487\pi$
$138$	800.735	+	8209.74i	0.0420466	+	0.431093i
$139$	17078.1	−	9860.04i	0.883913	−	0.510328i	0.0119667	−	0.999928i	$-0.496191\pi$
$139$	17078.1	−	9860.04i	0.883913	−	0.510328i	0.871947	+	0.489601i	$0.162857\pi$
$140$	−8829.65	−	32707.0i	−0.450492	−	1.66872i
$141$	−9747.12	+	5186.33i	−0.490273	+	0.260869i
$142$	2265.41	+	17083.6i	0.112349	+	0.847231i
$143$		−	2760.44i		−	0.134992i
$144$	−17241.2	−	11520.6i	−0.831460	−	0.555585i
$145$	−26792.5			−1.27432
$146$	−11938.5	+	1583.13i	−0.560072	+	0.0742697i
$147$	−60601.9	−	2098.34i	−2.80448	−	0.0971050i
$148$	−4922.18	+	1328.80i	−0.224716	+	0.0606649i
$149$	−14942.7	−	25881.6i	−0.673066	−	1.16578i	−0.977030	−	0.213101i	$-0.931644\pi$
$149$	−14942.7	−	25881.6i	−0.673066	−	1.16578i	0.303965	−	0.952683i	$-0.401690\pi$
$150$	−2814.89	−	3936.04i	−0.125106	−	0.174935i
$151$	−5164.11	−	2981.50i	−0.226486	−	0.130762i	0.382464	−	0.923970i	$-0.375076\pi$
$151$	−5164.11	−	2981.50i	−0.226486	−	0.130762i	−0.608950	+	0.793209i	$0.708409\pi$
$152$	−7982.56	−	19119.1i	−0.345506	−	0.827525i
$153$	10091.7	+	20660.1i	0.431104	+	0.882570i
$154$	5096.97	+	6629.60i	0.214917	+	0.279541i
$155$	−15915.6	−	9188.85i	−0.662458	−	0.382471i
$156$	17701.6	−	4127.26i	0.727382	−	0.169595i
$157$	17493.5	+	30299.6i	0.709704	+	1.22924i	0.964967	+	0.262372i	$0.0845048\pi$
$157$	17493.5	+	30299.6i	0.709704	+	1.22924i	−0.255262	+	0.966872i	$0.582162\pi$
$158$	26588.2	+	10984.0i	1.06506	+	0.439993i
$159$	13511.0	−	21636.4i	0.534435	−	0.855837i
$160$	−20994.7	−	8581.08i	−0.820107	−	0.335198i
$161$	21903.9			0.845027
$162$	13271.9	−	22640.8i	0.505710	−	0.862703i
$163$			14509.8i			0.546118i	0.961997	+	0.273059i	$0.0880354\pi$
$163$			14509.8i			0.546118i	−0.961997	+	0.273059i	$0.911965\pi$
$164$	−3727.34	−	3713.37i	−0.138584	−	0.138064i
$165$	−3697.72	−	2309.07i	−0.135821	−	0.0848144i
$166$	12283.0	+	5074.30i	0.445749	+	0.184145i
$167$	−38640.1	+	22308.9i	−1.38550	+	0.799917i	−0.992804	−	0.119753i	$-0.961790\pi$
$167$	−38640.1	+	22308.9i	−1.38550	+	0.799917i	−0.392693	+	0.919670i	$0.628457\pi$
$168$	−34892.2	+	42596.9i	−1.23626	+	1.50925i
$169$	6314.16	−	10936.5i	0.221076	−	0.382916i
$170$	15328.7	+	19938.0i	0.530406	+	0.689896i
$171$	23561.4	−	11508.9i	0.805767	−	0.393588i
$172$	3201.97	+	851.526i	0.108233	+	0.0287833i
$173$	26443.3	−	45801.1i	0.883534	−	1.53033i	0.0361488	−	0.999346i	$-0.488491\pi$
$173$	26443.3	−	45801.1i	0.883534	−	1.53033i	0.847385	−	0.530979i	$-0.178176\pi$
$174$	25331.7	+	35421.2i	0.836692	+	1.16994i
$175$	−11128.2	+	6424.86i	−0.363369	+	0.209791i
$176$	5598.50	−	21.0217i	0.180737	−	0.000678644i
$177$	459.639	−	13274.8i	0.0146714	−	0.423721i
$178$	6145.61	−	814.954i	0.193966	−	0.0257213i
$179$			32840.8i			1.02496i	0.858698	+	0.512482i	$0.171274\pi$
$179$			32840.8i			1.02496i	−0.858698	+	0.512482i	$0.828726\pi$
$180$	9278.49	−	27164.3i	0.286373	−	0.838405i
$181$	−22758.6			−0.694685			−0.347343	−	0.937738i	$-0.612916\pi$
$181$	−22758.6			−0.694685			−0.347343	+	0.937738i	$0.612916\pi$
$182$	−6344.93	−	47847.4i	−0.191551	−	1.44449i
$183$	7915.57	+	14876.4i	0.236363	+	0.444218i
$184$	8894.30	−	11659.1i	0.262710	−	0.344373i
$185$	−3528.90	−	6112.24i	−0.103109	−	0.178590i
$186$	2899.62	+	29729.1i	0.0838137	+	0.859322i
$187$	−5376.22	−	3103.96i	−0.153742	−	0.0887632i
$188$	18969.2	+	5044.62i	0.536701	+	0.142729i
$189$	−56416.2	−	40912.4i	−1.57936	−	1.14533i
$190$	22738.0	−	17481.4i	0.629860	−	0.484249i
$191$	−49799.3	−	28751.7i	−1.36508	−	0.788127i	−0.374782	−	0.927113i	$-0.622282\pi$
$191$	−49799.3	−	28751.7i	−1.36508	−	0.788127i	−0.990294	+	0.138986i	$0.955616\pi$
$192$	8505.37	+	35869.4i	0.230723	+	0.973020i
$193$	22470.8	+	38920.5i	0.603259	+	1.04488i	0.992324	+	0.123665i	$0.0394648\pi$
$193$	22470.8	+	38920.5i	0.603259	+	1.04488i	−0.389065	+	0.921210i	$0.627202\pi$
$194$	8915.21	−	21580.5i	0.236880	−	0.573400i
$195$	11819.4	+	22213.1i	0.310831	+	0.584172i
$196$	76370.0	+	76083.8i	1.98797	+	1.98052i
$197$	−44514.7			−1.14702			−0.573510	−	0.819198i	$-0.694419\pi$
$197$	−44514.7			−1.14702			−0.573510	+	0.819198i	$0.694419\pi$
$198$	443.385	+	7071.76i	0.0113097	+	0.180384i
$199$			19066.9i			0.481474i	0.970590	+	0.240737i	$0.0773892\pi$
$199$			19066.9i			0.481474i	−0.970590	+	0.240737i	$0.922611\pi$
$200$	−1098.85	+	8532.22i	−0.0274713	+	0.213305i
$201$	77.1966	−	2229.50i	0.00191076	−	0.0551844i
$202$	−8398.42	+	20329.5i	−0.205824	+	0.498224i
$203$	100145.	−	57818.5i	2.43016	−	1.40305i
$204$	11866.2	−	39116.3i	0.285135	−	0.939935i
$205$	3641.72	−	6307.65i	0.0866561	−	0.150093i
$206$	−56868.6	+	43721.7i	−1.34010	+	1.03030i
$207$	15392.7	+	10369.3i	0.359232	+	0.241996i
$208$	−28044.8	−	16051.6i	−0.648225	−	0.371014i
$209$	−3539.86	+	6131.22i	−0.0810389	+	0.140364i
$210$	−69400.9	−	31524.4i	−1.57372	−	0.714839i
$211$	825.251	−	476.459i	0.0185362	−	0.0107019i	−0.490703	−	0.871327i	$-0.663260\pi$
$211$	825.251	−	476.459i	0.0185362	−	0.0107019i	0.509239	+	0.860625i	$0.329927\pi$
$212$	−43781.1	+	11819.2i	−0.974125	+	0.262977i
$213$	32888.7	+	20537.6i	0.724916	+	0.452680i
$214$	−4582.67	−	34558.1i	−0.100067	−	0.754611i
$215$			4586.61i			0.0992237i
$216$	−44685.3	+	13416.6i	−0.957762	+	0.287563i
$217$	79318.5			1.68444
$218$	48226.2	−	6395.17i	1.01478	−	0.134567i
$219$	−14352.3	+	22983.6i	−0.299249	+	0.479214i
$220$	2019.94	+	7482.30i	0.0417343	+	0.154593i
$221$	17915.4	+	31030.4i	0.366810	+	0.635334i
$222$	−4744.22	+	10444.4i	−0.0962629	+	0.211922i
$223$	−37535.4	−	21671.1i	−0.754800	−	0.435784i	0.0726258	−	0.997359i	$-0.476862\pi$
$223$	−37535.4	−	21671.1i	−0.754800	−	0.435784i	−0.827426	+	0.561575i	$0.810195\pi$
$224$	96991.7	−	13232.6i	1.93303	−	0.263724i
$225$	−10861.7	−	753.076i	−0.214552	−	0.0148756i
$226$	−49914.6	−	64923.7i	−0.977262	−	1.27112i
$227$	−5202.66	−	3003.76i	−0.100966	−	0.0582925i	0.448667	−	0.893699i	$-0.351899\pi$
$227$	−5202.66	−	3003.76i	−0.100966	−	0.0582925i	−0.549633	+	0.835406i	$0.685232\pi$
$228$	−44609.6	−	13532.6i	−0.858140	−	0.260322i
$229$	2038.17	+	3530.22i	0.0388660	+	0.0673180i	0.884804	−	0.465963i	$-0.154292\pi$
$229$	2038.17	+	3530.22i	0.0388660	+	0.0673180i	−0.845938	+	0.533281i	$0.820959\pi$
$230$	18762.2	+	7750.92i	0.354673	+	0.146520i
$231$	18804.3	+	651.097i	0.352397	+	0.0122017i
$232$	9888.77	−	76783.0i	0.183724	−	1.42656i
$233$	−37427.6			−0.689414			−0.344707	−	0.938710i	$-0.612022\pi$
$233$	−37427.6			−0.689414			−0.344707	+	0.938710i	$0.612022\pi$
$234$	18192.1	−	36627.8i	0.332239	−	0.668928i
$235$			27172.1i			0.492025i
$236$	−16666.1	+	16728.7i	−0.299232	+	0.300358i
$237$	57141.9	−	30404.5i	1.01732	−	0.541305i
$238$	−100322.	−	41444.4i	−1.77109	−	0.731664i
$239$	−22212.3	+	12824.3i	−0.388865	+	0.224511i	−0.681668	−	0.731662i	$-0.738745\pi$
$239$	−22212.3	+	12824.3i	−0.388865	+	0.224511i	0.292804	+	0.956173i	$0.405412\pi$
$240$	−44960.8	+	24140.2i	−0.780569	+	0.419100i
$241$	−38300.8	+	66339.0i	−0.659438	+	1.14218i	0.321323	+	0.946970i	$0.395872\pi$
$241$	−38300.8	+	66339.0i	−0.659438	+	1.14218i	−0.980761	+	0.195211i	$0.937461\pi$
$242$	34529.1	+	44911.8i	0.589596	+	0.766884i
$243$	−20277.9	−	55458.0i	−0.343408	−	0.939186i
$244$	7699.30	−	28951.5i	0.129322	−	0.486285i
$245$	−74615.7	+	129238.i	−1.24308	+	2.15307i
$246$	−11782.2	+	1149.18i	−0.194696	+	0.0189896i
$247$	35388.1	−	20431.3i	0.580046	−	0.334890i
$248$	32208.0	−	42219.9i	0.523673	−	0.686458i
