LMFDB - Embedded newform 108.5.f.a.19.6

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			19.6
Character	$\chi$	$=$	108.19
Dual form			108.5.f.a.91.6

$q$-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 $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

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	0.996234	−	0.0867102i	$-0.0276354\pi$
$5$	10.5756	+	18.3175i	0.423024	+	0.732698i	−0.573210	+	0.819409i	$0.694302\pi$
$6$		0			0
$7$	−38.6407	−	22.3092i	−0.788586	−	0.455290i	0.0508787	−	0.998705i	$-0.483798\pi$
$7$	−38.6407	−	22.3092i	−0.788586	−	0.455290i	−0.839464	+	0.543415i	$0.817131\pi$
$8$	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	0.237472	−	0.971394i	$-0.423681\pi$
$11$	−58.6904	−	33.8849i	−0.485045	−	0.280041i	−0.722516	+	0.691354i	$0.757015\pi$
$12$		0			0
$13$	14.5519	+	25.2046i	0.0861058	+	0.149140i	0.905862	−	0.423573i	$-0.139224\pi$
$13$	14.5519	+	25.2046i	0.0861058	+	0.149140i	−0.819756	+	0.572713i	$0.805891\pi$
$14$	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	$-0.648601\pi$
$19$		−	644.741i		−	1.78599i	0.450070	−	0.892993i	$-0.351399\pi$
$20$	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	−0.148136	−	0.988967i	$-0.547327\pi$
$23$	335.527	−	193.717i	0.634267	−	0.366194i	0.782403	+	0.622773i	$0.213994\pi$
$24$		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	−0.566243	−	0.824238i	$-0.691604\pi$
$29$	362.210	−	627.366i	0.430690	−	0.745977i	0.996933	+	0.0782617i	$0.0249370\pi$
$30$		0			0
$31$	1090.90	−	629.833i	1.13517	−	0.655393i	0.189944	−	0.981795i	$-0.439169\pi$
$31$	1090.90	−	629.833i	1.13517	−	0.655393i	0.945231	+	0.326402i	$0.105836\pi$
$32$	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	0.998988	−	0.0449815i	$-0.0143229\pi$
$41$	774.166	+	1340.89i	0.460539	+	0.797677i	−0.538449	+	0.842658i	$0.680990\pi$
$42$		0			0
$43$	−1620.98	−	935.875i	−0.876681	−	0.506152i	−0.00711825	−	0.999975i	$-0.502266\pi$
$43$	−1620.98	−	935.875i	−0.876681	−	0.506152i	−0.869563	+	0.493823i	$0.835599\pi$
$44$	−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	−0.982679	−	0.185316i	$-0.940669\pi$
$47$	−3610.63	−	2084.60i	−1.63451	−	0.943683i	−0.651828	−	0.758367i	$-0.725998\pi$
$48$		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	−0.942696	−	0.333652i	$-0.891719\pi$
$59$	−3916.45	+	2261.16i	−1.12509	+	0.649573i	−0.182397	+	0.983225i	$0.558386\pi$
$60$		0			0
$61$	−1314.22	+	2276.30i	−0.353190	+	0.611743i	−0.986806	−	0.161904i	$-0.948236\pi$
$61$	−1314.22	+	2276.30i	−0.353190	+	0.611743i	0.633617	+	0.773647i	$0.281570\pi$
$62$	−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	−0.493446	−	0.869777i	$-0.664263\pi$
$67$	58.7165	−	33.9000i	0.0130801	−	0.00755179i	0.506526	+	0.862225i	$0.330930\pi$
$68$	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	$0.0416372\pi$
$71$			1315.04i			0.260869i	−0.991457	+	0.130434i	$0.958363\pi$
$72$		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	0.771518	−	0.636207i	$-0.219498\pi$
$79$	3783.95	+	2184.67i	0.606305	+	0.350050i	−0.165213	+	0.986258i	$0.552831\pi$
$80$	−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	0.451338	−	0.892353i	$-0.350947\pi$
