LMFDB - Embedded newform 63.6.p.b.17.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,6,Mod(17,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("63.17");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	63.p (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$10.1041806482$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.3
Character	$\chi$	$=$	63.17
Dual form			63.6.p.b.26.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-6.73742 + 3.88985i) q^{2} +(14.2619 - 24.7023i) q^{4} +(-46.8267 - 81.1063i) q^{5} +(58.7189 + 115.582i) q^{7} -27.0441i q^{8} +O(q^{10})$	\(q+(-6.73742 + 3.88985i) q^{2} +(14.2619 - 24.7023i) q^{4} +(-46.8267 - 81.1063i) q^{5} +(58.7189 + 115.582i) q^{7} -27.0441i q^{8} +(630.983 + 364.298i) q^{10} +(212.927 + 122.934i) q^{11} -592.325i q^{13} +(-845.209 - 550.314i) q^{14} +(561.578 + 972.681i) q^{16} +(-1015.44 + 1758.79i) q^{17} +(-703.867 + 406.378i) q^{19} -2671.35 q^{20} -1912.78 q^{22} +(-35.1283 + 20.2814i) q^{23} +(-2822.98 + 4889.55i) q^{25} +(2304.06 + 3990.74i) q^{26} +(3692.57 + 197.919i) q^{28} +5893.18i q^{29} +(-152.886 - 88.2690i) q^{31} +(-6817.70 - 3936.20i) q^{32} -15799.6i q^{34} +(6624.78 - 10174.8i) q^{35} +(2839.10 + 4917.47i) q^{37} +(3161.50 - 5475.88i) q^{38} +(-2193.44 + 1266.38i) q^{40} +2309.21 q^{41} +18360.2 q^{43} +(6073.49 - 3506.53i) q^{44} +(157.783 - 273.288i) q^{46} +(5134.85 + 8893.82i) q^{47} +(-9911.19 + 13573.6i) q^{49} -43924.0i q^{50} +(-14631.8 - 8447.67i) q^{52} +(34105.8 + 19691.0i) q^{53} -23026.3i q^{55} +(3125.79 - 1588.00i) q^{56} +(-22923.6 - 39704.8i) q^{58} +(-17836.4 + 30893.5i) q^{59} +(-19552.1 + 11288.4i) q^{61} +1373.41 q^{62} +25304.0 q^{64} +(-48041.3 + 27736.7i) q^{65} +(5727.31 - 9919.99i) q^{67} +(28964.1 + 50167.4i) q^{68} +(-5055.54 + 94321.1i) q^{70} -47986.7i q^{71} +(-51691.9 - 29844.4i) q^{73} +(-38256.5 - 22087.4i) q^{74} +23182.9i q^{76} +(-1706.01 + 31829.0i) q^{77} +(37220.8 + 64468.4i) q^{79} +(52593.7 - 91094.9i) q^{80} +(-15558.1 + 8982.50i) q^{82} -87877.8 q^{83} +190199. q^{85} +(-123700. + 71418.4i) q^{86} +(3324.63 - 5758.42i) q^{88} +(16626.9 + 28798.6i) q^{89} +(68461.9 - 34780.7i) q^{91} +1157.00i q^{92} +(-69191.2 - 39947.6i) q^{94} +(65919.6 + 38058.7i) q^{95} -96672.7i q^{97} +(13976.4 - 130004. i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 304 q^{4} - 436 q^{7}+O(q^{10}) $ 24 * q + 304 * q^4 - 436 * q^7	$ 24 q + 304 q^{4} - 436 q^{7} + 1992 q^{10} - 3644 q^{16} + 3804 q^{19} - 5648 q^{22} - 18852 q^{25} - 39172 q^{28} + 38652 q^{31} + 20548 q^{37} + 132060 q^{40} + 2200 q^{43} - 25712 q^{46} - 125676 q^{49} - 2940 q^{52} + 154300 q^{58} + 48504 q^{61} - 327880 q^{64} + 156324 q^{67} - 9468 q^{70} - 703236 q^{73} + 165756 q^{79} + 1081020 q^{82} - 284448 q^{85} + 582308 q^{88} - 19812 q^{91} - 1481724 q^{94}+O(q^{100}) $ 24 * q + 304 * q^4 - 436 * q^7 + 1992 * q^10 - 3644 * q^16 + 3804 * q^19 - 5648 * q^22 - 18852 * q^25 - 39172 * q^28 + 38652 * q^31 + 20548 * q^37 + 132060 * q^40 + 2200 * q^43 - 25712 * q^46 - 125676 * q^49 - 2940 * q^52 + 154300 * q^58 + 48504 * q^61 - 327880 * q^64 + 156324 * q^67 - 9468 * q^70 - 703236 * q^73 + 165756 * q^79 + 1081020 * q^82 - 284448 * q^85 + 582308 * q^88 - 19812 * q^91 - 1481724 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−6.73742	+	3.88985i	−1.19102	+	0.687635i	−0.958538	−	0.284966i	$-0.908018\pi$
$2$	−6.73742	+	3.88985i	−1.19102	+	0.687635i	−0.232481	+	0.972601i	$0.574684\pi$
$3$		0			0
$3$		0			0
$4$	14.2619	−	24.7023i	0.445684	−	0.771947i
$5$	−46.8267	−	81.1063i	−0.837662	−	1.45087i	−0.891845	−	0.452342i	$-0.850589\pi$
$5$	−46.8267	−	81.1063i	−0.837662	−	1.45087i	0.0541826	−	0.998531i	$-0.482745\pi$
$6$		0			0
$7$	58.7189	+	115.582i	0.452932	+	0.891545i
$7$	58.7189	+	115.582i	0.452932	+	0.891545i
$8$		−	27.0441i		−	0.149399i
$9$		0			0
$10$	630.983	+	364.298i	1.99534	+	1.15201i
$11$	212.927	+	122.934i	0.530579	+	0.306330i	0.741252	−	0.671227i	$-0.234232\pi$
$11$	212.927	+	122.934i	0.530579	+	0.306330i	−0.210673	+	0.977557i	$0.567566\pi$
$12$		0			0
$13$		−	592.325i		−	0.972080i	−0.873937	−	0.486040i	$-0.838441\pi$
$13$		−	592.325i		−	0.972080i	0.873937	−	0.486040i	$-0.161559\pi$
$14$	−845.209	−	550.314i	−1.15251	−	0.750396i
$15$		0			0
$16$	561.578	+	972.681i	0.548416	+	0.949884i
$17$	−1015.44	+	1758.79i	−0.852180	+	1.47602i	0.0270560	+	0.999634i	$0.491387\pi$
$17$	−1015.44	+	1758.79i	−0.852180	+	1.47602i	−0.879236	+	0.476386i	$0.841947\pi$
$18$		0			0
$19$	−703.867	+	406.378i	−0.447308	+	0.258253i	−0.706693	−	0.707521i	$-0.749814\pi$
$19$	−703.867	+	406.378i	−0.447308	+	0.258253i	0.259385	+	0.965774i	$0.416480\pi$
$20$	−2671.35			−1.49333
$21$		0			0
$22$	−1912.78			−0.842572
$23$	−35.1283	+	20.2814i	−0.0138464	+	0.00799424i	−0.506907	−	0.862001i	$-0.669211\pi$
$23$	−35.1283	+	20.2814i	−0.0138464	+	0.00799424i	0.493061	+	0.869995i	$0.335878\pi$
$24$		0			0
$25$	−2822.98	+	4889.55i	−0.903355	+	1.56466i
$26$	2304.06	+	3990.74i	0.668436	+	1.15777i
$27$		0			0
$28$	3692.57	+	197.919i	0.890090	+	0.0477081i
$29$			5893.18i			1.30123i	0.759407	+	0.650616i	$0.225489\pi$
$29$			5893.18i			1.30123i	−0.759407	+	0.650616i	$0.774511\pi$
$30$		0			0
$31$	−152.886	−	88.2690i	−0.0285736	−	0.0164970i	0.485645	−	0.874156i	$-0.338585\pi$
$31$	−152.886	−	88.2690i	−0.0285736	−	0.0164970i	−0.514219	+	0.857659i	$0.671918\pi$
$32$	−6817.70	−	3936.20i	−1.17696	−	0.679520i
$33$		0			0
$34$		−	15799.6i		−	2.34396i
$35$	6624.78	−	10174.8i	0.914115	−	1.40396i
$36$		0			0
$37$	2839.10	+	4917.47i	0.340939	+	0.590524i	0.984607	−	0.174781i	$-0.0559216\pi$
$37$	2839.10	+	4917.47i	0.340939	+	0.590524i	−0.643668	+	0.765305i	$0.722588\pi$
$38$	3161.50	−	5475.88i	0.355168	−	0.615169i
$39$		0			0
$40$	−2193.44	+	1266.38i	−0.216759	+	0.125146i
$41$	2309.21			0.214538			0.107269	−	0.994230i	$-0.465789\pi$
$41$	2309.21			0.214538			0.107269	+	0.994230i	$0.465789\pi$
$42$		0			0
$43$	18360.2			1.51428			0.757140	−	0.653252i	$-0.226596\pi$
$43$	18360.2			1.51428			0.757140	+	0.653252i	$0.226596\pi$
$44$	6073.49	−	3506.53i	0.472941	−	0.273052i
$45$		0			0
$46$	157.783	−	273.288i	0.0109942	−	0.0190426i
$47$	5134.85	+	8893.82i	0.339065	+	0.587278i	0.984257	−	0.176743i	$-0.0565560\pi$
$47$	5134.85	+	8893.82i	0.339065	+	0.587278i	−0.645192	+	0.764020i	$0.723223\pi$
$48$		0			0
$49$	−9911.19	+	13573.6i	−0.589706	+	0.807618i
$50$		−	43924.0i		−	2.48471i
$51$		0			0
$52$	−14631.8	−	8447.67i	−0.750394	−	0.433240i
$53$	34105.8	+	19691.0i	1.66778	+	0.962893i	0.968831	+	0.247722i	$0.0796819\pi$
$53$	34105.8	+	19691.0i	1.66778	+	0.962893i	0.698949	+	0.715171i	$0.253651\pi$
$54$		0			0
$55$		−	23026.3i		−	1.02640i
$56$	3125.79	−	1588.00i	0.133196	−	0.0676674i
$57$		0			0
$58$	−22923.6	−	39704.8i	−0.894772	−	1.54979i
$59$	−17836.4	+	30893.5i	−0.667078	+	1.15541i	0.311639	+	0.950201i	$0.399122\pi$
$59$	−17836.4	+	30893.5i	−0.667078	+	1.15541i	−0.978717	+	0.205213i	$0.934211\pi$
$60$		0			0
$61$	−19552.1	+	11288.4i	−0.672775	+	0.388427i	−0.797127	−	0.603811i	$-0.793648\pi$
$61$	−19552.1	+	11288.4i	−0.672775	+	0.388427i	0.124352	+	0.992238i	$0.460315\pi$
$62$	1373.41			0.0453755
$63$		0			0
$64$	25304.0			0.772216
$65$	−48041.3	+	27736.7i	−1.41036	+	0.814274i
$66$		0			0
$67$	5727.31	−	9919.99i	0.155870	−	0.269975i	−0.777505	−	0.628876i	$-0.783515\pi$
$67$	5727.31	−	9919.99i	0.155870	−	0.269975i	0.933376	+	0.358901i	$0.116848\pi$
$68$	28964.1	+	50167.4i	0.759606	+	1.31568i
$69$		0			0
$70$	−5055.54	+	94321.1i	−0.123317	+	2.30072i
