LMFDB - Embedded newform 192.9.l.a.175.23

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			175.23
Character	$\chi$	$=$	192.175
Dual form			192.9.l.a.79.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(33.0681 - 33.0681i) q^{3} +(260.136 - 260.136i) q^{5} +368.567 q^{7} -2187.00i q^{9} +O(q^{10})$	\(q+(33.0681 - 33.0681i) q^{3} +(260.136 - 260.136i) q^{5} +368.567 q^{7} -2187.00i q^{9} +(17059.0 + 17059.0i) q^{11} +(32217.3 + 32217.3i) q^{13} -17204.4i q^{15} -120640. q^{17} +(-5000.89 + 5000.89i) q^{19} +(12187.8 - 12187.8i) q^{21} -428464. q^{23} +255284. i q^{25} +(-72320.0 - 72320.0i) q^{27} +(669611. + 669611. i) q^{29} +35624.3i q^{31} +1.12821e6 q^{33} +(95877.5 - 95877.5i) q^{35} +(-1.95653e6 + 1.95653e6i) q^{37} +2.13073e6 q^{39} +2.75070e6i q^{41} +(-2.02704e6 - 2.02704e6i) q^{43} +(-568916. - 568916. i) q^{45} -5.13135e6i q^{47} -5.62896e6 q^{49} +(-3.98935e6 + 3.98935e6i) q^{51} +(-2.06872e6 + 2.06872e6i) q^{53} +8.87528e6 q^{55} +330740. i q^{57} +(9.48573e6 + 9.48573e6i) q^{59} +(8.73489e6 + 8.73489e6i) q^{61} -806057. i q^{63} +1.67617e7 q^{65} +(1.48877e7 - 1.48877e7i) q^{67} +(-1.41685e7 + 1.41685e7i) q^{69} -2.71789e7 q^{71} -7.57343e6i q^{73} +(8.44176e6 + 8.44176e6i) q^{75} +(6.28737e6 + 6.28737e6i) q^{77} -5.69812e6i q^{79} -4.78297e6 q^{81} +(-7.10472e6 + 7.10472e6i) q^{83} +(-3.13828e7 + 3.13828e7i) q^{85} +4.42856e7 q^{87} +9.01003e7i q^{89} +(1.18742e7 + 1.18742e7i) q^{91} +(1.17803e6 + 1.17803e6i) q^{93} +2.60182e6i q^{95} +1.12056e8 q^{97} +(3.73079e7 - 3.73079e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	260.136	−	260.136i	0.416217	−	0.416217i	−0.467681	−	0.883898i	$-0.654910\pi$
$5$	260.136	−	260.136i	0.416217	−	0.416217i	0.883898	+	0.467681i	$0.154910\pi$
$6$		0			0
$7$	368.567			0.153506			0.0767529	−	0.997050i	$-0.475545\pi$
$7$	368.567			0.153506			0.0767529	+	0.997050i	$0.475545\pi$
$8$		0			0
$9$		−	2187.00i		−	0.333333i
$10$		0			0
$11$	17059.0	+	17059.0i	1.16515	+	1.16515i	0.983332	+	0.181817i	$0.0581978\pi$
$11$	17059.0	+	17059.0i	1.16515	+	1.16515i	0.181817	+	0.983332i	$0.441802\pi$
$12$		0			0
$13$	32217.3	+	32217.3i	1.12802	+	1.12802i	0.990499	+	0.137518i	$0.0439124\pi$
$13$	32217.3	+	32217.3i	1.12802	+	1.12802i	0.137518	+	0.990499i	$0.456088\pi$
$14$		0			0
$15$		−	17204.4i		−	0.339840i
$16$		0			0
$17$	−120640.			−1.44443			−0.722215	−	0.691668i	$-0.756876\pi$
$17$	−120640.			−1.44443			−0.722215	+	0.691668i	$0.756876\pi$
$18$		0			0
$19$	−5000.89	+	5000.89i	−0.0383737	+	0.0383737i	−0.726033	−	0.687660i	$-0.758638\pi$
$19$	−5000.89	+	5000.89i	−0.0383737	+	0.0383737i	0.687660	+	0.726033i	$0.258638\pi$
$20$		0			0
$21$	12187.8	−	12187.8i	0.0626685	−	0.0626685i
$22$		0			0
$23$	−428464.			−1.53110			−0.765550	−	0.643377i	$-0.777533\pi$
$23$	−428464.			−1.53110			−0.765550	+	0.643377i	$0.777533\pi$
$24$		0			0
$25$			255284.i			0.653527i
$26$		0			0
$27$	−72320.0	−	72320.0i	−0.136083	−	0.136083i
$28$		0			0
$29$	669611.	+	669611.i	0.946740	+	0.946740i	0.998652	−	0.0519114i	$-0.0165313\pi$
$29$	669611.	+	669611.i	0.946740	+	0.946740i	−0.0519114	+	0.998652i	$0.516531\pi$
$30$		0			0
$31$			35624.3i			0.0385744i	0.999814	+	0.0192872i	$0.00613969\pi$
$31$			35624.3i			0.0385744i	−0.999814	+	0.0192872i	$0.993860\pi$
$32$		0			0
$33$	1.12821e6			0.951340
$34$		0			0
$35$	95877.5	−	95877.5i	0.0638917	−	0.0638917i
$36$		0			0
$37$	−1.95653e6	+	1.95653e6i	−1.04395	+	1.04395i	−0.0449597	+	0.998989i	$0.514316\pi$
$37$	−1.95653e6	+	1.95653e6i	−1.04395	+	1.04395i	−0.998989	+	0.0449597i	$0.985684\pi$
$38$		0			0
$39$	2.13073e6			0.921022
$40$		0			0
$41$			2.75070e6i			0.973436i	0.873559	+	0.486718i	$0.161806\pi$
$41$			2.75070e6i			0.973436i	−0.873559	+	0.486718i	$0.838194\pi$
$42$		0			0
$43$	−2.02704e6	−	2.02704e6i	−0.592910	−	0.592910i	0.345506	−	0.938417i	$-0.387707\pi$
$43$	−2.02704e6	−	2.02704e6i	−0.592910	−	0.592910i	−0.938417	+	0.345506i	$0.887707\pi$
$44$		0			0
$45$	−568916.	−	568916.i	−0.138739	−	0.138739i
$46$		0			0
$47$		−	5.13135e6i		−	1.05158i	−0.850616	−	0.525788i	$-0.823771\pi$
$47$		−	5.13135e6i		−	1.05158i	0.850616	−	0.525788i	$-0.176229\pi$
$48$		0			0
$49$	−5.62896e6			−0.976436
$50$		0			0
$51$	−3.98935e6	+	3.98935e6i	−0.589686	+	0.589686i
$52$		0			0
$53$	−2.06872e6	+	2.06872e6i	−0.262179	+	0.262179i	−0.825939	−	0.563760i	$-0.809354\pi$
$53$	−2.06872e6	+	2.06872e6i	−0.262179	+	0.262179i	0.563760	+	0.825939i	$0.309354\pi$
$54$		0			0
$55$	8.87528e6			0.969910
$56$		0			0
$57$			330740.i			0.0313320i
$58$		0			0
$59$	9.48573e6	+	9.48573e6i	0.782821	+	0.782821i	0.980306	−	0.197485i	$-0.0632772\pi$
$59$	9.48573e6	+	9.48573e6i	0.782821	+	0.782821i	−0.197485	+	0.980306i	$0.563277\pi$
$60$		0			0
$61$	8.73489e6	+	8.73489e6i	0.630868	+	0.630868i	0.948286	−	0.317418i	$-0.102816\pi$
$61$	8.73489e6	+	8.73489e6i	0.630868	+	0.630868i	−0.317418	+	0.948286i	$0.602816\pi$
$62$		0			0
$63$		−	806057.i		−	0.0511686i
$64$		0			0
$65$	1.67617e7			0.938999
$66$		0			0
$67$	1.48877e7	−	1.48877e7i	0.738802	−	0.738802i	−0.233544	−	0.972346i	$-0.575032\pi$
$67$	1.48877e7	−	1.48877e7i	0.738802	−	0.738802i	0.972346	+	0.233544i	$0.0750324\pi$
$68$		0			0
$69$	−1.41685e7	+	1.41685e7i	−0.625069	+	0.625069i
$70$		0			0
$71$	−2.71789e7			−1.06954			−0.534772	−	0.844996i	$-0.679602\pi$
$71$	−2.71789e7			−1.06954			−0.534772	+	0.844996i	$0.679602\pi$
$72$		0			0
$73$		−	7.57343e6i		−	0.266687i	−0.991070	−	0.133343i	$-0.957429\pi$
$73$		−	7.57343e6i		−	0.266687i	0.991070	−	0.133343i	$-0.0425713\pi$
$74$		0			0
$75$	8.44176e6	+	8.44176e6i	0.266801	+	0.266801i
$76$		0			0
$77$	6.28737e6	+	6.28737e6i	0.178857	+	0.178857i
$78$		0			0
$79$		−	5.69812e6i		−	0.146293i	−0.997321	−	0.0731465i	$-0.976696\pi$
$79$		−	5.69812e6i		−	0.146293i	0.997321	−	0.0731465i	$-0.0233041\pi$
$80$		0			0
$81$	−4.78297e6			−0.111111
$82$		0			0
$83$	−7.10472e6	+	7.10472e6i	−0.149704	+	0.149704i	−0.777986	−	0.628282i	$-0.783759\pi$
$83$	−7.10472e6	+	7.10472e6i	−0.149704	+	0.149704i	0.628282	+	0.777986i	$0.283759\pi$
$84$		0			0
$85$	−3.13828e7	+	3.13828e7i	−0.601197	+	0.601197i
$86$		0			0
$87$	4.42856e7			0.773010
$88$		0			0
$89$			9.01003e7i			1.43604i	0.696023	+	0.718019i	$0.254951\pi$
$89$			9.01003e7i			1.43604i	−0.696023	+	0.718019i	$0.745049\pi$
