LMFDB - Embedded newform 1008.2.bt.c.17.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(17,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1008.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.bt (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.3
Root			$-0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	1008.17
Dual form			1008.2.bt.c.593.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.358719 + 0.621320i) q^{5} +(-2.62132 - 0.358719i) q^{7} +(-2.59808 - 1.50000i) q^{11} +2.44949i q^{13} +(2.95680 - 5.12132i) q^{17} +(5.12132 - 2.95680i) q^{19} +(3.67423 - 2.12132i) q^{23} +(2.24264 - 3.88437i) q^{25} -7.24264i q^{29} +(7.86396 + 4.54026i) q^{31} +(-0.717439 - 1.75736i) q^{35} +(0.121320 + 0.210133i) q^{37} -11.8272 q^{41} +0.242641 q^{43} +(-2.95680 - 5.12132i) q^{47} +(6.74264 + 1.88064i) q^{49} +(6.27231 + 3.62132i) q^{53} -2.15232i q^{55} +(4.03295 - 6.98528i) q^{59} +(0.878680 - 0.507306i) q^{61} +(-1.52192 + 0.878680i) q^{65} +(-5.00000 + 8.66025i) q^{67} -1.75736i q^{71} +(-1.24264 - 0.717439i) q^{73} +(6.27231 + 4.86396i) q^{77} +(-1.37868 - 2.38794i) q^{79} +6.63103 q^{83} +4.24264 q^{85} +(-5.19615 - 9.00000i) q^{89} +(0.878680 - 6.42090i) q^{91} +(3.67423 + 2.12132i) q^{95} -13.5592i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{7} + 24 q^{19} - 16 q^{25} + 12 q^{31} - 16 q^{37} - 32 q^{43} + 20 q^{49} + 24 q^{61} - 40 q^{67} + 24 q^{73} - 28 q^{79} + 24 q^{91}+O(q^{100}) $ 8 * q - 4 * q^7 + 24 * q^19 - 16 * q^25 + 12 * q^31 - 16 * q^37 - 32 * q^43 + 20 * q^49 + 24 * q^61 - 40 * q^67 + 24 * q^73 - 28 * q^79 + 24 * q^91

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$	$-1$

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
$3$		0			0
$3$		0			0
$4$		0			0
$5$	0.358719	+	0.621320i	0.160424	+	0.277863i	0.935021	−	0.354593i	$-0.115380\pi$
$5$	0.358719	+	0.621320i	0.160424	+	0.277863i	−0.774597	+	0.632456i	$0.782047\pi$
$6$		0			0
$7$	−2.62132	−	0.358719i	−0.990766	−	0.135583i
$7$	−2.62132	−	0.358719i	−0.990766	−	0.135583i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−2.59808	−	1.50000i	−0.783349	−	0.452267i	0.0542666	−	0.998526i	$-0.482718\pi$
$11$	−2.59808	−	1.50000i	−0.783349	−	0.452267i	−0.837616	+	0.546259i	$0.816051\pi$
$12$		0			0
$13$			2.44949i			0.679366i	0.940540	+	0.339683i	$0.110320\pi$
$13$			2.44949i			0.679366i	−0.940540	+	0.339683i	$0.889680\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	2.95680	−	5.12132i	0.717128	−	1.24210i	−0.245005	−	0.969522i	$-0.578789\pi$
$17$	2.95680	−	5.12132i	0.717128	−	1.24210i	0.962133	−	0.272581i	$-0.0878772\pi$
$18$		0			0
$19$	5.12132	−	2.95680i	1.17491	−	0.678335i	0.220080	−	0.975482i	$-0.429368\pi$
$19$	5.12132	−	2.95680i	1.17491	−	0.678335i	0.954832	+	0.297146i	$0.0960350\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	3.67423	−	2.12132i	0.766131	−	0.442326i	−0.0653618	−	0.997862i	$-0.520820\pi$
$23$	3.67423	−	2.12132i	0.766131	−	0.442326i	0.831493	+	0.555536i	$0.187487\pi$
$24$		0			0
$25$	2.24264	−	3.88437i	0.448528	−	0.776874i
$26$		0			0
$27$		0			0
$28$		0			0
$29$		−	7.24264i		−	1.34492i	−0.740131	−	0.672462i	$-0.765237\pi$
$29$		−	7.24264i		−	1.34492i	0.740131	−	0.672462i	$-0.234763\pi$
$30$		0			0
$31$	7.86396	+	4.54026i	1.41241	+	0.815455i	0.995615	−	0.0935461i	$-0.0298203\pi$
$31$	7.86396	+	4.54026i	1.41241	+	0.815455i	0.416794	+	0.909001i	$0.363154\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−0.717439	−	1.75736i	−0.121269	−	0.297048i
$36$		0			0
$37$	0.121320	+	0.210133i	0.0199449	+	0.0345457i	0.875826	−	0.482628i	$-0.160318\pi$
$37$	0.121320	+	0.210133i	0.0199449	+	0.0345457i	−0.855881	+	0.517173i	$0.826984\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−11.8272			−1.84710			−0.923548	−	0.383483i	$-0.874724\pi$
$41$	−11.8272			−1.84710			−0.923548	+	0.383483i	$0.874724\pi$
$42$		0			0
$43$	0.242641			0.0370024			0.0185012	−	0.999829i	$-0.494111\pi$
$43$	0.242641			0.0370024			0.0185012	+	0.999829i	$0.494111\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−2.95680	−	5.12132i	−0.431293	−	0.747021i	0.565692	−	0.824617i	$-0.308609\pi$
$47$	−2.95680	−	5.12132i	−0.431293	−	0.747021i	−0.996985	+	0.0775953i	$0.975276\pi$
$48$		0			0
$49$	6.74264	+	1.88064i	0.963234	+	0.268662i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	6.27231	+	3.62132i	0.861568	+	0.497427i	0.864537	−	0.502569i	$-0.167612\pi$
$53$	6.27231	+	3.62132i	0.861568	+	0.497427i	−0.00296896	+	0.999996i	$0.500945\pi$
$54$		0			0
$55$		−	2.15232i		−	0.290218i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	4.03295	−	6.98528i	0.525046	−	0.909406i	−0.474529	−	0.880240i	$-0.657381\pi$
$59$	4.03295	−	6.98528i	0.525046	−	0.909406i	0.999575	−	0.0291661i	$-0.00928518\pi$
$60$		0			0
$61$	0.878680	−	0.507306i	0.112503	−	0.0649539i	−0.442692	−	0.896674i	$-0.645977\pi$
$61$	0.878680	−	0.507306i	0.112503	−	0.0649539i	0.555196	+	0.831720i	$0.312643\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1.52192	+	0.878680i	−0.188771	+	0.108987i
$66$		0			0
$67$	−5.00000	+	8.66025i	−0.610847	+	1.05802i	0.380251	+	0.924883i	$0.375838\pi$
$67$	−5.00000	+	8.66025i	−0.610847	+	1.05802i	−0.991098	+	0.133135i	$0.957496\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	1.75736i		−	0.208560i	−0.994548	−	0.104280i	$-0.966746\pi$
$71$		−	1.75736i		−	0.208560i	0.994548	−	0.104280i	$-0.0332538\pi$
$72$		0			0
$73$	−1.24264	−	0.717439i	−0.145440	−	0.0839699i	0.425514	−	0.904952i	$-0.360093\pi$
$73$	−1.24264	−	0.717439i	−0.145440	−	0.0839699i	−0.570954	+	0.820982i	$0.693427\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	6.27231	+	4.86396i	0.714796	+	0.554300i
$78$		0			0
$79$	−1.37868	−	2.38794i	−0.155114	−	0.268665i	0.777987	−	0.628281i	$-0.216241\pi$
$79$	−1.37868	−	2.38794i	−0.155114	−	0.268665i	−0.933100	+	0.359616i	$0.882908\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	6.63103			0.727850			0.363925	−	0.931428i	$-0.381436\pi$
$83$	6.63103			0.727850			0.363925	+	0.931428i	$0.381436\pi$
$84$		0			0
$85$	4.24264			0.460179
