LMFDB - Embedded newform 192.9.e.c.65.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [192,9,Mod(65,192)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(192, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("192.65");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 192 = 2^{6} \cdot 3 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	192.e (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$78.2166931317$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{-2}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 2 $ x^2 + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	no (minimal twist has level 6)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			65.1
Root			$1.41421i$ of defining polynomial
Character	$\chi$	$=$	192.65
Dual form			192.9.e.c.65.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-63.0000 - 50.9117i) q^{3} +576.999i q^{5} -2786.00 q^{7} +(1377.00 + 6414.87i) q^{9} +O(q^{10})$	\(q+(-63.0000 - 50.9117i) q^{3} +576.999i q^{5} -2786.00 q^{7} +(1377.00 + 6414.87i) q^{9} -22435.1i q^{11} +13150.0 q^{13} +(29376.0 - 36350.9i) q^{15} +66388.8i q^{17} +144002. q^{19} +(175518. + 141840. i) q^{21} +49350.4i q^{23} +57697.0 q^{25} +(239841. - 474242. i) q^{27} -627402. i q^{29} -728738. q^{31} +(-1.14221e6 + 1.41341e6i) q^{33} -1.60752e6i q^{35} +1.96445e6 q^{37} +(-828450. - 669489. i) q^{39} -986125. i q^{41} -78142.0 q^{43} +(-3.70138e6 + 794528. i) q^{45} -3.51969e6i q^{47} +1.99700e6 q^{49} +(3.37997e6 - 4.18250e6i) q^{51} +522048. i q^{53} +1.29450e7 q^{55} +(-9.07213e6 - 7.33138e6i) q^{57} +5.00425e6i q^{59} -1.75783e7 q^{61} +(-3.83632e6 - 1.78718e7i) q^{63} +7.58754e6i q^{65} -1.71368e7 q^{67} +(2.51251e6 - 3.10907e6i) q^{69} +2.58906e7i q^{71} +2.81393e7 q^{73} +(-3.63491e6 - 2.93745e6i) q^{75} +6.25041e7i q^{77} -9.18250e6 q^{79} +(-3.92545e7 + 1.76666e7i) q^{81} +8.71084e7i q^{83} -3.83063e7 q^{85} +(-3.19421e7 + 3.95263e7i) q^{87} +8.12528e7i q^{89} -3.66359e7 q^{91} +(4.59105e7 + 3.71013e7i) q^{93} +8.30890e7i q^{95} -1.28723e8 q^{97} +(1.43918e8 - 3.08931e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 126 q^{3} - 5572 q^{7} + 2754 q^{9}+O(q^{10}) $ 2 * q - 126 * q^3 - 5572 * q^7 + 2754 * q^9	$ 2 q - 126 q^{3} - 5572 q^{7} + 2754 q^{9} + 26300 q^{13} + 58752 q^{15} + 288004 q^{19} + 351036 q^{21} + 115394 q^{25} + 479682 q^{27} - 1457476 q^{31} - 2284416 q^{33} + 3928892 q^{37} - 1656900 q^{39} - 156284 q^{43} - 7402752 q^{45} + 3993990 q^{49} + 6759936 q^{51} + 25890048 q^{55} - 18144252 q^{57} - 35156548 q^{61} - 7672644 q^{63} - 34273532 q^{67} + 5025024 q^{69} + 56278660 q^{73} - 7269822 q^{75} - 18364996 q^{79} - 78508926 q^{81} - 76612608 q^{85} - 63884160 q^{87} - 73271800 q^{91} + 91820988 q^{93} - 257445116 q^{97} + 287836416 q^{99}+O(q^{100}) $ 2 * q - 126 * q^3 - 5572 * q^7 + 2754 * q^9 + 26300 * q^13 + 58752 * q^15 + 288004 * q^19 + 351036 * q^21 + 115394 * q^25 + 479682 * q^27 - 1457476 * q^31 - 2284416 * q^33 + 3928892 * q^37 - 1656900 * q^39 - 156284 * q^43 - 7402752 * q^45 + 3993990 * q^49 + 6759936 * q^51 + 25890048 * q^55 - 18144252 * q^57 - 35156548 * q^61 - 7672644 * q^63 - 34273532 * q^67 + 5025024 * q^69 + 56278660 * q^73 - 7269822 * q^75 - 18364996 * q^79 - 78508926 * q^81 - 76612608 * q^85 - 63884160 * q^87 - 73271800 * q^91 + 91820988 * q^93 - 257445116 * q^97 + 287836416 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$65$	$127$	$133$
$\chi(n)$	$-1$	$1$	$1$

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
$3$	−63.0000	−	50.9117i	−0.777778	−	0.628539i
$3$	−63.0000	−	50.9117i	−0.777778	−	0.628539i
$4$		0			0
$5$			576.999i			0.923199i	0.887089	+	0.461599i	$0.152724\pi$
$5$			576.999i			0.923199i	−0.887089	+	0.461599i	$0.847276\pi$
$6$		0			0
$7$	−2786.00			−1.16035			−0.580175	−	0.814492i	$-0.697016\pi$
$7$	−2786.00			−1.16035			−0.580175	+	0.814492i	$0.697016\pi$
$8$		0			0
$9$	1377.00	+	6414.87i	0.209877	+	0.977728i
$10$		0			0
$11$		−	22435.1i		−	1.53235i	−0.642634	−	0.766173i	$-0.722158\pi$
$11$		−	22435.1i		−	1.53235i	0.642634	−	0.766173i	$-0.277842\pi$
$12$		0			0
$13$	13150.0			0.460418			0.230209	−	0.973141i	$-0.426059\pi$
$13$	13150.0			0.460418			0.230209	+	0.973141i	$0.426059\pi$
$14$		0			0
$15$	29376.0	−	36350.9i	0.580267	−	0.718043i
$16$		0			0
$17$			66388.8i			0.794876i	0.917629	+	0.397438i	$0.130101\pi$
$17$			66388.8i			0.794876i	−0.917629	+	0.397438i	$0.869899\pi$
$18$		0			0
$19$	144002.			1.10498			0.552490	−	0.833520i	$-0.313678\pi$
$19$	144002.			1.10498			0.552490	+	0.833520i	$0.313678\pi$
$20$		0			0
$21$	175518.	+	141840.i	0.902494	+	0.729326i
$22$		0			0
$23$			49350.4i			0.176352i	0.996105	+	0.0881758i	$0.0281037\pi$
$23$			49350.4i			0.176352i	−0.996105	+	0.0881758i	$0.971896\pi$
$24$		0			0
$25$	57697.0			0.147704
$26$		0			0
$27$	239841.	−	474242.i	0.451303	−	0.892371i
$28$		0			0
$29$		−	627402.i		−	0.887061i	−0.896259	−	0.443531i	$-0.853726\pi$
$29$		−	627402.i		−	0.887061i	0.896259	−	0.443531i	$-0.146274\pi$
$30$		0			0
$31$	−728738.			−0.789087			−0.394543	−	0.918877i	$-0.629097\pi$
$31$	−728738.			−0.789087			−0.394543	+	0.918877i	$0.629097\pi$
$32$		0			0
$33$	−1.14221e6	+	1.41341e6i	−0.963140	+	1.19182i
$34$		0			0
$35$		−	1.60752e6i		−	1.07123i
$36$		0			0
$37$	1.96445e6			1.04817			0.524087	−	0.851665i	$-0.324407\pi$
$37$	1.96445e6			1.04817			0.524087	+	0.851665i	$0.324407\pi$
$38$		0			0
$39$	−828450.	−	669489.i	−0.358103	−	0.289391i
$40$		0			0
$41$		−	986125.i		−	0.348977i	−0.984659	−	0.174488i	$-0.944173\pi$
$41$		−	986125.i		−	0.348977i	0.984659	−	0.174488i	$-0.0558272\pi$
$42$		0			0
$43$	−78142.0			−0.0228566			−0.0114283	−	0.999935i	$-0.503638\pi$
$43$	−78142.0			−0.0228566			−0.0114283	+	0.999935i	$0.503638\pi$
$44$		0			0
$45$	−3.70138e6	+	794528.i	−0.902637	+	0.193758i
$46$		0			0
$47$		−	3.51969e6i		−	0.721296i	−0.932702	−	0.360648i	$-0.882556\pi$
$47$		−	3.51969e6i		−	0.721296i	0.932702	−	0.360648i	$-0.117444\pi$
$48$		0			0
$49$	1.99700e6			0.346412
$50$		0			0
$51$	3.37997e6	−	4.18250e6i	0.499611	−	0.618237i
$52$		0			0
$53$			522048.i			0.0661618i	0.999453	+	0.0330809i	$0.0105319\pi$
$53$			522048.i			0.0661618i	−0.999453	+	0.0330809i	$0.989468\pi$
$54$		0			0
$55$	1.29450e7			1.41466
$56$		0			0
$57$	−9.07213e6	−	7.33138e6i	−0.859428	−	0.694523i
$58$		0			0
