LMFDB - Embedded newform 200.6.d.b.101.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [200,6,Mod(101,200)]

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, 0]))

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

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

chi := DirichletCharacter("200.101");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 200 = 2^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	200.d (of order $2$, degree $1$, 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^{12} $
Twist minimal:	no (minimal twist has level 40)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			101.4
Root			$3.72553 - 1.45618i$ of defining polynomial
Character	$\chi$	$=$	200.101
Dual form			200.6.d.b.101.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-5.18171 + 2.26935i) q^{2} -10.8240i q^{3} +(21.7001 - 23.5182i) q^{4} +(24.5634 + 56.0868i) q^{6} -163.706 q^{7} +(-59.0729 + 171.109i) q^{8} +125.841 q^{9} +321.520i q^{11} +(-254.561 - 234.883i) q^{12} -128.246i q^{13} +(848.277 - 371.506i) q^{14} +(-82.2074 - 1020.69i) q^{16} +2110.72 q^{17} +(-652.070 + 285.576i) q^{18} -1454.37i q^{19} +1771.96i q^{21} +(-729.641 - 1666.02i) q^{22} +1231.18 q^{23} +(1852.09 + 639.406i) q^{24} +(291.033 + 664.531i) q^{26} -3992.34i q^{27} +(-3552.45 + 3850.07i) q^{28} +4073.19i q^{29} -3956.03 q^{31} +(2742.28 + 5102.38i) q^{32} +3480.14 q^{33} +(-10937.1 + 4789.95i) q^{34} +(2730.76 - 2959.54i) q^{36} -10656.6i q^{37} +(3300.46 + 7536.11i) q^{38} -1388.13 q^{39} -5907.19 q^{41} +(-4021.18 - 9181.76i) q^{42} +16439.6i q^{43} +(7561.57 + 6977.04i) q^{44} +(-6379.59 + 2793.96i) q^{46} -23238.8 q^{47} +(-11048.0 + 889.814i) q^{48} +9992.68 q^{49} -22846.5i q^{51} +(-3016.10 - 2782.95i) q^{52} -30634.0i q^{53} +(9059.99 + 20687.1i) q^{54} +(9670.60 - 28011.6i) q^{56} -15742.1 q^{57} +(-9243.47 - 21106.1i) q^{58} -25262.4i q^{59} -39115.5i q^{61} +(20499.0 - 8977.61i) q^{62} -20600.9 q^{63} +(-25788.8 - 20215.9i) q^{64} +(-18033.1 + 7897.64i) q^{66} -20894.5i q^{67} +(45803.0 - 49640.3i) q^{68} -13326.3i q^{69} +13889.1 q^{71} +(-7433.78 + 21532.5i) q^{72} +43451.2 q^{73} +(24183.6 + 55219.6i) q^{74} +(-34204.1 - 31560.0i) q^{76} -52634.8i q^{77} +(7192.89 - 3150.15i) q^{78} -12546.4 q^{79} -12633.8 q^{81} +(30609.3 - 13405.4i) q^{82} +6680.84i q^{83} +(41673.2 + 38451.7i) q^{84} +(-37307.1 - 85185.1i) q^{86} +44088.2 q^{87} +(-55015.1 - 18993.2i) q^{88} -90400.9 q^{89} +20994.6i q^{91} +(26716.7 - 28955.0i) q^{92} +42820.2i q^{93} +(120416. - 52736.8i) q^{94} +(55228.3 - 29682.5i) q^{96} -149616. q^{97} +(-51779.1 + 22676.8i) q^{98} +40460.4i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} - 32 q^{4} + 204 q^{6} + 196 q^{7} - 248 q^{8} - 1620 q^{9} + 1876 q^{12} + 2708 q^{14} + 3080 q^{16} + 5294 q^{18} - 13836 q^{22} + 4676 q^{23} + 1032 q^{24} - 8084 q^{26} - 2108 q^{28}+ \cdots - 216942 q^{98}+O(q^{100}) $ 20 * q - 2 * q^2 - 32 * q^4 + 204 * q^6 + 196 * q^7 - 248 * q^8 - 1620 * q^9 + 1876 * q^12 + 2708 * q^14 + 3080 * q^16 + 5294 * q^18 - 13836 * q^22 + 4676 * q^23 + 1032 * q^24 - 8084 * q^26 - 2108 * q^28 + 7160 * q^31 - 6792 * q^32 - 5672 * q^33 + 21132 * q^34 + 18344 * q^36 + 19580 * q^38 - 44904 * q^39 + 11608 * q^41 + 17116 * q^42 + 72296 * q^44 - 28516 * q^46 - 44180 * q^47 + 88856 * q^48 + 18756 * q^49 + 39680 * q^52 - 100584 * q^54 - 53624 * q^56 - 5032 * q^57 - 59496 * q^58 - 59824 * q^62 - 240620 * q^63 - 11264 * q^64 - 56688 * q^66 - 11576 * q^68 - 200312 * q^71 - 235912 * q^72 + 105136 * q^73 + 78876 * q^74 - 153872 * q^76 - 95864 * q^78 + 282080 * q^79 + 65172 * q^81 + 223032 * q^82 - 297128 * q^84 + 27452 * q^86 + 332592 * q^87 - 86896 * q^88 - 3160 * q^89 - 107916 * q^92 + 148820 * q^94 + 395168 * q^96 - 147376 * q^97 - 216942 * q^98

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 $

$2$	−5.18171	+	2.26935i	−0.916005	+	0.401167i
$2$	−5.18171	+	2.26935i	−0.916005	+	0.401167i
$3$		−	10.8240i		−	0.694361i	−0.937798	−	0.347180i	$-0.887139\pi$
$3$		−	10.8240i		−	0.694361i	0.937798	−	0.347180i	$-0.112861\pi$
$4$	21.7001	−	23.5182i	0.678130	−	0.734942i
$5$		0			0
$5$		0			0
$6$	24.5634	+	56.0868i	0.278555	+	0.636038i
$7$	−163.706			−1.26276			−0.631378	−	0.775475i	$-0.717510\pi$
$7$	−163.706			−1.26276			−0.631378	+	0.775475i	$0.717510\pi$
$8$	−59.0729	+	171.109i	−0.326335	+	0.945254i
$9$	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	$0.868806\pi$
$12$	−254.561	−	234.883i	−0.510315	−	0.470867i
$13$		−	128.246i		−	0.210467i	−0.994448	−	0.105233i	$-0.966441\pi$
$13$		−	128.246i		−	0.210467i	0.994448	−	0.105233i	$-0.0335590\pi$
$14$	848.277	−	371.506i	1.15669	−	0.506577i
$15$		0			0
$16$	−82.2074	−	1020.69i	−0.0802807	−	0.996772i
$17$	2110.72			1.77137			0.885683	−	0.464290i	$-0.153690\pi$
$17$	2110.72			1.77137			0.885683	+	0.464290i	$0.153690\pi$
$18$	−652.070	+	285.576i	−0.474365	+	0.207750i
$19$		−	1454.37i		−	0.924252i	−0.886814	−	0.462126i	$-0.847087\pi$
$19$		−	1454.37i		−	0.924252i	0.886814	−	0.462126i	$-0.152913\pi$
$20$		0			0
$21$			1771.96i			0.876809i
$22$	−729.641	−	1666.02i	−0.321405	−	0.733879i
$23$	1231.18			0.485289			0.242645	−	0.970115i	$-0.421985\pi$
$23$	1231.18			0.485289			0.242645	+	0.970115i	$0.421985\pi$
$24$	1852.09	+	639.406i	0.656347	+	0.226594i
$25$		0			0
$26$	291.033	+	664.531i	0.0844325	+	0.192789i
$27$		−	3992.34i		−	1.05394i
$28$	−3552.45	+	3850.07i	−0.856313	+	0.928053i
$29$			4073.19i			0.899372i	0.893187	+	0.449686i	$0.148464\pi$
$29$			4073.19i			0.899372i	−0.893187	+	0.449686i	$0.851536\pi$
$30$		0			0
$31$	−3956.03			−0.739360			−0.369680	−	0.929159i	$-0.620533\pi$
$31$	−3956.03			−0.739360			−0.369680	+	0.929159i	$0.620533\pi$
$32$	2742.28	+	5102.38i	0.473410	+	0.880842i
$33$	3480.14			0.556304
$34$	−10937.1	+	4789.95i	−1.62258	+	0.710615i
$35$		0			0
$36$	2730.76	−	2959.54i	0.351178	−	0.380600i
$37$		−	10656.6i		−	1.27972i	−0.768490	−	0.639861i	$-0.778992\pi$
$37$		−	10656.6i		−	1.27972i	0.768490	−	0.639861i	$-0.221008\pi$
$38$	3300.46	+	7536.11i	0.370780	+	0.846620i
$39$	−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	$0.588481\pi$
$42$	−4021.18	−	9181.76i	−0.351747	−	0.803161i
$43$			16439.6i			1.35588i	0.735119	+	0.677938i	$0.237126\pi$
$43$			16439.6i			1.35588i	−0.735119	+	0.677938i	$0.762874\pi$
$44$	7561.57	+	6977.04i	0.588817	+	0.543300i
$45$		0			0
$46$	−6379.59	+	2793.96i	−0.444527	+	0.194682i
$47$	−23238.8			−1.53450			−0.767252	−	0.641345i	$-0.778377\pi$
$47$	−23238.8			−1.53450			−0.767252	+	0.641345i	$0.778377\pi$
$48$	−11048.0	+	889.814i	−0.692120	+	0.0557438i
$49$	9992.68			0.594555
$50$		0			0
$51$		−	22846.5i		−	1.22997i
$52$	−3016.10	−	2782.95i	−0.154681	−	0.142724i
$53$		−	30634.0i		−	1.49801i	−0.662567	−	0.749003i	$-0.730533\pi$
$53$		−	30634.0i		−	1.49801i	0.662567	−	0.749003i	$-0.269467\pi$
$54$	9059.99	+	20687.1i	0.422808	+	0.965418i
$55$		0			0
$56$	9670.60	−	28011.6i	0.412082	−	1.19363i
$57$	−15742.1			−0.641764
$58$	−9243.47	−	21106.1i	−0.360799	−	0.823829i
$59$		−	25262.4i		−	0.944810i	−0.881382	−	0.472405i	$-0.843386\pi$
