LMFDB - Embedded newform 63.4.o.a.20.17

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			20.17
Character	$\chi$	$=$	63.20
Dual form			63.4.o.a.41.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.59186 + 1.49641i) q^{2} +(-1.03772 - 5.09148i) q^{3} +(0.478502 + 0.828790i) q^{4} +(-7.80147 - 13.5125i) q^{5} +(4.92933 - 14.7493i) q^{6} +(17.7116 + 5.41283i) q^{7} -21.0785i q^{8} +(-24.8463 + 10.5670i) q^{9} +O(q^{10})$	\(q+(2.59186 + 1.49641i) q^{2} +(-1.03772 - 5.09148i) q^{3} +(0.478502 + 0.828790i) q^{4} +(-7.80147 - 13.5125i) q^{5} +(4.92933 - 14.7493i) q^{6} +(17.7116 + 5.41283i) q^{7} -21.0785i q^{8} +(-24.8463 + 10.5670i) q^{9} -46.6969i q^{10} +(46.4700 + 26.8295i) q^{11} +(3.72322 - 3.29633i) q^{12} +(-29.1434 + 16.8260i) q^{13} +(37.8062 + 40.5332i) q^{14} +(-60.7031 + 53.7432i) q^{15} +(35.3701 - 61.2628i) q^{16} +43.5488 q^{17} +(-80.2108 - 9.79199i) q^{18} +32.2524i q^{19} +(7.46605 - 12.9316i) q^{20} +(9.17965 - 95.7953i) q^{21} +(80.2960 + 139.077i) q^{22} +(129.309 - 74.6565i) q^{23} +(-107.320 + 21.8735i) q^{24} +(-59.2260 + 102.582i) q^{25} -100.714 q^{26} +(79.5852 + 115.539i) q^{27} +(3.98894 + 17.2693i) q^{28} +(-127.390 - 73.5487i) q^{29} +(-237.756 + 48.4582i) q^{30} +(-61.1678 + 35.3153i) q^{31} +(37.3130 - 21.5427i) q^{32} +(88.3790 - 264.443i) q^{33} +(112.873 + 65.1670i) q^{34} +(-65.0355 - 281.557i) q^{35} +(-20.6469 - 15.5360i) q^{36} +40.3540 q^{37} +(-48.2629 + 83.5938i) q^{38} +(115.912 + 130.922i) q^{39} +(-284.824 + 164.443i) q^{40} +(179.454 + 310.824i) q^{41} +(167.142 - 234.552i) q^{42} +(-253.886 + 439.743i) q^{43} +51.3519i q^{44} +(336.625 + 253.298i) q^{45} +446.867 q^{46} +(228.160 - 395.185i) q^{47} +(-348.622 - 116.513i) q^{48} +(284.402 + 191.740i) q^{49} +(-307.011 + 177.253i) q^{50} +(-45.1914 - 221.728i) q^{51} +(-27.8904 - 16.1025i) q^{52} -213.420i q^{53} +(33.3805 + 418.553i) q^{54} -837.238i q^{55} +(114.094 - 373.333i) q^{56} +(164.212 - 33.4689i) q^{57} +(-220.118 - 381.256i) q^{58} +(-159.593 - 276.424i) q^{59} +(-73.5884 - 24.5939i) q^{60} +(303.662 + 175.319i) q^{61} -211.385 q^{62} +(-497.265 + 52.6705i) q^{63} -436.974 q^{64} +(454.723 + 262.535i) q^{65} +(624.782 - 553.148i) q^{66} +(-289.258 - 501.009i) q^{67} +(20.8382 + 36.0928i) q^{68} +(-514.298 - 580.900i) q^{69} +(252.762 - 827.077i) q^{70} +787.243i q^{71} +(222.737 + 523.721i) q^{72} +146.373i q^{73} +(104.592 + 60.3863i) q^{74} +(583.756 + 195.096i) q^{75} +(-26.7305 + 15.4329i) q^{76} +(677.836 + 726.728i) q^{77} +(104.513 + 512.785i) q^{78} +(-193.095 + 334.451i) q^{79} -1103.76 q^{80} +(505.676 - 525.103i) q^{81} +1074.15i q^{82} +(-98.9043 + 171.307i) q^{83} +(83.7867 - 38.2302i) q^{84} +(-339.745 - 588.455i) q^{85} +(-1316.07 + 759.835i) q^{86} +(-242.276 + 724.926i) q^{87} +(565.524 - 979.517i) q^{88} -596.020 q^{89} +(493.448 + 1160.24i) q^{90} +(-607.253 + 140.267i) q^{91} +(123.749 + 71.4466i) q^{92} +(243.282 + 274.787i) q^{93} +(1182.72 - 682.844i) q^{94} +(435.812 - 251.616i) q^{95} +(-148.404 - 167.623i) q^{96} +(631.485 + 364.588i) q^{97} +(450.210 + 922.547i) q^{98} +(-1438.12 - 175.563i) 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 $

$2$	2.59186	+	1.49641i	0.916362	+	0.529062i	0.882473	−	0.470364i	$-0.155877\pi$
$2$	2.59186	+	1.49641i	0.916362	+	0.529062i	0.0338893	+	0.999426i	$0.489211\pi$
$3$	−1.03772	−	5.09148i	−0.199709	−	0.979855i
$3$	−1.03772	−	5.09148i	−0.199709	−	0.979855i
$4$	0.478502	+	0.828790i	0.0598128	+	0.103599i
$5$	−7.80147	−	13.5125i	−0.697785	−	1.20860i	−0.969233	−	0.246146i	$-0.920836\pi$
$5$	−7.80147	−	13.5125i	−0.697785	−	1.20860i	0.271448	−	0.962453i	$-0.412498\pi$
$6$	4.92933	−	14.7493i	0.335398	−	1.00356i
$7$	17.7116	+	5.41283i	0.956337	+	0.292265i
$7$	17.7116	+	5.41283i	0.956337	+	0.292265i
$8$		−	21.0785i		−	0.931545i
$9$	−24.8463	+	10.5670i	−0.920233	+	0.391372i
$10$		−	46.6969i		−	1.47669i
$11$	46.4700	+	26.8295i	1.27375	+	0.735400i	0.975692	−	0.219148i	$-0.0703277\pi$
$11$	46.4700	+	26.8295i	1.27375	+	0.735400i	0.298058	+	0.954548i	$0.403661\pi$
$12$	3.72322	−	3.29633i	0.0895667	−	0.0792975i
$13$	−29.1434	+	16.8260i	−0.621764	+	0.358976i	−0.777555	−	0.628814i	$-0.783541\pi$
$13$	−29.1434	+	16.8260i	−0.621764	+	0.358976i	0.155791	+	0.987790i	$0.450207\pi$
$14$	37.8062	+	40.5332i	0.721725	+	0.773782i
$15$	−60.7031	+	53.7432i	−1.04490	+	0.925096i
$16$	35.3701	−	61.2628i	0.552658	−	0.957231i
$17$	43.5488			0.621302			0.310651	−	0.950524i	$-0.399453\pi$
$17$	43.5488			0.621302			0.310651	+	0.950524i	$0.399453\pi$
$18$	−80.2108	−	9.79199i	−1.05033	−	0.128222i
$19$			32.2524i			0.389432i	0.980860	+	0.194716i	$0.0623785\pi$
$19$			32.2524i			0.389432i	−0.980860	+	0.194716i	$0.937621\pi$
$20$	7.46605	−	12.9316i	0.0834729	−	0.144579i
$21$	9.17965	−	95.7953i	0.0953888	−	0.995440i
$22$	80.2960	+	139.077i	0.778144	+	1.34778i
$23$	129.309	−	74.6565i	1.17229	−	0.676824i	0.218074	−	0.975932i	$-0.430023\pi$
$23$	129.309	−	74.6565i	1.17229	−	0.676824i	0.954219	+	0.299108i	$0.0966892\pi$
$24$	−107.320	+	21.8735i	−0.912779	+	0.186038i
$25$	−59.2260	+	102.582i	−0.473808	+	0.820659i
$26$	−100.714			−0.759681
$27$	79.5852	+	115.539i	0.567266	+	0.823534i
$28$	3.98894	+	17.2693i	0.0269228	+	0.116557i
$29$	−127.390	−	73.5487i	−0.815715	−	0.470953i	0.0332217	−	0.999448i	$-0.489423\pi$
$29$	−127.390	−	73.5487i	−0.815715	−	0.470953i	−0.848937	+	0.528495i	$0.822757\pi$
$30$	−237.756	+	48.4582i	−1.44694	+	0.294907i
$31$	−61.1678	+	35.3153i	−0.354389	+	0.204607i	−0.666617	−	0.745401i	$-0.732258\pi$
$31$	−61.1678	+	35.3153i	−0.354389	+	0.204607i	0.312228	+	0.950007i	$0.398925\pi$
$32$	37.3130	−	21.5427i	0.206127	−	0.119008i
$33$	88.3790	−	264.443i	0.466206	−	1.39496i
$34$	112.873	+	65.1670i	0.569338	+	0.328707i
$35$	−65.0355	−	281.557i	−0.314086	−	1.35977i
$36$	−20.6469	−	15.5360i	−0.0955873	−	0.0719260i
$37$	40.3540			0.179302			0.0896509	−	0.995973i	$-0.471425\pi$
$37$	40.3540			0.179302			0.0896509	+	0.995973i	$0.471425\pi$
$38$	−48.2629	+	83.5938i	−0.206034	+	0.356861i
$39$	115.912	+	130.922i	0.475916	+	0.537548i
$40$	−284.824	+	164.443i	−1.12586	+	0.650018i
$41$	179.454	+	310.824i	0.683562	+	1.18396i	0.973886	+	0.227036i	$0.0729036\pi$
$41$	179.454	+	310.824i	0.683562	+	1.18396i	−0.290324	+	0.956928i	$0.593763\pi$
$42$	167.142	−	234.552i	0.614060	−	0.861717i
$43$	−253.886	+	439.743i	−0.900400	+	1.55954i	−0.0734235	+	0.997301i	$0.523392\pi$
$43$	−253.886	+	439.743i	−0.900400	+	1.55954i	−0.826976	+	0.562237i	$0.809941\pi$
$44$			51.3519i			0.175945i
$45$	336.625	+	253.298i	1.11514	+	0.839099i
$46$	446.867			1.43233
$47$	228.160	−	395.185i	0.708098	−	1.22646i	−0.257464	−	0.966288i	$-0.582887\pi$
$47$	228.160	−	395.185i	0.708098	−	1.22646i	0.965562	−	0.260174i	$-0.0837800\pi$
$48$	−348.622	−	116.513i	−1.04832	−	0.350357i
$49$	284.402	+	191.740i	0.829162	+	0.559009i
$50$	−307.011	+	177.253i	−0.868359	+	0.501347i
$51$	−45.1914	−	221.728i	−0.124080	−	0.608786i
$52$	−27.8904	−	16.1025i	−0.0743789	−	0.0429427i
$53$		−	213.420i		−	0.553123i	−0.960996	−	0.276561i	$-0.910805\pi$
$53$		−	213.420i		−	0.553123i	0.960996	−	0.276561i	$-0.0891949\pi$
$54$	33.3805	+	418.553i	0.0841205	+	1.05477i
$55$		−	837.238i		−	2.05260i
$56$	114.094	−	373.333i	0.272258	−	0.890871i
$57$	164.212	−	33.4689i	0.381587	−	0.0777731i
$58$	−220.118	−	381.256i	−0.498327	−	0.863127i
$59$	−159.593	−	276.424i	−0.352157	−	0.609954i	0.634470	−	0.772947i	$-0.281218\pi$
$59$	−159.593	−	276.424i	−0.352157	−	0.609954i	−0.986627	+	0.162993i	$0.947885\pi$
$60$	−73.5884	−	24.5939i	−0.158337	−	0.0529176i
$61$	303.662	+	175.319i	0.637375	+	0.367989i	0.783603	−	0.621262i	$-0.213380\pi$
$61$	303.662	+	175.319i	0.637375	+	0.367989i	−0.146227	+	0.989251i	$0.546713\pi$
$62$	−211.385			−0.432998
$63$	−497.265	+	52.6705i	−0.994437	+	0.105331i
$64$	−436.974			−0.853466
$65$	454.723	+	262.535i	0.867715	+	0.500976i
$66$	624.782	−	553.148i	1.16523	−	1.03163i
$67$	−289.258	−	501.009i	−0.527440	−	0.913553i	−0.999489	−	0.0319801i	$-0.989819\pi$
$67$	−289.258	−	501.009i	−0.527440	−	0.913553i	0.472049	−	0.881572i	$-0.343515\pi$
$68$	20.8382	+	36.0928i	0.0371618	+	0.0643662i
$69$	−514.298	−	580.900i	−0.897307	−	1.01351i
$70$	252.762	−	827.077i	0.431584	−	1.41221i
$71$			787.243i			1.31589i	0.753064	+	0.657947i	$0.228575\pi$
$71$			787.243i			1.31589i	−0.753064	+	0.657947i	$0.771425\pi$
$72$	222.737	+	523.721i	0.364580	+	0.857238i
$73$			146.373i			0.234681i	0.993092	+	0.117340i	$0.0374368\pi$
$73$			146.373i			0.234681i	−0.993092	+	0.117340i	$0.962563\pi$
$74$	104.592	+	60.3863i	0.164305	+	0.0948617i
$75$	583.756	+	195.096i	0.898751	+	0.300370i
$76$	−26.7305	+	15.4329i	−0.0403447	+	0.0232930i
$77$	677.836	+	726.728i	1.00320	+	1.07556i
$78$	104.513	+	512.785i	0.151715	+	0.744378i
