LMFDB - Embedded newform 36.5.f.a.7.15

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			7.15
Character	$\chi$	$=$	36.7
Dual form			36.5.f.a.31.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.52726 + 3.69695i) q^{2} +(4.76702 - 7.63384i) q^{3} +(-11.3349 + 11.2924i) q^{4} +(11.0746 + 19.1817i) q^{5} +(35.5025 + 5.96455i) q^{6} +(82.7885 + 47.7980i) q^{7} +(-59.0591 - 24.6582i) q^{8} +(-35.5511 - 72.7813i) q^{9} +O(q^{10})$	\(q+(1.52726 + 3.69695i) q^{2} +(4.76702 - 7.63384i) q^{3} +(-11.3349 + 11.2924i) q^{4} +(11.0746 + 19.1817i) q^{5} +(35.5025 + 5.96455i) 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} +(32.1709 + 140.360i) q^{12} +(-63.1124 - 109.314i) q^{13} +(-50.2669 + 379.065i) q^{14} +(199.223 + 6.89808i) q^{15} +(0.961243 - 255.998i) q^{16} -283.865 q^{17} +(214.773 - 242.587i) q^{18} -323.729i q^{19} +(-342.138 - 92.3643i) q^{20} +(759.536 - 404.141i) q^{21} +(11.4995 - 86.7180i) q^{22} +(198.433 - 114.565i) q^{23} +(-469.772 + 333.302i) 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} +(278.764 + 747.052i) q^{30} +(718.565 - 414.863i) q^{31} +(947.881 - 387.423i) q^{32} +(-173.758 + 92.4544i) q^{33} +(-433.537 - 1049.44i) q^{34} +2117.36i q^{35} +(1224.85 + 423.513i) q^{36} -318.650 q^{37} +(1196.81 - 494.420i) q^{38} +(-1135.34 - 39.3112i) q^{39} +(-181.068 - 1405.93i) q^{40} +(-164.418 - 284.781i) q^{41} +(2654.10 + 2190.74i) 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} +(-1949.67 - 1227.69i) q^{48} +(3368.79 + 5834.92i) q^{49} +(533.002 + 70.6801i) q^{50} +(-1353.19 + 2166.98i) q^{51} +(1949.79 + 526.371i) q^{52} -2834.27 q^{53} +(-828.042 - 2795.96i) q^{54} -484.385i q^{55} +(-3710.80 - 4864.32i) q^{56} +(-2471.30 - 1543.22i) q^{57} +(-4796.58 - 636.063i) q^{58} +(1278.13 - 737.929i) q^{59} +(-2336.07 + 2171.52i) 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} +(-607.173 - 501.171i) q^{66} +(214.663 - 123.936i) q^{67} +(3217.59 - 3205.53i) q^{68} +(71.3600 - 2060.94i) q^{69} +(-7827.80 + 3233.77i) q^{70} +4308.28i q^{71} +(304.960 + 5175.02i) q^{72} +3010.75 q^{73} +(-486.662 - 1178.03i) q^{74} +(-568.260 - 1067.98i) q^{75} +(3655.69 + 3669.45i) q^{76} +(-1045.31 - 1810.52i) q^{77} +(-1588.64 - 4257.34i) 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} +(-4045.56 + 13157.9i) q^{84} +(-3143.68 - 5445.01i) q^{85} +(108.888 - 821.128i) q^{86} +(5113.88 + 9610.95i) q^{87} +(848.913 + 1112.80i) q^{88} -1549.85 q^{89} +(7031.75 + 1433.17i) q^{90} -12066.6i q^{91} +(-955.500 + 3539.38i) q^{92} +(258.409 - 7463.07i) q^{93} +(645.075 - 4864.54i) q^{94} +(6209.67 - 3585.16i) q^{95} +(1561.04 - 9082.83i) 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 $

$2$	1.52726	+	3.69695i	0.381816	+	0.924238i
$2$	1.52726	+	3.69695i	0.381816	+	0.924238i
$3$	4.76702	−	7.63384i	0.529669	−	0.848205i
$3$	4.76702	−	7.63384i	0.529669	−	0.848205i
$4$	−11.3349	+	11.2924i	−0.708433	+	0.705778i
$5$	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	$0.687254\pi$
$6$	35.5025	+	5.96455i	0.986179	+	0.165682i
$7$	82.7885	+	47.7980i	1.68956	+	0.975469i	0.954850	+	0.297089i	$0.0960158\pi$
$7$	82.7885	+	47.7980i	1.68956	+	0.975469i	0.734711	+	0.678380i	$0.237318\pi$
$8$	−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	0.419692	−	0.907666i	$-0.362138\pi$
$11$	−18.9394	−	10.9346i	−0.156524	−	0.0903689i	−0.576216	+	0.817297i	$0.695471\pi$
$12$	32.1709	+	140.360i	0.223409	+	0.974725i
$13$	−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	$0.955157\pi$
$14$	−50.2669	+	379.065i	−0.256464	+	1.93401i
$15$	199.223	+	6.89808i	0.885434	+	0.0306581i
$16$	0.961243	−	255.998i	0.00375485	−	0.999993i
$17$	−283.865			−0.982232			−0.491116	−	0.871094i	$-0.663411\pi$
$17$	−283.865			−0.982232			−0.491116	+	0.871094i	$0.663411\pi$
$18$	214.773	−	242.587i	0.662881	−	0.748725i
$19$		−	323.729i		−	0.896756i	−0.893844	−	0.448378i	$-0.852002\pi$
$19$		−	323.729i		−	0.896756i	0.893844	−	0.448378i	$-0.147998\pi$
$20$	−342.138	−	92.3643i	−0.855344	−	0.230911i
$21$	759.536	−	404.141i	1.72230	−	0.916418i
$22$	11.4995	−	86.7180i	0.0237592	−	0.179169i
$23$	198.433	−	114.565i	0.375109	−	0.216570i	−0.300579	−	0.953757i	$-0.597180\pi$
$23$	198.433	−	114.565i	0.375109	−	0.216570i	0.675688	+	0.737187i	$0.263847\pi$
$24$	−469.772	+	333.302i	−0.815577	+	0.578649i
$25$	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	$0.911189\pi$
$30$	278.764	+	747.052i	0.309737	+	0.830058i
$31$	718.565	−	414.863i	0.747726	−	0.431700i	−0.0771458	−	0.997020i	$-0.524581\pi$
$31$	718.565	−	414.863i	0.747726	−	0.431700i	0.824872	+	0.565320i	$0.191247\pi$
$32$	947.881	−	387.423i	0.925666	−	0.378343i
$33$	−173.758	+	92.4544i	−0.159557	+	0.0848984i
$34$	−433.537	−	1049.44i	−0.375032	−	0.907816i
$35$			2117.36i			1.72846i
$36$	1224.85	+	423.513i	0.945099	+	0.326784i
$37$	−318.650			−0.232761			−0.116380	−	0.993205i	$-0.537129\pi$
$37$	−318.650			−0.232761			−0.116380	+	0.993205i	$0.537129\pi$
$38$	1196.81	−	494.420i	0.828817	−	0.342396i
$39$	−1135.34	−	39.3112i	−0.746444	−	0.0258456i
$40$	−181.068	−	1405.93i	−0.113167	−	0.878707i
$41$	−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	$0.864517\pi$
$42$	2654.10	+	2190.74i	1.50459	+	1.24192i
$43$	−179.336	−	103.539i	−0.0969906	−	0.0559976i	0.450720	−	0.892665i	$-0.351167\pi$
$43$	−179.336	−	103.539i	−0.0969906	−	0.0559976i	−0.547711	+	0.836668i	$0.684501\pi$
$44$	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	0.239861	−	0.970807i	$-0.422898\pi$
$47$	−1062.42	−	613.390i	−0.480952	−	0.277678i	−0.720813	+	0.693129i	$0.756231\pi$
$48$	−1949.67	−	1227.69i	−0.846210	−	0.532850i
$49$	3368.79	+	5834.92i	1.40308	+	2.43020i
$50$	533.002	+	70.6801i	0.213201	+	0.0282720i
$51$	−1353.19	+	2166.98i	−0.520258	+	0.833134i
$52$	1949.79	+	526.371i	0.721078	+	0.194664i
$53$	−2834.27			−1.00900			−0.504499	−	0.863412i	$-0.668323\pi$
$53$	−2834.27			−1.00900			−0.504499	+	0.863412i	$0.668323\pi$
$54$	−828.042	−	2795.96i	−0.283965	−	0.958835i
$55$		−	484.385i		−	0.160127i
$56$	−3710.80	−	4864.32i	−1.18329	−	1.55112i
$57$	−2471.30	−	1543.22i	−0.760633	−	0.474984i
$58$	−4796.58	−	636.063i	−1.42586	−	0.189079i
$59$	1278.13	−	737.929i	0.367173	−	0.211988i	−0.305049	−	0.952337i	$-0.598673\pi$
$59$	1278.13	−	737.929i	0.367173	−	0.211988i	0.672223	+	0.740349i	$0.265340\pi$
$60$	−2336.07	+	2171.52i	−0.648908	+	0.603200i
$61$	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
$66$	−607.173	−	501.171i	−0.139388	−	0.115053i
$67$	214.663	−	123.936i	0.0478197	−	0.0276087i	−0.475900	−	0.879500i	$-0.657877\pi$
$67$	214.663	−	123.936i	0.0478197	−	0.0276087i	0.523719	+	0.851891i	$0.324544\pi$
$68$	3217.59	−	3205.53i	0.695846	−	0.693238i
$69$	71.3600	−	2060.94i	0.0149885	−	0.432880i
$70$	−7827.80	+	3233.77i	−1.59751	+	0.659954i
$71$			4308.28i			0.854648i	0.904099	+	0.427324i	$0.140544\pi$
$71$			4308.28i			0.854648i	−0.904099	+	0.427324i	$0.859456\pi$
$72$	304.960	+	5175.02i	0.0588272	+	0.998268i
$73$	3010.75			0.564974			0.282487	−	0.959271i	$-0.408841\pi$
