LMFDB - Embedded newform 200.6.f.c.149.14

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			149.14
Root			$3.72553 + 1.45618i$ of defining polynomial
Character	$\chi$	$=$	200.149
Dual form			200.6.f.c.149.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.26935 + 5.18171i) q^{2} +10.8240 q^{3} +(-21.7001 + 23.5182i) q^{4} +(24.5634 + 56.0868i) q^{6} +163.706i q^{7} +(-171.109 - 59.0729i) q^{8} -125.841 q^{9} +O(q^{10})$	\(q+(2.26935 + 5.18171i) q^{2} +10.8240 q^{3} +(-21.7001 + 23.5182i) q^{4} +(24.5634 + 56.0868i) q^{6} +163.706i q^{7} +(-171.109 - 59.0729i) q^{8} -125.841 q^{9} +321.520i q^{11} +(-234.883 + 254.561i) q^{12} +128.246 q^{13} +(-848.277 + 371.506i) q^{14} +(-82.2074 - 1020.69i) q^{16} -2110.72i q^{17} +(-285.576 - 652.070i) q^{18} +1454.37i q^{19} +1771.96i q^{21} +(-1666.02 + 729.641i) q^{22} +1231.18i q^{23} +(-1852.09 - 639.406i) q^{24} +(291.033 + 664.531i) q^{26} -3992.34 q^{27} +(-3850.07 - 3552.45i) q^{28} -4073.19i q^{29} -3956.03 q^{31} +(5102.38 - 2742.28i) q^{32} +3480.14i q^{33} +(10937.1 - 4789.95i) q^{34} +(2730.76 - 2959.54i) q^{36} -10656.6 q^{37} +(-7536.11 + 3300.46i) q^{38} +1388.13 q^{39} -5907.19 q^{41} +(-9181.76 + 4021.18i) q^{42} -16439.6 q^{43} +(-7561.57 - 6977.04i) q^{44} +(-6379.59 + 2793.96i) q^{46} +23238.8i q^{47} +(-889.814 - 11048.0i) q^{48} -9992.68 q^{49} -22846.5i q^{51} +(-2782.95 + 3016.10i) q^{52} +30634.0 q^{53} +(-9059.99 - 20687.1i) q^{54} +(9670.60 - 28011.6i) q^{56} +15742.1i q^{57} +(21106.1 - 9243.47i) q^{58} +25262.4i q^{59} -39115.5i q^{61} +(-8977.61 - 20499.0i) q^{62} -20600.9i q^{63} +(25788.8 + 20215.9i) q^{64} +(-18033.1 + 7897.64i) q^{66} -20894.5 q^{67} +(49640.3 + 45803.0i) q^{68} +13326.3i q^{69} +13889.1 q^{71} +(21532.5 + 7433.78i) q^{72} +43451.2i q^{73} +(-24183.6 - 55219.6i) q^{74} +(-34204.1 - 31560.0i) q^{76} -52634.8 q^{77} +(3150.15 + 7192.89i) q^{78} +12546.4 q^{79} -12633.8 q^{81} +(-13405.4 - 30609.3i) q^{82} -6680.84 q^{83} +(-41673.2 - 38451.7i) q^{84} +(-37307.1 - 85185.1i) q^{86} -44088.2i q^{87} +(18993.2 - 55015.1i) q^{88} +90400.9 q^{89} +20994.6i q^{91} +(-28955.0 - 26716.7i) q^{92} -42820.2 q^{93} +(-120416. + 52736.8i) q^{94} +(55228.3 - 29682.5i) q^{96} +149616. i q^{97} +(-22676.8 - 51779.1i) q^{98} -40460.4i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.26935	+	5.18171i	0.401167	+	0.916005i
$2$	2.26935	+	5.18171i	0.401167	+	0.916005i
$3$	10.8240			0.694361			0.347180	−	0.937798i	$-0.387139\pi$
$3$	10.8240			0.694361			0.347180	+	0.937798i	$0.387139\pi$
$4$	−21.7001	+	23.5182i	−0.678130	+	0.734942i
$5$		0			0
$5$		0			0
$6$	24.5634	+	56.0868i	0.278555	+	0.636038i
$7$			163.706i			1.26276i	0.775475	+	0.631378i	$0.217510\pi$
$7$			163.706i			1.26276i	−0.775475	+	0.631378i	$0.782490\pi$
$8$	−171.109	−	59.0729i	−0.945254	−	0.326335i
$9$	−125.841			−0.517863
$10$		0			0
$11$			321.520i			0.801174i	0.916259	+	0.400587i	$0.131194\pi$
$11$			321.520i			0.801174i	−0.916259	+	0.400587i	$0.868806\pi$
$12$	−234.883	+	254.561i	−0.470867	+	0.510315i
$13$	128.246			0.210467			0.105233	−	0.994448i	$-0.466441\pi$
$13$	128.246			0.210467			0.105233	+	0.994448i	$0.466441\pi$
$14$	−848.277	+	371.506i	−1.15669	+	0.506577i
$15$		0			0
$16$	−82.2074	−	1020.69i	−0.0802807	−	0.996772i
$17$		−	2110.72i		−	1.77137i	−0.464290	−	0.885683i	$-0.653690\pi$
$17$		−	2110.72i		−	1.77137i	0.464290	−	0.885683i	$-0.346310\pi$
$18$	−285.576	−	652.070i	−0.207750	−	0.474365i
$19$			1454.37i			0.924252i	0.886814	+	0.462126i	$0.152913\pi$
$19$			1454.37i			0.924252i	−0.886814	+	0.462126i	$0.847087\pi$
$20$		0			0
$21$			1771.96i			0.876809i
$22$	−1666.02	+	729.641i	−0.733879	+	0.321405i
$23$			1231.18i			0.485289i	0.970115	+	0.242645i	$0.0780149\pi$
$23$			1231.18i			0.485289i	−0.970115	+	0.242645i	$0.921985\pi$
$24$	−1852.09	−	639.406i	−0.656347	−	0.226594i
$25$		0			0
$26$	291.033	+	664.531i	0.0844325	+	0.192789i
$27$	−3992.34			−1.05394
$28$	−3850.07	−	3552.45i	−0.928053	−	0.856313i
$29$		−	4073.19i		−	0.899372i	−0.893187	−	0.449686i	$-0.851536\pi$
$29$		−	4073.19i		−	0.899372i	0.893187	−	0.449686i	$-0.148464\pi$
$30$		0			0
$31$	−3956.03			−0.739360			−0.369680	−	0.929159i	$-0.620533\pi$
$31$	−3956.03			−0.739360			−0.369680	+	0.929159i	$0.620533\pi$
$32$	5102.38	−	2742.28i	0.880842	−	0.473410i
$33$			3480.14i			0.556304i
$34$	10937.1	−	4789.95i	1.62258	−	0.710615i
$35$		0			0
$36$	2730.76	−	2959.54i	0.351178	−	0.380600i
$37$	−10656.6			−1.27972			−0.639861	−	0.768490i	$-0.721008\pi$
$37$	−10656.6			−1.27972			−0.639861	+	0.768490i	$0.721008\pi$
$38$	−7536.11	+	3300.46i	−0.846620	+	0.370780i
$39$	1388.13			0.146140
$40$		0			0
$41$	−5907.19			−0.548809			−0.274404	−	0.961614i	$-0.588481\pi$
$41$	−5907.19			−0.548809			−0.274404	+	0.961614i	$0.588481\pi$
$42$	−9181.76	+	4021.18i	−0.803161	+	0.351747i
$43$	−16439.6			−1.35588			−0.677938	−	0.735119i	$-0.737126\pi$
$43$	−16439.6			−1.35588			−0.677938	+	0.735119i	$0.737126\pi$
$44$	−7561.57	−	6977.04i	−0.588817	−	0.543300i
$45$		0			0
$46$	−6379.59	+	2793.96i	−0.444527	+	0.194682i
$47$			23238.8i			1.53450i	0.641345	+	0.767252i	$0.278377\pi$
$47$			23238.8i			1.53450i	−0.641345	+	0.767252i	$0.721623\pi$
$48$	−889.814	−	11048.0i	−0.0557438	−	0.692120i
$49$	−9992.68			−0.594555
$50$		0			0
$51$		−	22846.5i		−	1.22997i
$52$	−2782.95	+	3016.10i	−0.142724	+	0.154681i
$53$	30634.0			1.49801			0.749003	−	0.662567i	$-0.230533\pi$
$53$	30634.0			1.49801			0.749003	+	0.662567i	$0.230533\pi$
$54$	−9059.99	−	20687.1i	−0.422808	−	0.965418i
$55$		0			0
$56$	9670.60	−	28011.6i	0.412082	−	1.19363i
$57$			15742.1i			0.641764i
$58$	21106.1	−	9243.47i	0.823829	−	0.360799i
$59$			25262.4i			0.944810i	0.881382	+	0.472405i	$0.156614\pi$
$59$			25262.4i			0.944810i	−0.881382	+	0.472405i	$0.843386\pi$
$60$		0			0
$61$		−	39115.5i		−	1.34594i	−0.739672	−	0.672968i	$-0.765019\pi$
$61$		−	39115.5i		−	1.34594i	0.739672	−	0.672968i	$-0.234981\pi$
$62$	−8977.61	−	20499.0i	−0.296607	−	0.677257i
$63$		−	20600.9i		−	0.653935i
$64$	25788.8	+	20215.9i	0.787011	+	0.616939i
$65$		0			0
$66$	−18033.1	+	7897.64i	−0.509577	+	0.223171i
$67$	−20894.5			−0.568651			−0.284325	−	0.958728i	$-0.591770\pi$
$67$	−20894.5			−0.568651			−0.284325	+	0.958728i	$0.591770\pi$
$68$	49640.3	+	45803.0i	1.30185	+	1.20122i
$69$			13326.3i			0.336966i
$70$		0			0
$71$	13889.1			0.326984			0.163492	−	0.986545i	$-0.447724\pi$
$71$	13889.1			0.326984			0.163492	+	0.986545i	$0.447724\pi$
$72$	21532.5	+	7433.78i	0.489512	+	0.168997i
$73$			43451.2i			0.954321i	0.878816	+	0.477161i	$0.158334\pi$
$73$			43451.2i			0.954321i	−0.878816	+	0.477161i	$0.841666\pi$
$74$	−24183.6	−	55219.6i	−0.513383	−	1.17223i
$75$		0			0
$76$	−34204.1	−	31560.0i	−0.679272	−	0.626763i
$77$	−52634.8			−1.01169
$78$	3150.15	+	7192.89i	0.0586266	+	0.133865i
$79$	12546.4			0.226179			0.113089	−	0.993585i	$-0.463925\pi$
$79$	12546.4			0.226179			0.113089	+	0.993585i	$0.463925\pi$
$80$		0			0
$81$	−12633.8			−0.213955
$82$	−13405.4	−	30609.3i	−0.220164	−	0.502711i
$83$	−6680.84			−0.106448			−0.0532238	−	0.998583i	$-0.516950\pi$
$83$	−6680.84			−0.106448			−0.0532238	+	0.998583i	$0.516950\pi$
$84$	−41673.2	−	38451.7i	−0.644404	−	0.594590i
$85$		0			0
