LMFDB - Embedded newform 192.9.l.a.79.25

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [192,9,Mod(79,192)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("192.79"); S:= CuspForms(chi, 9); N := Newforms(S);

sage: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")

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:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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			79.25
Character	$\chi$	$=$	192.79
Dual form			192.9.l.a.175.25

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(33.0681 + 33.0681i) q^{3} +(214.689 + 214.689i) q^{5} +321.411 q^{7} +2187.00i q^{9} +(13451.1 - 13451.1i) q^{11} +(-3434.55 + 3434.55i) q^{13} +14198.7i q^{15} +65954.5 q^{17} +(-113520. - 113520. i) q^{19} +(10628.4 + 10628.4i) q^{21} +99132.9 q^{23} -298442. i q^{25} +(-72320.0 + 72320.0i) q^{27} +(74218.8 - 74218.8i) q^{29} -783672. i q^{31} +889604. q^{33} +(69003.3 + 69003.3i) q^{35} +(385145. + 385145. i) q^{37} -227148. q^{39} +2.10509e6i q^{41} +(2.77452e6 - 2.77452e6i) q^{43} +(-469525. + 469525. i) q^{45} -6.61433e6i q^{47} -5.66150e6 q^{49} +(2.18099e6 + 2.18099e6i) q^{51} +(873055. + 873055. i) q^{53} +5.77560e6 q^{55} -7.50775e6i q^{57} +(1.79884e6 - 1.79884e6i) q^{59} +(-1.03492e7 + 1.03492e7i) q^{61} +702925. i q^{63} -1.47472e6 q^{65} +(1.57263e7 + 1.57263e7i) q^{67} +(3.27814e6 + 3.27814e6i) q^{69} +4.51284e7 q^{71} -1.41319e7i q^{73} +(9.86893e6 - 9.86893e6i) q^{75} +(4.32332e6 - 4.32332e6i) q^{77} -5.93775e6i q^{79} -4.78297e6 q^{81} +(-4.07467e7 - 4.07467e7i) q^{83} +(1.41597e7 + 1.41597e7i) q^{85} +4.90855e6 q^{87} +3.55568e7i q^{89} +(-1.10390e6 + 1.10390e6i) q^{91} +(2.59146e7 - 2.59146e7i) q^{93} -4.87428e7i q^{95} -1.43728e7 q^{97} +(2.94175e7 + 2.94175e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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}+ \cdots - 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

Character values

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

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

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
$5$	214.689	+	214.689i	0.343502	+	0.343502i	0.857682	−	0.514180i	$-0.171904\pi$
$5$	214.689	+	214.689i	0.343502	+	0.343502i	−0.514180	+	0.857682i	$0.671904\pi$
$6$		0			0
$7$	321.411			0.133865			0.0669326	−	0.997757i	$-0.478679\pi$
$7$	321.411			0.133865			0.0669326	+	0.997757i	$0.478679\pi$
$8$		0			0
$9$			2187.00i			0.333333i
$10$		0			0
$11$	13451.1	−	13451.1i	0.918727	−	0.918727i	−0.0782097	−	0.996937i	$-0.524920\pi$
$11$	13451.1	−	13451.1i	0.918727	−	0.918727i	0.996937	+	0.0782097i	$0.0249204\pi$
$12$		0			0
$13$	−3434.55	+	3434.55i	−0.120253	+	0.120253i	−0.764672	−	0.644419i	$-0.777099\pi$
$13$	−3434.55	+	3434.55i	−0.120253	+	0.120253i	0.644419	+	0.764672i	$0.277099\pi$
$14$		0			0
$15$			14198.7i			0.280468i
$16$		0			0
$17$	65954.5			0.789676			0.394838	−	0.918751i	$-0.370801\pi$
$17$	65954.5			0.789676			0.394838	+	0.918751i	$0.370801\pi$
$18$		0			0
$19$	−113520.	−	113520.i	−0.871076	−	0.871076i	0.121514	−	0.992590i	$-0.461225\pi$
$19$	−113520.	−	113520.i	−0.871076	−	0.871076i	−0.992590	+	0.121514i	$0.961225\pi$
$20$		0			0
$21$	10628.4	+	10628.4i	0.0546503	+	0.0546503i
$22$		0			0
$23$	99132.9			0.354247			0.177124	−	0.984189i	$-0.443321\pi$
$23$	99132.9			0.354247			0.177124	+	0.984189i	$0.443321\pi$
$24$		0			0
$25$		−	298442.i		−	0.764012i
$26$		0			0
$27$	−72320.0	+	72320.0i	−0.136083	+	0.136083i
$28$		0			0
$29$	74218.8	−	74218.8i	0.104935	−	0.104935i	−0.652690	−	0.757625i	$-0.726360\pi$
$29$	74218.8	−	74218.8i	0.104935	−	0.104935i	0.757625	+	0.652690i	$0.226360\pi$
$30$		0			0
$31$		−	783672.i		−	0.848570i	−0.905529	−	0.424285i	$-0.860525\pi$
$31$		−	783672.i		−	0.848570i	0.905529	−	0.424285i	$-0.139475\pi$
$32$		0			0
$33$	889604.			0.750138
$34$		0			0
$35$	69003.3	+	69003.3i	0.0459830	+	0.0459830i
$36$		0			0
$37$	385145.	+	385145.i	0.205502	+	0.205502i	0.802353	−	0.596850i	$-0.203581\pi$
$37$	385145.	+	385145.i	0.205502	+	0.205502i	−0.596850	+	0.802353i	$0.703581\pi$
$38$		0			0
$39$	−227148.			−0.0981863
$40$		0			0
$41$			2.10509e6i			0.744964i	0.928039	+	0.372482i	$0.121493\pi$
$41$			2.10509e6i			0.744964i	−0.928039	+	0.372482i	$0.878507\pi$
$42$		0			0
$43$	2.77452e6	−	2.77452e6i	0.811548	−	0.811548i	−0.173318	−	0.984866i	$-0.555449\pi$
$43$	2.77452e6	−	2.77452e6i	0.811548	−	0.811548i	0.984866	+	0.173318i	$0.0554489\pi$
$44$		0			0
$45$	−469525.	+	469525.i	−0.114501	+	0.114501i
$46$		0			0
$47$		−	6.61433e6i		−	1.35548i	−0.735300	−	0.677742i	$-0.762959\pi$
$47$		−	6.61433e6i		−	1.35548i	0.735300	−	0.677742i	$-0.237041\pi$
$48$		0			0
$49$	−5.66150e6			−0.982080
$50$		0			0
$51$	2.18099e6	+	2.18099e6i	0.322384	+	0.322384i
$52$		0			0
$53$	873055.	+	873055.i	0.110647	+	0.110647i	0.760263	−	0.649616i	$-0.225070\pi$
$53$	873055.	+	873055.i	0.110647	+	0.110647i	−0.649616	+	0.760263i	$0.725070\pi$
$54$		0			0
$55$	5.77560e6			0.631170
$56$		0			0
$57$		−	7.50775e6i		−	0.711231i
$58$		0			0
$59$	1.79884e6	−	1.79884e6i	0.148451	−	0.148451i	−0.628975	−	0.777426i	$-0.716525\pi$
$59$	1.79884e6	−	1.79884e6i	0.148451	−	0.148451i	0.777426	+	0.628975i	$0.216525\pi$
$60$		0			0
$61$	−1.03492e7	+	1.03492e7i	−0.747458	+	0.747458i	−0.974001	−	0.226543i	$-0.927258\pi$
$61$	−1.03492e7	+	1.03492e7i	−0.747458	+	0.747458i	0.226543	+	0.974001i	$0.427258\pi$
$62$		0			0
$63$			702925.i			0.0446218i
$64$		0			0
$65$	−1.47472e6			−0.0826144
$66$		0			0
$67$	1.57263e7	+	1.57263e7i	0.780418	+	0.780418i	0.979901	−	0.199483i	$-0.0639264\pi$
$67$	1.57263e7	+	1.57263e7i	0.780418	+	0.780418i	−0.199483	+	0.979901i	$0.563926\pi$
$68$		0			0
$69$	3.27814e6	+	3.27814e6i	0.144621	+	0.144621i
$70$		0			0
$71$	4.51284e7			1.77589			0.887945	−	0.459949i	$-0.152132\pi$
$71$	4.51284e7			1.77589			0.887945	+	0.459949i	$0.152132\pi$
$72$		0			0
$73$		−	1.41319e7i		−	0.497631i	−0.968551	−	0.248816i	$-0.919959\pi$
$73$		−	1.41319e7i		−	0.497631i	0.968551	−	0.248816i	$-0.0800413\pi$
$74$		0			0
$75$	9.86893e6	−	9.86893e6i	0.311907	−	0.311907i
$76$		0			0
$77$	4.32332e6	−	4.32332e6i	0.122986	−	0.122986i
$78$		0			0
$79$		−	5.93775e6i		−	0.152445i	−0.997091	−	0.0762225i	$-0.975714\pi$
$79$		−	5.93775e6i		−	0.152445i	0.997091	−	0.0762225i	$-0.0242859\pi$
$80$		0			0
$81$	−4.78297e6			−0.111111
