LMFDB - Embedded newform 147.8.c.b.146.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [147,8,Mod(146,147)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("147.146"); S:= CuspForms(chi, 8); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(147, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 8, names="a")

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	147.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [32] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$45.9205987462$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			146.1
Character	$\chi$	$=$	147.146
Dual form			147.8.c.b.146.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-14.6224i q^{2} +(34.6438 - 31.4135i) q^{3} -85.8156 q^{4} -538.208 q^{5} +(-459.342 - 506.577i) q^{6} -616.838i q^{8} +(213.384 - 2176.57i) q^{9} +7869.91i q^{10} +1898.48i q^{11} +(-2972.98 + 2695.77i) q^{12} -431.129i q^{13} +(-18645.5 + 16907.0i) q^{15} -20004.1 q^{16} -20815.9 q^{17} +(-31826.7 - 3120.20i) q^{18} +26676.2i q^{19} +46186.6 q^{20} +27760.4 q^{22} +30805.2i q^{23} +(-19377.0 - 21369.6i) q^{24} +211542. q^{25} -6304.16 q^{26} +(-60981.1 - 82107.6i) q^{27} -40183.4i q^{29} +(247221. + 272643. i) q^{30} -29020.1i q^{31} +213553. i q^{32} +(59638.0 + 65770.6i) q^{33} +304380. i q^{34} +(-18311.7 + 186783. i) q^{36} +286993. q^{37} +390071. q^{38} +(-13543.3 - 14935.9i) q^{39} +331987. i q^{40} +309693. q^{41} -47389.8 q^{43} -162920. i q^{44} +(-114845. + 1.17144e6i) q^{45} +450446. q^{46} -720054. q^{47} +(-693017. + 628398. i) q^{48} -3.09326e6i q^{50} +(-721143. + 653901. i) q^{51} +36997.6i q^{52} -784843. i q^{53} +(-1.20061e6 + 891692. i) q^{54} -1.02178e6i q^{55} +(837993. + 924165. i) q^{57} -587579. q^{58} +989928. q^{59} +(1.60008e6 - 1.45088e6i) q^{60} +1.50426e6i q^{61} -424344. q^{62} +562144. q^{64} +232037. i q^{65} +(961727. - 872053. i) q^{66} +1.99476e6 q^{67} +1.78633e6 q^{68} +(967698. + 1.06721e6i) q^{69} +672836. i q^{71} +(-1.34259e6 - 131624. i) q^{72} +3.69132e6i q^{73} -4.19653e6i q^{74} +(7.32863e6 - 6.64529e6i) q^{75} -2.28924e6i q^{76} +(-218400. + 198036. i) q^{78} -1.25310e6 q^{79} +1.07663e7 q^{80} +(-4.69190e6 - 928890. i) q^{81} -4.52847e6i q^{82} -4.44416e6 q^{83} +1.12033e7 q^{85} +692954. i q^{86} +(-1.26230e6 - 1.39211e6i) q^{87} +1.17106e6 q^{88} +1.47444e6 q^{89} +(1.71294e7 + 1.67931e6i) q^{90} -2.64356e6i q^{92} +(-911622. - 1.00536e6i) q^{93} +1.05289e7i q^{94} -1.43573e7i q^{95} +(6.70845e6 + 7.39829e6i) q^{96} +8.19557e6i q^{97} +(4.13217e6 + 405106. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2300 q^{4} + 7032 q^{9} + 27576 q^{15} + 39188 q^{16} - 66996 q^{18} + 105132 q^{22} + 662504 q^{25} + 81324 q^{30} - 227244 q^{36} + 1237496 q^{37} - 3992208 q^{39} - 1416064 q^{43} + 6985680 q^{46}+ \cdots + 35642232 q^{99}+O(q^{100}) $ 32 * q - 2300 * q^4 + 7032 * q^9 + 27576 * q^15 + 39188 * q^16 - 66996 * q^18 + 105132 * q^22 + 662504 * q^25 + 81324 * q^30 - 227244 * q^36 + 1237496 * q^37 - 3992208 * q^39 - 1416064 * q^43 + 6985680 * q^46 - 1354680 * q^51 - 6279408 * q^57 + 4128684 * q^58 - 15042564 * q^60 - 589508 * q^64 + 3889456 * q^67 + 3088944 * q^72 + 1917432 * q^78 - 15252656 * q^79 - 17406072 * q^81 + 3418848 * q^85 - 24626796 * q^88 + 49664208 * q^93 + 35642232 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

$n$	$50$	$52$
$\chi(n)$	$-1$	$-1$

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 $

$2$		−	14.6224i		−	1.29245i	−0.763146	−	0.646226i	$-0.776346\pi$
$2$		−	14.6224i		−	1.29245i	0.763146	−	0.646226i	$-0.223654\pi$
$3$	34.6438	−	31.4135i	0.740800	−	0.671726i
$3$	34.6438	−	31.4135i	0.740800	−	0.671726i
$4$	−85.8156			−0.670435
$5$	−538.208			−1.92555			−0.962775	−	0.270304i	$-0.912876\pi$
$5$	−538.208			−1.92555			−0.962775	+	0.270304i	$0.912876\pi$
$6$	−459.342	−	506.577i	−0.868174	−	0.957449i
$7$		0			0
$7$		0			0
$8$		−	616.838i		−	0.425948i
$9$	213.384	−	2176.57i	0.0975694	−	0.995229i
$10$			7869.91i			2.48868i
$11$			1898.48i			0.430063i	0.976607	+	0.215032i	$0.0689855\pi$
$11$			1898.48i			0.430063i	−0.976607	+	0.215032i	$0.931015\pi$
$12$	−2972.98	+	2695.77i	−0.496658	+	0.450348i
$13$		−	431.129i		−	0.0544259i	−0.999630	−	0.0272129i	$-0.991337\pi$
$13$		−	431.129i		−	0.0544259i	0.999630	−	0.0272129i	$-0.00866322\pi$
$14$		0			0
$15$	−18645.5	+	16907.0i	−1.42645	+	1.29344i
$16$	−20004.1			−1.22095
$17$	−20815.9			−1.02760			−0.513801	−	0.857910i	$-0.671763\pi$
$17$	−20815.9			−1.02760			−0.513801	+	0.857910i	$0.671763\pi$
$18$	−31826.7	−	3120.20i	−1.28629	−	0.126104i
$19$			26676.2i			0.892250i	0.894971	+	0.446125i	$0.147196\pi$
$19$			26676.2i			0.892250i	−0.894971	+	0.446125i	$0.852804\pi$
$20$	46186.6			1.29096
$21$		0			0
$22$	27760.4			0.555837
$23$			30805.2i			0.527930i	0.964532	+	0.263965i	$0.0850303\pi$
$23$			30805.2i			0.527930i	−0.964532	+	0.263965i	$0.914970\pi$
$24$	−19377.0	−	21369.6i	−0.286120	−	0.315542i
$25$	211542.			2.70774
$26$	−6304.16			−0.0703429
$27$	−60981.1	−	82107.6i	−0.596241	−	0.802805i
$28$		0			0
$29$		−	40183.4i		−	0.305952i	−0.988230	−	0.152976i	$-0.951114\pi$
$29$		−	40183.4i		−	0.305952i	0.988230	−	0.152976i	$-0.0488858\pi$
$30$	247221.	+	272643.i	1.67171	+	1.84362i
$31$		−	29020.1i		−	0.174957i	−0.996166	−	0.0874787i	$-0.972119\pi$
$31$		−	29020.1i		−	0.174957i	0.996166	−	0.0874787i	$-0.0278810\pi$
$32$			213553.i			1.15208i
$33$	59638.0	+	65770.6i	0.288885	+	0.318591i
$34$			304380.i			1.32813i
$35$		0			0
$36$	−18311.7	+	186783.i	−0.0654139	+	0.667236i
$37$	286993.			0.931461			0.465730	−	0.884927i	$-0.345792\pi$
$37$	286993.			0.931461			0.465730	+	0.884927i	$0.345792\pi$
$38$	390071.			1.15319
$39$	−13543.3	−	14935.9i	−0.0365593	−	0.0403187i
$40$			331987.i			0.820184i
$41$	309693.			0.701759			0.350879	−	0.936421i	$-0.385883\pi$
$41$	309693.			0.701759			0.350879	+	0.936421i	$0.385883\pi$
$42$		0			0
$43$	−47389.8			−0.0908961			−0.0454480	−	0.998967i	$-0.514472\pi$
$43$	−47389.8			−0.0908961			−0.0454480	+	0.998967i	$0.514472\pi$
$44$		−	162920.i		−	0.288329i
$45$	−114845.	+	1.17144e6i	−0.187875	+	1.91636i
$46$	450446.			0.682324
$47$	−720054.			−1.01163			−0.505816	−	0.862641i	$-0.668809\pi$
$47$	−720054.			−1.01163			−0.505816	+	0.862641i	$0.668809\pi$
$48$	−693017.	+	628398.i	−0.904481	+	0.820145i
$49$		0			0
$50$		−	3.09326e6i		−	3.49963i
$51$	−721143.	+	653901.i	−0.761247	+	0.690266i
$52$			36997.6i			0.0364890i
$53$		−	784843.i		−	0.724131i	−0.932153	−	0.362066i	$-0.882072\pi$
$53$		−	784843.i		−	0.724131i	0.932153	−	0.362066i	$-0.117928\pi$
$54$	−1.20061e6	+	891692.i	−1.03759	+	0.770614i
$55$		−	1.02178e6i		−	0.828108i
$56$		0			0
$57$	837993.	+	924165.i	0.599347	+	0.660979i
$58$	−587579.			−0.395429
$59$	989928.			0.627511			0.313756	−	0.949504i	$-0.398413\pi$
$59$	989928.			0.627511			0.313756	+	0.949504i	$0.398413\pi$
$60$	1.60008e6	−	1.45088e6i	0.956340	−	0.867168i
$61$			1.50426e6i			0.848534i	0.905537	+	0.424267i	$0.139468\pi$
$61$			1.50426e6i			0.848534i	−0.905537	+	0.424267i	$0.860532\pi$
$62$	−424344.			−0.226124
$63$		0			0
$64$	562144.			0.268051
$65$			232037.i			0.104800i
$66$	961727.	−	872053.i	0.411764	−	0.373370i
$67$	1.99476e6			0.810268			0.405134	−	0.914257i	$-0.367225\pi$
$67$	1.99476e6			0.810268			0.405134	+	0.914257i	$0.367225\pi$
