LMFDB - Embedded newform 192.9.l.a.79.6

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			79.6
Character	$\chi$	$=$	192.79
Dual form			192.9.l.a.175.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-33.0681 - 33.0681i) q^{3} +(306.323 + 306.323i) q^{5} -4330.12 q^{7} +2187.00i q^{9} +(-18335.5 + 18335.5i) q^{11} +(-24434.1 + 24434.1i) q^{13} -20259.0i q^{15} -35617.2 q^{17} +(-5513.54 - 5513.54i) q^{19} +(143189. + 143189. i) q^{21} +92940.4 q^{23} -202957. i q^{25} +(72320.0 - 72320.0i) q^{27} +(-311877. + 311877. i) q^{29} +122574. i q^{31} +1.21264e6 q^{33} +(-1.32641e6 - 1.32641e6i) q^{35} +(-1.50996e6 - 1.50996e6i) q^{37} +1.61598e6 q^{39} +2.41043e6i q^{41} +(952450. - 952450. i) q^{43} +(-669928. + 669928. i) q^{45} +4.39132e6i q^{47} +1.29851e7 q^{49} +(1.17779e6 + 1.17779e6i) q^{51} +(2.72881e6 + 2.72881e6i) q^{53} -1.12332e7 q^{55} +364645. i q^{57} +(-1.41908e7 + 1.41908e7i) q^{59} +(8.54559e6 - 8.54559e6i) q^{61} -9.46997e6i q^{63} -1.49695e7 q^{65} +(2.60963e7 + 2.60963e7i) q^{67} +(-3.07336e6 - 3.07336e6i) q^{69} -2.88819e7 q^{71} -3.78139e7i q^{73} +(-6.71142e6 + 6.71142e6i) q^{75} +(7.93950e7 - 7.93950e7i) q^{77} -7.03551e7i q^{79} -4.78297e6 q^{81} +(-4.08284e7 - 4.08284e7i) q^{83} +(-1.09104e7 - 1.09104e7i) q^{85} +2.06263e7 q^{87} +3.44569e6i q^{89} +(1.05803e8 - 1.05803e8i) q^{91} +(4.05328e6 - 4.05328e6i) q^{93} -3.37785e6i q^{95} -4.89049e7 q^{97} +(-4.00998e7 - 4.00998e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	306.323	+	306.323i	0.490117	+	0.490117i	0.908343	−	0.418226i	$-0.137348\pi$
$5$	306.323	+	306.323i	0.490117	+	0.490117i	−0.418226	+	0.908343i	$0.637348\pi$
$6$		0			0
$7$	−4330.12			−1.80346			−0.901732	−	0.432295i	$-0.857704\pi$
$7$	−4330.12			−1.80346			−0.901732	+	0.432295i	$0.857704\pi$
$8$		0			0
$9$			2187.00i			0.333333i
$10$		0			0
$11$	−18335.5	+	18335.5i	−1.25234	+	1.25234i	−0.297673	+	0.954668i	$0.596210\pi$
$11$	−18335.5	+	18335.5i	−1.25234	+	1.25234i	−0.954668	+	0.297673i	$0.903790\pi$
$12$		0			0
$13$	−24434.1	+	24434.1i	−0.855507	+	0.855507i	−0.990805	−	0.135298i	$-0.956801\pi$
$13$	−24434.1	+	24434.1i	−0.855507	+	0.855507i	0.135298	+	0.990805i	$0.456801\pi$
$14$		0			0
$15$		−	20259.0i		−	0.400179i
$16$		0			0
$17$	−35617.2			−0.426446			−0.213223	−	0.977004i	$-0.568396\pi$
$17$	−35617.2			−0.426446			−0.213223	+	0.977004i	$0.568396\pi$
$18$		0			0
$19$	−5513.54	−	5513.54i	−0.0423074	−	0.0423074i	0.685637	−	0.727944i	$-0.259524\pi$
$19$	−5513.54	−	5513.54i	−0.0423074	−	0.0423074i	−0.727944	+	0.685637i	$0.759524\pi$
$20$		0			0
$21$	143189.	+	143189.i	0.736261	+	0.736261i
$22$		0			0
$23$	92940.4			0.332118			0.166059	−	0.986116i	$-0.446896\pi$
$23$	92940.4			0.332118			0.166059	+	0.986116i	$0.446896\pi$
$24$		0			0
$25$		−	202957.i		−	0.519571i
$26$		0			0
$27$	72320.0	−	72320.0i	0.136083	−	0.136083i
$28$		0			0
$29$	−311877.	+	311877.i	−0.440952	+	0.440952i	−0.892332	−	0.451380i	$-0.850932\pi$
$29$	−311877.	+	311877.i	−0.440952	+	0.440952i	0.451380	+	0.892332i	$0.350932\pi$
$30$		0			0
$31$			122574.i			0.132724i	0.997796	+	0.0663622i	$0.0211393\pi$
$31$			122574.i			0.132724i	−0.997796	+	0.0663622i	$0.978861\pi$
$32$		0			0
$33$	1.21264e6			1.02253
$34$		0			0
$35$	−1.32641e6	−	1.32641e6i	−0.883908	−	0.883908i
$36$		0			0
$37$	−1.50996e6	−	1.50996e6i	−0.805670	−	0.805670i	0.178305	−	0.983975i	$-0.442939\pi$
$37$	−1.50996e6	−	1.50996e6i	−0.805670	−	0.805670i	−0.983975	+	0.178305i	$0.942939\pi$
$38$		0			0
$39$	1.61598e6			0.698518
$40$		0			0
$41$			2.41043e6i			0.853021i	0.904483	+	0.426510i	$0.140257\pi$
$41$			2.41043e6i			0.853021i	−0.904483	+	0.426510i	$0.859743\pi$
$42$		0			0
$43$	952450.	−	952450.i	0.278592	−	0.278592i	−0.553955	−	0.832547i	$-0.686882\pi$
$43$	952450.	−	952450.i	0.278592	−	0.278592i	0.832547	+	0.553955i	$0.186882\pi$
$44$		0			0
$45$	−669928.	+	669928.i	−0.163372	+	0.163372i
$46$		0			0
$47$			4.39132e6i			0.899920i	0.893049	+	0.449960i	$0.148562\pi$
$47$			4.39132e6i			0.899920i	−0.893049	+	0.449960i	$0.851438\pi$
$48$		0			0
$49$	1.29851e7			2.25248
$50$		0			0
$51$	1.17779e6	+	1.17779e6i	0.174096	+	0.174096i
$52$		0			0
$53$	2.72881e6	+	2.72881e6i	0.345836	+	0.345836i	0.858556	−	0.512720i	$-0.171362\pi$
$53$	2.72881e6	+	2.72881e6i	0.345836	+	0.345836i	−0.512720	+	0.858556i	$0.671362\pi$
$54$		0			0
$55$	−1.12332e7			−1.22759
$56$		0			0
$57$			364645.i			0.0345438i
$58$		0			0
$59$	−1.41908e7	+	1.41908e7i	−1.17112	+	1.17112i	−0.189173	+	0.981944i	$0.560581\pi$
$59$	−1.41908e7	+	1.41908e7i	−1.17112	+	1.17112i	−0.981944	+	0.189173i	$0.939419\pi$
$60$		0			0
$61$	8.54559e6	−	8.54559e6i	0.617195	−	0.617195i	−0.327616	−	0.944811i	$-0.606245\pi$
$61$	8.54559e6	−	8.54559e6i	0.617195	−	0.617195i	0.944811	+	0.327616i	$0.106245\pi$
$62$		0			0
$63$		−	9.46997e6i		−	0.601155i
$64$		0			0
$65$	−1.49695e7			−0.838596
$66$		0			0
$67$	2.60963e7	+	2.60963e7i	1.29503	+	1.29503i	0.931634	+	0.363398i	$0.118383\pi$
$67$	2.60963e7	+	2.60963e7i	1.29503	+	1.29503i	0.363398	+	0.931634i	$0.381617\pi$
$68$		0			0
$69$	−3.07336e6	−	3.07336e6i	−0.135587	−	0.135587i
$70$		0			0
$71$	−2.88819e7			−1.13656			−0.568280	−	0.822835i	$-0.692391\pi$
$71$	−2.88819e7			−1.13656			−0.568280	+	0.822835i	$0.692391\pi$
$72$		0			0
$73$		−	3.78139e7i		−	1.33156i	−0.746149	−	0.665779i	$-0.768099\pi$
$73$		−	3.78139e7i		−	1.33156i	0.746149	−	0.665779i	$-0.231901\pi$
$74$		0			0
$75$	−6.71142e6	+	6.71142e6i	−0.212114	+	0.212114i
$76$		0			0
$77$	7.93950e7	−	7.93950e7i	2.25855	−	2.25855i
$78$		0			0
$79$		−	7.03551e7i		−	1.80629i	−0.429337	−	0.903145i	$-0.641253\pi$
$79$		−	7.03551e7i		−	1.80629i	0.429337	−	0.903145i	$-0.358747\pi$
$80$		0			0
$81$	−4.78297e6			−0.111111
$82$		0			0
$83$	−4.08284e7	−	4.08284e7i	−0.860301	−	0.860301i	0.131072	−	0.991373i	$-0.458158\pi$
$83$	−4.08284e7	−	4.08284e7i	−0.860301	−	0.860301i	−0.991373	+	0.131072i	$0.958158\pi$
$84$		0			0
$85$	−1.09104e7	−	1.09104e7i	−0.209008	−	0.209008i
$86$		0			0
$87$	2.06263e7			0.360035
$88$		0			0
$89$			3.44569e6i			0.0549182i	0.999623	+	0.0274591i	$0.00874160\pi$
$89$			3.44569e6i			0.0549182i	−0.999623	+	0.0274591i	$0.991258\pi$
$90$		0			0
$91$	1.05803e8	−	1.05803e8i	1.54288	−	1.54288i
$92$		0			0
$93$	4.05328e6	−	4.05328e6i	0.0541845	−	0.0541845i
