LMFDB - Embedded newform 63.4.o.a.20.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,4,Mod(20,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 3]))

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

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

chi := DirichletCharacter("63.20");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	63.o (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:	$3.71712033036$
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			20.9
Character	$\chi$	$=$	63.20
Dual form			63.4.o.a.41.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.10556 - 0.638294i) q^{2} +(-0.213646 + 5.19176i) q^{3} +(-3.18516 - 5.51686i) q^{4} +(1.59510 + 2.76280i) q^{5} +(3.55007 - 5.60342i) q^{6} +(-13.1775 + 13.0136i) q^{7} +18.3450i q^{8} +(-26.9087 - 2.21839i) q^{9} +O(q^{10})$	\(q+(-1.10556 - 0.638294i) q^{2} +(-0.213646 + 5.19176i) q^{3} +(-3.18516 - 5.51686i) q^{4} +(1.59510 + 2.76280i) q^{5} +(3.55007 - 5.60342i) q^{6} +(-13.1775 + 13.0136i) q^{7} +18.3450i q^{8} +(-26.9087 - 2.21839i) q^{9} -4.07258i q^{10} +(-38.0908 - 21.9917i) q^{11} +(29.3227 - 15.3579i) q^{12} +(-65.6143 + 37.8824i) q^{13} +(22.8750 - 5.97614i) q^{14} +(-14.6846 + 7.69113i) q^{15} +(-13.7718 + 23.8534i) q^{16} +104.977 q^{17} +(28.3332 + 19.6282i) q^{18} +74.7068i q^{19} +(10.1613 - 17.5999i) q^{20} +(-64.7481 - 71.1947i) q^{21} +(28.0744 + 48.6262i) q^{22} +(46.6533 - 26.9353i) q^{23} +(-95.2428 - 3.91933i) q^{24} +(57.4113 - 99.4393i) q^{25} +96.7206 q^{26} +(17.2663 - 139.230i) q^{27} +(113.767 + 31.2481i) q^{28} +(-26.3321 - 15.2028i) q^{29} +(21.1439 + 0.870089i) q^{30} +(-111.231 + 64.2193i) q^{31} +(157.549 - 90.9609i) q^{32} +(122.314 - 193.060i) q^{33} +(-116.058 - 67.0062i) q^{34} +(-56.9734 - 15.6488i) q^{35} +(73.4700 + 155.518i) q^{36} +46.1138 q^{37} +(47.6849 - 82.5928i) q^{38} +(-182.658 - 348.747i) q^{39} +(-50.6835 + 29.2621i) q^{40} +(213.104 + 369.107i) q^{41} +(26.1396 + 120.038i) q^{42} +(-166.003 + 287.526i) q^{43} +280.188i q^{44} +(-36.7932 - 77.8819i) q^{45} -68.7706 q^{46} +(-170.147 + 294.704i) q^{47} +(-120.899 - 76.5959i) q^{48} +(4.29341 - 342.973i) q^{49} +(-126.943 + 73.2906i) q^{50} +(-22.4279 + 545.015i) q^{51} +(417.984 + 241.323i) q^{52} -235.233i q^{53} +(-107.958 + 142.905i) q^{54} -140.316i q^{55} +(-238.734 - 241.741i) q^{56} +(-387.860 - 15.9608i) q^{57} +(19.4078 + 33.6152i) q^{58} +(-272.093 - 471.279i) q^{59} +(89.2036 + 56.5152i) q^{60} +(-321.478 - 185.606i) q^{61} +163.963 q^{62} +(383.459 - 320.946i) q^{63} -11.8909 q^{64} +(-209.323 - 120.853i) q^{65} +(-258.454 + 135.367i) q^{66} +(-53.3481 - 92.4017i) q^{67} +(-334.368 - 579.143i) q^{68} +(129.874 + 247.967i) q^{69} +(52.9988 + 53.6665i) q^{70} +974.682i q^{71} +(40.6964 - 493.640i) q^{72} +576.299i q^{73} +(-50.9815 - 29.4342i) q^{74} +(503.999 + 319.310i) q^{75} +(412.147 - 237.953i) q^{76} +(788.132 - 205.901i) q^{77} +(-20.6639 + 502.150i) q^{78} +(-10.6691 + 18.4794i) q^{79} -87.8696 q^{80} +(719.157 + 119.388i) q^{81} -544.093i q^{82} +(-168.669 + 292.143i) q^{83} +(-186.538 + 583.973i) q^{84} +(167.449 + 290.030i) q^{85} +(367.053 - 211.918i) q^{86} +(84.5552 - 133.462i) q^{87} +(403.438 - 698.775i) q^{88} -1024.06 q^{89} +(-9.03458 + 109.588i) q^{90} +(371.647 - 1353.07i) q^{91} +(-297.197 - 171.586i) q^{92} +(-309.647 - 591.205i) q^{93} +(376.216 - 217.208i) q^{94} +(-206.400 + 119.165i) q^{95} +(438.587 + 837.389i) q^{96} +(63.5527 + 36.6922i) q^{97} +(-223.664 + 376.436i) q^{98} +(976.187 + 676.269i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 6 q^{2} + 78 q^{4} + 5 q^{7}+O(q^{10}) $ 44 * q - 6 * q^2 + 78 * q^4 + 5 * q^7	$ 44 q - 6 q^{2} + 78 q^{4} + 5 q^{7} - 18 q^{11} + 204 q^{14} + 66 q^{15} - 242 q^{16} - 210 q^{18} - 57 q^{21} - 34 q^{22} - 102 q^{23} - 352 q^{25} + 300 q^{28} + 246 q^{29} - 144 q^{30} + 1068 q^{32} - 1818 q^{36} + 328 q^{37} - 798 q^{39} - 1158 q^{42} - 170 q^{43} + 968 q^{46} - 79 q^{49} + 288 q^{50} - 204 q^{51} + 1212 q^{56} + 324 q^{57} - 538 q^{58} + 5316 q^{60} + 783 q^{63} - 808 q^{64} + 4350 q^{65} - 590 q^{67} + 384 q^{70} + 4284 q^{72} - 5304 q^{74} - 2787 q^{77} + 612 q^{78} - 302 q^{79} - 3720 q^{81} + 7050 q^{84} - 612 q^{85} - 13692 q^{86} + 1294 q^{88} + 210 q^{91} - 10194 q^{92} - 4266 q^{93} + 6336 q^{95} + 1014 q^{99}+O(q^{100}) $ 44 * q - 6 * q^2 + 78 * q^4 + 5 * q^7 - 18 * q^11 + 204 * q^14 + 66 * q^15 - 242 * q^16 - 210 * q^18 - 57 * q^21 - 34 * q^22 - 102 * q^23 - 352 * q^25 + 300 * q^28 + 246 * q^29 - 144 * q^30 + 1068 * q^32 - 1818 * q^36 + 328 * q^37 - 798 * q^39 - 1158 * q^42 - 170 * q^43 + 968 * q^46 - 79 * q^49 + 288 * q^50 - 204 * q^51 + 1212 * q^56 + 324 * q^57 - 538 * q^58 + 5316 * q^60 + 783 * q^63 - 808 * q^64 + 4350 * q^65 - 590 * q^67 + 384 * q^70 + 4284 * q^72 - 5304 * q^74 - 2787 * q^77 + 612 * q^78 - 302 * q^79 - 3720 * q^81 + 7050 * q^84 - 612 * q^85 - 13692 * q^86 + 1294 * q^88 + 210 * q^91 - 10194 * q^92 - 4266 * q^93 + 6336 * q^95 + 1014 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−1.10556	−	0.638294i	−0.390874	−	0.225671i	0.291665	−	0.956521i	$-0.405791\pi$
$2$	−1.10556	−	0.638294i	−0.390874	−	0.225671i	−0.682539	+	0.730849i	$0.739124\pi$
$3$	−0.213646	+	5.19176i	−0.0411161	+	0.999154i
$3$	−0.213646	+	5.19176i	−0.0411161	+	0.999154i
$4$	−3.18516	−	5.51686i	−0.398145	−	0.689607i
$5$	1.59510	+	2.76280i	0.142670	+	0.247112i	0.928501	−	0.371329i	$-0.121098\pi$
$5$	1.59510	+	2.76280i	0.142670	+	0.247112i	−0.785831	+	0.618441i	$0.787764\pi$
$6$	3.55007	−	5.60342i	0.241552	−	0.381265i
$7$	−13.1775	+	13.0136i	−0.711519	+	0.702667i
$7$	−13.1775	+	13.0136i	−0.711519	+	0.702667i
$8$			18.3450i			0.810742i
$9$	−26.9087	−	2.21839i	−0.996619	−	0.0821627i
$10$		−	4.07258i		−	0.128786i
$11$	−38.0908	−	21.9917i	−1.04407	−	0.602795i	−0.123088	−	0.992396i	$-0.539280\pi$
$11$	−38.0908	−	21.9917i	−1.04407	−	0.602795i	−0.920984	+	0.389600i	$0.872613\pi$
$12$	29.3227	−	15.3579i	0.705394	−	0.369454i
$13$	−65.6143	+	37.8824i	−1.39986	+	0.808208i	−0.994377	−	0.105896i	$-0.966229\pi$
$13$	−65.6143	+	37.8824i	−1.39986	+	0.808208i	−0.405480	+	0.914104i	$0.632895\pi$
$14$	22.8750	−	5.97614i	0.436686	−	0.114085i
$15$	−14.6846	+	7.69113i	−0.252769	+	0.132389i
$16$	−13.7718	+	23.8534i	−0.215184	+	0.372710i
$17$	104.977			1.49769			0.748843	−	0.662748i	$-0.230610\pi$
$17$	104.977			1.49769			0.748843	+	0.662748i	$0.230610\pi$
$18$	28.3332	+	19.6282i	0.371011	+	0.257023i
$19$			74.7068i			0.902048i	0.892512	+	0.451024i	$0.148941\pi$
$19$			74.7068i			0.902048i	−0.892512	+	0.451024i	$0.851059\pi$
$20$	10.1613	−	17.5999i	0.113607	−	0.196773i
$21$	−64.7481	−	71.1947i	−0.672818	−	0.739808i
$22$	28.0744	+	48.6262i	0.272067	+	0.471234i
$23$	46.6533	−	26.9353i	0.422952	−	0.244191i	−0.273388	−	0.961904i	$-0.588144\pi$
$23$	46.6533	−	26.9353i	0.422952	−	0.244191i	0.696339	+	0.717713i	$0.254811\pi$
$24$	−95.2428	−	3.91933i	−0.810056	−	0.0333346i
$25$	57.4113	−	99.4393i	0.459290	−	0.795514i
$26$	96.7206			0.729557
$27$	17.2663	−	139.230i	0.123070	−	0.992398i
$28$	113.767	+	31.2481i	0.767852	+	0.210905i
$29$	−26.3321	−	15.2028i	−0.168612	−	0.0973481i	0.413319	−	0.910586i	$-0.364369\pi$
$29$	−26.3321	−	15.2028i	−0.168612	−	0.0973481i	−0.581931	+	0.813238i	$0.697703\pi$
$30$	21.1439	+	0.870089i	0.128677	+	0.00529519i
$31$	−111.231	+	64.2193i	−0.644441	+	0.372068i	−0.786323	−	0.617815i	$-0.788018\pi$
$31$	−111.231	+	64.2193i	−0.644441	+	0.372068i	0.141882	+	0.989884i	$0.454685\pi$
$32$	157.549	−	90.9609i	0.870343	−	0.502493i
$33$	122.314	−	193.060i	0.645214	−	1.01840i
$34$	−116.058	−	67.0062i	−0.585406	−	0.337984i
$35$	−56.9734	−	15.6488i	−0.275150	−	0.0755751i
$36$	73.4700	+	155.518i	0.340139	+	0.719989i
$37$	46.1138			0.204894			0.102447	−	0.994738i	$-0.467333\pi$
$37$	46.1138			0.204894			0.102447	+	0.994738i	$0.467333\pi$
$38$	47.6849	−	82.5928i	0.203566	−	0.352587i
$39$	−182.658	−	348.747i	−0.749968	−	1.43190i
$40$	−50.6835	+	29.2621i	−0.200344	+	0.115669i
$41$	213.104	+	369.107i	0.811738	+	1.40597i	0.911647	+	0.410975i	$0.134812\pi$
$41$	213.104	+	369.107i	0.811738	+	1.40597i	−0.0999082	+	0.994997i	$0.531855\pi$
$42$	26.1396	+	120.038i	0.0960338	+	0.441007i
$43$	−166.003	+	287.526i	−0.588728	+	1.01971i	0.405672	+	0.914019i	$0.367038\pi$
$43$	−166.003	+	287.526i	−0.588728	+	1.01971i	−0.994399	+	0.105687i	$0.966296\pi$
$44$			280.188i			0.960000i
$45$	−36.7932	−	77.8819i	−0.121884	−	0.257999i
$46$	−68.7706			−0.220428
$47$	−170.147	+	294.704i	−0.528054	+	0.914616i	0.471411	+	0.881913i	$0.343745\pi$
$47$	−170.147	+	294.704i	−0.528054	+	0.914616i	−0.999465	+	0.0327026i	$0.989589\pi$
$48$	−120.899	−	76.5959i	−0.363547	−	0.230326i
$49$	4.29341	−	342.973i	0.0125172	−	0.999922i
$50$	−126.943	+	73.2906i	−0.359049	+	0.207297i
$51$	−22.4279	+	545.015i	−0.0615790	+	1.49642i
$52$	417.984	+	241.323i	1.11469	+	0.643568i
$53$		−	235.233i		−	0.609654i	−0.952408	−	0.304827i	$-0.901401\pi$
$53$		−	235.233i		−	0.609654i	0.952408	−	0.304827i	$-0.0985987\pi$
$54$	−107.958	+	142.905i	−0.272061	+	0.360129i
$55$		−	140.316i		−	0.344004i
$56$	−238.734	−	241.741i	−0.569682	−	0.576858i
$57$	−387.860	−	15.9608i	−0.901286	−	0.0370887i
$58$	19.4078	+	33.6152i	0.0439373	+	0.0761017i