$59$			5.00425e6i			0.412981i	0.978449	+	0.206491i	$0.0662043\pi$
$59$			5.00425e6i			0.412981i	−0.978449	+	0.206491i	$0.933796\pi$
$60$		0			0
$61$	−1.75783e7			−1.26957			−0.634785	−	0.772689i	$-0.718911\pi$
$61$	−1.75783e7			−1.26957			−0.634785	+	0.772689i	$0.718911\pi$
$62$		0			0
$63$	−3.83632e6	−	1.78718e7i	−0.243530	−	1.13451i
$64$		0			0
$65$			7.58754e6i			0.425057i
$66$		0			0
$67$	−1.71368e7			−0.850413			−0.425206	−	0.905096i	$-0.639798\pi$
$67$	−1.71368e7			−0.850413			−0.425206	+	0.905096i	$0.639798\pi$
$68$		0			0
$69$	2.51251e6	−	3.10907e6i	0.110844	−	0.137162i
$70$		0			0
$71$			2.58906e7i			1.01885i	0.860516	+	0.509424i	$0.170141\pi$
$71$			2.58906e7i			1.01885i	−0.860516	+	0.509424i	$0.829859\pi$
$72$		0			0
$73$	2.81393e7			0.990883			0.495441	−	0.868641i	$-0.335006\pi$
$73$	2.81393e7			0.990883			0.495441	+	0.868641i	$0.335006\pi$
$74$		0			0
$75$	−3.63491e6	−	2.93745e6i	−0.114881	−	0.0928380i
$76$		0			0
$77$			6.25041e7i			1.77806i
$78$		0			0
$79$	−9.18250e6			−0.235750			−0.117875	−	0.993028i	$-0.537608\pi$
$79$	−9.18250e6			−0.235750			−0.117875	+	0.993028i	$0.537608\pi$
$80$		0			0
$81$	−3.92545e7	+	1.76666e7i	−0.911904	+	0.410404i
$82$		0			0
$83$			8.71084e7i			1.83547i	0.397190	+	0.917736i	$0.369985\pi$
$83$			8.71084e7i			1.83547i	−0.397190	+	0.917736i	$0.630015\pi$
$84$		0			0
$85$	−3.83063e7			−0.733828
$86$		0			0
$87$	−3.19421e7	+	3.95263e7i	−0.557553	+	0.689937i
$88$		0			0
$89$			8.12528e7i			1.29503i	0.762055	+	0.647513i	$0.224191\pi$
$89$			8.12528e7i			1.29503i	−0.762055	+	0.647513i	$0.775809\pi$
$90$		0			0
$91$	−3.66359e7			−0.534246
$92$		0			0
$93$	4.59105e7	+	3.71013e7i	0.613734	+	0.495972i
$94$		0			0
$95$			8.30890e7i			1.02012i
$96$		0			0
$97$	−1.28723e8			−1.45401			−0.727006	−	0.686632i	$-0.759089\pi$
$97$	−1.28723e8			−1.45401			−0.727006	+	0.686632i	$0.759089\pi$
$98$		0			0
$99$	1.43918e8	−	3.08931e7i	1.49822	−	0.321604i
$100$		0			0
$101$		−	9.37809e7i		−	0.901216i	−0.892722	−	0.450608i	$-0.851207\pi$
$101$		−	9.37809e7i		−	0.901216i	0.892722	−	0.450608i	$-0.148793\pi$
$102$		0			0
$103$	5.30322e7			0.471184			0.235592	−	0.971852i	$-0.424297\pi$
$103$	5.30322e7			0.471184			0.235592	+	0.971852i	$0.424297\pi$
$104$		0			0
$105$	−8.18415e7	+	1.01274e8i	−0.673312	+	0.833182i
$106$		0			0
$107$		−	1.90801e8i		−	1.45561i	−0.685785	−	0.727804i	$-0.740541\pi$
$107$		−	1.90801e8i		−	1.45561i	0.685785	−	0.727804i	$-0.259459\pi$
$108$		0			0
$109$	−2.71959e8			−1.92662			−0.963312	−	0.268384i	$-0.913510\pi$
$109$	−2.71959e8			−1.92662			−0.963312	+	0.268384i	$0.913510\pi$
$110$		0			0
$111$	−1.23760e8	−	1.00013e8i	−0.815246	−	0.658818i
$112$		0			0
$113$		−	7.69189e7i		−	0.471758i	−0.971782	−	0.235879i	$-0.924203\pi$
$113$		−	7.69189e7i		−	0.471758i	0.971782	−	0.235879i	$-0.0757969\pi$
$114$		0			0
$115$	−2.84751e7			−0.162808
$116$		0			0
$117$	1.81076e7	+	8.43556e7i	0.0966309	+	0.450164i
$118$		0			0
$119$		−	1.84959e8i		−	0.922334i
$120$		0			0
$121$	−2.88974e8			−1.34809
$122$		0			0
$123$	−5.02053e7	+	6.21259e7i	−0.219346	+	0.271427i
$124$		0			0
$125$			2.58681e8i			1.05956i
$126$		0			0
$127$	1.25417e8			0.482104			0.241052	−	0.970512i	$-0.422508\pi$
$127$	1.25417e8			0.482104			0.241052	+	0.970512i	$0.422508\pi$
$128$		0			0
$129$	4.92295e6	+	3.97834e6i	0.0177773	+	0.0143662i
$130$		0			0
$131$			1.24051e8i			0.421225i	0.977570	+	0.210612i	$0.0675458\pi$
$131$			1.24051e8i			0.421225i	−0.977570	+	0.210612i	$0.932454\pi$
$132$		0			0
$133$	−4.01190e8			−1.28216
$134$		0			0
$135$	2.73637e8	+	1.38388e8i	0.823835	+	0.416642i
$136$		0			0
$137$			5.50746e8i			1.56340i	0.623656	+	0.781699i	$0.285647\pi$
$137$			5.50746e8i			1.56340i	−0.623656	+	0.781699i	$0.714353\pi$
$138$		0			0
$139$	−7.59262e7			−0.203391			−0.101696	−	0.994816i	$-0.532427\pi$
$139$	−7.59262e7			−0.203391			−0.101696	+	0.994816i	$0.532427\pi$
$140$		0			0
$141$	−1.79194e8	+	2.21741e8i	−0.453363	+	0.561008i
$142$		0			0
$143$		−	2.95021e8i		−	0.705520i
$144$		0			0
$145$	3.62010e8			0.818934
$146$		0			0
$147$	−1.25811e8	−	1.01670e8i	−0.269431	−	0.217733i
$148$		0			0
$149$			7.35143e8i			1.49151i	0.666219	+	0.745756i	$0.267912\pi$
$149$			7.35143e8i			1.49151i	−0.666219	+	0.745756i	$0.732088\pi$
$150$		0			0
$151$	−3.01637e8			−0.580198			−0.290099	−	0.956997i	$-0.593688\pi$
$151$	−3.01637e8			−0.580198			−0.290099	+	0.956997i	$0.593688\pi$
$152$		0			0
$153$	−4.25876e8	+	9.14174e7i	−0.777172	+	0.166826i
$154$		0			0
$155$		−	4.20481e8i		−	0.728484i
$156$		0			0
$157$	1.61241e8			0.265386			0.132693	−	0.991157i	$-0.457638\pi$
$157$	1.61241e8			0.265386			0.132693	+	0.991157i	$0.457638\pi$
$158$		0			0
$159$	2.65784e7	−	3.28891e7i	0.0415853	−	0.0514592i
$160$		0			0
$161$		−	1.37490e8i		−	0.204630i
$162$		0			0
$163$	−2.21232e8			−0.313399			−0.156700	−	0.987646i	$-0.550085\pi$
$163$	−2.21232e8			−0.313399			−0.156700	+	0.987646i	$0.550085\pi$
$164$		0			0
$165$	−8.15537e8	−	6.59053e8i	−1.10029	−	0.889170i
$166$		0			0
$167$		−	4.01854e8i		−	0.516657i	−0.966057	−	0.258328i	$-0.916828\pi$
$167$		−	4.01854e8i		−	0.516657i	0.966057	−	0.258328i	$-0.0831716\pi$
$168$		0			0
$169$	−6.42808e8			−0.788015
$170$		0			0
$171$	1.98291e8	+	9.23755e8i	0.231909	+	1.08037i
$172$		0			0
$173$		−	1.08224e7i		−	0.0120820i	−0.999982	−	0.00604099i	$-0.998077\pi$
$173$		−	1.08224e7i		−	0.0120820i	0.999982	−	0.00604099i	$-0.00192292\pi$
$174$		0			0
$175$	−1.60744e8			−0.171389
$176$		0			0
$177$	2.54775e8	−	3.15267e8i	0.259575	−	0.321208i
$178$		0			0
$179$		−	2.24822e8i		−	0.218991i	−0.993987	−	0.109495i	$-0.965076\pi$
$179$		−	2.24822e8i		−	0.218991i	0.993987	−	0.109495i	$-0.0349235\pi$
$180$		0			0
$181$	1.31026e9			1.22080			0.610398	−	0.792095i	$-0.291010\pi$
$181$	1.31026e9			1.22080			0.610398	+	0.792095i	$0.291010\pi$
$182$		0			0
$183$	1.10743e9	+	8.94940e8i	0.987444	+	0.797975i
$184$		0			0
$185$			1.13348e9i			0.967672i
$186$		0			0
$187$	1.48944e9			1.21803
$188$		0			0
$189$	−6.68197e8	+	1.32124e9i	−0.523670	+	1.03546i
$190$		0			0
$191$			2.18984e9i			1.64543i	0.568454	+	0.822715i	$0.307542\pi$
$191$			2.18984e9i			1.64543i	−0.568454	+	0.822715i	$0.692458\pi$
$192$		0			0
$193$	−1.71183e9			−1.23376			−0.616881	−	0.787057i	$-0.711604\pi$
$193$	−1.71183e9			−1.23376			−0.616881	+	0.787057i	$0.711604\pi$