$82$		0			0
$83$	−4.07467e7	−	4.07467e7i	−0.858579	−	0.858579i	0.132592	−	0.991171i	$-0.457670\pi$
$83$	−4.07467e7	−	4.07467e7i	−0.858579	−	0.858579i	−0.991171	+	0.132592i	$0.957670\pi$
$84$		0			0
$85$	1.41597e7	+	1.41597e7i	0.271255	+	0.271255i
$86$		0			0
$87$	4.90855e6			0.0856794
$88$		0			0
$89$			3.55568e7i			0.566712i	0.959015	+	0.283356i	$0.0914478\pi$
$89$			3.55568e7i			0.566712i	−0.959015	+	0.283356i	$0.908552\pi$
$90$		0			0
$91$	−1.10390e6	+	1.10390e6i	−0.0160977	+	0.0160977i
$92$		0			0
$93$	2.59146e7	−	2.59146e7i	0.346427	−	0.346427i
$94$		0			0
$95$		−	4.87428e7i		−	0.598433i
$96$		0			0
$97$	−1.43728e7			−0.162351			−0.0811755	−	0.996700i	$-0.525867\pi$
$97$	−1.43728e7			−0.162351			−0.0811755	+	0.996700i	$0.525867\pi$
$98$		0			0
$99$	2.94175e7	+	2.94175e7i	0.306242	+	0.306242i
$100$		0			0
$101$	1.27428e8	+	1.27428e8i	1.22456	+	1.22456i	0.965994	+	0.258565i	$0.0832495\pi$
$101$	1.27428e8	+	1.27428e8i	1.22456	+	1.22456i	0.258565	+	0.965994i	$0.416750\pi$
$102$		0			0
$103$	7.05349e7			0.626694			0.313347	−	0.949639i	$-0.398550\pi$
$103$	7.05349e7			0.626694			0.313347	+	0.949639i	$0.398550\pi$
$104$		0			0
$105$			4.56362e6i			0.0375450i
$106$		0			0
$107$	4.30920e7	−	4.30920e7i	0.328746	−	0.328746i	−0.523363	−	0.852110i	$-0.675323\pi$
$107$	4.30920e7	−	4.30920e7i	0.328746	−	0.328746i	0.852110	+	0.523363i	$0.175323\pi$
$108$		0			0
$109$	1.74484e8	−	1.74484e8i	1.23609	−	1.23609i	0.274502	−	0.961586i	$-0.411487\pi$
$109$	1.74484e8	−	1.74484e8i	1.23609	−	1.23609i	0.961586	−	0.274502i	$-0.0885131\pi$
$110$		0			0
$111$			2.54720e7i			0.167792i
$112$		0			0
$113$	1.52983e8			0.938275			0.469138	−	0.883125i	$-0.344565\pi$
$113$	1.52983e8			0.938275			0.469138	+	0.883125i	$0.344565\pi$
$114$		0			0
$115$	2.12827e7	+	2.12827e7i	0.121685	+	0.121685i
$116$		0			0
$117$	−7.51136e6	−	7.51136e6i	−0.0400844	−	0.0400844i
$118$		0			0
$119$	2.11985e7			0.105710
$120$		0			0
$121$		−	1.47504e8i		−	0.688119i
$122$		0			0
$123$	−6.96114e7	+	6.96114e7i	−0.304130	+	0.304130i
$124$		0			0
$125$	1.47935e8	−	1.47935e8i	0.605942	−	0.605942i
$126$		0			0
$127$			2.43669e8i			0.936667i	0.883552	+	0.468334i	$0.155145\pi$
$127$			2.43669e8i			0.936667i	−0.883552	+	0.468334i	$0.844855\pi$
$128$		0			0
$129$	1.83496e8			0.662626
$130$		0			0
$131$	1.01426e7	+	1.01426e7i	0.0344401	+	0.0344401i	0.724117	−	0.689677i	$-0.242247\pi$
$131$	1.01426e7	+	1.01426e7i	0.0344401	+	0.0344401i	−0.689677	+	0.724117i	$0.742247\pi$
$132$		0			0
$133$	−3.64864e7	−	3.64864e7i	−0.116607	−	0.116607i
$134$		0			0
$135$	−3.10526e7			−0.0934895
$136$		0			0
$137$		−	5.43447e8i		−	1.54268i	−0.636425	−	0.771339i	$-0.719587\pi$
$137$		−	5.43447e8i		−	1.54268i	0.636425	−	0.771339i	$-0.280413\pi$
$138$		0			0
$139$	5.06935e8	−	5.06935e8i	1.35798	−	1.35798i	0.481572	−	0.876407i	$-0.340066\pi$
$139$	5.06935e8	−	5.06935e8i	1.35798	−	1.35798i	0.876407	−	0.481572i	$-0.159934\pi$
$140$		0			0
$141$	2.18723e8	−	2.18723e8i	0.553374	−	0.553374i
$142$		0			0
$143$			9.23968e7i			0.220960i
$144$		0			0
$145$	3.18679e7			0.0720911
$146$		0			0
$147$	−1.87215e8	−	1.87215e8i	−0.400933	−	0.400933i
$148$		0			0
$149$	1.51435e8	+	1.51435e8i	0.307241	+	0.307241i	0.843839	−	0.536597i	$-0.180290\pi$
$149$	1.51435e8	+	1.51435e8i	0.307241	+	0.307241i	−0.536597	+	0.843839i	$0.680290\pi$
$150$		0			0
$151$	7.95362e8			1.52988			0.764939	−	0.644103i	$-0.222769\pi$
$151$	7.95362e8			1.52988			0.764939	+	0.644103i	$0.222769\pi$
$152$		0			0
$153$			1.44243e8i			0.263225i
$154$		0			0
$155$	1.68246e8	−	1.68246e8i	0.291486	−	0.291486i
$156$		0			0
$157$	6.55541e7	−	6.55541e7i	0.107895	−	0.107895i	−0.651098	−	0.758993i	$-0.725691\pi$
$157$	6.55541e7	−	6.55541e7i	0.107895	−	0.107895i	0.758993	+	0.651098i	$0.225691\pi$
$158$		0			0
$159$			5.77405e7i			0.0903425i
$160$		0			0
$161$	3.18623e7			0.0474214
$162$		0			0
$163$	4.97850e8	+	4.97850e8i	0.705258	+	0.705258i	0.965534	−	0.260277i	$-0.0838137\pi$
$163$	4.97850e8	+	4.97850e8i	0.705258	+	0.705258i	−0.260277	+	0.965534i	$0.583814\pi$
$164$		0			0
$165$	1.90988e8	+	1.90988e8i	0.257674	+	0.257674i
$166$		0			0
$167$	−6.10230e8			−0.784563			−0.392282	−	0.919845i	$-0.628314\pi$
$167$	−6.10230e8			−0.784563			−0.392282	+	0.919845i	$0.628314\pi$
$168$		0			0
$169$			7.92138e8i			0.971078i
$170$		0			0
$171$	2.48267e8	−	2.48267e8i	0.290359	−	0.290359i
$172$		0			0
$173$	3.08198e8	−	3.08198e8i	0.344068	−	0.344068i	−0.513826	−	0.857894i	$-0.671772\pi$
$173$	3.08198e8	−	3.08198e8i	0.344068	−	0.344068i	0.857894	+	0.513826i	$0.171772\pi$
$174$		0			0
$175$		−	9.59225e7i		−	0.102275i
$176$		0			0
$177$	1.18968e8			0.121210
$178$		0			0
$179$	−7.53399e8	−	7.53399e8i	−0.733859	−	0.733859i	0.237523	−	0.971382i	$-0.423665\pi$
$179$	−7.53399e8	−	7.53399e8i	−0.733859	−	0.733859i	−0.971382	+	0.237523i	$0.923665\pi$
$180$		0			0
$181$	1.14962e8	+	1.14962e8i	0.107112	+	0.107112i	0.758632	−	0.651520i	$-0.225868\pi$
$181$	1.14962e8	+	1.14962e8i	0.107112	+	0.107112i	−0.651520	+	0.758632i	$0.725868\pi$
$182$		0			0
$183$	−6.84456e8			−0.610297
$184$		0			0
$185$			1.65373e8i			0.141181i
$186$		0			0
$187$	8.87160e8	−	8.87160e8i	0.725497	−	0.725497i
$188$		0			0
$189$	−2.32444e7	+	2.32444e7i	−0.0182168	+	0.0182168i
$190$		0			0
$191$			1.97297e9i			1.48247i	0.671245	+	0.741236i	$0.265760\pi$
$191$			1.97297e9i			1.48247i	−0.671245	+	0.741236i	$0.734240\pi$
$192$		0			0
$193$	−2.10182e9			−1.51484			−0.757419	−	0.652929i	$-0.773540\pi$
$193$	−2.10182e9			−1.51484			−0.757419	+	0.652929i	$0.773540\pi$
$194$		0			0
$195$	−4.87662e7	−	4.87662e7i	−0.0337272	−	0.0337272i
$196$		0			0
$197$	9.25864e7	+	9.25864e7i	0.0614727	+	0.0614727i	0.737175	−	0.675702i	$-0.236159\pi$
$197$	9.25864e7	+	9.25864e7i	0.0614727	+	0.0614727i	−0.675702	+	0.737175i	$0.736159\pi$
$198$		0			0
$199$	−3.75161e8			−0.239225			−0.119612	−	0.992821i	$-0.538165\pi$
$199$	−3.75161e8			−0.239225			−0.119612	+	0.992821i	$0.538165\pi$
$200$		0			0
$201$			1.04008e9i			0.637208i
$202$		0			0
$203$	2.38547e7	−	2.38547e7i	0.0140472	−	0.0140472i
$204$		0			0
$205$	−4.51940e8	+	4.51940e8i	−0.255897	+	0.255897i
$206$		0			0
$207$			2.16804e8i			0.118082i
$208$		0			0
$209$	−3.05392e9			−1.60056
$210$		0			0
$211$	−8.36177e8	−	8.36177e8i	−0.421860	−	0.421860i	0.463984	−	0.885844i	$-0.346420\pi$
