LMFDB - Embedded newform 200.6.f.b.149.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [200,6,Mod(149,200)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(200, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("200.149");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 200 = 2^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	200.f (of order $2$, degree $1$, not 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:	$32.0767639626$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} - 17 x^{18} + 78 x^{17} + 253 x^{16} - 884 x^{15} + 2396 x^{14} + 19376 x^{13} + \cdots + 1099511627776 $ x^20 - 2x^19 - 17x^18 + 78x^17 + 253x^16 - 884x^15 + 2396x^14 + 19376x^13 - 109104x^12 - 96128x^11 + 3580672x^10 - 1538048x^9 - 27930624x^8 + 79364096x^7 + 157024256x^6 - 926941184x^5 + 4244635648x^4 + 20937965568x^3 - 73014444032x^2 - 137438953472*x + 1099511627776
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{45}\cdot 3^{4}\cdot 5^{8} $
Twist minimal:	no (minimal twist has level 40)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			149.19
Root			$-2.80358 + 2.85306i$ of defining polynomial
Character	$\chi$	$=$	200.149
Dual form			200.6.f.b.149.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.65664 - 0.0494789i) q^{2} +10.7455 q^{3} +(31.9951 - 0.559768i) q^{4} +(60.7833 - 0.531674i) q^{6} -198.733i q^{7} +(180.957 - 4.74949i) q^{8} -127.535 q^{9} +O(q^{10})$	\(q+(5.65664 - 0.0494789i) q^{2} +10.7455 q^{3} +(31.9951 - 0.559768i) q^{4} +(60.7833 - 0.531674i) q^{6} -198.733i q^{7} +(180.957 - 4.74949i) q^{8} -127.535 q^{9} -85.9303i q^{11} +(343.803 - 6.01498i) q^{12} +407.120 q^{13} +(-9.83309 - 1124.16i) q^{14} +(1023.37 - 35.8197i) q^{16} -1206.02i q^{17} +(-721.417 + 6.31026i) q^{18} -206.036i q^{19} -2135.48i q^{21} +(-4.25173 - 486.077i) q^{22} -2595.25i q^{23} +(1944.47 - 51.0355i) q^{24} +(2302.93 - 20.1438i) q^{26} -3981.57 q^{27} +(-111.244 - 6358.49i) q^{28} +6195.27i q^{29} -1862.42 q^{31} +(5787.08 - 253.254i) q^{32} -923.363i q^{33} +(-59.6727 - 6822.04i) q^{34} +(-4080.48 + 71.3897i) q^{36} +14708.1 q^{37} +(-10.1944 - 1165.47i) q^{38} +4374.70 q^{39} +18098.0 q^{41} +(-105.661 - 12079.7i) q^{42} -9260.46 q^{43} +(-48.1010 - 2749.35i) q^{44} +(-128.410 - 14680.4i) q^{46} +24363.7i q^{47} +(10996.6 - 384.900i) q^{48} -22687.9 q^{49} -12959.3i q^{51} +(13025.8 - 227.893i) q^{52} -12764.8 q^{53} +(-22522.3 + 197.004i) q^{54} +(-943.880 - 35962.2i) q^{56} -2213.96i q^{57} +(306.535 + 35044.4i) q^{58} -20719.7i q^{59} -11368.5i q^{61} +(-10535.0 + 92.1504i) q^{62} +25345.3i q^{63} +(32722.9 - 1718.91i) q^{64} +(-45.6869 - 5223.13i) q^{66} +62614.9 q^{67} +(-675.093 - 38586.8i) q^{68} -27887.3i q^{69} -61208.1 q^{71} +(-23078.3 + 605.723i) q^{72} +23236.4i q^{73} +(83198.1 - 727.738i) q^{74} +(-115.332 - 6592.14i) q^{76} -17077.2 q^{77} +(24746.1 - 216.455i) q^{78} -29172.5 q^{79} -11793.1 q^{81} +(102374. - 895.467i) q^{82} +48099.7 q^{83} +(-1195.38 - 68325.1i) q^{84} +(-52383.1 + 458.197i) q^{86} +66571.2i q^{87} +(-408.125 - 15549.7i) q^{88} -30118.4 q^{89} -80908.2i q^{91} +(-1452.74 - 83035.4i) q^{92} -20012.6 q^{93} +(1205.49 + 137817. i) q^{94} +(62185.0 - 2721.34i) q^{96} +113676. i q^{97} +(-128337. + 1122.57i) q^{98} +10959.1i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} - 36 q^{3} + 32 q^{4} + 204 q^{6} - 248 q^{8} + 1620 q^{9}+O(q^{10}) $ 20 * q - 2 * q^2 - 36 * q^3 + 32 * q^4 + 204 * q^6 - 248 * q^8 + 1620 * q^9	$ 20 q - 2 q^{2} - 36 q^{3} + 32 q^{4} + 204 q^{6} - 248 q^{8} + 1620 q^{9} - 1252 q^{12} - 2708 q^{14} + 3080 q^{16} - 2070 q^{18} - 8244 q^{22} - 1032 q^{24} - 8084 q^{26} - 11664 q^{27} - 22924 q^{28} + 7160 q^{31} - 14792 q^{32} - 21132 q^{34} + 18344 q^{36} + 3608 q^{37} + 16884 q^{38} + 44904 q^{39} + 11608 q^{41} + 49444 q^{42} + 51772 q^{43} - 72296 q^{44} - 28516 q^{46} + 85048 q^{48} - 18756 q^{49} + 111624 q^{52} - 928 q^{53} + 100584 q^{54} - 53624 q^{56} - 152344 q^{58} - 228648 q^{62} + 11264 q^{64} - 56688 q^{66} + 161604 q^{67} - 359040 q^{68} - 200312 q^{71} - 563448 q^{72} - 78876 q^{74} - 153872 q^{76} - 26008 q^{77} + 624640 q^{78} - 282080 q^{79} + 65172 q^{81} + 410576 q^{82} + 99092 q^{83} + 297128 q^{84} + 27452 q^{86} + 464496 q^{88} + 3160 q^{89} + 519244 q^{92} - 293472 q^{93} - 148820 q^{94} + 395168 q^{96} - 663674 q^{98}+O(q^{100}) $ 20 * q - 2 * q^2 - 36 * q^3 + 32 * q^4 + 204 * q^6 - 248 * q^8 + 1620 * q^9 - 1252 * q^12 - 2708 * q^14 + 3080 * q^16 - 2070 * q^18 - 8244 * q^22 - 1032 * q^24 - 8084 * q^26 - 11664 * q^27 - 22924 * q^28 + 7160 * q^31 - 14792 * q^32 - 21132 * q^34 + 18344 * q^36 + 3608 * q^37 + 16884 * q^38 + 44904 * q^39 + 11608 * q^41 + 49444 * q^42 + 51772 * q^43 - 72296 * q^44 - 28516 * q^46 + 85048 * q^48 - 18756 * q^49 + 111624 * q^52 - 928 * q^53 + 100584 * q^54 - 53624 * q^56 - 152344 * q^58 - 228648 * q^62 + 11264 * q^64 - 56688 * q^66 + 161604 * q^67 - 359040 * q^68 - 200312 * q^71 - 563448 * q^72 - 78876 * q^74 - 153872 * q^76 - 26008 * q^77 + 624640 * q^78 - 282080 * q^79 + 65172 * q^81 + 410576 * q^82 + 99092 * q^83 + 297128 * q^84 + 27452 * q^86 + 464496 * q^88 + 3160 * q^89 + 519244 * q^92 - 293472 * q^93 - 148820 * q^94 + 395168 * q^96 - 663674 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/200\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$177$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	5.65664	−	0.0494789i	0.999962	−	0.00874671i
$2$	5.65664	−	0.0494789i	0.999962	−	0.00874671i
$3$	10.7455			0.689323			0.344662	−	0.938727i	$-0.387994\pi$
$3$	10.7455			0.689323			0.344662	+	0.938727i	$0.387994\pi$
$4$	31.9951	−	0.559768i	0.999847	−	0.0174927i
$5$		0			0
$5$		0			0
$6$	60.7833	−	0.531674i	0.689297	−	0.00602931i
$7$		−	198.733i		−	1.53294i	−0.642280	−	0.766470i	$-0.722011\pi$
$7$		−	198.733i		−	1.53294i	0.642280	−	0.766470i	$-0.277989\pi$
$8$	180.957	−	4.74949i	0.999656	−	0.0262374i
$9$	−127.535			−0.524833
$10$		0			0
$11$		−	85.9303i		−	0.214124i	−0.994252	−	0.107062i	$-0.965856\pi$
$11$		−	85.9303i		−	0.214124i	0.994252	−	0.107062i	$-0.0341443\pi$
$12$	343.803	−	6.01498i	0.689218	−	0.0120582i
$13$	407.120			0.668134			0.334067	−	0.942549i	$-0.391579\pi$
$13$	407.120			0.668134			0.334067	+	0.942549i	$0.391579\pi$
$14$	−9.83309	−	1124.16i	−0.0134082	−	1.53288i
$15$		0			0
$16$	1023.37	−	35.8197i	0.999388	−	0.0349801i
$17$		−	1206.02i		−	1.01212i	−0.862497	−	0.506062i	$-0.831101\pi$
$17$		−	1206.02i		−	1.01212i	0.862497	−	0.506062i	$-0.168899\pi$
$18$	−721.417	+	6.31026i	−0.524813	+	0.00459056i
$19$		−	206.036i		−	0.130936i	−0.997855	−	0.0654680i	$-0.979146\pi$
$19$		−	206.036i		−	0.130936i	0.997855	−	0.0654680i	$-0.0208540\pi$
$20$		0			0
$21$		−	2135.48i		−	1.05669i
$22$	−4.25173	−	486.077i	−0.00187288	−	0.214115i
$23$		−	2595.25i		−	1.02296i	−0.859294	−	0.511482i	$-0.829097\pi$
$23$		−	2595.25i		−	1.02296i	0.859294	−	0.511482i	$-0.170903\pi$
$24$	1944.47	−	51.0355i	0.689086	−	0.0180861i
$25$		0			0
$26$	2302.93	−	20.1438i	0.668109	−	0.00584398i
$27$	−3981.57			−1.05110
$28$	−111.244	−	6358.49i	−0.0268153	−	1.53271i
$29$			6195.27i			1.36794i	0.729512	+	0.683968i	$0.239747\pi$
$29$			6195.27i			1.36794i	−0.729512	+	0.683968i	$0.760253\pi$
$30$		0			0
$31$	−1862.42			−0.348075			−0.174038	−	0.984739i	$-0.555681\pi$
$31$	−1862.42			−0.348075			−0.174038	+	0.984739i	$0.555681\pi$
$32$	5787.08	−	253.254i	0.999044	−	0.0437202i
$33$		−	923.363i		−	0.147600i
$34$	−59.6727	−	6822.04i	−0.00885275	−	1.01208i
$35$		0			0
$36$	−4080.48	+	71.3897i	−0.524753	+	0.00918078i
$37$	14708.1			1.76625			0.883123	−	0.469142i	$-0.155437\pi$
$37$	14708.1			1.76625			0.883123	+	0.469142i	$0.155437\pi$
$38$	−10.1944	−	1165.47i	−0.00114526	−	0.130931i
$39$	4374.70			0.460560
$40$		0			0
$41$	18098.0			1.68140			0.840699	−	0.541503i	$-0.182144\pi$
$41$	18098.0			1.68140			0.840699	+	0.541503i	$0.182144\pi$
