LMFDB - Embedded newform 216.3.j.a.125.2

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			125.2
Character	$\chi$	$=$	216.125
Dual form			216.3.j.a.197.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.96814 - 0.355563i) q^{2} +(3.74715 + 1.39960i) q^{4} +(4.28090 - 7.41474i) q^{5} +(-3.75800 - 6.50904i) q^{7} +(-6.87727 - 4.08695i) q^{8} +O(q^{10})$	\(q+(-1.96814 - 0.355563i) q^{2} +(3.74715 + 1.39960i) q^{4} +(4.28090 - 7.41474i) q^{5} +(-3.75800 - 6.50904i) q^{7} +(-6.87727 - 4.08695i) q^{8} +(-11.0618 + 13.0711i) q^{10} +(4.74705 + 8.22213i) q^{11} +(-9.54725 - 5.51211i) q^{13} +(5.08189 + 14.1469i) q^{14} +(12.0823 + 10.4890i) q^{16} -11.3516i q^{17} +18.3798i q^{19} +(26.4188 - 21.7926i) q^{20} +(-6.41937 - 17.8702i) q^{22} +(-22.8408 - 13.1871i) q^{23} +(-24.1522 - 41.8329i) q^{25} +(16.8304 + 14.2433i) q^{26} +(-4.97174 - 29.6500i) q^{28} +(-3.48316 - 6.03301i) q^{29} +(6.42393 - 11.1266i) q^{31} +(-20.0501 - 24.9398i) q^{32} +(-4.03621 + 22.3415i) q^{34} -64.3505 q^{35} -5.89614i q^{37} +(6.53519 - 36.1741i) q^{38} +(-59.7446 + 33.4973i) q^{40} +(-32.7049 - 18.8822i) q^{41} +(21.1756 - 12.2257i) q^{43} +(6.28023 + 37.4535i) q^{44} +(40.2650 + 34.0754i) q^{46} +(15.8834 - 9.17030i) q^{47} +(-3.74509 + 6.48669i) q^{49} +(32.6607 + 90.9207i) q^{50} +(-28.0603 - 34.0170i) q^{52} +58.4847 q^{53} +81.2866 q^{55} +(-0.757376 + 60.1232i) q^{56} +(4.71023 + 13.1123i) q^{58} +(13.1643 - 22.8013i) q^{59} +(56.0654 - 32.3694i) q^{61} +(-16.5994 + 19.6145i) q^{62} +(30.5937 + 56.2141i) q^{64} +(-81.7417 + 47.1936i) q^{65} +(28.4707 + 16.4376i) q^{67} +(15.8876 - 42.5361i) q^{68} +(126.651 + 22.8807i) q^{70} +84.5841i q^{71} -94.1083 q^{73} +(-2.09645 + 11.6044i) q^{74} +(-25.7243 + 68.8719i) q^{76} +(35.6788 - 61.7975i) q^{77} +(-12.3221 - 21.3425i) q^{79} +(129.496 - 44.6844i) q^{80} +(57.6540 + 48.7914i) q^{82} +(57.7838 + 100.085i) q^{83} +(-84.1691 - 48.5950i) q^{85} +(-46.0236 + 16.5327i) q^{86} +(0.956706 - 75.9467i) q^{88} -131.872i q^{89} +82.8580i q^{91} +(-67.1311 - 81.3820i) q^{92} +(-34.5214 + 12.4009i) q^{94} +(136.282 + 78.6822i) q^{95} +(94.1484 + 163.070i) q^{97} +(9.67730 - 11.4351i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.96814	−	0.355563i	−0.984070	−	0.177782i
$2$	−1.96814	−	0.355563i	−0.984070	−	0.177782i
$3$		0			0
$3$		0			0
$4$	3.74715	+	1.39960i	0.936787	+	0.349899i
$5$	4.28090	−	7.41474i	0.856180	−	1.48295i	−0.0193654	−	0.999812i	$-0.506165\pi$
$5$	4.28090	−	7.41474i	0.856180	−	1.48295i	0.875546	−	0.483135i	$-0.160502\pi$
$6$		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	0.997007	−	0.0773115i	$-0.0246336\pi$
$11$	4.74705	+	8.22213i	0.431550	+	0.747466i	−0.565457	+	0.824778i	$0.691300\pi$
$12$		0			0
$13$	−9.54725	−	5.51211i	−0.734404	−	0.424008i	0.0856271	−	0.996327i	$-0.472711\pi$
$13$	−9.54725	−	5.51211i	−0.734404	−	0.424008i	−0.820031	+	0.572319i	$0.806044\pi$
$14$	5.08189	+	14.1469i	0.362992	+	1.01049i
$15$		0			0
$16$	12.0823	+	10.4890i	0.755141	+	0.655562i
$17$		−	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	$0.160700\pi$
$19$			18.3798i			0.967359i	−0.875245	+	0.483680i	$0.839300\pi$
$20$	26.4188	−	21.7926i	1.32094	−	1.08963i
$21$		0			0
$22$	−6.41937	−	17.8702i	−0.291789	−	0.812281i
$23$	−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	0.799701	−	0.600398i	$-0.204991\pi$
$29$	−3.48316	−	6.03301i	−0.120109	−	0.208035i	−0.919810	+	0.392363i	$0.871658\pi$
$30$		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	$0.100224\pi$
$32$	−20.0501	−	24.9398i	−0.626565	−	0.779369i
$33$		0			0
$34$	−4.03621	+	22.3415i	−0.118712	+	0.657103i
$35$	−64.3505			−1.83859
$36$		0			0
$37$		−	5.89614i		−	0.159355i	−0.996821	−	0.0796776i	$-0.974611\pi$
$37$		−	5.89614i		−	0.159355i	0.996821	−	0.0796776i	$-0.0253891\pi$
$38$	6.53519	−	36.1741i	0.171979	−	0.951949i
$39$		0			0
$40$	−59.7446	+	33.4973i	−1.49361	+	0.837433i
$41$	−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	−0.233137	−	0.972444i	$-0.574899\pi$
$43$	21.1756	−	12.2257i	0.492456	−	0.284320i	0.725593	+	0.688124i	$0.241566\pi$
$44$	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
$50$	32.6607	+	90.9207i	0.653215	+	1.81841i
$51$		0			0
$52$	−28.0603	−	34.0170i	−0.539620	−	0.654173i
$53$	58.4847			1.10348			0.551742	−	0.834015i	$-0.313963\pi$
$53$	58.4847			1.10348			0.551742	+	0.834015i	$0.313963\pi$
$54$		0			0
$55$	81.2866			1.47794
$56$	−0.757376	+	60.1232i	−0.0135246	+	1.07363i
$57$		0			0
$58$	4.71023	+	13.1123i	0.0812109	+	0.226074i
$59$	13.1643	−	22.8013i	0.223124	−	0.386462i	−0.732631	−	0.680626i	$-0.761708\pi$
$59$	13.1643	−	22.8013i	0.223124	−	0.386462i	0.955755	+	0.294164i	$0.0950412\pi$
