LMFDB - Embedded newform 1600.2.s.d.207.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1600,2,Mod(207,1600)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1600, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 1]))

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

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

chi := DirichletCharacter("1600.207");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1600 = 2^{6} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1600.s (of order $4$, 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:	$12.7760643234$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 2 x^{16} - 4 x^{15} - 5 x^{14} - 14 x^{13} - 10 x^{12} + 6 x^{11} + 37 x^{10} + 70 x^{9} + \cdots + 512 $ x^18 + 2x^16 - 4x^15 - 5x^14 - 14x^13 - 10x^12 + 6x^11 + 37x^10 + 70x^9 + 74x^8 + 24x^7 - 80x^6 - 224x^5 - 160x^4 - 256x^3 + 256*x^2 + 512
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{15} $
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			207.7
Root			$1.41323 - 0.0526497i$ of defining polynomial
Character	$\chi$	$=$	1600.207
Dual form			1600.2.s.d.943.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.28110 q^{3} +(-1.13975 - 1.13975i) q^{7} -1.35879 q^{9} +O(q^{10})$	$q+1.28110 q^{3} +(-1.13975 - 1.13975i) q^{7} -1.35879 q^{9} +(2.32204 - 2.32204i) q^{11} +1.36502i q^{13} +(-5.25380 - 5.25380i) q^{17} +(3.69752 - 3.69752i) q^{19} +(-1.46013 - 1.46013i) q^{21} +(-0.911118 + 0.911118i) q^{23} -5.58403 q^{27} +(-2.37343 - 2.37343i) q^{29} -0.242577i q^{31} +(2.97475 - 2.97475i) q^{33} +3.34494i q^{37} +1.74872i q^{39} +2.66956i q^{41} -9.04874i q^{43} +(7.87820 - 7.87820i) q^{47} -4.40194i q^{49} +(-6.73063 - 6.73063i) q^{51} +5.80113 q^{53} +(4.73688 - 4.73688i) q^{57} +(-5.91474 - 5.91474i) q^{59} +(-6.67404 + 6.67404i) q^{61} +(1.54868 + 1.54868i) q^{63} -4.54673i q^{67} +(-1.16723 + 1.16723i) q^{69} -15.4389 q^{71} +(1.49307 + 1.49307i) q^{73} -5.29308 q^{77} +10.3024 q^{79} -3.07731 q^{81} +3.26589 q^{83} +(-3.04060 - 3.04060i) q^{87} +9.77206 q^{89} +(1.55578 - 1.55578i) q^{91} -0.310765i q^{93} +(1.63587 + 1.63587i) q^{97} +(-3.15516 + 3.15516i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 2 q^{7} + 10 q^{9}+O(q^{10}) $ 18 * q + 2 * q^7 + 10 * q^9	$ 18 q + 2 q^{7} + 10 q^{9} + 2 q^{11} + 6 q^{17} + 2 q^{19} - 16 q^{21} - 2 q^{23} - 24 q^{27} + 14 q^{29} + 8 q^{33} + 38 q^{47} - 8 q^{51} - 12 q^{53} + 24 q^{57} - 10 q^{59} + 14 q^{61} - 6 q^{63} - 32 q^{69} - 24 q^{71} + 14 q^{73} + 44 q^{77} + 16 q^{79} + 2 q^{81} + 40 q^{83} + 24 q^{87} + 12 q^{89} - 18 q^{97} - 22 q^{99}+O(q^{100}) $ 18 * q + 2 * q^7 + 10 * q^9 + 2 * q^11 + 6 * q^17 + 2 * q^19 - 16 * q^21 - 2 * q^23 - 24 * q^27 + 14 * q^29 + 8 * q^33 + 38 * q^47 - 8 * q^51 - 12 * q^53 + 24 * q^57 - 10 * q^59 + 14 * q^61 - 6 * q^63 - 32 * q^69 - 24 * q^71 + 14 * q^73 + 44 * q^77 + 16 * q^79 + 2 * q^81 + 40 * q^83 + 24 * q^87 + 12 * q^89 - 18 * q^97 - 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times$.

$n$	$577$	$901$	$1151$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{4}\right)$	$-1$

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
$3$	1.28110			0.739642			0.369821	−	0.929103i	$-0.379419\pi$
$3$	1.28110			0.739642			0.369821	+	0.929103i	$0.379419\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−1.13975	−	1.13975i	−0.430785	−	0.430785i	0.458111	−	0.888895i	$-0.348526\pi$
$7$	−1.13975	−	1.13975i	−0.430785	−	0.430785i	−0.888895	+	0.458111i	$0.848526\pi$
$8$		0			0
$9$	−1.35879			−0.452930
$10$		0			0
$11$	2.32204	−	2.32204i	0.700120	−	0.700120i	−0.264316	−	0.964436i	$-0.585146\pi$
$11$	2.32204	−	2.32204i	0.700120	−	0.700120i	0.964436	+	0.264316i	$0.0851462\pi$
$12$		0			0
$13$			1.36502i			0.378589i	0.981920	+	0.189294i	$0.0606201\pi$
$13$			1.36502i			0.378589i	−0.981920	+	0.189294i	$0.939380\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−5.25380	−	5.25380i	−1.27423	−	1.27423i	−0.943845	−	0.330389i	$-0.892820\pi$
$17$	−5.25380	−	5.25380i	−1.27423	−	1.27423i	−0.330389	−	0.943845i	$-0.607180\pi$
$18$		0			0
$19$	3.69752	−	3.69752i	0.848269	−	0.848269i	−0.141648	−	0.989917i	$-0.545240\pi$
$19$	3.69752	−	3.69752i	0.848269	−	0.848269i	0.989917	+	0.141648i	$0.0452403\pi$
$20$		0			0
$21$	−1.46013	−	1.46013i	−0.318626	−	0.318626i
$22$		0			0
$23$	−0.911118	+	0.911118i	−0.189981	+	0.189981i	−0.795688	−	0.605707i	$-0.792890\pi$
$23$	−0.911118	+	0.911118i	−0.189981	+	0.189981i	0.605707	+	0.795688i	$0.292890\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−5.58403			−1.07465
$28$		0			0
$29$	−2.37343	−	2.37343i	−0.440736	−	0.440736i	0.451524	−	0.892259i	$-0.350881\pi$
$29$	−2.37343	−	2.37343i	−0.440736	−	0.440736i	−0.892259	+	0.451524i	$0.850881\pi$
$30$		0			0
$31$		−	0.242577i		−	0.0435681i	−0.999763	−	0.0217841i	$-0.993065\pi$
$31$		−	0.242577i		−	0.0435681i	0.999763	−	0.0217841i	$-0.00693463\pi$
$32$		0			0
$33$	2.97475	−	2.97475i	0.517838	−	0.517838i
$34$		0			0
$35$		0			0
$36$		0			0
$37$			3.34494i			0.549905i	0.961458	+	0.274953i	$0.0886621\pi$
$37$			3.34494i			0.549905i	−0.961458	+	0.274953i	$0.911338\pi$
$38$		0			0
$39$			1.74872i			0.280020i
$40$		0			0
$41$			2.66956i			0.416915i	0.978031	+	0.208457i	$0.0668442\pi$
$41$			2.66956i			0.416915i	−0.978031	+	0.208457i	$0.933156\pi$
$42$		0			0
$43$		−	9.04874i		−	1.37992i	−0.723847	−	0.689960i	$-0.757628\pi$
$43$		−	9.04874i		−	1.37992i	0.723847	−	0.689960i	$-0.242372\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	7.87820	−	7.87820i	1.14915	−	1.14915i	0.162435	−	0.986719i	$-0.448065\pi$
$47$	7.87820	−	7.87820i	1.14915	−	1.14915i	0.986719	−	0.162435i	$-0.0519348\pi$
$48$		0			0
$49$		−	4.40194i		−	0.628849i
$50$		0			0
$51$	−6.73063	−	6.73063i	−0.942476	−	0.942476i
$52$		0			0
$53$	5.80113			0.796846			0.398423	−	0.917202i	$-0.369558\pi$
$53$	5.80113			0.796846			0.398423	+	0.917202i	$0.369558\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	4.73688	−	4.73688i	0.627415	−	0.627415i
$58$		0			0
$59$	−5.91474	−	5.91474i	−0.770033	−	0.770033i	0.208079	−	0.978112i	$-0.433279\pi$
$59$	−5.91474	−	5.91474i	−0.770033	−	0.770033i	−0.978112	+	0.208079i	$0.933279\pi$
