LMFDB - Embedded newform 40.5.i.a.13.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [40,5,Mod(13,40)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(40, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 3]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("40.13");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 40 = 2^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	40.i (of order $4$, 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:	$4.13479852335$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.12
Character	$\chi$	$=$	40.13
Dual form			40.5.i.a.37.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.133745 - 3.99776i) q^{2} +(-4.11430 + 4.11430i) q^{3} +(-15.9642 + 1.06936i) q^{4} +(3.95777 + 24.6847i) q^{5} +(16.9983 + 15.8977i) q^{6} +(-12.8562 + 12.8562i) q^{7} +(6.41019 + 63.6782i) q^{8} +47.1451i q^{9} +O(q^{10})$	\(q+(-0.133745 - 3.99776i) q^{2} +(-4.11430 + 4.11430i) q^{3} +(-15.9642 + 1.06936i) q^{4} +(3.95777 + 24.6847i) q^{5} +(16.9983 + 15.8977i) q^{6} +(-12.8562 + 12.8562i) q^{7} +(6.41019 + 63.6782i) q^{8} +47.1451i q^{9} +(98.1544 - 19.1237i) q^{10} -28.7483i q^{11} +(61.2819 - 70.0813i) q^{12} +(-21.7965 + 21.7965i) q^{13} +(53.1156 + 49.6767i) q^{14} +(-117.844 - 85.2769i) q^{15} +(253.713 - 34.1431i) q^{16} +(-308.195 + 308.195i) q^{17} +(188.475 - 6.30542i) q^{18} -85.6646 q^{19} +(-89.5796 - 389.840i) q^{20} -105.789i q^{21} +(-114.929 + 3.84495i) q^{22} +(-329.432 - 329.432i) q^{23} +(-288.364 - 235.618i) q^{24} +(-593.672 + 195.393i) q^{25} +(90.0526 + 84.2223i) q^{26} +(-527.227 - 527.227i) q^{27} +(191.492 - 218.988i) q^{28} +1284.31 q^{29} +(-325.156 + 482.517i) q^{30} +856.093 q^{31} +(-170.429 - 1009.72i) q^{32} +(118.279 + 118.279i) q^{33} +(1273.31 + 1190.87i) q^{34} +(-368.235 - 266.471i) q^{35} +(-50.4152 - 752.635i) q^{36} +(981.143 + 981.143i) q^{37} +(11.4572 + 342.467i) q^{38} -179.355i q^{39} +(-1546.51 + 410.257i) q^{40} +1653.37 q^{41} +(-422.918 + 14.1487i) q^{42} +(-2043.51 + 2043.51i) q^{43} +(30.7424 + 458.945i) q^{44} +(-1163.76 + 186.589i) q^{45} +(-1272.93 + 1361.05i) q^{46} +(2904.24 - 2904.24i) q^{47} +(-903.376 + 1184.33i) q^{48} +2070.43i q^{49} +(860.535 + 2347.23i) q^{50} -2536.02i q^{51} +(324.657 - 371.273i) q^{52} +(-648.030 + 648.030i) q^{53} +(-2037.22 + 2178.24i) q^{54} +(709.645 - 113.779i) q^{55} +(-901.072 - 736.250i) q^{56} +(352.450 - 352.450i) q^{57} +(-171.771 - 5134.38i) q^{58} +3546.69 q^{59} +(1972.48 + 1235.36i) q^{60} -1602.53i q^{61} +(-114.498 - 3422.46i) q^{62} +(-606.108 - 606.108i) q^{63} +(-4013.82 + 816.379i) q^{64} +(-624.308 - 451.776i) q^{65} +(457.033 - 488.672i) q^{66} +(1116.47 + 1116.47i) q^{67} +(4590.53 - 5249.67i) q^{68} +2710.76 q^{69} +(-1016.04 + 1507.75i) q^{70} -6649.74 q^{71} +(-3002.11 + 302.209i) q^{72} +(-2152.50 - 2152.50i) q^{73} +(3791.15 - 4053.60i) q^{74} +(1638.64 - 3246.45i) q^{75} +(1367.57 - 91.6065i) q^{76} +(369.595 + 369.595i) q^{77} +(-717.019 + 23.9878i) q^{78} +9290.39i q^{79} +(1846.95 + 6127.71i) q^{80} +519.588 q^{81} +(-221.131 - 6609.80i) q^{82} +(-5044.05 + 5044.05i) q^{83} +(113.126 + 1688.84i) q^{84} +(-8827.48 - 6387.95i) q^{85} +(8442.79 + 7896.17i) q^{86} +(-5284.05 + 5284.05i) q^{87} +(1830.64 - 184.282i) q^{88} -9904.95i q^{89} +(901.587 + 4627.50i) q^{90} -560.443i q^{91} +(5611.41 + 4906.85i) q^{92} +(-3522.22 + 3522.22i) q^{93} +(-11998.9 - 11222.0i) q^{94} +(-339.041 - 2114.61i) q^{95} +(4855.48 + 3453.09i) q^{96} +(-4549.17 + 4549.17i) q^{97} +(8277.11 - 276.910i) q^{98} +1355.34 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 2 q^{2} + 32 q^{6} - 4 q^{7} - 92 q^{8}+O(q^{10}) $ 44 * q - 2 * q^2 + 32 * q^6 - 4 * q^7 - 92 * q^8	$ 44 q - 2 q^{2} + 32 q^{6} - 4 q^{7} - 92 q^{8} - 154 q^{10} + 196 q^{12} - 4 q^{15} + 72 q^{16} + 236 q^{17} + 682 q^{18} - 904 q^{20} - 740 q^{22} - 4 q^{23} + 332 q^{25} - 2236 q^{26} + 2740 q^{28} + 3940 q^{30} - 264 q^{31} - 4352 q^{32} + 320 q^{33} - 4580 q^{36} - 4684 q^{38} + 5276 q^{40} - 8 q^{41} + 6676 q^{42} + 6784 q^{46} - 5764 q^{47} - 4000 q^{48} - 674 q^{50} + 5556 q^{52} + 2496 q^{55} + 13304 q^{56} - 328 q^{57} - 804 q^{58} + 3740 q^{60} - 13984 q^{62} + 9924 q^{63} - 3700 q^{65} - 12248 q^{66} - 11700 q^{68} - 10820 q^{70} - 19976 q^{71} - 17572 q^{72} + 13196 q^{73} - 12344 q^{76} + 23104 q^{78} - 24624 q^{80} - 13812 q^{81} + 15116 q^{82} + 16400 q^{86} + 48952 q^{87} + 35920 q^{88} + 49926 q^{90} + 25020 q^{92} - 27848 q^{95} + 42176 q^{96} + 3276 q^{97} - 65998 q^{98}+O(q^{100}) $ 44 * q - 2 * q^2 + 32 * q^6 - 4 * q^7 - 92 * q^8 - 154 * q^10 + 196 * q^12 - 4 * q^15 + 72 * q^16 + 236 * q^17 + 682 * q^18 - 904 * q^20 - 740 * q^22 - 4 * q^23 + 332 * q^25 - 2236 * q^26 + 2740 * q^28 + 3940 * q^30 - 264 * q^31 - 4352 * q^32 + 320 * q^33 - 4580 * q^36 - 4684 * q^38 + 5276 * q^40 - 8 * q^41 + 6676 * q^42 + 6784 * q^46 - 5764 * q^47 - 4000 * q^48 - 674 * q^50 + 5556 * q^52 + 2496 * q^55 + 13304 * q^56 - 328 * q^57 - 804 * q^58 + 3740 * q^60 - 13984 * q^62 + 9924 * q^63 - 3700 * q^65 - 12248 * q^66 - 11700 * q^68 - 10820 * q^70 - 19976 * q^71 - 17572 * q^72 + 13196 * q^73 - 12344 * q^76 + 23104 * q^78 - 24624 * q^80 - 13812 * q^81 + 15116 * q^82 + 16400 * q^86 + 48952 * q^87 + 35920 * q^88 + 49926 * q^90 + 25020 * q^92 - 27848 * q^95 + 42176 * q^96 + 3276 * q^97 - 65998 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/40\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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 $

$2$	−0.133745	−	3.99776i	−0.0334363	−	0.999441i
$2$	−0.133745	−	3.99776i	−0.0334363	−	0.999441i
$3$	−4.11430	+	4.11430i	−0.457144	+	0.457144i	−0.897717	−	0.440573i	$-0.854775\pi$
$3$	−4.11430	+	4.11430i	−0.457144	+	0.457144i	0.440573	+	0.897717i	$0.354775\pi$
$4$	−15.9642	+	1.06936i	−0.997764	+	0.0668351i
$5$	3.95777	+	24.6847i	0.158311	+	0.987389i
$5$	3.95777	+	24.6847i	0.158311	+	0.987389i
$6$	16.9983	+	15.8977i	0.472174	+	0.441603i
$7$	−12.8562	+	12.8562i	−0.262372	+	0.262372i	−0.826017	−	0.563645i	$-0.809399\pi$
$7$	−12.8562	+	12.8562i	−0.262372	+	0.262372i	0.563645	+	0.826017i	$0.309399\pi$
$8$	6.41019	+	63.6782i	0.100159	+	0.994971i
$9$			47.1451i			0.582038i
$10$	98.1544	−	19.1237i	0.981544	−	0.191237i
$11$		−	28.7483i		−	0.237590i	−0.992919	−	0.118795i	$-0.962097\pi$
$11$		−	28.7483i		−	0.237590i	0.992919	−	0.118795i	$-0.0379031\pi$
$12$	61.2819	−	70.0813i	0.425569	−	0.486675i
$13$	−21.7965	+	21.7965i	−0.128974	+	0.128974i	−0.768647	−	0.639673i	$-0.779070\pi$
$13$	−21.7965	+	21.7965i	−0.128974	+	0.128974i	0.639673	+	0.768647i	$0.279070\pi$
$14$	53.1156	+	49.6767i	0.270998	+	0.253453i
$15$	−117.844	−	85.2769i	−0.523750	−	0.379009i
$16$	253.713	−	34.1431i	0.991066	−	0.133371i
$17$	−308.195	+	308.195i	−1.06642	+	1.06642i	−0.0687884	+	0.997631i	$0.521913\pi$
$17$	−308.195	+	308.195i	−1.06642	+	1.06642i	−0.997631	+	0.0687884i	$0.978087\pi$
$18$	188.475	−	6.30542i	0.581713	−	0.0194612i
$19$	−85.6646			−0.237298			−0.118649	−	0.992936i	$-0.537856\pi$
$19$	−85.6646			−0.237298			−0.118649	+	0.992936i	$0.537856\pi$
$20$	−89.5796	−	389.840i	−0.223949	−	0.974601i
$21$		−	105.789i		−	0.239884i
$22$	−114.929	+	3.84495i	−0.237457	+	0.00794411i
$23$	−329.432	−	329.432i	−0.622745	−	0.622745i	0.323487	−	0.946232i	$-0.395145\pi$
$23$	−329.432	−	329.432i	−0.622745	−	0.622745i	−0.946232	+	0.323487i	$0.895145\pi$
$24$	−288.364	−	235.618i	−0.500633	−	0.409058i
$25$	−593.672	+	195.393i	−0.949875	+	0.312629i
$26$	90.0526	+	84.2223i	0.133214	+	0.124589i
$27$	−527.227	−	527.227i	−0.723220	−	0.723220i
$28$	191.492	−	218.988i	0.244250	−	0.279321i
$29$	1284.31			1.52713			0.763563	−	0.645733i	$-0.223448\pi$
$29$	1284.31			1.52713			0.763563	+	0.645733i	$0.223448\pi$
$30$	−325.156	+	482.517i	−0.361284	+	0.536130i
$31$	856.093			0.890835			0.445418	−	0.895323i	$-0.353055\pi$
$31$	856.093			0.890835			0.445418	+	0.895323i	$0.353055\pi$
$32$	−170.429	−	1009.72i	−0.166434	−	0.986053i
$33$	118.279	+	118.279i	0.108613	+	0.108613i
$34$	1273.31	+	1190.87i	1.10148	+	1.03017i
$35$	−368.235	−	266.471i	−0.300600	−	0.217527i
$36$	−50.4152	−	752.635i	−0.0389006	−	0.580737i
$37$	981.143	+	981.143i	0.716686	+	0.716686i	0.967925	−	0.251239i	$-0.0808381\pi$
$37$	981.143	+	981.143i	0.716686	+	0.716686i	−0.251239	+	0.967925i	$0.580838\pi$
$38$	11.4572	+	342.467i	0.00793436	+	0.237165i
$39$		−	179.355i		−	0.117919i
$40$	−1546.51	+	410.257i	−0.966568	+	0.256411i
$41$	1653.37			0.983566			0.491783	−	0.870718i	$-0.336345\pi$
$41$	1653.37			0.983566			0.491783	+	0.870718i	$0.336345\pi$
$42$	−422.918	+	14.1487i	−0.239750	+	0.00802082i
$43$	−2043.51	+	2043.51i	−1.10520	+	1.10520i	−0.111426	+	0.993773i	$0.535542\pi$
$43$	−2043.51	+	2043.51i	−1.10520	+	1.10520i	−0.993773	+	0.111426i	$0.964458\pi$
$44$	30.7424	+	458.945i	0.0158793	+	0.237058i
$45$	−1163.76	+	186.589i	−0.574698	+	0.0921428i
$46$	−1272.93	+	1361.05i	−0.601575	+	0.643219i
$47$	2904.24	−	2904.24i	1.31473	−	1.31473i	0.396848	−	0.917884i	$-0.370104\pi$
$47$	2904.24	−	2904.24i	1.31473	−	1.31473i	0.917884	−	0.396848i	$-0.129896\pi$
$48$	−903.376	+	1184.33i	−0.392090	+	0.514030i
$49$			2070.43i			0.862322i
$50$	860.535	+	2347.23i	0.344214	+	0.938891i
$51$		−	2536.02i		−	0.975015i