$90$		0			0
$91$	1.18742e7	+	1.18742e7i	0.173157	+	0.173157i
$92$		0			0
$93$	1.17803e6	+	1.17803e6i	0.0157479	+	0.0157479i
$94$		0			0
$95$			2.60182e6i			0.0319435i
$96$		0			0
$97$	1.12056e8			1.26575			0.632877	−	0.774252i	$-0.281874\pi$
$97$	1.12056e8			1.26575			0.632877	+	0.774252i	$0.281874\pi$
$98$		0			0
$99$	3.73079e7	−	3.73079e7i	0.388383	−	0.388383i
$100$		0			0
$101$	3.44480e6	−	3.44480e6i	0.0331039	−	0.0331039i	−0.690361	−	0.723465i	$-0.742548\pi$
$101$	3.44480e6	−	3.44480e6i	0.0331039	−	0.0331039i	0.723465	+	0.690361i	$0.242548\pi$
$102$		0			0
$103$	−1.82230e7			−0.161909			−0.0809544	−	0.996718i	$-0.525797\pi$
$103$	−1.82230e7			−0.161909			−0.0809544	+	0.996718i	$0.525797\pi$
$104$		0			0
$105$		−	6.34098e6i		−	0.0521674i
$106$		0			0
$107$	8.28894e7	+	8.28894e7i	0.632359	+	0.632359i	0.948659	−	0.316300i	$-0.102441\pi$
$107$	8.28894e7	+	8.28894e7i	0.632359	+	0.632359i	−0.316300	+	0.948659i	$0.602441\pi$
$108$		0			0
$109$	−3.77786e7	−	3.77786e7i	−0.267633	−	0.267633i	0.560513	−	0.828146i	$-0.310604\pi$
$109$	−3.77786e7	−	3.77786e7i	−0.267633	−	0.267633i	−0.828146	+	0.560513i	$0.810604\pi$
$110$		0			0
$111$			1.29397e8i			0.852380i
$112$		0			0
$113$	1.86917e8			1.14640			0.573198	−	0.819417i	$-0.305703\pi$
$113$	1.86917e8			1.14640			0.573198	+	0.819417i	$0.305703\pi$
$114$		0			0
$115$	−1.11459e8	+	1.11459e8i	−0.637269	+	0.637269i
$116$		0			0
$117$	7.04592e7	−	7.04592e7i	0.376006	−	0.376006i
$118$		0			0
$119$	−4.44641e7			−0.221729
$120$		0			0
$121$			3.67657e8i			1.71515i
$122$		0			0
$123$	9.09604e7	+	9.09604e7i	0.397404	+	0.397404i
$124$		0			0
$125$	1.68024e8	+	1.68024e8i	0.688226	+	0.688226i
$126$		0			0
$127$			2.77151e8i			1.06537i	0.846313	+	0.532686i	$0.178817\pi$
$127$			2.77151e8i			1.06537i	−0.846313	+	0.532686i	$0.821183\pi$
$128$		0			0
$129$	−1.34061e8			−0.484109
$130$		0			0
$131$	−1.78420e7	+	1.78420e7i	−0.0605841	+	0.0605841i	−0.736750	−	0.676166i	$-0.763640\pi$
$131$	−1.78420e7	+	1.78420e7i	−0.0605841	+	0.0605841i	0.676166	+	0.736750i	$0.263640\pi$
$132$		0			0
$133$	−1.84317e6	+	1.84317e6i	−0.00589058	+	0.00589058i
$134$		0			0
$135$	−3.76260e7			−0.113280
$136$		0			0
$137$		−	6.22804e8i		−	1.76795i	−0.467538	−	0.883973i	$-0.654859\pi$
$137$		−	6.22804e8i		−	1.76795i	0.467538	−	0.883973i	$-0.345141\pi$
$138$		0			0
$139$	1.77564e8	+	1.77564e8i	0.475658	+	0.475658i	0.903740	−	0.428082i	$-0.140810\pi$
$139$	1.77564e8	+	1.77564e8i	0.475658	+	0.475658i	−0.428082	+	0.903740i	$0.640810\pi$
$140$		0			0
$141$	−1.69684e8	−	1.69684e8i	−0.429304	−	0.429304i
$142$		0			0
$143$			1.09919e9i			2.62862i
$144$		0			0
$145$	3.48379e8			0.788099
$146$		0			0
$147$	−1.86139e8	+	1.86139e8i	−0.398628	+	0.398628i
$148$		0			0
$149$	−4.70908e8	+	4.70908e8i	−0.955413	+	0.955413i	−0.999048	−	0.0436346i	$-0.986106\pi$
$149$	−4.70908e8	+	4.70908e8i	−0.955413	+	0.955413i	0.0436346	+	0.999048i	$0.486106\pi$
$150$		0			0
$151$	3.38251e8			0.650626			0.325313	−	0.945606i	$-0.394530\pi$
$151$	3.38251e8			0.650626			0.325313	+	0.945606i	$0.394530\pi$
$152$		0			0
$153$			2.63840e8i			0.481477i
$154$		0			0
$155$	9.26714e6	+	9.26714e6i	0.0160553	+	0.0160553i
$156$		0			0
$157$	5.15512e8	+	5.15512e8i	0.848477	+	0.848477i	0.989943	−	0.141466i	$-0.0451816\pi$
$157$	5.15512e8	+	5.15512e8i	0.848477	+	0.848477i	−0.141466	+	0.989943i	$0.545182\pi$
$158$		0			0
$159$			1.36817e8i			0.214068i
$160$		0			0
$161$	−1.57918e8			−0.235033
$162$		0			0
$163$	6.02089e8	−	6.02089e8i	0.852924	−	0.852924i	−0.137568	−	0.990492i	$-0.543929\pi$
$163$	6.02089e8	−	6.02089e8i	0.852924	−	0.852924i	0.990492	+	0.137568i	$0.0439287\pi$
$164$		0			0
$165$	2.93489e8	−	2.93489e8i	0.395964	−	0.395964i
$166$		0			0
$167$	1.10432e8			0.141981			0.0709903	−	0.997477i	$-0.477384\pi$
$167$	1.10432e8			0.141981			0.0709903	+	0.997477i	$0.477384\pi$
$168$		0			0
$169$			1.26018e9i			1.54484i
$170$		0			0
$171$	1.09370e7	+	1.09370e7i	0.0127912	+	0.0127912i
$172$		0			0
$173$	−8.98116e8	−	8.98116e8i	−1.00265	−	1.00265i	−0.999996	−	0.00265061i	$-0.999156\pi$
$173$	−8.98116e8	−	8.98116e8i	−1.00265	−	1.00265i	−0.00265061	−	0.999996i	$-0.500844\pi$
$174$		0			0
$175$			9.40894e7i			0.100320i
$176$		0			0
$177$	6.27350e8			0.639171
$178$		0			0
$179$	2.98969e8	−	2.98969e8i	0.291215	−	0.291215i	−0.546345	−	0.837560i	$-0.683981\pi$
$179$	2.98969e8	−	2.98969e8i	0.291215	−	0.291215i	0.837560	+	0.546345i	$0.183981\pi$
$180$		0			0
$181$	7.32022e7	−	7.32022e7i	0.0682040	−	0.0682040i	−0.672182	−	0.740386i	$-0.734643\pi$
$181$	7.32022e7	−	7.32022e7i	0.0682040	−	0.0682040i	0.740386	+	0.672182i	$0.234643\pi$
$182$		0			0
$183$	5.77693e8			0.515101
$184$		0			0
$185$			1.01792e9i			0.869018i
$186$		0			0
$187$	−2.05800e9	−	2.05800e9i	−1.68298	−	1.68298i
$188$		0			0
$189$	−2.66548e7	−	2.66548e7i	−0.0208895	−	0.0208895i
$190$		0			0
$191$		−	1.38542e9i		−	1.04100i	−0.853863	−	0.520499i	$-0.825746\pi$
$191$		−	1.38542e9i		−	1.04100i	0.853863	−	0.520499i	$-0.174254\pi$
$192$		0			0
$193$	9.93916e8			0.716342			0.358171	−	0.933656i	$-0.383400\pi$
$193$	9.93916e8			0.716342			0.358171	+	0.933656i	$0.383400\pi$
$194$		0			0
$195$	5.54279e8	−	5.54279e8i	0.383345	−	0.383345i
$196$		0			0
$197$	6.71646e7	−	6.71646e7i	0.0445939	−	0.0445939i	−0.684458	−	0.729052i	$-0.739961\pi$
$197$	6.71646e7	−	6.71646e7i	0.0445939	−	0.0445939i	0.729052	+	0.684458i	$0.239961\pi$
$198$		0			0
$199$	−1.83807e9			−1.17206			−0.586030	−	0.810290i	$-0.699310\pi$
$199$	−1.83807e9			−1.17206			−0.586030	+	0.810290i	$0.699310\pi$
$200$		0			0
$201$		−	9.84615e8i		−	0.603229i
$202$		0			0
$203$	2.46797e8	+	2.46797e8i	0.145330	+	0.145330i
$204$		0			0
$205$	7.15555e8	+	7.15555e8i	0.405161	+	0.405161i
$206$		0			0
$207$			9.37052e8i			0.510367i
$208$		0			0
$209$	−1.70620e8			−0.0894221
$210$		0			0
$211$	1.74556e9	−	1.74556e9i	0.880656	−	0.880656i	−0.112945	−	0.993601i	$-0.536029\pi$
$211$	1.74556e9	−	1.74556e9i	0.880656	−	0.880656i	0.993601	+	0.112945i	$0.0360285\pi$
$212$		0			0
$213$	−8.98755e8	+	8.98755e8i	−0.436639	+	0.436639i
$214$		0			0
$215$	−1.05461e9			−0.493559
$216$		0			0
$217$			1.31299e7i			0.00592139i
$218$		0			0
$219$	−2.50439e8	−	2.50439e8i	−0.108874	−	0.108874i
$220$		0			0
$221$	−3.88670e9	−	3.88670e9i	−1.62934	−	1.62934i
