LMFDB - Embedded newform 192.9.l.a.79.12

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			79.12
Character	$\chi$	$=$	192.79
Dual form			192.9.l.a.175.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-33.0681 - 33.0681i) q^{3} +(508.668 + 508.668i) q^{5} +3253.34 q^{7} +2187.00i q^{9} +(-6777.24 + 6777.24i) q^{11} +(-26051.9 + 26051.9i) q^{13} -33641.4i q^{15} -155108. q^{17} +(98189.8 + 98189.8i) q^{19} +(-107582. - 107582. i) q^{21} -440378. q^{23} +126860. i q^{25} +(72320.0 - 72320.0i) q^{27} +(480071. - 480071. i) q^{29} +627305. i q^{31} +448221. q^{33} +(1.65487e6 + 1.65487e6i) q^{35} +(-1.48337e6 - 1.48337e6i) q^{37} +1.72298e6 q^{39} +42321.1i q^{41} +(1.53336e6 - 1.53336e6i) q^{43} +(-1.11246e6 + 1.11246e6i) q^{45} -8.84396e6i q^{47} +4.81940e6 q^{49} +(5.12911e6 + 5.12911e6i) q^{51} +(-6.41564e6 - 6.41564e6i) q^{53} -6.89473e6 q^{55} -6.49390e6i q^{57} +(9.15868e6 - 9.15868e6i) q^{59} +(-1.53578e7 + 1.53578e7i) q^{61} +7.11505e6i q^{63} -2.65035e7 q^{65} +(-9.64762e6 - 9.64762e6i) q^{67} +(1.45625e7 + 1.45625e7i) q^{69} +9.00590e6 q^{71} +1.17210e7i q^{73} +(4.19503e6 - 4.19503e6i) q^{75} +(-2.20486e7 + 2.20486e7i) q^{77} +3.38546e6i q^{79} -4.78297e6 q^{81} +(-1.31997e7 - 1.31997e7i) q^{83} +(-7.88982e7 - 7.88982e7i) q^{85} -3.17501e7 q^{87} +6.91877e7i q^{89} +(-8.47556e7 + 8.47556e7i) q^{91} +(2.07438e7 - 2.07438e7i) q^{93} +9.98919e7i q^{95} -1.04598e8 q^{97} +(-1.48218e7 - 1.48218e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	508.668	+	508.668i	0.813868	+	0.813868i	0.985211	−	0.171343i	$-0.0548107\pi$
$5$	508.668	+	508.668i	0.813868	+	0.813868i	−0.171343	+	0.985211i	$0.554811\pi$
$6$		0			0
$7$	3253.34			1.35499			0.677496	−	0.735526i	$-0.263065\pi$
$7$	3253.34			1.35499			0.677496	+	0.735526i	$0.263065\pi$
$8$		0			0
$9$			2187.00i			0.333333i
$10$		0			0
$11$	−6777.24	+	6777.24i	−0.462895	+	0.462895i	−0.899603	−	0.436708i	$-0.856144\pi$
$11$	−6777.24	+	6777.24i	−0.462895	+	0.462895i	0.436708	+	0.899603i	$0.356144\pi$
$12$		0			0
$13$	−26051.9	+	26051.9i	−0.912150	+	0.912150i	−0.996441	−	0.0842912i	$-0.973137\pi$
$13$	−26051.9	+	26051.9i	−0.912150	+	0.912150i	0.0842912	+	0.996441i	$0.473137\pi$
$14$		0			0
$15$		−	33641.4i		−	0.664521i
$16$		0			0
$17$	−155108.			−1.85711			−0.928554	−	0.371197i	$-0.878947\pi$
$17$	−155108.			−1.85711			−0.928554	+	0.371197i	$0.878947\pi$
$18$		0			0
$19$	98189.8	+	98189.8i	0.753445	+	0.753445i	0.975121	−	0.221675i	$-0.0711525\pi$
$19$	98189.8	+	98189.8i	0.753445	+	0.753445i	−0.221675	+	0.975121i	$0.571152\pi$
$20$		0			0
$21$	−107582.	−	107582.i	−0.553173	−	0.553173i
$22$		0			0
$23$	−440378.			−1.57367			−0.786835	−	0.617163i	$-0.788282\pi$
$23$	−440378.			−1.57367			−0.786835	+	0.617163i	$0.788282\pi$
$24$		0			0
$25$			126860.i			0.324763i
$26$		0			0
$27$	72320.0	−	72320.0i	0.136083	−	0.136083i
$28$		0			0
$29$	480071.	−	480071.i	0.678756	−	0.678756i	−0.280963	−	0.959719i	$-0.590654\pi$
$29$	480071.	−	480071.i	0.678756	−	0.678756i	0.959719	+	0.280963i	$0.0906537\pi$
$30$		0			0
$31$			627305.i			0.679253i	0.940560	+	0.339627i	$0.110301\pi$
$31$			627305.i			0.679253i	−0.940560	+	0.339627i	$0.889699\pi$
$32$		0			0
$33$	448221.			0.377952
$34$		0			0
$35$	1.65487e6	+	1.65487e6i	1.10279	+	1.10279i
$36$		0			0
$37$	−1.48337e6	−	1.48337e6i	−0.791484	−	0.791484i	0.190251	−	0.981735i	$-0.439070\pi$
$37$	−1.48337e6	−	1.48337e6i	−0.791484	−	0.791484i	−0.981735	+	0.190251i	$0.939070\pi$
$38$		0			0
$39$	1.72298e6			0.744767
$40$		0			0
$41$			42321.1i			0.0149769i	0.999972	+	0.00748845i	$0.00238367\pi$
$41$			42321.1i			0.0149769i	−0.999972	+	0.00748845i	$0.997616\pi$
$42$		0			0
$43$	1.53336e6	−	1.53336e6i	0.448508	−	0.448508i	−0.446350	−	0.894858i	$-0.647276\pi$
$43$	1.53336e6	−	1.53336e6i	0.448508	−	0.448508i	0.894858	+	0.446350i	$0.147276\pi$
$44$		0			0
$45$	−1.11246e6	+	1.11246e6i	−0.271289	+	0.271289i
$46$		0			0
$47$		−	8.84396e6i		−	1.81241i	−0.422844	−	0.906203i	$-0.638968\pi$
$47$		−	8.84396e6i		−	1.81241i	0.422844	−	0.906203i	$-0.361032\pi$
$48$		0			0
$49$	4.81940e6			0.836004
$50$		0			0
$51$	5.12911e6	+	5.12911e6i	0.758161	+	0.758161i
$52$		0			0
$53$	−6.41564e6	−	6.41564e6i	−0.813086	−	0.813086i	0.172010	−	0.985095i	$-0.444974\pi$
$53$	−6.41564e6	−	6.41564e6i	−0.813086	−	0.813086i	−0.985095	+	0.172010i	$0.944974\pi$
$54$		0			0
$55$	−6.89473e6			−0.753470
$56$		0			0
$57$		−	6.49390e6i		−	0.615186i
$58$		0			0
$59$	9.15868e6	−	9.15868e6i	0.755831	−	0.755831i	−0.219730	−	0.975561i	$-0.570518\pi$
$59$	9.15868e6	−	9.15868e6i	0.755831	−	0.755831i	0.975561	+	0.219730i	$0.0705176\pi$
$60$		0			0
$61$	−1.53578e7	+	1.53578e7i	−1.10920	+	1.10920i	−0.115946	+	0.993256i	$0.536990\pi$
$61$	−1.53578e7	+	1.53578e7i	−1.10920	+	1.10920i	−0.993256	+	0.115946i	$0.963010\pi$
$62$		0			0
$63$			7.11505e6i			0.451664i
$64$		0			0
$65$	−2.65035e7			−1.48474
$66$		0			0
$67$	−9.64762e6	−	9.64762e6i	−0.478764	−	0.478764i	0.425972	−	0.904736i	$-0.359932\pi$
$67$	−9.64762e6	−	9.64762e6i	−0.478764	−	0.478764i	−0.904736	+	0.425972i	$0.859932\pi$
$68$		0			0
$69$	1.45625e7	+	1.45625e7i	0.642448	+	0.642448i
$70$		0			0
$71$	9.00590e6			0.354400			0.177200	−	0.984175i	$-0.443296\pi$
$71$	9.00590e6			0.354400			0.177200	+	0.984175i	$0.443296\pi$
$72$		0			0
$73$			1.17210e7i			0.412736i	0.978474	+	0.206368i	$0.0661644\pi$
$73$			1.17210e7i			0.412736i	−0.978474	+	0.206368i	$0.933836\pi$
$74$		0			0
$75$	4.19503e6	−	4.19503e6i	0.132584	−	0.132584i
$76$		0			0
$77$	−2.20486e7	+	2.20486e7i	−0.627219	+	0.627219i
$78$		0			0
$79$			3.38546e6i			0.0869179i	0.999055	+	0.0434590i	$0.0138378\pi$
$79$			3.38546e6i			0.0869179i	−0.999055	+	0.0434590i	$0.986162\pi$
$80$		0			0
$81$	−4.78297e6			−0.111111
$82$		0			0
$83$	−1.31997e7	−	1.31997e7i	−0.278132	−	0.278132i	0.554231	−	0.832363i	$-0.313013\pi$
$83$	−1.31997e7	−	1.31997e7i	−0.278132	−	0.278132i	−0.832363	+	0.554231i	$0.813013\pi$
$84$		0			0
$85$	−7.88982e7	−	7.88982e7i	−1.51144	−	1.51144i
$86$		0			0
$87$	−3.17501e7			−0.554202
$88$		0			0
$89$			6.91877e7i			1.10273i	0.834264	+	0.551365i	$0.185893\pi$
$89$			6.91877e7i			1.10273i	−0.834264	+	0.551365i	$0.814107\pi$
$90$		0			0
$91$	−8.47556e7	+	8.47556e7i	−1.23596	+	1.23596i
$92$		0			0
$93$	2.07438e7	−	2.07438e7i	0.277304	−	0.277304i