$71$		−	47986.7i		−	1.12973i	−0.825183	−	0.564865i	$-0.808928\pi$
$71$		−	47986.7i		−	1.12973i	0.825183	−	0.564865i	$-0.191072\pi$
$72$		0			0
$73$	−51691.9	−	29844.4i	−1.13531	−	0.655473i	−0.190047	−	0.981775i	$-0.560864\pi$
$73$	−51691.9	−	29844.4i	−1.13531	−	0.655473i	−0.945266	+	0.326302i	$0.894197\pi$
$74$	−38256.5	−	22087.4i	−0.812130	−	0.468883i
$75$		0			0
$76$			23182.9i			0.460397i
$77$	−1706.01	+	31829.0i	−0.0327910	+	0.611781i
$78$		0			0
$79$	37220.8	+	64468.4i	0.670994	+	1.16220i	0.977623	+	0.210366i	$0.0674656\pi$
$79$	37220.8	+	64468.4i	0.670994	+	1.16220i	−0.306629	+	0.951829i	$0.599201\pi$
$80$	52593.7	−	91094.9i	0.918774	−	1.59136i
$81$		0			0
$82$	−15558.1	+	8982.50i	−0.255519	+	0.147524i
$83$	−87877.8			−1.40018			−0.700090	−	0.714054i	$-0.746857\pi$
$83$	−87877.8			−1.40018			−0.700090	+	0.714054i	$0.746857\pi$
$84$		0			0
$85$	190199.			2.85536
$86$	−123700.	+	71418.4i	−1.80354	+	1.04127i
$87$		0			0
$88$	3324.63	−	5758.42i	0.0457653	−	0.0792678i
$89$	16626.9	+	28798.6i	0.222503	+	0.385386i	0.955567	−	0.294773i	$-0.0952440\pi$
$89$	16626.9	+	28798.6i	0.222503	+	0.385386i	−0.733064	+	0.680159i	$0.761911\pi$
$90$		0			0
$91$	68461.9	−	34780.7i	0.866653	−	0.440286i
$92$			1157.00i			0.0142516i
$93$		0			0
$94$	−69191.2	−	39947.6i	−0.807665	−	0.466306i
$95$	65919.6	+	38058.7i	0.749386	+	0.432658i
$96$		0			0
$97$		−	96672.7i		−	1.04322i	−0.853185	−	0.521608i	$-0.825332\pi$
$97$		−	96672.7i		−	1.04322i	0.853185	−	0.521608i	$-0.174668\pi$
$98$	13976.4	−	130004.i	0.147004	−	1.36739i
$99$		0			0
$100$	80522.2	+	139468.i	0.805222	+	1.39468i
$101$	9686.45	−	16777.4i	0.0944846	−	0.163652i	−0.814909	−	0.579589i	$-0.803213\pi$
$101$	9686.45	−	16777.4i	0.0944846	−	0.163652i	0.909393	+	0.415937i	$0.136546\pi$
$102$		0			0
$103$	85999.1	−	49651.6i	0.798731	−	0.461148i	−0.0442961	−	0.999018i	$-0.514104\pi$
$103$	85999.1	−	49651.6i	0.798731	−	0.461148i	0.843027	+	0.537871i	$0.180771\pi$
$104$	−16018.9			−0.145227
$105$		0			0
$106$	−306380.			−2.64848
$107$	7121.68	−	4111.70i	0.0601344	−	0.0347186i	−0.469631	−	0.882863i	$-0.655613\pi$
$107$	7121.68	−	4111.70i	0.0601344	−	0.0347186i	0.529766	+	0.848144i	$0.322280\pi$
$108$		0			0
$109$	−71076.3	+	123108.i	−0.573005	+	0.992474i	0.423250	+	0.906013i	$0.360889\pi$
$109$	−71076.3	+	123108.i	−0.573005	+	0.992474i	−0.996255	+	0.0864612i	$0.972444\pi$
$110$	89569.0	+	155138.i	0.705791	+	1.22247i
$111$		0			0
$112$	−79448.8	+	122023.i	−0.598470	+	0.919170i
$113$		−	42730.4i		−	0.314804i	−0.987535	−	0.157402i	$-0.949688\pi$
$113$		−	42730.4i		−	0.314804i	0.987535	−	0.157402i	$-0.0503119\pi$
$114$		0			0
$115$	3289.89	+	1899.42i	0.0231973	+	0.0133929i
$116$	145575.	+	84047.8i	1.00448	+	0.579938i
$117$		0			0
$118$		−	277524.i		−	1.83483i
$119$	−262909.	−	14091.7i	−1.70192	−	0.0912214i
$120$		0			0
$121$	−50300.1	−	87122.3i	−0.312324	−	0.540961i
$122$	87820.7	−	152110.i	0.534192	−	0.925247i
$123$		0			0
$124$	−4360.89	+	2517.76i	−0.0254696	+	0.0147049i
$125$	236098.			1.35150
$126$		0			0
$127$	−308027.			−1.69465			−0.847324	−	0.531076i	$-0.821788\pi$
$127$	−308027.			−1.69465			−0.847324	+	0.531076i	$0.821788\pi$
$128$	47682.9	−	27529.7i	0.257239	−	0.148517i
$129$		0			0
$130$	215783.	−	373747.i	1.11985	−	1.93963i
$131$	77775.3	+	134711.i	0.395971	+	0.685842i	0.993225	−	0.116210i	$-0.0370747\pi$
$131$	77775.3	+	134711.i	0.395971	+	0.685842i	−0.597254	+	0.802053i	$0.703741\pi$
$132$		0			0
$133$	−88300.1	−	57492.0i	−0.432844	−	0.281824i
$134$			89113.5i			0.428728i
$135$		0			0
$136$	47564.9	+	27461.6i	0.220515	+	0.127315i
$137$	−60915.0	−	35169.3i	−0.277283	−	0.160089i	0.354910	−	0.934900i	$-0.384511\pi$
$137$	−60915.0	−	35169.3i	−0.277283	−	0.160089i	−0.632193	+	0.774811i	$0.717845\pi$
$138$		0			0
$139$			63588.8i			0.279154i	0.990211	+	0.139577i	$0.0445742\pi$
$139$			63588.8i			0.279154i	−0.990211	+	0.139577i	$0.955426\pi$
$140$	−156859.	−	308759.i	−0.676376	−	1.33137i
$141$		0			0
$142$	186661.	+	323306.i	0.776842	+	1.34553i
$143$	72816.7	−	126122.i	0.297777	−	0.515765i
$144$		0			0
$145$	477974.	−	275958.i	1.88792	−	1.08999i
$146$	464360.			1.80291
$147$		0			0
$148$	161964.			0.607804
$149$	−31985.6	+	18466.9i	−0.118029	+	0.0681440i	−0.557852	−	0.829940i	$-0.688374\pi$
$149$	−31985.6	+	18466.9i	−0.118029	+	0.0681440i	0.439823	+	0.898084i	$0.355041\pi$
$150$		0			0
$151$	−269005.	+	465931.i	−0.960105	+	1.66295i	−0.237877	+	0.971295i	$0.576452\pi$
$151$	−269005.	+	465931.i	−0.960105	+	1.66295i	−0.722228	+	0.691656i	$0.756882\pi$
$152$	10990.1	+	19035.4i	0.0385827	+	0.0668272i
$153$		0			0
$154$	−112316.	−	221082.i	−0.381628	−	0.751191i
$155$			16533.4i			0.0552755i
$156$		0			0
$157$	−42906.0	−	24771.8i	−0.138921	−	0.0802064i	0.428928	−	0.903338i	$-0.358891\pi$
$157$	−42906.0	−	24771.8i	−0.138921	−	0.0802064i	−0.567850	+	0.823132i	$0.692225\pi$
$158$	−501545.	−	289567.i	−1.59833	−	0.922797i
$159$		0			0
$160$			737278.i			2.27683i
$161$	−4406.85	−	2869.29i	−0.0133987	−	0.00872388i
$162$		0			0
$163$	80462.1	+	139364.i	0.237204	+	0.410849i	0.959911	−	0.280305i	$-0.0904357\pi$
$163$	80462.1	+	139364.i	0.237204	+	0.410849i	−0.722707	+	0.691155i	$0.757102\pi$
$164$	32933.7	−	57042.9i	0.0956162	−	0.165612i
$165$		0			0
$166$	592070.	−	341832.i	1.66764	−	0.962813i
$167$	151029.			0.419054			0.209527	−	0.977803i	$-0.432808\pi$
$167$	151029.			0.419054			0.209527	+	0.977803i	$0.432808\pi$
$168$		0			0
$169$	20443.7			0.0550608
$170$	−1.28145e6	+	739845.i	−3.40078	+	1.96344i
$171$		0			0
$172$	261851.	−	453539.i	0.674890	−	1.16894i
$173$	−48380.1	−	83796.9i	−0.122900	−	0.212869i	0.798010	−	0.602644i	$-0.205886\pi$
$173$	−48380.1	−	83796.9i	−0.122900	−	0.212869i	−0.920910	+	0.389775i	$0.872553\pi$
$174$		0			0
$175$	−730905.	−	39175.9i	−1.80412	−	0.0966994i
$176$			276147.i			0.671984i
$177$		0			0
$178$	−224044.	−	129352.i	−0.530010	−	0.306002i
$179$	55696.7	+	32156.5i	0.129926	+	0.0750130i	0.563554	−	0.826079i	$-0.309434\pi$
$179$	55696.7	+	32156.5i	0.129926	+	0.0750130i	−0.433628	+	0.901092i	$0.642767\pi$
$180$		0			0
$181$			465762.i			1.05674i	0.849015	+	0.528369i	$0.177196\pi$
$181$			465762.i			1.05674i	−0.849015	+	0.528369i	$0.822804\pi$
$182$	−325965.	+	500639.i	−0.729444	+	1.12033i
$183$		0			0
$184$	548.490	+	950.013i	0.00119433	+	0.00206864i
$185$	265892.	−	460538.i	0.571184	−	0.989319i
$186$		0			0
$187$	−432430.	+	249663.i	−0.904298	+	0.522096i
$188$	292930.			0.604463
$189$		0			0
$190$	−592171.			−1.19004
$191$	317171.	−	183119.i	0.629086	−	0.363203i	−0.151312	−	0.988486i	$-0.548350\pi$
$191$	317171.	−	183119.i	0.629086	−	0.363203i	0.780398	+	0.625283i	$0.215016\pi$
$192$		0			0
$193$	107364.	−	185960.i	0.207475	−	0.359357i	−0.743444	−	0.668799i	$-0.766809\pi$
$193$	107364.	−	185960.i	0.207475	−	0.359357i	0.950918	+	0.309442i	$0.100142\pi$
$194$	376042.	+	651325.i	0.717352	+	1.24249i
$195$		0			0
$196$	193948.	+	438415.i	0.360616	+	0.815164i
$197$			194807.i			0.357633i	0.983882	+	0.178817i	$0.0572269\pi$
$197$			194807.i			0.357633i	−0.983882	+	0.178817i	$0.942773\pi$
$198$		0			0
$199$	481226.	+	277836.i	0.861423	+	0.497343i	0.864489	−	0.502652i	$-0.167642\pi$
$199$	481226.	+	277836.i	0.861423	+	0.497343i	−0.00306524	+	0.999995i	$0.500976\pi$
$200$	132233.	+	76345.0i	0.233758	+	0.134960i
$201$		0			0
$202$			150715.i			0.259884i
$203$	−681143.	+	346041.i	−1.16011	+	0.589369i
$204$		0			0
$205$	−108133.	−	187292.i	−0.179710	−	0.311268i
$206$	−386275.	+	669047.i	−0.634203	+	1.09847i
$207$		0			0
$208$	576144.	−	332637.i	0.923363	−	0.533104i