$86$	−37307.1	−	85185.1i	−0.543933	−	1.24199i
$87$		−	44088.2i		−	0.624488i
$88$	18993.2	−	55015.1i	0.261451	−	0.757313i
$89$	90400.9			1.20976			0.604878	−	0.796318i	$-0.293222\pi$
$89$	90400.9			1.20976			0.604878	+	0.796318i	$0.293222\pi$
$90$		0			0
$91$			20994.6i			0.265769i
$92$	−28955.0	−	26716.7i	−0.356660	−	0.329089i
$93$	−42820.2			−0.513382
$94$	−120416.	+	52736.8i	−1.40561	+	0.615593i
$95$		0			0
$96$	55228.3	−	29682.5i	0.611622	−	0.328717i
$97$			149616.i			1.61454i	0.590184	+	0.807269i	$0.299055\pi$
$97$			149616.i			1.61454i	−0.590184	+	0.807269i	$0.700945\pi$
$98$	−22676.8	−	51779.1i	−0.238516	−	0.544615i
$99$		−	40460.4i		−	0.414898i
$100$		0			0
$101$		−	114822.i		−	1.12001i	−0.828491	−	0.560003i	$-0.810800\pi$
$101$		−	114822.i		−	1.12001i	0.828491	−	0.560003i	$-0.189200\pi$
$102$	118384.	−	51846.5i	1.12666	−	0.493423i
$103$		−	38586.9i		−	0.358382i	−0.983814	−	0.179191i	$-0.942652\pi$
$103$		−	38586.9i		−	0.358382i	0.983814	−	0.179191i	$-0.0573481\pi$
$104$	−21944.0	−	7575.84i	−0.198945	−	0.0686827i
$105$		0			0
$106$	69519.0	+	158736.i	0.600951	+	1.37218i
$107$	−189459.			−1.59976			−0.799881	−	0.600158i	$-0.795104\pi$
$107$	−189459.			−1.59976			−0.799881	+	0.600158i	$0.795104\pi$
$108$	86634.3	−	93892.4i	0.714711	−	0.774589i
$109$			24392.6i			0.196649i	0.995154	+	0.0983245i	$0.0313483\pi$
$109$			24392.6i			0.196649i	−0.995154	+	0.0983245i	$0.968652\pi$
$110$		0			0
$111$	−115348.			−0.888589
$112$	167094.	−	13457.9i	1.25868	−	0.101375i
$113$			52918.6i			0.389863i	0.980817	+	0.194932i	$0.0624485\pi$
$113$			52918.6i			0.389863i	−0.980817	+	0.194932i	$0.937552\pi$
$114$	−81571.0	+	35724.3i	−0.587859	+	0.257455i
$115$		0			0
$116$	95793.8	+	88388.7i	0.660987	+	0.609891i
$117$	−16138.5			−0.108993
$118$	−130902.	+	57329.1i	−0.865450	+	0.379027i
$119$	345538.			2.23681
$120$		0			0
$121$	57675.7			0.358120
$122$	202685.	−	88766.6i	1.23288	−	0.539945i
$123$	−63939.5			−0.381071
$124$	85846.5	−	93038.6i	0.501382	−	0.543387i
$125$		0			0
$126$	106748.	−	46750.5i	0.599008	−	0.262337i
$127$			293650.i			1.61555i	0.589489	+	0.807777i	$0.299329\pi$
$127$			293650.i			1.61555i	−0.589489	+	0.807777i	$0.700671\pi$
$128$	−46229.0	+	179507.i	−0.249396	+	0.968402i
$129$	−177942.			−0.941467
$130$		0			0
$131$			317738.i			1.61767i	0.588032	+	0.808837i	$0.299903\pi$
$131$			317738.i			1.61767i	−0.588032	+	0.808837i	$0.700097\pi$
$132$	−81846.5	−	75519.6i	−0.408851	−	0.377246i
$133$	−238089.			−1.16711
$134$	−47416.9	−	108269.i	−0.228124	−	0.520887i
$135$		0			0
$136$	−124687.	+	361164.i	−0.578059	+	1.67439i
$137$		−	162285.i		−	0.738717i	−0.929287	−	0.369358i	$-0.879577\pi$
$137$		−	162285.i		−	0.738717i	0.929287	−	0.369358i	$-0.120423\pi$
$138$	−69052.8	+	30241.9i	−0.308662	+	0.135180i
$139$			306759.i			1.34667i	0.739338	+	0.673334i	$0.235139\pi$
$139$			306759.i			1.34667i	−0.739338	+	0.673334i	$0.764861\pi$
$140$		0			0
$141$			251537.i			1.06550i
$142$	31519.1	+	71969.0i	0.131175	+	0.299519i
$143$			41233.5i			0.168621i
$144$	10345.0	+	128445.i	0.0415744	+	0.516192i
$145$		0			0
$146$	−225151.	+	98605.8i	−0.874163	+	0.382842i
$147$	−108161.			−0.412835
$148$	231251.	−	250625.i	0.867818	−	0.940523i
$149$			368107.i			1.35834i	0.733981	+	0.679170i	$0.237660\pi$
$149$			368107.i			1.35834i	−0.733981	+	0.679170i	$0.762340\pi$
$150$		0			0
$151$	336822.			1.20215			0.601075	−	0.799193i	$-0.294739\pi$
$151$	336822.			1.20215			0.601075	+	0.799193i	$0.294739\pi$
$152$	85913.8	−	248856.i	0.301616	−	0.873653i
$153$			265615.i			0.917326i
$154$	−119447.	−	272738.i	−0.405856	−	0.926711i
$155$		0			0
$156$	−30122.6	+	32646.3i	−0.0991018	+	0.107404i
$157$	271253.			0.878264			0.439132	−	0.898423i	$-0.355286\pi$
$157$	271253.			0.878264			0.439132	+	0.898423i	$0.355286\pi$
$158$	28472.1	+	65011.8i	0.0907356	+	0.207181i
$159$	331582.			1.04016
$160$		0			0
$161$	−201551.			−0.612802
$162$	−28670.5	−	65464.6i	−0.0858316	−	0.195983i
$163$	121354.			0.357756			0.178878	−	0.983871i	$-0.442753\pi$
$163$	121354.			0.357756			0.178878	+	0.983871i	$0.442753\pi$
$164$	128187.	−	138926.i	0.372163	−	0.403343i
$165$		0			0
$166$	−15161.1	−	34618.1i	−0.0427033	−	0.0975065i
$167$			56095.4i			0.155645i	0.996967	+	0.0778227i	$0.0247968\pi$
$167$			56095.4i			0.155645i	−0.996967	+	0.0778227i	$0.975203\pi$
$168$	104675.	−	303198.i	0.286133	−	0.828807i
$169$	−354846.			−0.955704
$170$		0			0
$171$		−	183019.i		−	0.478636i
$172$	356741.	−	386629.i	0.919459	−	0.996490i
$173$	−167666.			−0.425921			−0.212960	−	0.977061i	$-0.568311\pi$
$173$	−167666.			−0.425921			−0.212960	+	0.977061i	$0.568311\pi$
$174$	228452.	−	100051.i	0.572034	−	0.250524i
$175$		0			0
$176$	328174.	−	26431.4i	0.798588	−	0.0643188i
$177$			273440.i			0.656039i
$178$	205151.	+	468431.i	0.485314	+	1.10814i
$179$			535921.i			1.25017i	0.780558	+	0.625083i	$0.214935\pi$
$179$			535921.i			1.25017i	−0.780558	+	0.625083i	$0.785065\pi$
$180$		0			0
$181$			113446.i			0.257391i	0.991684	+	0.128696i	$0.0410790\pi$
$181$			113446.i			0.257391i	−0.991684	+	0.128696i	$0.958921\pi$
$182$	−108788.	+	47643.9i	−0.243445	+	0.106618i
$183$		−	423387.i		−	0.934565i
$184$	72729.2	−	210666.i	0.158367	−	0.458722i
$185$		0			0
$186$	−97173.7	−	221881.i	−0.205952	−	0.470261i
$187$	678640.			1.41917
$188$	−546533.	−	504284.i	−1.12777	−	1.04059i
$189$		−	653570.i		−	1.33088i
$190$		0			0
$191$	391808.			0.777124			0.388562	−	0.921423i	$-0.372972\pi$
$191$	391808.			0.777124			0.388562	+	0.921423i	$0.372972\pi$
$192$	279138.	+	218817.i	0.546470	+	0.428378i
$193$			261513.i			0.505359i	0.967550	+	0.252680i	$0.0813118\pi$
$193$			261513.i			0.505359i	−0.967550	+	0.252680i	$0.918688\pi$
$194$	−775265.	+	339530.i	−1.47892	+	0.647700i
$195$		0			0
$196$	216843.	−	235009.i	0.403185	−	0.436963i
$197$	−898947.			−1.65032			−0.825161	−	0.564898i	$-0.808916\pi$
$197$	−898947.			−1.65032			−0.825161	+	0.564898i	$0.808916\pi$
$198$	209654.	−	91818.5i	0.380049	−	0.166444i
$199$	83719.3			0.149862			0.0749312	−	0.997189i	$-0.476126\pi$
$199$	83719.3			0.149862			0.0749312	+	0.997189i	$0.476126\pi$
$200$		0			0
$201$	−226163.			−0.394849
$202$	594972.	−	260570.i	1.02593	−	0.449310i
$203$	666805.			1.13569
$204$	537307.	+	495772.i	0.903955	+	0.834077i
$205$		0			0
$206$	199946.	−	87566.9i	0.328280	−	0.143771i
$207$		−	154932.i		−	0.251313i
$208$	−10542.7	−	130900.i	−0.0168964	−	0.209788i
$209$	−467609.			−0.740487
$210$		0			0
$211$		−	553641.i		−	0.856095i	−0.903756	−	0.428047i	$-0.859202\pi$
$211$		−	553641.i		−	0.856095i	0.903756	−	0.428047i	$-0.140798\pi$
$212$	−664761.	+	720454.i	−1.01584	+	1.10095i
$213$	150335.			0.227045
$214$	−429948.	−	981720.i	−0.641772	−	1.46539i
$215$		0			0
$216$	683126.	+	235839.i	0.996246	+	0.343939i
$217$		−	647627.i		−	0.933632i
$218$	−126395.	+	55355.2i	−0.180131	+	0.0788892i
$219$			470316.i			0.662643i
$220$		0			0
$221$		−	270691.i		−	0.372814i
$222$	−261764.	−	597697.i	−0.356473	−	0.813952i
$223$		−	279400.i		−	0.376239i	−0.982146	−	0.188120i	$-0.939761\pi$
$223$		−	279400.i		−	0.376239i	0.982146	−	0.188120i	$-0.0602392\pi$
$224$	448929.	+	835291.i	0.597802	+	1.11229i
$225$		0			0
$226$	−274209.	+	120091.i	−0.357116	+	0.156400i