$94$		0			0
$95$			9.98919e7i			1.22641i
$96$		0			0
$97$	−1.04598e8			−1.18151			−0.590755	−	0.806851i	$-0.701170\pi$
$97$	−1.04598e8			−1.18151			−0.590755	+	0.806851i	$0.701170\pi$
$98$		0			0
$99$	−1.48218e7	−	1.48218e7i	−0.154298	−	0.154298i
$100$		0			0
$101$	−754525.	−	754525.i	−0.00725084	−	0.00725084i	0.703472	−	0.710723i	$-0.251632\pi$
$101$	−754525.	−	754525.i	−0.00725084	−	0.00725084i	−0.710723	+	0.703472i	$0.751632\pi$
$102$		0			0
$103$	−5.75624e7			−0.511435			−0.255717	−	0.966752i	$-0.582312\pi$
$103$	−5.75624e7			−0.511435			−0.255717	+	0.966752i	$0.582312\pi$
$104$		0			0
$105$		−	1.09447e8i		−	0.900420i
$106$		0			0
$107$	1.43345e8	−	1.43345e8i	1.09357	−	1.09357i	0.0984243	−	0.995145i	$-0.468620\pi$
$107$	1.43345e8	−	1.43345e8i	1.09357	−	1.09357i	0.995145	−	0.0984243i	$-0.0313802\pi$
$108$		0			0
$109$	9.63597e7	−	9.63597e7i	0.682637	−	0.682637i	−0.277957	−	0.960594i	$-0.589657\pi$
$109$	9.63597e7	−	9.63597e7i	0.682637	−	0.682637i	0.960594	+	0.277957i	$0.0896572\pi$
$110$		0			0
$111$			9.81044e7i			0.646244i
$112$		0			0
$113$	−1.40687e8			−0.862861			−0.431431	−	0.902146i	$-0.641991\pi$
$113$	−1.40687e8			−0.862861			−0.431431	+	0.902146i	$0.641991\pi$
$114$		0			0
$115$	−2.24006e8	−	2.24006e8i	−1.28076	−	1.28076i
$116$		0			0
$117$	−5.69755e7	−	5.69755e7i	−0.304050	−	0.304050i
$118$		0			0
$119$	−5.04617e8			−2.51637
$120$		0			0
$121$			1.22497e8i			0.571457i
$122$		0			0
$123$	1.39948e6	−	1.39948e6i	0.00611429	−	0.00611429i
$124$		0			0
$125$	1.34169e8	−	1.34169e8i	0.549554	−	0.549554i
$126$		0			0
$127$		−	1.18604e8i		−	0.455916i	−0.973671	−	0.227958i	$-0.926795\pi$
$127$		−	1.18604e8i		−	0.455916i	0.973671	−	0.227958i	$-0.0732048\pi$
$128$		0			0
$129$	−1.01411e8			−0.366206
$130$		0			0
$131$	7.63451e7	+	7.63451e7i	0.259236	+	0.259236i	0.824743	−	0.565507i	$-0.191320\pi$
$131$	7.63451e7	+	7.63451e7i	0.259236	+	0.259236i	−0.565507	+	0.824743i	$0.691320\pi$
$132$		0			0
$133$	3.19444e8	+	3.19444e8i	1.02091	+	1.02091i
$134$		0			0
$135$	7.35736e7			0.221507
$136$		0			0
$137$		−	2.67355e7i		−	0.0758938i	−0.999280	−	0.0379469i	$-0.987918\pi$
$137$		−	2.67355e7i		−	0.0758938i	0.999280	−	0.0379469i	$-0.0120818\pi$
$138$		0			0
$139$	−1.90673e8	+	1.90673e8i	−0.510776	+	0.510776i	−0.914764	−	0.403988i	$-0.867624\pi$
$139$	−1.90673e8	+	1.90673e8i	−0.510776	+	0.510776i	0.403988	+	0.914764i	$0.367624\pi$
$140$		0			0
$141$	−2.92453e8	+	2.92453e8i	−0.739911	+	0.739911i
$142$		0			0
$143$		−	3.53120e8i		−	0.844459i
$144$		0			0
$145$	4.88393e8			1.10484
$146$		0			0
$147$	−1.59368e8	−	1.59368e8i	−0.341297	−	0.341297i
$148$		0			0
$149$	−2.87068e8	−	2.87068e8i	−0.582424	−	0.582424i	0.353145	−	0.935569i	$-0.385112\pi$
$149$	−2.87068e8	−	2.87068e8i	−0.582424	−	0.582424i	−0.935569	+	0.353145i	$0.885112\pi$
$150$		0			0
$151$	−2.73453e7			−0.0525986			−0.0262993	−	0.999654i	$-0.508372\pi$
$151$	−2.73453e7			−0.0525986			−0.0262993	+	0.999654i	$0.508372\pi$
$152$		0			0
$153$		−	3.39220e8i		−	0.619036i
$154$		0			0
$155$	−3.19090e8	+	3.19090e8i	−0.552823	+	0.552823i
$156$		0			0
$157$	−3.95872e8	+	3.95872e8i	−0.651562	+	0.651562i	−0.953369	−	0.301807i	$-0.902410\pi$
$157$	−3.95872e8	+	3.95872e8i	−0.651562	+	0.651562i	0.301807	+	0.953369i	$0.402410\pi$
$158$		0			0
$159$			4.24306e8i			0.663882i
$160$		0			0
$161$	−1.43270e9			−2.13231
$162$		0			0
$163$	−7.13925e8	−	7.13925e8i	−1.01135	−	1.01135i	−0.999935	−	0.0114165i	$-0.996366\pi$
$163$	−7.13925e8	−	7.13925e8i	−1.01135	−	1.01135i	−0.0114165	−	0.999935i	$-0.503634\pi$
$164$		0			0
$165$	2.27996e8	+	2.27996e8i	0.307603	+	0.307603i
$166$		0			0
$167$	−6.13122e8			−0.788281			−0.394140	−	0.919050i	$-0.628958\pi$
$167$	−6.13122e8			−0.788281			−0.394140	+	0.919050i	$0.628958\pi$
$168$		0			0
$169$		−	5.41674e8i		−	0.664035i
$170$		0			0
$171$	−2.14741e8	+	2.14741e8i	−0.251148	+	0.251148i
$172$		0			0
$173$	−9.63205e7	+	9.63205e7i	−0.107531	+	0.107531i	−0.758825	−	0.651294i	$-0.774226\pi$
$173$	−9.63205e7	+	9.63205e7i	−0.107531	+	0.107531i	0.651294	+	0.758825i	$0.274226\pi$
$174$		0			0
$175$			4.12719e8i			0.440051i
$176$		0			0
$177$	−6.05720e8			−0.617133
$178$		0			0
$179$	1.44620e7	+	1.44620e7i	0.0140870	+	0.0140870i	0.714115	−	0.700028i	$-0.246829\pi$
$179$	1.44620e7	+	1.44620e7i	0.0140870	+	0.0140870i	−0.700028	+	0.714115i	$0.746829\pi$
$180$		0			0
$181$	1.15314e9	+	1.15314e9i	1.07440	+	1.07440i	0.997000	+	0.0774047i	$0.0246634\pi$
$181$	1.15314e9	+	1.15314e9i	1.07440	+	1.07440i	0.0774047	+	0.997000i	$0.475337\pi$
$182$		0			0
$183$	1.01571e9			0.905659
$184$		0			0
$185$		−	1.50908e9i		−	1.28833i
$186$		0			0
$187$	1.05120e9	−	1.05120e9i	0.859645	−	0.859645i
$188$		0			0
$189$	2.35281e8	−	2.35281e8i	0.184391	−	0.184391i
$190$		0			0
$191$			1.91013e9i			1.43526i	0.696426	+	0.717629i	$0.254772\pi$
$191$			1.91013e9i			1.43526i	−0.696426	+	0.717629i	$0.745228\pi$
$192$		0			0
$193$	−9.12672e8			−0.657788			−0.328894	−	0.944367i	$-0.606676\pi$
$193$	−9.12672e8			−0.657788			−0.328894	+	0.944367i	$0.606676\pi$
$194$		0			0
$195$	8.76422e8	+	8.76422e8i	0.606142	+	0.606142i
$196$		0			0
$197$	−6.71398e8	−	6.71398e8i	−0.445775	−	0.445775i	0.448172	−	0.893947i	$-0.352075\pi$
$197$	−6.71398e8	−	6.71398e8i	−0.445775	−	0.445775i	−0.893947	+	0.448172i	$0.852075\pi$
$198$		0			0
$199$	−2.52411e7			−0.0160952			−0.00804758	−	0.999968i	$-0.502562\pi$
$199$	−2.52411e7			−0.0160952			−0.00804758	+	0.999968i	$0.502562\pi$
$200$		0			0
$201$			6.38057e8i			0.390909i
$202$		0			0
$203$	1.56183e9	−	1.56183e9i	0.919709	−	0.919709i
$204$		0			0
$205$	−2.15274e7	+	2.15274e7i	−0.0121892	+	0.0121892i
$206$		0			0
$207$		−	9.63106e8i		−	0.524557i
$208$		0			0
$209$	−1.33091e9			−0.697532
$210$		0			0
$211$	6.60490e8	+	6.60490e8i	0.333224	+	0.333224i	0.853810	−	0.520585i	$-0.174286\pi$
$211$	6.60490e8	+	6.60490e8i	0.333224	+	0.333224i	−0.520585	+	0.853810i	$0.674286\pi$
$212$		0			0
$213$	−2.97808e8	−	2.97808e8i	−0.144683	−	0.144683i
$214$		0			0
$215$	1.55994e9			0.730053
$216$		0			0
$217$			2.04083e9i			0.920383i
$218$		0			0
$219$	3.87590e8	−	3.87590e8i	0.168499	−	0.168499i
$220$		0			0
$221$	4.04085e9	−	4.04085e9i	1.69396	−	1.69396i
$222$		0			0
$223$			2.95254e9i			1.19392i	0.802269	+	0.596962i	$0.203626\pi$