$59$	−272.093	−	471.279i	−0.600398	−	1.03992i	−0.992761	−	0.120109i	$-0.961676\pi$
$59$	−272.093	−	471.279i	−0.600398	−	1.03992i	0.392363	−	0.919811i	$-0.371658\pi$
$60$	89.2036	+	56.5152i	0.191936	+	0.121601i
$61$	−321.478	−	185.606i	−0.674772	−	0.389580i	0.123110	−	0.992393i	$-0.460713\pi$
$61$	−321.478	−	185.606i	−0.674772	−	0.389580i	−0.797882	+	0.602813i	$0.794046\pi$
$62$	163.963			0.335861
$63$	383.459	−	320.946i	0.766846	−	0.641831i
$64$	−11.8909			−0.0232244
$65$	−209.323	−	120.853i	−0.399436	−	0.230614i
$66$	−258.454	+	135.367i	−0.482022	+	0.252462i
$67$	−53.3481	−	92.4017i	−0.0972763	−	0.168487i	0.813280	−	0.581872i	$-0.197680\pi$
$67$	−53.3481	−	92.4017i	−0.0972763	−	0.168487i	−0.910556	+	0.413385i	$0.864346\pi$
$68$	−334.368	−	579.143i	−0.596296	−	1.03282i
$69$	129.874	+	247.967i	0.226595	+	0.432634i
$70$	52.9988	+	53.6665i	0.0904939	+	0.0916338i
$71$			974.682i			1.62920i	0.580020	+	0.814602i	$0.303045\pi$
$71$			974.682i			1.62920i	−0.580020	+	0.814602i	$0.696955\pi$
$72$	40.6964	−	493.640i	0.0666128	−	0.808001i
$73$			576.299i			0.923982i	0.886885	+	0.461991i	$0.152865\pi$
$73$			576.299i			0.923982i	−0.886885	+	0.461991i	$0.847135\pi$
$74$	−50.9815	−	29.4342i	−0.0800876	−	0.0462386i
$75$	503.999	+	319.310i	0.775957	+	0.491610i
$76$	412.147	−	237.953i	0.622059	−	0.359146i
$77$	788.132	−	205.901i	1.16644	−	0.304735i
$78$	−20.6639	+	502.150i	−0.0299965	+	0.728940i
$79$	−10.6691	+	18.4794i	−0.0151945	+	0.0263176i	−0.873523	−	0.486783i	$-0.838170\pi$
$79$	−10.6691	+	18.4794i	−0.0151945	+	0.0263176i	0.858328	+	0.513101i	$0.171503\pi$
$80$	−87.8696			−0.122801
$81$	719.157	+	119.388i	0.986499	+	0.163770i
$82$		−	544.093i		−	0.732744i
$83$	−168.669	+	292.143i	−0.223058	+	0.386348i	−0.955735	−	0.294229i	$-0.904937\pi$
$83$	−168.669	+	292.143i	−0.223058	+	0.386348i	0.732677	+	0.680576i	$0.238271\pi$
$84$	−186.538	+	583.973i	−0.242298	+	0.758531i
$85$	167.449	+	290.030i	0.213675	+	0.370096i
$86$	367.053	−	211.918i	0.460237	−	0.265718i
$87$	84.5552	−	133.462i	0.104198	−	0.164467i
$88$	403.438	−	698.775i	0.488711	−	0.846473i
$89$	−1024.06			−1.21967			−0.609834	−	0.792529i	$-0.708764\pi$
$89$	−1024.06			−1.21967			−0.609834	+	0.792529i	$0.708764\pi$
$90$	−9.03458	+	109.588i	−0.0105814	+	0.128351i
$91$	371.647	−	1353.07i	0.428123	−	1.55869i
$92$	−297.197	−	171.586i	−0.336792	−	0.194447i
$93$	−309.647	−	591.205i	−0.345257	−	0.659195i
$94$	376.216	−	217.208i	0.412805	−	0.238333i
$95$	−206.400	+	119.165i	−0.222907	+	0.128695i
$96$	438.587	+	837.389i	0.466283	+	0.890267i
$97$	63.5527	+	36.6922i	0.0665237	+	0.0384075i	0.532893	−	0.846183i	$-0.321105\pi$
$97$	63.5527	+	36.6922i	0.0665237	+	0.0384075i	−0.466369	+	0.884590i	$0.654438\pi$
$98$	−223.664	+	376.436i	−0.230546	+	0.388019i
$99$	976.187	+	676.269i	0.991015	+	0.686541i
$100$	−731.457			−0.731457
$101$	442.380	−	766.224i	0.435826	−	0.754873i	−0.561537	−	0.827452i	$-0.689790\pi$
$101$	442.380	−	766.224i	0.435826	−	0.754873i	0.997363	+	0.0725790i	$0.0231229\pi$
$102$	372.675	−	588.230i	0.361768	−	0.571015i
$103$	−38.7086	+	22.3484i	−0.0370299	+	0.0213792i	−0.518401	−	0.855138i	$-0.673472\pi$
$103$	−38.7086	+	22.3484i	−0.0370299	+	0.0213792i	0.481371	+	0.876517i	$0.340139\pi$
$104$	−694.953	−	1203.69i	−0.655248	−	1.13492i
$105$	93.4169	−	292.449i	0.0868243	−	0.271810i
$106$	−150.148	+	260.063i	−0.137581	+	0.238298i
$107$			517.187i			0.467274i	0.972324	+	0.233637i	$0.0750628\pi$
$107$			517.187i			0.467274i	−0.972324	+	0.233637i	$0.924937\pi$
$108$	−823.106	+	348.213i	−0.733365	+	0.310248i
$109$	−39.6511			−0.0348430			−0.0174215	−	0.999848i	$-0.505546\pi$
$109$	−39.6511			−0.0348430			−0.0174215	+	0.999848i	$0.505546\pi$
$110$	−89.5630	+	155.128i	−0.0776318	+	0.134462i
$111$	−9.85202	+	239.412i	−0.00842443	+	0.204720i
$112$	−128.941	−	493.549i	−0.108783	−	0.416393i
$113$	627.942	−	362.542i	0.522759	−	0.301815i	−0.215304	−	0.976547i	$-0.569074\pi$
$113$	627.942	−	362.542i	0.522759	−	0.301815i	0.738063	+	0.674732i	$0.235741\pi$
$114$	418.614	+	265.214i	0.343919	+	0.217891i
$115$	148.834	+	85.9291i	0.120685	+	0.0696777i
$116$			193.694i			0.155035i
$117$	1849.63	−	873.809i	1.46153	−	0.690459i
$118$			694.701i			0.541970i
$119$	−1383.33	+	1366.13i	−1.06563	+	1.05237i
$120$	−141.094	−	269.388i	−0.107334	−	0.204931i
$121$	301.771	+	522.682i	0.226725	+	0.392699i
$122$	236.942	+	410.396i	0.175834	+	0.304553i
$123$	−1961.84	+	1027.53i	−1.43816	+	0.753244i
$124$	708.577	+	409.097i	0.513162	+	0.296274i
$125$	765.083			0.547449
$126$	−628.794	+	110.065i	−0.444583	+	0.0778201i
$127$	−567.501			−0.396516			−0.198258	−	0.980150i	$-0.563528\pi$
$127$	−567.501			−0.396516			−0.198258	+	0.980150i	$0.563528\pi$
$128$	−1247.24	−	720.097i	−0.861265	−	0.497251i
$129$	−1457.30	−	923.279i	−0.994638	−	0.630156i
$130$	154.279	+	267.220i	0.104086	+	0.180282i
$131$	603.074	+	1044.55i	0.402220	+	0.696665i	0.993994	−	0.109439i	$-0.0349055\pi$
$131$	603.074	+	1044.55i	0.402220	+	0.696665i	−0.591774	+	0.806104i	$0.701572\pi$
$132$	−1454.67	−	59.8611i	−0.959188	−	0.0394715i
$133$	−972.203	−	984.450i	−0.633840	−	0.641824i
$134$			136.207i			0.0878098i
$135$	412.205	−	174.382i	0.262792	−	0.111174i
$136$			1925.80i			1.21424i
$137$	522.414	+	301.616i	0.325787	+	0.188093i	0.653969	−	0.756521i	$-0.273103\pi$
$137$	522.414	+	301.616i	0.325787	+	0.188093i	−0.328182	+	0.944615i	$0.606436\pi$
$138$	14.6925	−	357.040i	0.00906313	−	0.220241i
$139$	298.587	−	172.389i	0.182200	−	0.105193i	−0.406126	−	0.913817i	$-0.633121\pi$
$139$	298.587	−	172.389i	0.182200	−	0.105193i	0.588326	+	0.808624i	$0.299787\pi$
$140$	95.1371	+	364.158i	0.0574325	+	0.219835i
$141$	−1493.68	−	946.326i	−0.892131	−	0.565213i
$142$	622.134	−	1077.57i	0.367665	−	0.636814i
$143$	3332.40			1.94874
$144$	423.497	−	611.313i	0.245079	−	0.353769i
$145$		−	97.0003i		−	0.0555547i
$146$	367.848	−	637.132i	0.208516	−	0.361160i
$147$	1779.72	+	95.5651i	0.998561	+	0.0536195i
$148$	−146.880	−	254.403i	−0.0815774	−	0.141296i
$149$	197.969	−	114.298i	0.108847	−	0.0628431i	−0.444588	−	0.895735i	$-0.646650\pi$
$149$	197.969	−	114.298i	0.108847	−	0.0628431i	0.553435	+	0.832892i	$0.313317\pi$
$150$	−353.386	−	674.716i	−0.192359	−	0.367269i
$151$	−1697.35	+	2939.90i	−0.914758	+	1.58441i	−0.107502	+	0.994205i	$0.534285\pi$
$151$	−1697.35	+	2939.90i	−0.914758	+	1.58441i	−0.807256	+	0.590202i	$0.799048\pi$
$152$	−1370.50			−0.731328
$153$	−2824.79	−	232.880i	−1.49262	−	0.123054i
$154$	−1002.75	−	275.425i	−0.524702	−	0.144119i
$155$	−354.850	−	204.873i	−0.183885	−	0.106166i
$156$	−1342.19	+	2118.52i	−0.688855	+	1.08729i
$157$	−2829.60	+	1633.67i	−1.43838	+	0.830452i	−0.997738	−	0.0672287i	$-0.978584\pi$
$157$	−2829.60	+	1633.67i	−1.43838	+	0.830452i	−0.440647	+	0.897680i	$0.645251\pi$
$158$	23.5905	−	13.6200i	0.0118782	−	0.00685791i
$159$	1221.27	+	50.2564i	0.609139	+	0.0250666i
$160$	502.613	+	290.184i	0.248344	+	0.143382i
$161$	−264.250	+	962.067i	−0.129353	+	0.470941i
$162$	−718.866	−	591.025i	−0.348638	−	0.286638i
$163$	689.462			0.331306			0.165653	−	0.986184i	$-0.447027\pi$
$163$	689.462			0.331306			0.165653	+	0.986184i	$0.447027\pi$
$164$	1357.54	−	2351.33i	0.646379	−	1.11956i
$165$	728.487	+	29.9779i	0.343713	+	0.0141441i
$166$	372.946	−	215.321i	0.174375	−	0.100675i
$167$	683.829	+	1184.43i	0.316864	+	0.548824i	0.979832	−	0.199823i	$-0.0640368\pi$
$167$	683.829	+	1184.43i	0.316864	+	0.548824i	−0.662968	+	0.748648i	$0.730703\pi$
$168$	1306.07	−	1187.80i	0.599793	−	0.545482i
$169$	1771.66	−	3068.60i	0.806399	−	1.39672i
$170$		−	427.527i		−	0.192881i
$171$	165.729	−	2010.26i	0.0741147	−	0.898998i
$172$	2114.99			0.937596
$173$	−613.500	+	1062.61i	−0.269616	+	0.466988i	−0.968763	−	0.247990i	$-0.920230\pi$
$173$	−613.500	+	1062.61i	−0.269616	+	0.466988i	0.699147	+	0.714978i	$0.253563\pi$
$174$	−178.669	+	93.5787i	−0.0778438	+	0.0407712i
$175$	537.523	+	2057.49i	0.232188	+	0.888751i
$176$	1049.15	−	605.730i	0.449335	−	0.259424i
$177$	2504.90	−	1311.95i	1.06373	−	0.557133i
$178$	1132.16	+	653.654i	0.476737	+	0.275244i
$179$		−	1597.37i		−	0.667002i	−0.942750	−	0.333501i	$-0.891770\pi$
$179$		−	1597.37i		−	0.667002i	0.942750	−	0.333501i	$-0.108230\pi$
$180$	−312.471	+	451.049i	−0.129390	+	0.186773i
$181$			549.998i			0.225862i	0.993603	+	0.112931i	$0.0360239\pi$
$181$			549.998i			0.225862i	−0.993603	+	0.112931i	$0.963976\pi$
$182$	−1274.54	+	1258.68i	−0.519093	+	0.512636i
$183$	1032.30	−	1629.38i	0.416994	−	0.658183i
$184$	494.128	+	855.855i	0.197976	+	0.342905i
$185$	73.5562	+	127.403i	0.0292322	+	0.0506317i
$186$	−35.0300	+	851.258i	−0.0138093	+	0.335577i
$187$	−3998.65	−	2308.62i	−1.56369	−	0.902798i
$188$	2167.79			0.840968
$189$	1584.35	+	2059.40i	0.609759	+	0.792587i
$190$	304.249			0.116171
$191$	3253.62	+	1878.48i	1.23258	+	0.711633i	0.967568	−	0.252611i	$-0.0812891\pi$
$191$	3253.62	+	1878.48i	1.23258	+	0.711633i	0.265017	+	0.964244i	$0.414622\pi$
$192$	2.54044	−	61.7346i	0.000954897	−	0.0232047i
$193$	−1311.43	−	2271.46i	−0.489111	−	0.847165i	0.510810	−	0.859693i	$-0.329345\pi$
$193$	−1311.43	−	2271.46i	−0.489111	−	0.847165i	−0.999922	+	0.0125280i	$0.996012\pi$
$194$	−46.8408	−	81.1307i	−0.0173349	−	0.0300250i
$195$	672.159	−	1060.94i	0.246843	−	0.389616i