$60$		0			0
$61$	−6.67404	+	6.67404i	−0.854523	+	0.854523i	−0.990686	−	0.136163i	$-0.956523\pi$
$61$	−6.67404	+	6.67404i	−0.854523	+	0.854523i	0.136163	+	0.990686i	$0.456523\pi$
$62$		0			0
$63$	1.54868	+	1.54868i	0.195116	+	0.195116i
$64$		0			0
$65$		0			0
$66$		0			0
$67$		−	4.54673i		−	0.555471i	−0.960658	−	0.277736i	$-0.910416\pi$
$67$		−	4.54673i		−	0.555471i	0.960658	−	0.277736i	$-0.0895839\pi$
$68$		0			0
$69$	−1.16723	+	1.16723i	−0.140518	+	0.140518i
$70$		0			0
$71$	−15.4389			−1.83226			−0.916128	−	0.400885i	$-0.868703\pi$
$71$	−15.4389			−1.83226			−0.916128	+	0.400885i	$0.868703\pi$
$72$		0			0
$73$	1.49307	+	1.49307i	0.174750	+	0.174750i	0.789063	−	0.614313i	$-0.210567\pi$
$73$	1.49307	+	1.49307i	0.174750	+	0.174750i	−0.614313	+	0.789063i	$0.710567\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−5.29308			−0.603202
$78$		0			0
$79$	10.3024			1.15911			0.579556	−	0.814932i	$-0.303226\pi$
$79$	10.3024			1.15911			0.579556	+	0.814932i	$0.303226\pi$
$80$		0			0
$81$	−3.07731			−0.341924
$82$		0			0
$83$	3.26589			0.358478			0.179239	−	0.983806i	$-0.442636\pi$
$83$	3.26589			0.358478			0.179239	+	0.983806i	$0.442636\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−3.04060	−	3.04060i	−0.325986	−	0.325986i
$88$		0			0
$89$	9.77206			1.03584			0.517918	−	0.855430i	$-0.326707\pi$
$89$	9.77206			1.03584			0.517918	+	0.855430i	$0.326707\pi$
$90$		0			0
$91$	1.55578	−	1.55578i	0.163090	−	0.163090i
$92$		0			0
$93$		−	0.310765i		−	0.0322248i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	1.63587	+	1.63587i	0.166097	+	0.166097i	0.785262	−	0.619164i	$-0.212528\pi$
$97$	1.63587	+	1.63587i	0.166097	+	0.166097i	−0.619164	+	0.785262i	$0.712528\pi$
$98$		0			0
$99$	−3.15516	+	3.15516i	−0.317106	+	0.317106i
$100$		0			0
$101$	−6.63953	−	6.63953i	−0.660658	−	0.660658i	0.294877	−	0.955535i	$-0.404721\pi$
$101$	−6.63953	−	6.63953i	−0.660658	−	0.660658i	−0.955535	+	0.294877i	$0.904721\pi$
$102$		0			0
$103$	1.62219	−	1.62219i	0.159839	−	0.159839i	−0.622656	−	0.782496i	$-0.713946\pi$
$103$	1.62219	−	1.62219i	0.159839	−	0.159839i	0.782496	+	0.622656i	$0.213946\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	3.65206			0.353058			0.176529	−	0.984295i	$-0.443513\pi$
$107$	3.65206			0.353058			0.176529	+	0.984295i	$0.443513\pi$
$108$		0			0
$109$	5.20757	+	5.20757i	0.498795	+	0.498795i	0.911063	−	0.412268i	$-0.135263\pi$
$109$	5.20757	+	5.20757i	0.498795	+	0.498795i	−0.412268	+	0.911063i	$0.635263\pi$
$110$		0			0
$111$			4.28519i			0.406733i
$112$		0			0
$113$	4.27905	−	4.27905i	0.402539	−	0.402539i	−0.476588	−	0.879127i	$-0.658127\pi$
$113$	4.27905	−	4.27905i	0.402539	−	0.402539i	0.879127	+	0.476588i	$0.158127\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$		−	1.85478i		−	0.171474i
$118$		0			0
$119$			11.9760i			1.09784i
$120$		0			0
$121$			0.216302i			0.0196639i
$122$		0			0
$123$			3.41996i			0.308367i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−7.29257	+	7.29257i	−0.647111	+	0.647111i	−0.952294	−	0.305183i	$-0.901282\pi$
$127$	−7.29257	+	7.29257i	−0.647111	+	0.647111i	0.305183	+	0.952294i	$0.401282\pi$
$128$		0			0
$129$		−	11.5923i		−	1.02065i
$130$		0			0
$131$	11.9793	+	11.9793i	1.04664	+	1.04664i	0.998858	+	0.0477778i	$0.0152139\pi$
$131$	11.9793	+	11.9793i	1.04664	+	1.04664i	0.0477778	+	0.998858i	$0.484786\pi$
$132$		0			0
$133$	−8.42848			−0.730842
$134$		0			0
$135$		0			0
$136$		0			0
$137$	4.92762	−	4.92762i	0.420995	−	0.420995i	−0.464551	−	0.885546i	$-0.653784\pi$
$137$	4.92762	−	4.92762i	0.420995	−	0.420995i	0.885546	+	0.464551i	$0.153784\pi$
$138$		0			0
$139$	−10.3015	−	10.3015i	−0.873761	−	0.873761i	0.119119	−	0.992880i	$-0.461993\pi$
$139$	−10.3015	−	10.3015i	−0.873761	−	0.873761i	−0.992880	+	0.119119i	$0.961993\pi$
$140$		0			0
$141$	10.0927	−	10.0927i	0.849962	−	0.849962i
$142$		0			0
$143$	3.16963	+	3.16963i	0.265058	+	0.265058i
$144$		0			0
$145$		0			0
$146$		0			0
$147$		−	5.63931i		−	0.465123i
$148$		0			0
$149$	−15.2040	+	15.2040i	−1.24556	+	1.24556i	−0.287896	+	0.957662i	$0.592956\pi$
$149$	−15.2040	+	15.2040i	−1.24556	+	1.24556i	−0.957662	+	0.287896i	$0.907044\pi$
$150$		0			0
$151$	10.7055			0.871204			0.435602	−	0.900139i	$-0.356536\pi$
$151$	10.7055			0.871204			0.435602	+	0.900139i	$0.356536\pi$
$152$		0			0
$153$	7.13882	+	7.13882i	0.577139	+	0.577139i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−2.34588			−0.187222			−0.0936108	−	0.995609i	$-0.529841\pi$
$157$	−2.34588			−0.187222			−0.0936108	+	0.995609i	$0.529841\pi$
$158$		0			0
$159$	7.43180			0.589380
$160$		0			0
$161$	2.07689			0.163682
$162$		0			0
$163$	−2.73625			−0.214319			−0.107160	−	0.994242i	$-0.534176\pi$
$163$	−2.73625			−0.214319			−0.107160	+	0.994242i	$0.534176\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	10.1328	+	10.1328i	0.784097	+	0.784097i	0.980519	−	0.196423i	$-0.0629325\pi$
$167$	10.1328	+	10.1328i	0.784097	+	0.784097i	−0.196423	+	0.980519i	$0.562932\pi$
$168$		0			0
$169$	11.1367			0.856670
$170$		0			0
$171$	−5.02415	+	5.02415i	−0.384207	+	0.384207i
$172$		0			0
$173$		−	8.79590i		−	0.668740i	−0.942442	−	0.334370i	$-0.891477\pi$
$173$		−	8.79590i		−	0.668740i	0.942442	−	0.334370i	$-0.108523\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−7.57735	−	7.57735i	−0.569549	−	0.569549i
$178$		0			0
$179$	−6.62071	+	6.62071i	−0.494855	+	0.494855i	−0.909832	−	0.414977i	$-0.863790\pi$
$179$	−6.62071	+	6.62071i	−0.494855	+	0.494855i	0.414977	+	0.909832i	$0.363790\pi$
$180$		0			0
$181$	−5.84339	−	5.84339i	−0.434336	−	0.434336i	0.455765	−	0.890100i	$-0.349366\pi$
$181$	−5.84339	−	5.84339i	−0.434336	−	0.434336i	−0.890100	+	0.455765i	$0.849366\pi$
$182$		0			0
$183$	−8.55009	+	8.55009i	−0.632041	+	0.632041i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−24.3990			−1.78423
$188$		0			0
$189$	6.36440	+	6.36440i	0.462942	+	0.462942i
$190$		0			0
$191$		−	1.83906i		−	0.133070i	−0.997784	−	0.0665349i	$-0.978806\pi$
$191$		−	1.83906i		−	0.133070i	0.997784	−	0.0665349i	$-0.0211944\pi$
$192$		0			0
$193$	−6.18343	+	6.18343i	−0.445093	+	0.445093i	−0.893719	−	0.448626i	$-0.851913\pi$
