LMFDB - Embedded newform 108.4.h.b.35.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,4,Mod(35,108)]

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, 1]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("108.35");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	108.h (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:	$6.37220628062$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			35.8
Character	$\chi$	$=$	108.35
Dual form			108.4.h.b.71.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.38284 - 2.46734i) q^{2} +(-4.17551 - 6.82387i) q^{4} +(-14.6499 + 8.45813i) q^{5} +(-3.08966 - 1.78382i) q^{7} +(-22.6108 + 0.866066i) q^{8} +O(q^{10})$	\(q+(1.38284 - 2.46734i) q^{2} +(-4.17551 - 6.82387i) q^{4} +(-14.6499 + 8.45813i) q^{5} +(-3.08966 - 1.78382i) q^{7} +(-22.6108 + 0.866066i) q^{8} +(0.610574 + 47.8425i) q^{10} +(-25.0688 + 43.4205i) q^{11} +(-18.9966 - 32.9032i) q^{13} +(-8.67378 + 5.15650i) q^{14} +(-29.1303 + 56.9862i) q^{16} -84.3819i q^{17} +62.9237i q^{19} +(118.888 + 64.6521i) q^{20} +(72.4668 + 121.897i) q^{22} +(-37.6066 - 65.1366i) q^{23} +(80.5801 - 139.569i) q^{25} +(-107.453 + 1.37133i) q^{26} +(0.728372 + 28.5317i) q^{28} +(-105.644 - 60.9938i) q^{29} +(-17.2800 + 9.97659i) q^{31} +(100.322 + 150.677i) q^{32} +(-208.199 - 116.687i) q^{34} +60.3510 q^{35} +17.7622 q^{37} +(155.254 + 87.0135i) q^{38} +(323.922 - 203.933i) q^{40} +(-299.072 + 172.670i) q^{41} +(113.206 + 65.3596i) q^{43} +(400.970 - 10.2362i) q^{44} +(-212.718 + 2.71474i) q^{46} +(153.083 - 265.147i) q^{47} +(-165.136 - 286.024i) q^{49} +(-232.934 - 391.820i) q^{50} +(-145.206 + 267.018i) q^{52} -479.464i q^{53} -848.142i q^{55} +(71.4047 + 37.6577i) q^{56} +(-296.581 + 176.316i) q^{58} +(245.774 + 425.693i) q^{59} +(-49.9168 + 86.4585i) q^{61} +(0.720188 + 56.4315i) q^{62} +(510.500 - 39.1649i) q^{64} +(556.599 + 321.352i) q^{65} +(-536.669 + 309.846i) q^{67} +(-575.811 + 352.337i) q^{68} +(83.4558 - 148.906i) q^{70} -254.455 q^{71} +100.485 q^{73} +(24.5622 - 43.8253i) q^{74} +(429.383 - 262.738i) q^{76} +(154.908 - 89.4363i) q^{77} +(856.295 + 494.382i) q^{79} +(-55.2404 - 1081.23i) q^{80} +(12.4646 + 976.687i) q^{82} +(-251.755 + 436.053i) q^{83} +(713.714 + 1236.19i) q^{85} +(317.810 - 188.936i) q^{86} +(529.222 - 1003.48i) q^{88} +1019.86i q^{89} +135.546i q^{91} +(-287.457 + 528.601i) q^{92} +(-442.518 - 744.363i) q^{94} +(-532.217 - 921.828i) q^{95} +(-503.589 + 872.242i) q^{97} +(-934.074 + 11.9208i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 12 q^{4} + 72 q^{5}+O(q^{10}) $ 24 * q - 12 * q^4 + 72 * q^5	$ 24 q - 12 q^{4} + 72 q^{5} + 96 q^{10} - 216 q^{13} + 36 q^{14} - 72 q^{16} + 540 q^{20} - 192 q^{22} + 252 q^{25} - 672 q^{28} - 576 q^{29} - 360 q^{32} - 660 q^{34} + 1248 q^{37} + 144 q^{38} + 636 q^{40} - 1116 q^{41} + 960 q^{46} + 348 q^{49} + 648 q^{50} + 132 q^{52} + 1692 q^{56} + 516 q^{58} - 264 q^{61} + 960 q^{64} + 2592 q^{65} - 5688 q^{68} + 564 q^{70} - 4776 q^{73} - 5652 q^{74} - 600 q^{76} - 648 q^{77} - 4104 q^{82} + 720 q^{85} + 9540 q^{86} + 1956 q^{88} + 7416 q^{92} - 1188 q^{94} + 588 q^{97}+O(q^{100}) $ 24 * q - 12 * q^4 + 72 * q^5 + 96 * q^10 - 216 * q^13 + 36 * q^14 - 72 * q^16 + 540 * q^20 - 192 * q^22 + 252 * q^25 - 672 * q^28 - 576 * q^29 - 360 * q^32 - 660 * q^34 + 1248 * q^37 + 144 * q^38 + 636 * q^40 - 1116 * q^41 + 960 * q^46 + 348 * q^49 + 648 * q^50 + 132 * q^52 + 1692 * q^56 + 516 * q^58 - 264 * q^61 + 960 * q^64 + 2592 * q^65 - 5688 * q^68 + 564 * q^70 - 4776 * q^73 - 5652 * q^74 - 600 * q^76 - 648 * q^77 - 4104 * q^82 + 720 * q^85 + 9540 * q^86 + 1956 * q^88 + 7416 * q^92 - 1188 * q^94 + 588 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	1.38284	−	2.46734i	0.488908	−	0.872335i
$2$	1.38284	−	2.46734i	0.488908	−	0.872335i
$3$		0			0
$3$		0			0
$4$	−4.17551	−	6.82387i	−0.521938	−	0.852983i
$5$	−14.6499	+	8.45813i	−1.31033	+	0.756519i	−0.982150	−	0.188097i	$-0.939768\pi$
$5$	−14.6499	+	8.45813i	−1.31033	+	0.756519i	−0.328178	+	0.944616i	$0.606435\pi$
$6$		0			0
$7$	−3.08966	−	1.78382i	−0.166826	−	0.0963170i	0.414262	−	0.910157i	$-0.364040\pi$
$7$	−3.08966	−	1.78382i	−0.166826	−	0.0963170i	−0.581088	+	0.813841i	$0.697373\pi$
$8$	−22.6108	+	0.866066i	−0.999267	+	0.0382750i
$9$		0			0
$10$	0.610574	+	47.8425i	0.0193080	+	1.51291i
$11$	−25.0688	+	43.4205i	−0.687139	+	1.19016i	0.285620	+	0.958343i	$0.407801\pi$
$11$	−25.0688	+	43.4205i	−0.687139	+	1.19016i	−0.972759	+	0.231817i	$0.925533\pi$
$12$		0			0
$13$	−18.9966	−	32.9032i	−0.405286	−	0.701977i	0.589068	−	0.808083i	$-0.299495\pi$
$13$	−18.9966	−	32.9032i	−0.405286	−	0.701977i	−0.994355	+	0.106107i	$0.966162\pi$
$14$	−8.67378	+	5.15650i	−0.165583	+	0.0984380i
$15$		0			0
$16$	−29.1303	+	56.9862i	−0.455161	+	0.890409i
$17$		−	84.3819i		−	1.20386i	−0.798549	−	0.601930i	$-0.794399\pi$
$17$		−	84.3819i		−	1.20386i	0.798549	−	0.601930i	$-0.205601\pi$
$18$		0			0
$19$			62.9237i			0.759773i	0.925033	+	0.379887i	$0.124037\pi$
$19$			62.9237i			0.759773i	−0.925033	+	0.379887i	$0.875963\pi$
$20$	118.888	+	64.6521i	1.32921	+	0.722832i
$21$		0			0
$22$	72.4668	+	121.897i	0.702271	+	1.18129i
$23$	−37.6066	−	65.1366i	−0.340936	−	0.590518i	0.643671	−	0.765302i	$-0.277411\pi$
$23$	−37.6066	−	65.1366i	−0.340936	−	0.590518i	−0.984607	+	0.174784i	$0.944077\pi$
$24$		0			0
$25$	80.5801	−	139.569i	0.644641	−	1.11655i
$26$	−107.453	+	1.37133i	−0.810507	+	0.0103438i
$27$		0			0
$28$	0.728372	+	28.5317i	0.00491605	+	0.192571i
$29$	−105.644	−	60.9938i	−0.676471	−	0.390561i	0.122053	−	0.992524i	$-0.461052\pi$
$29$	−105.644	−	60.9938i	−0.676471	−	0.390561i	−0.798524	+	0.601963i	$0.794386\pi$
$30$		0			0
$31$	−17.2800	+	9.97659i	−0.100115	+	0.0578016i	−0.549222	−	0.835677i	$-0.685076\pi$
$31$	−17.2800	+	9.97659i	−0.100115	+	0.0578016i	0.449106	+	0.893478i	$0.351742\pi$
$32$	100.322	+	150.677i	0.554204	+	0.832381i
$33$		0			0
$34$	−208.199	−	116.687i	−1.05017	−	0.588577i
$35$	60.3510			0.291462
$36$		0			0
$37$	17.7622			0.0789211			0.0394606	−	0.999221i	$-0.487436\pi$
$37$	17.7622			0.0789211			0.0394606	+	0.999221i	$0.487436\pi$
$38$	155.254	+	87.0135i	0.662777	+	0.371459i
$39$		0			0
$40$	323.922	−	203.933i	1.28041	−	0.806117i
$41$	−299.072	+	172.670i	−1.13920	+	0.657718i	−0.946233	−	0.323486i	$-0.895145\pi$
$41$	−299.072	+	172.670i	−1.13920	+	0.657718i	−0.192969	+	0.981205i	$0.561812\pi$
$42$		0			0
$43$	113.206	+	65.3596i	0.401483	+	0.231796i	0.687124	−	0.726540i	$-0.258873\pi$
$43$	113.206	+	65.3596i	0.401483	+	0.231796i	−0.285641	+	0.958337i	$0.592206\pi$
$44$	400.970	−	10.2362i	1.37383	−	0.0350718i
$45$		0			0
$46$	−212.718	+	2.71474i	−0.681816	+	0.00870145i
$47$	153.083	−	265.147i	0.475094	−	0.822887i	−0.524499	−	0.851411i	$-0.675747\pi$
$47$	153.083	−	265.147i	0.475094	−	0.822887i	0.999593	+	0.0285243i	$0.00908080\pi$
$48$		0			0
$49$	−165.136	−	286.024i	−0.481446	−	0.833889i
$50$	−232.934	−	391.820i	−0.658837	−	1.10823i
$51$		0			0
$52$	−145.206	+	267.018i	−0.387240	+	0.712091i
$53$		−	479.464i		−	1.24263i	−0.783561	−	0.621315i	$-0.786599\pi$
$53$		−	479.464i		−	1.24263i	0.783561	−	0.621315i	$-0.213401\pi$
$54$		0			0
$55$		−	848.142i		−	2.07933i
$56$	71.4047	+	37.6577i	0.170390	+	0.0898611i
$57$		0			0
$58$	−296.581	+	176.316i	−0.671432	+	0.399161i
$59$	245.774	+	425.693i	0.542323	+	0.939330i	0.998770	+	0.0495801i	$0.0157883\pi$
$59$	245.774	+	425.693i	0.542323	+	0.939330i	−0.456447	+	0.889750i	$0.650878\pi$
$60$		0			0
$61$	−49.9168	+	86.4585i	−0.104774	+	0.181473i	−0.913646	−	0.406511i	$-0.866745\pi$
$61$	−49.9168	+	86.4585i	−0.104774	+	0.181473i	0.808872	+	0.587985i	$0.200079\pi$
