LMFDB - Embedded newform 1300.2.bb.a.1049.2

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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 260)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1049.2
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1300.1049
Dual form			1300.2.bb.a.549.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{3} +(-0.866025 + 0.500000i) q^{7} +(-1.00000 - 1.73205i) q^{9} +O(q^{10})$	$q+(0.866025 + 0.500000i) q^{3} +(-0.866025 + 0.500000i) q^{7} +(-1.00000 - 1.73205i) q^{9} +(-1.50000 + 2.59808i) q^{11} +(-3.46410 - 1.00000i) q^{13} +(-2.59808 + 1.50000i) q^{17} +(-3.50000 - 6.06218i) q^{19} -1.00000 q^{21} +(-2.59808 - 1.50000i) q^{23} -5.00000i q^{27} +(1.50000 - 2.59808i) q^{29} -4.00000 q^{31} +(-2.59808 + 1.50000i) q^{33} +(6.06218 + 3.50000i) q^{37} +(-2.50000 - 2.59808i) q^{39} +(4.50000 - 7.79423i) q^{41} +(-9.52628 + 5.50000i) q^{43} +(-3.00000 + 5.19615i) q^{49} -3.00000 q^{51} +6.00000i q^{53} -7.00000i q^{57} +(-1.50000 - 2.59808i) q^{59} +(-5.50000 - 9.52628i) q^{61} +(1.73205 + 1.00000i) q^{63} +(6.06218 + 3.50000i) q^{67} +(-1.50000 - 2.59808i) q^{69} +(1.50000 + 2.59808i) q^{71} -2.00000i q^{73} -3.00000i q^{77} -8.00000 q^{79} +(-0.500000 + 0.866025i) q^{81} +12.0000i q^{83} +(2.59808 - 1.50000i) q^{87} +(7.50000 - 12.9904i) q^{89} +(3.50000 - 0.866025i) q^{91} +(-3.46410 - 2.00000i) q^{93} +(-6.06218 + 3.50000i) q^{97} +6.00000 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^9	$ 4 q - 4 q^{9} - 6 q^{11} - 14 q^{19} - 4 q^{21} + 6 q^{29} - 16 q^{31} - 10 q^{39} + 18 q^{41} - 12 q^{49} - 12 q^{51} - 6 q^{59} - 22 q^{61} - 6 q^{69} + 6 q^{71} - 32 q^{79} - 2 q^{81} + 30 q^{89} + 14 q^{91} + 24 q^{99}+O(q^{100}) $ 4 * q - 4 * q^9 - 6 * q^11 - 14 * q^19 - 4 * q^21 + 6 * q^29 - 16 * q^31 - 10 * q^39 + 18 * q^41 - 12 * q^49 - 12 * q^51 - 6 * q^59 - 22 * q^61 - 6 * q^69 + 6 * q^71 - 32 * q^79 - 2 * q^81 + 30 * q^89 + 14 * q^91 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$301$	$651$	$677$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$-1$

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
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i	0.728714	−	0.684819i	$-0.240119\pi$
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i	−0.228714	+	0.973494i	$0.573452\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−0.866025	+	0.500000i	−0.327327	+	0.188982i	−0.654654	−	0.755929i	$-0.727186\pi$
$7$	−0.866025	+	0.500000i	−0.327327	+	0.188982i	0.327327	+	0.944911i	$0.393852\pi$
$8$		0			0
$9$	−1.00000	−	1.73205i	−0.333333	−	0.577350i
$10$		0			0
$11$	−1.50000	+	2.59808i	−0.452267	+	0.783349i	−0.998526	−	0.0542666i	$-0.982718\pi$
$11$	−1.50000	+	2.59808i	−0.452267	+	0.783349i	0.546259	+	0.837616i	$0.316051\pi$
$12$		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
$17$	−2.59808	+	1.50000i	−0.630126	+	0.363803i	−0.780801	−	0.624780i	$-0.785189\pi$
$17$	−2.59808	+	1.50000i	−0.630126	+	0.363803i	0.150675	+	0.988583i	$0.451855\pi$
$18$		0			0
$19$	−3.50000	−	6.06218i	−0.802955	−	1.39076i	−0.917663	−	0.397360i	$-0.869927\pi$
$19$	−3.50000	−	6.06218i	−0.802955	−	1.39076i	0.114708	−	0.993399i	$-0.463407\pi$
$20$		0			0
$21$	−1.00000			−0.218218
$22$		0			0
$23$	−2.59808	−	1.50000i	−0.541736	−	0.312772i	0.204046	−	0.978961i	$-0.434591\pi$
$23$	−2.59808	−	1.50000i	−0.541736	−	0.312772i	−0.745782	+	0.666190i	$0.767924\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$		−	5.00000i		−	0.962250i
$28$		0			0
$29$	1.50000	−	2.59808i	0.278543	−	0.482451i	−0.692480	−	0.721437i	$-0.743482\pi$
$29$	1.50000	−	2.59808i	0.278543	−	0.482451i	0.971023	+	0.238987i	$0.0768152\pi$
$30$		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
$33$	−2.59808	+	1.50000i	−0.452267	+	0.261116i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	6.06218	+	3.50000i	0.996616	+	0.575396i	0.907245	−	0.420602i	$-0.138181\pi$
$37$	6.06218	+	3.50000i	0.996616	+	0.575396i	0.0893706	+	0.995998i	$0.471514\pi$
$38$		0			0
$39$	−2.50000	−	2.59808i	−0.400320	−	0.416025i
$40$		0			0
$41$	4.50000	−	7.79423i	0.702782	−	1.21725i	−0.264704	−	0.964330i	$-0.585274\pi$
$41$	4.50000	−	7.79423i	0.702782	−	1.21725i	0.967486	−	0.252924i	$-0.0813924\pi$
$42$		0			0
$43$	−9.52628	+	5.50000i	−1.45274	+	0.838742i	−0.998636	−	0.0522047i	$-0.983375\pi$
$43$	−9.52628	+	5.50000i	−1.45274	+	0.838742i	−0.454108	+	0.890947i	$0.650042\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		0			0		1.00000			$0$
$47$		0			0		−1.00000			$\pi$
$48$		0			0
$49$	−3.00000	+	5.19615i	−0.428571	+	0.742307i
$50$		0			0
$51$	−3.00000			−0.420084
$52$		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
$57$		−	7.00000i		−	0.927173i
$58$		0			0
$59$	−1.50000	−	2.59808i	−0.195283	−	0.338241i	0.751710	−	0.659494i	$-0.229229\pi$
$59$	−1.50000	−	2.59808i	−0.195283	−	0.338241i	−0.946993	+	0.321253i	$0.895896\pi$
$60$		0			0
$61$	−5.50000	−	9.52628i	−0.704203	−	1.21972i	−0.966978	−	0.254858i	$-0.917971\pi$
$61$	−5.50000	−	9.52628i	−0.704203	−	1.21972i	0.262776	−	0.964857i	$-0.415362\pi$
$62$		0			0
$63$	1.73205	+	1.00000i	0.218218	+	0.125988i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	6.06218	+	3.50000i	0.740613	+	0.427593i	0.822292	−	0.569066i	$-0.192695\pi$
$67$	6.06218	+	3.50000i	0.740613	+	0.427593i	−0.0816792	+	0.996659i	$0.526028\pi$
$68$		0			0
$69$	−1.50000	−	2.59808i	−0.180579	−	0.312772i
$70$		0			0
$71$	1.50000	+	2.59808i	0.178017	+	0.308335i	0.941201	−	0.337846i	$-0.109698\pi$
$71$	1.50000	+	2.59808i	0.178017	+	0.308335i	−0.763184	+	0.646181i	$0.776365\pi$
$72$		0			0
$73$		−	2.00000i		−	0.234082i	−0.993127	−	0.117041i	$-0.962659\pi$
$73$		−	2.00000i		−	0.234082i	0.993127	−	0.117041i	$-0.0373409\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$		−	3.00000i		−	0.341882i
$78$		0			0
$79$	−8.00000			−0.900070			−0.450035	−	0.893011i	$-0.648589\pi$