$227$	−593068.			−0.763905			−0.381953	−	0.924182i	$-0.624748\pi$
$227$	−593068.			−0.763905			−0.381953	+	0.924182i	$0.624748\pi$
$228$	−370225.	−	341606.i	−0.471660	−	0.435199i
$229$		−	927873.i		−	1.16923i	−0.811311	−	0.584615i	$-0.801246\pi$
$229$		−	927873.i		−	1.16923i	0.811311	−	0.584615i	$-0.198754\pi$
$230$		0			0
$231$	−569720.			−0.702476
$232$	−240615.	+	696960.i	−0.293496	+	0.850135i
$233$			1.09279e6i			1.31871i	0.751833	+	0.659353i	$0.229170\pi$
$233$			1.09279e6i			1.31871i	−0.751833	+	0.659353i	$0.770830\pi$
$234$	−36623.9	−	83625.0i	−0.0437245	−	0.0998382i
$235$		0			0
$236$	−594125.	−	548197.i	−0.694381	−	0.640703i
$237$	135803.			0.157050
$238$	784145.	+	1.79048e6i	0.897333	+	2.04892i
$239$	797967.			0.903630			0.451815	−	0.892112i	$-0.350777\pi$
$239$	797967.			0.903630			0.451815	+	0.892112i	$0.350777\pi$
$240$		0			0
$241$	−1.61861e6			−1.79515			−0.897573	−	0.440865i	$-0.854672\pi$
$241$	−1.61861e6			−1.79515			−0.897573	+	0.440865i	$0.854672\pi$
$242$	130886.	+	298858.i	0.143666	+	0.328040i
$243$	833389.			0.905383
$244$	919924.	+	848812.i	0.989185	+	0.912719i
$245$		0			0
$246$	−145101.	−	331315.i	−0.152873	−	0.349063i
$247$			186516.i			0.194525i
$248$	676914.	+	233695.i	0.698883	+	0.241279i
$249$	−72313.5			−0.0739130
$250$		0			0
$251$		−	449688.i		−	0.450533i	−0.974297	−	0.225266i	$-0.927675\pi$
$251$		−	449688.i		−	0.450533i	0.974297	−	0.225266i	$-0.0723253\pi$
$252$	484495.	+	447042.i	0.480605	+	0.443453i
$253$	−395848.			−0.388801
$254$	−1.52161e6	+	666394.i	−1.47985	+	0.648107i
$255$		0			0
$256$	−1.03506e6	+	167817.i	−0.987110	+	0.160043i
$257$			396434.i			0.374402i	0.982322	+	0.187201i	$0.0599416\pi$
$257$			396434.i			0.374402i	−0.982322	+	0.187201i	$0.940058\pi$
$258$	−403813.	−	922045.i	−0.377686	−	0.862388i
$259$		−	1.74456e6i		−	1.61598i
$260$		0			0
$261$			512573.i			0.465752i
$262$	−1.64643e6	+	721058.i	−1.48180	+	0.648958i
$263$		−	1.93423e6i		−	1.72432i	−0.506635	−	0.862160i	$-0.669111\pi$
$263$		−	1.93423e6i		−	1.72432i	0.506635	−	0.862160i	$-0.330889\pi$
$264$	205582.	−	595484.i	0.181541	−	0.525848i
$265$		0			0
$266$	−540306.	−	1.23371e6i	−0.468205	−	1.06907i
$267$	978500.			0.840007
$268$	453414.	−	491401.i	0.385619	−	0.417926i
$269$		−	670016.i		−	0.564553i	−0.959333	−	0.282276i	$-0.908910\pi$
$269$		−	670016.i		−	0.564553i	0.959333	−	0.282276i	$-0.0910895\pi$
$270$		0			0
$271$	2.08940e6			1.72822			0.864109	−	0.503305i	$-0.167883\pi$
$271$	2.08940e6			1.72822			0.864109	+	0.503305i	$0.167883\pi$
$272$	−2.15440e6	+	173517.i	−1.76565	+	0.142207i
$273$			227246.i			0.184539i
$274$	840915.	−	368281.i	0.676668	−	0.296349i
$275$		0			0
$276$	−313409.	−	289182.i	−0.247651	−	0.228506i
$277$	828834.			0.649035			0.324517	−	0.945880i	$-0.394798\pi$
$277$	828834.			0.649035			0.324517	+	0.945880i	$0.394798\pi$
$278$	−1.58954e6	+	696143.i	−1.23356	+	0.540240i
$279$	497830.			0.382887
$280$		0			0
$281$	2.39932e6			1.81268			0.906342	−	0.422545i	$-0.138863\pi$
$281$	2.39932e6			1.81268			0.906342	+	0.422545i	$0.138863\pi$
$282$	−1.30339e6	+	570823.i	−0.976003	+	0.427444i
$283$	−2.00868e6			−1.49089			−0.745444	−	0.666568i	$-0.767763\pi$
$283$	−2.00868e6			−1.49089			−0.745444	+	0.666568i	$0.767763\pi$
$284$	−301395.	+	326645.i	−0.221738	+	0.240315i
$285$		0			0
$286$	−213660.	+	93573.2i	−0.154457	+	0.0676451i
$287$		−	967042.i		−	0.693012i
$288$	−642088.	+	345091.i	−0.456156	+	0.245162i
$289$	−3.03529e6			−2.13774
$290$		0			0
$291$			1.61944e6i			1.12107i
$292$	−1.02189e6	−	942897.i	−0.701371	−	0.647153i
$293$	−1.74203e6			−1.18546			−0.592729	−	0.805402i	$-0.701950\pi$
$293$	−1.74203e6			−1.18546			−0.592729	+	0.805402i	$0.701950\pi$
$294$	−245454.	−	560458.i	−0.165616	−	0.378159i
$295$		0			0
$296$	1.82345e6	+	629519.i	1.20966	+	0.417618i
$297$		−	1.28362e6i		−	0.844393i
$298$	−1.90742e6	+	835362.i	−1.24425	+	0.544922i
$299$			157893.i			0.102137i
$300$		0			0
$301$		−	2.69126e6i		−	1.71214i
$302$	764366.	+	1.74531e6i	0.482263	+	1.10118i
$303$		−	1.24283e6i		−	0.777688i
$304$	1.48447e6	−	119560.i	0.921269	−	0.0741996i
$305$		0			0
$306$	−1.37634e6	+	602772.i	−0.840275	+	0.368001i
$307$	−978690.			−0.592651			−0.296326	−	0.955087i	$-0.595761\pi$
$307$	−978690.			−0.592651			−0.296326	+	0.955087i	$0.595761\pi$
$308$	1.14218e6	−	1.23787e6i	0.686055	−	0.743532i
$309$		−	417665.i		−	0.248847i
$310$		0			0
$311$	−1.57652e6			−0.924268			−0.462134	−	0.886810i	$-0.652916\pi$
$311$	−1.57652e6			−0.924268			−0.462134	+	0.886810i	$0.652916\pi$
$312$	−237522.	−	82001.0i	−0.138139	−	0.0476906i
$313$		−	1.60962e6i		−	0.928670i	−0.885660	−	0.464335i	$-0.846293\pi$
$313$		−	1.60962e6i		−	0.928670i	0.885660	−	0.464335i	$-0.153707\pi$
$314$	615566.	+	1.40555e6i	0.352331	+	0.804494i
$315$		0			0
$316$	−272259.	+	295069.i	−0.153379	+	0.166228i
$317$	1.50670e6			0.842130			0.421065	−	0.907030i	$-0.361656\pi$
$317$	1.50670e6			0.842130			0.421065	+	0.907030i	$0.361656\pi$
$318$	752475.	+	1.71816e6i	0.417277	+	0.952788i
$319$	1.30961e6			0.720553
$320$		0			0
$321$	−2.05070e6			−1.11081
$322$	−457389.	−	1.04438e6i	−0.245836	−	0.561330i
$323$	3.06977e6			1.63719
$324$	274155.	−	297124.i	0.145089	−	0.157244i
$325$		0			0
$326$	275395.	+	628823.i	0.143520	+	0.327706i
$327$			264026.i			0.136545i
$328$	1.01077e6	+	348955.i	0.518764	+	0.179095i
$329$	−3.80433e6			−1.93771
$330$		0			0
$331$		−	394453.i		−	0.197891i	−0.995093	−	0.0989454i	$-0.968453\pi$
$331$		−	394453.i		−	0.197891i	0.995093	−	0.0989454i	$-0.0315469\pi$
$332$	144975.	−	157121.i	0.0721852	−	0.0782328i
$333$	1.34104e6			0.662721
$334$	−290670.	+	127300.i	−0.142572	+	0.0624398i
$335$		0			0
$336$	1.80863e6	−	145668.i	0.873979	−	0.0703908i
$337$		−	1.36879e6i		−	0.656543i	−0.944583	−	0.328272i	$-0.893534\pi$
$337$		−	1.36879e6i		−	0.656543i	0.944583	−	0.328272i	$-0.106466\pi$
$338$	−805268.	−	1.83871e6i	−0.383397	−	0.875429i
$339$			572791.i			0.270706i
$340$		0			0
$341$		−	1.27195e6i		−	0.592356i
$342$	948350.	−	415333.i	0.438433	−	0.192013i
$343$			1.11555e6i			0.511979i
$344$	2.81297e6	+	971135.i	1.28165	+	0.442470i
$345$		0			0
$346$	−380491.	−	868794.i	−0.170865	−	0.390145i
$347$	−569376.			−0.253849			−0.126925	−	0.991912i	$-0.540511\pi$
$347$	−569376.			−0.253849			−0.126925	+	0.991912i	$0.540511\pi$
$348$	1.03687e6	+	956721.i	0.458963	+	0.423484i
$349$		−	2.20053e6i		−	0.967081i	−0.875322	−	0.483541i	$-0.839351\pi$
$349$		−	2.20053e6i		−	0.967081i	0.875322	−	0.483541i	$-0.160649\pi$
$350$		0			0
$351$	−511999.			−0.221820
$352$	881700.	+	1.64052e6i	0.379284	+	0.705708i
$353$			2.51557e6i			1.07448i	0.843428	+	0.537242i	$0.180534\pi$
$353$			2.51557e6i			1.07448i	−0.843428	+	0.537242i	$0.819466\pi$
$354$	−1.41689e6	+	620531.i	−0.600935	+	0.263181i
$355$		0			0
$356$	−1.96171e6	+	2.12606e6i	−0.820371	+	0.889100i
$357$	3.74011e6			1.55315
$358$	−2.77698e6	+	1.21619e6i	−1.14516	+	0.501526i
$359$	794808.			0.325481			0.162741	−	0.986669i	$-0.447967\pi$
$359$	794808.			0.325481			0.162741	+	0.986669i	$0.447967\pi$
$360$		0			0
$361$	360911.			0.145758
$362$	−587845.	+	257449.i	−0.235772	+	0.103257i
$363$	624282.			0.248665
$364$	−493754.	−	455585.i	−0.195325	−	0.180225i
$365$		0			0
