LMFDB - Embedded newform 108.5.f.a.91.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,5,Mod(19,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("108.19");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	108.f (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:	$11.1639560131$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			91.6
Character	$\chi$	$=$	108.91
Dual form			108.5.f.a.19.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.63137 - 3.01262i) q^{2} +(-2.15179 + 15.8546i) q^{4} +(10.5756 - 18.3175i) q^{5} +(-38.6407 + 22.3092i) q^{7} +(53.4262 - 35.2369i) q^{8} +O(q^{10})$	\(q+(-2.63137 - 3.01262i) q^{2} +(-2.15179 + 15.8546i) q^{4} +(10.5756 - 18.3175i) q^{5} +(-38.6407 + 22.3092i) q^{7} +(53.4262 - 35.2369i) q^{8} +(-83.0119 + 16.3397i) q^{10} +(-58.6904 + 33.8849i) q^{11} +(14.5519 - 25.2046i) q^{13} +(168.887 + 57.7061i) q^{14} +(-246.740 - 68.2318i) q^{16} -402.841 q^{17} +644.741i q^{19} +(267.660 + 207.088i) q^{20} +(256.519 + 87.6483i) q^{22} +(335.527 + 193.717i) q^{23} +(88.8138 + 153.830i) q^{25} +(-114.223 + 22.4833i) q^{26} +(-270.558 - 660.639i) q^{28} +(362.210 + 627.366i) q^{29} +(1090.90 + 629.833i) q^{31} +(443.706 + 922.876i) q^{32} +(1060.02 + 1213.61i) q^{34} +943.733i q^{35} -1402.04 q^{37} +(1942.36 - 1696.55i) q^{38} +(-80.4363 - 1351.28i) q^{40} +(774.166 - 1340.89i) q^{41} +(-1620.98 + 935.875i) q^{43} +(-410.944 - 1003.43i) q^{44} +(-299.300 - 1520.56i) q^{46} +(-3610.63 + 2084.60i) q^{47} +(-205.097 + 355.239i) q^{49} +(229.730 - 672.346i) q^{50} +(368.297 + 284.950i) q^{52} -906.566 q^{53} +1433.41i q^{55} +(-1278.32 + 2553.48i) q^{56} +(936.910 - 2742.03i) q^{58} +(-3916.45 - 2261.16i) q^{59} +(-1314.22 - 2276.30i) q^{61} +(-973.119 - 4943.80i) q^{62} +(1612.72 - 3765.15i) q^{64} +(-307.789 - 533.107i) q^{65} +(58.7165 + 33.9000i) q^{67} +(866.831 - 6386.91i) q^{68} +(2843.11 - 2483.31i) q^{70} -1315.04i q^{71} +9470.72 q^{73} +(3689.27 + 4223.80i) q^{74} +(-10222.1 - 1387.35i) q^{76} +(1511.89 - 2618.67i) q^{77} +(3783.95 - 2184.67i) q^{79} +(-3859.25 + 3798.05i) q^{80} +(-6076.73 + 1196.12i) q^{82} +(-659.925 + 381.008i) q^{83} +(-4260.28 + 7379.03i) q^{85} +(7084.84 + 2420.78i) q^{86} +(-1941.61 + 3878.41i) q^{88} -8083.40 q^{89} +1298.56i q^{91} +(-3793.29 + 4902.82i) q^{92} +(15781.0 + 5392.11i) q^{94} +(11810.0 + 6818.52i) q^{95} +(-3332.71 - 5772.42i) q^{97} +(1609.89 - 316.884i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + q^{2} - q^{4} + 2 q^{5} - 122 q^{8}+O(q^{10}) $ 44 * q + q^2 - q^4 + 2 * q^5 - 122 * q^8	$ 44 q + q^{2} - q^{4} + 2 q^{5} - 122 q^{8} + 28 q^{10} - 2 q^{13} - 252 q^{14} - q^{16} + 56 q^{17} + 140 q^{20} - 33 q^{22} - 1752 q^{25} - 1096 q^{26} - 516 q^{28} - 526 q^{29} + 121 q^{32} + 385 q^{34} - 8 q^{37} - 1395 q^{38} - 2276 q^{40} + 2762 q^{41} - 6714 q^{44} + 3576 q^{46} + 3428 q^{49} - 6375 q^{50} + 1438 q^{52} + 10088 q^{53} + 7506 q^{56} - 4064 q^{58} - 2 q^{61} + 18324 q^{62} + 9026 q^{64} + 2014 q^{65} + 11405 q^{68} + 3666 q^{70} - 3416 q^{73} - 14620 q^{74} + 1581 q^{76} + 3942 q^{77} - 45520 q^{80} - 8486 q^{82} - 1252 q^{85} - 22113 q^{86} + 1995 q^{88} - 13048 q^{89} + 30294 q^{92} + 7524 q^{94} + 5638 q^{97} + 92938 q^{98}+O(q^{100}) $ 44 * q + q^2 - q^4 + 2 * q^5 - 122 * q^8 + 28 * q^10 - 2 * q^13 - 252 * q^14 - q^16 + 56 * q^17 + 140 * q^20 - 33 * q^22 - 1752 * q^25 - 1096 * q^26 - 516 * q^28 - 526 * q^29 + 121 * q^32 + 385 * q^34 - 8 * q^37 - 1395 * q^38 - 2276 * q^40 + 2762 * q^41 - 6714 * q^44 + 3576 * q^46 + 3428 * q^49 - 6375 * q^50 + 1438 * q^52 + 10088 * q^53 + 7506 * q^56 - 4064 * q^58 - 2 * q^61 + 18324 * q^62 + 9026 * q^64 + 2014 * q^65 + 11405 * q^68 + 3666 * q^70 - 3416 * q^73 - 14620 * q^74 + 1581 * q^76 + 3942 * q^77 - 45520 * q^80 - 8486 * q^82 - 1252 * q^85 - 22113 * q^86 + 1995 * q^88 - 13048 * q^89 + 30294 * q^92 + 7524 * q^94 + 5638 * q^97 + 92938 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.63137	−	3.01262i	−0.657842	−	0.753156i
$2$	−2.63137	−	3.01262i	−0.657842	−	0.753156i
$3$		0			0
$3$		0			0
$4$	−2.15179	+	15.8546i	−0.134487	+	0.990915i
$5$	10.5756	−	18.3175i	0.423024	−	0.732698i	−0.573210	−	0.819409i	$-0.694302\pi$
$5$	10.5756	−	18.3175i	0.423024	−	0.732698i	0.996234	+	0.0867102i	$0.0276354\pi$
$6$		0			0
$7$	−38.6407	+	22.3092i	−0.788586	+	0.455290i	−0.839464	−	0.543415i	$-0.817131\pi$
$7$	−38.6407	+	22.3092i	−0.788586	+	0.455290i	0.0508787	+	0.998705i	$0.483798\pi$
$8$	53.4262	−	35.2369i	0.834785	−	0.550576i
$9$		0			0
$10$	−83.0119	+	16.3397i	−0.830119	+	0.163397i
$11$	−58.6904	+	33.8849i	−0.485045	+	0.280041i	−0.722516	−	0.691354i	$-0.757015\pi$
$11$	−58.6904	+	33.8849i	−0.485045	+	0.280041i	0.237472	+	0.971394i	$0.423681\pi$
$12$		0			0
$13$	14.5519	−	25.2046i	0.0861058	−	0.149140i	−0.819756	−	0.572713i	$-0.805891\pi$
$13$	14.5519	−	25.2046i	0.0861058	−	0.149140i	0.905862	+	0.423573i	$0.139224\pi$
$14$	168.887	+	57.7061i	0.861669	+	0.294419i
$15$		0			0
$16$	−246.740	−	68.2318i	−0.963826	−	0.266531i
$17$	−402.841			−1.39391			−0.696957	−	0.717113i	$-0.745463\pi$
$17$	−402.841			−1.39391			−0.696957	+	0.717113i	$0.745463\pi$
$18$		0			0
$19$			644.741i			1.78599i	0.450070	+	0.892993i	$0.351399\pi$
$19$			644.741i			1.78599i	−0.450070	+	0.892993i	$0.648601\pi$
$20$	267.660	+	207.088i	0.669151	+	0.517719i
$21$		0			0
$22$	256.519	+	87.6483i	0.529997	+	0.181092i
$23$	335.527	+	193.717i	0.634267	+	0.366194i	0.782403	−	0.622773i	$-0.213994\pi$
$23$	335.527	+	193.717i	0.634267	+	0.366194i	−0.148136	+	0.988967i	$0.547327\pi$
$24$		0			0
$25$	88.8138	+	153.830i	0.142102	+	0.246128i
$26$	−114.223	+	22.4833i	−0.168969	+	0.0332593i
$27$		0			0
$28$	−270.558	−	660.639i	−0.345099	−	0.842652i
$29$	362.210	+	627.366i	0.430690	+	0.745977i	0.996933	−	0.0782617i	$-0.0249370\pi$
$29$	362.210	+	627.366i	0.430690	+	0.745977i	−0.566243	+	0.824238i	$0.691604\pi$
$30$		0			0
$31$	1090.90	+	629.833i	1.13517	+	0.655393i	0.945231	−	0.326402i	$-0.105836\pi$
$31$	1090.90	+	629.833i	1.13517	+	0.655393i	0.189944	+	0.981795i	$0.439169\pi$
$32$	443.706	+	922.876i	0.433307	+	0.901246i
$33$		0			0
$34$	1060.02	+	1213.61i	0.916976	+	1.04983i
$35$			943.733i			0.770394i
$36$		0			0
$37$	−1402.04			−1.02413			−0.512066	−	0.858946i	$-0.671120\pi$
$37$	−1402.04			−1.02413			−0.512066	+	0.858946i	$0.671120\pi$
$38$	1942.36	−	1696.55i	1.34513	−	1.17490i
$39$		0			0
$40$	−80.4363	−	1351.28i	−0.0502727	−	0.844552i
$41$	774.166	−	1340.89i	0.460539	−	0.797677i	−0.538449	−	0.842658i	$-0.680990\pi$
$41$	774.166	−	1340.89i	0.460539	−	0.797677i	0.998988	+	0.0449815i	$0.0143229\pi$
$42$		0			0
$43$	−1620.98	+	935.875i	−0.876681	+	0.506152i	−0.869563	−	0.493823i	$-0.835599\pi$
$43$	−1620.98	+	935.875i	−0.876681	+	0.506152i	−0.00711825	+	0.999975i	$0.502266\pi$
$44$	−410.944	−	1003.43i	−0.212264	−	0.518300i
$45$		0			0
$46$	−299.300	−	1520.56i	−0.141446	−	0.718599i
$47$	−3610.63	+	2084.60i	−1.63451	+	0.943683i	−0.651828	+	0.758367i	$0.725998\pi$
$47$	−3610.63	+	2084.60i	−1.63451	+	0.943683i	−0.982679	+	0.185316i	$0.940669\pi$
$48$		0			0
$49$	−205.097	+	355.239i	−0.0854217	+	0.147955i
$50$	229.730	−	672.346i	0.0918920	−	0.268938i
$51$		0			0
$52$	368.297	+	284.950i	0.136205	+	0.105381i
$53$	−906.566			−0.322736			−0.161368	−	0.986894i	$-0.551591\pi$
$53$	−906.566			−0.322736			−0.161368	+	0.986894i	$0.551591\pi$
$54$		0			0
$55$			1433.41i			0.473855i
$56$	−1278.32	+	2553.48i	−0.407627	+	0.814246i
$57$		0			0
$58$	936.910	−	2742.03i	0.278511	−	0.815111i
$59$	−3916.45	−	2261.16i	−1.12509	−	0.649573i	−0.182397	−	0.983225i	$-0.558386\pi$
$59$	−3916.45	−	2261.16i	−1.12509	−	0.649573i	−0.942696	+	0.333652i	$0.891719\pi$
$60$		0			0