$59$		−	25262.4i		−	0.944810i	0.881382	−	0.472405i	$-0.156614\pi$
$60$		0			0
$61$		−	39115.5i		−	1.34594i	−0.739672	−	0.672968i	$-0.765019\pi$
$61$		−	39115.5i		−	1.34594i	0.739672	−	0.672968i	$-0.234981\pi$
$62$	20499.0	−	8977.61i	0.677257	−	0.296607i
$63$	−20600.9			−0.653935
$64$	−25788.8	−	20215.9i	−0.787011	−	0.616939i
$65$		0			0
$66$	−18033.1	+	7897.64i	−0.509577	+	0.223171i
$67$		−	20894.5i		−	0.568651i	−0.958728	−	0.284325i	$-0.908230\pi$
$67$		−	20894.5i		−	0.568651i	0.958728	−	0.284325i	$-0.0917696\pi$
$68$	45803.0	−	49640.3i	1.20122	−	1.30185i
$69$		−	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	$0.447724\pi$
$72$	−7433.78	+	21532.5i	−0.168997	+	0.489512i
$73$	43451.2			0.954321			0.477161	−	0.878816i	$-0.341666\pi$
$73$	43451.2			0.954321			0.477161	+	0.878816i	$0.341666\pi$
$74$	24183.6	+	55219.6i	0.513383	+	1.17223i
$75$		0			0
$76$	−34204.1	−	31560.0i	−0.679272	−	0.626763i
$77$		−	52634.8i		−	1.01169i
$78$	7192.89	−	3150.15i	0.133865	−	0.0586266i
$79$	−12546.4			−0.226179			−0.113089	−	0.993585i	$-0.536075\pi$
$79$	−12546.4			−0.226179			−0.113089	+	0.993585i	$0.536075\pi$
$80$		0			0
$81$	−12633.8			−0.213955
$82$	30609.3	−	13405.4i	0.502711	−	0.220164i
$83$			6680.84i			0.106448i	0.998583	+	0.0532238i	$0.0169497\pi$
$83$			6680.84i			0.106448i	−0.998583	+	0.0532238i	$0.983050\pi$
$84$	41673.2	+	38451.7i	0.644404	+	0.594590i
$85$		0			0
$86$	−37307.1	−	85185.1i	−0.543933	−	1.24199i
$87$	44088.2			0.624488
$88$	−55015.1	−	18993.2i	−0.757313	−	0.261451i
$89$	−90400.9			−1.20976			−0.604878	−	0.796318i	$-0.706778\pi$
$89$	−90400.9			−1.20976			−0.604878	+	0.796318i	$0.706778\pi$
$90$		0			0
$91$			20994.6i			0.265769i
$92$	26716.7	−	28955.0i	0.329089	−	0.356660i
$93$			42820.2i			0.513382i
$94$	120416.	−	52736.8i	1.40561	−	0.615593i
$95$		0			0
$96$	55228.3	−	29682.5i	0.611622	−	0.328717i
$97$	−149616.			−1.61454			−0.807269	−	0.590184i	$-0.799055\pi$
$97$	−149616.			−1.61454			−0.807269	+	0.590184i	$0.799055\pi$
$98$	−51779.1	+	22676.8i	−0.544615	+	0.238516i
$99$			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	$-0.189200\pi$
$102$	51846.5	+	118384.i	0.493423	+	1.12666i
$103$	−38586.9			−0.358382			−0.179191	−	0.983814i	$-0.557348\pi$
$103$	−38586.9			−0.358382			−0.179191	+	0.983814i	$0.557348\pi$
$104$	21944.0	+	7575.84i	0.198945	+	0.0686827i
$105$		0			0
$106$	69519.0	+	158736.i	0.600951	+	1.37218i
$107$		−	189459.i		−	1.59976i	−0.600158	−	0.799881i	$-0.704896\pi$
$107$		−	189459.i		−	1.59976i	0.600158	−	0.799881i	$-0.295104\pi$
$108$	−93892.4	−	86634.3i	−0.774589	−	0.714711i
$109$		−	24392.6i		−	0.196649i	−0.995154	−	0.0983245i	$-0.968652\pi$
$109$		−	24392.6i		−	0.196649i	0.995154	−	0.0983245i	$-0.0313483\pi$
$110$		0			0
$111$	−115348.			−0.888589
$112$	13457.9	+	167094.i	0.101375	+	1.25868i
$113$	52918.6			0.389863			0.194932	−	0.980817i	$-0.437552\pi$
$113$	52918.6			0.389863			0.194932	+	0.980817i	$0.437552\pi$
$114$	81571.0	−	35724.3i	0.587859	−	0.257455i
$115$		0			0
$116$	95793.8	+	88388.7i	0.660987	+	0.609891i
$117$		−	16138.5i		−	0.108993i
$118$	57329.1	+	130902.i	0.379027	+	0.865450i
$119$	−345538.			−2.23681
$120$		0			0
$121$	57675.7			0.358120
$122$	88766.6	+	202685.i	0.539945	+	1.23288i
$123$			63939.5i			0.381071i
$124$	−85846.5	+	93038.6i	−0.501382	+	0.543387i
$125$		0			0
$126$	106748.	−	46750.5i	0.599008	−	0.262337i
$127$	−293650.			−1.61555			−0.807777	−	0.589489i	$-0.799329\pi$
$127$	−293650.			−1.61555			−0.807777	+	0.589489i	$0.799329\pi$
$128$	179507.	+	46229.0i	0.968402	+	0.249396i
$129$	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	$0.700097\pi$
$132$	75519.6	−	81846.5i	0.377246	−	0.408851i
$133$			238089.i			1.16711i
$134$	47416.9	+	108269.i	0.228124	+	0.520887i
$135$		0			0
$136$	−124687.	+	361164.i	−0.578059	+	1.67439i
$137$	162285.			0.738717			0.369358	−	0.929287i	$-0.379577\pi$
$137$	162285.			0.738717			0.369358	+	0.929287i	$0.379577\pi$
$138$	30241.9	+	69052.8i	0.135180	+	0.308662i
$139$		−	306759.i		−	1.34667i	−0.739338	−	0.673334i	$-0.764861\pi$
$139$		−	306759.i		−	1.34667i	0.739338	−	0.673334i	$-0.235139\pi$
$140$		0			0
$141$			251537.i			1.06550i
$142$	−71969.0	+	31519.1i	−0.299519	+	0.131175i
$143$	41233.5			0.168621
$144$	−10345.0	−	128445.i	−0.0415744	−	0.516192i
$145$		0			0
$146$	−225151.	+	98605.8i	−0.874163	+	0.382842i
$147$		−	108161.i		−	0.412835i
$148$	−250625.	−	231251.i	−0.940523	−	0.867818i
$149$		−	368107.i		−	1.35834i	−0.733981	−	0.679170i	$-0.762340\pi$
$149$		−	368107.i		−	1.35834i	0.733981	−	0.679170i	$-0.237660\pi$
$150$		0			0
$151$	336822.			1.20215			0.601075	−	0.799193i	$-0.294739\pi$
$151$	336822.			1.20215			0.601075	+	0.799193i	$0.294739\pi$
$152$	248856.	+	85913.8i	0.873653	+	0.301616i
$153$	265615.			0.917326
$154$	119447.	+	272738.i	0.405856	+	0.926711i
$155$		0			0
$156$	−30122.6	+	32646.3i	−0.0991018	+	0.107404i
$157$			271253.i			0.878264i	0.898423	+	0.439132i	$0.144714\pi$
$157$			271253.i			0.878264i	−0.898423	+	0.439132i	$0.855286\pi$
$158$	65011.8	−	28472.1i	0.207181	−	0.0907356i
$159$	−331582.			−1.04016
$160$		0			0
$161$	−201551.			−0.612802
$162$	65464.6	−	28670.5i	0.195983	−	0.0858316i
$163$		−	121354.i		−	0.357756i	−0.983871	−	0.178878i	$-0.942753\pi$
$163$		−	121354.i		−	0.357756i	0.983871	−	0.178878i	$-0.0572467\pi$
$164$	−128187.	+	138926.i	−0.372163	+	0.403343i
$165$		0			0
$166$	−15161.1	−	34618.1i	−0.0427033	−	0.0975065i
$167$	−56095.4			−0.155645			−0.0778227	−	0.996967i	$-0.524797\pi$
$167$	−56095.4			−0.155645			−0.0778227	+	0.996967i	$0.524797\pi$
$168$	−303198.	−	104675.i	−0.828807	−	0.286133i
$169$	354846.			0.955704
$170$		0			0
$171$		−	183019.i		−	0.478636i
$172$	386629.	+	356741.i	0.996490	+	0.919459i
$173$			167666.i			0.425921i	0.977061	+	0.212960i	$0.0683105\pi$
$173$			167666.i			0.425921i	−0.977061	+	0.212960i	$0.931689\pi$
$174$	−228452.	+	100051.i	−0.572034	+	0.250524i
$175$		0			0
$176$	328174.	−	26431.4i	0.798588	−	0.0643188i
$177$	−273440.			−0.656039
$178$	468431.	−	205151.i	1.10814	−	0.485314i
$179$		−	535921.i		−	1.25017i	−0.780558	−	0.625083i	$-0.785065\pi$
$179$		−	535921.i		−	1.25017i	0.780558	−	0.625083i	$-0.214935\pi$
$180$		0			0
$181$			113446.i			0.257391i	0.991684	+	0.128696i	$0.0410790\pi$
$181$			113446.i			0.257391i	−0.991684	+	0.128696i	$0.958921\pi$
$182$	−47643.9	−	108788.i	−0.106618	−	0.243445i
$183$	−423387.			−0.934565
$184$	−72729.2	+	210666.i	−0.158367	+	0.458722i
$185$		0			0
$186$	−97173.7	−	221881.i	−0.205952	−	0.470261i
$187$			678640.i			1.41917i
$188$	−504284.	+	546533.i	−1.04059	+	1.12777i
$189$			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	$0.372972\pi$
$192$	−218817.	+	279138.i	−0.428378	+	0.546470i
$193$	261513.			0.505359			0.252680	−	0.967550i	$-0.418688\pi$
$193$	261513.			0.505359			0.252680	+	0.967550i	$0.418688\pi$
$194$	775265.	−	339530.i	1.47892	−	0.647700i
$195$		0			0
$196$	216843.	−	235009.i	0.403185	−	0.436963i
$197$		−	898947.i		−	1.65032i	−0.564898	−	0.825161i	$-0.691084\pi$
$197$		−	898947.i		−	1.65032i	0.564898	−	0.825161i	$-0.308916\pi$