$209$	−199830.			−0.316443
$210$		0			0
$211$	−236704.			−0.366016			−0.183008	−	0.983111i	$-0.558583\pi$
$211$	−236704.			−0.366016			−0.183008	+	0.983111i	$0.558583\pi$
$212$	972826.	−	561662.i	1.48661	−	0.858292i
$213$		0			0
$214$	−31987.8	+	55404.6i	−0.0477475	+	0.0827011i
$215$	−859748.	−	1.48913e6i	−1.26845	−	2.19703i
$216$		0			0
$217$	1224.95	−	22853.9i	0.00176591	−	0.0329466i
$218$		−	1.10590e6i		−	1.57607i
$219$		0			0
$220$	−568804.	−	328399.i	−0.792329	−	0.457451i
$221$	1.04178e6	+	601470.i	1.43481	+	0.828387i
$222$		0			0
$223$		−	1.15994e6i		−	1.56197i	−0.624547	−	0.780987i	$-0.714716\pi$
$223$		−	1.15994e6i		−	1.56197i	0.624547	−	0.780987i	$-0.285284\pi$
$224$	54624.5	−	1.01913e6i	0.0727391	−	1.35709i
$225$		0			0
$226$	166215.	+	287892.i	0.216470	+	0.374938i
$227$	649781.	−	1.12545e6i	0.836956	−	1.44965i	−0.0554727	−	0.998460i	$-0.517667\pi$
$227$	649781.	−	1.12545e6i	0.836956	−	1.44965i	0.892428	−	0.451189i	$-0.149000\pi$
$228$		0			0
$229$	−11455.0	+	6613.53i	−0.0144346	+	0.00833383i	−0.507200	−	0.861828i	$-0.669319\pi$
$229$	−11455.0	+	6613.53i	−0.0144346	+	0.00833383i	0.492765	+	0.870162i	$0.335986\pi$
$230$	−29553.8			−0.0368378
$231$		0			0
$232$	159375.			0.194402
$233$	−852543.	+	492216.i	−1.02879	+	0.593972i	−0.916637	−	0.399720i	$-0.869108\pi$
$233$	−852543.	+	492216.i	−1.02879	+	0.593972i	−0.112151	+	0.993691i	$0.535774\pi$
$234$		0			0
$235$	480896.	−	832937.i	0.568044	−	0.983880i
$236$	508761.	+	881200.i	0.594612	+	1.02990i
$237$		0			0
$238$	1.82615e6	−	927736.i	2.08974	−	1.06165i
$239$		−	84518.9i		−	0.0957104i	−0.998854	−	0.0478552i	$-0.984761\pi$
$239$		−	84518.9i		−	0.0957104i	0.998854	−	0.0478552i	$-0.0152386\pi$
$240$		0			0
$241$	93542.5	+	54006.8i	0.103745	+	0.0598971i	0.550975	−	0.834522i	$-0.314256\pi$
$241$	93542.5	+	54006.8i	0.103745	+	0.0598971i	−0.447230	+	0.894419i	$0.647589\pi$
$242$	677786.	+	391320.i	0.743968	+	0.429530i
$243$		0			0
$244$			643977.i			0.692462i
$245$	1.56502e6	+	168250.i	1.66573	+	0.179078i
$246$		0			0
$247$	240708.	+	416918.i	0.251043	+	0.434819i
$248$	−2387.15	+	4134.67i	−0.00246462	+	0.00426885i
$249$		0			0
$250$	−1.59069e6	+	918384.i	−1.60966	+	0.929339i
$251$	−957846.			−0.959646			−0.479823	−	0.877365i	$-0.659299\pi$
$251$	−957846.			−0.959646			−0.479823	+	0.877365i	$0.659299\pi$
$252$		0			0
$253$	−9973.05			−0.00979550
$254$	2.07531e6	−	1.19818e6i	2.01836	−	1.16530i
$255$		0			0
$256$	−619037.	+	1.07220e6i	−0.590359	+	1.02253i
$257$	300830.	+	521054.i	0.284112	+	0.492096i	0.972393	−	0.233348i	$-0.0749681\pi$
$257$	300830.	+	521054.i	0.284112	+	0.492096i	−0.688282	+	0.725443i	$0.741635\pi$
$258$		0			0
$259$	−401660.	+	616896.i	−0.372057	+	0.571430i
$260$			1.58231e6i			1.45164i
$261$		0			0
$262$	−1.04801e6	−	605069.i	−0.943218	−	0.544567i
$263$	−1.63833e6	−	945888.i	−1.46053	−	0.843239i	−0.461496	−	0.887142i	$-0.652687\pi$
$263$	−1.63833e6	−	945888.i	−1.46053	−	0.843239i	−0.999036	+	0.0439037i	$0.986021\pi$
$264$		0			0
$265$		−	3.68826e6i		−	3.22632i
$266$	818550.	+	43873.6i	0.709318	+	0.0380189i
$267$		0			0
$268$	−163364.	−	282955.i	−0.138938	−	0.240647i
$269$	131399.	−	227590.i	0.110716	−	0.191766i	−0.805343	−	0.592809i	$-0.798019\pi$
$269$	131399.	−	227590.i	0.110716	−	0.191766i	0.916059	+	0.401043i	$0.131352\pi$
$270$		0			0
$271$	−967784.	+	558750.i	−0.800489	+	0.462162i	−0.843642	−	0.536906i	$-0.819593\pi$
$271$	−967784.	+	558750.i	−0.800489	+	0.462162i	0.0431532	+	0.999068i	$0.486260\pi$
$272$	−2.28099e6			−1.86940
$273$		0			0
$274$	547213.			0.440332
$275$	−1.20218e6	+	694080.i	−0.958602	+	0.553449i
$276$		0			0
$277$	−1.13495e6	+	1.96579e6i	−0.888745	+	1.53935i	−0.0473855	+	0.998877i	$0.515089\pi$
$277$	−1.13495e6	+	1.96579e6i	−0.888745	+	1.53935i	−0.841360	+	0.540475i	$0.818244\pi$
$278$	−247351.	−	428424.i	−0.191956	−	0.332477i
$279$		0			0
$280$	−275167.	−	179161.i	−0.209750	−	0.136568i
$281$			1.32116e6i			0.998137i	0.866563	+	0.499068i	$0.166324\pi$
$281$			1.32116e6i			0.998137i	−0.866563	+	0.499068i	$0.833676\pi$
$282$		0			0
$283$	1.91757e6	+	1.10711e6i	1.42326	+	0.821720i	0.996576	−	0.0826808i	$-0.0263482\pi$
$283$	1.91757e6	+	1.10711e6i	1.42326	+	0.821720i	0.426684	+	0.904401i	$0.359682\pi$
$284$	−1.18538e6	−	684380.i	−0.872092	−	0.503502i
$285$		0			0
$286$			1.13299e6i			0.819048i
$287$	135594.	+	266903.i	0.0971711	+	0.191271i
$288$		0			0
$289$	−1.35230e6	−	2.34226e6i	−0.952423	−	1.64964i
$290$	−2.14687e6	+	3.71849e6i	−1.49903	+	2.59640i
$291$		0			0
$292$	−1.47445e6	+	851273.i	−1.01198	+	0.584268i
$293$	185273.			0.126079			0.0630394	−	0.998011i	$-0.479921\pi$
$293$	185273.			0.126079			0.0630394	+	0.998011i	$0.479921\pi$
$294$		0			0
$295$	3.34088e6			2.23514
$296$	132988.	−	76780.9i	0.0882235	−	0.0509359i
$297$		0			0
$298$	143667.	−	248838.i	0.0937164	−	0.162322i
$299$	12013.2	+	20807.4i	0.00777104	+	0.0134598i
$300$		0			0
$301$	1.07809e6	+	2.12210e6i	0.685865	+	1.35005i
$302$		−	4.18556e6i		−	2.64081i
$303$		0			0
$304$	−790552.	−	456425.i	−0.490621	−	0.283260i
$305$	1.83113e6	+	1.05720e6i	1.12712	+	0.650741i
$306$		0			0
$307$			1.57311e6i			0.952603i	0.879282	+	0.476302i	$0.158023\pi$
$307$			1.57311e6i			0.952603i	−0.879282	+	0.476302i	$0.841977\pi$
$308$	761919.	+	496084.i	0.457648	+	0.297974i
$309$		0			0
$310$	−64312.4	−	111392.i	−0.0380094	−	0.0658341i
$311$	−1.05000e6	+	1.81865e6i	−0.615585	+	1.06623i	0.374696	+	0.927148i	$0.377747\pi$
$311$	−1.05000e6	+	1.81865e6i	−0.615585	+	1.06623i	−0.990281	+	0.139078i	$0.955586\pi$
$312$		0			0
$313$	1.34949e6	−	779129.i	0.778591	−	0.449519i	−0.0573400	−	0.998355i	$-0.518262\pi$
$313$	1.34949e6	−	779129.i	0.778591	−	0.449519i	0.835931	+	0.548835i	$0.184929\pi$
$314$	385435.			0.220611
$315$		0			0
$316$	2.12336e6			1.19620
$317$	2.08730e6	−	1.20510e6i	1.16664	−	0.673559i	0.213753	−	0.976888i	$-0.431431\pi$
$317$	2.08730e6	−	1.20510e6i	1.16664	−	0.673559i	0.952886	+	0.303328i	$0.0980979\pi$
$318$		0			0
$319$	−724470.	+	1.25482e6i	−0.398606	+	0.690406i
$320$	−1.18490e6	−	2.05231e6i	−0.646856	−	1.12039i
$321$		0			0
$322$	40851.9	+	2189.63i	0.0219570	+	0.00117688i
$323$		−	1.65061e6i		−	0.880314i
$324$		0			0
$325$	2.89621e6	+	1.67213e6i	1.52097	+	0.878133i
$326$	−1.08421e6	−	625971.i	−0.565029	−	0.326220i
$327$		0			0
$328$		−	62450.5i		−	0.0320517i
$329$	−726449.	+	1.11573e6i	−0.370011	+	0.568288i
$330$		0			0
$331$	−579027.	−	1.00290e6i	−0.290488	−	0.503141i	0.683437	−	0.730010i	$-0.260484\pi$
$331$	−579027.	−	1.00290e6i	−0.290488	−	0.503141i	−0.973925	+	0.226869i	$0.927151\pi$
$332$	−1.25330e6	+	2.17079e6i	−0.624038	+	1.08087i
$333$		0			0
$334$	−1.01755e6	+	587481.i	−0.499101	+	0.288156i
$335$	−1.07276e6			−0.522267
$336$		0			0
$337$	585639.			0.280902			0.140451	−	0.990088i	$-0.455145\pi$
$337$	585639.			0.280902			0.140451	+	0.990088i	$0.455145\pi$
$338$	−137738.	+	79522.9i	−0.0655785	+	0.0378618i
$339$		0			0
$340$	2.71259e6	−	4.69835e6i	1.27259	−	2.20418i
$341$	−21702.5	−	37589.8i	−0.0101070	−	0.0175059i
$342$		0			0
$343$	−2.15084e6	−	348522.i	−0.987125	−	0.159954i
$344$		−	496534.i		−	0.226232i
$345$		0			0
$346$	651915.	+	376383.i	0.292752	+	0.169021i
$347$	−1.57841e6	−	911294.i	−0.703713	−	0.406289i	0.105016	−	0.994471i	$-0.466511\pi$
$347$	−1.57841e6	−	911294.i	−0.703713	−	0.406289i	−0.808729	+	0.588182i	$0.799844\pi$
$348$		0			0
$349$		−	1.25184e6i		−	0.550155i	−0.961422	−	0.275077i	$-0.911296\pi$
$349$		−	1.25184e6i		−	0.550155i	0.961422	−	0.275077i	$-0.0887035\pi$