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−5.19615	−	9.00000i	−0.550791	−	0.953998i	−0.998218	−	0.0596775i	$-0.980993\pi$
$89$	−5.19615	−	9.00000i	−0.550791	−	0.953998i	0.447427	−	0.894321i	$-0.352341\pi$
$90$		0			0
$91$	0.878680	−	6.42090i	0.0921107	−	0.673093i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	3.67423	+	2.12132i	0.376969	+	0.217643i
$96$		0			0
$97$		−	13.5592i		−	1.37673i	−0.725364	−	0.688366i	$-0.758328\pi$
$97$		−	13.5592i		−	1.37673i	0.725364	−	0.688366i	$-0.241672\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$101$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$102$		0			0
$103$	4.75736	−	2.74666i	0.468757	−	0.270637i	−0.246963	−	0.969025i	$-0.579432\pi$
$103$	4.75736	−	2.74666i	0.468757	−	0.270637i	0.715719	+	0.698388i	$0.246099\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−9.94655	+	5.74264i	−0.961569	+	0.555162i	−0.896656	−	0.442729i	$-0.854010\pi$
$107$	−9.94655	+	5.74264i	−0.961569	+	0.555162i	−0.0649133	+	0.997891i	$0.520677\pi$
$108$		0			0
$109$	−9.24264	+	16.0087i	−0.885284	+	1.53336i	−0.0398971	+	0.999204i	$0.512703\pi$
$109$	−9.24264	+	16.0087i	−0.885284	+	1.53336i	−0.845387	+	0.534154i	$0.820630\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$		−	8.48528i		−	0.798228i	−0.916901	−	0.399114i	$-0.869318\pi$
$113$		−	8.48528i		−	0.798228i	0.916901	−	0.399114i	$-0.130682\pi$
$114$		0			0
$115$	2.63604	+	1.52192i	0.245812	+	0.141920i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−9.58783	+	12.3640i	−0.878915	+	1.13340i
$120$		0			0
$121$	−1.00000	−	1.73205i	−0.0909091	−	0.157459i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	6.80511			0.608668
$126$		0			0
$127$	−3.24264			−0.287738			−0.143869	−	0.989597i	$-0.545954\pi$
$127$	−3.24264			−0.287738			−0.143869	+	0.989597i	$0.545954\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−2.59808	−	4.50000i	−0.226995	−	0.393167i	0.729921	−	0.683531i	$-0.239557\pi$
$131$	−2.59808	−	4.50000i	−0.226995	−	0.393167i	−0.956916	+	0.290365i	$0.906223\pi$
$132$		0			0
$133$	−14.4853	+	5.91359i	−1.25603	+	0.512773i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	2.15232	+	1.24264i	0.183885	+	0.106166i	0.589117	−	0.808048i	$-0.299476\pi$
$137$	2.15232	+	1.24264i	0.183885	+	0.106166i	−0.405232	+	0.914214i	$0.632809\pi$
$138$		0			0
$139$		−	0.594346i		−	0.0504118i	−0.999682	−	0.0252059i	$-0.991976\pi$
$139$		−	0.594346i		−	0.0504118i	0.999682	−	0.0252059i	$-0.00802413\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	3.67423	−	6.36396i	0.307255	−	0.532181i
$144$		0			0
$145$	4.50000	−	2.59808i	0.373705	−	0.215758i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	3.04384	−	1.75736i	0.249361	−	0.143968i	−0.370111	−	0.928988i	$-0.620680\pi$
$149$	3.04384	−	1.75736i	0.249361	−	0.143968i	0.619472	+	0.785019i	$0.287347\pi$
$150$		0			0
$151$	2.62132	−	4.54026i	0.213320	−	0.369481i	−0.739432	−	0.673232i	$-0.764906\pi$
$151$	2.62132	−	4.54026i	0.213320	−	0.369481i	0.952752	+	0.303751i	$0.0982390\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$			6.51472i			0.523275i
$156$		0			0
$157$	12.7279	+	7.34847i	1.01580	+	0.586472i	0.912884	−	0.408219i	$-0.133850\pi$
$157$	12.7279	+	7.34847i	1.01580	+	0.586472i	0.102915	+	0.994690i	$0.467183\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−10.3923	+	4.24264i	−0.819028	+	0.334367i
$162$		0			0
$163$	−1.12132	−	1.94218i	−0.0878286	−	0.152124i	0.818764	−	0.574130i	$-0.194659\pi$
$163$	−1.12132	−	1.94218i	−0.0878286	−	0.152124i	−0.906593	+	0.422006i	$0.861326\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−16.1318			−1.24832			−0.624159	−	0.781298i	$-0.714558\pi$
$167$	−16.1318			−1.24832			−0.624159	+	0.781298i	$0.714558\pi$
$168$		0			0
$169$	7.00000			0.538462
$170$		0			0
$171$		0			0
$172$		0			0
$173$	10.3923	+	18.0000i	0.790112	+	1.36851i	0.925897	+	0.377776i	$0.123311\pi$
$173$	10.3923	+	18.0000i	0.790112	+	1.36851i	−0.135785	+	0.990738i	$0.543356\pi$
$174$		0			0
$175$	−7.27208	+	9.37769i	−0.549717	+	0.708887i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	22.9369	+	13.2426i	1.71439	+	0.989801i	0.928420	+	0.371532i	$0.121167\pi$
$179$	22.9369	+	13.2426i	1.71439	+	0.989801i	0.785966	+	0.618269i	$0.212166\pi$
$180$		0			0
$181$		−	11.8272i		−	0.879108i	−0.898216	−	0.439554i	$-0.855137\pi$
$181$		−	11.8272i		−	0.879108i	0.898216	−	0.439554i	$-0.144863\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−0.0870399	+	0.150758i	−0.00639930	+	0.0110839i
$186$		0			0
$187$	−15.3640	+	8.87039i	−1.12352	+	0.648667i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	7.34847	−	4.24264i	0.531717	−	0.306987i	−0.209999	−	0.977702i	$-0.567346\pi$
$191$	7.34847	−	4.24264i	0.531717	−	0.306987i	0.741715	+	0.670715i	$0.234013\pi$
$192$		0			0
$193$	−4.74264	+	8.21449i	−0.341383	+	0.591292i	−0.984690	−	0.174316i	$-0.944229\pi$
$193$	−4.74264	+	8.21449i	−0.341383	+	0.591292i	0.643307	+	0.765608i	$0.277562\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			26.4853i			1.88700i	0.331375	+	0.943499i	$0.392487\pi$
$197$			26.4853i			1.88700i	−0.331375	+	0.943499i	$0.607513\pi$
$198$		0			0
$199$	−19.9706	−	11.5300i	−1.41568	−	0.817341i	−0.419761	−	0.907635i	$-0.637886\pi$
$199$	−19.9706	−	11.5300i	−1.41568	−	0.817341i	−0.995915	+	0.0902942i	$0.971219\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−2.59808	+	18.9853i	−0.182349	+	1.33251i
$204$		0			0
$205$	−4.24264	−	7.34847i	−0.296319	−	0.513239i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−17.7408			−1.22716
$210$		0			0
$211$	0.242641			0.0167041			0.00835204	−	0.999965i	$-0.497341\pi$
$211$	0.242641			0.0167041			0.00835204	+	0.999965i	$0.497341\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	0.0870399	+	0.150758i	0.00593607	+	0.0102816i
$216$		0			0
$217$	−18.9853	−	14.7224i	−1.28880	−	0.999424i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	12.5446	+	7.24264i	0.843843	+	0.487193i
$222$		0			0
$223$			2.15232i			0.144130i	0.997400	+	0.0720649i	$0.0229589\pi$