$62$	0.720188	+	56.4315i	0.00147523	+	0.115594i
$63$		0			0
$64$	510.500	−	39.1649i	0.997070	−	0.0764940i
$65$	556.599	+	321.352i	1.06212	+	0.613213i
$66$		0			0
$67$	−536.669	+	309.846i	−0.978575	+	0.564980i	−0.901839	−	0.432071i	$-0.857783\pi$
$67$	−536.669	+	309.846i	−0.978575	+	0.564980i	−0.0767351	+	0.997052i	$0.524450\pi$
$68$	−575.811	+	352.337i	−1.02687	+	0.628341i
$69$		0			0
$70$	83.4558	−	148.906i	0.142498	−	0.254253i
$71$	−254.455			−0.425327			−0.212663	−	0.977125i	$-0.568214\pi$
$71$	−254.455			−0.425327			−0.212663	+	0.977125i	$0.568214\pi$
$72$		0			0
$73$	100.485			0.161108			0.0805541	−	0.996750i	$-0.474331\pi$
$73$	100.485			0.161108			0.0805541	+	0.996750i	$0.474331\pi$
$74$	24.5622	−	43.8253i	0.0385852	−	0.0688457i
$75$		0			0
$76$	429.383	−	262.738i	0.648074	−	0.396555i
$77$	154.908	−	89.4363i	0.229265	−	0.132366i
$78$		0			0
$79$	856.295	+	494.382i	1.21950	+	0.704080i	0.964812	−	0.262942i	$-0.0846928\pi$
$79$	856.295	+	494.382i	1.21950	+	0.704080i	0.254691	+	0.967022i	$0.418026\pi$
$80$	−55.2404	−	1081.23i	−0.0772008	−	1.51107i
$81$		0			0
$82$	12.4646	+	976.687i	0.0167864	+	1.31533i
$83$	−251.755	+	436.053i	−0.332936	+	0.576663i	−0.983086	−	0.183143i	$-0.941373\pi$
$83$	−251.755	+	436.053i	−0.332936	+	0.576663i	0.650150	+	0.759806i	$0.274706\pi$
$84$		0			0
$85$	713.714	+	1236.19i	0.910743	+	1.57745i
$86$	317.810	−	188.936i	0.398492	−	0.236901i
$87$		0			0
$88$	529.222	−	1003.48i	0.641082	−	1.21559i
$89$			1019.86i			1.21467i	0.794448	+	0.607333i	$0.207761\pi$
$89$			1019.86i			1.21467i	−0.794448	+	0.607333i	$0.792239\pi$
$90$		0			0
$91$			135.546i			0.156144i
$92$	−287.457	+	528.601i	−0.325755	+	0.599027i
$93$		0			0
$94$	−442.518	−	744.363i	−0.485556	−	0.816757i
$95$	−532.217	−	921.828i	−0.574783	−	0.995553i
$96$		0			0
$97$	−503.589	+	872.242i	−0.527131	+	0.913018i	0.472369	+	0.881401i	$0.343399\pi$
$97$	−503.589	+	872.242i	−0.527131	+	0.913018i	−0.999500	+	0.0316171i	$0.989934\pi$
$98$	−934.074	+	11.9208i	−0.962814	+	0.0122876i
$99$		0			0
$100$	−1288.86	+	32.9027i	−1.28886	+	0.0329027i
$101$	364.582	+	210.492i	0.359181	+	0.207373i	0.668721	−	0.743513i	$-0.266842\pi$
$101$	364.582	+	210.492i	0.359181	+	0.207373i	−0.309540	+	0.950886i	$0.600175\pi$
$102$		0			0
$103$	−1496.60	+	864.065i	−1.43170	+	0.826591i	−0.997250	−	0.0741066i	$-0.976389\pi$
$103$	−1496.60	+	864.065i	−1.43170	+	0.826591i	−0.434447	+	0.900697i	$0.643056\pi$
$104$	458.026	+	727.516i	0.431858	+	0.685950i
$105$		0			0
$106$	−1183.00	−	663.022i	−1.08399	−	0.607532i
$107$	−63.1607			−0.0570652			−0.0285326	−	0.999593i	$-0.509083\pi$
$107$	−63.1607			−0.0570652			−0.0285326	+	0.999593i	$0.509083\pi$
$108$		0			0
$109$	−835.373			−0.734076			−0.367038	−	0.930206i	$-0.619628\pi$
$109$	−835.373			−0.734076			−0.367038	+	0.930206i	$0.619628\pi$
$110$	−2092.65	−	1172.84i	−1.81388	−	1.01660i
$111$		0			0
$112$	191.656	−	124.105i	0.161694	−	0.104704i
$113$	891.915	−	514.947i	0.742516	−	0.428692i	−0.0804674	−	0.996757i	$-0.525641\pi$
$113$	891.915	−	514.947i	0.742516	−	0.428692i	0.822983	+	0.568065i	$0.192308\pi$
$114$		0			0
$115$	1101.87	+	636.164i	0.893476	+	0.515849i
$116$	24.9051	+	975.583i	0.0199343	+	0.780867i
$117$		0			0
$118$	1390.19	−	17.7419i	1.08456	−	0.0138413i
$119$	−150.522	+	260.711i	−0.115952	+	0.200835i
$120$		0			0
$121$	−591.391	−	1024.32i	−0.444321	−	0.769587i
$122$	144.295	+	242.720i	0.107081	+	0.180122i
$123$		0			0
$124$	140.231	+	76.2588i	0.101558	+	0.0552278i
$125$			611.695i			0.437693i
$126$		0			0
$127$		−	794.523i		−	0.555138i	−0.960706	−	0.277569i	$-0.910471\pi$
$127$		−	794.523i		−	0.555138i	0.960706	−	0.277569i	$-0.0895287\pi$
$128$	609.307	−	1313.73i	0.420747	−	0.907178i
$129$		0			0
$130$	1562.57	−	928.938i	1.05420	−	0.626717i
$131$	111.039	+	192.325i	0.0740575	+	0.128271i	0.900676	−	0.434491i	$-0.143072\pi$
$131$	111.039	+	192.325i	0.0740575	+	0.128271i	−0.826619	+	0.562763i	$0.809738\pi$
$132$		0			0
$133$	112.244	−	194.413i	0.0731791	−	0.126750i
$134$	22.3671	+	1752.61i	0.0144196	+	1.12987i
$135$		0			0
$136$	73.0803	+	1907.95i	0.0460778	+	1.20298i
$137$	−1054.28	−	608.690i	−0.657470	−	0.379591i	0.133842	−	0.991003i	$-0.457268\pi$
$137$	−1054.28	−	608.690i	−0.657470	−	0.379591i	−0.791312	+	0.611412i	$0.790602\pi$
$138$		0			0
$139$	1909.09	−	1102.21i	1.16494	−	0.672578i	0.212457	−	0.977170i	$-0.431854\pi$
$139$	1909.09	−	1102.21i	1.16494	−	0.672578i	0.952483	+	0.304592i	$0.0985202\pi$
$140$	−251.996	−	411.827i	−0.152125	−	0.248612i
$141$		0			0
$142$	−351.870	+	627.826i	−0.207946	+	0.371028i
$143$	1904.89			1.11395
$144$		0			0
$145$	2063.57			1.18187
$146$	138.955	−	247.931i	0.0787671	−	0.140540i
$147$		0			0
$148$	−74.1660	−	121.207i	−0.0411920	−	0.0673184i
$149$	352.120	−	203.297i	0.193603	−	0.111777i	−0.400065	−	0.916487i	$-0.631013\pi$
$149$	352.120	−	203.297i	0.193603	−	0.111777i	0.593668	+	0.804710i	$0.297679\pi$
$150$		0			0
$151$	−2990.17	−	1726.37i	−1.61150	−	0.930399i	−0.989023	−	0.147759i	$-0.952794\pi$
$151$	−2990.17	−	1726.37i	−1.61150	−	0.930399i	−0.622475	−	0.782640i	$-0.713873\pi$
$152$	−54.4961	−	1422.76i	−0.0290804	−	0.759217i
$153$		0			0
$154$	−6.45621	−	505.887i	−0.00337829	−	0.264711i
$155$	168.767	−	292.312i	0.0874559	−	0.151478i
$156$		0			0
$157$	440.287	+	762.599i	0.223813	+	0.387656i	0.955963	−	0.293488i	$-0.0948160\pi$
$157$	440.287	+	762.599i	0.223813	+	0.387656i	−0.732149	+	0.681144i	$0.761483\pi$
$158$	2403.93	−	1429.12i	1.21042	−	0.719585i
$159$		0			0
$160$	−2744.15	−	1358.87i	−1.35590	−	0.671427i
$161$			268.333i			0.131352i
$162$		0			0
$163$		−	1693.56i		−	0.813802i	−0.913472	−	0.406901i	$-0.866609\pi$
$163$		−	1693.56i		−	0.813802i	0.913472	−	0.406901i	$-0.133391\pi$
$164$	2427.05	+	1319.85i	1.15562	+	0.628432i
$165$		0			0
$166$	727.752	+	1224.16i	0.340268	+	0.572367i
$167$	820.051	+	1420.37i	0.379985	+	0.658153i	0.991060	−	0.133420i	$-0.0425959\pi$
$167$	820.051	+	1420.37i	0.379985	+	0.658153i	−0.611075	+	0.791573i	$0.709263\pi$
$168$		0			0
$169$	376.755	−	652.558i	0.171486	−	0.297022i
$170$	4037.05	−	51.5214i	1.82134	−	0.0232442i
$171$		0			0
$172$	−26.6878	−	1045.41i	−0.0118310	−	0.463442i
$173$	−1889.17	−	1090.71i	−0.830234	−	0.479336i	0.0236985	−	0.999719i	$-0.492456\pi$
$173$	−1889.17	−	1090.71i	−0.830234	−	0.479336i	−0.853933	+	0.520383i	$0.825789\pi$
$174$		0			0
$175$	−497.930	+	287.480i	−0.215085	+	0.124180i
$176$	−1744.10	−	2693.43i	−0.746971	−	1.15355i
$177$		0			0
$178$	2516.35	+	1410.31i	1.05960	+	0.593859i
$179$	−2350.24			−0.981370			−0.490685	−	0.871337i	$-0.663253\pi$
$179$	−2350.24			−0.981370			−0.490685	+	0.871337i	$0.663253\pi$
$180$		0			0
$181$	−2280.14			−0.936362			−0.468181	−	0.883633i	$-0.655090\pi$
$181$	−2280.14			−0.936362			−0.468181	+	0.883633i	$0.655090\pi$
$182$	334.438	+	187.439i	0.136210	+	0.0763399i
$183$		0			0
$184$	906.730	+	1440.22i	0.363288	+	0.577036i
$185$	−260.214	+	150.235i	−0.103413	+	0.0597053i
$186$		0			0
$187$	3663.90	+	2115.36i	1.43279	+	0.827220i
$188$	−2448.53	+	62.5071i	−0.949878	+	0.0242489i
$189$		0			0
$190$	−3010.43	+	38.4196i	−1.14947	+	0.0146697i
$191$	1966.48	−	3406.04i	0.744970	−	1.29033i	−0.205239	−	0.978712i	$-0.565797\pi$
$191$	1966.48	−	3406.04i	0.744970	−	1.29033i	0.950209	−	0.311614i	$-0.100870\pi$
$192$		0			0
$193$	−1356.60	−	2349.69i	−0.505958	−	0.876346i	−0.999976	−	0.00689392i	$-0.997806\pi$
$193$	−1356.60	−	2349.69i	−0.505958	−	0.876346i	0.494018	−	0.869452i	$-0.335528\pi$
$194$	1455.73	+	2448.70i	0.538739	+	0.906217i
$195$		0			0
$196$	−1262.26	+	2321.16i	−0.460008	+	0.845904i
$197$		−	1997.91i		−	0.722565i	−0.932456	−	0.361282i	$-0.882339\pi$
