LMFDB - Embedded newform 216.3.j.a.125.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,3,Mod(125,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("216.125");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	216.j (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:	$5.88557371018$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 72)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			125.9
Character	$\chi$	$=$	216.125
Dual form			216.3.j.a.197.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.676143 + 1.88224i) q^{2} +(-3.08566 - 2.54533i) q^{4} +(-4.28090 + 7.41474i) q^{5} +(-3.75800 - 6.50904i) q^{7} +(6.87727 - 4.08695i) q^{8} +O(q^{10})$	\(q+(-0.676143 + 1.88224i) q^{2} +(-3.08566 - 2.54533i) q^{4} +(-4.28090 + 7.41474i) q^{5} +(-3.75800 - 6.50904i) q^{7} +(6.87727 - 4.08695i) q^{8} +(-11.0618 - 13.0711i) q^{10} +(-4.74705 - 8.22213i) q^{11} +(9.54725 + 5.51211i) q^{13} +(14.7925 - 2.67241i) q^{14} +(3.04261 + 15.7080i) q^{16} -11.3516i q^{17} -18.3798i q^{19} +(32.0824 - 11.9831i) q^{20} +(18.6857 - 3.37575i) q^{22} +(-22.8408 - 13.1871i) q^{23} +(-24.1522 - 41.8329i) q^{25} +(-16.8304 + 14.2433i) q^{26} +(-4.97174 + 29.6500i) q^{28} +(3.48316 + 6.03301i) q^{29} +(6.42393 - 11.1266i) q^{31} +(-31.6236 - 4.89396i) q^{32} +(21.3664 + 7.67530i) q^{34} +64.3505 q^{35} +5.89614i q^{37} +(34.5953 + 12.4274i) q^{38} +(0.862760 + 68.4890i) q^{40} +(-32.7049 - 18.8822i) q^{41} +(-21.1756 + 12.2257i) q^{43} +(-6.28023 + 37.4535i) q^{44} +(40.2650 - 34.0754i) q^{46} +(15.8834 - 9.17030i) q^{47} +(-3.74509 + 6.48669i) q^{49} +(95.0700 - 17.1753i) q^{50} +(-15.4295 - 41.3094i) q^{52} -58.4847 q^{53} +81.2866 q^{55} +(-52.4469 - 29.4057i) q^{56} +(-13.7107 + 2.47697i) q^{58} +(-13.1643 + 22.8013i) q^{59} +(-56.0654 + 32.3694i) q^{61} +(16.5994 + 19.6145i) q^{62} +(30.5937 - 56.2141i) q^{64} +(-81.7417 + 47.1936i) q^{65} +(-28.4707 - 16.4376i) q^{67} +(-28.8935 + 35.0271i) q^{68} +(-43.5101 + 121.123i) q^{70} +84.5841i q^{71} -94.1083 q^{73} +(-11.0980 - 3.98664i) q^{74} +(-46.7827 + 56.7139i) q^{76} +(-35.6788 + 61.7975i) q^{77} +(-12.3221 - 21.3425i) q^{79} +(-129.496 - 44.6844i) q^{80} +(57.6540 - 48.7914i) q^{82} +(-57.7838 - 100.085i) q^{83} +(84.1691 + 48.5950i) q^{85} +(-8.69405 - 48.1239i) q^{86} +(-66.2502 - 37.1448i) q^{88} -131.872i q^{89} -82.8580i q^{91} +(36.9133 + 98.8282i) q^{92} +(6.52124 + 36.0969i) q^{94} +(136.282 + 78.6822i) q^{95} +(94.1484 + 163.070i) q^{97} +(-9.67730 - 11.4351i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 3 q^{2} - q^{4} - 2 q^{7}+O(q^{10}) $ 44 * q + 3 * q^2 - q^4 - 2 * q^7	$ 44 q + 3 q^{2} - q^{4} - 2 q^{7} + 4 q^{10} + 48 q^{14} - q^{16} + 66 q^{20} + 7 q^{22} + 6 q^{23} - 72 q^{25} + 28 q^{28} - 2 q^{31} + 93 q^{32} + 9 q^{34} - 99 q^{38} - 56 q^{40} - 66 q^{41} + 72 q^{46} + 6 q^{47} - 72 q^{49} - 189 q^{50} - 42 q^{52} + 92 q^{55} - 270 q^{56} - 38 q^{58} + 2 q^{64} + 6 q^{65} - 387 q^{68} - 4 q^{70} - 8 q^{73} + 432 q^{74} - 63 q^{76} - 2 q^{79} + 186 q^{82} + 615 q^{86} - 77 q^{88} + 624 q^{92} - 186 q^{94} - 144 q^{95} - 2 q^{97}+O(q^{100}) $ 44 * q + 3 * q^2 - q^4 - 2 * q^7 + 4 * q^10 + 48 * q^14 - q^16 + 66 * q^20 + 7 * q^22 + 6 * q^23 - 72 * q^25 + 28 * q^28 - 2 * q^31 + 93 * q^32 + 9 * q^34 - 99 * q^38 - 56 * q^40 - 66 * q^41 + 72 * q^46 + 6 * q^47 - 72 * q^49 - 189 * q^50 - 42 * q^52 + 92 * q^55 - 270 * q^56 - 38 * q^58 + 2 * q^64 + 6 * q^65 - 387 * q^68 - 4 * q^70 - 8 * q^73 + 432 * q^74 - 63 * q^76 - 2 * q^79 + 186 * q^82 + 615 * q^86 - 77 * q^88 + 624 * q^92 - 186 * q^94 - 144 * q^95 - 2 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.676143	+	1.88224i	−0.338072	+	0.941120i
$2$	−0.676143	+	1.88224i	−0.338072	+	0.941120i
$3$		0			0
$3$		0			0
$4$	−3.08566	−	2.54533i	−0.771415	−	0.636332i
$5$	−4.28090	+	7.41474i	−0.856180	+	1.48295i	0.0193654	+	0.999812i	$0.493835\pi$
$5$	−4.28090	+	7.41474i	−0.856180	+	1.48295i	−0.875546	+	0.483135i	$0.839498\pi$
$6$		0			0
$7$	−3.75800	−	6.50904i	−0.536857	−	0.929863i	−0.999071	−	0.0430950i	$-0.986278\pi$
$7$	−3.75800	−	6.50904i	−0.536857	−	0.929863i	0.462214	−	0.886768i	$-0.347055\pi$
$8$	6.87727	−	4.08695i	0.859659	−	0.510869i
$9$		0			0
$10$	−11.0618	−	13.0711i	−1.10618	−	1.30711i
$11$	−4.74705	−	8.22213i	−0.431550	−	0.747466i	0.565457	−	0.824778i	$-0.308700\pi$
$11$	−4.74705	−	8.22213i	−0.431550	−	0.747466i	−0.997007	+	0.0773115i	$0.975366\pi$
$12$		0			0
$13$	9.54725	+	5.51211i	0.734404	+	0.424008i	0.820031	−	0.572319i	$-0.193956\pi$
$13$	9.54725	+	5.51211i	0.734404	+	0.424008i	−0.0856271	+	0.996327i	$0.527289\pi$
$14$	14.7925	−	2.67241i	1.05661	−	0.190887i
$15$		0			0
$16$	3.04261	+	15.7080i	0.190163	+	0.981753i
$17$		−	11.3516i		−	0.667740i	−0.942619	−	0.333870i	$-0.891645\pi$
$17$		−	11.3516i		−	0.667740i	0.942619	−	0.333870i	$-0.108355\pi$
$18$		0			0
$19$		−	18.3798i		−	0.967359i	−0.875245	−	0.483680i	$-0.839300\pi$
$19$		−	18.3798i		−	0.967359i	0.875245	−	0.483680i	$-0.160700\pi$
$20$	32.0824	−	11.9831i	1.60412	−	0.599154i
$21$		0			0
$22$	18.6857	−	3.37575i	0.849350	−	0.153443i
$23$	−22.8408	−	13.1871i	−0.993077	−	0.573353i	−0.0868842	−	0.996218i	$-0.527691\pi$
$23$	−22.8408	−	13.1871i	−0.993077	−	0.573353i	−0.906193	+	0.422865i	$0.861024\pi$
$24$		0			0
$25$	−24.1522	−	41.8329i	−0.966090	−	1.67332i
$26$	−16.8304	+	14.2433i	−0.647324	+	0.547817i
$27$		0			0
$28$	−4.97174	+	29.6500i	−0.177562	+	1.05893i
$29$	3.48316	+	6.03301i	0.120109	+	0.208035i	0.919810	−	0.392363i	$-0.128342\pi$
$29$	3.48316	+	6.03301i	0.120109	+	0.208035i	−0.799701	+	0.600398i	$0.795009\pi$
$30$		0			0
$31$	6.42393	−	11.1266i	0.207224	−	0.358922i	−0.743615	−	0.668608i	$-0.766891\pi$
$31$	6.42393	−	11.1266i	0.207224	−	0.358922i	0.950839	+	0.309686i	$0.100224\pi$
$32$	−31.6236	−	4.89396i	−0.988236	−	0.152936i
$33$		0			0
$34$	21.3664	+	7.67530i	0.628424	+	0.225744i
$35$	64.3505			1.83859
$36$		0			0
$37$			5.89614i			0.159355i	0.996821	+	0.0796776i	$0.0253891\pi$
$37$			5.89614i			0.159355i	−0.996821	+	0.0796776i	$0.974611\pi$
$38$	34.5953	+	12.4274i	0.910401	+	0.327037i
$39$		0			0
$40$	0.862760	+	68.4890i	0.0215690	+	1.71222i
$41$	−32.7049	−	18.8822i	−0.797681	−	0.460541i	0.0449789	−	0.998988i	$-0.485678\pi$
$41$	−32.7049	−	18.8822i	−0.797681	−	0.460541i	−0.842659	+	0.538447i	$0.819011\pi$
$42$		0			0
$43$	−21.1756	+	12.2257i	−0.492456	+	0.284320i	−0.725593	−	0.688124i	$-0.758434\pi$
$43$	−21.1756	+	12.2257i	−0.492456	+	0.284320i	0.233137	+	0.972444i	$0.425101\pi$
$44$	−6.28023	+	37.4535i	−0.142733	+	0.851216i
$45$		0			0
$46$	40.2650	−	34.0754i	0.875325	−	0.740770i
$47$	15.8834	−	9.17030i	0.337945	−	0.195113i	−0.321418	−	0.946937i	$-0.604159\pi$
$47$	15.8834	−	9.17030i	0.337945	−	0.195113i	0.659363	+	0.751825i	$0.270826\pi$
$48$		0			0
$49$	−3.74509	+	6.48669i	−0.0764305	+	0.132382i
$50$	95.0700	−	17.1753i	1.90140	−	0.343506i
$51$		0			0
$52$	−15.4295	−	41.3094i	−0.296720	−	0.794411i
$53$	−58.4847			−1.10348			−0.551742	−	0.834015i	$-0.686037\pi$
$53$	−58.4847			−1.10348			−0.551742	+	0.834015i	$0.686037\pi$
$54$		0			0
$55$	81.2866			1.47794
$56$	−52.4469	−	29.4057i	−0.936552	−	0.525102i
$57$		0			0
$58$	−13.7107	+	2.47697i	−0.236391	+	0.0427064i
$59$	−13.1643	+	22.8013i	−0.223124	+	0.386462i	−0.955755	−	0.294164i	$-0.904959\pi$
$59$	−13.1643	+	22.8013i	−0.223124	+	0.386462i	0.732631	+	0.680626i	$0.238292\pi$
$60$		0			0
$61$	−56.0654	+	32.3694i	−0.919104	+	0.530645i	−0.883349	−	0.468715i	$-0.844717\pi$
$61$	−56.0654	+	32.3694i	−0.919104	+	0.530645i	−0.0357552	+	0.999361i	$0.511384\pi$
$62$	16.5994	+	19.6145i	0.267732	+	0.316364i
$63$		0			0
$64$	30.5937	−	56.2141i	0.478026	−	0.878346i
$65$	−81.7417	+	47.1936i	−1.25756	+	0.726055i