$193$	−6.18343	+	6.18343i	−0.445093	+	0.445093i	0.448626	+	0.893719i	$0.351913\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	5.55669i		−	0.395898i	−0.980212	−	0.197949i	$-0.936572\pi$
$197$		−	5.55669i		−	0.395898i	0.980212	−	0.197949i	$-0.0634280\pi$
$198$		0			0
$199$		−	6.96413i		−	0.493674i	−0.969057	−	0.246837i	$-0.920609\pi$
$199$		−	6.96413i		−	0.493674i	0.969057	−	0.246837i	$-0.0793912\pi$
$200$		0			0
$201$		−	5.82480i		−	0.410850i
$202$		0			0
$203$			5.41024i			0.379724i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	1.23802	−	1.23802i	0.0860483	−	0.0860483i
$208$		0			0
$209$		−	17.1715i		−	1.18778i
$210$		0			0
$211$	−5.43389	−	5.43389i	−0.374084	−	0.374084i	0.494878	−	0.868962i	$-0.335213\pi$
$211$	−5.43389	−	5.43389i	−0.374084	−	0.374084i	−0.868962	+	0.494878i	$0.835213\pi$
$212$		0			0
$213$	−19.7787			−1.35521
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−0.276477	+	0.276477i	−0.0187685	+	0.0187685i
$218$		0			0
$219$	1.91276	+	1.91276i	0.129253	+	0.129253i
$220$		0			0
$221$	7.17155	−	7.17155i	0.482411	−	0.482411i
$222$		0			0
$223$	8.61776	+	8.61776i	0.577088	+	0.577088i	0.934100	−	0.357012i	$-0.116204\pi$
$223$	8.61776	+	8.61776i	0.577088	+	0.577088i	−0.357012	+	0.934100i	$0.616204\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$			6.01977i			0.399546i	0.979842	+	0.199773i	$0.0640205\pi$
$227$			6.01977i			0.399546i	−0.979842	+	0.199773i	$0.935980\pi$
$228$		0			0
$229$	−0.568504	+	0.568504i	−0.0375678	+	0.0375678i	−0.725641	−	0.688073i	$-0.758457\pi$
$229$	−0.568504	+	0.568504i	−0.0375678	+	0.0375678i	0.688073	+	0.725641i	$0.258457\pi$
$230$		0			0
$231$	−6.78094			−0.446153
$232$		0			0
$233$	−12.6979	−	12.6979i	−0.831869	−	0.831869i	0.155904	−	0.987772i	$-0.450171\pi$
$233$	−12.6979	−	12.6979i	−0.831869	−	0.831869i	−0.987772	+	0.155904i	$0.950171\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	13.1984			0.857327
$238$		0			0
$239$	−1.78306			−0.115336			−0.0576682	−	0.998336i	$-0.518367\pi$
$239$	−1.78306			−0.115336			−0.0576682	+	0.998336i	$0.518367\pi$
$240$		0			0
$241$	10.4440			0.672754			0.336377	−	0.941727i	$-0.390798\pi$
$241$	10.4440			0.672754			0.336377	+	0.941727i	$0.390798\pi$
$242$		0			0
$243$	12.8098			0.821747
$244$		0			0
$245$		0			0
$246$		0			0
$247$	5.04719	+	5.04719i	0.321145	+	0.321145i
$248$		0			0
$249$	4.18392			0.265145
$250$		0			0
$251$	12.6497	−	12.6497i	0.798445	−	0.798445i	−0.184406	−	0.982850i	$-0.559036\pi$
$251$	12.6497	−	12.6497i	0.798445	−	0.798445i	0.982850	+	0.184406i	$0.0590360\pi$
$252$		0			0
$253$			4.23130i			0.266019i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	4.13062	+	4.13062i	0.257661	+	0.257661i	0.824102	−	0.566441i	$-0.191680\pi$
$257$	4.13062	+	4.13062i	0.257661	+	0.257661i	−0.566441	+	0.824102i	$0.691680\pi$
$258$		0			0
$259$	3.81240	−	3.81240i	0.236891	−	0.236891i
$260$		0			0
$261$	3.22500	+	3.22500i	0.199623	+	0.199623i
$262$		0			0
$263$	17.1303	−	17.1303i	1.05630	−	1.05630i	0.0579798	−	0.998318i	$-0.481534\pi$
$263$	17.1303	−	17.1303i	1.05630	−	1.05630i	0.998318	−	0.0579798i	$-0.0184659\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	12.5190			0.766147
$268$		0			0
$269$	−19.8075	−	19.8075i	−1.20768	−	1.20768i	−0.971775	−	0.235910i	$-0.924193\pi$
$269$	−19.8075	−	19.8075i	−1.20768	−	1.20768i	−0.235910	−	0.971775i	$-0.575807\pi$
$270$		0			0
$271$			27.9542i			1.69810i	0.528316	+	0.849048i	$0.322824\pi$
$271$			27.9542i			1.69810i	−0.528316	+	0.849048i	$0.677176\pi$
$272$		0			0
$273$	1.99311	−	1.99311i	0.120628	−	0.120628i
$274$		0			0
$275$		0			0
$276$		0			0
$277$			26.0257i			1.56373i	0.623447	+	0.781866i	$0.285732\pi$
$277$			26.0257i			1.56373i	−0.623447	+	0.781866i	$0.714268\pi$
$278$		0			0
$279$			0.329612i			0.0197333i
$280$		0			0
$281$			24.1001i			1.43769i	0.695170	+	0.718846i	$0.255329\pi$
$281$			24.1001i			1.43769i	−0.695170	+	0.718846i	$0.744671\pi$
$282$		0			0
$283$		−	4.73708i		−	0.281590i	−0.990039	−	0.140795i	$-0.955034\pi$
$283$		−	4.73708i		−	0.281590i	0.990039	−	0.140795i	$-0.0449658\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	3.04262	−	3.04262i	0.179600	−	0.179600i
$288$		0			0
$289$			38.2049i			2.24734i
$290$		0			0
$291$	2.09571	+	2.09571i	0.122852	+	0.122852i
$292$		0			0
$293$	3.11001			0.181689			0.0908445	−	0.995865i	$-0.471043\pi$
$293$	3.11001			0.181689			0.0908445	+	0.995865i	$0.471043\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−12.9663	+	12.9663i	−0.752382	+	0.752382i
$298$		0			0
$299$	−1.24370	−	1.24370i	−0.0719248	−	0.0719248i
$300$		0			0
$301$	−10.3133	+	10.3133i	−0.594449	+	0.594449i
$302$		0			0
$303$	−8.50588	−	8.50588i	−0.488650	−	0.488650i
$304$		0			0
$305$		0			0
$306$		0			0
$307$			14.5670i			0.831382i	0.909506	+	0.415691i	$0.136460\pi$
$307$			14.5670i			0.831382i	−0.909506	+	0.415691i	$0.863540\pi$
$308$		0			0
$309$	2.07819	−	2.07819i	0.118224	−	0.118224i
$310$		0			0
$311$	14.4572			0.819791			0.409896	−	0.912132i	$-0.365565\pi$
$311$	14.4572			0.819791			0.409896	+	0.912132i	$0.365565\pi$
$312$		0			0
$313$	10.1273	+	10.1273i	0.572429	+	0.572429i	0.932807	−	0.360377i	$-0.117352\pi$
$313$	10.1273	+	10.1273i	0.572429	+	0.572429i	−0.360377	+	0.932807i	$0.617352\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	13.8750			0.779295			0.389648	−	0.920964i	$-0.372597\pi$
$317$	13.8750			0.779295			0.389648	+	0.920964i	$0.372597\pi$
$318$		0			0
$319$	−11.0224			−0.617136
$320$		0			0
$321$	4.67864			0.261136
$322$		0			0
$323$	−38.8520			−2.16179
$324$		0			0
$325$		0			0
$326$		0			0
$327$	6.67140	+	6.67140i	0.368930	+	0.368930i
$328$		0			0
$329$	−17.9584			−0.990076
$330$		0			0
$331$	−1.69458	+	1.69458i	−0.0931425	+	0.0931425i	−0.752143	−	0.659000i	$-0.770980\pi$
$331$	−1.69458	+	1.69458i	−0.0931425	+	0.0931425i	0.659000	+	0.752143i	$0.270980\pi$
$332$		0			0
$333$		−	4.54508i		−	0.249069i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	9.53338	+	9.53338i	0.519316	+	0.519316i	0.917364	−	0.398048i	$-0.130312\pi$
$337$	9.53338	+	9.53338i	0.519316	+	0.519316i	−0.398048	+	0.917364i	$0.630312\pi$
$338$		0			0
$339$	5.48188	−	5.48188i	0.297735	−	0.297735i
$340$		0			0
$341$	−0.563273	−	0.563273i	−0.0305029	−	0.0305029i
