LMFDB - Embedded newform 1584.2.cd.b.161.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1584,2,Mod(17,1584)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1584, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 5, 9]))

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

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

chi := DirichletCharacter("1584.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1584 = 2^{4} \cdot 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1584.cd (of order $10$, degree $4$, 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:	$12.6483036802$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	8.0.64000000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{6} + 4x^{4} - 8x^{2} + 16 $ x^8 - 2x^6 + 4x^4 - 8*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 198)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			161.1
Root			$0.831254 - 1.14412i$ of defining polynomial
Character	$\chi$	$=$	1584.161
Dual form			1584.2.cd.b.305.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.604291 + 0.831735i) q^{5} +(-1.88947 + 0.613926i) q^{7} +O(q^{10})$	$q+(0.604291 + 0.831735i) q^{5} +(-1.88947 + 0.613926i) q^{7} +(2.07196 - 2.58978i) q^{11} +(1.72232 - 2.37058i) q^{13} +(-1.17625 + 0.854596i) q^{17} +(0.0598171 + 0.0194357i) q^{19} -0.0388715i q^{23} +(1.21847 - 3.75006i) q^{25} +(-2.64027 - 8.12592i) q^{29} +(8.52026 + 6.19033i) q^{31} +(-1.65241 - 1.20055i) q^{35} +(2.17625 + 6.69781i) q^{37} +(1.70998 - 5.26276i) q^{41} -5.07780i q^{43} +(6.68536 + 2.17220i) q^{47} +(-2.46992 + 1.79451i) q^{49} +(3.62455 - 4.98876i) q^{53} +(3.40608 + 0.158339i) q^{55} +(-4.53984 + 1.47508i) q^{59} +(6.24657 + 8.59766i) q^{61} +3.01248 q^{65} +15.6435 q^{67} +(-7.12516 - 9.80694i) q^{71} +(14.5120 - 4.71525i) q^{73} +(-2.32497 + 6.16535i) q^{77} +(-0.115040 + 0.158339i) q^{79} +(4.71124 - 3.42292i) q^{83} +(-1.42160 - 0.461904i) q^{85} +7.05342i q^{89} +(-1.79892 + 5.53652i) q^{91} +(0.0199815 + 0.0614968i) q^{95} +(-3.28214 - 2.38462i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q+O(q^{10}) $ 8 * q	$ 8 q + 4 q^{11} + 8 q^{17} + 6 q^{25} - 10 q^{29} + 14 q^{31} + 10 q^{35} + 8 q^{41} + 20 q^{47} + 6 q^{49} - 30 q^{53} - 28 q^{55} - 20 q^{59} + 20 q^{61} + 64 q^{65} + 56 q^{67} + 20 q^{71} - 10 q^{73} + 20 q^{79} - 12 q^{83} + 16 q^{95} - 12 q^{97}+O(q^{100}) $ 8 * q + 4 * q^11 + 8 * q^17 + 6 * q^25 - 10 * q^29 + 14 * q^31 + 10 * q^35 + 8 * q^41 + 20 * q^47 + 6 * q^49 - 30 * q^53 - 28 * q^55 - 20 * q^59 + 20 * q^61 + 64 * q^65 + 56 * q^67 + 20 * q^71 - 10 * q^73 + 20 * q^79 - 12 * q^83 + 16 * q^95 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1584\mathbb{Z}\right)^\times$.

$n$	$145$	$353$	$991$	$1189$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$-1$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	0.604291	+	0.831735i	0.270247	+	0.371963i	0.922473	−	0.386061i	$-0.126165\pi$
$5$	0.604291	+	0.831735i	0.270247	+	0.371963i	−0.652226	+	0.758025i	$0.726165\pi$
$6$		0			0
$7$	−1.88947	+	0.613926i	−0.714153	+	0.232042i	−0.643486	−	0.765458i	$-0.722513\pi$
$7$	−1.88947	+	0.613926i	−0.714153	+	0.232042i	−0.0706666	+	0.997500i	$0.522513\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	2.07196	−	2.58978i	0.624719	−	0.780849i
$11$	2.07196	−	2.58978i	0.624719	−	0.780849i
$12$		0			0
$13$	1.72232	−	2.37058i	0.477687	−	0.657480i	−0.500371	−	0.865811i	$-0.666803\pi$
$13$	1.72232	−	2.37058i	0.477687	−	0.657480i	0.978058	+	0.208331i	$0.0668032\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.17625	+	0.854596i	−0.285283	+	0.207270i	−0.721218	−	0.692708i	$-0.756418\pi$
$17$	−1.17625	+	0.854596i	−0.285283	+	0.207270i	0.435936	+	0.899978i	$0.356418\pi$
$18$		0			0
$19$	0.0598171	+	0.0194357i	0.0137230	+	0.00445887i	0.315870	−	0.948802i	$-0.397704\pi$
$19$	0.0598171	+	0.0194357i	0.0137230	+	0.00445887i	−0.302147	+	0.953261i	$0.597704\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$		−	0.0388715i		−	0.00810527i	−0.999992	−	0.00405263i	$-0.998710\pi$
$23$		−	0.0388715i		−	0.00810527i	0.999992	−	0.00405263i	$-0.00129000\pi$
$24$		0			0
$25$	1.21847	−	3.75006i	0.243694	−	0.750013i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−2.64027	−	8.12592i	−0.490286	−	1.50895i	−0.824176	−	0.566333i	$-0.808362\pi$
$29$	−2.64027	−	8.12592i	−0.490286	−	1.50895i	0.333890	−	0.942612i	$-0.391638\pi$
$30$		0			0
$31$	8.52026	+	6.19033i	1.53028	+	1.11182i	0.956081	+	0.293103i	$0.0946879\pi$
$31$	8.52026	+	6.19033i	1.53028	+	1.11182i	0.574203	+	0.818713i	$0.305312\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−1.65241	−	1.20055i	−0.279309	−	0.202930i
$36$		0			0
$37$	2.17625	+	6.69781i	0.357773	+	1.10111i	0.954384	+	0.298582i	$0.0965138\pi$
$37$	2.17625	+	6.69781i	0.357773	+	1.10111i	−0.596610	+	0.802531i	$0.703486\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	1.70998	−	5.26276i	0.267053	−	0.821906i	−0.724160	−	0.689632i	$-0.757772\pi$
$41$	1.70998	−	5.26276i	0.267053	−	0.821906i	0.991213	−	0.132274i	$-0.0422277\pi$
$42$		0			0
$43$		−	5.07780i		−	0.774357i	−0.922005	−	0.387179i	$-0.873450\pi$
$43$		−	5.07780i		−	0.774357i	0.922005	−	0.387179i	$-0.126550\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	6.68536	+	2.17220i	0.975159	+	0.316848i	0.752897	−	0.658138i	$-0.228656\pi$
$47$	6.68536	+	2.17220i	0.975159	+	0.316848i	0.222262	+	0.974987i	$0.428656\pi$
$48$		0			0
$49$	−2.46992	+	1.79451i	−0.352846	+	0.256358i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	3.62455	−	4.98876i	0.497870	−	0.685260i	−0.483945	−	0.875098i	$-0.660797\pi$
$53$	3.62455	−	4.98876i	0.497870	−	0.685260i	0.981815	+	0.189839i	$0.0607965\pi$
$54$		0			0
$55$	3.40608	+	0.158339i	0.459276	+	0.0213504i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−4.53984	+	1.47508i	−0.591036	+	0.192039i	−0.589239	−	0.807959i	$-0.700572\pi$
$59$	−4.53984	+	1.47508i	−0.591036	+	0.192039i	−0.00179763	+	0.999998i	$0.500572\pi$
$60$		0			0
$61$	6.24657	+	8.59766i	0.799791	+	1.10082i	0.992819	+	0.119625i	$0.0381691\pi$
$61$	6.24657	+	8.59766i	0.799791	+	1.10082i	−0.193028	+	0.981193i	$0.561831\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	3.01248			0.373652
