LMFDB - Embedded newform 1728.2.i.c.1153.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1728,2,Mod(577,1728)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1728, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1728.577");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1728 = 2^{6} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1728.i (of order $3$, 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:	$13.7981494693$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1153.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1728.1153
Dual form			1728.2.i.c.577.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 - 2.59808i) q^{5} +(-0.500000 + 0.866025i) q^{7} +O(q^{10})$	$q+(-1.50000 - 2.59808i) q^{5} +(-0.500000 + 0.866025i) q^{7} +(1.50000 - 2.59808i) q^{11} +(-0.500000 - 0.866025i) q^{13} -6.00000 q^{17} -4.00000 q^{19} +(1.50000 + 2.59808i) q^{23} +(-2.00000 + 3.46410i) q^{25} +(-1.50000 + 2.59808i) q^{29} +(2.50000 + 4.33013i) q^{31} +3.00000 q^{35} -2.00000 q^{37} +(1.50000 + 2.59808i) q^{41} +(0.500000 - 0.866025i) q^{43} +(4.50000 - 7.79423i) q^{47} +(3.00000 + 5.19615i) q^{49} -6.00000 q^{53} -9.00000 q^{55} +(-1.50000 - 2.59808i) q^{59} +(-6.50000 + 11.2583i) q^{61} +(-1.50000 + 2.59808i) q^{65} +(3.50000 + 6.06218i) q^{67} -12.0000 q^{71} -10.0000 q^{73} +(1.50000 + 2.59808i) q^{77} +(5.50000 - 9.52628i) q^{79} +(-4.50000 + 7.79423i) q^{83} +(9.00000 + 15.5885i) q^{85} -6.00000 q^{89} +1.00000 q^{91} +(6.00000 + 10.3923i) q^{95} +(-5.50000 + 9.52628i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 3 q^{5} - q^{7}+O(q^{10}) $ 2 * q - 3 * q^5 - q^7	$ 2 q - 3 q^{5} - q^{7} + 3 q^{11} - q^{13} - 12 q^{17} - 8 q^{19} + 3 q^{23} - 4 q^{25} - 3 q^{29} + 5 q^{31} + 6 q^{35} - 4 q^{37} + 3 q^{41} + q^{43} + 9 q^{47} + 6 q^{49} - 12 q^{53} - 18 q^{55} - 3 q^{59} - 13 q^{61} - 3 q^{65} + 7 q^{67} - 24 q^{71} - 20 q^{73} + 3 q^{77} + 11 q^{79} - 9 q^{83} + 18 q^{85} - 12 q^{89} + 2 q^{91} + 12 q^{95} - 11 q^{97}+O(q^{100}) $ 2 * q - 3 * q^5 - q^7 + 3 * q^11 - q^13 - 12 * q^17 - 8 * q^19 + 3 * q^23 - 4 * q^25 - 3 * q^29 + 5 * q^31 + 6 * q^35 - 4 * q^37 + 3 * q^41 + q^43 + 9 * q^47 + 6 * q^49 - 12 * q^53 - 18 * q^55 - 3 * q^59 - 13 * q^61 - 3 * q^65 + 7 * q^67 - 24 * q^71 - 20 * q^73 + 3 * q^77 + 11 * q^79 - 9 * q^83 + 18 * q^85 - 12 * q^89 + 2 * q^91 + 12 * q^95 - 11 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times$.

$n$	$325$	$703$	$1217$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−1.50000	−	2.59808i	−0.670820	−	1.16190i	−0.977672	−	0.210138i	$-0.932609\pi$
$5$	−1.50000	−	2.59808i	−0.670820	−	1.16190i	0.306851	−	0.951757i	$-0.400725\pi$
$6$		0			0
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i	−0.944911	−	0.327327i	$-0.893852\pi$
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i	0.755929	+	0.654654i	$0.227186\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	−0.546259	−	0.837616i	$-0.683949\pi$
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	0.998526	+	0.0542666i	$0.0172821\pi$
$12$		0			0
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i	0.788320	−	0.615265i	$-0.210951\pi$
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i	−0.926995	+	0.375073i	$0.877618\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−6.00000			−1.45521			−0.727607	−	0.685994i	$-0.759367\pi$
$17$	−6.00000			−1.45521			−0.727607	+	0.685994i	$0.759367\pi$
$18$		0			0
$19$	−4.00000			−0.917663			−0.458831	−	0.888523i	$-0.651732\pi$
$19$	−4.00000			−0.917663			−0.458831	+	0.888523i	$0.651732\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	1.50000	+	2.59808i	0.312772	+	0.541736i	0.978961	−	0.204046i	$-0.0654092\pi$
$23$	1.50000	+	2.59808i	0.312772	+	0.541736i	−0.666190	+	0.745782i	$0.732076\pi$
$24$		0			0
$25$	−2.00000	+	3.46410i	−0.400000	+	0.692820i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−1.50000	+	2.59808i	−0.278543	+	0.482451i	−0.971023	−	0.238987i	$-0.923185\pi$
$29$	−1.50000	+	2.59808i	−0.278543	+	0.482451i	0.692480	+	0.721437i	$0.256518\pi$
$30$		0			0
$31$	2.50000	+	4.33013i	0.449013	+	0.777714i	0.998322	−	0.0579057i	$-0.0184423\pi$
$31$	2.50000	+	4.33013i	0.449013	+	0.777714i	−0.549309	+	0.835619i	$0.685109\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	3.00000			0.507093
$36$		0			0
$37$	−2.00000			−0.328798			−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000			−0.328798			−0.164399	+	0.986394i	$0.552568\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	1.50000	+	2.59808i	0.234261	+	0.405751i	0.959058	−	0.283211i	$-0.0913998\pi$
$41$	1.50000	+	2.59808i	0.234261	+	0.405751i	−0.724797	+	0.688963i	$0.758066\pi$
$42$		0			0
$43$	0.500000	−	0.866025i	0.0762493	−	0.132068i	−0.825380	−	0.564578i	$-0.809039\pi$
$43$	0.500000	−	0.866025i	0.0762493	−	0.132068i	0.901629	+	0.432511i	$0.142372\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	4.50000	−	7.79423i	0.656392	−	1.13691i	−0.325150	−	0.945662i	$-0.605415\pi$
$47$	4.50000	−	7.79423i	0.656392	−	1.13691i	0.981543	−	0.191243i	$-0.0612518\pi$
$48$		0			0
$49$	3.00000	+	5.19615i	0.428571	+	0.742307i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−6.00000			−0.824163			−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000			−0.824163			−0.412082	+	0.911147i	$0.635198\pi$
$54$		0			0
$55$	−9.00000			−1.21356
$56$		0			0
$57$		0			0
$58$		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
$61$	−6.50000	+	11.2583i	−0.832240	+	1.44148i	0.0640184	+	0.997949i	$0.479608\pi$
$61$	−6.50000	+	11.2583i	−0.832240	+	1.44148i	−0.896258	+	0.443533i	$0.853725\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1.50000	+	2.59808i	−0.186052	+	0.322252i
$66$		0			0
$67$	3.50000	+	6.06218i	0.427593	+	0.740613i	0.996659	−	0.0816792i	$-0.0260283\pi$
$67$	3.50000	+	6.06218i	0.427593	+	0.740613i	−0.569066	+	0.822292i	$0.692695\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−12.0000			−1.42414			−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000			−1.42414			−0.712069	+	0.702109i	$0.752242\pi$
$72$		0			0
$73$	−10.0000			−1.17041			−0.585206	−	0.810885i	$-0.698986\pi$
$73$	−10.0000			−1.17041			−0.585206	+	0.810885i	$0.698986\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	1.50000	+	2.59808i	0.170941	+	0.296078i