$196$	−1905.81	+	1068.74i	−0.694537	+	0.389482i
$197$		−	4603.93i		−	1.66506i	−0.553982	−	0.832528i	$-0.686893\pi$
$197$		−	4603.93i		−	1.66506i	0.553982	−	0.832528i	$-0.313107\pi$
$198$	−647.573	−	1370.75i	−0.232429	−	0.491995i
$199$			3145.00i			1.12032i	0.828385	+	0.560158i	$0.189260\pi$
$199$			3145.00i			1.12032i	−0.828385	+	0.560158i	$0.810740\pi$
$200$	1824.21	+	1053.21i	0.644957	+	0.372366i
$201$	491.125	−	257.229i	0.172345	−	0.0902665i
$202$	−978.154	+	564.737i	−0.340706	+	0.196707i
$203$	544.834	−	142.339i	0.188374	−	0.0492131i
$204$	3078.21	−	1612.23i	1.05646	−	0.553326i
$205$	−679.846	+	1177.53i	−0.231622	+	0.401181i
$206$	57.0596			0.0192987
$207$	−1315.13	+	621.299i	−0.441585	+	0.208615i
$208$		−	2086.83i		−	0.695653i
$209$	1642.93	−	2845.64i	0.543751	−	0.941804i
$210$	−289.946	+	263.692i	−0.0952771	+	0.0866498i
$211$	341.927	+	592.236i	0.111560	+	0.193228i	0.916400	−	0.400265i	$-0.131082\pi$
$211$	341.927	+	592.236i	0.111560	+	0.193228i	−0.804839	+	0.593493i	$0.797748\pi$
$212$	−1297.74	+	749.253i	−0.420422	+	0.242731i
$213$	−5060.32	−	208.237i	−1.62783	−	0.0669866i
$214$	330.118	−	571.780i	0.105450	−	0.182645i
$215$	−1059.17			−0.335976
$216$	2554.17	+	316.750i	0.804578	+	0.0997783i
$217$	630.025	−	2293.76i	0.197092	−	0.717562i
$218$	43.8366	+	25.3091i	0.0136192	+	0.00786307i
$219$	−2992.00	−	123.124i	−0.923200	−	0.0379906i
$220$	−774.104	+	446.929i	−0.237228	+	0.136963i
$221$	−6887.99	+	3976.78i	−2.09655	+	1.21044i
$222$	163.707	−	258.395i	0.0494924	−	0.0781187i
$223$	2030.24	+	1172.16i	0.609664	+	0.351990i	0.772834	−	0.634608i	$-0.218839\pi$
$223$	2030.24	+	1172.16i	0.609664	+	0.351990i	−0.163170	+	0.986598i	$0.552172\pi$
$224$	−892.374	+	3248.91i	−0.266180	+	0.969094i
$225$	−1765.46	+	2548.42i	−0.523099	+	0.755088i
$226$	−925.635			−0.272444
$227$	1536.15	−	2660.69i	0.449154	−	0.777958i	−0.549177	−	0.835706i	$-0.685059\pi$
$227$	1536.15	−	2660.69i	0.449154	−	0.777958i	0.998331	+	0.0577480i	$0.0183920\pi$
$228$	1147.34	+	2190.61i	0.333266	+	0.636300i
$229$	1213.76	−	700.766i	0.350252	−	0.202218i	−0.314544	−	0.949243i	$-0.601852\pi$
$229$	1213.76	−	700.766i	0.350252	−	0.202218i	0.664796	+	0.747025i	$0.268518\pi$
$230$	−109.696	−	189.999i	−0.0314485	−	0.0544704i
$231$	900.609	+	4135.78i	0.256518	+	1.17798i
$232$	278.896	−	483.062i	0.0789242	−	0.136701i
$233$		−	5201.59i		−	1.46252i	−0.682098	−	0.731261i	$-0.738932\pi$
$233$		−	5201.59i		−	1.46252i	0.682098	−	0.731261i	$-0.261068\pi$
$234$	−2602.63	−	214.564i	−0.727090	−	0.0599424i
$235$	−1085.61			−0.301350
$236$	−1733.32	+	3002.20i	−0.478091	+	0.828078i
$237$	−93.6609	−	59.3392i	−0.0256706	−	0.0162637i
$238$	2401.35	−	627.358i	0.654018	−	0.170864i
$239$	−1811.86	+	1046.08i	−0.490373	+	0.283117i	−0.724729	−	0.689034i	$-0.758035\pi$
$239$	−1811.86	+	1046.08i	−0.490373	+	0.283117i	0.234356	+	0.972151i	$0.424702\pi$
$240$	18.7730	−	456.198i	0.00504912	−	0.122698i
$241$	6077.25	+	3508.70i	1.62436	+	0.937823i	0.985735	+	0.168303i	$0.0538287\pi$
$241$	6077.25	+	3508.70i	1.62436	+	0.937823i	0.638622	+	0.769520i	$0.279505\pi$
$242$		−	770.474i		−	0.204661i
$243$	−773.480	+	3708.19i	−0.204192	+	0.978931i
$244$			2364.73i			0.620437i
$245$	954.414	−	535.215i	0.248879	−	0.139566i
$246$	2824.80	+	116.243i	0.732124	+	0.0301276i
$247$	−2830.08	−	4901.84i	−0.729042	−	1.26274i
$248$	−1178.10	−	2040.53i	−0.301651	−	0.522476i
$249$	−1480.70	−	938.103i	−0.376850	−	0.238754i
$250$	−845.844	−	488.348i	−0.213984	−	0.123543i
$251$	−7255.60			−1.82458			−0.912290	−	0.409545i	$-0.865687\pi$
$251$	−7255.60			−1.82458			−0.912290	+	0.409545i	$0.865687\pi$
$252$	−2991.99	−	1093.23i	−0.747928	−	0.273281i
$253$	−2369.41			−0.588789
$254$	627.406	+	362.233i	0.154988	+	0.0894823i
$255$	−1541.54	+	807.391i	−0.378569	+	0.198278i
$256$	966.831	+	1674.60i	0.236043	+	0.408838i
$257$	505.462	+	875.487i	0.122684	+	0.212496i	0.920825	−	0.389975i	$-0.127516\pi$
$257$	505.462	+	875.487i	0.122684	+	0.212496i	−0.798141	+	0.602471i	$0.794183\pi$
$258$	1021.81	+	1950.93i	0.246570	+	0.470773i
$259$	−607.665	+	600.106i	−0.145786	+	0.143972i
$260$			1539.74i			0.367272i
$261$	674.836	+	467.503i	0.160043	+	0.110873i
$262$		−	1539.75i		−	0.363078i
$263$	2754.95	+	1590.57i	0.645921	+	0.372923i	0.786892	−	0.617091i	$-0.211689\pi$
$263$	2754.95	+	1590.57i	0.645921	+	0.372923i	−0.140971	+	0.990014i	$0.545022\pi$
$264$	3541.68	+	2243.84i	0.825663	+	0.523102i
$265$	649.900	−	375.220i	0.150653	−	0.0869795i
$266$	446.459	+	1708.92i	0.102910	+	0.393912i
$267$	218.787	−	5316.69i	0.0501480	−	1.21864i
$268$	−339.845	+	588.628i	−0.0774601	+	0.134165i
$269$	1227.12			0.278137			0.139069	−	0.990283i	$-0.455589\pi$
$269$	1227.12			0.278137			0.139069	+	0.990283i	$0.455589\pi$
$270$	−567.024	−	70.3184i	−0.127807	−	0.0158498i
$271$		−	7222.65i		−	1.61898i	−0.587131	−	0.809492i	$-0.699743\pi$
$271$		−	7222.65i		−	1.61898i	0.587131	−	0.809492i	$-0.300257\pi$
$272$	−1445.72	+	2504.06i	−0.322278	+	0.558202i
$273$	6945.43	+	2218.58i	1.53977	+	0.491848i
$274$	−385.039	−	666.908i	−0.0848945	−	0.147042i
$275$	−4373.68	+	2525.15i	−0.959065	+	0.553716i
$276$	954.330	−	1506.31i	0.208130	−	0.328512i
$277$	−1132.04	+	1960.75i	−0.245551	+	0.425306i	−0.962286	−	0.272039i	$-0.912302\pi$
$277$	−1132.04	+	1960.75i	−0.245551	+	0.425306i	0.716736	+	0.697345i	$0.245635\pi$
$278$	−440.141			−0.0949564
$279$	3135.55	−	1481.30i	0.672833	−	0.317861i
$280$	287.077	−	1045.18i	0.0612719	−	0.223076i
$281$	859.806	+	496.409i	0.182533	+	0.105385i	0.588482	−	0.808510i	$-0.299726\pi$
$281$	859.806	+	496.409i	0.182533	+	0.105385i	−0.405949	+	0.913896i	$0.633059\pi$
$282$	1047.32	+	1999.63i	0.221159	+	0.422255i
$283$	4936.03	−	2849.82i	1.03681	−	0.598601i	0.117880	−	0.993028i	$-0.462390\pi$
$283$	4936.03	−	2849.82i	1.03681	−	0.598601i	0.918927	+	0.394427i	$0.129057\pi$
$284$	5377.19	−	3104.52i	1.12351	−	0.648660i
$285$	−574.580	−	1097.04i	−0.119422	−	0.228010i
$286$	−3684.16	−	2127.05i	−0.761710	−	0.439773i
$287$	−7611.59	−	2090.66i	−1.56550	−	0.429993i
$288$	−4441.22	+	2098.13i	−0.908686	+	0.429284i
$289$	6107.16			1.24306
$290$	−61.9147	+	107.239i	−0.0125371	+	0.0217149i
$291$	−204.075	+	322.111i	−0.0411102	+	0.0648883i
$292$	3179.36	−	1835.60i	0.637185	−	0.367879i
$293$	−1110.55	−	1923.52i	−0.221429	−	0.383527i	0.733813	−	0.679352i	$-0.237739\pi$
$293$	−1110.55	−	1923.52i	−0.221429	−	0.383527i	−0.955242	+	0.295825i	$0.904406\pi$
$294$	−1906.58	−	1241.64i	−0.378211	−	0.246305i
$295$	868.032	−	1503.48i	0.171318	−	0.296731i
$296$			845.958i			0.166116i
$297$	−3719.58	+	4923.65i	−0.726707	+	0.961949i
$298$	−291.822			−0.0567275
$299$	−2040.75	+	3534.68i	−0.394714	+	0.683665i
$300$	156.273	−	3797.55i	0.0300747	−	0.730838i
$301$	−1554.24	−	5949.18i	−0.297624	−	1.13922i
$302$	3753.04	−	2166.82i	0.715110	−	0.412869i
$303$	3883.54	+	2460.43i	0.736315	+	0.466495i
$304$	−1782.01	−	1028.85i	−0.336202	−	0.194106i
$305$		−	1184.24i		−	0.222326i
$306$	2974.33	+	2060.51i	0.555657	+	0.384940i
$307$		−	3006.91i		−	0.559002i	−0.960145	−	0.279501i	$-0.909831\pi$
$307$		−	3006.91i		−	0.559002i	0.960145	−	0.279501i	$-0.0901690\pi$
$308$	−3646.26	−	3692.19i	−0.674561	−	0.683058i
$309$	−107.758	−	205.741i	−0.0198386	−	0.0378776i
$310$	261.538	+	452.997i	0.0479173	+	0.0829952i
$311$	−1269.29	−	2198.47i	−0.231430	−	0.400848i	0.726799	−	0.686850i	$-0.241007\pi$
$311$	−1269.29	−	2198.47i	−0.231430	−	0.400848i	−0.958229	+	0.286002i	$0.907674\pi$
$312$	6397.76	−	3350.86i	1.16090	−	0.608030i
$313$	4916.75	+	2838.69i	0.887895	+	0.512627i	0.873253	−	0.487266i	$-0.162006\pi$
$313$	4916.75	+	2838.69i	0.887895	+	0.512627i	0.0146418	+	0.999893i	$0.495339\pi$
$314$	4171.05			0.749636
$315$	1498.36	+	547.478i	0.268010	+	0.0979267i
$316$	135.931			0.0241984
$317$	6662.61	+	3846.66i	1.18047	+	0.681545i	0.956123	−	0.292964i	$-0.0946416\pi$
$317$	6662.61	+	3846.66i	1.18047	+	0.681545i	0.224347	+	0.974509i	$0.427975\pi$
$318$	−1318.11	−	835.092i	−0.232440	−	0.147263i
$319$	668.672	+	1158.17i	0.117362	+	0.203277i
$320$	−18.9672	−	32.8521i	−0.00331343	−	0.00573903i
$321$	−2685.11	−	110.495i	−0.466879	−	0.0192125i
$322$	906.225	−	894.952i	0.156838	−	0.154887i
$323$			7842.50i			1.35098i
$324$	−1631.98	−	4347.76i	−0.279833	−	0.745501i
$325$			8699.52i			1.48481i
$326$	−762.240	−	440.080i	−0.129499	−	0.0747661i
$327$	8.47129	−	205.859i	0.00143261	−	0.0348136i
$328$	−6771.27	+	3909.39i	−1.13988	+	0.658110i
$329$	−1593.03	−	6097.69i	−0.266951	−	1.02181i
$330$	−786.251	−	498.132i	−0.131157	−	0.0830947i
$331$	852.222	−	1476.09i	0.141518	−	0.245116i	−0.786551	−	0.617526i	$-0.788135\pi$
$331$	852.222	−	1476.09i	0.141518	−	0.245116i	0.928068	+	0.372410i	$0.121468\pi$
$332$	2148.95			0.355238
$333$	−1240.86	−	102.299i	−0.204201	−	0.0168346i
$334$		−	1745.94i		−	0.286028i
$335$	170.191	−	294.780i	0.0277569	−	0.0480763i
$336$	2589.93	−	563.984i	0.420513	−	0.0915710i
$337$	3770.46	+	6530.62i	0.609466	+	1.05563i	0.991329	+	0.131407i	$0.0419493\pi$
$337$	3770.46	+	6530.62i	0.609466	+	1.05563i	−0.381863	+	0.924219i	$0.624717\pi$
$338$	−3917.35	+	2261.68i	−0.630401	+	0.363962i
$339$	1748.08	+	3337.58i	0.280066	+	0.534727i
$340$	1066.70	−	1847.59i	0.170147	−	0.294704i
$341$	5649.17			0.897125
$342$	−1466.36	+	2116.68i	−0.231848	+	0.334670i
