LMFDB - Embedded newform 192.9.l.a.175.27

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [192,9,Mod(79,192)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(192, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("192.79");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 192 = 2^{6} \cdot 3 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	192.l (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$78.2166931317$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 48)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			175.27
Character	$\chi$	$=$	192.175
Dual form			192.9.l.a.79.27

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(33.0681 - 33.0681i) q^{3} +(271.296 - 271.296i) q^{5} -3140.01 q^{7} -2187.00i q^{9} +O(q^{10})$	\(q+(33.0681 - 33.0681i) q^{3} +(271.296 - 271.296i) q^{5} -3140.01 q^{7} -2187.00i q^{9} +(-13483.9 - 13483.9i) q^{11} +(53.7468 + 53.7468i) q^{13} -17942.5i q^{15} -49733.7 q^{17} +(81031.9 - 81031.9i) q^{19} +(-103834. + 103834. i) q^{21} -18878.1 q^{23} +243422. i q^{25} +(-72320.0 - 72320.0i) q^{27} +(169253. + 169253. i) q^{29} +928078. i q^{31} -891773. q^{33} +(-851871. + 851871. i) q^{35} +(766720. - 766720. i) q^{37} +3554.61 q^{39} +5.02634e6i q^{41} +(-2.95586e6 - 2.95586e6i) q^{43} +(-593324. - 593324. i) q^{45} +3.96840e6i q^{47} +4.09485e6 q^{49} +(-1.64460e6 + 1.64460e6i) q^{51} +(8.73814e6 - 8.73814e6i) q^{53} -7.31624e6 q^{55} -5.35915e6i q^{57} +(9.75112e6 + 9.75112e6i) q^{59} +(-4.29071e6 - 4.29071e6i) q^{61} +6.86720e6i q^{63} +29162.6 q^{65} +(-6.69650e6 + 6.69650e6i) q^{67} +(-624263. + 624263. i) q^{69} -2.38140e7 q^{71} -4.01505e7i q^{73} +(8.04952e6 + 8.04952e6i) q^{75} +(4.23395e7 + 4.23395e7i) q^{77} +7.02261e7i q^{79} -4.78297e6 q^{81} +(-7.55026e6 + 7.55026e6i) q^{83} +(-1.34926e7 + 1.34926e7i) q^{85} +1.11938e7 q^{87} +1.01023e8i q^{89} +(-168765. - 168765. i) q^{91} +(3.06898e7 + 3.06898e7i) q^{93} -4.39672e7i q^{95} +2.10782e7 q^{97} +(-2.94893e7 + 2.94893e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q+O(q^{10}) $ 64 * q	$ 64 q - 39552 q^{11} + 167552 q^{19} - 1691136 q^{23} - 2132352 q^{29} + 2415744 q^{35} - 4720512 q^{37} + 7244672 q^{43} + 52706752 q^{49} - 13862016 q^{51} - 5358720 q^{53} + 46326784 q^{55} - 44938752 q^{59} + 24476032 q^{61} + 29941632 q^{65} + 44244736 q^{67} - 8636544 q^{69} - 159664128 q^{71} - 12918528 q^{75} - 94964352 q^{77} - 306110016 q^{81} - 209328000 q^{83} + 106960000 q^{85} + 45401472 q^{91} - 86500224 q^{99}+O(q^{100}) $ 64 * q - 39552 * q^11 + 167552 * q^19 - 1691136 * q^23 - 2132352 * q^29 + 2415744 * q^35 - 4720512 * q^37 + 7244672 * q^43 + 52706752 * q^49 - 13862016 * q^51 - 5358720 * q^53 + 46326784 * q^55 - 44938752 * q^59 + 24476032 * q^61 + 29941632 * q^65 + 44244736 * q^67 - 8636544 * q^69 - 159664128 * q^71 - 12918528 * q^75 - 94964352 * q^77 - 306110016 * q^81 - 209328000 * q^83 + 106960000 * q^85 + 45401472 * q^91 - 86500224 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/192\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$133$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	33.0681	−	33.0681i	0.408248	−	0.408248i
$3$	33.0681	−	33.0681i	0.408248	−	0.408248i
$4$		0			0
$5$	271.296	−	271.296i	0.434073	−	0.434073i	−0.455938	−	0.890011i	$-0.650696\pi$
$5$	271.296	−	271.296i	0.434073	−	0.434073i	0.890011	+	0.455938i	$0.150696\pi$
$6$		0			0
$7$	−3140.01			−1.30779			−0.653896	−	0.756585i	$-0.726867\pi$
$7$	−3140.01			−1.30779			−0.653896	+	0.756585i	$0.726867\pi$
$8$		0			0
$9$		−	2187.00i		−	0.333333i
$10$		0			0
$11$	−13483.9	−	13483.9i	−0.920967	−	0.920967i	0.0761304	−	0.997098i	$-0.475743\pi$
$11$	−13483.9	−	13483.9i	−0.920967	−	0.920967i	−0.997098	+	0.0761304i	$0.975743\pi$
$12$		0			0
$13$	53.7468	+	53.7468i	0.00188183	+	0.00188183i	0.708047	−	0.706165i	$-0.249576\pi$
$13$	53.7468	+	53.7468i	0.00188183	+	0.00188183i	−0.706165	+	0.708047i	$0.749576\pi$
$14$		0			0
$15$		−	17942.5i		−	0.354419i
$16$		0			0
$17$	−49733.7			−0.595464			−0.297732	−	0.954649i	$-0.596230\pi$
$17$	−49733.7			−0.595464			−0.297732	+	0.954649i	$0.596230\pi$
$18$		0			0
$19$	81031.9	−	81031.9i	0.621787	−	0.621787i	−0.324201	−	0.945988i	$-0.605095\pi$
$19$	81031.9	−	81031.9i	0.621787	−	0.621787i	0.945988	+	0.324201i	$0.105095\pi$
$20$		0			0
$21$	−103834.	+	103834.i	−0.533904	+	0.533904i
$22$		0			0
$23$	−18878.1			−0.0674601			−0.0337301	−	0.999431i	$-0.510739\pi$
$23$	−18878.1			−0.0674601			−0.0337301	+	0.999431i	$0.510739\pi$
$24$		0			0
$25$			243422.i			0.623161i
$26$		0			0
$27$	−72320.0	−	72320.0i	−0.136083	−	0.136083i
$28$		0			0
$29$	169253.	+	169253.i	0.239301	+	0.239301i	0.816561	−	0.577259i	$-0.195878\pi$
$29$	169253.	+	169253.i	0.239301	+	0.239301i	−0.577259	+	0.816561i	$0.695878\pi$
$30$		0			0
$31$			928078.i			1.00493i	0.864596	+	0.502467i	$0.167574\pi$
$31$			928078.i			1.00493i	−0.864596	+	0.502467i	$0.832426\pi$
$32$		0			0
$33$	−891773.			−0.751967
$34$		0			0
$35$	−851871.	+	851871.i	−0.567677	+	0.567677i
$36$		0			0
$37$	766720.	−	766720.i	0.409100	−	0.409100i	−0.472325	−	0.881425i	$-0.656585\pi$
$37$	766720.	−	766720.i	0.409100	−	0.409100i	0.881425	+	0.472325i	$0.156585\pi$
$38$		0			0
$39$	3554.61			0.00153650
$40$		0			0
$41$			5.02634e6i			1.77876i	0.457172	+	0.889378i	$0.348862\pi$
$41$			5.02634e6i			1.77876i	−0.457172	+	0.889378i	$0.651138\pi$
$42$		0			0
$43$	−2.95586e6	−	2.95586e6i	−0.864590	−	0.864590i	0.127277	−	0.991867i	$-0.459376\pi$
$43$	−2.95586e6	−	2.95586e6i	−0.864590	−	0.864590i	−0.991867	+	0.127277i	$0.959376\pi$
$44$		0			0
$45$	−593324.	−	593324.i	−0.144691	−	0.144691i
$46$		0			0
$47$			3.96840e6i			0.813249i	0.913595	+	0.406624i	$0.133294\pi$
$47$			3.96840e6i			0.813249i	−0.913595	+	0.406624i	$0.866706\pi$
$48$		0			0
$49$	4.09485e6			0.710319
$50$		0			0
$51$	−1.64460e6	+	1.64460e6i	−0.243097	+	0.243097i
$52$		0			0
$53$	8.73814e6	−	8.73814e6i	1.10743	−	1.10743i	0.113941	−	0.993488i	$-0.463653\pi$
$53$	8.73814e6	−	8.73814e6i	1.10743	−	1.10743i	0.993488	−	0.113941i	$-0.0363474\pi$
$54$		0			0
$55$	−7.31624e6			−0.799534
$56$		0			0
$57$		−	5.35915e6i		−	0.507687i
$58$		0			0
$59$	9.75112e6	+	9.75112e6i	0.804723	+	0.804723i	0.983830	−	0.179107i	$-0.0573208\pi$
$59$	9.75112e6	+	9.75112e6i	0.804723	+	0.804723i	−0.179107	+	0.983830i	$0.557321\pi$
$60$		0			0
$61$	−4.29071e6	−	4.29071e6i	−0.309892	−	0.309892i	0.534976	−	0.844867i	$-0.320321\pi$
$61$	−4.29071e6	−	4.29071e6i	−0.309892	−	0.309892i	−0.844867	+	0.534976i	$0.820321\pi$
$62$		0			0
$63$			6.86720e6i			0.435931i
$64$		0			0
$65$	29162.6			0.00163370