$78$		0			0
$79$	5.50000	−	9.52628i	0.618798	−	1.07179i	−0.370907	−	0.928670i	$-0.620953\pi$
$79$	5.50000	−	9.52628i	0.618798	−	1.07179i	0.989705	−	0.143120i	$-0.0457135\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−4.50000	+	7.79423i	−0.493939	+	0.855528i	−0.999976	−	0.00698436i	$-0.997777\pi$
$83$	−4.50000	+	7.79423i	−0.493939	+	0.855528i	0.506036	+	0.862512i	$0.331110\pi$
$84$		0			0
$85$	9.00000	+	15.5885i	0.976187	+	1.69081i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−6.00000			−0.635999			−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000			−0.635999			−0.317999	+	0.948091i	$0.603011\pi$
$90$		0			0
$91$	1.00000			0.104828
$92$		0			0
$93$		0			0
$94$		0			0
$95$	6.00000	+	10.3923i	0.615587	+	1.06623i
$96$		0			0
$97$	−5.50000	+	9.52628i	−0.558440	+	0.967247i	0.439187	+	0.898396i	$0.355267\pi$
$97$	−5.50000	+	9.52628i	−0.558440	+	0.967247i	−0.997627	+	0.0688512i	$0.978067\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−7.50000	+	12.9904i	−0.746278	+	1.29259i	0.203317	+	0.979113i	$0.434828\pi$
$101$	−7.50000	+	12.9904i	−0.746278	+	1.29259i	−0.949595	+	0.313478i	$0.898506\pi$
$102$		0			0
$103$	−3.50000	−	6.06218i	−0.344865	−	0.597324i	0.640464	−	0.767988i	$-0.278742\pi$
$103$	−3.50000	−	6.06218i	−0.344865	−	0.597324i	−0.985329	+	0.170664i	$0.945409\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−12.0000			−1.16008			−0.580042	−	0.814587i	$-0.696964\pi$
$107$	−12.0000			−1.16008			−0.580042	+	0.814587i	$0.696964\pi$
$108$		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
$111$		0			0
$112$		0			0
$113$	−4.50000	−	7.79423i	−0.423324	−	0.733219i	0.572938	−	0.819599i	$-0.305804\pi$
$113$	−4.50000	−	7.79423i	−0.423324	−	0.733219i	−0.996262	+	0.0863794i	$0.972470\pi$
$114$		0			0
$115$	4.50000	−	7.79423i	0.419627	−	0.726816i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	3.00000	−	5.19615i	0.275010	−	0.476331i
$120$		0			0
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−3.00000			−0.268328
$126$		0			0
$127$	16.0000			1.41977			0.709885	−	0.704317i	$-0.248747\pi$
$127$	16.0000			1.41977			0.709885	+	0.704317i	$0.248747\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	10.5000	+	18.1865i	0.917389	+	1.58896i	0.803365	+	0.595487i	$0.203041\pi$
$131$	10.5000	+	18.1865i	0.917389	+	1.58896i	0.114024	+	0.993478i	$0.463626\pi$
$132$		0			0
$133$	2.00000	−	3.46410i	0.173422	−	0.300376i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	1.50000	−	2.59808i	0.128154	−	0.221969i	−0.794808	−	0.606861i	$-0.792428\pi$
$137$	1.50000	−	2.59808i	0.128154	−	0.221969i	0.922961	+	0.384893i	$0.125762\pi$
$138$		0			0
$139$	−2.50000	−	4.33013i	−0.212047	−	0.367277i	0.740308	−	0.672268i	$-0.234680\pi$
$139$	−2.50000	−	4.33013i	−0.212047	−	0.367277i	−0.952355	+	0.304991i	$0.901346\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−3.00000			−0.250873
$144$		0			0
$145$	9.00000			0.747409
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−7.50000	−	12.9904i	−0.614424	−	1.06421i	−0.990485	−	0.137619i	$-0.956055\pi$
$149$	−7.50000	−	12.9904i	−0.614424	−	1.06421i	0.376061	−	0.926595i	$-0.377278\pi$
$150$		0			0
$151$	−6.50000	+	11.2583i	−0.528962	+	0.916190i	0.470467	+	0.882418i	$0.344085\pi$
$151$	−6.50000	+	11.2583i	−0.528962	+	0.916190i	−0.999430	+	0.0337724i	$0.989248\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	7.50000	−	12.9904i	0.602414	−	1.04341i
$156$		0			0
$157$	−6.50000	−	11.2583i	−0.518756	−	0.898513i	−0.999762	−	0.0217953i	$-0.993062\pi$
$157$	−6.50000	−	11.2583i	−0.518756	−	0.898513i	0.481006	−	0.876717i	$-0.340272\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−3.00000			−0.236433
$162$		0			0
$163$	20.0000			1.56652			0.783260	−	0.621694i	$-0.213555\pi$
$163$	20.0000			1.56652			0.783260	+	0.621694i	$0.213555\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−4.50000	−	7.79423i	−0.348220	−	0.603136i	0.637713	−	0.770274i	$-0.279881\pi$
$167$	−4.50000	−	7.79423i	−0.348220	−	0.603136i	−0.985933	+	0.167139i	$0.946547\pi$
$168$		0			0
$169$	6.00000	−	10.3923i	0.461538	−	0.799408i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	4.50000	−	7.79423i	0.342129	−	0.592584i	−0.642699	−	0.766119i	$-0.722185\pi$
$173$	4.50000	−	7.79423i	0.342129	−	0.592584i	0.984828	+	0.173534i	$0.0555188\pi$
$174$		0			0
$175$	−2.00000	−	3.46410i	−0.151186	−	0.261861i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−12.0000			−0.896922			−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000			−0.896922			−0.448461	+	0.893802i	$0.648028\pi$
$180$		0			0
$181$	−2.00000			−0.148659			−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	−2.00000			−0.148659			−0.0743294	+	0.997234i	$0.523682\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	3.00000	+	5.19615i	0.220564	+	0.382029i
$186$		0			0
$187$	−9.00000	+	15.5885i	−0.658145	+	1.13994i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−7.50000	+	12.9904i	−0.542681	+	0.939951i	0.456068	+	0.889945i	$0.349257\pi$
$191$	−7.50000	+	12.9904i	−0.542681	+	0.939951i	−0.998749	+	0.0500060i	$0.984076\pi$
$192$		0			0
$193$	−5.50000	−	9.52628i	−0.395899	−	0.685717i	0.597317	−	0.802005i	$-0.296234\pi$
$193$	−5.50000	−	9.52628i	−0.395899	−	0.685717i	−0.993215	+	0.116289i	$0.962900\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	6.00000			0.427482			0.213741	−	0.976890i	$-0.431435\pi$
$197$	6.00000			0.427482			0.213741	+	0.976890i	$0.431435\pi$
$198$		0			0
$199$	4.00000			0.283552			0.141776	−	0.989899i	$-0.454719\pi$
$199$	4.00000			0.283552			0.141776	+	0.989899i	$0.454719\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−1.50000	−	2.59808i	−0.105279	−	0.182349i
$204$		0			0
$205$	4.50000	−	7.79423i	0.314294	−	0.544373i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−6.00000	+	10.3923i	−0.415029	+	0.718851i
$210$		0			0
$211$	−8.50000	−	14.7224i	−0.585164	−	1.01353i	−0.994855	−	0.101310i	$-0.967697\pi$
$211$	−8.50000	−	14.7224i	−0.585164	−	1.01353i	0.409691	−	0.912224i	$-0.365637\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−3.00000			−0.204598
$216$		0			0
$217$	−5.00000			−0.339422
$218$		0			0
$219$		0			0
$220$		0			0
$221$	3.00000	+	5.19615i	0.201802	+	0.349531i
$222$		0			0
