LMFDB - Embedded newform 1764.2.e.g.1079.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1764,2,Mod(1079,1764)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1764, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("1764.1079");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1764.e (of order $2$, degree $1$, 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:	$14.0856109166$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	12.0.653473922154496.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4x^{10} + 13x^{8} - 28x^{6} + 52x^{4} - 64x^{2} + 64 $ x^12 - 4x^10 + 13x^8 - 28x^6 + 52x^4 - 64*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{29}]$
Coefficient ring index:	$ 2^{9} $
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1079.2
Root			$-1.35489 - 0.405301i$ of defining polynomial
Character	$\chi$	$=$	1764.1079
Dual form			1764.2.e.g.1079.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.35489 + 0.405301i) q^{2} +(1.67146 - 1.09828i) q^{4} +3.31339i q^{5} +(-1.81951 + 2.16549i) q^{8} +O(q^{10})$	\(q+(-1.35489 + 0.405301i) q^{2} +(1.67146 - 1.09828i) q^{4} +3.31339i q^{5} +(-1.81951 + 2.16549i) q^{8} +(-1.34292 - 4.48929i) q^{10} -4.72761 q^{11} +4.97858 q^{13} +(1.58757 - 3.67146i) q^{16} +0.484966i q^{17} +2.29273i q^{19} +(3.63903 + 5.53821i) q^{20} +(6.40539 - 1.91611i) q^{22} +7.97002 q^{23} -5.97858 q^{25} +(-6.74543 + 2.01782i) q^{26} -1.41421i q^{29} +7.66442i q^{31} +(-0.662933 + 5.61788i) q^{32} +(-0.196558 - 0.657077i) q^{34} -2.39312 q^{37} +(-0.929247 - 3.10640i) q^{38} +(-7.17513 - 6.02877i) q^{40} +6.55580i q^{41} +5.37169i q^{43} +(-7.90201 + 5.19223i) q^{44} +(-10.7985 + 3.23026i) q^{46} -6.21280 q^{47} +(8.10032 - 2.42313i) q^{50} +(8.32150 - 5.46787i) q^{52} +1.00023i q^{53} -15.6644i q^{55} +(0.573183 + 1.91611i) q^{58} -1.38392 q^{59} -13.6644 q^{61} +(-3.10640 - 10.3845i) q^{62} +(-1.37873 - 7.88030i) q^{64} +16.4960i q^{65} +3.27131i q^{67} +(0.532628 + 0.810603i) q^{68} +3.34369 q^{71} +2.10038 q^{73} +(3.24241 - 0.969933i) q^{74} +(2.51806 + 3.83221i) q^{76} -12.0575i q^{79} +(12.1650 + 5.26024i) q^{80} +(-2.65708 - 8.88240i) q^{82} +3.24241 q^{83} -1.60688 q^{85} +(-2.17715 - 7.27806i) q^{86} +(8.60195 - 10.2376i) q^{88} +5.72784i q^{89} +(13.3216 - 8.75330i) q^{92} +(8.41767 - 2.51806i) q^{94} -7.59672 q^{95} -12.0575 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 8 q^{4}+O(q^{10}) $ 12 * q + 8 * q^4	$ 12 q + 8 q^{4} + 8 q^{10} - 20 q^{16} + 20 q^{22} - 12 q^{25} + 16 q^{34} + 8 q^{37} - 8 q^{40} - 36 q^{46} + 16 q^{52} + 4 q^{58} - 56 q^{61} - 16 q^{64} - 72 q^{76} - 56 q^{82} - 56 q^{85} + 28 q^{88} + 24 q^{94}+O(q^{100}) $ 12 * q + 8 * q^4 + 8 * q^10 - 20 * q^16 + 20 * q^22 - 12 * q^25 + 16 * q^34 + 8 * q^37 - 8 * q^40 - 36 * q^46 + 16 * q^52 + 4 * q^58 - 56 * q^61 - 16 * q^64 - 72 * q^76 - 56 * q^82 - 56 * q^85 + 28 * q^88 + 24 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times$.

$n$	$785$	$883$	$1081$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.35489	+	0.405301i	−0.958053	+	0.286591i
$2$	−1.35489	+	0.405301i	−0.958053	+	0.286591i
$3$		0			0
$3$		0			0
$4$	1.67146	−	1.09828i	0.835731	−	0.549139i
$5$			3.31339i			1.48179i	0.671618	+	0.740897i	$0.265600\pi$
$5$			3.31339i			1.48179i	−0.671618	+	0.740897i	$0.734400\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−1.81951	+	2.16549i	−0.643296	+	0.765618i
$9$		0			0
$10$	−1.34292	−	4.48929i	−0.424670	−	1.41964i
$11$	−4.72761			−1.42543			−0.712714	−	0.701455i	$-0.752534\pi$
$11$	−4.72761			−1.42543			−0.712714	+	0.701455i	$0.752534\pi$
$12$		0			0
$13$	4.97858			1.38081			0.690404	−	0.723424i	$-0.257433\pi$
$13$	4.97858			1.38081			0.690404	+	0.723424i	$0.257433\pi$
$14$		0			0
$15$		0			0
$16$	1.58757	−	3.67146i	0.396892	−	0.917865i
$17$			0.484966i			0.117622i	0.998269	+	0.0588108i	$0.0187309\pi$
$17$			0.484966i			0.117622i	−0.998269	+	0.0588108i	$0.981269\pi$
$18$		0			0
$19$			2.29273i			0.525989i	0.964797	+	0.262994i	$0.0847100\pi$
$19$			2.29273i			0.525989i	−0.964797	+	0.262994i	$0.915290\pi$
$20$	3.63903	+	5.53821i	0.813712	+	1.23838i
$21$		0			0
$22$	6.40539	−	1.91611i	1.36563	−	0.408515i
$23$	7.97002			1.66186			0.830932	−	0.556374i	$-0.187808\pi$
$23$	7.97002			1.66186			0.830932	+	0.556374i	$0.187808\pi$
$24$		0			0
$25$	−5.97858			−1.19572
$26$	−6.74543	+	2.01782i	−1.32289	+	0.395728i
$27$		0			0
$28$		0			0
$29$		−	1.41421i		−	0.262613i	−0.991342	−	0.131306i	$-0.958083\pi$
$29$		−	1.41421i		−	0.262613i	0.991342	−	0.131306i	$-0.0419172\pi$
$30$		0			0
$31$			7.66442i			1.37657i	0.725440	+	0.688286i	$0.241636\pi$
$31$			7.66442i			1.37657i	−0.725440	+	0.688286i	$0.758364\pi$
$32$	−0.662933	+	5.61788i	−0.117191	+	0.993109i
$33$		0			0
$34$	−0.196558	−	0.657077i	−0.0337093	−	0.112688i
$35$		0			0
$36$		0			0
$37$	−2.39312			−0.393426			−0.196713	−	0.980461i	$-0.563027\pi$
$37$	−2.39312			−0.393426			−0.196713	+	0.980461i	$0.563027\pi$
$38$	−0.929247	−	3.10640i	−0.150744	−	0.503925i
$39$		0			0
$40$	−7.17513	−	6.02877i	−1.13449	−	0.953232i
$41$			6.55580i			1.02384i	0.859032	+	0.511922i	$0.171066\pi$
$41$			6.55580i			1.02384i	−0.859032	+	0.511922i	$0.828934\pi$
$42$		0			0
$43$			5.37169i			0.819175i	0.912271	+	0.409588i	$0.134327\pi$
$43$			5.37169i			0.819175i	−0.912271	+	0.409588i	$0.865673\pi$
$44$	−7.90201	+	5.19223i	−1.19127	+	0.782758i
$45$		0			0
$46$	−10.7985	+	3.23026i	−1.59215	+	0.476276i
$47$	−6.21280			−0.906230			−0.453115	−	0.891452i	$-0.649687\pi$
$47$	−6.21280			−0.906230			−0.453115	+	0.891452i	$0.649687\pi$
$48$		0			0
$49$		0			0
$50$	8.10032	−	2.42313i	1.14556	−	0.342682i
$51$		0			0
$52$	8.32150	−	5.46787i	1.15398	−	0.758257i
$53$			1.00023i			0.137392i	0.997638	+	0.0686960i	$0.0218839\pi$