$366$	2.19386e6	−	960810.i	0.856066	−	0.374917i
$367$		−	874302.i		−	0.338841i	−0.985544	−	0.169421i	$-0.945810\pi$
$367$		−	874302.i		−	0.338841i	0.985544	−	0.169421i	$-0.0541896\pi$
$368$	1.25666e6	−	101212.i	0.483723	−	0.0389594i
$369$	743365.			0.284208
$370$		0			0
$371$			5.01497e6i			1.89162i
$372$	929204.	−	1.00705e6i	0.348140	−	0.377306i
$373$	4.86205e6			1.80945			0.904726	−	0.425994i	$-0.140076\pi$
$373$	4.86205e6			1.80945			0.904726	+	0.425994i	$0.140076\pi$
$374$	1.54007e6	+	3.51651e6i	0.569326	+	1.29997i
$375$		0			0
$376$	1.37278e6	−	3.97637e6i	0.500763	−	1.45050i
$377$		−	522368.i		−	0.189288i
$378$	3.38661e6	−	1.48318e6i	1.21909	−	0.533904i
$379$			1.24150e6i			0.443964i	0.975051	+	0.221982i	$0.0712527\pi$
$379$			1.24150e6i			0.443964i	−0.975051	+	0.221982i	$0.928747\pi$
$380$		0			0
$381$			3.17848e6i			1.12178i
$382$	889149.	+	2.03024e6i	0.311757	+	0.711849i
$383$			30969.9i			0.0107880i	0.999985	+	0.00539402i	$0.00171698\pi$
$383$			30969.9i			0.0107880i	−0.999985	+	0.00539402i	$0.998283\pi$
$384$	−500383.	+	1.94298e6i	−0.173171	+	0.672420i
$385$		0			0
$386$	−1.35508e6	+	593463.i	−0.462911	+	0.202734i
$387$	2.06877e6			0.702158
$388$	−3.51869e6	−	3.24669e6i	−1.18659	−	1.09487i
$389$			4.27860e6i			1.43360i	0.697279	+	0.716800i	$0.254394\pi$
$389$			4.27860e6i			1.43360i	−0.697279	+	0.716800i	$0.745606\pi$
$390$		0			0
$391$	2.59867e6			0.859626
$392$	1.70984e6	+	590297.i	0.562005	+	0.194024i
$393$			3.43920e6i			1.12325i
$394$	−2.04002e6	−	4.65808e6i	−0.662055	−	1.51170i
$395$		0			0
$396$	951553.	+	877996.i	0.304926	+	0.281355i
$397$	−2.31119e6			−0.735968			−0.367984	−	0.929832i	$-0.619952\pi$
$397$	−2.31119e6			−0.735968			−0.367984	+	0.929832i	$0.619952\pi$
$398$	189988.	+	433809.i	0.0601199	+	0.137275i
$399$	−2.57708e6			−0.810392
$400$		0			0
$401$	996347.			0.309421			0.154710	−	0.987960i	$-0.450556\pi$
$401$	996347.			0.309421			0.154710	+	0.987960i	$0.450556\pi$
$402$	−513241.	−	1.17191e6i	−0.158400	−	0.361683i
$403$	−507344.			−0.155611
$404$	2.70039e6	+	2.49165e6i	0.823140	+	0.759509i
$405$		0			0
$406$	1.51321e6	+	3.45519e6i	0.455601	+	1.04030i
$407$		−	3.42633e6i		−	1.02528i
$408$	−1.34961e6	+	3.90924e6i	−0.401381	+	1.16263i
$409$	5.17948e6			1.53101			0.765505	−	0.643430i	$-0.222489\pi$
$409$	5.17948e6			1.53101			0.765505	+	0.643430i	$0.222489\pi$
$410$		0			0
$411$		−	1.75658e6i		−	0.512936i
$412$	907492.	+	837341.i	0.263390	+	0.243030i
$413$	−4.13561e6			−1.19306
$414$	802813.	−	351595.i	0.230204	−	0.100819i
$415$		0			0
$416$	654358.	−	351686.i	0.185388	−	0.0996371i
$417$			3.32037e6i			0.935074i
$418$	−1.06117e6	−	2.42301e6i	−0.297059	−	0.678289i
$419$		−	3.57698e6i		−	0.995363i	−0.867360	−	0.497682i	$-0.834185\pi$
$419$		−	3.57698e6i		−	0.995363i	0.867360	−	0.497682i	$-0.165815\pi$
$420$		0			0
$421$			2.15848e6i			0.593531i	0.954950	+	0.296765i	$0.0959080\pi$
$421$			2.15848e6i			0.593531i	−0.954950	+	0.296765i	$0.904092\pi$
$422$	2.86880e6	−	1.25640e6i	0.784187	−	0.343437i
$423$		−	2.92438e6i		−	0.794664i
$424$	−5.24175e6	−	1.80964e6i	−1.41600	−	0.488852i
$425$		0			0
$426$	341163.	+	778993.i	0.0910831	+	0.207974i
$427$	6.40344e6			1.69959
$428$	4.11128e6	−	4.45572e6i	1.08485	−	1.17573i
$429$			446312.i			0.117084i
$430$		0			0
$431$	−1.80890e6			−0.469052			−0.234526	−	0.972110i	$-0.575354\pi$
$431$	−1.80890e6			−0.469052			−0.234526	+	0.972110i	$0.575354\pi$
$432$	328200.	+	4.07496e6i	0.0846114	+	1.05054i
$433$		−	1.28911e6i		−	0.330423i	−0.986258	−	0.165211i	$-0.947169\pi$
$433$		−	1.28911e6i		−	0.330423i	0.986258	−	0.165211i	$-0.0528306\pi$
$434$	3.35581e6	−	1.46969e6i	0.855211	−	0.374542i
$435$		0			0
$436$	−573669.	−	529323.i	−0.144526	−	0.133354i
$437$	−1.79058e6			−0.448530
$438$	−2.43704e6	+	1.06731e6i	−0.606984	+	0.265831i
$439$	−1.89694e6			−0.469777			−0.234889	−	0.972022i	$-0.575473\pi$
$439$	−1.89694e6			−0.469777			−0.234889	+	0.972022i	$0.575473\pi$
$440$		0			0
$441$	1.25749e6			0.307898
$442$	1.40264e6	−	614290.i	0.341500	−	0.149561i
$443$	−6.01979e6			−1.45738			−0.728689	−	0.684845i	$-0.759870\pi$
$443$	−6.01979e6			−1.45738			−0.728689	+	0.684845i	$0.759870\pi$
$444$	2.50306e6	−	2.71276e6i	0.602579	−	0.653062i
$445$		0			0
$446$	1.44777e6	−	634055.i	0.344637	−	0.150935i
$447$			3.98440e6i			0.943178i
$448$	−3.30946e6	+	4.22178e6i	−0.779044	+	0.993803i
$449$	2.40081e6			0.562007			0.281003	−	0.959707i	$-0.409333\pi$
$449$	2.40081e6			0.562007			0.281003	+	0.959707i	$0.409333\pi$
$450$		0			0
$451$		−	1.89928e6i		−	0.439691i
$452$	−1.24455e6	−	1.14834e6i	−0.286527	−	0.264378i
$453$	3.64577e6			0.834726
$454$	−1.34588e6	−	3.07310e6i	−0.306454	−	0.699741i
$455$		0			0
$456$	929933.	−	2.69362e6i	0.209430	−	0.606631i
$457$		−	858952.i		−	0.192388i	−0.995363	−	0.0961941i	$-0.969333\pi$
$457$		−	858952.i		−	0.192388i	0.995363	−	0.0961941i	$-0.0306669\pi$
$458$	4.80797e6	−	2.10567e6i	1.07102	−	0.469057i
$459$			8.42671e6i			1.86692i
$460$		0			0
$461$			2.33481e6i			0.511680i	0.966719	+	0.255840i	$0.0823521\pi$
$461$			2.33481e6i			0.511680i	−0.966719	+	0.255840i	$0.917648\pi$
$462$	−1.29289e6	−	2.95212e6i	−0.281811	−	0.643472i
$463$			1.35195e6i			0.293096i	0.989204	+	0.146548i	$0.0468162\pi$
$463$			1.35195e6i			0.293096i	−0.989204	+	0.146548i	$0.953184\pi$
$464$	−4.15748e6	+	334846.i	−0.896469	+	0.0722022i
$465$		0			0
$466$	−5.66253e6	+	2.47993e6i	−1.20794	+	0.529022i
$467$	−6.44013e6			−1.36648			−0.683239	−	0.730195i	$-0.739429\pi$
$467$	−6.44013e6			−1.36648			−0.683239	+	0.730195i	$0.739429\pi$
$468$	350208.	−	379548.i	0.0739114	−	0.0801036i
$469$		−	3.42056e6i		−	0.718068i
$470$		0			0
$471$	2.93604e6			0.609832
$472$	1.49232e6	−	4.32263e6i	0.308324	−	0.893085i
$473$		−	5.28566e6i		−	1.08629i
$474$	308183.	+	703689.i	0.0630032	+	0.143858i
$475$		0			0
$476$	−7.49822e6	+	8.12641e6i	−1.51684	+	1.64392i
$477$	−3.85500e6			−0.775762
$478$	1.81086e6	+	4.13483e6i	0.362507	+	0.827729i
$479$	1.85358e6			0.369124			0.184562	−	0.982821i	$-0.440913\pi$
$479$	1.85358e6			0.369124			0.184562	+	0.982821i	$0.440913\pi$
$480$		0			0
$481$	−1.36667e6			−0.269339
$482$	−3.67319e6	−	8.38717e6i	−0.720154	−	1.64436i
$483$	−2.18159e6			−0.425506
$484$	−1.25157e6	+	1.35643e6i	−0.242852	+	0.263198i
$485$		0			0
$486$	1.89125e6	+	4.31838e6i	0.363210	+	0.829335i
$487$			2.51668e6i			0.480846i	0.970668	+	0.240423i	$0.0772861\pi$
$487$			2.51668e6i			0.480846i	−0.970668	+	0.240423i	$0.922714\pi$
$488$	−2.31067e6	+	6.69302e6i	−0.439226	+	1.27225i
$489$	1.31354e6			0.248412
$490$		0			0
$491$		−	5.39115e6i		−	1.00920i	−0.863353	−	0.504601i	$-0.831640\pi$
$491$		−	5.39115e6i		−	1.00920i	0.863353	−	0.504601i	$-0.168360\pi$
$492$	1.38750e6	−	1.50374e6i	0.258416	−	0.280065i
$493$	−8.59736e6			−1.59312
$494$	−966472.	+	423270.i	−0.178185	+	0.0780369i
$495$		0			0
$496$	325215.	+	4.03790e6i	0.0593563	+	0.736973i
$497$			2.27372e6i			0.412902i
$498$	−164104.	−	374707.i	−0.0296515	−	0.0677047i
$499$		−	3.18358e6i		−	0.572353i	−0.958177	−	0.286177i	$-0.907616\pi$
$499$		−	3.18358e6i		−	0.572353i	0.958177	−	0.286177i	$-0.0923844\pi$
$500$		0			0
$501$			607177.i			0.108074i
$502$	2.33015e6	−	1.02050e6i	0.412690	−	0.180739i