$79$	−8.00000			−0.900070			−0.450035	+	0.893011i	$0.648589\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$			12.0000i			1.31717i	0.752506	+	0.658586i	$0.228845\pi$
$83$			12.0000i			1.31717i	−0.752506	+	0.658586i	$0.771155\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	2.59808	−	1.50000i	0.278543	−	0.160817i
$88$		0			0
$89$	7.50000	−	12.9904i	0.794998	−	1.37698i	−0.127842	−	0.991795i	$-0.540805\pi$
$89$	7.50000	−	12.9904i	0.794998	−	1.37698i	0.922840	−	0.385183i	$-0.125862\pi$
$90$		0			0
$91$	3.50000	−	0.866025i	0.366900	−	0.0907841i
$92$		0			0
$93$	−3.46410	−	2.00000i	−0.359211	−	0.207390i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−6.06218	+	3.50000i	−0.615521	+	0.355371i	−0.775123	−	0.631810i	$-0.782312\pi$
$97$	−6.06218	+	3.50000i	−0.615521	+	0.355371i	0.159602	+	0.987181i	$0.448979\pi$
$98$		0			0
$99$	6.00000			0.603023
$100$		0			0
$101$	4.50000	−	7.79423i	0.447767	−	0.775555i	−0.550474	−	0.834853i	$-0.685553\pi$
$101$	4.50000	−	7.79423i	0.447767	−	0.775555i	0.998240	+	0.0592978i	$0.0188862\pi$
$102$		0			0
$103$		−	8.00000i		−	0.788263i	−0.919054	−	0.394132i	$-0.871045\pi$
$103$		−	8.00000i		−	0.788263i	0.919054	−	0.394132i	$-0.128955\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−7.79423	−	4.50000i	−0.753497	−	0.435031i	0.0734594	−	0.997298i	$-0.476596\pi$
$107$	−7.79423	−	4.50000i	−0.753497	−	0.435031i	−0.826956	+	0.562267i	$0.809929\pi$
$108$		0			0
$109$	−2.00000			−0.191565			−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000			−0.191565			−0.0957826	+	0.995402i	$0.530535\pi$
$110$		0			0
$111$	3.50000	+	6.06218i	0.332205	+	0.575396i
$112$		0			0
$113$	−7.79423	+	4.50000i	−0.733219	+	0.423324i	−0.819599	−	0.572938i	$-0.805804\pi$
$113$	−7.79423	+	4.50000i	−0.733219	+	0.423324i	0.0863794	+	0.996262i	$0.472470\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	1.73205	+	7.00000i	0.160128	+	0.647150i
$118$		0			0
$119$	1.50000	−	2.59808i	0.137505	−	0.238165i
$120$		0			0
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$		0			0
$123$	7.79423	−	4.50000i	0.702782	−	0.405751i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	16.4545	+	9.50000i	1.46010	+	0.842989i	0.999015	−	0.0443678i	$-0.0141274\pi$
$127$	16.4545	+	9.50000i	1.46010	+	0.842989i	0.461084	+	0.887357i	$0.347461\pi$
$128$		0			0
$129$	−11.0000			−0.968496
$130$		0			0
$131$	−12.0000			−1.04844			−0.524222	−	0.851581i	$-0.675644\pi$
$131$	−12.0000			−1.04844			−0.524222	+	0.851581i	$0.675644\pi$
$132$		0			0
$133$	6.06218	+	3.50000i	0.525657	+	0.303488i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−12.9904	+	7.50000i	−1.10984	+	0.640768i	−0.938789	−	0.344493i	$-0.888051\pi$
$137$	−12.9904	+	7.50000i	−1.10984	+	0.640768i	−0.171054	+	0.985262i	$0.554717\pi$
$138$		0			0
$139$	2.50000	+	4.33013i	0.212047	+	0.367277i	0.952355	−	0.304991i	$-0.0986536\pi$
$139$	2.50000	+	4.33013i	0.212047	+	0.367277i	−0.740308	+	0.672268i	$0.765320\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	7.79423	−	7.50000i	0.651786	−	0.627182i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−5.19615	+	3.00000i	−0.428571	+	0.247436i
$148$		0			0
$149$	−10.5000	−	18.1865i	−0.860194	−	1.48990i	−0.871742	−	0.489966i	$-0.837009\pi$
$149$	−10.5000	−	18.1865i	−0.860194	−	1.48990i	0.0115483	−	0.999933i	$-0.496324\pi$
$150$		0			0
$151$	8.00000			0.651031			0.325515	−	0.945537i	$-0.394462\pi$
$151$	8.00000			0.651031			0.325515	+	0.945537i	$0.394462\pi$
$152$		0			0
$153$	5.19615	+	3.00000i	0.420084	+	0.242536i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		−	10.0000i		−	0.798087i	−0.916932	−	0.399043i	$-0.869342\pi$
$157$		−	10.0000i		−	0.798087i	0.916932	−	0.399043i	$-0.130658\pi$
$158$		0			0
$159$	−3.00000	+	5.19615i	−0.237915	+	0.412082i
$160$		0			0
$161$	3.00000			0.236433
$162$		0			0
$163$	0.866025	−	0.500000i	0.0678323	−	0.0391630i	−0.465700	−	0.884943i	$-0.654198\pi$
$163$	0.866025	−	0.500000i	0.0678323	−	0.0391630i	0.533533	+	0.845780i	$0.320864\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	2.59808	+	1.50000i	0.201045	+	0.116073i	0.597143	−	0.802135i	$-0.296303\pi$
$167$	2.59808	+	1.50000i	0.201045	+	0.116073i	−0.396098	+	0.918208i	$0.629636\pi$
$168$		0			0
$169$	11.0000	+	6.92820i	0.846154	+	0.532939i
$170$		0			0
$171$	−7.00000	+	12.1244i	−0.535303	+	0.927173i
$172$		0			0
$173$	2.59808	−	1.50000i	0.197528	−	0.114043i	−0.397974	−	0.917397i	$-0.630287\pi$
$173$	2.59808	−	1.50000i	0.197528	−	0.114043i	0.595502	+	0.803354i	$0.296953\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		−	3.00000i		−	0.225494i
$178$		0			0
$179$	−10.5000	+	18.1865i	−0.784807	+	1.35933i	0.144308	+	0.989533i	$0.453905\pi$
$179$	−10.5000	+	18.1865i	−0.784807	+	1.35933i	−0.929114	+	0.369792i	$0.879429\pi$
$180$		0			0
$181$	2.00000			0.148659			0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$		0			0
$183$		−	11.0000i		−	0.813143i
$184$		0			0
$185$		0			0
$186$		0			0
$187$		−	9.00000i		−	0.658145i
$188$		0			0
$189$	2.50000	+	4.33013i	0.181848	+	0.314970i
$190$		0			0
$191$	1.50000	+	2.59808i	0.108536	+	0.187990i	0.915177	−	0.403051i	$-0.132050\pi$
$191$	1.50000	+	2.59808i	0.108536	+	0.187990i	−0.806641	+	0.591041i	$0.798717\pi$
$192$		0			0
$193$	4.33013	+	2.50000i	0.311689	+	0.179954i	0.647682	−	0.761911i	$-0.275738\pi$
$193$	4.33013	+	2.50000i	0.311689	+	0.179954i	−0.335993	+	0.941865i	$0.609072\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−18.1865	−	10.5000i	−1.29574	−	0.748094i	−0.316072	−	0.948735i	$-0.602364\pi$
$197$	−18.1865	−	10.5000i	−1.29574	−	0.748094i	−0.979665	+	0.200641i	$0.935697\pi$
$198$		0			0
$199$	8.50000	+	14.7224i	0.602549	+	1.04365i	0.992434	+	0.122782i	$0.0391815\pi$
$199$	8.50000	+	14.7224i	0.602549	+	1.04365i	−0.389885	+	0.920864i	$0.627485\pi$
$200$		0			0
$201$	3.50000	+	6.06218i	0.246871	+	0.427593i
$202$		0			0
$203$			3.00000i			0.210559i
$204$		0			0
$205$		0			0
$206$		0			0
$207$			6.00000i			0.417029i
$208$		0			0
$209$	21.0000			1.45260