$73$	3010.75			0.564974			0.282487	+	0.959271i	$0.408841\pi$
$74$	−486.662	−	1178.03i	−0.0888718	−	0.215126i
$75$	−568.260	−	1067.98i	−0.101024	−	0.189863i
$76$	3655.69	+	3669.45i	0.632911	+	0.635292i
$77$	−1045.31	−	1810.52i	−0.176304	−	0.305368i
$78$	−1588.64	−	4257.34i	−0.261117	−	0.699761i
$79$	6228.39	+	3595.96i	0.997980	+	0.576184i	0.907650	−	0.419728i	$-0.137874\pi$
$79$	6228.39	+	3595.96i	0.997980	+	0.576184i	0.0903300	+	0.995912i	$0.471208\pi$
$80$	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	0.694081	−	0.719897i	$-0.255811\pi$
$83$	2877.35	+	1661.24i	0.417673	+	0.241144i	−0.276408	+	0.961040i	$0.589144\pi$
$84$	−4045.56	+	13157.9i	−0.573350	+	1.86479i
$85$	−3143.68	−	5445.01i	−0.435111	−	0.753635i
$86$	108.888	−	821.128i	0.0147225	−	0.111023i
$87$	5113.88	+	9610.95i	0.675634	+	1.26978i
$88$	848.913	+	1112.80i	0.109622	+	0.143698i
$89$	−1549.85			−0.195664			−0.0978318	−	0.995203i	$-0.531191\pi$
$89$	−1549.85			−0.195664			−0.0978318	+	0.995203i	$0.531191\pi$
$90$	7031.75	+	1433.17i	0.868117	+	0.176935i
$91$		−	12066.6i		−	1.45714i
$92$	−955.500	+	3539.38i	−0.112890	+	0.418169i
$93$	258.409	−	7463.07i	0.0298773	−	0.862882i
$94$	645.075	−	4864.54i	0.0730053	−	0.550536i
$95$	6209.67	−	3585.16i	0.688052	−	0.397247i
$96$	1561.04	−	9082.83i	0.169384	−	0.985550i
$97$	−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	$0.0797976\pi$
$102$	−10077.9	−	1693.13i	−0.968657	−	0.162738i
$103$	−15530.7	+	8966.63i	−1.46391	+	0.845191i	−0.999189	−	0.0402641i	$-0.987180\pi$
$103$	−15530.7	+	8966.63i	−1.46391	+	0.845191i	−0.464725	+	0.885455i	$0.653847\pi$
$104$	1031.88	+	8012.21i	0.0954032	+	0.740774i
$105$	16163.6	+	10093.5i	1.46609	+	0.915512i
$106$	−4328.69	−	10478.2i	−0.385251	−	0.932554i
$107$		−	8715.17i		−	0.761217i	−0.924736	−	0.380608i	$-0.875715\pi$
$107$		−	8715.17i		−	0.761217i	0.924736	−	0.380608i	$-0.124285\pi$
$108$	9071.90	−	7331.40i	0.777769	−	0.628550i
$109$	−12162.1			−1.02366			−0.511830	−	0.859087i	$-0.671032\pi$
$109$	−12162.1			−1.02366			−0.511830	+	0.859087i	$0.671032\pi$
$110$	1790.75	−	739.784i	0.147996	−	0.0611392i
$111$	−1519.01	+	2432.52i	−0.123286	+	0.197429i
$112$	12315.8	−	21147.8i	0.981806	−	1.68589i
$113$	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	$0.537271\pi$
$114$	1930.90	−	11493.2i	0.148576	−	0.884363i
$115$	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
$120$	−11595.8	−	5319.86i	−0.805265	−	0.369434i
$121$	−7081.37	−	12265.3i	−0.483667	−	0.837736i
$122$	7424.45	+	984.538i	0.498821	+	0.0661474i
$123$	−2957.76	−	102.412i	−0.195503	−	0.00676928i
$124$	−3460.05	+	12816.8i	−0.225030	+	0.833559i
$125$	16820.4			1.07651
$126$	29375.9	−	9817.68i	1.85034	−	0.618398i
$127$			8130.42i			0.504087i	0.967716	+	0.252044i	$0.0811026\pi$
$127$			8130.42i			0.504087i	−0.967716	+	0.252044i	$0.918897\pi$
$128$	−6369.21	+	15095.3i	−0.388746	+	0.921345i
$129$	−1645.30	+	875.445i	−0.0988703	+	0.0526077i
$130$	11086.0	+	1470.09i	0.655977	+	0.0869875i
$131$	−14095.1	+	8137.79i	−0.821343	+	0.474203i	−0.850879	−	0.525361i	$-0.823930\pi$
$131$	−14095.1	+	8137.79i	−0.821343	+	0.474203i	0.0295362	+	0.999564i	$0.490597\pi$
$132$	925.493	−	3010.11i	0.0531160	−	0.172757i
$133$	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	$0.938487\pi$
$138$	7728.18	−	2883.78i	0.405807	−	0.151427i
$139$	−17078.1	+	9860.04i	−0.883913	+	0.510328i	−0.871947	−	0.489601i	$-0.837143\pi$
$139$	−17078.1	+	9860.04i	−0.883913	+	0.510328i	−0.0119667	+	0.999928i	$0.503809\pi$
$140$	−23910.2	−	24000.2i	−1.21991	−	1.22450i
$141$	−9747.12	+	5186.33i	−0.490273	+	0.260869i
$142$	−15927.5	+	6579.88i	−0.789898	+	0.326318i
$143$			2760.44i			0.134992i
$144$	−18666.1	+	9031.05i	−0.900177	+	0.435525i
$145$	−26792.5			−1.27432
$146$	4598.21	+	11130.6i	0.215716	+	0.522171i
$147$	60601.9	+	2098.34i	2.80448	+	0.0971050i
$148$	3611.87	−	3598.33i	0.164895	−	0.164277i
$149$	−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	$-0.401690\pi$
$150$	3080.39	−	3731.92i	0.136906	−	0.165863i
$151$	5164.11	+	2981.50i	0.226486	+	0.130762i	0.608950	−	0.793209i	$-0.291591\pi$
$151$	5164.11	+	2981.50i	0.226486	+	0.130762i	−0.382464	+	0.923970i	$0.624924\pi$
$152$	−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
$156$	13312.9	−	12375.2i	0.547047	−	0.508514i
$157$	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	$0.582162\pi$
$158$	−3781.71	+	28518.1i	−0.151487	+	1.14237i
$159$	−13511.0	+	21636.4i	−0.534435	+	0.855837i
$160$	17928.8	+	13891.4i	0.700344	+	0.542634i
$161$	21903.9			0.845027
$162$	−25291.2	−	7007.26i	−0.963695	−	0.267004i
$163$		−	14509.8i		−	0.546118i	−0.961997	−	0.273059i	$-0.911965\pi$
$163$		−	14509.8i		−	0.546118i	0.961997	−	0.273059i	$-0.0880354\pi$
$164$	5079.55	+	1371.29i	0.188859	+	0.0509848i
$165$	−3697.72	−	2309.07i	−0.135821	−	0.0848144i
$166$	−1747.05	+	13174.6i	−0.0634000	+	0.478102i
$167$	38640.1	−	22308.9i	1.38550	−	0.799917i	0.392693	−	0.919670i	$-0.371543\pi$
$167$	38640.1	−	22308.9i	1.38550	−	0.799917i	0.992804	+	0.119753i	$0.0382102\pi$
$168$	−54822.9	+	5139.40i	−1.94242	+	0.182093i
$169$	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	$-0.178176\pi$
$174$	−27721.0	+	33584.2i	−0.915610	+	1.10927i
$175$	11128.2	−	6424.86i	0.363369	−	0.209791i
$176$	−2817.45	+	4837.93i	−0.0909560	+	0.156183i
$177$	459.639	−	13274.8i	0.0146714	−	0.423721i
$178$	−2367.03	−	5729.73i	−0.0747075	−	0.180840i
$179$		−	32840.8i		−	1.02496i	−0.858698	−	0.512482i	$-0.828726\pi$
$179$		−	32840.8i		−	1.02496i	0.858698	−	0.512482i	$-0.171274\pi$
$180$	5440.96	+	28184.9i	0.167931	+	0.869903i
$181$	−22758.6			−0.694685			−0.347343	−	0.937738i	$-0.612916\pi$
$181$	−22758.6			−0.694685			−0.347343	+	0.937738i	$0.612916\pi$
$182$	44609.5	−	18428.8i	1.34674	−	0.556359i
$183$	−7915.57	−	14876.4i	−0.236363	−	0.444218i
$184$	−14544.2	+	1873.13i	−0.429591	+	0.0553264i
$185$	−3528.90	−	6112.24i	−0.103109	−	0.178590i
$186$	27985.3	−	10442.8i	0.808917	−	0.301849i
$187$	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	0.990294	−	0.138986i	$-0.0443843\pi$
$191$	49799.3	+	28751.7i	1.36508	+	0.788127i	0.374782	+	0.927113i	$0.377718\pi$
$192$	35962.9	−	8100.78i	0.975557	−	0.219748i
$193$	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	$0.627202\pi$
$194$	−23146.9	−	3069.45i	−0.615019	−	0.0815562i
$195$	−11819.4	−	22213.1i	−0.310831	−	0.584172i
$196$	−104076.	−	28096.5i	−2.70917	−	0.731374i
$197$	−44514.7			−1.14702			−0.573510	−	0.819198i	$-0.694419\pi$
$197$	−44514.7			−1.14702			−0.573510	+	0.819198i	$0.694419\pi$
$198$	−6720.27	+	2245.97i	−0.171418	+	0.0572893i
$199$		−	19066.9i		−	0.481474i	−0.970590	−	0.240737i	$-0.922611\pi$
$199$		−	19066.9i		−	0.481474i	0.970590	−	0.240737i	$-0.0773892\pi$
$200$	−6839.69	+	5217.74i	−0.170992	+	0.130444i
$201$	77.1966	−	2229.50i	0.00191076	−	0.0551844i
$202$	21805.1	+	2891.52i	0.534387	+	0.0708637i
$203$	−100145.	+	57818.5i	−2.43016	+	1.40305i
$204$	−9132.20	−	39843.4i	−0.219440	−	0.957406i