$60$		0			0
$61$	56.0654	−	32.3694i	0.919104	−	0.530645i	0.0357552	−	0.999361i	$-0.488616\pi$
$61$	56.0654	−	32.3694i	0.919104	−	0.530645i	0.883349	+	0.468715i	$0.155283\pi$
$62$	−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	0.697187	−	0.716889i	$-0.254435\pi$
$67$	28.4707	+	16.4376i	0.424936	+	0.245337i	−0.272251	+	0.962226i	$0.587768\pi$
$68$	15.8876	−	42.5361i	0.233642	−	0.625531i
$69$		0			0
$70$	126.651	+	22.8807i	1.80930	+	0.326867i
$71$			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	$0.722967\pi$
$74$	−2.09645	+	11.6044i	−0.0283304	+	0.156817i
$75$		0			0
$76$	−25.7243	+	68.8719i	−0.338478	+	0.906210i
$77$	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	$0.0784566\pi$
$83$	57.7838	+	100.085i	0.696191	+	1.20584i	−0.273587	+	0.961847i	$0.588210\pi$
$84$		0			0
$85$	−84.1691	−	48.5950i	−0.990224	−	0.571706i
$86$	−46.0236	+	16.5327i	−0.535158	+	0.192241i
$87$		0			0
$88$	0.956706	−	75.9467i	0.0108717	−	0.863031i
$89$		−	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
$92$	−67.1311	−	81.3820i	−0.729686	−	0.884587i
$93$		0			0
$94$	−34.5214	+	12.4009i	−0.367249	+	0.131924i
$95$	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	0.971522	−	0.236951i	$-0.0761481\pi$
$101$	28.3361	+	49.0795i	0.280555	+	0.485936i	−0.690966	+	0.722887i	$0.742815\pi$
$102$		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	$0.183563\pi$
$104$	43.1313	+	76.9274i	0.414724	+	0.739687i
$105$		0			0
$106$	−115.106	−	20.7950i	−1.08591	−	0.196179i
$107$	−57.2955			−0.535472			−0.267736	−	0.963492i	$-0.586276\pi$
$107$	−57.2955			−0.535472			−0.267736	+	0.963492i	$0.586276\pi$
$108$		0			0
$109$		−	49.9283i		−	0.458058i	−0.973420	−	0.229029i	$-0.926445\pi$
$109$		−	49.9283i		−	0.458058i	0.973420	−	0.229029i	$-0.0735551\pi$
$110$	−159.983	−	28.9025i	−1.45439	−	0.262750i
$111$		0			0
$112$	22.8682	−	118.062i	0.204181	−	1.05412i
$113$	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
$122$	−121.854	+	43.7726i	−0.998802	+	0.358792i
$123$		0			0
$124$	39.6441	−	32.7020i	0.319711	−	0.263726i
$125$	−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	$0.476431\pi$
$128$	−40.2249	−	121.515i	−0.314257	−	0.949338i
$129$		0			0
$130$	177.659	−	63.8192i	1.36661	−	0.490917i
$131$	−18.9279	+	32.7842i	−0.144488	+	0.250261i	−0.929182	−	0.369623i	$-0.879487\pi$
$131$	−18.9279	+	32.7842i	−0.144488	+	0.250261i	0.784694	+	0.619884i	$0.212820\pi$
$132$		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	0.761370	−	0.648318i	$-0.224527\pi$
$139$	80.7028	+	46.5938i	0.580595	+	0.335207i	−0.180775	+	0.983525i	$0.557860\pi$
$140$	−241.131	−	90.0647i	−1.72236	−	0.643319i
$141$		0			0
$142$	30.0750	−	166.473i	0.211796	−	1.17235i
$143$		−	104.665i		−	0.731923i
$144$		0			0
$145$	−59.6443			−0.411340
$146$	185.218	+	33.4614i	1.26862	+	0.229188i
$147$		0			0
$148$	8.25222	−	22.0937i	0.0557583	−	0.149282i
$149$	90.5257	−	156.795i	0.607555	−	1.05232i	−0.384087	−	0.923297i	$-0.625484\pi$
$149$	90.5257	−	156.795i	0.607555	−	1.05232i	0.991642	−	0.129020i	$-0.0411830\pi$
$150$		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	0.205847	−	0.978584i	$-0.434005\pi$
$157$	−84.5771	−	48.8306i	−0.538707	−	0.311023i	−0.744555	+	0.667561i	$0.767338\pi$
$158$	16.6630	+	46.3862i	0.105462	+	0.293584i
$159$		0			0
$160$	−270.755	+	41.9012i	−1.69222	+	0.261882i
$161$			198.229i			1.23123i
$162$		0			0
$163$		−	275.467i		−	1.68998i	−0.534782	−	0.844990i	$-0.679606\pi$
$163$		−	275.467i		−	1.68998i	0.534782	−	0.844990i	$-0.320394\pi$
$164$	−96.1227	−	116.528i	−0.586114	−	0.710537i
$165$		0			0
$166$	−78.1403	−	217.526i	−0.470725	−	1.31040i
$167$	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	$0.00355414\pi$
$173$	88.1674	+	152.710i	0.509638	+	0.882720i	−0.490299	+	0.871554i	$0.663113\pi$
$174$		0			0
$175$	−181.528	+	314.416i	−1.03730	+	1.79666i
$176$	−28.8868	+	149.134i	−0.164130	+	0.847350i
$177$		0			0
$178$	−46.8890	+	259.543i	−0.263421	+	1.45811i
$179$	−21.4052			−0.119582			−0.0597911	−	0.998211i	$-0.519043\pi$
$179$	−21.4052			−0.119582			−0.0597911	+	0.998211i	$0.519043\pi$
$180$		0			0
$181$			319.291i			1.76404i	0.471215	+	0.882019i	$0.343816\pi$
$181$			319.291i			1.76404i	−0.471215	+	0.882019i	$0.656184\pi$
$182$	29.4613	−	163.076i	0.161875	−	0.896022i
$183$		0			0
$184$	103.187	+	184.040i	0.560799	+	1.00022i
$185$	−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	$0.132799\pi$
$194$	−127.316	−	354.420i	−0.656266	−	1.82691i
$195$		0			0
$196$	−23.1122	+	19.0650i	−0.117919	+	0.0972704i
$197$	−14.2759			−0.0724666			−0.0362333	−	0.999343i	$-0.511536\pi$
$197$	−14.2759			−0.0724666			−0.0362333	+	0.999343i	$0.511536\pi$