$223$			2.95254e9i			1.19392i	−0.802269	+	0.596962i	$0.796374\pi$
$224$		0			0
$225$	−2.77444e8			−0.108254
$226$		0			0
$227$	−1.18789e9	−	1.18789e9i	−0.447378	−	0.447378i	0.447104	−	0.894482i	$-0.352455\pi$
$227$	−1.18789e9	−	1.18789e9i	−0.447378	−	0.447378i	−0.894482	+	0.447104i	$0.852455\pi$
$228$		0			0
$229$	3.55495e9	+	3.55495e9i	1.29268	+	1.29268i	0.933122	+	0.359559i	$0.117073\pi$
$229$	3.55495e9	+	3.55495e9i	1.29268	+	1.29268i	0.359559	+	0.933122i	$0.382927\pi$
$230$		0			0
$231$	1.45821e9			0.512122
$232$		0			0
$233$			2.60000e9i			0.882165i	0.897467	+	0.441082i	$0.145405\pi$
$233$			2.60000e9i			0.882165i	−0.897467	+	0.441082i	$0.854595\pi$
$234$		0			0
$235$	4.49864e9	−	4.49864e9i	1.47506	−	1.47506i
$236$		0			0
$237$	1.11951e8	−	1.11951e8i	0.0354841	−	0.0354841i
$238$		0			0
$239$			1.22584e9i			0.375701i	0.982198	+	0.187850i	$0.0601520\pi$
$239$			1.22584e9i			0.375701i	−0.982198	+	0.187850i	$0.939848\pi$
$240$		0			0
$241$	−5.38574e9			−1.59653			−0.798265	−	0.602307i	$-0.794248\pi$
$241$	−5.38574e9			−1.59653			−0.798265	+	0.602307i	$0.794248\pi$
$242$		0			0
$243$	1.58164e8	+	1.58164e8i	0.0453609	+	0.0453609i
$244$		0			0
$245$	2.45147e9	+	2.45147e9i	0.680397	+	0.680397i
$246$		0			0
$247$	−5.11606e9			−1.37451
$248$		0			0
$249$			8.72978e8i			0.227094i
$250$		0			0
$251$	2.62200e8	−	2.62200e8i	0.0660599	−	0.0660599i	−0.673305	−	0.739365i	$-0.735126\pi$
$251$	2.62200e8	−	2.62200e8i	0.0660599	−	0.0660599i	0.739365	+	0.673305i	$0.235126\pi$
$252$		0			0
$253$	2.98454e9	−	2.98454e9i	0.728444	−	0.728444i
$254$		0			0
$255$			5.21803e9i			1.23409i
$256$		0			0
$257$	2.42435e9			0.555728			0.277864	−	0.960620i	$-0.410373\pi$
$257$	2.42435e9			0.555728			0.277864	+	0.960620i	$0.410373\pi$
$258$		0			0
$259$	−4.82590e9	−	4.82590e9i	−1.07245	−	1.07245i
$260$		0			0
$261$	1.04992e9	+	1.04992e9i	0.226252	+	0.226252i
$262$		0			0
$263$	3.25783e9			0.680934			0.340467	−	0.940256i	$-0.389415\pi$
$263$	3.25783e9			0.680934			0.340467	+	0.940256i	$0.389415\pi$
$264$		0			0
$265$		−	6.52685e9i		−	1.32349i
$266$		0			0
$267$	2.28791e9	−	2.28791e9i	0.450188	−	0.450188i
$268$		0			0
$269$	−1.83290e9	+	1.83290e9i	−0.350050	+	0.350050i	−0.860128	−	0.510078i	$-0.829617\pi$
$269$	−1.83290e9	+	1.83290e9i	−0.350050	+	0.350050i	0.510078	+	0.860128i	$0.329617\pi$
$270$		0			0
$271$			4.10341e9i			0.760796i	0.924823	+	0.380398i	$0.124213\pi$
$271$			4.10341e9i			0.760796i	−0.924823	+	0.380398i	$0.875787\pi$
$272$		0			0
$273$	5.60542e9			1.00915
$274$		0			0
$275$	−8.59763e8	−	8.59763e8i	−0.150331	−	0.150331i
$276$		0			0
$277$	4.59144e9	+	4.59144e9i	0.779884	+	0.779884i	0.979811	−	0.199927i	$-0.0640705\pi$
$277$	4.59144e9	+	4.59144e9i	0.779884	+	0.779884i	−0.199927	+	0.979811i	$0.564070\pi$
$278$		0			0
$279$	−1.37192e9			−0.226418
$280$		0			0
$281$		−	6.54546e9i		−	1.04982i	−0.851157	−	0.524910i	$-0.824099\pi$
$281$		−	6.54546e9i		−	1.04982i	0.851157	−	0.524910i	$-0.175901\pi$
$282$		0			0
$283$	−1.57393e9	+	1.57393e9i	−0.245381	+	0.245381i	−0.819072	−	0.573691i	$-0.805511\pi$
$283$	−1.57393e9	+	1.57393e9i	−0.245381	+	0.245381i	0.573691	+	0.819072i	$0.305511\pi$
$284$		0			0
$285$	3.30324e9	−	3.30324e9i	0.500680	−	0.500680i
$286$		0			0
$287$			1.37685e8i			0.0202936i
$288$		0			0
$289$	1.70826e10			2.44885
$290$		0			0
$291$	3.45887e9	+	3.45887e9i	0.482350	+	0.482350i
$292$		0			0
$293$	1.77618e9	+	1.77618e9i	0.240999	+	0.240999i	0.817263	−	0.576264i	$-0.195490\pi$
$293$	1.77618e9	+	1.77618e9i	0.240999	+	0.240999i	−0.576264	+	0.817263i	$0.695490\pi$
$294$		0			0
$295$	9.31744e9			1.23029
$296$		0			0
$297$			9.80260e8i			0.125984i
$298$		0			0
$299$	1.14727e10	−	1.14727e10i	1.43542	−	1.43542i
$300$		0			0
$301$	4.98854e9	−	4.98854e9i	0.607725	−	0.607725i
$302$		0			0
$303$			4.99015e7i			0.00592029i
$304$		0			0
$305$	−1.56241e10			−1.80549
$306$		0			0
$307$	1.15353e10	+	1.15353e10i	1.29860	+	1.29860i	0.929319	+	0.369278i	$0.120395\pi$
$307$	1.15353e10	+	1.15353e10i	1.29860	+	1.29860i	0.369278	+	0.929319i	$0.379605\pi$
$308$		0			0
$309$	1.90348e9	+	1.90348e9i	0.208792	+	0.208792i
$310$		0			0
$311$	−1.19033e10			−1.27241			−0.636204	−	0.771521i	$-0.719496\pi$
$311$	−1.19033e10			−1.27241			−0.636204	+	0.771521i	$0.719496\pi$
$312$		0			0
$313$			1.72755e10i			1.79992i	0.435968	+	0.899962i	$0.356406\pi$
$313$			1.72755e10i			1.79992i	−0.435968	+	0.899962i	$0.643594\pi$
$314$		0			0
$315$	−3.61919e9	+	3.61919e9i	−0.367595	+	0.367595i
$316$		0			0
$317$	−4.29968e9	+	4.29968e9i	−0.425794	+	0.425794i	−0.887193	−	0.461399i	$-0.847348\pi$
$317$	−4.29968e9	+	4.29968e9i	−0.425794	+	0.425794i	0.461399	+	0.887193i	$0.347348\pi$
$318$		0			0
$319$			6.50712e9i			0.628385i
$320$		0			0
$321$	−9.48027e9			−0.892895
$322$		0			0
$323$	−1.52300e10	−	1.52300e10i	−1.39923	−	1.39923i
$324$		0			0
$325$	−3.30496e9	−	3.30496e9i	−0.296232	−	0.296232i
$326$		0			0
$327$	−6.37287e9			−0.557370
$328$		0			0
$329$		−	2.87724e10i		−	2.45580i
$330$		0			0
$331$	−4.94130e9	+	4.94130e9i	−0.411651	+	0.411651i	−0.882313	−	0.470663i	$-0.844015\pi$
$331$	−4.94130e9	+	4.94130e9i	−0.411651	+	0.411651i	0.470663	+	0.882313i	$0.344015\pi$
$332$		0			0
$333$	3.24413e9	−	3.24413e9i	0.263828	−	0.263828i
$334$		0			0
$335$		−	9.81487e9i		−	0.779301i
$336$		0			0
$337$	−9.65157e9			−0.748305			−0.374152	−	0.927367i	$-0.622066\pi$
$337$	−9.65157e9			−0.748305			−0.374152	+	0.927367i	$0.622066\pi$
$338$		0			0
$339$	4.65226e9	+	4.65226e9i	0.352262	+	0.352262i
$340$		0			0
$341$	−4.25140e9	−	4.25140e9i	−0.314423	−	0.314423i
$342$		0			0
$343$	−3.07571e9			−0.222213
$344$		0			0
$345$			1.48149e10i			1.04574i
$346$		0			0
$347$	−1.26738e10	+	1.26738e10i	−0.874154	+	0.874154i	−0.992922	−	0.118768i	$-0.962106\pi$
$347$	−1.26738e10	+	1.26738e10i	−0.874154	+	0.874154i	0.118768	+	0.992922i	$0.462106\pi$
$348$		0			0
$349$	−5.75442e9	+	5.75442e9i	−0.387882	+	0.387882i	−0.873931	−	0.486049i	$-0.838438\pi$
$349$	−5.75442e9	+	5.75442e9i	−0.387882	+	0.387882i	0.486049	+	0.873931i	$0.338438\pi$
$350$		0			0
$351$			3.76815e9i			0.248256i
$352$		0			0
$353$	−9.23615e9			−0.594829			−0.297415	−	0.954748i	$-0.596124\pi$
$353$	−9.23615e9			−0.594829			−0.297415	+	0.954748i	$0.596124\pi$
$354$		0			0
