LMFDB - Embedded newform 1008.2.bt.b.593.1

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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			593.1
Root			$1.22474 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	1008.593
Dual form			1008.2.bt.b.17.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22474 + 2.12132i) q^{5} +(0.500000 + 2.59808i) q^{7} +O(q^{10})$	$q+(-1.22474 + 2.12132i) q^{5} +(0.500000 + 2.59808i) q^{7} +(1.22474 - 0.707107i) q^{11} +5.19615i q^{13} +(-2.44949 - 4.24264i) q^{17} +(-1.50000 - 0.866025i) q^{19} +(-4.89898 - 2.82843i) q^{23} +(-0.500000 - 0.866025i) q^{25} +2.82843i q^{29} +(-1.50000 + 0.866025i) q^{31} +(-6.12372 - 2.12132i) q^{35} +(0.500000 - 0.866025i) q^{37} -7.34847 q^{41} +1.00000 q^{43} +(-6.12372 + 10.6066i) q^{47} +(-6.50000 + 2.59808i) q^{49} +(2.44949 - 1.41421i) q^{53} +3.46410i q^{55} +(2.44949 + 4.24264i) q^{59} +(-3.00000 - 1.73205i) q^{61} +(-11.0227 - 6.36396i) q^{65} +(5.50000 + 9.52628i) q^{67} -7.07107i q^{71} +(1.50000 - 0.866025i) q^{73} +(2.44949 + 2.82843i) q^{77} +(2.50000 - 4.33013i) q^{79} -7.34847 q^{83} +12.0000 q^{85} +(2.44949 - 4.24264i) q^{89} +(-13.5000 + 2.59808i) q^{91} +(3.67423 - 2.12132i) q^{95} +10.3923i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{7}+O(q^{10}) $ 4 * q + 2 * q^7	$ 4 q + 2 q^{7} - 6 q^{19} - 2 q^{25} - 6 q^{31} + 2 q^{37} + 4 q^{43} - 26 q^{49} - 12 q^{61} + 22 q^{67} + 6 q^{73} + 10 q^{79} + 48 q^{85} - 54 q^{91}+O(q^{100}) $ 4 * q + 2 * q^7 - 6 * q^19 - 2 * q^25 - 6 * q^31 + 2 * q^37 + 4 * q^43 - 26 * q^49 - 12 * q^61 + 22 * q^67 + 6 * q^73 + 10 * q^79 + 48 * q^85 - 54 * q^91

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

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
$5$	−1.22474	+	2.12132i	−0.547723	+	0.948683i	0.450708	+	0.892672i	$0.351172\pi$
$5$	−1.22474	+	2.12132i	−0.547723	+	0.948683i	−0.998430	+	0.0560116i	$0.982162\pi$
$6$		0			0
$7$	0.500000	+	2.59808i	0.188982	+	0.981981i
$7$	0.500000	+	2.59808i	0.188982	+	0.981981i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.22474	−	0.707107i	0.369274	−	0.213201i	−0.303867	−	0.952714i	$-0.598278\pi$
$11$	1.22474	−	0.707107i	0.369274	−	0.213201i	0.673141	+	0.739514i	$0.264945\pi$
$12$		0			0
$13$			5.19615i			1.44115i	0.693375	+	0.720577i	$0.256123\pi$
$13$			5.19615i			1.44115i	−0.693375	+	0.720577i	$0.743877\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.44949	−	4.24264i	−0.594089	−	1.02899i	−0.993675	−	0.112296i	$-0.964180\pi$
$17$	−2.44949	−	4.24264i	−0.594089	−	1.02899i	0.399586	−	0.916696i	$-0.369154\pi$
$18$		0			0
$19$	−1.50000	−	0.866025i	−0.344124	−	0.198680i	0.317970	−	0.948101i	$-0.396999\pi$
$19$	−1.50000	−	0.866025i	−0.344124	−	0.198680i	−0.662094	+	0.749421i	$0.730332\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−4.89898	−	2.82843i	−1.02151	−	0.589768i	−0.106967	−	0.994263i	$-0.534114\pi$
$23$	−4.89898	−	2.82843i	−1.02151	−	0.589768i	−0.914540	+	0.404495i	$0.867447\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$		0			0
$28$		0			0
$29$			2.82843i			0.525226i	0.964901	+	0.262613i	$0.0845842\pi$
$29$			2.82843i			0.525226i	−0.964901	+	0.262613i	$0.915416\pi$
$30$		0			0
$31$	−1.50000	+	0.866025i	−0.269408	+	0.155543i	−0.628619	−	0.777714i	$-0.716379\pi$
$31$	−1.50000	+	0.866025i	−0.269408	+	0.155543i	0.359211	+	0.933257i	$0.383046\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−6.12372	−	2.12132i	−1.03510	−	0.358569i
$36$		0			0
$37$	0.500000	−	0.866025i	0.0821995	−	0.142374i	−0.821995	−	0.569495i	$-0.807139\pi$
$37$	0.500000	−	0.866025i	0.0821995	−	0.142374i	0.904194	+	0.427121i	$0.140472\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−7.34847			−1.14764			−0.573819	−	0.818982i	$-0.694539\pi$
$41$	−7.34847			−1.14764			−0.573819	+	0.818982i	$0.694539\pi$
$42$		0			0
$43$	1.00000			0.152499			0.0762493	−	0.997089i	$-0.475706\pi$
$43$	1.00000			0.152499			0.0762493	+	0.997089i	$0.475706\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−6.12372	+	10.6066i	−0.893237	+	1.54713i	−0.0572655	+	0.998359i	$0.518238\pi$
$47$	−6.12372	+	10.6066i	−0.893237	+	1.54713i	−0.835971	+	0.548773i	$0.815095\pi$
$48$		0			0
$49$	−6.50000	+	2.59808i	−0.928571	+	0.371154i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	2.44949	−	1.41421i	0.336463	−	0.194257i	−0.322244	−	0.946657i	$-0.604437\pi$
$53$	2.44949	−	1.41421i	0.336463	−	0.194257i	0.658707	+	0.752400i	$0.271104\pi$
$54$		0			0
$55$			3.46410i			0.467099i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	2.44949	+	4.24264i	0.318896	+	0.552345i	0.980258	−	0.197722i	$-0.0633545\pi$
$59$	2.44949	+	4.24264i	0.318896	+	0.552345i	−0.661362	+	0.750067i	$0.730021\pi$
$60$		0			0
$61$	−3.00000	−	1.73205i	−0.384111	−	0.221766i	0.295495	−	0.955344i	$-0.404516\pi$
$61$	−3.00000	−	1.73205i	−0.384111	−	0.221766i	−0.679605	+	0.733578i	$0.737849\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−11.0227	−	6.36396i	−1.36720	−	0.789352i
$66$		0			0
$67$	5.50000	+	9.52628i	0.671932	+	1.16382i	0.977356	+	0.211604i	$0.0678686\pi$
$67$	5.50000	+	9.52628i	0.671932	+	1.16382i	−0.305424	+	0.952217i	$0.598798\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	7.07107i		−	0.839181i	−0.907713	−	0.419591i	$-0.862174\pi$
$71$		−	7.07107i		−	0.839181i	0.907713	−	0.419591i	$-0.137826\pi$
$72$		0			0
$73$	1.50000	−	0.866025i	0.175562	−	0.101361i	−0.409644	−	0.912245i	$-0.634347\pi$
$73$	1.50000	−	0.866025i	0.175562	−	0.101361i	0.585206	+	0.810885i	$0.301014\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	2.44949	+	2.82843i	0.279145	+	0.322329i
$78$		0			0
$79$	2.50000	−	4.33013i	0.281272	−	0.487177i	−0.690426	−	0.723403i	$-0.742577\pi$
$79$	2.50000	−	4.33013i	0.281272	−	0.487177i	0.971698	+	0.236225i	$0.0759104\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−7.34847			−0.806599			−0.403300	−	0.915068i	$-0.632137\pi$
$83$	−7.34847			−0.806599			−0.403300	+	0.915068i	$0.632137\pi$
$84$		0			0
$85$	12.0000			1.30158
$86$		0			0
$87$		0			0
$88$		0			0
$89$	2.44949	−	4.24264i	0.259645	−	0.449719i	−0.706502	−	0.707712i	$-0.749728\pi$