$52$	324.657	−	371.273i	0.120065	−	0.137305i
$53$	−648.030	+	648.030i	−0.230698	+	0.230698i	−0.812984	−	0.582286i	$-0.802158\pi$
$53$	−648.030	+	648.030i	−0.230698	+	0.230698i	0.582286	+	0.812984i	$0.302158\pi$
$54$	−2037.22	+	2178.24i	−0.698634	+	0.746997i
$55$	709.645	−	113.779i	0.234593	−	0.0376130i
$56$	−901.072	−	736.250i	−0.287332	−	0.234774i
$57$	352.450	−	352.450i	0.108479	−	0.108479i
$58$	−171.771	−	5134.38i	−0.0510614	−	1.52627i
$59$	3546.69			1.01887			0.509435	−	0.860509i	$-0.329854\pi$
$59$	3546.69			1.01887			0.509435	+	0.860509i	$0.329854\pi$
$60$	1972.48	+	1235.36i	0.547910	+	0.343156i
$61$		−	1602.53i		−	0.430671i	−0.976540	−	0.215335i	$-0.930916\pi$
$61$		−	1602.53i		−	0.430671i	0.976540	−	0.215335i	$-0.0690845\pi$
$62$	−114.498	−	3422.46i	−0.0297862	−	0.890337i
$63$	−606.108	−	606.108i	−0.152711	−	0.152711i
$64$	−4013.82	+	816.379i	−0.979936	+	0.199311i
$65$	−624.308	−	451.776i	−0.147765	−	0.106929i
$66$	457.033	−	488.672i	0.104920	−	0.112184i
$67$	1116.47	+	1116.47i	0.248713	+	0.248713i	0.820442	−	0.571729i	$-0.193727\pi$
$67$	1116.47	+	1116.47i	0.248713	+	0.248713i	−0.571729	+	0.820442i	$0.693727\pi$
$68$	4590.53	−	5249.67i	0.992761	−	1.13531i
$69$	2710.76			0.569369
$70$	−1016.04	+	1507.75i	−0.207354	+	0.307705i
$71$	−6649.74			−1.31913			−0.659566	−	0.751647i	$-0.729260\pi$
$71$	−6649.74			−1.31913			−0.659566	+	0.751647i	$0.729260\pi$
$72$	−3002.11	+	302.209i	−0.579111	+	0.0582965i
$73$	−2152.50	−	2152.50i	−0.403923	−	0.403923i	0.475690	−	0.879613i	$-0.342198\pi$
$73$	−2152.50	−	2152.50i	−0.403923	−	0.403923i	−0.879613	+	0.475690i	$0.842198\pi$
$74$	3791.15	−	4053.60i	0.692322	−	0.740248i
$75$	1638.64	−	3246.45i	0.291314	−	0.577147i
$76$	1367.57	−	91.6065i	0.236768	−	0.0158599i
$77$	369.595	+	369.595i	0.0623369	+	0.0623369i
$78$	−717.019	+	23.9878i	−0.117853	+	0.00394278i
$79$			9290.39i			1.48861i	0.667842	+	0.744303i	$0.267218\pi$
$79$			9290.39i			1.48861i	−0.667842	+	0.744303i	$0.732782\pi$
$80$	1846.95	+	6127.71i	0.288586	+	0.957454i
$81$	519.588			0.0791934
$82$	−221.131	−	6609.80i	−0.0328868	−	0.983016i
$83$	−5044.05	+	5044.05i	−0.732189	+	0.732189i	−0.971053	−	0.238864i	$-0.923225\pi$
$83$	−5044.05	+	5044.05i	−0.732189	+	0.732189i	0.238864	+	0.971053i	$0.423225\pi$
$84$	113.126	+	1688.84i	0.0160327	+	0.239347i
$85$	−8827.48	−	6387.95i	−1.22180	−	0.884146i
$86$	8442.79	+	7896.17i	1.14153	+	1.06763i
$87$	−5284.05	+	5284.05i	−0.698117	+	0.698117i
$88$	1830.64	−	184.282i	0.236395	−	0.0237968i
$89$		−	9904.95i		−	1.25047i	−0.780438	−	0.625233i	$-0.785004\pi$
$89$		−	9904.95i		−	1.25047i	0.780438	−	0.625233i	$-0.214996\pi$
$90$	901.587	+	4627.50i	0.111307	+	0.571296i
$91$		−	560.443i		−	0.0676781i
$92$	5611.41	+	4906.85i	0.662974	+	0.579731i
$93$	−3522.22	+	3522.22i	−0.407240	+	0.407240i
$94$	−11998.9	−	11222.0i	−1.35796	−	1.27004i
$95$	−339.041	−	2114.61i	−0.0375668	−	0.234306i
$96$	4855.48	+	3453.09i	0.526853	+	0.374684i
$97$	−4549.17	+	4549.17i	−0.483491	+	0.483491i	−0.906245	−	0.422753i	$-0.861064\pi$
$97$	−4549.17	+	4549.17i	−0.483491	+	0.483491i	0.422753	+	0.906245i	$0.361064\pi$
$98$	8277.11	−	276.910i	0.861840	−	0.0288328i
$99$	1355.34			0.138286
$100$	9268.57	−	3754.15i	0.926857	−	0.375415i
$101$			1938.41i			0.190022i	0.995476	+	0.0950109i	$0.0302886\pi$
$101$			1938.41i			0.190022i	−0.995476	+	0.0950109i	$0.969711\pi$
$102$	−10138.4	+	339.180i	−0.974470	+	0.0326009i
$103$	9226.65	+	9226.65i	0.869700	+	0.869700i	0.992439	−	0.122739i	$-0.0391678\pi$
$103$	9226.65	+	9226.65i	0.869700	+	0.869700i	−0.122739	+	0.992439i	$0.539168\pi$
$104$	−1527.68	−	1248.24i	−0.141243	−	0.115407i
$105$	2611.37	−	418.687i	0.236859	−	0.0379762i
$106$	2677.34	+	2504.00i	0.238282	+	0.222855i
$107$	15947.7	+	15947.7i	1.39293	+	1.39293i	0.818672	+	0.574261i	$0.194711\pi$
$107$	15947.7	+	15947.7i	1.39293	+	1.39293i	0.574261	+	0.818672i	$0.305289\pi$
$108$	8980.57	+	7852.98i	0.769939	+	0.673266i
$109$	1035.03			0.0871163			0.0435582	−	0.999051i	$-0.486131\pi$
$109$	1035.03			0.0871163			0.0435582	+	0.999051i	$0.486131\pi$
$110$	−549.774	−	2821.78i	−0.0454359	−	0.233205i
$111$	−8073.43			−0.655258
$112$	−2822.84	+	3700.74i	−0.225035	+	0.295021i
$113$	473.361	+	473.361i	0.0370711	+	0.0370711i	0.725399	−	0.688328i	$-0.241655\pi$
$113$	473.361	+	473.361i	0.0370711	+	0.0370711i	−0.688328	+	0.725399i	$0.741655\pi$
$114$	−1456.15	−	1361.87i	−0.112046	−	0.104792i
$115$	6828.13	−	9435.76i	0.516305	−	0.713479i
$116$	−20503.1	+	1373.40i	−1.52371	+	0.102066i
$117$	−1027.60	−	1027.60i	−0.0750676	−	0.0750676i
$118$	−474.352	−	14178.8i	−0.0340672	−	1.01830i
$119$		−	7924.46i		−	0.559597i
$120$	4674.88	−	8050.72i	0.324644	−	0.559078i
$121$	13814.5			0.943551
$122$	−6406.52	+	214.330i	−0.430430	+	0.0144000i
$123$	−6802.48	+	6802.48i	−0.449632	+	0.449632i
$124$	−13666.9	+	915.473i	−0.888843	+	0.0595391i
$125$	−7172.84	−	13881.3i	−0.459061	−	0.888405i
$126$	−2342.01	+	2504.14i	−0.147519	+	0.157731i
$127$	−710.744	+	710.744i	−0.0440662	+	0.0440662i	−0.728797	−	0.684730i	$-0.759920\pi$
$127$	−710.744	+	710.744i	−0.0440662	+	0.0440662i	0.684730	+	0.728797i	$0.259920\pi$
$128$	3800.52	+	15937.1i	0.231965	+	0.972724i
$129$		−	16815.2i		−	1.01047i
$130$	−1722.60	+	2556.26i	−0.101929	+	0.151258i
$131$		−	24015.9i		−	1.39945i	−0.714414	−	0.699724i	$-0.753306\pi$
$131$		−	24015.9i		−	1.39945i	0.714414	−	0.699724i	$-0.246694\pi$
$132$	−2014.72	−	1761.75i	−0.115629	−	0.101111i
$133$	1101.32	−	1101.32i	0.0622604	−	0.0622604i
$134$	4314.07	−	4612.71i	0.240258	−	0.256890i
$135$	10927.8	−	15101.1i	0.599606	−	0.828593i
$136$	−21600.9	−	17649.7i	−1.16787	−	0.954245i
$137$	3603.80	−	3603.80i	0.192008	−	0.192008i	−0.604555	−	0.796563i	$-0.706649\pi$
$137$	3603.80	−	3603.80i	0.192008	−	0.192008i	0.796563	+	0.604555i	$0.206649\pi$
$138$	−362.551	−	10837.0i	−0.0190376	−	0.569050i
$139$	−12230.4			−0.633009			−0.316504	−	0.948591i	$-0.602509\pi$
$139$	−12230.4			−0.633009			−0.316504	+	0.948591i	$0.602509\pi$
$140$	6163.53	+	3860.22i	0.314466	+	0.196950i
$141$			23897.8i			1.20204i
$142$	889.371	+	26584.1i	0.0441069	+	1.31839i
$143$	626.614	+	626.614i	0.0306428	+	0.0306428i
$144$	1609.68	+	11961.3i	0.0776272	+	0.576838i
$145$	5083.01	+	31702.9i	0.241760	+	1.50787i
$146$	−8317.32	+	8893.09i	−0.390191	+	0.417203i
$147$	−8518.39	−	8518.39i	−0.394206	−	0.394206i
$148$	−16712.4	−	14614.0i	−0.762983	−	0.667183i
$149$	22723.6			1.02354			0.511771	−	0.859122i	$-0.328990\pi$
$149$	22723.6			1.02354			0.511771	+	0.859122i	$0.328990\pi$
$150$	−13197.7	−	6116.70i	−0.586564	−	0.271853i
$151$	10020.9			0.439494			0.219747	−	0.975557i	$-0.429477\pi$
$151$	10020.9			0.439494			0.219747	+	0.975557i	$0.429477\pi$
$152$	−549.127	−	5454.97i	−0.0237676	−	0.236105i
$153$	−14529.9	−	14529.9i	−0.620697	−	0.620697i
$154$	1428.12	−	1526.99i	0.0602177	−	0.0643863i
$155$	3388.21	+	21132.4i	0.141029	+	0.879601i
$156$	191.795	+	2863.26i	0.00788114	+	0.117655i
$157$	−59.1308	−	59.1308i	−0.00239891	−	0.00239891i	0.705906	−	0.708305i	$-0.250540\pi$
$157$	−59.1308	−	59.1308i	−0.00239891	−	0.00239891i	−0.708305	+	0.705906i	$0.750540\pi$
$158$	37140.8	−	1242.54i	1.48777	−	0.0497735i
$159$		−	5332.37i		−	0.210924i
$160$	24250.1	−	8203.22i	0.947269	−	0.320438i
$161$	8470.51			0.326782
$162$	−69.4923	−	2077.19i	−0.00264793	−	0.0791491i
$163$	−14.9176	+	14.9176i	−0.000561467	+	0.000561467i	−0.707387	−	0.706826i	$-0.750126\pi$
$163$	−14.9176	+	14.9176i	−0.000561467	+	0.000561467i	0.706826	+	0.707387i	$0.250126\pi$
$164$	−26394.8	+	1768.06i	−0.981367	+	0.0657368i
$165$	−2451.57	+	3387.81i	−0.0900485	+	0.124438i
$166$	20839.5	+	19490.3i	0.756261	+	0.707298i
$167$	15738.4	−	15738.4i	0.564322	−	0.564322i	−0.366210	−	0.930532i	$-0.619345\pi$
$167$	15738.4	−	15738.4i	0.564322	−	0.564322i	0.930532	+	0.366210i	$0.119345\pi$
$168$	6736.43	−	678.126i	0.238677	−	0.0240266i
$169$			27610.8i			0.966732i
$170$	−24356.9	+	36144.5i	−0.842799	+	1.25068i
$171$		−	4038.67i		−	0.138117i
$172$	30437.8	−	34808.3i	1.02886	−	1.17659i
$173$	26161.8	−	26161.8i	0.874130	−	0.874130i	−0.118790	−	0.992919i	$-0.537901\pi$
$173$	26161.8	−	26161.8i	0.874130	−	0.874130i	0.992919	+	0.118790i	$0.0379014\pi$
$174$	21831.1	+	20417.7i	0.721069	+	0.674384i
$175$	5120.37	−	10144.4i	0.167196	−	0.331246i
$176$	−981.557	−	7293.83i	−0.0316877	−	0.235467i
$177$	−14592.1	+	14592.1i	−0.465771	+	0.465771i
$178$	−39597.6	+	1324.74i	−1.24977	+	0.0418109i
$179$	−48997.1			−1.52920			−0.764599	−	0.644506i	$-0.777063\pi$
$179$	−48997.1			−1.52920			−0.764599	+	0.644506i	$0.777063\pi$
$180$	18379.1	−	4223.24i	0.567255	−	0.130347i
$181$			39459.0i			1.20445i	0.798326	+	0.602225i	$0.205719\pi$
$181$			39459.0i			1.20445i	−0.798326	+	0.602225i	$0.794281\pi$
$182$	−2240.52	+	74.9565i	−0.0676403	+	0.00226290i
$183$	6593.27	+	6593.27i	0.196879	+	0.196879i
$184$	18865.9	−	23089.4i	0.557240	−	0.681987i
$185$	−20336.1	+	28102.4i	−0.594189	+	0.821107i
$186$	14552.1	+	13609.9i	0.420629	+	0.393396i
$187$	8860.10	+	8860.10i	0.253370	+	0.253370i
$188$	−43258.3	+	49469.7i	−1.22392	+	1.39966i
$189$	13556.3			0.379505
$190$	−8408.36	+	1638.22i	−0.232919	+	0.0453801i
$191$	−52088.3			−1.42782			−0.713909	−	0.700238i	$-0.753077\pi$
$191$	−52088.3			−1.42782			−0.713909	+	0.700238i	$0.753077\pi$