$61$	−1314.22	−	2276.30i	−0.353190	−	0.611743i	0.633617	−	0.773647i	$-0.281570\pi$
$61$	−1314.22	−	2276.30i	−0.353190	−	0.611743i	−0.986806	+	0.161904i	$0.948236\pi$
$62$	−973.119	−	4943.80i	−0.253153	−	1.28611i
$63$		0			0
$64$	1612.72	−	3765.15i	0.393731	−	0.919226i
$65$	−307.789	−	533.107i	−0.0728496	−	0.126179i
$66$		0			0
$67$	58.7165	+	33.9000i	0.0130801	+	0.00755179i	0.506526	−	0.862225i	$-0.330930\pi$
$67$	58.7165	+	33.9000i	0.0130801	+	0.00755179i	−0.493446	+	0.869777i	$0.664263\pi$
$68$	866.831	−	6386.91i	0.187463	−	1.38125i
$69$		0			0
$70$	2843.11	−	2483.31i	0.580227	−	0.506798i
$71$		−	1315.04i		−	0.260869i	−0.991457	−	0.130434i	$-0.958363\pi$
$71$		−	1315.04i		−	0.260869i	0.991457	−	0.130434i	$-0.0416372\pi$
$72$		0			0
$73$	9470.72			1.77720			0.888602	−	0.458680i	$-0.151678\pi$
$73$	9470.72			1.77720			0.888602	+	0.458680i	$0.151678\pi$
$74$	3689.27	+	4223.80i	0.673717	+	0.771330i
$75$		0			0
$76$	−10222.1	−	1387.35i	−1.76976	−	0.240192i
$77$	1511.89	−	2618.67i	0.255000	−	0.441672i
$78$		0			0
$79$	3783.95	−	2184.67i	0.606305	−	0.350050i	−0.165213	−	0.986258i	$-0.552831\pi$
$79$	3783.95	−	2184.67i	0.606305	−	0.350050i	0.771518	+	0.636207i	$0.219498\pi$
$80$	−3859.25	+	3798.05i	−0.603008	+	0.593445i
$81$		0			0
$82$	−6076.73	+	1196.12i	−0.903737	+	0.177888i
$83$	−659.925	+	381.008i	−0.0957940	+	0.0553067i	−0.547132	−	0.837047i	$-0.684280\pi$
$83$	−659.925	+	381.008i	−0.0957940	+	0.0553067i	0.451338	+	0.892353i	$0.350947\pi$
$84$		0			0
$85$	−4260.28	+	7379.03i	−0.589659	+	1.02132i
$86$	7084.84	+	2420.78i	0.957929	+	0.327309i
$87$		0			0
$88$	−1941.61	+	3878.41i	−0.250724	+	0.500828i
$89$	−8083.40			−1.02050			−0.510251	−	0.860025i	$-0.670448\pi$
$89$	−8083.40			−1.02050			−0.510251	+	0.860025i	$0.670448\pi$
$90$		0			0
$91$			1298.56i			0.156813i
$92$	−3793.29	+	4902.82i	−0.448168	+	0.579256i
$93$		0			0
$94$	15781.0	+	5392.11i	1.78599	+	0.610244i
$95$	11810.0	+	6818.52i	1.30859	+	0.755514i
$96$		0			0
$97$	−3332.71	−	5772.42i	−0.354204	−	0.613500i	0.632777	−	0.774334i	$-0.281915\pi$
$97$	−3332.71	−	5772.42i	−0.354204	−	0.613500i	−0.986981	+	0.160834i	$0.948582\pi$
$98$	1609.89	−	316.884i	0.167627	−	0.0329950i
$99$		0			0
$100$	−2630.03	+	1077.10i	−0.263003	+	0.107710i
$101$	4643.04	+	8041.97i	0.455155	+	0.788352i	0.998697	−	0.0510303i	$-0.0162505\pi$
$101$	4643.04	+	8041.97i	0.455155	+	0.788352i	−0.543542	+	0.839382i	$0.682917\pi$
$102$		0			0
$103$	−9792.48	−	5653.69i	−0.923035	−	0.532915i	−0.0384332	−	0.999261i	$-0.512237\pi$
$103$	−9792.48	−	5653.69i	−0.923035	−	0.532915i	−0.884602	+	0.466346i	$0.845570\pi$
$104$	−110.679	−	1859.35i	−0.0102329	−	0.171907i
$105$		0			0
$106$	2385.51	+	2731.14i	0.212310	+	0.243071i
$107$		−	6261.61i		−	0.546913i	−0.961884	−	0.273456i	$-0.911833\pi$
$107$		−	6261.61i		−	0.546913i	0.961884	−	0.273456i	$-0.0881669\pi$
$108$		0			0
$109$	3452.85			0.290620			0.145310	−	0.989386i	$-0.453582\pi$
$109$	3452.85			0.290620			0.145310	+	0.989386i	$0.453582\pi$
$110$	4318.33	−	3771.84i	0.356887	−	0.311722i
$111$		0			0
$112$	11056.4	−	2868.04i	0.881409	−	0.228639i
$113$	−1272.55	+	2204.13i	−0.0996597	+	0.172616i	−0.911544	−	0.411203i	$-0.865109\pi$
$113$	−1272.55	+	2204.13i	−0.0996597	+	0.172616i	0.811884	+	0.583819i	$0.198442\pi$
$114$		0			0
$115$	7096.79	−	4097.33i	0.536619	−	0.309817i
$116$	−10726.1	+	4392.75i	−0.797122	+	0.326453i
$117$		0			0
$118$	3493.59	+	17748.7i	0.250904	+	1.27469i
$119$	15566.1	−	8987.07i	1.09922	−	0.634636i
$120$		0			0
$121$	−5024.12	+	8702.04i	−0.343154	+	0.594361i
$122$	−3399.42	+	9949.02i	−0.228394	+	0.668437i
$123$		0			0
$124$	−12333.2	+	15940.6i	−0.802106	+	1.03672i
$125$	16976.5			1.08650
$126$		0			0
$127$		−	530.060i		−	0.0328638i	−0.999865	−	0.0164319i	$-0.994769\pi$
$127$		−	530.060i		−	0.0328638i	0.999865	−	0.0164319i	$-0.00523067\pi$
$128$	−15586.6	+	5048.97i	−0.951333	+	0.308164i
$129$		0			0
$130$	−796.142	+	2330.05i	−0.0471090	+	0.137873i
$131$	802.198	+	463.149i	0.0467454	+	0.0269885i	0.523191	−	0.852216i	$-0.324742\pi$
$131$	802.198	+	463.149i	0.0467454	+	0.0269885i	−0.476445	+	0.879204i	$0.658075\pi$
$132$		0			0
$133$	−14383.7	−	24913.2i	−0.813142	−	1.40840i
$134$	−52.3769	−	266.094i	−0.00291696	−	0.0148192i
$135$		0			0
$136$	−21522.3	+	14194.9i	−1.16362	+	0.767456i
$137$	834.113	+	1444.73i	0.0444410	+	0.0769741i	0.887390	−	0.461019i	$-0.152516\pi$
$137$	834.113	+	1444.73i	0.0444410	+	0.0769741i	−0.842949	+	0.537993i	$0.819183\pi$
$138$		0			0
$139$	717.766	+	414.402i	0.0371495	+	0.0214483i	0.518460	−	0.855102i	$-0.326506\pi$
$139$	717.766	+	414.402i	0.0371495	+	0.0214483i	−0.481310	+	0.876550i	$0.659839\pi$
$140$	−14962.5	−	2030.72i	−0.763395	−	0.103608i
$141$		0			0
$142$	−3961.72	+	3460.36i	−0.196475	+	0.171611i
$143$			1972.36i			0.0964525i
$144$		0			0
$145$	15322.3			0.728768
$146$	−24920.9	−	28531.7i	−1.16912	−	1.33851i
$147$		0			0
$148$	3016.89	−	22228.8i	0.137732	−	1.01483i
$149$	1561.38	−	2704.39i	0.0703292	−	0.121814i	−0.828716	−	0.559669i	$-0.810928\pi$
$149$	1561.38	−	2704.39i	0.0703292	−	0.121814i	0.899046	+	0.437855i	$0.144262\pi$
$150$		0			0
$151$	−7932.37	+	4579.76i	−0.347896	+	0.200858i	−0.663758	−	0.747947i	$-0.731040\pi$
$151$	−7932.37	+	4579.76i	−0.347896	+	0.200858i	0.315862	+	0.948805i	$0.397706\pi$
$152$	22718.7	+	34446.1i	0.983322	+	1.49091i
$153$		0			0
$154$	−11867.4	+	2335.94i	−0.500397	+	0.0984963i
$155$	23073.9	−	13321.7i	0.960411	−	0.554494i
$156$		0			0
$157$	−10551.8	+	18276.3i	−0.428084	+	0.741463i	−0.996703	−	0.0811381i	$-0.974145\pi$
$157$	−10551.8	+	18276.3i	−0.428084	+	0.741463i	0.568619	+	0.822601i	$0.307478\pi$
$158$	−16538.5	−	5650.96i	−0.662496	−	0.226364i
$159$		0			0
$160$	21597.2	+	1632.39i	0.843641	+	0.0637653i
$161$	−17286.7			−0.666898
$162$		0			0
$163$		−	42771.0i		−	1.60981i	−0.593405	−	0.804904i	$-0.702217\pi$
$163$		−	42771.0i		−	1.60981i	0.593405	−	0.804904i	$-0.297783\pi$
$164$	19593.6	+	15159.5i	0.728494	+	0.563632i
$165$		0			0
$166$	2884.34	+	985.532i	0.104672	+	0.0357647i
$167$	−9568.12	−	5524.16i	−0.343079	−	0.198077i	0.318554	−	0.947905i	$-0.396803\pi$
$167$	−9568.12	−	5524.16i	−0.343079	−	0.198077i	−0.661633	+	0.749828i	$0.730136\pi$
$168$		0			0
$169$	13857.0	+	24001.0i	0.485172	+	0.840342i
$170$	33440.6	−	6582.32i	1.15711	−	0.227762i
$171$		0			0
$172$	−11349.9	−	27713.9i	−0.383651	−	0.936787i
$173$	−10967.8	−	18996.8i	−0.366461	−	0.634729i	0.622549	−	0.782581i	$-0.286097\pi$
$173$	−10967.8	−	18996.8i	−0.366461	−	0.634729i	−0.989009	+	0.147852i	$0.952764\pi$
$174$		0			0
$175$	−6863.66	−	3962.73i	−0.224119	−	0.129395i
$176$	16793.3	−	4356.20i	0.542138	−	0.140631i
$177$		0			0
$178$	21270.4	+	24352.2i	0.671329	+	0.768597i
$179$		−	11479.2i		−	0.358265i	−0.983825	−	0.179133i	$-0.942671\pi$
$179$		−	11479.2i		−	0.358265i	0.983825	−	0.179133i	$-0.0573291\pi$
$180$		0			0
$181$	45472.2			1.38800			0.693999	−	0.719976i	$-0.255847\pi$
$181$	45472.2			1.38800			0.693999	+	0.719976i	$0.255847\pi$
$182$	3912.08	−	3417.00i	0.118104	−	0.103158i
$183$		0			0
$184$	24751.9	−	1473.38i	0.731094	−	0.0435190i
$185$	−14827.4	+	25681.7i	−0.433232	+	0.750379i
$186$		0			0
$187$	23642.9	−	13650.2i	0.676111	−	0.390353i
$188$	−25281.2	−	61730.8i	−0.715290	−	1.74657i
$189$		0			0
$190$	−10534.9	−	53521.2i	−0.291825	−	1.48258i
$191$	−60657.0	+	35020.3i	−1.66270	+	0.959961i	−0.691283	+	0.722584i	$0.742954\pi$
$191$	−60657.0	+	35020.3i	−1.66270	+	0.959961i	−0.971418	+	0.237376i	$0.923713\pi$
$192$		0			0
$193$	17426.4	−	30183.5i	0.467836	−	0.810316i	−0.531488	−	0.847066i	$-0.678367\pi$
$193$	17426.4	−	30183.5i	0.467836	−	0.810316i	0.999325	+	0.0367497i	$0.0117004\pi$
$194$	−8620.54	+	25229.6i	−0.229050	+	0.670357i
$195$		0			0
$196$	−5190.87	−	4016.15i	−0.135122	−	0.104544i