$210$		0			0
$211$	−5.50000	+	9.52628i	−0.378636	+	0.655816i	−0.990864	−	0.134865i	$-0.956940\pi$
$211$	−5.50000	+	9.52628i	−0.378636	+	0.655816i	0.612228	+	0.790681i	$0.290273\pi$
$212$		0			0
$213$			3.00000i			0.205557i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	3.46410	−	2.00000i	0.235159	−	0.135769i
$218$		0			0
$219$	1.00000	−	1.73205i	0.0675737	−	0.117041i
$220$		0			0
$221$	10.5000	−	2.59808i	0.706306	−	0.174766i
$222$		0			0
$223$	−16.4545	−	9.50000i	−1.10187	−	0.636167i	−0.165161	−	0.986267i	$-0.552814\pi$
$223$	−16.4545	−	9.50000i	−1.10187	−	0.636167i	−0.936713	+	0.350100i	$0.886148\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	23.3827	−	13.5000i	1.55196	−	0.896026i	0.553981	−	0.832529i	$-0.313108\pi$
$227$	23.3827	−	13.5000i	1.55196	−	0.896026i	0.997982	−	0.0634974i	$-0.0202255\pi$
$228$		0			0
$229$	22.0000			1.45380			0.726900	−	0.686743i	$-0.240960\pi$
$229$	22.0000			1.45380			0.726900	+	0.686743i	$0.240960\pi$
$230$		0			0
$231$	1.50000	−	2.59808i	0.0986928	−	0.170941i
$232$		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
$237$	−6.92820	−	4.00000i	−0.450035	−	0.259828i
$238$		0			0
$239$		0			0			−	1.00000i	$-0.5\pi$
$239$		0			0				1.00000i	$0.5\pi$
$240$		0			0
$241$	0.500000	+	0.866025i	0.0322078	+	0.0557856i	0.881680	−	0.471848i	$-0.156413\pi$
$241$	0.500000	+	0.866025i	0.0322078	+	0.0557856i	−0.849472	+	0.527633i	$0.823079\pi$
$242$		0			0
$243$	−13.8564	+	8.00000i	−0.888889	+	0.513200i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	6.06218	+	24.5000i	0.385727	+	1.55890i
$248$		0			0
$249$	−6.00000	+	10.3923i	−0.380235	+	0.658586i
$250$		0			0
$251$	−10.5000	−	18.1865i	−0.662754	−	1.14792i	−0.979889	−	0.199543i	$-0.936054\pi$
$251$	−10.5000	−	18.1865i	−0.662754	−	1.14792i	0.317135	−	0.948380i	$-0.397279\pi$
$252$		0			0
$253$	7.79423	−	4.50000i	0.490019	−	0.282913i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−7.79423	−	4.50000i	−0.486191	−	0.280702i	0.236802	−	0.971558i	$-0.423901\pi$
$257$	−7.79423	−	4.50000i	−0.486191	−	0.280702i	−0.722993	+	0.690856i	$0.757234\pi$
$258$		0			0
$259$	−7.00000			−0.434959
$260$		0			0
$261$	−6.00000			−0.371391
$262$		0			0
$263$	−2.59808	−	1.50000i	−0.160204	−	0.0924940i	0.417755	−	0.908560i	$-0.362817\pi$
$263$	−2.59808	−	1.50000i	−0.160204	−	0.0924940i	−0.577959	+	0.816066i	$0.696151\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	12.9904	−	7.50000i	0.794998	−	0.458993i
$268$		0			0
$269$	13.5000	+	23.3827i	0.823110	+	1.42567i	0.903356	+	0.428892i	$0.141096\pi$
$269$	13.5000	+	23.3827i	0.823110	+	1.42567i	−0.0802460	+	0.996775i	$0.525571\pi$
$270$		0			0
$271$	−11.5000	+	19.9186i	−0.698575	+	1.20997i	0.270385	+	0.962752i	$0.412849\pi$
$271$	−11.5000	+	19.9186i	−0.698575	+	1.20997i	−0.968960	+	0.247216i	$0.920484\pi$
$272$		0			0
$273$	3.46410	+	1.00000i	0.209657	+	0.0605228i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−16.4545	+	9.50000i	−0.988654	+	0.570800i	−0.904872	−	0.425684i	$-0.860033\pi$
$277$	−16.4545	+	9.50000i	−0.988654	+	0.570800i	−0.0837823	+	0.996484i	$0.526700\pi$
$278$		0			0
$279$	4.00000	+	6.92820i	0.239474	+	0.414781i
$280$		0			0
$281$	6.00000			0.357930			0.178965	−	0.983855i	$-0.442725\pi$
$281$	6.00000			0.357930			0.178965	+	0.983855i	$0.442725\pi$
$282$		0			0
$283$	4.33013	+	2.50000i	0.257399	+	0.148610i	0.623148	−	0.782104i	$-0.285854\pi$
$283$	4.33013	+	2.50000i	0.257399	+	0.148610i	−0.365748	+	0.930714i	$0.619187\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$			9.00000i			0.531253i
$288$		0			0
$289$	−4.00000	+	6.92820i	−0.235294	+	0.407541i
$290$		0			0
$291$	−7.00000			−0.410347
$292$		0			0
$293$	23.3827	−	13.5000i	1.36603	−	0.788678i	0.375613	−	0.926777i	$-0.377432\pi$
$293$	23.3827	−	13.5000i	1.36603	−	0.788678i	0.990419	+	0.138098i	$0.0440990\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	12.9904	+	7.50000i	0.753778	+	0.435194i
$298$		0			0
$299$	7.50000	+	7.79423i	0.433736	+	0.450752i
$300$		0			0
$301$	5.50000	−	9.52628i	0.317015	−	0.549086i
$302$		0			0
$303$	7.79423	−	4.50000i	0.447767	−	0.258518i
$304$		0			0
$305$		0			0
$306$		0			0
$307$			20.0000i			1.14146i	0.821138	+	0.570730i	$0.193340\pi$
$307$			20.0000i			1.14146i	−0.821138	+	0.570730i	$0.806660\pi$
$308$		0			0
$309$	4.00000	−	6.92820i	0.227552	−	0.394132i
$310$		0			0
$311$	24.0000			1.36092			0.680458	−	0.732787i	$-0.261781\pi$
$311$	24.0000			1.36092			0.680458	+	0.732787i	$0.261781\pi$
$312$		0			0
$313$			22.0000i			1.24351i	0.783210	+	0.621757i	$0.213581\pi$
$313$			22.0000i			1.24351i	−0.783210	+	0.621757i	$0.786419\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		−	18.0000i		−	1.01098i	−0.862832	−	0.505490i	$-0.831312\pi$
$317$		−	18.0000i		−	1.01098i	0.862832	−	0.505490i	$-0.168688\pi$
$318$		0			0
$319$	4.50000	+	7.79423i	0.251952	+	0.436393i
$320$		0			0
$321$	−4.50000	−	7.79423i	−0.251166	−	0.435031i
$322$		0			0
$323$	18.1865	+	10.5000i	1.01193	+	0.584236i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−1.73205	−	1.00000i	−0.0957826	−	0.0553001i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	9.50000	+	16.4545i	0.522167	+	0.904420i	0.999667	+	0.0257885i	$0.00820965\pi$
$331$	9.50000	+	16.4545i	0.522167	+	0.904420i	−0.477500	+	0.878632i	$0.658457\pi$
$332$		0			0
$333$		−	14.0000i		−	0.767195i
$334$		0			0
$335$		0			0
$336$		0			0
$337$		−	34.0000i		−	1.85210i	−0.377403	−	0.926049i	$-0.623183\pi$
$337$		−	34.0000i		−	1.85210i	0.377403	−	0.926049i	$-0.376817\pi$
$338$		0			0
$339$	−9.00000			−0.488813
$340$		0			0
$341$	6.00000	−	10.3923i	0.324918	−	0.562775i
$342$		0			0
$343$		−	13.0000i		−	0.701934i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−28.5788	+	16.5000i	−1.53419	+	0.885766i	−0.535031	+	0.844833i	$0.679700\pi$
$347$	−28.5788	+	16.5000i	−1.53419	+	0.885766i	−0.999162	+	0.0409337i	$0.986967\pi$
$348$		0			0
