LMFDB - Embedded newform 63.4.p.a.26.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,4,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, 4, names="a")

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

chi := DirichletCharacter("63.17");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
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:	$3.71712033036$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 48 x^{14} + 1647 x^{12} - 27620 x^{10} + 336765 x^{8} - 1200006 x^{6} + 3242464 x^{4} + \cdots + 810000 $ x^16 - 48x^14 + 1647x^12 - 27620x^10 + 336765x^8 - 1200006x^6 + 3242464x^4 - 1762200*x^2 + 810000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			26.8
Root			$4.21355 + 2.43270i$ of defining polynomial
Character	$\chi$	$=$	63.26
Dual form			63.4.p.a.17.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.21355 + 2.43270i) q^{2} +(7.83601 + 13.5724i) q^{4} +(-6.38217 + 11.0542i) q^{5} +(2.53897 - 18.3454i) q^{7} +37.3274i q^{8} +O(q^{10})$	\(q+(4.21355 + 2.43270i) q^{2} +(7.83601 + 13.5724i) q^{4} +(-6.38217 + 11.0542i) q^{5} +(2.53897 - 18.3454i) q^{7} +37.3274i q^{8} +(-53.7832 + 31.0517i) q^{10} +(46.8633 - 27.0565i) q^{11} -8.85528i q^{13} +(55.3268 - 71.1228i) q^{14} +(-28.1181 + 48.7020i) q^{16} +(34.4587 + 59.6841i) q^{17} +(-141.898 - 81.9246i) q^{19} -200.043 q^{20} +263.281 q^{22} +(-81.3807 - 46.9852i) q^{23} +(-18.9642 - 32.8469i) q^{25} +(21.5422 - 37.3122i) q^{26} +(268.886 - 109.295i) q^{28} +119.620i q^{29} +(85.6311 - 49.4391i) q^{31} +(21.6577 - 12.5041i) q^{32} +335.310i q^{34} +(186.590 + 145.150i) q^{35} +(-47.0949 + 81.5708i) q^{37} +(-398.595 - 690.387i) q^{38} +(-412.626 - 238.230i) q^{40} -259.347 q^{41} +5.01418 q^{43} +(734.443 + 424.031i) q^{44} +(-228.601 - 395.949i) q^{46} +(-28.6747 + 49.6660i) q^{47} +(-330.107 - 93.1568i) q^{49} -184.536i q^{50} +(120.187 - 69.3901i) q^{52} +(-407.058 + 235.015i) q^{53} +690.718i q^{55} +(684.786 + 94.7731i) q^{56} +(-290.999 + 504.025i) q^{58} +(112.979 + 195.685i) q^{59} +(370.650 + 213.995i) q^{61} +481.082 q^{62} +571.564 q^{64} +(97.8884 + 56.5159i) q^{65} +(-81.9267 - 141.901i) q^{67} +(-540.037 + 935.372i) q^{68} +(433.103 + 1065.51i) q^{70} +79.8529i q^{71} +(666.447 - 384.774i) q^{73} +(-396.874 + 229.135i) q^{74} -2567.85i q^{76} +(-377.379 - 928.422i) q^{77} +(-267.408 + 463.165i) q^{79} +(-358.909 - 621.648i) q^{80} +(-1092.77 - 630.912i) q^{82} -438.520 q^{83} -879.684 q^{85} +(21.1275 + 12.1980i) q^{86} +(1009.95 + 1749.29i) q^{88} +(-12.8242 + 22.2121i) q^{89} +(-162.454 - 22.4833i) q^{91} -1472.71i q^{92} +(-241.644 + 139.513i) q^{94} +(1811.23 - 1045.71i) q^{95} -1381.00i q^{97} +(-1164.30 - 1195.57i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 32 q^{4} + 56 q^{7}+O(q^{10}) $ 16 * q + 32 * q^4 + 56 * q^7	$ 16 q + 32 q^{4} + 56 q^{7} - 72 q^{10} - 188 q^{16} - 612 q^{19} + 528 q^{22} - 20 q^{25} + 1036 q^{28} + 1128 q^{31} - 1196 q^{37} - 3204 q^{40} + 328 q^{43} - 1392 q^{46} + 784 q^{49} + 4452 q^{52} - 3372 q^{58} - 1632 q^{61} + 5432 q^{64} + 308 q^{67} + 3612 q^{70} + 4068 q^{73} - 2176 q^{79} - 10188 q^{82} - 4608 q^{85} + 708 q^{88} + 924 q^{91} - 2916 q^{94}+O(q^{100}) $ 16 * q + 32 * q^4 + 56 * q^7 - 72 * q^10 - 188 * q^16 - 612 * q^19 + 528 * q^22 - 20 * q^25 + 1036 * q^28 + 1128 * q^31 - 1196 * q^37 - 3204 * q^40 + 328 * q^43 - 1392 * q^46 + 784 * q^49 + 4452 * q^52 - 3372 * q^58 - 1632 * q^61 + 5432 * q^64 + 308 * q^67 + 3612 * q^70 + 4068 * q^73 - 2176 * q^79 - 10188 * q^82 - 4608 * q^85 + 708 * q^88 + 924 * q^91 - 2916 * q^94

Display 100 coefficients 10 coefficients

Character values

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

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	4.21355	+	2.43270i	1.48972	+	0.860088i	0.999931	−	0.0117558i	$-0.00374206\pi$
$2$	4.21355	+	2.43270i	1.48972	+	0.860088i	0.489785	+	0.871843i	$0.337075\pi$
$3$		0			0
$3$		0			0
$4$	7.83601	+	13.5724i	0.979502	+	1.69655i
$5$	−6.38217	+	11.0542i	−0.570839	+	0.988721i	0.425642	+	0.904892i	$0.360048\pi$
$5$	−6.38217	+	11.0542i	−0.570839	+	0.988721i	−0.996480	+	0.0838295i	$0.973285\pi$
$6$		0			0
$7$	2.53897	−	18.3454i	0.137091	−	0.990558i
$7$	2.53897	−	18.3454i	0.137091	−	0.990558i
$8$			37.3274i			1.64965i
$9$		0			0
$10$	−53.7832	+	31.0517i	−1.70077	+	0.981942i
$11$	46.8633	−	27.0565i	1.28453	−	0.741623i	0.306856	−	0.951756i	$-0.400723\pi$
$11$	46.8633	−	27.0565i	1.28453	−	0.741623i	0.977673	+	0.210133i	$0.0673897\pi$
$12$		0			0
$13$		−	8.85528i		−	0.188924i	−0.995528	−	0.0944620i	$-0.969887\pi$
$13$		−	8.85528i		−	0.188924i	0.995528	−	0.0944620i	$-0.0301131\pi$
$14$	55.3268	−	71.1228i	1.05619	−	1.35774i
$15$		0			0
$16$	−28.1181	+	48.7020i	−0.439345	+	0.760968i
$17$	34.4587	+	59.6841i	0.491615	+	0.851502i	0.999953	−	0.00965543i	$-0.00307347\pi$
$17$	34.4587	+	59.6841i	0.491615	+	0.851502i	−0.508339	+	0.861157i	$0.669740\pi$
$18$		0			0
$19$	−141.898	−	81.9246i	−1.71334	−	0.989199i	−0.929960	−	0.367660i	$-0.880159\pi$
$19$	−141.898	−	81.9246i	−1.71334	−	0.989199i	−0.783383	−	0.621540i	$-0.786508\pi$
$20$	−200.043			−2.23655
$21$		0			0
$22$	263.281			2.55144
$23$	−81.3807	−	46.9852i	−0.737785	−	0.425960i	0.0834783	−	0.996510i	$-0.473397\pi$
$23$	−81.3807	−	46.9852i	−0.737785	−	0.425960i	−0.821263	+	0.570549i	$0.806730\pi$
$24$		0			0
$25$	−18.9642	−	32.8469i	−0.151713	−	0.262775i
$26$	21.5422	−	37.3122i	0.162491	−	0.281443i
$27$		0			0
$28$	268.886	−	109.295i	1.81481	−	0.737672i
$29$			119.620i			0.765961i	0.923756	+	0.382981i	$0.125102\pi$
$29$			119.620i			0.765961i	−0.923756	+	0.382981i	$0.874898\pi$
$30$		0			0
$31$	85.6311	−	49.4391i	0.496123	−	0.286437i	−0.230988	−	0.972957i	$-0.574196\pi$
$31$	85.6311	−	49.4391i	0.496123	−	0.286437i	0.727111	+	0.686520i	$0.240863\pi$
$32$	21.6577	−	12.5041i	0.119643	−	0.0690760i
$33$		0			0
$34$			335.310i			1.69133i
$35$	186.590	+	145.150i	0.901129	+	0.700994i
$36$		0			0
$37$	−47.0949	+	81.5708i	−0.209253	+	0.362437i	−0.951479	−	0.307712i	$-0.900437\pi$
$37$	−47.0949	+	81.5708i	−0.209253	+	0.362437i	0.742227	+	0.670149i	$0.233770\pi$
$38$	−398.595	−	690.387i	−1.70160	−	2.94725i
$39$		0			0
$40$	−412.626	−	238.230i	−1.63105	−	0.941686i
$41$	−259.347			−0.987883			−0.493941	−	0.869495i	$-0.664444\pi$
$41$	−259.347			−0.987883			−0.493941	+	0.869495i	$0.664444\pi$
$42$		0			0
$43$	5.01418			0.0177827			0.00889133	−	0.999960i	$-0.497170\pi$
$43$	5.01418			0.0177827			0.00889133	+	0.999960i	$0.497170\pi$
$44$	734.443	+	424.031i	2.51640	+	1.45284i
$45$		0			0
$46$	−228.601	−	395.949i	−0.732727	−	1.26912i
$47$	−28.6747	+	49.6660i	−0.0889921	+	0.154139i	−0.907085	−	0.420947i	$-0.861698\pi$
$47$	−28.6747	+	49.6660i	−0.0889921	+	0.154139i	0.818093	+	0.575086i	$0.195031\pi$
$48$		0			0
$49$	−330.107	−	93.1568i	−0.962412	−	0.271594i
$50$		−	184.536i		−	0.521947i
$51$		0			0
$52$	120.187	−	69.3901i	0.320518	−	0.185051i
$53$	−407.058	+	235.015i	−1.05497	+	0.609090i	−0.924038	−	0.382301i	$-0.875132\pi$
$53$	−407.058	+	235.015i	−1.05497	+	0.609090i	−0.130937	+	0.991391i	$0.541798\pi$
$54$		0			0
$55$			690.718i			1.69339i
$56$	684.786	+	94.7731i	1.63408	+	0.226153i
$57$		0			0
$58$	−290.999	+	504.025i	−0.658794	+	1.14106i
$59$	112.979	+	195.685i	0.249299	+	0.431798i	0.963331	−	0.268314i	$-0.0864666\pi$
$59$	112.979	+	195.685i	0.249299	+	0.431798i	−0.714033	+	0.700112i	$0.753133\pi$
$60$		0			0