$53$			1.00023i			0.137392i	−0.997638	+	0.0686960i	$0.978116\pi$
$54$		0			0
$55$		−	15.6644i		−	2.11219i
$56$		0			0
$57$		0			0
$58$	0.573183	+	1.91611i	0.0752626	+	0.251597i
$59$	−1.38392			−0.180171			−0.0900853	−	0.995934i	$-0.528714\pi$
$59$	−1.38392			−0.180171			−0.0900853	+	0.995934i	$0.528714\pi$
$60$		0			0
$61$	−13.6644			−1.74955			−0.874775	−	0.484529i	$-0.838991\pi$
$61$	−13.6644			−1.74955			−0.874775	+	0.484529i	$0.838991\pi$
$62$	−3.10640	−	10.3845i	−0.394513	−	1.31883i
$63$		0			0
$64$	−1.37873	−	7.88030i	−0.172341	−	0.985037i
$65$			16.4960i			2.04608i
$66$		0			0
$67$			3.27131i			0.399654i	0.979831	+	0.199827i	$0.0640380\pi$
$67$			3.27131i			0.399654i	−0.979831	+	0.199827i	$0.935962\pi$
$68$	0.532628	+	0.810603i	0.0645907	+	0.0983000i
$69$		0			0
$70$		0			0
$71$	3.34369			0.396823			0.198412	−	0.980119i	$-0.436422\pi$
$71$	3.34369			0.396823			0.198412	+	0.980119i	$0.436422\pi$
$72$		0			0
$73$	2.10038			0.245831			0.122916	−	0.992417i	$-0.460776\pi$
$73$	2.10038			0.245831			0.122916	+	0.992417i	$0.460776\pi$
$74$	3.24241	−	0.969933i	0.376923	−	0.112752i
$75$		0			0
$76$	2.51806	+	3.83221i	0.288841	+	0.439585i
$77$		0			0
$78$		0			0
$79$		−	12.0575i		−	1.35658i	−0.734795	−	0.678290i	$-0.762722\pi$
$79$		−	12.0575i		−	1.35658i	0.734795	−	0.678290i	$-0.237278\pi$
$80$	12.1650	+	5.26024i	1.36009	+	0.588112i
$81$		0			0
$82$	−2.65708	−	8.88240i	−0.293425	−	0.980897i
$83$	3.24241			0.355901			0.177950	−	0.984039i	$-0.443053\pi$
$83$	3.24241			0.355901			0.177950	+	0.984039i	$0.443053\pi$
$84$		0			0
$85$	−1.60688			−0.174291
$86$	−2.17715	−	7.27806i	−0.234769	−	0.784813i
$87$		0			0
$88$	8.60195	−	10.2376i	0.916971	−	1.09133i
$89$			5.72784i			0.607149i	0.952808	+	0.303575i	$0.0981802\pi$
$89$			5.72784i			0.607149i	−0.952808	+	0.303575i	$0.901820\pi$
$90$		0			0
$91$		0			0
$92$	13.3216	−	8.75330i	1.38887	−	0.912595i
$93$		0			0
$94$	8.41767	−	2.51806i	0.868217	−	0.259718i
$95$	−7.59672			−0.779407
$96$		0			0
$97$	−12.0575			−1.22426			−0.612129	−	0.790758i	$-0.709687\pi$
$97$	−12.0575			−1.22426			−0.612129	+	0.790758i	$0.709687\pi$
$98$		0			0
$99$		0			0
$100$	−9.99296	+	6.56614i	−0.999296	+	0.656614i
$101$		−	14.5665i		−	1.44942i	−0.689053	−	0.724711i	$-0.741973\pi$
$101$		−	14.5665i		−	1.44942i	0.689053	−	0.724711i	$-0.258027\pi$
$102$		0			0
$103$		−	5.70727i		−	0.562354i	−0.959656	−	0.281177i	$-0.909275\pi$
$103$		−	5.70727i		−	0.562354i	0.959656	−	0.281177i	$-0.0907248\pi$
$104$	−9.05860	+	10.7811i	−0.888268	+	1.05717i
$105$		0			0
$106$	−0.405394	−	1.35520i	−0.0393754	−	0.131629i
$107$	−16.0413			−1.55077			−0.775386	−	0.631487i	$-0.782445\pi$
$107$	−16.0413			−1.55077			−0.775386	+	0.631487i	$0.782445\pi$
$108$		0			0
$109$	1.37169			0.131384			0.0656921	−	0.997840i	$-0.479074\pi$
$109$	1.37169			0.131384			0.0656921	+	0.997840i	$0.479074\pi$
$110$	6.34881	+	21.2236i	0.605336	+	2.02359i
$111$		0			0
$112$		0			0
$113$		−	11.2834i		−	1.06145i	−0.847543	−	0.530727i	$-0.821919\pi$
$113$		−	11.2834i		−	1.06145i	0.847543	−	0.530727i	$-0.178081\pi$
$114$		0			0
$115$			26.4078i			2.46254i
$116$	−1.55320	−	2.36380i	−0.144211	−	0.219474i
$117$		0			0
$118$	1.87506	−	0.560904i	0.172613	−	0.0516354i
$119$		0			0
$120$		0			0
$121$	11.3503			1.03184
$122$	18.5138	−	5.53821i	1.67616	−	0.501406i
$123$		0			0
$124$	8.41767	+	12.8108i	0.755929	+	1.15044i
$125$		−	3.24241i		−	0.290010i
$126$		0			0
$127$			16.6430i			1.47683i	0.674348	+	0.738414i	$0.264425\pi$
$127$			16.6430i			1.47683i	−0.674348	+	0.738414i	$0.735575\pi$
$128$	5.06193	+	10.1181i	0.447415	+	0.894326i
$129$		0			0
$130$	−6.68585	−	22.3503i	−0.586387	−	1.96025i
$131$	−7.59672			−0.663729			−0.331864	−	0.943327i	$-0.607678\pi$
$131$	−7.59672			−0.663729			−0.331864	+	0.943327i	$0.607678\pi$
$132$		0			0
$133$		0			0
$134$	−1.32587	−	4.43227i	−0.114537	−	0.382890i
$135$		0			0
$136$	−1.05019	−	0.882404i	−0.0900532	−	0.0756655i
$137$			9.42492i			0.805225i	0.915370	+	0.402613i	$0.131898\pi$
$137$			9.42492i			0.805225i	−0.915370	+	0.402613i	$0.868102\pi$
$138$		0			0
$139$			16.0000i			1.35710i	0.734553	+	0.678551i	$0.237392\pi$
$139$			16.0000i			1.35710i	−0.734553	+	0.678551i	$0.762608\pi$
$140$		0			0
$141$		0			0
$142$	−4.53034	+	1.35520i	−0.380177	+	0.113726i
$143$	−23.5368			−1.96824
$144$		0			0
$145$	4.68585			0.389138
$146$	−2.84579	+	0.851289i	−0.235519	+	0.0704532i
$147$		0			0
$148$	−4.00000	+	2.62831i	−0.328798	+	0.216046i
$149$		−	18.4661i		−	1.51281i	−0.654106	−	0.756403i	$-0.726955\pi$
$149$		−	18.4661i		−	1.51281i	0.654106	−	0.756403i	$-0.273045\pi$
$150$		0			0
$151$			23.3288i			1.89847i	0.314561	+	0.949237i	$0.398143\pi$
$151$			23.3288i			1.89847i	−0.314561	+	0.949237i	$0.601857\pi$
$152$	−4.96490	−	4.17166i	−0.402706	−	0.338366i
$153$		0			0
$154$		0			0
$155$	−25.3953			−2.03980
$156$		0			0
$157$	−22.2499			−1.77573			−0.887867	−	0.460100i	$-0.847814\pi$
$157$	−22.2499			−1.77573			−0.887867	+	0.460100i	$0.847814\pi$
$158$	4.88694	+	16.3367i	0.388784	+	1.29967i
$159$		0			0
$160$	−18.6142	−	2.19656i	−1.47158	−	0.173653i
$161$		0			0
$162$		0			0
$163$		−	16.6430i		−	1.30358i	−0.758399	−	0.651790i	$-0.774018\pi$
$163$		−	16.6430i		−	1.30358i	0.758399	−	0.651790i	$-0.225982\pi$
$164$	7.20010	+	10.9578i	0.562233	+	0.855659i
$165$		0			0
$166$	−4.39312	+	1.31415i	−0.340972	+	0.101998i
$167$	8.98064			0.694943			0.347471	−	0.937691i	$-0.387040\pi$
$167$	8.98064			0.694943			0.347471	+	0.937691i	$0.387040\pi$
$168$		0			0
$169$	11.7862			0.906633
$170$	2.17715	−	0.651273i	0.166980	−	0.0499503i
$171$		0			0
$172$	5.89962	+	8.97858i	0.449841	+	0.684610i
$173$			2.75744i			0.209645i	0.994491	+	0.104822i	$0.0334274\pi$
$173$			2.75744i			0.209645i	−0.994491	+	0.104822i	$0.966573\pi$
