LMFDB - Embedded newform 25.4.e.a.14.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,4,Mod(4,25)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(25, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("25.4");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	25.e (of order $10$, degree $4$, 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:	$1.47504775014$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			14.6
Character	$\chi$	$=$	25.14
Dual form			25.4.e.a.9.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.81526 + 3.87487i) q^{2} +(-3.96562 - 1.28851i) q^{3} +(-4.61680 + 14.2091i) q^{4} +(11.1717 - 0.439337i) q^{5} +(-6.17144 - 18.9937i) q^{6} -14.5499i q^{7} +(-31.6143 + 10.2721i) q^{8} +(-7.77757 - 5.65074i) q^{9} +O(q^{10})$	\(q+(2.81526 + 3.87487i) q^{2} +(-3.96562 - 1.28851i) q^{3} +(-4.61680 + 14.2091i) q^{4} +(11.1717 - 0.439337i) q^{5} +(-6.17144 - 18.9937i) q^{6} -14.5499i q^{7} +(-31.6143 + 10.2721i) q^{8} +(-7.77757 - 5.65074i) q^{9} +(33.1536 + 42.0521i) q^{10} +(37.4944 - 27.2413i) q^{11} +(36.6170 - 50.3989i) q^{12} +(-37.1739 + 51.1655i) q^{13} +(56.3791 - 40.9618i) q^{14} +(-44.8688 - 12.6526i) q^{15} +(-32.1098 - 23.3291i) q^{16} +(-108.429 + 35.2308i) q^{17} -46.0453i q^{18} +(-18.3935 - 56.6094i) q^{19} +(-45.3350 + 160.768i) q^{20} +(-18.7477 + 57.6995i) q^{21} +(211.113 + 68.5947i) q^{22} +(-30.1783 - 41.5369i) q^{23} +138.606 q^{24} +(124.614 - 9.81628i) q^{25} -302.914 q^{26} +(89.7358 + 123.511i) q^{27} +(206.741 + 67.1742i) q^{28} +(-7.57128 + 23.3020i) q^{29} +(-77.2902 - 209.481i) q^{30} +(6.68485 + 20.5739i) q^{31} +75.8309i q^{32} +(-183.789 + 59.7167i) q^{33} +(-441.771 - 320.965i) q^{34} +(-6.39232 - 162.548i) q^{35} +(116.199 - 84.4236i) q^{36} +(120.842 - 166.325i) q^{37} +(167.572 - 230.642i) q^{38} +(213.345 - 155.004i) q^{39} +(-348.673 + 128.646i) q^{40} +(255.528 + 185.652i) q^{41} +(-276.358 + 89.7941i) q^{42} +173.139i q^{43} +(213.969 + 658.528i) q^{44} +(-89.3713 - 59.7114i) q^{45} +(75.9903 - 233.874i) q^{46} +(-210.805 - 68.4946i) q^{47} +(97.2755 + 133.888i) q^{48} +131.299 q^{49} +(388.857 + 455.228i) q^{50} +475.384 q^{51} +(-555.389 - 764.428i) q^{52} +(-170.619 - 55.4375i) q^{53} +(-225.959 + 695.429i) q^{54} +(406.908 - 320.804i) q^{55} +(149.458 + 459.986i) q^{56} +248.192i q^{57} +(-111.607 + 36.2634i) q^{58} +(-352.077 - 255.799i) q^{59} +(386.932 - 579.129i) q^{60} +(-136.184 + 98.9435i) q^{61} +(-60.9014 + 83.8236i) q^{62} +(-82.2178 + 113.163i) q^{63} +(-550.713 + 400.117i) q^{64} +(-392.817 + 587.938i) q^{65} +(-748.808 - 544.041i) q^{66} +(198.942 - 64.6401i) q^{67} -1703.33i q^{68} +(66.1551 + 203.604i) q^{69} +(611.855 - 482.383i) q^{70} +(-113.945 + 350.686i) q^{71} +(303.927 + 98.7519i) q^{72} +(252.468 + 347.492i) q^{73} +984.688 q^{74} +(-506.820 - 121.638i) q^{75} +889.285 q^{76} +(-396.359 - 545.541i) q^{77} +(1201.24 + 390.307i) q^{78} +(161.227 - 496.204i) q^{79} +(-368.971 - 246.519i) q^{80} +(-116.503 - 358.559i) q^{81} +1512.79i q^{82} +(-161.373 + 52.4333i) q^{83} +(-733.301 - 532.775i) q^{84} +(-1195.86 + 441.225i) q^{85} +(-670.889 + 487.429i) q^{86} +(60.0497 - 82.6513i) q^{87} +(-905.533 + 1246.36i) q^{88} +(524.968 - 381.412i) q^{89} +(-20.2294 - 514.405i) q^{90} +(744.455 + 540.878i) q^{91} +(729.527 - 237.038i) q^{92} -90.2016i q^{93} +(-328.062 - 1009.67i) q^{94} +(-230.357 - 624.342i) q^{95} +(97.7087 - 300.716i) q^{96} +(154.858 + 50.3164i) q^{97} +(369.641 + 508.768i) q^{98} -445.549 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 5 q^{2} - 5 q^{3} + 13 q^{4} + 15 q^{5} - 7 q^{6} - 110 q^{8} + 47 q^{9}+O(q^{10}) $ 24 * q - 5 * q^2 - 5 * q^3 + 13 * q^4 + 15 * q^5 - 7 * q^6 - 110 * q^8 + 47 * q^9	\( 24 q - 5 q^{2} - 5 q^{3} + 13 q^{4} + 15 q^{5} - 7 q^{6} - 110 q^{8} + 47 q^{9} - 5 q^{10} + 83 q^{11} - 165 q^{12} - 5 q^{13} + 31 q^{14} - 225 q^{15} + 89 q^{16} - 165 q^{17} - 115 q^{19} + 395 q^{20} + 138 q^{21} + 30 q^{22} + 75 q^{23} + 640 q^{24} + 595 q^{25} - 822 q^{26} + 595 q^{27} + 675 q^{28} + 125 q^{29} - 965 q^{30} + 633 q^{31} - 1285 q^{33} - 779 q^{34} + 190 q^{35} - 531 q^{36} - 1510 q^{37} + 255 q^{38} - 1241 q^{39} - 2470 q^{40} - 117 q^{41} + 1745 q^{42} + 516 q^{44} + 1725 q^{45} + 1233 q^{46} - 95 q^{47} + 1410 q^{48} + 1148 q^{49} + 2165 q^{50} - 2022 q^{51} + 1740 q^{52} + 2580 q^{53} + 1745 q^{54} - 315 q^{55} + 3160 q^{56} - 4230 q^{58} - 1905 q^{59} + 560 q^{60} - 567 q^{61} - 6880 q^{62} - 1950 q^{63} - 3612 q^{64} - 3170 q^{65} - 2774 q^{66} + 4195 q^{67} + 539 q^{69} + 3630 q^{70} + 2473 q^{71} + 215 q^{72} - 845 q^{73} + 3596 q^{74} + 2045 q^{75} - 3280 q^{76} + 3870 q^{77} + 9295 q^{78} + 775 q^{79} - 3670 q^{80} + 3309 q^{81} - 4625 q^{83} - 5694 q^{84} - 1460 q^{85} - 3897 q^{86} - 8485 q^{87} - 1650 q^{88} - 2410 q^{89} - 8845 q^{90} - 382 q^{91} + 4090 q^{92} + 5401 q^{94} + 3545 q^{95} + 6488 q^{96} + 5185 q^{97} + 5180 q^{98} + 6024 q^{99}+O(q^{100}) \) 24 * q - 5 * q^2 - 5 * q^3 + 13 * q^4 + 15 * q^5 - 7 * q^6 - 110 * q^8 + 47 * q^9 - 5 * q^10 + 83 * q^11 - 165 * q^12 - 5 * q^13 + 31 * q^14 - 225 * q^15 + 89 * q^16 - 165 * q^17 - 115 * q^19 + 395 * q^20 + 138 * q^21 + 30 * q^22 + 75 * q^23 + 640 * q^24 + 595 * q^25 - 822 * q^26 + 595 * q^27 + 675 * q^28 + 125 * q^29 - 965 * q^30 + 633 * q^31 - 1285 * q^33 - 779 * q^34 + 190 * q^35 - 531 * q^36 - 1510 * q^37 + 255 * q^38 - 1241 * q^39 - 2470 * q^40 - 117 * q^41 + 1745 * q^42 + 516 * q^44 + 1725 * q^45 + 1233 * q^46 - 95 * q^47 + 1410 * q^48 + 1148 * q^49 + 2165 * q^50 - 2022 * q^51 + 1740 * q^52 + 2580 * q^53 + 1745 * q^54 - 315 * q^55 + 3160 * q^56 - 4230 * q^58 - 1905 * q^59 + 560 * q^60 - 567 * q^61 - 6880 * q^62 - 1950 * q^63 - 3612 * q^64 - 3170 * q^65 - 2774 * q^66 + 4195 * q^67 + 539 * q^69 + 3630 * q^70 + 2473 * q^71 + 215 * q^72 - 845 * q^73 + 3596 * q^74 + 2045 * q^75 - 3280 * q^76 + 3870 * q^77 + 9295 * q^78 + 775 * q^79 - 3670 * q^80 + 3309 * q^81 - 4625 * q^83 - 5694 * q^84 - 1460 * q^85 - 3897 * q^86 - 8485 * q^87 - 1650 * q^88 - 2410 * q^89 - 8845 * q^90 - 382 * q^91 + 4090 * q^92 + 5401 * q^94 + 3545 * q^95 + 6488 * q^96 + 5185 * q^97 + 5180 * q^98 + 6024 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{10}\right)$

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 $

$2$	2.81526	+	3.87487i	0.995344	+	1.36997i	0.928139	+	0.372234i	$0.121408\pi$
$2$	2.81526	+	3.87487i	0.995344	+	1.36997i	0.0672050	+	0.997739i	$0.478592\pi$
$3$	−3.96562	−	1.28851i	−0.763184	−	0.247973i	−0.0985393	−	0.995133i	$-0.531417\pi$
$3$	−3.96562	−	1.28851i	−0.763184	−	0.247973i	−0.664645	+	0.747160i	$0.731417\pi$
$4$	−4.61680	+	14.2091i	−0.577100	+	1.77613i
$5$	11.1717	−	0.439337i	0.999228	−	0.0392955i
$5$	11.1717	−	0.439337i	0.999228	−	0.0392955i
$6$	−6.17144	−	18.9937i	−0.419913	−	1.29236i
$7$		−	14.5499i		−	0.785623i	−0.919619	−	0.392811i	$-0.871503\pi$
$7$		−	14.5499i		−	0.785623i	0.919619	−	0.392811i	$-0.128497\pi$
$8$	−31.6143	+	10.2721i	−1.39717	+	0.453967i
$9$	−7.77757	−	5.65074i	−0.288058	−	0.209286i
$10$	33.1536	+	42.0521i	1.04841	+	1.32980i
$11$	37.4944	−	27.2413i	1.02773	−	0.746687i	0.0598737	−	0.998206i	$-0.480930\pi$
$11$	37.4944	−	27.2413i	1.02773	−	0.746687i	0.967852	+	0.251519i	$0.0809302\pi$
$12$	36.6170	−	50.3989i	0.880867	−	1.21241i
$13$	−37.1739	+	51.1655i	−0.793092	+	1.09160i	0.200625	+	0.979668i	$0.435703\pi$
$13$	−37.1739	+	51.1655i	−0.793092	+	1.09160i	−0.993716	+	0.111929i	$0.964297\pi$
$14$	56.3791	−	40.9618i	1.07628	−	0.781965i
$15$	−44.8688	−	12.6526i	−0.772339	−	0.217792i
$16$	−32.1098	−	23.3291i	−0.501716	−	0.364518i
$17$	−108.429	+	35.2308i	−1.54694	+	0.502631i	−0.953280	−	0.302087i	$-0.902317\pi$
$17$	−108.429	+	35.2308i	−1.54694	+	0.502631i	−0.593657	+	0.804718i	$0.702317\pi$
$18$		−	46.0453i		−	0.602944i
$19$	−18.3935	−	56.6094i	−0.222093	−	0.683531i	−0.998574	−	0.0533903i	$-0.982997\pi$
$19$	−18.3935	−	56.6094i	−0.222093	−	0.683531i	0.776481	−	0.630141i	$-0.217003\pi$
$20$	−45.3350	+	160.768i	−0.506861	+	1.79744i
$21$	−18.7477	+	57.6995i	−0.194814	+	0.599575i
$22$	211.113	+	68.5947i	2.04588	+	0.664747i
$23$	−30.1783	−	41.5369i	−0.273592	−	0.376567i	0.650006	−	0.759929i	$-0.274766\pi$
$23$	−30.1783	−	41.5369i	−0.273592	−	0.376567i	−0.923598	+	0.383362i	$0.874766\pi$
$24$	138.606			1.17887
$25$	124.614	−	9.81628i	0.996912	−	0.0785302i
$26$	−302.914			−2.28486
$27$	89.7358	+	123.511i	0.639617	+	0.880358i
$28$	206.741	+	67.1742i	1.39537	+	0.453383i
$29$	−7.57128	+	23.3020i	−0.0484811	+	0.149209i	−0.972366	−	0.233460i	$-0.924995\pi$
$29$	−7.57128	+	23.3020i	−0.0484811	+	0.149209i	0.923885	+	0.382669i	$0.124995\pi$
$30$	−77.2902	−	209.481i	−0.470373	−	1.27486i
$31$	6.68485	+	20.5739i	0.0387301	+	0.119199i	0.968552	−	0.248810i	$-0.0800395\pi$
$31$	6.68485	+	20.5739i	0.0387301	+	0.119199i	−0.929822	+	0.368009i	$0.880039\pi$
$32$			75.8309i			0.418910i
$33$	−183.789	+	59.7167i	−0.969502	+	0.315010i
$34$	−441.771	−	320.965i	−2.22833	−	1.61897i
$35$	−6.39232	−	162.548i	−0.0308714	−	0.785016i
$36$	116.199	−	84.4236i	0.537959	−	0.390850i
$37$	120.842	−	166.325i	0.536927	−	0.739017i	−0.451239	−	0.892403i	$-0.649018\pi$
$37$	120.842	−	166.325i	0.536927	−	0.739017i	0.988166	+	0.153386i	$0.0490179\pi$
$38$	167.572	−	230.642i	0.715360	−	0.984609i
$39$	213.345	−	155.004i	0.875962	−	0.636424i
$40$	−348.673	+	128.646i	−1.37825	+	0.508519i
$41$	255.528	+	185.652i	0.973335	+	0.707169i	0.956209	−	0.292684i	$-0.0945484\pi$
$41$	255.528	+	185.652i	0.973335	+	0.707169i	0.0171259	+	0.999853i	$0.494548\pi$
$42$	−276.358	+	89.7941i	−1.01531	+	0.329893i
$43$			173.139i			0.614032i	0.951704	+	0.307016i	$0.0993305\pi$