$205$	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
$210$	−12629.1	+	75171.6i	−0.286375	+	1.70457i
$211$	−825.251	+	476.459i	−0.0185362	+	0.0107019i	−0.509239	−	0.860625i	$-0.670073\pi$
$211$	−825.251	+	476.459i	−0.0185362	+	0.0107019i	0.490703	+	0.871327i	$0.336740\pi$
$212$	32126.3	−	32005.9i	0.714807	−	0.712128i
$213$	32888.7	+	20537.6i	0.724916	+	0.452680i
$214$	32219.6	−	13310.4i	0.703546	−	0.290645i
$215$		−	4586.61i		−	0.0992237i
$216$	40959.1	+	22341.4i	0.877895	+	0.478854i
$217$	79318.5			1.68444
$218$	−18574.7	−	44962.7i	−0.390850	−	0.946106i
$219$	14352.3	−	22983.6i	0.299249	−	0.479214i
$220$	5469.89	+	5490.47i	0.113014	+	0.113439i
$221$	17915.4	+	31030.4i	0.366810	+	0.635334i
$222$	−11312.8	−	1900.60i	−0.229544	−	0.0385643i
$223$	37535.4	+	21671.1i	0.754800	+	0.435784i	0.827426	−	0.561575i	$-0.189805\pi$
$223$	37535.4	+	21671.1i	0.754800	+	0.435784i	−0.0726258	+	0.997359i	$0.523138\pi$
$224$	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	0.549633	−	0.835406i	$-0.314768\pi$
$227$	5202.66	+	3003.76i	0.100966	+	0.0582925i	−0.448667	+	0.893699i	$0.648101\pi$
$228$	45438.7	−	10414.7i	0.874091	−	0.200344i
$229$	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	$0.820959\pi$
$230$	−2668.59	+	20124.0i	−0.0504460	+	0.380416i
$231$	−18804.3	−	651.097i	−0.352397	−	0.0122017i
$232$	61551.6	−	46955.4i	1.14357	−	0.872388i
$233$	−37427.6			−0.689414			−0.344707	−	0.938710i	$-0.612022\pi$
$233$	−37427.6			−0.689414			−0.344707	+	0.938710i	$0.612022\pi$
$234$	−40072.9	−	8167.45i	−0.731846	−	0.149161i
$235$		−	27172.1i		−	0.492025i
$236$	−6154.50	+	22797.6i	−0.110502	+	0.409322i
$237$	57141.9	−	30404.5i	1.01732	−	0.541305i
$238$	14269.0	−	107603.i	0.251907	−	1.89964i
$239$	22212.3	−	12824.3i	0.388865	−	0.224511i	−0.292804	−	0.956173i	$-0.594588\pi$
$239$	22212.3	−	12824.3i	0.388865	−	0.224511i	0.681668	+	0.731662i	$0.261255\pi$
$240$	1957.40	−	50994.0i	0.0339826	−	0.885312i
$241$	−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
$246$	−4138.67	−	11091.1i	−0.0683896	−	0.183276i
$247$	−35388.1	+	20431.3i	−0.580046	+	0.334890i
$248$	−52667.5	+	6782.98i	−0.856327	+	0.110285i
$249$	26398.0	−	14046.1i	0.425768	−	0.226546i
$250$	25689.2	+	62184.3i	0.411027	+	0.994948i
$251$			66642.6i			1.05780i	0.848683	+	0.528902i	$0.177396\pi$
$251$			66642.6i			1.05780i	−0.848683	+	0.528902i	$0.822604\pi$
$252$	81160.3	+	93607.2i	1.27803	+	1.47404i
$253$	−5010.92			−0.0782846
$254$	−30057.8	+	12417.3i	−0.465897	+	0.192468i
$255$	−56552.3	−	1958.12i	−0.869701	−	0.0301134i
$256$	−65534.2	−	492.153i	−0.999972	−	0.00750966i
$257$	−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	$0.981862\pi$
$258$	−5749.29	−	4745.56i	−0.0863723	−	0.0712932i
$259$	−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	0.334290	−	0.942470i	$-0.391503\pi$
$263$	−21772.1	−	12570.2i	−0.314767	−	0.181731i	−0.649058	+	0.760739i	$0.724837\pi$
$264$	12541.7	−	1175.73i	0.179949	−	0.0168694i
$265$	−31388.3	−	54366.2i	−0.446968	−	0.774171i
$266$	122714.	+	16272.9i	1.73433	+	0.229986i
$267$	−7388.17	+	11831.3i	−0.103637	+	0.165963i
$268$	−1033.65	+	3828.87i	−0.0143914	+	0.0533090i
$269$	2553.46			0.0352877			0.0176439	−	0.999844i	$-0.494383\pi$
$269$	2553.46			0.0352877			0.0176439	+	0.999844i	$0.494383\pi$
$270$	44461.1	−	46847.3i	0.609891	−	0.642624i
$271$			4623.11i			0.0629499i	0.999505	+	0.0314750i	$0.0100204\pi$
$271$			4623.11i			0.0629499i	−0.999505	+	0.0314750i	$0.989980\pi$
$272$	−272.863	+	72668.9i	−0.00368814	+	0.982225i
$273$	−92114.3	−	57521.6i	−1.23595	−	0.771801i
$274$	−97795.3	−	12968.4i	−1.30262	−	0.172737i
$275$	−2545.77	+	1469.80i	−0.0336631	+	0.0194354i
$276$	22464.2	+	24166.4i	0.294899	+	0.317245i
$277$	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	$0.0674789\pi$
$282$	−34060.0	−	28113.7i	−0.428299	−	0.353525i
$283$	114515.	−	66115.1i	1.42984	−	0.825520i	0.432735	−	0.901521i	$-0.357549\pi$
$283$	114515.	−	66115.1i	1.42984	−	0.825520i	0.997108	+	0.0760012i	$0.0242153\pi$
$284$	−48651.0	−	48834.0i	−0.603192	−	0.605461i
$285$	2233.11	−	64494.1i	0.0274929	−	0.794018i
$286$	−10205.2	+	4215.93i	−0.124764	+	0.0515420i
$287$		−	31435.5i		−	0.381642i
$288$	−61895.4	−	55214.8i	−0.746231	−	0.665687i
$289$	−2941.65			−0.0352205
$290$	−40919.2	−	99050.7i	−0.486555	−	1.17777i
$291$	24678.0	+	46379.5i	0.291423	+	0.547697i
$292$	−34126.6	+	33998.7i	−0.400247	+	0.398747i
$293$	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	$0.658752\pi$
$294$	84797.7	+	227247.i	0.981046	+	2.62908i
$295$	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
$300$	18501.3	+	5688.44i	0.205570	+	0.0632049i
$301$	−9897.95	−	17143.8i	−0.109248	−	0.189223i
$302$	−3135.51	+	23645.0i	−0.0343791	+	0.259254i
$303$	−23247.5	−	43691.1i	−0.253216	−	0.475891i
$304$	−82874.1	−	311.182i	−0.896750	−	0.00336719i
$305$	41471.1			0.445806
$306$	−60966.6	+	68861.9i	−0.651102	+	0.735422i
$307$		−	62726.9i		−	0.665545i	−0.943007	−	0.332772i	$-0.892016\pi$
$307$		−	62726.9i		−	0.665545i	0.943007	−	0.332772i	$-0.107984\pi$
$308$	32293.7	+	8718.10i	0.340421	+	0.0919010i
$309$	−5585.11	+	161303.i	−0.0584944	+	1.68937i
$310$	−9663.50	+	72872.9i	−0.100557	+	0.758303i
$311$	106333.	−	61391.4i	1.09938	−	0.634726i	0.163321	−	0.986573i	$-0.447779\pi$
$311$	106333.	−	61391.4i	1.09938	−	0.634726i	0.936058	+	0.351847i	$0.114446\pi$
$312$	66082.9	+	30317.1i	0.678860	+	0.311443i
$313$	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	$-0.0179393\pi$
$318$	−100624.	−	16905.2i	−0.995053	−	0.167173i
$319$	22909.9	−	13227.0i	0.225134	−	0.129981i
$320$	−23974.0	+	87497.8i	−0.234121	+	0.854471i
$321$	−66530.2	−	41545.4i	−0.645667	−	0.403193i
$322$	33453.1	+	80977.9i	0.322645	+	0.781006i
$323$			91895.4i			0.880823i
$324$	−12720.9	−	104202.i	−0.121179	−	0.992631i
$325$	−16966.7			−0.160632
$326$	53642.1	−	22160.3i	0.504743	−	0.208517i
$327$	−57977.0	+	92843.6i	−0.542201	+	0.868273i
$328$	2688.23	+	20873.2i	0.0249872	+	0.194017i
$329$	−58637.6	−	101563.i	−0.541732	−	0.938308i
$330$	2889.14	−	17196.9i	0.0265302	−	0.157914i
$331$	−159800.	−	92260.3i	−1.45854	−	0.842091i	−0.459605	−	0.888124i	$-0.652009\pi$
$331$	−159800.	−	92260.3i	−1.45854	−	0.842091i	−0.998940	+	0.0460325i	$0.985342\pi$
$332$	−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
$336$	−102729.	−	194828.i	−0.909945	−	1.72573i
$337$	−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	$0.926632\pi$
$338$	50074.9	+	6640.32i	0.438316	+	0.0581240i
$339$	184150.	+	6376.20i	1.60241	+	0.0554834i
$340$	97120.9	+	26219.0i	0.840146	+	0.226808i
$341$	−18145.5			−0.156049
$342$	−78532.4	−	69528.4i	−0.671424	−	0.594442i
$343$			414560.i			3.52370i
$344$	8038.31	+	10537.0i	0.0679278	+	0.0890433i
$345$	40322.6	−	21455.2i	0.338774	−	0.180258i
$346$	209710.	+	27809.2i	1.75173	+	0.232293i
$347$	90819.3	−	52434.6i	0.754257	−	0.435470i	−0.0729731	−	0.997334i	$-0.523249\pi$
$347$	90819.3	−	52434.6i	0.754257	−	0.435470i	0.827230	+	0.561864i	$0.189915\pi$