$66$		0			0
$67$	15.6435			1.91116			0.955581	−	0.294727i	$-0.0952288\pi$
$67$	15.6435			1.91116			0.955581	+	0.294727i	$0.0952288\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−7.12516	−	9.80694i	−0.845601	−	1.16387i	−0.984815	−	0.173608i	$-0.944458\pi$
$71$	−7.12516	−	9.80694i	−0.845601	−	1.16387i	0.139214	−	0.990262i	$-0.455542\pi$
$72$		0			0
$73$	14.5120	−	4.71525i	1.69851	−	0.551878i	0.710152	−	0.704049i	$-0.248626\pi$
$73$	14.5120	−	4.71525i	1.69851	−	0.551878i	0.988354	+	0.152170i	$0.0486263\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−2.32497	+	6.16535i	−0.264955	+	0.702607i
$78$		0			0
$79$	−0.115040	+	0.158339i	−0.0129430	+	0.0178145i	−0.815439	−	0.578842i	$-0.803505\pi$
$79$	−0.115040	+	0.158339i	−0.0129430	+	0.0178145i	0.802496	+	0.596657i	$0.203505\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	4.71124	−	3.42292i	0.517126	−	0.375714i	−0.298394	−	0.954443i	$-0.596451\pi$
$83$	4.71124	−	3.42292i	0.517126	−	0.375714i	0.815520	+	0.578729i	$0.196451\pi$
$84$		0			0
$85$	−1.42160	−	0.461904i	−0.154194	−	0.0501006i
$86$		0			0
$87$		0			0
$88$		0			0
$89$			7.05342i			0.747661i	0.927497	+	0.373831i	$0.121956\pi$
$89$			7.05342i			0.747661i	−0.927497	+	0.373831i	$0.878044\pi$
$90$		0			0
$91$	−1.79892	+	5.53652i	−0.188578	+	0.580385i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	0.0199815	+	0.0614968i	0.00205006	+	0.00630944i
$96$		0			0
$97$	−3.28214	−	2.38462i	−0.333251	−	0.242121i	0.408558	−	0.912732i	$-0.366032\pi$
$97$	−3.28214	−	2.38462i	−0.333251	−	0.242121i	−0.741809	+	0.670611i	$0.766032\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	11.5304	+	8.37729i	1.14731	+	0.833572i	0.988121	−	0.153676i	$-0.0491112\pi$
$101$	11.5304	+	8.37729i	1.14731	+	0.833572i	0.159192	+	0.987248i	$0.449111\pi$
$102$		0			0
$103$	−2.31713	−	7.13140i	−0.228314	−	0.702678i	−0.997938	−	0.0641810i	$-0.979557\pi$
$103$	−2.31713	−	7.13140i	−0.228314	−	0.702678i	0.769624	−	0.638497i	$-0.220443\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	2.93230	−	9.02469i	0.283476	−	0.872450i	−0.703375	−	0.710819i	$-0.748325\pi$
$107$	2.93230	−	9.02469i	0.283476	−	0.872450i	0.986851	−	0.161631i	$-0.0516755\pi$
$108$		0			0
$109$			14.1005i			1.35058i	0.737552	+	0.675290i	$0.235981\pi$
$109$			14.1005i			1.35058i	−0.737552	+	0.675290i	$0.764019\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−15.4528	−	5.02093i	−1.45368	−	0.472329i	−0.527547	−	0.849526i	$-0.676888\pi$
$113$	−15.4528	−	5.02093i	−1.45368	−	0.472329i	−0.926133	+	0.377196i	$0.876888\pi$
$114$		0			0
$115$	0.0323308	−	0.0234897i	0.00301486	−	0.00219042i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	1.69783	−	2.33687i	0.155640	−	0.214220i
$120$		0			0
$121$	−2.41396	−	10.7319i	−0.219451	−	0.975623i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	8.74418	−	2.84116i	0.782104	−	0.254121i
$126$		0			0
$127$	−7.04250	−	9.69316i	−0.624920	−	0.860129i	0.372779	−	0.927920i	$-0.378405\pi$
$127$	−7.04250	−	9.69316i	−0.624920	−	0.860129i	−0.997700	+	0.0677909i	$0.978405\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−16.2151			−1.41672			−0.708361	−	0.705850i	$-0.750565\pi$
$131$	−16.2151			−1.41672			−0.708361	+	0.705850i	$0.750565\pi$
$132$		0			0
$133$	−0.124955			−0.0108349
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−6.26069	−	8.61710i	−0.534887	−	0.736208i	0.452979	−	0.891521i	$-0.350361\pi$
$137$	−6.26069	−	8.61710i	−0.534887	−	0.736208i	−0.987865	+	0.155313i	$0.950361\pi$
$138$		0			0
$139$	−6.66251	+	2.16478i	−0.565107	+	0.183614i	−0.577618	−	0.816307i	$-0.696018\pi$
$139$	−6.66251	+	2.16478i	−0.565107	+	0.183614i	0.0125111	+	0.999922i	$0.496018\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−2.57069	−	9.37219i	−0.214972	−	0.783742i
$144$		0			0
$145$	5.16312	−	7.10642i	0.428774	−	0.590156i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	1.65401	−	1.20171i	0.135502	−	0.0984480i	−0.517969	−	0.855399i	$-0.673312\pi$
$149$	1.65401	−	1.20171i	0.135502	−	0.0984480i	0.653472	+	0.756951i	$0.273312\pi$
$150$		0			0
$151$	7.54955	+	2.45300i	0.614374	+	0.199622i	0.599641	−	0.800269i	$-0.295310\pi$
$151$	7.54955	+	2.45300i	0.614374	+	0.199622i	0.0147331	+	0.999891i	$0.495310\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$			10.8274i			0.869674i
$156$		0			0
$157$	−1.65214	+	5.08475i	−0.131855	+	0.405807i	−0.995088	−	0.0989987i	$-0.968436\pi$
$157$	−1.65214	+	5.08475i	−0.131855	+	0.405807i	0.863233	+	0.504806i	$0.168436\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	0.0238642	+	0.0734466i	0.00188076	+	0.00578840i
$162$		0			0
$163$	3.59321	+	2.61062i	0.281442	+	0.204479i	0.719546	−	0.694445i	$-0.244350\pi$
$163$	3.59321	+	2.61062i	0.281442	+	0.204479i	−0.438104	+	0.898924i	$0.644350\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	12.5193	+	9.09578i	0.968770	+	0.703853i	0.955171	−	0.296055i	$-0.0956711\pi$
$167$	12.5193	+	9.09578i	0.968770	+	0.703853i	0.0135992	+	0.999908i	$0.495671\pi$
$168$		0			0
$169$	1.36399	+	4.19793i	0.104922	+	0.322918i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	6.73771	−	20.7365i	0.512259	−	1.57657i	−0.275956	−	0.961170i	$-0.588994\pi$
$173$	6.73771	−	20.7365i	0.512259	−	1.57657i	0.788215	−	0.615400i	$-0.211006\pi$
$174$		0			0
$175$			7.83368i			0.592171i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	18.6613	+	6.06344i	1.39481	+	0.453203i	0.907510	−	0.420030i	$-0.137980\pi$
$179$	18.6613	+	6.06344i	1.39481	+	0.453203i	0.487304	+	0.873232i	$0.337980\pi$
$180$		0			0
$181$	−3.13928	+	2.28082i	−0.233341	+	0.169532i	−0.698311	−	0.715794i	$-0.746065\pi$
$181$	−3.13928	+	2.28082i	−0.233341	+	0.169532i	0.464970	+	0.885326i	$0.346065\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−4.25572	+	5.85749i	−0.312886	+	0.430651i
$186$		0			0
$187$	−0.223925	+	4.81693i	−0.0163750	+	0.352248i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−6.75929	+	2.19623i	−0.489085	+	0.158913i	−0.543170	−	0.839623i	$-0.682776\pi$
$191$	−6.75929	+	2.19623i	−0.489085	+	0.158913i	0.0540844	+	0.998536i	$0.482776\pi$
$192$		0			0
$193$	−6.41740	−	8.83279i	−0.461934	−	0.635798i	0.512974	−	0.858404i	$-0.328544\pi$
