LMFDB - Embedded newform 1300.2.bb.e.549.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1300,2,Mod(549,1300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1300, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("1300.549");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1300 = 2^{2} \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1300.bb (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$10.3805522628$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 260)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			549.2
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1300.549
Dual form			1300.2.bb.e.1049.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.59808 - 1.50000i) q^{3} +(-2.59808 - 1.50000i) q^{7} +(3.00000 - 5.19615i) q^{9} +O(q^{10})$	$q+(2.59808 - 1.50000i) q^{3} +(-2.59808 - 1.50000i) q^{7} +(3.00000 - 5.19615i) q^{9} +(-1.50000 - 2.59808i) q^{11} +(-3.46410 - 1.00000i) q^{13} +(6.06218 + 3.50000i) q^{17} +(0.500000 - 0.866025i) q^{19} -9.00000 q^{21} +(6.06218 - 3.50000i) q^{23} -9.00000i q^{27} +(-2.50000 - 4.33013i) q^{29} -4.00000 q^{31} +(-7.79423 - 4.50000i) q^{33} +(-2.59808 + 1.50000i) q^{37} +(-10.5000 + 2.59808i) q^{39} +(-3.50000 - 6.06218i) q^{41} +(-7.79423 - 4.50000i) q^{43} +8.00000i q^{47} +(1.00000 + 1.73205i) q^{49} +21.0000 q^{51} +6.00000i q^{53} -3.00000i q^{57} +(2.50000 - 4.33013i) q^{59} +(2.50000 - 4.33013i) q^{61} +(-15.5885 + 9.00000i) q^{63} +(11.2583 - 6.50000i) q^{67} +(10.5000 - 18.1865i) q^{69} +(1.50000 - 2.59808i) q^{71} +14.0000i q^{73} +9.00000i q^{77} +8.00000 q^{79} +(-4.50000 - 7.79423i) q^{81} -12.0000i q^{83} +(-12.9904 - 7.50000i) q^{87} +(3.50000 + 6.06218i) q^{89} +(7.50000 + 7.79423i) q^{91} +(-10.3923 + 6.00000i) q^{93} +(9.52628 + 5.50000i) q^{97} -18.0000 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 12 q^{9}+O(q^{10}) $ 4 * q + 12 * q^9	$ 4 q + 12 q^{9} - 6 q^{11} + 2 q^{19} - 36 q^{21} - 10 q^{29} - 16 q^{31} - 42 q^{39} - 14 q^{41} + 4 q^{49} + 84 q^{51} + 10 q^{59} + 10 q^{61} + 42 q^{69} + 6 q^{71} + 32 q^{79} - 18 q^{81} + 14 q^{89} + 30 q^{91} - 72 q^{99}+O(q^{100}) $ 4 * q + 12 * q^9 - 6 * q^11 + 2 * q^19 - 36 * q^21 - 10 * q^29 - 16 * q^31 - 42 * q^39 - 14 * q^41 + 4 * q^49 + 84 * q^51 + 10 * q^59 + 10 * q^61 + 42 * q^69 + 6 * q^71 + 32 * q^79 - 18 * q^81 + 14 * q^89 + 30 * q^91 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1300\mathbb{Z}\right)^\times$.

$n$	$301$	$651$	$677$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.59808	−	1.50000i	1.50000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$3$	2.59808	−	1.50000i	1.50000	−	0.866025i	1.00000			$0$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−2.59808	−	1.50000i	−0.981981	−	0.566947i	−0.0791130	−	0.996866i	$-0.525209\pi$
$7$	−2.59808	−	1.50000i	−0.981981	−	0.566947i	−0.902867	+	0.429919i	$0.858542\pi$
$8$		0			0
$9$	3.00000	−	5.19615i	1.00000	−	1.73205i
$10$		0			0
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	0.546259	−	0.837616i	$-0.316051\pi$
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	−0.998526	+	0.0542666i	$0.982718\pi$
$12$		0			0
$13$	−3.46410	−	1.00000i	−0.960769	−	0.277350i
$13$	−3.46410	−	1.00000i	−0.960769	−	0.277350i
$14$		0			0
$15$		0			0
$16$		0			0
$17$	6.06218	+	3.50000i	1.47029	+	0.848875i	0.999444	−	0.0333386i	$-0.0106140\pi$
$17$	6.06218	+	3.50000i	1.47029	+	0.848875i	0.470850	+	0.882213i	$0.343947\pi$
$18$		0			0
$19$	0.500000	−	0.866025i	0.114708	−	0.198680i	−0.802955	−	0.596040i	$-0.796740\pi$
$19$	0.500000	−	0.866025i	0.114708	−	0.198680i	0.917663	+	0.397360i	$0.130073\pi$
$20$		0			0
$21$	−9.00000			−1.96396
$22$		0			0
$23$	6.06218	−	3.50000i	1.26405	−	0.729800i	0.290196	−	0.956967i	$-0.406280\pi$
$23$	6.06218	−	3.50000i	1.26405	−	0.729800i	0.973856	+	0.227167i	$0.0729463\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$		−	9.00000i		−	1.73205i
$28$		0			0
$29$	−2.50000	−	4.33013i	−0.464238	−	0.804084i	0.534928	−	0.844897i	$-0.320339\pi$
$29$	−2.50000	−	4.33013i	−0.464238	−	0.804084i	−0.999167	+	0.0408130i	$0.987005\pi$
$30$		0			0
$31$	−4.00000			−0.718421			−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000			−0.718421			−0.359211	+	0.933257i	$0.616954\pi$
$32$		0			0
$33$	−7.79423	−	4.50000i	−1.35680	−	0.783349i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−2.59808	+	1.50000i	−0.427121	+	0.246598i	−0.698119	−	0.715981i	$-0.745980\pi$
$37$	−2.59808	+	1.50000i	−0.427121	+	0.246598i	0.270998	+	0.962580i	$0.412646\pi$
$38$		0			0
$39$	−10.5000	+	2.59808i	−1.68135	+	0.416025i
$40$		0			0
$41$	−3.50000	−	6.06218i	−0.546608	−	0.946753i	−0.998504	−	0.0546823i	$-0.982585\pi$
$41$	−3.50000	−	6.06218i	−0.546608	−	0.946753i	0.451896	−	0.892071i	$-0.350748\pi$
$42$		0			0
$43$	−7.79423	−	4.50000i	−1.18861	−	0.686244i	−0.230618	−	0.973044i	$-0.574075\pi$
$43$	−7.79423	−	4.50000i	−1.18861	−	0.686244i	−0.957990	+	0.286801i	$0.907408\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$			8.00000i			1.16692i	0.812142	+	0.583460i	$0.198301\pi$
$47$			8.00000i			1.16692i	−0.812142	+	0.583460i	$0.801699\pi$
$48$		0			0
$49$	1.00000	+	1.73205i	0.142857	+	0.247436i
$50$		0			0
$51$	21.0000			2.94059
$52$		0			0
$53$			6.00000i			0.824163i	0.911147	+	0.412082i	$0.135198\pi$
$53$			6.00000i			0.824163i	−0.911147	+	0.412082i	$0.864802\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		−	3.00000i		−	0.397360i
$58$		0			0
$59$	2.50000	−	4.33013i	0.325472	−	0.563735i	−0.656136	−	0.754643i	$-0.727810\pi$
$59$	2.50000	−	4.33013i	0.325472	−	0.563735i	0.981608	+	0.190909i	$0.0611434\pi$
$60$		0			0
$61$	2.50000	−	4.33013i	0.320092	−	0.554416i	−0.660415	−	0.750901i	$-0.729619\pi$
$61$	2.50000	−	4.33013i	0.320092	−	0.554416i	0.980507	+	0.196485i	$0.0629528\pi$
$62$		0			0
$63$	−15.5885	+	9.00000i	−1.96396	+	1.13389i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	11.2583	−	6.50000i	1.37542	−	0.794101i	0.383819	−	0.923408i	$-0.374609\pi$
$67$	11.2583	−	6.50000i	1.37542	−	0.794101i	0.991605	+	0.129307i	$0.0412752\pi$
$68$		0			0
$69$	10.5000	−	18.1865i	1.26405	−	2.18940i
$70$		0			0
$71$	1.50000	−	2.59808i	0.178017	−	0.308335i	−0.763184	−	0.646181i	$-0.776365\pi$