$83$	−659.925	−	381.008i	−0.0957940	−	0.0553067i	−0.547132	+	0.837047i	$0.684280\pi$
$84$		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	−0.986981	−	0.160834i	$-0.948582\pi$
$97$	−3332.71	+	5772.42i	−0.354204	+	0.613500i	0.632777	+	0.774334i	$0.281915\pi$
$98$	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	−0.543542	−	0.839382i	$-0.682917\pi$
$101$	4643.04	−	8041.97i	0.455155	−	0.788352i	0.998697	+	0.0510303i	$0.0162505\pi$
$102$		0			0
$103$	−9792.48	+	5653.69i	−0.923035	+	0.532915i	−0.884602	−	0.466346i	$-0.845570\pi$
$103$	−9792.48	+	5653.69i	−0.923035	+	0.532915i	−0.0384332	+	0.999261i	$0.512237\pi$
$104$	−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	$0.0881669\pi$
$107$			6261.61i			0.546913i	−0.961884	+	0.273456i	$0.911833\pi$
$108$		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	0.811884	−	0.583819i	$-0.198442\pi$
$113$	−1272.55	−	2204.13i	−0.0996597	−	0.172616i	−0.911544	+	0.411203i	$0.865109\pi$
$114$		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	$0.00523067\pi$
$127$			530.060i			0.0328638i	−0.999865	+	0.0164319i	$0.994769\pi$
$128$	−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	−0.476445	−	0.879204i	$-0.658075\pi$
$131$	802.198	−	463.149i	0.0467454	−	0.0269885i	0.523191	+	0.852216i	$0.324742\pi$
$132$		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	−0.842949	−	0.537993i	$-0.819183\pi$
$137$	834.113	−	1444.73i	0.0444410	−	0.0769741i	0.887390	+	0.461019i	$0.152516\pi$
$138$		0			0
$139$	717.766	−	414.402i	0.0371495	−	0.0214483i	−0.481310	−	0.876550i	$-0.659839\pi$
$139$	717.766	−	414.402i	0.0371495	−	0.0214483i	0.518460	+	0.855102i	$0.326506\pi$
$140$	−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	0.899046	−	0.437855i	$-0.144262\pi$
$149$	1561.38	+	2704.39i	0.0703292	+	0.121814i	−0.828716	+	0.559669i	$0.810928\pi$
$150$		0			0
$151$	−7932.37	−	4579.76i	−0.347896	−	0.200858i	0.315862	−	0.948805i	$-0.397706\pi$
$151$	−7932.37	−	4579.76i	−0.347896	−	0.200858i	−0.663758	+	0.747947i	$0.731040\pi$
$152$	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	0.568619	−	0.822601i	$-0.307478\pi$
$157$	−10551.8	−	18276.3i	−0.428084	−	0.741463i	−0.996703	+	0.0811381i	$0.974145\pi$
$158$	−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	$0.297783\pi$
$163$			42771.0i			1.60981i	−0.593405	+	0.804904i	$0.702217\pi$
$164$	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	−0.661633	−	0.749828i	$-0.730136\pi$
$167$	−9568.12	+	5524.16i	−0.343079	+	0.198077i	0.318554	+	0.947905i	$0.396803\pi$
$168$		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	−0.989009	−	0.147852i	$-0.952764\pi$
$173$	−10967.8	+	18996.8i	−0.366461	+	0.634729i	0.622549	+	0.782581i	$0.286097\pi$
$174$		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	$0.0573291\pi$
$179$			11479.2i			0.358265i	−0.983825	+	0.179133i	$0.942671\pi$
$180$		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	−0.971418	−	0.237376i	$-0.923713\pi$
$191$	−60657.0	−	35020.3i	−1.66270	−	0.959961i	−0.691283	−	0.722584i	$-0.742954\pi$
$192$		0			0
$193$	17426.4	+	30183.5i	0.467836	+	0.810316i	0.999325	−	0.0367497i	$-0.0117004\pi$
$193$	17426.4	+	30183.5i	0.467836	+	0.810316i	−0.531488	+	0.847066i	$0.678367\pi$
