LMFDB - Embedded newform 108.5.f.a.19.9

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			19.9
Character	$\chi$	$=$	108.19
Dual form			108.5.f.a.91.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.29332 + 3.78514i) q^{2} +(-12.6546 - 9.79083i) q^{4} +(10.5756 + 18.3175i) q^{5} +(38.6407 + 22.3092i) q^{7} +(53.4262 - 35.2369i) q^{8} +O(q^{10})$	\(q+(-1.29332 + 3.78514i) q^{2} +(-12.6546 - 9.79083i) q^{4} +(10.5756 + 18.3175i) q^{5} +(38.6407 + 22.3092i) q^{7} +(53.4262 - 35.2369i) q^{8} +(-83.0119 + 16.3397i) q^{10} +(58.6904 + 33.8849i) q^{11} +(14.5519 + 25.2046i) q^{13} +(-134.419 + 117.408i) q^{14} +(64.2793 + 247.799i) q^{16} -402.841 q^{17} +644.741i q^{19} +(45.5130 - 335.344i) q^{20} +(-204.165 + 178.327i) q^{22} +(-335.527 + 193.717i) q^{23} +(88.8138 - 153.830i) q^{25} +(-114.223 + 22.4833i) q^{26} +(-270.558 - 660.639i) q^{28} +(362.210 - 627.366i) q^{29} +(-1090.90 + 629.833i) q^{31} +(-1021.09 - 77.1774i) q^{32} +(521.004 - 1524.81i) q^{34} +943.733i q^{35} -1402.04 q^{37} +(-2440.44 - 833.859i) q^{38} +(1210.46 + 605.982i) q^{40} +(774.166 + 1340.89i) q^{41} +(1620.98 + 935.875i) q^{43} +(-410.944 - 1003.43i) q^{44} +(-299.300 - 1520.56i) q^{46} +(3610.63 + 2084.60i) q^{47} +(-205.097 - 355.239i) q^{49} +(467.404 + 535.125i) q^{50} +(62.6253 - 461.430i) q^{52} -906.566 q^{53} +1433.41i q^{55} +(2850.53 - 169.681i) q^{56} +(1906.22 + 2182.40i) q^{58} +(3916.45 - 2261.16i) q^{59} +(-1314.22 + 2276.30i) q^{61} +(-973.119 - 4943.80i) q^{62} +(1612.72 - 3765.15i) q^{64} +(-307.789 + 533.107i) q^{65} +(-58.7165 + 33.9000i) q^{67} +(5097.81 + 3944.15i) q^{68} +(-3572.16 - 1220.55i) q^{70} -1315.04i q^{71} +9470.72 q^{73} +(1813.29 - 5306.91i) q^{74} +(6312.55 - 8158.96i) q^{76} +(1511.89 + 2618.67i) q^{77} +(-3783.95 - 2184.67i) q^{79} +(-3859.25 + 3798.05i) q^{80} +(-6076.73 + 1196.12i) q^{82} +(659.925 + 381.008i) q^{83} +(-4260.28 - 7379.03i) q^{85} +(-5638.88 + 4925.26i) q^{86} +(4329.61 - 257.724i) q^{88} -8083.40 q^{89} +1298.56i q^{91} +(6142.62 + 833.676i) q^{92} +(-12560.2 + 10970.7i) q^{94} +(-11810.0 + 6818.52i) q^{95} +(-3332.71 + 5772.42i) q^{97} +(1609.89 - 316.884i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.29332	+	3.78514i	−0.323331	+	0.946286i
$2$	−1.29332	+	3.78514i	−0.323331	+	0.946286i
$3$		0			0
$3$		0			0
$4$	−12.6546	−	9.79083i	−0.790914	−	0.611927i
$5$	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	0.839464	−	0.543415i	$-0.182869\pi$
$7$	38.6407	+	22.3092i	0.788586	+	0.455290i	−0.0508787	+	0.998705i	$0.516202\pi$
$8$	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	$-0.242985\pi$
$11$	58.6904	+	33.8849i	0.485045	+	0.280041i	−0.237472	+	0.971394i	$0.576319\pi$
$12$		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	$0.805891\pi$
$14$	−134.419	+	117.408i	−0.685809	+	0.599018i
$15$		0			0
$16$	64.2793	+	247.799i	0.251091	+	0.967963i
$17$	−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	$0.648601\pi$
$20$	45.5130	−	335.344i	0.113782	−	0.838361i
$21$		0			0
$22$	−204.165	+	178.327i	−0.421828	+	0.368445i
$23$	−335.527	+	193.717i	−0.634267	+	0.366194i	−0.782403	−	0.622773i	$-0.786006\pi$
$23$	−335.527	+	193.717i	−0.634267	+	0.366194i	0.148136	+	0.988967i	$0.452673\pi$
$24$		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	−0.945231	−	0.326402i	$-0.894164\pi$
$31$	−1090.90	+	629.833i	−1.13517	+	0.655393i	−0.189944	+	0.981795i	$0.560831\pi$
$32$	−1021.09	−	77.1774i	−0.997156	−	0.0753685i
$33$		0			0
$34$	521.004	−	1524.81i	0.450695	−	1.31904i
$35$			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	$0.671120\pi$
$38$	−2440.44	−	833.859i	−1.69005	−	0.577464i
$39$		0			0
$40$	1210.46	+	605.982i	0.756540	+	0.378739i
$41$	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	0.869563	−	0.493823i	$-0.164401\pi$
$43$	1620.98	+	935.875i	0.876681	+	0.506152i	0.00711825	+	0.999975i	$0.497734\pi$
$44$	−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	$0.0593310\pi$
$47$	3610.63	+	2084.60i	1.63451	+	0.943683i	0.651828	+	0.758367i	$0.274002\pi$
$48$		0			0
$49$	−205.097	−	355.239i	−0.0854217	−	0.147955i
$50$	467.404	+	535.125i	0.186962	+	0.214050i
$51$		0			0
$52$	62.6253	−	461.430i	0.0231602	−	0.170647i