$71$	1.50000	−	2.59808i	0.178017	−	0.308335i	0.941201	+	0.337846i	$0.109698\pi$
$72$		0			0
$73$			14.0000i			1.63858i	0.573382	+	0.819288i	$0.305631\pi$
$73$			14.0000i			1.63858i	−0.573382	+	0.819288i	$0.694369\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$			9.00000i			1.02565i
$78$		0			0
$79$	8.00000			0.900070			0.450035	−	0.893011i	$-0.351411\pi$
$79$	8.00000			0.900070			0.450035	+	0.893011i	$0.351411\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$		0			0
$83$		−	12.0000i		−	1.31717i	−0.752506	−	0.658586i	$-0.771155\pi$
$83$		−	12.0000i		−	1.31717i	0.752506	−	0.658586i	$-0.228845\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−12.9904	−	7.50000i	−1.39272	−	0.804084i
$88$		0			0
$89$	3.50000	+	6.06218i	0.370999	+	0.642590i	0.989720	−	0.143022i	$-0.0456819\pi$
$89$	3.50000	+	6.06218i	0.370999	+	0.642590i	−0.618720	+	0.785611i	$0.712349\pi$
$90$		0			0
$91$	7.50000	+	7.79423i	0.786214	+	0.817057i
$92$		0			0
$93$	−10.3923	+	6.00000i	−1.07763	+	0.622171i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	9.52628	+	5.50000i	0.967247	+	0.558440i	0.898396	−	0.439187i	$-0.144733\pi$
$97$	9.52628	+	5.50000i	0.967247	+	0.558440i	0.0688512	+	0.997627i	$0.478067\pi$
$98$		0			0
$99$	−18.0000			−1.80907
$100$		0			0
$101$	4.50000	+	7.79423i	0.447767	+	0.775555i	0.998240	−	0.0592978i	$-0.0188862\pi$
$101$	4.50000	+	7.79423i	0.447767	+	0.775555i	−0.550474	+	0.834853i	$0.685553\pi$
$102$		0			0
$103$			16.0000i			1.57653i	0.615338	+	0.788263i	$0.289020\pi$
$103$			16.0000i			1.57653i	−0.615338	+	0.788263i	$0.710980\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−2.59808	+	1.50000i	−0.251166	+	0.145010i	−0.620298	−	0.784366i	$-0.712988\pi$
$107$	−2.59808	+	1.50000i	−0.251166	+	0.145010i	0.369132	+	0.929377i	$0.379655\pi$
$108$		0			0
$109$	14.0000			1.34096			0.670478	−	0.741929i	$-0.266089\pi$
$109$	14.0000			1.34096			0.670478	+	0.741929i	$0.266089\pi$
$110$		0			0
$111$	−4.50000	+	7.79423i	−0.427121	+	0.739795i
$112$		0			0
$113$	11.2583	+	6.50000i	1.05909	+	0.611469i	0.925182	−	0.379525i	$-0.123912\pi$
$113$	11.2583	+	6.50000i	1.05909	+	0.611469i	0.133913	+	0.990993i	$0.457246\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−15.5885	+	15.0000i	−1.44115	+	1.38675i
$118$		0			0
$119$	−10.5000	−	18.1865i	−0.962533	−	1.66716i
$120$		0			0
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$		0			0
$123$	−18.1865	−	10.5000i	−1.63982	−	0.946753i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	0.866025	−	0.500000i	0.0768473	−	0.0443678i	−0.461084	−	0.887357i	$-0.652539\pi$
$127$	0.866025	−	0.500000i	0.0768473	−	0.0443678i	0.537931	+	0.842989i	$0.319206\pi$
$128$		0			0
$129$	−27.0000			−2.37722
$130$		0			0
$131$	4.00000			0.349482			0.174741	−	0.984614i	$-0.444091\pi$
$131$	4.00000			0.349482			0.174741	+	0.984614i	$0.444091\pi$
$132$		0			0
$133$	−2.59808	+	1.50000i	−0.225282	+	0.130066i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	2.59808	+	1.50000i	0.221969	+	0.128154i	0.606861	−	0.794808i	$-0.292428\pi$
$137$	2.59808	+	1.50000i	0.221969	+	0.128154i	−0.384893	+	0.922961i	$0.625762\pi$
$138$		0			0
$139$	6.50000	−	11.2583i	0.551323	−	0.954919i	−0.446857	−	0.894606i	$-0.647457\pi$
$139$	6.50000	−	11.2583i	0.551323	−	0.954919i	0.998179	−	0.0603135i	$-0.0192101\pi$
$140$		0			0
$141$	12.0000	+	20.7846i	1.01058	+	1.75038i
$142$		0			0
$143$	2.59808	+	10.5000i	0.217262	+	0.878054i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	5.19615	+	3.00000i	0.428571	+	0.247436i
$148$		0			0
$149$	1.50000	−	2.59808i	0.122885	−	0.212843i	−0.798019	−	0.602632i	$-0.794119\pi$
$149$	1.50000	−	2.59808i	0.122885	−	0.212843i	0.920904	+	0.389789i	$0.127452\pi$
$150$		0			0
$151$	−8.00000			−0.651031			−0.325515	−	0.945537i	$-0.605538\pi$
$151$	−8.00000			−0.651031			−0.325515	+	0.945537i	$0.605538\pi$
$152$		0			0
$153$	36.3731	−	21.0000i	2.94059	−	1.69775i
$154$		0			0
$155$		0			0
$156$		0			0
$157$			6.00000i			0.478852i	0.970915	+	0.239426i	$0.0769593\pi$
$157$			6.00000i			0.478852i	−0.970915	+	0.239426i	$0.923041\pi$
$158$		0			0
$159$	9.00000	+	15.5885i	0.713746	+	1.23625i
$160$		0			0
$161$	−21.0000			−1.65503
$162$		0			0
$163$	9.52628	+	5.50000i	0.746156	+	0.430793i	0.824303	−	0.566149i	$-0.191567\pi$
$163$	9.52628	+	5.50000i	0.746156	+	0.430793i	−0.0781474	+	0.996942i	$0.524900\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	0.866025	−	0.500000i	0.0670151	−	0.0386912i	−0.466118	−	0.884723i	$-0.654348\pi$
$167$	0.866025	−	0.500000i	0.0670151	−	0.0386912i	0.533133	+	0.846031i	$0.321014\pi$
$168$		0			0
$169$	11.0000	+	6.92820i	0.846154	+	0.532939i
$170$		0			0
$171$	−3.00000	−	5.19615i	−0.229416	−	0.397360i
$172$		0			0
$173$	−12.9904	−	7.50000i	−0.987640	−	0.570214i	−0.0830722	−	0.996544i	$-0.526473\pi$
$173$	−12.9904	−	7.50000i	−0.987640	−	0.570214i	−0.904568	+	0.426329i	$0.859807\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		−	15.0000i		−	1.12747i
$178$		0			0
$179$	9.50000	+	16.4545i	0.710063	+	1.22987i	0.964833	+	0.262864i	$0.0846670\pi$
$179$	9.50000	+	16.4545i	0.710063	+	1.22987i	−0.254770	+	0.967002i	$0.582000\pi$
$180$		0			0
$181$	−14.0000			−1.04061			−0.520306	−	0.853980i	$-0.674182\pi$
$181$	−14.0000			−1.04061			−0.520306	+	0.853980i	$0.674182\pi$
$182$		0			0
$183$		−	15.0000i		−	1.10883i
$184$		0			0
$185$		0			0
$186$		0			0
$187$		−	21.0000i		−	1.53567i
$188$		0			0
$189$	−13.5000	+	23.3827i	−0.981981	+	1.70084i
$190$		0			0
$191$	1.50000	−	2.59808i	0.108536	−	0.187990i	−0.806641	−	0.591041i	$-0.798717\pi$
$191$	1.50000	−	2.59808i	0.108536	−	0.187990i	0.915177	+	0.403051i	$0.132050\pi$
$192$		0			0
$193$	12.9904	−	7.50000i	0.935068	−	0.539862i	0.0466572	−	0.998911i	$-0.485143\pi$
$193$	12.9904	−	7.50000i	0.935068	−	0.539862i	0.888411	+	0.459049i	$0.151810\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−19.9186	+	11.5000i	−1.41914	+	0.819341i	−0.996223	−	0.0868274i	$-0.972327\pi$
$197$	−19.9186	+	11.5000i	−1.41914	+	0.819341i	−0.422917	+	0.906168i	$0.638994\pi$
$198$		0			0
$199$	4.50000	−	7.79423i	0.318997	−	0.552518i	−0.661282	−	0.750137i	$-0.729987\pi$
$199$	4.50000	−	7.79423i	0.318997	−	0.552518i	0.980279	+	0.197619i	$0.0633208\pi$
$200$		0			0
