LMFDB - Embedded newform 63.4.o.a.41.10

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			41.10
Character	$\chi$	$=$	63.41
Dual form			63.4.o.a.20.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.10556 + 0.638294i) q^{2} +(0.213646 + 5.19176i) q^{3} +(-3.18516 + 5.51686i) q^{4} +(-1.59510 + 2.76280i) q^{5} +(-3.55007 - 5.60342i) q^{6} +(-4.68134 - 17.9188i) q^{7} -18.3450i q^{8} +(-26.9087 + 2.21839i) q^{9} +O(q^{10})$	\(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} +(-4.68134 - 17.9188i) 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} +(16.6130 + 16.8223i) 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} +(92.0302 - 28.1327i) 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} +(-83.7878 + 89.8447i) 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} +(-299.170 + 167.768i) 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} +(-328.721 + 85.8791i) 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} +(165.720 + 471.788i) 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} +(-72.9759 + 19.0651i) 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} +(572.382 + 579.592i) 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} +(-137.927 + 597.325i) 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 $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

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	−0.682539	−	0.730849i	$-0.739124\pi$
$2$	−1.10556	+	0.638294i	−0.390874	+	0.225671i	0.291665	+	0.956521i	$0.405791\pi$
$3$	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	$-0.878902\pi$
$5$	−1.59510	+	2.76280i	−0.142670	+	0.247112i	0.785831	+	0.618441i	$0.212236\pi$
$6$	−3.55007	−	5.60342i	−0.241552	−	0.381265i
$7$	−4.68134	−	17.9188i	−0.252769	−	0.967527i
$7$	−4.68134	−	17.9188i	−0.252769	−	0.967527i
$8$		−	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	−0.920984	−	0.389600i	$-0.872613\pi$
$11$	−38.0908	+	21.9917i	−1.04407	+	0.602795i	−0.123088	+	0.992396i	$0.539280\pi$
$12$	−29.3227	−	15.3579i	−0.705394	−	0.369454i
$13$	65.6143	+	37.8824i	1.39986	+	0.808208i	0.994377	−	0.105896i	$-0.0337712\pi$
$13$	65.6143	+	37.8824i	1.39986	+	0.808208i	0.405480	+	0.914104i	$0.367105\pi$
$14$	16.6130	+	16.8223i	0.317144	+	0.321138i
$15$	−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	$-0.769390\pi$
$17$	−104.977			−1.49769			−0.748843	+	0.662748i	$0.769390\pi$
$18$	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
$21$	92.0302	−	28.1327i	0.956316	−	0.292336i
$22$	28.0744	−	48.6262i	0.272067	−	0.471234i
$23$	46.6533	+	26.9353i	0.422952	+	0.244191i	0.696339	−	0.717713i	$-0.254811\pi$
$23$	46.6533	+	26.9353i	0.422952	+	0.244191i	−0.273388	+	0.961904i	$0.588144\pi$
$24$	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	−0.581931	−	0.813238i	$-0.697703\pi$
$29$	−26.3321	+	15.2028i	−0.168612	+	0.0973481i	0.413319	+	0.910586i	$0.364369\pi$
$30$	21.1439	−	0.870089i	0.128677	−	0.00529519i
$31$	111.231	+	64.2193i	0.644441	+	0.372068i	0.786323	−	0.617815i	$-0.211982\pi$
$31$	111.231	+	64.2193i	0.644441	+	0.372068i	−0.141882	+	0.989884i	$0.545315\pi$
$32$	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	0.0999082	+	0.994997i	$0.468145\pi$
$41$	−213.104	+	369.107i	−0.811738	+	1.40597i	−0.911647	+	0.410975i	$0.865188\pi$
$42$	−83.7878	+	89.8447i	−0.307827	+	0.330079i
$43$	−166.003	−	287.526i	−0.588728	−	1.01971i	−0.994399	−	0.105687i	$-0.966296\pi$
$43$	−166.003	−	287.526i	−0.588728	−	1.01971i	0.405672	−	0.914019i	$-0.367038\pi$
$44$		−	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	0.999465	+	0.0327026i	$0.0104114\pi$
$47$	170.147	+	294.704i	0.528054	+	0.914616i	−0.471411	+	0.881913i	$0.656255\pi$
$48$	120.899	−	76.5959i	0.363547	−	0.230326i
$49$	−299.170	+	167.768i	−0.872216	+	0.489121i
$50$	−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	$0.0985987\pi$
$53$			235.233i			0.609654i	−0.952408	+	0.304827i	$0.901401\pi$
$54$	107.958	+	142.905i	0.272061	+	0.360129i
$55$		−	140.316i		−	0.344004i
$56$	−328.721	+	85.8791i	−0.784414	+	0.204930i
$57$	−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	−0.392363	−	0.919811i	$-0.628342\pi$
$59$	272.093	−	471.279i	0.600398	−	1.03992i	0.992761	−	0.120109i	$-0.0383244\pi$
$60$	89.2036	−	56.5152i	0.191936	−	0.121601i
$61$	321.478	−	185.606i	0.674772	−	0.389580i	−0.123110	−	0.992393i	$-0.539287\pi$
$61$	321.478	−	185.606i	0.674772	−	0.389580i	0.797882	+	0.602813i	$0.205954\pi$
$62$	−163.963			−0.335861
$63$	165.720	+	471.788i	0.331409	+	0.943487i
$64$	−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	−0.910556	−	0.413385i	$-0.864346\pi$
$67$	−53.3481	+	92.4017i	−0.0972763	+	0.168487i	0.813280	+	0.581872i	$0.197680\pi$
$68$	334.368	−	579.143i	0.596296	−	1.03282i
$69$	−129.874	+	247.967i	−0.226595	+	0.432634i
$70$	−72.9759	+	19.0651i	−0.124604	+	0.0325531i
$71$		−	974.682i		−	1.62920i	−0.580020	−	0.814602i	$-0.696955\pi$
$71$		−	974.682i		−	1.62920i	0.580020	−	0.814602i	$-0.303045\pi$