$355$	4.58101e9	+	4.58101e9i	0.288435	+	0.288435i
$356$		0			0
$357$	1.66867e10	+	1.66867e10i	1.02730	+	1.02730i
$358$		0			0
$359$	−1.95347e10			−1.17606			−0.588029	−	0.808840i	$-0.700096\pi$
$359$	−1.95347e10			−1.17606			−0.588029	+	0.808840i	$0.700096\pi$
$360$		0			0
$361$			2.29889e9i			0.135360i
$362$		0			0
$363$	4.05074e9	−	4.05074e9i	0.233296	−	0.233296i
$364$		0			0
$365$	−5.96208e9	+	5.96208e9i	−0.335913	+	0.335913i
$366$		0			0
$367$			2.69559e10i			1.48590i	0.669346	+	0.742951i	$0.266574\pi$
$367$			2.69559e10i			1.48590i	−0.669346	+	0.742951i	$0.733426\pi$
$368$		0			0
$369$	−9.25563e7			−0.00499230
$370$		0			0
$371$	−2.08722e10	−	2.08722e10i	−1.10172	−	1.10172i
$372$		0			0
$373$	−2.16781e10	−	2.16781e10i	−1.11992	−	1.11992i	−0.991753	−	0.128166i	$-0.959091\pi$
$373$	−2.16781e10	−	2.16781e10i	−1.11992	−	1.11992i	−0.128166	−	0.991753i	$-0.540909\pi$
$374$		0			0
$375$	−8.87340e9			−0.448709
$376$		0			0
$377$			2.50135e10i			1.23825i
$378$		0			0
$379$	2.36973e10	−	2.36973e10i	1.14853	−	1.14853i	0.161686	−	0.986842i	$-0.448307\pi$
$379$	2.36973e10	−	2.36973e10i	1.14853	−	1.14853i	0.986842	−	0.161686i	$-0.0516933\pi$
$380$		0			0
$381$	−3.92201e9	+	3.92201e9i	−0.186127	+	0.186127i
$382$		0			0
$383$		−	2.26683e10i		−	1.05348i	−0.850028	−	0.526738i	$-0.823415\pi$
$383$		−	2.26683e10i		−	1.05348i	0.850028	−	0.526738i	$-0.176585\pi$
$384$		0			0
$385$	−2.24309e10			−1.02095
$386$		0			0
$387$	3.35346e9	+	3.35346e9i	0.149503	+	0.149503i
$388$		0			0
$389$	−1.99758e9	−	1.99758e9i	−0.0872379	−	0.0872379i	0.662141	−	0.749379i	$-0.269648\pi$
$389$	−1.99758e9	−	1.99758e9i	−0.0872379	−	0.0872379i	−0.749379	+	0.662141i	$0.769648\pi$
$390$		0			0
$391$	6.83059e10			2.92248
$392$		0			0
$393$		−	5.04918e9i		−	0.211666i
$394$		0			0
$395$	−1.72207e9	+	1.72207e9i	−0.0707397	+	0.0707397i
$396$		0			0
$397$	−1.46535e10	+	1.46535e10i	−0.589900	+	0.589900i	−0.937604	−	0.347704i	$-0.886961\pi$
$397$	−1.46535e10	+	1.46535e10i	−0.589900	+	0.589900i	0.347704	+	0.937604i	$0.386961\pi$
$398$		0			0
$399$		−	2.11268e10i		−	0.833572i
$400$		0			0
$401$	−3.06109e10			−1.18385			−0.591927	−	0.805991i	$-0.701633\pi$
$401$	−3.06109e10			−1.18385			−0.591927	+	0.805991i	$0.701633\pi$
$402$		0			0
$403$	−1.63425e10	−	1.63425e10i	−0.619581	−	0.619581i
$404$		0			0
$405$	−2.43294e9	−	2.43294e9i	−0.0904298	−	0.0904298i
$406$		0			0
$407$	2.01063e10			0.732748
$408$		0			0
$409$		−	4.58595e10i		−	1.63884i	−0.573194	−	0.819420i	$-0.694296\pi$
$409$		−	4.58595e10i		−	1.63884i	0.573194	−	0.819420i	$-0.305704\pi$
$410$		0			0
$411$	−8.84093e8	+	8.84093e8i	−0.0309835	+	0.0309835i
$412$		0			0
$413$	2.97963e10	−	2.97963e10i	1.02415	−	1.02415i
$414$		0			0
$415$		−	1.34285e10i		−	0.452726i
$416$		0			0
$417$	1.26104e10			0.417047
$418$		0			0
$419$	8.22572e9	+	8.22572e9i	0.266881	+	0.266881i	0.827842	−	0.560961i	$-0.189568\pi$
$419$	8.22572e9	+	8.22572e9i	0.266881	+	0.266881i	−0.560961	+	0.827842i	$0.689568\pi$
$420$		0			0
$421$	1.63287e10	+	1.63287e10i	0.519784	+	0.519784i	0.917506	−	0.397722i	$-0.130199\pi$
$421$	1.63287e10	+	1.63287e10i	0.519784	+	0.519784i	−0.397722	+	0.917506i	$0.630199\pi$
$422$		0			0
$423$	1.93417e10			0.604135
$424$		0			0
$425$		−	1.96770e10i		−	0.603119i
$426$		0			0
$427$	−4.99642e10	+	4.99642e10i	−1.50296	+	1.50296i
$428$		0			0
$429$	−1.16770e10	+	1.16770e10i	−0.344749	+	0.344749i
$430$		0			0
$431$			1.42893e9i			0.0414098i	0.999786	+	0.0207049i	$0.00659105\pi$
$431$			1.42893e9i			0.0414098i	−0.999786	+	0.0207049i	$0.993409\pi$
$432$		0			0
$433$	2.04819e10			0.582664			0.291332	−	0.956622i	$-0.405902\pi$
$433$	2.04819e10			0.582664			0.291332	+	0.956622i	$0.405902\pi$
$434$		0			0
$435$	−1.61502e10	−	1.61502e10i	−0.451047	−	0.451047i
$436$		0			0
$437$	−4.32406e10	−	4.32406e10i	−1.18567	−	1.18567i
$438$		0			0
$439$	−5.67014e10			−1.52664			−0.763318	−	0.646023i	$-0.776431\pi$
$439$	−5.67014e10			−1.52664			−0.763318	+	0.646023i	$0.776431\pi$
$440$		0			0
$441$			1.05400e10i			0.278668i
$442$		0			0
$443$	−3.09800e10	+	3.09800e10i	−0.804389	+	0.804389i	−0.983778	−	0.179389i	$-0.942588\pi$
$443$	−3.09800e10	+	3.09800e10i	−0.804389	+	0.804389i	0.179389	+	0.983778i	$0.442588\pi$
$444$		0			0
$445$	−3.51936e10	+	3.51936e10i	−0.897477	+	0.897477i
$446$		0			0
$447$			1.89856e10i			0.475547i
$448$		0			0
$449$	3.06686e10			0.754587			0.377293	−	0.926094i	$-0.376855\pi$
$449$	3.06686e10			0.754587			0.377293	+	0.926094i	$0.376855\pi$
$450$		0			0
$451$	−2.86821e8	−	2.86821e8i	−0.00693273	−	0.00693273i
$452$		0			0
$453$	9.04256e8	+	9.04256e8i	0.0214733	+	0.0214733i
$454$		0			0
$455$	−8.62249e10			−2.01181
$456$		0			0
$457$			9.64047e9i			0.221021i	0.993875	+	0.110510i	$0.0352486\pi$
$457$			9.64047e9i			0.221021i	−0.993875	+	0.110510i	$0.964751\pi$
$458$		0			0
$459$	−1.12174e10	+	1.12174e10i	−0.252720	+	0.252720i
$460$		0			0
$461$	3.69566e9	−	3.69566e9i	0.0818255	−	0.0818255i	−0.665009	−	0.746835i	$-0.731572\pi$
$461$	3.69566e9	−	3.69566e9i	0.0818255	−	0.0818255i	0.746835	+	0.665009i	$0.231572\pi$
$462$		0			0
$463$		−	5.80756e9i		−	0.126377i	−0.998002	−	0.0631887i	$-0.979873\pi$
$463$		−	5.80756e9i		−	0.126377i	0.998002	−	0.0631887i	$-0.0201270\pi$
$464$		0			0
$465$	2.11034e10			0.451378
$466$		0			0
$467$	4.63321e10	+	4.63321e10i	0.974125	+	0.974125i	0.999674	−	0.0255490i	$-0.00813337\pi$
$467$	4.63321e10	+	4.63321e10i	0.974125	+	0.974125i	−0.0255490	+	0.999674i	$0.508133\pi$
$468$		0			0
$469$	−3.13870e10	−	3.13870e10i	−0.648721	−	0.648721i
$470$		0			0
$471$	2.61815e10			0.531999
$472$		0			0
$473$			2.07839e10i			0.415224i
$474$		0			0
$475$	−1.24564e10	+	1.24564e10i	−0.244691	+	0.244691i
$476$		0			0
$477$	1.40310e10	−	1.40310e10i	0.271029	−	0.271029i
$478$		0			0
$479$		−	9.25763e10i		−	1.75856i	−0.476302	−	0.879282i	$-0.658023\pi$
$479$		−	9.25763e10i		−	1.75856i	0.476302	−	0.879282i	$-0.341977\pi$
$480$		0			0
$481$	7.72892e10			1.44390
$482$		0			0
$483$	4.73766e10	+	4.73766e10i	0.870513	+	0.870513i
$484$		0			0
$485$	−5.32058e10	−	5.32058e10i	−0.961594	−	0.961594i
$486$		0			0
$487$	−4.07553e10			−0.724550			−0.362275	−	0.932071i	$-0.618000\pi$
$487$	−4.07553e10			−0.724550			−0.362275	+	0.932071i	$0.618000\pi$
$488$		0			0
$489$			4.72163e10i			0.825765i