$61$	370.650	+	213.995i	0.777982	+	0.449168i	0.835715	−	0.549164i	$-0.185054\pi$
$61$	370.650	+	213.995i	0.777982	+	0.449168i	−0.0577325	+	0.998332i	$0.518387\pi$
$62$	481.082			0.985442
$63$		0			0
$64$	571.564			1.11634
$65$	97.8884	+	56.5159i	0.186793	+	0.107845i
$66$		0			0
$67$	−81.9267	−	141.901i	−0.149387	−	0.258746i	0.781614	−	0.623762i	$-0.214397\pi$
$67$	−81.9267	−	141.901i	−0.149387	−	0.258746i	−0.931001	+	0.365016i	$0.881063\pi$
$68$	−540.037	+	935.372i	−0.963075	+	1.66809i
$69$		0			0
$70$	433.103	+	1065.51i	0.739510	+	1.81933i
$71$			79.8529i			0.133476i	0.997771	+	0.0667380i	$0.0212592\pi$
$71$			79.8529i			0.133476i	−0.997771	+	0.0667380i	$0.978741\pi$
$72$		0			0
$73$	666.447	−	384.774i	1.06852	−	0.616909i	0.140741	−	0.990046i	$-0.455051\pi$
$73$	666.447	−	384.774i	1.06852	−	0.616909i	0.927776	+	0.373138i	$0.121718\pi$
$74$	−396.874	+	229.135i	−0.623454	+	0.359952i
$75$		0			0
$76$		−	2567.85i		−	3.87569i
$77$	−377.379	−	928.422i	−0.558523	−	1.37407i
$78$		0			0
$79$	−267.408	+	463.165i	−0.380833	+	0.659622i	−0.991182	−	0.132511i	$-0.957696\pi$
$79$	−267.408	+	463.165i	−0.380833	+	0.659622i	0.610349	+	0.792133i	$0.291029\pi$
$80$	−358.909	−	621.648i	−0.501590	−	0.868780i
$81$		0			0
$82$	−1092.77	−	630.912i	−1.47166	−	0.849666i
$83$	−438.520			−0.579926			−0.289963	−	0.957038i	$-0.593643\pi$
$83$	−438.520			−0.579926			−0.289963	+	0.957038i	$0.593643\pi$
$84$		0			0
$85$	−879.684			−1.12253
$86$	21.1275	+	12.1980i	0.0264911	+	0.0152947i
$87$		0			0
$88$	1009.95	+	1749.29i	1.22342	+	2.11903i
$89$	−12.8242	+	22.2121i	−0.0152737	+	0.0264548i	−0.873561	−	0.486714i	$-0.838195\pi$
$89$	−12.8242	+	22.2121i	−0.0152737	+	0.0264548i	0.858288	+	0.513169i	$0.171529\pi$
$90$		0			0
$91$	−162.454	−	22.4833i	−0.187140	−	0.0258999i
$92$		−	1472.71i		−	1.66892i
$93$		0			0
$94$	−241.644	+	139.513i	−0.265146	+	0.153082i
$95$	1811.23	−	1045.71i	1.95608	−	1.12935i
$96$		0			0
$97$		−	1381.00i		−	1.44555i	−0.691081	−	0.722777i	$-0.742865\pi$
$97$		−	1381.00i		−	1.44555i	0.691081	−	0.722777i	$-0.257135\pi$
$98$	−1164.30	−	1195.57i	−1.20013	−	1.23236i
$99$		0			0
$100$	297.207	−	514.777i	0.297207	−	0.514777i
$101$	356.808	+	618.009i	0.351522	+	0.608854i	0.986516	−	0.163663i	$-0.0523309\pi$
$101$	356.808	+	618.009i	0.351522	+	0.608854i	−0.634994	+	0.772517i	$0.718998\pi$
$102$		0			0
$103$	1552.42	+	896.288i	1.48509	+	0.857416i	0.999856	−	0.0169695i	$-0.00540182\pi$
$103$	1552.42	+	896.288i	1.48509	+	0.857416i	0.485232	+	0.874385i	$0.338735\pi$
$104$	330.544			0.311659
$105$		0			0
$106$	−2286.88			−2.09548
$107$	19.5366	+	11.2794i	0.0176511	+	0.0101909i	0.508800	−	0.860885i	$-0.330089\pi$
$107$	19.5366	+	11.2794i	0.0176511	+	0.0101909i	−0.491148	+	0.871076i	$0.663423\pi$
$108$		0			0
$109$	−476.210	−	824.820i	−0.418465	−	0.724802i	0.577320	−	0.816518i	$-0.304098\pi$
$109$	−476.210	−	824.820i	−0.418465	−	0.724802i	−0.995785	+	0.0917154i	$0.970765\pi$
$110$	−1680.31	+	2910.37i	−1.45646	+	2.52267i
$111$		0			0
$112$	822.066	+	639.490i	0.693553	+	0.539519i
$113$		−	120.145i		−	0.100020i	−0.998749	−	0.0500102i	$-0.984075\pi$
$113$		−	120.145i		−	0.100020i	0.998749	−	0.0500102i	$-0.0159254\pi$
$114$		0			0
$115$	1038.77	−	599.735i	0.842312	−	0.486309i
$116$	−1623.53	+	937.344i	−1.29949	+	0.750260i
$117$		0			0
$118$			1099.37i			0.857674i
$119$	1182.42	−	480.622i	0.910859	−	0.370240i
$120$		0			0
$121$	798.612	−	1383.24i	0.600009	−	1.03925i
$122$	1041.17	+	1803.36i	0.772648	+	1.33827i
$123$		0			0
$124$	1342.01	+	774.812i	0.971906	+	0.561130i
$125$	−1111.41			−0.795262
$126$		0			0
$127$	884.302			0.617867			0.308934	−	0.951084i	$-0.400028\pi$
$127$	884.302			0.617867			0.308934	+	0.951084i	$0.400028\pi$
$128$	2235.05	+	1290.41i	1.54338	+	0.891071i
$129$		0			0
$130$	274.972	+	476.265i	0.185512	+	0.321317i
$131$	803.439	−	1391.60i	0.535853	−	0.928125i	−0.463268	−	0.886218i	$-0.653323\pi$
$131$	803.439	−	1391.60i	0.535853	−	0.928125i	0.999122	−	0.0419070i	$-0.0133433\pi$
$132$		0			0
$133$	−1863.21	+	2395.16i	−1.21474	+	1.56156i
$134$		−	797.210i		−	0.513944i
$135$		0			0
$136$	−2227.85	+	1286.25i	−1.40468	+	0.810994i
$137$	615.297	−	355.242i	0.383711	−	0.221535i	−0.295721	−	0.955274i	$-0.595560\pi$
$137$	615.297	−	355.242i	0.383711	−	0.221535i	0.679431	+	0.733739i	$0.262227\pi$
$138$		0			0
$139$			1531.91i			0.934782i	0.884051	+	0.467391i	$0.154806\pi$
$139$			1531.91i			0.934782i	−0.884051	+	0.467391i	$0.845194\pi$
$140$	−507.903	+	3669.87i	−0.306612	+	2.21543i
$141$		0			0
$142$	−194.258	+	336.464i	−0.114801	+	0.198841i
$143$	−239.593	−	414.987i	−0.140110	−	0.242678i
$144$		0			0
$145$	−1322.31	−	763.435i	−0.757322	−	0.437240i
$146$	3744.15			2.12238
$147$		0			0
$148$	−1476.15			−0.819854
$149$	−2079.39	−	1200.54i	−1.14329	−	0.660079i	−0.196046	−	0.980595i	$-0.562810\pi$
$149$	−2079.39	−	1200.54i	−1.14329	−	0.660079i	−0.947243	+	0.320516i	$0.896144\pi$
$150$		0			0
$151$	−1233.99	−	2137.33i	−0.665035	−	1.15188i	−0.979276	−	0.202532i	$-0.935083\pi$
$151$	−1233.99	−	2137.33i	−0.665035	−	1.15188i	0.314240	−	0.949343i	$-0.398250\pi$
$152$	3058.03	−	5296.67i	1.63184	−	2.82642i
$153$		0			0
$154$	668.463	−	4830.00i	0.349781	−	2.52735i
$155$			1262.12i			0.654036i
$156$		0			0
$157$	2109.74	−	1218.06i	1.07246	−	0.619184i	0.143606	−	0.989635i	$-0.454130\pi$
$157$	2109.74	−	1218.06i	1.07246	−	0.619184i	0.928852	+	0.370451i	$0.120797\pi$
$158$	−2253.48	+	1301.05i	−1.13466	+	0.655099i
$159$		0			0
$160$			319.213i			0.157725i
$161$	−1068.59	+	1373.67i	−0.523083	+	0.672424i
$162$		0			0
$163$	−1638.50	+	2837.97i	−0.787347	+	1.36372i	0.140240	+	0.990118i	$0.455213\pi$
$163$	−1638.50	+	2837.97i	−0.787347	+	1.36372i	−0.927587	+	0.373607i	$0.878121\pi$
$164$	−2032.25	−	3519.95i	−0.967633	−	1.67599i
$165$		0			0
$166$	−1847.73	−	1066.79i	−0.863924	−	0.498787i
$167$	365.585			0.169400			0.0847000	−	0.996406i	$-0.473007\pi$
$167$	365.585			0.169400			0.0847000	+	0.996406i	$0.473007\pi$
$168$		0			0
$169$	2118.58			0.964308
$170$	−3706.59	−	2140.00i	−1.67225	−	0.965475i
$171$		0			0
$172$	39.2912	+	68.0543i	0.0174182	+	0.0301691i
$173$	−1046.47	+	1812.53i	−0.459892	+	0.796557i	−0.998955	−	0.0457089i	$-0.985445\pi$
$173$	−1046.47	+	1812.53i	−0.459892	+	0.796557i	0.539062	+	0.842266i	$0.318779\pi$
$174$		0			0
$175$	−650.739	+	264.508i	−0.281093	+	0.114257i
$176$			3043.11i			1.30331i
$177$		0			0
$178$	−108.071	+	62.3946i	−0.0455070	+	0.0262735i
$179$	1524.01	−	879.890i	0.636370	−	0.367408i	−0.146845	−	0.989160i	$-0.546912\pi$
$179$	1524.01	−	879.890i	0.636370	−	0.367408i	0.783215	+	0.621751i	$0.213578\pi$
$180$		0			0
$181$			3197.54i			1.31310i	0.754282	+	0.656551i	$0.227985\pi$
$181$			3197.54i			1.31310i	−0.754282	+	0.656551i	$0.772015\pi$
$182$	−629.812	−	489.934i	−0.256510	−	0.199540i
$183$		0			0
$184$	1753.84	−	3037.73i	0.702687	−	1.21709i
$185$	−601.135	−	1041.20i	−0.238899	−	0.413786i
$186$		0			0
$187$	3229.69	+	1864.66i	1.26299	+	0.729186i
$188$	−898.780			−0.348672
$189$		0			0
$190$	10175.6			3.88535
$191$	475.772	+	274.687i	0.180239	+	0.104061i	0.587405	−	0.809293i	$-0.300150\pi$
$191$	475.772	+	274.687i	0.180239	+	0.104061i	−0.407166	+	0.913354i	$0.633483\pi$
$192$		0			0
$193$	352.238	+	610.094i	0.131371	+	0.227542i	0.924205	−	0.381896i	$-0.124729\pi$
$193$	352.238	+	610.094i	0.131371	+	0.227542i	−0.792834	+	0.609437i	$0.791395\pi$