$193$	−6.41740	−	8.83279i	−0.461934	−	0.635798i	−0.974908	+	0.222606i	$0.928544\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−4.25626			−0.303246			−0.151623	−	0.988438i	$-0.548450\pi$
$197$	−4.25626			−0.303246			−0.151623	+	0.988438i	$0.548450\pi$
$198$		0			0
$199$	4.07769			0.289060			0.144530	−	0.989500i	$-0.453833\pi$
$199$	4.07769			0.289060			0.144530	+	0.989500i	$0.453833\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	9.97743	+	13.7328i	0.700278	+	0.963850i
$204$		0			0
$205$	5.41055	−	1.75799i	0.377889	−	0.122784i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	0.174273	−	0.114643i	0.0120547	−	0.00793004i
$210$		0			0
$211$	−1.61517	+	2.22309i	−0.111193	+	0.153044i	−0.860986	−	0.508628i	$-0.830153\pi$
$211$	−1.61517	+	2.22309i	−0.111193	+	0.153044i	0.749794	+	0.661672i	$0.230153\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	4.22338	−	3.06847i	0.288032	−	0.209268i
$216$		0			0
$217$	−19.8992	−	6.46564i	−1.35084	−	0.438916i
$218$		0			0
$219$		0			0
$220$		0			0
$221$			4.26029i			0.286578i
$222$		0			0
$223$	0.939572	−	2.89170i	0.0629184	−	0.193643i	−0.914656	−	0.404233i	$-0.867539\pi$
$223$	0.939572	−	2.89170i	0.0629184	−	0.193643i	0.977574	+	0.210590i	$0.0675385\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−3.44581	−	10.6051i	−0.228706	−	0.703886i	−0.997894	−	0.0648632i	$-0.979339\pi$
$227$	−3.44581	−	10.6051i	−0.228706	−	0.703886i	0.769188	−	0.639023i	$-0.220661\pi$
$228$		0			0
$229$	8.97804	+	6.52293i	0.593286	+	0.431047i	0.843489	−	0.537146i	$-0.180498\pi$
$229$	8.97804	+	6.52293i	0.593286	+	0.431047i	−0.250204	+	0.968193i	$0.580498\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	3.46894	+	2.52033i	0.227258	+	0.165112i	0.695588	−	0.718441i	$-0.255144\pi$
$233$	3.46894	+	2.52033i	0.227258	+	0.165112i	−0.468330	+	0.883554i	$0.655144\pi$
$234$		0			0
$235$	2.23320	+	6.87309i	0.145678	+	0.448351i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−4.76195	+	14.6558i	−0.308025	+	0.948004i	0.670506	+	0.741904i	$0.266077\pi$
$239$	−4.76195	+	14.6558i	−0.308025	+	0.948004i	−0.978531	+	0.206100i	$0.933923\pi$
$240$		0			0
$241$		−	25.2642i		−	1.62741i	−0.581279	−	0.813704i	$-0.697447\pi$
$241$		−	25.2642i		−	1.62741i	0.581279	−	0.813704i	$-0.302553\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−2.98511	−	0.969920i	−0.190711	−	0.0619659i
$246$		0			0
$247$	0.149098	−	0.108326i	0.00948690	−	0.00689264i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−1.04144	+	1.43341i	−0.0657348	+	0.0904762i	−0.840619	−	0.541627i	$-0.817808\pi$
$251$	−1.04144	+	1.43341i	−0.0657348	+	0.0904762i	0.774884	+	0.632104i	$0.217808\pi$
$252$		0			0
$253$	−0.100669	−	0.0805402i	−0.00632899	−	0.00506352i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−23.5800	+	7.66160i	−1.47088	+	0.477917i	−0.931374	−	0.364065i	$-0.881389\pi$
$257$	−23.5800	+	7.66160i	−1.47088	+	0.477917i	−0.539505	+	0.841982i	$0.681389\pi$
$258$		0			0
$259$	−8.22392	−	11.3193i	−0.511010	−	0.703345i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−6.57609			−0.405499			−0.202750	−	0.979231i	$-0.564988\pi$
$263$	−6.57609			−0.405499			−0.202750	+	0.979231i	$0.564988\pi$
$264$		0			0
$265$	6.33961			0.389439
$266$		0			0
$267$		0			0
$268$		0			0
$269$	11.8436	+	16.3013i	0.722117	+	0.993909i	0.999451	+	0.0331354i	$0.0105493\pi$
$269$	11.8436	+	16.3013i	0.722117	+	0.993909i	−0.277334	+	0.960774i	$0.589451\pi$
$270$		0			0
$271$	−16.8278	+	5.46770i	−1.02222	+	0.332139i	−0.771709	−	0.635975i	$-0.780598\pi$
$271$	−16.8278	+	5.46770i	−1.02222	+	0.332139i	−0.250509	+	0.968114i	$0.580598\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−7.18723	−	10.9256i	−0.433406	−	0.658836i
$276$		0			0
$277$	−6.29391	+	8.66282i	−0.378164	+	0.520498i	−0.955097	−	0.296293i	$-0.904249\pi$
$277$	−6.29391	+	8.66282i	−0.378164	+	0.520498i	0.576933	+	0.816792i	$0.304249\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−1.46463	+	1.06412i	−0.0873726	+	0.0634799i	−0.630614	−	0.776097i	$-0.717197\pi$
$281$	−1.46463	+	1.06412i	−0.0873726	+	0.0634799i	0.543241	+	0.839577i	$0.317197\pi$
$282$		0			0
$283$	−26.0096	−	8.45104i	−1.54611	−	0.502362i	−0.593057	−	0.805161i	$-0.702079\pi$
$283$	−26.0096	−	8.45104i	−1.54611	−	0.502362i	−0.953055	+	0.302799i	$0.902079\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$			10.9936i			0.648934i
$288$		0			0
$289$	−4.60006	+	14.1575i	−0.270592	+	0.832795i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	5.48466	+	16.8800i	0.320417	+	0.986142i	0.973467	+	0.228827i	$0.0734892\pi$
$293$	5.48466	+	16.8800i	0.320417	+	0.986142i	−0.653050	+	0.757315i	$0.726511\pi$
$294$		0			0
$295$	−3.97026	−	2.88456i	−0.231157	−	0.167946i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−0.0921479	−	0.0669493i	−0.00532905	−	0.00387178i
$300$		0			0
$301$	3.11740	+	9.59436i	0.179684	+	0.553010i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−3.37623	+	10.3910i	−0.193323	+	0.594986i
$306$		0			0
$307$			12.0009i			0.684928i	0.939531	+	0.342464i	$0.111261\pi$
$307$			12.0009i			0.684928i	−0.939531	+	0.342464i	$0.888739\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−26.6326	−	8.65346i	−1.51020	−	0.490693i	−0.567225	−	0.823563i	$-0.691983\pi$
$311$	−26.6326	−	8.65346i	−1.51020	−	0.490693i	−0.942973	+	0.332870i	$0.891983\pi$
$312$		0			0
$313$	3.47054	−	2.52149i	0.196166	−	0.142523i	−0.485366	−	0.874311i	$-0.661314\pi$
$313$	3.47054	−	2.52149i	0.196166	−	0.142523i	0.681533	+	0.731788i	$0.261314\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−4.33674	+	5.96901i	−0.243575	+	0.335253i	−0.913248	−	0.407403i	$-0.866434\pi$
$317$	−4.33674	+	5.96901i	−0.243575	+	0.335253i	0.669673	+	0.742656i	$0.266434\pi$
$318$		0			0
$319$	−26.5149	−	9.99885i	−1.48455	−	0.559828i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−0.0869696	+	0.0282581i	−0.00483912	+	0.00157232i
$324$		0			0
$325$	−6.79121	−	9.34730i	−0.376709	−	0.518495i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−13.9654			−0.769935
$330$		0			0
$331$	−11.1275			−0.611622			−0.305811	−	0.952092i	$-0.598928\pi$
$331$	−11.1275			−0.611622			−0.305811	+	0.952092i	$0.598928\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	9.45325	+	13.0113i	0.516486	+	0.710882i
$336$		0			0