$222$		0			0
$223$			9.03544e8i			0.365367i	0.983172	+	0.182684i	$0.0584784\pi$
$223$			9.03544e8i			0.365367i	−0.983172	+	0.182684i	$0.941522\pi$
$224$		0			0
$225$	5.58306e8			0.217842
$226$		0			0
$227$	3.61340e9	−	3.61340e9i	1.36086	−	1.36086i	0.488034	−	0.872825i	$-0.337714\pi$
$227$	3.61340e9	−	3.61340e9i	1.36086	−	1.36086i	0.872825	−	0.488034i	$-0.162286\pi$
$228$		0			0
$229$	−1.67209e9	+	1.67209e9i	−0.608018	+	0.608018i	−0.942428	−	0.334410i	$-0.891463\pi$
$229$	−1.67209e9	+	1.67209e9i	−0.608018	+	0.608018i	0.334410	+	0.942428i	$0.391463\pi$
$230$		0			0
$231$	4.15823e8			0.146036
$232$		0			0
$233$		−	5.04455e8i		−	0.171159i	−0.996331	−	0.0855794i	$-0.972726\pi$
$233$		−	5.04455e8i		−	0.171159i	0.996331	−	0.0855794i	$-0.0272741\pi$
$234$		0			0
$235$	−1.33485e9	−	1.33485e9i	−0.437683	−	0.437683i
$236$		0			0
$237$	−1.88426e8	−	1.88426e8i	−0.0597238	−	0.0597238i
$238$		0			0
$239$			4.64642e9i			1.42406i	0.702151	+	0.712028i	$0.252223\pi$
$239$			4.64642e9i			1.42406i	−0.702151	+	0.712028i	$0.747777\pi$
$240$		0			0
$241$	4.62173e9			1.37005			0.685025	−	0.728520i	$-0.259791\pi$
$241$	4.62173e9			1.37005			0.685025	+	0.728520i	$0.259791\pi$
$242$		0			0
$243$	−1.58164e8	+	1.58164e8i	−0.0453609	+	0.0453609i
$244$		0			0
$245$	−1.46429e9	+	1.46429e9i	−0.406409	+	0.406409i
$246$		0			0
$247$	−3.22231e8			−0.0865723
$248$		0			0
$249$			4.69879e8i			0.122233i
$250$		0			0
$251$	−2.41572e9	−	2.41572e9i	−0.608629	−	0.608629i	0.333959	−	0.942588i	$-0.391615\pi$
$251$	−2.41572e9	−	2.41572e9i	−0.608629	−	0.608629i	−0.942588	+	0.333959i	$0.891615\pi$
$252$		0			0
$253$	−7.30915e9	−	7.30915e9i	−1.78396	−	1.78396i
$254$		0			0
$255$			2.07554e9i			0.490875i
$256$		0			0
$257$	−5.42537e8			−0.124365			−0.0621823	−	0.998065i	$-0.519806\pi$
$257$	−5.42537e8			−0.124365			−0.0621823	+	0.998065i	$0.519806\pi$
$258$		0			0
$259$	−7.21112e8	+	7.21112e8i	−0.160252	+	0.160252i
$260$		0			0
$261$	1.46444e9	−	1.46444e9i	0.315580	−	0.315580i
$262$		0			0
$263$	−9.18981e9			−1.92081			−0.960403	−	0.278615i	$-0.910125\pi$
$263$	−9.18981e9			−1.92081			−0.960403	+	0.278615i	$0.910125\pi$
$264$		0			0
$265$			1.07629e9i			0.218246i
$266$		0			0
$267$	2.97945e9	+	2.97945e9i	0.586260	+	0.586260i
$268$		0			0
$269$	−2.52840e9	−	2.52840e9i	−0.482877	−	0.482877i	0.423172	−	0.906049i	$-0.360917\pi$
$269$	−2.52840e9	−	2.52840e9i	−0.482877	−	0.482877i	−0.906049	+	0.423172i	$0.860917\pi$
$270$		0			0
$271$		−	7.25111e9i		−	1.34440i	−0.740371	−	0.672199i	$-0.765350\pi$
$271$		−	7.25111e9i		−	1.34440i	0.740371	−	0.672199i	$-0.234650\pi$
$272$		0			0
$273$	7.85318e8			0.141382
$274$		0			0
$275$	−4.35488e9	+	4.35488e9i	−0.761457	+	0.761457i
$276$		0			0
$277$	2.62494e9	−	2.62494e9i	0.445861	−	0.445861i	−0.448115	−	0.893976i	$-0.647904\pi$
$277$	2.62494e9	−	2.62494e9i	0.445861	−	0.445861i	0.893976	+	0.448115i	$0.147904\pi$
$278$		0			0
$279$	7.79103e7			0.0128581
$280$		0			0
$281$		−	6.70840e9i		−	1.07595i	−0.842959	−	0.537977i	$-0.819189\pi$
$281$		−	6.70840e9i		−	1.07595i	0.842959	−	0.537977i	$-0.180811\pi$
$282$		0			0
$283$	3.91362e9	+	3.91362e9i	0.610145	+	0.610145i	0.942984	−	0.332839i	$-0.108006\pi$
$283$	3.91362e9	+	3.91362e9i	0.610145	+	0.610145i	−0.332839	+	0.942984i	$0.608006\pi$
$284$		0			0
$285$	8.60373e7	+	8.60373e7i	0.0130409	+	0.0130409i
$286$		0			0
$287$			1.01382e9i			0.149428i
$288$		0			0
$289$	7.57833e9			1.08638
$290$		0			0
$291$	3.70549e9	−	3.70549e9i	0.516742	−	0.516742i
$292$		0			0
$293$	−7.78723e8	+	7.78723e8i	−0.105661	+	0.105661i	−0.757961	−	0.652300i	$-0.773804\pi$
$293$	−7.78723e8	+	7.78723e8i	−0.105661	+	0.105661i	0.652300	+	0.757961i	$0.273804\pi$
$294$		0			0
$295$	4.93515e9			0.651647
$296$		0			0
$297$		−	2.46741e9i		−	0.317113i
$298$		0			0
$299$	−1.38040e10	−	1.38040e10i	−1.72711	−	1.72711i
$300$		0			0
$301$	−7.47102e8	−	7.47102e8i	−0.0910152	−	0.0910152i
$302$		0			0
$303$		−	2.27826e8i		−	0.0270292i
$304$		0			0
$305$	4.54451e9			0.525155
$306$		0			0
$307$	8.81000e9	−	8.81000e9i	0.991796	−	0.991796i	−0.00817102	−	0.999967i	$-0.502601\pi$
$307$	8.81000e9	−	8.81000e9i	0.991796	−	0.991796i	0.999967	+	0.00817102i	$0.00260094\pi$
$308$		0			0
$309$	−6.02600e8	+	6.02600e8i	−0.0660990	+	0.0660990i
$310$		0			0
$311$	−3.87027e9			−0.413713			−0.206857	−	0.978371i	$-0.566323\pi$
$311$	−3.87027e9			−0.413713			−0.206857	+	0.978371i	$0.566323\pi$
$312$		0			0
$313$		−	4.83707e9i		−	0.503970i	−0.967731	−	0.251985i	$-0.918917\pi$
$313$		−	4.83707e9i		−	0.503970i	0.967731	−	0.251985i	$-0.0810834\pi$
$314$		0			0
$315$	−2.09684e8	−	2.09684e8i	−0.0212972	−	0.0212972i
$316$		0			0
$317$	−5.54173e9	−	5.54173e9i	−0.548792	−	0.548792i	0.377299	−	0.926091i	$-0.376853\pi$
$317$	−5.54173e9	−	5.54173e9i	−0.548792	−	0.548792i	−0.926091	+	0.377299i	$0.876853\pi$
$318$		0			0
$319$			2.28457e10i			2.20619i
$320$		0			0
$321$	5.48199e9			0.516319
$322$		0			0
$323$	6.03309e8	−	6.03309e8i	0.0554281	−	0.0554281i
$324$		0			0
$325$	−8.22456e9	+	8.22456e9i	−0.737190	+	0.737190i
$326$		0			0
$327$	−2.49854e9			−0.218522
$328$		0			0
$329$		−	1.89125e9i		−	0.161423i
$330$		0			0
$331$	1.04186e9	+	1.04186e9i	0.0867958	+	0.0867958i	0.749172	−	0.662376i	$-0.230452\pi$
$331$	1.04186e9	+	1.04186e9i	0.0867958	+	0.0867958i	−0.662376	+	0.749172i	$0.730452\pi$
$332$		0			0
$333$	4.27893e9	+	4.27893e9i	0.347983	+	0.347983i
$334$		0			0
$335$		−	7.74563e9i		−	0.615003i
$336$		0			0
$337$	−5.14498e9			−0.398900			−0.199450	−	0.979908i	$-0.563916\pi$
$337$	−5.14498e9			−0.398900			−0.199450	+	0.979908i	$0.563916\pi$
$338$		0			0
$339$	6.18099e9	−	6.18099e9i	0.468014	−	0.468014i
$340$		0			0
$341$	−6.07713e8	+	6.07713e8i	−0.0449449	+	0.0449449i
$342$		0			0
$343$	−4.19937e9			−0.303394
$344$		0			0
$345$			7.37147e9i			0.520328i
$346$		0			0
$347$	−5.45394e9	−	5.45394e9i	−0.376177	−	0.376177i	0.493544	−	0.869721i	$-0.335701\pi$
$347$	−5.45394e9	−	5.45394e9i	−0.376177	−	0.376177i	−0.869721	+	0.493544i	$0.835701\pi$
$348$		0			0
$349$	4.95246e9	+	4.95246e9i	0.333825	+	0.333825i	0.854037	−	0.520212i	$-0.174147\pi$
$349$	4.95246e9	+	4.95246e9i	0.333825	+	0.333825i	−0.520212	+	0.854037i	$0.674147\pi$
$350$		0			0
$351$		−	4.65991e9i		−	0.307007i
$352$		0			0
$353$	−6.26529e9			−0.403499			−0.201750	−	0.979437i	$-0.564663\pi$