$194$	3359.54	−	5818.90i	1.24330	−	2.15347i
$195$		0			0
$196$	−1322.37	−	5210.32i	−0.481912	−	1.89880i
$197$			5317.81i			1.92324i	0.274384	+	0.961620i	$0.411526\pi$
$197$			5317.81i			1.92324i	−0.274384	+	0.961620i	$0.588474\pi$
$198$		0			0
$199$	−2155.80	+	1244.65i	−0.767942	+	0.443371i	−0.832140	−	0.554566i	$-0.812884\pi$
$199$	−2155.80	+	1244.65i	−0.767942	+	0.443371i	0.0641982	+	0.997937i	$0.479551\pi$
$200$	1226.09	−	707.883i	0.433488	−	0.250274i
$201$		0			0
$202$			3472.02i			1.20936i
$203$	2194.48	+	303.711i	0.758729	+	0.105007i
$204$		0			0
$205$	1655.20	−	2866.88i	0.563922	−	0.976741i
$206$	4360.79	+	7553.11i	1.47491	+	2.55461i
$207$		0			0
$208$	431.269	+	248.993i	0.143765	+	0.0830029i
$209$	−8866.38			−2.93445
$210$		0			0
$211$	−3454.31			−1.12704			−0.563519	−	0.826103i	$-0.690553\pi$
$211$	−3454.31			−1.12704			−0.563519	+	0.826103i	$0.690553\pi$
$212$	−6379.42	−	3683.16i	−2.06670	−	1.19321i
$213$		0			0
$214$	54.8789	+	95.0530i	0.0175301	+	0.0303630i
$215$	−32.0013	+	55.4279i	−0.0101510	+	0.0175821i
$216$		0			0
$217$	−689.566	−	1696.46i	−0.215718	−	0.530706i
$218$		−	4633.90i		−	1.43967i
$219$		0			0
$220$	−9374.68	+	5412.47i	−2.87291	+	1.65868i
$221$	528.520	−	305.141i	0.160869	−	0.0928778i
$222$		0			0
$223$		−	3896.38i		−	1.17005i	−0.811016	−	0.585024i	$-0.801085\pi$
$223$		−	3896.38i		−	1.17005i	0.811016	−	0.585024i	$-0.198915\pi$
$224$	−174.404	−	429.067i	−0.0520218	−	0.127983i
$225$		0			0
$226$	292.277	−	506.238i	0.0860263	−	0.149002i
$227$	302.747	+	524.374i	0.0885201	+	0.153321i	0.906886	−	0.421377i	$-0.138453\pi$
$227$	302.747	+	524.374i	0.0885201	+	0.153321i	−0.818366	+	0.574698i	$0.805120\pi$
$228$		0			0
$229$	−1912.98	−	1104.46i	−0.552023	−	0.318711i	0.197914	−	0.980219i	$-0.436583\pi$
$229$	−1912.98	−	1104.46i	−0.552023	−	0.318711i	−0.749938	+	0.661509i	$0.769917\pi$
$230$	5835.89			1.67307
$231$		0			0
$232$	−4465.10			−1.26357
$233$	2065.77	+	1192.67i	0.580829	+	0.335342i	0.761463	−	0.648209i	$-0.224482\pi$
$233$	2065.77	+	1192.67i	0.580829	+	0.335342i	−0.180634	+	0.983550i	$0.557815\pi$
$234$		0			0
$235$	−366.013	−	633.953i	−0.101600	−	0.175977i
$236$	−1770.61	+	3066.79i	−0.488377	+	0.845893i
$237$		0			0
$238$	6151.39	+	851.341i	1.67536	+	0.231866i
$239$			3017.95i			0.816798i	0.912803	+	0.408399i	$0.133913\pi$
$239$			3017.95i			0.816798i	−0.912803	+	0.408399i	$0.866087\pi$
$240$		0			0
$241$	−2178.48	+	1257.75i	−0.582275	+	0.336176i	−0.762037	−	0.647534i	$-0.775800\pi$
$241$	−2178.48	+	1257.75i	−0.582275	+	0.336176i	0.179762	+	0.983710i	$0.442467\pi$
$242$	6729.99	−	3885.56i	1.78769	−	1.03212i
$243$		0			0
$244$			6707.47i			1.75984i
$245$	3136.58	−	3054.54i	0.817913	−	0.796521i
$246$		0			0
$247$	−725.465	+	1256.54i	−0.186883	+	0.323692i
$248$	1845.44	+	3196.39i	0.472521	+	0.818431i
$249$		0			0
$250$	−4682.99	−	2703.73i	−1.18471	−	0.683995i
$251$	1306.11			0.328451			0.164226	−	0.986423i	$-0.447488\pi$
$251$	1306.11			0.328451			0.164226	+	0.986423i	$0.447488\pi$
$252$		0			0
$253$	−5085.03			−1.26361
$254$	3726.05	+	2151.24i	0.920447	+	0.531420i
$255$		0			0
$256$	3992.09	+	6914.50i	0.974630	+	1.68811i
$257$	3735.91	−	6470.79i	0.906770	−	1.57057i	0.0882460	−	0.996099i	$-0.471874\pi$
$257$	3735.91	−	6470.79i	0.906770	−	1.57057i	0.818524	−	0.574473i	$-0.194793\pi$
$258$		0			0
$259$	1376.88	+	1071.08i	0.330328	+	0.256964i
$260$			1771.44i			0.422538i
$261$		0			0
$262$	6770.66	−	3909.04i	1.59654	−	0.921762i
$263$	−1330.77	+	768.318i	−0.312010	+	0.180139i	−0.647825	−	0.761789i	$-0.724321\pi$
$263$	−1330.77	+	768.318i	−0.312010	+	0.180139i	0.335816	+	0.941928i	$0.390988\pi$
$264$		0			0
$265$		−	5999.62i		−	1.39077i
$266$	−13677.4	+	5559.51i	−3.15270	+	1.28149i
$267$		0			0
$268$	1283.96	−	2223.88i	0.292650	−	0.506884i
$269$	1958.09	+	3391.52i	0.443818	+	0.768715i	0.997969	−	0.0637010i	$-0.0202904\pi$
$269$	1958.09	+	3391.52i	0.443818	+	0.768715i	−0.554151	+	0.832416i	$0.686957\pi$
$270$		0			0
$271$	3117.42	+	1799.84i	0.698780	+	0.403441i	0.806893	−	0.590698i	$-0.201147\pi$
$271$	3117.42	+	1799.84i	0.698780	+	0.403441i	−0.108113	+	0.994139i	$0.534481\pi$
$272$	−3875.65			−0.863955
$273$		0			0
$274$	3456.78			0.762159
$275$	−1777.45	−	1026.21i	−0.389760	−	0.225028i
$276$		0			0
$277$	−142.040	−	246.021i	−0.0308100	−	0.0533645i	0.850209	−	0.526445i	$-0.176475\pi$
$277$	−142.040	−	246.021i	−0.0308100	−	0.0533645i	−0.881019	+	0.473080i	$0.843142\pi$
$278$	−3726.67	+	6454.77i	−0.803995	+	1.39256i
$279$		0			0
$280$	−5418.07	+	6964.93i	−1.15640	+	1.48655i
$281$		−	321.256i		−	0.0682011i	−0.999418	−	0.0341006i	$-0.989143\pi$
$281$		−	321.256i		−	0.0682011i	0.999418	−	0.0341006i	$-0.0108566\pi$
$282$		0			0
$283$	5891.40	−	3401.40i	1.23748	−	0.714460i	0.268903	−	0.963167i	$-0.413339\pi$
$283$	5891.40	−	3401.40i	1.23748	−	0.714460i	0.968579	+	0.248707i	$0.0800057\pi$
$284$	−1083.79	+	625.728i	−0.226448	+	0.130740i
$285$		0			0
$286$		−	2331.43i		−	0.482029i
$287$	−658.474	+	4757.82i	−0.135430	+	0.978556i
$288$		0			0
$289$	81.7017	−	141.511i	0.0166297	−	0.0288035i
$290$	−3714.41	−	6433.55i	−0.752130	−	1.30273i
$291$		0			0
$292$	10444.6	+	6030.18i	2.09323	+	1.20853i
$293$	3180.05			0.634063			0.317031	−	0.948415i	$-0.397314\pi$
$293$	3180.05			0.634063			0.317031	+	0.948415i	$0.397314\pi$
$294$		0			0
$295$	−2884.20			−0.569237
$296$	−3044.83	−	1757.93i	−0.597895	−	0.345195i
$297$		0			0
$298$	−5841.07	−	10117.0i	−1.13545	−	1.96666i
$299$	−416.067	+	720.649i	−0.0804741	+	0.139385i
$300$		0			0
$301$	12.7308	−	91.9871i	0.00243785	−	0.0176148i
$302$		−	12007.6i		−	2.28795i
$303$		0			0
$304$	7979.78	−	4607.13i	1.50550	−	0.869200i
$305$	−4731.11	+	2731.51i	−0.888204	+	0.512805i
$306$		0			0
$307$		−	2976.39i		−	0.553328i	−0.960967	−	0.276664i	$-0.910771\pi$
$307$		−	2976.39i		−	0.553328i	0.960967	−	0.276664i	$-0.0892289\pi$
$308$	9643.74	−	12397.0i	1.78410	−	2.29346i
$309$		0			0
$310$	−3070.34	+	5317.99i	−0.562528	+	0.974328i
$311$	−2340.89	−	4054.55i	−0.426817	−	0.739268i	0.569772	−	0.821803i	$-0.307032\pi$
$311$	−2340.89	−	4054.55i	−0.426817	−	0.739268i	−0.996588	+	0.0825352i	$0.973698\pi$
$312$		0			0
$313$	−850.477	−	491.023i	−0.153584	−	0.0886718i	0.421238	−	0.906950i	$-0.361596\pi$
$313$	−850.477	−	491.023i	−0.153584	−	0.0886718i	−0.574823	+	0.818278i	$0.694929\pi$
$314$	11852.7			2.13021
$315$		0			0
$316$	−8381.66			−1.49211
$317$	4269.80	+	2465.17i	0.756516	+	0.436775i	0.828044	−	0.560664i	$-0.189454\pi$
$317$	4269.80	+	2465.17i	0.756516	+	0.436775i	−0.0715272	+	0.997439i	$0.522787\pi$
$318$		0			0
$319$	3236.50	+	5605.79i	0.568055	+	0.983899i
$320$	−3647.82	+	6318.21i	−0.637248	+	1.10375i
$321$		0			0
$322$	−7844.26	+	3188.48i	−1.35759	+	0.551823i
$323$		−	11292.0i		−	1.94522i
$324$		0			0
$325$	−290.868	+	167.933i	−0.0496445	+	0.0286623i
$326$	−13807.8	+	7971.96i	−2.34585	+	1.35437i
$327$		0			0
$328$		−	9680.75i		−	1.62966i
$329$	838.338	+	652.148i	0.140483	+	0.109283i
$330$		0			0
$331$	2017.25	−	3493.99i	0.334980	−	0.580202i	−0.648501	−	0.761214i	$-0.724604\pi$
$331$	2017.25	−	3493.99i	0.334980	−	0.580202i	0.983481	+	0.181012i	$0.0579372\pi$
$332$	−3436.25	−	5951.76i	−0.568038	−	0.983871i
$333$		0			0
$334$	1540.41	+	889.356i	0.252358	+	0.145699i
$335$	2091.48			0.341104
$336$		0			0
$337$	2771.62			0.448011			0.224006	−	0.974588i	$-0.428087\pi$
$337$	2771.62			0.448011			0.224006	+	0.974588i	$0.428087\pi$