$249$	26398.0	−	14046.1i	0.425768	−	0.226546i
$250$	−66697.8	+	8844.63i	−1.06716	+	0.141514i
$251$		−	66642.6i		−	1.05780i	−0.848683	−	0.528902i	$-0.822604\pi$
$251$		−	66642.6i		−	1.05780i	0.848683	−	0.528902i	$-0.177396\pi$
$252$	23939.9	+	121557.i	0.376982	+	1.91417i
$253$	−5010.92			−0.0782846
$254$	4275.20	+	32239.5i	0.0662657	+	0.499713i
$255$	56552.3	+	1958.12i	0.869701	+	0.0301134i
$256$	32340.9	−	57000.3i	0.493482	−	0.869756i
$257$	−29713.2	−	51464.8i	−0.449866	−	0.779191i	0.548511	−	0.836143i	$-0.315195\pi$
$257$	−29713.2	−	51464.8i	−0.449866	−	0.779191i	−0.998377	+	0.0569526i	$0.981862\pi$
$258$	6063.76	−	4336.54i	0.0910966	−	0.0651484i
$259$	26380.5	+	15230.8i	0.393264	+	0.227051i
$260$	11496.4	−	43229.7i	0.170065	−	0.639492i
$261$	97746.4	+	6777.07i	1.43489	+	0.0994857i
$262$	−51611.9	+	39680.3i	−0.751878	+	0.578059i
$263$	21772.1	+	12570.2i	0.314767	+	0.181731i	0.649058	−	0.760739i	$-0.275163\pi$
$263$	21772.1	+	12570.2i	0.314767	+	0.181731i	−0.334290	+	0.942470i	$0.608497\pi$
$264$	7982.21	−	9744.81i	0.114529	−	0.139819i
$265$	−31388.3	−	54366.2i	−0.446968	−	0.774171i
$266$	−47264.5	+	114410.i	−0.667993	+	1.61697i
$267$	7388.17	−	11831.3i	0.103637	−	0.165963i
$268$	−2799.07	+	2809.60i	−0.0389712	+	0.0391179i
$269$	2553.46			0.0352877			0.0176439	−	0.999844i	$-0.494383\pi$
$269$	2553.46			0.0352877			0.0176439	+	0.999844i	$0.494383\pi$
$270$	−33847.0	−	55007.6i	−0.464293	−	0.754563i
$271$		−	4623.11i		−	0.0629499i	−0.999505	−	0.0314750i	$-0.989980\pi$
$271$		−	4623.11i		−	0.0629499i	0.999505	−	0.0314750i	$-0.0100204\pi$
$272$	−62796.7	+	36570.8i	−0.848788	+	0.494307i
$273$	−92114.3	−	57521.6i	−1.23595	−	0.771801i
$274$	37666.7	−	91177.4i	0.501714	−	1.21447i
$275$	2545.77	−	1469.80i	0.0336631	−	0.0194354i
$276$	−7492.05	−	32132.9i	−0.0983519	−	0.421825i
$277$	4927.19	−	8534.14i	0.0642154	−	0.111224i	−0.832130	−	0.554580i	$-0.812879\pi$
$277$	4927.19	−	8534.14i	0.0642154	−	0.111224i	0.896346	+	0.443356i	$0.146212\pi$
$278$	−62534.9	+	48078.0i	−0.809157	+	0.622095i
$279$	55740.0	+	37549.2i	0.716076	+	0.482384i
$280$	52210.3	+	125050.i	0.665948	+	1.59502i
$281$	24208.6	−	41930.5i	0.306589	−	0.531028i	−0.671025	−	0.741435i	$-0.734146\pi$
$281$	24208.6	−	41930.5i	0.306589	−	0.531028i	0.977614	+	0.210407i	$0.0674789\pi$
$282$	35923.0	−	25690.6i	0.451725	−	0.323054i
$283$	−114515.	+	66115.1i	−1.42984	+	0.825520i	−0.997108	−	0.0760012i	$-0.975785\pi$
$283$	−114515.	+	66115.1i	−1.42984	+	0.825520i	−0.432735	+	0.901521i	$0.642451\pi$
$284$	−17966.0	−	66550.0i	−0.222749	−	0.825110i
$285$	2233.11	−	64494.1i	0.0274929	−	0.794018i
$286$	1451.52	+	10946.0i	0.0177456	+	0.133820i
$287$			31435.5i			0.381642i
$288$	74424.0	+	36616.7i	0.897280	+	0.441462i
$289$	−2941.65			−0.0352205
$290$	106240.	−	14088.2i	1.26326	−	0.167518i
$291$	−24678.0	−	46379.5i	−0.291423	−	0.547697i
$292$	46507.1	−	12555.2i	0.545448	−	0.147250i
$293$	44759.6	+	77525.8i	0.521375	+	0.903049i	0.999691	+	0.0248607i	$0.00791423\pi$
$293$	44759.6	+	77525.8i	0.521375	+	0.903049i	−0.478315	+	0.878188i	$0.658752\pi$
$294$	241407.	−	23545.6i	2.79290	−	0.272405i
$295$	−28309.5	−	16344.5i	−0.325303	−	0.187814i
$296$	18819.1	−	7857.31i	0.214791	−	0.0896789i
$297$	12906.2	+	9359.45i	0.146314	+	0.106105i
$298$	72861.5	+	94770.6i	0.820475	+	1.06719i
$299$	25047.1	+	14461.0i	0.280166	+	0.161754i
$300$	13231.5	+	14127.4i	0.147017	+	0.156971i
$301$	−9897.95	−	17143.8i	−0.109248	−	0.189223i
$302$	22044.9	+	9107.08i	0.241710	+	0.0998540i
$303$	23247.5	+	43691.1i	0.253216	+	0.475891i
$304$	41706.5	+	71615.4i	0.451291	+	0.774925i
$305$	41471.1			0.445806
$306$	−50880.1	−	76616.6i	−0.543382	−	0.818239i
$307$			62726.9i			0.665545i	0.943007	+	0.332772i	$0.107984\pi$
$307$			62726.9i			0.665545i	−0.943007	+	0.332772i	$0.892016\pi$
$308$	−23697.0	−	23608.2i	−0.249799	−	0.248863i
$309$	−5585.11	+	161303.i	−0.0584944	+	1.68937i
$310$	67941.5	+	28067.6i	0.706988	+	0.292067i
$311$	−106333.	+	61391.4i	−1.09938	+	0.634726i	−0.936058	−	0.351847i	$-0.885554\pi$
$311$	−106333.	+	61391.4i	−1.09938	+	0.634726i	−0.163321	+	0.986573i	$0.552221\pi$
$312$	−68021.6	+	25673.8i	−0.698775	+	0.263743i
$313$	24294.6	−	42079.4i	0.247982	−	0.429518i	−0.714984	−	0.699141i	$-0.753566\pi$
$313$	24294.6	−	42079.4i	0.247982	−	0.429518i	0.962966	+	0.269623i	$0.0868992\pi$
$314$	−85299.2	−	110948.i	−0.865138	−	1.12528i
$315$	−154105.	+	75274.6i	−1.55308	+	0.758625i
$316$	−111206.	−	29573.8i	−1.11366	−	0.296164i
$317$	55066.7	−	95378.4i	0.547988	−	0.949143i	−0.450425	−	0.892815i	$-0.648727\pi$
$317$	55066.7	−	95378.4i	0.547988	−	0.949143i	0.998412	−	0.0563282i	$-0.0179393\pi$
$318$	−42198.1	+	92899.0i	−0.417291	+	0.918665i
$319$	−22909.9	+	13227.0i	−0.225134	+	0.129981i
$320$	87762.3	+	22986.8i	0.857054	+	0.224481i
$321$	−66530.2	−	41545.4i	−0.645667	−	0.403193i
$322$	−86855.5	+	11517.7i	−0.837694	+	0.111085i
$323$		−	91895.4i		−	0.880823i
$324$	−40721.6	+	96755.9i	−0.387913	+	0.921696i
$325$	−16966.7			−0.160632
$326$	−7629.65	−	57535.6i	−0.0717909	−	0.541379i
$327$	57977.0	−	92843.6i	0.542201	−	0.868273i
$328$	16732.6	+	12764.7i	0.155530	+	0.118648i
$329$	−58637.6	−	101563.i	−0.541732	−	0.938308i
$330$	15876.7	+	7211.78i	0.145791	+	0.0662238i
$331$	159800.	+	92260.3i	1.45854	+	0.842091i	0.998940	−	0.0460325i	$-0.0146578\pi$
$331$	159800.	+	92260.3i	1.45854	+	0.842091i	0.459605	+	0.888124i	$0.347991\pi$
$332$	−51374.0	−	13662.3i	−0.466087	−	0.123950i
$333$	11328.3	+	23191.7i	0.102159	+	0.209144i
$334$	141489.	−	108779.i	1.26832	−	0.975108i
$335$	−4754.59	−	2745.06i	−0.0423665	−	0.0244603i
$336$	115959.	−	187256.i	1.02713	−	1.65866i
$337$	−32813.1	−	56833.9i	−0.288926	−	0.500435i	0.684628	−	0.728893i	$-0.259965\pi$
$337$	−32813.1	−	56833.9i	−0.288926	−	0.500435i	−0.973554	+	0.228458i	$0.926632\pi$
$338$	−19286.8	+	46686.3i	−0.168821	+	0.408655i
$339$	−184150.	−	6376.20i	−1.60241	−	0.0554834i
$340$	−71266.7	−	70999.7i	−0.616494	−	0.614184i
$341$	−18145.5			−0.156049
$342$	−87376.1	+	58025.4i	−0.747035	+	0.496096i
$343$		−	414560.i		−	3.52370i
$344$	−13144.5	−	1692.86i	−0.111078	−	0.0143055i
$345$	40322.6	−	21455.2i	0.338774	−	0.180258i
$346$	−80771.7	+	195519.i	−0.674695	+	1.63319i
$347$	−90819.3	+	52434.6i	−0.754257	+	0.435470i	−0.827230	−	0.561864i	$-0.810085\pi$
$347$	−90819.3	+	52434.6i	−0.754257	+	0.435470i	0.0729731	+	0.997334i	$0.476751\pi$
$348$	−119073.	−	127135.i	−0.983228	−	1.04980i
$349$	−43672.0	+	75642.1i	−0.358552	+	0.621030i	−0.987719	−	0.156240i	$-0.950063\pi$
$349$	−43672.0	+	75642.1i	−0.358552	+	0.621030i	0.629167	+	0.777270i	$0.283396\pi$
$350$	40748.1	−	31327.9i	0.332637	−	0.255738i
$351$	−37501.5	−	84029.2i	−0.304393	−	0.682050i
$352$	−22188.6	+	3027.20i	−0.179079	+	0.0244318i
$353$	24354.3	−	42182.9i	0.195446	−	0.338522i	−0.751601	−	0.659618i	$-0.770718\pi$
$353$	24354.3	−	42182.9i	0.195446	−	0.338522i	0.947047	+	0.321096i	$0.104051\pi$
$354$	5157.64	+	52880.0i	0.0411570	+	0.421973i
$355$	82640.1	−	47712.3i	0.655744	−	0.378594i
$356$	−23940.6	+	6463.06i	−0.188901	+	0.0509962i
$357$	−215606.	+	114721.i	−1.69170	+	0.900135i
$358$	−17268.6	−	130223.i	−0.134738	−	1.01607i
$359$			109409.i			0.848911i	0.905449	+	0.424456i	$0.139535\pi$
$359$			109409.i			0.848911i	−0.905449	+	0.424456i	$0.860465\pi$
$360$	−22508.2	+	112593.i	−0.173674	+	0.868775i
$361$	25520.5			0.195828
$362$	90244.4	−	11967.1i	0.688657	−	0.0913211i