$201$	19.5000	−	33.7750i	1.37542	−	2.38230i
$202$		0			0
$203$			15.0000i			1.05279i
$204$		0			0
$205$		0			0
$206$		0			0
$207$		−	42.0000i		−	2.91920i
$208$		0			0
$209$	−3.00000			−0.207514
$210$		0			0
$211$	2.50000	+	4.33013i	0.172107	+	0.298098i	0.939156	−	0.343490i	$-0.111609\pi$
$211$	2.50000	+	4.33013i	0.172107	+	0.298098i	−0.767049	+	0.641588i	$0.778276\pi$
$212$		0			0
$213$		−	9.00000i		−	0.616670i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	10.3923	+	6.00000i	0.705476	+	0.407307i
$218$		0			0
$219$	21.0000	+	36.3731i	1.41905	+	2.45786i
$220$		0			0
$221$	−17.5000	−	18.1865i	−1.17718	−	1.22336i
$222$		0			0
$223$	19.9186	−	11.5000i	1.33385	−	0.770097i	0.347960	−	0.937509i	$-0.386874\pi$
$223$	19.9186	−	11.5000i	1.33385	−	0.770097i	0.985887	+	0.167412i	$0.0535411\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	0.866025	+	0.500000i	0.0574801	+	0.0331862i	0.528465	−	0.848955i	$-0.322768\pi$
$227$	0.866025	+	0.500000i	0.0574801	+	0.0331862i	−0.470985	+	0.882141i	$0.656101\pi$
$228$		0			0
$229$	−26.0000			−1.71813			−0.859064	−	0.511868i	$-0.828954\pi$
$229$	−26.0000			−1.71813			−0.859064	+	0.511868i	$0.828954\pi$
$230$		0			0
$231$	13.5000	+	23.3827i	0.888235	+	1.53847i
$232$		0			0
$233$		−	18.0000i		−	1.17922i	−0.807688	−	0.589610i	$-0.799282\pi$
$233$		−	18.0000i		−	1.17922i	0.807688	−	0.589610i	$-0.200718\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	20.7846	−	12.0000i	1.35011	−	0.779484i
$238$		0			0
$239$	16.0000			1.03495			0.517477	−	0.855697i	$-0.326871\pi$
$239$	16.0000			1.03495			0.517477	+	0.855697i	$0.326871\pi$
$240$		0			0
$241$	0.500000	−	0.866025i	0.0322078	−	0.0557856i	−0.849472	−	0.527633i	$-0.823079\pi$
$241$	0.500000	−	0.866025i	0.0322078	−	0.0557856i	0.881680	+	0.471848i	$0.156413\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−2.59808	+	2.50000i	−0.165312	+	0.159071i
$248$		0			0
$249$	−18.0000	−	31.1769i	−1.14070	−	1.97576i
$250$		0			0
$251$	−2.50000	+	4.33013i	−0.157799	+	0.273315i	−0.934075	−	0.357078i	$-0.883773\pi$
$251$	−2.50000	+	4.33013i	−0.157799	+	0.273315i	0.776276	+	0.630393i	$0.217106\pi$
$252$		0			0
$253$	−18.1865	−	10.5000i	−1.14338	−	0.660129i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−16.4545	+	9.50000i	−1.02640	+	0.592594i	−0.915952	−	0.401288i	$-0.868563\pi$
$257$	−16.4545	+	9.50000i	−1.02640	+	0.592594i	−0.110450	+	0.993882i	$0.535229\pi$
$258$		0			0
$259$	9.00000			0.559233
$260$		0			0
$261$	−30.0000			−1.85695
$262$		0			0
$263$	6.06218	−	3.50000i	0.373810	−	0.215819i	−0.301312	−	0.953526i	$-0.597424\pi$
$263$	6.06218	−	3.50000i	0.373810	−	0.215819i	0.675122	+	0.737706i	$0.264091\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	18.1865	+	10.5000i	1.11300	+	0.642590i
$268$		0			0
$269$	1.50000	−	2.59808i	0.0914566	−	0.158408i	−0.816668	−	0.577108i	$-0.804181\pi$
$269$	1.50000	−	2.59808i	0.0914566	−	0.158408i	0.908124	+	0.418701i	$0.137514\pi$
$270$		0			0
$271$	−11.5000	−	19.9186i	−0.698575	−	1.20997i	−0.968960	−	0.247216i	$-0.920484\pi$
$271$	−11.5000	−	19.9186i	−0.698575	−	1.20997i	0.270385	−	0.962752i	$-0.412849\pi$
$272$		0			0
$273$	31.1769	+	9.00000i	1.88691	+	0.544705i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	19.9186	+	11.5000i	1.19679	+	0.690968i	0.959839	−	0.280553i	$-0.0905179\pi$
$277$	19.9186	+	11.5000i	1.19679	+	0.690968i	0.236953	+	0.971521i	$0.423851\pi$
$278$		0			0
$279$	−12.0000	+	20.7846i	−0.718421	+	1.24434i
$280$		0			0
$281$	−10.0000			−0.596550			−0.298275	−	0.954480i	$-0.596411\pi$
$281$	−10.0000			−0.596550			−0.298275	+	0.954480i	$0.596411\pi$
$282$		0			0
$283$	−0.866025	+	0.500000i	−0.0514799	+	0.0297219i	−0.525519	−	0.850782i	$-0.676129\pi$
$283$	−0.866025	+	0.500000i	−0.0514799	+	0.0297219i	0.474039	+	0.880504i	$0.342796\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$			21.0000i			1.23959i
$288$		0			0
$289$	16.0000	+	27.7128i	0.941176	+	1.63017i
$290$		0			0
$291$	33.0000			1.93449
$292$		0			0
$293$	7.79423	+	4.50000i	0.455344	+	0.262893i	0.710084	−	0.704117i	$-0.248657\pi$
$293$	7.79423	+	4.50000i	0.455344	+	0.262893i	−0.254741	+	0.967009i	$0.581990\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−23.3827	+	13.5000i	−1.35680	+	0.783349i
$298$		0			0
$299$	−24.5000	+	6.06218i	−1.41687	+	0.350585i
$300$		0			0
$301$	13.5000	+	23.3827i	0.778127	+	1.34776i
$302$		0			0
$303$	23.3827	+	13.5000i	1.34330	+	0.775555i
$304$		0			0
$305$		0			0
$306$		0			0
$307$			28.0000i			1.59804i	0.601302	+	0.799022i	$0.294649\pi$
$307$			28.0000i			1.59804i	−0.601302	+	0.799022i	$0.705351\pi$
$308$		0			0
$309$	24.0000	+	41.5692i	1.36531	+	2.36479i
$310$		0			0
$311$	−24.0000			−1.36092			−0.680458	−	0.732787i	$-0.738219\pi$
$311$	−24.0000			−1.36092			−0.680458	+	0.732787i	$0.738219\pi$
$312$		0			0
$313$			6.00000i			0.339140i	0.985518	+	0.169570i	$0.0542379\pi$
$313$			6.00000i			0.339140i	−0.985518	+	0.169570i	$0.945762\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		−	2.00000i		−	0.112331i	−0.998421	−	0.0561656i	$-0.982113\pi$
$317$		−	2.00000i		−	0.112331i	0.998421	−	0.0561656i	$-0.0178875\pi$
$318$		0			0
$319$	−7.50000	+	12.9904i	−0.419919	+	0.727322i
$320$		0			0
$321$	−4.50000	+	7.79423i	−0.251166	+	0.435031i
$322$		0			0
$323$	6.06218	−	3.50000i	0.337309	−	0.194745i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	36.3731	−	21.0000i	2.01144	−	1.16130i
$328$		0			0
$329$	12.0000	−	20.7846i	0.661581	−	1.14589i
$330$		0			0
$331$	−6.50000	+	11.2583i	−0.357272	+	0.618814i	−0.987504	−	0.157593i	$-0.949627\pi$
$331$	−6.50000	+	11.2583i	−0.357272	+	0.618814i	0.630232	+	0.776407i	$0.282960\pi$
$332$		0			0
$333$			18.0000i			0.986394i
$334$		0			0
$335$		0			0
$336$		0			0
$337$		−	18.0000i		−	0.980522i	−0.871576	−	0.490261i	$-0.836901\pi$
$337$		−	18.0000i		−	0.980522i	0.871576	−	0.490261i	$-0.163099\pi$
$338$		0			0
$339$	39.0000			2.11819
$340$		0			0
$341$	6.00000	+	10.3923i	0.324918	+	0.562775i
$342$		0			0
$343$			15.0000i			0.809924i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	11.2583	+	6.50000i	0.604379	+	0.348938i	0.770762	−	0.637123i	$-0.219876\pi$
$347$	11.2583	+	6.50000i	0.604379	+	0.348938i	−0.166383	+	0.986061i	$0.553209\pi$