$198$		0			0
$199$	298.873			1.50188			0.750938	−	0.660373i	$-0.229602\pi$
$199$	298.873			1.50188			0.750938	+	0.660373i	$0.229602\pi$
$200$	−4.86757	+	386.405i	−0.0243379	+	1.93203i
$201$		0			0
$202$	−38.3185	−	106.671i	−0.189695	−	0.528072i
$203$	−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	0.895959	−	0.444136i	$-0.146489\pi$
$211$	202.413	+	116.863i	0.959305	+	0.553855i	0.0633463	+	0.997992i	$0.479823\pi$
$212$	219.151	+	81.8550i	1.03373	+	0.386108i
$213$		0			0
$214$	112.766	+	20.3722i	0.526942	+	0.0951971i
$215$		−	209.349i		−	0.973715i
$216$		0			0
$217$	−96.5645			−0.444998
$218$	−17.7527	+	98.2659i	−0.0814343	+	0.450761i
$219$		0			0
$220$	304.593	+	113.768i	1.38451	+	0.517129i
$221$	−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	0.806767	−	0.590870i	$-0.201215\pi$
$227$	−24.5897	−	42.5906i	−0.108325	−	0.187624i	−0.915092	+	0.403246i	$0.867882\pi$
$228$		0			0
$229$	227.507	+	131.351i	0.993481	+	0.573587i	0.906313	−	0.422607i	$-0.138885\pi$
$229$	227.507	+	131.351i	0.993481	+	0.573587i	0.0871681	+	0.996194i	$0.472218\pi$
$230$	425.031	−	152.681i	1.84796	−	0.663829i
$231$		0			0
$232$	−0.701986	+	55.7262i	−0.00302580	+	0.240199i
$233$			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
$236$	81.2412	−	67.0150i	0.344242	−	0.283962i
$237$		0			0
$238$	160.590	−	57.6875i	0.674748	−	0.242384i
$239$	−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
$248$	−89.6529	+	50.2662i	−0.361504	+	0.202686i
$249$		0			0
$250$	392.700	+	70.9449i	1.57080	+	0.283780i
$251$	255.233			1.01686			0.508432	−	0.861102i	$-0.330225\pi$
$251$	255.233			1.01686			0.508432	+	0.861102i	$0.330225\pi$
$252$		0			0
$253$		−	250.400i		−	0.989722i
$254$	−36.9809	−	6.68096i	−0.145594	−	0.0263030i
$255$		0			0
$256$	35.9619	+	253.462i	0.140476	+	0.990084i
$257$	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
$266$	−260.018	+	93.4042i	−0.977510	+	0.351144i
$267$		0			0
$268$	83.6781	+	101.442i	0.312232	+	0.378514i
$269$	−18.9169			−0.0703230			−0.0351615	−	0.999382i	$-0.511195\pi$
$269$	−18.9169			−0.0703230			−0.0351615	+	0.999382i	$0.511195\pi$
$270$		0			0
$271$	−502.339			−1.85365			−0.926824	−	0.375495i	$-0.877473\pi$
$271$	−502.339			−1.85365			−0.926824	+	0.375495i	$0.877473\pi$
$272$	119.067	−	137.153i	0.437745	−	0.504238i
$273$		0			0
$274$	−488.347	+	175.425i	−1.78229	+	0.640237i
$275$	229.304	−	397.166i	0.833831	−	1.44424i
$276$		0			0
$277$	164.430	−	94.9335i	0.593609	−	0.342720i	−0.172914	−	0.984937i	$-0.555318\pi$
$277$	164.430	−	94.9335i	0.593609	−	0.342720i	0.766523	+	0.642217i	$0.221985\pi$
$278$	−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	$-0.953260\pi$
$283$	−455.790	−	263.151i	−1.61057	−	0.929861i	−0.621327	−	0.783551i	$-0.713406\pi$
$284$	−118.384	+	316.949i	−0.416844	+	1.11602i
$285$		0			0
$286$	−37.2150	+	205.995i	−0.130122	+	0.720263i
$287$			283.837i			0.988979i
$288$		0			0
$289$	160.141			0.554123
$290$	117.388	+	21.2073i	0.404787	+	0.0731287i
$291$		0			0
$292$	−352.638	−	131.714i	−1.20766	−	0.451074i
$293$	−127.500	+	220.837i	−0.435154	+	0.753709i	−0.997308	−	0.0733236i	$-0.976639\pi$
$293$	−127.500	+	220.837i	−0.435154	+	0.753709i	0.562154	+	0.827032i	$0.309973\pi$
$294$		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
$302$	34.0476	+	94.7814i	0.112740	+	0.313846i
$303$		0			0
$304$	−192.786	+	222.070i	−0.634164	+	0.730493i
$305$		−	554.280i		−	1.81731i
$306$		0			0
$307$		−	365.110i		−	1.18928i	−0.803990	−	0.594642i	$-0.797294\pi$
$307$		−	365.110i		−	1.18928i	0.803990	−	0.594642i	$-0.202706\pi$
$308$	220.185	−	181.628i	0.714887	−	0.589703i
$309$		0			0
$310$	74.3763	+	207.048i	0.239924	+	0.667897i
$311$	−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	$-0.775391\pi$
$317$	−298.687	−	517.342i	−0.942231	−	1.63199i	−0.181029	−	0.983478i	$-0.557943\pi$
$318$		0			0
$319$	33.0695	−	57.2780i	0.103666	−	0.179555i
$320$	547.782	+	13.8031i	1.71182	+	0.0431346i
$321$		0			0
$322$	70.4828	−	390.142i	0.218891	−	1.21162i
$323$	208.640			0.645945
$324$		0			0
$325$			532.519i			1.63852i
$326$	−97.9459	+	542.157i	−0.300447	+	1.66306i
$327$		0			0
$328$	147.750	+	263.521i	0.450457	+	0.803418i
$329$	−119.380	−	68.9239i	−0.362856	−	0.209495i
$330$		0			0
$331$	−182.783	+	105.530i	−0.552215	+	0.318821i	−0.750015	−	0.661421i	$-0.769954\pi$
$331$	−182.783	+	105.530i	−0.552215	+	0.318821i	0.197800	+	0.980242i	$0.436620\pi$
$332$	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	$0.0143443\pi$
$338$	32.0942	+	89.3436i	0.0949533	+	0.264330i
$339$		0			0
$340$	−247.381	−	299.896i	−0.727590	−	0.882046i
$341$	121.979			0.357709
$342$		0			0
$343$	−311.988			−0.909585