$174$		0			0
$175$		0			0
$176$	−7.50539	+	17.3572i	−0.565740	+	1.30835i
$177$		0			0
$178$	−2.32150	−	7.76060i	−0.174004	−	0.581681i
$179$	−4.72761			−0.353358			−0.176679	−	0.984269i	$-0.556535\pi$
$179$	−4.72761			−0.353358			−0.176679	+	0.984269i	$0.556535\pi$
$180$		0			0
$181$	8.39312			0.623855			0.311928	−	0.950106i	$-0.399025\pi$
$181$	8.39312			0.623855			0.311928	+	0.950106i	$0.399025\pi$
$182$		0			0
$183$		0			0
$184$	−14.5016	+	17.2590i	−1.06907	+	1.27235i
$185$		−	7.92933i		−	0.582976i
$186$		0			0
$187$		−	2.29273i		−	0.167661i
$188$	−10.3845	+	6.82339i	−0.757365	+	0.497647i
$189$		0			0
$190$	10.2927	−	3.07896i	0.746713	−	0.223371i
$191$	1.48520			0.107465			0.0537325	−	0.998555i	$-0.482888\pi$
$191$	1.48520			0.107465			0.0537325	+	0.998555i	$0.482888\pi$
$192$		0			0
$193$	−8.35027			−0.601066			−0.300533	−	0.953771i	$-0.597164\pi$
$193$	−8.35027			−0.601066			−0.300533	+	0.953771i	$0.597164\pi$
$194$	16.3367	−	4.88694i	1.17290	−	0.350862i
$195$		0			0
$196$		0			0
$197$			3.82866i			0.272780i	0.990655	+	0.136390i	$0.0435501\pi$
$197$			3.82866i			0.272780i	−0.990655	+	0.136390i	$0.956450\pi$
$198$		0			0
$199$		−	6.04285i		−	0.428366i	−0.976794	−	0.214183i	$-0.931291\pi$
$199$		−	6.04285i		−	0.428366i	0.976794	−	0.214183i	$-0.0687089\pi$
$200$	10.8781	−	12.9466i	0.769199	−	0.915461i
$201$		0			0
$202$	5.90383	+	19.7360i	0.415392	+	1.38862i
$203$		0			0
$204$		0			0
$205$	−21.7220			−1.51713
$206$	2.31316	+	7.73273i	0.161166	+	0.538765i
$207$		0			0
$208$	7.90383	−	18.2787i	0.548032	−	1.26740i
$209$		−	10.8391i		−	0.749758i
$210$		0			0
$211$			9.95715i			0.685479i	0.939431	+	0.342739i	$0.111355\pi$
$211$			9.95715i			0.685479i	−0.939431	+	0.342739i	$0.888645\pi$
$212$	1.09853	+	1.67185i	0.0754474	+	0.114823i
$213$		0			0
$214$	21.7342	−	6.50157i	1.48572	−	0.444438i
$215$	−17.7985			−1.21385
$216$		0			0
$217$		0			0
$218$	−1.85849	+	0.555949i	−0.125873	+	0.0376536i
$219$		0			0
$220$	−17.2039	−	26.1825i	−1.15989	−	1.76522i
$221$			2.41444i			0.162413i
$222$		0			0
$223$		−	0.786230i		−	0.0526499i	−0.999653	−	0.0263249i	$-0.991620\pi$
$223$		−	0.786230i		−	0.0526499i	0.999653	−	0.0263249i	$-0.00838046\pi$
$224$		0			0
$225$		0			0
$226$	4.57318	+	15.2878i	0.304204	+	1.01693i
$227$	−20.2943			−1.34698			−0.673492	−	0.739195i	$-0.735206\pi$
$227$	−20.2943			−1.34698			−0.673492	+	0.739195i	$0.735206\pi$
$228$		0			0
$229$	4.97858			0.328994			0.164497	−	0.986378i	$-0.447400\pi$
$229$	4.97858			0.328994			0.164497	+	0.986378i	$0.447400\pi$
$230$	−10.7031	−	35.7797i	−0.705743	−	2.35924i
$231$		0			0
$232$	3.06247	+	2.57318i	0.201061	+	0.168938i
$233$		−	0.383688i		−	0.0251362i	−0.999921	−	0.0125681i	$-0.995999\pi$
$233$		−	0.383688i		−	0.0251362i	0.999921	−	0.0125681i	$-0.00400066\pi$
$234$		0			0
$235$		−	20.5855i		−	1.34285i
$236$	−2.31316	+	1.51993i	−0.150574	+	0.0989388i
$237$		0			0
$238$		0			0
$239$	−1.48520			−0.0960693			−0.0480347	−	0.998846i	$-0.515296\pi$
$239$	−1.48520			−0.0960693			−0.0480347	+	0.998846i	$0.515296\pi$
$240$		0			0
$241$	23.4721			1.51197			0.755985	−	0.654589i	$-0.227158\pi$
$241$	23.4721			1.51197			0.755985	+	0.654589i	$0.227158\pi$
$242$	−15.3784	+	4.60028i	−0.988560	+	0.295717i
$243$		0			0
$244$	−22.8396	+	15.0073i	−1.46215	+	0.960747i
$245$		0			0
$246$		0			0
$247$			11.4145i			0.726290i
$248$	−16.5973	−	13.9455i	−1.05393	−	0.885542i
$249$		0			0
$250$	1.31415	+	4.39312i	0.0831144	+	0.277845i
$251$	−4.62633			−0.292011			−0.146006	−	0.989284i	$-0.546642\pi$
$251$	−4.62633			−0.292011			−0.146006	+	0.989284i	$0.546642\pi$
$252$		0			0
$253$	−37.6791			−2.36887
$254$	−6.74543	−	22.5495i	−0.423246	−	1.41488i
$255$		0			0
$256$	−10.9593	−	11.6574i	−0.684954	−	0.728587i
$257$		−	3.78797i		−	0.236287i	−0.992997	−	0.118144i	$-0.962306\pi$
$257$		−	3.78797i		−	0.236287i	0.992997	−	0.118144i	$-0.0376943\pi$
$258$		0			0
$259$		0			0
$260$	18.1172	+	27.5724i	1.12358	+	1.70997i
$261$		0			0
$262$	10.2927	−	3.07896i	0.635887	−	0.190219i
$263$	12.7989			0.789214			0.394607	−	0.918850i	$-0.370881\pi$
$263$	12.7989			0.789214			0.394607	+	0.918850i	$0.370881\pi$
$264$		0			0
$265$	−3.31415			−0.203587
$266$		0			0
$267$		0			0
$268$	3.59281	+	5.46787i	0.219466	+	0.334003i
$269$			25.4662i			1.55270i	0.630300	+	0.776352i	$0.282932\pi$
$269$			25.4662i			1.55270i	−0.630300	+	0.776352i	$0.717068\pi$
$270$		0			0
$271$			21.0361i			1.27785i	0.769268	+	0.638927i	$0.220621\pi$
$271$			21.0361i			1.27785i	−0.769268	+	0.638927i	$0.779379\pi$
$272$	1.78054	+	0.769917i	0.107961	+	0.0466831i
$273$		0			0
$274$	−3.81993	−	12.7697i	−0.230771	−	0.771448i
$275$	28.2644			1.70441
$276$		0			0
$277$	8.39312			0.504293			0.252147	−	0.967689i	$-0.418863\pi$
$277$	8.39312			0.504293			0.252147	+	0.967689i	$0.418863\pi$
$278$	−6.48482	−	21.6783i	−0.388934	−	1.30018i
$279$		0			0
$280$		0			0
$281$			0.111668i			0.00666157i	0.999994	+	0.00333078i	$0.00106022\pi$
$281$			0.111668i			0.00666157i	−0.999994	+	0.00333078i	$0.998940\pi$
$282$		0			0
$283$			11.4637i			0.681444i	0.940164	+	0.340722i	$0.110671\pi$
$283$			11.4637i			0.681444i	−0.940164	+	0.340722i	$0.889329\pi$
$284$	5.58885	−	3.67230i	0.331637	−	0.217911i
$285$		0			0
$286$	31.8898	−	9.53948i	1.88568	−	0.564081i
$287$		0			0
$288$		0			0
$289$	16.7648			0.986165
$290$	−6.34881	+	1.89918i	−0.372815	+	0.111524i
$291$		0			0
$292$	3.51071	−	2.30681i	0.205449	−	0.134996i
$293$			17.8089i			1.04041i	0.854042	+	0.520204i	$0.174144\pi$
$293$			17.8089i			1.04041i	−0.854042	+	0.520204i	$0.825856\pi$
$294$		0			0
$295$		−	4.58546i		−	0.266976i
$296$	4.35431	−	5.18228i	0.253089	−	0.301214i
$297$		0			0
$298$	7.48436	+	25.0196i	0.433557	+	1.44935i
$299$	39.6794			2.29472
$300$		0			0
$301$		0			0
