LMFDB - Embedded newform 192.11.e.h.65.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [192,11,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, 11, names="a")

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

chi := DirichletCharacter("192.65");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 192 = 2^{6} \cdot 3 $
Weight:	$ k $	$=$	$ 11 $
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:	$121.988592513$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{85})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 37x^{2} + 38x + 531 $ x^4 - 2x^3 - 37x^2 + 38*x + 531
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{14}\cdot 3^{6} $
Twist minimal:	no (minimal twist has level 6)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			65.2
Root			$-4.10977 - 1.41421i$ of defining polynomial
Character	$\chi$	$=$	192.65
Dual form			192.11.e.h.65.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-200.269 + 137.627i) q^{3} -3630.47i q^{5} +23226.5 q^{7} +(21166.4 - 55125.0i) q^{9} +O(q^{10})$	\(q+(-200.269 + 137.627i) q^{3} -3630.47i q^{5} +23226.5 q^{7} +(21166.4 - 55125.0i) q^{9} -62442.7i q^{11} +170161. q^{13} +(499653. + 727072. i) q^{15} +2.66626e6i q^{17} +766825. q^{19} +(-4.65156e6 + 3.19661e6i) q^{21} +1.40327e6i q^{23} -3.41471e6 q^{25} +(3.34774e6 + 1.39529e7i) q^{27} +4.83245e6i q^{29} +4.18297e7 q^{31} +(8.59382e6 + 1.25053e7i) q^{33} -8.43233e7i q^{35} -5.01619e7 q^{37} +(-3.40779e7 + 2.34188e7i) q^{39} +1.49239e8i q^{41} -1.98719e8 q^{43} +(-2.00130e8 - 7.68440e7i) q^{45} -1.55059e8i q^{47} +2.56996e8 q^{49} +(-3.66951e8 - 5.33970e8i) q^{51} +4.21541e7i q^{53} -2.26696e8 q^{55} +(-1.53571e8 + 1.05536e8i) q^{57} -2.92026e8i q^{59} +5.30727e8 q^{61} +(4.91622e8 - 1.28036e9i) q^{63} -6.17764e8i q^{65} +5.22093e8 q^{67} +(-1.93128e8 - 2.81031e8i) q^{69} +5.71364e8i q^{71} +2.18588e9 q^{73} +(6.83861e8 - 4.69958e8i) q^{75} -1.45033e9i q^{77} -1.96592e9 q^{79} +(-2.59075e9 - 2.33360e9i) q^{81} +2.18558e9i q^{83} +9.67979e9 q^{85} +(-6.65078e8 - 9.67791e8i) q^{87} +2.38742e8i q^{89} +3.95224e9 q^{91} +(-8.37720e9 + 5.75692e9i) q^{93} -2.78394e9i q^{95} -8.84112e9 q^{97} +(-3.44215e9 - 1.32169e9i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 84 q^{3} + 45112 q^{7} + 159012 q^{9}+O(q^{10}) $ 4 * q + 84 * q^3 + 45112 * q^7 + 159012 * q^9	$ 4 q + 84 q^{3} + 45112 q^{7} + 159012 q^{9} - 275240 q^{13} + 1180800 q^{15} - 1568728 q^{19} - 9628008 q^{21} - 33732380 q^{25} + 34619508 q^{27} + 21785848 q^{31} + 25974144 q^{33} + 71014168 q^{37} - 217287240 q^{39} - 470688664 q^{43} - 312318720 q^{45} - 50058420 q^{49} - 708576768 q^{51} - 2701359360 q^{55} - 1058753208 q^{57} + 1184038744 q^{61} + 905007096 q^{63} - 297365848 q^{67} - 596268288 q^{69} + 6534269000 q^{73} - 5150031180 q^{75} - 199282568 q^{79} + 1458964548 q^{81} + 12880512000 q^{85} - 210268800 q^{87} + 8317232080 q^{91} - 31744468392 q^{93} - 39176355064 q^{97} - 2626912512 q^{99}+O(q^{100}) $ 4 * q + 84 * q^3 + 45112 * q^7 + 159012 * q^9 - 275240 * q^13 + 1180800 * q^15 - 1568728 * q^19 - 9628008 * q^21 - 33732380 * q^25 + 34619508 * q^27 + 21785848 * q^31 + 25974144 * q^33 + 71014168 * q^37 - 217287240 * q^39 - 470688664 * q^43 - 312318720 * q^45 - 50058420 * q^49 - 708576768 * q^51 - 2701359360 * q^55 - 1058753208 * q^57 + 1184038744 * q^61 + 905007096 * q^63 - 297365848 * q^67 - 596268288 * q^69 + 6534269000 * q^73 - 5150031180 * q^75 - 199282568 * q^79 + 1458964548 * q^81 + 12880512000 * q^85 - 210268800 * q^87 + 8317232080 * q^91 - 31744468392 * q^93 - 39176355064 * q^97 - 2626912512 * 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
$3$	−200.269	+	137.627i	−0.824153	+	0.566368i
$3$	−200.269	+	137.627i	−0.824153	+	0.566368i
$4$		0			0
$5$		−	3630.47i		−	1.16175i	−0.813992	−	0.580876i	$-0.802710\pi$
$5$		−	3630.47i		−	1.16175i	0.813992	−	0.580876i	$-0.197290\pi$
$6$		0			0
$7$	23226.5			1.38196			0.690978	−	0.722876i	$-0.257180\pi$
$7$	23226.5			1.38196			0.690978	+	0.722876i	$0.257180\pi$
$8$		0			0
$9$	21166.4	−	55125.0i	0.358455	−	0.933547i
$10$		0			0
$11$		−	62442.7i		−	0.387720i	−0.981029	−	0.193860i	$-0.937899\pi$
$11$		−	62442.7i		−	0.387720i	0.981029	−	0.193860i	$-0.0621007\pi$
$12$		0			0
$13$	170161.			0.458292			0.229146	−	0.973392i	$-0.426407\pi$
$13$	170161.			0.458292			0.229146	+	0.973392i	$0.426407\pi$
$14$		0			0
$15$	499653.	+	727072.i	0.657979	+	0.957460i
$16$		0			0
$17$			2.66626e6i			1.87784i	0.344139	+	0.938919i	$0.388171\pi$
$17$			2.66626e6i			1.87784i	−0.344139	+	0.938919i	$0.611829\pi$
$18$		0			0
$19$	766825.			0.309691			0.154845	−	0.987939i	$-0.450512\pi$
$19$	766825.			0.309691			0.154845	+	0.987939i	$0.450512\pi$
$20$		0			0
$21$	−4.65156e6	+	3.19661e6i	−1.13894	+	0.782695i
$22$		0			0
$23$			1.40327e6i			0.218022i	0.994041	+	0.109011i	$0.0347684\pi$
$23$			1.40327e6i			0.218022i	−0.994041	+	0.109011i	$0.965232\pi$
$24$		0			0
$25$	−3.41471e6			−0.349667
$26$		0			0
$27$	3.34774e6	+	1.39529e7i	0.233310	+	0.972402i
$28$		0			0
$29$			4.83245e6i			0.235601i	0.993037	+	0.117801i	$0.0375844\pi$
$29$			4.83245e6i			0.235601i	−0.993037	+	0.117801i	$0.962416\pi$
$30$		0			0
$31$	4.18297e7			1.46109			0.730544	−	0.682865i	$-0.239266\pi$
$31$	4.18297e7			1.46109			0.730544	+	0.682865i	$0.239266\pi$
$32$		0			0
$33$	8.59382e6	+	1.25053e7i	0.219592	+	0.319540i
$34$		0			0
$35$		−	8.43233e7i		−	1.60549i
$36$		0			0
$37$	−5.01619e7			−0.723378			−0.361689	−	0.932299i	$-0.617800\pi$
$37$	−5.01619e7			−0.723378			−0.361689	+	0.932299i	$0.617800\pi$
$38$		0			0
$39$	−3.40779e7	+	2.34188e7i	−0.377702	+	0.259562i
$40$		0			0
$41$			1.49239e8i			1.28814i	0.764967	+	0.644069i	$0.222755\pi$
$41$			1.49239e8i			1.28814i	−0.764967	+	0.644069i	$0.777245\pi$
$42$		0			0
$43$	−1.98719e8			−1.35175			−0.675876	−	0.737015i	$-0.736235\pi$
$43$	−1.98719e8			−1.35175			−0.675876	+	0.737015i	$0.736235\pi$
$44$		0			0
$45$	−2.00130e8	−	7.68440e7i	−1.08455	−	0.416435i
$46$		0			0
$47$		−	1.55059e8i		−	0.676093i	−0.941129	−	0.338047i	$-0.890234\pi$
$47$		−	1.55059e8i		−	0.676093i	0.941129	−	0.338047i	$-0.109766\pi$
$48$		0			0
$49$	2.56996e8			0.909802
$50$		0			0
$51$	−3.66951e8	−	5.33970e8i	−1.06355	−	1.54762i
$52$		0			0
$53$			4.21541e7i			0.100800i	0.998729	+	0.0503999i	$0.0160496\pi$
$53$			4.21541e7i			0.100800i	−0.998729	+	0.0503999i	$0.983950\pi$
$54$		0			0
$55$	−2.26696e8			−0.450434