$192$	13155.2	−	19872.9i	0.356858	−	0.539086i
$193$	−23187.6	−	23187.6i	−0.622504	−	0.622504i	0.323667	−	0.946171i	$-0.395084\pi$
$193$	−23187.6	−	23187.6i	−0.622504	−	0.622504i	−0.946171	+	0.323667i	$0.895084\pi$
$194$	18794.9	+	17578.1i	0.499387	+	0.467055i
$195$	4427.33	−	709.845i	0.116432	−	0.0186679i
$196$	−2214.04	−	33052.9i	−0.0576334	−	0.860394i
$197$	−22984.9	−	22984.9i	−0.592256	−	0.592256i	0.345984	−	0.938240i	$-0.387545\pi$
$197$	−22984.9	−	22984.9i	−0.592256	−	0.592256i	−0.938240	+	0.345984i	$0.887545\pi$
$198$	−181.270	−	5418.34i	−0.00462377	−	0.138209i
$199$			36864.9i			0.930909i	0.885072	+	0.465454i	$0.154109\pi$
$199$			36864.9i			0.930909i	−0.885072	+	0.465454i	$0.845891\pi$
$200$	−16247.8	−	36551.5i	−0.406195	−	0.913786i
$201$	−9187.00			−0.227395
$202$	7749.31	−	259.253i	0.189916	−	0.00635362i
$203$	−16511.4	+	16511.4i	−0.400675	+	0.400675i
$204$	2711.92	+	40485.5i	0.0651653	+	0.972835i
$205$	6543.67	+	40813.1i	0.155709	+	0.971163i
$206$	35651.9	−	38120.0i	0.840134	−	0.898293i
$207$	15531.1	−	15531.1i	0.362461	−	0.362461i
$208$	−4785.86	+	6274.27i	−0.110620	+	0.145023i
$209$			2462.72i			0.0563796i
$210$	−2023.07	−	10383.6i	−0.0458746	−	0.235456i
$211$		−	74222.0i		−	1.66712i	−0.552427	−	0.833561i	$-0.686298\pi$
$211$		−	74222.0i		−	1.66712i	0.552427	−	0.833561i	$-0.313702\pi$
$212$	9652.31	−	11038.3i	0.214763	−	0.245600i
$213$	27359.0	−	27359.0i	0.603034	−	0.603034i
$214$	61622.2	−	65888.0i	1.34558	−	1.43873i
$215$	−58531.3	−	42355.8i	−1.26623	−	0.916297i
$216$	30193.2	−	36952.5i	0.647146	−	0.792020i
$217$	−11006.1	+	11006.1i	−0.233730	+	0.233730i
$218$	−138.430	−	4137.80i	−0.00291284	−	0.0870676i
$219$	17712.1			0.369302
$220$	−11207.3	+	2575.26i	−0.231555	+	0.0532079i
$221$		−	13435.2i		−	0.275080i
$222$	1079.78	+	32275.7i	0.0219094	+	0.654891i
$223$	17996.0	+	17996.0i	0.361881	+	0.361881i	0.864505	−	0.502624i	$-0.167632\pi$
$223$	17996.0	+	17996.0i	0.361881	+	0.361881i	−0.502624	+	0.864505i	$0.667632\pi$
$224$	15172.2	+	10790.1i	0.302380	+	0.215045i
$225$	−9211.81	−	27988.7i	−0.181962	−	0.552864i
$226$	1829.08	−	1955.70i	0.0358109	−	0.0382899i
$227$	−35868.7	−	35868.7i	−0.696088	−	0.696088i	0.267477	−	0.963564i	$-0.413810\pi$
$227$	−35868.7	−	35868.7i	−0.696088	−	0.696088i	−0.963564	+	0.267477i	$0.913810\pi$
$228$	−5249.69	+	6003.49i	−0.100987	+	0.115487i
$229$	953.925			0.0181904			0.00909522	−	0.999959i	$-0.497105\pi$
$229$	953.925			0.0181904			0.00909522	+	0.999959i	$0.497105\pi$
$230$	−38635.2	−	26035.3i	−0.730343	−	0.492160i
$231$	−3041.25			−0.0569939
$232$	8232.70	+	81782.7i	0.152956	+	1.51945i
$233$	25388.1	+	25388.1i	0.467647	+	0.467647i	0.901151	−	0.433505i	$-0.142723\pi$
$233$	25388.1	+	25388.1i	0.467647	+	0.467647i	−0.433505	+	0.901151i	$0.642723\pi$
$234$	−3970.67	+	4245.54i	−0.0725156	+	0.0775356i
$235$	83184.8	+	60196.2i	1.50629	+	1.09002i
$236$	−56620.2	+	3792.70i	−1.01659	+	0.0680964i
$237$	−38223.5	−	38223.5i	−0.680508	−	0.680508i
$238$	−31680.1	+	1059.86i	−0.559284	+	0.0187108i
$239$			28697.1i			0.502392i	0.967936	+	0.251196i	$0.0808239\pi$
$239$			28697.1i			0.502392i	−0.967936	+	0.251196i	$0.919176\pi$
$240$	−32810.1	−	17612.3i	−0.569620	−	0.305769i
$241$	63465.5			1.09271			0.546353	−	0.837555i	$-0.316016\pi$
$241$	63465.5			1.09271			0.546353	+	0.837555i	$0.316016\pi$
$242$	−1847.63	−	55227.2i	−0.0315488	−	0.943024i
$243$	40567.7	−	40567.7i	0.687017	−	0.687017i
$244$	1713.68	+	25583.1i	0.0287840	+	0.429708i
$245$	−51108.1	+	8194.30i	−0.851447	+	0.136515i
$246$	28104.5	+	26284.9i	0.464414	+	0.434346i
$247$	1867.19	−	1867.19i	0.0306052	−	0.0306052i
$248$	5487.72	+	54514.4i	0.0892254	+	0.886356i
$249$		−	41505.4i		−	0.669432i
$250$	−54534.9	+	30531.9i	−0.872558	+	0.488510i
$251$			105134.i			1.66877i	0.551185	+	0.834383i	$0.314176\pi$
$251$			105134.i			1.66877i	−0.551185	+	0.834383i	$0.685824\pi$
$252$	10324.2	+	9027.90i	0.162575	+	0.142163i
$253$	−9470.63	+	9470.63i	−0.147958	+	0.147958i
$254$	2936.44	+	2746.33i	0.0455150	+	0.0425682i
$255$	62600.9	−	10037.0i	0.962720	−	0.154355i
$256$	63204.5	−	17325.1i	0.964424	−	0.264360i
$257$	47393.5	−	47393.5i	0.717551	−	0.717551i	−0.250552	−	0.968103i	$-0.580612\pi$
$257$	47393.5	−	47393.5i	0.717551	−	0.717551i	0.968103	+	0.250552i	$0.0806121\pi$
$258$	−67223.4	+	2248.96i	−1.00991	+	0.0337864i
$259$	−25227.6			−0.376077
$260$	10449.7	+	6544.65i	0.154581	+	0.0968143i
$261$			60549.1i			0.888846i
$262$	−96010.0	+	3212.01i	−1.39866	+	0.0467923i
$263$	15315.7	+	15315.7i	0.221424	+	0.221424i	0.809098	−	0.587674i	$-0.199956\pi$
$263$	15315.7	+	15315.7i	0.221424	+	0.221424i	−0.587674	+	0.809098i	$0.699956\pi$
$264$	−6773.61	+	8290.00i	−0.0971880	+	0.118945i
$265$	−18561.2	−	13431.7i	−0.264310	−	0.191266i
$266$	−4550.13	−	4255.54i	−0.0643073	−	0.0601438i
$267$	40751.9	+	40751.9i	0.571644	+	0.571644i
$268$	−19017.5	−	16629.7i	−0.264780	−	0.231534i
$269$	−57037.7			−0.788239			−0.394119	−	0.919059i	$-0.628950\pi$
$269$	−57037.7			−0.788239			−0.394119	+	0.919059i	$0.628950\pi$
$270$	−61832.2	−	41667.1i	−0.848178	−	0.571566i
$271$	43819.2			0.596658			0.298329	−	0.954463i	$-0.403571\pi$
$271$	43819.2			0.596658			0.298329	+	0.954463i	$0.403571\pi$
$272$	−67670.4	+	88715.9i	−0.914663	+	1.19912i
$273$	2305.83	+	2305.83i	0.0309387	+	0.0309387i
$274$	−14889.1	−	13925.1i	−0.198321	−	0.185481i
$275$	5617.22	+	17067.1i	0.0742773	+	0.225681i
$276$	−43275.3	+	2898.79i	−0.568096	+	0.0380538i
$277$	−17820.9	−	17820.9i	−0.232258	−	0.232258i	0.581376	−	0.813635i	$-0.302514\pi$
$277$	−17820.9	−	17820.9i	−0.232258	−	0.232258i	−0.813635	+	0.581376i	$0.802514\pi$
$278$	1635.75	+	48894.1i	0.0211654	+	0.632655i
$279$			40360.6i			0.518500i
$280$	14607.9	−	25156.6i	0.186325	−	0.320875i
$281$	95331.0			1.20732			0.603659	−	0.797243i	$-0.293709\pi$
$281$	95331.0			1.20732			0.603659	+	0.797243i	$0.293709\pi$
$282$	95537.9	−	3196.22i	1.20137	−	0.0401919i
$283$	−2515.67	+	2515.67i	−0.0314109	+	0.0314109i	−0.722638	−	0.691227i	$-0.757071\pi$
$283$	−2515.67	+	2515.67i	−0.0314109	+	0.0314109i	0.691227	+	0.722638i	$0.257071\pi$
$284$	106158.	−	7110.99i	1.31618	−	0.0881644i
$285$	10095.0	+	7305.22i	0.124285	+	0.0899380i
$286$	2421.25	−	2588.86i	0.0296011	−	0.0316502i
$287$	−21256.2	+	21256.2i	−0.258060	+	0.258060i
$288$	47603.2	−	8034.88i	0.573920	−	0.0968712i
$289$		−	106448.i		−	1.27450i
$290$	126061.	−	24560.8i	1.49894	−	0.292043i
$291$		−	37433.3i		−	0.442051i
$292$	36664.9	+	32061.3i	0.430016	+	0.376023i
$293$	86781.5	−	86781.5i	1.01086	−	1.01086i	0.0109221	−	0.999940i	$-0.496523\pi$
$293$	86781.5	−	86781.5i	1.01086	−	1.01086i	0.999940	−	0.0109221i	$-0.00347667\pi$
$294$	−32915.2	+	35193.8i	−0.380804	+	0.407166i
$295$	14037.0	+	87549.1i	0.161298	+	1.00602i
$296$	−56188.1	+	68766.7i	−0.641299	+	0.784865i
$297$	−15156.9	+	15156.9i	−0.171829	+	0.171829i
$298$	−3039.18	−	90843.7i	−0.0342234	−	1.02297i
$299$	14361.0			0.160635
$300$	−22688.0	+	53579.3i	−0.252089	+	0.595326i
$301$		−	52543.7i		−	0.579946i
$302$	−1340.25	−	40061.2i	−0.0146950	−	0.439248i
$303$	−7975.21	−	7975.21i	−0.0868674	−	0.0868674i
$304$	−21734.2	+	2924.85i	−0.235178	+	0.0316488i
$305$	39557.9	−	6342.43i	0.425240	−	0.0681798i
$306$	−56143.8	+	60030.4i	−0.599596	+	0.641104i
$307$	−73374.4	−	73374.4i	−0.778517	−	0.778517i	0.201062	−	0.979579i	$-0.435561\pi$
$307$	−73374.4	−	73374.4i	−0.778517	−	0.778517i	−0.979579	+	0.201062i	$0.935561\pi$
$308$	−6295.53	−	5505.07i	−0.0663638	−	0.0580312i
$309$	−75922.4			−0.795157
$310$	84029.3	−	16371.6i	0.874394	−	0.170360i
$311$	−145273.			−1.50198			−0.750989	−	0.660314i	$-0.770423\pi$
$311$	−145273.			−1.50198			−0.750989	+	0.660314i	$0.770423\pi$
$312$	11421.0	−	1149.70i	0.117326	−	0.0118107i
$313$	−68572.1	−	68572.1i	−0.699936	−	0.699936i	0.264460	−	0.964397i	$-0.414806\pi$
$313$	−68572.1	−	68572.1i	−0.699936	−	0.699936i	−0.964397	+	0.264460i	$0.914806\pi$
$314$	−228.482	+	244.299i	−0.00231736	+	0.00247778i
$315$	12562.8	−	17360.4i	0.126609	−	0.174960i
$316$	−9934.80	−	148314.i	−0.0994912	−	1.48528i
$317$	65494.2	+	65494.2i	0.651755	+	0.651755i	0.953415	−	0.301660i	$-0.0975408\pi$
$317$	65494.2	+	65494.2i	0.651755	+	0.651755i	−0.301660	+	0.953415i	$0.597541\pi$
$318$	−21317.6	+	713.179i	−0.210806	+	0.00705252i
$319$		−	36921.9i		−	0.362829i
$320$	−36037.9	−	95849.0i	−0.351932	−	0.936026i
$321$	−131227.			−1.27354
$322$	−1132.89	−	33863.1i	−0.0109264	−	0.326599i
$323$	26401.4	−	26401.4i	0.253059	−	0.253059i
$324$	−8294.82	+	555.628i	−0.0790164	+	0.00529290i
$325$	8681.11	−	17198.9i	0.0821881	−	0.162830i
$326$	61.6322	+	57.6419i	0.000579926	+	0.000542379i
$327$	−4258.42	+	4258.42i	−0.0398247	+	0.0398247i
$328$	10598.5	+	105284.i	0.0985133	+	0.978620i
$329$			74675.2i			0.689898i
$330$	13871.6	+	9347.69i	0.127379	+	0.0858374i
$331$			66352.6i			0.605623i	0.953051	+	0.302811i	$0.0979252\pi$
$331$			66352.6i			0.605623i	−0.953051	+	0.302811i	$0.902075\pi$
$332$	75130.4	−	85918.2i	0.681616	−	0.779488i
$333$	−46256.1	+	46256.1i	−0.417138	+	0.417138i
$334$	−65023.3	−	60813.4i	−0.582876	−	0.545138i
$335$	−23141.1	+	31978.6i	−0.206203	+	0.284950i
$336$	−3611.95	−	26840.0i	−0.0319936	−	0.237741i
$337$	−74402.4	+	74402.4i	−0.655130	+	0.655130i	−0.954224	−	0.299094i	$-0.903316\pi$