$353$	−6.26529e9			−0.403499			−0.201750	+	0.979437i	$0.564663\pi$
$354$		0			0
$355$	−7.07020e9	+	7.07020e9i	−0.445162	+	0.445162i
$356$		0			0
$357$	−1.47034e9	+	1.47034e9i	−0.0905203	+	0.0905203i
$358$		0			0
$359$	1.07114e10			0.644867			0.322434	−	0.946592i	$-0.395499\pi$
$359$	1.07114e10			0.644867			0.322434	+	0.946592i	$0.395499\pi$
$360$		0			0
$361$			1.69335e10i			0.997055i
$362$		0			0
$363$	1.21577e10	+	1.21577e10i	0.700205	+	0.700205i
$364$		0			0
$365$	−1.97012e9	−	1.97012e9i	−0.110999	−	0.110999i
$366$		0			0
$367$			1.44243e10i			0.795114i	0.917577	+	0.397557i	$0.130142\pi$
$367$			1.44243e10i			0.795114i	−0.917577	+	0.397557i	$0.869858\pi$
$368$		0			0
$369$	6.01578e9			0.324479
$370$		0			0
$371$	−7.62462e8	+	7.62462e8i	−0.0402460	+	0.0402460i
$372$		0			0
$373$	2.49909e10	−	2.49909e10i	1.29106	−	1.29106i	0.356927	−	0.934132i	$-0.383825\pi$
$373$	2.49909e10	−	2.49909e10i	1.29106	−	1.29106i	0.934132	−	0.356927i	$-0.116175\pi$
$374$		0			0
$375$	1.11125e10			0.561934
$376$		0			0
$377$			4.31461e10i			2.13588i
$378$		0			0
$379$	1.78697e10	+	1.78697e10i	0.866087	+	0.866087i	0.992037	−	0.125950i	$-0.0401979\pi$
$379$	1.78697e10	+	1.78697e10i	0.866087	+	0.866087i	−0.125950	+	0.992037i	$0.540198\pi$
$380$		0			0
$381$	9.16485e9	+	9.16485e9i	0.434936	+	0.434936i
$382$		0			0
$383$			2.14730e9i			0.0997924i	0.998754	+	0.0498962i	$0.0158891\pi$
$383$			2.14730e9i			0.0997924i	−0.998754	+	0.0498962i	$0.984111\pi$
$384$		0			0
$385$	3.27114e9			0.148887
$386$		0			0
$387$	−4.43314e9	+	4.43314e9i	−0.197637	+	0.197637i
$388$		0			0
$389$	−1.99746e10	+	1.99746e10i	−0.872329	+	0.872329i	−0.992726	−	0.120397i	$-0.961583\pi$
$389$	−1.99746e10	+	1.99746e10i	−0.872329	+	0.872329i	0.120397	+	0.992726i	$0.461583\pi$
$390$		0			0
$391$	5.16901e10			2.21157
$392$		0			0
$393$			1.18000e9i			0.0494667i
$394$		0			0
$395$	−1.48228e9	−	1.48228e9i	−0.0608896	−	0.0608896i
$396$		0			0
$397$	−2.26970e9	−	2.26970e9i	−0.0913705	−	0.0913705i	0.659944	−	0.751315i	$-0.270580\pi$
$397$	−2.26970e9	−	2.26970e9i	−0.0913705	−	0.0913705i	−0.751315	+	0.659944i	$0.770580\pi$
$398$		0			0
$399$			1.21900e8i			0.00480964i
$400$		0			0
$401$	−4.47840e10			−1.73199			−0.865995	−	0.500052i	$-0.833314\pi$
$401$	−4.47840e10			−1.73199			−0.865995	+	0.500052i	$0.833314\pi$
$402$		0			0
$403$	−1.14772e9	+	1.14772e9i	−0.0435126	+	0.0435126i
$404$		0			0
$405$	−1.24422e9	+	1.24422e9i	−0.0462463	+	0.0462463i
$406$		0			0
$407$	−6.67526e10			−2.43271
$408$		0			0
$409$			7.23017e9i			0.258378i	0.991620	+	0.129189i	$0.0412374\pi$
$409$			7.23017e9i			0.258378i	−0.991620	+	0.129189i	$0.958763\pi$
$410$		0			0
$411$	−2.05950e10	−	2.05950e10i	−0.721761	−	0.721761i
$412$		0			0
$413$	3.49613e9	+	3.49613e9i	0.120168	+	0.120168i
$414$		0			0
$415$			3.69638e9i			0.124619i
$416$		0			0
$417$	1.17434e10			0.388373
$418$		0			0
$419$	1.53530e10	−	1.53530e10i	0.498123	−	0.498123i	−0.412730	−	0.910853i	$-0.635425\pi$
$419$	1.53530e10	−	1.53530e10i	0.498123	−	0.498123i	0.910853	+	0.412730i	$0.135425\pi$
$420$		0			0
$421$	−1.31758e10	+	1.31758e10i	−0.419419	+	0.419419i	−0.885003	−	0.465585i	$-0.845844\pi$
$421$	−1.31758e10	+	1.31758e10i	−0.419419	+	0.419419i	0.465585	+	0.885003i	$0.345844\pi$
$422$		0			0
$423$	−1.12223e10			−0.350525
$424$		0			0
$425$		−	3.07975e10i		−	0.943975i
$426$		0			0
$427$	3.21940e9	+	3.21940e9i	0.0968418	+	0.0968418i
$428$		0			0
$429$	3.63480e10	+	3.63480e10i	1.07313	+	1.07313i
$430$		0			0
$431$			1.33196e10i			0.385995i	0.981199	+	0.192997i	$0.0618209\pi$
$431$			1.33196e10i			0.385995i	−0.981199	+	0.192997i	$0.938179\pi$
$432$		0			0
$433$	6.27714e10			1.78571			0.892853	−	0.450348i	$-0.148700\pi$
$433$	6.27714e10			1.78571			0.892853	+	0.450348i	$0.148700\pi$
$434$		0			0
$435$	1.15203e10	−	1.15203e10i	0.321740	−	0.321740i
$436$		0			0
$437$	2.14271e9	−	2.14271e9i	0.0587539	−	0.0587539i
$438$		0			0
$439$	2.72941e10			0.734870			0.367435	−	0.930049i	$-0.380236\pi$
$439$	2.72941e10			0.734870			0.367435	+	0.930049i	$0.380236\pi$
$440$		0			0
$441$			1.23105e10i			0.325479i
$442$		0			0
$443$	3.56345e10	+	3.56345e10i	0.925243	+	0.925243i	0.997394	−	0.0721508i	$-0.0229863\pi$
$443$	3.56345e10	+	3.56345e10i	0.925243	+	0.925243i	−0.0721508	+	0.997394i	$0.522986\pi$
$444$		0			0
$445$	2.34383e10	+	2.34383e10i	0.597704	+	0.597704i
$446$		0			0
$447$			3.11441e10i			0.780091i
$448$		0			0
$449$	−3.44494e10			−0.847610			−0.423805	−	0.905754i	$-0.639306\pi$
$449$	−3.44494e10			−0.847610			−0.423805	+	0.905754i	$0.639306\pi$
$450$		0			0
$451$	−4.69240e10	+	4.69240e10i	−1.13420	+	1.13420i
$452$		0			0
$453$	1.11853e10	−	1.11853e10i	0.265617	−	0.265617i
$454$		0			0
$455$	6.17783e9			0.144142
$456$		0			0
$457$			1.52723e10i			0.350139i	0.984556	+	0.175070i	$0.0560151\pi$
$457$			1.52723e10i			0.350139i	−0.984556	+	0.175070i	$0.943985\pi$
$458$		0			0
$459$	8.72470e9	+	8.72470e9i	0.196562	+	0.196562i
$460$		0			0
$461$	5.02225e10	+	5.02225e10i	1.11197	+	1.11197i	0.992883	+	0.119091i	$0.0379982\pi$
$461$	5.02225e10	+	5.02225e10i	1.11197	+	1.11197i	0.119091	+	0.992883i	$0.462002\pi$
$462$		0			0
$463$		−	8.27310e10i		−	1.80030i	−0.435583	−	0.900149i	$-0.643458\pi$
$463$		−	8.27310e10i		−	1.80030i	0.435583	−	0.900149i	$-0.356542\pi$
$464$		0			0
$465$	6.12893e8			0.0131091
$466$		0			0
$467$	−4.36358e10	+	4.36358e10i	−0.917436	+	0.917436i	−0.996842	−	0.0794061i	$-0.974698\pi$
$467$	−4.36358e10	+	4.36358e10i	−0.917436	+	0.917436i	0.0794061	+	0.996842i	$0.474698\pi$
$468$		0			0
$469$	5.48712e9	−	5.48712e9i	0.113410	−	0.113410i
$470$		0			0
$471$	3.40940e10			0.692779
$472$		0			0
$473$		−	6.91585e10i		−	1.38166i
$474$		0			0
$475$	−1.27665e9	−	1.27665e9i	−0.0250782	−	0.0250782i
$476$		0			0
$477$	4.52428e9	+	4.52428e9i	0.0873929	+	0.0873929i
$478$		0			0
$479$		−	7.29637e10i		−	1.38601i	−0.720935	−	0.693003i	$-0.756287\pi$
$479$		−	7.29637e10i		−	1.38601i	0.720935	−	0.693003i	$-0.243713\pi$
$480$		0			0
$481$	−1.26068e11			−2.35518
$482$		0			0
$483$	−5.22205e9	+	5.22205e9i	−0.0959517	+	0.0959517i
$484$		0			0
$485$	2.91498e10	−	2.91498e10i	0.526828	−	0.526828i
$486$		0			0
$487$	2.62997e10			0.467558			0.233779	−	0.972290i	$-0.424891\pi$
$487$	2.62997e10			0.467558			0.233779	+	0.972290i	$0.424891\pi$