$302$	−9.45521	−	31.6081i	−0.544086	−	1.81884i
$303$		0			0
$304$	8.41767	+	3.63986i	0.482787	+	0.208761i
$305$		−	45.2756i		−	2.59247i
$306$		0			0
$307$		−	20.2499i		−	1.15572i	−0.816135	−	0.577861i	$-0.803888\pi$
$307$		−	20.2499i		−	1.15572i	0.816135	−	0.577861i	$-0.196112\pi$
$308$		0			0
$309$		0			0
$310$	34.4078	−	10.2927i	1.95423	−	0.584588i
$311$	1.38392			0.0784747			0.0392374	−	0.999230i	$-0.487507\pi$
$311$	1.38392			0.0784747			0.0392374	+	0.999230i	$0.487507\pi$
$312$		0			0
$313$	30.1151			1.70220			0.851102	−	0.525000i	$-0.175935\pi$
$313$	30.1151			1.70220			0.851102	+	0.525000i	$0.175935\pi$
$314$	30.1462	−	9.01791i	1.70125	−	0.508910i
$315$		0			0
$316$	−13.2425	−	20.1537i	−0.744951	−	1.13373i
$317$		−	5.27317i		−	0.296171i	−0.988975	−	0.148085i	$-0.952689\pi$
$317$		−	5.27317i		−	0.296171i	0.988975	−	0.148085i	$-0.0473110\pi$
$318$		0			0
$319$			6.68585i			0.374336i
$320$	26.1105	−	4.56828i	1.45962	−	0.255374i
$321$		0			0
$322$		0			0
$323$	−1.11190			−0.0618676
$324$		0			0
$325$	−29.7648			−1.65105
$326$	6.74543	+	22.5495i	0.373595	+	1.24890i
$327$		0			0
$328$	−14.1966	−	11.9284i	−0.783874	−	0.658635i
$329$		0			0
$330$		0			0
$331$			9.95715i			0.547295i	0.961830	+	0.273647i	$0.0882301\pi$
$331$			9.95715i			0.547295i	−0.961830	+	0.273647i	$0.911770\pi$
$332$	5.41957	−	3.56107i	0.297437	−	0.195439i
$333$		0			0
$334$	−12.1678	+	3.63986i	−0.665792	+	0.199165i
$335$	−10.8391			−0.592205
$336$		0			0
$337$	−13.3717			−0.728402			−0.364201	−	0.931320i	$-0.618658\pi$
$337$	−13.3717			−0.728402			−0.364201	+	0.931320i	$0.618658\pi$
$338$	−15.9691	+	4.77698i	−0.868602	+	0.259833i
$339$		0			0
$340$	−2.68585	+	1.76481i	−0.145660	+	0.0957101i
$341$		−	36.2344i		−	1.96220i
$342$		0			0
$343$		0			0
$344$	−11.6324	−	9.77387i	−0.627175	−	0.526972i
$345$		0			0
$346$	−1.11760	−	3.73604i	−0.0600823	−	0.200851i
$347$	−11.2124			−0.601915			−0.300957	−	0.953638i	$-0.597306\pi$
$347$	−11.2124			−0.601915			−0.300957	+	0.953638i	$0.597306\pi$
$348$		0			0
$349$	4.29273			0.229785			0.114892	−	0.993378i	$-0.463348\pi$
$349$	4.29273			0.229785			0.114892	+	0.993378i	$0.463348\pi$
$350$		0			0
$351$		0			0
$352$	3.13409	−	26.5591i	0.167047	−	1.41561i
$353$		−	1.78751i		−	0.0951397i	−0.998868	−	0.0475698i	$-0.984852\pi$
$353$		−	1.78751i		−	0.0951397i	0.998868	−	0.0475698i	$-0.0151477\pi$
$354$		0			0
$355$			11.0790i			0.588010i
$356$	6.29076	+	9.57386i	0.333410	+	0.507413i
$357$		0			0
$358$	6.40539	−	1.91611i	0.338536	−	0.101269i
$359$	12.7989			0.675500			0.337750	−	0.941236i	$-0.390334\pi$
$359$	12.7989			0.675500			0.337750	+	0.941236i	$0.390334\pi$
$360$		0			0
$361$	13.7434			0.723336
$362$	−11.3718	+	3.40174i	−0.597686	+	0.178792i
$363$		0			0
$364$		0			0
$365$			6.95940i			0.364272i
$366$		0			0
$367$			30.1579i			1.57423i	0.616806	+	0.787115i	$0.288426\pi$
$367$			30.1579i			1.57423i	−0.616806	+	0.787115i	$0.711574\pi$
$368$	12.6529	−	29.2616i	0.659580	−	1.52537i
$369$		0			0
$370$	3.21377	+	10.7434i	0.167076	+	0.558522i
$371$		0			0
$372$		0			0
$373$	5.21377			0.269959			0.134979	−	0.990848i	$-0.456903\pi$
$373$	5.21377			0.269959			0.134979	+	0.990848i	$0.456903\pi$
$374$	0.929247	+	3.10640i	0.0480502	+	0.160628i
$375$		0			0
$376$	11.3043	−	13.4538i	0.582974	−	0.693826i
$377$		−	7.04077i		−	0.362618i
$378$		0			0
$379$		−	16.7862i		−	0.862251i	−0.902292	−	0.431125i	$-0.858117\pi$
$379$		−	16.7862i		−	0.862251i	0.902292	−	0.431125i	$-0.141883\pi$
$380$	−12.6976	+	8.34332i	−0.651374	+	0.428003i
$381$		0			0
$382$	−2.01228	+	0.601952i	−0.102957	+	0.0307985i
$383$	23.7393			1.21302			0.606511	−	0.795075i	$-0.292569\pi$
$383$	23.7393			1.21302			0.606511	+	0.795075i	$0.292569\pi$
$384$		0			0
$385$		0			0
$386$	11.3137	−	3.38438i	0.575853	−	0.172260i
$387$		0			0
$388$	−20.1537	+	13.2425i	−1.02315	+	0.672288i
$389$			17.7682i			0.900885i	0.892805	+	0.450443i	$0.148734\pi$
$389$			17.7682i			0.900885i	−0.892805	+	0.450443i	$0.851266\pi$
$390$		0			0
$391$			3.86519i			0.195471i
$392$		0			0
$393$		0			0
$394$	−1.55176	−	5.18741i	−0.0781765	−	0.261338i
$395$	39.9514			2.01017
$396$		0			0
$397$	−24.4078			−1.22499			−0.612496	−	0.790473i	$-0.709835\pi$
$397$	−24.4078			−1.22499			−0.612496	+	0.790473i	$0.709835\pi$
$398$	2.44917	+	8.18740i	0.122766	+	0.410397i
$399$		0			0
$400$	−9.49139	+	21.9501i	−0.474570	+	1.09751i
$401$			29.1633i			1.45635i	0.685393	+	0.728173i	$0.259630\pi$
$401$			29.1633i			1.45635i	−0.685393	+	0.728173i	$0.740370\pi$
$402$		0			0
$403$			38.1579i			1.90078i
$404$	−15.9981	−	24.3474i	−0.795935	−	1.21133i
$405$		0			0
$406$		0			0
$407$	11.3137			0.560800
$408$		0			0
$409$	10.4851			0.518454			0.259227	−	0.965816i	$-0.416532\pi$
$409$	10.4851			0.518454			0.259227	+	0.965816i	$0.416532\pi$
$410$	29.4309	−	8.80394i	1.45349	−	0.434796i
$411$		0			0
$412$	−6.26817	−	9.53948i	−0.308811	−	0.469976i
$413$		0			0
$414$		0			0
$415$			10.7434i			0.527372i
$416$	−3.30046	+	27.9690i	−0.161818	+	1.37129i
$417$		0			0
$418$	4.39312	+	14.6858i	0.214874	+	0.718308i
$419$	31.1335			1.52097			0.760485	−	0.649356i	$-0.224961\pi$
$419$	31.1335			1.52097			0.760485	+	0.649356i	$0.224961\pi$
$420$		0			0
$421$	30.2646			1.47501			0.737503	−	0.675344i	$-0.236005\pi$
$421$	30.2646			1.47501			0.737503	+	0.675344i	$0.236005\pi$
$422$	−4.03565	−	13.4909i	−0.196452	−	0.656725i
$423$		0			0
$424$	−2.16599	−	1.81993i	−0.105190	−	0.0883837i
$425$		−	2.89941i		−	0.140642i
$426$		0			0
$427$		0			0
$428$	−26.8124	+	17.6178i	−1.29603	+	0.851590i
$429$		0			0
$430$	24.1151	−	7.21377i	1.16293	−	0.347879i
$431$	−2.23179			−0.107502			−0.0537508	−	0.998554i	$-0.517118\pi$
$431$	−2.23179			−0.107502			−0.0537508	+	0.998554i	$0.517118\pi$
$432$		0			0