$89$	2.44949	−	4.24264i	0.259645	−	0.449719i	0.966147	+	0.257993i	$0.0830610\pi$
$90$		0			0
$91$	−13.5000	+	2.59808i	−1.41518	+	0.272352i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	3.67423	−	2.12132i	0.376969	−	0.217643i
$96$		0			0
$97$			10.3923i			1.05518i	0.849500	+	0.527589i	$0.176904\pi$
$97$			10.3923i			1.05518i	−0.849500	+	0.527589i	$0.823096\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	8.57321	+	14.8492i	0.853067	+	1.47755i	0.878427	+	0.477876i	$0.158593\pi$
$101$	8.57321	+	14.8492i	0.853067	+	1.47755i	−0.0253604	+	0.999678i	$0.508073\pi$
$102$		0			0
$103$	7.50000	+	4.33013i	0.738997	+	0.426660i	0.821705	−	0.569914i	$-0.193023\pi$
$103$	7.50000	+	4.33013i	0.738997	+	0.426660i	−0.0827075	+	0.996574i	$0.526357\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	2.44949	+	1.41421i	0.236801	+	0.136717i	0.613706	−	0.789535i	$-0.289678\pi$
$107$	2.44949	+	1.41421i	0.236801	+	0.136717i	−0.376905	+	0.926252i	$0.623012\pi$
$108$		0			0
$109$	0.500000	+	0.866025i	0.0478913	+	0.0829502i	0.888977	−	0.457951i	$-0.151417\pi$
$109$	0.500000	+	0.866025i	0.0478913	+	0.0829502i	−0.841086	+	0.540901i	$0.818083\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$		−	1.41421i		−	0.133038i	−0.997785	−	0.0665190i	$-0.978811\pi$
$113$		−	1.41421i		−	0.133038i	0.997785	−	0.0665190i	$-0.0211893\pi$
$114$		0			0
$115$	12.0000	−	6.92820i	1.11901	−	0.646058i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	9.79796	−	8.48528i	0.898177	−	0.777844i
$120$		0			0
$121$	−4.50000	+	7.79423i	−0.409091	+	0.708566i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−9.79796			−0.876356
$126$		0			0
$127$	−11.0000			−0.976092			−0.488046	−	0.872818i	$-0.662290\pi$
$127$	−11.0000			−0.976092			−0.488046	+	0.872818i	$0.662290\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	1.22474	−	2.12132i	0.107006	−	0.185341i	−0.807550	−	0.589799i	$-0.799207\pi$
$131$	1.22474	−	2.12132i	0.107006	−	0.185341i	0.914556	+	0.404459i	$0.132540\pi$
$132$		0			0
$133$	1.50000	−	4.33013i	0.130066	−	0.375470i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	9.79796	−	5.65685i	0.837096	−	0.483298i	−0.0191800	−	0.999816i	$-0.506106\pi$
$137$	9.79796	−	5.65685i	0.837096	−	0.483298i	0.856276	+	0.516518i	$0.172772\pi$
$138$		0			0
$139$		−	5.19615i		−	0.440732i	−0.975417	−	0.220366i	$-0.929275\pi$
$139$		−	5.19615i		−	0.440732i	0.975417	−	0.220366i	$-0.0707252\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	3.67423	+	6.36396i	0.307255	+	0.532181i
$144$		0			0
$145$	−6.00000	−	3.46410i	−0.498273	−	0.287678i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	4.89898	+	2.82843i	0.401340	+	0.231714i	0.687062	−	0.726599i	$-0.258900\pi$
$149$	4.89898	+	2.82843i	0.401340	+	0.231714i	−0.285722	+	0.958313i	$0.592233\pi$
$150$		0			0
$151$	−11.0000	−	19.0526i	−0.895167	−	1.55048i	−0.833597	−	0.552372i	$-0.813723\pi$
$151$	−11.0000	−	19.0526i	−0.895167	−	1.55048i	−0.0615699	−	0.998103i	$-0.519611\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		−	4.24264i		−	0.340777i
$156$		0			0
$157$	15.0000	−	8.66025i	1.19713	−	0.691164i	0.237216	−	0.971457i	$-0.423765\pi$
$157$	15.0000	−	8.66025i	1.19713	−	0.691164i	0.959914	+	0.280293i	$0.0904318\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	4.89898	−	14.1421i	0.386094	−	1.11456i
$162$		0			0
$163$	−5.00000	+	8.66025i	−0.391630	+	0.678323i	−0.992665	−	0.120900i	$-0.961422\pi$
$163$	−5.00000	+	8.66025i	−0.391630	+	0.678323i	0.601035	+	0.799223i	$0.294755\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	7.34847			0.568642			0.284321	−	0.958729i	$-0.408232\pi$
$167$	7.34847			0.568642			0.284321	+	0.958729i	$0.408232\pi$
$168$		0			0
$169$	−14.0000			−1.07692
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−4.89898	+	8.48528i	−0.372463	+	0.645124i	−0.989944	−	0.141462i	$-0.954820\pi$
$173$	−4.89898	+	8.48528i	−0.372463	+	0.645124i	0.617481	+	0.786586i	$0.288153\pi$
$174$		0			0
$175$	2.00000	−	1.73205i	0.151186	−	0.130931i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	8.57321	−	4.94975i	0.640792	−	0.369961i	−0.144127	−	0.989559i	$-0.546038\pi$
$179$	8.57321	−	4.94975i	0.640792	−	0.369961i	0.784920	+	0.619598i	$0.212704\pi$
$180$		0			0
$181$		−	15.5885i		−	1.15868i	−0.815086	−	0.579340i	$-0.803310\pi$
$181$		−	15.5885i		−	1.15868i	0.815086	−	0.579340i	$-0.196690\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	1.22474	+	2.12132i	0.0900450	+	0.155963i
$186$		0			0
$187$	−6.00000	−	3.46410i	−0.438763	−	0.253320i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−1.22474	−	0.707107i	−0.0886194	−	0.0511645i	0.455035	−	0.890473i	$-0.349627\pi$
$191$	−1.22474	−	0.707107i	−0.0886194	−	0.0511645i	−0.543655	+	0.839309i	$0.682960\pi$
$192$		0			0
$193$	−5.50000	−	9.52628i	−0.395899	−	0.685717i	0.597317	−	0.802005i	$-0.296234\pi$
$193$	−5.50000	−	9.52628i	−0.395899	−	0.685717i	−0.993215	+	0.116289i	$0.962900\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			19.7990i			1.41062i	0.708899	+	0.705310i	$0.249192\pi$
$197$			19.7990i			1.41062i	−0.708899	+	0.705310i	$0.750808\pi$
$198$		0			0
$199$	12.0000	−	6.92820i	0.850657	−	0.491127i	−0.0102152	−	0.999948i	$-0.503252\pi$
$199$	12.0000	−	6.92820i	0.850657	−	0.491127i	0.860873	+	0.508821i	$0.169918\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−7.34847	+	1.41421i	−0.515761	+	0.0992583i
$204$		0			0
$205$	9.00000	−	15.5885i	0.628587	−	1.08875i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−2.44949			−0.169435
$210$		0			0
$211$	22.0000			1.51454			0.757271	−	0.653101i	$-0.226532\pi$
$211$	22.0000			1.51454			0.757271	+	0.653101i	$0.226532\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−1.22474	+	2.12132i	−0.0835269	+	0.144673i
$216$		0			0
$217$	−3.00000	−	3.46410i	−0.203653	−	0.235159i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	22.0454	−	12.7279i	1.48293	−	0.856173i
$222$		0			0
$223$			20.7846i			1.39184i	0.718119	+	0.695920i	$0.245003\pi$
