LMFDB - Embedded newform 108.5.f.a.91.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("108.19");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	108.f (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$11.1639560131$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			91.17
Character	$\chi$	$=$	108.91
Dual form			108.5.f.a.19.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.73046 - 2.92312i) q^{2} +(-1.08921 - 15.9629i) q^{4} +(-19.5394 + 33.8433i) q^{5} +(-10.5700 + 6.10260i) q^{7} +(-49.6354 - 40.4021i) q^{8} +O(q^{10})$	\(q+(2.73046 - 2.92312i) q^{2} +(-1.08921 - 15.9629i) q^{4} +(-19.5394 + 33.8433i) q^{5} +(-10.5700 + 6.10260i) q^{7} +(-49.6354 - 40.4021i) q^{8} +(45.5763 + 149.524i) q^{10} +(-96.1446 + 55.5091i) q^{11} +(-104.491 + 180.984i) q^{13} +(-11.0224 + 47.5603i) q^{14} +(-253.627 + 34.7739i) q^{16} -93.3790 q^{17} -26.8894i q^{19} +(561.519 + 275.043i) q^{20} +(-100.259 + 432.607i) q^{22} +(757.577 + 437.387i) q^{23} +(-451.080 - 781.293i) q^{25} +(243.728 + 799.608i) q^{26} +(108.928 + 162.081i) q^{28} +(-650.809 - 1127.23i) q^{29} +(593.492 + 342.653i) q^{31} +(-590.870 + 836.330i) q^{32} +(-254.967 + 272.958i) q^{34} -476.966i q^{35} -1760.25 q^{37} +(-78.6008 - 73.4203i) q^{38} +(2337.19 - 890.392i) q^{40} +(39.0421 - 67.6229i) q^{41} +(-1405.46 + 811.442i) q^{43} +(990.807 + 1474.28i) q^{44} +(3347.06 - 1020.22i) q^{46} +(1999.54 - 1154.43i) q^{47} +(-1126.02 + 1950.32i) q^{49} +(-3515.46 - 814.729i) q^{50} +(3002.84 + 1470.85i) q^{52} +1313.48 q^{53} -4338.47i q^{55} +(771.205 + 124.146i) q^{56} +(-5072.04 - 1175.47i) q^{58} +(-4818.38 - 2781.89i) q^{59} +(-1090.13 - 1888.16i) q^{61} +(2622.12 - 799.247i) q^{62} +(831.345 + 4010.75i) q^{64} +(-4083.39 - 7072.65i) q^{65} +(-213.077 - 123.020i) q^{67} +(101.709 + 1490.60i) q^{68} +(-1394.23 - 1302.33i) q^{70} +4608.15i q^{71} +2564.79 q^{73} +(-4806.29 + 5145.42i) q^{74} +(-429.232 + 29.2882i) q^{76} +(677.500 - 1173.46i) q^{77} +(4486.29 - 2590.16i) q^{79} +(3778.87 - 9263.05i) q^{80} +(-91.0669 - 298.766i) q^{82} +(1622.37 - 936.677i) q^{83} +(1824.57 - 3160.25i) q^{85} +(-1465.61 + 6323.93i) q^{86} +(7014.86 + 1129.22i) q^{88} +1167.17 q^{89} -2550.67i q^{91} +(6156.80 - 12569.5i) q^{92} +(2085.11 - 8997.00i) q^{94} +(910.026 + 525.404i) q^{95} +(2869.58 + 4970.26i) q^{97} +(2626.47 + 8616.73i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + q^{2} - q^{4} + 2 q^{5} - 122 q^{8}+O(q^{10}) $ 44 * q + q^2 - q^4 + 2 * q^5 - 122 * q^8	$ 44 q + q^{2} - q^{4} + 2 q^{5} - 122 q^{8} + 28 q^{10} - 2 q^{13} - 252 q^{14} - q^{16} + 56 q^{17} + 140 q^{20} - 33 q^{22} - 1752 q^{25} - 1096 q^{26} - 516 q^{28} - 526 q^{29} + 121 q^{32} + 385 q^{34} - 8 q^{37} - 1395 q^{38} - 2276 q^{40} + 2762 q^{41} - 6714 q^{44} + 3576 q^{46} + 3428 q^{49} - 6375 q^{50} + 1438 q^{52} + 10088 q^{53} + 7506 q^{56} - 4064 q^{58} - 2 q^{61} + 18324 q^{62} + 9026 q^{64} + 2014 q^{65} + 11405 q^{68} + 3666 q^{70} - 3416 q^{73} - 14620 q^{74} + 1581 q^{76} + 3942 q^{77} - 45520 q^{80} - 8486 q^{82} - 1252 q^{85} - 22113 q^{86} + 1995 q^{88} - 13048 q^{89} + 30294 q^{92} + 7524 q^{94} + 5638 q^{97} + 92938 q^{98}+O(q^{100}) $ 44 * q + q^2 - q^4 + 2 * q^5 - 122 * q^8 + 28 * q^10 - 2 * q^13 - 252 * q^14 - q^16 + 56 * q^17 + 140 * q^20 - 33 * q^22 - 1752 * q^25 - 1096 * q^26 - 516 * q^28 - 526 * q^29 + 121 * q^32 + 385 * q^34 - 8 * q^37 - 1395 * q^38 - 2276 * q^40 + 2762 * q^41 - 6714 * q^44 + 3576 * q^46 + 3428 * q^49 - 6375 * q^50 + 1438 * q^52 + 10088 * q^53 + 7506 * q^56 - 4064 * q^58 - 2 * q^61 + 18324 * q^62 + 9026 * q^64 + 2014 * q^65 + 11405 * q^68 + 3666 * q^70 - 3416 * q^73 - 14620 * q^74 + 1581 * q^76 + 3942 * q^77 - 45520 * q^80 - 8486 * q^82 - 1252 * q^85 - 22113 * q^86 + 1995 * q^88 - 13048 * q^89 + 30294 * q^92 + 7524 * q^94 + 5638 * q^97 + 92938 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	2.73046	−	2.92312i	0.682614	−	0.730779i
$2$	2.73046	−	2.92312i	0.682614	−	0.730779i
$3$		0			0
$3$		0			0
$4$	−1.08921	−	15.9629i	−0.0680757	−	0.997680i
$5$	−19.5394	+	33.8433i	−0.781578	+	1.35373i	0.149444	+	0.988770i	$0.452251\pi$
$5$	−19.5394	+	33.8433i	−0.781578	+	1.35373i	−0.931022	+	0.364962i	$0.881082\pi$
$6$		0			0
$7$	−10.5700	+	6.10260i	−0.215715	+	0.124543i	−0.603964	−	0.797011i	$-0.706413\pi$
$7$	−10.5700	+	6.10260i	−0.215715	+	0.124543i	0.388250	+	0.921554i	$0.373080\pi$
$8$	−49.6354	−	40.4021i	−0.775553	−	0.631282i
$9$		0			0
$10$	45.5763	+	149.524i	0.455763	+	1.49524i
$11$	−96.1446	+	55.5091i	−0.794583	+	0.458753i	−0.841574	−	0.540142i	$-0.818370\pi$
$11$	−96.1446	+	55.5091i	−0.794583	+	0.458753i	0.0469902	+	0.998895i	$0.485037\pi$
$12$		0			0
$13$	−104.491	+	180.984i	−0.618290	+	1.07091i	0.371507	+	0.928430i	$0.378841\pi$
$13$	−104.491	+	180.984i	−0.618290	+	1.07091i	−0.989798	+	0.142480i	$0.954492\pi$
$14$	−11.0224	+	47.5603i	−0.0562366	+	0.242654i
$15$		0			0
$16$	−253.627	+	34.7739i	−0.990731	+	0.135835i
$17$	−93.3790			−0.323111			−0.161555	−	0.986864i	$-0.551651\pi$
$17$	−93.3790			−0.323111			−0.161555	+	0.986864i	$0.551651\pi$
$18$		0			0
$19$		−	26.8894i		−	0.0744859i	−0.999306	−	0.0372429i	$-0.988142\pi$
$19$		−	26.8894i		−	0.0744859i	0.999306	−	0.0372429i	$-0.0118575\pi$
$20$	561.519	+	275.043i	1.40380	+	0.687608i
$21$		0			0
$22$	−100.259	+	432.607i	−0.207147	+	0.893816i
$23$	757.577	+	437.387i	1.43209	+	0.826819i	0.997280	−	0.0737029i	$-0.0234816\pi$
$23$	757.577	+	437.387i	1.43209	+	0.826819i	0.434812	+	0.900521i	$0.356815\pi$
$24$		0			0
$25$	−451.080	−	781.293i	−0.721728	−	1.25007i
$26$	243.728	+	799.608i	0.360545	+	1.18285i
$27$		0			0
$28$	108.928	+	162.081i	0.138939	+	0.206736i
$29$	−650.809	−	1127.23i	−0.773851	−	1.34035i	−0.935438	−	0.353491i	$-0.884995\pi$
$29$	−650.809	−	1127.23i	−0.773851	−	1.34035i	0.161587	−	0.986858i	$-0.448339\pi$
$30$		0			0
$31$	593.492	+	342.653i	0.617577	+	0.356558i	0.775925	−	0.630825i	$-0.217283\pi$
$31$	593.492	+	342.653i	0.617577	+	0.356558i	−0.158348	+	0.987383i	$0.550617\pi$
$32$	−590.870	+	836.330i	−0.577022	+	0.816729i
$33$		0			0
$34$	−254.967	+	272.958i	−0.220560	+	0.236122i
$35$		−	476.966i		−	0.389360i
$36$		0			0
$37$	−1760.25			−1.28579			−0.642897	−	0.765953i	$-0.722268\pi$
$37$	−1760.25			−1.28579			−0.642897	+	0.765953i	$0.722268\pi$
$38$	−78.6008	−	73.4203i	−0.0544327	−	0.0508451i
$39$		0			0
$40$	2337.19	−	890.392i	1.46074	−	0.556495i
$41$	39.0421	−	67.6229i	0.0232255	−	0.0402278i	−0.854179	−	0.519979i	$-0.825940\pi$
$41$	39.0421	−	67.6229i	0.0232255	−	0.0402278i	0.877405	+	0.479751i	$0.159273\pi$
$42$		0			0
$43$	−1405.46	+	811.442i	−0.760118	+	0.438855i	−0.829338	−	0.558747i	$-0.811282\pi$
$43$	−1405.46	+	811.442i	−0.760118	+	0.438855i	0.0692198	+	0.997601i	$0.477949\pi$
$44$	990.807	+	1474.28i	0.511780	+	0.761510i
$45$		0			0
$46$	3347.06	−	1020.22i	1.58179	−	0.482144i
$47$	1999.54	−	1154.43i	0.905177	−	0.522604i	0.0263007	−	0.999654i	$-0.491627\pi$
$47$	1999.54	−	1154.43i	0.905177	−	0.522604i	0.878876	+	0.477050i	$0.158294\pi$
$48$		0			0
$49$	−1126.02	+	1950.32i	−0.468978	+	0.812294i
$50$	−3515.46	−	814.729i	−1.40619	−	0.325892i
$51$		0			0
$52$	3002.84	+	1470.85i	1.11052	+	0.543953i
$53$	1313.48			0.467598			0.233799	−	0.972285i	$-0.424884\pi$
$53$	1313.48			0.467598			0.233799	+	0.972285i	$0.424884\pi$
$54$		0			0
$55$		−	4338.47i		−	1.43420i
$56$	771.205	+	124.146i	0.245920	+	0.0395872i
$57$		0			0
$58$	−5072.04	−	1175.47i	−1.50774	−	0.349427i
$59$	−4818.38	−	2781.89i	−1.38419	−	0.799164i	−0.391540	−	0.920161i	$-0.628058\pi$