$337$	−74402.4	+	74402.4i	−0.655130	+	0.655130i	0.299094	+	0.954224i	$0.403316\pi$
$338$	110382.	−	3692.81i	0.966191	−	0.0323239i
$339$	−3895.10			−0.0338937
$340$	147755.	+	92539.0i	1.27816	+	0.800510i
$341$		−	24611.2i		−	0.211653i
$342$	−16145.6	+	540.152i	−0.138039	+	0.00461810i
$343$	−57485.8	−	57485.8i	−0.488621	−	0.488621i
$344$	−143226.	−	117028.i	−1.21034	−	0.988945i
$345$	10728.6	+	66914.5i	0.0901371	+	0.562189i
$346$	−108088.	−	101090.i	−0.902869	−	0.844413i
$347$	107202.	+	107202.i	0.890312	+	0.890312i	0.994552	−	0.104240i	$-0.0332410\pi$
$347$	107202.	+	107202.i	0.890312	+	0.890312i	−0.104240	+	0.994552i	$0.533241\pi$
$348$	78705.2	−	90006.3i	0.649897	−	0.743215i
$349$	−7592.02			−0.0623313			−0.0311657	−	0.999514i	$-0.509922\pi$
$349$	−7592.02			−0.0623313			−0.0311657	+	0.999514i	$0.509922\pi$
$350$	−41239.7	−	19113.3i	−0.336651	−	0.156027i
$351$	22983.5			0.186553
$352$	−29027.7	+	4899.55i	−0.234276	+	0.0395431i
$353$	86084.4	+	86084.4i	0.690836	+	0.690836i	0.962416	−	0.271580i	$-0.0875461\pi$
$353$	86084.4	+	86084.4i	0.690836	+	0.690836i	−0.271580	+	0.962416i	$0.587546\pi$
$354$	60287.6	+	56384.3i	0.481084	+	0.449937i
$355$	−26318.1	−	164147.i	−0.208833	−	1.30250i
$356$	10592.0	+	158125.i	0.0835751	+	1.24767i
$357$	32603.6	+	32603.6i	0.255817	+	0.255817i
$358$	6553.12	+	195879.i	0.0511307	+	1.52834i
$359$		−	157470.i		−	1.22183i	−0.791698	−	0.610913i	$-0.790803\pi$
$359$		−	157470.i		−	1.22183i	0.791698	−	0.610913i	$-0.209197\pi$
$360$	−19341.6	−	72910.3i	−0.149241	−	0.562579i
$361$	−122983.			−0.943690
$362$	157748.	−	5277.44i	1.20378	−	0.0402723i
$363$	−56837.1	+	56837.1i	−0.431339	+	0.431339i
$364$	599.316	+	8947.03i	0.00452328	+	0.0675268i
$365$	44614.9	−	61653.1i	0.334884	−	0.462774i
$366$	25476.5	−	27240.2i	0.190186	−	0.203352i
$367$	2311.12	−	2311.12i	0.0171589	−	0.0171589i	−0.698475	−	0.715634i	$-0.746138\pi$
$367$	2311.12	−	2311.12i	0.0171589	−	0.0171589i	0.715634	+	0.698475i	$0.246138\pi$
$368$	−94829.0	−	72333.4i	−0.700238	−	0.534125i
$369$			77948.5i			0.572473i
$370$	115067.	+	77540.4i	0.840515	+	0.566402i
$371$		−	16662.4i		−	0.121057i
$372$	52463.0	−	59996.1i	0.379112	−	0.433548i
$373$	−108657.	+	108657.i	−0.780979	+	0.780979i	−0.979996	−	0.199017i	$-0.936225\pi$
$373$	−108657.	+	108657.i	−0.780979	+	0.780979i	0.199017	+	0.979996i	$0.436225\pi$
$374$	34235.6	−	36605.6i	0.244757	−	0.261700i
$375$	86623.1	+	27600.7i	0.615986	+	0.196272i
$376$	203554.	+	166320.i	1.43980	+	1.17644i
$377$	−27993.6	+	27993.6i	−0.196959	+	0.196959i
$378$	−1813.09	−	54194.9i	−0.0126892	−	0.379293i
$379$	−1025.70			−0.00714074			−0.00357037	−	0.999994i	$-0.501136\pi$
$379$	−1025.70			−0.00714074			−0.00357037	+	0.999994i	$0.501136\pi$
$380$	7673.80	+	33395.5i	0.0531427	+	0.231271i
$381$		−	5848.42i		−	0.0402892i
$382$	6966.55	+	208237.i	0.0477409	+	1.42702i
$383$	−64930.1	−	64930.1i	−0.442638	−	0.442638i	0.450260	−	0.892898i	$-0.351331\pi$
$383$	−64930.1	−	64930.1i	−0.442638	−	0.442638i	−0.892898	+	0.450260i	$0.851331\pi$
$384$	−81206.5	−	49933.6i	−0.550717	−	0.338634i
$385$	−7660.59	+	10586.1i	−0.0516822	+	0.0714193i
$386$	−89597.5	+	95799.9i	−0.601341	+	0.642970i
$387$	−96341.6	−	96341.6i	−0.643268	−	0.643268i
$388$	67759.3	−	77488.7i	0.450096	−	0.514724i
$389$	219144.			1.44821			0.724104	−	0.689691i	$-0.242254\pi$
$389$	219144.			1.44821			0.724104	+	0.689691i	$0.242254\pi$
$390$	−3429.93	−	17604.5i	−0.0225505	−	0.115743i
$391$	203059.			1.32822
$392$	−131841.	+	13271.9i	−0.857986	+	0.0863695i
$393$	98808.7	+	98808.7i	0.639749	+	0.639749i
$394$	−88814.0	+	94962.2i	−0.572122	+	0.611728i
$395$	−229331.	+	36769.2i	−1.46983	+	0.235662i
$396$	−21637.0	+	1449.35i	−0.137977	+	0.00924238i
$397$	93113.1	+	93113.1i	0.590786	+	0.590786i	0.937844	−	0.347058i	$-0.112819\pi$
$397$	93113.1	+	93113.1i	0.590786	+	0.590786i	−0.347058	+	0.937844i	$0.612819\pi$
$398$	147377.	−	4930.50i	0.930388	−	0.0311261i
$399$			9062.35i			0.0569240i
$400$	−143951.	+	69843.5i	−0.899694	+	0.436522i
$401$	17865.1			0.111101			0.0555503	−	0.998456i	$-0.482309\pi$
$401$	17865.1			0.111101			0.0555503	+	0.998456i	$0.482309\pi$
$402$	1228.72	+	36727.4i	0.00760325	+	0.227268i
$403$	−18659.9	+	18659.9i	−0.114894	+	0.114894i
$404$	−2072.87	−	30945.3i	−0.0127001	−	0.189597i
$405$	2056.41	+	12825.9i	0.0125372	+	0.0781947i
$406$	68217.1	+	63800.4i	0.413848	+	0.387054i
$407$	28206.2	−	28206.2i	0.170277	−	0.170277i
$408$	161489.	−	16256.3i	0.970112	−	0.0976568i
$409$		−	39927.3i		−	0.238684i	−0.992853	−	0.119342i	$-0.961921\pi$
$409$		−	39927.3i		−	0.238684i	0.992853	−	0.119342i	$-0.0380785\pi$
$410$	162286.	−	31618.6i	0.965413	−	0.188094i
$411$			29654.2i			0.175551i
$412$	−157163.	−	137430.i	−0.925882	−	0.809629i
$413$	−45597.1	+	45597.1i	−0.267323	+	0.267323i
$414$	−64166.9	−	60012.5i	−0.374378	−	0.350139i
$415$	−144474.	−	104548.i	−0.838869	−	0.607042i
$416$	25723.1	+	18293.6i	0.148640	+	0.105709i
$417$	50319.3	−	50319.3i	0.289376	−	0.289376i
$418$	9845.35	−	329.376i	0.0563480	−	0.00188512i
$419$	7277.24			0.0414513			0.0207257	−	0.999785i	$-0.493402\pi$
$419$	7277.24			0.0414513			0.0207257	+	0.999785i	$0.493402\pi$
$420$	−41240.7	+	9476.51i	−0.233791	+	0.0537217i
$421$		−	55087.5i		−	0.310806i	−0.987851	−	0.155403i	$-0.950332\pi$
$421$		−	55087.5i		−	0.310806i	0.987851	−	0.155403i	$-0.0496676\pi$
$422$	−296722.	+	9926.82i	−1.66619	+	0.0557424i
$423$	136921.	+	136921.i	0.765224	+	0.765224i
$424$	−45419.3	−	37111.3i	−0.252644	−	0.206431i
$425$	122748.	−	243186.i	0.679573	−	1.34636i
$426$	−113034.	−	105716.i	−0.622860	−	0.582533i
$427$	20602.4	+	20602.4i	0.112996	+	0.112996i
$428$	−271646.	−	237539.i	−1.48292	−	1.29672i
$429$	−5156.16			−0.0280164
$430$	−161500.	+	239659.i	−0.873446	+	1.29616i
$431$	219183.			1.17992			0.589959	−	0.807434i	$-0.299144\pi$
$431$	219183.			1.17992			0.589959	+	0.807434i	$0.299144\pi$
$432$	−151766.	−	115763.i	−0.813215	−	0.620302i
$433$	−67090.9	−	67090.9i	−0.357839	−	0.357839i	0.505177	−	0.863016i	$-0.331427\pi$
$433$	−67090.9	−	67090.9i	−0.357839	−	0.357839i	−0.863016	+	0.505177i	$0.831427\pi$
$434$	45471.9	+	42527.9i	0.241415	+	0.225784i
$435$	−151348.	−	109522.i	−0.799833	−	0.578794i
$436$	−16523.4	+	1106.82i	−0.0869215	+	0.00582243i
$437$	28220.7	+	28220.7i	0.147776	+	0.147776i
$438$	−2368.91	−	70808.8i	−0.0123481	−	0.369096i
$439$		−	212568.i		−	1.10298i	−0.834180	−	0.551492i	$-0.814059\pi$
$439$		−	212568.i		−	1.10298i	0.834180	−	0.551492i	$-0.185941\pi$
$440$	11794.2	+	44459.6i	0.0609205	+	0.229646i
$441$	−97610.8			−0.501904
$442$	−53710.7	+	1796.89i	−0.274926	+	0.00919765i
$443$	8039.30	−	8039.30i	0.0409648	−	0.0409648i	−0.686328	−	0.727292i	$-0.740778\pi$
$443$	8039.30	−	8039.30i	0.0409648	−	0.0409648i	0.727292	+	0.686328i	$0.240778\pi$
$444$	128886.	−	8633.42i	0.653792	−	0.0437942i
$445$	244501.	−	39201.5i	1.23470	−	0.197962i
$446$	69536.8	−	74350.6i	0.349579	−	0.373779i
$447$	−93491.9	+	93491.9i	−0.467906	+	0.467906i
$448$	41107.0	−	62098.1i	0.204814	−	0.309402i
$449$			342397.i			1.69839i	0.528081	+	0.849194i	$0.322912\pi$
$449$			342397.i			1.69839i	−0.528081	+	0.849194i	$0.677088\pi$
$450$	−110660.	+	40570.0i	−0.546471	+	0.200346i
$451$		−	47531.8i		−	0.233685i
$452$	−8063.04	−	7050.65i	−0.0394659	−	0.0345106i
$453$	−41229.0	+	41229.0i	−0.200912	+	0.200912i
$454$	−138597.	+	148192.i	−0.672424	+	0.718973i
$455$	13834.4	−	2218.10i	0.0668247	−	0.0107142i
$456$	24702.6	+	20184.1i	0.118799	+	0.0970688i
$457$	156077.	−	156077.i	0.747318	−	0.747318i	−0.226657	−	0.973975i	$-0.572779\pi$
$457$	156077.	−	156077.i	0.747318	−	0.747318i	0.973975	+	0.226657i	$0.0727795\pi$
$458$	−127.583	−	3813.57i	−0.000608220	−	0.0181803i
$459$	324978.			1.54251
$460$	−98915.5	+	157936.i	−0.467465	+	0.746391i
$461$		−	367130.i		−	1.72750i	−0.503921	−	0.863750i	$-0.668110\pi$
$461$		−	367130.i		−	1.72750i	0.503921	−	0.863750i	$-0.331890\pi$
$462$	406.752	+	12158.2i	0.00190566	+	0.0569620i
$463$	−107453.	−	107453.i	−0.501251	−	0.501251i	0.410576	−	0.911826i	$-0.365328\pi$
$463$	−107453.	−	107453.i	−0.501251	−	0.501251i	−0.911826	+	0.410576i	$0.865328\pi$
$464$	325847.	−	43850.4i	1.51348	−	0.203675i
$465$	−100885.	−	73005.0i	−0.466575	−	0.337634i
$466$	98099.9	−	104891.i	0.451749	−	0.483021i
$467$	103819.	+	103819.i	0.476039	+	0.476039i	0.903862	−	0.427823i	$-0.140719\pi$
$467$	103819.	+	103819.i	0.476039	+	0.476039i	−0.427823	+	0.903862i	$0.640719\pi$
$468$	17503.7	+	15306.0i	0.0799169	+	0.0698826i
$469$	−28707.2			−0.130511
$470$	229524.	−	340604.i	1.03904	−	1.54189i
$471$	486.563			0.00219330
$472$	22735.0	+	225847.i	0.102049	+	1.01375i
$473$	58747.6	+	58747.6i	0.262584	+	0.262584i
$474$	−147696.	+	157921.i	−0.657374	+	0.702881i
$475$	50856.7	−	16738.3i	0.225404	−	0.0741862i
$476$	8474.12	+	126508.i	0.0374008	+	0.558346i
$477$	−30551.4	−	30551.4i	−0.134275	−	0.134275i
$478$	114724.	−	3838.10i	0.502111	−	0.0167981i
$479$			218917.i			0.954131i	0.878868	+	0.477065i	$0.158299\pi$
$479$			218917.i			0.954131i	−0.878868	+	0.477065i	$0.841701\pi$
$480$	−66021.7	+	133523.i	−0.286552	+	0.579525i
$481$	−42771.0			−0.184867
$482$	−8488.19	−	253720.i	−0.0365360	−	1.09210i
$483$	−34850.2	+	34850.2i	−0.149386	+	0.149386i
$484$	−220538.	+	14772.7i	−0.941441	+	0.0630624i
$485$	−130300.	−	94290.5i	−0.553936	−	0.400852i