$43$			173.139i			0.614032i	−0.951704	+	0.307016i	$0.900669\pi$
$44$	213.969	+	658.528i	0.733113	+	2.25629i
$45$	−89.3713	−	59.7114i	−0.296060	−	0.197805i
$46$	75.9903	−	233.874i	0.243569	−	0.749627i
$47$	−210.805	−	68.4946i	−0.654234	−	0.212574i	−0.0369541	−	0.999317i	$-0.511766\pi$
$47$	−210.805	−	68.4946i	−0.654234	−	0.212574i	−0.617280	+	0.786743i	$0.711766\pi$
$48$	97.2755	+	133.888i	0.292511	+	0.402607i
$49$	131.299			0.382797
$50$	388.857	+	455.228i	1.09985	+	1.28758i
$51$	475.384			1.30524
$52$	−555.389	−	764.428i	−1.48113	−	2.03860i
$53$	−170.619	−	55.4375i	−0.442195	−	0.143678i	0.0794532	−	0.996839i	$-0.474683\pi$
$53$	−170.619	−	55.4375i	−0.442195	−	0.143678i	−0.521648	+	0.853161i	$0.674683\pi$
$54$	−225.959	+	695.429i	−0.569427	+	1.75252i
$55$	406.908	−	320.804i	0.997591	−	0.786495i
$56$	149.458	+	459.986i	0.356647	+	1.09765i
$57$			248.192i			0.576733i
$58$	−111.607	+	36.2634i	−0.252668	+	0.0820969i
$59$	−352.077	−	255.799i	−0.776891	−	0.564444i	0.127153	−	0.991883i	$-0.459416\pi$
$59$	−352.077	−	255.799i	−0.776891	−	0.564444i	−0.904044	+	0.427439i	$0.859416\pi$
$60$	386.932	−	579.129i	0.832545	−	1.24609i
$61$	−136.184	+	98.9435i	−0.285845	+	0.207679i	−0.721463	−	0.692453i	$-0.756530\pi$
$61$	−136.184	+	98.9435i	−0.285845	+	0.207679i	0.435618	+	0.900132i	$0.356530\pi$
$62$	−60.9014	+	83.8236i	−0.124750	+	0.171703i
$63$	−82.2178	+	113.163i	−0.164420	+	0.226305i
$64$	−550.713	+	400.117i	−1.07561	+	0.781478i
$65$	−392.817	+	587.938i	−0.749584	+	1.12192i
$66$	−748.808	−	544.041i	−1.39654	−	1.01465i
$67$	198.942	−	64.6401i	0.362755	−	0.117866i	−0.121968	−	0.992534i	$-0.538920\pi$
$67$	198.942	−	64.6401i	0.362755	−	0.117866i	0.484723	+	0.874668i	$0.338920\pi$
$68$		−	1703.33i		−	3.03763i
$69$	66.1551	+	203.604i	0.115422	+	0.355233i
$70$	611.855	−	482.383i	1.04472	−	0.823654i
$71$	−113.945	+	350.686i	−0.190461	+	0.586179i	−1.00000		0.000887732i	$-0.999717\pi$
$71$	−113.945	+	350.686i	−0.190461	+	0.586179i	0.809538	+	0.587067i	$0.199717\pi$
$72$	303.927	+	98.7519i	0.497475	+	0.161639i
$73$	252.468	+	347.492i	0.404782	+	0.557135i	0.961936	−	0.273274i	$-0.0881066\pi$
$73$	252.468	+	347.492i	0.404782	+	0.557135i	−0.557154	+	0.830409i	$0.688107\pi$
$74$	984.688			1.54686
$75$	−506.820	−	121.638i	−0.780300	−	0.187275i
$76$	889.285			1.34221
$77$	−396.359	−	545.541i	−0.586614	−	0.807405i
$78$	1201.24	+	390.307i	1.74377	+	0.566584i
$79$	161.227	−	496.204i	0.229613	−	0.706675i	−0.768178	−	0.640237i	$-0.778836\pi$
$79$	161.227	−	496.204i	0.229613	−	0.706675i	0.997791	−	0.0664388i	$-0.0211637\pi$
$80$	−368.971	−	246.519i	−0.515652	−	0.344521i
$81$	−116.503	−	358.559i	−0.159812	−	0.491851i
$82$			1512.79i			2.03732i
$83$	−161.373	+	52.4333i	−0.213409	+	0.0693409i	−0.413771	−	0.910381i	$-0.635788\pi$
$83$	−161.373	+	52.4333i	−0.213409	+	0.0693409i	0.200361	+	0.979722i	$0.435788\pi$
$84$	−733.301	−	532.775i	−0.952497	−	0.692030i
$85$	−1195.86	+	441.225i	−1.52599	+	0.563030i
$86$	−670.889	+	487.429i	−0.841207	+	0.611173i
$87$	60.0497	−	82.6513i	0.0740000	−	0.101852i
$88$	−905.533	+	1246.36i	−1.09693	+	1.50980i
$89$	524.968	−	381.412i	0.625242	−	0.454265i	−0.229507	−	0.973307i	$-0.573711\pi$
$89$	524.968	−	381.412i	0.625242	−	0.454265i	0.854748	+	0.519042i	$0.173711\pi$
$90$	−20.2294	−	514.405i	−0.0236930	−	0.602478i
$91$	744.455	+	540.878i	0.857583	+	0.623071i
$92$	729.527	−	237.038i	0.826722	−	0.268618i
$93$		−	90.2016i		−	0.100575i
$94$	−328.062	−	1009.67i	−0.359968	−	1.10787i
$95$	−230.357	−	624.342i	−0.248781	−	0.674276i
$96$	97.7087	−	300.716i	0.103879	−	0.319706i
$97$	154.858	+	50.3164i	0.162097	+	0.0526686i	0.388941	−	0.921262i	$-0.372841\pi$
$97$	154.858	+	50.3164i	0.162097	+	0.0526686i	−0.226844	+	0.973931i	$0.572841\pi$
$98$	369.641	+	508.768i	0.381015	+	0.524422i
$99$	−445.549			−0.452316
$100$	−435.838	+	1815.97i	−0.435838	+	1.81597i
$101$	−1372.10			−1.35178			−0.675889	−	0.737004i	$-0.736240\pi$
$101$	−1372.10			−1.35178			−0.675889	+	0.737004i	$0.736240\pi$
$102$	1338.33	+	1842.05i	1.29916	+	1.78814i
$103$	1140.92	+	370.708i	1.09144	+	0.354631i	0.798803	−	0.601592i	$-0.205467\pi$
$103$	1140.92	+	370.708i	1.09144	+	0.354631i	0.292638	+	0.956223i	$0.405467\pi$
$104$	649.649	−	1999.42i	0.612532	−	1.88518i
$105$	−184.094	+	652.839i	−0.171103	+	0.606767i
$106$	−265.524	−	817.197i	−0.243301	−	0.748804i
$107$		−	1960.58i		−	1.77137i	−0.464285	−	0.885686i	$-0.653689\pi$
$107$		−	1960.58i		−	1.77137i	0.464285	−	0.885686i	$-0.346311\pi$
$108$	−2169.26	+	704.837i	−1.93276	+	0.627990i
$109$	1396.99	+	1014.97i	1.22759	+	0.891897i	0.996707	−	0.0810841i	$-0.0258382\pi$
$109$	1396.99	+	1014.97i	1.22759	+	0.891897i	0.230884	+	0.972981i	$0.425838\pi$
$110$	2388.63	+	673.570i	2.07042	+	0.583840i
$111$	−693.524	+	503.875i	−0.593031	+	0.430862i
$112$	−339.438	+	467.196i	−0.286374	+	0.394159i
$113$	513.462	−	706.720i	0.427455	−	0.588341i	−0.539912	−	0.841722i	$-0.681542\pi$
$113$	513.462	−	706.720i	0.427455	−	0.588341i	0.967367	+	0.253380i	$0.0815424\pi$
$114$	−961.710	+	698.723i	−0.790109	+	0.574047i
$115$	−355.392	−	450.779i	−0.288178	−	0.365525i
$116$	−296.145	−	215.162i	−0.237037	−	0.172218i
$117$	578.245	−	187.883i	0.456913	−	0.148460i
$118$		−	2084.39i		−	1.62614i
$119$	512.606	+	1577.64i	0.394878	+	1.21531i
$120$	1548.46	−	60.8946i	1.17796	−	0.0463241i
$121$	252.441	−	776.934i	0.189663	−	0.583722i
$122$	−766.786	−	249.144i	−0.569029	−	0.184889i
$123$	−774.112	−	1065.47i	−0.567474	−	0.781062i
$124$	−323.198			−0.234065
$125$	1387.84	−	164.412i	0.993056	−	0.117644i
$126$	−669.957			−0.473686
$127$	300.201	+	413.192i	0.209752	+	0.288699i	0.900911	−	0.434004i	$-0.142899\pi$
$127$	300.201	+	413.192i	0.209752	+	0.288699i	−0.691159	+	0.722703i	$0.742899\pi$
$128$	−2523.84	−	820.047i	−1.74280	−	0.566270i
$129$	223.090	−	686.602i	0.152264	−	0.468619i
$130$	−3384.06	+	133.081i	−2.28309	+	0.0897845i
$131$	−608.894	−	1873.98i	−0.406102	−	1.24985i	−0.919972	−	0.391985i	$-0.871789\pi$
$131$	−608.894	−	1873.98i	−0.406102	−	1.24985i	0.513870	−	0.857868i	$-0.328211\pi$
$132$		−	2887.17i		−	1.90376i
$133$	−823.663	+	267.624i	−0.536997	+	0.174481i
$134$	810.544	+	588.895i	0.522540	+	0.379647i
$135$	1056.77	+	1340.40i	0.673717	+	0.854544i
$136$	3066.02	−	2227.59i	1.93315	−	1.40452i
$137$	−402.493	+	553.984i	−0.251002	+	0.345474i	−0.915862	−	0.401494i	$-0.868491\pi$
$137$	−402.493	+	553.984i	−0.251002	+	0.345474i	0.664860	+	0.746968i	$0.268491\pi$
$138$	−602.697	+	829.541i	−0.371775	+	0.511705i
$139$	−1802.79	+	1309.80i	−1.10008	+	0.799253i	−0.981072	−	0.193641i	$-0.937970\pi$
$139$	−1802.79	+	1309.80i	−1.10008	+	0.799253i	−0.119005	+	0.992894i	$0.537970\pi$
$140$	2339.16	+	659.621i	1.41211	+	0.398201i
$141$	747.715	+	543.247i	0.446588	+	0.324466i
$142$	−1679.64	+	545.749i	−0.992624	+	0.322523i
$143$			2931.09i			1.71405i
$144$	117.910	+	362.888i	0.0682347	+	0.210005i
$145$	−74.3467	+	263.650i	−0.0425804	+	0.150999i
$146$	−635.725	+	1956.56i	−0.360363	+	1.10908i
$147$	−520.683	−	169.180i	−0.292144	−	0.0949235i
$148$	1805.41	+	2484.94i	1.00273	+	1.38014i
$149$	237.094			0.130359			0.0651796	−	0.997874i	$-0.479238\pi$
$149$	237.094			0.130359			0.0651796	+	0.997874i	$0.479238\pi$
$150$	−955.496	−	2306.31i	−0.520106	−	1.25539i
$151$	1669.11			0.899536			0.449768	−	0.893145i	$-0.351507\pi$
$151$	1669.11			0.899536			0.449768	+	0.893145i	$0.351507\pi$
$152$	1163.00	+	1600.73i	0.620601	+	0.854184i
$153$	1042.40	+	338.695i	0.550802	+	0.178966i
$154$	998.049	−	3071.68i	0.522241	−	1.60729i
$155$	83.7200	+	226.908i	0.0433842	+	0.117585i
$156$	1217.49	+	3747.05i	0.624855	+	1.92310i
$157$		−	1543.67i		−	0.784700i	−0.919816	−	0.392350i	$-0.871662\pi$
$157$		−	1543.67i		−	0.784700i	0.919816	−	0.392350i	$-0.128338\pi$
$158$	2376.62	−	772.211i	1.19667	−	0.388822i
$159$	605.179	+	439.688i	0.301848	+	0.219305i
$160$	33.3153	+	847.160i	0.0164613	+	0.418587i
$161$	−604.359	+	439.092i	−0.295839	+	0.214940i
$162$	1061.38	−	1460.87i	0.514754	−	0.708498i
$163$	579.524	−	797.647i	0.278478	−	0.383291i	−0.646751	−	0.762701i	$-0.723873\pi$
$163$	579.524	−	797.647i	0.278478	−	0.383291i	0.925229	+	0.379410i	$0.123873\pi$
$164$	−3817.66	+	2773.69i	−1.81774	+	1.32066i
$165$	−2027.00	+	747.883i	−0.956375	+	0.352864i
$166$	−657.479	−	477.686i	−0.307411	−	0.223347i
$167$	−659.533	+	214.295i	−0.305606	+	0.0992974i	−0.457805	−	0.889052i	$-0.651364\pi$
$167$	−659.533	+	214.295i	−0.305606	+	0.0992974i	0.152200	+	0.988350i	$0.451364\pi$
$168$		−	2016.71i		−	0.926145i
$169$	−557.099	−	1714.57i	−0.253573	−	0.780416i
$170$	−5076.34	−	3391.64i	−2.29022	−	1.53016i
$171$	−176.828	+	544.220i	−0.0790782	+	0.243378i
$172$	−2460.14	−	799.346i	−1.09060	−	0.354358i
$173$	−1177.97	−	1621.34i	−0.517686	−	0.712534i	0.467505	−	0.883990i	$-0.345153\pi$
$173$	−1177.97	−	1621.34i	−0.517686	−	0.712534i	−0.985192	+	0.171456i	$0.945153\pi$
$174$	489.318			0.213190
$175$	−142.826	−	1813.13i	−0.0616951	−	0.783197i
$176$	−1839.45			−0.787807
$177$	1066.61	+	1468.06i	0.452943	+	0.623423i
$178$	2955.84	+	960.411i	1.24466	+	0.404415i
$179$	116.627	−	358.941i	0.0486990	−	0.149880i	−0.923750	−	0.382996i	$-0.874892\pi$
$179$	116.627	−	358.941i	0.0486990	−	0.149880i	0.972449	+	0.233116i	$0.0748922\pi$
$180$	1261.05	−	994.206i	0.522185	−	0.411688i
$181$	−690.367	−	2124.73i	−0.283506	−	0.872541i	−0.986843	−	0.161684i	$-0.948307\pi$
$181$	−690.367	−	2124.73i	−0.283506	−	0.872541i	0.703337	−	0.710857i	$-0.251693\pi$
$182$			4407.38i			1.79504i
$183$	667.543	−	216.898i	0.269652	−	0.0876151i
$184$	1380.74	+	1003.16i	0.553202	+	0.401925i
$185$	1276.94	−	1911.22i	0.507472	−	0.759545i