$59$	−4818.38	−	2781.89i	−1.38419	−	0.799164i	−0.992653	+	0.120997i	$0.961391\pi$
$60$		0			0
$61$	−1090.13	−	1888.16i	−0.292967	−	0.507433i	0.681543	−	0.731778i	$-0.261309\pi$
$61$	−1090.13	−	1888.16i	−0.292967	−	0.507433i	−0.974510	+	0.224345i	$0.927976\pi$
$62$	2622.12	−	799.247i	0.682132	−	0.207921i
$63$		0			0
$64$	831.345	+	4010.75i	0.202965	+	0.979186i
$65$	−4083.39	−	7072.65i	−0.966484	−	1.67400i
$66$		0			0
$67$	−213.077	−	123.020i	−0.0474665	−	0.0274048i	0.476079	−	0.879403i	$-0.342058\pi$
$67$	−213.077	−	123.020i	−0.0474665	−	0.0274048i	−0.523545	+	0.851998i	$0.675391\pi$
$68$	101.709	+	1490.60i	0.0219960	+	0.322361i
$69$		0			0
$70$	−1394.23	−	1302.33i	−0.284536	−	0.265783i
$71$			4608.15i			0.914134i	0.889432	+	0.457067i	$0.151100\pi$
$71$			4608.15i			0.914134i	−0.889432	+	0.457067i	$0.848900\pi$
$72$		0			0
$73$	2564.79			0.481290			0.240645	−	0.970613i	$-0.422641\pi$
$73$	2564.79			0.481290			0.240645	+	0.970613i	$0.422641\pi$
$74$	−4806.29	+	5145.42i	−0.877701	+	0.939631i
$75$		0			0
$76$	−429.232	+	29.2882i	−0.0743131	+	0.00507067i
$77$	677.500	−	1173.46i	0.114269	−	0.197919i
$78$		0			0
$79$	4486.29	−	2590.16i	0.718842	−	0.415023i	−0.0954846	−	0.995431i	$-0.530440\pi$
$79$	4486.29	−	2590.16i	0.718842	−	0.415023i	0.814326	+	0.580408i	$0.197107\pi$
$80$	3778.87	−	9263.05i	0.590449	−	1.44735i
$81$		0			0
$82$	−91.0669	−	298.766i	−0.0135436	−	0.0444328i
$83$	1622.37	−	936.677i	0.235502	−	0.135967i	−0.377606	−	0.925966i	$-0.623253\pi$
$83$	1622.37	−	936.677i	0.235502	−	0.135967i	0.613108	+	0.789999i	$0.289919\pi$
$84$		0			0
$85$	1824.57	−	3160.25i	0.252536	−	0.437405i
$86$	−1465.61	+	6323.93i	−0.198162	+	0.855047i
$87$		0			0
$88$	7014.86	+	1129.22i	0.905844	+	0.145819i
$89$	1167.17			0.147352			0.0736759	−	0.997282i	$-0.476527\pi$
$89$	1167.17			0.147352			0.0736759	+	0.997282i	$0.476527\pi$
$90$		0			0
$91$		−	2550.67i		−	0.308015i
$92$	6156.80	−	12569.5i	0.727410	−	1.48506i
$93$		0			0
$94$	2085.11	−	8997.00i	0.235979	−	1.01822i
$95$	910.026	+	525.404i	0.100834	+	0.0582165i
$96$		0			0
$97$	2869.58	+	4970.26i	0.304983	+	0.528245i	0.977257	−	0.212056i	$-0.0680160\pi$
$97$	2869.58	+	4970.26i	0.304983	+	0.528245i	−0.672275	+	0.740302i	$0.734683\pi$
$98$	2626.47	+	8616.73i	0.273476	+	0.897203i
$99$		0			0
$100$	−11980.4	+	8051.53i	−1.19804	+	0.805153i
$101$	7793.37	+	13498.5i	0.763981	+	1.32325i	0.940783	+	0.339008i	$0.110091\pi$
$101$	7793.37	+	13498.5i	0.763981	+	1.32325i	−0.176802	+	0.984246i	$0.556575\pi$
$102$		0			0
$103$	9636.52	+	5563.65i	0.908334	+	0.524427i	0.879895	−	0.475168i	$-0.157613\pi$
$103$	9636.52	+	5563.65i	0.908334	+	0.524427i	0.0284395	+	0.999596i	$0.490946\pi$
$104$	12498.6	−	4761.55i	1.15556	−	0.440232i
$105$		0			0
$106$	3586.41	−	3839.46i	0.319189	−	0.341711i
$107$			4464.91i			0.389983i	0.980805	+	0.194991i	$0.0624679\pi$
$107$			4464.91i			0.389983i	−0.980805	+	0.194991i	$0.937532\pi$
$108$		0			0
$109$	−4736.05			−0.398624			−0.199312	−	0.979936i	$-0.563871\pi$
$109$	−4736.05			−0.398624			−0.199312	+	0.979936i	$0.563871\pi$
$110$	−12681.8	−	11846.0i	−1.04809	−	0.979008i
$111$		0			0
$112$	2468.63	−	1915.35i	0.196798	−	0.152690i
$113$	−9173.06	+	15888.2i	−0.718385	+	1.24428i	0.243254	+	0.969963i	$0.421785\pi$
$113$	−9173.06	+	15888.2i	−0.718385	+	1.24428i	−0.961639	+	0.274317i	$0.911548\pi$
$114$		0			0
$115$	−29605.3	+	17092.6i	−2.23858	+	1.29245i
$116$	−17285.0	+	11616.6i	−1.28456	+	0.863301i
$117$		0			0
$118$	−21288.2	+	6488.84i	−1.52888	+	0.466018i
$119$	987.017	−	569.855i	0.0696997	−	0.0402411i
$120$		0			0
$121$	−1157.98	+	2005.68i	−0.0790915	+	0.136990i
$122$	−8495.85	−	1968.96i	−0.570804	−	0.132287i
$123$		0			0
$124$	4823.29	−	9847.06i	0.313689	−	0.640417i
$125$	10831.1			0.693190
$126$		0			0
$127$			8169.42i			0.506505i	0.967400	+	0.253252i	$0.0815003\pi$
$127$			8169.42i			0.506505i	−0.967400	+	0.253252i	$0.918500\pi$
$128$	13993.8	+	8521.05i	0.854115	+	0.520084i
$129$		0			0
$130$	−31823.7	−	7375.32i	−1.88306	−	0.436410i
$131$	9131.01	+	5271.79i	0.532079	+	0.307196i	0.741863	−	0.670552i	$-0.233943\pi$
$131$	9131.01	+	5271.79i	0.532079	+	0.307196i	−0.209784	+	0.977748i	$0.567276\pi$
$132$		0			0
$133$	164.095	+	284.221i	0.00927669	+	0.0160677i
$134$	−941.399	+	286.948i	−0.0524281	+	0.0159806i
$135$		0			0
$136$	4634.90	+	3772.70i	0.250589	+	0.203974i
$137$	1612.85	+	2793.54i	0.0859318	+	0.148838i	0.905788	−	0.423731i	$-0.139280\pi$
$137$	1612.85	+	2793.54i	0.0859318	+	0.148838i	−0.819856	+	0.572570i	$0.805947\pi$
$138$		0			0
$139$	16276.4	+	9397.17i	0.842419	+	0.486371i	0.858086	−	0.513506i	$-0.171654\pi$
$139$	16276.4	+	9397.17i	0.842419	+	0.486371i	−0.0156666	+	0.999877i	$0.504987\pi$
$140$	−7613.75	+	519.516i	−0.388457	+	0.0265059i
$141$		0			0
$142$	13470.2	+	12582.4i	0.668030	+	0.624001i
$143$		−	23200.8i		−	1.13457i
$144$		0			0
$145$	50865.8			2.41930
$146$	7003.05	−	7497.18i	0.328535	−	0.351716i
$147$		0			0
$148$	1917.28	+	28098.7i	0.0875313	+	1.28281i
$149$	−3825.13	+	6625.31i	−0.172295	+	0.298424i	−0.939222	−	0.343311i	$-0.888452\pi$
$149$	−3825.13	+	6625.31i	−0.172295	+	0.298424i	0.766927	+	0.641735i	$0.221785\pi$
$150$		0			0
$151$	−974.974	+	562.901i	−0.0427601	+	0.0246876i	−0.521228	−	0.853418i	$-0.674526\pi$
$151$	−974.974	+	562.901i	−0.0427601	+	0.0246876i	0.478468	+	0.878105i	$0.341192\pi$
$152$	−1086.39	+	1334.67i	−0.0470216	+	0.0577677i
$153$		0			0
$154$	−1580.29	−	5184.51i	−0.0666338	−	0.218608i
$155$	−23193.0	+	13390.5i	−0.965369	+	0.557356i
$156$		0			0
$157$	1755.81	−	3041.15i	0.0712326	−	0.123378i	−0.828209	−	0.560419i	$-0.810640\pi$
$157$	1755.81	−	3041.15i	0.0712326	−	0.123378i	0.899442	+	0.437041i	$0.143973\pi$
$158$	4678.28	−	20186.3i	0.187401	−	0.808615i
$159$		0			0
$160$	−16758.9	−	36338.4i	−0.654645	−	1.41947i
$161$	−10676.8			−0.411898
$162$		0			0
$163$		−	41947.9i		−	1.57883i	−0.613861	−	0.789414i	$-0.710385\pi$
$163$		−	41947.9i		−	1.57883i	0.613861	−	0.789414i	$-0.289615\pi$
$164$	−1121.98	−	549.569i	−0.0417156	−	0.0204331i
$165$		0			0
$166$	1691.80	−	7299.94i	0.0613951	−	0.264913i
$167$	−5900.58	−	3406.70i	−0.211574	−	0.122152i	0.390469	−	0.920616i	$-0.372313\pi$
$167$	−5900.58	−	3406.70i	−0.211574	−	0.122152i	−0.602043	+	0.798464i	$0.705646\pi$
$168$		0			0
$169$	−7556.26	−	13087.8i	−0.264566	−	0.458241i
$170$	−4255.87	−	13962.4i	−0.147262	−	0.483127i
$171$		0			0
$172$	14483.8	+	21551.3i	0.489582	+	0.728480i
$173$	7874.16	+	13638.4i	0.263095	+	0.455693i	0.967063	−	0.254539i	$-0.0819236\pi$
$173$	7874.16	+	13638.4i	0.263095	+	0.455693i	−0.703968	+	0.710232i	$0.748590\pi$
$174$		0			0
$175$	9535.85	+	5505.52i	0.311375	+	0.179772i
$176$	22454.6	−	17421.9i	0.724904	−	0.562434i
$177$		0			0
$178$	3186.92	−	3411.79i	0.100584	−	0.107682i
$179$			22497.6i			0.702151i	0.936347	+	0.351075i	$0.114184\pi$
$179$			22497.6i			0.702151i	−0.936347	+	0.351075i	$0.885816\pi$
$180$		0			0
$181$	−21847.2			−0.666867			−0.333434	−	0.942774i	$-0.608207\pi$
$181$	−21847.2			−0.666867			−0.333434	+	0.942774i	$0.608207\pi$
$182$	−7455.90	−	6964.49i	−0.225091	−	0.210255i
$183$		0			0
$184$	−19931.3	−	52317.5i	−0.588707	−	1.54530i
$185$	34394.3	−	59572.7i	1.00495	−	1.74062i
$186$		0			0
$187$	8977.88	−	5183.38i	0.256738	−	0.148228i
$188$	−20606.0	−	30660.9i	−0.583012	−	0.867500i
$189$		0			0
$190$	4020.60	−	1225.52i	0.111374	−	0.0339479i
$191$	−16182.1	+	9342.76i	−0.443577	+	0.256099i	−0.705114	−	0.709094i	$-0.749104\pi$
$191$	−16182.1	+	9342.76i	−0.443577	+	0.256099i	0.261537	+	0.965194i	$0.415771\pi$