$344$	−195.596	−	2.46394i	−0.568594	−	0.00716261i
$345$		0			0
$346$	−119.228	−	331.905i	−0.344588	−	0.959262i
$347$	14.0423	−	24.3220i	0.0404678	−	0.0700923i	−0.845082	−	0.534637i	$-0.820449\pi$
$347$	14.0423	−	24.3220i	0.0404678	−	0.0700923i	0.885550	+	0.464544i	$0.153782\pi$
$348$		0			0
$349$	429.084	−	247.732i	1.22947	−	0.709833i	0.262549	−	0.964919i	$-0.415437\pi$
$349$	429.084	−	247.732i	1.22947	−	0.709833i	0.966918	+	0.255086i	$0.0821037\pi$
$350$	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
$356$	184.568	−	494.146i	0.518450	−	1.38805i
$357$		0			0
$358$	42.1284	+	7.61090i	0.117677	+	0.0212595i
$359$		−	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
$362$	113.528	−	628.409i	0.313613	−	1.73594i
$363$		0			0
$364$	−115.968	+	310.481i	−0.318593	+	0.852970i
$365$	−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	0.869099	−	0.494639i	$-0.164700\pi$
$373$	326.479	+	188.493i	0.875279	+	0.505342i	0.00617981	+	0.999981i	$0.498033\pi$
$374$	−202.855	+	72.8700i	−0.542393	+	0.194840i
$375$		0			0
$376$	−146.713	−	1.84815i	−0.390194	−	0.00491530i
$377$			76.7983i			0.203709i
$378$		0			0
$379$			385.660i			1.01757i	0.860893	+	0.508786i	$0.169905\pi$
$379$			385.660i			1.01757i	−0.860893	+	0.508786i	$0.830095\pi$
$380$	400.544	+	485.573i	1.05406	+	1.27782i
$381$		0			0
$382$	−365.712	+	131.372i	−0.957361	+	0.343905i
$383$	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	0.834772	−	0.550596i	$-0.185599\pi$
$389$	−23.1238	−	40.0515i	−0.0594441	−	0.102960i	−0.894216	+	0.447636i	$0.852266\pi$
$390$		0			0
$391$	−149.695	+	259.279i	−0.382851	+	0.663117i
$392$	52.2668	−	29.3047i	0.133334	−	0.0747570i
$393$		0			0
$394$	28.0970	+	5.07599i	0.0713122	+	0.0128832i
$395$	−210.998			−0.534173
$396$		0			0
$397$			301.305i			0.758955i	0.925201	+	0.379477i	$0.123896\pi$
$397$			301.305i			0.758955i	−0.925201	+	0.379477i	$0.876104\pi$
$398$	−588.225	−	106.268i	−1.47795	−	0.267006i
$399$		0			0
$400$	146.972	−	758.769i	0.367429	−	1.89692i
$401$	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	$0.870285\pi$
$410$	608.587	−	218.618i	1.48436	−	0.533215i
$411$		0			0
$412$	−33.7249	+	27.8193i	−0.0818566	+	0.0675226i
$413$	−197.886			−0.479142
$414$		0			0
$415$	989.468			2.38426
$416$	53.9521	+	348.625i	0.129693	+	0.838041i
$417$		0			0
$418$	328.451	−	117.987i	0.785767	−	0.282265i
$419$	−193.367	+	334.922i	−0.461497	+	0.799336i	−0.999036	−	0.0439028i	$-0.986021\pi$
$419$	−193.367	+	334.922i	−0.461497	+	0.799336i	0.537539	+	0.843239i	$0.319354\pi$
$420$		0			0
$421$	−280.678	+	162.049i	−0.666693	+	0.384916i	−0.794823	−	0.606842i	$-0.792436\pi$
$421$	−280.678	+	162.049i	−0.666693	+	0.384916i	0.128129	+	0.991757i	$0.459103\pi$
$422$	−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
$428$	−214.695	−	80.1906i	−0.501624	−	0.187361i
$429$		0			0
$430$	−74.4367	+	412.028i	−0.173109	+	0.958204i
$431$		−	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	$0.661505\pi$
$434$	190.052	+	34.3348i	0.437909	+	0.0791124i
$435$		0			0
$436$	69.8795	−	187.089i	0.160274	−	0.429103i
$437$	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	0.711190	−	0.703000i	$-0.248156\pi$
$443$	−112.177	−	194.296i	−0.253220	−	0.438591i	−0.964411	+	0.264409i	$0.914823\pi$
$444$		0			0
$445$	−977.799	−	564.533i	−2.19730	−	1.26861i
$446$	1.87081	+	5.20794i	0.00419464	+	0.0116770i
$447$		0			0
$448$	250.929	−	410.388i	0.560110	−	0.916045i
$449$		−	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
$452$	131.159	+	159.001i	0.290174	+	0.351773i
$453$		0			0
$454$	33.2523	+	92.5675i	0.0732430	+	0.203893i
$455$	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	0.751690	−	0.659517i	$-0.229239\pi$
$461$	−90.0395	−	155.953i	−0.195313	−	0.338293i	−0.947003	+	0.321224i	$0.895906\pi$
$462$		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	$0.308502\pi$
$464$	21.1958	−	109.427i	0.0456806	−	0.235835i
$465$		0			0
$466$	113.963	−	630.815i	0.244555	−	1.35368i
$467$	284.941			0.610153			0.305077	−	0.952328i	$-0.401318\pi$
$467$	284.941			0.610153			0.305077	+	0.952328i	$0.401318\pi$
$468$		0			0
$469$		−	247.090i		−	0.526844i
$470$	−55.8336	+	309.054i	−0.118795	+	0.657562i
$471$		0			0
$472$	−183.722	+	103.008i	−0.389242	+	0.218238i
$473$	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
$482$	−72.1503	−	200.851i	−0.149689	−	0.416704i
$483$		0			0
$484$	95.2302	−	78.5543i	0.196757	−	0.162302i
$485$	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	$0.332174\pi$
$488$	−517.869	−	6.52362i	−1.06121	−	0.0133681i
$489$		0			0
$490$	−43.3607	−	120.707i	−0.0884913	−	0.246341i
$491$	−167.001	+	289.254i	−0.340124	+	0.589113i	−0.984456	−	0.175634i	$-0.943802\pi$
