LMFDB - Embedded newform 192.7.i.a.113.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [192,7,Mod(17,192)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 3, 2]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("192.17");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 192 = 2^{6} \cdot 3 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	192.i (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$44.1703840550$
Analytic rank:	$0$
Dimension:	$92$
Relative dimension:	$46$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 48)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			113.9
Character	$\chi$	$=$	192.113
Dual form			192.7.i.a.17.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-20.6842 + 17.3541i) q^{3} +(-77.8915 + 77.8915i) q^{5} +310.530i q^{7} +(126.674 - 717.910i) q^{9} +O(q^{10})$	\(q+(-20.6842 + 17.3541i) q^{3} +(-77.8915 + 77.8915i) q^{5} +310.530i q^{7} +(126.674 - 717.910i) q^{9} +(-1027.05 + 1027.05i) q^{11} +(-1422.09 + 1422.09i) q^{13} +(259.392 - 2962.86i) q^{15} +6133.59i q^{17} +(-6349.13 + 6349.13i) q^{19} +(-5388.96 - 6423.08i) q^{21} -3000.58 q^{23} +3490.83i q^{25} +(9838.50 + 17047.7i) q^{27} +(17533.8 + 17533.8i) q^{29} -11354.1 q^{31} +(3420.26 - 39067.3i) q^{33} +(-24187.7 - 24187.7i) q^{35} +(-9399.09 - 9399.09i) q^{37} +(4735.79 - 54093.7i) q^{39} +81655.3 q^{41} +(-66104.5 - 66104.5i) q^{43} +(46052.3 + 65785.9i) q^{45} -39239.7i q^{47} +21219.9 q^{49} +(-106443. - 126869. i) q^{51} +(-199357. + 199357. i) q^{53} -159997. i q^{55} +(21143.7 - 241510. i) q^{57} +(-140266. + 140266. i) q^{59} +(279820. - 279820. i) q^{61} +(222933. + 39336.1i) q^{63} -221537. i q^{65} +(352782. - 352782. i) q^{67} +(62064.7 - 52072.3i) q^{69} +353151. q^{71} -365757. i q^{73} +(-60580.0 - 72205.0i) q^{75} +(-318931. - 318931. i) q^{77} -469445. q^{79} +(-499348. - 181881. i) q^{81} +(671838. + 671838. i) q^{83} +(-477755. - 477755. i) q^{85} +(-666955. - 58390.4i) q^{87} -289018. q^{89} +(-441601. - 441601. i) q^{91} +(234850. - 197039. i) q^{93} -989087. i q^{95} +356725. q^{97} +(607230. + 867431. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 92 q + 2 q^{3}+O(q^{10}) $ 92 * q + 2 * q^3	$ 92 q + 2 q^{3} - 4 q^{13} + 4 q^{15} + 3940 q^{19} + 1456 q^{21} + 34322 q^{27} + 8 q^{31} - 4 q^{33} - 4 q^{37} + 195268 q^{43} - 31252 q^{45} - 1142884 q^{49} - 385056 q^{51} - 326500 q^{61} - 470592 q^{63} - 1207676 q^{67} - 1460 q^{69} - 1413778 q^{75} - 860920 q^{79} - 4 q^{81} + 434496 q^{85} - 2320992 q^{91} - 1176260 q^{93} - 8 q^{97} + 4048228 q^{99}+O(q^{100}) $ 92 * q + 2 * q^3 - 4 * q^13 + 4 * q^15 + 3940 * q^19 + 1456 * q^21 + 34322 * q^27 + 8 * q^31 - 4 * q^33 - 4 * q^37 + 195268 * q^43 - 31252 * q^45 - 1142884 * q^49 - 385056 * q^51 - 326500 * q^61 - 470592 * q^63 - 1207676 * q^67 - 1460 * q^69 - 1413778 * q^75 - 860920 * q^79 - 4 * q^81 + 434496 * q^85 - 2320992 * q^91 - 1176260 * q^93 - 8 * q^97 + 4048228 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−20.6842	+	17.3541i	−0.766082	+	0.642743i
$3$	−20.6842	+	17.3541i	−0.766082	+	0.642743i
$4$		0			0
$5$	−77.8915	+	77.8915i	−0.623132	+	0.623132i	−0.946331	−	0.323199i	$-0.895242\pi$
$5$	−77.8915	+	77.8915i	−0.623132	+	0.623132i	0.323199	+	0.946331i	$0.395242\pi$
$6$		0			0
$7$			310.530i			0.905336i	0.891679	+	0.452668i	$0.149528\pi$
$7$			310.530i			0.905336i	−0.891679	+	0.452668i	$0.850472\pi$
$8$		0			0
$9$	126.674	−	717.910i	0.173764	−	0.984787i
$10$		0			0
$11$	−1027.05	+	1027.05i	−0.771639	+	0.771639i	−0.978393	−	0.206754i	$-0.933710\pi$
$11$	−1027.05	+	1027.05i	−0.771639	+	0.771639i	0.206754	+	0.978393i	$0.433710\pi$
$12$		0			0
$13$	−1422.09	+	1422.09i	−0.647285	+	0.647285i	−0.952336	−	0.305051i	$-0.901327\pi$
$13$	−1422.09	+	1422.09i	−0.647285	+	0.647285i	0.305051	+	0.952336i	$0.401327\pi$
$14$		0			0
$15$	259.392	−	2962.86i	0.0768569	−	0.877884i
$16$		0			0
$17$			6133.59i			1.24844i	0.781248	+	0.624221i	$0.214583\pi$
$17$			6133.59i			1.24844i	−0.781248	+	0.624221i	$0.785417\pi$
$18$		0			0
$19$	−6349.13	+	6349.13i	−0.925665	+	0.925665i	−0.997422	−	0.0717575i	$-0.977139\pi$
$19$	−6349.13	+	6349.13i	−0.925665	+	0.925665i	0.0717575	+	0.997422i	$0.477139\pi$
$20$		0			0
$21$	−5388.96	−	6423.08i	−0.581898	−	0.693562i
$22$		0			0
$23$	−3000.58			−0.246616			−0.123308	−	0.992368i	$-0.539350\pi$
$23$	−3000.58			−0.246616			−0.123308	+	0.992368i	$0.539350\pi$
$24$		0			0
$25$			3490.83i			0.223413i
$26$		0			0
$27$	9838.50	+	17047.7i	0.499847	+	0.866114i
$28$		0			0
$29$	17533.8	+	17533.8i	0.718922	+	0.718922i	0.968384	−	0.249463i	$-0.0802540\pi$
$29$	17533.8	+	17533.8i	0.718922	+	0.718922i	−0.249463	+	0.968384i	$0.580254\pi$
$30$		0			0
$31$	−11354.1			−0.381124			−0.190562	−	0.981675i	$-0.561031\pi$
$31$	−11354.1			−0.381124			−0.190562	+	0.981675i	$0.561031\pi$
$32$		0			0
$33$	3420.26	−	39067.3i	0.0951737	−	1.08710i
$34$		0			0
$35$	−24187.7	−	24187.7i	−0.564144	−	0.564144i
$36$		0			0
$37$	−9399.09	−	9399.09i	−0.185558	−	0.185558i	0.608214	−	0.793773i	$-0.291886\pi$
$37$	−9399.09	−	9399.09i	−0.185558	−	0.185558i	−0.793773	+	0.608214i	$0.791886\pi$
$38$		0			0
$39$	4735.79	−	54093.7i	0.0798359	−	0.911911i
$40$		0			0
$41$	81655.3			1.18477			0.592384	−	0.805656i	$-0.298187\pi$
$41$	81655.3			1.18477			0.592384	+	0.805656i	$0.298187\pi$
$42$		0			0
$43$	−66104.5	−	66104.5i	−0.831431	−	0.831431i	0.156282	−	0.987712i	$-0.450049\pi$
$43$	−66104.5	−	66104.5i	−0.831431	−	0.831431i	−0.987712	+	0.156282i	$0.950049\pi$
$44$		0			0
$45$	46052.3	+	65785.9i	0.505375	+	0.721930i
$46$		0			0
$47$		−	39239.7i		−	0.377948i	−0.981982	−	0.188974i	$-0.939484\pi$
$47$		−	39239.7i		−	0.377948i	0.981982	−	0.188974i	$-0.0605161\pi$
$48$		0			0
$49$	21219.9			0.180366
$50$		0			0
$51$	−106443.	−	126869.i	−0.802427	−	0.956409i
$52$		0			0
$53$	−199357.	+	199357.i	−1.33907	+	1.33907i	−0.442115	+	0.896959i	$0.645772\pi$
$53$	−199357.	+	199357.i	−1.33907	+	1.33907i	−0.896959	+	0.442115i	$0.854228\pi$
$54$		0			0
$55$		−	159997.i		−	0.961666i
$56$		0			0
$57$	21143.7	−	241510.i	0.114171	−	1.30410i
$58$		0			0
$59$	−140266.	+	140266.i	−0.682960	+	0.682960i	−0.960666	−	0.277706i	$-0.910426\pi$
$59$	−140266.	+	140266.i	−0.682960	+	0.682960i	0.277706	+	0.960666i	$0.410426\pi$
$60$		0			0
$61$	279820.	−	279820.i	1.23279	−	1.23279i	0.269902	−	0.962888i	$-0.413009\pi$
$61$	279820.	−	279820.i	1.23279	−	1.23279i	0.962888	−	0.269902i	$-0.0869912\pi$
$62$		0			0
$63$	222933.	+	39336.1i	0.891564	+	0.157315i
$64$		0			0
$65$		−	221537.i		−	0.806688i
$66$		0			0
$67$	352782.	−	352782.i	1.17296	−	1.17296i	0.191456	−	0.981501i	$-0.438679\pi$
$67$	352782.	−	352782.i	1.17296	−	1.17296i	0.981501	−	0.191456i	$-0.0613211\pi$
$68$		0			0