$348$		0			0
$349$	−12.5000	−	21.6506i	−0.669110	−	1.15893i	−0.978153	−	0.207884i	$-0.933342\pi$
$349$	−12.5000	−	21.6506i	−0.669110	−	1.15893i	0.309044	−	0.951048i	$-0.399991\pi$
$350$		0			0
$351$	−9.00000	+	31.1769i	−0.480384	+	1.66410i
$352$		0			0
$353$	−18.1865	+	10.5000i	−0.967972	+	0.558859i	−0.898617	−	0.438733i	$-0.855427\pi$
$353$	−18.1865	+	10.5000i	−0.967972	+	0.558859i	−0.0693543	+	0.997592i	$0.522094\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−54.5596	−	31.5000i	−2.88760	−	1.66716i
$358$		0			0
$359$	8.00000			0.422224			0.211112	−	0.977462i	$-0.432292\pi$
$359$	8.00000			0.422224			0.211112	+	0.977462i	$0.432292\pi$
$360$		0			0
$361$	9.00000	+	15.5885i	0.473684	+	0.820445i
$362$		0			0
$363$		−	6.00000i		−	0.314918i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	7.79423	−	4.50000i	0.406855	−	0.234898i	−0.282582	−	0.959243i	$-0.591191\pi$
$367$	7.79423	−	4.50000i	0.406855	−	0.234898i	0.689438	+	0.724345i	$0.257858\pi$
$368$		0			0
$369$	−42.0000			−2.18643
$370$		0			0
$371$	9.00000	−	15.5885i	0.467257	−	0.809312i
$372$		0			0
$373$	−23.3827	−	13.5000i	−1.21071	−	0.699004i	−0.247796	−	0.968812i	$-0.579706\pi$
$373$	−23.3827	−	13.5000i	−1.21071	−	0.699004i	−0.962914	+	0.269809i	$0.913039\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	4.33013	+	17.5000i	0.223013	+	0.901296i
$378$		0			0
$379$	−4.50000	−	7.79423i	−0.231149	−	0.400363i	0.726997	−	0.686640i	$-0.240915\pi$
$379$	−4.50000	−	7.79423i	−0.231149	−	0.400363i	−0.958147	+	0.286278i	$0.907582\pi$
$380$		0			0
$381$	1.50000	−	2.59808i	0.0768473	−	0.133103i
$382$		0			0
$383$	−11.2583	−	6.50000i	−0.575274	−	0.332134i	0.183979	−	0.982930i	$-0.441102\pi$
$383$	−11.2583	−	6.50000i	−0.575274	−	0.332134i	−0.759253	+	0.650796i	$0.774435\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−46.7654	+	27.0000i	−2.37722	+	1.37249i
$388$		0			0
$389$	−18.0000			−0.912636			−0.456318	−	0.889817i	$-0.650832\pi$
$389$	−18.0000			−0.912636			−0.456318	+	0.889817i	$0.650832\pi$
$390$		0			0
$391$	49.0000			2.47804
$392$		0			0
$393$	10.3923	−	6.00000i	0.524222	−	0.302660i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−28.5788	−	16.5000i	−1.43433	−	0.828111i	−0.436884	−	0.899518i	$-0.643918\pi$
$397$	−28.5788	−	16.5000i	−1.43433	−	0.828111i	−0.997447	+	0.0714068i	$0.977251\pi$
$398$		0			0
$399$	−4.50000	+	7.79423i	−0.225282	+	0.390199i
$400$		0			0
$401$	−7.50000	−	12.9904i	−0.374532	−	0.648709i	0.615725	−	0.787961i	$-0.288863\pi$
$401$	−7.50000	−	12.9904i	−0.374532	−	0.648709i	−0.990257	+	0.139253i	$0.955530\pi$
$402$		0			0
$403$	13.8564	+	4.00000i	0.690237	+	0.199254i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	7.79423	+	4.50000i	0.386346	+	0.223057i
$408$		0			0
$409$	−0.500000	+	0.866025i	−0.0247234	+	0.0428222i	−0.878122	−	0.478436i	$-0.841204\pi$
$409$	−0.500000	+	0.866025i	−0.0247234	+	0.0428222i	0.853399	+	0.521258i	$0.174537\pi$
$410$		0			0
$411$	9.00000			0.443937
$412$		0			0
$413$	−12.9904	+	7.50000i	−0.639215	+	0.369051i
$414$		0			0
$415$		0			0
$416$		0			0
$417$		−	39.0000i		−	1.90984i
$418$		0			0
$419$	−16.5000	−	28.5788i	−0.806078	−	1.39617i	−0.915561	−	0.402179i	$-0.868253\pi$
$419$	−16.5000	−	28.5788i	−0.806078	−	1.39617i	0.109483	−	0.993989i	$-0.465080\pi$
$420$		0			0
$421$	34.0000			1.65706			0.828529	−	0.559946i	$-0.189178\pi$
$421$	34.0000			1.65706			0.828529	+	0.559946i	$0.189178\pi$
$422$		0			0
$423$	41.5692	+	24.0000i	2.02116	+	1.16692i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−12.9904	+	7.50000i	−0.628649	+	0.362950i
$428$		0			0
$429$	22.5000	+	23.3827i	1.08631	+	1.12893i
$430$		0			0
$431$	4.50000	+	7.79423i	0.216757	+	0.375435i	0.953815	−	0.300395i	$-0.0971186\pi$
$431$	4.50000	+	7.79423i	0.216757	+	0.375435i	−0.737057	+	0.675830i	$0.763785\pi$
$432$		0			0
$433$	0.866025	+	0.500000i	0.0416185	+	0.0240285i	0.520665	−	0.853761i	$-0.325684\pi$
$433$	0.866025	+	0.500000i	0.0416185	+	0.0240285i	−0.479046	+	0.877790i	$0.659017\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		−	7.00000i		−	0.334855i
$438$		0			0
$439$	1.50000	+	2.59808i	0.0715911	+	0.123999i	0.899599	−	0.436717i	$-0.143859\pi$
$439$	1.50000	+	2.59808i	0.0715911	+	0.123999i	−0.828008	+	0.560717i	$0.810526\pi$
$440$		0			0
$441$	12.0000			0.571429
$442$		0			0
$443$		−	24.0000i		−	1.14027i	−0.821549	−	0.570137i	$-0.806890\pi$
$443$		−	24.0000i		−	1.14027i	0.821549	−	0.570137i	$-0.193110\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		−	9.00000i		−	0.425685i
$448$		0			0
$449$	−10.5000	+	18.1865i	−0.495526	+	0.858276i	−0.999987	−	0.00515887i	$-0.998358\pi$
$449$	−10.5000	+	18.1865i	−0.495526	+	0.858276i	0.504461	+	0.863434i	$0.331691\pi$
$450$		0			0
$451$	−10.5000	+	18.1865i	−0.494426	+	0.856370i
$452$		0			0
$453$	−20.7846	+	12.0000i	−0.976546	+	0.563809i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−19.9186	+	11.5000i	−0.931752	+	0.537947i	−0.887365	−	0.461067i	$-0.847467\pi$
$457$	−19.9186	+	11.5000i	−0.931752	+	0.537947i	−0.0443868	+	0.999014i	$0.514133\pi$
$458$		0			0
$459$	31.5000	−	54.5596i	1.47029	−	2.54662i
$460$		0			0
$461$	−5.50000	+	9.52628i	−0.256161	+	0.443683i	−0.965210	−	0.261476i	$-0.915791\pi$
$461$	−5.50000	+	9.52628i	−0.256161	+	0.443683i	0.709050	+	0.705159i	$0.249124\pi$
$462$		0			0
$463$			28.0000i			1.30127i	0.759390	+	0.650635i	$0.225497\pi$
$463$			28.0000i			1.30127i	−0.759390	+	0.650635i	$0.774503\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			20.0000i			0.925490i	0.886492	+	0.462745i	$0.153135\pi$
$467$			20.0000i			0.925490i	−0.886492	+	0.462745i	$0.846865\pi$
$468$		0			0
$469$	−39.0000			−1.80085
$470$		0			0
$471$	9.00000	+	15.5885i	0.414698	+	0.718278i
$472$		0			0
$473$			27.0000i			1.24146i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	31.1769	+	18.0000i	1.42749	+	0.824163i
$478$		0			0
$479$	−0.500000	−	0.866025i	−0.0228456	−	0.0395697i	0.854377	−	0.519654i	$-0.173939\pi$
$479$	−0.500000	−	0.866025i	−0.0228456	−	0.0395697i	−0.877222	+	0.480085i	$0.840606\pi$
$480$		0			0
$481$	10.5000	−	2.59808i	0.478759	−	0.118462i
$482$		0			0
$483$	−54.5596	+	31.5000i	−2.48255	+	1.43330i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	14.7224	+	8.50000i	0.667137	+	0.385172i	0.794991	−	0.606621i	$-0.207476\pi$
