LMFDB - Embedded newform 108.5.f.a.91.2

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			91.2
Character	$\chi$	$=$	108.91
Dual form			108.5.f.a.19.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.89672 + 0.903087i) q^{2} +(14.3689 - 7.03816i) q^{4} +(-19.5394 + 33.8433i) q^{5} +(10.5700 - 6.10260i) q^{7} +(-49.6354 + 40.4021i) q^{8} +O(q^{10})$	\(q+(-3.89672 + 0.903087i) q^{2} +(14.3689 - 7.03816i) q^{4} +(-19.5394 + 33.8433i) q^{5} +(10.5700 - 6.10260i) q^{7} +(-49.6354 + 40.4021i) q^{8} +(45.5763 - 149.524i) q^{10} +(96.1446 - 55.5091i) q^{11} +(-104.491 + 180.984i) q^{13} +(-35.6772 + 33.3258i) q^{14} +(156.929 - 202.261i) q^{16} -93.3790 q^{17} +26.8894i q^{19} +(-42.5651 + 623.812i) q^{20} +(-324.519 + 303.130i) q^{22} +(-757.577 - 437.387i) q^{23} +(-451.080 - 781.293i) q^{25} +(243.728 - 799.608i) q^{26} +(108.928 - 162.081i) q^{28} +(-650.809 - 1127.23i) q^{29} +(-593.492 - 342.653i) q^{31} +(-428.848 + 929.874i) q^{32} +(363.872 - 84.3293i) q^{34} +476.966i q^{35} -1760.25 q^{37} +(-24.2835 - 104.780i) q^{38} +(-397.492 - 2469.26i) q^{40} +(39.0421 - 67.6229i) q^{41} +(1405.46 - 811.442i) q^{43} +(990.807 - 1474.28i) q^{44} +(3347.06 + 1020.22i) q^{46} +(-1999.54 + 1154.43i) q^{47} +(-1126.02 + 1950.32i) q^{49} +(2463.31 + 2637.12i) q^{50} +(-227.626 + 3335.96i) q^{52} +1313.48 q^{53} +4338.47i q^{55} +(-278.089 + 729.956i) q^{56} +(3554.01 + 3804.78i) q^{58} +(4818.38 + 2781.89i) q^{59} +(-1090.13 - 1888.16i) q^{61} +(2622.12 + 799.247i) q^{62} +(831.345 - 4010.75i) q^{64} +(-4083.39 - 7072.65i) q^{65} +(213.077 + 123.020i) q^{67} +(-1341.75 + 657.216i) q^{68} +(-430.742 - 1858.60i) q^{70} -4608.15i q^{71} +2564.79 q^{73} +(6859.21 - 1589.66i) q^{74} +(189.252 + 386.370i) q^{76} +(677.500 - 1173.46i) q^{77} +(-4486.29 + 2590.16i) q^{79} +(3778.87 + 9263.05i) q^{80} +(-91.0669 + 298.766i) q^{82} +(-1622.37 + 936.677i) q^{83} +(1824.57 - 3160.25i) q^{85} +(-4743.88 + 4431.22i) q^{86} +(-2529.49 + 6639.66i) q^{88} +1167.17 q^{89} +2550.67i q^{91} +(-13963.9 - 952.813i) q^{92} +(6749.08 - 6304.26i) q^{94} +(-910.026 - 525.404i) q^{95} +(2869.58 + 4970.26i) q^{97} +(2626.47 - 8616.73i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−3.89672	+	0.903087i	−0.974180	+	0.225772i
$2$	−3.89672	+	0.903087i	−0.974180	+	0.225772i
$3$		0			0
$3$		0			0
$4$	14.3689	−	7.03816i	0.898054	−	0.439885i
$5$	−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	−0.388250	−	0.921554i	$-0.626920\pi$
$7$	10.5700	−	6.10260i	0.215715	−	0.124543i	0.603964	+	0.797011i	$0.293587\pi$
$8$	−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	−0.0469902	−	0.998895i	$-0.514963\pi$
$11$	96.1446	−	55.5091i	0.794583	−	0.458753i	0.841574	+	0.540142i	$0.181630\pi$
$12$		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	$0.954492\pi$
$14$	−35.6772	+	33.3258i	−0.182027	+	0.170030i
$15$		0			0
$16$	156.929	−	202.261i	0.613003	−	0.790081i
$17$	−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	$0.0118575\pi$
$19$			26.8894i			0.0744859i	−0.999306	+	0.0372429i	$0.988142\pi$
$20$	−42.5651	+	623.812i	−0.106413	+	1.55953i
$21$		0			0
$22$	−324.519	+	303.130i	−0.670494	+	0.626303i
$23$	−757.577	−	437.387i	−1.43209	−	0.826819i	−0.434812	−	0.900521i	$-0.643185\pi$
$23$	−757.577	−	437.387i	−1.43209	−	0.826819i	−0.997280	+	0.0737029i	$0.976518\pi$
$24$		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	0.158348	−	0.987383i	$-0.449383\pi$
$31$	−593.492	−	342.653i	−0.617577	−	0.356558i	−0.775925	+	0.630825i	$0.782717\pi$
$32$	−428.848	+	929.874i	−0.418797	+	0.908080i
$33$		0			0
$34$	363.872	−	84.3293i	0.314768	−	0.0729493i
$35$			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	$0.722268\pi$
$38$	−24.2835	−	104.780i	−0.0168168	−	0.0725626i
$39$		0			0
$40$	−397.492	−	2469.26i	−0.248432	−	1.54329i
$41$	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	−0.0692198	−	0.997601i	$-0.522051\pi$
$43$	1405.46	−	811.442i	0.760118	−	0.438855i	0.829338	+	0.558747i	$0.188718\pi$
$44$	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	−0.878876	−	0.477050i	$-0.841706\pi$
$47$	−1999.54	+	1154.43i	−0.905177	+	0.522604i	−0.0263007	+	0.999654i	$0.508373\pi$
$48$		0			0
$49$	−1126.02	+	1950.32i	−0.468978	+	0.812294i
$50$	2463.31	+	2637.12i	0.985323	+	1.05485i
$51$		0			0
$52$	−227.626	+	3335.96i	−0.0841811	+	1.23371i
$53$	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
$56$	−278.089	+	729.956i	−0.0886764	+	0.232767i
$57$		0			0
$58$	3554.01	+	3804.78i	1.05648	+	1.13103i
$59$	4818.38	+	2781.89i	1.38419	+	0.799164i	0.992653	−	0.120997i	$-0.0386091\pi$
$59$	4818.38	+	2781.89i	1.38419	+	0.799164i	0.391540	+	0.920161i	$0.371942\pi$