$486$	−167606.	−	156754.i	−0.709604	−	0.663661i
$487$	34469.5	−	34469.5i	0.145337	−	0.145337i	−0.630694	−	0.776032i	$-0.717230\pi$
$487$	34469.5	−	34469.5i	0.145337	−	0.145337i	0.776032	+	0.630694i	$0.217230\pi$
$488$	102046.	−	10272.5i	0.428505	−	0.0431357i
$489$		−	122.751i		−	0.000513342i
$490$	39594.3	+	203222.i	0.164908	+	0.846407i
$491$			63276.4i			0.262469i	0.991351	+	0.131235i	$0.0418941\pi$
$491$			63276.4i			0.262469i	−0.991351	+	0.131235i	$0.958106\pi$
$492$	101322.	−	115871.i	0.418575	−	0.478678i
$493$	−395819.	+	395819.i	−1.62856	+	1.62856i
$494$	−7714.32	−	7214.87i	−0.0316114	−	0.0295648i
$495$	5364.13	+	33456.3i	0.0218922	+	0.136542i
$496$	217202.	−	29229.6i	0.882877	−	0.118812i
$497$	85490.6	−	85490.6i	0.346103	−	0.346103i
$498$	−165929.	+	5551.15i	−0.669058	+	0.0223833i
$499$	198564.			0.797442			0.398721	−	0.917072i	$-0.369454\pi$
$499$	198564.			0.797442			0.398721	+	0.917072i	$0.369454\pi$
$500$	129353.	+	213934.i	0.517412	+	0.855737i
$501$			129505.i			0.515953i
$502$	420301.	−	14061.1i	1.66783	−	0.0557973i
$503$	−76098.2	−	76098.2i	−0.300773	−	0.300773i	0.540543	−	0.841316i	$-0.318219\pi$
$503$	−76098.2	−	76098.2i	−0.300773	−	0.300773i	−0.841316	+	0.540543i	$0.818219\pi$
$504$	34710.6	−	42481.1i	0.136647	−	0.167238i
$505$	−47849.2	+	7671.78i	−0.187626	+	0.0300825i
$506$	39128.0	+	36594.7i	0.152822	+	0.142928i
$507$	−113599.	−	113599.i	−0.441936	−	0.441936i
$508$	10586.4	−	12106.5i	0.0410225	−	0.0469128i
$509$	−179523.			−0.692923			−0.346462	−	0.938064i	$-0.612617\pi$
$509$	−179523.			−0.692923			−0.346462	+	0.938064i	$0.612617\pi$
$510$	−48497.9	−	248921.i	−0.186459	−	0.957020i
$511$	55346.2			0.211956
$512$	−77714.9	−	250359.i	−0.296459	−	0.955046i
$513$	45164.7	+	45164.7i	0.171619	+	0.171619i
$514$	−195807.	−	183130.i	−0.741142	−	0.693158i
$515$	−191240.	+	264274.i	−0.721050	+	0.996415i
$516$	17981.6	+	268442.i	0.0675349	+	1.00821i
$517$	−83492.2	−	83492.2i	−0.312367	−	0.312367i
$518$	3374.07	+	100854.i	0.0125746	+	0.375866i
$519$			215275.i			0.799207i
$520$	24766.4	−	42650.7i	0.0915916	−	0.157732i
$521$	−149919.			−0.552308			−0.276154	−	0.961113i	$-0.589060\pi$
$521$	−149919.			−0.552308			−0.276154	+	0.961113i	$0.589060\pi$
$522$	242061.	−	8098.14i	0.888349	−	0.0297197i
$523$	128725.	−	128725.i	0.470608	−	0.470608i	−0.431504	−	0.902111i	$-0.642017\pi$
$523$	128725.	−	128725.i	0.470608	−	0.470608i	0.902111	+	0.431504i	$0.142017\pi$
$524$	25681.7	+	383396.i	0.0935323	+	1.39632i
$525$	20670.4	+	62803.8i	0.0749945	+	0.227860i
$526$	59180.0	−	63276.8i	0.213896	−	0.228703i
$527$	−263844.	+	263844.i	−0.950004	+	0.950004i
$528$	34047.4	+	25970.6i	0.122128	+	0.0931566i
$529$		−	62789.9i		−	0.224377i
$530$	−51214.2	+	75999.7i	−0.182322	+	0.270558i
$531$			167209.i			0.593022i
$532$	−16404.1	+	18759.5i	−0.0579600	+	0.0662824i
$533$	−36037.9	+	36037.9i	−0.126854	+	0.126854i
$534$	157466.	−	168367.i	0.552210	−	0.590438i
$535$	−330547.	+	456782.i	−1.15485	+	1.59588i
$536$	−63938.1	+	78251.7i	−0.222551	+	0.272373i
$537$	201589.	−	201589.i	0.699065	−	0.699065i
$538$	7628.52	+	228023.i	0.0263558	+	0.787798i
$539$	59521.6			0.204879
$540$	−158306.	+	252763.i	−0.542886	+	0.866815i
$541$		−	337657.i		−	1.15367i	−0.816861	−	0.576834i	$-0.804288\pi$
$541$		−	337657.i		−	1.15367i	0.816861	−	0.576834i	$-0.195712\pi$
$542$	−5860.60	−	175179.i	−0.0199500	−	0.596325i
$543$	−162346.	−	162346.i	−0.550607	−	0.550607i
$544$	363716.	+	258665.i	1.22903	+	0.874057i
$545$	4096.40	+	25549.4i	0.0137914	+	0.0860177i
$546$	8909.77	−	9526.55i	0.0298869	−	0.0319559i
$547$	131973.	+	131973.i	0.441073	+	0.441073i	0.892372	−	0.451300i	$-0.149039\pi$
$547$	131973.	+	131973.i	0.441073	+	0.441073i	−0.451300	+	0.892372i	$0.649039\pi$
$548$	−53678.1	+	61385.6i	−0.178746	+	0.204412i
$549$	75551.3			0.250667
$550$	67478.9	−	24739.0i	0.223071	−	0.0817817i
$551$	−110020.			−0.362384
$552$	17376.5	+	172617.i	0.0570276	+	0.566506i
$553$	−119439.	−	119439.i	−0.390569	−	0.390569i
$554$	−68860.5	+	73627.4i	−0.224363	+	0.239894i
$555$	−31952.7	−	199290.i	−0.103734	−	0.646994i
$556$	195248.	−	13078.7i	0.631593	−	0.0423072i
$557$	97139.0	+	97139.0i	0.313100	+	0.313100i	0.846109	−	0.533009i	$-0.178939\pi$
$557$	97139.0	+	97139.0i	0.313100	+	0.313100i	−0.533009	+	0.846109i	$0.678939\pi$
$558$	161352.	−	5398.03i	0.518210	−	0.0173367i
$559$		−	89083.0i		−	0.285083i
$560$	−102524.	−	55034.4i	−0.326926	−	0.175492i
$561$	−72906.2			−0.231653
$562$	−12750.0	−	381111.i	−0.0403682	−	1.20664i
$563$	177245.	−	177245.i	0.559186	−	0.559186i	−0.369890	−	0.929076i	$-0.620604\pi$
$563$	177245.	−	177245.i	0.559186	−	0.559186i	0.929076	+	0.369890i	$0.120604\pi$
$564$	−25555.5	−	381511.i	−0.0803388	−	1.19936i
$565$	−9811.34	+	13558.2i	−0.0307349	+	0.0424724i
$566$	10393.5	+	9720.58i	0.0324436	+	0.0303431i
$567$	−6679.94	+	6679.94i	−0.0207781	+	0.0207781i
$568$	−42626.2	−	423444.i	−0.132123	−	1.31250i
$569$		−	48520.2i		−	0.149864i	−0.997189	−	0.0749322i	$-0.976126\pi$
$569$		−	48520.2i		−	0.149864i	0.997189	−	0.0749322i	$-0.0238740\pi$
$570$	27854.4	−	41334.6i	0.0857321	−	0.127223i
$571$			158590.i			0.486412i	0.969975	+	0.243206i	$0.0781991\pi$
$571$			158590.i			0.486412i	−0.969975	+	0.243206i	$0.921801\pi$
$572$	−10673.5	−	9333.34i	−0.0326223	−	0.0285263i
$573$	214307.	−	214307.i	0.652719	−	0.652719i
$574$	87820.0	+	82134.2i	0.266545	+	0.249287i
$575$	259943.	+	131206.i	0.786218	+	0.396842i
$576$	−38488.3	−	189232.i	−0.116007	−	0.570360i
$577$	−103707.	+	103707.i	−0.311499	+	0.311499i	−0.845490	−	0.533991i	$-0.820692\pi$
$577$	−103707.	+	103707.i	−0.311499	+	0.311499i	0.533991	+	0.845490i	$0.320692\pi$
$578$	−425553.	+	14236.9i	−1.27379	+	0.0426146i
$579$	190802.			0.569148
$580$	−115048.	−	500677.i	−0.341998	−	1.48834i
$581$		−	129695.i		−	0.384212i
$582$	−149649.	+	5006.52i	−0.441803	+	0.0147805i
$583$	18629.8	+	18629.8i	0.0548113	+	0.0548113i
$584$	123270.	−	150866.i	0.361435	−	0.442348i
$585$	21299.0	−	29433.0i	0.0622369	−	0.0860049i
$586$	−358539.	−	335325.i	−1.04410	−	0.976498i
$587$	−122008.	−	122008.i	−0.354088	−	0.354088i	0.507540	−	0.861628i	$-0.330555\pi$
$587$	−122008.	−	122008.i	−0.354088	−	0.354088i	−0.861628	+	0.507540i	$0.830555\pi$
$588$	145099.	+	126880.i	0.419671	+	0.366977i
$589$	−73336.9			−0.211394
$590$	348123.	−	67825.7i	1.00007	−	0.194846i
$591$	189133.			0.541493
$592$	282428.	+	215429.i	0.805868	+	0.614698i
$593$	−154016.	−	154016.i	−0.437983	−	0.437983i	0.453349	−	0.891333i	$-0.350229\pi$
$593$	−154016.	−	154016.i	−0.437983	−	0.437983i	−0.891333	+	0.453349i	$0.850229\pi$
$594$	62620.9	+	58566.6i	0.177479	+	0.165988i
$595$	195613.	−	31363.2i	0.552540	−	0.0885902i
$596$	−362765.	+	24299.8i	−1.02125	+	0.0684085i
$597$	−151673.	−	151673.i	−0.425560	−	0.425560i
$598$	−1920.71	−	57411.7i	−0.00537105	−	0.160546i
$599$		−	171604.i		−	0.478271i	−0.970986	−	0.239136i	$-0.923136\pi$
$599$		−	171604.i		−	0.478271i	0.970986	−	0.239136i	$-0.0768641\pi$
$600$	217232.	+	83535.2i	0.603422	+	0.232042i
$601$	89958.7			0.249054			0.124527	−	0.992216i	$-0.460259\pi$
$601$	89958.7			0.249054			0.124527	+	0.992216i	$0.460259\pi$
$602$	−210057.	+	7027.46i	−0.579622	+	0.0193912i
$603$	−52636.2	+	52636.2i	−0.144760	+	0.144760i
$604$	−159976.	+	10716.0i	−0.438511	+	0.0293736i
$605$	54674.7	+	341008.i	0.149374	+	0.931652i
$606$	−30816.4	+	32949.6i	−0.0839143	+	0.0897233i
$607$	180399.	−	180399.i	0.489617	−	0.489617i	−0.418569	−	0.908185i	$-0.637468\pi$
$607$	180399.	−	180399.i	0.489617	−	0.489617i	0.908185	+	0.418569i	$0.137468\pi$
$608$	14599.7	+	86497.1i	0.0394946	+	0.233988i
$609$		−	135866.i		−	0.366333i
$610$	−30646.2	−	157295.i	−0.0823601	−	0.422722i
$611$			126605.i			0.339132i
$612$	247496.	+	216421.i	0.660793	+	0.577825i
$613$	293864.	−	293864.i	0.782034	−	0.782034i	−0.198140	−	0.980174i	$-0.563490\pi$
$613$	293864.	−	293864.i	0.782034	−	0.782034i	0.980174	+	0.198140i	$0.0634899\pi$
$614$	−283520.	+	303147.i	−0.752051	+	0.804112i
$615$	−194840.	−	140995.i	−0.515143	−	0.372780i
$616$	−21166.0	+	25904.3i	−0.0557798	+	0.0682670i
$617$	−337318.	+	337318.i	−0.886072	+	0.886072i	−0.994143	−	0.108071i	$-0.965533\pi$
$617$	−337318.	+	337318.i	−0.886072	+	0.886072i	0.108071	+	0.994143i	$0.465533\pi$
$618$	10154.2	+	303520.i	0.0265871	+	0.794712i
$619$	−598874.			−1.56298			−0.781491	−	0.623917i	$-0.785540\pi$
$619$	−598874.			−1.56298			−0.781491	+	0.623917i	$0.785540\pi$
$620$	−76688.4	−	333739.i	−0.199502	−	0.868209i
$621$			347371.i			0.900763i
$622$	19429.5	+	580767.i	0.0502206	+	1.50114i
$623$	127340.	+	127340.i	0.328087	+	0.328087i
$624$	−6123.73	−	45504.7i	−0.0157270	−	0.116866i
$625$	314268.	−	231999.i	0.804527	−	0.593916i
$626$	−264964.	+	283306.i	−0.676142	+	0.722948i
$627$	−10132.3	−	10132.3i	−0.0257736	−	0.0257736i
$628$	1007.21	+	880.745i	0.00255388	+	0.00223322i
$629$	−604767.			−1.52858
$630$	−71083.2	−	47901.2i	−0.179096	−	0.120688i
$631$	102705.			0.257948			0.128974	−	0.991648i	$-0.458832\pi$
$631$	102705.			0.257948			0.128974	+	0.991648i	$0.458832\pi$
$632$	−591595.	+	59553.2i	−1.48112	+	0.149098i
$633$	305371.	+	305371.i	0.762115	+	0.762115i
$634$	253071.	−	270590.i	0.629599	−	0.673183i
$635$	−20357.5	−	14731.6i	−0.0504866	−	0.0365343i