$94$		0			0
$95$		−	3.37785e6i		−	0.0414711i
$96$		0			0
$97$	−4.89049e7			−0.552414			−0.276207	−	0.961098i	$-0.589078\pi$
$97$	−4.89049e7			−0.552414			−0.276207	+	0.961098i	$0.589078\pi$
$98$		0			0
$99$	−4.00998e7	−	4.00998e7i	−0.417447	−	0.417447i
$100$		0			0
$101$	1.66521e7	+	1.66521e7i	0.160023	+	0.160023i	0.782577	−	0.622554i	$-0.213905\pi$
$101$	1.66521e7	+	1.66521e7i	0.160023	+	0.160023i	−0.622554	+	0.782577i	$0.713905\pi$
$102$		0			0
$103$	−5.39271e7			−0.479136			−0.239568	−	0.970880i	$-0.577006\pi$
$103$	−5.39271e7			−0.479136			−0.239568	+	0.970880i	$0.577006\pi$
$104$		0			0
$105$			8.77241e7i			0.721708i
$106$		0			0
$107$	1.38480e8	−	1.38480e8i	1.05646	−	1.05646i	0.0581527	−	0.998308i	$-0.481479\pi$
$107$	1.38480e8	−	1.38480e8i	1.05646	−	1.05646i	0.998308	−	0.0581527i	$-0.0185210\pi$
$108$		0			0
$109$	−1.93669e8	+	1.93669e8i	−1.37200	+	1.37200i	−0.514523	+	0.857477i	$0.672031\pi$
$109$	−1.93669e8	+	1.93669e8i	−1.37200	+	1.37200i	−0.857477	+	0.514523i	$0.827969\pi$
$110$		0			0
$111$			9.98628e7i			0.657827i
$112$		0			0
$113$	1.66194e8			1.01930			0.509650	−	0.860382i	$-0.329775\pi$
$113$	1.66194e8			1.01930			0.509650	+	0.860382i	$0.329775\pi$
$114$		0			0
$115$	2.84698e7	+	2.84698e7i	0.162777	+	0.162777i
$116$		0			0
$117$	−5.34374e7	−	5.34374e7i	−0.285169	−	0.285169i
$118$		0			0
$119$	1.54227e8			0.769079
$120$		0			0
$121$		−	4.58024e8i		−	2.13671i
$122$		0			0
$123$	7.97085e7	−	7.97085e7i	0.348244	−	0.348244i
$124$		0			0
$125$	1.81828e8	−	1.81828e8i	0.744767	−	0.744767i
$126$		0			0
$127$			5.89844e7i			0.226737i	0.993553	+	0.113368i	$0.0361641\pi$
$127$			5.89844e7i			0.226737i	−0.993553	+	0.113368i	$0.963836\pi$
$128$		0			0
$129$	−6.29914e7			−0.227469
$130$		0			0
$131$	1.98376e8	+	1.98376e8i	0.673604	+	0.673604i	0.958545	−	0.284941i	$-0.0919740\pi$
$131$	1.98376e8	+	1.98376e8i	0.673604	+	0.673604i	−0.284941	+	0.958545i	$0.591974\pi$
$132$		0			0
$133$	2.38743e7	+	2.38743e7i	0.0762998	+	0.0762998i
$134$		0			0
$135$	4.43065e7			0.133393
$136$		0			0
$137$		−	2.70452e8i		−	0.767728i	−0.923390	−	0.383864i	$-0.874593\pi$
$137$		−	2.70452e8i		−	0.767728i	0.923390	−	0.383864i	$-0.125407\pi$
$138$		0			0
$139$	2.31422e8	−	2.31422e8i	0.619935	−	0.619935i	−0.325580	−	0.945515i	$-0.605559\pi$
$139$	2.31422e8	−	2.31422e8i	0.619935	−	0.619935i	0.945515	+	0.325580i	$0.105559\pi$
$140$		0			0
$141$	1.45213e8	−	1.45213e8i	0.367391	−	0.367391i
$142$		0			0
$143$		−	8.96025e8i		−	2.14277i
$144$		0			0
$145$	−1.91070e8			−0.432235
$146$		0			0
$147$	−4.29393e8	−	4.29393e8i	−0.919573	−	0.919573i
$148$		0			0
$149$	7.61640e7	+	7.61640e7i	0.154527	+	0.154527i	0.780137	−	0.625609i	$-0.215150\pi$
$149$	7.61640e7	+	7.61640e7i	0.154527	+	0.154527i	−0.625609	+	0.780137i	$0.715150\pi$
$150$		0			0
$151$	5.04866e8			0.971111			0.485555	−	0.874206i	$-0.338617\pi$
$151$	5.04866e8			0.971111			0.485555	+	0.874206i	$0.338617\pi$
$152$		0			0
$153$		−	7.78947e7i		−	0.142149i
$154$		0			0
$155$	−3.75471e7	+	3.75471e7i	−0.0650504	+	0.0650504i
$156$		0			0
$157$	1.53881e8	−	1.53881e8i	0.253271	−	0.253271i	−0.569039	−	0.822310i	$-0.692685\pi$
$157$	1.53881e8	−	1.53881e8i	0.253271	−	0.253271i	0.822310	+	0.569039i	$0.192685\pi$
$158$		0			0
$159$		−	1.80473e8i		−	0.282374i
$160$		0			0
$161$	−4.02443e8			−0.598964
$162$		0			0
$163$	5.89895e8	+	5.89895e8i	0.835650	+	0.835650i	0.988283	−	0.152633i	$-0.0487751\pi$
$163$	5.89895e8	+	5.89895e8i	0.835650	+	0.835650i	−0.152633	+	0.988283i	$0.548775\pi$
$164$		0			0
$165$	3.71460e8	+	3.71460e8i	0.501160	+	0.501160i
$166$		0			0
$167$	−1.12098e9			−1.44123			−0.720615	−	0.693335i	$-0.756140\pi$
$167$	−1.12098e9			−1.44123			−0.720615	+	0.693335i	$0.756140\pi$
$168$		0			0
$169$		−	3.78323e8i		−	0.463784i
$170$		0			0
$171$	1.20581e7	−	1.20581e7i	0.0141025	−	0.0141025i
$172$		0			0
$173$	−4.12801e8	+	4.12801e8i	−0.460846	+	0.460846i	−0.898933	−	0.438086i	$-0.855656\pi$
$173$	−4.12801e8	+	4.12801e8i	−0.460846	+	0.460846i	0.438086	+	0.898933i	$0.355656\pi$
$174$		0			0
$175$			8.78830e8i			0.937028i
$176$		0			0
$177$	9.38529e8			0.956213
$178$		0			0
$179$	−3.62969e8	−	3.62969e8i	−0.353556	−	0.353556i	0.507875	−	0.861431i	$-0.330431\pi$
$179$	−3.62969e8	−	3.62969e8i	−0.353556	−	0.353556i	−0.861431	+	0.507875i	$0.830431\pi$
$180$		0			0
$181$	−4.66109e8	−	4.66109e8i	−0.434284	−	0.434284i	0.455799	−	0.890083i	$-0.349354\pi$
$181$	−4.66109e8	−	4.66109e8i	−0.434284	−	0.434284i	−0.890083	+	0.455799i	$0.849354\pi$
$182$		0			0
$183$	−5.65173e8			−0.503938
$184$		0			0
$185$		−	9.25069e8i		−	0.789745i
$186$		0			0
$187$	6.53059e8	−	6.53059e8i	0.534055	−	0.534055i
$188$		0			0
$189$	−3.13154e8	+	3.13154e8i	−0.245420	+	0.245420i
$190$		0			0
$191$			4.70600e8i			0.353605i	0.984246	+	0.176803i	$0.0565754\pi$
$191$			4.70600e8i			0.353605i	−0.984246	+	0.176803i	$0.943425\pi$
$192$		0			0
$193$	−2.12140e8			−0.152895			−0.0764475	−	0.997074i	$-0.524358\pi$
$193$	−2.12140e8			−0.152895			−0.0764475	+	0.997074i	$0.524358\pi$
$194$		0			0
$195$	4.95012e8	+	4.95012e8i	0.342356	+	0.342356i
$196$		0			0
$197$	1.87958e9	+	1.87958e9i	1.24794	+	1.24794i	0.956626	+	0.291318i	$0.0940937\pi$
$197$	1.87958e9	+	1.87958e9i	1.24794	+	1.24794i	0.291318	+	0.956626i	$0.405906\pi$
$198$		0			0
$199$	−1.46175e9			−0.932097			−0.466049	−	0.884759i	$-0.654323\pi$
$199$	−1.46175e9			−0.932097			−0.466049	+	0.884759i	$0.654323\pi$
$200$		0			0
$201$		−	1.72591e9i		−	1.05739i
$202$		0			0
$203$	1.35046e9	−	1.35046e9i	0.795240	−	0.795240i
$204$		0			0
$205$	−7.38371e8	+	7.38371e8i	−0.418080	+	0.418080i
$206$		0			0
$207$			2.03261e8i			0.110706i
$208$		0			0
$209$	2.02187e8			0.105966
$210$		0			0
$211$	−2.06475e9	−	2.06475e9i	−1.04169	−	1.04169i	−0.999092	−	0.0425968i	$-0.986437\pi$
$211$	−2.06475e9	−	2.06475e9i	−1.04169	−	1.04169i	−0.0425968	−	0.999092i	$-0.513563\pi$
$212$		0			0
$213$	9.55070e8	+	9.55070e8i	0.463999	+	0.463999i
$214$		0			0
$215$	5.83515e8			0.273085
$216$		0			0
$217$		−	5.30759e8i		−	0.239364i
$218$		0			0
$219$	−1.25043e9	+	1.25043e9i	−0.543606	+	0.543606i
$220$		0			0
$221$	8.70274e8	−	8.70274e8i	0.364827	−	0.364827i
$222$		0			0
$223$			2.43335e9i			0.983978i	0.870601	+	0.491989i	$0.163730\pi$
$223$			2.43335e9i			0.983978i	−0.870601	+	0.491989i	$0.836270\pi$