$186$	349.519	−	253.941i	0.137785	−	0.100107i
$187$	−3105.76	+	4274.71i	−1.21452	+	1.67164i
$188$	1946.49	−	2679.11i	0.755118	−	1.03933i
$189$	1797.07	−	1305.65i	0.691629	−	0.502498i
$190$	1770.73	−	2650.29i	0.676117	−	1.01196i
$191$	1816.50	+	1319.76i	0.688153	+	0.499973i	0.876052	−	0.482216i	$-0.160168\pi$
$191$	1816.50	+	1319.76i	0.688153	+	0.499973i	−0.187899	+	0.982188i	$0.560168\pi$
$192$	2699.47	−	877.112i	1.01468	−	0.329688i
$193$		−	1535.61i		−	0.572722i	−0.958122	−	0.286361i	$-0.907554\pi$
$193$		−	1535.61i		−	0.572722i	0.958122	−	0.286361i	$-0.0924457\pi$
$194$	240.995	+	741.708i	0.0891879	+	0.274492i
$195$	2315.33	−	1825.39i	0.850277	−	0.670353i
$196$	−606.183	+	1865.64i	−0.220912	+	0.679898i
$197$	3238.08	+	1052.12i	1.17109	+	0.380509i	0.829048	−	0.559178i	$-0.188883\pi$
$197$	3238.08	+	1052.12i	1.17109	+	0.380509i	0.342037	+	0.939686i	$0.388883\pi$
$198$	−1254.33	−	1726.44i	−0.450210	−	0.619661i
$199$	−3490.16			−1.24327			−0.621636	−	0.783306i	$-0.713532\pi$
$199$	−3490.16			−1.24327			−0.621636	+	0.783306i	$0.713532\pi$
$200$	−3838.75	+	1590.38i	−1.35720	+	0.562285i
$201$	−872.216			−0.306077
$202$	−3862.83	−	5316.73i	−1.34548	−	1.85190i
$203$	339.043	+	110.162i	0.117222	+	0.0380879i
$204$	−2194.75	+	6754.76i	−0.753253	+	2.31827i
$205$	2936.24	+	1961.78i	1.00037	+	0.668376i
$206$	1775.55	+	5464.57i	0.600525	+	1.84823i
$207$			493.585i			0.165732i
$208$	2387.30	−	775.679i	0.795813	−	0.258575i
$209$	−2231.77	−	1621.47i	−0.738634	−	0.536649i
$210$	−3047.94	+	1124.57i	−1.00156	+	0.369536i
$211$	−4293.83	+	3119.65i	−1.40095	+	1.01785i	−0.406384	+	0.913702i	$0.633210\pi$
$211$	−4293.83	+	3119.65i	−1.40095	+	1.01785i	−0.994562	+	0.104144i	$0.966790\pi$
$212$	1575.43	−	2168.39i	0.510382	−	0.702480i
$213$	903.722	−	1243.87i	0.290714	−	0.400133i
$214$	7597.01	−	5519.55i	2.42673	−	1.76312i
$215$	76.0661	+	1934.25i	0.0241287	+	0.613558i
$216$	−4105.65	−	2982.93i	−1.29331	−	0.939642i
$217$	299.348	−	97.2641i	0.0936455	−	0.0304273i
$218$			8270.57i			2.56951i
$219$	−553.445	−	1703.33i	−0.170769	−	0.525572i
$220$	2679.71	+	7262.87i	0.821209	+	2.22574i
$221$	2228.14	−	6857.50i	0.678193	−	2.08726i
$222$	−3904.90	−	1268.78i	−1.18054	−	0.383580i
$223$	219.638	+	302.306i	0.0659554	+	0.0907798i	0.840720	−	0.541470i	$-0.182132\pi$
$223$	219.638	+	302.306i	0.0659554	+	0.0907798i	−0.774765	+	0.632249i	$0.782132\pi$
$224$	1103.33			0.329105
$225$	−1024.66	−	627.814i	−0.303604	−	0.186019i
$226$	4183.97			1.23148
$227$	−1991.64	−	2741.26i	−0.582334	−	0.801514i	0.411615	−	0.911358i	$-0.364965\pi$
$227$	−1991.64	−	2741.26i	−0.582334	−	0.801514i	−0.993949	+	0.109844i	$0.964965\pi$
$228$	−3526.57	−	1145.85i	−1.02435	−	0.332833i
$229$	−703.226	+	2164.31i	−0.202928	+	0.624548i	0.796864	+	0.604158i	$0.206491\pi$
$229$	−703.226	+	2164.31i	−0.202928	+	0.624548i	−0.999792	+	0.0203894i	$0.993509\pi$
$230$	746.191	−	2646.16i	0.213923	−	0.758619i
$231$	868.874	+	2674.12i	0.247479	+	0.761663i
$232$		−	814.449i		−	0.230479i
$233$	−6567.82	+	2134.01i	−1.84666	+	0.600017i	−0.849261	+	0.527974i	$0.822952\pi$
$233$	−6567.82	+	2134.01i	−1.84666	+	0.600017i	−0.997401	+	0.0720434i	$0.977048\pi$
$234$	2355.93	+	1711.69i	0.658172	+	0.478190i
$235$	−2385.14	−	672.587i	−0.662082	−	0.186701i
$236$	5260.14	−	3821.71i	1.45087	−	1.05412i
$237$	−1278.73	+	1760.02i	−0.350474	+	0.482385i
$238$	−4670.02	+	6427.74i	−1.27190	+	1.75062i
$239$	−3557.28	+	2584.52i	−0.962768	+	0.699492i	−0.953792	−	0.300468i	$-0.902857\pi$
$239$	−3557.28	+	2584.52i	−0.962768	+	0.699492i	−0.00897589	+	0.999960i	$0.502857\pi$
$240$	1145.56	+	1453.02i	0.308105	+	0.390801i
$241$	2184.17	+	1586.89i	0.583796	+	0.424153i	0.840091	−	0.542446i	$-0.182502\pi$
$241$	2184.17	+	1586.89i	0.583796	+	0.424153i	−0.256294	+	0.966599i	$0.582502\pi$
$242$	3721.21	−	1209.09i	0.988463	−	0.321171i
$243$		−	2550.01i		−	0.673181i
$244$	−777.159	−	2391.85i	−0.203904	−	0.627551i
$245$	1466.84	−	57.6846i	0.382501	−	0.0150422i
$246$	1949.25	−	5999.17i	0.505201	−	1.55485i
$247$	3580.21	+	1163.28i	0.922280	+	0.299667i
$248$	−422.673	−	581.760i	−0.108225	−	0.148959i
$249$	707.505			0.180065
$250$	4544.20	+	4914.83i	1.14960	+	1.24336i
$251$	−639.504			−0.160817			−0.0804086	−	0.996762i	$-0.525623\pi$
$251$	−639.504			−0.160817			−0.0804086	+	0.996762i	$0.525623\pi$
$252$	−1228.36	−	1690.69i	−0.307061	−	0.422633i
$253$	−2263.03	−	735.304i	−0.562355	−	0.182720i
$254$	−755.920	+	2326.48i	−0.186735	+	0.574710i
$255$	5310.85	−	208.854i	1.30423	−	0.0512899i
$256$	−2244.87	−	6908.99i	−0.548063	−	1.68676i
$257$			6291.12i			1.52696i	0.645831	+	0.763481i	$0.276511\pi$
$257$			6291.12i			1.52696i	−0.645831	+	0.763481i	$0.723489\pi$
$258$	3288.55	−	1068.51i	0.793551	−	0.257840i
$259$	−2420.01	−	1758.24i	−0.580588	−	0.421822i
$260$	−6540.48	−	8295.96i	−1.56009	−	1.97882i
$261$	190.560	−	138.450i	0.0451929	−	0.0328346i
$262$	5547.25	−	7635.13i	1.30805	−	1.80038i
$263$	1153.81	−	1588.08i	0.270521	−	0.372340i	−0.652045	−	0.758180i	$-0.726089\pi$
$263$	1153.81	−	1588.08i	0.270521	−	0.372340i	0.922565	+	0.385841i	$0.126089\pi$
$264$	5196.95	−	3775.80i	1.21155	−	0.880244i
$265$	−1930.46	−	544.372i	−0.447499	−	0.126191i
$266$	−3355.83	−	2438.16i	−0.773531	−	0.562003i
$267$	−2573.28	+	836.108i	−0.589820	+	0.191644i
$268$			3125.20i			0.712322i
$269$	1113.11	+	3425.80i	0.252295	+	0.776485i	0.994351	+	0.106146i	$0.0338512\pi$
$269$	1113.11	+	3425.80i	0.252295	+	0.776485i	−0.742055	+	0.670339i	$0.766149\pi$
$270$	−2218.82	+	7868.40i	−0.500122	+	1.77354i
$271$	−2174.84	+	6693.46i	−0.487498	+	1.50036i	0.340833	+	0.940124i	$0.389291\pi$
$271$	−2174.84	+	6693.46i	−0.487498	+	1.50036i	−0.828330	+	0.560240i	$0.810709\pi$
$272$	4303.55	+	1398.31i	0.959341	+	0.311709i
$273$	−2255.30	−	3104.15i	−0.499989	−	0.688176i
$274$	−3279.73			−0.723124
$275$	4404.92	−	3762.70i	0.965915	−	0.825088i
$276$	−3198.45			−0.697551
$277$	1880.35	+	2588.08i	0.407868	+	0.561382i	0.962697	−	0.270582i	$-0.0872163\pi$
$277$	1880.35	+	2588.08i	0.407868	+	0.561382i	−0.554829	+	0.831965i	$0.687216\pi$
$278$	−10150.6	−	3298.14i	−2.18991	−	0.711545i
$279$	64.2655	−	197.789i	0.0137902	−	0.0424420i
$280$	1871.79	+	5073.16i	0.399504	+	1.08278i
$281$	−2483.12	−	7642.26i	−0.527155	−	1.62242i	−0.760015	−	0.649906i	$-0.774808\pi$
$281$	−2483.12	−	7642.26i	−0.527155	−	1.62242i	0.232860	−	0.972510i	$-0.425192\pi$
$282$			4426.68i			0.934769i
$283$	7960.82	−	2586.63i	1.67216	−	0.543318i	0.688795	−	0.724956i	$-0.258140\pi$
$283$	7960.82	−	2586.63i	1.67216	−	0.543318i	0.983365	+	0.181639i	$0.0581401\pi$
$284$	−4456.85	−	3238.09i	−0.931216	−	0.676568i
$285$	109.040	+	2772.72i	0.0226630	+	0.576287i
$286$	−11357.6	+	8251.76i	−2.34821	+	1.70607i
$287$	2701.22	−	3717.91i	0.555568	−	0.764674i
$288$	428.500	−	589.780i	0.0876722	−	0.120670i
$289$	6540.98	−	4752.30i	1.33136	−	0.967291i
$290$	−1230.91	+	454.157i	−0.249247	+	0.0919622i
$291$	−549.274	−	399.071i	−0.110650	−	0.0803916i
$292$	−6103.13	+	1983.03i	−1.22315	+	0.397424i
$293$			7045.81i			1.40485i	0.711759	+	0.702424i	$0.247899\pi$
$293$			7045.81i			1.40485i	−0.711759	+	0.702424i	$0.752101\pi$
$294$	−810.306	−	2493.87i	−0.160742	−	0.494712i
$295$	−4045.69	−	2703.03i	−0.798471	−	0.533480i
$296$	−2111.83	+	6499.54i	−0.414687	+	1.27628i
$297$	6729.18	+	2186.44i	1.31470	+	0.427173i
$298$	667.482	+	918.710i	0.129752	+	0.178589i
$299$	3247.10			0.628042
$300$	4068.26	−	6639.85i	0.782936	−	1.27784i
$301$	2519.15			0.482397
$302$	4698.96	+	6467.57i	0.895347	+	1.23234i
$303$	5441.24	+	1767.97i	1.03165	+	0.335205i
$304$	−730.037	+	2246.82i	−0.137732	+	0.423895i
$305$	−1477.94	+	1165.20i	−0.277464	+	0.218751i
$306$	1622.21	+	4992.66i	0.303058	+	0.932717i
$307$		−	7332.79i		−	1.36321i	−0.731722	−	0.681603i	$-0.761283\pi$
$307$		−	7332.79i		−	1.36321i	0.731722	−	0.681603i	$-0.238717\pi$
$308$	9581.54	−	3113.23i	1.77259	−	0.575950i
$309$	−4046.81	−	2940.18i	−0.745032	−	0.541297i
$310$	−643.546	+	963.209i	−0.117906	+	0.176473i
$311$	6328.19	−	4597.70i	1.15382	−	0.838301i	0.164838	−	0.986321i	$-0.447290\pi$
$311$	6328.19	−	4597.70i	1.15382	−	0.838301i	0.988984	+	0.148020i	$0.0472899\pi$
$312$	−5152.53	+	7091.84i	−0.934950	+	1.28685i
$313$	1041.96	−	1434.14i	0.188164	−	0.258985i	−0.704504	−	0.709700i	$-0.748831\pi$
$313$	1041.96	−	1434.14i	0.188164	−	0.258985i	0.892668	+	0.450714i	$0.148831\pi$
$314$	5981.51	−	4345.82i	1.07502	−	0.781047i
$315$	−868.797	+	1300.35i	−0.155400	+	0.232591i
$316$	6306.25	+	4581.76i	1.12264	+	0.815645i
$317$	−5283.86	+	1716.83i	−0.936187	+	0.304186i	−0.737090	−	0.675794i	$-0.763801\pi$
$317$	−5283.86	+	1716.83i	−0.936187	+	0.304186i	−0.199097	+	0.979980i	$0.563801\pi$
$318$			3582.82i			0.631807i
$319$	350.896	+	1079.95i	0.0615874	+	0.189547i
$320$	−5976.62	+	4711.93i	−1.04407	+	0.823141i
$321$	−2526.23	+	7774.93i	−0.439253	+	1.35188i
$322$	−3402.85	−	1105.65i	−0.588924	−	0.191353i
$323$	3988.79	+	5490.09i	0.687127	+	0.945749i
$324$	5632.66			0.965819
$325$	−4130.13	+	6740.85i	−0.704919	+	1.15051i
$326$	4722.29			0.802280
$327$	−4232.13	−	5825.03i	−0.715711	−	0.985092i
$328$	−9985.36	−	3244.44i	−1.68094	−	0.546172i
$329$	−996.592	+	3067.19i	−0.167003	+	0.513981i
$330$	−8604.48	−	5748.89i	−1.43534	−	0.958987i
$331$	−2576.19	−	7928.71i	−0.427796	−	1.31662i	−0.900292	−	0.435287i	$-0.856647\pi$
$331$	−2576.19	−	7928.71i	−0.427796	−	1.31662i	0.472496	−	0.881333i	$-0.343353\pi$
$332$		−	2535.03i		−	0.419060i
$333$	−1879.71	+	610.756i	−0.309332	+	0.100508i
$334$	−2687.12	−	1952.31i	−0.440218	−	0.319837i
$335$	2194.12	−	809.542i	0.357843	−	0.132030i
$336$	1948.07	−	1415.35i	0.316297	−	0.229803i