$350$	5.07680e6	−	2.57917e6i	2.21524	−	1.12541i
$351$		0			0
$352$	−967784.	−	1.67625e6i	−0.416315	−	0.721078i
$353$	−331320.	+	573862.i	−0.141518	+	0.245116i	−0.928068	−	0.372410i	$-0.878532\pi$
$353$	−331320.	+	573862.i	−0.141518	+	0.245116i	0.786551	+	0.617526i	$0.211865\pi$
$354$		0			0
$355$	−3.89202e6	+	2.24706e6i	−1.63909	+	0.946332i
$356$	948522.			0.396664
$357$		0			0
$358$	−500336.			−0.206326
$359$	1.68613e6	−	973487.i	0.690486	−	0.398652i	−0.113308	−	0.993560i	$-0.536145\pi$
$359$	1.68613e6	−	973487.i	0.690486	−	0.398652i	0.803794	+	0.594908i	$0.202811\pi$
$360$		0			0
$361$	−907764.	+	1.57229e6i	−0.366610	+	0.634988i
$362$	−1.81175e6	−	3.13803e6i	−0.726651	−	1.25860i
$363$		0			0
$364$	117232.	−	2.18720e6i	0.0463761	−	0.865239i
$365$			5.59005e6i			2.19626i
$366$		0			0
$367$	−2.99252e6	−	1.72773e6i	−1.15977	−	0.669593i	−0.208521	−	0.978018i	$-0.566865\pi$
$367$	−2.99252e6	−	1.72773e6i	−1.15977	−	0.669593i	−0.951249	+	0.308425i	$0.900198\pi$
$368$	−39454.6	−	22779.1i	−0.0151872	−	0.00876834i
$369$		0			0
$370$			4.13712e6i			1.57106i
$371$	−273261.	+	5.09824e6i	−0.103073	+	1.92303i
$372$		0			0
$373$	−1.16752e6	−	2.02220e6i	−0.434502	−	0.752580i	0.562752	−	0.826625i	$-0.309742\pi$
$373$	−1.16752e6	−	2.02220e6i	−0.434502	−	0.752580i	−0.997255	+	0.0740452i	$0.976409\pi$
$374$	1.94231e6	−	3.36417e6i	0.718024	−	1.24365i
$375$		0			0
$376$	240525.	−	138867.i	0.0877385	−	0.0506559i
$377$	3.49068e6			1.26490
$378$		0			0
$379$	−1.01660e6			−0.363541			−0.181771	−	0.983341i	$-0.558183\pi$
$379$	−1.01660e6			−0.363541			−0.181771	+	0.983341i	$0.558183\pi$
$380$	1.88027e6	−	1.08558e6i	0.667978	−	0.385657i
$381$		0			0
$382$	−1.42461e6	+	2.46750e6i	−0.499502	+	0.865164i
$383$	1.17345e6	+	2.03247e6i	0.408759	+	0.707991i	0.994751	−	0.102326i	$-0.0326283\pi$
$383$	1.17345e6	+	2.03247e6i	0.408759	+	0.707991i	−0.585992	+	0.810317i	$0.699295\pi$
$384$		0			0
$385$	2.66142e6	−	1.35208e6i	0.915085	−	0.464890i
$386$			1.67052e6i			0.570668i
$387$		0			0
$388$	−2.38804e6	−	1.37873e6i	−0.805308	−	0.464945i
$389$	1.90457e6	+	1.09960e6i	0.638149	+	0.368436i	0.783901	−	0.620886i	$-0.213227\pi$
$389$	1.90457e6	+	1.09960e6i	0.638149	+	0.368436i	−0.145752	+	0.989321i	$0.546560\pi$
$390$		0			0
$391$		−	82377.9i		−	0.0272501i
$392$	367086.	+	268039.i	0.120657	+	0.0881013i
$393$		0			0
$394$	−757769.	−	1.31249e6i	−0.245921	−	0.425948i
$395$	3.48586e6	−	6.03769e6i	1.12413	−	1.94705i
$396$		0			0
$397$	4.09064e6	−	2.36173e6i	1.30261	−	0.752063i	0.321760	−	0.946821i	$-0.395726\pi$
$397$	4.09064e6	−	2.36173e6i	1.30261	−	0.752063i	0.980851	+	0.194758i	$0.0623922\pi$
$398$	−4.32297e6			−1.36796
$399$		0			0
$400$	−6.34130e6			−1.98166
$401$	369827.	−	213520.i	0.114852	−	0.0663096i	−0.441474	−	0.897274i	$-0.645544\pi$
$401$	369827.	−	213520.i	0.114852	−	0.0663096i	0.556325	+	0.830965i	$0.312211\pi$
$402$		0			0
$403$	−52283.9	+	90558.4i	−0.0160364	+	0.0277758i
$404$	−276294.	−	478555.i	−0.0842206	−	0.145874i
$405$		0			0
$406$	3.24310e6	−	4.98096e6i	0.976438	−	1.49968i
$407$			1.39609e6i			0.417759i
$408$		0			0
$409$	153620.	+	88692.4i	0.0454087	+	0.0262167i	0.522532	−	0.852619i	$-0.324987\pi$
$409$	153620.	+	88692.4i	0.0454087	+	0.0262167i	−0.477124	+	0.878836i	$0.658321\pi$
$410$	1.45707e6	+	841242.i	0.428077	+	0.247150i
$411$		0			0
$412$		−	2.83250e6i		−	0.822104i
$413$	−4.61805e6	−	247524.i	−1.33224	−	0.0714072i
$414$		0			0
$415$	4.11503e6	+	7.12744e6i	1.17288	+	2.03148i
$416$	−2.33151e6	+	4.03830e6i	−0.660548	+	1.14410i
$417$		0			0
$418$	1.34634e6	−	777309.i	0.376889	−	0.217597i
$419$	−2.88404e6			−0.802539			−0.401269	−	0.915960i	$-0.631431\pi$
$419$	−2.88404e6			−0.802539			−0.401269	+	0.915960i	$0.631431\pi$
$420$		0			0
$421$	779255.			0.214276			0.107138	−	0.994244i	$-0.465831\pi$
$421$	779255.			0.214276			0.107138	+	0.994244i	$0.465831\pi$
$422$	1.59478e6	−	920744.i	0.435932	−	0.251685i
$423$		0			0
$424$	532525.	−	922360.i	0.143855	−	0.249164i
$425$	−5.73314e6	−	9.93009e6i	−1.53964	−	2.66674i
$426$		0			0
$427$	−2.45281e6	−	1.59702e6i	−0.651021	−	0.423879i
$428$		−	234563.i		−	0.0618941i
$429$		0			0
$430$	1.15850e7	+	6.68858e6i	3.02151	+	1.74447i
$431$	−746695.	−	431105.i	−0.193620	−	0.111787i	0.400056	−	0.916491i	$-0.368991\pi$
$431$	−746695.	−	431105.i	−0.193620	−	0.111787i	−0.593676	+	0.804704i	$0.702324\pi$
$432$		0			0
$433$			2.90119e6i			0.743629i	0.928307	+	0.371815i	$0.121264\pi$
$433$			2.90119e6i			0.743629i	−0.928307	+	0.371815i	$0.878736\pi$
$434$	80645.2	+	158741.i	0.0205520	+	0.0404543i
$435$		0			0
$436$	2.02736e6	+	3.51150e6i	0.510758	+	0.884659i
$437$	16483.8	−	28550.8i	0.00412908	−	0.00715178i
$438$		0			0
$439$	−886538.	+	511843.i	−0.219551	+	0.126758i	−0.605743	−	0.795661i	$-0.707124\pi$
$439$	−886538.	+	511843.i	−0.219551	+	0.126758i	0.386191	+	0.922419i	$0.373791\pi$
$440$	−622725.			−0.153343
$441$		0			0
$442$	−9.35852e6			−2.27851
$443$	3.25534e6	−	1.87947e6i	0.788111	−	0.455016i	−0.0511864	−	0.998689i	$-0.516300\pi$
$443$	3.25534e6	−	1.87947e6i	0.788111	−	0.455016i	0.839297	+	0.543673i	$0.182967\pi$
$444$		0			0
$445$	1.55716e6	−	2.69709e6i	0.372764	−	0.645647i
$446$	4.51200e6	+	7.81501e6i	1.07407	+	1.86034i
$447$		0			0
$448$	1.48582e6	+	2.92467e6i	0.349761	+	0.688466i
$449$		−	741230.i		−	0.173515i	−0.996229	−	0.0867575i	$-0.972349\pi$
$449$		−	741230.i		−	0.173515i	0.996229	−	0.0867575i	$-0.0276505\pi$
$450$		0			0
$451$	491695.	+	283880.i	0.113829	+	0.0657194i
$452$	−1.05554e6	−	609415.i	−0.243012	−	0.140303i
$453$		0			0
$454$			1.01102e7i			2.30208i
$455$	−6.02678e6	−	3.92402e6i	−1.36476	−	0.888593i
$456$		0			0
$457$	−1.19819e6	−	2.07533e6i	−0.268372	−	0.464833i	0.700070	−	0.714074i	$-0.253152\pi$
$457$	−1.19819e6	−	2.07533e6i	−0.268372	−	0.464833i	−0.968441	+	0.249241i	$0.919819\pi$
$458$	51451.3	−	89116.3i	0.0114613	−	0.0198515i
$459$		0			0
$460$	93840.1	−	54178.6i	0.0206773	−	0.0119380i
$461$	5.93969e6			1.30170			0.650851	−	0.759206i	$-0.274412\pi$
$461$	5.93969e6			1.30170			0.650851	+	0.759206i	$0.274412\pi$
$462$		0			0
$463$	2.06910e6			0.448569			0.224284	−	0.974524i	$-0.427996\pi$
$463$	2.06910e6			0.448569			0.224284	+	0.974524i	$0.427996\pi$
$464$	−5.73218e6	+	3.30948e6i	−1.23602	+	0.713616i
$465$		0			0
$466$	3.82929e6	−	6.63253e6i	0.816871	−	1.41486i
$467$	−2.21202e6	−	3.83133e6i	−0.469350	−	0.812938i	0.530036	−	0.847975i	$-0.322178\pi$
$467$	−2.21202e6	−	3.83133e6i	−0.469350	−	0.812938i	−0.999386	+	0.0350370i	$0.988845\pi$
$468$		0			0
$469$	1.48287e6	+	79480.6i	0.311294	+	0.0166851i
$470$			7.48246e6i			1.56243i
$471$		0			0
$472$	835486.	+	482368.i	0.172617	+	0.0996606i
$473$	3.90939e6	+	2.25709e6i	0.803445	+	0.463869i
$474$		0			0
$475$		−	4.58879e6i		−	0.933178i
$476$	−4.09768e6	+	6.29349e6i	−0.828935	+	1.27313i
$477$		0			0
$478$	328766.	+	569439.i	0.0658138	+	0.113993i
$479$	−2.78502e6	+	4.82379e6i	−0.554612	+	0.960617i	0.443321	+	0.896363i	$0.353800\pi$
$479$	−2.78502e6	+	4.82379e6i	−0.554612	+	0.960617i	−0.997934	+	0.0642538i	$0.979533\pi$
$480$		0			0
$481$	2.91274e6	−	1.68167e6i	0.574036	−	0.331420i
$482$	−840314.			−0.164749
$483$		0			0
$484$	−2.86950e6			−0.556791
$485$	−7.84076e6	+	4.52687e6i	−1.51358	+	0.873863i
$486$		0			0
$487$	−1.77489e6	+	3.07420e6i	−0.339116	+	0.587367i	−0.984267	−	0.176689i	$-0.943461\pi$
$487$	−1.77489e6	+	3.07420e6i	−0.339116	+	0.587367i	0.645150	+	0.764056i	$0.276795\pi$
$488$	305285.	+	528769.i	0.0580305	+	0.100512i
$489$		0			0
$490$	−1.11986e7	+	4.95410e6i	−2.10705	+	0.932126i