$224$		0			0
$225$	4.43868e8			0.173190
$226$		0			0
$227$	1.73952e9	+	1.73952e9i	0.655129	+	0.655129i	0.954223	−	0.299095i	$-0.0966847\pi$
$227$	1.73952e9	+	1.73952e9i	0.655129	+	0.655129i	−0.299095	+	0.954223i	$0.596685\pi$
$228$		0			0
$229$	6.00973e8	+	6.00973e8i	0.218531	+	0.218531i	0.807879	−	0.589348i	$-0.200615\pi$
$229$	6.00973e8	+	6.00973e8i	0.218531	+	0.218531i	−0.589348	+	0.807879i	$0.700615\pi$
$230$		0			0
$231$	−5.25088e9			−1.84410
$232$		0			0
$233$		−	2.19736e9i		−	0.745552i	−0.927921	−	0.372776i	$-0.878406\pi$
$233$		−	2.19736e9i		−	0.745552i	0.927921	−	0.372776i	$-0.121594\pi$
$234$		0			0
$235$	−1.34516e9	+	1.34516e9i	−0.441066	+	0.441066i
$236$		0			0
$237$	−2.32651e9	+	2.32651e9i	−0.737414	+	0.737414i
$238$		0			0
$239$			5.38280e9i			1.64974i	0.565320	+	0.824872i	$0.308753\pi$
$239$			5.38280e9i			1.64974i	−0.565320	+	0.824872i	$0.691247\pi$
$240$		0			0
$241$	−5.86545e9			−1.73873			−0.869367	−	0.494168i	$-0.835473\pi$
$241$	−5.86545e9			−1.73873			−0.869367	+	0.494168i	$0.835473\pi$
$242$		0			0
$243$	1.58164e8	+	1.58164e8i	0.0453609	+	0.0453609i
$244$		0			0
$245$	3.97764e9	+	3.97764e9i	1.10398	+	1.10398i
$246$		0			0
$247$	2.69437e8			0.0723885
$248$		0			0
$249$			2.70024e9i			0.702432i
$250$		0			0
$251$	4.49568e9	−	4.49568e9i	1.13266	−	1.13266i	0.142929	−	0.989733i	$-0.454348\pi$
$251$	4.49568e9	−	4.49568e9i	1.13266	−	1.13266i	0.989733	−	0.142929i	$-0.0456521\pi$
$252$		0			0
$253$	−1.70411e9	+	1.70411e9i	−0.415925	+	0.415925i
$254$		0			0
$255$			7.21570e8i			0.170654i
$256$		0			0
$257$	1.17052e9			0.268316			0.134158	−	0.990960i	$-0.457167\pi$
$257$	1.17052e9			0.268316			0.134158	+	0.990960i	$0.457167\pi$
$258$		0			0
$259$	6.53829e9	+	6.53829e9i	1.45300	+	1.45300i
$260$		0			0
$261$	−6.82074e8	−	6.82074e8i	−0.146984	−	0.146984i
$262$		0			0
$263$	−8.17179e9			−1.70802			−0.854012	−	0.520253i	$-0.825838\pi$
$263$	−8.17179e9			−1.70802			−0.854012	+	0.520253i	$0.825838\pi$
$264$		0			0
$265$			1.67179e9i			0.339000i
$266$		0			0
$267$	1.13942e8	−	1.13942e8i	0.0224203	−	0.0224203i
$268$		0			0
$269$	−1.37316e9	+	1.37316e9i	−0.262248	+	0.262248i	−0.825967	−	0.563719i	$-0.809370\pi$
$269$	−1.37316e9	+	1.37316e9i	−0.262248	+	0.262248i	0.563719	+	0.825967i	$0.309370\pi$
$270$		0			0
$271$			5.63957e9i			1.04561i	0.852453	+	0.522804i	$0.175114\pi$
$271$			5.63957e9i			1.04561i	−0.852453	+	0.522804i	$0.824886\pi$
$272$		0			0
$273$	−6.99739e9			−1.25975
$274$		0			0
$275$	3.72133e9	+	3.72133e9i	0.650680	+	0.650680i
$276$		0			0
$277$	2.28396e9	+	2.28396e9i	0.387945	+	0.387945i	0.873954	−	0.486009i	$-0.161548\pi$
$277$	2.28396e9	+	2.28396e9i	0.387945	+	0.387945i	−0.486009	+	0.873954i	$0.661548\pi$
$278$		0			0
$279$	−2.68069e8			−0.0442414
$280$		0			0
$281$			1.97291e9i			0.316434i	0.987404	+	0.158217i	$0.0505745\pi$
$281$			1.97291e9i			0.316434i	−0.987404	+	0.158217i	$0.949425\pi$
$282$		0			0
$283$	4.46097e9	−	4.46097e9i	0.695478	−	0.695478i	−0.267954	−	0.963432i	$-0.586347\pi$
$283$	4.46097e9	−	4.46097e9i	0.695478	−	0.695478i	0.963432	+	0.267954i	$0.0863474\pi$
$284$		0			0
$285$	−1.11699e8	+	1.11699e8i	−0.0169305	+	0.0169305i
$286$		0			0
$287$		−	1.04375e10i		−	1.53839i
$288$		0			0
$289$	−5.70718e9			−0.818144
$290$		0			0
$291$	1.61719e9	+	1.61719e9i	0.225522	+	0.225522i
$292$		0			0
$293$	6.65882e8	+	6.65882e8i	0.0903497	+	0.0903497i	0.750837	−	0.660487i	$-0.229650\pi$
$293$	6.65882e8	+	6.65882e8i	0.0903497	+	0.0903497i	−0.660487	+	0.750837i	$0.729650\pi$
$294$		0			0
$295$	−8.69396e9			−1.14797
$296$		0			0
$297$			2.65205e9i			0.340844i
$298$		0			0
$299$	−2.27092e9	+	2.27092e9i	−0.284130	+	0.284130i
$300$		0			0
$301$	−4.12422e9	+	4.12422e9i	−0.502430	+	0.502430i
$302$		0			0
$303$		−	1.10130e9i		−	0.130658i
$304$		0			0
$305$	5.23542e9			0.604995
$306$		0			0
$307$	−1.01000e9	−	1.01000e9i	−0.113702	−	0.113702i	0.647967	−	0.761669i	$-0.275620\pi$
$307$	−1.01000e9	−	1.01000e9i	−0.113702	−	0.113702i	−0.761669	+	0.647967i	$0.775620\pi$
$308$		0			0
$309$	1.78327e9	+	1.78327e9i	0.195606	+	0.195606i
$310$		0			0
$311$	1.20144e10			1.28428			0.642139	−	0.766588i	$-0.278047\pi$
$311$	1.20144e10			1.28428			0.642139	+	0.766588i	$0.278047\pi$
$312$		0			0
$313$		−	9.06670e8i		−	0.0944652i	−0.998884	−	0.0472326i	$-0.984960\pi$
$313$		−	9.06670e8i		−	0.0944652i	0.998884	−	0.0472326i	$-0.0150402\pi$
$314$		0			0
$315$	2.90087e9	−	2.90087e9i	0.294636	−	0.294636i
$316$		0			0
$317$	−1.09662e9	+	1.09662e9i	−0.108598	+	0.108598i	−0.759318	−	0.650720i	$-0.774467\pi$
$317$	−1.09662e9	+	1.09662e9i	−0.108598	+	0.108598i	0.650720	+	0.759318i	$0.274467\pi$
$318$		0			0
$319$		−	1.14368e10i		−	1.10444i
$320$		0			0
$321$	−9.15857e9			−0.862596
$322$		0			0
$323$	1.96377e8	+	1.96377e8i	0.0180418	+	0.0180418i
$324$		0			0
$325$	4.95909e9	+	4.95909e9i	0.444497	+	0.444497i
$326$		0			0
$327$	1.28085e10			1.12023
$328$		0			0
$329$		−	1.90149e10i		−	1.62297i
$330$		0			0
$331$	1.58693e8	−	1.58693e8i	0.0132204	−	0.0132204i	−0.700466	−	0.713686i	$-0.747024\pi$
$331$	1.58693e8	−	1.58693e8i	0.0132204	−	0.0132204i	0.713686	+	0.700466i	$0.247024\pi$
$332$		0			0
$333$	3.30227e9	−	3.30227e9i	0.268557	−	0.268557i
$334$		0			0
$335$			1.59878e10i			1.26943i
$336$		0			0
$337$	4.41784e9			0.342523			0.171262	−	0.985226i	$-0.445216\pi$
$337$	4.41784e9			0.342523			0.171262	+	0.985226i	$0.445216\pi$
$338$		0			0
$339$	−5.49573e9	−	5.49573e9i	−0.416127	−	0.416127i
$340$		0			0
$341$	−2.24745e9	−	2.24745e9i	−0.166216	−	0.166216i
$342$		0			0
$343$	−3.12648e10			−2.25881
$344$		0			0
$345$		−	1.88288e9i		−	0.132907i
$346$		0			0
$347$	9.95116e9	−	9.95116e9i	0.686366	−	0.686366i	−0.275061	−	0.961427i	$-0.588698\pi$
$347$	9.95116e9	−	9.95116e9i	0.686366	−	0.686366i	0.961427	+	0.275061i	$0.0886979\pi$
$348$		0			0
$349$	−1.38855e10	+	1.38855e10i	−0.935967	+	0.935967i	−0.998070	−	0.0621027i	$-0.980219\pi$
$349$	−1.38855e10	+	1.38855e10i	−0.935967	+	0.935967i	0.0621027	+	0.998070i	$0.480219\pi$
$350$		0			0
$351$			3.53415e9i			0.232839i
$352$		0			0
$353$	1.88810e10			1.21598			0.607990	−	0.793944i	$-0.291976\pi$
$353$	1.88810e10			1.21598			0.607990	+	0.793944i	$0.291976\pi$
$354$		0			0
$355$	−8.84719e9	−	8.84719e9i	−0.557047	−	0.557047i
$356$		0			0