$194$	−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	$-0.857598\pi$
$199$		−	34262.5i		−	0.865192i	0.901588	−	0.432596i	$-0.142402\pi$
$200$	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	−0.322119	−	0.946699i	$-0.604395\pi$
$211$	14989.6	−	8654.27i	0.336687	−	0.194386i	0.658806	+	0.752313i	$0.271062\pi$
$212$	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	−0.175432	−	0.984492i	$-0.556132\pi$
$223$	−55484.8	−	32034.1i	−1.11574	−	0.644174i	−0.940311	+	0.340317i	$0.889466\pi$
$224$	−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	0.610627	−	0.791918i	$-0.290917\pi$
$227$	11857.8	+	6846.11i	0.230119	+	0.132859i	−0.380508	+	0.924778i	$0.624251\pi$
$228$		0			0
$229$	−32996.2	−	57151.0i	−0.629205	−	1.08982i	−0.987711	−	0.156288i	$-0.950047\pi$
$229$	−32996.2	−	57151.0i	−0.629205	−	1.08982i	0.358506	−	0.933527i	$-0.383286\pi$
$230$	−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	−0.497591	−	0.867412i	$-0.665782\pi$
$239$	275.008	−	158.776i	0.00481448	−	0.00277964i	0.502405	+	0.864632i	$0.332449\pi$
$240$		0			0
$241$	−12752.6	+	22088.2i	−0.219566	+	0.380300i	−0.954675	−	0.297649i	$-0.903798\pi$
$241$	−12752.6	+	22088.2i	−0.219566	+	0.380300i	0.735109	+	0.677949i	$0.237131\pi$
$242$	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	$-0.894537\pi$
$251$		−	40987.7i		−	0.650588i	0.945613	−	0.325294i	$-0.105463\pi$
$252$		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	0.959086	−	0.283116i	$-0.0913681\pi$
$257$	15479.1	+	26810.5i	0.234357	+	0.405919i	−0.724728	+	0.689035i	$0.758035\pi$
$258$		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	0.400678	−	0.916219i	$-0.368775\pi$
$263$	−13311.8	−	7685.54i	−0.192453	−	0.111113i	−0.593130	+	0.805107i	$0.702108\pi$
$264$		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	$-0.821606\pi$
$271$		−	78076.4i		−	1.06312i	0.847021	−	0.531559i	$-0.178394\pi$
$272$	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	−0.881056	−	0.473012i	$-0.843167\pi$
$277$	−2369.97	+	4104.90i	−0.0308875	+	0.0534987i	0.850168	+	0.526511i	$0.176500\pi$
$278$	−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	−0.696172	−	0.717875i	$-0.745115\pi$
$281$	21604.6	−	37420.3i	0.273612	−	0.473909i	0.969784	+	0.243966i	$0.0784484\pi$
$282$		0			0
$283$	31277.1	−	18057.8i	0.390529	−	0.225472i	−0.291860	−	0.956461i	$-0.594274\pi$
$283$	31277.1	−	18057.8i	0.390529	−	0.225472i	0.682389	+	0.730989i	$0.260941\pi$
$284$	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	−0.997524	−	0.0703243i	$-0.977597\pi$
$293$	−48046.7	−	83219.2i	−0.559665	−	0.969368i	0.437859	−	0.899043i	$-0.355737\pi$
$294$		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	$0.268083\pi$
$307$			140641.i			1.49223i	−0.665817	+	0.746115i	$0.731917\pi$
$308$	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	0.464453	−	0.885598i	$-0.346251\pi$
$311$	141564.	−	81731.8i	1.46363	−	0.845027i	0.999177	+	0.0405712i	$0.0129178\pi$
$312$		0			0
$313$	25645.1	−	44418.7i	0.261768	−	0.453395i	−0.704944	−	0.709263i	$-0.749028\pi$
$313$	25645.1	−	44418.7i	0.261768	−	0.453395i	0.966712	+	0.255868i	$0.0823611\pi$