$192$		0			0
$193$	−23049.7	+	39923.2i	−0.618800	+	1.07179i	0.370905	+	0.928671i	$0.379048\pi$
$193$	−23049.7	+	39923.2i	−0.618800	+	1.07179i	−0.989705	+	0.143123i	$0.954286\pi$
$194$	22363.9	+	5182.96i	0.594216	+	0.137713i
$195$		0			0
$196$	32359.2	+	15850.2i	0.842336	+	0.412593i
$197$	−15934.7			−0.410592			−0.205296	−	0.978700i	$-0.565816\pi$
$197$	−15934.7			−0.410592			−0.205296	+	0.978700i	$0.565816\pi$
$198$		0			0
$199$		−	73733.8i		−	1.86192i	−0.365124	−	0.930959i	$-0.618974\pi$
$199$		−	73733.8i		−	1.86192i	0.365124	−	0.930959i	$-0.381026\pi$
$200$	−9176.34	+	57004.4i	−0.229408	+	1.42511i
$201$		0			0
$202$	60737.2	+	14076.2i	1.48851	+	0.344971i
$203$	13758.1	+	7943.25i	0.333862	+	0.192755i
$204$		0			0
$205$	1525.72	+	2642.63i	0.0363051	+	0.0628823i
$206$	42575.3	−	12977.4i	1.00328	−	0.305810i
$207$		0			0
$208$	20208.3	−	49536.0i	0.467092	−	1.14497i
$209$	1492.61	+	2585.27i	0.0341706	+	0.0591852i
$210$		0			0
$211$	15431.2	+	8909.20i	0.346605	+	0.200112i	0.663189	−	0.748452i	$-0.269203\pi$
$211$	15431.2	+	8909.20i	0.346605	+	0.200112i	−0.316584	+	0.948564i	$0.602536\pi$
$212$	−1430.66	−	20967.0i	−0.0318321	−	0.466513i
$213$		0			0
$214$	13051.4	+	12191.2i	0.284991	+	0.266208i
$215$		−	63420.5i		−	1.37200i
$216$		0			0
$217$	−8364.29			−0.177627
$218$	−12931.6	+	13844.0i	−0.272106	+	0.291306i
$219$		0			0
$220$	−69254.5	+	4725.51i	−1.43088	+	0.0976344i
$221$	9757.27	−	16900.1i	0.199776	−	0.346022i
$222$		0			0
$223$	−58353.8	+	33690.6i	−1.17344	+	0.677483i	−0.954487	−	0.298253i	$-0.903596\pi$
$223$	−58353.8	+	33690.6i	−1.17344	+	0.677483i	−0.218949	+	0.975736i	$0.570263\pi$
$224$	1141.72	−	12445.9i	0.0227542	−	0.248044i
$225$		0			0
$226$	21396.4	+	70196.0i	0.418914	+	1.37434i
$227$	54381.5	−	31397.2i	1.05536	−	0.609310i	0.131212	−	0.991354i	$-0.458113\pi$
$227$	54381.5	−	31397.2i	1.05536	−	0.609310i	0.924144	+	0.382044i	$0.124780\pi$
$228$		0			0
$229$	20463.2	−	35443.2i	0.390213	−	0.675868i	−0.602265	−	0.798297i	$-0.705735\pi$
$229$	20463.2	−	35443.2i	0.390213	−	0.675868i	0.992477	+	0.122428i	$0.0390681\pi$
$230$	−30872.2	+	133210.i	−0.583596	+	2.51815i
$231$		0			0
$232$	−13239.4	+	82244.7i	−0.245976	+	1.52803i
$233$	−79254.5			−1.45986			−0.729932	−	0.683520i	$-0.760448\pi$
$233$	−79254.5			−1.45986			−0.729932	+	0.683520i	$0.760448\pi$
$234$		0			0
$235$			90227.9i			1.63382i
$236$	−39158.8	+	79945.2i	−0.703080	+	1.43539i
$237$		0			0
$238$	1029.26	−	4441.13i	0.0181706	−	0.0784042i
$239$	−39084.7	−	22565.5i	−0.684243	−	0.395048i	0.117209	−	0.993107i	$-0.462605\pi$
$239$	−39084.7	−	22565.5i	−0.684243	−	0.395048i	−0.801452	+	0.598059i	$0.795939\pi$
$240$		0			0
$241$	−37826.8	−	65517.9i	−0.651276	−	1.12804i	−0.982814	−	0.184601i	$-0.940901\pi$
$241$	−37826.8	−	65517.9i	−0.651276	−	1.12804i	0.331537	−	0.943442i	$-0.392433\pi$
$242$	2701.02	+	8861.32i	0.0461208	+	0.151310i
$243$		0			0
$244$	−28953.1	+	19458.2i	−0.486312	+	0.326831i
$245$	−44003.5	−	76216.3i	−0.733086	−	1.26974i
$246$		0			0
$247$	4866.55	+	2809.70i	0.0797677	+	0.0460539i
$248$	−15614.3	−	40986.0i	−0.253875	−	0.666395i
$249$		0			0
$250$	29573.8	−	31660.6i	0.473182	−	0.506569i
$251$			78270.9i			1.24238i	0.783662	+	0.621188i	$0.213350\pi$
$251$			78270.9i			1.24238i	−0.783662	+	0.621188i	$0.786650\pi$
$252$		0			0
$253$	−97115.9			−1.51722
$254$	23880.2	+	22306.2i	0.370143	+	0.345747i
$255$		0			0
$256$	63117.6	−	17639.2i	0.963097	−	0.269153i
$257$	−11506.3	+	19929.5i	−0.174209	+	0.301739i	−0.939887	−	0.341485i	$-0.889070\pi$
$257$	−11506.3	+	19929.5i	−0.174209	+	0.301739i	0.765678	+	0.643224i	$0.222403\pi$
$258$		0			0
$259$	18605.9	−	10742.1i	0.277365	−	0.160136i
$260$	−108452.	+	72886.4i	−1.60432	+	1.07820i
$261$		0			0
$262$	40341.9	−	12296.6i	0.587697	−	0.179136i
$263$	75237.8	−	43438.5i	1.08774	−	0.628006i	0.154765	−	0.987951i	$-0.450538\pi$
$263$	75237.8	−	43438.5i	1.08774	−	0.628006i	0.932973	+	0.359945i	$0.117205\pi$
$264$		0			0
$265$	−25664.7	+	44452.6i	−0.365464	+	0.633003i
$266$	1278.87	+	296.385i	0.0180743	+	0.00418883i
$267$		0			0
$268$	−1731.67	+	3535.32i	−0.0241099	+	0.0492220i
$269$	54083.3			0.747409			0.373705	−	0.927548i	$-0.378087\pi$
$269$	54083.3			0.747409			0.373705	+	0.927548i	$0.378087\pi$
$270$		0			0
$271$			47957.3i			0.653004i	0.945197	+	0.326502i	$0.105870\pi$
$271$			47957.3i			0.653004i	−0.945197	+	0.326502i	$0.894130\pi$
$272$	23683.5	−	3247.15i	0.320116	−	0.0438899i
$273$		0			0
$274$	12569.7	+	2913.09i	0.167426	+	0.0388019i
$275$	86737.8	+	50078.1i	1.14695	+	0.662190i
$276$		0			0
$277$	36861.8	+	63846.5i	0.480415	+	0.832103i	0.999748	−	0.0224689i	$-0.00715269\pi$
$277$	36861.8	+	63846.5i	0.480415	+	0.832103i	−0.519332	+	0.854572i	$0.673819\pi$
$278$	71911.0	−	21919.2i	0.930477	−	0.283618i
$279$		0			0
$280$	−19270.4	+	23674.4i	−0.245796	+	0.301969i
$281$	28062.0	+	48604.7i	0.355390	+	0.615554i	0.987185	−	0.159582i	$-0.0510147\pi$
$281$	28062.0	+	48604.7i	0.355390	+	0.615554i	−0.631795	+	0.775136i	$0.717681\pi$
$282$		0			0
$283$	−132300.	−	76383.2i	−1.65191	−	0.953730i	−0.976287	−	0.216481i	$-0.930542\pi$
$283$	−132300.	−	76383.2i	−1.65191	−	0.953730i	−0.675621	−	0.737249i	$-0.736124\pi$
$284$	73559.3	−	5019.25i	0.912013	−	0.0622303i
$285$		0			0
$286$	−67818.7	−	63348.8i	−0.829120	−	0.774474i
$287$			953.034i			0.0115703i
$288$		0			0
$289$	−74801.4			−0.895600
$290$	138887.	−	148687.i	1.65145	−	1.76797i
$291$		0			0
$292$	−2793.60	−	40941.5i	−0.0327641	−	0.480173i
$293$	−19420.1	+	33636.7i	−0.226213	+	0.391812i	−0.956683	−	0.291133i	$-0.905968\pi$
$293$	−19420.1	+	33636.7i	−0.226213	+	0.391812i	0.730470	+	0.682945i	$0.239301\pi$
$294$		0			0
$295$	188297.	−	108713.i	2.16371	−	1.24922i
$296$	87370.8	+	71117.8i	0.997201	+	0.811699i
$297$		0			0
$298$	8922.21	+	29271.4i	0.100471	+	0.329618i
$299$	−158320.	+	91406.1i	−1.77090	+	1.02243i
$300$		0			0
$301$	9903.82	−	17153.9i	0.109312	−	0.189335i
$302$	−1016.70	+	4386.94i	−0.0111475	+	0.0481003i
$303$		0			0
$304$	935.049	+	6819.88i	0.0101178	+	0.0737955i
$305$	85202.0			0.915905
$306$		0			0
$307$			457.528i			0.00485446i	0.999997	+	0.00242723i	$0.000772612\pi$
$307$			457.528i			0.00485446i	−0.999997	+	0.00242723i	$0.999227\pi$
$308$	−19469.8	−	9536.70i	−0.205239	−	0.100530i
$309$		0			0
$310$	−24185.5	+	104358.i	−0.251671	+	1.08593i
$311$	9285.82	+	5361.17i	0.0960062	+	0.0554292i	0.547234	−	0.836979i	$-0.315681\pi$
$311$	9285.82	+	5361.17i	0.0960062	+	0.0554292i	−0.451228	+	0.892409i	$0.649014\pi$
$312$		0			0
$313$	−8976.10	−	15547.1i	−0.0916218	−	0.158694i	0.816572	−	0.577244i	$-0.195872\pi$
$313$	−8976.10	−	15547.1i	−0.0916218	−	0.158694i	−0.908194	+	0.418550i	$0.862538\pi$
$314$	−4095.48	−	13436.2i	−0.0415380	−	0.136275i
$315$		0			0
$316$	−46232.9	−	68792.9i	−0.462996	−	0.688921i
$317$	−30685.9	−	53149.6i	−0.305366	−	0.528909i	0.671977	−	0.740572i	$-0.265445\pi$
$317$	−30685.9	−	53149.6i	−0.305366	−	0.528909i	−0.977343	+	0.211663i	$0.932112\pi$
$318$		0			0
$319$	125143.	+	72251.6i	1.22978	+	0.710013i
$320$	−151981.	−	50232.3i	−1.48419	−	0.490550i
$321$		0			0
$322$	−29152.5	+	31209.5i	−0.281167	+	0.301006i
$323$			2510.90i			0.0240672i
$324$		0			0
$325$	188535.			1.78495
$326$	−122619.	−	114537.i	−1.15377	−	1.07773i
$327$		0			0
$328$	−4669.98	+	1779.11i	−0.0434077	+	0.0165369i
$329$	−14090.1	+	24404.7i	−0.130173	+	0.225467i
$330$		0			0
$331$	−160993.	+	92949.3i	−1.46944	+	0.848379i	−0.999412	−	0.0342747i	$-0.989088\pi$
$331$	−160993.	+	92949.3i	−1.46944	+	0.848379i	−0.470023	+	0.882654i	$0.655755\pi$