$636$	5702.24	+	85127.2i	0.0140971	+	0.210453i
$637$	−45128.3	−	45128.3i	−0.111217	−	0.111217i
$638$	−147605.	+	4938.12i	−0.362626	+	0.0121317i
$639$		−	313503.i		−	0.767785i
$640$	−378362.	+	156890.i	−0.923735	+	0.383033i
$641$	122147.			0.297280			0.148640	−	0.988891i	$-0.452510\pi$
$641$	122147.			0.297280			0.148640	+	0.988891i	$0.452510\pi$
$642$	17551.0	+	524615.i	0.0425825	+	1.27283i
$643$	−67879.5	+	67879.5i	−0.164179	+	0.164179i	−0.784415	−	0.620236i	$-0.787037\pi$
$643$	−67879.5	+	67879.5i	−0.164179	+	0.164179i	0.620236	+	0.784415i	$0.287037\pi$
$644$	−135225.	+	9058.04i	−0.326051	+	0.0218405i
$645$	415080.	−	66550.8i	0.997728	−	0.159968i
$646$	−109078.	−	102016.i	−0.261379	−	0.244457i
$647$	186343.	−	186343.i	0.445148	−	0.445148i	−0.448590	−	0.893738i	$-0.648074\pi$
$647$	186343.	−	186343.i	0.445148	−	0.445148i	0.893738	+	0.448590i	$0.148074\pi$
$648$	3330.66	+	33086.4i	0.00793196	+	0.0787952i
$649$		−	101961.i		−	0.242073i
$650$	−69918.2	−	32404.8i	−0.165487	−	0.0766977i
$651$		−	90565.0i		−	0.213697i
$652$	222.196	−	254.100i	0.000522685	−	0.000597737i
$653$	200068.	−	200068.i	0.469194	−	0.469194i	−0.432459	−	0.901653i	$-0.642354\pi$
$653$	200068.	−	200068.i	0.469194	−	0.469194i	0.901653	+	0.432459i	$0.142354\pi$
$654$	17593.7	+	16454.6i	0.0411341	+	0.0384709i
$655$	592827.	−	95049.4i	1.38180	−	0.221547i
$656$	419483.	−	56451.3i	0.974779	−	0.131180i
$657$	101480.	−	101480.i	0.235099	−	0.235099i
$658$	298534.	−	9987.44i	0.689512	−	0.0230676i
$659$	−390624.			−0.899472			−0.449736	−	0.893162i	$-0.648482\pi$
$659$	−390624.			−0.899472			−0.449736	+	0.893162i	$0.648482\pi$
$660$	35514.6	−	56705.4i	0.0815303	−	0.130178i
$661$			381854.i			0.873966i	0.899470	+	0.436983i	$0.143953\pi$
$661$			381854.i			0.873966i	−0.899470	+	0.436983i	$0.856047\pi$
$662$	265262.	−	8874.34i	0.605284	−	0.0202498i
$663$	55276.4	+	55276.4i	0.125751	+	0.125751i
$664$	−353529.	−	288862.i	−0.801842	−	0.655171i
$665$	31544.7	+	22827.1i	0.0713317	+	0.0516188i
$666$	191107.	+	178734.i	0.430853	+	0.402958i
$667$	−423094.	−	423094.i	−0.951010	−	0.951010i
$668$	−234421.	+	268081.i	−0.525344	+	0.600777i
$669$	−148082.			−0.330864
$670$	130938.	+	88235.6i	0.291686	+	0.196560i
$671$	−46070.0			−0.102323
$672$	−106817.	+	18029.4i	−0.236538	+	0.0399249i
$673$	583756.	+	583756.i	1.28885	+	1.28885i	0.935488	+	0.353359i	$0.114960\pi$
$673$	583756.	+	583756.i	1.28885	+	1.28885i	0.353359	+	0.935488i	$0.385040\pi$
$674$	307394.	+	287492.i	0.676668	+	0.632858i
$675$	416017.	+	209984.i	0.913068	+	0.460870i
$676$	−29526.0	−	440785.i	−0.0646116	−	0.964570i
$677$	573993.	+	573993.i	1.25236	+	1.25236i	0.954659	+	0.297702i	$0.0962203\pi$
$677$	573993.	+	573993.i	1.25236	+	1.25236i	0.297702	+	0.954659i	$0.403780\pi$
$678$	520.950	+	15571.7i	0.00113328	+	0.0338747i
$679$		−	116970.i		−	0.253709i
$680$	350187.	−	603066.i	0.757326	−	1.30421i
$681$	295149.			0.636425
$682$	−98389.9	+	3291.63i	−0.211535	+	0.00707689i
$683$	460264.	−	460264.i	0.986655	−	0.986655i	−0.0132569	−	0.999912i	$-0.504220\pi$
$683$	460264.	−	460264.i	0.986655	−	0.986655i	0.999912	+	0.0132569i	$0.00421992\pi$
$684$	4318.80	+	64474.2i	0.00923104	+	0.137808i
$685$	103222.	+	74695.8i	0.219984	+	0.159190i
$686$	−222126.	+	237503.i	−0.472010	+	0.504686i
$687$	−3924.73	+	3924.73i	−0.00831566	+	0.00831566i
$688$	−448694.	+	588237.i	−0.947923	+	1.24273i
$689$		−	28249.6i		−	0.0595078i
$690$	266073.	−	51839.8i	0.558860	−	0.108884i
$691$			776619.i			1.62649i	0.581920	+	0.813246i	$0.302302\pi$
$691$			776619.i			1.62649i	−0.581920	+	0.813246i	$0.697698\pi$
$692$	−389677.	+	445630.i	−0.813753	+	0.930598i
$693$	−17424.6	+	17424.6i	−0.0362824	+	0.0362824i
$694$	414229.	−	442904.i	0.860046	−	0.919583i
$695$	−48404.9	−	301903.i	−0.100212	−	0.625026i
$696$	−370350.	−	302607.i	−0.764529	−	0.624684i
$697$	−509562.	+	509562.i	−1.04889	+	1.04889i
$698$	1015.40	+	30351.1i	0.00208413	+	0.0622965i
$699$	−208908.			−0.427564
$700$	−70894.7	+	167423.i	−0.144683	+	0.341680i
$701$			108075.i			0.219932i	0.993935	+	0.109966i	$0.0350742\pi$
$701$			108075.i			0.219932i	−0.993935	+	0.109966i	$0.964926\pi$
$702$	−3073.93	−	91882.4i	−0.00623762	−	0.186448i
$703$	−84049.2	−	84049.2i	−0.170068	−	0.170068i
$704$	23469.5	+	115391.i	0.0473543	+	0.232823i
$705$	−589912.	+	94582.1i	−1.18689	+	0.190296i
$706$	332632.	−	355658.i	0.667351	−	0.713549i
$707$	−24920.7	−	24920.7i	−0.0498564	−	0.0498564i
$708$	217348.	−	248557.i	0.433600	−	0.495859i
$709$	807048.			1.60549			0.802743	−	0.596325i	$-0.203373\pi$
$709$	807048.			1.60549			0.802743	+	0.596325i	$0.203373\pi$
$710$	−652702.	+	127168.i	−1.29479	+	0.252267i
$711$	−437996.			−0.866426
$712$	630729.	−	63492.6i	1.24418	−	0.125246i
$713$	−282024.	−	282024.i	−0.554763	−	0.554763i
$714$	125981.	−	134702.i	0.247120	−	0.264227i
$715$	−12987.8	+	17947.8i	−0.0254053	+	0.0351074i
$716$	782200.	−	52395.6i	1.52578	−	0.102204i
$717$	−118069.	−	118069.i	−0.229666	−	0.229666i
$718$	−629528.	+	21060.9i	−1.22114	+	0.0408533i
$719$		−	107517.i		−	0.207978i	−0.994578	−	0.103989i	$-0.966839\pi$
$719$		−	107517.i		−	0.207978i	0.994578	−	0.103989i	$-0.0331607\pi$
$720$	−288891.	+	87074.6i	−0.557275	+	0.167968i
$721$	−237240.			−0.456370
$722$	16448.3	+	491655.i	0.0315535	+	0.943162i
$723$	−261116.	+	261116.i	−0.499524	+	0.499524i
$724$	−42195.9	−	629932.i	−0.0804996	−	1.20176i
$725$	−762461.	+	250946.i	−1.45058	+	0.477423i
$726$	234823.	+	219620.i	0.445520	+	0.416676i
$727$	47143.0	−	47143.0i	0.0891967	−	0.0891967i	−0.661101	−	0.750297i	$-0.729910\pi$
$727$	47143.0	−	47143.0i	0.0891967	−	0.0891967i	0.750297	+	0.661101i	$0.229910\pi$
$728$	35688.0	−	3592.55i	0.0673378	−	0.00677859i
$729$			375902.i			0.707325i
$730$	−252442.	−	170114.i	−0.473713	−	0.319223i
$731$		−	1.25960e6i		−	2.35721i
$732$	−112307.	−	98205.9i	−0.209597	−	0.183280i
$733$	257955.	−	257955.i	0.480104	−	0.480104i	−0.425061	−	0.905165i	$-0.639747\pi$
$733$	257955.	−	257955.i	0.480104	−	0.480104i	0.905165	+	0.425061i	$0.139747\pi$
$734$	−9548.39	−	8930.19i	−0.0177230	−	0.0165756i
$735$	176560.	−	243988.i	0.326827	−	0.451641i
$736$	−276489.	+	388778.i	−0.510413	+	0.717706i
$737$	32096.7	−	32096.7i	0.0590916	−	0.0590916i
$738$	311620.	−	10425.2i	0.572153	−	0.0191414i
$739$	−44980.6			−0.0823638			−0.0411819	−	0.999152i	$-0.513112\pi$
$739$	−44980.6			−0.0823638			−0.0411819	+	0.999152i	$0.513112\pi$
$740$	294599.	−	470379.i	0.537981	−	0.858984i
$741$			15364.4i			0.0279820i
$742$	−66612.5	+	2228.52i	−0.120989	+	0.00404770i
$743$	425908.	+	425908.i	0.771504	+	0.771504i	0.978369	−	0.206865i	$-0.0663262\pi$
$743$	425908.	+	425908.i	0.771504	+	0.771504i	−0.206865	+	0.978369i	$0.566326\pi$
$744$	−246867.	−	201710.i	−0.445981	−	0.364404i
$745$	89934.9	+	560927.i	0.162038	+	1.01063i
$746$	448917.	+	419852.i	0.806655	+	0.754429i
$747$	−237802.	−	237802.i	−0.426162	−	0.426162i
$748$	−150919.	−	131970.i	−0.269738	−	0.235870i
$749$	−410054.			−0.730933
$750$	98755.7	−	349990.i	0.175566	−	0.622205i
$751$	−710003.			−1.25887			−0.629434	−	0.777054i	$-0.716713\pi$
$751$	−710003.			−1.25887			−0.629434	+	0.777054i	$0.716713\pi$
$752$	637684.	−	836004.i	1.12764	−	1.47833i
$753$	−432552.	−	432552.i	−0.762867	−	0.762867i
$754$	115656.	+	108168.i	0.203434	+	0.190263i
$755$	39660.4	+	247363.i	0.0695765	+	0.433951i
$756$	−216416.	+	14496.6i	−0.378657	+	0.0253643i
$757$	−658333.	−	658333.i	−1.14883	−	1.14883i	−0.986784	−	0.162042i	$-0.948192\pi$
$757$	−658333.	−	658333.i	−1.14883	−	1.14883i	−0.162042	−	0.986784i	$-0.551808\pi$
$758$	137.183	+	4100.52i	0.000238760	+	0.00713674i
$759$		−	77930.0i		−	0.135276i
$760$	132481.	−	35144.5i	0.229365	−	0.0608458i
$761$	−667556.			−1.15271			−0.576353	−	0.817201i	$-0.695525\pi$
$761$	−667556.			−1.15271			−0.576353	+	0.817201i	$0.695525\pi$
$762$	−23380.6	+	782.198i	−0.0402667	+	0.00134712i
$763$	−13306.6	+	13306.6i	−0.0228569	+	0.0228569i
$764$	831549.	−	55701.2i	1.42463	−	0.0954285i
$765$	301161.	−	416173.i	0.514607	−	0.711133i
$766$	−250891.	+	268259.i	−0.427590	+	0.457191i
$767$	−77305.6	+	77305.6i	−0.131407	+	0.131407i
$768$	−188762.	+	331323.i	−0.320030	+	0.561732i
$769$		−	175820.i		−	0.297315i	−0.988889	−	0.148657i	$-0.952505\pi$
$769$		−	175820.i		−	0.297315i	0.988889	−	0.148657i	$-0.0474952\pi$
$770$	43345.4	+	29209.4i	0.0731075	+	0.0492653i
$771$			389982.i			0.656049i
$772$	394969.	+	345377.i	0.662717	+	0.579507i
$773$	558519.	−	558519.i	0.934714	−	0.934714i	−0.0632814	−	0.997996i	$-0.520157\pi$
$773$	558519.	−	558519.i	0.934714	−	0.934714i	0.997996	+	0.0632814i	$0.0201566\pi$
$774$	−372266.	+	398036.i	−0.621400	+	0.664417i
$775$	−508238.	+	167274.i	−0.846183	+	0.278500i
$776$	−318844.	−	260522.i	−0.529486	−	0.432634i
$777$	103794.	−	103794.i	0.171921	−	0.171921i
$778$	−29309.5	−	876087.i	−0.0484227	−	1.44740i
$779$	−141636.			−0.233398
$780$	−69919.8	+	16066.5i	−0.114924	+	0.0264079i
$781$			191169.i			0.313412i
$782$	−27158.1	−	811781.i	−0.0444106	−	1.32747i
$783$	−677125.	−	677125.i	−1.10445	−	1.10445i
$784$	70691.0	+	525296.i	0.115009	+	0.854618i
$785$	1225.60	−	1693.65i	0.00198889	−	0.00274843i
$786$	381798.	−	408229.i	0.618001	−	0.660783i
$787$	470281.	+	470281.i	0.759291	+	0.759291i	0.976193	−	0.216902i	$-0.0695953\pi$