$198$	−91818.5	−	209654.i	−0.166444	−	0.380049i
$199$	−83719.3			−0.149862			−0.0749312	−	0.997189i	$-0.523874\pi$
$199$	−83719.3			−0.149862			−0.0749312	+	0.997189i	$0.523874\pi$
$200$		0			0
$201$	−226163.			−0.394849
$202$	260570.	+	594972.i	0.449310	+	1.02593i
$203$		−	666805.i		−	1.13569i
$204$	−537307.	−	495772.i	−0.903955	−	0.834077i
$205$		0			0
$206$	199946.	−	87566.9i	0.328280	−	0.143771i
$207$	154932.			0.251313
$208$	−130900.	+	10542.7i	−0.209788	+	0.0168964i
$209$	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	$-0.140798\pi$
$212$	−720454.	−	664761.i	−1.10095	−	1.01584i
$213$		−	150335.i		−	0.227045i
$214$	429948.	+	981720.i	0.641772	+	1.46539i
$215$		0			0
$216$	683126.	+	235839.i	0.996246	+	0.343939i
$217$	647627.			0.933632
$218$	55355.2	+	126395.i	0.0788892	+	0.180131i
$219$		−	470316.i		−	0.662643i
$220$		0			0
$221$		−	270691.i		−	0.372814i
$222$	597697.	−	261764.i	0.813952	−	0.356473i
$223$	−279400.			−0.376239			−0.188120	−	0.982146i	$-0.560239\pi$
$223$	−279400.			−0.376239			−0.188120	+	0.982146i	$0.560239\pi$
$224$	−448929.	−	835291.i	−0.597802	−	1.11229i
$225$		0			0
$226$	−274209.	+	120091.i	−0.357116	+	0.156400i
$227$		−	593068.i		−	0.763905i	−0.924182	−	0.381953i	$-0.875252\pi$
$227$		−	593068.i		−	0.763905i	0.924182	−	0.381953i	$-0.124748\pi$
$228$	−341606.	+	370225.i	−0.435199	+	0.471660i
$229$			927873.i			1.16923i	0.811311	+	0.584615i	$0.198754\pi$
$229$			927873.i			1.16923i	−0.811311	+	0.584615i	$0.801246\pi$
$230$		0			0
$231$	−569720.			−0.702476
$232$	−696960.	−	240615.i	−0.850135	−	0.293496i
$233$	1.09279e6			1.31871			0.659353	−	0.751833i	$-0.270830\pi$
$233$	1.09279e6			1.31871			0.659353	+	0.751833i	$0.270830\pi$
$234$	36623.9	+	83625.0i	0.0437245	+	0.0998382i
$235$		0			0
$236$	−594125.	−	548197.i	−0.694381	−	0.640703i
$237$			135803.i			0.157050i
$238$	1.79048e6	−	784145.i	2.04892	−	0.897333i
$239$	−797967.			−0.903630			−0.451815	−	0.892112i	$-0.649223\pi$
$239$	−797967.			−0.903630			−0.451815	+	0.892112i	$0.649223\pi$
$240$		0			0
$241$	−1.61861e6			−1.79515			−0.897573	−	0.440865i	$-0.854672\pi$
$241$	−1.61861e6			−1.79515			−0.897573	+	0.440865i	$0.854672\pi$
$242$	−298858.	+	130886.i	−0.328040	+	0.143666i
$243$		−	833389.i		−	0.905383i
$244$	−919924.	−	848812.i	−0.989185	−	0.912719i
$245$		0			0
$246$	−145101.	−	331315.i	−0.152873	−	0.349063i
$247$	−186516.			−0.194525
$248$	233695.	−	676914.i	0.241279	−	0.698883i
$249$	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	$-0.0723253\pi$
$252$	−447042.	+	484495.i	−0.443453	+	0.480605i
$253$			395848.i			0.388801i
$254$	1.52161e6	−	666394.i	1.47985	−	0.648107i
$255$		0			0
$256$	−1.03506e6	+	167817.i	−0.987110	+	0.160043i
$257$	−396434.			−0.374402			−0.187201	−	0.982322i	$-0.559942\pi$
$257$	−396434.			−0.374402			−0.187201	+	0.982322i	$0.559942\pi$
$258$	−922045.	+	403813.i	−0.862388	+	0.377686i
$259$			1.74456e6i			1.61598i
$260$		0			0
$261$			512573.i			0.465752i
$262$	−721058.	−	1.64643e6i	−0.648958	−	1.48180i
$263$	−1.93423e6			−1.72432			−0.862160	−	0.506635i	$-0.830889\pi$
$263$	−1.93423e6			−1.72432			−0.862160	+	0.506635i	$0.830889\pi$
$264$	−205582.	+	595484.i	−0.181541	+	0.525848i
$265$		0			0
$266$	−540306.	−	1.23371e6i	−0.468205	−	1.06907i
$267$			978500.i			0.840007i
$268$	−491401.	−	453414.i	−0.417926	−	0.385619i
$269$			670016.i			0.564553i	0.959333	+	0.282276i	$0.0910895\pi$
$269$			670016.i			0.564553i	−0.959333	+	0.282276i	$0.908910\pi$
$270$		0			0
$271$	2.08940e6			1.72822			0.864109	−	0.503305i	$-0.167883\pi$
$271$	2.08940e6			1.72822			0.864109	+	0.503305i	$0.167883\pi$
$272$	−173517.	−	2.15440e6i	−0.142207	−	1.76565i
$273$	227246.			0.184539
$274$	−840915.	+	368281.i	−0.676668	+	0.296349i
$275$		0			0
$276$	−313409.	−	289182.i	−0.247651	−	0.228506i
$277$			828834.i			0.649035i	0.945880	+	0.324517i	$0.105202\pi$
$277$			828834.i			0.649035i	−0.945880	+	0.324517i	$0.894798\pi$
$278$	696143.	+	1.58954e6i	0.540240	+	1.23356i
$279$	−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	$0.138863\pi$
$282$	−570823.	−	1.30339e6i	−0.427444	−	0.976003i
$283$			2.00868e6i			1.49089i	0.666568	+	0.745444i	$0.267763\pi$
$283$			2.00868e6i			1.49089i	−0.666568	+	0.745444i	$0.732237\pi$
$284$	301395.	−	326645.i	0.221738	−	0.240315i
$285$		0			0
$286$	−213660.	+	93573.2i	−0.154457	+	0.0676451i
$287$	967042.			0.693012
$288$	345091.	+	642088.i	0.245162	+	0.456156i
$289$	3.03529e6			2.13774
$290$		0			0
$291$			1.61944e6i			1.12107i
$292$	942897.	−	1.02189e6i	0.647153	−	0.701371i
$293$			1.74203e6i			1.18546i	0.805402	+	0.592729i	$0.201950\pi$
$293$			1.74203e6i			1.18546i	−0.805402	+	0.592729i	$0.798050\pi$
$294$	245454.	+	560458.i	0.165616	+	0.378159i
$295$		0			0
$296$	1.82345e6	+	629519.i	1.20966	+	0.417618i
$297$	1.28362e6			0.844393
$298$	835362.	+	1.90742e6i	0.544922	+	1.24425i
$299$		−	157893.i		−	0.102137i
$300$		0			0
$301$		−	2.69126e6i		−	1.71214i
$302$	−1.74531e6	+	764366.i	−1.10118	+	0.482263i
$303$	−1.24283e6			−0.777688
$304$	−1.48447e6	+	119560.i	−0.921269	+	0.0741996i
$305$		0			0
$306$	−1.37634e6	+	602772.i	−0.840275	+	0.368001i
$307$		−	978690.i		−	0.592651i	−0.955087	−	0.296326i	$-0.904239\pi$
$307$		−	978690.i		−	0.592651i	0.955087	−	0.296326i	$-0.0957614\pi$
$308$	−1.23787e6	−	1.14218e6i	−0.743532	−	0.686055i
$309$			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	$0.652916\pi$
$312$	82001.0	−	237522.i	0.0476906	−	0.138139i
$313$	−1.60962e6			−0.928670			−0.464335	−	0.885660i	$-0.653707\pi$
$313$	−1.60962e6			−0.928670			−0.464335	+	0.885660i	$0.653707\pi$
$314$	−615566.	−	1.40555e6i	−0.352331	−	0.804494i
$315$		0			0
$316$	−272259.	+	295069.i	−0.153379	+	0.166228i
$317$			1.50670e6i			0.842130i	0.907030	+	0.421065i	$0.138344\pi$
$317$			1.50670e6i			0.842130i	−0.907030	+	0.421065i	$0.861656\pi$
$318$	1.71816e6	−	752475.i	0.952788	−	0.417277i
$319$	−1.30961e6			−0.720553
$320$		0			0
$321$	−2.05070e6			−1.11081
$322$	1.04438e6	−	457389.i	0.561330	−	0.245836i
$323$		−	3.06977e6i		−	1.63719i
$324$	−274155.	+	297124.i	−0.145089	+	0.157244i
$325$		0			0
$326$	275395.	+	628823.i	0.143520	+	0.327706i
$327$	−264026.			−0.136545
$328$	348955.	−	1.01077e6i	0.179095	−	0.518764i
$329$	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	$-0.0315469\pi$
$332$	157121.	+	144975.i	0.0782328	+	0.0721852i
$333$		−	1.34104e6i		−	0.662721i
$334$	290670.	−	127300.i	0.142572	−	0.0624398i
$335$		0			0
$336$	1.80863e6	−	145668.i	0.873979	−	0.0703908i
$337$	1.36879e6			0.656543			0.328272	−	0.944583i	$-0.393534\pi$
$337$	1.36879e6			0.656543			0.328272	+	0.944583i	$0.393534\pi$
$338$	−1.83871e6	+	805268.i	−0.875429	+	0.383397i
$339$		−	572791.i		−	0.270706i
$340$		0			0
$341$		−	1.27195e6i		−	0.592356i
$342$	415333.	+	948350.i	0.192013	+	0.438433i
$343$	1.11555e6			0.511979
$344$	−2.81297e6	−	971135.i	−1.28165	−	0.442470i
$345$		0			0
$346$	−380491.	−	868794.i	−0.170865	−	0.390145i
$347$		−	569376.i		−	0.253849i	−0.991912	−	0.126925i	$-0.959489\pi$
$347$		−	569376.i		−	0.253849i	0.991912	−	0.126925i	$-0.0405106\pi$