$491$	−167.001	+	289.254i	−0.340124	+	0.589113i	0.644331	+	0.764747i	$0.277136\pi$
$492$		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	0.0248203	−	0.999692i	$-0.492099\pi$
$499$	−413.436	−	238.697i	−0.828528	−	0.478351i	−0.853348	+	0.521341i	$0.825432\pi$
$500$	−747.662	−	279.259i	−1.49532	−	0.558518i
$501$		0			0
$502$	−502.334	−	90.7515i	−1.00067	−	0.180780i
$503$			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
$506$	−89.0329	+	492.821i	−0.175954	+	0.973955i
$507$		0			0
$508$	70.4082	+	26.2981i	0.138599	+	0.0517680i
$509$	−75.5535	+	130.862i	−0.148435	+	0.257097i	−0.930649	−	0.365912i	$-0.880757\pi$
$509$	−75.5535	+	130.862i	−0.148435	+	0.257097i	0.782214	+	0.623010i	$0.214090\pi$
$510$		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
$518$	83.4122	−	29.9635i	0.161027	−	0.0578447i
$519$		0			0
$520$	755.038	+	9.51126i	1.45200	+	0.0182909i
$521$			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	$0.233704\pi$
$523$			700.814i			1.33999i	−0.742366	+	0.669994i	$0.766296\pi$
$524$	−116.810	+	96.3557i	−0.222921	+	0.183885i
$525$		0			0
$526$	762.026	−	273.737i	1.44872	−	0.520412i
$527$	−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
$536$	−128.621	−	229.404i	−0.239965	−	0.427993i
$537$		0			0
$538$	37.2311	+	6.72615i	0.0692028	+	0.0125021i
$539$	−71.1126			−0.131934
$540$		0			0
$541$		−	431.063i		−	0.796790i	−0.917214	−	0.398395i	$-0.869567\pi$
$541$		−	431.063i		−	0.796790i	0.917214	−	0.398395i	$-0.130433\pi$
$542$	988.673	+	178.613i	1.82412	+	0.329545i
$543$		0			0
$544$	−283.107	+	227.600i	−0.520416	+	0.418383i
$545$	−370.205	−	213.738i	−0.679276	−	0.392180i
$546$		0			0
$547$	−625.543	+	361.158i	−1.14359	+	0.660252i	−0.947317	−	0.320298i	$-0.896217\pi$
$547$	−625.543	+	361.158i	−1.14359	+	0.660252i	−0.196272	+	0.980549i	$0.562884\pi$
$548$	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
$554$	−357.375	+	128.377i	−0.645082	+	0.231728i
$555$		0			0
$556$	237.193	+	287.545i	0.426606	+	0.517167i
$557$	−907.654			−1.62954			−0.814770	−	0.579784i	$-0.803137\pi$
$557$	−907.654			−1.62954			−0.814770	+	0.579784i	$0.803137\pi$
$558$		0			0
$559$	−269.558			−0.482215
$560$	−777.499	−	674.972i	−1.38839	−	1.20531i
$561$		0			0
$562$	116.630	−	41.8962i	0.207527	−	0.0745484i
$563$	−521.945	+	904.036i	−0.927079	+	1.60575i	−0.138896	+	0.990307i	$0.544355\pi$
$563$	−521.945	+	904.036i	−0.927079	+	1.60575i	−0.788183	+	0.615441i	$0.788978\pi$
$564$		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	0.999922	−	0.0124934i	$-0.00397689\pi$
$571$	850.255	+	490.895i	1.48906	+	0.859711i	0.489141	+	0.872205i	$0.337310\pi$
$572$	146.489	−	392.195i	0.256099	−	0.685656i
$573$		0			0
$574$	100.922	−	558.631i	0.175822	−	0.973224i
$575$			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	$0.630834\pi$
$578$	−315.181	−	56.9404i	−0.545296	−	0.0985129i
$579$		0			0
$580$	−223.496	−	83.4779i	−0.385338	−	0.143927i
$581$	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	0.774694	−	0.632337i	$-0.217904\pi$
$587$	−94.0800	−	162.951i	−0.160273	−	0.277600i	−0.934966	+	0.354736i	$0.884571\pi$
$588$		0			0
$589$	204.504	+	118.071i	0.347206	+	0.200460i
$590$	152.416	+	424.296i	0.258333	+	0.719145i
$591$		0			0
$592$	61.8446	−	71.2387i	0.104467	−	0.120336i
$593$		−	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
$596$	558.663	−	460.835i	0.937355	−	0.773214i
$597$		0			0
$598$	−196.592	−	547.272i	−0.328750	−	0.915170i
$599$	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	$-0.213061\pi$
$608$	458.389	−	368.517i	0.753930	−	0.606113i
$609$		0			0
$610$	−197.082	+	1090.90i	−0.323085	+	1.78836i
$611$	−202.191			−0.330918
$612$		0			0
$613$		−	4.96469i		−	0.00809901i	−0.999992	−	0.00404951i	$-0.998711\pi$
$613$		−	4.96469i		−	0.00809901i	0.999992	−	0.00404951i	$-0.00128900\pi$
$614$	−129.820	+	718.588i	−0.211433	+	1.17034i
$615$		0			0
$616$	−497.936	+	279.180i	−0.808337	+	0.453215i
$617$	−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	−0.274053	−	0.961715i	$-0.588364\pi$
$619$	261.088	−	150.739i	0.421790	−	0.243521i	0.695843	+	0.718194i	$0.255031\pi$
$620$	−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
$626$	−360.194	−	1002.70i	−0.575390	−	1.60177i
$627$		0			0
$628$	−248.580	−	301.349i	−0.395828	−	0.479856i
$629$	−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	$0.750800\pi$
$632$	−2.48335	+	197.138i	−0.00392936	+	0.311927i
$633$		0			0
$634$	403.911	+	1124.40i	0.637083	+	1.77351i
$635$	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	0.623547	−	0.781786i	$-0.285691\pi$
$643$	166.070	+	95.8808i	0.258274	+	0.149115i	−0.365273	+	0.930901i	$0.619024\pi$
