LMFDB - Embedded newform 180.8.e.a.71.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [180,8,Mod(71,180)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(180, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("180.71");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 180 = 2^{2} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	180.e (of order $2$, degree $1$, 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:	$56.2293045871$
Analytic rank:	$0$
Dimension:	$56$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			71.3
Character	$\chi$	$=$	180.71
Dual form			180.8.e.a.71.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-11.0160 - 2.57826i) q^{2} +(114.705 + 56.8043i) q^{4} +125.000i q^{5} -118.084i q^{7} +(-1117.14 - 921.497i) q^{8} +O(q^{10})$	\(q+(-11.0160 - 2.57826i) q^{2} +(114.705 + 56.8043i) q^{4} +125.000i q^{5} -118.084i q^{7} +(-1117.14 - 921.497i) q^{8} +(322.283 - 1377.00i) q^{10} +4550.24 q^{11} -7997.80 q^{13} +(-304.451 + 1300.81i) q^{14} +(9930.53 + 13031.5i) q^{16} -24953.9i q^{17} +48910.8i q^{19} +(-7100.54 + 14338.1i) q^{20} +(-50125.5 - 11731.7i) q^{22} -47677.8 q^{23} -15625.0 q^{25} +(88103.8 + 20620.4i) q^{26} +(6707.67 - 13544.8i) q^{28} +41013.1i q^{29} +40062.4i q^{31} +(-75796.3 - 169159. i) q^{32} +(-64337.8 + 274893. i) q^{34} +14760.5 q^{35} +140476. q^{37} +(126105. - 538802. i) q^{38} +(115187. - 139642. i) q^{40} -559896. i q^{41} +343732. i q^{43} +(521936. + 258474. i) q^{44} +(525220. + 122926. i) q^{46} +994666. q^{47} +809599. q^{49} +(172125. + 40285.3i) q^{50} +(-917388. - 454310. i) q^{52} -202713. i q^{53} +568780. i q^{55} +(-108814. + 131916. i) q^{56} +(105743. - 451801. i) q^{58} -1.65755e6 q^{59} -3.11158e6 q^{61} +(103291. - 441328. i) q^{62} +(398837. + 2.05888e6i) q^{64} -999725. i q^{65} +395806. i q^{67} +(1.41749e6 - 2.86234e6i) q^{68} +(-162602. - 38056.4i) q^{70} +1.79702e6 q^{71} -3.77113e6 q^{73} +(-1.54748e6 - 362183. i) q^{74} +(-2.77834e6 + 5.61032e6i) q^{76} -537310. i q^{77} -1.67147e6i q^{79} +(-1.62894e6 + 1.24132e6i) q^{80} +(-1.44356e6 + 6.16783e6i) q^{82} -8.39036e6 q^{83} +3.11924e6 q^{85} +(886232. - 3.78656e6i) q^{86} +(-5.08324e6 - 4.19304e6i) q^{88} -9.29063e6i q^{89} +944410. i q^{91} +(-5.46889e6 - 2.70831e6i) q^{92} +(-1.09573e7 - 2.56451e6i) q^{94} -6.11385e6 q^{95} -1.46695e7 q^{97} +(-8.91856e6 - 2.08736e6i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 52 q^{4}+O(q^{10}) $ 56 * q + 52 * q^4	$ 56 q + 52 q^{4} - 6500 q^{10} + 14128 q^{13} - 8060 q^{16} + 259088 q^{22} - 875000 q^{25} - 490976 q^{28} + 40912 q^{34} + 1268048 q^{37} - 266500 q^{40} + 3108200 q^{46} - 3522056 q^{49} - 8882216 q^{52} + 8807592 q^{58} - 3944912 q^{61} - 16633580 q^{64} + 4533000 q^{70} + 7602384 q^{73} - 38876976 q^{76} + 33213064 q^{82} - 15068000 q^{85} - 56145472 q^{88} + 29409456 q^{94} - 45595824 q^{97}+O(q^{100}) $ 56 * q + 52 * q^4 - 6500 * q^10 + 14128 * q^13 - 8060 * q^16 + 259088 * q^22 - 875000 * q^25 - 490976 * q^28 + 40912 * q^34 + 1268048 * q^37 - 266500 * q^40 + 3108200 * q^46 - 3522056 * q^49 - 8882216 * q^52 + 8807592 * q^58 - 3944912 * q^61 - 16633580 * q^64 + 4533000 * q^70 + 7602384 * q^73 - 38876976 * q^76 + 33213064 * q^82 - 15068000 * q^85 - 56145472 * q^88 + 29409456 * q^94 - 45595824 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/180\mathbb{Z}\right)^\times$.

$n$	$37$	$91$	$101$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	−11.0160	−	2.57826i	−0.973687	−	0.227888i
$2$	−11.0160	−	2.57826i	−0.973687	−	0.227888i
$3$		0			0
$3$		0			0
$4$	114.705	+	56.8043i	0.896134	+	0.443784i
$5$			125.000i			0.447214i
$5$			125.000i			0.447214i
$6$		0			0
$7$		−	118.084i		−	0.130121i	−0.997881	−	0.0650604i	$-0.979276\pi$
$7$		−	118.084i		−	0.130121i	0.997881	−	0.0650604i	$-0.0207240\pi$
$8$	−1117.14	−	921.497i	−0.771421	−	0.636325i
$9$		0			0
$10$	322.283	−	1377.00i	0.101915	−	0.435446i
$11$	4550.24			1.03077			0.515383	−	0.856960i	$-0.327650\pi$
$11$	4550.24			1.03077			0.515383	+	0.856960i	$0.327650\pi$
$12$		0			0
$13$	−7997.80			−1.00964			−0.504822	−	0.863223i	$-0.668442\pi$
$13$	−7997.80			−1.00964			−0.504822	+	0.863223i	$0.668442\pi$
$14$	−304.451	+	1300.81i	−0.0296530	+	0.126697i
$15$		0			0
$16$	9930.53	+	13031.5i	0.606112	+	0.795380i
$17$		−	24953.9i		−	1.23188i	−0.787794	−	0.615939i	$-0.788777\pi$
$17$		−	24953.9i		−	1.23188i	0.787794	−	0.615939i	$-0.211223\pi$
$18$		0			0
$19$			48910.8i			1.63594i	0.575262	+	0.817969i	$0.304900\pi$
$19$			48910.8i			1.63594i	−0.575262	+	0.817969i	$0.695100\pi$
$20$	−7100.54	+	14338.1i	−0.198466	+	0.400763i
$21$		0			0
$22$	−50125.5	−	11731.7i	−1.00364	−	0.234900i
$23$	−47677.8			−0.817088			−0.408544	−	0.912739i	$-0.633963\pi$
$23$	−47677.8			−0.817088			−0.408544	+	0.912739i	$0.633963\pi$
$24$		0			0
$25$	−15625.0			−0.200000
$26$	88103.8	+	20620.4i	0.983078	+	0.230086i
$27$		0			0
$28$	6707.67	−	13544.8i	0.0577455	−	0.116606i
$29$			41013.1i			0.312270i	0.987736	+	0.156135i	$0.0499034\pi$
$29$			41013.1i			0.312270i	−0.987736	+	0.156135i	$0.950097\pi$
$30$		0			0
$31$			40062.4i			0.241530i	0.992681	+	0.120765i	$0.0385347\pi$
$31$			40062.4i			0.241530i	−0.992681	+	0.120765i	$0.961465\pi$
$32$	−75796.3	−	169159.i	−0.408905	−	0.912577i
$33$		0			0
$34$	−64337.8	+	274893.i	−0.280731	+	1.19946i
$35$	14760.5			0.0581918
$36$		0			0
$37$	140476.			0.455927			0.227963	−	0.973670i	$-0.426793\pi$
$37$	140476.			0.455927			0.227963	+	0.973670i	$0.426793\pi$
$38$	126105.	−	538802.i	0.372811	−	1.59289i
$39$		0			0
$40$	115187.	−	139642.i	0.284573	−	0.344990i
$41$		−	559896.i		−	1.26872i	−0.773040	−	0.634358i	$-0.781265\pi$
$41$		−	559896.i		−	1.26872i	0.773040	−	0.634358i	$-0.218735\pi$
$42$		0			0
$43$			343732.i			0.659296i	0.944104	+	0.329648i	$0.106930\pi$
$43$			343732.i			0.659296i	−0.944104	+	0.329648i	$0.893070\pi$
$44$	521936.	+	258474.i	0.923704	+	0.457437i
$45$		0			0
$46$	525220.	+	122926.i	0.795588	+	0.186205i
$47$	994666.			1.39745			0.698723	−	0.715393i	$-0.253752\pi$
$47$	994666.			1.39745			0.698723	+	0.715393i	$0.253752\pi$
$48$		0			0
$49$	809599.			0.983069
$50$	172125.	+	40285.3i	0.194737	+	0.0455777i
$51$		0			0
$52$	−917388.	−	454310.i	−0.904777	−	0.448064i
$53$		−	202713.i		−	0.187032i	−0.995618	−	0.0935159i	$-0.970189\pi$
$53$		−	202713.i		−	0.187032i	0.995618	−	0.0935159i	$-0.0298106\pi$
$54$		0			0
$55$			568780.i			0.460973i
$56$	−108814.	+	131916.i	−0.0827992	+	0.100378i
$57$		0			0
$58$	105743.	−	451801.i	0.0711626	−	0.304053i
$59$	−1.65755e6			−1.05071			−0.525357	−	0.850882i	$-0.676068\pi$
$59$	−1.65755e6			−1.05071			−0.525357	+	0.850882i	$0.676068\pi$
$60$		0			0
$61$	−3.11158e6			−1.75520			−0.877600	−	0.479393i	$-0.840857\pi$
$61$	−3.11158e6			−1.75520			−0.877600	+	0.479393i	$0.840857\pi$
$62$	103291.	−	441328.i	0.0550418	−	0.235174i
$63$		0			0
$64$	398837.	+	2.05888e6i	0.190180	+	0.981749i
$65$		−	999725.i		−	0.451527i
$66$		0			0
$67$			395806.i			0.160776i	0.996764	+	0.0803879i	$0.0256159\pi$