$53$	−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
$56$	2850.53	−	169.681i	0.908971	−	0.0541073i
$57$		0			0
$58$	1906.22	+	2182.40i	0.566652	+	0.648753i
$59$	3916.45	−	2261.16i	1.12509	−	0.649573i	0.182397	−	0.983225i	$-0.441614\pi$
$59$	3916.45	−	2261.16i	1.12509	−	0.649573i	0.942696	+	0.333652i	$0.108281\pi$
$60$		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	−0.506526	−	0.862225i	$-0.669070\pi$
$67$	−58.7165	+	33.9000i	−0.0130801	+	0.00755179i	0.493446	+	0.869777i	$0.335737\pi$
$68$	5097.81	+	3944.15i	1.10247	+	0.852974i
$69$		0			0
$70$	−3572.16	−	1220.55i	−0.729013	−	0.249092i
$71$		−	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	$0.151678\pi$
$74$	1813.29	−	5306.91i	0.331133	−	0.969121i
$75$		0			0
$76$	6312.55	−	8158.96i	1.09289	−	1.41256i
$77$	1511.89	+	2618.67i	0.255000	+	0.441672i
$78$		0			0
$79$	−3783.95	−	2184.67i	−0.606305	−	0.350050i	0.165213	−	0.986258i	$-0.447169\pi$
$79$	−3783.95	−	2184.67i	−0.606305	−	0.350050i	−0.771518	+	0.636207i	$0.780502\pi$
$80$	−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	$-0.315720\pi$
$83$	659.925	+	381.008i	0.0957940	+	0.0553067i	−0.451338	+	0.892353i	$0.649053\pi$
$84$		0			0
$85$	−4260.28	−	7379.03i	−0.589659	−	1.02132i
$86$	−5638.88	+	4925.26i	−0.762422	+	0.665936i
$87$		0			0
$88$	4329.61	−	257.724i	0.559092	−	0.0332804i
$89$	−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
$92$	6142.62	+	833.676i	0.725734	+	0.0984967i
$93$		0			0
$94$	−12560.2	+	10970.7i	−1.42148	+	1.24159i
$95$	−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	0.0384332	−	0.999261i	$-0.487763\pi$
$103$	9792.48	−	5653.69i	0.923035	−	0.532915i	0.884602	+	0.466346i	$0.154430\pi$
$104$	1665.58	+	833.824i	0.153993	+	0.0770917i
$105$		0			0
$106$	1172.48	−	3431.48i	0.104351	−	0.305401i
$107$		−	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	$0.453582\pi$
$110$	−5425.67	−	1853.87i	−0.448403	−	0.153212i
$111$		0			0
$112$	−3044.40	+	11009.1i	−0.242697	+	0.877641i
$113$	−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
$122$	−6916.39	−	7918.50i	−0.464687	−	0.532014i
$123$		0			0
$124$	19971.6	+	2710.54i	1.29888	+	0.176284i
$125$	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	$-0.00523067\pi$
$128$	12165.9	+	10973.9i	0.742545	+	0.669796i
$129$		0			0
$130$	−1619.82	−	1854.51i	−0.0958471	−	0.109734i
$131$	−802.198	+	463.149i	−0.0467454	+	0.0269885i	−0.523191	−	0.852216i	$-0.675258\pi$
$131$	−802.198	+	463.149i	−0.0467454	+	0.0269885i	0.476445	+	0.879204i	$0.341925\pi$
$132$		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	−0.518460	−	0.855102i	$-0.673494\pi$
$139$	−717.766	+	414.402i	−0.0371495	+	0.0214483i	0.481310	+	0.876550i	$0.340161\pi$
$140$	9239.93	−	11942.6i	0.471425	−	0.609316i
$141$		0			0
$142$	4977.62	+	1700.77i	0.246857	+	0.0843470i
$143$			1972.36i			0.0964525i
$144$		0			0
$145$	15322.3			0.728768
$146$	−12248.7	+	35848.0i	−0.574625	+	1.68174i
$147$		0			0
$148$	17742.2	+	13727.1i	0.810000	+	0.626693i
$149$	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	0.663758	−	0.747947i	$-0.268960\pi$
$151$	7932.37	+	4579.76i	0.347896	+	0.200858i	−0.315862	+	0.948805i	$0.602294\pi$
$152$	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	$0.974145\pi$
$158$	13163.1	−	11497.3i	0.527285	−	0.460556i
$159$		0			0
$160$	−9384.91	−	19519.9i	−0.366598	−	0.762497i
$161$	−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	$-0.297783\pi$
$164$	3331.69	−	24548.2i	0.123873	−	0.912710i
$165$		0			0
$166$	−2295.66	+	2005.14i	−0.0833091	+	0.0727661i
$167$	9568.12	−	5524.16i	0.343079	−	0.198077i	−0.318554	−	0.947905i	$-0.603197\pi$
$167$	9568.12	−	5524.16i	0.343079	−	0.198077i	0.661633	+	0.749828i	$0.269864\pi$
$168$		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
$176$	−4624.06	+	16721.5i	−0.149279	+	0.539821i
$177$		0			0
$178$	10454.4	−	30596.8i	0.329960	−	0.965687i
$179$		−	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	$0.255847\pi$
$182$	−4915.25	−	1679.46i	−0.148389	−	0.0507023i
$183$		0			0
$184$	−11100.0	+	22172.5i	−0.327858	+	0.654905i
$185$	−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	$0.0762875\pi$
$191$	60657.0	+	35020.3i	1.66270	+	0.959961i	0.691283	+	0.722584i	$0.257046\pi$