$363$	127388.	+	4410.82i	0.966754	+	0.0334739i
$364$	50318.9	+	186392.i	0.379777	+	1.40678i
$365$	33342.7	+	57751.3i	0.250274	+	0.433487i
$366$	−39210.0	−	54827.1i	−0.292708	−	0.409292i
$367$	−1112.82	−	642.487i	−0.00826215	−	0.00477015i	0.495863	−	0.868401i	$-0.334852\pi$
$367$	−1112.82	−	642.487i	−0.00826215	−	0.00477015i	−0.504125	+	0.863630i	$0.668185\pi$
$368$	−29137.8	+	50908.6i	−0.215160	+	0.375920i
$369$	−14881.5	+	22090.9i	−0.109293	+	0.162241i
$370$	17207.1	+	22381.2i	0.125691	+	0.163486i
$371$	234645.	+	135473.i	1.70476	+	0.984246i
$372$	−27130.2	−	116360.i	−0.196050	−	0.840847i
$373$	36777.2	+	63699.9i	0.264339	+	0.457848i	0.967390	−	0.253291i	$-0.0815130\pi$
$373$	36777.2	+	63699.9i	0.264339	+	0.457848i	−0.703052	+	0.711139i	$0.748180\pi$
$374$	22950.4	+	9481.14i	0.164077	+	0.0677825i
$375$	−80183.2	+	128404.i	−0.570192	+	0.913098i
$376$	−77870.8	−	10028.9i	−0.550807	−	0.0709376i
$377$	152687.			1.07428
$378$	245219.	+	132564.i	1.71621	+	0.927776i
$379$			139070.i			0.968176i	0.875019	+	0.484088i	$0.160848\pi$
$379$			139070.i			0.968176i	−0.875019	+	0.484088i	$0.839152\pi$
$380$	−80970.4	+	81275.0i	−0.560737	+	0.562846i
$381$	62066.3	+	38757.9i	0.427569	+	0.266999i
$382$	212587.	+	87822.8i	1.45683	+	0.601839i
$383$	90000.3	−	51961.7i	0.613545	−	0.354230i	−0.160807	−	0.986986i	$-0.551410\pi$
$383$	90000.3	−	51961.7i	0.613545	−	0.354230i	0.774352	+	0.632756i	$0.218076\pi$
$384$	−52587.3	−	137760.i	−0.356631	−	0.934245i
$385$	23152.6	−	40101.5i	0.156199	−	0.270545i
$386$	−109569.	−	142515.i	−0.735380	−	0.956505i
$387$	1160.17	−	16733.2i	0.00774638	−	0.111727i
$388$	−24003.7	+	90260.7i	−0.159447	+	0.599563i
$389$	50040.9	−	86673.4i	0.330694	−	0.572778i	−0.651954	−	0.758258i	$-0.726051\pi$
$389$	50040.9	−	86673.4i	0.330694	−	0.572778i	0.982648	+	0.185480i	$0.0593839\pi$
$390$	−58547.4	−	81866.5i	−0.384927	−	0.538241i
$391$	56328.2	−	32521.1i	0.368444	−	0.212721i
$392$	−342836.	−	261537.i	−2.23108	−	1.70200i
$393$	−5068.84	+	146393.i	−0.0328189	+	0.947838i
$394$	176514.	−	23407.1i	1.13707	−	0.150784i
$395$		−	159295.i		−	1.02096i
$396$	−5476.68	−	27808.4i	−0.0349242	−	0.177332i
$397$	164388.			1.04301			0.521507	−	0.853247i	$-0.325370\pi$
$397$	164388.			1.04301			0.521507	+	0.853247i	$0.325370\pi$
$398$	−10025.9	−	75605.6i	−0.0632931	−	0.477296i
$399$	130832.	+	245884.i	0.821804	+	1.54449i
$400$	−129.207	−	34410.5i	−0.000807546	−	0.215066i
$401$	78226.6	+	135492.i	0.486481	+	0.842609i	0.999879	−	0.0155412i	$-0.00494711\pi$
$401$	78226.6	+	135492.i	0.486481	+	0.842609i	−0.513399	+	0.858150i	$0.671614\pi$
$402$	866.227	+	8881.21i	0.00536018	+	0.0549567i
$403$	90700.6	+	52366.0i	0.558470	+	0.322433i
$404$	22612.3	−	85028.6i	0.138542	−	0.520958i
$405$	−143930.	−	20054.6i	−0.877487	−	0.122266i
$406$	−366699.	+	281926.i	−2.22463	+	1.71034i
$407$	−6035.02	−	3484.32i	−0.0364325	−	0.0210343i
$408$	−26484.4	+	161347.i	−0.159100	+	0.969261i
$409$	−135351.	−	234435.i	−0.809125	−	1.40145i	−0.913471	−	0.406904i	$-0.866608\pi$
$409$	−135351.	−	234435.i	−0.809125	−	1.40145i	0.104346	−	0.994541i	$-0.466725\pi$
$410$	−11123.7	+	26926.6i	−0.0661734	+	0.160182i
$411$	−104264.	−	195953.i	−0.617238	−	1.16003i
$412$	202510.	−	203272.i	1.19303	−	1.19752i
$413$	141086.			0.827149
$414$	−66489.0	−	33023.3i	−0.387926	−	0.192673i
$415$		−	73589.9i		−	0.427290i
$416$	119646.	+	48902.4i	0.691372	+	0.282581i
$417$	−6141.59	+	177374.i	−0.0353190	+	1.02004i
$418$	10812.6	−	26173.4i	0.0618839	−	0.149799i
$419$	49366.2	−	28501.6i	0.281191	−	0.162346i	−0.352771	−	0.935710i	$-0.614761\pi$
$419$	49366.2	−	28501.6i	0.281191	−	0.162346i	0.633963	+	0.773364i	$0.281427\pi$
$420$	291771.	+	88510.5i	1.65403	+	0.501760i
$421$	−116812.	+	202325.i	−0.659059	+	1.14152i	0.321801	+	0.946807i	$0.395712\pi$
$421$	−116812.	+	202325.i	−0.659059	+	1.14152i	−0.980860	+	0.194716i	$0.937621\pi$
$422$	−3021.82	+	2323.24i	−0.0169685	+	0.0130457i
$423$	6873.08	−	99131.3i	0.0384123	−	0.554026i
$424$	167390.	−	69888.0i	0.931101	−	0.388750i
$425$	−19078.1	+	33044.3i	−0.105623	+	0.182944i
$426$	−141213.	−	64143.9i	−0.778133	−	0.353457i
$427$	−155010.	+	89495.0i	−0.850166	+	0.490843i
$428$	36343.2	+	134623.i	0.198397	+	0.734908i
$429$	21072.8	+	13159.1i	0.114500	+	0.0715008i
$430$	−2411.77	−	18187.2i	−0.0130436	−	0.0983626i
$431$			333180.i			1.79360i	0.442439	+	0.896798i	$0.354113\pi$
$431$			333180.i			1.79360i	−0.442439	+	0.896798i	$0.645887\pi$
$432$	170135.	−	76697.3i	0.911648	−	0.410972i
$433$	−215343.			−1.14856			−0.574282	−	0.818657i	$-0.694719\pi$
$433$	−215343.			−1.14856			−0.574282	+	0.818657i	$0.694719\pi$
$434$	−314521.	+	41707.8i	−1.66982	+	0.221431i
$435$	127720.	−	204530.i	0.674966	−	1.08088i
$436$	−187868.	+	50717.3i	−0.988280	+	0.266799i
$437$	−37088.1	−	64238.5i	−0.194210	−	0.336382i
$438$	44825.6	−	98683.3i	0.233656	−	0.514394i
$439$	27053.2	+	15619.2i	0.140375	+	0.0810455i	0.568543	−	0.822654i	$-0.307507\pi$
$439$	27053.2	+	15619.2i	0.140375	+	0.0810455i	−0.428168	+	0.903699i	$0.640841\pi$
$440$	−11944.0	−	28607.3i	−0.0616944	−	0.147765i
$441$	304909.	−	452623.i	1.56781	−	2.32734i
$442$	−87356.3	−	113624.i	−0.447146	−	0.581601i
$443$	−184829.	−	106711.i	−0.941809	−	0.543754i	−0.0512822	−	0.998684i	$-0.516331\pi$
$443$	−184829.	−	106711.i	−0.941809	−	0.543754i	−0.890527	+	0.454930i	$0.849664\pi$
$444$	13320.3	−	43909.6i	0.0675689	−	0.222738i
$445$	−17163.9	−	29728.8i	−0.0866755	−	0.150126i
$446$	160234.	+	66195.0i	0.805536	+	0.332779i
$447$	268808.	+	9307.48i	1.34533	+	0.0465819i
$448$	−377642.	+	103472.i	−1.88159	+	0.515546i
$449$	−393053.			−1.94966			−0.974828	−	0.222956i	$-0.928429\pi$
$449$	−393053.			−1.94966			−0.974828	+	0.222956i	$0.928429\pi$
$450$	43465.8	−	2725.22i	0.214646	−	0.0134579i
$451$		−	7191.43i		−	0.0353559i
$452$	232065.	+	231195.i	1.13588	+	1.13162i
$453$	47377.7	−	25209.1i	0.230876	−	0.122846i
$454$	22209.5	+	9175.06i	0.107752	+	0.0445141i
$455$	−231457.	+	133632.i	−1.11802	+	0.645487i
$456$	184006.	+	30203.7i	0.884914	+	0.145255i
$457$	36178.7	−	62663.4i	0.173229	−	0.300042i	−0.766318	−	0.642462i	$-0.777913\pi$
$457$	36178.7	−	62663.4i	0.173229	−	0.300042i	0.939547	+	0.342420i	$0.111247\pi$
$458$	−9938.23	−	12926.6i	−0.0473782	−	0.0616246i
$459$	−205823.	−	21448.5i	−0.976942	−	0.101805i
$460$	−78473.1	−	20869.0i	−0.370856	−	0.0986246i
$461$	−29095.9	+	50395.5i	−0.136908	+	0.237132i	−0.926325	−	0.376726i	$-0.877050\pi$
$461$	−29095.9	+	50395.5i	−0.136908	+	0.237132i	0.789417	+	0.613858i	$0.210383\pi$
$462$	−74906.7	+	7306.00i	−0.350943	+	0.0342291i
$463$	−64721.6	+	37367.0i	−0.301917	+	0.174312i	−0.643304	−	0.765611i	$-0.722437\pi$
$463$	−64721.6	+	37367.0i	−0.301917	+	0.174312i	0.341387	+	0.939923i	$0.389103\pi$
$464$	1162.76	+	309666.i	0.00540075	+	1.43833i
$465$	146016.	−	77693.4i	0.675297	−	0.359318i
$466$	148411.	−	19680.5i	0.683431	−	0.0906282i
$467$		−	264366.i		−	1.21219i	−0.795392	−	0.606096i	$-0.792735\pi$
$467$		−	264366.i		−	1.21219i	0.795392	−	0.606096i	$-0.207265\pi$
$468$	−52876.8	+	154806.i	−0.241420	+	0.706798i
$469$	23695.5			0.107726
$470$	−14287.8	−	107745.i	−0.0646801	−	0.487756i
$471$	−314694.	−	10896.3i	−1.41856	−	0.0491176i
$472$	57289.3	−	75097.8i	0.257152	−	0.337088i
$473$	2264.33	+	3921.94i	0.0101209	+	0.0175299i
$474$	−210596.	+	150609.i	−0.937334	+	0.670341i
$475$	37684.8	+	21757.3i	0.167024	+	0.0964314i
$476$	419597.	+	111587.i	1.85191	+	0.492492i