$67$			395806.i			0.160776i	−0.996764	+	0.0803879i	$0.974384\pi$
$68$	1.41749e6	−	2.86234e6i	0.546688	−	1.10393i
$69$		0			0
$70$	−162602.	−	38056.4i	−0.0566606	−	0.0132612i
$71$	1.79702e6			0.595865			0.297933	−	0.954587i	$-0.403703\pi$
$71$	1.79702e6			0.595865			0.297933	+	0.954587i	$0.403703\pi$
$72$		0			0
$73$	−3.77113e6			−1.13460			−0.567298	−	0.823513i	$-0.692011\pi$
$73$	−3.77113e6			−1.13460			−0.567298	+	0.823513i	$0.692011\pi$
$74$	−1.54748e6	−	362183.i	−0.443930	−	0.103900i
$75$		0			0
$76$	−2.77834e6	+	5.61032e6i	−0.726003	+	1.46602i
$77$		−	537310.i		−	0.134124i
$78$		0			0
$79$		−	1.67147e6i		−	0.381421i	−0.981646	−	0.190710i	$-0.938921\pi$
$79$		−	1.67147e6i		−	0.381421i	0.981646	−	0.190710i	$-0.0610792\pi$
$80$	−1.62894e6	+	1.24132e6i	−0.355705	+	0.271061i
$81$		0			0
$82$	−1.44356e6	+	6.16783e6i	−0.289125	+	1.23533i
$83$	−8.39036e6			−1.61067			−0.805336	−	0.592818i	$-0.798015\pi$
$83$	−8.39036e6			−1.61067			−0.805336	+	0.592818i	$0.798015\pi$
$84$		0			0
$85$	3.11924e6			0.550913
$86$	886232.	−	3.78656e6i	0.150246	−	0.641948i
$87$		0			0
$88$	−5.08324e6	−	4.19304e6i	−0.795155	−	0.655903i
$89$		−	9.29063e6i		−	1.39695i	−0.715636	−	0.698474i	$-0.753863\pi$
$89$		−	9.29063e6i		−	1.39695i	0.715636	−	0.698474i	$-0.246137\pi$
$90$		0			0
$91$			944410.i			0.131376i
$92$	−5.46889e6	−	2.70831e6i	−0.732220	−	0.362611i
$93$		0			0
$94$	−1.09573e7	−	2.56451e6i	−1.36067	−	0.318462i
$95$	−6.11385e6			−0.731614
$96$		0			0
$97$	−1.46695e7			−1.63198			−0.815990	−	0.578066i	$-0.803807\pi$
$97$	−1.46695e7			−1.63198			−0.815990	+	0.578066i	$0.803807\pi$
$98$	−8.91856e6	−	2.08736e6i	−0.957201	−	0.224030i
$99$		0			0
$100$	−1.79227e6	−	887568.i	−0.179227	−	0.0887568i
$101$			1.37705e7i			1.32992i	0.746878	+	0.664961i	$0.231552\pi$
$101$			1.37705e7i			1.32992i	−0.746878	+	0.664961i	$0.768448\pi$
$102$		0			0
$103$		−	3.34505e6i		−	0.301628i	−0.988562	−	0.150814i	$-0.951811\pi$
$103$		−	3.34505e6i		−	0.301628i	0.988562	−	0.150814i	$-0.0481895\pi$
$104$	8.93463e6	+	7.36995e6i	0.778861	+	0.642463i
$105$		0			0
$106$	−522646.	+	2.23309e6i	−0.0426223	+	0.182110i
$107$	−1.46281e7			−1.15437			−0.577186	−	0.816613i	$-0.695849\pi$
$107$	−1.46281e7			−1.15437			−0.577186	+	0.816613i	$0.695849\pi$
$108$		0			0
$109$	−1.85969e7			−1.37546			−0.687730	−	0.725966i	$-0.741393\pi$
$109$	−1.85969e7			−1.37546			−0.687730	+	0.725966i	$0.741393\pi$
$110$	1.46646e6	−	6.26569e6i	0.105050	−	0.448843i
$111$		0			0
$112$	1.53881e6	−	1.17263e6i	0.103495	−	0.0788678i
$113$		−	5.39304e6i		−	0.351608i	−0.984425	−	0.175804i	$-0.943747\pi$
$113$		−	5.39304e6i		−	0.351608i	0.984425	−	0.175804i	$-0.0562525\pi$
$114$		0			0
$115$		−	5.95973e6i		−	0.365413i
$116$	−2.32972e6	+	4.70442e6i	−0.138580	+	0.279835i
$117$		0			0
$118$	1.82596e7	+	4.27360e6i	1.02307	+	0.239446i
$119$	−2.94665e6			−0.160293
$120$		0			0
$121$	1.21754e6			0.0624790
$122$	3.42772e7	+	8.02247e6i	1.70902	+	0.399990i
$123$		0			0
$124$	−2.27572e6	+	4.59536e6i	−0.107187	+	0.216443i
$125$		−	1.95312e6i		−	0.0894427i
$126$		0			0
$127$		−	1.93754e7i		−	0.839341i	−0.907677	−	0.419671i	$-0.862146\pi$
$127$		−	1.93754e7i		−	0.839341i	0.907677	−	0.419671i	$-0.137854\pi$
$128$	914726.	−	2.37089e7i	0.0385528	−	0.999257i
$129$		0			0
$130$	−2.57755e6	+	1.10130e7i	−0.102898	+	0.439646i
$131$	−2.85142e7			−1.10818			−0.554091	−	0.832456i	$-0.686934\pi$
$131$	−2.85142e7			−1.10818			−0.554091	+	0.832456i	$0.686934\pi$
$132$		0			0
$133$	5.77557e6			0.212870
$134$	1.02049e6	−	4.36021e6i	0.0366389	−	0.156545i
$135$		0			0
$136$	−2.29950e7	+	2.78770e7i	−0.783875	+	0.950297i
$137$		−	3.03968e6i		−	0.100996i	−0.998724	−	0.0504982i	$-0.983919\pi$
$137$		−	3.03968e6i		−	0.100996i	0.998724	−	0.0504982i	$-0.0160809\pi$
$138$		0			0
$139$		−	5.30895e6i		−	0.167671i	−0.996480	−	0.0838353i	$-0.973283\pi$
$139$		−	5.30895e6i		−	0.167671i	0.996480	−	0.0838353i	$-0.0267170\pi$
$140$	1.69310e6	+	838459.i	0.0521477	+	0.0258246i
$141$		0			0
$142$	−1.97960e7	−	4.63318e6i	−0.580187	−	0.135791i
$143$	−3.63919e7			−1.04071
$144$		0			0
$145$	−5.12664e6			−0.139651
$146$	4.15428e7	+	9.72296e6i	1.10474	+	0.258561i
$147$		0			0
$148$	1.61133e7	+	7.97963e6i	0.408571	+	0.202333i
$149$			1.89800e7i			0.470050i	0.971989	+	0.235025i	$0.0755171\pi$
$149$			1.89800e7i			0.470050i	−0.971989	+	0.235025i	$0.924483\pi$
$150$		0			0
$151$			5.14841e7i			1.21690i	0.793594	+	0.608448i	$0.208208\pi$
$151$			5.14841e7i			1.21690i	−0.793594	+	0.608448i	$0.791792\pi$
$152$	4.50711e7	−	5.46400e7i	1.04099	−	1.26200i
$153$		0			0
$154$	−1.38533e6	+	5.91901e6i	−0.0305653	+	0.130595i
$155$	−5.00780e6			−0.108015
$156$		0			0
$157$	2.10677e7			0.434479			0.217239	−	0.976118i	$-0.430295\pi$
$157$	2.10677e7			0.434479			0.217239	+	0.976118i	$0.430295\pi$
$158$	−4.30950e6	+	1.84130e7i	−0.0869214	+	0.371385i
$159$		0			0
$160$	2.11448e7	−	9.47453e6i	0.408117	−	0.182868i
$161$			5.62997e6i			0.106320i
$162$		0			0
$163$		−	8.90064e7i		−	1.60977i	−0.593429	−	0.804886i	$-0.702226\pi$
$163$		−	8.90064e7i		−	1.60977i	0.593429	−	0.804886i	$-0.297774\pi$
$164$	3.18045e7	−	6.42230e7i	0.563035	−	1.13694i
$165$		0			0
$166$	9.24283e7	+	2.16325e7i	1.56829	+	0.367053i
$167$	2.59571e7			0.431269			0.215634	−	0.976474i	$-0.430818\pi$
$167$	2.59571e7			0.431269			0.215634	+	0.976474i	$0.430818\pi$
$168$		0			0
$169$	1.21625e6			0.0193829
$170$	−3.43616e7	−	8.04222e6i	−0.536417	−	0.125547i
$171$		0			0
$172$	−1.95255e7	+	3.94279e7i	−0.292585	+	0.590818i
$173$		−	1.42176e7i		−	0.208769i	−0.994537	−	0.104384i	$-0.966713\pi$
$173$		−	1.42176e7i		−	0.208769i	0.994537	−	0.104384i	$-0.0332872\pi$
$174$		0			0
$175$			1.84506e6i			0.0260242i
$176$	4.51863e7	+	5.92965e7i	0.624759	+	0.819850i
$177$		0			0
$178$	−2.39537e7	+	1.02346e8i	−0.318348	+	1.36019i
$179$	−4.60454e7			−0.600068			−0.300034	−	0.953929i	$-0.596998\pi$
$179$	−4.60454e7			−0.600068			−0.300034	+	0.953929i	$0.596998\pi$
$180$		0			0
$181$	4.93422e7			0.618505			0.309253	−	0.950980i	$-0.399921\pi$
$181$	4.93422e7			0.618505			0.309253	+	0.950980i	$0.399921\pi$
$182$	2.43494e6	−	1.04036e7i	0.0299390	−	0.127919i
$183$		0			0
$184$	5.32626e7	+	4.39350e7i	0.630319	+	0.519934i
$185$			1.75595e7i			0.203897i
$186$		0			0
$187$		−	1.13546e8i		−	1.26978i
$188$	1.14093e8	+	5.65014e7i	1.25230	+	0.620164i
$189$		0			0
$190$	6.73502e7	+	1.57631e7i	0.712363	+	0.166726i
$191$	−1.27693e8			−1.32602			−0.663011	−	0.748610i	$-0.730722\pi$
$191$	−1.27693e8			−1.32602			−0.663011	+	0.748610i	$0.730722\pi$
$192$		0			0
$193$	2.35647e7			0.235945			0.117972	−	0.993017i	$-0.462361\pi$
$193$	2.35647e7			0.235945			0.117972	+	0.993017i	$0.462361\pi$
$194$	1.61600e8	+	3.78219e7i	1.58904	+	0.371909i
$195$		0			0
$196$	9.28652e7	+	4.59888e7i	0.880961	+	0.436270i
$197$		−	1.82950e7i		−	0.170491i	−0.996360	−	0.0852454i	$-0.972833\pi$
$197$		−	1.82950e7i		−	0.170491i	0.996360	−	0.0852454i	$-0.0271674\pi$
$198$		0			0