$69$	62064.7	−	52072.3i	0.188928	−	0.158511i
$70$		0			0
$71$	353151.			0.986700			0.493350	−	0.869831i	$-0.335772\pi$
$71$	353151.			0.986700			0.493350	+	0.869831i	$0.335772\pi$
$72$		0			0
$73$		−	365757.i		−	0.940208i	−0.882611	−	0.470104i	$-0.844216\pi$
$73$		−	365757.i		−	0.940208i	0.882611	−	0.470104i	$-0.155784\pi$
$74$		0			0
$75$	−60580.0	−	72205.0i	−0.143597	−	0.171153i
$76$		0			0
$77$	−318931.	−	318931.i	−0.698593	−	0.698593i
$78$		0			0
$79$	−469445.			−0.952146			−0.476073	−	0.879406i	$-0.657940\pi$
$79$	−469445.			−0.952146			−0.476073	+	0.879406i	$0.657940\pi$
$80$		0			0
$81$	−499348.	−	181881.i	−0.939612	−	0.342241i
$82$		0			0
$83$	671838.	+	671838.i	1.17498	+	1.17498i	0.981007	+	0.193973i	$0.0621374\pi$
$83$	671838.	+	671838.i	1.17498	+	1.17498i	0.193973	+	0.981007i	$0.437863\pi$
$84$		0			0
$85$	−477755.	−	477755.i	−0.777944	−	0.777944i
$86$		0			0
$87$	−666955.	−	58390.4i	−1.01283	−	0.0886715i
$88$		0			0
$89$	−289018.			−0.409972			−0.204986	−	0.978765i	$-0.565715\pi$
$89$	−289018.			−0.409972			−0.204986	+	0.978765i	$0.565715\pi$
$90$		0			0
$91$	−441601.	−	441601.i	−0.586011	−	0.586011i
$92$		0			0
$93$	234850.	−	197039.i	0.291972	−	0.244964i
$94$		0			0
$95$		−	989087.i		−	1.15362i
$96$		0			0
$97$	356725.			0.390858			0.195429	−	0.980718i	$-0.437390\pi$
$97$	356725.			0.390858			0.195429	+	0.980718i	$0.437390\pi$
$98$		0			0
$99$	607230.	+	867431.i	0.625817	+	0.893983i
$100$		0			0
$101$	−723463.	+	723463.i	−0.702186	+	0.702186i	−0.964879	−	0.262693i	$-0.915389\pi$
$101$	−723463.	+	723463.i	−0.702186	+	0.702186i	0.262693	+	0.964879i	$0.415389\pi$
$102$		0			0
$103$		−	878385.i		−	0.803847i	−0.915673	−	0.401923i	$-0.868342\pi$
$103$		−	878385.i		−	0.803847i	0.915673	−	0.401923i	$-0.131658\pi$
$104$		0			0
$105$	920057.	+	80549.0i	0.794780	+	0.0695813i
$106$		0			0
$107$	952833.	−	952833.i	0.777796	−	0.777796i	−0.201660	−	0.979456i	$-0.564634\pi$
$107$	952833.	−	952833.i	0.777796	−	0.777796i	0.979456	+	0.201660i	$0.0646336\pi$
$108$		0			0
$109$	−680307.	+	680307.i	−0.525322	+	0.525322i	−0.919174	−	0.393852i	$-0.871142\pi$
$109$	−680307.	+	680307.i	−0.525322	+	0.525322i	0.393852	+	0.919174i	$0.371142\pi$
$110$		0			0
$111$	357525.	+	31300.6i	0.261419	+	0.0228867i
$112$		0			0
$113$		−	138247.i		−	0.0958121i	−0.998852	−	0.0479060i	$-0.984745\pi$
$113$		−	138247.i		−	0.0958121i	0.998852	−	0.0479060i	$-0.0152548\pi$
$114$		0			0
$115$	233720.	−	233720.i	0.153675	−	0.153675i
$116$		0			0
$117$	840788.	+	1.20107e6i	0.524964	+	0.749913i
$118$		0			0
$119$	−1.90467e6			−1.13026
$120$		0			0
$121$		−	338109.i		−	0.190854i
$122$		0			0
$123$	−1.68898e6	+	1.41705e6i	−0.907629	+	0.761500i
$124$		0			0
$125$	−1.48896e6	−	1.48896e6i	−0.762348	−	0.762348i
$126$		0			0
$127$	−369091.			−0.180187			−0.0900934	−	0.995933i	$-0.528717\pi$
$127$	−369091.			−0.180187			−0.0900934	+	0.995933i	$0.528717\pi$
$128$		0			0
$129$	2.51450e6	+	220139.i	1.17134	+	0.102548i
$130$		0			0
$131$	2.05595e6	+	2.05595e6i	0.914530	+	0.914530i	0.996625	−	0.0820941i	$-0.0261608\pi$
$131$	2.05595e6	+	2.05595e6i	0.914530	+	0.914530i	−0.0820941	+	0.996625i	$0.526161\pi$
$132$		0			0
$133$	−1.97160e6	−	1.97160e6i	−0.838038	−	0.838038i
$134$		0			0
$135$	−2.09421e6	−	561537.i	−0.851174	−	0.228232i
$136$		0			0
$137$	3.22146e6			1.25283			0.626413	−	0.779491i	$-0.284522\pi$
$137$	3.22146e6			1.25283			0.626413	+	0.779491i	$0.284522\pi$
$138$		0			0
$139$	1.27858e6	+	1.27858e6i	0.476083	+	0.476083i	0.903877	−	0.427793i	$-0.140709\pi$
$139$	1.27858e6	+	1.27858e6i	0.476083	+	0.476083i	−0.427793	+	0.903877i	$0.640709\pi$
$140$		0			0
$141$	680967.	+	811642.i	0.242923	+	0.289539i
$142$		0			0
$143$		−	2.92111e6i		−	0.998941i
$144$		0			0
$145$	−2.73146e6			−0.895966
$146$		0			0
$147$	−438918.	+	368252.i	−0.138175	+	0.115929i
$148$		0			0
$149$	−3.08453e6	+	3.08453e6i	−0.932461	+	0.932461i	−0.997859	−	0.0653987i	$-0.979168\pi$
$149$	−3.08453e6	+	3.08453e6i	−0.932461	+	0.932461i	0.0653987	+	0.997859i	$0.479168\pi$
$150$		0			0
$151$			3.73589e6i			1.08508i	0.840028	+	0.542542i	$0.182538\pi$
$151$			3.73589e6i			1.08508i	−0.840028	+	0.542542i	$0.817462\pi$
$152$		0			0
$153$	4.40337e6	+	776966.i	1.22945	+	0.216934i
$154$		0			0
$155$	884384.	−	884384.i	0.237490	−	0.237490i
$156$		0			0
$157$	1.30900e6	−	1.30900e6i	0.338253	−	0.338253i	−0.517457	−	0.855710i	$-0.673121\pi$
$157$	1.30900e6	−	1.30900e6i	0.338253	−	0.338253i	0.855710	+	0.517457i	$0.173121\pi$
$158$		0			0
$159$	663893.	−	7.58320e6i	0.165161	−	1.88652i
$160$		0			0
$161$		−	931772.i		−	0.223271i
$162$		0			0
$163$	59111.6	−	59111.6i	0.0136493	−	0.0136493i	−0.700249	−	0.713898i	$-0.746928\pi$
$163$	59111.6	−	59111.6i	0.0136493	−	0.0136493i	0.713898	+	0.700249i	$0.246928\pi$
$164$		0			0
$165$	2.77660e6	+	3.30942e6i	0.618104	+	0.736715i
$166$		0			0
$167$	−2.28355e6			−0.490300			−0.245150	−	0.969485i	$-0.578837\pi$
$167$	−2.28355e6			−0.490300			−0.245150	+	0.969485i	$0.578837\pi$
$168$		0			0
$169$			782154.i			0.162044i
$170$		0			0
$171$	3.75384e6	+	5.36238e6i	0.750736	+	1.07243i
$172$		0			0
$173$	3.47518e6	+	3.47518e6i	0.671180	+	0.671180i	0.957988	−	0.286808i	$-0.0925942\pi$
$173$	3.47518e6	+	3.47518e6i	0.671180	+	0.671180i	−0.286808	+	0.957988i	$0.592594\pi$
$174$		0			0
$175$	−1.08401e6			−0.202264
$176$		0			0
$177$	467108.	−	5.33546e6i	0.0842360	−	0.962171i
$178$		0			0
$179$	2.91510e6	+	2.91510e6i	0.508269	+	0.508269i	0.913995	−	0.405726i	$-0.132981\pi$
$179$	2.91510e6	+	2.91510e6i	0.508269	+	0.508269i	−0.405726	+	0.913995i	$0.632981\pi$
$180$		0			0
$181$	5.86054e6	+	5.86054e6i	0.988330	+	0.988330i	0.999933	−	0.0116025i	$-0.00369326\pi$
$181$	5.86054e6	+	5.86054e6i	0.988330	+	0.988330i	−0.0116025	+	0.999933i	$0.503693\pi$
$182$		0			0
$183$	−931847.	+	1.06439e7i	−0.152052	+	1.73678i
$184$		0			0
$185$	1.46422e6			0.231255
$186$		0			0
$187$	−6.29952e6	−	6.29952e6i	−0.963347	−	0.963347i
$188$		0			0
$189$	−5.29383e6	+	3.05515e6i	−0.784124	+	0.452530i
$190$		0			0
$191$			3.40903e6i			0.489250i	0.969618	+	0.244625i	$0.0786649\pi$
$191$			3.40903e6i			0.489250i	−0.969618	+	0.244625i	$0.921335\pi$
$192$		0			0
$193$	−6.11510e6			−0.850613			−0.425306	−	0.905049i	$-0.639834\pi$
$193$	−6.11510e6			−0.850613			−0.425306	+	0.905049i	$0.639834\pi$
$194$		0			0
$195$	3.84456e6	+	4.58232e6i	0.518493	+	0.617990i
$196$		0			0
$197$	−7.02036e6	+	7.02036e6i	−0.918250	+	0.918250i	−0.996902	−	0.0786521i	$-0.974938\pi$
$197$	−7.02036e6	+	7.02036e6i	−0.918250	+	0.918250i	0.0786521	+	0.996902i	$0.474938\pi$
$198$		0			0
$199$		−	4.41617e6i		−	0.560385i	−0.959944	−	0.280193i	$-0.909602\pi$
$199$		−	4.41617e6i		−	0.560385i	0.959944	−	0.280193i	$-0.0903984\pi$
$200$		0			0