$337$	−24.5466	+	7.97568i	−1.33714	+	0.434463i	−0.888347	−	0.459173i	$-0.848146\pi$
$337$	−24.5466	+	7.97568i	−1.33714	+	0.434463i	−0.448793	+	0.893636i	$0.648146\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	33.6853	−	9.23951i	1.82416	−	0.500348i
$342$		0			0
$343$	11.7395	−	16.1580i	0.633871	−	0.872449i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	8.54024	−	6.20485i	0.458464	−	0.333094i	−0.334464	−	0.942408i	$-0.608555\pi$
$347$	8.54024	−	6.20485i	0.458464	−	0.333094i	0.792928	+	0.609315i	$0.208555\pi$
$348$		0			0
$349$	−16.8321	−	5.46909i	−0.901004	−	0.292754i	−0.178353	−	0.983967i	$-0.557077\pi$
$349$	−16.8321	−	5.46909i	−0.901004	−	0.292754i	−0.722651	+	0.691213i	$0.757077\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$			15.0780i			0.802521i	0.915964	+	0.401260i	$0.131428\pi$
$353$			15.0780i			0.802521i	−0.915964	+	0.401260i	$0.868572\pi$
$354$		0			0
$355$	3.85111	−	11.8525i	0.204396	−	0.629065i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−6.51948	−	20.0649i	−0.344085	−	1.05898i	−0.962072	−	0.272796i	$-0.912052\pi$
$359$	−6.51948	−	20.0649i	−0.344085	−	1.05898i	0.617987	−	0.786188i	$-0.287948\pi$
$360$		0			0
$361$	−15.3681	−	11.1656i	−0.808849	−	0.587663i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	12.6913	+	9.22079i	0.664295	+	0.482638i
$366$		0			0
$367$	6.32154	+	19.4557i	0.329982	+	1.01558i	0.969142	+	0.246505i	$0.0792822\pi$
$367$	6.32154	+	19.4557i	0.329982	+	1.01558i	−0.639160	+	0.769074i	$0.720718\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−3.78575	+	11.6513i	−0.196546	+	0.604907i
$372$		0			0
$373$			16.8547i			0.872705i	0.899776	+	0.436352i	$0.143730\pi$
$373$			16.8547i			0.872705i	−0.899776	+	0.436352i	$0.856270\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−23.8105	−	7.73651i	−1.22630	−	0.398450i
$378$		0			0
$379$	1.34766	−	0.979130i	0.0692245	−	0.0502945i	−0.552635	−	0.833424i	$-0.686378\pi$
$379$	1.34766	−	0.979130i	0.0692245	−	0.0502945i	0.621859	+	0.783129i	$0.286378\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−13.9409	+	19.1880i	−0.712345	+	0.980459i	0.287399	+	0.957811i	$0.407210\pi$
$383$	−13.9409	+	19.1880i	−0.712345	+	0.980459i	−0.999744	+	0.0226476i	$0.992790\pi$
$384$		0			0
$385$	−6.53290	+	1.79191i	−0.332947	+	0.0913240i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−12.9907	+	4.22094i	−0.658656	+	0.214010i	−0.619227	−	0.785212i	$-0.712554\pi$
$389$	−12.9907	+	4.22094i	−0.658656	+	0.214010i	−0.0394290	+	0.999222i	$0.512554\pi$
$390$		0			0
$391$	0.0332194	+	0.0457226i	0.00167998	+	0.00231229i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−0.201214			−0.0101242
$396$		0			0
$397$	3.38639			0.169958			0.0849790	−	0.996383i	$-0.472918\pi$
$397$	3.38639			0.169958			0.0849790	+	0.996383i	$0.472918\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	4.67807	+	6.43881i	0.233611	+	0.321539i	0.909688	−	0.415293i	$-0.136321\pi$
$401$	4.67807	+	6.43881i	0.233611	+	0.321539i	−0.676076	+	0.736832i	$0.736321\pi$
$402$		0			0
$403$	29.3493	−	9.53617i	1.46199	−	0.475030i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	21.8550	+	8.24158i	1.08331	+	0.408520i
$408$		0			0
$409$	12.3646	−	17.0184i	0.611390	−	0.841506i	−0.385301	−	0.922791i	$-0.625902\pi$
$409$	12.3646	−	17.0184i	0.611390	−	0.841506i	0.996691	+	0.0812847i	$0.0259023\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	7.67230	−	5.57425i	0.377529	−	0.274291i
$414$		0			0
$415$	5.69392	+	1.85007i	0.279504	+	0.0908162i
$416$		0			0
$417$		0			0
$418$		0			0
$419$			36.2149i			1.76921i	0.466338	+	0.884607i	$0.345573\pi$
$419$			36.2149i			1.76921i	−0.466338	+	0.884607i	$0.654427\pi$
$420$		0			0
$421$	−11.9336	+	36.7277i	−0.581606	+	1.79000i	0.0308844	+	0.999523i	$0.490168\pi$
$421$	−11.9336	+	36.7277i	−0.581606	+	1.79000i	−0.612491	+	0.790478i	$0.709832\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	1.77156	+	5.45231i	0.0859335	+	0.264476i
$426$		0			0
$427$	−17.0810	−	12.4101i	−0.826609	−	0.600567i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	26.4754	+	19.2355i	1.27527	+	0.926540i	0.999399	−	0.0346541i	$-0.0110329\pi$
$431$	26.4754	+	19.2355i	1.27527	+	0.926540i	0.275873	+	0.961194i	$0.411033\pi$
$432$		0			0
$433$	−10.5045	−	32.3296i	−0.504815	−	1.55366i	−0.801082	−	0.598554i	$-0.795742\pi$
$433$	−10.5045	−	32.3296i	−0.504815	−	1.55366i	0.296268	−	0.955105i	$-0.404258\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	0.000755497	−	0.00232518i	3.61403e−5	−	0.000111228i
$438$		0			0
$439$			4.25200i			0.202937i	0.994839	+	0.101468i	$0.0323541\pi$
$439$			4.25200i			0.202937i	−0.994839	+	0.101468i	$0.967646\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−31.3807	−	10.1962i	−1.49094	−	0.484437i	−0.553581	−	0.832795i	$-0.686739\pi$
$443$	−31.3807	−	10.1962i	−1.49094	−	0.484437i	−0.937361	+	0.348359i	$0.886739\pi$
$444$		0			0
$445$	−5.86658	+	4.26232i	−0.278103	+	0.202053i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	23.7671	−	32.7127i	1.12164	−	1.54381i	0.318592	−	0.947892i	$-0.396790\pi$
$449$	23.7671	−	32.7127i	1.12164	−	1.54381i	0.803048	−	0.595914i	$-0.203210\pi$
$450$		0			0
$451$	−10.0864	−	15.3327i	−0.474951	−	0.721989i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−5.69199	+	1.84944i	−0.266844	+	0.0867030i
$456$		0			0
$457$	−11.1358	−	15.3272i	−0.520912	−	0.716974i	0.464799	−	0.885416i	$-0.346126\pi$
$457$	−11.1358	−	15.3272i	−0.520912	−	0.716974i	−0.985712	+	0.168442i	$0.946126\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−16.3807			−0.762927			−0.381464	−	0.924384i	$-0.624580\pi$
$461$	−16.3807			−0.762927			−0.381464	+	0.924384i	$0.624580\pi$
$462$		0			0
$463$	1.67874			0.0780177			0.0390088	−	0.999239i	$-0.487580\pi$
$463$	1.67874			0.0780177			0.0390088	+	0.999239i	$0.487580\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−7.89548	−	10.8672i	−0.365359	−	0.502874i	0.586273	−	0.810114i	$-0.300595\pi$
$467$	−7.89548	−	10.8672i	−0.365359	−	0.502874i	−0.951632	+	0.307240i	$0.900595\pi$
$468$		0			0
$469$	−29.5580	+	9.60398i	−1.36486	+	0.443471i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−13.1504	−	10.5210i	−0.604656	−	0.483756i
$474$		0			0