$488$		0			0
$489$		−	3.98199e10i		−	0.696409i
$490$		0			0
$491$	7.24101e9	+	7.24101e9i	0.124587	+	0.124587i	0.766651	−	0.642064i	$-0.221922\pi$
$491$	7.24101e9	+	7.24101e9i	0.124587	+	0.124587i	−0.642064	+	0.766651i	$0.721922\pi$
$492$		0			0
$493$	−8.07821e10	−	8.07821e10i	−1.36750	−	1.36750i
$494$		0			0
$495$		−	1.94102e10i		−	0.323303i
$496$		0			0
$497$	−1.00173e10			−0.164181
$498$		0			0
$499$	−8.68602e10	+	8.68602e10i	−1.40094	+	1.40094i	−0.603805	+	0.797132i	$0.706349\pi$
$499$	−8.68602e10	+	8.68602e10i	−1.40094	+	1.40094i	−0.797132	+	0.603805i	$0.793651\pi$
$500$		0			0
$501$	3.65178e9	−	3.65178e9i	0.0579633	−	0.0579633i
$502$		0			0
$503$	2.47257e9			0.0386257			0.0193129	−	0.999813i	$-0.493852\pi$
$503$	2.47257e9			0.0386257			0.0193129	+	0.999813i	$0.493852\pi$
$504$		0			0
$505$		−	1.79223e9i		−	0.0275568i
$506$		0			0
$507$	4.16717e10	+	4.16717e10i	0.630680	+	0.630680i
$508$		0			0
$509$	−4.02845e10	−	4.02845e10i	−0.600160	−	0.600160i	0.340195	−	0.940355i	$-0.389507\pi$
$509$	−4.02845e10	−	4.02845e10i	−0.600160	−	0.600160i	−0.940355	+	0.340195i	$0.889507\pi$
$510$		0			0
$511$		−	2.79132e9i		−	0.0409380i
$512$		0			0
$513$	7.23329e8			0.0104440
$514$		0			0
$515$	−4.74045e9	+	4.74045e9i	−0.0673892	+	0.0673892i
$516$		0			0
$517$	8.75355e10	−	8.75355e10i	1.22524	−	1.22524i
$518$		0			0
$519$	−5.93980e10			−0.818658
$520$		0			0
$521$		−	1.03647e11i		−	1.40671i	−0.710839	−	0.703354i	$-0.751685\pi$
$521$		−	1.03647e11i		−	1.40671i	0.710839	−	0.703354i	$-0.248315\pi$
$522$		0			0
$523$	3.32468e10	+	3.32468e10i	0.444368	+	0.444368i	0.893477	−	0.449109i	$-0.148258\pi$
$523$	3.32468e10	+	3.32468e10i	0.444368	+	0.444368i	−0.449109	+	0.893477i	$0.648258\pi$
$524$		0			0
$525$	3.11136e9	+	3.11136e9i	0.0409556	+	0.0409556i
$526$		0			0
$527$		−	4.29772e9i		−	0.0557180i
$528$		0			0
$529$	1.05271e11			1.34427
$530$		0			0
$531$	2.07453e10	−	2.07453e10i	0.260940	−	0.260940i
$532$		0			0
$533$	−8.86201e10	+	8.86201e10i	−1.09805	+	1.09805i
$534$		0			0
$535$	4.31250e10			0.526397
$536$		0			0
$537$		−	1.97727e10i		−	0.237776i
$538$		0			0
$539$	−9.60241e10	−	9.60241e10i	−1.13769	−	1.13769i
$540$		0			0
$541$	8.78525e10	+	8.78525e10i	1.02557	+	1.02557i	0.999664	+	0.0259045i	$0.00824659\pi$
$541$	8.78525e10	+	8.78525e10i	1.02557	+	1.02557i	0.0259045	+	0.999664i	$0.491753\pi$
$542$		0			0
$543$		−	4.84132e9i		−	0.0556883i
$544$		0			0
$545$	−1.96551e10			−0.222787
$546$		0			0
$547$	6.47090e10	−	6.47090e10i	0.722796	−	0.722796i	−0.246378	−	0.969174i	$-0.579241\pi$
$547$	6.47090e10	−	6.47090e10i	0.722796	−	0.722796i	0.969174	+	0.246378i	$0.0792405\pi$
$548$		0			0
$549$	1.91032e10	−	1.91032e10i	0.210289	−	0.210289i
$550$		0			0
$551$	−6.69731e9			−0.0726598
$552$		0			0
$553$		−	2.10014e9i		−	0.0224568i
$554$		0			0
$555$	3.36608e10	+	3.36608e10i	0.354775	+	0.354775i
$556$		0			0
$557$	1.49269e10	+	1.49269e10i	0.155078	+	0.155078i	0.780381	−	0.625304i	$-0.215025\pi$
$557$	1.49269e10	+	1.49269e10i	0.155078	+	0.155078i	−0.625304	+	0.780381i	$0.715025\pi$
$558$		0			0
$559$		−	1.30612e11i		−	1.33763i
$560$		0			0
$561$	−1.36108e11			−1.37415
$562$		0			0
$563$	−7.72511e10	+	7.72511e10i	−0.768902	+	0.768902i	−0.977913	−	0.209011i	$-0.932975\pi$
$563$	−7.72511e10	+	7.72511e10i	−0.768902	+	0.768902i	0.209011	+	0.977913i	$0.432975\pi$
$564$		0			0
$565$	4.86237e10	−	4.86237e10i	0.477149	−	0.477149i
$566$		0			0
$567$	−1.76285e9			−0.0170562
$568$		0			0
$569$		−	4.51125e10i		−	0.430375i	−0.976573	−	0.215188i	$-0.930964\pi$
$569$		−	4.51125e10i		−	0.430375i	0.976573	−	0.215188i	$-0.0690363\pi$
$570$		0			0
$571$	−9.32366e10	−	9.32366e10i	−0.877086	−	0.877086i	0.116147	−	0.993232i	$-0.462946\pi$
$571$	−9.32366e10	−	9.32366e10i	−0.877086	−	0.877086i	−0.993232	+	0.116147i	$0.962946\pi$
$572$		0			0
$573$	−4.58134e10	−	4.58134e10i	−0.424985	−	0.424985i
$574$		0			0
$575$		−	1.09380e11i		−	1.00062i
$576$		0			0
$577$	−1.05867e11			−0.955119			−0.477559	−	0.878599i	$-0.658478\pi$
$577$	−1.05867e11			−0.955119			−0.477559	+	0.878599i	$0.658478\pi$
$578$		0			0
$579$	3.28669e10	−	3.28669e10i	0.292445	−	0.292445i
$580$		0			0
$581$	−2.61857e9	+	2.61857e9i	−0.0229805	+	0.0229805i
$582$		0			0
$583$	−7.05803e10			−0.610955
$584$		0			0
$585$		−	3.66579e10i		−	0.313000i
$586$		0			0
$587$	6.57079e10	+	6.57079e10i	0.553433	+	0.553433i	0.927430	−	0.373997i	$-0.122013\pi$
$587$	6.57079e10	+	6.57079e10i	0.553433	+	0.553433i	−0.373997	+	0.927430i	$0.622013\pi$
$588$		0			0
$589$	−1.78153e8	−	1.78153e8i	−0.00148024	−	0.00148024i
$590$		0			0
$591$		−	4.44201e9i		−	0.0364108i
$592$		0			0
$593$	−1.02722e11			−0.830702			−0.415351	−	0.909661i	$-0.636341\pi$
$593$	−1.02722e11			−0.830702			−0.415351	+	0.909661i	$0.636341\pi$
$594$		0			0
$595$	−1.15667e10	+	1.15667e10i	−0.0922872	+	0.0922872i
$596$		0			0
$597$	−6.07815e10	+	6.07815e10i	−0.478491	+	0.478491i
$598$		0			0
$599$	−1.83037e11			−1.42178			−0.710889	−	0.703305i	$-0.751707\pi$
$599$	−1.83037e11			−1.42178			−0.710889	+	0.703305i	$0.751707\pi$
$600$		0			0
$601$			2.04443e11i			1.56702i	0.621381	+	0.783509i	$0.286572\pi$
$601$			2.04443e11i			1.56702i	−0.621381	+	0.783509i	$0.713428\pi$
$602$		0			0
$603$	−3.25594e10	−	3.25594e10i	−0.246267	−	0.246267i
$604$		0			0
$605$	9.56406e10	+	9.56406e10i	0.713873	+	0.713873i
$606$		0			0
$607$		−	1.68583e11i		−	1.24182i	−0.783883	−	0.620909i	$-0.786764\pi$
$607$		−	1.68583e11i		−	1.24182i	0.783883	−	0.620909i	$-0.213236\pi$
$608$		0			0
$609$	1.63222e10			0.118662
$610$		0			0
$611$	1.65318e11	−	1.65318e11i	1.18619	−	1.18619i
$612$		0			0
$613$	−1.63425e11	+	1.63425e11i	−1.15739	+	1.15739i	−0.172349	+	0.985036i	$0.555136\pi$
$613$	−1.63425e11	+	1.63425e11i	−1.15739	+	1.15739i	−0.985036	+	0.172349i	$0.944864\pi$
$614$		0			0
$615$	4.73241e10			0.330812
$616$		0			0
$617$			4.85931e10i			0.335301i	0.985847	+	0.167650i	$0.0536179\pi$
$617$			4.85931e10i			0.335301i	−0.985847	+	0.167650i	$0.946382\pi$
$618$		0			0
$619$	−8.31685e10	−	8.31685e10i	−0.566495	−	0.566495i	0.364649	−	0.931145i	$-0.381189\pi$
$619$	−8.31685e10	−	8.31685e10i	−0.566495	−	0.566495i	−0.931145	+	0.364649i	$0.881189\pi$
$620$		0			0
$621$	3.09865e10	+	3.09865e10i	0.208356	+	0.208356i
$622$		0			0