$72$	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
$77$	572.382	+	579.592i	0.847129	+	0.857800i
$78$	−20.6639	−	502.150i	−0.0299965	−	0.728940i
$79$	−10.6691	−	18.4794i	−0.0151945	−	0.0263176i	0.858328	−	0.513101i	$-0.171503\pi$
$79$	−10.6691	−	18.4794i	−0.0151945	−	0.0263176i	−0.873523	+	0.486783i	$0.838170\pi$
$80$	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	$-0.0950628\pi$
$83$	168.669	+	292.143i	0.223058	+	0.386348i	−0.732677	+	0.680576i	$0.761729\pi$
$84$	−137.927	+	597.325i	−0.179155	+	0.775874i
$85$	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	$-0.291236\pi$
$89$	1024.06			1.21967			0.609834	+	0.792529i	$0.291236\pi$
$90$	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	$-0.678895\pi$
$97$	−63.5527	+	36.6922i	−0.0665237	+	0.0384075i	0.466369	+	0.884590i	$0.345562\pi$
$98$	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	$-0.310210\pi$
$101$	−442.380	−	766.224i	−0.435826	−	0.754873i	−0.997363	+	0.0725790i	$0.976877\pi$
$102$	372.675	+	588.230i	0.361768	+	0.571015i
$103$	38.7086	+	22.3484i	0.0370299	+	0.0213792i	0.518401	−	0.855138i	$-0.326528\pi$
$103$	38.7086	+	22.3484i	0.0370299	+	0.0213792i	−0.481371	+	0.876517i	$0.659861\pi$
$104$	694.953	−	1203.69i	0.655248	−	1.13492i
$105$	−69.0727	+	299.135i	−0.0641981	+	0.278025i
$106$	−150.148	−	260.063i	−0.137581	−	0.238298i
$107$		−	517.187i		−	0.467274i	−0.972324	−	0.233637i	$-0.924937\pi$
$107$		−	517.187i		−	0.467274i	0.972324	−	0.233637i	$-0.0750628\pi$
$108$	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
$112$	−362.955	+	358.440i	−0.306215	+	0.302406i
$113$	627.942	+	362.542i	0.522759	+	0.301815i	0.738063	−	0.674732i	$-0.235741\pi$
$113$	627.942	+	362.542i	0.522759	+	0.301815i	−0.215304	+	0.976547i	$0.569074\pi$
$114$	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
$119$	491.433	+	1881.07i	0.378568	+	1.44905i
$120$	−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
$126$	−484.353	−	415.811i	−0.342457	−	0.293995i
$127$	−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	$-0.965095\pi$
$131$	−603.074	+	1044.55i	−0.402220	+	0.696665i	0.591774	+	0.806104i	$0.298428\pi$
$132$	1454.67	−	59.8611i	0.959188	−	0.0394715i
$133$	1338.66	−	349.728i	0.872756	−	0.228009i
$134$		−	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	−0.328182	−	0.944615i	$-0.606436\pi$
$137$	522.414	−	301.616i	0.325787	−	0.188093i	0.653969	+	0.756521i	$0.273103\pi$
$138$	−14.6925	−	357.040i	−0.00906313	−	0.220241i
$139$	−298.587	−	172.389i	−0.182200	−	0.105193i	0.406126	−	0.913817i	$-0.366879\pi$
$139$	−298.587	−	172.389i	−0.182200	−	0.105193i	−0.588326	+	0.808624i	$0.700213\pi$
$140$	−267.802	+	264.470i	−0.161667	+	0.159656i
$141$	−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
$147$	−934.929	−	1517.38i	−0.524569	−	0.851368i
$148$	−146.880	+	254.403i	−0.0815774	+	0.141296i
$149$	197.969	+	114.298i	0.108847	+	0.0628431i	0.553435	−	0.832892i	$-0.313317\pi$
$149$	197.969	+	114.298i	0.108847	+	0.0628431i	−0.444588	+	0.895735i	$0.646650\pi$
$150$	353.386	−	674.716i	0.192359	−	0.367269i
$151$	−1697.35	−	2939.90i	−0.914758	−	1.58441i	−0.807256	−	0.590202i	$-0.799048\pi$
$151$	−1697.35	−	2939.90i	−0.914758	−	1.58441i	−0.107502	−	0.994205i	$-0.534285\pi$
$152$	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	$-0.0214157\pi$
$157$	2829.60	+	1633.67i	1.43838	+	0.830452i	0.440647	+	0.897680i	$0.354749\pi$
$158$	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	$-0.935963\pi$
$167$	−683.829	+	1184.43i	−0.316864	+	0.548824i	0.662968	+	0.748648i	$0.269297\pi$
$168$	−516.093	−	1688.29i	−0.237009	−	0.775325i
$169$	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	$-0.0797699\pi$
$173$	613.500	+	1062.61i	0.269616	+	0.466988i	−0.699147	+	0.714978i	$0.746437\pi$
$174$	178.669	+	93.5787i	0.0778438	+	0.0407712i
$175$	1513.08	−	1494.25i	0.653587	−	0.645457i
$176$	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	$0.108230\pi$
$179$			1597.37i			0.667002i	−0.942750	+	0.333501i	$0.891770\pi$
$180$	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	$0.963976\pi$
$182$	452.782	+	1733.12i	0.184409	+	0.705866i
$183$	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
$189$	−2414.00	+	961.173i	−0.929063	+	0.369921i
$190$	304.249			0.116171
$191$	3253.62	−	1878.48i	1.23258	−	0.711633i	0.265017	−	0.964244i	$-0.414622\pi$
$191$	3253.62	−	1878.48i	1.23258	−	0.711633i	0.967568	+	0.252611i	$0.0812891\pi$
$192$	−2.54044	−	61.7346i	−0.000954897	−	0.0232047i
$193$	−1311.43	+	2271.46i	−0.489111	+	0.847165i	−0.999922	−	0.0125280i	$-0.996012\pi$
$193$	−1311.43	+	2271.46i	−0.489111	+	0.847165i	0.510810	+	0.859693i	$0.329345\pi$
$194$	46.8408	−	81.1307i	0.0173349	−	0.0300250i
$195$	−672.159	−	1060.94i	−0.246843	−	0.389616i
$196$	27.3504	−	2184.85i	0.00996734	−	0.796228i
$197$			4603.93i			1.66506i	0.553982	+	0.832528i	$0.313107\pi$
$197$			4603.93i			1.66506i	−0.553982	+	0.832528i	$0.686893\pi$