$314$	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	−0.927333	−	0.374237i	$-0.877905\pi$
$317$	−14025.0	+	24292.0i	−0.139568	+	0.241738i	0.787765	+	0.615975i	$0.211238\pi$
$318$		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	0.874446	−	0.485123i	$-0.161225\pi$
$331$	97678.0	+	56394.4i	0.891540	+	0.514731i	0.0170938	+	0.999854i	$0.494559\pi$
$332$	−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	0.908210	−	0.418515i	$-0.137449\pi$
$337$	10409.8	+	18030.3i	0.0916606	+	0.158761i	−0.816549	+	0.577276i	$0.804116\pi$
$338$	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	−0.951185	−	0.308621i	$-0.900132\pi$
$347$	−139615.	+	80606.6i	−1.15950	+	0.669440i	−0.208318	+	0.978061i	$0.566799\pi$
$348$		0			0
$349$	110742.	−	191811.i	0.909205	−	1.57479i	0.0940341	−	0.995569i	$-0.470024\pi$
$349$	110742.	−	191811.i	0.909205	−	1.57479i	0.815171	−	0.579220i	$-0.196643\pi$
$350$	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	0.0242676	−	0.999705i	$-0.492275\pi$
$353$	109395.	−	189477.i	0.877904	−	1.52057i	0.853637	−	0.520869i	$-0.174392\pi$
$354$		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	$0.00114180\pi$
$359$			924.606i			0.00717411i	−0.999994	+	0.00358705i	$0.998858\pi$
$360$		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	0.363071	−	0.931762i	$-0.381728\pi$
$367$	−35332.0	−	20398.9i	−0.262323	−	0.151452i	−0.625394	+	0.780309i	$0.715062\pi$
$368$	−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	0.887474	+	0.460858i	$0.152458\pi$
$373$	117265.	+	203109.i	0.842851	+	1.45986i	−0.0446228	+	0.999004i	$0.514209\pi$
$374$	−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	$0.223515\pi$
$379$			185553.i			1.29178i	−0.763428	+	0.645892i	$0.776485\pi$
$380$	−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	−0.311443	−	0.950265i	$-0.600812\pi$
$383$	52190.3	−	30132.1i	0.355789	−	0.205415i	0.667232	+	0.744850i	$0.267479\pi$
$384$		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	−0.885184	−	0.465241i	$-0.845968\pi$
$389$	−6004.66	+	10400.4i	−0.0396816	+	0.0687306i	0.845502	+	0.533971i	$0.179301\pi$
$390$		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	−0.995033	−	0.0995418i	$-0.968262\pi$
$401$	−93863.1	−	162576.i	−0.583722	−	1.01104i	0.411311	−	0.911495i	$-0.365071\pi$
$402$		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	0.993985	−	0.109515i	$-0.0349299\pi$
$409$	67272.0	+	116518.i	0.402149	+	0.696543i	−0.591836	+	0.806059i	$0.701597\pi$
$410$	−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	−0.276429	−	0.961034i	$-0.589151\pi$
$419$	73320.7	−	42331.7i	0.417637	−	0.241123i	0.694066	+	0.719912i	$0.255818\pi$
$420$		0			0
$421$	57849.8	−	100199.i	0.326391	−	0.565325i	−0.655402	−	0.755280i	$-0.727501\pi$
$421$	57849.8	−	100199.i	0.326391	−	0.565325i	0.981793	+	0.189955i	$0.0608341\pi$
$422$	−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	$-0.708125\pi$
$431$		−	294896.i		−	1.58750i	0.608241	−	0.793752i	$-0.291875\pi$
$432$		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	0.544294	−	0.838895i	$-0.316798\pi$
$439$	17332.7	+	10007.1i	0.0899369	+	0.0519251i	−0.454357	+	0.890820i	$0.650131\pi$
$440$	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	0.582837	−	0.812589i	$-0.301943\pi$