$68$	1.78633e6			0.688939
$69$	967698.	+	1.06721e6i	0.354624	+	0.391090i
$70$		0			0
$71$			672836.i			0.223103i	0.993759	+	0.111551i	$0.0355820\pi$
$71$			672836.i			0.223103i	−0.993759	+	0.111551i	$0.964418\pi$
$72$	−1.34259e6	−	131624.i	−0.423916	−	0.0415595i
$73$			3.69132e6i			1.11059i	0.831655	+	0.555293i	$0.187394\pi$
$73$			3.69132e6i			1.11059i	−0.831655	+	0.555293i	$0.812606\pi$
$74$		−	4.19653e6i		−	1.20387i
$75$	7.32863e6	−	6.64529e6i	2.00590	−	1.81886i
$76$		−	2.28924e6i		−	0.598195i
$77$		0			0
$78$	−218400.	+	198036.i	−0.0521100	+	0.0472511i
$79$	−1.25310e6			−0.285951			−0.142976	−	0.989726i	$-0.545667\pi$
$79$	−1.25310e6			−0.285951			−0.142976	+	0.989726i	$0.545667\pi$
$80$	1.07663e7			2.35100
$81$	−4.69190e6	−	928890.i	−0.980960	−	0.194208i
$82$		−	4.52847e6i		−	0.906990i
$83$	−4.44416e6			−0.853133			−0.426566	−	0.904456i	$-0.640277\pi$
$83$	−4.44416e6			−0.853133			−0.426566	+	0.904456i	$0.640277\pi$
$84$		0			0
$85$	1.12033e7			1.97870
$86$			692954.i			0.117479i
$87$	−1.26230e6	−	1.39211e6i	−0.205516	−	0.226650i
$88$	1.17106e6			0.183185
$89$	1.47444e6			0.221698			0.110849	−	0.993837i	$-0.464643\pi$
$89$	1.47444e6			0.221698			0.110849	+	0.993837i	$0.464643\pi$
$90$	1.71294e7	+	1.67931e6i	2.47681	+	0.242819i
$91$		0			0
$92$		−	2.64356e6i		−	0.353942i
$93$	−911622.	−	1.00536e6i	−0.117523	−	0.129608i
$94$			1.05289e7i			1.30749i
$95$		−	1.43573e7i		−	1.71807i
$96$	6.70845e6	+	7.39829e6i	0.773878	+	0.853457i
$97$			8.19557e6i			0.911755i	0.890043	+	0.455877i	$0.150674\pi$
$97$			8.19557e6i			0.911755i	−0.890043	+	0.455877i	$0.849326\pi$
$98$		0			0
$99$	4.13217e6	+	405106.i	0.428011	+	0.0419610i
$100$	−1.81536e7			−1.81536
$101$	−1.35241e7			−1.30613			−0.653063	−	0.757304i	$-0.726516\pi$
$101$	−1.35241e7			−1.30613			−0.653063	+	0.757304i	$0.726516\pi$
$102$	9.56163e6	+	1.05449e7i	0.892136	+	0.983876i
$103$			9.46626e6i			0.853587i	0.904349	+	0.426794i	$0.140357\pi$
$103$			9.46626e6i			0.853587i	−0.904349	+	0.426794i	$0.859643\pi$
$104$	−265937.			−0.0231826
$105$		0			0
$106$	−1.14763e7			−0.935906
$107$		−	197098.i		−	0.0155539i	−0.999970	−	0.00777696i	$-0.997524\pi$
$107$		−	197098.i		−	0.0155539i	0.999970	−	0.00777696i	$-0.00247551\pi$
$108$	5.23313e6	+	7.04612e6i	0.399741	+	0.538228i
$109$	−1.84917e6			−0.136768			−0.0683840	−	0.997659i	$-0.521784\pi$
$109$	−1.84917e6			−0.136768			−0.0683840	+	0.997659i	$0.521784\pi$
$110$	−1.49409e7			−1.07029
$111$	9.94251e6	−	9.01544e6i	0.690026	−	0.625686i
$112$		0			0
$113$		−	1.54177e7i		−	1.00518i	−0.864525	−	0.502590i	$-0.832380\pi$
$113$		−	1.54177e7i		−	1.00518i	0.864525	−	0.502590i	$-0.167620\pi$
$114$	1.35135e7	−	1.22535e7i	0.854284	−	0.774628i
$115$		−	1.65796e7i		−	1.01655i
$116$			3.44837e6i			0.205121i
$117$	−938380.	−	91996.2i	−0.0541662	−	0.00531030i
$118$		−	1.44752e7i		−	0.811029i
$119$		0			0
$120$	1.04289e7	+	1.15013e7i	0.550938	+	0.607592i
$121$	1.58829e7			0.815046
$122$	2.19960e7			1.09669
$123$	1.07289e7	−	9.72854e6i	0.519863	−	0.471389i
$124$			2.49037e6i			0.117298i
$125$	−7.18062e7			−3.28834
$126$		0			0
$127$	−1.74020e7			−0.753853			−0.376926	−	0.926243i	$-0.623019\pi$
$127$	−1.74020e7			−0.753853			−0.376926	+	0.926243i	$0.623019\pi$
$128$			1.91149e7i			0.805632i
$129$	−1.64176e6	+	1.48868e6i	−0.0673358	+	0.0610572i
$130$	3.39294e6			0.135449
$131$	−4.56458e7			−1.77399			−0.886995	−	0.461780i	$-0.847211\pi$
$131$	−4.56458e7			−1.77399			−0.886995	+	0.461780i	$0.847211\pi$
$132$	−5.11787e6	−	5.64415e6i	−0.193678	−	0.213594i
$133$		0			0
$134$		−	2.91682e7i		−	1.04723i
$135$	3.28205e7	+	4.41909e7i	1.14809	+	1.54584i
$136$			1.28401e7i			0.437704i
$137$			2.94610e7i			0.978872i	0.872039	+	0.489436i	$0.162797\pi$
$137$			2.94610e7i			0.978872i	−0.872039	+	0.489436i	$0.837203\pi$
$138$	1.56052e7	−	1.41501e7i	0.505466	−	0.458335i
$139$			6.02035e7i			1.90138i	0.310136	+	0.950692i	$0.399625\pi$
$139$			6.02035e7i			1.90138i	−0.310136	+	0.950692i	$0.600375\pi$
$140$		0			0
$141$	−2.49454e7	+	2.26194e7i	−0.749417	+	0.679539i
$142$	9.83850e6			0.288350
$143$	818491.			0.0234066
$144$	−4.26856e6	+	4.35402e7i	−0.119128	+	1.21513i
$145$			2.16270e7i			0.589127i
$146$	5.39761e7			1.43538
$147$		0			0
$148$	−2.46284e7			−0.624484
$149$		−	1.04236e7i		−	0.258147i	−0.991635	−	0.129073i	$-0.958800\pi$
$149$		−	1.04236e7i		−	0.258147i	0.991635	−	0.129073i	$-0.0412003\pi$
$150$	−9.71703e7	−	1.07162e8i	−2.35079	−	2.59253i
$151$	−3.81678e7			−0.902147			−0.451074	−	0.892487i	$-0.648959\pi$
$151$	−3.81678e7			−0.902147			−0.451074	+	0.892487i	$0.648959\pi$
$152$	1.64549e7			0.380052
$153$	−4.44179e6	+	4.53072e7i	−0.100262	+	1.02270i
$154$		0			0
$155$			1.56188e7i			0.336889i
$156$	1.16222e6	+	1.28174e6i	0.0245106	+	0.0270310i
$157$			5.47864e7i			1.12986i	0.825139	+	0.564929i	$0.191097\pi$
$157$			5.47864e7i			1.12986i	−0.825139	+	0.564929i	$0.808903\pi$
$158$			1.83234e7i			0.369579i
$159$	−2.46547e7	−	2.71899e7i	−0.486418	−	0.536436i
$160$		−	1.14936e8i		−	2.21838i
$161$		0			0
$162$	−1.35826e7	+	6.86071e7i	−0.251004	+	1.26785i
$163$	−6.02898e7			−1.09040			−0.545202	−	0.838305i	$-0.683547\pi$
$163$	−6.02898e7			−1.09040			−0.545202	+	0.838305i	$0.683547\pi$
$164$	−2.65765e7			−0.470483
$165$	−3.20976e7	−	3.53983e7i	−0.556262	−	0.613463i
$166$			6.49845e7i			1.10263i
$167$	3.16225e7			0.525398			0.262699	−	0.964878i	$-0.415387\pi$
$167$	3.16225e7			0.525398			0.262699	+	0.964878i	$0.415387\pi$
$168$		0			0
$169$	6.25626e7			0.997038
$170$		−	1.63819e8i		−	2.55737i
$171$	5.80625e7	+	5.69228e6i	0.887993	+	0.0870563i
$172$	4.06678e6			0.0609399
$173$	−3.55124e6			−0.0521457			−0.0260729	−	0.999660i	$-0.508300\pi$
$173$	−3.55124e6			−0.0521457			−0.0260729	+	0.999660i	$0.508300\pi$
$174$	−2.03560e7	+	1.84579e7i	−0.292934	+	0.265620i
$175$		0			0
$176$		−	3.79774e7i		−	0.525087i
$177$	3.42949e7	−	3.10971e7i	0.464860	−	0.421515i
$178$		−	2.15599e7i		−	0.286535i
$179$			8.80409e7i			1.14736i	0.819080	+	0.573679i	$0.194484\pi$
$179$			8.80409e7i			1.14736i	−0.819080	+	0.573679i	$0.805516\pi$
$180$	9.85550e6	−	1.00528e8i	0.125958	−	1.28480i
$181$		−	1.12564e8i		−	1.41099i	−0.708714	−	0.705496i	$-0.750724\pi$
$181$		−	1.12564e8i		−	1.41099i	0.708714	−	0.705496i	$-0.249276\pi$
$182$		0			0
$183$	4.72541e7	+	5.21133e7i	0.569982	+	0.628594i
$184$	1.90018e7			0.224870
$185$	−1.54462e8			−1.79357
$186$	−1.47009e7	+	1.33301e7i	−0.167513	+	0.151893i
$187$		−	3.95187e7i		−	0.441933i
$188$	6.17919e7			0.678233
$189$		0			0
$190$	−2.09939e8			−2.22053
$191$			8.50236e7i			0.882923i	0.897280	+	0.441461i	$0.145540\pi$
$191$			8.50236e7i			0.882923i	−0.897280	+	0.441461i	$0.854460\pi$
$192$	1.94748e7	−	1.76589e7i	0.198572	−	0.180057i
$193$	−1.80486e8			−1.80714			−0.903571	−	0.428438i	$-0.859064\pi$
$193$	−1.80486e8			−1.80714			−0.903571	+	0.428438i	$0.859064\pi$
$194$	1.19839e8			1.17840
$195$	7.28909e6	+	8.03864e6i	0.0703967	+	0.0776357i
$196$		0			0
$197$			2.09911e8i			1.95616i	0.208239	+	0.978078i	$0.433227\pi$
$197$			2.09911e8i			1.95616i	−0.208239	+	0.978078i	$0.566773\pi$
$198$	5.92364e6	−	6.04224e7i	0.0542326	−	0.553184i
$199$		−	1.46599e8i		−	1.31870i	−0.751836	−	0.659350i	$-0.770831\pi$
$199$		−	1.46599e8i		−	1.31870i	0.751836	−	0.659350i	$-0.229169\pi$