$223$			20.7846i			1.39184i	−0.718119	+	0.695920i	$0.754997\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	13.4722	+	23.3345i	0.894181	+	1.54877i	0.834815	+	0.550530i	$0.185575\pi$
$227$	13.4722	+	23.3345i	0.894181	+	1.54877i	0.0593658	+	0.998236i	$0.481092\pi$
$228$		0			0
$229$	19.5000	+	11.2583i	1.28860	+	0.743971i	0.978404	−	0.206702i	$-0.0662732\pi$
$229$	19.5000	+	11.2583i	1.28860	+	0.743971i	0.310192	+	0.950674i	$0.399607\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	8.57321	+	4.94975i	0.561650	+	0.324269i	0.753807	−	0.657095i	$-0.228215\pi$
$233$	8.57321	+	4.94975i	0.561650	+	0.324269i	−0.192158	+	0.981364i	$0.561548\pi$
$234$		0			0
$235$	−15.0000	−	25.9808i	−0.978492	−	1.69480i
$236$		0			0
$237$		0			0
$238$		0			0
$239$			26.8701i			1.73808i	0.494742	+	0.869040i	$0.335262\pi$
$239$			26.8701i			1.73808i	−0.494742	+	0.869040i	$0.664738\pi$
$240$		0			0
$241$	−12.0000	+	6.92820i	−0.772988	+	0.446285i	−0.833939	−	0.551856i	$-0.813920\pi$
$241$	−12.0000	+	6.92820i	−0.772988	+	0.446285i	0.0609515	+	0.998141i	$0.480586\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	2.44949	−	16.9706i	0.156492	−	1.08421i
$246$		0			0
$247$	4.50000	−	7.79423i	0.286328	−	0.495935i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$		0			0
$253$	−8.00000			−0.502956
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−1.22474	+	2.12132i	−0.0763975	+	0.132324i	−0.901693	−	0.432377i	$-0.857675\pi$
$257$	−1.22474	+	2.12132i	−0.0763975	+	0.132324i	0.825296	+	0.564701i	$0.191008\pi$
$258$		0			0
$259$	2.50000	+	0.866025i	0.155342	+	0.0538122i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	12.2474	−	7.07107i	0.755210	−	0.436021i	−0.0723633	−	0.997378i	$-0.523054\pi$
$263$	12.2474	−	7.07107i	0.755210	−	0.436021i	0.827573	+	0.561358i	$0.189721\pi$
$264$		0			0
$265$			6.92820i			0.425596i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	8.57321	+	14.8492i	0.522718	+	0.905374i	0.999651	+	0.0264343i	$0.00841529\pi$
$269$	8.57321	+	14.8492i	0.522718	+	0.905374i	−0.476932	+	0.878940i	$0.658251\pi$
$270$		0			0
$271$	12.0000	+	6.92820i	0.728948	+	0.420858i	0.818037	−	0.575165i	$-0.195062\pi$
$271$	12.0000	+	6.92820i	0.728948	+	0.420858i	−0.0890891	+	0.996024i	$0.528396\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−1.22474	−	0.707107i	−0.0738549	−	0.0426401i
$276$		0			0
$277$	−11.5000	−	19.9186i	−0.690968	−	1.19679i	−0.971521	−	0.236953i	$-0.923851\pi$
$277$	−11.5000	−	19.9186i	−0.690968	−	1.19679i	0.280553	−	0.959839i	$-0.409482\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		−	22.6274i		−	1.34984i	−0.737892	−	0.674919i	$-0.764178\pi$
$281$		−	22.6274i		−	1.34984i	0.737892	−	0.674919i	$-0.235822\pi$
$282$		0			0
$283$	−1.50000	+	0.866025i	−0.0891657	+	0.0514799i	−0.543920	−	0.839137i	$-0.683060\pi$
$283$	−1.50000	+	0.866025i	−0.0891657	+	0.0514799i	0.454754	+	0.890617i	$0.349727\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−3.67423	−	19.0919i	−0.216883	−	1.12696i
$288$		0			0
$289$	−3.50000	+	6.06218i	−0.205882	+	0.356599i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	14.6969			0.858604			0.429302	−	0.903161i	$-0.358760\pi$
$293$	14.6969			0.858604			0.429302	+	0.903161i	$0.358760\pi$
$294$		0			0
$295$	−12.0000			−0.698667
$296$		0			0
$297$		0			0
$298$		0			0
$299$	14.6969	−	25.4558i	0.849946	−	1.47215i
$300$		0			0
$301$	0.500000	+	2.59808i	0.0288195	+	0.149751i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	7.34847	−	4.24264i	0.420772	−	0.242933i
$306$		0			0
$307$		−	15.5885i		−	0.889680i	−0.895610	−	0.444840i	$-0.853260\pi$
$307$		−	15.5885i		−	0.889680i	0.895610	−	0.444840i	$-0.146740\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−8.57321	−	14.8492i	−0.486142	−	0.842023i	0.513731	−	0.857951i	$-0.328263\pi$
$311$	−8.57321	−	14.8492i	−0.486142	−	0.842023i	−0.999873	+	0.0159282i	$0.994930\pi$
$312$		0			0
$313$	10.5000	+	6.06218i	0.593495	+	0.342655i	0.766478	−	0.642270i	$-0.222007\pi$
$313$	10.5000	+	6.06218i	0.593495	+	0.342655i	−0.172983	+	0.984925i	$0.555341\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	12.2474	+	7.07107i	0.687885	+	0.397151i	0.802819	−	0.596222i	$-0.203332\pi$
$317$	12.2474	+	7.07107i	0.687885	+	0.397151i	−0.114934	+	0.993373i	$0.536666\pi$
$318$		0			0
$319$	2.00000	+	3.46410i	0.111979	+	0.193952i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			8.48528i			0.472134i
$324$		0			0
$325$	4.50000	−	2.59808i	0.249615	−	0.144115i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−30.6186	−	10.6066i	−1.68806	−	0.584761i
$330$		0			0
$331$	−15.5000	+	26.8468i	−0.851957	+	1.47563i	0.0274825	+	0.999622i	$0.491251\pi$
$331$	−15.5000	+	26.8468i	−0.851957	+	1.47563i	−0.879440	+	0.476011i	$0.842082\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−26.9444			−1.47213
$336$		0			0
$337$	23.0000			1.25289			0.626445	−	0.779466i	$-0.284509\pi$
$337$	23.0000			1.25289			0.626445	+	0.779466i	$0.284509\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−1.22474	+	2.12132i	−0.0663237	+	0.114876i
$342$		0			0
$343$	−10.0000	−	15.5885i	−0.539949	−	0.841698i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	26.9444	−	15.5563i	1.44645	−	0.835109i	0.448183	−	0.893942i	$-0.352071\pi$
$347$	26.9444	−	15.5563i	1.44645	−	0.835109i	0.998268	+	0.0588334i	$0.0187381\pi$
$348$		0			0
$349$			10.3923i			0.556287i	0.960539	+	0.278144i	$0.0897191\pi$
$349$			10.3923i			0.556287i	−0.960539	+	0.278144i	$0.910281\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	8.57321	+	14.8492i	0.456306	+	0.790345i	0.998762	−	0.0497387i	$-0.0158389\pi$
$353$	8.57321	+	14.8492i	0.456306	+	0.790345i	−0.542456	+	0.840084i	$0.682506\pi$
$354$		0			0
$355$	15.0000	+	8.66025i	0.796117	+	0.459639i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	24.4949	+	14.1421i	1.29279	+	0.746393i	0.979148	−	0.203148i	$-0.0651171\pi$
$359$	24.4949	+	14.1421i	1.29279	+	0.746393i	0.313643	+	0.949541i	$0.398450\pi$
$360$		0			0
$361$	−8.00000	−	13.8564i	−0.421053	−	0.729285i
$362$		0			0
$363$		0			0
$364$		0			0
$365$			4.24264i			0.222070i
$366$		0			0