$197$		−	1997.91i		−	0.722565i	0.932456	−	0.361282i	$-0.117661\pi$
$198$		0			0
$199$			2409.09i			0.858170i	0.903264	+	0.429085i	$0.141164\pi$
$199$			2409.09i			0.858170i	−0.903264	+	0.429085i	$0.858836\pi$
$200$	−1701.11	+	3225.55i	−0.601432	+	1.14041i
$201$		0			0
$202$	1023.51	−	608.471i	0.356505	−	0.211940i
$203$	217.603	+	376.900i	0.0752353	+	0.130311i
$204$		0			0
$205$	2920.92	−	5059.19i	0.995152	−	1.72365i
$206$	62.3750	+	4887.49i	0.0210965	+	1.65305i
$207$		0			0
$208$	2428.40	−	124.068i	0.809517	−	0.0413584i
$209$	−2732.18	−	1577.42i	−0.904252	−	0.522070i
$210$		0			0
$211$	−1575.68	+	909.717i	−0.514095	+	0.296813i	−0.734515	−	0.678592i	$-0.762590\pi$
$211$	−1575.68	+	909.717i	−0.514095	+	0.296813i	0.220420	+	0.975405i	$0.429257\pi$
$212$	−3271.80	+	2002.00i	−1.05994	+	0.648577i
$213$		0			0
$214$	−87.3411	+	155.839i	−0.0278996	+	0.0497800i
$215$	−2211.28			−0.701433
$216$		0			0
$217$	71.1856			0.0222691
$218$	−1155.19	+	2061.15i	−0.358895	+	0.640360i
$219$		0			0
$220$	−5787.61	+	3541.42i	−1.77364	+	1.08528i
$221$	−2776.43	+	1602.97i	−0.845082	+	0.487908i
$222$		0			0
$223$	−2316.13	−	1337.22i	−0.695514	−	0.401555i	0.110160	−	0.993914i	$-0.464864\pi$
$223$	−2316.13	−	1337.22i	−0.695514	−	0.401555i	−0.805674	+	0.592359i	$0.798197\pi$
$224$	−41.1795	−	644.496i	−0.0122831	−	0.192242i
$225$		0			0
$226$	−37.1729	−	2912.74i	−0.0109412	−	0.857314i
$227$	−2949.58	+	5108.82i	−0.862425	+	1.49376i	0.00715576	+	0.999974i	$0.497722\pi$
$227$	−2949.58	+	5108.82i	−0.862425	+	1.49376i	−0.869581	+	0.493790i	$0.835611\pi$
$228$		0			0
$229$	−1516.38	−	2626.44i	−0.437576	−	0.757904i	0.559926	−	0.828543i	$-0.310830\pi$
$229$	−1516.38	−	2626.44i	−0.437576	−	0.757904i	−0.997502	+	0.0706386i	$0.977496\pi$
$230$	3093.34	−	1838.97i	0.886821	−	0.527208i
$231$		0			0
$232$	2441.53	+	1287.63i	0.690924	+	0.364383i
$233$		−	1294.13i		−	0.363867i	−0.983311	−	0.181934i	$-0.941764\pi$
$233$		−	1294.13i		−	0.363867i	0.983311	−	0.181934i	$-0.0582356\pi$
$234$		0			0
$235$			5179.18i			1.43767i
$236$	1878.64	−	3454.61i	0.518174	−	0.952865i
$237$		0			0
$238$	435.115	+	731.910i	0.118506	+	0.199339i
$239$	−2875.14	−	4979.89i	−0.778149	−	1.34779i	−0.933008	−	0.359856i	$-0.882826\pi$
$239$	−2875.14	−	4979.89i	−0.778149	−	1.34779i	0.154859	−	0.987937i	$-0.450508\pi$
$240$		0			0
$241$	−3008.82	+	5211.43i	−0.804212	+	1.39294i	0.112611	+	0.993639i	$0.464079\pi$
$241$	−3008.82	+	5211.43i	−0.804212	+	1.39294i	−0.916822	+	0.399296i	$0.869255\pi$
$242$	−3345.14	+	42.6912i	−0.888570	+	0.0113401i
$243$		0			0
$244$	798.409	−	20.3822i	0.209479	−	0.00534769i
$245$	4838.46	+	2793.49i	1.26171	+	0.728446i
$246$		0			0
$247$	2070.39	−	1195.34i	0.533343	−	0.307926i
$248$	382.074	−	240.545i	0.0978295	−	0.0615911i
$249$		0			0
$250$	1509.26	+	845.876i	0.381815	+	0.213992i
$251$	3207.28			0.806541			0.403270	−	0.915081i	$-0.367873\pi$
$251$	3207.28			0.806541			0.403270	+	0.915081i	$0.367873\pi$
$252$		0			0
$253$	3771.02			0.937082
$254$	−1960.36	−	1098.70i	−0.484266	−	0.271411i
$255$		0			0
$256$	−2398.85	−	3320.05i	−0.585657	−	0.810559i
$257$	2518.27	−	1453.92i	0.611226	−	0.352892i	−0.162219	−	0.986755i	$-0.551865\pi$
$257$	2518.27	−	1453.92i	0.611226	−	0.352892i	0.773445	+	0.633863i	$0.218532\pi$
$258$		0			0
$259$	−54.8790	−	31.6844i	−0.0131661	−	0.00760144i
$260$	−131.215	−	5139.96i	−0.0312986	−	1.22603i
$261$		0			0
$262$	628.081	−	8.01567i	0.148103	−	0.00189011i
$263$	156.053	−	270.292i	0.0365880	−	0.0633723i	−0.847152	−	0.531351i	$-0.821684\pi$
$263$	156.053	−	270.292i	0.0365880	−	0.0633723i	0.883740	+	0.467979i	$0.155018\pi$
$264$		0			0
$265$	4055.37	+	7024.11i	0.940073	+	1.62825i
$266$	−324.466	−	545.787i	−0.0747906	−	0.125806i
$267$		0			0
$268$	4355.21	+	2368.39i	0.992674	+	0.539823i
$269$			1826.27i			0.413939i	0.978347	+	0.206969i	$0.0663600\pi$
$269$			1826.27i			0.413939i	−0.978347	+	0.206969i	$0.933640\pi$
$270$		0			0
$271$		−	4987.26i		−	1.11791i	−0.829197	−	0.558956i	$-0.811202\pi$
$271$		−	4987.26i		−	1.11791i	0.829197	−	0.558956i	$-0.188798\pi$
$272$	4808.60	+	2458.07i	1.07193	+	0.547950i
$273$		0			0
$274$	−2959.75	+	1759.55i	−0.652573	+	0.387950i
$275$	4040.09	+	6997.65i	0.885916	+	1.53445i
$276$		0			0
$277$	−2125.92	+	3682.20i	−0.461134	+	0.798708i	−0.999018	−	0.0443112i	$-0.985891\pi$
$277$	−2125.92	+	3682.20i	−0.461134	+	0.798708i	0.537884	+	0.843019i	$0.319224\pi$
$278$	−79.5662	−	6234.54i	−0.0171657	−	1.34505i
$279$		0			0
$280$	−1364.59	+	52.2679i	−0.291249	+	0.0111557i
$281$	2541.67	+	1467.43i	0.539585	+	0.311529i	0.744911	−	0.667164i	$-0.232492\pi$
$281$	2541.67	+	1467.43i	0.539585	+	0.311529i	−0.205326	+	0.978694i	$0.565825\pi$
$282$		0			0
$283$	3467.24	−	2001.81i	0.728289	−	0.420478i	−0.0895066	−	0.995986i	$-0.528529\pi$
$283$	3467.24	−	2001.81i	0.728289	−	0.420478i	0.817796	+	0.575508i	$0.195196\pi$
$284$	1062.48	+	1736.36i	0.221994	+	0.362797i
$285$		0			0
$286$	2634.16	−	4700.02i	0.544620	−	0.971741i
$287$	1232.04			0.253398
$288$		0			0
$289$	−2207.31			−0.449280
$290$	2853.59	−	5091.53i	0.577823	−	1.03098i
$291$		0			0
$292$	−419.576	−	685.697i	−0.0840886	−	0.137423i
$293$	−2334.26	+	1347.69i	−0.465423	+	0.268712i	−0.714322	−	0.699817i	$-0.753265\pi$
$293$	−2334.26	+	1347.69i	−0.465423	+	0.268712i	0.248899	+	0.968530i	$0.419931\pi$
$294$		0			0
$295$	−7201.14	−	4157.58i	−1.42124	−	0.820554i
$296$	−401.617	+	15.3832i	−0.0788633	+	0.00302071i
$297$		0			0
$298$	−14.6755	−	1149.93i	−0.00285279	−	0.223535i
$299$	−1428.80	+	2474.75i	−0.276353	+	0.478658i
$300$		0			0
$301$	−233.179	−	403.878i	−0.0446518	−	0.0773393i
$302$	−8394.46	+	4990.45i	−1.59949	+	0.950888i
$303$		0			0
$304$	−3585.78	−	1832.99i	−0.676509	−	0.345819i
$305$		−	1688.81i		−	0.317053i
$306$		0			0
$307$			4575.16i			0.850547i	0.905065	+	0.425274i	$0.139822\pi$
$307$			4575.16i			0.850547i	−0.905065	+	0.425274i	$0.860178\pi$
$308$	−1257.12	−	683.631i	−0.232569	−	0.126472i
$309$		0			0
$310$	−487.856	−	820.626i	−0.0893818	−	0.150350i
$311$	−4119.46	−	7135.11i	−0.751103	−	1.30095i	−0.947289	−	0.320381i	$-0.896189\pi$
$311$	−4119.46	−	7135.11i	−0.751103	−	1.30095i	0.196186	−	0.980567i	$-0.437144\pi$
$312$		0			0
$313$	2659.91	−	4607.09i	0.480341	−	0.831975i	−0.519405	−	0.854528i	$-0.673846\pi$
$313$	2659.91	−	4607.09i	0.480341	−	0.831975i	0.999746	+	0.0225534i	$0.00717958\pi$
$314$	2490.44	−	31.7833i	0.447591	−	0.00571222i
$315$		0			0
$316$	−201.867	−	7907.54i	−0.0359365	−	1.40770i
$317$	7641.35	+	4411.73i	1.35388	+	0.781665i	0.988791	−	0.149307i	$-0.0477042\pi$
$317$	7641.35	+	4411.73i	1.35388	+	0.781665i	0.365092	+	0.930971i	$0.381038\pi$
$318$		0			0
$319$	5296.76	−	3058.08i	0.929660	−	0.536739i
$320$	−7147.52	+	4891.64i	−1.24862	+	0.854534i
$321$		0			0
$322$	662.068	+	371.062i	0.114583	+	0.0642189i
$323$	5309.63			0.914661
$324$		0			0
$325$	−6123.01			−1.04506
$326$	−4178.58	−	2341.92i	−0.709908	−	0.397874i
$327$		0			0
$328$	6612.74	−	4163.22i	1.11319	−	0.700840i
$329$	−945.947	+	546.143i	−0.158516	+	0.0915192i
$330$		0			0
$331$	−2056.23	−	1187.17i	−0.341452	−	0.197138i	0.319462	−	0.947599i	$-0.396498\pi$
$331$	−2056.23	−	1187.17i	−0.341452	−	0.197138i	−0.660914	+	0.750462i	$0.729831\pi$
$332$	4026.77	−	102.797i	0.665656	−	0.0169932i
$333$		0			0
$334$	4638.53	−	59.1977i	0.759908	−	0.00969806i
$335$	5241.43	−	9078.43i	0.854836	−	1.48062i
$336$		0			0
$337$	321.888	+	557.527i	0.0520308	+	0.0901199i	0.890868	−	0.454263i	$-0.150097\pi$
$337$	321.888	+	557.527i	0.0520308	+	0.0901199i	−0.838837	+	0.544383i	$0.816764\pi$
$338$	−1089.09	−	1831.96i	−0.175262	−	0.294810i
$339$		0			0
$340$	5455.47	−	10032.0i	0.870189	−	1.60018i