$223$			2.15232i			0.144130i	−0.997400	+	0.0720649i	$0.977041\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	7.79423	−	13.5000i	0.517321	−	0.896026i	−0.482476	−	0.875909i	$-0.660263\pi$
$227$	7.79423	−	13.5000i	0.517321	−	0.896026i	0.999798	−	0.0201176i	$-0.00640405\pi$
$228$		0			0
$229$	−12.0000	+	6.92820i	−0.792982	+	0.457829i	−0.841011	−	0.541017i	$-0.818039\pi$
$229$	−12.0000	+	6.92820i	−0.792982	+	0.457829i	0.0480291	+	0.998846i	$0.484706\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−16.2189	+	9.36396i	−1.06253	+	0.613453i	−0.926132	−	0.377200i	$-0.876887\pi$
$233$	−16.2189	+	9.36396i	−1.06253	+	0.613453i	−0.136401	+	0.990654i	$0.543554\pi$
$234$		0			0
$235$	2.12132	−	3.67423i	0.138380	−	0.239681i
$236$		0			0
$237$		0			0
$238$		0			0
$239$			12.7279i			0.823301i	0.911342	+	0.411650i	$0.135048\pi$
$239$			12.7279i			0.823301i	−0.911342	+	0.411650i	$0.864952\pi$
$240$		0			0
$241$	6.25736	+	3.61269i	0.403072	+	0.232714i	0.687809	−	0.725892i	$-0.258573\pi$
$241$	6.25736	+	3.61269i	0.403072	+	0.232714i	−0.284737	+	0.958606i	$0.591906\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	1.25024	+	4.86396i	0.0798748	+	0.310747i
$246$		0			0
$247$	7.24264	+	12.5446i	0.460838	+	0.798195i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−27.4156			−1.73046			−0.865230	−	0.501375i	$-0.832828\pi$
$251$	−27.4156			−1.73046			−0.865230	+	0.501375i	$0.832828\pi$
$252$		0			0
$253$	−12.7279			−0.800198
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−2.15232	−	3.72792i	−0.134258	−	0.232541i	0.791056	−	0.611744i	$-0.209532\pi$
$257$	−2.15232	−	3.72792i	−0.134258	−	0.232541i	−0.925314	+	0.379203i	$0.876198\pi$
$258$		0			0
$259$	−0.242641	−	0.594346i	−0.0150770	−	0.0369309i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	13.1750	+	7.60660i	0.812407	+	0.469043i	0.847791	−	0.530331i	$-0.177932\pi$
$263$	13.1750	+	7.60660i	0.812407	+	0.469043i	−0.0353843	+	0.999374i	$0.511266\pi$
$264$		0			0
$265$			5.19615i			0.319197i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	6.98975	−	12.1066i	0.426173	−	0.738153i	−0.570357	−	0.821397i	$-0.693195\pi$
$269$	6.98975	−	12.1066i	0.426173	−	0.738153i	0.996529	+	0.0832447i	$0.0265283\pi$
$270$		0			0
$271$	5.37868	−	3.10538i	0.326732	−	0.188639i	−0.327658	−	0.944797i	$-0.606259\pi$
$271$	5.37868	−	3.10538i	0.326732	−	0.188639i	0.654389	+	0.756158i	$0.272926\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−11.6531	+	6.72792i	−0.702709	+	0.405709i
$276$		0			0
$277$	−6.48528	+	11.2328i	−0.389663	+	0.674916i	−0.992404	−	0.123021i	$-0.960742\pi$
$277$	−6.48528	+	11.2328i	−0.389663	+	0.674916i	0.602741	+	0.797937i	$0.294075\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		−	6.00000i		−	0.357930i	−0.983855	−	0.178965i	$-0.942725\pi$
$281$		−	6.00000i		−	0.357930i	0.983855	−	0.178965i	$-0.0572749\pi$
$282$		0			0
$283$	18.3640	+	10.6024i	1.09162	+	0.630250i	0.934008	−	0.357251i	$-0.116286\pi$
$283$	18.3640	+	10.6024i	1.09162	+	0.630250i	0.157616	+	0.987501i	$0.449619\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	31.0028	+	4.24264i	1.83004	+	0.250435i
$288$		0			0
$289$	−8.98528	−	15.5630i	−0.528546	−	0.915468i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	0.717439			0.0419132			0.0209566	−	0.999780i	$-0.493329\pi$
$293$	0.717439			0.0419132			0.0209566	+	0.999780i	$0.493329\pi$
$294$		0			0
$295$	5.78680			0.336920
$296$		0			0
$297$		0			0
$298$		0			0
$299$	5.19615	+	9.00000i	0.300501	+	0.520483i
$300$		0			0
$301$	−0.636039	−	0.0870399i	−0.0366607	−	0.00501690i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	0.630399	+	0.363961i	0.0360965	+	0.0208403i
$306$		0			0
$307$		−	9.97204i		−	0.569134i	−0.958656	−	0.284567i	$-0.908150\pi$
$307$		−	9.97204i		−	0.569134i	0.958656	−	0.284567i	$-0.0918499\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−4.47871	+	7.75736i	−0.253965	+	0.439879i	−0.964614	−	0.263667i	$-0.915068\pi$
$311$	−4.47871	+	7.75736i	−0.253965	+	0.439879i	0.710649	+	0.703547i	$0.248401\pi$
$312$		0			0
$313$	15.9853	−	9.22911i	0.903542	−	0.521660i	0.0251940	−	0.999683i	$-0.491980\pi$
$313$	15.9853	−	9.22911i	0.903542	−	0.521660i	0.878348	+	0.478023i	$0.158646\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−1.07616	+	0.621320i	−0.0604431	+	0.0348968i	−0.529917	−	0.848050i	$-0.677777\pi$
$317$	−1.07616	+	0.621320i	−0.0604431	+	0.0348968i	0.469474	+	0.882946i	$0.344444\pi$
$318$		0			0
$319$	−10.8640	+	18.8169i	−0.608265	+	1.05355i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	34.9706i		−	1.94581i
$324$		0			0
$325$	9.51472	+	5.49333i	0.527782	+	0.304715i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	5.91359	+	14.4853i	0.326027	+	0.798599i
$330$		0			0
$331$	−16.7279	−	28.9736i	−0.919450	−	1.59253i	−0.800253	−	0.599663i	$-0.795301\pi$
$331$	−16.7279	−	28.9736i	−0.919450	−	1.59253i	−0.119197	−	0.992871i	$-0.538032\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−7.17439			−0.391979
$336$		0			0
$337$	−5.00000			−0.272367			−0.136184	−	0.990684i	$-0.543484\pi$
$337$	−5.00000			−0.272367			−0.136184	+	0.990684i	$0.543484\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−13.6208	−	23.5919i	−0.737607	−	1.27757i
$342$		0			0
$343$	−17.0000	−	7.34847i	−0.917914	−	0.396780i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	2.15232	+	1.24264i	0.115542	+	0.0667084i	0.556657	−	0.830742i	$-0.312084\pi$
$347$	2.15232	+	1.24264i	0.115542	+	0.0667084i	−0.441115	+	0.897451i	$0.645417\pi$
$348$		0			0
$349$			2.27541i			0.121800i	0.998144	+	0.0608999i	$0.0193971\pi$
$349$			2.27541i			0.121800i	−0.998144	+	0.0608999i	$0.980603\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	4.47871	−	7.75736i	0.238378	−	0.412883i	−0.721871	−	0.692028i	$-0.756718\pi$
$353$	4.47871	−	7.75736i	0.238378	−	0.412883i	0.960249	+	0.279145i	$0.0900510\pi$
$354$		0			0
$355$	1.09188	−	0.630399i	0.0579511	−	0.0334581i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−15.5885	+	9.00000i	−0.822727	+	0.475002i	−0.851356	−	0.524588i	$-0.824219\pi$
$359$	−15.5885	+	9.00000i	−0.822727	+	0.475002i	0.0286287	+	0.999590i	$0.490886\pi$
$360$		0			0