$433$	8.54262			0.410532			0.205266	−	0.978706i	$-0.434194\pi$
$433$	8.54262			0.410532			0.205266	+	0.978706i	$0.434194\pi$
$434$		0			0
$435$		0			0
$436$	2.29273	−	1.50650i	0.109802	−	0.0721483i
$437$			18.2731i			0.874121i
$438$		0			0
$439$		−	1.17092i		−	0.0558851i	−0.999610	−	0.0279426i	$-0.991104\pi$
$439$		−	1.17092i		−	0.0558851i	0.999610	−	0.0279426i	$-0.00889556\pi$
$440$	33.9212	+	28.5017i	1.61713	+	1.35876i
$441$		0			0
$442$	−0.978577	−	3.27131i	−0.0465462	−	0.155600i
$443$	6.58610			0.312915			0.156458	−	0.987685i	$-0.449993\pi$
$443$	6.58610			0.312915			0.156458	+	0.987685i	$0.449993\pi$
$444$		0			0
$445$	−18.9786			−0.899671
$446$	0.318660	+	1.06526i	0.0150890	+	0.0504414i
$447$		0			0
$448$		0			0
$449$			11.2228i			0.529638i	0.964298	+	0.264819i	$0.0853121\pi$
$449$			11.2228i			0.529638i	−0.964298	+	0.264819i	$0.914688\pi$
$450$		0			0
$451$		−	30.9933i		−	1.45942i
$452$	−12.3923	−	18.8598i	−0.582886	−	0.887090i
$453$		0			0
$454$	27.4966	−	8.22533i	1.29048	−	0.386034i
$455$		0			0
$456$		0			0
$457$	11.9143			0.557328			0.278664	−	0.960389i	$-0.410108\pi$
$457$	11.9143			0.557328			0.278664	+	0.960389i	$0.410108\pi$
$458$	−6.74543	+	2.01782i	−0.315193	+	0.0942867i
$459$		0			0
$460$	29.0031	+	44.1396i	1.35228	+	2.05802i
$461$		−	18.4255i		−	0.858159i	−0.903267	−	0.429080i	$-0.858838\pi$
$461$		−	18.4255i		−	0.858159i	0.903267	−	0.429080i	$-0.141162\pi$
$462$		0			0
$463$		−	7.47208i		−	0.347257i	−0.984811	−	0.173628i	$-0.944451\pi$
$463$		−	7.47208i		−	0.347257i	0.984811	−	0.173628i	$-0.0555492\pi$
$464$	−5.19223	−	2.24516i	−0.241043	−	0.104229i
$465$		0			0
$466$	0.155509	+	0.519855i	0.00720382	+	0.0240818i
$467$	−5.57548			−0.258003			−0.129001	−	0.991644i	$-0.541177\pi$
$467$	−5.57548			−0.258003			−0.129001	+	0.991644i	$0.541177\pi$
$468$		0			0
$469$		0			0
$470$	8.34332	+	27.8911i	0.384849	+	1.28652i
$471$		0			0
$472$	2.51806	−	2.99686i	0.115903	−	0.137942i
$473$		−	25.3953i		−	1.16767i
$474$		0			0
$475$		−	13.7073i		−	0.628933i
$476$		0			0
$477$		0			0
$478$	2.01228	−	0.601952i	0.0920395	−	0.0275326i
$479$	15.9400			0.728319			0.364159	−	0.931337i	$-0.381356\pi$
$479$	15.9400			0.728319			0.364159	+	0.931337i	$0.381356\pi$
$480$		0			0
$481$	−11.9143			−0.543246
$482$	−31.8021	+	9.51327i	−1.44855	+	0.433317i
$483$		0			0
$484$	18.9715	−	12.4658i	0.862343	−	0.566625i
$485$		−	39.9514i		−	1.81410i
$486$		0			0
$487$		−	34.0722i		−	1.54396i	−0.635647	−	0.771980i	$-0.719266\pi$
$487$		−	34.0722i		−	1.54396i	0.635647	−	0.771980i	$-0.280734\pi$
$488$	24.8626	−	29.5902i	1.12548	−	1.33949i
$489$		0			0
$490$		0			0
$491$	34.0026			1.53452			0.767258	−	0.641339i	$-0.221621\pi$
$491$	34.0026			1.53452			0.767258	+	0.641339i	$0.221621\pi$
$492$		0			0
$493$	0.685846			0.0308890
$494$	−4.62633	−	15.4655i	−0.208148	−	0.695824i
$495$		0			0
$496$	28.1396	+	12.1678i	1.26351	+	0.546350i
$497$		0			0
$498$		0			0
$499$			5.37169i			0.240470i	0.992745	+	0.120235i	$0.0383648\pi$
$499$			5.37169i			0.240470i	−0.992745	+	0.120235i	$0.961635\pi$
$500$	−3.56107	−	5.41957i	−0.159256	−	0.242370i
$501$		0			0
$502$	6.26817	−	1.87506i	0.279762	−	0.0836879i
$503$	−37.3463			−1.66519			−0.832594	−	0.553884i	$-0.813145\pi$
$503$	−37.3463			−1.66519			−0.832594	+	0.553884i	$0.813145\pi$
$504$		0			0
$505$	48.2646			2.14775
$506$	51.0511	−	15.2714i	2.26950	−	0.678896i
$507$		0			0
$508$	18.2787	+	27.8181i	0.810984	+	1.23423i
$509$			0.403595i			0.0178890i	0.999960	+	0.00894451i	$0.00284716\pi$
$509$			0.403595i			0.0178890i	−0.999960	+	0.00894451i	$0.997153\pi$
$510$		0			0
$511$		0			0
$512$	19.5734	+	11.3527i	0.865029	+	0.501723i
$513$		0			0
$514$	1.53527	+	5.13229i	0.0677179	+	0.226376i
$515$	18.9104			0.833293
$516$		0			0
$517$	29.3717			1.29177
$518$		0			0
$519$		0			0
$520$	−35.7220	−	30.0147i	−1.56651	−	1.31623i
$521$		−	42.9927i		−	1.88355i	−0.336249	−	0.941773i	$-0.609158\pi$
$521$		−	42.9927i		−	1.88355i	0.336249	−	0.941773i	$-0.390842\pi$
$522$		0			0
$523$			16.0000i			0.699631i	0.936819	+	0.349816i	$0.113756\pi$
$523$			16.0000i			0.699631i	−0.936819	+	0.349816i	$0.886244\pi$
$524$	−12.6976	+	8.34332i	−0.554698	+	0.364479i
$525$		0			0
$526$	−17.3411	+	5.18741i	−0.756109	+	0.226182i
$527$	−3.71699			−0.161915
$528$		0			0
$529$	40.5212			1.76179
$530$	4.49032	−	1.34323i	0.195047	−	0.0583462i
$531$		0			0
$532$		0			0
$533$			32.6386i			1.41373i
$534$		0			0
$535$		−	53.1512i		−	2.29793i
$536$	−7.08400	−	5.95219i	−0.305982	−	0.257096i
$537$		0			0
$538$	−10.3215	−	34.5040i	−0.444991	−	1.48757i
$539$		0			0
$540$		0			0
$541$	19.1365			0.822742			0.411371	−	0.911468i	$-0.365050\pi$
$541$	19.1365			0.822742			0.411371	+	0.911468i	$0.365050\pi$
$542$	−8.52597	−	28.5017i	−0.366222	−	1.22425i
$543$		0			0
$544$	−2.72448	−	0.321500i	−0.116811	−	0.0137842i
$545$			4.54496i			0.194685i
$546$		0			0
$547$			8.14323i			0.348179i	0.984730	+	0.174090i	$0.0556983\pi$
$547$			8.14323i			0.348179i	−0.984730	+	0.174090i	$0.944302\pi$
$548$	10.3512	+	15.7534i	0.442181	+	0.672951i
$549$		0			0
$550$	−38.2951	+	11.4556i	−1.63291	+	0.488468i
$551$	3.24241			0.138131
$552$		0			0
$553$		0			0
$554$	−11.3718	+	3.40174i	−0.483140	+	0.144526i
$555$		0			0
$556$	17.5725	+	26.7434i	0.745238	+	1.13417i
$557$			39.0931i			1.65643i	0.560412	+	0.828214i	$0.310643\pi$
$557$			39.0931i			1.65643i	−0.560412	+	0.828214i	$0.689357\pi$
$558$		0			0
$559$			26.7434i			1.13112i
$560$		0			0
$561$		0			0
$562$	−0.0452593	−	0.151298i	−0.00190915	−	0.00638213i
$563$	−13.6468			−0.575143			−0.287572	−	0.957759i	$-0.592848\pi$
$563$	−13.6468			−0.575143			−0.287572	+	0.957759i	$0.592848\pi$
$564$		0			0
$565$	37.3864			1.57286
$566$	−4.64624	−	15.5320i	−0.195296	−	0.652859i
$567$		0			0