$338$	8926.76	+	5153.87i	1.43654	+	0.829389i
$339$		0			0
$340$	−6893.21	−	11939.4i	−1.09952	−	1.90443i
$341$	2675.30	−	4633.76i	0.424856	−	0.735872i
$342$		0			0
$343$	−2547.13	+	5819.43i	−0.400968	+	0.916092i
$344$			187.166i			0.0293352i
$345$		0			0
$346$	−8818.68	+	5091.47i	−1.37022	+	0.791095i
$347$	−3743.15	+	2161.11i	−0.579085	+	0.334335i	−0.760770	−	0.649022i	$-0.775178\pi$
$347$	−3743.15	+	2161.11i	−0.579085	+	0.334335i	0.181685	+	0.983357i	$0.441845\pi$
$348$		0			0
$349$			1331.65i			0.204245i	0.994772	+	0.102122i	$0.0325634\pi$
$349$			1331.65i			0.204245i	−0.994772	+	0.102122i	$0.967437\pi$
$350$	−3385.39	−	468.531i	−0.517019	−	0.0715545i
$351$		0			0
$352$	676.635	−	1171.97i	0.102457	−	0.177460i
$353$	−5674.26	−	9828.10i	−0.855553	−	1.48186i	−0.876131	−	0.482073i	$-0.839884\pi$
$353$	−5674.26	−	9828.10i	−0.855553	−	1.48186i	0.0205782	−	0.999788i	$-0.493449\pi$
$354$		0			0
$355$	−882.713	−	509.634i	−0.131970	−	0.0761932i
$356$	−401.962			−0.0598425
$357$		0			0
$358$	8562.02			1.26401
$359$	−7247.49	−	4184.34i	−1.06548	−	0.615156i	−0.138538	−	0.990357i	$-0.544240\pi$
$359$	−7247.49	−	4184.34i	−1.06548	−	0.615156i	−0.926943	+	0.375201i	$0.877574\pi$
$360$		0			0
$361$	9993.77	+	17309.7i	1.45703	+	2.52365i
$362$	−7778.64	+	13473.0i	−1.12938	+	1.95615i
$363$		0			0
$364$	−967.837	−	2381.06i	−0.139364	−	0.342861i
$365$			9822.76i			1.40862i
$366$		0			0
$367$	2351.31	−	1357.53i	0.334434	−	0.193086i	−0.323374	−	0.946271i	$-0.604817\pi$
$367$	2351.31	−	1357.53i	0.334434	−	0.193086i	0.657808	+	0.753186i	$0.271484\pi$
$368$	4576.54	−	2642.27i	0.648285	−	0.374287i
$369$		0			0
$370$		−	5849.52i		−	0.821897i
$371$	3277.93	+	8064.33i	0.458711	+	1.12851i
$372$		0			0
$373$	−3048.56	+	5280.25i	−0.423186	+	0.732979i	−0.996249	−	0.0865320i	$-0.972422\pi$
$373$	−3048.56	+	5280.25i	−0.423186	+	0.732979i	0.573063	+	0.819511i	$0.305755\pi$
$374$	9072.32	+	15713.7i	1.25433	+	2.17256i
$375$		0			0
$376$	−1853.90	−	1070.35i	−0.254276	−	0.146806i
$377$	1059.27			0.144708
$378$		0			0
$379$	−9922.24			−1.34478			−0.672389	−	0.740198i	$-0.734732\pi$
$379$	−9922.24			−1.34478			−0.672389	+	0.740198i	$0.734732\pi$
$380$	28385.6	+	16388.4i	3.83198	+	2.21239i
$381$		0			0
$382$	1336.46	+	2314.82i	0.179003	+	0.310043i
$383$	−609.532	+	1055.74i	−0.0813202	+	0.140851i	−0.903817	−	0.427919i	$-0.859247\pi$
$383$	−609.532	+	1055.74i	−0.0813202	+	0.140851i	0.822497	+	0.568769i	$0.192580\pi$
$384$		0			0
$385$	12671.5	+	1753.71i	1.67740	+	0.232149i
$386$			3427.55i			0.451963i
$387$		0			0
$388$	18743.4	−	10821.5i	2.45245	−	1.41592i
$389$	11374.6	−	6567.15i	1.48256	−	0.855958i	0.482759	−	0.875753i	$-0.339635\pi$
$389$	11374.6	−	6567.15i	1.48256	−	0.855958i	0.999804	+	0.0197949i	$0.00630133\pi$
$390$		0			0
$391$		−	6476.19i		−	0.837634i
$392$	3477.30	−	12322.0i	0.448036	−	1.58765i
$393$		0			0
$394$	−12936.6	+	22406.9i	−1.65416	+	2.86508i
$395$	−3413.29	−	5911.99i	−0.434788	−	0.753075i
$396$		0			0
$397$	2697.68	+	1557.51i	0.341040	+	0.196900i	0.660732	−	0.750622i	$-0.270246\pi$
$397$	2697.68	+	1557.51i	0.341040	+	0.196900i	−0.319692	+	0.947522i	$0.603579\pi$
$398$	−12111.4			−1.52535
$399$		0			0
$400$	2132.94			0.266618
$401$	−9724.47	−	5614.42i	−1.21101	−	0.699179i	−0.248034	−	0.968751i	$-0.579784\pi$
$401$	−9724.47	−	5614.42i	−1.21101	−	0.699179i	−0.962980	+	0.269572i	$0.913118\pi$
$402$		0			0
$403$	−437.797	−	758.287i	−0.0541147	−	0.0937295i
$404$	−5591.90	+	9685.46i	−0.688633	+	1.19275i
$405$		0			0
$406$	8507.70	+	6618.20i	1.03998	+	0.809004i
$407$			5096.90i			0.620747i
$408$		0			0
$409$	−10739.4	+	6200.41i	−1.29836	+	0.749610i	−0.980121	−	0.198399i	$-0.936426\pi$
$409$	−10739.4	+	6200.41i	−1.29836	+	0.749610i	−0.318242	+	0.948010i	$0.603092\pi$
$410$	13948.5	−	8053.18i	1.68017	−	0.970044i
$411$		0			0
$412$			28093.3i			3.35936i
$413$	3876.78	−	1575.81i	0.461898	−	0.187749i
$414$		0			0
$415$	2798.71	−	4847.51i	0.331044	−	0.573385i
$416$	−110.727	−	191.785i	−0.0130501	−	0.0226035i
$417$		0			0
$418$	−37359.0	−	21569.2i	−4.37150	−	2.52389i
$419$	−8260.19			−0.963095			−0.481547	−	0.876420i	$-0.659925\pi$
$419$	−8260.19			−0.963095			−0.481547	+	0.876420i	$0.659925\pi$
$420$		0			0
$421$	5571.81			0.645020			0.322510	−	0.946566i	$-0.395473\pi$
$421$	5571.81			0.645020			0.322510	+	0.946566i	$0.395473\pi$
$422$	−14554.9	−	8403.30i	−1.67896	−	0.969351i
$423$		0			0
$424$	−8772.49	−	15194.4i	−1.00479	−	1.74034i
$425$	1306.96	−	2263.72i	0.149169	−	0.258368i
$426$		0			0
$427$	4866.89	−	6256.40i	0.551582	−	0.709060i
$428$			353.543i			0.0399279i
$429$		0			0
$430$	−269.678	+	155.699i	−0.0302443	+	0.0174616i
$431$	−6094.88	+	3518.88i	−0.681160	+	0.393268i	−0.800292	−	0.599611i	$-0.795322\pi$
$431$	−6094.88	+	3518.88i	−0.681160	+	0.393268i	0.119132	+	0.992878i	$0.461989\pi$
$432$		0			0
$433$		−	9212.26i		−	1.02243i	−0.859452	−	0.511216i	$-0.829195\pi$
$433$		−	9212.26i		−	1.02243i	0.859452	−	0.511216i	$-0.170805\pi$
$434$	1221.45	−	8825.63i	0.135096	−	0.976138i
$435$		0			0
$436$	7463.18	−	12926.6i	0.819774	−	1.41989i
$437$	7698.48	+	13334.2i	0.842719	+	1.45963i
$438$		0			0
$439$	−7345.30	−	4240.81i	−0.798570	−	0.461054i	0.0444012	−	0.999014i	$-0.485862\pi$
$439$	−7345.30	−	4240.81i	−0.798570	−	0.461054i	−0.842971	+	0.537959i	$0.819195\pi$
$440$	−25782.7			−2.79350
$441$		0			0
$442$	2969.26			0.319532
$443$	11305.9	+	6527.49i	1.21255	+	0.700068i	0.963315	−	0.268374i	$-0.0864863\pi$
$443$	11305.9	+	6527.49i	1.21255	+	0.700068i	0.249239	+	0.968442i	$0.419820\pi$
$444$		0			0
$445$	−163.692	−	283.523i	−0.0174376	−	0.0302029i
$446$	9478.70	−	16417.6i	1.00634	−	1.74304i
$447$		0			0
$448$	1451.18	−	10485.6i	0.153040	−	1.10580i
$449$		−	14114.0i		−	1.48348i	−0.670689	−	0.741738i	$-0.734002\pi$
$449$		−	14114.0i		−	1.48348i	0.670689	−	0.741738i	$-0.265998\pi$
$450$		0			0
$451$	−12153.9	+	7017.03i	−1.26896	+	0.732637i
$452$	1630.66	−	941.459i	0.169689	−	0.0979702i
$453$		0			0
$454$			2945.97i			0.304540i
$455$	1285.34	−	1652.31i	0.132435	−	0.170245i
$456$		0			0
$457$	4486.87	−	7771.49i	0.459271	−	0.795481i	−0.539651	−	0.841889i	$-0.681444\pi$
$457$	4486.87	−	7771.49i	0.459271	−	0.795481i	0.998923	+	0.0464073i	$0.0147772\pi$
$458$	−5373.63	−	9307.40i	−0.548238	−	0.949577i
$459$		0			0
$460$	16279.7	+	9399.06i	1.65009	+	0.952682i
$461$	955.010			0.0964842			0.0482421	−	0.998836i	$-0.484638\pi$
$461$	955.010			0.0964842			0.0482421	+	0.998836i	$0.484638\pi$
$462$		0			0
$463$	12004.5			1.20496			0.602479	−	0.798135i	$-0.294180\pi$
$463$	12004.5			1.20496			0.602479	+	0.798135i	$0.294180\pi$
$464$	−5825.73	−	3363.49i	−0.582872	−	0.336521i
$465$		0			0
$466$	5802.82	+	10050.8i	0.576846	+	0.999127i
$467$	2532.46	−	4386.34i	0.250938	−	0.434638i	−0.712846	−	0.701320i	$-0.752594\pi$
$467$	2532.46	−	4386.34i	0.250938	−	0.434638i	0.963784	+	0.266683i	$0.0859276\pi$
$468$		0			0
$469$	−2811.24	+	1142.69i	−0.276783	+	0.112505i
$470$		−	3561.59i		−	0.349540i
$471$		0			0
$472$	−7304.43	+	4217.21i	−0.712317	+	0.411256i
$473$	234.981	−	135.666i	0.0228423	−	0.0131880i
$474$		0			0
$475$			6214.52i			0.600299i
$476$	15788.6	+	12282.1i	1.52032	+	1.18266i
$477$		0			0
$478$	−7341.75	+	12716.3i	−0.702518	+	1.21680i
$479$	−7606.85	−	13175.5i	−0.725607	−	1.25679i	−0.958724	−	0.284340i	$-0.908226\pi$
$479$	−7606.85	−	13175.5i	−0.725607	−	1.25679i	0.233116	−	0.972449i	$-0.425108\pi$