$367$	−1.50000	+	0.866025i	−0.0782994	+	0.0452062i	−0.538639	−	0.842537i	$-0.681061\pi$
$367$	−1.50000	+	0.866025i	−0.0782994	+	0.0452062i	0.460339	+	0.887743i	$0.347728\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	4.89898	+	5.65685i	0.254342	+	0.293689i
$372$		0			0
$373$	−14.5000	+	25.1147i	−0.750782	+	1.30039i	0.196663	+	0.980471i	$0.436990\pi$
$373$	−14.5000	+	25.1147i	−0.750782	+	1.30039i	−0.947444	+	0.319921i	$0.896344\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−14.6969			−0.756931
$378$		0			0
$379$	7.00000			0.359566			0.179783	−	0.983706i	$-0.442460\pi$
$379$	7.00000			0.359566			0.179783	+	0.983706i	$0.442460\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−9.79796	+	16.9706i	−0.500652	+	0.867155i	0.499347	+	0.866402i	$0.333573\pi$
$383$	−9.79796	+	16.9706i	−0.500652	+	0.867155i	−1.00000		0.000753393i	$0.999760\pi$
$384$		0			0
$385$	−9.00000	+	1.73205i	−0.458682	+	0.0882735i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−23.2702	+	13.4350i	−1.17984	+	0.681183i	−0.955978	−	0.293437i	$-0.905201\pi$
$389$	−23.2702	+	13.4350i	−1.17984	+	0.681183i	−0.223865	+	0.974620i	$0.571868\pi$
$390$		0			0
$391$			27.7128i			1.40150i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	6.12372	+	10.6066i	0.308118	+	0.533676i
$396$		0			0
$397$	1.50000	+	0.866025i	0.0752828	+	0.0434646i	0.537169	−	0.843475i	$-0.319494\pi$
$397$	1.50000	+	0.866025i	0.0752828	+	0.0434646i	−0.461886	+	0.886939i	$0.652827\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−17.1464	−	9.89949i	−0.856252	−	0.494357i	0.00650355	−	0.999979i	$-0.497930\pi$
$401$	−17.1464	−	9.89949i	−0.856252	−	0.494357i	−0.862755	+	0.505622i	$0.831263\pi$
$402$		0			0
$403$	−4.50000	−	7.79423i	−0.224161	−	0.388258i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	1.41421i		−	0.0701000i
$408$		0			0
$409$	28.5000	−	16.4545i	1.40923	−	0.813622i	0.413920	−	0.910313i	$-0.364159\pi$
$409$	28.5000	−	16.4545i	1.40923	−	0.813622i	0.995314	+	0.0966915i	$0.0308260\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−9.79796	+	8.48528i	−0.482126	+	0.417533i
$414$		0			0
$415$	9.00000	−	15.5885i	0.441793	−	0.765207i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−36.7423			−1.79498			−0.897491	−	0.441034i	$-0.854612\pi$
$419$	−36.7423			−1.79498			−0.897491	+	0.441034i	$0.854612\pi$
$420$		0			0
$421$	−1.00000			−0.0487370			−0.0243685	−	0.999703i	$-0.507758\pi$
$421$	−1.00000			−0.0487370			−0.0243685	+	0.999703i	$0.507758\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−2.44949	+	4.24264i	−0.118818	+	0.205798i
$426$		0			0
$427$	3.00000	−	8.66025i	0.145180	−	0.419099i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−13.4722	+	7.77817i	−0.648933	+	0.374661i	−0.788047	−	0.615615i	$-0.788908\pi$
$431$	−13.4722	+	7.77817i	−0.648933	+	0.374661i	0.139114	+	0.990276i	$0.455574\pi$
$432$		0			0
$433$		−	15.5885i		−	0.749133i	−0.927200	−	0.374567i	$-0.877791\pi$
$433$		−	15.5885i		−	0.749133i	0.927200	−	0.374567i	$-0.122209\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	4.89898	+	8.48528i	0.234350	+	0.405906i
$438$		0			0
$439$	−24.0000	−	13.8564i	−1.14546	−	0.661330i	−0.197681	−	0.980266i	$-0.563341\pi$
$439$	−24.0000	−	13.8564i	−1.14546	−	0.661330i	−0.947776	+	0.318936i	$0.896674\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−34.2929	−	19.7990i	−1.62930	−	0.940678i	−0.984301	−	0.176497i	$-0.943523\pi$
$443$	−34.2929	−	19.7990i	−1.62930	−	0.940678i	−0.645002	−	0.764181i	$-0.723143\pi$
$444$		0			0
$445$	6.00000	+	10.3923i	0.284427	+	0.492642i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			7.07107i			0.333704i	0.985982	+	0.166852i	$0.0533603\pi$
$449$			7.07107i			0.333704i	−0.985982	+	0.166852i	$0.946640\pi$
$450$		0			0
$451$	−9.00000	+	5.19615i	−0.423793	+	0.244677i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	11.0227	−	31.8198i	0.516752	−	1.49174i
$456$		0			0
$457$	−2.50000	+	4.33013i	−0.116945	+	0.202555i	−0.918556	−	0.395292i	$-0.870643\pi$
$457$	−2.50000	+	4.33013i	−0.116945	+	0.202555i	0.801611	+	0.597847i	$0.203977\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−14.6969			−0.684505			−0.342252	−	0.939608i	$-0.611190\pi$
$461$	−14.6969			−0.684505			−0.342252	+	0.939608i	$0.611190\pi$
$462$		0			0
$463$	13.0000			0.604161			0.302081	−	0.953282i	$-0.402319\pi$
$463$	13.0000			0.604161			0.302081	+	0.953282i	$0.402319\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−13.4722	+	23.3345i	−0.623419	+	1.07979i	0.365426	+	0.930841i	$0.380923\pi$
$467$	−13.4722	+	23.3345i	−0.623419	+	1.07979i	−0.988844	+	0.148952i	$0.952410\pi$
$468$		0			0
$469$	−22.0000	+	19.0526i	−1.01587	+	0.879765i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	1.22474	−	0.707107i	0.0563138	−	0.0325128i
$474$		0			0
$475$			1.73205i			0.0794719i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	2.44949	+	4.24264i	0.111920	+	0.193851i	0.916544	−	0.399933i	$-0.130967\pi$
$479$	2.44949	+	4.24264i	0.111920	+	0.193851i	−0.804624	+	0.593784i	$0.797633\pi$
$480$		0			0
$481$	4.50000	+	2.59808i	0.205182	+	0.118462i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−22.0454	−	12.7279i	−1.00103	−	0.577945i
$486$		0			0
$487$	8.50000	+	14.7224i	0.385172	+	0.667137i	0.991793	−	0.127854i	$-0.0408089\pi$
$487$	8.50000	+	14.7224i	0.385172	+	0.667137i	−0.606621	+	0.794991i	$0.707476\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$		−	11.3137i		−	0.510581i	−0.966864	−	0.255290i	$-0.917829\pi$
$491$		−	11.3137i		−	0.510581i	0.966864	−	0.255290i	$-0.0821710\pi$
$492$		0			0
$493$	12.0000	−	6.92820i	0.540453	−	0.312031i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	18.3712	−	3.53553i	0.824060	−	0.158590i
$498$		0			0
$499$	−12.5000	+	21.6506i	−0.559577	+	0.969216i	0.437955	+	0.898997i	$0.355703\pi$
$499$	−12.5000	+	21.6506i	−0.559577	+	0.969216i	−0.997532	+	0.0702185i	$0.977630\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−22.0454			−0.982956			−0.491478	−	0.870890i	$-0.663543\pi$
$503$	−22.0454			−0.982956			−0.491478	+	0.870890i	$0.663543\pi$
$504$		0			0
$505$	−42.0000			−1.86898