$66$		0			0
$67$	−28.4707	−	16.4376i	−0.424936	−	0.245337i	0.272251	−	0.962226i	$-0.412232\pi$
$67$	−28.4707	−	16.4376i	−0.424936	−	0.245337i	−0.697187	+	0.716889i	$0.745565\pi$
$68$	−28.8935	+	35.0271i	−0.424905	+	0.515105i
$69$		0			0
$70$	−43.5101	+	121.123i	−0.621573	+	1.73033i
$71$			84.5841i			1.19132i	0.803235	+	0.595662i	$0.203110\pi$
$71$			84.5841i			1.19132i	−0.803235	+	0.595662i	$0.796890\pi$
$72$		0			0
$73$	−94.1083			−1.28915			−0.644577	−	0.764539i	$-0.722967\pi$
$73$	−94.1083			−1.28915			−0.644577	+	0.764539i	$0.722967\pi$
$74$	−11.0980	−	3.98664i	−0.149972	−	0.0538735i
$75$		0			0
$76$	−46.7827	+	56.7139i	−0.615562	+	0.746236i
$77$	−35.6788	+	61.7975i	−0.463361	+	0.802565i
$78$		0			0
$79$	−12.3221	−	21.3425i	−0.155976	−	0.270158i	0.777438	−	0.628959i	$-0.216519\pi$
$79$	−12.3221	−	21.3425i	−0.155976	−	0.270158i	−0.933414	+	0.358802i	$0.883185\pi$
$80$	−129.496	−	44.6844i	−1.61870	−	0.558555i
$81$		0			0
$82$	57.6540	−	48.7914i	0.703098	−	0.595018i
$83$	−57.7838	−	100.085i	−0.696191	−	1.20584i	−0.969778	−	0.243991i	$-0.921543\pi$
$83$	−57.7838	−	100.085i	−0.696191	−	1.20584i	0.273587	−	0.961847i	$-0.411790\pi$
$84$		0			0
$85$	84.1691	+	48.5950i	0.990224	+	0.571706i
$86$	−8.69405	−	48.1239i	−0.101094	−	0.559581i
$87$		0			0
$88$	−66.2502	−	37.1448i	−0.752843	−	0.422100i
$89$		−	131.872i		−	1.48171i	−0.671664	−	0.740856i	$-0.734420\pi$
$89$		−	131.872i		−	1.48171i	0.671664	−	0.740856i	$-0.265580\pi$
$90$		0			0
$91$		−	82.8580i		−	0.910527i
$92$	36.9133	+	98.8282i	0.401232	+	1.07422i
$93$		0			0
$94$	6.52124	+	36.0969i	0.0693749	+	0.384009i
$95$	136.282	+	78.6822i	1.43454	+	0.828234i
$96$		0			0
$97$	94.1484	+	163.070i	0.970603	+	1.68113i	0.693743	+	0.720223i	$0.255960\pi$
$97$	94.1484	+	163.070i	0.970603	+	1.68113i	0.276859	+	0.960910i	$0.410706\pi$
$98$	−9.67730	−	11.4351i	−0.0987480	−	0.116685i
$99$		0			0
$100$	−31.9529	+	190.558i	−0.319529	+	1.90558i
$101$	−28.3361	−	49.0795i	−0.280555	−	0.485936i	0.690966	−	0.722887i	$-0.257185\pi$
$101$	−28.3361	−	49.0795i	−0.280555	−	0.485936i	−0.971522	+	0.236951i	$0.923852\pi$
$102$		0			0
$103$	−5.46478	+	9.46528i	−0.0530561	+	0.0918959i	−0.891334	−	0.453348i	$-0.850230\pi$
$103$	−5.46478	+	9.46528i	−0.0530561	+	0.0918959i	0.838278	+	0.545244i	$0.183563\pi$
$104$	88.1867	−	1.11089i	0.847950	−	0.0106817i
$105$		0			0
$106$	39.5440	−	110.082i	0.373057	−	1.03851i
$107$	57.2955			0.535472			0.267736	−	0.963492i	$-0.413724\pi$
$107$	57.2955			0.535472			0.267736	+	0.963492i	$0.413724\pi$
$108$		0			0
$109$			49.9283i			0.458058i	0.973420	+	0.229029i	$0.0735551\pi$
$109$			49.9283i			0.458058i	−0.973420	+	0.229029i	$0.926445\pi$
$110$	−54.9614	+	153.001i	−0.499649	+	1.39092i
$111$		0			0
$112$	90.8102	−	78.8352i	0.810805	−	0.703886i
$113$	44.6255	+	25.7646i	0.394916	+	0.228005i	0.684288	−	0.729212i	$-0.260113\pi$
$113$	44.6255	+	25.7646i	0.394916	+	0.228005i	−0.289372	+	0.957217i	$0.593446\pi$
$114$		0			0
$115$	195.558	−	112.906i	1.70051	−	0.981787i
$116$	4.60814	−	27.4816i	0.0397254	−	0.236911i
$117$		0			0
$118$	−34.0165	−	40.1953i	−0.288275	−	0.340638i
$119$	−73.8880	+	42.6592i	−0.620907	+	0.358481i
$120$		0			0
$121$	15.4311	−	26.7274i	0.127530	−	0.220888i
$122$	−23.0187	−	127.415i	−0.188678	−	1.04438i
$123$		0			0
$124$	−48.1429	+	17.9818i	−0.388249	+	0.145015i
$125$	199.528			1.59623
$126$		0			0
$127$	18.7898			0.147951			0.0739756	−	0.997260i	$-0.476431\pi$
$127$	18.7898			0.147951			0.0739756	+	0.997260i	$0.476431\pi$
$128$	85.1228	+	95.5934i	0.665022	+	0.746824i
$129$		0			0
$130$	−33.5606	−	185.767i	−0.258159	−	1.42898i
$131$	18.9279	−	32.7842i	0.144488	−	0.250261i	−0.784694	−	0.619884i	$-0.787180\pi$
$131$	18.9279	−	32.7842i	0.144488	−	0.250261i	0.929182	+	0.369623i	$0.120513\pi$
$132$		0			0
$133$	−119.635	+	69.0713i	−0.899512	+	0.519333i
$134$	50.1898	−	42.4746i	0.374551	−	0.316975i
$135$		0			0
$136$	−46.3934	−	78.0679i	−0.341128	−	0.574029i
$137$	224.690	−	129.725i	1.64007	−	0.946896i	0.659266	−	0.751909i	$-0.270867\pi$
$137$	224.690	−	129.725i	1.64007	−	0.946896i	0.980806	−	0.194987i	$-0.0624664\pi$
$138$		0			0
$139$	−80.7028	−	46.5938i	−0.580595	−	0.335207i	0.180775	−	0.983525i	$-0.442140\pi$
$139$	−80.7028	−	46.5938i	−0.580595	−	0.335207i	−0.761370	+	0.648318i	$0.775473\pi$
$140$	−198.564	−	163.793i	−1.41831	−	1.16995i
$141$		0			0
$142$	−159.208	−	57.1909i	−1.12118	−	0.402753i
$143$		−	104.665i		−	0.731923i
$144$		0			0
$145$	−59.6443			−0.411340
$146$	63.6307	−	177.134i	0.435826	−	1.21325i
$147$		0			0
$148$	15.0076	−	18.1935i	0.101403	−	0.122929i
$149$	−90.5257	+	156.795i	−0.607555	+	1.05232i	0.384087	+	0.923297i	$0.374516\pi$
$149$	−90.5257	+	156.795i	−0.607555	+	1.05232i	−0.991642	+	0.129020i	$0.958817\pi$
$150$		0			0
$151$	−25.1778	−	43.6092i	−0.166740	−	0.288803i	0.770532	−	0.637402i	$-0.219991\pi$
$151$	−25.1778	−	43.6092i	−0.166740	−	0.288803i	−0.937272	+	0.348599i	$0.886658\pi$
$152$	−75.1174	−	126.403i	−0.494194	−	0.831599i
$153$		0			0
$154$	−92.1938	−	108.940i	−0.598661	−	0.707403i
$155$	55.0004	+	95.2635i	0.354842	+	0.614604i
$156$		0			0
$157$	84.5771	+	48.8306i	0.538707	+	0.311023i	0.744555	−	0.667561i	$-0.232662\pi$
$157$	84.5771	+	48.8306i	0.538707	+	0.311023i	−0.205847	+	0.978584i	$0.565995\pi$
$158$	48.5031	−	8.76256i	0.306982	−	0.0554592i
$159$		0			0
$160$	171.665	−	213.530i	1.07290	−	1.33456i
$161$			198.229i			1.23123i
$162$		0			0
$163$			275.467i			1.68998i	0.534782	+	0.844990i	$0.320394\pi$
$163$			275.467i			1.68998i	−0.534782	+	0.844990i	$0.679606\pi$
$164$	52.8549	+	141.509i	0.322286	+	0.862858i
$165$		0			0
$166$	227.453	−	41.0916i	1.37020	−	0.247540i
$167$	81.5588	+	47.0880i	0.488376	+	0.281964i	0.723900	−	0.689904i	$-0.242347\pi$
$167$	81.5588	+	47.0880i	0.488376	+	0.281964i	−0.235525	+	0.971868i	$0.575681\pi$
$168$		0			0
$169$	−23.7333	−	41.1073i	−0.140434	−	0.243238i
$170$	−148.378	+	125.569i	−0.872811	+	0.738643i
$171$		0			0
$172$	96.4592	+	16.1744i	0.560810	+	0.0940370i
$173$	−88.1674	−	152.710i	−0.509638	−	0.882720i	−0.999938	−	0.0111654i	$-0.996446\pi$
$173$	−88.1674	−	152.710i	−0.509638	−	0.882720i	0.490299	−	0.871554i	$-0.336887\pi$
$174$		0			0
$175$	−181.528	+	314.416i	−1.03730	+	1.79666i
$176$	114.710	−	99.5835i	0.651762	−	0.565815i
$177$		0			0
$178$	248.216	+	89.1646i	1.39447	+	0.500925i
$179$	21.4052			0.119582			0.0597911	−	0.998211i	$-0.480957\pi$
$179$	21.4052			0.119582			0.0597911	+	0.998211i	$0.480957\pi$
$180$		0			0
$181$		−	319.291i		−	1.76404i	−0.471215	−	0.882019i	$-0.656184\pi$
$181$		−	319.291i		−	1.76404i	0.471215	−	0.882019i	$-0.343816\pi$
$182$	155.959	+	56.0239i	0.856916	+	0.307823i
$183$		0			0
$184$	−210.977	+	2.65769i	−1.14662	+	0.0144440i
$185$	−43.7184	−	25.2408i	−0.236315	−	0.136437i
$186$		0			0
$187$	−93.3342	+	53.8865i	−0.499113	+	0.288163i
$188$	−72.3523	−	12.1321i	−0.384852	−	0.0645324i
$189$		0			0
$190$	−240.245	+	203.314i	−1.26445	+	1.07008i
$191$	168.265	−	97.1480i	0.880970	−	0.508628i	0.00999168	−	0.999950i	$-0.496819\pi$
$191$	168.265	−	97.1480i	0.880970	−	0.508628i	0.870978	+	0.491322i	$0.163486\pi$
$192$		0			0
$193$	20.4962	−	35.5005i	0.106198	−	0.183940i	−0.808029	−	0.589143i	$-0.799466\pi$
$193$	20.4962	−	35.5005i	0.106198	−	0.183940i	0.914227	+	0.405202i	$0.132799\pi$
$194$	−370.595	+	66.9515i	−1.91028	+	0.345111i
$195$		0			0
$196$	28.0669	−	10.4832i	0.143198	−	0.0534859i
$197$	14.2759			0.0724666			0.0362333	−	0.999343i	$-0.488464\pi$
$197$	14.2759			0.0724666			0.0362333	+	0.999343i	$0.488464\pi$
$198$		0			0
$199$	298.873			1.50188			0.750938	−	0.660373i	$-0.229602\pi$
$199$	298.873			1.50188			0.750938	+	0.660373i	$0.229602\pi$
$200$	−337.070	−	188.987i	−1.68535	−	0.944936i