$503$			8.99291e6i			1.58482i	0.609989	+	0.792410i	$0.291174\pi$
$503$			8.99291e6i			1.58482i	−0.609989	+	0.792410i	$0.708826\pi$
$504$	−1.21696e6	+	3.52500e6i	−0.213402	+	0.618135i
$505$		0			0
$506$	−898317.	−	2.05117e6i	−0.155974	−	0.356144i
$507$	−3.84086e6			−0.663603
$508$	−6.90612e6	−	6.37226e6i	−1.18734	−	1.09555i
$509$			5.35388e6i			0.915956i	0.888964	+	0.457978i	$0.151426\pi$
$509$			5.35388e6i			0.915956i	−0.888964	+	0.457978i	$0.848574\pi$
$510$		0			0
$511$	−7.11322e6			−1.20508
$512$	−3.21849e6	−	4.98254e6i	−0.542597	−	0.839993i
$513$		−	5.80633e6i		−	0.974111i
$514$	−2.05420e6	+	899646.i	−0.342954	+	0.150198i
$515$		0			0
$516$	3.86137e6	−	4.18488e6i	0.638436	−	0.691924i
$517$	−7.47173e6			−1.22941
$518$	9.03978e6	−	3.95900e6i	1.48024	−	0.648278i
$519$	−1.81481e6			−0.295743
$520$		0			0
$521$	−2.62401e6			−0.423518			−0.211759	−	0.977322i	$-0.567919\pi$
$521$	−2.62401e6			−0.423518			−0.211759	+	0.977322i	$0.567919\pi$
$522$	−2.65600e6	+	1.16320e6i	−0.426631	+	0.186844i
$523$	−1.31228e6			−0.209784			−0.104892	−	0.994484i	$-0.533450\pi$
$523$	−1.31228e6			−0.209784			−0.104892	+	0.994484i	$0.533450\pi$
$524$	−7.47262e6	−	6.89497e6i	−1.18890	−	1.09699i
$525$		0			0
$526$	1.00226e7	−	4.38943e6i	1.57949	−	0.691741i
$527$			8.35008e6i			1.30968i
$528$	3.55216e6	−	286093.i	0.554508	−	0.0446605i
$529$	4.92055e6			0.764494
$530$		0			0
$531$		−	3.17904e6i		−	0.489282i
$532$	5.16657e6	−	5.59941e6i	0.791449	−	0.857756i
$533$	−757570.			−0.115506
$534$	2.22055e6	+	5.07030e6i	0.336983	+	0.769450i
$535$		0			0
$536$	3.57525e6	+	1.23430e6i	0.537520	+	0.185571i
$537$			5.80081e6i			0.868067i
$538$	3.47183e6	−	1.52050e6i	0.517133	−	0.226480i
$539$		−	3.21285e6i		−	0.476342i
$540$		0			0
$541$		−	6.84935e6i		−	1.00613i	−0.864247	−	0.503067i	$-0.832205\pi$
$541$		−	6.84935e6i		−	1.00613i	0.864247	−	0.503067i	$-0.167795\pi$
$542$	4.74157e6	+	1.08267e7i	0.693304	+	1.58306i
$543$			1.22794e6i			0.178722i
$544$	−5.78820e6	−	1.07697e7i	−0.838583	−	1.56029i
$545$		0			0
$546$	−1.17752e6	+	515698.i	−0.169039	+	0.0740311i
$547$	−6.39084e6			−0.913251			−0.456625	−	0.889659i	$-0.650942\pi$
$547$	−6.39084e6			−0.913251			−0.456625	+	0.889659i	$0.650942\pi$
$548$	3.81665e6	+	3.52162e6i	0.542914	+	0.500946i
$549$			4.92232e6i			0.697010i
$550$		0			0
$551$	5.92391e6			0.831246
$552$	787222.	−	2.28025e6i	0.109964	−	0.318518i
$553$			2.05392e6i			0.285609i
$554$	1.88091e6	+	4.29477e6i	0.260372	+	0.594519i
$555$		0			0
$556$	−7.21441e6	−	6.65672e6i	−0.989724	−	0.913216i
$557$	463389.			0.0632861			0.0316430	−	0.999499i	$-0.489926\pi$
$557$	463389.			0.0632861			0.0316430	+	0.999499i	$0.489926\pi$
$558$	1.12975e6	+	2.57961e6i	0.153602	+	0.350726i
$559$	−2.10830e6			−0.285367
$560$		0			0
$561$	7.34561e6			0.985418
$562$	5.44488e6	+	1.24326e7i	0.727189	+	1.66043i
$563$	1.07609e7			1.43080			0.715400	−	0.698715i	$-0.246244\pi$
$563$	1.07609e7			1.43080			0.715400	+	0.698715i	$0.246244\pi$
$564$	−5.91568e6	−	5.45838e6i	−0.783081	−	0.722547i
$565$		0			0
$566$	−4.55839e6	−	1.04084e7i	−0.598096	−	1.36566i
$567$		−	2.06823e6i		−	0.270173i
$568$	−2.37655e6	−	820467.i	−0.309083	−	0.106706i
$569$	1.04253e7			1.34992			0.674961	−	0.737853i	$-0.264160\pi$
$569$	1.04253e7			1.34992			0.674961	+	0.737853i	$0.264160\pi$
$570$		0			0
$571$		−	1.58675e6i		−	0.203666i	−0.994802	−	0.101833i	$-0.967529\pi$
$571$		−	1.58675e6i		−	0.203666i	0.994802	−	0.101833i	$-0.0324707\pi$
$572$	−969737.	−	894774.i	−0.123926	−	0.114347i
$573$	4.24094e6			0.539605
$574$	5.01093e6	−	2.19455e6i	0.634802	−	0.278014i
$575$		0			0
$576$	−3.24528e6	−	2.54398e6i	−0.407564	−	0.319490i
$577$		−	2.79056e6i		−	0.348941i	−0.984662	−	0.174471i	$-0.944179\pi$
$577$		−	2.79056e6i		−	0.348941i	0.984662	−	0.174471i	$-0.0558214\pi$
$578$	−6.88811e6	−	1.57280e7i	−0.857592	−	1.95818i
$579$			2.83062e6i			0.350901i
$580$		0			0
$581$		−	1.09369e6i		−	0.134417i
$582$	−8.39148e6	+	3.67508e6i	−1.02691	+	0.449737i
$583$			9.84944e6i			1.20016i
$584$	2.56679e6	−	7.43490e6i	0.311428	−	0.902076i
$585$		0			0
$586$	−3.95327e6	−	9.02668e6i	−0.475567	−	1.08589i
$587$	−1.94272e6			−0.232710			−0.116355	−	0.993208i	$-0.537121\pi$
$587$	−1.94272e6			−0.232710			−0.116355	+	0.993208i	$0.537121\pi$
$588$	2.34711e6	−	2.54374e6i	0.279956	−	0.303410i
$589$		−	5.75353e6i		−	0.683355i
$590$		0			0
$591$	−9.73022e6			−1.14592
$592$	876055.	+	1.08772e7i	0.102737	+	1.27559i
$593$		−	8.14862e6i		−	0.951584i	−0.879558	−	0.475792i	$-0.842161\pi$
$593$		−	8.14862e6i		−	0.951584i	0.879558	−	0.475792i	$-0.157839\pi$
$594$	6.65133e6	−	2.91297e6i	0.773468	−	0.338743i
$595$		0			0
$596$	−8.65720e6	−	7.98798e6i	−0.998302	−	0.921131i
$597$	906179.			0.104059
$598$	−818154.	+	358313.i	−0.0935583	+	0.0409742i
$599$	−1.49677e6			−0.170447			−0.0852234	−	0.996362i	$-0.527160\pi$
$599$	−1.49677e6			−0.170447			−0.0852234	+	0.996362i	$0.527160\pi$
$600$		0			0
$601$	−9.04082e6			−1.02099			−0.510495	−	0.859881i	$-0.670538\pi$
$601$	−9.04082e6			−1.02099			−0.510495	+	0.859881i	$0.670538\pi$
$602$	1.39453e7	−	6.10740e6i	1.56833	−	0.686855i
$603$	2.62938e6			0.294483
$604$	−7.30910e6	+	7.92144e6i	−0.815213	+	0.883511i
$605$		0			0
$606$	6.43998e6	−	2.82041e6i	0.712366	−	0.311983i
$607$		−	3.63200e6i		−	0.400105i	−0.979785	−	0.200052i	$-0.935889\pi$
$607$		−	3.63200e6i		−	0.400105i	0.979785	−	0.200052i	$-0.0641112\pi$
$608$	3.98829e6	+	7.42075e6i	0.437550	+	0.814120i
$609$	7.21751e6			0.788577
$610$		0			0
$611$			2.98027e6i			0.322962i
$612$	−6.24677e6	−	5.76388e6i	−0.674182	−	0.622066i
$613$	1.89937e6			0.204154			0.102077	−	0.994776i	$-0.467451\pi$
$613$	1.89937e6			0.204154			0.102077	+	0.994776i	$0.467451\pi$
$614$	−2.22099e6	−	5.07128e6i	−0.237752	−	0.542871i
$615$		0			0
$616$	9.00631e6	+	3.10929e6i	0.956302	+	0.330149i
$617$			5.96746e6i			0.631069i	0.948914	+	0.315534i	$0.102184\pi$
$617$			5.96746e6i			0.631069i	−0.948914	+	0.315534i	$0.897816\pi$
$618$	2.16422e6	−	947826.i	0.227945	−	0.0998291i
$619$		−	1.46307e7i		−	1.53475i	−0.641196	−	0.767377i	$-0.721561\pi$
$619$		−	1.46307e7i		−	1.53475i	0.641196	−	0.767377i	$-0.278439\pi$
$620$		0			0
$621$		−	4.91527e6i		−	0.511468i
$622$	−3.57766e6	−	8.16905e6i	−0.370786	−	0.846634i
$623$			1.47992e7i			1.52763i
$624$	−114115.	−	1.41686e6i	−0.0117322	−	0.145668i
$625$		0			0
$626$	8.34055e6	−	3.65277e6i	0.850666	−	0.372552i
$627$	−5.06141e6			−0.514165
$628$	−5.88622e6	+	6.37936e6i	−0.595577	+	0.645473i
$629$			2.24932e7i			2.26686i
$630$		0			0
$631$	−1.47747e7			−1.47722			−0.738609	−	0.674134i	$-0.764517\pi$
$631$	−1.47747e7			−1.47722			−0.738609	+	0.674134i	$0.764517\pi$
$632$	−2.14681e6	−	741154.i	−0.213796	−	0.0738101i
$633$		−	5.99261e6i		−	0.594438i
$634$	3.41923e6	+	7.80729e6i	0.337835	+	0.771395i
$635$		0			0
$636$	−7.19538e6	+	7.79821e6i	−0.705361	+	0.764455i
$637$	−1.28152e6			−0.125134
$638$	2.97196e6	+	6.78603e6i	0.289062	+	0.660030i
$639$	−1.74781e6			−0.169333
$640$		0			0
$641$	1.81017e7			1.74010			0.870050	−	0.492964i	$-0.164087\pi$
$641$	1.81017e7			1.74010			0.870050	+	0.492964i	$0.164087\pi$
$642$	−4.65376e6	−	1.06261e7i	−0.445622	−	1.01751i
$643$	−7.21849e6			−0.688524			−0.344262	−	0.938874i	$-0.611871\pi$