$343$	4406.73	+	4575.40i	0.693706	+	0.720258i
$344$	−5274.67	−	3045.33i	−0.826718	−	0.477306i
$345$	−477.921	+	754.350i	−0.0745808	+	0.117718i
$346$	1356.52	−	783.188i	0.210772	−	0.121689i
$347$	−1623.73	+	937.459i	−0.251199	+	0.145030i	−0.620313	−	0.784354i	$-0.712995\pi$
$347$	−1623.73	+	937.459i	−0.251199	+	0.145030i	0.369114	+	0.929384i	$0.379661\pi$
$348$	−1005.61	−	41.3818i	−0.154904	−	0.00637442i
$349$	1501.48	+	866.879i	0.230293	+	0.132960i	0.610707	−	0.791856i	$-0.290885\pi$
$349$	1501.48	+	866.879i	0.230293	+	0.132960i	−0.380414	+	0.924816i	$0.624219\pi$
$350$	719.020	−	2617.77i	0.109809	−	0.399788i
$351$	4141.44	+	9789.54i	0.629783	+	1.48868i
$352$	−8001.54			−1.21160
$353$	4678.78	−	8103.88i	0.705457	−	1.22189i	−0.261070	−	0.965320i	$-0.584075\pi$
$353$	4678.78	−	8103.88i	0.705457	−	1.22189i	0.966526	−	0.256567i	$-0.0825914\pi$
$354$	−3606.72	−	148.420i	−0.541512	−	0.0222837i
$355$	−2692.85	+	1554.72i	−0.402596	+	0.232439i
$356$	3261.81	+	5649.61i	0.485605	+	0.841092i
$357$	−6797.05	−	7473.81i	−1.00767	−	1.10800i
$358$	−1019.60	+	1765.99i	−0.150523	+	0.260714i
$359$		−	11558.3i		−	1.69923i	−0.527401	−	0.849616i	$-0.676833\pi$
$359$		−	11558.3i		−	1.69923i	0.527401	−	0.849616i	$-0.323167\pi$
$360$	1428.74	−	674.970i	0.209170	−	0.0988169i
$361$	1277.89			0.186309
$362$	351.061	−	608.055i	0.0509706	−	0.0882836i
$363$	−2778.11	+	1455.05i	−0.401689	+	0.210387i
$364$	−8648.47	+	2259.43i	−1.24534	+	0.325347i
$365$	−1592.20	+	919.255i	−0.228327	+	0.131825i
$366$	−2181.30	+	1142.47i	−0.311525	+	0.163163i
$367$	−7156.41	−	4131.76i	−1.01788	−	0.587673i	−0.104390	−	0.994536i	$-0.533289\pi$
$367$	−7156.41	−	4131.76i	−1.01788	−	0.587673i	−0.913489	+	0.406864i	$0.866622\pi$
$368$			1483.79i			0.210184i
$369$	−4915.53	−	10404.9i	−0.693475	−	1.46791i
$370$		−	187.802i		−	0.0263875i
$371$	3061.22	+	3099.78i	0.428384	+	0.433780i
$372$	−2275.32	+	3591.36i	−0.317123	+	0.500547i
$373$	4591.28	+	7952.33i	0.637339	+	1.10390i	0.986014	+	0.166660i	$0.0532981\pi$
$373$	4591.28	+	7952.33i	0.637339	+	1.10390i	−0.348676	+	0.937243i	$0.613369\pi$
$374$	2947.16	+	5104.64i	0.407471	+	0.705761i
$375$	−163.457	+	3972.13i	−0.0225090	+	0.546986i
$376$	−5406.34	−	3121.35i	−0.741517	−	0.428115i
$377$	2303.68			0.314710
$378$	−437.090	−	3288.06i	−0.0594748	−	0.447407i
$379$	−9297.03			−1.26004			−0.630022	−	0.776577i	$-0.716954\pi$
$379$	−9297.03			−1.26004			−0.630022	+	0.776577i	$0.716954\pi$
$380$	1314.83	+	759.119i	0.177499	+	0.102479i
$381$	121.244	−	2946.33i	0.0163032	−	0.396181i
$382$	−2398.05	−	4153.54i	−0.321190	−	0.556318i
$383$	3674.74	+	6364.84i	0.490262	+	0.849159i	0.999937	−	0.0112079i	$-0.00356767\pi$
$383$	3674.74	+	6364.84i	0.490262	+	0.849159i	−0.509675	+	0.860367i	$0.670234\pi$
$384$	4005.04	−	6321.55i	0.532243	−	0.840091i
$385$	1826.02	+	1849.02i	0.241720	+	0.244765i
$386$			3348.30i			0.441513i
$387$	5104.79	−	7368.70i	0.670519	−	0.967887i
$388$		−	467.482i		−	0.0611670i
$389$	−4531.66	−	2616.35i	−0.590653	−	0.341014i	0.174702	−	0.984621i	$-0.444104\pi$
$389$	−4531.66	−	2616.35i	−0.590653	−	0.341014i	−0.765356	+	0.643607i	$0.777437\pi$
$390$	−1420.30	+	743.890i	−0.184410	+	0.0965855i
$391$	4897.52	−	2827.59i	0.633448	−	0.365722i
$392$	6291.84	+	78.7625i	0.810678	+	0.0101482i
$393$	−5551.92	+	2907.85i	−0.712614	+	0.373235i
$394$	−2938.66	+	5089.91i	−0.375755	+	0.650827i
$395$	−68.0730			−0.00867120
$396$	621.568	−	7539.51i	0.0788762	−	0.956754i
$397$			10045.1i			1.26990i	0.772554	+	0.634949i	$0.218979\pi$
$397$			10045.1i			1.26990i	−0.772554	+	0.634949i	$0.781021\pi$
$398$	2007.44	−	3476.98i	0.252823	−	0.437903i
$399$	5318.73	−	4837.12i	0.667342	−	0.606915i
$400$	1581.31	+	2738.91i	0.197664	+	0.342364i
$401$	−6480.01	+	3741.24i	−0.806974	+	0.465906i	−0.845904	−	0.533335i	$-0.820938\pi$
$401$	−6480.01	+	3741.24i	−0.806974	+	0.465906i	0.0389302	+	0.999242i	$0.487605\pi$
$402$	−707.155	−	29.1001i	−0.0877356	−	0.00361040i
$403$	4865.57	−	8427.41i	0.601417	−	1.04169i
$404$	−5636.20			−0.694088
$405$	817.284	+	2177.32i	0.100275	+	0.267141i
$406$	−693.201	−	190.400i	−0.0847364	−	0.0232744i
$407$	−1756.51	−	1014.12i	−0.213924	−	0.123509i
$408$	−9998.30	−	411.439i	−1.21321	−	0.0499247i
$409$	−9878.34	+	5703.26i	−1.19426	+	0.689506i	−0.959270	−	0.282491i	$-0.908839\pi$
$409$	−9878.34	+	5703.26i	−1.19426	+	0.689506i	−0.234990	+	0.971998i	$0.575506\pi$
$410$	1503.22	−	867.883i	0.181070	−	0.104541i
$411$	−1677.53	+	2647.81i	−0.201329	+	0.317778i
$412$	246.587	+	142.367i	0.0294865	+	0.0170240i
$413$	9718.53	+	2669.38i	1.15791	+	0.318042i
$414$	1850.53	+	152.560i	0.219682	+	0.0181109i
$415$	−1076.18			−0.127295
$416$	−6891.64	+	11936.7i	−0.812237	+	1.40684i
$417$	831.212	+	1587.02i	0.0976130	+	0.186371i
$418$	−3632.71	+	2097.35i	−0.425076	+	0.245418i
$419$	−3027.27	−	5243.38i	−0.352964	−	0.611351i	0.633804	−	0.773494i	$-0.281493\pi$
$419$	−3027.27	−	5243.38i	−0.352964	−	0.611351i	−0.986767	+	0.162143i	$0.948159\pi$
$420$	−1910.95	+	416.128i	−0.222011	+	0.0483452i
$421$	−3434.60	+	5948.91i	−0.397606	+	0.688674i	−0.993430	−	0.114441i	$-0.963492\pi$
$421$	−3434.60	+	5948.91i	−0.397606	+	0.688674i	0.595824	+	0.803115i	$0.296826\pi$
$422$		−	873.002i		−	0.100704i
$423$	5232.21	−	7552.64i	0.601416	−	0.868137i
$424$	4315.34			0.494272
$425$	6026.86	−	10438.8i	0.687873	−	1.19143i
$426$	5461.56	+	3460.19i	0.621158	+	0.393537i
$427$	6651.68	−	1737.77i	0.753858	−	0.196947i
$428$	2853.25	−	1647.32i	0.322236	−	0.186043i
$429$	−711.953	+	17301.0i	−0.0801245	+	1.94709i
$430$	1170.97	+	676.062i	0.131324	+	0.0758200i
$431$		−	7761.64i		−	0.867436i	−0.901049	−	0.433718i	$-0.857201\pi$
$431$		−	7761.64i		−	0.867436i	0.901049	−	0.433718i	$-0.142799\pi$
$432$	3083.31	+	2329.30i	0.343393	+	0.259418i
$433$			7474.70i			0.829586i	0.909916	+	0.414793i	$0.136146\pi$
$433$			7474.70i			0.829586i	−0.909916	+	0.414793i	$0.863854\pi$
$434$	−2160.63	+	2133.75i	−0.238971	+	0.235998i
$435$	503.602	+	20.7237i	0.0555077	+	0.00228420i
$436$	126.295	+	218.750i	0.0138726	+	0.0240280i
$437$	2012.25	+	3485.32i	0.220272	+	0.381523i
$438$	3229.25	+	2045.90i	0.352282	+	0.223189i
$439$	804.050	+	464.219i	0.0874151	+	0.0504691i	0.543070	−	0.839687i	$-0.317262\pi$
$439$	804.050	+	464.219i	0.0874151	+	0.0504691i	−0.455655	+	0.890156i	$0.650595\pi$
$440$	2574.10			0.278898
$441$	−876.379	+	9219.44i	−0.0946312	+	0.995512i
$442$	10153.4			1.09265
$443$	4799.04	+	2770.72i	0.514693	+	0.297158i	0.734761	−	0.678326i	$-0.237294\pi$
$443$	4799.04	+	2770.72i	0.514693	+	0.297158i	−0.220068	+	0.975485i	$0.570628\pi$
$444$	1352.18	−	708.213i	0.144531	−	0.0756988i
$445$	−1633.49	−	2829.28i	−0.174010	−	0.301395i
$446$	−1496.37	−	2591.78i	−0.158868	−	0.275167i
$447$	551.110	+	1052.23i	0.0583146	+	0.111339i
$448$	156.692	−	154.743i	0.0165246	−	0.0163190i
$449$			13088.2i			1.37566i	0.725873	+	0.687829i	$0.241436\pi$
$449$			13088.2i			1.37566i	−0.725873	+	0.687829i	$0.758564\pi$
$450$	3578.46	−	1690.55i	0.374867	−	0.177096i
$451$		−	18746.1i		−	1.95725i
$452$	−4000.19	−	2309.51i	−0.416268	−	0.240332i
$453$	−14900.6	−	9440.33i	−1.54546	−	0.979129i
$454$	−3396.61	+	1961.04i	−0.351126	+	0.202722i
$455$	4331.08	−	1131.51i	0.446251	−	0.116584i
$456$	292.801	−	7115.28i	0.0300694	−	0.730710i
$457$	5771.25	−	9996.10i	0.590739	−	1.02319i	−0.403394	−	0.915026i	$-0.632170\pi$
$457$	5771.25	−	9996.10i	0.590739	−	1.02319i	0.994133	−	0.108164i	$-0.0344971\pi$
$458$	−1789.18			−0.182539
$459$	1812.56	−	14615.9i	0.184321	−	1.48630i
$460$		−	1094.79i		−	0.110967i
$461$	−4557.29	+	7893.46i	−0.460421	+	0.797473i	−0.998982	−	0.0451139i	$-0.985635\pi$
$461$	−4557.29	+	7893.46i	−0.460421	+	0.797473i	0.538561	+	0.842587i	$0.318968\pi$
$462$	1644.17	−	5147.20i	0.165571	−	0.518332i
$463$	−1592.53	−	2758.34i	−0.159851	−	0.276871i	0.774964	−	0.632006i	$-0.217768\pi$
$463$	−1592.53	−	2758.34i	−0.159851	−	0.276871i	−0.934815	+	0.355135i	$0.884435\pi$
$464$	725.279	−	418.740i	0.0725651	−	0.0418955i
$465$	1139.46	−	1798.52i	0.113637	−	0.179365i
$466$	−3320.15	+	5750.66i	−0.330049	+	0.571662i
$467$	995.144			0.0986077			0.0493038	−	0.998784i	$-0.484300\pi$
$467$	995.144			0.0986077			0.0493038	+	0.998784i	$0.484300\pi$
$468$	−10712.1	−	7420.95i	−1.05805	−	0.732978i
$469$	1905.47	+	523.373i	0.187605	+	0.0515291i
$470$	1200.20	+	692.938i	0.117790	+	0.0680061i
$471$	−7877.08	−	15039.6i	−0.770609	−	1.47131i
$472$	8645.60	−	4991.54i	0.843106	−	0.486768i
$473$	12646.4	−	7301.40i	1.22935	−	0.709765i
$474$	65.6718	+	125.386i	0.00636372	+	0.0121502i
$475$	7428.79	+	4289.02i	0.717592	+	0.414302i
$476$	11942.9	+	3280.33i	1.15000	+	0.315869i
$477$	−521.838	+	6329.80i	−0.0500908	+	0.607593i
$478$	2670.82			0.255565
$479$	−6951.30	+	12040.0i	−0.663075	+	1.14848i	0.316728	+	0.948516i	$0.397416\pi$
$479$	−6951.30	+	12040.0i	−0.663075	+	1.14848i	−0.979803	+	0.199964i	$0.935917\pi$
$480$	−1613.95	+	2547.45i	−0.153471	+	0.242239i
$481$	−3025.73	+	1746.90i	−0.286822	+	0.165597i
$482$	−4479.17	−	7758.15i	−0.423279	−	0.733141i
$483$	−4938.36	−	1577.46i	−0.465224	−	0.148607i
$484$	1922.38	−	3329.65i	0.180539	−	0.312702i
$485$			234.111i			0.0219184i
$486$	3222.04	−	3605.91i	0.300730	−	0.336558i
$487$	−7608.36			−0.707942			−0.353971	−	0.935256i	$-0.615169\pi$