$475$	0.145771	−	0.200636i	0.00668841	−	0.00920581i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	16.1343	−	11.7223i	0.737195	−	0.535604i	−0.154636	−	0.987971i	$-0.549421\pi$
$479$	16.1343	−	11.7223i	0.737195	−	0.535604i	0.891832	+	0.452368i	$0.149421\pi$
$480$		0			0
$481$	19.6259	+	6.37684i	0.894863	+	0.290759i
$482$		0			0
$483$		0			0
$484$		0			0
$485$		−	4.17087i		−	0.189390i
$486$		0			0
$487$	−0.606141	+	1.86551i	−0.0274669	+	0.0845344i	−0.963850	−	0.266444i	$-0.914151\pi$
$487$	−0.606141	+	1.86551i	−0.0274669	+	0.0845344i	0.936383	+	0.350979i	$0.114151\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	5.38926	+	16.5865i	0.243214	+	0.748536i	0.995925	+	0.0901849i	$0.0287458\pi$
$491$	5.38926	+	16.5865i	0.243214	+	0.748536i	−0.752711	+	0.658351i	$0.771254\pi$
$492$		0			0
$493$	10.0500	+	7.30175i	0.452629	+	0.328854i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	19.4835	+	14.1556i	0.873955	+	0.634966i
$498$		0			0
$499$	−1.89584	−	5.83479i	−0.0848693	−	0.261201i	0.899612	−	0.436690i	$-0.143849\pi$
$499$	−1.89584	−	5.83479i	−0.0848693	−	0.261201i	−0.984481	+	0.175489i	$0.943849\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	10.8851	−	33.5008i	0.485342	−	1.49373i	−0.346143	−	0.938182i	$-0.612509\pi$
$503$	10.8851	−	33.5008i	0.485342	−	1.49373i	0.831485	−	0.555547i	$-0.187491\pi$
$504$		0			0
$505$			14.6525i			0.652029i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	15.1634	+	4.92689i	0.672106	+	0.218380i	0.625136	−	0.780516i	$-0.285044\pi$
$509$	15.1634	+	4.92689i	0.672106	+	0.218380i	0.0469698	+	0.998896i	$0.485044\pi$
$510$		0			0
$511$	−24.5253	+	17.8186i	−1.08493	+	0.788251i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	4.53121	−	6.23668i	0.199669	−	0.274821i
$516$		0			0
$517$	19.4773	−	12.8129i	0.856612	−	0.563511i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	0.483930	−	0.157238i	0.0212014	−	0.00688874i	−0.298397	−	0.954442i	$-0.596452\pi$
$521$	0.483930	−	0.157238i	0.0212014	−	0.00688874i	0.319598	+	0.947553i	$0.396452\pi$
$522$		0			0
$523$	6.34601	+	8.73454i	0.277492	+	0.381935i	0.924901	−	0.380208i	$-0.124148\pi$
$523$	6.34601	+	8.73454i	0.277492	+	0.381935i	−0.647409	+	0.762143i	$0.724148\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−15.3122			−0.667010
$528$		0			0
$529$	22.9985			0.999934
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−9.53065	−	13.1178i	−0.412818	−	0.568196i
$534$		0			0
$535$	9.27811	−	3.01464i	0.401128	−	0.130334i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−0.470204	+	10.1147i	−0.0202531	+	0.435672i
$540$		0			0
$541$	8.24071	−	11.3424i	0.354296	−	0.487646i	−0.594253	−	0.804278i	$-0.702552\pi$
$541$	8.24071	−	11.3424i	0.354296	−	0.487646i	0.948548	+	0.316632i	$0.102552\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−11.7279	+	8.52078i	−0.502366	+	0.364990i
$546$		0			0
$547$	4.66837	+	1.51684i	0.199605	+	0.0648556i	0.407113	−	0.913378i	$-0.366535\pi$
$547$	4.66837	+	1.51684i	0.199605	+	0.0648556i	−0.207508	+	0.978233i	$0.566535\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		−	0.537384i		−	0.0228933i
$552$		0			0
$553$	0.120156	−	0.369803i	0.00510956	−	0.0157256i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−1.28181	−	3.94500i	−0.0543120	−	0.167155i	0.920221	−	0.391399i	$-0.128009\pi$
$557$	−1.28181	−	3.94500i	−0.0543120	−	0.167155i	−0.974533	+	0.224244i	$0.928009\pi$
$558$		0			0
$559$	−12.0373	−	8.74562i	−0.509124	−	0.369900i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−22.1234	−	16.0736i	−0.932390	−	0.677421i	0.0141871	−	0.999899i	$-0.495484\pi$
$563$	−22.1234	−	16.0736i	−0.932390	−	0.677421i	−0.946577	+	0.322479i	$0.895484\pi$
$564$		0			0
$565$	−5.16192	−	15.8868i	−0.217164	−	0.668361i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	1.71162	−	5.26782i	0.0717548	−	0.220839i	−0.908747	−	0.417347i	$-0.862960\pi$
$569$	1.71162	−	5.26782i	0.0717548	−	0.220839i	0.980502	+	0.196508i	$0.0629601\pi$
$570$		0			0
$571$			40.0601i			1.67646i	0.545313	+	0.838232i	$0.316411\pi$
$571$			40.0601i			1.67646i	−0.545313	+	0.838232i	$0.683589\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−0.145771	−	0.0473637i	−0.00607905	−	0.00197520i
$576$		0			0
$577$	24.3076	−	17.6605i	1.01194	−	0.735216i	0.0473236	−	0.998880i	$-0.484931\pi$
$577$	24.3076	−	17.6605i	1.01194	−	0.735216i	0.964615	+	0.263663i	$0.0849308\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−6.80033	+	9.35986i	−0.282125	+	0.388312i
$582$		0			0
$583$	−5.40990	−	19.7233i	−0.224055	−	0.816857i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	37.3102	−	12.1228i	1.53996	−	0.500362i	0.588593	−	0.808430i	$-0.299682\pi$
$587$	37.3102	−	12.1228i	1.53996	−	0.500362i	0.951365	+	0.308067i	$0.0996822\pi$
$588$		0			0
$589$	0.389343	+	0.535885i	0.0160426	+	0.0220808i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−37.9764			−1.55950			−0.779752	−	0.626088i	$-0.784655\pi$
$593$	−37.9764			−1.55950			−0.779752	+	0.626088i	$0.784655\pi$
$594$		0			0
$595$	2.96964			0.121743
$596$		0			0
$597$		0			0
$598$		0			0
$599$	0.0332926	+	0.0458233i	0.00136030	+	0.00187229i	0.809697	−	0.586849i	$-0.199632\pi$
$599$	0.0332926	+	0.0458233i	0.00136030	+	0.00187229i	−0.808336	+	0.588721i	$0.799632\pi$
$600$		0			0
$601$	−12.7604	+	4.14609i	−0.520506	+	0.169123i	−0.557475	−	0.830194i	$-0.688230\pi$
$601$	−12.7604	+	4.14609i	−0.520506	+	0.169123i	0.0369691	+	0.999316i	$0.488230\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	7.46733	−	8.49294i	0.303590	−	0.345287i
$606$		0			0
$607$	−6.63755	+	9.13581i	−0.269410	+	0.370811i	−0.922190	−	0.386736i	$-0.873602\pi$
$607$	−6.63755	+	9.13581i	−0.269410	+	0.370811i	0.652780	+	0.757547i	$0.273602\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	16.6637	−	12.1069i	0.674142	−	0.489793i
$612$		0			0
$613$	16.1894	+	5.26026i	0.653884	+	0.212460i	0.617126	−	0.786864i	$-0.288297\pi$
$613$	16.1894	+	5.26026i	0.653884	+	0.212460i	0.0367581	+	0.999324i	$0.488297\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			38.8680i			1.56477i	0.622796	+	0.782384i	$0.285997\pi$
$617$			38.8680i			1.56477i	−0.622796	+	0.782384i	$0.714003\pi$
$618$		0			0
$619$	−11.1070	+	34.1839i	−0.446429	+	1.37397i	0.434480	+	0.900682i	$0.356932\pi$