$200$		−	1.30487e8i		−	1.15336i
$201$	6.91060e7	−	6.26623e7i	0.600246	−	0.544277i
$202$			1.97756e8i			1.68811i
$203$		0			0
$204$	6.18853e7	−	5.61149e7i	0.510366	−	0.462778i
$205$	−1.66679e8			−1.35127
$206$	1.38420e8			1.10322
$207$	6.70494e7	+	6.57334e6i	0.525411	+	0.0515098i
$208$			8.62434e6i			0.0664514i
$209$	−5.06443e7			−0.383724
$210$		0			0
$211$	1.44961e8			1.06233			0.531167	−	0.847267i	$-0.321754\pi$
$211$	1.44961e8			1.06233			0.531167	+	0.847267i	$0.321754\pi$
$212$			6.73518e7i			0.485483i
$213$	2.11361e7	+	2.33096e7i	0.149864	+	0.165275i
$214$	−2.88206e6			−0.0201027
$215$	2.55055e7			0.175025
$216$	−5.06471e7	+	3.76155e7i	−0.341953	+	0.253968i
$217$		0			0
$218$			2.70394e7i			0.176766i
$219$	1.15957e8	+	1.27881e8i	0.746009	+	0.822722i
$220$			8.76845e7i			0.555192i
$221$			8.97435e6i			0.0559281i
$222$	−1.31828e8	−	1.45384e8i	−0.808670	−	0.891826i
$223$		−	1.90116e8i		−	1.14803i	−0.818846	−	0.574013i	$-0.805386\pi$
$223$		−	1.90116e8i		−	1.14803i	0.818846	−	0.574013i	$-0.194614\pi$
$224$		0			0
$225$	4.51398e7	−	4.60436e8i	0.264193	−	2.69482i
$226$	−2.25444e8			−1.29915
$227$	4.49155e7			0.254862			0.127431	−	0.991847i	$-0.459327\pi$
$227$	4.49155e7			0.254862			0.127431	+	0.991847i	$0.459327\pi$
$228$	−7.19129e7	−	7.93078e7i	−0.401823	−	0.443143i
$229$		−	8.21767e7i		−	0.452193i	−0.974105	−	0.226097i	$-0.927403\pi$
$229$		−	8.21767e7i		−	0.452193i	0.974105	−	0.226097i	$-0.0725965\pi$
$230$	−2.42434e8			−1.31385
$231$		0			0
$232$	−2.47867e7			−0.130320
$233$			3.64031e7i			0.188535i	0.995547	+	0.0942676i	$0.0300509\pi$
$233$			3.64031e7i			0.188535i	−0.995547	+	0.0942676i	$0.969949\pi$
$234$	−1.34521e6	+	1.37214e7i	−0.00686331	+	0.0700073i
$235$	3.87539e8			1.94795
$236$	−8.49513e7			−0.420705
$237$	−4.34123e7	+	3.93644e7i	−0.211833	+	0.192081i
$238$		0			0
$239$			1.04151e8i			0.493482i	0.969081	+	0.246741i	$0.0793597\pi$
$239$			1.04151e8i			0.493482i	−0.969081	+	0.246741i	$0.920640\pi$
$240$	3.72987e8	−	3.38209e8i	1.74162	−	1.57923i
$241$			2.81090e8i			1.29356i	0.762679	+	0.646778i	$0.223884\pi$
$241$			2.81090e8i			1.29356i	−0.762679	+	0.646778i	$0.776116\pi$
$242$		−	2.32247e8i		−	1.05341i
$243$	−1.91725e8	+	1.15209e8i	−0.857150	+	0.515067i
$244$		−	1.29089e8i		−	0.568886i
$245$		0			0
$246$	−1.42255e8	−	1.56883e8i	−0.609249	−	0.671899i
$247$	1.15009e7			0.0485615
$248$	−1.79007e7			−0.0745227
$249$	−1.53963e8	+	1.39607e8i	−0.632001	+	0.573071i
$250$			1.04998e9i			4.25003i
$251$	3.23864e8			1.29272			0.646360	−	0.763033i	$-0.276290\pi$
$251$	3.23864e8			1.29272			0.646360	+	0.763033i	$0.276290\pi$
$252$		0			0
$253$	−5.84831e7			−0.227043
$254$			2.54460e8i			0.974319i
$255$	3.88124e8	−	3.51935e8i	1.46582	−	1.32914i
$256$	3.51461e8			1.30929
$257$	−2.00680e8			−0.737458			−0.368729	−	0.929537i	$-0.620207\pi$
$257$	−2.00680e8			−0.737458			−0.368729	+	0.929537i	$0.620207\pi$
$258$	2.17681e7	+	2.40066e7i	0.0789136	+	0.0870284i
$259$		0			0
$260$		−	1.99124e7i		−	0.0702614i
$261$	−8.74618e7	−	8.57451e6i	−0.304493	−	0.0298516i
$262$			6.67452e8i			2.29280i
$263$			4.30533e8i			1.45936i	0.683790	+	0.729679i	$0.260330\pi$
$263$			4.30533e8i			1.45936i	−0.683790	+	0.729679i	$0.739670\pi$
$264$	4.05699e7	−	3.67870e7i	0.135703	−	0.123050i
$265$			4.22408e8i			1.39435i
$266$		0			0
$267$	5.10802e7	−	4.63174e7i	0.164234	−	0.148920i
$268$	−1.71181e8			−0.543231
$269$	−2.42668e8			−0.760116			−0.380058	−	0.924963i	$-0.624096\pi$
$269$	−2.42668e8			−0.760116			−0.380058	+	0.924963i	$0.624096\pi$
$270$	6.46179e8	−	4.79915e8i	1.99793	−	1.48386i
$271$		−	1.47356e8i		−	0.449756i	−0.974387	−	0.224878i	$-0.927802\pi$
$271$		−	1.47356e8i		−	0.449756i	0.974387	−	0.224878i	$-0.0721983\pi$
$272$	4.16403e8			1.25465
$273$		0			0
$274$	4.30792e8			1.26515
$275$			4.01610e8i			1.16450i
$276$	−8.30436e7	−	9.15831e7i	−0.237752	−	0.262200i
$277$	−5.15102e8			−1.45618			−0.728089	−	0.685483i	$-0.759591\pi$
$277$	−5.15102e8			−1.45618			−0.728089	+	0.685483i	$0.759591\pi$
$278$	8.80322e8			2.45745
$279$	−6.31641e7	−	6.19242e6i	−0.174123	−	0.0170705i
$280$		0			0
$281$		−	3.74214e8i		−	1.00612i	−0.864253	−	0.503058i	$-0.832208\pi$
$281$		−	3.74214e8i		−	1.00612i	0.864253	−	0.503058i	$-0.167792\pi$
$282$	3.30751e8	+	3.64763e8i	0.878273	+	0.968587i
$283$			3.75895e8i			0.985858i	0.870070	+	0.492929i	$0.164074\pi$
$283$			3.75895e8i			0.985858i	−0.870070	+	0.492929i	$0.835926\pi$
$284$		−	5.77398e7i		−	0.149576i
$285$	−4.51014e8	−	4.97393e8i	−1.15407	−	1.27275i
$286$		−	1.19683e7i		−	0.0302519i
$287$		0			0
$288$	4.64812e8	+	4.55689e7i	1.14658	+	0.112407i
$289$	2.29642e7			0.0559640
$290$	3.16240e8			0.761418
$291$	2.57452e8	+	2.83926e8i	0.612449	+	0.675428i
$292$		−	3.16773e8i		−	0.744575i
$293$	−1.82974e7			−0.0424964			−0.0212482	−	0.999774i	$-0.506764\pi$
$293$	−1.82974e7			−0.0424964			−0.0212482	+	0.999774i	$0.506764\pi$
$294$		0			0
$295$	−5.32787e8			−1.20830
$296$		−	1.77028e8i		−	0.396754i
$297$	1.55880e8	−	1.15772e8i	0.345257	−	0.256421i
$298$	−1.52419e8			−0.333642
$299$	1.32810e7			0.0287330
$300$	−6.28911e8	+	5.70269e8i	−1.34482	+	1.21943i
$301$		0			0
$302$			5.58106e8i			1.16598i
$303$	−4.68528e8	+	4.24841e8i	−0.967578	+	0.877358i
$304$		−	5.33633e8i		−	1.08939i
$305$		−	8.09605e8i		−	1.63389i
$306$	6.62502e8	+	6.49498e7i	1.32179	+	0.129584i
$307$		−	6.99449e8i		−	1.37966i	−0.723972	−	0.689830i	$-0.757685\pi$
$307$		−	6.99449e8i		−	1.37966i	0.723972	−	0.689830i	$-0.242315\pi$
$308$		0			0
$309$	2.97368e8	+	3.27947e8i	0.573376	+	0.632338i
$310$	2.28385e8			0.435413
$311$	4.23553e8			0.798448			0.399224	−	0.916853i	$-0.369280\pi$
$311$	4.23553e8			0.798448			0.399224	+	0.916853i	$0.369280\pi$
$312$	−9.21306e6	+	8.35401e6i	−0.0171737	+	0.0155723i
$313$			3.36360e8i			0.620010i	0.950735	+	0.310005i	$0.100331\pi$
$313$			3.36360e8i			0.620010i	−0.950735	+	0.310005i	$0.899669\pi$
$314$	8.01111e8			1.46029
$315$		0			0
$316$	1.07536e8			0.191712
$317$		−	6.91081e8i		−	1.21849i	−0.792983	−	0.609244i	$-0.791473\pi$
$317$		−	6.91081e8i		−	1.21849i	0.792983	−	0.609244i	$-0.208527\pi$
$318$	−3.97583e8	+	3.60511e8i	−0.693319	+	0.628672i
$319$	7.62875e7			0.131579
$320$	−3.02550e8			−0.516145
$321$	−6.19155e6	−	6.82823e6i	−0.0104480	−	0.0115223i
$322$		0			0
$323$		−	5.55290e8i		−	0.916877i
$324$	4.02639e8	+	7.97132e7i	0.657670	+	0.130204i
$325$		−	9.12020e7i		−	0.147371i
$326$			8.81584e8i			1.40929i
$327$	−6.40623e7	+	5.80890e7i	−0.101318	+	0.0918706i
$328$		−	1.91031e8i		−	0.298913i
$329$		0			0
$330$	−5.17609e8	+	4.69345e8i	−0.792872	+	0.718942i
$331$	−8.56181e8			−1.29768			−0.648840	−	0.760925i	$-0.724746\pi$
$331$	−8.56181e8			−1.29768			−0.648840	+	0.760925i	$0.724746\pi$
$332$	3.81379e8			0.571970
$333$	6.12397e7	−	6.24658e8i	0.0908821	−	0.927017i
$334$		−	4.62398e8i		−	0.679052i
$335$	−1.07359e9			−1.56021
$336$		0			0
$337$	−8.30714e8			−1.18235			−0.591176	−	0.806542i	$-0.701336\pi$
$337$	−8.30714e8			−1.18235			−0.591176	+	0.806542i	$0.701336\pi$
$338$		−	9.14818e8i		−	1.28862i
$339$	−4.84323e8	−	5.34127e8i	−0.675206	−	0.744638i
$340$	−9.61417e8			−1.32659
$341$	5.50941e7			0.0752428
$342$	8.32351e7	−	8.49015e8i	0.112516	−	1.14769i
$343$		0			0
$344$			2.92318e7i			0.0387170i
$345$	−5.20822e8	−	5.74379e8i	−0.682846	−	0.753064i
$346$			5.19278e7i			0.0673959i