$490$		0			0
$491$	2.12853e10	−	2.12853e10i	0.366229	−	0.366229i	−0.499871	−	0.866100i	$-0.666619\pi$
$491$	2.12853e10	−	2.12853e10i	0.366229	−	0.366229i	0.866100	+	0.499871i	$0.166619\pi$
$492$		0			0
$493$	−7.44626e10	+	7.44626e10i	−1.26052	+	1.26052i
$494$		0			0
$495$		−	1.50788e10i		−	0.251157i
$496$		0			0
$497$	2.92992e10			0.480209
$498$		0			0
$499$	6.20782e8	+	6.20782e8i	0.0100124	+	0.0100124i	0.712095	−	0.702083i	$-0.247746\pi$
$499$	6.20782e8	+	6.20782e8i	0.0100124	+	0.0100124i	−0.702083	+	0.712095i	$0.747746\pi$
$500$		0			0
$501$	2.02748e10	+	2.02748e10i	0.321814	+	0.321814i
$502$		0			0
$503$	−5.71269e10			−0.892419			−0.446210	−	0.894928i	$-0.647226\pi$
$503$	−5.71269e10			−0.892419			−0.446210	+	0.894928i	$0.647226\pi$
$504$		0			0
$505$		−	7.67605e8i		−	0.0118025i
$506$		0			0
$507$	−1.79121e10	+	1.79121e10i	−0.271091	+	0.271091i
$508$		0			0
$509$	7.08210e9	−	7.08210e9i	0.105509	−	0.105509i	−0.652381	−	0.757891i	$-0.726230\pi$
$509$	7.08210e9	−	7.08210e9i	0.105509	−	0.105509i	0.757891	+	0.652381i	$0.226230\pi$
$510$		0			0
$511$			3.81323e10i			0.559254i
$512$		0			0
$513$	1.42022e10			0.205062
$514$		0			0
$515$	−2.92801e10	−	2.92801e10i	−0.416240	−	0.416240i
$516$		0			0
$517$	5.99377e10	+	5.99377e10i	0.838953	+	0.838953i
$518$		0			0
$519$	6.37027e9			0.0877988
$520$		0			0
$521$			7.39836e10i			1.00412i	0.864833	+	0.502059i	$0.167424\pi$
$521$			7.39836e10i			1.00412i	−0.864833	+	0.502059i	$0.832576\pi$
$522$		0			0
$523$	4.85141e10	−	4.85141e10i	0.648427	−	0.648427i	−0.304186	−	0.952613i	$-0.598384\pi$
$523$	4.85141e10	−	4.85141e10i	0.648427	−	0.648427i	0.952613	+	0.304186i	$0.0983844\pi$
$524$		0			0
$525$	1.36479e10	−	1.36479e10i	0.179650	−	0.179650i
$526$		0			0
$527$		−	9.72997e10i		−	1.26145i
$528$		0			0
$529$	1.15621e11			1.47644
$530$		0			0
$531$	2.00300e10	+	2.00300e10i	0.251944	+	0.251944i
$532$		0			0
$533$	−1.10255e9	−	1.10255e9i	−0.0136612	−	0.0136612i
$534$		0			0
$535$	1.45829e11			1.78004
$536$		0			0
$537$		−	9.56464e8i		−	0.0115019i
$538$		0			0
$539$	−3.26622e10	+	3.26622e10i	−0.386982	+	0.386982i
$540$		0			0
$541$	7.14242e10	−	7.14242e10i	0.833789	−	0.833789i	−0.154244	−	0.988033i	$-0.549294\pi$
$541$	7.14242e10	−	7.14242e10i	0.833789	−	0.833789i	0.988033	+	0.154244i	$0.0492941\pi$
$542$		0			0
$543$		−	7.62643e10i		−	0.877248i
$544$		0			0
$545$	9.80301e10			1.11115
$546$		0			0
$547$	4.85657e10	+	4.85657e10i	0.542476	+	0.542476i	0.924254	−	0.381778i	$-0.124688\pi$
$547$	4.85657e10	+	4.85657e10i	0.542476	+	0.542476i	−0.381778	+	0.924254i	$0.624688\pi$
$548$		0			0
$549$	−3.35876e10	−	3.35876e10i	−0.369734	−	0.369734i
$550$		0			0
$551$	9.42761e10			1.02281
$552$		0			0
$553$			1.10140e10i			0.117773i
$554$		0			0
$555$	−4.99025e10	+	4.99025e10i	−0.525957	+	0.525957i
$556$		0			0
$557$	2.15340e10	−	2.15340e10i	0.223720	−	0.223720i	−0.586343	−	0.810063i	$-0.699433\pi$
$557$	2.15340e10	−	2.15340e10i	0.223720	−	0.223720i	0.810063	+	0.586343i	$0.199433\pi$
$558$		0			0
$559$			7.98940e10i			0.818214i
$560$		0			0
$561$	−6.95225e10			−0.701898
$562$		0			0
$563$	6.79499e10	+	6.79499e10i	0.676325	+	0.676325i	0.959167	−	0.282842i	$-0.0912772\pi$
$563$	6.79499e10	+	6.79499e10i	0.676325	+	0.676325i	−0.282842	+	0.959167i	$0.591277\pi$
$564$		0			0
$565$	−7.15631e10	−	7.15631e10i	−0.702255	−	0.702255i
$566$		0			0
$567$	−1.55606e10			−0.150555
$568$		0			0
$569$			5.33123e10i			0.508603i	0.967125	+	0.254301i	$0.0818455\pi$
$569$			5.33123e10i			0.508603i	−0.967125	+	0.254301i	$0.918155\pi$
$570$		0			0
$571$	4.45623e10	−	4.45623e10i	0.419202	−	0.419202i	−0.465727	−	0.884929i	$-0.654207\pi$
$571$	4.45623e10	−	4.45623e10i	0.419202	−	0.419202i	0.884929	+	0.465727i	$0.154207\pi$
$572$		0			0
$573$	6.31644e10	−	6.31644e10i	0.585941	−	0.585941i
$574$		0			0
$575$		−	5.58665e10i		−	0.511069i
$576$		0			0
$577$	1.92831e11			1.73969			0.869847	−	0.493322i	$-0.164218\pi$
$577$	1.92831e11			1.73969			0.869847	+	0.493322i	$0.164218\pi$
$578$		0			0
$579$	3.01804e10	+	3.01804e10i	0.268541	+	0.268541i
$580$		0			0
$581$	−4.29430e10	−	4.29430e10i	−0.376867	−	0.376867i
$582$		0			0
$583$	8.69606e10			0.752746
$584$		0			0
$585$		−	5.79632e10i		−	0.494913i
$586$		0			0
$587$	1.57969e10	−	1.57969e10i	0.133051	−	0.133051i	−0.637445	−	0.770496i	$-0.720009\pi$
$587$	1.57969e10	−	1.57969e10i	0.133051	−	0.133051i	0.770496	+	0.637445i	$0.220009\pi$
$588$		0			0
$589$	−6.15949e10	+	6.15949e10i	−0.511780	+	0.511780i
$590$		0			0
$591$			4.44038e10i			0.363973i
$592$		0			0
$593$	−1.82931e11			−1.47934			−0.739669	−	0.672970i	$-0.765018\pi$
$593$	−1.82931e11			−1.47934			−0.739669	+	0.672970i	$0.765018\pi$
$594$		0			0
$595$	−2.56682e11	−	2.56682e11i	−2.04799	−	2.04799i
$596$		0			0
$597$	8.34674e8	+	8.34674e8i	0.00657082	+	0.00657082i
$598$		0			0
$599$	1.91701e11			1.48908			0.744538	−	0.667580i	$-0.232670\pi$
$599$	1.91701e11			1.48908			0.744538	+	0.667580i	$0.232670\pi$
$600$		0			0
$601$		−	9.59781e10i		−	0.735655i	−0.929894	−	0.367828i	$-0.880102\pi$
$601$		−	9.59781e10i		−	0.735655i	0.929894	−	0.367828i	$-0.119898\pi$
$602$		0			0
$603$	2.10994e10	−	2.10994e10i	0.159588	−	0.159588i
$604$		0			0
$605$	−6.23102e10	+	6.23102e10i	−0.465091	+	0.465091i
$606$		0			0
$607$		−	8.08524e10i		−	0.595577i	−0.954632	−	0.297789i	$-0.903751\pi$
$607$		−	8.08524e10i		−	0.595577i	0.954632	−	0.297789i	$-0.0962491\pi$
$608$		0			0
$609$	−1.03294e11			−0.750939
$610$		0			0
$611$	2.30402e11	+	2.30402e11i	1.65319	+	1.65319i
$612$		0			0
$613$	8.34407e10	+	8.34407e10i	0.590930	+	0.590930i	0.937883	−	0.346953i	$-0.112784\pi$
$613$	8.34407e10	+	8.34407e10i	0.590930	+	0.590930i	−0.346953	+	0.937883i	$0.612784\pi$
$614$		0			0
$615$	1.42374e9			0.00995246
$616$		0			0
$617$		−	2.09834e11i		−	1.44789i	−0.689859	−	0.723943i	$-0.742328\pi$
$617$		−	2.09834e11i		−	1.44789i	0.689859	−	0.723943i	$-0.257672\pi$
$618$		0			0
$619$	−2.75000e10	+	2.75000e10i	−0.187314	+	0.187314i	−0.794534	−	0.607220i	$-0.792285\pi$
$619$	−2.75000e10	+	2.75000e10i	−0.187314	+	0.187314i	0.607220	+	0.794534i	$0.292285\pi$
$620$		0			0
$621$	−3.18481e10	+	3.18481e10i	−0.214149	+	0.214149i
$622$		0			0
$623$			2.25091e11i			1.49419i
$624$		0			0
$625$	1.86049e11			1.21929
$626$		0			0