$332$	−16719.2	−	24877.5i	−0.151684	−	0.225700i
$333$		0			0
$334$	−26069.4	+	7946.22i	−0.233689	+	0.0712308i
$335$	8326.81	−	4807.49i	0.0741975	−	0.0428379i
$336$		0			0
$337$	73998.8	−	128170.i	0.651576	−	1.12856i	−0.331165	−	0.943573i	$-0.607442\pi$
$337$	73998.8	−	128170.i	0.651576	−	1.12856i	0.982741	−	0.184989i	$-0.0592251\pi$
$338$	−58889.3	−	13647.9i	−0.515469	−	0.119463i
$339$		0			0
$340$	−52434.1	−	25683.3i	−0.453582	−	0.222174i
$341$	−76081.3			−0.654289
$342$		0			0
$343$		−	56791.2i		−	0.482717i
$344$	102544.	+	16507.2i	0.866553	+	0.139494i
$345$		0			0
$346$	61366.8	+	14222.1i	0.512603	+	0.118799i
$347$	−125556.	−	72490.0i	−1.04275	−	0.602031i	−0.122138	−	0.992513i	$-0.538975\pi$
$347$	−125556.	−	72490.0i	−1.04275	−	0.602031i	−0.920611	+	0.390482i	$0.872308\pi$
$348$		0			0
$349$	89475.8	+	154977.i	0.734606	+	1.27238i	0.954896	+	0.296941i	$0.0959664\pi$
$349$	89475.8	+	154977.i	0.734606	+	1.27238i	−0.220290	+	0.975435i	$0.570700\pi$
$350$	42130.5	−	12841.8i	0.343922	−	0.104831i
$351$		0			0
$352$	10385.0	−	113207.i	0.0838150	−	0.913670i
$353$	13197.7	+	22859.1i	0.105913	+	0.183446i	0.914111	−	0.405465i	$-0.132890\pi$
$353$	13197.7	+	22859.1i	0.105913	+	0.183446i	−0.808198	+	0.588911i	$0.799557\pi$
$354$		0			0
$355$	−155955.	−	90040.7i	−1.23749	−	0.714467i
$356$	−1271.30	−	18631.5i	−0.0100311	−	0.147010i
$357$		0			0
$358$	65763.1	+	61428.8i	0.513117	+	0.479298i
$359$		−	181364.i		−	1.40722i	−0.710587	−	0.703609i	$-0.751571\pi$
$359$		−	181364.i		−	1.40722i	0.710587	−	0.703609i	$-0.248429\pi$
$360$		0			0
$361$	129598.			0.994452
$362$	−59652.9	+	63862.0i	−0.455213	+	0.487333i
$363$		0			0
$364$	−40716.0	+	2778.22i	−0.307300	+	0.0209683i
$365$	−50114.6	+	86801.1i	−0.376165	+	0.651537i
$366$		0			0
$367$	181000.	−	104500.i	1.34383	−	0.775863i	0.356467	−	0.934308i	$-0.383981\pi$
$367$	181000.	−	104500.i	1.34383	−	0.775863i	0.987368	+	0.158445i	$0.0506481\pi$
$368$	−207352.	−	84589.4i	−1.53113	−	0.624626i
$369$		0			0
$370$	−80225.8	−	263199.i	−0.586017	−	1.92257i
$371$	−13883.5	+	8015.67i	−0.100868	+	0.0582360i
$372$		0			0
$373$	38298.0	−	66334.0i	0.275269	−	0.476781i	−0.694934	−	0.719074i	$-0.744566\pi$
$373$	38298.0	−	66334.0i	0.275269	−	0.476781i	0.970203	+	0.242293i	$0.0778996\pi$
$374$	9362.09	−	40396.4i	0.0669314	−	0.288801i
$375$		0			0
$376$	−145889.	−	23484.7i	−1.03192	−	0.166115i
$377$	272015.			1.91386
$378$		0			0
$379$			232118.i			1.61596i	0.589211	+	0.807979i	$0.299439\pi$
$379$			232118.i			1.61596i	−0.589211	+	0.807979i	$0.700561\pi$
$380$	7395.75	−	15098.9i	0.0512171	−	0.104563i
$381$		0			0
$382$	−16874.7	+	72812.3i	−0.115640	+	0.498974i
$383$	−74119.1	−	42792.7i	−0.505280	−	0.291724i	0.225611	−	0.974217i	$-0.427562\pi$
$383$	−74119.1	−	42792.7i	−0.505280	−	0.291724i	−0.730891	+	0.682494i	$0.760895\pi$
$384$		0			0
$385$	26476.0	+	45857.7i	0.178620	+	0.309379i
$386$	53764.1	+	176386.i	0.360842	+	1.18383i
$387$		0			0
$388$	76214.1	−	51220.4i	0.506258	−	0.340236i
$389$	60869.2	+	105429.i	0.402252	+	0.696721i	0.993997	−	0.109404i	$-0.0348942\pi$
$389$	60869.2	+	105429.i	0.402252	+	0.696721i	−0.591745	+	0.806125i	$0.701561\pi$
$390$		0			0
$391$	−70741.7	−	40842.8i	−0.462724	−	0.267154i
$392$	134687.	−	51311.4i	0.876504	−	0.333919i
$393$		0			0
$394$	−43508.9	+	46578.9i	−0.280276	+	0.300052i
$395$			202441.i			1.29749i
$396$		0			0
$397$	−71690.8			−0.454865			−0.227432	−	0.973794i	$-0.573033\pi$
$397$	−71690.8			−0.454865			−0.227432	+	0.973794i	$0.573033\pi$
$398$	−215532.	−	201327.i	−1.36065	−	1.27097i
$399$		0			0
$400$	141575.	+	182471.i	0.884842	+	1.14045i
$401$	−43140.3	+	74721.1i	−0.268283	+	0.464681i	−0.968419	−	0.249330i	$-0.919790\pi$
$401$	−43140.3	+	74721.1i	−0.268283	+	0.464681i	0.700135	+	0.714010i	$0.253123\pi$
$402$		0			0
$403$	−124029.	+	71608.3i	−0.763684	+	0.440913i
$404$	206987.	−	139107.i	1.26818	−	0.852291i
$405$		0			0
$406$	60785.0	−	18527.9i	0.368761	−	0.112402i
$407$	169239.	−	97710.0i	1.02167	−	0.589862i
$408$		0			0
$409$	−115231.	+	199585.i	−0.688844	+	1.19311i	0.283368	+	0.959011i	$0.408548\pi$
$409$	−115231.	+	199585.i	−0.688844	+	1.19311i	−0.972212	+	0.234102i	$0.924785\pi$
$410$	11890.6	+	2755.72i	0.0707355	+	0.0163933i
$411$		0			0
$412$	78315.6	−	159887.i	0.461375	−	0.941928i
$413$	67907.1			0.398121
$414$		0			0
$415$			73208.6i			0.425075i
$416$	−89621.6	−	194327.i	−0.517876	−	1.12291i
$417$		0			0
$418$	11632.5	+	2695.91i	0.0665767	+	0.0154295i
$419$	−48172.3	−	27812.3i	−0.274391	−	0.158420i	0.356491	−	0.934299i	$-0.383973\pi$
$419$	−48172.3	−	27812.3i	−0.274391	−	0.158420i	−0.630881	+	0.775879i	$0.717307\pi$
$420$		0			0
$421$	−70485.7	−	122085.i	−0.397683	−	0.688807i	0.595757	−	0.803165i	$-0.296852\pi$
$421$	−70485.7	−	122085.i	−0.397683	−	0.688807i	−0.993440	+	0.114358i	$0.963519\pi$
$422$	68176.8	−	20781.0i	0.382835	−	0.116692i
$423$		0			0
$424$	−65195.3	−	53067.4i	−0.362647	−	0.295186i
$425$	42121.4	+	72956.4i	0.233198	+	0.403911i
$426$		0			0
$427$	23045.4	+	13305.2i	0.126394	+	0.0729738i
$428$	71272.8	−	4863.23i	0.389078	−	0.0265483i
$429$		0			0
$430$	−185386.	−	173167.i	−1.00263	−	0.936544i
$431$			191015.i			1.02828i	0.857705	+	0.514142i	$0.171889\pi$
$431$			191015.i			1.02828i	−0.857705	+	0.514142i	$0.828111\pi$
$432$		0			0
$433$	48243.4			0.257313			0.128657	−	0.991689i	$-0.458933\pi$
$433$	48243.4			0.257313			0.128657	+	0.991689i	$0.458933\pi$
$434$	−22838.3	+	24449.8i	−0.121251	+	0.129806i
$435$		0			0
$436$	5158.56	+	75601.0i	0.0271366	+	0.397699i
$437$	11761.1	−	20370.8i	0.0615863	−	0.106671i
$438$		0			0
$439$	227081.	−	131105.i	1.17829	−	0.680285i	0.222670	−	0.974894i	$-0.428523\pi$
$439$	227081.	−	131105.i	1.17829	−	0.680285i	0.955618	+	0.294609i	$0.0951893\pi$
$440$	−175283.	+	215342.i	−0.905388	+	1.11230i
$441$		0			0
$442$	−22759.1	−	74666.6i	−0.116496	−	0.382192i
$443$	78793.6	−	45491.5i	0.401498	−	0.231805i	−0.285632	−	0.958339i	$-0.592204\pi$
$443$	78793.6	−	45491.5i	0.401498	−	0.231805i	0.687130	+	0.726534i	$0.258870\pi$
$444$		0			0
$445$	−22805.9	+	39501.0i	−0.115167	+	0.199475i
$446$	−60851.0	+	262566.i	−0.305913	+	1.31998i
$447$		0			0
$448$	−33263.3	−	37320.3i	−0.165733	−	0.185947i
$449$	−283350.			−1.40550			−0.702748	−	0.711438i	$-0.748044\pi$
$449$	−283350.			−1.40550			−0.702748	+	0.711438i	$0.748044\pi$
$450$		0			0
$451$			8668.77i			0.0426191i
$452$	263613.	+	129123.i	1.29030	+	0.632014i
$453$		0			0
$454$	56708.7	−	244692.i	0.275130	−	1.18716i
$455$	86323.1	+	49838.7i	0.416970	+	0.240737i
$456$		0			0
$457$	−99226.7	−	171866.i	−0.475112	−	0.822918i	0.524482	−	0.851422i	$-0.324259\pi$
$457$	−99226.7	−	171866.i	−0.475112	−	0.822918i	−0.999594	+	0.0285035i	$0.990926\pi$
$458$	−47730.9	−	156592.i	−0.227546	−	0.746517i
$459$		0			0
$460$	305094.	+	453968.i	1.44184	+	2.14541i
$461$	−104347.	−	180735.i	−0.490998	−	0.850433i	0.508949	−	0.860797i	$-0.330034\pi$
$461$	−104347.	−	180735.i	−0.490998	−	0.850433i	−0.999946	+	0.0103639i	$0.996701\pi$
$462$		0			0
$463$	−22687.9	−	13098.9i	−0.105836	−	0.0611044i	0.446148	−	0.894959i	$-0.352796\pi$
$463$	−22687.9	−	13098.9i	−0.105836	−	0.0611044i	−0.551984	+	0.833855i	$0.686129\pi$
$464$	204261.	+	263266.i	0.948746	+	1.22281i
$465$		0			0
$466$	−216401.	+	231670.i	−0.996524	+	1.06684i
$467$			96607.8i			0.442974i	0.975163	+	0.221487i	$0.0710911\pi$
$467$			96607.8i			0.442974i	−0.975163	+	0.221487i	$0.928909\pi$
$468$		0			0
$469$	3002.97			0.0136523
$470$	263747.	+	246363.i	1.19396	+	1.11527i
$471$		0			0