$211$	−8.36177e8	−	8.36177e8i	−0.421860	−	0.421860i	−0.885844	+	0.463984i	$0.846420\pi$
$212$		0			0
$213$	1.49231e9	+	1.49231e9i	0.725004	+	0.725004i
$214$		0			0
$215$	1.19132e9			0.557537
$216$		0			0
$217$		−	2.51881e8i		−	0.113594i
$218$		0			0
$219$	4.67314e8	−	4.67314e8i	0.203157	−	0.203157i
$220$		0			0
$221$	−2.26524e8	+	2.26524e8i	−0.0949610	+	0.0949610i
$222$		0			0
$223$			3.15369e9i			1.27526i	0.770342	+	0.637631i	$0.220086\pi$
$223$			3.15369e9i			1.27526i	−0.770342	+	0.637631i	$0.779914\pi$
$224$		0			0
$225$	6.52693e8			0.254671
$226$		0			0
$227$	−2.85405e9	−	2.85405e9i	−1.07487	−	1.07487i	−0.996960	−	0.0779139i	$-0.975174\pi$
$227$	−2.85405e9	−	2.85405e9i	−1.07487	−	1.07487i	−0.0779139	−	0.996960i	$-0.524826\pi$
$228$		0			0
$229$	4.08940e8	+	4.08940e8i	0.148702	+	0.148702i	0.777538	−	0.628836i	$-0.216468\pi$
$229$	4.08940e8	+	4.08940e8i	0.148702	+	0.148702i	−0.628836	+	0.777538i	$0.716468\pi$
$230$		0			0
$231$	2.85928e8			0.100417
$232$		0			0
$233$			3.36265e8i			0.114093i	0.998372	+	0.0570463i	$0.0181683\pi$
$233$			3.36265e8i			0.114093i	−0.998372	+	0.0570463i	$0.981832\pi$
$234$		0			0
$235$	1.42002e9	−	1.42002e9i	0.465612	−	0.465612i
$236$		0			0
$237$	1.96350e8	−	1.96350e8i	0.0622354	−	0.0622354i
$238$		0			0
$239$			4.68464e8i			0.143577i	0.997420	+	0.0717885i	$0.0228707\pi$
$239$			4.68464e8i			0.143577i	−0.997420	+	0.0717885i	$0.977129\pi$
$240$		0			0
$241$	−6.11577e9			−1.81294			−0.906469	−	0.422273i	$-0.861232\pi$
$241$	−6.11577e9			−1.81294			−0.906469	+	0.422273i	$0.861232\pi$
$242$		0			0
$243$	−1.58164e8	−	1.58164e8i	−0.0453609	−	0.0453609i
$244$		0			0
$245$	−1.21546e9	−	1.21546e9i	−0.337347	−	0.337347i
$246$		0			0
$247$	7.79777e8			0.209499
$248$		0			0
$249$		−	2.69483e9i		−	0.701027i
$250$		0			0
$251$	−8.62591e8	+	8.62591e8i	−0.217325	+	0.217325i	−0.807370	−	0.590045i	$-0.799110\pi$
$251$	−8.62591e8	+	8.62591e8i	−0.217325	+	0.217325i	0.590045	+	0.807370i	$0.299110\pi$
$252$		0			0
$253$	1.33344e9	−	1.33344e9i	0.325456	−	0.325456i
$254$		0			0
$255$			9.36469e8i			0.221479i
$256$		0			0
$257$	−6.89191e9			−1.57982			−0.789909	−	0.613223i	$-0.789873\pi$
$257$	−6.89191e9			−1.57982			−0.789909	+	0.613223i	$0.789873\pi$
$258$		0			0
$259$	1.23790e8	+	1.23790e8i	0.0275096	+	0.0275096i
$260$		0			0
$261$	1.62316e8	+	1.62316e8i	0.0349785	+	0.0349785i
$262$		0			0
$263$	−8.36743e9			−1.74892			−0.874459	−	0.485100i	$-0.838783\pi$
$263$	−8.36743e9			−1.74892			−0.874459	+	0.485100i	$0.838783\pi$
$264$		0			0
$265$			3.74870e8i			0.0760147i
$266$		0			0
$267$	−1.17580e9	+	1.17580e9i	−0.231359	+	0.231359i
$268$		0			0
$269$	4.28997e9	−	4.28997e9i	0.819304	−	0.819304i	−0.166703	−	0.986007i	$-0.553312\pi$
$269$	4.28997e9	−	4.28997e9i	0.819304	−	0.819304i	0.986007	+	0.166703i	$0.0533122\pi$
$270$		0			0
$271$			6.13114e9i			1.13675i	0.822770	+	0.568374i	$0.192427\pi$
$271$			6.13114e9i			1.13675i	−0.822770	+	0.568374i	$0.807573\pi$
$272$		0			0
$273$	−7.30078e7			−0.0131437
$274$		0			0
$275$	−4.01437e9	−	4.01437e9i	−0.701919	−	0.701919i
$276$		0			0
$277$	4.63135e9	+	4.63135e9i	0.786662	+	0.786662i	0.980945	−	0.194283i	$-0.0622381\pi$
$277$	4.63135e9	+	4.63135e9i	0.786662	+	0.786662i	−0.194283	+	0.980945i	$0.562238\pi$
$278$		0			0
$279$	1.71389e9			0.282857
$280$		0			0
$281$		−	2.92015e9i		−	0.468361i	−0.972193	−	0.234180i	$-0.924759\pi$
$281$		−	2.92015e9i		−	0.468361i	0.972193	−	0.234180i	$-0.0752406\pi$
$282$		0			0
$283$	−4.73143e9	+	4.73143e9i	−0.737644	+	0.737644i	−0.972122	−	0.234477i	$-0.924662\pi$
$283$	−4.73143e9	+	4.73143e9i	−0.737644	+	0.737644i	0.234477	+	0.972122i	$0.424662\pi$
$284$		0			0
$285$	1.61183e9	−	1.61183e9i	0.244309	−	0.244309i
$286$		0			0
$287$			6.76598e8i			0.0997249i
$288$		0			0
$289$	−2.62576e9			−0.376412
$290$		0			0
$291$	−4.75282e8	−	4.75282e8i	−0.0662795	−	0.0662795i
$292$		0			0
$293$	4.99670e9	+	4.99670e9i	0.677973	+	0.677973i	0.959541	−	0.281568i	$-0.0908546\pi$
$293$	4.99670e9	+	4.99670e9i	0.677973	+	0.677973i	−0.281568	+	0.959541i	$0.590855\pi$
$294$		0			0
$295$	7.72381e8			0.101987
$296$		0			0
$297$			1.94556e9i			0.250046i
$298$		0			0
$299$	−3.40477e8	+	3.40477e8i	−0.0425993	+	0.0425993i
$300$		0			0
$301$	8.91760e8	−	8.91760e8i	0.108638	−	0.108638i
$302$		0			0
$303$			8.42761e9i			0.999848i
$304$		0			0
$305$	−4.44371e9			−0.513507
$306$		0			0
$307$	−2.24003e9	−	2.24003e9i	−0.252174	−	0.252174i	0.569687	−	0.821861i	$-0.307064\pi$
$307$	−2.24003e9	−	2.24003e9i	−0.252174	−	0.252174i	−0.821861	+	0.569687i	$0.807064\pi$
$308$		0			0
$309$	2.33246e9	+	2.33246e9i	0.255847	+	0.255847i
$310$		0			0
$311$	−1.74578e10			−1.86616			−0.933080	−	0.359669i	$-0.882890\pi$
$311$	−1.74578e10			−1.86616			−0.933080	+	0.359669i	$0.882890\pi$
$312$		0			0
$313$		−	5.39649e8i		−	0.0562256i	−0.999605	−	0.0281128i	$-0.991050\pi$
$313$		−	5.39649e8i		−	0.0562256i	0.999605	−	0.0281128i	$-0.00894976\pi$
$314$		0			0
$315$	−1.50910e8	+	1.50910e8i	−0.0153277	+	0.0153277i
$316$		0			0
$317$	−1.14777e10	+	1.14777e10i	−1.13663	+	1.13663i	−0.147581	+	0.989050i	$0.547149\pi$
$317$	−1.14777e10	+	1.14777e10i	−1.13663	+	1.13663i	−0.989050	+	0.147581i	$0.952851\pi$
$318$		0			0
$319$		−	1.99665e9i		−	0.192814i
$320$		0			0
$321$	2.84994e9			0.268420
$322$		0			0
$323$	−7.48713e9	−	7.48713e9i	−0.687868	−	0.687868i
$324$		0			0
$325$	1.02502e9	+	1.02502e9i	0.0918749	+	0.0918749i
$326$		0			0
$327$	1.15397e10			1.00926
$328$		0			0
$329$		−	2.12591e9i		−	0.181452i
$330$		0			0
$331$	4.68871e9	−	4.68871e9i	0.390608	−	0.390608i	−0.484296	−	0.874904i	$-0.660924\pi$
$331$	4.68871e9	−	4.68871e9i	0.390608	−	0.390608i	0.874904	+	0.484296i	$0.160924\pi$
$332$		0			0
$333$	−8.42312e8	+	8.42312e8i	−0.0685008	+	0.0685008i
$334$		0			0
$335$			6.75252e9i			0.536150i
$336$		0			0
$337$	1.49622e10			1.16005			0.580025	−	0.814599i	$-0.303043\pi$
$337$	1.49622e10			1.16005			0.580025	+	0.814599i	$0.303043\pi$
$338$		0			0
$339$	5.05887e9	+	5.05887e9i	0.383049	+	0.383049i
$340$		0			0
$341$	−1.05412e10	−	1.05412e10i	−0.779604	−	0.779604i
$342$		0			0
$343$	−3.67253e9			−0.265332
$344$		0			0
$345$			1.40756e9i			0.0993551i
$346$		0			0
$347$	1.34112e10	−	1.34112e10i	0.925016	−	0.925016i	−0.0723626	−	0.997378i	$-0.523054\pi$
$347$	1.34112e10	−	1.34112e10i	0.925016	−	0.925016i	0.997378	+	0.0723626i	$0.0230539\pi$
$348$		0			0