$201$		0			0
$202$	111.539	−	20.1505i	0.552172	−	0.0997551i
$203$	26.1794	−	45.3441i	0.128963	−	0.223370i
$204$		0			0
$205$	280.013	−	161.666i	1.36592	−	0.788613i
$206$	−14.1210	−	16.6859i	−0.0685484	−	0.0809996i
$207$		0			0
$208$	−57.5359	+	166.740i	−0.276615	+	0.801634i
$209$	−151.121	+	87.2499i	−0.723068	+	0.417464i
$210$		0			0
$211$	−202.413	−	116.863i	−0.959305	−	0.553855i	−0.0633463	−	0.997992i	$-0.520177\pi$
$211$	−202.413	−	116.863i	−0.959305	−	0.553855i	−0.895959	+	0.444136i	$0.853511\pi$
$212$	180.464	+	148.863i	0.851245	+	0.702183i
$213$		0			0
$214$	−38.7400	+	107.844i	−0.181028	+	0.503944i
$215$		−	209.349i		−	0.973715i
$216$		0			0
$217$	−96.5645			−0.444998
$218$	−93.9771	−	33.7587i	−0.431088	−	0.154856i
$219$		0			0
$220$	−250.823	−	206.901i	−1.14010	−	0.940459i
$221$	62.5712	−	108.376i	0.283128	−	0.490391i
$222$		0			0
$223$	−1.38344	−	2.39619i	−0.00620377	−	0.0107452i	0.862907	−	0.505363i	$-0.168641\pi$
$223$	−1.38344	−	2.39619i	−0.00620377	−	0.0107452i	−0.869111	+	0.494618i	$0.835308\pi$
$224$	86.9862	+	224.231i	0.388331	+	1.00103i
$225$		0			0
$226$	−78.6684	+	66.5755i	−0.348090	+	0.294582i
$227$	24.5897	+	42.5906i	0.108325	+	0.187624i	0.915092	−	0.403246i	$-0.132118\pi$
$227$	24.5897	+	42.5906i	0.108325	+	0.187624i	−0.806767	+	0.590870i	$0.798785\pi$
$228$		0			0
$229$	−227.507	−	131.351i	−0.993481	−	0.573587i	−0.0871681	−	0.996194i	$-0.527782\pi$
$229$	−227.507	−	131.351i	−0.993481	−	0.573587i	−0.906313	+	0.422607i	$0.861115\pi$
$230$	80.2901	+	444.428i	0.349088	+	1.93229i
$231$		0			0
$232$	48.6113	+	27.2551i	0.209531	+	0.117479i
$233$			320.513i			1.37559i	0.725903	+	0.687797i	$0.241422\pi$
$233$			320.513i			1.37559i	−0.725903	+	0.687797i	$0.758578\pi$
$234$		0			0
$235$			157.029i			0.668207i
$236$	98.6573	−	36.8494i	0.418039	−	0.156142i
$237$		0			0
$238$	−30.3361	−	167.919i	−0.127463	−	0.705541i
$239$	−317.949	−	183.568i	−1.33033	−	0.768066i	−0.344979	−	0.938610i	$-0.612114\pi$
$239$	−317.949	−	183.568i	−1.33033	−	0.768066i	−0.985350	+	0.170545i	$0.945447\pi$
$240$		0			0
$241$	53.3543	+	92.4123i	0.221387	+	0.383454i	0.955229	−	0.295866i	$-0.0956082\pi$
$241$	53.3543	+	92.4123i	0.221387	+	0.383454i	−0.733842	+	0.679320i	$0.762275\pi$
$242$	39.8738	+	47.1166i	0.164768	+	0.194697i
$243$		0			0
$244$	255.389	+	42.8239i	1.04668	+	0.175508i
$245$	−32.0648	−	55.5378i	−0.130877	−	0.226685i
$246$		0			0
$247$	101.312	−	175.477i	0.410168	−	0.710432i
$248$	−1.29466	−	102.775i	−0.00522040	−	0.414414i
$249$		0			0
$250$	−134.910	+	375.560i	−0.539639	+	1.50224i
$251$	−255.233			−1.01686			−0.508432	−	0.861102i	$-0.669775\pi$
$251$	−255.233			−1.01686			−0.508432	+	0.861102i	$0.669775\pi$
$252$		0			0
$253$			250.400i			0.989722i
$254$	−12.7046	+	35.3669i	−0.0500181	+	0.139240i
$255$		0			0
$256$	−237.485	+	95.5868i	−0.927676	+	0.373386i
$257$	138.828	+	80.1521i	0.540185	+	0.311876i	0.745154	−	0.666893i	$-0.232376\pi$
$257$	138.828	+	80.1521i	0.540185	+	0.311876i	−0.204969	+	0.978768i	$0.565709\pi$
$258$		0			0
$259$	38.3783	−	22.1577i	0.148179	−	0.0855509i
$260$	372.350	+	62.4360i	1.43212	+	0.240139i
$261$		0			0
$262$	48.9097	+	57.7937i	0.186678	+	0.220587i
$263$	−350.611	+	202.425i	−1.33312	+	0.769678i	−0.985777	−	0.168060i	$-0.946250\pi$
$263$	−350.611	+	202.425i	−1.33312	+	0.769678i	−0.347345	+	0.937738i	$0.612917\pi$
$264$		0			0
$265$	250.367	−	433.649i	0.944782	−	1.63641i
$266$	−49.1185	−	271.884i	−0.184656	−	1.02212i
$267$		0			0
$268$	46.0120	+	123.188i	0.171687	+	0.459658i
$269$	18.9169			0.0703230			0.0351615	−	0.999382i	$-0.488805\pi$
$269$	18.9169			0.0703230			0.0351615	+	0.999382i	$0.488805\pi$
$270$		0			0
$271$	−502.339			−1.85365			−0.926824	−	0.375495i	$-0.877473\pi$
$271$	−502.339			−1.85365			−0.926824	+	0.375495i	$0.877473\pi$
$272$	178.311	−	34.5384i	0.655556	−	0.126979i
$273$		0			0
$274$	92.2507	+	510.633i	0.336682	+	1.86362i
$275$	−229.304	+	397.166i	−0.833831	+	1.44424i
$276$		0			0
$277$	−164.430	+	94.9335i	−0.593609	+	0.342720i	−0.766523	−	0.642217i	$-0.778015\pi$
$277$	−164.430	+	94.9335i	−0.593609	+	0.342720i	0.172914	+	0.984937i	$0.444682\pi$
$278$	142.267	−	120.398i	0.511753	−	0.433086i
$279$		0			0
$280$	442.556	−	262.997i	1.58056	−	0.939276i
$281$	−53.6619	+	30.9817i	−0.190968	+	0.110255i	−0.592436	−	0.805618i	$-0.701834\pi$
$281$	−53.6619	+	30.9817i	−0.190968	+	0.110255i	0.401468	+	0.915873i	$0.368500\pi$
$282$		0			0
$283$	455.790	+	263.151i	1.61057	+	0.929861i	0.989239	+	0.146310i	$0.0467396\pi$
$283$	455.790	+	263.151i	1.61057	+	0.929861i	0.621327	+	0.783551i	$0.286594\pi$
$284$	215.294	−	260.998i	0.758078	−	0.919006i
$285$		0			0
$286$	197.005	+	70.7685i	0.688828	+	0.247442i
$287$			283.837i			0.988979i
$288$		0			0
$289$	160.141			0.554123
$290$	40.3281	−	112.265i	0.139062	−	0.387120i
$291$		0			0
$292$	290.386	+	239.536i	0.994473	+	0.820330i
$293$	127.500	−	220.837i	0.435154	−	0.753709i	−0.562154	−	0.827032i	$-0.690027\pi$
$293$	127.500	−	220.837i	0.435154	−	0.753709i	0.997308	+	0.0733236i	$0.0233606\pi$
$294$		0			0
$295$	−112.710	−	195.220i	−0.382069	−	0.661762i
$296$	24.0972	+	40.5494i	0.0814096	+	0.136991i
$297$		0			0
$298$	−233.918	−	276.407i	−0.784959	−	0.927541i
$299$	−145.378	−	251.802i	−0.486213	−	0.842146i
$300$		0			0
$301$	159.156	+	91.8886i	0.528757	+	0.305278i
$302$	99.1069	−	17.9046i	0.328168	−	0.0592868i
$303$		0			0
$304$	288.711	−	55.9226i	0.949707	−	0.183956i
$305$		−	554.280i		−	1.81731i
$306$		0			0
$307$			365.110i			1.18928i	0.803990	+	0.594642i	$0.202706\pi$
$307$			365.110i			1.18928i	−0.803990	+	0.594642i	$0.797294\pi$
$308$	267.388	−	99.8718i	0.868141	−	0.324259i
$309$		0			0
$310$	−216.497	+	39.1123i	−0.698378	+	0.126169i
$311$	−359.227	−	207.400i	−1.15507	−	0.666881i	−0.204953	−	0.978772i	$-0.565704\pi$
$311$	−359.227	−	207.400i	−1.15507	−	0.666881i	−0.950118	+	0.311891i	$0.899038\pi$
$312$		0			0
$313$	266.359	+	461.348i	0.850988	+	1.47396i	0.880317	+	0.474385i	$0.157330\pi$
$313$	266.359	+	461.348i	0.850988	+	1.47396i	−0.0293289	+	0.999570i	$0.509337\pi$
$314$	−149.097	+	126.178i	−0.474832	+	0.401841i
$315$		0			0
$316$	−16.3018	+	97.2193i	−0.0515881	+	0.307656i
$317$	298.687	+	517.342i	0.942231	+	1.63199i	0.761202	+	0.648514i	$0.224609\pi$
$317$	298.687	+	517.342i	0.942231	+	1.63199i	0.181029	+	0.983478i	$0.442057\pi$
$318$		0			0
$319$	33.0695	−	57.2780i	0.103666	−	0.179555i
$320$	285.845	+	467.491i	0.893264	+	1.46091i
$321$		0			0
$322$	−373.114	−	134.031i	−1.15874	−	0.416245i
$323$	−208.640			−0.645945
$324$		0			0
$325$		−	532.519i		−	1.63852i
$326$	−518.495	−	186.255i	−1.59047	−	0.571334i
$327$		0			0
$328$	−302.091	+	3.80546i	−0.921009	+	0.0116020i
$329$	−119.380	−	68.9239i	−0.362856	−	0.209495i
$330$		0			0
$331$	182.783	−	105.530i	0.552215	−	0.318821i	−0.197800	−	0.980242i	$-0.563380\pi$
$331$	182.783	−	105.530i	0.552215	−	0.318821i	0.750015	+	0.661421i	$0.230046\pi$
$332$	−76.4467	+	455.906i	−0.230261	+	1.37321i
$333$		0			0
$334$	−143.776	+	121.675i	−0.430468	+	0.364297i
$335$	243.761	−	140.735i	0.727644	−	0.420106i
$336$		0			0
$337$	155.181	−	268.782i	0.460479	−	0.797573i	−0.538506	−	0.842622i	$-0.681011\pi$
$337$	155.181	−	268.782i	0.460479	−	0.797573i	0.998985	+	0.0450488i	$0.0143443\pi$
$338$	93.4209	−	16.8774i	0.276393	−	0.0499331i
$339$		0			0
$340$	−136.027	−	364.186i	−0.400079	−	1.07113i
$341$	−121.979			−0.357709
$342$		0			0
$343$	−311.988			−0.909585
$344$	−95.6643	+	170.623i	−0.278094	+	0.495998i
$345$		0			0
$346$	347.052	−	62.6982i	1.00304	−	0.181209i
$347$	−14.0423	+	24.3220i	−0.0404678	+	0.0700923i	−0.885550	−	0.464544i	$-0.846218\pi$
$347$	−14.0423	+	24.3220i	−0.0404678	+	0.0700923i	0.845082	+	0.534637i	$0.179551\pi$