$357$	−5.09998e9	−	5.09998e9i	−0.313975	−	0.313975i
$358$		0			0
$359$	1.13365e10			0.682500			0.341250	−	0.939973i	$-0.389150\pi$
$359$	1.13365e10			0.682500			0.341250	+	0.939973i	$0.389150\pi$
$360$		0			0
$361$		−	1.69228e10i		−	0.996420i
$362$		0			0
$363$	−1.51460e10	+	1.51460e10i	−0.872310	+	0.872310i
$364$		0			0
$365$	1.15833e10	−	1.15833e10i	0.652619	−	0.652619i
$366$		0			0
$367$			2.50329e10i			1.37990i	0.723859	+	0.689948i	$0.242367\pi$
$367$			2.50329e10i			1.37990i	−0.723859	+	0.689948i	$0.757633\pi$
$368$		0			0
$369$	−5.27162e9			−0.284340
$370$		0			0
$371$	−1.18161e10	−	1.18161e10i	−0.623702	−	0.623702i
$372$		0			0
$373$	−9.40421e9	−	9.40421e9i	−0.485833	−	0.485833i	0.421155	−	0.906989i	$-0.361625\pi$
$373$	−9.40421e9	−	9.40421e9i	−0.485833	−	0.485833i	−0.906989	+	0.421155i	$0.861625\pi$
$374$		0			0
$375$	−1.20254e10			−0.608100
$376$		0			0
$377$		−	1.52409e10i		−	0.754474i
$378$		0			0
$379$	1.04093e10	−	1.04093e10i	0.504505	−	0.504505i	−0.408330	−	0.912835i	$-0.633889\pi$
$379$	1.04093e10	−	1.04093e10i	0.504505	−	0.504505i	0.912835	+	0.408330i	$0.133889\pi$
$380$		0			0
$381$	1.95050e9	−	1.95050e9i	0.0925650	−	0.0925650i
$382$		0			0
$383$		−	1.73370e10i		−	0.805711i	−0.915263	−	0.402856i	$-0.868018\pi$
$383$		−	1.73370e10i		−	0.805711i	0.915263	−	0.402856i	$-0.131982\pi$
$384$		0			0
$385$	4.86410e10			2.21391
$386$		0			0
$387$	2.08301e9	+	2.08301e9i	0.0928639	+	0.0928639i
$388$		0			0
$389$	1.06696e10	+	1.06696e10i	0.465961	+	0.465961i	0.900603	−	0.434642i	$-0.143125\pi$
$389$	1.06696e10	+	1.06696e10i	0.465961	+	0.465961i	−0.434642	+	0.900603i	$0.643125\pi$
$390$		0			0
$391$	−3.31027e9			−0.141630
$392$		0			0
$393$		−	1.31199e10i		−	0.549995i
$394$		0			0
$395$	2.15514e10	−	2.15514e10i	0.885293	−	0.885293i
$396$		0			0
$397$	1.79515e10	−	1.79515e10i	0.722668	−	0.722668i	−0.246480	−	0.969148i	$-0.579274\pi$
$397$	1.79515e10	−	1.79515e10i	0.722668	−	0.722668i	0.969148	+	0.246480i	$0.0792740\pi$
$398$		0			0
$399$		−	1.57895e9i		−	0.0622985i
$400$		0			0
$401$	−1.23789e10			−0.478744			−0.239372	−	0.970928i	$-0.576942\pi$
$401$	−1.23789e10			−0.478744			−0.239372	+	0.970928i	$0.576942\pi$
$402$		0			0
$403$	−2.99498e9	−	2.99498e9i	−0.113547	−	0.113547i
$404$		0			0
$405$	−1.46513e9	−	1.46513e9i	−0.0544574	−	0.0544574i
$406$		0			0
$407$	5.53717e10			2.01795
$408$		0			0
$409$			1.46189e10i			0.522421i	0.965282	+	0.261211i	$0.0841217\pi$
$409$			1.46189e10i			0.522421i	−0.965282	+	0.261211i	$0.915878\pi$
$410$		0			0
$411$	−8.94332e9	+	8.94332e9i	−0.313424	+	0.313424i
$412$		0			0
$413$	6.14480e10	−	6.14480e10i	2.11207	−	2.11207i
$414$		0			0
$415$		−	2.50134e10i		−	0.843295i
$416$		0			0
$417$	−1.53054e10			−0.506175
$418$		0			0
$419$	1.47232e10	+	1.47232e10i	0.477691	+	0.477691i	0.904393	−	0.426701i	$-0.140324\pi$
$419$	1.47232e10	+	1.47232e10i	0.477691	+	0.477691i	−0.426701	+	0.904393i	$0.640324\pi$
$420$		0			0
$421$	2.64201e10	+	2.64201e10i	0.841021	+	0.841021i	0.988992	−	0.147971i	$-0.0472741\pi$
$421$	2.64201e10	+	2.64201e10i	0.841021	+	0.841021i	−0.147971	+	0.988992i	$0.547274\pi$
$422$		0			0
$423$	−9.60382e9			−0.299973
$424$		0			0
$425$			7.22877e9i			0.221569i
$426$		0			0
$427$	−3.70034e10	+	3.70034e10i	−1.11309	+	1.11309i
$428$		0			0
$429$	−2.96299e10	+	2.96299e10i	−0.874783	+	0.874783i
$430$		0			0
$431$		−	3.67427e10i		−	1.06478i	−0.846498	−	0.532392i	$-0.821293\pi$
$431$		−	3.67427e10i		−	1.06478i	0.846498	−	0.532392i	$-0.178707\pi$
$432$		0			0
$433$	−2.81639e10			−0.801200			−0.400600	−	0.916253i	$-0.631198\pi$
$433$	−2.81639e10			−0.801200			−0.400600	+	0.916253i	$0.631198\pi$
$434$		0			0
$435$	6.31832e9	+	6.31832e9i	0.176459	+	0.176459i
$436$		0			0
$437$	−5.12430e8	−	5.12430e8i	−0.0140511	−	0.0140511i
$438$		0			0
$439$	−7.33053e9			−0.197368			−0.0986842	−	0.995119i	$-0.531463\pi$
$439$	−7.33053e9			−0.197368			−0.0986842	+	0.995119i	$0.531463\pi$
$440$		0			0
$441$			2.83985e10i			0.750828i
$442$		0			0
$443$	−2.93084e9	+	2.93084e9i	−0.0760988	+	0.0760988i	−0.744132	−	0.668033i	$-0.767137\pi$
$443$	−2.93084e9	+	2.93084e9i	−0.0760988	+	0.0760988i	0.668033	+	0.744132i	$0.267137\pi$
$444$		0			0
$445$	−1.05549e9	+	1.05549e9i	−0.0269163	+	0.0269163i
$446$		0			0
$447$		−	5.03720e9i		−	0.126171i
$448$		0			0
$449$	−3.95466e10			−0.973025			−0.486513	−	0.873674i	$-0.661731\pi$
$449$	−3.95466e10			−0.973025			−0.486513	+	0.873674i	$0.661731\pi$
$450$		0			0
$451$	−4.41965e10	−	4.41965e10i	−1.06827	−	1.06827i
$452$		0			0
$453$	−1.66950e10	−	1.66950e10i	−0.396454	−	0.396454i
$454$		0			0
$455$	6.48196e10			1.51238
$456$		0			0
$457$			4.96923e10i			1.13926i	0.821900	+	0.569632i	$0.192914\pi$
$457$			4.96923e10i			1.13926i	−0.821900	+	0.569632i	$0.807086\pi$
$458$		0			0
$459$	−2.57583e9	+	2.57583e9i	−0.0580319	+	0.0580319i
$460$		0			0
$461$	−3.71863e10	+	3.71863e10i	−0.823341	+	0.823341i	−0.986586	−	0.163245i	$-0.947804\pi$
$461$	−3.71863e10	+	3.71863e10i	−0.823341	+	0.823341i	0.163245	+	0.986586i	$0.447804\pi$
$462$		0			0
$463$		−	2.29012e10i		−	0.498349i	−0.968459	−	0.249175i	$-0.919841\pi$
$463$		−	2.29012e10i		−	0.498349i	0.968459	−	0.249175i	$-0.0801593\pi$
$464$		0			0
$465$	2.48323e9			0.0531134
$466$		0			0
$467$	4.90133e10	+	4.90133e10i	1.03050	+	1.03050i	0.999520	+	0.0309756i	$0.00986142\pi$
$467$	4.90133e10	+	4.90133e10i	1.03050	+	1.03050i	0.0309756	+	0.999520i	$0.490139\pi$
$468$		0			0
$469$	−1.13000e11	−	1.13000e11i	−2.33554	−	2.33554i
$470$		0			0
$471$	−1.01771e10			−0.206795
$472$		0			0
$473$			3.49273e10i			0.697784i
$474$		0			0
$475$	−1.11901e9	+	1.11901e9i	−0.0219817	+	0.0219817i
$476$		0			0
$477$	−5.96790e9	+	5.96790e9i	−0.115279	+	0.115279i
$478$		0			0
$479$		−	7.22421e10i		−	1.37230i	−0.727461	−	0.686149i	$-0.759300\pi$
$479$		−	7.22421e10i		−	1.37230i	0.727461	−	0.686149i	$-0.240700\pi$
$480$		0			0
$481$	7.37889e10			1.37851
$482$		0			0
$483$	1.33080e10	+	1.33080e10i	0.244526	+	0.244526i
$484$		0			0
$485$	−1.49807e10	−	1.49807e10i	−0.270748	−	0.270748i
$486$		0			0
$487$	8.60718e10			1.53019			0.765095	−	0.643918i	$-0.222692\pi$
$487$	8.60718e10			1.53019			0.765095	+	0.643918i	$0.222692\pi$
$488$		0			0
$489$		−	3.90135e10i		−	0.682306i
$490$		0			0