$42$	−105.661	−	12079.7i	−0.00924257	−	1.05665i
$43$	−9260.46			−0.763768			−0.381884	−	0.924210i	$-0.624725\pi$
$43$	−9260.46			−0.763768			−0.381884	+	0.924210i	$0.624725\pi$
$44$	−48.1010	−	2749.35i	−0.00374561	−	0.214091i
$45$		0			0
$46$	−128.410	−	14680.4i	−0.00894757	−	1.02292i
$47$			24363.7i			1.60879i	0.594095	+	0.804395i	$0.297510\pi$
$47$			24363.7i			1.60879i	−0.594095	+	0.804395i	$0.702490\pi$
$48$	10996.6	−	384.900i	0.688901	−	0.0241126i
$49$	−22687.9			−1.34991
$50$		0			0
$51$		−	12959.3i		−	0.697680i
$52$	13025.8	−	227.893i	0.668032	−	0.0116875i
$53$	−12764.8			−0.624202			−0.312101	−	0.950049i	$-0.601033\pi$
$53$	−12764.8			−0.624202			−0.312101	+	0.950049i	$0.601033\pi$
$54$	−22522.3	+	197.004i	−1.05106	+	0.00919369i
$55$		0			0
$56$	−943.880	−	35962.2i	−0.0402204	−	1.53241i
$57$		−	2213.96i		−	0.0902572i
$58$	306.535	+	35044.4i	0.0119649	+	1.36788i
$59$		−	20719.7i		−	0.774913i	−0.921888	−	0.387457i	$-0.873354\pi$
$59$		−	20719.7i		−	0.774913i	0.921888	−	0.387457i	$-0.126646\pi$
$60$		0			0
$61$		−	11368.5i		−	0.391183i	−0.980686	−	0.195591i	$-0.937337\pi$
$61$		−	11368.5i		−	0.391183i	0.980686	−	0.195591i	$-0.0626626\pi$
$62$	−10535.0	+	92.1504i	−0.348062	+	0.00304451i
$63$			25345.3i			0.804538i
$64$	32722.9	−	1718.91i	0.998623	−	0.0524568i
$65$		0			0
$66$	−45.6869	−	5223.13i	−0.00129102	−	0.147595i
$67$	62614.9			1.70408			0.852041	−	0.523475i	$-0.175365\pi$
$67$	62614.9			1.70408			0.852041	+	0.523475i	$0.175365\pi$
$68$	−675.093	−	38586.8i	−0.0177048	−	1.01197i
$69$		−	27887.3i		−	0.705153i
$70$		0			0
$71$	−61208.1			−1.44100			−0.720498	−	0.693457i	$-0.756087\pi$
$71$	−61208.1			−1.44100			−0.720498	+	0.693457i	$0.756087\pi$
$72$	−23078.3	+	605.723i	−0.524653	+	0.0137703i
$73$			23236.4i			0.510342i	0.966896	+	0.255171i	$0.0821318\pi$
$73$			23236.4i			0.510342i	−0.966896	+	0.255171i	$0.917868\pi$
$74$	83198.1	−	727.738i	1.76618	−	0.0154488i
$75$		0			0
$76$	−115.332	−	6592.14i	−0.00229043	−	0.130916i
$77$	−17077.2			−0.328239
$78$	24746.1	−	216.455i	0.460543	−	0.00402839i
$79$	−29172.5			−0.525904			−0.262952	−	0.964809i	$-0.584696\pi$
$79$	−29172.5			−0.525904			−0.262952	+	0.964809i	$0.584696\pi$
$80$		0			0
$81$	−11793.1			−0.199717
$82$	102374.	−	895.467i	1.68133	−	0.0147067i
$83$	48099.7			0.766386			0.383193	−	0.923668i	$-0.374824\pi$
$83$	48099.7			0.766386			0.383193	+	0.923668i	$0.374824\pi$
$84$	−1195.38	−	68325.1i	−0.0184844	−	1.05653i
$85$		0			0
$86$	−52383.1	+	458.197i	−0.763739	+	0.00668046i
$87$			66571.2i			0.942950i
$88$	−408.125	−	15549.7i	−0.00561806	−	0.214050i
$89$	−30118.4			−0.403048			−0.201524	−	0.979484i	$-0.564589\pi$
$89$	−30118.4			−0.403048			−0.201524	+	0.979484i	$0.564589\pi$
$90$		0			0
$91$		−	80908.2i		−	1.02421i
$92$	−1452.74	−	83035.4i	−0.0178945	−	1.02281i
$93$	−20012.6			−0.239937
$94$	1205.49	+	137817.i	0.0140716	+	1.60873i
$95$		0			0
$96$	62185.0	−	2721.34i	0.688664	−	0.0301373i
$97$			113676.i			1.22670i	0.789811	+	0.613351i	$0.210179\pi$
$97$			113676.i			1.22670i	−0.789811	+	0.613351i	$0.789821\pi$
$98$	−128337.	+	1122.57i	−1.34985	+	0.0118072i
$99$			10959.1i			0.112379i
$100$		0			0
$101$		−	21867.4i		−	0.213302i	−0.994297	−	0.106651i	$-0.965987\pi$
$101$		−	21867.4i		−	0.213302i	0.994297	−	0.106651i	$-0.0340127\pi$
$102$	−641.212	−	73306.1i	−0.00610241	−	0.697654i
$103$			156608.i			1.45452i	0.686360	+	0.727262i	$0.259208\pi$
$103$			156608.i			1.45452i	−0.686360	+	0.727262i	$0.740792\pi$
$104$	73671.2	−	1933.61i	0.667904	−	0.0175301i
$105$		0			0
$106$	−72206.0	+	631.589i	−0.624178	+	0.00545971i
$107$	−91401.1			−0.771777			−0.385889	−	0.922545i	$-0.626105\pi$
$107$	−91401.1			−0.771777			−0.385889	+	0.922545i	$0.626105\pi$
$108$	−127391.	+	2228.76i	−1.05094	+	0.0183867i
$109$			48973.9i			0.394819i	0.980321	+	0.197410i	$0.0632529\pi$
$109$			48973.9i			0.394819i	−0.980321	+	0.197410i	$0.936747\pi$
$110$		0			0
$111$	158045.			1.21751
$112$	−7118.56	−	203378.i	−0.0536225	−	1.53200i
$113$		−	153638.i		−	1.13188i	−0.824445	−	0.565942i	$-0.808513\pi$
$113$		−	153638.i		−	1.13188i	0.824445	−	0.565942i	$-0.191487\pi$
$114$	−109.544	−	12523.5i	−0.000789453	−	0.0902537i
$115$		0			0
$116$	3467.92	+	198218.i	0.0239289	+	1.36773i
$117$	−51921.8			−0.350659
$118$	−1025.19	−	117204.i	−0.00677794	−	0.774883i
$119$	−239677.			−1.55152
$120$		0			0
$121$	153667.			0.954151
$122$	−562.502	−	64307.6i	−0.00342156	−	0.391168i
$123$	194472.			1.15903
$124$	−59588.3	+	1042.52i	−0.348022	+	0.00608880i
$125$		0			0
$126$	1254.06	+	143369.i	0.00703706	+	0.804507i
$127$			122092.i			0.671705i	0.941915	+	0.335852i	$0.109024\pi$
$127$			122092.i			0.671705i	−0.941915	+	0.335852i	$0.890976\pi$
$128$	185016.	−	11342.3i	0.998126	−	0.0611895i
$129$	−99508.2			−0.526483
$130$		0			0
$131$			179438.i			0.913560i	0.889580	+	0.456780i	$0.150997\pi$
$131$			179438.i			0.913560i	−0.889580	+	0.456780i	$0.849003\pi$
$132$	−516.869	−	29543.1i	−0.00258194	−	0.147578i
$133$	−40946.2			−0.200717
$134$	354190.	−	3098.11i	1.70402	−	0.0149051i
$135$		0			0
$136$	−5727.99	−	218238.i	−0.0265555	−	1.01177i
$137$			327113.i			1.48900i	0.667620	+	0.744502i	$0.267313\pi$
$137$			327113.i			1.48900i	−0.667620	+	0.744502i	$0.732687\pi$
$138$	−1379.83	−	157748.i	−0.00616777	−	0.705126i
$139$		−	359354.i		−	1.57756i	−0.614678	−	0.788778i	$-0.710714\pi$
$139$		−	359354.i		−	1.57756i	0.614678	−	0.788778i	$-0.289286\pi$
$140$		0			0
$141$			261800.i			1.10898i
$142$	−346232.	+	3028.51i	−1.44094	+	0.0126040i
$143$		−	34983.9i		−	0.143063i
$144$	−130515.	+	4568.24i	−0.524512	+	0.0183587i
$145$		0			0
$146$	1149.71	+	131440.i	0.00446381	+	0.510322i
$147$	−243792.			−0.930522
$148$	470586.	−	8233.10i	1.76597	−	0.0308965i
$149$			494795.i			1.82583i	0.408152	+	0.912914i	$0.366173\pi$
$149$			494795.i			1.82583i	−0.408152	+	0.912914i	$0.633827\pi$
$150$		0			0
$151$	−9960.81			−0.0355511			−0.0177755	−	0.999842i	$-0.505658\pi$
$151$	−9960.81			−0.0355511			−0.0177755	+	0.999842i	$0.505658\pi$
$152$	−978.565	−	37283.6i	−0.00343543	−	0.130891i
$153$			153810.i			0.531196i
$154$	−96599.5	+	844.960i	−0.328226	+	0.00287101i
$155$		0			0
$156$	139969.	−	2448.82i	0.460490	−	0.00805647i
$157$	243819.			0.789439			0.394719	−	0.918802i	$-0.370842\pi$
$157$	243819.			0.789439			0.394719	+	0.918802i	$0.370842\pi$
$158$	−165018.	+	1443.42i	−0.525884	+	0.00459993i
$159$	−137164.			−0.430277
$160$		0			0
$161$	−515763.			−1.56814
$162$	−66709.1	+	583.507i	−0.199709	+	0.00174686i
$163$	−268182.			−0.790608			−0.395304	−	0.918550i	$-0.629361\pi$
$163$	−268182.			−0.790608			−0.395304	+	0.918550i	$0.629361\pi$
$164$	579047.	−	10130.7i	1.68114	−	0.0294123i
$165$		0			0
$166$	272083.	−	2379.92i	0.766356	−	0.00670335i
$167$			17404.1i			0.0482905i	0.999708	+	0.0241452i	$0.00768641\pi$
$167$			17404.1i			0.0482905i	−0.999708	+	0.0241452i	$0.992314\pi$
$168$	−10142.5	−	386431.i	−0.0277249	−	1.05633i
$169$	−205547.			−0.553597
$170$		0			0
$171$			26276.7i			0.0687195i
$172$	−296289.	+	5183.71i	−0.763651	+	0.0133604i
$173$	−534365.			−1.35745			−0.678723	−	0.734394i	$-0.737466\pi$
$173$	−534365.			−1.35745			−0.678723	+	0.734394i	$0.737466\pi$
$174$	3293.87	+	376569.i	0.00824771	+	0.942914i
$175$		0			0
$176$	−3077.99	−	87938.8i	−0.00749008	−	0.213993i
$177$		−	222643.i		−	0.534166i
$178$	−170369.	+	1490.22i	−0.403032	+	0.00352534i
$179$		−	342831.i		−	0.799738i	−0.916572	−	0.399869i	$-0.869056\pi$
$179$		−	342831.i		−	0.799738i	0.916572	−	0.399869i	$-0.130944\pi$
$180$		0			0
$181$			593221.i			1.34592i	0.739678	+	0.672961i	$0.234978\pi$
$181$			593221.i			1.34592i	−0.739678	+	0.672961i	$0.765022\pi$
$182$	−4003.24	−	457668.i	−0.00895847	−	1.02417i
$183$		−	122160.i		−	0.269651i
$184$	−12326.1	−	469630.i	−0.0268400	−	1.02261i
$185$		0			0
$186$	−113204.	+	990.201i	−0.239927	+	0.00209865i