$348$	956721.	−	1.03687e6i	0.423484	−	0.458963i
$349$			2.20053e6i			0.967081i	0.875322	+	0.483541i	$0.160649\pi$
$349$			2.20053e6i			0.967081i	−0.875322	+	0.483541i	$0.839351\pi$
$350$		0			0
$351$	−511999.			−0.221820
$352$	−1.64052e6	+	881700.i	−0.705708	+	0.379284i
$353$	2.51557e6			1.07448			0.537242	−	0.843428i	$-0.319466\pi$
$353$	2.51557e6			1.07448			0.537242	+	0.843428i	$0.319466\pi$
$354$	1.41689e6	−	620531.i	0.600935	−	0.263181i
$355$		0			0
$356$	−1.96171e6	+	2.12606e6i	−0.820371	+	0.889100i
$357$			3.74011e6i			1.55315i
$358$	1.21619e6	+	2.77698e6i	0.501526	+	1.14516i
$359$	−794808.			−0.325481			−0.162741	−	0.986669i	$-0.552033\pi$
$359$	−794808.			−0.325481			−0.162741	+	0.986669i	$0.552033\pi$
$360$		0			0
$361$	360911.			0.145758
$362$	−257449.	−	587845.i	−0.103257	−	0.235772i
$363$		−	624282.i		−	0.248665i
$364$	493754.	+	455585.i	0.195325	+	0.180225i
$365$		0			0
$366$	2.19386e6	−	960810.i	0.856066	−	0.374917i
$367$	874302.			0.338841			0.169421	−	0.985544i	$-0.445810\pi$
$367$	874302.			0.338841			0.169421	+	0.985544i	$0.445810\pi$
$368$	−101212.	−	1.25666e6i	−0.0389594	−	0.483723i
$369$	−743365.			−0.284208
$370$		0			0
$371$			5.01497e6i			1.89162i
$372$	1.00705e6	+	929204.i	0.377306	+	0.348140i
$373$		−	4.86205e6i		−	1.80945i	−0.425994	−	0.904726i	$-0.640076\pi$
$373$		−	4.86205e6i		−	1.80945i	0.425994	−	0.904726i	$-0.359924\pi$
$374$	−1.54007e6	−	3.51651e6i	−0.569326	−	1.29997i
$375$		0			0
$376$	1.37278e6	−	3.97637e6i	0.500763	−	1.45050i
$377$	522368.			0.189288
$378$	−1.48318e6	−	3.38661e6i	−0.533904	−	1.21909i
$379$		−	1.24150e6i		−	0.443964i	−0.975051	−	0.221982i	$-0.928747\pi$
$379$		−	1.24150e6i		−	0.443964i	0.975051	−	0.221982i	$-0.0712527\pi$
$380$		0			0
$381$			3.17848e6i			1.12178i
$382$	−2.03024e6	+	889149.i	−0.711849	+	0.311757i
$383$	30969.9			0.0107880			0.00539402	−	0.999985i	$-0.498283\pi$
$383$	30969.9			0.0107880			0.00539402	+	0.999985i	$0.498283\pi$
$384$	500383.	−	1.94298e6i	0.173171	−	0.672420i
$385$		0			0
$386$	−1.35508e6	+	593463.i	−0.462911	+	0.202734i
$387$			2.06877e6i			0.702158i
$388$	−3.24669e6	+	3.51869e6i	−1.09487	+	1.18659i
$389$		−	4.27860e6i		−	1.43360i	−0.697279	−	0.716800i	$-0.745606\pi$
$389$		−	4.27860e6i		−	1.43360i	0.697279	−	0.716800i	$-0.254394\pi$
$390$		0			0
$391$	2.59867e6			0.859626
$392$	−590297.	+	1.70984e6i	−0.194024	+	0.562005i
$393$	3.43920e6			1.12325
$394$	2.04002e6	+	4.65808e6i	0.662055	+	1.51170i
$395$		0			0
$396$	951553.	+	877996.i	0.304926	+	0.281355i
$397$		−	2.31119e6i		−	0.735968i	−0.929832	−	0.367984i	$-0.880048\pi$
$397$		−	2.31119e6i		−	0.735968i	0.929832	−	0.367984i	$-0.119952\pi$
$398$	433809.	−	189988.i	0.137275	−	0.0601199i
$399$	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	$0.450556\pi$
$402$	1.17191e6	−	513241.i	0.361683	−	0.158400i
$403$			507344.i			0.155611i
$404$	−2.70039e6	−	2.49165e6i	−0.823140	−	0.759509i
$405$		0			0
$406$	1.51321e6	+	3.45519e6i	0.455601	+	1.04030i
$407$	3.42633e6			1.02528
$408$	3.90924e6	+	1.34961e6i	1.16263	+	0.401381i
$409$	−5.17948e6			−1.53101			−0.765505	−	0.643430i	$-0.777511\pi$
$409$	−5.17948e6			−1.53101			−0.765505	+	0.643430i	$0.777511\pi$
$410$		0			0
$411$		−	1.75658e6i		−	0.512936i
$412$	−837341.	+	907492.i	−0.243030	+	0.263390i
$413$			4.13561e6i			1.19306i
$414$	−802813.	+	351595.i	−0.230204	+	0.100819i
$415$		0			0
$416$	654358.	−	351686.i	0.185388	−	0.0996371i
$417$	−3.32037e6			−0.935074
$418$	−2.42301e6	+	1.06117e6i	−0.678289	+	0.297059i
$419$			3.57698e6i			0.995363i	0.867360	+	0.497682i	$0.165815\pi$
$419$			3.57698e6i			0.995363i	−0.867360	+	0.497682i	$0.834185\pi$
$420$		0			0
$421$			2.15848e6i			0.593531i	0.954950	+	0.296765i	$0.0959080\pi$
$421$			2.15848e6i			0.593531i	−0.954950	+	0.296765i	$0.904092\pi$
$422$	1.25640e6	+	2.86880e6i	0.343437	+	0.784187i
$423$	−2.92438e6			−0.794664
$424$	5.24175e6	+	1.80964e6i	1.41600	+	0.488852i
$425$		0			0
$426$	341163.	+	778993.i	0.0910831	+	0.207974i
$427$			6.40344e6i			1.69959i
$428$	−4.45572e6	−	4.11128e6i	−1.17573	−	1.08485i
$429$		−	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	$0.575354\pi$
$432$	−4.07496e6	+	328200.i	−1.05054	+	0.0846114i
$433$	−1.28911e6			−0.330423			−0.165211	−	0.986258i	$-0.552831\pi$
$433$	−1.28911e6			−0.330423			−0.165211	+	0.986258i	$0.552831\pi$
$434$	−3.35581e6	+	1.46969e6i	−0.855211	+	0.374542i
$435$		0			0
$436$	−573669.	−	529323.i	−0.144526	−	0.133354i
$437$		−	1.79058e6i		−	0.448530i
$438$	1.06731e6	+	2.43704e6i	0.265831	+	0.606984i
$439$	1.89694e6			0.469777			0.234889	−	0.972022i	$-0.424527\pi$
$439$	1.89694e6			0.469777			0.234889	+	0.972022i	$0.424527\pi$
$440$		0			0
$441$	1.25749e6			0.307898
$442$	614290.	+	1.40264e6i	0.149561	+	0.341500i
$443$			6.01979e6i			1.45738i	0.684845	+	0.728689i	$0.259870\pi$
$443$			6.01979e6i			1.45738i	−0.684845	+	0.728689i	$0.740130\pi$
$444$	−2.50306e6	+	2.71276e6i	−0.602579	+	0.653062i
$445$		0			0
$446$	1.44777e6	−	634055.i	0.344637	−	0.150935i
$447$	−3.98440e6			−0.943178
$448$	4.22178e6	+	3.30946e6i	0.993803	+	0.779044i
$449$	−2.40081e6			−0.562007			−0.281003	−	0.959707i	$-0.590667\pi$
$449$	−2.40081e6			−0.562007			−0.281003	+	0.959707i	$0.590667\pi$
$450$		0			0
$451$		−	1.89928e6i		−	0.439691i
$452$	1.14834e6	−	1.24455e6i	0.264378	−	0.286527i
$453$		−	3.64577e6i		−	0.834726i
$454$	1.34588e6	+	3.07310e6i	0.306454	+	0.699741i
$455$		0			0
$456$	929933.	−	2.69362e6i	0.209430	−	0.606631i
$457$	858952.			0.192388			0.0961941	−	0.995363i	$-0.469333\pi$
$457$	858952.			0.192388			0.0961941	+	0.995363i	$0.469333\pi$
$458$	−2.10567e6	−	4.80797e6i	−0.469057	−	1.07102i
$459$		−	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	$0.917648\pi$
$462$	2.95212e6	−	1.29289e6i	0.643472	−	0.281811i
$463$	1.35195e6			0.293096			0.146548	−	0.989204i	$-0.453184\pi$
$463$	1.35195e6			0.293096			0.146548	+	0.989204i	$0.453184\pi$
$464$	4.15748e6	−	334846.i	0.896469	−	0.0722022i
$465$		0			0
$466$	−5.66253e6	+	2.47993e6i	−1.20794	+	0.529022i
$467$		−	6.44013e6i		−	1.36648i	−0.730195	−	0.683239i	$-0.760571\pi$
$467$		−	6.44013e6i		−	1.36648i	0.730195	−	0.683239i	$-0.239429\pi$
$468$	−379548.	−	350208.i	−0.0801036	−	0.0739114i
$469$			3.42056e6i			0.718068i
$470$		0			0
$471$	2.93604e6			0.609832
$472$	4.32263e6	+	1.49232e6i	0.893085	+	0.308324i
$473$	−5.28566e6			−1.08629
$474$	−308183.	−	703689.i	−0.0630032	−	0.143858i
$475$		0			0
$476$	−7.49822e6	+	8.12641e6i	−1.51684	+	1.64392i
$477$		−	3.85500e6i		−	0.775762i
$478$	4.13483e6	−	1.81086e6i	0.827729	−	0.362507i
$479$	−1.85358e6			−0.369124			−0.184562	−	0.982821i	$-0.559087\pi$
$479$	−1.85358e6			−0.369124			−0.184562	+	0.982821i	$0.559087\pi$
$480$		0			0
$481$	−1.36667e6			−0.269339
$482$	8.38717e6	−	3.67319e6i	1.64436	−	0.720154i
$483$			2.18159e6i			0.425506i
$484$	1.25157e6	−	1.35643e6i	0.242852	−	0.263198i
$485$		0			0
$486$	1.89125e6	+	4.31838e6i	0.363210	+	0.829335i
$487$	−2.51668e6			−0.480846			−0.240423	−	0.970668i	$-0.577286\pi$
$487$	−2.51668e6			−0.480846			−0.240423	+	0.970668i	$0.577286\pi$