$643$	−7.21849e6			−0.688524			−0.344262	+	0.938874i	$0.611871\pi$
$644$	4.37369e6	−	4.74011e6i	0.415559	−	0.450374i
$645$		0			0
$646$	6.96636e6	+	1.59066e7i	0.656787	+	1.49967i
$647$			2.44672e6i			0.229786i	0.993378	+	0.114893i	$0.0366526\pi$
$647$			2.44672e6i			0.229786i	−0.993378	+	0.114893i	$0.963347\pi$
$648$	2.16176e6	+	746316.i	0.202241	+	0.0698209i
$649$	−8.12237e6			−0.756957
$650$		0			0
$651$		−	7.00992e6i		−	0.648277i
$652$	−2.63341e6	+	2.85403e6i	−0.242605	+	0.262930i
$653$	5.92231e6			0.543511			0.271755	−	0.962366i	$-0.412396\pi$
$653$	5.92231e6			0.543511			0.271755	+	0.962366i	$0.412396\pi$
$654$	−1.36810e6	+	599166.i	−0.125076	+	0.0547776i
$655$		0			0
$656$	485615.	+	6.02943e6i	0.0440587	+	0.547037i
$657$		−	5.46793e6i		−	0.494208i
$658$	−8.63333e6	−	1.97129e7i	−0.777345	−	1.77495i
$659$		−	2.68146e6i		−	0.240523i	−0.992742	−	0.120262i	$-0.961627\pi$
$659$		−	2.68146e6i		−	0.240523i	0.992742	−	0.120262i	$-0.0383734\pi$
$660$		0			0
$661$			1.14098e7i			1.01572i	0.861440	+	0.507859i	$0.169563\pi$
$661$			1.14098e7i			1.01572i	−0.861440	+	0.507859i	$0.830437\pi$
$662$	2.04394e6	−	895150.i	0.181269	−	0.0793873i
$663$		−	2.92996e6i		−	0.258868i
$664$	1.14315e6	+	394657.i	0.100620	+	0.0347376i
$665$		0			0
$666$	3.04328e6	+	6.94887e6i	0.265862	+	0.607056i
$667$	5.01481e6			0.436456
$668$	−1.31926e6	−	1.21728e6i	−0.114390	−	0.105548i
$669$		−	3.02423e6i		−	0.261246i
$670$		0			0
$671$	1.25764e7			1.07833
$672$	4.85921e6	+	9.04120e6i	0.415090	+	0.772330i
$673$			5.13646e6i			0.437146i	0.975821	+	0.218573i	$0.0701402\pi$
$673$			5.13646e6i			0.437146i	−0.975821	+	0.218573i	$0.929860\pi$
$674$	7.09269e6	−	3.10627e6i	0.601397	−	0.263384i
$675$		0			0
$676$	7.70021e6	−	8.34533e6i	0.648091	−	0.702387i
$677$	4.91407e6			0.412068			0.206034	−	0.978545i	$-0.433944\pi$
$677$	4.91407e6			0.412068			0.206034	+	0.978545i	$0.433944\pi$
$678$	−2.96804e6	+	1.29986e6i	−0.247968	+	0.108598i
$679$	−2.44930e7			−2.03877
$680$		0			0
$681$	−6.41937e6			−0.530426
$682$	6.59085e6	−	2.88648e6i	0.542601	−	0.237634i
$683$	−4.30841e6			−0.353399			−0.176700	−	0.984265i	$-0.556542\pi$
$683$	−4.30841e6			−0.353399			−0.176700	+	0.984265i	$0.556542\pi$
$684$	4.30427e6	+	3.97154e6i	0.351770	+	0.324577i
$685$		0			0
$686$	−5.78043e6	+	2.53156e6i	−0.468975	+	0.205389i
$687$		−	1.00433e7i		−	0.811868i
$688$	1.35146e6	+	1.67798e7i	0.108851	+	1.35150i
$689$	3.92867e6			0.315281
$690$		0			0
$691$		−	2.17672e6i		−	0.173423i	−0.996233	−	0.0867116i	$-0.972364\pi$
$691$		−	2.17672e6i		−	0.173423i	0.996233	−	0.0867116i	$-0.0276359\pi$
$692$	3.63837e6	−	3.94319e6i	0.288829	−	0.313027i
$693$	6.62361e6			0.523916
$694$	−1.29211e6	−	2.95034e6i	−0.101836	−	0.232527i
$695$		0			0
$696$	−2.60442e6	+	7.54390e6i	−0.203792	+	0.590300i
$697$			1.24684e7i			0.972142i
$698$	1.14025e7	−	4.99375e6i	0.885851	−	0.387961i
$699$			1.18284e7i			0.915658i
$700$		0			0
$701$			1.31991e6i			0.101450i	0.998713	+	0.0507248i	$0.0161531\pi$
$701$			1.31991e6i			0.101450i	−0.998713	+	0.0507248i	$0.983847\pi$
$702$	−1.16190e6	−	2.65303e6i	−0.0889871	−	0.203189i
$703$		−	1.54987e7i		−	1.18279i
$704$	−6.49981e6	+	8.29162e6i	−0.494275	+	0.630533i
$705$		0			0
$706$	−1.30349e7	+	5.70870e6i	−0.984232	+	0.431048i
$707$	1.87970e7			1.41429
$708$	−6.43081e6	−	5.93370e6i	−0.482151	−	0.444879i
$709$			1.33410e7i			0.996721i	0.866970	+	0.498360i	$0.166064\pi$
$709$			1.33410e7i			0.996721i	−0.866970	+	0.498360i	$0.833936\pi$
$710$		0			0
$711$	−1.57885e6			−0.117130
$712$	−1.54684e7	−	5.34024e6i	−1.14353	−	0.394785i
$713$		−	4.87058e6i		−	0.358803i
$714$	8.48759e6	+	1.93801e7i	0.623073	+	1.42269i
$715$		0			0
$716$	−1.26039e7	−	1.16296e7i	−0.918800	−	0.847775i
$717$	8.63721e6			0.627445
$718$	1.80369e6	+	4.11846e6i	0.130573	+	0.298143i
$719$	−2.25289e7			−1.62524			−0.812620	−	0.582794i	$-0.801960\pi$
$719$	−2.25289e7			−1.62524			−0.812620	+	0.582794i	$0.801960\pi$
$720$		0			0
$721$	6.31691e6			0.452550
$722$	819031.	+	1.87013e6i	0.0584732	+	0.133515i
$723$	−1.75199e7			−1.24648
$724$	−2.66805e6	−	2.46180e6i	−0.189168	−	0.174545i
$725$		0			0
$726$	1.41671e6	+	3.23485e6i	0.0997562	+	0.227778i
$727$		−	1.49088e7i		−	1.04618i	−0.852277	−	0.523091i	$-0.824779\pi$
$727$		−	1.49088e7i		−	1.04618i	0.852277	−	0.523091i	$-0.175221\pi$
$728$	1.24021e6	−	3.59237e6i	0.0867296	−	0.251219i
$729$	1.20906e7			0.842617
$730$		0			0
$731$			3.46994e7i			2.40175i
$732$	9.95727e6	+	9.18755e6i	0.686851	+	0.633756i
$733$	−7.98329e6			−0.548810			−0.274405	−	0.961614i	$-0.588481\pi$
$733$	−7.98329e6			−0.548810			−0.274405	+	0.961614i	$0.588481\pi$
$734$	4.53037e6	−	1.98409e6i	0.310380	−	0.135932i
$735$		0			0
$736$	3.37624e6	+	6.28193e6i	0.229741	+	0.427463i
$737$		−	6.71802e6i		−	0.455588i
$738$	1.68695e6	+	3.85190e6i	0.114015	+	0.260336i
$739$		−	3.81018e6i		−	0.256646i	−0.991732	−	0.128323i	$-0.959041\pi$
$739$		−	3.81018e6i		−	0.256646i	0.991732	−	0.128323i	$-0.0409594\pi$
$740$		0			0
$741$			2.01885e6i			0.135070i
$742$	−2.59861e7	+	1.13807e7i	−1.73273	+	0.758855i
$743$		−	8.99457e6i		−	0.597734i	−0.954295	−	0.298867i	$-0.903391\pi$
$743$		−	8.99457e6i		−	0.597734i	0.954295	−	0.298867i	$-0.0966088\pi$
$744$	7.32693e6	+	2.52951e6i	0.485277	+	0.167535i
$745$		0			0
$746$	1.10337e7	+	2.51937e7i	0.725893	+	1.65747i
$747$	840722.			0.0551253
$748$	−1.47266e7	+	1.59604e7i	−0.962383	+	1.04301i
$749$		−	3.10156e7i		−	2.02011i
$750$		0			0
$751$	1.18325e7			0.765559			0.382779	−	0.923840i	$-0.374967\pi$
$751$	1.18325e7			0.765559			0.382779	+	0.923840i	$0.374967\pi$
$752$	2.37197e7	−	1.91040e6i	1.52955	−	0.123191i
$753$		−	4.86742e6i		−	0.312832i
$754$	2.70676e6	−	1.18543e6i	0.173389	−	0.0759362i
$755$		0			0
$756$	1.53708e7	+	1.41826e7i	0.978117	+	0.902506i
$757$	−5.14086e6			−0.326059			−0.163030	−	0.986621i	$-0.552127\pi$
$757$	−5.14086e6			−0.326059			−0.163030	+	0.986621i	$0.552127\pi$
$758$	−6.43308e6	+	2.81739e6i	−0.406673	+	0.178104i
$759$	−4.28467e6			−0.269968
$760$		0			0
$761$	8.21979e6			0.514516			0.257258	−	0.966343i	$-0.417181\pi$
$761$	8.21979e6			0.514516			0.257258	+	0.966343i	$0.417181\pi$
$762$	−1.64699e7	+	7.21306e6i	−1.02755	+	0.450020i
$763$	−3.99322e6			−0.248320
$764$	−8.50230e6	+	9.21461e6i	−0.526991	+	0.571142i
$765$		0			0
$766$	−160477.	+	70281.3i	−0.00988189	+	0.00432781i
$767$			3.23979e6i			0.198851i
$768$	−1.12035e7	+	1.81646e6i	−0.685410	+	0.111128i
$769$	1.11390e7			0.679251			0.339626	−	0.940561i	$-0.389700\pi$
$769$	1.11390e7			0.679251			0.339626	+	0.940561i	$0.389700\pi$
$770$		0			0
$771$			4.29101e6i			0.259970i
$772$	−6.15030e6	−	5.67487e6i	−0.371410	−	0.342699i
$773$	5.63671e6			0.339294			0.169647	−	0.985505i	$-0.445737\pi$
$773$	5.63671e6			0.339294			0.169647	+	0.985505i	$0.445737\pi$
$774$	4.69475e6	+	1.07198e7i	0.281683	+	0.643180i
$775$		0			0
$776$	8.83825e6	−	2.56007e7i	0.526880	−	1.52615i
$777$		−	1.88831e7i		−	1.12207i
$778$	−2.21705e7	+	9.70963e6i	−1.31318	+	0.575113i
$779$		−	8.59123e6i		−	0.507238i
$780$		0			0
$781$			4.46561e6i			0.261971i
$782$	5.89728e6	+	1.34655e7i	0.344854	+	0.787421i
$783$			1.62615e7i			0.947888i
$784$	821473.	+	1.01995e7i	0.0477313	+	0.592636i
$785$		0			0
$786$	−1.78209e7	+	7.80474e6i	−1.02890	+	0.450611i