$66$		0			0
$67$	−6.69650e6	+	6.69650e6i	−0.332314	+	0.332314i	−0.853465	−	0.521151i	$-0.825503\pi$
$67$	−6.69650e6	+	6.69650e6i	−0.332314	+	0.332314i	0.521151	+	0.853465i	$0.325503\pi$
$68$		0			0
$69$	−624263.	+	624263.i	−0.0275405	+	0.0275405i
$70$		0			0
$71$	−2.38140e7			−0.937127			−0.468563	−	0.883430i	$-0.655228\pi$
$71$	−2.38140e7			−0.937127			−0.468563	+	0.883430i	$0.655228\pi$
$72$		0			0
$73$		−	4.01505e7i		−	1.41384i	−0.707295	−	0.706918i	$-0.750085\pi$
$73$		−	4.01505e7i		−	1.41384i	0.707295	−	0.706918i	$-0.249915\pi$
$74$		0			0
$75$	8.04952e6	+	8.04952e6i	0.254404	+	0.254404i
$76$		0			0
$77$	4.23395e7	+	4.23395e7i	1.20443	+	1.20443i
$78$		0			0
$79$			7.02261e7i			1.80298i	0.432803	+	0.901489i	$0.357525\pi$
$79$			7.02261e7i			1.80298i	−0.432803	+	0.901489i	$0.642475\pi$
$80$		0			0
$81$	−4.78297e6			−0.111111
$82$		0			0
$83$	−7.55026e6	+	7.55026e6i	−0.159093	+	0.159093i	−0.782165	−	0.623072i	$-0.785884\pi$
$83$	−7.55026e6	+	7.55026e6i	−0.159093	+	0.159093i	0.623072	+	0.782165i	$0.285884\pi$
$84$		0			0
$85$	−1.34926e7	+	1.34926e7i	−0.258475	+	0.258475i
$86$		0			0
$87$	1.11938e7			0.195389
$88$		0			0
$89$			1.01023e8i			1.61013i	0.593184	+	0.805067i	$0.297871\pi$
$89$			1.01023e8i			1.61013i	−0.593184	+	0.805067i	$0.702129\pi$
$90$		0			0
$91$	−168765.	−	168765.i	−0.00246104	−	0.00246104i
$92$		0			0
$93$	3.06898e7	+	3.06898e7i	0.410263	+	0.410263i
$94$		0			0
$95$		−	4.39672e7i		−	0.539802i
$96$		0			0
$97$	2.10782e7			0.238093			0.119047	−	0.992889i	$-0.462016\pi$
$97$	2.10782e7			0.238093			0.119047	+	0.992889i	$0.462016\pi$
$98$		0			0
$99$	−2.94893e7	+	2.94893e7i	−0.306989	+	0.306989i
$100$		0			0
$101$	−2.83838e6	+	2.83838e6i	−0.0272763	+	0.0272763i	−0.720613	−	0.693337i	$-0.756140\pi$
$101$	−2.83838e6	+	2.83838e6i	−0.0272763	+	0.0272763i	0.693337	+	0.720613i	$0.256140\pi$
$102$		0			0
$103$	1.80583e8			1.60445			0.802226	−	0.597020i	$-0.203649\pi$
$103$	1.80583e8			1.60445			0.802226	+	0.597020i	$0.203649\pi$
$104$		0			0
$105$			5.63395e7i			0.463507i
$106$		0			0
$107$	−1.10577e8	−	1.10577e8i	−0.843584	−	0.843584i	0.145739	−	0.989323i	$-0.453444\pi$
$107$	−1.10577e8	−	1.10577e8i	−0.843584	−	0.843584i	−0.989323	+	0.145739i	$0.953444\pi$
$108$		0			0
$109$	2.48326e7	+	2.48326e7i	0.175920	+	0.175920i	0.789575	−	0.613655i	$-0.210301\pi$
$109$	2.48326e7	+	2.48326e7i	0.175920	+	0.175920i	−0.613655	+	0.789575i	$0.710301\pi$
$110$		0			0
$111$		−	5.07079e7i		−	0.334029i
$112$		0			0
$113$	−2.38114e8			−1.46040			−0.730199	−	0.683235i	$-0.760573\pi$
$113$	−2.38114e8			−1.46040			−0.730199	+	0.683235i	$0.760573\pi$
$114$		0			0
$115$	−5.12155e6	+	5.12155e6i	−0.0292826	+	0.0292826i
$116$		0			0
$117$	117544.	−	117544.i	0.000627275	−	0.000627275i
$118$		0			0
$119$	1.56164e8			0.778743
$120$		0			0
$121$			1.49271e8i			0.696362i
$122$		0			0
$123$	1.66212e8	+	1.66212e8i	0.726174	+	0.726174i
$124$		0			0
$125$	1.72014e8	+	1.72014e8i	0.704571	+	0.704571i
$126$		0			0
$127$			4.29074e8i			1.64937i	0.565595	+	0.824683i	$0.308646\pi$
$127$			4.29074e8i			1.64937i	−0.565595	+	0.824683i	$0.691354\pi$
$128$		0			0
$129$	−1.95489e8			−0.705935
$130$		0			0
$131$	−2.20360e8	+	2.20360e8i	−0.748250	+	0.748250i	−0.974150	−	0.225900i	$-0.927468\pi$
$131$	−2.20360e8	+	2.20360e8i	−0.748250	+	0.748250i	0.225900	+	0.974150i	$0.427468\pi$
$132$		0			0
$133$	−2.54441e8	+	2.54441e8i	−0.813168	+	0.813168i
$134$		0			0
$135$	−3.92402e7			−0.118140
$136$		0			0
$137$			2.66288e8i			0.755910i	0.925824	+	0.377955i	$0.123373\pi$
$137$			2.66288e8i			0.755910i	−0.925824	+	0.377955i	$0.876627\pi$
$138$		0			0
$139$	4.27337e8	+	4.27337e8i	1.14475	+	1.14475i	0.987570	+	0.157181i	$0.0502406\pi$
$139$	4.27337e8	+	4.27337e8i	1.14475	+	1.14475i	0.157181	+	0.987570i	$0.449759\pi$
$140$		0			0
$141$	1.31227e8	+	1.31227e8i	0.332007	+	0.332007i
$142$		0			0
$143$		−	1.44943e6i		−	0.00346620i
$144$		0			0
$145$	9.18354e7			0.207748
$146$		0			0
$147$	1.35409e8	−	1.35409e8i	0.289987	−	0.289987i
$148$		0			0
$149$	−3.09770e8	+	3.09770e8i	−0.628485	+	0.628485i	−0.947687	−	0.319202i	$-0.896585\pi$
$149$	−3.09770e8	+	3.09770e8i	−0.628485	+	0.628485i	0.319202	+	0.947687i	$0.396585\pi$
$150$		0			0
$151$	−7.12363e8			−1.37023			−0.685115	−	0.728435i	$-0.740248\pi$
$151$	−7.12363e8			−1.37023			−0.685115	+	0.728435i	$0.740248\pi$
$152$		0			0
$153$			1.08768e8i			0.198488i
$154$		0			0
$155$	2.51784e8	+	2.51784e8i	0.436215	+	0.436215i
$156$		0			0
$157$	2.02672e8	+	2.02672e8i	0.333577	+	0.333577i	0.853943	−	0.520366i	$-0.174205\pi$
$157$	2.02672e8	+	2.02672e8i	0.333577	+	0.333577i	−0.520366	+	0.853943i	$0.674205\pi$
$158$		0			0
$159$		−	5.77908e8i		−	0.904211i
$160$		0			0
$161$	5.92774e7			0.0882238
$162$		0			0
$163$	−9.79943e8	+	9.79943e8i	−1.38820	+	1.38820i	−0.559085	+	0.829110i	$0.688848\pi$
$163$	−9.79943e8	+	9.79943e8i	−1.38820	+	1.38820i	−0.829110	+	0.559085i	$0.811152\pi$
$164$		0			0
$165$	−2.41934e8	+	2.41934e8i	−0.326409	+	0.326409i
$166$		0			0
$167$	7.98570e8			1.02671			0.513354	−	0.858177i	$-0.328403\pi$
$167$	7.98570e8			1.02671			0.513354	+	0.858177i	$0.328403\pi$
$168$		0			0
$169$		−	8.15725e8i		−	0.999993i
$170$		0			0
$171$	−1.77217e8	−	1.77217e8i	−0.207262	−	0.207262i
$172$		0			0
$173$	4.12260e7	+	4.12260e7i	0.0460243	+	0.0460243i	0.729744	−	0.683720i	$-0.239639\pi$
$173$	4.12260e7	+	4.12260e7i	0.0460243	+	0.0460243i	−0.683720	+	0.729744i	$0.739639\pi$
$174$		0			0
$175$		−	7.64348e8i		−	0.814965i
$176$		0			0
$177$	6.44902e8			0.657053
$178$		0			0
$179$	−2.80091e7	+	2.80091e7i	−0.0272827	+	0.0272827i	−0.720617	−	0.693334i	$-0.756141\pi$
$179$	−2.80091e7	+	2.80091e7i	−0.0272827	+	0.0272827i	0.693334	+	0.720617i	$0.256141\pi$
$180$		0			0
$181$	8.25608e8	−	8.25608e8i	0.769236	−	0.769236i	−0.208736	−	0.977972i	$-0.566935\pi$
$181$	8.25608e8	−	8.25608e8i	0.769236	−	0.769236i	0.977972	+	0.208736i	$0.0669350\pi$
$182$		0			0
$183$	−2.83771e8			−0.253025
$184$		0			0
$185$		−	4.16015e8i		−	0.355159i
$186$		0			0
$187$	6.70604e8	+	6.70604e8i	0.548403	+	0.548403i
$188$		0			0
$189$	2.27085e8	+	2.27085e8i	0.177968	+	0.177968i
$190$		0			0
$191$		−	1.01764e9i		−	0.764644i	−0.924029	−	0.382322i	$-0.875125\pi$
$191$		−	1.01764e9i		−	0.764644i	0.924029	−	0.382322i	$-0.124875\pi$
$192$		0			0
$193$	−6.23062e8			−0.449057			−0.224529	−	0.974467i	$-0.572084\pi$
$193$	−6.23062e8			−0.449057			−0.224529	+	0.974467i	$0.572084\pi$
$194$		0			0
$195$	964351.	−	964351.i	0.000666955	−	0.000666955i
$196$		0			0
$197$	9.82885e8	−	9.82885e8i	0.652586	−	0.652586i	−0.301029	−	0.953615i	$-0.597330\pi$