$477$	100761.	+	206282.i	0.442851	+	0.906620i
$478$	81334.9	−	62531.9i	0.355976	−	0.273682i
$479$	−242211.	−	139840.i	−1.05566	−	0.609483i	−0.131429	−	0.991326i	$-0.541956\pi$
$479$	−242211.	−	139840.i	−1.05566	−	0.609483i	−0.924228	+	0.381842i	$0.875290\pi$
$480$	165589.	−	119364.i	0.718702	−	0.518074i
$481$	20110.7	+	34832.8i	0.0869236	+	0.150556i
$482$	116991.	−	283193.i	0.503568	−	1.21896i
$483$	−104417.	+	167211.i	−0.447584	+	0.716756i
$484$	−160534.	−	159932.i	−0.685291	−	0.682723i
$485$	−129293.			−0.549655
$486$	109569.	+	209244.i	0.463890	+	0.885893i
$487$			62506.3i			0.263552i	0.991280	+	0.131776i	$0.0420679\pi$
$487$			62506.3i			0.263552i	−0.991280	+	0.131776i	$0.957932\pi$
$488$	−15306.5	+	118849.i	−0.0642739	+	0.499065i
$489$	−110766.	−	69168.5i	−0.463220	−	0.289262i
$490$	227916.	−	551702.i	0.949254	−	2.29780i
$491$	291742.	−	168437.i	1.21014	−	0.698674i	0.247350	−	0.968926i	$-0.420440\pi$
$491$	291742.	−	168437.i	1.21014	−	0.698674i	0.962790	+	0.270252i	$0.0871070\pi$
$492$	46115.6	−	10752.2i	0.190510	−	0.0444189i
$493$	171688.	−	297372.i	0.706391	−	1.22351i
$494$	−129580.	+	99624.0i	−0.530989	+	0.408235i
$495$	35254.2	−	17220.4i	0.143880	−	0.0702802i
$496$	−105514.	+	184350.i	−0.428889	+	0.749342i
$497$	−205927.	+	356676.i	−0.833682	+	1.44398i
$498$	−97289.9	+	69577.6i	−0.392292	+	0.280550i
$499$	−276635.	+	159715.i	−1.11098	+	0.641424i	−0.939083	−	0.343691i	$-0.888323\pi$
$499$	−276635.	+	159715.i	−1.11098	+	0.641424i	−0.171896	+	0.985115i	$0.554989\pi$
$500$	259825.	−	70143.0i	1.03930	−	0.280572i
$501$	13895.7	−	401319.i	0.0553611	−	1.59888i
$502$	35042.5	+	264257.i	0.139055	+	1.04862i
$503$		−	28287.7i		−	0.111805i	−0.998436	−	0.0559025i	$-0.982196\pi$
$503$		−	28287.7i		−	0.111805i	0.998436	−	0.0559025i	$-0.0178036\pi$
$504$	−158847.	−	469422.i	−0.625341	−	1.84800i
$505$	121798.			0.477592
$506$	19869.7	−	2634.88i	0.0776053	−	0.0102910i
$507$	53387.4	+	100336.i	0.207693	+	0.390336i
$508$	−33904.8	−	125591.i	−0.131381	−	0.486665i
$509$	−47278.6	−	81888.9i	−0.182486	−	0.316074i	0.760241	−	0.649641i	$-0.225081\pi$
$509$	−47278.6	−	81888.9i	−0.182486	−	0.316074i	−0.942726	+	0.333567i	$0.891748\pi$
$510$	−225276.	+	21972.2i	−0.866113	+	0.0844761i
$511$	−249255.	−	143908.i	−0.954559	−	0.551115i
$512$	−98268.5	+	243028.i	−0.374865	+	0.927080i
$513$	−24460.5	+	234727.i	−0.0929462	+	0.891927i
$514$	144883.	+	188449.i	0.548392	+	0.713291i
$515$	343990.	+	198603.i	1.29698	+	0.748809i
$516$	−21764.3	+	20384.1i	−0.0817419	+	0.0765583i
$517$	13414.4	+	23234.4i	0.0501869	+	0.0869263i
$518$	−112615.	−	46522.9i	−0.419698	−	0.173383i
$519$	223583.	+	420199.i	0.830049	+	1.55998i
$520$	−22855.2	+	177463.i	−0.0845238	+	0.656299i
$521$	369932.			1.36285			0.681423	−	0.731890i	$-0.261362\pi$
$521$	369932.			1.36285			0.681423	+	0.731890i	$0.261362\pi$
$522$	−391156.	+	24524.7i	−1.43552	+	0.0900043i
$523$		−	65267.4i		−	0.238612i	−0.992858	−	0.119306i	$-0.961933\pi$
$523$		−	65267.4i		−	0.238612i	0.992858	−	0.119306i	$-0.0380670\pi$
$524$	183791.	−	184483.i	0.669364	−	0.671882i
$525$	4001.90	−	115578.i	0.0145193	−	0.419331i
$526$	−92942.5	−	38395.9i	−0.335925	−	0.138776i
$527$	203975.	−	117765.i	0.734440	−	0.424029i
$528$	−26527.7	+	42838.2i	−0.0951549	+	0.153661i
$529$	−113670.	+	196882.i	−0.406195	+	0.703551i
$530$	153051.	+	199073.i	0.544859	+	0.708696i
$531$	99146.4	+	66789.9i	0.351632	+	0.236876i
$532$	127257.	−	478523.i	0.449634	−	1.69075i
$533$	−20753.7	+	35946.4i	−0.0730534	+	0.126532i
$534$	−23075.0	+	50799.5i	−0.0809206	+	0.178146i
$535$	−167172.	+	96516.6i	−0.584057	+	0.337205i
$536$	9621.76	−	12612.7i	0.0334907	−	0.0439014i
$537$	−250702.	−	156553.i	−0.869378	−	0.542891i
$538$	−10125.2	+	1342.68i	−0.0349815	+	0.00463882i
$539$			147346.i			0.507179i
$540$	163137.	+	200323.i	0.559456	+	0.686980i
$541$	176002.			0.601343			0.300671	−	0.953728i	$-0.402789\pi$
$541$	176002.			0.601343			0.300671	+	0.953728i	$0.402789\pi$
$542$	2430.96	+	18331.9i	0.00827520	+	0.0624036i
$543$	108491.	−	173735.i	0.367953	−	0.589235i
$544$	229777.	−	178034.i	0.776442	−	0.601596i
$545$	−134690.	−	233290.i	−0.453463	−	0.785421i
$546$	395506.	+	179653.i	1.32668	+	0.602629i
$547$	236509.	+	136549.i	0.790448	+	0.456365i	0.840120	−	0.542400i	$-0.182484\pi$
$547$	236509.	+	136549.i	0.790448	+	0.456365i	−0.0496725	+	0.998766i	$0.515818\pi$
$548$	−101416.	+	381351.i	−0.337710	+	1.26988i
$549$	−151298.	−	10490.0i	−0.501982	−	0.0348040i
$550$	−9321.85	+	7166.82i	−0.0308160	+	0.0236920i
$551$	−339133.	−	195798.i	−1.11703	−	0.644920i
$552$	46604.5	+	123477.i	0.152950	+	0.405235i
$553$	343760.	+	595409.i	1.12410	+	1.94700i
$554$	−15050.2	+	36431.2i	−0.0490370	+	0.118701i
$555$	63482.2	+	2198.07i	0.206094	+	0.00713601i
$556$	222688.	−	223526.i	0.720356	−	0.723066i
$557$	−454335.			−1.46442			−0.732211	−	0.681078i	$-0.761511\pi$
$557$	−454335.			−1.46442			−0.732211	+	0.681078i	$0.761511\pi$
$558$	−240770.	−	119584.i	−0.773274	−	0.384065i
$559$		−	26138.5i		−	0.0836482i
$560$	−272783.	−	468404.i	−0.869845	−	1.49364i
$561$	49323.7	−	26244.6i	0.156722	−	0.0833899i
$562$	−73945.8	+	178996.i	−0.234121	+	0.566723i
$563$	27753.2	−	16023.3i	0.0875582	−	0.0505518i	−0.455582	−	0.890194i	$-0.650569\pi$
$563$	27753.2	−	16023.3i	0.0875582	−	0.0505518i	0.543140	+	0.839642i	$0.317235\pi$
$564$	−128936.	+	120760.i	−0.405338	+	0.379633i
$565$	−226734.	+	392714.i	−0.710263	+	1.23021i
$566$	419318.	−	322380.i	1.30891	−	1.00632i
$567$	581256.	−	235642.i	1.80801	−	0.732971i
$568$	106234.	+	254443.i	0.329282	+	0.788667i
$569$	138564.	−	240000.i	0.427982	−	0.741287i	−0.568712	−	0.822537i	$-0.692558\pi$
$569$	138564.	−	240000.i	0.427982	−	0.741287i	0.996694	+	0.0812502i	$0.0258913\pi$
$570$	25057.9	+	256912.i	0.0771248	+	0.790742i
$571$	556449.	−	321266.i	1.70668	−	0.985355i	0.768085	−	0.640348i	$-0.221210\pi$
$571$	556449.	−	321266.i	1.70668	−	0.985355i	0.938600	−	0.345007i	$-0.112123\pi$
$572$	−11511.4	−	42640.6i	−0.0351831	−	0.130326i
$573$	456880.	−	243101.i	1.39153	−	0.740418i
$574$	−16529.6	−	124651.i	−0.0501694	−	0.378330i
$575$			30799.0i			0.0931540i
$576$	−314366.	−	106061.i	−0.947526	−	0.319678i
$577$	451002.			1.35465			0.677324	−	0.735685i	$-0.263140\pi$
$577$	451002.			1.35465			0.677324	+	0.735685i	$0.263140\pi$
$578$	11664.5	−	1546.80i	0.0349148	−	0.00462997i
$579$	−404232.	−	13996.5i	−1.20580	−	0.0417507i
$580$	−413864.	+	111728.i	−1.23027	+	0.332128i
$581$	158808.	+	275063.i	0.470456	+	0.814854i
$582$	122243.	+	170932.i	0.360893	+	0.504635i
$583$	−53679.3	−	30991.8i	−0.157932	−	0.0911820i
$584$	−177812.	+	74239.5i	−0.521357	+	0.217675i
$585$	−225915.	−	15663.4i	−0.660135	−	0.0457692i
$586$	−218250.	−	283876.i	−0.635563	−	0.826674i
$587$	−327761.	−	189233.i	−0.951221	−	0.549188i	−0.0577610	−	0.998330i	$-0.518396\pi$
$587$	−327761.	−	189233.i	−0.951221	−	0.549188i	−0.893460	+	0.449143i	$0.851729\pi$
$588$	−944869.	+	220304.i	−2.73286	+	0.637187i
$589$	−134303.	−	232620.i	−0.387129	−	0.670528i
$590$	120850.	+	49924.6i	0.347169	+	0.143420i
$591$	212202.	−	339818.i	0.607541	−	0.972908i
$592$	−70491.8	+	41052.1i	−0.201138	+	0.117136i
$593$	137966.			0.392339			0.196170	−	0.980570i	$-0.437150\pi$
$593$	137966.			0.392339			0.196170	+	0.980570i	$0.437150\pi$
$594$	−56098.3	−	30326.5i	−0.158993	−	0.0859506i
$595$			601046.i			1.69775i
$596$	−338750.	−	337480.i	−0.953644	−	0.950070i