$56$		0			0
$57$	−1.53571e8	+	1.05536e8i	−0.255233	+	0.175399i
$58$		0			0
$59$		−	2.92026e8i		−	0.408471i	−0.978922	−	0.204236i	$-0.934529\pi$
$59$		−	2.92026e8i		−	0.408471i	0.978922	−	0.204236i	$-0.0654708\pi$
$60$		0			0
$61$	5.30727e8			0.628379			0.314190	−	0.949360i	$-0.398267\pi$
$61$	5.30727e8			0.628379			0.314190	+	0.949360i	$0.398267\pi$
$62$		0			0
$63$	4.91622e8	−	1.28036e9i	0.495369	−	1.29012i
$64$		0			0
$65$		−	6.17764e8i		−	0.532421i
$66$		0			0
$67$	5.22093e8			0.386700			0.193350	−	0.981130i	$-0.438065\pi$
$67$	5.22093e8			0.386700			0.193350	+	0.981130i	$0.438065\pi$
$68$		0			0
$69$	−1.93128e8	−	2.81031e8i	−0.123481	−	0.179684i
$70$		0			0
$71$			5.71364e8i			0.316681i	0.987385	+	0.158340i	$0.0506143\pi$
$71$			5.71364e8i			0.316681i	−0.987385	+	0.158340i	$0.949386\pi$
$72$		0			0
$73$	2.18588e9			1.05441			0.527207	−	0.849737i	$-0.323239\pi$
$73$	2.18588e9			1.05441			0.527207	+	0.849737i	$0.323239\pi$
$74$		0			0
$75$	6.83861e8	−	4.69958e8i	0.288179	−	0.198040i
$76$		0			0
$77$		−	1.45033e9i		−	0.535812i
$78$		0			0
$79$	−1.96592e9			−0.638897			−0.319449	−	0.947604i	$-0.603498\pi$
$79$	−1.96592e9			−0.638897			−0.319449	+	0.947604i	$0.603498\pi$
$80$		0			0
$81$	−2.59075e9	−	2.33360e9i	−0.743020	−	0.669269i
$82$		0			0
$83$			2.18558e9i			0.554850i	0.960747	+	0.277425i	$0.0894810\pi$
$83$			2.18558e9i			0.554850i	−0.960747	+	0.277425i	$0.910519\pi$
$84$		0			0
$85$	9.67979e9			2.18158
$86$		0			0
$87$	−6.65078e8	−	9.67791e8i	−0.133437	−	0.194171i
$88$		0			0
$89$			2.38742e8i			0.0427542i	0.999771	+	0.0213771i	$0.00680506\pi$
$89$			2.38742e8i			0.0427542i	−0.999771	+	0.0213771i	$0.993195\pi$
$90$		0			0
$91$	3.95224e9			0.633339
$92$		0			0
$93$	−8.37720e9	+	5.75692e9i	−1.20416	+	0.827514i
$94$		0			0
$95$		−	2.78394e9i		−	0.359784i
$96$		0			0
$97$	−8.84112e9			−1.02955			−0.514776	−	0.857324i	$-0.672125\pi$
$97$	−8.84112e9			−1.02955			−0.514776	+	0.857324i	$0.672125\pi$
$98$		0			0
$99$	−3.44215e9	−	1.32169e9i	−0.361955	−	0.138980i
$100$		0			0
$101$			1.67928e10i			1.59778i	0.601477	+	0.798890i	$0.294579\pi$
$101$			1.67928e10i			1.59778i	−0.601477	+	0.798890i	$0.705421\pi$
$102$		0			0
$103$	−8.36865e9			−0.721887			−0.360944	−	0.932588i	$-0.617545\pi$
$103$	−8.36865e9			−0.721887			−0.360944	+	0.932588i	$0.617545\pi$
$104$		0			0
$105$	1.16052e10	+	1.68873e10i	0.909297	+	1.32317i
$106$		0			0
$107$			1.43555e10i			1.02353i	0.859126	+	0.511764i	$0.171008\pi$
$107$			1.43555e10i			1.02353i	−0.859126	+	0.511764i	$0.828992\pi$
$108$		0			0
$109$	4.72564e9			0.307134			0.153567	−	0.988138i	$-0.450924\pi$
$109$	4.72564e9			0.307134			0.153567	+	0.988138i	$0.450924\pi$
$110$		0			0
$111$	1.00459e10	−	6.90365e9i	0.596174	−	0.409698i
$112$		0			0
$113$			1.32158e10i			0.717303i	0.933472	+	0.358651i	$0.116763\pi$
$113$			1.32158e10i			0.717303i	−0.933472	+	0.358651i	$0.883237\pi$
$114$		0			0
$115$	5.09452e9			0.253288
$116$		0			0
$117$	3.60169e9	−	9.38011e9i	0.164277	−	0.427837i
$118$		0			0
$119$			6.19280e10i			2.59509i
$120$		0			0
$121$	2.20383e10			0.849673
$122$		0			0
$123$	−2.05393e10	−	2.98879e10i	−0.729560	−	1.06162i
$124$		0			0
$125$		−	2.30568e10i		−	0.755526i
$126$		0			0
$127$	3.17814e10			0.961953			0.480976	−	0.876733i	$-0.340282\pi$
$127$	3.17814e10			0.961953			0.480976	+	0.876733i	$0.340282\pi$
$128$		0			0
$129$	3.97973e10	−	2.73492e10i	1.11405	−	0.765589i
$130$		0			0
$131$			5.01094e10i			1.29886i	0.760421	+	0.649430i	$0.224993\pi$
$131$			5.01094e10i			1.29886i	−0.760421	+	0.649430i	$0.775007\pi$
$132$		0			0
$133$	1.78107e10			0.427979
$134$		0			0
$135$	5.06557e10	−	1.21539e10i	1.12969	−	0.271048i
$136$		0			0
$137$			2.74744e10i			0.569279i	0.958635	+	0.284639i	$0.0918738\pi$
$137$			2.74744e10i			0.569279i	−0.958635	+	0.284639i	$0.908126\pi$
$138$		0			0
$139$	6.32488e10			1.21893			0.609464	−	0.792814i	$-0.291385\pi$
$139$	6.32488e10			1.21893			0.609464	+	0.792814i	$0.291385\pi$
$140$		0			0
$141$	2.13403e10	+	3.10534e10i	0.382917	+	0.557204i
$142$		0			0
$143$		−	1.06253e10i		−	0.177689i
$144$		0			0
$145$	1.75441e10			0.273710
$146$		0			0
$147$	−5.14684e10	+	3.53697e10i	−0.749815	+	0.515282i
$148$		0			0
$149$			3.38479e10i			0.460893i	0.973085	+	0.230446i	$0.0740186\pi$
$149$			3.38479e10i			0.460893i	−0.973085	+	0.230446i	$0.925981\pi$
$150$		0			0
$151$	−1.22386e11			−1.55901			−0.779503	−	0.626399i	$-0.784528\pi$
$151$	−1.22386e11			−1.55901			−0.779503	+	0.626399i	$0.784528\pi$
$152$		0			0
$153$	1.46978e11	+	5.64351e10i	1.75305	+	0.673120i
$154$		0			0
$155$		−	1.51862e11i		−	1.69742i
$156$		0			0
$157$	1.58971e11			1.66656			0.833279	−	0.552853i	$-0.186461\pi$
$157$	1.58971e11			1.66656			0.833279	+	0.552853i	$0.186461\pi$
$158$		0			0
$159$	−5.80155e9	−	8.44215e9i	−0.0570898	−	0.0830745i
$160$		0			0
$161$			3.25930e10i			0.301297i
$162$		0			0
$163$	−9.20831e10			−0.800280			−0.400140	−	0.916454i	$-0.631038\pi$
$163$	−9.20831e10			−0.800280			−0.400140	+	0.916454i	$0.631038\pi$
$164$		0			0
$165$	4.54003e10	−	3.11996e10i	0.371226	−	0.255111i
$166$		0			0
$167$		−	2.12416e11i		−	1.63533i	−0.575697	−	0.817663i	$-0.695269\pi$
$167$		−	2.12416e11i		−	1.63533i	0.575697	−	0.817663i	$-0.304731\pi$
$168$		0			0
$169$	−1.08904e11			−0.789968
$170$		0			0
$171$	1.62309e10	−	4.22713e10i	0.111010	−	0.289111i
$172$		0			0
$173$			3.04132e11i			1.96260i	0.192482	+	0.981300i	$0.438346\pi$
$173$			3.04132e11i			1.96260i	−0.192482	+	0.981300i	$0.561654\pi$
$174$		0			0
$175$	−7.93119e10			−0.483224
$176$		0			0
$177$	4.01908e10	+	5.84837e10i	0.231345	+	0.336642i
$178$		0			0
$179$		−	7.07114e9i		−	0.0384791i	−0.999815	−	0.0192395i	$-0.993875\pi$
$179$		−	7.07114e9i		−	0.0384791i	0.999815	−	0.0192395i	$-0.00612451\pi$
$180$		0			0
$181$	1.27309e11			0.655337			0.327669	−	0.944793i	$-0.393737\pi$
$181$	1.27309e11			0.655337			0.327669	+	0.944793i	$0.393737\pi$
$182$		0			0
$183$	−1.06288e11	+	7.30425e10i	−0.517880	+	0.355894i
$184$		0			0
$185$			1.82111e11i			0.840386i
$186$		0			0
$187$	1.66488e11			0.728075
$188$		0			0
$189$	7.77563e10	+	3.24078e11i	0.322424	+	1.34382i
$190$		0			0
$191$		−	2.06460e11i		−	0.812209i	−0.913827	−	0.406105i	$-0.866887\pi$
$191$		−	2.06460e11i		−	0.812209i	0.913827	−	0.406105i	$-0.133113\pi$
$192$		0			0
$193$	3.11606e11			1.16364			0.581821	−	0.813317i	$-0.302340\pi$