$619$	−11.1070	+	34.1839i	−0.446429	+	1.37397i	−0.880909	+	0.473286i	$0.843068\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−4.33028	−	13.3272i	−0.173489	−	0.533944i
$624$		0			0
$625$	−8.30285	−	6.03237i	−0.332114	−	0.241295i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−8.28374	−	6.01849i	−0.330294	−	0.239973i
$630$		0			0
$631$	8.72572	+	26.8550i	0.347366	+	1.06908i	0.960305	+	0.278952i	$0.0899869\pi$
$631$	8.72572	+	26.8550i	0.347366	+	1.06908i	−0.612940	+	0.790130i	$0.710013\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	3.80643	−	11.7150i	0.151053	−	0.464895i
$636$		0			0
$637$			8.94587i			0.354448i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	20.7616	+	6.74586i	0.820035	+	0.266445i	0.688842	−	0.724911i	$-0.258119\pi$
$641$	20.7616	+	6.74586i	0.820035	+	0.266445i	0.131193	+	0.991357i	$0.458119\pi$
$642$		0			0
$643$	22.4184	−	16.2879i	0.884095	−	0.642332i	−0.0502368	−	0.998737i	$-0.515998\pi$
$643$	22.4184	−	16.2879i	0.884095	−	0.642332i	0.934332	+	0.356405i	$0.115998\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−0.433857	+	0.597152i	−0.0170567	+	0.0234765i	−0.817460	−	0.575985i	$-0.804619\pi$
$647$	−0.433857	+	0.597152i	−0.0170567	+	0.0234765i	0.800404	+	0.599462i	$0.204619\pi$
$648$		0			0
$649$	−5.58621	+	14.8135i	−0.219278	+	0.581481i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−0.994083	+	0.322997i	−0.0389015	+	0.0126399i	−0.328403	−	0.944538i	$-0.606510\pi$
$653$	−0.994083	+	0.322997i	−0.0389015	+	0.0126399i	0.289502	+	0.957178i	$0.406510\pi$
$654$		0			0
$655$	−9.79865	−	13.4867i	−0.382865	−	0.526968i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−17.9109			−0.697708			−0.348854	−	0.937177i	$-0.613429\pi$
$659$	−17.9109			−0.697708			−0.348854	+	0.937177i	$0.613429\pi$
$660$		0			0
$661$	23.3842			0.909540			0.454770	−	0.890609i	$-0.349721\pi$
$661$	23.3842			0.909540			0.454770	+	0.890609i	$0.349721\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−0.0755090	−	0.103929i	−0.00292811	−	0.00403020i
$666$		0			0
$667$	−0.315867	+	0.102631i	−0.0122304	+	0.00397390i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	35.2087	+	1.63675i	1.35922	+	0.0631861i
$672$		0			0
$673$	4.18304	−	5.75746i	0.161244	−	0.221934i	−0.720748	−	0.693197i	$-0.756202\pi$
$673$	4.18304	−	5.75746i	0.161244	−	0.221934i	0.881993	+	0.471263i	$0.156202\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	23.3752	−	16.9831i	0.898384	−	0.652714i	−0.0396665	−	0.999213i	$-0.512630\pi$
$677$	23.3752	−	16.9831i	0.898384	−	0.652714i	0.938050	+	0.346499i	$0.112630\pi$
$678$		0			0
$679$	7.66549	+	2.49067i	0.294174	+	0.0955831i
$680$		0			0
$681$		0			0
$682$		0			0
$683$			36.7306i			1.40546i	0.711458	+	0.702728i	$0.248035\pi$
$683$			36.7306i			1.40546i	−0.711458	+	0.702728i	$0.751965\pi$
$684$		0			0
$685$	3.38387	−	10.4145i	0.129291	−	0.397916i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−5.58360	−	17.1845i	−0.212718	−	0.654679i
$690$		0			0
$691$	0.489251	+	0.355462i	0.0186120	+	0.0135224i	0.597052	−	0.802202i	$-0.296338\pi$
$691$	0.489251	+	0.355462i	0.0186120	+	0.0135224i	−0.578440	+	0.815725i	$0.696338\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−5.82662	−	4.23328i	−0.221016	−	0.160578i
$696$		0			0
$697$	2.48618	+	7.65167i	0.0941707	+	0.289828i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	1.55911	−	4.79843i	0.0588866	−	0.181234i	−0.917286	−	0.398228i	$-0.869625\pi$
$701$	1.55911	−	4.79843i	0.0588866	−	0.181234i	0.976173	+	0.216994i	$0.0696252\pi$
$702$		0			0
$703$			0.442941i			0.0167058i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−26.9293	−	8.74986i	−1.01278	−	0.329072i
$708$		0			0
$709$	24.9345	−	18.1159i	0.936433	−	0.680358i	−0.0111263	−	0.999938i	$-0.503542\pi$
$709$	24.9345	−	18.1159i	0.936433	−	0.680358i	0.947559	+	0.319580i	$0.103542\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	0.240627	−	0.331195i	0.00901157	−	0.0124034i
$714$		0			0
$715$	6.24173	−	7.80166i	0.233428	−	0.291766i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−29.9223	+	9.72235i	−1.11591	+	0.362582i	−0.808207	−	0.588899i	$-0.799562\pi$
$719$	−29.9223	+	9.72235i	−1.11591	+	0.362582i	−0.307707	+	0.951481i	$0.599562\pi$
$720$		0			0
$721$	8.75631	+	12.0520i	0.326102	+	0.448841i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−33.6898			−1.25121
$726$		0			0
$727$	41.6268			1.54385			0.771926	−	0.635713i	$-0.219294\pi$
$727$	41.6268			1.54385			0.771926	+	0.635713i	$0.219294\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	4.33947	+	5.97277i	0.160501	+	0.220911i
$732$		0			0
$733$	−7.57302	+	2.46062i	−0.279716	+	0.0908852i	−0.445515	−	0.895274i	$-0.646980\pi$
$733$	−7.57302	+	2.46062i	−0.279716	+	0.0908852i	0.165800	+	0.986159i	$0.446980\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	32.4128	−	40.5134i	1.19394	−	1.49233i
$738$		0			0
$739$	20.6182	−	28.3785i	0.758452	−	1.04392i	−0.238890	−	0.971047i	$-0.576783\pi$
$739$	20.6182	−	28.3785i	0.758452	−	1.04392i	0.997341	−	0.0728723i	$-0.0232165\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−16.7155	+	12.1445i	−0.613232	+	0.445539i	−0.850551	−	0.525892i	$-0.823731\pi$
$743$	−16.7155	+	12.1445i	−0.613232	+	0.445539i	0.237319	+	0.971432i	$0.423731\pi$
$744$		0			0
$745$	1.99901	+	0.649518i	0.0732381	+	0.0237965i
$746$		0			0
$747$		0			0
$748$		0			0
$749$			18.8521i			0.688841i
$750$		0			0
$751$	1.90663	−	5.86800i	0.0695739	−	0.214126i	−0.910224	−	0.414116i	$-0.864091\pi$
$751$	1.90663	−	5.86800i	0.0695739	−	0.214126i	0.979798	+	0.199989i	$0.0640908\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	2.52188	+	7.76155i	0.0917806	+	0.282472i
$756$		0			0
$757$	8.84926	+	6.42936i	0.321632	+	0.233679i	0.736871	−	0.676033i	$-0.236302\pi$
$757$	8.84926	+	6.42936i	0.321632	+	0.233679i	−0.415240	+	0.909712i	$0.636302\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−0.600364	−	0.436190i	−0.0217632	−	0.0158119i	0.576850	−	0.816850i	$-0.304282\pi$
$761$	−0.600364	−	0.436190i	−0.0217632	−	0.0158119i	−0.598614	+	0.801038i	$0.704282\pi$
$762$		0			0
$763$	−8.65665	−	26.6424i	−0.313392	−	0.964520i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−4.32228	+	13.3026i	−0.156068	+	0.480329i