$348$	−166497.	−	51191.3i	−1.37482	−	0.422705i
$349$	−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	$0.104051\pi$
$354$	49778.2	−	18574.8i	0.397221	−	0.148224i
$355$	−82640.1	+	47712.3i	−0.655744	+	0.378594i
$356$	17567.5	−	17501.6i	0.138615	−	0.138095i
$357$	−215606.	+	114721.i	−1.69170	+	0.900135i
$358$	121411.	−	50156.6i	0.947310	−	0.391347i
$359$		−	109409.i		−	0.848911i	−0.905449	−	0.424456i	$-0.860465\pi$
$359$		−	109409.i		−	0.848911i	0.905449	−	0.424456i	$-0.139535\pi$
$360$	−95888.4	+	63160.7i	−0.739879	+	0.487351i
$361$	25520.5			0.195828
$362$	−34758.4	−	84137.4i	−0.265242	−	0.642055i
$363$	−127388.	−	4410.82i	−0.966754	−	0.0334739i
$364$	136261.	+	136774.i	1.02842	+	1.03229i
$365$	33342.7	+	57751.3i	0.250274	+	0.433487i
$366$	42908.3	−	51983.7i	0.320316	−	0.388066i
$367$	1112.82	+	642.487i	0.00826215	+	0.00477015i	0.504125	−	0.863630i	$-0.331815\pi$
$367$	1112.82	+	642.487i	0.00826215	+	0.00477015i	−0.495863	+	0.868401i	$0.665148\pi$
$368$	−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
$372$	81347.3	+	87511.4i	0.587837	+	0.632381i
$373$	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	$0.748180\pi$
$374$	−3264.30	+	24616.2i	−0.0233371	+	0.175986i
$375$	80183.2	−	128404.i	0.570192	−	0.913098i
$376$	47620.7	+	62423.7i	0.336837	+	0.441544i
$377$	152687.			1.07428
$378$	65088.9	−	271052.i	0.455537	−	1.89701i
$379$		−	139070.i		−	0.968176i	−0.875019	−	0.484088i	$-0.839152\pi$
$379$		−	139070.i		−	0.968176i	0.875019	−	0.484088i	$-0.160848\pi$
$380$	−29901.0	+	110760.i	−0.207071	+	0.767035i
$381$	62066.3	+	38757.9i	0.427569	+	0.266999i
$382$	−30236.8	+	228017.i	−0.207209	+	1.56258i
$383$	−90000.3	+	51961.7i	−0.613545	+	0.354230i	−0.774352	−	0.632756i	$-0.781924\pi$
$383$	−90000.3	+	51961.7i	−0.613545	+	0.354230i	0.160807	+	0.986986i	$0.448590\pi$
$384$	84873.1	+	120581.i	0.575582	+	0.817744i
$385$	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	$0.0593839\pi$
$390$	64069.6	−	77620.9i	0.421234	−	0.510328i
$391$	−56328.2	+	32521.1i	−0.368444	+	0.212721i
$392$	−55079.4	−	427673.i	−0.358441	−	2.78317i
$393$	−5068.84	+	146393.i	−0.0328189	+	0.947838i
$394$	−67985.7	−	164569.i	−0.437951	−	1.06012i
$395$			159295.i			1.02096i
$396$	−18566.9	−	21414.3i	−0.118399	−	0.136557i
$397$	164388.			1.04301			0.521507	−	0.853247i	$-0.325370\pi$
$397$	164388.			1.04301			0.521507	+	0.853247i	$0.325370\pi$
$398$	70489.3	−	29120.1i	0.444997	−	0.183835i
$399$	−130832.	−	245884.i	−0.821804	−	1.54449i
$400$	−29735.8	−	17317.2i	−0.185849	−	0.108232i
$401$	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	$0.671614\pi$
$402$	8360.27	−	3119.65i	0.0517331	−	0.0193043i
$403$	−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
$408$	133352.	−	94612.7i	0.801085	−	0.568367i
$409$	−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	$-0.466725\pi$
$410$	28881.0	+	3829.83i	0.171808	+	0.0227831i
$411$	104264.	+	195953.i	0.617238	+	1.16003i
$412$	74783.7	−	277015.i	0.440568	−	1.63196i
$413$	141086.			0.827149
$414$	14826.0	−	72742.8i	0.0865017	−	0.424414i
$415$			73589.9i			0.427290i
$416$	−102174.	−	79165.3i	−0.590408	−	0.457455i
$417$	−6141.59	+	177374.i	−0.0353190	+	1.02004i
$418$	−28073.1	−	3722.71i	−0.160671	−	0.0213062i
$419$	−49366.2	+	28501.6i	−0.281191	+	0.162346i	−0.633963	−	0.773364i	$-0.718573\pi$
$419$	−49366.2	+	28501.6i	−0.281191	+	0.162346i	0.352771	+	0.935710i	$0.385239\pi$
$420$	−297194.	+	68117.6i	−1.68477	+	0.386154i
$421$	−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
$426$	−25697.0	+	152954.i	−0.141600	+	0.842836i
$427$	155010.	−	89495.0i	0.850166	−	0.490843i
$428$	98415.6	+	98785.8i	0.537250	+	0.539271i
$429$	21072.8	+	13159.1i	0.114500	+	0.0715008i
$430$	16956.5	−	7004.97i	0.0917063	−	0.0378852i
$431$		−	333180.i		−	1.79360i	−0.442439	−	0.896798i	$-0.645887\pi$
$431$		−	333180.i		−	1.79360i	0.442439	−	0.896798i	$-0.354113\pi$
$432$	−20039.9	+	185545.i	−0.107381	+	0.994218i
$433$	−215343.			−1.14856			−0.574282	−	0.818657i	$-0.694719\pi$
$433$	−215343.			−1.14856			−0.574282	+	0.818657i	$0.694719\pi$
$434$	121140.	+	293237.i	0.643145	+	1.55682i
$435$	−127720.	+	204530.i	−0.674966	+	1.08088i
$436$	137857.	−	137340.i	0.725194	−	0.722477i
$437$	−37088.1	−	64238.5i	−0.194210	−	0.336382i
$438$	106889.	+	17957.8i	0.557166	+	0.0936061i
$439$	−27053.2	−	15619.2i	−0.140375	−	0.0810455i	0.428168	−	0.903699i	$-0.359159\pi$
$439$	−27053.2	−	15619.2i	−0.140375	−	0.0810455i	−0.568543	+	0.822654i	$0.692493\pi$
$440$	−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	0.890527	−	0.454930i	$-0.150336\pi$
$443$	184829.	+	106711.i	0.941809	+	0.543754i	0.0512822	+	0.998684i	$0.483669\pi$
$444$	−10251.3	−	44725.8i	−0.0520009	−	0.226878i
$445$	−17163.9	−	29728.8i	−0.0866755	−	0.150126i
$446$	−22790.5	+	171864.i	−0.114574	+	0.864004i
$447$	−268808.	−	9307.48i	−1.34533	−	0.0465819i
$448$	99211.6	+	378784.i	0.494318	+	1.88727i
$449$	−393053.			−1.94966			−0.974828	−	0.222956i	$-0.928429\pi$
$449$	−393053.			−1.94966			−0.974828	+	0.222956i	$0.928429\pi$
$450$	−13804.6	−	41305.3i	−0.0681709	−	0.203977i
$451$			7191.43i			0.0353559i
$452$	−316253.	−	85376.4i	−1.54795	−	0.417889i
$453$	47377.7	−	25209.1i	0.230876	−	0.122846i
$454$	−3158.91	+	23821.5i	−0.0153259	+	0.115573i
$455$	231457.	−	133632.i	1.11802	−	0.645487i
$456$	107899.	+	152079.i	0.518907	+	0.731374i
$457$	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	$0.210383\pi$
$462$	−26312.0	−	70512.9i	−0.123274	−	0.330358i
$463$	64721.6	−	37367.0i	0.301917	−	0.174312i	−0.341387	−	0.939923i	$-0.610897\pi$
$463$	64721.6	−	37367.0i	0.301917	−	0.174312i	0.643304	+	0.765611i	$0.277563\pi$
$464$	267598.	+	155840.i	1.24293	+	0.723842i
$465$	146016.	−	77693.4i	0.675297	−	0.359318i
$466$	−57161.8	−	138368.i	−0.263229	−	0.637183i
$467$			264366.i			1.21219i	0.795392	+	0.606096i	$0.207265\pi$
$467$			264366.i			1.21219i	−0.795392	+	0.606096i	$0.792735\pi$
$468$	−31007.3	−	160622.i	−0.141570	−	0.733352i
$469$	23695.5			0.107726
$470$	100454.	−	41499.0i	0.454749	−	0.187863i
$471$	314694.	+	10896.3i	1.41856	+	0.0491176i
$472$	−93681.2	+	12065.1i	−0.420502	+	0.0541559i
$473$	2264.33	+	3921.94i	0.0101209	+	0.0175299i
$474$	199675.	+	164815.i	0.888724	+	0.733568i
$475$	−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	0.924228	−	0.381842i	$-0.124710\pi$
$479$	242211.	+	139840.i	1.05566	+	0.609483i	0.131429	+	0.991326i	$0.458044\pi$
$480$	191512.	−	70644.9i	0.831215	−	0.306618i
$481$	20110.7	+	34832.8i	0.0869236	+	0.150556i
$482$	−303748.	−	40279.2i	−1.30743	−	0.173375i
$483$	104417.	−	167211.i	0.447584	−	0.716756i
$484$	218772.	+	59060.2i	0.933901	+	0.252118i
$485$	−129293.			−0.549655
$486$	−174056.	+	159665.i	−0.736914	+	0.675987i
$487$		−	62506.3i		−	0.263552i	−0.991280	−	0.131776i	$-0.957932\pi$
$487$		−	62506.3i		−	0.263552i	0.991280	−	0.131776i	$-0.0420679\pi$
$488$	−95273.4	+	72680.5i	−0.400066	+	0.305196i
$489$	−110766.	−	69168.5i	−0.463220	−	0.289262i
$490$	−591746.	−	78470.0i	−2.46458	−	0.326822i