$79$	−193.095	+	334.451i	−0.274999	+	0.476312i	−0.970135	−	0.242566i	$-0.922011\pi$
$79$	−193.095	+	334.451i	−0.274999	+	0.476312i	0.695136	+	0.718878i	$0.255344\pi$
$80$	−1103.76			−1.54254
$81$	505.676	−	525.103i	0.693656	−	0.720306i
$82$			1074.15i			1.44659i
$83$	−98.9043	+	171.307i	−0.130797	+	0.226547i	−0.923984	−	0.382431i	$-0.875087\pi$
$83$	−98.9043	+	171.307i	−0.130797	+	0.226547i	0.793187	+	0.608978i	$0.208420\pi$
$84$	83.7867	−	38.2302i	0.108832	−	0.0496579i
$85$	−339.745	−	588.455i	−0.433535	−	0.750905i
$86$	−1316.07	+	759.835i	−1.65018	+	0.952734i
$87$	−242.276	+	724.926i	−0.298560	+	0.893336i
$88$	565.524	−	979.517i	0.685058	−	1.18656i
$89$	−596.020			−0.709865			−0.354932	−	0.934892i	$-0.615496\pi$
$89$	−596.020			−0.709865			−0.354932	+	0.934892i	$0.615496\pi$
$90$	493.448	+	1160.24i	0.577933	+	1.35889i
$91$	−607.253	+	140.267i	−0.699532	+	0.161582i
$92$	123.749	+	71.4466i	0.140236	+	0.0809654i
$93$	243.282	+	274.787i	0.271260	+	0.306388i
$94$	1182.72	−	682.844i	1.29775	−	0.749255i
$95$	435.812	−	251.616i	0.470667	−	0.271740i
$96$	−148.404	−	167.623i	−0.157776	−	0.178208i
$97$	631.485	+	364.588i	0.661006	+	0.381632i	0.792660	−	0.609664i	$-0.208696\pi$
$97$	631.485	+	364.588i	0.661006	+	0.381632i	−0.131654	+	0.991296i	$0.542029\pi$
$98$	450.210	+	922.547i	0.464062	+	0.950932i
$99$	−1438.12	−	175.563i	−1.45996	−	0.178229i
$100$	−113.359			−0.113359
$101$	−286.723	+	496.619i	−0.282476	+	0.489262i	−0.971994	−	0.235006i	$-0.924489\pi$
$101$	−286.723	+	496.619i	−0.282476	+	0.489262i	0.689518	+	0.724268i	$0.257822\pi$
$102$	214.666	−	642.313i	0.208384	−	0.623514i
$103$	−1420.04	+	819.860i	−1.35845	+	0.784303i	−0.989415	−	0.145111i	$-0.953646\pi$
$103$	−1420.04	+	819.860i	−1.35845	+	0.784303i	−0.369038	+	0.929414i	$0.620313\pi$
$104$	354.665	+	614.298i	0.334402	+	0.579201i
$105$	−1366.05	+	623.304i	−1.26965	+	0.579316i
$106$	319.365	−	553.156i	0.292636	−	0.506861i
$107$		−	377.596i		−	0.341155i	−0.985344	−	0.170577i	$-0.945437\pi$
$107$		−	377.596i		−	0.341155i	0.985344	−	0.170577i	$-0.0545633\pi$
$108$	−57.6756	+	121.245i	−0.0513874	+	0.108026i
$109$	−1166.06			−1.02467			−0.512334	−	0.858787i	$-0.671219\pi$
$109$	−1166.06			−1.02467			−0.512334	+	0.858787i	$0.671219\pi$
$110$	1252.85	−	2170.01i	1.08595	−	1.88093i
$111$	−41.8761	−	205.462i	−0.0358081	−	0.175690i
$112$	958.067	−	893.611i	0.808293	−	0.753913i
$113$	−279.069	+	161.121i	−0.232324	+	0.134132i	−0.611644	−	0.791133i	$-0.709491\pi$
$113$	−279.069	+	161.121i	−0.232324	+	0.134132i	0.379320	+	0.925266i	$0.376158\pi$
$114$	475.699	+	158.983i	0.390819	+	0.130615i
$115$	−2017.60	−	1164.86i	−1.63602	−	0.944555i
$116$		−	140.773i		−	0.112676i
$117$	546.305	−	726.022i	0.431675	−	0.573682i
$118$		−	955.269i		−	0.745252i
$119$	771.320	+	235.722i	0.594175	+	0.181585i
$120$	1132.82	+	1279.53i	0.861769	+	0.973370i
$121$	774.144	+	1340.86i	0.581626	+	1.00741i
$122$	524.700	+	908.806i	0.389378	+	0.674422i
$123$	1396.33	−	1236.24i	1.02360	−	0.906241i
$124$	−58.5379	−	33.7969i	−0.0423940	−	0.0244762i
$125$	−102.169			−0.0731064
$126$	−1367.66	−	607.600i	−0.966991	−	0.429597i
$127$	1356.31			0.947663			0.473832	−	0.880615i	$-0.342871\pi$
$127$	1356.31			0.947663			0.473832	+	0.880615i	$0.342871\pi$
$128$	−1431.08	−	826.236i	−0.988211	−	0.570544i
$129$	2502.40	+	836.324i	1.70794	+	0.570808i
$130$	785.720	+	1360.91i	0.530094	+	0.918150i
$131$	−978.999	−	1695.68i	−0.652943	−	1.13093i	−0.982405	−	0.186762i	$-0.940201\pi$
$131$	−978.999	−	1695.68i	−0.652943	−	1.13093i	0.329462	−	0.944169i	$-0.393133\pi$
$132$	261.457	−	53.2888i	0.172401	−	0.0351378i
$133$	−174.577	+	571.242i	−0.113818	+	0.372428i
$134$		−	1731.40i		−	1.11619i
$135$	940.340	−	1976.77i	0.599493	−	1.26025i
$136$		−	917.942i		−	0.578771i
$137$	−859.395	−	496.172i	−0.535935	−	0.309422i	0.207495	−	0.978236i	$-0.433469\pi$
$137$	−859.395	−	496.172i	−0.535935	−	0.309422i	−0.743430	+	0.668814i	$0.766802\pi$
$138$	−463.722	−	2275.22i	−0.286048	−	1.40347i
$139$	722.161	−	416.940i	0.440668	−	0.254420i	−0.263213	−	0.964738i	$-0.584782\pi$
$139$	722.161	−	416.940i	0.440668	−	0.254420i	0.703881	+	0.710318i	$0.251449\pi$
$140$	202.232	−	188.627i	0.122084	−	0.113870i
$141$	−2248.84	−	751.583i	−1.34317	−	0.448898i
$142$	−1178.04	+	2040.43i	−0.696190	+	1.20584i
$143$	−1805.73			−1.05596
$144$	−231.449	+	1895.91i	−0.133941	+	1.09717i
$145$			2295.15i			1.31450i
$146$	−219.035	+	379.379i	−0.124161	+	0.215052i
$147$	681.110	−	1647.00i	0.382157	−	0.924098i
$148$	19.3095	+	33.4450i	0.0107245	+	0.0185754i
$149$	1324.03	−	764.428i	0.727978	−	0.420298i	−0.0897042	−	0.995968i	$-0.528592\pi$
$149$	1324.03	−	764.428i	0.727978	−	0.420298i	0.817682	+	0.575670i	$0.195259\pi$
$150$	1221.07	+	1379.20i	0.664667	+	0.750742i
$151$	−373.571	+	647.044i	−0.201330	+	0.348713i	−0.948957	−	0.315405i	$-0.897860\pi$
$151$	−373.571	+	647.044i	−0.201330	+	0.348713i	0.747627	+	0.664118i	$0.231193\pi$
$152$	679.831			0.362774
$153$	−1082.03	+	460.182i	−0.571743	+	0.243160i
$154$	669.373	+	2897.90i	0.350257	+	1.51636i
$155$	954.398	+	551.022i	0.494575	+	0.285543i
$156$	−53.0433	+	158.713i	−0.0272235	+	0.0814566i
$157$	1193.21	−	688.900i	0.606551	−	0.350192i	−0.165064	−	0.986283i	$-0.552783\pi$
$157$	1193.21	−	688.900i	0.606551	−	0.350192i	0.771614	+	0.636091i	$0.219450\pi$
$158$	−1000.95	+	577.901i	−0.503997	+	0.290983i
$159$	−1086.62	+	221.470i	−0.541980	+	0.110464i
$160$	−582.193	−	336.129i	−0.287665	−	0.166083i
$161$	2694.37	−	622.360i	1.31892	−	0.304651i
$162$	2096.41	−	604.296i	1.01673	−	0.293074i
$163$	1900.28			0.913139			0.456569	−	0.889688i	$-0.349078\pi$
$163$	1900.28			0.913139			0.456569	+	0.889688i	$0.349078\pi$
$164$	−171.739	+	297.460i	−0.0817715	+	0.141632i
$165$	−4262.78	+	868.817i	−2.01125	+	0.409923i
$166$	−512.693	+	296.003i	−0.239715	+	0.138399i
$167$	836.404	+	1448.69i	0.387562	+	0.671277i	0.992121	−	0.125283i	$-0.0399839\pi$
$167$	836.404	+	1448.69i	0.387562	+	0.671277i	−0.604559	+	0.796560i	$0.706651\pi$
$168$	−2019.22	−	193.493i	−0.927297	−	0.0888590i
$169$	−532.274	+	921.925i	−0.242273	+	0.419629i
$170$		−	2033.59i		−	0.917468i
$171$	−340.812	−	801.353i	−0.152413	−	0.358368i
$172$	−485.939			−0.215422
$173$	−496.398	+	859.787i	−0.218153	+	0.377852i	−0.954243	−	0.299031i	$-0.903336\pi$
$173$	−496.398	+	859.787i	−0.218153	+	0.377852i	0.736090	+	0.676883i	$0.236670\pi$
$174$	−1712.74	+	1516.36i	−0.746219	+	0.660662i
$175$	−1604.25	+	1496.32i	−0.692970	+	0.646349i
$176$	3287.30	−	1897.92i	1.40790	−	0.812849i
$177$	−1241.79	+	1099.42i	−0.527338	+	0.466876i
$178$	−1544.80	−	891.891i	−0.650493	−	0.375562i
$179$			145.772i			0.0608687i	0.999537	+	0.0304343i	$0.00968905\pi$
$179$			145.772i			0.0608687i	−0.999537	+	0.0304343i	$0.990311\pi$
$180$	−48.8551	+	400.195i	−0.0202303	+	0.165716i
$181$		−	2253.56i		−	0.925448i	−0.886502	−	0.462724i	$-0.846872\pi$
$181$		−	2253.56i		−	0.925448i	0.886502	−	0.462724i	$-0.153128\pi$
$182$	−1783.81	−	545.150i	−0.726511	−	0.222029i
$183$	577.518	−	1728.02i	0.233286	−	0.698026i
$184$	−1573.64	−	2725.63i	−0.630492	−	1.09204i
$185$	−314.821	−	545.286i	−0.125114	−	0.216704i
$186$	219.358	+	1076.26i	0.0864736	+	0.424276i
$187$	2023.72	+	1168.39i	0.791384	+	0.456906i
$188$	436.701			0.169413
$189$	784.192	+	2477.16i	0.301807	+	0.953369i
$190$	1506.09			0.575069
$191$	3201.45	+	1848.36i	1.21282	+	0.700222i	0.963373	−	0.268166i	$-0.0864175\pi$
$191$	3201.45	+	1848.36i	1.21282	+	0.700222i	0.249448	+	0.968388i	$0.419751\pi$
$192$	453.456	+	2224.85i	0.170445	+	0.836273i
$193$	2194.75	+	3801.42i	0.818559	+	1.41779i	0.906744	+	0.421681i	$0.138560\pi$
$193$	2194.75	+	3801.42i	0.818559	+	1.41779i	−0.0881856	+	0.996104i	$0.528107\pi$
$194$	1091.15	+	1889.92i	0.403814	+	0.699426i
$195$	864.815	−	2587.65i	0.317593	−	0.950285i
$196$	−22.8250	+	327.458i	−0.00831814	+	0.119336i
$197$			2110.35i			0.763229i	0.924322	+	0.381615i	$0.124632\pi$
$197$			2110.35i			0.763229i	−0.924322	+	0.381615i	$0.875368\pi$
$198$	−3464.69	−	2607.05i	−1.24356	−	0.935732i
$199$		−	3443.20i		−	1.22654i	−0.789873	−	0.613271i	$-0.789854\pi$
$199$		−	3443.20i		−	1.22654i	0.789873	−	0.613271i	$-0.210146\pi$
$200$	2162.28	+	1248.39i	0.764481	+	0.441373i
$201$	−2250.71	+	1992.66i	−0.789815	+	0.699259i
$202$	−1486.29	+	858.113i	−0.517700	+	0.298894i
$203$	−1858.18	−	1992.21i	−0.642455	−	0.688795i
$204$	162.142	−	143.551i	0.0556480	−	0.0492677i
$205$	2800.02	−	4849.77i	0.953959	−	1.65231i
$206$	−4907.40			−1.65978
$207$	−2423.95	+	3221.35i	−0.813893	+	1.08164i
$208$			2380.54i			0.793562i
$209$	−865.316	+	1498.77i	−0.286388	+	0.496039i
$210$	−4473.34	−	428.661i	−1.46995	−	0.140859i
$211$	−1865.08	−	3230.41i	−0.608518	−	1.05398i	−0.991485	−	0.130223i	$-0.958431\pi$
$211$	−1865.08	−	3230.41i	−0.608518	−	1.05398i	0.382966	−	0.923762i	$-0.374903\pi$