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−1.22474	+	2.12132i	−0.0542859	+	0.0940259i	−0.891891	−	0.452250i	$-0.850622\pi$
$509$	−1.22474	+	2.12132i	−0.0542859	+	0.0940259i	0.837605	+	0.546276i	$0.183955\pi$
$510$		0			0
$511$	3.00000	+	3.46410i	0.132712	+	0.153243i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−18.3712	+	10.6066i	−0.809531	+	0.467383i
$516$		0			0
$517$			17.3205i			0.761755i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−2.44949	−	4.24264i	−0.107314	−	0.185873i	0.807367	−	0.590049i	$-0.200892\pi$
$521$	−2.44949	−	4.24264i	−0.107314	−	0.185873i	−0.914681	+	0.404176i	$0.867558\pi$
$522$		0			0
$523$	−1.50000	−	0.866025i	−0.0655904	−	0.0378686i	0.466846	−	0.884339i	$-0.345390\pi$
$523$	−1.50000	−	0.866025i	−0.0655904	−	0.0378686i	−0.532437	+	0.846470i	$0.678724\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	7.34847	+	4.24264i	0.320104	+	0.184812i
$528$		0			0
$529$	4.50000	+	7.79423i	0.195652	+	0.338880i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		−	38.1838i		−	1.65392i
$534$		0			0
$535$	−6.00000	+	3.46410i	−0.259403	+	0.149766i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−6.12372	+	7.77817i	−0.263767	+	0.335030i
$540$		0			0
$541$	−8.50000	+	14.7224i	−0.365444	+	0.632967i	−0.988847	−	0.148933i	$-0.952416\pi$
$541$	−8.50000	+	14.7224i	−0.365444	+	0.632967i	0.623404	+	0.781900i	$0.285749\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−2.44949			−0.104925
$546$		0			0
$547$	10.0000			0.427569			0.213785	−	0.976881i	$-0.431421\pi$
$547$	10.0000			0.427569			0.213785	+	0.976881i	$0.431421\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	2.44949	−	4.24264i	0.104352	−	0.180743i
$552$		0			0
$553$	12.5000	+	4.33013i	0.531554	+	0.184136i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	13.4722	−	7.77817i	0.570835	−	0.329572i	−0.186648	−	0.982427i	$-0.559762\pi$
$557$	13.4722	−	7.77817i	0.570835	−	0.329572i	0.757483	+	0.652855i	$0.226429\pi$
$558$		0			0
$559$			5.19615i			0.219774i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	13.4722	+	23.3345i	0.567785	+	0.983433i	0.996785	+	0.0801281i	$0.0255329\pi$
$563$	13.4722	+	23.3345i	0.567785	+	0.983433i	−0.428999	+	0.903305i	$0.641134\pi$
$564$		0			0
$565$	3.00000	+	1.73205i	0.126211	+	0.0728679i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	1.22474	+	0.707107i	0.0513440	+	0.0296435i	0.525452	−	0.850823i	$-0.323896\pi$
$569$	1.22474	+	0.707107i	0.0513440	+	0.0296435i	−0.474108	+	0.880467i	$0.657229\pi$
$570$		0			0
$571$	5.50000	+	9.52628i	0.230168	+	0.398662i	0.957857	−	0.287244i	$-0.0927391\pi$
$571$	5.50000	+	9.52628i	0.230168	+	0.398662i	−0.727690	+	0.685907i	$0.759406\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			5.65685i			0.235907i
$576$		0			0
$577$	1.50000	−	0.866025i	0.0624458	−	0.0360531i	−0.468452	−	0.883489i	$-0.655188\pi$
$577$	1.50000	−	0.866025i	0.0624458	−	0.0360531i	0.530898	+	0.847436i	$0.321855\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−3.67423	−	19.0919i	−0.152433	−	0.792065i
$582$		0			0
$583$	2.00000	−	3.46410i	0.0828315	−	0.143468i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	14.6969			0.606608			0.303304	−	0.952894i	$-0.401910\pi$
$587$	14.6969			0.606608			0.303304	+	0.952894i	$0.401910\pi$
$588$		0			0
$589$	3.00000			0.123613
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−8.57321	+	14.8492i	−0.352060	+	0.609785i	−0.986610	−	0.163096i	$-0.947852\pi$
$593$	−8.57321	+	14.8492i	−0.352060	+	0.609785i	0.634550	+	0.772881i	$0.281185\pi$
$594$		0			0
$595$	6.00000	+	31.1769i	0.245976	+	1.27813i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	4.89898	−	2.82843i	0.200167	−	0.115566i	−0.396566	−	0.918006i	$-0.629798\pi$
$599$	4.89898	−	2.82843i	0.200167	−	0.115566i	0.596733	+	0.802440i	$0.296465\pi$
$600$		0			0
$601$			25.9808i			1.05978i	0.848067	+	0.529889i	$0.177766\pi$
$601$			25.9808i			1.05978i	−0.848067	+	0.529889i	$0.822234\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−11.0227	−	19.0919i	−0.448137	−	0.776195i
$606$		0			0
$607$	34.5000	+	19.9186i	1.40031	+	0.808470i	0.994424	−	0.105453i	$-0.0336291\pi$
$607$	34.5000	+	19.9186i	1.40031	+	0.808470i	0.405887	+	0.913923i	$0.366962\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−55.1135	−	31.8198i	−2.22965	−	1.28729i
$612$		0			0
$613$	−4.00000	−	6.92820i	−0.161558	−	0.279827i	0.773869	−	0.633345i	$-0.218319\pi$
$613$	−4.00000	−	6.92820i	−0.161558	−	0.279827i	−0.935428	+	0.353518i	$0.884985\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			24.0416i			0.967880i	0.875101	+	0.483940i	$0.160795\pi$
$617$			24.0416i			0.967880i	−0.875101	+	0.483940i	$0.839205\pi$
$618$		0			0
$619$	25.5000	−	14.7224i	1.02493	−	0.591744i	0.109403	−	0.993997i	$-0.465106\pi$
$619$	25.5000	−	14.7224i	1.02493	−	0.591744i	0.915529	+	0.402253i	$0.131773\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	12.2474	+	4.24264i	0.490684	+	0.169978i
$624$		0			0
$625$	14.5000	−	25.1147i	0.580000	−	1.00459i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−4.89898			−0.195335
$630$		0			0
$631$	−38.0000			−1.51276			−0.756378	−	0.654135i	$-0.773033\pi$
$631$	−38.0000			−1.51276			−0.756378	+	0.654135i	$0.773033\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	13.4722	−	23.3345i	0.534628	−	0.926002i
$636$		0			0
$637$	−13.5000	−	33.7750i	−0.534889	−	1.33821i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−12.2474	+	7.07107i	−0.483745	+	0.279290i	−0.721976	−	0.691918i	$-0.756766\pi$
$641$	−12.2474	+	7.07107i	−0.483745	+	0.279290i	0.238231	+	0.971209i	$0.423433\pi$
$642$		0			0
$643$			25.9808i			1.02458i	0.858812	+	0.512291i	$0.171203\pi$
$643$			25.9808i			1.02458i	−0.858812	+	0.512291i	$0.828797\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−8.57321	−	14.8492i	−0.337048	−	0.583784i	0.646828	−	0.762636i	$-0.276095\pi$
$647$	−8.57321	−	14.8492i	−0.337048	−	0.583784i	−0.983876	+	0.178852i	$0.942762\pi$
$648$		0			0
$649$	6.00000	+	3.46410i	0.235521	+	0.135978i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−6.12372	−	3.53553i	−0.239640	−	0.138356i	0.375371	−	0.926875i	$-0.377515\pi$