$627$	4.40107e10	+	4.40107e10i	0.284766	+	0.284766i
$628$		0			0
$629$	2.30082e11	+	2.30082e11i	1.46987	+	1.46987i
$630$		0			0
$631$	1.92278e11			1.21286			0.606432	−	0.795135i	$-0.292600\pi$
$631$	1.92278e11			1.21286			0.606432	+	0.795135i	$0.292600\pi$
$632$		0			0
$633$		−	4.36823e10i		−	0.272076i
$634$		0			0
$635$	6.03300e10	−	6.03300e10i	0.371055	−	0.371055i
$636$		0			0
$637$	−1.25555e11	+	1.25555e11i	−0.762561	+	0.762561i
$638$		0			0
$639$			1.96959e10i			0.118133i
$640$		0			0
$641$	−2.38418e11			−1.41223			−0.706117	−	0.708095i	$-0.749555\pi$
$641$	−2.38418e11			−1.41223			−0.706117	+	0.708095i	$0.749555\pi$
$642$		0			0
$643$	4.68691e10	+	4.68691e10i	0.274184	+	0.274184i	0.830782	−	0.556598i	$-0.187894\pi$
$643$	4.68691e10	+	4.68691e10i	0.274184	+	0.274184i	−0.556598	+	0.830782i	$0.687894\pi$
$644$		0			0
$645$	−5.15843e10	−	5.15843e10i	−0.298043	−	0.298043i
$646$		0			0
$647$	9.62172e10			0.549080			0.274540	−	0.961576i	$-0.411474\pi$
$647$	9.62172e10			0.549080			0.274540	+	0.961576i	$0.411474\pi$
$648$		0			0
$649$			1.24141e11i			0.699740i
$650$		0			0
$651$	6.74865e10	−	6.74865e10i	0.375745	−	0.375745i
$652$		0			0
$653$	1.55526e11	−	1.55526e11i	0.855360	−	0.855360i	−0.135427	−	0.990787i	$-0.543241\pi$
$653$	1.55526e11	−	1.55526e11i	0.855360	−	0.855360i	0.990787	+	0.135427i	$0.0432407\pi$
$654$		0			0
$655$			7.76685e10i			0.421968i
$656$		0			0
$657$	−2.56338e10			−0.137579
$658$		0			0
$659$	−7.24722e10	−	7.24722e10i	−0.384264	−	0.384264i	0.488372	−	0.872636i	$-0.337591\pi$
$659$	−7.24722e10	−	7.24722e10i	−0.384264	−	0.384264i	−0.872636	+	0.488372i	$0.837591\pi$
$660$		0			0
$661$	−1.45594e11	−	1.45594e11i	−0.762673	−	0.762673i	0.214132	−	0.976805i	$-0.431308\pi$
$661$	−1.45594e11	−	1.45594e11i	−0.762673	−	0.762673i	−0.976805	+	0.214132i	$0.931308\pi$
$662$		0			0
$663$	−2.67246e11			−1.38311
$664$		0			0
$665$			3.24982e11i			1.66178i
$666$		0			0
$667$	−2.11413e11	+	2.11413e11i	−1.06814	+	1.06814i
$668$		0			0
$669$	9.76350e10	−	9.76350e10i	0.487418	−	0.487418i
$670$		0			0
$671$		−	2.08167e11i		−	1.02689i
$672$		0			0
$673$	−5.95017e10			−0.290048			−0.145024	−	0.989428i	$-0.546326\pi$
$673$	−5.95017e10			−0.290048			−0.145024	+	0.989428i	$0.546326\pi$
$674$		0			0
$675$	9.17454e9	+	9.17454e9i	0.0441946	+	0.0441946i
$676$		0			0
$677$	6.38020e10	+	6.38020e10i	0.303724	+	0.303724i	0.842469	−	0.538745i	$-0.181101\pi$
$677$	6.38020e10	+	6.38020e10i	0.303724	+	0.303724i	−0.538745	+	0.842469i	$0.681101\pi$
$678$		0			0
$679$	−3.40293e11			−1.60094
$680$		0			0
$681$			7.85629e10i			0.365283i
$682$		0			0
$683$	−9.14398e10	+	9.14398e10i	−0.420196	+	0.420196i	−0.885271	−	0.465075i	$-0.846027\pi$
$683$	−9.14398e10	+	9.14398e10i	−0.420196	+	0.420196i	0.465075	+	0.885271i	$0.346027\pi$
$684$		0			0
$685$	1.35995e10	−	1.35995e10i	0.0617675	−	0.0617675i
$686$		0			0
$687$		−	2.35111e11i		−	1.05547i
$688$		0			0
$689$	3.34279e11			1.48331
$690$		0			0
$691$	−2.29971e11	−	2.29971e11i	−1.00870	−	1.00870i	−0.999962	−	0.00873733i	$-0.997219\pi$
$691$	−2.29971e11	−	2.29971e11i	−1.00870	−	1.00870i	−0.00873733	−	0.999962i	$-0.502781\pi$
$692$		0			0
$693$	−4.82204e10	−	4.82204e10i	−0.209073	−	0.209073i
$694$		0			0
$695$	−1.93979e11			−0.831408
$696$		0			0
$697$		−	6.56433e9i		−	0.0278137i
$698$		0			0
$699$	8.59771e10	−	8.59771e10i	0.360142	−	0.360142i
$700$		0			0
$701$	−2.53372e11	+	2.53372e11i	−1.04927	+	1.04927i	−0.0505476	+	0.998722i	$0.516097\pi$
$701$	−2.53372e11	+	2.53372e11i	−1.04927	+	1.04927i	−0.998722	+	0.0505476i	$0.983903\pi$
$702$		0			0
$703$		−	2.91303e11i		−	1.19268i
$704$		0			0
$705$	−2.97523e11			−1.20438
$706$		0			0
$707$	−2.45473e9	−	2.45473e9i	−0.00982483	−	0.00982483i
$708$		0			0
$709$	−1.66916e11	−	1.66916e11i	−0.660561	−	0.660561i	0.294951	−	0.955512i	$-0.404697\pi$
$709$	−1.66916e11	−	1.66916e11i	−0.660561	−	0.660561i	−0.955512	+	0.294951i	$0.904697\pi$
$710$		0			0
$711$	−7.40400e9			−0.0289726
$712$		0			0
$713$		−	2.76251e11i		−	1.06892i
$714$		0			0
$715$	1.79621e11	−	1.79621e11i	0.687278	−	0.687278i
$716$		0			0
$717$	4.05362e10	−	4.05362e10i	0.153379	−	0.153379i
$718$		0			0
$719$			4.08434e11i			1.52829i	0.645042	+	0.764147i	$0.276840\pi$
$719$			4.08434e11i			1.52829i	−0.645042	+	0.764147i	$0.723160\pi$
$720$		0			0
$721$	−1.87270e11			−0.692990
$722$		0			0
$723$	1.78096e11	+	1.78096e11i	0.651780	+	0.651780i
$724$		0			0
$725$	6.09020e10	+	6.09020e10i	0.220434	+	0.220434i
$726$		0			0
$727$	−1.75647e11			−0.628785			−0.314392	−	0.949293i	$-0.601801\pi$
$727$	−1.75647e11			−0.628785			−0.314392	+	0.949293i	$0.601801\pi$
$728$		0			0
$729$		−	1.04604e10i		−	0.0370370i
$730$		0			0
$731$	−2.37836e11	+	2.37836e11i	−0.832929	+	0.832929i
$732$		0			0
$733$	−2.15517e11	+	2.15517e11i	−0.746563	+	0.746563i	−0.973832	−	0.227269i	$-0.927020\pi$
$733$	−2.15517e11	+	2.15517e11i	−0.746563	+	0.746563i	0.227269	+	0.973832i	$0.427020\pi$
$734$		0			0
$735$		−	1.62131e11i		−	0.555542i
$736$		0			0
$737$	1.30769e11			0.443234
$738$		0			0
$739$	−2.36391e11	−	2.36391e11i	−0.792598	−	0.792598i	0.189318	−	0.981916i	$-0.439372\pi$
$739$	−2.36391e11	−	2.36391e11i	−0.792598	−	0.792598i	−0.981916	+	0.189318i	$0.939372\pi$
$740$		0			0
$741$	1.69179e11	+	1.69179e11i	0.561141	+	0.561141i
$742$		0			0
$743$	−8.00989e10			−0.262828			−0.131414	−	0.991328i	$-0.541952\pi$
$743$	−8.00989e10			−0.262828			−0.131414	+	0.991328i	$0.541952\pi$
$744$		0			0
$745$		−	2.92044e11i		−	0.948033i
$746$		0			0
$747$	2.88677e10	−	2.88677e10i	0.0927108	−	0.0927108i
$748$		0			0
$749$	4.66348e11	−	4.66348e11i	1.48178	−	1.48178i
$750$		0			0
$751$			4.40769e11i			1.38564i	0.721110	+	0.692821i	$0.243632\pi$
$751$			4.40769e11i			1.38564i	−0.721110	+	0.692821i	$0.756368\pi$
$752$		0			0
$753$	−1.73409e10			−0.0539377
$754$		0			0
$755$	−1.39096e10	−	1.39096e10i	−0.0428083	−	0.0428083i
$756$		0			0
$757$	3.82170e11	+	3.82170e11i	1.16379	+	1.16379i	0.983640	+	0.180147i	$0.0576575\pi$
$757$	3.82170e11	+	3.82170e11i	1.16379	+	1.16379i	0.180147	+	0.983640i	$0.442343\pi$
$758$		0			0
$759$	−1.97387e11			−0.594772
$760$		0			0
$761$		−	4.89963e10i		−	0.146092i	−0.997329	−	0.0730458i	$-0.976728\pi$
$761$		−	4.89963e10i		−	0.146092i	0.997329	−	0.0730458i	$-0.0232719\pi$
$762$		0			0