$488$	6.69302e6	+	2.31067e6i	1.27225	+	0.439226i
$489$	−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	$-0.168360\pi$
$492$	1.50374e6	+	1.38750e6i	0.280065	+	0.258416i
$493$			8.59736e6i			1.59312i
$494$	966472.	−	423270.i	0.178185	−	0.0780369i
$495$		0			0
$496$	325215.	+	4.03790e6i	0.0593563	+	0.736973i
$497$	−2.27372e6			−0.412902
$498$	−374707.	+	164104.i	−0.0677047	+	0.0296515i
$499$			3.18358e6i			0.572353i	0.958177	+	0.286177i	$0.0923844\pi$
$499$			3.18358e6i			0.572353i	−0.958177	+	0.286177i	$0.907616\pi$
$500$		0			0
$501$			607177.i			0.108074i
$502$	1.02050e6	+	2.33015e6i	0.180739	+	0.412690i
$503$	8.99291e6			1.58482			0.792410	−	0.609989i	$-0.208826\pi$
$503$	8.99291e6			1.58482			0.792410	+	0.609989i	$0.208826\pi$
$504$	1.21696e6	−	3.52500e6i	0.213402	−	0.618135i
$505$		0			0
$506$	−898317.	−	2.05117e6i	−0.155974	−	0.356144i
$507$		−	3.84086e6i		−	0.663603i
$508$	−6.37226e6	+	6.90612e6i	−1.09555	+	1.18734i
$509$		−	5.35388e6i		−	0.915956i	−0.888964	−	0.457978i	$-0.848574\pi$
$509$		−	5.35388e6i		−	0.915956i	0.888964	−	0.457978i	$-0.151426\pi$
$510$		0			0
$511$	−7.11322e6			−1.20508
$512$	4.98254e6	−	3.21849e6i	0.839993	−	0.542597i
$513$	−5.80633e6			−0.974111
$514$	2.05420e6	−	899646.i	0.342954	−	0.150198i
$515$		0			0
$516$	3.86137e6	−	4.18488e6i	0.638436	−	0.691924i
$517$		−	7.47173e6i		−	1.22941i
$518$	−3.95900e6	−	9.03978e6i	−0.648278	−	1.48024i
$519$	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	$0.567919\pi$
$522$	−1.16320e6	−	2.65600e6i	−0.186844	−	0.426631i
$523$			1.31228e6i			0.209784i	0.994484	+	0.104892i	$0.0334497\pi$
$523$			1.31228e6i			0.209784i	−0.994484	+	0.104892i	$0.966550\pi$
$524$	7.47262e6	+	6.89497e6i	1.18890	+	1.09699i
$525$		0			0
$526$	1.00226e7	−	4.38943e6i	1.57949	−	0.691741i
$527$	−8.35008e6			−1.30968
$528$	−286093.	−	3.55216e6i	−0.0446605	−	0.554508i
$529$	−4.92055e6			−0.764494
$530$		0			0
$531$		−	3.17904e6i		−	0.489282i
$532$	5.59941e6	+	5.16657e6i	0.857756	+	0.791449i
$533$			757570.i			0.115506i
$534$	−2.22055e6	−	5.07030e6i	−0.336983	−	0.769450i
$535$		0			0
$536$	3.57525e6	+	1.23430e6i	0.537520	+	0.185571i
$537$	−5.80081e6			−0.868067
$538$	−1.52050e6	−	3.47183e6i	−0.226480	−	0.517133i
$539$			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	$-0.167795\pi$
$542$	−1.08267e7	+	4.74157e6i	−1.58306	+	0.693304i
$543$	1.22794e6			0.178722
$544$	5.78820e6	+	1.07697e7i	0.838583	+	1.56029i
$545$		0			0
$546$	−1.17752e6	+	515698.i	−0.169039	+	0.0740311i
$547$		−	6.39084e6i		−	0.913251i	−0.889659	−	0.456625i	$-0.849058\pi$
$547$		−	6.39084e6i		−	0.913251i	0.889659	−	0.456625i	$-0.150942\pi$
$548$	3.52162e6	−	3.81665e6i	0.500946	−	0.542914i
$549$		−	4.92232e6i		−	0.697010i
$550$		0			0
$551$	5.92391e6			0.831246
$552$	2.28025e6	+	787222.i	0.318518	+	0.109964i
$553$	2.05392e6			0.285609
$554$	−1.88091e6	−	4.29477e6i	−0.260372	−	0.594519i
$555$		0			0
$556$	−7.21441e6	−	6.65672e6i	−0.989724	−	0.913216i
$557$			463389.i			0.0632861i	0.999499	+	0.0316430i	$0.0100740\pi$
$557$			463389.i			0.0632861i	−0.999499	+	0.0316430i	$0.989926\pi$
$558$	2.57961e6	−	1.12975e6i	0.350726	−	0.153602i
$559$	2.10830e6			0.285367
$560$		0			0
$561$	7.34561e6			0.985418
$562$	−1.24326e7	+	5.44488e6i	−1.66043	+	0.727189i
$563$		−	1.07609e7i		−	1.43080i	−0.698715	−	0.715400i	$-0.746244\pi$
$563$		−	1.07609e7i		−	1.43080i	0.698715	−	0.715400i	$-0.253756\pi$
$564$	5.91568e6	+	5.45838e6i	0.783081	+	0.722547i
$565$		0			0
$566$	−4.55839e6	−	1.04084e7i	−0.598096	−	1.36566i
$567$	2.06823e6			0.270173
$568$	−820467.	+	2.37655e6i	−0.106706	+	0.309083i
$569$	−1.04253e7			−1.34992			−0.674961	−	0.737853i	$-0.735840\pi$
$569$	−1.04253e7			−1.34992			−0.674961	+	0.737853i	$0.735840\pi$
$570$		0			0
$571$		−	1.58675e6i		−	0.203666i	−0.994802	−	0.101833i	$-0.967529\pi$
$571$		−	1.58675e6i		−	0.203666i	0.994802	−	0.101833i	$-0.0324707\pi$
$572$	894774.	−	969737.i	0.114347	−	0.123926i
$573$		−	4.24094e6i		−	0.539605i
$574$	−5.01093e6	+	2.19455e6i	−0.634802	+	0.278014i
$575$		0			0
$576$	−3.24528e6	−	2.54398e6i	−0.407564	−	0.319490i
$577$	2.79056e6			0.348941			0.174471	−	0.984662i	$-0.444179\pi$
$577$	2.79056e6			0.348941			0.174471	+	0.984662i	$0.444179\pi$
$578$	−1.57280e7	+	6.88811e6i	−1.95818	+	0.857592i
$579$		−	2.83062e6i		−	0.350901i
$580$		0			0
$581$		−	1.09369e6i		−	0.134417i
$582$	−3.67508e6	−	8.39148e6i	−0.449737	−	1.02691i
$583$	9.84944e6			1.20016
$584$	−2.56679e6	+	7.43490e6i	−0.311428	+	0.902076i
$585$		0			0
$586$	−3.95327e6	−	9.02668e6i	−0.475567	−	1.08589i
$587$		−	1.94272e6i		−	0.232710i	−0.993208	−	0.116355i	$-0.962879\pi$
$587$		−	1.94272e6i		−	0.232710i	0.993208	−	0.116355i	$-0.0371210\pi$
$588$	−2.54374e6	−	2.34711e6i	−0.303410	−	0.279956i
$589$			5.75353e6i			0.683355i
$590$		0			0
$591$	−9.73022e6			−1.14592
$592$	−1.08772e7	+	876055.i	−1.27559	+	0.102737i
$593$	−8.14862e6			−0.951584			−0.475792	−	0.879558i	$-0.657839\pi$
$593$	−8.14862e6			−0.951584			−0.475792	+	0.879558i	$0.657839\pi$
$594$	−6.65133e6	+	2.91297e6i	−0.773468	+	0.338743i
$595$		0			0
$596$	−8.65720e6	−	7.98798e6i	−0.998302	−	0.921131i
$597$			906179.i			0.104059i
$598$	358313.	+	818154.i	0.0409742	+	0.0935583i
$599$	1.49677e6			0.170447			0.0852234	−	0.996362i	$-0.472840\pi$
$599$	1.49677e6			0.170447			0.0852234	+	0.996362i	$0.472840\pi$
$600$		0			0
$601$	−9.04082e6			−1.02099			−0.510495	−	0.859881i	$-0.670538\pi$
$601$	−9.04082e6			−1.02099			−0.510495	+	0.859881i	$0.670538\pi$
$602$	6.10740e6	+	1.39453e7i	0.686855	+	1.56833i
$603$		−	2.62938e6i		−	0.294483i
$604$	7.30910e6	−	7.92144e6i	0.815213	−	0.883511i
$605$		0			0
$606$	6.43998e6	−	2.82041e6i	0.712366	−	0.311983i
$607$	3.63200e6			0.400105			0.200052	−	0.979785i	$-0.435889\pi$
$607$	3.63200e6			0.400105			0.200052	+	0.979785i	$0.435889\pi$
$608$	7.42075e6	−	3.98829e6i	0.814120	−	0.437550i
$609$	−7.21751e6			−0.788577
$610$		0			0
$611$			2.98027e6i			0.322962i
$612$	5.76388e6	−	6.24677e6i	0.622066	−	0.674182i
$613$		−	1.89937e6i		−	0.204154i	−0.994776	−	0.102077i	$-0.967451\pi$
$613$		−	1.89937e6i		−	0.204154i	0.994776	−	0.102077i	$-0.0325488\pi$
$614$	2.22099e6	+	5.07128e6i	0.237752	+	0.542871i
$615$		0			0
$616$	9.00631e6	+	3.10929e6i	0.956302	+	0.330149i
$617$	−5.96746e6			−0.631069			−0.315534	−	0.948914i	$-0.602184\pi$
$617$	−5.96746e6			−0.631069			−0.315534	+	0.948914i	$0.602184\pi$
$618$	−947826.	−	2.16422e6i	−0.0998291	−	0.227945i
$619$			1.46307e7i			1.53475i	0.641196	+	0.767377i	$0.278439\pi$
$619$			1.46307e7i			1.53475i	−0.641196	+	0.767377i	$0.721561\pi$
$620$		0			0
$621$		−	4.91527e6i		−	0.511468i
$622$	8.16905e6	−	3.57766e6i	0.846634	−	0.370786i
$623$	1.47992e7			1.52763
$624$	114115.	+	1.41686e6i	0.0117322	+	0.145668i
$625$		0			0
$626$	8.34055e6	−	3.65277e6i	0.850666	−	0.372552i
$627$		−	5.06141e6i		−	0.514165i
$628$	6.37936e6	+	5.88622e6i	0.645473	+	0.595577i
$629$		−	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	$0.764517\pi$
$632$	741154.	−	2.14681e6i	0.0738101	−	0.213796i
$633$	−5.99261e6			−0.594438