$193$	3.11606e11			1.16364			0.581821	+	0.813317i	$0.302340\pi$
$194$		0			0
$195$	8.50212e10	+	1.23719e11i	0.301546	+	0.438796i
$196$		0			0
$197$		−	1.51694e11i		−	0.511255i	−0.966775	−	0.255628i	$-0.917718\pi$
$197$		−	1.51694e11i		−	0.511255i	0.966775	−	0.255628i	$-0.0822821\pi$
$198$		0			0
$199$	1.11692e11			0.357895			0.178947	−	0.983859i	$-0.442731\pi$
$199$	1.11692e11			0.357895			0.178947	+	0.983859i	$0.442731\pi$
$200$		0			0
$201$	−1.04559e11	+	7.18543e10i	−0.318700	+	0.219014i
$202$		0			0
$203$			1.12241e11i			0.325591i
$204$		0			0
$205$	5.41807e11			1.49650
$206$		0			0
$207$	7.73551e10	+	2.97021e10i	0.203534	+	0.0781512i
$208$		0			0
$209$		−	4.78826e10i		−	0.120073i
$210$		0			0
$211$	1.53066e11			0.365987			0.182994	−	0.983114i	$-0.441421\pi$
$211$	1.53066e11			0.365987			0.182994	+	0.983114i	$0.441421\pi$
$212$		0			0
$213$	−7.86354e10	−	1.14427e11i	−0.179358	−	0.260993i
$214$		0			0
$215$			7.21444e11i			1.57040i
$216$		0			0
$217$	9.71560e11			2.01916
$218$		0			0
$219$	−4.37763e11	+	3.00836e11i	−0.868998	+	0.597186i
$220$		0			0
$221$			4.53693e11i			0.860598i
$222$		0			0
$223$	6.05759e11			1.09844			0.549219	−	0.835678i	$-0.314925\pi$
$223$	6.05759e11			1.09844			0.549219	+	0.835678i	$0.314925\pi$
$224$		0			0
$225$	−7.22772e10	+	1.88236e11i	−0.125340	+	0.326430i
$226$		0			0
$227$		−	6.70588e11i		−	1.11257i	−0.830992	−	0.556284i	$-0.812227\pi$
$227$		−	6.70588e11i		−	1.11257i	0.830992	−	0.556284i	$-0.187773\pi$
$228$		0			0
$229$	−3.53356e11			−0.561094			−0.280547	−	0.959840i	$-0.590516\pi$
$229$	−3.53356e11			−0.561094			−0.280547	+	0.959840i	$0.590516\pi$
$230$		0			0
$231$	1.99605e11	+	2.90456e11i	0.303467	+	0.441591i
$232$		0			0
$233$			1.12390e12i			1.63662i	0.574779	+	0.818309i	$0.305088\pi$
$233$			1.12390e12i			1.63662i	−0.574779	+	0.818309i	$0.694912\pi$
$234$		0			0
$235$	−5.62936e11			−0.785452
$236$		0			0
$237$	3.93714e11	−	2.70565e11i	0.526549	−	0.361851i
$238$		0			0
$239$		−	2.64603e11i		−	0.339317i	−0.985503	−	0.169658i	$-0.945734\pi$
$239$		−	2.64603e11i		−	0.339317i	0.985503	−	0.169658i	$-0.0542665\pi$
$240$		0			0
$241$	8.86768e11			1.09075			0.545375	−	0.838192i	$-0.316387\pi$
$241$	8.86768e11			1.09075			0.545375	+	0.838192i	$0.316387\pi$
$242$		0			0
$243$	8.40014e11	+	1.10789e11i	0.991414	+	0.130757i
$244$		0			0
$245$		−	9.33019e11i		−	1.05696i
$246$		0			0
$247$	1.30483e11			0.141929
$248$		0			0
$249$	−3.00795e11	−	4.37704e11i	−0.314249	−	0.457281i
$250$		0			0
$251$			8.59494e11i			0.862729i	0.902178	+	0.431364i	$0.141968\pi$
$251$			8.59494e11i			0.862729i	−0.902178	+	0.431364i	$0.858032\pi$
$252$		0			0
$253$	8.76237e10			0.0845316
$254$		0			0
$255$	−1.93856e12	+	1.33220e12i	−1.79796	+	1.23558i
$256$		0			0
$257$		−	2.17900e12i		−	1.94353i	−0.235954	−	0.971764i	$-0.575821\pi$
$257$		−	2.17900e12i		−	1.94353i	0.235954	−	0.971764i	$-0.424179\pi$
$258$		0			0
$259$	−1.16509e12			−0.999677
$260$		0			0
$261$	2.66389e11	+	1.02286e11i	0.219945	+	0.0844524i
$262$		0			0
$263$		−	1.37942e12i		−	1.09627i	−0.836391	−	0.548134i	$-0.815339\pi$
$263$		−	1.37942e12i		−	1.09627i	0.836391	−	0.548134i	$-0.184661\pi$
$264$		0			0
$265$	1.53039e11			0.117104
$266$		0			0
$267$	−3.28574e10	−	4.78126e10i	−0.0242146	−	0.0352360i
$268$		0			0
$269$			1.18129e12i			0.838680i	0.907829	+	0.419340i	$0.137738\pi$
$269$			1.18129e12i			0.838680i	−0.907829	+	0.419340i	$0.862262\pi$
$270$		0			0
$271$	1.42251e12			0.973213			0.486606	−	0.873621i	$-0.338235\pi$
$271$	1.42251e12			0.973213			0.486606	+	0.873621i	$0.338235\pi$
$272$		0			0
$273$	−7.91511e11	+	5.43937e11i	−0.521968	+	0.358703i
$274$		0			0
$275$			2.13224e11i			0.135573i
$276$		0			0
$277$	−5.29960e11			−0.324971			−0.162485	−	0.986711i	$-0.551951\pi$
$277$	−5.29960e11			−0.324971			−0.162485	+	0.986711i	$0.551951\pi$
$278$		0			0
$279$	8.85385e11	−	2.30587e12i	0.523734	−	1.36400i
$280$		0			0
$281$			2.28441e12i			1.30389i	0.758265	+	0.651946i	$0.226047\pi$
$281$			2.28441e12i			1.30389i	−0.758265	+	0.651946i	$0.773953\pi$
$282$		0			0
$283$	2.31274e12			1.27408			0.637038	−	0.770833i	$-0.280160\pi$
$283$	2.31274e12			1.27408			0.637038	+	0.770833i	$0.280160\pi$
$284$		0			0
$285$	3.83146e11	+	5.57537e11i	0.203770	+	0.296517i
$286$		0			0
$287$			3.46630e12i			1.78015i
$288$		0			0
$289$	−5.09295e12			−2.52627
$290$		0			0
$291$	1.77060e12	−	1.21678e12i	0.848509	−	0.583106i
$292$		0			0
$293$			1.05989e12i			0.490822i	0.969419	+	0.245411i	$0.0789229\pi$
$293$			1.05989e12i			0.490822i	−0.969419	+	0.245411i	$0.921077\pi$
$294$		0			0
$295$	−1.06019e12			−0.474542
$296$		0			0
$297$	8.71257e11	−	2.09042e11i	0.377020	−	0.0904588i
$298$		0			0
$299$			2.38781e11i			0.0999179i
$300$		0			0
$301$	−4.61555e12			−1.86806
$302$		0			0
$303$	−2.31115e12	−	3.36308e12i	−0.904931	−	1.31681i
$304$		0			0
$305$		−	1.92679e12i		−	0.730020i
$306$		0			0
$307$	6.89209e11			0.252731			0.126366	−	0.991984i	$-0.459669\pi$
$307$	6.89209e11			0.252731			0.126366	+	0.991984i	$0.459669\pi$
$308$		0			0
$309$	1.67598e12	−	1.15176e12i	0.594945	−	0.408854i
$310$		0			0
$311$		−	1.95674e12i		−	0.672559i	−0.941762	−	0.336280i	$-0.890831\pi$
$311$		−	1.95674e12i		−	0.672559i	0.941762	−	0.336280i	$-0.109169\pi$
$312$		0			0
$313$	−2.48821e11			−0.0828256			−0.0414128	−	0.999142i	$-0.513186\pi$
$313$	−2.48821e11			−0.0828256			−0.0414128	+	0.999142i	$0.513186\pi$
$314$		0			0
$315$	−4.64832e12	−	1.78482e12i	−1.49880	−	0.575495i
$316$		0			0
$317$		−	4.63675e12i		−	1.44850i	−0.689539	−	0.724249i	$-0.742187\pi$
$317$		−	4.63675e12i		−	1.44850i	0.689539	−	0.724249i	$-0.257813\pi$
$318$		0			0
$319$	3.01751e11			0.0913473
$320$		0			0
$321$	−1.97571e12	−	2.87497e12i	−0.579694	−	0.843544i
$322$		0			0
$323$			2.04456e12i			0.581549i
$324$		0			0
$325$	−5.81050e11			−0.160249
$326$		0			0
$327$	−9.46400e11	+	6.50378e11i	−0.253125	+	0.173951i
$328$		0			0
$329$		−	3.60147e12i		−	0.934331i
$330$		0			0
$331$	−1.41443e12			−0.355994			−0.177997	−	0.984031i	$-0.556962\pi$
$331$	−1.41443e12			−0.355994			−0.177997	+	0.984031i	$0.556962\pi$
$332$		0			0
$333$	−1.06175e12	+	2.76518e12i	−0.259298	+	0.675308i
$334$		0			0
$335$		−	1.89545e12i		−	0.449249i
$336$		0			0
$337$	8.67755e11			0.199640			0.0998201	−	0.995006i	$-0.468173\pi$
$337$	8.67755e11			0.199640			0.0998201	+	0.995006i	$0.468173\pi$
$338$		0			0
$339$	−1.81886e12	−	2.64672e12i	−0.406257	−	0.591167i
$340$		0			0