$480$		0			0
$481$	722.332	+	417.038i	0.0684730	+	0.0395329i
$482$	−12238.8			−1.15656
$483$		0			0
$484$	25031.7			2.35084
$485$	15265.9	+	8813.75i	1.42925	+	0.825179i
$486$		0			0
$487$	−7905.92	−	13693.5i	−0.735629	−	1.27415i	−0.954447	−	0.298382i	$-0.903553\pi$
$487$	−7905.92	−	13693.5i	−0.735629	−	1.27415i	0.218817	−	0.975766i	$-0.429780\pi$
$488$	−7987.88	+	13835.4i	−0.740972	+	1.28340i
$489$		0			0
$490$	20646.9	−	5240.14i	1.90354	−	0.483113i
$491$			18064.2i			1.66034i	0.557512	+	0.830169i	$0.311756\pi$
$491$			18064.2i			1.66034i	−0.557512	+	0.830169i	$0.688244\pi$
$492$		0			0
$493$	−7139.42	+	4121.94i	−0.652217	+	0.376558i
$494$	−6113.57	+	3529.67i	−0.556806	+	0.321472i
$495$		0			0
$496$			5560.54i			0.503378i
$497$	1464.93	+	202.744i	0.132216	+	0.0182984i
$498$		0			0
$499$	5262.33	−	9114.62i	0.472092	−	0.817688i	−0.527398	−	0.849619i	$-0.676832\pi$
$499$	5262.33	−	9114.62i	0.472092	−	0.817688i	0.999490	+	0.0319305i	$0.0101655\pi$
$500$	−8709.04	−	15084.5i	−0.778960	−	1.34920i
$501$		0			0
$502$	5503.38	+	3177.38i	0.489299	+	0.282497i
$503$	7790.82			0.690607			0.345304	−	0.938491i	$-0.387776\pi$
$503$	7790.82			0.690607			0.345304	+	0.938491i	$0.387776\pi$
$504$		0			0
$505$	−9108.83			−0.802649
$506$	−21426.0	−	12370.3i	−1.88242	−	1.08681i
$507$		0			0
$508$	6929.41	+	12002.1i	0.605202	+	1.04824i
$509$	−5098.24	+	8830.41i	−0.443960	+	0.768961i	−0.997979	−	0.0635430i	$-0.979760\pi$
$509$	−5098.24	+	8830.41i	−0.443960	+	0.768961i	0.554019	+	0.832504i	$0.313093\pi$
$510$		0			0
$511$	−5366.74	−	13203.2i	−0.464600	−	1.14300i
$512$			18199.6i			1.57093i
$513$		0			0
$514$	31482.9	−	18176.7i	2.70166	−	1.55980i
$515$	−19815.6	+	11440.5i	−1.69549	+	0.978892i
$516$		0			0
$517$			3103.35i			0.263994i
$518$	3195.93	+	7862.57i	0.271083	+	0.666914i
$519$		0			0
$520$	−2109.59	+	3653.92i	−0.177907	+	0.308144i
$521$	−963.789	−	1669.33i	−0.0810449	−	0.140374i	0.822654	−	0.568542i	$-0.192492\pi$
$521$	−963.789	−	1669.33i	−0.0810449	−	0.140374i	−0.903699	+	0.428168i	$0.859159\pi$
$522$		0			0
$523$	−6716.70	−	3877.89i	−0.561569	−	0.324222i	0.192206	−	0.981355i	$-0.438436\pi$
$523$	−6716.70	−	3877.89i	−0.561569	−	0.324222i	−0.753775	+	0.657133i	$0.771769\pi$
$524$	25183.0			2.09948
$525$		0			0
$526$	−7476.33			−0.619741
$527$	5901.47	+	3407.21i	0.487803	+	0.281633i
$528$		0			0
$529$	−1668.28	−	2889.55i	−0.137115	−	0.237491i
$530$	14595.2	−	25279.7i	1.19618	−	2.07185i
$531$		0			0
$532$	−47108.2	−	6519.68i	−3.83910	−	0.531324i
$533$			2296.59i			0.186635i
$534$		0			0
$535$	−249.371	+	143.975i	−0.0201519	+	0.0116347i
$536$	5296.80	−	3058.11i	0.426841	−	0.246437i
$537$		0			0
$538$			19053.8i			1.52689i
$539$	−17990.4	+	4565.93i	−1.43767	+	0.364876i
$540$		0			0
$541$	−8380.42	+	14515.3i	−0.665993	+	1.15353i	0.313022	+	0.949746i	$0.398659\pi$
$541$	−8380.42	+	14515.3i	−0.665993	+	1.15353i	−0.979015	+	0.203788i	$0.934675\pi$
$542$	8756.93	+	15167.4i	0.693989	+	1.20202i
$543$		0			0
$544$	1492.59	+	861.748i	0.117637	+	0.0679176i
$545$	12157.0			0.955503
$546$		0			0
$547$	5869.79			0.458819			0.229410	−	0.973330i	$-0.426320\pi$
$547$	5869.79			0.458819			0.229410	+	0.973330i	$0.426320\pi$
$548$	9642.95	+	5567.36i	0.751690	+	0.433989i
$549$		0			0
$550$	−4992.91	−	8647.97i	−0.387088	−	0.670456i
$551$	9799.82	−	16973.8i	0.757688	−	1.31235i
$552$		0			0
$553$	7818.00	+	6081.67i	0.601185	+	0.467666i
$554$		−	1382.16i		−	0.105997i
$555$		0			0
$556$	−20791.6	+	12004.1i	−1.58590	+	0.915621i
$557$	18756.5	−	10829.1i	1.42682	−	0.823774i	0.429951	−	0.902852i	$-0.358531\pi$
$557$	18756.5	−	10829.1i	1.42682	−	0.823774i	0.996868	+	0.0790779i	$0.0251976\pi$
$558$		0			0
$559$		−	44.4019i		−	0.00335957i
$560$	−12315.6	+	5005.98i	−0.929341	+	0.377752i
$561$		0			0
$562$	781.517	−	1353.63i	0.0586589	−	0.101600i
$563$	−4795.36	−	8305.80i	−0.358970	−	0.621755i	0.628819	−	0.777552i	$-0.283539\pi$
$563$	−4795.36	−	8305.80i	−0.358970	−	0.621755i	−0.987789	+	0.155797i	$0.950205\pi$
$564$		0			0
$565$	1328.11	+	766.787i	0.0988923	+	0.0570955i
$566$	33098.3			2.45799
$567$		0			0
$568$	−2980.70			−0.220189
$569$	−14405.5	−	8317.01i	−1.06135	−	0.612772i	−0.135546	−	0.990771i	$-0.543279\pi$
$569$	−14405.5	−	8317.01i	−1.06135	−	0.612772i	−0.925806	+	0.377999i	$0.876612\pi$
$570$		0			0
$571$	−3165.51	−	5482.83i	−0.232001	−	0.401838i	0.726396	−	0.687277i	$-0.241194\pi$
$571$	−3165.51	−	5482.83i	−0.232001	−	0.401838i	−0.958397	+	0.285439i	$0.907861\pi$
$572$	3754.91	−	6503.69i	0.274477	−	0.475408i
$573$		0			0
$574$	−14348.8	+	18445.5i	−1.04340	+	1.34129i
$575$			3564.14i			0.258495i
$576$		0			0
$577$	8431.94	−	4868.18i	0.608364	−	0.351239i	−0.163961	−	0.986467i	$-0.552427\pi$
$577$	8431.94	−	4868.18i	0.608364	−	0.351239i	0.772325	+	0.635228i	$0.219094\pi$
$578$	688.509	−	397.511i	0.0495470	−	0.0286060i
$579$		0			0
$580$		−	23929.1i		−	1.71311i
$581$	−1113.39	+	8044.83i	−0.0795028	+	0.574450i
$582$		0			0
$583$	−12717.4	+	22027.1i	−0.903430	+	1.56479i
$584$	14362.6	+	24876.8i	1.01769	+	1.76268i
$585$		0			0
$586$	13399.3	+	7736.09i	0.944573	+	0.545350i
$587$	−10940.3			−0.769255			−0.384628	−	0.923072i	$-0.625670\pi$
$587$	−10940.3			−0.769255			−0.384628	+	0.923072i	$0.625670\pi$
$588$		0			0
$589$	−16201.1			−1.13337
$590$	−12152.7	−	7016.39i	−0.848001	−	0.489594i
$591$		0			0
$592$	−2648.44	−	4587.23i	−0.183869	−	0.318470i
$593$	−12430.4	+	21530.0i	−0.860799	+	1.49095i	0.0103608	+	0.999946i	$0.496702\pi$
$593$	−12430.4	+	21530.0i	−0.860799	+	1.49095i	−0.871159	+	0.491000i	$0.836631\pi$
$594$		0			0
$595$	−2233.49	+	16138.2i	−0.153889	+	1.11193i
$596$		−	37629.6i		−	2.58619i
$597$		0			0
$598$	−3506.24	+	2024.33i	−0.239767	+	0.138430i
$599$	−20207.8	+	11667.0i	−1.37841	+	0.795825i	−0.991968	−	0.126488i	$-0.959629\pi$
$599$	−20207.8	+	11667.0i	−1.37841	+	0.795825i	−0.386442	+	0.922314i	$0.626296\pi$
$600$		0			0
$601$		−	13012.4i		−	0.883175i	−0.897218	−	0.441587i	$-0.854416\pi$
$601$		−	13012.4i		−	0.883175i	0.897218	−	0.441587i	$-0.145584\pi$
$602$	277.419	−	356.622i	0.0187820	−	0.0241442i
$603$		0			0
$604$	19339.1	−	33496.2i	1.30281	−	2.25653i
$605$	10193.8	+	17656.1i	0.685017	+	1.18648i
$606$		0			0
$607$	7355.69	+	4246.81i	0.491859	+	0.283975i	0.725345	−	0.688385i	$-0.241680\pi$
$607$	7355.69	+	4246.81i	0.491859	+	0.283975i	−0.233486	+	0.972360i	$0.575013\pi$
$608$	−4097.57			−0.273320
$609$		0			0
$610$	−26579.7			−1.76423
$611$	439.806	+	253.922i	0.0291205	+	0.0168127i
$612$		0			0
$613$	4569.79	+	7915.11i	0.301097	+	0.521514i	0.976385	−	0.216040i	$-0.0693140\pi$
$613$	4569.79	+	7915.11i	0.301097	+	0.521514i	−0.675288	+	0.737554i	$0.735981\pi$
$614$	7240.66	−	12541.2i	0.475911	−	0.824302i
$615$		0			0
$616$	34655.6	−	14086.6i	2.26674	−	0.921370i
$617$		−	7360.91i		−	0.480290i	−0.970737	−	0.240145i	$-0.922805\pi$
$617$		−	7360.91i		−	0.480290i	0.970737	−	0.240145i	$-0.0771950\pi$
$618$		0			0
$619$	19878.5	−	11476.9i	1.29077	−	0.745225i	0.311978	−	0.950089i	$-0.399009\pi$
$619$	19878.5	−	11476.9i	1.29077	−	0.745225i	0.978790	+	0.204864i	$0.0656753\pi$
$620$	−17129.9	+	9889.96i	−1.10960	+	0.640629i
$621$		0			0
$622$		−	22778.7i		−	1.46840i
$623$	374.930	+	291.660i	0.0241112	+	0.0187562i
$624$		0			0
$625$	9463.74	−	16391.7i	0.605679	−	1.04907i
$626$	−2389.02	−	4137.91i	−0.152531	−	0.264192i
$627$		0			0
$628$	33064.0	+	19089.5i	2.10095	+	1.21298i
$629$	−6491.31			−0.411487