$337$	−453.709	+	624.477i	−0.0733386	+	0.100942i	−0.844110	−	0.536169i	$-0.819871\pi$
$337$	−453.709	+	624.477i	−0.0733386	+	0.100942i	0.770772	+	0.637111i	$0.219871\pi$
$338$	5075.37	−	6985.65i	0.816757	−	1.12417i
$339$	−2946.81	+	2140.98i	−0.472120	+	0.343015i
$340$	−748.335	−	19029.1i	−0.119365	−	3.03529i
$341$	811.102	+	589.300i	0.128808	+	0.0935848i
$342$	−2606.60	+	846.935i	−0.412131	+	0.133909i
$343$		−	6901.03i		−	1.08636i
$344$	−1778.50	−	5473.65i	−0.278750	−	0.857905i
$345$	828.516	+	2245.54i	0.129292	+	0.350423i
$346$	2966.19	−	9129.00i	0.460877	−	1.41843i
$347$	−4348.40	−	1412.88i	−0.672721	−	0.218580i	−0.0473154	−	0.998880i	$-0.515067\pi$
$347$	−4348.40	−	1412.88i	−0.672721	−	0.218580i	−0.625406	+	0.780300i	$0.715067\pi$
$348$	897.159	+	1234.83i	0.138198	+	0.190213i
$349$	1688.12			0.258919			0.129460	−	0.991585i	$-0.458676\pi$
$349$	1688.12			0.258919			0.129460	+	0.991585i	$0.458676\pi$
$350$	6623.53	−	5657.85i	1.01155	−	0.864071i
$351$	−9655.33			−1.46827
$352$	2065.73	+	2843.23i	0.312795	+	0.430525i
$353$	−1524.11	−	495.212i	−0.229802	−	0.0746670i	0.191853	−	0.981424i	$-0.438550\pi$
$353$	−1524.11	−	495.212i	−0.229802	−	0.0746670i	−0.421654	+	0.906757i	$0.638550\pi$
$354$	−2685.76	+	8265.91i	−0.403239	+	1.24104i
$355$	−1118.89	+	3967.82i	−0.167280	+	0.593211i
$356$	2995.83	+	9220.20i	0.446007	+	1.37267i
$357$		−	6916.81i		−	1.02542i
$358$	1719.19	−	558.598i	0.253804	−	0.0824659i
$359$	10551.2	+	7665.88i	1.55117	+	1.12699i	0.942811	+	0.333329i	$0.108172\pi$
$359$	10551.2	+	7665.88i	1.55117	+	1.12699i	0.608359	+	0.793662i	$0.291828\pi$
$360$	3438.77	+	969.701i	0.503442	+	0.141966i
$361$	2682.75	−	1949.13i	0.391128	−	0.284171i
$362$	6289.49	−	8656.74i	0.913172	−	1.25687i
$363$	−2002.17	+	2755.75i	−0.289495	+	0.398456i
$364$	−11122.4	+	8080.88i	−1.60157	+	1.16361i
$365$	2973.16	+	3771.16i	0.426363	+	0.540799i
$366$	2719.76	+	1976.02i	0.388426	+	0.282208i
$367$	−2310.87	+	750.849i	−0.328683	+	0.106796i	−0.468710	−	0.883352i	$-0.655281\pi$
$367$	−2310.87	+	750.849i	−0.328683	+	0.106796i	0.140027	+	0.990148i	$0.455281\pi$
$368$			2037.78i			0.288659i
$369$	−938.316	−	2887.84i	−0.132376	−	0.407412i
$370$	11000.6	−	432.609i	1.54567	−	0.0607846i
$371$	−806.612	+	2482.50i	−0.112877	+	0.347398i
$372$	1281.68	+	416.443i	0.178634	+	0.0580418i
$373$	−2586.62	−	3560.18i	−0.359062	−	0.494207i	0.590825	−	0.806800i	$-0.298802\pi$
$373$	−2586.62	−	3560.18i	−0.359062	−	0.494207i	−0.949887	+	0.312593i	$0.898802\pi$
$374$	−25307.4			−3.49897
$375$	−5715.48	−	1136.24i	−0.787057	−	0.156468i
$376$	7368.02			1.01058
$377$	−910.805	−	1253.62i	−0.124427	−	0.171259i
$378$	10118.5	+	3287.68i	1.37682	+	0.447355i
$379$	−2947.97	+	9072.92i	−0.399544	+	1.22967i	0.525822	+	0.850595i	$0.323758\pi$
$379$	−2947.97	+	9072.92i	−0.399544	+	1.22967i	−0.925366	+	0.379075i	$0.876242\pi$
$380$	9934.83	−	390.696i	1.34117	−	0.0527428i
$381$	−658.083	−	2025.37i	−0.0884898	−	0.272344i
$382$			10754.2i			1.44040i
$383$	−2366.70	+	768.987i	−0.315751	+	0.102594i	−0.462605	−	0.886564i	$-0.653085\pi$
$383$	−2366.70	+	768.987i	−0.315751	+	0.102594i	0.146854	+	0.989158i	$0.453085\pi$
$384$	8951.97	+	6503.99i	1.18966	+	0.864336i
$385$	−4667.68	−	5920.49i	−0.617888	−	0.783730i
$386$	5950.27	−	4323.13i	0.784614	−	0.570055i
$387$	978.360	−	1346.60i	0.128509	−	0.176877i
$388$	−1429.90	+	1968.08i	−0.187093	+	0.257511i
$389$	−4923.75	+	3577.32i	−0.641759	+	0.466265i	−0.860454	−	0.509528i	$-0.829820\pi$
$389$	−4923.75	+	3577.32i	−0.641759	+	0.466265i	0.218695	+	0.975793i	$0.429820\pi$
$390$	13591.4	+	3832.64i	1.76468	+	0.497624i
$391$	4735.58	+	3440.60i	0.612503	+	0.445010i
$392$	−4150.93	+	1348.72i	−0.534831	+	0.173777i
$393$			8216.07i			1.05457i
$394$	5039.22	+	15509.1i	0.644346	+	1.98309i
$395$	1583.18	−	5614.28i	0.201666	−	0.715152i
$396$	2057.01	−	6330.83i	0.261032	−	0.803374i
$397$	1591.28	+	517.037i	0.201169	+	0.0653636i	0.407868	−	0.913041i	$-0.366272\pi$
$397$	1591.28	+	517.037i	0.201169	+	0.0653636i	−0.206700	+	0.978404i	$0.566272\pi$
$398$	−9825.70	−	13523.9i	−1.23748	−	1.70325i
$399$	3611.17			0.453094
$400$	−4230.34	−	2591.94i	−0.528792	−	0.323992i
$401$	−11329.7			−1.41092			−0.705462	−	0.708748i	$-0.749261\pi$
$401$	−11329.7			−1.41092			−0.705462	+	0.708748i	$0.749261\pi$
$402$	−2455.51	−	3379.72i	−0.304651	−	0.419317i
$403$	−1301.17	−	422.777i	−0.160834	−	0.0522581i
$404$	6334.74	−	19496.3i	0.780111	−	2.40094i
$405$	−1459.06	−	3954.53i	−0.179016	−	0.485191i
$406$	527.631	+	1623.88i	0.0644972	+	0.198502i
$407$		−	9528.13i		−	1.16042i
$408$	−15028.9	+	4883.19i	−1.82363	+	0.592535i
$409$	7342.54	+	5334.66i	0.887690	+	0.644944i	0.935275	−	0.353923i	$-0.115153\pi$
$409$	7342.54	+	5334.66i	0.887690	+	0.644944i	−0.0475850	+	0.998867i	$0.515153\pi$
$410$	664.626	+	16900.5i	0.0800574	+	2.03575i
$411$	2309.94	−	1678.27i	0.277229	−	0.201419i
$412$	−10534.8	+	14500.0i	−1.25974	+	1.73389i
$413$	−3721.86	+	5122.70i	−0.443440	+	0.610343i
$414$	−1912.58	+	1389.57i	−0.227049	+	0.164960i
$415$	−1779.78	+	656.666i	−0.210520	+	0.0776734i
$416$	−3879.92	−	2818.93i	−0.457281	−	0.332234i
$417$	8836.88	−	2871.28i	1.03775	−	0.337187i
$418$		−	13212.7i		−	1.54606i
$419$	−2365.19	−	7279.30i	−0.275768	−	0.848728i	−0.989015	−	0.147815i	$-0.952776\pi$
$419$	−2365.19	−	7279.30i	−0.275768	−	0.848728i	0.713247	−	0.700913i	$-0.247224\pi$
$420$	−8426.29	−	5629.84i	−0.978955	−	0.654066i
$421$	2024.77	−	6231.59i	0.234397	−	0.721399i	−0.762804	−	0.646630i	$-0.776178\pi$
$421$	2024.77	−	6231.59i	0.234397	−	0.721399i	0.997201	−	0.0747696i	$-0.0238221\pi$
$422$	−24176.5	−	7855.42i	−2.78885	−	0.906151i
$423$	1252.50	+	1723.92i	0.143969	+	0.198156i
$424$	5963.46			0.683045
$425$	−13166.0	+	5454.62i	−1.50269	+	0.622560i
$426$	7364.03			0.837532
$427$	1439.62	+	1981.47i	0.163157	+	0.224567i
$428$	27858.1	+	9051.63i	3.14619	+	1.02226i
$429$	3776.73	−	11623.6i	0.425040	−	1.30814i
$430$	−7280.83	+	5740.16i	−0.816541	+	0.643757i
$431$	4797.50	+	14765.2i	0.536166	+	1.65015i	0.741116	+	0.671377i	$0.234297\pi$
$431$	4797.50	+	14765.2i	0.536166	+	1.65015i	−0.204950	+	0.978773i	$0.565703\pi$
$432$		−	6059.37i		−	0.674842i
$433$	9236.47	−	3001.11i	1.02512	−	0.333081i	0.252260	−	0.967659i	$-0.418826\pi$
$433$	9236.47	−	3001.11i	1.02512	−	0.333081i	0.772859	+	0.634578i	$0.218826\pi$
$434$	1219.63	+	886.112i	0.134894	+	0.0980063i
$435$	634.545	−	949.737i	0.0699405	−	0.104681i
$436$	−20871.4	+	15164.0i	−2.29257	+	1.66565i
$437$	−1796.29	+	2472.38i	−0.196632	+	0.270641i
$438$	5042.08	−	6939.83i	0.550046	−	0.757073i
$439$	3625.13	−	2633.81i	0.394118	−	0.286344i	−0.373023	−	0.927822i	$-0.621679\pi$
$439$	3625.13	−	2633.81i	0.394118	−	0.286344i	0.767141	+	0.641478i	$0.221679\pi$
$440$	−9568.78	+	14321.8i	−1.03676	+	1.55174i
$441$	−1021.19	−	741.938i	−0.110268	−	0.0801142i
$442$	32844.7	−	10671.9i	3.53453	−	1.14844i
$443$		−	7663.64i		−	0.821919i	−0.911653	−	0.410960i	$-0.865194\pi$
$443$		−	7663.64i		−	0.821919i	0.911653	−	0.410960i	$-0.134806\pi$
$444$	−3957.72	−	12180.6i	−0.423030	−	1.30195i
$445$	5697.22	−	4491.66i	0.606908	−	0.478483i
$446$	−553.058	+	1702.14i	−0.0587176	+	0.180714i
$447$	−940.226	−	305.498i	−0.0994881	−	0.0323256i
$448$	5821.67	+	8012.84i	0.613947	+	0.845025i
$449$	9789.69			1.02896			0.514481	−	0.857502i	$-0.327985\pi$
$449$	9789.69			1.02896			0.514481	+	0.857502i	$0.327985\pi$
$450$	−451.994	−	5737.89i	−0.0473493	−	0.601082i
$451$	14638.3			1.52836
$452$	7671.27	+	10558.6i	0.798288	+	1.09875i
$453$	−6619.04	−	2150.66i	−0.686511	−	0.223061i
$454$	5015.03	−	15434.7i	0.518430	−	1.59556i
$455$	8554.46	+	5715.47i	0.881405	+	0.588890i
$456$	−2549.45	−	7846.40i	−0.261818	−	0.805792i
$457$			4876.27i			0.499130i	0.968358	+	0.249565i	$0.0802876\pi$
$457$			4876.27i			0.499130i	−0.968358	+	0.249565i	$0.919712\pi$
$458$	−10366.2	+	3368.17i	−1.05760	+	0.343634i
$459$	−14081.4	−	10230.7i	−1.43194	−	1.04037i
$460$	8045.92	−	2968.62i	0.815528	−	0.300897i
$461$	654.078	−	475.216i	0.0660813	−	0.0480108i	−0.554254	−	0.832347i	$-0.686996\pi$
$461$	654.078	−	475.216i	0.0660813	−	0.0480108i	0.620335	+	0.784337i	$0.286996\pi$
$462$	−7915.76	+	10895.1i	−0.797131	+	1.09716i
$463$	−5765.47	+	7935.49i	−0.578713	+	0.796531i	−0.993554	−	0.113364i	$-0.963837\pi$
$463$	−5765.47	+	7935.49i	−0.578713	+	0.796531i	0.414840	+	0.909894i	$0.363837\pi$
$464$	786.729	−	571.592i	0.0787133	−	0.0571885i
$465$	−39.6288	−	1007.71i	−0.00395214	−	0.100497i
$466$	−26759.1	−	19441.7i	−2.66007	−	1.93265i
$467$	1426.71	−	463.566i	0.141371	−	0.0459342i	−0.237477	−	0.971393i	$-0.576320\pi$
$467$	1426.71	−	463.566i	0.141371	−	0.0459342i	0.378848	+	0.925459i	$0.376320\pi$
$468$			9083.74i			0.897214i
$469$	−940.509	−	2894.59i	−0.0925984	−	0.284989i
$470$	−4108.59	−	11135.6i	−0.403224	−	1.09287i
$471$	−1989.03	+	6121.59i	−0.194585	+	0.598871i
$472$	13758.3	+	4470.33i	1.34169	+	0.435940i
$473$	4716.51	+	6491.72i	0.458489	+	0.631057i
$474$	−10419.8			−1.00970
$475$	−2847.78	−	6873.77i	−0.275085	−	0.663979i
$476$	−24783.3			−2.38643
$477$	1013.74	+	1395.29i	0.0973080	+	0.133933i
$478$	−20029.3	−	6507.93i	−1.91657	−	0.622731i
$479$	2833.73	−	8721.32i	0.270306	−	0.831915i	−0.720118	−	0.693852i	$-0.755912\pi$
$479$	2833.73	−	8721.32i	0.270306	−	0.831915i	0.990423	−	0.138063i	$-0.0440877\pi$
$480$	959.457	−	3402.44i	0.0912354	−	0.323541i
$481$	4017.92	+	12365.9i	0.380876	+	1.17222i
$482$			12930.9i			1.22196i
$483$	2962.43	−	962.552i	0.279079	−	0.0906784i
$484$	9874.03	+	7173.90i	0.927313	+	0.673733i
$485$	1752.13	+	494.085i	0.164042	+	0.0462582i
$486$	9880.94	−	7178.92i	0.922240	−	0.670046i
$487$	−2976.83	+	4097.26i	−0.276988	+	0.381241i	−0.924733	−	0.380616i	$-0.875712\pi$