$361$	7.98528	−	13.8309i	0.420278	−	0.727943i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		−	1.02944i		−	0.0538832i
$366$		0			0
$367$	13.3492	+	7.70719i	0.696825	+	0.402312i	0.806164	−	0.591693i	$-0.201540\pi$
$367$	13.3492	+	7.70719i	0.696825	+	0.402312i	−0.109339	+	0.994005i	$0.534873\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−15.1427	−	11.7426i	−0.786170	−	0.609648i
$372$		0			0
$373$	14.7279	+	25.5095i	0.762583	+	1.32083i	0.941515	+	0.336971i	$0.109402\pi$
$373$	14.7279	+	25.5095i	0.762583	+	1.32083i	−0.178932	+	0.983861i	$0.557264\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	17.7408			0.913696
$378$		0			0
$379$	−12.4853			−0.641326			−0.320663	−	0.947193i	$-0.603906\pi$
$379$	−12.4853			−0.641326			−0.320663	+	0.947193i	$0.603906\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−11.1097	−	19.2426i	−0.567681	−	0.983253i	−0.996795	−	0.0800023i	$-0.974507\pi$
$383$	−11.1097	−	19.2426i	−0.567681	−	0.983253i	0.429113	−	0.903251i	$-0.358826\pi$
$384$		0			0
$385$	−0.772078	+	5.64191i	−0.0393487	+	0.287538i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	27.2416	+	15.7279i	1.38120	+	0.797437i	0.992302	−	0.123843i	$-0.0395218\pi$
$389$	27.2416	+	15.7279i	1.38120	+	0.797437i	0.388900	+	0.921280i	$0.372855\pi$
$390$		0			0
$391$		−	25.0892i		−	1.26882i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	0.989118	−	1.71320i	0.0497680	−	0.0862006i
$396$		0			0
$397$	12.0000	−	6.92820i	0.602263	−	0.347717i	−0.167668	−	0.985843i	$-0.553624\pi$
$397$	12.0000	−	6.92820i	0.602263	−	0.347717i	0.769931	+	0.638127i	$0.220290\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$401$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$402$		0			0
$403$	−11.1213	+	19.2627i	−0.553992	+	0.959543i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	0.727922i		−	0.0360818i
$408$		0			0
$409$	12.9853	+	7.49706i	0.642081	+	0.370706i	0.785416	−	0.618969i	$-0.212449\pi$
$409$	12.9853	+	7.49706i	0.642081	+	0.370706i	−0.143335	+	0.989674i	$0.545783\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−13.0774	+	16.8640i	−0.643498	+	0.829821i
$414$		0			0
$415$	2.37868	+	4.11999i	0.116765	+	0.202243i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	23.6544			1.15559			0.577796	−	0.816181i	$-0.303913\pi$
$419$	23.6544			1.15559			0.577796	+	0.816181i	$0.303913\pi$
$420$		0			0
$421$	−14.2426			−0.694144			−0.347072	−	0.937839i	$-0.612824\pi$
$421$	−14.2426			−0.694144			−0.347072	+	0.937839i	$0.612824\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−13.2621	−	22.9706i	−0.643304	−	1.11424i
$426$		0			0
$427$	−2.48528	+	1.01461i	−0.120271	+	0.0491005i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−3.04384	−	1.75736i	−0.146616	−	0.0846490i	0.424897	−	0.905242i	$-0.360310\pi$
$431$	−3.04384	−	1.75736i	−0.146616	−	0.0846490i	−0.571514	+	0.820593i	$0.693644\pi$
$432$		0			0
$433$			3.46410i			0.166474i	0.996530	+	0.0832370i	$0.0265259\pi$
$433$			3.46410i			0.166474i	−0.996530	+	0.0832370i	$0.973474\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	12.5446	−	21.7279i	0.600091	−	1.03939i
$438$		0			0
$439$	14.5919	−	8.42463i	0.696433	−	0.402086i	−0.109585	−	0.993977i	$-0.534952\pi$
$439$	14.5919	−	8.42463i	0.696433	−	0.402086i	0.806017	+	0.591892i	$0.201619\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−14.2512	+	8.22792i	−0.677094	+	0.390920i	−0.798759	−	0.601651i	$-0.794510\pi$
$443$	−14.2512	+	8.22792i	−0.677094	+	0.390920i	0.121665	+	0.992571i	$0.461177\pi$
$444$		0			0
$445$	3.72792	−	6.45695i	0.176720	−	0.306089i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			1.75736i			0.0829349i	0.999140	+	0.0414675i	$0.0132033\pi$
$449$			1.75736i			0.0829349i	−0.999140	+	0.0414675i	$0.986797\pi$
$450$		0			0
$451$	30.7279	+	17.7408i	1.44692	+	0.835380i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	4.30463	−	1.75736i	0.201804	−	0.0823863i
$456$		0			0
$457$	11.5000	+	19.9186i	0.537947	+	0.931752i	0.999014	+	0.0443868i	$0.0141334\pi$
$457$	11.5000	+	19.9186i	0.537947	+	0.931752i	−0.461067	+	0.887365i	$0.652533\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−32.6118			−1.51888			−0.759441	−	0.650576i	$-0.774528\pi$
$461$	−32.6118			−1.51888			−0.759441	+	0.650576i	$0.774528\pi$
$462$		0			0
$463$	29.4558			1.36893			0.684465	−	0.729046i	$-0.260036\pi$
$463$	29.4558			1.36893			0.684465	+	0.729046i	$0.260036\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	19.8931	+	34.4558i	0.920542	+	1.59443i	0.798578	+	0.601892i	$0.205586\pi$
$467$	19.8931	+	34.4558i	0.920542	+	1.59443i	0.121965	+	0.992534i	$0.461080\pi$
$468$		0			0
$469$	16.2132	−	20.9077i	0.748656	−	0.965428i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−0.630399	−	0.363961i	−0.0289858	−	0.0167349i
$474$		0			0
$475$		−	26.5241i		−	1.21701i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	6.00063	−	10.3934i	0.274176	−	0.474886i	−0.695751	−	0.718283i	$-0.744928\pi$
$479$	6.00063	−	10.3934i	0.274176	−	0.474886i	0.969927	+	0.243397i	$0.0782616\pi$
$480$		0			0
$481$	−0.514719	+	0.297173i	−0.0234691	+	0.0135499i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	8.42463	−	4.86396i	0.382543	−	0.220861i
$486$		0			0
$487$	−7.10660	+	12.3090i	−0.322031	+	0.557774i	−0.980907	−	0.194478i	$-0.937699\pi$
$487$	−7.10660	+	12.3090i	−0.322031	+	0.557774i	0.658876	+	0.752251i	$0.271032\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$		−	13.9706i		−	0.630483i	−0.949012	−	0.315241i	$-0.897915\pi$
$491$		−	13.9706i		−	0.630483i	0.949012	−	0.315241i	$-0.102085\pi$
$492$		0			0
$493$	−37.0919	−	21.4150i	−1.67053	−	0.964483i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−0.630399	+	4.60660i	−0.0282773	+	0.206634i
$498$		0			0
$499$	15.9706	+	27.6618i	0.714941	+	1.23831i	0.962982	+	0.269564i	$0.0868796\pi$
$499$	15.9706	+	27.6618i	0.714941	+	1.23831i	−0.248042	+	0.968749i	$0.579787\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−31.0028			−1.38235			−0.691174	−	0.722688i	$-0.742906\pi$