$349$	−0.500000	+	0.866025i	−0.0267644	+	0.0463573i	−0.879097	−	0.476642i	$-0.841854\pi$
$349$	−0.500000	+	0.866025i	−0.0267644	+	0.0463573i	0.852333	+	0.523000i	$0.175187\pi$
$350$		0			0
$351$	−5.00000	+	17.3205i	−0.266880	+	0.924500i
$352$		0			0
$353$	7.79423	+	4.50000i	0.414845	+	0.239511i	0.692869	−	0.721063i	$-0.256346\pi$
$353$	7.79423	+	4.50000i	0.414845	+	0.239511i	−0.278024	+	0.960574i	$0.589680\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	2.59808	−	1.50000i	0.137505	−	0.0793884i
$358$		0			0
$359$	24.0000			1.26667			0.633336	−	0.773877i	$-0.281685\pi$
$359$	24.0000			1.26667			0.633336	+	0.773877i	$0.281685\pi$
$360$		0			0
$361$	−15.0000	+	25.9808i	−0.789474	+	1.36741i
$362$		0			0
$363$			2.00000i			0.104973i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−4.33013	−	2.50000i	−0.226031	−	0.130499i	0.382709	−	0.923869i	$-0.374991\pi$
$367$	−4.33013	−	2.50000i	−0.226031	−	0.130499i	−0.608740	+	0.793370i	$0.708325\pi$
$368$		0			0
$369$	−18.0000			−0.937043
$370$		0			0
$371$	−3.00000	−	5.19615i	−0.155752	−	0.269771i
$372$		0			0
$373$	26.8468	−	15.5000i	1.39007	−	0.802560i	0.396751	−	0.917926i	$-0.370138\pi$
$373$	26.8468	−	15.5000i	1.39007	−	0.802560i	0.993323	+	0.115367i	$0.0368043\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−7.79423	+	7.50000i	−0.401423	+	0.386270i
$378$		0			0
$379$	−0.500000	+	0.866025i	−0.0256833	+	0.0444847i	−0.878581	−	0.477593i	$-0.841509\pi$
$379$	−0.500000	+	0.866025i	−0.0256833	+	0.0444847i	0.852898	+	0.522077i	$0.174843\pi$
$380$		0			0
$381$	9.50000	+	16.4545i	0.486700	+	0.842989i
$382$		0			0
$383$	7.79423	−	4.50000i	0.398266	−	0.229939i	−0.287469	−	0.957790i	$-0.592814\pi$
$383$	7.79423	−	4.50000i	0.398266	−	0.229939i	0.685736	+	0.727851i	$0.259481\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	19.0526	+	11.0000i	0.968496	+	0.559161i
$388$		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
$391$	9.00000			0.455150
$392$		0			0
$393$	−10.3923	−	6.00000i	−0.524222	−	0.302660i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	4.33013	−	2.50000i	0.217323	−	0.125471i	−0.387387	−	0.921917i	$-0.626622\pi$
$397$	4.33013	−	2.50000i	0.217323	−	0.125471i	0.604710	+	0.796446i	$0.293289\pi$
$398$		0			0
$399$	3.50000	+	6.06218i	0.175219	+	0.303488i
$400$		0			0
$401$	16.5000	−	28.5788i	0.823971	−	1.42716i	−0.0787327	−	0.996896i	$-0.525087\pi$
$401$	16.5000	−	28.5788i	0.823971	−	1.42716i	0.902703	−	0.430263i	$-0.141579\pi$
$402$		0			0
$403$	13.8564	+	4.00000i	0.690237	+	0.199254i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−18.1865	+	10.5000i	−0.901473	+	0.520466i
$408$		0			0
$409$	−12.5000	−	21.6506i	−0.618085	−	1.07056i	−0.989835	−	0.142222i	$-0.954575\pi$
$409$	−12.5000	−	21.6506i	−0.618085	−	1.07056i	0.371750	−	0.928333i	$-0.378758\pi$
$410$		0			0
$411$	−15.0000			−0.739895
$412$		0			0
$413$	2.59808	+	1.50000i	0.127843	+	0.0738102i
$414$		0			0
$415$		0			0
$416$		0			0
$417$			5.00000i			0.244851i
$418$		0			0
$419$	−4.50000	+	7.79423i	−0.219839	+	0.380773i	−0.954759	−	0.297382i	$-0.903887\pi$
$419$	−4.50000	+	7.79423i	−0.219839	+	0.380773i	0.734919	+	0.678155i	$0.237220\pi$
$420$		0			0
$421$	2.00000			0.0974740			0.0487370	−	0.998812i	$-0.484480\pi$
$421$	2.00000			0.0974740			0.0487370	+	0.998812i	$0.484480\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		0			0
$426$		0			0
$427$	9.52628	+	5.50000i	0.461009	+	0.266164i
$428$		0			0
$429$	10.5000	−	2.59808i	0.506945	−	0.125436i
$430$		0			0
$431$	4.50000	−	7.79423i	0.216757	−	0.375435i	−0.737057	−	0.675830i	$-0.763785\pi$
$431$	4.50000	−	7.79423i	0.216757	−	0.375435i	0.953815	+	0.300395i	$0.0971186\pi$
$432$		0			0
$433$	−25.1147	+	14.5000i	−1.20694	+	0.696826i	−0.962089	−	0.272736i	$-0.912071\pi$
$433$	−25.1147	+	14.5000i	−1.20694	+	0.696826i	−0.244848	+	0.969561i	$0.578738\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$			21.0000i			1.00457i
$438$		0			0
$439$	5.50000	−	9.52628i	0.262501	−	0.454665i	−0.704405	−	0.709798i	$-0.748786\pi$
$439$	5.50000	−	9.52628i	0.262501	−	0.454665i	0.966906	+	0.255134i	$0.0821195\pi$
$440$		0			0
$441$	12.0000			0.571429
$442$		0			0
$443$		0			0		1.00000			$0$
$443$		0			0		−1.00000			$\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		−	21.0000i		−	0.993266i
$448$		0			0
$449$	1.50000	+	2.59808i	0.0707894	+	0.122611i	0.899247	−	0.437440i	$-0.144115\pi$
$449$	1.50000	+	2.59808i	0.0707894	+	0.122611i	−0.828458	+	0.560051i	$0.810782\pi$
$450$		0			0
$451$	13.5000	+	23.3827i	0.635690	+	1.10105i
$452$		0			0
$453$	6.92820	+	4.00000i	0.325515	+	0.187936i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−4.33013	−	2.50000i	−0.202555	−	0.116945i	0.395292	−	0.918556i	$-0.370643\pi$
$457$	−4.33013	−	2.50000i	−0.202555	−	0.116945i	−0.597847	+	0.801611i	$0.703977\pi$
$458$		0			0
$459$	7.50000	+	12.9904i	0.350070	+	0.606339i
$460$		0			0
$461$	−13.5000	−	23.3827i	−0.628758	−	1.08904i	−0.987801	−	0.155719i	$-0.950230\pi$
$461$	−13.5000	−	23.3827i	−0.628758	−	1.08904i	0.359044	−	0.933321i	$-0.383103\pi$
$462$		0			0
$463$			4.00000i			0.185896i	0.995671	+	0.0929479i	$0.0296290\pi$
$463$			4.00000i			0.185896i	−0.995671	+	0.0929479i	$0.970371\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	36.0000i		−	1.66588i	−0.553362	−	0.832941i	$-0.686655\pi$
$467$		−	36.0000i		−	1.66588i	0.553362	−	0.832941i	$-0.313345\pi$
$468$		0			0
$469$	−7.00000			−0.323230
$470$		0			0
$471$	5.00000	−	8.66025i	0.230388	−	0.399043i
$472$		0			0
$473$		−	33.0000i		−	1.51734i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	10.3923	−	6.00000i	0.475831	−	0.274721i
$478$		0			0
$479$	19.5000	−	33.7750i	0.890978	−	1.54322i	0.0522726	−	0.998633i	$-0.483354\pi$
$479$	19.5000	−	33.7750i	0.890978	−	1.54322i	0.838705	−	0.544586i	$-0.183313\pi$
$480$		0			0
$481$	−17.5000	−	18.1865i	−0.797931	−	0.829235i
$482$		0			0
$483$	2.59808	+	1.50000i	0.118217	+	0.0682524i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	9.52628	−	5.50000i	0.431677	−	0.249229i	−0.268384	−	0.963312i	$-0.586490\pi$