$187$	−103634.			−0.216720
$188$	13638.0	+	779520.i	0.0281421	+	1.60854i
$189$			791271.i			1.61128i
$190$		0			0
$191$	−1448.97			−0.00287392			−0.00143696	−	0.999999i	$-0.500457\pi$
$191$	−1448.97			−0.00287392			−0.00143696	+	0.999999i	$0.500457\pi$
$192$	351623.	−	18470.5i	0.688374	−	0.0361597i
$193$			888526.i			1.71703i	0.512791	+	0.858513i	$0.328612\pi$
$193$			888526.i			1.71703i	−0.512791	+	0.858513i	$0.671388\pi$
$194$	5624.55	+	643023.i	0.0107296	+	1.22665i
$195$		0			0
$196$	−725901.	+	12699.9i	−1.34970	+	0.0236136i
$197$	−356565.			−0.654595			−0.327298	−	0.944921i	$-0.606138\pi$
$197$	−356565.			−0.654595			−0.327298	+	0.944921i	$0.606138\pi$
$198$	542.243	+	61991.5i	0.000982948	+	0.112375i
$199$	406304.			0.727307			0.363654	−	0.931534i	$-0.381529\pi$
$199$	406304.			0.727307			0.363654	+	0.931534i	$0.381529\pi$
$200$		0			0
$201$	672827.			1.17466
$202$	−1081.98	−	123696.i	−0.00186569	−	0.213294i
$203$	1.23121e6			2.09696
$204$	−7254.21	−	414634.i	−0.0122043	−	0.697573i
$205$		0			0
$206$	7748.79	+	885875.i	0.0127223	+	1.45447i
$207$			330984.i			0.536886i
$208$	416635.	−	14582.9i	0.667725	−	0.0233714i
$209$	−17704.7			−0.0280365
$210$		0			0
$211$		−	582646.i		−	0.900945i	−0.892790	−	0.450473i	$-0.851256\pi$
$211$		−	582646.i		−	0.900945i	0.892790	−	0.450473i	$-0.148744\pi$
$212$	−408412.	+	7145.34i	−0.624106	+	0.0109190i
$213$	−657711.			−0.993312
$214$	−517023.	+	4522.42i	−0.771748	+	0.00675051i
$215$		0			0
$216$	−720494.	+	18910.4i	−1.05074	+	0.0275783i
$217$			370125.i			0.533579i
$218$	2423.17	+	277027.i	0.00345337	+	0.394804i
$219$			249686.i			0.351791i
$220$		0			0
$221$		−	490996.i		−	0.676234i
$222$	894005.	−	7819.90i	1.21747	−	0.0106492i
$223$		−	789020.i		−	1.06249i	−0.847218	−	0.531246i	$-0.821724\pi$
$223$		−	789020.i		−	1.06249i	0.847218	−	0.531246i	$-0.178276\pi$
$224$	−50330.0	−	1.15008e6i	−0.0670204	−	1.53147i
$225$		0			0
$226$	−7601.82	−	869073.i	−0.00990026	−	1.13184i
$227$	872412.			1.12372			0.561858	−	0.827233i	$-0.310087\pi$
$227$	872412.			1.12372			0.561858	+	0.827233i	$0.310087\pi$
$228$	−1239.30	−	70835.8i	−0.00157885	−	0.0902434i
$229$		−	404072.i		−	0.509178i	−0.967049	−	0.254589i	$-0.918060\pi$
$229$		−	404072.i		−	0.509178i	0.967049	−	0.254589i	$-0.0819402\pi$
$230$		0			0
$231$	−183503.			−0.226263
$232$	29424.4	+	1.12108e6i	0.0358911	+	1.36746i
$233$		−	198854.i		−	0.239963i	−0.992776	−	0.119982i	$-0.961716\pi$
$233$		−	198854.i		−	0.239963i	0.992776	−	0.119982i	$-0.0382836\pi$
$234$	−293703.	+	2569.03i	−0.350646	+	0.00306711i
$235$		0			0
$236$	−11598.2	−	662928.i	−0.0135554	−	0.774795i
$237$	−313473.			−0.362518
$238$	−1.35577e6	+	11858.9i	−1.55147	+	0.0135707i
$239$	388433.			0.439868			0.219934	−	0.975515i	$-0.429416\pi$
$239$	388433.			0.439868			0.219934	+	0.975515i	$0.429416\pi$
$240$		0			0
$241$	−714818.			−0.792780			−0.396390	−	0.918082i	$-0.629737\pi$
$241$	−714818.			−0.792780			−0.396390	+	0.918082i	$0.629737\pi$
$242$	869238.	−	7603.27i	0.954115	−	0.00834568i
$243$	840800.			0.913434
$244$	−6363.73	−	363737.i	−0.00684286	−	0.391123i
$245$		0			0
$246$	1.10006e6	−	9622.23i	1.15898	−	0.0101377i
$247$		−	83881.3i		−	0.0874828i
$248$	−337018.	+	8845.54i	−0.347956	+	0.00913261i
$249$	516855.			0.528287
$250$		0			0
$251$		−	1.57948e6i		−	1.58244i	−0.611529	−	0.791222i	$-0.709445\pi$
$251$		−	1.57948e6i		−	1.58244i	0.611529	−	0.791222i	$-0.290555\pi$
$252$	14187.5	+	810927.i	0.0140736	+	0.804415i
$253$	−223011.			−0.219041
$254$	6040.98	+	690631.i	0.00587521	+	0.671679i
$255$		0			0
$256$	1.04601e6	−	73313.8i	0.997553	−	0.0699175i
$257$		−	1.80546e6i		−	1.70512i	−0.522632	−	0.852558i	$-0.675050\pi$
$257$		−	1.80546e6i		−	1.70512i	0.522632	−	0.852558i	$-0.324950\pi$
$258$	−562882.	+	4923.55i	−0.526463	+	0.00460500i
$259$		−	2.92298e6i		−	2.70755i
$260$		0			0
$261$		−	790111.i		−	0.717938i
$262$	8878.41	+	1.01502e6i	0.00799065	+	0.913526i
$263$			185503.i			0.165372i	0.996576	+	0.0826860i	$0.0263499\pi$
$263$			185503.i			0.165372i	−0.996576	+	0.0826860i	$0.973650\pi$
$264$	−4385.50	−	167089.i	−0.00387266	−	0.147550i
$265$		0			0
$266$	−231618.	+	2025.97i	−0.200709	+	0.00175561i
$267$	−323637.			−0.277830
$268$	2.00337e6	−	35049.8i	1.70382	−	0.0298091i
$269$			1.12615e6i			0.948887i	0.880286	+	0.474444i	$0.157351\pi$
$269$			1.12615e6i			0.948887i	−0.880286	+	0.474444i	$0.842649\pi$
$270$		0			0
$271$	157610.			0.130365			0.0651825	−	0.997873i	$-0.479237\pi$
$271$	157610.			0.130365			0.0651825	+	0.997873i	$0.479237\pi$
$272$	−43199.4	−	1.23421e6i	−0.0354042	−	1.01150i
$273$		−	869398.i		−	0.706012i
$274$	16185.2	+	1.85036e6i	0.0130239	+	1.48895i
$275$		0			0
$276$	−15610.4	−	892256.i	−0.0123351	−	0.705045i
$277$	1.93510e6			1.51532			0.757660	−	0.652650i	$-0.226343\pi$
$277$	1.93510e6			1.51532			0.757660	+	0.652650i	$0.226343\pi$
$278$	−17780.4	−	2.03273e6i	−0.0137984	−	1.57750i
$279$	237523.			0.182682
$280$		0			0
$281$	394102.			0.297744			0.148872	−	0.988856i	$-0.452436\pi$
$281$	394102.			0.297744			0.148872	+	0.988856i	$0.452436\pi$
$282$	12953.6	+	1.48091e6i	0.00969989	+	1.10893i
$283$	538592.			0.399755			0.199878	−	0.979821i	$-0.435946\pi$
$283$	538592.			0.399755			0.199878	+	0.979821i	$0.435946\pi$
$284$	−1.95836e6	+	34262.3i	−1.44078	+	0.0252070i
$285$		0			0
$286$	−1730.96	−	197891.i	−0.00125133	−	0.143058i
$287$		−	3.59667e6i		−	2.57748i
$288$	−738052.	+	32298.7i	−0.524332	+	0.0229458i
$289$	−34635.4			−0.0243936
$290$		0			0
$291$			1.22150e6i			0.845594i
$292$	13007.0	+	743450.i	0.00892728	+	0.510264i
$293$	−1.25662e6			−0.855134			−0.427567	−	0.903984i	$-0.640629\pi$
$293$	−1.25662e6			−0.855134			−0.427567	+	0.903984i	$0.640629\pi$
$294$	−1.37904e6	+	12062.6i	−0.930486	+	0.00813900i
$295$		0			0
$296$	2.66153e6	−	69855.7i	1.76564	−	0.0463418i
$297$			342138.i			0.225066i
$298$	24481.9	+	2.79888e6i	0.0159700	+	1.82576i
$299$		−	1.05658e6i		−	0.683477i
$300$		0			0
$301$			1.84036e6i			1.17081i
$302$	−56344.7	+	492.850i	−0.0355497	+	0.000310955i
$303$		−	234976.i		−	0.147034i
$304$	−7380.14	−	210852.i	−0.00458016	−	0.130856i
$305$		0			0
$306$	7610.32	+	870045.i	0.00464622	+	0.531176i
$307$	227401.			0.137704			0.0688519	−	0.997627i	$-0.478066\pi$
$307$	227401.			0.137704			0.0688519	+	0.997627i	$0.478066\pi$
$308$	−546387.	+	9559.27i	−0.328189	+	0.00574180i
$309$			1.68283e6i			1.00264i
$310$		0			0
$311$	1.13530e6			0.665593			0.332796	−	0.942999i	$-0.392008\pi$
$311$	1.13530e6			0.665593			0.332796	+	0.942999i	$0.392008\pi$
$312$	791633.	−	20777.6i	0.460402	−	0.0120839i
$313$		−	2.32737e6i		−	1.34278i	−0.741105	−	0.671390i	$-0.765698\pi$
$313$		−	2.32737e6i		−	1.34278i	0.741105	−	0.671390i	$-0.234302\pi$
$314$	1.37920e6	−	12063.9i	0.789409	−	0.00690499i
$315$		0			0
$316$	−933378.	+	16329.8i	−0.525823	+	0.00919950i
$317$	1.50212e6			0.839570			0.419785	−	0.907624i	$-0.362106\pi$
$317$	1.50212e6			0.839570			0.419785	+	0.907624i	$0.362106\pi$
$318$	−775888.	+	6786.73i	−0.430261	+	0.00376351i
$319$	532362.			0.292907
$320$		0			0
$321$	−982149.			−0.532004
$322$	−2.91749e6	+	25519.4i	−1.56808	+	0.0137161i
$323$	−248484.			−0.132523
$324$	−377320.	+	6601.38i	−0.199686	+	0.00349359i
$325$		0			0
$326$	−1.51701e6	+	13269.4i	−0.790578	+	0.00691522i
$327$			526248.i			0.272158i
$328$	3.27496e6	−	85956.1i	1.68082	−	0.0441156i
$329$	4.84188e6			2.46618
$330$		0			0
$331$		−	2.72477e6i		−	1.36697i	−0.729964	−	0.683486i	$-0.760463\pi$
$331$		−	2.72477e6i		−	1.36697i	0.729964	−	0.683486i	$-0.239537\pi$
$332$	1.53896e6	−	26924.7i	0.766268	−	0.0134062i
$333$	−1.87578e6			−0.926984
$334$	861.137	+	98448.9i	0.000422383	+	0.0482886i
$335$		0			0
$336$	−76492.4	−	2.18540e6i	−0.0369632	−	1.05604i
$337$		−	2.04270e6i		−	0.979784i	−0.871783	−	0.489892i	$-0.837036\pi$
$337$		−	2.04270e6i		−	0.979784i	0.871783	−	0.489892i	$-0.162964\pi$