$503$	−31.0028			−1.38235			−0.691174	+	0.722688i	$0.742906\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−8.59871	−	14.8934i	−0.381131	−	0.660138i	0.610093	−	0.792330i	$-0.291132\pi$
$509$	−8.59871	−	14.8934i	−0.381131	−	0.660138i	−0.991224	+	0.132191i	$0.957799\pi$
$510$		0			0
$511$	3.00000	+	2.32640i	0.132712	+	0.102914i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	3.41311	+	1.97056i	0.150400	+	0.0868334i
$516$		0			0
$517$			17.7408i			0.780238i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	16.9363	−	29.3345i	0.741993	−	1.28517i	−0.209594	−	0.977788i	$-0.567214\pi$
$521$	16.9363	−	29.3345i	0.741993	−	1.28517i	0.951587	−	0.307380i	$-0.0994524\pi$
$522$		0			0
$523$	−5.84924	+	3.37706i	−0.255770	+	0.147669i	−0.622403	−	0.782697i	$-0.713844\pi$
$523$	−5.84924	+	3.37706i	−0.255770	+	0.147669i	0.366634	+	0.930365i	$0.380510\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	46.5043	−	26.8492i	2.02576	−	1.16957i
$528$		0			0
$529$	−2.50000	+	4.33013i	−0.108696	+	0.188266i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		−	28.9706i		−	1.25485i
$534$		0			0
$535$	−7.13604	−	4.11999i	−0.308518	−	0.178123i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−14.6969	−	15.0000i	−0.633042	−	0.646096i
$540$		0			0
$541$	−7.36396	−	12.7548i	−0.316601	−	0.548370i	0.663175	−	0.748464i	$-0.269208\pi$
$541$	−7.36396	−	12.7548i	−0.316601	−	0.548370i	−0.979777	+	0.200094i	$0.935875\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−13.2621			−0.568084
$546$		0			0
$547$	39.6985			1.69738			0.848692	−	0.528887i	$-0.177390\pi$
$547$	39.6985			1.69738			0.848692	+	0.528887i	$0.177390\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−21.4150	−	37.0919i	−0.912310	−	1.58017i
$552$		0			0
$553$	2.75736	+	6.75412i	0.117255	+	0.287215i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−8.42463	−	4.86396i	−0.356963	−	0.206093i	0.310785	−	0.950480i	$-0.399408\pi$
$557$	−8.42463	−	4.86396i	−0.356963	−	0.206093i	−0.667748	+	0.744388i	$0.732741\pi$
$558$		0			0
$559$			0.594346i			0.0251382i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	17.2950	−	29.9558i	0.728898	−	1.26249i	−0.228451	−	0.973555i	$-0.573366\pi$
$563$	17.2950	−	29.9558i	0.728898	−	1.26249i	0.957349	−	0.288933i	$-0.0933005\pi$
$564$		0			0
$565$	5.27208	−	3.04384i	0.221798	−	0.128055i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	8.87039	−	5.12132i	0.371866	−	0.214697i	−0.302407	−	0.953179i	$-0.597790\pi$
$569$	8.87039	−	5.12132i	0.371866	−	0.214697i	0.674273	+	0.738482i	$0.264457\pi$
$570$		0			0
$571$	4.36396	−	7.55860i	0.182626	−	0.316318i	−0.760148	−	0.649750i	$-0.774874\pi$
$571$	4.36396	−	7.55860i	0.182626	−	0.316318i	0.942774	+	0.333432i	$0.108207\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	19.0294i		−	0.793582i
$576$		0			0
$577$	9.25736	+	5.34474i	0.385389	+	0.222504i	0.680160	−	0.733063i	$-0.261910\pi$
$577$	9.25736	+	5.34474i	0.385389	+	0.222504i	−0.294771	+	0.955568i	$0.595243\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−17.3821	−	2.37868i	−0.721129	−	0.0986843i
$582$		0			0
$583$	−10.8640	−	18.8169i	−0.449939	−	0.779318i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	5.19615			0.214468			0.107234	−	0.994234i	$-0.465801\pi$
$587$	5.19615			0.214468			0.107234	+	0.994234i	$0.465801\pi$
$588$		0			0
$589$	53.6985			2.21261
$590$		0			0
$591$		0			0
$592$		0			0
$593$	11.7401	+	20.3345i	0.482110	+	0.835039i	0.999789	−	0.0205360i	$-0.00653726\pi$
$593$	11.7401	+	20.3345i	0.482110	+	0.835039i	−0.517679	+	0.855575i	$0.673204\pi$
$594$		0			0
$595$	−11.1213	−	1.52192i	−0.455930	−	0.0623925i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−6.45695	−	3.72792i	−0.263824	−	0.152319i	0.362254	−	0.932079i	$-0.382007\pi$
$599$	−6.45695	−	3.72792i	−0.263824	−	0.152319i	−0.626078	+	0.779761i	$0.715341\pi$
$600$		0			0
$601$		−	23.3572i		−	0.952760i	−0.879240	−	0.476380i	$-0.841949\pi$
$601$		−	23.3572i		−	0.952760i	0.879240	−	0.476380i	$-0.158051\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	0.717439	−	1.24264i	0.0291680	−	0.0505205i
$606$		0			0
$607$	17.3787	−	10.0336i	0.705379	−	0.407251i	−0.103969	−	0.994581i	$-0.533154\pi$
$607$	17.3787	−	10.0336i	0.705379	−	0.407251i	0.809348	+	0.587330i	$0.199821\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	12.5446	−	7.24264i	0.507501	−	0.293006i
$612$		0			0
$613$	18.6066	−	32.2276i	0.751514	−	1.30166i	−0.195575	−	0.980689i	$-0.562657\pi$
$613$	18.6066	−	32.2276i	0.751514	−	1.30166i	0.947089	−	0.320971i	$-0.104009\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			17.6985i			0.712514i	0.934388	+	0.356257i	$0.115947\pi$
$617$			17.6985i			0.712514i	−0.934388	+	0.356257i	$0.884053\pi$
$618$		0			0
$619$	−5.33452	−	3.07989i	−0.214413	−	0.123791i	0.388948	−	0.921260i	$-0.372839\pi$
$619$	−5.33452	−	3.07989i	−0.214413	−	0.123791i	−0.603360	+	0.797469i	$0.706172\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	10.3923	+	25.4558i	0.416359	+	1.01987i
$624$		0			0
$625$	−8.77208	−	15.1937i	−0.350883	−	0.607747i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	1.43488			0.0572123
$630$		0			0
$631$	−24.7574			−0.985575			−0.492787	−	0.870150i	$-0.664022\pi$
$631$	−24.7574			−0.985575			−0.492787	+	0.870150i	$0.664022\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−1.16320	−	2.01472i	−0.0461601	−	0.0799517i
$636$		0			0
$637$	−4.60660	+	16.5160i	−0.182520	+	0.654389i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	15.3273	+	8.84924i	0.605393	+	0.349524i	0.771160	−	0.636641i	$-0.219677\pi$
$641$	15.3273	+	8.84924i	0.605393	+	0.349524i	−0.165767	+	0.986165i	$0.553010\pi$
$642$		0			0
$643$			32.0174i			1.26264i	0.775520	+	0.631322i	$0.217488\pi$
$643$			32.0174i			1.26264i	−0.775520	+	0.631322i	$0.782512\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−16.2189	+	28.0919i	−0.637629	+	1.10441i	0.348323	+	0.937375i	$0.386751\pi$
$647$	−16.2189	+	28.0919i	−0.637629	+	1.10441i	−0.985952	+	0.167031i	$0.946582\pi$
$648$		0			0
$649$	−20.9558	+	12.0989i	−0.822589	+	0.474922i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−16.6646	+	9.62132i	−0.652137	+	0.376511i	−0.789274	−	0.614041i	$-0.789543\pi$