$223$	−0.500000	+	0.866025i	−0.0334825	+	0.0579934i	−0.882281	−	0.470723i	$-0.843993\pi$
$223$	−0.500000	+	0.866025i	−0.0334825	+	0.0579934i	0.848799	+	0.528716i	$0.177326\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	13.5000	−	23.3827i	0.896026	−	1.55196i	0.0634974	−	0.997982i	$-0.479775\pi$
$227$	13.5000	−	23.3827i	0.896026	−	1.55196i	0.832529	−	0.553981i	$-0.186892\pi$
$228$		0			0
$229$	−6.50000	−	11.2583i	−0.429532	−	0.743971i	0.567300	−	0.823511i	$-0.307988\pi$
$229$	−6.50000	−	11.2583i	−0.429532	−	0.743971i	−0.996832	+	0.0795401i	$0.974655\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	6.00000			0.393073			0.196537	−	0.980497i	$-0.437031\pi$
$233$	6.00000			0.393073			0.196537	+	0.980497i	$0.437031\pi$
$234$		0			0
$235$	−27.0000			−1.76129
$236$		0			0
$237$		0			0
$238$		0			0
$239$	13.5000	+	23.3827i	0.873242	+	1.51250i	0.858623	+	0.512607i	$0.171320\pi$
$239$	13.5000	+	23.3827i	0.873242	+	1.51250i	0.0146191	+	0.999893i	$0.495346\pi$
$240$		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
$245$	9.00000	−	15.5885i	0.574989	−	0.995910i
$246$		0			0
$247$	2.00000	+	3.46410i	0.127257	+	0.220416i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−12.0000			−0.757433			−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000			−0.757433			−0.378717	+	0.925513i	$0.623635\pi$
$252$		0			0
$253$	9.00000			0.565825
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−4.50000	−	7.79423i	−0.280702	−	0.486191i	0.690856	−	0.722993i	$-0.257234\pi$
$257$	−4.50000	−	7.79423i	−0.280702	−	0.486191i	−0.971558	+	0.236802i	$0.923901\pi$
$258$		0			0
$259$	1.00000	−	1.73205i	0.0621370	−	0.107624i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	10.5000	−	18.1865i	0.647458	−	1.12143i	−0.336270	−	0.941766i	$-0.609166\pi$
$263$	10.5000	−	18.1865i	0.647458	−	1.12143i	0.983728	−	0.179664i	$-0.0575011\pi$
$264$		0			0
$265$	9.00000	+	15.5885i	0.552866	+	0.957591i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−6.00000			−0.365826			−0.182913	−	0.983129i	$-0.558553\pi$
$269$	−6.00000			−0.365826			−0.182913	+	0.983129i	$0.558553\pi$
$270$		0			0
$271$	−8.00000			−0.485965			−0.242983	−	0.970031i	$-0.578126\pi$
$271$	−8.00000			−0.485965			−0.242983	+	0.970031i	$0.578126\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	6.00000	+	10.3923i	0.361814	+	0.626680i
$276$		0			0
$277$	−0.500000	+	0.866025i	−0.0300421	+	0.0520344i	−0.880656	−	0.473757i	$-0.842897\pi$
$277$	−0.500000	+	0.866025i	−0.0300421	+	0.0520344i	0.850613	+	0.525792i	$0.176231\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	1.50000	−	2.59808i	0.0894825	−	0.154988i	−0.817810	−	0.575488i	$-0.804812\pi$
$281$	1.50000	−	2.59808i	0.0894825	−	0.154988i	0.907293	+	0.420500i	$0.138145\pi$
$282$		0			0
$283$	−2.50000	−	4.33013i	−0.148610	−	0.257399i	0.782104	−	0.623148i	$-0.214146\pi$
$283$	−2.50000	−	4.33013i	−0.148610	−	0.257399i	−0.930714	+	0.365748i	$0.880813\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−3.00000			−0.177084
$288$		0			0
$289$	19.0000			1.11765
$290$		0			0
$291$		0			0
$292$		0			0
$293$	10.5000	+	18.1865i	0.613417	+	1.06247i	0.990660	+	0.136355i	$0.0435386\pi$
$293$	10.5000	+	18.1865i	0.613417	+	1.06247i	−0.377244	+	0.926114i	$0.623128\pi$
$294$		0			0
$295$	−4.50000	+	7.79423i	−0.262000	+	0.453798i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	1.50000	−	2.59808i	0.0867472	−	0.150251i
$300$		0			0
$301$	0.500000	+	0.866025i	0.0288195	+	0.0499169i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	39.0000			2.23313
$306$		0			0
$307$	20.0000			1.14146			0.570730	−	0.821138i	$-0.306660\pi$
$307$	20.0000			1.14146			0.570730	+	0.821138i	$0.306660\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−10.5000	−	18.1865i	−0.595400	−	1.03126i	−0.993490	−	0.113917i	$-0.963660\pi$
$311$	−10.5000	−	18.1865i	−0.595400	−	1.03126i	0.398090	−	0.917346i	$-0.369673\pi$
$312$		0			0
$313$	0.500000	−	0.866025i	0.0282617	−	0.0489506i	−0.851549	−	0.524276i	$-0.824336\pi$
$313$	0.500000	−	0.866025i	0.0282617	−	0.0489506i	0.879810	+	0.475325i	$0.157669\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	10.5000	−	18.1865i	0.589739	−	1.02146i	−0.404528	−	0.914526i	$-0.632564\pi$
$317$	10.5000	−	18.1865i	0.589739	−	1.02146i	0.994266	−	0.106932i	$-0.0341026\pi$
$318$		0			0
$319$	4.50000	+	7.79423i	0.251952	+	0.436393i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	24.0000			1.33540
$324$		0			0
$325$	4.00000			0.221880
$326$		0			0
$327$		0			0
$328$		0			0
$329$	4.50000	+	7.79423i	0.248093	+	0.429710i
$330$		0			0
$331$	−5.50000	+	9.52628i	−0.302307	+	0.523612i	−0.976658	−	0.214799i	$-0.931090\pi$
$331$	−5.50000	+	9.52628i	−0.302307	+	0.523612i	0.674351	+	0.738411i	$0.264424\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	10.5000	−	18.1865i	0.573676	−	0.993636i
$336$		0			0
$337$	−11.5000	−	19.9186i	−0.626445	−	1.08503i	−0.988260	−	0.152784i	$-0.951176\pi$
$337$	−11.5000	−	19.9186i	−0.626445	−	1.08503i	0.361815	−	0.932250i	$-0.382157\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	15.0000			0.812296
$342$		0			0
$343$	−13.0000			−0.701934
$344$		0			0
$345$		0			0
$346$		0			0
$347$	4.50000	+	7.79423i	0.241573	+	0.418416i	0.961162	−	0.275983i	$-0.0890035\pi$
$347$	4.50000	+	7.79423i	0.241573	+	0.418416i	−0.719590	+	0.694399i	$0.755670\pi$
$348$		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
$351$		0			0
$352$		0			0
$353$	1.50000	−	2.59808i	0.0798369	−	0.138282i	−0.823343	−	0.567545i	$-0.807893\pi$
$353$	1.50000	−	2.59808i	0.0798369	−	0.138282i	0.903179	+	0.429263i	$0.141227\pi$
$354$		0			0
$355$	18.0000	+	31.1769i	0.955341	+	1.65470i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		0			0			−	1.00000i	$-0.5\pi$
$359$		0			0				1.00000i	$0.5\pi$
$360$		0			0
$361$	−3.00000			−0.157895
$362$		0			0
$363$		0			0
$364$		0			0
$365$	15.0000	+	25.9808i	0.785136	+	1.35990i
$366$		0			0
$367$	−6.50000	+	11.2583i	−0.339297	+	0.587680i	−0.984301	−	0.176500i	$-0.943523\pi$
$367$	−6.50000	+	11.2583i	−0.339297	+	0.587680i	0.645003	+	0.764180i	$0.276856\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	3.00000	−	5.19615i	0.155752	−	0.269771i
$372$		0			0
$373$	−0.500000	−	0.866025i	−0.0258890	−	0.0448411i	0.852791	−	0.522253i	$-0.174908\pi$