$487$	14.7224	+	8.50000i	0.667137	+	0.385172i	−0.127854	+	0.991793i	$0.540809\pi$
$488$		0			0
$489$	33.0000			1.49231
$490$		0			0
$491$	−11.5000	−	19.9186i	−0.518988	−	0.898913i	−0.999757	−	0.0220657i	$-0.992976\pi$
$491$	−11.5000	−	19.9186i	−0.518988	−	0.898913i	0.480769	−	0.876847i	$-0.340358\pi$
$492$		0			0
$493$		−	35.0000i		−	1.57632i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−7.79423	+	4.50000i	−0.349619	+	0.201853i
$498$		0			0
$499$	16.0000			0.716258			0.358129	−	0.933672i	$-0.383415\pi$
$499$	16.0000			0.716258			0.358129	+	0.933672i	$0.383415\pi$
$500$		0			0
$501$	1.50000	−	2.59808i	0.0670151	−	0.116073i
$502$		0			0
$503$	9.52628	+	5.50000i	0.424756	+	0.245233i	0.697110	−	0.716964i	$-0.254469\pi$
$503$	9.52628	+	5.50000i	0.424756	+	0.245233i	−0.272354	+	0.962197i	$0.587802\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	38.9711	+	1.50000i	1.73077	+	0.0666173i
$508$		0			0
$509$	7.50000	+	12.9904i	0.332432	+	0.575789i	0.982988	−	0.183669i	$-0.0587976\pi$
$509$	7.50000	+	12.9904i	0.332432	+	0.575789i	−0.650556	+	0.759458i	$0.725464\pi$
$510$		0			0
$511$	21.0000	−	36.3731i	0.928985	−	1.60905i
$512$		0			0
$513$	−7.79423	−	4.50000i	−0.344124	−	0.198680i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	20.7846	−	12.0000i	0.914106	−	0.527759i
$518$		0			0
$519$	−45.0000			−1.97528
$520$		0			0
$521$	−34.0000			−1.48957			−0.744784	−	0.667306i	$-0.767447\pi$
$521$	−34.0000			−1.48957			−0.744784	+	0.667306i	$0.767447\pi$
$522$		0			0
$523$	19.9186	−	11.5000i	0.870979	−	0.502860i	0.00330547	−	0.999995i	$-0.498948\pi$
$523$	19.9186	−	11.5000i	0.870979	−	0.502860i	0.867673	+	0.497135i	$0.165615\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−24.2487	−	14.0000i	−1.05629	−	0.609850i
$528$		0			0
$529$	13.0000	−	22.5167i	0.565217	−	0.978985i
$530$		0			0
$531$	−15.0000	−	25.9808i	−0.650945	−	1.12747i
$532$		0			0
$533$	6.06218	+	24.5000i	0.262582	+	1.06121i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	49.3634	+	28.5000i	2.13019	+	1.22987i
$538$		0			0
$539$	3.00000	−	5.19615i	0.129219	−	0.223814i
$540$		0			0
$541$	10.0000			0.429934			0.214967	−	0.976621i	$-0.431036\pi$
$541$	10.0000			0.429934			0.214967	+	0.976621i	$0.431036\pi$
$542$		0			0
$543$	−36.3731	+	21.0000i	−1.56092	+	0.901196i
$544$		0			0
$545$		0			0
$546$		0			0
$547$		−	16.0000i		−	0.684111i	−0.939680	−	0.342055i	$-0.888877\pi$
$547$		−	16.0000i		−	0.684111i	0.939680	−	0.342055i	$-0.111123\pi$
$548$		0			0
$549$	−15.0000	−	25.9808i	−0.640184	−	1.10883i
$550$		0			0
$551$	−5.00000			−0.213007
$552$		0			0
$553$	−20.7846	−	12.0000i	−0.883852	−	0.510292i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−16.4545	+	9.50000i	−0.697199	+	0.402528i	−0.806303	−	0.591502i	$-0.798535\pi$
$557$	−16.4545	+	9.50000i	−0.697199	+	0.402528i	0.109104	+	0.994030i	$0.465202\pi$
$558$		0			0
$559$	22.5000	+	23.3827i	0.951649	+	0.988982i
$560$		0			0
$561$	−31.5000	−	54.5596i	−1.32993	−	2.30351i
$562$		0			0
$563$	−38.9711	−	22.5000i	−1.64244	−	0.948262i	−0.979963	−	0.199177i	$-0.936173\pi$
$563$	−38.9711	−	22.5000i	−1.64244	−	0.948262i	−0.662474	−	0.749085i	$-0.730494\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$			27.0000i			1.13389i
$568$		0			0
$569$	9.50000	+	16.4545i	0.398261	+	0.689808i	0.993511	−	0.113732i	$-0.0362806\pi$
$569$	9.50000	+	16.4545i	0.398261	+	0.689808i	−0.595251	+	0.803540i	$0.702947\pi$
$570$		0			0
$571$	−40.0000			−1.67395			−0.836974	−	0.547243i	$-0.815677\pi$
$571$	−40.0000			−1.67395			−0.836974	+	0.547243i	$0.815677\pi$
$572$		0			0
$573$		−	9.00000i		−	0.375980i
$574$		0			0
$575$		0			0
$576$		0			0
$577$			2.00000i			0.0832611i	0.999133	+	0.0416305i	$0.0132552\pi$
$577$			2.00000i			0.0832611i	−0.999133	+	0.0416305i	$0.986745\pi$
$578$		0			0
$579$	22.5000	−	38.9711i	0.935068	−	1.61959i
$580$		0			0
$581$	−18.0000	+	31.1769i	−0.746766	+	1.29344i
$582$		0			0
$583$	15.5885	−	9.00000i	0.645608	−	0.372742i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	32.0429	−	18.5000i	1.32255	−	0.763577i	0.338418	−	0.940996i	$-0.390108\pi$
$587$	32.0429	−	18.5000i	1.32255	−	0.763577i	0.984135	+	0.177419i	$0.0567748\pi$
$588$		0			0
$589$	−2.00000	+	3.46410i	−0.0824086	+	0.142736i
$590$		0			0
$591$	−34.5000	+	59.7558i	−1.41914	+	2.45802i
$592$		0			0
$593$		−	26.0000i		−	1.06769i	−0.845582	−	0.533846i	$-0.820746\pi$
$593$		−	26.0000i		−	1.06769i	0.845582	−	0.533846i	$-0.179254\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		−	27.0000i		−	1.10504i
$598$		0			0
$599$	−8.00000			−0.326871			−0.163436	−	0.986554i	$-0.552258\pi$
$599$	−8.00000			−0.326871			−0.163436	+	0.986554i	$0.552258\pi$
$600$		0			0
$601$	6.50000	+	11.2583i	0.265141	+	0.459237i	0.967600	−	0.252486i	$-0.0812483\pi$
$601$	6.50000	+	11.2583i	0.265141	+	0.459237i	−0.702460	+	0.711723i	$0.747915\pi$
$602$		0			0
$603$		−	78.0000i		−	3.17641i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	7.79423	+	4.50000i	0.316358	+	0.182649i	0.649768	−	0.760133i	$-0.274866\pi$
$607$	7.79423	+	4.50000i	0.316358	+	0.182649i	−0.333410	+	0.942782i	$0.608199\pi$
$608$		0			0
$609$	22.5000	+	38.9711i	0.911746	+	1.57919i
$610$		0			0
$611$	8.00000	−	27.7128i	0.323645	−	1.12114i
$612$		0			0
$613$	26.8468	−	15.5000i	1.08433	−	0.626039i	0.152270	−	0.988339i	$-0.451342\pi$
$613$	26.8468	−	15.5000i	1.08433	−	0.626039i	0.932062	+	0.362300i	$0.118008\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−25.1147	−	14.5000i	−1.01108	−	0.583748i	−0.0995732	−	0.995030i	$-0.531748\pi$
$617$	−25.1147	−	14.5000i	−1.01108	−	0.583748i	−0.911508	+	0.411282i	$0.865081\pi$
$618$		0			0
$619$	−12.0000			−0.482321			−0.241160	−	0.970485i	$-0.577528\pi$
$619$	−12.0000			−0.482321			−0.241160	+	0.970485i	$0.577528\pi$
$620$		0			0
$621$	−31.5000	−	54.5596i	−1.26405	−	2.18940i
$622$		0			0
$623$		−	21.0000i		−	0.841347i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−7.79423	+	4.50000i	−0.311272	+	0.179713i
$628$		0			0
$629$	−21.0000			−0.837325
$630$		0			0
$631$	7.50000	−	12.9904i	0.298570	−	0.517139i	−0.677239	−	0.735763i	$-0.736824\pi$
