LMFDB - Embedded newform 441.4.p.c.215.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,4,Mod(80,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, 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("441.80");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	441.p (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$26.0198423125$
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:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{8} $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			215.8
Root			$4.21355 + 2.43270i$ of defining polynomial
Character	$\chi$	$=$	441.215
Dual form			441.4.p.c.80.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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	$-0.639952\pi$
$5$	6.38217	−	11.0542i	0.570839	−	0.988721i	0.996480	−	0.0838295i	$-0.0267151\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$			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	$0.0301131\pi$
$13$			8.85528i			0.188924i	−0.995528	+	0.0944620i	$0.969887\pi$
$14$		0			0
$15$		0			0
$16$	−28.1181	+	48.7020i	−0.439345	+	0.760968i
$17$	−34.4587	−	59.6841i	−0.491615	−	0.851502i	0.508339	−	0.861157i	$-0.330260\pi$
$17$	−34.4587	−	59.6841i	−0.491615	−	0.851502i	−0.999953	+	0.00965543i	$0.996927\pi$
$18$		0			0
$19$	141.898	+	81.9246i	1.71334	+	0.989199i	0.929960	+	0.367660i	$0.119841\pi$
$19$	141.898	+	81.9246i	1.71334	+	0.989199i	0.783383	+	0.621540i	$0.213492\pi$
$20$	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
$28$		0			0
$29$			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	−0.727111	−	0.686520i	$-0.759137\pi$
$31$	−85.6311	+	49.4391i	−0.496123	+	0.286437i	0.230988	+	0.972957i	$0.425804\pi$
$32$	21.6577	−	12.5041i	0.119643	−	0.0690760i
$33$		0			0
$34$		−	335.310i		−	1.69133i
$35$		0			0
$36$		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	$-0.335556\pi$
$41$	259.347			0.987883			0.493941	+	0.869495i	$0.335556\pi$
$42$		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	−0.818093	−	0.575086i	$-0.804969\pi$
$47$	28.6747	−	49.6660i	0.0889921	−	0.154139i	0.907085	+	0.420947i	$0.138302\pi$
$48$		0			0
$49$		0			0
$50$		−	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
$56$		0			0
$57$		0			0
$58$	−290.999	+	504.025i	−0.658794	+	1.14106i
$59$	−112.979	−	195.685i	−0.249299	−	0.431798i	0.714033	−	0.700112i	$-0.246867\pi$
$59$	−112.979	−	195.685i	−0.249299	−	0.431798i	−0.963331	+	0.268314i	$0.913533\pi$
$60$		0			0
$61$	−370.650	−	213.995i	−0.777982	−	0.449168i	0.0577325	−	0.998332i	$-0.481613\pi$
$61$	−370.650	−	213.995i	−0.777982	−	0.449168i	−0.835715	+	0.549164i	$0.814946\pi$
$62$	−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
$70$		0			0
$71$			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	−0.927776	−	0.373138i	$-0.878282\pi$
$73$	−666.447	+	384.774i	−1.06852	+	0.616909i	−0.140741	+	0.990046i	$0.544949\pi$
$74$	−396.874	+	229.135i	−0.623454	+	0.359952i
$75$		0			0
$76$			2567.85i			3.87569i
$77$		0			0
$78$		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	$-0.406357\pi$
$83$	438.520			0.579926			0.289963	+	0.957038i	$0.406357\pi$
$84$		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	−0.858288	−	0.513169i	$-0.828471\pi$
$89$	12.8242	−	22.2121i	0.0152737	−	0.0264548i	0.873561	+	0.486714i	$0.161805\pi$