$197$	9.82885e8	−	9.82885e8i	0.652586	−	0.652586i	0.953615	+	0.301029i	$0.0973301\pi$
$198$		0			0
$199$	1.94440e9			1.23986			0.619931	−	0.784656i	$-0.287160\pi$
$199$	1.94440e9			1.23986			0.619931	+	0.784656i	$0.287160\pi$
$200$		0			0
$201$			4.42882e8i			0.271333i
$202$		0			0
$203$	−5.31457e8	−	5.31457e8i	−0.312956	−	0.312956i
$204$		0			0
$205$	1.36362e9	+	1.36362e9i	0.772110	+	0.772110i
$206$		0			0
$207$			4.12864e7i			0.0224867i
$208$		0			0
$209$	−2.18525e9			−1.14529
$210$		0			0
$211$	−1.17826e9	+	1.17826e9i	−0.594443	+	0.594443i	−0.938828	−	0.344385i	$-0.888087\pi$
$211$	−1.17826e9	+	1.17826e9i	−0.594443	+	0.594443i	0.344385	+	0.938828i	$0.388087\pi$
$212$		0			0
$213$	−7.87483e8	+	7.87483e8i	−0.382580	+	0.382580i
$214$		0			0
$215$	−1.60382e9			−0.750590
$216$		0			0
$217$		−	2.91417e9i		−	1.31424i
$218$		0			0
$219$	−1.32770e9	−	1.32770e9i	−0.577196	−	0.577196i
$220$		0			0
$221$	−2.67303e6	−	2.67303e6i	−0.00112056	−	0.00112056i
$222$		0			0
$223$		−	1.43941e9i		−	0.582056i	−0.956715	−	0.291028i	$-0.906003\pi$
$223$		−	1.43941e9i		−	0.582056i	0.956715	−	0.291028i	$-0.0939972\pi$
$224$		0			0
$225$	5.32365e8			0.207720
$226$		0			0
$227$	−2.47247e9	+	2.47247e9i	−0.931167	+	0.931167i	−0.997779	−	0.0666116i	$-0.978781\pi$
$227$	−2.47247e9	+	2.47247e9i	−0.931167	+	0.931167i	0.0666116	+	0.997779i	$0.478781\pi$
$228$		0			0
$229$	2.82439e9	−	2.82439e9i	1.02703	−	1.02703i	0.0274030	−	0.999624i	$-0.491276\pi$
$229$	2.82439e9	−	2.82439e9i	1.02703	−	1.02703i	0.999624	−	0.0274030i	$-0.00872373\pi$
$230$		0			0
$231$	2.80017e9			0.983416
$232$		0			0
$233$		−	4.00466e9i		−	1.35876i	−0.733788	−	0.679379i	$-0.762249\pi$
$233$		−	4.00466e9i		−	1.35876i	0.733788	−	0.679379i	$-0.237751\pi$
$234$		0			0
$235$	1.07661e9	+	1.07661e9i	0.353009	+	0.353009i
$236$		0			0
$237$	2.32224e9	+	2.32224e9i	0.736062	+	0.736062i
$238$		0			0
$239$		−	4.00603e9i		−	1.22779i	−0.789389	−	0.613893i	$-0.789603\pi$
$239$		−	4.00603e9i		−	1.22779i	0.789389	−	0.613893i	$-0.210397\pi$
$240$		0			0
$241$	−3.87088e9			−1.14747			−0.573736	−	0.819040i	$-0.694506\pi$
$241$	−3.87088e9			−1.14747			−0.573736	+	0.819040i	$0.694506\pi$
$242$		0			0
$243$	−1.58164e8	+	1.58164e8i	−0.0453609	+	0.0453609i
$244$		0			0
$245$	1.11091e9	−	1.11091e9i	0.308330	−	0.308330i
$246$		0			0
$247$	8.71042e6			0.00234019
$248$		0			0
$249$			4.99346e8i			0.129898i
$250$		0			0
$251$	−4.32665e9	−	4.32665e9i	−1.09008	−	1.09008i	−0.995520	−	0.0945555i	$-0.969857\pi$
$251$	−4.32665e9	−	4.32665e9i	−1.09008	−	1.09008i	−0.0945555	−	0.995520i	$-0.530143\pi$
$252$		0			0
$253$	2.54550e8	+	2.54550e8i	0.0621286	+	0.0621286i
$254$		0			0
$255$			8.92346e8i			0.211044i
$256$		0			0
$257$	−6.30105e9			−1.44438			−0.722188	−	0.691697i	$-0.756863\pi$
$257$	−6.30105e9			−1.44438			−0.722188	+	0.691697i	$0.756863\pi$
$258$		0			0
$259$	−2.40751e9	+	2.40751e9i	−0.535018	+	0.535018i
$260$		0			0
$261$	3.70157e8	−	3.70157e8i	0.0797671	−	0.0797671i
$262$		0			0
$263$	1.92249e9			0.401828			0.200914	−	0.979609i	$-0.435609\pi$
$263$	1.92249e9			0.401828			0.200914	+	0.979609i	$0.435609\pi$
$264$		0			0
$265$		−	4.74124e9i		−	0.961410i
$266$		0			0
$267$	3.34065e9	+	3.34065e9i	0.657334	+	0.657334i
$268$		0			0
$269$	−1.23805e9	−	1.23805e9i	−0.236444	−	0.236444i	0.578932	−	0.815376i	$-0.303470\pi$
$269$	−1.23805e9	−	1.23805e9i	−0.236444	−	0.236444i	−0.815376	+	0.578932i	$0.803470\pi$
$270$		0			0
$271$		−	3.07221e9i		−	0.569604i	−0.958586	−	0.284802i	$-0.908072\pi$
$271$		−	3.07221e9i		−	0.569604i	0.958586	−	0.284802i	$-0.0919279\pi$
$272$		0			0
$273$	−1.11615e7			−0.00200943
$274$		0			0
$275$	3.28228e9	−	3.28228e9i	0.573911	−	0.573911i
$276$		0			0
$277$	−2.14710e8	+	2.14710e8i	−0.0364697	+	0.0364697i	−0.725106	−	0.688637i	$-0.758209\pi$
$277$	−2.14710e8	+	2.14710e8i	−0.0364697	+	0.0364697i	0.688637	+	0.725106i	$0.258209\pi$
$278$		0			0
$279$	2.02971e9			0.334978
$280$		0			0
$281$		−	2.59845e9i		−	0.416763i	−0.978048	−	0.208381i	$-0.933180\pi$
$281$		−	2.59845e9i		−	0.416763i	0.978048	−	0.208381i	$-0.0668196\pi$
$282$		0			0
$283$	−1.05105e9	−	1.05105e9i	−0.163862	−	0.163862i	0.620413	−	0.784275i	$-0.286965\pi$
$283$	−1.05105e9	−	1.05105e9i	−0.163862	−	0.163862i	−0.784275	+	0.620413i	$0.786965\pi$
$284$		0			0
$285$	−1.45391e9	−	1.45391e9i	−0.220373	−	0.220373i
$286$		0			0
$287$		−	1.57828e10i		−	2.32624i
$288$		0			0
$289$	−4.50231e9			−0.645423
$290$		0			0
$291$	6.97017e8	−	6.97017e8i	0.0972011	−	0.0972011i
$292$		0			0
$293$	−7.05749e9	+	7.05749e9i	−0.957591	+	0.957591i	−0.999137	−	0.0415456i	$-0.986772\pi$
$293$	−7.05749e9	+	7.05749e9i	−0.957591	+	0.957591i	0.0415456	+	0.999137i	$0.486772\pi$
$294$		0			0
$295$	5.29087e9			0.698617
$296$		0			0
$297$			1.95031e9i			0.250656i
$298$		0			0
$299$	−1.01464e6	−	1.01464e6i	−0.000126948	−	0.000126948i
$300$		0			0
$301$	9.28142e9	+	9.28142e9i	1.13070	+	1.13070i
$302$		0			0
$303$			1.87720e8i			0.0222710i
$304$		0			0
$305$	−2.32810e9			−0.269031
$306$		0			0
$307$	8.00453e9	−	8.00453e9i	0.901119	−	0.901119i	−0.0944136	−	0.995533i	$-0.530098\pi$
$307$	8.00453e9	−	8.00453e9i	0.901119	−	0.901119i	0.995533	+	0.0944136i	$0.0300976\pi$
$308$		0			0
$309$	5.97152e9	−	5.97152e9i	0.655015	−	0.655015i
$310$		0			0
$311$	−3.34398e9			−0.357456			−0.178728	−	0.983899i	$-0.557198\pi$
$311$	−3.34398e9			−0.357456			−0.178728	+	0.983899i	$0.557198\pi$
$312$		0			0
$313$			8.74516e9i			0.911151i	0.890197	+	0.455575i	$0.150566\pi$
$313$			8.74516e9i			0.911151i	−0.890197	+	0.455575i	$0.849434\pi$
$314$		0			0
$315$	1.86304e9	+	1.86304e9i	0.189226	+	0.189226i
$316$		0			0
$317$	4.28630e9	+	4.28630e9i	0.424468	+	0.424468i	0.886739	−	0.462271i	$-0.152965\pi$
$317$	4.28630e9	+	4.28630e9i	0.424468	+	0.424468i	−0.462271	+	0.886739i	$0.652965\pi$
$318$		0			0
$319$		−	4.56438e9i		−	0.440777i
$320$		0			0
$321$	−7.31312e9			−0.688783
$322$		0			0
$323$	−4.03002e9	+	4.03002e9i	−0.370252	+	0.370252i
$324$		0			0
$325$	−1.30832e7	+	1.30832e7i	−0.00117268	+	0.00117268i
$326$		0			0
$327$	1.64233e9			0.143638
$328$		0			0
$329$		−	1.24608e10i		−	1.06356i
$330$		0			0
$331$	4.73680e9	+	4.73680e9i	0.394615	+	0.394615i	0.876329	−	0.481714i	$-0.159986\pi$
$331$	4.73680e9	+	4.73680e9i	0.394615	+	0.394615i	−0.481714	+	0.876329i	$0.659986\pi$
$332$		0			0
$333$	−1.67682e9	−	1.67682e9i	−0.136367	−	0.136367i
$334$		0			0
$335$			3.63347e9i			0.288497i
$336$		0			0
$337$	7.25132e9			0.562209			0.281104	−	0.959677i	$-0.409299\pi$
$337$	7.25132e9			0.562209			0.281104	+	0.959677i	$0.409299\pi$
$338$		0			0