$341$		−	2.61196e12i		−	0.566493i
$342$		0			0
$343$	−5.91785e11			−0.124650
$344$		0			0
$345$	−1.02028e12	+	7.01146e11i	−0.208748	+	0.143454i
$346$		0			0
$347$		−	5.20712e12i		−	1.03502i	−0.855676	−	0.517512i	$-0.826858\pi$
$347$		−	5.20712e12i		−	1.03502i	0.855676	−	0.517512i	$-0.173142\pi$
$348$		0			0
$349$	−1.11953e12			−0.216226			−0.108113	−	0.994139i	$-0.534481\pi$
$349$	−1.11953e12			−0.216226			−0.108113	+	0.994139i	$0.534481\pi$
$350$		0			0
$351$	5.69653e11	+	2.37424e12i	0.106924	+	0.445644i
$352$		0			0
$353$		−	3.73952e12i		−	0.682248i	−0.940018	−	0.341124i	$-0.889192\pi$
$353$		−	3.73952e12i		−	0.682248i	0.940018	−	0.341124i	$-0.110808\pi$
$354$		0			0
$355$	2.07432e12			0.367904
$356$		0			0
$357$	−8.52299e12	−	1.24023e13i	−1.46977	−	2.13875i
$358$		0			0
$359$			3.54489e12i			0.594471i	0.954804	+	0.297235i	$0.0960646\pi$
$359$			3.54489e12i			0.594471i	−0.954804	+	0.297235i	$0.903935\pi$
$360$		0			0
$361$	−5.54305e12			−0.904092
$362$		0			0
$363$	−4.41360e12	+	3.03308e12i	−0.700260	+	0.481228i
$364$		0			0
$365$		−	7.93577e12i		−	1.22497i
$366$		0			0
$367$	1.01161e13			1.51944			0.759722	−	0.650248i	$-0.225335\pi$
$367$	1.01161e13			1.51944			0.759722	+	0.650248i	$0.225335\pi$
$368$		0			0
$369$	8.22679e12	+	3.15885e12i	1.20254	+	0.461739i
$370$		0			0
$371$			9.79093e11i			0.139301i
$372$		0			0
$373$	−3.81055e12			−0.527769			−0.263885	−	0.964554i	$-0.585004\pi$
$373$	−3.81055e12			−0.527769			−0.263885	+	0.964554i	$0.585004\pi$
$374$		0			0
$375$	3.17325e12	+	4.61757e12i	0.427906	+	0.622669i
$376$		0			0
$377$			8.22293e11i			0.107974i
$378$		0			0
$379$	1.11052e13			1.42014			0.710069	−	0.704132i	$-0.248664\pi$
$379$	1.11052e13			1.42014			0.710069	+	0.704132i	$0.248664\pi$
$380$		0			0
$381$	−6.36482e12	+	4.37399e12i	−0.792796	+	0.544819i
$382$		0			0
$383$			4.29169e12i			0.520756i	0.965507	+	0.260378i	$0.0838472\pi$
$383$			4.29169e12i			0.520756i	−0.965507	+	0.260378i	$0.916153\pi$
$384$		0			0
$385$	−5.26537e12			−0.622480
$386$		0			0
$387$	−4.20617e12	+	1.09544e13i	−0.484542	+	1.26192i
$388$		0			0
$389$			1.50554e13i			1.69023i	0.534588	+	0.845113i	$0.320467\pi$
$389$			1.50554e13i			1.69023i	−0.534588	+	0.845113i	$0.679533\pi$
$390$		0			0
$391$	−3.74148e12			−0.409411
$392$		0			0
$393$	−6.89642e12	−	1.00354e13i	−0.735633	−	1.07046i
$394$		0			0
$395$			7.13723e12i			0.742240i
$396$		0			0
$397$	1.11669e13			1.13235			0.566174	−	0.824286i	$-0.308423\pi$
$397$	1.11669e13			1.13235			0.566174	+	0.824286i	$0.308423\pi$
$398$		0			0
$399$	−3.56693e12	+	2.45124e12i	−0.352720	+	0.242394i
$400$		0			0
$401$			1.15685e13i			1.11572i	0.829935	+	0.557861i	$0.188378\pi$
$401$			1.15685e13i			1.11572i	−0.829935	+	0.557861i	$0.811622\pi$
$402$		0			0
$403$	7.11777e12			0.669605
$404$		0			0
$405$	−8.47206e12	+	9.40565e12i	−0.777524	+	0.863205i
$406$		0			0
$407$			3.13224e12i			0.280468i
$408$		0			0
$409$	−1.07411e13			−0.938498			−0.469249	−	0.883066i	$-0.655475\pi$
$409$	−1.07411e13			−0.938498			−0.469249	+	0.883066i	$0.655475\pi$
$410$		0			0
$411$	−3.78123e12	−	5.50227e12i	−0.322421	−	0.469172i
$412$		0			0
$413$		−	6.78275e12i		−	0.564489i
$414$		0			0
$415$	7.93468e12			0.644598
$416$		0			0
$417$	−1.26668e13	+	8.70477e12i	−1.00458	+	0.690362i
$418$		0			0
$419$			8.81717e12i			0.682746i	0.939928	+	0.341373i	$0.110892\pi$
$419$			8.81717e12i			0.682746i	−0.939928	+	0.341373i	$0.889108\pi$
$420$		0			0
$421$	5.69741e12			0.430792			0.215396	−	0.976527i	$-0.430896\pi$
$421$	5.69741e12			0.430792			0.215396	+	0.976527i	$0.430896\pi$
$422$		0			0
$423$	−8.54761e12	−	3.28203e12i	−0.631165	−	0.242349i
$424$		0			0
$425$		−	9.10451e12i		−	0.656617i
$426$		0			0
$427$	1.23269e13			0.868392
$428$		0			0
$429$	1.46233e12	+	2.12792e12i	0.100637	+	0.146443i
$430$		0			0
$431$		−	1.80323e13i		−	1.21245i	−0.795293	−	0.606226i	$-0.792683\pi$
$431$		−	1.80323e13i		−	1.21245i	0.795293	−	0.606226i	$-0.207317\pi$
$432$		0			0
$433$	2.06339e13			1.35563			0.677816	−	0.735232i	$-0.262927\pi$
$433$	2.06339e13			1.35563			0.677816	+	0.735232i	$0.262927\pi$
$434$		0			0
$435$	−3.51354e12	+	2.41455e12i	−0.225579	+	0.155021i
$436$		0			0
$437$			1.07606e12i			0.0675195i
$438$		0			0
$439$	−1.95313e13			−1.19787			−0.598935	−	0.800798i	$-0.704409\pi$
$439$	−1.95313e13			−1.19787			−0.598935	+	0.800798i	$0.704409\pi$
$440$		0			0
$441$	5.43969e12	−	1.41669e13i	0.326123	−	0.849343i
$442$		0			0
$443$		−	2.97469e13i		−	1.74351i	−0.489946	−	0.871753i	$-0.662984\pi$
$443$		−	2.97469e13i		−	1.74351i	0.489946	−	0.871753i	$-0.337016\pi$
$444$		0			0
$445$	8.66747e11			0.0496698
$446$		0			0
$447$	−4.65839e12	−	6.77868e12i	−0.261035	−	0.379846i
$448$		0			0
$449$		−	1.37505e13i		−	0.753509i	−0.926313	−	0.376754i	$-0.877040\pi$
$449$		−	1.37505e13i		−	0.753509i	0.926313	−	0.376754i	$-0.122960\pi$
$450$		0			0
$451$	9.31887e12			0.499437
$452$		0			0
$453$	2.45102e13	−	1.68437e13i	1.28486	−	0.882971i
$454$		0			0
$455$		−	1.43485e13i		−	0.735783i
$456$		0			0
$457$	4.10224e11			0.0205798			0.0102899	−	0.999947i	$-0.496725\pi$
$457$	4.10224e11			0.0205798			0.0102899	+	0.999947i	$0.496725\pi$
$458$		0			0
$459$	−3.72021e13	+	8.92594e12i	−1.82601	+	0.438118i
$460$		0			0
$461$			2.10914e11i			0.0101298i	0.999987	+	0.00506490i	$0.00161221\pi$
$461$			2.10914e11i			0.0101298i	−0.999987	+	0.00506490i	$0.998388\pi$
$462$		0			0
$463$	1.96738e13			0.924660			0.462330	−	0.886708i	$-0.347013\pi$
$463$	1.96738e13			0.924660			0.462330	+	0.886708i	$0.347013\pi$
$464$		0			0
$465$	2.09003e13	+	3.04132e13i	0.961365	+	1.39893i
$466$		0			0
$467$		−	1.21902e13i		−	0.548815i	−0.961614	−	0.274407i	$-0.911518\pi$
$467$		−	1.21902e13i		−	0.548815i	0.961614	−	0.274407i	$-0.0884817\pi$
$468$		0			0
$469$	1.21264e13			0.534402
$470$		0			0
$471$	−3.18370e13	+	2.18788e13i	−1.37350	+	0.943885i
$472$		0			0
$473$			1.24085e13i			0.524101i
$474$		0			0
$475$	−2.61849e12			−0.108289
$476$		0			0
$477$	2.32374e12	+	8.92250e11i	0.0941014	+	0.0361322i
$478$		0			0
$479$		−	5.00886e12i		−	0.198637i	−0.995056	−	0.0993187i	$-0.968334\pi$
$479$		−	5.00886e12i		−	0.198637i	0.995056	−	0.0993187i	$-0.0316663\pi$
$480$		0			0
$481$	−8.53558e12			−0.331518
$482$		0			0
$483$	−4.48569e12	−	6.52737e12i	−0.170645	−	0.248315i
$484$		0			0
$485$			3.20975e13i			1.19608i
$486$		0			0
$487$	4.17000e13			1.52227			0.761134	−	0.648595i	$-0.224643\pi$