$491$			2.35429e6i			0.440713i	0.975419	+	0.220356i	$0.0707221\pi$
$491$			2.35429e6i			0.440713i	−0.975419	+	0.220356i	$0.929278\pi$
$492$		0			0
$493$	−1.03649e7	−	5.98416e6i	−1.92064	−	1.10888i
$494$	−3.24350e6	−	1.87264e6i	−0.597994	−	0.345252i
$495$		0			0
$496$		−	198279.i		−	0.0361888i
$497$	5.54637e6	−	2.81772e6i	1.00721	−	0.511690i
$498$		0			0
$499$	−389036.	−	673830.i	−0.0699420	−	0.121143i	0.828934	−	0.559347i	$-0.188948\pi$
$499$	−389036.	−	673830.i	−0.0699420	−	0.121143i	−0.898876	+	0.438204i	$0.855615\pi$
$500$	3.36720e6	−	5.83215e6i	0.602342	−	1.04329i
$501$		0			0
$502$	6.45341e6	−	3.72588e6i	1.14296	−	0.659886i
$503$	8.32976e6			1.46795			0.733977	−	0.679175i	$-0.237662\pi$
$503$	8.32976e6			1.46795			0.733977	+	0.679175i	$0.237662\pi$
$504$		0			0
$505$	−1.81434e6			−0.316585
$506$	67192.6	−	38793.7i	0.0116666	−	0.00673573i
$507$		0			0
$508$	−4.39304e6	+	7.60898e6i	−0.755277	+	1.30818i
$509$	−1.24589e6	−	2.15794e6i	−0.213150	−	0.369186i	0.739549	−	0.673103i	$-0.235039\pi$
$509$	−1.24589e6	−	2.15794e6i	−0.213150	−	0.369186i	−0.952699	+	0.303917i	$0.901706\pi$
$510$		0			0
$511$	414164.	−	7.72706e6i	0.0701650	−	1.30907i
$512$		−	7.86994e6i		−	1.32677i
$513$		0			0
$514$	−4.05364e6	−	2.34037e6i	−0.676764	−	0.390730i
$515$	−8.05411e6	−	4.65004e6i	−1.33813	−	0.772572i
$516$		0			0
$517$			2.52498e6i			0.415463i
$518$	306517.	−	5.71869e6i	0.0501915	−	0.936423i
$519$		0			0
$520$	750112.	+	1.29923e6i	0.121652	+	0.210707i
$521$	−590637.	+	1.02301e6i	−0.0953294	+	0.165115i	−0.909746	−	0.415165i	$-0.863724\pi$
$521$	−590637.	+	1.02301e6i	−0.0953294	+	0.165115i	0.814417	+	0.580281i	$0.197057\pi$
$522$		0			0
$523$	−5.16423e6	+	2.98157e6i	−0.825565	+	0.476640i	−0.852332	−	0.523002i	$-0.824812\pi$
$523$	−5.16423e6	+	2.98157e6i	−0.825565	+	0.476640i	0.0267669	+	0.999642i	$0.491479\pi$
$524$	4.43689e6			0.705912
$525$		0			0
$526$	1.47175e7			2.31936
$527$	310493.	−	179263.i	0.0486997	−	0.0281168i
$528$		0			0
$529$	−3.21735e6	+	5.57261e6i	−0.499872	+	0.865804i
$530$	1.43468e7	+	2.48494e7i	2.21853	+	3.84260i
$531$		0			0
$532$	−2.67951e6	+	1.36127e6i	−0.410465	+	0.208529i
$533$		−	1.36781e6i		−	0.208548i
$534$		0			0
$535$	−666970.	−	385075.i	−0.100745	−	0.0581649i
$536$	−268277.	−	154890.i	−0.0403340	−	0.0232868i
$537$		0			0
$538$			2.04449e6i			0.304530i
$539$	−3.77902e6	+	1.67178e6i	−0.560283	+	0.247860i
$540$		0			0
$541$	−771540.	−	1.33635e6i	−0.113335	−	0.196303i	0.803778	−	0.594930i	$-0.202820\pi$
$541$	−771540.	−	1.33635e6i	−0.113335	−	0.196303i	−0.917113	+	0.398627i	$0.869487\pi$
$542$	4.34691e6	−	7.52907e6i	0.635598	−	1.10089i
$543$		0			0
$544$	1.38459e7	−	7.99395e6i	2.00597	−	1.15815i
$545$	1.33131e7			1.91994
$546$		0			0
$547$	7.77667e6			1.11129			0.555643	−	0.831421i	$-0.312472\pi$
$547$	7.77667e6			1.11129			0.555643	+	0.831421i	$0.312472\pi$
$548$	−1.73752e6	+	1.00316e6i	−0.247161	+	0.142698i
$549$		0			0
$550$	5.39974e6	−	9.35262e6i	0.761142	−	1.31834i
$551$	−2.39486e6	−	4.14801e6i	−0.336047	−	0.582051i
$552$		0			0
$553$	−5.26579e6	+	8.08755e6i	−0.732235	+	1.12462i
$554$		−	1.76591e7i		−	2.44453i
$555$		0			0
$556$	1.57079e6	+	906896.i	0.215492	+	0.124414i
$557$	−6.40208e6	−	3.69624e6i	−0.874346	−	0.504804i	−0.00555602	−	0.999985i	$-0.501769\pi$
$557$	−6.40208e6	−	3.69624e6i	−0.874346	−	0.504804i	−0.868790	+	0.495181i	$0.835102\pi$
$558$		0			0
$559$		−	1.08752e7i		−	1.47200i
$560$	1.36171e7	+	729867.i	1.83491	+	0.0983499i
$561$		0			0
$562$	−5.13912e6	−	8.90122e6i	−0.686354	−	1.18880i
$563$	5.22242e6	−	9.04550e6i	0.694386	−	1.20271i	−0.276001	−	0.961157i	$-0.589009\pi$
$563$	5.22242e6	−	9.04550e6i	0.694386	−	1.20271i	0.970387	−	0.241555i	$-0.0776574\pi$
$564$		0			0
$565$	−3.46570e6	+	2.00092e6i	−0.456741	+	0.263699i
$566$	−1.72259e7			−2.26017
$567$		0			0
$568$	−1.29775e6			−0.168780
$569$	4.16431e6	−	2.40427e6i	0.539216	−	0.311316i	−0.205545	−	0.978648i	$-0.565897\pi$
$569$	4.16431e6	−	2.40427e6i	0.539216	−	0.311316i	0.744761	+	0.667331i	$0.232563\pi$
$570$		0			0
$571$	5.34054e6	−	9.25008e6i	0.685480	−	1.18729i	−0.287806	−	0.957689i	$-0.592926\pi$
$571$	5.34054e6	−	9.25008e6i	0.685480	−	1.18729i	0.973286	−	0.229597i	$-0.0737408\pi$
$572$	−2.07701e6	−	3.59748e6i	−0.265429	−	0.459736i
$573$		0			0
$574$	−1.95177e6	−	1.27079e6i	−0.247257	−	0.160989i
$575$		−	229016.i		−	0.0288866i
$576$		0			0
$577$	−1.00975e6	−	582981.i	−0.126263	−	0.0728979i	0.435538	−	0.900170i	$-0.356558\pi$
$577$	−1.00975e6	−	582981.i	−0.126263	−	0.0728979i	−0.561801	+	0.827272i	$0.689891\pi$
$578$	1.82221e7	+	1.05205e7i	2.26871	+	1.30984i
$579$		0			0
$580$		−	1.57427e7i		−	1.94317i
$581$	−5.16009e6	−	1.01571e7i	−0.634186	−	1.24832i
$582$		0			0
$583$	4.84138e6	+	8.38551e6i	0.589926	+	1.02178i
$584$	−807112.	+	1.39796e6i	−0.0979269	+	0.169614i
$585$		0			0
$586$	−1.24826e6	+	720683.i	−0.150162	+	0.0866962i
$587$	90616.7			0.0108546			0.00542729	−	0.999985i	$-0.498272\pi$
$587$	90616.7			0.0108546			0.00542729	+	0.999985i	$0.498272\pi$
$588$		0			0
$589$	143482.			0.0170416
$590$	−2.25089e7	+	1.29955e7i	−2.66210	+	1.53696i
$591$		0			0
$592$	−3.18875e6	+	5.52308e6i	−0.373953	+	0.647705i
$593$	7.73816e6	+	1.34029e7i	0.903651	+	1.56517i	0.822717	+	0.568451i	$0.192457\pi$
$593$	7.73816e6	+	1.34029e7i	0.903651	+	1.56517i	0.0809342	+	0.996719i	$0.474210\pi$
$594$		0			0
$595$	1.11683e7	+	2.19835e7i	1.29328	+	2.54568i
$596$			1.05349e6i			0.121483i
$597$		0			0
$598$	−161875.	−	93458.8i	−0.0185109	−	0.0106873i
$599$	1.01493e7	+	5.85973e6i	1.15577	+	0.667284i	0.950286	−	0.311377i	$-0.100790\pi$
$599$	1.01493e7	+	5.85973e6i	1.15577	+	0.667284i	0.205483	+	0.978661i	$0.434124\pi$
$600$		0			0
$601$			3.43153e6i			0.387527i	0.981048	+	0.193764i	$0.0620695\pi$
$601$			3.43153e6i			0.387527i	−0.981048	+	0.193764i	$0.937931\pi$
$602$	−1.55182e7	−	1.01039e7i	−1.74522	−	1.13631i
$603$		0			0
$604$	7.67305e6	+	1.32901e7i	0.855807	+	1.48230i
$605$	−4.71078e6	+	8.15931e6i	−0.523244	+	0.906285i
$606$		0			0
$607$	−1.39375e7	+	8.04681e6i	−1.53537	+	0.886446i	−0.536268	+	0.844048i	$0.680166\pi$
$607$	−1.39375e7	+	8.04681e6i	−1.53537	+	0.886446i	−0.999101	+	0.0423977i	$0.986500\pi$
$608$	6.39834e6			0.701954
$609$		0			0
$610$	−1.64494e7			−1.78989
$611$	5.26803e6	−	3.04150e6i	0.570881	−	0.329598i
$612$		0			0
$613$	−1.15527e6	+	2.00099e6i	−0.124175	+	0.215077i	−0.921410	−	0.388592i	$-0.872962\pi$
$613$	−1.15527e6	+	2.00099e6i	−0.124175	+	0.215077i	0.797235	+	0.603669i	$0.206295\pi$
$614$	−6.11915e6	−	1.05987e7i	−0.655043	−	1.13457i
$615$		0			0
$616$	860785.	+	46137.4i	0.0913994	+	0.00489893i
$617$			3.72656e6i			0.394090i	0.980394	+	0.197045i	$0.0631345\pi$
$617$			3.72656e6i			0.394090i	−0.980394	+	0.197045i	$0.936866\pi$
$618$		0			0
$619$	−1.19584e7	−	6.90416e6i	−1.25443	−	0.724243i	−0.282440	−	0.959285i	$-0.591144\pi$
$619$	−1.19584e7	−	6.90416e6i	−1.25443	−	0.724243i	−0.971985	+	0.235042i	$0.924477\pi$
$620$	408413.	+	235797.i	0.0426697	+	0.0246354i
$621$		0			0
$622$		−	1.63374e7i		−	1.69319i
$623$	−2.35227e6	+	3.61278e6i	−0.242811	+	0.372925i
$624$		0			0
$625$	−2.23385e6	−	3.86913e6i	−0.228746	−	0.396199i
$626$	−6.06139e6	+	1.04986e7i	−0.618211	+	1.07077i
$627$		0			0
$628$	−1.22384e6	+	706586.i	−0.123830	+	0.0714934i
$629$	−1.15317e7			−1.16217
$630$		0			0
$631$	9.04954e6			0.904801			0.452401	−	0.891815i	$-0.350568\pi$
$631$	9.04954e6			0.904801			0.452401	+	0.891815i	$0.350568\pi$
$632$	1.74349e6	−	1.00660e6i	0.173630	−	0.100246i
$633$		0			0
$634$	−9.37534e6	+	1.62386e7i	−0.926326	+	1.60444i