$487$	−7608.36			−0.707942			−0.353971	+	0.935256i	$0.615169\pi$
$488$	3404.93	−	5897.52i	0.315849	−	0.547066i
$489$	−147.301	+	3579.52i	−0.0136220	+	0.331025i
$490$	−1396.79	−	17.4852i	−0.128776	−	0.00161205i
$491$	14278.7	−	8243.83i	1.31240	−	0.757717i	0.329910	−	0.944012i	$-0.392982\pi$
$491$	14278.7	−	8243.83i	1.31240	−	0.757717i	0.982494	+	0.186296i	$0.0596482\pi$
$492$	11917.5	+	7550.38i	1.09204	+	0.691865i
$493$	−2764.26	−	1595.95i	−0.252528	−	0.145797i
$494$			7225.69i			0.658095i
$495$	−311.276	+	3775.73i	−0.0282643	+	0.342841i
$496$		−	3537.65i		−	0.320253i
$497$	−12684.1	−	12843.9i	−1.14479	−	1.15921i
$498$	1038.21	+	1982.25i	0.0934207	+	0.178367i
$499$	1546.08	+	2677.88i	0.138701	+	0.240237i	0.927005	−	0.375049i	$-0.122374\pi$
$499$	1546.08	+	2677.88i	0.138701	+	0.240237i	−0.788304	+	0.615286i	$0.789041\pi$
$500$	−2436.91	−	4220.86i	−0.217964	−	0.377525i
$501$	−6295.35	+	3297.23i	−0.561389	+	0.294030i
$502$	8021.49	+	4631.21i	0.713181	+	0.411755i
$503$	−5624.21			−0.498551			−0.249275	−	0.968433i	$-0.580192\pi$
$503$	−5624.21			−0.498551			−0.249275	+	0.968433i	$0.580192\pi$
$504$	5887.75	+	7034.55i	0.520359	+	0.621714i
$505$	2822.56			0.248718
$506$	2619.52	+	1512.38i	0.230142	+	0.132873i
$507$	15552.9	+	9853.62i	1.36239	+	0.863145i
$508$	1807.58	+	3130.82i	0.157871	+	0.273441i
$509$	−2174.06	−	3765.58i	−0.189319	−	0.327910i	0.755704	−	0.654913i	$-0.227295\pi$
$509$	−2174.06	−	3765.58i	−0.189319	−	0.327910i	−0.945023	+	0.327003i	$0.893961\pi$
$510$	2219.62	+	91.3393i	0.192718	+	0.00793053i
$511$	−7499.71	−	7594.18i	−0.649252	−	0.657430i
$512$			9053.06i			0.781431i
$513$	10401.4	+	1289.91i	0.895191	+	0.111015i
$514$		−	1290.54i		−	0.110745i
$515$	−123.489	−	71.2961i	−0.0105661	−	0.00610035i
$516$	−451.859	+	10980.5i	−0.0385503	+	0.936803i
$517$	12962.1	−	7483.66i	1.10265	−	0.636617i
$518$	1054.85	−	275.583i	0.0894741	−	0.0233753i
$519$	−5385.76	−	3412.17i	−0.455508	−	0.288589i
$520$	2217.04	−	3840.03i	0.186969	−	0.323839i
$521$	−16584.8			−1.39461			−0.697305	−	0.716774i	$-0.745618\pi$
$521$	−16584.8			−1.39461			−0.697305	+	0.716774i	$0.745618\pi$
$522$	−447.666	−	947.597i	−0.0375360	−	0.0794544i
$523$			15080.9i			1.26088i	0.776237	+	0.630441i	$0.217126\pi$
$523$			15080.9i			1.26088i	−0.776237	+	0.630441i	$0.782874\pi$
$524$	3841.77	−	6654.14i	0.320284	−	0.554747i
$525$	−10796.8	+	2351.12i	−0.897547	+	0.195450i
$526$	−2030.50	−	3516.93i	−0.168316	−	0.291532i
$527$	−11676.7	+	6741.54i	−0.965171	+	0.557242i
$528$	2920.66	+	5576.37i	0.240730	+	0.459622i
$529$	−4632.48	+	8023.69i	−0.380741	+	0.659463i
$530$	−958.003			−0.0785151
$531$	6276.19	+	13285.1i	0.512925	+	1.08573i
$532$	−2334.45	+	8499.14i	−0.190246	+	0.692640i
$533$	−27965.4	−	16145.8i	−2.27263	−	1.31211i
$534$	−3635.49	+	5738.26i	−0.294613	+	0.465016i
$535$	−1428.88	+	824.966i	−0.115469	+	0.0666662i
$536$	1695.11	−	978.671i	0.136600	−	0.0788660i
$537$	8293.18	+	341.272i	0.666438	+	0.0274245i
$538$	−1356.65	−	783.264i	−0.108717	−	0.0627675i
$539$	−7706.10	+	12969.7i	−0.615817	+	1.03645i
$540$	−2274.98	−	1718.64i	−0.181295	−	0.136960i
$541$	−17064.6			−1.35613			−0.678064	−	0.735003i	$-0.737181\pi$
$541$	−17064.6			−1.35613			−0.678064	+	0.735003i	$0.737181\pi$
$542$	−4610.18	+	7985.06i	−0.365358	+	0.632819i
$543$	−2855.46	−	117.505i	−0.225671	−	0.00928658i
$544$	16539.0	−	9548.80i	1.30350	−	0.752576i
$545$	−63.2476	−	109.548i	−0.00497106	−	0.00861013i
$546$	−6262.47	−	6886.00i	−0.490859	−	0.539732i
$547$	226.704	−	392.663i	0.0177206	−	0.0306929i	−0.857029	−	0.515268i	$-0.827692\pi$
$547$	226.704	−	392.663i	0.0177206	−	0.0306929i	0.874750	+	0.484575i	$0.161026\pi$
$548$		−	3842.78i		−	0.299554i
$549$	8238.82	+	5707.57i	0.640482	+	0.443704i
$550$	6447.15			0.499831
$551$	1135.76	−	1967.19i	0.0878127	−	0.152096i
$552$	−4548.96	+	2382.54i	−0.350755	+	0.183710i
$553$	−99.8910	−	382.355i	−0.00768137	−	0.0294021i
$554$	2503.07	−	1445.15i	0.191959	−	0.110827i
$555$	−677.161	+	354.667i	−0.0517908	+	0.0271257i
$556$	−1902.10	−	1098.18i	−0.145084	−	0.0837644i
$557$			19320.2i			1.46970i	0.678229	+	0.734850i	$0.262748\pi$
$557$			19320.2i			1.46970i	−0.678229	+	0.734850i	$0.737252\pi$
$558$	−4412.04	−	363.735i	−0.334725	−	0.0275952i
$559$		−	25154.5i		−	1.90326i
$560$	1157.90	−	1143.50i	0.0873755	−	0.0862886i
$561$	12840.1	−	20266.8i	0.966328	−	1.52525i
$562$	−633.710	−	1097.62i	−0.0475649	−	0.0823848i
$563$	1038.78	+	1799.22i	0.0777608	+	0.134686i	0.902283	−	0.431143i	$-0.141890\pi$
$563$	1038.78	+	1799.22i	0.0777608	+	0.134686i	−0.824523	+	0.565829i	$0.808556\pi$
$564$	−463.138	+	11254.6i	−0.0345774	+	0.840257i
$565$	2003.26	+	1156.58i	0.149164	+	0.0861201i
$566$	−7276.09			−0.540348
$567$	−11030.4	+	7785.57i	−0.816988	+	0.576655i
$568$	−17880.5			−1.32086
$569$	16935.0	+	9777.42i	1.24772	+	0.720370i	0.970654	−	0.240481i	$-0.0773052\pi$
$569$	16935.0	+	9777.42i	1.24772	+	0.720370i	0.277064	+	0.960851i	$0.410639\pi$
$570$	−65.0016	+	1579.59i	−0.00477652	+	0.116073i
$571$	−3001.96	−	5199.54i	−0.220014	−	0.381075i	0.734798	−	0.678286i	$-0.237277\pi$
$571$	−3001.96	−	5199.54i	−0.220014	−	0.381075i	−0.954812	+	0.297211i	$0.903944\pi$
$572$	−10614.2	−	18384.4i	−0.775879	−	1.34386i
$573$	−10447.7	+	16490.7i	−0.761711	+	1.20228i
$574$	7080.59	+	7169.79i	0.514875	+	0.521361i
$575$		−	6185.56i		−	0.448619i
$576$	319.968	+	26.3787i	0.0231459	+	0.00190818i
$577$		−	18306.7i		−	1.32083i	−0.750901	−	0.660415i	$-0.770381\pi$
$577$		−	18306.7i		−	1.32083i	0.750901	−	0.660415i	$-0.229619\pi$
$578$	−6751.83	−	3898.17i	−0.485881	−	0.280523i
$579$	12073.0	−	6323.32i	0.866559	−	0.453865i
$580$	−535.137	+	308.961i	−0.0383109	+	0.0221188i
$581$	−1579.19	−	6044.70i	−0.112764	−	0.431629i
$582$	431.218	−	225.853i	0.0307123	−	0.0160858i
$583$	−5173.17	+	8960.18i	−0.367497	+	0.636523i
$584$	−10572.2			−0.749111
$585$	5364.52	+	3716.35i	0.379137	+	0.262653i
$586$			2835.42i			0.199881i
$587$	−10160.7	+	17598.8i	−0.714440	+	1.23745i	0.248735	+	0.968572i	$0.419985\pi$
$587$	−10160.7	+	17598.8i	−0.714440	+	1.23745i	−0.963175	+	0.268875i	$0.913348\pi$
$588$	−5141.46	−	10122.8i	−0.360596	−	0.709964i
$589$	−4797.62	−	8309.72i	−0.335624	−	0.581317i
$590$	−1919.32	+	1108.12i	−0.133927	+	0.0773230i
$591$	23902.5	+	983.609i	1.66365	+	0.0684607i
$592$	−635.069	+	1099.97i	−0.0440898	+	0.0763658i
$593$	27525.8			1.90616			0.953078	−	0.302725i	$-0.0978965\pi$
$593$	27525.8			1.90616			0.953078	+	0.302725i	$0.0978965\pi$
$594$	7254.95	−	3069.19i	0.501135	−	0.212004i
$595$	−5980.89	−	1642.76i	−0.412088	−	0.113188i
$596$	−1261.13	−	728.112i	−0.0866741	−	0.0500413i
$597$	−16328.1	−	671.915i	−1.11937	−	0.0460631i
$598$	4512.34	−	2605.20i	0.308567	−	0.178151i
$599$	−17841.0	+	10300.5i	−1.21697	+	0.702616i	−0.964268	−	0.264929i	$-0.914652\pi$
$599$	−17841.0	+	10300.5i	−1.21697	+	0.702616i	−0.252699	+	0.967545i	$0.581318\pi$
$600$	−5857.75	+	9245.86i	−0.398569	+	0.629101i
$601$	−13383.7	−	7727.08i	−0.908374	−	0.524450i	−0.0284661	−	0.999595i	$-0.509062\pi$
$601$	−13383.7	−	7727.08i	−0.908374	−	0.524450i	−0.879907	+	0.475145i	$0.842396\pi$
$602$	−2079.03	+	7569.23i	−0.140756	+	0.512456i
$603$	1230.55	+	2604.76i	0.0831040	+	0.175910i
$604$	21625.3			1.45682
$605$	−962.710	+	1667.46i	−0.0646938	+	0.112053i
$606$	−2723.00	−	5198.99i	−0.182532	−	0.348506i
$607$	−21073.4	+	12166.7i	−1.40913	+	0.813562i	−0.995305	−	0.0967932i	$-0.969141\pi$
$607$	−21073.4	+	12166.7i	−1.40913	+	0.813562i	−0.413827	+	0.910356i	$0.635808\pi$
$608$	6795.40	+	11770.0i	0.453273	+	0.785091i
$609$	622.589	+	2859.06i	0.0414262	+	0.190238i
$610$	−755.894	+	1309.25i	−0.0501725	+	0.0869014i
$611$		−	25782.4i		−	1.70711i
$612$	7712.66	+	16325.8i	0.509421	+	1.07832i
$613$	16221.1			1.06879			0.534393	−	0.845236i	$-0.320540\pi$
$613$	16221.1			1.06879			0.534393	+	0.845236i	$0.320540\pi$
$614$	−1919.30	+	3324.32i	−0.126151	+	0.218499i
$615$	−5968.19	−	3781.17i	−0.391318	−	0.247921i
$616$	3777.26	+	14458.3i	0.247062	+	0.945683i
$617$	17506.0	−	10107.1i	1.14224	−	0.659475i	0.195259	−	0.980752i	$-0.437445\pi$
$617$	17506.0	−	10107.1i	1.14224	−	0.659475i	0.946986	+	0.321276i	$0.104112\pi$
$618$	−12.1905	+	296.239i	−0.000793487	+	0.0192824i
$619$	−14613.8	−	8437.29i	−0.948915	−	0.547857i	−0.0561715	−	0.998421i	$-0.517889\pi$
$619$	−14613.8	−	8437.29i	−0.948915	−	0.547857i	−0.892744	+	0.450565i	$0.851223\pi$
$620$			2610.21i			0.169078i
$621$	−2944.66	−	6960.59i	−0.190282	−	0.449789i
$622$			3240.71i			0.208908i
$623$	13494.6	−	13326.7i	0.867817	−	0.857021i
$624$	10834.3	+	445.843i	0.695065	+	0.0286026i
$625$	−5956.03	−	10316.1i	−0.381186	−	0.660233i
$626$	−3623.84	−	6276.67i	−0.231370	−	0.400745i
$627$	14422.9	+	9137.66i	0.918650	+	0.582014i
$628$	18025.4	+	10407.0i	1.14537	+	0.661280i
$629$	4840.89			0.306866
$630$	−1307.08	−	1561.67i	−0.0826591	−	0.0987592i
$631$	30726.8			1.93853			0.969266	−	0.246014i	$-0.0791209\pi$
$631$	30726.8			1.93853			0.969266	+	0.246014i	$0.0791209\pi$
$632$	−339.004	−	195.724i	−0.0213368	−	0.0123188i
$633$	−3147.80	+	1648.68i	−0.197652	+	0.103521i
$634$	−4910.60	−	8505.41i	−0.307610	−	0.532797i
$635$	−905.222	−	1567.89i	−0.0565711	−	0.0979840i
$636$	−3612.68	−	6897.65i	−0.225239	−	0.430047i
$637$	12711.0	+	22666.6i	0.790622	+	1.40986i