$787$	3.07197e7			1.76799			0.883996	−	0.467495i	$-0.154843\pi$
$787$	3.07197e7			1.76799			0.883996	+	0.467495i	$0.154843\pi$
$788$	1.95073e7	−	2.11416e7i	1.11913	−	1.21289i
$789$		−	2.09361e7i		−	1.19730i
$790$		0			0
$791$	−8.66309e6			−0.492302
$792$	−2.39011e6	+	6.92314e6i	−0.135396	+	0.392184i
$793$		−	5.01639e6i		−	0.283275i
$794$	−5.24489e6	−	1.19759e7i	−0.295246	−	0.674151i
$795$		0			0
$796$	−1.81672e6	+	1.96892e6i	−0.101626	+	0.110140i
$797$	2.22339e7			1.23985			0.619926	−	0.784660i	$-0.287163\pi$
$797$	2.22339e7			1.23985			0.619926	+	0.784660i	$0.287163\pi$
$798$	−5.84828e6	−	1.33537e7i	−0.325103	−	0.742323i
$799$	4.90505e7			2.71817
$800$		0			0
$801$	−1.13761e7			−0.626488
$802$	2.26106e6	+	5.16278e6i	0.124130	+	0.283431i
$803$	−1.39704e7			−0.764577
$804$	4.90776e6	−	5.31893e6i	0.267759	−	0.290191i
$805$		0			0
$806$	−1.15134e6	−	2.62891e6i	−0.0624260	−	0.142540i
$807$		−	7.25226e6i		−	0.392003i
$808$	−6.78285e6	+	1.96470e7i	−0.365497	+	1.05869i
$809$	−1.51247e7			−0.812484			−0.406242	−	0.913765i	$-0.633161\pi$
$809$	−1.51247e7			−0.812484			−0.406242	+	0.913765i	$0.633161\pi$
$810$		0			0
$811$		−	1.35982e7i		−	0.725990i	−0.931791	−	0.362995i	$-0.881754\pi$
$811$		−	1.35982e7i		−	0.725990i	0.931791	−	0.362995i	$-0.118246\pi$
$812$	−1.44698e7	+	1.56820e7i	−0.770143	+	0.834665i
$813$	2.26157e7			1.20001
$814$	1.77542e7	−	7.77552e6i	0.939162	−	0.411309i
$815$		0			0
$816$	−2.33193e7	+	1.87815e6i	−1.22600	+	0.0987427i
$817$		−	2.39092e7i		−	1.25317i
$818$	1.17540e7	+	2.68385e7i	0.614191	+	1.40241i
$819$		−	2.64197e6i		−	0.137632i
$820$		0			0
$821$			2.56951e7i			1.33043i	0.746651	+	0.665216i	$0.231660\pi$
$821$			2.56951e7i			1.33043i	−0.746651	+	0.665216i	$0.768340\pi$
$822$	9.10207e6	−	3.98628e6i	0.469852	−	0.205773i
$823$		−	8.73184e6i		−	0.449372i	−0.974431	−	0.224686i	$-0.927864\pi$
$823$		−	8.73184e6i		−	0.449372i	0.974431	−	0.224686i	$-0.0721357\pi$
$824$	−2.27944e6	+	6.60257e6i	−0.116953	+	0.338762i
$825$		0			0
$826$	−9.38512e6	−	2.14295e7i	−0.478619	−	1.09285i
$827$	1.46565e6			0.0745191			0.0372596	−	0.999306i	$-0.488137\pi$
$827$	1.46565e6			0.0745191			0.0372596	+	0.999306i	$0.488137\pi$
$828$	3.64372e6	+	3.36205e6i	0.184701	+	0.170423i
$829$		−	4.49887e6i		−	0.227362i	−0.993517	−	0.113681i	$-0.963736\pi$
$829$		−	4.49887e6i		−	0.227362i	0.993517	−	0.113681i	$-0.0362641\pi$
$830$		0			0
$831$	8.97130e6			0.450664
$832$	3.30729e6	+	2.59259e6i	0.165640	+	0.129845i
$833$			2.10918e7i			1.05317i
$834$	−1.72052e7	+	7.53506e6i	−0.856532	+	0.375121i
$835$		0			0
$836$	1.01472e7	−	1.09973e7i	0.502146	−	0.544215i
$837$	1.57938e7			0.779244
$838$	1.85349e7	−	8.11741e6i	0.911758	−	0.399307i
$839$	1.43801e7			0.705273			0.352636	−	0.935760i	$-0.385285\pi$
$839$	1.43801e7			0.705273			0.352636	+	0.935760i	$0.385285\pi$
$840$		0			0
$841$	3.92030e6			0.191130
$842$	−1.11846e7	+	4.89834e6i	−0.543677	+	0.238105i
$843$	2.59702e7			1.25866
$844$	1.30206e7	+	1.20141e7i	0.629180	+	0.580543i
$845$		0			0
$846$	1.51533e7	−	6.63643e6i	0.727916	−	0.318793i
$847$			9.44185e6i			0.452219i
$848$	−2.51834e6	−	3.12679e7i	−0.120261	−	1.49317i
$849$	−2.17420e7			−1.03521
$850$		0			0
$851$		−	1.31202e7i		−	0.621036i
$852$	−3.26230e6	+	3.53561e6i	−0.153966	+	0.166865i
$853$	2.62365e7			1.23462			0.617310	−	0.786720i	$-0.288222\pi$
$853$	2.62365e7			1.23462			0.617310	+	0.786720i	$0.288222\pi$
$854$	1.45316e7	+	3.31808e7i	0.681820	+	1.55683i
$855$		0			0
$856$	3.24182e7	+	1.11919e7i	1.51218	+	0.522058i
$857$		−	6.34066e6i		−	0.294905i	−0.989069	−	0.147453i	$-0.952893\pi$
$857$		−	6.34066e6i		−	0.294905i	0.989069	−	0.147453i	$-0.0471074\pi$
$858$	−2.31266e6	+	1.01284e6i	−0.107249	+	0.0469701i
$859$		−	1.09488e7i		−	0.506273i	−0.967431	−	0.253137i	$-0.918538\pi$
$859$		−	1.09488e7i		−	0.506273i	0.967431	−	0.253137i	$-0.0814622\pi$
$860$		0			0
$861$		−	1.04673e7i		−	0.481200i
$862$	−4.10501e6	−	9.37318e6i	−0.188168	−	0.429654i
$863$			3.28604e6i			0.150192i	0.997176	+	0.0750958i	$0.0239263\pi$
$863$			3.28604e6i			0.150192i	−0.997176	+	0.0750958i	$0.976074\pi$
$864$	−2.03704e7	+	1.09481e7i	−0.928359	+	0.498948i
$865$		0			0
$866$	6.67978e6	−	2.92543e6i	0.302669	−	0.132555i
$867$	−3.28540e7			−1.48436
$868$	1.52310e7	+	1.40536e7i	0.686165	+	0.633123i
$869$			4.03393e6i			0.181209i
$870$		0			0
$871$	−2.67963e6			−0.119682
$872$	1.44094e6	−	4.17380e6i	0.0641735	−	0.185883i
$873$		−	1.88278e7i		−	0.836110i
$874$	−4.06345e6	−	9.27828e6i	−0.179936	−	0.410855i
$875$		0			0
$876$	−1.10610e7	−	1.02059e7i	−0.487005	−	0.449358i
$877$	7.75326e6			0.340397			0.170198	−	0.985410i	$-0.445559\pi$
$877$	7.75326e6			0.340397			0.170198	+	0.985410i	$0.445559\pi$
$878$	−4.30481e6	−	9.82937e6i	−0.188459	−	0.430318i
$879$	−1.88557e7			−0.823136
$880$		0			0
$881$	−449453.			−0.0195094			−0.00975471	−	0.999952i	$-0.503105\pi$
$881$	−449453.			−0.0195094			−0.00975471	+	0.999952i	$0.503105\pi$
$882$	2.85367e6	+	6.51592e6i	0.123519	+	0.282036i
$883$	2.42001e7			1.04452			0.522259	−	0.852787i	$-0.325089\pi$
$883$	2.42001e7			1.04452			0.522259	+	0.852787i	$0.325089\pi$
$884$	6.36614e6	+	5.87402e6i	0.273997	+	0.252816i
$885$		0			0
$886$	−1.36610e7	−	3.11928e7i	−0.584652	−	1.33496i
$887$			8.80204e6i			0.375642i	0.982203	+	0.187821i	$0.0601425\pi$
$887$			8.80204e6i			0.375642i	−0.982203	+	0.187821i	$0.939857\pi$
$888$	1.97370e7	+	6.81392e6i	0.839943	+	0.289978i
$889$	−4.80724e7			−2.04005
$890$		0			0
$891$		−	4.06203e6i		−	0.171415i
$892$	6.57097e6	+	6.06302e6i	0.276514	+	0.255139i
$893$	−3.37977e7			−1.41827
$894$	−2.06460e7	+	9.04197e6i	−0.863956	+	0.378372i
$895$		0			0
$896$	−2.93863e7	−	7.56797e6i	−1.22286	−	0.314926i
$897$			1.70903e6i			0.0709202i
$898$	5.44826e6	+	1.24403e7i	0.225459	+	0.514801i
$899$			1.61137e7i			0.664959i
$900$		0			0
$901$		−	6.46597e7i		−	2.65352i
$902$	9.84151e6	−	4.31012e6i	0.402759	−	0.176390i
$903$		−	2.91302e7i		−	1.18884i
$904$	3.12606e6	−	9.05486e6i	0.127226	−	0.368520i
$905$		0			0
$906$	8.27351e6	+	1.88913e7i	0.334865	+	0.764613i
$907$	−1.35035e7			−0.545040			−0.272520	−	0.962150i	$-0.587857\pi$
$907$	−1.35035e7			−0.545040			−0.272520	+	0.962150i	$0.587857\pi$
$908$	1.28697e7	−	1.39479e7i	0.518027	−	0.561426i
$909$			1.44492e7i			0.580010i
$910$		0			0
$911$	−1.74802e7			−0.697831			−0.348915	−	0.937154i	$-0.613450\pi$
$911$	−1.74802e7			−0.697831			−0.348915	+	0.937154i	$0.613450\pi$
$912$	1.60679e7	−	1.29412e6i	0.639693	−	0.0515213i
$913$		−	2.14803e6i		−	0.0852830i
$914$	4.45083e6	−	1.94926e6i	0.176228	−	0.0771798i
$915$		0			0
$916$	2.18219e7	+	2.01350e7i	0.859317	+	0.792890i
$917$	−5.20157e7			−2.04273
$918$	−4.36647e7	+	1.91231e7i	−1.71011	+	0.748948i
$919$	−3.84416e7			−1.50146			−0.750728	−	0.660612i	$-0.770297\pi$
$919$	−3.84416e7			−1.50146			−0.750728	+	0.660612i	$0.770297\pi$
$920$		0			0
$921$	−1.05934e7			−0.411514
$922$	−1.20983e7	+	5.29849e6i	−0.468702	+	0.205270i
$923$	1.78121e6			0.0688194
$924$	1.23630e7	−	1.33988e7i	0.476370	−	0.516280i
$925$		0			0
$926$	−7.00542e6	+	3.06805e6i	−0.268477	+	0.117580i
$927$			4.85580e6i			0.185593i
$928$	−1.11698e7	−	2.07830e7i	−0.425772	−	0.792205i
$929$	694053.			0.0263848			0.0131924	−	0.999913i	$-0.495801\pi$