$597$	−145553.	−	90892.1i	−0.408389	−	0.255022i
$598$	−106923.	−	44171.4i	−0.298998	−	0.123521i
$599$	−180870.	+	104426.i	−0.504096	+	0.291040i	−0.730404	−	0.683016i	$-0.760668\pi$
$599$	−180870.	+	104426.i	−0.504096	+	0.291040i	0.226307	+	0.974056i	$0.427335\pi$
$600$	−59895.4	−	49061.7i	−0.166376	−	0.136283i
$601$	−180004.	+	311775.i	−0.498348	+	0.863163i	−0.999998	−	0.00190701i	$-0.999393\pi$
$601$	−180004.	+	311775.i	−0.498348	+	0.863163i	0.501651	+	0.865070i	$0.332726\pi$
$602$	48262.9	+	62775.3i	0.133174	+	0.173219i
$603$	16651.7	+	11217.4i	0.0457956	+	0.0308501i
$604$	−92203.3	−	24520.4i	−0.252739	−	0.0672130i
$605$	156846.	−	271665.i	0.428512	−	0.742204i
$606$	−115157.	−	161024.i	−0.313578	−	0.438474i
$607$	279709.	−	161490.i	0.759152	−	0.438297i	−0.0698392	−	0.997558i	$-0.522249\pi$
$607$	279709.	−	161490.i	0.759152	−	0.438297i	0.828991	+	0.559262i	$0.188915\pi$
$608$	−203036.	−	262045.i	−0.549244	−	0.708875i
$609$	−36013.8	+	1.04011e6i	−0.0971034	+	2.80443i
$610$	−164445.	+	21806.6i	−0.441937	+	0.0586042i
$611$		−	154850.i		−	0.414791i
$612$	242042.	+	277053.i	0.646230	+	0.739707i
$613$	−392554.			−1.04467			−0.522334	−	0.852741i	$-0.674939\pi$
$613$	−392554.			−1.04467			−0.522334	+	0.852741i	$0.674939\pi$
$614$	−32983.5	−	248730.i	−0.0874904	−	0.659769i
$615$	30791.4	+	57869.0i	0.0814103	+	0.153002i
$616$	106379.	+	81152.6i	0.280346	+	0.213866i
$617$	−192102.	−	332730.i	−0.504616	−	0.874020i	−0.999986	−	0.00533786i	$-0.998301\pi$
$617$	−192102.	−	332730.i	−0.504616	−	0.874020i	0.495370	−	0.868682i	$-0.335032\pi$
$618$	−62670.8	−	642548.i	−0.164092	−	1.68240i
$619$	−602573.	−	347896.i	−1.57264	−	0.907962i	−0.995844	−	0.0910712i	$-0.970971\pi$
$619$	−602573.	−	347896.i	−1.57264	−	0.907962i	−0.576792	−	0.816891i	$-0.695696\pi$
$620$	−284166.	−	75570.6i	−0.739247	−	0.196594i
$621$	−152535.	+	68074.9i	−0.395536	+	0.176524i
$622$	389360.	−	299347.i	1.00640	−	0.773739i
$623$	128310.	+	74079.7i	0.330586	+	0.190864i
$624$	256225.	−	137571.i	0.658041	−	0.353313i
$625$	144273.	+	249889.i	0.369339	+	0.639715i
$626$	−74208.4	+	179632.i	−0.189367	+	0.458389i
$627$	−29930.2	−	56250.4i	−0.0761332	−	0.143084i
$628$	396575.	+	395089.i	1.00556	+	1.00179i
$629$	90453.5			0.228625
$630$	571488.	−	379518.i	1.43988	−	0.956205i
$631$			230753.i			0.579546i	0.957095	+	0.289773i	$0.0935798\pi$
$631$			230753.i			0.579546i	−0.957095	+	0.289773i	$0.906420\pi$
$632$	456513.	+	58793.7i	1.14293	+	0.147196i
$633$	−296.775	+	8571.13i	−0.000740662	+	0.0213910i
$634$	−168203.	+	407158.i	−0.418461	+	1.01294i
$635$	155955.	−	90040.8i	0.386770	−	0.223302i
$636$	118479.	−	390560.i	0.292905	−	0.965548i
$637$	425225.	−	736511.i	1.04795	−	1.81510i
$638$	83889.0	−	64495.5i	0.206093	−	0.158449i
$639$	−313562.	+	153164.i	−0.767931	+	0.375107i
$640$	−360090.	−	45001.6i	−0.879126	−	0.109867i
$641$	−259471.	+	449416.i	−0.631498	+	1.09379i	0.355747	+	0.934582i	$0.384226\pi$
$641$	−259471.	+	449416.i	−0.631498	+	1.09379i	−0.987246	+	0.159205i	$0.949107\pi$
$642$	285657.	+	129756.i	0.693067	+	0.314816i
$643$	−195039.	+	112606.i	−0.471738	+	0.272358i	−0.716967	−	0.697107i	$-0.754470\pi$
$643$	−195039.	+	112606.i	−0.471738	+	0.272358i	0.245229	+	0.969465i	$0.421137\pi$
$644$	338351.	−	91341.9i	0.815821	−	0.220241i
$645$	−35013.5	−	21864.5i	−0.0841620	−	0.0525557i
$646$	48321.1	+	364392.i	0.115790	+	0.873179i
$647$		−	153505.i		−	0.366703i	−0.983047	−	0.183352i	$-0.941305\pi$
$647$		−	153505.i		−	0.366703i	0.983047	−	0.183352i	$-0.0586947\pi$
$648$	110596.	−	405078.i	0.263384	−	0.964691i
$649$	−32276.0			−0.0766284
$650$	67278.0	−	8921.58i	0.159238	−	0.0211162i
$651$	−378113.	+	605505.i	−0.892194	+	1.42875i
$652$	60507.5	+	224133.i	0.142336	+	0.527243i
$653$	−36120.4	−	62562.3i	−0.0847082	−	0.146719i	0.820559	−	0.571562i	$-0.193662\pi$
$653$	−36120.4	−	62562.3i	−0.0847082	−	0.146719i	−0.905267	+	0.424843i	$0.860329\pi$
$654$	−181076.	+	398637.i	−0.423355	+	0.932014i
$655$	312193.	+	180245.i	0.727681	+	0.420127i
$656$	−73061.5	−	41817.1i	−0.169778	−	0.0971731i
$657$	−107035.	−	219126.i	−0.247968	−	0.507649i
$658$	285920.	+	371895.i	0.660378	+	0.858950i
$659$	203157.	+	117293.i	0.467802	+	0.270086i	0.715319	−	0.698798i	$-0.246281\pi$
$659$	203157.	+	117293.i	0.467802	+	0.270086i	−0.247517	+	0.968883i	$0.579615\pi$
$660$	−66747.8	−	20248.4i	−0.153232	−	0.0464838i
$661$	−298973.	−	517837.i	−0.684274	−	1.18520i	−0.973665	−	0.227986i	$-0.926786\pi$
$661$	−298973.	−	517837.i	−0.684274	−	1.18520i	0.289391	−	0.957211i	$-0.406547\pi$
$662$	−682164.	−	281812.i	−1.55659	−	0.643048i
$663$	−322284.	−	11159.1i	−0.733182	−	0.0253864i
$664$	210897.	+	27161.1i	0.478337	+	0.0616043i
$665$	685452.			1.55001
$666$	−57114.9	−	86005.2i	−0.128766	−	0.193899i
$667$		−	277166.i		−	0.623001i
$668$	−503844.	+	505739.i	−1.12913	+	1.13338i
$669$	344366.	−	183233.i	0.769428	−	0.409404i
$670$	20296.7	+	8384.87i	0.0452144	+	0.0186787i
$671$	35461.3	−	20473.6i	0.0787607	−	0.0454725i
$672$	−361346.	+	803500.i	−0.800174	+	1.77929i
$673$	375852.	−	650996.i	0.829826	−	1.43730i	−0.0683477	−	0.997662i	$-0.521773\pi$
$673$	375852.	−	650996.i	0.829826	−	1.43730i	0.898174	−	0.439640i	$-0.144894\pi$
$674$	159998.	+	208109.i	0.352204	+	0.458111i
$675$	57526.8	−	79326.6i	0.126259	−	0.174105i
$676$	51928.7	−	195266.i	0.113636	−	0.427301i
$677$	42323.8	−	73307.0i	0.0923437	−	0.159944i	−0.816153	−	0.577836i	$-0.803897\pi$
$677$	42323.8	−	73307.0i	0.0923437	−	0.159944i	0.908497	+	0.417892i	$0.137231\pi$
$678$	733561.	−	71547.7i	1.59580	−	0.155645i
$679$	483267.	−	279014.i	1.04821	−	0.605183i
$680$	319927.	+	244060.i	0.691883	+	0.527812i
$681$	47731.4	−	25397.3i	0.102922	−	0.0547638i
$682$	71952.2	−	9541.41i	0.154695	−	0.0205137i
$683$			635506.i			1.36232i	0.732136	+	0.681159i	$0.238524\pi$
$683$			635506.i			1.36232i	−0.732136	+	0.681159i	$0.761476\pi$
$684$	315960.	−	276032.i	0.675336	−	0.589994i
$685$	−546260.			−1.16418
$686$	217987.	+	1.64385e6i	0.463214	+	3.49312i
$687$	−36665.2	−	1269.53i	−0.0776855	−	0.00268986i
$688$	53011.8	−	199.053i	0.111994	−	0.000420525i
$689$	178878.	+	309825.i	0.376806	+	0.652647i
$690$	−148609.	+	106279.i	−0.312138	+	0.223228i
$691$	−384843.	−	222189.i	−0.805986	−	0.465336i	0.0395741	−	0.999217i	$-0.487400\pi$
$691$	−384843.	−	222189.i	−0.805986	−	0.465336i	−0.845560	+	0.533881i	$0.820733\pi$
$692$	217474.	−	817762.i	0.454145	−	1.70771i
$693$	−94610.6	+	140445.i	−0.197003	+	0.292442i
$694$	332553.	−	255673.i	0.690466	−	0.530844i
$695$	378265.	+	218391.i	0.783116	+	0.452132i
$696$	539009.	+	441515.i	1.11270	+	0.911438i
$697$	46672.6	+	80839.4i	0.0960720	+	0.166402i
$698$	133397.	−	322906.i	0.273802	−	0.662775i
$699$	178418.	−	285716.i	0.365161	−	0.584764i
$700$	−145105.	+	145651.i	−0.296132	+	0.297246i
$701$	−374624.			−0.762359			−0.381179	−	0.924501i	$-0.624482\pi$
$701$	−374624.			−0.762359			−0.381179	+	0.924501i	$0.624482\pi$
$702$	192889.	+	313481.i	0.391411	+	0.636117i
$703$		−	103156.i		−	0.208730i
$704$	86392.4	−	23671.1i	0.174313	−	0.0477609i
$705$	−207428.	−	129530.i	−0.417338	−	0.260610i
$706$	−74390.9	+	180073.i	−0.149249	+	0.361277i
$707$	−455254.	+	262841.i	−0.910783	+	0.525841i
$708$	−48257.2	−	206972.i	−0.0962711	−	0.412901i
$709$	−92815.5	+	160761.i	−0.184641	+	0.319808i	−0.943456	−	0.331499i	$-0.892446\pi$
$709$	−92815.5	+	160761.i	−0.184641	+	0.319808i	0.758814	+	0.651307i	$0.225779\pi$