$349$	1.93059e10	−	1.93059e10i	1.30134	−	1.30134i	0.373843	−	0.927492i	$-0.378040\pi$
$349$	1.93059e10	−	1.93059e10i	1.30134	−	1.30134i	0.927492	−	0.373843i	$-0.121960\pi$
$350$		0			0
$351$		−	4.96773e8i		−	0.0327288i
$352$		0			0
$353$	−2.03892e10			−1.31311			−0.656555	−	0.754278i	$-0.727987\pi$
$353$	−2.03892e10			−1.31311			−0.656555	+	0.754278i	$0.727987\pi$
$354$		0			0
$355$	9.68856e9	+	9.68856e9i	0.610022	+	0.610022i
$356$		0			0
$357$	7.00994e8	+	7.00994e8i	0.0431560	+	0.0431560i
$358$		0			0
$359$	2.14611e10			1.29203			0.646016	−	0.763324i	$-0.276434\pi$
$359$	2.14611e10			1.29203			0.646016	+	0.763324i	$0.276434\pi$
$360$		0			0
$361$			8.78979e9i			0.517547i
$362$		0			0
$363$	4.87769e9	−	4.87769e9i	0.280924	−	0.280924i
$364$		0			0
$365$	3.03395e9	−	3.03395e9i	0.170937	−	0.170937i
$366$		0			0
$367$			5.54772e9i			0.305809i	0.988241	+	0.152905i	$0.0488627\pi$
$367$			5.54772e9i			0.305809i	−0.988241	+	0.152905i	$0.951137\pi$
$368$		0			0
$369$	−4.60383e9			−0.248321
$370$		0			0
$371$	2.80609e8	+	2.80609e8i	0.0148117	+	0.0148117i
$372$		0			0
$373$	2.11197e10	+	2.11197e10i	1.09107	+	1.09107i	0.995414	+	0.0956566i	$0.0304951\pi$
$373$	2.11197e10	+	2.11197e10i	1.09107	+	1.09107i	0.0956566	+	0.995414i	$0.469505\pi$
$374$		0			0
$375$	9.78387e9			0.494750
$376$		0			0
$377$			5.09816e8i			0.0252376i
$378$		0			0
$379$	1.43672e10	−	1.43672e10i	0.696329	−	0.696329i	−0.267288	−	0.963617i	$-0.586127\pi$
$379$	1.43672e10	−	1.43672e10i	0.696329	−	0.696329i	0.963617	+	0.267288i	$0.0861273\pi$
$380$		0			0
$381$	−8.05767e9	+	8.05767e9i	−0.382393	+	0.382393i
$382$		0			0
$383$		−	2.68615e10i		−	1.24835i	−0.781285	−	0.624174i	$-0.785435\pi$
$383$		−	2.68615e10i		−	1.24835i	0.781285	−	0.624174i	$-0.214565\pi$
$384$		0			0
$385$	1.85634e9			0.0844917
$386$		0			0
$387$	6.06788e9	+	6.06788e9i	0.270516	+	0.270516i
$388$		0			0
$389$	−2.88548e10	−	2.88548e10i	−1.26014	−	1.26014i	−0.951023	−	0.309121i	$-0.899965\pi$
$389$	−2.88548e10	−	2.88548e10i	−1.26014	−	1.26014i	−0.309121	−	0.951023i	$-0.600035\pi$
$390$		0			0
$391$	6.53826e9			0.279740
$392$		0			0
$393$			6.70794e8i			0.0281202i
$394$		0			0
$395$	1.27477e9	−	1.27477e9i	0.0523652	−	0.0523652i
$396$		0			0
$397$	9.47205e9	−	9.47205e9i	0.381313	−	0.381313i	−0.490262	−	0.871575i	$-0.663099\pi$
$397$	9.47205e9	−	9.47205e9i	0.381313	−	0.381313i	0.871575	+	0.490262i	$0.163099\pi$
$398$		0			0
$399$		−	2.41307e9i		−	0.0952091i
$400$		0			0
$401$	1.16717e10			0.451397			0.225698	−	0.974197i	$-0.427534\pi$
$401$	1.16717e10			0.451397			0.225698	+	0.974197i	$0.427534\pi$
$402$		0			0
$403$	2.69156e9	+	2.69156e9i	0.102043	+	0.102043i
$404$		0			0
$405$	−1.02685e9	−	1.02685e9i	−0.0381669	−	0.0381669i
$406$		0			0
$407$	1.03612e10			0.377601
$408$		0			0
$409$			2.04558e10i			0.731008i	0.930810	+	0.365504i	$0.119103\pi$
$409$			2.04558e10i			0.731008i	−0.930810	+	0.365504i	$0.880897\pi$
$410$		0			0
$411$	1.79708e10	−	1.79708e10i	0.629796	−	0.629796i
$412$		0			0
$413$	5.78165e8	−	5.78165e8i	0.0198725	−	0.0198725i
$414$		0			0
$415$		−	1.74957e10i		−	0.589847i
$416$		0			0
$417$	3.35268e10			1.10878
$418$		0			0
$419$	−1.07657e10	−	1.07657e10i	−0.349291	−	0.349291i	0.510554	−	0.859845i	$-0.329440\pi$
$419$	−1.07657e10	−	1.07657e10i	−0.349291	−	0.349291i	−0.859845	+	0.510554i	$0.829440\pi$
$420$		0			0
$421$	1.52423e9	+	1.52423e9i	0.0485203	+	0.0485203i	0.730951	−	0.682430i	$-0.239077\pi$
$421$	1.52423e9	+	1.52423e9i	0.0485203	+	0.0485203i	−0.682430	+	0.730951i	$0.739077\pi$
$422$		0			0
$423$	1.44655e10			0.451828
$424$		0			0
$425$		−	1.96836e10i		−	0.603322i
$426$		0			0
$427$	−3.32634e9	+	3.32634e9i	−0.100059	+	0.100059i
$428$		0			0
$429$	−3.05539e9	+	3.05539e9i	−0.0902064	+	0.0902064i
$430$		0			0
$431$			1.69058e10i			0.489923i	0.969533	+	0.244962i	$0.0787753\pi$
$431$			1.69058e10i			0.489923i	−0.969533	+	0.244962i	$0.921225\pi$
$432$		0			0
$433$	6.20156e10			1.76421			0.882103	−	0.471057i	$-0.156128\pi$
$433$	6.20156e10			1.76421			0.882103	+	0.471057i	$0.156128\pi$
$434$		0			0
$435$	1.05381e9	+	1.05381e9i	0.0294311	+	0.0294311i
$436$		0			0
$437$	−1.12535e10	−	1.12535e10i	−0.308576	−	0.308576i
$438$		0			0
$439$	−1.12319e10			−0.302408			−0.151204	−	0.988503i	$-0.548315\pi$
$439$	−1.12319e10			−0.302408			−0.151204	+	0.988503i	$0.548315\pi$
$440$		0			0
$441$		−	1.23817e10i		−	0.327360i
$442$		0			0
$443$	−3.31396e10	+	3.31396e10i	−0.860464	+	0.860464i	−0.991392	−	0.130928i	$-0.958204\pi$
$443$	−3.31396e10	+	3.31396e10i	−0.860464	+	0.860464i	0.130928	+	0.991392i	$0.458204\pi$
$444$		0			0
$445$	−7.63365e9	+	7.63365e9i	−0.194667	+	0.194667i
$446$		0			0
$447$			1.00153e10i			0.250862i
$448$		0			0
$449$	1.60349e10			0.394531			0.197266	−	0.980350i	$-0.436794\pi$
$449$	1.60349e10			0.394531			0.197266	+	0.980350i	$0.436794\pi$
$450$		0			0
$451$	2.83158e10	+	2.83158e10i	0.684419	+	0.684419i
$452$		0			0
$453$	2.63011e10	+	2.63011e10i	0.624570	+	0.624570i
$454$		0			0
$455$	−4.73990e8			−0.0110592
$456$		0			0
$457$			1.43942e9i			0.0330008i	0.999864	+	0.0165004i	$0.00525247\pi$
$457$			1.43942e9i			0.0330008i	−0.999864	+	0.0165004i	$0.994748\pi$
$458$		0			0
$459$	−4.76983e9	+	4.76983e9i	−0.107461	+	0.107461i
$460$		0			0
$461$	−9.71534e8	+	9.71534e8i	−0.0215107	+	0.0215107i	−0.717780	−	0.696270i	$-0.754842\pi$
$461$	−9.71534e8	+	9.71534e8i	−0.0215107	+	0.0215107i	0.696270	+	0.717780i	$0.254842\pi$
$462$		0			0
$463$		−	8.99701e10i		−	1.95783i	−0.204278	−	0.978913i	$-0.565485\pi$
$463$		−	8.99701e10i		−	1.95783i	0.204278	−	0.978913i	$-0.434515\pi$
$464$		0			0
$465$	1.11271e10			0.237997
$466$		0			0
$467$	−5.62958e9	−	5.62958e9i	−0.118361	−	0.118361i	0.645445	−	0.763806i	$-0.276672\pi$
$467$	−5.62958e9	−	5.62958e9i	−0.118361	−	0.118361i	−0.763806	+	0.645445i	$0.776672\pi$
$468$		0			0
$469$	5.05460e9	+	5.05460e9i	0.104471	+	0.104471i
$470$		0			0
$471$	4.33550e9			0.0880959
$472$		0			0
$473$		−	7.46406e10i		−	1.49118i
$474$		0			0
$475$	−3.38790e10	+	3.38790e10i	−0.665513	+	0.665513i
$476$		0			0
$477$	−1.90937e9	+	1.90937e9i	−0.0368822	+	0.0368822i
$478$		0			0
$479$		−	2.84189e10i		−	0.539841i	−0.962883	−	0.269921i	$-0.913003\pi$
$479$		−	2.84189e10i		−	0.539841i	0.962883	−	0.269921i	$-0.0869974\pi$
$480$		0			0
$481$	−2.64560e9			−0.0494246
$482$		0			0
$483$	1.05363e9	+	1.05363e9i	0.0193597	+	0.0193597i