$763$	3.13491e11	−	3.13491e11i	0.924967	−	0.924967i
$764$		0			0
$765$	1.72550e11	−	1.72550e11i	0.503814	−	0.503814i
$766$		0			0
$767$			4.77202e11i			1.37886i
$768$		0			0
$769$	−4.61794e11			−1.32051			−0.660257	−	0.751040i	$-0.729553\pi$
$769$	−4.61794e11			−1.32051			−0.660257	+	0.751040i	$0.729553\pi$
$770$		0			0
$771$	−8.01686e10	−	8.01686e10i	−0.226875	−	0.226875i
$772$		0			0
$773$	1.57922e11	+	1.57922e11i	0.442307	+	0.442307i	0.892787	−	0.450480i	$-0.148747\pi$
$773$	1.57922e11	+	1.57922e11i	0.442307	+	0.442307i	−0.450480	+	0.892787i	$0.648747\pi$
$774$		0			0
$775$	−7.95801e10			−0.220596
$776$		0			0
$777$			3.19167e11i			0.875656i
$778$		0			0
$779$	−4.15550e9	+	4.15550e9i	−0.0112843	+	0.0112843i
$780$		0			0
$781$	−6.10352e10	+	6.10352e10i	−0.164050	+	0.164050i
$782$		0			0
$783$		−	6.94375e10i		−	0.184734i
$784$		0			0
$785$	−4.02734e11			−1.06057
$786$		0			0
$787$	−3.89880e11	−	3.89880e11i	−1.01632	−	1.01632i	−0.999865	−	0.0164595i	$-0.994761\pi$
$787$	−3.89880e11	−	3.89880e11i	−1.01632	−	1.01632i	−0.0164595	−	0.999865i	$-0.505239\pi$
$788$		0			0
$789$	−1.07730e11	−	1.07730e11i	−0.277990	−	0.277990i
$790$		0			0
$791$	−4.57703e11			−1.16917
$792$		0			0
$793$		−	8.00201e11i		−	2.02352i
$794$		0			0
$795$	−2.15831e11	+	2.15831e11i	−0.540312	+	0.540312i
$796$		0			0
$797$	−1.28611e11	+	1.28611e11i	−0.318745	+	0.318745i	−0.848285	−	0.529540i	$-0.822365\pi$
$797$	−1.28611e11	+	1.28611e11i	−0.318745	+	0.318745i	0.529540	+	0.848285i	$0.322365\pi$
$798$		0			0
$799$			1.37176e12i			3.36583i
$800$		0			0
$801$	−1.51314e11			−0.367577
$802$		0			0
$803$	−7.94359e10	−	7.94359e10i	−0.191053	−	0.191053i
$804$		0			0
$805$	−7.28766e11	−	7.28766e11i	−1.73542	−	1.73542i
$806$		0			0
$807$	1.21221e11			0.285815
$808$		0			0
$809$			3.20778e11i			0.748877i	0.927252	+	0.374439i	$0.122165\pi$
$809$			3.20778e11i			0.748877i	−0.927252	+	0.374439i	$0.877835\pi$
$810$		0			0
$811$	1.06682e11	−	1.06682e11i	0.246608	−	0.246608i	−0.572969	−	0.819577i	$-0.694208\pi$
$811$	1.06682e11	−	1.06682e11i	0.246608	−	0.246608i	0.819577	+	0.572969i	$0.194208\pi$
$812$		0			0
$813$	1.35692e11	−	1.35692e11i	0.310594	−	0.310594i
$814$		0			0
$815$		−	7.26301e11i		−	1.64621i
$816$		0			0
$817$	3.01121e11			0.675853
$818$		0			0
$819$	−1.85361e11	−	1.85361e11i	−0.411985	−	0.411985i
$820$		0			0
$821$	4.40491e11	+	4.40491e11i	0.969537	+	0.969537i	0.999550	−	0.0300127i	$-0.00955477\pi$
$821$	4.40491e11	+	4.40491e11i	0.969537	+	0.969537i	−0.0300127	+	0.999550i	$0.509555\pi$
$822$		0			0
$823$	3.96401e11			0.864042			0.432021	−	0.901864i	$-0.357801\pi$
$823$	3.96401e11			0.864042			0.432021	+	0.901864i	$0.357801\pi$
$824$		0			0
$825$			5.68615e10i			0.122745i
$826$		0			0
$827$	4.18792e11	−	4.18792e11i	0.895316	−	0.895316i	−0.0997016	−	0.995017i	$-0.531789\pi$
$827$	4.18792e11	−	4.18792e11i	0.895316	−	0.895316i	0.995017	+	0.0997016i	$0.0317888\pi$
$828$		0			0
$829$	−3.69338e11	+	3.69338e11i	−0.781999	+	0.781999i	−0.980168	−	0.198169i	$-0.936501\pi$
$829$	−3.69338e11	+	3.69338e11i	−0.781999	+	0.781999i	0.198169	+	0.980168i	$0.436501\pi$
$830$		0			0
$831$		−	3.03661e11i		−	0.636773i
$832$		0			0
$833$	−7.47525e11			−1.55255
$834$		0			0
$835$	−3.11875e11	−	3.11875e11i	−0.641557	−	0.641557i
$836$		0			0
$837$	4.53666e10	+	4.53666e10i	0.0924347	+	0.0924347i
$838$		0			0
$839$	5.35390e11			1.08049			0.540247	−	0.841506i	$-0.318331\pi$
$839$	5.35390e11			1.08049			0.540247	+	0.841506i	$0.318331\pi$
$840$		0			0
$841$			3.93097e10i			0.0785807i
$842$		0			0
$843$	−2.16446e11	+	2.16446e11i	−0.428588	+	0.428588i
$844$		0			0
$845$	2.75532e11	−	2.75532e11i	0.540437	−	0.540437i
$846$		0			0
$847$			3.98524e11i			0.774320i
$848$		0			0
$849$	1.04094e11			0.200353
$850$		0			0
$851$	6.53242e11	+	6.53242e11i	1.24554	+	1.24554i
$852$		0			0
$853$	−1.25669e11	−	1.25669e11i	−0.237373	−	0.237373i	0.578388	−	0.815762i	$-0.303682\pi$
$853$	−1.25669e11	−	1.25669e11i	−0.237373	−	0.237373i	−0.815762	+	0.578388i	$0.803682\pi$
$854$		0			0
$855$	−2.18464e11			−0.408803
$856$		0			0
$857$			9.60332e11i			1.78032i	0.455648	+	0.890160i	$0.349407\pi$
$857$			9.60332e11i			1.78032i	−0.455648	+	0.890160i	$0.650593\pi$
$858$		0			0
$859$	3.78436e11	−	3.78436e11i	0.695056	−	0.695056i	−0.268284	−	0.963340i	$-0.586457\pi$
$859$	3.78436e11	−	3.78436e11i	0.695056	−	0.695056i	0.963340	+	0.268284i	$0.0864565\pi$
$860$		0			0
$861$	4.55298e9	−	4.55298e9i	0.00828482	−	0.00828482i
$862$		0			0
$863$			2.22812e11i			0.401693i	0.979623	+	0.200847i	$0.0643693\pi$
$863$			2.22812e11i			0.401693i	−0.979623	+	0.200847i	$0.935631\pi$
$864$		0			0
$865$	−9.79902e10			−0.175032
$866$		0			0
$867$	−5.64889e11	−	5.64889e11i	−0.999739	−	0.999739i
$868$		0			0
$869$	−2.29441e10	−	2.29441e10i	−0.0402339	−	0.0402339i
$870$		0			0
$871$	5.02678e11			0.873408
$872$		0			0
$873$		−	2.28756e11i		−	0.393837i
$874$		0			0
$875$	4.36495e11	−	4.36495e11i	0.744642	−	0.744642i
$876$		0			0
$877$	2.02917e10	−	2.02917e10i	0.0343021	−	0.0343021i	−0.689748	−	0.724050i	$-0.742279\pi$
$877$	2.02917e10	−	2.02917e10i	0.0343021	−	0.0343021i	0.724050	+	0.689748i	$0.242279\pi$
$878$		0			0
$879$		−	1.17470e11i		−	0.196775i
$880$		0			0
$881$	−5.75202e11			−0.954809			−0.477405	−	0.878684i	$-0.658422\pi$
$881$	−5.75202e11			−0.954809			−0.477405	+	0.878684i	$0.658422\pi$
$882$		0			0
$883$	9.76084e10	+	9.76084e10i	0.160563	+	0.160563i	0.782816	−	0.622253i	$-0.213783\pi$
$883$	9.76084e10	+	9.76084e10i	0.160563	+	0.160563i	−0.622253	+	0.782816i	$0.713783\pi$
$884$		0			0
$885$	−3.08110e11	−	3.08110e11i	−0.502265	−	0.502265i
$886$		0			0
$887$	−8.61421e11			−1.39162			−0.695811	−	0.718225i	$-0.744955\pi$
$887$	−8.61421e11			−1.39162			−0.695811	+	0.718225i	$0.744955\pi$
$888$		0			0
$889$		−	3.85859e11i		−	0.617762i
$890$		0			0
$891$	3.24153e10	−	3.24153e10i	0.0514327	−	0.0514327i
$892$		0			0
$893$	8.68386e11	−	8.68386e11i	1.36555	−	1.36555i
$894$		0			0
$895$			1.47127e10i			0.0229298i
$896$		0			0
$897$	−7.58760e11			−1.17202
$898$		0			0
$899$	3.01151e11	+	3.01151e11i	0.461047	+	0.461047i
$900$		0			0
$901$	9.95113e11	+	9.95113e11i	1.50999	+	1.50999i
$902$		0			0
$903$	−3.29923e11			−0.496206
$904$		0			0
$905$			1.17313e12i			1.74885i
$906$		0			0