$768$		0			0
$769$			14.8937i			0.537079i	0.963269	+	0.268540i	$0.0865410\pi$
$769$			14.8937i			0.537079i	−0.963269	+	0.268540i	$0.913459\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−25.6945	−	8.34865i	−0.924166	−	0.300280i	−0.191992	−	0.981397i	$-0.561495\pi$
$773$	−25.6945	−	8.34865i	−0.924166	−	0.300280i	−0.732175	+	0.681117i	$0.761495\pi$
$774$		0			0
$775$	33.5958	−	24.4088i	1.20680	−	0.876789i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	0.204571	−	0.281568i	0.00732953	−	0.0100882i
$780$		0			0
$781$	−40.1609	−	1.86697i	−1.43707	−	0.0668053i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−5.22754	+	1.69853i	−0.186579	+	0.0606231i
$786$		0			0
$787$	27.1818	+	37.4125i	0.968926	+	1.33361i	0.942588	+	0.333959i	$0.108385\pi$
$787$	27.1818	+	37.4125i	0.968926	+	1.33361i	0.0263384	+	0.999653i	$0.491615\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	32.2802			1.14775
$792$		0			0
$793$	31.1400			1.10582
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−2.81411	−	3.87329i	−0.0996810	−	0.137199i	0.756263	−	0.654268i	$-0.227023\pi$
$797$	−2.81411	−	3.87329i	−0.0996810	−	0.137199i	−0.855944	+	0.517069i	$0.827023\pi$
$798$		0			0
$799$	−9.72001	+	3.15822i	−0.343869	+	0.111730i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	17.8569	−	47.3529i	0.630156	−	1.67105i
$804$		0			0
$805$	−0.0466671	+	0.0642318i	−0.00164480	+	0.00226387i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	33.7562	−	24.5253i	1.18681	−	0.862265i	0.193883	−	0.981025i	$-0.437892\pi$
$809$	33.7562	−	24.5253i	1.18681	−	0.862265i	0.992923	+	0.118760i	$0.0378919\pi$
$810$		0			0
$811$	−28.8252	−	9.36587i	−1.01219	−	0.328880i	−0.244463	−	0.969659i	$-0.578612\pi$
$811$	−28.8252	−	9.36587i	−1.01219	−	0.328880i	−0.767726	+	0.640778i	$0.778612\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$			4.56617i			0.159946i
$816$		0			0
$817$	0.0986909	−	0.303739i	0.00345276	−	0.0106265i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−10.6440	−	32.7589i	−0.371478	−	1.14329i	−0.945824	−	0.324679i	$-0.894744\pi$
$821$	−10.6440	−	32.7589i	−0.371478	−	1.14329i	0.574346	−	0.818613i	$-0.305256\pi$
$822$		0			0
$823$	25.4636	+	18.5004i	0.887605	+	0.644883i	0.935252	−	0.353982i	$-0.115172\pi$
$823$	25.4636	+	18.5004i	0.887605	+	0.644883i	−0.0476476	+	0.998864i	$0.515172\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	39.8526	+	28.9546i	1.38581	+	1.00685i	0.996310	+	0.0858232i	$0.0273520\pi$
$827$	39.8526	+	28.9546i	1.38581	+	1.00685i	0.389500	+	0.921027i	$0.372648\pi$
$828$		0			0
$829$	9.41962	+	28.9906i	0.327157	+	1.00689i	0.970458	+	0.241272i	$0.0775645\pi$
$829$	9.41962	+	28.9906i	0.327157	+	1.00689i	−0.643301	+	0.765614i	$0.722436\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	1.37167	−	4.22158i	0.0475257	−	0.146269i
$834$		0			0
$835$			15.9092i			0.550561i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−42.2725	−	13.7352i	−1.45941	−	0.474191i	−0.531519	−	0.847046i	$-0.678379\pi$
$839$	−42.2725	−	13.7352i	−1.45941	−	0.474191i	−0.927889	+	0.372855i	$0.878379\pi$
$840$		0			0
$841$	−35.5980	+	25.8635i	−1.22752	+	0.891844i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−2.66732	+	3.67125i	−0.0917585	+	0.126295i
$846$		0			0
$847$	11.1497	+	18.7955i	0.383108	+	0.645822i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	0.260354	−	0.0845941i	0.00892482	−	0.00289985i
$852$		0			0
$853$	−0.796675	−	1.09653i	−0.0272776	−	0.0375445i	0.795160	−	0.606399i	$-0.207387\pi$
$853$	−0.796675	−	1.09653i	−0.0272776	−	0.0375445i	−0.822438	+	0.568855i	$0.807387\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	47.3025			1.61582			0.807911	−	0.589304i	$-0.200598\pi$
$857$	47.3025			1.61582			0.807911	+	0.589304i	$0.200598\pi$
$858$		0			0
$859$	37.1178			1.26644			0.633221	−	0.773971i	$-0.281732\pi$
$859$	37.1178			1.26644			0.633221	+	0.773971i	$0.281732\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−10.8948	−	14.9954i	−0.370864	−	0.510451i	0.582271	−	0.812994i	$-0.302164\pi$
$863$	−10.8948	−	14.9954i	−0.370864	−	0.510451i	−0.953135	+	0.302544i	$0.902164\pi$
$864$		0			0
$865$	21.3188	−	6.92691i	0.724863	−	0.235522i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	0.171705	+	0.626000i	0.00582471	+	0.0212356i
$870$		0			0
$871$	26.9433	−	37.0842i	0.912938	−	1.25655i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−14.7776	+	10.7366i	−0.499575	+	0.362962i
$876$		0			0
$877$	−11.0714	−	3.59732i	−0.373855	−	0.121473i	0.116062	−	0.993242i	$-0.462973\pi$
$877$	−11.0714	−	3.59732i	−0.373855	−	0.121473i	−0.489917	+	0.871769i	$0.662973\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	5.22971i		−	0.176193i	−0.996112	−	0.0880966i	$-0.971922\pi$
$881$		−	5.22971i		−	0.176193i	0.996112	−	0.0880966i	$-0.0280784\pi$
$882$		0			0
$883$	0.241668	−	0.743777i	0.00813277	−	0.0250301i	−0.946908	−	0.321505i	$-0.895811\pi$
$883$	0.241668	−	0.743777i	0.00813277	−	0.0250301i	0.955041	+	0.296475i	$0.0958112\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−9.64805	−	29.6937i	−0.323950	−	0.997015i	−0.971912	−	0.235343i	$-0.924379\pi$
$887$	−9.64805	−	29.6937i	−0.323950	−	0.997015i	0.647962	−	0.761672i	$-0.275621\pi$
$888$		0			0
$889$	19.2575	+	13.9914i	0.645875	+	0.469256i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	0.357680	+	0.259870i	0.0119693	+	0.00869621i
$894$		0			0
$895$	6.23371	+	19.1854i	0.208370	+	0.641296i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	27.8063	−	85.5791i	0.927393	−	2.85422i
$900$		0			0
$901$			8.96557i			0.298686i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−3.79408	−	1.23277i	−0.126119	−	0.0409787i
$906$		0			0
$907$	−22.0578	+	16.0260i	−0.732419	+	0.532133i	−0.890328	−	0.455320i	$-0.849525\pi$
$907$	−22.0578	+	16.0260i	−0.732419	+	0.532133i	0.157909	+	0.987454i	$0.449525\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	32.8872	−	45.2653i	1.08960	−	1.49971i	0.241109	−	0.970498i	$-0.422489\pi$
$911$	32.8872	−	45.2653i	1.08960	−	1.49971i	0.848492	−	0.529208i	$-0.177511\pi$
$912$		0			0
$913$	0.896888	−	19.2932i	0.0296826	−	0.638513i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	30.6380	−	9.95489i	1.01176	−	0.328739i