$201$	−1.17482e6	+	1.34192e7i	−0.144672	+	1.65249i
$202$		0			0
$203$	−5.44477e6	+	5.44477e6i	−0.650866	+	0.650866i
$204$		0			0
$205$	−6.36026e6	+	6.36026e6i	−0.738266	+	0.738266i
$206$		0			0
$207$	−380095.	+	2.15415e6i	−0.0428530	+	0.242865i
$208$		0			0
$209$		−	1.30418e7i		−	1.42856i
$210$		0			0
$211$	−8.74430e6	+	8.74430e6i	−0.930846	+	0.930846i	−0.997759	−	0.0669131i	$-0.978685\pi$
$211$	−8.74430e6	+	8.74430e6i	−0.930846	+	0.930846i	0.0669131	+	0.997759i	$0.478685\pi$
$212$		0			0
$213$	−7.30465e6	+	6.12860e6i	−0.755894	+	0.634194i
$214$		0			0
$215$	1.02980e7			1.03618
$216$		0			0
$217$		−	3.52578e6i		−	0.345045i
$218$		0			0
$219$	6.34736e6	+	7.56540e6i	0.604312	+	0.720277i
$220$		0			0
$221$	−8.72250e6	−	8.72250e6i	−0.808098	−	0.808098i
$222$		0			0
$223$	−7.67162e6			−0.691787			−0.345894	−	0.938274i	$-0.612424\pi$
$223$	−7.67162e6			−0.691787			−0.345894	+	0.938274i	$0.612424\pi$
$224$		0			0
$225$	2.50610e6	+	442196.i	0.220014	+	0.0388211i
$226$		0			0
$227$	−3.03062e6	−	3.03062e6i	−0.259092	−	0.259092i	0.565593	−	0.824685i	$-0.308647\pi$
$227$	−3.03062e6	−	3.03062e6i	−0.259092	−	0.259092i	−0.824685	+	0.565593i	$0.808647\pi$
$228$		0			0
$229$	−5.57443e6	−	5.57443e6i	−0.464188	−	0.464188i	0.435837	−	0.900026i	$-0.356452\pi$
$229$	−5.57443e6	−	5.57443e6i	−0.464188	−	0.464188i	−0.900026	+	0.435837i	$0.856452\pi$
$230$		0			0
$231$	1.21316e7	+	1.06209e6i	0.984195	+	0.0861642i
$232$		0			0
$233$	2.31313e7			1.82865			0.914327	−	0.404976i	$-0.132720\pi$
$233$	2.31313e7			1.82865			0.914327	+	0.404976i	$0.132720\pi$
$234$		0			0
$235$	3.05644e6	+	3.05644e6i	0.235511	+	0.235511i
$236$		0			0
$237$	9.71010e6	−	8.14677e6i	0.729422	−	0.611984i
$238$		0			0
$239$		−	8.10890e6i		−	0.593975i	−0.954881	−	0.296987i	$-0.904018\pi$
$239$		−	8.10890e6i		−	0.593975i	0.954881	−	0.296987i	$-0.0959820\pi$
$240$		0			0
$241$	5.60281e6			0.400272			0.200136	−	0.979768i	$-0.435862\pi$
$241$	5.60281e6			0.400272			0.200136	+	0.979768i	$0.435862\pi$
$242$		0			0
$243$	1.34850e7	−	4.90365e6i	0.939793	−	0.341744i
$244$		0			0
$245$	−1.65285e6	+	1.65285e6i	−0.112392	+	0.112392i
$246$		0			0
$247$		−	1.80580e7i		−	1.19834i
$248$		0			0
$249$	−2.55556e7	−	2.23733e6i	−1.65534	−	0.144922i
$250$		0			0
$251$	6.97970e6	−	6.97970e6i	0.441383	−	0.441383i	−0.451094	−	0.892477i	$-0.648966\pi$
$251$	6.97970e6	−	6.97970e6i	0.441383	−	0.441383i	0.892477	+	0.451094i	$0.148966\pi$
$252$		0			0
$253$	3.08175e6	−	3.08175e6i	0.190299	−	0.190299i
$254$		0			0
$255$	1.81730e7	+	1.59100e6i	1.09599	+	0.0959513i
$256$		0			0
$257$			1.05065e7i			0.618953i	0.950907	+	0.309477i	$0.100154\pi$
$257$			1.05065e7i			0.618953i	−0.950907	+	0.309477i	$0.899846\pi$
$258$		0			0
$259$	2.91870e6	−	2.91870e6i	0.167993	−	0.167993i
$260$		0			0
$261$	1.48087e7	−	1.03666e7i	0.832907	−	0.583062i
$262$		0			0
$263$	−3.43943e7			−1.89068			−0.945342	−	0.326080i	$-0.894272\pi$
$263$	−3.43943e7			−1.89068			−0.945342	+	0.326080i	$0.894272\pi$
$264$		0			0
$265$		−	3.10565e7i		−	1.66884i
$266$		0			0
$267$	5.97810e6	−	5.01563e6i	0.314072	−	0.263507i
$268$		0			0
$269$	−1.47409e6	−	1.47409e6i	−0.0757296	−	0.0757296i	0.668227	−	0.743957i	$-0.267053\pi$
$269$	−1.47409e6	−	1.47409e6i	−0.0757296	−	0.0757296i	−0.743957	+	0.668227i	$0.767053\pi$
$270$		0			0
$271$	2.60363e6			0.130819			0.0654096	−	0.997858i	$-0.479165\pi$
$271$	2.60363e6			0.130819			0.0654096	+	0.997858i	$0.479165\pi$
$272$		0			0
$273$	1.67977e7	+	1.47060e6i	0.825586	+	0.0722783i
$274$		0			0
$275$	−3.58526e6	−	3.58526e6i	−0.172394	−	0.172394i
$276$		0			0
$277$	−2.21180e7	−	2.21180e7i	−1.04065	−	1.04065i	−0.999138	−	0.0415157i	$-0.986781\pi$
$277$	−2.21180e7	−	2.21180e7i	−1.04065	−	1.04065i	−0.0415157	−	0.999138i	$-0.513219\pi$
$278$		0			0
$279$	−1.43826e6	+	8.15119e6i	−0.0662255	+	0.375326i
$280$		0			0
$281$	−3.37592e6			−0.152151			−0.0760753	−	0.997102i	$-0.524239\pi$
$281$	−3.37592e6			−0.152151			−0.0760753	+	0.997102i	$0.524239\pi$
$282$		0			0
$283$	−2.77260e7	−	2.77260e7i	−1.22329	−	1.22329i	−0.966456	−	0.256831i	$-0.917322\pi$
$283$	−2.77260e7	−	2.77260e7i	−1.22329	−	1.22329i	−0.256831	−	0.966456i	$-0.582678\pi$
$284$		0			0
$285$	1.71647e7	+	2.04585e7i	0.741482	+	0.883770i
$286$		0			0
$287$			2.53565e7i			1.07261i
$288$		0			0
$289$	−1.34834e7			−0.558607
$290$		0			0
$291$	−7.37858e6	+	6.19063e6i	−0.299429	+	0.251221i
$292$		0			0
$293$	3.29847e7	−	3.29847e7i	1.31132	−	1.31132i	0.390884	−	0.920440i	$-0.372169\pi$
$293$	3.29847e7	−	3.29847e7i	1.31132	−	1.31132i	0.920440	−	0.390884i	$-0.127831\pi$
$294$		0			0
$295$		−	2.18510e7i		−	0.851148i
$296$		0			0
$297$	−2.76135e7	−	7.40424e6i	−1.05403	−	0.282625i
$298$		0			0
$299$	4.26708e6	−	4.26708e6i	0.159631	−	0.159631i
$300$		0			0
$301$	2.05275e7	−	2.05275e7i	0.752724	−	0.752724i
$302$		0			0
$303$	2.40926e6	−	2.75193e7i	0.0866074	−	0.989258i
$304$		0			0
$305$			4.35912e7i			1.53638i
$306$		0			0
$307$	3.51931e7	−	3.51931e7i	1.21630	−	1.21630i	0.247387	−	0.968917i	$-0.420428\pi$
$307$	3.51931e7	−	3.51931e7i	1.21630	−	1.21630i	0.968917	−	0.247387i	$-0.0795718\pi$
$308$		0			0
$309$	1.52435e7	+	1.81687e7i	0.516667	+	0.615813i
$310$		0			0
$311$	−1.12861e7			−0.375199			−0.187599	−	0.982246i	$-0.560071\pi$
$311$	−1.12861e7			−0.375199			−0.187599	+	0.982246i	$0.560071\pi$
$312$		0			0
$313$			1.74518e7i			0.569123i	0.958658	+	0.284562i	$0.0918480\pi$
$313$			1.74518e7i			0.569123i	−0.958658	+	0.284562i	$0.908152\pi$
$314$		0			0
$315$	−2.04285e7	+	1.43006e7i	−0.653590	+	0.457534i
$316$		0			0
$317$	−1.47576e7	−	1.47576e7i	−0.463273	−	0.463273i	0.436454	−	0.899727i	$-0.356234\pi$
$317$	−1.47576e7	−	1.47576e7i	−0.463273	−	0.463273i	−0.899727	+	0.436454i	$0.856234\pi$
$318$		0			0
$319$	−3.60162e7			−1.10950
$320$		0			0
$321$	−3.17309e6	+	3.62441e7i	−0.0959330	+	1.09578i
$322$		0			0
$323$	−3.89430e7	−	3.89430e7i	−1.15564	−	1.15564i
$324$		0			0
$325$	−4.96425e6	−	4.96425e6i	−0.144612	−	0.144612i
$326$		0			0
$327$	2.26554e6	−	2.58777e7i	0.0647930	−	0.740086i
$328$		0			0
$329$	1.21851e7			0.342170
$330$		0			0
$331$	−912322.	−	912322.i	−0.0251573	−	0.0251573i	0.694416	−	0.719574i	$-0.255663\pi$
$331$	−912322.	−	912322.i	−0.0251573	−	0.0251573i	−0.719574	+	0.694416i	$0.755663\pi$
$332$		0			0
$333$	−7.93832e6	+	5.55708e6i	−0.214979	+	0.150492i
$334$		0			0
$335$			5.49575e7i			1.46181i
$336$		0			0
$337$	−2.91976e7			−0.762881			−0.381440	−	0.924393i	$-0.624572\pi$
$337$	−2.91976e7			−0.762881			−0.381440	+	0.924393i	$0.624572\pi$
$338$		0			0
$339$	2.39914e6	+	2.85953e6i	0.0615825	+	0.0733999i
$340$		0			0
$341$	1.16612e7	−	1.16612e7i	0.294090	−	0.294090i
$342$		0			0
$343$			4.31230e7i			1.06863i
$344$		0			0