$443$	33466.7	+	19322.0i	0.170532	+	0.0984567i	−0.412305	+	0.911046i	$0.635276\pi$
$444$		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	−0.356392	−	0.934337i	$-0.615993\pi$
$457$	131776.	−	228243.i	0.630963	−	1.09286i	0.987355	−	0.158524i	$-0.0506735\pi$
$458$	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	−0.999486	−	0.0320624i	$-0.989792\pi$
$461$	−100305.	+	173733.i	−0.471976	+	0.817487i	0.527510	+	0.849549i	$0.323126\pi$
$462$		0			0
$463$	205297.	−	118528.i	0.957679	−	0.552916i	0.0622210	−	0.998062i	$-0.480182\pi$
$463$	205297.	−	118528.i	0.957679	−	0.552916i	0.895458	+	0.445146i	$0.146848\pi$
$464$	−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	$0.177197\pi$
$467$			230464.i			1.05674i	−0.849014	+	0.528371i	$0.822803\pi$
$468$		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	0.504525	−	0.863397i	$-0.331668\pi$
$479$	2079.74	+	1200.74i	0.00906438	+	0.00523332i	−0.495461	+	0.868630i	$0.665001\pi$
$480$		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	$-0.673986\pi$
$487$		−	405227.i		−	1.70860i	0.519781	−	0.854300i	$-0.326014\pi$
$488$	−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	−0.251016	−	0.967983i	$-0.580765\pi$
$491$	111325.	−	64273.4i	0.461773	−	0.266605i	0.712790	+	0.701378i	$0.247431\pi$
$492$		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	−0.259392	−	0.965772i	$-0.583522\pi$
$499$	111377.	−	64303.6i	0.447296	−	0.258246i	0.706687	+	0.707526i	$0.250189\pi$
$500$	−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	$-0.740683\pi$
$503$		−	368128.i		−	1.45500i	0.686109	−	0.727499i	$-0.259317\pi$
$504$		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	0.776730	−	0.629834i	$-0.216877\pi$
$509$	−40698.4	−	70491.6i	−0.157087	−	0.272083i	−0.933817	+	0.357751i	$0.883544\pi$
$510$		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	$-0.969700\pi$
$523$		−	51996.2i		−	0.190094i	0.995473	−	0.0950470i	$-0.0303001\pi$
$524$	−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	0.914915	−	0.403646i	$-0.132257\pi$
$547$	306032.	+	176688.i	1.02280	+	0.590517i	0.107890	+	0.994163i	$0.465591\pi$
$548$	−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	−0.785765	−	0.618526i	$-0.787730\pi$
$563$	−203807.	+	117668.i	−0.642988	+	0.371229i	0.142776	+	0.989755i	$0.454397\pi$
$564$		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	−0.984944	−	0.172875i	$-0.944694\pi$
$569$	−110971.	+	192208.i	−0.342757	+	0.593673i	0.642186	+	0.766549i	$0.278028\pi$
$570$		0			0
$571$	34588.3	−	19969.5i	0.106086	−	0.0612486i	−0.446018	−	0.895024i	$-0.647158\pi$
$571$	34588.3	−	19969.5i	0.106086	−	0.0612486i	0.552104	+	0.833775i	$0.313825\pi$
$572$	−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	0.585228	−	0.810869i	$-0.301005\pi$
$587$	60509.5	+	34935.2i	0.175609	+	0.101388i	−0.409619	+	0.912257i	$0.634338\pi$
$588$		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	−0.124757	−	0.992187i	$-0.539815\pi$
$599$	241159.	−	139233.i	0.672123	−	0.388051i	0.796881	+	0.604137i	$0.206482\pi$
$600$		0			0
$601$	−213736.	+	370201.i	−0.591737	+	1.02492i	0.402262	+	0.915525i	$0.368224\pi$