$634$	−3.41923e6	−	7.80729e6i	−0.337835	−	0.771395i
$635$		0			0
$636$	−7.19538e6	+	7.79821e6i	−0.705361	+	0.764455i
$637$		−	1.28152e6i		−	0.125134i
$638$	6.78603e6	−	2.97196e6i	0.660030	−	0.289062i
$639$	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	$0.164087\pi$
$642$	1.06261e7	−	4.65376e6i	1.01751	−	0.445622i
$643$			7.21849e6i			0.688524i	0.938874	+	0.344262i	$0.111871\pi$
$643$			7.21849e6i			0.688524i	−0.938874	+	0.344262i	$0.888129\pi$
$644$	−4.37369e6	+	4.74011e6i	−0.415559	+	0.450374i
$645$		0			0
$646$	6.96636e6	+	1.59066e7i	0.656787	+	1.49967i
$647$	−2.44672e6			−0.229786			−0.114893	−	0.993378i	$-0.536653\pi$
$647$	−2.44672e6			−0.229786			−0.114893	+	0.993378i	$0.536653\pi$
$648$	746316.	−	2.16176e6i	0.0698209	−	0.202241i
$649$	8.12237e6			0.756957
$650$		0			0
$651$		−	7.00992e6i		−	0.648277i
$652$	−2.85403e6	−	2.63341e6i	−0.262930	−	0.242605i
$653$		−	5.92231e6i		−	0.543511i	−0.962366	−	0.271755i	$-0.912396\pi$
$653$		−	5.92231e6i		−	0.543511i	0.962366	−	0.271755i	$-0.0876041\pi$
$654$	1.36810e6	−	599166.i	0.125076	−	0.0547776i
$655$		0			0
$656$	485615.	+	6.02943e6i	0.0440587	+	0.547037i
$657$	5.46793e6			0.494208
$658$	−1.97129e7	+	8.63333e6i	−1.77495	+	0.777345i
$659$			2.68146e6i			0.240523i	0.992742	+	0.120262i	$0.0383734\pi$
$659$			2.68146e6i			0.240523i	−0.992742	+	0.120262i	$0.961627\pi$
$660$		0			0
$661$			1.14098e7i			1.01572i	0.861440	+	0.507859i	$0.169563\pi$
$661$			1.14098e7i			1.01572i	−0.861440	+	0.507859i	$0.830437\pi$
$662$	895150.	+	2.04394e6i	0.0793873	+	0.181269i
$663$	−2.92996e6			−0.258868
$664$	−1.14315e6	−	394657.i	−0.100620	−	0.0347376i
$665$		0			0
$666$	3.04328e6	+	6.94887e6i	0.265862	+	0.607056i
$667$			5.01481e6i			0.436456i
$668$	−1.21728e6	+	1.31926e6i	−0.105548	+	0.114390i
$669$			3.02423e6i			0.261246i
$670$		0			0
$671$	1.25764e7			1.07833
$672$	−9.04120e6	+	4.85921e6i	−0.772330	+	0.415090i
$673$	5.13646e6			0.437146			0.218573	−	0.975821i	$-0.429860\pi$
$673$	5.13646e6			0.437146			0.218573	+	0.975821i	$0.429860\pi$
$674$	−7.09269e6	+	3.10627e6i	−0.601397	+	0.263384i
$675$		0			0
$676$	7.70021e6	−	8.34533e6i	0.648091	−	0.702387i
$677$			4.91407e6i			0.412068i	0.978545	+	0.206034i	$0.0660558\pi$
$677$			4.91407e6i			0.412068i	−0.978545	+	0.206034i	$0.933944\pi$
$678$	1.29986e6	+	2.96804e6i	0.108598	+	0.247968i
$679$	2.44930e7			2.03877
$680$		0			0
$681$	−6.41937e6			−0.530426
$682$	2.88648e6	+	6.59085e6i	0.237634	+	0.542601i
$683$			4.30841e6i			0.353399i	0.984265	+	0.176700i	$0.0565421\pi$
$683$			4.30841e6i			0.353399i	−0.984265	+	0.176700i	$0.943458\pi$
$684$	−4.30427e6	−	3.97154e6i	−0.351770	−	0.324577i
$685$		0			0
$686$	−5.78043e6	+	2.53156e6i	−0.468975	+	0.205389i
$687$	1.00433e7			0.811868
$688$	1.67798e7	−	1.35146e6i	1.35150	−	0.108851i
$689$	−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	$-0.0276359\pi$
$692$	3.94319e6	+	3.63837e6i	0.313027	+	0.288829i
$693$		−	6.62361e6i		−	0.523916i
$694$	1.29211e6	+	2.95034e6i	0.101836	+	0.232527i
$695$		0			0
$696$	−2.60442e6	+	7.54390e6i	−0.203792	+	0.590300i
$697$	−1.24684e7			−0.972142
$698$	−4.99375e6	−	1.14025e7i	−0.387961	−	0.885851i
$699$		−	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	$0.983847\pi$
$702$	2.65303e6	−	1.16190e6i	0.203189	−	0.0889871i
$703$	−1.54987e7			−1.18279
$704$	6.49981e6	−	8.29162e6i	0.494275	−	0.630533i
$705$		0			0
$706$	−1.30349e7	+	5.70870e6i	−0.984232	+	0.431048i
$707$			1.87970e7i			1.41429i
$708$	−5.93370e6	+	6.43081e6i	−0.444879	+	0.482151i
$709$		−	1.33410e7i		−	0.996721i	−0.866970	−	0.498360i	$-0.833936\pi$
$709$		−	1.33410e7i		−	0.996721i	0.866970	−	0.498360i	$-0.166064\pi$
$710$		0			0
$711$	−1.57885e6			−0.117130
$712$	5.34024e6	−	1.54684e7i	0.394785	−	1.14353i
$713$	−4.87058e6			−0.358803
$714$	−8.48759e6	−	1.93801e7i	−0.623073	−	1.42269i
$715$		0			0
$716$	−1.26039e7	−	1.16296e7i	−0.918800	−	0.847775i
$717$			8.63721e6i			0.627445i
$718$	4.11846e6	−	1.80369e6i	0.298143	−	0.130573i
$719$	2.25289e7			1.62524			0.812620	−	0.582794i	$-0.198040\pi$
$719$	2.25289e7			1.62524			0.812620	+	0.582794i	$0.198040\pi$
$720$		0			0
$721$	6.31691e6			0.452550
$722$	−1.87013e6	+	819031.i	−0.133515	+	0.0584732i
$723$			1.75199e7i			1.24648i
$724$	2.66805e6	+	2.46180e6i	0.189168	+	0.174545i
$725$		0			0
$726$	1.41671e6	+	3.23485e6i	0.0997562	+	0.227778i
$727$	1.49088e7			1.04618			0.523091	−	0.852277i	$-0.324779\pi$
$727$	1.49088e7			1.04618			0.523091	+	0.852277i	$0.324779\pi$
$728$	−3.59237e6	−	1.24021e6i	−0.251219	−	0.0867296i
$729$	−1.20906e7			−0.842617
$730$		0			0
$731$			3.46994e7i			2.40175i
$732$	−9.18755e6	+	9.95727e6i	−0.633756	+	0.686851i
$733$			7.98329e6i			0.548810i	0.961614	+	0.274405i	$0.0884809\pi$
$733$			7.98329e6i			0.548810i	−0.961614	+	0.274405i	$0.911519\pi$
$734$	−4.53037e6	+	1.98409e6i	−0.310380	+	0.135932i
$735$		0			0
$736$	3.37624e6	+	6.28193e6i	0.229741	+	0.427463i
$737$	6.71802e6			0.455588
$738$	3.85190e6	−	1.68695e6i	0.260336	−	0.114015i
$739$			3.81018e6i			0.256646i	0.991732	+	0.128323i	$0.0409594\pi$
$739$			3.81018e6i			0.256646i	−0.991732	+	0.128323i	$0.959041\pi$
$740$		0			0
$741$			2.01885e6i			0.135070i
$742$	−1.13807e7	−	2.59861e7i	−0.758855	−	1.73273i
$743$	−8.99457e6			−0.597734			−0.298867	−	0.954295i	$-0.596609\pi$
$743$	−8.99457e6			−0.597734			−0.298867	+	0.954295i	$0.596609\pi$
$744$	−7.32693e6	−	2.52951e6i	−0.485277	−	0.167535i
$745$		0			0
$746$	1.10337e7	+	2.51937e7i	0.725893	+	1.65747i
$747$			840722.i			0.0551253i
$748$	1.59604e7	+	1.47266e7i	1.04301	+	0.962383i
$749$			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	$0.374967\pi$
$752$	1.91040e6	+	2.37197e7i	0.123191	+	1.52955i
$753$	−4.86742e6			−0.312832
$754$	−2.70676e6	+	1.18543e6i	−0.173389	+	0.0759362i
$755$		0			0
$756$	1.53708e7	+	1.41826e7i	0.978117	+	0.902506i
$757$		−	5.14086e6i		−	0.326059i	−0.986621	−	0.163030i	$-0.947873\pi$
$757$		−	5.14086e6i		−	0.326059i	0.986621	−	0.163030i	$-0.0521266\pi$
$758$	2.81739e6	+	6.43308e6i	0.178104	+	0.406673i
$759$	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	$0.417181\pi$
$762$	−7.21306e6	−	1.64699e7i	−0.450020	−	1.02755i
$763$			3.99322e6i			0.248320i
$764$	8.50230e6	−	9.21461e6i	0.526991	−	0.571142i
$765$		0			0
$766$	−160477.	+	70281.3i	−0.00988189	+	0.00432781i
$767$	−3.23979e6			−0.198851
$768$	1.81646e6	+	1.12035e7i	0.111128	+	0.685410i
$769$	−1.11390e7			−0.679251			−0.339626	−	0.940561i	$-0.610300\pi$
$769$	−1.11390e7			−0.679251			−0.339626	+	0.940561i	$0.610300\pi$
$770$		0			0
$771$			4.29101e6i			0.259970i
$772$	5.67487e6	−	6.15030e6i	0.342699	−	0.371410i
$773$		−	5.63671e6i		−	0.339294i	−0.985505	−	0.169647i	$-0.945737\pi$
$773$		−	5.63671e6i		−	0.339294i	0.985505	−	0.169647i	$-0.0542628\pi$
$774$	−4.69475e6	−	1.07198e7i	−0.281683	−	0.643180i
$775$		0			0
$776$	8.83825e6	−	2.56007e7i	0.526880	−	1.52615i
$777$	1.88831e7			1.12207
$778$	9.70963e6	+	2.21705e7i	0.575113	+	1.31318i
$779$			8.59123e6i			0.507238i
$780$		0			0
$781$			4.46561e6i			0.261971i
$782$	−1.34655e7	+	5.89728e6i	−0.787421	+	0.344854i