$644$	−277.440	+	742.793i	−0.430808	+	1.15340i
$645$		0			0
$646$	−410.633	−	74.1848i	−0.635655	−	0.114837i
$647$		−	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
$650$	189.344	−	1048.07i	0.291299	−	1.61242i
$651$		0			0
$652$	385.542	−	1032.22i	0.591323	−	1.58315i
$653$	353.929	−	613.023i	0.542004	−	0.938779i	−0.456785	−	0.889577i	$-0.650999\pi$
$653$	353.929	−	613.023i	0.542004	−	0.938779i	0.998789	−	0.0492016i	$-0.0156677\pi$
$654$		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	0.996991	−	0.0775154i	$-0.0246987\pi$
$659$	284.270	+	492.370i	0.431365	+	0.747147i	−0.565626	+	0.824662i	$0.691365\pi$
$660$		0			0
$661$	394.236	+	227.612i	0.596424	+	0.344346i	0.767634	−	0.640889i	$-0.221434\pi$
$661$	394.236	+	227.612i	0.596424	+	0.344346i	−0.171209	+	0.985235i	$0.554767\pi$
$662$	397.265	−	142.707i	0.600098	−	0.215569i
$663$		0			0
$664$	11.6456	−	924.468i	0.0175385	−	1.39227i
$665$		−	1182.75i		−	1.77857i
$666$		0			0
$667$			183.731i			0.275459i
$668$	239.709	+	290.595i	0.358845	+	0.435023i
$669$		0			0
$670$	−529.796	+	190.315i	−0.790740	+	0.284052i
$671$	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	0.955517	−	0.294937i	$-0.0952986\pi$
$677$	150.521	+	260.711i	0.222336	+	0.385097i	−0.733181	+	0.680033i	$0.761965\pi$
$678$		0			0
$679$	707.619	−	1225.63i	1.04215	−	1.80506i
$680$	380.248	+	678.196i	0.559188	+	0.997347i
$681$		0			0
$682$	−240.071	−	43.3712i	−0.352011	−	0.0635941i
$683$	−244.466			−0.357930			−0.178965	−	0.983855i	$-0.557275\pi$
$683$	−244.466			−0.357930			−0.178965	+	0.983855i	$0.557275\pi$
$684$		0			0
$685$		−	2221.36i		−	3.24286i
$686$	614.035	+	110.931i	0.895095	+	0.161707i
$687$		0			0
$688$	384.085	+	74.3962i	0.558263	+	0.108134i
$689$	−558.368	−	322.374i	−0.810404	−	0.467887i
$690$		0			0
$691$	−37.7206	+	21.7780i	−0.0545884	+	0.0315166i	−0.527046	−	0.849837i	$-0.676700\pi$
$691$	−37.7206	+	21.7780i	−0.0545884	+	0.0315166i	0.472457	+	0.881353i	$0.343367\pi$
$692$	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
$698$	−932.582	+	335.004i	−1.33608	+	0.479949i
$699$		0			0
$700$	−1120.27	+	924.097i	−1.60038	+	1.32014i
$701$	−505.146			−0.720607			−0.360304	−	0.932835i	$-0.617327\pi$
$701$	−505.146			−0.720607			−0.360304	+	0.932835i	$0.617327\pi$
$702$		0			0
$703$	108.370			0.154154
$704$	−316.970	+	518.396i	−0.450242	+	0.736358i
$705$		0			0
$706$	−210.143	+	75.4880i	−0.297653	+	0.106924i
$707$	212.974	−	368.881i	0.301236	−	0.521756i
$708$		0			0
$709$	−940.019	+	542.720i	−1.32584	+	0.765473i	−0.984653	−	0.174524i	$-0.944161\pi$
$709$	−940.019	+	542.720i	−1.32584	+	0.765473i	−0.341185	+	0.939996i	$0.610828\pi$
$710$	−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
$716$	−80.2085	−	29.9586i	−0.112023	−	0.0418417i
$717$		0			0
$718$	−22.8234	+	126.334i	−0.0317875	+	0.175952i
$719$		−	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
$722$	−45.6256	−	8.24270i	−0.0631934	−	0.0114165i
$723$		0			0
$724$	−446.878	+	1196.43i	−0.617235	+	1.65253i
$725$	−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	0.349422	−	0.936965i	$-0.386378\pi$
$733$	−210.592	−	121.586i	−0.287302	−	0.165874i	−0.636724	+	0.771091i	$0.719711\pi$
$734$	427.035	+	1188.78i	0.581792	+	1.61959i
$735$		0			0
$736$	129.075	+	834.047i	0.175373	+	1.13322i
$737$			312.120i			0.423501i
$738$		0			0
$739$		−	315.637i		−	0.427113i	−0.976931	−	0.213557i	$-0.931495\pi$
$739$		−	315.637i		−	0.427113i	0.976931	−	0.213557i	$-0.0685048\pi$
$740$	−128.492	−	155.769i	−0.173638	−	0.210499i
$741$		0			0
$742$	297.213	+	827.378i	0.400556	+	1.11506i
$743$	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	$0.000317176\pi$
$752$	288.095	+	55.8032i	0.383105	+	0.0742064i
$753$		0			0
$754$	27.3066	−	151.150i	0.0362157	−	0.200464i
$755$	−431.135			−0.571040
$756$		0			0
$757$			731.923i			0.966873i	0.875379	+	0.483436i	$0.160612\pi$
$757$			731.923i			0.966873i	−0.875379	+	0.483436i	$0.839388\pi$
$758$	137.126	−	759.032i	0.180906	−	1.00136i
$759$		0			0
$760$	−615.675	−	1098.09i	−0.810099	−	1.44486i
$761$	−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	$0.0500882\pi$
$770$	413.089	+	1149.95i	0.536480	+	1.49345i
$771$		0			0
$772$	126.489	−	104.339i	0.163845	−	0.135154i
$773$	328.803			0.425360			0.212680	−	0.977122i	$-0.431781\pi$
$773$	328.803			0.425360			0.212680	+	0.977122i	$0.431781\pi$
$774$		0			0
$775$	−620.609			−0.800786
$776$	18.9744	−	1506.26i	0.0244515	−	1.94105i
$777$		0			0
$778$	31.2700	+	87.0490i	0.0401927	+	0.111888i
$779$	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	0.262937	−	0.964813i	$-0.415309\pi$
$787$	−347.183	−	200.446i	−0.441147	−	0.254696i	−0.704084	+	0.710117i	$0.748642\pi$