$348$		0			0
$349$	−429.084	+	247.732i	−1.22947	+	0.709833i	−0.966918	−	0.255086i	$-0.917896\pi$
$349$	−429.084	+	247.732i	−1.22947	+	0.709833i	−0.262549	+	0.964919i	$0.584563\pi$
$350$	−469.067	−	554.270i	−1.34019	−	1.58363i
$351$		0			0
$352$	109.880	+	283.245i	0.312158	+	0.804673i
$353$	96.6875	−	55.8225i	0.273902	−	0.158137i	−0.356757	−	0.934197i	$-0.616118\pi$
$353$	96.6875	−	55.8225i	0.273902	−	0.158137i	0.630660	+	0.776060i	$0.282784\pi$
$354$		0			0
$355$	−627.169	−	362.096i	−1.76667	−	1.01999i
$356$	−335.659	+	406.913i	−0.942861	+	1.14302i
$357$		0			0
$358$	−14.4730	+	40.2897i	−0.0404273	+	0.112541i
$359$		−	64.1895i		−	0.178801i	−0.995996	−	0.0894004i	$-0.971505\pi$
$359$		−	64.1895i		−	0.178801i	0.995996	−	0.0894004i	$-0.0284951\pi$
$360$		0			0
$361$	23.1821			0.0642163
$362$	600.982	+	215.886i	1.66017	+	0.596371i
$363$		0			0
$364$	−210.901	+	255.672i	−0.579398	+	0.702395i
$365$	402.868	−	697.788i	1.10375	−	1.91175i
$366$		0			0
$367$	−315.787	−	546.960i	−0.860456	−	1.49035i	−0.871489	−	0.490415i	$-0.836845\pi$
$367$	−315.787	−	546.960i	−0.860456	−	1.49035i	0.0110327	−	0.999939i	$-0.496488\pi$
$368$	137.648	−	398.907i	0.374044	−	1.08399i
$369$		0			0
$370$	77.0692	−	65.2221i	0.208295	−	0.176276i
$371$	219.785	+	380.679i	0.592413	+	1.02609i
$372$		0			0
$373$	−326.479	−	188.493i	−0.875279	−	0.505342i	−0.00617981	−	0.999981i	$-0.501967\pi$
$373$	−326.479	−	188.493i	−0.875279	−	0.505342i	−0.869099	+	0.494639i	$0.835300\pi$
$374$	−38.3201	−	212.112i	−0.102460	−	0.567146i
$375$		0			0
$376$	71.7560	−	127.981i	0.190840	−	0.340376i
$377$			76.7983i			0.203709i
$378$		0			0
$379$		−	385.660i		−	1.01757i	−0.860893	−	0.508786i	$-0.830095\pi$
$379$		−	385.660i		−	1.01757i	0.860893	−	0.508786i	$-0.169905\pi$
$380$	−220.247	−	589.668i	−0.579597	−	1.55176i
$381$		0			0
$382$	69.0845	+	382.402i	0.180849	+	1.00105i
$383$	92.9952	+	53.6908i	0.242807	+	0.140185i	0.616466	−	0.787381i	$-0.288564\pi$
$383$	92.9952	+	53.6908i	0.242807	+	0.140185i	−0.373659	+	0.927566i	$0.621897\pi$
$384$		0			0
$385$	−305.475	−	529.098i	−0.793441	−	1.37428i
$386$	52.9620	+	62.5822i	0.137207	+	0.162130i
$387$		0			0
$388$	124.556	−	742.817i	0.321021	−	1.91448i
$389$	23.1238	+	40.0515i	0.0594441	+	0.102960i	0.894216	−	0.447636i	$-0.147734\pi$
$389$	23.1238	+	40.0515i	0.0594441	+	0.102960i	−0.834772	+	0.550596i	$0.814401\pi$
$390$		0			0
$391$	−149.695	+	259.279i	−0.382851	+	0.663117i
$392$	0.754775	+	59.9168i	0.00192545	+	0.152849i
$393$		0			0
$394$	−9.65256	+	26.8707i	−0.0244989	+	0.0681998i
$395$	210.998			0.534173
$396$		0			0
$397$		−	301.305i		−	0.758955i	−0.925201	−	0.379477i	$-0.876104\pi$
$397$		−	301.305i		−	0.758955i	0.925201	−	0.379477i	$-0.123896\pi$
$398$	−202.081	+	562.552i	−0.507742	+	1.41345i
$399$		0			0
$400$	583.627	−	506.665i	1.45907	−	1.26666i
$401$	188.370	+	108.755i	0.469751	+	0.271211i	0.716135	−	0.697962i	$-0.245909\pi$
$401$	188.370	+	108.755i	0.469751	+	0.271211i	−0.246385	+	0.969172i	$0.579243\pi$
$402$		0			0
$403$	122.662	−	70.8188i	0.304372	−	0.175729i
$404$	−37.4880	+	223.567i	−0.0927920	+	0.553384i
$405$		0			0
$406$	67.6475	+	79.9351i	0.166619	+	0.196884i
$407$	48.4788	−	27.9893i	0.119113	−	0.0687697i
$408$		0			0
$409$	−328.133	+	568.344i	−0.802282	+	1.38959i	0.115828	+	0.993269i	$0.463048\pi$
$409$	−328.133	+	568.344i	−0.802282	+	1.38959i	−0.918110	+	0.396325i	$0.870285\pi$
$410$	114.965	+	636.361i	0.280402	+	1.55210i
$411$		0			0
$412$	40.9547	−	15.2970i	0.0994046	−	0.0371286i
$413$	197.886			0.479142
$414$		0			0
$415$	989.468			2.38426
$416$	−274.942	−	221.036i	−0.660918	−	0.531337i
$417$		0			0
$418$	−62.0457	−	343.440i	−0.148435	−	0.821627i
$419$	193.367	−	334.922i	0.461497	−	0.799336i	−0.537539	−	0.843239i	$-0.680646\pi$
$419$	193.367	−	334.922i	0.461497	−	0.799336i	0.999036	+	0.0439028i	$0.0139792\pi$
$420$		0			0
$421$	280.678	−	162.049i	0.666693	−	0.384916i	−0.128129	−	0.991757i	$-0.540897\pi$
$421$	280.678	−	162.049i	0.666693	−	0.384916i	0.794823	+	0.606842i	$0.207564\pi$
$422$	356.826	−	301.974i	0.845558	−	0.715579i
$423$		0			0
$424$	−402.215	+	239.024i	−0.948620	+	0.563736i
$425$	−474.870	+	274.166i	−1.11734	+	0.645097i
$426$		0			0
$427$	421.387	+	243.288i	0.986855	+	0.569761i
$428$	−176.795	−	145.836i	−0.413071	−	0.340738i
$429$		0			0
$430$	394.045	+	141.550i	0.916383	+	0.329185i
$431$		−	417.635i		−	0.968991i	−0.874794	−	0.484495i	$-0.839003\pi$
$431$		−	417.635i		−	0.968991i	0.874794	−	0.484495i	$-0.160997\pi$
$432$		0			0
$433$	−420.782			−0.971784			−0.485892	−	0.874019i	$-0.661505\pi$
$433$	−420.782			−0.971784			−0.485892	+	0.874019i	$0.661505\pi$
$434$	65.2914	−	181.758i	0.150441	−	0.418796i
$435$		0			0
$436$	127.084	−	154.062i	0.291477	−	0.353353i
$437$	−242.377	+	419.809i	−0.554638	+	0.960662i
$438$		0			0
$439$	93.9396	+	162.708i	0.213985	+	0.370634i	0.952958	−	0.303102i	$-0.0980222\pi$
$439$	93.9396	+	162.708i	0.213985	+	0.370634i	−0.738973	+	0.673735i	$0.764689\pi$
$440$	559.030	−	332.214i	1.27052	−	0.755032i
$441$		0			0
$442$	161.684	+	191.052i	0.365800	+	0.432244i
$443$	112.177	+	194.296i	0.253220	+	0.438591i	0.964411	−	0.264409i	$-0.0851769\pi$
$443$	112.177	+	194.296i	0.253220	+	0.438591i	−0.711190	+	0.703000i	$0.751844\pi$
$444$		0			0
$445$	977.799	+	564.533i	2.19730	+	1.26861i
$446$	5.44561	−	0.983802i	0.0122099	−	0.00220583i
$447$		0			0
$448$	−480.871	+	12.1171i	−1.07337	+	0.0270470i
$449$		−	207.466i		−	0.462063i	−0.972946	−	0.231032i	$-0.925790\pi$
$449$		−	207.466i		−	0.462063i	0.972946	−	0.231032i	$-0.0742101\pi$
$450$		0			0
$451$			358.539i			0.794986i
$452$	−72.1200	−	193.087i	−0.159557	−	0.427184i
$453$		0			0
$454$	−96.7919	+	17.4864i	−0.213198	+	0.0385163i
$455$	614.370	+	354.707i	1.35026	+	0.779575i
$456$		0			0
$457$	29.9392	+	51.8562i	0.0655124	+	0.113471i	0.896921	−	0.442190i	$-0.145798\pi$
$457$	29.9392	+	51.8562i	0.0655124	+	0.113471i	−0.831409	+	0.555661i	$0.812465\pi$
$458$	401.062	−	339.411i	0.875682	−	0.741072i
$459$		0			0
$460$	−890.808	−	149.371i	−1.93654	−	0.324721i
$461$	90.0395	+	155.953i	0.195313	+	0.338293i	0.947003	−	0.321224i	$-0.104094\pi$
$461$	90.0395	+	155.953i	0.195313	+	0.338293i	−0.751690	+	0.659517i	$0.770761\pi$
$462$		0			0
$463$	−199.548	+	345.627i	−0.430989	+	0.746496i	−0.996959	−	0.0779307i	$-0.975169\pi$
$463$	−199.548	+	345.627i	−0.430989	+	0.746496i	0.565969	+	0.824426i	$0.308502\pi$
$464$	−84.1689	+	73.0697i	−0.181399	+	0.157478i
$465$		0			0
$466$	−603.283	−	216.713i	−1.29460	−	0.465049i
$467$	−284.941			−0.610153			−0.305077	−	0.952328i	$-0.598682\pi$
$467$	−284.941			−0.610153			−0.305077	+	0.952328i	$0.598682\pi$
$468$		0			0
$469$			247.090i			0.526844i
$470$	−295.566	−	106.174i	−0.628863	−	0.225902i
$471$		0			0
$472$	2.65310	+	210.612i	0.00562097	+	0.446212i
$473$	201.043	+	116.072i	0.425038	+	0.245396i
$474$		0			0
$475$	−768.881	+	443.914i	−1.61870	+	0.934555i
$476$	336.575	+	56.4372i	0.707090	+	0.118566i
$477$		0			0
$478$	560.497	−	474.338i	1.17259	−	0.992338i
$479$	243.933	−	140.835i	0.509255	−	0.294018i	−0.223272	−	0.974756i	$-0.571674\pi$
$479$	243.933	−	140.835i	0.509255	−	0.294018i	0.732527	+	0.680738i	$0.238341\pi$
$480$		0			0
$481$	−32.5002	+	56.2920i	−0.0675680	+	0.117031i
$482$	−210.017	+	37.9416i	−0.435721	+	0.0787171i
$483$		0			0
$484$	−115.645	+	43.1946i	−0.238936	+	0.0892450i
$485$	−1612.16			−3.32404
$486$		0			0
$487$	490.070			1.00630			0.503152	−	0.864198i	$-0.332174\pi$
$487$	490.070			1.00630			0.503152	+	0.864198i	$0.332174\pi$
$488$	−253.285	+	451.749i	−0.519026	+	0.925716i
$489$		0			0
$490$	126.216	−	22.8021i	0.257583	−	0.0465349i
$491$	167.001	−	289.254i	0.340124	−	0.589113i	−0.644331	−	0.764747i	$-0.722864\pi$