$635$	1.44239e7	+	2.49829e7i	1.41954	+	2.45872i
$636$		0			0
$637$	8.04001e6	+	5.87065e6i	0.785069	+	0.573241i
$638$		−	1.12723e7i		−	1.09638i
$639$		0			0
$640$	−4.46566e6	−	2.57825e6i	−0.430959	−	0.248814i
$641$	−5.32452e6	−	3.07412e6i	−0.511842	−	0.295512i	0.221749	−	0.975104i	$-0.428824\pi$
$641$	−5.32452e6	−	3.07412e6i	−0.511842	−	0.295512i	−0.733590	+	0.679592i	$0.762157\pi$
$642$		0			0
$643$		−	5.13071e6i		−	0.489384i	−0.969601	−	0.244692i	$-0.921313\pi$
$643$		−	5.13071e6i		−	0.489384i	0.969601	−	0.244692i	$-0.0786869\pi$
$644$	−133728.	+	67937.8i	−0.0127060	+	0.00645501i
$645$		0			0
$646$	6.42062e6	+	1.11208e7i	0.605335	+	1.04847i
$647$	3.78852e6	−	6.56190e6i	0.355802	−	0.616267i	−0.631453	−	0.775414i	$-0.717541\pi$
$647$	3.78852e6	−	6.56190e6i	0.355802	−	0.616267i	0.987255	+	0.159147i	$0.0508744\pi$
$648$		0			0
$649$	−7.59571e6	+	4.38539e6i	−0.707875	+	0.408692i
$650$	−2.60173e7			−2.41534
$651$		0			0
$652$	4.59016e6			0.422872
$653$	−1.08612e7	+	6.27074e6i	−0.996773	+	0.575487i	−0.907292	−	0.420501i	$-0.861854\pi$
$653$	−1.08612e7	+	6.27074e6i	−0.996773	+	0.575487i	−0.0894813	+	0.995988i	$0.528521\pi$
$654$		0			0
$655$	7.28393e6	−	1.26161e7i	0.663380	−	1.14901i
$656$	1.29680e6	+	2.24613e6i	0.117656	+	0.203786i
$657$		0			0
$658$	554372.	−	1.03429e7i	0.0499156	−	0.931275i
$659$			8.97219e6i			0.804795i	0.915465	+	0.402397i	$0.131823\pi$
$659$			8.97219e6i			0.804795i	−0.915465	+	0.402397i	$0.868177\pi$
$660$		0			0
$661$	−15373.7	−	8876.02i	−0.00136860	−	0.000790159i	0.499316	−	0.866420i	$-0.333585\pi$
$661$	−15373.7	−	8876.02i	−0.00136860	−	0.000790159i	−0.500684	+	0.865630i	$0.666918\pi$
$662$	7.80230e6	+	4.50466e6i	0.691954	+	0.399500i
$663$		0			0
$664$			2.37657e6i			0.209185i
$665$	−528158.	+	9.85385e6i	−0.0463138	+	0.864076i
$666$		0			0
$667$	−119522.	−	207018.i	−0.0104024	−	0.0180174i
$668$	2.15396e6	−	3.73077e6i	0.186765	−	0.323487i
$669$		0			0
$670$	7.22767e6	−	4.17289e6i	0.622030	−	0.359129i
$671$	−5.55092e6			−0.475947
$672$		0			0
$673$	−235445.			−0.0200379			−0.0100189	−	0.999950i	$-0.503189\pi$
$673$	−235445.			−0.0200379			−0.0100189	+	0.999950i	$0.503189\pi$
$674$	−3.94570e6	+	2.27805e6i	−0.334560	+	0.193158i
$675$		0			0
$676$	291566.	−	505007.i	0.0245397	−	0.0425040i
$677$	−6.31071e6	−	1.09305e7i	−0.529184	−	0.916573i	−0.999421	−	0.0340329i	$-0.989165\pi$
$677$	−6.31071e6	−	1.09305e7i	−0.529184	−	0.916573i	0.470237	−	0.882540i	$-0.344168\pi$
$678$		0			0
$679$	1.11736e7	−	5.67651e6i	0.930075	−	0.472506i
$680$		−	5.14375e6i		−	0.426587i
$681$		0			0
$682$	292437.	+	168839.i	0.0240753	+	0.0138999i
$683$	−6.84555e6	−	3.95228e6i	−0.561509	−	0.324187i	0.192242	−	0.981348i	$-0.438424\pi$
$683$	−6.84555e6	−	3.95228e6i	−0.561509	−	0.324187i	−0.753751	+	0.657160i	$0.771757\pi$
$684$		0			0
$685$			6.58745e6i			0.536402i
$686$	1.58468e7	−	6.01829e6i	1.28567	−	0.488273i
$687$		0			0
$688$	1.03107e7	+	1.78586e7i	0.830455	+	1.43839i
$689$	1.16635e7	−	2.02017e7i	0.936009	−	1.62122i
$690$		0			0
$691$	1.05423e7	−	6.08661e6i	0.839925	−	0.484931i	−0.0173134	−	0.999850i	$-0.505511\pi$
$691$	1.05423e7	−	6.08661e6i	0.839925	−	0.484931i	0.857239	+	0.514919i	$0.172178\pi$
$692$	−2.75997e6			−0.219098
$693$		0			0
$694$	1.41792e7			1.11751
$695$	5.15745e6	−	2.97765e6i	0.405017	−	0.233836i
$696$		0			0
$697$	−2.34487e6	+	4.06143e6i	−0.182825	+	0.316663i
$698$	4.86947e6	+	8.43417e6i	0.378306	+	0.655245i
$699$		0			0
$700$	−1.13918e7	+	1.74963e7i	−0.878714	+	1.34959i
$701$			1.11324e7i			0.855643i	0.903863	+	0.427821i	$0.140719\pi$
$701$			1.11324e7i			0.855643i	−0.903863	+	0.427821i	$0.859281\pi$
$702$		0			0
$703$	−3.99670e6	−	2.30750e6i	−0.305010	−	0.176097i
$704$	5.38791e6	+	3.11071e6i	0.409722	+	0.236553i
$705$		0			0
$706$		−	5.15514e6i		−	0.389250i
$707$	2.50794e6	+	134423.i	0.188698	+	0.0101141i
$708$		0			0
$709$	−275013.	−	476337.i	−0.0205465	−	0.0355876i	0.855569	−	0.517688i	$-0.173207\pi$
$709$	−275013.	−	476337.i	−0.0205465	−	0.0355876i	−0.876116	+	0.482101i	$0.839874\pi$
$710$	1.74814e7	−	3.02788e7i	1.30146	−	2.25420i
$711$		0			0
$712$	778831.	−	449658.i	0.0575762	−	0.0332416i
$713$	7160.86			0.000527523
$714$		0			0
$715$	−1.36391e7			−0.997746
$716$	1.58868e6	−	917225.i	0.115812	−	0.0668641i
$717$		0			0
$718$	−7.57344e6	+	1.31176e7i	−0.548254	+	0.949604i
$719$	−1.86659e6	−	3.23302e6i	−0.134656	−	0.233231i	0.790810	−	0.612062i	$-0.209660\pi$
$719$	−1.86659e6	−	3.23302e6i	−0.134656	−	0.233231i	−0.925466	+	0.378831i	$0.876326\pi$
$720$		0			0
$721$	1.07886e7	+	7.02442e6i	0.772905	+	0.503237i
$722$		−	1.41243e7i		−	1.00838i
$723$		0			0
$724$	1.15054e7	+	6.64264e6i	0.815746	+	0.470971i
$725$	−2.88150e7	−	1.66364e7i	−2.03598	−	1.17547i
$726$		0			0
$727$			1.07995e7i			0.757825i	0.925433	+	0.378913i	$0.123702\pi$
$727$			1.07995e7i			0.757825i	−0.925433	+	0.378913i	$0.876298\pi$
$728$	−940611.	−	1.85149e6i	−0.0657781	−	0.129477i
$729$		0			0
$730$	−2.17445e7	−	3.76625e7i	−1.51023	−	2.61579i
$731$	−1.86437e7	+	3.22918e7i	−1.29044	+	2.23511i
$732$		0			0
$733$	1.12726e7	−	6.50822e6i	0.774931	−	0.447406i	−0.0597000	−	0.998216i	$-0.519014\pi$
$733$	1.12726e7	−	6.50822e6i	0.774931	−	0.447406i	0.834631	+	0.550810i	$0.185681\pi$
$734$	2.68825e7			1.84174
$735$		0			0
$736$	319326.			0.0217290
$737$	2.43900e6	−	1.40816e6i	0.165403	−	0.0954955i
$738$		0			0
$739$	1.40330e7	−	2.43058e7i	0.945232	−	1.63719i	0.189947	−	0.981794i	$-0.439168\pi$
$739$	1.40330e7	−	2.43058e7i	0.945232	−	1.63719i	0.755285	−	0.655396i	$-0.227498\pi$
$740$	−7.58424e6	−	1.31363e7i	−0.509135	−	0.881847i
$741$		0			0
$742$	−1.79903e7	−	3.54119e7i	−1.19958	−	2.36124i
$743$			1.08931e7i			0.723901i	0.932197	+	0.361951i	$0.117889\pi$
$743$			1.08931e7i			0.723901i	−0.932197	+	0.361951i	$0.882111\pi$
$744$		0			0
$745$	2.99556e6	+	1.72949e6i	0.197737	+	0.114163i
$746$	1.57321e7	+	9.08296e6i	1.03500	+	0.597558i
$747$		0			0
$748$			1.42427e7i			0.930760i
$749$	893414.	+	581700.i	0.0581900	+	0.0378874i
$750$		0			0
$751$	−7.92719e6	−	1.37303e7i	−0.512884	−	0.888341i	−0.999888	−	0.0149418i	$-0.995244\pi$
$751$	−7.92719e6	−	1.37303e7i	−0.512884	−	0.888341i	0.487004	−	0.873400i	$-0.338090\pi$
$752$	−5.76723e6	+	9.98914e6i	−0.371897	+	0.644145i
$753$		0			0
$754$	−2.35182e7	+	1.35782e7i	−1.50652	+	0.869790i
$755$	5.03866e7			3.21697
$756$		0			0
$757$	1.74726e7			1.10820			0.554100	−	0.832450i	$-0.313063\pi$
$757$	1.74726e7			1.10820			0.554100	+	0.832450i	$0.313063\pi$
$758$	6.84929e6	−	3.95444e6i	0.432985	−	0.249984i
$759$		0			0
$760$	1.02926e6	−	1.78273e6i	0.0646386	−	0.111957i
$761$	−1.03862e7	−	1.79894e7i	−0.650122	−	1.12604i	−0.983093	−	0.183107i	$-0.941385\pi$
$761$	−1.03862e7	−	1.79894e7i	−0.650122	−	1.12604i	0.332971	−	0.942937i	$-0.391949\pi$
$762$		0			0
$763$	−1.84025e7	−	986359.i	−1.14437	−	0.0613372i
$764$		−	1.04465e7i		−	0.647495i
$765$		0			0
$766$	−1.58120e7	−	9.12908e6i	−0.973679	−	0.562154i
$767$	1.82990e7	+	1.05649e7i	1.12315	+	0.648453i
$768$		0			0
$769$		−	2.69450e7i		−	1.64309i	−0.570141	−	0.821547i	$-0.693111\pi$
$769$		−	2.69450e7i		−	1.64309i	0.570141	−	0.821547i	$-0.306889\pi$
$770$	−1.26717e7	+	1.94621e7i	−0.770208	+	1.18294i
$771$		0			0
$772$	−3.06242e6	−	5.30428e6i	−0.184936	−	0.320319i
$773$	−8.34621e6	+	1.44561e7i	−0.502390	+	0.870165i	0.497606	+	0.867403i	$0.334212\pi$
$773$	−8.34621e6	+	1.44561e7i	−0.502390	+	0.870165i	−0.999996	+	0.00276163i	$0.999121\pi$
$774$		0			0
$775$	863192.	−	498364.i	0.0516241	−	0.0298052i
$776$	−2.61442e6			−0.155855