$788$	−53.4940	−	19.9805i	−0.0678858	−	0.0253560i
$789$		0			0
$790$	415.274	+	75.0233i	0.525664	+	0.0949662i
$791$		−	387.293i		−	0.489624i
$792$		0			0
$793$	−713.694			−0.899992
$794$	107.133	−	593.011i	0.134928	−	0.746865i
$795$		0			0
$796$	1119.92	+	418.302i	1.40694	+	0.525505i
$797$	−129.797	+	224.815i	−0.162857	+	0.282077i	−0.935892	−	0.352286i	$-0.885404\pi$
$797$	−129.797	+	224.815i	−0.162857	+	0.282077i	0.773035	+	0.634363i	$0.218738\pi$
$798$		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
$806$	266.596	−	95.7673i	0.330764	−	0.118818i
$807$		0			0
$808$	5.71077	−	453.341i	0.00706778	−	0.561066i
$809$		−	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	$-0.953691\pi$
$811$		−	235.144i		−	0.289943i	0.989436	−	0.144972i	$-0.0463091\pi$
$812$	−161.562	+	133.270i	−0.198968	+	0.164126i
$813$		0			0
$814$	−105.365	+	37.8495i	−0.129441	+	0.0464982i
$815$	−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	0.830106	−	0.557606i	$-0.188280\pi$
$821$	−55.7034	−	96.4812i	−0.0678483	−	0.117517i	−0.897954	+	0.440089i	$0.854947\pi$
$822$		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	$0.262714\pi$
$824$	76.2669	−	42.7610i	0.0925569	−	0.0518944i
$825$		0			0
$826$	389.467	+	70.3609i	0.471510	+	0.0851827i
$827$	595.430			0.719988			0.359994	−	0.932955i	$-0.382779\pi$
$827$	595.430			0.719988			0.359994	+	0.932955i	$0.382779\pi$
$828$		0			0
$829$			952.457i			1.14892i	0.818532	+	0.574461i	$0.194788\pi$
$829$			952.457i			1.14892i	−0.818532	+	0.574461i	$0.805212\pi$
$830$	−1947.41	−	351.818i	−2.34628	−	0.423878i
$831$		0			0
$832$	17.7729	−	705.326i	0.0213617	−	0.847748i
$833$	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
$842$	610.032	−	219.137i	0.724504	−	0.260258i
$843$		0			0
$844$	594.912	+	721.202i	0.704872	+	0.854505i
$845$	−406.400			−0.480946
$846$		0			0
$847$	−231.960			−0.273861
$848$	706.627	+	613.446i	0.833287	+	0.723403i
$849$		0			0
$850$	1032.09	−	370.751i	1.21423	−	0.436178i
$851$	−77.7532	+	134.672i	−0.0913668	+	0.158252i
$852$		0			0
$853$	463.386	−	267.536i	0.543243	−	0.313641i	−0.203149	−	0.979148i	$-0.565118\pi$
$853$	463.386	−	267.536i	0.543243	−	0.313641i	0.746392	+	0.665506i	$0.231784\pi$
$854$	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	0.684754	−	0.728774i	$-0.259910\pi$
$859$	340.158	+	196.391i	0.395993	+	0.228627i	−0.288760	+	0.957401i	$0.593243\pi$
$860$	293.004	−	784.461i	0.340702	−	0.912164i
$861$		0			0
$862$	−148.496	+	821.964i	−0.172269	+	0.953555i
$863$			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
$866$	828.159	+	149.615i	0.956303	+	0.172765i
$867$		0			0
$868$	−361.842	−	135.151i	−0.416868	−	0.155704i
$869$	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	0.185896	−	0.982569i	$-0.440481\pi$
$877$	−501.720	−	289.668i	−0.572087	−	0.330294i	−0.757982	+	0.652275i	$0.773815\pi$
$878$	−127.033	−	353.634i	−0.144685	−	0.402772i
$879$		0			0
$880$	982.125	+	852.614i	1.11605	+	0.968880i
$881$			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	$0.166729\pi$
$883$			883.300i			1.00034i	−0.865927	+	0.500170i	$0.833271\pi$
$884$	−386.147	+	318.528i	−0.436818	+	0.360326i
$885$		0			0
$886$	151.695	+	422.287i	0.171213	+	0.476622i
$887$	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
$896$	−639.783	+	718.480i	−0.714043	+	0.801875i
$897$		0			0
$898$	−73.7674	+	408.323i	−0.0821464	+	0.454703i
$899$	−89.5023			−0.0995577
$900$		0			0
$901$		−	663.894i		−	0.736841i
$902$	−127.483	+	705.654i	−0.141334	+	0.782322i
$903$		0			0
$904$	−201.603	−	359.572i	−0.223012	−	0.397757i
$905$	2367.46	+	1366.85i	2.61597	+	1.51033i
$906$		0			0
$907$	−335.644	+	193.784i	−0.370060	+	0.213654i	−0.673485	−	0.739201i	$-0.735203\pi$
$907$	−335.644	+	193.784i	−0.370060	+	0.213654i	0.303425	+	0.952855i	$0.401870\pi$
$908$	−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
$914$	−40.4863	−	112.705i	−0.0442958	−	0.123310i
$915$		0			0
$916$	668.664	+	810.611i	0.729983	+	0.884947i
$917$	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	$0.501382\pi$
$920$	1806.35	+	22.7546i	1.96342	+	0.0247333i
$921$		0			0
$922$	121.759	+	338.952i	0.132060	+	0.367627i
$923$	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
$932$	−448.590	+	1201.01i	−0.481319	+	1.28864i
$933$		0			0
$934$	−560.805	−	101.315i	−0.600433	−	0.108474i
$935$		−	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	$0.446707\pi$
$938$	−87.8560	+	486.307i	−0.0936631	+	0.518451i
$939$		0			0
$940$	219.777	−	588.409i	0.233805	−	0.625967i
$941$	−466.897	+	808.689i	−0.496171	+	0.859393i	−0.999990	−	0.00441583i	$-0.998594\pi$
$941$	−466.897	+	808.689i	−0.496171	+	0.859393i	0.503819	+	0.863809i	$0.331928\pi$