$198$	−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
$203$	395.687	+	400.671i	0.136807	+	0.138530i
$204$	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
$210$	−114.573	−	374.800i	−0.0376488	−	0.123160i
$211$	341.927	−	592.236i	0.111560	−	0.193228i	−0.804839	−	0.593493i	$-0.797748\pi$
$211$	341.927	−	592.236i	0.111560	−	0.193228i	0.916400	+	0.400265i	$0.131082\pi$
$212$	−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	$-0.781161\pi$
$223$	−2030.24	+	1172.16i	−0.609664	+	0.351990i	0.163170	+	0.986598i	$0.447828\pi$
$224$	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	$-0.314941\pi$
$227$	−1536.15	−	2660.69i	−0.449154	−	0.777958i	−0.998331	+	0.0577480i	$0.981608\pi$
$228$	1147.34	−	2190.61i	0.333266	−	0.636300i
$229$	−1213.76	−	700.766i	−0.350252	−	0.202218i	0.314544	−	0.949243i	$-0.398148\pi$
$229$	−1213.76	−	700.766i	−0.350252	−	0.202218i	−0.664796	+	0.747025i	$0.731482\pi$
$230$	109.696	−	189.999i	0.0314485	−	0.0544704i
$231$	−2886.81	+	3095.50i	−0.822244	+	0.881682i
$232$	278.896	+	483.062i	0.0789242	+	0.136701i
$233$			5201.59i			1.46252i	0.682098	+	0.731261i	$0.261068\pi$
$233$			5201.59i			1.46252i	−0.682098	+	0.731261i	$0.738932\pi$
$234$	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
$238$	−1743.98	−	1765.95i	−0.474981	−	0.480964i
$239$	−1811.86	−	1046.08i	−0.490373	−	0.283117i	0.234356	−	0.972151i	$-0.424702\pi$
$239$	−1811.86	−	1046.08i	−0.490373	−	0.283117i	−0.724729	+	0.689034i	$0.758035\pi$
$240$	18.7730	+	456.198i	0.00504912	+	0.122698i
$241$	−6077.25	+	3508.70i	−1.62436	+	0.937823i	−0.638622	+	0.769520i	$0.720495\pi$
$241$	−6077.25	+	3508.70i	−1.62436	+	0.937823i	−0.985735	+	0.168303i	$0.946171\pi$
$242$			770.474i			0.204661i
$243$	773.480	+	3708.19i	0.204192	+	0.978931i
$244$			2364.73i			0.620437i
$245$	13.6968	−	1094.15i	0.00357167	−	0.285318i
$246$	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	$-0.134313\pi$
$251$	7255.60			1.82458			0.912290	+	0.409545i	$0.134313\pi$
$252$	−3130.63	−	588.467i	−0.782585	−	0.147103i
$253$	−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	$-0.872484\pi$
$257$	−505.462	+	875.487i	−0.122684	+	0.212496i	0.798141	+	0.602471i	$0.205817\pi$
$258$	−1021.81	+	1950.93i	−0.246570	+	0.470773i
$259$	−215.874	−	826.306i	−0.0517907	−	0.198240i
$260$		−	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	−0.140971	−	0.990014i	$-0.545022\pi$
$263$	2754.95	−	1590.57i	0.645921	−	0.372923i	0.786892	+	0.617091i	$0.211689\pi$
$264$	−3541.68	+	2243.84i	−0.825663	+	0.523102i
$265$	−649.900	−	375.220i	−0.150653	−	0.0869795i
$266$	−1256.74	+	1241.10i	−0.289682	+	0.286079i
$267$	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	$-0.544411\pi$
$269$	−1227.12			−0.278137			−0.139069	+	0.990283i	$0.544411\pi$
$270$	−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
$273$	7104.23	+	1640.42i	1.57497	+	0.363674i
$274$	−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	0.716736	−	0.697345i	$-0.245635\pi$
$277$	−1132.04	−	1960.75i	−0.245551	−	0.425306i	−0.962286	+	0.272039i	$0.912302\pi$
$278$	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	−0.405949	−	0.913896i	$-0.633059\pi$
$281$	859.806	−	496.409i	0.182533	−	0.105385i	0.588482	+	0.808510i	$0.299726\pi$
$282$	1047.32	−	1999.63i	0.221159	−	0.422255i
$283$	−4936.03	−	2849.82i	−1.03681	−	0.598601i	−0.117880	−	0.993028i	$-0.537610\pi$
$283$	−4936.03	−	2849.82i	−1.03681	−	0.598601i	−0.918927	+	0.394427i	$0.870943\pi$
$284$	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	$-0.762261\pi$
$293$	1110.55	−	1923.52i	0.221429	−	0.383527i	0.955242	+	0.295825i	$0.0955944\pi$
$294$	2002.15	+	1080.79i	0.397170	+	0.214397i
$295$	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
$301$	−4375.02	+	4320.60i	−0.837781	+	0.827359i
$302$	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	$-0.0901690\pi$
$308$	−5020.65	+	1311.66i	−0.928826	+	0.242658i
$309$	−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	$-0.758993\pi$
$311$	1269.29	−	2198.47i	0.231430	−	0.400848i	0.958229	+	0.286002i	$0.0923264\pi$
$312$	6397.76	+	3350.86i	1.16090	+	0.608030i
$313$	−4916.75	+	2838.69i	−0.887895	+	0.512627i	−0.873253	−	0.487266i	$-0.837994\pi$
$313$	−4916.75	+	2838.69i	−0.887895	+	0.512627i	−0.0146418	+	0.999893i	$0.504661\pi$
$314$	−4171.05			−0.749636
$315$	−1567.80	−	294.700i	−0.280429	−	0.0527125i
$316$	135.931			0.0241984
$317$	6662.61	−	3846.66i	1.18047	−	0.681545i	0.224347	−	0.974509i	$-0.427975\pi$
$317$	6662.61	−	3846.66i	1.18047	−	0.681545i	0.956123	+	0.292964i	$0.0946416\pi$
$318$	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
$322$	321.938	+	1232.29i	0.0557172	+	0.213270i
$323$		−	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
$329$	4484.23	−	4428.45i	0.751440	−	0.742092i
$330$	−786.251	+	498.132i	−0.131157	+	0.0830947i
$331$	852.222	+	1476.09i	0.141518	+	0.245116i	0.928068	−	0.372410i	$-0.121468\pi$