$491$	167.001	−	289.254i	0.340124	−	0.589113i	0.984456	+	0.175634i	$0.0561975\pi$
$492$		0			0
$493$	68.4843	−	39.5394i	0.138913	−	0.0802016i
$494$	261.789	+	309.340i	0.529936	+	0.626195i
$495$		0			0
$496$	194.322	+	67.0536i	0.391779	+	0.135189i
$497$	550.561	−	317.867i	1.10777	−	0.639571i
$498$		0			0
$499$	413.436	+	238.697i	0.828528	+	0.478351i	0.853348	−	0.521341i	$-0.174568\pi$
$499$	413.436	+	238.697i	0.828528	+	0.478351i	−0.0248203	+	0.999692i	$0.507901\pi$
$500$	−615.677	−	507.865i	−1.23135	−	1.01573i
$501$		0			0
$502$	172.574	−	480.410i	0.343773	−	0.956992i
$503$			413.724i			0.822512i	0.911520	+	0.411256i	$0.134910\pi$
$503$			413.724i			0.822512i	−0.911520	+	0.411256i	$0.865090\pi$
$504$		0			0
$505$	485.216			0.960823
$506$	−471.312	−	169.306i	−0.931447	−	0.334597i
$507$		0			0
$508$	−57.9789	−	47.8262i	−0.114132	−	0.0941460i
$509$	75.5535	−	130.862i	0.148435	−	0.257097i	−0.782214	−	0.623010i	$-0.785910\pi$
$509$	75.5535	−	130.862i	0.148435	−	0.257097i	0.930649	+	0.365912i	$0.119243\pi$
$510$		0			0
$511$	353.659	+	612.555i	0.692091	+	1.19874i
$512$	−19.3435	−	511.634i	−0.0377802	−	0.999286i
$513$		0			0
$514$	−244.733	+	207.113i	−0.476134	+	0.402943i
$515$	−46.7884	−	81.0399i	−0.0908512	−	0.157359i
$516$		0			0
$517$	−150.799	−	87.0637i	−0.291680	−	0.168402i
$518$	15.7569	+	87.2189i	0.0304188	+	0.168376i
$519$		0			0
$520$	−369.282	+	658.637i	−0.710157	+	1.26661i
$521$			1031.73i			1.98029i	0.140063	+	0.990143i	$0.455269\pi$
$521$			1031.73i			1.98029i	−0.140063	+	0.990143i	$0.544731\pi$
$522$		0			0
$523$		−	700.814i		−	1.33999i	−0.742366	−	0.669994i	$-0.766296\pi$
$523$		−	700.814i		−	1.33999i	0.742366	−	0.669994i	$-0.233704\pi$
$524$	−141.852	+	52.9830i	−0.270709	+	0.101113i
$525$		0			0
$526$	−143.950	−	796.803i	−0.273669	−	1.51483i
$527$	−126.304	−	72.9218i	−0.239667	−	0.138372i
$528$		0			0
$529$	83.3004	+	144.280i	0.157468	+	0.272742i
$530$	646.947	+	764.460i	1.22066	+	1.44238i
$531$		0			0
$532$	544.962	+	91.3798i	1.02437	+	0.171767i
$533$	−208.161	−	360.546i	−0.390547	−	0.676447i
$534$		0			0
$535$	−245.276	+	424.831i	−0.458461	+	0.794077i
$536$	−262.981	+	3.31278i	−0.490635	+	0.00618057i
$537$		0			0
$538$	−12.7905	+	35.6062i	−0.0237742	+	0.0661824i
$539$	71.1126			0.131934
$540$		0			0
$541$			431.063i			0.796790i	0.917214	+	0.398395i	$0.130433\pi$
$541$			431.063i			0.796790i	−0.917214	+	0.398395i	$0.869567\pi$
$542$	339.653	−	945.523i	0.626666	−	1.74451i
$543$		0			0
$544$	−55.5543	+	358.978i	−0.102122	+	0.659885i
$545$	−370.205	−	213.738i	−0.679276	−	0.392180i
$546$		0			0
$547$	625.543	−	361.158i	1.14359	−	0.660252i	0.196272	−	0.980549i	$-0.437116\pi$
$547$	625.543	−	361.158i	1.14359	−	0.660252i	0.947317	+	0.320298i	$0.103783\pi$
$548$	−1023.51	−	171.623i	−1.86772	−	0.313180i
$549$		0			0
$550$	−592.519	−	700.145i	−1.07731	−	1.27299i
$551$	110.886	−	64.0199i	0.201244	−	0.116189i
$552$		0			0
$553$	−92.6127	+	160.410i	−0.167473	+	0.290072i
$554$	−67.5097	−	373.685i	−0.121859	−	0.674521i
$555$		0			0
$556$	130.425	+	349.188i	0.234577	+	0.628035i
$557$	907.654			1.62954			0.814770	−	0.579784i	$-0.196863\pi$
$557$	907.654			1.62954			0.814770	+	0.579784i	$0.196863\pi$
$558$		0			0
$559$	−269.558			−0.482215
$560$	195.793	+	1010.82i	0.349631	+	1.80504i
$561$		0			0
$562$	−22.0319	−	121.953i	−0.0392027	−	0.216998i
$563$	521.945	−	904.036i	0.927079	−	1.60575i	0.138896	−	0.990307i	$-0.455645\pi$
$563$	521.945	−	904.036i	0.927079	−	1.60575i	0.788183	−	0.615441i	$-0.211022\pi$
$564$		0			0
$565$	−382.075	+	220.591i	−0.676239	+	0.390427i
$566$	−803.492	+	679.979i	−1.41960	+	1.20138i
$567$		0			0
$568$	345.691	+	581.707i	0.608611	+	1.02413i
$569$	493.155	−	284.723i	0.866705	−	0.500392i	0.000453262	−	1.00000i	$-0.499856\pi$
$569$	493.155	−	284.723i	0.866705	−	0.500392i	0.866252	+	0.499607i	$0.166522\pi$
$570$		0			0
$571$	−850.255	−	490.895i	−1.48906	−	0.859711i	−0.489141	−	0.872205i	$-0.662690\pi$
$571$	−850.255	−	490.895i	−1.48906	−	0.859711i	−0.999922	+	0.0124934i	$0.996023\pi$
$572$	−266.407	+	322.961i	−0.465746	+	0.564616i
$573$		0			0
$574$	−534.249	−	191.914i	−0.930748	−	0.334346i
$575$			1273.99i			2.21564i
$576$		0			0
$577$	−461.080			−0.799099			−0.399550	−	0.916712i	$-0.630834\pi$
$577$	−461.080			−0.799099			−0.399550	+	0.916712i	$0.630834\pi$
$578$	−108.279	+	301.425i	−0.187333	+	0.521496i
$579$		0			0
$580$	184.042	+	151.814i	0.317314	+	0.261749i
$581$	−434.303	+	752.235i	−0.747510	+	1.29472i
$582$		0			0
$583$	277.630	+	480.869i	0.476209	+	0.824818i
$584$	−647.208	+	384.616i	−1.10823	+	0.658589i
$585$		0			0
$586$	329.459	+	389.303i	0.562218	+	0.664340i
$587$	94.0800	+	162.951i	0.160273	+	0.277600i	0.934966	−	0.354736i	$-0.115429\pi$
$587$	94.0800	+	162.951i	0.160273	+	0.277600i	−0.774694	+	0.632337i	$0.782096\pi$
$588$		0			0
$589$	−204.504	−	118.071i	−0.347206	−	0.200460i
$590$	443.659	−	80.1512i	0.751964	−	0.135850i
$591$		0			0
$592$	−92.6169	+	17.9396i	−0.156447	+	0.0303035i
$593$		−	127.877i		−	0.215644i	−0.994170	−	0.107822i	$-0.965612\pi$
$593$		−	127.877i		−	0.215644i	0.994170	−	0.107822i	$-0.0343877\pi$
$594$		0			0
$595$		−	730.480i		−	1.22770i
$596$	678.427	−	253.399i	1.13830	−	0.425166i
$597$		0			0
$598$	572.247	−	103.382i	0.956935	−	0.172880i
$599$	21.9156	+	12.6530i	0.0365869	+	0.0211235i	0.518182	−	0.855270i	$-0.326609\pi$
$599$	21.9156	+	12.6530i	0.0365869	+	0.0211235i	−0.481595	+	0.876394i	$0.659942\pi$
$600$		0			0
$601$	125.146	+	216.760i	0.208230	+	0.360665i	0.951157	−	0.308708i	$-0.0998964\pi$
$601$	125.146	+	216.760i	0.208230	+	0.360665i	−0.742927	+	0.669372i	$0.766563\pi$
$602$	−280.569	+	237.440i	−0.466061	+	0.394418i
$603$		0			0
$604$	−33.3097	+	198.649i	−0.0551484	+	0.328889i
$605$	132.118	+	228.835i	0.218377	+	0.378239i
$606$		0			0
$607$	564.183	−	977.193i	0.929461	−	1.60987i	0.145236	−	0.989397i	$-0.453606\pi$
$607$	564.183	−	977.193i	0.929461	−	1.60987i	0.784225	−	0.620477i	$-0.213061\pi$
$608$	−89.9502	+	581.235i	−0.147944	+	0.955979i
$609$		0			0
$610$	1043.29	+	374.773i	1.71031	+	0.614382i
$611$	202.191			0.330918
$612$		0			0
$613$			4.96469i			0.00809901i	0.999992	+	0.00404951i	$0.00128900\pi$
$613$			4.96469i			0.00809901i	−0.999992	+	0.00404951i	$0.998711\pi$
$614$	−687.226	−	246.867i	−1.11926	−	0.402063i
$615$		0			0
$616$	7.19060	+	570.815i	0.0116730	+	0.926648i
$617$	−196.879	−	113.668i	−0.319090	−	0.184227i	0.331897	−	0.943316i	$-0.392311\pi$
$617$	−196.879	−	113.668i	−0.319090	−	0.184227i	−0.650987	+	0.759089i	$0.725645\pi$
$618$		0			0
$619$	−261.088	+	150.739i	−0.421790	+	0.243521i	−0.695843	−	0.718194i	$-0.744969\pi$
$619$	−261.088	+	150.739i	−0.421790	+	0.243521i	0.274053	+	0.961715i	$0.411636\pi$
$620$	72.7643	−	433.945i	0.117362	−	0.699912i
$621$		0			0
$622$	633.266	−	535.920i	1.01811	−	0.861608i
$623$	−858.363	+	495.576i	−1.37779	+	0.795467i
$624$		0			0
$625$	−250.355	+	433.628i	−0.400568	+	0.693805i
$626$	−1048.47	+	189.415i	−1.67486	+	0.302580i
$627$		0			0
$628$	−136.686	−	365.951i	−0.217653	−	0.582725i
$629$	66.9306			0.106408
$630$		0			0
$631$	−894.608			−1.41776			−0.708881	−	0.705328i	$-0.750800\pi$
$631$	−894.608			−1.41776			−0.708881	+	0.705328i	$0.750800\pi$
$632$	−171.968	−	96.4181i	−0.272101	−	0.152560i
$633$		0			0
$634$	−1175.72	+	212.404i	−1.85444	+	0.335023i
$635$	−80.4373	+	139.321i	−0.126673	+	0.219404i
$636$		0			0
$637$	−71.5107	+	41.2867i	−0.112262	+	0.0648143i
$638$	85.4513	+	100.973i	0.133936	+	0.158265i
$639$		0			0
$640$	−1073.20	+	221.937i	−1.67688	+	0.346777i
$641$	−112.447	+	64.9216i	−0.175425	+	0.101282i	−0.585141	−	0.810931i	$-0.698961\pi$
$641$	−112.447	+	64.9216i	−0.175425	+	0.101282i	0.409716	+	0.912213i	$0.365628\pi$