$339$	−7.87398e9	+	7.87398e9i	−0.596205	+	0.596205i
$340$		0			0
$341$	1.25141e10	−	1.25141e10i	0.925512	−	0.925512i
$342$		0			0
$343$	5.24366e9			0.378842
$344$		0			0
$345$			3.38720e8i			0.0239092i
$346$		0			0
$347$	−9.09788e9	−	9.09788e9i	−0.627512	−	0.627512i	0.319929	−	0.947441i	$-0.396341\pi$
$347$	−9.09788e9	−	9.09788e9i	−0.627512	−	0.627512i	−0.947441	+	0.319929i	$0.896341\pi$
$348$		0			0
$349$	−3.60901e9	−	3.60901e9i	−0.243269	−	0.243269i	0.574932	−	0.818201i	$-0.305028\pi$
$349$	−3.60901e9	−	3.60901e9i	−0.243269	−	0.243269i	−0.818201	+	0.574932i	$0.805028\pi$
$350$		0			0
$351$		−	7.77394e6i		−	0.000512168i
$352$		0			0
$353$	−6.40769e9			−0.412670			−0.206335	−	0.978481i	$-0.566154\pi$
$353$	−6.40769e9			−0.412670			−0.206335	+	0.978481i	$0.566154\pi$
$354$		0			0
$355$	−6.46063e9	+	6.46063e9i	−0.406781	+	0.406781i
$356$		0			0
$357$	5.16406e9	−	5.16406e9i	0.317920	−	0.317920i
$358$		0			0
$359$	−1.09610e10			−0.659891			−0.329946	−	0.944000i	$-0.607030\pi$
$359$	−1.09610e10			−0.659891			−0.329946	+	0.944000i	$0.607030\pi$
$360$		0			0
$361$			3.85121e9i			0.226761i
$362$		0			0
$363$	4.93612e9	+	4.93612e9i	0.284289	+	0.284289i
$364$		0			0
$365$	−1.08926e10	−	1.08926e10i	−0.613708	−	0.613708i
$366$		0			0
$367$			3.06694e10i			1.69060i	0.534291	+	0.845300i	$0.320579\pi$
$367$			3.06694e10i			1.69060i	−0.534291	+	0.845300i	$0.679421\pi$
$368$		0			0
$369$	1.09926e10			0.592919
$370$		0			0
$371$	−2.74378e10	+	2.74378e10i	−1.44829	+	1.44829i
$372$		0			0
$373$	−1.99773e10	+	1.99773e10i	−1.03205	+	1.03205i	−0.0325850	+	0.999469i	$0.510374\pi$
$373$	−1.99773e10	+	1.99773e10i	−1.03205	+	1.03205i	−0.999469	+	0.0325850i	$0.989626\pi$
$374$		0			0
$375$	1.13764e10			0.575279
$376$		0			0
$377$			1.81936e7i			0.000900646i
$378$		0			0
$379$	7.49423e8	+	7.49423e8i	0.0363220	+	0.0363220i	0.725035	−	0.688713i	$-0.241824\pi$
$379$	7.49423e8	+	7.49423e8i	0.0363220	+	0.0363220i	−0.688713	+	0.725035i	$0.741824\pi$
$380$		0			0
$381$	1.41887e10	+	1.41887e10i	0.673351	+	0.673351i
$382$		0			0
$383$		−	5.73000e9i		−	0.266293i	−0.991096	−	0.133146i	$-0.957492\pi$
$383$		−	5.73000e9i		−	0.266293i	0.991096	−	0.133146i	$-0.0425080\pi$
$384$		0			0
$385$	2.29731e10			1.04562
$386$		0			0
$387$	−6.46447e9	+	6.46447e9i	−0.288197	+	0.288197i
$388$		0			0
$389$	−4.07315e9	+	4.07315e9i	−0.177882	+	0.177882i	−0.790432	−	0.612550i	$-0.790144\pi$
$389$	−4.07315e9	+	4.07315e9i	−0.177882	+	0.177882i	0.612550	+	0.790432i	$0.290144\pi$
$390$		0			0
$391$	9.38879e8			0.0401701
$392$		0			0
$393$			1.45738e10i			0.610944i
$394$		0			0
$395$	1.90520e10	+	1.90520e10i	0.782624	+	0.782624i
$396$		0			0
$397$	3.21221e10	+	3.21221e10i	1.29313	+	1.29313i	0.932842	+	0.360287i	$0.117321\pi$
$397$	3.21221e10	+	3.21221e10i	1.29313	+	1.29313i	0.360287	+	0.932842i	$0.382679\pi$
$398$		0			0
$399$			1.68278e10i			0.663949i
$400$		0			0
$401$	−3.00084e9			−0.116055			−0.0580277	−	0.998315i	$-0.518481\pi$
$401$	−3.00084e9			−0.116055			−0.0580277	+	0.998315i	$0.518481\pi$
$402$		0			0
$403$	−4.98812e7	+	4.98812e7i	−0.00189111	+	0.00189111i
$404$		0			0
$405$	−1.29760e9	+	1.29760e9i	−0.0482303	+	0.0482303i
$406$		0			0
$407$	−2.06767e10			−0.753536
$408$		0			0
$409$			1.45503e10i			0.519970i	0.965613	+	0.259985i	$0.0837177\pi$
$409$			1.45503e10i			0.519970i	−0.965613	+	0.259985i	$0.916282\pi$
$410$		0			0
$411$	8.80565e9	+	8.80565e9i	0.308599	+	0.308599i
$412$		0			0
$413$	−3.06186e10	−	3.06186e10i	−1.05241	−	1.05241i
$414$		0			0
$415$			4.09671e9i			0.138116i
$416$		0			0
$417$	2.82624e10			0.934685
$418$		0			0
$419$	6.20388e9	−	6.20388e9i	0.201283	−	0.201283i	−0.599267	−	0.800550i	$-0.704541\pi$
$419$	6.20388e9	−	6.20388e9i	0.201283	−	0.201283i	0.800550	+	0.599267i	$0.204541\pi$
$420$		0			0
$421$	−3.11957e10	+	3.11957e10i	−0.993040	+	0.993040i	−0.999976	−	0.00693560i	$-0.997792\pi$
$421$	−3.11957e10	+	3.11957e10i	−0.993040	+	0.993040i	0.00693560	+	0.999976i	$0.497792\pi$
$422$		0			0
$423$	8.67888e9			0.271083
$424$		0			0
$425$		−	1.21063e10i		−	0.371070i
$426$		0			0
$427$	1.34729e10	+	1.34729e10i	0.405274	+	0.405274i
$428$		0			0
$429$	−4.79300e7	−	4.79300e7i	−0.00141507	−	0.00141507i
$430$		0			0
$431$			1.45305e10i			0.421087i	0.977584	+	0.210544i	$0.0675234\pi$
$431$			1.45305e10i			0.421087i	−0.977584	+	0.210544i	$0.932477\pi$
$432$		0			0
$433$	9.84633e9			0.280106			0.140053	−	0.990144i	$-0.455273\pi$
$433$	9.84633e9			0.280106			0.140053	+	0.990144i	$0.455273\pi$
$434$		0			0
$435$	3.03682e9	−	3.03682e9i	0.0848130	−	0.0848130i
$436$		0			0
$437$	−1.52973e9	+	1.52973e9i	−0.0419458	+	0.0419458i
$438$		0			0
$439$	−5.46119e10			−1.47038			−0.735189	−	0.677862i	$-0.762907\pi$
$439$	−5.46119e10			−1.47038			−0.735189	+	0.677862i	$0.762907\pi$
$440$		0			0
$441$		−	8.95543e9i		−	0.236773i
$442$		0			0
$443$	−2.33132e10	−	2.33132e10i	−0.605323	−	0.605323i	0.336397	−	0.941720i	$-0.390792\pi$
$443$	−2.33132e10	−	2.33132e10i	−0.605323	−	0.605323i	−0.941720	+	0.336397i	$0.890792\pi$
$444$		0			0
$445$	2.74072e10	+	2.74072e10i	0.698916	+	0.698916i
$446$		0			0
$447$			2.04870e10i			0.513156i
$448$		0			0
$449$	−4.03382e10			−0.992502			−0.496251	−	0.868179i	$-0.665290\pi$
$449$	−4.03382e10			−0.992502			−0.496251	+	0.868179i	$0.665290\pi$
$450$		0			0
$451$	6.77746e10	−	6.77746e10i	1.63818	−	1.63818i
$452$		0			0
$453$	−2.35565e10	+	2.35565e10i	−0.559394	+	0.559394i
$454$		0			0
$455$	−9.15707e7			−0.00213654
$456$		0			0
$457$			1.77877e10i			0.407808i	0.978991	+	0.203904i	$0.0653630\pi$
$457$			1.77877e10i			0.407808i	−0.978991	+	0.203904i	$0.934637\pi$
$458$		0			0
$459$	3.59674e9	+	3.59674e9i	0.0810324	+	0.0810324i
$460$		0			0
$461$	−5.65754e10	−	5.65754e10i	−1.25263	−	1.25263i	−0.954535	−	0.298099i	$-0.903647\pi$
$461$	−5.65754e10	−	5.65754e10i	−1.25263	−	1.25263i	−0.298099	−	0.954535i	$-0.596353\pi$
$462$		0			0
$463$		−	6.34281e10i		−	1.38025i	−0.723690	−	0.690125i	$-0.757555\pi$
$463$		−	6.34281e10i		−	1.38025i	0.723690	−	0.690125i	$-0.242445\pi$
$464$		0			0
$465$	1.66520e10			0.356168
$466$		0			0
$467$	2.52894e10	−	2.52894e10i	0.531706	−	0.531706i	−0.389374	−	0.921080i	$-0.627309\pi$
$467$	2.52894e10	−	2.52894e10i	0.531706	−	0.531706i	0.921080	+	0.389374i	$0.127309\pi$
$468$		0			0
$469$	2.10271e10	−	2.10271e10i	0.434598	−	0.434598i
$470$		0			0
$471$	1.34040e10			0.272364
$472$		0			0
$473$			7.97130e10i			1.59252i
$474$		0			0
$475$	1.97250e10	+	1.97250e10i	0.387474	+	0.387474i
$476$		0			0
$477$	−1.91103e10	−	1.91103e10i	−0.369143	−	0.369143i
$478$		0			0
$479$			8.00871e10i			1.52132i	0.649151	+	0.760660i	$0.275124\pi$