$630$		0			0
$631$	21126.0			1.33282			0.666412	−	0.745584i	$-0.267829\pi$
$631$	21126.0			1.33282			0.666412	+	0.745584i	$0.267829\pi$
$632$	−17288.7	−	9981.66i	−1.08815	−	0.628242i
$633$		0			0
$634$	11994.0	+	20774.2i	0.751330	+	1.30134i
$635$	−5643.77	+	9775.29i	−0.352703	+	0.610899i
$636$		0			0
$637$	−824.929	+	2923.19i	−0.0513106	+	0.181823i
$638$			31493.7i			1.95431i
$639$		0			0
$640$	−28529.0	+	16471.2i	−1.76204	+	1.01732i
$641$	15447.5	−	8918.61i	0.951855	−	0.549554i	0.0581985	−	0.998305i	$-0.481464\pi$
$641$	15447.5	−	8918.61i	0.951855	−	0.549554i	0.893657	+	0.448751i	$0.148131\pi$
$642$		0			0
$643$			25449.0i			1.56082i	0.625266	+	0.780412i	$0.284991\pi$
$643$			25449.0i			1.56082i	−0.625266	+	0.780412i	$0.715009\pi$
$644$	−27017.4	−	3739.16i	−1.65316	−	0.228794i
$645$		0			0
$646$	27470.1	−	47579.6i	1.67306	−	2.89782i
$647$	13149.2	+	22775.1i	0.798993	+	1.38390i	0.920273	+	0.391277i	$0.127967\pi$
$647$	13149.2	+	22775.1i	0.798993	+	1.38390i	−0.121280	+	0.992618i	$0.538700\pi$
$648$		0			0
$649$	10589.1	+	6113.64i	0.640462	+	0.369771i
$650$	−1634.12			−0.0986083
$651$		0			0
$652$	−51357.4			−3.08483
$653$	−8203.79	−	4736.46i	−0.491637	−	0.283847i	0.233616	−	0.972329i	$-0.424944\pi$
$653$	−8203.79	−	4736.46i	−0.491637	−	0.283847i	−0.725253	+	0.688482i	$0.758277\pi$
$654$		0			0
$655$	10255.4	+	17762.8i	0.611771	+	1.05962i
$656$	7292.34	−	12630.7i	0.434022	−	0.751747i
$657$		0			0
$658$	1945.90	+	4787.28i	0.115287	+	0.283629i
$659$		−	22384.5i		−	1.32318i	−0.749865	−	0.661591i	$-0.769882\pi$
$659$		−	22384.5i		−	1.32318i	0.749865	−	0.661591i	$-0.230118\pi$
$660$		0			0
$661$	−19857.3	+	11464.6i	−1.16847	+	0.674618i	−0.953320	−	0.301962i	$-0.902359\pi$
$661$	−19857.3	+	11464.6i	−1.16847	+	0.674618i	−0.215153	+	0.976580i	$0.569025\pi$
$662$	16999.6	−	9814.73i	0.998049	−	0.576224i
$663$		0			0
$664$		−	16368.8i		−	0.956677i
$665$	−14585.4	−	35882.7i	−0.850521	−	2.09244i
$666$		0			0
$667$	5620.37	−	9734.77i	0.326269	−	0.565115i
$668$	2864.73	+	4961.85i	0.165928	+	0.287395i
$669$		0			0
$670$	8812.56	+	5087.93i	0.508147	+	0.293379i
$671$	23159.9			1.33245
$672$		0			0
$673$	−4873.86			−0.279158			−0.139579	−	0.990211i	$-0.544575\pi$
$673$	−4873.86			−0.279158			−0.139579	+	0.990211i	$0.544575\pi$
$674$	11678.4	+	6742.51i	0.667409	+	0.385329i
$675$		0			0
$676$	16601.3	+	28754.2i	0.944541	+	1.63599i
$677$	−8123.71	+	14070.7i	−0.461181	+	0.798789i	−0.999020	−	0.0442583i	$-0.985908\pi$
$677$	−8123.71	+	14070.7i	−0.461181	+	0.798789i	0.537839	+	0.843048i	$0.319241\pi$
$678$		0			0
$679$	−25334.9	−	3506.30i	−1.43191	−	0.198173i
$680$		−	32836.3i		−	1.85179i
$681$		0			0
$682$	22545.1	−	13016.4i	1.26583	−	0.730827i
$683$	18786.2	−	10846.2i	1.05247	−	0.607641i	0.129127	−	0.991628i	$-0.458783\pi$
$683$	18786.2	−	10846.2i	1.05247	−	0.607641i	0.923339	+	0.383987i	$0.125449\pi$
$684$		0			0
$685$			9068.85i			0.505844i
$686$	−24889.4	+	18324.1i	−1.38525	+	1.01985i
$687$		0			0
$688$	−140.989	+	244.200i	−0.00781273	+	0.0135320i
$689$	2081.12	+	3604.61i	0.115072	+	0.199310i
$690$		0			0
$691$	−19499.9	−	11258.3i	−1.07353	−	0.619803i	−0.144387	−	0.989521i	$-0.546121\pi$
$691$	−19499.9	−	11258.3i	−1.07353	−	0.619803i	−0.929144	+	0.369718i	$0.879454\pi$
$692$	−32800.5			−1.80186
$693$		0			0
$694$	−21029.2			−1.15023
$695$	−16934.1	−	9776.90i	−0.924239	−	0.533610i
$696$		0			0
$697$	−8936.75	−	15478.9i	−0.485658	−	0.841184i
$698$	−3239.49	+	5610.97i	−0.175669	+	0.304267i
$699$		0			0
$700$	−8689.20	−	6759.38i	−0.469173	−	0.364972i
$701$		−	33929.0i		−	1.82807i	−0.405631	−	0.914037i	$-0.632948\pi$
$701$		−	33929.0i		−	1.82807i	0.405631	−	0.914037i	$-0.367052\pi$
$702$		0			0
$703$	13365.3	−	7716.46i	0.717044	−	0.413986i
$704$	26785.4	−	15464.5i	1.43397	−	0.827901i
$705$		0			0
$706$		−	55214.9i		−	2.94340i
$707$	12243.6	−	4976.68i	0.651296	−	0.264734i
$708$		0			0
$709$	−9593.62	+	16616.6i	−0.508175	+	0.880185i	0.491780	+	0.870719i	$0.336346\pi$
$709$	−9593.62	+	16616.6i	−0.508175	+	0.880185i	−0.999955	+	0.00946553i	$0.996987\pi$
$710$	−2479.57	−	4294.74i	−0.131066	−	0.227012i
$711$		0			0
$712$	−829.121	−	478.693i	−0.0436413	−	0.0251963i
$713$	−9291.63			−0.488043
$714$		0			0
$715$	6116.49			0.319922
$716$	23884.4	+	13789.7i	1.24665	+	0.719754i
$717$		0			0
$718$	−20358.4	−	35261.8i	−1.05818	−	1.83281i
$719$	−6883.43	+	11922.4i	−0.357036	+	0.618404i	−0.987464	−	0.157844i	$-0.949546\pi$
$719$	−6883.43	+	11922.4i	−0.357036	+	0.618404i	0.630429	+	0.776247i	$0.282879\pi$
$720$		0			0
$721$	20384.3	−	26204.0i	1.05291	−	1.35352i
$722$			97247.2i			5.01269i
$723$		0			0
$724$	−43398.2	+	25056.0i	−2.22774	+	1.28618i
$725$	3929.15	−	2268.49i	0.201276	−	0.116207i
$726$		0			0
$727$			12226.1i			0.623717i	0.950129	+	0.311858i	$0.100951\pi$
$727$			12226.1i			0.623717i	−0.950129	+	0.311858i	$0.899049\pi$
$728$	839.242	−	6063.97i	0.0427258	−	0.308717i
$729$		0			0
$730$	−23895.8	+	41388.7i	−1.21154	+	2.09845i
$731$	172.782	+	299.267i	0.00874222	+	0.0151420i
$732$		0			0
$733$	2256.76	+	1302.94i	0.113718	+	0.0656553i	0.555780	−	0.831329i	$-0.312420\pi$
$733$	2256.76	+	1302.94i	0.113718	+	0.0656553i	−0.442062	+	0.896984i	$0.645753\pi$
$734$	13209.8			0.664282
$735$		0			0
$736$	−2350.03			−0.117695
$737$	−7678.71	−	4433.30i	−0.383784	−	0.221578i
$738$		0			0
$739$	−16871.7	−	29222.7i	−0.839833	−	1.45463i	−0.890034	−	0.455894i	$-0.849320\pi$
$739$	−16871.7	−	29222.7i	−0.839833	−	1.45463i	0.0502016	−	0.998739i	$-0.484014\pi$
$740$	9421.01	−	16317.7i	0.468004	−	0.810607i
$741$		0			0
$742$	−5806.31	+	41953.7i	−0.287273	+	2.07570i
$743$		−	14586.9i		−	0.720244i	−0.932905	−	0.360122i	$-0.882735\pi$
$743$		−	14586.9i		−	0.720244i	0.932905	−	0.360122i	$-0.117265\pi$
$744$		0			0
$745$	26542.0	−	15324.0i	1.30527	−	0.753597i
$746$	−25690.5	+	14832.4i	−1.26085	+	0.727953i
$747$		0			0
$748$			58446.1i			2.85695i
$749$	256.528	−	329.768i	0.0125145	−	0.0160874i
$750$		0			0
$751$	3757.62	−	6508.39i	0.182580	−	0.316238i	−0.760178	−	0.649714i	$-0.774889\pi$
$751$	3757.62	−	6508.39i	0.182580	−	0.316238i	0.942758	+	0.333477i	$0.108222\pi$
$752$	−1612.55	−	2793.02i	−0.0781965	−	0.135440i
$753$		0			0
$754$	4463.28	+	2576.88i	0.215574	+	0.124462i
$755$	31502.0			1.51851
$756$		0			0
$757$	23917.4			1.14834			0.574169	−	0.818737i	$-0.305325\pi$
$757$	23917.4			1.14834			0.574169	+	0.818737i	$0.305325\pi$
$758$	−41807.9	−	24137.8i	−2.00334	−	1.15663i
$759$		0			0
$760$	39033.7	+	67608.4i	1.86303	+	3.22686i
$761$	6099.27	−	10564.2i	0.290537	−	0.503224i	−0.683400	−	0.730044i	$-0.739500\pi$
$761$	6099.27	−	10564.2i	0.290537	−	0.503224i	0.973937	+	0.226820i	$0.0728328\pi$
$762$		0			0
$763$	−16340.7	+	6642.07i	−0.775327	+	0.315150i
$764$			8609.80i			0.407712i
$765$		0			0
$766$	−5136.59	+	2965.61i	−0.242288	+	0.139885i
$767$	1732.85	−	1000.46i	0.0815769	−	0.0470985i
$768$		0			0
$769$			2013.08i			0.0943999i	0.998885	+	0.0471999i	$0.0150298\pi$
$769$			2013.08i			0.0943999i	−0.998885	+	0.0471999i	$0.984970\pi$
$770$	49125.7	+	38215.2i	2.29918	+	1.78855i
$771$		0			0
$772$	−5520.28	+	9561.41i	−0.257357	+	0.445755i
$773$	15139.1	+	26221.7i	0.704418	+	1.22009i	0.966901	+	0.255152i	$0.0821254\pi$
$773$	15139.1	+	26221.7i	0.704418	+	1.22009i	−0.262483	+	0.964937i	$0.584541\pi$
$774$		0			0
$775$	−3247.85	−	1875.14i	−0.150537	−	0.0869125i
$776$	51549.0			2.38467
$777$		0			0