$487$	9.52628	−	5.50000i	0.431677	−	0.249229i	0.700061	+	0.714083i	$0.253156\pi$
$488$		0			0
$489$	1.00000			0.0452216
$490$		0			0
$491$	4.50000	−	7.79423i	0.203082	−	0.351749i	−0.746438	−	0.665455i	$-0.768237\pi$
$491$	4.50000	−	7.79423i	0.203082	−	0.351749i	0.949520	+	0.313707i	$0.101571\pi$
$492$		0			0
$493$			9.00000i			0.405340i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−2.59808	−	1.50000i	−0.116540	−	0.0672842i
$498$		0			0
$499$	−32.0000			−1.43252			−0.716258	−	0.697835i	$-0.754147\pi$
$499$	−32.0000			−1.43252			−0.716258	+	0.697835i	$0.754147\pi$
$500$		0			0
$501$	1.50000	+	2.59808i	0.0670151	+	0.116073i
$502$		0			0
$503$	−12.9904	+	7.50000i	−0.579212	+	0.334408i	−0.760820	−	0.648963i	$-0.775203\pi$
$503$	−12.9904	+	7.50000i	−0.579212	+	0.334408i	0.181608	+	0.983371i	$0.441870\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	6.06218	+	11.5000i	0.269231	+	0.510733i
$508$		0			0
$509$	−4.50000	+	7.79423i	−0.199459	+	0.345473i	−0.948353	−	0.317217i	$-0.897252\pi$
$509$	−4.50000	+	7.79423i	−0.199459	+	0.345473i	0.748894	+	0.662690i	$0.230585\pi$
$510$		0			0
$511$	1.00000	+	1.73205i	0.0442374	+	0.0766214i
$512$		0			0
$513$	−30.3109	+	17.5000i	−1.33826	+	0.772644i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	3.00000			0.131685
$520$		0			0
$521$	30.0000			1.31432			0.657162	−	0.753749i	$-0.271757\pi$
$521$	30.0000			1.31432			0.657162	+	0.753749i	$0.271757\pi$
$522$		0			0
$523$	25.1147	+	14.5000i	1.09819	+	0.634041i	0.935745	−	0.352677i	$-0.114728\pi$
$523$	25.1147	+	14.5000i	1.09819	+	0.634041i	0.162446	+	0.986718i	$0.448062\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	10.3923	−	6.00000i	0.452696	−	0.261364i
$528$		0			0
$529$	−7.00000	−	12.1244i	−0.304348	−	0.527146i
$530$		0			0
$531$	−3.00000	+	5.19615i	−0.130189	+	0.225494i
$532$		0			0
$533$	−23.3827	+	22.5000i	−1.01282	+	0.974583i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−18.1865	+	10.5000i	−0.784807	+	0.453108i
$538$		0			0
$539$	−9.00000	−	15.5885i	−0.387657	−	0.671442i
$540$		0			0
$541$	−22.0000			−0.945854			−0.472927	−	0.881102i	$-0.656803\pi$
$541$	−22.0000			−0.945854			−0.472927	+	0.881102i	$0.656803\pi$
$542$		0			0
$543$	1.73205	+	1.00000i	0.0743294	+	0.0429141i
$544$		0			0
$545$		0			0
$546$		0			0
$547$			8.00000i			0.342055i	0.985266	+	0.171028i	$0.0547087\pi$
$547$			8.00000i			0.342055i	−0.985266	+	0.171028i	$0.945291\pi$
$548$		0			0
$549$	−11.0000	+	19.0526i	−0.469469	+	0.813143i
$550$		0			0
$551$	−21.0000			−0.894630
$552$		0			0
$553$	6.92820	−	4.00000i	0.294617	−	0.170097i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	33.7750	+	19.5000i	1.43109	+	0.826242i	0.997204	−	0.0747252i	$-0.0238080\pi$
$557$	33.7750	+	19.5000i	1.43109	+	0.826242i	0.433888	+	0.900967i	$0.357141\pi$
$558$		0			0
$559$	38.5000	−	9.52628i	1.62838	−	0.402919i
$560$		0			0
$561$	4.50000	−	7.79423i	0.189990	−	0.329073i
$562$		0			0
$563$	−33.7750	+	19.5000i	−1.42345	+	0.821827i	−0.996592	−	0.0824933i	$-0.973712\pi$
$563$	−33.7750	+	19.5000i	−1.42345	+	0.821827i	−0.426855	+	0.904320i	$0.640378\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$		−	1.00000i		−	0.0419961i
$568$		0			0
$569$	13.5000	−	23.3827i	0.565949	−	0.980253i	−0.431011	−	0.902347i	$-0.641843\pi$
$569$	13.5000	−	23.3827i	0.565949	−	0.980253i	0.996961	−	0.0779066i	$-0.0248236\pi$
$570$		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
$573$			3.00000i			0.125327i
$574$		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
$579$	2.50000	+	4.33013i	0.103896	+	0.179954i
$580$		0			0
$581$	−6.00000	−	10.3923i	−0.248922	−	0.431145i
$582$		0			0
$583$	−15.5885	−	9.00000i	−0.645608	−	0.372742i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−28.5788	−	16.5000i	−1.17957	−	0.681028i	−0.223659	−	0.974668i	$-0.571800\pi$
$587$	−28.5788	−	16.5000i	−1.17957	−	0.681028i	−0.955916	+	0.293640i	$0.905133\pi$
$588$		0			0
$589$	14.0000	+	24.2487i	0.576860	+	0.999151i
$590$		0			0
$591$	−10.5000	−	18.1865i	−0.431912	−	0.748094i
$592$		0			0
$593$			6.00000i			0.246390i	0.992382	+	0.123195i	$0.0393141\pi$
$593$			6.00000i			0.246390i	−0.992382	+	0.123195i	$0.960686\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$			17.0000i			0.695764i
$598$		0			0
$599$	−24.0000			−0.980613			−0.490307	−	0.871550i	$-0.663115\pi$
$599$	−24.0000			−0.980613			−0.490307	+	0.871550i	$0.663115\pi$
$600$		0			0
$601$	−17.5000	+	30.3109i	−0.713840	+	1.23641i	0.249565	+	0.968358i	$0.419712\pi$
$601$	−17.5000	+	30.3109i	−0.713840	+	1.23641i	−0.963405	+	0.268049i	$0.913621\pi$
$602$		0			0
$603$		−	14.0000i		−	0.570124i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−11.2583	+	6.50000i	−0.456962	+	0.263827i	−0.710766	−	0.703429i	$-0.751651\pi$
$607$	−11.2583	+	6.50000i	−0.456962	+	0.263827i	0.253804	+	0.967256i	$0.418318\pi$
$608$		0			0
$609$	−1.50000	+	2.59808i	−0.0607831	+	0.105279i
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−37.2391	−	21.5000i	−1.50407	−	0.868377i	−0.999989	−	0.00472215i	$-0.998497\pi$
$613$	−37.2391	−	21.5000i	−1.50407	−	0.868377i	−0.504084	−	0.863655i	$-0.668170\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	28.5788	−	16.5000i	1.15054	−	0.664265i	0.201522	−	0.979484i	$-0.435411\pi$
$617$	28.5788	−	16.5000i	1.15054	−	0.664265i	0.949019	+	0.315219i	$0.102078\pi$
$618$		0			0
$619$	−44.0000			−1.76851			−0.884255	−	0.467005i	$-0.845333\pi$
$619$	−44.0000			−1.76851			−0.884255	+	0.467005i	$0.845333\pi$
$620$		0			0
$621$	−7.50000	+	12.9904i	−0.300965	+	0.521286i
$622$		0			0
$623$			15.0000i			0.600962i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	18.1865	+	10.5000i	0.726300	+	0.419330i
$628$		0			0
$629$	−21.0000			−0.837325
$630$		0			0
$631$	−8.50000	−	14.7224i	−0.338380	−	0.586091i	0.645748	−	0.763550i	$-0.276545\pi$