$479$			8.00871e10i			1.52132i	−0.649151	+	0.760660i	$0.724876\pi$
$480$		0			0
$481$	8.24175e7			0.00153971
$482$		0			0
$483$	1.96019e9	−	1.96019e9i	0.0360172	−	0.0360172i
$484$		0			0
$485$	5.71843e9	−	5.71843e9i	0.103350	−	0.103350i
$486$		0			0
$487$	2.29804e9			0.0408546			0.0204273	−	0.999791i	$-0.493497\pi$
$487$	2.29804e9			0.0408546			0.0204273	+	0.999791i	$0.493497\pi$
$488$		0			0
$489$			6.48098e10i			1.13346i
$490$		0			0
$491$	−6.62220e10	−	6.62220e10i	−1.13940	−	1.13940i	−0.988558	−	0.150842i	$-0.951801\pi$
$491$	−6.62220e10	−	6.62220e10i	−1.13940	−	1.13940i	−0.150842	−	0.988558i	$-0.548199\pi$
$492$		0			0
$493$	−8.41760e9	−	8.41760e9i	−0.142495	−	0.142495i
$494$		0			0
$495$			1.60006e10i			0.266511i
$496$		0			0
$497$	7.47760e10			1.22557
$498$		0			0
$499$	5.75501e9	−	5.75501e9i	0.0928205	−	0.0928205i	−0.659172	−	0.751992i	$-0.729093\pi$
$499$	5.75501e9	−	5.75501e9i	0.0928205	−	0.0928205i	0.751992	+	0.659172i	$0.229093\pi$
$500$		0			0
$501$	2.64072e10	−	2.64072e10i	0.419152	−	0.419152i
$502$		0			0
$503$	5.76352e10			0.900359			0.450180	−	0.892938i	$-0.351360\pi$
$503$	5.76352e10			0.900359			0.450180	+	0.892938i	$0.351360\pi$
$504$		0			0
$505$			1.54008e9i			0.0236798i
$506$		0			0
$507$	−2.69745e10	−	2.69745e10i	−0.408245	−	0.408245i
$508$		0			0
$509$	−2.41241e10	−	2.41241e10i	−0.359401	−	0.359401i	0.504191	−	0.863592i	$-0.331791\pi$
$509$	−2.41241e10	−	2.41241e10i	−0.359401	−	0.359401i	−0.863592	+	0.504191i	$0.831791\pi$
$510$		0			0
$511$			1.26073e11i			1.84900i
$512$		0			0
$513$	−1.17205e10			−0.169229
$514$		0			0
$515$	4.89913e10	−	4.89913e10i	0.696450	−	0.696450i
$516$		0			0
$517$	5.35094e10	−	5.35094e10i	0.748976	−	0.748976i
$518$		0			0
$519$	2.72654e9			0.0375787
$520$		0			0
$521$			2.14533e10i			0.291168i	0.989346	+	0.145584i	$0.0465061\pi$
$521$			2.14533e10i			0.291168i	−0.989346	+	0.145584i	$0.953494\pi$
$522$		0			0
$523$	1.31508e10	+	1.31508e10i	0.175770	+	0.175770i	0.789509	−	0.613739i	$-0.210335\pi$
$523$	1.31508e10	+	1.31508e10i	0.175770	+	0.175770i	−0.613739	+	0.789509i	$0.710335\pi$
$524$		0			0
$525$	−2.52755e10	−	2.52755e10i	−0.332708	−	0.332708i
$526$		0			0
$527$		−	4.61568e10i		−	0.598402i
$528$		0			0
$529$	−7.79546e10			−0.995449
$530$		0			0
$531$	2.13257e10	−	2.13257e10i	0.268241	−	0.268241i
$532$		0			0
$533$	−2.70150e8	+	2.70150e8i	−0.00334731	+	0.00334731i
$534$		0			0
$535$	−5.99979e10			−0.732354
$536$		0			0
$537$			1.85242e9i			0.0222762i
$538$		0			0
$539$	−5.52145e10	−	5.52145e10i	−0.654181	−	0.654181i
$540$		0			0
$541$	−1.06324e11	−	1.06324e11i	−1.24121	−	1.24121i	−0.959501	−	0.281704i	$-0.909100\pi$
$541$	−1.06324e11	−	1.06324e11i	−1.24121	−	1.24121i	−0.281704	−	0.959501i	$-0.590900\pi$
$542$		0			0
$543$		−	5.46026e10i		−	0.628078i
$544$		0			0
$545$	1.34739e10			0.152724
$546$		0			0
$547$	7.97862e10	−	7.97862e10i	0.891207	−	0.891207i	−0.103430	−	0.994637i	$-0.532982\pi$
$547$	7.97862e10	−	7.97862e10i	0.891207	−	0.891207i	0.994637	+	0.103430i	$0.0329817\pi$
$548$		0			0
$549$	−9.38378e9	+	9.38378e9i	−0.103297	+	0.103297i
$550$		0			0
$551$	2.74298e10			0.297589
$552$		0			0
$553$		−	2.20511e11i		−	2.35792i
$554$		0			0
$555$	−1.37568e10	−	1.37568e10i	−0.144993	−	0.144993i
$556$		0			0
$557$	−4.43348e8	−	4.43348e8i	−0.00460600	−	0.00460600i	0.704800	−	0.709406i	$-0.251037\pi$
$557$	−4.43348e8	−	4.43348e8i	−0.00460600	−	0.00460600i	−0.709406	+	0.704800i	$0.751037\pi$
$558$		0			0
$559$		−	3.17736e8i		−	0.00325401i
$560$		0			0
$561$	4.43512e10			0.447769
$562$		0			0
$563$	−1.99839e9	+	1.99839e9i	−0.0198906	+	0.0198906i	−0.716982	−	0.697092i	$-0.754477\pi$
$563$	−1.99839e9	+	1.99839e9i	−0.0198906	+	0.0198906i	0.697092	+	0.716982i	$0.254477\pi$
$564$		0			0
$565$	−6.45993e10	+	6.45993e10i	−0.633920	+	0.633920i
$566$		0			0
$567$	1.50186e10			0.145310
$568$		0			0
$569$		−	8.53338e10i		−	0.814089i	−0.913408	−	0.407044i	$-0.866559\pi$
$569$		−	8.53338e10i		−	0.814089i	0.913408	−	0.407044i	$-0.133441\pi$
$570$		0			0
$571$	6.51521e10	+	6.51521e10i	0.612892	+	0.612892i	0.943698	−	0.330807i	$-0.107321\pi$
$571$	6.51521e10	+	6.51521e10i	0.612892	+	0.612892i	−0.330807	+	0.943698i	$0.607321\pi$
$572$		0			0
$573$	−3.36513e10	−	3.36513e10i	−0.312165	−	0.312165i
$574$		0			0
$575$		−	4.59535e9i		−	0.0420385i
$576$		0			0
$577$	1.10409e11			0.996099			0.498050	−	0.867148i	$-0.334050\pi$
$577$	1.10409e11			0.996099			0.498050	+	0.867148i	$0.334050\pi$
$578$		0			0
$579$	−2.06035e10	+	2.06035e10i	−0.183327	+	0.183327i
$580$		0			0
$581$	2.37079e10	−	2.37079e10i	0.208060	−	0.208060i
$582$		0			0
$583$	−2.35648e11			−2.03981
$584$		0			0
$585$		−	6.37785e7i		−	0.000544567i
$586$		0			0
$587$	−9.02561e10	−	9.02561e10i	−0.760193	−	0.760193i	0.216164	−	0.976357i	$-0.430645\pi$
$587$	−9.02561e10	−	9.02561e10i	−0.760193	−	0.760193i	−0.976357	+	0.216164i	$0.930645\pi$
$588$		0			0
$589$	7.52040e10	+	7.52040e10i	0.624855	+	0.624855i
$590$		0			0
$591$		−	6.50043e10i		−	0.532834i
$592$		0			0
$593$	1.75238e11			1.41713			0.708566	−	0.705644i	$-0.249342\pi$
$593$	1.75238e11			1.41713			0.708566	+	0.705644i	$0.249342\pi$
$594$		0			0
$595$	4.23667e10	−	4.23667e10i	0.338031	−	0.338031i
$596$		0			0
$597$	6.42977e10	−	6.42977e10i	0.506172	−	0.506172i
$598$		0			0
$599$	−1.74002e11			−1.35160			−0.675799	−	0.737086i	$-0.736201\pi$
$599$	−1.74002e11			−1.35160			−0.675799	+	0.737086i	$0.736201\pi$
$600$		0			0
$601$		−	7.22356e10i		−	0.553673i	−0.960917	−	0.276837i	$-0.910714\pi$
$601$		−	7.22356e10i		−	0.553673i	0.960917	−	0.276837i	$-0.0892861\pi$
$602$		0			0
$603$	1.46453e10	+	1.46453e10i	0.110771	+	0.110771i
$604$		0			0
$605$	4.04967e10	+	4.04967e10i	0.302272	+	0.302272i
$606$		0			0
$607$			1.60214e11i			1.18017i	0.807341	+	0.590086i	$0.200906\pi$
$607$			1.60214e11i			1.18017i	−0.807341	+	0.590086i	$0.799094\pi$
$608$		0			0
$609$	−3.51485e10			−0.255528
$610$		0			0
$611$	−2.13289e8	+	2.13289e8i	−0.00153039	+	0.00153039i
$612$		0			0
$613$	−7.01772e10	+	7.01772e10i	−0.496997	+	0.496997i	−0.910502	−	0.413505i	$-0.864305\pi$
$613$	−7.01772e10	+	7.01772e10i	−0.496997	+	0.496997i	0.413505	+	0.910502i	$0.364305\pi$
$614$		0			0
$615$	9.01850e10			0.630426
$616$		0			0
$617$			2.04847e11i			1.41348i	0.707476	+	0.706738i	$0.249834\pi$
$617$			2.04847e11i			1.41348i	−0.707476	+	0.706738i	$0.750166\pi$
$618$		0			0
$619$	−3.37307e10	−	3.37307e10i	−0.229754	−	0.229754i	0.582836	−	0.812590i	$-0.301943\pi$
$619$	−3.37307e10	−	3.37307e10i	−0.229754	−	0.229754i	−0.812590	+	0.582836i	$0.801943\pi$
$620$		0			0