$373$	−0.500000	−	0.866025i	−0.0258890	−	0.0448411i	−0.878680	+	0.477412i	$0.841575\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	3.00000			0.154508
$378$		0			0
$379$	−16.0000			−0.821865			−0.410932	−	0.911666i	$-0.634797\pi$
$379$	−16.0000			−0.821865			−0.410932	+	0.911666i	$0.634797\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	7.50000	+	12.9904i	0.383232	+	0.663777i	0.991522	−	0.129937i	$-0.0414776\pi$
$383$	7.50000	+	12.9904i	0.383232	+	0.663777i	−0.608290	+	0.793715i	$0.708144\pi$
$384$		0			0
$385$	4.50000	−	7.79423i	0.229341	−	0.397231i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−7.50000	+	12.9904i	−0.380265	+	0.658638i	−0.991100	−	0.133120i	$-0.957501\pi$
$389$	−7.50000	+	12.9904i	−0.380265	+	0.658638i	0.610835	+	0.791758i	$0.290834\pi$
$390$		0			0
$391$	−9.00000	−	15.5885i	−0.455150	−	0.788342i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−33.0000			−1.66041
$396$		0			0
$397$	−2.00000			−0.100377			−0.0501886	−	0.998740i	$-0.515982\pi$
$397$	−2.00000			−0.100377			−0.0501886	+	0.998740i	$0.515982\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	1.50000	+	2.59808i	0.0749064	+	0.129742i	0.901046	−	0.433724i	$-0.142801\pi$
$401$	1.50000	+	2.59808i	0.0749064	+	0.129742i	−0.826139	+	0.563466i	$0.809468\pi$
$402$		0			0
$403$	2.50000	−	4.33013i	0.124534	−	0.215699i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−3.00000	+	5.19615i	−0.148704	+	0.257564i
$408$		0			0
$409$	−11.5000	−	19.9186i	−0.568638	−	0.984911i	−0.996701	−	0.0811615i	$-0.974137\pi$
$409$	−11.5000	−	19.9186i	−0.568638	−	0.984911i	0.428063	−	0.903749i	$-0.359196\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	3.00000			0.147620
$414$		0			0
$415$	27.0000			1.32538
$416$		0			0
$417$		0			0
$418$		0			0
$419$	4.50000	+	7.79423i	0.219839	+	0.380773i	0.954759	−	0.297382i	$-0.0961133\pi$
$419$	4.50000	+	7.79423i	0.219839	+	0.380773i	−0.734919	+	0.678155i	$0.762780\pi$
$420$		0			0
$421$	17.5000	−	30.3109i	0.852898	−	1.47726i	−0.0256838	−	0.999670i	$-0.508176\pi$
$421$	17.5000	−	30.3109i	0.852898	−	1.47726i	0.878582	−	0.477592i	$-0.158490\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	12.0000	−	20.7846i	0.582086	−	1.00820i
$426$		0			0
$427$	−6.50000	−	11.2583i	−0.314557	−	0.544829i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	24.0000			1.15604			0.578020	−	0.816023i	$-0.303826\pi$
$431$	24.0000			1.15604			0.578020	+	0.816023i	$0.303826\pi$
$432$		0			0
$433$	−34.0000			−1.63394			−0.816968	−	0.576683i	$-0.804347\pi$
$433$	−34.0000			−1.63394			−0.816968	+	0.576683i	$0.804347\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−6.00000	−	10.3923i	−0.287019	−	0.497131i
$438$		0			0
$439$	17.5000	−	30.3109i	0.835229	−	1.44666i	−0.0586141	−	0.998281i	$-0.518668\pi$
$439$	17.5000	−	30.3109i	0.835229	−	1.44666i	0.893843	−	0.448379i	$-0.147999\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−4.50000	+	7.79423i	−0.213801	+	0.370315i	−0.952901	−	0.303281i	$-0.901918\pi$
$443$	−4.50000	+	7.79423i	−0.213801	+	0.370315i	0.739100	+	0.673596i	$0.235251\pi$
$444$		0			0
$445$	9.00000	+	15.5885i	0.426641	+	0.738964i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	18.0000			0.849473			0.424736	−	0.905317i	$-0.360367\pi$
$449$	18.0000			0.849473			0.424736	+	0.905317i	$0.360367\pi$
$450$		0			0
$451$	9.00000			0.423793
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−1.50000	−	2.59808i	−0.0703211	−	0.121800i
$456$		0			0
$457$	18.5000	−	32.0429i	0.865393	−	1.49891i	−0.00126243	−	0.999999i	$-0.500402\pi$
$457$	18.5000	−	32.0429i	0.865393	−	1.49891i	0.866656	−	0.498906i	$-0.166265\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−1.50000	+	2.59808i	−0.0698620	+	0.121004i	−0.898840	−	0.438276i	$-0.855589\pi$
$461$	−1.50000	+	2.59808i	−0.0698620	+	0.121004i	0.828978	+	0.559281i	$0.188923\pi$
$462$		0			0
$463$	−9.50000	−	16.4545i	−0.441502	−	0.764705i	0.556299	−	0.830982i	$-0.312221\pi$
$463$	−9.50000	−	16.4545i	−0.441502	−	0.764705i	−0.997801	+	0.0662777i	$0.978888\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−12.0000			−0.555294			−0.277647	−	0.960683i	$-0.589555\pi$
$467$	−12.0000			−0.555294			−0.277647	+	0.960683i	$0.589555\pi$
$468$		0			0
$469$	−7.00000			−0.323230
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−1.50000	−	2.59808i	−0.0689701	−	0.119460i
$474$		0			0
$475$	8.00000	−	13.8564i	0.367065	−	0.635776i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−13.5000	+	23.3827i	−0.616831	+	1.06838i	0.373230	+	0.927739i	$0.378250\pi$
$479$	−13.5000	+	23.3827i	−0.616831	+	1.06838i	−0.990060	+	0.140643i	$0.955083\pi$
$480$		0			0
$481$	1.00000	+	1.73205i	0.0455961	+	0.0789747i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	33.0000			1.49845
$486$		0			0
$487$	−32.0000			−1.45006			−0.725029	−	0.688718i	$-0.758174\pi$
$487$	−32.0000			−1.45006			−0.725029	+	0.688718i	$0.758174\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−1.50000	−	2.59808i	−0.0676941	−	0.117250i	0.830192	−	0.557478i	$-0.188231\pi$
$491$	−1.50000	−	2.59808i	−0.0676941	−	0.117250i	−0.897886	+	0.440228i	$0.854898\pi$
$492$		0			0
$493$	9.00000	−	15.5885i	0.405340	−	0.702069i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	6.00000	−	10.3923i	0.269137	−	0.466159i
$498$		0			0
$499$	−2.50000	−	4.33013i	−0.111915	−	0.193843i	0.804627	−	0.593780i	$-0.202365\pi$
$499$	−2.50000	−	4.33013i	−0.111915	−	0.193843i	−0.916542	+	0.399937i	$0.869032\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−36.0000			−1.60516			−0.802580	−	0.596544i	$-0.796540\pi$
$503$	−36.0000			−1.60516			−0.802580	+	0.596544i	$0.796540\pi$
$504$		0			0
$505$	45.0000			2.00247
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−19.5000	−	33.7750i	−0.864322	−	1.49705i	−0.867719	−	0.497056i	$-0.834414\pi$
$509$	−19.5000	−	33.7750i	−0.864322	−	1.49705i	0.00339621	−	0.999994i	$-0.498919\pi$
$510$		0			0
$511$	5.00000	−	8.66025i	0.221187	−	0.383107i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−10.5000	+	18.1865i	−0.462685	+	0.801394i
$516$		0			0
$517$	−13.5000	−	23.3827i	−0.593729	−	1.02837i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−42.0000			−1.84005			−0.920027	−	0.391856i	$-0.871833\pi$
$521$	−42.0000			−1.84005			−0.920027	+	0.391856i	$0.871833\pi$