$192$		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	$0.678367\pi$
$194$	−17539.2	−	20080.4i	−0.466021	−	0.533542i
$195$		0			0
$196$	−882.655	+	6503.50i	−0.0229762	+	0.169291i
$197$	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	$0.857598\pi$
$200$	−675.504	−	11348.1i	−0.0168876	−	0.283702i
$201$		0			0
$202$	24435.1	+	27975.4i	0.598840	+	0.685605i
$203$	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	$-0.728938\pi$
$211$	−14989.6	+	8654.27i	−0.336687	+	0.194386i	0.322119	+	0.946699i	$0.395605\pi$
$212$	11472.3	+	8876.03i	0.255257	+	0.197491i
$213$		0			0
$214$	23701.1	+	8098.28i	0.517536	+	0.176834i
$215$			39589.7i			0.856457i
$216$		0			0
$217$	−56204.3			−1.19358
$218$	−4465.65	+	13069.5i	−0.0939663	+	0.275009i
$219$		0			0
$220$	14034.3	−	18139.3i	0.289965	−	0.374779i
$221$	−5862.10	−	10153.5i	−0.120024	−	0.207888i
$222$		0			0
$223$	55484.8	+	32034.1i	1.11574	+	0.644174i	0.940311	−	0.340317i	$-0.110534\pi$
$223$	55484.8	+	32034.1i	1.11574	+	0.644174i	0.175432	+	0.984492i	$0.443868\pi$
$224$	−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	$-0.375749\pi$
$227$	−11857.8	−	6846.11i	−0.230119	−	0.132859i	−0.610627	+	0.791918i	$0.709083\pi$
$228$		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	$-0.383286\pi$
$230$	24687.4	−	21563.2i	0.466681	−	0.407622i
$231$		0			0
$232$	−2754.91	−	46281.0i	−0.0511838	−	0.859857i
$233$	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
$236$	−71699.9	−	9731.11i	−1.28734	−	0.174718i
$237$		0			0
$238$	54149.3	−	47296.6i	0.955959	−	0.834980i
$239$	−275.008	+	158.776i	−0.00481448	+	0.00277964i	−0.502405	−	0.864632i	$-0.667551\pi$
$239$	−275.008	+	158.776i	−0.00481448	+	0.00277964i	0.497591	+	0.867412i	$0.334218\pi$
$240$		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
$248$	−36089.5	+	72089.6i	−0.586783	+	1.17211i
$249$		0			0
$250$	−21956.1	+	64258.6i	−0.351298	+	1.02814i
$251$			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
$254$	2006.35	+	685.539i	0.0310986	+	0.0106259i
$255$		0			0
$256$	−57272.3	+	31856.6i	−0.873907	+	0.486094i
$257$	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	0.593130	−	0.805107i	$-0.297892\pi$
$263$	13311.8	+	7685.54i	0.192453	+	0.111113i	−0.400678	+	0.916219i	$0.631225\pi$
$264$		0			0
$265$	−9587.47	−	16606.0i	−0.136525	−	0.236468i
$266$	−75697.5	−	86665.1i	−1.06984	−	1.22485i
$267$		0			0
$268$	1074.94	+	145.891i	0.0149664	+	0.00203124i
$269$	−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	$0.821606\pi$
$272$	−25894.4	−	99823.5i	−0.349999	−	1.34926i
$273$		0			0
$274$	4389.72	+	5025.74i	0.0584704	+	0.0669420i
$275$	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	−0.682389	−	0.730989i	$-0.739059\pi$
$283$	−31277.1	+	18057.8i	−0.390529	+	0.225472i	0.291860	+	0.956461i	$0.405726\pi$
$284$	−12875.3	+	16641.3i	−0.159633	+	0.206325i
$285$		0			0
$286$	−7465.66	−	2550.90i	−0.0912717	−	0.0311861i
$287$			69084.1i			0.838715i
$288$		0			0
$289$	78760.1			0.942997
$290$	−19816.7	+	57997.3i	−0.235633	+	0.689623i
$291$		0			0
$292$	−119848.	−	92726.2i	−1.40562	−	1.08752i
$293$	−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
$302$	−27594.2	+	24102.1i	−0.302554	+	0.264265i
$303$		0			0
$304$	−159766.	+	41443.5i	−1.72877	+	0.448445i
$305$	−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	$-0.268083\pi$
$308$	6506.56	−	47941.0i	0.0685883	−	0.505366i
$309$		0			0
$310$	80266.6	−	70108.7i	0.835240	−	0.729539i
$311$	−141564.	+	81731.8i	−1.46363	+	0.845027i	−0.999177	−	0.0405712i	$-0.987082\pi$
$311$	−141564.	+	81731.8i	−1.46363	+	0.845027i	−0.464453	+	0.885598i	$0.653749\pi$
$312$		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
$320$	86023.4	−	10277.7i	0.840073	−	0.100368i
$321$		0			0
$322$	22357.2	−	65432.5i	0.215629	−	0.631076i
$323$		−	259728.i		−	2.48951i
$324$		0			0
$325$	5169.63			0.0489433
$326$	161894.	+	55316.7i	1.52334	+	0.520500i
$327$		0			0
$328$	88609.7	+	44359.7i	0.823633	+	0.412327i
$329$	93011.4	+	161101.i	0.859299	+	1.48835i
$330$		0			0
$331$	−97678.0	−	56394.4i	−0.891540	−	0.514731i	−0.0170938	−	0.999854i	$-0.505441\pi$
$331$	−97678.0	−	56394.4i	−0.891540	−	0.514731i	−0.874446	+	0.485123i	$0.838775\pi$