$199$		−	1.83197e8i		−	1.64791i	−0.566656	−	0.823954i	$-0.691763\pi$
$199$		−	1.83197e8i		−	1.64791i	0.566656	−	0.823954i	$-0.308237\pi$
$200$	1.74553e7	+	1.43984e7i	0.154284	+	0.127265i
$201$		0			0
$202$	3.55041e7	−	1.51697e8i	0.303074	−	1.29493i
$203$	4.84298e6			0.0406328
$204$		0			0
$205$	6.99870e7			0.567387
$206$	−8.62441e6	+	3.68491e7i	−0.0687375	+	0.293692i
$207$		0			0
$208$	−7.94224e7	−	1.04223e8i	−0.611958	−	0.803051i
$209$			2.22556e8i			1.68627i
$210$		0			0
$211$		−	1.36796e8i		−	1.00250i	−0.865303	−	0.501249i	$-0.832874\pi$
$211$		−	1.36796e8i		−	1.00250i	0.865303	−	0.501249i	$-0.167126\pi$
$212$	1.15150e7	−	2.32522e7i	0.0830017	−	0.167605i
$213$		0			0
$214$	1.61144e8	+	3.77152e7i	1.12400	+	0.263068i
$215$	−4.29665e7			−0.294846
$216$		0			0
$217$	4.73071e6			0.0314281
$218$	2.04864e8	+	4.79477e7i	1.33927	+	0.313451i
$219$		0			0
$220$	−3.23092e7	+	6.52420e7i	−0.204572	+	0.413093i
$221$			1.99577e8i			1.24376i
$222$		0			0
$223$		−	3.59857e7i		−	0.217301i	−0.994080	−	0.108651i	$-0.965347\pi$
$223$		−	3.59857e7i		−	0.217301i	0.994080	−	0.108651i	$-0.0346530\pi$
$224$	−1.99749e7	+	8.95031e6i	−0.118745	+	0.0532071i
$225$		0			0
$226$	−1.39047e7	+	5.94098e7i	−0.0801274	+	0.342357i
$227$	−1.81742e8			−1.03125			−0.515627	−	0.856813i	$-0.672441\pi$
$227$	−1.81742e8			−1.03125			−0.515627	+	0.856813i	$0.672441\pi$
$228$		0			0
$229$	−1.27335e8			−0.700685			−0.350343	−	0.936622i	$-0.613935\pi$
$229$	−1.27335e8			−0.700685			−0.350343	+	0.936622i	$0.613935\pi$
$230$	−1.53657e7	+	6.56524e7i	−0.0832733	+	0.355798i
$231$		0			0
$232$	3.77935e7	−	4.58173e7i	0.198705	−	0.240891i
$233$			1.51184e8i			0.782996i	0.920179	+	0.391498i	$0.128043\pi$
$233$			1.51184e8i			0.782996i	−0.920179	+	0.391498i	$0.871957\pi$
$234$		0			0
$235$			1.24333e8i			0.624957i
$236$	−1.90130e8	−	9.41561e7i	−0.941581	−	0.466290i
$237$		0			0
$238$	3.24604e7	+	7.59725e6i	0.156075	+	0.0365289i
$239$	7.35426e6			0.0348455			0.0174227	−	0.999848i	$-0.494454\pi$
$239$	7.35426e6			0.0348455			0.0174227	+	0.999848i	$0.494454\pi$
$240$		0			0
$241$	2.96918e8			1.36640			0.683199	−	0.730232i	$-0.260588\pi$
$241$	2.96918e8			1.36640			0.683199	+	0.730232i	$0.260588\pi$
$242$	−1.34124e7	−	3.13914e6i	−0.0608350	−	0.0142382i
$243$		0			0
$244$	−3.56914e8	−	1.76751e8i	−1.57289	−	0.778930i
$245$			1.01200e8i			0.439642i
$246$		0			0
$247$		−	3.91178e8i		−	1.65172i
$248$	3.69174e7	−	4.47551e7i	0.153691	−	0.186321i
$249$		0			0
$250$	−5.03567e6	+	2.15157e7i	−0.0203830	+	0.0870892i
$251$	−3.40368e8			−1.35860			−0.679298	−	0.733862i	$-0.737716\pi$
$251$	−3.40368e8			−1.35860			−0.679298	+	0.733862i	$0.737716\pi$
$252$		0			0
$253$	−2.16946e8			−0.842227
$254$	−4.99550e7	+	2.13440e8i	−0.191276	+	0.817256i
$255$		0			0
$256$	−7.12045e7	+	2.58819e8i	−0.265257	+	0.964178i
$257$		−	3.51815e8i		−	1.29285i	−0.762977	−	0.646426i	$-0.776263\pi$
$257$		−	3.51815e8i		−	1.29285i	0.762977	−	0.646426i	$-0.223737\pi$
$258$		0			0
$259$		−	1.65879e7i		−	0.0593256i
$260$	5.67887e7	−	1.14674e8i	0.200380	−	0.404629i
$261$		0			0
$262$	3.14113e8	+	7.35170e7i	1.07902	+	0.252542i
$263$	−2.02325e8			−0.685811			−0.342905	−	0.939370i	$-0.611411\pi$
$263$	−2.02325e8			−0.685811			−0.342905	+	0.939370i	$0.611411\pi$
$264$		0			0
$265$	2.53391e7			0.0836431
$266$	−6.36237e7	−	1.48909e7i	−0.207269	−	0.0485105i
$267$		0			0
$268$	−2.24835e7	+	4.54010e7i	−0.0713497	+	0.144077i
$269$		−	3.09089e8i		−	0.968169i	−0.875021	−	0.484084i	$-0.839153\pi$
$269$		−	3.09089e8i		−	0.968169i	0.875021	−	0.484084i	$-0.160847\pi$
$270$		0			0
$271$			2.23772e8i			0.682987i	0.939884	+	0.341494i	$0.110933\pi$
$271$			2.23772e8i			0.682987i	−0.939884	+	0.341494i	$0.889067\pi$
$272$	3.25187e8	−	2.47806e8i	0.979811	−	0.746656i
$273$		0			0
$274$	−7.83710e6	+	3.34852e7i	−0.0230159	+	0.0983390i
$275$	−7.10975e7			−0.206153
$276$		0			0
$277$	−3.74217e8			−1.05790			−0.528950	−	0.848653i	$-0.677414\pi$
$277$	−3.74217e8			−1.05790			−0.528950	+	0.848653i	$0.677414\pi$
$278$	−1.36879e7	+	5.84835e7i	−0.0382102	+	0.163259i
$279$		0			0
$280$	−1.64895e7	−	1.36017e7i	−0.0448904	−	0.0370289i
$281$		−	1.00973e8i		−	0.271476i	−0.990745	−	0.135738i	$-0.956660\pi$
$281$		−	1.00973e8i		−	0.271476i	0.990745	−	0.135738i	$-0.0433405\pi$
$282$		0			0
$283$			6.58710e8i			1.72759i	0.503839	+	0.863797i	$0.331920\pi$
$283$			6.58710e8i			1.72759i	−0.503839	+	0.863797i	$0.668080\pi$
$284$	2.06127e8	+	1.02078e8i	0.533975	+	0.264436i
$285$		0			0
$286$	4.00894e8	+	9.38279e7i	1.01332	+	0.237165i
$287$	−6.61147e7			−0.165086
$288$		0			0
$289$	−2.12360e8			−0.517524
$290$	5.64751e7	+	1.32178e7i	0.135977	+	0.0318249i
$291$		0			0
$292$	−4.32568e8	−	2.14216e8i	−1.01675	−	0.503515i
$293$			6.57088e8i			1.52611i	0.646331	+	0.763057i	$0.276302\pi$
$293$			6.57088e8i			1.52611i	−0.646331	+	0.763057i	$0.723698\pi$
$294$		0			0
$295$		−	2.07194e8i		−	0.469894i
$296$	−1.56931e8	−	1.29448e8i	−0.351711	−	0.290118i
$297$		0			0
$298$	4.89354e7	−	2.09084e8i	0.107119	−	0.457681i
$299$	3.81318e8			0.824969
$300$		0			0
$301$	4.05892e7			0.0857882
$302$	1.32739e8	−	5.67149e8i	0.277316	−	1.18488i
$303$		0			0
$304$	−6.37381e8	+	4.85710e8i	−1.30119	+	0.991561i
$305$		−	3.88948e8i		−	0.784950i
$306$		0			0
$307$		−	2.75336e8i		−	0.543098i	−0.962425	−	0.271549i	$-0.912464\pi$
$307$		−	2.75336e8i		−	0.543098i	0.962425	−	0.271549i	$-0.0875359\pi$
$308$	3.05215e7	−	6.16322e7i	0.0595222	−	0.120193i
$309$		0			0
$310$	5.51660e7	+	1.29114e7i	0.105173	+	0.0246154i
$311$	2.03449e8			0.383525			0.191762	−	0.981441i	$-0.438580\pi$
$311$	2.03449e8			0.383525			0.191762	+	0.981441i	$0.438580\pi$
$312$		0			0
$313$	−1.85440e8			−0.341820			−0.170910	−	0.985287i	$-0.554671\pi$
$313$	−1.85440e8			−0.341820			−0.170910	+	0.985287i	$0.554671\pi$
$314$	−2.32082e8	−	5.43181e7i	−0.423047	−	0.0990127i
$315$		0			0
$316$	9.49469e7	−	1.91727e8i	0.169268	−	0.341804i
$317$		−	8.28795e8i		−	1.46130i	−0.682751	−	0.730651i	$-0.739217\pi$
$317$		−	8.28795e8i		−	1.46130i	0.682751	−	0.730651i	$-0.260783\pi$
$318$		0			0
$319$			1.86620e8i			0.321877i
$320$	−2.57360e8	+	4.98547e7i	−0.439052	+	0.0850513i
$321$		0			0
$322$	1.45156e7	−	6.20199e7i	0.0242291	−	0.103523i
$323$	1.22052e9			2.01528
$324$		0			0
$325$	1.24966e8			0.201929
$326$	−2.29482e8	+	9.80495e8i	−0.366848	+	1.56741i
$327$		0			0
$328$	−5.15943e8	+	6.25481e8i	−0.807315	+	0.978713i
$329$		−	1.17454e8i		−	0.181837i
$330$		0			0
$331$			7.94404e8i			1.20405i	0.798479	+	0.602023i	$0.205639\pi$
$331$			7.94404e8i			1.20405i	−0.798479	+	0.602023i	$0.794361\pi$
$332$	−9.62417e8	−	4.76609e8i	−1.44338	−	0.714791i
$333$		0			0
$334$	−2.85943e8	−	6.69241e7i	−0.419921	−	0.0982811i
$335$	−4.94758e7			−0.0719011
$336$		0			0
$337$	1.07979e9			1.53687			0.768433	−	0.639930i	$-0.221037\pi$
$337$	1.07979e9			1.53687			0.768433	+	0.639930i	$0.221037\pi$
$338$	−1.33982e7	−	3.13581e6i	−0.0188729	−	0.00441714i
$339$		0			0
$340$	3.57793e8	+	1.77186e8i	0.493692	+	0.244486i
$341$			1.82294e8i			0.248961i