$342$		0			0
$343$	−12.9954	+	12.9954i	−0.701683	+	0.701683i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−6.67273			−0.358211			−0.179105	−	0.983830i	$-0.557320\pi$
$347$	−6.67273			−0.358211			−0.179105	+	0.983830i	$0.557320\pi$
$348$		0			0
$349$	2.02618	+	2.02618i	0.108459	+	0.108459i	0.759254	−	0.650795i	$-0.225564\pi$
$349$	2.02618	+	2.02618i	0.108459	+	0.108459i	−0.650795	+	0.759254i	$0.725564\pi$
$350$		0			0
$351$		−	7.62233i		−	0.406850i
$352$		0			0
$353$	5.36542	−	5.36542i	0.285572	−	0.285572i	−0.549754	−	0.835327i	$-0.685279\pi$
$353$	5.36542	−	5.36542i	0.285572	−	0.285572i	0.835327	+	0.549754i	$0.185279\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$			15.3425i			0.812009i
$358$		0			0
$359$			7.76117i			0.409619i	0.978802	+	0.204809i	$0.0656574\pi$
$359$			7.76117i			0.409619i	−0.978802	+	0.204809i	$0.934343\pi$
$360$		0			0
$361$		−	8.34326i		−	0.439119i
$362$		0			0
$363$			0.277104i			0.0145442i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	18.0536	−	18.0536i	0.942389	−	0.942389i	−0.0560392	−	0.998429i	$-0.517847\pi$
$367$	18.0536	−	18.0536i	0.942389	−	0.942389i	0.998429	+	0.0560392i	$0.0178472\pi$
$368$		0			0
$369$		−	3.62737i		−	0.188833i
$370$		0			0
$371$	−6.61183	−	6.61183i	−0.343269	−	0.343269i
$372$		0			0
$373$	4.36197			0.225854			0.112927	−	0.993603i	$-0.463977\pi$
$373$	4.36197			0.225854			0.112927	+	0.993603i	$0.463977\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	3.23979	−	3.23979i	0.166858	−	0.166858i
$378$		0			0
$379$	5.93072	+	5.93072i	0.304641	+	0.304641i	0.842826	−	0.538186i	$-0.180890\pi$
$379$	5.93072	+	5.93072i	0.304641	+	0.304641i	−0.538186	+	0.842826i	$0.680890\pi$
$380$		0			0
$381$	−9.34249	+	9.34249i	−0.478630	+	0.478630i
$382$		0			0
$383$	−19.3340	−	19.3340i	−0.987922	−	0.987922i	0.0120057	−	0.999928i	$-0.496178\pi$
$383$	−19.3340	−	19.3340i	−0.987922	−	0.987922i	−0.999928	+	0.0120057i	$0.996178\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$			12.2954i			0.625008i
$388$		0			0
$389$	6.28607	−	6.28607i	0.318716	−	0.318716i	−0.529558	−	0.848274i	$-0.677642\pi$
$389$	6.28607	−	6.28607i	0.318716	−	0.318716i	0.848274	+	0.529558i	$0.177642\pi$
$390$		0			0
$391$	9.57367			0.484161
$392$		0			0
$393$	15.3466	+	15.3466i	0.774135	+	0.774135i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−6.58413			−0.330448			−0.165224	−	0.986256i	$-0.552835\pi$
$397$	−6.58413			−0.330448			−0.165224	+	0.986256i	$0.552835\pi$
$398$		0			0
$399$	−10.7977			−0.540561
$400$		0			0
$401$	19.7951			0.988522			0.494261	−	0.869313i	$-0.335439\pi$
$401$	19.7951			0.988522			0.494261	+	0.869313i	$0.335439\pi$
$402$		0			0
$403$	0.331123			0.0164944
$404$		0			0
$405$		0			0
$406$		0			0
$407$	7.76707	+	7.76707i	0.385000	+	0.385000i
$408$		0			0
$409$	5.76937			0.285277			0.142638	−	0.989775i	$-0.454441\pi$
$409$	5.76937			0.285277			0.142638	+	0.989775i	$0.454441\pi$
$410$		0			0
$411$	6.31276	−	6.31276i	0.311385	−	0.311385i
$412$		0			0
$413$			13.4826i			0.663437i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−13.1972	−	13.1972i	−0.646270	−	0.646270i
$418$		0			0
$419$	−8.68932	+	8.68932i	−0.424501	+	0.424501i	−0.886750	−	0.462249i	$-0.847043\pi$
$419$	−8.68932	+	8.68932i	−0.424501	+	0.424501i	0.462249	+	0.886750i	$0.347043\pi$
$420$		0			0
$421$	20.1193	+	20.1193i	0.980555	+	0.980555i	0.999815	−	0.0192594i	$-0.00613083\pi$
$421$	20.1193	+	20.1193i	0.980555	+	0.980555i	−0.0192594	+	0.999815i	$0.506131\pi$
$422$		0			0
$423$	−10.7048	+	10.7048i	−0.520487	+	0.520487i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	15.2135			0.736231
$428$		0			0
$429$	4.06060	+	4.06060i	0.196048	+	0.196048i
$430$		0			0
$431$		−	33.6247i		−	1.61965i	−0.586675	−	0.809823i	$-0.699563\pi$
$431$		−	33.6247i		−	1.61965i	0.586675	−	0.809823i	$-0.300437\pi$
$432$		0			0
$433$	−7.46558	+	7.46558i	−0.358773	+	0.358773i	−0.863361	−	0.504588i	$-0.831645\pi$
$433$	−7.46558	+	7.46558i	−0.358773	+	0.358773i	0.504588	+	0.863361i	$0.331645\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$			6.73775i			0.322310i
$438$		0			0
$439$			7.91929i			0.377967i	0.981980	+	0.188984i	$0.0605193\pi$
$439$			7.91929i			0.377967i	−0.981980	+	0.188984i	$0.939481\pi$
$440$		0			0
$441$			5.98132i			0.284825i
$442$		0			0
$443$		−	10.6463i		−	0.505823i	−0.967489	−	0.252911i	$-0.918612\pi$
$443$		−	10.6463i		−	0.505823i	0.967489	−	0.252911i	$-0.0813881\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−19.4778	+	19.4778i	−0.921266	+	0.921266i
$448$		0			0
$449$		−	6.08115i		−	0.286987i	−0.989651	−	0.143494i	$-0.954166\pi$
$449$		−	6.08115i		−	0.286987i	0.989651	−	0.143494i	$-0.0458336\pi$
$450$		0			0
$451$	6.19880	+	6.19880i	0.291890	+	0.291890i
$452$		0			0
$453$	13.7148			0.644379
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−0.313815	+	0.313815i	−0.0146796	+	0.0146796i	−0.714409	−	0.699729i	$-0.753304\pi$
$457$	−0.313815	+	0.313815i	−0.0146796	+	0.0146796i	0.699729	+	0.714409i	$0.253304\pi$
$458$		0			0
$459$	29.3374	+	29.3374i	1.36935	+	1.36935i
$460$		0			0
$461$	9.90949	−	9.90949i	0.461531	−	0.461531i	−0.437626	−	0.899157i	$-0.644181\pi$
$461$	9.90949	−	9.90949i	0.461531	−	0.461531i	0.899157	+	0.437626i	$0.144181\pi$
$462$		0			0
$463$	17.3430	+	17.3430i	0.805999	+	0.805999i	0.984026	−	0.178027i	$-0.0569714\pi$
$463$	17.3430	+	17.3430i	0.805999	+	0.805999i	−0.178027	+	0.984026i	$0.556971\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			1.52267i			0.0704606i	0.999379	+	0.0352303i	$0.0112165\pi$
$467$			1.52267i			0.0704606i	−0.999379	+	0.0352303i	$0.988784\pi$
$468$		0			0
$469$	−5.18213	+	5.18213i	−0.239289	+	0.239289i
$470$		0			0
$471$	−3.00530			−0.138477
$472$		0			0
$473$	−21.0115	−	21.0115i	−0.966110	−	0.966110i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−7.88252			−0.360916
$478$		0			0
$479$	−0.507657			−0.0231955			−0.0115977	−	0.999933i	$-0.503692\pi$
$479$	−0.507657			−0.0231955			−0.0115977	+	0.999933i	$0.503692\pi$
$480$		0			0
$481$	−4.56592			−0.208188
$482$		0			0
$483$	2.66070			0.121066
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−25.9809	−	25.9809i	−1.17730	−	1.17730i	−0.980428	−	0.196876i	$-0.936920\pi$