$338$	−1.16270e6	+	10170.2i	−0.553576	+	0.00484215i
$339$		−	1.65091e6i		−	0.780234i
$340$		0			0
$341$			160038.i			0.0745312i
$342$	1300.14	+	148638.i	0.000601070	+	0.0687169i
$343$			1.16872e6i			0.536385i
$344$	−1.67575e6	+	43982.4i	−0.763505	+	0.0200393i
$345$		0			0
$346$	−3.02271e6	+	26439.8i	−1.35739	+	0.0118732i
$347$	−2.57456e6			−1.14783			−0.573916	−	0.818914i	$-0.694577\pi$
$347$	−2.57456e6			−1.14783			−0.573916	+	0.818914i	$0.694577\pi$
$348$	37264.4	+	2.12995e6i	0.0164948	+	0.942805i
$349$			1.97991e6i			0.870125i	0.900400	+	0.435062i	$0.143274\pi$
$349$			1.97991e6i			0.870125i	−0.900400	+	0.435062i	$0.856726\pi$
$350$		0			0
$351$	−1.62098e6			−0.702278
$352$	−21762.2	−	497285.i	−0.00936152	−	0.213919i
$353$		−	1.02870e6i		−	0.439394i	−0.975568	−	0.219697i	$-0.929493\pi$
$353$		−	1.02870e6i		−	0.439394i	0.975568	−	0.219697i	$-0.0705068\pi$
$354$	−11016.1	−	1.25941e6i	−0.00467219	−	0.534145i
$355$		0			0
$356$	−963641.	+	16859.3i	−0.402986	+	0.00705041i
$357$	−2.57544e6			−1.06950
$358$	−16962.9	−	1.93927e6i	−0.00699508	−	0.799708i
$359$	979196.			0.400990			0.200495	−	0.979695i	$-0.435745\pi$
$359$	979196.			0.400990			0.200495	+	0.979695i	$0.435745\pi$
$360$		0			0
$361$	2.43365e6			0.982856
$362$	29351.9	+	3.35564e6i	0.0117724	+	1.34587i
$363$	1.65123e6			0.657719
$364$	−45289.8	−	2.58867e6i	−0.0179162	−	1.02405i
$365$		0			0
$366$	−6044.35	−	691017.i	−0.00235856	−	0.269641i
$367$			1.07920e6i			0.418250i	0.977889	+	0.209125i	$0.0670616\pi$
$367$			1.07920e6i			0.418250i	−0.977889	+	0.209125i	$0.932938\pi$
$368$	−92961.2	−	2.65591e6i	−0.0357834	−	1.02234i
$369$	−2.30812e6			−0.882454
$370$		0			0
$371$			2.53679e6i			0.956864i
$372$	−640305.	+	11202.4i	−0.239900	+	0.00419715i
$373$	3.65291e6			1.35946			0.679731	−	0.733461i	$-0.262096\pi$
$373$	3.65291e6			1.35946			0.679731	+	0.733461i	$0.262096\pi$
$374$	−586220.	+	5127.69i	−0.216711	+	0.00189558i
$375$		0			0
$376$	115715.	+	4.40879e6i	0.0422105	+	1.60824i
$377$			2.52222e6i			0.913964i
$378$	39151.2	+	4.47593e6i	0.0140934	+	1.61122i
$379$			2.99413e6i			1.07071i	0.844627	+	0.535355i	$0.179822\pi$
$379$			2.99413e6i			1.07071i	−0.844627	+	0.535355i	$0.820178\pi$
$380$		0			0
$381$			1.31194e6i			0.463022i
$382$	−8196.27	+	71.6932i	−0.00287381	+	2.51373e-5i
$383$			4.15754e6i			1.44824i	0.689675	+	0.724119i	$0.257753\pi$
$383$			4.15754e6i			1.44824i	−0.689675	+	0.724119i	$0.742247\pi$
$384$	1.98809e6	−	121879.i	0.688032	−	0.0421793i
$385$		0			0
$386$	43963.3	+	5.02607e6i	0.0150183	+	1.71696i
$387$	1.18103e6			0.400851
$388$	63632.1	+	3.63707e6i	0.0214584	+	1.22651i
$389$			1.08421e6i			0.363278i	0.983365	+	0.181639i	$0.0581402\pi$
$389$			1.08421e6i			0.363278i	−0.983365	+	0.181639i	$0.941860\pi$
$390$		0			0
$391$	−3.12994e6			−1.03537
$392$	−4.10553e6	+	107756.i	−1.34944	+	0.0354181i
$393$			1.92815e6i			0.629739i
$394$	−2.01696e6	+	17642.4i	−0.654570	+	0.00572555i
$395$		0			0
$396$	6134.54	+	350637.i	0.00196582	+	0.112362i
$397$	−3.11966e6			−0.993415			−0.496708	−	0.867918i	$-0.665458\pi$
$397$	−3.11966e6			−0.993415			−0.496708	+	0.867918i	$0.665458\pi$
$398$	2.29831e6	−	20103.4i	0.727280	−	0.00636155i
$399$	−439987.			−0.138359
$400$		0			0
$401$	−3.18432e6			−0.988908			−0.494454	−	0.869204i	$-0.664632\pi$
$401$	−3.18432e6			−0.988908			−0.494454	+	0.869204i	$0.664632\pi$
$402$	3.80594e6	−	33290.7i	1.17462	−	0.0102744i
$403$	−758228.			−0.232561
$404$	−12240.7	−	699651.i	−0.00373123	−	0.213269i
$405$		0			0
$406$	6.96449e6	−	60918.7i	2.09688	−	0.0183415i
$407$		−	1.26387e6i		−	0.378195i
$408$	−61550.1	−	2.34508e6i	−0.0183053	−	0.697440i
$409$	−3.76338e6			−1.11242			−0.556211	−	0.831041i	$-0.687745\pi$
$409$	−3.76338e6			−1.11242			−0.556211	+	0.831041i	$0.687745\pi$
$410$		0			0
$411$			3.51499e6i			1.02641i
$412$	87664.2	+	5.01069e6i	0.0254436	+	1.45430i
$413$	−4.11769e6			−1.18790
$414$	16376.7	+	1.87226e6i	0.00469598	+	0.536865i
$415$		0			0
$416$	2.35603e6	−	103105.i	0.667495	−	0.0292109i
$417$		−	3.86143e6i		−	1.08745i
$418$	−100149.	+	876.010i	−0.0280354	+	0.000245227i
$419$			2.73449e6i			0.760924i	0.924797	+	0.380462i	$0.124235\pi$
$419$			2.73449e6i			0.760924i	−0.924797	+	0.380462i	$0.875765\pi$
$420$		0			0
$421$			450371.i			0.123841i	0.998081	+	0.0619206i	$0.0197225\pi$
$421$			450371.i			0.123841i	−0.998081	+	0.0619206i	$0.980277\pi$
$422$	−28828.6	−	3.29581e6i	−0.00788030	−	0.900911i
$423$		−	3.10722e6i		−	0.844346i
$424$	−2.30988e6	+	60626.3i	−0.623987	+	0.0163775i
$425$		0			0
$426$	−3.72043e6	+	32542.8i	−0.993274	+	0.00868821i
$427$	−2.25930e6			−0.599659
$428$	−2.92439e6	+	51163.4i	−0.771659	+	0.0135005i
$429$		−	375919.i		−	0.0986169i
$430$		0			0
$431$	517327.			0.134144			0.0670721	−	0.997748i	$-0.478634\pi$
$431$	517327.			0.134144			0.0670721	+	0.997748i	$0.478634\pi$
$432$	−4.07464e6	+	142619.i	−1.05046	+	0.0367677i
$433$			2.24867e6i			0.576375i	0.957574	+	0.288188i	$0.0930527\pi$
$433$			2.24867e6i			0.576375i	−0.957574	+	0.288188i	$0.906947\pi$
$434$	18313.3	+	2.09366e6i	0.00466706	+	0.533558i
$435$		0			0
$436$	27414.0	+	1.56692e6i	0.00690647	+	0.394759i
$437$	−534716.			−0.133943
$438$	12354.2	+	1.41238e6i	0.00307701	+	0.351777i
$439$	−862979.			−0.213717			−0.106858	−	0.994274i	$-0.534079\pi$
$439$	−862979.			−0.213717			−0.106858	+	0.994274i	$0.534079\pi$
$440$		0			0
$441$	2.89349e6			0.708476
$442$	−24293.9	−	2.77739e6i	−0.00591482	−	0.676208i
$443$	972329.			0.235399			0.117699	−	0.993049i	$-0.462448\pi$
$443$	972329.			0.235399			0.117699	+	0.993049i	$0.462448\pi$
$444$	5.05667e6	−	88468.7i	1.21733	−	0.0212977i
$445$		0			0
$446$	−39039.8	−	4.46320e6i	−0.00929331	−	1.06245i
$447$			5.31682e6i			1.25859i
$448$	−341604.	−	6.50312e6i	−0.0804132	−	1.53083i
$449$	28297.9			0.00662428			0.00331214	−	0.999995i	$-0.498946\pi$
$449$	28297.9			0.00662428			0.00331214	+	0.999995i	$0.498946\pi$
$450$		0			0
$451$		−	1.55516e6i		−	0.360027i
$452$	−86001.5	−	4.91566e6i	−0.0197998	−	1.13171i
$453$	−107034.			−0.0245062
$454$	4.93492e6	−	43165.9i	1.12367	−	0.00982882i
$455$		0			0
$456$	−10515.2	−	400631.i	−0.00236812	−	0.0902261i
$457$		−	456269.i		−	0.102195i	−0.998694	−	0.0510976i	$-0.983728\pi$
$457$		−	456269.i		−	0.102195i	0.998694	−	0.0510976i	$-0.0162720\pi$
$458$	−19993.0	−	2.28569e6i	−0.00445363	−	0.509159i
$459$			4.80187e6i			1.06385i
$460$		0			0
$461$		−	11198.5i		−	0.00245418i	−0.999999	−	0.00122709i	$-0.999609\pi$
$461$		−	11198.5i		−	0.00245418i	0.999999	−	0.00122709i	$-0.000390595\pi$
$462$	−1.03801e6	+	9079.51i	−0.226254	+	0.00197905i
$463$		−	7.93015e6i		−	1.71921i	−0.510959	−	0.859605i	$-0.670710\pi$
$463$		−	7.93015e6i		−	1.71921i	0.510959	−	0.859605i	$-0.329290\pi$
$464$	221913.	+	6.34008e6i	0.0478506	+	1.36710i
$465$		0			0
$466$	−9839.07	−	1.12485e6i	−0.00209889	−	0.239954i
$467$	6.59151e6			1.39860			0.699298	−	0.714830i	$-0.253496\pi$
$467$	6.59151e6			1.39860			0.699298	+	0.714830i	$0.253496\pi$
$468$	−1.66124e6	+	29064.2i	−0.350605	+	0.00613399i
$469$		−	1.24437e7i		−	2.61226i
$470$		0			0
$471$	2.61995e6			0.544179
$472$	−98407.8	−	3.74937e6i	−0.0203317	−	0.774646i
$473$			795754.i			0.163541i
$474$	−1.77320e6	+	15510.3i	−0.362504	+	0.00317084i
$475$		0			0
$476$	−7.66849e6	+	134163.i	−1.55129	+	0.0271404i
$477$	1.62796e6			0.327602
$478$	2.19723e6	−	19219.2i	0.439851	−	0.00384739i
$479$	1.60702e6			0.320023			0.160012	−	0.987115i	$-0.448847\pi$
$479$	1.60702e6			0.320023			0.160012	+	0.987115i	$0.448847\pi$
$480$		0			0
$481$	5.98794e6			1.18009
$482$	−4.04347e6	+	35368.4i	−0.792750	+	0.00693422i
$483$	−5.54213e6			−1.08096
$484$	4.91659e6	−	86017.9i	0.954005	−	0.0166907i
$485$		0			0
$486$	4.75610e6	−	41601.8i	0.913399	−	0.00798954i
$487$			1.81230e6i			0.346264i	0.984899	+	0.173132i	$0.0553888\pi$
$487$			1.81230e6i			0.346264i	−0.984899	+	0.173132i	$0.944611\pi$