$487$	−2976.83	+	4097.26i	−0.276988	+	0.381241i	0.647745	+	0.761857i	$0.275712\pi$
$488$	3289.00	−	4526.92i	0.305094	−	0.419927i
$489$	−3325.95	+	2416.44i	−0.307576	+	0.223467i
$490$	4353.05	+	5521.41i	0.401328	+	0.509044i
$491$	−5258.69	−	3820.66i	−0.483343	−	0.351169i	0.319276	−	0.947662i	$-0.396560\pi$
$491$	−5258.69	−	3820.66i	−0.483343	−	0.351169i	−0.802618	+	0.596493i	$0.796560\pi$
$492$	18713.3	−	6080.32i	1.71476	−	0.557159i
$493$		−	2793.36i		−	0.255186i
$494$	5571.65	+	17147.8i	0.507450	+	1.56177i
$495$	−4977.54	+	195.746i	−0.451967	+	0.0177740i
$496$	265.321	−	816.575i	0.0240187	−	0.0739219i
$497$	5102.45	+	1657.89i	0.460516	+	0.149631i
$498$	1991.81	+	2741.49i	0.179227	+	0.246685i
$499$	−11412.5			−1.02384			−0.511918	−	0.859034i	$-0.671065\pi$
$499$	−11412.5			−1.02384			−0.511918	+	0.859034i	$0.671065\pi$
$500$	−4071.23	+	20478.9i	−0.364142	+	1.83169i
$501$	2891.58			0.257857
$502$	−1800.37	−	2477.99i	−0.160068	−	0.220315i
$503$	−391.363	−	127.162i	−0.0346919	−	0.0112721i	0.291620	−	0.956534i	$-0.405806\pi$
$503$	−391.363	−	127.162i	−0.0346919	−	0.0112721i	−0.326312	+	0.945262i	$0.605806\pi$
$504$	1436.83	−	4422.12i	0.126987	−	0.390827i
$505$	−15328.7	+	602.816i	−1.35073	+	0.0531187i
$506$	−3521.82	−	10839.0i	−0.309415	−	0.952280i
$507$			7517.18i			0.658480i
$508$	−7257.03	+	2357.95i	−0.633816	+	0.205939i
$509$	9046.75	+	6572.85i	0.787800	+	0.572370i	0.907310	−	0.420463i	$-0.138132\pi$
$509$	9046.75	+	6572.85i	0.787800	+	0.572370i	−0.119510	+	0.992833i	$0.538132\pi$
$510$	15760.7	+	19990.9i	1.36842	+	1.73571i
$511$	5055.99	−	3673.39i	0.437698	−	0.318006i
$512$	7972.98	−	10973.9i	0.688202	−	0.947229i
$513$	5341.31	−	7351.69i	0.459697	−	0.632719i
$514$	−24377.3	+	17711.1i	−2.09190	+	1.51985i
$515$	12908.9	+	3640.20i	1.10453	+	0.311468i
$516$	8726.00	+	6339.81i	0.744459	+	0.540881i
$517$	−9769.87	+	3174.42i	−0.831100	+	0.270041i
$518$		−	14327.1i		−	1.21525i
$519$	2582.29	+	7947.46i	0.218400	+	0.672167i
$520$	6379.27	−	22622.3i	0.537980	−	1.90779i
$521$	172.998	−	532.432i	0.0145473	−	0.0447721i	−0.943519	−	0.331317i	$-0.892507\pi$
$521$	172.998	−	532.432i	0.0145473	−	0.0447721i	0.958067	+	0.286545i	$0.0925069\pi$
$522$	1072.95	+	348.622i	0.0899649	+	0.0292314i
$523$	5268.76	+	7251.82i	0.440510	+	0.606310i	0.970325	−	0.241803i	$-0.0777389\pi$
$523$	5268.76	+	7251.82i	0.440510	+	0.606310i	−0.529816	+	0.848113i	$0.677739\pi$
$524$	29438.7			2.45427
$525$	−1769.83	+	7374.20i	−0.147127	+	0.613022i
$526$	9401.88			0.779356
$527$	−1449.67	−	1995.29i	−0.119826	−	0.164927i
$528$	7294.58	+	2370.15i	0.601242	+	0.195355i
$529$	2945.23	−	9064.48i	0.242067	−	0.745005i
$530$	−3325.37	−	9012.83i	−0.272538	−	0.738665i
$531$	1292.85	+	3978.99i	0.105659	+	0.325186i
$532$		−	12939.0i		−	1.05447i
$533$	−18997.9	+	6172.81i	−1.54389	+	0.501640i
$534$	−10484.2	−	7617.25i	−0.849621	−	0.617286i
$535$	−861.356	−	21903.1i	−0.0696069	−	1.77000i
$536$	−5625.41	+	4087.10i	−0.453322	+	0.329358i
$537$	−924.998	+	1273.15i	−0.0743326	+	0.102310i
$538$	−10140.8	+	13957.7i	−0.812643	+	1.11851i
$539$	4922.99	−	3576.76i	0.393410	−	0.285829i
$540$	−23924.7	+	8827.27i	−1.90659	+	0.703454i
$541$	7270.66	+	5282.44i	0.577800	+	0.419796i	0.837930	−	0.545777i	$-0.183765\pi$
$541$	7270.66	+	5282.44i	0.577800	+	0.419796i	−0.260130	+	0.965574i	$0.583765\pi$
$542$	−32059.0	+	10416.6i	−2.54069	+	0.825519i
$543$			9315.41i			0.736211i
$544$	−2671.58	−	8222.28i	−0.210557	−	0.648028i
$545$	16052.7	+	10725.2i	1.26169	+	0.842970i
$546$	5678.94	−	17478.0i	0.445121	−	1.36994i
$547$	6074.72	+	1973.80i	0.474838	+	0.154284i	0.536652	−	0.843804i	$-0.319689\pi$
$547$	6074.72	+	1973.80i	0.474838	+	0.154284i	−0.0618145	+	0.998088i	$0.519689\pi$
$548$	−6013.36	−	8276.67i	−0.468755	−	0.645186i
$549$	1618.28			0.125804
$550$	26980.9	+	6475.52i	2.09177	+	0.502031i
$551$	1458.38			0.112757
$552$	−4182.89	−	5757.26i	−0.322528	−	0.443922i
$553$	−7219.74	−	2345.84i	−0.555180	−	0.180389i
$554$	−4734.81	+	14572.2i	−0.363110	+	1.11754i
$555$	−7526.47	+	5933.83i	−0.575642	+	0.453833i
$556$	−10288.0	−	31663.1i	−0.784724	−	2.41513i
$557$		−	20270.1i		−	1.54196i	−0.636860	−	0.770979i	$-0.719767\pi$
$557$		−	20270.1i		−	1.54196i	0.636860	−	0.770979i	$-0.280233\pi$
$558$	947.330	−	307.806i	0.0718704	−	0.0233521i
$559$	−8858.72	−	6436.24i	−0.670275	−	0.486984i
$560$	−3586.84	+	5368.50i	−0.270664	+	0.405108i
$561$	17824.2	−	12950.1i	1.34143	−	0.974603i
$562$	22622.1	−	31136.7i	1.69797	−	2.33705i
$563$	−6643.02	+	9143.33i	−0.497282	+	0.684450i	−0.981710	−	0.190381i	$-0.939028\pi$
$563$	−6643.02	+	9143.33i	−0.497282	+	0.684450i	0.484428	+	0.874831i	$0.339028\pi$
$564$	−11171.1	+	8116.27i	−0.834020	+	0.605951i
$565$	5425.76	−	8120.85i	0.404006	−	0.604684i
$566$	32434.6	+	23565.1i	2.40871	+	1.75003i
$567$	−5217.01	+	1695.11i	−0.386409	+	0.125552i
$568$		−	12257.1i		−	0.905453i
$569$	−4188.67	−	12891.4i	−0.308608	−	0.949798i	−0.978306	−	0.207165i	$-0.933576\pi$
$569$	−4188.67	−	12891.4i	−0.308608	−	0.949798i	0.669698	−	0.742634i	$-0.266424\pi$
$570$	−10437.0	+	8228.44i	−0.766941	+	0.604652i
$571$	−5468.55	+	16830.5i	−0.400791	+	1.23351i	0.523568	+	0.851984i	$0.324601\pi$
$571$	−5468.55	+	16830.5i	−0.400791	+	1.23351i	−0.924359	+	0.381524i	$0.875399\pi$
$572$	−41648.0	−	13532.2i	−3.04439	−	0.989181i
$573$	−5503.02	−	7574.25i	−0.401207	−	0.552215i
$574$	22011.1			1.60056
$575$	−4168.37	−	4879.84i	−0.302319	−	0.353919i
$576$	6544.16			0.473391
$577$	−5102.35	−	7022.79i	−0.368135	−	0.506694i	0.584258	−	0.811568i	$-0.301386\pi$
$577$	−5102.35	−	7022.79i	−0.368135	−	0.506694i	−0.952393	+	0.304874i	$0.901386\pi$
$578$	36829.1	+	11966.5i	2.65033	+	0.861143i
$579$	−1978.64	+	6089.63i	−0.142020	+	0.437092i
$580$	−3402.97	−	2273.61i	−0.243622	−	0.162770i
$581$	762.901	+	2347.97i	0.0544758	+	0.167659i
$582$		−	3251.85i		−	0.231604i
$583$	−7907.45	+	2569.28i	−0.561737	+	0.182520i
$584$	−11551.1	−	8392.34i	−0.818470	−	0.594653i
$585$	6377.44	−	2353.02i	0.450726	−	0.166300i
$586$	−27301.6	+	19835.8i	−1.92460	+	1.39831i
$587$	−8603.63	+	11841.9i	−0.604957	+	0.832652i	−0.996151	−	0.0876563i	$-0.972062\pi$
$587$	−8603.63	+	11841.9i	−0.604957	+	0.832652i	0.391194	+	0.920308i	$0.372062\pi$
$588$	4807.78	−	6617.35i	0.337193	−	0.464107i
$589$	1041.72	−	756.851i	0.0728746	−	0.0529465i
$590$	−915.750	−	23286.2i	−0.0638997	−	1.62488i
$591$	−11485.3	−	8344.59i	−0.799397	−	0.580796i
$592$	−7760.43	+	2521.52i	−0.538770	+	0.175057i
$593$		−	13780.9i		−	0.954326i	−0.878815	−	0.477163i	$-0.841665\pi$
$593$		−	13780.9i		−	0.954326i	0.878815	−	0.477163i	$-0.158335\pi$
$594$	10472.2	+	32230.1i	0.723366	+	2.22629i
$595$	6419.79	+	17399.7i	0.442329	+	1.19885i
$596$	−1094.62	+	3368.89i	−0.0752304	+	0.231535i
$597$	13840.7	+	4497.10i	0.948845	+	0.308298i
$598$	9141.42	+	12582.1i	0.625118	+	0.860401i
$599$	−4263.27			−0.290805			−0.145403	−	0.989373i	$-0.546448\pi$
$599$	−4263.27			−0.290805			−0.145403	+	0.989373i	$0.546448\pi$
$600$	17272.2	−	1360.59i	1.17523	−	0.0925767i
$601$	−23201.7			−1.57474			−0.787369	−	0.616483i	$-0.788557\pi$
$601$	−23201.7			−1.57474			−0.787369	+	0.616483i	$0.788557\pi$
$602$	7092.07	+	9761.39i	0.480151	+	0.660872i
$603$	−1912.55	−	621.424i	−0.129162	−	0.0419674i
$604$	−7705.93	+	23716.4i	−0.519122	+	1.59769i
$605$	2478.86	−	8790.59i	0.166579	−	0.590724i
$606$	8467.86	+	26061.4i	0.567629	+	1.74698i
$607$			5055.32i			0.338038i	0.985613	+	0.169019i	$0.0540599\pi$
$607$			5055.32i			0.338038i	−0.985613	+	0.169019i	$0.945940\pi$
$608$	4292.74	−	1394.80i	0.286338	−	0.0930369i
$609$	−1202.57	−	873.719i	−0.0800174	−	0.0581361i
$610$	−8675.77	−	2446.48i	−0.575855	−	0.162386i
$611$	11341.0	−	8239.71i	0.750912	−	0.545570i
$612$	−9625.07	+	13247.8i	−0.635736	+	0.875015i
$613$	9250.88	−	12732.7i	0.609526	−	0.838941i	−0.387012	−	0.922074i	$-0.626493\pi$
$613$	9250.88	−	12732.7i	0.609526	−	0.838941i	0.996538	+	0.0831340i	$0.0264930\pi$
$614$	28413.6	−	20643.7i	1.86756	−	1.35686i
$615$	−9116.26	−	11563.1i	−0.597728	−	0.758159i
$616$	18134.5	+	13175.5i	1.18613	+	0.861776i
$617$	−6147.00	+	1997.28i	−0.401084	+	0.130320i	−0.502611	−	0.864513i	$-0.667627\pi$
$617$	−6147.00	+	1997.28i	−0.401084	+	0.130320i	0.101527	+	0.994833i	$0.467627\pi$
$618$		−	23958.2i		−	1.55945i
$619$	8200.30	+	25237.9i	0.532468	+	1.63877i	0.749057	+	0.662506i	$0.230507\pi$
$619$	8200.30	+	25237.9i	0.532468	+	1.63877i	−0.216588	+	0.976263i	$0.569493\pi$
$620$	−3610.67	+	141.993i	−0.233884	+	0.00919767i
$621$	2422.18	−	7454.69i	0.156519	−	0.481717i
$622$	35631.0	+	11577.2i	2.29690	+	0.746308i
$623$	−5549.52	−	7638.25i	−0.356881	−	0.491204i
$624$	−10466.6			−0.671472
$625$	15432.3	−	2446.49i	0.987666	−	0.156575i
$626$	8490.50			0.542090
$627$	6761.05	+	9305.79i	0.430639	+	0.592723i
$628$	21934.0	+	7126.80i	1.39373	+	0.452851i
$629$	−7243.05	+	22291.8i	−0.459140	+	1.41309i
$630$	−7484.56	+	294.336i	−0.473321	+	0.0186137i
$631$	−4298.88	−	13230.6i	−0.271213	−	0.834708i	−0.990197	−	0.139681i	$-0.955392\pi$
$631$	−4298.88	−	13230.6i	−0.271213	−	0.834708i	0.718983	−	0.695027i	$-0.244608\pi$
$632$			17343.3i			1.09158i
$633$	21047.4	−	6838.72i	1.32158	−	0.429407i
$634$	−21527.9	−	15641.0i	−1.34855	−	0.979782i
$635$	3535.29	+	4484.16i	0.220935	+	0.280234i
$636$	−9041.54	+	6569.07i	−0.563712	+	0.409560i
$637$	−4880.91	+	6718.00i	−0.303593	+	0.417860i
$638$	−3196.79	+	4400.00i	−0.198373	+	0.273037i
$639$	2867.84	−	2083.61i	0.177543	−	0.128993i
$640$	−28555.9	−	8052.50i	−1.76371	−	0.497348i
$641$	−10379.3	−	7541.01i	−0.639560	−	0.464668i	0.220139	−	0.975469i	$-0.429349\pi$