$487$	4.17000e13			1.52227			0.761134	+	0.648595i	$0.224643\pi$
$488$		0			0
$489$	1.84414e13	−	1.26732e13i	0.659553	−	0.453253i
$490$		0			0
$491$		−	2.10340e12i		−	0.0737081i	−0.999321	−	0.0368540i	$-0.988266\pi$
$491$		−	2.10340e12i		−	0.0737081i	0.999321	−	0.0368540i	$-0.0117337\pi$
$492$		0			0
$493$	−1.28846e13			−0.442421
$494$		0			0
$495$	−4.79835e12	+	1.24966e13i	−0.161460	+	0.420501i
$496$		0			0
$497$			1.32708e13i			0.437639i
$498$		0			0
$499$	2.74482e13			0.887179			0.443589	−	0.896230i	$-0.353705\pi$
$499$	2.74482e13			0.887179			0.443589	+	0.896230i	$0.353705\pi$
$500$		0			0
$501$	2.92342e13	+	4.25403e13i	0.926197	+	1.34776i
$502$		0			0
$503$		−	2.26985e13i		−	0.704949i	−0.935822	−	0.352474i	$-0.885340\pi$
$503$		−	2.26985e13i		−	0.704949i	0.935822	−	0.352474i	$-0.114660\pi$
$504$		0			0
$505$	6.09659e13			1.85622
$506$		0			0
$507$	2.18101e13	−	1.49882e13i	0.651055	−	0.447413i
$508$		0			0
$509$		−	4.21460e13i		−	1.23358i	−0.787127	−	0.616791i	$-0.788433\pi$
$509$		−	4.21460e13i		−	1.23358i	0.787127	−	0.616791i	$-0.211567\pi$
$510$		0			0
$511$	5.07703e13			1.45715
$512$		0			0
$513$	2.56713e12	+	1.06994e13i	0.0722539	+	0.301144i
$514$		0			0
$515$			3.03822e13i			0.838653i
$516$		0			0
$517$	−9.68227e12			−0.262135
$518$		0			0
$519$	−4.18569e13	−	6.09083e13i	−1.11155	−	1.61748i
$520$		0			0
$521$			6.54420e13i			1.70478i	0.522907	+	0.852390i	$0.324848\pi$
$521$			6.54420e13i			1.70478i	−0.522907	+	0.852390i	$0.675152\pi$
$522$		0			0
$523$	−6.14531e13			−1.57049			−0.785245	−	0.619185i	$-0.787463\pi$
$523$	−6.14531e13			−1.57049			−0.785245	+	0.619185i	$0.787463\pi$
$524$		0			0
$525$	1.58837e13	−	1.09155e13i	0.398250	−	0.273682i
$526$		0			0
$527$			1.11529e14i			2.74369i
$528$		0			0
$529$	3.94574e13			0.952466
$530$		0			0
$531$	−1.60979e13	−	6.18114e12i	−0.381327	−	0.146418i
$532$		0			0
$533$			2.53946e13i			0.590343i
$534$		0			0
$535$	5.21173e13			1.18909
$536$		0			0
$537$	9.73183e11	+	1.41613e12i	0.0217933	+	0.0317126i
$538$		0			0
$539$		−	1.60475e13i		−	0.352748i
$540$		0			0
$541$	−1.50207e13			−0.324118			−0.162059	−	0.986781i	$-0.551813\pi$
$541$	−1.50207e13			−0.324118			−0.162059	+	0.986781i	$0.551813\pi$
$542$		0			0
$543$	−2.54960e13	+	1.75211e13i	−0.540098	+	0.371162i
$544$		0			0
$545$		−	1.71563e13i		−	0.356814i
$546$		0			0
$547$	7.15097e13			1.46025			0.730127	−	0.683312i	$-0.239461\pi$
$547$	7.15097e13			1.46025			0.730127	+	0.683312i	$0.239461\pi$
$548$		0			0
$549$	1.12336e13	−	2.92563e13i	0.225245	−	0.586621i
$550$		0			0
$551$			3.70565e12i			0.0729636i
$552$		0			0
$553$	−4.56616e13			−0.882928
$554$		0			0
$555$	−2.50635e13	−	3.64713e13i	−0.475967	−	0.692606i
$556$		0			0
$557$			7.34107e13i			1.36925i	0.728895	+	0.684626i	$0.240034\pi$
$557$			7.34107e13i			1.36925i	−0.728895	+	0.684626i	$0.759966\pi$
$558$		0			0
$559$	−3.38141e13			−0.619497
$560$		0			0
$561$	−3.33425e13	+	2.29134e13i	−0.600045	+	0.412358i
$562$		0			0
$563$			4.77347e13i			0.843902i	0.906619	+	0.421951i	$0.138655\pi$
$563$			4.77347e13i			0.843902i	−0.906619	+	0.421951i	$0.861345\pi$
$564$		0			0
$565$	4.79797e13			0.833327
$566$		0			0
$567$	−6.01742e13	−	5.42013e13i	−1.02682	−	0.924900i
$568$		0			0
$569$			1.90951e13i			0.320156i	0.987104	+	0.160078i	$0.0511745\pi$
$569$			1.90951e13i			0.320156i	−0.987104	+	0.160078i	$0.948825\pi$
$570$		0			0
$571$	−2.09448e13			−0.345060			−0.172530	−	0.985004i	$-0.555194\pi$
$571$	−2.09448e13			−0.345060			−0.172530	+	0.985004i	$0.555194\pi$
$572$		0			0
$573$	2.84145e13	+	4.13475e13i	0.460009	+	0.669385i
$574$		0			0
$575$		−	4.79175e12i		−	0.0762351i
$576$		0			0
$577$	3.56688e13			0.557711			0.278855	−	0.960333i	$-0.410045\pi$
$577$	3.56688e13			0.557711			0.278855	+	0.960333i	$0.410045\pi$
$578$		0			0
$579$	−6.24051e13	+	4.28856e13i	−0.959019	+	0.659050i
$580$		0			0
$581$			5.07634e13i			0.766778i
$582$		0			0
$583$	2.63221e12			0.0390821
$584$		0			0
$585$	−3.40542e13	−	1.30758e13i	−0.497040	−	0.190849i
$586$		0			0
$587$			1.29418e14i			1.85697i	0.371375	+	0.928483i	$0.378886\pi$
$587$			1.29418e14i			1.85697i	−0.371375	+	0.928483i	$0.621114\pi$
$588$		0			0
$589$	3.20761e13			0.452486
$590$		0			0
$591$	2.08773e13	+	3.03797e13i	0.289559	+	0.421352i
$592$		0			0
$593$		−	3.96596e13i		−	0.540848i	−0.962741	−	0.270424i	$-0.912836\pi$
$593$		−	3.96596e13i		−	0.540848i	0.962741	−	0.270424i	$-0.0871639\pi$
$594$		0			0
$595$	2.24828e14			3.01485
$596$		0			0
$597$	−2.23684e13	+	1.53718e13i	−0.294960	+	0.202700i
$598$		0			0
$599$		−	4.57555e13i		−	0.593347i	−0.954979	−	0.296674i	$-0.904123\pi$
$599$		−	4.57555e13i		−	0.593347i	0.954979	−	0.296674i	$-0.0958774\pi$
$600$		0			0
$601$	1.06033e14			1.35229			0.676143	−	0.736770i	$-0.263650\pi$
$601$	1.06033e14			1.35229			0.676143	+	0.736770i	$0.263650\pi$
$602$		0			0
$603$	1.10508e13	−	2.87804e13i	0.138614	−	0.361003i
$604$		0			0
$605$		−	8.00096e13i		−	0.987109i
$606$		0			0
$607$	9.55067e13			1.15902			0.579509	−	0.814966i	$-0.303244\pi$
$607$	9.55067e13			1.15902			0.579509	+	0.814966i	$0.303244\pi$
$608$		0			0
$609$	−1.54475e13	−	2.24784e13i	−0.184404	−	0.268336i
$610$		0			0
$611$		−	2.63849e13i		−	0.309848i
$612$		0			0
$613$	5.18411e13			0.598924			0.299462	−	0.954108i	$-0.403193\pi$
$613$	5.18411e13			0.598924			0.299462	+	0.954108i	$0.403193\pi$
$614$		0			0
$615$	−1.08507e14	+	7.45675e13i	−1.23334	+	0.847567i
$616$		0			0
$617$		−	8.05443e13i		−	0.900760i	−0.892837	−	0.450380i	$-0.851289\pi$
$617$		−	8.05443e13i		−	0.900760i	0.892837	−	0.450380i	$-0.148711\pi$
$618$		0			0
$619$	−5.14946e13			−0.566642			−0.283321	−	0.959025i	$-0.591436\pi$
$619$	−5.14946e13			−0.566642			−0.283321	+	0.959025i	$0.591436\pi$
$620$		0			0
$621$	−1.95797e13	+	4.69777e12i	−0.212005	+	0.0508667i
$622$		0			0
$623$			5.54515e12i			0.0590844i
$624$		0			0
$625$	−1.17054e14			−1.22740
$626$		0			0
$627$	6.58996e12	+	9.58941e12i	0.0680057	+	0.0989587i
$628$		0			0
$629$		−	1.33745e14i		−	1.35839i
$630$		0			0
$631$	1.02922e13			0.102887			0.0514435	−	0.998676i	$-0.483618\pi$
$631$	1.02922e13			0.102887			0.0514435	+	0.998676i	$0.483618\pi$
$632$		0			0
$633$	−3.06543e13	+	2.10660e13i	−0.301629	+	0.207283i
$634$		0			0
$635$		−	1.15381e14i		−	1.11755i
$636$		0			0
$637$	4.37307e13			0.416955
$638$		0			0
$639$	3.14965e13	+	1.20937e13i	0.295636	+	0.113516i
$640$		0			0