$331$	852.222	+	1476.09i	0.141518	+	0.245116i	−0.786551	+	0.617526i	$0.788135\pi$
$332$	−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
$336$	−1938.48	−	1807.80i	−0.314740	−	0.293522i
$337$	3770.46	−	6530.62i	0.609466	−	1.05563i	−0.381863	−	0.924219i	$-0.624717\pi$
$337$	3770.46	−	6530.62i	0.609466	−	1.05563i	0.991329	−	0.131407i	$-0.0419493\pi$
$338$	−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	0.369114	−	0.929384i	$-0.379661\pi$
$347$	−1623.73	−	937.459i	−0.251199	−	0.145030i	−0.620313	+	0.784354i	$0.712995\pi$
$348$	1005.61	−	41.3818i	0.154904	−	0.00637442i
$349$	−1501.48	+	866.879i	−0.230293	+	0.132960i	−0.610707	−	0.791856i	$-0.709115\pi$
$349$	−1501.48	+	866.879i	−0.230293	+	0.132960i	0.380414	+	0.924816i	$0.375781\pi$
$350$	−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	−0.966526	−	0.256567i	$-0.917409\pi$
$353$	−4678.78	−	8103.88i	−0.705457	−	1.22189i	0.261070	−	0.965320i	$-0.415925\pi$
$354$	−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
$357$	−9661.05	+	2953.28i	−1.43226	+	0.437827i
$358$	−1019.60	−	1765.99i	−0.150523	−	0.260714i
$359$			11558.3i			1.69923i	0.527401	+	0.849616i	$0.323167\pi$
$359$			11558.3i			1.69923i	−0.527401	+	0.849616i	$0.676833\pi$
$360$	−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
$364$	6280.96	+	6360.08i	0.904428	+	0.915821i
$365$	−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	$-0.466711\pi$
$367$	7156.41	−	4131.76i	1.01788	−	0.587673i	0.913489	+	0.406864i	$0.133378\pi$
$368$		−	1483.79i		−	0.210184i
$369$	4915.53	−	10404.9i	0.693475	−	1.46791i
$370$		−	187.802i		−	0.0263875i
$371$	4215.10	−	1101.20i	0.589857	−	0.154101i
$372$	−2275.32	−	3591.36i	−0.317123	−	0.500547i
$373$	4591.28	−	7952.33i	0.637339	−	1.10390i	−0.348676	−	0.937243i	$-0.613369\pi$
$373$	4591.28	−	7952.33i	0.637339	−	1.10390i	0.986014	−	0.166660i	$-0.0532981\pi$
$374$	−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
$378$	2055.31	−	2603.48i	0.279666	−	0.354255i
$379$	−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	$-0.996432\pi$
$383$	−3674.74	+	6364.84i	−0.490262	+	0.849159i	0.509675	+	0.860367i	$0.329766\pi$
$384$	−4005.04	−	6321.55i	−0.532243	−	0.840091i
$385$	−2514.30	+	656.867i	−0.332833	+	0.0869534i
$386$		−	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	−0.765356	−	0.643607i	$-0.777437\pi$
$389$	−4531.66	+	2616.35i	−0.590653	+	0.341014i	0.174702	+	0.984621i	$0.444104\pi$
$390$	1420.30	+	743.890i	0.184410	+	0.0965855i
$391$	−4897.52	−	2827.59i	−0.633448	−	0.365722i
$392$	3077.71	+	5488.27i	0.396551	+	0.707142i
$393$	−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
$399$	2101.70	+	6875.28i	0.263701	+	0.862643i
$400$	1581.31	−	2738.91i	0.197664	−	0.342364i
$401$	−6480.01	−	3741.24i	−0.806974	−	0.465906i	0.0389302	−	0.999242i	$-0.487605\pi$
$401$	−6480.01	−	3741.24i	−0.806974	−	0.465906i	−0.845904	+	0.533335i	$0.820938\pi$
$402$	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	$-0.0911609\pi$
$409$	9878.34	+	5703.26i	1.19426	+	0.689506i	0.234990	+	0.971998i	$0.424494\pi$
$410$	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	$-0.718507\pi$
$419$	3027.27	−	5243.38i	0.352964	−	0.611351i	0.986767	+	0.162143i	$0.0518406\pi$
$420$	−1430.28	−	1333.86i	−0.166168	−	0.154966i
$421$	−3434.60	−	5948.91i	−0.397606	−	0.688674i	0.595824	−	0.803115i	$-0.296826\pi$
$421$	−3434.60	−	5948.91i	−0.397606	−	0.688674i	−0.993430	+	0.114441i	$0.963492\pi$
$422$			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
$427$	−4830.79	−	4891.64i	−0.547490	−	0.554386i
$428$	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	$0.142799\pi$
$431$			7761.64i			0.867436i	−0.901049	+	0.433718i	$0.857201\pi$
$432$	−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	$0.863854\pi$
$434$	767.567	+	2938.03i	0.0848950	+	0.324954i
$435$	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	$-0.682738\pi$
$439$	−804.050	+	464.219i	−0.0874151	+	0.0504691i	0.455655	+	0.890156i	$0.349405\pi$
$440$	−2574.10			−0.278898
$441$	7678.11	−	5178.11i	0.829080	−	0.559131i
$442$	10153.4			1.09265
$443$	4799.04	−	2770.72i	0.514693	−	0.297158i	−0.220068	−	0.975485i	$-0.570628\pi$
$443$	4799.04	−	2770.72i	0.514693	−	0.297158i	0.734761	+	0.678326i	$0.237294\pi$
$444$	−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
$448$	55.6653	+	213.071i	0.00587039	+	0.0224702i
$449$		−	13088.2i		−	1.37566i	−0.725873	−	0.687829i	$-0.758564\pi$
$449$		−	13088.2i		−	1.37566i	0.725873	−	0.687829i	$-0.241436\pi$
$450$	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
$455$	3145.45	+	3185.08i	0.324090	+	0.328173i
$456$	292.801	+	7115.28i	0.0300694	+	0.730710i
$457$	5771.25	+	9996.10i	0.590739	+	1.02319i	0.994133	+	0.108164i	$0.0344971\pi$
$457$	5771.25	+	9996.10i	0.590739	+	1.02319i	−0.403394	+	0.915026i	$0.632170\pi$
$458$	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	$-0.0143651\pi$
$461$	4557.29	+	7893.46i	0.460421	+	0.797473i	−0.538561	+	0.842587i	$0.681032\pi$