$491$	3.44025e10	−	3.44025e10i	0.591921	−	0.591921i	−0.346229	−	0.938150i	$-0.612538\pi$
$491$	3.44025e10	−	3.44025e10i	0.591921	−	0.591921i	0.938150	+	0.346229i	$0.112538\pi$
$492$		0			0
$493$	1.11082e10	−	1.11082e10i	0.188042	−	0.188042i
$494$		0			0
$495$		−	2.45670e10i		−	0.409195i
$496$		0			0
$497$	1.25062e11			2.04975
$498$		0			0
$499$	−7.69193e10	−	7.69193e10i	−1.24060	−	1.24060i	−0.959751	−	0.280854i	$-0.909382\pi$
$499$	−7.69193e10	−	7.69193e10i	−1.24060	−	1.24060i	−0.280854	−	0.959751i	$-0.590618\pi$
$500$		0			0
$501$	3.70688e10	+	3.70688e10i	0.588380	+	0.588380i
$502$		0			0
$503$	−8.07309e10			−1.26115			−0.630577	−	0.776127i	$-0.717182\pi$
$503$	−8.07309e10			−1.26115			−0.630577	+	0.776127i	$0.717182\pi$
$504$		0			0
$505$			1.02018e10i			0.156860i
$506$		0			0
$507$	−1.25104e10	+	1.25104e10i	−0.189339	+	0.189339i
$508$		0			0
$509$	1.02860e10	−	1.02860e10i	0.153242	−	0.153242i	−0.626323	−	0.779564i	$-0.715441\pi$
$509$	1.02860e10	−	1.02860e10i	0.153242	−	0.153242i	0.779564	+	0.626323i	$0.215441\pi$
$510$		0			0
$511$			1.63739e11i			2.40142i
$512$		0			0
$513$	−7.97478e8			−0.0115146
$514$		0			0
$515$	−1.65191e10	−	1.65191e10i	−0.234832	−	0.234832i
$516$		0			0
$517$	−8.05172e10	−	8.05172e10i	−1.12701	−	1.12701i
$518$		0			0
$519$	2.73011e10			0.376280
$520$		0			0
$521$			3.34398e10i			0.453850i	0.973912	+	0.226925i	$0.0728672\pi$
$521$			3.34398e10i			0.453850i	−0.973912	+	0.226925i	$0.927133\pi$
$522$		0			0
$523$	6.15955e10	−	6.15955e10i	0.823270	−	0.823270i	−0.163305	−	0.986576i	$-0.552216\pi$
$523$	6.15955e10	−	6.15955e10i	0.823270	−	0.823270i	0.986576	+	0.163305i	$0.0522156\pi$
$524$		0			0
$525$	2.90612e10	−	2.90612e10i	0.382540	−	0.382540i
$526$		0			0
$527$		−	4.36573e9i		−	0.0565997i
$528$		0			0
$529$	−6.96731e10			−0.889697
$530$		0			0
$531$	−3.10354e10	−	3.10354e10i	−0.390372	−	0.390372i
$532$		0			0
$533$	−5.88968e10	−	5.88968e10i	−0.729765	−	0.729765i
$534$		0			0
$535$	8.48395e10			1.03558
$536$		0			0
$537$			2.40054e10i			0.288677i
$538$		0			0
$539$	−2.38089e11	+	2.38089e11i	−2.82088	+	2.82088i
$540$		0			0
$541$	−2.84956e10	+	2.84956e10i	−0.332651	+	0.332651i	−0.853592	−	0.520941i	$-0.825581\pi$
$541$	−2.84956e10	+	2.84956e10i	−0.332651	+	0.332651i	0.520941	+	0.853592i	$0.325581\pi$
$542$		0			0
$543$			3.08267e10i			0.354591i
$544$		0			0
$545$	−1.18650e11			−1.34488
$546$		0			0
$547$	9.74078e10	+	9.74078e10i	1.08804	+	1.08804i	0.995730	+	0.0923090i	$0.0294248\pi$
$547$	9.74078e10	+	9.74078e10i	1.08804	+	1.08804i	0.0923090	+	0.995730i	$0.470575\pi$
$548$		0			0
$549$	1.86892e10	+	1.86892e10i	0.205732	+	0.205732i
$550$		0			0
$551$	3.43909e9			0.0373110
$552$		0			0
$553$			3.04646e11i			3.25758i
$554$		0			0
$555$	−3.05903e10	+	3.05903e10i	−0.322412	+	0.322412i
$556$		0			0
$557$	−2.76223e10	+	2.76223e10i	−0.286972	+	0.286972i	−0.835882	−	0.548910i	$-0.815043\pi$
$557$	−2.76223e10	+	2.76223e10i	−0.286972	+	0.286972i	0.548910	+	0.835882i	$0.315043\pi$
$558$		0			0
$559$			4.65446e10i			0.476674i
$560$		0			0
$561$	−4.31909e10			−0.436054
$562$		0			0
$563$	4.36554e10	+	4.36554e10i	0.434515	+	0.434515i	0.890161	−	0.455646i	$-0.150592\pi$
$563$	4.36554e10	+	4.36554e10i	0.434515	+	0.434515i	−0.455646	+	0.890161i	$0.650592\pi$
$564$		0			0
$565$	5.09091e10	+	5.09091e10i	0.499576	+	0.499576i
$566$		0			0
$567$	2.07108e10			0.200385
$568$		0			0
$569$		−	8.25526e9i		−	0.0787556i	−0.999224	−	0.0393778i	$-0.987462\pi$
$569$		−	8.25526e9i		−	0.0787556i	0.999224	−	0.0393778i	$-0.0125376\pi$
$570$		0			0
$571$	−6.81132e10	+	6.81132e10i	−0.640748	+	0.640748i	−0.950739	−	0.309992i	$-0.899674\pi$
$571$	−6.81132e10	+	6.81132e10i	−0.640748	+	0.640748i	0.309992	+	0.950739i	$0.399674\pi$
$572$		0			0
$573$	1.55619e10	−	1.55619e10i	0.144359	−	0.144359i
$574$		0			0
$575$		−	1.88629e10i		−	0.172559i
$576$		0			0
$577$	7.97472e10			0.719469			0.359734	−	0.933055i	$-0.382867\pi$
$577$	7.97472e10			0.719469			0.359734	+	0.933055i	$0.382867\pi$
$578$		0			0
$579$	7.01507e9	+	7.01507e9i	0.0624191	+	0.0624191i
$580$		0			0
$581$	1.76792e11	+	1.76792e11i	1.55152	+	1.55152i
$582$		0			0
$583$	−1.00068e11			−0.866208
$584$		0			0
$585$		−	3.27382e10i		−	0.279532i
$586$		0			0
$587$	−2.38620e10	+	2.38620e10i	−0.200981	+	0.200981i	−0.800420	−	0.599439i	$-0.795390\pi$
$587$	−2.38620e10	+	2.38620e10i	−0.200981	+	0.200981i	0.599439	+	0.800420i	$0.295390\pi$
$588$		0			0
$589$	6.75815e8	−	6.75815e8i	0.00561522	−	0.00561522i
$590$		0			0
$591$		−	1.24308e11i		−	1.01894i
$592$		0			0
$593$	3.00612e10			0.243101			0.121551	−	0.992585i	$-0.461213\pi$
$593$	3.00612e10			0.243101			0.121551	+	0.992585i	$0.461213\pi$
$594$		0			0
$595$	4.72431e10	+	4.72431e10i	0.376939	+	0.376939i
$596$		0			0
$597$	4.83374e10	+	4.83374e10i	0.380527	+	0.380527i
$598$		0			0
$599$	−1.35624e10			−0.105349			−0.0526746	−	0.998612i	$-0.516775\pi$
$599$	−1.35624e10			−0.105349			−0.0526746	+	0.998612i	$0.516775\pi$
$600$		0			0
$601$			9.45767e9i			0.0724913i	0.999343	+	0.0362457i	$0.0115399\pi$
$601$			9.45767e9i			0.0724913i	−0.999343	+	0.0362457i	$0.988460\pi$
$602$		0			0
$603$	−5.70727e10	+	5.70727e10i	−0.431677	+	0.431677i
$604$		0			0
$605$	1.40303e11	−	1.40303e11i	1.04724	−	1.04724i
$606$		0			0
$607$			7.49215e10i			0.551889i	0.961174	+	0.275944i	$0.0889905\pi$
$607$			7.49215e10i			0.551889i	−0.961174	+	0.275944i	$0.911009\pi$
$608$		0			0
$609$	−8.93145e10			−0.649311
$610$		0			0
$611$	−1.07298e11	−	1.07298e11i	−0.769888	−	0.769888i
$612$		0			0
$613$	−1.05145e11	−	1.05145e11i	−0.744639	−	0.744639i	0.228828	−	0.973467i	$-0.426511\pi$
$613$	−1.05145e11	−	1.05145e11i	−0.744639	−	0.744639i	−0.973467	+	0.228828i	$0.926511\pi$
$614$		0			0
$615$	4.88331e10			0.341361
$616$		0			0
$617$			6.60503e10i			0.455758i	0.973689	+	0.227879i	$0.0731791\pi$
$617$			6.60503e10i			0.455758i	−0.973689	+	0.227879i	$0.926821\pi$
$618$		0			0
$619$	1.61893e11	−	1.61893e11i	1.10272	−	1.10272i	0.108643	−	0.994081i	$-0.465350\pi$
$619$	1.61893e11	−	1.61893e11i	1.10272	−	1.10272i	0.994081	−	0.108643i	$-0.0346504\pi$
$620$		0			0
$621$	6.72144e9	−	6.72144e9i	0.0451956	−	0.0451956i
$622$		0			0
$623$		−	1.49202e10i		−	0.0990430i
$624$		0			0
$625$	3.21159e10			0.210475
$626$		0			0
$627$	−6.68595e9	−	6.68595e9i	−0.0432606	−	0.0432606i