$783$	1.62615e7			0.947888
$784$	−821473.	−	1.01995e7i	−0.0477313	−	0.592636i
$785$		0			0
$786$	−1.78209e7	+	7.80474e6i	−1.02890	+	0.450611i
$787$			3.07197e7i			1.76799i	0.467495	+	0.883996i	$0.345157\pi$
$787$			3.07197e7i			1.76799i	−0.467495	+	0.883996i	$0.654843\pi$
$788$	−2.11416e7	−	1.95073e7i	−1.21289	−	1.11913i
$789$			2.09361e7i			1.19730i
$790$		0			0
$791$	−8.66309e6			−0.492302
$792$	−6.92314e6	−	2.39011e6i	−0.392184	−	0.135396i
$793$	−5.01639e6			−0.283275
$794$	5.24489e6	+	1.19759e7i	0.295246	+	0.674151i
$795$		0			0
$796$	−1.81672e6	+	1.96892e6i	−0.101626	+	0.110140i
$797$			2.22339e7i			1.23985i	0.784660	+	0.619926i	$0.212837\pi$
$797$			2.22339e7i			1.23985i	−0.784660	+	0.619926i	$0.787163\pi$
$798$	−1.33537e7	+	5.84828e6i	−0.742323	+	0.325103i
$799$	−4.90505e7			−2.71817
$800$		0			0
$801$	−1.13761e7			−0.626488
$802$	−5.16278e6	+	2.26106e6i	−0.283431	+	0.124130i
$803$			1.39704e7i			0.764577i
$804$	−4.90776e6	+	5.31893e6i	−0.267759	+	0.290191i
$805$		0			0
$806$	−1.15134e6	−	2.62891e6i	−0.0624260	−	0.142540i
$807$	7.25226e6			0.392003
$808$	1.96470e7	+	6.78285e6i	1.05869	+	0.365497i
$809$	1.51247e7			0.812484			0.406242	−	0.913765i	$-0.366839\pi$
$809$	1.51247e7			0.812484			0.406242	+	0.913765i	$0.366839\pi$
$810$		0			0
$811$		−	1.35982e7i		−	0.725990i	−0.931791	−	0.362995i	$-0.881754\pi$
$811$		−	1.35982e7i		−	0.725990i	0.931791	−	0.362995i	$-0.118246\pi$
$812$	−1.56820e7	−	1.44698e7i	−0.834665	−	0.770143i
$813$		−	2.26157e7i		−	1.20001i
$814$	−1.77542e7	+	7.77552e6i	−0.939162	+	0.411309i
$815$		0			0
$816$	−2.33193e7	+	1.87815e6i	−1.22600	+	0.0987427i
$817$	2.39092e7			1.25317
$818$	2.68385e7	−	1.17540e7i	1.40241	−	0.614191i
$819$			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	$0.768340\pi$
$822$	3.98628e6	+	9.10207e6i	0.205773	+	0.469852i
$823$	−8.73184e6			−0.449372			−0.224686	−	0.974431i	$-0.572136\pi$
$823$	−8.73184e6			−0.449372			−0.224686	+	0.974431i	$0.572136\pi$
$824$	2.27944e6	−	6.60257e6i	0.116953	−	0.338762i
$825$		0			0
$826$	−9.38512e6	−	2.14295e7i	−0.478619	−	1.09285i
$827$			1.46565e6i			0.0745191i	0.999306	+	0.0372596i	$0.0118628\pi$
$827$			1.46565e6i			0.0745191i	−0.999306	+	0.0372596i	$0.988137\pi$
$828$	3.36205e6	−	3.64372e6i	0.170423	−	0.184701i
$829$			4.49887e6i			0.227362i	0.993517	+	0.113681i	$0.0362641\pi$
$829$			4.49887e6i			0.227362i	−0.993517	+	0.113681i	$0.963736\pi$
$830$		0			0
$831$	8.97130e6			0.450664
$832$	−2.59259e6	+	3.30729e6i	−0.129845	+	0.165640i
$833$	2.10918e7			1.05317
$834$	1.72052e7	−	7.53506e6i	0.856532	−	0.375121i
$835$		0			0
$836$	1.01472e7	−	1.09973e7i	0.502146	−	0.544215i
$837$			1.57938e7i			0.779244i
$838$	−8.11741e6	−	1.85349e7i	−0.399307	−	0.911758i
$839$	−1.43801e7			−0.705273			−0.352636	−	0.935760i	$-0.614715\pi$
$839$	−1.43801e7			−0.705273			−0.352636	+	0.935760i	$0.614715\pi$
$840$		0			0
$841$	3.92030e6			0.191130
$842$	−4.89834e6	−	1.11846e7i	−0.238105	−	0.543677i
$843$		−	2.59702e7i		−	1.25866i
$844$	−1.30206e7	−	1.20141e7i	−0.629180	−	0.580543i
$845$		0			0
$846$	1.51533e7	−	6.63643e6i	0.727916	−	0.318793i
$847$	−9.44185e6			−0.452219
$848$	−3.12679e7	+	2.51834e6i	−1.49317	+	0.120261i
$849$	2.17420e7			1.03521
$850$		0			0
$851$		−	1.31202e7i		−	0.621036i
$852$	−3.53561e6	−	3.26230e6i	−0.166865	−	0.153966i
$853$		−	2.62365e7i		−	1.23462i	−0.786720	−	0.617310i	$-0.788222\pi$
$853$		−	2.62365e7i		−	1.23462i	0.786720	−	0.617310i	$-0.211778\pi$
$854$	−1.45316e7	−	3.31808e7i	−0.681820	−	1.55683i
$855$		0			0
$856$	3.24182e7	+	1.11919e7i	1.51218	+	0.522058i
$857$	6.34066e6			0.294905			0.147453	−	0.989069i	$-0.452893\pi$
$857$	6.34066e6			0.294905			0.147453	+	0.989069i	$0.452893\pi$
$858$	1.01284e6	+	2.31266e6i	0.0469701	+	0.107249i
$859$			1.09488e7i			0.506273i	0.967431	+	0.253137i	$0.0814622\pi$
$859$			1.09488e7i			0.506273i	−0.967431	+	0.253137i	$0.918538\pi$
$860$		0			0
$861$		−	1.04673e7i		−	0.481200i
$862$	9.37318e6	−	4.10501e6i	0.429654	−	0.188168i
$863$	3.28604e6			0.150192			0.0750958	−	0.997176i	$-0.476074\pi$
$863$	3.28604e6			0.150192			0.0750958	+	0.997176i	$0.476074\pi$
$864$	2.03704e7	−	1.09481e7i	0.928359	−	0.498948i
$865$		0			0
$866$	6.67978e6	−	2.92543e6i	0.302669	−	0.132555i
$867$		−	3.28540e7i		−	1.48436i
$868$	1.40536e7	−	1.52310e7i	0.633123	−	0.686165i
$869$		−	4.03393e6i		−	0.181209i
$870$		0			0
$871$	−2.67963e6			−0.119682
$872$	4.17380e6	+	1.44094e6i	0.185883	+	0.0641735i
$873$	−1.88278e7			−0.836110
$874$	4.06345e6	+	9.27828e6i	0.179936	+	0.410855i
$875$		0			0
$876$	−1.10610e7	−	1.02059e7i	−0.487005	−	0.449358i
$877$			7.75326e6i			0.340397i	0.985410	+	0.170198i	$0.0544409\pi$
$877$			7.75326e6i			0.340397i	−0.985410	+	0.170198i	$0.945559\pi$
$878$	−9.82937e6	+	4.30481e6i	−0.430318	+	0.188459i
$879$	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	$0.503105\pi$
$882$	−6.51592e6	+	2.85367e6i	−0.282036	+	0.123519i
$883$		−	2.42001e7i		−	1.04452i	−0.852787	−	0.522259i	$-0.825089\pi$
$883$		−	2.42001e7i		−	1.04452i	0.852787	−	0.522259i	$-0.174911\pi$
$884$	−6.36614e6	−	5.87402e6i	−0.273997	−	0.252816i
$885$		0			0
$886$	−1.36610e7	−	3.11928e7i	−0.584652	−	1.33496i
$887$	−8.80204e6			−0.375642			−0.187821	−	0.982203i	$-0.560143\pi$
$887$	−8.80204e6			−0.375642			−0.187821	+	0.982203i	$0.560143\pi$
$888$	6.81392e6	−	1.97370e7i	0.289978	−	0.839943i
$889$	4.80724e7			2.04005
$890$		0			0
$891$		−	4.06203e6i		−	0.171415i
$892$	−6.06302e6	+	6.57097e6i	−0.255139	+	0.276514i
$893$			3.37977e7i			1.41827i
$894$	2.06460e7	−	9.04197e6i	0.863956	−	0.378372i
$895$		0			0
$896$	−2.93863e7	−	7.56797e6i	−1.22286	−	0.314926i
$897$	−1.70903e6			−0.0709202
$898$	1.24403e7	−	5.44826e6i	0.514801	−	0.225459i
$899$		−	1.61137e7i		−	0.664959i
$900$		0			0
$901$		−	6.46597e7i		−	2.65352i
$902$	4.31012e6	+	9.84151e6i	0.176390	+	0.402759i
$903$	−2.91302e7			−1.18884
$904$	−3.12606e6	+	9.05486e6i	−0.127226	+	0.368520i
$905$		0			0
$906$	8.27351e6	+	1.88913e7i	0.334865	+	0.764613i
$907$		−	1.35035e7i		−	0.545040i	−0.962150	−	0.272520i	$-0.912143\pi$
$907$		−	1.35035e7i		−	0.545040i	0.962150	−	0.272520i	$-0.0878571\pi$
$908$	−1.39479e7	−	1.28697e7i	−0.561426	−	0.518027i
$909$		−	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	$0.613450\pi$
$912$	1.29412e6	+	1.60679e7i	0.0515213	+	0.639693i
$913$	−2.14803e6			−0.0852830
$914$	−4.45083e6	+	1.94926e6i	−0.176228	+	0.0771798i
$915$		0			0
$916$	2.18219e7	+	2.01350e7i	0.859317	+	0.792890i
$917$		−	5.20157e7i		−	2.04273i
$918$	1.91231e7	+	4.36647e7i	0.748948	+	1.71011i
$919$	3.84416e7			1.50146			0.750728	−	0.660612i	$-0.229703\pi$
$919$	3.84416e7			1.50146			0.750728	+	0.660612i	$0.229703\pi$
$920$		0			0
$921$	−1.05934e7			−0.411514
$922$	−5.29849e6	−	1.20983e7i	−0.205270	−	0.468702i
$923$		−	1.78121e6i		−	0.0688194i
$924$	−1.23630e7	+	1.33988e7i	−0.476370	+	0.516280i
$925$		0			0
$926$	−7.00542e6	+	3.06805e6i	−0.268477	+	0.117580i
$927$	−4.85580e6			−0.185593
$928$	−2.07830e7	+	1.11698e7i	−0.792205	+	0.425772i
$929$	−694053.			−0.0263848			−0.0131924	−	0.999913i	$-0.504199\pi$