$601$	−213736.	+	370201.i	−0.591737	+	1.02492i	−0.993999	+	0.109393i	$0.965109\pi$
$602$	−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	−0.902597	−	0.430487i	$-0.858342\pi$
$607$	−361479.	+	208700.i	−0.981082	+	0.566428i	−0.0784853	+	0.996915i	$0.525008\pi$
$608$	−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	0.913108	−	0.407719i	$-0.133676\pi$
$617$	39385.7	+	68218.0i	0.103459	+	0.179196i	−0.809649	+	0.586915i	$0.800342\pi$
$618$		0			0
$619$	382655.	+	220926.i	0.998679	+	0.576587i	0.907857	−	0.419280i	$-0.137717\pi$
$619$	382655.	+	220926.i	0.998679	+	0.576587i	0.0908215	+	0.995867i	$0.471051\pi$
$620$	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	$-0.914390\pi$
$631$		−	211599.i		−	0.531440i	0.964050	−	0.265720i	$-0.0856097\pi$
$632$	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	−0.869115	−	0.494610i	$-0.835311\pi$
$641$	−2552.74	+	4421.47i	−0.00621284	+	0.0107610i	0.862902	+	0.505371i	$0.168644\pi$
$642$		0			0
$643$	−69127.8	+	39911.0i	−0.167198	+	0.0965318i	−0.581264	−	0.813715i	$-0.697442\pi$
$643$	−69127.8	+	39911.0i	−0.167198	+	0.0965318i	0.414066	+	0.910247i	$0.364108\pi$
$644$	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	$0.218942\pi$
$647$			531516.i			1.26972i	−0.772628	+	0.634859i	$0.781058\pi$
$648$		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	−0.998089	−	0.0617897i	$-0.980319\pi$
$653$	−235615.	−	408097.i	−0.552556	−	0.957055i	0.445533	−	0.895265i	$-0.353014\pi$
$654$		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	0.812023	−	0.583625i	$-0.198366\pi$
$659$	309469.	+	178672.i	0.712601	+	0.411420i	−0.0994224	+	0.995045i	$0.531700\pi$
$660$		0			0
$661$	282792.	+	489809.i	0.647237	+	1.12105i	0.983780	+	0.179380i	$0.0574090\pi$
$661$	282792.	+	489809.i	0.647237	+	1.12105i	−0.336543	+	0.941668i	$0.609258\pi$
$662$	−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	−0.636988	−	0.770874i	$-0.719820\pi$
$673$	158119.	−	273870.i	0.349103	−	0.604663i	0.986090	+	0.166211i	$0.0531532\pi$
$674$	−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	0.324959	+	0.945728i	$0.394649\pi$
$677$	−300914.	+	521198.i	−0.656545	+	1.13717i	−0.981504	+	0.191441i	$0.938684\pi$
$678$		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	$-0.864497\pi$
$683$		−	385277.i		−	0.825909i	0.910752	−	0.412955i	$-0.135503\pi$
$684$		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	0.0218438	−	0.999761i	$-0.493046\pi$
$691$	−397767.	−	229651.i	−0.833053	−	0.480963i	−0.854897	+	0.518798i	$0.826380\pi$
$692$	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	−0.999959	−	0.00901014i	$-0.997132\pi$
$709$	−247408.	+	428523.i	−0.492177	+	0.852475i	0.507783	+	0.861485i	$0.330465\pi$
$710$	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	$0.202629\pi$
$719$			614613.i			1.18890i	−0.804134	+	0.594448i	$0.797371\pi$
$720$		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	0.203286	−	0.979119i	$-0.434838\pi$
$727$	−286999.	−	165699.i	−0.543014	−	0.313509i	−0.746299	+	0.665610i	$0.768171\pi$
$728$	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	0.889043	−	0.457824i	$-0.151371\pi$
$733$	25808.4	+	44701.5i	0.0480345	+	0.0831982i	−0.841008	+	0.541022i	$0.818038\pi$