$462$	1215.70	−	5264.89i	0.122424	−	0.530184i
$463$	−1592.53	+	2758.34i	−0.159851	+	0.276871i	−0.934815	−	0.355135i	$-0.884435\pi$
$463$	−1592.53	+	2758.34i	−0.159851	+	0.276871i	0.774964	+	0.632006i	$0.217768\pi$
$464$	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	$-0.515700\pi$
$467$	−995.144			−0.0986077			−0.0493038	+	0.998784i	$0.515700\pi$
$468$	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	0.979803	+	0.199964i	$0.0640825\pi$
$479$	6951.30	+	12040.0i	0.663075	+	1.14848i	−0.316728	+	0.948516i	$0.602584\pi$
$480$	−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
$483$	5051.27	+	1166.38i	0.475861	+	0.109880i
$484$	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
$490$	683.250	+	1218.39i	0.0629920	+	0.112329i
$491$	14278.7	+	8243.83i	1.31240	+	0.757717i	0.982494	−	0.186296i	$-0.0596482\pi$
$491$	14278.7	+	8243.83i	1.31240	+	0.757717i	0.329910	+	0.944012i	$0.392982\pi$
$492$	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
$497$	−17465.2	+	4562.82i	−1.57630	+	0.411812i
$498$	1038.21	−	1982.25i	0.0934207	−	0.178367i
$499$	1546.08	−	2677.88i	0.138701	−	0.240237i	−0.788304	−	0.615286i	$-0.789041\pi$
$499$	1546.08	−	2677.88i	0.138701	−	0.240237i	0.927005	+	0.375049i	$0.122374\pi$
$500$	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	$-0.419808\pi$
$503$	5624.21			0.498551			0.249275	+	0.968433i	$0.419808\pi$
$504$	8654.95	−	3040.13i	0.764925	−	0.268687i
$505$	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	$-0.772705\pi$
$509$	2174.06	−	3765.58i	0.189319	−	0.327910i	0.945023	+	0.327003i	$0.106039\pi$
$510$	−2219.62	+	91.3393i	−0.192718	+	0.00793053i
$511$	10326.6	−	2697.85i	0.893977	−	0.233553i
$512$		−	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
$518$	766.088	+	775.739i	0.0649807	+	0.0657992i
$519$	−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	$-0.254382\pi$
$521$	16584.8			1.39461			0.697305	+	0.716774i	$0.254382\pi$
$522$	−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
$525$	8081.06	+	7536.28i	0.671784	+	0.626496i
$526$	−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
$546$	−8901.22	+	2721.01i	−0.697687	+	0.213275i
$547$	226.704	+	392.663i	0.0177206	+	0.0306929i	0.874750	−	0.484575i	$-0.161026\pi$
$547$	226.704	+	392.663i	0.0177206	+	0.0306929i	−0.857029	+	0.515268i	$0.827692\pi$
$548$			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
$553$	−281.183	+	277.685i	−0.0216223	+	0.0213533i
$554$	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	$-0.737252\pi$
$557$		−	19320.2i		−	1.46970i	0.678229	−	0.734850i	$-0.262748\pi$
$558$	4412.04	−	363.735i	0.334725	−	0.0275952i
$559$		−	25154.5i		−	1.90326i
$560$	−411.347	−	1574.52i	−0.0310403	−	0.118814i
$561$	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	$-0.858110\pi$
$563$	−1038.78	+	1799.22i	−0.0777608	+	0.134686i	0.824523	+	0.565829i	$0.191444\pi$
$564$	−463.138	−	11254.6i	−0.0345774	−	0.840257i
$565$	−2003.26	+	1156.58i	−0.149164	+	0.0861201i
$566$	7276.09			0.540348
$567$	−5505.92	−	12327.6i	−0.407807	−	0.913068i
$568$	−17880.5			−1.32086
$569$	16935.0	−	9777.42i	1.24772	−	0.720370i	0.277064	−	0.960851i	$-0.410639\pi$
$569$	16935.0	−	9777.42i	1.24772	−	0.720370i	0.970654	+	0.240481i	$0.0773052\pi$
$570$	65.0016	+	1579.59i	0.00477652	+	0.116073i
$571$	−3001.96	+	5199.54i	−0.220014	+	0.381075i	−0.954812	−	0.297211i	$-0.903944\pi$
$571$	−3001.96	+	5199.54i	−0.220014	+	0.381075i	0.734798	+	0.678286i	$0.237277\pi$
$572$	10614.2	−	18384.4i	0.775879	−	1.34386i
$573$	10447.7	+	16490.7i	0.761711	+	1.20228i
$574$	−9749.51	+	2547.08i	−0.708949	+	0.185215i
$575$			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
$581$	4445.27	−	4389.97i	0.317420	−	0.313471i
$582$	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	0.963175	+	0.268875i	$0.0866519\pi$
$587$	10160.7	+	17598.8i	0.714440	+	1.23745i	−0.248735	+	0.968572i	$0.580015\pi$
$588$	11349.1	−	324.787i	0.795964	−	0.0227789i
$589$	−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	$-0.902104\pi$
$593$	−27525.8			−1.90616			−0.953078	+	0.302725i	$0.902104\pi$
$594$	−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	−0.252699	−	0.967545i	$-0.581318\pi$
$599$	−17841.0	−	10300.5i	−1.21697	−	0.702616i	−0.964268	+	0.264929i	$0.914652\pi$
$600$	5857.75	+	9245.86i	0.398569	+	0.629101i
$601$	13383.7	−	7727.08i	0.908374	−	0.524450i	0.0284661	−	0.999595i	$-0.490938\pi$
$601$	13383.7	−	7727.08i	0.908374	−	0.524450i	0.879907	+	0.475145i	$0.157604\pi$
$602$	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	$-0.0308585\pi$
$607$	21073.4	+	12166.7i	1.40913	+	0.813562i	0.413827	+	0.910356i	$0.364192\pi$
$608$	−6795.40	+	11770.0i	−0.453273	+	0.785091i
$609$	−1995.65	+	2139.91i	−0.132788	+	0.142387i
$610$	−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
$616$	10632.6	−	10500.3i	0.695455	−	0.686803i
$617$	17506.0	+	10107.1i	1.14224	+	0.659475i	0.946986	−	0.321276i	$-0.104112\pi$