$777$		0			0
$778$	−1.71092e7			−1.01340
$779$	−1.62538e6	+	938414.i	−0.0959646	+	0.0554052i
$780$		0			0
$781$	5.89918e6	−	1.02177e7i	0.346070	−	0.599411i
$782$	320438.	+	555015.i	0.0187382	+	0.0324554i
$783$		0			0
$784$	−1.87687e7	−	2.01777e6i	−1.09055	−	0.117242i
$785$			4.63993e6i			0.268743i
$786$		0			0
$787$	2.26325e7	+	1.30669e7i	1.30255	+	0.752028i	0.980841	−	0.194810i	$-0.0624090\pi$
$787$	2.26325e7	+	1.30669e7i	1.30255	+	0.752028i	0.321710	+	0.946838i	$0.395742\pi$
$788$	4.81217e6	+	2.77831e6i	0.276074	+	0.159391i
$789$		0			0
$790$			5.42379e7i			3.09197i
$791$	4.93884e6	−	2.50908e6i	0.280662	−	0.142585i
$792$		0			0
$793$	6.68643e6	+	1.15812e7i	0.377582	+	0.653991i
$794$	−1.83736e7	+	3.18240e7i	−1.03429	+	1.79144i
$795$		0			0
$796$	1.37264e7	−	7.92493e6i	0.767845	−	0.443316i
$797$	−3.57013e6			−0.199085			−0.0995423	−	0.995033i	$-0.531738\pi$
$797$	−3.57013e6			−0.199085			−0.0995423	+	0.995033i	$0.531738\pi$
$798$		0			0
$799$	−2.08565e7			−1.15578
$800$	3.84925e7	−	2.22237e7i	2.12643	−	1.22770i
$801$		0			0
$802$	−1.66112e6	+	2.87714e6i	−0.0911937	+	0.157952i
$803$	−7.33775e6	−	1.27094e7i	−0.401582	−	0.695560i
$804$		0			0
$805$	−26359.1	+	491782.i	−0.00143364	+	0.0267475i
$806$		−	813507.i		−	0.0441086i
$807$		0			0
$808$	−453730.	−	261961.i	−0.0244494	−	0.0141159i
$809$	−1.54161e7	−	8.90052e6i	−0.828141	−	0.478128i	0.0250745	−	0.999686i	$-0.492018\pi$
$809$	−1.54161e7	−	8.90052e6i	−0.828141	−	0.478128i	−0.853216	+	0.521558i	$0.825351\pi$
$810$		0			0
$811$			3.44374e7i			1.83856i	0.393604	+	0.919280i	$0.371228\pi$
$811$			3.44374e7i			1.83856i	−0.393604	+	0.919280i	$0.628772\pi$
$812$	−1.16637e6	+	2.17610e7i	−0.0620793	+	1.15821i
$813$		0			0
$814$	−5.43057e6	−	9.40602e6i	−0.287266	−	0.497559i
$815$	7.53555e6	−	1.30520e7i	0.397394	−	0.688306i
$816$		0			0
$817$	−1.29231e7	+	7.46118e6i	−0.677350	+	0.391068i
$818$	−1.38000e6			−0.0721101
$819$		0			0
$820$	−6.16872e6			−0.320376
$821$	9.54659e6	−	5.51173e6i	0.494300	−	0.285384i	−0.232057	−	0.972702i	$-0.574545\pi$
$821$	9.54659e6	−	5.51173e6i	0.494300	−	0.285384i	0.726357	+	0.687318i	$0.241212\pi$
$822$		0			0
$823$	−1.13845e6	+	1.97185e6i	−0.0585886	+	0.101478i	−0.893832	−	0.448402i	$-0.851993\pi$
$823$	−1.13845e6	+	1.97185e6i	−0.0585886	+	0.101478i	0.835243	+	0.549880i	$0.185327\pi$
$824$	−1.34278e6	−	2.32576e6i	−0.0688949	−	0.119329i
$825$		0			0
$826$	3.20766e7	−	1.62959e7i	1.63583	−	0.831050i
$827$			8.44456e6i			0.429352i	0.976685	+	0.214676i	$0.0688695\pi$
$827$			8.44456e6i			0.429352i	−0.976685	+	0.214676i	$0.931130\pi$
$828$		0			0
$829$	3.63761e6	+	2.10018e6i	0.183836	+	0.106138i	0.589094	−	0.808065i	$-0.299485\pi$
$829$	3.63761e6	+	2.10018e6i	0.183836	+	0.106138i	−0.405258	+	0.914202i	$0.632818\pi$
$830$	−5.54494e7	−	3.20137e7i	−2.79384	−	1.61302i
$831$		0			0
$832$		−	1.49882e7i		−	0.750656i
$833$	−1.38090e7	−	3.12149e7i	−0.689524	−	1.55865i
$834$		0			0
$835$	−7.07220e6	−	1.22494e7i	−0.351025	−	0.607994i
$836$	−2.84995e6	+	4.93627e6i	−0.141033	+	0.244277i
$837$		0			0
$838$	1.94310e7	−	1.12185e7i	0.955839	−	0.551854i
$839$	308450.			0.0151279			0.00756397	−	0.999971i	$-0.497592\pi$
$839$	308450.			0.0151279			0.00756397	+	0.999971i	$0.497592\pi$
$840$		0			0
$841$	−1.42184e7			−0.693203
$842$	−5.25016e6	+	3.03118e6i	−0.255207	+	0.147344i
$843$		0			0
$844$	−3.37585e6	+	5.84714e6i	−0.163127	+	0.282545i
$845$	−957312.	−	1.65811e6i	−0.0461224	−	0.0798863i
$846$		0			0
$847$	7.11617e6	−	1.09295e7i	0.340830	−	0.523470i
$848$			4.42321e7i			2.11226i
$849$		0			0
$850$	7.72531e7	+	4.46021e7i	3.66749	+	2.11742i
$851$	−199466.	−	115162.i	−0.00944158	−	0.00545110i
$852$		0			0
$853$			5.93710e6i			0.279384i	0.990195	+	0.139692i	$0.0446113\pi$
$853$			5.93710e6i			0.279384i	−0.990195	+	0.139692i	$0.955389\pi$
$854$	2.27378e7	+	1.21873e6i	1.06685	+	0.0571824i
$855$		0			0
$856$	−111197.	−	192599.i	−0.00518692	−	0.00898400i
$857$	4.12425e6	−	7.14341e6i	0.191820	−	0.332241i	−0.754034	−	0.656836i	$-0.771894\pi$
$857$	4.12425e6	−	7.14341e6i	0.191820	−	0.332241i	0.945853	+	0.324594i	$0.105228\pi$
$858$		0			0
$859$	2.27857e7	−	1.31553e7i	1.05361	−	0.608300i	0.129950	−	0.991521i	$-0.458518\pi$
$859$	2.27857e7	−	1.31553e7i	1.05361	−	0.608300i	0.923657	+	0.383220i	$0.125185\pi$
$860$	−4.90465e7			−2.26132
$861$		0			0
$862$	6.70773e6			0.307473
$863$	−3.11798e7	+	1.80017e7i	−1.42510	+	0.822784i	−0.996729	−	0.0808178i	$-0.974247\pi$
$863$	−3.11798e7	+	1.80017e7i	−1.42510	+	0.822784i	−0.428374	+	0.903601i	$0.640913\pi$
$864$		0			0
$865$	−4.53097e6	+	7.84786e6i	−0.205897	+	0.356625i
$866$	−1.12852e7	−	1.95465e7i	−0.511346	−	0.885677i
$867$		0			0
$868$	−547074.	−	356199.i	−0.0246460	−	0.0160470i
$869$			1.83028e7i			0.822181i
$870$		0			0
$871$	−5.87586e6	−	3.39243e6i	−0.262438	−	0.151518i
$872$	3.32933e6	+	1.92219e6i	0.148274	+	0.0856062i
$873$		0			0
$874$			256478.i			0.0113572i
$875$	1.38634e7	+	2.72885e7i	0.612137	+	1.20492i
$876$		0			0
$877$	2.03213e7	+	3.51975e7i	0.892179	+	1.54530i	0.837258	+	0.546808i	$0.184157\pi$
$877$	2.03213e7	+	3.51975e7i	0.892179	+	1.54530i	0.0549211	+	0.998491i	$0.482509\pi$
$878$	3.98199e6	−	6.89701e6i	0.174327	−	0.301943i
$879$		0			0
$880$	2.23973e7	−	1.29311e7i	0.974964	−	0.562896i
$881$	1.74116e7			0.755787			0.377894	−	0.925849i	$-0.376649\pi$
$881$	1.74116e7			0.755787			0.377894	+	0.925849i	$0.376649\pi$
$882$		0			0
$883$	2.31051e7			0.997255			0.498628	−	0.866816i	$-0.333838\pi$
$883$	2.31051e7			0.997255			0.498628	+	0.866816i	$0.333838\pi$
$884$	2.97154e7	−	1.71562e7i	1.27894	−	0.738398i
$885$		0			0
$886$	−1.46217e7	+	2.53256e7i	−0.625770	+	1.08386i
$887$	−1.32420e7	−	2.29359e7i	−0.565126	−	0.978828i	−0.997038	−	0.0769117i	$-0.975494\pi$
$887$	−1.32420e7	−	2.29359e7i	−0.565126	−	0.978828i	0.431911	−	0.901916i	$-0.357839\pi$
$888$		0			0
$889$	−1.80870e7	−	3.56022e7i	−0.767560	−	1.51086i
$890$			2.42285e7i			1.02530i
$891$		0			0
$892$	−2.86532e7	−	1.65429e7i	−1.20576	−	0.696147i
$893$	−7.22850e6	−	4.17338e6i	−0.303333	−	0.175129i
$894$		0			0
$895$		−	6.02314e6i		−	0.251342i
$896$	5.98181e6	+	3.89474e6i	0.248922	+	0.162072i
$897$		0			0
$898$	2.88327e6	+	4.99398e6i	0.119315	+	0.206660i
$899$	520185.	−	900986.i	0.0214664	−	0.0371808i
$900$		0			0
$901$	−6.92648e7	+	3.99900e7i	−2.84250	+	1.64112i
$902$	−4.41701e6			−0.180764
$903$		0			0
$904$	−1.15560e6			−0.0470313
$905$	3.77762e7	−	2.18101e7i	1.53319	−	0.885190i
$906$		0			0
$907$	−1.08942e7	+	1.88692e7i	−0.439719	+	0.761616i	−0.997668	−	0.0682597i	$-0.978255\pi$
$907$	−1.08942e7	+	1.88692e7i	−0.439719	+	0.761616i	0.557948	+	0.829876i	$0.311589\pi$
$908$	−1.85342e7	−	3.21022e7i	−0.746035	−	1.29217i
$909$		0			0
$910$	5.58688e7	+	2.99452e6i	2.23648	+	0.119874i
$911$			560911.i			0.0223923i	0.999937	+	0.0111961i	$0.00356391\pi$
$911$			560911.i			0.0223923i	−0.999937	+	0.0111961i	$0.996436\pi$
$912$		0			0
$913$	−1.87116e7	−	1.08031e7i	−0.742906	−	0.428917i
$914$	1.61455e7	+	9.32159e6i	0.639271	+	0.369083i
$915$		0			0
$916$			377286.i			0.0148570i
$917$	−1.10032e7	+	1.68995e7i	−0.432111	+	0.663666i
$918$		0			0
$919$	7.84712e6	+	1.35916e7i	0.306494	+	0.530863i	0.977593	−	0.210505i	$-0.0675109\pi$
$919$	7.84712e6	+	1.35916e7i	0.306494	+	0.530863i	−0.671099	+	0.741368i	$0.734178\pi$
$920$	51368.0	−	88972.0i	0.00200089	−	0.00346564i
$921$		0			0
$922$	−4.00182e7	+	2.31045e7i	−1.55035	+	0.895095i
$923$	−2.84237e7			−1.09819
$924$		0			0
$925$	−3.20590e7			−1.23196
$926$	−1.39404e7	+	8.04850e6i	−0.534254	+	0.308452i
$927$		0			0