$628$		0			0
$629$	5.37804e10	+	5.37804e10i	0.343575	+	0.343575i
$630$		0			0
$631$	−2.05441e11			−1.29590			−0.647948	−	0.761685i	$-0.724372\pi$
$631$	−2.05441e11			−1.29590			−0.647948	+	0.761685i	$0.724372\pi$
$632$		0			0
$633$			1.36555e11i			0.850536i
$634$		0			0
$635$	−1.80683e10	+	1.80683e10i	−0.111128	+	0.111128i
$636$		0			0
$637$	−3.17280e11	+	3.17280e11i	−1.92702	+	1.92702i
$638$		0			0
$639$		−	6.31647e10i		−	0.378853i
$640$		0			0
$641$	5.29531e10			0.313660			0.156830	−	0.987626i	$-0.449873\pi$
$641$	5.29531e10			0.313660			0.156830	+	0.987626i	$0.449873\pi$
$642$		0			0
$643$	−3.27501e9	−	3.27501e9i	−0.0191588	−	0.0191588i	0.697462	−	0.716621i	$-0.254312\pi$
$643$	−3.27501e9	−	3.27501e9i	−0.0191588	−	0.0191588i	−0.716621	+	0.697462i	$0.754312\pi$
$644$		0			0
$645$	−1.92957e10	−	1.92957e10i	−0.111486	−	0.111486i
$646$		0			0
$647$	9.77431e10			0.557788			0.278894	−	0.960322i	$-0.410032\pi$
$647$	9.77431e10			0.557788			0.278894	+	0.960322i	$0.410032\pi$
$648$		0			0
$649$		−	5.20393e11i		−	2.93327i
$650$		0			0
$651$	−1.75512e10	+	1.75512e10i	−0.0977198	+	0.0977198i
$652$		0			0
$653$	4.84458e10	−	4.84458e10i	0.266443	−	0.266443i	−0.561222	−	0.827665i	$-0.689669\pi$
$653$	4.84458e10	−	4.84458e10i	0.266443	−	0.266443i	0.827665	+	0.561222i	$0.189669\pi$
$654$		0			0
$655$			1.21534e11i			0.660289i
$656$		0			0
$657$	8.26990e10			0.443852
$658$		0			0
$659$	−1.64966e11	−	1.64966e11i	−0.874689	−	0.874689i	0.118290	−	0.992979i	$-0.462259\pi$
$659$	−1.64966e11	−	1.64966e11i	−0.874689	−	0.874689i	−0.992979	+	0.118290i	$0.962259\pi$
$660$		0			0
$661$	−1.97855e11	−	1.97855e11i	−1.03643	−	1.03643i	−0.999311	−	0.0371236i	$-0.988180\pi$
$661$	−1.97855e11	−	1.97855e11i	−1.03643	−	1.03643i	−0.0371236	−	0.999311i	$-0.511820\pi$
$662$		0			0
$663$	−5.75567e10			−0.297880
$664$		0			0
$665$			1.46265e10i			0.0747916i
$666$		0			0
$667$	−2.89859e10	+	2.89859e10i	−0.146448	+	0.146448i
$668$		0			0
$669$	8.04663e10	−	8.04663e10i	0.401707	−	0.401707i
$670$		0			0
$671$			3.13376e11i			1.54588i
$672$		0			0
$673$	2.82133e11			1.37529			0.687643	−	0.726049i	$-0.258645\pi$
$673$	2.82133e11			1.37529			0.687643	+	0.726049i	$0.258645\pi$
$674$		0			0
$675$	−1.46779e10	−	1.46779e10i	−0.0707047	−	0.0707047i
$676$		0			0
$677$	−1.34053e11	−	1.34053e11i	−0.638150	−	0.638150i	0.311949	−	0.950099i	$-0.399018\pi$
$677$	−1.34053e11	−	1.34053e11i	−0.638150	−	0.638150i	−0.950099	+	0.311949i	$0.899018\pi$
$678$		0			0
$679$	2.11764e11			0.996260
$680$		0			0
$681$		−	1.15045e11i		−	0.534910i
$682$		0			0
$683$	2.73998e10	−	2.73998e10i	0.125911	−	0.125911i	−0.641343	−	0.767254i	$-0.721622\pi$
$683$	2.73998e10	−	2.73998e10i	0.125911	−	0.125911i	0.767254	+	0.641343i	$0.221622\pi$
$684$		0			0
$685$	8.28455e10	−	8.28455e10i	0.376276	−	0.376276i
$686$		0			0
$687$		−	3.97461e10i		−	0.178430i
$688$		0			0
$689$	−1.33352e11			−0.591729
$690$		0			0
$691$	−6.68395e9	−	6.68395e9i	−0.0293171	−	0.0293171i	0.692296	−	0.721613i	$-0.256599\pi$
$691$	−6.68395e9	−	6.68395e9i	−0.0293171	−	0.0293171i	−0.721613	+	0.692296i	$0.756599\pi$
$692$		0			0
$693$	1.73637e11	+	1.73637e11i	0.752851	+	0.752851i
$694$		0			0
$695$	1.41780e11			0.607681
$696$		0			0
$697$		−	8.58528e10i		−	0.363767i
$698$		0			0
$699$	−7.26626e10	+	7.26626e10i	−0.304370	+	0.304370i
$700$		0			0
$701$	−2.08502e11	+	2.08502e11i	−0.863451	+	0.863451i	−0.991737	−	0.128286i	$-0.959052\pi$
$701$	−2.08502e11	+	2.08502e11i	−0.863451	+	0.863451i	0.128286	+	0.991737i	$0.459052\pi$
$702$		0			0
$703$			1.66504e10i			0.0681716i
$704$		0			0
$705$	8.89640e10			0.360129
$706$		0			0
$707$	−7.21054e10	−	7.21054e10i	−0.288596	−	0.288596i
$708$		0			0
$709$	7.90632e10	+	7.90632e10i	0.312888	+	0.312888i	0.846028	−	0.533139i	$-0.178988\pi$
$709$	7.90632e10	+	7.90632e10i	0.312888	+	0.312888i	−0.533139	+	0.846028i	$0.678988\pi$
$710$		0			0
$711$	1.53867e11			0.602096
$712$		0			0
$713$			1.13920e10i			0.0440802i
$714$		0			0
$715$	2.74473e11	−	2.74473e11i	1.05021	−	1.05021i
$716$		0			0
$717$	1.77999e11	−	1.77999e11i	0.673505	−	0.673505i
$718$		0			0
$719$		−	1.25473e11i		−	0.469497i	−0.972056	−	0.234749i	$-0.924573\pi$
$719$		−	1.25473e11i		−	0.469497i	0.972056	−	0.234749i	$-0.0754267\pi$
$720$		0			0
$721$	2.33511e11			0.864104
$722$		0			0
$723$	1.93959e11	+	1.93959e11i	0.709835	+	0.709835i
$724$		0			0
$725$	6.32977e10	+	6.32977e10i	0.229106	+	0.229106i
$726$		0			0
$727$	−1.90558e11			−0.682167			−0.341083	−	0.940033i	$-0.610794\pi$
$727$	−1.90558e11			−0.682167			−0.341083	+	0.940033i	$0.610794\pi$
$728$		0			0
$729$		−	1.04604e10i		−	0.0370370i
$730$		0			0
$731$	−3.39236e10	+	3.39236e10i	−0.118804	+	0.118804i
$732$		0			0
$733$	8.87689e10	−	8.87689e10i	0.307500	−	0.307500i	−0.536439	−	0.843939i	$-0.680231\pi$
$733$	8.87689e10	−	8.87689e10i	0.307500	−	0.307500i	0.843939	+	0.536439i	$0.180231\pi$
$734$		0			0
$735$		−	2.63066e11i		−	0.901396i
$736$		0			0
$737$	−9.56980e11			−3.24364
$738$		0			0
$739$	1.39620e11	+	1.39620e11i	0.468135	+	0.468135i	0.901310	−	0.433175i	$-0.142607\pi$
$739$	1.39620e11	+	1.39620e11i	0.468135	+	0.468135i	−0.433175	+	0.901310i	$0.642607\pi$
$740$		0			0
$741$	−8.90977e9	−	8.90977e9i	−0.0295525	−	0.0295525i
$742$		0			0
$743$	−3.26857e11			−1.07251			−0.536257	−	0.844055i	$-0.680162\pi$
$743$	−3.26857e11			−1.07251			−0.536257	+	0.844055i	$0.680162\pi$
$744$		0			0
$745$			4.66616e10i			0.151473i
$746$		0			0
$747$	8.92918e10	−	8.92918e10i	0.286767	−	0.286767i
$748$		0			0
$749$	−5.99637e11	+	5.99637e11i	−1.90529	+	1.90529i
$750$		0			0
$751$		−	1.43379e11i		−	0.450739i	−0.974273	−	0.225369i	$-0.927641\pi$
$751$		−	1.43379e11i		−	0.450739i	0.974273	−	0.225369i	$-0.0723589\pi$
$752$		0			0
$753$	−2.97327e11			−0.924815
$754$		0			0
$755$	1.54652e11	+	1.54652e11i	0.475958	+	0.475958i
$756$		0			0
$757$	1.38716e11	+	1.38716e11i	0.422419	+	0.422419i	0.886036	−	0.463617i	$-0.153449\pi$
$757$	1.38716e11	+	1.38716e11i	0.422419	+	0.422419i	−0.463617	+	0.886036i	$0.653449\pi$
$758$		0			0
$759$	1.12703e11			0.339602
$760$		0			0
$761$		−	5.66134e11i		−	1.68803i	−0.536317	−	0.844017i	$-0.680185\pi$
$761$		−	5.66134e11i		−	1.68803i	0.536317	−	0.844017i	$-0.319815\pi$
$762$		0			0
$763$	8.38609e11	−	8.38609e11i	2.47435	−	2.47435i