$484$		0			0
$485$	−3.08568e9	−	3.08568e9i	−0.0557679	−	0.0557679i
$486$		0			0
$487$	−4.99046e10			−0.887206			−0.443603	−	0.896223i	$-0.646300\pi$
$487$	−4.99046e10			−0.887206			−0.443603	+	0.896223i	$0.646300\pi$
$488$		0			0
$489$			3.29259e10i			0.575840i
$490$		0			0
$491$	−2.50716e10	+	2.50716e10i	−0.431376	+	0.431376i	−0.889096	−	0.457720i	$-0.848666\pi$
$491$	−2.50716e10	+	2.50716e10i	−0.431376	+	0.431376i	0.457720	+	0.889096i	$0.348666\pi$
$492$		0			0
$493$	4.89507e9	−	4.89507e9i	0.0828649	−	0.0828649i
$494$		0			0
$495$			1.26312e10i			0.210390i
$496$		0			0
$497$	1.45047e10			0.237730
$498$		0			0
$499$	6.45686e10	+	6.45686e10i	1.04140	+	1.04140i	0.999105	+	0.0422994i	$0.0134683\pi$
$499$	6.45686e10	+	6.45686e10i	1.04140	+	1.04140i	0.0422994	+	0.999105i	$0.486532\pi$
$500$		0			0
$501$	−2.01792e10	−	2.01792e10i	−0.320297	−	0.320297i
$502$		0			0
$503$	−3.98044e10			−0.621813			−0.310906	−	0.950441i	$-0.600633\pi$
$503$	−3.98044e10			−0.621813			−0.310906	+	0.950441i	$0.600633\pi$
$504$		0			0
$505$			5.47148e10i			0.841277i
$506$		0			0
$507$	−2.61945e10	+	2.61945e10i	−0.396441	+	0.396441i
$508$		0			0
$509$	−8.83621e10	+	8.83621e10i	−1.31642	+	1.31642i	−0.399832	+	0.916588i	$0.630932\pi$
$509$	−8.83621e10	+	8.83621e10i	−1.31642	+	1.31642i	−0.916588	+	0.399832i	$0.869068\pi$
$510$		0			0
$511$		−	4.54213e9i		−	0.0666156i
$512$		0			0
$513$	1.64195e10			0.237077
$514$		0			0
$515$	1.51431e10	+	1.51431e10i	0.215271	+	0.215271i
$516$		0			0
$517$	−8.89699e10	−	8.89699e10i	−1.24532	−	1.24532i
$518$		0			0
$519$	2.03830e10			0.280931
$520$		0			0
$521$		−	3.23543e9i		−	0.0439118i	−0.999759	−	0.0219559i	$-0.993011\pi$
$521$		−	3.23543e9i		−	0.0439118i	0.999759	−	0.0219559i	$-0.00698935\pi$
$522$		0			0
$523$	−5.28959e10	+	5.28959e10i	−0.706994	+	0.706994i	−0.965902	−	0.258908i	$-0.916637\pi$
$523$	−5.28959e10	+	5.28959e10i	−0.706994	+	0.706994i	0.258908	+	0.965902i	$0.416637\pi$
$524$		0			0
$525$	3.17198e9	−	3.17198e9i	0.0417535	−	0.0417535i
$526$		0			0
$527$		−	5.16867e10i		−	0.670095i
$528$		0			0
$529$	−6.84837e10			−0.874509
$530$		0			0
$531$	3.93406e9	+	3.93406e9i	0.0494838	+	0.0494838i
$532$		0			0
$533$	−7.23004e9	−	7.23004e9i	−0.0895843	−	0.0895843i
$534$		0			0
$535$	1.85027e10			0.225850
$536$		0			0
$537$		−	4.98270e10i		−	0.599194i
$538$		0			0
$539$	−7.61533e10	+	7.61533e10i	−0.902264	+	0.902264i
$540$		0			0
$541$	7.06245e10	−	7.06245e10i	0.824454	−	0.824454i	−0.162289	−	0.986743i	$-0.551888\pi$
$541$	7.06245e10	−	7.06245e10i	0.824454	−	0.824454i	0.986743	+	0.162289i	$0.0518878\pi$
$542$		0			0
$543$			7.60314e9i			0.0874568i
$544$		0			0
$545$	7.49196e10			0.849199
$546$		0			0
$547$	6.56817e10	+	6.56817e10i	0.733660	+	0.733660i	0.971343	−	0.237683i	$-0.0763879\pi$
$547$	6.56817e10	+	6.56817e10i	0.733660	+	0.733660i	−0.237683	+	0.971343i	$0.576388\pi$
$548$		0			0
$549$	−2.26337e10	−	2.26337e10i	−0.249153	−	0.249153i
$550$		0			0
$551$	−1.68506e10			−0.182813
$552$		0			0
$553$		−	1.90845e9i		−	0.0204071i
$554$		0			0
$555$	−5.46856e9	+	5.46856e9i	−0.0576369	+	0.0576369i
$556$		0			0
$557$	−1.17862e11	+	1.17862e11i	−1.22449	+	1.22449i	−0.258468	+	0.966020i	$0.583218\pi$
$557$	−1.17862e11	+	1.17862e11i	−1.22449	+	1.22449i	−0.966020	+	0.258468i	$0.916782\pi$
$558$		0			0
$559$			1.90585e10i			0.195182i
$560$		0			0
$561$	5.86734e10			0.592366
$562$		0			0
$563$	−1.16659e11	−	1.16659e11i	−1.16114	−	1.16114i	−0.984226	−	0.176917i	$-0.943388\pi$
$563$	−1.16659e11	−	1.16659e11i	−1.16114	−	1.16114i	−0.176917	−	0.984226i	$-0.556612\pi$
$564$		0			0
$565$	3.28438e10	+	3.28438e10i	0.322300	+	0.322300i
$566$		0			0
$567$	−1.53730e9			−0.0148739
$568$		0			0
$569$		−	1.87613e9i		−	0.0178984i	−0.999960	−	0.00894921i	$-0.997151\pi$
$569$		−	1.87613e9i		−	0.0178984i	0.999960	−	0.00894921i	$-0.00284866\pi$
$570$		0			0
$571$	−4.05487e10	+	4.05487e10i	−0.381445	+	0.381445i	−0.871623	−	0.490177i	$-0.836932\pi$
$571$	−4.05487e10	+	4.05487e10i	−0.381445	+	0.381445i	0.490177	+	0.871623i	$0.336932\pi$
$572$		0			0
$573$	−6.52423e10	+	6.52423e10i	−0.605216	+	0.605216i
$574$		0			0
$575$		−	2.95854e10i		−	0.270649i
$576$		0			0
$577$	−1.27347e11			−1.14891			−0.574456	−	0.818536i	$-0.694786\pi$
$577$	−1.27347e11			−1.14891			−0.574456	+	0.818536i	$0.694786\pi$
$578$		0			0
$579$	−6.95032e10	−	6.95032e10i	−0.618430	−	0.618430i
$580$		0			0
$581$	−1.30964e10	−	1.30964e10i	−0.114934	−	0.114934i
$582$		0			0
$583$	2.34871e10			0.203308
$584$		0			0
$585$		−	3.22521e9i		−	0.0275381i
$586$		0			0
$587$	9.06324e10	−	9.06324e10i	0.763363	−	0.763363i	−0.213566	−	0.976929i	$-0.568508\pi$
$587$	9.06324e10	−	9.06324e10i	0.763363	−	0.763363i	0.976929	+	0.213566i	$0.0685077\pi$
$588$		0			0
$589$	−8.89621e10	+	8.89621e10i	−0.739169	+	0.739169i
$590$		0			0
$591$			6.12331e9i			0.0501922i
$592$		0			0
$593$	−4.31542e10			−0.348983			−0.174491	−	0.984659i	$-0.555828\pi$
$593$	−4.31542e10			−0.348983			−0.174491	+	0.984659i	$0.555828\pi$
$594$		0			0
$595$	4.55108e9	+	4.55108e9i	0.0363117	+	0.0363117i
$596$		0			0
$597$	−1.24059e10	−	1.24059e10i	−0.0976630	−	0.0976630i
$598$		0			0
$599$	−1.08451e10			−0.0842415			−0.0421207	−	0.999113i	$-0.513411\pi$
$599$	−1.08451e10			−0.0842415			−0.0421207	+	0.999113i	$0.513411\pi$
$600$		0			0
$601$			1.29082e11i			0.989387i	0.869068	+	0.494693i	$0.164720\pi$
$601$			1.29082e11i			0.989387i	−0.869068	+	0.494693i	$0.835280\pi$
$602$		0			0
$603$	−3.43934e10	+	3.43934e10i	−0.260139	+	0.260139i
$604$		0			0
$605$	3.16676e10	−	3.16676e10i	0.236371	−	0.236371i
$606$		0			0
$607$		−	2.41012e11i		−	1.77535i	−0.460468	−	0.887676i	$-0.652319\pi$
$607$		−	2.41012e11i		−	1.77535i	0.460468	−	0.887676i	$-0.347681\pi$
$608$		0			0
$609$	1.57766e9			0.0114695
$610$		0			0
$611$	2.27172e10	+	2.27172e10i	0.163001	+	0.163001i
$612$		0			0
$613$	−6.99206e10	−	6.99206e10i	−0.495180	−	0.495180i	0.414754	−	0.909934i	$-0.363868\pi$
$613$	−6.99206e10	−	6.99206e10i	−0.495180	−	0.495180i	−0.909934	+	0.414754i	$0.863868\pi$
$614$		0			0
$615$	−2.98896e10			−0.208939
$616$		0			0
$617$			2.02589e11i			1.39790i	0.715171	+	0.698949i	$0.246349\pi$
$617$			2.02589e11i			1.39790i	−0.715171	+	0.698949i	$0.753651\pi$
$618$		0			0
$619$	1.56596e11	−	1.56596e11i	1.06664	−	1.06664i	0.0690266	−	0.997615i	$-0.478011\pi$