$90$		0			0
$91$		0			0
$92$		−	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	$0.257135\pi$
$97$			1381.00i			1.44555i	−0.691081	+	0.722777i	$0.742865\pi$
$98$		0			0
$99$		0			0
$100$	297.207	−	514.777i	0.297207	−	0.514777i
$101$	−356.808	−	618.009i	−0.351522	−	0.608854i	0.634994	−	0.772517i	$-0.281002\pi$
$101$	−356.808	−	618.009i	−0.351522	−	0.608854i	−0.986516	+	0.163663i	$0.947669\pi$
$102$		0			0
$103$	−1552.42	−	896.288i	−1.48509	−	0.857416i	−0.485232	−	0.874385i	$-0.661265\pi$
$103$	−1552.42	−	896.288i	−1.48509	−	0.857416i	−0.999856	+	0.0169695i	$0.994598\pi$
$104$	−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
$112$		0			0
$113$		−	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
$119$		0			0
$120$		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	$0.346677\pi$
$131$	−803.439	+	1391.60i	−0.535853	+	0.928125i	−0.999122	+	0.0419070i	$0.986657\pi$
$132$		0			0
$133$		0			0
$134$		−	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	$-0.845194\pi$
$139$		−	1531.91i		−	0.934782i	0.884051	−	0.467391i	$-0.154806\pi$
$140$		0			0
$141$		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
$154$		0			0
$155$			1262.12i			0.654036i
$156$		0			0
$157$	−2109.74	+	1218.06i	−1.07246	+	0.619184i	−0.928852	−	0.370451i	$-0.879203\pi$
$157$	−2109.74	+	1218.06i	−1.07246	+	0.619184i	−0.143606	+	0.989635i	$0.545870\pi$
$158$	−2253.48	+	1301.05i	−1.13466	+	0.655099i
$159$		0			0
$160$		−	319.213i		−	0.157725i
$161$		0			0
$162$		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	$-0.526993\pi$
$167$	−365.585			−0.169400			−0.0847000	+	0.996406i	$0.526993\pi$
$168$		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	−0.539062	−	0.842266i	$-0.681221\pi$
$173$	1046.47	−	1812.53i	0.459892	−	0.796557i	0.998955	+	0.0457089i	$0.0145547\pi$
$174$		0			0
$175$		0			0
$176$			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	$-0.772015\pi$
$181$		−	3197.54i		−	1.31310i	0.754282	−	0.656551i	$-0.227985\pi$
$182$		0			0
$183$		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
$196$		0			0
$197$			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	−0.0641982	−	0.997937i	$-0.520449\pi$
$199$	2155.80	−	1244.65i	0.767942	−	0.443371i	0.832140	+	0.554566i	$0.187116\pi$
$200$	1226.09	−	707.883i	0.433488	−	0.250274i
$201$		0			0
$202$		−	3472.02i		−	1.20936i
$203$		0			0
$204$		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
$217$		0			0
$218$		−	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	$0.198915\pi$
$223$			3896.38i			1.17005i	−0.811016	+	0.585024i	$0.801085\pi$
$224$		0			0
$225$		0			0
$226$	292.277	−	506.238i	0.0860263	−	0.149002i
$227$	−302.747	−	524.374i	−0.0885201	−	0.153321i	0.818366	−	0.574698i	$-0.194880\pi$
$227$	−302.747	−	524.374i	−0.0885201	−	0.153321i	−0.906886	+	0.421377i	$0.861547\pi$
$228$		0			0
$229$	1912.98	+	1104.46i	0.552023	+	0.318711i	0.749938	−	0.661509i	$-0.230083\pi$
$229$	1912.98	+	1104.46i	0.552023	+	0.318711i	−0.197914	+	0.980219i	$0.563417\pi$
$230$	−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
$238$		0			0
$239$			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	−0.179762	−	0.983710i	$-0.557533\pi$
$241$	2178.48	−	1257.75i	0.582275	−	0.336176i	0.762037	+	0.647534i	$0.224200\pi$
$242$	6729.99	−	3885.56i	1.78769	−	1.03212i