$653$	−16.6646	+	9.62132i	−0.652137	+	0.376511i	0.137138	+	0.990552i	$0.456210\pi$
$654$		0			0
$655$	1.86396	−	3.22848i	0.0728310	−	0.126147i
$656$		0			0
$657$		0			0
$658$		0			0
$659$			6.00000i			0.233727i	0.993148	+	0.116863i	$0.0372840\pi$
$659$			6.00000i			0.233727i	−0.993148	+	0.116863i	$0.962716\pi$
$660$		0			0
$661$	30.8787	+	17.8278i	1.20104	+	0.693422i	0.960787	−	0.277288i	$-0.0894357\pi$
$661$	30.8787	+	17.8278i	1.20104	+	0.693422i	0.240255	+	0.970710i	$0.422769\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−8.87039	−	6.87868i	−0.343979	−	0.266744i
$666$		0			0
$667$	−15.3640	−	26.6112i	−0.594895	−	1.03039i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−3.04384			−0.117506
$672$		0			0
$673$	17.9706			0.692714			0.346357	−	0.938103i	$-0.387419\pi$
$673$	17.9706			0.692714			0.346357	+	0.938103i	$0.387419\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−1.07616	−	1.86396i	−0.0413601	−	0.0716378i	0.844604	−	0.535391i	$-0.179836\pi$
$677$	−1.07616	−	1.86396i	−0.0413601	−	0.0716378i	−0.885964	+	0.463753i	$0.846502\pi$
$678$		0			0
$679$	−4.86396	+	35.5431i	−0.186662	+	1.36402i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−6.90271	−	3.98528i	−0.264125	−	0.152493i	0.362090	−	0.932143i	$-0.382063\pi$
$683$	−6.90271	−	3.98528i	−0.264125	−	0.152493i	−0.626215	+	0.779651i	$0.715397\pi$
$684$		0			0
$685$			1.78304i			0.0681264i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−8.87039	+	15.3640i	−0.337935	+	0.585320i
$690$		0			0
$691$	−24.7279	+	14.2767i	−0.940694	+	0.543110i	−0.890178	−	0.455613i	$-0.849420\pi$
$691$	−24.7279	+	14.2767i	−0.940694	+	0.543110i	−0.0505165	+	0.998723i	$0.516087\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	0.369279	−	0.213203i	0.0140076	−	0.00808727i
$696$		0			0
$697$	−34.9706	+	60.5708i	−1.32460	+	2.29428i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	20.6985i		−	0.781771i	−0.920439	−	0.390885i	$-0.872169\pi$
$701$		−	20.6985i		−	0.781771i	0.920439	−	0.390885i	$-0.127831\pi$
$702$		0			0
$703$	1.24264	+	0.717439i	0.0468671	+	0.0270587i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−13.4853	−	23.3572i	−0.506450	−	0.877198i	−0.999972	−	0.00746433i	$-0.997624\pi$
$709$	−13.4853	−	23.3572i	−0.506450	−	0.877198i	0.493522	−	0.869733i	$-0.335709\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	38.5254			1.44279
$714$		0			0
$715$	5.27208			0.197165
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−8.06591	−	13.9706i	−0.300808	−	0.521014i	0.675511	−	0.737349i	$-0.263923\pi$
$719$	−8.06591	−	13.9706i	−0.300808	−	0.521014i	−0.976319	+	0.216335i	$0.930590\pi$
$720$		0			0
$721$	−13.4558	+	5.49333i	−0.501122	+	0.204582i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−28.1331	−	16.2426i	−1.04484	−	0.603237i
$726$		0			0
$727$		−	11.7041i		−	0.434081i	−0.976163	−	0.217040i	$-0.930360\pi$
$727$		−	11.7041i		−	0.434081i	0.976163	−	0.217040i	$-0.0696403\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	0.717439	−	1.24264i	0.0265354	−	0.0459607i
$732$		0			0
$733$	4.09188	−	2.36245i	0.151137	−	0.0872591i	−0.422524	−	0.906352i	$-0.638856\pi$
$733$	4.09188	−	2.36245i	0.151137	−	0.0872591i	0.573661	+	0.819093i	$0.305523\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	25.9808	−	15.0000i	0.957014	−	0.552532i
$738$		0			0
$739$	7.72792	−	13.3852i	0.284276	−	0.492381i	−0.688157	−	0.725562i	$-0.741580\pi$
$739$	7.72792	−	13.3852i	0.284276	−	0.492381i	0.972433	+	0.233181i	$0.0749134\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$			38.4853i			1.41189i	0.708268	+	0.705944i	$0.249477\pi$
$743$			38.4853i			1.41189i	−0.708268	+	0.705944i	$0.750523\pi$
$744$		0			0
$745$	2.18377	+	1.26080i	0.0800070	+	0.0461921i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	28.1331	−	11.4853i	1.02796	−	0.419663i
$750$		0			0
$751$	17.6213	+	30.5210i	0.643011	+	1.11373i	0.984757	+	0.173936i	$0.0556484\pi$
$751$	17.6213	+	30.5210i	0.643011	+	1.11373i	−0.341746	+	0.939792i	$0.611018\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	3.76127			0.136887
$756$		0			0
$757$	−33.7574			−1.22693			−0.613466	−	0.789721i	$-0.710225\pi$
$757$	−33.7574			−1.22693			−0.613466	+	0.789721i	$0.710225\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	14.7840	+	25.6066i	0.535919	+	0.928239i	0.999118	+	0.0419845i	$0.0133680\pi$
$761$	14.7840	+	25.6066i	0.535919	+	0.928239i	−0.463199	+	0.886254i	$0.653299\pi$
$762$		0			0
$763$	29.9706	−	38.6485i	1.08501	−	1.39917i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	17.1104	+	9.87868i	0.617820	+	0.356698i
$768$		0			0
$769$		−	9.84895i		−	0.355162i	−0.984106	−	0.177581i	$-0.943173\pi$
$769$		−	9.84895i		−	0.355162i	0.984106	−	0.177581i	$-0.0568272\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−8.06591	+	13.9706i	−0.290111	+	0.502486i	−0.973836	−	0.227253i	$-0.927025\pi$
$773$	−8.06591	+	13.9706i	−0.290111	+	0.502486i	0.683725	+	0.729740i	$0.260359\pi$
$774$		0			0
$775$	35.2721	−	20.3643i	1.26701	−	0.731509i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−60.5708	+	34.9706i	−2.17017	+	1.25295i
$780$		0			0
$781$	−2.63604	+	4.56575i	−0.0943249	+	0.163376i
$782$		0			0
$783$		0			0
$784$		0			0
$785$			10.5442i			0.376337i
$786$		0			0
$787$	−27.8787	−	16.0958i	−0.993768	−	0.573752i	−0.0873693	−	0.996176i	$-0.527846\pi$
$787$	−27.8787	−	16.0958i	−0.993768	−	0.573752i	−0.906398	+	0.422424i	$0.861179\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−3.04384	+	22.2426i	−0.108226	+	0.790857i
$792$		0			0
$793$	1.24264	+	2.15232i	0.0441275	+	0.0764310i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−6.45695			−0.228717			−0.114358	−	0.993440i	$-0.536481\pi$
$797$	−6.45695			−0.228717			−0.114358	+	0.993440i	$0.536481\pi$
$798$		0			0
$799$	−34.9706			−1.23717
$800$		0			0
$801$		0			0
$802$		0			0
$803$	2.15232	+	3.72792i	0.0759536	+	0.131556i
$804$		0			0
$805$	−6.36396	−	4.93503i	−0.224300	−	0.173937i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	6.08767	+	3.51472i	0.214031	+	0.123571i	0.603183	−	0.797602i	$-0.293899\pi$