$778$	63903.5			2.94480
$779$	36800.7	+	21246.9i	1.69258	+	0.977213i
$780$		0			0
$781$	2160.54	+	3742.17i	0.0989888	+	0.171454i
$782$	15754.6	−	27287.8i	0.720439	−	1.24784i
$783$		0			0
$784$	13818.9	−	13457.5i	0.629506	−	0.613041i
$785$			31095.5i			1.41382i
$786$		0			0
$787$	24839.3	−	14341.0i	1.12507	−	0.649557i	0.182377	−	0.983229i	$-0.441621\pi$
$787$	24839.3	−	14341.0i	1.12507	−	0.649557i	0.942689	+	0.333671i	$0.108288\pi$
$788$	−72175.3	+	41670.4i	−3.26287	+	1.88382i
$789$		0			0
$790$		−	33214.0i		−	1.49582i
$791$	−2204.11	−	305.045i	−0.0990761	−	0.0137119i
$792$		0			0
$793$	1894.99	−	3282.21i	0.0848586	−	0.146979i
$794$	7577.89	+	13125.3i	0.338702	+	0.586649i
$795$		0			0
$796$	−33785.7	−	19506.2i	−1.50440	−	0.868566i
$797$	−27108.9			−1.20483			−0.602413	−	0.798184i	$-0.705794\pi$
$797$	−27108.9			−1.20483			−0.602413	+	0.798184i	$0.705794\pi$
$798$		0			0
$799$	−3952.36			−0.174999
$800$	−821.441	−	474.259i	−0.0363029	−	0.0209595i
$801$		0			0
$802$	−27316.4	−	47313.3i	−1.20271	−	2.08316i
$803$	20821.3	−	36063.5i	0.915028	−	1.58487i
$804$		0			0
$805$	−8364.97	−	20579.4i	−0.366244	−	0.901029i
$806$		−	4260.11i		−	0.186174i
$807$		0			0
$808$	−23068.7	+	13318.7i	−1.00440	+	0.579890i
$809$	−17128.3	+	9889.03i	−0.744375	+	0.429765i	−0.823658	−	0.567087i	$-0.808070\pi$
$809$	−17128.3	+	9889.03i	−0.744375	+	0.429765i	0.0792832	+	0.996852i	$0.474737\pi$
$810$		0			0
$811$			44456.6i			1.92488i	0.271487	+	0.962442i	$0.412484\pi$
$811$			44456.6i			1.92488i	−0.271487	+	0.962442i	$0.587516\pi$
$812$	13073.9	+	32164.1i	0.565028	+	1.39007i
$813$		0			0
$814$	−12399.2	+	21476.1i	−0.533897	+	0.924736i
$815$	−20914.4	−	36224.8i	−0.898896	−	1.55693i
$816$		0			0
$817$	−711.499	−	410.784i	−0.0304678	−	0.0175906i
$818$	−60334.8			−2.57892
$819$		0			0
$820$	51880.6			2.20945
$821$	9958.57	+	5749.58i	0.423333	+	0.244411i	0.696502	−	0.717555i	$-0.254739\pi$
$821$	9958.57	+	5749.58i	0.423333	+	0.244411i	−0.273169	+	0.961966i	$0.588072\pi$
$822$		0			0
$823$	−596.549	−	1033.25i	−0.0252666	−	0.0437630i	0.853116	−	0.521722i	$-0.174710\pi$
$823$	−596.549	−	1033.25i	−0.0252666	−	0.0437630i	−0.878382	+	0.477959i	$0.841377\pi$
$824$	−33456.1	+	57947.6i	−1.41444	+	2.44988i
$825$		0			0
$826$	20168.5	+	2791.28i	0.849577	+	0.117580i
$827$		−	29552.9i		−	1.24263i	−0.783561	−	0.621315i	$-0.786599\pi$
$827$		−	29552.9i		−	1.24263i	0.783561	−	0.621315i	$-0.213401\pi$
$828$		0			0
$829$	−11762.7	+	6791.21i	−0.492806	+	0.284521i	−0.725738	−	0.687972i	$-0.758501\pi$
$829$	−11762.7	+	6791.21i	−0.492806	+	0.284521i	0.232932	+	0.972493i	$0.425168\pi$
$830$	23585.0	−	13616.8i	0.986323	−	0.569454i
$831$		0			0
$832$		−	5061.36i		−	0.210903i
$833$	−5815.07	−	22912.2i	−0.241873	−	0.953015i
$834$		0			0
$835$	−2333.22	+	4041.26i	−0.0967000	+	0.167489i
$836$	−69477.1	−	120338.i	−2.87430	−	4.97843i
$837$		0			0
$838$	−34804.7	−	20094.5i	−1.43474	−	0.828346i
$839$	11623.6			0.478297			0.239149	−	0.970983i	$-0.423132\pi$
$839$	11623.6			0.478297			0.239149	+	0.970983i	$0.423132\pi$
$840$		0			0
$841$	10080.1			0.413303
$842$	23477.1	+	13554.5i	0.960896	+	0.554774i
$843$		0			0
$844$	−27068.1	−	46883.2i	−1.10393	−	1.91207i
$845$	−13521.2	+	23419.3i	−0.550464	+	0.953432i
$846$		0			0
$847$	−23348.4	−	18162.9i	−0.947178	−	0.736816i
$848$		−	26432.7i		−	1.07040i
$849$		0			0
$850$	11013.9	−	6358.87i	0.444439	−	0.256597i
$851$	7665.24	−	4425.53i	0.308767	−	0.178267i
$852$		0			0
$853$		−	1019.82i		−	0.0409354i	−0.999791	−	0.0204677i	$-0.993484\pi$
$853$		−	1019.82i		−	0.0409354i	0.999791	−	0.0204677i	$-0.00651553\pi$
$854$	35726.8	−	14522.0i	1.43155	−	0.581888i
$855$		0			0
$856$	−421.032	+	729.249i	−0.0168114	+	0.0291182i
$857$	4299.43	+	7446.83i	0.171372	+	0.296825i	0.938900	−	0.344191i	$-0.111847\pi$
$857$	4299.43	+	7446.83i	0.171372	+	0.296825i	−0.767528	+	0.641016i	$0.778513\pi$
$858$		0			0
$859$	32182.1	+	18580.4i	1.27828	+	0.738013i	0.976531	−	0.215375i	$-0.0690974\pi$
$859$	32182.1	+	18580.4i	1.27828	+	0.738013i	0.301745	+	0.953389i	$0.402431\pi$
$860$	−1003.05			−0.0397718
$861$		0			0
$862$	−34241.4			−1.35298
$863$	10634.2	+	6139.68i	0.419459	+	0.242175i	0.694846	−	0.719159i	$-0.255473\pi$
$863$	10634.2	+	6139.68i	0.419459	+	0.242175i	−0.275387	+	0.961334i	$0.588806\pi$
$864$		0			0
$865$	−13357.5	−	23135.8i	−0.525049	−	0.909411i
$866$	22410.6	−	38816.3i	0.879381	−	1.52313i
$867$		0			0
$868$	17621.6	−	22652.5i	0.689072	−	0.885803i
$869$			28940.6i			1.12974i
$870$		0			0
$871$	−1256.57	+	725.483i	−0.0488833	+	0.0282228i
$872$	30788.4	−	17775.7i	1.19567	−	0.690322i
$873$		0			0
$874$			74912.3i			2.89925i
$875$	−2821.84	+	20389.3i	−0.109024	+	0.787753i
$876$		0			0
$877$	−15935.8	+	27601.6i	−0.613583	+	1.06276i	0.377048	+	0.926194i	$0.376939\pi$
$877$	−15935.8	+	27601.6i	−0.613583	+	1.06276i	−0.990631	+	0.136564i	$0.956394\pi$
$878$	−20633.2	−	35737.8i	−0.793094	−	1.37368i
$879$		0			0
$880$	−33639.3	−	19421.7i	−1.28861	−	0.743982i
$881$	−29427.6			−1.12536			−0.562679	−	0.826676i	$-0.690229\pi$
$881$	−29427.6			−1.12536			−0.562679	+	0.826676i	$0.690229\pi$
$882$		0			0
$883$	846.860			0.0322753			0.0161377	−	0.999870i	$-0.494863\pi$
$883$	846.860			0.0322753			0.0161377	+	0.999870i	$0.494863\pi$
$884$	8282.97	+	4782.18i	0.315143	+	0.181948i
$885$		0			0
$886$	31758.8	+	55007.8i	1.20424	+	2.08580i
$887$	−3940.07	+	6824.39i	−0.149148	+	0.258332i	−0.930913	−	0.365241i	$-0.880986\pi$
$887$	−3940.07	+	6824.39i	−0.149148	+	0.258332i	0.781765	+	0.623574i	$0.214320\pi$
$888$		0			0
$889$	2245.22	−	16222.9i	0.0847043	−	0.612034i
$890$		−	1592.85i		−	0.0599916i
$891$		0			0
$892$	52883.1	−	30532.1i	1.98504	−	1.14606i
$893$	8137.73	−	4698.32i	0.304948	−	0.176062i
$894$		0			0
$895$			22462.4i			0.838923i
$896$	29347.8	−	37726.6i	1.09424	−	1.40665i
$897$		0			0
$898$	34335.1	−	59470.1i	1.27592	−	2.20996i
$899$	5913.91	+	10243.2i	0.219399	+	0.380011i
$900$		0			0
$901$	−28053.3	−	16196.6i	−1.03728	−	0.598875i
$902$	−68281.2			−2.52053
$903$		0			0
$904$	4484.71			0.164999
$905$	−35346.4	−	20407.2i	−1.29829	−	0.749569i
$906$		0			0
$907$	−10646.6	−	18440.4i	−0.389762	−	0.675088i	0.602655	−	0.798002i	$-0.294109\pi$
$907$	−10646.6	−	18440.4i	−0.389762	−	0.675088i	−0.992417	+	0.122914i	$0.960776\pi$
$908$	−4744.67	+	8218.00i	−0.173411	+	0.300357i
$909$		0			0
$910$	9435.42	−	3835.24i	0.343715	−	0.139711i
$911$			14634.3i			0.532225i	0.963942	+	0.266112i	$0.0857393\pi$
$911$			14634.3i			0.532225i	−0.963942	+	0.266112i	$0.914261\pi$
$912$		0			0
$913$	−20550.5	+	11864.8i	−0.744931	+	0.430086i
$914$	37811.3	−	21830.4i	1.36837	−	0.790027i
$915$		0			0
$916$		−	34618.2i		−	1.24871i
$917$	−23489.5	−	18272.6i	−0.845901	−	0.658032i
$918$		0			0
$919$	−6098.61	+	10563.1i	−0.218906	+	0.379156i	−0.954474	−	0.298295i	$-0.903582\pi$
$919$	−6098.61	+	10563.1i	−0.218906	+	0.379156i	0.735568	+	0.677451i	$0.236915\pi$
$920$	22386.5	+	38774.6i	0.802242	+	1.38952i
$921$		0			0
$922$	4023.98	+	2323.25i	0.143734	+	0.0829849i
$923$	707.119			0.0252168
$924$		0			0
$925$	3572.46			0.126986
$926$	50581.5	+	29203.2i	1.79504	+	1.03637i
$927$		0			0
$928$	1495.74	+	2590.70i	0.0529095	+	0.0916420i
$929$	−12348.1	+	21387.5i	−0.436091	+	0.755331i	−0.997384	−	0.0722858i	$-0.976971\pi$
$929$	−12348.1	+	21387.5i	−0.436091	+	0.755331i	0.561293	+	0.827617i	$0.310304\pi$
$930$		0			0
$931$	39209.6	+	40262.6i	1.38028	+	1.41735i