$487$	−25.9809	−	25.9809i	−1.17730	−	1.17730i	−0.196876	−	0.980428i	$-0.563080\pi$
$488$		0			0
$489$	−3.50539			−0.158519
$490$		0			0
$491$	3.28208	−	3.28208i	0.148118	−	0.148118i	−0.629159	−	0.777277i	$-0.716600\pi$
$491$	3.28208	−	3.28208i	0.148118	−	0.148118i	0.777277	+	0.629159i	$0.216600\pi$
$492$		0			0
$493$			24.9391i			1.12320i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	17.5964	+	17.5964i	0.789308	+	0.789308i
$498$		0			0
$499$	6.73907	−	6.73907i	0.301682	−	0.301682i	−0.539990	−	0.841672i	$-0.681572\pi$
$499$	6.73907	−	6.73907i	0.301682	−	0.301682i	0.841672	+	0.539990i	$0.181572\pi$
$500$		0			0
$501$	12.9810	+	12.9810i	0.579950	+	0.579950i
$502$		0			0
$503$	−6.12090	+	6.12090i	−0.272918	+	0.272918i	−0.830274	−	0.557356i	$-0.811816\pi$
$503$	−6.12090	+	6.12090i	−0.272918	+	0.272918i	0.557356	+	0.830274i	$0.311816\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	14.2672			0.633629
$508$		0			0
$509$	13.8727	+	13.8727i	0.614894	+	0.614894i	0.944217	−	0.329323i	$-0.106820\pi$
$509$	13.8727	+	13.8727i	0.614894	+	0.614894i	−0.329323	+	0.944217i	$0.606820\pi$
$510$		0			0
$511$		−	3.40344i		−	0.150559i
$512$		0			0
$513$	−20.6471	+	20.6471i	−0.911590	+	0.911590i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		−	36.5869i		−	1.60909i
$518$		0			0
$519$		−	11.2684i		−	0.494628i
$520$		0			0
$521$		−	5.87686i		−	0.257470i	−0.991679	−	0.128735i	$-0.958908\pi$
$521$		−	5.87686i		−	0.257470i	0.991679	−	0.128735i	$-0.0410917\pi$
$522$		0			0
$523$			26.0176i			1.13767i	0.822452	+	0.568834i	$0.192605\pi$
$523$			26.0176i			1.13767i	−0.822452	+	0.568834i	$0.807395\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.27445	+	1.27445i	−0.0555160	+	0.0555160i
$528$		0			0
$529$			21.3397i			0.927814i
$530$		0			0
$531$	8.03690	+	8.03690i	0.348772	+	0.348772i
$532$		0			0
$533$	−3.64400			−0.157839
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−8.48177	+	8.48177i	−0.366016	+	0.366016i
$538$		0			0
$539$	−10.2215	−	10.2215i	−0.440270	−	0.440270i
$540$		0			0
$541$	−6.57691	+	6.57691i	−0.282764	+	0.282764i	−0.834210	−	0.551447i	$-0.814076\pi$
$541$	−6.57691	+	6.57691i	−0.282764	+	0.282764i	0.551447	+	0.834210i	$0.314076\pi$
$542$		0			0
$543$	−7.48594	−	7.48594i	−0.321253	−	0.321253i
$544$		0			0
$545$		0			0
$546$		0			0
$547$		−	10.6170i		−	0.453951i	−0.973900	−	0.226976i	$-0.927116\pi$
$547$		−	10.6170i		−	0.453951i	0.973900	−	0.226976i	$-0.0728838\pi$
$548$		0			0
$549$	9.06863	−	9.06863i	0.387040	−	0.387040i
$550$		0			0
$551$	−17.5516			−0.747724
$552$		0			0
$553$	−11.7422	−	11.7422i	−0.499328	−	0.499328i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−20.9610			−0.888146			−0.444073	−	0.895991i	$-0.646467\pi$
$557$	−20.9610			−0.888146			−0.444073	+	0.895991i	$0.646467\pi$
$558$		0			0
$559$	12.3517			0.522422
$560$		0			0
$561$	−31.2575			−1.31969
$562$		0			0
$563$	16.5598			0.697911			0.348955	−	0.937139i	$-0.386536\pi$
$563$	16.5598			0.697911			0.348955	+	0.937139i	$0.386536\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	3.50736	+	3.50736i	0.147295	+	0.147295i
$568$		0			0
$569$	−39.6751			−1.66327			−0.831634	−	0.555325i	$-0.812594\pi$
$569$	−39.6751			−1.66327			−0.831634	+	0.555325i	$0.812594\pi$
$570$		0			0
$571$	−24.0292	+	24.0292i	−1.00559	+	1.00559i	−0.00560819	+	0.999984i	$0.501785\pi$
$571$	−24.0292	+	24.0292i	−1.00559	+	1.00559i	−0.999984	+	0.00560819i	$0.998215\pi$
$572$		0			0
$573$		−	2.35602i		−	0.0984240i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	28.7705	+	28.7705i	1.19773	+	1.19773i	0.974844	+	0.222888i	$0.0715485\pi$
$577$	28.7705	+	28.7705i	1.19773	+	1.19773i	0.222888	+	0.974844i	$0.428451\pi$
$578$		0			0
$579$	−7.92157	+	7.92157i	−0.329209	+	0.329209i
$580$		0			0
$581$	−3.72230	−	3.72230i	−0.154427	−	0.154427i
$582$		0			0
$583$	13.4704	−	13.4704i	0.557888	−	0.557888i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	33.4854			1.38209			0.691046	−	0.722811i	$-0.257150\pi$
$587$	33.4854			1.38209			0.691046	+	0.722811i	$0.257150\pi$
$588$		0			0
$589$	−0.896933	−	0.896933i	−0.0369575	−	0.0369575i
$590$		0			0
$591$		−	7.11866i		−	0.292822i
$592$		0			0
$593$	−11.5298	+	11.5298i	−0.473472	+	0.473472i	−0.903036	−	0.429564i	$-0.858667\pi$
$593$	−11.5298	+	11.5298i	−0.473472	+	0.473472i	0.429564	+	0.903036i	$0.358667\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		−	8.92172i		−	0.365142i
$598$		0			0
$599$		−	20.0148i		−	0.817781i	−0.912583	−	0.408891i	$-0.865916\pi$
$599$		−	20.0148i		−	0.817781i	0.912583	−	0.408891i	$-0.134084\pi$
$600$		0			0
$601$		−	27.5924i		−	1.12552i	−0.826621	−	0.562759i	$-0.809740\pi$
$601$		−	27.5924i		−	1.12552i	0.826621	−	0.562759i	$-0.190260\pi$
$602$		0			0
$603$			6.17806i			0.251590i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−30.4850	+	30.4850i	−1.23735	+	1.23735i	−0.276265	+	0.961081i	$0.589097\pi$
$607$	−30.4850	+	30.4850i	−1.23735	+	1.23735i	−0.961081	+	0.276265i	$0.910903\pi$
$608$		0			0
$609$			6.93104i			0.280860i
$610$		0			0
$611$	10.7539	+	10.7539i	0.435057	+	0.435057i
$612$		0			0
$613$	20.2657			0.818523			0.409261	−	0.912417i	$-0.365786\pi$
$613$	20.2657			0.818523			0.409261	+	0.912417i	$0.365786\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−1.61302	+	1.61302i	−0.0649378	+	0.0649378i	−0.738830	−	0.673892i	$-0.764621\pi$
$617$	−1.61302	+	1.61302i	−0.0649378	+	0.0649378i	0.673892	+	0.738830i	$0.264621\pi$
$618$		0			0
$619$	2.46756	+	2.46756i	0.0991797	+	0.0991797i	0.754956	−	0.655776i	$-0.227658\pi$
$619$	2.46756	+	2.46756i	0.0991797	+	0.0991797i	−0.655776	+	0.754956i	$0.727658\pi$
$620$		0			0
$621$	5.08771	−	5.08771i	0.204163	−	0.204163i
$622$		0			0
$623$	−11.1377	−	11.1377i	−0.446222	−	0.446222i
$624$		0			0
$625$		0			0
$626$		0			0
$627$		−	21.9984i		−	0.878531i
$628$		0			0
$629$	17.5737	−	17.5737i	0.700708	−	0.700708i
$630$		0			0
$631$	29.9602			1.19270			0.596348	−	0.802726i	$-0.296618\pi$
$631$	29.9602			1.19270			0.596348	+	0.802726i	$0.296618\pi$
$632$		0			0
$633$	−6.96133	−	6.96133i	−0.276688	−	0.276688i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	6.00875			0.238075
$638$		0			0