$522$		0			0
$523$	8.00000			0.349816			0.174908	−	0.984585i	$-0.444037\pi$
$523$	8.00000			0.349816			0.174908	+	0.984585i	$0.444037\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−15.0000	−	25.9808i	−0.653410	−	1.13174i
$528$		0			0
$529$	7.00000	−	12.1244i	0.304348	−	0.527146i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	1.50000	−	2.59808i	0.0649722	−	0.112535i
$534$		0			0
$535$	18.0000	+	31.1769i	0.778208	+	1.34790i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	18.0000			0.775315
$540$		0			0
$541$	34.0000			1.46177			0.730887	−	0.682498i	$-0.239107\pi$
$541$	34.0000			1.46177			0.730887	+	0.682498i	$0.239107\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	3.00000	+	5.19615i	0.128506	+	0.222579i
$546$		0			0
$547$	6.50000	−	11.2583i	0.277920	−	0.481371i	−0.692948	−	0.720988i	$-0.743688\pi$
$547$	6.50000	−	11.2583i	0.277920	−	0.481371i	0.970868	+	0.239616i	$0.0770217\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	6.00000	−	10.3923i	0.255609	−	0.442727i
$552$		0			0
$553$	5.50000	+	9.52628i	0.233884	+	0.405099i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−30.0000			−1.27114			−0.635570	−	0.772043i	$-0.719235\pi$
$557$	−30.0000			−1.27114			−0.635570	+	0.772043i	$0.719235\pi$
$558$		0			0
$559$	−1.00000			−0.0422955
$560$		0			0
$561$		0			0
$562$		0			0
$563$	4.50000	+	7.79423i	0.189652	+	0.328488i	0.945134	−	0.326682i	$-0.105931\pi$
$563$	4.50000	+	7.79423i	0.189652	+	0.328488i	−0.755482	+	0.655169i	$0.772597\pi$
$564$		0			0
$565$	−13.5000	+	23.3827i	−0.567949	+	0.983717i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	7.50000	−	12.9904i	0.314416	−	0.544585i	−0.664897	−	0.746935i	$-0.731525\pi$
$569$	7.50000	−	12.9904i	0.314416	−	0.544585i	0.979313	+	0.202350i	$0.0648579\pi$
$570$		0			0
$571$	15.5000	+	26.8468i	0.648655	+	1.12350i	0.983444	+	0.181210i	$0.0580014\pi$
$571$	15.5000	+	26.8468i	0.648655	+	1.12350i	−0.334790	+	0.942293i	$0.608665\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−12.0000			−0.500435
$576$		0			0
$577$	−10.0000			−0.416305			−0.208153	−	0.978096i	$-0.566745\pi$
$577$	−10.0000			−0.416305			−0.208153	+	0.978096i	$0.566745\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−4.50000	−	7.79423i	−0.186691	−	0.323359i
$582$		0			0
$583$	−9.00000	+	15.5885i	−0.372742	+	0.645608i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	7.50000	−	12.9904i	0.309558	−	0.536170i	−0.668708	−	0.743525i	$-0.733152\pi$
$587$	7.50000	−	12.9904i	0.309558	−	0.536170i	0.978266	+	0.207355i	$0.0664855\pi$
$588$		0			0
$589$	−10.0000	−	17.3205i	−0.412043	−	0.713679i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−6.00000			−0.246390			−0.123195	−	0.992382i	$-0.539314\pi$
$593$	−6.00000			−0.246390			−0.123195	+	0.992382i	$0.539314\pi$
$594$		0			0
$595$	−18.0000			−0.737928
$596$		0			0
$597$		0			0
$598$		0			0
$599$	19.5000	+	33.7750i	0.796748	+	1.38001i	0.921723	+	0.387849i	$0.126782\pi$
$599$	19.5000	+	33.7750i	0.796748	+	1.38001i	−0.124975	+	0.992160i	$0.539885\pi$
$600$		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
$603$		0			0
$604$		0			0
$605$	3.00000	−	5.19615i	0.121967	−	0.211254i
$606$		0			0
$607$	20.5000	+	35.5070i	0.832069	+	1.44119i	0.896394	+	0.443257i	$0.146177\pi$
$607$	20.5000	+	35.5070i	0.832069	+	1.44119i	−0.0643251	+	0.997929i	$0.520489\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−9.00000			−0.364101
$612$		0			0
$613$	−26.0000			−1.05013			−0.525065	−	0.851062i	$-0.675959\pi$
$613$	−26.0000			−1.05013			−0.525065	+	0.851062i	$0.675959\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	1.50000	+	2.59808i	0.0603877	+	0.104595i	0.894639	−	0.446790i	$-0.147433\pi$
$617$	1.50000	+	2.59808i	0.0603877	+	0.104595i	−0.834251	+	0.551385i	$0.814100\pi$
$618$		0			0
$619$	6.50000	−	11.2583i	0.261257	−	0.452510i	−0.705319	−	0.708890i	$-0.749196\pi$
$619$	6.50000	−	11.2583i	0.261257	−	0.452510i	0.966576	+	0.256379i	$0.0825296\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	3.00000	−	5.19615i	0.120192	−	0.208179i
$624$		0			0
$625$	14.5000	+	25.1147i	0.580000	+	1.00459i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	12.0000			0.478471
$630$		0			0
$631$	16.0000			0.636950			0.318475	−	0.947931i	$-0.396829\pi$
$631$	16.0000			0.636950			0.318475	+	0.947931i	$0.396829\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−24.0000	−	41.5692i	−0.952411	−	1.64962i
$636$		0			0
$637$	3.00000	−	5.19615i	0.118864	−	0.205879i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−16.5000	+	28.5788i	−0.651711	+	1.12880i	0.330997	+	0.943632i	$0.392615\pi$
$641$	−16.5000	+	28.5788i	−0.651711	+	1.12880i	−0.982708	+	0.185164i	$0.940718\pi$
$642$		0			0
$643$	−20.5000	−	35.5070i	−0.808441	−	1.40026i	−0.913943	−	0.405842i	$-0.866978\pi$
$643$	−20.5000	−	35.5070i	−0.808441	−	1.40026i	0.105502	−	0.994419i	$-0.466355\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0			−	1.00000i	$-0.5\pi$
$647$		0			0				1.00000i	$0.5\pi$
$648$		0			0
$649$	−9.00000			−0.353281
$650$		0			0
$651$		0			0
$652$		0			0
$653$	10.5000	+	18.1865i	0.410897	+	0.711694i	0.994988	−	0.0999939i	$-0.0318823\pi$
$653$	10.5000	+	18.1865i	0.410897	+	0.711694i	−0.584091	+	0.811688i	$0.698549\pi$
$654$		0			0
$655$	31.5000	−	54.5596i	1.23081	−	2.13182i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−10.5000	+	18.1865i	−0.409022	+	0.708447i	−0.994780	−	0.102039i	$-0.967463\pi$
$659$	−10.5000	+	18.1865i	−0.409022	+	0.708447i	0.585758	+	0.810486i	$0.300797\pi$
$660$		0			0
$661$	5.50000	+	9.52628i	0.213925	+	0.370529i	0.952940	−	0.303160i	$-0.0980418\pi$
$661$	5.50000	+	9.52628i	0.213925	+	0.370529i	−0.739014	+	0.673690i	$0.764708\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−12.0000			−0.465340
$666$		0			0
$667$	−9.00000			−0.348481
$668$		0			0
$669$		0			0
$670$		0			0
$671$	19.5000	+	33.7750i	0.752789	+	1.30387i
$672$		0			0
$673$	−5.50000	+	9.52628i	−0.212009	+	0.367211i	−0.952343	−	0.305028i	$-0.901334\pi$
$673$	−5.50000	+	9.52628i	−0.212009	+	0.367211i	0.740334	+	0.672239i	$0.234667\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−7.50000	+	12.9904i	−0.288248	+	0.499261i	−0.973392	−	0.229147i	$-0.926406\pi$
$677$	−7.50000	+	12.9904i	−0.288248	+	0.499261i	0.685143	+	0.728408i	$0.259740\pi$