$918$		0			0
$919$	−1.02766	−	1.41445i	−0.0338993	−	0.0466584i	0.791731	−	0.610870i	$-0.209180\pi$
$919$	−1.02766	−	1.41445i	−0.0338993	−	0.0466584i	−0.825630	+	0.564212i	$0.809180\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−35.5200			−1.16915
$924$		0			0
$925$	27.7689			0.913036
$926$		0			0
$927$		0			0
$928$		0			0
$929$	3.06522	+	4.21891i	0.100566	+	0.138418i	0.856334	−	0.516422i	$-0.172736\pi$
$929$	3.06522	+	4.21891i	0.100566	+	0.138418i	−0.755768	+	0.654839i	$0.772736\pi$
$930$		0			0
$931$	−0.182621	+	0.0593372i	−0.00598517	+	0.00194470i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−4.14172	+	2.72458i	−0.135449	+	0.0891032i
$936$		0			0
$937$	2.18339	−	3.00519i	0.0713284	−	0.0981751i	−0.771862	−	0.635790i	$-0.780674\pi$
$937$	2.18339	−	3.00519i	0.0713284	−	0.0981751i	0.843191	+	0.537615i	$0.180674\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−5.44587	+	3.95666i	−0.177530	+	0.128983i	−0.673002	−	0.739641i	$-0.734995\pi$
$941$	−5.44587	+	3.95666i	−0.177530	+	0.128983i	0.495471	+	0.868624i	$0.334995\pi$
$942$		0			0
$943$	−0.204571	−	0.0664693i	−0.00666176	−	0.00216454i
$944$		0			0
$945$		0			0
$946$		0			0
$947$		−	32.2097i		−	1.04667i	−0.852126	−	0.523337i	$-0.824687\pi$
$947$		−	32.2097i		−	1.04667i	0.852126	−	0.523337i	$-0.175313\pi$
$948$		0			0
$949$	13.8166	−	42.5231i	0.448506	−	1.38036i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−2.44111	−	7.51296i	−0.0790753	−	0.243369i	0.903702	−	0.428162i	$-0.140839\pi$
$953$	−2.44111	−	7.51296i	−0.0790753	−	0.243369i	−0.982777	+	0.184793i	$0.940839\pi$
$954$		0			0
$955$	−5.91126	−	4.29478i	−0.191284	−	0.138976i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	17.1196	+	12.4382i	0.552822	+	0.401649i
$960$		0			0
$961$	24.6951	+	76.0037i	0.796616	+	2.45173i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	3.46857	−	10.6751i	0.111657	−	0.343645i
$966$		0			0
$967$		−	37.2874i		−	1.19908i	−0.800343	−	0.599542i	$-0.795350\pi$
$967$		−	37.2874i		−	1.19908i	0.800343	−	0.599542i	$-0.204650\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	20.2063	+	6.56541i	0.648450	+	0.210694i	0.614730	−	0.788737i	$-0.289265\pi$
$971$	20.2063	+	6.56541i	0.648450	+	0.210694i	0.0337193	+	0.999431i	$0.489265\pi$
$972$		0			0
$973$	11.2596	−	8.18058i	0.360966	−	0.262257i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−27.9910	+	38.5263i	−0.895511	+	1.23257i	0.0763666	+	0.997080i	$0.475668\pi$
$977$	−27.9910	+	38.5263i	−0.895511	+	1.23257i	−0.971878	+	0.235486i	$0.924332\pi$
$978$		0			0
$979$	18.2668	+	14.6144i	0.583811	+	0.467079i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−38.3809	+	12.4707i	−1.22416	+	0.397754i	−0.848595	−	0.529042i	$-0.822551\pi$
$983$	−38.3809	+	12.4707i	−1.22416	+	0.397754i	−0.375565	+	0.926796i	$0.622551\pi$
$984$		0			0
$985$	−2.57202	−	3.54008i	−0.0819513	−	0.112796i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−0.197382			−0.00627637
$990$		0			0
$991$	−33.5742			−1.06652			−0.533260	−	0.845951i	$-0.679033\pi$
$991$	−33.5742			−1.06652			−0.533260	+	0.845951i	$0.679033\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	2.46411	+	3.39156i	0.0781176	+	0.107520i
$996$		0			0
$997$	26.3247	−	8.55343i	0.833713	−	0.270890i	0.139104	−	0.990278i	$-0.455578\pi$
$997$	26.3247	−	8.55343i	0.833713	−	0.270890i	0.694608	+	0.719388i	$0.255578\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1584.2.cd.b.161.1		8
3.2	odd	2		1584.2.cd.a.161.2		8
4.3	odd	2		198.2.l.b.161.1	yes	8
11.8	odd	10		1584.2.cd.a.305.2		8
12.11	even	2		198.2.l.a.161.2	yes	8
33.8	even	10	inner	1584.2.cd.b.305.1		8
44.19	even	10		198.2.l.a.107.2	✓	8
44.27	odd	10		2178.2.b.i.2177.4		8
44.39	even	10		2178.2.b.j.2177.4		8
132.71	even	10		2178.2.b.j.2177.5		8
132.83	odd	10		2178.2.b.i.2177.5		8
132.107	odd	10		198.2.l.b.107.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
198.2.l.a.107.2	✓	8	44.19	even	10
198.2.l.a.161.2	yes	8	12.11	even	2
198.2.l.b.107.1	yes	8	132.107	odd	10
198.2.l.b.161.1	yes	8	4.3	odd	2
1584.2.cd.a.161.2		8	3.2	odd	2
1584.2.cd.a.305.2		8	11.8	odd	10
1584.2.cd.b.161.1		8	1.1	even	1	trivial
1584.2.cd.b.305.1		8	33.8	even	10	inner
2178.2.b.i.2177.4		8	44.27	odd	10
2178.2.b.i.2177.5		8	132.83	odd	10
2178.2.b.j.2177.4		8	44.39	even	10
2178.2.b.j.2177.5		8	132.71	even	10

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:	\( N \)	\(=\)	\( 1584 = 2^{4} \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1584.cd (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.604291 + 0.831735i) q^{5} +(-1.88947 + 0.613926i) q^{7} +O(q^{10})\)	\(q+(0.604291 + 0.831735i) q^{5} +(-1.88947 + 0.613926i) q^{7} +(2.07196 - 2.58978i) q^{11} +(1.72232 - 2.37058i) q^{13} +(-1.17625 + 0.854596i) q^{17} +(0.0598171 + 0.0194357i) q^{19} -0.0388715i q^{23} +(1.21847 - 3.75006i) q^{25} +(-2.64027 - 8.12592i) q^{29} +(8.52026 + 6.19033i) q^{31} +(-1.65241 - 1.20055i) q^{35} +(2.17625 + 6.69781i) q^{37} +(1.70998 - 5.26276i) q^{41} -5.07780i q^{43} +(6.68536 + 2.17220i) q^{47} +(-2.46992 + 1.79451i) q^{49} +(3.62455 - 4.98876i) q^{53} +(3.40608 + 0.158339i) q^{55} +(-4.53984 + 1.47508i) q^{59} +(6.24657 + 8.59766i) q^{61} +3.01248 q^{65} +15.6435 q^{67} +(-7.12516 - 9.80694i) q^{71} +(14.5120 - 4.71525i) q^{73} +(-2.32497 + 6.16535i) q^{77} +(-0.115040 + 0.158339i) q^{79} +(4.71124 - 3.42292i) q^{83} +(-1.42160 - 0.461904i) q^{85} +7.05342i q^{89} +(-1.79892 + 5.53652i) q^{91} +(0.0199815 + 0.0614968i) q^{95} +(-3.28214 - 2.38462i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q+O(q^{10}) \) 8 * q	\( 8 q + 4 q^{11} + 8 q^{17} + 6 q^{25} - 10 q^{29} + 14 q^{31} + 10 q^{35} + 8 q^{41} + 20 q^{47} + 6 q^{49} - 30 q^{53} - 28 q^{55} - 20 q^{59} + 20 q^{61} + 64 q^{65} + 56 q^{67} + 20 q^{71} - 10 q^{73} + 20 q^{79} - 12 q^{83} + 16 q^{95} - 12 q^{97}+O(q^{100}) \) 8 * q + 4 * q^11 + 8 * q^17 + 6 * q^25 - 10 * q^29 + 14 * q^31 + 10 * q^35 + 8 * q^41 + 20 * q^47 + 6 * q^49 - 30 * q^53 - 28 * q^55 - 20 * q^59 + 20 * q^61 + 64 * q^65 + 56 * q^67 + 20 * q^71 - 10 * q^73 + 20 * q^79 - 12 * q^83 + 16 * q^95 - 12 * q^97

Introduction

L-functions

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