$345$	−778327.	+	8.89030e6i	−0.0189542	+	0.216501i
$346$		0			0
$347$	2.35265e7	−	2.35265e7i	0.563078	−	0.563078i	−0.367103	−	0.930180i	$-0.619650\pi$
$347$	2.35265e7	−	2.35265e7i	0.563078	−	0.563078i	0.930180	+	0.367103i	$0.119650\pi$
$348$		0			0
$349$	−3.43475e6	+	3.43475e6i	−0.0808013	+	0.0808013i	−0.746352	−	0.665551i	$-0.768197\pi$
$349$	−3.43475e6	+	3.43475e6i	−0.0808013	+	0.0808013i	0.665551	+	0.746352i	$0.268197\pi$
$350$		0			0
$351$	−3.82345e7	−	1.02521e7i	−0.884166	−	0.237079i
$352$		0			0
$353$			519893.i			0.0118193i	0.999983	+	0.00590963i	$0.00188110\pi$
$353$			519893.i			0.0118193i	−0.999983	+	0.00590963i	$0.998119\pi$
$354$		0			0
$355$	−2.75075e7	+	2.75075e7i	−0.614845	+	0.614845i
$356$		0			0
$357$	3.93966e7	−	3.30537e7i	0.865872	−	0.726466i
$358$		0			0
$359$	8.00215e7			1.72951			0.864755	−	0.502194i	$-0.167474\pi$
$359$	8.00215e7			1.72951			0.864755	+	0.502194i	$0.167474\pi$
$360$		0			0
$361$		−	3.35771e7i		−	0.713710i
$362$		0			0
$363$	5.86757e6	+	6.99353e6i	0.122670	+	0.146210i
$364$		0			0
$365$	2.84894e7	+	2.84894e7i	0.585874	+	0.585874i
$366$		0			0
$367$	8.64094e7			1.74809			0.874043	−	0.485848i	$-0.161489\pi$
$367$	8.64094e7			1.74809			0.874043	+	0.485848i	$0.161489\pi$
$368$		0			0
$369$	1.03436e7	−	5.86212e7i	0.205870	−	1.16674i
$370$		0			0
$371$	−6.19065e7	−	6.19065e7i	−1.21231	−	1.21231i
$372$		0			0
$373$	−3.64362e7	−	3.64362e7i	−0.702112	−	0.702112i	0.262752	−	0.964863i	$-0.415370\pi$
$373$	−3.64362e7	−	3.64362e7i	−0.702112	−	0.702112i	−0.964863	+	0.262752i	$0.915370\pi$
$374$		0			0
$375$	5.66375e7	+	4.95849e6i	1.07401	+	0.0940277i
$376$		0			0
$377$	−4.98691e7			−0.930695
$378$		0			0
$379$	9.14432e6	+	9.14432e6i	0.167971	+	0.167971i	0.786087	−	0.618116i	$-0.212104\pi$
$379$	9.14432e6	+	9.14432e6i	0.167971	+	0.167971i	−0.618116	+	0.786087i	$0.712104\pi$
$380$		0			0
$381$	7.63437e6	−	6.40523e6i	0.138038	−	0.115814i
$382$		0			0
$383$			1.02744e8i			1.82878i	0.404839	+	0.914388i	$0.367328\pi$
$383$			1.02744e8i			1.82878i	−0.404839	+	0.914388i	$0.632672\pi$
$384$		0			0
$385$	4.96840e7			0.870631
$386$		0			0
$387$	−5.58308e7	+	3.90834e7i	−0.963255	+	0.674310i
$388$		0			0
$389$	−5.76988e7	+	5.76988e7i	−0.980208	+	0.980208i	−0.999808	−	0.0195997i	$-0.993761\pi$
$389$	−5.76988e7	+	5.76988e7i	−0.980208	+	0.980208i	0.0195997	+	0.999808i	$0.493761\pi$
$390$		0			0
$391$		−	1.84044e7i		−	0.307886i
$392$		0			0
$393$	−7.82047e7	−	6.84665e6i	−1.28841	−	0.112798i
$394$		0			0
$395$	3.65658e7	−	3.65658e7i	0.593312	−	0.593312i
$396$		0			0
$397$	−3.38251e7	+	3.38251e7i	−0.540590	+	0.540590i	−0.923702	−	0.383112i	$-0.874852\pi$
$397$	−3.38251e7	+	3.38251e7i	−0.540590	+	0.540590i	0.383112	+	0.923702i	$0.374852\pi$
$398$		0			0
$399$	7.49962e7	+	6.56576e6i	1.18065	+	0.103363i
$400$		0			0
$401$		−	1.80656e7i		−	0.280169i	−0.990140	−	0.140084i	$-0.955263\pi$
$401$		−	1.80656e7i		−	0.280169i	0.990140	−	0.140084i	$-0.0447374\pi$
$402$		0			0
$403$	1.61464e7	−	1.61464e7i	0.246696	−	0.246696i
$404$		0			0
$405$	5.30620e7	−	2.47280e7i	0.798764	−	0.372241i
$406$		0			0
$407$	1.93067e7			0.286368
$408$		0			0
$409$			8.45299e7i			1.23549i	0.786377	+	0.617746i	$0.211954\pi$
$409$			8.45299e7i			1.23549i	−0.786377	+	0.617746i	$0.788046\pi$
$410$		0			0
$411$	−6.66334e7	+	5.59054e7i	−0.959768	+	0.805245i
$412$		0			0
$413$	−4.35567e7	−	4.35567e7i	−0.618308	−	0.618308i
$414$		0			0
$415$	−1.04661e8			−1.46434
$416$		0			0
$417$	−4.86349e7	−	4.25788e6i	−0.670718	−	0.0587199i
$418$		0			0
$419$	4.87260e7	+	4.87260e7i	0.662397	+	0.662397i	0.955944	−	0.293548i	$-0.0948359\pi$
$419$	4.87260e7	+	4.87260e7i	0.662397	+	0.662397i	−0.293548	+	0.955944i	$0.594836\pi$
$420$		0			0
$421$	6.36969e7	+	6.36969e7i	0.853635	+	0.853635i	0.990579	−	0.136944i	$-0.0437281\pi$
$421$	6.36969e7	+	6.36969e7i	0.853635	+	0.853635i	−0.136944	+	0.990579i	$0.543728\pi$
$422$		0			0
$423$	−2.81705e7	−	4.97064e6i	−0.372198	−	0.0656737i
$424$		0			0
$425$	−2.14113e7			−0.278918
$426$		0			0
$427$	8.68925e7	+	8.68925e7i	1.11609	+	1.11609i
$428$		0			0
$429$	5.06931e7	+	6.04209e7i	0.642062	+	0.765271i
$430$		0			0
$431$			6.42503e7i			0.802497i	0.915969	+	0.401248i	$0.131424\pi$
$431$			6.42503e7i			0.802497i	−0.915969	+	0.401248i	$0.868576\pi$
$432$		0			0
$433$	5.28277e7			0.650726			0.325363	−	0.945589i	$-0.394514\pi$
$433$	5.28277e7			0.650726			0.325363	+	0.945589i	$0.394514\pi$
$434$		0			0
$435$	5.64982e7	−	4.74020e7i	0.686384	−	0.575876i
$436$		0			0
$437$	1.90511e7	−	1.90511e7i	0.228284	−	0.228284i
$438$		0			0
$439$			3.37695e6i			0.0399146i	0.999801	+	0.0199573i	$0.00635302\pi$
$439$			3.37695e6i			0.0399146i	−0.999801	+	0.0199573i	$0.993647\pi$
$440$		0			0
$441$	2.68801e6	−	1.52340e7i	0.0313412	−	0.177623i
$442$		0			0
$443$	3.55956e7	−	3.55956e7i	0.409435	−	0.409435i	−0.472106	−	0.881542i	$-0.656506\pi$
$443$	3.55956e7	−	3.55956e7i	0.409435	−	0.409435i	0.881542	+	0.472106i	$0.156506\pi$
$444$		0			0
$445$	2.25120e7	−	2.25120e7i	0.255467	−	0.255467i
$446$		0			0
$447$	1.02720e7	−	1.17330e8i	0.115009	−	1.31367i
$448$		0			0
$449$			1.40962e7i			0.155726i	0.996964	+	0.0778631i	$0.0248097\pi$
$449$			1.40962e7i			0.155726i	−0.996964	+	0.0778631i	$0.975190\pi$
$450$		0			0
$451$	−8.38642e7	+	8.38642e7i	−0.914213	+	0.914213i
$452$		0			0
$453$	−6.48329e7	−	7.72740e7i	−0.697430	−	0.831264i
$454$		0			0
$455$	6.87939e7			0.730324
$456$		0			0
$457$			1.53031e8i			1.60336i	0.597756	+	0.801678i	$0.296059\pi$
$457$			1.53031e8i			1.60336i	−0.597756	+	0.801678i	$0.703941\pi$
$458$		0			0
$459$	−1.04564e8	+	6.03453e7i	−1.08129	+	0.624030i
$460$		0			0
$461$	−1.00667e8	−	1.00667e8i	−1.02751	−	1.02751i	−0.999611	−	0.0278951i	$-0.991120\pi$
$461$	−1.00667e8	−	1.00667e8i	−1.02751	−	1.02751i	−0.0278951	−	0.999611i	$-0.508880\pi$
$462$		0			0
$463$	2.24428e7			0.226117			0.113059	−	0.993588i	$-0.463935\pi$
$463$	2.24428e7			0.226117			0.113059	+	0.993588i	$0.463935\pi$
$464$		0			0
$465$	−2.94515e6	+	3.36405e7i	−0.0292920	+	0.334582i
$466$		0			0
$467$	−1.02611e8	−	1.02611e8i	−1.00749	−	1.00749i	−0.999972	−	0.00752324i	$-0.997605\pi$
$467$	−1.02611e8	−	1.02611e8i	−1.00749	−	1.00749i	−0.00752324	−	0.999972i	$-0.502395\pi$
$468$		0			0
$469$	1.09550e8	+	1.09550e8i	1.06192	+	1.06192i
$470$		0			0
$471$	−4.35920e6	+	4.97922e7i	−0.0417200	+	0.476539i
$472$		0			0
$473$	1.35786e8			1.28313
$474$		0			0
$475$	−2.21637e7	−	2.21637e7i	−0.206805	−	0.206805i
$476$		0			0
$477$	1.17867e8	+	1.68374e8i	1.08602	+	1.55138i
$478$		0			0
$479$		−	3.89026e7i		−	0.353975i	−0.984213	−	0.176987i	$-0.943365\pi$
$479$		−	3.89026e7i		−	0.353975i	0.984213	−	0.176987i	$-0.0566351\pi$
$480$		0			0
$481$	2.67326e7			0.240219
$482$		0			0
$483$	1.61700e7	+	1.92730e7i	0.143506	+	0.171044i