$243$		0			0
$244$		−	6707.47i		−	1.75984i
$245$		0			0
$246$		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	$-0.552512\pi$
$251$	−1306.11			−0.328451			−0.164226	+	0.986423i	$0.552512\pi$
$252$		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	$0.528126\pi$
$257$	−3735.91	+	6470.79i	−0.906770	+	1.57057i	−0.818524	+	0.574473i	$0.805207\pi$
$258$		0			0
$259$		0			0
$260$			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
$266$		0			0
$267$		0			0
$268$	1283.96	−	2223.88i	0.292650	−	0.506884i
$269$	−1958.09	−	3391.52i	−0.443818	−	0.768715i	0.554151	−	0.832416i	$-0.313043\pi$
$269$	−1958.09	−	3391.52i	−0.443818	−	0.768715i	−0.997969	+	0.0637010i	$0.979710\pi$
$270$		0			0
$271$	−3117.42	−	1799.84i	−0.698780	−	0.403441i	0.108113	−	0.994139i	$-0.465519\pi$
$271$	−3117.42	−	1799.84i	−0.698780	−	0.403441i	−0.806893	+	0.590698i	$0.798853\pi$
$272$	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
$280$		0			0
$281$		−	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	−0.968579	−	0.248707i	$-0.919994\pi$
$283$	−5891.40	+	3401.40i	−1.23748	+	0.714460i	−0.268903	+	0.963167i	$0.586661\pi$
$284$	−1083.79	+	625.728i	−0.226448	+	0.130740i
$285$		0			0
$286$			2331.43i			0.482029i
$287$		0			0
$288$		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	$-0.602686\pi$
$293$	−3180.05			−0.634063			−0.317031	+	0.948415i	$0.602686\pi$
$294$		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
$301$		0			0
$302$		−	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	$0.0892289\pi$
$307$			2976.39i			0.553328i	−0.960967	+	0.276664i	$0.910771\pi$
$308$		0			0
$309$		0			0
$310$	−3070.34	+	5317.99i	−0.562528	+	0.974328i
$311$	2340.89	+	4054.55i	0.426817	+	0.739268i	0.996588	−	0.0825352i	$-0.0263017\pi$
$311$	2340.89	+	4054.55i	0.426817	+	0.739268i	−0.569772	+	0.821803i	$0.692968\pi$
$312$		0			0
$313$	850.477	+	491.023i	0.153584	+	0.0886718i	0.574823	−	0.818278i	$-0.305071\pi$
$313$	850.477	+	491.023i	0.153584	+	0.0886718i	−0.421238	+	0.906950i	$0.638404\pi$
$314$	−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
$322$		0			0
$323$		−	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
$329$		0			0
$330$		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
$343$		0			0
$344$			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	$-0.967437\pi$
$349$		−	1331.65i		−	0.204245i	0.994772	−	0.102122i	$-0.0325634\pi$
$350$		0			0
$351$		0			0
$352$	676.635	−	1171.97i	0.102457	−	0.177460i
$353$	5674.26	+	9828.10i	0.855553	+	1.48186i	0.876131	+	0.482073i	$0.160116\pi$
$353$	5674.26	+	9828.10i	0.855553	+	1.48186i	−0.0205782	+	0.999788i	$0.506551\pi$
$354$		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
$364$		0			0
$365$			9822.76i			1.40862i
$366$		0			0
$367$	−2351.31	+	1357.53i	−0.334434	+	0.193086i	−0.657808	−	0.753186i	$-0.728516\pi$
$367$	−2351.31	+	1357.53i	−0.334434	+	0.193086i	0.323374	+	0.946271i	$0.395183\pi$
$368$	4576.54	−	2642.27i	0.648285	−	0.374287i
$369$		0			0
$370$			5849.52i			0.821897i
$371$		0			0
$372$		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	−0.822497	−	0.568769i	$-0.807420\pi$
$383$	609.532	−	1055.74i	0.0813202	−	0.140851i	0.903817	+	0.427919i	$0.140753\pi$
$384$		0			0
$385$		0			0
$386$			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