$568$	−6.08389	+	7.24074i	−0.255275	+	0.303815i
$569$		−	2.32355i		−	0.0974084i	−0.998813	−	0.0487042i	$-0.984491\pi$
$569$		−	2.32355i		−	0.0974084i	0.998813	−	0.0487042i	$-0.0155092\pi$
$570$		0			0
$571$		−	2.88661i		−	0.120801i	−0.998174	−	0.0604005i	$-0.980762\pi$
$571$		−	2.88661i		−	0.120801i	0.998174	−	0.0604005i	$-0.0192378\pi$
$572$	−39.3408	+	25.8499i	−1.64492	+	1.08084i
$573$		0			0
$574$		0			0
$575$	−47.6494			−1.98712
$576$		0			0
$577$	18.5855			0.773723			0.386861	−	0.922138i	$-0.373559\pi$
$577$	18.5855			0.773723			0.386861	+	0.922138i	$0.373559\pi$
$578$	−22.7145	+	6.79480i	−0.944798	+	0.282626i
$579$		0			0
$580$	7.83221	−	5.14637i	0.325215	−	0.213691i
$581$		0			0
$582$		0			0
$583$		−	4.72869i		−	0.195842i
$584$	−3.82168	+	4.54837i	−0.158142	+	0.188213i
$585$		0			0
$586$	−7.21798	−	24.1292i	−0.298172	−	0.996766i
$587$	9.92979			0.409846			0.204923	−	0.978778i	$-0.434306\pi$
$587$	9.92979			0.409846			0.204923	+	0.978778i	$0.434306\pi$
$588$		0			0
$589$	−17.5725			−0.724061
$590$	1.85849	+	6.21280i	0.0765130	+	0.255777i
$591$		0			0
$592$	−3.79923	+	8.78623i	−0.156147	+	0.361112i
$593$		−	24.0823i		−	0.988942i	−0.869194	−	0.494471i	$-0.835362\pi$
$593$		−	24.0823i		−	0.988942i	0.869194	−	0.494471i	$-0.164638\pi$
$594$		0			0
$595$		0			0
$596$	−20.2810	−	30.8655i	−0.830741	−	1.26430i
$597$		0			0
$598$	−53.7612	+	16.0821i	−2.19846	+	0.657646i
$599$	19.2837			0.787912			0.393956	−	0.919129i	$-0.371106\pi$
$599$	19.2837			0.787912			0.393956	+	0.919129i	$0.371106\pi$
$600$		0			0
$601$	−10.5855			−0.431790			−0.215895	−	0.976417i	$-0.569267\pi$
$601$	−10.5855			−0.431790			−0.215895	+	0.976417i	$0.569267\pi$
$602$		0			0
$603$		0			0
$604$	25.6216	+	38.9933i	1.04253	+	1.58661i
$605$			37.6079i			1.52898i
$606$		0			0
$607$		−	34.0722i		−	1.38295i	−0.722401	−	0.691475i	$-0.756961\pi$
$607$		−	34.0722i		−	1.38295i	0.722401	−	0.691475i	$-0.243039\pi$
$608$	−12.8803	−	1.51993i	−0.522364	−	0.0616412i
$609$		0			0
$610$	18.3503	+	61.3435i	0.742981	+	2.48373i
$611$	−30.9309			−1.25133
$612$		0			0
$613$	−17.3288			−0.699906			−0.349953	−	0.936767i	$-0.613802\pi$
$613$	−17.3288			−0.699906			−0.349953	+	0.936767i	$0.613802\pi$
$614$	8.20731	+	27.4364i	0.331220	+	1.10724i
$615$		0			0
$616$		0			0
$617$			1.76760i			0.0711611i	0.999367	+	0.0355805i	$0.0113280\pi$
$617$			1.76760i			0.0711611i	−0.999367	+	0.0355805i	$0.988672\pi$
$618$		0			0
$619$		−	47.0424i		−	1.89079i	−0.325922	−	0.945397i	$-0.605675\pi$
$619$		−	47.0424i		−	1.89079i	0.325922	−	0.945397i	$-0.394325\pi$
$620$	−42.4472	+	27.8911i	−1.70472	+	1.12013i
$621$		0			0
$622$	−1.87506	+	0.560904i	−0.0751830	+	0.0224902i
$623$		0			0
$624$		0			0
$625$	−19.1495			−0.765980
$626$	−40.8027	+	12.2057i	−1.63080	+	0.487837i
$627$		0			0
$628$	−37.1898	+	24.4366i	−1.48404	+	0.975126i
$629$		−	1.16058i		−	0.0462754i
$630$		0			0
$631$		−	14.0147i		−	0.557916i	−0.960303	−	0.278958i	$-0.910011\pi$
$631$		−	14.0147i		−	0.557916i	0.960303	−	0.278958i	$-0.0899890\pi$
$632$	26.1105	+	21.9389i	1.03862	+	0.872681i
$633$		0			0
$634$	2.13722	+	7.14457i	0.0848799	+	0.283747i
$635$	−55.1448			−2.18836
$636$		0			0
$637$		0			0
$638$	−2.70978	−	9.05860i	−0.107281	−	0.358633i
$639$		0			0
$640$	−33.5254	+	16.7722i	−1.32521	+	0.662978i
$641$		−	8.92956i		−	0.352696i	−0.984328	−	0.176348i	$-0.943572\pi$
$641$		−	8.92956i		−	0.352696i	0.984328	−	0.176348i	$-0.0564285\pi$
$642$		0			0
$643$		−	4.53635i		−	0.178896i	−0.995991	−	0.0894480i	$-0.971490\pi$
$643$		−	4.53635i		−	0.178896i	0.995991	−	0.0894480i	$-0.0285103\pi$
$644$		0			0
$645$		0			0
$646$	1.50650	−	0.450654i	0.0592725	−	0.0177307i
$647$	−5.10091			−0.200537			−0.100269	−	0.994960i	$-0.531970\pi$
$647$	−5.10091			−0.200537			−0.100269	+	0.994960i	$0.531970\pi$
$648$		0			0
$649$	6.54262			0.256820
$650$	40.3281	−	12.0637i	1.58180	−	0.473178i
$651$		0			0
$652$	−18.2787	−	27.8181i	−0.715847	−	1.08944i
$653$			26.2535i			1.02738i	0.857976	+	0.513690i	$0.171722\pi$
$653$			26.2535i			1.02738i	−0.857976	+	0.513690i	$0.828278\pi$
$654$		0			0
$655$		−	25.1709i		−	0.983509i
$656$	24.0694	+	10.4078i	0.939752	+	0.406356i
$657$		0			0
$658$		0			0
$659$	16.0413			0.624881			0.312440	−	0.949937i	$-0.398854\pi$
$659$	16.0413			0.624881			0.312440	+	0.949937i	$0.398854\pi$
$660$		0			0
$661$	−29.8652			−1.16162			−0.580811	−	0.814039i	$-0.697264\pi$
$661$	−29.8652			−1.16162			−0.580811	+	0.814039i	$0.697264\pi$
$662$	−4.03565	−	13.4909i	−0.156850	−	0.524337i
$663$		0			0
$664$	−5.89962	+	7.02142i	−0.228949	+	0.272484i
$665$		0			0
$666$		0			0
$667$		−	11.2713i		−	0.436427i
$668$	15.0108	−	9.86324i	0.580785	−	0.381620i
$669$		0			0
$670$	14.6858	−	4.39312i	0.567364	−	0.169721i
$671$	64.6000			2.49386
$672$		0			0
$673$	−35.0080			−1.34946			−0.674729	−	0.738066i	$-0.735739\pi$
$673$	−35.0080			−1.34946			−0.674729	+	0.738066i	$0.735739\pi$
$674$	18.1172	−	5.41957i	0.697848	−	0.208754i
$675$		0			0
$676$	19.7002	−	12.9446i	0.757701	−	0.497868i
$677$			37.6893i			1.44852i	0.689529	+	0.724258i	$0.257818\pi$
$677$			37.6893i			1.44852i	−0.689529	+	0.724258i	$0.742182\pi$
$678$		0			0
$679$		0			0
$680$	2.92375	−	3.47970i	0.112121	−	0.133440i
$681$		0			0
$682$	14.6858	+	49.0937i	0.562350	+	1.87989i
$683$	21.5770			0.825620			0.412810	−	0.910817i	$-0.364547\pi$
$683$	21.5770			0.825620			0.412810	+	0.910817i	$0.364547\pi$
$684$		0			0
$685$	−31.2285			−1.19318
$686$		0			0
$687$		0			0
$688$	19.7220	+	8.52792i	0.751893	+	0.325124i
$689$			4.97972i			0.189712i
$690$		0			0
$691$		−	14.0428i		−	0.534215i	−0.963667	−	0.267108i	$-0.913932\pi$
$691$		−	14.0428i		−	0.534215i	0.963667	−	0.267108i	$-0.0860679\pi$
$692$	3.02844	+	4.60896i	0.115124	+	0.175206i
$693$		0			0
$694$	15.1916	−	4.54441i	0.576666	−	0.172504i