$332$	−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	$0.804116\pi$
$338$	72925.7	+	83491.7i	0.638333	+	0.730819i
$339$		0			0
$340$	−18334.5	+	135091.i	−0.158603	+	1.16860i
$341$	−85367.4			−0.734147
$342$		0			0
$343$		−	125431.i		−	1.06615i
$344$	119580.	−	7118.12i	1.01052	−	0.0601518i
$345$		0			0
$346$	−57720.7	−	66083.7i	−0.482147	−	0.552004i
$347$	139615.	−	80606.6i	1.15950	−	0.669440i	0.208318	−	0.978061i	$-0.433201\pi$
$347$	139615.	−	80606.6i	1.15950	−	0.669440i	0.951185	+	0.308621i	$0.0998676\pi$
$348$		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
$356$	102292.	+	79143.2i	0.807130	+	0.624473i
$357$		0			0
$358$	43450.3	+	14846.3i	0.339021	+	0.115838i
$359$		−	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
$362$	−58810.2	+	172119.i	−0.448782	+	1.31344i
$363$		0			0
$364$	12714.0	−	16432.9i	0.0959578	−	0.124025i
$365$	100158.	+	173479.i	0.751799	+	1.30215i
$366$		0			0
$367$	35332.0	+	20398.9i	0.262323	+	0.151452i	0.625394	−	0.780309i	$-0.284938\pi$
$367$	35332.0	+	20398.9i	0.262323	+	0.151452i	−0.363071	+	0.931762i	$0.618272\pi$
$368$	−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	$0.514209\pi$
$374$	82246.1	−	71837.7i	0.587993	−	0.513581i
$375$		0			0
$376$	266357.	−	15855.1i	1.88403	−	0.112149i
$377$	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	$-0.223515\pi$
$380$	216210.	+	29344.1i	1.49730	+	0.203214i
$381$		0			0
$382$	−211006.	+	184303.i	−1.44600	+	1.26301i
$383$	−52190.3	+	30132.1i	−0.355789	+	0.205415i	−0.667232	−	0.744850i	$-0.732521\pi$
$383$	−52190.3	+	30132.1i	−0.355789	+	0.205415i	0.311443	+	0.950265i	$0.399188\pi$
$384$		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
$392$	−23475.1	−	11752.1i	−0.152769	−	0.0764792i
$393$		0			0
$394$	−39909.3	+	116802.i	−0.257088	+	0.752415i
$395$		−	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	$0.467350\pi$
$398$	−129688.	−	44312.4i	−0.818719	−	0.279743i
$399$		0			0
$400$	43827.8	+	12119.9i	0.273924	+	0.0757491i
$401$	−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	$0.701597\pi$
$410$	−86174.8	−	98660.5i	−0.512640	−	0.586916i
$411$		0			0
$412$	−179275.	−	24331.1i	−1.05615	−	0.143340i
$413$	201779.			1.18298
$414$		0			0
$415$			16117.5i			0.0935841i
$416$	−12913.5	−	26859.2i	−0.0746205	−	0.155205i
$417$		0			0
$418$	−114975.	−	131634.i	−0.658038	−	0.753380i
$419$	−73320.7	+	42331.7i	−0.417637	+	0.241123i	−0.694066	−	0.719912i	$-0.744182\pi$
$419$	−73320.7	+	42331.7i	−0.417637	+	0.241123i	0.276429	+	0.961034i	$0.410849\pi$
$420$		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
$428$	−61306.3	+	79238.3i	−0.334671	+	0.432561i
$429$		0			0
$430$	−149853.	−	51202.3i	−0.810453	−	0.276919i
$431$			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	$0.632188\pi$
$434$	72690.4	−	212742.i	0.385920	−	1.12947i
$435$		0			0
$436$	−43694.6	−	33806.3i	−0.229855	−	0.177838i
$437$	−124897.	−	216328.i	−0.654017	−	1.13279i
$438$		0			0
$439$	−17332.7	−	10007.1i	−0.0899369	−	0.0519251i	0.454357	−	0.890820i	$-0.349869\pi$
$439$	−17332.7	−	10007.1i	−0.0899369	−	0.0519251i	−0.544294	+	0.838895i	$0.683202\pi$
$440$	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	$-0.364724\pi$
$443$	−33466.7	−	19322.0i	−0.170532	−	0.0984567i	−0.582837	+	0.812589i	$0.698057\pi$
$444$		0			0
$445$	−85486.7	−	148067.i	−0.431696	−	0.747720i
$446$	−193014.	+	168587.i	−0.970327	+	0.847530i
$447$		0			0
$448$	146314.	−	109509.i	0.729005	−	0.545626i
$449$	−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
$452$	−5476.55	+	40351.8i	−0.0268059	+	0.197509i
$453$		0			0
$454$	41249.5	−	36029.3i	0.200128	−	0.174801i
$455$	−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	−0.895458	−	0.445146i	$-0.853152\pi$
$463$	−205297.	+	118528.i	−0.957679	+	0.552916i	−0.0622210	+	0.998062i	$0.519818\pi$
$464$	178743.	+	49428.5i	0.830220	+	0.229584i
$465$		0			0
$466$	−81922.2	+	239760.i	−0.377250	+	1.10409i
$467$		−	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
$470$	−333787.	−	114050.i	−1.51103	−	0.516295i
$471$		0			0
$472$	129565.	−	258809.i	0.581571	−	1.16170i
$473$	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	$-0.334999\pi$
$479$	−2079.74	−	1200.74i	−0.00906438	−	0.00523332i	−0.504525	+	0.863397i	$0.668332\pi$