$60$		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	0.523545	−	0.851998i	$-0.324609\pi$
$67$	213.077	+	123.020i	0.0474665	+	0.0274048i	−0.476079	+	0.879403i	$0.657942\pi$
$68$	−1341.75	+	657.216i	−0.290171	+	0.142131i
$69$		0			0
$70$	−430.742	−	1858.60i	−0.0879065	−	0.379307i
$71$		−	4608.15i		−	0.914134i	−0.889432	−	0.457067i	$-0.848900\pi$
$71$		−	4608.15i		−	0.914134i	0.889432	−	0.457067i	$-0.151100\pi$
$72$		0			0
$73$	2564.79			0.481290			0.240645	−	0.970613i	$-0.422641\pi$
$73$	2564.79			0.481290			0.240645	+	0.970613i	$0.422641\pi$
$74$	6859.21	−	1589.66i	1.25259	−	0.290296i
$75$		0			0
$76$	189.252	+	386.370i	0.0327652	+	0.0668923i
$77$	677.500	−	1173.46i	0.114269	−	0.197919i
$78$		0			0
$79$	−4486.29	+	2590.16i	−0.718842	+	0.415023i	−0.814326	−	0.580408i	$-0.802893\pi$
$79$	−4486.29	+	2590.16i	−0.718842	+	0.415023i	0.0954846	+	0.995431i	$0.469560\pi$
$80$	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	−0.613108	−	0.789999i	$-0.710081\pi$
$83$	−1622.37	+	936.677i	−0.235502	+	0.135967i	0.377606	+	0.925966i	$0.376747\pi$
$84$		0			0
$85$	1824.57	−	3160.25i	0.252536	−	0.437405i
$86$	−4743.88	+	4431.22i	−0.641411	+	0.599137i
$87$		0			0
$88$	−2529.49	+	6639.66i	−0.326639	+	0.857394i
$89$	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
$92$	−13963.9	−	952.813i	−1.64980	−	0.112572i
$93$		0			0
$94$	6749.08	−	6304.26i	0.763816	−	0.713474i
$95$	−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	−0.0284395	−	0.999596i	$-0.509054\pi$
$103$	−9636.52	−	5563.65i	−0.908334	−	0.524427i	−0.879895	+	0.475168i	$0.842387\pi$
$104$	−2125.67	−	13204.9i	−0.196530	−	1.22086i
$105$		0			0
$106$	−5118.28	+	1186.19i	−0.455525	+	0.105570i
$107$		−	4464.91i		−	0.389983i	−0.980805	−	0.194991i	$-0.937532\pi$
$107$		−	4464.91i		−	0.389983i	0.980805	−	0.194991i	$-0.0624679\pi$
$108$		0			0
$109$	−4736.05			−0.398624			−0.199312	−	0.979936i	$-0.563871\pi$
$109$	−4736.05			−0.398624			−0.199312	+	0.979936i	$0.563871\pi$
$110$	−3918.02	−	16905.8i	−0.323803	−	1.39717i
$111$		0			0
$112$	424.422	−	3095.57i	0.0338347	−	0.246777i
$113$	−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
$122$	5953.10	+	6373.14i	0.399966	+	0.428188i
$123$		0			0
$124$	−10939.4	−	746.442i	−0.711462	−	0.0485459i
$125$	10831.1			0.693190
$126$		0			0
$127$		−	8169.42i		−	0.506505i	−0.967400	−	0.253252i	$-0.918500\pi$
$127$		−	8169.42i		−	0.506505i	0.967400	−	0.253252i	$-0.0815003\pi$
$128$	382.534	+	16379.5i	0.0233480	+	0.999727i
$129$		0			0
$130$	22299.1	+	23872.5i	1.31947	+	1.41257i
$131$	−9131.01	−	5271.79i	−0.532079	−	0.307196i	0.209784	−	0.977748i	$-0.432724\pi$
$131$	−9131.01	−	5271.79i	−0.532079	−	0.307196i	−0.741863	+	0.670552i	$0.766057\pi$
$132$		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	0.0156666	−	0.999877i	$-0.495013\pi$
$139$	−16276.4	−	9397.17i	−0.842419	−	0.486371i	−0.858086	+	0.513506i	$0.828346\pi$
$140$	3356.96	+	6853.46i	0.171274	+	0.349666i
$141$		0			0
$142$	4161.56	+	17956.7i	0.206386	+	0.890531i
$143$			23200.8i			1.13457i
$144$		0			0
$145$	50865.8			2.41930
$146$	−9994.28	+	2316.23i	−0.468863	+	0.108662i
$147$		0			0
$148$	−25292.8	+	12388.9i	−1.15471	+	0.565601i
$149$	−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	−0.478468	−	0.878105i	$-0.658808\pi$
$151$	974.974	−	562.901i	0.0427601	−	0.0246876i	0.521228	+	0.853418i	$0.325474\pi$
$152$	−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	$0.143973\pi$
$158$	15142.7	−	14144.6i	0.606581	−	0.566602i
$159$		0			0
$160$	−23090.6	−	32682.9i	−0.901975	−	1.27667i
$161$	−10676.8			−0.411898
$162$		0			0
$163$			41947.9i			1.57883i	0.613861	+	0.789414i	$0.289615\pi$
$163$			41947.9i			1.57883i	−0.613861	+	0.789414i	$0.710385\pi$
$164$	85.0502	−	1246.45i	0.00316219	−	0.0463433i
$165$		0			0
$166$	5476.03	−	5115.11i	0.198724	−	0.185626i
$167$	5900.58	+	3406.70i	0.211574	+	0.122152i	0.602043	−	0.798464i	$-0.294354\pi$
$167$	5900.58	+	3406.70i	0.211574	+	0.122152i	−0.390469	+	0.920616i	$0.627687\pi$
$168$		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
$176$	3860.53	−	28157.2i	0.124630	−	0.909002i
$177$		0			0
$178$	−4548.15	+	1054.06i	−0.143547	+	0.0332679i
$179$		−	22497.6i		−	0.702151i	−0.936347	−	0.351075i	$-0.885816\pi$
$179$		−	22497.6i		−	0.702151i	0.936347	−	0.351075i	$-0.114184\pi$
$180$		0			0
$181$	−21847.2			−0.666867			−0.333434	−	0.942774i	$-0.608207\pi$
$181$	−21847.2			−0.666867			−0.333434	+	0.942774i	$0.608207\pi$
$182$	−2303.48	−	9939.25i	−0.0695410	−	0.300062i
$183$		0			0
$184$	55274.0	−	8897.79i	1.63262	−	0.262813i
$185$	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	−0.261537	−	0.965194i	$-0.584229\pi$