$631$	−8.50000	−	14.7224i	−0.338380	−	0.586091i	−0.984128	+	0.177459i	$0.943212\pi$
$632$		0			0
$633$	−9.52628	+	5.50000i	−0.378636	+	0.218605i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	15.5885	−	15.0000i	0.617637	−	0.594322i
$638$		0			0
$639$	3.00000	−	5.19615i	0.118678	−	0.205557i
$640$		0			0
$641$	−13.5000	−	23.3827i	−0.533218	−	0.923561i	−0.999247	−	0.0387913i	$-0.987649\pi$
$641$	−13.5000	−	23.3827i	−0.533218	−	0.923561i	0.466029	−	0.884769i	$-0.345684\pi$
$642$		0			0
$643$	−9.52628	+	5.50000i	−0.375680	+	0.216899i	−0.675937	−	0.736959i	$-0.736261\pi$
$643$	−9.52628	+	5.50000i	−0.375680	+	0.216899i	0.300257	+	0.953858i	$0.402928\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−38.9711	−	22.5000i	−1.53211	−	0.884566i	−0.999264	−	0.0383563i	$-0.987788\pi$
$647$	−38.9711	−	22.5000i	−1.53211	−	0.884566i	−0.532850	−	0.846210i	$-0.678879\pi$
$648$		0			0
$649$	9.00000			0.353281
$650$		0			0
$651$	4.00000			0.156772
$652$		0			0
$653$	−33.7750	−	19.5000i	−1.32172	−	0.763094i	−0.337715	−	0.941248i	$-0.609654\pi$
$653$	−33.7750	−	19.5000i	−1.32172	−	0.763094i	−0.984003	+	0.178154i	$0.942987\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−3.46410	+	2.00000i	−0.135147	+	0.0780274i
$658$		0			0
$659$	−19.5000	−	33.7750i	−0.759612	−	1.31569i	−0.943049	−	0.332655i	$-0.892055\pi$
$659$	−19.5000	−	33.7750i	−0.759612	−	1.31569i	0.183436	−	0.983032i	$-0.441278\pi$
$660$		0			0
$661$	0.500000	−	0.866025i	0.0194477	−	0.0336845i	−0.856138	−	0.516748i	$-0.827143\pi$
$661$	0.500000	−	0.866025i	0.0194477	−	0.0336845i	0.875585	+	0.483063i	$0.160476\pi$
$662$		0			0
$663$	10.3923	+	3.00000i	0.403604	+	0.116510i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−7.79423	+	4.50000i	−0.301794	+	0.174241i
$668$		0			0
$669$	−9.50000	−	16.4545i	−0.367291	−	0.636167i
$670$		0			0
$671$	33.0000			1.27395
$672$		0			0
$673$	14.7224	+	8.50000i	0.567508	+	0.327651i	0.756153	−	0.654394i	$-0.227076\pi$
$673$	14.7224	+	8.50000i	0.567508	+	0.327651i	−0.188645	+	0.982045i	$0.560410\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$		−	42.0000i		−	1.61419i	−0.590421	−	0.807096i	$-0.701038\pi$
$677$		−	42.0000i		−	1.61419i	0.590421	−	0.807096i	$-0.298962\pi$
$678$		0			0
$679$	3.50000	−	6.06218i	0.134318	−	0.232645i
$680$		0			0
$681$	27.0000			1.03464
$682$		0			0
$683$	−44.1673	+	25.5000i	−1.69001	+	0.975730i	−0.735520	+	0.677503i	$0.763062\pi$
$683$	−44.1673	+	25.5000i	−1.69001	+	0.975730i	−0.954495	+	0.298227i	$0.903605\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	19.0526	+	11.0000i	0.726900	+	0.419676i
$688$		0			0
$689$	6.00000	−	20.7846i	0.228582	−	0.791831i
$690$		0			0
$691$	−11.5000	+	19.9186i	−0.437481	+	0.757739i	−0.997494	−	0.0707446i	$-0.977462\pi$
$691$	−11.5000	+	19.9186i	−0.437481	+	0.757739i	0.560014	+	0.828483i	$0.310796\pi$
$692$		0			0
$693$	−5.19615	+	3.00000i	−0.197386	+	0.113961i
$694$		0			0
$695$		0			0
$696$		0			0
$697$			27.0000i			1.02270i
$698$		0			0
$699$	9.00000	−	15.5885i	0.340411	−	0.589610i
$700$		0			0
$701$	18.0000			0.679851			0.339925	−	0.940452i	$-0.389598\pi$
$701$	18.0000			0.679851			0.339925	+	0.940452i	$0.389598\pi$
$702$		0			0
$703$		−	49.0000i		−	1.84807i
$704$		0			0
$705$		0			0
$706$		0			0
$707$			9.00000i			0.338480i
$708$		0			0
$709$	−18.5000	−	32.0429i	−0.694782	−	1.20340i	−0.970254	−	0.242089i	$-0.922167\pi$
$709$	−18.5000	−	32.0429i	−0.694782	−	1.20340i	0.275472	−	0.961309i	$-0.411166\pi$
$710$		0			0
$711$	8.00000	+	13.8564i	0.300023	+	0.519656i
$712$		0			0
$713$	10.3923	+	6.00000i	0.389195	+	0.224702i
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$	4.50000	+	7.79423i	0.167822	+	0.290676i	0.937654	−	0.347571i	$-0.112993\pi$
$719$	4.50000	+	7.79423i	0.167822	+	0.290676i	−0.769832	+	0.638247i	$0.779660\pi$
$720$		0			0
$721$	4.00000	+	6.92820i	0.148968	+	0.258020i
$722$		0			0
$723$			1.00000i			0.0371904i
$724$		0			0
$725$		0			0
$726$		0			0
$727$		−	52.0000i		−	1.92857i	−0.264861	−	0.964287i	$-0.585326\pi$
$727$		−	52.0000i		−	1.92857i	0.264861	−	0.964287i	$-0.414674\pi$
$728$		0			0
$729$	−13.0000			−0.481481
$730$		0			0
$731$	16.5000	−	28.5788i	0.610275	−	1.05703i
$732$		0			0
$733$			34.0000i			1.25582i	0.778287	+	0.627909i	$0.216089\pi$
$733$			34.0000i			1.25582i	−0.778287	+	0.627909i	$0.783911\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−18.1865	+	10.5000i	−0.669910	+	0.386772i
$738$		0			0
$739$	23.5000	−	40.7032i	0.864461	−	1.49729i	−0.00311943	−	0.999995i	$-0.500993\pi$
$739$	23.5000	−	40.7032i	0.864461	−	1.49729i	0.867581	−	0.497296i	$-0.165674\pi$
$740$		0			0
$741$	−7.00000	+	24.2487i	−0.257151	+	0.890799i
$742$		0			0
$743$	18.1865	+	10.5000i	0.667199	+	0.385208i	0.795015	−	0.606590i	$-0.207463\pi$
$743$	18.1865	+	10.5000i	0.667199	+	0.385208i	−0.127815	+	0.991798i	$0.540796\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	20.7846	−	12.0000i	0.760469	−	0.439057i
$748$		0			0
$749$	9.00000			0.328853
$750$		0			0
$751$	6.50000	−	11.2583i	0.237188	−	0.410822i	−0.722718	−	0.691143i	$-0.757107\pi$
$751$	6.50000	−	11.2583i	0.237188	−	0.410822i	0.959906	+	0.280321i	$0.0904408\pi$
$752$		0			0
$753$		−	21.0000i		−	0.765283i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−25.1147	−	14.5000i	−0.912811	−	0.527011i	−0.0314762	−	0.999505i	$-0.510021\pi$
$757$	−25.1147	−	14.5000i	−0.912811	−	0.527011i	−0.881334	+	0.472493i	$0.843354\pi$
$758$		0			0
$759$	9.00000			0.326679
$760$		0			0
$761$	−1.50000	−	2.59808i	−0.0543750	−	0.0941802i	0.837557	−	0.546350i	$-0.183983\pi$
$761$	−1.50000	−	2.59808i	−0.0543750	−	0.0941802i	−0.891932	+	0.452170i	$0.850650\pi$
$762$		0			0
$763$	1.73205	−	1.00000i	0.0627044	−	0.0362024i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	2.59808	+	10.5000i	0.0938111	+	0.379133i
$768$		0			0
$769$	−6.50000	+	11.2583i	−0.234396	+	0.405986i	−0.959097	−	0.283078i	$-0.908645\pi$
$769$	−6.50000	+	11.2583i	−0.234396	+	0.405986i	0.724701	+	0.689063i	$0.241978\pi$