$197$	30858.0			0.795124			0.397562	−	0.917575i	$-0.369856\pi$
$197$	30858.0			0.795124			0.397562	+	0.917575i	$0.369856\pi$
$198$		0			0
$199$			34262.5i			0.865192i	0.901588	+	0.432596i	$0.142402\pi$
$199$			34262.5i			0.865192i	−0.901588	+	0.432596i	$0.857598\pi$
$200$	10165.5	+	5089.04i	0.254137	+	0.127226i
$201$		0			0
$202$	12009.9	−	35149.1i	0.294331	−	0.861414i
$203$	−27992.1	−	16161.2i	−0.679272	−	0.392178i
$204$		0			0
$205$	−16374.5	−	28361.5i	−0.389638	−	0.674872i
$206$	8735.19	+	44378.0i	0.205844	+	1.04576i
$207$		0			0
$208$	−5310.28	+	5226.07i	−0.122741	+	0.120795i
$209$	−21847.0	−	37840.1i	−0.500149	−	0.866283i
$210$		0			0
$211$	14989.6	+	8654.27i	0.336687	+	0.194386i	0.658806	−	0.752313i	$-0.271062\pi$
$211$	14989.6	+	8654.27i	0.336687	+	0.194386i	−0.322119	+	0.946699i	$0.604395\pi$
$212$	1950.74	−	14373.3i	0.0434038	−	0.319804i
$213$		0			0
$214$	−18863.9	+	16476.6i	−0.411911	+	0.359782i
$215$			39589.7i			0.856457i
$216$		0			0
$217$	−56204.3			−1.19358
$218$	−9085.73	−	10402.1i	−0.191182	−	0.218882i
$219$		0			0
$220$	−22726.2	−	3084.41i	−0.469550	−	0.0637274i
$221$	−5862.10	+	10153.5i	−0.120024	+	0.207888i
$222$		0			0
$223$	−55484.8	+	32034.1i	−1.11574	+	0.644174i	−0.940311	−	0.340317i	$-0.889466\pi$
$223$	−55484.8	+	32034.1i	−1.11574	+	0.644174i	−0.175432	+	0.984492i	$0.556132\pi$
$224$	−37733.8	−	25761.9i	−0.752028	−	0.513430i
$225$		0			0
$226$	9988.77	−	1966.15i	0.195567	−	0.0384946i
$227$	11857.8	−	6846.11i	0.230119	−	0.132859i	−0.380508	−	0.924778i	$-0.624251\pi$
$227$	11857.8	−	6846.11i	0.230119	−	0.132859i	0.610627	+	0.791918i	$0.290917\pi$
$228$		0			0
$229$	−32996.2	+	57151.0i	−0.629205	+	1.08982i	0.358506	+	0.933527i	$0.383286\pi$
$229$	−32996.2	+	57151.0i	−0.629205	+	1.08982i	−0.987711	+	0.156288i	$0.950047\pi$
$230$	−31018.0	−	10598.4i	−0.586352	−	0.200347i
$231$		0			0
$232$	41458.0	+	20754.7i	0.770250	+	0.385602i
$233$	63342.4			1.16676			0.583381	−	0.812198i	$-0.301729\pi$
$233$	63342.4			1.16676			0.583381	+	0.812198i	$0.301729\pi$
$234$		0			0
$235$			88183.3i			1.59680i
$236$	44277.3	−	57228.4i	0.794982	−	1.02751i
$237$		0			0
$238$	−68034.7	−	23246.4i	−1.20109	−	0.410394i
$239$	275.008	+	158.776i	0.00481448	+	0.00277964i	0.502405	−	0.864632i	$-0.332449\pi$
$239$	275.008	+	158.776i	0.00481448	+	0.00277964i	−0.497591	+	0.867412i	$0.665782\pi$
$240$		0			0
$241$	−12752.6	−	22088.2i	−0.219566	−	0.380300i	0.735109	−	0.677949i	$-0.237131\pi$
$241$	−12752.6	−	22088.2i	−0.219566	−	0.380300i	−0.954675	+	0.297649i	$0.903798\pi$
$242$	39436.3	−	7762.48i	0.673388	−	0.132547i
$243$		0			0
$244$	38917.8	−	15938.4i	0.653685	−	0.267710i
$245$	4338.05	+	7513.73i	0.0722708	+	0.125177i
$246$		0			0
$247$	16250.4	+	9382.19i	0.266361	+	0.153784i
$248$	80476.2	−	4790.41i	1.30847	−	0.0778878i
$249$		0			0
$250$	−44671.5	−	51143.9i	−0.714744	−	0.818302i
$251$			40987.7i			0.650588i	0.945613	+	0.325294i	$0.105463\pi$
$251$			40987.7i			0.650588i	−0.945613	+	0.325294i	$0.894537\pi$
$252$		0			0
$253$	−26256.3			−0.410197
$254$	−1596.87	+	1394.78i	−0.0247516	+	0.0216192i
$255$		0			0
$256$	56224.8	+	33671.0i	0.857923	+	0.513778i
$257$	15479.1	−	26810.5i	0.234357	−	0.405919i	−0.724728	−	0.689035i	$-0.758035\pi$
$257$	15479.1	−	26810.5i	0.234357	−	0.405919i	0.959086	+	0.283116i	$0.0913681\pi$
$258$		0			0
$259$	54175.6	−	31278.3i	0.807615	−	0.466277i
$260$	9114.52	−	3732.76i	0.134830	−	0.0552183i
$261$		0			0
$262$	−715.585	−	3635.44i	−0.0104246	−	0.0529607i
$263$	−13311.8	+	7685.54i	−0.192453	+	0.111113i	−0.593130	−	0.805107i	$-0.702108\pi$
$263$	−13311.8	+	7685.54i	−0.192453	+	0.111113i	0.400678	+	0.916219i	$0.368775\pi$
$264$		0			0
$265$	−9587.47	+	16606.0i	−0.136525	+	0.236468i
$266$	−37205.5	+	108889.i	−0.525828	+	1.53893i
$267$		0			0
$268$	−663.818	+	857.983i	−0.00924228	+	0.0119456i
$269$	−76105.5			−1.05175			−0.525873	−	0.850563i	$-0.676261\pi$
$269$	−76105.5			−1.05175			−0.525873	+	0.850563i	$0.676261\pi$
$270$		0			0
$271$			78076.4i			1.06312i	0.847021	+	0.531559i	$0.178394\pi$
$271$			78076.4i			1.06312i	−0.847021	+	0.531559i	$0.821606\pi$
$272$	99396.9	+	27486.6i	1.34349	+	0.371521i
$273$		0			0
$274$	2157.56	−	6314.48i	0.0287383	−	0.0841078i
$275$	−10425.0	−	6018.90i	−0.137852	−	0.0795887i
$276$		0			0
$277$	−2369.97	−	4104.90i	−0.0308875	−	0.0534987i	0.850168	−	0.526511i	$-0.176500\pi$
$277$	−2369.97	−	4104.90i	−0.0308875	−	0.0534987i	−0.881056	+	0.473012i	$0.843167\pi$
$278$	−640.269	−	3252.80i	−0.00828463	−	0.0420890i
$279$		0			0
$280$	33254.2	+	50420.1i	0.424161	+	0.643113i
$281$	21604.6	+	37420.3i	0.273612	+	0.473909i	0.969784	−	0.243966i	$-0.0784484\pi$
$281$	21604.6	+	37420.3i	0.273612	+	0.473909i	−0.696172	+	0.717875i	$0.745115\pi$
$282$		0			0
$283$	31277.1	+	18057.8i	0.390529	+	0.225472i	0.682389	−	0.730989i	$-0.260941\pi$
$283$	31277.1	+	18057.8i	0.390529	+	0.225472i	−0.291860	+	0.956461i	$0.594274\pi$
$284$	20849.5	+	2829.69i	0.258499	+	0.0350835i
$285$		0			0
$286$	5941.97	−	5190.00i	0.0726438	−	0.0634505i
$287$			69084.1i			0.838715i
$288$		0			0
$289$	78760.1			0.942997
$290$	−40318.7	−	46160.4i	−0.479414	−	0.548876i
$291$		0			0
$292$	−20379.0	+	150155.i	−0.239011	+	1.76106i
$293$	−48046.7	+	83219.2i	−0.559665	+	0.969368i	0.437859	+	0.899043i	$0.355737\pi$
$293$	−48046.7	+	83219.2i	−0.559665	+	0.969368i	−0.997524	+	0.0703243i	$0.977597\pi$
$294$		0			0
$295$	−82837.5	+	47826.3i	−0.951882	+	0.549569i
$296$	−74905.5	+	49403.4i	−0.854929	+	0.563862i
$297$		0			0
$298$	−12255.9	+	2412.40i	−0.138010	+	0.0271654i
$299$	9765.10	−	5637.88i	0.109228	−	0.0630628i
$300$		0			0
$301$	41757.3	−	72325.7i	0.460892	−	0.798288i
$302$	34670.1	+	11846.2i	0.380138	+	0.129887i
$303$		0			0
$304$	43991.9	−	159083.i	0.476020	−	1.72138i
$305$	−55594.6			−0.597631
$306$		0			0
$307$		−	140641.i		−	1.49223i	−0.665817	−	0.746115i	$-0.731917\pi$
$307$		−	140641.i		−	1.49223i	0.665817	−	0.746115i	$-0.268083\pi$
$308$	38264.9	+	29605.4i	0.403366	+	0.312082i
$309$		0			0
$310$	−100849.	−	34458.6i	−1.04942	−	0.358570i
$311$	141564.	+	81731.8i	1.46363	+	0.845027i	0.999177	−	0.0405712i	$-0.0129178\pi$
$311$	141564.	+	81731.8i	1.46363	+	0.845027i	0.464453	+	0.885598i	$0.346251\pi$
$312$		0			0
$313$	25645.1	+	44418.7i	0.261768	+	0.453395i	0.966712	−	0.255868i	$-0.0823611\pi$
$313$	25645.1	+	44418.7i	0.261768	+	0.453395i	−0.704944	+	0.709263i	$0.749028\pi$
$314$	82825.4	−	16303.0i	0.840049	−	0.165352i
$315$		0			0
$316$	26494.8	+	64694.1i	0.265330	+	0.647874i
$317$	−14025.0	−	24292.0i	−0.139568	−	0.241738i	0.787765	−	0.615975i	$-0.211238\pi$
$317$	−14025.0	−	24292.0i	−0.139568	−	0.241738i	−0.927333	+	0.374237i	$0.877905\pi$
$318$		0			0
$319$	−42516.5	−	24546.9i	−0.417808	−	0.241221i
$320$	−51912.4	−	69359.7i	−0.506957	−	0.677340i
$321$		0			0
$322$	45487.6	+	52078.2i	0.438714	+	0.502278i
$323$		−	259728.i		−	2.48951i
$324$		0			0
$325$	5169.63			0.0489433
$326$	−128853.	+	112546.i	−1.21244	+	1.05900i
$327$		0			0
$328$	−5888.19	−	98918.1i	−0.0547311	−	0.919450i
$329$	93011.4	−	161101.i	0.859299	−	1.48835i
$330$		0			0
$331$	97678.0	−	56394.4i	0.891540	−	0.514731i	0.0170938	−	0.999854i	$-0.494559\pi$
$331$	97678.0	−	56394.4i	0.891540	−	0.514731i	0.874446	+	0.485123i	$0.161225\pi$
$332$	−4620.72	−	11282.7i	−0.0419212	−	0.102362i
$333$		0			0
$334$	8535.06	+	43361.2i	0.0765092	+	0.388695i
$335$	1241.92	−	717.024i	0.0110664	−	0.00638917i
$336$		0			0
$337$	10409.8	−	18030.3i	0.0916606	−	0.158761i	−0.816549	−	0.577276i	$-0.804116\pi$
$337$	10409.8	−	18030.3i	0.0916606	−	0.158761i	0.908210	+	0.418515i	$0.137449\pi$
$338$	35843.1	−	104901.i	0.313742	−	0.918222i
$339$		0			0
$340$	−107825.	−	83423.4i	−0.932739	−	0.721656i
$341$	−85367.4			−0.734147