$617$	17506.0	+	10107.1i	1.14224	+	0.659475i	0.195259	+	0.980752i	$0.437445\pi$
$618$	−12.1905	−	296.239i	−0.000793487	−	0.0192824i
$619$	14613.8	−	8437.29i	0.948915	−	0.547857i	0.0561715	−	0.998421i	$-0.482111\pi$
$619$	14613.8	−	8437.29i	0.948915	−	0.547857i	0.892744	+	0.450565i	$0.148777\pi$
$620$		−	2610.21i		−	0.169078i
$621$	2944.66	−	6960.59i	0.190282	−	0.449789i
$622$			3240.71i			0.208908i
$623$	−4793.99	−	18350.0i	−0.308294	−	1.18006i
$624$	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
$630$	1921.39	−	674.907i	0.121508	−	0.0426809i
$631$	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
$637$	−25985.3	−	325.289i	−1.61629	−	0.0202330i
$638$			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	−0.0122166	−	0.999925i	$-0.503889\pi$
$641$	13756.1	−	7942.11i	0.847636	−	0.489383i	0.859852	+	0.510543i	$0.170555\pi$
$642$	−2898.02	+	1836.05i	−0.178155	+	0.112871i
$643$	−1909.66	−	1102.54i	−0.117122	−	0.0676206i	0.440294	−	0.897853i	$-0.354874\pi$
$643$	−1909.66	−	1102.54i	−0.117122	−	0.0676206i	−0.557417	+	0.830233i	$0.688207\pi$
$644$	4465.91	+	4522.16i	0.273263	+	0.276705i
$645$	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	$-0.465262\pi$
$647$	3584.90			0.217831			0.108916	+	0.994051i	$0.465262\pi$
$648$	−2190.18	−	13192.9i	−0.132775	−	0.799796i
$649$			23935.1i			1.44767i
$650$	−5552.86	−	9617.83i	−0.335078	−	0.580373i
$651$	12043.3	+	2780.89i	0.725058	+	0.167422i
$652$	−2196.05	+	3803.66i	−0.131908	+	0.228471i
$653$	−394.355	−	227.681i	−0.0236329	−	0.0136445i	0.488137	−	0.872767i	$-0.337677\pi$
$653$	−394.355	−	227.681i	−0.0236329	−	0.0136445i	−0.511770	+	0.859123i	$0.671010\pi$
$654$	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	−0.212291	−	0.977207i	$-0.568092\pi$
$659$	8929.73	−	5155.58i	0.527850	−	0.304754i	0.740140	+	0.672452i	$0.234759\pi$
$660$	−2154.96	+	4114.45i	−0.127094	+	0.242659i
$661$	−7083.52	−	4089.67i	−0.416818	−	0.240650i	0.276897	−	0.960900i	$-0.410694\pi$
$661$	−7083.52	−	4089.67i	−0.416818	−	0.240650i	−0.693715	+	0.720250i	$0.744027\pi$
$662$	−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
$672$	17058.2	+	3938.88i	0.979219	+	0.226109i
$673$	11433.9	+	19804.0i	0.654893	+	1.13431i	0.981921	+	0.189293i	$0.0606195\pi$
$673$	11433.9	+	19804.0i	0.654893	+	1.13431i	−0.327028	+	0.945015i	$0.606047\pi$
$674$			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	$-0.211296\pi$
$677$	−2461.68	−	4263.75i	−0.139749	−	0.242052i	−0.927401	+	0.374067i	$0.877963\pi$
$678$	−197.758	−	4805.67i	−0.0112018	−	0.272214i
$679$	954.993	+	967.023i	0.0539754	+	0.0546553i
$680$	−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	$0.139956\pi$
$683$			15195.6i			0.851310i	−0.904885	+	0.425655i	$0.860044\pi$
$684$	11618.2	+	5488.71i	0.649464	+	0.306822i
$685$			1924.43i			0.107341i
$686$	−7792.36	−	2245.58i	−0.433693	−	0.124981i
$687$	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	$-0.618469\pi$
$691$	4745.60	−	2739.88i	0.261261	−	0.150839i	0.624910	+	0.780697i	$0.285136\pi$
$692$	−7816.39			−0.429385
$693$	−16687.8	−	14326.3i	−0.914744	−	0.785298i
$694$	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
$700$	3424.20	+	13106.9i	0.184889	+	0.707704i
$701$		−	5356.09i		−	0.288583i	−0.989535	−	0.144292i	$-0.953910\pi$
$701$		−	5356.09i		−	0.288583i	0.989535	−	0.144292i	$-0.0460903\pi$
$702$	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
$707$	−11658.9	+	11513.9i	−0.620197	+	0.612482i
$708$	−15216.4	+	9640.38i	−0.807720	+	0.511734i
$709$	−6540.71	−	11328.8i	−0.346462	−	0.600090i	0.639156	−	0.769077i	$-0.279284\pi$
$709$	−6540.71	−	11328.8i	−0.346462	−	0.600090i	−0.985618	+	0.168987i	$0.945950\pi$
$710$	−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
$714$	8795.79	−	9431.62i	0.461028	−	0.494355i
$715$	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	$-0.596807\pi$
$719$	−11546.9			−0.598925			−0.299463	+	0.954108i	$0.596807\pi$
$720$	−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	$-0.590773\pi$
$727$	8018.50	−	4629.49i	0.409064	−	0.236173i	0.690388	+	0.723440i	$0.257440\pi$
$728$	−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	0.998185	+	0.0602216i	$0.0191808\pi$
$733$	30748.8	+	17752.8i	1.54943	+	0.894564i	0.551246	+	0.834343i	$0.314153\pi$
$734$	−5274.55	+	9135.79i	−0.265242	+	0.459412i
$735$	5683.51	−	162.651i	0.285224	−	0.00816253i
$736$	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
$742$	−3957.14	+	3907.92i	−0.195783	+	0.193348i
$743$	9171.95	+	5295.43i	0.452875	+	0.261468i	0.709044	−	0.705164i	$-0.249127\pi$
$743$	9171.95	+	5295.43i	0.452875	+	0.261468i	−0.256168	+	0.966632i	$0.582460\pi$
$744$	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
$749$	−9267.39	+	2421.13i	−0.452100	+	0.118112i
$750$	2716.10	+	4287.08i	0.132237	+	0.208723i
$751$	−2521.66	+	4367.64i	−0.122525	+	0.212220i	−0.920763	−	0.390123i	$-0.872433\pi$
$751$	−2521.66	+	4367.64i	−0.122525	+	0.212220i	0.798238	+	0.602343i	$0.205766\pi$