$641$	−10379.3	−	7541.01i	−0.639560	−	0.464668i	−0.859699	+	0.510801i	$0.829349\pi$
$642$	−37238.8	+	12099.6i	−2.28925	+	0.743823i
$643$		−	14527.1i		−	0.890972i	−0.895289	−	0.445486i	$-0.853031\pi$
$643$		−	14527.1i		−	0.890972i	0.895289	−	0.445486i	$-0.146969\pi$
$644$	−3448.88	−	10614.6i	−0.211033	−	0.649492i
$645$	2190.65	−	7768.52i	0.133731	−	0.474241i
$646$	−10043.9	+	30912.1i	−0.611723	+	1.88269i
$647$	18707.3	+	6078.36i	1.13672	+	0.369343i	0.816127	−	0.577873i	$-0.196117\pi$
$647$	18707.3	+	6078.36i	1.13672	+	0.369343i	0.320595	+	0.947216i	$0.396117\pi$
$648$	7366.31	+	10138.9i	0.446568	+	0.614648i
$649$	−20169.2			−1.21989
$650$	−37747.3	+	2973.49i	−2.27780	+	0.179430i
$651$	−1312.43			−0.0790139
$652$	8658.26	+	11917.1i	0.520067	+	0.715811i
$653$	5803.14	+	1885.56i	0.347771	+	0.112998i	0.477694	−	0.878526i	$-0.341473\pi$
$653$	5803.14	+	1885.56i	0.347771	+	0.112998i	−0.129923	+	0.991524i	$0.541473\pi$
$654$	10656.7	−	32797.9i	0.637171	−	1.96101i
$655$	−7625.69	−	20668.1i	−0.454902	−	1.23293i
$656$	−3873.85	−	11922.5i	−0.230562	−	0.709596i
$657$		−	4129.27i		−	0.245203i
$658$	−14690.6	+	4773.28i	−0.870366	+	0.282799i
$659$	−11656.3	−	8468.79i	−0.689020	−	0.500603i	0.187317	−	0.982299i	$-0.440021\pi$
$659$	−11656.3	−	8468.79i	−0.689020	−	0.500603i	−0.876338	+	0.481697i	$0.840021\pi$
$660$	−1268.44	−	32254.6i	−0.0748090	−	1.90229i
$661$	−8540.95	+	6205.36i	−0.502578	+	0.365145i	−0.810001	−	0.586428i	$-0.800533\pi$
$661$	−8540.95	+	6205.36i	−0.502578	+	0.365145i	0.307423	+	0.951573i	$0.400533\pi$
$662$	23470.1	−	32303.8i	1.37793	−	1.89656i
$663$	−17671.9	+	24323.3i	−1.03517	+	1.42479i
$664$	4563.09	−	3315.28i	0.266690	−	0.193762i
$665$	−9084.14	+	3351.69i	−0.529726	+	0.195448i
$666$	−7658.48	−	5564.21i	−0.445586	−	0.323737i
$667$	1196.38	−	388.728i	0.0694514	−	0.0225661i
$668$		−	10360.7i		−	0.600101i
$669$	−481.477	−	1481.83i	−0.0278251	−	0.0856368i
$670$	9313.88	+	6222.86i	0.537055	+	0.358821i
$671$	−2410.79	+	7419.65i	−0.138700	+	0.426874i
$672$	−4375.40	−	1421.65i	−0.251168	−	0.0816094i
$673$	17098.0	+	23533.3i	0.979314	+	1.34791i	0.937198	+	0.348797i	$0.113410\pi$
$673$	17098.0	+	23533.3i	0.979314	+	1.34791i	0.0421155	+	0.999113i	$0.486590\pi$
$674$	−3697.08			−0.211285
$675$	12394.8	+	14510.3i	0.706777	+	0.827410i
$676$	26934.5			1.53246
$677$	−6800.51	−	9360.10i	−0.386063	−	0.531371i	0.571115	−	0.820870i	$-0.306511\pi$
$677$	−6800.51	−	9360.10i	−0.386063	−	0.531371i	−0.957178	+	0.289499i	$0.906511\pi$
$678$	−16592.0	−	5391.08i	−0.939843	−	0.305374i
$679$	732.100	−	2253.17i	0.0413776	−	0.127347i
$680$	33274.0	−	26233.0i	1.87647	−	1.47940i
$681$	4365.95	+	13437.0i	0.245674	+	0.756106i
$682$			4801.95i			0.269613i
$683$	29385.0	−	9547.75i	1.64624	−	0.534897i	0.668323	−	0.743872i	$-0.267013\pi$
$683$	29385.0	−	9547.75i	1.64624	−	0.534897i	0.977921	+	0.208975i	$0.0670126\pi$
$684$	−6916.48	−	5025.12i	−0.386635	−	0.280907i
$685$	−4253.14	+	6365.77i	−0.237232	+	0.355071i
$686$	26740.6	−	19428.2i	1.48828	−	1.08130i
$687$	5577.45	−	7676.71i	0.309743	−	0.426324i
$688$	4039.17	−	5559.45i	0.223826	−	0.308070i
$689$	9179.07	−	6668.98i	0.507539	−	0.368749i
$690$	−6368.70	+	9532.18i	−0.351380	+	0.525918i
$691$	−9587.93	−	6966.04i	−0.527847	−	0.383503i	0.291705	−	0.956508i	$-0.405777\pi$
$691$	−9587.93	−	6966.04i	−0.527847	−	0.383503i	−0.819552	+	0.573005i	$0.805777\pi$
$692$	28476.2	−	9252.49i	1.56431	−	0.508276i
$693$			6482.70i			0.355350i
$694$	−6767.13	−	20827.1i	−0.370140	−	1.13917i
$695$	−19564.8	+	15424.8i	−1.06782	+	0.841864i
$696$	−1049.42	+	3229.80i	−0.0571528	+	0.175898i
$697$	−34247.3	−	11127.6i	−1.86113	−	0.604719i
$698$	4752.48	+	6541.23i	0.257713	+	0.354712i
$699$	28795.2			1.55813
$700$	26422.2	+	6341.42i	1.42667	+	0.342404i
$701$	−3433.64			−0.185002			−0.0925012	−	0.995713i	$-0.529486\pi$
$701$	−3433.64			−0.185002			−0.0925012	+	0.995713i	$0.529486\pi$
$702$	−27182.2	−	37413.1i	−1.46143	−	2.01149i
$703$	−11638.2	−	3781.50i	−0.624388	−	0.202876i
$704$	−9748.98	+	30004.3i	−0.521915	+	1.60629i
$705$	8591.92	+	5740.49i	0.458994	+	0.306666i
$706$	−2371.87	−	7299.86i	−0.126440	−	0.389141i
$707$			19964.0i			1.06199i
$708$	−25784.0	+	8377.73i	−1.36868	+	0.444710i
$709$	18482.3	+	13428.2i	0.979008	+	0.711291i	0.957487	−	0.288478i	$-0.0931491\pi$
$709$	18482.3	+	13428.2i	0.979008	+	0.711291i	0.0215209	+	0.999768i	$0.493149\pi$
$710$	−18524.7	+	6834.88i	−0.979184	+	0.361280i
$711$	−4057.87	+	2948.22i	−0.214039	+	0.155509i
$712$	−12678.6	+	17450.6i	−0.667346	+	0.918523i
$713$	652.836	−	898.552i	0.0342902	−	0.0471964i
$714$	26801.7	−	19472.6i	1.40480	−	1.02065i
$715$	1287.73	+	32745.2i	0.0673545	+	1.71273i
$716$	4561.77	+	3314.32i	0.238103	+	0.172992i
$717$	17437.0	−	5665.63i	0.908224	−	0.295100i
$718$			62465.9i			3.24680i
$719$	−3677.38	−	11317.8i	−0.190742	−	0.587042i	0.809258	−	0.587453i	$-0.199869\pi$
$719$	−3677.38	−	11317.8i	−0.190742	−	0.587042i	−1.00000		0.000410732i	$0.999869\pi$
$720$	1476.68	+	4002.28i	0.0764342	+	0.207161i
$721$	5393.78	−	16600.4i	0.278606	−	0.857461i
$722$	15105.2	+	4907.99i	0.778613	+	0.252987i
$723$	−6616.87	−	9107.34i	−0.340365	−	0.468473i
$724$	33377.7			1.71336
$725$	−714.749	+	2978.08i	−0.0366139	+	0.152556i
$726$	−16314.8			−0.834021
$727$	−8790.88	−	12099.6i	−0.448467	−	0.617262i	0.523600	−	0.851964i	$-0.324589\pi$
$727$	−8790.88	−	12099.6i	−0.448467	−	0.617262i	−0.972067	+	0.234702i	$0.924589\pi$
$728$	−29091.4	−	9452.36i	−1.48104	−	0.481219i
$729$	−6431.28	+	19793.4i	−0.326743	+	1.00561i
$730$	−6242.54	+	22137.4i	−0.316502	+	1.12239i
$731$	−6099.80	−	18773.3i	−0.308631	−	0.949869i
$732$			10486.5i			0.529500i
$733$	11541.2	−	3749.95i	0.581559	−	0.188960i	−0.00344008	−	0.999994i	$-0.501095\pi$
$733$	11541.2	−	3749.95i	0.581559	−	0.188960i	0.584999	+	0.811034i	$0.301095\pi$
$734$	−9415.15	−	6840.50i	−0.473460	−	0.343989i
$735$	−5891.25	−	1661.28i	−0.295649	−	0.0833702i
$736$	3149.78	−	2288.45i	0.157748	−	0.114610i
$737$	5698.32	−	7843.07i	0.284804	−	0.391999i
$738$	8548.40	−	11765.9i	0.426383	−	0.586867i
$739$	−16217.1	+	11782.4i	−0.807248	+	0.586500i	−0.913032	−	0.407889i	$-0.866265\pi$
$739$	−16217.1	+	11782.4i	−0.807248	+	0.586500i	0.105783	+	0.994389i	$0.466265\pi$
$740$	21261.3	+	26967.8i	1.05619	+	1.33967i
$741$	−12698.8	−	9226.25i	−0.629560	−	0.457402i
$742$	−11890.2	+	3863.35i	−0.588277	+	0.191143i
$743$		−	18987.2i		−	0.937515i	−0.883327	−	0.468757i	$-0.844702\pi$
$743$		−	18987.2i		−	0.937515i	0.883327	−	0.468757i	$-0.155298\pi$
$744$	926.560	+	2851.66i	0.0456577	+	0.140520i
$745$	2648.75	−	104.164i	0.130259	−	0.00512252i
$746$	6513.23	−	20045.7i	0.319660	−	0.983812i
$747$	1551.38	+	504.073i	0.0759865	+	0.0246895i
$748$	−46400.9	−	63865.3i	−2.26816	−	3.12186i
$749$	−28526.4			−1.39163
$750$	−11687.8	−	25345.6i	−0.569035	−	1.23399i
$751$	14542.7			0.706620			0.353310	−	0.935506i	$-0.385056\pi$
$751$	14542.7			0.706620			0.353310	+	0.935506i	$0.385056\pi$
$752$	5170.98	+	7117.24i	0.250753	+	0.345132i
$753$	2536.03	+	824.006i	0.122733	+	0.0398784i
$754$	2293.45	−	7058.50i	0.110772	−	0.340922i
$755$	18646.8	−	733.299i	0.898841	−	0.0353477i
$756$	10255.3	+	31562.7i	0.493364	+	1.51842i
$757$		−	1745.51i		−	0.0838064i	−0.999122	−	0.0419032i	$-0.986658\pi$
$757$		−	1745.51i		−	0.0838064i	0.999122	−	0.0419032i	$-0.0133421\pi$
$758$	−43455.7	+	14119.6i	−2.08230	+	0.676580i
$759$	8026.89	+	5831.88i	0.383870	+	0.278898i
$760$	13695.9	+	17371.9i	0.653687	+	0.829137i
$761$	−10368.6	+	7533.26i	−0.493906	+	0.358844i	−0.806685	−	0.590982i	$-0.798740\pi$
$761$	−10368.6	+	7533.26i	−0.493906	+	0.358844i	0.312778	+	0.949826i	$0.398740\pi$
$762$	5995.38	−	8251.93i	0.285026	−	0.392304i
$763$	14767.8	−	20326.1i	0.700695	−	0.964424i
$764$	−27139.0	+	19717.7i	−1.28515	+	0.933717i
$765$	11794.1	+	3325.84i	0.557409	+	0.157184i
$766$	−9642.59	−	7005.75i	−0.454831	−	0.330454i
$767$	26176.2	−	8505.16i	1.23229	−	0.400396i
$768$			30291.0i			1.42322i
$769$	10882.6	+	33493.2i	0.510321	+	1.57061i	0.791637	+	0.610991i	$0.209229\pi$
$769$	10882.6	+	33493.2i	0.510321	+	1.57061i	−0.281316	+	0.959615i	$0.590771\pi$
$770$	9800.40	−	34754.4i	0.458678	−	1.62657i
$771$	8106.15	−	24948.2i	0.378646	−	1.16535i
$772$	21819.5	+	7089.59i	1.01723	+	0.330518i
$773$	16168.9	+	22254.6i	0.752337	+	1.03550i	0.997813	+	0.0661002i	$0.0210557\pi$
$773$	16168.9	+	22254.6i	0.752337	+	1.03550i	−0.245476	+	0.969403i	$0.578944\pi$
$774$	7972.22			0.370227
$775$	1034.98	+	2498.17i	0.0479713	+	0.115790i
$776$	−5412.57			−0.250387
$777$	7331.35	+	10090.7i	0.338495	+	0.465898i
$778$	−27723.3	−	9007.84i	−1.27754	−	0.415098i
$779$	5809.58	−	17880.1i	0.267202	−	0.822362i
$780$	15247.7	+	41326.1i	0.699941	+	1.89707i
$781$	5280.84	+	16252.7i	0.241950	+	0.744646i
$782$			28036.0i			1.28205i
$783$	−3557.47	+	1155.89i	−0.162367	+	0.0527563i
$784$	−4216.00	−	3063.10i	−0.192055	−	0.139536i
$785$	−678.189	−	17245.4i	−0.0308352	−	0.784094i
$786$	−31836.2	+	23130.4i	−1.44473	+	1.04966i
$787$	−8488.48	+	11683.4i	−0.384475	+	0.529184i	−0.956763	−	0.290868i	$-0.906056\pi$
$787$	−8488.48	+	11683.4i	−0.384475	+	0.529184i	0.572288	+	0.820053i	$0.306056\pi$
$788$	−29899.2	+	41152.7i	−1.35167	+	1.86041i
$789$	−6621.82	+	4811.04i	−0.298787	+	0.217082i
$790$	26211.7	−	9671.05i	1.18047	−	0.435545i
$791$	−10282.7	−	7470.84i	−0.462214	−	0.335818i
$792$	14085.7	−	4576.72i	0.631961	−	0.205337i
$793$		−	10646.0i		−	0.476736i
$794$	2476.40	+	7621.59i	0.110685	+	0.340655i
$795$	6954.05	+	4646.19i	0.310232	+	0.207275i
$796$	16113.4	−	49591.9i	0.717492	−	2.20821i
$797$	−10207.0	−	3316.44i	−0.453638	−	0.147396i	0.0732813	−	0.997311i	$-0.476653\pi$