$491$	−291742.	+	168437.i	−1.21014	+	0.698674i	−0.962790	−	0.270252i	$-0.912893\pi$
$491$	−291742.	+	168437.i	−1.21014	+	0.698674i	−0.247350	+	0.968926i	$0.579560\pi$
$492$	34682.5	−	32239.5i	0.143278	−	0.133186i
$493$	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
$498$	92244.5	+	76140.2i	0.371947	+	0.307012i
$499$	276635.	−	159715.i	1.11098	−	0.641424i	0.171896	−	0.985115i	$-0.445011\pi$
$499$	276635.	−	159715.i	1.11098	−	0.641424i	0.939083	+	0.343691i	$0.111677\pi$
$500$	−190658.	+	189944.i	−0.762633	+	0.759774i
$501$	13895.7	−	401319.i	0.0553611	−	1.59888i
$502$	−246375.	+	101781.i	−0.977662	+	0.403886i
$503$			28287.7i			0.111805i	0.998436	+	0.0559025i	$0.0178036\pi$
$503$			28287.7i			0.111805i	−0.998436	+	0.0559025i	$0.982196\pi$
$504$	−222108.	+	443009.i	−0.874387	+	1.74402i
$505$	121798.			0.477592
$506$	−7653.00	−	18525.1i	−0.0298903	−	0.0723536i
$507$	−53387.4	−	100336.i	−0.207693	−	0.390336i
$508$	−91812.3	−	92157.7i	−0.355774	−	0.357112i
$509$	−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	$0.891748\pi$
$510$	−79131.2	−	212062.i	−0.304234	−	0.815309i
$511$	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
$516$	8763.44	−	28502.6i	0.0329136	−	0.107050i
$517$	13414.4	+	23234.4i	0.0501869	+	0.0869263i
$518$	16017.5	−	120789.i	0.0596948	−	0.450161i
$519$	−223583.	−	420199.i	−0.830049	−	1.55998i
$520$	−142260.	+	108525.i	−0.526110	+	0.401349i
$521$	369932.			1.36285			0.681423	−	0.731890i	$-0.261362\pi$
$521$	369932.			1.36285			0.681423	+	0.731890i	$0.261362\pi$
$522$	124230.	+	371714.i	0.455917	+	1.36417i
$523$			65267.4i			0.238612i	0.992858	+	0.119306i	$0.0380670\pi$
$523$			65267.4i			0.238612i	−0.992858	+	0.119306i	$0.961933\pi$
$524$	67871.0	−	251409.i	0.247185	−	0.915627i
$525$	4001.90	−	115578.i	0.0145193	−	0.419331i
$526$	13219.5	−	99688.5i	0.0477796	−	0.360308i
$527$	−203975.	+	117765.i	−0.734440	+	0.424029i
$528$	23501.1	+	44570.5i	0.0842987	+	0.159875i
$529$	−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
$534$	−55023.5	−	9244.17i	−0.192959	−	0.0324180i
$535$	167172.	−	96516.6i	0.584057	−	0.337205i
$536$	−15733.8	+	2026.33i	−0.0547651	+	0.00705312i
$537$	−250702.	−	156553.i	−0.869378	−	0.542891i
$538$	3899.80	+	9440.01i	0.0134734	+	0.0326143i
$539$		−	147346.i		−	0.507179i
$540$	241096.	+	92822.4i	0.826804	+	0.318321i
$541$	176002.			0.601343			0.300671	−	0.953728i	$-0.402789\pi$
$541$	176002.			0.601343			0.300671	+	0.953728i	$0.402789\pi$
$542$	−17091.4	+	7060.70i	−0.0581807	+	0.0240353i
$543$	−108491.	+	173735.i	−0.367953	+	0.589235i
$544$	−269070.	+	109976.i	−0.909218	+	0.371620i
$545$	−134690.	−	233290.i	−0.453463	−	0.785421i
$546$	71971.7	−	428393.i	0.241422	−	1.43700i
$547$	−236509.	−	136549.i	−0.790448	−	0.456365i	0.0496725	−	0.998766i	$-0.484182\pi$
$547$	−236509.	−	136549.i	−0.790448	−	0.456365i	−0.840120	+	0.542400i	$0.817516\pi$
$548$	−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
$552$	−55033.4	+	119958.i	−0.180613	+	0.393686i
$553$	343760.	+	595409.i	1.12410	+	1.94700i
$554$	39075.4	+	5181.70i	0.127316	+	0.0168831i
$555$	−63482.2	−	2198.07i	−0.206094	−	0.00713601i
$556$	82235.0	−	304616.i	0.266016	−	0.985380i
$557$	−454335.			−1.46442			−0.732211	−	0.681078i	$-0.761511\pi$
$557$	−454335.			−1.46442			−0.732211	+	0.681078i	$0.761511\pi$
$558$	53688.0	−	263416.i	0.172428	−	0.846006i
$559$			26138.5i			0.0836482i
$560$	542042.	+	2035.30i	1.72845	+	0.00649012i
$561$	49323.7	−	26244.6i	0.156722	−	0.0833899i
$562$	191988.	+	25459.1i	0.607857	+	0.0806065i
$563$	−27753.2	+	16023.3i	−0.0875582	+	0.0505518i	−0.543140	−	0.839642i	$-0.682765\pi$
$563$	−27753.2	+	16023.3i	−0.0875582	+	0.0505518i	0.455582	+	0.890194i	$0.349431\pi$
$564$	51916.5	−	168855.i	0.163210	−	0.530832i
$565$	−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	$0.0258913\pi$
$570$	241842.	−	90243.9i	0.744359	−	0.277759i
$571$	−556449.	+	321266.i	−1.70668	+	0.985355i	−0.768085	+	0.640348i	$0.778790\pi$
$571$	−556449.	+	321266.i	−1.70668	+	0.985355i	−0.938600	+	0.345007i	$0.887877\pi$
$572$	−31172.2	−	31289.4i	−0.0952741	−	0.0956325i
$573$	456880.	−	243101.i	1.39153	−	0.740418i
$574$	116215.	−	48010.3i	0.352728	−	0.145717i
$575$		−	30799.0i		−	0.0931540i
$576$	109596.	−	313152.i	0.330331	−	0.943865i
$577$	451002.			1.35465			0.677324	−	0.735685i	$-0.263140\pi$
$577$	451002.			1.35465			0.677324	+	0.735685i	$0.263140\pi$
$578$	−4492.68	−	10875.1i	−0.0134477	−	0.0325521i
$579$	404232.	+	13996.5i	1.20580	+	0.0417507i
$580$	303691.	−	302553.i	0.902768	−	0.899385i
$581$	158808.	+	275063.i	0.470456	+	0.814854i
$582$	−133773.	+	162067.i	−0.394933	+	0.478464i
$583$	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	0.893460	−	0.449143i	$-0.148271\pi$
$587$	327761.	+	189233.i	0.951221	+	0.549188i	0.0577610	+	0.998330i	$0.481604\pi$
$588$	−710614.	+	660559.i	−2.05532	+	1.91054i
$589$	−134303.	−	232620.i	−0.387129	−	0.670528i
$590$	−17188.7	+	129621.i	−0.0493787	+	0.372367i
$591$	−212202.	+	339818.i	−0.607541	+	0.972908i
$592$	−306.300	+	81573.7i	−0.000873983	+	0.232759i
$593$	137966.			0.392339			0.196170	−	0.980570i	$-0.437150\pi$
$593$	137966.			0.392339			0.196170	+	0.980570i	$0.437150\pi$
$594$	−14890.3	+	62008.0i	−0.0422016	+	0.175742i
$595$		−	601046.i		−	1.69775i
$596$	461641.	+	124626.i	1.29961	+	0.350845i
$597$	−145553.	−	90892.1i	−0.408389	−	0.255022i
$598$	15207.9	−	114684.i	0.0425273	−	0.320701i
$599$	180870.	−	104426.i	0.504096	−	0.291040i	−0.226307	−	0.974056i	$-0.572665\pi$
$599$	180870.	−	104426.i	0.504096	−	0.291040i	0.730404	+	0.683016i	$0.239332\pi$
$600$	7226.49	+	77086.2i	0.0200736	+	0.214128i
$601$	−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
$606$	126019.	−	152673.i	0.343155	−	0.415735i
$607$	−279709.	+	161490.i	−0.759152	+	0.438297i	−0.828991	−	0.559262i	$-0.811085\pi$
$607$	−279709.	+	161490.i	−0.759152	+	0.438297i	0.0698392	+	0.997558i	$0.477751\pi$
$608$	−125420.	−	306857.i	−0.339281	−	0.830096i
$609$	−36013.8	+	1.04011e6i	−0.0971034	+	2.80443i
$610$	63337.3	+	153317.i	0.170216	+	0.412031i
$611$			154850.i			0.414791i
$612$	−347692.	−	120220.i	−0.928306	−	0.320978i
$613$	−392554.			−1.04467			−0.522334	−	0.852741i	$-0.674939\pi$
$613$	−392554.			−1.04467			−0.522334	+	0.852741i	$0.674939\pi$
$614$	231899.	−	95800.6i	0.615122	−	0.254116i
$615$	−30791.4	−	57869.0i	−0.0814103	−	0.153002i
$616$	17090.7	+	132703.i	0.0450399	+	0.349720i
$617$	−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	$-0.335032\pi$
$618$	−604859.	+	225704.i	−1.58371	+	0.590966i
$619$	602573.	+	347896.i	1.57264	+	0.907962i	0.995844	+	0.0910712i	$0.0290291\pi$
$619$	602573.	+	347896.i	1.57264	+	0.907962i	0.576792	+	0.816891i	$0.304304\pi$
$620$	−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
$624$	−11154.9	+	290608.i	−0.0286482	+	0.746342i
$625$	144273.	+	249889.i	0.369339	+	0.639715i
$626$	192670.	+	25549.5i	0.491660	+	0.0651979i
$627$	29930.2	+	56250.4i	0.0761332	+	0.143084i
$628$	−540445.	−	145900.i	−1.37035	−	0.369943i