$194$		0			0
$195$	3.86294e8	−	4.78015e8i	0.267165	−	0.330600i
$196$		0			0
$197$		−	2.63287e9i		−	1.74810i	−0.485840	−	0.874048i	$-0.661486\pi$
$197$		−	2.63287e9i		−	1.74810i	0.485840	−	0.874048i	$-0.338514\pi$
$198$		0			0
$199$	−2.95243e9			−1.88264			−0.941319	−	0.337517i	$-0.890413\pi$
$199$	−2.95243e9			−1.88264			−0.941319	+	0.337517i	$0.890413\pi$
$200$		0			0
$201$	1.07962e9	+	8.72462e8i	0.661432	+	0.534518i
$202$		0			0
$203$			1.74794e9i			1.02930i
$204$		0			0
$205$	5.68994e8			0.322175
$206$		0			0
$207$	−3.16577e8	+	6.79555e7i	−0.172424	+	0.0370121i
$208$		0			0
$209$		−	3.23070e9i		−	1.69321i
$210$		0			0
$211$	−2.66349e9			−1.34376			−0.671880	−	0.740660i	$-0.734513\pi$
$211$	−2.66349e9			−1.34376			−0.671880	+	0.740660i	$0.734513\pi$
$212$		0			0
$213$	1.31814e9	−	1.63111e9i	0.640386	−	0.792437i
$214$		0			0
$215$		−	4.50879e7i		−	0.0211011i
$216$		0			0
$217$	2.03026e9			0.915616
$218$		0			0
$219$	−1.77278e9	−	1.43262e9i	−0.770687	−	0.622809i
$220$		0			0
$221$			8.73013e8i			0.365975i
$222$		0			0
$223$	2.04266e8			0.0825993			0.0412996	−	0.999147i	$-0.486850\pi$
$223$	2.04266e8			0.0825993			0.0412996	+	0.999147i	$0.486850\pi$
$224$		0			0
$225$	7.94488e7	+	3.70119e8i	0.0309997	+	0.144415i
$226$		0			0
$227$			4.26163e8i			0.160499i	0.996775	+	0.0802495i	$0.0255717\pi$
$227$			4.26163e8i			0.160499i	−0.996775	+	0.0802495i	$0.974428\pi$
$228$		0			0
$229$	3.05784e8			0.111192			0.0555960	−	0.998453i	$-0.482294\pi$
$229$	3.05784e8			0.111192			0.0555960	+	0.998453i	$0.482294\pi$
$230$		0			0
$231$	3.18219e9	−	3.93776e9i	1.11758	−	1.38293i
$232$		0			0
$233$		−	1.40915e9i		−	0.478117i	−0.971005	−	0.239059i	$-0.923161\pi$
$233$		−	1.40915e9i		−	0.478117i	0.971005	−	0.239059i	$-0.0768388\pi$
$234$		0			0
$235$	2.03086e9			0.665900
$236$		0			0
$237$	5.78497e8	+	4.67496e8i	0.183361	+	0.148178i
$238$		0			0
$239$		−	2.28759e9i		−	0.701109i	−0.936542	−	0.350555i	$-0.885993\pi$
$239$		−	2.28759e9i		−	0.701109i	0.936542	−	0.350555i	$-0.114007\pi$
$240$		0			0
$241$	4.37370e9			1.29653			0.648263	−	0.761417i	$-0.275496\pi$
$241$	4.37370e9			1.29653			0.648263	+	0.761417i	$0.275496\pi$
$242$		0			0
$243$	3.37247e9	+	8.85518e8i	0.967214	+	0.253964i
$244$		0			0
$245$			1.15226e9i			0.319807i
$246$		0			0
$247$	1.89363e9			0.508752
$248$		0			0
$249$	4.43484e9	−	5.48783e9i	1.15367	−	1.42759i
$250$		0			0
$251$		−	1.78995e9i		−	0.450969i	−0.974247	−	0.225484i	$-0.927604\pi$
$251$		−	1.78995e9i		−	0.450969i	0.974247	−	0.225484i	$-0.0723965\pi$
$252$		0			0
$253$	1.10718e9			0.270232
$254$		0			0
$255$	2.41330e9	+	1.95024e9i	0.570755	+	0.461240i
$256$		0			0
$257$			2.20683e9i			0.505867i	0.967484	+	0.252933i	$0.0813954\pi$
$257$			2.20683e9i			0.505867i	−0.967484	+	0.252933i	$0.918605\pi$
$258$		0			0
$259$	−5.47295e9			−1.21625
$260$		0			0
$261$	4.02470e9	−	8.63932e8i	0.867305	−	0.186173i
$262$		0			0
$263$		−	1.77804e9i		−	0.371636i	−0.982584	−	0.185818i	$-0.940506\pi$
$263$		−	1.77804e9i		−	0.371636i	0.982584	−	0.185818i	$-0.0594935\pi$
$264$		0			0
$265$	−3.01222e8			−0.0610805
$266$		0			0
$267$	4.13672e9	−	5.11893e9i	0.813975	−	1.00724i
$268$		0			0
$269$		−	5.97276e9i		−	1.14069i	−0.821406	−	0.570343i	$-0.806810\pi$
$269$		−	5.97276e9i		−	1.14069i	0.821406	−	0.570343i	$-0.193190\pi$
$270$		0			0
$271$	−3.24555e9			−0.601744			−0.300872	−	0.953665i	$-0.597278\pi$
$271$	−3.24555e9			−0.601744			−0.300872	+	0.953665i	$0.597278\pi$
$272$		0			0
$273$	2.30806e9	+	1.86520e9i	0.415525	+	0.335795i
$274$		0			0
$275$		−	1.29444e9i		−	0.226334i
$276$		0			0
$277$	1.34137e9			0.227841			0.113920	−	0.993490i	$-0.463659\pi$
$277$	1.34137e9			0.227841			0.113920	+	0.993490i	$0.463659\pi$
$278$		0			0
$279$	−1.00347e9	−	4.67476e9i	−0.165611	−	0.771512i
$280$		0			0
$281$		−	1.89253e9i		−	0.303541i	−0.988416	−	0.151771i	$-0.951502\pi$
$281$		−	1.89253e9i		−	0.303541i	0.988416	−	0.151771i	$-0.0484975\pi$
$282$		0			0
$283$	−6.88292e9			−1.07307			−0.536534	−	0.843879i	$-0.680267\pi$
$283$	−6.88292e9			−1.07307			−0.536534	+	0.843879i	$0.680267\pi$
$284$		0			0
$285$	4.23020e9	−	5.23461e9i	0.641183	−	0.793423i
$286$		0			0
$287$			2.74735e9i			0.404935i
$288$		0			0
$289$	2.56828e9			0.368172
$290$		0			0
$291$	8.10952e9	+	6.55348e9i	1.13090	+	0.913903i
$292$		0			0
$293$			4.31371e9i			0.585302i	0.956219	+	0.292651i	$0.0945375\pi$
$293$			4.31371e9i			0.585302i	−0.956219	+	0.292651i	$0.905463\pi$
$294$		0			0
$295$	−2.88745e9			−0.381264
$296$		0			0
$297$	−1.06397e10	−	5.38085e9i	−1.36742	−	0.691553i
$298$		0			0
$299$			6.48958e8i			0.0811954i
$300$		0			0
$301$	2.17704e8			0.0265216
$302$		0			0
$303$	−4.77455e9	+	5.90820e9i	−0.566450	+	0.700946i
$304$		0			0
$305$		−	1.01426e10i		−	1.17207i
$306$		0			0
$307$	−8.32155e9			−0.936809			−0.468404	−	0.883514i	$-0.655171\pi$
$307$	−8.32155e9			−0.936809			−0.468404	+	0.883514i	$0.655171\pi$
$308$		0			0
$309$	−3.34103e9	−	2.69996e9i	−0.366477	−	0.296158i
$310$		0			0
$311$			1.09184e10i			1.16712i	0.812069	+	0.583561i	$0.198341\pi$
$311$			1.09184e10i			1.16712i	−0.812069	+	0.583561i	$0.801659\pi$
$312$		0			0
$313$	6.19953e9			0.645924			0.322962	−	0.946412i	$-0.395321\pi$
$313$	6.19953e9			0.645924			0.322962	+	0.946412i	$0.395321\pi$
$314$		0			0
$315$	1.03120e10	−	2.21355e9i	1.04737	−	0.224827i
$316$		0			0
$317$		−	1.86870e10i		−	1.85056i	−0.379289	−	0.925278i	$-0.623831\pi$
$317$		−	1.86870e10i		−	1.85056i	0.379289	−	0.925278i	$-0.376169\pi$
$318$		0			0
$319$	−1.40758e10			−1.35929
$320$		0			0
$321$	−9.71398e9	+	1.20204e10i	−0.914907	+	1.13214i
$322$		0			0
$323$			9.56013e9i			0.878322i
$324$		0			0
$325$	7.58716e8			0.0680057
$326$		0			0
$327$	1.71334e10	+	1.38459e10i	1.49849	+	1.21096i
$328$		0			0
$329$			9.80587e9i			0.836956i
$330$		0			0
$331$	3.24478e9			0.270317			0.135158	−	0.990824i	$-0.456846\pi$
$331$	3.24478e9			0.270317			0.135158	+	0.990824i	$0.456846\pi$
$332$		0			0
$333$	2.70504e9	+	1.26017e10i	0.219987	+	1.02483i
$334$		0			0
$335$		−	9.88790e9i		−	0.785100i
$336$		0			0
$337$	4.89137e9			0.379237			0.189619	−	0.981858i	$-0.439275\pi$
$337$	4.89137e9			0.379237			0.189619	+	0.981858i	$0.439275\pi$
$338$		0			0
$339$	−3.91607e9	+	4.84589e9i	−0.296518	+	0.366923i
$340$		0			0
$341$			1.63493e10i			1.20915i
$342$		0			0