$480$		0			0
$481$	−20402.3	−	35337.7i	−0.0881836	−	0.152739i
$482$	−67113.8	−	76837.7i	−0.288880	−	0.330735i
$483$		0			0
$484$	−21621.7	+	159311.i	−0.0922997	+	0.680074i
$485$	−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	$0.673986\pi$
$488$	9995.75	+	167923.i	0.0419736	+	0.705132i
$489$		0			0
$490$	22830.0	+	26137.8i	0.0950855	+	0.108862i
$491$	−111325.	+	64273.4i	−0.461773	+	0.266605i	−0.712790	−	0.701378i	$-0.752569\pi$
$491$	−111325.	+	64273.4i	−0.461773	+	0.266605i	0.251016	+	0.967983i	$0.419235\pi$
$492$		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	$-0.749811\pi$
$499$	−111377.	+	64303.6i	−0.447296	+	0.258246i	0.259392	+	0.965772i	$0.416478\pi$
$500$	−214832.	−	166214.i	−0.859326	−	0.664857i
$501$		0			0
$502$	−155144.	−	53010.3i	−0.615642	−	0.210355i
$503$			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
$506$	33957.9	−	99383.8i	0.132629	−	0.388163i
$507$		0			0
$508$	−5189.73	+	6707.72i	−0.0201102	+	0.0259925i
$509$	−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
$518$	188460.	−	164610.i	0.702358	−	0.613473i
$519$		0			0
$520$	2341.00	+	39327.4i	0.00865754	+	0.145442i
$521$	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	$0.969700\pi$
$524$	14686.1	+	1993.20i	0.0534866	+	0.00725920i
$525$		0			0
$526$	−46307.3	+	40447.0i	−0.167370	+	0.146189i
$527$	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
$536$	−1942.47	+	3880.13i	−0.00676122	+	0.0135057i
$537$		0			0
$538$	98429.0	−	288070.i	0.340062	−	0.995253i
$539$		−	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	$0.690524\pi$
$542$	−295530.	−	100978.i	−1.00601	−	0.343739i
$543$		0			0
$544$	411336.	+	31090.2i	1.38995	+	0.105057i
$545$	36515.9	+	63247.5i	0.122939	+	0.212936i
$546$		0			0
$547$	−306032.	−	176688.i	−1.02280	−	0.590517i	−0.107890	−	0.994163i	$-0.534409\pi$
$547$	−306032.	−	176688.i	−1.02280	−	0.590517i	−0.914915	+	0.403646i	$0.867743\pi$
$548$	−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
$554$	−12472.5	−	14279.6i	−0.0406382	−	0.0465262i
$555$		0			0
$556$	13140.4	+	1783.42i	0.0425069	+	0.00576903i
$557$	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
$560$	−233856.	+	60662.5i	−0.745713	+	0.193439i
$561$		0			0
$562$	113700.	+	130173.i	0.359987	+	0.412144i
$563$	203807.	−	117668.i	0.642988	−	0.371229i	−0.142776	−	0.989755i	$-0.545603\pi$
$563$	203807.	−	117668.i	0.642988	−	0.371229i	0.785765	+	0.618526i	$0.212270\pi$
$564$		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	−0.552104	−	0.833775i	$-0.686175\pi$
$571$	−34588.3	+	19969.5i	−0.106086	+	0.0612486i	0.446018	+	0.895024i	$0.352842\pi$
$572$	19311.0	−	24959.5i	0.0590219	−	0.0762857i
$573$		0			0
$574$	−261493.	−	89348.1i	−0.793664	−	0.271182i
$575$			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	$0.221434\pi$
$578$	−101862.	+	298118.i	−0.304900	+	0.892345i
$579$		0			0
$580$	−193899.	−	150018.i	−0.576393	−	0.445953i
$581$	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	$-0.365662\pi$
$587$	−60509.5	−	34935.2i	−0.175609	−	0.101388i	−0.585228	+	0.810869i	$0.698995\pi$
$588$		0			0
$589$	−406079.	−	703350.i	−1.17052	−	2.02741i
$590$	−288165.	+	251697.i	−0.827823	+	0.723060i
$591$		0			0
$592$	−90121.9	−	347423.i	−0.257150	−	0.991322i
$593$	−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
$596$	6719.53	−	49510.2i	0.0189167	−	0.139381i
$597$		0			0
$598$	33969.6	−	29670.7i	0.0949923	−	0.0829708i
$599$	−241159.	+	139233.i	−0.672123	+	0.388051i	−0.796881	−	0.604137i	$-0.793518\pi$
$599$	−241159.	+	139233.i	−0.672123	+	0.388051i	0.124757	+	0.992187i	$0.460185\pi$
$600$		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	0.0784853	−	0.996915i	$-0.474992\pi$
$607$	361479.	−	208700.i	0.981082	−	0.566428i	0.902597	+	0.430487i	$0.141658\pi$
$608$	49759.4	−	658337.i	0.134607	−	1.78091i
$609$		0			0
$610$	71901.8	−	210434.i	0.193232	−	0.565530i
$611$			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	$0.509882\pi$
$614$	532347.	+	181895.i	1.41208	+	0.482484i
$615$		0			0
$616$	173049.	+	86631.5i	0.456044	+	0.228305i
$617$	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	−0.0908215	−	0.995867i	$-0.528949\pi$
$619$	−382655.	−	220926.i	−0.998679	−	0.576587i	−0.907857	+	0.419280i	$0.862283\pi$