$638$		−	1707.24i		−	0.105941i
$639$	2162.23	−	26227.4i	0.133860	−	1.62370i
$640$		−	4594.51i		−	0.283772i
$641$	13756.1	+	7942.11i	0.847636	+	0.489383i	0.859852	−	0.510543i	$-0.170555\pi$
$641$	13756.1	+	7942.11i	0.847636	+	0.489383i	−0.0122166	+	0.999925i	$0.503889\pi$
$642$	2898.02	+	1836.05i	0.178155	+	0.112871i
$643$	1909.66	−	1102.54i	0.117122	−	0.0676206i	−0.440294	−	0.897853i	$-0.645126\pi$
$643$	1909.66	−	1102.54i	0.117122	−	0.0676206i	0.557417	+	0.830233i	$0.311793\pi$
$644$	6149.26	−	1606.51i	0.376265	−	0.0983002i
$645$	226.287	−	5498.95i	0.0138140	−	0.335692i
$646$	5005.82	−	8670.34i	0.304878	−	0.528065i
$647$	−3584.90			−0.217831			−0.108916	−	0.994051i	$-0.534738\pi$
$647$	−3584.90			−0.217831			−0.108916	+	0.994051i	$0.534738\pi$
$648$	−2190.18	+	13192.9i	−0.132775	+	0.799796i
$649$			23935.1i			1.44767i
$650$	5552.86	−	9617.83i	0.335078	−	0.580373i
$651$	11774.1	+	3760.99i	0.708851	+	0.226428i
$652$	−2196.05	−	3803.66i	−0.131908	−	0.228471i
$653$	−394.355	+	227.681i	−0.0236329	+	0.0136445i	−0.511770	−	0.859123i	$-0.671010\pi$
$653$	−394.355	+	227.681i	−0.0236329	+	0.0136445i	0.488137	+	0.872767i	$0.337677\pi$
$654$	−140.764	+	222.182i	−0.00841639	+	0.0132844i
$655$	−1923.93	+	3332.34i	−0.114770	+	0.198787i
$656$	−11739.3			−0.698692
$657$	1278.46	−	15507.5i	0.0759169	−	0.920858i
$658$	−2130.93	+	7758.17i	−0.126250	+	0.459643i
$659$	8929.73	+	5155.58i	0.527850	+	0.304754i	0.740140	−	0.672452i	$-0.234759\pi$
$659$	8929.73	+	5155.58i	0.527850	+	0.304754i	−0.212291	+	0.977207i	$0.568092\pi$
$660$	−2154.96	−	4114.45i	−0.127094	−	0.242659i
$661$	7083.52	−	4089.67i	0.416818	−	0.240650i	−0.276897	−	0.960900i	$-0.589306\pi$
$661$	7083.52	−	4089.67i	0.416818	−	0.240650i	0.693715	+	0.720250i	$0.255973\pi$
$662$	−1884.36	+	1087.94i	−0.110631	+	0.0638730i
$663$	−19174.9	−	36610.4i	−1.12322	−	2.14454i
$664$	−5359.36	−	3094.23i	−0.313228	−	0.180842i
$665$	1169.07	−	4256.30i	0.0681724	−	0.248199i
$666$	1306.55	+	905.133i	0.0760177	+	0.0526625i
$667$	−1637.97			−0.0950862
$668$	4356.21	−	7545.18i	0.252316	−	0.437023i
$669$	−6519.33	+	10290.1i	−0.376759	+	0.594676i
$670$	−376.313	+	217.265i	−0.0216989	+	0.0125279i
$671$	8163.57	+	14139.7i	0.469674	+	0.813499i
$672$	−16676.9	−	5327.11i	−0.957330	−	0.305800i
$673$	11433.9	−	19804.0i	0.654893	−	1.13431i	−0.327028	−	0.945015i	$-0.606047\pi$
$673$	11433.9	−	19804.0i	0.654893	−	1.13431i	0.981921	−	0.189293i	$-0.0606195\pi$
$674$		−	9626.65i		−	0.550155i
$675$	−12853.6	−	9710.30i	−0.732942	−	0.553703i
$676$	−22572.1			−1.28426
$677$	2461.68	−	4263.75i	0.139749	−	0.242052i	−0.787653	−	0.616120i	$-0.788704\pi$
$677$	2461.68	−	4263.75i	0.139749	−	0.242052i	0.927401	+	0.374067i	$0.122037\pi$
$678$	197.758	−	4805.67i	0.0112018	−	0.272214i
$679$	−1314.96	+	343.537i	−0.0743205	+	0.0194164i
$680$	−5320.60	+	3071.85i	−0.300053	+	0.173235i
$681$	13485.5	+	8543.78i	0.758833	+	0.480761i
$682$	−6245.48	−	3605.83i	−0.350663	−	0.202455i
$683$		−	15195.6i		−	0.851310i	−0.904885	−	0.425655i	$-0.860044\pi$
$683$		−	15195.6i		−	0.851310i	0.904885	−	0.425655i	$-0.139956\pi$
$684$	−11618.2	+	5488.71i	−0.649464	+	0.306822i
$685$			1924.43i			0.107341i
$686$	−1951.45	−	7871.17i	−0.108610	−	0.438080i
$687$	3378.89	+	6451.28i	0.187646	+	0.358270i
$688$	−4572.32	−	7919.50i	−0.253370	−	0.438849i
$689$	8911.18	+	15434.6i	0.492727	+	0.853428i
$690$	1009.87	−	528.923i	0.0557173	−	0.0291823i
$691$	−4745.60	−	2739.88i	−0.261261	−	0.150839i	0.363649	−	0.931536i	$-0.381531\pi$
$691$	−4745.60	−	2739.88i	−0.261261	−	0.150839i	−0.624910	+	0.780697i	$0.714864\pi$
$692$	7816.39			0.429385
$693$	−21664.4	+	3792.15i	−1.18754	+	0.207867i
$694$	2393.50			0.130916
$695$	952.554	+	549.957i	0.0519891	+	0.0300159i
$696$	2448.35	+	1551.16i	0.133340	+	0.0844780i
$697$	22371.0	+	38747.7i	1.21573	+	2.10570i
$698$	−1106.65	−	1916.77i	−0.0600104	−	0.103941i
$699$	27005.4	+	1111.30i	1.46128	+	0.0601332i
$700$	9638.78	−	9518.87i	0.520445	−	0.513971i
$701$			5356.09i			0.288583i	0.989535	+	0.144292i	$0.0460903\pi$
$701$			5356.09i			0.288583i	−0.989535	+	0.144292i	$0.953910\pi$
$702$	1670.01	−	13466.4i	0.0897868	−	0.724011i
$703$			3445.02i			0.184824i
$704$	452.933	+	261.501i	0.0242479	+	0.0139996i
$705$	231.936	−	5636.22i	0.0123904	−	0.301096i
$706$	−10345.3	+	5972.88i	−0.551489	+	0.318402i
$707$	4141.86	+	15853.9i	0.220326	+	0.843347i
$708$	−15216.4	−	9640.38i	−0.807720	−	0.511734i
$709$	−6540.71	+	11328.8i	−0.346462	+	0.600090i	−0.985618	−	0.168987i	$-0.945950\pi$
$709$	−6540.71	+	11328.8i	−0.346462	+	0.600090i	0.639156	+	0.769077i	$0.279284\pi$
$710$	3969.47			0.209819
$711$	328.085	−	473.587i	0.0173054	−	0.0249802i
$712$		−	18786.4i		−	0.988836i
$713$	−3459.53	+	5992.08i	−0.181712	+	0.314734i
$714$	2744.05	+	12601.3i	0.143828	+	0.660490i
$715$	5315.52	+	9206.75i	0.278027	+	0.481556i
$716$	−8812.49	+	5087.89i	−0.459970	+	0.265564i
$717$	−5043.88	−	9630.21i	−0.262715	−	0.501599i
$718$	−7377.61	+	12778.4i	−0.383468	+	0.664186i
$719$	11546.9			0.598925			0.299463	−	0.954108i	$-0.403193\pi$
$719$	11546.9			0.598925			0.299463	+	0.954108i	$0.403193\pi$
$720$	2364.46	+	194.929i	0.122386	+	0.0100897i
$721$	219.250	−	798.235i	0.0113250	−	0.0412314i
$722$	−1412.78	−	815.671i	−0.0728232	−	0.0420445i
$723$	−19514.7	+	30802.0i	−1.00382	+	1.58442i
$724$	3034.26	−	1751.83i	0.155756	−	0.0899259i
$725$	−3023.52	+	1745.63i	−0.154884	+	0.0894221i
$726$	4000.12	+	164.608i	0.204488	+	0.00841487i
$727$	−8018.50	−	4629.49i	−0.409064	−	0.236173i	0.281323	−	0.959613i	$-0.409227\pi$
$727$	−8018.50	−	4629.49i	−0.409064	−	0.236173i	−0.690388	+	0.723440i	$0.742560\pi$
$728$	24822.1	+	6817.86i	1.26369	+	0.347097i
$729$	−19086.8	−	4807.96i	−0.969707	−	0.244270i
$730$	2347.02			0.118996
$731$	−17426.5	+	30183.7i	−0.881729	+	1.52720i
$732$	−12277.1	−	505.215i	−0.619912	−	0.0255100i
$733$	−30748.8	+	17752.8i	−1.54943	+	0.894564i	−0.551246	+	0.834343i	$0.685847\pi$
$733$	−30748.8	+	17752.8i	−1.54943	+	0.894564i	−0.998185	+	0.0602216i	$0.980819\pi$
$734$	5274.55	+	9135.79i	0.265242	+	0.459412i
$735$	2574.80	+	5069.43i	0.129215	+	0.254407i
$736$	4900.12	−	8487.25i	0.245409	−	0.425060i
$737$			4692.87i			0.234551i
$738$	−1207.01	+	14640.8i	−0.0602042	+	0.730266i
$739$	−17773.8			−0.884734			−0.442367	−	0.896834i	$-0.645861\pi$
$739$	−17773.8			−0.884734			−0.442367	+	0.896834i	$0.645861\pi$
$740$	468.577	−	811.599i	0.0232773	−	0.0403175i
$741$	26053.8	−	13645.8i	1.29165	−	0.676507i
$742$	−1405.78	−	5380.94i	−0.0695525	−	0.266227i
$743$	9171.95	−	5295.43i	0.452875	−	0.261468i	−0.256168	−	0.966632i	$-0.582460\pi$
$743$	9171.95	−	5295.43i	0.452875	−	0.261468i	0.709044	+	0.705164i	$0.249127\pi$
$744$	10845.6	−	5680.47i	0.534437	−	0.279914i
$745$	631.562	+	364.633i	0.0310586	+	0.0179317i
$746$		−	11722.3i		−	0.575316i
$747$	5186.75	−	7487.02i	0.254047	−	0.366714i
$748$			29413.3i			1.43778i
$749$	−6730.45	−	6815.24i	−0.328338	−	0.332474i
$750$	2716.10	−	4287.08i	0.132237	−	0.208723i
$751$	−2521.66	−	4367.64i	−0.122525	−	0.212220i	0.798238	−	0.602343i	$-0.205766\pi$
$751$	−2521.66	−	4367.64i	−0.122525	−	0.212220i	−0.920763	+	0.390123i	$0.872433\pi$
$752$	−4686.46	−	8117.19i	−0.227257	−	0.393621i
$753$	1550.13	−	37669.3i	0.0750197	−	1.82304i
$754$	−2546.85	−	1470.43i	−0.123012	−	0.0710210i
$755$	−10829.8			−0.522035
$756$	6314.99	−	15300.1i	0.303801	−	0.736059i
$757$	−36576.1			−1.75612			−0.878060	−	0.478551i	$-0.841162\pi$
$757$	−36576.1			−1.75612			−0.878060	+	0.478551i	$0.841162\pi$
$758$	10278.4	+	5934.25i	0.492518	+	0.284356i
$759$	506.215	−	12301.4i	0.0242087	−	0.588292i
$760$	−2186.08	−	3786.40i	−0.104339	−	0.180720i
$761$	9686.08	+	16776.8i	0.461393	+	0.799157i	0.999031	−	0.0440195i	$-0.0140164\pi$
$761$	9686.08	+	16776.8i	0.461393	+	0.799157i	−0.537637	+	0.843176i	$0.680683\pi$
$762$	−2014.67	+	3179.95i	−0.0957792	+	0.151178i
$763$	522.503	−	516.003i	0.0247915	−	0.0244831i
$764$		−	23933.0i		−	1.13333i
$765$	−3862.44	−	8175.81i	−0.182545	−	0.386401i
$766$		−	9382.26i		−	0.442552i
$767$	35706.4	+	20615.1i	1.68094	+	0.970492i
$768$	−8900.68	+	4661.78i	−0.418198	+	0.219033i
$769$	−983.118	+	567.603i	−0.0461016	+	0.0266168i	−0.522874	−	0.852410i	$-0.675140\pi$
$769$	−983.118	+	567.603i	−0.0461016	+	0.0266168i	0.476772	+	0.879027i	$0.341807\pi$
$770$	−838.549	−	3209.73i	−0.0392457	−	0.150222i
$771$	−4653.30	+	2437.19i	−0.217360	+	0.113844i
$772$	−8354.20	+	14469.9i	−0.389474	+	0.674589i
$773$	4858.97			0.226087			0.113043	−	0.993590i	$-0.463940\pi$
$773$	4858.97			0.226087			0.113043	+	0.993590i	$0.463940\pi$
$774$	−10347.0	+	4888.18i	−0.480513	+	0.227005i
$775$			14747.6i			0.683550i
$776$	−673.118	+	1165.87i	−0.0311385	+	0.0539335i
$777$	−2985.78	−	3283.06i	−0.137856	−	0.151582i
$778$	3340.01	+	5785.06i	0.153914	+	0.266587i
$779$	−27574.8	+	15920.3i	−1.26825	+	0.732227i
$780$	−7993.97	−	328.959i	−0.366961	−	0.0151008i
$781$	21434.9	−	37126.4i	0.982077	−	1.70101i
$782$	−7219.33			−0.330131
$783$	−2571.34	+	3403.71i	−0.117359	+	0.155349i
$784$	8121.95	+	4825.76i	0.369987	+	0.219832i
$785$	−9026.99	−	5211.74i	−0.410429	−	0.236962i
$786$	7994.03	+	328.962i	0.362771	+	0.0149283i
$787$	−6311.59	+	3644.00i	−0.285875	+	0.165050i	−0.636080	−	0.771623i	$-0.719445\pi$