$619$	1.56596e11	−	1.56596e11i	1.06664	−	1.06664i	0.997615	−	0.0690266i	$-0.0219893\pi$
$620$		0			0
$621$	−7.16928e9	+	7.16928e9i	−0.0482069	+	0.0482069i
$622$		0			0
$623$			1.14283e10i			0.0758631i
$624$		0			0
$625$	−5.30590e10			−0.347727
$626$		0			0
$627$	−1.00987e11	−	1.00987e11i	−0.653427	−	0.653427i
$628$		0			0
$629$	2.54020e10	+	2.54020e10i	0.162280	+	0.162280i
$630$		0			0
$631$	−1.60818e11			−1.01442			−0.507210	−	0.861823i	$-0.669323\pi$
$631$	−1.60818e11			−1.01442			−0.507210	+	0.861823i	$0.669323\pi$
$632$		0			0
$633$		−	5.53016e10i		−	0.344447i
$634$		0			0
$635$	−5.23130e10	+	5.23130e10i	−0.321747	+	0.321747i
$636$		0			0
$637$	1.94447e10	−	1.94447e10i	0.118098	−	0.118098i
$638$		0			0
$639$			9.86957e10i			0.591964i
$640$		0			0
$641$	2.42585e11			1.43692			0.718459	−	0.695569i	$-0.244848\pi$
$641$	2.42585e11			1.43692			0.718459	+	0.695569i	$0.244848\pi$
$642$		0			0
$643$	2.09870e11	+	2.09870e11i	1.22774	+	1.22774i	0.964817	+	0.262923i	$0.0846866\pi$
$643$	2.09870e11	+	2.09870e11i	1.22774	+	1.22774i	0.262923	+	0.964817i	$0.415313\pi$
$644$		0			0
$645$	3.93946e10	+	3.93946e10i	0.227614	+	0.227614i
$646$		0			0
$647$	5.01468e10			0.286171			0.143086	−	0.989710i	$-0.454298\pi$
$647$	5.01468e10			0.286171			0.143086	+	0.989710i	$0.454298\pi$
$648$		0			0
$649$		−	4.83926e10i		−	0.272772i
$650$		0			0
$651$	8.32921e9	−	8.32921e9i	0.0463746	−	0.0463746i
$652$		0			0
$653$	9.32411e10	−	9.32411e10i	0.512808	−	0.512808i	−0.402578	−	0.915386i	$-0.631886\pi$
$653$	9.32411e10	−	9.32411e10i	0.512808	−	0.512808i	0.915386	+	0.402578i	$0.131886\pi$
$654$		0			0
$655$			4.35501e9i			0.0236605i
$656$		0			0
$657$	3.09064e10			0.165877
$658$		0			0
$659$	3.78176e9	+	3.78176e9i	0.0200517	+	0.0200517i	0.717062	−	0.697010i	$-0.245487\pi$
$659$	3.78176e9	+	3.78176e9i	0.0200517	+	0.0200517i	−0.697010	+	0.717062i	$0.745487\pi$
$660$		0			0
$661$	−1.89156e11	−	1.89156e11i	−0.990864	−	0.990864i	0.00909472	−	0.999959i	$-0.497105\pi$
$661$	−1.89156e11	−	1.89156e11i	−0.990864	−	0.990864i	−0.999959	+	0.00909472i	$0.997105\pi$
$662$		0			0
$663$	−1.49814e10			−0.0775353
$664$		0			0
$665$		−	1.56664e10i		−	0.0801094i
$666$		0			0
$667$	7.35752e9	−	7.35752e9i	0.0371730	−	0.0371730i
$668$		0			0
$669$	−1.04287e11	+	1.04287e11i	−0.520624	+	0.520624i
$670$		0			0
$671$			2.78416e11i			1.37342i
$672$		0			0
$673$	−3.72954e11			−1.81801			−0.909003	−	0.416789i	$-0.863155\pi$
$673$	−3.72954e11			−1.81801			−0.909003	+	0.416789i	$0.863155\pi$
$674$		0			0
$675$	2.15833e10	+	2.15833e10i	0.103969	+	0.103969i
$676$		0			0
$677$	6.10238e10	+	6.10238e10i	0.290499	+	0.290499i	0.837277	−	0.546778i	$-0.184146\pi$
$677$	6.10238e10	+	6.10238e10i	0.290499	+	0.290499i	−0.546778	+	0.837277i	$0.684146\pi$
$678$		0			0
$679$	−4.61957e9			−0.0217332
$680$		0			0
$681$		−	1.88756e11i		−	0.877631i
$682$		0			0
$683$	1.46023e10	−	1.46023e10i	0.0671023	−	0.0671023i	−0.672759	−	0.739862i	$-0.734891\pi$
$683$	1.46023e10	−	1.46023e10i	0.0671023	−	0.0671023i	0.739862	+	0.672759i	$0.234891\pi$
$684$		0			0
$685$	1.16672e11	−	1.16672e11i	0.529913	−	0.529913i
$686$		0			0
$687$			2.70457e10i			0.121415i
$688$		0			0
$689$	−5.99710e9			−0.0266112
$690$		0			0
$691$	1.40475e9	+	1.40475e9i	0.00616152	+	0.00616152i	0.710181	−	0.704019i	$-0.248613\pi$
$691$	1.40475e9	+	1.40475e9i	0.00616152	+	0.00616152i	−0.704019	+	0.710181i	$0.748613\pi$
$692$		0			0
$693$	9.45510e9	+	9.45510e9i	0.0409952	+	0.0409952i
$694$		0			0
$695$	2.17667e11			0.932937
$696$		0			0
$697$			1.38840e11i			0.588280i
$698$		0			0
$699$	−1.11196e10	+	1.11196e10i	−0.0465781	+	0.0465781i
$700$		0			0
$701$	4.98964e10	−	4.98964e10i	0.206632	−	0.206632i	−0.596202	−	0.802834i	$-0.703324\pi$
$701$	4.98964e10	−	4.98964e10i	0.206632	−	0.206632i	0.802834	+	0.596202i	$0.203324\pi$
$702$		0			0
$703$		−	8.74429e10i		−	0.358017i
$704$		0			0
$705$	9.39149e10			0.380170
$706$		0			0
$707$	4.09567e10	+	4.09567e10i	0.163926	+	0.163926i
$708$		0			0
$709$	1.81955e11	+	1.81955e11i	0.720076	+	0.720076i	0.968620	−	0.248545i	$-0.0799523\pi$
$709$	1.81955e11	+	1.81955e11i	0.720076	+	0.720076i	−0.248545	+	0.968620i	$0.579952\pi$
$710$		0			0
$711$	1.29858e10			0.0508150
$712$		0			0
$713$		−	7.76877e10i		−	0.300603i
$714$		0			0
$715$	−1.98366e10	+	1.98366e10i	−0.0759001	+	0.0759001i
$716$		0			0
$717$	−1.54912e10	+	1.54912e10i	−0.0586151	+	0.0586151i
$718$		0			0
$719$			4.21431e11i			1.57692i	0.615084	+	0.788462i	$0.289122\pi$
$719$			4.21431e11i			1.57692i	−0.615084	+	0.788462i	$0.710878\pi$
$720$		0			0
$721$	2.26707e10			0.0838926
$722$		0			0
$723$	−2.02237e11	−	2.02237e11i	−0.740129	−	0.740129i
$724$		0			0
$725$	−2.21500e10	−	2.21500e10i	−0.0801719	−	0.0801719i
$726$		0			0
$727$	−3.61832e11			−1.29530			−0.647649	−	0.761939i	$-0.724248\pi$
$727$	−3.61832e11			−1.29530			−0.647649	+	0.761939i	$0.724248\pi$
$728$		0			0
$729$		−	1.04604e10i		−	0.0370370i
$730$		0			0
$731$	1.82992e11	−	1.82992e11i	0.640860	−	0.640860i
$732$		0			0
$733$	2.27256e11	−	2.27256e11i	0.787227	−	0.787227i	−0.193812	−	0.981039i	$-0.562085\pi$
$733$	2.27256e11	−	2.27256e11i	0.787227	−	0.787227i	0.981039	+	0.193812i	$0.0620851\pi$
$734$		0			0
$735$		−	8.03860e10i		−	0.275442i
$736$		0			0
$737$	4.23071e11			1.43398
$738$		0			0
$739$	−8.64797e10	−	8.64797e10i	−0.289959	−	0.289959i	0.547105	−	0.837064i	$-0.315730\pi$
$739$	−8.64797e10	−	8.64797e10i	−0.289959	−	0.289959i	−0.837064	+	0.547105i	$0.815730\pi$
$740$		0			0
$741$	2.57857e10	+	2.57857e10i	0.0855277	+	0.0855277i
$742$		0			0
$743$	4.53548e11			1.48822			0.744112	−	0.668055i	$-0.232873\pi$
$743$	4.53548e11			1.48822			0.744112	+	0.668055i	$0.232873\pi$
$744$		0			0
$745$			6.50226e10i			0.211076i
$746$		0			0
$747$	8.91130e10	−	8.91130e10i	0.286193	−	0.286193i
$748$		0			0
$749$	1.38502e10	−	1.38502e10i	0.0440077	−	0.0440077i
$750$		0			0
$751$			1.33549e11i			0.419836i	0.977719	+	0.209918i	$0.0673198\pi$
$751$			1.33549e11i			0.419836i	−0.977719	+	0.209918i	$0.932680\pi$
$752$		0			0
$753$	−5.70485e10			−0.177445
$754$		0			0
$755$	1.70755e11	+	1.70755e11i	0.525517	+	0.525517i
$756$		0			0
$757$	4.18661e11	+	4.18661e11i	1.27491	+	1.27491i	0.943481	+	0.331427i	$0.107530\pi$
$757$	4.18661e11	+	4.18661e11i	1.27491	+	1.27491i	0.331427	+	0.943481i	$0.392470\pi$
$758$		0			0
$759$	8.81890e10			0.265734
$760$		0			0