$641$			4.62451e13i			0.427342i	0.976906	+	0.213671i	$0.0685420\pi$
$641$			4.62451e13i			0.427342i	−0.976906	+	0.213671i	$0.931458\pi$
$642$		0			0
$643$	2.73102e13			0.248468			0.124234	−	0.992253i	$-0.460353\pi$
$643$	2.73102e13			0.248468			0.124234	+	0.992253i	$0.460353\pi$
$644$		0			0
$645$	−9.92905e13	−	1.44483e14i	−0.889424	−	1.29425i
$646$		0			0
$647$			1.34984e13i			0.119059i	0.998227	+	0.0595293i	$0.0189600\pi$
$647$			1.34984e13i			0.119059i	−0.998227	+	0.0595293i	$0.981040\pi$
$648$		0			0
$649$	−1.82349e13			−0.158372
$650$		0			0
$651$	−1.94573e14	+	1.33713e14i	−1.66410	+	1.14359i
$652$		0			0
$653$			8.41840e13i			0.709029i	0.935051	+	0.354514i	$0.115354\pi$
$653$			8.41840e13i			0.709029i	−0.935051	+	0.354514i	$0.884646\pi$
$654$		0			0
$655$	1.81921e14			1.50895
$656$		0			0
$657$	4.62671e13	−	1.20496e14i	0.377960	−	0.984345i
$658$		0			0
$659$		−	1.65464e14i		−	1.33130i	−0.746264	−	0.665650i	$-0.768154\pi$
$659$		−	1.65464e14i		−	1.33130i	0.746264	−	0.665650i	$-0.231846\pi$
$660$		0			0
$661$	−2.01681e14			−1.59830			−0.799148	−	0.601135i	$-0.794716\pi$
$661$	−2.01681e14			−1.59830			−0.799148	+	0.601135i	$0.794716\pi$
$662$		0			0
$663$	−6.24405e13	−	9.08606e13i	−0.487415	−	0.709264i
$664$		0			0
$665$		−	6.46612e13i		−	0.497205i
$666$		0			0
$667$	−6.78122e12			−0.0513664
$668$		0			0
$669$	−1.21315e14	+	8.33691e13i	−0.905281	+	0.622120i
$670$		0			0
$671$		−	3.31400e13i		−	0.243635i
$672$		0			0
$673$	6.04368e12			0.0437750			0.0218875	−	0.999760i	$-0.493032\pi$
$673$	6.04368e12			0.0437750			0.0218875	+	0.999760i	$0.493032\pi$
$674$		0			0
$675$	−1.14316e13	−	4.76452e13i	−0.0815806	−	0.340017i
$676$		0			0
$677$		−	1.21474e14i		−	0.854164i	−0.904213	−	0.427082i	$-0.859542\pi$
$677$		−	1.21474e14i		−	0.854164i	0.904213	−	0.427082i	$-0.140458\pi$
$678$		0			0
$679$	−2.05349e14			−1.42280
$680$		0			0
$681$	9.22913e13	+	1.34298e14i	0.630123	+	0.916926i
$682$		0			0
$683$		−	1.51629e14i		−	1.02019i	−0.860119	−	0.510094i	$-0.829611\pi$
$683$		−	1.51629e14i		−	1.02019i	0.860119	−	0.510094i	$-0.170389\pi$
$684$		0			0
$685$	9.97450e13			0.661360
$686$		0			0
$687$	7.07663e13	−	4.86315e13i	0.462427	−	0.317785i
$688$		0			0
$689$			7.17296e12i			0.0461958i
$690$		0			0
$691$	6.62249e13			0.420369			0.210185	−	0.977662i	$-0.432593\pi$
$691$	6.62249e13			0.420369			0.210185	+	0.977662i	$0.432593\pi$
$692$		0			0
$693$	−7.99493e13	−	3.06982e13i	−0.500205	−	0.192064i
$694$		0			0
$695$		−	2.29623e14i		−	1.41609i
$696$		0			0
$697$	−3.97909e14			−2.41891
$698$		0			0
$699$	−1.54679e14	−	2.25082e14i	−0.926928	−	1.34882i
$700$		0			0
$701$		−	5.78990e13i		−	0.342043i	−0.985267	−	0.171022i	$-0.945293\pi$
$701$		−	5.78990e13i		−	0.342043i	0.985267	−	0.171022i	$-0.0547068\pi$
$702$		0			0
$703$	−3.84654e13			−0.224024
$704$		0			0
$705$	1.12739e14	−	7.74754e13i	0.647332	−	0.444855i
$706$		0			0
$707$			3.90039e14i			2.20806i
$708$		0			0
$709$	−2.70077e14			−1.50750			−0.753750	−	0.657162i	$-0.771757\pi$
$709$	−2.70077e14			−1.50750			−0.753750	+	0.657162i	$0.771757\pi$
$710$		0			0
$711$	−4.16115e13	+	1.08372e14i	−0.229016	+	0.596441i
$712$		0			0
$713$			5.86983e13i			0.318550i
$714$		0			0
$715$	−3.85748e13			−0.206430
$716$		0			0
$717$	3.64166e13	+	5.29918e13i	0.192178	+	0.279649i
$718$		0			0
$719$			1.48102e14i			0.770755i	0.922759	+	0.385377i	$0.125929\pi$
$719$			1.48102e14i			0.770755i	−0.922759	+	0.385377i	$0.874071\pi$
$720$		0			0
$721$	−1.94375e14			−0.997616
$722$		0			0
$723$	−1.77592e14	+	1.22044e14i	−0.898944	+	0.617765i
$724$		0			0
$725$		−	1.65014e13i		−	0.0823819i
$726$		0			0
$727$	−5.21602e13			−0.256842			−0.128421	−	0.991720i	$-0.540991\pi$
$727$	−5.21602e13			−0.256842			−0.128421	+	0.991720i	$0.540991\pi$
$728$		0			0
$729$	−1.83476e14	+	9.34214e13i	−0.891133	+	0.453742i
$730$		0			0
$731$		−	5.29837e14i		−	2.53837i
$732$		0			0
$733$	−3.21782e14			−1.52069			−0.760346	−	0.649518i	$-0.774971\pi$
$733$	−3.21782e14			−1.52069			−0.760346	+	0.649518i	$0.774971\pi$
$734$		0			0
$735$	1.28409e14	+	1.86855e14i	0.598630	+	0.871099i
$736$		0			0
$737$		−	3.26009e13i		−	0.149931i
$738$		0			0
$739$	1.66542e14			0.755617			0.377809	−	0.925884i	$-0.376678\pi$
$739$	1.66542e14			0.755617			0.377809	+	0.925884i	$0.376678\pi$
$740$		0			0
$741$	−2.61318e13	+	1.79581e13i	−0.116971	+	0.0803839i
$742$		0			0
$743$		−	1.13631e14i		−	0.501825i	−0.968010	−	0.250912i	$-0.919269\pi$
$743$		−	1.13631e14i		−	0.501825i	0.968010	−	0.250912i	$-0.0807306\pi$
$744$		0			0
$745$	1.22884e14			0.535443
$746$		0			0
$747$	1.20480e14	+	4.62608e13i	0.517979	+	0.198889i
$748$		0			0
$749$			3.33429e14i			1.41447i
$750$		0			0
$751$	1.64956e14			0.690508			0.345254	−	0.938509i	$-0.387793\pi$
$751$	1.64956e14			0.690508			0.345254	+	0.938509i	$0.387793\pi$
$752$		0			0
$753$	−1.18290e14	−	1.72130e14i	−0.488622	−	0.711020i
$754$		0			0
$755$			4.44320e14i			1.81118i
$756$		0			0
$757$	2.67990e14			1.07805			0.539026	−	0.842289i	$-0.318793\pi$
$757$	2.67990e14			1.07805			0.539026	+	0.842289i	$0.318793\pi$
$758$		0			0
$759$	−1.75483e13	+	1.20594e13i	−0.0696669	+	0.0478760i
$760$		0			0
$761$		−	1.29795e14i		−	0.508550i	−0.967132	−	0.254275i	$-0.918163\pi$
$761$		−	1.29795e14i		−	0.508550i	0.967132	−	0.254275i	$-0.0818368\pi$
$762$		0			0
$763$	1.09760e14			0.424446
$764$		0			0
$765$	2.04886e14	−	5.33599e14i	0.781998	−	2.03661i
$766$		0			0
$767$		−	4.96913e13i		−	0.187199i
$768$		0			0
$769$	−2.19185e14			−0.815041			−0.407521	−	0.913196i	$-0.633607\pi$
$769$	−2.19185e14			−0.815041			−0.407521	+	0.913196i	$0.633607\pi$
$770$		0			0
$771$	2.99890e14	+	4.36386e14i	1.10075	+	1.60176i
$772$		0			0
$773$		−	4.05042e14i		−	1.46758i	−0.679374	−	0.733792i	$-0.737749\pi$
$773$		−	4.05042e14i		−	1.46758i	0.679374	−	0.733792i	$-0.262251\pi$
$774$		0			0
$775$	−1.42837e14			−0.510894
$776$		0			0
$777$	2.33331e14	−	1.60348e14i	0.823886	−	0.566185i
$778$		0			0
$779$			1.14440e14i			0.398925i
$780$		0			0
$781$	3.56775e13			0.122783
$782$		0			0
$783$	−6.74268e13	+	1.61778e13i	−0.229099	+	0.0549681i
$784$		0			0
$785$		−	5.77141e14i		−	1.93613i
$786$		0			0
$787$	4.98729e14			1.65193			0.825963	−	0.563724i	$-0.190632\pi$
$787$	4.98729e14			1.65193			0.825963	+	0.563724i	$0.190632\pi$
$788$		0			0
$789$	1.89845e14	+	2.76254e14i	0.620890	+	0.903491i
$790$		0			0
$791$			3.06958e14i			0.991280i
$792$		0			0