$347$		−	1.14776e8i		−	0.147468i	−0.997278	−	0.0737340i	$-0.976508\pi$
$347$		−	1.14776e8i		−	0.147468i	0.997278	−	0.0737340i	$-0.0234916\pi$
$348$	1.08325e8	+	1.19464e8i	0.137785	+	0.151954i
$349$		−	2.74148e8i		−	0.345220i	−0.984990	−	0.172610i	$-0.944780\pi$
$349$		−	2.74148e8i		−	0.345220i	0.984990	−	0.172610i	$-0.0552200\pi$
$350$		0			0
$351$	−3.53990e7	+	2.62907e7i	−0.0436934	+	0.0324510i
$352$	−4.05427e8			−0.495465
$353$	−1.24812e9			−1.51023			−0.755117	−	0.655590i	$-0.772420\pi$
$353$	−1.24812e9			−1.51023			−0.755117	+	0.655590i	$0.772420\pi$
$354$	−4.54715e8	−	5.01474e8i	−0.544789	−	0.600810i
$355$		−	3.62125e8i		−	0.429596i
$356$	−1.26530e8			−0.148634
$357$		0			0
$358$	1.28737e9			1.48291
$359$		−	6.14848e8i		−	0.701354i	−0.936496	−	0.350677i	$-0.885951\pi$
$359$		−	6.14848e8i		−	0.701354i	0.936496	−	0.350677i	$-0.114049\pi$
$360$	7.22591e8	+	7.08408e7i	0.816270	+	0.0800248i
$361$	1.82251e8			0.203890
$362$	−1.64596e9			−1.82364
$363$	5.50245e8	−	4.98938e8i	0.603786	−	0.547487i
$364$		0			0
$365$		−	1.98670e9i		−	2.13849i
$366$	7.62024e8	−	6.90971e8i	0.812428	−	0.736675i
$367$		−	5.37976e8i		−	0.568109i	−0.958808	−	0.284055i	$-0.908320\pi$
$367$		−	5.37976e8i		−	0.568109i	0.958808	−	0.284055i	$-0.0916797\pi$
$368$		−	6.16229e8i		−	0.644577i
$369$	6.60836e7	−	6.74067e8i	0.0684702	−	0.698411i
$370$			2.25860e9i			2.31811i
$371$		0			0
$372$	7.82314e7	+	8.62760e7i	0.0787917	+	0.0868940i
$373$	−1.07909e9			−1.07665			−0.538327	−	0.842736i	$-0.680943\pi$
$373$	−1.07909e9			−1.07665			−0.538327	+	0.842736i	$0.680943\pi$
$374$	−5.77859e8			−0.571178
$375$	−2.48764e9	+	2.25569e9i	−2.43600	+	2.20886i
$376$			4.44157e8i			0.430903i
$377$	−1.73242e7			−0.0166517
$378$		0			0
$379$	1.22890e9			1.15952			0.579761	−	0.814787i	$-0.303146\pi$
$379$	1.22890e9			1.15952			0.579761	+	0.814787i	$0.303146\pi$
$380$			1.23208e9i			1.15185i
$381$	−6.02872e8	+	5.46658e8i	−0.558454	+	0.506382i
$382$	1.24325e9			1.14114
$383$	1.03799e9			0.944053			0.472027	−	0.881584i	$-0.343523\pi$
$383$	1.03799e9			0.944053			0.472027	+	0.881584i	$0.343523\pi$
$384$	6.00465e8	+	6.62212e8i	0.541164	+	0.596812i
$385$		0			0
$386$			2.63914e9i			2.33565i
$387$	−1.01122e7	+	1.03147e8i	−0.00886868	+	0.0904624i
$388$		−	7.03308e8i		−	0.611272i
$389$			5.33269e8i			0.459328i	0.973270	+	0.229664i	$0.0737627\pi$
$389$			5.33269e8i			0.459328i	−0.973270	+	0.229664i	$0.926237\pi$
$390$	1.17544e8	−	1.06584e8i	0.100340	−	0.0909844i
$391$		−	6.41238e8i		−	0.542501i
$392$		0			0
$393$	−1.58134e9	+	1.43389e9i	−1.31417	+	1.19163i
$394$	3.06941e9			2.52824
$395$	6.74430e8			0.550614
$396$	−3.54605e8	−	3.47645e7i	−0.286954	−	0.0281321i
$397$		−	1.07357e9i		−	0.861119i	−0.902562	−	0.430560i	$-0.858316\pi$
$397$		−	1.07357e9i		−	0.861119i	0.902562	−	0.430560i	$-0.141684\pi$
$398$	−2.14364e9			−1.70436
$399$		0			0
$400$	−4.23171e9			−3.30602
$401$			2.29391e9i			1.77652i	0.459338	+	0.888262i	$0.348087\pi$
$401$			2.29391e9i			1.77652i	−0.459338	+	0.888262i	$0.651913\pi$
$402$	−9.16276e8	−	1.01050e9i	−0.703453	−	0.775790i
$403$	−1.25114e7			−0.00952221
$404$	1.16058e9			0.875672
$405$	2.52522e9	+	4.99935e8i	1.88889	+	0.373957i
$406$		0			0
$407$			5.44851e8i			0.400587i
$408$	4.03351e8	+	4.44828e8i	0.294017	+	0.324251i
$409$		−	1.70804e9i		−	1.23443i	−0.786795	−	0.617214i	$-0.788261\pi$
$409$		−	1.70804e9i		−	1.23443i	0.786795	−	0.617214i	$-0.211739\pi$
$410$			2.43726e9i			1.74646i
$411$	9.25474e8	+	1.02064e9i	0.657533	+	0.725149i
$412$		−	8.12353e8i		−	0.572274i
$413$		0			0
$414$	9.61182e7	−	9.80426e8i	0.0665740	−	0.679069i
$415$	2.39188e9			1.64275
$416$	9.20689e7			0.0627027
$417$	1.89120e9	+	2.08568e9i	1.27721	+	1.40855i
$418$			7.40544e8i			0.495945i
$419$	−1.93716e9			−1.28652			−0.643261	−	0.765647i	$-0.722419\pi$
$419$	−1.93716e9			−1.28652			−0.643261	+	0.765647i	$0.722419\pi$
$420$		0			0
$421$	2.15401e9			1.40689			0.703447	−	0.710748i	$-0.251643\pi$
$421$	2.15401e9			1.40689			0.703447	+	0.710748i	$0.251643\pi$
$422$		−	2.11968e9i		−	1.37302i
$423$	−1.53648e8	+	1.56725e9i	−0.0987044	+	1.00681i
$424$	−4.84121e8			−0.308442
$425$	−4.40345e9			−2.78248
$426$	3.40843e8	−	3.09062e8i	0.213610	−	0.193692i
$427$		0			0
$428$			1.69141e7i			0.0104279i
$429$	2.83556e7	−	2.57117e7i	0.0173396	−	0.0157228i
$430$		−	3.72953e8i		−	0.226212i
$431$		−	2.91784e9i		−	1.75546i	−0.479158	−	0.877729i	$-0.659058\pi$
$431$		−	2.91784e9i		−	1.75546i	0.479158	−	0.877729i	$-0.340942\pi$
$432$	1.21987e9	+	1.64249e9i	0.727982	+	0.980187i
$433$		−	1.75910e9i		−	1.04132i	−0.853765	−	0.520659i	$-0.825686\pi$
$433$		−	1.75910e9i		−	1.04132i	0.853765	−	0.520659i	$-0.174314\pi$
$434$		0			0
$435$	6.79380e8	+	7.49242e8i	0.395731	+	0.436425i
$436$	1.58688e8			0.0916940
$437$	−8.21765e8			−0.471045
$438$	1.86994e9	−	1.69558e9i	1.06333	−	0.964181i
$439$		−	1.28094e9i		−	0.722606i	−0.932448	−	0.361303i	$-0.882332\pi$
$439$		−	1.28094e9i		−	0.722606i	0.932448	−	0.361303i	$-0.117668\pi$
$440$	−6.30272e8			−0.352731
$441$		0			0
$442$	1.31227e8			0.0722844
$443$			1.33104e9i			0.727407i	0.931515	+	0.363703i	$0.118488\pi$
$443$			1.33104e9i			0.727407i	−0.931515	+	0.363703i	$0.881512\pi$
$444$	−8.53223e8	+	7.73666e8i	−0.462617	+	0.419482i
$445$	−7.93556e8			−0.426891
$446$	−2.77996e9			−1.48377
$447$	−3.27442e8	−	3.61114e8i	−0.173404	−	0.191235i
$448$		0			0
$449$			9.16466e8i			0.477809i	0.971043	+	0.238905i	$0.0767883\pi$
$449$			9.16466e8i			0.477809i	−0.971043	+	0.238905i	$0.923212\pi$
$450$	−6.73269e9	−	6.60054e8i	−3.48293	−	0.341457i
$451$			5.87947e8i			0.301801i
$452$			1.32308e9i			0.673908i
$453$	−1.32228e9	+	1.19898e9i	−0.668311	+	0.605996i
$454$		−	6.56773e8i		−	0.329397i
$455$		0			0
$456$	5.70060e8	−	5.16906e8i	0.281542	−	0.255291i
$457$	6.44098e8			0.315679			0.157839	−	0.987465i	$-0.449547\pi$
$457$	6.44098e8			0.315679			0.157839	+	0.987465i	$0.449547\pi$
$458$	−1.20162e9			−0.584439
$459$	1.26938e9	+	1.70915e9i	0.612698	+	0.824964i
$460$			1.42279e9i			0.681534i
$461$	1.81792e9			0.864215			0.432108	−	0.901822i	$-0.357770\pi$
$461$	1.81792e9			0.864215			0.432108	+	0.901822i	$0.357770\pi$
$462$		0			0
$463$	−1.41455e9			−0.662348			−0.331174	−	0.943570i	$-0.607445\pi$
$463$	−1.41455e9			−0.662348			−0.331174	+	0.943570i	$0.607445\pi$
$464$			8.03832e8i			0.373553i
$465$	4.90642e8	+	5.41095e8i	0.226297	+	0.249568i
$466$	5.32302e8			0.243673
$467$	4.08012e9			1.85380			0.926902	−	0.375303i	$-0.122461\pi$
$467$	4.08012e9			1.85380			0.926902	+	0.375303i	$0.122461\pi$
$468$	8.05277e7	+	7.89471e6i	0.0363149	+	0.00356021i
$469$		0			0
$470$		−	5.66676e9i		−	2.51763i
$471$	1.72103e9	+	1.89801e9i	0.758955	+	0.836999i
$472$		−	6.10625e8i		−	0.267287i
$473$		−	8.99687e7i		−	0.0390911i
$474$	5.75603e8	+	6.34793e8i	0.248255	+	0.273784i
$475$			5.64315e9i			2.41598i
$476$		0			0
$477$	−1.70826e9	−	1.67473e8i	−0.720676	−	0.0706531i
$478$	1.52294e9			0.637802
$479$	−1.03198e6			−0.000429037			−0.000214519	−	1.00000i	$-0.500068\pi$
$479$	−1.03198e6			−0.000429037			−0.000214519		1.00000i	$0.500068\pi$
$480$	−3.61054e9	−	3.98181e9i	−1.49014	−	1.64337i
$481$		−	1.23731e8i		−	0.0506956i
$482$	4.11021e9			1.67186
$483$		0			0
$484$	−1.36300e9			−0.546435
$485$		−	4.41092e9i		−	1.75563i
$486$	1.68463e9	+	2.80349e9i	0.665700	+	1.10783i