$695$	−53.0143			−2.01095
$696$		0			0
$697$	−3.17935			−0.120426
$698$	−5.81618	+	1.73985i	−0.220146	+	0.0658543i
$699$		0			0
$700$		0			0
$701$		−	27.9214i		−	1.05458i	−0.849687	−	0.527288i	$-0.823209\pi$
$701$		−	27.9214i		−	1.05458i	0.849687	−	0.527288i	$-0.176791\pi$
$702$		0			0
$703$		−	5.48677i		−	0.206937i
$704$	6.51810	+	37.2550i	0.245660	+	1.40410i
$705$		0			0
$706$	0.724481	+	2.42188i	0.0272662	+	0.0911488i
$707$		0			0
$708$		0			0
$709$	−10.5426			−0.395936			−0.197968	−	0.980208i	$-0.563434\pi$
$709$	−10.5426			−0.395936			−0.197968	+	0.980208i	$0.563434\pi$
$710$	−4.49032	−	15.0108i	−0.168519	−	0.563345i
$711$		0			0
$712$	−12.4036	−	10.4219i	−0.464844	−	0.390577i
$713$			61.0856i			2.28767i
$714$		0			0
$715$		−	77.9865i		−	2.91653i
$716$	−7.90201	+	5.19223i	−0.295312	+	0.194043i
$717$		0			0
$718$	−17.3411	+	5.18741i	−0.647165	+	0.193593i
$719$	31.8801			1.18893			0.594463	−	0.804123i	$-0.297365\pi$
$719$	31.8801			1.18893			0.594463	+	0.804123i	$0.297365\pi$
$720$		0			0
$721$		0			0
$722$	−18.6208	+	5.57021i	−0.692994	+	0.207302i
$723$		0			0
$724$	14.0288	−	9.21798i	0.521375	−	0.342584i
$725$			8.45498i			0.314010i
$726$		0			0
$727$			46.2070i			1.71372i	0.515546	+	0.856862i	$0.327589\pi$
$727$			46.2070i			1.71372i	−0.515546	+	0.856862i	$0.672411\pi$
$728$		0			0
$729$		0			0
$730$	−2.82065	−	9.42923i	−0.104397	−	0.348991i
$731$	−2.60509			−0.0963528
$732$		0			0
$733$	−22.4360			−0.828691			−0.414346	−	0.910120i	$-0.635990\pi$
$733$	−22.4360			−0.828691			−0.414346	+	0.910120i	$0.635990\pi$
$734$	−12.2230	−	40.8607i	−0.451161	−	1.50820i
$735$		0			0
$736$	−5.28359	+	44.7746i	−0.194756	+	1.65041i
$737$		−	15.4655i		−	0.569678i
$738$		0			0
$739$		−	14.0147i		−	0.515539i	−0.966206	−	0.257769i	$-0.917013\pi$
$739$		−	14.0147i		−	0.515539i	0.966206	−	0.257769i	$-0.0829875\pi$
$740$	−8.70862	−	13.2536i	−0.320135	−	0.487211i
$741$		0			0
$742$		0			0
$743$	25.9313			0.951327			0.475663	−	0.879627i	$-0.342208\pi$
$743$	25.9313			0.951327			0.475663	+	0.879627i	$0.342208\pi$
$744$		0			0
$745$	61.1856			2.24167
$746$	−7.06409	+	2.11315i	−0.258635	+	0.0773679i
$747$		0			0
$748$	−2.51806	−	3.83221i	−0.0920693	−	0.140120i
$749$		0			0
$750$		0			0
$751$			2.74338i			0.100108i	0.998747	+	0.0500538i	$0.0159393\pi$
$751$			2.74338i			0.100108i	−0.998747	+	0.0500538i	$0.984061\pi$
$752$	−9.86324	+	22.8101i	−0.359675	+	0.831798i
$753$		0			0
$754$	2.85363	+	9.53948i	0.103923	+	0.347407i
$755$	−77.2977			−2.81315
$756$		0			0
$757$	−15.7992			−0.574233			−0.287116	−	0.957896i	$-0.592697\pi$
$757$	−15.7992			−0.574233			−0.287116	+	0.957896i	$0.592697\pi$
$758$	6.80348	+	22.7435i	0.247114	+	0.826082i
$759$		0			0
$760$	13.8223	−	16.4507i	0.501389	−	0.596728i
$761$			27.0527i			0.980660i	0.871537	+	0.490330i	$0.163124\pi$
$761$			27.0527i			0.980660i	−0.871537	+	0.490330i	$0.836876\pi$
$762$		0			0
$763$		0			0
$764$	2.48245	−	1.63116i	0.0898118	−	0.0590133i
$765$		0			0
$766$	−32.1642	+	9.62158i	−1.16214	+	0.347642i
$767$	−6.88994			−0.248781
$768$		0			0
$769$	−39.8715			−1.43780			−0.718901	−	0.695113i	$-0.755354\pi$
$769$	−39.8715			−1.43780			−0.718901	+	0.695113i	$0.755354\pi$
$770$		0			0
$771$		0			0
$772$	−13.9572	+	9.17092i	−0.502329	+	0.330069i
$773$			34.4261i			1.23822i	0.785304	+	0.619110i	$0.212507\pi$
$773$			34.4261i			1.23822i	−0.785304	+	0.619110i	$0.787493\pi$
$774$		0			0
$775$		−	45.8223i		−	1.64599i
$776$	21.9389	−	26.1105i	0.787560	−	0.937313i
$777$		0			0
$778$	−7.20149	−	24.0740i	−0.258186	−	0.863096i
$779$	−15.0307			−0.538531
$780$		0			0
$781$	−15.8077			−0.565642
$782$	−1.56657	−	5.23692i	−0.0560203	−	0.187272i
$783$		0			0
$784$		0			0
$785$		−	73.7226i		−	2.63127i
$786$		0			0
$787$		−	24.1151i		−	0.859610i	−0.902922	−	0.429805i	$-0.858582\pi$
$787$		−	24.1151i		−	0.859610i	0.902922	−	0.429805i	$-0.141418\pi$
$788$	4.20493	+	6.39945i	0.149795	+	0.227971i
$789$		0			0
$790$	−54.1298	+	16.1923i	−1.92585	+	0.576098i
$791$		0			0
$792$		0			0
$793$	−68.0294			−2.41579
$794$	33.0699	−	9.89252i	1.17361	−	0.351072i
$795$		0			0
$796$	−6.63673	−	10.1004i	−0.235233	−	0.357999i
$797$		−	35.0634i		−	1.24201i	−0.783807	−	0.621005i	$-0.786725\pi$
$797$		−	35.0634i		−	1.24201i	0.783807	−	0.621005i	$-0.213275\pi$
$798$		0			0
$799$		−	3.01300i		−	0.106592i
$800$	3.96340	−	33.5869i	0.140127	−	1.18748i
$801$		0			0
$802$	−11.8199	−	39.5131i	−0.417376	−	1.39526i
$803$	−9.92979			−0.350415
$804$		0			0
$805$		0			0
$806$	−15.4655	−	51.6998i	−0.544748	−	1.82105i
$807$		0			0
$808$	31.5437	+	26.5040i	1.10970	+	0.932407i
$809$			21.9806i			0.772796i	0.922332	+	0.386398i	$0.126281\pi$
$809$			21.9806i			0.772796i	−0.922332	+	0.386398i	$0.873719\pi$
$810$		0			0
$811$			44.7005i			1.56965i	0.619719	+	0.784824i	$0.287247\pi$
$811$			44.7005i			1.56965i	−0.619719	+	0.784824i	$0.712753\pi$
$812$		0			0
$813$		0			0
$814$	−15.3288	+	4.58546i	−0.537276	+	0.160720i
$815$	55.1448			1.93164
$816$		0			0
$817$	−12.3158			−0.430877
$818$	−14.2061	+	4.24962i	−0.496706	+	0.148584i
$819$		0			0
$820$	−36.3074	+	23.8568i	−1.26791	+	0.833115i
$821$		−	39.3651i		−	1.37385i	−0.726727	−	0.686926i	$-0.758960\pi$
$821$		−	39.3651i		−	1.37385i	0.726727	−	0.686926i	$-0.241040\pi$
$822$		0			0
$823$		−	31.9718i		−	1.11447i	−0.830355	−	0.557234i	$-0.811863\pi$
$823$		−	31.9718i		−	1.11447i	0.830355	−	0.557234i	$-0.188137\pi$
$824$	12.3591	+	10.3845i	0.430548	+	0.361760i
$825$		0			0
$826$		0			0
$827$	20.8702			0.725728			0.362864	−	0.931842i	$-0.381799\pi$
$827$	20.8702			0.725728			0.362864	+	0.931842i	$0.381799\pi$
$828$		0			0
$829$	32.2217			1.11911			0.559554	−	0.828794i	$-0.310973\pi$
$829$	32.2217			1.11911			0.559554	+	0.828794i	$0.310973\pi$