$343$	1.04971e10			0.758391
$344$		0			0
$345$	1.79393e9	+	1.44972e9i	0.126628	+	0.102331i
$346$		0			0
$347$		−	1.44263e10i		−	0.995030i	−0.867455	−	0.497515i	$-0.834246\pi$
$347$		−	1.44263e10i		−	0.995030i	0.867455	−	0.497515i	$-0.165754\pi$
$348$		0			0
$349$	5.34169e9			0.360062			0.180031	−	0.983661i	$-0.442380\pi$
$349$	5.34169e9			0.360062			0.180031	+	0.983661i	$0.442380\pi$
$350$		0			0
$351$	3.15391e9	−	6.23629e9i	0.207788	−	0.410864i
$352$		0			0
$353$			7.82366e9i			0.503861i	0.967745	+	0.251931i	$0.0810655\pi$
$353$			7.82366e9i			0.503861i	−0.967745	+	0.251931i	$0.918935\pi$
$354$		0			0
$355$	−1.49389e10			−0.940599
$356$		0			0
$357$	−9.41659e9	+	1.16524e10i	−0.579723	+	0.717371i
$358$		0			0
$359$		−	1.66718e10i		−	1.00370i	−0.864955	−	0.501850i	$-0.832653\pi$
$359$		−	1.66718e10i		−	1.00370i	0.864955	−	0.501850i	$-0.167347\pi$
$360$		0			0
$361$	3.75301e9			0.220979
$362$		0			0
$363$	1.82054e10	+	1.47122e10i	1.04851	+	0.847325i
$364$		0			0
$365$			1.62364e10i			0.914782i
$366$		0			0
$367$	−1.86456e10			−1.02781			−0.513905	−	0.857847i	$-0.671802\pi$
$367$	−1.86456e10			−1.02781			−0.513905	+	0.857847i	$0.671802\pi$
$368$		0			0
$369$	6.32587e9	−	1.35789e9i	0.341205	−	0.0732421i
$370$		0			0
$371$		−	1.45443e9i		−	0.0767708i
$372$		0			0
$373$	−3.38390e10			−1.74817			−0.874083	−	0.485776i	$-0.838537\pi$
$373$	−3.38390e10			−1.74817			−0.874083	+	0.485776i	$0.838537\pi$
$374$		0			0
$375$	1.31699e10	−	1.62969e10i	0.665975	−	0.824101i
$376$		0			0
$377$		−	8.25033e9i		−	0.408419i
$378$		0			0
$379$	−2.82088e10			−1.36719			−0.683594	−	0.729863i	$-0.739584\pi$
$379$	−2.82088e10			−1.36719			−0.683594	+	0.729863i	$0.739584\pi$
$380$		0			0
$381$	−7.90126e9	−	6.38518e9i	−0.374970	−	0.303021i
$382$		0			0
$383$			1.82405e10i			0.847698i	0.905733	+	0.423849i	$0.139321\pi$
$383$			1.82405e10i			0.847698i	−0.905733	+	0.423849i	$0.860679\pi$
$384$		0			0
$385$	−3.60648e10			−1.64150
$386$		0			0
$387$	−1.07602e8	−	5.01271e8i	−0.00479705	−	0.0223475i
$388$		0			0
$389$			1.94375e10i			0.848871i	0.905458	+	0.424435i	$0.139527\pi$
$389$			1.94375e10i			0.848871i	−0.905458	+	0.424435i	$0.860473\pi$
$390$		0			0
$391$	−3.27632e9			−0.140178
$392$		0			0
$393$	6.31563e9	−	7.81519e9i	0.264756	−	0.327619i
$394$		0			0
$395$		−	5.29829e9i		−	0.217644i
$396$		0			0
$397$	−1.66719e10			−0.671157			−0.335578	−	0.942012i	$-0.608932\pi$
$397$	−1.66719e10			−0.671157			−0.335578	+	0.942012i	$0.608932\pi$
$398$		0			0
$399$	2.52749e10	+	2.04252e10i	0.997238	+	0.805890i
$400$		0			0
$401$			3.30836e10i			1.27949i	0.768589	+	0.639743i	$0.220959\pi$
$401$			3.30836e10i			1.27949i	−0.768589	+	0.639743i	$0.779041\pi$
$402$		0			0
$403$	−9.58290e9			−0.363310
$404$		0			0
$405$	−1.01936e10	−	2.26498e10i	−0.378885	−	0.841868i
$406$		0			0
$407$		−	4.40725e10i		−	1.60616i
$408$		0			0
$409$	−5.03326e10			−1.79869			−0.899345	−	0.437240i	$-0.855956\pi$
$409$	−5.03326e10			−1.79869			−0.899345	+	0.437240i	$0.855956\pi$
$410$		0			0
$411$	2.80394e10	−	3.46970e10i	0.982657	−	1.21598i
$412$		0			0
$413$		−	1.39418e10i		−	0.479203i
$414$		0			0
$415$	−5.02615e10			−1.69451
$416$		0			0
$417$	4.78335e9	+	3.86553e9i	0.158193	+	0.127839i
$418$		0			0
$419$			2.94280e10i			0.954782i	0.878691	+	0.477391i	$0.158418\pi$
$419$			2.94280e10i			0.954782i	−0.878691	+	0.477391i	$0.841582\pi$
$420$		0			0
$421$	3.33243e10			1.06080			0.530399	−	0.847748i	$-0.322042\pi$
$421$	3.33243e10			1.06080			0.530399	+	0.847748i	$0.322042\pi$
$422$		0			0
$423$	2.25784e10	−	4.84662e9i	0.705231	−	0.151383i
$424$		0			0
$425$			3.83044e9i			0.117407i
$426$		0			0
$427$	4.89731e10			1.47315
$428$		0			0
$429$	−1.50200e10	+	1.85863e10i	−0.443447	+	0.548738i
$430$		0			0
$431$			5.62271e10i			1.62943i	0.579860	+	0.814716i	$0.303107\pi$
$431$			5.62271e10i			1.62943i	−0.579860	+	0.814716i	$0.696893\pi$
$432$		0			0
$433$	−2.18807e10			−0.622457			−0.311229	−	0.950335i	$-0.600740\pi$
$433$	−2.18807e10			−0.622457			−0.311229	+	0.950335i	$0.600740\pi$
$434$		0			0
$435$	−2.28066e10	−	1.84306e10i	−0.636949	−	0.514732i
$436$		0			0
$437$			7.10656e9i			0.194865i
$438$		0			0
$439$	−1.87990e10			−0.506146			−0.253073	−	0.967447i	$-0.581441\pi$
$439$	−1.87990e10			−0.506146			−0.253073	+	0.967447i	$0.581441\pi$
$440$		0			0
$441$	2.74986e9	+	1.28105e10i	0.0727037	+	0.338696i
$442$		0			0
$443$		−	6.53593e10i		−	1.69704i	−0.529163	−	0.848520i	$-0.677494\pi$
$443$		−	6.53593e10i		−	1.69704i	0.529163	−	0.848520i	$-0.322506\pi$
$444$		0			0
$445$	−4.68828e10			−1.19557
$446$		0			0
$447$	3.74274e10	−	4.63140e10i	0.937474	−	1.16006i
$448$		0			0
$449$			1.58084e10i			0.388959i	0.980907	+	0.194479i	$0.0623017\pi$
$449$			1.58084e10i			0.388959i	−0.980907	+	0.194479i	$0.937698\pi$
$450$		0			0
$451$	−2.21238e10			−0.534754
$452$		0			0
$453$	1.90031e10	+	1.53568e10i	0.451265	+	0.364677i
$454$		0			0
$455$		−	2.11389e10i		−	0.493215i
$456$		0			0
$457$	3.30400e9			0.0757486			0.0378743	−	0.999283i	$-0.487941\pi$
$457$	3.30400e9			0.0757486			0.0378743	+	0.999283i	$0.487941\pi$
$458$		0			0
$459$	3.14844e10	+	1.59228e10i	0.709324	+	0.358730i
$460$		0			0
$461$			3.30139e10i			0.730960i	0.930819	+	0.365480i	$0.119095\pi$
$461$			3.30139e10i			0.730960i	−0.930819	+	0.365480i	$0.880905\pi$
$462$		0			0
$463$	−5.63117e10			−1.22539			−0.612696	−	0.790319i	$-0.709915\pi$
$463$	−5.63117e10			−1.22539			−0.612696	+	0.790319i	$0.709915\pi$
$464$		0			0
$465$	−2.14074e10	+	2.64903e10i	−0.457881	+	0.566598i
$466$		0			0
$467$			5.38175e10i			1.13150i	0.824576	+	0.565752i	$0.191414\pi$
$467$			5.38175e10i			1.13150i	−0.824576	+	0.565752i	$0.808586\pi$
$468$		0			0
$469$	4.77430e10			0.986776
$470$		0			0
$471$	−1.01582e10	−	8.20907e9i	−0.206411	−	0.166805i
$472$		0			0
$473$			1.75312e9i			0.0350242i
$474$		0			0
$475$	8.30848e9			0.163210
$476$		0			0
$477$	−3.34887e9	+	7.18861e8i	−0.0646882	+	0.0138858i
$478$		0			0
$479$			8.02692e10i			1.52478i	0.647119	+	0.762389i	$0.275974\pi$
$479$			8.02692e10i			1.52478i	−0.647119	+	0.762389i	$0.724026\pi$
$480$		0			0
$481$	2.58325e10			0.482598
$482$		0			0
$483$	−6.99986e9	+	8.66188e9i	−0.128618	+	0.159156i
$484$		0			0
$485$		−	7.42728e10i		−	1.34234i
$486$		0			0
$487$	7.07093e10			1.25707			0.628537	−	0.777780i	$-0.283654\pi$