$472$	126768.	+	332753.i	0.569017	+	1.49361i
$473$	90084.9	−	156032.i	0.402652	−	0.697413i
$474$		0			0
$475$	−21008.5	+	12129.3i	−0.0931125	+	0.0537585i
$476$	−10171.6	−	15135.0i	−0.0448926	−	0.0667986i
$477$		0			0
$478$	−172681.	+	52634.7i	−0.755767	+	0.230365i
$479$	29664.3	−	17126.7i	0.129289	−	0.0746453i	−0.433960	−	0.900932i	$-0.642884\pi$
$479$	29664.3	−	17126.7i	0.129289	−	0.0746453i	0.563250	+	0.826287i	$0.309551\pi$
$480$		0			0
$481$	183931.	−	318577.i	0.794994	−	1.37697i
$482$	−294801.	−	68321.7i	−1.26892	−	0.294080i
$483$		0			0
$484$	33277.7	+	16300.1i	0.142057	+	0.0695823i
$485$	−224280.			−0.953470
$486$		0			0
$487$			69521.4i			0.293130i	0.989201	+	0.146565i	$0.0468218\pi$
$487$			69521.4i			0.293130i	−0.989201	+	0.146565i	$0.953178\pi$
$488$	−22176.5	+	137763.i	−0.0931224	+	0.578486i
$489$		0			0
$490$	−342939.	−	79477.9i	−1.42832	−	0.331020i
$491$	174305.	+	100635.i	0.723016	+	0.417433i	0.815862	−	0.578247i	$-0.196263\pi$
$491$	174305.	+	100635.i	0.723016	+	0.417433i	−0.0928458	+	0.995681i	$0.529596\pi$
$492$		0			0
$493$	60771.9	+	105260.i	0.250040	+	0.433081i
$494$	21501.0	−	6553.71i	0.0881057	−	0.0268555i
$495$		0			0
$496$	−162441.	−	66268.0i	−0.660286	−	0.269365i
$497$	−28121.7	−	48708.2i	−0.113849	−	0.197192i
$498$		0			0
$499$	46850.8	+	27049.3i	0.188155	+	0.108631i	0.591119	−	0.806585i	$-0.298687\pi$
$499$	46850.8	+	27049.3i	0.188155	+	0.108631i	−0.402964	+	0.915216i	$0.632020\pi$
$500$	−11797.3	−	172896.i	−0.0471894	−	0.691582i
$501$		0			0
$502$	228795.	+	213715.i	0.907902	+	0.848064i
$503$		−	239548.i		−	0.946795i	−0.880849	−	0.473397i	$-0.843027\pi$
$503$		−	239548.i		−	0.946795i	0.880849	−	0.473397i	$-0.156973\pi$
$504$		0			0
$505$	−609113.			−2.38844
$506$	−265171.	+	283881.i	−1.03568	+	1.10875i
$507$		0			0
$508$	130407.	−	8898.22i	0.505330	−	0.0344807i
$509$	57738.0	−	100005.i	0.222857	−	0.386000i	−0.732817	−	0.680425i	$-0.761795\pi$
$509$	57738.0	−	100005.i	0.222857	−	0.386000i	0.955674	+	0.294426i	$0.0951284\pi$
$510$		0			0
$511$	−27109.9	+	15651.9i	−0.103821	+	0.0599412i
$512$	120778.	−	232663.i	0.460733	−	0.887539i
$513$		0			0
$514$	26838.8	+	88051.1i	0.101587	+	0.333279i
$515$	−376584.	+	217421.i	−1.41987	+	0.819761i
$516$		0			0
$517$	−128163.	+	221985.i	−0.479492	+	0.830505i
$518$	19402.1	−	83718.1i	0.0723086	−	0.312004i
$519$		0			0
$520$	−83068.7	+	516031.i	−0.307207	+	1.90840i
$521$	−217267.			−0.800420			−0.400210	−	0.916424i	$-0.631063\pi$
$521$	−217267.			−0.800420			−0.400210	+	0.916424i	$0.631063\pi$
$522$		0			0
$523$		−	39683.4i		−	0.145079i	−0.997366	−	0.0725397i	$-0.976890\pi$
$523$		−	39683.4i		−	0.145079i	0.997366	−	0.0725397i	$-0.0231104\pi$
$524$	74207.4	−	151499.i	0.270262	−	0.551757i
$525$		0			0
$526$	78457.6	−	338536.i	0.283572	−	1.22358i
$527$	−55419.6	−	31996.5i	−0.199546	−	0.115208i
$528$		0			0
$529$	242694.	+	420359.i	0.867258	+	1.50213i
$530$	59863.7	+	196397.i	0.213114	+	0.699170i
$531$		0			0
$532$	4358.26	−	2929.01i	0.0153989	−	0.0103490i
$533$	8159.11	+	14132.0i	0.0287202	+	0.0497449i
$534$		0			0
$535$	−151107.	−	87241.9i	−0.527932	−	0.304802i
$536$	5605.90	+	14714.9i	0.0195126	+	0.0512186i
$537$		0			0
$538$	147672.	−	158092.i	0.510192	−	0.546191i
$539$		−	250017.i		−	0.860580i
$540$		0			0
$541$	−194992.			−0.666228			−0.333114	−	0.942887i	$-0.608099\pi$
$541$	−194992.			−0.666228			−0.333114	+	0.942887i	$0.608099\pi$
$542$	140185.	+	130945.i	0.477201	+	0.445750i
$543$		0			0
$544$	55174.8	−	78095.7i	0.186442	−	0.263894i
$545$	92539.8	−	160284.i	0.311556	−	0.539630i
$546$		0			0
$547$	81637.9	−	47133.6i	0.272846	−	0.157527i	−0.357335	−	0.933976i	$-0.616314\pi$
$547$	81637.9	−	47133.6i	0.272846	−	0.157527i	0.630180	+	0.776449i	$0.282981\pi$
$548$	42836.3	−	28788.5i	0.142643	−	0.0958647i
$549$		0			0
$550$	383218.	−	116809.i	1.26684	−	0.386144i
$551$	−30310.6	+	17499.9i	−0.0998371	+	0.0576410i
$552$		0			0
$553$	−31613.4	+	54756.1i	−0.103376	+	0.179053i
$554$	287280.	+	66578.8i	0.936022	+	0.216928i
$555$		0			0
$556$	132278.	−	270053.i	0.427894	−	0.873575i
$557$	563587.			1.81656			0.908282	−	0.418358i	$-0.137394\pi$
$557$	563587.			1.81656			0.908282	+	0.418358i	$0.137394\pi$
$558$		0			0
$559$		−	339154.i		−	1.08536i
$560$	16586.0	+	120972.i	0.0528889	+	0.385751i
$561$		0			0
$562$	218699.	+	50684.8i	0.692428	+	0.160474i
$563$	543509.	+	313795.i	1.71471	+	0.989986i	0.927935	+	0.372741i	$0.121582\pi$
$563$	543509.	+	313795.i	1.71471	+	0.989986i	0.786771	+	0.617245i	$0.211751\pi$
$564$		0			0
$565$	−358473.	−	620894.i	−1.12295	−	1.94500i
$566$	−584516.	+	178166.i	−1.82458	+	0.556150i
$567$		0			0
$568$	186179.	−	228727.i	0.577077	−	0.708959i
$569$	−38859.9	−	67307.3i	−0.120026	−	0.207892i	0.799751	−	0.600331i	$-0.204965\pi$
$569$	−38859.9	−	67307.3i	−0.120026	−	0.207892i	−0.919778	+	0.392439i	$0.871631\pi$
$570$		0			0
$571$	−276094.	−	159403.i	−0.846809	−	0.488905i	0.0127640	−	0.999919i	$-0.495937\pi$
$571$	−276094.	−	159403.i	−0.846809	−	0.488905i	−0.859573	+	0.511013i	$0.829270\pi$
$572$	−370352.	+	25270.6i	−1.13194	+	0.0772366i
$573$		0			0
$574$	2785.83	+	2602.22i	0.00845533	+	0.00789805i
$575$		−	789186.i		−	2.38695i
$576$		0			0
$577$	40053.7			0.120307			0.0601534	−	0.998189i	$-0.480841\pi$
$577$	40053.7			0.120307			0.0601534	+	0.998189i	$0.480841\pi$
$578$	−204242.	+	218653.i	−0.611349	+	0.654485i
$579$		0			0
$580$	−55403.5	−	811964.i	−0.164695	−	2.41369i
$581$	−11432.3	+	19801.4i	−0.0338675	+	0.0586602i
$582$		0			0
$583$	−126284.	+	72910.3i	−0.371546	+	0.214512i
$584$	−127304.	−	103623.i	−0.373266	−	0.303830i
$585$		0			0
$586$	45298.0	+	148611.i	0.131912	+	0.432768i
$587$	11894.5	−	6867.28i	0.0345199	−	0.0199301i	−0.482641	−	0.875818i	$-0.660322\pi$
$587$	11894.5	−	6867.28i	0.0345199	−	0.0199301i	0.517161	+	0.855888i	$0.326989\pi$
$588$		0			0
$589$	9213.72	−	15958.6i	0.0265586	−	0.0460008i
$590$	196355.	−	847250.i	0.564076	−	2.43393i
$591$		0			0
$592$	446448.	−	61210.8i	1.27388	−	0.174656i
$593$	−537582.			−1.52875			−0.764373	−	0.644775i	$-0.776951\pi$
$593$	−537582.			−1.52875			−0.764373	+	0.644775i	$0.776951\pi$
$594$		0			0
$595$			44538.6i			0.125806i
$596$	109925.	+	53843.7i	0.309461	+	0.151580i
$597$		0			0
$598$	−165095.	+	712368.i	−0.461671	+	1.99206i
$599$	−394401.	−	227708.i	−1.09922	−	0.634635i	−0.163204	−	0.986592i	$-0.552183\pi$
$599$	−394401.	−	227708.i	−1.09922	−	0.634635i	−0.936016	+	0.351958i	$0.885516\pi$
$600$		0			0
$601$	118996.	+	206108.i	0.329446	+	0.570618i	0.982402	−	0.186778i	$-0.0598046\pi$
$601$	118996.	+	206108.i	0.329446	+	0.570618i	−0.652956	+	0.757396i	$0.726471\pi$
$602$	−23100.9	−	75788.0i	−0.0637436	−	0.209126i
$603$		0			0
$604$	10047.5	+	14950.3i	0.0275412	+	0.0409803i
$605$	−45252.5	−	78379.7i	−0.123632	−	0.214137i
$606$		0			0
$607$	516142.	+	297995.i	1.40085	+	0.808781i	0.994480	−	0.104927i	$-0.0334608\pi$
$607$	516142.	+	297995.i	1.40085	+	0.808781i	0.406371	+	0.913708i	$0.366794\pi$
$608$	22488.4	+	15888.1i	0.0608347	+	0.0429799i
$609$		0			0
$610$	232640.	−	249055.i	0.625209	−	0.669324i
$611$			482511.i			1.29248i
$612$		0			0
$613$	547275.			1.45641			0.728206	−	0.685358i	$-0.240354\pi$
$613$	547275.			1.45641			0.728206	+	0.685358i	$0.240354\pi$
$614$	1337.41	+	1249.26i	0.00354754	+	0.00331372i
$615$		0			0
$616$	−81038.4	+	30873.0i	−0.213565	+	0.0813611i
$617$	259077.	−	448735.i	0.680549	−	1.17874i	−0.294265	−	0.955724i	$-0.595075\pi$
$617$	259077.	−	448735.i	0.680549	−	1.17874i	0.974814	−	0.223021i	$-0.0715919\pi$
$618$		0			0