$642$		0			0
$643$	−166.070	−	95.8808i	−0.258274	−	0.149115i	0.365273	−	0.930901i	$-0.380976\pi$
$643$	−166.070	−	95.8808i	−0.258274	−	0.149115i	−0.623547	+	0.781786i	$0.714309\pi$
$644$	504.557	−	611.667i	0.783474	−	0.949793i
$645$		0			0
$646$	141.071	−	392.711i	0.218376	−	0.607912i
$647$		−	940.799i		−	1.45409i	−0.686588	−	0.727047i	$-0.740892\pi$
$647$		−	940.799i		−	1.45409i	0.686588	−	0.727047i	$-0.259108\pi$
$648$		0			0
$649$	249.966			0.385156
$650$	1002.33	+	360.059i	1.54204	+	0.553937i
$651$		0			0
$652$	701.153	−	849.997i	1.07539	−	1.30368i
$653$	−353.929	+	613.023i	−0.542004	+	0.938779i	0.456785	+	0.889577i	$0.349001\pi$
$653$	−353.929	+	613.023i	−0.542004	+	0.938779i	−0.998789	+	0.0492016i	$0.984332\pi$
$654$		0			0
$655$	162.057	+	280.692i	0.247416	+	0.428537i
$656$	197.094	−	571.181i	0.300448	−	0.870703i
$657$		0			0
$658$	210.449	−	178.099i	0.319832	−	0.270667i
$659$	−284.270	−	492.370i	−0.431365	−	0.747147i	0.565626	−	0.824662i	$-0.308635\pi$
$659$	−284.270	−	492.370i	−0.431365	−	0.747147i	−0.996991	+	0.0775154i	$0.975301\pi$
$660$		0			0
$661$	−394.236	−	227.612i	−0.596424	−	0.344346i	0.171209	−	0.985235i	$-0.445233\pi$
$661$	−394.236	−	227.612i	−0.596424	−	0.344346i	−0.767634	+	0.640889i	$0.778566\pi$
$662$	75.0451	+	415.395i	0.113361	+	0.627485i
$663$		0			0
$664$	−806.436	−	452.149i	−1.21451	−	0.680947i
$665$		−	1182.75i		−	1.77857i
$666$		0			0
$667$		−	183.731i		−	0.275459i
$668$	−131.808	−	352.891i	−0.197318	−	0.528281i
$669$		0			0
$670$	100.081	+	553.974i	0.149374	+	0.826827i
$671$	532.290	+	307.318i	0.793279	+	0.458000i
$672$		0			0
$673$	−301.556	−	522.311i	−0.448078	−	0.776093i	0.550183	−	0.835044i	$-0.314558\pi$
$673$	−301.556	−	522.311i	−0.448078	−	0.776093i	−0.998261	+	0.0589506i	$0.981225\pi$
$674$	400.988	+	473.824i	0.594937	+	0.703003i
$675$		0			0
$676$	−31.3986	+	187.252i	−0.0464477	+	0.277000i
$677$	−150.521	−	260.711i	−0.222336	−	0.385097i	0.733181	−	0.680033i	$-0.238035\pi$
$677$	−150.521	−	260.711i	−0.222336	−	0.385097i	−0.955517	+	0.294937i	$0.904701\pi$
$678$		0			0
$679$	707.619	−	1225.63i	1.04215	−	1.80506i
$680$	777.459	−	9.79370i	1.14332	−	0.0144025i
$681$		0			0
$682$	82.4751	−	229.594i	0.120931	−	0.336647i
$683$	244.466			0.357930			0.178965	−	0.983855i	$-0.442725\pi$
$683$	244.466			0.357930			0.178965	+	0.983855i	$0.442725\pi$
$684$		0			0
$685$			2221.36i			3.24286i
$686$	210.948	−	587.236i	0.307505	−	0.856029i
$687$		0			0
$688$	−256.471	−	295.429i	−0.372778	−	0.429403i
$689$	−558.368	−	322.374i	−0.810404	−	0.467887i
$690$		0			0
$691$	37.7206	−	21.7780i	0.0545884	−	0.0315166i	−0.472457	−	0.881353i	$-0.656633\pi$
$691$	37.7206	−	21.7780i	0.0545884	−	0.0315166i	0.527046	+	0.849837i	$0.323300\pi$
$692$	−116.643	+	695.628i	−0.168560	+	1.00524i
$693$		0			0
$694$	−36.2853	−	42.8762i	−0.0522843	−	0.0617813i
$695$	690.961	−	398.927i	0.994189	−	0.573995i
$696$		0			0
$697$	−214.343	+	371.253i	−0.307522	+	0.532644i
$698$	−176.169	−	975.141i	−0.252391	−	1.39705i
$699$		0			0
$700$	1360.43	−	508.132i	1.94347	−	0.725903i
$701$	505.146			0.720607			0.360304	−	0.932835i	$-0.382673\pi$
$701$	505.146			0.720607			0.360304	+	0.932835i	$0.382673\pi$
$702$		0			0
$703$	108.370			0.154154
$704$	−607.429	+	15.3061i	−0.862826	+	0.0217416i
$705$		0			0
$706$	39.6969	+	219.733i	0.0562279	+	0.311237i
$707$	−212.974	+	368.881i	−0.301236	+	0.521756i
$708$		0			0
$709$	940.019	−	542.720i	1.32584	−	0.765473i	0.341185	−	0.939996i	$-0.389172\pi$
$709$	940.019	−	542.720i	1.32584	−	0.765473i	0.984653	+	0.174524i	$0.0558386\pi$
$710$	1105.61	−	935.654i	1.55719	−	1.31782i
$711$		0			0
$712$	−538.956	−	906.922i	−0.756961	−	1.27377i
$713$	−293.455	+	169.426i	−0.411578	+	0.237625i
$714$		0			0
$715$	776.063	+	448.060i	1.08540	+	0.626658i
$716$	−66.0492	−	54.4833i	−0.0922475	−	0.0760939i
$717$		0			0
$718$	120.820	+	43.4013i	0.168273	+	0.0604474i
$719$		−	508.844i		−	0.707710i	−0.935300	−	0.353855i	$-0.884871\pi$
$719$		−	508.844i		−	0.707710i	0.935300	−	0.353855i	$-0.115129\pi$
$720$		0			0
$721$	82.1465			0.113934
$722$	−15.6744	+	43.6343i	−0.0217097	+	0.0604353i
$723$		0			0
$724$	−812.700	+	985.223i	−1.12251	+	1.36081i
$725$	168.252	−	291.421i	0.232072	−	0.401961i
$726$		0			0
$727$	−197.956	−	342.870i	−0.272292	−	0.471623i	0.697156	−	0.716919i	$-0.254448\pi$
$727$	−197.956	−	342.870i	−0.272292	−	0.471623i	−0.969448	+	0.245296i	$0.921115\pi$
$728$	−338.636	−	569.837i	−0.465160	−	0.782743i
$729$		0			0
$730$	1041.01	+	1230.10i	1.42604	+	1.68507i
$731$	138.782	+	240.377i	0.189852	+	0.328833i
$732$		0			0
$733$	210.592	+	121.586i	0.287302	+	0.165874i	0.636724	−	0.771091i	$-0.280289\pi$
$733$	210.592	+	121.586i	0.287302	+	0.165874i	−0.349422	+	0.936965i	$0.613622\pi$
$734$	1243.03	−	224.565i	1.69350	−	0.305947i
$735$		0			0
$736$	657.769	+	528.806i	0.893708	+	0.718486i
$737$			312.120i			0.423501i
$738$		0			0
$739$			315.637i			0.427113i	0.976931	+	0.213557i	$0.0685048\pi$
$739$			315.637i			0.427113i	−0.976931	+	0.213557i	$0.931495\pi$
$740$	70.6539	+	189.162i	0.0954783	+	0.255625i
$741$		0			0
$742$	−865.137	+	156.295i	−1.16595	+	0.210640i
$743$	855.729	+	494.055i	1.15172	+	0.664947i	0.949306	−	0.314353i	$-0.101788\pi$
$743$	855.729	+	494.055i	1.15172	+	0.664947i	0.202415	+	0.979300i	$0.435121\pi$
$744$		0			0
$745$	−775.064	−	1342.45i	−1.04035	−	1.80195i
$746$	575.535	−	487.064i	0.771495	−	0.652901i
$747$		0			0
$748$	425.157	+	71.2906i	0.568391	+	0.0953083i
$749$	−215.316	−	372.939i	−0.287472	−	0.497916i
$750$		0			0
$751$	374.852	−	649.262i	0.499137	−	0.864530i	−0.500863	−	0.865527i	$-0.666984\pi$
$751$	374.852	−	649.262i	0.499137	−	0.864530i	1.00000		0.000996439i	$0.000317176\pi$
$752$	192.374	+	221.596i	0.255817	+	0.294675i
$753$		0			0
$754$	−144.553	−	51.9266i	−0.191715	−	0.0688682i
$755$	431.135			0.571040
$756$		0			0
$757$		−	731.923i		−	0.966873i	−0.875379	−	0.483436i	$-0.839388\pi$
$757$		−	731.923i		−	0.966873i	0.875379	−	0.483436i	$-0.160612\pi$
$758$	725.904	+	260.761i	0.957657	+	0.344012i
$759$		0			0
$760$	1258.82	−	15.8574i	1.65634	−	0.0208650i
$761$	−777.865	−	449.101i	−1.02216	−	0.590146i	−0.107433	−	0.994212i	$-0.534263\pi$
$761$	−777.865	−	449.101i	−1.02216	−	0.590146i	−0.914729	+	0.404067i	$0.867596\pi$
$762$		0			0
$763$	324.986	−	187.630i	0.425931	−	0.245912i
$764$	−766.483	−	128.525i	−1.00325	−	0.168226i
$765$		0			0
$766$	−163.937	+	138.737i	−0.214017	+	0.181118i
$767$	−251.366	+	145.126i	−0.327726	+	0.189213i
$768$		0			0
$769$	275.386	−	476.983i	0.358109	−	0.620264i	−0.629536	−	0.776972i	$-0.716755\pi$
$769$	275.386	−	476.983i	0.358109	−	0.620264i	0.987645	+	0.156708i	$0.0500882\pi$
$770$	1202.43	−	217.231i	1.56160	−	0.282118i
$771$		0			0
$772$	−153.605	+	57.3728i	−0.198970	+	0.0743171i
$773$	−328.803			−0.425360			−0.212680	−	0.977122i	$-0.568219\pi$
$773$	−328.803			−0.425360			−0.212680	+	0.977122i	$0.568219\pi$
$774$		0			0
$775$	−620.609			−0.800786
$776$	1313.94	+	736.696i	1.69323	+	0.949350i
$777$		0			0
$778$	−91.0216	+	16.4439i	−0.116994	+	0.0211362i
$779$	−347.051	+	601.110i	−0.445509	+	0.771644i
$780$		0			0
$781$	695.461	−	401.525i	0.890475	−	0.514116i
$782$	−386.810	−	457.071i	−0.494642	−	0.584490i
$783$		0			0
$784$	−113.288	−	39.0916i	−0.144500	−	0.0498618i
$785$	−724.132	+	418.078i	−0.922461	+	0.532583i
$786$		0			0
$787$	347.183	+	200.446i	0.441147	+	0.254696i	0.704084	−	0.710117i	$-0.251358\pi$
$787$	347.183	+	200.446i	0.441147	+	0.254696i	−0.262937	+	0.964813i	$0.584691\pi$
$788$	−44.0506	−	36.3369i	−0.0559018	−	0.0461128i
$789$		0			0
$790$	−142.665	+	397.150i	−0.180589	+	0.502721i
$791$		−	387.293i		−	0.489624i
$792$		0			0
$793$	−713.694			−0.899992