$392$		0			0
$393$		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	0.319692	−	0.947522i	$-0.396421\pi$
$397$	−2697.68	−	1557.51i	−0.341040	−	0.196900i	−0.660732	+	0.750622i	$0.729754\pi$
$398$	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
$406$		0			0
$407$			5096.90i			0.620747i
$408$		0			0
$409$	10739.4	−	6200.41i	1.29836	−	0.749610i	0.318242	−	0.948010i	$-0.396908\pi$
$409$	10739.4	−	6200.41i	1.29836	−	0.749610i	0.980121	+	0.198399i	$0.0635743\pi$
$410$	13948.5	−	8053.18i	1.68017	−	0.970044i
$411$		0			0
$412$		−	28093.3i		−	3.35936i
$413$		0			0
$414$		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	$-0.340075\pi$
$419$	8260.19			0.963095			0.481547	+	0.876420i	$0.340075\pi$
$420$		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
$427$		0			0
$428$			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	$0.170805\pi$
$433$			9212.26i			1.02243i	−0.859452	+	0.511216i	$0.829195\pi$
$434$		0			0
$435$		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	0.842971	−	0.537959i	$-0.180805\pi$
$439$	7345.30	+	4240.81i	0.798570	+	0.461054i	−0.0444012	+	0.999014i	$0.514138\pi$
$440$	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
$448$		0			0
$449$		−	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
$455$		0			0
$456$		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	$-0.515362\pi$
$461$	−955.010			−0.0964842			−0.0482421	+	0.998836i	$0.515362\pi$
$462$		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	−0.963784	−	0.266683i	$-0.914072\pi$
$467$	−2532.46	+	4386.34i	−0.250938	+	0.434638i	0.712846	+	0.701320i	$0.247406\pi$
$468$		0			0
$469$		0			0
$470$		−	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
$476$		0			0
$477$		0			0
$478$	−7341.75	+	12716.3i	−0.702518	+	1.21680i
$479$	7606.85	+	13175.5i	0.725607	+	1.25679i	0.958724	+	0.284340i	$0.0917744\pi$
$479$	7606.85	+	13175.5i	0.725607	+	1.25679i	−0.233116	+	0.972449i	$0.574892\pi$
$480$		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
$490$		0			0
$491$			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
$497$		0			0
$498$		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	$-0.612224\pi$
$503$	−7790.82			−0.690607			−0.345304	+	0.938491i	$0.612224\pi$
$504$		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	−0.554019	−	0.832504i	$-0.686907\pi$
$509$	5098.24	−	8830.41i	0.443960	−	0.768961i	0.997979	+	0.0635430i	$0.0202400\pi$
$510$		0			0
$511$		0			0
$512$			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
$518$		0			0
$519$		0			0
$520$	−2109.59	+	3653.92i	−0.177907	+	0.308144i
$521$	963.789	+	1669.33i	0.0810449	+	0.140374i	0.903699	−	0.428168i	$-0.140841\pi$
$521$	963.789	+	1669.33i	0.0810449	+	0.140374i	−0.822654	+	0.568542i	$0.807508\pi$
$522$		0			0
$523$	6716.70	+	3877.89i	0.561569	+	0.324222i	0.753775	−	0.657133i	$-0.228231\pi$
$523$	6716.70	+	3877.89i	0.561569	+	0.324222i	−0.192206	+	0.981355i	$0.561564\pi$
$524$	−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
$532$		0			0
$533$			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
$539$		0			0
$540$		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
$553$		0			0
$554$		−	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
$560$		0			0
$561$		0			0
$562$	781.517	−	1353.63i	0.0586589	−	0.101600i