$678$		0			0
$679$	−5.50000	−	9.52628i	−0.211071	−	0.365585i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	36.0000			1.37750			0.688751	−	0.724998i	$-0.258159\pi$
$683$	36.0000			1.37750			0.688751	+	0.724998i	$0.258159\pi$
$684$		0			0
$685$	−9.00000			−0.343872
$686$		0			0
$687$		0			0
$688$		0			0
$689$	3.00000	+	5.19615i	0.114291	+	0.197958i
$690$		0			0
$691$	0.500000	−	0.866025i	0.0190209	−	0.0329452i	−0.856358	−	0.516382i	$-0.827278\pi$
$691$	0.500000	−	0.866025i	0.0190209	−	0.0329452i	0.875379	+	0.483437i	$0.160612\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−7.50000	+	12.9904i	−0.284491	+	0.492753i
$696$		0			0
$697$	−9.00000	−	15.5885i	−0.340899	−	0.590455i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−6.00000			−0.226617			−0.113308	−	0.993560i	$-0.536145\pi$
$701$	−6.00000			−0.226617			−0.113308	+	0.993560i	$0.536145\pi$
$702$		0			0
$703$	8.00000			0.301726
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−7.50000	−	12.9904i	−0.282067	−	0.488554i
$708$		0			0
$709$	−12.5000	+	21.6506i	−0.469447	+	0.813107i	−0.999390	−	0.0349269i	$-0.988880\pi$
$709$	−12.5000	+	21.6506i	−0.469447	+	0.813107i	0.529943	+	0.848034i	$0.322213\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−7.50000	+	12.9904i	−0.280877	+	0.486494i
$714$		0			0
$715$	4.50000	+	7.79423i	0.168290	+	0.291488i
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0			−	1.00000i	$-0.5\pi$
$719$		0			0				1.00000i	$0.5\pi$
$720$		0			0
$721$	7.00000			0.260694
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−6.00000	−	10.3923i	−0.222834	−	0.385961i
$726$		0			0
$727$	−18.5000	+	32.0429i	−0.686127	+	1.18841i	0.286954	+	0.957944i	$0.407357\pi$
$727$	−18.5000	+	32.0429i	−0.686127	+	1.18841i	−0.973081	+	0.230463i	$0.925976\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−3.00000	+	5.19615i	−0.110959	+	0.192187i
$732$		0			0
$733$	11.5000	+	19.9186i	0.424762	+	0.735710i	0.996398	−	0.0847976i	$-0.0270244\pi$
$733$	11.5000	+	19.9186i	0.424762	+	0.735710i	−0.571636	+	0.820507i	$0.693691\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	21.0000			0.773545
$738$		0			0
$739$	−16.0000			−0.588570			−0.294285	−	0.955718i	$-0.595081\pi$
$739$	−16.0000			−0.588570			−0.294285	+	0.955718i	$0.595081\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−4.50000	−	7.79423i	−0.165089	−	0.285943i	0.771598	−	0.636111i	$-0.219458\pi$
$743$	−4.50000	−	7.79423i	−0.165089	−	0.285943i	−0.936687	+	0.350168i	$0.886124\pi$
$744$		0			0
$745$	−22.5000	+	38.9711i	−0.824336	+	1.42779i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	6.00000	−	10.3923i	0.219235	−	0.379727i
$750$		0			0
$751$	−15.5000	−	26.8468i	−0.565603	−	0.979653i	−0.996993	−	0.0774878i	$-0.975310\pi$
$751$	−15.5000	−	26.8468i	−0.565603	−	0.979653i	0.431390	−	0.902165i	$-0.358023\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	39.0000			1.41936
$756$		0			0
$757$	10.0000			0.363456			0.181728	−	0.983349i	$-0.441831\pi$
$757$	10.0000			0.363456			0.181728	+	0.983349i	$0.441831\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	13.5000	+	23.3827i	0.489375	+	0.847622i	0.999925	−	0.0122260i	$-0.00389175\pi$
$761$	13.5000	+	23.3827i	0.489375	+	0.847622i	−0.510551	+	0.859848i	$0.670558\pi$
$762$		0			0
$763$	1.00000	−	1.73205i	0.0362024	−	0.0627044i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−1.50000	+	2.59808i	−0.0541619	+	0.0938111i
$768$		0			0
$769$	0.500000	+	0.866025i	0.0180305	+	0.0312297i	0.874900	−	0.484304i	$-0.160927\pi$
$769$	0.500000	+	0.866025i	0.0180305	+	0.0312297i	−0.856869	+	0.515534i	$0.827594\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	18.0000			0.647415			0.323708	−	0.946157i	$-0.395071\pi$
$773$	18.0000			0.647415			0.323708	+	0.946157i	$0.395071\pi$
$774$		0			0
$775$	−20.0000			−0.718421
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−6.00000	−	10.3923i	−0.214972	−	0.372343i
$780$		0			0
$781$	−18.0000	+	31.1769i	−0.644091	+	1.11560i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−19.5000	+	33.7750i	−0.695985	+	1.20548i
$786$		0			0
$787$	21.5000	+	37.2391i	0.766392	+	1.32743i	0.939507	+	0.342529i	$0.111283\pi$
$787$	21.5000	+	37.2391i	0.766392	+	1.32743i	−0.173115	+	0.984902i	$0.555383\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	9.00000			0.320003
$792$		0			0
$793$	13.0000			0.461644
$794$		0			0
$795$		0			0
$796$		0			0
$797$	4.50000	+	7.79423i	0.159398	+	0.276086i	0.934652	−	0.355564i	$-0.115711\pi$
$797$	4.50000	+	7.79423i	0.159398	+	0.276086i	−0.775254	+	0.631650i	$0.782378\pi$
$798$		0			0
$799$	−27.0000	+	46.7654i	−0.955191	+	1.65444i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−15.0000	+	25.9808i	−0.529339	+	0.916841i
$804$		0			0
$805$	4.50000	+	7.79423i	0.158604	+	0.274710i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−6.00000			−0.210949			−0.105474	−	0.994422i	$-0.533636\pi$
$809$	−6.00000			−0.210949			−0.105474	+	0.994422i	$0.533636\pi$
$810$		0			0
$811$	20.0000			0.702295			0.351147	−	0.936320i	$-0.385792\pi$
$811$	20.0000			0.702295			0.351147	+	0.936320i	$0.385792\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−30.0000	−	51.9615i	−1.05085	−	1.82013i
$816$		0			0
$817$	−2.00000	+	3.46410i	−0.0699711	+	0.121194i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−25.5000	+	44.1673i	−0.889956	+	1.54145i	−0.0500305	+	0.998748i	$0.515932\pi$
$821$	−25.5000	+	44.1673i	−0.889956	+	1.54145i	−0.839926	+	0.542702i	$0.817401\pi$
$822$		0			0
$823$	−9.50000	−	16.4545i	−0.331149	−	0.573567i	0.651588	−	0.758573i	$-0.274103\pi$
$823$	−9.50000	−	16.4545i	−0.331149	−	0.573567i	−0.982737	+	0.185006i	$0.940770\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	12.0000			0.417281			0.208640	−	0.977992i	$-0.433096\pi$
$827$	12.0000			0.417281			0.208640	+	0.977992i	$0.433096\pi$
$828$		0			0
$829$	−50.0000			−1.73657			−0.868286	−	0.496064i	$-0.834778\pi$
$829$	−50.0000			−1.73657			−0.868286	+	0.496064i	$0.834778\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−18.0000	−	31.1769i	−0.623663	−	1.08022i
$834$		0			0
$835$	−13.5000	+	23.3827i	−0.467187	+	0.809191i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	4.50000	−	7.79423i	0.155357	−	0.269087i	−0.777832	−	0.628473i	$-0.783680\pi$