$623$			3.32080e10i			0.220440i
$624$		0			0
$625$	−1.23023e10			−0.0806247
$626$		0			0
$627$	−5.64208e9	+	5.64208e9i	−0.0365064	+	0.0365064i
$628$		0			0
$629$	2.36036e11	−	2.36036e11i	1.50791	−	1.50791i
$630$		0			0
$631$	2.65899e11			1.67725			0.838627	−	0.544706i	$-0.183359\pi$
$631$	2.65899e11			1.67725			0.838627	+	0.544706i	$0.183359\pi$
$632$		0			0
$633$		−	1.15445e11i		−	0.719052i
$634$		0			0
$635$	7.20967e10	+	7.20967e10i	0.443426	+	0.443426i
$636$		0			0
$637$	−1.81350e11	−	1.81350e11i	−1.10144	−	1.10144i
$638$		0			0
$639$			5.94403e10i			0.356515i
$640$		0			0
$641$	4.51636e10			0.267520			0.133760	−	0.991014i	$-0.457295\pi$
$641$	4.51636e10			0.267520			0.133760	+	0.991014i	$0.457295\pi$
$642$		0			0
$643$	−2.09447e11	+	2.09447e11i	−1.22526	+	1.22526i	−0.259528	+	0.965736i	$0.583567\pi$
$643$	−2.09447e11	+	2.09447e11i	−1.22526	+	1.22526i	−0.965736	+	0.259528i	$0.916433\pi$
$644$		0			0
$645$	−3.48740e10	+	3.48740e10i	−0.201494	+	0.201494i
$646$		0			0
$647$	1.55025e11			0.884679			0.442339	−	0.896848i	$-0.354149\pi$
$647$	1.55025e11			0.884679			0.442339	+	0.896848i	$0.354149\pi$
$648$		0			0
$649$			3.23633e11i			1.82421i
$650$		0			0
$651$	4.34182e8	+	4.34182e8i	0.00241740	+	0.00241740i
$652$		0			0
$653$	8.70484e10	+	8.70484e10i	0.478749	+	0.478749i	0.904731	−	0.425982i	$-0.140071\pi$
$653$	8.70484e10	+	8.70484e10i	0.478749	+	0.478749i	−0.425982	+	0.904731i	$0.640071\pi$
$654$		0			0
$655$			9.28269e9i			0.0504323i
$656$		0			0
$657$	−1.65631e10			−0.0888956
$658$		0			0
$659$	1.49023e11	−	1.49023e11i	0.790155	−	0.790155i	−0.191364	−	0.981519i	$-0.561291\pi$
$659$	1.49023e11	−	1.49023e11i	0.790155	−	0.790155i	0.981519	+	0.191364i	$0.0612910\pi$
$660$		0			0
$661$	4.42316e10	−	4.42316e10i	0.231701	−	0.231701i	−0.581702	−	0.813402i	$-0.697613\pi$
$661$	4.42316e10	−	4.42316e10i	0.231701	−	0.231701i	0.813402	+	0.581702i	$0.197613\pi$
$662$		0			0
$663$	−2.57052e11			−1.33035
$664$		0			0
$665$			9.58946e8i			0.00490352i
$666$		0			0
$667$	−2.86905e11	−	2.86905e11i	−1.44955	−	1.44955i
$668$		0			0
$669$	2.98785e10	+	2.98785e10i	0.149161	+	0.149161i
$670$		0			0
$671$			2.98016e11i			1.47011i
$672$		0			0
$673$	2.86738e11			1.39773			0.698867	−	0.715251i	$-0.253688\pi$
$673$	2.86738e11			1.39773			0.698867	+	0.715251i	$0.253688\pi$
$674$		0			0
$675$	1.84621e10	−	1.84621e10i	0.0889338	−	0.0889338i
$676$		0			0
$677$	4.43597e10	−	4.43597e10i	0.211171	−	0.211171i	−0.593594	−	0.804765i	$-0.702291\pi$
$677$	4.43597e10	−	4.43597e10i	0.211171	−	0.211171i	0.804765	+	0.593594i	$0.202291\pi$
$678$		0			0
$679$	4.13003e10			0.194301
$680$		0			0
$681$		−	2.38977e11i		−	1.11114i
$682$		0			0
$683$	5.53539e10	+	5.53539e10i	0.254370	+	0.254370i	0.822760	−	0.568390i	$-0.192433\pi$
$683$	5.53539e10	+	5.53539e10i	0.254370	+	0.254370i	−0.568390	+	0.822760i	$0.692433\pi$
$684$		0			0
$685$	−1.62013e11	−	1.62013e11i	−0.735849	−	0.735849i
$686$		0			0
$687$			1.10585e11i			0.496445i
$688$		0			0
$689$	−1.33297e11			−0.591484
$690$		0			0
$691$	−1.44286e11	+	1.44286e11i	−0.632868	+	0.632868i	−0.948786	−	0.315919i	$-0.897687\pi$
$691$	−1.44286e11	+	1.44286e11i	−0.632868	+	0.632868i	0.315919	+	0.948786i	$0.397687\pi$
$692$		0			0
$693$	1.37505e10	−	1.37505e10i	0.0596191	−	0.0596191i
$694$		0			0
$695$	9.23813e10			0.395954
$696$		0			0
$697$		−	3.31845e11i		−	1.40606i
$698$		0			0
$699$	−1.66814e10	−	1.66814e10i	−0.0698753	−	0.0698753i
$700$		0			0
$701$	−4.48422e10	−	4.48422e10i	−0.185701	−	0.185701i	0.608134	−	0.793835i	$-0.291918\pi$
$701$	−4.48422e10	−	4.48422e10i	−0.185701	−	0.185701i	−0.793835	+	0.608134i	$0.791918\pi$
$702$		0			0
$703$		−	1.95688e10i		−	0.0801203i
$704$		0			0
$705$	−8.82817e10			−0.357367
$706$		0			0
$707$	1.26964e9	−	1.26964e9i	0.00508164	−	0.00508164i
$708$		0			0
$709$	−7.07748e9	+	7.07748e9i	−0.0280088	+	0.0280088i	−0.720972	−	0.692964i	$-0.756305\pi$
$709$	−7.07748e9	+	7.07748e9i	−0.0280088	+	0.0280088i	0.692964	+	0.720972i	$0.256305\pi$
$710$		0			0
$711$	−1.24618e10			−0.0487643
$712$		0			0
$713$		−	1.52637e10i		−	0.0590612i
$714$		0			0
$715$	2.85937e11	+	2.85937e11i	1.09407	+	1.09407i
$716$		0			0
$717$	1.53648e11	+	1.53648e11i	0.581368	+	0.581368i
$718$		0			0
$719$			2.28853e11i			0.856329i	0.903701	+	0.428164i	$0.140840\pi$
$719$			2.28853e11i			0.856329i	−0.903701	+	0.428164i	$0.859160\pi$
$720$		0			0
$721$	−6.71640e9			−0.0248540
$722$		0			0
$723$	1.52832e11	−	1.52832e11i	0.559320	−	0.559320i
$724$		0			0
$725$	−1.70941e11	+	1.70941e11i	−0.618720	+	0.618720i
$726$		0			0
$727$	−3.57335e9			−0.0127920			−0.00639599	−	0.999980i	$-0.502036\pi$
$727$	−3.57335e9			−0.0127920			−0.00639599	+	0.999980i	$0.502036\pi$
$728$		0			0
$729$			1.04604e10i			0.0370370i
$730$		0			0
$731$	2.44543e11	+	2.44543e11i	0.856418	+	0.856418i
$732$		0			0
$733$	−1.90758e9	−	1.90758e9i	−0.00660797	−	0.00660797i	0.703795	−	0.710403i	$-0.251487\pi$
$733$	−1.90758e9	−	1.90758e9i	−0.00660797	−	0.00660797i	−0.710403	+	0.703795i	$0.751487\pi$
$734$		0			0
$735$			9.68428e10i			0.331832i
$736$		0			0
$737$	5.07937e11			1.72163
$738$		0			0
$739$	2.04883e11	−	2.04883e11i	0.686955	−	0.686955i	−0.274603	−	0.961558i	$-0.588546\pi$
$739$	2.04883e11	−	2.04883e11i	0.686955	−	0.686955i	0.961558	+	0.274603i	$0.0885463\pi$
$740$		0			0
$741$	−1.06556e10	+	1.06556e10i	−0.0353430	+	0.0353430i
$742$		0			0
$743$	2.28437e11			0.749569			0.374785	−	0.927112i	$-0.377717\pi$
$743$	2.28437e11			0.749569			0.374785	+	0.927112i	$0.377717\pi$
$744$		0			0
$745$			2.45000e11i			0.795318i
$746$		0			0
$747$	1.55380e10	+	1.55380e10i	0.0499014	+	0.0499014i
$748$		0			0
$749$	3.05503e10	+	3.05503e10i	0.0970708	+	0.0970708i
$750$		0			0
$751$			6.71665e10i			0.211151i	0.994411	+	0.105575i	$0.0336685\pi$
$751$			6.71665e10i			0.211151i	−0.994411	+	0.105575i	$0.966332\pi$
$752$		0			0
$753$	−1.59767e11			−0.496943
$754$		0			0
$755$	8.79912e10	−	8.79912e10i	0.270802	−	0.270802i
$756$		0			0
$757$	1.99263e11	−	1.99263e11i	0.606797	−	0.606797i	−0.335311	−	0.942108i	$-0.608841\pi$
$757$	1.99263e11	−	1.99263e11i	0.606797	−	0.606797i	0.942108	+	0.335311i	$0.108841\pi$
$758$		0			0
$759$	−4.83400e11			−1.45660
$760$		0			0
$761$			3.19590e11i			0.952917i	0.879197	+	0.476458i	$0.158080\pi$