$563$	4795.36	+	8305.80i	0.358970	+	0.621755i	0.987789	−	0.155797i	$-0.0497946\pi$
$563$	4795.36	+	8305.80i	0.358970	+	0.621755i	−0.628819	+	0.777552i	$0.716461\pi$
$564$		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
$574$		0			0
$575$			3564.14i			0.258495i
$576$		0			0
$577$	−8431.94	+	4868.18i	−0.608364	+	0.351239i	−0.772325	−	0.635228i	$-0.780906\pi$
$577$	−8431.94	+	4868.18i	−0.608364	+	0.351239i	0.163961	+	0.986467i	$0.447573\pi$
$578$	688.509	−	397.511i	0.0495470	−	0.0286060i
$579$		0			0
$580$			23929.1i			1.71311i
$581$		0			0
$582$		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	$-0.374330\pi$
$587$	10940.3			0.769255			0.384628	+	0.923072i	$0.374330\pi$
$588$		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	$-0.503298\pi$
$593$	12430.4	−	21530.0i	0.860799	−	1.49095i	0.871159	−	0.491000i	$-0.163369\pi$
$594$		0			0
$595$		0			0
$596$		−	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	$0.145584\pi$
$601$			13012.4i			0.883175i	−0.897218	+	0.441587i	$0.854416\pi$
$602$		0			0
$603$		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	0.233486	−	0.972360i	$-0.424987\pi$
$607$	−7355.69	−	4246.81i	−0.491859	−	0.283975i	−0.725345	+	0.688385i	$0.758320\pi$
$608$	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
$616$		0			0
$617$		−	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	−0.978790	−	0.204864i	$-0.934325\pi$
$619$	−19878.5	+	11476.9i	−1.29077	+	0.745225i	−0.311978	+	0.950089i	$0.600991\pi$
$620$	−17129.9	+	9889.96i	−1.10960	+	0.640629i
$621$		0			0
$622$			22778.7i			1.46840i
$623$		0			0
$624$		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
$637$		0			0
$638$			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	$-0.715009\pi$
$643$		−	25449.0i		−	1.56082i	0.625266	−	0.780412i	$-0.284991\pi$
$644$		0			0
$645$		0			0
$646$	27470.1	−	47579.6i	1.67306	−	2.89782i
$647$	−13149.2	−	22775.1i	−0.798993	−	1.38390i	−0.920273	−	0.391277i	$-0.872033\pi$
$647$	−13149.2	−	22775.1i	−0.798993	−	1.38390i	0.121280	−	0.992618i	$-0.461300\pi$
$648$		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
$658$		0			0
$659$		−	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	0.215153	−	0.976580i	$-0.430975\pi$
$661$	19857.3	−	11464.6i	1.16847	−	0.674618i	0.953320	+	0.301962i	$0.0976415\pi$
$662$	16999.6	−	9814.73i	0.998049	−	0.576224i
$663$		0			0
$664$			16368.8i			0.956677i
$665$		0			0
$666$		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	−0.537839	−	0.843048i	$-0.680759\pi$
$677$	8123.71	−	14070.7i	0.461181	−	0.798789i	0.999020	+	0.0442583i	$0.0140925\pi$
$678$		0			0
$679$		0			0
$680$		−	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
$686$		0			0
$687$		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	0.929144	−	0.369718i	$-0.120546\pi$
$691$	19499.9	+	11258.3i	1.07353	+	0.619803i	0.144387	+	0.989521i	$0.453879\pi$
$692$	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
$700$		0			0
$701$		−	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
$707$		0			0
$708$		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	−0.630429	−	0.776247i	$-0.717121\pi$
$719$	6883.43	−	11922.4i	0.357036	−	0.618404i	0.987464	+	0.157844i	$0.0504542\pi$
$720$		0			0
$721$		0			0
$722$			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	$-0.899049\pi$