$212$	176.881	−	102.122i	0.0573028	−	0.0330838i
$213$	4008.23	−	816.936i	1.28939	−	0.262796i
$214$	565.039	−	978.676i	0.180492	−	0.312621i
$215$	7922.73			2.51314
$216$	2435.38	−	1677.53i	0.767159	−	0.528434i
$217$	−1274.54	+	294.399i	−0.398715	+	0.0920973i
$218$	−3022.28	−	1744.91i	−0.938966	−	0.542112i
$219$	745.256	−	151.894i	0.229953	−	0.0468678i
$220$	693.895	−	400.620i	0.212647	−	0.122772i
$221$	−1269.16	+	732.751i	−0.386303	+	0.223032i
$222$	198.918	−	595.192i	0.0601375	−	0.179940i
$223$	2359.66	+	1362.35i	0.708585	+	0.409101i	0.810537	−	0.585688i	$-0.199176\pi$
$223$	2359.66	+	1362.35i	0.708585	+	0.409101i	−0.101952	+	0.994789i	$0.532509\pi$
$224$	777.481	−	179.587i	0.231909	−	0.0535675i
$225$	387.554	−	3174.63i	0.114831	−	0.940632i
$226$	−964.411			−0.283857
$227$	−2832.72	+	4906.41i	−0.828256	+	1.43458i	0.0711495	+	0.997466i	$0.477333\pi$
$227$	−2832.72	+	4906.41i	−0.828256	+	1.43458i	−0.899405	+	0.437116i	$0.856000\pi$
$228$	106.315	+	120.083i	0.0308810	+	0.0348801i
$229$	366.827	−	211.787i	0.105854	−	0.0611149i	−0.446138	−	0.894964i	$-0.647201\pi$
$229$	366.827	−	211.787i	0.105854	−	0.0611149i	0.551992	+	0.833849i	$0.313868\pi$
$230$	−3486.22	−	6038.32i	−0.999456	−	1.73111i
$231$	2996.72	−	4205.33i	0.853548	−	1.19779i
$232$	−1550.29	+	2685.18i	−0.438714	+	0.759875i
$233$			234.803i			0.0660192i	0.999455	+	0.0330096i	$0.0105092\pi$
$233$			234.803i			0.0660192i	−0.999455	+	0.0330096i	$0.989491\pi$
$234$	2502.38	−	1064.25i	0.699083	−	0.297318i
$235$	−7119.95			−1.97640
$236$	152.731	−	264.539i	0.0421270	−	0.0729661i
$237$	1903.23	+	636.075i	0.521637	+	0.174335i
$238$	1646.42	+	1765.17i	0.448409	+	0.480753i
$239$	1575.90	−	909.844i	0.426511	−	0.246246i	−0.271348	−	0.962481i	$-0.587469\pi$
$239$	1575.90	−	909.844i	0.426511	−	0.246246i	0.697859	+	0.716235i	$0.254136\pi$
$240$	1145.39	+	5619.74i	0.308060	+	1.51147i
$241$	2358.44	+	1361.65i	0.630377	+	0.363948i	0.780898	−	0.624659i	$-0.214762\pi$
$241$	2358.44	+	1361.65i	0.630377	+	0.363948i	−0.150521	+	0.988607i	$0.548095\pi$
$242$			4633.75i			1.23086i
$243$	−3198.30	−	2029.73i	−0.844325	−	0.535831i
$244$			335.562i			0.0880417i
$245$	372.137	−	5338.86i	0.0970407	−	1.39219i
$246$	5469.02	−	1114.67i	1.41745	−	0.288896i
$247$	−542.678	−	939.946i	−0.139797	−	0.242135i
$248$	744.391	+	1289.32i	0.190600	+	0.330129i
$249$	974.842	+	325.800i	0.248105	+	0.0829187i
$250$	−264.809	−	152.887i	−0.0669919	−	0.0386778i
$251$	−4214.66			−1.05987			−0.529934	−	0.848039i	$-0.677783\pi$
$251$	−4214.66			−1.05987			−0.529934	+	0.848039i	$0.677783\pi$
$252$	−281.595	−	386.926i	−0.0703922	−	0.0967223i
$253$	8011.98			1.99094
$254$	3515.38	+	2029.60i	0.868403	+	0.501372i
$255$	−2643.55	+	2340.45i	−0.649198	+	0.574764i
$256$	−724.881	−	1255.53i	−0.176973	−	0.306526i
$257$	−1388.99	−	2405.80i	−0.337132	−	0.583929i	0.646760	−	0.762693i	$-0.276123\pi$
$257$	−1388.99	−	2405.80i	−0.337132	−	0.583929i	−0.983892	+	0.178764i	$0.942790\pi$
$258$	5234.40	+	5912.26i	1.26310	+	1.42667i
$259$	714.735	+	218.430i	0.171473	+	0.0524037i
$260$			502.494i			0.119859i
$261$	3942.36	+	481.276i	0.934965	+	0.114139i
$262$		−	5859.95i		−	1.38179i
$263$	−2737.40	−	1580.44i	−0.641808	−	0.370548i	0.143503	−	0.989650i	$-0.454163\pi$
$263$	−2737.40	−	1580.44i	−0.641808	−	0.370548i	−0.785311	+	0.619102i	$0.787497\pi$
$264$	−5574.04	−	1862.89i	−1.29946	−	0.434292i
$265$	−2883.85	+	1664.99i	−0.668504	+	0.385961i
$266$	−1307.29	+	1219.34i	−0.301336	+	0.281063i
$267$	618.500	+	3034.62i	0.141766	+	0.695565i
$268$	276.821	−	479.468i	0.0630953	−	0.109284i
$269$	4337.32			0.983088			0.491544	−	0.870853i	$-0.336433\pi$
$269$	4337.32			0.983088			0.491544	+	0.870853i	$0.336433\pi$
$270$	5395.30	−	3716.38i	1.21610	−	0.837674i
$271$		−	8399.64i		−	1.88281i	−0.337276	−	0.941406i	$-0.609505\pi$
$271$		−	8399.64i		−	1.88281i	0.337276	−	0.941406i	$-0.390495\pi$
$272$	1540.33	−	2667.92i	0.343368	−	0.594730i
$273$	1344.32	+	2946.26i	0.298029	+	0.653171i
$274$	−1484.96	−	2572.02i	−0.327407	−	0.567085i
$275$	−5504.47	+	3178.01i	−1.20702	+	0.696876i
$276$	235.352	−	704.207i	0.0513280	−	0.153581i
$277$	1826.45	−	3163.50i	0.396176	−	0.686197i	−0.597075	−	0.802186i	$-0.703670\pi$
$277$	1826.45	−	3163.50i	0.396176	−	0.686197i	0.993250	+	0.115989i	$0.0370038\pi$
$278$	2495.66			0.538415
$279$	1146.62	−	1523.82i	0.246043	−	0.326984i
$280$	−5934.79	+	1370.85i	−1.26668	+	0.292585i
$281$	−7198.88	−	4156.27i	−1.52829	−	0.882358i	−0.999434	−	0.0336451i	$-0.989288\pi$
$281$	−7198.88	−	4156.27i	−1.52829	−	0.882358i	−0.528854	−	0.848713i	$-0.677378\pi$
$282$	−4704.02	−	5313.20i	−0.993334	−	1.12197i
$283$	1294.63	−	747.458i	0.271937	−	0.157003i	−0.357831	−	0.933786i	$-0.616484\pi$
$283$	1294.63	−	747.458i	0.271937	−	0.157003i	0.629767	+	0.776784i	$0.283150\pi$
$284$	−652.459	+	376.697i	−0.136325	+	0.0787073i
$285$	−1733.35	−	1957.82i	−0.360262	−	0.406917i
$286$	−4680.20	−	2702.12i	−0.967644	−	0.558669i
$287$	1495.99	+	6476.55i	0.307684	+	1.33205i
$288$	−699.448	+	929.543i	−0.143109	+	0.190187i
$289$	−3016.50			−0.613983
$290$	−3434.49	+	5948.72i	−0.695450	+	1.20455i
$291$	1200.99	−	3593.53i	0.241935	−	0.723905i
$292$	−121.313	+	70.0399i	−0.0243126	+	0.0140369i
$293$	−139.838	−	242.207i	−0.0278820	−	0.0482931i	0.851748	−	0.523952i	$-0.175543\pi$
$293$	−139.838	−	242.207i	−0.0278820	−	0.0482931i	−0.879630	+	0.475659i	$0.842210\pi$
$294$	4229.94	−	3249.58i	0.839099	−	0.644623i
$295$	−2490.12	+	4313.02i	−0.491460	+	0.851233i
$296$		−	850.601i		−	0.167028i
$297$	598.486	+	7504.32i	0.116928	+	1.46614i
$298$	4575.60			0.889455
$299$	−2512.33	+	4351.49i	−0.485926	+	0.841649i
$300$	117.635	+	577.165i	0.0226388	+	0.111075i
$301$	−6876.98	+	6414.31i	−1.31688	+	1.22829i
$302$	−1936.49	+	1118.03i	−0.368982	+	0.213032i
$303$	2826.06	+	944.494i	0.535819	+	0.179075i
$304$	1975.87	+	1140.77i	0.372777	+	0.215223i
$305$		−	5470.99i		−	1.02711i
$306$	−3493.09	−	426.430i	−0.652570	−	0.0796646i
$307$			10727.5i			1.99430i	0.0754451	+	0.997150i	$0.475962\pi$
$307$			10727.5i			1.99430i	−0.0754451	+	0.997150i	$0.524038\pi$
$308$	−277.959	+	909.525i	−0.0514227	+	0.168263i
$309$	5647.90	+	6379.32i	1.03980	+	1.17446i
$310$	1649.11	+	2856.35i	0.302140	+	0.523321i
$311$	−4776.34	−	8272.87i	−0.870873	−	1.50840i	−0.861095	−	0.508445i	$-0.830221\pi$
$311$	−4776.34	−	8272.87i	−0.870873	−	1.50840i	−0.00977881	−	0.999952i	$-0.503113\pi$
$312$	2759.64	−	2443.24i	0.500750	−	0.443337i
$313$	3195.36	+	1844.84i	0.577037	+	0.333153i	0.759955	−	0.649976i	$-0.225221\pi$
$313$	3195.36	+	1844.84i	0.577037	+	0.333153i	−0.182918	+	0.983128i	$0.558554\pi$
$314$	4123.51			0.741093
$315$	4591.11	+	6308.41i	0.821206	+	1.12838i
$316$	−369.586			−0.0657938
$317$	−652.484	−	376.712i	−0.115606	−	0.0667453i	0.441082	−	0.897467i	$-0.354595\pi$
$317$	−652.484	−	376.712i	−0.115606	−	0.0667453i	−0.556688	+	0.830722i	$0.687928\pi$
$318$	−3147.79	−	1052.02i	−0.555092	−	0.185516i
$319$	−3946.55	−	6835.62i	−0.692678	−	1.19975i
$320$	3409.04	+	5904.64i	0.595536	+	1.03150i
$321$	−1922.52	+	391.838i	−0.334282	+	0.0681316i
$322$	7914.74	+	2418.82i	1.36979	+	0.418620i
$323$			1404.55i			0.241955i
$324$	677.167	+	167.836i	0.116112	+	0.0287785i
$325$		−	3986.14i		−	0.680342i
$326$	4925.27	+	2843.61i	0.836766	+	0.483107i
$327$	1210.05	+	5936.99i	0.204635	+	1.00403i
$328$	6551.69	−	3782.62i	1.10292	−	0.636769i
$329$	6180.16	−	5764.38i	1.03563	−	0.965959i
$330$	−12348.7	−	4127.02i	−2.05991	−	0.688440i
$331$	−3119.34	+	5402.86i	−0.517989	+	0.897184i	0.481792	+	0.876285i	$0.339986\pi$
$331$	−3119.34	+	5402.86i	−0.517989	+	0.897184i	−0.999782	+	0.0208983i	$0.993347\pi$
$332$	−189.304			−0.0312933
$333$	−1002.65	+	426.423i	−0.164999	+	0.0701736i
$334$			5006.42i			0.820177i
$335$	−4513.27	+	7817.22i	−0.736079	+	1.27493i
$336$	−5544.00	−	3950.66i	−0.900149	−	0.641447i
$337$	−3929.76	−	6806.55i	−0.635216	−	1.10023i	−0.986469	−	0.163946i	$-0.947578\pi$
$337$	−3929.76	−	6806.55i	−0.635216	−	1.10023i	0.351254	−	0.936280i	$-0.385756\pi$
$338$	−2759.16	+	1593.00i	−0.444020	+	0.256355i
$339$	1109.94	+	1253.68i	0.177827	+	0.200856i
$340$	325.137	−	563.155i	0.0518619	−	0.0898275i
$341$	−3789.96			−0.601871
$342$	315.815	−	2586.99i	0.0499337	−	0.409031i
$343$	3999.37	+	4935.45i	0.629579	+	0.776936i
$344$	9269.10	+	5351.52i	1.45278	+	0.838763i
$345$	−3837.16	+	11481.4i	−0.598800	+	1.79170i
$346$	−2573.19	+	1485.63i	−0.399814	+	0.230833i
$347$	1142.47	−	659.607i	0.176747	−	0.102045i	−0.409016	−	0.912527i	$-0.634128\pi$
$347$	1142.47	−	659.607i	0.176747	−	0.102045i	0.585763	+	0.810482i	$0.300795\pi$
$348$	−716.742	+	146.082i	−0.110406	+	0.0225024i
$349$	−4291.07	−	2477.45i	−0.658153	−	0.379985i	0.133420	−	0.991060i	$-0.457404\pi$
$349$	−4291.07	−	2477.45i	−0.658153	−	0.379985i	−0.791573	+	0.611075i	$0.790738\pi$