$341$		−	1000.41i		−	0.158871i
$342$		0			0
$343$			2401.99i			0.378120i
$344$	−2616.29	−	1379.79i	−0.410061	−	0.216260i
$345$		0			0
$346$	−5303.56	+	3152.93i	−0.824050	+	0.489892i
$347$	768.265	+	1330.67i	0.118855	+	0.205863i	0.919314	−	0.393525i	$-0.128744\pi$
$347$	768.265	+	1330.67i	0.118855	+	0.205863i	−0.800459	+	0.599387i	$0.795411\pi$
$348$		0			0
$349$	−3432.65	+	5945.53i	−0.526492	+	0.911910i	0.473032	+	0.881045i	$0.343160\pi$
$349$	−3432.65	+	5945.53i	−0.526492	+	0.911910i	−0.999524	+	0.0308650i	$0.990174\pi$
$350$	20.7525	+	1626.10i	0.00316934	+	0.248339i
$351$		0			0
$352$	−9057.41	+	578.715i	−1.37148	+	0.0876296i
$353$	−107.968	−	62.3355i	−0.0162792	−	0.00939881i	0.491838	−	0.870687i	$-0.336325\pi$
$353$	−107.968	−	62.3355i	−0.0162792	−	0.00939881i	−0.508118	+	0.861288i	$0.669658\pi$
$354$		0			0
$355$	3727.74	−	2152.21i	0.557318	−	0.321768i
$356$	6959.41	−	4258.44i	1.03609	−	0.633980i
$357$		0			0
$358$	−3250.01	+	5798.84i	−0.479799	+	0.856084i
$359$	−4489.49			−0.660017			−0.330009	−	0.943978i	$-0.607052\pi$
$359$	−4489.49			−0.660017			−0.330009	+	0.943978i	$0.607052\pi$
$360$		0			0
$361$	2899.60			0.422744
$362$	−3153.07	+	5625.87i	−0.457794	+	0.816821i
$363$		0			0
$364$	924.948	−	565.973i	0.133188	−	0.0814974i
$365$	−1472.10	+	849.917i	−0.211105	+	0.121881i
$366$		0			0
$367$	−750.997	−	433.589i	−0.106817	−	0.0616707i	0.445640	−	0.895212i	$-0.352976\pi$
$367$	−750.997	−	433.589i	−0.106817	−	0.0616707i	−0.552457	+	0.833542i	$0.686310\pi$
$368$	4807.38	−	245.610i	0.680984	−	0.0347916i
$369$		0			0
$370$	10.8451	+	849.787i	0.00152381	+	0.119401i
$371$	−855.275	+	1481.38i	−0.119686	+	0.207303i
$372$		0			0
$373$	2169.58	+	3757.82i	0.301170	+	0.521642i	0.976401	−	0.215964i	$-0.0692895\pi$
$373$	2169.58	+	3757.82i	0.301170	+	0.521642i	−0.675231	+	0.737606i	$0.735956\pi$
$374$	10285.9	−	6114.89i	1.42211	−	0.845436i
$375$		0			0
$376$	−3231.69	+	6127.78i	−0.443250	+	0.840468i
$377$			4634.71i			0.633156i
$378$		0			0
$379$			14096.9i			1.91058i	0.295677	+	0.955288i	$0.404455\pi$
$379$			14096.9i			1.91058i	−0.295677	+	0.955288i	$0.595545\pi$
$380$	−4068.15	+	7480.88i	−0.549189	+	1.00990i
$381$		0			0
$382$	−5684.52	−	9561.97i	−0.761375	−	1.28071i
$383$	4134.45	+	7161.08i	0.551594	+	0.955390i	0.998160	+	0.0606386i	$0.0193137\pi$
$383$	4134.45	+	7161.08i	0.551594	+	0.955390i	−0.446565	+	0.894751i	$0.647353\pi$
$384$		0			0
$385$	−1512.93	+	2620.47i	−0.200275	+	0.346887i
$386$	−7673.45	+	97.9297i	−1.01183	+	0.0129132i
$387$		0			0
$388$	8054.80	−	205.627i	1.05392	−	0.0269050i
$389$	−4972.96	−	2871.14i	−0.648173	−	0.374223i	0.139583	−	0.990210i	$-0.455424\pi$
$389$	−4972.96	−	2871.14i	−0.648173	−	0.374223i	−0.787756	+	0.615987i	$0.788757\pi$
$390$		0			0
$391$	−5496.35	+	3173.32i	−0.710902	+	0.410439i
$392$	3981.58	+	6324.22i	0.513010	+	0.814851i
$393$		0			0
$394$	−4929.52	−	2762.79i	−0.630319	−	0.353267i
$395$	−16726.2			−2.13060
$396$		0			0
$397$	10494.4			1.32670			0.663349	−	0.748310i	$-0.269134\pi$
$397$	10494.4			1.32670			0.663349	+	0.748310i	$0.269134\pi$
$398$	5944.04	+	3331.39i	0.748612	+	0.419566i
$399$		0			0
$400$	5606.17	+	8657.63i	0.700771	+	1.08220i
$401$	7070.19	−	4081.97i	0.880469	−	0.508339i	0.00965631	−	0.999953i	$-0.496926\pi$
$401$	7070.19	−	4081.97i	0.880469	−	0.508339i	0.870813	+	0.491614i	$0.163593\pi$
$402$		0			0
$403$	656.523	+	379.044i	0.0811507	+	0.0468524i
$404$	−85.9485	−	3366.77i	−0.0105844	−	0.414611i
$405$		0			0
$406$	1230.85	−	15.7083i	0.150458	−	0.00192017i
$407$	−445.277	+	771.242i	−0.0542298	+	0.0939288i
$408$		0			0
$409$	−2037.43	−	3528.93i	−0.246319	−	0.426637i	0.716183	−	0.697913i	$-0.245888\pi$
$409$	−2037.43	−	3528.93i	−0.246319	−	0.426637i	−0.962502	+	0.271276i	$0.912554\pi$
$410$	−8443.56	−	14203.0i	−1.01707	−	1.71081i
$411$		0			0
$412$	12145.3	+	6604.72i	1.45233	+	0.789784i
$413$		−	1753.66i		−	0.208940i
$414$		0			0
$415$		−	8517.52i		−	1.00749i
$416$	3051.98	−	6163.26i	0.359701	−	0.726391i
$417$		0			0
$418$	−7670.20	+	4559.88i	−0.897516	+	0.533567i
$419$	−346.536	−	600.219i	−0.0404043	−	0.0699823i	0.845116	−	0.534583i	$-0.179531\pi$
$419$	−346.536	−	600.219i	−0.0404043	−	0.0699823i	−0.885520	+	0.464601i	$0.846198\pi$
$420$		0			0
$421$	5362.68	−	9288.44i	0.620810	−	1.07527i	−0.368525	−	0.929618i	$-0.620137\pi$
$421$	5362.68	−	9288.44i	0.620810	−	1.07527i	0.989335	−	0.145657i	$-0.0465296\pi$
$422$	65.6705	+	5145.72i	0.00757533	+	0.593577i
$423$		0			0
$424$	415.247	+	10841.1i	0.0475618	+	1.24172i
$425$	−11777.1	−	6799.50i	−1.34417	−	0.776057i
$426$		0			0
$427$	308.452	−	178.085i	0.0349579	−	0.0201830i
$428$	263.728	+	431.000i	0.0297845	+	0.0486756i
$429$		0			0
$430$	−3057.85	+	5455.98i	−0.342936	+	0.611885i
$431$	10013.8			1.11914			0.559569	−	0.828784i	$-0.310967\pi$
$431$	10013.8			1.11914			0.559569	+	0.828784i	$0.310967\pi$
$432$		0			0
$433$	−9726.02			−1.07945			−0.539726	−	0.841841i	$-0.681472\pi$
$433$	−9726.02			−1.07945			−0.539726	+	0.841841i	$0.681472\pi$
$434$	98.4383	−	175.639i	0.0108875	−	0.0194261i
$435$		0			0
$436$	3488.11	+	5700.47i	0.383142	+	0.626154i
$437$	4098.64	−	2366.35i	0.448660	−	0.259034i
$438$		0			0
$439$	5675.95	+	3277.01i	0.617080	+	0.356271i	0.775731	−	0.631063i	$-0.217381\pi$
$439$	5675.95	+	3277.01i	0.617080	+	0.356271i	−0.158651	+	0.987335i	$0.550715\pi$
$440$	734.546	+	19177.2i	0.0795866	+	2.07781i
$441$		0			0
$442$	115.715	+	9067.05i	0.0124525	+	0.975737i
$443$	−2939.61	+	5091.55i	−0.315271	+	0.546065i	−0.979495	−	0.201468i	$-0.935429\pi$
$443$	−2939.61	+	5091.55i	−0.315271	+	0.546065i	0.664224	+	0.747533i	$0.268762\pi$
$444$		0			0
$445$	−8626.14	−	14940.9i	−0.918917	−	1.59161i
$446$	−6502.21	+	3865.52i	−0.690333	+	0.410398i
$447$		0			0
$448$	−1647.13	−	789.631i	−0.173705	−	0.0832736i
$449$			6761.00i			0.710627i	0.934747	+	0.355313i	$0.115626\pi$
$449$			6761.00i			0.710627i	−0.934747	+	0.355313i	$0.884374\pi$
$450$		0			0
$451$		−	17314.5i		−	1.80778i
$452$	−7238.13	−	3936.14i	−0.753214	−	0.409603i
$453$		0			0
$454$	8526.39	+	14342.3i	0.881417	+	1.48264i
$455$	−1146.47	−	1985.74i	−0.118126	−	0.204600i
$456$		0			0
$457$	7620.16	−	13198.5i	0.779992	−	1.35099i	−0.151954	−	0.988388i	$-0.548557\pi$
$457$	7620.16	−	13198.5i	0.779992	−	1.35099i	0.931946	−	0.362598i	$-0.118110\pi$
$458$	−8577.22	+	109.464i	−0.875081	+	0.0111679i
$459$		0			0
$460$	−259.760	−	10175.3i	−0.0263291	−	1.03136i
$461$	−11900.4	−	6870.68i	−1.20229	−	0.694142i	−0.241226	−	0.970469i	$-0.577550\pi$
$461$	−11900.4	−	6870.68i	−1.20229	−	0.694142i	−0.961064	+	0.276327i	$0.910883\pi$
$462$		0			0
$463$	−15291.7	+	8828.66i	−1.53491	+	0.886183i	−0.535789	+	0.844352i	$0.679986\pi$
$463$	−15291.7	+	8828.66i	−1.53491	+	0.886183i	−0.999125	+	0.0418305i	$0.986681\pi$
$464$	6553.25	−	4243.50i	0.655662	−	0.424568i
$465$		0			0
$466$	−3193.05	−	1789.57i	−0.317414	−	0.177898i
$467$	6165.12			0.610895			0.305447	−	0.952209i	$-0.401194\pi$
$467$	6165.12			0.610895			0.305447	+	0.952209i	$0.401194\pi$
$468$		0			0
$469$	2210.83			0.217669
$470$	12778.8	+	7161.97i	1.25413	+	0.702888i
$471$		0			0
$472$	−5925.83	−	9412.42i	−0.577878	−	0.917885i
$473$	−5675.89	+	3276.98i	−0.551750	+	0.318553i
$474$		0			0
$475$	8782.19	+	5070.40i	0.848325	+	0.489781i
$476$	2407.56	−	61.4614i	0.231829	−	0.00591824i
$477$		0			0
$478$	−16262.9	+	207.550i	−1.55617	+	0.0198601i
$479$	−8659.06	+	14997.9i	−0.825976	+	1.43063i	0.0751944	+	0.997169i	$0.476042\pi$
$479$	−8659.06	+	14997.9i	−0.825976	+	1.43063i	−0.901171	+	0.433464i	$0.857291\pi$
$480$		0			0
$481$	−337.422	−	584.431i	−0.0319857	−	0.0554008i
$482$	8697.63	+	14630.3i	0.821921	+	1.38256i
$483$		0			0