$487$	−9.59255e8			−0.376342			−0.188171	−	0.982136i	$-0.560256\pi$
$487$	−9.59255e8			−0.376342			−0.188171	+	0.982136i	$0.560256\pi$
$488$	9.27887e8			0.361431
$489$	−2.08867e9	+	1.89391e9i	−0.807771	+	0.732452i
$490$		0			0
$491$		−	6.85759e8i		−	0.261449i	−0.991419	−	0.130724i	$-0.958270\pi$
$491$		−	6.85759e8i		−	0.261449i	0.991419	−	0.130724i	$-0.0417303\pi$
$492$	−9.20711e8	+	8.34861e8i	−0.348534	+	0.316036i
$493$			8.36455e8i			0.314397i
$494$		−	1.68171e8i		−	0.0627634i
$495$	−2.22397e9	−	2.18031e8i	−0.824157	−	0.0807980i
$496$			5.80520e8i			0.213615i
$497$		0			0
$498$	2.04139e9	+	2.25131e9i	0.740668	+	0.816831i
$499$	−2.98010e9			−1.07369			−0.536844	−	0.843681i	$-0.680384\pi$
$499$	−2.98010e9			−1.07369			−0.536844	+	0.843681i	$0.680384\pi$
$500$	6.16210e9			2.20462
$501$	1.09552e9	−	9.93373e8i	0.389215	−	0.352923i
$502$		−	4.73568e9i		−	1.67078i
$503$	−2.90478e9			−1.01771			−0.508856	−	0.860852i	$-0.669931\pi$
$503$	−2.90478e9			−1.01771			−0.508856	+	0.860852i	$0.669931\pi$
$504$		0			0
$505$	7.27880e9			2.51501
$506$			8.55165e8i			0.293443i
$507$	2.16741e9	−	1.96531e9i	0.738606	−	0.669736i
$508$	1.49336e9			0.505409
$509$	5.01080e8			0.168420			0.0842102	−	0.996448i	$-0.473163\pi$
$509$	5.01080e8			0.168420			0.0842102	+	0.996448i	$0.473163\pi$
$510$	−5.14614e9	−	5.67532e9i	−1.71785	−	1.89450i
$511$		0			0
$512$		−	2.69250e9i		−	0.886567i
$513$	2.19032e9	−	1.62674e9i	0.716303	−	0.531996i
$514$			2.93442e9i			0.953130i
$515$		−	5.09481e9i		−	1.64363i
$516$	1.40889e8	−	1.27752e8i	0.0451443	−	0.0409349i
$517$		−	1.36701e9i		−	0.435066i
$518$		0			0
$519$	−1.23028e8	+	1.11557e8i	−0.0386296	+	0.0350276i
$520$	1.43129e8			0.0446392
$521$	4.62618e9			1.43315			0.716573	−	0.697512i	$-0.245710\pi$
$521$	4.62618e9			1.43315			0.716573	+	0.697512i	$0.245710\pi$
$522$	−1.25380e8	+	1.27890e9i	−0.0385818	+	0.393542i
$523$		−	4.52155e9i		−	1.38207i	−0.722819	−	0.691037i	$-0.757154\pi$
$523$		−	4.52155e9i		−	1.38207i	0.722819	−	0.691037i	$-0.242846\pi$
$524$	3.91712e9			1.18934
$525$		0			0
$526$	6.29545e9			1.88615
$527$			6.04079e8i			0.179786i
$528$	−1.19300e9	−	1.31568e9i	−0.352714	−	0.388984i
$529$	2.45587e9			0.721290
$530$	6.17664e9			1.80213
$531$	2.11235e8	−	2.15464e9i	0.0612259	−	0.624517i
$532$		0			0
$533$		−	1.33518e8i		−	0.0381939i
$534$	−6.77273e8	−	7.46918e8i	−0.192473	−	0.212265i
$535$			1.06080e8i			0.0299498i
$536$		−	1.23044e9i		−	0.345132i
$537$	2.76567e9	+	3.05007e9i	0.770710	+	0.849963i
$538$			3.54840e9i			0.982414i
$539$		0			0
$540$	−2.81651e9	−	3.79227e9i	−0.769721	−	1.03639i
$541$	1.09886e9			0.298367			0.149183	−	0.988810i	$-0.452336\pi$
$541$	1.09886e9			0.298367			0.149183	+	0.988810i	$0.452336\pi$
$542$	−2.15471e9			−0.581288
$543$	−3.53603e9	−	3.89964e9i	−0.947799	−	1.04526i
$544$		−	4.44530e9i		−	1.18387i
$545$	9.95238e8			0.263354
$546$		0			0
$547$	−4.60429e9			−1.20284			−0.601419	−	0.798934i	$-0.705398\pi$
$547$	−4.60429e9			−1.20284			−0.601419	+	0.798934i	$0.705398\pi$
$548$		−	2.52822e9i		−	0.656270i
$549$	3.27412e9	+	3.20986e8i	0.844485	+	0.0827909i
$550$	5.87251e9			1.50506
$551$	1.07194e9			0.272986
$552$	6.58295e8	−	5.96913e8i	0.166584	−	0.151051i
$553$		0			0
$554$			7.53205e9i			1.88204i
$555$	−5.35113e9	+	4.85218e9i	−1.32868	+	1.20479i
$556$		−	5.16640e9i		−	1.27475i
$557$			4.14818e9i			1.01710i	0.861032	+	0.508551i	$0.169819\pi$
$557$			4.14818e9i			1.01710i	−0.861032	+	0.508551i	$0.830181\pi$
$558$	−9.05483e7	+	9.23612e8i	−0.0220628	+	0.225045i
$559$			2.04311e7i			0.00494710i
$560$		0			0
$561$	−1.24142e9	−	1.36908e9i	−0.296858	−	0.327384i
$562$	−5.47192e9			−1.30036
$563$	−6.59764e9			−1.55815			−0.779075	−	0.626930i	$-0.784311\pi$
$563$	−6.59764e9			−1.55815			−0.779075	+	0.626930i	$0.784311\pi$
$564$	2.14071e9	−	1.94110e9i	0.502435	−	0.455587i
$565$			8.29791e9i			1.93553i
$566$	5.49650e9			1.27417
$567$		0			0
$568$	4.15031e8			0.0950301
$569$			1.08631e9i			0.247208i	0.992332	+	0.123604i	$0.0394453\pi$
$569$			1.08631e9i			0.247208i	−0.992332	+	0.123604i	$0.960555\pi$
$570$	−7.27309e9	+	6.59493e9i	−1.64497	+	1.49158i
$571$	−1.50879e9			−0.339158			−0.169579	−	0.985517i	$-0.554241\pi$
$571$	−1.50879e9			−0.339158			−0.169579	+	0.985517i	$0.554241\pi$
$572$	−7.02393e7			−0.0156926
$573$	2.67089e9	+	2.94554e9i	0.593082	+	0.654069i
$574$		0			0
$575$			6.51660e9i			1.42950i
$576$	1.19953e8	−	1.22354e9i	0.0261536	−	0.266772i
$577$		−	7.97534e8i		−	0.172836i	−0.996259	−	0.0864180i	$-0.972458\pi$
$577$		−	7.97534e8i		−	0.172836i	0.996259	−	0.0864180i	$-0.0275420\pi$
$578$		−	3.35793e8i		−	0.0723309i
$579$	−6.25271e9	+	5.66969e9i	−1.33873	+	1.21390i
$580$		−	1.85594e9i		−	0.394971i
$581$		0			0
$582$	4.15168e9	−	3.76457e9i	0.872959	−	0.791562i
$583$	1.49001e9			0.311422
$584$	2.27695e9			0.473052
$585$	5.05043e8	+	4.95130e7i	0.104300	+	0.0102252i
$586$			2.67552e8i			0.0549246i
$587$	3.14642e9			0.642072			0.321036	−	0.947067i	$-0.395969\pi$
$587$	3.14642e9			0.642072			0.321036	+	0.947067i	$0.395969\pi$
$588$		0			0
$589$	7.74145e8			0.156106
$590$			7.79064e9i			1.56168i
$591$	6.59404e9	+	7.27211e9i	1.31400	+	1.44912i
$592$	−5.74102e9			−1.13727
$593$	2.04659e9			0.403031			0.201516	−	0.979485i	$-0.435413\pi$
$593$	2.04659e9			0.403031			0.201516	+	0.979485i	$0.435413\pi$
$594$	−1.69286e9	−	2.27934e9i	−0.331413	−	0.446229i
$595$		0			0
$596$			8.94509e8i			0.173070i
$597$	−4.60520e9	−	5.07876e9i	−0.885805	−	0.976894i
$598$		−	1.94201e8i		−	0.0371361i
$599$			5.45015e8i			0.103613i	0.998657	+	0.0518066i	$0.0164979\pi$
$599$			5.45015e8i			0.103613i	−0.998657	+	0.0518066i	$0.983502\pi$
$600$	−4.09907e9	−	4.52058e9i	−0.774739	−	0.854407i
$601$			1.21229e9i			0.227796i	0.993492	+	0.113898i	$0.0363336\pi$
$601$			1.21229e9i			0.227796i	−0.993492	+	0.113898i	$0.963666\pi$
$602$		0			0
$603$	4.25650e8	−	4.34172e9i	0.0790573	−	0.806402i
$604$	3.27539e9			0.604831
$605$	−8.54831e9			−1.56941
$606$	6.21220e9	+	6.85101e9i	1.13394	+	1.25055i
$607$			1.59406e9i			0.289296i	0.989483	+	0.144648i	$0.0462050\pi$
$607$			1.59406e9i			0.289296i	−0.989483	+	0.144648i	$0.953795\pi$
$608$	−5.69679e9			−1.02794
$609$		0			0
$610$	−1.18384e10			−2.11173
$611$			3.10436e8i			0.0550590i
$612$	3.81175e8	−	3.88807e9i	0.0672194	−	0.685652i
$613$	−1.69702e9			−0.297561			−0.148780	−	0.988870i	$-0.547535\pi$
$613$	−1.69702e9			−0.297561			−0.148780	+	0.988870i	$0.547535\pi$
$614$	−1.02277e10			−1.78314
$615$	−5.77440e9	+	5.23598e9i	−1.00102	+	0.907684i
$616$		0			0
$617$		−	1.19915e9i		−	0.205530i	−0.994706	−	0.102765i	$-0.967231\pi$
$617$		−	1.19915e9i		−	0.205530i	0.994706	−	0.102765i	$-0.0327690\pi$
$618$	4.79538e9	−	4.34825e9i	0.817267	−	0.741062i
$619$			6.05428e9i			1.02599i	0.858390	+	0.512997i	$0.171465\pi$
$619$			6.05428e9i			1.02599i	−0.858390	+	0.512997i	$0.828535\pi$
$620$		−	1.34034e9i		−	0.225862i
$621$	2.52934e9	−	1.87853e9i	0.423825	−	0.314773i
$622$		−	6.19338e9i		−	1.03196i
$623$		0			0
$624$	2.70921e8	+	2.98780e8i	0.0446371	+	0.0492272i
$625$	2.21199e10			3.62413
$626$	4.91840e9			0.801334
$627$	−1.75451e9	+	1.59092e9i	−0.284263	+	0.257757i
$628$		−	4.70153e9i		−	0.757496i
$629$	−5.97402e9			−0.957170
$630$		0			0
$631$	−4.25664e8			−0.0674472			−0.0337236	−	0.999431i	$-0.510737\pi$