$629$	90453.5			0.228625
$630$	513645.	+	454753.i	1.29414	+	1.14576i
$631$		−	230753.i		−	0.579546i	−0.957095	−	0.289773i	$-0.906420\pi$
$631$		−	230753.i		−	0.579546i	0.957095	−	0.289773i	$-0.0935798\pi$
$632$	−279173.	−	365955.i	−0.698940	−	0.916207i
$633$	−296.775	+	8571.13i	−0.000740662	+	0.0213910i
$634$	436711.	+	57911.2i	1.08646	+	0.144073i
$635$	−155955.	+	90040.8i	−0.386770	+	0.223302i
$636$	−91181.3	−	397820.i	−0.225419	−	0.983495i
$637$	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	$0.949107\pi$
$642$	51982.1	−	309410.i	0.126120	−	0.750696i
$643$	195039.	−	112606.i	0.471738	−	0.272358i	−0.245229	−	0.969465i	$-0.578863\pi$
$643$	195039.	−	112606.i	0.471738	−	0.272358i	0.716967	+	0.697107i	$0.245530\pi$
$644$	−248280.	+	247349.i	−0.598645	+	0.596402i
$645$	−35013.5	−	21864.5i	−0.0841620	−	0.0525557i
$646$	−339733.	+	140348.i	−0.814090	+	0.336312i
$647$			153505.i			0.366703i	0.983047	+	0.183352i	$0.0586947\pi$
$647$			153505.i			0.366703i	−0.983047	+	0.183352i	$0.941305\pi$
$648$	365803.	−	206173.i	0.871159	−	0.491000i
$649$	−32276.0			−0.0766284
$650$	−25912.7	−	62725.3i	−0.0613318	−	0.148462i
$651$	378113.	−	605505.i	0.892194	−	1.42875i
$652$	163851.	+	164468.i	0.385438	+	0.386888i
$653$	−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	$0.860329\pi$
$654$	−431784.	−	72541.5i	−1.00951	−	0.169602i
$655$	−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	0.247517	−	0.968883i	$-0.420385\pi$
$659$	−203157.	−	117293.i	−0.467802	−	0.270086i	−0.715319	+	0.698798i	$0.753719\pi$
$660$	67988.5	−	15583.1i	0.156080	−	0.0357739i
$661$	−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	$-0.406547\pi$
$662$	97026.0	−	731678.i	0.221397	−	1.66957i
$663$	322284.	+	11159.1i	0.733182	+	0.0253864i
$664$	−128971.	−	169061.i	−0.292519	−	0.383450i
$665$	685452.			1.55001
$666$	−68437.4	+	77300.2i	−0.154293	+	0.174274i
$667$			277166.i			0.623001i
$668$	−186061.	+	689211.i	−0.416968	+	1.54454i
$669$	344366.	−	183233.i	0.769428	−	0.409404i
$670$	−2886.86	+	21769.9i	−0.00643096	+	0.0484961i
$671$	−35461.3	+	20473.6i	−0.0787607	+	0.0454725i
$672$	563377.	−	677339.i	1.24756	−	1.49992i
$673$	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	$0.137231\pi$
$678$	257674.	+	690533.i	0.560545	+	1.50219i
$679$	−483267.	+	279014.i	−1.04821	+	0.605183i
$680$	51398.8	+	399095.i	0.111157	+	0.863094i
$681$	47731.4	−	25397.3i	0.102922	−	0.0547638i
$682$	−27713.0	−	67083.2i	−0.0595820	−	0.144226i
$683$		−	635506.i		−	1.36232i	−0.732136	−	0.681159i	$-0.761476\pi$
$683$		−	635506.i		−	1.36232i	0.732136	−	0.681159i	$-0.238524\pi$
$684$	137103.	−	396519.i	0.293046	−	0.847524i
$685$	−546260.			−1.16418
$686$	−1.53261e6	+	633142.i	−3.25674	+	1.34540i
$687$	36665.2	+	1269.53i	0.0776855	+	0.00268986i
$688$	−26678.3	+	45810.1i	−0.0563614	+	0.0967797i
$689$	178878.	+	309825.i	0.376806	+	0.652647i
$690$	140902.	+	116303.i	0.295951	+	0.244283i
$691$	384843.	+	222189.i	0.805986	+	0.465336i	0.845560	−	0.533881i	$-0.179267\pi$
$691$	384843.	+	222189.i	0.805986	+	0.465336i	−0.0395741	+	0.999217i	$0.512600\pi$
$692$	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
$696$	−65032.5	−	693713.i	−0.134249	−	1.43206i
$697$	46672.6	+	80839.4i	0.0960720	+	0.166402i
$698$	−346344.	−	45927.8i	−0.710880	−	0.0942682i
$699$	−178418.	+	285716.i	−0.365161	+	0.584764i
$700$	−53584.8	+	198490.i	−0.109357	+	0.405081i
$701$	−374624.			−0.762359			−0.381179	−	0.924501i	$-0.624482\pi$
$701$	−374624.			−0.762359			−0.381179	+	0.924501i	$0.624482\pi$
$702$	−253378.	+	266976.i	−0.514155	+	0.541749i
$703$			103156.i			0.208730i
$704$	−22696.4	−	86653.5i	−0.0457944	−	0.174840i
$705$	−207428.	−	129530.i	−0.417338	−	0.260610i
$706$	193144.	+	25612.3i	0.387499	+	0.0513854i
$707$	455254.	−	262841.i	0.910783	−	0.525841i
$708$	144695.	+	155659.i	0.288660	+	0.310533i
$709$	−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
$714$	−753407.	−	621875.i	−1.47786	−	1.21985i
$715$	−52950.0	+	30570.7i	−0.103575	+	0.0597989i
$716$	370854.	+	372249.i	0.723396	+	0.726118i
$717$	7987.96	−	230699.i	0.0155381	−	0.448753i
$718$	404478.	−	167096.i	0.784596	−	0.324128i
$719$		−	651163.i		−	1.25960i	−0.776759	−	0.629799i	$-0.783137\pi$
$719$		−	651163.i		−	1.25960i	0.776759	−	0.629799i	$-0.216863\pi$
$720$	−379949.	−	258032.i	−0.732927	−	0.497746i
$721$	−1.71435e6			−3.29783
$722$	38976.5	+	94348.1i	0.0747702	+	0.180992i
$723$	323840.	+	608621.i	0.619519	+	1.16432i
$724$	257967.	−	257000.i	0.492138	−	0.490294i
$725$	81298.3	+	140813.i	0.154670	+	0.267896i
$726$	−178249.	−	477685.i	−0.338184	−	0.906292i
$727$	207917.	+	120041.i	0.393389	+	0.227123i	0.683627	−	0.729831i	$-0.260401\pi$
$727$	207917.	+	120041.i	0.393389	+	0.227123i	−0.290239	+	0.956954i	$0.593735\pi$
$728$	−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
$732$	257714.	+	79237.0i	0.480967	+	0.147879i
$733$	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	$0.816832\pi$
$734$	−675.675	+	5095.29i	−0.00125414	+	0.00945751i
$735$	630889.	+	1.18569e6i	1.16783	+	2.19480i
$736$	143706.	−	185472.i	0.265288	−	0.342391i
$737$	−5420.76			−0.00997988
$738$	−104397.	−	21277.6i	−0.191679	−	0.0390670i
$739$			327859.i			0.600341i	0.953886	+	0.300170i	$0.0970435\pi$
$739$			327859.i			0.600341i	−0.953886	+	0.300170i	$0.902957\pi$
$740$	109022.	+	29431.8i	0.199091	+	0.0537470i
$741$	−12726.2	+	367543.i	−0.0231772	+	0.669379i
$742$	142470.	−	1.07438e6i	0.258772	−	1.95141i
$743$	−11150.8	+	6437.91i	−0.0201989	+	0.0116618i	−0.510065	−	0.860136i	$-0.670379\pi$
$743$	−11150.8	+	6437.91i	−0.0201989	+	0.0116618i	0.489867	+	0.871797i	$0.337045\pi$
$744$	−199287.	+	434390.i	−0.360025	+	0.784755i
$745$	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
$750$	597166.	+	100326.i	1.06163	+	0.178358i
$751$	460430.	−	265829.i	0.816363	−	0.471328i	−0.0327975	−	0.999462i	$-0.510442\pi$
$751$	460430.	−	265829.i	0.816363	−	0.471328i	0.849161	+	0.528134i	$0.177108\pi$
$752$	−158048.	+	271389.i	−0.279482	+	0.479906i
$753$	508739.	+	317687.i	0.897233	+	0.560285i
$754$	233193.	+	564476.i	0.410179	+	0.992894i
$755$			132075.i			0.231701i
$756$	1.10148e6	−	173338.i	1.92722	−	0.303284i
$757$	614542.			1.07241			0.536204	−	0.844089i	$-0.319858\pi$
$757$	614542.			1.07241			0.536204	+	0.844089i	$0.319858\pi$
$758$	514134.	−	212396.i	0.894825	−	0.369665i
$759$	−23887.1	+	38252.6i	−0.0414649	+	0.0664014i
$760$	−455141.	+	58616.9i	−0.787986	+	0.101484i
$761$	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	$0.582673\pi$
$762$	−48494.3	+	288650.i	−0.0835182	+	0.497120i
$763$	−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
$768$	−316160.	+	497931.i	−0.536024	+	0.844203i
$769$	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	$0.797884\pi$
$770$	183614.	+	24348.6i	0.309687	+	0.0410669i
$771$	−534517.	−	18507.7i	−0.899193	−	0.0311346i
$772$	−694213.	−	187411.i	−1.16482	−	0.314457i
$773$	−629.598			−0.00105367			−0.000526834	−	1.00000i	$-0.500168\pi$