$484$	−4520.46	+	8312.63i	−0.424536	+	0.780675i
$485$		−	17037.7i		−	1.59514i
$486$		0			0
$487$			7352.14i			0.684101i	0.939682	+	0.342050i	$0.111121\pi$
$487$			7352.14i			0.684101i	−0.939682	+	0.342050i	$0.888879\pi$
$488$	1053.78	−	1998.13i	0.0977510	−	0.185351i
$489$		0			0
$490$	13583.3	−	8075.16i	1.25231	−	0.744487i
$491$	−4221.27	−	7311.46i	−0.387991	−	0.672019i	0.604189	−	0.796841i	$-0.293497\pi$
$491$	−4221.27	−	7311.46i	−0.387991	−	0.672019i	−0.992179	+	0.124822i	$0.960164\pi$
$492$		0			0
$493$	−5146.77	+	8914.47i	−0.470181	+	0.814377i
$494$	−86.2890	−	6761.31i	−0.00785896	−	0.615801i
$495$		0			0
$496$	−65.1574	−	1275.34i	−0.00589850	−	0.115453i
$497$	786.178	+	453.900i	0.0709555	+	0.0409662i
$498$		0			0
$499$	6542.34	−	3777.22i	0.586924	−	0.338861i	−0.176956	−	0.984219i	$-0.556625\pi$
$499$	6542.34	−	3777.22i	0.586924	−	0.338861i	0.763880	+	0.645358i	$0.223292\pi$
$500$	4174.12	−	2554.14i	0.373345	−	0.228449i
$501$		0			0
$502$	4435.16	−	7913.44i	0.394324	−	0.703574i
$503$	604.632			0.0535968			0.0267984	−	0.999641i	$-0.491469\pi$
$503$	604.632			0.0535968			0.0267984	+	0.999641i	$0.491469\pi$
$504$		0			0
$505$	−7121.47			−0.627527
$506$	5214.71	−	9304.37i	0.458147	−	0.817450i
$507$		0			0
$508$	−5421.72	+	3317.54i	−0.473523	+	0.289748i
$509$	−8861.66	+	5116.28i	−0.771682	+	0.445531i	−0.833474	−	0.552558i	$-0.813652\pi$
$509$	−8861.66	+	5116.28i	−0.771682	+	0.445531i	0.0617925	+	0.998089i	$0.480318\pi$
$510$		0			0
$511$	−310.465	−	179.247i	−0.0268770	−	0.0155175i
$512$	−11508.9	+	1327.68i	−0.993412	+	0.114601i
$513$		0			0
$514$	−104.955	−	8223.96i	−0.00900659	−	0.705726i
$515$	14616.8	−	25317.0i	1.25066	−	2.16621i
$516$		0			0
$517$	7675.21	+	13293.8i	0.652911	+	1.13088i
$518$	−154.065	+	91.5906i	−0.0130680	+	0.00776884i
$519$		0			0
$520$	−12863.5	−	6784.00i	−1.08481	−	0.572111i
$521$			18465.3i			1.55274i	0.630276	+	0.776371i	$0.282942\pi$
$521$			18465.3i			1.55274i	−0.630276	+	0.776371i	$0.717058\pi$
$522$		0			0
$523$		−	15941.5i		−	1.33284i	−0.745579	−	0.666418i	$-0.767827\pi$
$523$		−	15941.5i		−	1.33284i	0.745579	−	0.666418i	$-0.232173\pi$
$524$	848.759	−	1560.77i	0.0707599	−	0.130120i
$525$		0			0
$526$	−451.105	−	758.807i	−0.0373938	−	0.0629003i
$527$	841.844	+	1458.12i	0.0695850	+	0.120525i
$528$		0			0
$529$	3254.98	−	5637.79i	0.267525	−	0.463368i
$530$	22938.8	−	292.748i	1.87999	−	0.0239928i
$531$		0			0
$532$	−1795.32	+	45.8319i	−0.146310	+	0.00373508i
$533$	11362.7	+	6560.29i	0.923406	+	0.533129i
$534$		0			0
$535$	925.299	−	534.221i	0.0747741	−	0.0431709i
$536$	11866.2	−	7470.66i	0.956233	−	0.602021i
$537$		0			0
$538$	4506.02	+	2525.44i	0.361093	+	0.202378i
$539$	16559.1			1.32328
$540$		0			0
$541$	7256.04			0.576638			0.288319	−	0.957534i	$-0.406904\pi$
$541$	7256.04			0.576638			0.288319	+	0.957534i	$0.406904\pi$
$542$	−12305.2	−	6896.58i	−0.975195	−	0.546556i
$543$		0			0
$544$	12714.4	−	8465.33i	1.00207	−	0.667184i
$545$	12238.1	−	7065.70i	0.961880	−	0.555342i
$546$		0			0
$547$	−374.999	−	216.506i	−0.0293122	−	0.0169234i	0.485272	−	0.874363i	$-0.338720\pi$
$547$	−374.999	−	216.506i	−0.0293122	−	0.0169234i	−0.514585	+	0.857440i	$0.672054\pi$
$548$	248.542	+	9735.87i	0.0193744	+	0.758934i
$549$		0			0
$550$	22852.4	−	291.646i	1.77169	−	0.0226106i
$551$	3837.96	−	6647.54i	0.296738	−	0.513965i
$552$		0			0
$553$	−1763.77	−	3054.94i	−0.135630	−	0.234918i
$554$	6145.43	+	10337.3i	0.471289	+	0.792758i
$555$		0			0
$556$	−15492.7	−	8425.06i	−1.18172	−	0.642630i
$557$		−	9185.88i		−	0.698776i	−0.936978	−	0.349388i	$-0.886390\pi$
$557$		−	9185.88i		−	0.698776i	0.936978	−	0.349388i	$-0.113610\pi$
$558$		0			0
$559$		−	4966.45i		−	0.375776i
$560$	−1758.04	+	3439.17i	−0.132662	+	0.259521i
$561$		0			0
$562$	7135.38	−	4241.93i	0.535565	−	0.318390i
$563$	−6499.11	−	11256.8i	−0.486510	−	0.842659i	0.513370	−	0.858167i	$-0.328397\pi$
$563$	−6499.11	−	11256.8i	−0.486510	−	0.842659i	−0.999880	+	0.0155079i	$0.995063\pi$
$564$		0			0
$565$	−8710.99	+	15087.9i	−0.648627	+	1.12345i
$566$	−144.506	−	11323.0i	−0.0107315	−	0.840888i
$567$		0			0
$568$	5753.43	−	220.374i	0.425015	−	0.0162794i
$569$	−5424.42	−	3131.79i	−0.399655	−	0.230741i	0.286680	−	0.958026i	$-0.407448\pi$
$569$	−5424.42	−	3131.79i	−0.399655	−	0.230741i	−0.686335	+	0.727286i	$0.740782\pi$
$570$		0			0
$571$	−21837.8	+	12608.1i	−1.60050	+	0.924047i	−0.609109	+	0.793086i	$0.708473\pi$
$571$	−21837.8	+	12608.1i	−1.60050	+	0.924047i	−0.991388	+	0.130961i	$0.958194\pi$
$572$	−7953.90	−	12998.7i	−0.581415	−	0.950183i
$573$		0			0
$574$	1703.72	−	3039.86i	0.123888	−	0.221048i
$575$	−12121.4			−0.879125
$576$		0			0
$577$	18112.2			1.30680			0.653398	−	0.757014i	$-0.273343\pi$
$577$	18112.2			1.30680			0.653398	+	0.757014i	$0.273343\pi$
$578$	−3052.36	+	5446.18i	−0.219656	+	0.391923i
$579$		0			0
$580$	−8616.47	−	14081.6i	−0.616861	−	1.00811i
$581$	1555.67	−	898.169i	0.111085	−	0.0641348i
$582$		0			0
$583$	20818.6	+	12019.6i	1.47893	+	0.853861i
$584$	−2272.05	+	87.0268i	−0.160990	+	0.00616643i
$585$		0			0
$586$	97.2865	+	7623.04i	0.00685813	+	0.537380i
$587$	−13172.1	+	22814.8i	−0.926189	+	1.60421i	−0.136551	+	0.990633i	$0.543602\pi$
$587$	−13172.1	+	22814.8i	−0.926189	+	1.60421i	−0.789638	+	0.613573i	$0.789732\pi$
$588$		0			0
$589$	−627.764	−	1087.32i	−0.0439161	−	0.0760649i
$590$	−20216.2	+	12018.4i	−1.41065	+	0.838624i
$591$		0			0
$592$	−517.417	+	1012.20i	−0.0359218	+	0.0702721i
$593$			11633.4i			0.805609i	0.915286	+	0.402804i	$0.131965\pi$
$593$			11633.4i			0.805609i	−0.915286	+	0.402804i	$0.868035\pi$
$594$		0			0
$595$		−	5092.53i		−	0.350880i
$596$	−2857.55	−	1553.96i	−0.196392	−	0.106799i
$597$		0			0
$598$	4130.25	+	6947.52i	0.282439	+	0.475092i
$599$	11060.5	+	19157.3i	0.754454	+	1.30675i	0.945645	+	0.325200i	$0.105432\pi$
$599$	11060.5	+	19157.3i	0.754454	+	1.30675i	−0.191191	+	0.981553i	$0.561235\pi$
$600$		0			0
$601$	846.923	−	1466.91i	0.0574820	−	0.0995618i	−0.835852	−	0.548954i	$-0.815026\pi$
$601$	846.923	−	1466.91i	0.0574820	−	0.0995618i	0.893334	+	0.449392i	$0.148359\pi$
$602$	−1318.95	+	16.8327i	−0.0892964	+	0.00113962i
$603$		0			0
$604$	704.917	+	27613.0i	0.0474879	+	1.86019i
$605$	17327.7	+	10004.1i	1.16441	+	0.672274i
$606$		0			0
$607$	11418.4	−	6592.43i	0.763525	−	0.440821i	−0.0670351	−	0.997751i	$-0.521354\pi$
$607$	11418.4	−	6592.43i	0.763525	−	0.440821i	0.830560	+	0.556929i	$0.188021\pi$
$608$	−9481.16	+	6312.61i	−0.632421	+	0.421069i
$609$		0			0
$610$	−4166.87	−	2335.36i	−0.276577	−	0.155010i
$611$	−11632.2			−0.770196
$612$		0			0
$613$	−18052.3			−1.18944			−0.594719	−	0.803934i	$-0.702737\pi$
$613$	−18052.3			−1.18944			−0.594719	+	0.803934i	$0.702737\pi$
$614$	11288.5	+	6326.71i	0.741962	+	0.415839i
$615$		0			0
$616$	−3425.15	+	2156.39i	−0.224031	+	0.141045i
$617$	18897.2	−	10910.3i	1.23302	−	0.711884i	0.265361	−	0.964149i	$-0.414509\pi$
$617$	18897.2	−	10910.3i	1.23302	−	0.711884i	0.967658	+	0.252266i	$0.0811756\pi$
$618$		0			0
$619$	−15640.0	−	9029.74i	−1.01555	−	0.586326i	−0.102736	−	0.994709i	$-0.532760\pi$
$619$	−15640.0	−	9029.74i	−1.01555	−	0.586326i	−0.912811	+	0.408382i	$0.866093\pi$
$620$	−2699.39	+	68.9112i	−0.174855	+	0.00446378i
$621$		0			0
$622$	−23301.3	+	297.374i	−1.50208	+	0.0191698i
$623$	1819.25	−	3151.03i	0.116993	−	0.202638i
$624$		0			0
$625$	4898.71	+	8484.82i	0.313518	+	0.543028i
$626$	−7689.02	−	12933.8i	−0.490919	−	0.825778i
$627$		0			0
$628$	3365.45	−	6188.70i	0.213848	−	0.393242i
$629$		−	1498.81i		−	0.0950100i
$630$		0			0
$631$			7301.94i			0.460674i	0.973111	+	0.230337i	$0.0739829\pi$
$631$			7301.94i			0.460674i	−0.973111	+	0.230337i	$0.926017\pi$