$620$	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
$626$	134964.	+	154518.i	0.344404	+	0.394304i
$627$		0			0
$628$	−45410.7	+	334591.i	−0.115143	+	0.848390i
$629$	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	$0.914390\pi$
$632$	−279143.	+	16616.2i	−0.698864	+	0.0416005i
$633$		0			0
$634$	−73809.9	−	84504.1i	−0.183627	−	0.210232i
$635$	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	−0.414066	−	0.910247i	$-0.635892\pi$
$643$	69127.8	−	39911.0i	0.167198	−	0.0965318i	0.581264	+	0.813715i	$0.302558\pi$
$644$	218756.	+	169251.i	0.527459	+	0.408093i
$645$		0			0
$646$	983109.	+	335913.i	2.35579	+	0.804936i
$647$		−	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
$650$	−6686.01	+	19567.8i	−0.0158249	+	0.0463143i
$651$		0			0
$652$	−418763.	+	541251.i	−0.985085	+	1.27322i
$653$	−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	0.0994224	−	0.995045i	$-0.468300\pi$
$659$	−309469.	−	178672.i	−0.712601	−	0.411420i	−0.812023	+	0.583625i	$0.801634\pi$
$660$		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	$0.609258\pi$
$662$	339790.	−	296789.i	0.775345	−	0.677223i
$663$		0			0
$664$	48682.8	−	2897.89i	0.110418	−	0.00657272i
$665$	−608463.			−1.37591
$666$		0			0
$667$			280664.i			0.630864i
$668$	−175167.	−	23773.7i	−0.392554	−	0.0532775i
$669$		0			0
$670$	4320.25	−	3773.51i	0.00962408	−	0.00840613i
$671$	−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
$680$	−487625.	−	244115.i	−1.05455	−	0.527929i
$681$		0			0
$682$	110408.	−	323128.i	0.237372	−	0.694713i
$683$			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
$686$	474775.	+	162223.i	1.00888	+	0.344718i
$687$		0			0
$688$	−127713.	+	461835.i	−0.269810	+	0.975685i
$689$	−13192.2	−	22849.6i	−0.0277895	−	0.0481328i
$690$		0			0
$691$	397767.	+	229651.i	0.833053	+	0.480963i	0.854897	−	0.518798i	$-0.173620\pi$
$691$	397767.	+	229651.i	0.833053	+	0.480963i	−0.0218438	+	0.999761i	$0.506954\pi$
$692$	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
$698$	582807.	+	667248.i	1.19623	+	1.36955i
$699$		0			0
$700$	−125655.	−	17054.0i	−0.256440	−	0.0348040i
$701$	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
$704$	222233.	−	166331.i	0.448398	−	0.335605i
$705$		0			0
$706$	575716.	+	659130.i	1.15504	+	1.32240i
$707$	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
$716$	−112391.	+	145265.i	−0.219232	+	0.283357i
$717$		0			0
$718$	3499.77	+	1195.82i	0.00678876	+	0.00231961i
$719$		−	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
$722$	369076.	−	1.08017e6i	0.708013	−	2.07213i
$723$		0			0
$724$	−575434.	−	445210.i	−1.09779	−	0.849353i
$725$	−64338.5	−	111438.i	−0.122404	−	0.212010i
$726$		0			0
$727$	286999.	+	165699.i	0.543014	+	0.313509i	0.746299	−	0.665610i	$-0.231829\pi$
$727$	286999.	+	165699.i	0.543014	+	0.313509i	−0.203286	+	0.979119i	$0.565162\pi$
$728$	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	$0.818038\pi$
$734$	−122909.	+	107354.i	−0.228134	+	0.199263i
$735$		0			0
$736$	357553.	−	171906.i	0.660062	−	0.317349i
$737$	−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	$-0.0672264\pi$
$740$	−63810.8	+	470165.i	−0.116528	+	0.858592i
$741$		0			0
$742$	121859.	−	106438.i	0.221335	−	0.193325i
$743$	−910009.	+	525394.i	−1.64842	+	0.951716i	−0.670720	+	0.741711i	$0.734015\pi$
$743$	−910009.	+	525394.i	−1.64842	+	0.951716i	−0.977700	+	0.210005i	$0.932652\pi$
$744$		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	$-0.589907\pi$
$751$	233295.	−	134693.i	0.413643	−	0.238817i	0.692354	+	0.721558i	$0.256574\pi$
$752$	−284472.	+	1.02870e6i	−0.503041	+	1.81909i
$753$		0			0
$754$	−27267.6	+	79803.5i	−0.0479627	+	0.140372i
$755$			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	$0.636385\pi$
$758$	702346.	+	239980.i	1.22240	+	0.417674i
$759$		0			0
$760$	−390701.	+	780436.i	−0.676422	+	1.35117i
$761$	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	$0.972901\pi$
$770$	−168293.	−	192677.i	−0.283848	−	0.324974i
$771$		0			0
$772$	74996.1	−	552580.i	0.125836	−	0.927172i
$773$	−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
$776$	25348.1	+	425833.i	0.0420941	+	0.707157i
$777$		0			0
$778$	−31601.0	−	36179.6i	−0.0522085	−	0.0597729i