$773$	−629.598			−0.00105367			−0.000526834		1.00000i	$0.500168\pi$
$774$	−63633.8	+	21267.0i	−0.106220	+	0.0354996i
$775$		−	111529.i		−	0.185689i
$776$	297029.	−	226593.i	0.493260	−	0.376290i
$777$	−242026.	+	128779.i	−0.400885	+	0.213306i
$778$	396853.	+	52625.8i	0.655648	+	0.0869439i
$779$	−92191.9	+	53227.0i	−0.151921	+	0.0877117i
$780$	384812.	+	118315.i	0.632499	+	0.194469i
$781$	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
$786$	−548948.	+	204841.i	−0.888559	+	0.331567i
$787$	−415038.	+	239622.i	−0.670098	+	0.386881i	−0.796114	−	0.605147i	$-0.793114\pi$
$787$	−415038.	+	239622.i	−0.670098	+	0.386881i	0.126016	+	0.992028i	$0.459781\pi$
$788$	504571.	−	502680.i	0.812587	−	0.809542i
$789$	−199747.	+	106283.i	−0.320867	+	0.170730i
$790$	−588905.	+	243285.i	−0.943608	+	0.389818i
$791$			1.95717e6i			3.12807i
$792$	50811.3	−	101346.i	0.0810046	−	0.161569i
$793$	−236338.			−0.375826
$794$	251064.	+	607736.i	0.398239	+	0.963994i
$795$	−564652.	−	19551.1i	−0.893401	−	0.0309340i
$796$	215312.	+	216122.i	0.339814	+	0.341092i
$797$	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	$0.651165\pi$
$798$	709207.	−	859210.i	1.11370	−	1.34925i
$799$	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
$804$	24301.5	+	26143.0i	0.0375943	+	0.0404430i
$805$	242576.	+	420155.i	0.374332	+	0.648362i
$806$	55071.0	−	415293.i	0.0847720	−	0.639270i
$807$	12172.4	−	19492.7i	0.0186908	−	0.0299312i
$808$	−279812.	+	213458.i	−0.428591	+	0.326956i
$809$	−423910.			−0.647703			−0.323852	−	0.946108i	$-0.604978\pi$
$809$	−423910.			−0.647703			−0.323852	+	0.946108i	$0.604978\pi$
$810$	−145678.	−	562731.i	−0.222036	−	0.857690i
$811$		−	257508.i		−	0.391515i	−0.980652	−	0.195757i	$-0.937283\pi$
$811$		−	257508.i		−	0.391515i	0.980652	−	0.195757i	$-0.0627165\pi$
$812$	482219.	−	1.78625e6i	0.731362	−	2.70913i
$813$	35292.1	+	22038.4i	0.0533944	+	0.0333426i
$814$	−3664.30	+	27632.6i	−0.00553022	+	0.0417036i
$815$	278323.	−	160690.i	0.419019	−	0.241921i
$816$	553442.	+	348497.i	0.831174	+	0.523382i
$817$	−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	$-0.0591289\pi$
$822$	−565191.	+	684733.i	−0.836472	+	1.01339i
$823$	−571229.	+	329799.i	−0.843355	+	0.486911i	−0.858403	−	0.512976i	$-0.828543\pi$
$823$	−571229.	+	329799.i	−0.843355	+	0.486911i	0.0150484	+	0.999887i	$0.495210\pi$
$824$	1.13833e6	−	146604.i	1.67654	−	0.215919i
$825$	−915.505	+	26440.6i	−0.00134509	+	0.0388475i
$826$	215476.	+	521589.i	0.315819	+	0.764483i
$827$		−	853638.i		−	1.24814i	−0.781369	−	0.624069i	$-0.785478\pi$
$827$		−	853638.i		−	1.24814i	0.781369	−	0.624069i	$-0.214522\pi$
$828$	291570.	−	56286.2i	0.425287	−	0.0820997i
$829$	542017.			0.788685			0.394343	−	0.918963i	$-0.370972\pi$
$829$	542017.			0.788685			0.394343	+	0.918963i	$0.370972\pi$
$830$	−272059.	+	112391.i	−0.394917	+	0.163146i
$831$	−41660.3	−	78295.7i	−0.0603281	−	0.113380i
$832$	136624.	−	498638.i	0.197370	−	0.720342i
$833$	−956282.	−	1.65633e6i	−1.37815	−	2.38702i
$834$	−665125.	+	248192.i	−0.956249	+	0.356826i
$835$	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	−0.447259	−	0.894404i	$-0.647600\pi$
$839$	−1.01749e6	−	587450.i	−1.44547	−	0.834540i	−0.998207	+	0.0598644i	$0.980933\pi$
$840$	−705721.	−	994679.i	−1.00017	−	1.40969i
$841$	−377978.	−	654677.i	−0.534410	−	0.925625i
$842$	−926388.	−	122846.i	−1.30668	−	0.173276i
$843$	−204688.	−	384688.i	−0.288030	−	0.541319i
$844$	3973.78	−	14719.7i	0.00557851	−	0.0206640i
$845$	279706.			0.391732
$846$	−376981.	+	125990.i	−0.526718	+	0.176034i
$847$		−	1.35390e6i		−	1.88721i
$848$	−2724.43	+	725569.i	−0.00378864	+	1.00899i
$849$	41181.5	−	1.18936e6i	0.0571330	−	1.65005i
$850$	−151301.	−	20063.6i	−0.209413	−	0.0277697i
$851$	−63230.5	+	36506.2i	−0.0873108	+	0.0504089i
$852$	−604712.	+	138601.i	−0.833046	+	0.190936i
$853$	−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	$0.958009\pi$
$858$	−16464.8	+	98002.5i	−0.0223657	+	0.133126i
$859$	−918319.	+	530192.i	−1.24454	+	0.718533i	−0.970014	−	0.243048i	$-0.921853\pi$
$859$	−918319.	+	530192.i	−1.24454	+	0.718533i	−0.274521	+	0.961581i	$0.588519\pi$
$860$	51794.1	+	51989.0i	0.0700299	+	0.0702933i
$861$	−239973.	−	149853.i	−0.323711	−	0.202144i
$862$	1.23175e6	−	508854.i	1.65771	−	0.684824i
$863$			150213.i			0.201691i	0.994902	+	0.100845i	$0.0321547\pi$
$863$			150213.i			0.201691i	−0.994902	+	0.100845i	$0.967845\pi$
$864$	−716557.	+	209290.i	−0.959894	+	0.280363i
$865$	1.17139e6			1.56556
$866$	−328886.	−	796114.i	−0.438540	−	1.06155i
$867$	−14022.9	+	22456.1i	−0.0186552	+	0.0298742i
$868$	−899070.	+	895700.i	−1.19331	+	1.18884i
$869$	−78641.1	−	136210.i	−0.104138	−	0.180373i
$870$	−951200.	−	159805.i	−1.25671	−	0.211131i
$871$	−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
$876$	96858.6	+	422590.i	0.126221	+	0.550695i
$877$	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	$0.555760\pi$
$878$	16426.0	−	123869.i	0.0213080	−	0.160684i
$879$	805190.	+	27879.7i	1.04213	+	0.0360836i
$880$	−124002.	−	465.612i	−0.160126	−	0.000601255i
$881$	1.15136e6			1.48341			0.741703	−	0.670728i	$-0.234018\pi$
$881$	1.15136e6			1.48341			0.741703	+	0.670728i	$0.234018\pi$
$882$	2.13900e6	+	435960.i	2.74963	+	0.560414i
$883$			109897.i			0.140950i	0.997514	+	0.0704752i	$0.0224516\pi$
$883$			109897.i			0.140950i	−0.997514	+	0.0704752i	$0.977548\pi$
$884$	−553478.	−	149418.i	−0.708266	−	0.191205i
$885$	259723.	−	138195.i	0.331607	−	0.176444i
$886$	−112223.	+	846281.i	−0.142960	+	1.07807i
$887$	856444.	−	494468.i	1.08856	−	0.628480i	0.155366	−	0.987857i	$-0.450344\pi$
$887$	856444.	−	494468.i	1.08856	−	0.628480i	0.933192	+	0.359377i	$0.117011\pi$
$888$	149693.	−	106206.i	0.189834	−	0.134687i
$889$	−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
$894$	−376132.	−	1.00799e6i	−0.470614	−	1.26119i
$895$	629943.	−	363698.i	0.786421	−	0.454040i
$896$	−1.24882e6	+	945283.i	−1.55555	+	1.17746i
$897$	−229793.	+	122270.i	−0.285596	+	0.151962i
$898$	−600295.	−	1.45310e6i	−0.744410	−	1.80195i
$899$			1.00367e6i			1.24186i
$900$	131621.	−	114119.i	0.162495	−	0.140888i
$901$	804551.			0.991070
$902$	−26586.4	+	10983.2i	−0.0326773	+	0.0134995i
$903$	−178056.	−	6165.21i	−0.218365	−	0.00756087i
$904$	−167369.	−	1.29956e6i	−0.204804	−	1.59023i
$905$	−252041.	−	436548.i	−0.307733	−	0.533010i
$906$	165555.	+	136652.i	0.201691	+	0.166479i
$907$	445673.	+	257309.i	0.541753	+	0.312781i	0.745789	−	0.666182i	$-0.232073\pi$
$907$	445673.	+	257309.i	0.541753	+	0.312781i	−0.204036	+	0.978963i	$0.565406\pi$
$908$	−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	−0.235829	−	0.971795i	$-0.575780\pi$
$911$	−992039.	−	572754.i	−1.19534	−	0.690131i	−0.959513	+	0.281664i	$0.909114\pi$
$912$	−397438.	+	631164.i	−0.477837	+	0.758844i
$913$	−36330.1	−	62925.6i	−0.0435838	−	0.0754894i
$914$	286918.	+	38047.5i	0.343452	+	0.0455443i
$915$	197694.	−	316584.i	0.236129	−	0.378135i
$916$	−62967.4	−	16998.8i	−0.0750455	−	0.0202595i
$917$	−1.55588e6			−1.85028