$191$	16182.1	−	9342.76i	0.443577	−	0.256099i	0.705114	+	0.709094i	$0.250896\pi$
$192$		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	$0.954286\pi$
$194$	−15670.5	−	16776.2i	−0.416371	−	0.445750i
$195$		0			0
$196$	−2452.94	+	35948.9i	−0.0638520	+	0.935780i
$197$	−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	$0.381026\pi$
$199$			73733.8i			1.86192i	−0.365124	+	0.930959i	$0.618974\pi$
$200$	53955.4	+	20555.2i	1.34888	+	0.513881i
$201$		0			0
$202$	−42558.9	−	45561.9i	−1.04301	−	1.11660i
$203$	−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	0.316584	−	0.948564i	$-0.397464\pi$
$211$	−15431.2	−	8909.20i	−0.346605	−	0.200112i	−0.663189	+	0.748452i	$0.730797\pi$
$212$	18873.3	−	9244.50i	0.419929	−	0.205689i
$213$		0			0
$214$	4032.20	+	17398.5i	0.0880471	+	0.379913i
$215$			63420.5i			1.37200i
$216$		0			0
$217$	−8364.29			−0.177627
$218$	18455.1	−	4277.07i	0.388332	−	0.0899980i
$219$		0			0
$220$	30534.8	+	62338.9i	0.630885	+	1.28799i
$221$	9757.27	−	16900.1i	0.199776	−	0.346022i
$222$		0			0
$223$	58353.8	−	33690.6i	1.17344	−	0.677483i	0.218949	−	0.975736i	$-0.429737\pi$
$223$	58353.8	−	33690.6i	1.17344	−	0.677483i	0.954487	+	0.298253i	$0.0964039\pi$
$224$	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	−0.924144	−	0.382044i	$-0.875220\pi$
$227$	−54381.5	+	31397.2i	−1.05536	+	0.609310i	−0.131212	+	0.991354i	$0.541887\pi$
$228$		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	$0.0390681\pi$
$230$	−99927.3	+	93341.2i	−1.88898	+	1.76448i
$231$		0			0
$232$	77845.7	+	29656.7i	1.44630	+	0.550993i
$233$	−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
$236$	88814.0	+	6060.13i	1.59462	+	0.108807i
$237$		0			0
$238$	3331.50	−	3111.93i	0.0588148	−	0.0549383i
$239$	39084.7	+	22565.5i	0.684243	+	0.395048i	0.801452	−	0.598059i	$-0.204061\pi$
$239$	39084.7	+	22565.5i	0.684243	+	0.395048i	−0.117209	+	0.993107i	$0.537395\pi$
$240$		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
$248$	43302.1	−	6970.60i	0.704053	−	0.113336i
$249$		0			0
$250$	−42205.8	+	9781.43i	−0.675292	+	0.156503i
$251$		−	78270.9i		−	1.24238i	−0.783662	−	0.621188i	$-0.786650\pi$
$251$		−	78270.9i		−	1.24238i	0.783662	−	0.621188i	$-0.213350\pi$
$252$		0			0
$253$	−97115.9			−1.51722
$254$	7377.70	+	31833.9i	0.114355	+	0.493427i
$255$		0			0
$256$	−16282.8	−	63481.0i	−0.248455	−	0.968643i
$257$	−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	−0.932973	−	0.359945i	$-0.882795\pi$
$263$	−75237.8	+	43438.5i	−1.08774	+	0.628006i	−0.154765	+	0.987951i	$0.549462\pi$
$264$		0			0
$265$	−25664.7	+	44452.6i	−0.365464	+	0.633003i
$266$	−896.110	−	959.339i	−0.0126648	−	0.0135584i
$267$		0			0
$268$	3927.51	+	267.990i	0.0546824	+	0.00373120i
$269$	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	$-0.894130\pi$
$271$		−	47957.3i		−	0.653004i	0.945197	−	0.326502i	$-0.105870\pi$
$272$	−14653.8	+	18886.9i	−0.198068	+	0.255284i
$273$		0			0
$274$	−8807.65	−	9429.11i	−0.117316	−	0.125594i
$275$	−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	$0.0694578\pi$
$283$	132300.	+	76383.2i	1.65191	+	0.953730i	0.675621	+	0.737249i	$0.263876\pi$
$284$	−32432.9	−	66213.9i	−0.402114	−	0.820942i
$285$		0			0
$286$	−20952.4	−	90407.1i	−0.256154	−	1.10528i
$287$		−	953.034i		−	0.0115703i
$288$		0			0
$289$	−74801.4			−0.895600
$290$	−198210.	+	45936.2i	−2.35683	+	0.546210i
$291$		0			0
$292$	36853.2	−	18051.4i	0.432224	−	0.211712i
$293$	−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
$302$	−3290.85	+	3073.96i	−0.0360823	+	0.0337042i
$303$		0			0
$304$	5438.67	+	4219.72i	0.0588498	+	0.0456600i
$305$	85202.0			0.915905
$306$		0			0
$307$		−	457.528i		−	0.00485446i	−0.999997	−	0.00242723i	$-0.999227\pi$
$307$		−	457.528i		−	0.00485446i	0.999997	−	0.00242723i	$-0.000772612\pi$
$308$	1475.88	−	21629.7i	0.0155579	−	0.228008i
$309$		0			0
$310$	−78283.9	+	73124.3i	−0.814608	+	0.760919i
$311$	−9285.82	−	5361.17i	−0.0960062	−	0.0554292i	0.451228	−	0.892409i	$-0.350986\pi$
$311$	−9285.82	−	5361.17i	−0.0960062	−	0.0554292i	−0.547234	+	0.836979i	$0.684319\pi$
$312$		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
$320$	119493.	+	106503.i	1.16692	+	1.04007i
$321$		0			0
$322$	41604.5	−	9642.08i	0.401262	−	0.0929949i
$323$		−	2510.90i		−	0.0240672i
$324$		0			0
$325$	188535.			1.78495
$326$	−37882.6	−	163459.i	−0.356455	−	1.53806i
$327$		0			0
$328$	794.236	+	4933.87i	0.00738247	+	0.0458607i
$329$	−14090.1	+	24404.7i	−0.130173	+	0.225467i
$330$		0			0
$331$	160993.	−	92949.3i	1.46944	−	0.848379i	0.470023	−	0.882654i	$-0.344245\pi$
$331$	160993.	−	92949.3i	1.46944	−	0.848379i	0.999412	+	0.0342747i	$0.0109121\pi$
$332$	−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	$-0.0592251\pi$