$764$		0			0
$765$	2.38609e10	−	2.38609e10i	0.0696694	−	0.0696694i
$766$		0			0
$767$		−	6.93482e11i		−	2.00380i
$768$		0			0
$769$	4.31818e11			1.23480			0.617398	−	0.786651i	$-0.288187\pi$
$769$	4.31818e11			1.23480			0.617398	+	0.786651i	$0.288187\pi$
$770$		0			0
$771$	−3.87068e10	−	3.87068e10i	−0.109539	−	0.109539i
$772$		0			0
$773$	−2.02081e10	−	2.02081e10i	−0.0565987	−	0.0565987i	0.678241	−	0.734840i	$-0.262743\pi$
$773$	−2.02081e10	−	2.02081e10i	−0.0565987	−	0.0565987i	−0.734840	+	0.678241i	$0.762743\pi$
$774$		0			0
$775$	2.48773e10			0.0689597
$776$		0			0
$777$		−	4.32418e11i		−	1.18637i
$778$		0			0
$779$	1.32900e10	−	1.32900e10i	0.0360891	−	0.0360891i
$780$		0			0
$781$	5.29565e11	−	5.29565e11i	1.42336	−	1.42336i
$782$		0			0
$783$			4.51098e10i			0.120012i
$784$		0			0
$785$	9.42743e10			0.248265
$786$		0			0
$787$	−3.68011e11	−	3.68011e11i	−0.959317	−	0.959317i	0.0398868	−	0.999204i	$-0.487300\pi$
$787$	−3.68011e11	−	3.68011e11i	−0.959317	−	0.959317i	−0.999204	+	0.0398868i	$0.987300\pi$
$788$		0			0
$789$	2.70226e11	+	2.70226e11i	0.697298	+	0.697298i
$790$		0			0
$791$	−7.19640e11			−1.83827
$792$		0			0
$793$			4.17608e11i			1.05603i
$794$		0			0
$795$	5.52831e10	−	5.52831e10i	0.138396	−	0.138396i
$796$		0			0
$797$	2.71828e11	−	2.71828e11i	0.673692	−	0.673692i	−0.284873	−	0.958565i	$-0.591952\pi$
$797$	2.71828e11	−	2.71828e11i	0.673692	−	0.673692i	0.958565	+	0.284873i	$0.0919515\pi$
$798$		0			0
$799$		−	1.56406e11i		−	0.383767i
$800$		0			0
$801$	−7.53572e9			−0.0183061
$802$		0			0
$803$	6.93337e11	+	6.93337e11i	1.66756	+	1.66756i
$804$		0			0
$805$	−1.23277e11	−	1.23277e11i	−0.293562	−	0.293562i
$806$		0			0
$807$	9.08157e10			0.214125
$808$		0			0
$809$			2.86516e10i			0.0668889i	0.999441	+	0.0334444i	$0.0106477\pi$
$809$			2.86516e10i			0.0668889i	−0.999441	+	0.0334444i	$0.989352\pi$
$810$		0			0
$811$	1.44668e11	−	1.44668e11i	0.334417	−	0.334417i	−0.519844	−	0.854261i	$-0.674010\pi$
$811$	1.44668e11	−	1.44668e11i	0.334417	−	0.334417i	0.854261	+	0.519844i	$0.174010\pi$
$812$		0			0
$813$	1.86490e11	−	1.86490e11i	0.426867	−	0.426867i
$814$		0			0
$815$			3.61397e11i			0.819133i
$816$		0			0
$817$	−1.05027e10			−0.0235730
$818$		0			0
$819$	2.31390e11	+	2.31390e11i	0.514292	+	0.514292i
$820$		0			0
$821$	2.52880e10	+	2.52880e10i	0.0556597	+	0.0556597i	0.734389	−	0.678729i	$-0.237469\pi$
$821$	2.52880e10	+	2.52880e10i	0.0556597	+	0.0556597i	−0.678729	+	0.734389i	$0.737469\pi$
$822$		0			0
$823$	−2.41332e11			−0.526035			−0.263018	−	0.964791i	$-0.584718\pi$
$823$	−2.41332e11			−0.526035			−0.263018	+	0.964791i	$0.584718\pi$
$824$		0			0
$825$		−	2.46115e11i		−	0.531278i
$826$		0			0
$827$	9.83527e10	−	9.83527e10i	0.210264	−	0.210264i	−0.594116	−	0.804379i	$-0.702498\pi$
$827$	9.83527e10	−	9.83527e10i	0.210264	−	0.210264i	0.804379	+	0.594116i	$0.202498\pi$
$828$		0			0
$829$	−1.23040e11	+	1.23040e11i	−0.260512	+	0.260512i	−0.825262	−	0.564750i	$-0.808973\pi$
$829$	−1.23040e11	+	1.23040e11i	−0.260512	+	0.260512i	0.564750	+	0.825262i	$0.308973\pi$
$830$		0			0
$831$		−	1.51053e11i		−	0.316755i
$832$		0			0
$833$	−4.62493e11			−0.960562
$834$		0			0
$835$	−3.43383e11	−	3.43383e11i	−0.706371	−	0.706371i
$836$		0			0
$837$	8.86453e9	+	8.86453e9i	0.0180615	+	0.0180615i
$838$		0			0
$839$	1.70487e11			0.344068			0.172034	−	0.985091i	$-0.444966\pi$
$839$	1.70487e11			0.344068			0.172034	+	0.985091i	$0.444966\pi$
$840$		0			0
$841$			3.05712e11i			0.611124i
$842$		0			0
$843$	6.52406e10	−	6.52406e10i	0.129184	−	0.129184i
$844$		0			0
$845$	1.15889e11	−	1.15889e11i	0.227308	−	0.227308i
$846$		0			0
$847$			1.98330e12i			3.85349i
$848$		0			0
$849$	−2.95032e11			−0.567856
$850$		0			0
$851$	−1.40336e11	−	1.40336e11i	−0.267578	−	0.267578i
$852$		0			0
$853$	−2.44629e11	−	2.44629e11i	−0.462074	−	0.462074i	0.437261	−	0.899335i	$-0.355949\pi$
$853$	−2.44629e11	−	2.44629e11i	−0.462074	−	0.462074i	−0.899335	+	0.437261i	$0.855949\pi$
$854$		0			0
$855$	7.38735e9			0.0138237
$856$		0			0
$857$		−	4.87245e11i		−	0.903283i	−0.892199	−	0.451642i	$-0.850839\pi$
$857$		−	4.87245e11i		−	0.903283i	0.892199	−	0.451642i	$-0.149161\pi$
$858$		0			0
$859$	8.11679e10	−	8.11679e10i	0.149077	−	0.149077i	−0.628628	−	0.777706i	$-0.716383\pi$
$859$	8.11679e10	−	8.11679e10i	0.149077	−	0.149077i	0.777706	+	0.628628i	$0.216383\pi$
$860$		0			0
$861$	−3.45147e11	+	3.45147e11i	−0.628046	+	0.628046i
$862$		0			0
$863$		−	1.75798e11i		−	0.316935i	−0.987364	−	0.158467i	$-0.949345\pi$
$863$		−	1.75798e11i		−	0.316935i	0.987364	−	0.158467i	$-0.0506553\pi$
$864$		0			0
$865$	−2.52901e11			−0.451737
$866$		0			0
$867$	1.88726e11	+	1.88726e11i	0.334006	+	0.334006i
$868$		0			0
$869$	1.29000e12	+	1.29000e12i	2.26209	+	2.26209i
$870$		0			0
$871$	−1.27528e12			−2.21582
$872$		0			0
$873$		−	1.06955e11i		−	0.184138i
$874$		0			0
$875$	−7.87336e11	+	7.87336e11i	−1.34316	+	1.34316i
$876$		0			0
$877$	−9.37586e10	+	9.37586e10i	−0.158494	+	0.158494i	−0.781899	−	0.623405i	$-0.785749\pi$
$877$	−9.37586e10	+	9.37586e10i	−0.158494	+	0.158494i	0.623405	+	0.781899i	$0.285749\pi$
$878$		0			0
$879$		−	4.40389e10i		−	0.0737702i
$880$		0			0
$881$	8.48336e11			1.40820			0.704100	−	0.710101i	$-0.251351\pi$
$881$	8.48336e11			1.40820			0.704100	+	0.710101i	$0.251351\pi$
$882$		0			0
$883$	−2.34420e11	−	2.34420e11i	−0.385613	−	0.385613i	0.487507	−	0.873119i	$-0.337906\pi$
$883$	−2.34420e11	−	2.34420e11i	−0.385613	−	0.385613i	−0.873119	+	0.487507i	$0.837906\pi$
$884$		0			0
$885$	2.87493e11	+	2.87493e11i	0.468656	+	0.468656i
$886$		0			0
$887$	−7.65512e11			−1.23668			−0.618340	−	0.785911i	$-0.712195\pi$
$887$	−7.65512e11			−1.23668			−0.618340	+	0.785911i	$0.712195\pi$
$888$		0			0
$889$		−	2.55409e11i		−	0.408912i
$890$		0			0
$891$	8.76982e10	−	8.76982e10i	0.139149	−	0.139149i
$892$		0			0
$893$	2.42117e10	−	2.42117e10i	0.0380732	−	0.0380732i
$894$		0			0
$895$		−	2.22372e11i		−	0.346567i
$896$		0			0
$897$	1.50190e11			0.231991
$898$		0			0
$899$	−3.82279e10	−	3.82279e10i	−0.0585250	−	0.0585250i
$900$		0			0
$901$	−9.71924e10	−	9.71924e10i	−0.147480	−	0.147480i
$902$		0			0
$903$	2.72760e11			0.410233
$904$		0			0
$905$		−	2.85560e11i		−	0.425699i
$906$		0			0