$839$	4.50000	−	7.79423i	0.155357	−	0.269087i	0.933189	+	0.359386i	$0.117014\pi$
$840$		0			0
$841$	10.0000	+	17.3205i	0.344828	+	0.597259i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−36.0000			−1.23844
$846$		0			0
$847$	−2.00000			−0.0687208
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−3.00000	−	5.19615i	−0.102839	−	0.178122i
$852$		0			0
$853$	−6.50000	+	11.2583i	−0.222556	+	0.385478i	−0.955583	−	0.294721i	$-0.904773\pi$
$853$	−6.50000	+	11.2583i	−0.222556	+	0.385478i	0.733028	+	0.680199i	$0.238107\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	13.5000	−	23.3827i	0.461151	−	0.798737i	−0.537867	−	0.843029i	$-0.680770\pi$
$857$	13.5000	−	23.3827i	0.461151	−	0.798737i	0.999019	+	0.0442921i	$0.0141032\pi$
$858$		0			0
$859$	−20.5000	−	35.5070i	−0.699451	−	1.21148i	−0.968657	−	0.248402i	$-0.920095\pi$
$859$	−20.5000	−	35.5070i	−0.699451	−	1.21148i	0.269206	−	0.963083i	$-0.413239\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	24.0000			0.816970			0.408485	−	0.912765i	$-0.366057\pi$
$863$	24.0000			0.816970			0.408485	+	0.912765i	$0.366057\pi$
$864$		0			0
$865$	−27.0000			−0.918028
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−16.5000	−	28.5788i	−0.559724	−	0.969471i
$870$		0			0
$871$	3.50000	−	6.06218i	0.118593	−	0.205409i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	1.50000	−	2.59808i	0.0507093	−	0.0878310i
$876$		0			0
$877$	11.5000	+	19.9186i	0.388327	+	0.672603i	0.992225	−	0.124459i	$-0.0397196\pi$
$877$	11.5000	+	19.9186i	0.388327	+	0.672603i	−0.603897	+	0.797062i	$0.706386\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−30.0000			−1.01073			−0.505363	−	0.862907i	$-0.668641\pi$
$881$	−30.0000			−1.01073			−0.505363	+	0.862907i	$0.668641\pi$
$882$		0			0
$883$	−4.00000			−0.134611			−0.0673054	−	0.997732i	$-0.521440\pi$
$883$	−4.00000			−0.134611			−0.0673054	+	0.997732i	$0.521440\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−10.5000	−	18.1865i	−0.352555	−	0.610644i	0.634141	−	0.773217i	$-0.281354\pi$
$887$	−10.5000	−	18.1865i	−0.352555	−	0.610644i	−0.986696	+	0.162573i	$0.948021\pi$
$888$		0			0
$889$	−8.00000	+	13.8564i	−0.268311	+	0.464729i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−18.0000	+	31.1769i	−0.602347	+	1.04330i
$894$		0			0
$895$	18.0000	+	31.1769i	0.601674	+	1.04213i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−15.0000			−0.500278
$900$		0			0
$901$	36.0000			1.19933
$902$		0			0
$903$		0			0
$904$		0			0
$905$	3.00000	+	5.19615i	0.0997234	+	0.172726i
$906$		0			0
$907$	−23.5000	+	40.7032i	−0.780305	+	1.35153i	0.151460	+	0.988463i	$0.451603\pi$
$907$	−23.5000	+	40.7032i	−0.780305	+	1.35153i	−0.931764	+	0.363064i	$0.881731\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	22.5000	−	38.9711i	0.745458	−	1.29117i	−0.204522	−	0.978862i	$-0.565564\pi$
$911$	22.5000	−	38.9711i	0.745458	−	1.29117i	0.949980	−	0.312310i	$-0.101103\pi$
$912$		0			0
$913$	13.5000	+	23.3827i	0.446785	+	0.773854i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−21.0000			−0.693481
$918$		0			0
$919$	16.0000			0.527791			0.263896	−	0.964551i	$-0.414993\pi$
$919$	16.0000			0.527791			0.263896	+	0.964551i	$0.414993\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	6.00000	+	10.3923i	0.197492	+	0.342067i
$924$		0			0
$925$	4.00000	−	6.92820i	0.131519	−	0.227798i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	13.5000	−	23.3827i	0.442921	−	0.767161i	−0.554984	−	0.831861i	$-0.687276\pi$
$929$	13.5000	−	23.3827i	0.442921	−	0.767161i	0.997905	+	0.0646999i	$0.0206090\pi$
$930$		0			0
$931$	−12.0000	−	20.7846i	−0.393284	−	0.681188i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	54.0000			1.76599
$936$		0			0
$937$	−34.0000			−1.11073			−0.555366	−	0.831606i	$-0.687422\pi$
$937$	−34.0000			−1.11073			−0.555366	+	0.831606i	$0.687422\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	10.5000	+	18.1865i	0.342290	+	0.592864i	0.984858	−	0.173365i	$-0.0554641\pi$
$941$	10.5000	+	18.1865i	0.342290	+	0.592864i	−0.642567	+	0.766229i	$0.722131\pi$
$942$		0			0
$943$	−4.50000	+	7.79423i	−0.146540	+	0.253815i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	13.5000	−	23.3827i	0.438691	−	0.759835i	−0.558898	−	0.829237i	$-0.688776\pi$
$947$	13.5000	−	23.3827i	0.438691	−	0.759835i	0.997589	+	0.0694014i	$0.0221089\pi$
$948$		0			0
$949$	5.00000	+	8.66025i	0.162307	+	0.281124i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−54.0000			−1.74923			−0.874616	−	0.484817i	$-0.838886\pi$
$953$	−54.0000			−1.74923			−0.874616	+	0.484817i	$0.838886\pi$
$954$		0			0
$955$	45.0000			1.45617
$956$		0			0
$957$		0			0
$958$		0			0
$959$	1.50000	+	2.59808i	0.0484375	+	0.0838963i
$960$		0			0
$961$	3.00000	−	5.19615i	0.0967742	−	0.167618i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−16.5000	+	28.5788i	−0.531154	+	0.919985i
$966$		0			0
$967$	−21.5000	−	37.2391i	−0.691393	−	1.19753i	−0.971381	−	0.237525i	$-0.923664\pi$
$967$	−21.5000	−	37.2391i	−0.691393	−	1.19753i	0.279988	−	0.960003i	$-0.409669\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$		0			0			−	1.00000i	$-0.5\pi$
$971$		0			0				1.00000i	$0.5\pi$
$972$		0			0
$973$	5.00000			0.160293
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−28.5000	−	49.3634i	−0.911796	−	1.57928i	−0.811526	−	0.584316i	$-0.801363\pi$
$977$	−28.5000	−	49.3634i	−0.911796	−	1.57928i	−0.100270	−	0.994960i	$-0.531971\pi$
$978$		0			0
$979$	−9.00000	+	15.5885i	−0.287641	+	0.498209i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−25.5000	+	44.1673i	−0.813324	+	1.40872i	0.0972017	+	0.995265i	$0.469011\pi$
$983$	−25.5000	+	44.1673i	−0.813324	+	1.40872i	−0.910525	+	0.413453i	$0.864323\pi$
$984$		0			0
$985$	−9.00000	−	15.5885i	−0.286764	−	0.496690i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	3.00000			0.0953945
$990$		0			0
$991$	−8.00000			−0.254128			−0.127064	−	0.991894i	$-0.540555\pi$
$991$	−8.00000			−0.254128			−0.127064	+	0.991894i	$0.540555\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−6.00000	−	10.3923i	−0.190213	−	0.329458i
$996$		0			0
$997$	−0.500000	+	0.866025i	−0.0158352	+	0.0274273i	−0.873834	−	0.486224i	$-0.838374\pi$
$997$	−0.500000	+	0.866025i	−0.0158352	+	0.0274273i	0.857999	+	0.513651i	$0.171707\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1728.2.i.c.1153.1		2