$907$	7.63561e11	−	7.63561e11i	1.12827	−	1.12827i	0.137817	−	0.990458i	$-0.455991\pi$
$907$	7.63561e11	−	7.63561e11i	1.12827	−	1.12827i	0.990458	−	0.137817i	$-0.0440086\pi$
$908$		0			0
$909$	1.65015e9	−	1.65015e9i	0.00241695	−	0.00241695i
$910$		0			0
$911$			1.00379e11i			0.145736i	0.997342	+	0.0728682i	$0.0232153\pi$
$911$			1.00379e11i			0.145736i	−0.997342	+	0.0728682i	$0.976785\pi$
$912$		0			0
$913$	1.78915e11			0.257492
$914$		0			0
$915$	5.16658e11	+	5.16658e11i	0.737087	+	0.737087i
$916$		0			0
$917$	2.48376e11	+	2.48376e11i	0.351263	+	0.351263i
$918$		0			0
$919$	−4.24302e10			−0.0594858			−0.0297429	−	0.999558i	$-0.509469\pi$
$919$	−4.24302e10			−0.0594858			−0.0297429	+	0.999558i	$0.509469\pi$
$920$		0			0
$921$		−	7.62900e11i		−	1.06030i
$922$		0			0
$923$	−2.34621e11	+	2.34621e11i	−0.323266	+	0.323266i
$924$		0			0
$925$	1.88181e11	−	1.88181e11i	0.257044	−	0.257044i
$926$		0			0
$927$		−	1.25889e11i		−	0.170478i
$928$		0			0
$929$	1.03495e12			1.38949			0.694745	−	0.719256i	$-0.255517\pi$
$929$	1.03495e12			1.38949			0.694745	+	0.719256i	$0.255517\pi$
$930$		0			0
$931$	4.73216e11	+	4.73216e11i	0.629884	+	0.629884i
$932$		0			0
$933$	3.93620e11	+	3.93620e11i	0.519458	+	0.519458i
$934$		0			0
$935$	1.06942e12			1.39928
$936$		0			0
$937$		−	8.71654e11i		−	1.13080i	−0.824817	−	0.565400i	$-0.808722\pi$
$937$		−	8.71654e11i		−	1.13080i	0.824817	−	0.565400i	$-0.191278\pi$
$938$		0			0
$939$	5.71269e11	−	5.71269e11i	0.734816	−	0.734816i
$940$		0			0
$941$	−8.26055e11	+	8.26055e11i	−1.05354	+	1.05354i	−0.0550553	+	0.998483i	$0.517533\pi$
$941$	−8.26055e11	+	8.26055e11i	−1.05354	+	1.05354i	−0.998483	+	0.0550553i	$0.982467\pi$
$942$		0			0
$943$		−	1.86373e10i		−	0.0235687i
$944$		0			0
$945$	2.39360e11			0.300140
$946$		0			0
$947$	2.32021e11	+	2.32021e11i	0.288487	+	0.288487i	0.836482	−	0.547994i	$-0.184609\pi$
$947$	2.32021e11	+	2.32021e11i	0.288487	+	0.288487i	−0.547994	+	0.836482i	$0.684609\pi$
$948$		0			0
$949$	−3.05354e11	−	3.05354e11i	−0.376477	−	0.376477i
$950$		0			0
$951$	2.84365e11			0.347659
$952$		0			0
$953$			1.33518e10i			0.0161871i	0.999967	+	0.00809355i	$0.00257628\pi$
$953$			1.33518e10i			0.0161871i	−0.999967	+	0.00809355i	$0.997424\pi$
$954$		0			0
$955$	−9.71622e11	+	9.71622e11i	−1.16811	+	1.16811i
$956$		0			0
$957$	2.15178e11	−	2.15178e11i	0.256537	−	0.256537i
$958$		0			0
$959$		−	8.69796e10i		−	0.102836i
$960$		0			0
$961$	4.59380e11			0.538615
$962$		0			0
$963$	3.13495e11	+	3.13495e11i	0.364523	+	0.364523i
$964$		0			0
$965$	−4.64247e11	−	4.64247e11i	−0.535352	−	0.535352i
$966$		0			0
$967$	6.56705e11			0.751042			0.375521	−	0.926814i	$-0.377464\pi$
$967$	6.56705e11			0.751042			0.375521	+	0.926814i	$0.377464\pi$
$968$		0			0
$969$			1.00725e12i			1.14247i
$970$		0			0
$971$	−9.77017e10	+	9.77017e10i	−0.109907	+	0.109907i	−0.759922	−	0.650015i	$-0.774763\pi$
$971$	−9.77017e10	+	9.77017e10i	−0.109907	+	0.109907i	0.650015	+	0.759922i	$0.274763\pi$
$972$		0			0
$973$	−6.20324e11	+	6.20324e11i	−0.692097	+	0.692097i
$974$		0			0
$975$			2.18577e11i			0.241873i
$976$		0			0
$977$	8.10989e11			0.890095			0.445048	−	0.895507i	$-0.353187\pi$
$977$	8.10989e11			0.890095			0.445048	+	0.895507i	$0.353187\pi$
$978$		0			0
$979$	−4.68902e11	−	4.68902e11i	−0.510448	−	0.510448i
$980$		0			0
$981$	2.10739e11	+	2.10739e11i	0.227546	+	0.227546i
$982$		0			0
$983$	−5.69686e11			−0.610129			−0.305064	−	0.952332i	$-0.598678\pi$
$983$	−5.69686e11			−0.610129			−0.305064	+	0.952332i	$0.598678\pi$
$984$		0			0
$985$		−	6.83037e11i		−	0.725604i
$986$		0			0
$987$	−9.51448e11	+	9.51448e11i	−1.00257	+	1.00257i
$988$		0			0
$989$	−6.75258e11	+	6.75258e11i	−0.705804	+	0.705804i
$990$		0			0
$991$		−	1.31899e12i		−	1.36757i	−0.729685	−	0.683783i	$-0.760333\pi$
$991$		−	1.31899e12i		−	1.36757i	0.729685	−	0.683783i	$-0.239667\pi$
$992$		0			0
$993$	3.26799e11			0.336111
$994$		0			0
$995$	−1.28393e10	−	1.28393e10i	−0.0130993	−	0.0130993i
$996$		0			0
$997$	4.63158e10	+	4.63158e10i	0.0468758	+	0.0468758i	0.730156	−	0.683280i	$-0.239447\pi$
$997$	4.63158e10	+	4.63158e10i	0.0468758	+	0.0468758i	−0.683280	+	0.730156i	$0.739447\pi$
$998$		0			0
$999$	−2.14554e11			−0.215415

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	192.9.l.a.79.12		64
4.3	odd	2		48.9.l.a.43.15	yes	64
16.3	odd	4	inner	192.9.l.a.175.12		64
16.13	even	4		48.9.l.a.19.15	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.9.l.a.19.15	✓	64	16.13	even	4
48.9.l.a.43.15	yes	64	4.3	odd	2
192.9.l.a.79.12		64	1.1	even	1	trivial
192.9.l.a.175.12		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)

\(f(q)\)	\(=\)	\(q+(-33.0681 - 33.0681i) q^{3} +(508.668 + 508.668i) q^{5} +3253.34 q^{7} +2187.00i q^{9} +(-6777.24 + 6777.24i) q^{11} +(-26051.9 + 26051.9i) q^{13} -33641.4i q^{15} -155108. q^{17} +(98189.8 + 98189.8i) q^{19} +(-107582. - 107582. i) q^{21} -440378. q^{23} +126860. i q^{25} +(72320.0 - 72320.0i) q^{27} +(480071. - 480071. i) q^{29} +627305. i q^{31} +448221. q^{33} +(1.65487e6 + 1.65487e6i) q^{35} +(-1.48337e6 - 1.48337e6i) q^{37} +1.72298e6 q^{39} +42321.1i q^{41} +(1.53336e6 - 1.53336e6i) q^{43} +(-1.11246e6 + 1.11246e6i) q^{45} -8.84396e6i q^{47} +4.81940e6 q^{49} +(5.12911e6 + 5.12911e6i) q^{51} +(-6.41564e6 - 6.41564e6i) q^{53} -6.89473e6 q^{55} -6.49390e6i q^{57} +(9.15868e6 - 9.15868e6i) q^{59} +(-1.53578e7 + 1.53578e7i) q^{61} +7.11505e6i q^{63} -2.65035e7 q^{65} +(-9.64762e6 - 9.64762e6i) q^{67} +(1.45625e7 + 1.45625e7i) q^{69} +9.00590e6 q^{71} +1.17210e7i q^{73} +(4.19503e6 - 4.19503e6i) q^{75} +(-2.20486e7 + 2.20486e7i) q^{77} +3.38546e6i q^{79} -4.78297e6 q^{81} +(-1.31997e7 - 1.31997e7i) q^{83} +(-7.88982e7 - 7.88982e7i) q^{85} -3.17501e7 q^{87} +6.91877e7i q^{89} +(-8.47556e7 + 8.47556e7i) q^{91} +(2.07438e7 - 2.07438e7i) q^{93} +9.98919e7i q^{95} -1.04598e8 q^{97} +(-1.48218e7 - 1.48218e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 39552 q^{11} + 167552 q^{19} - 1691136 q^{23} - 2132352 q^{29} + 2415744 q^{35} - 4720512 q^{37} + 7244672 q^{43} + 52706752 q^{49} - 13862016 q^{51} - 5358720 q^{53} + 46326784 q^{55} - 44938752 q^{59}+ \cdots - 86500224 q^{99}+O(q^{100}) \) 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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