$342$		0			0
$343$		−	125431.i		−	1.06615i
$344$	−53625.7	+	107119.i	−0.453165	+	0.905208i
$345$		0			0
$346$	−28369.8	+	83029.5i	−0.236976	+	0.693554i
$347$	−139615.	−	80606.6i	−1.15950	−	0.669440i	−0.208318	−	0.978061i	$-0.566799\pi$
$347$	−139615.	−	80606.6i	−1.15950	−	0.669440i	−0.951185	+	0.308621i	$0.900132\pi$
$348$		0			0
$349$	110742.	+	191811.i	0.909205	+	1.57479i	0.815171	+	0.579220i	$0.196643\pi$
$349$	110742.	+	191811.i	0.909205	+	1.57479i	0.0940341	+	0.995569i	$0.470024\pi$
$350$	6122.59	+	31105.0i	0.0499803	+	0.253919i
$351$		0			0
$352$	−57312.9	−	39129.0i	−0.462559	−	0.315801i
$353$	109395.	+	189477.i	0.877904	+	1.52057i	0.853637	+	0.520869i	$0.174392\pi$
$353$	109395.	+	189477.i	0.877904	+	1.52057i	0.0242676	+	0.999705i	$0.492275\pi$
$354$		0			0
$355$	−24088.2	−	13907.3i	−0.191138	−	0.110354i
$356$	17393.8	−	128159.i	0.137244	−	1.01123i
$357$		0			0
$358$	−34582.4	+	30206.0i	−0.269830	+	0.235682i
$359$		−	924.606i		−	0.00717411i	−0.999994	−	0.00358705i	$-0.998858\pi$
$359$		−	924.606i		−	0.00717411i	0.999994	−	0.00358705i	$-0.00114180\pi$
$360$		0			0
$361$	−285370.			−2.18975
$362$	−119654.	−	136991.i	−0.913084	−	1.04538i
$363$		0			0
$364$	−20588.3	−	2794.24i	−0.155388	−	0.0210893i
$365$	100158.	−	173479.i	0.751799	−	1.30215i
$366$		0			0
$367$	−35332.0	+	20398.9i	−0.262323	+	0.151452i	−0.625394	−	0.780309i	$-0.715062\pi$
$367$	−35332.0	+	20398.9i	−0.262323	+	0.151452i	0.363071	+	0.931762i	$0.381728\pi$
$368$	−69570.1	−	70691.2i	−0.513721	−	0.521999i
$369$		0			0
$370$	116386.	−	22908.9i	0.850150	−	0.167340i
$371$	35030.3	−	20224.8i	0.254505	−	0.146939i
$372$		0			0
$373$	117265.	−	203109.i	0.842851	−	1.45986i	−0.0446228	−	0.999004i	$-0.514209\pi$
$373$	117265.	−	203109.i	0.842851	−	1.45986i	0.887474	−	0.460858i	$-0.152458\pi$
$374$	−103336.	−	35308.4i	−0.738771	−	0.252426i
$375$		0			0
$376$	−119447.	+	238599.i	−0.844892	+	1.68769i
$377$	21083.4			0.148340
$378$		0			0
$379$		−	185553.i		−	1.29178i	−0.763428	−	0.645892i	$-0.776485\pi$
$379$		−	185553.i		−	1.29178i	0.763428	−	0.645892i	$-0.223515\pi$
$380$	−133518.	+	172572.i	−0.924639	+	1.19509i
$381$		0			0
$382$	265114.	+	90585.2i	1.81679	+	0.620770i
$383$	52190.3	+	30132.1i	0.355789	+	0.205415i	0.667232	−	0.744850i	$-0.267479\pi$
$383$	52190.3	+	30132.1i	0.355789	+	0.205415i	−0.311443	+	0.950265i	$0.600812\pi$
$384$		0			0
$385$	−31978.3	−	55388.1i	−0.215742	−	0.373675i
$386$	−136787.	+	26924.6i	−0.918056	+	0.180707i
$387$		0			0
$388$	98691.0	−	40417.8i	0.655562	−	0.268479i
$389$	−6004.66	−	10400.4i	−0.0396816	−	0.0687306i	0.845502	−	0.533971i	$-0.179301\pi$
$389$	−6004.66	−	10400.4i	−0.0396816	−	0.0687306i	−0.885184	+	0.465241i	$0.845968\pi$
$390$		0			0
$391$	−135164.	−	78037.0i	−0.884113	−	0.510443i
$392$	1559.94	+	26206.1i	0.0101516	+	0.170542i
$393$		0			0
$394$	−81198.7	−	92963.4i	−0.523066	−	0.598852i
$395$		−	92416.5i		−	0.592318i
$396$		0			0
$397$	32276.3			0.204787			0.102394	−	0.994744i	$-0.467350\pi$
$397$	32276.3			0.204787			0.102394	+	0.994744i	$0.467350\pi$
$398$	103220.	−	90157.2i	0.651624	−	0.569160i
$399$		0			0
$400$	−11417.8	−	44015.9i	−0.0713611	−	0.275099i
$401$	−93863.1	+	162576.i	−0.583722	+	1.01104i	0.411311	+	0.911495i	$0.365071\pi$
$401$	−93863.1	+	162576.i	−0.583722	+	1.01104i	−0.995033	+	0.0995418i	$0.968262\pi$
$402$		0			0
$403$	31749.4	−	18330.5i	0.195490	−	0.112866i
$404$	−137494.	+	56309.0i	−0.842402	+	0.344997i
$405$		0			0
$406$	24969.8	+	126856.i	0.151483	+	0.769588i
$407$	82286.0	−	47507.9i	0.496749	−	0.286798i
$408$		0			0
$409$	67272.0	−	116518.i	0.402149	−	0.696543i	−0.591836	−	0.806059i	$-0.701597\pi$
$409$	67272.0	−	116518.i	0.402149	−	0.696543i	0.993985	+	0.109515i	$0.0349299\pi$
$410$	−42355.1	+	123960.i	−0.251964	+	0.737417i
$411$		0			0
$412$	110709.	−	143091.i	0.652210	−	0.842980i
$413$	201779.			1.18298
$414$		0			0
$415$			16117.5i			0.0935841i
$416$	29717.5	+	2246.15i	0.171722	+	0.0129793i
$417$		0			0
$418$	−56510.5	+	165388.i	−0.323427	+	0.946568i
$419$	73320.7	+	42331.7i	0.417637	+	0.241123i	0.694066	−	0.719912i	$-0.255818\pi$
$419$	73320.7	+	42331.7i	0.417637	+	0.241123i	−0.276429	+	0.961034i	$0.589151\pi$
$420$		0			0
$421$	57849.8	+	100199.i	0.326391	+	0.565325i	0.981793	−	0.189955i	$-0.0608341\pi$
$421$	57849.8	+	100199.i	0.326391	+	0.565325i	−0.655402	+	0.755280i	$0.727501\pi$
$422$	−13371.2	−	67930.7i	−0.0750837	−	0.381453i
$423$		0			0
$424$	−48434.4	+	31944.6i	−0.269415	+	0.177691i
$425$	−35777.9	−	61969.1i	−0.198078	−	0.343081i
$426$		0			0
$427$	101565.	+	58638.4i	0.557041	+	0.321608i
$428$	99275.5	+	13473.7i	0.541944	+	0.0735527i
$429$		0			0
$430$	119269.	−	104175.i	0.645045	−	0.563413i
$431$			294896.i			1.58750i	0.608241	+	0.793752i	$0.291875\pi$
$431$			294896.i			1.58750i	−0.608241	+	0.793752i	$0.708125\pi$
$432$		0			0
$433$	−151284.			−0.806895			−0.403447	−	0.915003i	$-0.632188\pi$
$433$	−151284.			−0.806895			−0.403447	+	0.915003i	$0.632188\pi$
$434$	147894.	+	169322.i	0.785185	+	0.898949i
$435$		0			0
$436$	−7429.82	+	54743.7i	−0.0390846	+	0.287979i
$437$	−124897.	+	216328.i	−0.654017	+	1.13279i
$438$		0			0
$439$	17332.7	−	10007.1i	0.0899369	−	0.0519251i	−0.454357	−	0.890820i	$-0.650131\pi$
$439$	17332.7	−	10007.1i	0.0899369	−	0.0519251i	0.544294	+	0.838895i	$0.316798\pi$
$440$	50509.0	+	76581.8i	0.260893	+	0.395567i
$441$		0			0
$442$	46013.9	−	9057.19i	0.235529	−	0.0463606i
$443$	33466.7	−	19322.0i	0.170532	−	0.0984567i	−0.412305	−	0.911046i	$-0.635276\pi$
$443$	33466.7	−	19322.0i	0.170532	−	0.0984567i	0.582837	+	0.812589i	$0.301943\pi$
$444$		0			0
$445$	−85486.7	+	148067.i	−0.431696	+	0.747720i
$446$	242508.	+	82861.0i	1.21915	+	0.416563i
$447$		0			0
$448$	21680.7	+	181467.i	0.108023	+	0.904150i
$449$	−79457.9			−0.394135			−0.197067	−	0.980390i	$-0.563142\pi$
$449$	−79457.9			−0.394135			−0.197067	+	0.980390i	$0.563142\pi$
$450$		0			0
$451$			104930.i			0.515878i
$452$	−32207.4	−	24918.7i	−0.157645	−	0.121969i
$453$		0			0
$454$	−51827.0	−	17708.5i	−0.251446	−	0.0859151i
$455$	23786.4	+	13733.1i	0.114896	+	0.0663354i
$456$		0			0
$457$	131776.	+	228243.i	0.630963	+	1.09286i	0.987355	+	0.158524i	$0.0506735\pi$
$457$	131776.	+	228243.i	0.630963	+	1.09286i	−0.356392	+	0.934337i	$0.615993\pi$
$458$	259000.	−	50980.5i	1.23472	−	0.243037i
$459$		0			0
$460$	49691.0	+	121334.i	0.234834	+	0.573411i
$461$	−100305.	−	173733.i	−0.471976	−	0.817487i	0.527510	−	0.849549i	$-0.323126\pi$
$461$	−100305.	−	173733.i	−0.471976	−	0.817487i	−0.999486	+	0.0320624i	$0.989792\pi$
$462$		0			0
$463$	205297.	+	118528.i	0.957679	+	0.552916i	0.895458	−	0.445146i	$-0.146848\pi$
$463$	205297.	+	118528.i	0.957679	+	0.552916i	0.0622210	+	0.998062i	$0.480182\pi$
$464$	−46565.2	−	179510.i	−0.216285	−	0.833784i
$465$		0			0
$466$	−166677.	−	190827.i	−0.767546	−	0.878754i
$467$		−	230464.i		−	1.05674i	−0.849014	−	0.528371i	$-0.822803\pi$
$467$		−	230464.i		−	1.05674i	0.849014	−	0.528371i	$-0.177197\pi$
$468$		0			0
$469$	−3025.13			−0.0137530
$470$	265663.	−	232043.i	1.20264	−	1.05044i
$471$		0			0
$472$	−288918.	+	17198.1i	−1.29685	+	0.0771961i
$473$	63424.1	−	109854.i	0.283486	−	0.491013i
$474$		0			0
$475$	−99180.5	+	57261.9i	−0.439581	+	0.253792i
$476$	108992.	+	266133.i	0.481039	+	1.17459i
$477$		0			0
$478$	−245.315	−	1246.29i	−0.00107366	−	0.00545461i
$479$	2079.74	−	1200.74i	0.00906438	−	0.00523332i	−0.495461	−	0.868630i	$-0.665001\pi$
$479$	2079.74	−	1200.74i	0.00906438	−	0.00523332i	0.504525	+	0.863397i	$0.331668\pi$
$480$		0			0
$481$	−20402.3	+	35337.7i	−0.0881836	+	0.152739i
$482$	−32986.6	+	96541.1i	−0.141985	+	0.415545i
$483$		0			0
$484$	−127157.	−	98380.7i	−0.542812	−	0.419971i
$485$	−140981.			−0.599347