$342$		0			0
$343$		−	1.92848e8i		−	0.258039i
$344$	3.16748e8	−	3.83996e8i	0.419527	−	0.508595i
$345$		0			0
$346$	−3.66568e7	+	1.56622e8i	−0.0475760	+	0.203276i
$347$	2.05401e8			0.263905			0.131953	−	0.991256i	$-0.457875\pi$
$347$	2.05401e8			0.263905			0.131953	+	0.991256i	$0.457875\pi$
$348$		0			0
$349$	−3.73229e8			−0.469987			−0.234994	−	0.971997i	$-0.575507\pi$
$349$	−3.73229e8			−0.469987			−0.234994	+	0.971997i	$0.575507\pi$
$350$	4.75704e6	−	2.03252e7i	0.00593060	−	0.0253394i
$351$		0			0
$352$	−3.44891e8	−	7.69713e8i	−0.421486	−	0.940653i
$353$		−	1.15204e9i		−	1.39398i	−0.717083	−	0.696988i	$-0.754523\pi$
$353$		−	1.15204e9i		−	1.39398i	0.717083	−	0.696988i	$-0.245477\pi$
$354$		0			0
$355$			2.24627e8i			0.266479i
$356$	5.27748e8	−	1.06568e9i	0.619943	−	1.25185i
$357$		0			0
$358$	5.07236e8	+	1.18717e8i	0.584278	+	0.136748i
$359$	9.76301e8			1.11366			0.556831	−	0.830626i	$-0.312017\pi$
$359$	9.76301e8			1.11366			0.556831	+	0.830626i	$0.312017\pi$
$360$		0			0
$361$	−1.49839e9			−1.67629
$362$	−5.43554e8	−	1.27217e8i	−0.602230	−	0.140950i
$363$		0			0
$364$	−5.36466e7	+	1.08329e8i	−0.0583025	+	0.117730i
$365$		−	4.71391e8i		−	0.507407i
$366$		0			0
$367$			1.48160e9i			1.56459i	0.622907	+	0.782296i	$0.285952\pi$
$367$			1.48160e9i			1.56459i	−0.622907	+	0.782296i	$0.714048\pi$
$368$	−4.73466e8	−	6.21313e8i	−0.495247	−	0.649895i
$369$		0			0
$370$	4.52729e7	−	1.93435e8i	0.0464657	−	0.198532i
$371$	−2.39371e7			−0.0243367
$372$		0			0
$373$	−3.58274e8			−0.357465			−0.178733	−	0.983898i	$-0.557200\pi$
$373$	−3.58274e8			−0.357465			−0.178733	+	0.983898i	$0.557200\pi$
$374$	−2.92753e8	+	1.25083e9i	−0.289368	+	1.23637i
$375$		0			0
$376$	−1.11118e9	−	9.16582e8i	−1.07802	−	0.889230i
$377$		−	3.28015e8i		−	0.315282i
$378$		0			0
$379$			1.07824e8i			0.101736i	0.998705	+	0.0508682i	$0.0161989\pi$
$379$			1.07824e8i			0.101736i	−0.998705	+	0.0508682i	$0.983801\pi$
$380$	−7.01290e8	−	3.47293e8i	−0.655624	−	0.324678i
$381$		0			0
$382$	1.40667e9	+	3.29226e8i	1.29113	+	0.302185i
$383$	−1.63524e9			−1.48725			−0.743627	−	0.668594i	$-0.766896\pi$
$383$	−1.63524e9			−1.48725			−0.743627	+	0.668594i	$0.766896\pi$
$384$		0			0
$385$	6.71637e7			0.0599822
$386$	−2.59589e8	−	6.07559e7i	−0.229737	−	0.0537691i
$387$		0			0
$388$	−1.68267e9	−	8.33292e8i	−1.46247	−	0.724246i
$389$			2.17561e9i			1.87395i	0.349402	+	0.936973i	$0.386385\pi$
$389$			2.17561e9i			1.87395i	−0.349402	+	0.936973i	$0.613615\pi$
$390$		0			0
$391$			1.18975e9i			1.00655i
$392$	−9.04433e8	−	7.46044e8i	−0.758360	−	0.625551i
$393$		0			0
$394$	−4.71694e7	+	2.01538e8i	−0.0388529	+	0.166005i
$395$	2.08934e8			0.170577
$396$		0			0
$397$	3.01024e8			0.241454			0.120727	−	0.992686i	$-0.461478\pi$
$397$	3.01024e8			0.241454			0.120727	+	0.992686i	$0.461478\pi$
$398$	−4.72331e8	+	2.01810e9i	−0.375539	+	1.60455i
$399$		0			0
$400$	−1.55165e8	−	2.03617e8i	−0.121222	−	0.159076i
$401$		−	5.13709e8i		−	0.397843i	−0.980015	−	0.198921i	$-0.936256\pi$
$401$		−	5.13709e8i		−	0.397843i	0.980015	−	0.198921i	$-0.0637439\pi$
$402$		0			0
$403$		−	3.20411e8i		−	0.243859i
$404$	−7.82227e8	+	1.57955e9i	−0.590198	+	1.19179i
$405$		0			0
$406$	−5.33504e7	−	1.24865e7i	−0.0395636	−	0.00925974i
$407$	6.39198e8			0.469954
$408$		0			0
$409$	−1.46200e9			−1.05662			−0.528308	−	0.849053i	$-0.677173\pi$
$409$	−1.46200e9			−1.05662			−0.528308	+	0.849053i	$0.677173\pi$
$410$	−7.70978e8	−	1.80445e8i	−0.552457	−	0.129301i
$411$		0			0
$412$	1.90013e8	−	3.83694e8i	0.133858	−	0.270299i
$413$			1.95730e8i			0.136720i
$414$		0			0
$415$		−	1.04879e9i		−	0.720315i
$416$	6.06203e8	+	1.35290e9i	0.412849	+	0.921378i
$417$		0			0
$418$	5.73807e8	−	2.45168e9i	0.384281	−	1.64190i
$419$	8.75174e8			0.581226			0.290613	−	0.956841i	$-0.406141\pi$
$419$	8.75174e8			0.581226			0.290613	+	0.956841i	$0.406141\pi$
$420$		0			0
$421$	2.16862e9			1.41643			0.708216	−	0.705995i	$-0.249500\pi$
$421$	2.16862e9			1.41643			0.708216	+	0.705995i	$0.249500\pi$
$422$	−3.52695e8	+	1.50694e9i	−0.228458	+	0.976120i
$423$		0			0
$424$	−1.86799e8	+	2.26458e8i	−0.119013	+	0.144280i
$425$			3.89905e8i			0.246376i
$426$		0			0
$427$			3.67427e8i			0.228388i
$428$	−1.67792e9	−	8.30942e8i	−1.03447	−	0.512292i
$429$		0			0
$430$	4.73320e8	+	1.10779e8i	0.287088	+	0.0671920i
$431$	3.29066e9			1.97976			0.989880	−	0.141907i	$-0.0453233\pi$
$431$	3.29066e9			1.97976			0.989880	+	0.141907i	$0.0453233\pi$
$432$		0			0
$433$	1.32799e9			0.786119			0.393060	−	0.919513i	$-0.371417\pi$
$433$	1.32799e9			0.786119			0.393060	+	0.919513i	$0.371417\pi$
$434$	−5.21136e7	−	1.21970e7i	−0.0306011	−	0.00716209i
$435$		0			0
$436$	−2.13316e9	−	1.05639e9i	−1.23260	−	0.610407i
$437$		−	2.33196e9i		−	1.33671i
$438$		0			0
$439$			1.54053e9i			0.869050i	0.900660	+	0.434525i	$0.143084\pi$
$439$			1.54053e9i			0.869050i	−0.900660	+	0.434525i	$0.856916\pi$
$440$	5.24130e8	−	6.35405e8i	0.293329	−	0.355604i
$441$		0			0
$442$	5.14561e8	−	2.19854e9i	0.283438	−	1.21103i
$443$	1.71780e9			0.938770			0.469385	−	0.882994i	$-0.344476\pi$
$443$	1.71780e9			0.938770			0.469385	+	0.882994i	$0.344476\pi$
$444$		0			0
$445$	1.16133e9			0.624734
$446$	−9.27805e7	+	3.96419e8i	−0.0495205	+	0.211584i
$447$		0			0
$448$	2.43120e8	−	4.70962e7i	0.127746	−	0.0247465i
$449$			3.22082e9i			1.67921i	0.543198	+	0.839604i	$0.317213\pi$
$449$			3.22082e9i			1.67921i	−0.543198	+	0.839604i	$0.682787\pi$
$450$		0			0
$451$		−	2.54766e9i		−	1.30775i
$452$	3.06348e8	−	6.18609e8i	0.156038	−	0.315088i
$453$		0			0
$454$	2.00208e9	+	4.68580e8i	1.00412	+	0.235011i
$455$	−1.18051e8			−0.0587531
$456$		0			0
$457$	3.10061e9			1.51964			0.759820	−	0.650133i	$-0.225287\pi$
$457$	3.10061e9			1.51964			0.759820	+	0.650133i	$0.225287\pi$
$458$	1.40272e9	+	3.28303e8i	0.682249	+	0.159678i
$459$		0			0
$460$	3.38538e8	−	6.83611e8i	0.162164	−	0.327459i
$461$			2.30103e9i			1.09388i	0.837173	+	0.546939i	$0.184207\pi$
$461$			2.30103e9i			1.09388i	−0.837173	+	0.546939i	$0.815793\pi$
$462$		0			0
$463$			3.55958e9i			1.66673i	0.552723	+	0.833365i	$0.313589\pi$
$463$			3.55958e9i			1.66673i	−0.552723	+	0.833365i	$0.686411\pi$
$464$	−5.34462e8	+	4.07282e8i	−0.248373	+	0.189270i
$465$		0			0
$466$	3.89792e8	−	1.66544e9i	0.178436	−	0.762394i
$467$	−3.69666e9			−1.67958			−0.839790	−	0.542911i	$-0.817322\pi$
$467$	−3.69666e9			−1.67958			−0.839790	+	0.542911i	$0.817322\pi$
$468$		0			0
$469$	4.67383e7			0.0209203
$470$	3.20564e8	−	1.36966e9i	0.142420	−	0.608512i
$471$		0			0
$472$	1.85171e9	+	1.52743e9i	0.810544	+	0.668596i
$473$			1.56407e9i			0.679580i
$474$		0			0
$475$		−	7.64231e8i		−	0.327188i
$476$	−3.37996e8	−	1.67383e8i	−0.143644	−	0.0711355i
$477$		0			0
$478$	−8.10147e7	−	1.89612e7i	−0.0339286	−	0.00794088i
$479$	4.23795e9			1.76190			0.880951	−	0.473208i	$-0.156904\pi$
$479$	4.23795e9			1.76190			0.880951	+	0.473208i	$0.156904\pi$
$480$		0			0
$481$	−1.12350e9			−0.460324
$482$	−3.27085e9	−	7.65533e8i	−1.33044	−	0.311386i