$761$			3.19590e11i			0.952917i	−0.879197	+	0.476458i	$0.841920\pi$
$762$		0			0
$763$	−1.39240e10	−	1.39240e10i	−0.0410833	−	0.0410833i
$764$		0			0
$765$	6.86343e10	+	6.86343e10i	0.200399	+	0.200399i
$766$		0			0
$767$			6.11209e11i			1.76607i
$768$		0			0
$769$	5.20977e11			1.48975			0.744875	−	0.667204i	$-0.232509\pi$
$769$	5.20977e11			1.48975			0.744875	+	0.667204i	$0.232509\pi$
$770$		0			0
$771$	−1.79407e10	+	1.79407e10i	−0.0507717	+	0.0507717i
$772$		0			0
$773$	−1.63711e11	+	1.63711e11i	−0.458520	+	0.458520i	−0.898170	−	0.439649i	$-0.855103\pi$
$773$	−1.63711e11	+	1.63711e11i	−0.458520	+	0.458520i	0.439649	+	0.898170i	$0.355103\pi$
$774$		0			0
$775$	−9.09430e9			−0.0252094
$776$		0			0
$777$			4.76917e10i			0.130845i
$778$		0			0
$779$	−1.37560e10	−	1.37560e10i	−0.0373543	−	0.0373543i
$780$		0			0
$781$	−4.63644e11	−	4.63644e11i	−1.24618	−	1.24618i
$782$		0			0
$783$		−	9.68525e10i		−	0.257670i
$784$		0			0
$785$	2.68206e11			0.706301
$786$		0			0
$787$	−5.37625e11	+	5.37625e11i	−1.40146	+	1.40146i	−0.605978	+	0.795481i	$0.707218\pi$
$787$	−5.37625e11	+	5.37625e11i	−1.40146	+	1.40146i	−0.795481	+	0.605978i	$0.792782\pi$
$788$		0			0
$789$	−3.03890e11	+	3.03890e11i	−0.784166	+	0.784166i
$790$		0			0
$791$	6.88915e10			0.175979
$792$		0			0
$793$			5.62829e11i			1.42326i
$794$		0			0
$795$	3.55910e10	+	3.55910e10i	0.0890987	+	0.0890987i
$796$		0			0
$797$	3.65947e11	+	3.65947e11i	0.906953	+	0.906953i	0.996025	−	0.0890724i	$-0.0283902\pi$
$797$	3.65947e11	+	3.65947e11i	0.906953	+	0.906953i	−0.0890724	+	0.996025i	$0.528390\pi$
$798$		0			0
$799$			6.19048e11i			1.51893i
$800$		0			0
$801$	1.97049e11			0.478680
$802$		0			0
$803$	1.29195e11	−	1.29195e11i	0.310730	−	0.310730i
$804$		0			0
$805$	−4.10801e10	+	4.10801e10i	−0.0978246	+	0.0978246i
$806$		0			0
$807$	−1.67219e11			−0.394268
$808$		0			0
$809$		−	1.21954e11i		−	0.284708i	−0.989816	−	0.142354i	$-0.954533\pi$
$809$		−	1.21954e11i		−	0.284708i	0.989816	−	0.142354i	$-0.0454672\pi$
$810$		0			0
$811$	−4.22150e11	−	4.22150e11i	−0.975851	−	0.975851i	0.0238639	−	0.999715i	$-0.492403\pi$
$811$	−4.22150e11	−	4.22150e11i	−0.975851	−	0.975851i	−0.999715	+	0.0238639i	$0.992403\pi$
$812$		0			0
$813$	−2.39781e11	−	2.39781e11i	−0.548848	−	0.548848i
$814$		0			0
$815$		−	3.13249e11i		−	0.710003i
$816$		0			0
$817$	2.02741e10			0.0455043
$818$		0			0
$819$	2.59690e10	−	2.59690e10i	0.0577191	−	0.0577191i
$820$		0			0
$821$	−2.99390e11	+	2.99390e11i	−0.658970	+	0.658970i	−0.955136	−	0.296167i	$-0.904292\pi$
$821$	−2.99390e11	+	2.99390e11i	−0.658970	+	0.658970i	0.296167	+	0.955136i	$0.404292\pi$
$822$		0			0
$823$	−1.81497e11			−0.395614			−0.197807	−	0.980241i	$-0.563382\pi$
$823$	−1.81497e11			−0.395614			−0.197807	+	0.980241i	$0.563382\pi$
$824$		0			0
$825$			2.88015e11i			0.621727i
$826$		0			0
$827$	1.99402e11	+	1.99402e11i	0.426292	+	0.426292i	0.887363	−	0.461071i	$-0.152535\pi$
$827$	1.99402e11	+	1.99402e11i	0.426292	+	0.426292i	−0.461071	+	0.887363i	$0.652535\pi$
$828$		0			0
$829$	−4.15130e11	−	4.15130e11i	−0.878953	−	0.878953i	0.114473	−	0.993426i	$-0.463482\pi$
$829$	−4.15130e11	−	4.15130e11i	−0.878953	−	0.878953i	−0.993426	+	0.114473i	$0.963482\pi$
$830$		0			0
$831$		−	1.73603e11i		−	0.364044i
$832$		0			0
$833$	6.79079e11			1.41039
$834$		0			0
$835$	2.87273e10	−	2.87273e10i	0.0590947	−	0.0590947i
$836$		0			0
$837$	2.57635e9	−	2.57635e9i	0.00524931	−	0.00524931i
$838$		0			0
$839$	−1.79380e11			−0.362014			−0.181007	−	0.983482i	$-0.557936\pi$
$839$	−1.79380e11			−0.362014			−0.181007	+	0.983482i	$0.557936\pi$
$840$		0			0
$841$			3.96512e11i			0.792634i
$842$		0			0
$843$	−2.21834e11	−	2.21834e11i	−0.439257	−	0.439257i
$844$		0			0
$845$	3.27817e11	+	3.27817e11i	0.642990	+	0.642990i
$846$		0			0
$847$			1.35506e11i			0.263285i
$848$		0			0
$849$	2.58832e11			0.498181
$850$		0			0
$851$	8.38303e11	−	8.38303e11i	1.59839	−	1.59839i
$852$		0			0
$853$	−3.38129e11	+	3.38129e11i	−0.638684	+	0.638684i	−0.950231	−	0.311547i	$-0.899153\pi$
$853$	−3.38129e11	+	3.38129e11i	−0.638684	+	0.638684i	0.311547	+	0.950231i	$0.399153\pi$
$854$		0			0
$855$	5.69018e9			0.0106478
$856$		0			0
$857$		−	2.97481e11i		−	0.551488i	−0.961231	−	0.275744i	$-0.911076\pi$
$857$		−	2.97481e11i		−	0.551488i	0.961231	−	0.275744i	$-0.0889242\pi$
$858$		0			0
$859$	5.13114e11	+	5.13114e11i	0.942412	+	0.942412i	0.998430	−	0.0560173i	$-0.0178402\pi$
$859$	5.13114e11	+	5.13114e11i	0.942412	+	0.942412i	−0.0560173	+	0.998430i	$0.517840\pi$
$860$		0			0
$861$	3.35251e10	+	3.35251e10i	0.0610038	+	0.0610038i
$862$		0			0
$863$			2.73974e11i			0.493931i	0.969024	+	0.246966i	$0.0794334\pi$
$863$			2.73974e11i			0.493931i	−0.969024	+	0.246966i	$0.920567\pi$
$864$		0			0
$865$	−4.67264e11			−0.834637
$866$		0			0
$867$	2.50601e11	−	2.50601e11i	0.443513	−	0.443513i
$868$		0			0
$869$	9.72040e10	−	9.72040e10i	0.170453	−	0.170453i
$870$		0			0
$871$	9.59282e11			1.66676
$872$		0			0
$873$		−	2.45067e11i		−	0.421918i
$874$		0			0
$875$	6.19281e10	+	6.19281e10i	0.105647	+	0.105647i
$876$		0			0
$877$	−5.69921e11	−	5.69921e11i	−0.963421	−	0.963421i	0.0359328	−	0.999354i	$-0.488560\pi$
$877$	−5.69921e11	−	5.69921e11i	−0.963421	−	0.963421i	−0.999354	+	0.0359328i	$0.988560\pi$
$878$		0			0
$879$			5.15018e10i			0.0862714i
$880$		0			0
$881$	5.83934e11			0.969303			0.484652	−	0.874707i	$-0.338946\pi$
$881$	5.83934e11			0.969303			0.484652	+	0.874707i	$0.338946\pi$
$882$		0			0
$883$	2.75500e11	−	2.75500e11i	0.453188	−	0.453188i	−0.443223	−	0.896411i	$-0.646165\pi$
$883$	2.75500e11	−	2.75500e11i	0.453188	−	0.453188i	0.896411	+	0.443223i	$0.146165\pi$
$884$		0			0
$885$	1.63196e11	−	1.63196e11i	0.266034	−	0.266034i
$886$		0			0
$887$	−7.28074e11			−1.17620			−0.588100	−	0.808788i	$-0.700124\pi$
$887$	−7.28074e11			−1.17620			−0.588100	+	0.808788i	$0.700124\pi$
$888$		0			0
$889$			1.02149e11i			0.163541i
$890$		0			0
$891$	−8.15924e10	−	8.15924e10i	−0.129461	−	0.129461i
$892$		0			0
$893$	2.56613e10	+	2.56613e10i	0.0403528	+	0.0403528i
$894$		0			0
$895$		−	1.55545e11i		−	0.242417i
$896$		0			0
$897$	−9.12942e11			−1.41018
$898$		0			0
$899$	−2.38544e10	+	2.38544e10i	−0.0365199	+	0.0365199i
$900$		0			0
$901$	2.49571e11	−	2.49571e11i	0.378699	−	0.378699i
$902$		0			0