$734$	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	$0.0672264\pi$
$739$			228968.i			0.419263i	−0.977780	+	0.209631i	$0.932774\pi$
$740$	−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	0.670720	−	0.741711i	$-0.265985\pi$
$743$	910009.	−	525394.i	1.64842	−	0.951716i	0.977700	−	0.210005i	$-0.0673480\pi$
$744$		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	−0.692354	−	0.721558i	$-0.743426\pi$
$751$	−233295.	+	134693.i	−0.413643	+	0.238817i	0.278711	+	0.960375i	$0.410093\pi$
$752$	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	0.995760	−	0.0919890i	$-0.0293225\pi$
$761$	242197.	+	419498.i	0.418215	+	0.724370i	−0.577545	+	0.816359i	$0.695989\pi$
$762$		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	0.571830	−	0.820372i	$-0.306234\pi$
$769$	−251061.	−	434851.i	−0.424549	−	0.735340i	−0.996378	+	0.0850327i	$0.972901\pi$
$770$	−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	−0.769247	−	0.638952i	$-0.779368\pi$
$787$	−371945.	+	214742.i	−0.600522	+	0.346711i	0.168725	+	0.985663i	$0.446035\pi$
$788$	−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	0.996462	+	0.0840446i	$0.0267838\pi$
$797$	362714.	+	628240.i	0.571016	+	0.989028i	−0.425446	+	0.904984i	$0.639883\pi$
$798$		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	$-0.921301\pi$
$811$		−	321928.i		−	0.489460i	0.969591	−	0.244730i	$-0.0786993\pi$
$812$	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	−0.303549	−	0.952816i	$-0.598172\pi$
$821$	453891.	−	786162.i	0.673388	−	1.16634i	0.976937	−	0.213527i	$-0.0684950\pi$
$822$		0			0
$823$	730902.	−	421987.i	1.07909	−	0.623016i	0.148443	−	0.988921i	$-0.452574\pi$
$823$	730902.	−	421987.i	1.07909	−	0.623016i	0.930652	+	0.365905i	$0.119241\pi$
$824$	−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	$0.159824\pi$
$827$			658309.i			0.962540i	−0.876572	+	0.481270i	$0.840176\pi$
$828$		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	0.467299	−	0.884099i	$-0.345227\pi$
$839$	−45546.9	−	26296.5i	−0.0647045	−	0.0373572i	−0.532003	+	0.846742i	$0.678561\pi$
$840$		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	−0.555003	−	0.831848i	$-0.687283\pi$
$853$	322258.	−	558168.i	0.442900	−	0.767126i	0.997903	+	0.0647226i	$0.0206163\pi$
$854$	−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	−0.721150	−	0.692779i	$-0.756386\pi$
$857$	175819.	−	304528.i	0.239390	−	0.414635i	0.960539	+	0.278144i	$0.0897194\pi$
$858$		0			0
$859$	−658817.	+	380368.i	−0.892851	+	0.515487i	−0.874874	−	0.484351i	$-0.839056\pi$
$859$	−658817.	+	380368.i	−0.892851	+	0.515487i	−0.0179767	+	0.999838i	$0.505722\pi$
$860$	−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	$-0.921559\pi$
$863$		−	363360.i		−	0.487883i	0.969790	−	0.243942i	$-0.0784406\pi$
$864$		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	0.841649	−	0.540026i	$-0.181585\pi$
$877$	−36035.0	−	62414.4i	−0.0468516	−	0.0811494i	−0.888500	+	0.458876i	$0.848252\pi$
$878$	−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	$-0.857293\pi$
$883$		−	675925.i		−	0.866916i	0.901174	−	0.433458i	$-0.142707\pi$
$884$	−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	−0.943602	−	0.331082i	$-0.892586\pi$