$484$		0			0
$485$	−2.77859e7	+	2.77859e7i	−0.243556	+	0.243556i
$486$		0			0
$487$			1.47719e8i			1.27894i	0.768816	+	0.639470i	$0.220846\pi$
$487$			1.47719e8i			1.27894i	−0.768816	+	0.639470i	$0.779154\pi$
$488$		0			0
$489$	−196852.	+	2.24850e6i	−0.00168350	+	0.0192295i
$490$		0			0
$491$	1.15929e8	−	1.15929e8i	0.979371	−	0.979371i	−0.0204209	−	0.999791i	$-0.506501\pi$
$491$	1.15929e8	−	1.15929e8i	0.979371	−	0.979371i	0.999791	+	0.0204209i	$0.00650064\pi$
$492$		0			0
$493$	−1.07545e8	+	1.07545e8i	−0.897532	+	0.897532i
$494$		0			0
$495$	−1.14864e8	−	2.02675e7i	−0.947037	−	0.167103i
$496$		0			0
$497$			1.09664e8i			0.893295i
$498$		0			0
$499$	−1.07143e6	+	1.07143e6i	−0.00862307	+	0.00862307i	−0.711405	−	0.702782i	$-0.751941\pi$
$499$	−1.07143e6	+	1.07143e6i	−0.00862307	+	0.00862307i	0.702782	+	0.711405i	$0.251941\pi$
$500$		0			0
$501$	4.72335e7	−	3.96289e7i	0.375610	−	0.315136i
$502$		0			0
$503$	−1.42268e8			−1.11790			−0.558950	−	0.829201i	$-0.688796\pi$
$503$	−1.42268e8			−1.11790			−0.558950	+	0.829201i	$0.688796\pi$
$504$		0			0
$505$		−	1.12703e8i		−	0.875110i
$506$		0			0
$507$	−1.35735e7	−	1.61782e7i	−0.104152	−	0.124139i
$508$		0			0
$509$	−4.19418e7	−	4.19418e7i	−0.318049	−	0.318049i	0.529969	−	0.848017i	$-0.322204\pi$
$509$	−4.19418e7	−	4.19418e7i	−0.318049	−	0.318049i	−0.848017	+	0.529969i	$0.822204\pi$
$510$		0			0
$511$	1.13579e8			0.851204
$512$		0			0
$513$	−1.70704e8	−	4.57723e7i	−1.26442	−	0.339040i
$514$		0			0
$515$	6.84187e7	+	6.84187e7i	0.500903	+	0.500903i
$516$		0			0
$517$	4.03012e7	+	4.03012e7i	0.291639	+	0.291639i
$518$		0			0
$519$	−1.32190e8	−	1.15729e7i	−0.945575	−	0.0827831i
$520$		0			0
$521$	2.07003e8			1.46374			0.731870	−	0.681444i	$-0.238648\pi$
$521$	2.07003e8			1.46374			0.731870	+	0.681444i	$0.238648\pi$
$522$		0			0
$523$	−9.02749e6	−	9.02749e6i	−0.0631047	−	0.0631047i	0.674850	−	0.737955i	$-0.264208\pi$
$523$	−9.02749e6	−	9.02749e6i	−0.0631047	−	0.0631047i	−0.737955	+	0.674850i	$0.764208\pi$
$524$		0			0
$525$	2.24218e7	−	1.88119e7i	0.154951	−	0.130004i
$526$		0			0
$527$		−	6.96412e7i		−	0.475811i
$528$		0			0
$529$	−1.39032e8			−0.939180
$530$		0			0
$531$	8.29301e7	+	1.18466e8i	0.553897	+	0.791244i
$532$		0			0
$533$	−1.16121e8	+	1.16121e8i	−0.766882	+	0.766882i
$534$		0			0
$535$			1.48435e8i			0.969339i
$536$		0			0
$537$	−1.10885e8	−	9.70776e6i	−0.716062	−	0.0626897i
$538$		0			0
$539$	−2.17940e7	+	2.17940e7i	−0.139178	+	0.139178i
$540$		0			0
$541$	1.36157e8	−	1.36157e8i	0.859900	−	0.859900i	−0.131426	−	0.991326i	$-0.541956\pi$
$541$	1.36157e8	−	1.36157e8i	0.859900	−	0.859900i	0.991326	+	0.131426i	$0.0419556\pi$
$542$		0			0
$543$	−2.22925e8	−	1.95166e7i	−1.39238	−	0.121900i
$544$		0			0
$545$		−	1.05980e8i		−	0.654690i
$546$		0			0
$547$	3.49263e7	−	3.49263e7i	0.213398	−	0.213398i	−0.592311	−	0.805709i	$-0.701784\pi$
$547$	3.49263e7	−	3.49263e7i	0.213398	−	0.213398i	0.805709	+	0.592311i	$0.201784\pi$
$548$		0			0
$549$	−1.65440e8	−	2.36331e8i	−0.999821	−	1.42825i
$550$		0			0
$551$	−2.22649e8			−1.33096
$552$		0			0
$553$		−	1.45777e8i		−	0.862012i
$554$		0			0
$555$	−3.02862e7	+	2.54101e7i	−0.177160	+	0.148637i
$556$		0			0
$557$	−6.40563e7	−	6.40563e7i	−0.370678	−	0.370678i	0.497046	−	0.867724i	$-0.334418\pi$
$557$	−6.40563e7	−	6.40563e7i	−0.370678	−	0.370678i	−0.867724	+	0.497046i	$0.834418\pi$
$558$		0			0
$559$	1.88013e8			1.07635
$560$		0			0
$561$	2.39623e8	+	2.09785e7i	1.35719	+	0.118819i
$562$		0			0
$563$	1.63635e8	+	1.63635e8i	0.916963	+	0.916963i	0.996807	−	0.0798445i	$-0.0254424\pi$
$563$	1.63635e8	+	1.63635e8i	0.916963	+	0.916963i	−0.0798445	+	0.996807i	$0.525442\pi$
$564$		0			0
$565$	1.07683e7	+	1.07683e7i	0.0597036	+	0.0597036i
$566$		0			0
$567$	5.64795e7	−	1.55063e8i	0.309843	−	0.850665i
$568$		0			0
$569$	2.26122e8			1.22745			0.613727	−	0.789518i	$-0.289670\pi$
$569$	2.26122e8			1.22745			0.613727	+	0.789518i	$0.289670\pi$
$570$		0			0
$571$	7.51046e7	+	7.51046e7i	0.403421	+	0.403421i	0.879437	−	0.476016i	$-0.157920\pi$
$571$	7.51046e7	+	7.51046e7i	0.403421	+	0.403421i	−0.476016	+	0.879437i	$0.657920\pi$
$572$		0			0
$573$	−5.91605e7	−	7.05132e7i	−0.314462	−	0.374806i
$574$		0			0
$575$		−	1.04745e7i		−	0.0550973i
$576$		0			0
$577$	1.40140e8			0.729513			0.364757	−	0.931103i	$-0.381152\pi$
$577$	1.40140e8			0.729513			0.364757	+	0.931103i	$0.381152\pi$
$578$		0			0
$579$	1.26486e8	−	1.06122e8i	0.651639	−	0.546725i
$580$		0			0
$581$	−2.08626e8	+	2.08626e8i	−1.06375	+	1.06375i
$582$		0			0
$583$		−	4.09500e8i		−	2.06656i
$584$		0			0
$585$	−1.59043e8	−	2.80629e7i	−0.794416	−	0.140173i
$586$		0			0
$587$	−8.78044e7	+	8.78044e7i	−0.434112	+	0.434112i	−0.890025	−	0.455913i	$-0.849313\pi$
$587$	−8.78044e7	+	8.78044e7i	−0.434112	+	0.434112i	0.455913	+	0.890025i	$0.349313\pi$
$588$		0			0
$589$	7.20884e7	−	7.20884e7i	0.352793	−	0.352793i
$590$		0			0
$591$	2.33790e7	−	2.67043e8i	0.113257	−	1.29365i
$592$		0			0
$593$			8.83985e7i			0.423917i	0.977279	+	0.211959i	$0.0679842\pi$
$593$			8.83985e7i			0.423917i	−0.977279	+	0.211959i	$0.932016\pi$
$594$		0			0
$595$	1.48357e8	−	1.48357e8i	0.704301	−	0.704301i
$596$		0			0
$597$	7.66385e7	+	9.13451e7i	0.360184	+	0.429301i
$598$		0			0
$599$	−8.79846e7			−0.409380			−0.204690	−	0.978827i	$-0.565619\pi$
$599$	−8.79846e7			−0.409380			−0.204690	+	0.978827i	$0.565619\pi$
$600$		0			0
$601$			1.41134e8i			0.650142i	0.945690	+	0.325071i	$0.105388\pi$
$601$			1.41134e8i			0.650142i	−0.945690	+	0.325071i	$0.894612\pi$
$602$		0			0
$603$	−2.08578e8	−	2.97954e8i	−0.951296	−	1.35893i
$604$		0			0
$605$	2.63359e7	+	2.63359e7i	0.118927	+	0.118927i
$606$		0			0
$607$	5.90432e7			0.264000			0.132000	−	0.991250i	$-0.457860\pi$
$607$	5.90432e7			0.264000			0.132000	+	0.991250i	$0.457860\pi$
$608$		0			0
$609$	1.81320e7	−	2.07110e8i	0.0802775	−	0.916956i
$610$		0			0
$611$	5.58022e7	+	5.58022e7i	0.244640	+	0.244640i
$612$		0			0
$613$	−1.57380e8	−	1.57380e8i	−0.683234	−	0.683234i	0.277494	−	0.960727i	$-0.410496\pi$
$613$	−1.57380e8	−	1.57380e8i	−0.683234	−	0.683234i	−0.960727	+	0.277494i	$0.910496\pi$
$614$		0			0
$615$	2.11807e7	−	2.41933e8i	0.0910575	−	1.04009i
$616$		0			0
$617$	−1.38269e7			−0.0588669			−0.0294334	−	0.999567i	$-0.509370\pi$
$617$	−1.38269e7			−0.0588669			−0.0294334	+	0.999567i	$0.509370\pi$
$618$		0			0
$619$	1.34517e7	+	1.34517e7i	0.0567159	+	0.0567159i	0.734896	−	0.678180i	$-0.237231\pi$
$619$	1.34517e7	+	1.34517e7i	0.0567159	+	0.0567159i	−0.678180	+	0.734896i	$0.737231\pi$
$620$		0			0
$621$	−2.95212e7	−	5.11531e7i	−0.123271	−	0.213598i
$622$		0			0
$623$		−	8.97487e7i		−	0.371163i
$624$		0			0
$625$	1.77411e8			0.726674
$626$		0			0
$627$	2.26328e8	+	2.69759e8i	0.918195	+	1.09439i