$483$		0			0
$484$	1.39658e8	+	6.91615e7i	0.0559896	+	0.0277272i
$485$		−	1.83369e9i		−	0.729843i
$486$		0			0
$487$		−	3.67241e9i		−	1.44079i	−0.693565	−	0.720394i	$-0.743961\pi$
$487$		−	3.67241e9i		−	1.44079i	0.693565	−	0.720394i	$-0.256039\pi$
$488$	3.47606e9	+	2.86731e9i	1.35400	+	1.11688i
$489$		0			0
$490$	2.60920e8	−	1.11482e9i	0.100189	−	0.428073i
$491$	1.28282e9			0.489079			0.244540	−	0.969639i	$-0.421363\pi$
$491$	1.28282e9			0.489079			0.244540	+	0.969639i	$0.421363\pi$
$492$		0			0
$493$	1.02344e9			0.384678
$494$	−1.00856e9	+	4.30923e9i	−0.376407	+	1.60826i
$495$		0			0
$496$	−5.22073e8	+	3.97841e8i	−0.192108	+	0.146394i
$497$		−	2.12199e8i		−	0.0775345i
$498$		0			0
$499$		−	1.32776e9i		−	0.478375i	−0.970973	−	0.239187i	$-0.923119\pi$
$499$		−	1.32776e9i		−	0.478375i	0.970973	−	0.239187i	$-0.0768810\pi$
$500$	1.10946e8	−	2.24033e8i	0.0396932	−	0.0801526i
$501$		0			0
$502$	3.74950e9	+	8.77558e8i	1.32285	+	0.309608i
$503$	−9.33528e8			−0.327069			−0.163535	−	0.986538i	$-0.552290\pi$
$503$	−9.33528e8			−0.327069			−0.163535	+	0.986538i	$0.552290\pi$
$504$		0			0
$505$	−1.72132e9			−0.594759
$506$	2.38988e9	+	5.59343e8i	0.820066	+	0.191934i
$507$		0			0
$508$	1.10061e9	−	2.22246e9i	0.372486	−	0.752162i
$509$		−	3.14058e9i		−	1.05560i	−0.849370	−	0.527798i	$-0.823018\pi$
$509$		−	3.14058e9i		−	1.05560i	0.849370	−	0.527798i	$-0.176982\pi$
$510$		0			0
$511$			4.45309e8i			0.147635i
$512$	1.45169e9	−	2.66758e9i	0.478002	−	0.878358i
$513$		0			0
$514$	−9.07072e8	+	3.87560e9i	−0.294626	+	1.25883i
$515$	4.18131e8			0.134892
$516$		0			0
$517$	4.52597e9			1.44044
$518$	−4.27679e7	+	1.82732e8i	−0.0135196	+	0.0577646i
$519$		0			0
$520$	−9.21244e8	+	1.11683e9i	−0.287318	+	0.348317i
$521$		−	4.94545e9i		−	1.53205i	−0.642809	−	0.766026i	$-0.722231\pi$
$521$		−	4.94545e9i		−	1.53205i	0.642809	−	0.766026i	$-0.277769\pi$
$522$		0			0
$523$			4.60919e9i			1.40886i	0.709773	+	0.704431i	$0.248798\pi$
$523$			4.60919e9i			1.40886i	−0.709773	+	0.704431i	$0.751202\pi$
$524$	−3.27072e9	−	1.61973e9i	−0.993080	−	0.491794i
$525$		0			0
$526$	2.22882e9	+	5.21647e8i	0.667765	+	0.156288i
$527$	9.99714e8			0.297535
$528$		0			0
$529$	−1.13165e9			−0.332367
$530$	−2.79136e8	−	6.53308e7i	−0.0814422	−	0.0190613i
$531$		0			0
$532$	6.62487e8	+	3.28077e8i	0.190760	+	0.0944681i
$533$			4.47794e9i			1.28095i
$534$		0			0
$535$		−	1.82852e9i		−	0.516251i
$536$	3.64734e8	−	4.42170e8i	0.102306	−	0.124026i
$537$		0			0
$538$	−7.96913e8	+	3.40493e9i	−0.220634	+	0.942694i
$539$	3.68387e9			1.01331
$540$		0			0
$541$	−4.10635e9			−1.11498			−0.557489	−	0.830185i	$-0.688235\pi$
$541$	−4.10635e9			−1.11498			−0.557489	+	0.830185i	$0.688235\pi$
$542$	5.76942e8	−	2.46507e9i	0.155645	−	0.665016i
$543$		0			0
$544$	−4.22118e9	+	1.89142e9i	−1.12418	+	0.503722i
$545$		−	2.32461e9i		−	0.615125i
$546$		0			0
$547$			5.14921e9i			1.34519i	0.740009	+	0.672597i	$0.234821\pi$
$547$			5.14921e9i			1.34519i	−0.740009	+	0.672597i	$0.765179\pi$
$548$	1.72667e8	−	3.48667e8i	0.0448206	−	0.0905063i
$549$		0			0
$550$	7.83212e8	+	1.83308e8i	0.200729	+	0.0469799i
$551$	−2.00598e9			−0.510854
$552$		0			0
$553$	−1.97374e8			−0.0496308
$554$	4.12238e9	+	9.64830e8i	1.03006	+	0.241083i
$555$		0			0
$556$	3.01571e8	−	6.08964e8i	0.0744095	−	0.150255i
$557$			1.01836e8i			0.0249693i	0.999922	+	0.0124847i	$0.00397410\pi$
$557$			1.01836e8i			0.0249693i	−0.999922	+	0.0124847i	$0.996026\pi$
$558$		0			0
$559$		−	2.74910e9i		−	0.665655i
$560$	1.46579e8	+	1.92351e8i	0.0352707	+	0.0462846i
$561$		0			0
$562$	−2.60334e8	+	1.11231e9i	−0.0618661	+	0.264332i
$563$	−2.14024e9			−0.505455			−0.252728	−	0.967537i	$-0.581328\pi$
$563$	−2.14024e9			−0.505455			−0.252728	+	0.967537i	$0.581328\pi$
$564$		0			0
$565$	6.74130e8			0.157244
$566$	1.69833e9	−	7.25636e9i	0.393699	−	1.68214i
$567$		0			0
$568$	−2.00752e9	−	1.65595e9i	−0.459663	−	0.379164i
$569$			6.31144e9i			1.43627i	0.695905	+	0.718134i	$0.255003\pi$
$569$			6.31144e9i			1.43627i	−0.695905	+	0.718134i	$0.744997\pi$
$570$		0			0
$571$		−	2.42566e9i		−	0.545261i	−0.962119	−	0.272630i	$-0.912106\pi$
$571$		−	2.42566e9i		−	0.545261i	0.962119	−	0.272630i	$-0.0878936\pi$
$572$	−4.17434e9	−	2.06722e9i	−0.932614	−	0.461849i
$573$		0			0
$574$	7.28320e8	+	1.70461e8i	0.160742	+	0.0376212i
$575$	7.44966e8			0.163418
$576$		0			0
$577$	5.05611e9			1.09573			0.547863	−	0.836568i	$-0.315442\pi$
$577$	5.05611e9			1.09573			0.547863	+	0.836568i	$0.315442\pi$
$578$	2.33936e9	+	5.47520e8i	0.503907	+	0.117938i
$579$		0			0
$580$	−5.88052e8	−	2.91215e8i	−0.125146	−	0.0619750i
$581$			9.90765e8i			0.209582i
$582$		0			0
$583$		−	9.22392e8i		−	0.192786i
$584$	4.21287e9	+	3.47508e9i	0.875251	+	0.721972i
$585$		0			0
$586$	1.69415e9	−	7.23849e9i	0.347784	−	1.48596i
$587$	−7.87947e9			−1.60792			−0.803959	−	0.594685i	$-0.797277\pi$
$587$	−7.87947e9			−1.60792			−0.803959	+	0.594685i	$0.797277\pi$
$588$		0			0
$589$	−1.95948e9			−0.395128
$590$	−5.34200e8	+	2.28245e9i	−0.107083	+	0.457530i
$591$		0			0
$592$	1.39500e9	+	1.83061e9i	0.276343	+	0.362635i
$593$			1.77627e9i			0.349798i	0.984586	+	0.174899i	$0.0559599\pi$
$593$			1.77627e9i			0.349798i	−0.984586	+	0.174899i	$0.944040\pi$
$594$		0			0
$595$		−	3.68332e8i		−	0.0716852i
$596$	−1.07815e9	+	2.17710e9i	−0.208600	+	0.421227i
$597$		0			0
$598$	−4.20060e9	−	9.83137e8i	−0.803262	−	0.188001i
$599$	−8.68302e9			−1.65073			−0.825366	−	0.564598i	$-0.809031\pi$
$599$	−8.68302e9			−1.65073			−0.825366	+	0.564598i	$0.809031\pi$
$600$		0			0
$601$	−2.08141e9			−0.391108			−0.195554	−	0.980693i	$-0.562650\pi$
$601$	−2.08141e9			−0.391108			−0.195554	+	0.980693i	$0.562650\pi$
$602$	−4.47131e8	−	1.04650e8i	−0.0835309	−	0.0195501i
$603$		0			0
$604$	−2.92452e9	+	5.90549e9i	−0.540039	+	1.09050i
$605$			1.52192e8i			0.0279415i
$606$		0			0
$607$		−	1.69991e9i		−	0.308508i	−0.988031	−	0.154254i	$-0.950703\pi$
$607$		−	1.69991e9i		−	0.308508i	0.988031	−	0.154254i	$-0.0492974\pi$
$608$	8.27368e9	−	3.70725e9i	1.49292	−	0.668944i
$609$		0			0
$610$	−1.00281e9	+	4.28465e9i	−0.178881	+	0.764296i
$611$	−7.95514e9			−1.41092
$612$		0			0
$613$	−9.45514e9			−1.65789			−0.828946	−	0.559329i	$-0.811059\pi$
$613$	−9.45514e9			−1.65789			−0.828946	+	0.559329i	$0.811059\pi$
$614$	−7.09888e8	+	3.03310e9i	−0.123766	+	0.528808i
$615$		0			0
$616$	−4.95129e8	+	6.00248e8i	−0.0853466	+	0.103466i
$617$		−	8.21339e9i		−	1.40775i	−0.710326	−	0.703873i	$-0.751452\pi$
$617$		−	8.21339e9i		−	1.40775i	0.710326	−	0.703873i	$-0.248548\pi$
$618$		0			0
$619$		−	1.13973e10i		−	1.93146i	−0.259553	−	0.965729i	$-0.583575\pi$
$619$		−	1.13973e10i		−	1.93146i	0.259553	−	0.965729i	$-0.416425\pi$
$620$	−5.74420e8	−	2.84465e8i	−0.0967963	−	0.0479355i
$621$		0			0
$622$	−2.24119e9	−	5.24544e8i	−0.373433	−	0.0874008i
$623$	−1.09707e9			−0.181772
$624$		0			0
$625$	2.44141e8			0.0400000
$626$	2.04281e9	+	4.78113e8i	0.332826	+	0.0778969i
$627$		0			0
$628$	2.41658e9	+	1.19674e9i	0.389351	+	0.192815i