$793$	9.03088e13			0.287981
$794$		0			0
$795$	−3.06490e13	+	2.10624e13i	−0.0965119	+	0.0663242i
$796$		0			0
$797$		−	1.48672e14i		−	0.462314i	−0.972917	−	0.231157i	$-0.925749\pi$
$797$		−	1.48672e14i		−	0.462314i	0.972917	−	0.231157i	$-0.0742510\pi$
$798$		0			0
$799$	4.13427e14			1.26959
$800$		0			0
$801$	1.31607e13	+	5.05331e12i	0.0399131	+	0.0153255i
$802$		0			0
$803$		−	1.36492e14i		−	0.408817i
$804$		0			0
$805$	1.18328e14			0.350033
$806$		0			0
$807$	−1.62578e14	−	2.36576e14i	−0.475001	−	0.691200i
$808$		0			0
$809$			1.32296e14i			0.381772i	0.981612	+	0.190886i	$0.0611361\pi$
$809$			1.32296e14i			0.381772i	−0.981612	+	0.190886i	$0.938864\pi$
$810$		0			0
$811$	−3.75449e14			−1.07016			−0.535078	−	0.844803i	$-0.679718\pi$
$811$	−3.75449e14			−1.07016			−0.535078	+	0.844803i	$0.679718\pi$
$812$		0			0
$813$	−2.84884e14	+	1.95776e14i	−0.802076	+	0.551197i
$814$		0			0
$815$			3.34305e14i			0.929726i
$816$		0			0
$817$	−1.52383e14			−0.418625
$818$		0			0
$819$	8.36547e13	−	2.17867e14i	0.227023	−	0.591252i
$820$		0			0
$821$		−	4.64480e12i		−	0.0124524i	−0.999981	−	0.00622618i	$-0.998018\pi$
$821$		−	4.64480e12i		−	0.0124524i	0.999981	−	0.00622618i	$-0.00198187\pi$
$822$		0			0
$823$	−6.38146e14			−1.69013			−0.845067	−	0.534661i	$-0.820439\pi$
$823$	−6.38146e14			−1.69013			−0.845067	+	0.534661i	$0.820439\pi$
$824$		0			0
$825$	−2.93454e13	−	4.27021e13i	−0.0767840	−	0.111733i
$826$		0			0
$827$			5.33624e14i			1.37946i	0.724068	+	0.689728i	$0.242270\pi$
$827$			5.33624e14i			1.37946i	−0.724068	+	0.689728i	$0.757730\pi$
$828$		0			0
$829$	8.63626e13			0.220573			0.110287	−	0.993900i	$-0.464823\pi$
$829$	8.63626e13			0.220573			0.110287	+	0.993900i	$0.464823\pi$
$830$		0			0
$831$	1.06135e14	−	7.29370e13i	0.267825	−	0.184053i
$832$		0			0
$833$			6.85220e14i			1.70846i
$834$		0			0
$835$	−7.71170e14			−1.89984
$836$		0			0
$837$	1.40035e14	+	5.83647e14i	0.340886	+	1.42077i
$838$		0			0
$839$		−	4.28770e14i		−	1.03137i	−0.856778	−	0.515685i	$-0.827538\pi$
$839$		−	4.28770e14i		−	1.03137i	0.856778	−	0.515685i	$-0.172462\pi$
$840$		0			0
$841$	3.97355e14			0.944492
$842$		0			0
$843$	−3.14397e14	−	4.57496e14i	−0.738483	−	1.07461i
$844$		0			0
$845$			3.95373e14i			0.917747i
$846$		0			0
$847$	5.11874e14			1.17421
$848$		0			0
$849$	−4.63171e14	+	3.18297e14i	−1.05003	+	0.721595i
$850$		0			0
$851$		−	7.03905e13i		−	0.157713i
$852$		0			0
$853$	8.99493e10			0.000199183			9.95916e−5	−	1.00000i	$-0.499968\pi$
$853$	8.99493e10			0.000199183			9.95916e−5		1.00000i	$0.499968\pi$
$854$		0			0
$855$	−1.53465e14	−	5.89260e13i	−0.335875	−	0.128966i
$856$		0			0
$857$			1.45265e14i			0.314238i	0.987580	+	0.157119i	$0.0502205\pi$
$857$			1.45265e14i			0.314238i	−0.987580	+	0.157119i	$0.949779\pi$
$858$		0			0
$859$	−3.53555e14			−0.755947			−0.377974	−	0.925816i	$-0.623379\pi$
$859$	−3.53555e14			−0.755947			−0.377974	+	0.925816i	$0.623379\pi$
$860$		0			0
$861$	−4.77058e14	−	6.94192e14i	−1.00822	−	1.46711i
$862$		0			0
$863$			5.16372e14i			1.07872i	0.842075	+	0.539360i	$0.181334\pi$
$863$			5.16372e14i			1.07872i	−0.842075	+	0.539360i	$0.818666\pi$
$864$		0			0
$865$	1.10414e15			2.28005
$866$		0			0
$867$	1.01996e15	−	7.00930e14i	2.08204	−	1.43080i
$868$		0			0
$869$			1.22757e14i			0.247713i
$870$		0			0
$871$	8.88397e13			0.177221
$872$		0			0
$873$	−1.87135e14	+	4.87367e14i	−0.369048	+	0.961136i
$874$		0			0
$875$		−	5.35530e14i		−	1.04410i
$876$		0			0
$877$	−3.23487e13			−0.0623532			−0.0311766	−	0.999514i	$-0.509925\pi$
$877$	−3.23487e13			−0.0623532			−0.0311766	+	0.999514i	$0.509925\pi$
$878$		0			0
$879$	−1.45870e14	−	2.12264e14i	−0.277986	−	0.404512i
$880$		0			0
$881$			3.45484e14i			0.650950i	0.945551	+	0.325475i	$0.105524\pi$
$881$			3.45484e14i			0.650950i	−0.945551	+	0.325475i	$0.894476\pi$
$882$		0			0
$883$	−1.94069e14			−0.361537			−0.180769	−	0.983526i	$-0.557859\pi$
$883$	−1.94069e14			−0.361537			−0.180769	+	0.983526i	$0.557859\pi$
$884$		0			0
$885$	2.12324e14	−	1.45911e14i	0.391095	−	0.268765i
$886$		0			0
$887$			2.06383e14i			0.375885i	0.982180	+	0.187943i	$0.0601819\pi$
$887$			2.06383e14i			0.375885i	−0.982180	+	0.187943i	$0.939818\pi$
$888$		0			0
$889$	7.38171e14			1.32938
$890$		0			0
$891$	−1.45716e14	+	1.61773e14i	−0.259489	+	0.288084i
$892$		0			0
$893$		−	1.18903e14i		−	0.209380i
$894$		0			0
$895$	−2.56716e13			−0.0447031
$896$		0			0
$897$	−3.28628e13	−	4.78204e13i	−0.0565903	−	0.0823476i
$898$		0			0
$899$			2.02140e14i			0.344234i
$900$		0			0
$901$	−1.12394e14			−0.189286
$902$		0			0
$903$	9.24353e14	−	6.35227e14i	1.53957	−	1.05801i
$904$		0			0
$905$		−	4.62190e14i		−	0.761339i
$906$		0			0
$907$	−3.53646e14			−0.576145			−0.288073	−	0.957609i	$-0.593014\pi$
$907$	−3.53646e14			−0.576145			−0.288073	+	0.957609i	$0.593014\pi$
$908$		0			0
$909$	9.25705e14	+	3.55444e14i	1.49160	+	0.572732i
$910$		0			0
$911$		−	4.57044e14i		−	0.728394i	−0.931322	−	0.364197i	$-0.881344\pi$
$911$		−	4.57044e14i		−	0.728394i	0.931322	−	0.364197i	$-0.118656\pi$
$912$		0			0
$913$	1.36473e14			0.215126
$914$		0			0
$915$	2.65179e14	+	3.85876e14i	0.413460	+	0.601648i
$916$		0			0
$917$			1.16387e15i			1.79497i
$918$		0			0
$919$	−4.85254e14			−0.740273			−0.370136	−	0.928977i	$-0.620689\pi$
$919$	−4.85254e14			−0.740273			−0.370136	+	0.928977i	$0.620689\pi$
$920$		0			0
$921$	−1.38027e14	+	9.48541e13i	−0.208289	+	0.143139i
$922$		0			0
$923$			9.72237e13i			0.145132i
$924$		0			0
$925$	1.71288e14			0.252941
$926$		0			0
$927$	−1.77134e14	+	4.61322e14i	−0.258764	+	0.673916i
$928$		0			0
$929$			8.16207e14i			1.17957i	0.807562	+	0.589783i	$0.200787\pi$
$929$			8.16207e14i			1.17957i	−0.807562	+	0.589783i	$0.799213\pi$
$930$		0			0
$931$	1.97071e14			0.281757
$932$		0			0
$933$	2.69301e14	+	3.91874e14i	0.380916	+	0.554292i
$934$		0			0
$935$		−	6.04432e14i		−	0.845842i
$936$		0			0
$937$	−6.90133e14			−0.955510			−0.477755	−	0.878493i	$-0.658549\pi$
$937$	−6.90133e14			−0.955510			−0.477755	+	0.878493i	$0.658549\pi$
$938$		0			0
$939$	4.98311e13	−	3.42445e13i	0.0682609	−	0.0469098i
$940$		0			0
$941$		−	1.26481e14i		−	0.171426i	−0.996320	−	0.0857129i	$-0.972683\pi$
$941$		−	1.26481e14i		−	0.171426i	0.996320	−	0.0857129i	$-0.0273168\pi$
$942$		0			0
$943$	−2.09422e14			−0.280843
$944$		0			0
$945$	1.17656e15	−	2.82292e14i	1.56118	−	0.374576i
$946$		0			0
$947$		−	3.05743e14i		−	0.401427i	−0.979650	−	0.200713i	$-0.935674\pi$