$797$	−10207.0	−	3316.44i	−0.453638	−	0.147396i	−0.526919	+	0.849915i	$0.676653\pi$
$798$	10166.4	+	13992.8i	0.450985	+	0.620727i
$799$	25270.5			1.11891
$800$	744.377	+	9449.58i	0.0328971	+	0.417617i
$801$	−6238.23			−0.275177
$802$	−31896.2	−	43901.3i	−1.40435	−	1.93293i
$803$	18932.3	+	6151.46i	0.832011	+	0.270337i
$804$	4026.85	−	12393.4i	0.176637	−	0.543633i
$805$	−6558.81	+	5170.93i	−0.287165	+	0.226399i
$806$	−2024.93	−	6232.10i	−0.0884929	−	0.272353i
$807$		−	15019.7i		−	0.655164i
$808$	43378.1	−	14094.4i	1.88866	−	0.613662i
$809$	−18356.4	−	13336.7i	−0.797747	−	0.579597i	0.112505	−	0.993651i	$-0.464112\pi$
$809$	−18356.4	−	13336.7i	−0.797747	−	0.579597i	−0.910252	+	0.414054i	$0.864112\pi$
$810$	11215.7	−	16786.7i	0.486516	−	0.728179i
$811$	14084.4	−	10232.9i	0.609826	−	0.443064i	−0.239527	−	0.970890i	$-0.576992\pi$
$811$	14084.4	−	10232.9i	0.609826	−	0.443064i	0.849353	+	0.527825i	$0.176992\pi$
$812$	−3130.59	+	4308.88i	−0.135298	+	0.186222i
$813$	17249.2	−	23741.4i	0.744101	−	1.02417i
$814$	36920.3	−	26824.1i	1.58975	−	1.15502i
$815$	6123.84	−	9165.68i	0.263201	−	0.393938i
$816$	−15264.5	−	11090.3i	−0.654858	−	0.475782i
$817$	9801.27	−	3184.62i	0.419710	−	0.136372i
$818$			43469.8i			1.85805i
$819$	−2733.69	−	8413.44i	−0.116634	−	0.358961i
$820$	−41431.2	+	32664.1i	−1.76444	+	1.39107i
$821$	−9708.28	+	29879.0i	−0.412693	+	1.27014i	0.501605	+	0.865097i	$0.332743\pi$
$821$	−9708.28	+	29879.0i	−0.412693	+	1.27014i	−0.914298	+	0.405042i	$0.867257\pi$
$822$	13006.2	+	4225.96i	0.551877	+	0.179316i
$823$	−24374.7	−	33548.9i	−1.03238	−	1.42095i	−0.903146	−	0.429333i	$-0.858749\pi$
$823$	−24374.7	−	33548.9i	−1.03238	−	1.42095i	−0.129233	−	0.991614i	$-0.541251\pi$
$824$	−39877.4			−1.68592
$825$	−22316.5	+	9245.66i	−0.941771	+	0.390173i
$826$	−30327.8			−1.27753
$827$	18602.4	+	25604.0i	0.782187	+	1.07659i	0.995037	+	0.0995027i	$0.0317252\pi$
$827$	18602.4	+	25604.0i	0.782187	+	1.07659i	−0.212851	+	0.977085i	$0.568275\pi$
$828$	−7013.38	−	2278.79i	−0.294362	−	0.0956441i
$829$	4722.33	−	14533.8i	0.197845	−	0.608904i	−0.802087	−	0.597208i	$-0.796277\pi$
$829$	4722.33	−	14533.8i	0.197845	−	0.608904i	0.999932	−	0.0116963i	$-0.00372315\pi$
$830$	−7555.02	−	5047.71i	−0.315950	−	0.211095i
$831$	−4122.00	−	12686.2i	−0.172070	−	0.529578i
$832$		−	43051.4i		−	1.79392i
$833$	−14236.7	+	4625.78i	−0.592163	+	0.192405i
$834$	36003.9	+	26158.4i	1.49486	+	1.08608i
$835$	−7273.96	+	2683.80i	−0.301468	+	0.111230i
$836$	33343.2	−	24225.3i	1.37943	−	1.00221i
$837$	−1941.22	+	2671.86i	−0.0801654	+	0.110338i
$838$	21547.7	−	29657.9i	0.888250	−	1.22257i
$839$	−4836.99	+	3514.28i	−0.199036	+	0.144608i	−0.682839	−	0.730569i	$-0.739255\pi$
$839$	−4836.99	+	3514.28i	−0.199036	+	0.144608i	0.483803	+	0.875177i	$0.339255\pi$
$840$	−886.013	−	22530.1i	−0.0363933	−	0.925430i
$841$	19245.5	+	13982.6i	0.789104	+	0.573318i
$842$	29846.8	−	9697.83i	1.22160	−	0.396923i
$843$			33505.8i			1.36892i
$844$	−24503.5	−	75414.1i	−0.999344	−	3.07567i
$845$	−6977.02	−	18910.0i	−0.284043	−	0.769849i
$846$	−3153.86	+	9706.57i	−0.128170	+	0.394467i
$847$	−11304.3	−	3673.00i	−0.458585	−	0.149003i
$848$	4185.24	+	5760.48i	0.169483	+	0.233273i
$849$	−34902.5			−1.41089
$850$	−58201.5	−	35660.2i	−2.34858	−	1.43898i
$851$	−10555.4			−0.425188
$852$	13501.9	+	18583.7i	0.542918	+	0.747263i
$853$	3404.13	+	1106.07i	0.136641	+	0.0443975i	0.376539	−	0.926401i	$-0.377114\pi$
$853$	3404.13	+	1106.07i	0.136641	+	0.0443975i	−0.239898	+	0.970798i	$0.577114\pi$
$854$	−3625.03	+	11156.7i	−0.145253	+	0.447042i
$855$	−1736.37	+	6157.56i	−0.0694535	+	0.246297i
$856$	20139.3	+	61982.5i	0.804145	+	2.47490i
$857$			26211.5i			1.04477i	0.852710	+	0.522385i	$0.174958\pi$
$857$			26211.5i			1.04477i	−0.852710	+	0.522385i	$0.825042\pi$
$858$	55672.3	−	18089.0i	2.21517	−	0.719754i
$859$	2188.24	+	1589.85i	0.0869171	+	0.0631489i	0.630395	−	0.776274i	$-0.282893\pi$
$859$	2188.24	+	1589.85i	0.0869171	+	0.0631489i	−0.543478	+	0.839423i	$0.682893\pi$
$860$	−27835.1	−	7849.23i	−1.10368	−	0.311229i
$861$	−15502.6	+	11263.3i	−0.613620	+	0.445821i
$862$	−43707.0	+	60157.5i	−1.72699	+	2.37700i
$863$	−12739.1	+	17533.8i	−0.502484	+	0.691610i	−0.982629	−	0.185579i	$-0.940584\pi$
$863$	−12739.1	+	17533.8i	−0.502484	+	0.691610i	0.480146	+	0.877189i	$0.340584\pi$
$864$	−9365.93	+	6804.75i	−0.368791	+	0.267942i
$865$	−13872.3	−	17595.6i	−0.545286	−	0.691641i
$866$	37632.0	+	27341.2i	1.47666	+	1.07285i
$867$	−32062.4	+	10417.7i	−1.25594	+	0.408078i
$868$			4702.51i			0.183886i
$869$	−7472.15	−	22996.9i	−0.291686	−	0.897718i
$870$	5466.52	−	214.975i	0.213026	−	0.00837741i
$871$	−4088.10	+	12581.9i	−0.159036	+	0.489461i
$872$	−54590.8	−	17737.6i	−2.12004	−	0.688843i
$873$	−920.093	−	1266.40i	−0.0356706	−	0.0490964i
$874$	−14637.2			−0.566488
$875$	−2392.18	−	20193.0i	−0.0924235	−	0.780167i
$876$	26757.8			1.03204
$877$	24952.3	+	34344.0i	0.960754	+	1.32236i	0.946582	+	0.322464i	$0.104511\pi$
$877$	24952.3	+	34344.0i	0.960754	+	1.32236i	0.0141719	+	0.999900i	$0.495489\pi$
$878$	20411.3	+	6632.05i	0.784567	+	0.254921i
$879$	9078.58	−	27941.0i	0.348365	−	1.07216i
$880$	−20549.8	+	808.139i	−0.787199	+	0.0309572i
$881$	1381.37	+	4251.43i	0.0528259	+	0.162581i	0.973989	−	0.226595i	$-0.0727595\pi$
$881$	1381.37	+	4251.43i	0.0528259	+	0.162581i	−0.921163	+	0.389177i	$0.872760\pi$
$882$		−	6045.72i		−	0.230805i
$883$	−4542.15	+	1475.83i	−0.173109	+	0.0562466i	−0.394289	−	0.918986i	$-0.629009\pi$
$883$	−4542.15	+	1475.83i	−0.173109	+	0.0562466i	0.221180	+	0.975233i	$0.429009\pi$
$884$	87151.8	+	63319.5i	3.31587	+	2.40912i
$885$	12560.8	+	15932.1i	0.477091	+	0.605143i
$886$	29695.6	−	21575.1i	1.12601	−	0.818093i
$887$	30878.5	−	42500.6i	1.16888	−	1.60883i	0.498255	−	0.867031i	$-0.333974\pi$
$887$	30878.5	−	42500.6i	1.16888	−	1.60883i	0.670626	−	0.741796i	$-0.266026\pi$
$888$	16749.4	−	23053.6i	0.632966	−	0.871202i
$889$	6011.91	−	4367.91i	0.226809	−	0.164786i
$890$	33443.7	+	9430.82i	1.25959	+	0.355193i
$891$	−14135.8	−	10270.3i	−0.531501	−	0.386158i
$892$	−5309.50	+	1725.16i	−0.199300	+	0.0647564i
$893$			13193.4i			0.494400i
$894$	−1463.21	−	4503.31i	−0.0547396	−	0.168471i
$895$	1145.23	−	4061.23i	0.0427718	−	0.151678i
$896$	−11931.6	+	36721.8i	−0.444875	+	1.36918i
$897$	−12876.8	−	4183.92i	−0.479312	−	0.155738i
$898$	27560.5	+	37933.8i	1.02417	+	1.40965i
$899$	−530.025			−0.0196633
$900$	13651.3	−	11661.0i	0.505604	−	0.431889i
$901$	20453.2			0.756265
$902$	41210.5	+	56721.3i	1.52124	+	2.09381i
$903$	−9990.01	−	3245.95i	−0.368158	−	0.119622i
$904$	−8973.23	+	27616.8i	−0.330139	+	1.01606i
$905$	−8646.04	−	23433.6i	−0.317574	−	0.860727i
$906$	−10300.8	−	31702.6i	−0.377727	−	1.16252i
$907$			9861.27i			0.361012i	0.983574	+	0.180506i	$0.0577735\pi$
$907$			9861.27i			0.361012i	−0.983574	+	0.180506i	$0.942226\pi$
$908$	48145.7	−	15643.5i	1.75966	−	0.571748i
$909$	10671.6	+	7753.40i	0.389390	+	0.282909i
$910$	1936.32	+	49237.9i	0.0705367	+	1.79365i
$911$	−24663.5	+	17919.1i	−0.896969	+	0.651686i	−0.937686	−	0.347484i	$-0.887036\pi$
$911$	−24663.5	+	17919.1i	−0.896969	+	0.651686i	0.0407166	+	0.999171i	$0.487036\pi$
$912$	5790.10	−	7969.39i	0.210229	−	0.289356i
$913$	−4622.23	+	6361.96i	−0.167551	+	0.230614i
$914$	−18894.9	+	13728.0i	−0.683795	+	0.496806i
$915$	7362.31	−	2716.40i	0.266000	−	0.0981435i
$916$	−27506.1	−	19984.4i	−0.992170	−	0.720854i
$917$	−27266.3	+	8859.37i	−0.981913	+	0.319043i
$918$		−	83365.5i		−	2.99725i
$919$	9150.97	+	28163.8i	0.328469	+	1.01092i	0.969851	+	0.243700i	$0.0783614\pi$
$919$	9150.97	+	28163.8i	0.328469	+	1.01092i	−0.641382	+	0.767222i	$0.721639\pi$
$920$	15865.9	+	10600.4i	0.568569	+	0.379876i
$921$	−9448.36	+	29079.1i	−0.338039	+	1.04038i
$922$	3682.80	+	1196.61i	0.131547	+	0.0427423i
$923$	−13707.2	−	18866.4i	−0.488818	−	0.672800i
$924$	−42008.2			−1.49564
$925$	13425.9	−	21912.6i	0.477234	−	0.778899i
$926$	−46980.3			−1.66724
$927$	−6778.83	−	9330.26i	−0.240179	−	0.330578i
$928$	−1767.01	−	574.137i	−0.0625054	−	0.0203092i
$929$	−3801.35	+	11699.3i	−0.134250	+	0.413179i	−0.995473	−	0.0950491i	$-0.969699\pi$
$929$	−3801.35	+	11699.3i	−0.134250	+	0.413179i	0.861223	+	0.508228i	$0.169699\pi$
$930$	3793.16	−	2990.51i	0.133745	−	0.105444i
$931$	−2415.06	−	7432.78i	−0.0850164	−	0.261653i
$932$		−	103175.i		−	3.62619i
$933$	−31019.4	+	10078.8i	−1.08846	+	0.353660i
$934$	5812.82	+	4223.26i	0.203641	+	0.147954i
$935$	−32818.6	+	49120.2i	−1.14789	+	1.71808i
$936$	−16350.9	+	11879.6i	−0.570988	+	0.414847i
$937$	−1494.19	+	2056.58i	−0.0520952	+	0.0717028i	−0.834270	−	0.551356i	$-0.814110\pi$
$937$	−1494.19	+	2056.58i	−0.0520952	+	0.0717028i	0.782175	+	0.623059i	$0.214110\pi$
$938$	8568.38	−	11793.4i	0.298260	−	0.410519i
$939$	−5979.93	+	4344.67i	−0.207825	+	0.150994i
$940$	20568.5	−	30785.4i	0.713694	−	1.06820i
$941$	37245.0	+	27060.1i	1.29028	+	0.937443i	0.999811	−	0.0194414i	$-0.00618877\pi$
$941$	37245.0	+	27060.1i	1.29028	+	0.937443i	0.290469	+	0.956884i	$0.406189\pi$
$942$	−29320.0	+	9526.64i	−1.01412	+	0.329506i
$943$		−	16216.5i		−	0.560001i
$944$	5337.56	+	16427.3i	0.184028	+	0.566381i
$945$	19502.8	−	15375.9i	0.671349	−	0.529288i
$946$	−11876.4	+	36551.8i	−0.408176	+	1.25624i
$947$	−9791.91	−	3181.58i	−0.336002	−	0.109174i	0.136156	−	0.990687i	$-0.456525\pi$
$947$	−9791.91	−	3181.58i	−0.336002	−	0.109174i	−0.472159	+	0.881514i	$0.656525\pi$
$948$	−19104.5	−	26295.2i	−0.654522	−	0.900872i
$949$	−27164.8			−0.929196
$950$	18617.7	−	30386.2i	0.635830	−	1.03775i
$951$	23165.9			0.789913
$952$	−32411.3	−	44610.3i	−1.10342	−	1.51873i
$953$	−40224.1	−	13069.6i	−1.36725	−	0.444246i	−0.468791	−	0.883309i	$-0.655310\pi$