$488$	−53994.6	−	2.05721e6i	−0.0102636	−	0.391048i
$489$	−2.88175e6			−0.544985
$490$		0			0
$491$		−	292083.i		−	0.0546768i	−0.999626	−	0.0273384i	$-0.991297\pi$
$491$		−	292083.i		−	0.0546768i	0.999626	−	0.0273384i	$-0.00870317\pi$
$492$	6.22214e6	−	108859.i	1.15885	−	0.0202746i
$493$	7.47164e6			1.38452
$494$	−4150.35	−	474486.i	−0.000765186	−	0.0874794i
$495$		0			0
$496$	−1.90595e6	+	66711.3i	−0.347862	+	0.0121757i
$497$			1.21641e7i			2.20896i
$498$	2.92366e6	−	25573.4i	0.528267	−	0.00462078i
$499$		−	8.47619e6i		−	1.52388i	−0.647650	−	0.761938i	$-0.724248\pi$
$499$		−	8.47619e6i		−	1.52388i	0.647650	−	0.761938i	$-0.275752\pi$
$500$		0			0
$501$			187016.i			0.0332877i
$502$	−78150.6	−	8.93452e6i	−0.0138412	−	1.58238i
$503$			2.07725e6i			0.366074i	0.983106	+	0.183037i	$0.0585929\pi$
$503$			2.07725e6i			0.366074i	−0.983106	+	0.183037i	$0.941407\pi$
$504$	120377.	+	4.58642e6i	0.0211090	+	0.804261i
$505$		0			0
$506$	−1.26149e6	+	11034.3i	−0.219032	+	0.00191589i
$507$	−2.20870e6			−0.381607
$508$	68343.3	+	3.90635e6i	0.0117500	+	0.671602i
$509$		−	739081.i		−	0.126444i	−0.997999	−	0.0632219i	$-0.979862\pi$
$509$		−	739081.i		−	0.126444i	0.997999	−	0.0632219i	$-0.0201376\pi$
$510$		0			0
$511$	4.61784e6			0.782324
$512$	5.91327e6	−	466465.i	0.996903	−	0.0786401i
$513$			820347.i			0.137627i
$514$	−89331.9	−	1.02128e7i	−0.0149142	−	1.70505i
$515$		0			0
$516$	−3.18377e6	+	55701.5i	−0.526403	+	0.00920964i
$517$	2.09358e6			0.344480
$518$	−144626.	−	1.65342e7i	−0.0236821	−	2.70744i
$519$	−5.74201e6			−0.935719
$520$		0			0
$521$	−7.18449e6			−1.15958			−0.579791	−	0.814765i	$-0.696866\pi$
$521$	−7.18449e6			−1.15958			−0.579791	+	0.814765i	$0.696866\pi$
$522$	−39093.8	−	4.46937e6i	−0.00627959	−	0.717911i
$523$	1.94687e6			0.311231			0.155616	−	0.987818i	$-0.450264\pi$
$523$	1.94687e6			0.311231			0.155616	+	0.987818i	$0.450264\pi$
$524$	100444.	+	5.74115e6i	0.0159807	+	0.913421i
$525$		0			0
$526$	9178.48	+	1.04932e6i	0.00144646	+	0.165366i
$527$			2.24612e6i			0.352295i
$528$	−33074.6	−	944945.i	−0.00516308	−	0.147510i
$529$	−299003.			−0.0464554
$530$		0			0
$531$			2.64247e6i			0.406700i
$532$	−1.31008e6	+	22920.4i	−0.200686	+	0.00351109i
$533$	7.36804e6			1.12340
$534$	−1.83070e6	+	16013.2i	−0.277820	+	0.00243010i
$535$		0			0
$536$	1.13306e7	−	297388.i	1.70350	−	0.0447108i
$537$		−	3.68389e6i		−	0.551278i
$538$	55720.5	+	6.37021e6i	0.00829964	+	0.948851i
$539$			1.94958e6i			0.289047i
$540$		0			0
$541$		−	1.18585e7i		−	1.74195i	−0.491330	−	0.870973i	$-0.663489\pi$
$541$		−	1.18585e7i		−	1.74195i	0.491330	−	0.870973i	$-0.336511\pi$
$542$	891543.	−	7798.37i	0.130360	−	0.00114026i
$543$			6.37445e6i			0.927776i
$544$	−305431.	−	6.97935e6i	−0.0442502	−	1.01116i
$545$		0			0
$546$	−43016.8	−	4.91787e6i	−0.00617528	−	0.705985i
$547$	−2.10343e6			−0.300580			−0.150290	−	0.988642i	$-0.548021\pi$
$547$	−2.10343e6			−0.300580			−0.150290	+	0.988642i	$0.548021\pi$
$548$	183107.	+	1.04660e7i	0.0260468	+	1.48878i
$549$			1.44988e6i			0.205306i
$550$		0			0
$551$	1.27645e6			0.179112
$552$	−132450.	−	5.04640e6i	−0.0185014	−	0.704910i
$553$			5.79755e6i			0.806179i
$554$	1.09462e7	−	95746.6i	1.51526	−	0.0132541i
$555$		0			0
$556$	−201155.	−	1.14976e7i	−0.0275958	−	1.57731i
$557$	4.61967e6			0.630918			0.315459	−	0.948939i	$-0.397842\pi$
$557$	4.61967e6			0.630918			0.315459	+	0.948939i	$0.397842\pi$
$558$	1.34358e6	−	11752.4i	0.182675	−	0.00159786i
$559$	−3.77012e6			−0.510300
$560$		0			0
$561$	−1.11360e6			−0.149390
$562$	2.22929e6	−	19499.7i	0.297732	−	0.00260428i
$563$	−1.23357e7			−1.64019			−0.820096	−	0.572227i	$-0.806080\pi$
$563$	−1.23357e7			−1.64019			−0.820096	+	0.572227i	$0.806080\pi$
$564$	146547.	+	8.37632e6i	0.0193990	+	1.10881i
$565$		0			0
$566$	3.04662e6	−	26648.9i	0.399740	−	0.00349654i
$567$			2.34367e6i			0.306154i
$568$	−1.10760e7	+	290707.i	−1.44050	+	0.0378081i
$569$	−7.85222e6			−1.01674			−0.508372	−	0.861138i	$-0.669753\pi$
$569$	−7.85222e6			−1.01674			−0.508372	+	0.861138i	$0.669753\pi$
$570$		0			0
$571$		−	1.14825e7i		−	1.47383i	−0.675984	−	0.736916i	$-0.736281\pi$
$571$		−	1.14825e7i		−	1.47383i	0.675984	−	0.736916i	$-0.263719\pi$
$572$	−19582.9	−	1.11931e6i	−0.00250257	−	0.143041i
$573$	−15569.8			−0.00198106
$574$	−177959.	−	2.03451e7i	−0.0225445	−	2.57738i
$575$		0			0
$576$	−4.17330e6	+	219220.i	−0.524111	+	0.0275311i
$577$			1.10508e7i			1.38183i	0.722938	+	0.690913i	$0.242791\pi$
$577$			1.10508e7i			1.38183i	−0.722938	+	0.690913i	$0.757209\pi$
$578$	−195920.	+	1713.72i	−0.0243926	+	0.000213363i
$579$			9.54765e6i			1.18359i
$580$		0			0
$581$		−	9.55901e6i		−	1.17482i
$582$	60438.5	+	6.90960e6i	0.00739616	+	0.845561i
$583$			1.09689e6i			0.133656i
$584$	110361.	+	4.20479e6i	0.0133901	+	0.510166i
$585$		0			0
$586$	−7.10823e6	+	62176.0i	−0.855101	+	0.00747961i
$587$	1.22974e6			0.147305			0.0736524	−	0.997284i	$-0.476534\pi$
$587$	1.22974e6			0.147305			0.0736524	+	0.997284i	$0.476534\pi$
$588$	−7.80016e6	+	136467.i	−0.930379	+	0.0162774i
$589$			383725.i			0.0455756i
$590$		0			0
$591$	−3.83146e6			−0.451228
$592$	1.50518e7	−	526838.i	1.76516	−	0.0617835i
$593$			4.14520e6i			0.484071i	0.970267	+	0.242035i	$0.0778150\pi$
$593$			4.14520e6i			0.484071i	−0.970267	+	0.242035i	$0.922185\pi$
$594$	16928.6	+	1.93535e6i	0.00196859	+	0.225057i
$595$		0			0
$596$	276971.	+	1.58310e7i	0.0319387	+	1.82555i
$597$	4.36593e6			0.501350
$598$	−52278.3	−	5.97669e6i	−0.00597818	−	0.683451i
$599$	−1.54313e7			−1.75726			−0.878629	−	0.477505i	$-0.841541\pi$
$599$	−1.54313e7			−1.75726			−0.878629	+	0.477505i	$0.841541\pi$
$600$		0			0
$601$	−1.20526e7			−1.36111			−0.680556	−	0.732696i	$-0.738262\pi$
$601$	−1.20526e7			−1.36111			−0.680556	+	0.732696i	$0.738262\pi$
$602$	91059.0	+	1.04103e7i	0.0102407	+	1.17077i
$603$	−7.98556e6			−0.894359
$604$	−318697.	+	5575.74i	−0.0355456	+	0.000621886i
$605$		0			0
$606$	−11626.4	−	1.32918e6i	−0.00128606	−	0.147028i
$607$		−	7.95296e6i		−	0.876107i	−0.898949	−	0.438053i	$-0.855668\pi$
$607$		−	7.95296e6i		−	0.876107i	0.898949	−	0.438053i	$-0.144332\pi$
$608$	−52179.5	−	1.19235e6i	−0.00572454	−	0.130811i
$609$	1.32299e7			1.44549
$610$		0			0
$611$			9.91895e6i			1.07489i
$612$	86097.7	+	4.92115e6i	0.00929208	+	0.531115i
$613$	1.04301e7			1.12108			0.560538	−	0.828128i	$-0.310594\pi$
$613$	1.04301e7			1.12108			0.560538	+	0.828128i	$0.310594\pi$
$614$	1.28632e6	−	11251.5i	0.137699	−	0.00120445i
$615$		0			0
$616$	−3.09024e6	+	81107.9i	−0.328126	+	0.00861215i
$617$			6.91606e6i			0.731384i	0.930736	+	0.365692i	$0.119168\pi$
$617$			6.91606e6i			0.731384i	−0.930736	+	0.365692i	$0.880832\pi$
$618$	83264.5	+	9.51916e6i	0.00876978	+	1.00260i
$619$			1.15145e7i			1.20786i	0.797037	+	0.603931i	$0.206400\pi$
$619$			1.15145e7i			1.20786i	−0.797037	+	0.603931i	$0.793600\pi$
$620$		0			0
$621$			1.03332e7i			1.07524i
$622$	6.42196e6	−	56173.2i	0.665567	−	0.00582175i
$623$			5.98552e6i			0.617848i
$624$	4.47695e6	−	156700.i	0.460279	−	0.0161105i
$625$		0			0
$626$	−115156.	−	1.31651e7i	−0.0117449	−	1.34273i
$627$	−190246.			−0.0193262
$628$	7.80102e6	−	136482.i	0.789318	−	0.0138095i
$629$		−	1.77383e7i		−	1.78766i
$630$		0			0
$631$	5.76766e6			0.576669			0.288334	−	0.957530i	$-0.406899\pi$
$631$	5.76766e6			0.576669			0.288334	+	0.957530i	$0.406899\pi$
$632$	−5.27897e6	+	138554.i	−0.525723	+	0.0137984i
$633$		−	6.26081e6i		−	0.621042i
$634$	8.49695e6	−	74323.2i	0.839537	−	0.00734347i
$635$		0			0
$636$	−4.38858e6	+	76780.2i	−0.430211	+	0.00752673i
$637$	−9.23668e6			−0.901919
$638$	3.01138e6	−	26340.6i	0.292896	−	0.00256197i
$639$	7.80614e6			0.756283
$640$		0			0
$641$	−518990.			−0.0498901			−0.0249450	−	0.999689i	$-0.507941\pi$
$641$	−518990.			−0.0498901			−0.0249450	+	0.999689i	$0.507941\pi$
$642$	−5.55566e6	+	48595.6i	−0.531984	+	0.00465328i