$632$	−19789.7	−	10436.8i	−1.24556	−	0.656888i
$633$		0			0
$634$	21452.0	−	12753.1i	1.34380	−	0.798878i
$635$	6720.18	+	11639.7i	0.419972	+	0.727413i
$636$		0			0
$637$	−6274.06	+	10867.0i	−0.390247	+	0.675928i
$638$	−220.756	−	17297.7i	−0.0136988	−	1.07339i
$639$		0			0
$640$	2185.45	+	24399.7i	0.134980	+	1.50700i
$641$	−735.990	−	424.924i	−0.0453508	−	0.0261833i	0.477153	−	0.878820i	$-0.341669\pi$
$641$	−735.990	−	424.924i	−0.0453508	−	0.0261833i	−0.522504	+	0.852637i	$0.675002\pi$
$642$		0			0
$643$	−984.538	+	568.423i	−0.0603832	+	0.0348622i	−0.529888	−	0.848068i	$-0.677766\pi$
$643$	−984.538	+	568.423i	−0.0603832	+	0.0348622i	0.469504	+	0.882930i	$0.344433\pi$
$644$	1831.07	−	1120.43i	0.112041	−	0.0685575i
$645$		0			0
$646$	7342.37	−	13100.6i	0.447185	−	0.797891i
$647$	−995.889			−0.0605138			−0.0302569	−	0.999542i	$-0.509633\pi$
$647$	−995.889			−0.0605138			−0.0302569	+	0.999542i	$0.509633\pi$
$648$		0			0
$649$	−24645.0			−1.49061
$650$	−8467.14	+	15107.5i	−0.510936	+	0.911640i
$651$		0			0
$652$	−11556.6	+	7071.46i	−0.694160	+	0.424754i
$653$	−24496.2	+	14142.9i	−1.46801	+	0.847557i	−0.999358	−	0.0358245i	$-0.988594\pi$
$653$	−24496.2	+	14142.9i	−1.46801	+	0.847557i	−0.468654	+	0.883382i	$0.655261\pi$
$654$		0			0
$655$	−3253.43	−	1878.37i	−0.194079	−	0.112052i
$656$	−1127.71	−	22072.9i	−0.0671185	−	1.31372i
$657$		0			0
$658$	39.4248	+	3089.20i	0.00233577	+	0.183023i
$659$	12722.0	−	22035.1i	0.752014	−	1.30253i	−0.194831	−	0.980837i	$-0.562416\pi$
$659$	12722.0	−	22035.1i	0.752014	−	1.30253i	0.946845	−	0.321690i	$-0.104251\pi$
$660$		0			0
$661$	2109.30	+	3653.42i	0.124119	+	0.214980i	0.921388	−	0.388644i	$-0.127056\pi$
$661$	2109.30	+	3653.42i	0.124119	+	0.214980i	−0.797269	+	0.603624i	$0.793723\pi$
$662$	−5772.58	+	3431.76i	−0.338909	+	0.201479i
$663$		0			0
$664$	5314.74	−	10077.6i	0.310621	−	0.588983i
$665$			3797.51i			0.221445i
$666$		0			0
$667$			9175.09i			0.532625i
$668$	6268.29	−	11526.7i	0.363065	−	0.667636i
$669$		0			0
$670$	−15151.5	−	25486.4i	−0.873661	−	1.46959i
$671$	−2502.71	−	4334.83i	−0.143988	−	0.249395i
$672$		0			0
$673$	−7212.87	+	12493.0i	−0.413129	+	0.715560i	−0.995230	−	0.0975565i	$-0.968897\pi$
$673$	−7212.87	+	12493.0i	−0.413129	+	0.715560i	0.582101	+	0.813116i	$0.302231\pi$
$674$	1820.73	−	23.2364i	0.104053	−	0.00132794i
$675$		0			0
$676$	−6026.11	+	153.837i	−0.342860	+	0.00875270i
$677$	27870.5	+	16091.1i	1.58220	+	0.913486i	0.994537	+	0.104382i	$0.0332865\pi$
$677$	27870.5	+	16091.1i	1.58220	+	0.913486i	0.587666	+	0.809103i	$0.300047\pi$
$678$		0			0
$679$	3111.84	−	1796.62i	0.175878	−	0.101543i
$680$	−17208.3	−	27333.1i	−0.970452	−	1.54144i
$681$		0			0
$682$	−2468.34	−	1383.40i	−0.138589	−	0.0776732i
$683$	−28383.3			−1.59012			−0.795062	−	0.606528i	$-0.792562\pi$
$683$	−28383.3			−1.59012			−0.795062	+	0.606528i	$0.792562\pi$
$684$		0			0
$685$	20593.5			1.14867
$686$	5926.51	+	3321.56i	0.329847	+	0.184866i
$687$		0			0
$688$	−7022.32	+	4547.24i	−0.389133	+	0.251980i
$689$	−15775.9	+	9108.21i	−0.872298	+	0.503621i
$690$		0			0
$691$	4592.61	+	2651.54i	0.252838	+	0.145976i	0.621063	−	0.783761i	$-0.286701\pi$
$691$	4592.61	+	2651.54i	0.252838	+	0.145976i	−0.368225	+	0.929737i	$0.620034\pi$
$692$	445.362	+	17445.7i	0.0244655	+	0.958360i
$693$		0			0
$694$	4345.61	−	55.4594i	0.237690	−	0.00303344i
$695$	−18645.3	+	32294.6i	−1.01764	+	1.76260i
$696$		0			0
$697$	14570.2	+	25236.3i	0.791801	+	1.37144i
$698$	9922.81	+	16691.2i	0.538086	+	0.905117i
$699$		0			0
$700$	4040.83	+	2197.43i	0.218185	+	0.118650i
$701$		−	10087.7i		−	0.543519i	−0.962365	−	0.271760i	$-0.912394\pi$
$701$		−	10087.7i		−	0.543519i	0.962365	−	0.271760i	$-0.0876056\pi$
$702$		0			0
$703$			1117.66i			0.0599622i
$704$	−11097.1	+	23148.0i	−0.594086	+	1.23924i
$705$		0			0
$706$	−303.105	+	180.194i	−0.0161580	+	0.00960579i
$707$	−750.956	−	1300.69i	−0.0399471	−	0.0691905i
$708$		0			0
$709$	12869.6	−	22290.9i	0.681706	−	1.18075i	−0.292754	−	0.956188i	$-0.594572\pi$
$709$	12869.6	−	22290.9i	0.681706	−	1.18075i	0.974460	−	0.224561i	$-0.0720949\pi$
$710$	−155.363	−	12173.8i	−0.00821223	−	0.643483i
$711$		0			0
$712$	−883.268	−	23059.9i	−0.0464914	−	1.21378i
$713$	1299.68	+	750.372i	0.0682658	+	0.0394133i
$714$		0			0
$715$	−27906.5	+	16111.9i	−1.45964	+	0.842726i
$716$	9813.44	+	16037.7i	0.512215	+	0.837092i
$717$		0			0
$718$	−6208.25	+	11077.1i	−0.322688	+	0.575757i
$719$	7178.86			0.372359			0.186180	−	0.982516i	$-0.440389\pi$
$719$	7178.86			0.372359			0.186180	+	0.982516i	$0.440389\pi$
$720$		0			0
$721$	6165.33			0.318459
$722$	4009.69	−	7154.30i	0.206683	−	0.368775i
$723$		0			0
$724$	9520.74	+	15559.4i	0.488723	+	0.798701i
$725$	−17025.7	+	9829.77i	−0.872161	+	0.503543i
$726$		0			0
$727$	18250.7	+	10537.0i	0.931061	+	0.537548i	0.887147	−	0.461487i	$-0.152684\pi$
$727$	18250.7	+	10537.0i	0.931061	+	0.537548i	0.0439138	+	0.999035i	$0.486017\pi$
$728$	−117.392	−	3064.81i	−0.00597641	−	0.156029i
$729$		0			0
$730$	61.3537	+	4807.47i	0.00311069	+	0.243743i
$731$	5515.17	−	9552.55i	0.279050	−	0.483330i
$732$		0			0
$733$	−10114.0	−	17518.0i	−0.509645	−	0.882730i	−0.999938	−	0.0111727i	$-0.996444\pi$
$733$	−10114.0	−	17518.0i	−0.509645	−	0.882730i	0.490293	−	0.871558i	$-0.336890\pi$
$734$	−2108.32	+	1253.38i	−0.106021	+	0.0630288i
$735$		0			0
$736$	6041.83	−	12201.1i	0.302588	−	0.611056i
$737$		−	31069.9i		−	1.55288i
$738$		0			0
$739$		−	8782.55i		−	0.437173i	−0.975818	−	0.218587i	$-0.929855\pi$
$739$		−	8782.55i		−	0.437173i	0.975818	−	0.218587i	$-0.0701447\pi$
$740$	2111.71	+	1148.36i	0.104903	+	0.0570467i
$741$		0			0
$742$	2472.36	+	4158.76i	0.122322	+	0.205759i
$743$	−11676.8	−	20224.8i	−0.576553	−	0.998620i	−0.995871	−	0.0907800i	$-0.971064\pi$
$743$	−11676.8	−	20224.8i	−0.576553	−	0.998620i	0.419318	−	0.907840i	$-0.362269\pi$
$744$		0			0
$745$	−3439.02	+	5956.56i	−0.169122	+	0.292928i
$746$	12272.0	−	156.617i	0.602291	−	0.00768654i
$747$		0			0
$748$	−863.747	−	33834.7i	−0.0422216	−	1.65390i
$749$	195.145	+	112.667i	0.00951995	+	0.00549634i
$750$		0			0
$751$	14625.3	−	8443.94i	0.710634	−	0.410285i	−0.100662	−	0.994921i	$-0.532096\pi$
$751$	14625.3	−	8443.94i	0.710634	−	0.410285i	0.811296	+	0.584636i	$0.198763\pi$
$752$	10650.4	+	16447.4i	0.516462	+	0.797574i
$753$		0			0
$754$	11435.4	+	6409.06i	0.552324	+	0.309555i
$755$	58407.6			2.81546
$756$		0			0
$757$	6838.01			0.328311			0.164156	−	0.986434i	$-0.447510\pi$
$757$	6838.01			0.328311			0.164156	+	0.986434i	$0.447510\pi$
$758$	34781.8	+	19493.7i	1.66666	+	0.934095i
$759$		0			0
$760$	12832.2	+	20382.4i	0.612466	+	0.972824i
$761$	20503.9	−	11837.9i	0.976696	−	0.563896i	0.0754248	−	0.997151i	$-0.475969\pi$
$761$	20503.9	−	11837.9i	0.976696	−	0.563896i	0.901271	+	0.433256i	$0.142635\pi$
$762$		0			0
$763$	2581.02	+	1490.15i	0.122463	+	0.0707039i
$764$	−31453.4	+	802.957i	−1.48945	+	0.0380235i
$765$		0			0
$766$	23386.1	−	298.457i	1.10310	−	0.0140779i
$767$	9337.76	−	16173.5i	0.439592	−	0.761396i
$768$		0			0
$769$	−18418.7	−	31902.0i	−0.863711	−	1.49599i	−0.868322	−	0.496002i	$-0.834801\pi$
$769$	−18418.7	−	31902.0i	−0.863711	−	1.49599i	0.00461075	−	0.999989i	$-0.498532\pi$
$770$	4373.44	+	7356.59i	0.204686	+	0.344303i
$771$		0			0
$772$	−10369.5	+	19068.4i	−0.483429	+	0.888972i
$773$		−	7505.51i		−	0.349230i	−0.984637	−	0.174615i	$-0.944132\pi$
$773$		−	7505.51i		−	0.349230i	0.984637	−	0.174615i	$-0.0558680\pi$
$774$		0			0
$775$			3215.66i			0.149045i
$776$	10631.2	−	20158.3i	0.491799	−	0.932525i
$777$		0			0
$778$	−13960.9	+	8299.65i	−0.643345	+	0.382464i
$779$	−10865.0	−	18818.8i	−0.499717	−	0.865535i
$780$		0			0