$929$	−694053.			−0.0263848			−0.0131924	+	0.999913i	$0.504199\pi$
$930$		0			0
$931$		−	1.45330e7i		−	0.549518i
$932$	2.37138e7	−	2.57005e7i	0.894254	−	0.969174i
$933$			1.70643e7i			0.641776i
$934$	1.46149e7	+	3.33709e7i	0.548186	+	1.25170i
$935$		0			0
$936$	2.76145e6	+	953349.i	0.103026	+	0.0355682i
$937$	−4.08849e7			−1.52130			−0.760648	−	0.649165i	$-0.775119\pi$
$937$	−4.08849e7			−1.52130			−0.760648	+	0.649165i	$0.775119\pi$
$938$	−7.76244e6	−	1.77243e7i	−0.288065	−	0.657753i
$939$			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	$0.928308\pi$
$942$	−1.52137e7	+	6.66289e6i	−0.558609	+	0.244645i
$943$	−7.27279e6			−0.266331
$944$	−2.57852e7	+	2.07676e6i	−0.941760	+	0.0758500i
$945$		0			0
$946$	2.73887e7	−	1.19950e7i	0.995049	−	0.435785i
$947$			3.38948e7i			1.22817i	0.789241	+	0.614084i	$0.210474\pi$
$947$			3.38948e7i			1.22817i	−0.789241	+	0.614084i	$0.789526\pi$
$948$	3.19383e6	+	2.94694e6i	0.115422	+	0.106500i
$949$		−	5.57242e6i		−	0.200853i
$950$		0			0
$951$	1.63086e7			0.584742
$952$	2.04119e7	−	5.91247e7i	0.729948	−	2.11435i
$953$	5.18152e7			1.84810			0.924049	−	0.382274i	$-0.124859\pi$
$953$	5.18152e7			1.84810			0.924049	+	0.382274i	$0.124859\pi$
$954$	8.74833e6	+	1.99755e7i	0.311210	+	0.710602i
$955$		0			0
$956$	−1.73160e7	+	1.87667e7i	−0.612778	+	0.664116i
$957$			1.41753e7i			0.500324i
$958$	9.60470e6	−	4.20641e6i	0.338119	−	0.148080i
$959$	−2.65671e7			−0.932819
$960$		0			0
$961$	−1.29789e7			−0.453347
$962$	7.08166e6	−	3.10144e6i	0.246716	−	0.108050i
$963$		−	2.38416e7i		−	0.828458i
$964$	−3.51241e7	+	3.80667e7i	−1.21734	+	1.31933i
$965$		0			0
$966$	−4.95078e6	−	1.13044e7i	−0.170699	−	0.389765i
$967$	4.41440e7			1.51812			0.759058	−	0.651023i	$-0.225660\pi$
$967$	4.41440e7			1.51812			0.759058	+	0.651023i	$0.225660\pi$
$968$	−3.40707e6	+	9.86884e6i	−0.116867	+	0.338515i
$969$	−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	$0.874703\pi$
$972$	−1.95998e7	−	1.80847e7i	−0.665404	−	0.613967i
$973$			5.02184e7i			1.70052i
$974$	1.30407e7	−	5.71122e6i	0.440457	−	0.192900i
$975$		0			0
$976$	−3.99250e7	+	3.21558e6i	−1.34159	+	0.108053i
$977$	508955.			0.0170586			0.00852929	−	0.999964i	$-0.497285\pi$
$977$	508955.			0.0170586			0.00852929	+	0.999964i	$0.497285\pi$
$978$	6.80639e6	−	2.98088e6i	0.227546	−	0.0996546i
$979$		−	2.90657e7i		−	0.969224i
$980$		0			0
$981$		−	3.06958e6i		−	0.101837i
$982$	1.22344e7	+	2.79354e7i	0.404859	+	0.924433i
$983$	1.38312e7			0.456536			0.228268	−	0.973598i	$-0.426694\pi$
$983$	1.38312e7			0.456536			0.228268	+	0.973598i	$0.426694\pi$
$984$	−1.09406e7	−	3.77709e6i	−0.360209	−	0.124357i
$985$		0			0
$986$	−1.95104e7	−	4.45490e7i	−0.639107	−	1.45930i
$987$		−	4.11781e7i		−	1.34547i
$988$	−4.04743e6	+	4.38652e6i	−0.131913	+	0.142964i
$989$			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	$0.441307\pi$
$992$	−1.08486e7	−	2.01852e7i	−0.350020	−	0.651259i
$993$	−4.26957e6			−0.137408
$994$	1.17818e7	−	5.15986e6i	0.378220	−	0.165643i
$995$		0			0
$996$	1.56921e6	−	1.70068e6i	0.0501226	−	0.0543218i
$997$			3.66390e7i			1.16736i	0.811983	+	0.583681i	$0.198388\pi$
$997$			3.66390e7i			1.16736i	−0.811983	+	0.583681i	$0.801612\pi$
$998$	−7.22464e6	−	1.64964e7i	−0.229609	−	0.524278i
$999$	−4.25449e7			−1.34876

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.6.d.a.21.17	✓	20	5.4	even	2
40.6.d.a.21.18	yes	20	40.29	even	2
160.6.d.a.81.7		20	20.19	odd	2
160.6.d.a.81.14		20	40.19	odd	2
200.6.d.b.101.3		20	8.5	even	2	inner
200.6.d.b.101.4		20	1.1	even	1	trivial
200.6.f.b.149.7		20	5.2	odd	4
200.6.f.b.149.8		20	40.13	odd	4
200.6.f.c.149.13		20	40.37	odd	4
200.6.f.c.149.14		20	5.3	odd	4
360.6.k.b.181.3		20	120.29	odd	2
360.6.k.b.181.4		20	15.14	odd	2
800.6.d.c.401.7		20	8.3	odd	2
800.6.d.c.401.14		20	4.3	odd	2
800.6.f.b.49.7		20	20.3	even	4
800.6.f.b.49.8		20	40.27	even	4
800.6.f.c.49.13		20	40.3	even	4
800.6.f.c.49.14		20	20.7	even	4

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.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.18171 + 2.26935i) q^{2} -10.8240i q^{3} +(21.7001 - 23.5182i) q^{4} +(24.5634 + 56.0868i) q^{6} -163.706 q^{7} +(-59.0729 + 171.109i) q^{8} +125.841 q^{9} +321.520i q^{11} +(-254.561 - 234.883i) q^{12} -128.246i q^{13} +(848.277 - 371.506i) q^{14} +(-82.2074 - 1020.69i) q^{16} +2110.72 q^{17} +(-652.070 + 285.576i) q^{18} -1454.37i q^{19} +1771.96i q^{21} +(-729.641 - 1666.02i) q^{22} +1231.18 q^{23} +(1852.09 + 639.406i) q^{24} +(291.033 + 664.531i) q^{26} -3992.34i q^{27} +(-3552.45 + 3850.07i) q^{28} +4073.19i q^{29} -3956.03 q^{31} +(2742.28 + 5102.38i) q^{32} +3480.14 q^{33} +(-10937.1 + 4789.95i) q^{34} +(2730.76 - 2959.54i) q^{36} -10656.6i q^{37} +(3300.46 + 7536.11i) q^{38} -1388.13 q^{39} -5907.19 q^{41} +(-4021.18 - 9181.76i) q^{42} +16439.6i q^{43} +(7561.57 + 6977.04i) q^{44} +(-6379.59 + 2793.96i) q^{46} -23238.8 q^{47} +(-11048.0 + 889.814i) q^{48} +9992.68 q^{49} -22846.5i q^{51} +(-3016.10 - 2782.95i) q^{52} -30634.0i q^{53} +(9059.99 + 20687.1i) q^{54} +(9670.60 - 28011.6i) q^{56} -15742.1 q^{57} +(-9243.47 - 21106.1i) q^{58} -25262.4i q^{59} -39115.5i q^{61} +(20499.0 - 8977.61i) q^{62} -20600.9 q^{63} +(-25788.8 - 20215.9i) q^{64} +(-18033.1 + 7897.64i) q^{66} -20894.5i q^{67} +(45803.0 - 49640.3i) q^{68} -13326.3i q^{69} +13889.1 q^{71} +(-7433.78 + 21532.5i) q^{72} +43451.2 q^{73} +(24183.6 + 55219.6i) q^{74} +(-34204.1 - 31560.0i) q^{76} -52634.8i q^{77} +(7192.89 - 3150.15i) q^{78} -12546.4 q^{79} -12633.8 q^{81} +(30609.3 - 13405.4i) q^{82} +6680.84i q^{83} +(41673.2 + 38451.7i) q^{84} +(-37307.1 - 85185.1i) q^{86} +44088.2 q^{87} +(-55015.1 - 18993.2i) q^{88} -90400.9 q^{89} +20994.6i q^{91} +(26716.7 - 28955.0i) q^{92} +42820.2i q^{93} +(120416. - 52736.8i) q^{94} +(55228.3 - 29682.5i) q^{96} -149616. q^{97} +(-51779.1 + 22676.8i) q^{98} +40460.4i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} - 32 q^{4} + 204 q^{6} + 196 q^{7} - 248 q^{8} - 1620 q^{9} + 1876 q^{12} + 2708 q^{14} + 3080 q^{16} + 5294 q^{18} - 13836 q^{22} + 4676 q^{23} + 1032 q^{24} - 8084 q^{26} - 2108 q^{28}+ \cdots - 216942 q^{98}+O(q^{100}) \) 20 * q - 2 * q^2 - 32 * q^4 + 204 * q^6 + 196 * q^7 - 248 * q^8 - 1620 * q^9 + 1876 * q^12 + 2708 * q^14 + 3080 * q^16 + 5294 * q^18 - 13836 * q^22 + 4676 * q^23 + 1032 * q^24 - 8084 * q^26 - 2108 * q^28 + 7160 * q^31 - 6792 * q^32 - 5672 * q^33 + 21132 * q^34 + 18344 * q^36 + 19580 * q^38 - 44904 * q^39 + 11608 * q^41 + 17116 * q^42 + 72296 * q^44 - 28516 * q^46 - 44180 * q^47 + 88856 * q^48 + 18756 * q^49 + 39680 * q^52 - 100584 * q^54 - 53624 * q^56 - 5032 * q^57 - 59496 * q^58 - 59824 * q^62 - 240620 * q^63 - 11264 * q^64 - 56688 * q^66 - 11576 * q^68 - 200312 * q^71 - 235912 * q^72 + 105136 * q^73 + 78876 * q^74 - 153872 * q^76 - 95864 * q^78 + 282080 * q^79 + 65172 * q^81 + 223032 * q^82 - 297128 * q^84 + 27452 * q^86 + 332592 * q^87 - 86896 * q^88 - 3160 * q^89 - 107916 * q^92 + 148820 * q^94 + 395168 * q^96 - 147376 * q^97 - 216942 * q^98

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