$487$	7.07093e10			1.25707			0.628537	+	0.777780i	$0.283654\pi$
$488$		0			0
$489$	1.39376e10	+	1.12633e10i	0.243755	+	0.196984i
$490$		0			0
$491$			6.06876e10i			1.04418i	0.852892	+	0.522088i	$0.174847\pi$
$491$			6.06876e10i			1.04418i	−0.852892	+	0.522088i	$0.825153\pi$
$492$		0			0
$493$	4.16525e10			0.705104
$494$		0			0
$495$	1.78253e10	+	8.30407e10i	0.296904	+	1.38315i
$496$		0			0
$497$		−	7.21313e10i		−	1.18222i
$498$		0			0
$499$	−1.04926e11			−1.69232			−0.846158	−	0.532932i	$-0.821090\pi$
$499$	−1.04926e11			−1.69232			−0.846158	+	0.532932i	$0.821090\pi$
$500$		0			0
$501$	−2.04590e10	+	2.53168e10i	−0.324739	+	0.401844i
$502$		0			0
$503$		−	4.73262e9i		−	0.0739315i	−0.999317	−	0.0369657i	$-0.988231\pi$
$503$		−	4.73262e9i		−	0.0739315i	0.999317	−	0.0369657i	$-0.0117692\pi$
$504$		0			0
$505$	5.41115e10			0.832002
$506$		0			0
$507$	4.04969e10	+	3.27265e10i	0.612901	+	0.495299i
$508$		0			0
$509$		−	8.34402e7i		−	0.00124309i	−1.00000		0.000621547i	$-0.999802\pi$
$509$		−	8.34402e7i		−	0.00124309i	1.00000		0.000621547i	$-0.000197845\pi$
$510$		0			0
$511$	−7.83962e10			−1.14977
$512$		0			0
$513$	3.45376e10	−	6.82919e10i	0.498681	−	0.986051i
$514$		0			0
$515$			3.05995e10i			0.434997i
$516$		0			0
$517$	−7.89646e10			−1.10528
$518$		0			0
$519$	−5.50985e8	+	6.81809e8i	−0.00759399	+	0.00939709i
$520$		0			0
$521$			3.30179e10i			0.448124i	0.974575	+	0.224062i	$0.0719318\pi$
$521$			3.30179e10i			0.448124i	−0.974575	+	0.224062i	$0.928068\pi$
$522$		0			0
$523$	−7.60491e9			−0.101645			−0.0508227	−	0.998708i	$-0.516184\pi$
$523$	−7.60491e9			−0.101645			−0.0508227	+	0.998708i	$0.516184\pi$
$524$		0			0
$525$	1.01269e10	+	8.18374e9i	0.133302	+	0.107725i
$526$		0			0
$527$		−	4.83801e10i		−	0.627226i
$528$		0			0
$529$	7.58755e10			0.968900
$530$		0			0
$531$	−3.21016e10	+	6.89085e9i	−0.403784	+	0.0866751i
$532$		0			0
$533$		−	1.29675e10i		−	0.160675i
$534$		0			0
$535$	1.10092e11			1.34382
$536$		0			0
$537$	−1.14460e10	+	1.41638e10i	−0.137644	+	0.170326i
$538$		0			0
$539$		−	4.48028e10i		−	0.530823i
$540$		0			0
$541$	1.18116e11			1.37885			0.689427	−	0.724355i	$-0.257862\pi$
$541$	1.18116e11			1.37885			0.689427	+	0.724355i	$0.257862\pi$
$542$		0			0
$543$	−8.25464e10	−	6.67075e10i	−0.949508	−	0.767318i
$544$		0			0
$545$		−	1.56920e11i		−	1.77866i
$546$		0			0
$547$	−6.60454e10			−0.737723			−0.368862	−	0.929484i	$-0.620252\pi$
$547$	−6.60454e10			−0.737723			−0.368862	+	0.929484i	$0.620252\pi$
$548$		0			0
$549$	−2.42053e10	−	1.12762e11i	−0.266453	−	1.24129i
$550$		0			0
$551$		−	9.03471e10i		−	0.980184i
$552$		0			0
$553$	2.55824e10			0.273553
$554$		0			0
$555$	5.77076e10	−	7.14095e10i	0.608220	−	0.752634i
$556$		0			0
$557$			1.38850e11i			1.44253i	0.692659	+	0.721265i	$0.256439\pi$
$557$			1.38850e11i			1.44253i	−0.692659	+	0.721265i	$0.743561\pi$
$558$		0			0
$559$	−1.02757e9			−0.0105236
$560$		0			0
$561$	−9.38347e10	−	7.58299e10i	−0.947353	−	0.765577i
$562$		0			0
$563$		−	3.29834e10i		−	0.328294i	−0.986436	−	0.164147i	$-0.947513\pi$
$563$		−	3.29834e10i		−	0.328294i	0.986436	−	0.164147i	$-0.0524871\pi$
$564$		0			0
$565$	4.43821e10			0.435526
$566$		0			0
$567$	1.09363e11	−	4.92190e10i	1.05813	−	0.476213i
$568$		0			0
$569$			7.16018e10i			0.683085i	0.939866	+	0.341543i	$0.110949\pi$
$569$			7.16018e10i			0.683085i	−0.939866	+	0.341543i	$0.889051\pi$
$570$		0			0
$571$	4.20250e10			0.395333			0.197667	−	0.980269i	$-0.436664\pi$
$571$	4.20250e10			0.395333			0.197667	+	0.980269i	$0.436664\pi$
$572$		0			0
$573$	1.11489e11	−	1.37960e11i	1.03422	−	1.27978i
$574$		0			0
$575$			2.84737e9i			0.0260479i
$576$		0			0
$577$	2.19502e11			1.98032			0.990162	−	0.139927i	$-0.0446868\pi$
$577$	2.19502e11			1.98032			0.990162	+	0.139927i	$0.0446868\pi$
$578$		0			0
$579$	1.07845e11	+	8.71521e10i	0.959592	+	0.775468i
$580$		0			0
$581$		−	2.42684e11i		−	2.12979i
$582$		0			0
$583$	1.17122e10			0.101383
$584$		0			0
$585$	−4.86731e10	+	1.04480e10i	−0.415590	+	0.0892096i
$586$		0			0
$587$		−	2.05299e11i		−	1.72916i	−0.502496	−	0.864580i	$-0.667585\pi$
$587$		−	2.05299e11i		−	1.72916i	0.502496	−	0.864580i	$-0.332415\pi$
$588$		0			0
$589$	−1.04940e11			−0.871924
$590$		0			0
$591$	−1.34044e11	+	1.65871e11i	−1.09875	+	1.35963i
$592$		0			0
$593$			1.01405e11i			0.820052i	0.912074	+	0.410026i	$0.134480\pi$
$593$			1.01405e11i			0.820052i	−0.912074	+	0.410026i	$0.865520\pi$
$594$		0			0
$595$	1.06721e11			0.851498
$596$		0			0
$597$	1.86003e11	+	1.50313e11i	1.46427	+	1.18331i
$598$		0			0
$599$			9.27543e10i			0.720488i	0.932858	+	0.360244i	$0.117307\pi$
$599$			9.27543e10i			0.720488i	−0.932858	+	0.360244i	$0.882693\pi$
$600$		0			0
$601$	−1.18263e11			−0.906464			−0.453232	−	0.891393i	$-0.649729\pi$
$601$	−1.18263e11			−0.906464			−0.453232	+	0.891393i	$0.649729\pi$
$602$		0			0
$603$	−2.35973e10	−	1.09930e11i	−0.178482	−	0.831472i
$604$		0			0
$605$		−	1.66738e11i		−	1.24455i
$606$		0			0
$607$	7.78725e10			0.573627			0.286813	−	0.957986i	$-0.407404\pi$
$607$	7.78725e10			0.573627			0.286813	+	0.957986i	$0.407404\pi$
$608$		0			0
$609$	8.89906e10	−	1.10120e11i	0.646957	−	0.800568i
$610$		0			0
$611$		−	4.62840e10i		−	0.332098i
$612$		0			0
$613$	6.04009e10			0.427761			0.213881	−	0.976860i	$-0.431390\pi$
$613$	6.04009e10			0.427761			0.213881	+	0.976860i	$0.431390\pi$
$614$		0			0
$615$	−3.58466e10	−	2.89684e10i	−0.250581	−	0.202500i
$616$		0			0
$617$		−	1.86030e11i		−	1.28364i	−0.766856	−	0.641819i	$-0.778180\pi$
$617$		−	1.86030e11i		−	1.28364i	0.766856	−	0.641819i	$-0.221820\pi$
$618$		0			0
$619$	1.54130e11			1.04984			0.524922	−	0.851151i	$-0.324095\pi$
$619$	1.54130e11			1.04984			0.524922	+	0.851151i	$0.324095\pi$
$620$		0			0
$621$	2.34040e10	+	1.18362e10i	0.157371	+	0.0795880i
$622$		0			0
$623$		−	2.26370e11i		−	1.50268i
$624$		0			0
$625$	−1.26721e11			−0.830479
$626$		0			0
$627$	−1.64480e11	+	2.03534e11i	−1.06425	+	1.31694i
$628$		0			0
$629$			1.30417e11i			0.833168i
$630$		0			0
$631$	−4.35140e10			−0.274480			−0.137240	−	0.990538i	$-0.543823\pi$
$631$	−4.35140e10			−0.274480			−0.137240	+	0.990538i	$0.543823\pi$
$632$		0			0
$633$	1.67800e11	+	1.35603e11i	1.04515	+	0.844606i
$634$		0			0
$635$			7.23654e10i			0.445078i
$636$		0			0
$637$	2.62605e10			0.159494
$638$		0			0
$639$	−1.66085e11	+	3.56514e10i	−0.996156	+	0.213832i