$710$	−302603.	+	232647.i	−0.600284	+	0.461510i
$711$	−40293.0	+	581151.i	−0.0797059	+	1.14961i
$712$	91532.8	−	38216.5i	0.180558	−	0.0753860i
$713$	95057.9	−	164645.i	0.186986	−	0.323869i
$714$	794615.	−	568275.i	1.55869	−	1.11471i
$715$	52950.0	−	30570.7i	0.103575	−	0.0597989i
$716$	136950.	+	507293.i	0.267138	+	0.989539i
$717$	7987.96	−	230699.i	0.0155381	−	0.448753i
$718$	−57530.0	−	433836.i	−0.111595	−	0.841544i
$719$			651163.i			1.25960i	0.776759	+	0.629799i	$0.216863\pi$
$719$			651163.i			1.25960i	−0.776759	+	0.629799i	$0.783137\pi$
$720$	30046.7	−	458300.i	0.0579604	−	0.884066i
$721$	−1.71435e6			−3.29783
$722$	−101196.	+	13419.4i	−0.194129	+	0.0257429i
$723$	−323840.	−	608621.i	−0.619519	−	1.16432i
$724$	−351552.	+	94905.9i	−0.670676	+	0.181057i
$725$	81298.3	+	140813.i	0.154670	+	0.267896i
$726$	−507450.	+	49494.1i	−0.962765	+	0.0939031i
$727$	−207917.	−	120041.i	−0.393389	−	0.227123i	0.290239	−	0.956954i	$-0.406265\pi$
$727$	−207917.	−	120041.i	−0.393389	−	0.227123i	−0.683627	+	0.729831i	$0.739599\pi$
$728$	−297539.	−	712640.i	−0.561412	−	1.34465i
$729$	520023.	+	109571.i	0.978515	+	0.206178i
$730$	−162581.	−	211468.i	−0.305086	−	0.396825i
$731$	−50907.1	−	29391.2i	−0.0952673	−	0.0550026i
$732$	184308.	+	196787.i	0.343972	+	0.367261i
$733$	27840.0	+	48220.4i	0.0518158	+	0.0897475i	0.890770	−	0.454455i	$-0.150166\pi$
$733$	27840.0	+	48220.4i	0.0518158	+	0.0897475i	−0.838954	+	0.544202i	$0.816832\pi$
$734$	4750.49	+	1962.49i	0.00881752	+	0.00364264i
$735$	−630889.	−	1.18569e6i	−1.16783	−	2.19480i
$736$	88770.5	−	217189.i	0.163875	−	0.400942i
$737$	−5420.76			−0.00997988
$738$	47393.4	−	95421.7i	0.0870173	−	0.175200i
$739$		−	327859.i		−	0.600341i	−0.953886	−	0.300170i	$-0.902957\pi$
$739$		−	327859.i		−	0.600341i	0.953886	−	0.300170i	$-0.0970435\pi$
$740$	−79999.7	−	79699.9i	−0.146091	−	0.145544i
$741$	−12726.2	+	367543.i	−0.0231772	+	0.669379i
$742$	−1.00167e6	−	413805.i	−1.81936	−	0.751602i
$743$	11150.8	−	6437.91i	0.0201989	−	0.0116618i	−0.489867	−	0.871797i	$-0.662955\pi$
$743$	11150.8	−	6437.91i	0.0201989	−	0.0116618i	0.510065	+	0.860136i	$0.329621\pi$
$744$	168764.	+	447134.i	0.304884	+	0.807777i
$745$	330968.	−	573254.i	0.596312	−	1.03284i
$746$	−179327.	−	233250.i	−0.322232	−	0.419126i
$747$	−18614.3	+	268476.i	−0.0333584	+	0.481132i
$748$	−95990.4	−	25527.5i	−0.171563	−	0.0456252i
$749$	416567.	−	721516.i	0.742543	−	1.28612i
$750$	250431.	−	551323.i	0.445211	−	0.980129i
$751$	−460430.	+	265829.i	−0.816363	+	0.471328i	−0.849161	−	0.528134i	$-0.822892\pi$
$751$	−460430.	+	265829.i	−0.816363	+	0.471328i	0.0327975	+	0.999462i	$0.489558\pi$
$752$	314054.	−	1179.23i	0.555352	−	0.00208528i
$753$	508739.	+	317687.i	0.897233	+	0.560285i
$754$	−605447.	+	80286.9i	−1.06496	+	0.141222i
$755$		−	132075.i		−	0.231701i
$756$	−1.04207e6	−	396713.i	−1.82328	−	0.694117i
$757$	614542.			1.07241			0.536204	−	0.844089i	$-0.319858\pi$
$757$	614542.			1.07241			0.536204	+	0.844089i	$0.319858\pi$
$758$	−73126.6	−	551451.i	−0.127273	−	0.959774i
$759$	23887.1	−	38252.6i	0.0414649	−	0.0664014i
$760$	278334.	−	364855.i	0.481880	−	0.631674i
$761$	410349.	+	710745.i	0.708571	+	1.22728i	0.965387	+	0.260821i	$0.0839933\pi$
$761$	410349.	+	710745.i	0.708571	+	1.22728i	−0.256816	+	0.966460i	$0.582673\pi$
$762$	−266491.	−	121050.i	−0.458957	−	0.208475i
$763$	1.00688e6	+	581324.i	1.72954	+	0.998548i
$764$	−889149.	−	236458.i	−1.52331	−	0.405105i
$765$	−284534.	+	422377.i	−0.486196	+	0.721734i
$766$	−329554.	+	253368.i	−0.561654	+	0.431811i
$767$	161332.	+	93144.9i	0.274239	+	0.158332i
$768$	280962.	+	518607.i	0.476349	+	0.879256i
$769$	65721.6	+	113833.i	0.111136	+	0.192494i	0.916229	−	0.400656i	$-0.131218\pi$
$769$	65721.6	+	113833.i	0.111136	+	0.192494i	−0.805092	+	0.593149i	$0.797884\pi$
$770$	−70720.3	+	171188.i	−0.119279	+	0.288730i
$771$	534517.	+	18507.7i	0.899193	+	0.0311346i
$772$	509410.	+	507500.i	0.854737	+	0.851534i
$773$	−629.598			−0.00105367			−0.000526834	−	1.00000i	$-0.500168\pi$
$773$	−629.598			−0.00105367			−0.000526834		1.00000i	$0.500168\pi$
$774$	4198.39	+	66962.1i	0.00700811	+	0.111776i
$775$			111529.i			0.185689i
$776$	47720.2	−	370531.i	0.0792463	−	0.615321i
$777$	−242026.	+	128779.i	−0.400885	+	0.213306i
$778$	−152851.	+	369998.i	−0.252528	+	0.611280i
$779$	92191.9	−	53227.0i	0.151921	−	0.0877117i
$780$	275205.	+	293838.i	0.452342	+	0.482969i
$781$	47109.5	−	81596.0i	0.0772336	−	0.133773i
$782$	−206257.	+	158574.i	−0.337283	+	0.259310i
$783$	−517694.	+	713874.i	−0.844403	+	1.16439i
$784$	1.49697e6	+	856796.i	2.43545	+	1.39394i
$785$	−387466.	+	671110.i	−0.628773	+	1.08907i
$786$	−56877.8	−	583154.i	−0.0920656	−	0.943926i
$787$	415038.	−	239622.i	0.670098	−	0.386881i	−0.126016	−	0.992028i	$-0.540219\pi$
$787$	415038.	−	239622.i	0.670098	−	0.386881i	0.796114	+	0.605147i	$0.206886\pi$
$788$	−687619.	+	185631.i	−1.10738	+	0.298950i
$789$	−199747.	+	106283.i	−0.320867	+	0.170730i
$790$	83761.6	+	631650.i	0.134212	+	1.01210i
$791$		−	1.95717e6i		−	3.12807i
$792$	36339.0	+	107389.i	0.0579326	+	0.171202i
$793$	−236338.			−0.375826
$794$	−651847.	+	86439.9i	−1.03396	+	0.137111i
$795$	564652.	+	19551.1i	0.893401	+	0.0309340i
$796$	79511.0	+	294526.i	0.125488	+	0.464834i
$797$	344008.	+	595840.i	0.541567	+	0.938021i	0.998814	+	0.0486819i	$0.0155020\pi$
$797$	344008.	+	595840.i	0.541567	+	0.938021i	−0.457247	+	0.889340i	$0.651165\pi$
$798$	−648079.	−	906206.i	−1.01771	−	1.42305i
$799$	−301585.	−	174120.i	−0.472407	−	0.272744i
$800$	18606.3	+	136380.i	0.0290724	+	0.213093i
$801$	55098.9	+	112800.i	0.0858772	+	0.175811i
$802$	−381436.	−	496133.i	−0.593026	−	0.771346i
$803$	57021.6	+	32921.5i	0.0884318	+	0.0510561i
$804$	−8104.82	−	34761.1i	−0.0125381	−	0.0537751i
$805$	242576.	+	420155.i	0.374332	+	0.648362i
$806$	−387189.	−	159953.i	−0.596010	−	0.246220i
$807$	−12172.4	+	19492.7i	−0.0186908	+	0.0299312i
$808$	−44954.1	+	349053.i	−0.0688567	+	0.534649i
$809$	−423910.			−0.647703			−0.323852	−	0.946108i	$-0.604978\pi$
$809$	−423910.			−0.647703			−0.323852	+	0.946108i	$0.604978\pi$
$810$	581269.	+	3840.08i	0.885945	+	0.00585289i
$811$			257508.i			0.391515i	0.980652	+	0.195757i	$0.0627165\pi$
$811$			257508.i			0.391515i	−0.980652	+	0.195757i	$0.937283\pi$
$812$	1.30582e6	−	1.31074e6i	1.98049	−	1.98794i
$813$	35292.1	+	22038.4i	0.0533944	+	0.0333426i
$814$	25762.7	+	10642.9i	0.0388815	+	0.0160625i
$815$	−278323.	+	160690.i	−0.419019	+	0.241921i
$816$	20177.6	−	653714.i	0.0303032	−	0.981764i
$817$	−33518.7	+	58056.2i	−0.0502162	+	0.0869770i
$818$	659979.	+	858432.i	0.986333	+	1.28292i
$819$	878221.	−	428979.i	1.30929	−	0.639541i
$820$	29950.1	−	112621.i	0.0445421	−	0.167491i
$821$	439034.	−	760430.i	0.651347	−	1.12817i	−0.331450	−	0.943473i	$-0.607538\pi$
$821$	439034.	−	760430.i	0.651347	−	1.12817i	0.982796	−	0.184692i	$-0.0591289\pi$
$822$	516476.	+	722186.i	0.764376	+	1.06882i
$823$	571229.	−	329799.i	0.843355	−	0.486911i	−0.0150484	−	0.999887i	$-0.504790\pi$
$823$	571229.	−	329799.i	0.843355	−	0.486911i	0.858403	+	0.512976i	$0.171457\pi$
$824$	−696126.	+	912519.i	−1.02526	+	1.34396i
$825$	−915.505	+	26440.6i	−0.00134509	+	0.0388475i
$826$	−559447.	+	74186.9i	−0.819971	+	0.108734i
$827$			853638.i			1.24814i	0.781369	+	0.624069i	$0.214522\pi$
$827$			853638.i			1.24814i	−0.781369	+	0.624069i	$0.785478\pi$
$828$	281013.	+	95985.2i	0.409888	+	0.140005i