$350$	−6397.10	+	1477.64i	−0.976970	+	0.225666i
$351$	−4263.44	−	2028.09i	−0.648335	−	0.308409i
$352$	2311.92			0.350073
$353$	2690.76	−	4660.53i	0.405707	−	0.702706i	−0.588696	−	0.808354i	$-0.700359\pi$
$353$	2690.76	−	4660.53i	0.405707	−	0.702706i	0.994404	+	0.105648i	$0.0336918\pi$
$354$	−4863.73	+	991.300i	−0.730239	+	0.148833i
$355$	10637.7	−	6141.65i	1.59039	−	0.918211i
$356$	−285.197	−	493.975i	−0.0424590	−	0.0735411i
$357$	399.763	−	4171.77i	0.0592653	−	0.618469i
$358$	−218.135	+	377.820i	−0.0322033	+	0.0557777i
$359$		−	3814.03i		−	0.560715i	−0.959896	−	0.280357i	$-0.909547\pi$
$359$		−	3814.03i		−	0.560715i	0.959896	−	0.280357i	$-0.0904530\pi$
$360$	5339.13	−	7095.54i	0.781659	−	1.03880i
$361$	5818.78			0.848343
$362$	3372.26	−	5840.93i	0.489619	−	0.848046i
$363$	6023.60	−	5332.97i	0.870955	−	0.771097i
$364$	−406.824	−	436.168i	−0.0585806	−	0.0628060i
$365$	1977.88	−	1141.93i	0.283635	−	0.163757i
$366$	4082.68	−	3614.58i	0.583074	−	0.516222i
$367$	−10883.1	−	6283.37i	−1.54794	−	0.893704i	−0.998299	−	0.0583038i	$-0.981431\pi$
$367$	−10883.1	−	6283.37i	−1.54794	−	0.893704i	−0.549642	−	0.835400i	$-0.685236\pi$
$368$		−	10562.4i		−	1.49621i
$369$	−7743.26	−	5826.52i	−1.09241	−	0.821996i
$370$		−	1884.41i		−	0.264772i
$371$	1155.21	−	3780.01i	0.161659	−	0.528972i
$372$	−111.330	+	333.116i	−0.0155167	+	0.0464281i
$373$	2338.60	+	4050.58i	0.324633	+	0.562281i	0.981438	−	0.191779i	$-0.0614258\pi$
$373$	2338.60	+	4050.58i	0.324633	+	0.562281i	−0.656805	+	0.754061i	$0.728092\pi$
$374$	3496.80	+	6056.63i	0.483463	+	0.837382i
$375$	106.023	+	520.193i	0.0146000	+	0.0716337i
$376$	−8329.90	−	4809.27i	−1.14250	−	0.659625i
$377$	4950.11			0.676243
$378$	−1674.33	+	7593.93i	−0.227827	+	1.03331i
$379$	−4851.71			−0.657561			−0.328780	−	0.944406i	$-0.606638\pi$
$379$	−4851.71			−0.657561			−0.328780	+	0.944406i	$0.606638\pi$
$380$	417.074	+	240.798i	0.0563038	+	0.0325070i
$381$	−1407.47	−	6905.63i	−0.189257	−	0.928573i
$382$	5531.81	+	9581.38i	0.740922	+	1.28331i
$383$	2456.18	+	4254.22i	0.327689	+	0.567573i	0.982053	−	0.188606i	$-0.0603970\pi$
$383$	2456.18	+	4254.22i	0.327689	+	0.567573i	−0.654364	+	0.756180i	$0.727064\pi$
$384$	−2721.70	+	8143.72i	−0.361696	+	1.08225i
$385$	4531.83	−	14828.8i	0.599905	−	1.96298i
$386$			13137.0i			1.73227i
$387$	1661.34	−	13608.8i	0.218218	−	1.78753i
$388$			697.825i			0.0913059i
$389$	−4621.95	−	2668.48i	−0.602421	−	0.347808i	0.167572	−	0.985860i	$-0.446407\pi$
$389$	−4621.95	−	2668.48i	−0.602421	−	0.347808i	−0.769994	+	0.638052i	$0.779741\pi$
$390$	6113.67	−	5412.72i	0.793790	−	0.702778i
$391$	5631.24	−	3251.20i	0.728349	−	0.420512i
$392$	4041.58	−	5994.77i	0.520742	−	0.772401i
$393$	−7617.57	+	6744.18i	−0.977750	+	0.865646i
$394$	−3157.95	+	5469.74i	−0.403795	+	0.699394i
$395$	6025.71			0.767561
$396$	−542.637	−	1275.90i	−0.0688600	−	0.161911i
$397$			1308.17i			0.165378i	0.996575	+	0.0826889i	$0.0263508\pi$
$397$			1308.17i			0.165378i	−0.996575	+	0.0826889i	$0.973649\pi$
$398$	5152.44	−	8924.29i	0.648916	−	1.12396i
$399$	3089.63	+	296.066i	0.387656	+	0.0371475i
$400$	4189.66	+	7256.70i	0.523707	+	0.907087i
$401$	−1742.21	+	1005.86i	−0.216962	+	0.125263i	−0.604543	−	0.796573i	$-0.706644\pi$
$401$	−1742.21	+	1005.86i	−0.216962	+	0.125263i	0.387581	+	0.921836i	$0.373311\pi$
$402$	−8815.37	+	1796.70i	−1.09371	+	0.222914i
$403$	1188.43	−	2058.42i	0.146898	−	0.254434i
$404$	−548.791			−0.0675826
$405$	−11040.5	−	2736.39i	−1.35458	−	0.335734i
$406$	−1834.98	−	7944.12i	−0.224306	−	0.971084i
$407$	1875.25	+	1082.68i	0.228386	+	0.131858i
$408$	−4673.68	+	952.565i	−0.567112	+	0.115586i
$409$	61.5250	−	35.5215i	0.00743818	−	0.00429444i	−0.496276	−	0.868165i	$-0.665300\pi$
$409$	61.5250	−	35.5215i	0.00743818	−	0.00429444i	0.503714	+	0.863870i	$0.331966\pi$
$410$	14514.5	−	8379.96i	1.74834	−	1.00941i
$411$	−1634.44	+	4890.48i	−0.196158	+	0.586933i
$412$	−1358.98	−	784.610i	−0.162506	−	0.0938227i
$413$	−1330.42	−	5759.76i	−0.158512	−	0.686245i
$414$	−11103.0	+	4722.06i	−1.31807	+	0.560572i
$415$	3086.40			0.365073
$416$	−724.953	+	1255.66i	−0.0854417	+	0.147989i
$417$	−2872.24	−	3244.20i	−0.337300	−	0.380981i
$418$	−4485.56	+	2589.74i	−0.524871	+	0.303034i
$419$	−1825.15	−	3161.25i	−0.212803	−	0.368585i	0.739788	−	0.672840i	$-0.234926\pi$
$419$	−1825.15	−	3161.25i	−0.212803	−	0.368585i	−0.952591	+	0.304255i	$0.901592\pi$
$420$	−1170.25	−	833.919i	−0.135958	−	0.0968835i
$421$	−2970.12	+	5144.40i	−0.343836	+	0.595541i	−0.985142	−	0.171744i	$-0.945060\pi$
$421$	−2970.12	+	5144.40i	−0.343836	+	0.595541i	0.641306	+	0.767285i	$0.278393\pi$
$422$		−	11163.7i		−	1.28778i
$423$	−1493.00	+	12229.9i	−0.171613	+	1.40576i
$424$	−4498.57			−0.515259
$425$	−2579.22	+	4467.34i	−0.294378	+	0.509877i
$426$	11611.3	+	3880.58i	1.32058	+	0.441349i
$427$	4429.37	+	4748.85i	0.501995	+	0.538204i
$428$	312.948	−	180.680i	0.0353432	−	0.0204054i
$429$	1873.84	+	9193.83i	0.210885	+	1.03469i
$430$	20534.6	+	11855.7i	2.30295	+	1.32961i
$431$			7508.08i			0.839098i	0.907733	+	0.419549i	$0.137812\pi$
$431$			7508.08i			0.839098i	−0.907733	+	0.419549i	$0.862188\pi$
$432$	9893.16	−	789.001i	1.10182	−	0.0878723i
$433$			6880.95i			0.763689i	0.924227	+	0.381845i	$0.124711\pi$
$433$			6880.95i			0.763689i	−0.924227	+	0.381845i	$0.875289\pi$
$434$	−3743.97	−	1144.19i	−0.414092	−	0.126550i
$435$	11685.7	−	2381.72i	1.28802	−	0.262517i
$436$	−557.964	−	966.423i	−0.0612882	−	0.106154i
$437$	2407.85	+	4170.52i	0.263577	+	0.456529i
$438$	2158.90	+	721.522i	0.235516	+	0.0787115i
$439$	4495.14	+	2595.27i	0.488705	+	0.282154i	0.724037	−	0.689761i	$-0.242285\pi$
$439$	4495.14	+	2595.27i	0.488705	+	0.282154i	−0.235332	+	0.971915i	$0.575618\pi$
$440$	−17647.7			−1.91209
$441$	−9092.47	−	1758.73i	−0.981802	−	0.189908i
$442$	−4385.99			−0.471992
$443$	−878.510	−	507.208i	−0.0942196	−	0.0543977i	0.452150	−	0.891942i	$-0.350657\pi$
$443$	−878.510	−	507.208i	−0.0942196	−	0.0543977i	−0.546369	+	0.837544i	$0.683991\pi$
$444$	150.247	−	133.020i	0.0160595	−	0.0142182i
$445$	4649.83	+	8053.74i	0.495333	+	0.857942i
$446$	4077.27	+	7062.04i	0.432880	+	0.749770i
$447$	−5266.04	−	5948.00i	−0.557215	−	0.629376i
$448$	−7739.52	−	2365.27i	−0.816201	−	0.249439i
$449$		−	6361.05i		−	0.668589i	−0.942469	−	0.334295i	$-0.891502\pi$
$449$		−	6361.05i		−	0.668589i	0.942469	−	0.334295i	$-0.108498\pi$
$450$	5755.05	−	7648.27i	0.602879	−	0.801207i
$451$			19258.7i			2.01077i
$452$	−267.070	−	154.193i	−0.0277919	−	0.0160456i
$453$	3682.07	+	1230.58i	0.381896	+	0.127633i
$454$	−14684.0	+	8477.83i	−1.51796	+	0.876397i
$455$	6632.83	+	7111.25i	0.683410	+	0.732705i
$456$	−705.473	−	3461.34i	−0.0724491	−	0.355466i
$457$	−2808.03	+	4863.65i	−0.287427	+	0.497838i	−0.973195	−	0.229982i	$-0.926133\pi$
$457$	−2808.03	+	4863.65i	−0.287427	+	0.497838i	0.685768	+	0.727820i	$0.259467\pi$
$458$	1267.69			0.129334
$459$	3465.84	+	5031.57i	0.352444	+	0.511664i
$460$		−	2229.55i		−	0.225986i
$461$	2311.52	−	4003.68i	0.233532	−	0.404490i	−0.725313	−	0.688420i	$-0.758305\pi$
$461$	2311.52	−	4003.68i	0.233532	−	0.404490i	0.958845	+	0.283929i	$0.0916382\pi$
$462$	14060.0	−	6415.30i	1.41587	−	0.646032i
$463$	2180.04	+	3775.94i	0.218823	+	0.379012i	0.954448	−	0.298376i	$-0.0964450\pi$
$463$	2180.04	+	3775.94i	0.218823	+	0.379012i	−0.735626	+	0.677388i	$0.763112\pi$
$464$	−9011.59	+	5202.85i	−0.901622	+	0.520552i
$465$	1815.12	−	5431.10i	0.181020	−	0.541637i
$466$	−351.363	+	608.578i	−0.0349283	+	0.0604975i
$467$	−10923.9			−1.08243			−0.541216	−	0.840884i	$-0.682036\pi$
$467$	−10923.9			−1.08243			−0.541216	+	0.840884i	$0.682036\pi$
$468$	863.129	+	105.369i	0.0852524	+	0.0104075i
$469$	−2411.34	−	10439.4i	−0.237410	−	1.02782i
$470$	−18453.9	−	10654.4i	−1.81110	−	1.04564i
$471$	−4745.73	−	5360.31i	−0.464271	−	0.524395i
$472$	−5826.58	+	3363.98i	−0.568200	+	0.328050i
$473$	−23596.1	+	13623.2i	−2.29377	+	1.32431i
$474$	3981.07	+	4496.63i	0.385774	+	0.435732i
$475$	−3308.53	−	1910.18i	−0.319591	−	0.184516i
$476$	173.714	+	752.056i	0.0167272	+	0.0724169i
$477$	2255.22	+	5302.70i	0.216477	+	0.509002i
$478$	5446.01			0.521118
$479$	4797.57	−	8309.64i	0.457634	−	0.792645i	−0.541202	−	0.840893i	$-0.682030\pi$
$479$	4797.57	−	8309.64i	0.457634	−	0.792645i	0.998835	+	0.0482479i	$0.0153637\pi$
$480$	−1107.24	+	3313.03i	−0.105288	+	0.315038i
$481$	−1176.06	+	678.996i	−0.111483	+	0.0643649i
$482$	4075.18	+	7058.41i	0.385102	+	0.667016i
$483$	−5964.73	−	13072.5i	−0.561914	−	1.23151i
$484$	−740.859	+	1283.21i	−0.0695773	+	0.120511i
$485$		−	11377.3i		−	1.06519i
$486$	−5252.24	−	10046.7i	−0.490219	−	0.937716i
$487$	−8240.46			−0.766758			−0.383379	−	0.923591i	$-0.625240\pi$
$487$	−8240.46			−0.766758			−0.383379	+	0.923591i	$0.625240\pi$
$488$	3695.46	−	6400.72i	0.342798	−	0.593744i