$631$	−4.25664e8			−0.0674472			−0.0337236	+	0.999431i	$0.510737\pi$
$632$			7.72962e8i			0.121800i
$633$	5.02198e9	−	4.55372e9i	0.786978	−	0.713597i
$634$	−1.01053e10			−1.57484
$635$	9.36590e9			1.45158
$636$	2.11576e9	+	2.33332e9i	0.326111	+	0.359646i
$637$		0			0
$638$		−	1.11551e9i		−	0.170060i
$639$	1.46447e9	+	1.43573e8i	0.222038	+	0.0217680i
$640$		−	1.02878e10i		−	1.55128i
$641$			8.60758e9i			1.29086i	0.763821	+	0.645428i	$0.223321\pi$
$641$			8.60758e9i			1.29086i	−0.763821	+	0.645428i	$0.776679\pi$
$642$	−9.98454e7	+	9.05355e7i	−0.0148921	+	0.0135035i
$643$			2.22868e9i			0.330605i	0.986243	+	0.165303i	$0.0528601\pi$
$643$			2.22868e9i			0.330605i	−0.986243	+	0.165303i	$0.947140\pi$
$644$		0			0
$645$	8.83609e8	−	8.01218e8i	0.129659	−	0.117569i
$646$	−8.11969e9			−1.18502
$647$	−4.78565e9			−0.694665			−0.347333	−	0.937742i	$-0.612912\pi$
$647$	−4.78565e9			−0.694665			−0.347333	+	0.937742i	$0.612912\pi$
$648$	−5.72975e8	+	2.89415e9i	−0.0827224	+	0.417838i
$649$			1.87936e9i			0.269870i
$650$	−1.33360e9			−0.190470
$651$		0			0
$652$	5.17381e9			0.731044
$653$			4.58570e9i			0.644480i	0.946658	+	0.322240i	$0.104436\pi$
$653$			4.58570e9i			0.644480i	−0.946658	+	0.322240i	$0.895564\pi$
$654$	8.49402e8	+	9.36747e8i	0.118738	+	0.130948i
$655$	2.45669e10			3.41590
$656$	−6.19512e9			−0.856814
$657$	8.03441e9	+	7.87670e8i	1.10529	+	0.108359i
$658$		0			0
$659$			1.15059e10i			1.56610i	0.621956	+	0.783052i	$0.286338\pi$
$659$			1.15059e10i			1.56610i	−0.621956	+	0.783052i	$0.713662\pi$
$660$	2.75448e9	+	3.03772e9i	0.372937	+	0.411287i
$661$		−	3.97278e9i		−	0.535044i	−0.963552	−	0.267522i	$-0.913795\pi$
$661$		−	3.97278e9i		−	0.535044i	0.963552	−	0.267522i	$-0.0862047\pi$
$662$			1.25195e10i			1.67719i
$663$	2.81916e8	+	3.10905e8i	0.0375683	+	0.0414315i
$664$			2.74133e9i			0.363390i
$665$		0			0
$666$	−9.13402e9	−	8.95474e8i	−1.19813	−	0.117461i
$667$	1.23786e9			0.161521
$668$	−2.71370e9			−0.352245
$669$	−5.97221e9	−	6.58634e9i	−0.771158	−	0.850457i
$670$			1.56986e10i			2.01650i
$671$	−2.85582e9			−0.364923
$672$		0			0
$673$	2.68753e9			0.339861			0.169931	−	0.985456i	$-0.445646\pi$
$673$	2.68753e9			0.339861			0.169931	+	0.985456i	$0.445646\pi$
$674$			1.21471e10i			1.52814i
$675$	−1.29001e10	−	1.73692e10i	−1.61447	−	2.17379i
$676$	−5.36885e9			−0.668449
$677$	−7.56073e9			−0.936491			−0.468245	−	0.883599i	$-0.655114\pi$
$677$	−7.56073e9			−0.936491			−0.468245	+	0.883599i	$0.655114\pi$
$678$	−7.81023e9	+	7.08198e9i	−0.962410	+	0.872672i
$679$		0			0
$680$		−	6.91062e9i		−	0.842822i
$681$	1.55604e9	−	1.41095e9i	0.188802	−	0.171197i
$682$		−	8.05610e8i		−	0.0972477i
$683$		−	1.41723e10i		−	1.70204i	−0.525137	−	0.851018i	$-0.675986\pi$
$683$		−	1.41723e10i		−	1.70204i	0.525137	−	0.851018i	$-0.324014\pi$
$684$	−4.98267e9	−	4.88487e8i	−0.595341	−	0.0583656i
$685$		−	1.58561e10i		−	1.88487i
$686$		0			0
$687$	−2.58146e9	−	2.84691e9i	−0.303750	−	0.334985i
$688$	9.47989e8			0.110980
$689$	−3.38369e8			−0.0394115
$690$	−8.39882e9	+	7.61569e9i	−0.973300	+	0.882546i
$691$		−	8.72892e9i		−	1.00644i	−0.864159	−	0.503219i	$-0.832149\pi$
$691$		−	8.72892e9i		−	1.00644i	0.864159	−	0.503219i	$-0.167851\pi$
$692$	3.04752e8			0.0349603
$693$		0			0
$694$	−1.67830e9			−0.190596
$695$		−	3.24020e10i		−	3.66121i
$696$	−8.58704e8	+	7.78636e8i	−0.0965409	+	0.0875391i
$697$	−6.44655e9			−0.721128
$698$	−4.00871e9			−0.446181
$699$	1.14355e9	+	1.26114e9i	0.126644	+	0.139667i
$700$		0			0
$701$		−	1.45093e9i		−	0.159086i	−0.996831	−	0.0795432i	$-0.974654\pi$
$701$		−	1.45093e9i		−	0.159086i	0.996831	−	0.0795432i	$-0.0253461\pi$
$702$	3.84434e8	+	5.17619e8i	0.0419413	+	0.0564716i
$703$			7.65587e9i			0.831096i
$704$			1.06722e9i			0.115279i
$705$	1.34258e10	−	1.21739e10i	1.44304	−	1.30849i
$706$			1.82505e10i			1.95191i
$707$		0			0
$708$	−2.94303e9	+	2.66862e9i	−0.311658	+	0.282598i
$709$	−1.58354e10			−1.66866			−0.834331	−	0.551264i	$-0.814146\pi$
$709$	−1.58354e10			−1.66866			−0.834331	+	0.551264i	$0.814146\pi$
$710$	−5.29516e9			−0.555232
$711$	−2.67393e8	+	2.72746e9i	−0.0279001	+	0.284587i
$712$		−	9.09492e8i		−	0.0944320i
$713$	8.93968e8			0.0923652
$714$		0			0
$715$	−4.40518e8			−0.0450705
$716$		−	7.55528e9i		−	0.769228i
$717$	3.27175e9	+	3.60819e9i	0.331484	+	0.365571i
$718$	−8.99058e9			−0.906467
$719$	−1.49545e9			−0.150045			−0.0750225	−	0.997182i	$-0.523903\pi$
$719$	−1.49545e9			−0.150045			−0.0750225	+	0.997182i	$0.523903\pi$
$720$	2.29737e9	−	2.34337e10i	0.229386	−	2.33979i
$721$		0			0
$722$		−	2.66496e9i		−	0.263518i
$723$	8.83001e9	+	9.73801e9i	0.868914	+	0.958266i
$724$			9.65975e9i			0.945978i
$725$		−	8.50050e9i		−	0.828440i
$726$	−7.29570e9	−	8.04592e9i	−0.707601	−	0.780365i
$727$		−	1.76815e10i		−	1.70667i	−0.521364	−	0.853334i	$-0.674577\pi$
$727$		−	1.76815e10i		−	1.70667i	0.521364	−	0.853334i	$-0.325423\pi$
$728$		0			0
$729$	−3.02297e9	+	1.00140e10i	−0.288993	+	0.957331i
$730$	−2.90504e10			−2.76390
$731$	9.86463e8			0.0934049
$732$	−4.05514e9	−	4.47214e9i	−0.382136	−	0.421431i
$733$		−	2.98987e9i		−	0.280407i	−0.990123	−	0.140203i	$-0.955224\pi$
$733$		−	2.98987e9i		−	0.280407i	0.990123	−	0.140203i	$-0.0447756\pi$
$734$	−7.86652e9			−0.734254
$735$		0			0
$736$	−6.57854e9			−0.608215
$737$			3.78701e9i			0.348466i
$738$	−9.85650e9	−	9.66304e8i	−0.902663	−	0.0884945i
$739$	−1.06042e10			−0.966544			−0.483272	−	0.875470i	$-0.660552\pi$
$739$	−1.06042e10			−0.966544			−0.483272	+	0.875470i	$0.660552\pi$
$740$	1.32552e10			1.20247
$741$	3.98434e8	−	3.61283e8i	0.0359744	−	0.0326200i
$742$		0			0
$743$			6.92790e9i			0.619642i	0.950795	+	0.309821i	$0.100269\pi$
$743$			6.92790e9i			0.619642i	−0.950795	+	0.309821i	$0.899731\pi$
$744$	−6.20148e8	+	5.62323e8i	−0.0552064	+	0.0500588i
$745$			5.61007e9i			0.497074i
$746$			1.57789e10i			1.39152i
$747$	−9.48315e8	+	9.67301e9i	−0.0832397	+	0.849062i
$748$			3.39132e9i			0.296287i
$749$		0			0
$750$	3.29836e10	+	3.63754e10i	2.85485	+	3.14842i
$751$	−7.24144e9			−0.623857			−0.311929	−	0.950106i	$-0.600975\pi$
$751$	−7.24144e9			−0.623857			−0.311929	+	0.950106i	$0.600975\pi$
$752$	1.44040e10			1.23515
$753$	1.12199e10	−	1.01737e10i	0.957647	−	0.868353i
$754$			2.53323e8i			0.0215216i
$755$	2.05422e10			1.73713
$756$		0			0
$757$	−1.94667e10			−1.63101			−0.815507	−	0.578747i	$-0.803542\pi$
$757$	−1.94667e10			−1.63101			−0.815507	+	0.578747i	$0.803542\pi$
$758$		−	1.79695e10i		−	1.49863i
$759$	−2.02608e9	+	1.83716e9i	−0.168194	+	0.152511i
$760$	−8.85616e9			−0.731809
$761$	1.63880e10			1.34797			0.673984	−	0.738746i	$-0.264582\pi$
$761$	1.63880e10			1.34797			0.673984	+	0.738746i	$0.264582\pi$
$762$	7.99347e9	+	8.81545e9i	0.654475	+	0.721776i
$763$		0			0
$764$		−	7.29635e9i		−	0.591942i
$765$	2.39061e9	−	2.43847e10i	0.193060	−	1.96926i
$766$		−	1.51779e10i		−	1.22014i
$767$		−	4.26787e8i		−	0.0341529i
$768$	1.21759e10	−	1.10406e10i	0.969924	−	0.879485i
$769$			1.90743e10i			1.51254i	0.654259	+	0.756270i	$0.272980\pi$
$769$			1.90743e10i			1.51254i	−0.654259	+	0.756270i	$0.727020\pi$
$770$		0			0
$771$	−6.95230e9	+	6.30405e9i	−0.546309	+	0.495369i
$772$	1.54885e10			1.21157
$773$	5.87243e9			0.457288			0.228644	−	0.973510i	$-0.426571\pi$
$773$	5.87243e9			0.457288			0.228644	+	0.973510i	$0.426571\pi$