$486$		0			0
$487$			405227.i			1.70860i	0.519781	+	0.854300i	$0.326014\pi$
$487$			405227.i			1.70860i	−0.519781	+	0.854300i	$0.673986\pi$
$488$	−150423.	−	75304.9i	−0.631649	−	0.316216i
$489$		0			0
$490$	11221.0	−	32840.3i	0.0467347	−	0.136778i
$491$	111325.	+	64273.4i	0.461773	+	0.266605i	0.712790	−	0.701378i	$-0.247431\pi$
$491$	111325.	+	64273.4i	0.461773	+	0.266605i	−0.251016	+	0.967983i	$0.580765\pi$
$492$		0			0
$493$	−145913.	−	252729.i	−0.600345	−	1.03983i
$494$	−14495.9	−	73644.5i	−0.0594006	−	0.301777i
$495$		0			0
$496$	−226194.	−	229839.i	−0.919429	−	0.934244i
$497$	29337.5	+	50814.1i	0.118771	+	0.205717i
$498$		0			0
$499$	111377.	+	64303.6i	0.447296	+	0.258246i	0.706687	−	0.707526i	$-0.250189\pi$
$499$	111377.	+	64303.6i	0.447296	+	0.258246i	−0.259392	+	0.965772i	$0.583522\pi$
$500$	−36530.0	+	269157.i	−0.146120	+	1.07663i
$501$		0			0
$502$	123480.	−	107854.i	0.489994	−	0.427984i
$503$			368128.i			1.45500i	0.686109	+	0.727499i	$0.259317\pi$
$503$			368128.i			1.45500i	−0.686109	+	0.727499i	$0.740683\pi$
$504$		0			0
$505$	196411.			0.770165
$506$	69090.0	+	79100.3i	0.269845	+	0.308942i
$507$		0			0
$508$	8403.92	+	1140.58i	0.0325653	+	0.00441976i
$509$	−40698.4	+	70491.6i	−0.157087	+	0.272083i	−0.933817	−	0.357751i	$-0.883544\pi$
$509$	−40698.4	+	70491.6i	−0.157087	+	0.272083i	0.776730	+	0.629834i	$0.216877\pi$
$510$		0			0
$511$	−365955.	+	211284.i	−1.40148	+	0.809143i
$512$	−46510.3	−	257985.i	−0.177423	−	0.984135i
$513$		0			0
$514$	−121501.	+	23915.8i	−0.459890	+	0.0905230i
$515$	−207123.	+	119582.i	−0.780931	+	0.450871i
$516$		0			0
$517$	141273.	−	244692.i	0.528539	−	0.915457i
$518$	−236786.	−	80906.0i	−0.882463	−	0.301523i
$519$		0			0
$520$	−35229.1	−	17636.4i	−0.130285	−	0.0652232i
$521$	17832.5			0.0656956			0.0328478	−	0.999460i	$-0.489542\pi$
$521$	17832.5			0.0656956			0.0328478	+	0.999460i	$0.489542\pi$
$522$		0			0
$523$			51996.2i			0.190094i	0.995473	+	0.0950470i	$0.0303001\pi$
$523$			51996.2i			0.190094i	−0.995473	+	0.0950470i	$0.969700\pi$
$524$	−9069.23	+	11722.0i	−0.0330299	+	0.0426911i
$525$		0			0
$526$	58181.8	+	19879.8i	0.210289	+	0.0718522i
$527$	−439461.	−	253723.i	−1.58234	−	0.913562i
$528$		0			0
$529$	−64868.3	−	112355.i	−0.231804	−	0.401496i
$530$	75255.7	−	14813.0i	0.267909	−	0.0527342i
$531$		0			0
$532$	425941.	−	174440.i	1.50497	−	0.616343i
$533$	−22531.1	−	39025.1i	−0.0793101	−	0.137369i
$534$		0			0
$535$	−114697.	−	66220.2i	−0.400722	−	0.231357i
$536$	4331.53	−	257.838i	0.0150769	−	0.000897465i
$537$		0			0
$538$	200262.	+	229277.i	0.691884	+	0.792129i
$539$		−	27798.8i		−	0.0956862i
$540$		0			0
$541$	−329819.			−1.12689			−0.563444	−	0.826154i	$-0.690524\pi$
$541$	−329819.			−1.12689			−0.563444	+	0.826154i	$0.690524\pi$
$542$	235215.	−	205448.i	0.800693	−	0.699364i
$543$		0			0
$544$	−178743.	−	371773.i	−0.603993	−	1.25626i
$545$	36515.9	−	63247.5i	0.122939	−	0.212936i
$546$		0			0
$547$	306032.	−	176688.i	1.02280	−	0.590517i	0.107890	−	0.994163i	$-0.465591\pi$
$547$	306032.	−	176688.i	1.02280	−	0.590517i	0.914915	+	0.403646i	$0.132257\pi$
$548$	−24700.5	+	10115.8i	−0.0822516	+	0.0336853i
$549$		0			0
$550$	9299.45	+	47244.6i	0.0307420	+	0.156181i
$551$	−404489.	+	233532.i	−1.33230	+	0.769206i
$552$		0			0
$553$	−97476.3	+	168834.i	−0.318749	+	0.552090i
$554$	−6130.27	+	17941.3i	−0.0199738	+	0.0584568i
$555$		0			0
$556$	−8114.69	+	10488.2i	−0.0262496	+	0.0339275i
$557$	381405.			1.22935			0.614676	−	0.788780i	$-0.289287\pi$
$557$	381405.			1.22935			0.614676	+	0.788780i	$0.289287\pi$
$558$		0			0
$559$			54475.0i			0.174330i
$560$	64392.6	−	232856.i	0.205334	−	0.742526i
$561$		0			0
$562$	55883.6	−	163553.i	0.176934	−	0.517830i
$563$	−203807.	−	117668.i	−0.642988	−	0.371229i	0.142776	−	0.989755i	$-0.454397\pi$
$563$	−203807.	−	117668.i	−0.642988	−	0.371229i	−0.785765	+	0.618526i	$0.787730\pi$
$564$		0			0
$565$	26916.0	+	46619.9i	0.0843168	+	0.146041i
$566$	−27900.1	−	141743.i	−0.0870909	−	0.442454i
$567$		0			0
$568$	−46337.9	−	70257.6i	−0.143628	−	0.217769i
$569$	−110971.	−	192208.i	−0.342757	−	0.593673i	0.642186	−	0.766549i	$-0.278028\pi$
$569$	−110971.	−	192208.i	−0.342757	−	0.593673i	−0.984944	+	0.172875i	$0.944694\pi$
$570$		0			0
$571$	34588.3	+	19969.5i	0.106086	+	0.0612486i	0.552104	−	0.833775i	$-0.313825\pi$
$571$	34588.3	+	19969.5i	0.106086	+	0.0612486i	−0.446018	+	0.895024i	$0.647158\pi$
$572$	−31271.0	−	4244.10i	−0.0955763	−	0.0129716i
$573$		0			0
$574$	208124.	−	181786.i	0.631683	−	0.551742i
$575$			68818.8i			0.208148i
$576$		0			0
$577$	511135.			1.53527			0.767634	−	0.640889i	$-0.221434\pi$
$577$	511135.			1.53527			0.767634	+	0.640889i	$0.221434\pi$
$578$	−207247.	−	237274.i	−0.620343	−	0.710224i
$579$		0			0
$580$	−32970.5	+	242930.i	−0.0980098	+	0.722147i
$581$	17000.0	−	29444.8i	0.0503612	−	0.0872281i
$582$		0			0
$583$	53206.7	−	30718.9i	0.156541	−	0.0903793i
$584$	505985.	−	333719.i	1.48358	−	0.978486i
$585$		0			0
$586$	377137.	−	74234.1i	1.09826	−	0.216176i
$587$	60509.5	−	34935.2i	0.175609	−	0.101388i	−0.409619	−	0.912257i	$-0.634338\pi$
$587$	60509.5	−	34935.2i	0.175609	−	0.101388i	0.585228	+	0.810869i	$0.301005\pi$
$588$		0			0
$589$	−406079.	+	703350.i	−1.17052	+	2.02741i
$590$	362059.	+	123710.i	1.04010	+	0.355385i
$591$		0			0
$592$	345938.	+	95663.4i	0.987085	+	0.272962i
$593$	−206980.			−0.588599			−0.294299	−	0.955713i	$-0.595086\pi$
$593$	−206980.			−0.588599			−0.294299	+	0.955713i	$0.595086\pi$
$594$		0			0
$595$		−	380174.i		−	1.07386i
$596$	39517.3	+	30574.4i	0.111249	+	0.0860726i
$597$		0			0
$598$	−42680.4	−	14583.2i	−0.119351	−	0.0407803i
$599$	241159.	+	139233.i	0.672123	+	0.388051i	0.796881	−	0.604137i	$-0.206482\pi$
$599$	241159.	+	139233.i	0.672123	+	0.388051i	−0.124757	+	0.992187i	$0.539815\pi$
$600$		0			0
$601$	−213736.	−	370201.i	−0.591737	−	1.02492i	−0.993999	−	0.109393i	$-0.965109\pi$
$601$	−213736.	−	370201.i	−0.591737	−	1.02492i	0.402262	−	0.915525i	$-0.368224\pi$
$602$	−327769.	+	64516.8i	−0.904430	+	0.178024i
$603$		0			0
$604$	−55541.6	−	135620.i	−0.152246	−	0.371748i
$605$	106266.	+	184058.i	0.290325	+	0.502857i
$606$		0			0
$607$	−361479.	−	208700.i	−0.981082	−	0.566428i	−0.0784853	−	0.996915i	$-0.525008\pi$
$607$	−361479.	−	208700.i	−0.981082	−	0.566428i	−0.902597	+	0.430487i	$0.858342\pi$
$608$	−595016.	+	286076.i	−1.60961	+	0.773880i
$609$		0			0
$610$	146290.	+	167486.i	0.393147	+	0.450109i
$611$			121339.i			0.325026i
$612$		0			0
$613$	−23327.6			−0.0620796			−0.0310398	−	0.999518i	$-0.509882\pi$
$613$	−23327.6			−0.0620796			−0.0310398	+	0.999518i	$0.509882\pi$
$614$	−423699.	+	370079.i	−1.12388	+	0.981652i
$615$		0			0
$616$	−11499.2	−	193180.i	−0.0303045	−	0.509098i
$617$	39385.7	−	68218.0i	0.103459	−	0.179196i	−0.809649	−	0.586915i	$-0.800342\pi$
$617$	39385.7	−	68218.0i	0.103459	−	0.179196i	0.913108	+	0.407719i	$0.133676\pi$
$618$		0			0
$619$	382655.	−	220926.i	0.998679	−	0.576587i	0.0908215	−	0.995867i	$-0.471051\pi$
$619$	382655.	−	220926.i	0.998679	−	0.576587i	0.907857	+	0.419280i	$0.137717\pi$
$620$	161561.	+	394494.i	0.420293	+	1.02626i
$621$		0			0
$622$	−126279.	−	641545.i	−0.326401	−	1.65824i
$623$	312348.	−	180334.i	0.804753	−	0.464625i
$624$		0			0
$625$	124028.	−	214823.i	0.317512	−	0.549947i
$626$	66334.9	−	194141.i	0.169275	−	0.495415i
$627$		0			0
$628$	−267059.	−	206623.i	−0.677155	−	0.523912i
$629$	564798.			1.42755
$630$		0			0
$631$			211599.i			0.531440i	0.964050	+	0.265720i	$0.0856097\pi$
$631$			211599.i			0.531440i	−0.964050	+	0.265720i	$0.914390\pi$
$632$	125181.	−	250053.i	0.313405	−	0.626034i
$633$		0			0
$634$	−36277.7	+	106173.i	−0.0902530	+	0.264142i
$635$	−9709.36	−	5605.70i	−0.0240793	−	0.0139022i