$489$	−1971.96	−	9675.25i	−0.182362	−	0.894744i
$490$	8953.66	−	13280.7i	0.825480	−	1.22441i
$491$	1742.44	−	1006.00i	0.160153	−	0.0924645i	−0.417781	−	0.908548i	$-0.637192\pi$
$491$	1742.44	−	1006.00i	0.160153	−	0.0924645i	0.577935	+	0.816083i	$0.303859\pi$
$492$	1692.73	+	565.724i	0.155110	+	0.0518390i
$493$	−5547.68	−	3202.96i	−0.506806	−	0.292604i
$494$		−	3248.28i		−	0.295844i
$495$	8847.13	+	20802.3i	0.803331	+	1.88887i
$496$			4996.42i			0.452310i
$497$	−4261.21	+	13943.3i	−0.384591	+	1.25844i
$498$	2039.12	+	2303.20i	0.183485	+	0.207246i
$499$	−7186.51	−	12447.4i	−0.644714	−	1.11668i	−0.984367	−	0.176127i	$-0.943643\pi$
$499$	−7186.51	−	12447.4i	−0.644714	−	1.11668i	0.339653	−	0.940551i	$-0.389690\pi$
$500$	−48.8883	−	84.6769i	−0.00437270	−	0.00757374i
$501$	6508.04	−	5761.87i	0.580355	−	0.513815i
$502$	−10923.8	−	6306.87i	−0.971222	−	0.560735i
$503$	12261.8			1.08693			0.543467	−	0.839430i	$-0.317111\pi$
$503$	12261.8			1.08693			0.543467	+	0.839430i	$0.317111\pi$
$504$	1110.21	+	10481.6i	0.0981206	+	0.926363i
$505$	8947.46			0.788429
$506$	20766.0	+	11989.2i	1.82443	+	1.05333i
$507$	5246.31	+	1753.36i	0.459560	+	0.153589i
$508$	648.998	+	1124.10i	0.0566824	+	0.0981768i
$509$	−10985.2	−	19026.9i	−0.956602	−	1.65688i	−0.730658	−	0.682744i	$-0.760787\pi$
$509$	−10985.2	−	19026.9i	−0.956602	−	1.65688i	−0.225945	−	0.974140i	$-0.572547\pi$
$510$	−10354.0	+	2110.30i	−0.898986	+	0.183227i
$511$	−792.294	+	2592.51i	−0.0685891	+	0.224434i
$512$			8880.88i			0.766569i
$513$	−3726.40	+	2566.82i	−0.320711	+	0.220912i
$514$		−	8314.01i		−	0.713454i
$515$	22156.8	+	12792.2i	1.89582	+	1.09455i
$516$	504.268	+	2474.15i	0.0430216	+	0.211082i
$517$	21205.3	−	12242.9i	1.80388	−	1.04147i
$518$	1525.63	+	1635.68i	0.129406	+	0.138741i
$519$	4892.71	+	1635.18i	0.413807	+	0.138298i
$520$	5533.82	−	9584.87i	0.466681	−	0.808316i
$521$	−9869.79			−0.829949			−0.414974	−	0.909833i	$-0.636209\pi$
$521$	−9869.79			−0.829949			−0.414974	+	0.909833i	$0.636209\pi$
$522$	9497.87	+	7146.80i	0.796380	+	0.599247i
$523$		−	4243.21i		−	0.354766i	−0.984142	−	0.177383i	$-0.943237\pi$
$523$		−	4243.21i		−	0.354766i	0.984142	−	0.177383i	$-0.0567632\pi$
$524$	936.906	−	1622.77i	0.0781087	−	0.135288i
$525$	9283.23	+	6615.24i	0.771721	+	0.549929i
$526$	−4729.98	−	8192.57i	−0.392086	−	0.679112i
$527$	−2663.79	+	1537.94i	−0.220183	+	0.127123i
$528$	−13074.5	−	14767.7i	−1.07764	−	1.21720i
$529$	5063.67	−	8770.54i	0.416181	−	0.720846i
$530$	−9966.06			−0.816788
$531$	6886.28	+	5181.67i	0.562785	+	0.423475i
$532$	−556.976	+	128.653i	−0.0453909	+	0.0104846i
$533$	−10459.8	−	6038.99i	−0.850029	−	0.490765i
$534$	−2937.98	+	8790.85i	−0.238087	+	0.712392i
$535$	−5102.28	+	2945.80i	−0.412319	+	0.238053i
$536$	−10560.5	+	6097.11i	−0.851015	+	0.491334i
$537$	742.194	−	151.270i	0.0596425	−	0.0121560i
$538$	11241.7	+	6490.41i	0.900865	+	0.520115i
$539$	8071.91	+	16540.5i	0.645050	+	1.32180i
$540$	2088.28	−	166.545i	0.166417	−	0.0132721i
$541$	3649.63			0.290037			0.145018	−	0.989429i	$-0.453676\pi$
$541$	3649.63			0.290037			0.145018	+	0.989429i	$0.453676\pi$
$542$	12569.3	−	21770.7i	0.996124	−	1.72534i
$543$	−11474.0	+	2338.56i	−0.906805	+	0.184820i
$544$	1624.94	−	938.158i	0.128067	−	0.0739397i
$545$	9097.02	+	15756.5i	0.714997	+	1.23841i
$546$	−924.523	+	9647.96i	−0.0724651	+	0.756217i
$547$	758.912	−	1314.47i	0.0593212	−	0.102747i	−0.834840	−	0.550493i	$-0.814440\pi$
$547$	758.912	−	1314.47i	0.0593212	−	0.102747i	0.894161	+	0.447746i	$0.147773\pi$
$548$		−	949.678i		−	0.0740296i
$549$	−9397.47	−	1147.23i	−0.730554	−	0.0891847i
$550$	−19022.4			−1.47476
$551$	2372.12	−	4108.64i	0.183404	−	0.317666i
$552$	−12244.5	+	10840.6i	−0.944130	+	0.835882i
$553$	−5230.36	+	4878.47i	−0.402201	+	0.375142i
$554$	9467.81	−	5466.24i	0.726081	−	0.419203i
$555$	−2449.62	+	2168.76i	−0.187352	+	0.165871i
$556$	691.111	+	399.013i	0.0527152	+	0.0304351i
$557$			3101.35i			0.235922i	0.993018	+	0.117961i	$0.0376357\pi$
$557$			3101.35i			0.235922i	−0.993018	+	0.117961i	$0.962364\pi$
$558$	5252.13	−	2233.71i	0.398459	−	0.169463i
$559$		−	17087.5i		−	1.29289i
$560$	−19549.3	−	5974.44i	−1.47519	−	0.450833i
$561$	3848.80	−	11516.2i	0.289655	−	0.866690i
$562$	−12439.0	−	21545.0i	−0.933643	−	1.61712i
$563$	−488.465	−	846.047i	−0.0365655	−	0.0633333i	0.847164	−	0.531332i	$-0.178308\pi$
$563$	−488.465	−	846.047i	−0.0365655	−	0.0633333i	−0.883729	+	0.467999i	$0.844975\pi$
$564$	−453.173	−	2223.45i	−0.0338333	−	0.166001i
$565$	4354.30	+	2513.96i	0.324224	+	0.187191i
$566$	4474.02			0.332256
$567$	11798.6	−	6563.29i	0.873890	−	0.486124i
$568$	16593.9			1.22581
$569$	14997.0	+	8658.53i	1.10493	+	0.637934i	0.937513	−	0.347952i	$-0.113123\pi$
$569$	14997.0	+	8658.53i	1.10493	+	0.637934i	0.167421	+	0.985885i	$0.446456\pi$
$570$	−1562.89	−	7668.21i	−0.114846	−	0.563484i
$571$	−9602.72	−	16632.4i	−0.703785	−	1.21899i	−0.967128	−	0.254289i	$-0.918158\pi$
$571$	−9602.72	−	16632.4i	−0.703785	−	1.21899i	0.263343	−	0.964702i	$-0.415175\pi$
$572$	−864.045	−	1496.57i	−0.0631601	−	0.109396i
$573$	6088.67	−	18218.2i	0.443906	−	1.32823i
$574$	−5814.20	+	19024.9i	−0.422787	+	1.38343i
$575$			17686.4i			1.28274i
$576$	10857.2	−	4617.52i	0.785387	−	0.334022i
$577$			19299.1i			1.39243i	0.717832	+	0.696216i	$0.245134\pi$
$577$			19299.1i			1.39243i	−0.717832	+	0.696216i	$0.754866\pi$
$578$	−7818.36	−	4513.93i	−0.562631	−	0.324835i
$579$	17077.3	−	15119.3i	1.22575	−	1.08521i
$580$	−1902.20	+	1098.24i	−0.136180	+	0.0786237i
$581$	−2679.01	+	2498.78i	−0.191298	+	0.178428i
$582$	8490.20	−	7516.76i	0.604691	−	0.535361i
$583$	5725.95	−	9917.64i	0.406766	−	0.704540i
$584$	3085.32			0.218616
$585$	−14072.4	−	1717.93i	−0.994568	−	0.121415i
$586$		−	837.023i		−	0.0590053i
$587$	−4690.62	+	8124.39i	−0.329817	+	0.571260i	−0.982475	−	0.186392i	$-0.940320\pi$
$587$	−4690.62	+	8124.39i	−0.329817	+	0.571260i	0.652658	+	0.757652i	$0.273654\pi$
$588$	1690.93	−	223.596i	0.118593	−	0.0156819i
$589$	−1139.00	−	1972.81i	−0.0796804	−	0.138011i
$590$	−12908.1	+	7452.51i	−0.900710	+	0.520025i
$591$	10744.8	−	2189.95i	0.747854	−	0.152424i
$592$	1427.33	−	2472.20i	0.0990925	−	0.171633i
$593$	−21351.5			−1.47859			−0.739294	−	0.673383i	$-0.764841\pi$
$593$	−21351.5			−1.47859			−0.739294	+	0.673383i	$0.764841\pi$
$594$	−9678.37	+	20345.8i	−0.668532	+	1.40538i
$595$	−2832.22	−	12261.5i	−0.195142	−	0.844826i
$596$	1267.10	+	731.562i	0.0870847	+	0.0502784i
$597$	−17531.0	+	3573.07i	−1.20183	+	0.244951i
$598$	−13023.2	+	7518.98i	−0.890569	+	0.514170i
$599$	15576.0	−	8992.82i	1.06247	−	0.613417i	0.136355	−	0.990660i	$-0.456461\pi$
$599$	15576.0	−	8992.82i	1.06247	−	0.613417i	0.926114	+	0.377243i	$0.123128\pi$
$600$	4112.32	−	12304.7i	0.279808	−	0.837227i
$601$	14051.1	+	8112.39i	0.953669	+	0.550601i	0.894219	−	0.447630i	$-0.147732\pi$
$601$	14051.1	+	8112.39i	0.953669	+	0.550601i	0.0594502	+	0.998231i	$0.481065\pi$
$602$	−27422.6	+	6334.22i	−1.85658	+	0.428843i
$603$	12481.2	+	9391.62i	0.842906	+	0.634256i
$604$	−715.019			−0.0481684
$605$	12078.9	−	20921.3i	0.811699	−	1.40590i
$606$	5911.42	+	6676.96i	0.396262	+	0.447579i
$607$	−9689.02	+	5593.96i	−0.647883	+	0.374055i	−0.787645	−	0.616130i	$-0.788700\pi$
$607$	−9689.02	+	5593.96i	−0.647883	+	0.374055i	0.139762	+	0.990185i	$0.455366\pi$
$608$	694.803	+	1203.43i	0.0463454	+	0.0802726i
$609$	−8215.01	+	11528.2i	−0.546616	+	0.767072i
$610$	8186.86	−	14180.1i	0.543404	−	0.941203i
$611$			15356.1i			1.01676i
$612$	−899.146	−	676.575i	−0.0593886	−	0.0446878i
$613$	26379.5			1.73810			0.869052	−	0.494720i	$-0.164729\pi$
$613$	26379.5			1.73810			0.869052	+	0.494720i	$0.164729\pi$
$614$	−16052.7	+	27804.2i	−1.05511	+	1.82750i
$615$	−27598.1	−	9223.53i	−1.80953	−	0.604762i
$616$	15318.3	−	14287.7i	1.00194	−	0.934528i
$617$	18989.8	−	10963.8i	1.23906	−	0.715371i	0.270157	−	0.962816i	$-0.412924\pi$
$617$	18989.8	−	10963.8i	1.23906	−	0.715371i	0.968902	+	0.247445i	$0.0795909\pi$
$618$	5092.49	+	24985.9i	0.331473	+	1.62634i
$619$	15019.6	+	8671.59i	0.975267	+	0.563071i	0.900838	−	0.434156i	$-0.142953\pi$
$619$	15019.6	+	8671.59i	0.975267	+	0.563071i	0.0744291	+	0.997226i	$0.476287\pi$
$620$			1054.66i			0.0683165i
$621$	18916.8	+	8998.61i	1.22239	+	0.581485i
$622$		−	28589.5i		−	1.84298i
$623$	−10556.5	−	3226.15i	−0.678870	−	0.207469i
$624$	12120.5	−	2470.33i	0.777576	−	0.158481i
$625$	8200.32	+	14203.4i	0.524820	+	0.909015i
$626$	5521.30	+	9563.17i	0.352517	+	0.610577i
$627$	8528.91	+	2850.44i	0.543241	+	0.181556i
$628$	1141.91	+	659.280i	0.0725590	+	0.0418919i
$629$	1757.37			0.111401
$630$	2459.55	+	23220.7i	0.155541	+	1.46847i
$631$	−30543.8			−1.92699			−0.963495	−	0.267727i	$-0.913727\pi$
$631$	−30543.8			−1.92699			−0.963495	+	0.267727i	$0.913727\pi$