$639$	20.9782			0.829885
$640$		0			0
$641$	−37.3386			−1.47478			−0.737392	−	0.675465i	$-0.763943\pi$
$641$	−37.3386			−1.47478			−0.737392	+	0.675465i	$0.763943\pi$
$642$		0			0
$643$	24.5635			0.968691			0.484345	−	0.874877i	$-0.339058\pi$
$643$	24.5635			0.968691			0.484345	+	0.874877i	$0.339058\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−23.1347	−	23.1347i	−0.909519	−	0.909519i	0.0867142	−	0.996233i	$-0.472363\pi$
$647$	−23.1347	−	23.1347i	−0.909519	−	0.909519i	−0.996233	+	0.0867142i	$0.972363\pi$
$648$		0			0
$649$	−27.4685			−1.07823
$650$		0			0
$651$	−0.354194	+	0.354194i	−0.0138820	+	0.0138820i
$652$		0			0
$653$		−	50.8060i		−	1.98819i	−0.108496	−	0.994097i	$-0.534603\pi$
$653$		−	50.8060i		−	1.98819i	0.108496	−	0.994097i	$-0.465397\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−2.02877	−	2.02877i	−0.0791497	−	0.0791497i
$658$		0			0
$659$	9.97780	−	9.97780i	0.388680	−	0.388680i	−0.485537	−	0.874216i	$-0.661376\pi$
$659$	9.97780	−	9.97780i	0.388680	−	0.388680i	0.874216	+	0.485537i	$0.161376\pi$
$660$		0			0
$661$	−5.09643	−	5.09643i	−0.198228	−	0.198228i	0.601012	−	0.799240i	$-0.294764\pi$
$661$	−5.09643	−	5.09643i	−0.198228	−	0.198228i	−0.799240	+	0.601012i	$0.794764\pi$
$662$		0			0
$663$	9.18745	−	9.18745i	0.356811	−	0.356811i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	4.32496			0.167463
$668$		0			0
$669$	11.0402	+	11.0402i	0.426838	+	0.426838i
$670$		0			0
$671$			30.9947i			1.19654i
$672$		0			0
$673$	31.6322	−	31.6322i	1.21933	−	1.21933i	0.251464	−	0.967867i	$-0.419088\pi$
$673$	31.6322	−	31.6322i	1.21933	−	1.21933i	0.967867	−	0.251464i	$-0.0809121\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$		−	25.6600i		−	0.986196i	−0.869974	−	0.493098i	$-0.835864\pi$
$677$		−	25.6600i		−	0.986196i	0.869974	−	0.493098i	$-0.164136\pi$
$678$		0			0
$679$		−	3.72896i		−	0.143104i
$680$		0			0
$681$			7.71190i			0.295521i
$682$		0			0
$683$		−	12.3536i		−	0.472698i	−0.971668	−	0.236349i	$-0.924049\pi$
$683$		−	12.3536i		−	0.472698i	0.971668	−	0.236349i	$-0.0759509\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−0.728309	+	0.728309i	−0.0277867	+	0.0277867i
$688$		0			0
$689$			7.91866i			0.301677i
$690$		0			0
$691$	−22.5426	−	22.5426i	−0.857561	−	0.857561i	0.133489	−	0.991050i	$-0.457382\pi$
$691$	−22.5426	−	22.5426i	−0.857561	−	0.857561i	−0.991050	+	0.133489i	$0.957382\pi$
$692$		0			0
$693$	7.19219			0.273209
$694$		0			0
$695$		0			0
$696$		0			0
$697$	14.0253	−	14.0253i	0.531247	−	0.531247i
$698$		0			0
$699$	−16.2673	−	16.2673i	−0.615285	−	0.615285i
$700$		0			0
$701$	26.9530	−	26.9530i	1.01800	−	1.01800i	0.0181663	−	0.999835i	$-0.494217\pi$
$701$	26.9530	−	26.9530i	1.01800	−	1.01800i	0.999835	−	0.0181663i	$-0.00578284\pi$
$702$		0			0
$703$	12.3680	+	12.3680i	0.466467	+	0.466467i
$704$		0			0
$705$		0			0
$706$		0			0
$707$			15.1348i			0.569203i
$708$		0			0
$709$	7.78615	−	7.78615i	0.292415	−	0.292415i	−0.545619	−	0.838034i	$-0.683705\pi$
$709$	7.78615	−	7.78615i	0.292415	−	0.292415i	0.838034	+	0.545619i	$0.183705\pi$
$710$		0			0
$711$	−13.9988			−0.524997
$712$		0			0
$713$	0.221016	+	0.221016i	0.00827713	+	0.00827713i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−2.28427			−0.0853076
$718$		0			0
$719$	−20.6777			−0.771150			−0.385575	−	0.922677i	$-0.625997\pi$
$719$	−20.6777			−0.771150			−0.385575	+	0.922677i	$0.625997\pi$
$720$		0			0
$721$	−3.69779			−0.137713
$722$		0			0
$723$	13.3797			0.497597
$724$		0			0
$725$		0			0
$726$		0			0
$727$	20.4994	+	20.4994i	0.760280	+	0.760280i	0.976373	−	0.216093i	$-0.0693315\pi$
$727$	20.4994	+	20.4994i	0.760280	+	0.760280i	−0.216093	+	0.976373i	$0.569331\pi$
$728$		0			0
$729$	25.6425			0.949722
$730$		0			0
$731$	−47.5403	+	47.5403i	−1.75834	+	1.75834i
$732$		0			0
$733$			10.7306i			0.396344i	0.980167	+	0.198172i	$0.0635005\pi$
$733$			10.7306i			0.396344i	−0.980167	+	0.198172i	$0.936500\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−10.5577	−	10.5577i	−0.388897	−	0.388897i
$738$		0			0
$739$	−2.93837	+	2.93837i	−0.108090	+	0.108090i	−0.759083	−	0.650994i	$-0.774352\pi$
$739$	−2.93837	+	2.93837i	−0.108090	+	0.108090i	0.650994	+	0.759083i	$0.274352\pi$
$740$		0			0
$741$	6.46594	+	6.46594i	0.237532	+	0.237532i
$742$		0			0
$743$	−0.223404	+	0.223404i	−0.00819590	+	0.00819590i	−0.711193	−	0.702997i	$-0.751845\pi$
$743$	−0.223404	+	0.223404i	−0.00819590	+	0.00819590i	0.702997	+	0.711193i	$0.251845\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−4.43766			−0.162366
$748$		0			0
$749$	−4.16243	−	4.16243i	−0.152092	−	0.152092i
$750$		0			0
$751$		−	39.9939i		−	1.45940i	−0.683769	−	0.729699i	$-0.739660\pi$
$751$		−	39.9939i		−	1.45940i	0.683769	−	0.729699i	$-0.260340\pi$
$752$		0			0
$753$	16.2055	−	16.2055i	0.590563	−	0.590563i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		−	32.9120i		−	1.19621i	−0.801419	−	0.598103i	$-0.795921\pi$
$757$		−	32.9120i		−	1.19621i	0.801419	−	0.598103i	$-0.204079\pi$
$758$		0			0
$759$			5.42070i			0.196759i
$760$		0			0
$761$		−	33.9591i		−	1.23102i	−0.788130	−	0.615509i	$-0.788951\pi$
$761$		−	33.9591i		−	1.23102i	0.788130	−	0.615509i	$-0.211049\pi$
$762$		0			0
$763$		−	11.8707i		−	0.429747i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	8.07375	−	8.07375i	0.291526	−	0.291526i
$768$		0			0
$769$		−	40.2535i		−	1.45158i	−0.687917	−	0.725789i	$-0.741475\pi$
$769$		−	40.2535i		−	1.45158i	0.687917	−	0.725789i	$-0.258525\pi$
$770$		0			0
$771$	5.29172	+	5.29172i	0.190577	+	0.190577i
$772$		0			0
$773$	−9.47175			−0.340675			−0.170338	−	0.985386i	$-0.554486\pi$
$773$	−9.47175			−0.340675			−0.170338	+	0.985386i	$0.554486\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	4.88405	−	4.88405i	0.175214	−	0.175214i
$778$		0			0
$779$	9.87073	+	9.87073i	0.353656	+	0.353656i
$780$		0			0
$781$	−35.8496	+	35.8496i	−1.28280	+	1.28280i
$782$		0			0
$783$	13.2533	+	13.2533i	0.473636	+	0.473636i
$784$		0			0
$785$		0			0
$786$		0			0
$787$		−	48.1367i		−	1.71589i	−0.513742	−	0.857945i	$-0.671741\pi$
$787$		−	48.1367i		−	1.71589i	0.513742	−	0.857945i	$-0.328259\pi$
$788$		0			0
$789$	21.9455	−	21.9455i	0.781282	−	0.781282i