$829$	542017.			0.788685			0.394343	−	0.918963i	$-0.370972\pi$
$829$	542017.			0.788685			0.394343	+	0.918963i	$0.370972\pi$
$830$	38695.6	+	291805.i	0.0561701	+	0.423581i
$831$	41660.3	+	78295.7i	0.0603281	+	0.113380i
$832$	−500145.	−	130999.i	−0.722519	−	0.189243i
$833$	−956282.	−	1.65633e6i	−1.37815	−	2.38702i
$834$	−68915.2	−	706570.i	−0.0990792	−	1.01583i
$835$	−855844.	−	494122.i	−1.22750	−	0.708698i
$836$	−29112.4	+	109471.i	−0.0416548	+	0.156634i
$837$	−552359.	+	246513.i	−0.788443	+	0.351875i
$838$	−180764.	+	138975.i	−0.257410	+	0.197901i
$839$	1.01749e6	+	587450.i	1.44547	+	0.834540i	0.998207	−	0.0598644i	$-0.0190668\pi$
$839$	1.01749e6	+	587450.i	1.44547	+	0.834540i	0.447259	+	0.894404i	$0.352400\pi$
$840$	−1.20350e6	−	197549.i	−1.70564	−	0.279973i
$841$	−377978.	−	654677.i	−0.534410	−	0.925625i
$842$	356806.	−	863699.i	0.503278	−	1.21826i
$843$	204688.	+	384688.i	0.288030	+	0.541319i
$844$	10760.8	−	10801.3i	0.0151063	−	0.0151632i
$845$	279706.			0.391732
$846$	24872.2	+	396698.i	0.0347515	+	0.554267i
$847$			1.35390e6i			1.88721i
$848$	−626999.	+	365144.i	−0.871917	+	0.507776i
$849$	41181.5	−	1.18936e6i	0.0571330	−	1.65005i
$850$	58274.7	−	141062.i	0.0806570	−	0.195242i
$851$	63230.5	−	36506.2i	0.0873108	−	0.0504089i
$852$	593677.	+	180096.i	0.817845	+	0.248098i
$853$	−587574.	+	1.01771e6i	−0.807541	+	1.39870i	0.107021	+	0.994257i	$0.465869\pi$
$853$	−587574.	+	1.01771e6i	−0.807541	+	1.39870i	−0.914562	+	0.404445i	$0.867465\pi$
$854$	567600.	−	436382.i	0.778263	−	0.598344i
$855$	481693.	+	324492.i	0.658928	+	0.443886i
$856$	−214900.	−	514710.i	−0.293284	−	0.702449i
$857$	−447698.	+	775436.i	−0.609570	+	1.05581i	0.381741	+	0.924269i	$0.375325\pi$
$857$	−447698.	+	775436.i	−0.609570	+	1.05581i	−0.991311	+	0.131538i	$0.958009\pi$
$858$	−90479.1	−	41098.9i	−0.122906	−	0.0558285i
$859$	918319.	−	530192.i	1.24454	−	0.718533i	0.274521	−	0.961581i	$-0.411481\pi$
$859$	918319.	−	530192.i	1.24454	−	0.718533i	0.970014	+	0.243048i	$0.0781473\pi$
$860$	19126.7	+	70849.5i	0.0258609	+	0.0957943i
$861$	−239973.	−	149853.i	−0.323711	−	0.202144i
$862$	−175195.	−	1.32116e6i	−0.235781	−	1.77803i
$863$		−	150213.i		−	0.201691i	−0.994902	−	0.100845i	$-0.967845\pi$
$863$		−	150213.i		−	0.201691i	0.994902	−	0.100845i	$-0.0321547\pi$
$864$	−634306.	+	393589.i	−0.849711	+	0.527248i
$865$	1.17139e6			1.56556
$866$	853898.	−	113233.i	1.13860	−	0.150987i
$867$	14022.9	−	22456.1i	0.0186552	−	0.0298742i
$868$	1.22523e6	−	330767.i	1.62622	−	0.439019i
$869$	−78641.1	−	136210.i	−0.104138	−	0.180373i
$870$	−398901.	+	878178.i	−0.527019	+	1.16023i
$871$	27095.7	+	15643.7i	0.0357161	+	0.0206207i
$872$	718283.	−	299895.i	0.944631	−	0.394399i
$873$	471695.	+	32704.1i	0.618917	+	0.0429114i
$874$	180843.	+	235222.i	0.236744	+	0.307932i
$875$	−1.39254e6	−	803981.i	−1.81882	−	1.05010i
$876$	−125856.	+	414878.i	−0.164008	+	0.540645i
$877$	588870.	+	1.01995e6i	0.765632	+	1.32611i	0.939912	+	0.341418i	$0.110907\pi$
$877$	588870.	+	1.01995e6i	0.765632	+	1.32611i	−0.174280	+	0.984696i	$0.555760\pi$
$878$	−115487.	−	47709.2i	−0.149811	−	0.0618890i
$879$	−805190.	−	27879.7i	−1.04213	−	0.0360836i
$880$	62404.1	+	107156.i	0.0805838	+	0.138373i
$881$	1.15136e6			1.48341			0.741703	−	0.670728i	$-0.234018\pi$
$881$	1.15136e6			1.48341			0.741703	+	0.670728i	$0.234018\pi$
$882$	−971050.	+	1.95511e6i	−1.24826	+	2.51324i
$883$		−	109897.i		−	0.140950i	−0.997514	−	0.0704752i	$-0.977548\pi$
$883$		−	109897.i		−	0.140950i	0.997514	−	0.0704752i	$-0.0224516\pi$
$884$	406139.	+	404617.i	0.519721	+	0.517773i
$885$	259723.	−	138195.i	0.331607	−	0.176444i
$886$	789012.	+	325952.i	1.00512	+	0.415228i
$887$	−856444.	+	494468.i	−1.08856	+	0.628480i	−0.933192	−	0.359377i	$-0.882989\pi$
$887$	−856444.	+	494468.i	−1.08856	+	0.628480i	−0.155366	+	0.987857i	$0.549656\pi$
$888$	−29729.8	+	181118.i	−0.0377021	+	0.229687i
$889$	−388618.	+	673105.i	−0.491721	+	0.851686i
$890$	83692.1	+	108858.i	0.105658	+	0.137429i
$891$	−132973.	+	53907.3i	−0.167497	+	0.0679036i
$892$	−670181.	−	178227.i	−0.842292	−	0.223997i
$893$	−198572.	+	343937.i	−0.249009	+	0.431297i
$894$	−1.07080e6	+	104440.i	−1.33977	+	0.130675i
$895$	−629943.	+	363698.i	−0.786421	+	0.454040i
$896$	1.44305e6	−	608871.i	1.79749	−	0.758419i
$897$	−229793.	+	122270.i	−0.285596	+	0.151962i
$898$	1.55857e6	−	206678.i	1.93274	−	0.256296i
$899$		−	1.00367e6i		−	1.24186i
$900$	−170921.	+	33661.8i	−0.211014	+	0.0415577i
$901$	804551.			0.991070
$902$	3781.45	+	28516.1i	0.00464777	+	0.0350491i
$903$	178056.	+	6165.21i	0.218365	+	0.00756087i
$904$	−1.04177e6	−	794728.i	−1.27478	−	0.972482i
$905$	−252041.	−	436548.i	−0.307733	−	0.533010i
$906$	−174611.	+	124874.i	−0.212723	+	0.152130i
$907$	−445673.	−	257309.i	−0.541753	−	0.312781i	0.204036	−	0.978963i	$-0.434594\pi$
$907$	−445673.	−	257309.i	−0.541753	−	0.312781i	−0.745789	+	0.666182i	$0.767927\pi$
$908$	−92891.5	−	24703.4i	−0.112669	−	0.0299630i
$909$	−444352.	−	30808.3i	−0.537774	−	0.0372855i
$910$	847527.	−	651595.i	1.02346	−	0.786856i
$911$	992039.	+	572754.i	1.19534	+	0.690131i	0.959513	−	0.281664i	$-0.0908862\pi$
$911$	992039.	+	572754.i	1.19534	+	0.690131i	0.235829	+	0.971795i	$0.424220\pi$
$912$	−745517.	−	23011.2i	−0.896330	−	0.0276662i
$913$	−36330.1	−	62925.6i	−0.0435838	−	0.0754894i
$914$	−110509.	+	267502.i	−0.132283	+	0.320210i
$915$	−197694.	+	316584.i	−0.236129	+	0.378135i
$916$	46205.1	+	46032.0i	0.0550680	+	0.0548616i
$917$	−1.55588e6			−1.85028
$918$	827426.	−	23178.0i	0.981847	−	0.0275037i
$919$		−	329486.i		−	0.390127i	−0.980791	−	0.195063i	$-0.937509\pi$
$919$		−	329486.i		−	0.390127i	0.980791	−	0.195063i	$-0.0624913\pi$
$920$	322142.	+	41488.2i	0.380602	+	0.0490172i
$921$	−478848.	−	299021.i	−0.564518	−	0.352518i
$922$	88874.2	−	215132.i	0.104548	−	0.253072i
$923$	−470954.	+	271906.i	−0.552809	+	0.319165i
$924$	293185.	−	68358.4i	0.343398	−	0.0800659i
$925$	−21416.0	+	37093.5i	−0.0250296	+	0.0433525i
$926$	236991.	−	182203.i	0.276382	−	0.212488i
$927$	−1.20474e6	−	811569.i	−1.40195	−	0.944422i
$928$	−167442.	−	1.22731e6i	−0.194432	−	1.42514i
$929$	453534.	−	785545.i	0.525507	−	0.910205i	−0.474051	−	0.880497i	$-0.657209\pi$
$929$	453534.	−	785545.i	0.525507	−	0.910205i	0.999559	−	0.0297082i	$-0.00945781\pi$
$930$	−538142.	+	384856.i	−0.622202	+	0.444972i
$931$	−1.88893e6	+	1.09058e6i	−2.17930	+	1.25822i
$932$	−578145.	+	156077.i	−0.665587	+	0.179683i
$933$	38239.3	−	1.10438e6i	0.0439285	−	1.26869i
$934$	139011.	+	1.04829e6i	0.159351	+	1.20167i
$935$		−	137500.i		−	0.157282i
$936$	128271.	−	641653.i	0.146412	−	0.732401i
$937$	1.29741e6			1.47774			0.738872	−	0.673846i	$-0.235359\pi$
$937$	1.29741e6			1.47774			0.738872	+	0.673846i	$0.235359\pi$
$938$	−93959.3	+	12459.7i	−0.106791	+	0.0141613i
$939$	205415.	+	386054.i	0.232971	+	0.437842i
$940$	113311.	+	419728.i	0.128238	+	0.475020i
$941$	−54978.4	−	95225.4i	−0.0620888	−	0.107541i	0.833310	−	0.552806i	$-0.186443\pi$
$941$	−54978.4	−	95225.4i	−0.0620888	−	0.107541i	−0.895399	+	0.445265i	$0.853110\pi$
$942$	1.25358e6	−	122268.i	1.41271	−	0.137788i
$943$	65252.1	+	37673.3i	0.0733788	+	0.0423653i
$944$	−187680.	+	327908.i	−0.210608	+	0.367967i
$945$	159985.	−	1.53525e6i	0.179150	−	1.71915i
$946$	−11041.0	−	14361.0i	−0.0123375	−	0.0160473i
$947$	−476861.	−	275316.i	−0.531730	−	0.306995i	0.209990	−	0.977703i	$-0.432657\pi$