$628$		0			0
$629$	5.76502e7	−	5.76502e7i	0.231659	−	0.231659i
$630$		0			0
$631$			1.19101e7i			0.0474053i	0.999719	+	0.0237026i	$0.00754549\pi$
$631$			1.19101e7i			0.0474053i	−0.999719	+	0.0237026i	$0.992455\pi$
$632$		0			0
$633$	2.91200e7	−	3.32618e8i	0.114810	−	1.31140i
$634$		0			0
$635$	2.87491e7	−	2.87491e7i	0.112280	−	0.112280i
$636$		0			0
$637$	−3.01765e7	+	3.01765e7i	−0.116748	+	0.116748i
$638$		0			0
$639$	4.47350e7	−	2.53531e8i	0.171453	−	0.971690i
$640$		0			0
$641$		−	2.81769e8i		−	1.06984i	−0.844902	−	0.534921i	$-0.820341\pi$
$641$		−	2.81769e8i		−	1.06984i	0.844902	−	0.534921i	$-0.179659\pi$
$642$		0			0
$643$	−3.91150e7	+	3.91150e7i	−0.147133	+	0.147133i	−0.776836	−	0.629703i	$-0.783177\pi$
$643$	−3.91150e7	+	3.91150e7i	−0.147133	+	0.147133i	0.629703	+	0.776836i	$0.283177\pi$
$644$		0			0
$645$	−2.13005e8	+	1.78711e8i	−0.793801	+	0.665998i
$646$		0			0
$647$	2.11543e8			0.781064			0.390532	−	0.920589i	$-0.372291\pi$
$647$	2.11543e8			0.781064			0.390532	+	0.920589i	$0.372291\pi$
$648$		0			0
$649$		−	2.88120e8i		−	1.05400i
$650$		0			0
$651$	6.11865e7	+	7.29280e7i	0.221775	+	0.264333i
$652$		0			0
$653$	−1.91048e8	−	1.91048e8i	−0.686124	−	0.686124i	0.275249	−	0.961373i	$-0.411240\pi$
$653$	−1.91048e8	−	1.91048e8i	−0.686124	−	0.686124i	−0.961373	+	0.275249i	$0.911240\pi$
$654$		0			0
$655$	−3.20282e8			−1.13975
$656$		0			0
$657$	−2.62581e8	−	4.63318e7i	−0.925905	−	0.163374i
$658$		0			0
$659$	−8.63327e7	−	8.63327e7i	−0.301661	−	0.301661i	0.540003	−	0.841663i	$-0.318423\pi$
$659$	−8.63327e7	−	8.63327e7i	−0.301661	−	0.301661i	−0.841663	+	0.540003i	$0.818423\pi$
$660$		0			0
$661$	7.97831e7	+	7.97831e7i	0.276253	+	0.276253i	0.831611	−	0.555358i	$-0.187419\pi$
$661$	7.97831e7	+	7.97831e7i	0.276253	+	0.276253i	−0.555358	+	0.831611i	$0.687419\pi$
$662$		0			0
$663$	3.31789e8	+	2.90474e7i	1.13847	+	0.0996705i
$664$		0			0
$665$	3.07142e8			1.04442
$666$		0			0
$667$	−5.26115e7	−	5.26115e7i	−0.177298	−	0.177298i
$668$		0			0
$669$	1.58681e8	−	1.33134e8i	0.529966	−	0.444641i
$670$		0			0
$671$			5.74779e8i			1.90254i
$672$		0			0
$673$	−3.42984e8			−1.12520			−0.562598	−	0.826730i	$-0.690198\pi$
$673$	−3.42984e8			−1.12520			−0.562598	+	0.826730i	$0.690198\pi$
$674$		0			0
$675$	−5.95106e7	+	3.43445e7i	−0.193501	+	0.111672i
$676$		0			0
$677$	−1.34358e8	+	1.34358e8i	−0.433010	+	0.433010i	−0.889651	−	0.456641i	$-0.849052\pi$
$677$	−1.34358e8	+	1.34358e8i	−0.433010	+	0.433010i	0.456641	+	0.889651i	$0.349052\pi$
$678$		0			0
$679$			1.10774e8i			0.353858i
$680$		0			0
$681$	1.15279e8	+	1.00925e7i	0.365015	+	0.0319563i
$682$		0			0
$683$	−1.06305e8	+	1.06305e8i	−0.333651	+	0.333651i	−0.853971	−	0.520320i	$-0.825813\pi$
$683$	−1.06305e8	+	1.06305e8i	−0.333651	+	0.333651i	0.520320	+	0.853971i	$0.325813\pi$
$684$		0			0
$685$	−2.50924e8	+	2.50924e8i	−0.780677	+	0.780677i
$686$		0			0
$687$	2.12042e8	+	1.85638e7i	0.653960	+	0.0572528i
$688$		0			0
$689$		−	5.67006e8i		−	1.73352i
$690$		0			0
$691$	−4.39787e7	+	4.39787e7i	−0.133293	+	0.133293i	−0.770606	−	0.637312i	$-0.780046\pi$
$691$	−4.39787e7	+	4.39787e7i	−0.133293	+	0.133293i	0.637312	+	0.770606i	$0.280046\pi$
$692$		0			0
$693$	−2.69364e8	+	1.88563e8i	−0.809356	+	0.566575i
$694$		0			0
$695$	−1.99181e8			−0.593325
$696$		0			0
$697$			5.00841e8i			1.47911i
$698$		0			0
$699$	−4.78452e8	+	4.01421e8i	−1.40090	+	1.17535i
$700$		0			0
$701$	2.30678e8	+	2.30678e8i	0.669657	+	0.669657i	0.957637	−	0.287980i	$-0.0929836\pi$
$701$	2.30678e8	+	2.30678e8i	0.669657	+	0.669657i	−0.287980	+	0.957637i	$0.592984\pi$
$702$		0			0
$703$	1.19352e8			0.343530
$704$		0			0
$705$	−1.16262e8	−	1.01785e7i	−0.331794	−	0.0290479i
$706$		0			0
$707$	−2.24657e8	−	2.24657e8i	−0.635715	−	0.635715i
$708$		0			0
$709$	8.22692e6	+	8.22692e6i	0.0230833	+	0.0230833i	0.718554	−	0.695471i	$-0.244804\pi$
$709$	8.22692e6	+	8.22692e6i	0.0230833	+	0.0230833i	−0.695471	+	0.718554i	$0.744804\pi$
$710$		0			0
$711$	−5.94664e7	+	3.37019e8i	−0.165448	+	0.937661i
$712$		0			0
$713$	3.40688e7			0.0939913
$714$		0			0
$715$	2.27530e8	+	2.27530e8i	0.622472	+	0.622472i
$716$		0			0
$717$	1.40722e8	+	1.67726e8i	0.381773	+	0.455034i
$718$		0			0
$719$		−	1.76750e8i		−	0.475525i	−0.971323	−	0.237762i	$-0.923586\pi$
$719$		−	1.76750e8i		−	0.475525i	0.971323	−	0.237762i	$-0.0764139\pi$
$720$		0			0
$721$	2.72765e8			0.727751
$722$		0			0
$723$	−1.15890e8	+	9.72315e7i	−0.306641	+	0.257272i
$724$		0			0
$725$	−6.12074e7	+	6.12074e7i	−0.160616	+	0.160616i
$726$		0			0
$727$			4.03065e8i			1.04899i	0.851413	+	0.524495i	$0.175746\pi$
$727$			4.03065e8i			1.04899i	−0.851413	+	0.524495i	$0.824254\pi$
$728$		0			0
$729$	−1.93828e8	+	3.35448e8i	−0.500305	+	0.865849i
$730$		0			0
$731$	4.05459e8	−	4.05459e8i	1.03799	−	1.03799i
$732$		0			0
$733$	4.11168e8	−	4.11168e8i	1.04402	−	1.04402i	0.0450300	−	0.998986i	$-0.485662\pi$
$733$	4.11168e8	−	4.11168e8i	1.04402	−	1.04402i	0.998986	−	0.0450300i	$-0.0143384\pi$
$734$		0			0
$735$	5.50428e6	−	6.28716e7i	0.0138624	−	0.158341i
$736$		0			0
$737$			7.24651e8i			1.81020i
$738$		0			0
$739$	1.14783e8	−	1.14783e8i	0.284409	−	0.284409i	−0.550455	−	0.834865i	$-0.685546\pi$
$739$	1.14783e8	−	1.14783e8i	0.284409	−	0.284409i	0.834865	+	0.550455i	$0.185546\pi$
$740$		0			0
$741$	3.13380e8	+	3.73516e8i	0.770223	+	0.918025i
$742$		0			0
$743$	−2.26310e8			−0.551744			−0.275872	−	0.961194i	$-0.588967\pi$
$743$	−2.26310e8			−0.551744			−0.275872	+	0.961194i	$0.588967\pi$
$744$		0			0
$745$		−	4.80518e8i		−	1.16209i
$746$		0			0
$747$	5.67424e8	−	3.97215e8i	1.36127	−	0.952936i
$748$		0			0
$749$	2.95884e8	+	2.95884e8i	0.704166	+	0.704166i
$750$		0			0
$751$	−5.05620e8			−1.19373			−0.596863	−	0.802343i	$-0.703586\pi$
$751$	−5.05620e8			−1.19373			−0.596863	+	0.802343i	$0.703586\pi$
$752$		0			0
$753$	−2.32436e7	+	2.65496e8i	−0.0544400	+	0.621831i
$754$		0			0
$755$	−2.90994e8	−	2.90994e8i	−0.676151	−	0.676151i
$756$		0			0
$757$	−3.02200e7	−	3.02200e7i	−0.0696637	−	0.0696637i	0.671416	−	0.741080i	$-0.265686\pi$
$757$	−3.02200e7	−	3.02200e7i	−0.0696637	−	0.0696637i	−0.741080	+	0.671416i	$0.765686\pi$
$758$		0			0
$759$	−1.02628e7	+	1.17225e8i	−0.0234714	+	0.268098i
$760$		0			0
$761$	1.46101e8			0.331513			0.165756	−	0.986167i	$-0.446993\pi$
$761$	1.46101e8			0.331513			0.165756	+	0.986167i	$0.446993\pi$
$762$		0			0
$763$	−2.11256e8	−	2.11256e8i	−0.475593	−	0.475593i
$764$		0			0
$765$	−4.03504e8	+	2.82466e8i	−0.901288	+	0.630931i
$766$		0			0
$767$		−	3.98939e8i		−	0.884140i
$768$		0			0
$769$	−3.00236e8			−0.660213			−0.330107	−	0.943944i	$-0.607085\pi$
$769$	−3.00236e8			−0.660213			−0.330107	+	0.943944i	$0.607085\pi$
$770$		0			0