$770$		0			0
$771$	−4.50000	−	7.79423i	−0.162064	−	0.280702i
$772$		0			0
$773$	23.3827	−	13.5000i	0.841017	−	0.485561i	−0.0165929	−	0.999862i	$-0.505282\pi$
$773$	23.3827	−	13.5000i	0.841017	−	0.485561i	0.857610	+	0.514301i	$0.171949\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−6.06218	−	3.50000i	−0.217479	−	0.125562i
$778$		0			0
$779$	−63.0000			−2.25721
$780$		0			0
$781$	−9.00000			−0.322045
$782$		0			0
$783$	−12.9904	−	7.50000i	−0.464238	−	0.268028i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−32.0429	+	18.5000i	−1.14221	+	0.659454i	−0.946976	−	0.321303i	$-0.895879\pi$
$787$	−32.0429	+	18.5000i	−1.14221	+	0.659454i	−0.195231	+	0.980757i	$0.562546\pi$
$788$		0			0
$789$	−1.50000	−	2.59808i	−0.0534014	−	0.0924940i
$790$		0			0
$791$	4.50000	−	7.79423i	0.160002	−	0.277131i
$792$		0			0
$793$	9.52628	+	38.5000i	0.338288	+	1.36718i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−44.1673	+	25.5000i	−1.56449	+	0.903256i	−0.567692	+	0.823241i	$0.692164\pi$
$797$	−44.1673	+	25.5000i	−1.56449	+	0.903256i	−0.996794	+	0.0800155i	$0.974503\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	−30.0000			−1.06000
$802$		0			0
$803$	5.19615	+	3.00000i	0.183368	+	0.105868i
$804$		0			0
$805$		0			0
$806$		0			0
$807$			27.0000i			0.950445i
$808$		0			0
$809$	7.50000	−	12.9904i	0.263686	−	0.456717i	−0.703533	−	0.710663i	$-0.748395\pi$
$809$	7.50000	−	12.9904i	0.263686	−	0.456717i	0.967219	+	0.253946i	$0.0817284\pi$
$810$		0			0
$811$	32.0000			1.12367			0.561836	−	0.827249i	$-0.310095\pi$
$811$	32.0000			1.12367			0.561836	+	0.827249i	$0.310095\pi$
$812$		0			0
$813$	−19.9186	+	11.5000i	−0.698575	+	0.403323i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	66.6840	+	38.5000i	2.33298	+	1.34694i
$818$		0			0
$819$	−5.00000	−	5.19615i	−0.174714	−	0.181568i
$820$		0			0
$821$	−7.50000	+	12.9904i	−0.261752	+	0.453367i	−0.966708	−	0.255884i	$-0.917634\pi$
$821$	−7.50000	+	12.9904i	−0.261752	+	0.453367i	0.704956	+	0.709251i	$0.250967\pi$
$822$		0			0
$823$	11.2583	−	6.50000i	0.392441	−	0.226576i	−0.290776	−	0.956791i	$-0.593914\pi$
$823$	11.2583	−	6.50000i	0.392441	−	0.226576i	0.683217	+	0.730215i	$0.260580\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	12.0000i		−	0.417281i	−0.977992	−	0.208640i	$-0.933096\pi$
$827$		−	12.0000i		−	0.417281i	0.977992	−	0.208640i	$-0.0669038\pi$
$828$		0			0
$829$	5.50000	−	9.52628i	0.191023	−	0.330861i	−0.754567	−	0.656223i	$-0.772153\pi$
$829$	5.50000	−	9.52628i	0.191023	−	0.330861i	0.945589	+	0.325362i	$0.105486\pi$
$830$		0			0
$831$	−19.0000			−0.659103
$832$		0			0
$833$		−	18.0000i		−	0.623663i
$834$		0			0
$835$		0			0
$836$		0			0
$837$			20.0000i			0.691301i
$838$		0			0
$839$	10.5000	+	18.1865i	0.362500	+	0.627869i	0.988372	−	0.152057i	$-0.0485899\pi$
$839$	10.5000	+	18.1865i	0.362500	+	0.627869i	−0.625871	+	0.779926i	$0.715257\pi$
$840$		0			0
$841$	10.0000	+	17.3205i	0.344828	+	0.597259i
$842$		0			0
$843$	5.19615	+	3.00000i	0.178965	+	0.103325i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−1.73205	−	1.00000i	−0.0595140	−	0.0343604i
$848$		0			0
$849$	2.50000	+	4.33013i	0.0857998	+	0.148610i
$850$		0			0
$851$	−10.5000	−	18.1865i	−0.359935	−	0.623426i
$852$		0			0
$853$			22.0000i			0.753266i	0.926363	+	0.376633i	$0.122918\pi$
$853$			22.0000i			0.753266i	−0.926363	+	0.376633i	$0.877082\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		−	30.0000i		−	1.02478i	−0.858753	−	0.512390i	$-0.828760\pi$
$857$		−	30.0000i		−	1.02478i	0.858753	−	0.512390i	$-0.171240\pi$
$858$		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
$861$	−4.50000	+	7.79423i	−0.153360	+	0.265627i
$862$		0			0
$863$		−	24.0000i		−	0.816970i	−0.912765	−	0.408485i	$-0.866057\pi$
$863$		−	24.0000i		−	0.816970i	0.912765	−	0.408485i	$-0.133943\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−6.92820	+	4.00000i	−0.235294	+	0.135847i
$868$		0			0
$869$	12.0000	−	20.7846i	0.407072	−	0.705070i
$870$		0			0
$871$	−17.5000	−	18.1865i	−0.592965	−	0.616227i
$872$		0			0
$873$	12.1244	+	7.00000i	0.410347	+	0.236914i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	35.5070	−	20.5000i	1.19899	−	0.692236i	0.238658	−	0.971104i	$-0.423292\pi$
$877$	35.5070	−	20.5000i	1.19899	−	0.692236i	0.960329	+	0.278868i	$0.0899591\pi$
$878$		0			0
$879$	27.0000			0.910687
$880$		0			0
$881$	−13.5000	+	23.3827i	−0.454827	+	0.787783i	−0.998678	−	0.0513987i	$-0.983632\pi$
$881$	−13.5000	+	23.3827i	−0.454827	+	0.787783i	0.543852	+	0.839181i	$0.316965\pi$
$882$		0			0
$883$			4.00000i			0.134611i	0.997732	+	0.0673054i	$0.0214402\pi$
$883$			4.00000i			0.134611i	−0.997732	+	0.0673054i	$0.978560\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−7.79423	−	4.50000i	−0.261705	−	0.151095i	0.363407	−	0.931630i	$-0.381613\pi$
$887$	−7.79423	−	4.50000i	−0.261705	−	0.151095i	−0.625112	+	0.780535i	$0.714947\pi$
$888$		0			0
$889$	−19.0000			−0.637240
$890$		0			0
$891$	−1.50000	−	2.59808i	−0.0502519	−	0.0870388i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$	2.59808	+	10.5000i	0.0867472	+	0.350585i
$898$		0			0
$899$	−6.00000	+	10.3923i	−0.200111	+	0.346603i
$900$		0			0
$901$	−9.00000	−	15.5885i	−0.299833	−	0.519327i
$902$		0			0
$903$	9.52628	−	5.50000i	0.317015	−	0.183029i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	16.4545	+	9.50000i	0.546362	+	0.315442i	0.747653	−	0.664089i	$-0.231180\pi$
$907$	16.4545	+	9.50000i	0.546362	+	0.315442i	−0.201291	+	0.979531i	$0.564514\pi$
$908$		0			0
$909$	−18.0000			−0.597022
$910$		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
$919$	14.5000	+	25.1147i	0.478311	+	0.828459i	0.999691	−	0.0248659i	$-0.00791589\pi$
$919$	14.5000	+	25.1147i	0.478311	+	0.828459i	−0.521380	+	0.853325i	$0.674583\pi$
$920$		0			0
$921$	−10.0000	+	17.3205i	−0.329511	+	0.570730i
$922$		0			0
$923$	−2.59808	−	10.5000i	−0.0855167	−	0.345612i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−13.8564	+	8.00000i	−0.455104	+	0.262754i