$338$	41264.1	+	44175.7i	0.361193	+	0.386678i
$339$		0			0
$340$	3974.69	−	58250.9i	0.0343831	−	0.503901i
$341$	−76081.3			−0.654289
$342$		0			0
$343$			56791.2i			0.482717i
$344$	−36976.6	+	97059.7i	−0.312471	+	0.820204i
$345$		0			0
$346$	−43000.1	−	46034.1i	−0.359184	−	0.384528i
$347$	125556.	+	72490.0i	1.04275	+	0.602031i	0.920611	−	0.390482i	$-0.127692\pi$
$347$	125556.	+	72490.0i	1.04275	+	0.602031i	0.122138	+	0.992513i	$0.461025\pi$
$348$		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
$356$	16771.0	−	8214.76i	0.132330	−	0.0648179i
$357$		0			0
$358$	20317.3	+	87666.9i	0.158526	+	0.684022i
$359$			181364.i			1.40722i	0.710587	+	0.703609i	$0.248429\pi$
$359$			181364.i			1.40722i	−0.710587	+	0.703609i	$0.751571\pi$
$360$		0			0
$361$	129598.			0.994452
$362$	85132.6	−	19730.0i	0.649649	−	0.150560i
$363$		0			0
$364$	17952.0	+	36650.2i	0.135491	+	0.276614i
$365$	−50114.6	+	86801.1i	−0.376165	+	0.651537i
$366$		0			0
$367$	−181000.	+	104500.i	−1.34383	+	0.775863i	−0.987368	−	0.158445i	$-0.949352\pi$
$367$	−181000.	+	104500.i	−1.34383	+	0.775863i	−0.356467	+	0.934308i	$0.616019\pi$
$368$	−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	$0.0778996\pi$
$374$	30303.3	−	28306.0i	0.216644	−	0.202365i
$375$		0			0
$376$	52606.3	−	138086.i	0.372102	−	0.976729i
$377$	272015.			1.91386
$378$		0			0
$379$		−	232118.i		−	1.61596i	−0.589211	−	0.807979i	$-0.700561\pi$
$379$		−	232118.i		−	1.61596i	0.589211	−	0.807979i	$-0.299439\pi$
$380$	−16773.9	−	1144.55i	−0.116163	−	0.00792625i
$381$		0			0
$382$	−54620.0	+	51020.0i	−0.374304	+	0.349634i
$383$	74119.1	+	42792.7i	0.505280	+	0.291724i	0.730891	−	0.682494i	$-0.239105\pi$
$383$	74119.1	+	42792.7i	0.505280	+	0.291724i	−0.225611	+	0.974217i	$0.572438\pi$
$384$		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
$392$	−22906.6	−	142298.i	−0.149069	−	0.926035i
$393$		0			0
$394$	62092.9	−	14390.4i	0.399990	−	0.0927001i
$395$		−	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	$0.573033\pi$
$398$	−66588.0	−	287320.i	−0.420368	−	1.81384i
$399$		0			0
$400$	−228812.	−	31371.6i	−1.43008	−	0.196073i
$401$	−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	$0.924785\pi$
$410$	−8331.84	−	8919.73i	−0.0495648	−	0.0530620i
$411$		0			0
$412$	−177624.	−	12120.0i	−1.04642	−	0.0714015i
$413$	67907.1			0.398121
$414$		0			0
$415$		−	73208.6i		−	0.425075i
$416$	−123481.	−	174778.i	−0.713534	−	1.00995i
$417$		0			0
$418$	−8150.99	−	8726.12i	−0.0466507	−	0.0499423i
$419$	48172.3	+	27812.3i	0.274391	+	0.158420i	0.630881	−	0.775879i	$-0.282693\pi$
$419$	48172.3	+	27812.3i	0.274391	+	0.158420i	−0.356491	+	0.934299i	$0.616027\pi$
$420$		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
$428$	−31424.7	−	64155.7i	−0.171547	−	0.350225i
$429$		0			0
$430$	−57274.3	−	247132.i	−0.309758	−	1.33657i
$431$		−	191015.i		−	1.02828i	−0.857705	−	0.514142i	$-0.828111\pi$
$431$		−	191015.i		−	1.02828i	0.857705	−	0.514142i	$-0.171889\pi$
$432$		0			0
$433$	48243.4			0.257313			0.128657	−	0.991689i	$-0.458933\pi$
$433$	48243.4			0.257313			0.128657	+	0.991689i	$0.458933\pi$
$434$	32593.3	−	7553.68i	0.173041	−	0.0401032i
$435$		0			0
$436$	−68051.7	+	33333.1i	−0.357986	+	0.175349i
$437$	11761.1	−	20370.8i	0.0615863	−	0.106671i
$438$		0			0
$439$	−227081.	+	131105.i	−1.17829	+	0.680285i	−0.955618	−	0.294609i	$-0.904811\pi$
$439$	−227081.	+	131105.i	−1.17829	+	0.680285i	−0.222670	+	0.974894i	$0.571477\pi$
$440$	−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	−0.687130	−	0.726534i	$-0.741130\pi$
$443$	−78793.6	+	45491.5i	−0.401498	+	0.231805i	0.285632	+	0.958339i	$0.407796\pi$
$444$		0			0
$445$	−22805.9	+	39501.0i	−0.115167	+	0.199475i
$446$	−196963.	+	183981.i	−0.990181	+	0.924920i
$447$		0			0
$448$	−15688.7	−	47467.0i	−0.0781681	−	0.236503i
$449$	−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
$452$	−19982.8	+	292857.i	−0.0978091	+	1.43344i
$453$		0			0
$454$	183555.	−	171457.i	0.890542	−	0.831848i
$455$	−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	0.551984	−	0.833855i	$-0.313871\pi$
$463$	22687.9	+	13098.9i	0.105836	+	0.0611044i	−0.446148	+	0.894959i	$0.647204\pi$
$464$	−330126.	−	45262.3i	−1.53336	−	0.210233i
$465$		0			0
$466$	308833.	−	71573.7i	1.42217	−	0.329596i
$467$		−	96607.8i		−	0.442974i	−0.975163	−	0.221487i	$-0.928909\pi$
$467$		−	96607.8i		−	0.442974i	0.975163	−	0.221487i	$-0.0710911\pi$
$468$		0			0
$469$	3002.97			0.0136523
$470$	81483.6	+	351593.i	0.368871	+	1.59164i
$471$		0			0
$472$	−351556.	+	56592.1i	−1.57801	+	0.254022i
$473$	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	−0.563250	−	0.826287i	$-0.690449\pi$