$887$	−888008.	+	512692.i	−1.12868	+	0.651642i	−0.185075	+	0.982724i	$0.559253\pi$
$888$		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	−0.944785	−	0.327690i	$-0.893730\pi$
$907$	−1.39930e6	−	807885.i	−1.70097	−	0.982053i	−0.756181	−	0.654363i	$-0.772937\pi$
$908$	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	0.343860	−	0.939021i	$-0.388266\pi$
$911$	−246841.	−	142514.i	−0.297427	−	0.171719i	−0.641286	+	0.767302i	$0.721599\pi$
$912$		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	$-0.871743\pi$
$919$		−	662333.i		−	0.784233i	0.919916	−	0.392117i	$-0.128257\pi$
$920$	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	−0.242803	−	0.970076i	$-0.578067\pi$
$929$	620275.	−	1.07435e6i	0.718708	−	1.24484i	0.961512	−	0.274764i	$-0.0885997\pi$
$930$		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	−0.970899	−	0.239491i	$-0.923020\pi$
$941$	−613509.	−	1.06263e6i	−0.692854	−	1.20006i	0.278044	−	0.960568i	$-0.410314\pi$
$942$		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	−0.974720	−	0.223431i	$-0.928274\pi$
$947$	−1.48474e6	−	857213.i	−1.65558	−	0.955848i	−0.680857	−	0.732416i	$-0.738393\pi$
$948$		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	0.0350720	−	0.999385i	$-0.488834\pi$
$967$	858506.	−	495659.i	0.918101	−	0.530066i	0.883029	+	0.469319i	$0.155501\pi$
$968$	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	$-0.720296\pi$
$971$		−	1.45182e6i		−	1.53984i	0.638141	−	0.769920i	$-0.279704\pi$
$972$		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	0.980627	−	0.195886i	$-0.0627583\pi$
$977$	306090.	+	530163.i	0.320671	+	0.555418i	−0.659956	+	0.751304i	$0.729425\pi$
$978$		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	0.931323	−	0.364195i	$-0.118656\pi$
$983$	1.04512e6	+	603401.i	1.08158	+	0.624452i	0.150259	+	0.988647i	$0.451989\pi$
$984$		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	$0.144350\pi$
$991$			860509.i			0.876210i	−0.898924	+	0.438105i	$0.855650\pi$
$992$	−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	−0.717167	−	0.696901i	$-0.754562\pi$
$997$	243483.	−	421725.i	0.244951	−	0.424267i	0.962118	+	0.272634i	$0.0878949\pi$
$998$	−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.19.6		44
3.2	odd	2		36.5.f.a.7.17	yes	44
4.3	odd	2	inner	108.5.f.a.19.9		44
9.2	odd	6		324.5.d.f.163.1		22
9.4	even	3	inner	108.5.f.a.91.9		44
9.5	odd	6		36.5.f.a.31.14	yes	44
9.7	even	3		324.5.d.e.163.22		22
12.11	even	2		36.5.f.a.7.14	✓	44
36.7	odd	6		324.5.d.e.163.21		22
36.11	even	6		324.5.d.f.163.2		22
36.23	even	6		36.5.f.a.31.17	yes	44
36.31	odd	6	inner	108.5.f.a.91.6		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.5.f.a.7.14	✓	44	12.11	even	2
36.5.f.a.7.17	yes	44	3.2	odd	2
36.5.f.a.31.14	yes	44	9.5	odd	6
36.5.f.a.31.17	yes	44	36.23	even	6
108.5.f.a.19.6		44	1.1	even	1	trivial
108.5.f.a.19.9		44	4.3	odd	2	inner
108.5.f.a.91.6		44	36.31	odd	6	inner
108.5.f.a.91.9		44	9.4	even	3	inner
324.5.d.e.163.21		22	36.7	odd	6
324.5.d.e.163.22		22	9.7	even	3
324.5.d.f.163.1		22	9.2	odd	6
324.5.d.f.163.2		22	36.11	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:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more