$643$	6.52874e6			0.622733			0.311367	−	0.950290i	$-0.399213\pi$
$643$	6.52874e6			0.622733			0.311367	+	0.950290i	$0.399213\pi$
$644$	−1.65019e7	+	288708.i	−1.56790	+	0.0274311i
$645$		0			0
$646$	−1.40558e6	+	12294.7i	−0.132518	+	0.00115914i
$647$			6.41651e6i			0.602613i	0.953527	+	0.301306i	$0.0974227\pi$
$647$			6.41651e6i			0.602613i	−0.953527	+	0.301306i	$0.902577\pi$
$648$	−2.13404e6	+	56011.0i	−0.199648	+	0.00524005i
$649$	−1.78045e6			−0.165927
$650$		0			0
$651$			3.97717e6i			0.367808i
$652$	−8.58053e6	+	150120.i	−0.790487	+	0.0138299i
$653$	−9.11065e6			−0.836116			−0.418058	−	0.908420i	$-0.637289\pi$
$653$	−9.11065e6			−0.836116			−0.418058	+	0.908420i	$0.637289\pi$
$654$	26038.2	+	2.97680e6i	0.00238049	+	0.272148i
$655$		0			0
$656$	1.85210e7	−	648264.i	1.68037	−	0.0588155i
$657$		−	2.96344e6i		−	0.267844i
$658$	2.73888e7	−	239571.i	2.46608	−	0.0215709i
$659$			1.97306e7i			1.76981i	0.465775	+	0.884903i	$0.345776\pi$
$659$			1.97306e7i			1.76981i	−0.465775	+	0.884903i	$0.654224\pi$
$660$		0			0
$661$		−	9.04530e6i		−	0.805228i	−0.915370	−	0.402614i	$-0.868102\pi$
$661$		−	9.04530e6i		−	0.805228i	0.915370	−	0.402614i	$-0.131898\pi$
$662$	−134818.	−	1.54130e7i	−0.0119565	−	1.36692i
$663$		−	5.27599e6i		−	0.466144i
$664$	8.70398e6	−	228449.i	0.766122	−	0.0201080i
$665$		0			0
$666$	−1.06106e7	+	92811.7i	−0.926949	+	0.00810806i
$667$	1.60783e7			1.39935
$668$	9742.28	+	556847.i	0.000844733	+	0.0482831i
$669$		−	8.47840e6i		−	0.732401i
$670$		0			0
$671$	−976900.			−0.0837614
$672$	−540821.	−	1.23582e7i	−0.0461987	−	1.05568i
$673$		−	1.11387e7i		−	0.947974i	−0.880532	−	0.473987i	$-0.842814\pi$
$673$		−	1.11387e7i		−	0.947974i	0.880532	−	0.473987i	$-0.157186\pi$
$674$	−101071.	−	1.15548e7i	−0.00856989	−	0.979747i
$675$		0			0
$676$	−6.57648e6	+	115058.i	−0.553512	+	0.00968393i
$677$	−1.13338e7			−0.950395			−0.475198	−	0.879879i	$-0.657623\pi$
$677$	−1.13338e7			−0.950395			−0.475198	+	0.879879i	$0.657623\pi$
$678$	−81685.3	−	9.33862e6i	−0.00682448	−	0.780204i
$679$	2.25912e7			1.88046
$680$		0			0
$681$	9.37449e6			0.774604
$682$	7918.51	+	905279.i	0.000651902	+	0.0745283i
$683$	−1.06005e7			−0.869514			−0.434757	−	0.900548i	$-0.643166\pi$
$683$	−1.06005e7			−0.869514			−0.434757	+	0.900548i	$0.643166\pi$
$684$	14708.8	+	840725.i	0.00120209	+	0.0687090i
$685$		0			0
$686$	57827.2	+	6.61105e6i	0.00469161	+	0.536365i
$687$		−	4.34195e6i		−	0.350988i
$688$	−9.47691e6	+	331707.i	−0.763301	+	0.0267167i
$689$	−5.19681e6			−0.417051
$690$		0			0
$691$			1.18528e7i			0.944331i	0.881510	+	0.472165i	$0.156527\pi$
$691$			1.18528e7i			0.944331i	−0.881510	+	0.472165i	$0.843473\pi$
$692$	−1.70971e7	+	299120.i	−1.35724	+	0.0237455i
$693$	2.17793e6			0.172271
$694$	−1.45633e7	+	127386.i	−1.14779	+	0.0100398i
$695$		0			0
$696$	316179.	+	1.20465e7i	0.0247406	+	0.942625i
$697$		−	2.18266e7i		−	1.70178i
$698$	97963.6	+	1.11996e7i	0.00761073	+	0.870092i
$699$		−	2.13678e6i		−	0.165412i
$700$		0			0
$701$			1.42728e7i			1.09702i	0.836144	+	0.548511i	$0.184805\pi$
$701$			1.42728e7i			1.09702i	−0.836144	+	0.548511i	$0.815195\pi$
$702$	−9.16928e6	+	80204.1i	−0.702251	+	0.00614262i
$703$		−	3.03039e6i		−	0.231265i
$704$	−147706.	−	2.81189e6i	−0.0112322	−	0.213829i
$705$		0			0
$706$	−50899.1	−	5.81901e6i	−0.00384325	−	0.439377i
$707$	−4.34578e6			−0.326979
$708$	−124628.	−	7.12349e6i	−0.00934403	−	0.534084i
$709$		−	1.40052e7i		−	1.04635i	−0.852227	−	0.523173i	$-0.824748\pi$
$709$		−	1.40052e7i		−	1.04635i	0.852227	−	0.523173i	$-0.175252\pi$
$710$		0			0
$711$	3.72050e6			0.276012
$712$	−5.45013e6	+	143047.i	−0.402909	+	0.0105749i
$713$			4.83345e6i			0.356069i
$714$	−1.45684e7	+	127430.i	−1.06946	+	0.00935462i
$715$		0			0
$716$	−191906.	−	1.09689e7i	−0.0139896	−	0.799616i
$717$	4.17391e6			0.303211
$718$	5.53895e6	−	48449.5i	0.400974	−	0.00350734i
$719$	−7.28309e6			−0.525404			−0.262702	−	0.964877i	$-0.584614\pi$
$719$	−7.28309e6			−0.525404			−0.262702	+	0.964877i	$0.584614\pi$
$720$		0			0
$721$	3.11232e7			2.22970
$722$	1.37663e7	−	120414.i	0.982818	−	0.00859675i
$723$	−7.68107e6			−0.546482
$724$	332066.	+	1.89802e7i	0.0235439	+	1.34572i
$725$		0			0
$726$	9.34039e6	−	81700.8i	0.657693	−	0.00575287i
$727$		−	3.41888e6i		−	0.239910i	−0.992779	−	0.119955i	$-0.961725\pi$
$727$		−	3.41888e6i		−	0.239910i	0.992779	−	0.119955i	$-0.0382750\pi$
$728$	−384272.	−	1.46409e7i	−0.0268727	−	1.02386i
$729$	1.19005e7			0.829368
$730$		0			0
$731$			1.11683e7i			0.773028i
$732$	−68381.4	−	3.90853e6i	−0.00471694	−	0.269610i
$733$	2.11502e6			0.145397			0.0726983	−	0.997354i	$-0.476839\pi$
$733$	2.11502e6			0.145397			0.0726983	+	0.997354i	$0.476839\pi$
$734$	53397.5	+	6.10463e6i	0.00365831	+	0.418234i
$735$		0			0
$736$	−657259.	−	1.50189e7i	−0.0447242	−	1.02199i
$737$		−	5.38051e6i		−	0.364884i
$738$	−1.30562e7	+	114203.i	−0.882420	+	0.00771857i
$739$		−	4.97420e6i		−	0.335052i	−0.985868	−	0.167526i	$-0.946422\pi$
$739$		−	4.97420e6i		−	0.335052i	0.985868	−	0.167526i	$-0.0535778\pi$
$740$		0			0
$741$		−	901345.i		−	0.0603039i
$742$	125518.	+	1.43497e7i	0.00836941	+	0.956828i
$743$			6.04483e6i			0.401709i	0.979621	+	0.200855i	$0.0643719\pi$
$743$			6.04483e6i			0.401709i	−0.979621	+	0.200855i	$0.935628\pi$
$744$	−3.62142e6	+	95049.6i	−0.239854	+	0.00629532i
$745$		0			0
$746$	2.06632e7	−	180742.i	1.35941	−	0.0118908i
$747$	−6.13437e6			−0.402225
$748$	−3.31578e6	+	58011.0i	−0.216686	+	0.00379102i
$749$			1.81644e7i			1.18309i
$750$		0			0
$751$	−2.14521e7			−1.38794			−0.693970	−	0.720004i	$-0.744140\pi$
$751$	−2.14521e7			−1.38794			−0.693970	+	0.720004i	$0.744140\pi$
$752$	872701.	+	2.49332e7i	0.0562757	+	1.60780i
$753$		−	1.69722e7i		−	1.09082i
$754$	124796.	+	1.42673e7i	0.00799418	+	0.913929i
$755$		0			0
$756$	442928.	+	2.53168e7i	0.0281857	+	1.61103i
$757$	−1.22790e7			−0.778794			−0.389397	−	0.921070i	$-0.627317\pi$
$757$	−1.22790e7			−0.778794			−0.389397	+	0.921070i	$0.627317\pi$
$758$	148146.	+	1.69367e7i	0.00936520	+	1.07067i
$759$	−2.39636e6			−0.150990
$760$		0			0
$761$	−1.38648e7			−0.867867			−0.433933	−	0.900945i	$-0.642875\pi$
$761$	−1.38648e7			−0.867867			−0.433933	+	0.900945i	$0.642875\pi$
$762$	64913.3	+	7.42117e6i	0.00404992	+	0.463004i
$763$	9.73273e6			0.605234
$764$	−46359.8	+	811.084i	−0.00287348	+	5.02728e-5i
$765$		0			0
$766$	205711.	+	2.35177e7i	0.0126673	+	1.44818i
$767$		−	8.43539e6i		−	0.517746i
$768$	1.12399e7	−	787792.i	0.687636	−	0.0481957i
$769$	−1.92248e6			−0.117232			−0.0586158	−	0.998281i	$-0.518669\pi$
$769$	−1.92248e6			−0.117232			−0.0586158	+	0.998281i	$0.518669\pi$
$770$		0			0
$771$		−	1.94005e7i		−	1.17538i
$772$	497369.	+	2.84285e7i	0.0300355	+	1.71676i
$773$	2.66728e7			1.60554			0.802768	−	0.596291i	$-0.203360\pi$
$773$	2.66728e7			1.60554			0.802768	+	0.596291i	$0.203360\pi$
$774$	6.68065e6	−	58435.9i	0.400836	−	0.00350613i
$775$		0			0
$776$	539902.	+	2.05704e7i	0.0321855	+	1.22628i
$777$		−	3.14088e7i		−	1.86638i
$778$	53645.4	+	6.13298e6i	0.00317749	+	0.363264i
$779$		−	3.72883e6i		−	0.220155i
$780$		0			0
$781$			5.25963e6i			0.308551i
$782$	−1.77049e7	+	154866.i	−1.03533	+	0.00905604i
$783$		−	2.46669e7i		−	1.43784i
$784$	−2.32182e7	+	812672.i	−1.34908	+	0.0472199i
$785$		0			0
$786$	95402.8	+	1.09069e7i	0.00550814	+	0.629714i
$787$	−7.22979e6			−0.416092			−0.208046	−	0.978119i	$-0.566710\pi$
$787$	−7.22979e6			−0.416092			−0.208046	+	0.978119i	$0.566710\pi$
$788$	−1.14083e7	+	199593.i	−0.654495	+	0.0114507i
$789$			1.99332e6i			0.113995i
$790$		0			0
$791$	−3.05329e7			−1.73511
$792$	52050.0	+	1.98312e6i	0.00294854	+	0.112341i
$793$		−	4.62835e6i		−	0.261362i
$794$	−1.76468e7	+	154357.i	−0.993377	+	0.00868911i
$795$		0			0
$796$	1.29997e7	−	227436.i	0.727196	−	0.0127226i
$797$	4.41257e6			0.246062			0.123031	−	0.992403i	$-0.460738\pi$
$797$	4.41257e6			0.246062			0.123031	+	0.992403i	$0.460738\pi$