$479$	−29664.3	+	17126.7i	−0.129289	+	0.0746453i	0.433960	+	0.900932i	$0.357116\pi$
$480$		0			0
$481$	183931.	−	318577.i	0.794994	−	1.37697i
$482$	206569.	+	221144.i	0.889141	+	0.951878i
$483$		0			0
$484$	−2522.57	+	36969.4i	−0.0107684	+	0.157816i
$485$	−224280.			−0.953470
$486$		0			0
$487$		−	69521.4i		−	0.293130i	−0.989201	−	0.146565i	$-0.953178\pi$
$487$		−	69521.4i		−	0.293130i	0.989201	−	0.146565i	$-0.0468218\pi$
$488$	130394.	+	49676.0i	0.547545	+	0.208597i
$489$		0			0
$490$	240299.	+	257255.i	1.00083	+	1.07145i
$491$	−174305.	−	100635.i	−0.723016	−	0.417433i	0.0928458	−	0.995681i	$-0.470404\pi$
$491$	−174305.	−	100635.i	−0.723016	−	0.417433i	−0.815862	+	0.578247i	$0.803737\pi$
$492$		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	0.402964	−	0.915216i	$-0.367980\pi$
$499$	−46850.8	−	27049.3i	−0.188155	−	0.108631i	−0.591119	+	0.806585i	$0.701313\pi$
$500$	155631.	−	76231.0i	0.622522	−	0.304924i
$501$		0			0
$502$	70685.5	+	305000.i	0.280493	+	1.21030i
$503$			239548.i			0.946795i	0.880849	+	0.473397i	$0.156973\pi$
$503$			239548.i			0.946795i	−0.880849	+	0.473397i	$0.843027\pi$
$504$		0			0
$505$	−609113.			−2.38844
$506$	378433.	−	87704.1i	1.47805	−	0.342546i
$507$		0			0
$508$	−57497.6	−	117385.i	−0.222804	−	0.454869i
$509$	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
$518$	62800.9	−	58661.8i	0.234049	−	0.218623i
$519$		0			0
$520$	488431.	+	186076.i	1.80633	+	0.688151i
$521$	−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	$0.0231104\pi$
$523$			39683.4i			0.145079i	−0.997366	+	0.0725397i	$0.976890\pi$
$524$	−168306.	−	11484.2i	−0.612967	−	0.0418251i
$525$		0			0
$526$	253952.	−	237214.i	0.917867	−	0.857372i
$527$	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
$536$	−15546.4	+	2502.60i	−0.0541129	+	0.00871089i
$537$		0			0
$538$	−210747.	+	48841.9i	−0.728111	+	0.168744i
$539$			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	$0.608099\pi$
$542$	43309.6	+	186876.i	0.147430	+	0.636143i
$543$		0			0
$544$	40045.4	−	86830.7i	0.135318	−	0.293410i
$545$	92539.8	−	160284.i	0.311556	−	0.539630i
$546$		0			0
$547$	−81637.9	+	47133.6i	−0.272846	+	0.157527i	−0.630180	−	0.776449i	$-0.717019\pi$
$547$	−81637.9	+	47133.6i	−0.272846	+	0.157527i	0.357335	+	0.933976i	$0.383686\pi$
$548$	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
$554$	−201299.	−	215502.i	−0.655876	−	0.702154i
$555$		0			0
$556$	−300012.	−	20471.0i	−0.970485	−	0.0662201i
$557$	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
$560$	96471.5	+	74849.6i	0.307626	+	0.238679i
$561$		0			0
$562$	−153244.	−	164057.i	−0.485189	−	0.519423i
$563$	−543509.	−	313795.i	−1.71471	−	0.989986i	−0.927935	−	0.372741i	$-0.878418\pi$
$563$	−543509.	−	313795.i	−1.71471	−	0.989986i	−0.786771	−	0.617245i	$-0.788249\pi$
$564$		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	0.859573	−	0.511013i	$-0.170730\pi$
$571$	276094.	+	159403.i	0.846809	+	0.488905i	−0.0127640	+	0.999919i	$0.504063\pi$
$572$	163291.	+	333370.i	0.499080	+	1.01891i
$573$		0			0
$574$	860.673	+	3713.71i	0.00261225	+	0.0112716i
$575$			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	$0.480841\pi$
$578$	291480.	−	67552.2i	0.872475	−	0.202201i
$579$		0			0
$580$	730883.	−	358001.i	2.17266	−	1.06421i
$581$	−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	−0.517161	−	0.855888i	$-0.673011\pi$
$587$	−11894.5	+	6867.28i	−0.0345199	+	0.0199301i	0.482641	+	0.875818i	$0.339678\pi$
$588$		0			0
$589$	9213.72	−	15958.6i	0.0265586	−	0.0460008i
$590$	635563.	−	593673.i	1.82580	−	1.70547i
$591$		0			0
$592$	−276234.	+	356030.i	−0.788195	+	1.01588i
$593$	−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
$596$	−8332.74	+	122120.i	−0.0234582	+	0.343791i
$597$		0			0
$598$	−534381.	+	499161.i	−1.49434	+	1.39585i
$599$	394401.	+	227708.i	1.09922	+	0.634635i	0.936016	−	0.351958i	$-0.114484\pi$
$599$	394401.	+	227708.i	1.09922	+	0.634635i	0.163204	+	0.986592i	$0.447817\pi$
$600$		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	−0.406371	−	0.913708i	$-0.633206\pi$
$607$	−516142.	−	297995.i	−1.40085	−	0.808781i	−0.994480	+	0.104927i	$0.966539\pi$
$608$	−25003.7	−	11531.5i	−0.0676391	−	0.0311945i
$609$		0			0
$610$	−332008.	+	76944.8i	−0.892256	+	0.206785i
$611$		−	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	$0.240354\pi$
$614$	413.188	+	1782.86i	0.00109600	+	0.00472912i
$615$		0			0
$616$	13782.4	+	85617.8i	0.0363215	+	0.225633i
$617$	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	−0.712719	−	0.701450i	$-0.752537\pi$
$619$	−176869.	+	102115.i	−0.461605	+	0.266508i	0.251114	+	0.967958i	$0.419203\pi$