$928$		0			0
$929$	25.5000	+	44.1673i	0.836628	+	1.44908i	0.892698	+	0.450655i	$0.148810\pi$
$929$	25.5000	+	44.1673i	0.836628	+	1.44908i	−0.0560703	+	0.998427i	$0.517857\pi$
$930$		0			0
$931$	42.0000			1.37649
$932$		0			0
$933$	20.7846	+	12.0000i	0.680458	+	0.392862i
$934$		0			0
$935$		0			0
$936$		0			0
$937$			2.00000i			0.0653372i	0.999466	+	0.0326686i	$0.0104006\pi$
$937$			2.00000i			0.0653372i	−0.999466	+	0.0326686i	$0.989599\pi$
$938$		0			0
$939$	−11.0000	+	19.0526i	−0.358971	+	0.621757i
$940$		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
$943$	−23.3827	+	13.5000i	−0.761445	+	0.439620i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−18.1865	−	10.5000i	−0.590983	−	0.341204i	0.174503	−	0.984657i	$-0.444168\pi$
$947$	−18.1865	−	10.5000i	−0.590983	−	0.341204i	−0.765486	+	0.643452i	$0.777501\pi$
$948$		0			0
$949$	−2.00000	+	6.92820i	−0.0649227	+	0.224899i
$950$		0			0
$951$	9.00000	−	15.5885i	0.291845	−	0.505490i
$952$		0			0
$953$	44.1673	−	25.5000i	1.43072	−	0.826026i	0.433544	−	0.901133i	$-0.357263\pi$
$953$	44.1673	−	25.5000i	1.43072	−	0.826026i	0.997176	+	0.0751066i	$0.0239297\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$			9.00000i			0.290929i
$958$		0			0
$959$	7.50000	−	12.9904i	0.242188	−	0.419481i
$960$		0			0
$961$	−15.0000			−0.483871
$962$		0			0
$963$			18.0000i			0.580042i
$964$		0			0
$965$		0			0
$966$		0			0
$967$		−	40.0000i		−	1.28631i	−0.765735	−	0.643157i	$-0.777624\pi$
$967$		−	40.0000i		−	1.28631i	0.765735	−	0.643157i	$-0.222376\pi$
$968$		0			0
$969$	10.5000	+	18.1865i	0.337309	+	0.584236i
$970$		0			0
$971$	−10.5000	−	18.1865i	−0.336961	−	0.583634i	0.646899	−	0.762576i	$-0.276066\pi$
$971$	−10.5000	−	18.1865i	−0.336961	−	0.583634i	−0.983860	+	0.178942i	$0.942732\pi$
$972$		0			0
$973$	−4.33013	−	2.50000i	−0.138817	−	0.0801463i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−7.79423	−	4.50000i	−0.249359	−	0.143968i	0.370111	−	0.928987i	$-0.379319\pi$
$977$	−7.79423	−	4.50000i	−0.249359	−	0.143968i	−0.619471	+	0.785020i	$0.712653\pi$
$978$		0			0
$979$	22.5000	+	38.9711i	0.719103	+	1.24552i
$980$		0			0
$981$	2.00000	+	3.46410i	0.0638551	+	0.110600i
$982$		0			0
$983$			36.0000i			1.14822i	0.818778	+	0.574111i	$0.194652\pi$
$983$			36.0000i			1.14822i	−0.818778	+	0.574111i	$0.805348\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$	33.0000			1.04934
$990$		0			0
$991$	30.5000	−	52.8275i	0.968864	−	1.67812i	0.270011	−	0.962857i	$-0.412973\pi$
$991$	30.5000	−	52.8275i	0.968864	−	1.67812i	0.698853	−	0.715265i	$-0.253694\pi$
$992$		0			0
$993$			19.0000i			0.602947i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−26.8468	+	15.5000i	−0.850246	+	0.490890i	−0.860734	−	0.509055i	$-0.829995\pi$
$997$	−26.8468	+	15.5000i	−0.850246	+	0.490890i	0.0104877	+	0.999945i	$0.496662\pi$
$998$		0			0
$999$	17.5000	−	30.3109i	0.553675	−	0.958994i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1300.2.bb.a.1049.2		4
5.2	odd	4		1300.2.i.e.1101.1		2
5.3	odd	4		260.2.i.b.61.1	✓	2
5.4	even	2	inner	1300.2.bb.a.1049.1		4
13.3	even	3	inner	1300.2.bb.a.549.1		4
15.8	even	4		2340.2.q.b.1621.1		2
20.3	even	4		1040.2.q.j.321.1		2
65.3	odd	12		260.2.i.b.81.1	yes	2
65.29	even	6	inner	1300.2.bb.a.549.2		4
65.33	even	12		3380.2.f.e.3041.2		2
65.42	odd	12		1300.2.i.e.601.1		2
65.43	odd	12		3380.2.a.g.1.1		1
65.48	odd	12		3380.2.a.h.1.1		1
65.58	even	12		3380.2.f.e.3041.1		2
195.68	even	12		2340.2.q.b.2161.1		2
260.3	even	12		1040.2.q.j.81.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.i.b.61.1	✓	2	5.3	odd	4
260.2.i.b.81.1	yes	2	65.3	odd	12
1040.2.q.j.81.1		2	260.3	even	12
1040.2.q.j.321.1		2	20.3	even	4
1300.2.i.e.601.1		2	65.42	odd	12
1300.2.i.e.1101.1		2	5.2	odd	4
1300.2.bb.a.549.1		4	13.3	even	3	inner
1300.2.bb.a.549.2		4	65.29	even	6	inner
1300.2.bb.a.1049.1		4	5.4	even	2	inner
1300.2.bb.a.1049.2		4	1.1	even	1	trivial
2340.2.q.b.1621.1		2	15.8	even	4
2340.2.q.b.2161.1		2	195.68	even	12
3380.2.a.g.1.1		1	65.43	odd	12
3380.2.a.h.1.1		1	65.48	odd	12
3380.2.f.e.3041.1		2	65.58	even	12
3380.2.f.e.3041.2		2	65.33	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)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{3} +(-0.866025 + 0.500000i) q^{7} +(-1.00000 - 1.73205i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{3} +(-0.866025 + 0.500000i) q^{7} +(-1.00000 - 1.73205i) q^{9} +(-1.50000 + 2.59808i) q^{11} +(-3.46410 - 1.00000i) q^{13} +(-2.59808 + 1.50000i) q^{17} +(-3.50000 - 6.06218i) q^{19} -1.00000 q^{21} +(-2.59808 - 1.50000i) q^{23} -5.00000i q^{27} +(1.50000 - 2.59808i) q^{29} -4.00000 q^{31} +(-2.59808 + 1.50000i) q^{33} +(6.06218 + 3.50000i) q^{37} +(-2.50000 - 2.59808i) q^{39} +(4.50000 - 7.79423i) q^{41} +(-9.52628 + 5.50000i) q^{43} +(-3.00000 + 5.19615i) q^{49} -3.00000 q^{51} +6.00000i q^{53} -7.00000i q^{57} +(-1.50000 - 2.59808i) q^{59} +(-5.50000 - 9.52628i) q^{61} +(1.73205 + 1.00000i) q^{63} +(6.06218 + 3.50000i) q^{67} +(-1.50000 - 2.59808i) q^{69} +(1.50000 + 2.59808i) q^{71} -2.00000i q^{73} -3.00000i q^{77} -8.00000 q^{79} +(-0.500000 + 0.866025i) q^{81} +12.0000i q^{83} +(2.59808 - 1.50000i) q^{87} +(7.50000 - 12.9904i) q^{89} +(3.50000 - 0.866025i) q^{91} +(-3.46410 - 2.00000i) q^{93} +(-6.06218 + 3.50000i) q^{97} +6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^9	\( 4 q - 4 q^{9} - 6 q^{11} - 14 q^{19} - 4 q^{21} + 6 q^{29} - 16 q^{31} - 10 q^{39} + 18 q^{41} - 12 q^{49} - 12 q^{51} - 6 q^{59} - 22 q^{61} - 6 q^{69} + 6 q^{71} - 32 q^{79} - 2 q^{81} + 30 q^{89} + 14 q^{91} + 24 q^{99}+O(q^{100}) \) 4 * q - 4 * q^9 - 6 * q^11 - 14 * q^19 - 4 * q^21 + 6 * q^29 - 16 * q^31 - 10 * q^39 + 18 * q^41 - 12 * q^49 - 12 * q^51 - 6 * q^59 - 22 * q^61 - 6 * q^69 + 6 * q^71 - 32 * q^79 - 2 * q^81 + 30 * q^89 + 14 * q^91 + 24 * q^99

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