$774$	1.50826e9	+	1.47866e8i	0.116918	+	0.0114623i
$775$		−	6.13897e9i		−	0.473740i
$776$	5.05534e9			0.388360
$777$		0			0
$778$	7.79769e9			0.593660
$779$			8.26144e9i			0.626144i
$780$	−6.25518e8	−	6.89841e8i	−0.0471964	−	0.0520496i
$781$	−1.27737e9			−0.0959483
$782$	−9.37646e9			−0.701157
$783$	−3.29936e9	+	2.45043e9i	−0.245620	+	0.182421i
$784$		0			0
$785$		−	2.94865e10i		−	2.17560i
$786$	2.09670e10	+	2.31231e10i	1.54013	+	1.69850i
$787$		−	1.18200e10i		−	0.864384i	−0.901781	−	0.432192i	$-0.857740\pi$
$787$		−	1.18200e10i		−	0.864384i	0.901781	−	0.432192i	$-0.142260\pi$
$788$		−	1.80136e10i		−	1.31147i
$789$	1.35246e10	+	1.49153e10i	0.980288	+	1.08109i
$790$		−	9.86181e9i		−	0.711642i
$791$		0			0
$792$	2.49885e8	−	2.54888e9i	0.0178732	−	0.182310i
$793$	6.48531e8			0.0461822
$794$	−1.56982e10			−1.11296
$795$	1.32693e10	+	1.46338e10i	0.936621	+	1.03294i
$796$			1.25805e10i			0.884103i
$797$	1.19819e9			0.0838345			0.0419173	−	0.999121i	$-0.486653\pi$
$797$	1.19819e9			0.0838345			0.0419173	+	0.999121i	$0.486653\pi$
$798$		0			0
$799$	1.49886e10			1.03955
$800$			4.51755e10i			3.11952i
$801$	3.14623e8	−	3.20922e9i	0.0216310	−	0.220641i
$802$	3.35425e10			2.29607
$803$	−7.00791e9			−0.477622
$804$	−5.93037e9	+	5.37741e9i	−0.402426	+	0.364902i
$805$		0			0
$806$			1.82947e8i			0.0123070i
$807$	−8.40694e9	+	7.62306e9i	−0.563094	+	0.510589i
$808$			8.34221e9i			0.556341i
$809$			1.60213e10i			1.06384i	0.846793	+	0.531922i	$0.178530\pi$
$809$			1.60213e10i			1.06384i	−0.846793	+	0.531922i	$0.821470\pi$
$810$	7.31027e9	−	3.69248e10i	0.483321	−	2.44130i
$811$		−	1.85573e10i		−	1.22164i	−0.791770	−	0.610819i	$-0.790840\pi$
$811$		−	1.85573e10i		−	1.22164i	0.791770	−	0.610819i	$-0.209160\pi$
$812$		0			0
$813$	−4.62898e9	−	5.10498e9i	−0.302112	−	0.333179i
$814$	7.96704e9			0.517740
$815$	3.24484e10			2.09963
$816$	1.44258e10	−	1.30807e10i	0.929446	−	0.842782i
$817$		−	1.26418e9i		−	0.0811020i
$818$	−2.49757e10			−1.59544
$819$		0			0
$820$	1.43037e10			0.905939
$821$		−	1.41474e10i		−	0.892226i	−0.894977	−	0.446113i	$-0.852808\pi$
$821$		−	1.41474e10i		−	0.892226i	0.894977	−	0.446113i	$-0.147192\pi$
$822$	1.49243e10	−	1.35327e10i	0.937220	−	0.849831i
$823$	−5.04223e9			−0.315299			−0.157650	−	0.987495i	$-0.550392\pi$
$823$	−5.04223e9			−0.315299			−0.157650	+	0.987495i	$0.550392\pi$
$824$	5.83915e9			0.363584
$825$	1.26160e10	+	1.39133e10i	0.782225	+	0.862662i
$826$		0			0
$827$		−	2.69970e10i		−	1.65976i	−0.557941	−	0.829881i	$-0.688408\pi$
$827$		−	2.69970e10i		−	1.65976i	0.557941	−	0.829881i	$-0.311592\pi$
$828$	−5.75389e9	−	5.64095e8i	−0.352254	−	0.0345339i
$829$			2.65474e10i			1.61838i	0.587545	+	0.809191i	$0.300094\pi$
$829$			2.65474e10i			1.61838i	−0.587545	+	0.809191i	$0.699906\pi$
$830$		−	3.49751e10i		−	2.12318i
$831$	−1.78451e10	+	1.61812e10i	−1.07874	+	0.978151i
$832$		−	2.42356e8i		−	0.0145889i
$833$		0			0
$834$	3.04977e10	−	2.76540e10i	1.82048	−	1.65073i
$835$	−1.70195e10			−1.01168
$836$	4.34608e9			0.257262
$837$	−2.38277e9	+	1.76967e9i	−0.140457	+	0.104317i
$838$			2.83261e10i			1.66277i
$839$	−1.50756e10			−0.881266			−0.440633	−	0.897687i	$-0.645246\pi$
$839$	−1.50756e10			−0.881266			−0.440633	+	0.897687i	$0.645246\pi$
$840$		0			0
$841$	1.56352e10			0.906393
$842$		−	3.14969e10i		−	1.81834i
$843$	−1.17554e10	−	1.29642e10i	−0.675834	−	0.745331i
$844$	−1.24399e10			−0.712226
$845$	−3.36717e10			−1.91985
$846$	2.29169e10	+	2.24671e9i	1.30125	+	0.127571i
$847$		0			0
$848$			1.57001e10i			0.884130i
$849$	1.18082e10	+	1.30224e10i	0.662226	+	0.730323i
$850$			6.43892e10i			3.59622i
$851$			8.84085e9i			0.491746i
$852$	−1.81381e9	−	2.00033e9i	−0.100474	−	0.110806i
$853$			1.92731e10i			1.06324i	0.846984	+	0.531618i	$0.178416\pi$
$853$			1.92731e10i			1.06324i	−0.846984	+	0.531618i	$0.821584\pi$
$854$		0			0
$855$	−3.12497e10	−	3.06363e9i	−1.70987	−	0.167631i
$856$	−1.21578e8			−0.00662516
$857$	1.21714e10			0.660554			0.330277	−	0.943884i	$-0.392858\pi$
$857$	1.21714e10			0.660554			0.330277	+	0.943884i	$0.392858\pi$
$858$	−3.75967e8	−	4.14628e8i	−0.0203210	−	0.0224106i
$859$			2.09276e10i			1.12653i	0.826277	+	0.563264i	$0.190455\pi$
$859$			2.09276e10i			1.12653i	−0.826277	+	0.563264i	$0.809545\pi$
$860$	−2.18877e9			−0.117343
$861$		0			0
$862$	−4.26659e10			−2.26885
$863$			1.19006e10i			0.630279i	0.949045	+	0.315140i	$0.102051\pi$
$863$			1.19006e10i			0.630279i	−0.949045	+	0.315140i	$0.897949\pi$
$864$	1.75343e10	−	1.30227e10i	0.924892	−	0.686915i
$865$	1.91130e9			0.100409
$866$	−2.57224e10			−1.34586
$867$	7.95567e8	−	7.21386e8i	0.0414582	−	0.0375925i
$868$		0			0
$869$		−	2.37900e9i		−	0.122977i
$870$	1.09557e10	−	9.93420e9i	0.564059	−	0.511464i
$871$		−	8.59998e8i		−	0.0440995i
$872$			1.14064e9i			0.0582560i
$873$	1.78382e10	+	1.74881e9i	0.907405	+	0.0889594i
$874$			1.20162e10i			0.608804i
$875$		0			0
$876$	−9.95095e9	−	1.09742e10i	−0.500150	−	0.551581i
$877$	−2.60925e10			−1.30622			−0.653112	−	0.757261i	$-0.726537\pi$
$877$	−2.60925e10			−1.30622			−0.653112	+	0.757261i	$0.726537\pi$
$878$	−1.87304e10			−0.933934
$879$	−6.33891e8	+	5.74785e8i	−0.0314814	+	0.0285459i
$880$			2.04397e10i			1.01108i
$881$	−2.60616e10			−1.28406			−0.642031	−	0.766678i	$-0.721908\pi$
$881$	−2.60616e10			−1.28406			−0.642031	+	0.766678i	$0.721908\pi$
$882$		0			0
$883$	−7.75021e9			−0.378836			−0.189418	−	0.981897i	$-0.560660\pi$
$883$	−7.75021e9			−0.378836			−0.189418	+	0.981897i	$0.560660\pi$
$884$		−	7.70139e8i		−	0.0374961i
$885$	−1.84577e10	+	1.67367e10i	−0.895112	+	0.811649i
$886$	1.94630e10			0.940139
$887$	6.90376e9			0.332165			0.166082	−	0.986112i	$-0.446888\pi$
$887$	6.90376e9			0.332165			0.166082	+	0.986112i	$0.446888\pi$
$888$	−5.56107e9	−	6.13292e9i	−0.266510	−	0.293915i
$889$		0			0
$890$			1.16037e10i			0.551737i
$891$	1.76348e9	−	8.90750e9i	0.0835216	−	0.421875i
$892$			1.63149e10i			0.769676i
$893$		−	1.92083e10i		−	0.902629i
$894$	−5.28036e9	+	4.78800e9i	−0.247162	+	0.224116i
$895$		−	4.73843e10i		−	2.20929i
$896$		0			0
$897$	4.60104e8	−	4.17203e8i	0.0212854	−	0.0193007i
$898$	1.34010e10			0.617546
$899$	−1.16613e9			−0.0535286
$900$	−3.87370e9	+	3.95126e10i	−0.177124	+	1.80670i
$901$			1.63372e10i			0.744118i
$902$	8.59722e9			0.390063
$903$		0			0
$904$	−9.51021e9			−0.428155
$905$			6.05828e10i			2.71693i
$906$	1.75321e10	+	1.93349e10i	0.783221	+	0.863760i
$907$	3.64835e10			1.62357			0.811784	−	0.583957i	$-0.198496\pi$
$907$	3.64835e10			1.62357			0.811784	+	0.583957i	$0.198496\pi$
$908$	−3.85445e9			−0.170868
$909$	−2.88584e9	+	2.94362e10i	−0.127438	+	1.29989i
$910$		0			0
$911$		−	2.78042e8i		−	0.0121842i	−0.999981	−	0.00609209i	$-0.998061\pi$
$911$		−	2.78042e8i		−	0.0121842i	0.999981	−	0.00609209i	$-0.00193918\pi$
$912$	−1.67633e10	−	1.84871e10i	−0.731774	−	0.807023i
$913$		−	8.43717e9i		−	0.366901i
$914$		−	9.41828e9i		−	0.408000i
$915$	−2.54325e10	−	2.80478e10i	−1.09753	−	1.21039i
$916$			7.05204e9i			0.303166i
$917$		0			0
$918$	2.49919e10	−	1.85614e10i	1.06623	−	0.791883i
$919$	2.41019e10			1.02435			0.512174	−	0.858882i	$-0.328840\pi$
$919$	2.41019e10			1.02435			0.512174	+	0.858882i	$0.328840\pi$
$920$	−1.02269e10			−0.432999
$921$	−2.19721e10	−	2.42316e10i	−0.926753	−	1.02205i
$922$		−	2.65824e10i		−	1.11696i