$636$		0			0
$637$	5969.11	+	10338.8i	0.0147106	+	0.0254795i
$638$	37926.0	+	192678.i	0.0931743	+	0.473360i
$639$		0			0
$640$	−72353.7	+	338903.i	−0.176645	+	0.827401i
$641$	−2552.74	−	4421.47i	−0.00621284	−	0.0107610i	0.862902	−	0.505371i	$-0.168644\pi$
$641$	−2552.74	−	4421.47i	−0.00621284	−	0.0107610i	−0.869115	+	0.494610i	$0.835311\pi$
$642$		0			0
$643$	−69127.8	−	39911.0i	−0.167198	−	0.0965318i	0.414066	−	0.910247i	$-0.364108\pi$
$643$	−69127.8	−	39911.0i	−0.167198	−	0.0965318i	−0.581264	+	0.813715i	$0.697442\pi$
$644$	37197.3	−	274074.i	0.0896891	−	0.660839i
$645$		0			0
$646$	−782463.	+	683441.i	−1.87499	+	1.63771i
$647$		−	531516.i		−	1.26972i	−0.772628	−	0.634859i	$-0.781058\pi$
$647$		−	531516.i		−	1.26972i	0.772628	−	0.634859i	$-0.218942\pi$
$648$		0			0
$649$	306477.			0.727627
$650$	−13603.2	−	15574.2i	−0.0321969	−	0.0368619i
$651$		0			0
$652$	678119.	+	92034.3i	1.59518	+	0.216498i
$653$	−235615.	+	408097.i	−0.552556	+	0.957055i	0.445533	+	0.895265i	$0.353014\pi$
$653$	−235615.	+	408097.i	−0.552556	+	0.957055i	−0.998089	+	0.0617897i	$0.980319\pi$
$654$		0			0
$655$	16967.4	−	9796.15i	0.0395488	−	0.0228335i
$656$	−282509.	+	278029.i	−0.656485	+	0.646074i
$657$		0			0
$658$	−730082.	+	143707.i	−1.68624	+	0.331913i
$659$	309469.	−	178672.i	0.712601	−	0.411420i	−0.0994224	−	0.995045i	$-0.531700\pi$
$659$	309469.	−	178672.i	0.712601	−	0.411420i	0.812023	+	0.583625i	$0.198366\pi$
$660$		0			0
$661$	282792.	−	489809.i	0.647237	−	1.12105i	−0.336543	−	0.941668i	$-0.609258\pi$
$661$	282792.	−	489809.i	0.647237	−	1.12105i	0.983780	−	0.179380i	$-0.0574090\pi$
$662$	−426922.	−	145872.i	−0.974165	−	0.332857i
$663$		0			0
$664$	−21831.8	+	43609.5i	−0.0495168	+	0.0989111i
$665$	−608463.			−1.37591
$666$		0			0
$667$			280664.i			0.630864i
$668$	108172.	−	139812.i	0.242417	−	0.313323i
$669$		0			0
$670$	−5428.08	−	1854.69i	−0.0120920	−	0.00413163i
$671$	154264.	+	89064.5i	0.342626	+	0.197815i
$672$		0			0
$673$	158119.	+	273870.i	0.349103	+	0.604663i	0.986090	−	0.166211i	$-0.0531532\pi$
$673$	158119.	+	273870.i	0.349103	+	0.604663i	−0.636988	+	0.770874i	$0.719820\pi$
$674$	−81710.5	+	16083.6i	−0.179870	+	0.0354049i
$675$		0			0
$676$	−410345.	+	168052.i	−0.897957	+	0.367749i
$677$	−300914.	−	521198.i	−0.656545	−	1.13717i	−0.981504	−	0.191441i	$-0.938684\pi$
$677$	−300914.	−	521198.i	−0.656545	−	1.13717i	0.324959	−	0.945728i	$-0.394649\pi$
$678$		0			0
$679$	257556.	+	148700.i	0.558641	+	0.322531i
$680$	32403.1	+	544353.i	0.0700758	+	1.17723i
$681$		0			0
$682$	224633.	+	257180.i	0.482953	+	0.552927i
$683$			385277.i			0.825909i	0.910752	+	0.412955i	$0.135503\pi$
$683$			385277.i			0.825909i	−0.910752	+	0.412955i	$0.864497\pi$
$684$		0			0
$685$	35285.0			0.0751984
$686$	−377877.	+	330056.i	−0.802975	+	0.701357i
$687$		0			0
$688$	463817.	−	120315.i	0.979873	−	0.254180i
$689$	−13192.2	+	22849.6i	−0.0277895	+	0.0481328i
$690$		0			0
$691$	−397767.	+	229651.i	−0.833053	+	0.480963i	−0.854897	−	0.518798i	$-0.826380\pi$
$691$	−397767.	+	229651.i	−0.833053	+	0.480963i	0.0218438	+	0.999761i	$0.493046\pi$
$692$	324788.	−	133014.i	0.678247	−	0.277769i
$693$		0			0
$694$	124541.	+	632712.i	0.258578	+	1.31367i
$695$	15181.6	−	8765.10i	0.0314303	−	0.0181463i
$696$		0			0
$697$	−311866.	+	540168.i	−0.641952	+	1.11189i
$698$	286451.	−	838349.i	0.587948	−	1.72074i
$699$		0			0
$700$	77596.9	−	100294.i	0.158361	−	0.204681i
$701$	127011.			0.258467			0.129234	−	0.991614i	$-0.458748\pi$
$701$	127011.			0.258467			0.129234	+	0.991614i	$0.458748\pi$
$702$		0			0
$703$		−	903950.i		−	1.82908i
$704$	32930.3	+	275625.i	0.0664432	+	0.556126i
$705$		0			0
$706$	282966.	−	828150.i	0.567707	−	1.66150i
$707$	−358820.	−	207165.i	−0.717857	−	0.414455i
$708$		0			0
$709$	−247408.	−	428523.i	−0.492177	−	0.852475i	0.507783	−	0.861485i	$-0.330465\pi$
$709$	−247408.	−	428523.i	−0.492177	−	0.852475i	−0.999959	+	0.00901014i	$0.997132\pi$
$710$	21487.4	+	109164.i	0.0426253	+	0.216552i
$711$		0			0
$712$	−431865.	+	284834.i	−0.851900	+	0.561864i
$713$	244018.	+	422652.i	0.480002	+	0.831388i
$714$		0			0
$715$	36128.6	+	20858.8i	0.0706706	+	0.0408017i
$716$	181998.	+	24700.8i	0.355011	+	0.0481820i
$717$		0			0
$718$	−2785.49	+	2432.98i	−0.00540322	+	0.00471943i
$719$		−	614613.i		−	1.18890i	−0.804134	−	0.594448i	$-0.797371\pi$
$719$		−	614613.i		−	1.18890i	0.804134	−	0.594448i	$-0.202629\pi$
$720$		0			0
$721$	504518.			0.970523
$722$	750914.	+	859712.i	1.44051	+	1.64922i
$723$		0			0
$724$	−97846.7	+	720945.i	−0.186668	+	1.37539i
$725$	−64338.5	+	111438.i	−0.122404	+	0.212010i
$726$		0			0
$727$	−286999.	+	165699.i	−0.543014	+	0.313509i	−0.746299	−	0.665610i	$-0.768171\pi$
$727$	−286999.	+	165699.i	−0.543014	+	0.313509i	0.203286	+	0.979119i	$0.434838\pi$
$728$	45757.4	+	69377.4i	0.0863373	+	0.130905i
$729$		0			0
$730$	−786182.	+	154749.i	−1.47529	+	0.290390i
$731$	652999.	−	377009.i	1.22202	−	0.705532i
$732$		0			0
$733$	25808.4	−	44701.5i	0.0480345	−	0.0831982i	−0.841008	−	0.541022i	$-0.818038\pi$
$733$	25808.4	−	44701.5i	0.0480345	−	0.0831982i	0.889043	+	0.457824i	$0.151371\pi$
$734$	154426.	+	52764.9i	0.286634	+	0.0979383i
$735$		0			0
$736$	−29901.1	+	395603.i	−0.0551990	+	0.730305i
$737$	−4594.79			−0.00845923
$738$		0			0
$739$		−	228968.i		−	0.419263i	−0.977780	−	0.209631i	$-0.932774\pi$
$739$		−	228968.i		−	0.419263i	0.977780	−	0.209631i	$-0.0672264\pi$
$740$	−375269.	−	290344.i	−0.685298	−	0.530212i
$741$		0			0
$742$	−153107.	−	52314.4i	−0.278092	−	0.0950196i
$743$	910009.	+	525394.i	1.64842	+	0.951716i	0.977700	+	0.210005i	$0.0673480\pi$
$743$	910009.	+	525394.i	1.64842	+	0.951716i	0.670720	+	0.741711i	$0.265985\pi$
$744$		0			0
$745$	−33025.0	−	57201.0i	−0.0595018	−	0.103060i
$746$	−920459.	+	181179.i	−1.65397	+	0.325560i
$747$		0			0
$748$	165545.	+	404223.i	0.295878	+	0.722466i
$749$	139692.	+	241953.i	0.249004	+	0.431288i
$750$		0			0
$751$	−233295.	−	134693.i	−0.413643	−	0.238817i	0.278711	−	0.960375i	$-0.410093\pi$
$751$	−233295.	−	134693.i	−0.413643	−	0.238817i	−0.692354	+	0.721558i	$0.743426\pi$
$752$	1.03312e6	−	267993.i	1.82690	−	0.473901i
$753$		0			0
$754$	−55478.1	−	63516.2i	−0.0975840	−	0.111723i
$755$			193735.i			0.339870i
$756$		0			0
$757$	−476176.			−0.830952			−0.415476	−	0.909604i	$-0.636385\pi$
$757$	−476176.			−0.830952			−0.415476	+	0.909604i	$0.636385\pi$
$758$	−559002.	+	488259.i	−0.972915	+	0.849791i
$759$		0			0
$760$	871228.	−	51860.6i	1.50836	−	0.0897863i
$761$	242197.	−	419498.i	0.418215	−	0.724370i	−0.577545	−	0.816359i	$-0.695989\pi$
$761$	242197.	−	419498.i	0.418215	−	0.724370i	0.995760	+	0.0919890i	$0.0293225\pi$
$762$		0			0
$763$	−133421.	+	77030.4i	−0.229178	+	0.132316i
$764$	−424714.	−	1.03705e6i	−0.727628	−	1.77670i
$765$		0			0
$766$	−46555.3	−	236518.i	−0.0793436	−	0.403095i
$767$	−113983.	+	65808.4i	−0.193754	+	0.111864i
$768$		0			0
$769$	−251061.	+	434851.i	−0.424549	+	0.735340i	−0.996378	−	0.0850327i	$-0.972901\pi$
$769$	−251061.	+	434851.i	−0.424549	+	0.735340i	0.571830	+	0.820372i	$0.306234\pi$
$770$	−82716.6	+	242085.i	−0.139512	+	0.408307i
$771$		0			0
$772$	441050.	+	341238.i	0.740037	+	0.572563i
$773$	−435529.			−0.728884			−0.364442	−	0.931226i	$-0.618740\pi$
$773$	−435529.			−0.728884			−0.364442	+	0.931226i	$0.618740\pi$
$774$		0			0
$775$			223752.i			0.372531i
$776$	−381456.	−	190964.i	−0.633463	−	0.317124i
$777$		0			0
$778$	−15531.9	+	45457.0i	−0.0256606	+	0.0751004i
$779$	864530.	+	499136.i	1.42464	+	0.822516i
$780$		0			0
$781$	44560.0	+	77180.2i	0.0730539	+	0.126533i
$782$	120571.	+	612543.i	0.197164	+	1.00167i
$783$		0			0
$784$	74844.3	−	73657.4i	0.121766	−	0.119835i
$785$	223184.	+	386566.i	0.362179	+	0.627313i
$786$		0			0