$809$	6.08767	+	3.51472i	0.214031	+	0.123571i	−0.389152	+	0.921173i	$0.627232\pi$
$810$		0			0
$811$			31.1769i			1.09477i	0.836881	+	0.547385i	$0.184377\pi$
$811$			31.1769i			1.09477i	−0.836881	+	0.547385i	$0.815623\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	0.804479	−	1.39340i	0.0281797	−	0.0488086i
$816$		0			0
$817$	1.24264	−	0.717439i	0.0434745	−	0.0251000i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−35.2969	+	20.3787i	−1.23187	+	0.711221i	−0.967420	−	0.253178i	$-0.918524\pi$
$821$	−35.2969	+	20.3787i	−1.23187	+	0.711221i	−0.264451	+	0.964399i	$0.585191\pi$
$822$		0			0
$823$	14.9706	−	25.9298i	0.521841	−	0.903855i	−0.477836	−	0.878449i	$-0.658579\pi$
$823$	14.9706	−	25.9298i	0.521841	−	0.903855i	0.999677	−	0.0254062i	$-0.00808791\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			37.9706i			1.32037i	0.751105	+	0.660183i	$0.229521\pi$
$827$			37.9706i			1.32037i	−0.751105	+	0.660183i	$0.770479\pi$
$828$		0			0
$829$	11.3345	+	6.54399i	0.393664	+	0.227282i	0.683747	−	0.729720i	$-0.260349\pi$
$829$	11.3345	+	6.54399i	0.393664	+	0.227282i	−0.290082	+	0.957002i	$0.593683\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	29.5680	−	28.9706i	1.02447	−	1.00377i
$834$		0			0
$835$	−5.78680	−	10.0230i	−0.200260	−	0.346861i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	10.2182			0.352772			0.176386	−	0.984321i	$-0.443559\pi$
$839$	10.2182			0.352772			0.176386	+	0.984321i	$0.443559\pi$
$840$		0			0
$841$	−23.4558			−0.808822
$842$		0			0
$843$		0			0
$844$		0			0
$845$	2.51104	+	4.34924i	0.0863823	+	0.149618i
$846$		0			0
$847$	2.00000	+	4.89898i	0.0687208	+	0.168331i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	0.891519	+	0.514719i	0.0305609	+	0.0176443i
$852$		0			0
$853$		−	36.9164i		−	1.26399i	−0.774971	−	0.631997i	$-0.782235\pi$
$853$		−	36.9164i		−	1.26399i	0.774971	−	0.631997i	$-0.217765\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−16.9363	+	29.3345i	−0.578533	+	1.00205i	0.417115	+	0.908854i	$0.363041\pi$
$857$	−16.9363	+	29.3345i	−0.578533	+	1.00205i	−0.995648	+	0.0931946i	$0.970292\pi$
$858$		0			0
$859$	−8.12132	+	4.68885i	−0.277096	+	0.159981i	−0.632108	−	0.774880i	$-0.717810\pi$
$859$	−8.12132	+	4.68885i	−0.277096	+	0.159981i	0.355012	+	0.934862i	$0.384477\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	29.0246	−	16.7574i	0.988009	−	0.570427i	0.0833303	−	0.996522i	$-0.473444\pi$
$863$	29.0246	−	16.7574i	0.988009	−	0.570427i	0.904679	+	0.426095i	$0.140111\pi$
$864$		0			0
$865$	−7.45584	+	12.9139i	−0.253506	+	0.439086i
$866$		0			0
$867$		0			0
$868$		0			0
$869$			8.27208i			0.280611i
$870$		0			0
$871$	−21.2132	−	12.2474i	−0.718782	−	0.414989i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−17.8384	−	2.44113i	−0.603047	−	0.0825251i
$876$		0			0
$877$	−2.24264	−	3.88437i	−0.0757286	−	0.131166i	0.825674	−	0.564147i	$-0.190795\pi$
$877$	−2.24264	−	3.88437i	−0.0757286	−	0.131166i	−0.901403	+	0.432981i	$0.857462\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−19.0016			−0.640179			−0.320090	−	0.947387i	$-0.603713\pi$
$881$	−19.0016			−0.640179			−0.320090	+	0.947387i	$0.603713\pi$
$882$		0			0
$883$	−41.4558			−1.39510			−0.697550	−	0.716536i	$-0.745727\pi$
$883$	−41.4558			−1.39510			−0.697550	+	0.716536i	$0.745727\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	5.28319	+	9.15076i	0.177392	+	0.307252i	0.940987	−	0.338444i	$-0.109901\pi$
$887$	5.28319	+	9.15076i	0.177392	+	0.307252i	−0.763594	+	0.645696i	$0.776567\pi$
$888$		0			0
$889$	8.50000	+	1.16320i	0.285081	+	0.0390124i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−30.2854	−	17.4853i	−1.01346	−	0.585123i
$894$		0			0
$895$			19.0016i			0.635153i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	32.8835	−	56.9558i	1.09673	−	1.89958i
$900$		0			0
$901$	37.0919	−	21.4150i	1.23571	−	0.713437i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	7.34847	−	4.24264i	0.244271	−	0.141030i
$906$		0			0
$907$	−15.8492	+	27.4517i	−0.526265	+	0.911519i	0.473266	+	0.880919i	$0.343075\pi$
$907$	−15.8492	+	27.4517i	−0.526265	+	0.911519i	−0.999532	+	0.0305991i	$0.990258\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$		−	6.72792i		−	0.222906i	−0.993770	−	0.111453i	$-0.964450\pi$
$911$		−	6.72792i		−	0.222906i	0.993770	−	0.111453i	$-0.0355505\pi$
$912$		0			0
$913$	−17.2279	−	9.94655i	−0.570161	−	0.329183i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	5.19615	+	12.7279i	0.171592	+	0.420313i
$918$		0			0
$919$	18.2426	+	31.5972i	0.601769	+	1.04229i	0.992553	+	0.121812i	$0.0388706\pi$
$919$	18.2426	+	31.5972i	0.601769	+	1.04229i	−0.390784	+	0.920482i	$0.627796\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	4.30463			0.141689
$924$		0			0
$925$	1.08831			0.0357835
$926$		0			0
$927$		0			0
$928$		0			0
$929$	15.5014	+	26.8492i	0.508585	+	0.880895i	0.999951	+	0.00994164i	$0.00316458\pi$
$929$	15.5014	+	26.8492i	0.508585	+	0.880895i	−0.491366	+	0.870953i	$0.663502\pi$
$930$		0			0
$931$	40.0919	−	10.3053i	1.31396	−	0.337741i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−11.0227	−	6.36396i	−0.360481	−	0.208124i
$936$		0			0
$937$			35.1844i			1.14942i	0.818356	+	0.574712i	$0.194886\pi$
$937$			35.1844i			1.14942i	−0.818356	+	0.574712i	$0.805114\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−13.7949	+	23.8934i	−0.449700	+	0.778903i	−0.998366	−	0.0571387i	$-0.981802\pi$
$941$	−13.7949	+	23.8934i	−0.449700	+	0.778903i	0.548667	+	0.836041i	$0.315136\pi$
$942$		0			0
$943$	−43.4558	+	25.0892i	−1.41512	+	0.817018i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−9.50079	+	5.48528i	−0.308734	+	0.178248i	−0.646360	−	0.763033i	$-0.723709\pi$
$947$	−9.50079	+	5.48528i	−0.308734	+	0.178248i	0.337626	+	0.941280i	$0.390376\pi$
$948$		0			0
$949$	1.75736	−	3.04384i	0.0570463	−	0.0988071i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			17.6985i			0.573310i	0.958034	+	0.286655i	$0.0925434\pi$
$953$			17.6985i			0.573310i	−0.958034	+	0.286655i	$0.907457\pi$