$653$	−6.12372	−	3.53553i	−0.239640	−	0.138356i	−0.615011	+	0.788518i	$0.710849\pi$
$654$		0			0
$655$	3.00000	+	5.19615i	0.117220	+	0.203030i
$656$		0			0
$657$		0			0
$658$		0			0
$659$			22.6274i			0.881439i	0.897645	+	0.440720i	$0.145277\pi$
$659$			22.6274i			0.881439i	−0.897645	+	0.440720i	$0.854723\pi$
$660$		0			0
$661$	−25.5000	+	14.7224i	−0.991835	+	0.572636i	−0.905822	−	0.423658i	$-0.860746\pi$
$661$	−25.5000	+	14.7224i	−0.991835	+	0.572636i	−0.0860127	+	0.996294i	$0.527413\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	7.34847	+	8.48528i	0.284961	+	0.329045i
$666$		0			0
$667$	8.00000	−	13.8564i	0.309761	−	0.536522i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−4.89898			−0.189123
$672$		0			0
$673$	35.0000			1.34915			0.674575	−	0.738206i	$-0.264327\pi$
$673$	35.0000			1.34915			0.674575	+	0.738206i	$0.264327\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−4.89898	+	8.48528i	−0.188283	+	0.326116i	−0.944678	−	0.327999i	$-0.893626\pi$
$677$	−4.89898	+	8.48528i	−0.188283	+	0.326116i	0.756395	+	0.654115i	$0.226959\pi$
$678$		0			0
$679$	−27.0000	+	5.19615i	−1.03616	+	0.199410i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	41.6413	−	24.0416i	1.59336	−	0.919927i	0.600636	−	0.799522i	$-0.294914\pi$
$683$	41.6413	−	24.0416i	1.59336	−	0.919927i	0.992725	−	0.120405i	$-0.0384193\pi$
$684$		0			0
$685$			27.7128i			1.05885i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	7.34847	+	12.7279i	0.279954	+	0.484895i
$690$		0			0
$691$	−37.5000	−	21.6506i	−1.42657	−	0.823629i	−0.429719	−	0.902963i	$-0.641387\pi$
$691$	−37.5000	−	21.6506i	−1.42657	−	0.823629i	−0.996848	+	0.0793336i	$0.974721\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	11.0227	+	6.36396i	0.418115	+	0.241399i
$696$		0			0
$697$	18.0000	+	31.1769i	0.681799	+	1.18091i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	5.65685i		−	0.213656i	−0.994277	−	0.106828i	$-0.965931\pi$
$701$		−	5.65685i		−	0.213656i	0.994277	−	0.106828i	$-0.0340695\pi$
$702$		0			0
$703$	−1.50000	+	0.866025i	−0.0565736	+	0.0326628i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−34.2929	+	29.6985i	−1.28972	+	1.11693i
$708$		0			0
$709$	20.0000	−	34.6410i	0.751116	−	1.30097i	−0.196167	−	0.980571i	$-0.562849\pi$
$709$	20.0000	−	34.6410i	0.751116	−	1.30097i	0.947282	−	0.320400i	$-0.103817\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	9.79796			0.366936
$714$		0			0
$715$	−18.0000			−0.673162
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−13.4722	+	23.3345i	−0.502428	+	0.870231i	0.497568	+	0.867425i	$0.334226\pi$
$719$	−13.4722	+	23.3345i	−0.502428	+	0.870231i	−0.999996	+	0.00280593i	$0.999107\pi$
$720$		0			0
$721$	−7.50000	+	21.6506i	−0.279315	+	0.806312i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	2.44949	−	1.41421i	0.0909718	−	0.0525226i
$726$		0			0
$727$		−	25.9808i		−	0.963573i	−0.876289	−	0.481787i	$-0.839988\pi$
$727$		−	25.9808i		−	0.963573i	0.876289	−	0.481787i	$-0.160012\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−2.44949	−	4.24264i	−0.0905977	−	0.156920i
$732$		0			0
$733$	−34.5000	−	19.9186i	−1.27429	−	0.735710i	−0.298495	−	0.954411i	$-0.596485\pi$
$733$	−34.5000	−	19.9186i	−1.27429	−	0.735710i	−0.975792	+	0.218702i	$0.929818\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	13.4722	+	7.77817i	0.496255	+	0.286513i
$738$		0			0
$739$	−0.500000	−	0.866025i	−0.0183928	−	0.0318573i	0.856683	−	0.515844i	$-0.172522\pi$
$739$	−0.500000	−	0.866025i	−0.0183928	−	0.0318573i	−0.875075	+	0.483987i	$0.839188\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		−	24.0416i		−	0.882002i	−0.897507	−	0.441001i	$-0.854624\pi$
$743$		−	24.0416i		−	0.882002i	0.897507	−	0.441001i	$-0.145376\pi$
$744$		0			0
$745$	−12.0000	+	6.92820i	−0.439646	+	0.253830i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−2.44949	+	7.07107i	−0.0895024	+	0.258371i
$750$		0			0
$751$	14.5000	−	25.1147i	0.529113	−	0.916450i	−0.470311	−	0.882501i	$-0.655858\pi$
$751$	14.5000	−	25.1147i	0.529113	−	0.916450i	0.999424	−	0.0339490i	$-0.0108084\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	53.8888			1.96121
$756$		0			0
$757$	2.00000			0.0726912			0.0363456	−	0.999339i	$-0.488428\pi$
$757$	2.00000			0.0726912			0.0363456	+	0.999339i	$0.488428\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−12.2474	+	21.2132i	−0.443970	+	0.768978i	−0.997980	−	0.0635319i	$-0.979764\pi$
$761$	−12.2474	+	21.2132i	−0.443970	+	0.768978i	0.554010	+	0.832510i	$0.313097\pi$
$762$		0			0
$763$	−2.00000	+	1.73205i	−0.0724049	+	0.0627044i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−22.0454	+	12.7279i	−0.796014	+	0.459579i
$768$		0			0
$769$		−	25.9808i		−	0.936890i	−0.883493	−	0.468445i	$-0.844814\pi$
$769$		−	25.9808i		−	0.936890i	0.883493	−	0.468445i	$-0.155186\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−13.4722	−	23.3345i	−0.484561	−	0.839284i	0.515282	−	0.857021i	$-0.327687\pi$
$773$	−13.4722	−	23.3345i	−0.484561	−	0.839284i	−0.999843	+	0.0177365i	$0.994354\pi$
$774$		0			0
$775$	1.50000	+	0.866025i	0.0538816	+	0.0311086i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	11.0227	+	6.36396i	0.394929	+	0.228013i
$780$		0			0
$781$	−5.00000	−	8.66025i	−0.178914	−	0.309888i
$782$		0			0
$783$		0			0
$784$		0			0
$785$			42.4264i			1.51426i
$786$		0			0
$787$	39.0000	−	22.5167i	1.39020	−	0.802632i	0.396863	−	0.917878i	$-0.370099\pi$
$787$	39.0000	−	22.5167i	1.39020	−	0.802632i	0.993337	+	0.115246i	$0.0367655\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	3.67423	−	0.707107i	0.130641	−	0.0251418i
$792$		0			0
$793$	9.00000	−	15.5885i	0.319599	−	0.553562i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−29.3939			−1.04118			−0.520592	−	0.853805i	$-0.674289\pi$
$797$	−29.3939			−1.04118			−0.520592	+	0.853805i	$0.674289\pi$
$798$		0			0
$799$	60.0000			2.12265
$800$		0			0
$801$		0			0
$802$		0			0
$803$	1.22474	−	2.12132i	0.0432203	−	0.0748598i
$804$		0			0