$640$		0			0
$641$			1.74736e11i			1.03502i	0.855676	+	0.517512i	$0.173142\pi$
$641$			1.74736e11i			1.03502i	−0.855676	+	0.517512i	$0.826858\pi$
$642$		0			0
$643$	−2.46091e11			−1.43963			−0.719817	−	0.694164i	$-0.755774\pi$
$643$	−2.46091e11			−1.43963			−0.719817	+	0.694164i	$0.755774\pi$
$644$		0			0
$645$	−2.29550e9	+	2.84054e9i	−0.0132629	+	0.0164120i
$646$		0			0
$647$		−	1.89739e10i		−	0.108278i	−0.998533	−	0.0541390i	$-0.982759\pi$
$647$		−	1.89739e10i		−	0.108278i	0.998533	−	0.0541390i	$-0.0172414\pi$
$648$		0			0
$649$	1.12271e11			0.632831
$650$		0			0
$651$	−1.27907e11	−	1.03364e11i	−0.712146	−	0.575501i
$652$		0			0
$653$			1.53366e11i			0.843484i	0.906716	+	0.421742i	$0.138581\pi$
$653$			1.53366e11i			0.843484i	−0.906716	+	0.421742i	$0.861419\pi$
$654$		0			0
$655$	−7.15771e10			−0.388874
$656$		0			0
$657$	3.87479e10	+	1.80510e11i	0.207963	+	0.968814i
$658$		0			0
$659$			1.47234e11i			0.780667i	0.920674	+	0.390333i	$0.127640\pi$
$659$			1.47234e11i			0.780667i	−0.920674	+	0.390333i	$0.872360\pi$
$660$		0			0
$661$	6.61159e10			0.346338			0.173169	−	0.984892i	$-0.444599\pi$
$661$	6.61159e10			0.346338			0.173169	+	0.984892i	$0.444599\pi$
$662$		0			0
$663$	4.44466e10	−	5.49998e10i	0.230030	−	0.284647i
$664$		0			0
$665$		−	2.31486e11i		−	1.18369i
$666$		0			0
$667$	3.09625e10			0.156435
$668$		0			0
$669$	−1.28687e10	−	1.03995e10i	−0.0642439	−	0.0519169i
$670$		0			0
$671$			3.94370e11i			1.94542i
$672$		0			0
$673$	−1.67142e11			−0.814753			−0.407377	−	0.913260i	$-0.633556\pi$
$673$	−1.67142e11			−0.814753			−0.407377	+	0.913260i	$0.633556\pi$
$674$		0			0
$675$	1.38381e10	−	2.73624e10i	0.0666594	−	0.131807i
$676$		0			0
$677$			7.82435e10i			0.372472i	0.982505	+	0.186236i	$0.0596289\pi$
$677$			7.82435e10i			0.372472i	−0.982505	+	0.186236i	$0.940371\pi$
$678$		0			0
$679$	3.58621e11			1.68716
$680$		0			0
$681$	2.16967e10	−	2.68483e10i	0.100880	−	0.124832i
$682$		0			0
$683$			1.21724e11i			0.559361i	0.960093	+	0.279681i	$0.0902286\pi$
$683$			1.21724e11i			0.559361i	−0.960093	+	0.279681i	$0.909771\pi$
$684$		0			0
$685$	−3.17780e11			−1.44333
$686$		0			0
$687$	−1.92644e10	−	1.55680e10i	−0.0864827	−	0.0698885i
$688$		0			0
$689$			6.86494e9i			0.0304621i
$690$		0			0
$691$	3.71272e11			1.62847			0.814236	−	0.580535i	$-0.197156\pi$
$691$	3.71272e11			1.62847			0.814236	+	0.580535i	$0.197156\pi$
$692$		0			0
$693$	−4.00956e11	+	8.60682e10i	−1.73846	+	0.373173i
$694$		0			0
$695$		−	4.38094e10i		−	0.187771i
$696$		0			0
$697$	6.54677e10			0.277393
$698$		0			0
$699$	−7.17424e10	+	8.87767e10i	−0.300516	+	0.371869i
$700$		0			0
$701$		−	2.35914e11i		−	0.976970i	−0.872572	−	0.488485i	$-0.837550\pi$
$701$		−	2.35914e11i		−	0.976970i	0.872572	−	0.488485i	$-0.162450\pi$
$702$		0			0
$703$	2.82884e11			1.15821
$704$		0			0
$705$	−1.27944e11	−	1.03395e11i	−0.517922	−	0.418544i
$706$		0			0
$707$			2.61274e11i			1.04573i
$708$		0			0
$709$	1.51154e11			0.598184			0.299092	−	0.954224i	$-0.403316\pi$
$709$	1.51154e11			0.598184			0.299092	+	0.954224i	$0.403316\pi$
$710$		0			0
$711$	−1.26443e10	−	5.89046e10i	−0.0494785	−	0.230500i
$712$		0			0
$713$		−	3.59635e10i		−	0.139157i
$714$		0			0
$715$	1.70227e11			0.651335
$716$		0			0
$717$	−1.16465e11	+	1.44118e11i	−0.440675	+	0.545307i
$718$		0			0
$719$			1.57719e10i			0.0590158i	0.999565	+	0.0295079i	$0.00939402\pi$
$719$			1.57719e10i			0.0590158i	−0.999565	+	0.0295079i	$0.990606\pi$
$720$		0			0
$721$	−1.47748e11			−0.546739
$722$		0			0
$723$	−2.75543e11	−	2.22673e11i	−1.00841	−	0.814918i
$724$		0			0
$725$		−	3.61992e10i		−	0.131023i
$726$		0			0
$727$	−3.61913e11			−1.29559			−0.647794	−	0.761816i	$-0.724308\pi$
$727$	−3.61913e11			−1.29559			−0.647794	+	0.761816i	$0.724308\pi$
$728$		0			0
$729$	−1.67382e11	−	2.27486e11i	−0.592651	−	0.805459i
$730$		0			0
$731$		−	5.18776e9i		−	0.0181681i
$732$		0			0
$733$	−5.75659e10			−0.199411			−0.0997056	−	0.995017i	$-0.531790\pi$
$733$	−5.75659e10			−0.199411			−0.0997056	+	0.995017i	$0.531790\pi$
$734$		0			0
$735$	5.86637e10	−	7.25927e10i	0.201011	−	0.248739i
$736$		0			0
$737$			3.84465e11i			1.30313i
$738$		0			0
$739$	−2.30778e11			−0.773780			−0.386890	−	0.922126i	$-0.626451\pi$
$739$	−2.30778e11			−0.773780			−0.386890	+	0.922126i	$0.626451\pi$
$740$		0			0
$741$	−1.19298e11	−	9.64077e10i	−0.395696	−	0.319771i
$742$		0			0
$743$		−	4.84430e10i		−	0.158956i	−0.996837	−	0.0794778i	$-0.974675\pi$
$743$		−	4.84430e10i		−	0.158956i	0.996837	−	0.0794778i	$-0.0253253\pi$
$744$		0			0
$745$	−4.24177e11			−1.37696
$746$		0			0
$747$	−5.58790e11	+	1.19948e11i	−1.79459	+	0.385223i
$748$		0			0
$749$			5.31571e11i			1.68902i
$750$		0			0
$751$	−1.03467e11			−0.325269			−0.162635	−	0.986686i	$-0.551999\pi$
$751$	−1.03467e11			−0.325269			−0.162635	+	0.986686i	$0.551999\pi$
$752$		0			0
$753$	−9.11295e10	+	1.12767e11i	−0.283452	+	0.350753i
$754$		0			0
$755$		−	1.74044e11i		−	0.535638i
$756$		0			0
$757$	−3.09395e11			−0.942170			−0.471085	−	0.882088i	$-0.656137\pi$
$757$	−3.09395e11			−0.942170			−0.471085	+	0.882088i	$0.656137\pi$
$758$		0			0
$759$	−6.97524e10	−	5.63684e10i	−0.210180	−	0.169851i
$760$		0			0
$761$			3.57736e11i			1.06665i	0.845909	+	0.533327i	$0.179059\pi$
$761$			3.57736e11i			1.06665i	−0.845909	+	0.533327i	$0.820941\pi$
$762$		0			0
$763$	7.57677e11			2.23556
$764$		0			0
$765$	−5.27478e10	−	2.45730e11i	−0.154013	−	0.717485i
$766$		0			0
$767$			6.58058e10i			0.190144i
$768$		0			0
$769$	6.91156e10			0.197638			0.0988190	−	0.995105i	$-0.468494\pi$
$769$	6.91156e10			0.197638			0.0988190	+	0.995105i	$0.468494\pi$
$770$		0			0
$771$	1.12353e11	−	1.39030e11i	0.317957	−	0.393452i
$772$		0			0
$773$			4.96225e11i			1.38983i	0.719093	+	0.694914i	$0.244557\pi$
$773$			4.96225e11i			1.38983i	−0.719093	+	0.694914i	$0.755443\pi$
$774$		0			0
$775$	−4.20460e10			−0.116551
$776$		0			0
$777$	3.44796e11	+	2.78637e11i	0.945971	+	0.764460i
$778$		0			0
$779$		−	1.42004e11i		−	0.385612i
$780$		0			0
$781$	5.80858e11			1.56123
$782$		0			0
$783$	−2.97540e11	−	1.50477e11i	−0.791588	−	0.400334i
$784$		0			0
$785$			9.30361e10i			0.245004i
$786$		0			0
$787$	1.30010e11			0.338906			0.169453	−	0.985538i	$-0.445800\pi$
$787$	1.30010e11			0.338906			0.169453	+	0.985538i	$0.445800\pi$
$788$		0			0