$787$	−371945.	−	214742.i	−0.600522	−	0.346711i	0.168725	−	0.985663i	$-0.446035\pi$
$787$	−371945.	−	214742.i	−0.600522	−	0.346711i	−0.769247	+	0.638952i	$0.779368\pi$
$788$	−66399.9	+	489242.i	−0.106934	+	0.787900i
$789$		0			0
$790$	−278416.	+	243182.i	−0.446108	+	0.389652i
$791$		−	113559.i		−	0.181496i
$792$		0			0
$793$	−76497.5			−0.121647
$794$	−84930.9	−	97236.4i	−0.134718	−	0.154237i
$795$		0			0
$796$	−543219.	−	73725.7i	−0.857332	−	0.116357i
$797$	362714.	−	628240.i	0.571016	−	0.989028i	−0.425446	−	0.904984i	$-0.639883\pi$
$797$	362714.	−	628240.i	0.571016	−	0.989028i	0.996462	−	0.0840446i	$-0.0267838\pi$
$798$		0			0
$799$	1.45451e6	−	839761.i	2.27836	−	1.31541i
$800$	−102559.	+	150220.i	−0.160248	+	0.234718i
$801$		0			0
$802$	736768.	−	145023.i	1.14547	−	0.225469i
$803$	−555840.	+	320914.i	−0.862023	+	0.497689i
$804$		0			0
$805$	−182817.	+	316648.i	−0.282114	+	0.488635i
$806$	−138767.	−	47414.6i	−0.213608	−	0.0729863i
$807$		0			0
$808$	531434.	+	266046.i	0.814004	+	0.407506i
$809$	−144295.			−0.220473			−0.110237	−	0.993905i	$-0.535161\pi$
$809$	−144295.			−0.220473			−0.110237	+	0.993905i	$0.535161\pi$
$810$		0			0
$811$			321928.i			0.489460i	0.969591	+	0.244730i	$0.0786993\pi$
$811$			321928.i			0.489460i	−0.969591	+	0.244730i	$0.921301\pi$
$812$	316464.	−	409029.i	0.479968	−	0.620358i
$813$		0			0
$814$	−359648.	−	122886.i	−0.542787	−	0.185462i
$815$	−783456.	−	452328.i	−1.17950	−	0.680987i
$816$		0			0
$817$	−603397.	−	1.04511e6i	−0.903980	−	1.56574i
$818$	−528044.	+	103938.i	−0.789156	+	0.155334i
$819$		0			0
$820$	484896.	−	198584.i	0.721142	−	0.295336i
$821$	453891.	+	786162.i	0.673388	+	1.16634i	0.976937	+	0.213527i	$0.0684950\pi$
$821$	453891.	+	786162.i	0.673388	+	1.16634i	−0.303549	+	0.952816i	$0.598172\pi$
$822$		0			0
$823$	730902.	+	421987.i	1.07909	+	0.623016i	0.930652	−	0.365905i	$-0.119241\pi$
$823$	730902.	+	421987.i	1.07909	+	0.623016i	0.148443	+	0.988921i	$0.452574\pi$
$824$	−722394.	+	43001.1i	−1.06395	+	0.0633323i
$825$		0			0
$826$	−530955.	−	607885.i	−0.778212	−	0.890966i
$827$		−	658309.i		−	0.962540i	−0.876572	−	0.481270i	$-0.840176\pi$
$827$		−	658309.i		−	0.962540i	0.876572	−	0.481270i	$-0.159824\pi$
$828$		0			0
$829$	1.22965e6			1.78925			0.894625	−	0.446818i	$-0.147443\pi$
$829$	1.22965e6			1.78925			0.894625	+	0.446818i	$0.147443\pi$
$830$	48556.0	−	42411.2i	0.0704834	−	0.0615636i
$831$		0			0
$832$	−71430.9	−	95438.0i	−0.103190	−	0.137872i
$833$	82621.7	−	143105.i	0.119071	−	0.206236i
$834$		0			0
$835$	−202377.	+	116842.i	−0.290261	+	0.167582i
$836$	646952.	−	264952.i	0.925677	−	0.379101i
$837$		0			0
$838$	−65404.3	−	332278.i	−0.0931362	−	0.473166i
$839$	−45546.9	+	26296.5i	−0.0647045	+	0.0373572i	−0.532003	−	0.846742i	$-0.678561\pi$
$839$	−45546.9	+	26296.5i	−0.0647045	+	0.0373572i	0.467299	+	0.884099i	$0.345227\pi$
$840$		0			0
$841$	91248.2	−	158047.i	0.129013	−	0.223456i
$842$	149637.	−	437940.i	0.211064	−	0.617718i
$843$		0			0
$844$	−169465.	+	219033.i	−0.237900	+	0.307486i
$845$	586183.			0.820956
$846$		0			0
$847$		−	448337.i		−	0.624939i
$848$	223686.	+	61856.6i	0.311062	+	0.0860191i
$849$		0			0
$850$	−92544.7	+	270849.i	−0.128090	+	0.374877i
$851$	−470421.	−	271598.i	−0.649572	−	0.375031i
$852$		0			0
$853$	322258.	+	558168.i	0.442900	+	0.767126i	0.997903	−	0.0647226i	$-0.0206163\pi$
$853$	322258.	+	558168.i	0.442900	+	0.767126i	−0.555003	+	0.831848i	$0.687283\pi$
$854$	−90598.9	−	460276.i	−0.124224	−	0.631106i
$855$		0			0
$856$	−220639.	−	334534.i	−0.301117	−	0.456555i
$857$	175819.	+	304528.i	0.239390	+	0.414635i	0.960539	−	0.278144i	$-0.0897194\pi$
$857$	175819.	+	304528.i	0.239390	+	0.414635i	−0.721150	+	0.692779i	$0.756386\pi$
$858$		0			0
$859$	−658817.	−	380368.i	−0.892851	−	0.515487i	−0.0179767	−	0.999838i	$-0.505722\pi$
$859$	−658817.	−	380368.i	−0.892851	−	0.515487i	−0.874874	+	0.484351i	$0.839056\pi$
$860$	−627681.	−	85188.9i	−0.848676	−	0.115182i
$861$		0			0
$862$	888412.	−	775981.i	1.19564	−	1.04433i
$863$			363360.i			0.487883i	0.969790	+	0.243942i	$0.0784406\pi$
$863$			363360.i			0.487883i	−0.969790	+	0.243942i	$0.921559\pi$
$864$		0			0
$865$	−463964.			−0.620086
$866$	398084.	+	455761.i	0.530809	+	0.607717i
$867$		0			0
$868$	120940.	−	891100.i	0.160521	−	1.18273i
$869$	−148054.	+	256438.i	−0.196057	+	0.339580i
$870$		0			0
$871$	1708.87	−	986.617i	0.00225254	−	0.00130051i
$872$	184473.	−	121668.i	0.242605	−	0.160008i
$873$		0			0
$874$	980365.	−	192971.i	1.28341	−	0.252621i
$875$	−655985.	+	378733.i	−0.856796	+	0.494672i
$876$		0			0
$877$	−36035.0	+	62414.4i	−0.0468516	+	0.0811494i	−0.888500	−	0.458876i	$-0.848252\pi$
$877$	−36035.0	+	62414.4i	−0.0468516	+	0.0811494i	0.841649	+	0.540026i	$0.181585\pi$
$878$	−75756.3	−	25884.7i	−0.0982720	−	0.0335780i
$879$		0			0
$880$	97804.3	−	353680.i	0.126297	−	0.456714i
$881$	−1.34754e6			−1.73616			−0.868082	−	0.496422i	$-0.834647\pi$
$881$	−1.34754e6			−1.73616			−0.868082	+	0.496422i	$0.834647\pi$
$882$		0			0
$883$			675925.i			0.866916i	0.901174	+	0.433458i	$0.142707\pi$
$883$			675925.i			0.866916i	−0.901174	+	0.433458i	$0.857293\pi$
$884$	−148365.	−	114790.i	−0.189858	−	0.146892i
$885$		0			0
$886$	−146273.	−	49979.2i	−0.186336	−	0.0636681i
$887$	−888008.	−	512692.i	−1.12868	−	0.651642i	−0.185075	−	0.982724i	$-0.559253\pi$
$887$	−888008.	−	512692.i	−1.12868	−	0.651642i	−0.943602	+	0.331082i	$0.892586\pi$
$888$		0			0
$889$	11825.2	+	20481.9i	0.0149626	+	0.0259159i
$890$	671018.	−	132081.i	0.847138	−	0.166747i
$891$		0			0
$892$	−388498.	−	948622.i	−0.488269	−	1.19224i
$893$	−1.34402e6	−	2.32792e6i	−1.68540	−	2.91921i
$894$		0			0
$895$	−210269.	−	121399.i	−0.262500	−	0.151555i
$896$	489640.	−	542821.i	0.609904	−	0.676147i
$897$		0			0
$898$	209083.	+	239377.i	0.259278	+	0.296845i
$899$			912528.i			1.12908i
$900$		0			0
$901$	365202.			0.449867
$902$	316115.	−	276110.i	0.388537	−	0.339367i
$903$		0			0
$904$	9678.86	+	162599.i	0.0118437	+	0.198967i
$905$	480895.	−	832935.i	0.587156	−	1.01698i
$906$		0			0
$907$	−1.39930e6	+	807885.i	−1.70097	+	0.982053i	−0.756181	+	0.654363i	$0.772937\pi$
$907$	−1.39930e6	+	807885.i	−1.70097	+	0.982053i	−0.944785	+	0.327690i	$0.893730\pi$
$908$	83027.1	+	202733.i	0.100704	+	0.245896i
$909$		0			0
$910$	−21218.2	−	107796.i	−0.0256227	−	0.130173i
$911$	−246841.	+	142514.i	−0.297427	+	0.171719i	−0.641286	−	0.767302i	$-0.721599\pi$
$911$	−246841.	+	142514.i	−0.297427	+	0.171719i	0.343860	+	0.939021i	$0.388266\pi$
$912$		0			0
$913$	25820.8	−	44723.0i	0.0309762	−	0.0536524i
$914$	340858.	−	997583.i	0.408020	−	1.19414i
$915$		0			0
$916$	−835108.	−	646119.i	−0.995295	−	0.770055i
$917$	−41330.0			−0.0491503
$918$		0			0
$919$			662333.i			0.784233i	0.919916	+	0.392117i	$0.128257\pi$
$919$			662333.i			0.784233i	−0.919916	+	0.392117i	$0.871743\pi$
$920$	234777.	−	468974.i	0.277384	−	0.554081i
$921$		0			0
$922$	−259453.	+	759336.i	−0.305209	+	0.893249i
$923$	−33145.1	−	19136.3i	−0.0389059	−	0.0224623i
$924$		0			0
$925$	−124520.	−	215675.i	−0.145531	−	0.252067i
$926$	−183131.	−	930373.i	−0.213570	−	1.08501i
$927$		0			0
$928$	−418267.	+	612641.i	−0.485688	+	0.711394i
$929$	620275.	+	1.07435e6i	0.718708	+	1.24484i	0.961512	+	0.274764i	$0.0885997\pi$
$929$	620275.	+	1.07435e6i	0.718708	+	1.24484i	−0.242803	+	0.970076i	$0.578067\pi$
$930$		0			0
$931$	−229037.	−	132235.i	−0.264245	−	0.152562i
$932$	−136300.	+	1.00427e6i	−0.156914	+	1.15616i
$933$		0			0
$934$	−694300.	+	606435.i	−0.795891	+	0.695169i
$935$		−	577438.i		−	0.660514i
$936$		0			0
$937$	−593717.			−0.676239			−0.338119	−	0.941103i	$-0.609791\pi$
$937$	−593717.			−0.676239			−0.338119	+	0.941103i	$0.609791\pi$
$938$	7960.23	+	9113.57i	0.00904732	+	0.0103582i