$631$	7.50000	−	12.9904i	0.298570	−	0.517139i	0.975809	+	0.218624i	$0.0701569\pi$
$632$		0			0
$633$	12.9904	+	7.50000i	0.516321	+	0.298098i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−1.73205	−	7.00000i	−0.0686264	−	0.277350i
$638$		0			0
$639$	−9.00000	−	15.5885i	−0.356034	−	0.616670i
$640$		0			0
$641$	10.5000	−	18.1865i	0.414725	−	0.718325i	−0.580674	−	0.814136i	$-0.697211\pi$
$641$	10.5000	−	18.1865i	0.414725	−	0.718325i	0.995400	+	0.0958109i	$0.0305444\pi$
$642$		0			0
$643$	6.06218	+	3.50000i	0.239069	+	0.138027i	0.614749	−	0.788723i	$-0.289257\pi$
$643$	6.06218	+	3.50000i	0.239069	+	0.138027i	−0.375680	+	0.926750i	$0.622591\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	14.7224	−	8.50000i	0.578799	−	0.334169i	−0.181857	−	0.983325i	$-0.558211\pi$
$647$	14.7224	−	8.50000i	0.578799	−	0.334169i	0.760656	+	0.649155i	$0.224878\pi$
$648$		0			0
$649$	−15.0000			−0.588802
$650$		0			0
$651$	36.0000			1.41095
$652$		0			0
$653$	9.52628	−	5.50000i	0.372792	−	0.215232i	−0.301885	−	0.953344i	$-0.597616\pi$
$653$	9.52628	−	5.50000i	0.372792	−	0.215232i	0.674678	+	0.738113i	$0.264283\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	72.7461	+	42.0000i	2.83810	+	1.63858i
$658$		0			0
$659$	−7.50000	+	12.9904i	−0.292159	+	0.506033i	−0.974320	−	0.225168i	$-0.927707\pi$
$659$	−7.50000	+	12.9904i	−0.292159	+	0.506033i	0.682161	+	0.731202i	$0.261040\pi$
$660$		0			0
$661$	8.50000	+	14.7224i	0.330612	+	0.572636i	0.982632	−	0.185565i	$-0.0594116\pi$
$661$	8.50000	+	14.7224i	0.330612	+	0.572636i	−0.652020	+	0.758202i	$0.726078\pi$
$662$		0			0
$663$	−72.7461	−	21.0000i	−2.82523	−	0.815572i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−30.3109	−	17.5000i	−1.17364	−	0.677603i
$668$		0			0
$669$	34.5000	−	59.7558i	1.33385	−	2.31029i
$670$		0			0
$671$	−15.0000			−0.579069
$672$		0			0
$673$	−11.2583	+	6.50000i	−0.433977	+	0.250557i	−0.701039	−	0.713123i	$-0.747280\pi$
$673$	−11.2583	+	6.50000i	−0.433977	+	0.250557i	0.267063	+	0.963679i	$0.413947\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$			22.0000i			0.845529i	0.906240	+	0.422764i	$0.138940\pi$
$677$			22.0000i			0.845529i	−0.906240	+	0.422764i	$0.861060\pi$
$678$		0			0
$679$	−16.5000	−	28.5788i	−0.633212	−	1.09676i
$680$		0			0
$681$	3.00000			0.114960
$682$		0			0
$683$	26.8468	+	15.5000i	1.02726	+	0.593091i	0.916200	−	0.400722i	$-0.131241\pi$
$683$	26.8468	+	15.5000i	1.02726	+	0.593091i	0.111064	+	0.993813i	$0.464574\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−67.5500	+	39.0000i	−2.57719	+	1.48794i
$688$		0			0
$689$	6.00000	−	20.7846i	0.228582	−	0.791831i
$690$		0			0
$691$	12.5000	+	21.6506i	0.475522	+	0.823629i	0.999607	−	0.0280373i	$-0.00892572\pi$
$691$	12.5000	+	21.6506i	0.475522	+	0.823629i	−0.524084	+	0.851666i	$0.675592\pi$
$692$		0			0
$693$	46.7654	+	27.0000i	1.77647	+	1.02565i
$694$		0			0
$695$		0			0
$696$		0			0
$697$		−	49.0000i		−	1.85601i
$698$		0			0
$699$	−27.0000	−	46.7654i	−1.02123	−	1.76883i
$700$		0			0
$701$	2.00000			0.0755390			0.0377695	−	0.999286i	$-0.487975\pi$
$701$	2.00000			0.0755390			0.0377695	+	0.999286i	$0.487975\pi$
$702$		0			0
$703$			3.00000i			0.113147i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		−	27.0000i		−	1.01544i
$708$		0			0
$709$	17.5000	−	30.3109i	0.657226	−	1.13835i	−0.324104	−	0.946021i	$-0.605063\pi$
$709$	17.5000	−	30.3109i	0.657226	−	1.13835i	0.981331	−	0.192328i	$-0.0616038\pi$
$710$		0			0
$711$	24.0000	−	41.5692i	0.900070	−	1.55897i
$712$		0			0
$713$	−24.2487	+	14.0000i	−0.908121	+	0.524304i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	41.5692	−	24.0000i	1.55243	−	0.896296i
$718$		0			0
$719$	0.500000	−	0.866025i	0.0186469	−	0.0322973i	−0.856551	−	0.516062i	$-0.827398\pi$
$719$	0.500000	−	0.866025i	0.0186469	−	0.0322973i	0.875198	+	0.483764i	$0.160731\pi$
$720$		0			0
$721$	24.0000	−	41.5692i	0.893807	−	1.54812i
$722$		0			0
$723$		−	3.00000i		−	0.111571i
$724$		0			0
$725$		0			0
$726$		0			0
$727$		−	28.0000i		−	1.03846i	−0.854634	−	0.519231i	$-0.826218\pi$
$727$		−	28.0000i		−	1.03846i	0.854634	−	0.519231i	$-0.173782\pi$
$728$		0			0
$729$	27.0000			1.00000
$730$		0			0
$731$	−31.5000	−	54.5596i	−1.16507	−	2.01796i
$732$		0			0
$733$		−	14.0000i		−	0.517102i	−0.965998	−	0.258551i	$-0.916755\pi$
$733$		−	14.0000i		−	0.517102i	0.965998	−	0.258551i	$-0.0832450\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−33.7750	−	19.5000i	−1.24412	−	0.718292i
$738$		0			0
$739$	19.5000	+	33.7750i	0.717319	+	1.24243i	0.962058	+	0.272844i	$0.0879643\pi$
$739$	19.5000	+	33.7750i	0.717319	+	1.24243i	−0.244739	+	0.969589i	$0.578702\pi$
$740$		0			0
$741$	−3.00000	+	10.3923i	−0.110208	+	0.381771i
$742$		0			0
$743$	−0.866025	+	0.500000i	−0.0317714	+	0.0183432i	−0.515802	−	0.856708i	$-0.672506\pi$
$743$	−0.866025	+	0.500000i	−0.0317714	+	0.0183432i	0.484030	+	0.875051i	$0.339172\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−62.3538	−	36.0000i	−2.28141	−	1.31717i
$748$		0			0
$749$	9.00000			0.328853
$750$		0			0
$751$	6.50000	+	11.2583i	0.237188	+	0.410822i	0.959906	−	0.280321i	$-0.0904408\pi$
$751$	6.50000	+	11.2583i	0.237188	+	0.410822i	−0.722718	+	0.691143i	$0.757107\pi$
$752$		0			0
$753$			15.0000i			0.546630i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	0.866025	−	0.500000i	0.0314762	−	0.0181728i	−0.484179	−	0.874969i	$-0.660882\pi$
$757$	0.866025	−	0.500000i	0.0314762	−	0.0181728i	0.515656	+	0.856796i	$0.327548\pi$
$758$		0			0
$759$	−63.0000			−2.28676
$760$		0			0
$761$	−25.5000	+	44.1673i	−0.924374	+	1.60106i	−0.131810	+	0.991275i	$0.542079\pi$
$761$	−25.5000	+	44.1673i	−0.924374	+	1.60106i	−0.792564	+	0.609788i	$0.791255\pi$
$762$		0			0
$763$	−36.3731	−	21.0000i	−1.31679	−	0.760251i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−12.9904	+	12.5000i	−0.469055	+	0.451349i
$768$		0			0
$769$	−2.50000	−	4.33013i	−0.0901523	−	0.156148i	0.817423	−	0.576038i	$-0.195402\pi$
$769$	−2.50000	−	4.33013i	−0.0901523	−	0.156148i	−0.907575	+	0.419890i	$0.862069\pi$
$770$		0			0
$771$	−28.5000	+	49.3634i	−1.02640	+	1.77778i
$772$		0			0
$773$	21.6506	+	12.5000i	0.778719	+	0.449594i	0.835976	−	0.548766i	$-0.184902\pi$