$727$		−	12226.1i		−	0.623717i	0.950129	−	0.311858i	$-0.100951\pi$
$728$		0			0
$729$		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	0.442062	−	0.896984i	$-0.354247\pi$
$733$	−2256.76	−	1302.94i	−0.113718	−	0.0656553i	−0.555780	+	0.831329i	$0.687580\pi$
$734$	−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
$742$		0			0
$743$		−	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
$749$		0			0
$750$		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	−0.973937	−	0.226820i	$-0.927167\pi$
$761$	−6099.27	+	10564.2i	−0.290537	+	0.503224i	0.683400	+	0.730044i	$0.260500\pi$
$762$		0			0
$763$		0			0
$764$			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	$-0.984970\pi$
$769$		−	2013.08i		−	0.0943999i	0.998885	−	0.0471999i	$-0.0150298\pi$
$770$		0			0
$771$		0			0
$772$	−5520.28	+	9561.41i	−0.257357	+	0.445755i
$773$	−15139.1	−	26221.7i	−0.704418	−	1.22009i	−0.966901	−	0.255152i	$-0.917875\pi$
$773$	−15139.1	−	26221.7i	−0.704418	−	1.22009i	0.262483	−	0.964937i	$-0.415459\pi$
$774$		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
$784$		0			0
$785$			31095.5i			1.41382i
$786$		0			0
$787$	−24839.3	+	14341.0i	−1.12507	+	0.649557i	−0.942689	−	0.333671i	$-0.891712\pi$
$787$	−24839.3	+	14341.0i	−1.12507	+	0.649557i	−0.182377	+	0.983229i	$0.558379\pi$
$788$	−72175.3	+	41670.4i	−3.26287	+	1.88382i
$789$		0			0
$790$			33214.0i			1.49582i
$791$		0			0
$792$		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	$-0.294206\pi$
$797$	27108.9			1.20483			0.602413	+	0.798184i	$0.294206\pi$
$798$		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
$805$		0			0
$806$		−	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	$-0.587516\pi$
$811$		−	44456.6i		−	1.92488i	0.271487	−	0.962442i	$-0.412484\pi$
$812$		0			0
$813$		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
$826$		0			0
$827$		−	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	−0.232932	−	0.972493i	$-0.574832\pi$
$829$	11762.7	−	6791.21i	0.492806	−	0.284521i	0.725738	+	0.687972i	$0.241499\pi$
$830$	23585.0	−	13616.8i	0.986323	−	0.569454i
$831$		0			0
$832$			5061.36i			0.210903i
$833$		0			0
$834$		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	$-0.576868\pi$
$839$	−11623.6			−0.478297			−0.239149	+	0.970983i	$0.576868\pi$
$840$		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
$847$		0			0
$848$		−	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	$0.00651553\pi$
$853$			1019.82i			0.0409354i	−0.999791	+	0.0204677i	$0.993484\pi$
$854$		0			0
$855$		0			0
$856$	−421.032	+	729.249i	−0.0168114	+	0.0291182i
$857$	−4299.43	−	7446.83i	−0.171372	−	0.296825i	0.767528	−	0.641016i	$-0.221487\pi$
$857$	−4299.43	−	7446.83i	−0.171372	−	0.296825i	−0.938900	+	0.344191i	$0.888153\pi$
$858$		0			0
$859$	−32182.1	−	18580.4i	−1.27828	−	0.738013i	−0.301745	−	0.953389i	$-0.597569\pi$
$859$	−32182.1	−	18580.4i	−1.27828	−	0.738013i	−0.976531	+	0.215375i	$0.930903\pi$
$860$	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
$868$		0			0
$869$			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
$875$		0			0
$876$		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	$-0.309771\pi$
$881$	29427.6			1.12536			0.562679	+	0.826676i	$0.309771\pi$
$882$		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	−0.781765	−	0.623574i	$-0.785680\pi$