$805$	24.0000	+	27.7128i	0.845889	+	0.976748i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	35.5176	−	20.5061i	1.24873	−	0.720956i	0.277876	−	0.960617i	$-0.410370\pi$
$809$	35.5176	−	20.5061i	1.24873	−	0.720956i	0.970857	+	0.239661i	$0.0770363\pi$
$810$		0			0
$811$		−	31.1769i		−	1.09477i	−0.836881	−	0.547385i	$-0.815623\pi$
$811$		−	31.1769i		−	1.09477i	0.836881	−	0.547385i	$-0.184377\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−12.2474	−	21.2132i	−0.429009	−	0.743066i
$816$		0			0
$817$	−1.50000	−	0.866025i	−0.0524784	−	0.0302984i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−20.8207	−	12.0208i	−0.726646	−	0.419529i	0.0905478	−	0.995892i	$-0.471138\pi$
$821$	−20.8207	−	12.0208i	−0.726646	−	0.419529i	−0.817194	+	0.576363i	$0.804472\pi$
$822$		0			0
$823$	−17.0000	−	29.4449i	−0.592583	−	1.02638i	−0.993883	−	0.110437i	$-0.964775\pi$
$823$	−17.0000	−	29.4449i	−0.592583	−	1.02638i	0.401300	−	0.915947i	$-0.368558\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	7.07107i		−	0.245885i	−0.992414	−	0.122943i	$-0.960767\pi$
$827$		−	7.07107i		−	0.245885i	0.992414	−	0.122943i	$-0.0392331\pi$
$828$		0			0
$829$	1.50000	−	0.866025i	0.0520972	−	0.0300783i	−0.473725	−	0.880673i	$-0.657091\pi$
$829$	1.50000	−	0.866025i	0.0520972	−	0.0300783i	0.525822	+	0.850594i	$0.323758\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	26.9444	+	21.2132i	0.933568	+	0.734994i
$834$		0			0
$835$	−9.00000	+	15.5885i	−0.311458	+	0.539461i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	14.6969			0.507395			0.253697	−	0.967284i	$-0.418353\pi$
$839$	14.6969			0.507395			0.253697	+	0.967284i	$0.418353\pi$
$840$		0			0
$841$	21.0000			0.724138
$842$		0			0
$843$		0			0
$844$		0			0
$845$	17.1464	−	29.6985i	0.589855	−	1.02166i
$846$		0			0
$847$	−22.5000	−	7.79423i	−0.773109	−	0.267813i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−4.89898	+	2.82843i	−0.167935	+	0.0969572i
$852$		0			0
$853$		−	36.3731i		−	1.24539i	−0.782465	−	0.622695i	$-0.786038\pi$
$853$		−	36.3731i		−	1.24539i	0.782465	−	0.622695i	$-0.213962\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	19.5959	+	33.9411i	0.669384	+	1.15941i	0.978077	+	0.208245i	$0.0667751\pi$
$857$	19.5959	+	33.9411i	0.669384	+	1.15941i	−0.308693	+	0.951162i	$0.599892\pi$
$858$		0			0
$859$	−33.0000	−	19.0526i	−1.12595	−	0.650065i	−0.183033	−	0.983107i	$-0.558592\pi$
$859$	−33.0000	−	19.0526i	−1.12595	−	0.650065i	−0.942912	+	0.333042i	$0.891925\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	35.5176	+	20.5061i	1.20903	+	0.698036i	0.962548	−	0.271111i	$-0.0873910\pi$
$863$	35.5176	+	20.5061i	1.20903	+	0.698036i	0.246485	+	0.969147i	$0.420724\pi$
$864$		0			0
$865$	−12.0000	−	20.7846i	−0.408012	−	0.706698i
$866$		0			0
$867$		0			0
$868$		0			0
$869$		−	7.07107i		−	0.239870i
$870$		0			0
$871$	−49.5000	+	28.5788i	−1.67724	+	0.968357i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−4.89898	−	25.4558i	−0.165616	−	0.860565i
$876$		0			0
$877$	−10.0000	+	17.3205i	−0.337676	+	0.584872i	−0.983995	−	0.178195i	$-0.942974\pi$
$877$	−10.0000	+	17.3205i	−0.337676	+	0.584872i	0.646319	+	0.763067i	$0.276307\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		0			0			−	1.00000i	$-0.5\pi$
$881$		0			0				1.00000i	$0.5\pi$
$882$		0			0
$883$	−11.0000			−0.370179			−0.185090	−	0.982722i	$-0.559258\pi$
$883$	−11.0000			−0.370179			−0.185090	+	0.982722i	$0.559258\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−20.8207	+	36.0624i	−0.699089	+	1.21086i	0.269693	+	0.962946i	$0.413078\pi$
$887$	−20.8207	+	36.0624i	−0.699089	+	1.21086i	−0.968783	+	0.247912i	$0.920256\pi$
$888$		0			0
$889$	−5.50000	−	28.5788i	−0.184464	−	0.958503i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	18.3712	−	10.6066i	0.614768	−	0.354936i
$894$		0			0
$895$			24.2487i			0.810545i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−2.44949	−	4.24264i	−0.0816951	−	0.141500i
$900$		0			0
$901$	−12.0000	−	6.92820i	−0.399778	−	0.230812i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	33.0681	+	19.0919i	1.09922	+	0.634636i
$906$		0			0
$907$	2.50000	+	4.33013i	0.0830111	+	0.143780i	0.904542	−	0.426385i	$-0.140213\pi$
$907$	2.50000	+	4.33013i	0.0830111	+	0.143780i	−0.821531	+	0.570164i	$0.806880\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$		−	53.7401i		−	1.78049i	−0.455483	−	0.890245i	$-0.650533\pi$
$911$		−	53.7401i		−	1.78049i	0.455483	−	0.890245i	$-0.349467\pi$
$912$		0			0
$913$	−9.00000	+	5.19615i	−0.297857	+	0.171968i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	6.12372	+	2.12132i	0.202223	+	0.0700522i
$918$		0			0
$919$	8.50000	−	14.7224i	0.280389	−	0.485648i	−0.691091	−	0.722767i	$-0.742870\pi$
$919$	8.50000	−	14.7224i	0.280389	−	0.485648i	0.971481	+	0.237119i	$0.0762032\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	36.7423			1.20939
$924$		0			0
$925$	−1.00000			−0.0328798
$926$		0			0
$927$		0			0
$928$		0			0
$929$	28.1691	−	48.7904i	0.924199	−	1.60076i	0.131355	−	0.991335i	$-0.458067\pi$
$929$	28.1691	−	48.7904i	0.924199	−	1.60076i	0.792844	−	0.609425i	$-0.208600\pi$
$930$		0			0
$931$	12.0000	+	1.73205i	0.393284	+	0.0567657i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	14.6969	−	8.48528i	0.480641	−	0.277498i
$936$		0			0
$937$		−	46.7654i		−	1.52776i	−0.645359	−	0.763879i	$-0.723292\pi$
$937$		−	46.7654i		−	1.52776i	0.645359	−	0.763879i	$-0.276708\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−24.4949	−	42.4264i	−0.798511	−	1.38306i	−0.920586	−	0.390540i	$-0.872288\pi$
$941$	−24.4949	−	42.4264i	−0.798511	−	1.38306i	0.122075	−	0.992521i	$-0.461045\pi$
$942$		0			0
$943$	36.0000	+	20.7846i	1.17232	+	0.676840i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	42.8661	+	24.7487i	1.39296	+	0.804226i	0.993642	−	0.112586i	$-0.0359135\pi$
$947$	42.8661	+	24.7487i	1.39296	+	0.804226i	0.399318	+	0.916812i	$0.369247\pi$
$948$		0			0
$949$	4.50000	+	7.79423i	0.146076	+	0.253011i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	5.65685i		−	0.183243i	−0.995794	−	0.0916217i	$-0.970795\pi$