$761$		−	3.87386e11i		−	1.15506i	−0.816368	−	0.577532i	$-0.804016\pi$
$761$		−	3.87386e11i		−	1.15506i	0.816368	−	0.577532i	$-0.195984\pi$
$762$		0			0
$763$	5.60810e10	−	5.60810e10i	0.165469	−	0.165469i
$764$		0			0
$765$	−3.09673e10	+	3.09673e10i	−0.0904185	+	0.0904185i
$766$		0			0
$767$			1.23564e10i			0.0357035i
$768$		0			0
$769$	−1.11931e11			−0.320070			−0.160035	−	0.987111i	$-0.551161\pi$
$769$	−1.11931e11			−0.320070			−0.160035	+	0.987111i	$0.551161\pi$
$770$		0			0
$771$	−2.27903e11	−	2.27903e11i	−0.644958	−	0.644958i
$772$		0			0
$773$	3.26989e11	+	3.26989e11i	0.915829	+	0.915829i	0.996723	−	0.0808934i	$-0.0257773\pi$
$773$	3.26989e11	+	3.26989e11i	0.915829	+	0.915829i	−0.0808934	+	0.996723i	$0.525777\pi$
$774$		0			0
$775$	−2.33881e11			−0.648318
$776$		0			0
$777$			8.18698e9i			0.0224615i
$778$		0			0
$779$	2.38969e11	−	2.38969e11i	0.648921	−	0.648921i
$780$		0			0
$781$	6.07025e11	−	6.07025e11i	1.63156	−	1.63156i
$782$		0			0
$783$			1.07350e10i			0.0285598i
$784$		0			0
$785$	2.81475e10			0.0741244
$786$		0			0
$787$	3.95177e10	+	3.95177e10i	0.103013	+	0.103013i	0.756735	−	0.653722i	$-0.226793\pi$
$787$	3.95177e10	+	3.95177e10i	0.103013	+	0.103013i	−0.653722	+	0.756735i	$0.726793\pi$
$788$		0			0
$789$	−2.76695e11	−	2.76695e11i	−0.713993	−	0.713993i
$790$		0			0
$791$	4.91704e10			0.125602
$792$		0			0
$793$		−	7.10896e10i		−	0.179768i
$794$		0			0
$795$	−1.23963e10	+	1.23963e10i	−0.0310329	+	0.0310329i
$796$		0			0
$797$	2.90803e11	−	2.90803e11i	0.720718	−	0.720718i	−0.248034	−	0.968751i	$-0.579784\pi$
$797$	2.90803e11	−	2.90803e11i	0.720718	−	0.720718i	0.968751	+	0.248034i	$0.0797844\pi$
$798$		0			0
$799$		−	4.36245e11i		−	1.07039i
$800$		0			0
$801$	−7.77627e10			−0.188904
$802$		0			0
$803$	−1.90089e11	−	1.90089e11i	−0.457187	−	0.457187i
$804$		0			0
$805$	6.84049e9	+	6.84049e9i	0.0162894	+	0.0162894i
$806$		0			0
$807$	2.83722e11			0.668959
$808$		0			0
$809$		−	3.45805e11i		−	0.807304i	−0.914913	−	0.403652i	$-0.867741\pi$
$809$		−	3.45805e11i		−	0.807304i	0.914913	−	0.403652i	$-0.132259\pi$
$810$		0			0
$811$	−2.27058e11	+	2.27058e11i	−0.524871	+	0.524871i	−0.919039	−	0.394167i	$-0.871033\pi$
$811$	−2.27058e11	+	2.27058e11i	−0.524871	+	0.524871i	0.394167	+	0.919039i	$0.371033\pi$
$812$		0			0
$813$	−2.02745e11	+	2.02745e11i	−0.464076	+	0.464076i
$814$		0			0
$815$			2.13766e11i			0.484515i
$816$		0			0
$817$	−6.29924e11			−1.41384
$818$		0			0
$819$	−2.41423e9	−	2.41423e9i	−0.00536591	−	0.00536591i
$820$		0			0
$821$	6.01905e11	+	6.01905e11i	1.32481	+	1.32481i	0.909827	+	0.414988i	$0.136214\pi$
$821$	6.01905e11	+	6.01905e11i	1.32481	+	1.32481i	0.414988	+	0.909827i	$0.363786\pi$
$822$		0			0
$823$	−2.08094e10			−0.0453586			−0.0226793	−	0.999743i	$-0.507220\pi$
$823$	−2.08094e10			−0.0453586			−0.0226793	+	0.999743i	$0.507220\pi$
$824$		0			0
$825$		−	2.65495e11i		−	0.573114i
$826$		0			0
$827$	2.85750e11	−	2.85750e11i	0.610892	−	0.610892i	−0.332287	−	0.943178i	$-0.607820\pi$
$827$	2.85750e11	−	2.85750e11i	0.610892	−	0.610892i	0.943178	+	0.332287i	$0.107820\pi$
$828$		0			0
$829$	6.34081e11	−	6.34081e11i	1.34254	−	1.34254i	0.449014	−	0.893525i	$-0.351776\pi$
$829$	6.34081e11	−	6.34081e11i	1.34254	−	1.34254i	0.893525	−	0.449014i	$-0.148224\pi$
$830$		0			0
$831$			3.06300e11i			0.642307i
$832$		0			0
$833$	−3.73401e11			−0.775525
$834$		0			0
$835$	−1.31010e11	−	1.31010e11i	−0.269499	−	0.269499i
$836$		0			0
$837$	5.66751e10	+	5.66751e10i	0.115476	+	0.115476i
$838$		0			0
$839$	3.96094e11			0.799375			0.399688	−	0.916651i	$-0.369119\pi$
$839$	3.96094e11			0.799375			0.399688	+	0.916651i	$0.369119\pi$
$840$		0			0
$841$			4.89230e11i			0.977977i
$842$		0			0
$843$	9.65640e10	−	9.65640e10i	0.191207	−	0.191207i
$844$		0			0
$845$	−1.70063e11	+	1.70063e11i	−0.333568	+	0.333568i
$846$		0			0
$847$		−	4.74095e10i		−	0.0921153i
$848$		0			0
$849$	−3.12919e11			−0.602284
$850$		0			0
$851$	3.81805e10	+	3.81805e10i	0.0727987	+	0.0727987i
$852$		0			0
$853$	−2.36449e11	−	2.36449e11i	−0.446624	−	0.446624i	0.447607	−	0.894231i	$-0.352276\pi$
$853$	−2.36449e11	−	2.36449e11i	−0.446624	−	0.446624i	−0.894231	+	0.447607i	$0.852276\pi$
$854$		0			0
$855$	1.06600e11			0.199478
$856$		0			0
$857$			5.75350e11i			1.06662i	0.845921	+	0.533309i	$0.179052\pi$
$857$			5.75350e11i			1.06662i	−0.845921	+	0.533309i	$0.820948\pi$
$858$		0			0
$859$	4.54656e11	−	4.54656e11i	0.835046	−	0.835046i	−0.153156	−	0.988202i	$-0.548944\pi$
$859$	4.54656e11	−	4.54656e11i	0.835046	−	0.835046i	0.988202	+	0.153156i	$0.0489438\pi$
$860$		0			0
$861$	−2.23738e10	+	2.23738e10i	−0.0407125	+	0.0407125i
$862$		0			0
$863$			5.63595e11i			1.01607i	0.861336	+	0.508035i	$0.169628\pi$
$863$			5.63595e11i			1.01607i	−0.861336	+	0.508035i	$0.830372\pi$
$864$		0			0
$865$	1.32333e11			0.236377
$866$		0			0
$867$	−8.68288e10	−	8.68288e10i	−0.153669	−	0.153669i
$868$		0			0
$869$	−7.98691e10	−	7.98691e10i	−0.140055	−	0.140055i
$870$		0			0
$871$	−1.08025e11			−0.187695
$872$		0			0
$873$		−	3.14333e10i		−	0.0541170i
$874$		0			0
$875$	4.75479e10	−	4.75479e10i	0.0811146	−	0.0811146i
$876$		0			0
$877$	−4.72278e11	+	4.72278e11i	−0.798361	+	0.798361i	−0.982837	−	0.184476i	$-0.940941\pi$
$877$	−4.72278e11	+	4.72278e11i	−0.798361	+	0.798361i	0.184476	+	0.982837i	$0.440941\pi$
$878$		0			0
$879$			3.30463e11i			0.553563i
$880$		0			0
$881$	−1.91927e11			−0.318590			−0.159295	−	0.987231i	$-0.550922\pi$
$881$	−1.91927e11			−0.318590			−0.159295	+	0.987231i	$0.550922\pi$
$882$		0			0
$883$	−5.35958e10	−	5.35958e10i	−0.0881634	−	0.0881634i	0.661650	−	0.749813i	$-0.269857\pi$
$883$	−5.35958e10	−	5.35958e10i	−0.0881634	−	0.0881634i	−0.749813	+	0.661650i	$0.769857\pi$
$884$		0			0
$885$	2.55412e10	+	2.55412e10i	0.0416359	+	0.0416359i
$886$		0			0
$887$	5.32731e11			0.860623			0.430312	−	0.902680i	$-0.358404\pi$
$887$	5.32731e11			0.860623			0.430312	+	0.902680i	$0.358404\pi$
$888$		0			0
$889$			7.83178e10i			0.125387i
$890$		0			0
$891$	−6.43361e10	+	6.43361e10i	−0.102081	+	0.102081i
$892$		0			0
$893$	−7.50855e11	+	7.50855e11i	−1.18073	+	1.18073i
$894$		0			0
$895$		−	3.23493e11i		−	0.504165i
$896$		0			0
$897$	−2.25178e10			−0.0347822
$898$		0			0
$899$	−5.81632e10	−	5.81632e10i	−0.0890450	−	0.0890450i
$900$		0			0
$901$	5.75819e10	+	5.75819e10i	0.0873750	+	0.0873750i
$902$		0			0