$787$	−6311.59	+	3644.00i	−0.285875	+	0.165050i	0.350205	+	0.936673i	$0.386112\pi$
$788$	−25399.2	+	14664.2i	−1.14824	+	0.662934i
$789$	−8846.43	+	13963.2i	−0.399165	+	0.630042i
$790$	75.2586	+	43.4506i	0.00338934	+	0.00195684i
$791$	−3556.73	+	12949.2i	−0.159877	+	0.582073i
$792$	−12406.1	+	17908.1i	−0.556608	+	0.803457i
$793$	28124.8			1.25945
$794$	6411.74	−	11105.5i	0.286580	−	0.496370i
$795$	1809.20	+	3454.29i	0.0807117	+	0.154102i
$796$	17350.5	−	10017.3i	0.772579	−	0.446049i
$797$	−4956.07	−	8584.16i	−0.220267	−	0.381514i	0.734622	−	0.678477i	$-0.237360\pi$
$797$	−4956.07	−	8584.16i	−0.220267	−	0.381514i	−0.954889	+	0.296963i	$0.904026\pi$
$798$	−8967.68	+	1952.80i	−0.397810	+	0.0866272i
$799$	−17861.5	+	30937.1i	−0.790859	+	1.36981i
$800$		−	20888.7i		−	0.923160i
$801$	27556.2	+	2271.78i	1.21554	+	0.100211i
$802$	9552.05			0.420567
$803$	12673.8	−	21951.7i	0.556972	−	0.964704i
$804$	−2983.41	−	1890.15i	−0.130867	−	0.0829110i
$805$	−3079.50	+	804.526i	−0.134830	+	0.0352246i
$806$	−10758.3	+	6211.33i	−0.470157	+	0.271445i
$807$	−262.169	+	6370.91i	−0.0114359	+	0.277902i
$808$	14056.4	+	8115.45i	0.612007	+	0.353342i
$809$		−	39890.5i		−	1.73359i	−0.498664	−	0.866795i	$-0.666176\pi$
$809$		−	39890.5i		−	1.73359i	0.498664	−	0.866795i	$-0.333824\pi$
$810$	486.218	−	2928.83i	0.0210913	−	0.127047i
$811$		−	17543.5i		−	0.759601i	−0.925069	−	0.379800i	$-0.875993\pi$
$811$		−	17543.5i		−	0.759601i	0.925069	−	0.379800i	$-0.124007\pi$
$812$	−2520.65	−	2552.40i	−0.108938	−	0.110310i
$813$	37498.2	+	1543.09i	1.61761	+	0.0665663i
$814$	1294.62	+	2242.34i	0.0557448	+	0.0965529i
$815$	1099.76	+	1904.84i	0.0472675	+	0.0818697i
$816$	−12691.6	−	8040.81i	−0.544479	−	0.344957i
$817$	−21480.2	−	12401.6i	−0.919824	−	0.531061i
$818$	14561.4			0.622407
$819$	−13002.2	+	35585.0i	−0.554741	+	1.51824i
$820$	8661.67			0.368876
$821$	−869.844	−	502.205i	−0.0369766	−	0.0213484i	0.481398	−	0.876502i	$-0.340129\pi$
$821$	−869.844	−	502.205i	−0.0369766	−	0.0213484i	−0.518374	+	0.855154i	$0.673463\pi$
$822$	3544.69	−	1856.55i	0.150408	−	0.0787769i
$823$	404.664	+	700.898i	0.0171394	+	0.0296862i	0.874468	−	0.485083i	$-0.161211\pi$
$823$	404.664	+	700.898i	0.0171394	+	0.0296862i	−0.857329	+	0.514770i	$0.827877\pi$
$824$	−409.982	−	710.110i	−0.0173330	−	0.0300217i
$825$	−12175.5	−	23246.6i	−0.513815	−	0.981020i
$826$	−9040.55	−	9154.43i	−0.380825	−	0.385622i
$827$			27558.4i			1.15877i	0.815056	+	0.579383i	$0.196706\pi$
$827$			27558.4i			1.15877i	−0.815056	+	0.579383i	$0.803294\pi$
$828$	7616.53	+	5276.47i	0.319677	+	0.221461i
$829$			11232.4i			0.470588i	0.971924	+	0.235294i	$0.0756053\pi$
$829$			11232.4i			0.470588i	−0.971924	+	0.235294i	$0.924395\pi$
$830$	1189.78	+	686.917i	0.0497563	+	0.0287268i
$831$	−9937.87	−	6296.17i	−0.414851	−	0.262830i
$832$	780.212	−	450.456i	0.0325108	−	0.0187701i
$833$	450.709	−	36004.3i	0.0187469	−	1.49757i
$834$	94.0341	−	2285.10i	0.00390424	−	0.0948761i
$835$	−2181.55	+	3778.56i	−0.0904141	+	0.156602i
$836$	−20932.0			−0.865967
$837$	7020.67	+	16595.5i	0.289928	+	0.685333i
$838$			7729.16i			0.318615i
$839$	10338.7	−	17907.2i	0.425425	−	0.736859i	−0.571035	−	0.820926i	$-0.693458\pi$
$839$	10338.7	−	17907.2i	0.425425	−	0.736859i	0.996460	+	0.0840675i	$0.0267911\pi$
$840$	5364.97	+	1713.73i	0.220368	+	0.0703921i
$841$	−11732.2	−	20320.8i	−0.481047	−	0.833197i
$842$	7594.31	−	4384.58i	0.310828	−	0.179457i
$843$	−2760.93	+	4357.85i	−0.112801	+	0.178045i
$844$	2178.19	−	3772.73i	0.0888345	−	0.153866i
$845$	11303.9			0.460197
$846$	−10605.3	+	5010.20i	−0.430991	+	0.203610i
$847$	−10778.6	−	2960.53i	−0.437256	−	0.120100i
$848$	5611.10	+	3239.57i	0.227224	+	0.131188i
$849$	13741.0	+	26235.5i	0.555465	+	1.06054i
$850$	−13326.1	+	7693.83i	−0.537743	+	0.310466i
$851$	2151.36	−	1242.09i	0.0866601	−	0.0500332i
$852$	14969.1	+	28580.3i	0.601917	+	1.14923i
$853$	12678.1	+	7319.71i	0.508899	+	0.293813i	0.732381	−	0.680895i	$-0.238409\pi$
$853$	12678.1	+	7319.71i	0.508899	+	0.293813i	−0.223482	+	0.974708i	$0.571742\pi$
$854$	−8463.02	−	2324.53i	−0.339109	−	0.0931425i
$855$	5818.31	−	2748.70i	0.232727	−	0.109946i
$856$	−9487.79			−0.378839
$857$	5363.52	−	9289.90i	0.213786	−	0.370288i	−0.739110	−	0.673584i	$-0.764754\pi$
$857$	5363.52	−	9289.90i	0.213786	−	0.370288i	0.952896	+	0.303296i	$0.0980872\pi$
$858$	11830.2	−	18672.8i	0.470720	−	0.742984i
$859$	37326.6	−	21550.5i	1.48262	−	0.855988i	0.482810	−	0.875725i	$-0.339616\pi$
$859$	37326.6	−	21550.5i	1.48262	−	0.855988i	0.999805	+	0.0197364i	$0.00628272\pi$
$860$	3373.63	+	5843.29i	0.133767	+	0.231691i
$861$	12480.4	−	39070.9i	0.493997	−	1.54649i
$862$	−4954.21	+	8580.94i	−0.195755	+	0.339058i
$863$			2755.10i			0.108673i	0.998523	+	0.0543363i	$0.0173043\pi$
$863$			2755.10i			0.108673i	−0.998523	+	0.0543363i	$0.982696\pi$
$864$	−9944.16	−	23506.0i	−0.391559	−	0.925568i
$865$	−3914.38			−0.153865
$866$	4771.06	−	8263.71i	0.187214	−	0.324264i
$867$	−1304.77	+	31706.9i	−0.0511099	+	1.24201i
$868$	−14661.1	+	3830.25i	−0.573307	+	0.149778i
$869$	812.785	−	469.262i	0.0317283	−	0.0183183i
$870$	−543.534	−	344.358i	−0.0211811	−	0.0134193i
$871$	7000.80	+	4041.92i	0.272346	+	0.157239i
$872$		−	727.400i		−	0.0282487i
$873$	−1628.72	−	1128.32i	−0.0631431	−	0.0437434i
$874$		−	5137.63i		−	0.198836i
$875$	−10081.9	+	9956.47i	−0.389520	+	0.384674i
$876$	8850.76	+	16898.6i	0.341369	+	0.651772i
$877$	14479.0	+	25078.4i	0.557494	+	0.965609i	0.997705	+	0.0677140i	$0.0215705\pi$
$877$	14479.0	+	25078.4i	0.557494	+	0.965609i	−0.440210	+	0.897895i	$0.645096\pi$
$878$	−592.617	−	1026.44i	−0.0227789	−	0.0394541i
$879$	10223.7	−	5354.74i	0.392307	−	0.205473i
$880$	3347.02	+	1932.40i	0.128214	+	0.0740242i
$881$	−41511.7			−1.58747			−0.793737	−	0.608261i	$-0.791867\pi$
$881$	−41511.7			−1.58747			−0.793737	+	0.608261i	$0.791867\pi$
$882$	6853.61	−	9633.24i	0.261647	−	0.367764i
$883$	34478.4			1.31403			0.657016	−	0.753877i	$-0.271818\pi$
$883$	34478.4			1.31403			0.657016	+	0.753877i	$0.271818\pi$
$884$	43878.7	+	25333.4i	1.66946	+	0.963862i
$885$	7620.23	+	4827.82i	0.289436	+	0.183373i
$886$	−3537.08	−	6126.40i	−0.134120	−	0.232303i
$887$	19033.5	+	32967.0i	0.720499	+	1.24794i	0.960800	+	0.277242i	$0.0894203\pi$
$887$	19033.5	+	32967.0i	0.720499	+	1.24794i	−0.240302	+	0.970698i	$0.577246\pi$
$888$	−4392.01	−	180.735i	−0.165975	−	0.00683004i
$889$	7478.25	−	7385.22i	0.282129	−	0.278619i
$890$			4170.58i			0.157077i
$891$	−24767.7	−	20363.1i	−0.931256	−	0.765644i
$892$		−	14934.1i		−	0.560572i
$893$	−22016.4	−	12711.2i	−0.825028	−	0.476330i
$894$	62.3465	−	1515.07i	0.00233241	−	0.0566795i
$895$	4413.22	−	2547.98i	0.164824	−	0.0951614i
$896$	25806.6	−	6742.04i	0.962208	−	0.251379i
$897$	−17915.2	−	11350.2i	−0.666858	−	0.422490i
$898$	8354.13	−	14469.8i	0.310446	−	0.537709i
$899$	3905.26			0.144881
$900$	19682.6	+	1622.66i	0.728984	+	0.0600985i
$901$		−	24694.0i		−	0.913070i
$902$	−11965.5	+	20724.9i	−0.441695	+	0.765037i
$903$	31218.8	−	6798.20i	1.15049	−	0.250532i
$904$	6650.84	+	11519.6i	0.244694	+	0.423823i
$905$	−1519.53	+	877.303i	−0.0558133	+	0.0322238i
$906$	10447.8	+	19947.8i	0.383117	+	0.731481i
$907$	13062.6	−	22625.2i	0.478212	−	0.828287i	−0.521476	−	0.853266i	$-0.674619\pi$
$907$	13062.6	−	22625.2i	0.478212	−	0.828287i	0.999688	+	0.0249790i	$0.00795188\pi$
$908$	−19571.6			−0.715314
$909$	−13603.7	+	19636.7i	−0.496375	+	0.716512i
$910$	−5510.50	−	1513.56i	−0.200738	−	0.0551364i
$911$	13990.6	+	8077.47i	0.508813	+	0.293763i	0.732346	−	0.680933i	$-0.238426\pi$
$911$	13990.6	+	8077.47i	0.508813	+	0.293763i	−0.223532	+	0.974696i	$0.571759\pi$
$912$	5722.24	−	9031.97i	0.207766	−	0.327937i
$913$	12849.4	−	7418.63i	0.465777	−	0.268917i
$914$	−12760.9	+	7367.52i	−0.461809	+	0.266626i
$915$	6148.29	+	253.008i	0.222138	+	0.00914118i
$916$	−7732.06	−	4464.11i	−0.278902	−	0.161024i
$917$	−21540.4	−	5916.47i	−0.775710	−	0.213063i
$918$	−11333.1	+	15001.8i	−0.407461	+	0.539360i
$919$	−26587.5			−0.954344			−0.477172	−	0.878810i	$-0.658338\pi$
$919$	−26587.5			−0.954344			−0.477172	+	0.878810i	$0.658338\pi$
$920$	−1576.37	+	2730.35i	−0.0564906	+	0.0978446i
$921$	15611.2	+	642.414i	0.558529	+	0.0229840i
$922$	10076.7	−	5817.79i	0.359933	−	0.207808i
$923$	−36923.4	−	63953.1i	−1.31674	−	2.28065i
$924$	19947.9	−	18141.7i	0.710216	−	0.645906i
$925$	2647.45	−	4585.52i	0.0941057	−	0.162996i
$926$			4066.01i			0.144295i
$927$	1091.18	−	515.497i	0.0386612	−	0.0182644i
$928$	−5531.45			−0.195667
$929$	−14089.6	+	24403.9i	−0.497594	+	0.861857i	−0.999996	−	0.00277655i	$-0.999116\pi$
$929$	−14089.6	+	24403.9i	−0.497594	+	0.861857i	0.502403	+	0.864634i	$0.332450\pi$
$930$	−2407.73	+	1261.06i	−0.0848952	+	0.0444644i
$931$	25622.4	+	320.747i	0.901978	+	0.0112911i
$932$	−28696.4	+	16567.9i	−1.00857	+	0.582296i
$933$	11685.1	−	6120.13i	0.410024	−	0.214753i
$934$	−1100.19	−	635.195i	−0.0385432	−	0.0222529i
$935$		−	14730.0i		−	0.515210i
$936$	16030.0	+	33931.5i	0.559784	+	1.18492i
$937$		−	10247.7i		−	0.357288i	−0.983914	−	0.178644i	$-0.942829\pi$
$937$		−	10247.7i		−	0.357288i	0.983914	−	0.178644i	$-0.0571711\pi$
$938$	−1772.54	−	1794.87i	−0.0617011	−	0.0624783i
$939$	−15788.2	+	24920.1i	−0.548700	+	0.866067i