$953$	−40224.1	−	13069.6i	−1.36725	−	0.444246i	−0.898456	+	0.439063i	$0.855310\pi$
$954$	−2552.64	+	7856.21i	−0.0866297	+	0.266619i
$955$	20873.2	+	13946.0i	0.707268	+	0.472545i
$956$	−20300.3	−	62477.9i	−0.686776	−	2.11368i
$957$		−	4734.79i		−	0.159931i
$958$	41771.6	−	13572.4i	1.40875	−	0.457730i
$959$	8060.43	+	5856.24i	0.271413	+	0.197193i
$960$	29772.4	−	10984.8i	1.00094	−	0.369305i
$961$	23722.8	−	17235.6i	0.796309	−	0.578552i
$962$	−36604.7	+	50382.1i	−1.22680	+	1.68855i
$963$	−11078.7	+	15248.6i	−0.370724	+	0.510258i
$964$	−32632.2	+	23708.7i	−1.09026	+	0.792121i
$965$	−674.648	−	17155.3i	−0.0225054	−	0.572280i
$966$	12069.8	+	8769.20i	0.402007	+	0.292075i
$967$	19761.9	−	6421.04i	0.657188	−	0.213533i	0.0386070	−	0.999254i	$-0.487708\pi$
$967$	19761.9	−	6421.04i	0.657188	−	0.213533i	0.618581	+	0.785721i	$0.287708\pi$
$968$			27155.3i			0.901658i
$969$	−8743.98	−	26911.2i	−0.289884	−	0.892170i
$970$	3018.19	+	8180.26i	0.0999054	+	0.270776i
$971$	17399.7	−	53550.7i	0.575059	−	1.76985i	−0.0609180	−	0.998143i	$-0.519403\pi$
$971$	17399.7	−	53550.7i	0.575059	−	1.76985i	0.635977	−	0.771708i	$-0.280597\pi$
$972$	36233.2	+	11772.9i	1.19566	+	0.388493i
$973$	19057.6	+	26230.5i	0.627911	+	0.864246i
$974$	−24256.9			−0.797989
$975$	25064.2	−	21409.9i	0.823278	−	0.703248i
$976$	6681.11			0.219116
$977$	−7237.69	−	9961.83i	−0.237005	−	0.326210i	0.673902	−	0.738821i	$-0.264617\pi$
$977$	−7237.69	−	9961.83i	−0.237005	−	0.326210i	−0.910907	+	0.412611i	$0.864617\pi$
$978$	−18726.8	−	6084.70i	−0.612287	−	0.198944i
$979$	9293.22	−	28601.6i	0.303384	−	0.933719i
$980$	−5952.46	+	21108.7i	−0.194025	+	0.688054i
$981$	−5129.85	−	15788.0i	−0.166956	−	0.513837i
$982$		−	31132.9i		−	1.01170i
$983$	−11167.0	+	3628.37i	−0.362331	+	0.117728i	−0.484524	−	0.874778i	$-0.661007\pi$
$983$	−11167.0	+	3628.37i	−0.362331	+	0.117728i	0.122193	+	0.992506i	$0.461007\pi$
$984$	35417.7	+	25732.4i	1.14743	+	0.833659i
$985$	36637.1	+	10331.3i	1.18513	+	0.334196i
$986$	10823.9	−	7864.03i	0.349598	−	0.253998i
$987$	7904.21	−	10879.2i	0.254908	−	0.350850i
$988$	−33058.2	+	45500.7i	−1.06450	+	1.46515i
$989$	7191.63	−	5225.03i	0.231224	−	0.167994i
$990$	−14771.5	−	18736.2i	−0.474212	−	0.601491i
$991$	36896.1	+	26806.6i	1.18269	+	0.859273i	0.992472	−	0.122469i	$-0.0390812\pi$
$991$	36896.1	+	26806.6i	1.18269	+	0.859273i	0.190216	+	0.981742i	$0.439081\pi$
$992$	−1560.13	+	506.918i	−0.0499337	+	0.0162245i
$993$			34761.7i			1.11091i
$994$	7940.62	+	24438.7i	0.253381	+	0.779828i
$995$	−38991.1	+	1533.36i	−1.24231	+	0.0488549i
$996$	−3266.41	+	10053.0i	−0.103916	+	0.319820i
$997$	−52392.6	−	17023.4i	−1.66428	−	0.540758i	−0.682520	−	0.730867i	$-0.739116\pi$
$997$	−52392.6	−	17023.4i	−1.66428	−	0.540758i	−0.981763	+	0.190109i	$0.939116\pi$
$998$	−32129.2	−	44222.0i	−1.01907	−	1.40263i
$999$	31386.8			0.994027

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.4.e.a.14.6	yes	24
3.2	odd	2		225.4.m.a.64.1		24
5.2	odd	4		125.4.d.b.51.1		48
5.3	odd	4		125.4.d.b.51.12		48
5.4	even	2		125.4.e.a.74.1		24
25.3	odd	20		625.4.a.g.1.2		24
25.9	even	10	inner	25.4.e.a.9.6	✓	24
25.12	odd	20		125.4.d.b.76.1		48
25.13	odd	20		125.4.d.b.76.12		48
25.16	even	5		125.4.e.a.49.1		24
25.22	odd	20		625.4.a.g.1.23		24
75.59	odd	10		225.4.m.a.109.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.4.e.a.9.6	✓	24	25.9	even	10	inner
25.4.e.a.14.6	yes	24	1.1	even	1	trivial
125.4.d.b.51.1		48	5.2	odd	4
125.4.d.b.51.12		48	5.3	odd	4
125.4.d.b.76.1		48	25.12	odd	20
125.4.d.b.76.12		48	25.13	odd	20
125.4.e.a.49.1		24	25.16	even	5
125.4.e.a.74.1		24	5.4	even	2
225.4.m.a.64.1		24	3.2	odd	2
225.4.m.a.109.1		24	75.59	odd	10
625.4.a.g.1.2		24	25.3	odd	20
625.4.a.g.1.23		24	25.22	odd	20

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:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	25.e (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.81526 + 3.87487i) q^{2} +(-3.96562 - 1.28851i) q^{3} +(-4.61680 + 14.2091i) q^{4} +(11.1717 - 0.439337i) q^{5} +(-6.17144 - 18.9937i) q^{6} -14.5499i q^{7} +(-31.6143 + 10.2721i) q^{8} +(-7.77757 - 5.65074i) q^{9} +O(q^{10})\)	\(q+(2.81526 + 3.87487i) q^{2} +(-3.96562 - 1.28851i) q^{3} +(-4.61680 + 14.2091i) q^{4} +(11.1717 - 0.439337i) q^{5} +(-6.17144 - 18.9937i) q^{6} -14.5499i q^{7} +(-31.6143 + 10.2721i) q^{8} +(-7.77757 - 5.65074i) q^{9} +(33.1536 + 42.0521i) q^{10} +(37.4944 - 27.2413i) q^{11} +(36.6170 - 50.3989i) q^{12} +(-37.1739 + 51.1655i) q^{13} +(56.3791 - 40.9618i) q^{14} +(-44.8688 - 12.6526i) q^{15} +(-32.1098 - 23.3291i) q^{16} +(-108.429 + 35.2308i) q^{17} -46.0453i q^{18} +(-18.3935 - 56.6094i) q^{19} +(-45.3350 + 160.768i) q^{20} +(-18.7477 + 57.6995i) q^{21} +(211.113 + 68.5947i) q^{22} +(-30.1783 - 41.5369i) q^{23} +138.606 q^{24} +(124.614 - 9.81628i) q^{25} -302.914 q^{26} +(89.7358 + 123.511i) q^{27} +(206.741 + 67.1742i) q^{28} +(-7.57128 + 23.3020i) q^{29} +(-77.2902 - 209.481i) q^{30} +(6.68485 + 20.5739i) q^{31} +75.8309i q^{32} +(-183.789 + 59.7167i) q^{33} +(-441.771 - 320.965i) q^{34} +(-6.39232 - 162.548i) q^{35} +(116.199 - 84.4236i) q^{36} +(120.842 - 166.325i) q^{37} +(167.572 - 230.642i) q^{38} +(213.345 - 155.004i) q^{39} +(-348.673 + 128.646i) q^{40} +(255.528 + 185.652i) q^{41} +(-276.358 + 89.7941i) q^{42} +173.139i q^{43} +(213.969 + 658.528i) q^{44} +(-89.3713 - 59.7114i) q^{45} +(75.9903 - 233.874i) q^{46} +(-210.805 - 68.4946i) q^{47} +(97.2755 + 133.888i) q^{48} +131.299 q^{49} +(388.857 + 455.228i) q^{50} +475.384 q^{51} +(-555.389 - 764.428i) q^{52} +(-170.619 - 55.4375i) q^{53} +(-225.959 + 695.429i) q^{54} +(406.908 - 320.804i) q^{55} +(149.458 + 459.986i) q^{56} +248.192i q^{57} +(-111.607 + 36.2634i) q^{58} +(-352.077 - 255.799i) q^{59} +(386.932 - 579.129i) q^{60} +(-136.184 + 98.9435i) q^{61} +(-60.9014 + 83.8236i) q^{62} +(-82.2178 + 113.163i) q^{63} +(-550.713 + 400.117i) q^{64} +(-392.817 + 587.938i) q^{65} +(-748.808 - 544.041i) q^{66} +(198.942 - 64.6401i) q^{67} -1703.33i q^{68} +(66.1551 + 203.604i) q^{69} +(611.855 - 482.383i) q^{70} +(-113.945 + 350.686i) q^{71} +(303.927 + 98.7519i) q^{72} +(252.468 + 347.492i) q^{73} +984.688 q^{74} +(-506.820 - 121.638i) q^{75} +889.285 q^{76} +(-396.359 - 545.541i) q^{77} +(1201.24 + 390.307i) q^{78} +(161.227 - 496.204i) q^{79} +(-368.971 - 246.519i) q^{80} +(-116.503 - 358.559i) q^{81} +1512.79i q^{82} +(-161.373 + 52.4333i) q^{83} +(-733.301 - 532.775i) q^{84} +(-1195.86 + 441.225i) q^{85} +(-670.889 + 487.429i) q^{86} +(60.0497 - 82.6513i) q^{87} +(-905.533 + 1246.36i) q^{88} +(524.968 - 381.412i) q^{89} +(-20.2294 - 514.405i) q^{90} +(744.455 + 540.878i) q^{91} +(729.527 - 237.038i) q^{92} -90.2016i q^{93} +(-328.062 - 1009.67i) q^{94} +(-230.357 - 624.342i) q^{95} +(97.7087 - 300.716i) q^{96} +(154.858 + 50.3164i) q^{97} +(369.641 + 508.768i) q^{98} -445.549 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 5 q^{2} - 5 q^{3} + 13 q^{4} + 15 q^{5} - 7 q^{6} - 110 q^{8} + 47 q^{9}+O(q^{10}) \) 24 * q - 5 * q^2 - 5 * q^3 + 13 * q^4 + 15 * q^5 - 7 * q^6 - 110 * q^8 + 47 * q^9	\( 24 q - 5 q^{2} - 5 q^{3} + 13 q^{4} + 15 q^{5} - 7 q^{6} - 110 q^{8} + 47 q^{9} - 5 q^{10} + 83 q^{11} - 165 q^{12} - 5 q^{13} + 31 q^{14} - 225 q^{15} + 89 q^{16} - 165 q^{17} - 115 q^{19} + 395 q^{20} + 138 q^{21} + 30 q^{22} + 75 q^{23} + 640 q^{24} + 595 q^{25} - 822 q^{26} + 595 q^{27} + 675 q^{28} + 125 q^{29} - 965 q^{30} + 633 q^{31} - 1285 q^{33} - 779 q^{34} + 190 q^{35} - 531 q^{36} - 1510 q^{37} + 255 q^{38} - 1241 q^{39} - 2470 q^{40} - 117 q^{41} + 1745 q^{42} + 516 q^{44} + 1725 q^{45} + 1233 q^{46} - 95 q^{47} + 1410 q^{48} + 1148 q^{49} + 2165 q^{50} - 2022 q^{51} + 1740 q^{52} + 2580 q^{53} + 1745 q^{54} - 315 q^{55} + 3160 q^{56} - 4230 q^{58} - 1905 q^{59} + 560 q^{60} - 567 q^{61} - 6880 q^{62} - 1950 q^{63} - 3612 q^{64} - 3170 q^{65} - 2774 q^{66} + 4195 q^{67} + 539 q^{69} + 3630 q^{70} + 2473 q^{71} + 215 q^{72} - 845 q^{73} + 3596 q^{74} + 2045 q^{75} - 3280 q^{76} + 3870 q^{77} + 9295 q^{78} + 775 q^{79} - 3670 q^{80} + 3309 q^{81} - 4625 q^{83} - 5694 q^{84} - 1460 q^{85} - 3897 q^{86} - 8485 q^{87} - 1650 q^{88} - 2410 q^{89} - 8845 q^{90} - 382 q^{91} + 4090 q^{92} + 5401 q^{94} + 3545 q^{95} + 6488 q^{96} + 5185 q^{97} + 5180 q^{98} + 6024 q^{99}+O(q^{100}) \) 24 * q - 5 * q^2 - 5 * q^3 + 13 * q^4 + 15 * q^5 - 7 * q^6 - 110 * q^8 + 47 * q^9 - 5 * q^10 + 83 * q^11 - 165 * q^12 - 5 * q^13 + 31 * q^14 - 225 * q^15 + 89 * q^16 - 165 * q^17 - 115 * q^19 + 395 * q^20 + 138 * q^21 + 30 * q^22 + 75 * q^23 + 640 * q^24 + 595 * q^25 - 822 * q^26 + 595 * q^27 + 675 * q^28 + 125 * q^29 - 965 * q^30 + 633 * q^31 - 1285 * q^33 - 779 * q^34 + 190 * q^35 - 531 * q^36 - 1510 * q^37 + 255 * q^38 - 1241 * q^39 - 2470 * q^40 - 117 * q^41 + 1745 * q^42 + 516 * q^44 + 1725 * q^45 + 1233 * q^46 - 95 * q^47 + 1410 * q^48 + 1148 * q^49 + 2165 * q^50 - 2022 * q^51 + 1740 * q^52 + 2580 * q^53 + 1745 * q^54 - 315 * q^55 + 3160 * q^56 - 4230 * q^58 - 1905 * q^59 + 560 * q^60 - 567 * q^61 - 6880 * q^62 - 1950 * q^63 - 3612 * q^64 - 3170 * q^65 - 2774 * q^66 + 4195 * q^67 + 539 * q^69 + 3630 * q^70 + 2473 * q^71 + 215 * q^72 - 845 * q^73 + 3596 * q^74 + 2045 * q^75 - 3280 * q^76 + 3870 * q^77 + 9295 * q^78 + 775 * q^79 - 3670 * q^80 + 3309 * q^81 - 4625 * q^83 - 5694 * q^84 - 1460 * q^85 - 3897 * q^86 - 8485 * q^87 - 1650 * q^88 - 2410 * q^89 - 8845 * q^90 - 382 * q^91 + 4090 * q^92 + 5401 * q^94 + 3545 * q^95 + 6488 * q^96 + 5185 * q^97 + 5180 * q^98 + 6024 * q^99

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