$621$	1.36526e9	+	1.36526e9i	0.00918016	+	0.00918016i
$622$		0			0
$623$		−	3.17214e11i		−	2.10572i
$624$		0			0
$625$	−1.75335e9			−0.0114908
$626$		0			0
$627$	−7.22621e10	+	7.22621e10i	−0.467563	+	0.467563i
$628$		0			0
$629$	−3.81318e10	+	3.81318e10i	−0.243604	+	0.243604i
$630$		0			0
$631$	4.86240e10			0.306714			0.153357	−	0.988171i	$-0.450992\pi$
$631$	4.86240e10			0.306714			0.153357	+	0.988171i	$0.450992\pi$
$632$		0			0
$633$			7.79255e10i			0.485361i
$634$		0			0
$635$	1.16406e11	+	1.16406e11i	0.715945	+	0.715945i
$636$		0			0
$637$	2.20085e8	+	2.20085e8i	0.00133670	+	0.00133670i
$638$		0			0
$639$			5.20811e10i			0.312376i
$640$		0			0
$641$	−1.56196e11			−0.925206			−0.462603	−	0.886566i	$-0.653084\pi$
$641$	−1.56196e11			−0.925206			−0.462603	+	0.886566i	$0.653084\pi$
$642$		0			0
$643$	−7.22237e10	+	7.22237e10i	−0.422509	+	0.422509i	−0.886067	−	0.463558i	$-0.846573\pi$
$643$	−7.22237e10	+	7.22237e10i	−0.422509	+	0.422509i	0.463558	+	0.886067i	$0.346573\pi$
$644$		0			0
$645$	−5.30354e10	+	5.30354e10i	−0.306427	+	0.306427i
$646$		0			0
$647$	1.71618e11			0.979370			0.489685	−	0.871899i	$-0.337112\pi$
$647$	1.71618e11			0.979370			0.489685	+	0.871899i	$0.337112\pi$
$648$		0			0
$649$		−	2.62966e11i		−	1.48225i
$650$		0			0
$651$	−9.63662e10	−	9.63662e10i	−0.536538	−	0.536538i
$652$		0			0
$653$	−2.44488e11	−	2.44488e11i	−1.34464	−	1.34464i	−0.891381	−	0.453255i	$-0.850263\pi$
$653$	−2.44488e11	−	2.44488e11i	−1.34464	−	1.34464i	−0.453255	−	0.891381i	$-0.649737\pi$
$654$		0			0
$655$			1.19565e11i			0.649590i
$656$		0			0
$657$	−8.78091e10			−0.471279
$658$		0			0
$659$	−1.29470e11	+	1.29470e11i	−0.686478	+	0.686478i	−0.961452	−	0.274973i	$-0.911331\pi$
$659$	−1.29470e11	+	1.29470e11i	−0.686478	+	0.686478i	0.274973	+	0.961452i	$0.411331\pi$
$660$		0			0
$661$	7.86836e10	−	7.86836e10i	0.412172	−	0.412172i	−0.470322	−	0.882495i	$-0.655862\pi$
$661$	7.86836e10	−	7.86836e10i	0.412172	−	0.412172i	0.882495	+	0.470322i	$0.155862\pi$
$662$		0			0
$663$	−1.76784e8			−0.000914933
$664$		0			0
$665$			1.38057e11i			0.705949i
$666$		0			0
$667$	−3.19518e9	−	3.19518e9i	−0.0161433	−	0.0161433i
$668$		0			0
$669$	−4.75985e10	−	4.75985e10i	−0.237623	−	0.237623i
$670$		0			0
$671$			1.15711e11i			0.570800i
$672$		0			0
$673$	2.87102e11			1.39951			0.699754	−	0.714384i	$-0.253293\pi$
$673$	2.87102e11			1.39951			0.699754	+	0.714384i	$0.253293\pi$
$674$		0			0
$675$	1.76043e10	−	1.76043e10i	0.0848015	−	0.0848015i
$676$		0			0
$677$	1.63329e11	−	1.63329e11i	0.777517	−	0.777517i	−0.201891	−	0.979408i	$-0.564709\pi$
$677$	1.63329e11	−	1.63329e11i	0.777517	−	0.777517i	0.979408	+	0.201891i	$0.0647087\pi$
$678$		0			0
$679$	−6.61857e10			−0.311376
$680$		0			0
$681$			1.63520e11i			0.760295i
$682$		0			0
$683$	2.47151e11	+	2.47151e11i	1.13574	+	1.13574i	0.989205	+	0.146539i	$0.0468133\pi$
$683$	2.47151e11	+	2.47151e11i	1.13574	+	1.13574i	0.146539	+	0.989205i	$0.453187\pi$
$684$		0			0
$685$	7.22429e10	+	7.22429e10i	0.328120	+	0.328120i
$686$		0			0
$687$		−	1.86794e11i		−	0.838564i
$688$		0			0
$689$	9.39295e8			0.00416797
$690$		0			0
$691$	8.24396e10	−	8.24396e10i	0.361596	−	0.361596i	−0.502804	−	0.864400i	$-0.667698\pi$
$691$	8.24396e10	−	8.24396e10i	0.361596	−	0.361596i	0.864400	+	0.502804i	$0.167698\pi$
$692$		0			0
$693$	9.25965e10	−	9.25965e10i	0.401478	−	0.401478i
$694$		0			0
$695$	2.31869e11			0.993811
$696$		0			0
$697$		−	2.49979e11i		−	1.05919i
$698$		0			0
$699$	−1.32426e11	−	1.32426e11i	−0.554710	−	0.554710i
$700$		0			0
$701$	2.95574e11	+	2.95574e11i	1.22404	+	1.22404i	0.966184	+	0.257853i	$0.0830152\pi$
$701$	2.95574e11	+	2.95574e11i	1.22404	+	1.22404i	0.257853	+	0.966184i	$0.416985\pi$
$702$		0			0
$703$		−	1.24258e11i		−	0.508747i
$704$		0			0
$705$	7.12028e10			0.288231
$706$		0			0
$707$	8.91255e9	−	8.91255e9i	0.0356717	−	0.0356717i
$708$		0			0
$709$	−9.26548e10	+	9.26548e10i	−0.366676	+	0.366676i	−0.866264	−	0.499587i	$-0.833485\pi$
$709$	−9.26548e10	+	9.26548e10i	−0.366676	+	0.366676i	0.499587	+	0.866264i	$0.333485\pi$
$710$		0			0
$711$	1.53585e11			0.600992
$712$		0			0
$713$		−	1.75204e10i		−	0.0677930i
$714$		0			0
$715$	−3.93225e8	−	3.93225e8i	−0.00150458	−	0.00150458i
$716$		0			0
$717$	−1.32472e11	−	1.32472e11i	−0.501241	−	0.501241i
$718$		0			0
$719$			2.75614e11i			1.03130i	0.856799	+	0.515651i	$0.172450\pi$
$719$			2.75614e11i			1.03130i	−0.856799	+	0.515651i	$0.827550\pi$
$720$		0			0
$721$	−5.67031e11			−2.09829
$722$		0			0
$723$	−1.28003e11	+	1.28003e11i	−0.468453	+	0.468453i
$724$		0			0
$725$	−4.12000e10	+	4.12000e10i	−0.149123	+	0.149123i
$726$		0			0
$727$	−2.56071e11			−0.916689			−0.458345	−	0.888775i	$-0.651557\pi$
$727$	−2.56071e11			−0.916689			−0.458345	+	0.888775i	$0.651557\pi$
$728$		0			0
$729$			1.04604e10i			0.0370370i
$730$		0			0
$731$	1.47006e11	+	1.47006e11i	0.514832	+	0.514832i
$732$		0			0
$733$	1.70023e11	+	1.70023e11i	0.588967	+	0.588967i	0.937352	−	0.348385i	$-0.113270\pi$
$733$	1.70023e11	+	1.70023e11i	0.588967	+	0.588967i	−0.348385	+	0.937352i	$0.613270\pi$
$734$		0			0
$735$		−	7.34717e10i		−	0.251751i
$736$		0			0
$737$	1.80590e11			0.612101
$738$		0			0
$739$	3.69241e11	−	3.69241e11i	1.23803	−	1.23803i	0.277228	−	0.960804i	$-0.410584\pi$
$739$	3.69241e11	−	3.69241e11i	1.23803	−	1.23803i	0.960804	−	0.277228i	$-0.0894157\pi$
$740$		0			0
$741$	2.88037e8	−	2.88037e8i	0.000955379	−	0.000955379i
$742$		0			0
$743$	1.74679e11			0.573173			0.286587	−	0.958054i	$-0.407479\pi$
$743$	1.74679e11			0.573173			0.286587	+	0.958054i	$0.407479\pi$
$744$		0			0
$745$			1.68079e11i			0.545617i
$746$		0			0
$747$	1.65124e10	+	1.65124e10i	0.0530308	+	0.0530308i
$748$		0			0
$749$	3.47211e11	+	3.47211e11i	1.10323	+	1.10323i
$750$		0			0
$751$		−	2.76638e11i		−	0.869665i	−0.900511	−	0.434833i	$-0.856807\pi$
$751$		−	2.76638e11i		−	0.869665i	0.900511	−	0.434833i	$-0.143193\pi$
$752$		0			0
$753$	−2.86148e11			−0.890043
$754$		0			0
$755$	−1.93261e11	+	1.93261e11i	−0.594780	+	0.594780i
$756$		0			0
$757$	−4.35648e11	+	4.35648e11i	−1.32664	+	1.32664i	−0.418355	+	0.908283i	$0.637393\pi$
$757$	−4.35648e11	+	4.35648e11i	−1.32664	+	1.32664i	−0.908283	+	0.418355i	$0.862607\pi$
$758$		0			0
$759$	1.68350e10			0.0507278
$760$		0			0
$761$			4.59202e11i			1.36920i	0.728921	+	0.684598i	$0.240022\pi$
$761$			4.59202e11i			1.36920i	−0.728921	+	0.684598i	$0.759978\pi$
$762$		0			0
$763$	−7.79744e10	−	7.79744e10i	−0.230067	−	0.230067i
$764$		0			0
$765$	2.95082e10	+	2.95082e10i	0.0861583	+	0.0861583i
$766$		0			0
$767$			1.04818e9i			0.00302870i
$768$		0			0