$771$	−1.82330e8	−	2.17318e8i	−0.397828	−	0.474169i
$772$		0			0
$773$	5.62030e8	−	5.62030e8i	1.21680	−	1.21680i	0.248060	−	0.968745i	$-0.420207\pi$
$773$	5.62030e8	−	5.62030e8i	1.21680	−	1.21680i	0.968745	−	0.248060i	$-0.0797931\pi$
$774$		0			0
$775$		−	3.96350e7i		−	0.0851479i
$776$		0			0
$777$	−9.71978e6	+	1.11022e8i	−0.0207202	+	0.236672i
$778$		0			0
$779$	−5.18441e8	+	5.18441e8i	−1.09670	+	1.09670i
$780$		0			0
$781$	−3.62704e8	+	3.62704e8i	−0.761377	+	0.761377i
$782$		0			0
$783$	−1.26405e8	+	4.71417e8i	−0.263317	+	0.982019i
$784$		0			0
$785$			2.03920e8i			0.421553i
$786$		0			0
$787$	−2.21139e8	+	2.21139e8i	−0.453671	+	0.453671i	−0.896571	−	0.442900i	$-0.853950\pi$
$787$	−2.21139e8	+	2.21139e8i	−0.453671	+	0.453671i	0.442900	+	0.896571i	$0.353950\pi$
$788$		0			0
$789$	7.11419e8	−	5.96880e8i	1.44842	−	1.21522i
$790$		0			0
$791$	4.29299e7			0.0867421
$792$		0			0
$793$			7.95855e8i			1.59593i
$794$		0			0
$795$	5.38955e8	+	6.42379e8i	1.07263	+	1.27847i
$796$		0			0
$797$	−2.76872e8	−	2.76872e8i	−0.546895	−	0.546895i	0.378647	−	0.925541i	$-0.376390\pi$
$797$	−2.76872e8	−	2.76872e8i	−0.546895	−	0.546895i	−0.925541	+	0.378647i	$0.876390\pi$
$798$		0			0
$799$	2.40680e8			0.471846
$800$		0			0
$801$	−3.66110e7	+	2.07489e8i	−0.0712383	+	0.403735i
$802$		0			0
$803$	3.75651e8	+	3.75651e8i	0.725501	+	0.725501i
$804$		0			0
$805$	7.25771e7	+	7.25771e7i	0.139127	+	0.139127i
$806$		0			0
$807$	5.60716e7	+	4.90895e6i	0.106690	+	0.00934046i
$808$		0			0
$809$	−6.13120e8			−1.15798			−0.578988	−	0.815336i	$-0.696552\pi$
$809$	−6.13120e8			−1.15798			−0.578988	+	0.815336i	$0.696552\pi$
$810$		0			0
$811$	−5.50342e8	−	5.50342e8i	−1.03174	−	1.03174i	−0.999479	−	0.0322606i	$-0.989729\pi$
$811$	−5.50342e8	−	5.50342e8i	−1.03174	−	1.03174i	−0.0322606	−	0.999479i	$-0.510271\pi$
$812$		0			0
$813$	−5.38541e7	+	4.51836e7i	−0.100218	+	0.0840831i
$814$		0			0
$815$			9.20858e6i			0.0170106i
$816$		0			0
$817$	8.39413e8			1.53925
$818$		0			0
$819$	−3.72969e8	+	2.61090e8i	−0.678923	+	0.475268i
$820$		0			0
$821$	2.13638e8	−	2.13638e8i	0.386055	−	0.386055i	−0.487223	−	0.873278i	$-0.661990\pi$
$821$	2.13638e8	−	2.13638e8i	0.386055	−	0.386055i	0.873278	+	0.487223i	$0.161990\pi$
$822$		0			0
$823$		−	6.57403e8i		−	1.17932i	−0.807651	−	0.589661i	$-0.799261\pi$
$823$		−	6.57403e8i		−	1.17932i	0.807651	−	0.589661i	$-0.200739\pi$
$824$		0			0
$825$	1.36377e8	+	1.19395e7i	0.242873	+	0.0212630i
$826$		0			0
$827$	1.81552e8	−	1.81552e8i	0.320985	−	0.320985i	−0.528160	−	0.849145i	$-0.677118\pi$
$827$	1.81552e8	−	1.81552e8i	0.320985	−	0.320985i	0.849145	+	0.528160i	$0.177118\pi$
$828$		0			0
$829$	7.81081e7	−	7.81081e7i	0.137098	−	0.137098i	−0.635227	−	0.772325i	$-0.719093\pi$
$829$	7.81081e7	−	7.81081e7i	0.137098	−	0.137098i	0.772325	+	0.635227i	$0.219093\pi$
$830$		0			0
$831$	8.41330e8	+	7.36566e7i	1.46610	+	0.128354i
$832$		0			0
$833$			1.30154e8i			0.225177i
$834$		0			0
$835$	1.77869e8	−	1.77869e8i	0.305521	−	0.305521i
$836$		0			0
$837$	−1.11707e8	−	1.93561e8i	−0.190504	−	0.330096i
$838$		0			0
$839$	4.70764e8			0.797109			0.398554	−	0.917145i	$-0.369512\pi$
$839$	4.70764e8			0.797109			0.398554	+	0.917145i	$0.369512\pi$
$840$		0			0
$841$			2.00434e7i			0.0336965i
$842$		0			0
$843$	6.98283e7	−	5.85859e7i	0.116560	−	0.0977936i
$844$		0			0
$845$	−6.09232e7	−	6.09232e7i	−0.100975	−	0.100975i
$846$		0			0
$847$	1.04993e8			0.172787
$848$		0			0
$849$	1.05465e9	+	9.23324e7i	1.72340	+	0.150880i
$850$		0			0
$851$	2.82027e7	+	2.82027e7i	0.0457618	+	0.0457618i
$852$		0			0
$853$	5.14265e7	+	5.14265e7i	0.0828590	+	0.0828590i	0.747322	−	0.664463i	$-0.231339\pi$
$853$	5.14265e7	+	5.14265e7i	0.0828590	+	0.0828590i	−0.664463	+	0.747322i	$0.731339\pi$
$854$		0			0
$855$	−7.10076e8	−	1.25292e8i	−1.13607	−	0.200458i
$856$		0			0
$857$	−9.46343e8			−1.50351			−0.751755	−	0.659443i	$-0.770792\pi$
$857$	−9.46343e8			−1.50351			−0.751755	+	0.659443i	$0.770792\pi$
$858$		0			0
$859$	6.35758e8	+	6.35758e8i	1.00303	+	1.00303i	0.999995	+	0.00303137i	$0.000964917\pi$
$859$	6.35758e8	+	6.35758e8i	1.00303	+	1.00303i	0.00303137	+	0.999995i	$0.499035\pi$
$860$		0			0
$861$	−4.40037e8	−	5.24478e8i	−0.689414	−	0.821709i
$862$		0			0
$863$		−	2.56659e7i		−	0.0399322i	−0.999801	−	0.0199661i	$-0.993644\pi$
$863$		−	2.56659e7i		−	0.0399322i	0.999801	−	0.0199661i	$-0.00635583\pi$
$864$		0			0
$865$	−5.41374e8			−0.836468
$866$		0			0
$867$	2.78894e8	−	2.33992e8i	0.427939	−	0.359041i
$868$		0			0
$869$	4.82144e8	−	4.82144e8i	0.734713	−	0.734713i
$870$		0			0
$871$			1.00337e9i			1.51848i
$872$		0			0
$873$	4.51878e7	−	2.56097e8i	0.0679169	−	0.384912i
$874$		0			0
$875$	4.62367e8	−	4.62367e8i	0.690181	−	0.690181i
$876$		0			0
$877$	−6.11052e7	+	6.11052e7i	−0.0905898	+	0.0905898i	−0.750949	−	0.660360i	$-0.770404\pi$
$877$	−6.11052e7	+	6.11052e7i	−0.0905898	+	0.0905898i	0.660360	+	0.750949i	$0.270404\pi$
$878$		0			0
$879$	−1.09845e8	+	1.25468e9i	−0.161738	+	1.84743i
$880$		0			0
$881$			3.34838e8i			0.489674i	0.969564	+	0.244837i	$0.0787344\pi$
$881$			3.34838e8i			0.489674i	−0.969564	+	0.244837i	$0.921266\pi$
$882$		0			0
$883$	−4.79823e8	+	4.79823e8i	−0.696945	+	0.696945i	−0.963751	−	0.266805i	$-0.914032\pi$
$883$	−4.79823e8	+	4.79823e8i	−0.696945	+	0.696945i	0.266805	+	0.963751i	$0.414032\pi$
$884$		0			0
$885$	3.79203e8	+	4.51971e8i	0.547069	+	0.652050i
$886$		0			0
$887$	7.22095e8			1.03472			0.517361	−	0.855767i	$-0.326915\pi$
$887$	7.22095e8			1.03472			0.517361	+	0.855767i	$0.326915\pi$
$888$		0			0
$889$		−	1.14614e8i		−	0.163130i
$890$		0			0
$891$	6.99658e8	−	3.26056e8i	0.989128	−	0.460955i
$892$		0			0
$893$	2.49138e8	+	2.49138e8i	0.349853	+	0.349853i
$894$		0			0
$895$	−4.54122e8			−0.633438
$896$		0			0
$897$	−1.42101e7	+	1.62313e8i	−0.0196888	+	0.224892i
$898$		0			0
$899$	−1.99079e8	−	1.99079e8i	−0.273998	−	0.273998i
$900$		0			0
$901$	−1.22278e9	−	1.22278e9i	−1.67176	−	1.67176i
$902$		0			0
$903$	−6.83599e7	+	7.80829e8i	−0.0928407	+	1.06046i
$904$		0			0
$905$	−9.12973e8			−1.23172
$906$		0			0
$907$	−3.01488e8	−	3.01488e8i	−0.404062	−	0.404062i	0.475600	−	0.879662i	$-0.342231\pi$
$907$	−3.01488e8	−	3.01488e8i	−0.404062	−	0.404062i	−0.879662	+	0.475600i	$0.842231\pi$
$908$		0			0
$909$	4.27738e8	+	6.11026e8i	0.569490	+	0.813519i
$910$		0			0
$911$			8.37188e8i			1.10731i	0.832747	+	0.553654i	$0.186767\pi$
$911$			8.37188e8i			1.10731i	−0.832747	+	0.553654i	$0.813233\pi$
$912$		0			0
$913$	−1.38003e9			−1.81332
$914$		0			0
$915$	−7.56483e8	−	9.01649e8i	−0.987498	−	1.17699i
$916$		0			0
$917$	−6.38434e8	+	6.38434e8i	−0.827958	+	0.827958i
$918$		0			0
$919$		−	1.00319e9i		−	1.29251i	−0.763120	−	0.646257i	$-0.776333\pi$
$919$		−	1.00319e9i		−	1.29251i	0.763120	−	0.646257i	$-0.223667\pi$