$619$	176869.	−	102115.i	0.461605	−	0.266508i	−0.251114	−	0.967958i	$-0.580797\pi$
$619$	176869.	−	102115.i	0.461605	−	0.266508i	0.712719	+	0.701450i	$0.247463\pi$
$620$	239013.	+	355642.i	0.621781	+	0.925187i
$621$		0			0
$622$	41025.8	−	12505.1i	0.106042	−	0.0323226i
$623$	−12337.1	+	7122.80i	−0.0317860	+	0.0183516i
$624$		0			0
$625$	70291.3	−	121748.i	0.179946	−	0.311675i
$626$	−69954.7	−	16212.4i	−0.178512	−	0.0413712i
$627$		0			0
$628$	−50458.0	−	24715.4i	−0.127941	−	0.0626683i
$629$	164370.			0.415454
$630$		0			0
$631$			177036.i			0.444633i	0.974975	+	0.222317i	$0.0713618\pi$
$631$			177036.i			0.444633i	−0.974975	+	0.222317i	$0.928638\pi$
$632$	−327327.	−	52691.8i	−0.819497	−	0.131919i
$633$		0			0
$634$	−239149.	−	55424.1i	−0.594963	−	0.137886i
$635$	−276480.	−	159626.i	−0.685672	−	0.395873i
$636$		0			0
$637$	−235317.	−	407582.i	−0.579929	−	1.00447i
$638$	552899.	−	168529.i	1.35833	−	0.414031i
$639$		0			0
$640$	−561812.	+	307101.i	−1.37161	+	0.749758i
$641$	109444.	+	189562.i	0.266364	+	0.461356i	0.967920	−	0.251258i	$-0.0808444\pi$
$641$	109444.	+	189562.i	0.266364	+	0.461356i	−0.701556	+	0.712614i	$0.747511\pi$
$642$		0			0
$643$	298938.	+	172592.i	0.723035	+	0.417445i	0.815869	−	0.578237i	$-0.196259\pi$
$643$	298938.	+	172592.i	0.723035	+	0.417445i	−0.0928336	+	0.995682i	$0.529592\pi$
$644$	11629.3	+	170432.i	0.0280402	+	0.410942i
$645$		0			0
$646$	7339.66	+	6855.91i	0.0175878	+	0.0164286i
$647$			398251.i			0.951366i	0.879617	+	0.475683i	$0.157799\pi$
$647$			398251.i			0.951366i	−0.879617	+	0.475683i	$0.842201\pi$
$648$		0			0
$649$	617681.			1.46648
$650$	514787.	−	551110.i	1.21843	−	1.30440i
$651$		0			0
$652$	−669609.	+	45690.1i	−1.57517	+	0.107480i
$653$	−171144.	+	296430.i	−0.401361	+	0.695178i	−0.993890	−	0.110371i	$-0.964796\pi$
$653$	−171144.	+	296430.i	−0.401361	+	0.695178i	0.592529	+	0.805549i	$0.298129\pi$
$654$		0			0
$655$	−356830.	+	206016.i	−0.831722	+	0.480195i
$656$	−7550.63	+	18508.7i	−0.0175459	+	0.0430098i
$657$		0			0
$658$	32865.5	+	107823.i	0.0759082	+	0.249035i
$659$	452868.	−	261464.i	1.04280	−	0.602061i	0.122175	−	0.992509i	$-0.461013\pi$
$659$	452868.	−	261464.i	1.04280	−	0.602061i	0.920625	+	0.390447i	$0.127680\pi$
$660$		0			0
$661$	−154294.	+	267245.i	−0.353140	+	0.611656i	−0.986798	−	0.161957i	$-0.948219\pi$
$661$	−154294.	+	267245.i	−0.353140	+	0.611656i	0.633658	+	0.773613i	$0.281553\pi$
$662$	−167883.	+	724395.i	−0.383080	+	1.65295i
$663$		0			0
$664$	−118371.	−	19054.9i	−0.268478	−	0.0432185i
$665$	−12825.3			−0.0290018
$666$		0			0
$667$		−	1.13862e6i		−	2.55934i
$668$	−47953.8	+	97900.8i	−0.107466	+	0.219398i
$669$		0			0
$670$	8683.16	−	37466.9i	0.0193432	−	0.0834637i
$671$	209620.	+	121024.i	0.465573	+	0.268798i
$672$		0			0
$673$	124260.	+	215225.i	0.274348	+	0.475184i	0.969970	−	0.243223i	$-0.0782047\pi$
$673$	124260.	+	215225.i	0.274348	+	0.475184i	−0.695623	+	0.718407i	$0.744871\pi$
$674$	−172604.	−	566269.i	−0.379955	−	1.24653i
$675$		0			0
$676$	−200689.	+	134875.i	−0.439168	+	0.295147i
$677$	134761.	+	233413.i	0.294027	+	0.509270i	0.974758	−	0.223264i	$-0.0716711\pi$
$677$	134761.	+	233413.i	0.294027	+	0.509270i	−0.680731	+	0.732533i	$0.738338\pi$
$678$		0			0
$679$	−60663.0	−	35023.8i	−0.131578	−	0.0759668i
$680$	−218244.	+	83143.9i	−0.471981	+	0.179809i
$681$		0			0
$682$	−207737.	+	222395.i	−0.446627	+	0.478140i
$683$			124482.i			0.266848i	0.991059	+	0.133424i	$0.0425972\pi$
$683$			124482.i			0.266848i	−0.991059	+	0.133424i	$0.957403\pi$
$684$		0			0
$685$	−126057.			−0.268649
$686$	−166007.	−	155066.i	−0.352760	−	0.329510i
$687$		0			0
$688$	328246.	−	254677.i	0.693461	−	0.538038i
$689$	−137247.	+	237719.i	−0.289111	+	0.500756i
$690$		0			0
$691$	−771402.	+	445369.i	−1.61557	+	0.932747i	−0.627518	+	0.778602i	$0.715929\pi$
$691$	−771402.	+	445369.i	−1.61557	+	0.932747i	−0.988048	+	0.154145i	$0.950738\pi$
$692$	209132.	−	140549.i	0.436726	−	0.293506i
$693$		0			0
$694$	−554723.	+	169085.i	−1.15175	+	0.351064i
$695$	−636063.	+	367231.i	−1.31683	+	0.760274i
$696$		0			0
$697$	−3645.71	+	6314.56i	−0.00750442	+	0.0129980i
$698$	697324.	+	161609.i	1.43128	+	0.331707i
$699$		0			0
$700$	77497.5	−	158216.i	0.158158	−	0.322890i
$701$	170934.			0.347851			0.173925	−	0.984759i	$-0.444355\pi$
$701$	170934.			0.347851			0.173925	+	0.984759i	$0.444355\pi$
$702$		0			0
$703$			47332.1i			0.0957734i
$704$	−302562.	−	339464.i	−0.610477	−	0.684934i
$705$		0			0
$706$	102855.	+	23837.3i	0.206356	+	0.0478242i
$707$	−164752.	−	95119.7i	−0.329604	−	0.190297i
$708$		0			0
$709$	350963.	+	607886.i	0.698183	+	1.20929i	0.969096	+	0.246684i	$0.0793410\pi$
$709$	350963.	+	607886.i	0.698183	+	1.20929i	−0.270913	+	0.962604i	$0.587326\pi$
$710$	−689028.	+	210022.i	−1.36685	+	0.416628i
$711$		0			0
$712$	−57933.2	−	47156.3i	−0.114279	−	0.0930206i
$713$	299744.	+	519171.i	0.589618	+	1.02125i
$714$		0			0
$715$	785193.	+	453331.i	1.53590	+	0.886755i
$716$	359127.	−	24504.6i	0.700522	−	0.0477994i
$717$		0			0
$718$	−530147.	−	495206.i	−1.02837	−	0.960587i
$719$			768366.i			1.48631i	0.669117	+	0.743157i	$0.266672\pi$
$719$			768366.i			1.48631i	−0.669117	+	0.743157i	$0.733328\pi$
$720$		0			0
$721$	−135811.			−0.261255
$722$	353862.	−	378830.i	0.678827	−	0.726724i
$723$		0			0
$724$	23796.2	+	348745.i	0.0453974	+	0.665320i
$725$	−587133.	+	1.01695e6i	−1.11702	+	1.93473i
$726$		0			0
$727$	−221493.	+	127879.i	−0.419074	+	0.241952i	−0.694681	−	0.719318i	$-0.744454\pi$
$727$	−221493.	+	127879.i	−0.419074	+	0.241952i	0.275607	+	0.961270i	$0.411121\pi$
$728$	−103052.	+	126604.i	−0.194444	+	0.238882i
$729$		0			0
$730$	116894.	+	383497.i	0.219354	+	0.719642i
$731$	131240.	−	75771.6i	0.245602	−	0.141799i
$732$		0			0
$733$	−184829.	+	320133.i	−0.344003	+	0.595831i	−0.985172	−	0.171569i	$-0.945116\pi$
$733$	−184829.	+	320133.i	−0.344003	+	0.595831i	0.641169	+	0.767400i	$0.278450\pi$
$734$	188746.	−	814416.i	0.350336	−	1.51166i
$735$		0			0
$736$	−813429.	+	375145.i	−1.50163	+	0.692539i
$737$	27314.9			0.0502881
$738$		0			0
$739$			1.03557e6i			1.89623i	0.317932	+	0.948114i	$0.397012\pi$
$739$			1.03557e6i			1.89623i	−0.317932	+	0.948114i	$0.602988\pi$
$740$	−988415.	−	484146.i	−1.80500	−	0.884123i
$741$		0			0
$742$	−14477.7	+	62469.6i	−0.0262961	+	0.113465i
$743$	−486002.	−	280593.i	−0.880360	−	0.508276i	−0.00958322	−	0.999954i	$-0.503050\pi$
$743$	−486002.	−	280593.i	−0.880360	−	0.508276i	−0.870777	+	0.491678i	$0.836384\pi$
$744$		0			0
$745$	−149482.	−	258910.i	−0.269324	−	0.466483i
$746$	−89331.1	−	293072.i	−0.160518	−	0.526618i
$747$		0			0
$748$	−92520.5	−	137667.i	−0.165362	−	0.246052i
$749$	−27247.6	−	47194.2i	−0.0485696	−	0.0841250i
$750$		0			0
$751$	−164898.	−	95204.1i	−0.292372	−	0.168801i	0.346639	−	0.937999i	$-0.387323\pi$
$751$	−164898.	−	95204.1i	−0.292372	−	0.168801i	−0.639011	+	0.769197i	$0.720656\pi$
$752$	−466993.	+	362327.i	−0.825799	+	0.640715i
$753$		0			0
$754$	742725.	−	795131.i	1.30643	−	1.39861i
$755$		−	43995.1i		−	0.0771810i
$756$		0			0
$757$	523077.			0.912797			0.456398	−	0.889776i	$-0.349139\pi$
$757$	523077.			0.912797			0.456398	+	0.889776i	$0.349139\pi$
$758$	678508.	+	633788.i	1.18091	+	1.10308i
$759$		0			0
$760$	−23942.1	−	62845.6i	−0.0414510	−	0.108805i
$761$	−80448.7	+	139341.i	−0.138915	+	0.240608i	−0.927086	−	0.374848i	$-0.877695\pi$
$761$	−80448.7	+	139341.i	−0.138915	+	0.240608i	0.788171	+	0.615456i	$0.211028\pi$
$762$		0			0
$763$	50060.1	−	28902.2i	0.0859890	−	0.0496458i
$764$	166763.	+	248137.i	0.285702	+	0.425114i