$629$		−	3.50542e9i		−	0.561646i
$630$		0			0
$631$		−	2.87818e8i		−	0.0456053i	−0.999740	−	0.0228027i	$-0.992741\pi$
$631$		−	2.87818e8i		−	0.0456053i	0.999740	−	0.0228027i	$-0.00725894\pi$
$632$	−1.54026e9	+	1.86726e9i	−0.242708	+	0.294236i
$633$		0			0
$634$	−2.13685e9	+	9.13002e9i	−0.333014	+	1.42285i
$635$	2.42193e9			0.375365
$636$		0			0
$637$	−6.47501e9			−0.992550
$638$	4.81154e8	−	2.05580e9i	0.0733520	−	0.313408i
$639$		0			0
$640$	2.96362e9	+	1.14341e8i	0.446881	+	0.0172414i
$641$			3.58683e9i			0.537908i	0.963153	+	0.268954i	$0.0866780\pi$
$641$			3.58683e9i			0.537908i	−0.963153	+	0.268954i	$0.913322\pi$
$642$		0			0
$643$			2.91686e9i			0.432690i	0.976317	+	0.216345i	$0.0694136\pi$
$643$			2.91686e9i			0.432690i	−0.976317	+	0.216345i	$0.930586\pi$
$644$	−3.19807e8	+	6.45787e8i	−0.0471832	+	0.0952771i
$645$		0			0
$646$	−1.34452e10	−	3.14681e9i	−1.96225	−	0.459258i
$647$	−9.34838e9			−1.35697			−0.678487	−	0.734612i	$-0.737364\pi$
$647$	−9.34838e9			−1.35697			−0.678487	+	0.734612i	$0.737364\pi$
$648$		0			0
$649$	−7.54226e9			−1.08304
$650$	−1.37662e9	−	3.22194e8i	−0.196616	−	0.0460173i
$651$		0			0
$652$	5.05595e9	−	1.02095e10i	0.714391	−	1.44257i
$653$			3.20796e9i			0.450850i	0.974261	+	0.225425i	$0.0723771\pi$
$653$			3.20796e9i			0.450850i	−0.974261	+	0.225425i	$0.927623\pi$
$654$		0			0
$655$		−	3.56427e9i		−	0.495594i
$656$	7.29629e9	−	5.56007e9i	1.00911	−	0.768983i
$657$		0			0
$658$	−3.02827e8	+	1.29387e9i	−0.0414385	+	0.177052i
$659$	5.61516e9			0.764299			0.382149	−	0.924101i	$-0.375184\pi$
$659$	5.61516e9			0.764299			0.382149	+	0.924101i	$0.375184\pi$
$660$		0			0
$661$	6.37531e9			0.858611			0.429305	−	0.903159i	$-0.358758\pi$
$661$	6.37531e9			0.858611			0.429305	+	0.903159i	$0.358758\pi$
$662$	2.04818e9	−	8.75116e9i	0.274388	−	1.17236i
$663$		0			0
$664$	9.37318e9	+	7.73169e9i	1.24251	+	1.02491i
$665$			7.21946e8i			0.0951982i
$666$		0			0
$667$		−	1.95542e9i		−	0.255152i
$668$	2.97741e9	+	1.47447e9i	0.386474	+	0.191390i
$669$		0			0
$670$	5.45026e8	+	1.27561e8i	0.0700092	+	0.0163854i
$671$	−1.41585e10			−1.80920
$672$		0			0
$673$	−4.66091e9			−0.589410			−0.294705	−	0.955588i	$-0.595221\pi$
$673$	−4.66091e9			−0.589410			−0.294705	+	0.955588i	$0.595221\pi$
$674$	−1.18950e10	−	2.78399e9i	−1.49643	−	0.350234i
$675$		0			0
$676$	1.39510e8	+	6.90882e7i	0.0173697	+	0.00860182i
$677$		−	2.19388e9i		−	0.271740i	−0.990727	−	0.135870i	$-0.956617\pi$
$677$		−	2.19388e9i		−	0.271740i	0.990727	−	0.135870i	$-0.0433829\pi$
$678$		0			0
$679$			1.73223e9i			0.212355i
$680$	−3.48462e9	−	2.87437e9i	−0.424986	−	0.350560i
$681$		0			0
$682$	4.70000e8	−	2.00815e9i	0.0567352	−	0.242410i
$683$	−1.15048e10			−1.38168			−0.690840	−	0.723007i	$-0.742759\pi$
$683$	−1.15048e10			−1.38168			−0.690840	+	0.723007i	$0.742759\pi$
$684$		0			0
$685$	3.79960e8			0.0451670
$686$	−4.97211e8	+	2.12441e9i	−0.0588040	+	0.251249i
$687$		0			0
$688$	−4.47935e9	+	3.41344e9i	−0.524391	+	0.399607i
$689$			1.62125e9i			0.188836i
$690$		0			0
$691$			8.72298e9i			1.00575i	0.864358	+	0.502877i	$0.167725\pi$
$691$			8.72298e9i			1.00575i	−0.864358	+	0.502877i	$0.832275\pi$
$692$	8.07623e8	−	1.63083e9i	0.0926482	−	0.187085i
$693$		0			0
$694$	−2.26269e9	−	5.29576e8i	−0.256961	−	0.0601410i
$695$	6.63619e8			0.0749846
$696$		0			0
$697$	−1.39716e10			−1.56290
$698$	4.11150e9	+	9.62282e8i	0.457621	+	0.107105i
$699$		0			0
$700$	−1.04807e8	+	2.11638e8i	−0.0115491	+	0.0233211i
$701$			3.29096e8i			0.0360836i	0.999837	+	0.0180418i	$0.00574319\pi$
$701$			3.29096e8i			0.0360836i	−0.999837	+	0.0180418i	$0.994257\pi$
$702$		0			0
$703$			6.87077e9i			0.745868i
$704$	1.81481e9	+	9.36839e9i	0.196032	+	1.01195i
$705$		0			0
$706$	−2.97025e9	+	1.26909e10i	−0.317671	+	1.35730i
$707$	1.62608e9			0.173051
$708$		0			0
$709$	1.97511e9			0.208128			0.104064	−	0.994571i	$-0.466815\pi$
$709$	1.97511e9			0.208128			0.104064	+	0.994571i	$0.466815\pi$
$710$	5.79148e8	−	2.47450e9i	0.0607275	−	0.259467i
$711$		0			0
$712$	−8.56129e9	+	1.03789e10i	−0.888913	+	1.07763i
$713$		−	1.91009e9i		−	0.197351i
$714$		0			0
$715$		−	4.54899e9i		−	0.465419i
$716$	−5.28164e9	−	2.61558e9i	−0.537741	−	0.266300i
$717$		0			0
$718$	−1.07549e10	−	2.51716e9i	−1.08436	−	0.253791i
$719$	4.83310e9			0.484925			0.242463	−	0.970161i	$-0.422045\pi$
$719$	4.83310e9			0.484925			0.242463	+	0.970161i	$0.422045\pi$
$720$		0			0
$721$	−3.94996e8			−0.0392481
$722$	1.65063e10	+	3.86325e9i	1.63219	+	0.382008i
$723$		0			0
$724$	5.65980e9	+	2.80285e9i	0.554263	+	0.274483i
$725$		−	6.40830e8i		−	0.0624539i
$726$		0			0
$727$		−	1.13903e10i		−	1.09942i	−0.835355	−	0.549711i	$-0.814738\pi$
$727$		−	1.13903e10i		−	1.09942i	0.835355	−	0.549711i	$-0.185262\pi$
$728$	8.70271e8	−	1.05503e9i	0.0835978	−	0.101346i
$729$		0			0
$730$	−1.21537e9	+	5.19285e9i	−0.115632	+	0.494055i
$731$	8.57747e9			0.812173
$732$		0			0
$733$	1.47773e10			1.38589			0.692947	−	0.720989i	$-0.256312\pi$
$733$	1.47773e10			1.38589			0.692947	+	0.720989i	$0.256312\pi$
$734$	3.81997e9	−	1.63214e10i	0.356552	−	1.52342i
$735$		0			0
$736$	3.61380e9	+	8.06512e9i	0.334112	+	0.745656i
$737$			1.80101e9i			0.165722i
$738$		0			0
$739$		−	1.99415e10i		−	1.81762i	−0.417212	−	0.908809i	$-0.636993\pi$
$739$		−	1.99415e10i		−	1.81762i	0.417212	−	0.908809i	$-0.363007\pi$
$740$	−9.97453e8	+	2.01416e9i	−0.0904861	+	0.182719i
$741$		0			0
$742$	2.63691e8	+	6.17160e7i	0.0236964	+	0.00554606i
$743$	−9.70396e9			−0.867937			−0.433968	−	0.900928i	$-0.642887\pi$
$743$	−9.70396e9			−0.867937			−0.433968	+	0.900928i	$0.642887\pi$
$744$		0			0
$745$	−2.37250e9			−0.210213
$746$	3.94675e9	+	9.23724e8i	0.348060	+	0.0814622i
$747$		0			0
$748$	6.44993e9	−	1.30244e10i	0.563507	−	1.13789i
$749$			1.72735e9i			0.150208i
$750$		0			0
$751$			4.21101e9i			0.362783i	0.983411	+	0.181391i	$0.0580601\pi$
$751$			4.21101e9i			0.362783i	−0.983411	+	0.181391i	$0.941940\pi$
$752$	9.87757e9	+	1.29620e10i	0.847008	+	1.11150i
$753$		0			0
$754$	−8.45708e8	+	3.61341e9i	−0.0718490	+	0.306986i
$755$	−6.43551e9			−0.544213
$756$		0			0
$757$	1.91616e10			1.60545			0.802724	−	0.596350i	$-0.203383\pi$
$757$	1.91616e10			1.60545			0.802724	+	0.596350i	$0.203383\pi$
$758$	2.77998e8	−	1.18779e9i	0.0231846	−	0.0990595i
$759$		0			0
$760$	6.83000e9	+	5.63389e9i	0.564382	+	0.465544i
$761$			1.52044e9i			0.125061i	0.998043	+	0.0625306i	$0.0199171\pi$
$761$			1.52044e9i			0.125061i	−0.998043	+	0.0625306i	$0.980083\pi$
$762$		0			0
$763$			2.19599e9i			0.178976i
$764$	−1.46471e10	−	7.25352e9i	−1.18829	−	0.588467i
$765$		0			0
$766$	1.80138e10	+	4.21607e9i	1.44812	+	0.338928i
$767$	1.32568e10			1.06085
$768$		0			0
$769$	−1.40272e10			−1.11231			−0.556157	−	0.831077i	$-0.687725\pi$
$769$	−1.40272e10			−1.11231			−0.556157	+	0.831077i	$0.687725\pi$
$770$	−7.39876e8	−	1.73166e8i	−0.0584039	−	0.0136692i
$771$		0			0
$772$	2.70299e9	+	1.33857e9i	0.211438	+	0.104709i
$773$		−	7.71866e9i		−	0.601054i	−0.953773	−	0.300527i	$-0.902837\pi$