$939$		0			0
$940$	−1.39812e6	−	189752.i	−1.58229	−	0.214749i
$941$	−613509.	+	1.06263e6i	−0.692854	+	1.20006i	0.278044	+	0.960568i	$0.410314\pi$
$941$	−613509.	+	1.06263e6i	−0.692854	+	1.20006i	−0.970899	+	0.239491i	$0.923020\pi$
$942$		0			0
$943$	519507.	−	299938.i	0.584209	−	0.337293i
$944$	812060.	+	825145.i	0.911264	+	0.925947i
$945$		0			0
$946$	−497840.	+	97992.9i	−0.556298	+	0.109500i
$947$	−1.48474e6	+	857213.i	−1.65558	+	0.955848i	−0.680857	+	0.732416i	$0.738393\pi$
$947$	−1.48474e6	+	857213.i	−1.65558	+	0.955848i	−0.974720	+	0.223431i	$0.928274\pi$
$948$		0			0
$949$	137817.	−	238706.i	0.153027	−	0.265051i
$950$	433489.	+	148116.i	0.480320	+	0.164118i
$951$		0			0
$952$	514960.	−	1.02865e6i	0.568198	−	1.13499i
$953$	1.23751e6			1.36258			0.681290	−	0.732014i	$-0.261419\pi$
$953$	1.23751e6			1.36258			0.681290	+	0.732014i	$0.261419\pi$
$954$		0			0
$955$			1.48144e6i			1.62434i
$956$	−3109.09	+	4018.50i	−0.00340187	+	0.00439691i
$957$		0			0
$958$	−9089.93	−	3105.89i	−0.00990443	−	0.00338419i
$959$	−64461.5	−	37216.8i	−0.0700911	−	0.0404671i
$960$		0			0
$961$	331619.	+	574381.i	0.359081	+	0.621947i
$962$	160145.	−	31522.3i	0.173047	−	0.0340619i
$963$		0			0
$964$	377642.	−	154659.i	0.406374	−	0.166426i
$965$	−368589.	−	638416.i	−0.395811	−	0.685565i
$966$		0			0
$967$	858506.	+	495659.i	0.918101	+	0.530066i	0.883029	−	0.469319i	$-0.155501\pi$
$967$	858506.	+	495659.i	0.918101	+	0.530066i	0.0350720	+	0.999385i	$0.488834\pi$
$968$	38212.7	+	641952.i	0.0407809	+	0.685096i
$969$		0			0
$970$	370974.	+	424724.i	0.394276	+	0.451402i
$971$			1.45182e6i			1.53984i	0.638141	+	0.769920i	$0.279704\pi$
$971$			1.45182e6i			1.53984i	−0.638141	+	0.769920i	$0.720296\pi$
$972$		0			0
$973$	−36980.0			−0.0390608
$974$	1.22080e6	−	1.06630e6i	1.28684	−	1.12399i
$975$		0			0
$976$	168954.	+	651324.i	0.177366	+	0.683750i
$977$	306090.	−	530163.i	0.320671	−	0.555418i	−0.659956	−	0.751304i	$-0.729425\pi$
$977$	306090.	−	530163.i	0.320671	−	0.555418i	0.980627	+	0.195886i	$0.0627583\pi$
$978$		0			0
$979$	474418.	−	273905.i	0.494989	−	0.285782i
$980$	−128462.	+	52610.3i	−0.133759	+	0.0547796i
$981$		0			0
$982$	−99305.1	−	504507.i	−0.102979	−	0.523171i
$983$	1.04512e6	−	603401.i	1.08158	−	0.624452i	0.150259	−	0.988647i	$-0.451989\pi$
$983$	1.04512e6	−	603401.i	1.08158	−	0.624452i	0.931323	+	0.364195i	$0.118656\pi$
$984$		0			0
$985$	326341.	−	565239.i	0.336356	−	0.582586i
$986$	−377426.	+	1.10460e6i	−0.388220	+	1.13620i
$987$		0			0
$988$	−183719.	+	237456.i	−0.188209	+	0.243260i
$989$	−725178.			−0.741399
$990$		0			0
$991$		−	860509.i		−	0.876210i	−0.898924	−	0.438105i	$-0.855650\pi$
$991$		−	860509.i		−	0.876210i	0.898924	−	0.438105i	$-0.144350\pi$
$992$	−97217.8	+	1.28623e6i	−0.0987921	+	1.30706i
$993$		0			0
$994$	75885.8	−	222093.i	0.0768047	−	0.224783i
$995$	627601.	+	362346.i	0.633924	+	0.365996i
$996$		0			0
$997$	243483.	+	421725.i	0.244951	+	0.424267i	0.962118	−	0.272634i	$-0.0878949\pi$
$997$	243483.	+	421725.i	0.244951	+	0.424267i	−0.717167	+	0.696901i	$0.754562\pi$
$998$	−99351.8	−	504744.i	−0.0997504	−	0.506769i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.5.f.a.91.6		44
3.2	odd	2		36.5.f.a.31.17	yes	44
4.3	odd	2	inner	108.5.f.a.91.9		44
9.2	odd	6		36.5.f.a.7.14	✓	44
9.4	even	3		324.5.d.e.163.21		22
9.5	odd	6		324.5.d.f.163.2		22
9.7	even	3	inner	108.5.f.a.19.9		44
12.11	even	2		36.5.f.a.31.14	yes	44
36.7	odd	6	inner	108.5.f.a.19.6		44
36.11	even	6		36.5.f.a.7.17	yes	44
36.23	even	6		324.5.d.f.163.1		22
36.31	odd	6		324.5.d.e.163.22		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.5.f.a.7.14	✓	44	9.2	odd	6
36.5.f.a.7.17	yes	44	36.11	even	6
36.5.f.a.31.14	yes	44	12.11	even	2
36.5.f.a.31.17	yes	44	3.2	odd	2
108.5.f.a.19.6		44	36.7	odd	6	inner
108.5.f.a.19.9		44	9.7	even	3	inner
108.5.f.a.91.6		44	1.1	even	1	trivial
108.5.f.a.91.9		44	4.3	odd	2	inner
324.5.d.e.163.21		22	9.4	even	3
324.5.d.e.163.22		22	36.31	odd	6
324.5.d.f.163.1		22	36.23	even	6
324.5.d.f.163.2		22	9.5	odd	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:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	108.f (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.63137 - 3.01262i) q^{2} +(-2.15179 + 15.8546i) q^{4} +(10.5756 - 18.3175i) q^{5} +(-38.6407 + 22.3092i) q^{7} +(53.4262 - 35.2369i) q^{8} +O(q^{10})\)	\(q+(-2.63137 - 3.01262i) q^{2} +(-2.15179 + 15.8546i) q^{4} +(10.5756 - 18.3175i) q^{5} +(-38.6407 + 22.3092i) q^{7} +(53.4262 - 35.2369i) q^{8} +(-83.0119 + 16.3397i) q^{10} +(-58.6904 + 33.8849i) q^{11} +(14.5519 - 25.2046i) q^{13} +(168.887 + 57.7061i) q^{14} +(-246.740 - 68.2318i) q^{16} -402.841 q^{17} +644.741i q^{19} +(267.660 + 207.088i) q^{20} +(256.519 + 87.6483i) q^{22} +(335.527 + 193.717i) q^{23} +(88.8138 + 153.830i) q^{25} +(-114.223 + 22.4833i) q^{26} +(-270.558 - 660.639i) q^{28} +(362.210 + 627.366i) q^{29} +(1090.90 + 629.833i) q^{31} +(443.706 + 922.876i) q^{32} +(1060.02 + 1213.61i) q^{34} +943.733i q^{35} -1402.04 q^{37} +(1942.36 - 1696.55i) q^{38} +(-80.4363 - 1351.28i) q^{40} +(774.166 - 1340.89i) q^{41} +(-1620.98 + 935.875i) q^{43} +(-410.944 - 1003.43i) q^{44} +(-299.300 - 1520.56i) q^{46} +(-3610.63 + 2084.60i) q^{47} +(-205.097 + 355.239i) q^{49} +(229.730 - 672.346i) q^{50} +(368.297 + 284.950i) q^{52} -906.566 q^{53} +1433.41i q^{55} +(-1278.32 + 2553.48i) q^{56} +(936.910 - 2742.03i) q^{58} +(-3916.45 - 2261.16i) q^{59} +(-1314.22 - 2276.30i) q^{61} +(-973.119 - 4943.80i) q^{62} +(1612.72 - 3765.15i) q^{64} +(-307.789 - 533.107i) q^{65} +(58.7165 + 33.9000i) q^{67} +(866.831 - 6386.91i) q^{68} +(2843.11 - 2483.31i) q^{70} -1315.04i q^{71} +9470.72 q^{73} +(3689.27 + 4223.80i) q^{74} +(-10222.1 - 1387.35i) q^{76} +(1511.89 - 2618.67i) q^{77} +(3783.95 - 2184.67i) q^{79} +(-3859.25 + 3798.05i) q^{80} +(-6076.73 + 1196.12i) q^{82} +(-659.925 + 381.008i) q^{83} +(-4260.28 + 7379.03i) q^{85} +(7084.84 + 2420.78i) q^{86} +(-1941.61 + 3878.41i) q^{88} -8083.40 q^{89} +1298.56i q^{91} +(-3793.29 + 4902.82i) q^{92} +(15781.0 + 5392.11i) q^{94} +(11810.0 + 6818.52i) q^{95} +(-3332.71 - 5772.42i) q^{97} +(1609.89 - 316.884i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + q^{2} - q^{4} + 2 q^{5} - 122 q^{8}+O(q^{10}) \) 44 * q + q^2 - q^4 + 2 * q^5 - 122 * q^8	\( 44 q + q^{2} - q^{4} + 2 q^{5} - 122 q^{8} + 28 q^{10} - 2 q^{13} - 252 q^{14} - q^{16} + 56 q^{17} + 140 q^{20} - 33 q^{22} - 1752 q^{25} - 1096 q^{26} - 516 q^{28} - 526 q^{29} + 121 q^{32} + 385 q^{34} - 8 q^{37} - 1395 q^{38} - 2276 q^{40} + 2762 q^{41} - 6714 q^{44} + 3576 q^{46} + 3428 q^{49} - 6375 q^{50} + 1438 q^{52} + 10088 q^{53} + 7506 q^{56} - 4064 q^{58} - 2 q^{61} + 18324 q^{62} + 9026 q^{64} + 2014 q^{65} + 11405 q^{68} + 3666 q^{70} - 3416 q^{73} - 14620 q^{74} + 1581 q^{76} + 3942 q^{77} - 45520 q^{80} - 8486 q^{82} - 1252 q^{85} - 22113 q^{86} + 1995 q^{88} - 13048 q^{89} + 30294 q^{92} + 7524 q^{94} + 5638 q^{97} + 92938 q^{98}+O(q^{100}) \) 44 * q + q^2 - q^4 + 2 * q^5 - 122 * q^8 + 28 * q^10 - 2 * q^13 - 252 * q^14 - q^16 + 56 * q^17 + 140 * q^20 - 33 * q^22 - 1752 * q^25 - 1096 * q^26 - 516 * q^28 - 526 * q^29 + 121 * q^32 + 385 * q^34 - 8 * q^37 - 1395 * q^38 - 2276 * q^40 + 2762 * q^41 - 6714 * q^44 + 3576 * q^46 + 3428 * q^49 - 6375 * q^50 + 1438 * q^52 + 10088 * q^53 + 7506 * q^56 - 4064 * q^58 - 2 * q^61 + 18324 * q^62 + 9026 * q^64 + 2014 * q^65 + 11405 * q^68 + 3666 * q^70 - 3416 * q^73 - 14620 * q^74 + 1581 * q^76 + 3942 * q^77 - 45520 * q^80 - 8486 * q^82 - 1252 * q^85 - 22113 * q^86 + 1995 * q^88 - 13048 * q^89 + 30294 * q^92 + 7524 * q^94 + 5638 * q^97 + 92938 * q^98

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