$781$	6378.88	−	11048.5i	0.292259	−	0.506207i
$782$	229.075	+	17949.6i	0.0104753	+	0.820812i
$783$		0			0
$784$	21109.9	−	1078.51i	0.961638	−	0.0491303i
$785$	−12900.3	−	7448.01i	−0.586538	−	0.338638i
$786$		0			0
$787$	16864.0	−	9736.41i	0.763832	−	0.440998i	−0.0668382	−	0.997764i	$-0.521291\pi$
$787$	16864.0	−	9736.41i	0.763832	−	0.440998i	0.830670	+	0.556765i	$0.187958\pi$
$788$	−13633.5	+	8342.29i	−0.616335	+	0.377134i
$789$		0			0
$790$	−23129.7	+	41269.2i	−1.04167	+	1.85860i
$791$	−3674.28			−0.165161
$792$		0			0
$793$	3793.01			0.169853
$794$	14512.1	−	25893.2i	0.648633	−	1.15733i
$795$		0			0
$796$	16439.3	−	10059.2i	0.732005	−	0.447912i
$797$	30984.0	−	17888.6i	1.37705	−	0.795040i	0.385247	−	0.922814i	$-0.374116\pi$
$797$	30984.0	−	17888.6i	1.37705	−	0.795040i	0.991803	+	0.127773i	$0.0407830\pi$
$798$		0			0
$799$	−22373.6	−	12917.4i	−0.990640	−	0.571947i
$800$	29113.7	−	1860.20i	1.28666	−	0.0822098i
$801$		0			0
$802$	−294.669	−	23089.3i	−0.0129740	−	1.01660i
$803$	−2519.04	+	4363.11i	−0.110704	+	0.191745i
$804$		0			0
$805$	−2269.60	−	3931.06i	−0.0993700	−	0.172114i
$806$	1843.09	−	1095.71i	0.0805462	−	0.0478841i
$807$		0			0
$808$	−8425.81	−	4443.64i	−0.366855	−	0.193474i
$809$			16519.8i			0.717932i	0.933351	+	0.358966i	$0.116871\pi$
$809$			16519.8i			0.717932i	−0.933351	+	0.358966i	$0.883129\pi$
$810$		0			0
$811$		−	18594.4i		−	0.805103i	−0.915397	−	0.402552i	$-0.868123\pi$
$811$		−	18594.4i		−	0.805103i	0.915397	−	0.402552i	$-0.131877\pi$
$812$	1663.31	−	3058.64i	0.0718852	−	0.132189i
$813$		0			0
$814$	1287.17	+	2165.15i	0.0554240	+	0.0932291i
$815$	14324.3	+	24810.5i	0.615656	+	1.06635i
$816$		0			0
$817$	−4112.67	+	7123.35i	−0.176113	+	0.305036i
$818$	−11524.5	+	147.078i	−0.492598	+	0.00628661i
$819$		0			0
$820$	−46719.6	+	1192.68i	−1.98966	+	0.0507929i
$821$	−35701.8	−	20612.4i	−1.51766	−	0.876222i	−0.999784	−	0.0207677i	$-0.993389\pi$
$821$	−35701.8	−	20612.4i	−1.51766	−	0.876222i	−0.517878	−	0.855455i	$-0.673278\pi$
$822$		0			0
$823$	3713.28	−	2143.86i	0.157274	−	0.0908025i	−0.419297	−	0.907849i	$-0.637723\pi$
$823$	3713.28	−	2143.86i	0.157274	−	0.0908025i	0.576572	+	0.817047i	$0.304390\pi$
$824$	33091.1	−	20833.4i	1.39901	−	0.880783i
$825$		0			0
$826$	−4326.87	−	2425.03i	−0.182265	−	0.102152i
$827$	−24944.4			−1.04885			−0.524426	−	0.851456i	$-0.675720\pi$
$827$	−24944.4			−1.04885			−0.524426	+	0.851456i	$0.675720\pi$
$828$		0			0
$829$	−31040.8			−1.30047			−0.650235	−	0.759733i	$-0.725330\pi$
$829$	−31040.8			−1.30047			−0.650235	+	0.759733i	$0.725330\pi$
$830$	−21015.6	−	11778.4i	−0.878869	−	0.492570i
$831$		0			0
$832$	−10986.4	−	16053.1i	−0.457796	−	0.668918i
$833$	−24135.3	+	13934.5i	−1.00389	+	0.579594i
$834$		0			0
$835$	−24027.4	−	13872.2i	−0.995810	−	0.574931i
$836$	644.098	+	25230.6i	0.0266466	+	1.04380i
$837$		0			0
$838$	−1960.15	+	25.0157i	−0.0808021	+	0.00103121i
$839$	−6393.60	+	11074.0i	−0.263089	+	0.455683i	−0.967061	−	0.254544i	$-0.918075\pi$
$839$	−6393.60	+	11074.0i	−0.263089	+	0.455683i	0.703972	+	0.710228i	$0.251408\pi$
$840$		0			0
$841$	−4754.02	−	8234.20i	−0.194925	−	0.337619i
$842$	−15502.0	−	26076.0i	−0.634481	−	1.06727i
$843$		0			0
$844$	12787.0	+	6953.67i	0.521502	+	0.283596i
$845$			12746.6i			0.518929i
$846$		0			0
$847$			4219.73i			0.171183i
$848$	27322.8	+	13966.9i	1.10645	+	0.565597i
$849$		0			0
$850$	−33062.5	+	19655.4i	−1.33416	+	0.793147i
$851$	−667.975	−	1156.97i	−0.0269070	−	0.0466044i
$852$		0			0
$853$	23491.5	−	40688.4i	0.942946	−	1.63323i	0.183132	−	0.983088i	$-0.441376\pi$
$853$	23491.5	−	40688.4i	0.942946	−	1.63323i	0.759813	−	0.650141i	$-0.225290\pi$
$854$	−12.8556	−	1007.32i	−0.000515115	−	0.0403627i
$855$		0			0
$856$	1428.12	−	54.7013i	0.0570234	−	0.00218417i
$857$	−39991.4	−	23089.0i	−1.59402	−	0.920310i	−0.992607	−	0.121375i	$-0.961269\pi$
$857$	−39991.4	−	23089.0i	−1.59402	−	0.920310i	−0.601418	−	0.798935i	$-0.705397\pi$
$858$		0			0
$859$	−5670.77	+	3274.02i	−0.225244	+	0.130045i	−0.608376	−	0.793649i	$-0.708179\pi$
$859$	−5670.77	+	3274.02i	−0.225244	+	0.130045i	0.383132	+	0.923694i	$0.374845\pi$
$860$	9233.22	+	15089.5i	0.366105	+	0.598311i
$861$		0			0
$862$	13847.5	−	24707.5i	0.547156	−	0.976264i
$863$	29442.2			1.16133			0.580663	−	0.814144i	$-0.302793\pi$
$863$	29442.2			1.16133			0.580663	+	0.814144i	$0.302793\pi$
$864$		0			0
$865$	36901.5			1.45051
$866$	−13449.5	+	23997.4i	−0.527752	+	0.941644i
$867$		0			0
$868$	−297.236	−	485.761i	−0.0116231	−	0.0189952i
$869$	−42932.6	+	24787.2i	−1.67594	+	0.967603i
$870$		0			0
$871$	20389.8	+	11772.1i	0.793206	+	0.457958i
$872$	18888.5	−	723.488i	0.733538	−	0.0280968i
$873$		0			0
$874$	−170.822	−	13385.0i	−0.00661113	−	0.518026i
$875$	1091.15	−	1889.93i	0.0421573	−	0.0730186i
$876$		0			0
$877$	16384.3	+	28378.4i	0.630853	+	1.09267i	0.987378	+	0.158383i	$0.0506282\pi$
$877$	16384.3	+	28378.4i	0.630853	+	1.09267i	−0.356525	+	0.934286i	$0.616039\pi$
$878$	15934.4	−	9472.89i	0.612483	−	0.364117i
$879$		0			0
$880$	48332.4	+	24706.6i	1.85146	+	0.946432i
$881$			15082.2i			0.576769i	0.957515	+	0.288384i	$0.0931181\pi$
$881$			15082.2i			0.576769i	−0.957515	+	0.288384i	$0.906882\pi$
$882$		0			0
$883$			425.340i			0.0162105i	0.999967	+	0.00810523i	$0.00258000\pi$
$883$			425.340i			0.0162105i	−0.999967	+	0.00810523i	$0.997420\pi$
$884$	22531.5	+	12252.8i	0.857258	+	0.466183i
$885$		0			0
$886$	8497.56	+	14293.8i	0.322214	+	0.541997i
$887$	6078.41	+	10528.1i	0.230094	+	0.398534i	0.957835	−	0.287317i	$-0.0927634\pi$
$887$	6078.41	+	10528.1i	0.230094	+	0.398534i	−0.727742	+	0.685851i	$0.759430\pi$
$888$		0			0
$889$	−1417.28	+	2454.80i	−0.0534692	+	0.0926114i
$890$	−48792.8	+	622.702i	−1.83768	+	0.0234528i
$891$		0			0
$892$	546.017	+	21388.5i	0.0204955	+	0.802849i
$893$	16684.0	+	9632.54i	0.625207	+	0.360964i
$894$		0			0
$895$	34430.8	−	19878.7i	1.28592	−	0.742425i
$896$	−4226.01	+	2972.10i	−0.157568	+	0.110816i
$897$		0			0
$898$	16681.7	+	9349.38i	0.619905	+	0.347431i
$899$	2434.04			0.0903001
$900$		0			0
$901$	−40458.1			−1.49595
$902$	−42720.7	−	23943.2i	−1.57699	−	0.883836i
$903$		0			0
$904$	−19721.0	+	12415.8i	−0.725564	+	0.456798i
$905$	33403.9	−	19285.7i	1.22694	−	0.708375i
$906$		0			0
$907$	−39674.6	−	22906.2i	−1.45245	−	0.838574i	−0.453832	−	0.891087i	$-0.649944\pi$
$907$	−39674.6	−	22906.2i	−1.45245	−	0.838574i	−0.998620	+	0.0525131i	$0.983277\pi$
$908$	47177.9	−	1204.38i	1.72429	−	0.0440185i
$909$		0			0
$910$	−6484.87	+	82.7609i	−0.236232	+	0.00301483i
$911$	−14411.9	+	24962.1i	−0.524134	+	0.907827i	0.475471	+	0.879732i	$0.342278\pi$
$911$	−14411.9	+	24962.1i	−0.524134	+	0.907827i	−0.999605	+	0.0280960i	$0.991056\pi$
$912$		0			0
$913$	−12622.4	−	21862.7i	−0.457547	−	0.792495i
$914$	−22027.7	−	37052.9i	−0.797168	−	1.34092i
$915$		0			0
$916$	−11590.8	+	21314.3i	−0.418092	+	0.768824i
$917$		−	792.293i		−	0.0285320i
$918$		0			0
$919$			41488.4i			1.48920i	0.667511	+	0.744600i	$0.267360\pi$
$919$			41488.4i			1.48920i	−0.667511	+	0.744600i	$0.732640\pi$
$920$	−25465.1	−	13429.9i	−0.912566	−	0.481273i
$921$		0			0
$922$	−33408.6	+	19861.2i	−1.19333	+	0.709428i
$923$	4833.79	+	8372.36i	0.172379	+	0.298570i
$924$		0			0
$925$	1431.28	−	2479.04i	0.0508758	−	0.0881194i
$926$	637.321	+	49938.4i	0.0226174	+	1.77222i
$927$		0			0
$928$	−1408.04	−	22037.2i	−0.0498075	−	0.779532i
$929$	−3659.97	−	2113.09i	−0.129257	−	0.0746266i	0.433977	−	0.900924i	$-0.357110\pi$
$929$	−3659.97	−	2113.09i	−0.129257	−	0.0746266i	−0.563234	+	0.826297i	$0.690443\pi$
$930$		0			0
$931$	17997.7	−	10391.0i	0.633567	−	0.365790i
$932$	−8830.95	+	5403.64i	−0.310373	+	0.189916i