$787$	470281.	+	470281.i	0.759291	+	0.759291i	−0.216902	+	0.976193i	$0.569595\pi$
$788$	391515.	+	342356.i	0.630515	+	0.551348i
$789$	−126026.			−0.202445
$790$	177666.	+	911893.i	0.284676	+	1.46113i
$791$	−12171.3			−0.0194528
$792$	8688.01	+	86305.8i	0.0138506	+	0.137591i
$793$	34929.5	+	34929.5i	0.0555452	+	0.0555452i
$794$	359791.	−	384698.i	0.570702	−	0.610209i
$795$	131628.	−	21104.3i	0.208264	−	0.0333915i
$796$	−39422.0	−	588520.i	−0.0622174	−	0.928827i
$797$	304660.	+	304660.i	0.479621	+	0.479621i	0.905011	−	0.425389i	$-0.139863\pi$
$797$	304660.	+	304660.i	0.479621	+	0.479621i	−0.425389	+	0.905011i	$0.639863\pi$
$798$	36229.1	−	1212.04i	0.0568921	−	0.00190333i
$799$			1.79015e6i			2.80411i
$800$	298470.	+	566141.i	0.466360	+	0.884595i
$801$	466970.			0.727819
$802$	−2389.37	−	71420.3i	−0.00371479	−	0.111038i
$803$	−61880.9	+	61880.9i	−0.0959679	+	0.0959679i
$804$	146663.	−	9824.23i	0.226887	−	0.0151980i
$805$	33524.3	+	209092.i	0.0517330	+	0.322661i
$806$	77093.4	+	72102.1i	0.118672	+	0.110988i
$807$	234670.	−	234670.i	0.360339	−	0.360339i
$808$	−123435.	+	12425.6i	−0.189066	+	0.0190324i
$809$		−	364865.i		−	0.557487i	−0.960366	−	0.278744i	$-0.910082\pi$
$809$		−	364865.i		−	0.557487i	0.960366	−	0.278744i	$-0.0899180\pi$
$810$	50999.9	−	9936.43i	0.0777318	−	0.0151447i
$811$		−	494953.i		−	0.752527i	−0.926513	−	0.376263i	$-0.877209\pi$
$811$		−	494953.i		−	0.752527i	0.926513	−	0.376263i	$-0.122791\pi$
$812$	245935.	−	281249.i	0.373000	−	0.426558i
$813$	−180285.	+	180285.i	−0.272759	+	0.272759i
$814$	−116534.	−	108989.i	−0.175875	−	0.164488i
$815$	−427.278	−	309.197i	−0.000643272	−	0.000465500i
$816$	−86587.4	−	643420.i	−0.130039	−	0.966305i
$817$	175057.	−	175057.i	0.262262	−	0.262262i
$818$	−159620.	+	5340.08i	−0.238551	+	0.00798070i
$819$	26422.1			0.0393913
$820$	−148109.	−	644552.i	−0.220269	−	0.958584i
$821$			594185.i			0.881527i	0.897623	+	0.440763i	$0.145292\pi$
$821$			594185.i			0.881527i	−0.897623	+	0.440763i	$0.854708\pi$
$822$	118550.	−	3966.10i	0.175453	−	0.00586976i
$823$	844023.	+	844023.i	1.24610	+	1.24610i	0.957426	+	0.288678i	$0.0932158\pi$
$823$	844023.	+	844023.i	1.24610	+	1.24610i	0.288678	+	0.957426i	$0.406784\pi$
$824$	−528391.	+	646681.i	−0.778218	+	0.952435i
$825$	−93330.0	−	47108.2i	−0.137124	−	0.0692131i
$826$	188385.	+	176188.i	0.276112	+	0.258235i
$827$	346935.	+	346935.i	0.507268	+	0.507268i	0.913687	−	0.406419i	$-0.133223\pi$
$827$	346935.	+	346935.i	0.507268	+	0.507268i	−0.406419	+	0.913687i	$0.633223\pi$
$828$	−231334.	+	264550.i	−0.337426	+	0.385876i
$829$	910626.			1.32505			0.662523	−	0.749041i	$-0.269486\pi$
$829$	910626.			1.32505			0.662523	+	0.749041i	$0.269486\pi$
$830$	−398635.	+	591556.i	−0.578654	+	0.858697i
$831$	146641.			0.212351
$832$	69693.1	−	105282.i	0.100680	−	0.152092i
$833$	−638098.	−	638098.i	−0.919597	−	0.919597i
$834$	−207895.	−	194435.i	−0.298890	−	0.279539i
$835$	450787.	+	326209.i	0.646544	+	0.467868i
$836$	−2633.54	−	39315.3i	−0.00376814	−	0.0562535i
$837$	−451355.	−	451355.i	−0.644270	−	0.644270i
$838$	−973.295	−	29092.7i	−0.00138598	−	0.0414282i
$839$		−	440279.i		−	0.625466i	−0.949841	−	0.312733i	$-0.898756\pi$
$839$		−	440279.i		−	0.625466i	0.949841	−	0.312733i	$-0.101244\pi$
$840$	43400.6	+	163603.i	0.0615088	+	0.231864i
$841$	942179.			1.33211
$842$	−220227.	+	7367.69i	−0.310632	+	0.0103922i
$843$	−392220.	+	392220.i	−0.551918	+	0.551918i
$844$	79370.2	+	1.18490e6i	0.111422	+	1.66339i
$845$	−681566.	+	109277.i	−0.954540	+	0.153044i
$846$	529065.	−	565690.i	0.739210	−	0.790383i
$847$	−177603.	+	177603.i	−0.247561	+	0.247561i
$848$	−142288.	+	186539.i	−0.197868	+	0.259405i
$849$		−	20700.4i		−	0.0287186i
$850$	−988617.	−	458192.i	−1.36833	−	0.634176i
$851$		−	646440.i		−	0.892625i
$852$	−407509.	+	466023.i	−0.561381	+	0.641989i
$853$	−807188.	+	807188.i	−1.10937	+	1.10937i	−0.116137	+	0.993233i	$0.537051\pi$
$853$	−807188.	+	807188.i	−1.10937	+	1.10937i	−0.993233	+	0.116137i	$0.962949\pi$
$854$	79608.2	−	85119.2i	0.109155	−	0.116711i
$855$	99693.4	−	15984.1i	0.136375	−	0.0218653i
$856$	−913292.	+	1.11775e6i	−1.24641	+	1.52544i
$857$	830066.	−	830066.i	1.13019	−	1.13019i	0.140044	−	0.990145i	$-0.455276\pi$
$857$	830066.	−	830066.i	1.13019	−	1.13019i	0.990145	−	0.140044i	$-0.0447243\pi$
$858$	689.611	+	20613.1i	0.000936762	+	0.0280007i
$859$	−258032.			−0.349693			−0.174846	−	0.984596i	$-0.555943\pi$
$859$	−258032.			−0.349693			−0.174846	+	0.984596i	$0.555943\pi$
$860$	979701.	+	613587.i	1.32464	+	0.829619i
$861$		−	174908.i		−	0.235942i
$862$	−29314.6	−	876240.i	−0.0394520	−	1.17926i
$863$	−62029.1	−	62029.1i	−0.0832863	−	0.0832863i	0.664236	−	0.747523i	$-0.268757\pi$
$863$	−62029.1	−	62029.1i	−0.0832863	−	0.0832863i	−0.747523	+	0.664236i	$0.768757\pi$
$864$	−442496.	+	622205.i	−0.592764	+	0.833501i
$865$	749340.	+	542255.i	1.00149	+	0.724722i
$866$	−259241.	+	277187.i	−0.345674	+	0.369604i
$867$	437958.	+	437958.i	0.582631	+	0.582631i
$868$	163935.	−	187474.i	0.217586	−	0.248829i
$869$	267083.			0.353677
$870$	−417602.	+	619703.i	−0.551727	+	0.818738i
$871$	−48670.5			−0.0641548
$872$	6634.74	+	65908.8i	0.00872551	+	0.0866783i
$873$	−214471.	−	214471.i	−0.281410	−	0.281410i
$874$	109045.	−	116594.i	0.142753	−	0.152635i
$875$	270677.	+	86245.8i	0.353537	+	0.112648i
$876$	−282760.	+	18940.6i	−0.368476	+	0.0246824i
$877$	−838093.	−	838093.i	−1.08967	−	1.08967i	−0.995562	−	0.0941029i	$-0.970002\pi$
$877$	−838093.	−	838093.i	−1.08967	−	1.08967i	−0.0941029	−	0.995562i	$-0.529998\pi$
$878$	−849797.	+	28430.0i	−1.10237	+	0.0368797i
$879$			714090.i			0.924220i
$880$	176161.	−	53096.7i	0.227481	−	0.0685650i
$881$	864619.			1.11397			0.556984	−	0.830523i	$-0.311958\pi$
$881$	864619.			1.11397			0.556984	+	0.830523i	$0.311958\pi$
$882$	13055.0	+	390225.i	0.0167818	+	0.501624i
$883$	−91584.4	+	91584.4i	−0.117463	+	0.117463i	−0.763395	−	0.645932i	$-0.776469\pi$
$883$	−91584.4	+	91584.4i	−0.117463	+	0.117463i	0.645932	+	0.763395i	$0.276469\pi$
$884$	14367.1	+	214482.i	0.0183850	+	0.274465i
$885$	−417955.	−	302451.i	−0.533634	−	0.386161i
$886$	−33214.4	−	31064.0i	−0.0423116	−	0.0395722i
$887$	299983.	−	299983.i	0.381284	−	0.381284i	−0.490280	−	0.871565i	$-0.663106\pi$
$887$	299983.	−	299983.i	0.381284	−	0.381284i	0.871565	+	0.490280i	$0.163106\pi$
$888$	−51752.2	−	514101.i	−0.0656301	−	0.651963i
$889$		−	18275.0i		−	0.0231235i
$890$	−189419.	−	972214.i	−0.239135	−	1.22739i
$891$		−	14937.3i		−	0.0188155i
$892$	−306536.	−	268048.i	−0.385258	−	0.336886i
$893$	−248791.	+	248791.i	−0.311983	+	0.311983i
$894$	386262.	+	361254.i	0.483290	+	0.451999i
$895$	−193919.	−	1.20948e6i	−0.242088	−	1.50991i
$896$	−253751.	−	156031.i	−0.316077	−	0.194354i
$897$	−59085.3	+	59085.3i	−0.0734336	+	0.0734336i
$898$	1.36882e6	−	45793.9i	1.69744	−	0.0567877i
$899$	1.09949e6			1.36042
$900$	176990.	+	436968.i	0.218506	+	0.539466i
$901$		−	399439.i		−	0.492041i
$902$	−190021.	+	6357.14i	−0.233554	+	0.00781356i
$903$	216181.	+	216181.i	0.265119	+	0.265119i
$904$	−27108.4	+	33177.1i	−0.0331717	+	0.0405977i
$905$	−974034.	+	156169.i	−1.18926	+	0.190677i
$906$	170338.	+	159309.i	0.207517	+	0.194082i
$907$	−152114.	−	152114.i	−0.184907	−	0.184907i	0.608583	−	0.793490i	$-0.291738\pi$
$907$	−152114.	−	152114.i	−0.184907	−	0.184907i	−0.793490	+	0.608583i	$0.791738\pi$
$908$	610973.	+	534259.i	0.741054	+	0.648008i
$909$	−91386.6			−0.110600
$910$	−10717.7	−	55009.9i	−0.0129425	−	0.0664291i
$911$	881164.			1.06174			0.530872	−	0.847452i	$-0.321864\pi$
$911$	881164.			1.06174			0.530872	+	0.847452i	$0.321864\pi$
$912$	77387.4	−	101455.i	0.0930423	−	0.121978i
$913$	145008.	+	145008.i	0.173960	+	0.173960i
$914$	−644832.	−	603083.i	−0.771888	−	0.721913i
$915$	−136659.	+	188848.i	−0.163228	+	0.225564i
$916$	−15228.7	+	1020.09i	−0.0181498	+	0.00121576i
$917$	308754.	+	308754.i	0.367176	+	0.367176i
$918$	−43464.2	−	1.29918e6i	−0.0515758	−	1.54165i
$919$		−	375250.i		−	0.444313i	−0.975011	−	0.222157i	$-0.928690\pi$
$919$		−	375250.i		−	0.444313i	0.975011	−	0.222157i	$-0.0713096\pi$
$920$	644622.	+	374318.i	0.761604	+	0.442247i
$921$	603769.			0.711789
$922$	−1.46770e6	+	49101.8i	−1.72653	+	0.0577612i
$923$	144941.	−	144941.i	0.170133	−	0.170133i
$924$	48551.2	−	3252.20i	0.0568664	−	0.00380919i
$925$	−774185.	−	390769.i	−0.904819	−	0.456706i
$926$	−415199.	+	443941.i	−0.484210	+	0.517730i
$927$	−434991.	+	434991.i	−0.506199	+	0.506199i
$928$	−218884.	−	1.29679e6i	−0.254166	−	1.50583i
$929$		−	1.09922e6i		−	1.27366i	−0.771004	−	0.636831i	$-0.780245\pi$
$929$		−	1.09922e6i		−	1.27366i	0.771004	−	0.636831i	$-0.219755\pi$
$930$	−278364.	+	413079.i	−0.321845	+	0.477603i
$931$		−	177363.i		−	0.204627i
$932$	−432450.	−	378152.i	−0.497856	−	0.435346i
$933$	597696.	−	597696.i	0.686621	−	0.686621i
$934$	401158.	−	428928.i	0.459856	−	0.491690i
$935$	−183643.	+	253775.i	−0.210064	+	0.290286i
$936$	58848.6	−	72022.8i	0.0671714	−	0.0822088i
$937$	−196706.	+	196706.i	−0.224047	+	0.224047i	−0.810200	−	0.586153i	$-0.800642\pi$
$937$	−196706.	+	196706.i	−0.224047	+	0.224047i	0.586153	+	0.810200i	$0.300642\pi$
$938$	3839.45	+	114765.i	0.00436379	+	0.130438i
$939$	564252.			0.639944
$940$	−1.39235e6	−	872030.i	−1.57577	−	0.986906i
$941$			682887.i			0.771204i	0.922665	+	0.385602i	$0.126006\pi$