$932$			37383.2i			1.31387i
$933$		0			0
$934$	21341.3	−	12321.4i	0.747653	−	0.431658i
$935$	−41224.9	+	23801.2i	−1.44192	+	0.832495i
$936$		0			0
$937$			14448.0i			0.503730i	0.967762	+	0.251865i	$0.0810439\pi$
$937$			14448.0i			0.503730i	−0.967762	+	0.251865i	$0.918956\pi$
$938$	−14625.1	−	2024.09i	−0.509092	−	0.0704573i
$939$		0			0
$940$	5736.17	−	9935.33i	0.199035	−	0.344739i
$941$	15580.4	+	26986.0i	0.539752	+	0.934878i	0.998917	+	0.0465268i	$0.0148153\pi$
$941$	15580.4	+	26986.0i	0.539752	+	0.934878i	−0.459165	+	0.888351i	$0.651851\pi$
$942$		0			0
$943$	21105.9	+	12185.5i	0.728845	+	0.420799i
$944$	−12707.0			−0.438113
$945$		0			0
$946$	1320.14			0.0453715
$947$	−8887.48	−	5131.19i	−0.304968	−	0.176073i	0.339705	−	0.940532i	$-0.389673\pi$
$947$	−8887.48	−	5131.19i	−0.304968	−	0.176073i	−0.644672	+	0.764459i	$0.723006\pi$
$948$		0			0
$949$	−3407.28	−	5901.58i	−0.116549	−	0.201869i
$950$	−15118.0	+	26185.2i	−0.516310	+	0.894274i
$951$		0			0
$952$	17940.4	+	44136.6i	0.610767	+	1.50260i
$953$		−	12686.9i		−	0.431236i	−0.976478	−	0.215618i	$-0.930823\pi$
$953$		−	12686.9i		−	0.431236i	0.976478	−	0.215618i	$-0.0691766\pi$
$954$		0			0
$955$	−6072.91	+	3506.20i	−0.205775	+	0.118804i
$956$	−40960.7	+	23648.7i	−1.38574	+	0.800055i
$957$		0			0
$958$		−	74020.6i		−	2.49634i
$959$	−4954.83	−	12189.8i	−0.166840	−	0.410458i
$960$		0			0
$961$	−10007.0	+	17332.7i	−0.335908	+	0.581810i
$962$	2029.05	+	3514.43i	0.0680035	+	0.117785i
$963$		0			0
$964$	−34141.2	−	19711.4i	−1.14068	−	0.658571i
$965$	−8992.17			−0.299967
$966$		0			0
$967$	16129.8			0.536401			0.268200	−	0.963363i	$-0.413571\pi$
$967$	16129.8			0.536401			0.268200	+	0.963363i	$0.413571\pi$
$968$	51632.7	+	29810.1i	1.71440	+	0.989808i
$969$		0			0
$970$	42882.3	+	74274.4i	1.41945	+	2.45856i
$971$	−26382.4	+	45695.6i	−0.871937	+	1.51024i	−0.0119472	+	0.999929i	$0.503803\pi$
$971$	−26382.4	+	45695.6i	−0.871937	+	1.51024i	−0.859990	+	0.510311i	$0.829530\pi$
$972$		0			0
$973$	28103.5	+	3889.47i	0.925956	+	0.128151i
$974$		−	76930.8i		−	2.53082i
$975$		0			0
$976$	−20844.0	+	12034.3i	−0.683606	+	0.394680i
$977$	46759.5	−	26996.6i	1.53118	−	0.884030i	0.531877	−	0.846821i	$-0.321487\pi$
$977$	46759.5	−	26996.6i	1.53118	−	0.884030i	0.999308	−	0.0372085i	$-0.0118466\pi$
$978$		0			0
$979$			1387.91i			0.0453093i
$980$	66035.7	+	18635.4i	2.15248	+	0.607434i
$981$		0			0
$982$	−43944.7	+	76114.4i	−1.42804	+	2.47343i
$983$	26119.2	+	45239.8i	0.847480	+	1.46788i	0.883450	+	0.468526i	$0.155215\pi$
$983$	26119.2	+	45239.8i	0.847480	+	1.46788i	−0.0359696	+	0.999353i	$0.511452\pi$
$984$		0			0
$985$	−58784.4	−	33939.2i	−1.90155	−	1.09786i
$986$	−40109.7			−1.29549
$987$		0			0
$988$	−22739.0			−0.732211
$989$	−408.057	−	235.592i	−0.0131198	−	0.00757471i
$990$		0			0
$991$	4812.21	+	8334.99i	0.154253	+	0.267174i	0.932787	−	0.360429i	$-0.117370\pi$
$991$	4812.21	+	8334.99i	0.154253	+	0.267174i	−0.778534	+	0.627603i	$0.784036\pi$
$992$	1236.38	−	2141.48i	0.0395718	−	0.0685403i
$993$		0			0
$994$	5679.35	+	4418.01i	0.181226	+	0.140977i
$995$		−	31774.3i		−	1.01237i
$996$		0			0
$997$	−25023.0	+	14447.0i	−0.794871	+	0.458919i	−0.841675	−	0.539985i	$-0.818430\pi$
$997$	−25023.0	+	14447.0i	−0.794871	+	0.458919i	0.0468034	+	0.998904i	$0.485097\pi$
$998$	44346.2	−	25603.3i	1.40657	−	0.812082i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.4.p.a.26.8	yes	16
3.2	odd	2	inner	63.4.p.a.26.1	yes	16
4.3	odd	2		1008.4.bt.a.593.2		16
7.2	even	3		441.4.c.a.440.2		16
7.3	odd	6	inner	63.4.p.a.17.1	✓	16
7.4	even	3		441.4.p.c.80.1		16
7.5	odd	6		441.4.c.a.440.1		16
7.6	odd	2		441.4.p.c.215.8		16
12.11	even	2		1008.4.bt.a.593.7		16
21.2	odd	6		441.4.c.a.440.15		16
21.5	even	6		441.4.c.a.440.16		16
21.11	odd	6		441.4.p.c.80.8		16
21.17	even	6	inner	63.4.p.a.17.8	yes	16
21.20	even	2		441.4.p.c.215.1		16
28.3	even	6		1008.4.bt.a.17.7		16
84.59	odd	6		1008.4.bt.a.17.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.p.a.17.1	✓	16	7.3	odd	6	inner
63.4.p.a.17.8	yes	16	21.17	even	6	inner
63.4.p.a.26.1	yes	16	3.2	odd	2	inner
63.4.p.a.26.8	yes	16	1.1	even	1	trivial
441.4.c.a.440.1		16	7.5	odd	6
441.4.c.a.440.2		16	7.2	even	3
441.4.c.a.440.15		16	21.2	odd	6
441.4.c.a.440.16		16	21.5	even	6
441.4.p.c.80.1		16	7.4	even	3
441.4.p.c.80.8		16	21.11	odd	6
441.4.p.c.215.1		16	21.20	even	2
441.4.p.c.215.8		16	7.6	odd	2
1008.4.bt.a.17.2		16	84.59	odd	6
1008.4.bt.a.17.7		16	28.3	even	6
1008.4.bt.a.593.2		16	4.3	odd	2
1008.4.bt.a.593.7		16	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	63.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(4.21355 + 2.43270i) q^{2} +(7.83601 + 13.5724i) q^{4} +(-6.38217 + 11.0542i) q^{5} +(2.53897 - 18.3454i) q^{7} +37.3274i q^{8} +O(q^{10})\)	\(q+(4.21355 + 2.43270i) q^{2} +(7.83601 + 13.5724i) q^{4} +(-6.38217 + 11.0542i) q^{5} +(2.53897 - 18.3454i) q^{7} +37.3274i q^{8} +(-53.7832 + 31.0517i) q^{10} +(46.8633 - 27.0565i) q^{11} -8.85528i q^{13} +(55.3268 - 71.1228i) q^{14} +(-28.1181 + 48.7020i) q^{16} +(34.4587 + 59.6841i) q^{17} +(-141.898 - 81.9246i) q^{19} -200.043 q^{20} +263.281 q^{22} +(-81.3807 - 46.9852i) q^{23} +(-18.9642 - 32.8469i) q^{25} +(21.5422 - 37.3122i) q^{26} +(268.886 - 109.295i) q^{28} +119.620i q^{29} +(85.6311 - 49.4391i) q^{31} +(21.6577 - 12.5041i) q^{32} +335.310i q^{34} +(186.590 + 145.150i) q^{35} +(-47.0949 + 81.5708i) q^{37} +(-398.595 - 690.387i) q^{38} +(-412.626 - 238.230i) q^{40} -259.347 q^{41} +5.01418 q^{43} +(734.443 + 424.031i) q^{44} +(-228.601 - 395.949i) q^{46} +(-28.6747 + 49.6660i) q^{47} +(-330.107 - 93.1568i) q^{49} -184.536i q^{50} +(120.187 - 69.3901i) q^{52} +(-407.058 + 235.015i) q^{53} +690.718i q^{55} +(684.786 + 94.7731i) q^{56} +(-290.999 + 504.025i) q^{58} +(112.979 + 195.685i) q^{59} +(370.650 + 213.995i) q^{61} +481.082 q^{62} +571.564 q^{64} +(97.8884 + 56.5159i) q^{65} +(-81.9267 - 141.901i) q^{67} +(-540.037 + 935.372i) q^{68} +(433.103 + 1065.51i) q^{70} +79.8529i q^{71} +(666.447 - 384.774i) q^{73} +(-396.874 + 229.135i) q^{74} -2567.85i q^{76} +(-377.379 - 928.422i) q^{77} +(-267.408 + 463.165i) q^{79} +(-358.909 - 621.648i) q^{80} +(-1092.77 - 630.912i) q^{82} -438.520 q^{83} -879.684 q^{85} +(21.1275 + 12.1980i) q^{86} +(1009.95 + 1749.29i) q^{88} +(-12.8242 + 22.2121i) q^{89} +(-162.454 - 22.4833i) q^{91} -1472.71i q^{92} +(-241.644 + 139.513i) q^{94} +(1811.23 - 1045.71i) q^{95} -1381.00i q^{97} +(-1164.30 - 1195.57i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 32 q^{4} + 56 q^{7}+O(q^{10}) \) 16 * q + 32 * q^4 + 56 * q^7	\( 16 q + 32 q^{4} + 56 q^{7} - 72 q^{10} - 188 q^{16} - 612 q^{19} + 528 q^{22} - 20 q^{25} + 1036 q^{28} + 1128 q^{31} - 1196 q^{37} - 3204 q^{40} + 328 q^{43} - 1392 q^{46} + 784 q^{49} + 4452 q^{52} - 3372 q^{58} - 1632 q^{61} + 5432 q^{64} + 308 q^{67} + 3612 q^{70} + 4068 q^{73} - 2176 q^{79} - 10188 q^{82} - 4608 q^{85} + 708 q^{88} + 924 q^{91} - 2916 q^{94}+O(q^{100}) \) 16 * q + 32 * q^4 + 56 * q^7 - 72 * q^10 - 188 * q^16 - 612 * q^19 + 528 * q^22 - 20 * q^25 + 1036 * q^28 + 1128 * q^31 - 1196 * q^37 - 3204 * q^40 + 328 * q^43 - 1392 * q^46 + 784 * q^49 + 4452 * q^52 - 3372 * q^58 - 1632 * q^61 + 5432 * q^64 + 308 * q^67 + 3612 * q^70 + 4068 * q^73 - 2176 * q^79 - 10188 * q^82 - 4608 * q^85 + 708 * q^88 + 924 * q^91 - 2916 * q^94

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