$933$		0			0
$934$	8525.38	−	15211.4i	0.298671	−	0.532905i
$935$	−71567.8			−2.50323
$936$		0			0
$937$	31514.2			1.09875			0.549373	−	0.835577i	$-0.314867\pi$
$937$	31514.2			1.09875			0.549373	+	0.835577i	$0.314867\pi$
$938$	3057.22	−	5454.86i	0.106420	−	0.189880i
$939$		0			0
$940$	35342.0	−	21625.7i	1.22631	−	0.750374i
$941$	23040.3	−	13302.3i	0.798185	−	0.460832i	−0.0446514	−	0.999003i	$-0.514218\pi$
$941$	23040.3	−	13302.3i	0.798185	−	0.460832i	0.842836	+	0.538171i	$0.180884\pi$
$942$		0			0
$943$	22494.2	+	12987.0i	0.776790	+	0.448480i
$944$	−31418.1	+	1605.16i	−1.08323	+	0.0553426i
$945$		0			0
$946$	236.558	+	18535.9i	0.00813018	+	0.637054i
$947$	25814.6	−	44712.3i	0.885811	−	1.53427i	0.0410299	−	0.999158i	$-0.486936\pi$
$947$	25814.6	−	44712.3i	0.885811	−	1.53427i	0.844781	−	0.535112i	$-0.179731\pi$
$948$		0			0
$949$	−1908.88	−	3306.28i	−0.0652950	−	0.113094i
$950$	24654.8	−	14657.1i	0.842006	−	0.500567i
$951$		0			0
$952$	3177.63	−	6025.26i	0.108180	−	0.205126i
$953$		−	25766.7i		−	0.875829i	−0.899017	−	0.437915i	$-0.855717\pi$
$953$		−	25766.7i		−	0.875829i	0.899017	−	0.437915i	$-0.144283\pi$
$954$		0			0
$955$			66530.9i			2.25433i
$956$	−21976.9	+	40413.2i	−0.743499	+	1.36721i
$957$		0			0
$958$	25030.9	+	42104.6i	0.844166	+	1.41998i
$959$	2171.58	+	3761.29i	0.0731220	+	0.126651i
$960$		0			0
$961$	−14696.4	+	25455.0i	−0.493318	+	0.854452i
$962$	−1908.59	+	24.3577i	−0.0639661	+	0.000816346i
$963$		0			0
$964$	48125.4	−	1228.57i	1.60790	−	0.0410472i
$965$	39748.1	+	22948.6i	1.32594	+	0.765534i
$966$		0			0
$967$	−39828.3	+	22994.9i	−1.32450	+	0.764700i	−0.984443	−	0.175705i	$-0.943779\pi$
$967$	−39828.3	+	22994.9i	−1.32450	+	0.764700i	−0.340056	+	0.940405i	$0.610446\pi$
$968$	14259.0	+	22648.5i	0.473451	+	0.752016i
$969$		0			0
$970$	−42037.7	−	23560.4i	−1.39150	−	0.779876i
$971$	−22109.4			−0.730714			−0.365357	−	0.930867i	$-0.619053\pi$
$971$	−22109.4			−0.730714			−0.365357	+	0.930867i	$0.619053\pi$
$972$		0			0
$973$	−7864.57			−0.259123
$974$	18140.2	+	10166.8i	0.596765	+	0.334462i
$975$		0			0
$976$	−3472.85	−	5363.13i	−0.113897	−	0.175891i
$977$	43850.9	−	25317.3i	1.43594	−	0.829040i	0.438375	−	0.898792i	$-0.355554\pi$
$977$	43850.9	−	25317.3i	1.43594	−	0.829040i	0.997564	+	0.0697519i	$0.0222208\pi$
$978$		0			0
$979$	−44282.9	−	25566.8i	−1.44565	−	0.834645i
$980$	−1140.64	−	44681.2i	−0.0371801	−	1.45642i
$981$		0			0
$982$	−23877.2	+	304.724i	−0.775918	+	0.00990239i
$983$	−6989.79	+	12106.7i	−0.226795	+	0.392821i	−0.956856	−	0.290561i	$-0.906158\pi$
$983$	−6989.79	+	12106.7i	−0.226795	+	0.392821i	0.730061	+	0.683382i	$0.239491\pi$
$984$		0			0
$985$	16898.6	+	29269.2i	0.546633	+	0.946797i
$986$	14877.8	+	25026.1i	0.480535	+	0.808310i
$987$		0			0
$988$	−16801.8	−	9136.91i	−0.541028	−	0.294215i
$989$		−	9831.82i		−	0.316111i
$990$		0			0
$991$			29526.4i			0.946456i	0.880940	+	0.473228i	$0.156911\pi$
$991$			29526.4i			0.946456i	−0.880940	+	0.473228i	$0.843089\pi$
$992$	−3236.80	−	1602.83i	−0.103597	−	0.0513002i
$993$		0			0
$994$	2207.08	−	1312.10i	0.0704270	−	0.0418683i
$995$	−20376.4	−	35293.0i	−0.649222	−	1.12448i
$996$		0			0
$997$	−2513.86	+	4354.14i	−0.0798545	+	0.138312i	−0.903187	−	0.429247i	$-0.858779\pi$
$997$	−2513.86	+	4354.14i	−0.0798545	+	0.138312i	0.823333	+	0.567559i	$0.192112\pi$
$998$	−272.669	−	21365.4i	−0.00864849	−	0.677667i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.4.h.b.35.8		24
3.2	odd	2		36.4.h.b.11.5	✓	24
4.3	odd	2	inner	108.4.h.b.35.4		24
9.2	odd	6		324.4.b.c.323.23		24
9.4	even	3		36.4.h.b.23.9	yes	24
9.5	odd	6	inner	108.4.h.b.71.4		24
9.7	even	3		324.4.b.c.323.2		24
12.11	even	2		36.4.h.b.11.9	yes	24
36.7	odd	6		324.4.b.c.323.24		24
36.11	even	6		324.4.b.c.323.1		24
36.23	even	6	inner	108.4.h.b.71.8		24
36.31	odd	6		36.4.h.b.23.5	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.4.h.b.11.5	✓	24	3.2	odd	2
36.4.h.b.11.9	yes	24	12.11	even	2
36.4.h.b.23.5	yes	24	36.31	odd	6
36.4.h.b.23.9	yes	24	9.4	even	3
108.4.h.b.35.4		24	4.3	odd	2	inner
108.4.h.b.35.8		24	1.1	even	1	trivial
108.4.h.b.71.4		24	9.5	odd	6	inner
108.4.h.b.71.8		24	36.23	even	6	inner
324.4.b.c.323.1		24	36.11	even	6
324.4.b.c.323.2		24	9.7	even	3
324.4.b.c.323.23		24	9.2	odd	6
324.4.b.c.323.24		24	36.7	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:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	108.h (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.38284 - 2.46734i) q^{2} +(-4.17551 - 6.82387i) q^{4} +(-14.6499 + 8.45813i) q^{5} +(-3.08966 - 1.78382i) q^{7} +(-22.6108 + 0.866066i) q^{8} +O(q^{10})\)	\(q+(1.38284 - 2.46734i) q^{2} +(-4.17551 - 6.82387i) q^{4} +(-14.6499 + 8.45813i) q^{5} +(-3.08966 - 1.78382i) q^{7} +(-22.6108 + 0.866066i) q^{8} +(0.610574 + 47.8425i) q^{10} +(-25.0688 + 43.4205i) q^{11} +(-18.9966 - 32.9032i) q^{13} +(-8.67378 + 5.15650i) q^{14} +(-29.1303 + 56.9862i) q^{16} -84.3819i q^{17} +62.9237i q^{19} +(118.888 + 64.6521i) q^{20} +(72.4668 + 121.897i) q^{22} +(-37.6066 - 65.1366i) q^{23} +(80.5801 - 139.569i) q^{25} +(-107.453 + 1.37133i) q^{26} +(0.728372 + 28.5317i) q^{28} +(-105.644 - 60.9938i) q^{29} +(-17.2800 + 9.97659i) q^{31} +(100.322 + 150.677i) q^{32} +(-208.199 - 116.687i) q^{34} +60.3510 q^{35} +17.7622 q^{37} +(155.254 + 87.0135i) q^{38} +(323.922 - 203.933i) q^{40} +(-299.072 + 172.670i) q^{41} +(113.206 + 65.3596i) q^{43} +(400.970 - 10.2362i) q^{44} +(-212.718 + 2.71474i) q^{46} +(153.083 - 265.147i) q^{47} +(-165.136 - 286.024i) q^{49} +(-232.934 - 391.820i) q^{50} +(-145.206 + 267.018i) q^{52} -479.464i q^{53} -848.142i q^{55} +(71.4047 + 37.6577i) q^{56} +(-296.581 + 176.316i) q^{58} +(245.774 + 425.693i) q^{59} +(-49.9168 + 86.4585i) q^{61} +(0.720188 + 56.4315i) q^{62} +(510.500 - 39.1649i) q^{64} +(556.599 + 321.352i) q^{65} +(-536.669 + 309.846i) q^{67} +(-575.811 + 352.337i) q^{68} +(83.4558 - 148.906i) q^{70} -254.455 q^{71} +100.485 q^{73} +(24.5622 - 43.8253i) q^{74} +(429.383 - 262.738i) q^{76} +(154.908 - 89.4363i) q^{77} +(856.295 + 494.382i) q^{79} +(-55.2404 - 1081.23i) q^{80} +(12.4646 + 976.687i) q^{82} +(-251.755 + 436.053i) q^{83} +(713.714 + 1236.19i) q^{85} +(317.810 - 188.936i) q^{86} +(529.222 - 1003.48i) q^{88} +1019.86i q^{89} +135.546i q^{91} +(-287.457 + 528.601i) q^{92} +(-442.518 - 744.363i) q^{94} +(-532.217 - 921.828i) q^{95} +(-503.589 + 872.242i) q^{97} +(-934.074 + 11.9208i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{4} + 72 q^{5}+O(q^{10}) \) 24 * q - 12 * q^4 + 72 * q^5	\( 24 q - 12 q^{4} + 72 q^{5} + 96 q^{10} - 216 q^{13} + 36 q^{14} - 72 q^{16} + 540 q^{20} - 192 q^{22} + 252 q^{25} - 672 q^{28} - 576 q^{29} - 360 q^{32} - 660 q^{34} + 1248 q^{37} + 144 q^{38} + 636 q^{40} - 1116 q^{41} + 960 q^{46} + 348 q^{49} + 648 q^{50} + 132 q^{52} + 1692 q^{56} + 516 q^{58} - 264 q^{61} + 960 q^{64} + 2592 q^{65} - 5688 q^{68} + 564 q^{70} - 4776 q^{73} - 5652 q^{74} - 600 q^{76} - 648 q^{77} - 4104 q^{82} + 720 q^{85} + 9540 q^{86} + 1956 q^{88} + 7416 q^{92} - 1188 q^{94} + 588 q^{97}+O(q^{100}) \) 24 * q - 12 * q^4 + 72 * q^5 + 96 * q^10 - 216 * q^13 + 36 * q^14 - 72 * q^16 + 540 * q^20 - 192 * q^22 + 252 * q^25 - 672 * q^28 - 576 * q^29 - 360 * q^32 - 660 * q^34 + 1248 * q^37 + 144 * q^38 + 636 * q^40 - 1116 * q^41 + 960 * q^46 + 348 * q^49 + 648 * q^50 + 132 * q^52 + 1692 * q^56 + 516 * q^58 - 264 * q^61 + 960 * q^64 + 2592 * q^65 - 5688 * q^68 + 564 * q^70 - 4776 * q^73 - 5652 * q^74 - 600 * q^76 - 648 * q^77 - 4104 * q^82 + 720 * q^85 + 9540 * q^86 + 1956 * q^88 + 7416 * q^92 - 1188 * q^94 + 588 * q^97

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