$941$			682887.i			0.771204i	−0.922665	+	0.385602i	$0.873994\pi$
$942$	−65.0755	−	1945.17i	−7.33357e−5	−	0.00219207i
$943$	−544675.	−	544675.i	−0.612511	−	0.612511i
$944$	899841.	−	121095.i	1.00977	−	0.135888i
$945$	53652.7	+	334634.i	0.0600797	+	0.374719i
$946$	227002.	−	242716.i	0.253657	−	0.271217i
$947$	922613.	+	922613.i	1.02877	+	1.02877i	0.999574	+	0.0292000i	$0.00929598\pi$
$947$	922613.	+	922613.i	1.02877	+	1.02877i	0.0292000	+	0.999574i	$0.490704\pi$
$948$	651083.	+	569333.i	0.724468	+	0.633505i
$949$	93834.3			0.104191
$950$	−73717.4	−	201074.i	−0.0816813	−	0.222797i
$951$	−538926.			−0.595892
$952$	504615.	−	50797.3i	0.556783	−	0.0560489i
$953$	−382778.	−	382778.i	−0.421465	−	0.421465i	0.464243	−	0.885708i	$-0.346326\pi$
$953$	−382778.	−	382778.i	−0.421465	−	0.421465i	−0.885708	+	0.464243i	$0.846326\pi$
$954$	−118051.	+	126223.i	−0.129710	+	0.138689i
$955$	−206153.	−	1.28578e6i	−0.226039	−	1.40981i
$956$	−30687.6	−	458127.i	−0.0335774	−	0.501269i
$957$	151908.	+	151908.i	0.165865	+	0.165865i
$958$	875177.	−	29279.0i	0.953597	−	0.0319026i
$959$			92662.5i			0.100755i
$960$	542622.	+	246081.i	0.588783	+	0.267015i
$961$	−190626.			−0.206413
$962$	5720.42	+	170989.i	0.00618127	+	0.184764i
$963$	−751856.	+	751856.i	−0.810740	+	0.810740i
$964$	−1.01318e6	+	67867.6i	−1.09026	+	0.0730312i
$965$	480609.	−	664152.i	0.516104	−	0.713202i
$966$	143984.	+	134662.i	0.154298	+	0.144308i
$967$	−125397.	+	125397.i	−0.134102	+	0.134102i	−0.770972	−	0.636870i	$-0.780229\pi$
$967$	−125397.	+	125397.i	−0.134102	+	0.134102i	0.636870	+	0.770972i	$0.280229\pi$
$968$	88553.8	+	879684.i	0.0945054	+	0.938806i
$969$			217247.i			0.231369i
$970$	−359524.	+	533518.i	−0.382107	+	0.567029i
$971$		−	1.38138e6i		−	1.46512i	−0.680701	−	0.732561i	$-0.738325\pi$
$971$		−	1.38138e6i		−	1.46512i	0.680701	−	0.732561i	$-0.261675\pi$
$972$	−604250.	+	691013.i	−0.639564	+	0.731398i
$973$	157236.	−	157236.i	0.166084	−	0.166084i
$974$	−142411.	−	133191.i	−0.150116	−	0.140397i
$975$	35044.7	+	106478.i	0.0368649	+	0.112008i
$976$	−54715.2	−	406582.i	−0.0574392	−	0.426823i
$977$	−1.00612e6	+	1.00612e6i	−1.05405	+	1.05405i	−0.0555928	+	0.998454i	$0.517705\pi$
$977$	−1.00612e6	+	1.00612e6i	−1.05405	+	1.05405i	−0.998454	+	0.0555928i	$0.982295\pi$
$978$	−490.729	+	16.4173i	−0.000513055	+	1.71643e-5i
$979$	−284751.			−0.297098
$980$	807139.	−	185469.i	0.840420	−	0.193116i
$981$			48796.5i			0.0507050i
$982$	252964.	−	8462.90i	0.262323	−	0.00877600i
$983$	1.33309e6	+	1.33309e6i	1.37959	+	1.37959i	0.845295	+	0.534300i	$0.179425\pi$
$983$	1.33309e6	+	1.33309e6i	1.37959	+	1.37959i	0.534300	+	0.845295i	$0.320575\pi$
$984$	−476775.	−	389564.i	−0.492405	−	0.402336i
$985$	476407.	−	658344.i	0.491027	−	0.678548i
$986$	1.63533e6	+	1.52945e6i	1.68210	+	1.57319i
$987$	−307236.	−	307236.i	−0.315383	−	0.315383i
$988$	−27811.6	+	31805.0i	−0.0284913	+	0.0325823i
$989$	1.34640e6			1.37651
$990$	133033.	−	25919.1i	0.135734	−	0.0264454i
$991$	−321150.			−0.327010			−0.163505	−	0.986543i	$-0.552280\pi$
$991$	−321150.			−0.327010			−0.163505	+	0.986543i	$0.552280\pi$
$992$	−145903.	−	864412.i	−0.148266	−	0.878410i
$993$	−272994.	−	272994.i	−0.276857	−	0.276857i
$994$	−353205.	−	330337.i	−0.357482	−	0.334337i
$995$	−910001.	+	145903.i	−0.919169	+	0.147373i
$996$	44384.4	+	662602.i	0.0447416	+	0.667935i
$997$	540978.	+	540978.i	0.544239	+	0.544239i	0.924769	−	0.380530i	$-0.124258\pi$
$997$	540978.	+	540978.i	0.544239	+	0.544239i	−0.380530	+	0.924769i	$0.624258\pi$
$998$	−26556.9	−	793812.i	−0.0266635	−	0.796996i
$999$		−	1.03457e6i		−	1.03664i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	40.5.i.a.13.12	✓	44
4.3	odd	2		160.5.m.a.113.15		44
5.2	odd	4	inner	40.5.i.a.37.22	yes	44
8.3	odd	2		160.5.m.a.113.8		44
8.5	even	2	inner	40.5.i.a.13.22	yes	44
20.7	even	4		160.5.m.a.17.8		44
40.27	even	4		160.5.m.a.17.15		44
40.37	odd	4	inner	40.5.i.a.37.12	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.5.i.a.13.12	✓	44	1.1	even	1	trivial
40.5.i.a.13.22	yes	44	8.5	even	2	inner
40.5.i.a.37.12	yes	44	40.37	odd	4	inner
40.5.i.a.37.22	yes	44	5.2	odd	4	inner
160.5.m.a.17.8		44	20.7	even	4
160.5.m.a.17.15		44	40.27	even	4
160.5.m.a.113.8		44	8.3	odd	2
160.5.m.a.113.15		44	4.3	odd	2

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:	\( N \)	\(=\)	\( 40 = 2^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	40.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.133745 - 3.99776i) q^{2} +(-4.11430 + 4.11430i) q^{3} +(-15.9642 + 1.06936i) q^{4} +(3.95777 + 24.6847i) q^{5} +(16.9983 + 15.8977i) q^{6} +(-12.8562 + 12.8562i) q^{7} +(6.41019 + 63.6782i) q^{8} +47.1451i q^{9} +O(q^{10})\)	\(q+(-0.133745 - 3.99776i) q^{2} +(-4.11430 + 4.11430i) q^{3} +(-15.9642 + 1.06936i) q^{4} +(3.95777 + 24.6847i) q^{5} +(16.9983 + 15.8977i) q^{6} +(-12.8562 + 12.8562i) q^{7} +(6.41019 + 63.6782i) q^{8} +47.1451i q^{9} +(98.1544 - 19.1237i) q^{10} -28.7483i q^{11} +(61.2819 - 70.0813i) q^{12} +(-21.7965 + 21.7965i) q^{13} +(53.1156 + 49.6767i) q^{14} +(-117.844 - 85.2769i) q^{15} +(253.713 - 34.1431i) q^{16} +(-308.195 + 308.195i) q^{17} +(188.475 - 6.30542i) q^{18} -85.6646 q^{19} +(-89.5796 - 389.840i) q^{20} -105.789i q^{21} +(-114.929 + 3.84495i) q^{22} +(-329.432 - 329.432i) q^{23} +(-288.364 - 235.618i) q^{24} +(-593.672 + 195.393i) q^{25} +(90.0526 + 84.2223i) q^{26} +(-527.227 - 527.227i) q^{27} +(191.492 - 218.988i) q^{28} +1284.31 q^{29} +(-325.156 + 482.517i) q^{30} +856.093 q^{31} +(-170.429 - 1009.72i) q^{32} +(118.279 + 118.279i) q^{33} +(1273.31 + 1190.87i) q^{34} +(-368.235 - 266.471i) q^{35} +(-50.4152 - 752.635i) q^{36} +(981.143 + 981.143i) q^{37} +(11.4572 + 342.467i) q^{38} -179.355i q^{39} +(-1546.51 + 410.257i) q^{40} +1653.37 q^{41} +(-422.918 + 14.1487i) q^{42} +(-2043.51 + 2043.51i) q^{43} +(30.7424 + 458.945i) q^{44} +(-1163.76 + 186.589i) q^{45} +(-1272.93 + 1361.05i) q^{46} +(2904.24 - 2904.24i) q^{47} +(-903.376 + 1184.33i) q^{48} +2070.43i q^{49} +(860.535 + 2347.23i) q^{50} -2536.02i q^{51} +(324.657 - 371.273i) q^{52} +(-648.030 + 648.030i) q^{53} +(-2037.22 + 2178.24i) q^{54} +(709.645 - 113.779i) q^{55} +(-901.072 - 736.250i) q^{56} +(352.450 - 352.450i) q^{57} +(-171.771 - 5134.38i) q^{58} +3546.69 q^{59} +(1972.48 + 1235.36i) q^{60} -1602.53i q^{61} +(-114.498 - 3422.46i) q^{62} +(-606.108 - 606.108i) q^{63} +(-4013.82 + 816.379i) q^{64} +(-624.308 - 451.776i) q^{65} +(457.033 - 488.672i) q^{66} +(1116.47 + 1116.47i) q^{67} +(4590.53 - 5249.67i) q^{68} +2710.76 q^{69} +(-1016.04 + 1507.75i) q^{70} -6649.74 q^{71} +(-3002.11 + 302.209i) q^{72} +(-2152.50 - 2152.50i) q^{73} +(3791.15 - 4053.60i) q^{74} +(1638.64 - 3246.45i) q^{75} +(1367.57 - 91.6065i) q^{76} +(369.595 + 369.595i) q^{77} +(-717.019 + 23.9878i) q^{78} +9290.39i q^{79} +(1846.95 + 6127.71i) q^{80} +519.588 q^{81} +(-221.131 - 6609.80i) q^{82} +(-5044.05 + 5044.05i) q^{83} +(113.126 + 1688.84i) q^{84} +(-8827.48 - 6387.95i) q^{85} +(8442.79 + 7896.17i) q^{86} +(-5284.05 + 5284.05i) q^{87} +(1830.64 - 184.282i) q^{88} -9904.95i q^{89} +(901.587 + 4627.50i) q^{90} -560.443i q^{91} +(5611.41 + 4906.85i) q^{92} +(-3522.22 + 3522.22i) q^{93} +(-11998.9 - 11222.0i) q^{94} +(-339.041 - 2114.61i) q^{95} +(4855.48 + 3453.09i) q^{96} +(-4549.17 + 4549.17i) q^{97} +(8277.11 - 276.910i) q^{98} +1355.34 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 2 q^{2} + 32 q^{6} - 4 q^{7} - 92 q^{8}+O(q^{10}) \) 44 * q - 2 * q^2 + 32 * q^6 - 4 * q^7 - 92 * q^8	\( 44 q - 2 q^{2} + 32 q^{6} - 4 q^{7} - 92 q^{8} - 154 q^{10} + 196 q^{12} - 4 q^{15} + 72 q^{16} + 236 q^{17} + 682 q^{18} - 904 q^{20} - 740 q^{22} - 4 q^{23} + 332 q^{25} - 2236 q^{26} + 2740 q^{28} + 3940 q^{30} - 264 q^{31} - 4352 q^{32} + 320 q^{33} - 4580 q^{36} - 4684 q^{38} + 5276 q^{40} - 8 q^{41} + 6676 q^{42} + 6784 q^{46} - 5764 q^{47} - 4000 q^{48} - 674 q^{50} + 5556 q^{52} + 2496 q^{55} + 13304 q^{56} - 328 q^{57} - 804 q^{58} + 3740 q^{60} - 13984 q^{62} + 9924 q^{63} - 3700 q^{65} - 12248 q^{66} - 11700 q^{68} - 10820 q^{70} - 19976 q^{71} - 17572 q^{72} + 13196 q^{73} - 12344 q^{76} + 23104 q^{78} - 24624 q^{80} - 13812 q^{81} + 15116 q^{82} + 16400 q^{86} + 48952 q^{87} + 35920 q^{88} + 49926 q^{90} + 25020 q^{92} - 27848 q^{95} + 42176 q^{96} + 3276 q^{97} - 65998 q^{98}+O(q^{100}) \) 44 * q - 2 * q^2 + 32 * q^6 - 4 * q^7 - 92 * q^8 - 154 * q^10 + 196 * q^12 - 4 * q^15 + 72 * q^16 + 236 * q^17 + 682 * q^18 - 904 * q^20 - 740 * q^22 - 4 * q^23 + 332 * q^25 - 2236 * q^26 + 2740 * q^28 + 3940 * q^30 - 264 * q^31 - 4352 * q^32 + 320 * q^33 - 4580 * q^36 - 4684 * q^38 + 5276 * q^40 - 8 * q^41 + 6676 * q^42 + 6784 * q^46 - 5764 * q^47 - 4000 * q^48 - 674 * q^50 + 5556 * q^52 + 2496 * q^55 + 13304 * q^56 - 328 * q^57 - 804 * q^58 + 3740 * q^60 - 13984 * q^62 + 9924 * q^63 - 3700 * q^65 - 12248 * q^66 - 11700 * q^68 - 10820 * q^70 - 19976 * q^71 - 17572 * q^72 + 13196 * q^73 - 12344 * q^76 + 23104 * q^78 - 24624 * q^80 - 13812 * q^81 + 15116 * q^82 + 16400 * q^86 + 48952 * q^87 + 35920 * q^88 + 49926 * q^90 + 25020 * q^92 - 27848 * q^95 + 42176 * q^96 + 3276 * q^97 - 65998 * q^98

Introduction

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