$928$	2.31967e7	−	4.01779e7i	0.884213	−	1.53150i
$929$	8.68727e6	+	1.50468e7i	0.330251	+	0.572012i	0.982561	−	0.185941i	$-0.0595333\pi$
$929$	8.68727e6	+	1.50468e7i	0.330251	+	0.572012i	−0.652310	+	0.757952i	$0.726200\pi$
$930$		0			0
$931$	1.46013e6	−	1.35817e7i	0.0552101	−	0.513548i
$932$			2.80797e7i			1.05889i
$933$		0			0
$934$	2.98066e7	+	1.72089e7i	1.11801	+	0.645483i
$935$	4.04985e7	+	2.33818e7i	1.51499	+	0.874681i
$936$		0			0
$937$		−	276622.i		−	0.0102929i	−0.999987	−	0.00514646i	$-0.998362\pi$
$937$		−	276622.i		−	0.0102929i	0.999987	−	0.00514646i	$-0.00163818\pi$
$938$	−1.02999e7	+	5.23265e6i	−0.382230	+	0.194184i
$939$		0			0
$940$	−1.37170e7	−	2.37585e7i	−0.506336	−	0.876999i
$941$	−1.43311e7	+	2.48222e7i	−0.527601	+	0.913831i	0.471882	+	0.881662i	$0.343575\pi$
$941$	−1.43311e7	+	2.48222e7i	−0.527601	+	0.913831i	−0.999482	+	0.0321695i	$0.989758\pi$
$942$		0			0
$943$	−81118.9	+	46834.0i	−0.00297059	+	0.00171507i
$944$	−4.00661e7			−1.46334
$945$		0			0
$946$	−3.51189e7			−1.27589
$947$	2.43615e7	−	1.40651e7i	0.882733	−	0.509646i	0.0111747	−	0.999938i	$-0.496443\pi$
$947$	2.43615e7	−	1.40651e7i	0.882733	−	0.509646i	0.871559	+	0.490291i	$0.163110\pi$
$948$		0			0
$949$	−1.76776e7	+	3.06184e7i	−0.637172	+	1.10361i
$950$	1.78497e7	+	3.09166e7i	0.641686	+	1.11143i
$951$		0			0
$952$	−381097.	+	7.11013e6i	−0.0136284	+	0.254264i
$953$		−	4.83932e7i		−	1.72604i	−0.505166	−	0.863022i	$-0.668569\pi$
$953$		−	4.83932e7i		−	1.72604i	0.505166	−	0.863022i	$-0.331431\pi$
$954$		0			0
$955$	−2.97042e7	−	1.71497e7i	−1.05392	−	0.608483i
$956$	−2.08781e6	−	1.20540e6i	−0.0738834	−	0.0426566i
$957$		0			0
$958$		−	4.33332e7i		−	1.52548i
$959$	488061.	−	9.10574e6i	0.0171367	−	0.319719i
$960$		0			0
$961$	−1.42990e7	−	2.47666e7i	−0.499456	−	0.865083i
$962$	−1.30829e7	+	2.26603e7i	−0.455792	+	0.789455i
$963$		0			0
$964$	2.66819e6	−	1.54048e6i	0.0924748	−	0.0533904i
$965$	−2.01100e7			−0.695175
$966$		0			0
$967$	1.31731e7			0.453023			0.226512	−	0.974008i	$-0.427268\pi$
$967$	1.31731e7			0.453023			0.226512	+	0.974008i	$0.427268\pi$
$968$	−2.35614e6	+	1.36032e6i	−0.0808189	+	0.0466608i
$969$		0			0
$970$	3.52177e7	−	6.09988e7i	1.20180	−	2.08157i
$971$	−1.74045e7	−	3.01455e7i	−0.592397	−	1.02606i	−0.993909	−	0.110208i	$-0.964848\pi$
$971$	−1.74045e7	−	3.01455e7i	−0.592397	−	1.02606i	0.401511	−	0.915854i	$-0.368485\pi$
$972$		0			0
$973$	−7.34969e6	+	3.73386e6i	−0.248878	+	0.126438i
$974$		−	2.76162e7i		−	0.932753i
$975$		0			0
$976$	−2.19601e7	−	1.26787e7i	−0.737921	−	0.426039i
$977$	3.91689e7	+	2.26142e7i	1.31282	+	0.757956i	0.982562	−	0.185935i	$-0.0595315\pi$
$977$	3.91689e7	+	2.26142e7i	1.31282	+	0.757956i	0.330256	+	0.943891i	$0.392865\pi$
$978$		0			0
$979$			8.17601e6i			0.272637i
$980$	2.64762e7	−	3.62599e7i	0.880625	−	1.20604i
$981$		0			0
$982$	−9.15783e6	−	1.58618e7i	−0.303050	−	0.524897i
$983$	2.18408e7	−	3.78293e7i	0.720915	−	1.24866i	−0.239718	−	0.970842i	$-0.577055\pi$
$983$	2.18408e7	−	3.78293e7i	0.720915	−	1.24866i	0.960633	−	0.277819i	$-0.0896116\pi$
$984$		0			0
$985$	1.58000e7	−	9.12216e6i	0.518881	−	0.299576i
$986$	9.31100e7			3.05003
$987$		0			0
$988$	1.37318e7			0.447543
$989$	−644963.	+	372370.i	−0.0209674	+	0.0121055i
$990$		0			0
$991$	−2.58972e6	+	4.48552e6i	−0.0837661	+	0.145087i	−0.904865	−	0.425699i	$-0.860028\pi$
$991$	−2.58972e6	+	4.48552e6i	−0.0837661	+	0.145087i	0.821099	+	0.570786i	$0.193362\pi$
$992$	694889.	+	1.20358e6i	0.0224200	+	0.0388326i
$993$		0			0
$994$	−2.64077e7	+	4.05587e7i	−0.847744	+	1.30202i
$995$		−	5.20406e7i		−	1.66642i
$996$		0			0
$997$	3.66534e7	+	2.11619e7i	1.16782	+	0.674242i	0.953166	−	0.302447i	$-0.0978037\pi$
$997$	3.66534e7	+	2.11619e7i	1.16782	+	0.674242i	0.214656	+	0.976690i	$0.431137\pi$
$998$	5.24219e6	+	3.02658e6i	0.166605	+	0.0961892i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.6.p.b.17.3	✓	24
3.2	odd	2	inner	63.6.p.b.17.10	yes	24
7.3	odd	6		441.6.c.b.440.1		24
7.4	even	3		441.6.c.b.440.23		24
7.5	odd	6	inner	63.6.p.b.26.10	yes	24
21.5	even	6	inner	63.6.p.b.26.3	yes	24
21.11	odd	6		441.6.c.b.440.2		24
21.17	even	6		441.6.c.b.440.24		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.6.p.b.17.3	✓	24	1.1	even	1	trivial
63.6.p.b.17.10	yes	24	3.2	odd	2	inner
63.6.p.b.26.3	yes	24	21.5	even	6	inner
63.6.p.b.26.10	yes	24	7.5	odd	6	inner
441.6.c.b.440.1		24	7.3	odd	6
441.6.c.b.440.2		24	21.11	odd	6
441.6.c.b.440.23		24	7.4	even	3
441.6.c.b.440.24		24	21.17	even	6

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:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	63.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-6.73742 + 3.88985i) q^{2} +(14.2619 - 24.7023i) q^{4} +(-46.8267 - 81.1063i) q^{5} +(58.7189 + 115.582i) q^{7} -27.0441i q^{8} +O(q^{10})\)	\(q+(-6.73742 + 3.88985i) q^{2} +(14.2619 - 24.7023i) q^{4} +(-46.8267 - 81.1063i) q^{5} +(58.7189 + 115.582i) q^{7} -27.0441i q^{8} +(630.983 + 364.298i) q^{10} +(212.927 + 122.934i) q^{11} -592.325i q^{13} +(-845.209 - 550.314i) q^{14} +(561.578 + 972.681i) q^{16} +(-1015.44 + 1758.79i) q^{17} +(-703.867 + 406.378i) q^{19} -2671.35 q^{20} -1912.78 q^{22} +(-35.1283 + 20.2814i) q^{23} +(-2822.98 + 4889.55i) q^{25} +(2304.06 + 3990.74i) q^{26} +(3692.57 + 197.919i) q^{28} +5893.18i q^{29} +(-152.886 - 88.2690i) q^{31} +(-6817.70 - 3936.20i) q^{32} -15799.6i q^{34} +(6624.78 - 10174.8i) q^{35} +(2839.10 + 4917.47i) q^{37} +(3161.50 - 5475.88i) q^{38} +(-2193.44 + 1266.38i) q^{40} +2309.21 q^{41} +18360.2 q^{43} +(6073.49 - 3506.53i) q^{44} +(157.783 - 273.288i) q^{46} +(5134.85 + 8893.82i) q^{47} +(-9911.19 + 13573.6i) q^{49} -43924.0i q^{50} +(-14631.8 - 8447.67i) q^{52} +(34105.8 + 19691.0i) q^{53} -23026.3i q^{55} +(3125.79 - 1588.00i) q^{56} +(-22923.6 - 39704.8i) q^{58} +(-17836.4 + 30893.5i) q^{59} +(-19552.1 + 11288.4i) q^{61} +1373.41 q^{62} +25304.0 q^{64} +(-48041.3 + 27736.7i) q^{65} +(5727.31 - 9919.99i) q^{67} +(28964.1 + 50167.4i) q^{68} +(-5055.54 + 94321.1i) q^{70} -47986.7i q^{71} +(-51691.9 - 29844.4i) q^{73} +(-38256.5 - 22087.4i) q^{74} +23182.9i q^{76} +(-1706.01 + 31829.0i) q^{77} +(37220.8 + 64468.4i) q^{79} +(52593.7 - 91094.9i) q^{80} +(-15558.1 + 8982.50i) q^{82} -87877.8 q^{83} +190199. q^{85} +(-123700. + 71418.4i) q^{86} +(3324.63 - 5758.42i) q^{88} +(16626.9 + 28798.6i) q^{89} +(68461.9 - 34780.7i) q^{91} +1157.00i q^{92} +(-69191.2 - 39947.6i) q^{94} +(65919.6 + 38058.7i) q^{95} -96672.7i q^{97} +(13976.4 - 130004. i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 304 q^{4} - 436 q^{7}+O(q^{10}) \) 24 * q + 304 * q^4 - 436 * q^7	\( 24 q + 304 q^{4} - 436 q^{7} + 1992 q^{10} - 3644 q^{16} + 3804 q^{19} - 5648 q^{22} - 18852 q^{25} - 39172 q^{28} + 38652 q^{31} + 20548 q^{37} + 132060 q^{40} + 2200 q^{43} - 25712 q^{46} - 125676 q^{49} - 2940 q^{52} + 154300 q^{58} + 48504 q^{61} - 327880 q^{64} + 156324 q^{67} - 9468 q^{70} - 703236 q^{73} + 165756 q^{79} + 1081020 q^{82} - 284448 q^{85} + 582308 q^{88} - 19812 q^{91} - 1481724 q^{94}+O(q^{100}) \) 24 * q + 304 * q^4 - 436 * q^7 + 1992 * q^10 - 3644 * q^16 + 3804 * q^19 - 5648 * q^22 - 18852 * q^25 - 39172 * q^28 + 38652 * q^31 + 20548 * q^37 + 132060 * q^40 + 2200 * q^43 - 25712 * q^46 - 125676 * q^49 - 2940 * q^52 + 154300 * q^58 + 48504 * q^61 - 327880 * q^64 + 156324 * q^67 - 9468 * q^70 - 703236 * q^73 + 165756 * q^79 + 1081020 * q^82 - 284448 * q^85 + 582308 * q^88 - 19812 * q^91 - 1481724 * q^94

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