$953$		−	5.65685i		−	0.183243i	0.995794	−	0.0916217i	$-0.0292051\pi$
$954$		0			0
$955$	3.00000	−	1.73205i	0.0970777	−	0.0560478i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	19.5959	+	22.6274i	0.632785	+	0.730677i
$960$		0			0
$961$	−14.0000	+	24.2487i	−0.451613	+	0.782216i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	26.9444			0.867371
$966$		0			0
$967$	13.0000			0.418052			0.209026	−	0.977910i	$-0.432971\pi$
$967$	13.0000			0.418052			0.209026	+	0.977910i	$0.432971\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	19.5959	−	33.9411i	0.628863	−	1.08922i	−0.358917	−	0.933369i	$-0.616854\pi$
$971$	19.5959	−	33.9411i	0.628863	−	1.08922i	0.987780	−	0.155853i	$-0.0498127\pi$
$972$		0			0
$973$	13.5000	−	2.59808i	0.432790	−	0.0832905i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	6.12372	−	3.53553i	0.195915	−	0.113112i	−0.398833	−	0.917023i	$-0.630585\pi$
$977$	6.12372	−	3.53553i	0.195915	−	0.113112i	0.594749	+	0.803912i	$0.297252\pi$
$978$		0			0
$979$		−	6.92820i		−	0.221426i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	2.44949	+	4.24264i	0.0781266	+	0.135319i	0.902442	−	0.430812i	$-0.141773\pi$
$983$	2.44949	+	4.24264i	0.0781266	+	0.135319i	−0.824315	+	0.566131i	$0.808439\pi$
$984$		0			0
$985$	−42.0000	−	24.2487i	−1.33823	−	0.772628i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−4.89898	−	2.82843i	−0.155778	−	0.0899388i
$990$		0			0
$991$	17.5000	+	30.3109i	0.555906	+	0.962857i	0.997832	+	0.0658059i	$0.0209618\pi$
$991$	17.5000	+	30.3109i	0.555906	+	0.962857i	−0.441927	+	0.897051i	$0.645705\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$			33.9411i			1.07601i
$996$		0			0
$997$	−25.5000	+	14.7224i	−0.807593	+	0.466264i	−0.846119	−	0.532993i	$-0.821067\pi$
$997$	−25.5000	+	14.7224i	−0.807593	+	0.466264i	0.0385262	+	0.999258i	$0.487734\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.bt.b.593.1		4
3.2	odd	2	inner	1008.2.bt.b.593.2		4
4.3	odd	2		63.2.p.a.26.2	yes	4
7.2	even	3		7056.2.k.b.881.4		4
7.3	odd	6	inner	1008.2.bt.b.17.2		4
7.5	odd	6		7056.2.k.b.881.2		4
12.11	even	2		63.2.p.a.26.1	yes	4
20.3	even	4		1575.2.bc.a.1349.3		8
20.7	even	4		1575.2.bc.a.1349.2		8
20.19	odd	2		1575.2.bk.c.26.1		4
21.2	odd	6		7056.2.k.b.881.1		4
21.5	even	6		7056.2.k.b.881.3		4
21.17	even	6	inner	1008.2.bt.b.17.1		4
28.3	even	6		63.2.p.a.17.1	✓	4
28.11	odd	6		441.2.p.a.80.1		4
28.19	even	6		441.2.c.a.440.1		4
28.23	odd	6		441.2.c.a.440.2		4
28.27	even	2		441.2.p.a.215.2		4
36.7	odd	6		567.2.i.d.215.1		4
36.11	even	6		567.2.i.d.215.2		4
36.23	even	6		567.2.s.d.26.2		4
36.31	odd	6		567.2.s.d.26.1		4
60.23	odd	4		1575.2.bc.a.1349.1		8
60.47	odd	4		1575.2.bc.a.1349.4		8
60.59	even	2		1575.2.bk.c.26.2		4
84.11	even	6		441.2.p.a.80.2		4
84.23	even	6		441.2.c.a.440.3		4
84.47	odd	6		441.2.c.a.440.4		4
84.59	odd	6		63.2.p.a.17.2	yes	4
84.83	odd	2		441.2.p.a.215.1		4
140.3	odd	12		1575.2.bc.a.899.4		8
140.59	even	6		1575.2.bk.c.1151.2		4
140.87	odd	12		1575.2.bc.a.899.1		8
252.31	even	6		567.2.i.d.269.1		4
252.59	odd	6		567.2.i.d.269.2		4
252.115	even	6		567.2.s.d.458.2		4
252.227	odd	6		567.2.s.d.458.1		4
420.59	odd	6		1575.2.bk.c.1151.1		4
420.143	even	12		1575.2.bc.a.899.2		8
420.227	even	12		1575.2.bc.a.899.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.p.a.17.1	✓	4	28.3	even	6
63.2.p.a.17.2	yes	4	84.59	odd	6
63.2.p.a.26.1	yes	4	12.11	even	2
63.2.p.a.26.2	yes	4	4.3	odd	2
441.2.c.a.440.1		4	28.19	even	6
441.2.c.a.440.2		4	28.23	odd	6
441.2.c.a.440.3		4	84.23	even	6
441.2.c.a.440.4		4	84.47	odd	6
441.2.p.a.80.1		4	28.11	odd	6
441.2.p.a.80.2		4	84.11	even	6
441.2.p.a.215.1		4	84.83	odd	2
441.2.p.a.215.2		4	28.27	even	2
567.2.i.d.215.1		4	36.7	odd	6
567.2.i.d.215.2		4	36.11	even	6
567.2.i.d.269.1		4	252.31	even	6
567.2.i.d.269.2		4	252.59	odd	6
567.2.s.d.26.1		4	36.31	odd	6
567.2.s.d.26.2		4	36.23	even	6
567.2.s.d.458.1		4	252.227	odd	6
567.2.s.d.458.2		4	252.115	even	6
1008.2.bt.b.17.1		4	21.17	even	6	inner
1008.2.bt.b.17.2		4	7.3	odd	6	inner
1008.2.bt.b.593.1		4	1.1	even	1	trivial
1008.2.bt.b.593.2		4	3.2	odd	2	inner
1575.2.bc.a.899.1		8	140.87	odd	12
1575.2.bc.a.899.2		8	420.143	even	12
1575.2.bc.a.899.3		8	420.227	even	12
1575.2.bc.a.899.4		8	140.3	odd	12
1575.2.bc.a.1349.1		8	60.23	odd	4
1575.2.bc.a.1349.2		8	20.7	even	4
1575.2.bc.a.1349.3		8	20.3	even	4
1575.2.bc.a.1349.4		8	60.47	odd	4
1575.2.bk.c.26.1		4	20.19	odd	2
1575.2.bk.c.26.2		4	60.59	even	2
1575.2.bk.c.1151.1		4	420.59	odd	6
1575.2.bk.c.1151.2		4	140.59	even	6
7056.2.k.b.881.1		4	21.2	odd	6
7056.2.k.b.881.2		4	7.5	odd	6
7056.2.k.b.881.3		4	21.5	even	6
7056.2.k.b.881.4		4	7.2	even	3

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)

\(f(q)\)	\(=\)	\(q+(-1.22474 + 2.12132i) q^{5} +(0.500000 + 2.59808i) q^{7} +O(q^{10})\)	\(q+(-1.22474 + 2.12132i) q^{5} +(0.500000 + 2.59808i) q^{7} +(1.22474 - 0.707107i) q^{11} +5.19615i q^{13} +(-2.44949 - 4.24264i) q^{17} +(-1.50000 - 0.866025i) q^{19} +(-4.89898 - 2.82843i) q^{23} +(-0.500000 - 0.866025i) q^{25} +2.82843i q^{29} +(-1.50000 + 0.866025i) q^{31} +(-6.12372 - 2.12132i) q^{35} +(0.500000 - 0.866025i) q^{37} -7.34847 q^{41} +1.00000 q^{43} +(-6.12372 + 10.6066i) q^{47} +(-6.50000 + 2.59808i) q^{49} +(2.44949 - 1.41421i) q^{53} +3.46410i q^{55} +(2.44949 + 4.24264i) q^{59} +(-3.00000 - 1.73205i) q^{61} +(-11.0227 - 6.36396i) q^{65} +(5.50000 + 9.52628i) q^{67} -7.07107i q^{71} +(1.50000 - 0.866025i) q^{73} +(2.44949 + 2.82843i) q^{77} +(2.50000 - 4.33013i) q^{79} -7.34847 q^{83} +12.0000 q^{85} +(2.44949 - 4.24264i) q^{89} +(-13.5000 + 2.59808i) q^{91} +(3.67423 - 2.12132i) q^{95} +10.3923i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{7}+O(q^{10}) \) 4 * q + 2 * q^7	\( 4 q + 2 q^{7} - 6 q^{19} - 2 q^{25} - 6 q^{31} + 2 q^{37} + 4 q^{43} - 26 q^{49} - 12 q^{61} + 22 q^{67} + 6 q^{73} + 10 q^{79} + 48 q^{85} - 54 q^{91}+O(q^{100}) \) 4 * q + 2 * q^7 - 6 * q^19 - 2 * q^25 - 6 * q^31 + 2 * q^37 + 4 * q^43 - 26 * q^49 - 12 * q^61 + 22 * q^67 + 6 * q^73 + 10 * q^79 + 48 * q^85 - 54 * q^91

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