$632$	7049.71	+	4070.15i	0.443706	+	0.256174i
$633$	−14512.1	+	12848.3i	−0.911226	+	0.806750i
$634$	−1127.43	−	1952.77i	−0.0706248	−	0.122326i
$635$	−10581.2	−	18327.2i	−0.661265	−	1.14534i
$636$	−703.504	−	794.609i	−0.0438612	−	0.0495414i
$637$	−11514.7	−	802.614i	−0.716213	−	0.0499226i
$638$		−	23622.7i		−	1.46588i
$639$	−8318.82	−	19560.1i	−0.515004	−	1.21093i
$640$			25783.4i			1.59247i
$641$	−513.438	−	296.433i	−0.0316374	−	0.0182659i	0.484098	−	0.875014i	$-0.339148\pi$
$641$	−513.438	−	296.433i	−0.0316374	−	0.0182659i	−0.515735	+	0.856748i	$0.672481\pi$
$642$	−5569.26	−	1861.29i	−0.342369	−	0.114423i
$643$	−27553.5	+	15908.0i	−1.68990	+	0.975661i	−0.735307	+	0.677735i	$0.762962\pi$
$643$	−27553.5	+	15908.0i	−1.68990	+	0.975661i	−0.954589	+	0.297927i	$0.903705\pi$
$644$	1805.07	+	1935.27i	0.110450	+	0.118416i
$645$	−8221.55	−	40338.4i	−0.501897	−	2.46251i
$646$	−2101.79	+	3640.41i	−0.128009	+	0.221718i
$647$	14337.8			0.871218			0.435609	−	0.900136i	$-0.356533\pi$
$647$	14337.8			0.871218			0.435609	+	0.900136i	$0.356533\pi$
$648$	−11068.4	−	10658.9i	−0.670997	−	0.646172i
$649$		−	17127.2i		−	1.03591i
$650$	5964.90	−	10331.5i	0.359943	−	0.623439i
$651$	2821.54	+	6183.77i	0.169869	+	0.372290i
$652$	909.290	+	1574.94i	0.0546174	+	0.0946001i
$653$	1310.50	−	756.617i	0.0785356	−	0.0453426i	−0.460218	−	0.887806i	$-0.652229\pi$
$653$	1310.50	−	756.617i	0.0785356	−	0.0453426i	0.538754	+	0.842463i	$0.318895\pi$
$654$	−5747.92	+	17198.6i	−0.343672	+	1.02832i
$655$	−15275.3	+	26457.5i	−0.911228	+	1.57829i
$656$	25389.3			1.51110
$657$	−1546.73	−	3636.83i	−0.0918474	−	0.215961i
$658$	24644.0	−	5692.40i	1.46007	−	0.337254i
$659$	2743.47	+	1583.94i	0.162171	+	0.0936293i	0.578889	−	0.815406i	$-0.303486\pi$
$659$	2743.47	+	1583.94i	0.162171	+	0.0936293i	−0.416718	+	0.909036i	$0.636820\pi$
$660$	−2759.82	−	3117.22i	−0.162766	−	0.183845i
$661$	4954.29	−	2860.36i	0.291527	−	0.168313i	−0.347103	−	0.937827i	$-0.612835\pi$
$661$	4954.29	−	2860.36i	0.291527	−	0.168313i	0.638630	+	0.769514i	$0.279501\pi$
$662$	−16169.8	+	9335.64i	−0.949331	+	0.548097i
$663$	5047.82	+	5701.52i	0.295688	+	0.333980i
$664$	3610.89	+	2084.75i	0.211039	+	0.121843i
$665$	9080.90	−	2097.55i	0.529537	−	0.122315i
$666$	−3236.83	−	395.146i	−0.188325	−	0.0229904i
$667$	−21963.5			−1.27501
$668$	−800.442	+	1386.41i	−0.0463623	+	0.0803019i
$669$	4487.71	−	13427.9i	0.259350	−	0.776011i
$670$	−23395.6	+	13507.4i	−1.34903	+	0.778863i
$671$	9407.45	+	16294.2i	0.541238	+	0.937451i
$672$	−1721.17	−	3772.16i	−0.0988027	−	0.216539i
$673$	3370.28	−	5837.50i	0.193038	−	0.334352i	−0.753217	−	0.657772i	$-0.771499\pi$
$673$	3370.28	−	5837.50i	0.193038	−	0.334352i	0.946256	+	0.323420i	$0.104833\pi$
$674$		−	23522.2i		−	1.34427i
$675$	−16565.7	+	1321.15i	−0.944616	+	0.0753352i
$676$	−1018.78			−0.0579641
$677$	2209.63	−	3827.20i	0.125440	−	0.217269i	−0.796465	−	0.604685i	$-0.793299\pi$
$677$	2209.63	−	3827.20i	0.125440	−	0.217269i	0.921905	+	0.387416i	$0.126632\pi$
$678$	1000.79	+	4910.28i	0.0566888	+	0.278139i
$679$	9211.16	+	9875.56i	0.520607	+	0.558158i
$680$	−12403.7	+	7161.30i	−0.699502	+	0.403858i
$681$	27920.4	+	9331.25i	1.57109	+	0.525072i
$682$	−9823.06	−	5671.35i	−0.551532	−	0.318427i
$683$		−	25188.7i		−	1.41115i	−0.708633	−	0.705577i	$-0.750688\pi$
$683$		−	25188.7i		−	1.41115i	0.708633	−	0.705577i	$-0.249312\pi$
$684$	501.074	−	665.911i	0.0280103	−	0.0372248i
$685$			15483.5i			0.863640i
$686$	2980.35	+	18776.7i	0.165875	+	1.04504i
$687$	−1458.97	−	1647.91i	−0.0810237	−	0.0915165i
$688$	17959.9	+	31107.5i	0.995225	+	1.72378i
$689$	3591.00	+	6219.79i	0.198558	+	0.343912i
$690$	−27126.2	+	24016.1i	−1.49664	+	1.32504i
$691$	−21.1593	−	12.2163i	−0.00116489	−	0.000672548i	0.499417	−	0.866361i	$-0.333547\pi$
$691$	−21.1593	−	12.2163i	−0.00116489	−	0.000672548i	−0.500582	+	0.865689i	$0.666881\pi$
$692$	−950.111			−0.0521933
$693$	−24521.1	−	10893.8i	−1.34412	−	0.597144i
$694$	3948.18			0.215952
$695$	−11267.8	−	6505.49i	−0.614983	−	0.355061i
$696$	15280.3	+	5106.81i	0.832183	+	0.278122i
$697$	7815.02	+	13536.0i	0.424699	+	0.735600i
$698$	−7414.57	−	12842.4i	−0.402071	−	0.696408i
$699$	1195.50	−	243.660i	0.0646893	−	0.0131846i
$700$	−2007.77	−	613.593i	−0.108409	−	0.0331309i
$701$		−	5989.84i		−	0.322729i	−0.986895	−	0.161365i	$-0.948411\pi$
$701$		−	5989.84i		−	0.322729i	0.986895	−	0.161365i	$-0.0515895\pi$
$702$	−8015.38	−	11636.4i	−0.430941	−	0.625624i
$703$			1301.52i			0.0698259i
$704$	−20306.2	−	11723.8i	−1.08710	−	0.627639i
$705$	7388.50	+	36251.1i	0.394705	+	1.93659i
$706$	13948.2	−	8052.98i	0.743550	−	0.429289i
$707$	−7766.45	+	7243.94i	−0.413136	+	0.385342i
$708$	−1505.38	−	503.112i	−0.0799094	−	0.0267064i
$709$	−2214.14	+	3835.00i	−0.117283	+	0.203140i	−0.918690	−	0.394979i	$-0.870752\pi$
$709$	−2214.14	+	3835.00i	−0.117283	+	0.203140i	0.801407	+	0.598119i	$0.204085\pi$
$710$	36761.8			1.94316
$711$	1263.55	−	10350.3i	0.0666480	−	0.545945i
$712$			12563.2i			0.661271i
$713$	−5273.02	+	9133.15i	−0.276965	+	0.479718i
$714$	7278.82	−	10214.4i	0.381517	−	0.535387i
$715$	14087.3	+	24400.0i	0.736835	+	1.27624i
$716$	−120.814	+	69.7521i	−0.00630592	+	0.00364073i
$717$	−6267.78	−	7079.48i	−0.326464	−	0.368742i
$718$	5707.36	−	9885.44i	0.296653	−	0.513818i
$719$	−28053.6			−1.45511			−0.727554	−	0.686050i	$-0.759343\pi$
$719$	−28053.6			−1.45511			−0.727554	+	0.686050i	$0.759343\pi$
$720$	27424.2	−	11663.4i	1.41950	−	0.603708i
$721$	−29589.0	+	6834.61i	−1.52836	+	0.353030i
$722$	15081.5	+	8707.30i	0.777389	+	0.448826i
$723$	4485.40	−	13421.0i	0.230725	−	0.690361i
$724$	1867.73	−	1078.34i	0.0958753	−	0.0553536i
$725$	15089.6	−	8711.98i	0.772984	−	0.446282i
$726$	23592.7	−	4808.53i	1.20607	−	0.245814i
$727$	−13620.1	−	7863.54i	−0.694828	−	0.401159i	0.110590	−	0.993866i	$-0.464726\pi$
$727$	−13620.1	−	7863.54i	−0.694828	−	0.401159i	−0.805418	+	0.592707i	$0.798059\pi$
$728$	2956.60	+	12800.0i	0.150521	+	0.651646i
$729$	−7015.38	+	18390.4i	−0.356418	+	0.934327i
$730$	6835.18			0.346550
$731$	−11056.4	+	19150.3i	−0.559420	+	0.968945i
$732$	1708.51	−	348.219i	0.0862682	−	0.0175827i
$733$	28543.9	−	16479.8i	1.43833	−	0.830418i	0.440593	−	0.897707i	$-0.354768\pi$
$733$	28543.9	−	16479.8i	1.43833	−	0.830418i	0.997734	+	0.0672892i	$0.0214350\pi$
$734$	−18805.0	−	32571.3i	−0.945649	−	1.63791i
$735$	−27568.8	+	3645.50i	−1.38353	+	0.182947i
$736$	3216.60	−	5571.32i	0.161094	−	0.279024i
$737$		−	31042.6i		−	1.55152i
$738$	−11350.6	−	26688.7i	−0.566153	−	1.33120i
$739$	18483.4			0.920056			0.460028	−	0.887905i	$-0.347839\pi$
$739$	18483.4			0.920056			0.460028	+	0.887905i	$0.347839\pi$
$740$	301.285	−	521.841i	0.0149668	−	0.0259233i
$741$	−4222.57	+	3738.43i	−0.209339	+	0.185337i
$742$	8650.60	−	8068.61i	0.427997	−	0.399202i
$743$	27952.9	−	16138.6i	1.38020	−	0.796861i	0.388020	−	0.921651i	$-0.373159\pi$
$743$	27952.9	−	16138.6i	1.38020	−	0.796861i	0.992183	+	0.124790i	$0.0398257\pi$
$744$	5792.09	−	5128.00i	0.285415	−	0.252691i
$745$	−20658.8	−	11927.3i	−1.01594	−	0.586555i
$746$			13998.0i			0.687004i
$747$	647.194	−	5301.47i	0.0316996	−	0.259666i
$748$			2236.31i			0.109315i
$749$	2043.86	−	6687.83i	0.0997077	−	0.326259i
$750$	−503.626	+	1506.92i	−0.0245198	+	0.0733667i
$751$	12875.3	+	22300.7i	0.625601	+	1.08357i	0.988424	+	0.151715i	$0.0484796\pi$
$751$	12875.3	+	22300.7i	0.625601	+	1.08357i	−0.362823	+	0.931858i	$0.618187\pi$
$752$	−16140.1	−	27955.5i	−0.782672	−	1.35563i
$753$	4373.62	+	21458.8i	0.211665	+	1.03852i
$754$	12830.0	+	7407.41i	0.619683	+	0.357774i
$755$	11657.6			0.561939
$756$	−1677.81	+	1835.26i	−0.0807159	+	0.0882905i
$757$	14678.2			0.704741			0.352371	−	0.935861i	$-0.385376\pi$
$757$	14678.2			0.704741			0.352371	+	0.935861i	$0.385376\pi$
$758$	−12575.0	−	7260.16i	−0.602564	−	0.347890i
$759$	−8314.18	−	40792.8i	−0.397609	−	1.95084i
$760$	−5303.68	−	9186.25i	−0.253138	−	0.438448i
$761$	15248.7	+	26411.6i	0.726369	+	1.25811i	0.958408	+	0.285401i	$0.0921268\pi$
$761$	15248.7	+	26411.6i	0.726369	+	1.25811i	−0.232039	+	0.972706i	$0.574540\pi$
$762$	6685.71	−	20004.6i	0.317845	−	0.951037i
$763$	−20652.9	−	6311.71i	−0.979927	−	0.299475i
$764$			3537.77i			0.167529i
$765$	14659.6	+	11030.8i	0.692837	+	0.521334i
$766$			14701.8i			0.693470i
$767$	9302.19	+	5370.62i	0.437917	+	0.252832i
$768$	−5640.29	+	4993.60i	−0.265008	+	0.234624i
$769$	−30619.6	+	17678.2i	−1.43585	+	0.828989i	−0.997558	−	0.0698425i	$-0.977750\pi$
$769$	−30619.6	+	17678.2i	−1.43585	+	0.828989i	−0.438294	+	0.898832i	$0.644417\pi$
$770$	33936.0	−	31652.8i	1.58827	−	1.48141i
$771$	−10807.7	+	9568.56i	−0.504838	+	0.446956i
$772$	−2100.39	+	3637.98i	−0.0979205	+	0.169603i
$773$	−4097.47			−0.190654			−0.0953272	−	0.995446i	$-0.530390\pi$
$773$	−4097.47			−0.190654			−0.0953272	+	0.995446i	$0.530390\pi$