$929$	694053.			0.0263848			0.0131924	+	0.999913i	$0.495801\pi$
$930$		0			0
$931$		−	1.45330e7i		−	0.549518i
$932$	−2.57005e7	−	2.37138e7i	−0.969174	−	0.894254i
$933$	−1.70643e7			−0.641776
$934$	−1.46149e7	−	3.33709e7i	−0.548186	−	1.25170i
$935$		0			0
$936$	2.76145e6	+	953349.i	0.103026	+	0.0355682i
$937$			4.08849e7i			1.52130i	0.649165	+	0.760648i	$0.275119\pi$
$937$			4.08849e7i			1.52130i	−0.649165	+	0.760648i	$0.724881\pi$
$938$	1.77243e7	−	7.76244e6i	0.657753	−	0.288065i
$939$		−	1.74225e7i		−	0.644832i
$940$		0			0
$941$			1.21324e7i			0.446655i	0.974743	+	0.223328i	$0.0716920\pi$
$941$			1.21324e7i			0.446655i	−0.974743	+	0.223328i	$0.928308\pi$
$942$	6.66289e6	+	1.52137e7i	0.244645	+	0.558609i
$943$		−	7.27279e6i		−	0.266331i
$944$	2.57852e7	−	2.07676e6i	0.941760	−	0.0758500i
$945$		0			0
$946$	2.73887e7	−	1.19950e7i	0.995049	−	0.435785i
$947$	3.38948e7			1.22817			0.614084	−	0.789241i	$-0.289526\pi$
$947$	3.38948e7			1.22817			0.614084	+	0.789241i	$0.289526\pi$
$948$	−2.94694e6	+	3.19383e6i	−0.106500	+	0.115422i
$949$			5.57242e6i			0.200853i
$950$		0			0
$951$	1.63086e7			0.584742
$952$	−5.91247e7	−	2.04119e7i	−2.11435	−	0.729948i
$953$			5.18152e7i			1.84810i	0.382274	+	0.924049i	$0.375141\pi$
$953$			5.18152e7i			1.84810i	−0.382274	+	0.924049i	$0.624859\pi$
$954$	−8.74833e6	−	1.99755e7i	−0.311210	−	0.710602i
$955$		0			0
$956$	−1.73160e7	+	1.87667e7i	−0.612778	+	0.664116i
$957$	1.41753e7			0.500324
$958$	4.20641e6	+	9.60470e6i	0.148080	+	0.338119i
$959$	2.65671e7			0.932819
$960$		0			0
$961$	−1.29789e7			−0.453347
$962$	−3.10144e6	−	7.08166e6i	−0.108050	−	0.246716i
$963$	2.38416e7			0.828458
$964$	3.51241e7	−	3.80667e7i	1.21734	−	1.31933i
$965$		0			0
$966$	−4.95078e6	−	1.13044e7i	−0.170699	−	0.389765i
$967$		−	4.41440e7i		−	1.51812i	−0.651023	−	0.759058i	$-0.725660\pi$
$967$		−	4.41440e7i		−	1.51812i	0.651023	−	0.759058i	$-0.274340\pi$
$968$	−9.86884e6	−	3.40707e6i	−0.338515	−	0.116867i
$969$	3.32272e7			1.13680
$970$		0			0
$971$			2.25369e7i			0.767091i	0.923522	+	0.383546i	$0.125297\pi$
$971$			2.25369e7i			0.767091i	−0.923522	+	0.383546i	$0.874703\pi$
$972$	−1.80847e7	+	1.95998e7i	−0.613967	+	0.665404i
$973$	−5.02184e7			−1.70052
$974$	−1.30407e7	+	5.71122e6i	−0.440457	+	0.192900i
$975$		0			0
$976$	−3.99250e7	+	3.21558e6i	−1.34159	+	0.108053i
$977$		−	508955.i		−	0.0170586i	−0.999964	−	0.00852929i	$-0.997285\pi$
$977$		−	508955.i		−	0.0170586i	0.999964	−	0.00852929i	$-0.00271499\pi$
$978$	2.98088e6	+	6.80639e6i	0.0996546	+	0.227546i
$979$			2.90657e7i			0.969224i
$980$		0			0
$981$		−	3.06958e6i		−	0.101837i
$982$	2.79354e7	−	1.22344e7i	0.924433	−	0.404859i
$983$			1.38312e7i			0.456536i	0.973598	+	0.228268i	$0.0733063\pi$
$983$			1.38312e7i			0.456536i	−0.973598	+	0.228268i	$0.926694\pi$
$984$	1.09406e7	+	3.77709e6i	0.360209	+	0.124357i
$985$		0			0
$986$	−1.95104e7	−	4.45490e7i	−0.639107	−	1.45930i
$987$	−4.11781e7			−1.34547
$988$	−4.38652e6	−	4.04743e6i	−0.142964	−	0.131913i
$989$		−	2.02400e7i		−	0.657992i
$990$		0			0
$991$	1.13368e7			0.366696			0.183348	−	0.983048i	$-0.441307\pi$
$991$	1.13368e7			0.366696			0.183348	+	0.983048i	$0.441307\pi$
$992$	−2.01852e7	+	1.08486e7i	−0.651259	+	0.350020i
$993$		−	4.26957e6i		−	0.137408i
$994$	−1.17818e7	+	5.15986e6i	−0.378220	+	0.165643i
$995$		0			0
$996$	1.56921e6	−	1.70068e6i	0.0501226	−	0.0543218i
$997$	3.66390e7			1.16736			0.583681	−	0.811983i	$-0.301612\pi$
$997$	3.66390e7			1.16736			0.583681	+	0.811983i	$0.301612\pi$
$998$	1.64964e7	−	7.22464e6i	0.524278	−	0.229609i
$999$	4.25449e7			1.34876

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	200.6.f.c.149.14		20
4.3	odd	2		800.6.f.b.49.7		20
5.2	odd	4		200.6.d.b.101.4		20
5.3	odd	4		40.6.d.a.21.17	✓	20
5.4	even	2		200.6.f.b.149.7		20
8.3	odd	2		800.6.f.c.49.13		20
8.5	even	2		200.6.f.b.149.8		20
15.8	even	4		360.6.k.b.181.4		20
20.3	even	4		160.6.d.a.81.7		20
20.7	even	4		800.6.d.c.401.14		20
20.19	odd	2		800.6.f.c.49.14		20
40.3	even	4		160.6.d.a.81.14		20
40.13	odd	4		40.6.d.a.21.18	yes	20
40.19	odd	2		800.6.f.b.49.8		20
40.27	even	4		800.6.d.c.401.7		20
40.29	even	2	inner	200.6.f.c.149.13		20
40.37	odd	4		200.6.d.b.101.3		20
120.53	even	4		360.6.k.b.181.3		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.6.d.a.21.17	✓	20	5.3	odd	4
40.6.d.a.21.18	yes	20	40.13	odd	4
160.6.d.a.81.7		20	20.3	even	4
160.6.d.a.81.14		20	40.3	even	4
200.6.d.b.101.3		20	40.37	odd	4
200.6.d.b.101.4		20	5.2	odd	4
200.6.f.b.149.7		20	5.4	even	2
200.6.f.b.149.8		20	8.5	even	2
200.6.f.c.149.13		20	40.29	even	2	inner
200.6.f.c.149.14		20	1.1	even	1	trivial
360.6.k.b.181.3		20	120.53	even	4
360.6.k.b.181.4		20	15.8	even	4
800.6.d.c.401.7		20	40.27	even	4
800.6.d.c.401.14		20	20.7	even	4
800.6.f.b.49.7		20	4.3	odd	2
800.6.f.b.49.8		20	40.19	odd	2
800.6.f.c.49.13		20	8.3	odd	2
800.6.f.c.49.14		20	20.19	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)

\(f(q)\)	\(=\)	\(q+(2.26935 + 5.18171i) q^{2} +10.8240 q^{3} +(-21.7001 + 23.5182i) q^{4} +(24.5634 + 56.0868i) q^{6} +163.706i q^{7} +(-171.109 - 59.0729i) q^{8} -125.841 q^{9} +O(q^{10})\)	\(q+(2.26935 + 5.18171i) q^{2} +10.8240 q^{3} +(-21.7001 + 23.5182i) q^{4} +(24.5634 + 56.0868i) q^{6} +163.706i q^{7} +(-171.109 - 59.0729i) q^{8} -125.841 q^{9} +321.520i q^{11} +(-234.883 + 254.561i) q^{12} +128.246 q^{13} +(-848.277 + 371.506i) q^{14} +(-82.2074 - 1020.69i) q^{16} -2110.72i q^{17} +(-285.576 - 652.070i) q^{18} +1454.37i q^{19} +1771.96i q^{21} +(-1666.02 + 729.641i) q^{22} +1231.18i q^{23} +(-1852.09 - 639.406i) q^{24} +(291.033 + 664.531i) q^{26} -3992.34 q^{27} +(-3850.07 - 3552.45i) q^{28} -4073.19i q^{29} -3956.03 q^{31} +(5102.38 - 2742.28i) q^{32} +3480.14i q^{33} +(10937.1 - 4789.95i) q^{34} +(2730.76 - 2959.54i) q^{36} -10656.6 q^{37} +(-7536.11 + 3300.46i) q^{38} +1388.13 q^{39} -5907.19 q^{41} +(-9181.76 + 4021.18i) q^{42} -16439.6 q^{43} +(-7561.57 - 6977.04i) q^{44} +(-6379.59 + 2793.96i) q^{46} +23238.8i q^{47} +(-889.814 - 11048.0i) q^{48} -9992.68 q^{49} -22846.5i q^{51} +(-2782.95 + 3016.10i) q^{52} +30634.0 q^{53} +(-9059.99 - 20687.1i) q^{54} +(9670.60 - 28011.6i) q^{56} +15742.1i q^{57} +(21106.1 - 9243.47i) q^{58} +25262.4i q^{59} -39115.5i q^{61} +(-8977.61 - 20499.0i) q^{62} -20600.9i q^{63} +(25788.8 + 20215.9i) q^{64} +(-18033.1 + 7897.64i) q^{66} -20894.5 q^{67} +(49640.3 + 45803.0i) q^{68} +13326.3i q^{69} +13889.1 q^{71} +(21532.5 + 7433.78i) q^{72} +43451.2i q^{73} +(-24183.6 - 55219.6i) q^{74} +(-34204.1 - 31560.0i) q^{76} -52634.8 q^{77} +(3150.15 + 7192.89i) q^{78} +12546.4 q^{79} -12633.8 q^{81} +(-13405.4 - 30609.3i) q^{82} -6680.84 q^{83} +(-41673.2 - 38451.7i) q^{84} +(-37307.1 - 85185.1i) q^{86} -44088.2i q^{87} +(18993.2 - 55015.1i) q^{88} +90400.9 q^{89} +20994.6i q^{91} +(-28955.0 - 26716.7i) q^{92} -42820.2 q^{93} +(-120416. + 52736.8i) q^{94} +(55228.3 - 29682.5i) q^{96} +149616. i q^{97} +(-22676.8 - 51779.1i) q^{98} -40460.4i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{2} + 36 q^{3} + 32 q^{4} + 204 q^{6} + 248 q^{8} + 1620 q^{9}+O(q^{10}) \) 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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