$903$	5.89776e10			0.0887026
$904$		0			0
$905$			4.93621e10i			0.0735866i
$906$		0			0
$907$	−1.14644e11	+	1.14644e11i	−0.169403	+	0.169403i	−0.786717	−	0.617314i	$-0.788221\pi$
$907$	−1.14644e11	+	1.14644e11i	−0.169403	+	0.169403i	0.617314	+	0.786717i	$0.288221\pi$
$908$		0			0
$909$	−2.78685e11	+	2.78685e11i	−0.408186	+	0.408186i
$910$		0			0
$911$			6.94812e10i			0.100877i	0.998727	+	0.0504387i	$0.0160620\pi$
$911$			6.94812e10i			0.100877i	−0.998727	+	0.0504387i	$0.983938\pi$
$912$		0			0
$913$	−1.09617e12			−1.57760
$914$		0			0
$915$	−1.46945e11	−	1.46945e11i	−0.209638	−	0.209638i
$916$		0			0
$917$	3.25994e9	+	3.25994e9i	0.00461034	+	0.00461034i
$918$		0			0
$919$	−9.17244e11			−1.28595			−0.642973	−	0.765889i	$-0.722299\pi$
$919$	−9.17244e11			−1.28595			−0.642973	+	0.765889i	$0.722299\pi$
$920$		0			0
$921$		−	1.48147e11i		−	0.205899i
$922$		0			0
$923$	−1.54996e11	+	1.54996e11i	−0.213556	+	0.213556i
$924$		0			0
$925$	1.14943e11	−	1.14943e11i	0.157006	−	0.157006i
$926$		0			0
$927$			1.54260e11i			0.208898i
$928$		0			0
$929$	−2.02150e11			−0.271400			−0.135700	−	0.990750i	$-0.543328\pi$
$929$	−2.02150e11			−0.271400			−0.135700	+	0.990750i	$0.543328\pi$
$930$		0			0
$931$	6.42690e11	+	6.42690e11i	0.855466	+	0.855466i
$932$		0			0
$933$	−5.77298e11	−	5.77298e11i	−0.761857	−	0.761857i
$934$		0			0
$935$	3.80927e11			0.498420
$936$		0			0
$937$			4.55072e11i			0.590367i	0.955441	+	0.295184i	$0.0953808\pi$
$937$			4.55072e11i			0.590367i	−0.955441	+	0.295184i	$0.904619\pi$
$938$		0			0
$939$	1.78452e10	−	1.78452e10i	0.0229540	−	0.0229540i
$940$		0			0
$941$	−2.30280e11	+	2.30280e11i	−0.293696	+	0.293696i	−0.838539	−	0.544842i	$-0.816590\pi$
$941$	−2.30280e11	+	2.30280e11i	−0.293696	+	0.293696i	0.544842	+	0.838539i	$0.316590\pi$
$942$		0			0
$943$			2.08684e11i			0.263901i
$944$		0			0
$945$	−9.98063e9			−0.0125150
$946$		0			0
$947$	−9.29338e11	−	9.29338e11i	−1.15551	−	1.15551i	−0.985430	−	0.170080i	$-0.945597\pi$
$947$	−9.29338e11	−	9.29338e11i	−1.15551	−	1.15551i	−0.170080	−	0.985430i	$-0.554403\pi$
$948$		0			0
$949$	4.85366e10	+	4.85366e10i	0.0598417	+	0.0598417i
$950$		0			0
$951$	−7.59095e11			−0.928055
$952$		0			0
$953$			2.94264e11i			0.356751i	0.983962	+	0.178376i	$0.0570842\pi$
$953$			2.94264e11i			0.356751i	−0.983962	+	0.178376i	$0.942916\pi$
$954$		0			0
$955$	−4.23574e11	+	4.23574e11i	−0.509232	+	0.509232i
$956$		0			0
$957$	6.60253e10	−	6.60253e10i	0.0787160	−	0.0787160i
$958$		0			0
$959$		−	1.74670e11i		−	0.206511i
$960$		0			0
$961$	2.38749e11			0.279929
$962$		0			0
$963$	9.42421e10	+	9.42421e10i	0.109582	+	0.109582i
$964$		0			0
$965$	−4.51238e11	−	4.51238e11i	−0.520350	−	0.520350i
$966$		0			0
$967$	−1.17556e12			−1.34443			−0.672216	−	0.740355i	$-0.734657\pi$
$967$	−1.17556e12			−1.34443			−0.672216	+	0.740355i	$0.734657\pi$
$968$		0			0
$969$		−	4.95170e11i		−	0.561642i
$970$		0			0
$971$	−2.62616e11	+	2.62616e11i	−0.295423	+	0.295423i	−0.839218	−	0.543795i	$-0.816987\pi$
$971$	−2.62616e11	+	2.62616e11i	−0.295423	+	0.295423i	0.543795	+	0.839218i	$0.316987\pi$
$972$		0			0
$973$	1.62934e11	−	1.62934e11i	0.181786	−	0.181786i
$974$		0			0
$975$			6.77906e10i			0.0750155i
$976$		0			0
$977$	6.52580e11			0.716235			0.358117	−	0.933677i	$-0.383419\pi$
$977$	6.52580e11			0.716235			0.358117	+	0.933677i	$0.383419\pi$
$978$		0			0
$979$	4.78277e11	+	4.78277e11i	0.520654	+	0.520654i
$980$		0			0
$981$	3.81597e11	+	3.81597e11i	0.412030	+	0.412030i
$982$		0			0
$983$	−1.10301e12			−1.18132			−0.590659	−	0.806922i	$-0.701132\pi$
$983$	−1.10301e12			−1.18132			−0.590659	+	0.806922i	$0.701132\pi$
$984$		0			0
$985$			3.97545e10i			0.0422320i
$986$		0			0
$987$	7.03000e10	−	7.03000e10i	0.0740776	−	0.0740776i
$988$		0			0
$989$	2.75046e11	−	2.75046e11i	0.287488	−	0.287488i
$990$		0			0
$991$			3.11647e11i			0.323124i	0.986863	+	0.161562i	$0.0516531\pi$
$991$			3.11647e11i			0.323124i	−0.986863	+	0.161562i	$0.948347\pi$
$992$		0			0
$993$	3.10094e11			0.318930
$994$		0			0
$995$	−8.05430e10	−	8.05430e10i	−0.0821742	−	0.0821742i
$996$		0			0
$997$	1.44432e11	+	1.44432e11i	0.146178	+	0.146178i	0.776408	−	0.630230i	$-0.217039\pi$
$997$	1.44432e11	+	1.44432e11i	0.146178	+	0.146178i	−0.630230	+	0.776408i	$0.717039\pi$
$998$		0			0
$999$	−5.57073e10			−0.0559307

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	192.9.l.a.79.25		64
4.3	odd	2		48.9.l.a.43.21	yes	64
16.3	odd	4	inner	192.9.l.a.175.25		64
16.13	even	4		48.9.l.a.19.21	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.9.l.a.19.21	✓	64	16.13	even	4
48.9.l.a.43.21	yes	64	4.3	odd	2
192.9.l.a.79.25		64	1.1	even	1	trivial
192.9.l.a.175.25		64	16.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(33.0681 + 33.0681i) q^{3} +(214.689 + 214.689i) q^{5} +321.411 q^{7} +2187.00i q^{9} +(13451.1 - 13451.1i) q^{11} +(-3434.55 + 3434.55i) q^{13} +14198.7i q^{15} +65954.5 q^{17} +(-113520. - 113520. i) q^{19} +(10628.4 + 10628.4i) q^{21} +99132.9 q^{23} -298442. i q^{25} +(-72320.0 + 72320.0i) q^{27} +(74218.8 - 74218.8i) q^{29} -783672. i q^{31} +889604. q^{33} +(69003.3 + 69003.3i) q^{35} +(385145. + 385145. i) q^{37} -227148. q^{39} +2.10509e6i q^{41} +(2.77452e6 - 2.77452e6i) q^{43} +(-469525. + 469525. i) q^{45} -6.61433e6i q^{47} -5.66150e6 q^{49} +(2.18099e6 + 2.18099e6i) q^{51} +(873055. + 873055. i) q^{53} +5.77560e6 q^{55} -7.50775e6i q^{57} +(1.79884e6 - 1.79884e6i) q^{59} +(-1.03492e7 + 1.03492e7i) q^{61} +702925. i q^{63} -1.47472e6 q^{65} +(1.57263e7 + 1.57263e7i) q^{67} +(3.27814e6 + 3.27814e6i) q^{69} +4.51284e7 q^{71} -1.41319e7i q^{73} +(9.86893e6 - 9.86893e6i) q^{75} +(4.32332e6 - 4.32332e6i) q^{77} -5.93775e6i q^{79} -4.78297e6 q^{81} +(-4.07467e7 - 4.07467e7i) q^{83} +(1.41597e7 + 1.41597e7i) q^{85} +4.90855e6 q^{87} +3.55568e7i q^{89} +(-1.10390e6 + 1.10390e6i) q^{91} +(2.59146e7 - 2.59146e7i) q^{93} -4.87428e7i q^{95} -1.43728e7 q^{97} +(2.94175e7 + 2.94175e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 39552 q^{11} + 167552 q^{19} - 1691136 q^{23} - 2132352 q^{29} + 2415744 q^{35} - 4720512 q^{37} + 7244672 q^{43} + 52706752 q^{49} - 13862016 q^{51} - 5358720 q^{53} + 46326784 q^{55} - 44938752 q^{59}+ \cdots - 86500224 q^{99}+O(q^{100}) \) 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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