$923$	2.90079e8			0.0121426
$924$		0			0
$925$	6.07111e10			2.52216
$926$			2.06842e10i			0.856054i
$927$	2.06039e10	+	2.01995e9i	0.849515	+	0.0832840i
$928$	8.58129e9			0.352480
$929$	1.89119e9			0.0773891			0.0386945	−	0.999251i	$-0.487680\pi$
$929$	1.89119e9			0.0773891			0.0386945	+	0.999251i	$0.487680\pi$
$930$	7.91213e9	−	7.17438e9i	0.322554	−	0.292478i
$931$		0			0
$932$		−	3.12395e9i		−	0.126401i
$933$	1.46735e10	−	1.33053e10i	0.591490	−	0.536338i
$934$		−	5.96613e10i		−	2.39595i
$935$			2.12693e10i			0.850965i
$936$	−5.67468e7	+	5.78829e8i	−0.00226191	+	0.0230720i
$937$			3.00074e9i			0.119163i	0.998223	+	0.0595813i	$0.0189766\pi$
$937$			3.00074e9i			0.119163i	−0.998223	+	0.0595813i	$0.981023\pi$
$938$		0			0
$939$	1.05662e10	+	1.16528e10i	0.416476	+	0.459303i
$940$	−3.32569e10			−1.30597
$941$	1.71379e8			0.00670491			0.00335246	−	0.999994i	$-0.498933\pi$
$941$	1.71379e8			0.00670491			0.00335246	+	0.999994i	$0.498933\pi$
$942$	2.77535e10	−	2.51657e10i	1.08178	−	0.980913i
$943$			9.54015e9i			0.370479i
$944$	−1.98026e10			−0.766161
$945$		0			0
$946$	−1.31556e9			−0.0505234
$947$		−	2.15658e10i		−	0.825164i	−0.910920	−	0.412582i	$-0.864627\pi$
$947$		−	2.15658e10i		−	0.825164i	0.910920	−	0.412582i	$-0.135373\pi$
$948$	3.72545e9	−	3.37808e9i	0.142020	−	0.128778i
$949$	1.59144e9			0.0604446
$950$	8.25166e10			3.12254
$951$	−2.17093e10	−	2.39417e10i	−0.818490	−	0.902656i
$952$		0			0
$953$			2.27050e10i			0.849760i	0.905250	+	0.424880i	$0.139684\pi$
$953$			2.27050e10i			0.849760i	−0.905250	+	0.424880i	$0.860316\pi$
$954$	−2.44887e9	+	2.49790e10i	−0.0913157	+	0.931440i
$955$		−	4.57603e10i		−	1.70011i
$956$		−	8.93779e9i		−	0.330847i
$957$	2.64289e9	−	2.39646e9i	0.0974737	−	0.0883849i
$958$			1.50900e7i			0.000554510i
$959$		0			0
$960$	−1.04815e10	+	9.50415e9i	−0.382361	+	0.346708i
$961$	2.66705e10			0.969390
$962$	−1.80925e9			−0.0655217
$963$	−4.28997e8	−	4.20577e7i	−0.0154797	−	0.00151759i
$964$		−	2.41219e10i		−	0.867244i
$965$	9.71388e10			3.47974
$966$		0			0
$967$	−3.81459e10			−1.35661			−0.678306	−	0.734780i	$-0.737285\pi$
$967$	−3.81459e10			−1.35661			−0.678306	+	0.734780i	$0.737285\pi$
$968$		−	9.79720e9i		−	0.347167i
$969$	−1.74436e10	−	1.92374e10i	−0.615890	−	0.679223i
$970$	−6.44984e10			−2.26907
$971$	2.80457e10			0.983102			0.491551	−	0.870849i	$-0.336430\pi$
$971$	2.80457e10			0.983102			0.491551	+	0.870849i	$0.336430\pi$
$972$	1.64530e10	−	9.88672e9i	0.574663	−	0.345319i
$973$		0			0
$974$			1.40266e10i			0.486404i
$975$	−2.86498e9	−	3.15958e9i	−0.0989931	−	0.109173i
$976$		−	3.00914e10i		−	1.03602i
$977$			2.41960e10i			0.830065i	0.909807	+	0.415032i	$0.136230\pi$
$977$			2.41960e10i			0.830065i	−0.909807	+	0.415032i	$0.863770\pi$
$978$	2.76936e10	+	3.05414e10i	0.946659	+	1.04401i
$979$			2.79920e9i			0.0953443i
$980$		0			0
$981$	−3.94584e8	+	4.02484e9i	−0.0133444	+	0.136115i
$982$	−1.00275e10			−0.337910
$983$	−1.50841e10			−0.506502			−0.253251	−	0.967401i	$-0.581500\pi$
$983$	−1.50841e10			−0.506502			−0.253251	+	0.967401i	$0.581500\pi$
$984$	−6.00094e9	−	6.61802e9i	−0.200787	−	0.221435i
$985$		−	1.12976e11i		−	3.76668i
$986$	1.22310e10			0.406343
$987$		0			0
$988$	−9.86956e8			−0.0325573
$989$		−	1.45985e9i		−	0.0479867i
$990$	−3.18815e9	+	3.25198e10i	−0.104428	+	1.06518i
$991$	−3.68938e10			−1.20419			−0.602096	−	0.798424i	$-0.705667\pi$
$991$	−3.68938e10			−1.20419			−0.602096	+	0.798424i	$0.705667\pi$
$992$	6.19732e9			0.201564
$993$	−2.96614e10	+	2.68956e10i	−0.961321	+	0.871685i
$994$		0			0
$995$			7.89009e10i			2.53922i
$996$	1.32124e10	−	1.19804e10i	0.423715	−	0.384207i
$997$			4.12487e10i			1.31819i	0.752060	+	0.659094i	$0.229060\pi$
$997$			4.12487e10i			1.31819i	−0.752060	+	0.659094i	$0.770940\pi$
$998$			4.35762e10i			1.38769i
$999$	−1.75011e10	−	2.35643e10i	−0.555375	−	0.747782i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.8.c.b.146.1		32
3.2	odd	2	inner	147.8.c.b.146.32		32
7.2	even	3		21.8.g.b.17.4	yes	32
7.3	odd	6		21.8.g.b.5.13	yes	32
7.6	odd	2	inner	147.8.c.b.146.31		32
21.2	odd	6		21.8.g.b.17.13	yes	32
21.17	even	6		21.8.g.b.5.4	✓	32
21.20	even	2	inner	147.8.c.b.146.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.8.g.b.5.4	✓	32	21.17	even	6
21.8.g.b.5.13	yes	32	7.3	odd	6
21.8.g.b.17.4	yes	32	7.2	even	3
21.8.g.b.17.13	yes	32	21.2	odd	6
147.8.c.b.146.1		32	1.1	even	1	trivial
147.8.c.b.146.2		32	21.20	even	2	inner
147.8.c.b.146.31		32	7.6	odd	2	inner
147.8.c.b.146.32		32	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	147.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-14.6224i q^{2} +(34.6438 - 31.4135i) q^{3} -85.8156 q^{4} -538.208 q^{5} +(-459.342 - 506.577i) q^{6} -616.838i q^{8} +(213.384 - 2176.57i) q^{9} +7869.91i q^{10} +1898.48i q^{11} +(-2972.98 + 2695.77i) q^{12} -431.129i q^{13} +(-18645.5 + 16907.0i) q^{15} -20004.1 q^{16} -20815.9 q^{17} +(-31826.7 - 3120.20i) q^{18} +26676.2i q^{19} +46186.6 q^{20} +27760.4 q^{22} +30805.2i q^{23} +(-19377.0 - 21369.6i) q^{24} +211542. q^{25} -6304.16 q^{26} +(-60981.1 - 82107.6i) q^{27} -40183.4i q^{29} +(247221. + 272643. i) q^{30} -29020.1i q^{31} +213553. i q^{32} +(59638.0 + 65770.6i) q^{33} +304380. i q^{34} +(-18311.7 + 186783. i) q^{36} +286993. q^{37} +390071. q^{38} +(-13543.3 - 14935.9i) q^{39} +331987. i q^{40} +309693. q^{41} -47389.8 q^{43} -162920. i q^{44} +(-114845. + 1.17144e6i) q^{45} +450446. q^{46} -720054. q^{47} +(-693017. + 628398. i) q^{48} -3.09326e6i q^{50} +(-721143. + 653901. i) q^{51} +36997.6i q^{52} -784843. i q^{53} +(-1.20061e6 + 891692. i) q^{54} -1.02178e6i q^{55} +(837993. + 924165. i) q^{57} -587579. q^{58} +989928. q^{59} +(1.60008e6 - 1.45088e6i) q^{60} +1.50426e6i q^{61} -424344. q^{62} +562144. q^{64} +232037. i q^{65} +(961727. - 872053. i) q^{66} +1.99476e6 q^{67} +1.78633e6 q^{68} +(967698. + 1.06721e6i) q^{69} +672836. i q^{71} +(-1.34259e6 - 131624. i) q^{72} +3.69132e6i q^{73} -4.19653e6i q^{74} +(7.32863e6 - 6.64529e6i) q^{75} -2.28924e6i q^{76} +(-218400. + 198036. i) q^{78} -1.25310e6 q^{79} +1.07663e7 q^{80} +(-4.69190e6 - 928890. i) q^{81} -4.52847e6i q^{82} -4.44416e6 q^{83} +1.12033e7 q^{85} +692954. i q^{86} +(-1.26230e6 - 1.39211e6i) q^{87} +1.17106e6 q^{88} +1.47444e6 q^{89} +(1.71294e7 + 1.67931e6i) q^{90} -2.64356e6i q^{92} +(-911622. - 1.00536e6i) q^{93} +1.05289e7i q^{94} -1.43573e7i q^{95} +(6.70845e6 + 7.39829e6i) q^{96} +8.19557e6i q^{97} +(4.13217e6 + 405106. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2300 q^{4} + 7032 q^{9} + 27576 q^{15} + 39188 q^{16} - 66996 q^{18} + 105132 q^{22} + 662504 q^{25} + 81324 q^{30} - 227244 q^{36} + 1237496 q^{37} - 3992208 q^{39} - 1416064 q^{43} + 6985680 q^{46}+ \cdots + 35642232 q^{99}+O(q^{100}) \) 32 * q - 2300 * q^4 + 7032 * q^9 + 27576 * q^15 + 39188 * q^16 - 66996 * q^18 + 105132 * q^22 + 662504 * q^25 + 81324 * q^30 - 227244 * q^36 + 1237496 * q^37 - 3992208 * q^39 - 1416064 * q^43 + 6985680 * q^46 - 1354680 * q^51 - 6279408 * q^57 + 4128684 * q^58 - 15042564 * q^60 - 589508 * q^64 + 3889456 * q^67 + 3088944 * q^72 + 1917432 * q^78 - 15252656 * q^79 - 17406072 * q^81 + 3418848 * q^85 - 24626796 * q^88 + 49664208 * q^93 + 35642232 * q^99

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