$798$	−2.48884e6	+	21770.0i	−0.138354	+	0.00121019i
$799$	2.93832e7			1.62829
$800$		0			0
$801$	3.84113e6			0.211533
$802$	−1.80126e7	+	157557.i	−0.988871	+	0.00864969i
$803$	1.99671e6			0.109276
$804$	2.15272e7	−	376627.i	1.17448	−	0.0205481i
$805$		0			0
$806$	−4.28902e6	+	37516.2i	−0.232552	+	0.00203414i
$807$			1.21010e7i			0.654090i
$808$	−103859.	−	3.95707e6i	−0.00559649	−	0.213228i
$809$	−6.04388e6			−0.324672			−0.162336	−	0.986736i	$-0.551903\pi$
$809$	−6.04388e6			−0.324672			−0.162336	+	0.986736i	$0.551903\pi$
$810$		0			0
$811$			2.40664e7i			1.28487i	0.766340	+	0.642435i	$0.222076\pi$
$811$			2.40664e7i			1.28487i	−0.766340	+	0.642435i	$0.777924\pi$
$812$	3.93926e7	−	689190.i	2.09664	−	0.0366816i
$813$	1.69360e6			0.0898636
$814$	−62534.7	−	7.14924e6i	−0.00330796	−	0.378180i
$815$		0			0
$816$	−464198.	−	1.32622e7i	−0.0244050	−	0.697253i
$817$			1.90799e6i			0.100005i
$818$	−2.12881e7	+	186208.i	−1.11238	+	0.00973003i
$819$			1.03186e7i			0.537540i
$820$		0			0
$821$			1.16527e7i			0.603350i	0.953411	+	0.301675i	$0.0975458\pi$
$821$			1.16527e7i			0.603350i	−0.953411	+	0.301675i	$0.902454\pi$
$822$	173917.	+	1.98830e7i	0.00897767	+	1.02637i
$823$		−	161156.i		−	0.00829369i	−0.999991	−	0.00414684i	$-0.998680\pi$
$823$		−	161156.i		−	0.00829369i	0.999991	−	0.00414684i	$-0.00131999\pi$
$824$	743808.	+	2.83393e7i	0.0381630	+	1.45402i
$825$		0			0
$826$	−2.32923e7	+	203738.i	−1.18785	+	0.0103902i
$827$	−2.85594e7			−1.45206			−0.726031	−	0.687661i	$-0.758637\pi$
$827$	−2.85594e7			−1.45206			−0.726031	+	0.687661i	$0.758637\pi$
$828$	185275.	+	1.05899e7i	0.00939161	+	0.536803i
$829$			1.49564e7i			0.755859i	0.925834	+	0.377929i	$0.123364\pi$
$829$			1.49564e7i			0.755859i	−0.925834	+	0.377929i	$0.876636\pi$
$830$		0			0
$831$	2.07936e7			1.04455
$832$	1.33221e7	−	699800.i	0.667214	−	0.0350482i
$833$			2.73621e7i			1.36627i
$834$	−191059.	−	2.18427e7i	−0.00951158	−	1.08740i
$835$		0			0
$836$	−566465.	+	9910.54i	−0.0280322	+	0.000490435i
$837$	7.41536e6			0.365863
$838$	135299.	+	1.54680e7i	0.00665558	+	0.760895i
$839$	1.76445e7			0.865374			0.432687	−	0.901544i	$-0.357565\pi$
$839$	1.76445e7			0.865374			0.432687	+	0.901544i	$0.357565\pi$
$840$		0			0
$841$	−1.78703e7			−0.871246
$842$	22283.8	+	2.54758e6i	0.00108320	+	0.123836i
$843$	4.23482e6			0.205242
$844$	−326146.	−	1.86418e7i	−0.0157600	−	0.900807i
$845$		0			0
$846$	−153742.	−	1.75764e7i	−0.00738525	−	0.844314i
$847$		−	3.05387e7i		−	1.46266i
$848$	−1.30632e7	+	457232.i	−0.623820	+	0.0218347i
$849$	5.78744e6			0.275561
$850$		0			0
$851$		−	3.81711e7i		−	1.80681i
$852$	−2.10435e7	+	368165.i	−0.993160	+	0.0173758i
$853$	−3.43356e7			−1.61574			−0.807870	−	0.589361i	$-0.799380\pi$
$853$	−3.43356e7			−1.61574			−0.807870	+	0.589361i	$0.799380\pi$
$854$	−1.27801e7	+	111788.i	−0.599637	+	0.00524505i
$855$		0			0
$856$	−1.65397e7	+	434108.i	−0.771512	+	0.0202495i
$857$			1.27760e7i			0.594216i	0.954844	+	0.297108i	$0.0960221\pi$
$857$			1.27760e7i			0.594216i	−0.954844	+	0.297108i	$0.903978\pi$
$858$	−18600.1	−	2.12644e6i	−0.000862573	−	0.0986131i
$859$		−	3.23768e7i		−	1.49710i	−0.663077	−	0.748551i	$-0.730750\pi$
$859$		−	3.23768e7i		−	1.49710i	0.663077	−	0.748551i	$-0.269250\pi$
$860$		0			0
$861$		−	3.86480e7i		−	1.77672i
$862$	2.92633e6	−	25596.8i	0.134139	−	0.00117332i
$863$			2.57138e7i			1.17527i	0.809125	+	0.587637i	$0.199942\pi$
$863$			2.57138e7i			1.17527i	−0.809125	+	0.587637i	$0.800058\pi$
$864$	−2.30417e7	+	1.00835e6i	−1.05010	+	0.0459544i
$865$		0			0
$866$	111261.	+	1.27199e7i	0.00504139	+	0.576353i
$867$	−372174.			−0.0168151
$868$	207184.	+	1.18422e7i	0.00933376	+	0.533497i
$869$			2.50680e6i			0.112608i
$870$		0			0
$871$	2.54917e7			1.13856
$872$	232601.	+	8.86217e6i	0.0103590	+	0.394683i
$873$		−	1.44976e7i		−	0.643814i
$874$	−3.02469e6	+	26457.1i	−0.133938	+	0.00117156i
$875$		0			0
$876$	139766.	+	7.98874e6i	0.00615378	+	0.351737i
$877$	4.69271e6			0.206027			0.103014	−	0.994680i	$-0.467151\pi$
$877$	4.69271e6			0.206027			0.103014	+	0.994680i	$0.467151\pi$
$878$	−4.88156e6	+	42699.2i	−0.213709	+	0.00186932i
$879$	−1.35030e7			−0.589464
$880$		0			0
$881$	446984.			0.0194023			0.00970113	−	0.999953i	$-0.496912\pi$
$881$	446984.			0.0194023			0.00970113	+	0.999953i	$0.496912\pi$
$882$	1.63674e7	−	143166.i	0.708449	−	0.00619683i
$883$	3.04436e7			1.31400			0.656999	−	0.753892i	$-0.271826\pi$
$883$	3.04436e7			1.31400			0.656999	+	0.753892i	$0.271826\pi$
$884$	−274844.	−	1.57095e7i	−0.0118292	−	0.676131i
$885$		0			0
$886$	5.50011e6	−	48109.7i	0.235390	−	0.00205896i
$887$			1.40477e7i			0.599508i	0.954016	+	0.299754i	$0.0969046\pi$
$887$			1.40477e7i			0.599508i	−0.954016	+	0.299754i	$0.903095\pi$
$888$	2.85994e7	−	750634.i	1.21709	−	0.0319445i
$889$	2.42638e7			1.02968
$890$		0			0
$891$			1.01338e6i			0.0427640i
$892$	−441668.	−	2.52448e7i	−0.0185859	−	1.06233i
$893$	5.01980e6			0.210648
$894$	263070.	+	3.00753e7i	0.0110085	+	1.25854i
$895$		0			0
$896$	−2.25409e6	−	3.67689e7i	−0.0937998	−	1.53007i
$897$		−	1.13535e7i		−	0.471137i
$898$	160071.	−	1400.15i	0.00662402	−	5.79406e-5i
$899$		−	1.15382e7i		−	0.476145i
$900$		0			0
$901$			1.53947e7i			0.631769i
$902$	−76947.8	−	8.79700e6i	−0.00314905	−	0.360013i
$903$			1.97756e7i			0.807067i
$904$	−729701.	−	2.78018e7i	−0.0296978	−	1.13149i
$905$		0			0
$906$	−605451.	+	5295.91i	−0.0245052	+	0.000214348i
$907$	3.03623e7			1.22551			0.612755	−	0.790273i	$-0.290061\pi$
$907$	3.03623e7			1.22551			0.612755	+	0.790273i	$0.290061\pi$
$908$	2.79129e7	−	488348.i	1.12354	−	0.0196569i
$909$			2.78885e6i			0.111948i
$910$		0			0
$911$	−1.87844e7			−0.749896			−0.374948	−	0.927046i	$-0.622339\pi$
$911$	−1.87844e7			−0.749896			−0.374948	+	0.927046i	$0.622339\pi$
$912$	−79303.2	−	2.26570e6i	−0.00315721	−	0.0902020i
$913$		−	4.13322e6i		−	0.164101i
$914$	−22575.7	−	2.58095e6i	−0.000893871	−	0.102191i
$915$		0			0
$916$	−226186.	−	1.29283e7i	−0.00890693	−	0.509100i
$917$	3.56604e7			1.40043
$918$	237591.	+	2.71624e7i	0.00930515	+	1.06381i
$919$	−4.38053e7			−1.71095			−0.855476	−	0.517842i	$-0.826735\pi$
$919$	−4.38053e7			−1.71095			−0.855476	+	0.517842i	$0.826735\pi$
$920$		0			0
$921$	2.44353e6			0.0949224
$922$	−554.087	−	63345.6i	−2.14660e−5	−	0.00245408i
$923$	−2.49190e7			−0.962779
$924$	−5.87119e6	+	102719.i	−0.226228	+	0.00395796i
$925$		0			0
$926$	−392375.	−	4.48580e7i	−0.0150374	−	1.71914i
$927$		−	1.99729e7i		−	0.763383i
$928$	1.56898e6	+	3.58525e7i	0.0598063	+	1.36663i
$929$	1.88925e7			0.718208			0.359104	−	0.933298i	$-0.383082\pi$
$929$	1.88925e7			0.718208			0.359104	+	0.933298i	$0.383082\pi$
$930$		0			0
$931$			4.67452e6i			0.176751i
$932$	−111312.	−	6.36236e6i	−0.00419762	−	0.239926i
$933$	1.21993e7			0.458809
$934$	3.72858e7	−	326140.i	1.39854	−	0.0122331i
$935$		0			0
$936$	−9.39561e6	+	246602.i	−0.350538	+	0.00920040i
$937$			3.00651e7i			1.11870i	0.828931	+	0.559350i	$0.188949\pi$
$937$			3.00651e7i			1.11870i	−0.828931	+	0.559350i	$0.811051\pi$
$938$	−615698.	−	7.03892e7i	−0.0228486	−	2.61216i
$939$		−	2.50087e7i		−	0.925609i
$940$		0			0
$941$			368874.i			0.0135801i	0.999977	+	0.00679006i	$0.00216136\pi$
$941$			368874.i			0.0135801i	−0.999977	+	0.00679006i	$0.997839\pi$
$942$	1.48201e7	−	129632.i	0.544158	−	0.00475977i
$943$		−	4.69689e7i		−	1.72001i
$944$	−742172.	−	2.12040e7i	−0.0271066	−	0.774439i
$945$		0			0
$946$	39373.0	+	4.50129e6i	0.00143044	+	0.163535i
$947$	3.31548e6			0.120135			0.0600677	−	0.998194i	$-0.480868\pi$
$947$	3.31548e6			0.120135			0.0600677	+	0.998194i	$0.480868\pi$
$948$	−1.00296e7	+	175472.i	−0.362462	+	0.00634143i
$949$			9.45999e6i			0.340977i
$950$		0			0
$951$	1.61410e7			0.578735
$952$	−4.33712e7	+	1.13834e6i	−1.55099	+	0.0407081i
$953$			1.89980e7i			0.677604i	0.940858	+	0.338802i	$0.110022\pi$