$903$	−4.94105e10			−0.0743136
$904$		0			0
$905$		−	3.80850e10i		−	0.0567753i
$906$		0			0
$907$	−2.39872e11	−	2.39872e11i	−0.354446	−	0.354446i	0.507315	−	0.861761i	$-0.330638\pi$
$907$	−2.39872e11	−	2.39872e11i	−0.354446	−	0.354446i	−0.861761	+	0.507315i	$0.830638\pi$
$908$		0			0
$909$	−7.53378e9	−	7.53378e9i	−0.0110346	−	0.0110346i
$910$		0			0
$911$		−	4.20108e11i		−	0.609941i	−0.952362	−	0.304970i	$-0.901353\pi$
$911$		−	4.20108e11i		−	0.609941i	0.952362	−	0.304970i	$-0.0986466\pi$
$912$		0			0
$913$	−2.42398e11			−0.348856
$914$		0			0
$915$	1.50278e11	−	1.50278e11i	0.214394	−	0.214394i
$916$		0			0
$917$	−6.57599e9	+	6.57599e9i	−0.00930001	+	0.00930001i
$918$		0			0
$919$	3.87216e11			0.542864			0.271432	−	0.962458i	$-0.412503\pi$
$919$	3.87216e11			0.542864			0.271432	+	0.962458i	$0.412503\pi$
$920$		0			0
$921$		−	5.82660e11i		−	0.809798i
$922$		0			0
$923$	−8.75631e11	−	8.75631e11i	−1.20646	−	1.20646i
$924$		0			0
$925$	−4.99470e11	−	4.99470e11i	−0.682249	−	0.682249i
$926$		0			0
$927$			3.98537e10i			0.0539696i
$928$		0			0
$929$	−1.07580e12			−1.44433			−0.722167	−	0.691718i	$-0.756854\pi$
$929$	−1.07580e12			−1.44433			−0.722167	+	0.691718i	$0.756854\pi$
$930$		0			0
$931$	2.81498e10	−	2.81498e10i	0.0374694	−	0.0374694i
$932$		0			0
$933$	−1.27982e11	+	1.27982e11i	−0.168898	+	0.168898i
$934$		0			0
$935$	−1.07072e12			−1.40097
$936$		0			0
$937$		−	3.02180e11i		−	0.392019i	−0.980602	−	0.196009i	$-0.937202\pi$
$937$		−	3.02180e11i		−	0.392019i	0.980602	−	0.196009i	$-0.0627983\pi$
$938$		0			0
$939$	−1.59953e11	−	1.59953e11i	−0.205745	−	0.205745i
$940$		0			0
$941$	−3.74179e11	−	3.74179e11i	−0.477222	−	0.477222i	0.427020	−	0.904242i	$-0.359563\pi$
$941$	−3.74179e11	−	3.74179e11i	−0.477222	−	0.477222i	−0.904242	+	0.427020i	$0.859563\pi$
$942$		0			0
$943$		−	1.17858e12i		−	1.49043i
$944$		0			0
$945$	−1.38677e10			−0.0173891
$946$		0			0
$947$	2.62216e11	−	2.62216e11i	0.326032	−	0.326032i	−0.525044	−	0.851075i	$-0.675951\pi$
$947$	2.62216e11	−	2.62216e11i	0.326032	−	0.326032i	0.851075	+	0.525044i	$0.175951\pi$
$948$		0			0
$949$	2.43995e11	−	2.43995e11i	0.300827	−	0.300827i
$950$		0			0
$951$	−3.66509e11			−0.448087
$952$		0			0
$953$		−	1.64130e11i		−	0.198983i	−0.995038	−	0.0994914i	$-0.968278\pi$
$953$		−	1.64130e11i		−	0.198983i	0.995038	−	0.0994914i	$-0.0317216\pi$
$954$		0			0
$955$	−3.60398e11	−	3.60398e11i	−0.433281	−	0.433281i
$956$		0			0
$957$	7.55465e11	+	7.55465e11i	0.900672	+	0.900672i
$958$		0			0
$959$		−	2.29545e11i		−	0.271390i
$960$		0			0
$961$	8.51622e11			0.998512
$962$		0			0
$963$	1.81279e11	−	1.81279e11i	0.210786	−	0.210786i
$964$		0			0
$965$	2.58553e11	−	2.58553e11i	0.298154	−	0.298154i
$966$		0			0
$967$	8.28232e11			0.947210			0.473605	−	0.880737i	$-0.342952\pi$
$967$	8.28232e11			0.947210			0.473605	+	0.880737i	$0.342952\pi$
$968$		0			0
$969$		−	3.99006e10i		−	0.0452569i
$970$		0			0
$971$	6.42797e11	+	6.42797e11i	0.723097	+	0.723097i	0.969235	−	0.246138i	$-0.0791615\pi$
$971$	6.42797e11	+	6.42797e11i	0.723097	+	0.723097i	−0.246138	+	0.969235i	$0.579161\pi$
$972$		0			0
$973$	6.54442e10	+	6.54442e10i	0.0730163	+	0.0730163i
$974$		0			0
$975$			5.43941e11i			0.601913i
$976$		0			0
$977$	−3.97049e10			−0.0435779			−0.0217889	−	0.999763i	$-0.506936\pi$
$977$	−3.97049e10			−0.0435779			−0.0217889	+	0.999763i	$0.506936\pi$
$978$		0			0
$979$	−1.53702e12	+	1.53702e12i	−1.67320	+	1.67320i
$980$		0			0
$981$	−8.26219e10	+	8.26219e10i	−0.0892111	+	0.0892111i
$982$		0			0
$983$	9.75459e11			1.04471			0.522354	−	0.852729i	$-0.325054\pi$
$983$	9.75459e11			1.04471			0.522354	+	0.852729i	$0.325054\pi$
$984$		0			0
$985$		−	3.49438e10i		−	0.0371215i
$986$		0			0
$987$	−6.25400e10	−	6.25400e10i	−0.0659006	−	0.0659006i
$988$		0			0
$989$	8.68516e11	+	8.68516e11i	0.907805	+	0.907805i
$990$		0			0
$991$		−	2.75678e11i		−	0.285829i	−0.989735	−	0.142915i	$-0.954353\pi$
$991$		−	2.75678e11i		−	0.285829i	0.989735	−	0.142915i	$-0.0456475\pi$
$992$		0			0
$993$	6.89049e10			0.0708684
$994$		0			0
$995$	−4.78147e11	+	4.78147e11i	−0.487831	+	0.487831i
$996$		0			0
$997$	2.12118e11	−	2.12118e11i	0.214683	−	0.214683i	−0.591570	−	0.806253i	$-0.701492\pi$
$997$	2.12118e11	−	2.12118e11i	0.214683	−	0.214683i	0.806253	+	0.591570i	$0.201492\pi$
$998$		0			0
$999$	2.82992e11			0.284127

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	192.9.l.a.175.23		64
4.3	odd	2		48.9.l.a.19.9	✓	64
16.5	even	4		48.9.l.a.43.9	yes	64
16.11	odd	4	inner	192.9.l.a.79.23		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.9.l.a.19.9	✓	64	4.3	odd	2
48.9.l.a.43.9	yes	64	16.5	even	4
192.9.l.a.79.23		64	16.11	odd	4	inner
192.9.l.a.175.23		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)

\(f(q)\)	\(=\)	\(q+(33.0681 - 33.0681i) q^{3} +(260.136 - 260.136i) q^{5} +368.567 q^{7} -2187.00i q^{9} +O(q^{10})\)	\(q+(33.0681 - 33.0681i) q^{3} +(260.136 - 260.136i) q^{5} +368.567 q^{7} -2187.00i q^{9} +(17059.0 + 17059.0i) q^{11} +(32217.3 + 32217.3i) q^{13} -17204.4i q^{15} -120640. q^{17} +(-5000.89 + 5000.89i) q^{19} +(12187.8 - 12187.8i) q^{21} -428464. q^{23} +255284. i q^{25} +(-72320.0 - 72320.0i) q^{27} +(669611. + 669611. i) q^{29} +35624.3i q^{31} +1.12821e6 q^{33} +(95877.5 - 95877.5i) q^{35} +(-1.95653e6 + 1.95653e6i) q^{37} +2.13073e6 q^{39} +2.75070e6i q^{41} +(-2.02704e6 - 2.02704e6i) q^{43} +(-568916. - 568916. i) q^{45} -5.13135e6i q^{47} -5.62896e6 q^{49} +(-3.98935e6 + 3.98935e6i) q^{51} +(-2.06872e6 + 2.06872e6i) q^{53} +8.87528e6 q^{55} +330740. i q^{57} +(9.48573e6 + 9.48573e6i) q^{59} +(8.73489e6 + 8.73489e6i) q^{61} -806057. i q^{63} +1.67617e7 q^{65} +(1.48877e7 - 1.48877e7i) q^{67} +(-1.41685e7 + 1.41685e7i) q^{69} -2.71789e7 q^{71} -7.57343e6i q^{73} +(8.44176e6 + 8.44176e6i) q^{75} +(6.28737e6 + 6.28737e6i) q^{77} -5.69812e6i q^{79} -4.78297e6 q^{81} +(-7.10472e6 + 7.10472e6i) q^{83} +(-3.13828e7 + 3.13828e7i) q^{85} +4.42856e7 q^{87} +9.01003e7i q^{89} +(1.18742e7 + 1.18742e7i) q^{91} +(1.17803e6 + 1.17803e6i) q^{93} +2.60182e6i q^{95} +1.12056e8 q^{97} +(3.73079e7 - 3.73079e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q+O(q^{10}) \) 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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