$752$	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
$756$	2386.33	−	16379.2i	0.114802	−	0.787971i
$757$	−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	$-0.985984\pi$
$761$	−9686.08	+	16776.8i	−0.461393	+	0.799157i	0.537637	+	0.843176i	$0.319317\pi$
$762$	2014.67	+	3179.95i	0.0957792	+	0.151178i
$763$	185.620	+	710.502i	0.00880722	+	0.0337116i
$764$			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	$-0.324860\pi$
$769$	983.118	+	567.603i	0.0461016	+	0.0266168i	−0.476772	+	0.879027i	$0.658193\pi$
$770$	2360.43	−	2331.07i	0.110473	−	0.109099i
$771$	−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	$-0.536060\pi$
$773$	−4858.97			−0.226087			−0.113043	+	0.993590i	$0.536060\pi$
$774$	−10347.0	−	4888.18i	−0.480513	−	0.227005i
$775$			14747.6i			0.683550i
$776$	673.118	+	1165.87i	0.0311385	+	0.0539335i
$777$	4243.86	−	1297.30i	0.195943	−	0.0598977i
$778$	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	$-0.280555\pi$
$787$	6311.59	+	3644.00i	0.285875	+	0.165050i	−0.350205	+	0.936673i	$0.613888\pi$
$788$	−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	$-0.762640\pi$
$797$	4956.07	−	8584.16i	0.220267	−	0.381514i	0.954889	+	0.296963i	$0.0959738\pi$
$798$	−6712.01	−	6259.52i	−0.297748	−	0.277675i
$799$	−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
$805$	2236.49	+	2264.66i	0.0979204	+	0.0991539i
$806$	−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	$0.333824\pi$
$809$			39890.5i			1.73359i	−0.498664	+	0.866795i	$0.666176\pi$
$810$	−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	$-0.124007\pi$
$812$	−3470.77	+	906.746i	−0.150000	+	0.0391879i
$813$	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
$819$	−6998.89	+	37233.9i	−0.298609	+	1.58859i
$820$	8661.67			0.368876
$821$	−869.844	+	502.205i	−0.0369766	+	0.0213484i	−0.518374	−	0.855154i	$-0.673463\pi$
$821$	−869.844	+	502.205i	−0.0369766	+	0.0213484i	0.481398	+	0.876502i	$0.340129\pi$
$822$	−3544.69	−	1856.55i	−0.150408	−	0.0787769i
$823$	404.664	−	700.898i	0.0171394	−	0.0296862i	−0.857329	−	0.514770i	$-0.827877\pi$
$823$	404.664	−	700.898i	0.0171394	−	0.0296862i	0.874468	+	0.485083i	$0.161211\pi$
$824$	409.982	−	710.110i	0.0173330	−	0.0300217i
$825$	12175.5	−	23246.6i	0.513815	−	0.981020i
$826$	12448.2	−	3252.13i	0.524370	−	0.136993i
$827$		−	27558.4i		−	1.15877i	−0.815056	−	0.579383i	$-0.803294\pi$
$827$		−	27558.4i		−	1.15877i	0.815056	−	0.579383i	$-0.196706\pi$
$828$	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
$833$	31406.0	−	17611.8i	1.30631	−	0.732549i
$834$	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	$-0.306542\pi$
$839$	−10338.7	−	17907.2i	−0.425425	−	0.736859i	−0.996460	+	0.0840675i	$0.973209\pi$
$840$	5487.63	+	1267.14i	0.225406	+	0.0520481i
$841$	−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	$-0.761591\pi$
$853$	−12678.1	+	7319.71i	−0.508899	+	0.293813i	0.223482	+	0.974708i	$0.428258\pi$
$854$	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	$-0.235246\pi$
$857$	−5363.52	−	9289.90i	−0.213786	−	0.370288i	−0.952896	+	0.303296i	$0.901913\pi$
$858$	11830.2	+	18672.8i	0.470720	+	0.742984i
$859$	−37326.6	−	21550.5i	−1.48262	−	0.855988i	−0.482810	−	0.875725i	$-0.660384\pi$
$859$	−37326.6	−	21550.5i	−1.48262	−	0.855988i	−0.999805	+	0.0197364i	$0.993717\pi$
$860$	−3373.63	+	5843.29i	−0.133767	+	0.231691i
$861$	−9228.04	+	39964.2i	−0.365262	+	1.58185i
$862$	−4954.21	−	8580.94i	−0.195755	−	0.339058i
$863$		−	2755.10i		−	0.108673i	−0.998523	−	0.0543363i	$-0.982696\pi$
$863$		−	2755.10i		−	0.108673i	0.998523	−	0.0543363i	$-0.0173043\pi$
$864$	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
$868$	10647.6	+	10781.8i	0.416365	+	0.421609i
$869$	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
$875$	3581.61	+	13709.4i	0.138378	+	0.529671i
$876$	8850.76	−	16898.6i	0.341369	−	0.651772i
$877$	14479.0	−	25078.4i	0.557494	−	0.965609i	−0.440210	−	0.897895i	$-0.645096\pi$
$877$	14479.0	−	25078.4i	0.557494	−	0.965609i	0.997705	−	0.0677140i	$-0.0215705\pi$
$878$	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	$-0.208133\pi$
$881$	41511.7			1.58747			0.793737	+	0.608261i	$0.208133\pi$
$882$	−5183.44	+	10625.6i	−0.197886	+	0.405649i
$883$	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	0.240302	+	0.970698i	$0.422754\pi$
$887$	−19033.5	+	32967.0i	−0.720499	+	1.24794i	−0.960800	+	0.277242i	$0.910580\pi$
$888$	4392.01	−	180.735i	0.165975	−	0.00683004i
$889$	2656.67	+	10169.0i	0.100227	+	0.383640i
$890$		−	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
$896$	18742.1	+	18978.2i	0.698805	+	0.707607i
$897$	−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
$903$	−23366.2	−	21791.0i	−0.861106	−	0.803055i
$904$	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	0.999688	−	0.0249790i	$-0.00795188\pi$
$907$	13062.6	+	22625.2i	0.478212	+	0.828287i	−0.521476	+	0.853266i	$0.674619\pi$