$790$		0			0
$791$	−9.75409			−0.346815
$792$		0			0
$793$	−9.11021	−	9.11021i	−0.323513	−	0.323513i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	33.8962			1.20066			0.600332	−	0.799751i	$-0.295035\pi$
$797$	33.8962			1.20066			0.600332	+	0.799751i	$0.295035\pi$
$798$		0			0
$799$	−82.7810			−2.92858
$800$		0			0
$801$	−13.2782			−0.469162
$802$		0			0
$803$	6.93391			0.244692
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−25.3753	−	25.3753i	−0.893254	−	0.893254i
$808$		0			0
$809$	27.5625			0.969047			0.484523	−	0.874778i	$-0.338993\pi$
$809$	27.5625			0.969047			0.484523	+	0.874778i	$0.338993\pi$
$810$		0			0
$811$	24.1817	−	24.1817i	0.849133	−	0.849133i	−0.140892	−	0.990025i	$-0.544997\pi$
$811$	24.1817	−	24.1817i	0.849133	−	0.849133i	0.990025	+	0.140892i	$0.0449970\pi$
$812$		0			0
$813$			35.8120i			1.25598i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−33.4579	−	33.4579i	−1.17054	−	1.17054i
$818$		0			0
$819$	−2.11398	+	2.11398i	−0.0738686	+	0.0738686i
$820$		0			0
$821$	0.0575735	+	0.0575735i	0.00200933	+	0.00200933i	0.708111	−	0.706101i	$-0.249548\pi$
$821$	0.0575735	+	0.0575735i	0.00200933	+	0.00200933i	−0.706101	+	0.708111i	$0.749548\pi$
$822$		0			0
$823$	28.5594	−	28.5594i	0.995518	−	0.995518i	−0.00447159	−	0.999990i	$-0.501423\pi$
$823$	28.5594	−	28.5594i	0.995518	−	0.995518i	0.999990	+	0.00447159i	$0.00142335\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−23.0863			−0.802788			−0.401394	−	0.915905i	$-0.631474\pi$
$827$	−23.0863			−0.802788			−0.401394	+	0.915905i	$0.631474\pi$
$828$		0			0
$829$	−33.3543	−	33.3543i	−1.15844	−	1.15844i	−0.984811	−	0.173631i	$-0.944450\pi$
$829$	−33.3543	−	33.3543i	−1.15844	−	1.15844i	−0.173631	−	0.984811i	$-0.555550\pi$
$830$		0			0
$831$			33.3414i			1.15660i
$832$		0			0
$833$	−23.1269	+	23.1269i	−0.801301	+	0.801301i
$834$		0			0
$835$		0			0
$836$		0			0
$837$			1.35456i			0.0468204i
$838$		0			0
$839$		−	49.4524i		−	1.70729i	−0.520859	−	0.853643i	$-0.674388\pi$
$839$		−	49.4524i		−	1.70729i	0.520859	−	0.853643i	$-0.325612\pi$
$840$		0			0
$841$		−	17.7336i		−	0.611504i
$842$		0			0
$843$			30.8746i			1.06338i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	0.246530	−	0.246530i	0.00847089	−	0.00847089i
$848$		0			0
$849$		−	6.06865i		−	0.208276i
$850$		0			0
$851$	−3.04764	−	3.04764i	−0.104472	−	0.104472i
$852$		0			0
$853$	31.3639			1.07388			0.536939	−	0.843621i	$-0.319581\pi$
$853$	31.3639			1.07388			0.536939	+	0.843621i	$0.319581\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−16.1594	+	16.1594i	−0.551996	+	0.551996i	−0.927016	−	0.375021i	$-0.877636\pi$
$857$	−16.1594	+	16.1594i	−0.551996	+	0.551996i	0.375021	+	0.927016i	$0.377636\pi$
$858$		0			0
$859$	30.7369	+	30.7369i	1.04873	+	1.04873i	0.998750	+	0.0499792i	$0.0159155\pi$
$859$	30.7369	+	30.7369i	1.04873	+	1.04873i	0.0499792	+	0.998750i	$0.484085\pi$
$860$		0			0
$861$	3.89790	−	3.89790i	0.132840	−	0.132840i
$862$		0			0
$863$	−18.9353	−	18.9353i	−0.644565	−	0.644565i	0.307109	−	0.951674i	$-0.400638\pi$
$863$	−18.9353	−	18.9353i	−0.644565	−	0.644565i	−0.951674	+	0.307109i	$0.900638\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$			48.9441i			1.66223i
$868$		0			0
$869$	23.9226	−	23.9226i	0.811517	−	0.811517i
$870$		0			0
$871$	6.20638			0.210295
$872$		0			0
$873$	−2.22280	−	2.22280i	−0.0752305	−	0.0752305i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−49.7461			−1.67981			−0.839903	−	0.542737i	$-0.817388\pi$
$877$	−49.7461			−1.67981			−0.839903	+	0.542737i	$0.817388\pi$
$878$		0			0
$879$	3.98423			0.134385
$880$		0			0
$881$	27.7694			0.935574			0.467787	−	0.883841i	$-0.345051\pi$
$881$	27.7694			0.935574			0.467787	+	0.883841i	$0.345051\pi$
$882$		0			0
$883$	−42.4602			−1.42890			−0.714450	−	0.699686i	$-0.753323\pi$
$883$	−42.4602			−1.42890			−0.714450	+	0.699686i	$0.753323\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−16.1076	−	16.1076i	−0.540842	−	0.540842i	0.382934	−	0.923776i	$-0.374914\pi$
$887$	−16.1076	−	16.1076i	−0.540842	−	0.540842i	−0.923776	+	0.382934i	$0.874914\pi$
$888$		0			0
$889$	16.6234			0.557531
$890$		0			0
$891$	−7.14563	+	7.14563i	−0.239388	+	0.239388i
$892$		0			0
$893$		−	58.2596i		−	1.94958i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−1.59329	−	1.59329i	−0.0531986	−	0.0531986i
$898$		0			0
$899$	−0.575741	+	0.575741i	−0.0192020	+	0.0192020i
$900$		0			0
$901$	−30.4780	−	30.4780i	−1.01537	−	1.01537i
$902$		0			0
$903$	−13.2123	+	13.2123i	−0.439679	+	0.439679i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−9.20991			−0.305810			−0.152905	−	0.988241i	$-0.548863\pi$
$907$	−9.20991			−0.305810			−0.152905	+	0.988241i	$0.548863\pi$
$908$		0			0
$909$	9.02174	+	9.02174i	0.299232	+	0.299232i
$910$		0			0
$911$		−	45.8065i		−	1.51764i	−0.651302	−	0.758819i	$-0.725777\pi$
$911$		−	45.8065i		−	1.51764i	0.651302	−	0.758819i	$-0.274223\pi$
$912$		0			0
$913$	7.58351	−	7.58351i	0.250978	−	0.250978i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		−	27.3068i		−	0.901749i
$918$		0			0
$919$		−	5.52468i		−	0.182242i	−0.995840	−	0.0911211i	$-0.970955\pi$
$919$		−	5.52468i		−	0.182242i	0.995840	−	0.0911211i	$-0.0290450\pi$
$920$		0			0
$921$			18.6617i			0.614924i
$922$		0			0
$923$		−	21.0744i		−	0.693672i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−2.20422	+	2.20422i	−0.0723961	+	0.0723961i
$928$		0			0
$929$			43.4288i			1.42485i	0.701746	+	0.712427i	$0.252404\pi$
$929$			43.4288i			1.42485i	−0.701746	+	0.712427i	$0.747596\pi$
$930$		0			0
$931$	−16.2763	−	16.2763i	−0.533433	−	0.533433i
$932$		0			0
$933$	18.5210			0.606352
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−20.7275	+	20.7275i	−0.677138	+	0.677138i	−0.959352	−	0.282213i	$-0.908931\pi$
$937$	−20.7275	+	20.7275i	−0.677138	+	0.677138i	0.282213	+	0.959352i	$0.408931\pi$
$938$		0			0
$939$	12.9741	+	12.9741i	0.423392	+	0.423392i
$940$		0			0
$941$	12.3393	−	12.3393i	0.402251	−	0.402251i	−0.476775	−	0.879026i	$-0.658194\pi$
$941$	12.3393	−	12.3393i	0.402251	−	0.402251i	0.879026	+	0.476775i	$0.158194\pi$
$942$		0			0
$943$	−2.43228	−	2.43228i	−0.0792060	−	0.0792060i
$944$		0			0
$945$		0			0
$946$		0			0