$947$		−	3.05743e14i		−	0.401427i	0.979650	−	0.200713i	$-0.0643260\pi$
$948$		0			0
$949$	3.71950e14			0.483230
$950$		0			0
$951$	6.38144e14	+	9.28598e14i	0.820382	+	1.19378i
$952$		0			0
$953$		−	7.71039e14i		−	0.980870i	−0.871478	−	0.490435i	$-0.836838\pi$
$953$		−	7.71039e14i		−	0.980870i	0.871478	−	0.490435i	$-0.163162\pi$
$954$		0			0
$955$	−7.49546e14			−0.943586
$956$		0			0
$957$	−6.04315e13	+	4.15292e13i	−0.0752841	+	0.0517362i
$958$		0			0
$959$			6.38134e14i			0.786718i
$960$		0			0
$961$	9.30098e14			1.13478
$962$		0			0
$963$	7.91348e14	+	3.03855e14i	0.955512	+	0.366889i
$964$		0			0
$965$		−	1.13128e15i		−	1.35186i
$966$		0			0
$967$	−1.27364e15			−1.50631			−0.753154	−	0.657845i	$-0.771468\pi$
$967$	−1.27364e15			−1.50631			−0.753154	+	0.657845i	$0.771468\pi$
$968$		0			0
$969$	−2.81387e14	−	4.09461e14i	−0.329371	−	0.479285i
$970$		0			0
$971$		−	4.71364e14i		−	0.546085i	−0.962002	−	0.273043i	$-0.911970\pi$
$971$		−	4.71364e14i		−	0.546085i	0.962002	−	0.273043i	$-0.0880300\pi$
$972$		0			0
$973$	1.46905e15			1.68451
$974$		0			0
$975$	1.16366e14	−	7.99683e13i	0.132070	−	0.0907601i
$976$		0			0
$977$			1.09733e15i			1.23272i	0.787465	+	0.616360i	$0.211393\pi$
$977$			1.09733e15i			1.23272i	−0.787465	+	0.616360i	$0.788607\pi$
$978$		0			0
$979$	1.49077e13			0.0165767
$980$		0			0
$981$	1.00025e14	−	2.60501e14i	0.110094	−	0.286724i
$982$		0			0
$983$		−	1.52240e15i		−	1.65867i	−0.558751	−	0.829336i	$-0.688719\pi$
$983$		−	1.52240e15i		−	1.65867i	0.558751	−	0.829336i	$-0.311281\pi$
$984$		0			0
$985$	−5.50722e14			−0.593952
$986$		0			0
$987$	4.95661e14	+	7.21264e14i	0.529175	+	0.770031i
$988$		0			0
$989$		−	2.78856e14i		−	0.294712i
$990$		0			0
$991$	−3.79461e14			−0.397008			−0.198504	−	0.980100i	$-0.563608\pi$
$991$	−3.79461e14			−0.397008			−0.198504	+	0.980100i	$0.563608\pi$
$992$		0			0
$993$	2.83267e14	−	1.94665e14i	0.293393	−	0.201623i
$994$		0			0
$995$		−	4.05493e14i		−	0.415785i
$996$		0			0
$997$	−3.25337e13			−0.0330262			−0.0165131	−	0.999864i	$-0.505257\pi$
$997$	−3.25337e13			−0.0330262			−0.0165131	+	0.999864i	$0.505257\pi$
$998$		0			0
$999$	−1.67929e14	−	6.99905e14i	−0.168771	−	0.703415i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	192.11.e.h.65.2		4
3.2	odd	2	inner	192.11.e.h.65.1		4
4.3	odd	2		192.11.e.g.65.3		4
8.3	odd	2		6.11.b.a.5.1	✓	4
8.5	even	2		48.11.e.d.17.3		4
12.11	even	2		192.11.e.g.65.4		4
24.5	odd	2		48.11.e.d.17.4		4
24.11	even	2		6.11.b.a.5.3	yes	4
40.3	even	4		150.11.b.a.149.1		8
40.19	odd	2		150.11.d.a.101.4		4
40.27	even	4		150.11.b.a.149.8		8
72.11	even	6		162.11.d.d.53.4		8
72.43	odd	6		162.11.d.d.53.1		8
72.59	even	6		162.11.d.d.107.1		8
72.67	odd	6		162.11.d.d.107.4		8
120.59	even	2		150.11.d.a.101.2		4
120.83	odd	4		150.11.b.a.149.7		8
120.107	odd	4		150.11.b.a.149.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6.11.b.a.5.1	✓	4	8.3	odd	2
6.11.b.a.5.3	yes	4	24.11	even	2
48.11.e.d.17.3		4	8.5	even	2
48.11.e.d.17.4		4	24.5	odd	2
150.11.b.a.149.1		8	40.3	even	4
150.11.b.a.149.2		8	120.107	odd	4
150.11.b.a.149.7		8	120.83	odd	4
150.11.b.a.149.8		8	40.27	even	4
150.11.d.a.101.2		4	120.59	even	2
150.11.d.a.101.4		4	40.19	odd	2
162.11.d.d.53.1		8	72.43	odd	6
162.11.d.d.53.4		8	72.11	even	6
162.11.d.d.107.1		8	72.59	even	6
162.11.d.d.107.4		8	72.67	odd	6
192.11.e.g.65.3		4	4.3	odd	2
192.11.e.g.65.4		4	12.11	even	2
192.11.e.h.65.1		4	3.2	odd	2	inner
192.11.e.h.65.2		4	1.1	even	1	trivial

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:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	192.e (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(-200.269 + 137.627i) q^{3} -3630.47i q^{5} +23226.5 q^{7} +(21166.4 - 55125.0i) q^{9} +O(q^{10})\)	\(q+(-200.269 + 137.627i) q^{3} -3630.47i q^{5} +23226.5 q^{7} +(21166.4 - 55125.0i) q^{9} -62442.7i q^{11} +170161. q^{13} +(499653. + 727072. i) q^{15} +2.66626e6i q^{17} +766825. q^{19} +(-4.65156e6 + 3.19661e6i) q^{21} +1.40327e6i q^{23} -3.41471e6 q^{25} +(3.34774e6 + 1.39529e7i) q^{27} +4.83245e6i q^{29} +4.18297e7 q^{31} +(8.59382e6 + 1.25053e7i) q^{33} -8.43233e7i q^{35} -5.01619e7 q^{37} +(-3.40779e7 + 2.34188e7i) q^{39} +1.49239e8i q^{41} -1.98719e8 q^{43} +(-2.00130e8 - 7.68440e7i) q^{45} -1.55059e8i q^{47} +2.56996e8 q^{49} +(-3.66951e8 - 5.33970e8i) q^{51} +4.21541e7i q^{53} -2.26696e8 q^{55} +(-1.53571e8 + 1.05536e8i) q^{57} -2.92026e8i q^{59} +5.30727e8 q^{61} +(4.91622e8 - 1.28036e9i) q^{63} -6.17764e8i q^{65} +5.22093e8 q^{67} +(-1.93128e8 - 2.81031e8i) q^{69} +5.71364e8i q^{71} +2.18588e9 q^{73} +(6.83861e8 - 4.69958e8i) q^{75} -1.45033e9i q^{77} -1.96592e9 q^{79} +(-2.59075e9 - 2.33360e9i) q^{81} +2.18558e9i q^{83} +9.67979e9 q^{85} +(-6.65078e8 - 9.67791e8i) q^{87} +2.38742e8i q^{89} +3.95224e9 q^{91} +(-8.37720e9 + 5.75692e9i) q^{93} -2.78394e9i q^{95} -8.84112e9 q^{97} +(-3.44215e9 - 1.32169e9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 84 q^{3} + 45112 q^{7} + 159012 q^{9}+O(q^{10}) \) 4 * q + 84 * q^3 + 45112 * q^7 + 159012 * q^9	\( 4 q + 84 q^{3} + 45112 q^{7} + 159012 q^{9} - 275240 q^{13} + 1180800 q^{15} - 1568728 q^{19} - 9628008 q^{21} - 33732380 q^{25} + 34619508 q^{27} + 21785848 q^{31} + 25974144 q^{33} + 71014168 q^{37} - 217287240 q^{39} - 470688664 q^{43} - 312318720 q^{45} - 50058420 q^{49} - 708576768 q^{51} - 2701359360 q^{55} - 1058753208 q^{57} + 1184038744 q^{61} + 905007096 q^{63} - 297365848 q^{67} - 596268288 q^{69} + 6534269000 q^{73} - 5150031180 q^{75} - 199282568 q^{79} + 1458964548 q^{81} + 12880512000 q^{85} - 210268800 q^{87} + 8317232080 q^{91} - 31744468392 q^{93} - 39176355064 q^{97} - 2626912512 q^{99}+O(q^{100}) \) 4 * q + 84 * q^3 + 45112 * q^7 + 159012 * q^9 - 275240 * q^13 + 1180800 * q^15 - 1568728 * q^19 - 9628008 * q^21 - 33732380 * q^25 + 34619508 * q^27 + 21785848 * q^31 + 25974144 * q^33 + 71014168 * q^37 - 217287240 * q^39 - 470688664 * q^43 - 312318720 * q^45 - 50058420 * q^49 - 708576768 * q^51 - 2701359360 * q^55 - 1058753208 * q^57 + 1184038744 * q^61 + 905007096 * q^63 - 297365848 * q^67 - 596268288 * q^69 + 6534269000 * q^73 - 5150031180 * q^75 - 199282568 * q^79 + 1458964548 * q^81 + 12880512000 * q^85 - 210268800 * q^87 + 8317232080 * q^91 - 31744468392 * q^93 - 39176355064 * q^97 - 2626912512 * q^99

Introduction

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