$773$	21.6506	+	12.5000i	0.778719	+	0.449594i	−0.0572570	+	0.998359i	$0.518235\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	23.3827	−	13.5000i	0.838849	−	0.484310i
$778$		0			0
$779$	−7.00000			−0.250801
$780$		0			0
$781$	−9.00000			−0.322045
$782$		0			0
$783$	−38.9711	+	22.5000i	−1.39272	+	0.804084i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	0.866025	+	0.500000i	0.0308705	+	0.0178231i	0.515356	−	0.856976i	$-0.327660\pi$
$787$	0.866025	+	0.500000i	0.0308705	+	0.0178231i	−0.484485	+	0.874799i	$0.660993\pi$
$788$		0			0
$789$	10.5000	−	18.1865i	0.373810	−	0.647458i
$790$		0			0
$791$	−19.5000	−	33.7750i	−0.693340	−	1.20090i
$792$		0			0
$793$	−12.9904	+	12.5000i	−0.461302	+	0.443888i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	6.06218	+	3.50000i	0.214733	+	0.123976i	0.603509	−	0.797356i	$-0.293769\pi$
$797$	6.06218	+	3.50000i	0.214733	+	0.123976i	−0.388776	+	0.921332i	$0.627102\pi$
$798$		0			0
$799$	−28.0000	+	48.4974i	−0.990569	+	1.71572i
$800$		0			0
$801$	42.0000			1.48400
$802$		0			0
$803$	36.3731	−	21.0000i	1.28358	−	0.741074i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		−	9.00000i		−	0.316815i
$808$		0			0
$809$	−12.5000	−	21.6506i	−0.439477	−	0.761196i	0.558173	−	0.829725i	$-0.311503\pi$
$809$	−12.5000	−	21.6506i	−0.439477	−	0.761196i	−0.997649	+	0.0685291i	$0.978169\pi$
$810$		0			0
$811$		0			0			−	1.00000i	$-0.5\pi$
$811$		0			0				1.00000i	$0.5\pi$
$812$		0			0
$813$	−59.7558	−	34.5000i	−2.09573	−	1.20997i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−7.79423	+	4.50000i	−0.272686	+	0.157435i
$818$		0			0
$819$	63.0000	−	15.5885i	2.20140	−	0.544705i
$820$		0			0
$821$	−7.50000	−	12.9904i	−0.261752	−	0.453367i	0.704956	−	0.709251i	$-0.250967\pi$
$821$	−7.50000	−	12.9904i	−0.261752	−	0.453367i	−0.966708	+	0.255884i	$0.917634\pi$
$822$		0			0
$823$	40.7032	+	23.5000i	1.41882	+	0.819159i	0.996196	−	0.0871445i	$-0.0277742\pi$
$823$	40.7032	+	23.5000i	1.41882	+	0.819159i	0.422628	+	0.906303i	$0.361108\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			12.0000i			0.417281i	0.977992	+	0.208640i	$0.0669038\pi$
$827$			12.0000i			0.417281i	−0.977992	+	0.208640i	$0.933096\pi$
$828$		0			0
$829$	−6.50000	−	11.2583i	−0.225754	−	0.391018i	0.730791	−	0.682601i	$-0.239151\pi$
$829$	−6.50000	−	11.2583i	−0.225754	−	0.391018i	−0.956545	+	0.291583i	$0.905818\pi$
$830$		0			0
$831$	69.0000			2.39358
$832$		0			0
$833$			14.0000i			0.485071i
$834$		0			0
$835$		0			0
$836$		0			0
$837$			36.0000i			1.24434i
$838$		0			0
$839$	6.50000	−	11.2583i	0.224405	−	0.388681i	−0.731736	−	0.681588i	$-0.761290\pi$
$839$	6.50000	−	11.2583i	0.224405	−	0.388681i	0.956141	+	0.292908i	$0.0946228\pi$
$840$		0			0
$841$	2.00000	−	3.46410i	0.0689655	−	0.119452i
$842$		0			0
$843$	−25.9808	+	15.0000i	−0.894825	+	0.516627i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−5.19615	+	3.00000i	−0.178542	+	0.103081i
$848$		0			0
$849$	−1.50000	+	2.59808i	−0.0514799	+	0.0891657i
$850$		0			0
$851$	−10.5000	+	18.1865i	−0.359935	+	0.623426i
$852$		0			0
$853$		−	10.0000i		−	0.342393i	−0.985237	−	0.171197i	$-0.945237\pi$
$853$		−	10.0000i		−	0.342393i	0.985237	−	0.171197i	$-0.0547634\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$			18.0000i			0.614868i	0.951569	+	0.307434i	$0.0994704\pi$
$857$			18.0000i			0.614868i	−0.951569	+	0.307434i	$0.900530\pi$
$858$		0			0
$859$	−44.0000			−1.50126			−0.750630	−	0.660722i	$-0.770250\pi$
$859$	−44.0000			−1.50126			−0.750630	+	0.660722i	$0.770250\pi$
$860$		0			0
$861$	31.5000	+	54.5596i	1.07352	+	1.85939i
$862$		0			0
$863$		−	16.0000i		−	0.544646i	−0.962206	−	0.272323i	$-0.912208\pi$
$863$		−	16.0000i		−	0.544646i	0.962206	−	0.272323i	$-0.0877920\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	83.1384	+	48.0000i	2.82353	+	1.63017i
$868$		0			0
$869$	−12.0000	−	20.7846i	−0.407072	−	0.705070i
$870$		0			0
$871$	−45.5000	+	11.2583i	−1.54171	+	0.381474i
$872$		0			0
$873$	57.1577	−	33.0000i	1.93449	−	1.11688i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−4.33013	−	2.50000i	−0.146218	−	0.0844190i	0.425106	−	0.905143i	$-0.360237\pi$
$877$	−4.33013	−	2.50000i	−0.146218	−	0.0844190i	−0.571324	+	0.820724i	$0.693570\pi$
$878$		0			0
$879$	27.0000			0.910687
$880$		0			0
$881$	−5.50000	−	9.52628i	−0.185300	−	0.320949i	0.758378	−	0.651815i	$-0.225992\pi$
$881$	−5.50000	−	9.52628i	−0.185300	−	0.320949i	−0.943677	+	0.330867i	$0.892659\pi$
$882$		0			0
$883$			44.0000i			1.48072i	0.672212	+	0.740359i	$0.265344\pi$
$883$			44.0000i			1.48072i	−0.672212	+	0.740359i	$0.734656\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−16.4545	+	9.50000i	−0.552487	+	0.318979i	−0.750125	−	0.661296i	$-0.770007\pi$
$887$	−16.4545	+	9.50000i	−0.552487	+	0.318979i	0.197637	+	0.980275i	$0.436673\pi$
$888$		0			0
$889$	−3.00000			−0.100617
$890$		0			0
$891$	−13.5000	+	23.3827i	−0.452267	+	0.783349i
$892$		0			0
$893$	6.92820	+	4.00000i	0.231843	+	0.133855i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−54.5596	+	52.5000i	−1.82169	+	1.75292i
$898$		0			0
$899$	10.0000	+	17.3205i	0.333519	+	0.577671i
$900$		0			0
$901$	−21.0000	+	36.3731i	−0.699611	+	1.21176i
$902$		0			0
$903$	70.1481	+	40.5000i	2.33438	+	1.34776i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	14.7224	−	8.50000i	0.488850	−	0.282238i	−0.235247	−	0.971936i	$-0.575590\pi$
$907$	14.7224	−	8.50000i	0.488850	−	0.282238i	0.724097	+	0.689698i	$0.242257\pi$
$908$		0			0
$909$	54.0000			1.79107
$910$		0			0
$911$	−12.0000			−0.397578			−0.198789	−	0.980042i	$-0.563701\pi$
$911$	−12.0000			−0.397578			−0.198789	+	0.980042i	$0.563701\pi$
$912$		0			0
$913$	−31.1769	+	18.0000i	−1.03181	+	0.595713i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−10.3923	−	6.00000i	−0.343184	−	0.198137i
$918$		0			0
$919$	−21.5000	+	37.2391i	−0.709220	+	1.22840i	0.255927	+	0.966696i	$0.417619\pi$
$919$	−21.5000	+	37.2391i	−0.709220	+	1.22840i	−0.965147	+	0.261708i	$0.915714\pi$
$920$		0			0
$921$	42.0000	+	72.7461i	1.38395	+	2.39707i
$922$		0			0
$923$	−7.79423	+	7.50000i	−0.256550	+	0.246866i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	83.1384	+	48.0000i	2.73062	+	1.57653i
$928$		0			0
$929$	−26.5000	+	45.8993i	−0.869437	+	1.50591i	−0.00686358	+	0.999976i	$0.502185\pi$