$947$		−	48.3611i		−	1.57152i	−0.618529	−	0.785762i	$-0.712271\pi$
$947$		−	48.3611i		−	1.57152i	0.618529	−	0.785762i	$-0.287729\pi$
$948$		0			0
$949$	−2.03807	+	2.03807i	−0.0661585	+	0.0661585i
$950$		0			0
$951$	17.7752			0.576399
$952$		0			0
$953$	34.0371	+	34.0371i	1.10257	+	1.10257i	0.994100	+	0.108471i	$0.0345953\pi$
$953$	34.0371	+	34.0371i	1.10257	+	1.10257i	0.108471	+	0.994100i	$0.465405\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−14.1208			−0.456459
$958$		0			0
$959$	−11.2325			−0.362716
$960$		0			0
$961$	30.9412			0.998102
$962$		0			0
$963$	−4.96238			−0.159911
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−18.9307	−	18.9307i	−0.608770	−	0.608770i	0.333855	−	0.942625i	$-0.391651\pi$
$967$	−18.9307	−	18.9307i	−0.608770	−	0.608770i	−0.942625	+	0.333855i	$0.891651\pi$
$968$		0			0
$969$	−49.7732			−1.59895
$970$		0			0
$971$	21.2698	−	21.2698i	0.682580	−	0.682580i	−0.278001	−	0.960581i	$-0.589672\pi$
$971$	21.2698	−	21.2698i	0.682580	−	0.682580i	0.960581	+	0.278001i	$0.0896719\pi$
$972$		0			0
$973$			23.4822i			0.752805i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−2.13884	−	2.13884i	−0.0684275	−	0.0684275i	0.672065	−	0.740492i	$-0.265408\pi$
$977$	−2.13884	−	2.13884i	−0.0684275	−	0.0684275i	−0.740492	+	0.672065i	$0.765408\pi$
$978$		0			0
$979$	22.6911	−	22.6911i	0.725210	−	0.725210i
$980$		0			0
$981$	−7.07601	−	7.07601i	−0.225919	−	0.225919i
$982$		0			0
$983$	−6.18193	+	6.18193i	−0.197173	+	0.197173i	−0.798787	−	0.601614i	$-0.794525\pi$
$983$	−6.18193	+	6.18193i	−0.197173	+	0.197173i	0.601614	+	0.798787i	$0.294525\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−23.0064			−0.732302
$988$		0			0
$989$	8.24447	+	8.24447i	0.262159	+	0.262159i
$990$		0			0
$991$			43.4847i			1.38134i	0.723172	+	0.690668i	$0.242683\pi$
$991$			43.4847i			1.38134i	−0.723172	+	0.690668i	$0.757317\pi$
$992$		0			0
$993$	−2.17092	+	2.17092i	−0.0688921	+	0.0688921i
$994$		0			0
$995$		0			0
$996$		0			0
$997$			33.4043i			1.05793i	0.848645	+	0.528963i	$0.177419\pi$
$997$			33.4043i			1.05793i	−0.848645	+	0.528963i	$0.822581\pi$
$998$		0			0
$999$		−	18.6783i		−	0.590954i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1600.2.s.d.207.7		18
4.3	odd	2		400.2.s.d.107.6		18
5.2	odd	4		320.2.j.b.143.3		18
5.3	odd	4		1600.2.j.d.143.7		18
5.4	even	2		320.2.s.b.207.3		18
16.3	odd	4		1600.2.j.d.1007.3		18
16.13	even	4		400.2.j.d.307.8		18
20.3	even	4		400.2.j.d.43.8		18
20.7	even	4		80.2.j.b.43.2	✓	18
20.19	odd	2		80.2.s.b.27.4	yes	18
40.19	odd	2		640.2.s.d.287.3		18
40.27	even	4		640.2.j.d.543.3		18
40.29	even	2		640.2.s.c.287.7		18
40.37	odd	4		640.2.j.c.543.7		18
60.47	odd	4		720.2.bd.g.523.8		18
60.59	even	2		720.2.z.g.667.6		18
80.3	even	4	inner	1600.2.s.d.943.7		18
80.13	odd	4		400.2.s.d.243.6		18
80.19	odd	4		320.2.j.b.47.7		18
80.27	even	4		640.2.s.c.223.7		18
80.29	even	4		80.2.j.b.67.2	yes	18
80.37	odd	4		640.2.s.d.223.3		18
80.59	odd	4		640.2.j.c.607.3		18
80.67	even	4		320.2.s.b.303.3		18
80.69	even	4		640.2.j.d.607.7		18
80.77	odd	4		80.2.s.b.3.4	yes	18
240.29	odd	4		720.2.bd.g.307.8		18
240.77	even	4		720.2.z.g.163.6		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.j.b.43.2	✓	18	20.7	even	4
80.2.j.b.67.2	yes	18	80.29	even	4
80.2.s.b.3.4	yes	18	80.77	odd	4
80.2.s.b.27.4	yes	18	20.19	odd	2
320.2.j.b.47.7		18	80.19	odd	4
320.2.j.b.143.3		18	5.2	odd	4
320.2.s.b.207.3		18	5.4	even	2
320.2.s.b.303.3		18	80.67	even	4
400.2.j.d.43.8		18	20.3	even	4
400.2.j.d.307.8		18	16.13	even	4
400.2.s.d.107.6		18	4.3	odd	2
400.2.s.d.243.6		18	80.13	odd	4
640.2.j.c.543.7		18	40.37	odd	4
640.2.j.c.607.3		18	80.59	odd	4
640.2.j.d.543.3		18	40.27	even	4
640.2.j.d.607.7		18	80.69	even	4
640.2.s.c.223.7		18	80.27	even	4
640.2.s.c.287.7		18	40.29	even	2
640.2.s.d.223.3		18	80.37	odd	4
640.2.s.d.287.3		18	40.19	odd	2
720.2.z.g.163.6		18	240.77	even	4
720.2.z.g.667.6		18	60.59	even	2
720.2.bd.g.307.8		18	240.29	odd	4
720.2.bd.g.523.8		18	60.47	odd	4
1600.2.j.d.143.7		18	5.3	odd	4
1600.2.j.d.1007.3		18	16.3	odd	4
1600.2.s.d.207.7		18	1.1	even	1	trivial
1600.2.s.d.943.7		18	80.3	even	4	inner

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:	\( N \)	\(=\)	\( 1600 = 2^{6} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1600.s (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.28110 q^{3} +(-1.13975 - 1.13975i) q^{7} -1.35879 q^{9} +O(q^{10})\)	\(q+1.28110 q^{3} +(-1.13975 - 1.13975i) q^{7} -1.35879 q^{9} +(2.32204 - 2.32204i) q^{11} +1.36502i q^{13} +(-5.25380 - 5.25380i) q^{17} +(3.69752 - 3.69752i) q^{19} +(-1.46013 - 1.46013i) q^{21} +(-0.911118 + 0.911118i) q^{23} -5.58403 q^{27} +(-2.37343 - 2.37343i) q^{29} -0.242577i q^{31} +(2.97475 - 2.97475i) q^{33} +3.34494i q^{37} +1.74872i q^{39} +2.66956i q^{41} -9.04874i q^{43} +(7.87820 - 7.87820i) q^{47} -4.40194i q^{49} +(-6.73063 - 6.73063i) q^{51} +5.80113 q^{53} +(4.73688 - 4.73688i) q^{57} +(-5.91474 - 5.91474i) q^{59} +(-6.67404 + 6.67404i) q^{61} +(1.54868 + 1.54868i) q^{63} -4.54673i q^{67} +(-1.16723 + 1.16723i) q^{69} -15.4389 q^{71} +(1.49307 + 1.49307i) q^{73} -5.29308 q^{77} +10.3024 q^{79} -3.07731 q^{81} +3.26589 q^{83} +(-3.04060 - 3.04060i) q^{87} +9.77206 q^{89} +(1.55578 - 1.55578i) q^{91} -0.310765i q^{93} +(1.63587 + 1.63587i) q^{97} +(-3.15516 + 3.15516i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 2 q^{7} + 10 q^{9}+O(q^{10}) \) 18 * q + 2 * q^7 + 10 * q^9	\( 18 q + 2 q^{7} + 10 q^{9} + 2 q^{11} + 6 q^{17} + 2 q^{19} - 16 q^{21} - 2 q^{23} - 24 q^{27} + 14 q^{29} + 8 q^{33} + 38 q^{47} - 8 q^{51} - 12 q^{53} + 24 q^{57} - 10 q^{59} + 14 q^{61} - 6 q^{63} - 32 q^{69} - 24 q^{71} + 14 q^{73} + 44 q^{77} + 16 q^{79} + 2 q^{81} + 40 q^{83} + 24 q^{87} + 12 q^{89} - 18 q^{97} - 22 q^{99}+O(q^{100}) \) 18 * q + 2 * q^7 + 10 * q^9 + 2 * q^11 + 6 * q^17 + 2 * q^19 - 16 * q^21 - 2 * q^23 - 24 * q^27 + 14 * q^29 + 8 * q^33 + 38 * q^47 - 8 * q^51 - 12 * q^53 + 24 * q^57 - 10 * q^59 + 14 * q^61 - 6 * q^63 - 32 * q^69 - 24 * q^71 + 14 * q^73 + 44 * q^77 + 16 * q^79 + 2 * q^81 + 40 * q^83 + 24 * q^87 + 12 * q^89 - 18 * q^97 - 22 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more