$620$	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
$626$	49017.7	+	52476.4i	0.125085	+	0.133911i
$627$		0			0
$628$	3824.90	−	56055.6i	0.00969841	−	0.142135i
$629$	164370.			0.415454
$630$		0			0
$631$		−	177036.i		−	0.444633i	−0.974975	−	0.222317i	$-0.928638\pi$
$631$		−	177036.i		−	0.444633i	0.974975	−	0.222317i	$-0.0713618\pi$
$632$	118031.	−	309819.i	0.295503	−	0.775665i
$633$		0			0
$634$	167573.	+	179397.i	0.416894	+	0.446310i
$635$	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	0.0928336	−	0.995682i	$-0.470408\pi$
$643$	−298938.	−	172592.i	−0.723035	−	0.417445i	−0.815869	+	0.578237i	$0.803741\pi$
$644$	−153413.	+	75145.0i	−0.369906	+	0.181187i
$645$		0			0
$646$	2267.56	+	9784.29i	0.00543369	+	0.0234458i
$647$		−	398251.i		−	0.951366i	−0.879617	−	0.475683i	$-0.842201\pi$
$647$		−	398251.i		−	0.951366i	0.879617	−	0.475683i	$-0.157799\pi$
$648$		0			0
$649$	617681.			1.46648
$650$	−734669.	+	170264.i	−1.73886	+	0.402991i
$651$		0			0
$652$	295236.	+	602744.i	0.694502	+	1.41787i
$653$	−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	−0.920625	−	0.390447i	$-0.872320\pi$
$659$	−452868.	+	261464.i	−1.04280	+	0.602061i	−0.122175	+	0.992509i	$0.538987\pi$
$660$		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	$0.281553\pi$
$662$	−543403.	+	507588.i	−1.23996	+	1.15823i
$663$		0			0
$664$	42683.4	−	112040.i	0.0968106	−	0.254118i
$665$	−12825.3			−0.0290018
$666$		0			0
$667$			1.13862e6i			2.55934i
$668$	108761.	+	7421.23i	0.243737	+	0.0166312i
$669$		0			0
$670$	28105.7	−	26253.3i	0.0626101	−	0.0584836i
$671$	−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
$680$	37117.4	+	230577.i	0.0802712	+	0.498653i
$681$		0			0
$682$	296468.	−	68708.1i	0.637395	−	0.147720i
$683$		−	124482.i		−	0.266848i	−0.991059	−	0.133424i	$-0.957403\pi$
$683$		−	124482.i		−	0.266848i	0.991059	−	0.133424i	$-0.0425972\pi$
$684$		0			0
$685$	−126057.			−0.268649
$686$	−51287.4	−	221300.i	−0.108984	−	0.470254i
$687$		0			0
$688$	56434.0	−	411608.i	0.119224	−	0.869574i
$689$	−137247.	+	237719.i	−0.289111	+	0.500756i
$690$		0			0
$691$	771402.	−	445369.i	1.61557	−	0.932747i	0.627518	−	0.778602i	$-0.284071\pi$
$691$	771402.	−	445369.i	1.61557	−	0.932747i	0.988048	−	0.154145i	$-0.0492623\pi$
$692$	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
$698$	−488619.	−	523096.i	−1.00291	−	1.07367i
$699$		0			0
$700$	−175768.	−	11993.3i	−0.358710	−	0.0244762i
$701$	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
$704$	−142704.	−	431759.i	−0.287932	−	0.871156i
$705$		0			0
$706$	−72071.4	−	77156.7i	−0.144595	−	0.154798i
$707$	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
$716$	−158342.	−	323265.i	−0.308866	−	0.630570i
$717$		0			0
$718$	−163787.	−	706724.i	−0.317710	−	1.37088i
$719$		−	768366.i		−	1.48631i	−0.669117	−	0.743157i	$-0.733328\pi$
$719$		−	768366.i		−	1.48631i	0.669117	−	0.743157i	$-0.266672\pi$
$720$		0			0
$721$	−135811.			−0.261255
$722$	−505007.	+	117038.i	−0.968775	+	0.224519i
$723$		0			0
$724$	−313920.	+	153764.i	−0.598883	+	0.293345i
$725$	−587133.	+	1.01695e6i	−1.11702	+	1.93473i
$726$		0			0
$727$	221493.	−	127879.i	0.419074	−	0.241952i	−0.275607	−	0.961270i	$-0.588879\pi$
$727$	221493.	−	127879.i	0.419074	−	0.241952i	0.694681	+	0.719318i	$0.255546\pi$
$728$	−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	$0.278450\pi$
$734$	610932.	−	570667.i	1.13397	−	1.05923i
$735$		0			0
$736$	731600.	−	516878.i	1.35057	−	0.954184i
$737$	27314.9			0.0502881
$738$		0			0
$739$		−	1.03557e6i		−	1.89623i	−0.317932	−	0.948114i	$-0.602988\pi$
$739$		−	1.03557e6i		−	1.89623i	0.317932	−	0.948114i	$-0.397012\pi$
$740$	74925.4	−	1.09807e6i	0.136825	−	2.00523i
$741$		0			0
$742$	−46861.4	+	43772.9i	−0.0851153	+	0.0795055i
$743$	486002.	+	280593.i	0.880360	+	0.508276i	0.870777	−	0.491678i	$-0.163616\pi$
$743$	486002.	+	280593.i	0.880360	+	0.508276i	0.00958322	+	0.999954i	$0.496950\pi$
$744$		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	0.639011	−	0.769197i	$-0.279344\pi$
$751$	164898.	+	95204.1i	0.292372	+	0.168801i	−0.346639	+	0.937999i	$0.612677\pi$
$752$	−80288.2	+	585591.i	−0.141976	+	1.03552i
$753$		0			0
$754$	−1.05997e6	+	245653.i	−1.86444	+	0.432095i
$755$			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	$0.349139\pi$
$758$	209623.	+	904499.i	0.364838	+	1.57424i
$759$		0			0
$760$	66396.9	−	10688.3i	0.114953	−	0.0185047i
$761$	−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	$-0.00132158\pi$
$770$	−144583.	−	154785.i	−0.243857	−	0.261063i
$771$		0			0
$772$	−50212.0	+	735879.i	−0.0842505	+	1.23473i
$773$	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
$776$	−343242.	−	130764.i	−0.570002	−	0.217152i