$769$	−5.72952e11			−1.63837			−0.819187	−	0.573526i	$-0.805575\pi$
$769$	−5.72952e11			−1.63837			−0.819187	+	0.573526i	$0.805575\pi$
$770$		0			0
$771$	−2.08364e11	+	2.08364e11i	−0.589664	+	0.589664i
$772$		0			0
$773$	−9.66765e10	+	9.66765e10i	−0.270771	+	0.270771i	−0.829411	−	0.558639i	$-0.811324\pi$
$773$	−9.66765e10	+	9.66765e10i	−0.270771	+	0.270771i	0.558639	+	0.829411i	$0.311324\pi$
$774$		0			0
$775$	−2.25915e11			−0.626236
$776$		0			0
$777$			1.59223e11i			0.436840i
$778$		0			0
$779$	4.07294e11	+	4.07294e11i	1.10601	+	1.10601i
$780$		0			0
$781$	3.21105e11	+	3.21105e11i	0.863063	+	0.863063i
$782$		0			0
$783$		−	2.44808e10i		−	0.0651296i
$784$		0			0
$785$	1.09968e11			0.289594
$786$		0			0
$787$	−3.70067e11	+	3.70067e11i	−0.964675	+	0.964675i	−0.999397	−	0.0347224i	$-0.988945\pi$
$787$	−3.70067e11	+	3.70067e11i	−0.964675	+	0.964675i	0.0347224	+	0.999397i	$0.488945\pi$
$788$		0			0
$789$	6.35730e10	−	6.35730e10i	0.164046	−	0.164046i
$790$		0			0
$791$	7.47680e11			1.90990
$792$		0			0
$793$		−	4.61224e8i		−	0.00116632i
$794$		0			0
$795$	−1.56784e11	−	1.56784e11i	−0.392494	−	0.392494i
$796$		0			0
$797$	1.78890e11	+	1.78890e11i	0.443357	+	0.443357i	0.893139	−	0.449782i	$-0.148498\pi$
$797$	1.78890e11	+	1.78890e11i	0.443357	+	0.443357i	−0.449782	+	0.893139i	$0.648498\pi$
$798$		0			0
$799$		−	1.97363e11i		−	0.484260i
$800$		0			0
$801$	2.20938e11			0.536711
$802$		0			0
$803$	−5.41384e11	+	5.41384e11i	−1.30210	+	1.30210i
$804$		0			0
$805$	1.60817e10	−	1.60817e10i	0.0382956	−	0.0382956i
$806$		0			0
$807$	−8.18798e10			−0.193056
$808$		0			0
$809$		−	2.64934e11i		−	0.618506i	−0.950980	−	0.309253i	$-0.899921\pi$
$809$		−	2.64934e11i		−	0.618506i	0.950980	−	0.309253i	$-0.100079\pi$
$810$		0			0
$811$	5.54367e11	+	5.54367e11i	1.28149	+	1.28149i	0.939822	+	0.341665i	$0.110991\pi$
$811$	5.54367e11	+	5.54367e11i	1.28149	+	1.28149i	0.341665	+	0.939822i	$0.389009\pi$
$812$		0			0
$813$	−1.01592e11	−	1.01592e11i	−0.232540	−	0.232540i
$814$		0			0
$815$			5.31709e11i			1.20516i
$816$		0			0
$817$	−4.79038e11			−1.07518
$818$		0			0
$819$	−3.69090e8	+	3.69090e8i	−0.000820345	+	0.000820345i
$820$		0			0
$821$	−3.67950e11	+	3.67950e11i	−0.809872	+	0.809872i	−0.984614	−	0.174742i	$-0.944091\pi$
$821$	−3.67950e11	+	3.67950e11i	−0.809872	+	0.809872i	0.174742	+	0.984614i	$0.444091\pi$
$822$		0			0
$823$	−3.90849e11			−0.851942			−0.425971	−	0.904737i	$-0.640067\pi$
$823$	−3.90849e11			−0.851942			−0.425971	+	0.904737i	$0.640067\pi$
$824$		0			0
$825$		−	2.17077e11i		−	0.468596i
$826$		0			0
$827$	−4.78084e11	−	4.78084e11i	−1.02207	−	1.02207i	−0.999751	−	0.0223220i	$-0.992894\pi$
$827$	−4.78084e11	−	4.78084e11i	−1.02207	−	1.02207i	−0.0223220	−	0.999751i	$-0.507106\pi$
$828$		0			0
$829$	5.05866e11	+	5.05866e11i	1.07107	+	1.07107i	0.997273	+	0.0737948i	$0.0235110\pi$
$829$	5.05866e11	+	5.05866e11i	1.07107	+	1.07107i	0.0737948	+	0.997273i	$0.476489\pi$
$830$		0			0
$831$			1.42001e10i			0.0297774i
$832$		0			0
$833$	−2.03652e11			−0.422969
$834$		0			0
$835$	2.16648e11	−	2.16648e11i	0.445666	−	0.445666i
$836$		0			0
$837$	6.71186e10	−	6.71186e10i	0.136754	−	0.136754i
$838$		0			0
$839$	7.72532e11			1.55908			0.779541	−	0.626351i	$-0.215452\pi$
$839$	7.72532e11			1.55908			0.779541	+	0.626351i	$0.215452\pi$
$840$		0			0
$841$		−	4.42953e11i		−	0.885470i
$842$		0			0
$843$	−8.59258e10	−	8.59258e10i	−0.170143	−	0.170143i
$844$		0			0
$845$	−2.21303e11	−	2.21303e11i	−0.434070	−	0.434070i
$846$		0			0
$847$		−	4.68713e11i		−	0.910697i
$848$		0			0
$849$	−6.95124e10			−0.133792
$850$		0			0
$851$	−1.44742e10	+	1.44742e10i	−0.0275979	+	0.0275979i
$852$		0			0
$853$	4.84413e11	−	4.84413e11i	0.914998	−	0.914998i	−0.0816625	−	0.996660i	$-0.526023\pi$
$853$	4.84413e11	−	4.84413e11i	0.914998	−	0.914998i	0.996660	+	0.0816625i	$0.0260230\pi$
$854$		0			0
$855$	−9.61563e10			−0.179934
$856$		0			0
$857$			3.47582e11i			0.644369i	0.946677	+	0.322184i	$0.104417\pi$
$857$			3.47582e11i			0.644369i	−0.946677	+	0.322184i	$0.895583\pi$
$858$		0			0
$859$	−3.27033e9	−	3.27033e9i	−0.00600647	−	0.00600647i	0.704097	−	0.710104i	$-0.251352\pi$
$859$	−3.27033e9	−	3.27033e9i	−0.00600647	−	0.00600647i	−0.710104	+	0.704097i	$0.751352\pi$
$860$		0			0
$861$	−5.21906e11	−	5.21906e11i	−0.949685	−	0.949685i
$862$		0			0
$863$		−	3.08551e11i		−	0.556268i	−0.960542	−	0.278134i	$-0.910284\pi$
$863$		−	3.08551e11i		−	0.556268i	0.960542	−	0.278134i	$-0.0897160\pi$
$864$		0			0
$865$	2.23689e10			0.0399558
$866$		0			0
$867$	−1.48883e11	+	1.48883e11i	−0.263493	+	0.263493i
$868$		0			0
$869$	9.46921e11	−	9.46921e11i	1.66048	−	1.66048i
$870$		0			0
$871$	−7.19832e8			−0.00125071
$872$		0			0
$873$		−	4.60980e10i		−	0.0793644i
$874$		0			0
$875$	−5.40126e11	−	5.40126e11i	−0.921432	−	0.921432i
$876$		0			0
$877$	6.47410e11	+	6.47410e11i	1.09441	+	1.09441i	0.995052	+	0.0993605i	$0.0316797\pi$
$877$	6.47410e11	+	6.47410e11i	1.09441	+	1.09441i	0.0993605	+	0.995052i	$0.468320\pi$
$878$		0			0
$879$			4.66756e11i			0.781870i
$880$		0			0
$881$	3.52208e10			0.0584650			0.0292325	−	0.999573i	$-0.490694\pi$
$881$	3.52208e10			0.0584650			0.0292325	+	0.999573i	$0.490694\pi$
$882$		0			0
$883$	−2.70170e11	+	2.70170e11i	−0.444421	+	0.444421i	−0.893495	−	0.449074i	$-0.851754\pi$
$883$	−2.70170e11	+	2.70170e11i	−0.444421	+	0.444421i	0.449074	+	0.893495i	$0.351754\pi$
$884$		0			0
$885$	1.74959e11	−	1.74959e11i	0.285209	−	0.285209i
$886$		0			0
$887$	−8.56295e11			−1.38334			−0.691670	−	0.722214i	$-0.743125\pi$
$887$	−8.56295e11			−1.38334			−0.691670	+	0.722214i	$0.743125\pi$
$888$		0			0
$889$		−	1.34729e12i		−	2.15703i
$890$		0			0
$891$	6.44930e10	+	6.44930e10i	0.102330	+	0.102330i
$892$		0			0
$893$	3.21567e11	+	3.21567e11i	0.505668	+	0.505668i
$894$		0			0
$895$			1.51975e10i			0.0236854i
$896$		0			0
$897$	−6.71043e7			−0.000103653
$898$		0			0
$899$	−1.57080e11	+	1.57080e11i	−0.240482	+	0.240482i
$900$		0			0
$901$	−4.34581e11	+	4.34581e11i	−0.659434	+	0.659434i
$902$		0			0
$903$	6.13838e11			0.923215
$904$		0			0
$905$		−	4.47968e11i		−	0.667809i
$906$		0			0
$907$	3.34116e10	+	3.34116e10i	0.0493705	+	0.0493705i	0.731361	−	0.681991i	$-0.238885\pi$
$907$	3.34116e10	+	3.34116e10i	0.0493705	+	0.0493705i	−0.681991	+	0.731361i	$0.738885\pi$
$908$		0			0
$909$	6.20755e9	+	6.20755e9i	0.00909211	+	0.00909211i
$910$		0			0
$911$			1.39499e10i			0.0202534i	0.999949	+	0.0101267i	$0.00322348\pi$
$911$			1.39499e10i			0.0202534i	−0.999949	+	0.0101267i	$0.996777\pi$
$912$		0			0
$913$	2.03614e11			0.293038
$914$		0			0
$915$	−7.69860e10	+	7.69860e10i	−0.109832	+	0.109832i