$774$	24670.3	−	32786.1i	1.14568	−	1.52257i
$775$		−	8366.32i		−	0.387777i
$776$	7684.95	−	13310.7i	0.355507	−	0.615757i
$777$	370.436	−	3865.73i	0.0171034	−	0.178484i
$778$	−7986.30	−	13832.7i	−0.368024	−	0.637436i
$779$	−10024.8	+	5787.84i	−0.461074	+	0.266201i
$780$	2558.44	−	521.447i	0.117444	−	0.0239369i
$781$	−21121.3	+	36583.2i	−0.967709	+	1.67612i
$782$	19460.6			0.889908
$783$	−1640.65	−	20571.9i	−0.0748813	−	0.938925i
$784$	21805.9	−	10641.4i	0.993343	−	0.484759i
$785$	−18617.6	−	10748.9i	−0.846484	−	0.488718i
$786$	−29835.8	+	6080.97i	−1.35395	+	0.275956i
$787$	29205.4	−	16861.7i	1.32282	−	0.763730i	0.338642	−	0.940915i	$-0.390032\pi$
$787$	29205.4	−	16861.7i	1.32282	−	0.763730i	0.984178	+	0.177185i	$0.0566990\pi$
$788$	−1749.04	+	1009.81i	−0.0790696	+	0.0456509i
$789$	−5206.13	+	15577.5i	−0.234909	+	0.702881i
$790$	15617.8	+	9016.95i	0.703363	+	0.406087i
$791$	−5814.88	+	1343.15i	−0.261382	+	0.0603754i
$792$	−3700.59	+	30313.3i	−0.166029	+	1.36002i
$793$	−11799.7			−0.528396
$794$	−1957.56	+	3390.59i	−0.0874950	+	0.151546i
$795$	11469.9	+	12955.3i	0.511692	+	0.577957i
$796$	2853.69	−	1647.58i	0.127068	−	0.0733628i
$797$	−7132.81	−	12354.4i	−0.317010	−	0.549077i	0.662853	−	0.748750i	$-0.269346\pi$
$797$	−7132.81	−	12354.4i	−0.317010	−	0.549077i	−0.979863	+	0.199672i	$0.936012\pi$
$798$	7564.86	+	5390.72i	0.335580	+	0.239135i
$799$	9936.12	−	17209.9i	0.439943	−	0.762004i
$800$			5103.54i			0.225547i
$801$	14808.9	−	6298.16i	0.653241	−	0.277821i
$802$	−6020.75			−0.265087
$803$	−3927.12	+	6801.97i	−0.172584	+	0.298925i
$804$	−2728.46	−	911.876i	−0.119683	−	0.0399992i
$805$	−29429.7	−	31552.5i	−1.28852	−	1.38146i
$806$	6160.48	−	3556.75i	0.269223	−	0.155436i
$807$	−4500.91	−	22083.3i	−0.196332	−	0.963284i
$808$	10468.0	+	6043.68i	0.455770	+	0.263139i
$809$			13916.9i			0.604812i	0.953179	+	0.302406i	$0.0977898\pi$
$809$			13916.9i			0.604812i	−0.953179	+	0.302406i	$0.902210\pi$
$810$	−24520.7	−	23613.5i	−1.06367	−	1.02431i
$811$		−	7296.14i		−	0.315909i	−0.987446	−	0.157954i	$-0.949510\pi$
$811$		−	7296.14i		−	0.315909i	0.987446	−	0.157954i	$-0.0504899\pi$
$812$	761.980	−	2493.31i	0.0329313	−	0.107756i
$813$	−42766.6	+	8716.46i	−1.84488	+	0.376014i
$814$	3240.27	+	5612.31i	0.139523	+	0.241660i
$815$	−14825.0	−	25677.7i	−0.637175	−	1.10362i
$816$	−15182.1	−	5073.98i	−0.651323	−	0.217678i
$817$	−14182.8	−	8188.42i	−0.607334	−	0.350645i
$818$	212.619			0.00908809
$819$	13605.8	−	9901.97i	0.580494	−	0.422470i
$820$	5359.26			0.228236
$821$	30269.4	+	17476.0i	1.28673	+	0.742897i	0.978070	−	0.208274i	$-0.0667846\pi$
$821$	30269.4	+	17476.0i	1.28673	+	0.742897i	0.308664	+	0.951171i	$0.400118\pi$
$822$	−11554.4	+	10229.7i	−0.490275	+	0.434063i
$823$	−11765.3	−	20378.1i	−0.498314	−	0.863105i	0.501684	−	0.865051i	$-0.332714\pi$
$823$	−11765.3	−	20378.1i	−0.498314	−	0.863105i	−0.999998	+	0.00194598i	$0.999381\pi$
$824$	17281.4	+	29932.2i	0.730614	+	1.26546i
$825$	21892.8	+	24728.0i	0.923891	+	1.04354i
$826$	5170.71	−	16919.4i	0.217811	−	0.712712i
$827$			40158.9i			1.68859i	0.535880	+	0.844294i	$0.319980\pi$
$827$			40158.9i			1.68859i	−0.535880	+	0.844294i	$0.680020\pi$
$828$	−3829.68	−	467.521i	−0.160738	−	0.0196226i
$829$			10739.4i			0.449934i	0.974366	+	0.224967i	$0.0722275\pi$
$829$			10739.4i			0.449934i	−0.974366	+	0.224967i	$0.927773\pi$
$830$	7999.52	+	4618.52i	0.334539	+	0.193146i
$831$	−18002.2	−	6016.50i	−0.751493	−	0.251155i
$832$	12734.9	−	7352.52i	0.530654	−	0.306373i
$833$	12385.4	+	8350.05i	0.515160	+	0.347313i
$834$	−2589.79	−	12706.6i	−0.107526	−	0.527569i
$835$	13050.4	−	22603.9i	0.540870	−	0.936814i
$836$	−1656.22			−0.0685187
$837$	−8948.34	−	4256.68i	−0.369534	−	0.175785i
$838$		−	10924.7i		−	0.450343i
$839$	−9285.04	+	16082.2i	−0.382068	+	0.661762i	−0.991358	−	0.131186i	$-0.958121\pi$
$839$	−9285.04	+	16082.2i	−0.382068	+	0.661762i	0.609289	+	0.792948i	$0.291455\pi$
$840$	13138.3	+	28794.3i	0.539659	+	1.18273i
$841$	−1375.69	−	2382.76i	−0.0564062	−	0.0976983i
$842$	−15396.3	+	8889.05i	−0.630156	+	0.363821i
$843$	−13691.2	+	40966.0i	−0.559370	+	1.67372i
$844$	1784.89	−	3091.52i	0.0727944	−	0.126084i
$845$	16610.1			0.676218
$846$	−22170.6	+	29464.0i	−0.900993	+	1.19739i
$847$	6453.50	+	27939.0i	0.261801	+	1.13341i
$848$	−13074.7	−	7548.69i	−0.529466	−	0.305688i
$849$	−5149.13	−	5815.95i	−0.208148	−	0.235104i
$850$	−13370.0	+	7719.16i	−0.539513	+	0.311488i
$851$	5218.13	−	3012.69i	0.210194	−	0.121356i
$852$	2595.01	+	2931.07i	0.104347	+	0.117860i
$853$	4663.07	+	2692.22i	0.187175	+	0.108066i	0.590659	−	0.806921i	$-0.298868\pi$
$853$	4663.07	+	2692.22i	0.187175	+	0.108066i	−0.403484	+	0.914987i	$0.632201\pi$
$854$	4374.06	+	18936.5i	0.175266	+	0.758776i
$855$	−8169.48	+	10857.0i	−0.326772	+	0.434270i
$856$	−7959.13			−0.317801
$857$	−5528.79	+	9576.15i	−0.220373	+	0.381698i	−0.954921	−	0.296859i	$-0.904061\pi$
$857$	−5528.79	+	9576.15i	−0.220373	+	0.381698i	0.734548	+	0.678557i	$0.237394\pi$
$858$	−8901.03	+	26633.2i	−0.354168	+	1.05972i
$859$	14136.9	−	8161.94i	0.561519	−	0.324193i	−0.192236	−	0.981349i	$-0.561574\pi$
$859$	14136.9	−	8161.94i	0.561519	−	0.324193i	0.753755	+	0.657156i	$0.228241\pi$
$860$	3791.04	+	6566.28i	0.150318	+	0.260358i
$861$	31422.8	−	14337.6i	1.24377	−	0.567508i
$862$	−11235.2	+	19459.9i	−0.443935	+	0.768917i
$863$		−	37617.5i		−	1.48379i	−0.670515	−	0.741896i	$-0.733927\pi$
$863$		−	37617.5i		−	1.48379i	0.670515	−	0.741896i	$-0.266073\pi$
$864$	5458.58	+	2596.62i	0.214936	+	0.102244i
$865$	15490.5			0.608895
$866$	−10296.7	+	17834.5i	−0.404039	+	0.699816i
$867$	3130.28	+	15358.4i	0.122618	+	0.601615i
$868$	−853.864	−	915.453i	−0.0333894	−	0.0357978i
$869$	−17946.3	+	10361.3i	−0.700560	+	0.404468i
$870$	33851.8	+	11313.6i	1.31918	+	0.440880i
$871$	16859.9	+	9734.08i	0.655886	+	0.378676i
$872$			24578.8i			0.954523i
$873$	−19542.7	−	2385.73i	−0.757639	−	0.0924912i
$874$			14412.6i			0.557794i
$875$	−1809.58	−	553.025i	−0.0699144	−	0.0213665i
$876$	482.495	+	544.979i	0.0186096	+	0.0210196i
$877$	−21070.2	−	36494.6i	−0.811275	−	1.40517i	−0.911972	−	0.410253i	$-0.865440\pi$
$877$	−21070.2	−	36494.6i	−0.811275	−	1.40517i	0.100696	−	0.994917i	$-0.467893\pi$
$878$	7767.19	+	13453.2i	0.298553	+	0.517110i
$879$	−1088.08	+	963.326i	−0.0417520	+	0.0369649i
$880$	−51291.6	−	29613.2i	−1.96482	−	1.13439i
$881$	17255.0			0.659861			0.329930	−	0.944005i	$-0.392975\pi$
$881$	17255.0			0.659861			0.329930	+	0.944005i	$0.392975\pi$
$882$	−20934.6	−	18164.5i	−0.799213	−	0.693458i
$883$	−26461.1			−1.00848			−0.504240	−	0.863564i	$-0.668227\pi$
$883$	−26461.1			−1.00848			−0.504240	+	0.863564i	$0.668227\pi$
$884$	−1214.59	−	701.246i	−0.0462118	−	0.0266804i
$885$	24543.7	+	8202.71i	0.932235	+	0.311561i
$886$	−1517.98	−	2629.23i	−0.0575595	−	0.0996959i
$887$	−9683.24	−	16771.9i	−0.366552	−	0.634886i	0.622472	−	0.782642i	$-0.286128\pi$
$887$	−9683.24	−	16771.9i	−0.366552	−	0.634886i	−0.989024	+	0.147756i	$0.952795\pi$
$888$	−4330.82	+	882.684i	−0.163663	+	0.0333569i
$889$	24022.5	+	7341.49i	0.906286	+	0.276969i
$890$			27832.3i			1.04825i
$891$	37587.0	−	10834.5i	1.41326	−	0.407375i
$892$			2607.55i			0.0978780i
$893$	12745.7	+	7358.72i	0.477624	+	0.275756i
$894$	−4748.18	−	23296.6i	−0.177632	−	0.871537i
$895$	1969.75	−	1137.23i	0.0735658	−	0.0424732i
$896$	−20874.5	−	22380.2i	−0.778313	−	0.834452i
$897$	24762.6	+	8275.87i	0.921738	+	0.308053i
$898$	9518.76	−	16487.0i	0.353725	−	0.612670i
$899$	10389.6			0.385441
$900$	2816.55	−	1197.87i	0.104317	−	0.0443655i
$901$		−	9294.19i		−	0.343656i
$902$	−28818.9	+	49915.9i	−1.06382	+	1.84259i
$903$	39794.7	+	28357.7i	1.46654	+	1.04506i
$904$	3396.17	+	5882.34i	0.124950	+	0.216420i
$905$	−30451.4	+	17581.1i	−1.11850	+	0.645764i
$906$	7701.97	+	8699.39i	0.282429	+	0.319004i
$907$	569.688	−	986.728i	0.0208558	−	0.0361232i	−0.855409	−	0.517953i	$-0.826694\pi$
$907$	569.688	−	986.728i	0.0208558	−	0.0361232i	0.876265	+	0.481830i	$0.160028\pi$
$908$	−5421.85			−0.198161
$909$	1876.21	−	15369.0i	0.0684600	−	0.560788i
$910$	6550.01	+	28356.8i	0.238605	+	1.03299i
$911$	−7531.25	−	4348.17i	−0.273898	−	0.158135i	0.356760	−	0.934196i	$-0.383882\pi$
$911$	−7531.25	−	4348.17i	−0.273898	−	0.158135i	−0.630658	+	0.776061i	$0.717215\pi$
$912$	3757.81	−	11243.9i	0.136440	−	0.408249i
$913$	−9192.18	+	5307.10i	−0.333205	+	0.192376i
$914$	−14556.1	+	8403.95i	−0.526775	+	0.304133i
$915$	−27855.4	+	5677.34i	−1.00642	+	0.205123i
$916$	351.055	+	202.682i	0.0126629	+	0.00731090i
$917$	−8161.24	−	35332.3i	−0.293902	−	1.27238i
$918$	1453.68	+	18227.5i	0.0522643	+	0.655334i
$919$	−2297.46			−0.0824659			−0.0412330	−	0.999150i	$-0.513129\pi$
$919$	−2297.46			−0.0824659			−0.0412330	+	0.999150i	$0.513129\pi$