$947$	−476861.	−	275316.i	−0.531730	−	0.306995i	−0.741721	+	0.670709i	$0.765990\pi$
$948$	755881.	−	707947.i	0.841079	−	0.787742i
$949$	−190015.	−	329116.i	−0.210987	−	0.365441i
$950$	−160872.	−	66458.4i	−0.178251	−	0.0736381i
$951$	465599.	+	875041.i	0.514815	+	0.967537i
$952$	−1.72250e6	−	221838.i	−1.90058	−	0.244772i
$953$	−802951.			−0.884104			−0.442052	−	0.896989i	$-0.645749\pi$
$953$	−802951.			−0.884104			−0.442052	+	0.896989i	$0.645749\pi$
$954$	−508017.	−	764985.i	−0.558189	−	0.840536i
$955$		−	1.27365e6i		−	1.39650i
$956$	−289635.	+	290725.i	−0.316910	+	0.318102i
$957$	8238.80	−	237944.i	0.00899580	−	0.259807i
$958$	1.03397e6	+	427147.i	1.12662	+	0.465421i
$959$	2.04180e6	−	1.17883e6i	2.22012	−	1.28179i
$960$	−593842.	+	560385.i	−0.644360	+	0.608056i
$961$	−117537.	+	203580.i	−0.127271	+	0.220439i
$962$	−98060.8	−	127547.i	−0.105961	−	0.137823i
$963$	634301.	−	309834.i	0.683980	−	0.334100i
$964$	−314992.	+	1.18446e6i	−0.338958	+	1.27458i
$965$	−497708.	+	862055.i	−0.534466	+	0.925722i
$966$	326117.	−	717946.i	0.349478	−	0.769374i
$967$	−826524.	+	477194.i	−0.883898	+	0.510319i	−0.871942	−	0.489610i	$-0.837139\pi$
$967$	−826524.	+	477194.i	−0.883898	+	0.510319i	−0.0119565	+	0.999929i	$0.503806\pi$
$968$	720658.	+	549763.i	0.769093	+	0.586712i
$969$	701515.	+	438067.i	0.747118	+	0.466544i
$970$	512682.	−	67985.5i	0.544885	−	0.0722559i
$971$			708749.i			0.751716i	0.926677	+	0.375858i	$0.122652\pi$
$971$			708749.i			0.751716i	−0.926677	+	0.375858i	$0.877348\pi$
$972$	−544499.	−	772100.i	−0.576321	−	0.817223i
$973$	−1.88516e6			−1.99123
$974$	−32867.5	−	247856.i	−0.0346457	−	0.261265i
$975$	80880.8	−	129521.i	0.0850817	−	0.136249i
$976$	−1799.79	−	479321.i	−0.00188939	−	0.503184i
$977$	311552.	+	539625.i	0.326394	+	0.565331i	0.981793	−	0.189952i	$-0.0608331\pi$
$977$	311552.	+	539625.i	0.326394	+	0.565331i	−0.655400	+	0.755282i	$0.727500\pi$
$978$	475588.	+	216030.i	0.497225	+	0.225858i
$979$	−29353.2	−	16947.1i	−0.0306260	−	0.0176819i
$980$	−613652.	+	2.30750e6i	−0.638954	+	2.40264i
$981$	432376.	+	885174.i	0.449286	+	0.919794i
$982$	−1.06827e6	+	821307.i	−1.10779	+	0.851692i
$983$	−1.50312e6	−	867829.i	−1.55556	−	0.898105i	−0.997672	−	0.0681909i	$-0.978277\pi$
$983$	−1.50312e6	−	867829.i	−1.55556	−	0.898105i	−0.557891	−	0.829914i	$-0.688389\pi$
$984$	−177208.	+	66884.5i	−0.183018	+	0.0690773i
$985$	−492981.	−	853867.i	−0.508110	−	0.880072i
$986$	−524425.	+	1.26944e6i	−0.539423	+	1.30575i
$987$	1.05485e6	+	36524.0i	1.08282	+	0.0374925i
$988$	461439.	−	463175.i	0.472716	−	0.474494i
$989$	−47448.1			−0.0485095
$990$	−130738.	+	86821.5i	−0.133393	+	0.0885843i
$991$			106256.i			0.108195i	0.998536	+	0.0540974i	$0.0172282\pi$
$991$			106256.i			0.108195i	−0.998536	+	0.0540974i	$0.982772\pi$
$992$	321455.	−	786483.i	0.326661	−	0.799219i
$993$	−1.46607e6	+	780078.i	−1.48681	+	0.791115i
$994$	629010.	−	1.52261e6i	0.636626	−	1.54104i
$995$	−365735.	+	211157.i	−0.369420	+	0.213285i
$996$	349197.	−	327053.i	0.352007	−	0.329685i
$997$	765045.	−	1.32510e6i	0.769656	−	1.33308i	−0.168094	−	0.985771i	$-0.553761\pi$
$997$	765045.	−	1.32510e6i	0.769656	−	1.33308i	0.937750	−	0.347312i	$-0.112905\pi$
$998$	1.01295e6	−	778779.i	1.01702	−	0.781903i
$999$	−231044.	−	24076.7i	−0.231507	−	0.0241250i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	36.5.f.a.7.1	✓	44
3.2	odd	2		108.5.f.a.19.22		44
4.3	odd	2	inner	36.5.f.a.7.15	yes	44
9.2	odd	6		324.5.d.e.163.7		22
9.4	even	3	inner	36.5.f.a.31.15	yes	44
9.5	odd	6		108.5.f.a.91.8		44
9.7	even	3		324.5.d.f.163.16		22
12.11	even	2		108.5.f.a.19.8		44
36.7	odd	6		324.5.d.f.163.15		22
36.11	even	6		324.5.d.e.163.8		22
36.23	even	6		108.5.f.a.91.22		44
36.31	odd	6	inner	36.5.f.a.31.1	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.5.f.a.7.1	✓	44	1.1	even	1	trivial
36.5.f.a.7.15	yes	44	4.3	odd	2	inner
36.5.f.a.31.1	yes	44	36.31	odd	6	inner
36.5.f.a.31.15	yes	44	9.4	even	3	inner
108.5.f.a.19.8		44	12.11	even	2
108.5.f.a.19.22		44	3.2	odd	2
108.5.f.a.91.8		44	9.5	odd	6
108.5.f.a.91.22		44	36.23	even	6
324.5.d.e.163.7		22	9.2	odd	6
324.5.d.e.163.8		22	36.11	even	6
324.5.d.f.163.15		22	36.7	odd	6
324.5.d.f.163.16		22	9.7	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)

\(f(q)\)	\(=\)	\(q+(-3.96529 + 0.525827i) q^{2} +(-4.76702 + 7.63384i) q^{3} +(15.4470 - 4.17011i) q^{4} +(11.0746 + 19.1817i) q^{5} +(14.8885 - 32.7770i) q^{6} +(-82.7885 - 47.7980i) q^{7} +(-59.0591 + 24.6582i) q^{8} +(-35.5511 - 72.7813i) q^{9} +O(q^{10})\)	\(q+(-3.96529 + 0.525827i) q^{2} +(-4.76702 + 7.63384i) q^{3} +(15.4470 - 4.17011i) q^{4} +(11.0746 + 19.1817i) q^{5} +(14.8885 - 32.7770i) q^{6} +(-82.7885 - 47.7980i) q^{7} +(-59.0591 + 24.6582i) q^{8} +(-35.5511 - 72.7813i) q^{9} +(-54.0000 - 70.2376i) q^{10} +(18.9394 + 10.9346i) q^{11} +(-41.8022 + 137.799i) q^{12} +(-63.1124 - 109.314i) q^{13} +(353.414 + 146.000i) q^{14} +(-199.223 - 6.89808i) q^{15} +(221.220 - 128.832i) q^{16} -283.865 q^{17} +(179.241 + 269.905i) q^{18} +323.729i q^{19} +(251.059 + 250.118i) q^{20} +(759.536 - 404.141i) q^{21} +(-80.8497 - 33.4002i) q^{22} +(-198.433 + 114.565i) q^{23} +(93.2993 - 568.394i) q^{24} +(67.2085 - 116.409i) q^{25} +(307.739 + 400.274i) q^{26} +(725.074 + 75.5587i) q^{27} +(-1478.16 - 393.098i) q^{28} +(-604.822 + 1047.58i) q^{29} +(793.602 - 77.4038i) q^{30} +(-718.565 + 414.863i) q^{31} +(-809.459 + 627.178i) q^{32} +(-173.758 + 92.4544i) q^{33} +(1125.61 - 149.264i) q^{34} -2117.36i q^{35} +(-852.664 - 976.002i) q^{36} -318.650 q^{37} +(-170.226 - 1283.68i) q^{38} +(1135.34 + 39.3112i) q^{39} +(-1127.04 - 859.775i) q^{40} +(-164.418 - 284.781i) q^{41} +(-2799.27 + 2001.92i) q^{42} +(179.336 + 103.539i) q^{43} +(338.155 + 89.9283i) q^{44} +(1002.36 - 1487.95i) q^{45} +(726.602 - 558.626i) q^{46} +(1062.42 + 613.390i) q^{47} +(-71.0817 + 2302.90i) q^{48} +(3368.79 + 5834.92i) q^{49} +(-205.290 + 496.933i) q^{50} +(1353.19 - 2166.98i) q^{51} +(-1430.75 - 1425.39i) q^{52} -2834.27 q^{53} +(-2914.86 + 81.6516i) q^{54} +484.385i q^{55} +(6068.02 + 781.492i) q^{56} +(-2471.30 - 1543.22i) q^{57} +(1847.44 - 4471.99i) q^{58} +(-1278.13 + 737.929i) q^{59} +(-3106.16 + 724.226i) q^{60} +(936.180 - 1621.51i) q^{61} +(2631.17 - 2022.89i) q^{62} +(-535.579 + 7724.73i) q^{63} +(2879.95 - 2912.58i) q^{64} +(1397.88 - 2421.20i) q^{65} +(640.384 - 457.975i) q^{66} +(-214.663 + 123.936i) q^{67} +(-4384.87 + 1183.75i) q^{68} +(71.3600 - 2060.94i) q^{69} +(1113.37 + 8395.96i) q^{70} -4308.28i q^{71} +(3894.27 + 3421.77i) q^{72} +3010.75 q^{73} +(1263.54 - 167.555i) q^{74} +(568.260 + 1067.98i) q^{75} +(1349.99 + 5000.65i) q^{76} +(-1045.31 - 1810.52i) q^{77} +(-4522.63 + 441.113i) q^{78} +(-6228.39 - 3595.96i) q^{79} +(4921.12 + 2816.63i) q^{80} +(-4033.24 + 5174.91i) q^{81} +(801.712 + 1042.78i) q^{82} +(-2877.35 - 1661.24i) q^{83} +(10047.3 - 9410.12i) q^{84} +(-3143.68 - 5445.01i) q^{85} +(-765.561 - 316.264i) q^{86} +(-5113.88 - 9610.95i) q^{87} +(-1388.17 - 178.780i) q^{88} -1549.85 q^{89} +(-3192.23 + 6427.22i) q^{90} +12066.6i q^{91} +(-2587.44 + 2597.18i) q^{92} +(258.409 - 7463.07i) q^{93} +(-4535.35 - 1873.62i) q^{94} +(-6209.67 + 3585.16i) q^{95} +(-929.070 - 9169.05i) q^{96} +(-2918.68 + 5055.31i) q^{97} +(-16426.4 - 21365.7i) q^{98} +(122.523 - 1767.17i) 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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