$789$	−9.05229e10	+	1.12016e11i	−0.233588	+	0.289050i
$790$		0			0
$791$			2.14296e11i			0.547404i
$792$		0			0
$793$	−2.31154e11			−0.584533
$794$		0			0
$795$	1.89770e10	+	1.53357e10i	0.0475070	+	0.0383915i
$796$		0			0
$797$		−	4.08242e11i		−	1.01178i	−0.862599	−	0.505888i	$-0.831165\pi$
$797$		−	4.08242e11i		−	1.01178i	0.862599	−	0.505888i	$-0.168835\pi$
$798$		0			0
$799$	2.33668e11			0.573341
$800$		0			0
$801$	−5.21226e11	+	1.11885e11i	−1.26618	+	0.271796i
$802$		0			0
$803$		−	6.31308e11i		−	1.51838i
$804$		0			0
$805$	7.93317e10			0.188914
$806$		0			0
$807$	−3.04084e11	+	3.76284e11i	−0.716966	+	0.887201i
$808$		0			0
$809$			2.23269e11i			0.521235i	0.965442	+	0.260618i	$0.0839262\pi$
$809$			2.23269e11i			0.521235i	−0.965442	+	0.260618i	$0.916074\pi$
$810$		0			0
$811$	1.75526e11			0.405750			0.202875	−	0.979205i	$-0.434972\pi$
$811$	1.75526e11			0.405750			0.202875	+	0.979205i	$0.434972\pi$
$812$		0			0
$813$	2.04470e11	+	1.65237e11i	0.468023	+	0.378220i
$814$		0			0
$815$		−	1.27651e11i		−	0.289330i
$816$		0			0
$817$	−1.12526e10			−0.0252560
$818$		0			0
$819$	−5.04476e10	−	2.35015e11i	−0.112126	−	0.522347i
$820$		0			0
$821$			8.37441e10i			0.184324i	0.995744	+	0.0921619i	$0.0293777\pi$
$821$			8.37441e10i			0.184324i	−0.995744	+	0.0921619i	$0.970622\pi$
$822$		0			0
$823$	5.41972e11			1.18135			0.590673	−	0.806911i	$-0.298862\pi$
$823$	5.41972e11			1.18135			0.590673	+	0.806911i	$0.298862\pi$
$824$		0			0
$825$	−6.59020e10	+	8.15495e10i	−0.142260	+	0.176038i
$826$		0			0
$827$			5.30564e11i			1.13427i	0.823626	+	0.567134i	$0.191948\pi$
$827$			5.30564e11i			1.13427i	−0.823626	+	0.567134i	$0.808052\pi$
$828$		0			0
$829$	−4.65551e11			−0.985710			−0.492855	−	0.870111i	$-0.664047\pi$
$829$	−4.65551e11			−0.985710			−0.492855	+	0.870111i	$0.664047\pi$
$830$		0			0
$831$	−8.45066e10	−	6.82916e10i	−0.177209	−	0.143207i
$832$		0			0
$833$			1.32578e11i			0.275354i
$834$		0			0
$835$	2.31869e11			0.476977
$836$		0			0
$837$	−1.74781e11	+	3.45598e11i	−0.356117	+	0.704158i
$838$		0			0
$839$		−	7.93304e11i		−	1.60100i	−0.599332	−	0.800501i	$-0.704567\pi$
$839$		−	7.93304e11i		−	1.60100i	0.599332	−	0.800501i	$-0.295433\pi$
$840$		0			0
$841$	1.06614e11			0.213122
$842$		0			0
$843$	−9.63520e10	+	1.19229e11i	−0.190788	+	0.236088i
$844$		0			0
$845$		−	3.70900e11i		−	0.727495i
$846$		0			0
$847$	8.05082e11			1.56425
$848$		0			0
$849$	4.33624e11	+	3.50421e11i	0.834608	+	0.674465i
$850$		0			0
$851$			9.69462e10i			0.184847i
$852$		0			0
$853$	−4.55056e10			−0.0859545			−0.0429772	−	0.999076i	$-0.513684\pi$
$853$	−4.55056e10			−0.0859545			−0.0429772	+	0.999076i	$0.513684\pi$
$854$		0			0
$855$	−5.33006e11	+	1.14414e11i	−0.997395	+	0.214098i
$856$		0			0
$857$		−	8.48487e11i		−	1.57297i	−0.617606	−	0.786487i	$-0.711898\pi$
$857$		−	8.48487e11i		−	1.57297i	0.617606	−	0.786487i	$-0.288102\pi$
$858$		0			0
$859$	−7.64741e11			−1.40456			−0.702282	−	0.711899i	$-0.747836\pi$
$859$	−7.64741e11			−1.40456			−0.702282	+	0.711899i	$0.747836\pi$
$860$		0			0
$861$	1.39872e11	−	1.73083e11i	0.254518	−	0.314950i
$862$		0			0
$863$		−	4.55374e11i		−	0.820966i	−0.911868	−	0.410483i	$-0.865360\pi$
$863$		−	4.55374e11i		−	0.820966i	0.911868	−	0.410483i	$-0.134640\pi$
$864$		0			0
$865$	6.24450e9			0.0111541
$866$		0			0
$867$	−1.61802e11	−	1.30755e11i	−0.286356	−	0.231411i
$868$		0			0
$869$			2.06010e11i			0.361251i
$870$		0			0
$871$	−2.25348e11			−0.391545
$872$		0			0
$873$	−1.77251e11	−	8.25739e11i	−0.305163	−	1.42163i
$874$		0			0
$875$		−	7.20686e11i		−	1.22946i
$876$		0			0
$877$	−8.42742e11			−1.42461			−0.712306	−	0.701869i	$-0.752349\pi$
$877$	−8.42742e11			−1.42461			−0.712306	+	0.701869i	$0.752349\pi$
$878$		0			0
$879$	2.19618e11	−	2.71764e11i	0.367886	−	0.455235i
$880$		0			0
$881$		−	1.12314e12i		−	1.86436i	−0.361994	−	0.932181i	$-0.617904\pi$
$881$		−	1.12314e12i		−	1.86436i	0.361994	−	0.932181i	$-0.382096\pi$
$882$		0			0
$883$	6.25330e11			1.02865			0.514323	−	0.857596i	$-0.328043\pi$
$883$	6.25330e11			1.02865			0.514323	+	0.857596i	$0.328043\pi$
$884$		0			0
$885$	1.81909e11	+	1.47005e11i	0.296539	+	0.239639i
$886$		0			0
$887$			4.73224e11i			0.764491i	0.924061	+	0.382246i	$0.124849\pi$
$887$			4.73224e11i			0.764491i	−0.924061	+	0.382246i	$0.875151\pi$
$888$		0			0
$889$	−3.49411e11			−0.559409
$890$		0			0
$891$	3.96351e11	+	8.80677e11i	0.628882	+	1.39735i
$892$		0			0
$893$		−	5.06843e11i		−	0.797017i
$894$		0			0
$895$	1.29722e11			0.202172
$896$		0			0
$897$	3.30395e10	−	4.08843e10i	0.0510345	−	0.0631520i
$898$		0			0
$899$			4.57211e11i			0.699968i
$900$		0			0
$901$	−3.46582e10			−0.0525904
$902$		0			0
$903$	−1.37153e10	−	1.10837e10i	−0.0206279	−	0.0166699i
$904$		0			0
$905$			7.56019e11i			1.12704i
$906$		0			0
$907$	−9.14524e11			−1.35134			−0.675672	−	0.737202i	$-0.736147\pi$
$907$	−9.14524e11			−1.35134			−0.675672	+	0.737202i	$0.736147\pi$
$908$		0			0
$909$	6.01593e11	−	1.29136e11i	0.881144	−	0.189144i
$910$		0			0
$911$			8.57040e11i			1.24431i	0.782895	+	0.622154i	$0.213742\pi$
$911$			8.57040e11i			1.24431i	−0.782895	+	0.622154i	$0.786258\pi$
$912$		0			0
$913$	1.95429e12			2.81258
$914$		0			0
$915$	−5.16379e11	+	6.38987e11i	−0.736690	+	0.911607i
$916$		0			0
$917$		−	3.45605e11i		−	0.488768i
$918$		0			0
$919$	−9.47490e10			−0.132835			−0.0664175	−	0.997792i	$-0.521157\pi$
$919$	−9.47490e10			−0.132835			−0.0664175	+	0.997792i	$0.521157\pi$
$920$		0			0
$921$	5.24258e11	+	4.23664e11i	0.728629	+	0.588821i
$922$		0			0
$923$			3.40462e11i			0.469096i
$924$		0			0
$925$	1.13343e11			0.154820
$926$		0			0
$927$	7.30254e10	+	3.40195e11i	0.0988906	+	0.460690i
$928$		0			0
$929$			2.06406e11i			0.277115i	0.990354	+	0.138557i	$0.0442466\pi$
$929$			2.06406e11i			0.277115i	−0.990354	+	0.138557i	$0.955753\pi$
$930$		0			0
$931$	2.87571e11			0.382778
$932$		0			0
$933$	5.55873e11	−	6.87858e11i	0.733583	−	0.907762i
$934$		0			0
$935$			8.59405e11i			1.12448i
$936$		0			0
$937$	−2.99452e11			−0.388480			−0.194240	−	0.980954i	$-0.562224\pi$
$937$	−2.99452e11			−0.388480			−0.194240	+	0.980954i	$0.562224\pi$
$938$		0			0
$939$	−3.90571e11	−	3.15629e11i	−0.502386	−	0.405989i
$940$		0			0
$941$			9.75658e11i			1.24434i	0.782882	+	0.622170i	$0.213749\pi$
$941$			9.75658e11i			1.24434i	−0.782882	+	0.622170i	$0.786251\pi$