3.2	odd	2		576.2.i.e.385.1		2
4.3	odd	2		1728.2.i.d.1153.1		2
8.3	odd	2		108.2.e.a.73.1		2
8.5	even	2		432.2.i.c.289.1		2
9.2	odd	6		5184.2.a.f.1.1		1
9.4	even	3	inner	1728.2.i.c.577.1		2
9.5	odd	6		576.2.i.e.193.1		2
9.7	even	3		5184.2.a.bb.1.1		1
12.11	even	2		576.2.i.f.385.1		2
24.5	odd	2		144.2.i.a.97.1		2
24.11	even	2		36.2.e.a.25.1	yes	2
36.7	odd	6		5184.2.a.ba.1.1		1
36.11	even	6		5184.2.a.e.1.1		1
36.23	even	6		576.2.i.f.193.1		2
36.31	odd	6		1728.2.i.d.577.1		2
40.3	even	4		2700.2.s.b.2449.1		4
40.19	odd	2		2700.2.i.b.1801.1		2
40.27	even	4		2700.2.s.b.2449.2		4
56.3	even	6		5292.2.l.c.3313.1		2
56.11	odd	6		5292.2.l.a.3313.1		2
56.19	even	6		5292.2.i.a.2125.1		2
56.27	even	2		5292.2.j.a.3529.1		2
56.51	odd	6		5292.2.i.c.2125.1		2
72.5	odd	6		144.2.i.a.49.1		2
72.11	even	6		324.2.a.c.1.1		1
72.13	even	6		432.2.i.c.145.1		2
72.29	odd	6		1296.2.a.k.1.1		1
72.43	odd	6		324.2.a.a.1.1		1
72.59	even	6		36.2.e.a.13.1	✓	2
72.61	even	6		1296.2.a.b.1.1		1
72.67	odd	6		108.2.e.a.37.1		2
120.59	even	2		900.2.i.b.601.1		2
120.83	odd	4		900.2.s.b.349.1		4
120.107	odd	4		900.2.s.b.349.2		4
168.11	even	6		1764.2.l.c.961.1		2
168.59	odd	6		1764.2.l.a.961.1		2
168.83	odd	2		1764.2.j.b.1177.1		2
168.107	even	6		1764.2.i.a.1537.1		2
168.131	odd	6		1764.2.i.c.1537.1		2
360.43	even	12		8100.2.d.c.649.2		2
360.59	even	6		900.2.i.b.301.1		2
360.67	even	12		2700.2.s.b.1549.1		4
360.83	odd	12		8100.2.d.h.649.2		2
360.139	odd	6		2700.2.i.b.901.1		2
360.187	even	12		8100.2.d.c.649.1		2
360.203	odd	12		900.2.s.b.49.2		4
360.227	odd	12		8100.2.d.h.649.1		2
360.259	odd	6		8100.2.a.g.1.1		1
360.283	even	12		2700.2.s.b.1549.2		4
360.299	even	6		8100.2.a.j.1.1		1
360.347	odd	12		900.2.s.b.49.1		4
504.59	odd	6		1764.2.i.c.373.1		2
504.67	odd	6		5292.2.i.c.1549.1		2
504.131	odd	6		1764.2.l.a.949.1		2
504.139	even	6		5292.2.j.a.1765.1		2
504.275	even	6		1764.2.l.c.949.1		2
504.283	even	6		5292.2.i.a.1549.1		2
504.347	even	6		1764.2.i.a.373.1		2
504.355	even	6		5292.2.l.c.361.1		2
504.419	odd	6		1764.2.j.b.589.1		2
504.499	odd	6		5292.2.l.a.361.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.2.e.a.13.1	✓	2	72.59	even	6
36.2.e.a.25.1	yes	2	24.11	even	2
108.2.e.a.37.1		2	72.67	odd	6
108.2.e.a.73.1		2	8.3	odd	2
144.2.i.a.49.1		2	72.5	odd	6
144.2.i.a.97.1		2	24.5	odd	2
324.2.a.a.1.1		1	72.43	odd	6
324.2.a.c.1.1		1	72.11	even	6
432.2.i.c.145.1		2	72.13	even	6
432.2.i.c.289.1		2	8.5	even	2
576.2.i.e.193.1		2	9.5	odd	6
576.2.i.e.385.1		2	3.2	odd	2
576.2.i.f.193.1		2	36.23	even	6
576.2.i.f.385.1		2	12.11	even	2
900.2.i.b.301.1		2	360.59	even	6
900.2.i.b.601.1		2	120.59	even	2
900.2.s.b.49.1		4	360.347	odd	12
900.2.s.b.49.2		4	360.203	odd	12
900.2.s.b.349.1		4	120.83	odd	4
900.2.s.b.349.2		4	120.107	odd	4
1296.2.a.b.1.1		1	72.61	even	6
1296.2.a.k.1.1		1	72.29	odd	6
1728.2.i.c.577.1		2	9.4	even	3	inner
1728.2.i.c.1153.1		2	1.1	even	1	trivial
1728.2.i.d.577.1		2	36.31	odd	6
1728.2.i.d.1153.1		2	4.3	odd	2
1764.2.i.a.373.1		2	504.347	even	6
1764.2.i.a.1537.1		2	168.107	even	6
1764.2.i.c.373.1		2	504.59	odd	6
1764.2.i.c.1537.1		2	168.131	odd	6
1764.2.j.b.589.1		2	504.419	odd	6
1764.2.j.b.1177.1		2	168.83	odd	2
1764.2.l.a.949.1		2	504.131	odd	6
1764.2.l.a.961.1		2	168.59	odd	6
1764.2.l.c.949.1		2	504.275	even	6
1764.2.l.c.961.1		2	168.11	even	6
2700.2.i.b.901.1		2	360.139	odd	6
2700.2.i.b.1801.1		2	40.19	odd	2
2700.2.s.b.1549.1		4	360.67	even	12
2700.2.s.b.1549.2		4	360.283	even	12
2700.2.s.b.2449.1		4	40.3	even	4
2700.2.s.b.2449.2		4	40.27	even	4
5184.2.a.e.1.1		1	36.11	even	6
5184.2.a.f.1.1		1	9.2	odd	6
5184.2.a.ba.1.1		1	36.7	odd	6
5184.2.a.bb.1.1		1	9.7	even	3
5292.2.i.a.1549.1		2	504.283	even	6
5292.2.i.a.2125.1		2	56.19	even	6
5292.2.i.c.1549.1		2	504.67	odd	6
5292.2.i.c.2125.1		2	56.51	odd	6
5292.2.j.a.1765.1		2	504.139	even	6
5292.2.j.a.3529.1		2	56.27	even	2
5292.2.l.a.361.1		2	504.499	odd	6
5292.2.l.a.3313.1		2	56.11	odd	6
5292.2.l.c.361.1		2	504.355	even	6
5292.2.l.c.3313.1		2	56.3	even	6
8100.2.a.g.1.1		1	360.259	odd	6
8100.2.a.j.1.1		1	360.299	even	6
8100.2.d.c.649.1		2	360.187	even	12
8100.2.d.c.649.2		2	360.43	even	12
8100.2.d.h.649.1		2	360.227	odd	12
8100.2.d.h.649.2		2	360.83	odd	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:	\( N \)	\(=\)	\( 1728 = 2^{6} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1728.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 - 2.59808i) q^{5} +(-0.500000 + 0.866025i) q^{7} +O(q^{10})\)	\(q+(-1.50000 - 2.59808i) q^{5} +(-0.500000 + 0.866025i) q^{7} +(1.50000 - 2.59808i) q^{11} +(-0.500000 - 0.866025i) q^{13} -6.00000 q^{17} -4.00000 q^{19} +(1.50000 + 2.59808i) q^{23} +(-2.00000 + 3.46410i) q^{25} +(-1.50000 + 2.59808i) q^{29} +(2.50000 + 4.33013i) q^{31} +3.00000 q^{35} -2.00000 q^{37} +(1.50000 + 2.59808i) q^{41} +(0.500000 - 0.866025i) q^{43} +(4.50000 - 7.79423i) q^{47} +(3.00000 + 5.19615i) q^{49} -6.00000 q^{53} -9.00000 q^{55} +(-1.50000 - 2.59808i) q^{59} +(-6.50000 + 11.2583i) q^{61} +(-1.50000 + 2.59808i) q^{65} +(3.50000 + 6.06218i) q^{67} -12.0000 q^{71} -10.0000 q^{73} +(1.50000 + 2.59808i) q^{77} +(5.50000 - 9.52628i) q^{79} +(-4.50000 + 7.79423i) q^{83} +(9.00000 + 15.5885i) q^{85} -6.00000 q^{89} +1.00000 q^{91} +(6.00000 + 10.3923i) q^{95} +(-5.50000 + 9.52628i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 3 q^{5} - q^{7}+O(q^{10}) \) 2 * q - 3 * q^5 - q^7	\( 2 q - 3 q^{5} - q^{7} + 3 q^{11} - q^{13} - 12 q^{17} - 8 q^{19} + 3 q^{23} - 4 q^{25} - 3 q^{29} + 5 q^{31} + 6 q^{35} - 4 q^{37} + 3 q^{41} + q^{43} + 9 q^{47} + 6 q^{49} - 12 q^{53} - 18 q^{55} - 3 q^{59} - 13 q^{61} - 3 q^{65} + 7 q^{67} - 24 q^{71} - 20 q^{73} + 3 q^{77} + 11 q^{79} - 9 q^{83} + 18 q^{85} - 12 q^{89} + 2 q^{91} + 12 q^{95} - 11 q^{97}+O(q^{100}) \) 2 * q - 3 * q^5 - q^7 + 3 * q^11 - q^13 - 12 * q^17 - 8 * q^19 + 3 * q^23 - 4 * q^25 - 3 * q^29 + 5 * q^31 + 6 * q^35 - 4 * q^37 + 3 * q^41 + q^43 + 9 * q^47 + 6 * q^49 - 12 * q^53 - 18 * q^55 - 3 * q^59 - 13 * q^61 - 3 * q^65 + 7 * q^67 - 24 * q^71 - 20 * q^73 + 3 * q^77 + 11 * q^79 - 9 * q^83 + 18 * q^85 - 12 * q^89 + 2 * q^91 + 12 * q^95 - 11 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more