$794$	567.129	+	203.725i	0.714268	+	0.256581i
$795$		0			0
$796$	−922.222	−	760.731i	−1.15857	−	0.955692i
$797$	129.797	−	224.815i	0.162857	−	0.282077i	−0.773035	−	0.634363i	$-0.781262\pi$
$797$	129.797	−	224.815i	0.162857	−	0.282077i	0.935892	+	0.352286i	$0.114596\pi$
$798$		0			0
$799$	−104.097	−	180.302i	−0.130285	−	0.225660i
$800$	559.051	+	1441.11i	0.698814	+	1.80138i
$801$		0			0
$802$	−332.069	+	281.023i	−0.414051	+	0.350403i
$803$	446.736	+	773.770i	0.556334	+	0.963599i
$804$		0			0
$805$	−1469.81	−	848.598i	−1.82586	−	1.05416i
$806$	50.3611	+	278.763i	0.0624828	+	0.345859i
$807$		0			0
$808$	−395.460	−	221.725i	−0.489431	−	0.274412i
$809$		−	934.520i		−	1.15515i	−0.816336	−	0.577577i	$-0.803998\pi$
$809$		−	934.520i		−	1.15515i	0.816336	−	0.577577i	$-0.196002\pi$
$810$		0			0
$811$			235.144i			0.289943i	0.989436	+	0.144972i	$0.0463091\pi$
$811$			235.144i			0.289943i	−0.989436	+	0.144972i	$0.953691\pi$
$812$	−196.196	+	73.2813i	−0.241621	+	0.0902479i
$813$		0			0
$814$	19.9039	+	110.174i	0.0244520	+	0.135348i
$815$	−2042.51	−	1179.25i	−2.50615	−	1.44693i
$816$		0			0
$817$	224.707	+	389.204i	0.275039	+	0.476382i
$818$	−847.895	−	1001.91i	−1.03655	−	1.22483i
$819$		0			0
$820$	−1275.52	−	213.880i	−1.55551	−	0.260829i
$821$	55.7034	+	96.4812i	0.0678483	+	0.117517i	0.897954	−	0.440089i	$-0.145053\pi$
$821$	55.7034	+	96.4812i	0.0678483	+	0.117517i	−0.830106	+	0.557606i	$0.811720\pi$
$822$		0			0
$823$	−244.582	+	423.628i	−0.297183	+	0.514736i	−0.975490	−	0.220042i	$-0.929380\pi$
$823$	−244.582	+	423.628i	−0.297183	+	0.514736i	0.678307	+	0.734778i	$0.262714\pi$
$824$	1.10136	+	87.4296i	0.00133660	+	0.106104i
$825$		0			0
$826$	−133.799	+	372.469i	−0.161984	+	0.450931i
$827$	−595.430			−0.719988			−0.359994	−	0.932955i	$-0.617221\pi$
$827$	−595.430			−0.719988			−0.359994	+	0.932955i	$0.617221\pi$
$828$		0			0
$829$		−	952.457i		−	1.14892i	−0.818532	−	0.574461i	$-0.805212\pi$
$829$		−	952.457i		−	1.14892i	0.818532	−	0.574461i	$-0.194788\pi$
$830$	−669.022	+	1862.42i	−0.806050	+	2.24388i
$831$		0			0
$832$	601.944	−	368.055i	0.723490	−	0.442374i
$833$	73.6343	+	42.5128i	0.0883965	+	0.0510357i
$834$		0			0
$835$	−698.290	+	403.158i	−0.836276	+	0.482824i
$836$	688.389	+	115.430i	0.823431	+	0.138074i
$837$		0			0
$838$	499.660	+	590.419i	0.596253	+	0.704557i
$839$	−719.566	+	415.442i	−0.857647	+	0.495163i	−0.863224	−	0.504821i	$-0.831558\pi$
$839$	−719.566	+	415.442i	−0.857647	+	0.495163i	0.00557635	+	0.999984i	$0.498225\pi$
$840$		0			0
$841$	396.235	−	686.299i	0.471148	−	0.816052i
$842$	115.238	+	637.872i	0.136862	+	0.757568i
$843$		0			0
$844$	327.123	+	875.810i	0.387587	+	1.03769i
$845$	406.400			0.480946
$846$		0			0
$847$	−231.960			−0.273861
$848$	−177.946	−	918.680i	−0.209842	−	1.08335i
$849$		0			0
$850$	−194.967	−	1079.19i	−0.229373	−	1.26964i
$851$	77.7532	−	134.672i	0.0913668	−	0.158252i
$852$		0			0
$853$	−463.386	+	267.536i	−0.543243	+	0.313641i	−0.746392	−	0.665506i	$-0.768216\pi$
$853$	−463.386	+	267.536i	−0.543243	+	0.313641i	0.203149	+	0.979148i	$0.434882\pi$
$854$	−742.845	+	628.655i	−0.869841	+	0.736129i
$855$		0			0
$856$	394.037	−	234.164i	0.460323	−	0.273556i
$857$	−91.7985	+	52.9999i	−0.107116	+	0.0618435i	−0.552601	−	0.833446i	$-0.686365\pi$
$857$	−91.7985	+	52.9999i	−0.107116	+	0.0618435i	0.445485	+	0.895289i	$0.353031\pi$
$858$		0			0
$859$	−340.158	−	196.391i	−0.395993	−	0.228627i	0.288760	−	0.957401i	$-0.406757\pi$
$859$	−340.158	−	196.391i	−0.395993	−	0.228627i	−0.684754	+	0.728774i	$0.740090\pi$
$860$	−532.861	+	645.979i	−0.619606	+	0.751139i
$861$		0			0
$862$	786.090	+	282.381i	0.911937	+	0.327588i
$863$			989.382i			1.14644i	0.819400	+	0.573222i	$0.194307\pi$
$863$			989.382i			1.14644i	−0.819400	+	0.573222i	$0.805693\pi$
$864$		0			0
$865$	1509.74			1.74537
$866$	284.509	−	792.014i	0.328533	−	0.914566i
$867$		0			0
$868$	297.965	+	245.788i	0.343278	+	0.283166i
$869$	−116.987	+	202.627i	−0.134623	+	0.233173i
$870$		0			0
$871$	−181.212	−	313.868i	−0.208050	−	0.360353i
$872$	204.055	+	343.370i	0.234008	+	0.393773i
$873$		0			0
$874$	−626.301	−	740.063i	−0.716591	−	0.846754i
$875$	−749.827	−	1298.74i	−0.856945	−	1.48427i
$876$		0			0
$877$	501.720	+	289.668i	0.572087	+	0.330294i	0.757982	−	0.652275i	$-0.226185\pi$
$877$	501.720	+	289.668i	0.572087	+	0.330294i	−0.185896	+	0.982569i	$0.559519\pi$
$878$	−369.772	+	66.8029i	−0.421153	+	0.0760853i
$879$		0			0
$880$	247.323	+	1276.85i	0.281049	+	1.45097i
$881$			1186.52i			1.34679i	0.739284	+	0.673394i	$0.235164\pi$
$881$			1186.52i			1.34679i	−0.739284	+	0.673394i	$0.764836\pi$
$882$		0			0
$883$		−	883.300i		−	1.00034i	−0.865927	−	0.500170i	$-0.833271\pi$
$883$		−	883.300i		−	1.00034i	0.865927	−	0.500170i	$-0.166729\pi$
$884$	−468.927	+	175.149i	−0.530461	+	0.198132i
$885$		0			0
$886$	−441.559	+	79.7718i	−0.498373	+	0.0900359i
$887$	659.656	+	380.853i	0.743694	+	0.429372i	0.823411	−	0.567446i	$-0.192068\pi$
$887$	659.656	+	380.853i	0.743694	+	0.429372i	−0.0797171	+	0.996818i	$0.525402\pi$
$888$		0			0
$889$	−70.6120	−	122.304i	−0.0794286	−	0.137574i
$890$	−1723.72	+	1458.75i	−1.93676	+	1.63904i
$891$		0			0
$892$	−1.83026	+	10.9151i	−0.00205186	+	0.0122367i
$893$	−168.548	−	291.934i	−0.188744	−	0.326914i
$894$		0			0
$895$	−91.6336	+	158.714i	−0.102384	+	0.177334i
$896$	302.330	−	913.308i	0.337422	−	1.01932i
$897$		0			0
$898$	390.502	+	140.277i	0.434857	+	0.156210i
$899$	89.5023			0.0995577
$900$		0			0
$901$			663.894i			0.736841i
$902$	−674.856	−	242.423i	−0.748177	−	0.268762i
$903$		0			0
$904$	412.200	−	5.19251i	0.455974	−	0.00574393i
$905$	2367.46	+	1366.85i	2.61597	+	1.51033i
$906$		0			0
$907$	335.644	−	193.784i	0.370060	−	0.213654i	−0.303425	−	0.952855i	$-0.598130\pi$
$907$	335.644	−	193.784i	0.370060	−	0.213654i	0.673485	+	0.739201i	$0.264797\pi$
$908$	32.5316	−	194.009i	0.0358278	−	0.213666i
$909$		0			0
$910$	−1083.05	+	916.560i	−1.19016	+	1.00721i
$911$	748.017	−	431.868i	0.821094	−	0.474059i	−0.0296996	−	0.999559i	$-0.509455\pi$
$911$	748.017	−	431.868i	0.821094	−	0.474059i	0.850794	+	0.525500i	$0.176122\pi$
$912$		0			0
$913$	−548.605	+	950.212i	−0.600882	+	1.04076i
$914$	−117.849	+	21.2905i	−0.128938	+	0.0232938i
$915$		0			0
$916$	367.678	+	984.386i	0.401395	+	1.07466i
$917$	−284.525			−0.310278
$918$		0			0
$919$	−7.98109			−0.00868453			−0.00434227	−	0.999991i	$-0.501382\pi$
$919$	−7.98109			−0.00868453			−0.00434227	+	0.999991i	$0.501382\pi$
$920$	883.467	−	1575.72i	0.960290	−	1.71274i
$921$		0			0
$922$	−354.421	+	64.0295i	−0.384404	+	0.0694463i
$923$	−466.237	+	807.546i	−0.505132	+	0.874914i
$924$		0			0
$925$	246.653	−	142.405i	0.266652	−	0.153951i
$926$	−515.631	−	609.291i	−0.556837	−	0.657982i
$927$		0			0
$928$	−80.6246	−	207.832i	−0.0868799	−	0.223957i
$929$	402.056	−	232.127i	0.432783	−	0.249867i	−0.267748	−	0.963489i	$-0.586280\pi$
$929$	402.056	−	232.127i	0.432783	−	0.249867i	0.700532	+	0.713621i	$0.252946\pi$
$930$		0			0
$931$	119.224	+	68.8342i	0.128060	+	0.0739357i
$932$	815.812	−	988.996i	0.875335	−	1.06115i
$933$		0			0
$934$	192.661	−	536.328i	0.206275	−	0.574227i
$935$		−	922.732i		−	0.986879i
$936$		0			0
$937$	312.292			0.333289			0.166645	−	0.986017i	$-0.446707\pi$
$937$	312.292			0.333289			0.166645	+	0.986017i	$0.446707\pi$
$938$	−465.082	−	167.068i	−0.495823	−	0.178111i
$939$		0			0
$940$	399.689	−	484.537i	0.425201	−	0.515465i
$941$	466.897	−	808.689i	0.496171	−	0.859393i	−0.503819	−	0.863809i	$-0.668072\pi$
$941$	466.897	−	808.689i	0.496171	−	0.859393i	0.999990	+	0.00441583i	$0.00140561\pi$
$942$		0			0
$943$	498.003	+	862.567i	0.528105	+	0.914705i
$944$	−398.217	−	137.410i	−0.421840	−	0.145562i
$945$		0			0