$907$	−4.15441e11	+	4.15441e11i	−0.613875	+	0.613875i	−0.943953	−	0.330079i	$-0.892925\pi$
$907$	−4.15441e11	+	4.15441e11i	−0.613875	+	0.613875i	0.330079	+	0.943953i	$0.392925\pi$
$908$		0			0
$909$	−3.64181e10	+	3.64181e10i	−0.0533410	+	0.0533410i
$910$		0			0
$911$		−	2.81870e11i		−	0.409237i	−0.978842	−	0.204619i	$-0.934405\pi$
$911$		−	2.81870e11i		−	0.409237i	0.978842	−	0.204619i	$-0.0655954\pi$
$912$		0			0
$913$	1.49722e12			2.15478
$914$		0			0
$915$	−1.73125e11	−	1.73125e11i	−0.246988	−	0.246988i
$916$		0			0
$917$	−8.58993e11	−	8.58993e11i	−1.21482	−	1.21482i
$918$		0			0
$919$	1.14242e12			1.60164			0.800819	−	0.598907i	$-0.204398\pi$
$919$	1.14242e12			1.60164			0.800819	+	0.598907i	$0.204398\pi$
$920$		0			0
$921$			6.67975e10i			0.0928372i
$922$		0			0
$923$	7.05704e11	−	7.05704e11i	0.972335	−	0.972335i
$924$		0			0
$925$	−3.06457e11	+	3.06457e11i	−0.418603	+	0.418603i
$926$		0			0
$927$		−	1.17939e11i		−	0.159712i
$928$		0			0
$929$	−1.20297e12			−1.61507			−0.807534	−	0.589821i	$-0.799198\pi$
$929$	−1.20297e12			−1.61507			−0.807534	+	0.589821i	$0.799198\pi$
$930$		0			0
$931$	−7.15940e10	−	7.15940e10i	−0.0952966	−	0.0952966i
$932$		0			0
$933$	−3.97292e11	−	3.97292e11i	−0.524304	−	0.524304i
$934$		0			0
$935$	4.00094e11			0.523499
$936$		0			0
$937$		−	3.18711e11i		−	0.413465i	−0.978398	−	0.206732i	$-0.933717\pi$
$937$		−	3.18711e11i		−	0.413465i	0.978398	−	0.206732i	$-0.0662829\pi$
$938$		0			0
$939$	−2.99819e10	+	2.99819e10i	−0.0385653	+	0.0385653i
$940$		0			0
$941$	1.63380e11	−	1.63380e11i	0.208373	−	0.208373i	−0.595203	−	0.803576i	$-0.702928\pi$
$941$	1.63380e11	−	1.63380e11i	0.208373	−	0.208373i	0.803576	+	0.595203i	$0.202928\pi$
$942$		0			0
$943$			2.24026e11i			0.283304i
$944$		0			0
$945$	−1.91853e11			−0.240569
$946$		0			0
$947$	9.47600e10	+	9.47600e10i	0.117822	+	0.117822i	0.763559	−	0.645738i	$-0.223450\pi$
$947$	9.47600e10	+	9.47600e10i	0.117822	+	0.117822i	−0.645738	+	0.763559i	$0.723450\pi$
$948$		0			0
$949$	9.23950e11	+	9.23950e11i	1.13916	+	1.13916i
$950$		0			0
$951$	7.25266e10			0.0886696
$952$		0			0
$953$		−	6.71332e11i		−	0.813890i	−0.913453	−	0.406945i	$-0.866594\pi$
$953$		−	6.71332e11i		−	0.813890i	0.913453	−	0.406945i	$-0.133406\pi$
$954$		0			0
$955$	−1.44156e11	+	1.44156e11i	−0.173308	+	0.173308i
$956$		0			0
$957$	−3.78195e11	+	3.78195e11i	−0.450887	+	0.450887i
$958$		0			0
$959$			1.17109e12i			1.38457i
$960$		0			0
$961$	8.37867e11			0.982384
$962$		0			0
$963$	3.02857e11	+	3.02857e11i	0.352153	+	0.352153i
$964$		0			0
$965$	−6.49833e10	−	6.49833e10i	−0.0749364	−	0.0749364i
$966$		0			0
$967$	−9.54179e11			−1.09125			−0.545625	−	0.838030i	$-0.683708\pi$
$967$	−9.54179e11			−1.09125			−0.545625	+	0.838030i	$0.683708\pi$
$968$		0			0
$969$		−	1.29876e10i		−	0.0147311i
$970$		0			0
$971$	−7.04263e11	+	7.04263e11i	−0.792242	+	0.792242i	−0.981858	−	0.189616i	$-0.939276\pi$
$971$	−7.04263e11	+	7.04263e11i	−0.792242	+	0.792242i	0.189616	+	0.981858i	$0.439276\pi$
$972$		0			0
$973$	−1.00209e12	+	1.00209e12i	−1.11803	+	1.11803i
$974$		0			0
$975$		−	3.27975e11i		−	0.362930i
$976$		0			0
$977$	−1.19293e12			−1.30929			−0.654645	−	0.755937i	$-0.727182\pi$
$977$	−1.19293e12			−1.30929			−0.654645	+	0.755937i	$0.727182\pi$
$978$		0			0
$979$	−6.31785e10	−	6.31785e10i	−0.0687763	−	0.0687763i
$980$		0			0
$981$	−4.23554e11	−	4.23554e11i	−0.457333	−	0.457333i
$982$		0			0
$983$	4.11584e11			0.440803			0.220401	−	0.975409i	$-0.429263\pi$
$983$	4.11584e11			0.440803			0.220401	+	0.975409i	$0.429263\pi$
$984$		0			0
$985$			1.15151e12i			1.22328i
$986$		0			0
$987$	−6.28788e11	+	6.28788e11i	−0.662576	+	0.662576i
$988$		0			0
$989$	8.85210e10	−	8.85210e10i	0.0925255	−	0.0925255i
$990$		0			0
$991$		−	3.99488e11i		−	0.414199i	−0.978320	−	0.207099i	$-0.933598\pi$
$991$		−	3.99488e11i		−	0.414199i	0.978320	−	0.207099i	$-0.0664024\pi$
$992$		0			0
$993$	−1.04954e10			−0.0107944
$994$		0			0
$995$	−4.47768e11	−	4.47768e11i	−0.456836	−	0.456836i
$996$		0			0
$997$	−1.30861e12	−	1.30861e12i	−1.32443	−	1.32443i	−0.910147	−	0.414285i	$-0.864032\pi$
$997$	−1.30861e12	−	1.30861e12i	−1.32443	−	1.32443i	−0.414285	−	0.910147i	$-0.635968\pi$
$998$		0			0
$999$	−2.18400e11			−0.219276

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	192.9.l.a.79.6		64
4.3	odd	2		48.9.l.a.43.24	yes	64
16.3	odd	4	inner	192.9.l.a.175.6		64
16.13	even	4		48.9.l.a.19.24	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.9.l.a.19.24	✓	64	16.13	even	4
48.9.l.a.43.24	yes	64	4.3	odd	2
192.9.l.a.79.6		64	1.1	even	1	trivial
192.9.l.a.175.6		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)

\(f(q)\)	\(=\)	\(q+(-33.0681 - 33.0681i) q^{3} +(306.323 + 306.323i) q^{5} -4330.12 q^{7} +2187.00i q^{9} +(-18335.5 + 18335.5i) q^{11} +(-24434.1 + 24434.1i) q^{13} -20259.0i q^{15} -35617.2 q^{17} +(-5513.54 - 5513.54i) q^{19} +(143189. + 143189. i) q^{21} +92940.4 q^{23} -202957. i q^{25} +(72320.0 - 72320.0i) q^{27} +(-311877. + 311877. i) q^{29} +122574. i q^{31} +1.21264e6 q^{33} +(-1.32641e6 - 1.32641e6i) q^{35} +(-1.50996e6 - 1.50996e6i) q^{37} +1.61598e6 q^{39} +2.41043e6i q^{41} +(952450. - 952450. i) q^{43} +(-669928. + 669928. i) q^{45} +4.39132e6i q^{47} +1.29851e7 q^{49} +(1.17779e6 + 1.17779e6i) q^{51} +(2.72881e6 + 2.72881e6i) q^{53} -1.12332e7 q^{55} +364645. i q^{57} +(-1.41908e7 + 1.41908e7i) q^{59} +(8.54559e6 - 8.54559e6i) q^{61} -9.46997e6i q^{63} -1.49695e7 q^{65} +(2.60963e7 + 2.60963e7i) q^{67} +(-3.07336e6 - 3.07336e6i) q^{69} -2.88819e7 q^{71} -3.78139e7i q^{73} +(-6.71142e6 + 6.71142e6i) q^{75} +(7.93950e7 - 7.93950e7i) q^{77} -7.03551e7i q^{79} -4.78297e6 q^{81} +(-4.08284e7 - 4.08284e7i) q^{83} +(-1.09104e7 - 1.09104e7i) q^{85} +2.06263e7 q^{87} +3.44569e6i q^{89} +(1.05803e8 - 1.05803e8i) q^{91} +(4.05328e6 - 4.05328e6i) q^{93} -3.37785e6i q^{95} -4.89049e7 q^{97} +(-4.00998e7 - 4.00998e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 39552 q^{11} + 167552 q^{19} - 1691136 q^{23} - 2132352 q^{29} + 2415744 q^{35} - 4720512 q^{37} + 7244672 q^{43} + 52706752 q^{49} - 13862016 q^{51} - 5358720 q^{53} + 46326784 q^{55} - 44938752 q^{59}+ \cdots - 86500224 q^{99}+O(q^{100}) \) 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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