$942$		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	$0.0966724\pi$
$947$	697.096	+	1207.40i	0.736109	+	1.27498i	−0.218126	+	0.975921i	$0.569994\pi$
$948$		0			0
$949$	898.475	+	518.735i	0.946760	+	0.546612i
$950$	−1671.11	+	600.299i	−1.75906	+	0.631893i
$951$		0			0
$952$	682.494	+	8.59742i	0.716905	+	0.00903090i
$953$		−	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
$956$	−934.480	−	1132.86i	−0.977490	−	1.18500i
$957$		0			0
$958$	−530.170	+	190.449i	−0.553413	+	0.198799i
$959$	−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	$0.840276\pi$
$968$	−215.357	+	120.746i	−0.222477	+	0.124737i
$969$		0			0
$970$	−3172.96	−	573.225i	−3.27109	−	0.590954i
$971$	−677.141			−0.697365			−0.348683	−	0.937241i	$-0.613371\pi$
$971$	−677.141			−0.697365			−0.348683	+	0.937241i	$0.613371\pi$
$972$		0			0
$973$		−	700.397i		−	0.719832i
$974$	−964.527	−	174.251i	−0.990274	−	0.178902i
$975$		0			0
$976$	1016.92	+	196.974i	1.04192	+	0.201818i
$977$	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
$986$	148.845	−	53.4686i	0.150959	−	0.0542278i
$987$		0			0
$988$	625.226	−	515.743i	0.632820	−	0.522007i
$989$	−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	$0.519907\pi$
$992$	−406.295	+	62.8770i	−0.409572	+	0.0633840i
$993$		0			0
$994$	−1196.60	+	429.847i	−1.20383	+	0.432441i
$995$	1279.45	−	2216.07i	1.28588	−	2.22720i
$996$		0			0
$997$	591.638	−	341.582i	0.593418	−	0.342610i	−0.173030	−	0.984917i	$-0.555356\pi$
$997$	591.638	−	341.582i	0.593418	−	0.342610i	0.766448	+	0.642307i	$0.222022\pi$
$998$	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.125.2		44
3.2	odd	2		72.3.j.a.5.21	yes	44
4.3	odd	2		864.3.n.a.17.22		44
8.3	odd	2		864.3.n.a.17.1		44
8.5	even	2	inner	216.3.j.a.125.9		44
9.2	odd	6	inner	216.3.j.a.197.9		44
9.4	even	3		648.3.h.a.485.31		44
9.5	odd	6		648.3.h.a.485.14		44
9.7	even	3		72.3.j.a.29.14	yes	44
12.11	even	2		288.3.n.a.113.5		44
24.5	odd	2		72.3.j.a.5.14	✓	44
24.11	even	2		288.3.n.a.113.18		44
36.7	odd	6		288.3.n.a.209.18		44
36.11	even	6		864.3.n.a.305.1		44
36.23	even	6		2592.3.h.a.1457.44		44
36.31	odd	6		2592.3.h.a.1457.1		44
72.5	odd	6		648.3.h.a.485.32		44
72.11	even	6		864.3.n.a.305.22		44
72.13	even	6		648.3.h.a.485.13		44
72.29	odd	6	inner	216.3.j.a.197.2		44
72.43	odd	6		288.3.n.a.209.5		44
72.59	even	6		2592.3.h.a.1457.2		44
72.61	even	6		72.3.j.a.29.21	yes	44
72.67	odd	6		2592.3.h.a.1457.43		44

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

\(f(q)\)	\(=\)	\(q+(-1.96814 - 0.355563i) q^{2} +(3.74715 + 1.39960i) q^{4} +(4.28090 - 7.41474i) q^{5} +(-3.75800 - 6.50904i) q^{7} +(-6.87727 - 4.08695i) q^{8} +O(q^{10})\)	\(q+(-1.96814 - 0.355563i) q^{2} +(3.74715 + 1.39960i) q^{4} +(4.28090 - 7.41474i) q^{5} +(-3.75800 - 6.50904i) q^{7} +(-6.87727 - 4.08695i) q^{8} +(-11.0618 + 13.0711i) q^{10} +(4.74705 + 8.22213i) q^{11} +(-9.54725 - 5.51211i) q^{13} +(5.08189 + 14.1469i) q^{14} +(12.0823 + 10.4890i) q^{16} -11.3516i q^{17} +18.3798i q^{19} +(26.4188 - 21.7926i) q^{20} +(-6.41937 - 17.8702i) q^{22} +(-22.8408 - 13.1871i) q^{23} +(-24.1522 - 41.8329i) q^{25} +(16.8304 + 14.2433i) q^{26} +(-4.97174 - 29.6500i) q^{28} +(-3.48316 - 6.03301i) q^{29} +(6.42393 - 11.1266i) q^{31} +(-20.0501 - 24.9398i) q^{32} +(-4.03621 + 22.3415i) q^{34} -64.3505 q^{35} -5.89614i q^{37} +(6.53519 - 36.1741i) q^{38} +(-59.7446 + 33.4973i) q^{40} +(-32.7049 - 18.8822i) q^{41} +(21.1756 - 12.2257i) q^{43} +(6.28023 + 37.4535i) q^{44} +(40.2650 + 34.0754i) q^{46} +(15.8834 - 9.17030i) q^{47} +(-3.74509 + 6.48669i) q^{49} +(32.6607 + 90.9207i) q^{50} +(-28.0603 - 34.0170i) q^{52} +58.4847 q^{53} +81.2866 q^{55} +(-0.757376 + 60.1232i) q^{56} +(4.71023 + 13.1123i) q^{58} +(13.1643 - 22.8013i) q^{59} +(56.0654 - 32.3694i) q^{61} +(-16.5994 + 19.6145i) q^{62} +(30.5937 + 56.2141i) q^{64} +(-81.7417 + 47.1936i) q^{65} +(28.4707 + 16.4376i) q^{67} +(15.8876 - 42.5361i) q^{68} +(126.651 + 22.8807i) q^{70} +84.5841i q^{71} -94.1083 q^{73} +(-2.09645 + 11.6044i) q^{74} +(-25.7243 + 68.8719i) q^{76} +(35.6788 - 61.7975i) q^{77} +(-12.3221 - 21.3425i) q^{79} +(129.496 - 44.6844i) q^{80} +(57.6540 + 48.7914i) q^{82} +(57.7838 + 100.085i) q^{83} +(-84.1691 - 48.5950i) q^{85} +(-46.0236 + 16.5327i) q^{86} +(0.956706 - 75.9467i) q^{88} -131.872i q^{89} +82.8580i q^{91} +(-67.1311 - 81.3820i) q^{92} +(-34.5214 + 12.4009i) q^{94} +(136.282 + 78.6822i) q^{95} +(94.1484 + 163.070i) q^{97} +(9.67730 - 11.4351i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 3 q^{2} - q^{4} - 2 q^{7}+O(q^{10}) \) 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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