$918$	235052.	+	793676.i	0.278920	+	0.941798i
$919$			329486.i			0.390127i	0.980791	+	0.195063i	$0.0624913\pi$
$919$			329486.i			0.390127i	−0.980791	+	0.195063i	$0.937509\pi$
$920$	−197001.	−	258239.i	−0.232751	−	0.305103i
$921$	−478848.	−	299021.i	−0.564518	−	0.352518i
$922$	−230747.	−	30598.8i	−0.271440	−	0.0359950i
$923$	470954.	−	271906.i	0.552809	−	0.319165i
$924$	220497.	−	204966.i	0.258261	−	0.240070i
$925$	−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	$-0.00945781\pi$
$930$	510234.	+	421156.i	0.589934	+	0.486942i
$931$	1.88893e6	−	1.09058e6i	2.17930	−	1.25822i
$932$	424239.	−	422649.i	0.488404	−	0.486573i
$933$	38239.3	−	1.10438e6i	0.0439285	−	1.26869i
$934$	−977348.	+	403756.i	−1.12035	+	0.462834i
$935$			137500.i			0.157282i
$936$	546455.	−	359944.i	0.623738	−	0.410850i
$937$	1.29741e6			1.47774			0.738872	−	0.673846i	$-0.235359\pi$
$937$	1.29741e6			1.47774			0.738872	+	0.673846i	$0.235359\pi$
$938$	36189.2	+	87601.0i	0.0411314	+	0.0995643i
$939$	−205415.	−	386054.i	−0.232971	−	0.437842i
$940$	306840.	+	307994.i	0.347261	+	0.348567i
$941$	−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	$0.853110\pi$
$942$	440338.	+	1.18005e6i	0.496232	+	1.32984i
$943$	−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	0.741721	−	0.670709i	$-0.234010\pi$
$947$	476861.	+	275316.i	0.531730	+	0.306995i	−0.209990	+	0.977703i	$0.567343\pi$
$948$	−304358.	+	989905.i	−0.338663	+	1.10148i
$949$	−190015.	−	329116.i	−0.210987	−	0.365441i
$950$	22881.2	−	172548.i	0.0253531	−	0.191189i
$951$	−465599.	−	875041.i	−0.514815	−	0.967537i
$952$	1.05337e6	+	1.38081e6i	1.16227	+	1.52356i
$953$	−802951.			−0.884104			−0.442052	−	0.896989i	$-0.645749\pi$
$953$	−802951.			−0.884104			−0.442052	+	0.896989i	$0.645749\pi$
$954$	−608727.	+	687558.i	−0.668845	+	0.755462i
$955$			1.27365e6i			1.39650i
$956$	−106958.	+	396194.i	−0.117030	+	0.433503i
$957$	8238.80	−	237944.i	0.00899580	−	0.259807i
$958$	−147064.	+	1.10902e6i	−0.160241	+	1.20839i
$959$	−2.04180e6	+	1.17883e6i	−2.22012	+	1.28179i
$960$	553660.	+	600117.i	0.600760	+	0.651169i
$961$	−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
$966$	777644.	+	130647.i	0.833348	+	0.140006i
$967$	826524.	−	477194.i	0.883898	−	0.510319i	0.0119565	−	0.999929i	$-0.496194\pi$
$967$	826524.	−	477194.i	0.883898	−	0.510319i	0.871942	+	0.489610i	$0.162861\pi$
$968$	115780.	+	898990.i	0.123561	+	0.959410i
$969$	701515.	+	438067.i	0.747118	+	0.466544i
$970$	−197464.	−	477988.i	−0.209867	−	0.508012i
$971$		−	708749.i		−	0.751716i	−0.926677	−	0.375858i	$-0.877348\pi$
$971$		−	708749.i		−	0.751716i	0.926677	−	0.375858i	$-0.122652\pi$
$972$	−856105.	−	399626.i	−0.906139	−	0.422981i
$973$	−1.88516e6			−1.99123
$974$	231083.	−	95463.7i	0.243585	−	0.100628i
$975$	−80880.8	+	129521.i	−0.0850817	+	0.136249i
$976$	−414204.	−	241219.i	−0.434825	−	0.253228i
$977$	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	$0.727500\pi$
$978$	86544.6	−	515134.i	0.0904820	−	0.538570i
$979$	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	$0.0217227\pi$
$983$	1.50312e6	+	867829.i	1.55556	+	0.898105i	0.557891	+	0.829914i	$0.311611\pi$
$984$	172157.	+	78981.3i	0.177801	+	0.0815707i
$985$	−492981.	−	853867.i	−0.508110	−	0.880072i
$986$	1.36158e6	+	180556.i	1.40052	+	0.185720i
$987$	−1.05485e6	−	36524.0i	−1.08282	−	0.0374925i
$988$	170402.	−	631205.i	0.174566	−	0.646631i
$989$	−47448.1			−0.0485095
$990$	−117505.	−	104033.i	−0.119891	−	0.106145i
$991$		−	106256.i		−	0.108195i	−0.998536	−	0.0540974i	$-0.982772\pi$
$991$		−	106256.i		−	0.108195i	0.998536	−	0.0540974i	$-0.0172282\pi$
$992$	520386.	−	671630.i	0.528813	−	0.682506i
$993$	−1.46607e6	+	780078.i	−1.48681	+	0.791115i
$994$	−1.63312e6	−	216564.i	−1.65289	−	0.219186i
$995$	365735.	−	211157.i	0.369420	−	0.213285i
$996$	−140605.	+	457310.i	−0.141737	+	0.460990i
$997$	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.7.15	yes	44
3.2	odd	2		108.5.f.a.19.8		44
4.3	odd	2	inner	36.5.f.a.7.1	✓	44
9.2	odd	6		324.5.d.e.163.8		22
9.4	even	3	inner	36.5.f.a.31.1	yes	44
9.5	odd	6		108.5.f.a.91.22		44
9.7	even	3		324.5.d.f.163.15		22
12.11	even	2		108.5.f.a.19.22		44
36.7	odd	6		324.5.d.f.163.16		22
36.11	even	6		324.5.d.e.163.7		22
36.23	even	6		108.5.f.a.91.8		44
36.31	odd	6	inner	36.5.f.a.31.15	yes	44

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

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)

\(f(q)\)	\(=\)	\(q+(1.52726 + 3.69695i) q^{2} +(4.76702 - 7.63384i) q^{3} +(-11.3349 + 11.2924i) q^{4} +(11.0746 + 19.1817i) q^{5} +(35.5025 + 5.96455i) q^{6} +(82.7885 + 47.7980i) q^{7} +(-59.0591 - 24.6582i) q^{8} +(-35.5511 - 72.7813i) q^{9} +O(q^{10})\)	\(q+(1.52726 + 3.69695i) q^{2} +(4.76702 - 7.63384i) q^{3} +(-11.3349 + 11.2924i) q^{4} +(11.0746 + 19.1817i) q^{5} +(35.5025 + 5.96455i) 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} +(32.1709 + 140.360i) q^{12} +(-63.1124 - 109.314i) q^{13} +(-50.2669 + 379.065i) q^{14} +(199.223 + 6.89808i) q^{15} +(0.961243 - 255.998i) q^{16} -283.865 q^{17} +(214.773 - 242.587i) q^{18} -323.729i q^{19} +(-342.138 - 92.3643i) q^{20} +(759.536 - 404.141i) q^{21} +(11.4995 - 86.7180i) q^{22} +(198.433 - 114.565i) q^{23} +(-469.772 + 333.302i) 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} +(278.764 + 747.052i) q^{30} +(718.565 - 414.863i) q^{31} +(947.881 - 387.423i) q^{32} +(-173.758 + 92.4544i) q^{33} +(-433.537 - 1049.44i) q^{34} +2117.36i q^{35} +(1224.85 + 423.513i) q^{36} -318.650 q^{37} +(1196.81 - 494.420i) q^{38} +(-1135.34 - 39.3112i) q^{39} +(-181.068 - 1405.93i) q^{40} +(-164.418 - 284.781i) q^{41} +(2654.10 + 2190.74i) 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} +(-1949.67 - 1227.69i) q^{48} +(3368.79 + 5834.92i) q^{49} +(533.002 + 70.6801i) q^{50} +(-1353.19 + 2166.98i) q^{51} +(1949.79 + 526.371i) q^{52} -2834.27 q^{53} +(-828.042 - 2795.96i) q^{54} -484.385i q^{55} +(-3710.80 - 4864.32i) q^{56} +(-2471.30 - 1543.22i) q^{57} +(-4796.58 - 636.063i) q^{58} +(1278.13 - 737.929i) q^{59} +(-2336.07 + 2171.52i) 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} +(-607.173 - 501.171i) q^{66} +(214.663 - 123.936i) q^{67} +(3217.59 - 3205.53i) q^{68} +(71.3600 - 2060.94i) q^{69} +(-7827.80 + 3233.77i) q^{70} +4308.28i q^{71} +(304.960 + 5175.02i) q^{72} +3010.75 q^{73} +(-486.662 - 1178.03i) q^{74} +(-568.260 - 1067.98i) q^{75} +(3655.69 + 3669.45i) q^{76} +(-1045.31 - 1810.52i) q^{77} +(-1588.64 - 4257.34i) 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} +(-4045.56 + 13157.9i) q^{84} +(-3143.68 - 5445.01i) q^{85} +(108.888 - 821.128i) q^{86} +(5113.88 + 9610.95i) q^{87} +(848.913 + 1112.80i) q^{88} -1549.85 q^{89} +(7031.75 + 1433.17i) q^{90} -12066.6i q^{91} +(-955.500 + 3539.38i) q^{92} +(258.409 - 7463.07i) q^{93} +(645.075 - 4864.54i) q^{94} +(6209.67 - 3585.16i) q^{95} +(1561.04 - 9082.83i) 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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