$773$		−	7.71866e9i		−	0.601054i	0.953773	−	0.300527i	$-0.0971626\pi$
$774$		0			0
$775$		−	6.25975e8i		−	0.0483060i
$776$	1.63879e10	+	1.35179e10i	1.25894	+	1.03847i
$777$		0			0
$778$	5.60929e9	−	2.39665e10i	0.427050	−	1.82464i
$779$	2.73850e10			2.07554
$780$		0			0
$781$	8.17687e9			0.614198
$782$	3.06749e9	−	1.31063e10i	0.229382	−	0.980068i
$783$		0			0
$784$	8.03975e9	+	1.05503e10i	0.595849	+	0.781913i
$785$			2.63346e9i			0.194305i
$786$		0			0
$787$			3.34524e9i			0.244633i	0.992491	+	0.122317i	$0.0390323\pi$
$787$			3.34524e9i			0.244633i	−0.992491	+	0.122317i	$0.960968\pi$
$788$	1.03924e9	−	2.09853e9i	0.0756611	−	0.152783i
$789$		0			0
$790$	−2.30162e9	−	5.38687e8i	−0.166088	−	0.0388724i
$791$	−6.36830e8			−0.0457516
$792$		0			0
$793$	2.48858e10			1.77213
$794$	−3.31608e9	−	7.76118e8i	−0.235100	−	0.0550245i
$795$		0			0
$796$	1.04064e10	−	2.10137e10i	0.731315	−	1.47675i
$797$			1.05441e10i			0.737747i	0.929480	+	0.368873i	$0.120256\pi$
$797$			1.05441e10i			0.737747i	−0.929480	+	0.368873i	$0.879744\pi$
$798$		0			0
$799$		−	2.48208e10i		−	1.72148i
$800$	1.18432e9	+	2.64310e9i	0.0817811	+	0.182515i
$801$		0			0
$802$	−1.32448e9	+	5.65902e9i	−0.0906637	+	0.387375i
$803$	−1.71595e10			−1.16950
$804$		0			0
$805$	−7.03747e8			−0.0475478
$806$	−8.26103e8	+	3.52965e9i	−0.0555727	+	0.237443i
$807$		0			0
$808$	1.26895e10	−	1.53836e10i	0.846263	−	1.02593i
$809$		−	1.05270e10i		−	0.699011i	−0.936934	−	0.349506i	$-0.886350\pi$
$809$		−	1.05270e10i		−	0.699011i	0.936934	−	0.349506i	$-0.113650\pi$
$810$		0			0
$811$			2.70841e10i			1.78296i	0.453061	+	0.891479i	$0.350332\pi$
$811$			2.70841e10i			1.78296i	−0.453061	+	0.891479i	$0.649668\pi$
$812$	5.55515e8	+	2.75102e8i	0.0364124	+	0.0180322i
$813$		0			0
$814$	−7.04142e9	−	1.64802e9i	−0.457588	−	0.107097i
$815$	1.11258e10			0.719912
$816$		0			0
$817$	−1.68122e10			−1.07857
$818$	1.61055e10	+	3.76943e9i	1.02881	+	0.240790i
$819$		0			0
$820$	8.02787e9	+	3.97557e9i	0.508454	+	0.251797i
$821$			1.52681e10i			0.962904i	0.876472	+	0.481452i	$0.159890\pi$
$821$			1.52681e10i			0.962904i	−0.876472	+	0.481452i	$0.840110\pi$
$822$		0			0
$823$			3.06809e10i			1.91853i	0.282509	+	0.959265i	$0.408833\pi$
$823$			3.06809e10i			1.91853i	−0.282509	+	0.959265i	$0.591167\pi$
$824$	−3.08245e9	+	3.73688e9i	−0.191934	+	0.232682i
$825$		0			0
$826$	5.04643e8	−	2.15616e9i	0.0311569	−	0.133122i
$827$	4.32469e9			0.265880			0.132940	−	0.991124i	$-0.457558\pi$
$827$	4.32469e9			0.265880			0.132940	+	0.991124i	$0.457558\pi$
$828$		0			0
$829$	8.88539e9			0.541671			0.270836	−	0.962626i	$-0.412700\pi$
$829$	8.88539e9			0.541671			0.270836	+	0.962626i	$0.412700\pi$
$830$	−2.70407e9	+	1.15535e10i	−0.164151	+	0.701361i
$831$		0			0
$832$	−3.18982e9	−	1.64665e10i	−0.192015	−	0.991218i
$833$		−	2.02027e10i		−	1.21102i
$834$		0			0
$835$			3.24463e9i			0.192869i
$836$	−1.26421e10	+	2.55283e10i	−0.748339	+	1.51112i
$837$		0			0
$838$	−9.64093e9	−	2.25643e9i	−0.565933	−	0.132455i
$839$	2.20836e10			1.29093			0.645464	−	0.763790i	$-0.276664\pi$
$839$	2.20836e10			1.29093			0.645464	+	0.763790i	$0.276664\pi$
$840$		0			0
$841$	1.55678e10			0.902488
$842$	−2.38895e10	−	5.59127e9i	−1.37916	−	0.322788i
$843$		0			0
$844$	7.77059e9	−	1.56912e10i	0.444893	−	0.898373i
$845$			1.52031e8i			0.00866830i
$846$		0			0
$847$		−	1.43772e8i		−	0.00812982i
$848$	2.64165e9	−	2.01304e9i	0.148761	−	0.113362i
$849$		0			0
$850$	1.00528e9	−	4.29520e9i	0.0561461	−	0.239893i
$851$	−6.69757e9			−0.372532
$852$		0			0
$853$	1.80040e10			0.993224			0.496612	−	0.867973i	$-0.334577\pi$
$853$	1.80040e10			0.993224			0.496612	+	0.867973i	$0.334577\pi$
$854$	9.47324e8	−	4.04758e9i	0.0520470	−	0.222379i
$855$		0			0
$856$	1.63416e10	+	1.34798e10i	0.890507	+	0.734556i
$857$			2.07001e10i			1.12341i	0.827337	+	0.561707i	$0.189855\pi$
$857$			2.07001e10i			1.12341i	−0.827337	+	0.561707i	$0.810145\pi$
$858$		0			0
$859$		−	2.50897e10i		−	1.35058i	−0.737553	−	0.675289i	$-0.764019\pi$
$859$		−	2.50897e10i		−	1.35058i	0.737553	−	0.675289i	$-0.235981\pi$
$860$	−4.92848e9	−	2.44069e9i	−0.264222	−	0.130848i
$861$		0			0
$862$	−3.62500e10	−	8.48418e9i	−1.92767	−	0.451164i
$863$	−5.69072e9			−0.301391			−0.150695	−	0.988580i	$-0.548151\pi$
$863$	−5.69072e9			−0.301391			−0.150695	+	0.988580i	$0.548151\pi$
$864$		0			0
$865$	1.77720e9			0.0933643
$866$	−1.46292e10	−	3.42392e9i	−0.765434	−	0.179147i
$867$		0			0
$868$	5.42637e8	+	2.68725e8i	0.0281638	+	0.0139473i
$869$		−	7.60561e9i		−	0.393156i
$870$		0			0
$871$		−	3.16558e9i		−	0.162326i
$872$	2.07753e10	+	1.71370e10i	1.06106	+	0.875240i
$873$		0			0
$874$	−6.01240e9	+	2.56889e10i	−0.304620	+	1.30153i
$875$	−2.30632e8			−0.0116384
$876$		0			0
$877$	−4.33055e8			−0.0216793			−0.0108396	−	0.999941i	$-0.503450\pi$
$877$	−4.33055e8			−0.0216793			−0.0108396	+	0.999941i	$0.503450\pi$
$878$	3.97190e9	−	1.69705e10i	0.198046	−	0.846183i
$879$		0			0
$880$	−7.41206e9	+	5.64829e9i	−0.366648	+	0.279401i
$881$			7.10988e9i			0.350305i	0.984541	+	0.175152i	$0.0560418\pi$
$881$			7.10988e9i			0.350305i	−0.984541	+	0.175152i	$0.943958\pi$
$882$		0			0
$883$		−	2.01969e9i		−	0.0987238i	−0.998781	−	0.0493619i	$-0.984281\pi$
$883$		−	2.01969e9i		−	0.0987238i	0.998781	−	0.0493619i	$-0.0157188\pi$
$884$	−1.13368e10	+	2.28925e10i	−0.551961	+	1.11458i
$885$		0			0
$886$	−1.89233e10	−	4.42894e9i	−0.914068	−	0.213935i
$887$	2.39368e10			1.15168			0.575841	−	0.817562i	$-0.304675\pi$
$887$	2.39368e10			1.15168			0.575841	+	0.817562i	$0.304675\pi$
$888$		0			0
$889$	−2.28792e9			−0.109216
$890$	−1.27932e10	−	2.99421e9i	−0.608295	−	0.142370i
$891$		0			0
$892$	2.04414e9	−	4.12774e9i	0.0964349	−	0.194731i
$893$			4.86499e10i			2.28613i
$894$		0			0
$895$		−	5.75567e9i		−	0.268358i
$896$	−2.79964e9	−	1.08014e8i	−0.130024	−	0.00501653i
$897$		0			0
$898$	8.30413e9	−	3.54806e10i	0.382672	−	1.63502i
$899$	−1.64308e9			−0.0754224
$900$		0			0
$901$	−5.05848e9			−0.230400
$902$	−6.56855e9	+	2.80651e10i	−0.298021	+	1.27334i
$903$		0			0
$904$	−4.96967e9	+	6.02476e9i	−0.223737	+	0.271238i
$905$			6.16777e9i			0.276604i
$906$		0			0
$907$			2.79121e10i			1.24213i	0.783760	+	0.621064i	$0.213299\pi$
$907$			2.79121e10i			1.24213i	−0.783760	+	0.621064i	$0.786701\pi$
$908$	−2.08468e10	−	1.03238e10i	−0.924142	−	0.457654i
$909$		0			0
$910$	1.30045e9	+	3.04367e8i	0.0572071	+	0.0133891i
$911$	−9.81331e9			−0.430033			−0.215016	−	0.976610i	$-0.568980\pi$
$911$	−9.81331e9			−0.430033			−0.215016	+	0.976610i	$0.568980\pi$
$912$		0			0
$913$	−3.81782e10			−1.66023
$914$	−3.41564e10	−	7.99419e9i	−1.47965	−	0.346308i
$915$		0			0
$916$	−1.46060e10	−	7.23317e9i	−0.627908	−	0.310953i
$917$			3.36706e9i			0.144198i
$918$		0			0
$919$		−	1.46930e10i		−	0.624464i	−0.950006	−	0.312232i	$-0.898923\pi$
$919$		−	1.46930e10i		−	0.624464i	0.950006	−	0.312232i	$-0.101077\pi$
$920$	−5.49187e9	+	6.65783e9i	−0.232521	+	0.281887i
$921$		0			0
$922$	5.93266e9	−	2.53482e10i	0.249282	−	1.06509i