$765$		0			0
$766$	−327467.	+	99815.1i	−0.558097	+	0.170113i
$767$	1.00695e6	−	581365.i	1.71167	−	0.988231i
$768$		0			0
$769$	297804.	−	515812.i	0.503591	−	0.872246i	−0.496400	−	0.868094i	$-0.665345\pi$
$769$	297804.	−	515812.i	0.503591	−	0.872246i	0.999991	−	0.00415186i	$-0.00132158\pi$
$770$	206339.	+	47820.2i	0.348016	+	0.0806547i
$771$		0			0
$772$	662396.	+	324455.i	1.11143	+	0.544402i
$773$	583394.			0.976345			0.488172	−	0.872747i	$-0.337664\pi$
$773$	583394.			0.976345			0.488172	+	0.872747i	$0.337664\pi$
$774$		0			0
$775$		−	618255.i		−	1.02935i
$776$	58376.0	−	362638.i	0.0969418	−	0.602212i
$777$		0			0
$778$	474381.	+	109940.i	0.783732	+	0.181634i
$779$	−1818.34	−	1049.82i	−0.00299640	−	0.00172997i
$780$		0			0
$781$	−255794.	−	443049.i	−0.419362	−	0.726356i
$782$	−312545.	+	95266.9i	−0.511092	+	0.155786i
$783$		0			0
$784$	217768.	−	533810.i	0.354293	−	0.868469i
$785$	68615.2	+	118845.i	0.111348	+	0.192860i
$786$		0			0
$787$	151046.	+	87206.2i	0.243870	+	0.140798i	0.616954	−	0.786999i	$-0.288366\pi$
$787$	151046.	+	87206.2i	0.243870	+	0.140798i	−0.373084	+	0.927798i	$0.621700\pi$
$788$	17356.2	+	254363.i	0.0279513	+	0.409639i
$789$		0			0
$790$	591759.	+	552757.i	0.948180	+	0.885687i
$791$		−	223918.i		−	0.357879i
$792$		0			0
$793$	455635.			0.724553
$794$	−195749.	+	209560.i	−0.310497	+	0.332406i
$795$		0			0
$796$	−1.17700e6	+	80311.6i	−1.85760	+	0.126751i
$797$	423576.	−	733655.i	0.666829	−	1.15498i	−0.311957	−	0.950096i	$-0.600984\pi$
$797$	423576.	−	733655.i	0.666829	−	1.15498i	0.978786	−	0.204886i	$-0.0656823\pi$
$798$		0			0
$799$	−186715.	+	107800.i	−0.292472	+	0.168859i
$800$	919949.	+	84391.1i	1.43742	+	0.131861i
$801$		0			0
$802$	100626.	+	330127.i	0.156445	+	0.513254i
$803$	−246591.	+	142369.i	−0.382425	+	0.220793i
$804$		0			0
$805$	208619.	−	361338.i	0.321930	−	0.557599i
$806$	−129337.	+	558075.i	−0.199091	+	0.859058i
$807$		0			0
$808$	158541.	−	984873.i	0.242839	−	1.50854i
$809$	−43118.8			−0.0658824			−0.0329412	−	0.999457i	$-0.510487\pi$
$809$	−43118.8			−0.0658824			−0.0329412	+	0.999457i	$0.510487\pi$
$810$		0			0
$811$		−	372984.i		−	0.567085i	−0.958960	−	0.283543i	$-0.908490\pi$
$811$		−	372984.i		−	0.567085i	0.958960	−	0.283543i	$-0.0915097\pi$
$812$	111812.	−	228271.i	0.169580	−	0.346209i
$813$		0			0
$814$	176481.	−	761497.i	0.266348	−	1.14926i
$815$	1.41966e6	+	819638.i	2.13731	+	1.23398i
$816$		0			0
$817$	21819.2	+	37791.9i	0.0326885	+	0.0566181i
$818$	268778.	+	881791.i	0.401687	+	1.31783i
$819$		0			0
$820$	40522.2	−	27233.3i	0.0602650	−	0.0405017i
$821$	−665022.	−	1.15185e6i	−0.986620	−	1.70888i	−0.634504	−	0.772920i	$-0.718796\pi$
$821$	−665022.	−	1.15185e6i	−0.986620	−	1.70888i	−0.352116	−	0.935956i	$-0.614538\pi$
$822$		0			0
$823$	636230.	+	367328.i	0.939322	+	0.542318i	0.889748	−	0.456452i	$-0.150880\pi$
$823$	636230.	+	367328.i	0.939322	+	0.542318i	0.0495745	+	0.998770i	$0.484213\pi$
$824$	−253530.	−	665489.i	−0.373400	−	0.980136i
$825$		0			0
$826$	185417.	−	198500.i	0.271763	−	0.290938i
$827$		−	1.27112e6i		−	1.85856i	−0.369375	−	0.929281i	$-0.620428\pi$
$827$		−	1.27112e6i		−	1.85856i	0.369375	−	0.929281i	$-0.379572\pi$
$828$		0			0
$829$	−427267.			−0.621714			−0.310857	−	0.950457i	$-0.600616\pi$
$829$	−427267.			−0.621714			−0.310857	+	0.950457i	$0.600616\pi$
$830$	213997.	+	199893.i	0.310636	+	0.290163i
$831$		0			0
$832$	−812748.	−	268627.i	−1.17411	−	0.388064i
$833$	105146.	−	182119.i	0.151532	−	0.262461i
$834$		0			0
$835$	230588.	−	133130.i	0.330723	−	0.190943i
$836$	39642.6	−	26642.2i	0.0567217	−	0.0381204i
$837$		0			0
$838$	−212831.	+	64873.0i	−0.303073	+	0.0923796i
$839$	−601815.	+	347458.i	−0.854947	+	0.493604i	−0.862317	−	0.506369i	$-0.830987\pi$
$839$	−601815.	+	347458.i	−0.854947	+	0.493604i	0.00737025	+	0.999973i	$0.497654\pi$
$840$		0			0
$841$	−493464.	+	854704.i	−0.697691	+	1.20844i
$842$	−549327.	−	127310.i	−0.774830	−	0.179571i
$843$		0			0
$844$	125409.	−	256030.i	0.176053	−	0.359423i
$845$	590581.			0.827115
$846$		0			0
$847$		−	28266.7i		−	0.0394011i
$848$	−333135.	+	45674.9i	−0.463264	+	0.0635164i
$849$		0			0
$850$	328270.	+	76078.5i	0.454354	+	0.105299i
$851$	−1.33353e6	−	769911.i	−1.84137	−	1.06312i
$852$		0			0
$853$	−72314.7	−	125253.i	−0.0993867	−	0.172143i	0.812044	−	0.583596i	$-0.198355\pi$
$853$	−72314.7	−	125253.i	−0.0993867	−	0.172143i	−0.911431	+	0.411453i	$0.865021\pi$
$854$	101817.	−	31034.8i	0.139606	−	0.0425534i
$855$		0			0
$856$	180392.	−	221618.i	0.246189	−	0.302452i
$857$	−318005.	−	550800.i	−0.432984	−	0.749951i	0.564145	−	0.825676i	$-0.309206\pi$
$857$	−318005.	−	550800.i	−0.432984	−	0.749951i	−0.997129	+	0.0757255i	$0.975873\pi$
$858$		0			0
$859$	−1.16908e6	−	674970.i	−1.58438	−	0.914741i	−0.994209	−	0.107460i	$-0.965728\pi$
$859$	−1.16908e6	−	674970.i	−1.58438	−	0.914741i	−0.590168	−	0.807281i	$-0.700938\pi$
$860$	−1.01237e6	+	69078.3i	−1.36881	+	0.0933996i
$861$		0			0
$862$	558359.	+	521558.i	0.751448	+	0.701921i
$863$			916363.i			1.23040i	0.788372	+	0.615199i	$0.210924\pi$
$863$			916363.i			1.23040i	−0.788372	+	0.615199i	$0.789076\pi$
$864$		0			0
$865$	−615427.			−0.822515
$866$	131727.	−	141021.i	0.175646	−	0.188039i
$867$		0			0
$868$	9110.47	+	133518.i	0.0120921	+	0.177215i
$869$	−287555.	+	498060.i	−0.380786	+	0.659541i
$870$		0			0
$871$	44529.3	−	25709.0i	0.0586961	−	0.0338882i
$872$	235076.	+	191346.i	0.309154	+	0.251644i
$873$		0			0
$874$	−27433.0	−	90000.5i	−0.0359129	−	0.117821i
$875$	−114485.	+	66097.9i	−0.149531	+	0.0863319i
$876$		0			0
$877$	273128.	−	473071.i	0.355113	−	0.615074i	−0.632024	−	0.774949i	$-0.717776\pi$
$877$	273128.	−	473071.i	0.355113	−	0.615074i	0.987137	+	0.159875i	$0.0511090\pi$
$878$	236799.	−	1.02176e6i	0.307178	−	1.32544i
$879$		0			0
$880$	150865.	+	1.10035e6i	0.194816	+	1.42091i
$881$	−446863.			−0.575735			−0.287867	−	0.957670i	$-0.592946\pi$
$881$	−446863.			−0.575735			−0.287867	+	0.957670i	$0.592946\pi$
$882$		0			0
$883$			140436.i			0.180119i	0.995936	+	0.0900593i	$0.0287056\pi$
$883$			140436.i			0.180119i	−0.995936	+	0.0900593i	$0.971294\pi$
$884$	−280402.	−	137346.i	−0.358820	−	0.175757i
$885$		0			0
$886$	82165.5	−	354535.i	0.104670	−	0.451639i
$887$	307169.	+	177344.i	0.390418	+	0.225408i	0.682341	−	0.731034i	$-0.260962\pi$
$887$	307169.	+	177344.i	0.390418	+	0.225408i	−0.291923	+	0.956442i	$0.594295\pi$
$888$		0			0
$889$	−49854.7	−	86350.9i	−0.0630816	−	0.109261i
$890$	53195.5	+	174520.i	0.0671575	+	0.220326i
$891$		0			0
$892$	601358.	+	894798.i	0.755794	+	1.12459i
$893$	−31042.0	−	53766.3i	−0.0389266	−	0.0674229i
$894$		0			0
$895$	−761394.	−	439591.i	−0.950525	−	0.548786i
$896$	−199916.	−	4668.90i	−0.249018	−	0.00581565i
$897$		0			0
$898$	−773674.	+	828264.i	−0.959412	+	1.02711i
$899$		−	892005.i		−	1.10369i
$900$		0			0
$901$	−122652.			−0.151086
$902$	25339.8	+	23669.7i	0.0311452	+	0.0290924i
$903$		0			0
$904$	1.09723e6	−	418007.i	1.34264	−	0.511501i
$905$	426883.	−	739383.i	0.521209	−	0.902760i
$906$		0			0
$907$	1.27955e6	−	738746.i	1.55540	−	0.898008i	0.557709	−	0.830037i	$-0.311681\pi$
$907$	1.27955e6	−	738746.i	1.55540	−	0.898008i	0.997687	−	0.0679717i	$-0.0216528\pi$
$908$	−560422.	−	833887.i	−0.679741	−	1.01143i
$909$		0			0
$910$	381386.	−	116250.i	0.460555	−	0.140382i
$911$	−41701.0	+	24076.1i	−0.0502470	+	0.0290101i	−0.524913	−	0.851156i	$-0.675902\pi$
$911$	−41701.0	+	24076.1i	−0.0502470	+	0.0290101i	0.474666	+	0.880166i	$0.342569\pi$
$912$		0			0
$913$	−103988.	+	180113.i	−0.124751	+	0.216074i