$953$			1.89980e7i			0.677604i	−0.940858	+	0.338802i	$0.889978\pi$
$954$	9.20875e6	−	80549.4i	0.327589	−	0.00286544i
$955$		0			0
$956$	1.24280e7	−	217433.i	0.439800	−	0.00769449i
$957$	5.72049e6			0.201908
$958$	9.09032e6	−	79513.4i	0.320011	−	0.00279915i
$959$	6.50082e7			2.28256
$960$		0			0
$961$	−2.51605e7			−0.878844
$962$	3.38716e7	−	296276.i	1.18004	−	0.0103219i
$963$	1.16568e7			0.405054
$964$	−2.28707e7	+	400132.i	−0.792659	+	0.0138679i
$965$		0			0
$966$	−3.13498e7	+	274218.i	−1.08092	+	0.00945482i
$967$		−	1.00131e7i		−	0.344354i	−0.985066	−	0.172177i	$-0.944920\pi$
$967$		−	1.00131e7i		−	0.344354i	0.985066	−	0.172177i	$-0.0550800\pi$
$968$	2.78071e7	−	729839.i	0.953823	−	0.0250345i
$969$	−2.67008e6			−0.0913514
$970$		0			0
$971$		−	2.66607e6i		−	0.0907453i	−0.998970	−	0.0453726i	$-0.985552\pi$
$971$		−	2.66607e6i		−	0.0907453i	0.998970	−	0.0453726i	$-0.0144475\pi$
$972$	2.69015e7	−	470653.i	0.913294	−	0.0159785i
$973$	−7.14155e7			−2.41830
$974$	89670.6	+	1.02515e7i	0.00302867	+	0.346251i
$975$		0			0
$976$	−407217.	−	1.16342e7i	−0.0136836	−	0.390943i
$977$			3.15935e6i			0.105891i	0.998597	+	0.0529457i	$0.0168610\pi$
$977$			3.15935e6i			0.105891i	−0.998597	+	0.0529457i	$0.983139\pi$
$978$	−1.63010e7	+	142586.i	−0.544964	+	0.00476682i
$979$			2.58808e6i			0.0863021i
$980$		0			0
$981$		−	6.24586e6i		−	0.207214i
$982$	−14451.9	−	1.65221e6i	−0.000478242	−	0.0546747i
$983$			2.50171e6i			0.0825758i	0.999147	+	0.0412879i	$0.0131461\pi$
$983$			2.50171e6i			0.0825758i	−0.999147	+	0.0412879i	$0.986854\pi$
$984$	3.51910e7	−	923640.i	1.15863	−	0.0304099i
$985$		0			0
$986$	4.22644e7	−	369688.i	1.38447	−	0.0121100i
$987$	5.20284e7			1.69999
$988$	−46954.0	−	2.68379e6i	−0.00153031	−	0.0874694i
$989$			2.40333e7i			0.781307i
$990$		0			0
$991$	4.14173e7			1.33967			0.669835	−	0.742510i	$-0.266365\pi$
$991$	4.14173e7			1.33967			0.669835	+	0.742510i	$0.266365\pi$
$992$	−1.07780e7	+	471666.i	−0.347743	+	0.0152179i
$993$		−	2.92790e7i		−	0.942286i
$994$	601864.	+	6.88078e7i	0.0193211	+	2.20888i
$995$		0			0
$996$	1.65368e7	−	289319.i	0.528207	−	0.00924120i
$997$	−3.80654e7			−1.21281			−0.606405	−	0.795156i	$-0.707389\pi$
$997$	−3.80654e7			−1.21281			−0.606405	+	0.795156i	$0.707389\pi$
$998$	−419392.	−	4.79468e7i	−0.0133289	−	1.52382i
$999$	−5.85612e7			−1.85651

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	200.6.f.b.149.19		20
4.3	odd	2		800.6.f.c.49.8		20
5.2	odd	4		40.6.d.a.21.10	yes	20
5.3	odd	4		200.6.d.b.101.11		20
5.4	even	2		200.6.f.c.149.2		20
8.3	odd	2		800.6.f.b.49.14		20
8.5	even	2		200.6.f.c.149.1		20
15.2	even	4		360.6.k.b.181.11		20
20.3	even	4		800.6.d.c.401.8		20
20.7	even	4		160.6.d.a.81.13		20
20.19	odd	2		800.6.f.b.49.13		20
40.3	even	4		800.6.d.c.401.13		20
40.13	odd	4		200.6.d.b.101.12		20
40.19	odd	2		800.6.f.c.49.7		20
40.27	even	4		160.6.d.a.81.8		20
40.29	even	2	inner	200.6.f.b.149.20		20
40.37	odd	4		40.6.d.a.21.9	✓	20
120.77	even	4		360.6.k.b.181.12		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.6.d.a.21.9	✓	20	40.37	odd	4
40.6.d.a.21.10	yes	20	5.2	odd	4
160.6.d.a.81.8		20	40.27	even	4
160.6.d.a.81.13		20	20.7	even	4
200.6.d.b.101.11		20	5.3	odd	4
200.6.d.b.101.12		20	40.13	odd	4
200.6.f.b.149.19		20	1.1	even	1	trivial
200.6.f.b.149.20		20	40.29	even	2	inner
200.6.f.c.149.1		20	8.5	even	2
200.6.f.c.149.2		20	5.4	even	2
360.6.k.b.181.11		20	15.2	even	4
360.6.k.b.181.12		20	120.77	even	4
800.6.d.c.401.8		20	20.3	even	4
800.6.d.c.401.13		20	40.3	even	4
800.6.f.b.49.13		20	20.19	odd	2
800.6.f.b.49.14		20	8.3	odd	2
800.6.f.c.49.7		20	40.19	odd	2
800.6.f.c.49.8		20	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:	\( N \)	\(=\)	\( 200 = 2^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	200.f (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(5.65664 - 0.0494789i) q^{2} +10.7455 q^{3} +(31.9951 - 0.559768i) q^{4} +(60.7833 - 0.531674i) q^{6} -198.733i q^{7} +(180.957 - 4.74949i) q^{8} -127.535 q^{9} +O(q^{10})\)	\(q+(5.65664 - 0.0494789i) q^{2} +10.7455 q^{3} +(31.9951 - 0.559768i) q^{4} +(60.7833 - 0.531674i) q^{6} -198.733i q^{7} +(180.957 - 4.74949i) q^{8} -127.535 q^{9} -85.9303i q^{11} +(343.803 - 6.01498i) q^{12} +407.120 q^{13} +(-9.83309 - 1124.16i) q^{14} +(1023.37 - 35.8197i) q^{16} -1206.02i q^{17} +(-721.417 + 6.31026i) q^{18} -206.036i q^{19} -2135.48i q^{21} +(-4.25173 - 486.077i) q^{22} -2595.25i q^{23} +(1944.47 - 51.0355i) q^{24} +(2302.93 - 20.1438i) q^{26} -3981.57 q^{27} +(-111.244 - 6358.49i) q^{28} +6195.27i q^{29} -1862.42 q^{31} +(5787.08 - 253.254i) q^{32} -923.363i q^{33} +(-59.6727 - 6822.04i) q^{34} +(-4080.48 + 71.3897i) q^{36} +14708.1 q^{37} +(-10.1944 - 1165.47i) q^{38} +4374.70 q^{39} +18098.0 q^{41} +(-105.661 - 12079.7i) q^{42} -9260.46 q^{43} +(-48.1010 - 2749.35i) q^{44} +(-128.410 - 14680.4i) q^{46} +24363.7i q^{47} +(10996.6 - 384.900i) q^{48} -22687.9 q^{49} -12959.3i q^{51} +(13025.8 - 227.893i) q^{52} -12764.8 q^{53} +(-22522.3 + 197.004i) q^{54} +(-943.880 - 35962.2i) q^{56} -2213.96i q^{57} +(306.535 + 35044.4i) q^{58} -20719.7i q^{59} -11368.5i q^{61} +(-10535.0 + 92.1504i) q^{62} +25345.3i q^{63} +(32722.9 - 1718.91i) q^{64} +(-45.6869 - 5223.13i) q^{66} +62614.9 q^{67} +(-675.093 - 38586.8i) q^{68} -27887.3i q^{69} -61208.1 q^{71} +(-23078.3 + 605.723i) q^{72} +23236.4i q^{73} +(83198.1 - 727.738i) q^{74} +(-115.332 - 6592.14i) q^{76} -17077.2 q^{77} +(24746.1 - 216.455i) q^{78} -29172.5 q^{79} -11793.1 q^{81} +(102374. - 895.467i) q^{82} +48099.7 q^{83} +(-1195.38 - 68325.1i) q^{84} +(-52383.1 + 458.197i) q^{86} +66571.2i q^{87} +(-408.125 - 15549.7i) q^{88} -30118.4 q^{89} -80908.2i q^{91} +(-1452.74 - 83035.4i) q^{92} -20012.6 q^{93} +(1205.49 + 137817. i) q^{94} +(62185.0 - 2721.34i) q^{96} +113676. i q^{97} +(-128337. + 1122.57i) q^{98} +10959.1i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} - 36 q^{3} + 32 q^{4} + 204 q^{6} - 248 q^{8} + 1620 q^{9}+O(q^{10}) \) 20 * q - 2 * q^2 - 36 * q^3 + 32 * q^4 + 204 * q^6 - 248 * q^8 + 1620 * q^9	\( 20 q - 2 q^{2} - 36 q^{3} + 32 q^{4} + 204 q^{6} - 248 q^{8} + 1620 q^{9} - 1252 q^{12} - 2708 q^{14} + 3080 q^{16} - 2070 q^{18} - 8244 q^{22} - 1032 q^{24} - 8084 q^{26} - 11664 q^{27} - 22924 q^{28} + 7160 q^{31} - 14792 q^{32} - 21132 q^{34} + 18344 q^{36} + 3608 q^{37} + 16884 q^{38} + 44904 q^{39} + 11608 q^{41} + 49444 q^{42} + 51772 q^{43} - 72296 q^{44} - 28516 q^{46} + 85048 q^{48} - 18756 q^{49} + 111624 q^{52} - 928 q^{53} + 100584 q^{54} - 53624 q^{56} - 152344 q^{58} - 228648 q^{62} + 11264 q^{64} - 56688 q^{66} + 161604 q^{67} - 359040 q^{68} - 200312 q^{71} - 563448 q^{72} - 78876 q^{74} - 153872 q^{76} - 26008 q^{77} + 624640 q^{78} - 282080 q^{79} + 65172 q^{81} + 410576 q^{82} + 99092 q^{83} + 297128 q^{84} + 27452 q^{86} + 464496 q^{88} + 3160 q^{89} + 519244 q^{92} - 293472 q^{93} - 148820 q^{94} + 395168 q^{96} - 663674 q^{98}+O(q^{100}) \) 20 * q - 2 * q^2 - 36 * q^3 + 32 * q^4 + 204 * q^6 - 248 * q^8 + 1620 * q^9 - 1252 * q^12 - 2708 * q^14 + 3080 * q^16 - 2070 * q^18 - 8244 * q^22 - 1032 * q^24 - 8084 * q^26 - 11664 * q^27 - 22924 * q^28 + 7160 * q^31 - 14792 * q^32 - 21132 * q^34 + 18344 * q^36 + 3608 * q^37 + 16884 * q^38 + 44904 * q^39 + 11608 * q^41 + 49444 * q^42 + 51772 * q^43 - 72296 * q^44 - 28516 * q^46 + 85048 * q^48 - 18756 * q^49 + 111624 * q^52 - 928 * q^53 + 100584 * q^54 - 53624 * q^56 - 152344 * q^58 - 228648 * q^62 + 11264 * q^64 - 56688 * q^66 + 161604 * q^67 - 359040 * q^68 - 200312 * q^71 - 563448 * q^72 - 78876 * q^74 - 153872 * q^76 - 26008 * q^77 + 624640 * q^78 - 282080 * q^79 + 65172 * q^81 + 410576 * q^82 + 99092 * q^83 + 297128 * q^84 + 27452 * q^86 + 464496 * q^88 + 3160 * q^89 + 519244 * q^92 - 293472 * q^93 - 148820 * q^94 + 395168 * q^96 - 663674 * q^98

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