$946$	−354.410	+	299.930i	−0.374641	+	0.317051i
$947$	−697.096	−	1207.40i	−0.736109	−	1.27498i	−0.954235	−	0.299058i	$-0.903328\pi$
$947$	−697.096	−	1207.40i	−0.736109	−	1.27498i	0.218126	−	0.975921i	$-0.430006\pi$
$948$		0			0
$949$	−898.475	−	518.735i	−0.946760	−	0.546612i
$950$	−315.679	−	1747.37i	−0.332294	−	1.83934i
$951$		0			0
$952$	−333.801	+	595.356i	−0.350632	+	0.625373i
$953$		−	1110.04i		−	1.16478i	−0.812909	−	0.582390i	$-0.802118\pi$
$953$		−	1110.04i		−	1.16478i	0.812909	−	0.582390i	$-0.197882\pi$
$954$		0			0
$955$			1663.52i			1.74191i
$956$	513.842	+	1375.71i	0.537491	+	1.43903i
$957$		0			0
$958$	100.151	+	554.365i	0.104542	+	0.578669i
$959$	−1688.77	−	975.011i	−1.76097	−	1.01670i
$960$		0			0
$961$	397.966	+	689.298i	0.414117	+	0.717271i
$962$	−83.9803	−	99.2346i	−0.0872976	−	0.103154i
$963$		0			0
$964$	70.5865	−	420.957i	0.0732225	−	0.436678i
$965$	175.484	+	303.948i	0.181849	+	0.314972i
$966$		0			0
$967$	−826.703	+	1431.89i	−0.854915	+	1.48076i	0.0218081	+	0.999762i	$0.493058\pi$
$967$	−826.703	+	1431.89i	−0.854915	+	1.48076i	−0.876723	+	0.480995i	$0.840276\pi$
$968$	−3.10993	−	246.878i	−0.00321274	−	0.255039i
$969$		0			0
$970$	1090.05	−	3034.48i	1.12376	−	3.12832i
$971$	677.141			0.697365			0.348683	−	0.937241i	$-0.386629\pi$
$971$	677.141			0.697365			0.348683	+	0.937241i	$0.386629\pi$
$972$		0			0
$973$			700.397i			0.719832i
$974$	−331.358	+	922.430i	−0.340203	+	0.947054i
$975$		0			0
$976$	−679.044	−	782.190i	−0.695742	−	0.801424i
$977$	816.419	+	471.360i	0.835639	+	0.482456i	0.855779	−	0.517341i	$-0.173078\pi$
$977$	816.419	+	471.360i	0.835639	+	0.482456i	−0.0201405	+	0.999797i	$0.506411\pi$
$978$		0			0
$979$	−1084.27	+	626.005i	−1.10753	+	0.639433i
$980$	−42.4209	+	252.986i	−0.0432867	+	0.258149i
$981$		0			0
$982$	431.530	+	509.914i	0.439440	+	0.519260i
$983$	−1071.25	+	618.485i	−1.08977	+	0.629181i	−0.933516	−	0.358536i	$-0.883276\pi$
$983$	−1071.25	+	618.485i	−1.08977	+	0.629181i	−0.156257	+	0.987716i	$0.549943\pi$
$984$		0			0
$985$	−61.1138	+	105.852i	−0.0620445	+	0.107464i
$986$	28.1175	+	155.638i	0.0285168	+	0.157848i
$987$		0			0
$988$	−759.259	+	283.591i	−0.768481	+	0.287035i
$989$	644.889			0.652062
$990$		0			0
$991$	−123.871			−0.124996			−0.0624979	−	0.998045i	$-0.519907\pi$
$991$	−123.871			−0.124996			−0.0624979	+	0.998045i	$0.519907\pi$
$992$	−257.601	+	320.423i	−0.259678	+	0.323007i
$993$		0			0
$994$	226.044	+	1251.21i	0.227408	+	1.25877i
$995$	−1279.45	+	2216.07i	−1.28588	+	2.22720i
$996$		0			0
$997$	−591.638	+	341.582i	−0.593418	+	0.342610i	−0.766448	−	0.642307i	$-0.777978\pi$
$997$	−591.638	+	341.582i	−0.593418	+	0.342610i	0.173030	+	0.984917i	$0.444644\pi$
$998$	−728.827	+	616.792i	−0.730288	+	0.618028i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.3.j.a.125.9		44
3.2	odd	2		72.3.j.a.5.14	✓	44
4.3	odd	2		864.3.n.a.17.1		44
8.3	odd	2		864.3.n.a.17.22		44
8.5	even	2	inner	216.3.j.a.125.2		44
9.2	odd	6	inner	216.3.j.a.197.2		44
9.4	even	3		648.3.h.a.485.13		44
9.5	odd	6		648.3.h.a.485.32		44
9.7	even	3		72.3.j.a.29.21	yes	44
12.11	even	2		288.3.n.a.113.18		44
24.5	odd	2		72.3.j.a.5.21	yes	44
24.11	even	2		288.3.n.a.113.5		44
36.7	odd	6		288.3.n.a.209.5		44
36.11	even	6		864.3.n.a.305.22		44
36.23	even	6		2592.3.h.a.1457.2		44
36.31	odd	6		2592.3.h.a.1457.43		44
72.5	odd	6		648.3.h.a.485.14		44
72.11	even	6		864.3.n.a.305.1		44
72.13	even	6		648.3.h.a.485.31		44
72.29	odd	6	inner	216.3.j.a.197.9		44
72.43	odd	6		288.3.n.a.209.18		44
72.59	even	6		2592.3.h.a.1457.44		44
72.61	even	6		72.3.j.a.29.14	yes	44
72.67	odd	6		2592.3.h.a.1457.1		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.3.j.a.5.14	✓	44	3.2	odd	2
72.3.j.a.5.21	yes	44	24.5	odd	2
72.3.j.a.29.14	yes	44	72.61	even	6
72.3.j.a.29.21	yes	44	9.7	even	3
216.3.j.a.125.2		44	8.5	even	2	inner
216.3.j.a.125.9		44	1.1	even	1	trivial
216.3.j.a.197.2		44	9.2	odd	6	inner
216.3.j.a.197.9		44	72.29	odd	6	inner
288.3.n.a.113.5		44	24.11	even	2
288.3.n.a.113.18		44	12.11	even	2
288.3.n.a.209.5		44	36.7	odd	6
288.3.n.a.209.18		44	72.43	odd	6
648.3.h.a.485.13		44	9.4	even	3
648.3.h.a.485.14		44	72.5	odd	6
648.3.h.a.485.31		44	72.13	even	6
648.3.h.a.485.32		44	9.5	odd	6
864.3.n.a.17.1		44	4.3	odd	2
864.3.n.a.17.22		44	8.3	odd	2
864.3.n.a.305.1		44	72.11	even	6
864.3.n.a.305.22		44	36.11	even	6
2592.3.h.a.1457.1		44	72.67	odd	6
2592.3.h.a.1457.2		44	36.23	even	6
2592.3.h.a.1457.43		44	36.31	odd	6
2592.3.h.a.1457.44		44	72.59	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	216.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.676143 + 1.88224i) q^{2} +(-3.08566 - 2.54533i) q^{4} +(-4.28090 + 7.41474i) q^{5} +(-3.75800 - 6.50904i) q^{7} +(6.87727 - 4.08695i) q^{8} +O(q^{10})\)	\(q+(-0.676143 + 1.88224i) q^{2} +(-3.08566 - 2.54533i) q^{4} +(-4.28090 + 7.41474i) q^{5} +(-3.75800 - 6.50904i) q^{7} +(6.87727 - 4.08695i) q^{8} +(-11.0618 - 13.0711i) q^{10} +(-4.74705 - 8.22213i) q^{11} +(9.54725 + 5.51211i) q^{13} +(14.7925 - 2.67241i) q^{14} +(3.04261 + 15.7080i) q^{16} -11.3516i q^{17} -18.3798i q^{19} +(32.0824 - 11.9831i) q^{20} +(18.6857 - 3.37575i) q^{22} +(-22.8408 - 13.1871i) q^{23} +(-24.1522 - 41.8329i) q^{25} +(-16.8304 + 14.2433i) q^{26} +(-4.97174 + 29.6500i) q^{28} +(3.48316 + 6.03301i) q^{29} +(6.42393 - 11.1266i) q^{31} +(-31.6236 - 4.89396i) q^{32} +(21.3664 + 7.67530i) q^{34} +64.3505 q^{35} +5.89614i q^{37} +(34.5953 + 12.4274i) q^{38} +(0.862760 + 68.4890i) q^{40} +(-32.7049 - 18.8822i) q^{41} +(-21.1756 + 12.2257i) q^{43} +(-6.28023 + 37.4535i) q^{44} +(40.2650 - 34.0754i) q^{46} +(15.8834 - 9.17030i) q^{47} +(-3.74509 + 6.48669i) q^{49} +(95.0700 - 17.1753i) q^{50} +(-15.4295 - 41.3094i) q^{52} -58.4847 q^{53} +81.2866 q^{55} +(-52.4469 - 29.4057i) q^{56} +(-13.7107 + 2.47697i) q^{58} +(-13.1643 + 22.8013i) q^{59} +(-56.0654 + 32.3694i) q^{61} +(16.5994 + 19.6145i) q^{62} +(30.5937 - 56.2141i) q^{64} +(-81.7417 + 47.1936i) q^{65} +(-28.4707 - 16.4376i) q^{67} +(-28.8935 + 35.0271i) q^{68} +(-43.5101 + 121.123i) q^{70} +84.5841i q^{71} -94.1083 q^{73} +(-11.0980 - 3.98664i) q^{74} +(-46.7827 + 56.7139i) q^{76} +(-35.6788 + 61.7975i) q^{77} +(-12.3221 - 21.3425i) q^{79} +(-129.496 - 44.6844i) q^{80} +(57.6540 - 48.7914i) q^{82} +(-57.7838 - 100.085i) q^{83} +(84.1691 + 48.5950i) q^{85} +(-8.69405 - 48.1239i) q^{86} +(-66.2502 - 37.1448i) q^{88} -131.872i q^{89} -82.8580i q^{91} +(36.9133 + 98.8282i) q^{92} +(6.52124 + 36.0969i) q^{94} +(136.282 + 78.6822i) q^{95} +(94.1484 + 163.070i) q^{97} +(-9.67730 - 11.4351i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 3 q^{2} - q^{4} - 2 q^{7}+O(q^{10}) \) 44 * q + 3 * q^2 - q^4 - 2 * q^7	\( 44 q + 3 q^{2} - q^{4} - 2 q^{7} + 4 q^{10} + 48 q^{14} - q^{16} + 66 q^{20} + 7 q^{22} + 6 q^{23} - 72 q^{25} + 28 q^{28} - 2 q^{31} + 93 q^{32} + 9 q^{34} - 99 q^{38} - 56 q^{40} - 66 q^{41} + 72 q^{46} + 6 q^{47} - 72 q^{49} - 189 q^{50} - 42 q^{52} + 92 q^{55} - 270 q^{56} - 38 q^{58} + 2 q^{64} + 6 q^{65} - 387 q^{68} - 4 q^{70} - 8 q^{73} + 432 q^{74} - 63 q^{76} - 2 q^{79} + 186 q^{82} + 615 q^{86} - 77 q^{88} + 624 q^{92} - 186 q^{94} - 144 q^{95} - 2 q^{97}+O(q^{100}) \) 44 * q + 3 * q^2 - q^4 - 2 * q^7 + 4 * q^10 + 48 * q^14 - q^16 + 66 * q^20 + 7 * q^22 + 6 * q^23 - 72 * q^25 + 28 * q^28 - 2 * q^31 + 93 * q^32 + 9 * q^34 - 99 * q^38 - 56 * q^40 - 66 * q^41 + 72 * q^46 + 6 * q^47 - 72 * q^49 - 189 * q^50 - 42 * q^52 + 92 * q^55 - 270 * q^56 - 38 * q^58 + 2 * q^64 + 6 * q^65 - 387 * q^68 - 4 * q^70 - 8 * q^73 + 432 * q^74 - 63 * q^76 - 2 * q^79 + 186 * q^82 + 615 * q^86 - 77 * q^88 + 624 * q^92 - 186 * q^94 - 144 * q^95 - 2 * q^97

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