$916$		0			0
$917$	6.91931e11	−	6.91931e11i	0.978555	−	0.978555i
$918$		0			0
$919$	−1.93733e11			−0.271607			−0.135804	−	0.990736i	$-0.543362\pi$
$919$	−1.93733e11			−0.271607			−0.135804	+	0.990736i	$0.543362\pi$
$920$		0			0
$921$		−	5.29389e11i		−	0.735761i
$922$		0			0
$923$	−1.27992e9	−	1.27992e9i	−0.00176351	−	0.00176351i
$924$		0			0
$925$	1.86637e11	+	1.86637e11i	0.254935	+	0.254935i
$926$		0			0
$927$		−	3.94934e11i		−	0.534818i
$928$		0			0
$929$	3.31956e11			0.445674			0.222837	−	0.974856i	$-0.428468\pi$
$929$	3.31956e11			0.445674			0.222837	+	0.974856i	$0.428468\pi$
$930$		0			0
$931$	3.31814e11	−	3.31814e11i	0.441667	−	0.441667i
$932$		0			0
$933$	−1.10579e11	+	1.10579e11i	−0.145931	+	0.145931i
$934$		0			0
$935$	3.63864e11			0.476094
$936$		0			0
$937$			9.83338e11i			1.27569i	0.770166	+	0.637844i	$0.220174\pi$
$937$			9.83338e11i			1.27569i	−0.770166	+	0.637844i	$0.779826\pi$
$938$		0			0
$939$	2.89186e11	+	2.89186e11i	0.371976	+	0.371976i
$940$		0			0
$941$	−9.92581e11	−	9.92581e11i	−1.26592	−	1.26592i	−0.948175	−	0.317749i	$-0.897073\pi$
$941$	−9.92581e11	−	9.92581e11i	−1.26592	−	1.26592i	−0.317749	−	0.948175i	$-0.602927\pi$
$942$		0			0
$943$		−	9.48878e10i		−	0.119995i
$944$		0			0
$945$	1.23214e11			0.154502
$946$		0			0
$947$	−1.02380e11	+	1.02380e11i	−0.127296	+	0.127296i	−0.767884	−	0.640588i	$-0.778691\pi$
$947$	−1.02380e11	+	1.02380e11i	−0.127296	+	0.127296i	0.640588	+	0.767884i	$0.278691\pi$
$948$		0			0
$949$	2.15796e9	−	2.15796e9i	0.00266059	−	0.00266059i
$950$		0			0
$951$	2.83479e11			0.346577
$952$		0			0
$953$			6.24354e11i			0.756936i	0.925614	+	0.378468i	$0.123549\pi$
$953$			6.24354e11i			0.756936i	−0.925614	+	0.378468i	$0.876451\pi$
$954$		0			0
$955$	−2.76080e11	−	2.76080e11i	−0.331911	−	0.331911i
$956$		0			0
$957$	−1.50936e11	−	1.50936e11i	−0.179947	−	0.179947i
$958$		0			0
$959$		−	8.36148e11i		−	0.988573i
$960$		0			0
$961$	−8.43758e9			−0.00989291
$962$		0			0
$963$	−2.41831e11	+	2.41831e11i	−0.281195	+	0.281195i
$964$		0			0
$965$	−1.69034e11	+	1.69034e11i	−0.194924	+	0.194924i
$966$		0			0
$967$	−8.54464e11			−0.977209			−0.488605	−	0.872505i	$-0.662494\pi$
$967$	−8.54464e11			−0.977209			−0.488605	+	0.872505i	$0.662494\pi$
$968$		0			0
$969$			2.66530e11i			0.302309i
$970$		0			0
$971$	7.23940e11	+	7.23940e11i	0.814377	+	0.814377i	0.985287	−	0.170909i	$-0.0546706\pi$
$971$	7.23940e11	+	7.23940e11i	0.814377	+	0.814377i	−0.170909	+	0.985287i	$0.554671\pi$
$972$		0			0
$973$	−1.34184e12	−	1.34184e12i	−1.49710	−	1.49710i
$974$		0			0
$975$			8.65272e8i			0.000957490i
$976$		0			0
$977$	2.95655e11			0.324494			0.162247	−	0.986750i	$-0.448126\pi$
$977$	2.95655e11			0.324494			0.162247	+	0.986750i	$0.448126\pi$
$978$		0			0
$979$	1.36219e12	−	1.36219e12i	1.48288	−	1.48288i
$980$		0			0
$981$	5.43088e10	−	5.43088e10i	0.0586400	−	0.0586400i
$982$		0			0
$983$	−9.94055e9			−0.0106462			−0.00532312	−	0.999986i	$-0.501694\pi$
$983$	−9.94055e9			−0.0106462			−0.00532312	+	0.999986i	$0.501694\pi$
$984$		0			0
$985$		−	5.33305e11i		−	0.566540i
$986$		0			0
$987$	−4.12055e11	−	4.12055e11i	−0.434197	−	0.434197i
$988$		0			0
$989$	5.58010e10	+	5.58010e10i	0.0583253	+	0.0583253i
$990$		0			0
$991$		−	4.44574e11i		−	0.460945i	−0.973079	−	0.230473i	$-0.925973\pi$
$991$		−	4.44574e11i		−	0.460945i	0.973079	−	0.230473i	$-0.0740272\pi$
$992$		0			0
$993$	3.13274e11			0.322201
$994$		0			0
$995$	5.27508e11	−	5.27508e11i	0.538191	−	0.538191i
$996$		0			0
$997$	−8.77613e11	+	8.77613e11i	−0.888224	+	0.888224i	−0.994352	−	0.106129i	$-0.966155\pi$
$997$	−8.77613e11	+	8.77613e11i	−0.888224	+	0.888224i	0.106129	+	0.994352i	$0.466155\pi$
$998$		0			0
$999$	−1.10898e11			−0.111343

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	192.9.l.a.175.27		64
4.3	odd	2		48.9.l.a.19.25	✓	64
16.5	even	4		48.9.l.a.43.25	yes	64
16.11	odd	4	inner	192.9.l.a.79.27		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.9.l.a.19.25	✓	64	4.3	odd	2
48.9.l.a.43.25	yes	64	16.5	even	4
192.9.l.a.79.27		64	16.11	odd	4	inner
192.9.l.a.175.27		64	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	192.l (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(33.0681 - 33.0681i) q^{3} +(271.296 - 271.296i) q^{5} -3140.01 q^{7} -2187.00i q^{9} +O(q^{10})\)	\(q+(33.0681 - 33.0681i) q^{3} +(271.296 - 271.296i) q^{5} -3140.01 q^{7} -2187.00i q^{9} +(-13483.9 - 13483.9i) q^{11} +(53.7468 + 53.7468i) q^{13} -17942.5i q^{15} -49733.7 q^{17} +(81031.9 - 81031.9i) q^{19} +(-103834. + 103834. i) q^{21} -18878.1 q^{23} +243422. i q^{25} +(-72320.0 - 72320.0i) q^{27} +(169253. + 169253. i) q^{29} +928078. i q^{31} -891773. q^{33} +(-851871. + 851871. i) q^{35} +(766720. - 766720. i) q^{37} +3554.61 q^{39} +5.02634e6i q^{41} +(-2.95586e6 - 2.95586e6i) q^{43} +(-593324. - 593324. i) q^{45} +3.96840e6i q^{47} +4.09485e6 q^{49} +(-1.64460e6 + 1.64460e6i) q^{51} +(8.73814e6 - 8.73814e6i) q^{53} -7.31624e6 q^{55} -5.35915e6i q^{57} +(9.75112e6 + 9.75112e6i) q^{59} +(-4.29071e6 - 4.29071e6i) q^{61} +6.86720e6i q^{63} +29162.6 q^{65} +(-6.69650e6 + 6.69650e6i) q^{67} +(-624263. + 624263. i) q^{69} -2.38140e7 q^{71} -4.01505e7i q^{73} +(8.04952e6 + 8.04952e6i) q^{75} +(4.23395e7 + 4.23395e7i) q^{77} +7.02261e7i q^{79} -4.78297e6 q^{81} +(-7.55026e6 + 7.55026e6i) q^{83} +(-1.34926e7 + 1.34926e7i) q^{85} +1.11938e7 q^{87} +1.01023e8i q^{89} +(-168765. - 168765. i) q^{91} +(3.06898e7 + 3.06898e7i) q^{93} -4.39672e7i q^{95} +2.10782e7 q^{97} +(-2.94893e7 + 2.94893e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q+O(q^{10}) \) 64 * q	\( 64 q - 39552 q^{11} + 167552 q^{19} - 1691136 q^{23} - 2132352 q^{29} + 2415744 q^{35} - 4720512 q^{37} + 7244672 q^{43} + 52706752 q^{49} - 13862016 q^{51} - 5358720 q^{53} + 46326784 q^{55} - 44938752 q^{59} + 24476032 q^{61} + 29941632 q^{65} + 44244736 q^{67} - 8636544 q^{69} - 159664128 q^{71} - 12918528 q^{75} - 94964352 q^{77} - 306110016 q^{81} - 209328000 q^{83} + 106960000 q^{85} + 45401472 q^{91} - 86500224 q^{99}+O(q^{100}) \) 64 * q - 39552 * q^11 + 167552 * q^19 - 1691136 * q^23 - 2132352 * q^29 + 2415744 * q^35 - 4720512 * q^37 + 7244672 * q^43 + 52706752 * q^49 - 13862016 * q^51 - 5358720 * q^53 + 46326784 * q^55 - 44938752 * q^59 + 24476032 * q^61 + 29941632 * q^65 + 44244736 * q^67 - 8636544 * q^69 - 159664128 * q^71 - 12918528 * q^75 - 94964352 * q^77 - 306110016 * q^81 - 209328000 * q^83 + 106960000 * q^85 + 45401472 * q^91 - 86500224 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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