$942$		0			0
$943$	4.86657e10			0.0615426
$944$		0			0
$945$	−7.62354e11	−	3.85549e11i	−0.955937	−	0.483451i
$946$		0			0
$947$			6.85570e11i			0.852416i	0.904625	+	0.426208i	$0.140151\pi$
$947$			6.85570e11i			0.852416i	−0.904625	+	0.426208i	$0.859849\pi$
$948$		0			0
$949$	3.70032e11			0.456220
$950$		0			0
$951$	−9.51386e11	+	1.17728e12i	−1.16315	+	1.43932i
$952$		0			0
$953$			1.81880e11i			0.220502i	0.993904	+	0.110251i	$0.0351655\pi$
$953$			1.81880e11i			0.220502i	−0.993904	+	0.110251i	$0.964835\pi$
$954$		0			0
$955$	−1.26354e12			−1.51906
$956$		0			0
$957$	8.86776e11	+	7.16623e11i	1.05722	+	0.854364i
$958$		0			0
$959$		−	1.53438e12i		−	1.81409i
$960$		0			0
$961$	−3.21832e11			−0.377342
$962$		0			0
$963$	1.22396e12	−	2.62732e11i	1.42319	−	0.305498i
$964$		0			0
$965$		−	9.87724e11i		−	1.13901i
$966$		0			0
$967$	1.51799e11			0.173605			0.0868024	−	0.996226i	$-0.472335\pi$
$967$	1.51799e11			0.173605			0.0868024	+	0.996226i	$0.472335\pi$
$968$		0			0
$969$	4.86722e11	−	6.02288e11i	0.552060	−	0.683139i
$970$		0			0
$971$			2.30877e11i			0.259718i	0.991532	+	0.129859i	$0.0414525\pi$
$971$			2.30877e11i			0.259718i	−0.991532	+	0.129859i	$0.958547\pi$
$972$		0			0
$973$	2.11530e11			0.236005
$974$		0			0
$975$	−4.77991e10	−	3.86275e10i	−0.0528933	−	0.0427443i
$976$		0			0
$977$		−	1.10823e12i		−	1.21633i	−0.793812	−	0.608163i	$-0.791907\pi$
$977$		−	1.10823e12i		−	1.21633i	0.793812	−	0.608163i	$-0.208093\pi$
$978$		0			0
$979$	1.82291e12			1.98443
$980$		0			0
$981$	−3.74487e11	−	1.74458e12i	−0.404353	−	1.88371i
$982$		0			0
$983$		−	3.64534e11i		−	0.390413i	−0.980762	−	0.195207i	$-0.937462\pi$
$983$		−	3.64534e11i		−	0.390413i	0.980762	−	0.195207i	$-0.0625377\pi$
$984$		0			0
$985$	1.51917e12			1.61384
$986$		0			0
$987$	4.99233e11	−	6.17770e11i	0.526060	−	0.650966i
$988$		0			0
$989$		−	3.85634e9i		−	0.00403079i
$990$		0			0
$991$	−1.27281e10			−0.0131968			−0.00659842	−	0.999978i	$-0.502100\pi$
$991$	−1.27281e10			−0.0131968			−0.00659842	+	0.999978i	$0.502100\pi$
$992$		0			0
$993$	−2.04421e11	−	1.65197e11i	−0.210247	−	0.169905i
$994$		0			0
$995$		−	1.70355e12i		−	1.73805i
$996$		0			0
$997$	1.56439e12			1.58330			0.791651	−	0.610973i	$-0.209222\pi$
$997$	1.56439e12			1.58330			0.791651	+	0.610973i	$0.209222\pi$
$998$		0			0
$999$	4.71155e11	−	9.31624e11i	0.473044	−	0.935359i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	192.9.e.c.65.1		2
3.2	odd	2	inner	192.9.e.c.65.2		2
4.3	odd	2		192.9.e.h.65.2		2
8.3	odd	2		6.9.b.a.5.1	✓	2
8.5	even	2		48.9.e.d.17.2		2
12.11	even	2		192.9.e.h.65.1		2
24.5	odd	2		48.9.e.d.17.1		2
24.11	even	2		6.9.b.a.5.2	yes	2
40.3	even	4		150.9.b.a.149.1		4
40.19	odd	2		150.9.d.a.101.2		2
40.27	even	4		150.9.b.a.149.4		4
72.11	even	6		162.9.d.a.53.2		4
72.43	odd	6		162.9.d.a.53.1		4
72.59	even	6		162.9.d.a.107.1		4
72.67	odd	6		162.9.d.a.107.2		4
120.59	even	2		150.9.d.a.101.1		2
120.83	odd	4		150.9.b.a.149.3		4
120.107	odd	4		150.9.b.a.149.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6.9.b.a.5.1	✓	2	8.3	odd	2
6.9.b.a.5.2	yes	2	24.11	even	2
48.9.e.d.17.1		2	24.5	odd	2
48.9.e.d.17.2		2	8.5	even	2
150.9.b.a.149.1		4	40.3	even	4
150.9.b.a.149.2		4	120.107	odd	4
150.9.b.a.149.3		4	120.83	odd	4
150.9.b.a.149.4		4	40.27	even	4
150.9.d.a.101.1		2	120.59	even	2
150.9.d.a.101.2		2	40.19	odd	2
162.9.d.a.53.1		4	72.43	odd	6
162.9.d.a.53.2		4	72.11	even	6
162.9.d.a.107.1		4	72.59	even	6
162.9.d.a.107.2		4	72.67	odd	6
192.9.e.c.65.1		2	1.1	even	1	trivial
192.9.e.c.65.2		2	3.2	odd	2	inner
192.9.e.h.65.1		2	12.11	even	2
192.9.e.h.65.2		2	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	192.e (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(-63.0000 - 50.9117i) q^{3} +576.999i q^{5} -2786.00 q^{7} +(1377.00 + 6414.87i) q^{9} +O(q^{10})\)	\(q+(-63.0000 - 50.9117i) q^{3} +576.999i q^{5} -2786.00 q^{7} +(1377.00 + 6414.87i) q^{9} -22435.1i q^{11} +13150.0 q^{13} +(29376.0 - 36350.9i) q^{15} +66388.8i q^{17} +144002. q^{19} +(175518. + 141840. i) q^{21} +49350.4i q^{23} +57697.0 q^{25} +(239841. - 474242. i) q^{27} -627402. i q^{29} -728738. q^{31} +(-1.14221e6 + 1.41341e6i) q^{33} -1.60752e6i q^{35} +1.96445e6 q^{37} +(-828450. - 669489. i) q^{39} -986125. i q^{41} -78142.0 q^{43} +(-3.70138e6 + 794528. i) q^{45} -3.51969e6i q^{47} +1.99700e6 q^{49} +(3.37997e6 - 4.18250e6i) q^{51} +522048. i q^{53} +1.29450e7 q^{55} +(-9.07213e6 - 7.33138e6i) q^{57} +5.00425e6i q^{59} -1.75783e7 q^{61} +(-3.83632e6 - 1.78718e7i) q^{63} +7.58754e6i q^{65} -1.71368e7 q^{67} +(2.51251e6 - 3.10907e6i) q^{69} +2.58906e7i q^{71} +2.81393e7 q^{73} +(-3.63491e6 - 2.93745e6i) q^{75} +6.25041e7i q^{77} -9.18250e6 q^{79} +(-3.92545e7 + 1.76666e7i) q^{81} +8.71084e7i q^{83} -3.83063e7 q^{85} +(-3.19421e7 + 3.95263e7i) q^{87} +8.12528e7i q^{89} -3.66359e7 q^{91} +(4.59105e7 + 3.71013e7i) q^{93} +8.30890e7i q^{95} -1.28723e8 q^{97} +(1.43918e8 - 3.08931e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 126 q^{3} - 5572 q^{7} + 2754 q^{9}+O(q^{10}) \) 2 * q - 126 * q^3 - 5572 * q^7 + 2754 * q^9	\( 2 q - 126 q^{3} - 5572 q^{7} + 2754 q^{9} + 26300 q^{13} + 58752 q^{15} + 288004 q^{19} + 351036 q^{21} + 115394 q^{25} + 479682 q^{27} - 1457476 q^{31} - 2284416 q^{33} + 3928892 q^{37} - 1656900 q^{39} - 156284 q^{43} - 7402752 q^{45} + 3993990 q^{49} + 6759936 q^{51} + 25890048 q^{55} - 18144252 q^{57} - 35156548 q^{61} - 7672644 q^{63} - 34273532 q^{67} + 5025024 q^{69} + 56278660 q^{73} - 7269822 q^{75} - 18364996 q^{79} - 78508926 q^{81} - 76612608 q^{85} - 63884160 q^{87} - 73271800 q^{91} + 91820988 q^{93} - 257445116 q^{97} + 287836416 q^{99}+O(q^{100}) \) 2 * q - 126 * q^3 - 5572 * q^7 + 2754 * q^9 + 26300 * q^13 + 58752 * q^15 + 288004 * q^19 + 351036 * q^21 + 115394 * q^25 + 479682 * q^27 - 1457476 * q^31 - 2284416 * q^33 + 3928892 * q^37 - 1656900 * q^39 - 156284 * q^43 - 7402752 * q^45 + 3993990 * q^49 + 6759936 * q^51 + 25890048 * q^55 - 18144252 * q^57 - 35156548 * q^61 - 7672644 * q^63 - 34273532 * q^67 + 5025024 * q^69 + 56278660 * q^73 - 7269822 * q^75 - 18364996 * q^79 - 78508926 * q^81 - 76612608 * q^85 - 63884160 * q^87 - 73271800 * q^91 + 91820988 * q^93 - 257445116 * q^97 + 287836416 * q^99

Introduction

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