$923$	−1.43722e10			−0.601613
$924$		0			0
$925$	−2.19493e9			−0.0911853
$926$	9.17753e9	−	3.92124e10i	0.379828	−	1.62287i
$927$		0			0
$928$	6.93773e9	−	3.10864e9i	0.284970	−	0.127689i
$929$		−	4.82435e10i		−	1.97417i	−0.160209	−	0.987083i	$-0.551217\pi$
$929$		−	4.82435e10i		−	1.97417i	0.160209	−	0.987083i	$-0.448783\pi$
$930$		0			0
$931$			3.95981e10i			1.60824i
$932$	−8.58790e9	+	1.73416e10i	−0.347481	+	0.701669i
$933$		0			0
$934$	4.07225e10	+	9.53097e9i	1.63539	+	0.382757i
$935$	1.41933e10			0.567862
$936$		0			0
$937$	−1.61883e10			−0.642856			−0.321428	−	0.946934i	$-0.604163\pi$
$937$	−1.61883e10			−0.642856			−0.321428	+	0.946934i	$0.604163\pi$
$938$	−5.14869e8	−	1.20504e8i	−0.0203698	−	0.00476749i
$939$		0			0
$940$	−7.06267e9	+	1.42617e10i	−0.277346	+	0.560045i
$941$		−	1.03237e10i		−	0.403897i	−0.979396	−	0.201949i	$-0.935273\pi$
$941$		−	1.03237e10i		−	0.403897i	0.979396	−	0.201949i	$-0.0647274\pi$
$942$		0			0
$943$			2.66946e10i			1.03665i
$944$	−1.64604e10	−	2.16004e10i	−0.636851	−	0.835717i
$945$		0			0
$946$	4.03257e9	−	1.72298e10i	0.154868	−	0.661699i
$947$	3.41592e10			1.30702			0.653510	−	0.756918i	$-0.273296\pi$
$947$	3.41592e10			1.30702			0.653510	+	0.756918i	$0.273296\pi$
$948$		0			0
$949$	3.01607e10			1.14554
$950$	−1.97039e9	+	8.41878e9i	−0.0745622	+	0.318578i
$951$		0			0
$952$	3.29182e9	+	2.71533e9i	0.123653	+	0.101999i
$953$		−	1.22587e10i		−	0.458797i	−0.973333	−	0.229399i	$-0.926324\pi$
$953$		−	1.22587e10i		−	0.458797i	0.973333	−	0.229399i	$-0.0736759\pi$
$954$		0			0
$955$		−	1.59616e10i		−	0.593015i
$956$	8.43572e8	+	4.17754e8i	0.0312262	+	0.0154639i
$957$		0			0
$958$	−4.66853e10	−	1.09265e10i	−1.71554	−	0.401517i
$959$	−3.58937e8			−0.0131417
$960$		0			0
$961$	2.59076e10			0.941663
$962$	1.23764e10	+	2.89667e9i	0.448212	+	0.104902i
$963$		0			0
$964$	3.40580e10	+	1.68662e10i	1.22448	+	0.606385i
$965$			2.94558e9i			0.105518i
$966$		0			0
$967$			8.35640e9i			0.297185i	0.988899	+	0.148592i	$0.0474742\pi$
$967$			8.35640e9i			0.297185i	−0.988899	+	0.148592i	$0.952526\pi$
$968$	−1.36016e9	−	1.12196e9i	−0.0481976	−	0.0397570i
$969$		0			0
$970$	−4.72773e9	+	2.01999e10i	−0.166323	+	0.710639i
$971$	6.88696e9			0.241413			0.120706	−	0.992688i	$-0.461484\pi$
$971$	6.88696e9			0.241413			0.120706	+	0.992688i	$0.461484\pi$
$972$		0			0
$973$	−6.26901e8			−0.0218174
$974$	−9.46844e9	+	4.04553e10i	−0.328339	+	1.40288i
$975$		0			0
$976$	−3.08997e10	−	4.05486e10i	−1.06385	−	1.39605i
$977$		−	2.54107e10i		−	0.871736i	−0.900011	−	0.435868i	$-0.856441\pi$
$977$		−	2.54107e10i		−	0.871736i	0.900011	−	0.435868i	$-0.143559\pi$
$978$		0			0
$979$		−	4.22746e10i		−	1.43993i
$980$	−5.74859e9	+	1.16081e10i	−0.195106	+	0.393978i
$981$		0			0
$982$	−1.41315e10	−	3.30743e9i	−0.476210	−	0.111455i
$983$	3.59296e10			1.20647			0.603233	−	0.797565i	$-0.293879\pi$
$983$	3.59296e10			1.20647			0.603233	+	0.797565i	$0.293879\pi$
$984$		0			0
$985$	2.28688e9			0.0762458
$986$	−1.12742e10	−	2.63869e9i	−0.374556	−	0.0876637i
$987$		0			0
$988$	2.22206e10	−	4.48702e10i	0.733005	−	1.48016i
$989$		−	1.63884e10i		−	0.538703i
$990$		0			0
$991$			2.12344e10i			0.693078i	0.938036	+	0.346539i	$0.112643\pi$
$991$			2.12344e10i			0.693078i	−0.938036	+	0.346539i	$0.887357\pi$
$992$	6.77690e9	−	3.03658e9i	0.220414	−	0.0987629i
$993$		0			0
$994$	−5.47104e8	+	2.33758e9i	−0.0176692	+	0.0754944i
$995$	2.28997e10			0.736967
$996$		0			0
$997$	−5.07758e10			−1.62264			−0.811322	−	0.584599i	$-0.801252\pi$
$997$	−5.07758e10			−1.62264			−0.811322	+	0.584599i	$0.801252\pi$
$998$	−3.42332e9	+	1.46266e10i	−0.109016	+	0.465787i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	180.8.e.a.71.3	✓	56
3.2	odd	2	inner	180.8.e.a.71.54	yes	56
4.3	odd	2	inner	180.8.e.a.71.53	yes	56
12.11	even	2	inner	180.8.e.a.71.4	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.8.e.a.71.3	✓	56	1.1	even	1	trivial
180.8.e.a.71.4	yes	56	12.11	even	2	inner
180.8.e.a.71.53	yes	56	4.3	odd	2	inner
180.8.e.a.71.54	yes	56	3.2	odd	2	inner

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:	\( N \)	\(=\)	\( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	180.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-11.0160 - 2.57826i) q^{2} +(114.705 + 56.8043i) q^{4} +125.000i q^{5} -118.084i q^{7} +(-1117.14 - 921.497i) q^{8} +O(q^{10})\)	\(q+(-11.0160 - 2.57826i) q^{2} +(114.705 + 56.8043i) q^{4} +125.000i q^{5} -118.084i q^{7} +(-1117.14 - 921.497i) q^{8} +(322.283 - 1377.00i) q^{10} +4550.24 q^{11} -7997.80 q^{13} +(-304.451 + 1300.81i) q^{14} +(9930.53 + 13031.5i) q^{16} -24953.9i q^{17} +48910.8i q^{19} +(-7100.54 + 14338.1i) q^{20} +(-50125.5 - 11731.7i) q^{22} -47677.8 q^{23} -15625.0 q^{25} +(88103.8 + 20620.4i) q^{26} +(6707.67 - 13544.8i) q^{28} +41013.1i q^{29} +40062.4i q^{31} +(-75796.3 - 169159. i) q^{32} +(-64337.8 + 274893. i) q^{34} +14760.5 q^{35} +140476. q^{37} +(126105. - 538802. i) q^{38} +(115187. - 139642. i) q^{40} -559896. i q^{41} +343732. i q^{43} +(521936. + 258474. i) q^{44} +(525220. + 122926. i) q^{46} +994666. q^{47} +809599. q^{49} +(172125. + 40285.3i) q^{50} +(-917388. - 454310. i) q^{52} -202713. i q^{53} +568780. i q^{55} +(-108814. + 131916. i) q^{56} +(105743. - 451801. i) q^{58} -1.65755e6 q^{59} -3.11158e6 q^{61} +(103291. - 441328. i) q^{62} +(398837. + 2.05888e6i) q^{64} -999725. i q^{65} +395806. i q^{67} +(1.41749e6 - 2.86234e6i) q^{68} +(-162602. - 38056.4i) q^{70} +1.79702e6 q^{71} -3.77113e6 q^{73} +(-1.54748e6 - 362183. i) q^{74} +(-2.77834e6 + 5.61032e6i) q^{76} -537310. i q^{77} -1.67147e6i q^{79} +(-1.62894e6 + 1.24132e6i) q^{80} +(-1.44356e6 + 6.16783e6i) q^{82} -8.39036e6 q^{83} +3.11924e6 q^{85} +(886232. - 3.78656e6i) q^{86} +(-5.08324e6 - 4.19304e6i) q^{88} -9.29063e6i q^{89} +944410. i q^{91} +(-5.46889e6 - 2.70831e6i) q^{92} +(-1.09573e7 - 2.56451e6i) q^{94} -6.11385e6 q^{95} -1.46695e7 q^{97} +(-8.91856e6 - 2.08736e6i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 52 q^{4}+O(q^{10}) \) 56 * q + 52 * q^4	\( 56 q + 52 q^{4} - 6500 q^{10} + 14128 q^{13} - 8060 q^{16} + 259088 q^{22} - 875000 q^{25} - 490976 q^{28} + 40912 q^{34} + 1268048 q^{37} - 266500 q^{40} + 3108200 q^{46} - 3522056 q^{49} - 8882216 q^{52} + 8807592 q^{58} - 3944912 q^{61} - 16633580 q^{64} + 4533000 q^{70} + 7602384 q^{73} - 38876976 q^{76} + 33213064 q^{82} - 15068000 q^{85} - 56145472 q^{88} + 29409456 q^{94} - 45595824 q^{97}+O(q^{100}) \) 56 * q + 52 * q^4 - 6500 * q^10 + 14128 * q^13 - 8060 * q^16 + 259088 * q^22 - 875000 * q^25 - 490976 * q^28 + 40912 * q^34 + 1268048 * q^37 - 266500 * q^40 + 3108200 * q^46 - 3522056 * q^49 - 8882216 * q^52 + 8807592 * q^58 - 3944912 * q^61 - 16633580 * q^64 + 4533000 * q^70 + 7602384 * q^73 - 38876976 * q^76 + 33213064 * q^82 - 15068000 * q^85 - 56145472 * q^88 + 29409456 * q^94 - 45595824 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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