$914$	−773317.	−	179221.i	−0.925690	−	0.214534i
$915$		0			0
$916$	−588065.	−	288046.i	−0.700865	−	0.343297i
$917$	−128687.			−0.153036
$918$		0			0
$919$		−	346372.i		−	0.410120i	−0.978749	−	0.205060i	$-0.934261\pi$
$919$		−	346372.i		−	0.410120i	0.978749	−	0.205060i	$-0.0657390\pi$
$920$	2.16004e6	+	347716.i	2.55204	+	0.410817i
$921$		0			0
$922$	−813225.	−	188469.i	−0.956641	−	0.221707i
$923$	−834000.	−	481510.i	−0.978955	−	0.565200i
$924$		0			0
$925$	794014.	+	1.37527e6i	0.927993	+	1.60733i
$926$	−100238.	+	30553.5i	−0.116899	+	0.0356319i
$927$		0			0
$928$	1.32728e6	+	121758.i	1.54123	+	0.141384i
$929$	435392.	+	754120.i	0.504485	+	0.873794i	0.999987	+	0.00518706i	$0.00165110\pi$
$929$	435392.	+	754120.i	0.504485	+	0.873794i	−0.495501	+	0.868607i	$0.665016\pi$
$930$		0			0
$931$	52442.9	+	30277.9i	0.0605044	+	0.0349322i
$932$	86324.9	+	1.26513e6i	0.0993812	+	1.45648i
$933$		0			0
$934$	282396.	+	263783.i	0.323716	+	0.302380i
$935$			405122.i			0.463407i
$936$		0			0
$937$	−1.00280e6			−1.14219			−0.571094	−	0.820885i	$-0.693481\pi$
$937$	−1.00280e6			−1.14219			−0.571094	+	0.820885i	$0.693481\pi$
$938$	8199.48	−	8778.03i	0.00931924	−	0.00997680i
$939$		0			0
$940$	1.44030e6	−	98277.2i	1.63003	−	0.111224i
$941$	−630949.	+	1.09284e6i	−0.712550	+	1.23417i	0.251348	+	0.967897i	$0.419126\pi$
$941$	−630949.	+	1.09284e6i	−0.712550	+	1.23417i	−0.963897	+	0.266275i	$0.914207\pi$
$942$		0			0
$943$	59154.8	−	34153.0i	0.0665222	−	0.0384066i
$944$	1.31881e6	+	538010.i	1.47992	+	0.603735i
$945$		0			0
$946$	−210125.	−	689366.i	−0.234799	−	0.770314i
$947$	162072.	−	93572.3i	0.180721	−	0.104339i	−0.406910	−	0.913468i	$-0.633394\pi$
$947$	162072.	−	93572.3i	0.180721	−	0.104339i	0.587631	+	0.809129i	$0.300061\pi$
$948$		0			0
$949$	−267998.	+	464186.i	−0.297577	+	0.515418i
$950$	−21907.6	+	94528.7i	−0.0242743	+	0.104741i
$951$		0			0
$952$	−72014.3	−	11592.6i	−0.0794593	−	0.0127911i
$953$	−194925.			−0.214626			−0.107313	−	0.994225i	$-0.534225\pi$
$953$	−194925.			−0.214626			−0.107313	+	0.994225i	$0.534225\pi$
$954$		0			0
$955$		−	730210.i		−	0.800647i
$956$	−317640.	+	648482.i	−0.347551	+	0.709549i
$957$		0			0
$958$	30933.8	−	133476.i	0.0337056	−	0.145436i
$959$	−34095.8	−	19685.2i	−0.0370735	−	0.0214044i
$960$		0			0
$961$	−226939.	−	393070.i	−0.245732	−	0.425621i
$962$	−429023.	−	1.40751e6i	−0.463586	−	1.52090i
$963$		0			0
$964$	−1.00465e6	+	675187.i	−1.08109	+	0.726557i
$965$	−900757.	−	1.56016e6i	−0.967281	−	1.67538i
$966$		0			0
$967$	374342.	+	216127.i	0.400328	+	0.231129i	0.686625	−	0.727011i	$-0.259091\pi$
$967$	374342.	+	216127.i	0.400328	+	0.231129i	−0.286298	+	0.958141i	$0.592425\pi$
$968$	138510.	−	52767.9i	0.147819	−	0.0563143i
$969$		0			0
$970$	−612387.	+	655597.i	−0.650852	+	0.696776i
$971$			756598.i			0.802467i	0.915976	+	0.401233i	$0.131418\pi$
$971$			756598.i			0.802467i	−0.915976	+	0.401233i	$0.868582\pi$
$972$		0			0
$973$	−229389.			−0.242296
$974$	203219.	+	189825.i	0.214213	+	0.200095i
$975$		0			0
$976$	342145.	+	440980.i	0.359179	+	0.462934i
$977$	903593.	−	1.56507e6i	0.946638	−	1.63962i	0.194200	−	0.980962i	$-0.437789\pi$
$977$	903593.	−	1.56507e6i	0.946638	−	1.63962i	0.752438	−	0.658663i	$-0.228878\pi$
$978$		0			0
$979$	−112217.	+	64788.8i	−0.117083	+	0.0675981i
$980$	−1.16870e6	+	785438.i	−1.21689	+	0.817824i
$981$		0			0
$982$	770102.	−	234735.i	0.798593	−	0.243419i
$983$	−181852.	+	104992.i	−0.188196	+	0.108655i	−0.591138	−	0.806570i	$-0.701321\pi$
$983$	−181852.	+	104992.i	−0.188196	+	0.108655i	0.402942	+	0.915226i	$0.367988\pi$
$984$		0			0
$985$	311354.	−	539282.i	0.320910	−	0.555832i
$986$	473622.	+	109765.i	0.487167	+	0.112904i
$987$		0			0
$988$	39550.2	−	80744.4i	0.0405168	−	0.0827178i
$989$	−1.41966e6			−1.45141
$990$		0			0
$991$			1.66713e6i			1.69755i	0.528754	+	0.848775i	$0.322659\pi$
$991$			1.66713e6i			1.69755i	−0.528754	+	0.848775i	$0.677341\pi$
$992$	−637247.	+	293892.i	−0.647567	+	0.298651i
$993$		0			0
$994$	−219165.	−	50792.7i	−0.221819	−	0.0514077i
$995$	2.49540e6	+	1.44072e6i	2.52054	+	1.45523i
$996$		0			0
$997$	−671417.	−	1.16293e6i	−0.675464	−	1.16994i	−0.976333	−	0.216273i	$-0.930610\pi$
$997$	−671417.	−	1.16293e6i	−0.675464	−	1.16994i	0.300869	−	0.953666i	$-0.402723\pi$
$998$	206992.	−	63093.3i	0.207823	−	0.0633464i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.5.f.a.91.17		44
3.2	odd	2		36.5.f.a.31.6	yes	44
4.3	odd	2	inner	108.5.f.a.91.2		44
9.2	odd	6		36.5.f.a.7.21	yes	44
9.4	even	3		324.5.d.e.163.14		22
9.5	odd	6		324.5.d.f.163.9		22
9.7	even	3	inner	108.5.f.a.19.2		44
12.11	even	2		36.5.f.a.31.21	yes	44
36.7	odd	6	inner	108.5.f.a.19.17		44
36.11	even	6		36.5.f.a.7.6	✓	44
36.23	even	6		324.5.d.f.163.10		22
36.31	odd	6		324.5.d.e.163.13		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.5.f.a.7.6	✓	44	36.11	even	6
36.5.f.a.7.21	yes	44	9.2	odd	6
36.5.f.a.31.6	yes	44	3.2	odd	2
36.5.f.a.31.21	yes	44	12.11	even	2
108.5.f.a.19.2		44	9.7	even	3	inner
108.5.f.a.19.17		44	36.7	odd	6	inner
108.5.f.a.91.2		44	4.3	odd	2	inner
108.5.f.a.91.17		44	1.1	even	1	trivial
324.5.d.e.163.13		22	36.31	odd	6
324.5.d.e.163.14		22	9.4	even	3
324.5.d.f.163.9		22	9.5	odd	6
324.5.d.f.163.10		22	36.23	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	108.f (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.73046 - 2.92312i) q^{2} +(-1.08921 - 15.9629i) q^{4} +(-19.5394 + 33.8433i) q^{5} +(-10.5700 + 6.10260i) q^{7} +(-49.6354 - 40.4021i) q^{8} +O(q^{10})\)	\(q+(2.73046 - 2.92312i) q^{2} +(-1.08921 - 15.9629i) q^{4} +(-19.5394 + 33.8433i) q^{5} +(-10.5700 + 6.10260i) q^{7} +(-49.6354 - 40.4021i) q^{8} +(45.5763 + 149.524i) q^{10} +(-96.1446 + 55.5091i) q^{11} +(-104.491 + 180.984i) q^{13} +(-11.0224 + 47.5603i) q^{14} +(-253.627 + 34.7739i) q^{16} -93.3790 q^{17} -26.8894i q^{19} +(561.519 + 275.043i) q^{20} +(-100.259 + 432.607i) q^{22} +(757.577 + 437.387i) q^{23} +(-451.080 - 781.293i) q^{25} +(243.728 + 799.608i) q^{26} +(108.928 + 162.081i) q^{28} +(-650.809 - 1127.23i) q^{29} +(593.492 + 342.653i) q^{31} +(-590.870 + 836.330i) q^{32} +(-254.967 + 272.958i) q^{34} -476.966i q^{35} -1760.25 q^{37} +(-78.6008 - 73.4203i) q^{38} +(2337.19 - 890.392i) q^{40} +(39.0421 - 67.6229i) q^{41} +(-1405.46 + 811.442i) q^{43} +(990.807 + 1474.28i) q^{44} +(3347.06 - 1020.22i) q^{46} +(1999.54 - 1154.43i) q^{47} +(-1126.02 + 1950.32i) q^{49} +(-3515.46 - 814.729i) q^{50} +(3002.84 + 1470.85i) q^{52} +1313.48 q^{53} -4338.47i q^{55} +(771.205 + 124.146i) q^{56} +(-5072.04 - 1175.47i) q^{58} +(-4818.38 - 2781.89i) q^{59} +(-1090.13 - 1888.16i) q^{61} +(2622.12 - 799.247i) q^{62} +(831.345 + 4010.75i) q^{64} +(-4083.39 - 7072.65i) q^{65} +(-213.077 - 123.020i) q^{67} +(101.709 + 1490.60i) q^{68} +(-1394.23 - 1302.33i) q^{70} +4608.15i q^{71} +2564.79 q^{73} +(-4806.29 + 5145.42i) q^{74} +(-429.232 + 29.2882i) q^{76} +(677.500 - 1173.46i) q^{77} +(4486.29 - 2590.16i) q^{79} +(3778.87 - 9263.05i) q^{80} +(-91.0669 - 298.766i) q^{82} +(1622.37 - 936.677i) q^{83} +(1824.57 - 3160.25i) q^{85} +(-1465.61 + 6323.93i) q^{86} +(7014.86 + 1129.22i) q^{88} +1167.17 q^{89} -2550.67i q^{91} +(6156.80 - 12569.5i) q^{92} +(2085.11 - 8997.00i) q^{94} +(910.026 + 525.404i) q^{95} +(2869.58 + 4970.26i) q^{97} +(2626.47 + 8616.73i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + q^{2} - q^{4} + 2 q^{5} - 122 q^{8}+O(q^{10}) \) 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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