$908$	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	−0.223532	−	0.974696i	$-0.571759\pi$
$911$	13990.6	−	8077.47i	0.508813	−	0.293763i	0.732346	+	0.680933i	$0.238426\pi$
$912$	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
$924$	−7882.45	−	25785.8i	−0.280642	−	0.918063i
$925$	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	$-0.000883805\pi$
$929$	14089.6	+	24403.9i	0.497594	+	0.861857i	−0.502403	+	0.864634i	$0.667550\pi$
$930$	2407.73	+	1261.06i	0.0848952	+	0.0444644i
$931$	−12533.4	−	22350.0i	−0.441210	−	0.786781i
$932$	−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	$-0.0571711\pi$
$938$	−2440.68	+	637.632i	−0.0849584	+	0.0221956i
$939$	−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	$-0.744480\pi$
$941$	7953.42	−	13775.7i	0.275530	−	0.477232i	0.970269	+	0.242030i	$0.0778132\pi$
$942$	−891.126	−	21655.1i	−0.0308221	−	0.749002i
$943$	−19884.0	+	11480.0i	−0.686652	+	0.396439i
$944$	−14988.8			−0.516784
$945$	1195.06	−	8202.57i	0.0411378	−	0.282360i
$946$	−18641.8			−0.640694
$947$	−28572.1	+	16496.1i	−0.980432	+	0.566053i	−0.902401	−	0.430898i	$-0.858197\pi$
$947$	−28572.1	+	16496.1i	−0.980432	+	0.566053i	−0.0780317	+	0.996951i	$0.524864\pi$
$948$	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
$952$	34508.1	−	9015.33i	1.17481	−	0.306921i
$953$		−	37129.3i		−	1.26205i	−0.775761	−	0.631027i	$-0.782634\pi$
$953$		−	37129.3i		−	1.26205i	0.775761	−	0.631027i	$-0.217366\pi$
$954$	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
$959$	−7850.20	−	7949.09i	−0.264334	−	0.267664i
$960$	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
$966$	−6328.97	+	1934.70i	−0.210798	+	0.0644389i
$967$	−31.4682	+	54.5045i	−0.00104648	+	0.00181256i	−0.866548	−	0.499093i	$-0.833666\pi$
$967$	−31.4682	+	54.5045i	−0.00104648	+	0.00181256i	0.865502	+	0.500906i	$0.167000\pi$
$968$	−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	$-0.353999\pi$
$971$	26793.4			0.885521			0.442761	+	0.896640i	$0.353999\pi$
$972$	−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	0.826140	−	0.563465i	$-0.190532\pi$
$977$	22941.3	+	13245.2i	0.751235	+	0.433726i	−0.0749048	+	0.997191i	$0.523865\pi$
$978$	−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	$-0.293356\pi$
$983$	−11945.2	−	20689.7i	−0.387582	−	0.671313i	−0.992124	+	0.125261i	$0.960023\pi$
$984$	−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
$987$	23949.5	+	22334.9i	0.772361	+	0.720293i
$988$	−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
$994$	16396.4	−	16192.4i	0.523200	−	0.516692i
$995$	−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	$-0.661680\pi$
$997$	854.102	−	493.116i	0.0271311	−	0.0156641i	0.513504	+	0.858087i	$0.328347\pi$
$998$			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.41.10	yes	44
3.2	odd	2		189.4.o.a.125.14		44
7.6	odd	2	inner	63.4.o.a.41.9	yes	44
9.2	odd	6	inner	63.4.o.a.20.9	✓	44
9.4	even	3		567.4.c.c.566.19		44
9.5	odd	6		567.4.c.c.566.26		44
9.7	even	3		189.4.o.a.62.13		44
21.20	even	2		189.4.o.a.125.13		44
63.13	odd	6		567.4.c.c.566.25		44
63.20	even	6	inner	63.4.o.a.20.10	yes	44
63.34	odd	6		189.4.o.a.62.14		44
63.41	even	6		567.4.c.c.566.20		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.o.a.20.9	✓	44	9.2	odd	6	inner
63.4.o.a.20.10	yes	44	63.20	even	6	inner
63.4.o.a.41.9	yes	44	7.6	odd	2	inner
63.4.o.a.41.10	yes	44	1.1	even	1	trivial
189.4.o.a.62.13		44	9.7	even	3
189.4.o.a.62.14		44	63.34	odd	6
189.4.o.a.125.13		44	21.20	even	2
189.4.o.a.125.14		44	3.2	odd	2
567.4.c.c.566.19		44	9.4	even	3
567.4.c.c.566.20		44	63.41	even	6
567.4.c.c.566.25		44	63.13	odd	6
567.4.c.c.566.26		44	9.5	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:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	63.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.10556 + 0.638294i) q^{2} +(0.213646 + 5.19176i) q^{3} +(-3.18516 + 5.51686i) q^{4} +(-1.59510 + 2.76280i) q^{5} +(-3.55007 - 5.60342i) q^{6} +(-4.68134 - 17.9188i) q^{7} -18.3450i q^{8} +(-26.9087 + 2.21839i) q^{9} +O(q^{10})\)	\(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} +(-4.68134 - 17.9188i) 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} +(16.6130 + 16.8223i) 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} +(92.0302 - 28.1327i) 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} +(-83.7878 + 89.8447i) 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} +(-299.170 + 167.768i) 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} +(-328.721 + 85.8791i) 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} +(165.720 + 471.788i) 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} +(-72.9759 + 19.0651i) 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} +(572.382 + 579.592i) 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} +(-137.927 + 597.325i) 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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