$779$	−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	$-0.553965\pi$
$787$	371945.	−	214742.i	0.600522	−	0.346711i	0.769247	+	0.638952i	$0.220632\pi$
$788$	−390496.	−	302125.i	−0.628875	−	0.486558i
$789$		0			0
$790$	349810.	+	119524.i	0.560503	+	0.191515i
$791$		−	113559.i		−	0.181496i
$792$		0			0
$793$	−76497.5			−0.121647
$794$	−41743.7	+	122171.i	−0.0662140	+	0.193787i
$795$		0			0
$796$	335458.	−	433579.i	0.529434	−	0.684292i
$797$	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
$806$	110446.	−	96468.7i	0.170012	−	0.148497i
$807$		0			0
$808$	−35314.2	−	593258.i	−0.0540912	−	0.908701i
$809$	−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	$0.921301\pi$
$812$	−512462.	−	69551.3i	−0.777230	−	0.105486i
$813$		0			0
$814$	286247.	−	250021.i	0.432008	−	0.377336i
$815$	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	−0.930652	−	0.365905i	$-0.880759\pi$
$823$	−730902.	+	421987.i	−1.07909	+	0.623016i	−0.148443	+	0.988921i	$0.547426\pi$
$824$	323957.	−	647112.i	0.477126	−	0.953070i
$825$		0			0
$826$	−260966.	+	763763.i	−0.382493	+	1.11943i
$827$		−	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	$0.147443\pi$
$830$	−61007.1	−	20845.2i	−0.0885573	−	0.0302586i
$831$		0			0
$832$	118367.	−	14141.9i	0.170996	−	0.0204297i
$833$	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	$-0.321439\pi$
$839$	45546.9	+	26296.5i	0.0647045	+	0.0373572i	−0.467299	+	0.884099i	$0.654773\pi$
$840$		0			0
$841$	91248.2	+	158047.i	0.129013	+	0.223456i
$842$	304449.	+	348559.i	0.429427	+	0.491646i
$843$		0			0
$844$	274421.	+	37244.4i	0.385241	+	0.0522849i
$845$	586183.			0.820956
$846$		0			0
$847$		−	448337.i		−	0.624939i
$848$	−58273.4	−	224646.i	−0.0810362	−	0.312397i
$849$		0			0
$850$	−188290.	−	215570.i	−0.260608	−	0.298367i
$851$	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	0.0179767	−	0.999838i	$-0.494278\pi$
$859$	658817.	−	380368.i	0.892851	−	0.515487i	0.874874	+	0.484351i	$0.160944\pi$
$860$	387616.	−	500993.i	0.524089	−	0.677384i
$861$		0			0
$862$	−1.11623e6	−	381396.i	−1.50223	−	0.513289i
$863$			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
$866$	195659.	−	572631.i	0.260894	−	0.763553i
$867$		0			0
$868$	711245.	+	550287.i	0.944017	+	0.730382i
$869$	−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	$0.848252\pi$
$878$	60295.0	−	52664.5i	0.0782154	−	0.0683171i
$879$		0			0
$880$	−355198.	+	92138.7i	−0.458675	+	0.118981i
$881$	−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	$0.857293\pi$
$884$	−25228.0	+	185883.i	−0.0322834	+	0.237867i
$885$		0			0
$886$	116420.	−	101687.i	0.148306	−	0.129538i
$887$	888008.	−	512692.i	1.12868	−	0.651642i	0.185075	−	0.982724i	$-0.440747\pi$
$887$	888008.	−	512692.i	1.12868	−	0.651642i	0.943602	+	0.331082i	$0.107414\pi$
$888$		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
$896$	225277.	+	695452.i	0.280608	+	0.866265i
$897$		0			0
$898$	102765.	−	300760.i	0.127436	−	0.372964i
$899$			912528.i			1.12908i
$900$		0			0
$901$	365202.			0.449867
$902$	−397176.	−	135709.i	−0.488169	−	0.166799i
$903$		0			0
$904$	−145654.	−	72917.5i	−0.178232	−	0.0892267i
$905$	480895.	+	832935.i	0.587156	+	1.01698i
$906$		0			0
$907$	1.39930e6	+	807885.i	1.70097	+	0.982053i	0.944785	+	0.327690i	$0.106270\pi$
$907$	1.39930e6	+	807885.i	1.70097	+	0.982053i	0.756181	+	0.654363i	$0.227063\pi$
$908$	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	$-0.278401\pi$
$911$	246841.	+	142514.i	0.297427	+	0.171719i	−0.343860	+	0.939021i	$0.611734\pi$
$912$		0			0
$913$	25820.8	+	44723.0i	0.0309762	+	0.0536524i
$914$	693503.	+	793983.i	0.830149	+	0.950427i
$915$		0			0
$916$	−142002.	+	1.04628e6i	−0.169240	+	1.24698i
$917$	−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	$0.871743\pi$
$920$	−523532.	+	31163.7i	−0.618540	+	0.0368191i
$921$		0			0
$922$	−527878.	−	604361.i	−0.620972	−	0.710943i
$923$	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
$932$	−801574.	−	620174.i	−0.922809	−	0.713973i
$933$		0			0
$934$	872338.	+	298064.i	0.999980	+	0.341677i
$935$		−	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	$0.609791\pi$
$938$	3912.47	−	11450.5i	0.00444677	−	0.0130143i
$939$		0			0