$777$		0			0
$778$	−332401.	−	355855.i	−0.549166	−	0.587915i
$779$	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	0.373084	−	0.927798i	$-0.378300\pi$
$787$	−151046.	−	87206.2i	−0.243870	−	0.140798i	−0.616954	+	0.786999i	$0.711634\pi$
$788$	−228963.	+	112151.i	−0.368734	+	0.180613i
$789$		0			0
$790$	182822.	+	788857.i	0.292937	+	1.26399i
$791$			223918.i			0.357879i
$792$		0			0
$793$	455635.			0.724553
$794$	279359.	−	64743.0i	0.443120	−	0.102696i
$795$		0			0
$796$	518950.	+	1.05947e6i	0.819029	+	1.67210i
$797$	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
$806$	−418638.	+	391047.i	−0.644420	+	0.601947i
$807$		0			0
$808$	−932195.	−	355136.i	−1.42786	−	0.543966i
$809$	−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	$0.0915097\pi$
$811$			372984.i			0.567085i	−0.958960	+	0.283543i	$0.908490\pi$
$812$	−253594.	−	17303.8i	−0.384616	−	0.0262439i
$813$		0			0
$814$	571235.	−	533586.i	0.862117	−	0.805296i
$815$	−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	−0.0495745	−	0.998770i	$-0.515787\pi$
$823$	−636230.	−	367328.i	−0.939322	−	0.542318i	−0.889748	+	0.456452i	$0.849120\pi$
$824$	703095.	−	113182.i	1.03552	−	0.166694i
$825$		0			0
$826$	−264615.	+	61326.0i	−0.387842	+	0.0898845i
$827$			1.27112e6i			1.85856i	0.369375	+	0.929281i	$0.379572\pi$
$827$			1.27112e6i			1.85856i	−0.369375	+	0.929281i	$0.620428\pi$
$828$		0			0
$829$	−427267.			−0.621714			−0.310857	−	0.950457i	$-0.600616\pi$
$829$	−427267.			−0.621714			−0.310857	+	0.950457i	$0.600616\pi$
$830$	66113.8	+	285274.i	0.0959700	+	0.414100i
$831$		0			0
$832$	639012.	+	569547.i	0.923129	+	0.822779i
$833$	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	−0.00737025	−	0.999973i	$-0.502346\pi$
$839$	601815.	−	347458.i	0.854947	−	0.493604i	0.862317	+	0.506369i	$0.169013\pi$
$840$		0			0
$841$	−493464.	+	854704.i	−0.697691	+	1.20844i
$842$	384917.	+	412076.i	0.542928	+	0.581237i
$843$		0			0
$844$	−284433.	−	19408.0i	−0.399296	−	0.0272456i
$845$	590581.			0.827115
$846$		0			0
$847$			28266.7i			0.0394011i
$848$	206123.	−	265666.i	0.286639	−	0.369440i
$849$		0			0
$850$	−230021.	−	246251.i	−0.318368	−	0.340832i
$851$	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	$0.0342718\pi$
$859$	1.16908e6	+	674970.i	1.58438	+	0.914741i	0.590168	+	0.807281i	$0.299062\pi$
$860$	446364.	+	911281.i	0.603520	+	1.23213i
$861$		0			0
$862$	172503.	+	744332.i	0.232157	+	1.00173i
$863$		−	916363.i		−	1.23040i	−0.788372	−	0.615199i	$-0.789076\pi$
$863$		−	916363.i		−	1.23040i	0.788372	−	0.615199i	$-0.210924\pi$
$864$		0			0
$865$	−615427.			−0.822515
$866$	−187991.	+	43568.0i	−0.250670	+	0.0580941i
$867$		0			0
$868$	−120185.	+	58869.2i	−0.159519	+	0.0781355i
$869$	−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	$0.0511090\pi$
$878$	766471.	−	715954.i	0.994276	−	0.928744i
$879$		0			0
$880$	877502.	+	680830.i	1.13314	+	0.879171i
$881$	−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	$-0.971294\pi$
$883$		−	140436.i		−	0.180119i	0.995936	−	0.0900593i	$-0.0287056\pi$
$884$	21255.4	−	311508.i	0.0271998	−	0.398625i
$885$		0			0
$886$	265954.	−	248425.i	0.338796	−	0.316467i
$887$	−307169.	−	177344.i	−0.390418	−	0.225408i	0.291923	−	0.956442i	$-0.405705\pi$
$887$	−307169.	−	177344.i	−0.390418	−	0.225408i	−0.682341	+	0.731034i	$0.739038\pi$
$888$		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
$896$	104001.	+	170798.i	0.129545	+	0.212748i
$897$		0			0
$898$	1.10413e6	−	255889.i	1.36921	−	0.317322i
$899$			892005.i			1.10369i
$900$		0			0
$901$	−122652.			−0.151086
$902$	7828.66	+	33779.8i	0.00962220	+	0.0415187i
$903$		0			0
$904$	−186608.	−	1.15923e6i	−0.228346	−	1.41851i
$905$	426883.	−	739383.i	0.521209	−	0.902760i
$906$		0			0
$907$	−1.27955e6	+	738746.i	−1.55540	+	0.898008i	−0.557709	+	0.830037i	$0.688319\pi$
$907$	−1.27955e6	+	738746.i	−1.55540	+	0.898008i	−0.997687	+	0.0679717i	$0.978347\pi$
$908$	−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	−0.474666	−	0.880166i	$-0.657431\pi$
$911$	41701.0	−	24076.1i	0.0502470	−	0.0290101i	0.524913	+	0.851156i	$0.324098\pi$
$912$		0			0
$913$	−103988.	+	180113.i	−0.124751	+	0.216074i
$914$	541868.	+	580102.i	0.648637	+	0.694404i
$915$		0			0
$916$	44577.4	−	653302.i	0.0531280	−	0.778615i
$917$	−128687.			−0.153036
$918$		0			0
$919$			346372.i			0.410120i	0.978749	+	0.205060i	$0.0657390\pi$
$919$			346372.i			0.410120i	−0.978749	+	0.205060i	$0.934261\pi$
$920$	−778892.	+	2.04451e6i	−0.920241	+	2.41554i
$921$		0			0
$922$	569832.	+	610039.i	0.670324	+	0.717622i
$923$	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
$932$	−1.13880e6	+	557806.i	−1.31104	+	0.642172i
$933$		0			0