$920$	−24553.5	+	42527.8i	−0.879895	+	1.52402i
$921$	54618.8	−	11132.1i	1.95413	−	0.398279i
$922$	11982.3	−	6917.99i	0.428000	−	0.247106i
$923$	−13246.1	−	22942.9i	−0.472374	−	0.818176i
$924$	4919.27	+	471.393i	0.175143	+	0.0167832i
$925$	−2390.01	+	4139.61i	−0.0849545	+	0.147146i
$926$			13048.9i			0.463083i
$927$	26619.2	−	35376.1i	0.943139	−	1.25340i
$928$	−6337.74			−0.224188
$929$	24197.9	−	41911.9i	0.854581	−	1.48018i	−0.0224522	−	0.999748i	$-0.507147\pi$
$929$	24197.9	−	41911.9i	0.854581	−	1.48018i	0.877033	−	0.480430i	$-0.159519\pi$
$930$	12831.7	−	11360.5i	0.452439	−	0.400565i
$931$	−6184.08	+	9172.67i	−0.217696	+	0.322902i
$932$	−194.603	+	112.354i	−0.00683951	+	0.00394879i
$933$	−37164.6	+	32903.6i	−1.30409	+	1.15457i
$934$	−28313.1	−	16346.6i	−0.991900	−	0.572673i
$935$		−	36460.7i		−	1.27529i
$936$	−15303.4	−	11515.3i	−0.534410	−	0.402124i
$937$			23667.6i			0.825172i	0.910919	+	0.412586i	$0.135374\pi$
$937$			23667.6i			0.825172i	−0.910919	+	0.412586i	$0.864626\pi$
$938$	9371.76	−	30665.8i	0.326225	−	1.06746i
$939$	6077.10	−	18183.6i	0.211202	−	0.631947i
$940$	−3406.91	−	5900.94i	−0.118214	−	0.204753i
$941$	5099.48	+	8832.56i	0.176661	+	0.305987i	0.940735	−	0.339143i	$-0.110137\pi$
$941$	5099.48	+	8832.56i	0.176661	+	0.305987i	−0.764074	+	0.645129i	$0.776804\pi$
$942$	−4279.04	−	20994.8i	−0.148003	−	0.726164i
$943$	46410.0	+	26794.9i	1.60267	+	0.925303i
$944$	−22579.3			−0.778489
$945$	27354.9	−	29921.9i	0.941644	−	1.03001i
$946$	−81544.0			−2.80256
$947$	−2943.58	−	1699.47i	−0.101007	−	0.0583163i	0.448646	−	0.893710i	$-0.351907\pi$
$947$	−2943.58	−	1699.47i	−0.101007	−	0.0583163i	−0.549652	+	0.835393i	$0.685240\pi$
$948$	383.526	+	1881.74i	0.0131396	+	0.0644684i
$949$	−2462.87	−	4265.82i	−0.0842447	−	0.145916i
$950$	−5716.84	−	9901.85i	−0.195241	−	0.338167i
$951$	−1240.93	+	3713.03i	−0.0423131	+	0.126607i
$952$	4968.67	−	16258.2i	0.169155	−	0.553500i
$953$			27410.8i			0.931714i	0.884860	+	0.465857i	$0.154254\pi$
$953$			27410.8i			0.931714i	−0.884860	+	0.465857i	$0.845746\pi$
$954$	−2089.81	+	17118.6i	−0.0709225	+	0.580959i
$955$		−	57679.7i		−	1.95442i
$956$	1508.14	+	870.725i	0.0510217	+	0.0294574i
$957$	−30708.0	+	27187.2i	−1.03725	+	0.918325i
$958$	24869.3	−	14358.3i	0.838716	−	0.484233i
$959$	−12535.6	−	13439.8i	−0.422101	−	0.452547i
$960$	26525.7	−	23484.4i	0.891785	−	0.789538i
$961$	−12401.2	+	21479.4i	−0.416272	+	0.721005i
$962$	−4064.23			−0.136212
$963$	3990.07	+	9381.85i	0.133518	+	0.313942i
$964$			2606.21i			0.0870750i
$965$	34244.6	−	59313.4i	1.14236	−	1.97862i
$966$	4102.09	−	42807.8i	0.136628	−	1.42580i
$967$	18511.5	+	32062.9i	0.615606	+	1.06626i	0.990278	+	0.139103i	$0.0444221\pi$
$967$	18511.5	+	32062.9i	0.615606	+	1.06626i	−0.374672	+	0.927158i	$0.622245\pi$
$968$	28263.2	−	16317.8i	0.938443	−	0.541810i
$969$	7151.26	−	1457.53i	0.237081	−	0.0483206i
$970$	17025.1	−	29488.4i	0.563550	−	0.976098i
$971$	−17050.2			−0.563509			−0.281754	−	0.959487i	$-0.590916\pi$
$971$	−17050.2			−0.563509			−0.281754	+	0.959487i	$0.590916\pi$
$972$	151.825	−	3621.95i	0.00501006	−	0.119521i
$973$	15047.5	−	3475.74i	0.495786	−	0.114519i
$974$	−21358.2	−	12331.1i	−0.702628	−	0.405662i
$975$	−20295.3	+	4136.48i	−0.666636	+	0.135870i
$976$	21481.1	−	12402.1i	0.704501	−	0.406744i
$977$	−14180.0	+	8186.83i	−0.464338	+	0.268086i	−0.713867	−	0.700282i	$-0.753058\pi$
$977$	−14180.0	+	8186.83i	−0.464338	+	0.268086i	0.249528	+	0.968367i	$0.419724\pi$
$978$	9367.12	−	28027.8i	0.306265	−	0.916390i
$979$	−27697.1	−	15990.9i	−0.904190	−	0.522034i
$980$	4602.86	−	2246.23i	0.150034	−	0.0732176i
$981$	28972.4	−	12321.8i	0.942932	−	0.401026i
$982$	6021.56			0.195678
$983$	10769.1	−	18652.7i	0.349423	−	0.605218i	−0.636724	−	0.771092i	$-0.719711\pi$
$983$	10769.1	−	18652.7i	0.349423	−	0.605218i	0.986147	+	0.165874i	$0.0530444\pi$
$984$	−26057.9	−	29432.5i	−0.844204	−	0.953530i
$985$	28516.2	−	16463.8i	0.922438	−	0.532570i
$986$	−9585.89	−	16603.3i	−0.309612	−	0.536263i
$987$	−35762.5	−	25484.4i	−1.15332	−	0.821860i
$988$	519.345	−	899.533i	0.0167233	−	0.0289655i
$989$			75816.8i			2.43765i
$990$	−8198.23	+	67155.6i	−0.263189	+	2.15590i
$991$	39248.1			1.25808			0.629040	−	0.777373i	$-0.283448\pi$
$991$	39248.1			1.25808			0.629040	+	0.777373i	$0.283448\pi$
$992$	−1521.57	+	2635.44i	−0.0486995	+	0.0843500i
$993$	30745.5	+	10275.4i	0.982557	+	0.328379i
$994$	−31909.5	+	29762.7i	−1.01822	+	0.949713i
$995$	−46526.3	+	26862.0i	−1.48240	+	0.855862i
$996$	196.444	+	963.836i	0.00624956	+	0.0306630i
$997$	3452.73	+	1993.43i	0.109678	+	0.0633226i	0.553836	−	0.832626i	$-0.313164\pi$
$997$	3452.73	+	1993.43i	0.109678	+	0.0633226i	−0.444158	+	0.895949i	$0.646497\pi$
$998$		−	43015.9i		−	1.36437i
$999$	3211.59	+	4662.45i	0.101712	+	0.147661i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.4.o.a.20.17	✓	44
3.2	odd	2		189.4.o.a.62.6		44
7.6	odd	2	inner	63.4.o.a.20.18	yes	44
9.2	odd	6		567.4.c.c.566.8		44
9.4	even	3		189.4.o.a.125.5		44
9.5	odd	6	inner	63.4.o.a.41.18	yes	44
9.7	even	3		567.4.c.c.566.37		44
21.20	even	2		189.4.o.a.62.5		44
63.13	odd	6		189.4.o.a.125.6		44
63.20	even	6		567.4.c.c.566.38		44
63.34	odd	6		567.4.c.c.566.7		44
63.41	even	6	inner	63.4.o.a.41.17	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.o.a.20.17	✓	44	1.1	even	1	trivial
63.4.o.a.20.18	yes	44	7.6	odd	2	inner
63.4.o.a.41.17	yes	44	63.41	even	6	inner
63.4.o.a.41.18	yes	44	9.5	odd	6	inner
189.4.o.a.62.5		44	21.20	even	2
189.4.o.a.62.6		44	3.2	odd	2
189.4.o.a.125.5		44	9.4	even	3
189.4.o.a.125.6		44	63.13	odd	6
567.4.c.c.566.7		44	63.34	odd	6
567.4.c.c.566.8		44	9.2	odd	6
567.4.c.c.566.37		44	9.7	even	3
567.4.c.c.566.38		44	63.20	even	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)

\(f(q)\)	\(=\)	\(q+(2.59186 + 1.49641i) q^{2} +(-1.03772 - 5.09148i) q^{3} +(0.478502 + 0.828790i) q^{4} +(-7.80147 - 13.5125i) q^{5} +(4.92933 - 14.7493i) q^{6} +(17.7116 + 5.41283i) q^{7} -21.0785i q^{8} +(-24.8463 + 10.5670i) q^{9} +O(q^{10})\)	\(q+(2.59186 + 1.49641i) q^{2} +(-1.03772 - 5.09148i) q^{3} +(0.478502 + 0.828790i) q^{4} +(-7.80147 - 13.5125i) q^{5} +(4.92933 - 14.7493i) q^{6} +(17.7116 + 5.41283i) q^{7} -21.0785i q^{8} +(-24.8463 + 10.5670i) q^{9} -46.6969i q^{10} +(46.4700 + 26.8295i) q^{11} +(3.72322 - 3.29633i) q^{12} +(-29.1434 + 16.8260i) q^{13} +(37.8062 + 40.5332i) q^{14} +(-60.7031 + 53.7432i) q^{15} +(35.3701 - 61.2628i) q^{16} +43.5488 q^{17} +(-80.2108 - 9.79199i) q^{18} +32.2524i q^{19} +(7.46605 - 12.9316i) q^{20} +(9.17965 - 95.7953i) q^{21} +(80.2960 + 139.077i) q^{22} +(129.309 - 74.6565i) q^{23} +(-107.320 + 21.8735i) q^{24} +(-59.2260 + 102.582i) q^{25} -100.714 q^{26} +(79.5852 + 115.539i) q^{27} +(3.98894 + 17.2693i) q^{28} +(-127.390 - 73.5487i) q^{29} +(-237.756 + 48.4582i) q^{30} +(-61.1678 + 35.3153i) q^{31} +(37.3130 - 21.5427i) q^{32} +(88.3790 - 264.443i) q^{33} +(112.873 + 65.1670i) q^{34} +(-65.0355 - 281.557i) q^{35} +(-20.6469 - 15.5360i) q^{36} +40.3540 q^{37} +(-48.2629 + 83.5938i) q^{38} +(115.912 + 130.922i) q^{39} +(-284.824 + 164.443i) q^{40} +(179.454 + 310.824i) q^{41} +(167.142 - 234.552i) q^{42} +(-253.886 + 439.743i) q^{43} +51.3519i q^{44} +(336.625 + 253.298i) q^{45} +446.867 q^{46} +(228.160 - 395.185i) q^{47} +(-348.622 - 116.513i) q^{48} +(284.402 + 191.740i) q^{49} +(-307.011 + 177.253i) q^{50} +(-45.1914 - 221.728i) q^{51} +(-27.8904 - 16.1025i) q^{52} -213.420i q^{53} +(33.3805 + 418.553i) q^{54} -837.238i q^{55} +(114.094 - 373.333i) q^{56} +(164.212 - 33.4689i) q^{57} +(-220.118 - 381.256i) q^{58} +(-159.593 - 276.424i) q^{59} +(-73.5884 - 24.5939i) q^{60} +(303.662 + 175.319i) q^{61} -211.385 q^{62} +(-497.265 + 52.6705i) q^{63} -436.974 q^{64} +(454.723 + 262.535i) q^{65} +(624.782 - 553.148i) q^{66} +(-289.258 - 501.009i) q^{67} +(20.8382 + 36.0928i) q^{68} +(-514.298 - 580.900i) q^{69} +(252.762 - 827.077i) q^{70} +787.243i q^{71} +(222.737 + 523.721i) q^{72} +146.373i q^{73} +(104.592 + 60.3863i) q^{74} +(583.756 + 195.096i) q^{75} +(-26.7305 + 15.4329i) q^{76} +(677.836 + 726.728i) q^{77} +(104.513 + 512.785i) q^{78} +(-193.095 + 334.451i) q^{79} -1103.76 q^{80} +(505.676 - 525.103i) q^{81} +1074.15i q^{82} +(-98.9043 + 171.307i) q^{83} +(83.7867 - 38.2302i) q^{84} +(-339.745 - 588.455i) q^{85} +(-1316.07 + 759.835i) q^{86} +(-242.276 + 724.926i) q^{87} +(565.524 - 979.517i) q^{88} -596.020 q^{89} +(493.448 + 1160.24i) q^{90} +(-607.253 + 140.267i) q^{91} +(123.749 + 71.4466i) q^{92} +(243.282 + 274.787i) q^{93} +(1182.72 - 682.844i) q^{94} +(435.812 - 251.616i) q^{95} +(-148.404 - 167.623i) q^{96} +(631.485 + 364.588i) q^{97} +(450.210 + 922.547i) q^{98} +(-1438.12 - 175.563i) 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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