$940$	863388.	−	1.11593e6i	0.977125	−	1.26293i
$941$	−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	$0.0717258\pi$
$947$	1.48474e6	+	857213.i	1.65558	+	0.955848i	0.680857	+	0.732416i	$0.261607\pi$
$948$		0			0
$949$	137817.	+	238706.i	0.153027	+	0.265051i
$950$	−345017.	+	301354.i	−0.382290	+	0.333911i
$951$		0			0
$952$	−1.14831e6	+	68354.3i	−1.26703	+	0.0754210i
$953$	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
$956$	5034.67	+	683.305i	0.00550877	+	0.000747651i
$957$		0			0
$958$	7234.74	−	6319.17i	0.00788301	−	0.00688540i
$959$	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	$-0.844499\pi$
$967$	−858506.	+	495659.i	−0.918101	+	0.530066i	−0.0350720	+	0.999385i	$0.511166\pi$
$968$	−575053.	−	287883.i	−0.613701	−	0.307231i
$969$		0			0
$970$	182335.	−	533635.i	0.193787	−	0.567154i
$971$			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
$974$	−1.53384e6	−	524089.i	−1.61682	−	0.552443i
$975$		0			0
$976$	−648540.	−	179343.i	−0.680828	−	0.188272i
$977$	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	−0.150259	−	0.988647i	$-0.548011\pi$
$983$	−1.04512e6	−	603401.i	−1.08158	−	0.624452i	−0.931323	+	0.364195i	$0.881344\pi$
$984$		0			0
$985$	326341.	+	565239.i	0.336356	+	0.582586i
$986$	−767903.	−	879163.i	−0.789864	−	0.904306i
$987$		0			0
$988$	297503.	+	40377.1i	0.304773	+	0.0413638i
$989$	−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	$-0.144350\pi$
$992$	1.16252e6	−	558922.i	1.18134	−	0.567973i
$993$		0			0
$994$	154396.	+	176766.i	0.156265	+	0.178906i
$995$	−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.19.9		44
3.2	odd	2		36.5.f.a.7.14	✓	44
4.3	odd	2	inner	108.5.f.a.19.6		44
9.2	odd	6		324.5.d.f.163.2		22
9.4	even	3	inner	108.5.f.a.91.6		44
9.5	odd	6		36.5.f.a.31.17	yes	44
9.7	even	3		324.5.d.e.163.21		22
12.11	even	2		36.5.f.a.7.17	yes	44
36.7	odd	6		324.5.d.e.163.22		22
36.11	even	6		324.5.d.f.163.1		22
36.23	even	6		36.5.f.a.31.14	yes	44
36.31	odd	6	inner	108.5.f.a.91.9		44

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

\(f(q)\)	\(=\)	\(q+(-1.29332 + 3.78514i) q^{2} +(-12.6546 - 9.79083i) q^{4} +(10.5756 + 18.3175i) q^{5} +(38.6407 + 22.3092i) q^{7} +(53.4262 - 35.2369i) q^{8} +O(q^{10})\)	\(q+(-1.29332 + 3.78514i) q^{2} +(-12.6546 - 9.79083i) q^{4} +(10.5756 + 18.3175i) q^{5} +(38.6407 + 22.3092i) q^{7} +(53.4262 - 35.2369i) q^{8} +(-83.0119 + 16.3397i) q^{10} +(58.6904 + 33.8849i) q^{11} +(14.5519 + 25.2046i) q^{13} +(-134.419 + 117.408i) q^{14} +(64.2793 + 247.799i) q^{16} -402.841 q^{17} +644.741i q^{19} +(45.5130 - 335.344i) q^{20} +(-204.165 + 178.327i) q^{22} +(-335.527 + 193.717i) q^{23} +(88.8138 - 153.830i) q^{25} +(-114.223 + 22.4833i) q^{26} +(-270.558 - 660.639i) q^{28} +(362.210 - 627.366i) q^{29} +(-1090.90 + 629.833i) q^{31} +(-1021.09 - 77.1774i) q^{32} +(521.004 - 1524.81i) q^{34} +943.733i q^{35} -1402.04 q^{37} +(-2440.44 - 833.859i) q^{38} +(1210.46 + 605.982i) q^{40} +(774.166 + 1340.89i) q^{41} +(1620.98 + 935.875i) q^{43} +(-410.944 - 1003.43i) q^{44} +(-299.300 - 1520.56i) q^{46} +(3610.63 + 2084.60i) q^{47} +(-205.097 - 355.239i) q^{49} +(467.404 + 535.125i) q^{50} +(62.6253 - 461.430i) q^{52} -906.566 q^{53} +1433.41i q^{55} +(2850.53 - 169.681i) q^{56} +(1906.22 + 2182.40i) q^{58} +(3916.45 - 2261.16i) q^{59} +(-1314.22 + 2276.30i) q^{61} +(-973.119 - 4943.80i) q^{62} +(1612.72 - 3765.15i) q^{64} +(-307.789 + 533.107i) q^{65} +(-58.7165 + 33.9000i) q^{67} +(5097.81 + 3944.15i) q^{68} +(-3572.16 - 1220.55i) q^{70} -1315.04i q^{71} +9470.72 q^{73} +(1813.29 - 5306.91i) q^{74} +(6312.55 - 8158.96i) q^{76} +(1511.89 + 2618.67i) q^{77} +(-3783.95 - 2184.67i) q^{79} +(-3859.25 + 3798.05i) q^{80} +(-6076.73 + 1196.12i) q^{82} +(659.925 + 381.008i) q^{83} +(-4260.28 - 7379.03i) q^{85} +(-5638.88 + 4925.26i) q^{86} +(4329.61 - 257.724i) q^{88} -8083.40 q^{89} +1298.56i q^{91} +(6142.62 + 833.676i) q^{92} +(-12560.2 + 10970.7i) q^{94} +(-11810.0 + 6818.52i) q^{95} +(-3332.71 + 5772.42i) q^{97} +(1609.89 - 316.884i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + q^{2} - q^{4} + 2 q^{5} - 122 q^{8}+O(q^{10}) \) 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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