$920$		0			0
$921$	−1.17199e8	+	1.33868e9i	−0.150018	+	1.71356i
$922$		0			0
$923$	−5.02211e8	+	5.02211e8i	−0.638676	+	0.638676i
$924$		0			0
$925$	3.28106e7	−	3.28106e7i	0.0414561	−	0.0414561i
$926$		0			0
$927$	−6.30601e8	−	1.11268e8i	−0.791618	−	0.139680i
$928$		0			0
$929$			3.39676e8i			0.423660i	0.977307	+	0.211830i	$0.0679423\pi$
$929$			3.39676e8i			0.423660i	−0.977307	+	0.211830i	$0.932058\pi$
$930$		0			0
$931$	−1.34728e8	+	1.34728e8i	−0.166959	+	0.166959i
$932$		0			0
$933$	2.33443e8	−	1.95859e8i	0.287433	−	0.241156i
$934$		0			0
$935$	9.81358e8			1.20058
$936$		0			0
$937$		−	1.22832e9i		−	1.49311i	−0.665324	−	0.746554i	$-0.731707\pi$
$937$		−	1.22832e9i		−	1.49311i	0.665324	−	0.746554i	$-0.268293\pi$
$938$		0			0
$939$	−3.02859e8	−	3.60976e8i	−0.365800	−	0.435995i
$940$		0			0
$941$	−2.73475e8	−	2.73475e8i	−0.328208	−	0.328208i	0.523697	−	0.851905i	$-0.324552\pi$
$941$	−2.73475e8	−	2.73475e8i	−0.328208	−	0.328208i	−0.851905	+	0.523697i	$0.824552\pi$
$942$		0			0
$943$	−2.45014e8			−0.292183
$944$		0			0
$945$	1.74374e8	−	6.50315e8i	0.206627	−	0.770599i
$946$		0			0
$947$	2.23209e8	+	2.23209e8i	0.262822	+	0.262822i	0.826200	−	0.563378i	$-0.190498\pi$
$947$	2.23209e8	+	2.23209e8i	0.262822	+	0.262822i	−0.563378	+	0.826200i	$0.690498\pi$
$948$		0			0
$949$	5.20138e8	+	5.20138e8i	0.608583	+	0.608583i
$950$		0			0
$951$	5.61352e8	+	4.91452e7i	0.652670	+	0.0571399i
$952$		0			0
$953$	−1.15460e9			−1.33399			−0.666995	−	0.745062i	$-0.732420\pi$
$953$	−1.15460e9			−1.33399			−0.666995	+	0.745062i	$0.732420\pi$
$954$		0			0
$955$	−2.65535e8	−	2.65535e8i	−0.304867	−	0.304867i
$956$		0			0
$957$	7.44967e8	−	6.25027e8i	0.849965	−	0.713120i
$958$		0			0
$959$			1.00036e9i			1.13423i
$960$		0			0
$961$	−7.58589e8			−0.854745
$962$		0			0
$963$	−5.63349e8	−	8.04747e8i	−0.630810	−	0.901116i
$964$		0			0
$965$	4.76315e8	−	4.76315e8i	0.530044	−	0.530044i
$966$		0			0
$967$		−	5.96724e8i		−	0.659924i	−0.943994	−	0.329962i	$-0.892964\pi$
$967$		−	5.96724e8i		−	0.659924i	0.943994	−	0.329962i	$-0.107036\pi$
$968$		0			0
$969$	1.48132e9	+	1.29687e8i	1.62809	+	0.142536i
$970$		0			0
$971$	−3.36566e8	+	3.36566e8i	−0.367631	+	0.367631i	−0.866613	−	0.498982i	$-0.833708\pi$
$971$	−3.36566e8	+	3.36566e8i	−0.367631	+	0.367631i	0.498982	+	0.866613i	$0.333708\pi$
$972$		0			0
$973$	−3.97037e8	+	3.97037e8i	−0.431015	+	0.431015i
$974$		0			0
$975$	1.88832e8	+	1.65318e7i	0.203733	+	0.0178364i
$976$		0			0
$977$		−	8.45394e8i		−	0.906516i	−0.891379	−	0.453258i	$-0.850262\pi$
$977$		−	8.45394e8i		−	0.906516i	0.891379	−	0.453258i	$-0.149738\pi$
$978$		0			0
$979$	2.96836e8	−	2.96836e8i	0.316351	−	0.316351i
$980$		0			0
$981$	4.02222e8	+	5.74576e8i	0.426048	+	0.608612i
$982$		0			0
$983$	3.82375e7			0.0402558			0.0201279	−	0.999797i	$-0.493593\pi$
$983$	3.82375e7			0.0402558			0.0201279	+	0.999797i	$0.493593\pi$
$984$		0			0
$985$		−	1.09365e9i		−	1.14438i
$986$		0			0
$987$	−2.52039e8	+	2.11461e8i	−0.262130	+	0.219927i
$988$		0			0
$989$	1.98352e8	+	1.98352e8i	0.205044	+	0.205044i
$990$		0			0
$991$	1.25057e9			1.28495			0.642474	−	0.766307i	$-0.277908\pi$
$991$	1.25057e9			1.28495			0.642474	+	0.766307i	$0.277908\pi$
$992$		0			0
$993$	3.47031e7	+	3.03818e6i	0.0354422	+	0.00310289i
$994$		0			0
$995$	3.43982e8	+	3.43982e8i	0.349194	+	0.349194i
$996$		0			0
$997$	−3.82791e8	−	3.82791e8i	−0.386257	−	0.386257i	0.487093	−	0.873350i	$-0.338057\pi$
$997$	−3.82791e8	−	3.82791e8i	−0.386257	−	0.386257i	−0.873350	+	0.487093i	$0.838057\pi$
$998$		0			0
$999$	6.77601e7	−	2.52706e8i	0.0679638	−	0.253466i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	192.7.i.a.113.9		92
3.2	odd	2	inner	192.7.i.a.113.14		92
4.3	odd	2		48.7.i.a.5.37	yes	92
12.11	even	2		48.7.i.a.5.10	✓	92
16.3	odd	4		48.7.i.a.29.10	yes	92
16.13	even	4	inner	192.7.i.a.17.14		92
48.29	odd	4	inner	192.7.i.a.17.9		92
48.35	even	4		48.7.i.a.29.37	yes	92

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.7.i.a.5.10	✓	92	12.11	even	2
48.7.i.a.5.37	yes	92	4.3	odd	2
48.7.i.a.29.10	yes	92	16.3	odd	4
48.7.i.a.29.37	yes	92	48.35	even	4
192.7.i.a.17.9		92	48.29	odd	4	inner
192.7.i.a.17.14		92	16.13	even	4	inner
192.7.i.a.113.9		92	1.1	even	1	trivial
192.7.i.a.113.14		92	3.2	odd	2	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	192.i (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-20.6842 + 17.3541i) q^{3} +(-77.8915 + 77.8915i) q^{5} +310.530i q^{7} +(126.674 - 717.910i) q^{9} +O(q^{10})\)	\(q+(-20.6842 + 17.3541i) q^{3} +(-77.8915 + 77.8915i) q^{5} +310.530i q^{7} +(126.674 - 717.910i) q^{9} +(-1027.05 + 1027.05i) q^{11} +(-1422.09 + 1422.09i) q^{13} +(259.392 - 2962.86i) q^{15} +6133.59i q^{17} +(-6349.13 + 6349.13i) q^{19} +(-5388.96 - 6423.08i) q^{21} -3000.58 q^{23} +3490.83i q^{25} +(9838.50 + 17047.7i) q^{27} +(17533.8 + 17533.8i) q^{29} -11354.1 q^{31} +(3420.26 - 39067.3i) q^{33} +(-24187.7 - 24187.7i) q^{35} +(-9399.09 - 9399.09i) q^{37} +(4735.79 - 54093.7i) q^{39} +81655.3 q^{41} +(-66104.5 - 66104.5i) q^{43} +(46052.3 + 65785.9i) q^{45} -39239.7i q^{47} +21219.9 q^{49} +(-106443. - 126869. i) q^{51} +(-199357. + 199357. i) q^{53} -159997. i q^{55} +(21143.7 - 241510. i) q^{57} +(-140266. + 140266. i) q^{59} +(279820. - 279820. i) q^{61} +(222933. + 39336.1i) q^{63} -221537. i q^{65} +(352782. - 352782. i) q^{67} +(62064.7 - 52072.3i) q^{69} +353151. q^{71} -365757. i q^{73} +(-60580.0 - 72205.0i) q^{75} +(-318931. - 318931. i) q^{77} -469445. q^{79} +(-499348. - 181881. i) q^{81} +(671838. + 671838. i) q^{83} +(-477755. - 477755. i) q^{85} +(-666955. - 58390.4i) q^{87} -289018. q^{89} +(-441601. - 441601. i) q^{91} +(234850. - 197039. i) q^{93} -989087. i q^{95} +356725. q^{97} +(607230. + 867431. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 92 q + 2 q^{3}+O(q^{10}) \) 92 * q + 2 * q^3	\( 92 q + 2 q^{3} - 4 q^{13} + 4 q^{15} + 3940 q^{19} + 1456 q^{21} + 34322 q^{27} + 8 q^{31} - 4 q^{33} - 4 q^{37} + 195268 q^{43} - 31252 q^{45} - 1142884 q^{49} - 385056 q^{51} - 326500 q^{61} - 470592 q^{63} - 1207676 q^{67} - 1460 q^{69} - 1413778 q^{75} - 860920 q^{79} - 4 q^{81} + 434496 q^{85} - 2320992 q^{91} - 1176260 q^{93} - 8 q^{97} + 4048228 q^{99}+O(q^{100}) \) 92 * q + 2 * q^3 - 4 * q^13 + 4 * q^15 + 3940 * q^19 + 1456 * q^21 + 34322 * q^27 + 8 * q^31 - 4 * q^33 - 4 * q^37 + 195268 * q^43 - 31252 * q^45 - 1142884 * q^49 - 385056 * q^51 - 326500 * q^61 - 470592 * q^63 - 1207676 * q^67 - 1460 * q^69 - 1413778 * q^75 - 860920 * q^79 - 4 * q^81 + 434496 * q^85 - 2320992 * q^91 - 1176260 * q^93 - 8 * q^97 + 4048228 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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