$940$	3457.84	+	5989.15i	0.119981	+	0.207813i
$941$	−7953.42	−	13775.7i	−0.275530	−	0.477232i	0.694739	−	0.719262i	$-0.255520\pi$
$941$	−7953.42	−	13775.7i	−0.275530	−	0.477232i	−0.970269	+	0.242030i	$0.922187\pi$
$942$	−891.126	+	21655.1i	−0.0308221	+	0.749002i
$943$	19884.0	+	11480.0i	0.686652	+	0.396439i
$944$	14988.8			0.516784
$945$	−3162.49	+	7662.18i	−0.108863	+	0.263757i
$946$	−18641.8			−0.640694
$947$	−28572.1	−	16496.1i	−0.980432	−	0.566053i	−0.0780317	−	0.996951i	$-0.524864\pi$
$947$	−28572.1	−	16496.1i	−0.980432	−	0.566053i	−0.902401	+	0.430898i	$0.858197\pi$
$948$	−29.0410	+	705.719i	−0.000994945	+	0.0241779i
$949$	−21831.6	−	37813.5i	−0.746769	−	1.29344i
$950$	−5475.31	−	9483.51i	−0.186992	−	0.323880i
$951$	−21394.4	+	33768.8i	−0.729505	+	1.15145i
$952$	−25061.6	−	25377.3i	−0.853204	−	0.863952i
$953$			37129.3i			1.26205i	0.775761	+	0.631027i	$0.217366\pi$
$953$			37129.3i			1.26205i	−0.775761	+	0.631027i	$0.782634\pi$
$954$	4617.20	−	6664.88i	0.156695	−	0.226188i
$955$			11985.5i			0.406116i
$956$	11542.1	+	6663.84i	0.390479	+	0.225443i
$957$	−6155.82	+	3224.15i	−0.207930	+	0.108905i
$958$	15370.1	−	8873.96i	0.518358	−	0.299274i
$959$	−10809.2	+	2823.93i	−0.363971	+	0.0950881i
$960$	174.613	−	91.4543i	0.00587041	−	0.00307466i
$961$	−6647.27	+	11513.4i	−0.223130	+	0.386473i
$962$	4460.16			0.149482
$963$	1147.32	−	13916.8i	0.0383925	−	0.465694i
$964$		−	44703.1i		−	1.49356i
$965$	4183.71	−	7246.41i	0.139563	−	0.241731i
$966$	4452.76	+	4896.10i	0.148308	+	0.163074i
$967$	−31.4682	−	54.5045i	−0.00104648	−	0.00181256i	0.865502	−	0.500906i	$-0.167000\pi$
$967$	−31.4682	−	54.5045i	−0.00104648	−	0.00181256i	−0.866548	+	0.499093i	$0.833666\pi$
$968$	−9588.60	+	5535.98i	−0.318377	+	0.183815i
$969$	−40716.3	−	1675.52i	−1.34984	−	0.0555473i
$970$	149.432	−	258.823i	0.00494636	−	0.00856734i
$971$	−26793.4			−0.885521			−0.442761	−	0.896640i	$-0.646001\pi$
$971$	−26793.4			−0.885521			−0.442761	+	0.896640i	$0.646001\pi$
$972$	22921.2	−	7543.99i	0.756376	−	0.248944i
$973$	−1691.23	+	6157.35i	−0.0557229	+	0.202873i
$974$	8411.49	+	4856.38i	0.276716	+	0.159762i
$975$	−45165.8	−	1858.62i	−1.48355	−	0.0610496i
$976$	8854.66	−	5112.24i	0.290400	−	0.167663i
$977$	22941.3	−	13245.2i	0.751235	−	0.433726i	−0.0749048	−	0.997191i	$-0.523865\pi$
$977$	22941.3	−	13245.2i	0.751235	−	0.433726i	0.826140	+	0.563465i	$0.190532\pi$
$978$	2447.64	−	3863.35i	0.0800274	−	0.126315i
$979$	39007.3	+	22520.9i	1.27342	+	0.735211i
$980$	−5992.67	−	3560.62i	−0.195336	−	0.116061i
$981$	1066.96	+	87.9618i	0.0347252	+	0.00286280i
$982$	−21048.0			−0.683979
$983$	11945.2	−	20689.7i	0.387582	−	0.671313i	−0.604541	−	0.796574i	$-0.706644\pi$
$983$	11945.2	−	20689.7i	0.387582	−	0.671313i	0.992124	+	0.125261i	$0.0399769\pi$
$984$	−18850.0	−	35990.0i	−0.610686	−	1.16598i
$985$	12719.7	−	7343.73i	0.411456	−	0.237554i
$986$	2037.37	+	3528.83i	0.0658043	+	0.113976i
$987$	31998.1	−	6967.90i	1.03192	−	0.224712i
$988$	−18028.5	+	31226.3i	−0.580529	+	1.00551i
$989$			17885.4i			0.575048i
$990$	2754.16	−	3975.60i	0.0884171	−	0.127629i
$991$	377.774			0.0121094			0.00605468	−	0.999982i	$-0.498073\pi$
$991$	377.774			0.0121094			0.00605468	+	0.999982i	$0.498073\pi$
$992$	−11682.9	+	20235.3i	−0.373923	+	0.647654i
$993$	7481.44	+	4739.89i	0.239090	+	0.151476i
$994$	5824.84	+	22295.9i	0.185868	+	0.711451i
$995$	−8689.00	+	5016.59i	−0.276844	+	0.159836i
$996$	−459.114	+	11156.8i	−0.0146060	+	0.354937i
$997$	−854.102	−	493.116i	−0.0271311	−	0.0156641i	0.486373	−	0.873751i	$-0.338320\pi$
$997$	−854.102	−	493.116i	−0.0271311	−	0.0156641i	−0.513504	+	0.858087i	$0.671653\pi$
$998$		−	3947.40i		−	0.125203i
$999$	796.215	−	6420.41i	0.0252163	−	0.203336i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.4.o.a.20.9	✓	44
3.2	odd	2		189.4.o.a.62.13		44
7.6	odd	2	inner	63.4.o.a.20.10	yes	44
9.2	odd	6		567.4.c.c.566.19		44
9.4	even	3		189.4.o.a.125.14		44
9.5	odd	6	inner	63.4.o.a.41.10	yes	44
9.7	even	3		567.4.c.c.566.26		44
21.20	even	2		189.4.o.a.62.14		44
63.13	odd	6		189.4.o.a.125.13		44
63.20	even	6		567.4.c.c.566.25		44
63.34	odd	6		567.4.c.c.566.20		44
63.41	even	6	inner	63.4.o.a.41.9	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.o.a.20.9	✓	44	1.1	even	1	trivial
63.4.o.a.20.10	yes	44	7.6	odd	2	inner
63.4.o.a.41.9	yes	44	63.41	even	6	inner
63.4.o.a.41.10	yes	44	9.5	odd	6	inner
189.4.o.a.62.13		44	3.2	odd	2
189.4.o.a.62.14		44	21.20	even	2
189.4.o.a.125.13		44	63.13	odd	6
189.4.o.a.125.14		44	9.4	even	3
567.4.c.c.566.19		44	9.2	odd	6
567.4.c.c.566.20		44	63.34	odd	6
567.4.c.c.566.25		44	63.20	even	6
567.4.c.c.566.26		44	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:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	63.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.10556 - 0.638294i) q^{2} +(-0.213646 + 5.19176i) q^{3} +(-3.18516 - 5.51686i) q^{4} +(1.59510 + 2.76280i) q^{5} +(3.55007 - 5.60342i) q^{6} +(-13.1775 + 13.0136i) q^{7} +18.3450i q^{8} +(-26.9087 - 2.21839i) q^{9} +O(q^{10})\)	\(q+(-1.10556 - 0.638294i) q^{2} +(-0.213646 + 5.19176i) q^{3} +(-3.18516 - 5.51686i) q^{4} +(1.59510 + 2.76280i) q^{5} +(3.55007 - 5.60342i) q^{6} +(-13.1775 + 13.0136i) q^{7} +18.3450i q^{8} +(-26.9087 - 2.21839i) q^{9} -4.07258i q^{10} +(-38.0908 - 21.9917i) q^{11} +(29.3227 - 15.3579i) q^{12} +(-65.6143 + 37.8824i) q^{13} +(22.8750 - 5.97614i) q^{14} +(-14.6846 + 7.69113i) q^{15} +(-13.7718 + 23.8534i) q^{16} +104.977 q^{17} +(28.3332 + 19.6282i) q^{18} +74.7068i q^{19} +(10.1613 - 17.5999i) q^{20} +(-64.7481 - 71.1947i) q^{21} +(28.0744 + 48.6262i) q^{22} +(46.6533 - 26.9353i) q^{23} +(-95.2428 - 3.91933i) q^{24} +(57.4113 - 99.4393i) q^{25} +96.7206 q^{26} +(17.2663 - 139.230i) q^{27} +(113.767 + 31.2481i) q^{28} +(-26.3321 - 15.2028i) q^{29} +(21.1439 + 0.870089i) q^{30} +(-111.231 + 64.2193i) q^{31} +(157.549 - 90.9609i) q^{32} +(122.314 - 193.060i) q^{33} +(-116.058 - 67.0062i) q^{34} +(-56.9734 - 15.6488i) q^{35} +(73.4700 + 155.518i) q^{36} +46.1138 q^{37} +(47.6849 - 82.5928i) q^{38} +(-182.658 - 348.747i) q^{39} +(-50.6835 + 29.2621i) q^{40} +(213.104 + 369.107i) q^{41} +(26.1396 + 120.038i) q^{42} +(-166.003 + 287.526i) q^{43} +280.188i q^{44} +(-36.7932 - 77.8819i) q^{45} -68.7706 q^{46} +(-170.147 + 294.704i) q^{47} +(-120.899 - 76.5959i) q^{48} +(4.29341 - 342.973i) q^{49} +(-126.943 + 73.2906i) q^{50} +(-22.4279 + 545.015i) q^{51} +(417.984 + 241.323i) q^{52} -235.233i q^{53} +(-107.958 + 142.905i) q^{54} -140.316i q^{55} +(-238.734 - 241.741i) q^{56} +(-387.860 - 15.9608i) q^{57} +(19.4078 + 33.6152i) q^{58} +(-272.093 - 471.279i) q^{59} +(89.2036 + 56.5152i) q^{60} +(-321.478 - 185.606i) q^{61} +163.963 q^{62} +(383.459 - 320.946i) q^{63} -11.8909 q^{64} +(-209.323 - 120.853i) q^{65} +(-258.454 + 135.367i) q^{66} +(-53.3481 - 92.4017i) q^{67} +(-334.368 - 579.143i) q^{68} +(129.874 + 247.967i) q^{69} +(52.9988 + 53.6665i) q^{70} +974.682i q^{71} +(40.6964 - 493.640i) q^{72} +576.299i q^{73} +(-50.9815 - 29.4342i) q^{74} +(503.999 + 319.310i) q^{75} +(412.147 - 237.953i) q^{76} +(788.132 - 205.901i) q^{77} +(-20.6639 + 502.150i) q^{78} +(-10.6691 + 18.4794i) q^{79} -87.8696 q^{80} +(719.157 + 119.388i) q^{81} -544.093i q^{82} +(-168.669 + 292.143i) q^{83} +(-186.538 + 583.973i) q^{84} +(167.449 + 290.030i) q^{85} +(367.053 - 211.918i) q^{86} +(84.5552 - 133.462i) q^{87} +(403.438 - 698.775i) q^{88} -1024.06 q^{89} +(-9.03458 + 109.588i) q^{90} +(371.647 - 1353.07i) q^{91} +(-297.197 - 171.586i) q^{92} +(-309.647 - 591.205i) q^{93} +(376.216 - 217.208i) q^{94} +(-206.400 + 119.165i) q^{95} +(438.587 + 837.389i) q^{96} +(63.5527 + 36.6922i) q^{97} +(-223.664 + 376.436i) q^{98} +(976.187 + 676.269i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 6 q^{2} + 78 q^{4} + 5 q^{7}+O(q^{10}) \) 44 * q - 6 * q^2 + 78 * q^4 + 5 * q^7	\( 44 q - 6 q^{2} + 78 q^{4} + 5 q^{7} - 18 q^{11} + 204 q^{14} + 66 q^{15} - 242 q^{16} - 210 q^{18} - 57 q^{21} - 34 q^{22} - 102 q^{23} - 352 q^{25} + 300 q^{28} + 246 q^{29} - 144 q^{30} + 1068 q^{32} - 1818 q^{36} + 328 q^{37} - 798 q^{39} - 1158 q^{42} - 170 q^{43} + 968 q^{46} - 79 q^{49} + 288 q^{50} - 204 q^{51} + 1212 q^{56} + 324 q^{57} - 538 q^{58} + 5316 q^{60} + 783 q^{63} - 808 q^{64} + 4350 q^{65} - 590 q^{67} + 384 q^{70} + 4284 q^{72} - 5304 q^{74} - 2787 q^{77} + 612 q^{78} - 302 q^{79} - 3720 q^{81} + 7050 q^{84} - 612 q^{85} - 13692 q^{86} + 1294 q^{88} + 210 q^{91} - 10194 q^{92} - 4266 q^{93} + 6336 q^{95} + 1014 q^{99}+O(q^{100}) \) 44 * q - 6 * q^2 + 78 * q^4 + 5 * q^7 - 18 * q^11 + 204 * q^14 + 66 * q^15 - 242 * q^16 - 210 * q^18 - 57 * q^21 - 34 * q^22 - 102 * q^23 - 352 * q^25 + 300 * q^28 + 246 * q^29 - 144 * q^30 + 1068 * q^32 - 1818 * q^36 + 328 * q^37 - 798 * q^39 - 1158 * q^42 - 170 * q^43 + 968 * q^46 - 79 * q^49 + 288 * q^50 - 204 * q^51 + 1212 * q^56 + 324 * q^57 - 538 * q^58 + 5316 * q^60 + 783 * q^63 - 808 * q^64 + 4350 * q^65 - 590 * q^67 + 384 * q^70 + 4284 * q^72 - 5304 * q^74 - 2787 * q^77 + 612 * q^78 - 302 * q^79 - 3720 * q^81 + 7050 * q^84 - 612 * q^85 - 13692 * q^86 + 1294 * q^88 + 210 * q^91 - 10194 * q^92 - 4266 * q^93 + 6336 * q^95 + 1014 * q^99

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