$934$	87245.3	+	376454.i	0.100011	+	0.431537i
$935$		−	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	$0.693481\pi$
$938$	−11701.7	+	2711.94i	−0.0132998	+	0.00308230i
$939$		0			0
$940$	−635038.	−	1.29647e6i	−0.718694	−	1.46726i
$941$	−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	−0.587631	−	0.809129i	$-0.699939\pi$
$947$	−162072.	+	93572.3i	−0.180721	+	0.104339i	0.406910	+	0.913468i	$0.366606\pi$
$948$		0			0
$949$	−267998.	+	464186.i	−0.297577	+	0.515418i
$950$	−70910.5	+	66236.9i	−0.0785712	+	0.0733927i
$951$		0			0
$952$	25967.7	−	68162.5i	0.0286523	−	0.0752093i
$953$	−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
$956$	720422.	+	49157.2i	0.788263	+	0.0537863i
$957$		0			0
$958$	100127.	−	93527.4i	0.109098	−	0.101908i
$959$	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	0.286298	−	0.958141i	$-0.407575\pi$
$967$	−374342.	−	216127.i	−0.400328	−	0.231129i	−0.686625	+	0.727011i	$0.740909\pi$
$968$	−23556.8	−	146337.i	−0.0251400	−	0.156172i
$969$		0			0
$970$	873957.	−	202544.i	0.928852	−	0.215267i
$971$		−	756598.i		−	0.802467i	−0.915976	−	0.401233i	$-0.868582\pi$
$971$		−	756598.i		−	0.802467i	0.915976	−	0.401233i	$-0.131418\pi$
$972$		0			0
$973$	−229389.			−0.242296
$974$	62783.9	+	270906.i	0.0661806	+	0.285562i
$975$		0			0
$976$	−552973.	−	75816.0i	−0.580502	−	0.0795905i
$977$	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	−0.402942	−	0.915226i	$-0.632012\pi$
$983$	181852.	−	104992.i	0.188196	−	0.108655i	0.591138	+	0.806570i	$0.298679\pi$
$984$		0			0
$985$	311354.	−	539282.i	0.320910	−	0.555832i
$986$	−331870.	−	355286.i	−0.341361	−	0.365447i
$987$		0			0
$988$	−89701.9	−	6120.71i	−0.0918941	−	0.00627030i
$989$	−1.41966e6			−1.45141
$990$		0			0
$991$		−	1.66713e6i		−	1.69755i	−0.528754	−	0.848775i	$-0.677341\pi$
$991$		−	1.66713e6i		−	1.69755i	0.528754	−	0.848775i	$-0.322659\pi$
$992$	573141.	−	404926.i	0.582423	−	0.411484i
$993$		0			0
$994$	153570.	+	164406.i	0.155430	+	0.166397i
$995$	−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.91.2		44
3.2	odd	2		36.5.f.a.31.21	yes	44
4.3	odd	2	inner	108.5.f.a.91.17		44
9.2	odd	6		36.5.f.a.7.6	✓	44
9.4	even	3		324.5.d.e.163.13		22
9.5	odd	6		324.5.d.f.163.10		22
9.7	even	3	inner	108.5.f.a.19.17		44
12.11	even	2		36.5.f.a.31.6	yes	44
36.7	odd	6	inner	108.5.f.a.19.2		44
36.11	even	6		36.5.f.a.7.21	yes	44
36.23	even	6		324.5.d.f.163.9		22
36.31	odd	6		324.5.d.e.163.14		22

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-3.89672 + 0.903087i) q^{2} +(14.3689 - 7.03816i) q^{4} +(-19.5394 + 33.8433i) q^{5} +(10.5700 - 6.10260i) q^{7} +(-49.6354 + 40.4021i) q^{8} +O(q^{10})\)	\(q+(-3.89672 + 0.903087i) q^{2} +(14.3689 - 7.03816i) q^{4} +(-19.5394 + 33.8433i) q^{5} +(10.5700 - 6.10260i) q^{7} +(-49.6354 + 40.4021i) q^{8} +(45.5763 - 149.524i) q^{10} +(96.1446 - 55.5091i) q^{11} +(-104.491 + 180.984i) q^{13} +(-35.6772 + 33.3258i) q^{14} +(156.929 - 202.261i) q^{16} -93.3790 q^{17} +26.8894i q^{19} +(-42.5651 + 623.812i) q^{20} +(-324.519 + 303.130i) q^{22} +(-757.577 - 437.387i) q^{23} +(-451.080 - 781.293i) q^{25} +(243.728 - 799.608i) q^{26} +(108.928 - 162.081i) q^{28} +(-650.809 - 1127.23i) q^{29} +(-593.492 - 342.653i) q^{31} +(-428.848 + 929.874i) q^{32} +(363.872 - 84.3293i) q^{34} +476.966i q^{35} -1760.25 q^{37} +(-24.2835 - 104.780i) q^{38} +(-397.492 - 2469.26i) q^{40} +(39.0421 - 67.6229i) q^{41} +(1405.46 - 811.442i) q^{43} +(990.807 - 1474.28i) q^{44} +(3347.06 + 1020.22i) q^{46} +(-1999.54 + 1154.43i) q^{47} +(-1126.02 + 1950.32i) q^{49} +(2463.31 + 2637.12i) q^{50} +(-227.626 + 3335.96i) q^{52} +1313.48 q^{53} +4338.47i q^{55} +(-278.089 + 729.956i) q^{56} +(3554.01 + 3804.78i) q^{58} +(4818.38 + 2781.89i) q^{59} +(-1090.13 - 1888.16i) q^{61} +(2622.12 + 799.247i) q^{62} +(831.345 - 4010.75i) q^{64} +(-4083.39 - 7072.65i) q^{65} +(213.077 + 123.020i) q^{67} +(-1341.75 + 657.216i) q^{68} +(-430.742 - 1858.60i) q^{70} -4608.15i q^{71} +2564.79 q^{73} +(6859.21 - 1589.66i) q^{74} +(189.252 + 386.370i) q^{76} +(677.500 - 1173.46i) q^{77} +(-4486.29 + 2590.16i) q^{79} +(3778.87 + 9263.05i) q^{80} +(-91.0669 + 298.766i) q^{82} +(-1622.37 + 936.677i) q^{83} +(1824.57 - 3160.25i) q^{85} +(-4743.88 + 4431.22i) q^{86} +(-2529.49 + 6639.66i) q^{88} +1167.17 q^{89} +2550.67i q^{91} +(-13963.9 - 952.813i) q^{92} +(6749.08 - 6304.26i) q^{94} +(-910.026 - 525.404i) q^{95} +(2869.58 + 4970.26i) q^{97} +(2626.47 - 8616.73i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + q^{2} - q^{4} + 2 q^{5} - 122 q^{8}+O(q^{10}) \) 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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