$887$	3940.07	−	6824.39i	0.149148	−	0.258332i	0.930913	+	0.365241i	$0.119014\pi$
$888$		0			0
$889$		0			0
$890$		−	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
$896$		0			0
$897$		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
$910$		0			0
$911$			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
$917$		0			0
$918$		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	−0.561293	−	0.827617i	$-0.689696\pi$
$929$	12348.1	−	21387.5i	0.436091	−	0.755331i	0.997384	+	0.0722858i	$0.0230294\pi$
$930$		0			0
$931$		0			0
$932$			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	$-0.918956\pi$
$937$		−	14448.0i		−	0.503730i	0.967762	−	0.251865i	$-0.0810439\pi$
$938$		0			0
$939$		0			0
$940$	5736.17	−	9935.33i	0.199035	−	0.344739i
$941$	−15580.4	−	26986.0i	−0.539752	−	0.934878i	−0.998917	−	0.0465268i	$-0.985185\pi$
$941$	−15580.4	−	26986.0i	−0.539752	−	0.934878i	0.459165	−	0.888351i	$-0.348149\pi$
$942$		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
$952$		0			0
$953$		−	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
$959$		0			0
$960$		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	$-0.496197\pi$
$971$	26382.4	−	45695.6i	0.871937	−	1.51024i	0.859990	−	0.510311i	$-0.170470\pi$
$972$		0			0
$973$		0			0
$974$		−	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
$980$		0			0
$981$		0			0
$982$	−43944.7	+	76114.4i	−1.42804	+	2.47343i
$983$	−26119.2	−	45239.8i	−0.847480	−	1.46788i	−0.883450	−	0.468526i	$-0.844785\pi$
$983$	−26119.2	−	45239.8i	−0.847480	−	1.46788i	0.0359696	−	0.999353i	$-0.488548\pi$
$984$		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
$994$		0			0
$995$		−	31774.3i		−	1.01237i
$996$		0			0
$997$	25023.0	−	14447.0i	0.794871	−	0.458919i	−0.0468034	−	0.998904i	$-0.514903\pi$
$997$	25023.0	−	14447.0i	0.794871	−	0.458919i	0.841675	+	0.539985i	$0.181570\pi$
$998$	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	441.4.p.c.215.8		16
3.2	odd	2	inner	441.4.p.c.215.1		16
7.2	even	3		441.4.c.a.440.1		16
7.3	odd	6	inner	441.4.p.c.80.1		16
7.4	even	3		63.4.p.a.17.1	✓	16
7.5	odd	6		441.4.c.a.440.2		16
7.6	odd	2		63.4.p.a.26.8	yes	16
21.2	odd	6		441.4.c.a.440.16		16
21.5	even	6		441.4.c.a.440.15		16
21.11	odd	6		63.4.p.a.17.8	yes	16
21.17	even	6	inner	441.4.p.c.80.8		16
21.20	even	2		63.4.p.a.26.1	yes	16
28.11	odd	6		1008.4.bt.a.17.7		16
28.27	even	2		1008.4.bt.a.593.2		16
84.11	even	6		1008.4.bt.a.17.2		16
84.83	odd	2		1008.4.bt.a.593.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.p.a.17.1	✓	16	7.4	even	3
63.4.p.a.17.8	yes	16	21.11	odd	6
63.4.p.a.26.1	yes	16	21.20	even	2
63.4.p.a.26.8	yes	16	7.6	odd	2
441.4.c.a.440.1		16	7.2	even	3
441.4.c.a.440.2		16	7.5	odd	6
441.4.c.a.440.15		16	21.5	even	6
441.4.c.a.440.16		16	21.2	odd	6
441.4.p.c.80.1		16	7.3	odd	6	inner
441.4.p.c.80.8		16	21.17	even	6	inner
441.4.p.c.215.1		16	3.2	odd	2	inner
441.4.p.c.215.8		16	1.1	even	1	trivial
1008.4.bt.a.17.2		16	84.11	even	6
1008.4.bt.a.17.7		16	28.11	odd	6
1008.4.bt.a.593.2		16	28.27	even	2
1008.4.bt.a.593.7		16	84.83	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	441.p (of order \(6\), degree \(2\), not minimal)

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

Introduction

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