$929$	−26.5000	+	45.8993i	−0.869437	+	1.50591i	−0.862573	+	0.505932i	$0.831149\pi$
$930$		0			0
$931$	2.00000			0.0655474
$932$		0			0
$933$	−62.3538	+	36.0000i	−2.04137	+	1.17859i
$934$		0			0
$935$		0			0
$936$		0			0
$937$			50.0000i			1.63343i	0.577042	+	0.816714i	$0.304207\pi$
$937$			50.0000i			1.63343i	−0.577042	+	0.816714i	$0.695793\pi$
$938$		0			0
$939$	9.00000	+	15.5885i	0.293704	+	0.508710i
$940$		0			0
$941$	42.0000			1.36916			0.684580	−	0.728937i	$-0.259985\pi$
$941$	42.0000			1.36916			0.684580	+	0.728937i	$0.259985\pi$
$942$		0			0
$943$	−42.4352	−	24.5000i	−1.38188	−	0.797830i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−47.6314	+	27.5000i	−1.54781	+	0.893630i	−0.549504	+	0.835491i	$0.685183\pi$
$947$	−47.6314	+	27.5000i	−1.54781	+	0.893630i	−0.998309	+	0.0581388i	$0.981483\pi$
$948$		0			0
$949$	14.0000	−	48.4974i	0.454459	−	1.57429i
$950$		0			0
$951$	−3.00000	−	5.19615i	−0.0972817	−	0.168497i
$952$		0			0
$953$	−26.8468	−	15.5000i	−0.869653	−	0.502094i	−0.00241992	−	0.999997i	$-0.500770\pi$
$953$	−26.8468	−	15.5000i	−0.869653	−	0.502094i	−0.867233	+	0.497903i	$0.834104\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$			45.0000i			1.45464i
$958$		0			0
$959$	−4.50000	−	7.79423i	−0.145313	−	0.251689i
$960$		0			0
$961$	−15.0000			−0.483871
$962$		0			0
$963$			18.0000i			0.580042i
$964$		0			0
$965$		0			0
$966$		0			0
$967$		−	48.0000i		−	1.54358i	−0.635880	−	0.771788i	$-0.719363\pi$
$967$		−	48.0000i		−	1.54358i	0.635880	−	0.771788i	$-0.280637\pi$
$968$		0			0
$969$	10.5000	−	18.1865i	0.337309	−	0.584236i
$970$		0			0
$971$	21.5000	−	37.2391i	0.689968	−	1.19506i	−0.281880	−	0.959450i	$-0.590958\pi$
$971$	21.5000	−	37.2391i	0.689968	−	1.19506i	0.971848	−	0.235610i	$-0.0757087\pi$
$972$		0			0
$973$	−33.7750	+	19.5000i	−1.08278	+	0.625141i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−2.59808	+	1.50000i	−0.0831198	+	0.0479893i	−0.540984	−	0.841033i	$-0.681948\pi$
$977$	−2.59808	+	1.50000i	−0.0831198	+	0.0479893i	0.457864	+	0.889022i	$0.348615\pi$
$978$		0			0
$979$	10.5000	−	18.1865i	0.335581	−	0.581244i
$980$		0			0
$981$	42.0000	−	72.7461i	1.34096	−	2.32261i
$982$		0			0
$983$		−	36.0000i		−	1.14822i	−0.818778	−	0.574111i	$-0.805348\pi$
$983$		−	36.0000i		−	1.14822i	0.818778	−	0.574111i	$-0.194652\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		−	72.0000i		−	2.29179i
$988$		0			0
$989$	−63.0000			−2.00328
$990$		0			0
$991$	6.50000	+	11.2583i	0.206479	+	0.357633i	0.950603	−	0.310409i	$-0.100466\pi$
$991$	6.50000	+	11.2583i	0.206479	+	0.357633i	−0.744124	+	0.668042i	$0.767133\pi$
$992$		0			0
$993$			39.0000i			1.23763i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−11.2583	−	6.50000i	−0.356555	−	0.205857i	0.311014	−	0.950405i	$-0.399332\pi$
$997$	−11.2583	−	6.50000i	−0.356555	−	0.205857i	−0.667568	+	0.744548i	$0.732665\pi$
$998$		0			0
$999$	13.5000	+	23.3827i	0.427121	+	0.739795i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1300.2.bb.e.549.2		4
5.2	odd	4		1300.2.i.a.601.1		2
5.3	odd	4		260.2.i.d.81.1	yes	2
5.4	even	2	inner	1300.2.bb.e.549.1		4
13.9	even	3	inner	1300.2.bb.e.1049.1		4
15.8	even	4		2340.2.q.a.2161.1		2
20.3	even	4		1040.2.q.b.81.1		2
65.3	odd	12		3380.2.a.b.1.1		1
65.9	even	6	inner	1300.2.bb.e.1049.2		4
65.22	odd	12		1300.2.i.a.1101.1		2
65.23	odd	12		3380.2.a.a.1.1		1
65.28	even	12		3380.2.f.a.3041.1		2
65.48	odd	12		260.2.i.d.61.1	✓	2
65.63	even	12		3380.2.f.a.3041.2		2
195.113	even	12		2340.2.q.a.1621.1		2
260.243	even	12		1040.2.q.b.321.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.i.d.61.1	✓	2	65.48	odd	12
260.2.i.d.81.1	yes	2	5.3	odd	4
1040.2.q.b.81.1		2	20.3	even	4
1040.2.q.b.321.1		2	260.243	even	12
1300.2.i.a.601.1		2	5.2	odd	4
1300.2.i.a.1101.1		2	65.22	odd	12
1300.2.bb.e.549.1		4	5.4	even	2	inner
1300.2.bb.e.549.2		4	1.1	even	1	trivial
1300.2.bb.e.1049.1		4	13.9	even	3	inner
1300.2.bb.e.1049.2		4	65.9	even	6	inner
2340.2.q.a.1621.1		2	195.113	even	12
2340.2.q.a.2161.1		2	15.8	even	4
3380.2.a.a.1.1		1	65.23	odd	12
3380.2.a.b.1.1		1	65.3	odd	12
3380.2.f.a.3041.1		2	65.28	even	12
3380.2.f.a.3041.2		2	65.63	even	12

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:	\( N \)	\(=\)	\( 1300 = 2^{2} \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1300.bb (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.59808 - 1.50000i) q^{3} +(-2.59808 - 1.50000i) q^{7} +(3.00000 - 5.19615i) q^{9} +O(q^{10})\)	\(q+(2.59808 - 1.50000i) q^{3} +(-2.59808 - 1.50000i) q^{7} +(3.00000 - 5.19615i) q^{9} +(-1.50000 - 2.59808i) q^{11} +(-3.46410 - 1.00000i) q^{13} +(6.06218 + 3.50000i) q^{17} +(0.500000 - 0.866025i) q^{19} -9.00000 q^{21} +(6.06218 - 3.50000i) q^{23} -9.00000i q^{27} +(-2.50000 - 4.33013i) q^{29} -4.00000 q^{31} +(-7.79423 - 4.50000i) q^{33} +(-2.59808 + 1.50000i) q^{37} +(-10.5000 + 2.59808i) q^{39} +(-3.50000 - 6.06218i) q^{41} +(-7.79423 - 4.50000i) q^{43} +8.00000i q^{47} +(1.00000 + 1.73205i) q^{49} +21.0000 q^{51} +6.00000i q^{53} -3.00000i q^{57} +(2.50000 - 4.33013i) q^{59} +(2.50000 - 4.33013i) q^{61} +(-15.5885 + 9.00000i) q^{63} +(11.2583 - 6.50000i) q^{67} +(10.5000 - 18.1865i) q^{69} +(1.50000 - 2.59808i) q^{71} +14.0000i q^{73} +9.00000i q^{77} +8.00000 q^{79} +(-4.50000 - 7.79423i) q^{81} -12.0000i q^{83} +(-12.9904 - 7.50000i) q^{87} +(3.50000 + 6.06218i) q^{89} +(7.50000 + 7.79423i) q^{91} +(-10.3923 + 6.00000i) q^{93} +(9.52628 + 5.50000i) q^{97} -18.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 12 q^{9}+O(q^{10}) \) 4 * q + 12 * q^9	\( 4 q + 12 q^{9} - 6 q^{11} + 2 q^{19} - 36 q^{21} - 10 q^{29} - 16 q^{31} - 42 q^{39} - 14 q^{41} + 4 q^{49} + 84 q^{51} + 10 q^{59} + 10 q^{61} + 42 q^{69} + 6 q^{71} + 32 q^{79} - 18 q^{81} + 14 q^{89} + 30 q^{91} - 72 q^{99}+O(q^{100}) \) 4 * q + 12 * q^9 - 6 * q^11 + 2 * q^19 - 36 * q^21 - 10 * q^29 - 16 * q^31 - 42 * q^39 - 14 * q^41 + 4 * q^49 + 84 * q^51 + 10 * q^59 + 10 * q^61 + 42 * q^69 + 6 * q^71 + 32 * q^79 - 18 * q^81 + 14 * q^89 + 30 * q^91 - 72 * q^99

Introduction

L-functions

Modular forms

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Database

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