$954$		0			0
$955$	5.27208	+	3.04384i	0.170600	+	0.0984962i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−5.19615	−	4.02944i	−0.167793	−	0.130117i
$960$		0			0
$961$	25.7279	+	44.5621i	0.829933	+	1.43749i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−6.80511			−0.219064
$966$		0			0
$967$	−47.7279			−1.53483			−0.767413	−	0.641153i	$-0.778456\pi$
$967$	−47.7279			−1.53483			−0.767413	+	0.641153i	$0.778456\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	13.5337	+	23.4411i	0.434318	+	0.752262i	0.997240	−	0.0742490i	$-0.0236559\pi$
$971$	13.5337	+	23.4411i	0.434318	+	0.752262i	−0.562921	+	0.826510i	$0.690323\pi$
$972$		0			0
$973$	−0.213203	+	1.55797i	−0.00683499	+	0.0499463i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	34.8511	+	20.1213i	1.11499	+	0.643738i	0.940116	−	0.340853i	$-0.110716\pi$
$977$	34.8511	+	20.1213i	1.11499	+	0.643738i	0.174871	+	0.984591i	$0.444049\pi$
$978$		0			0
$979$			31.1769i			0.996419i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−23.6544	+	40.9706i	−0.754457	+	1.30676i	0.191187	+	0.981554i	$0.438766\pi$
$983$	−23.6544	+	40.9706i	−0.754457	+	1.30676i	−0.945644	+	0.325204i	$0.894567\pi$
$984$		0			0
$985$	−16.4558	+	9.50079i	−0.524327	+	0.302720i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	0.891519	−	0.514719i	0.0283486	−	0.0163671i
$990$		0			0
$991$	26.1066	−	45.2180i	0.829304	−	1.43640i	−0.0692818	−	0.997597i	$-0.522071\pi$
$991$	26.1066	−	45.2180i	0.829304	−	1.43640i	0.898585	−	0.438799i	$-0.144596\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		−	16.5442i		−	0.524485i
$996$		0			0
$997$	−33.7279	−	19.4728i	−1.06817	−	0.616711i	−0.140492	−	0.990082i	$-0.544868\pi$
$997$	−33.7279	−	19.4728i	−1.06817	−	0.616711i	−0.927682	+	0.373371i	$0.878202\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.bt.c.17.3		8
3.2	odd	2	inner	1008.2.bt.c.17.2		8
4.3	odd	2		126.2.k.a.17.2	✓	8
7.3	odd	6		7056.2.k.f.881.6		8
7.4	even	3		7056.2.k.f.881.4		8
7.5	odd	6	inner	1008.2.bt.c.593.2		8
12.11	even	2		126.2.k.a.17.3	yes	8
20.3	even	4		3150.2.bp.e.899.3		8
20.7	even	4		3150.2.bp.b.899.2		8
20.19	odd	2		3150.2.bf.a.1151.3		8
21.5	even	6	inner	1008.2.bt.c.593.3		8
21.11	odd	6		7056.2.k.f.881.5		8
21.17	even	6		7056.2.k.f.881.3		8
28.3	even	6		882.2.d.a.881.3		8
28.11	odd	6		882.2.d.a.881.2		8
28.19	even	6		126.2.k.a.89.3	yes	8
28.23	odd	6		882.2.k.a.215.4		8
28.27	even	2		882.2.k.a.521.1		8
36.7	odd	6		1134.2.t.e.1025.3		8
36.11	even	6		1134.2.t.e.1025.2		8
36.23	even	6		1134.2.l.f.269.3		8
36.31	odd	6		1134.2.l.f.269.2		8
60.23	odd	4		3150.2.bp.b.899.3		8
60.47	odd	4		3150.2.bp.e.899.2		8
60.59	even	2		3150.2.bf.a.1151.1		8
84.11	even	6		882.2.d.a.881.7		8
84.23	even	6		882.2.k.a.215.1		8
84.47	odd	6		126.2.k.a.89.2	yes	8
84.59	odd	6		882.2.d.a.881.6		8
84.83	odd	2		882.2.k.a.521.4		8
140.19	even	6		3150.2.bf.a.1601.1		8
140.47	odd	12		3150.2.bp.b.1349.3		8
140.103	odd	12		3150.2.bp.e.1349.2		8
252.47	odd	6		1134.2.l.f.215.4		8
252.103	even	6		1134.2.t.e.593.2		8
252.131	odd	6		1134.2.t.e.593.3		8
252.187	even	6		1134.2.l.f.215.1		8
420.47	even	12		3150.2.bp.e.1349.3		8
420.299	odd	6		3150.2.bf.a.1601.3		8
420.383	even	12		3150.2.bp.b.1349.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.k.a.17.2	✓	8	4.3	odd	2
126.2.k.a.17.3	yes	8	12.11	even	2
126.2.k.a.89.2	yes	8	84.47	odd	6
126.2.k.a.89.3	yes	8	28.19	even	6
882.2.d.a.881.2		8	28.11	odd	6
882.2.d.a.881.3		8	28.3	even	6
882.2.d.a.881.6		8	84.59	odd	6
882.2.d.a.881.7		8	84.11	even	6
882.2.k.a.215.1		8	84.23	even	6
882.2.k.a.215.4		8	28.23	odd	6
882.2.k.a.521.1		8	28.27	even	2
882.2.k.a.521.4		8	84.83	odd	2
1008.2.bt.c.17.2		8	3.2	odd	2	inner
1008.2.bt.c.17.3		8	1.1	even	1	trivial
1008.2.bt.c.593.2		8	7.5	odd	6	inner
1008.2.bt.c.593.3		8	21.5	even	6	inner
1134.2.l.f.215.1		8	252.187	even	6
1134.2.l.f.215.4		8	252.47	odd	6
1134.2.l.f.269.2		8	36.31	odd	6
1134.2.l.f.269.3		8	36.23	even	6
1134.2.t.e.593.2		8	252.103	even	6
1134.2.t.e.593.3		8	252.131	odd	6
1134.2.t.e.1025.2		8	36.11	even	6
1134.2.t.e.1025.3		8	36.7	odd	6
3150.2.bf.a.1151.1		8	60.59	even	2
3150.2.bf.a.1151.3		8	20.19	odd	2
3150.2.bf.a.1601.1		8	140.19	even	6
3150.2.bf.a.1601.3		8	420.299	odd	6
3150.2.bp.b.899.2		8	20.7	even	4
3150.2.bp.b.899.3		8	60.23	odd	4
3150.2.bp.b.1349.2		8	420.383	even	12
3150.2.bp.b.1349.3		8	140.47	odd	12
3150.2.bp.e.899.2		8	60.47	odd	4
3150.2.bp.e.899.3		8	20.3	even	4
3150.2.bp.e.1349.2		8	140.103	odd	12
3150.2.bp.e.1349.3		8	420.47	even	12
7056.2.k.f.881.3		8	21.17	even	6
7056.2.k.f.881.4		8	7.4	even	3
7056.2.k.f.881.5		8	21.11	odd	6
7056.2.k.f.881.6		8	7.3	odd	6

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:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.bt (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.358719 + 0.621320i) q^{5} +(-2.62132 - 0.358719i) q^{7} +(-2.59808 - 1.50000i) q^{11} +2.44949i q^{13} +(2.95680 - 5.12132i) q^{17} +(5.12132 - 2.95680i) q^{19} +(3.67423 - 2.12132i) q^{23} +(2.24264 - 3.88437i) q^{25} -7.24264i q^{29} +(7.86396 + 4.54026i) q^{31} +(-0.717439 - 1.75736i) q^{35} +(0.121320 + 0.210133i) q^{37} -11.8272 q^{41} +0.242641 q^{43} +(-2.95680 - 5.12132i) q^{47} +(6.74264 + 1.88064i) q^{49} +(6.27231 + 3.62132i) q^{53} -2.15232i q^{55} +(4.03295 - 6.98528i) q^{59} +(0.878680 - 0.507306i) q^{61} +(-1.52192 + 0.878680i) q^{65} +(-5.00000 + 8.66025i) q^{67} -1.75736i q^{71} +(-1.24264 - 0.717439i) q^{73} +(6.27231 + 4.86396i) q^{77} +(-1.37868 - 2.38794i) q^{79} +6.63103 q^{83} +4.24264 q^{85} +(-5.19615 - 9.00000i) q^{89} +(0.878680 - 6.42090i) q^{91} +(3.67423 + 2.12132i) q^{95} -13.5592i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{7} + 24 q^{19} - 16 q^{25} + 12 q^{31} - 16 q^{37} - 32 q^{43} + 20 q^{49} + 24 q^{61} - 40 q^{67} + 24 q^{73} - 28 q^{79} + 24 q^{91}+O(q^{100}) \) 8 * q - 4 * q^7 + 24 * q^19 - 16 * q^25 + 12 * q^31 - 16 * q^37 - 32 * q^43 + 20 * q^49 + 24 * q^61 - 40 * q^67 + 24 * q^73 - 28 * q^79 + 24 * q^91

Introduction

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