$830$	−4.35431	−	14.5561i	−0.151140	−	0.505250i
$831$		0			0
$832$	−6.86412	−	39.2327i	−0.237970	−	1.36015i
$833$		0			0
$834$		0			0
$835$			29.7564i			1.02976i
$836$	−11.9044	−	18.1172i	−0.411722	−	0.626596i
$837$		0			0
$838$	−42.1825	+	12.6184i	−1.45717	+	0.435897i
$839$	−48.9320			−1.68932			−0.844660	−	0.535303i	$-0.820198\pi$
$839$	−48.9320			−1.68932			−0.844660	+	0.535303i	$0.820198\pi$
$840$		0			0
$841$	27.0000			0.931034
$842$	−41.0052	+	12.2663i	−1.41313	+	0.422724i
$843$		0			0
$844$	10.9357	+	16.6430i	0.376423	+	0.572876i
$845$			39.0524i			1.34344i
$846$		0			0
$847$		0			0
$848$	3.67230	+	1.58793i	0.126107	+	0.0545298i
$849$		0			0
$850$	1.17513	+	3.92839i	0.0403068	+	0.134742i
$851$	−19.0732			−0.653820
$852$		0			0
$853$	−12.2927			−0.420895			−0.210448	−	0.977605i	$-0.567492\pi$
$853$	−12.2927			−0.420895			−0.210448	+	0.977605i	$0.567492\pi$
$854$		0			0
$855$		0			0
$856$	29.1874	−	34.7374i	0.997605	−	1.18730i
$857$		−	57.1349i		−	1.95169i	−0.218463	−	0.975845i	$-0.570104\pi$
$857$		−	57.1349i		−	1.95169i	0.218463	−	0.975845i	$-0.429896\pi$
$858$		0			0
$859$		−	21.8223i		−	0.744569i	−0.928119	−	0.372284i	$-0.878575\pi$
$859$		−	21.8223i		−	0.744569i	0.928119	−	0.372284i	$-0.121425\pi$
$860$	−29.7496	+	19.5477i	−1.01445	+	0.666573i
$861$		0			0
$862$	3.02384	−	0.904549i	0.102992	−	0.0308090i
$863$	−42.2764			−1.43911			−0.719553	−	0.694437i	$-0.755653\pi$
$863$	−42.2764			−1.43911			−0.719553	+	0.694437i	$0.755653\pi$
$864$		0			0
$865$	−9.13650			−0.310650
$866$	−11.5743	+	3.46233i	−0.393311	+	0.117655i
$867$		0			0
$868$		0			0
$869$			57.0033i			1.93370i
$870$		0			0
$871$			16.2865i			0.551846i
$872$	−2.49581	+	2.97039i	−0.0845190	+	0.100590i
$873$		0			0
$874$	−7.40612	−	24.7581i	−0.250516	−	0.837454i
$875$		0			0
$876$		0			0
$877$	26.2008			0.884737			0.442369	−	0.896833i	$-0.354138\pi$
$877$	26.2008			0.884737			0.442369	+	0.896833i	$0.354138\pi$
$878$	0.474577	+	1.58647i	0.0160162	+	0.0535409i
$879$		0			0
$880$	−57.5113	−	24.8683i	−1.93871	−	0.838311i
$881$		−	47.4165i		−	1.59750i	−0.601661	−	0.798752i	$-0.705494\pi$
$881$		−	47.4165i		−	1.59750i	0.601661	−	0.798752i	$-0.294506\pi$
$882$		0			0
$883$			26.6283i			0.896114i	0.894005	+	0.448057i	$0.147884\pi$
$883$			26.6283i			0.896114i	−0.894005	+	0.448057i	$0.852116\pi$
$884$	2.65173	+	4.03565i	0.0891874	+	0.135734i
$885$		0			0
$886$	−8.92345	+	2.66936i	−0.299789	+	0.0896788i
$887$	6.75684			0.226873			0.113436	−	0.993545i	$-0.463814\pi$
$887$	6.75684			0.226873			0.113436	+	0.993545i	$0.463814\pi$
$888$		0			0
$889$		0			0
$890$	25.7139	−	7.69204i	0.861932	−	0.257838i
$891$		0			0
$892$	−0.863500	−	1.31415i	−0.0289121	−	0.0440011i
$893$		−	14.2443i		−	0.476667i
$894$		0			0
$895$		−	15.6644i		−	0.523604i
$896$		0			0
$897$		0			0
$898$	−4.54862	−	15.2057i	−0.151790	−	0.507421i
$899$	10.8391			0.361505
$900$		0			0
$901$	−0.485078			−0.0161603
$902$	12.5616	+	41.9925i	0.418256	+	1.39820i
$903$		0			0
$904$	24.4342	+	20.5303i	0.812668	+	0.682829i
$905$			27.8097i			0.924426i
$906$		0			0
$907$		−	25.2860i		−	0.839608i	−0.907615	−	0.419804i	$-0.862099\pi$
$907$		−	25.2860i		−	0.839608i	0.907615	−	0.419804i	$-0.137901\pi$
$908$	−33.9212	+	22.2888i	−1.12572	+	0.739681i
$909$		0			0
$910$		0			0
$911$	21.3050			0.705865			0.352932	−	0.935649i	$-0.385185\pi$
$911$	21.3050			0.705865			0.352932	+	0.935649i	$0.385185\pi$
$912$		0			0
$913$	−15.3288			−0.507311
$914$	−16.1426	+	4.82889i	−0.533950	+	0.159725i
$915$		0			0
$916$	8.32150	−	5.46787i	0.274950	−	0.180663i
$917$		0			0
$918$		0			0
$919$			48.4998i			1.59986i	0.600093	+	0.799930i	$0.295130\pi$
$919$			48.4998i			1.59986i	−0.600093	+	0.799930i	$0.704870\pi$
$920$	−57.1860	−	48.0494i	−1.88537	−	1.58414i
$921$		0			0
$922$	7.46787	+	24.9645i	0.245941	+	0.822162i
$923$	16.6468			0.547937
$924$		0			0
$925$	14.3074			0.470425
$926$	3.02844	+	10.1239i	0.0995208	+	0.332690i
$927$		0			0
$928$	7.94488	+	0.937529i	0.260803	+	0.0307759i
$929$		−	10.5567i		−	0.346355i	−0.984891	−	0.173177i	$-0.944597\pi$
$929$		−	10.5567i		−	0.346355i	0.984891	−	0.173177i	$-0.0554034\pi$
$930$		0			0
$931$		0			0
$932$	−0.421396	−	0.641319i	−0.0138033	−	0.0210071i
$933$		0			0
$934$	7.55417	−	2.25975i	0.247180	−	0.0739413i
$935$	7.59672			0.248439
$936$		0			0
$937$	29.5296			0.964690			0.482345	−	0.875981i	$-0.339785\pi$
$937$	29.5296			0.964690			0.482345	+	0.875981i	$0.339785\pi$
$938$		0			0
$939$		0			0
$940$	−22.6086	−	34.4078i	−0.737410	−	1.12226i
$941$			6.53503i			0.213036i	0.994311	+	0.106518i	$0.0339701\pi$
$941$			6.53503i			0.213036i	−0.994311	+	0.106518i	$0.966030\pi$
$942$		0			0
$943$			52.2499i			1.70149i
$944$	−2.19706	+	5.08100i	−0.0715083	+	0.165372i
$945$		0			0
$946$	10.2927	+	34.4078i	0.334646	+	1.11869i
$947$	43.2951			1.40690			0.703450	−	0.710745i	$-0.251642\pi$
$947$	43.2951			1.40690			0.703450	+	0.710745i	$0.251642\pi$
$948$		0			0
$949$	10.4569			0.339446
$950$	5.55558	+	18.5719i	0.180247	+	0.602551i
$951$		0			0
$952$		0			0
$953$		−	19.4848i		−	0.631173i	−0.948897	−	0.315587i	$-0.897799\pi$
$953$		−	19.4848i		−	0.631173i	0.948897	−	0.315587i	$-0.102201\pi$
$954$		0			0
$955$			4.92104i			0.159241i
$956$	−2.48245	+	1.63116i	−0.0802881	+	0.0527555i
$957$		0			0
$958$	−21.5970	+	6.46052i	−0.697768	+	0.208730i
$959$		0			0
$960$		0			0
$961$	−27.7434			−0.894948
$962$	16.1426	−	4.82889i	0.520458	−	0.155690i
$963$		0			0
$964$	39.2327	−	25.7789i	1.26360	−	0.830282i
$965$		−	27.6677i		−	0.890656i
$966$		0			0
$967$			28.4422i			0.914641i	0.889302	+	0.457320i	$0.151191\pi$
$967$			28.4422i			0.914641i	−0.889302	+	0.457320i	$0.848809\pi$
$968$	−20.6520	+	24.5789i	−0.663780	+	0.789997i
$969$		0			0
$970$	16.1923	+	54.1298i	0.519905	+	1.73800i
$971$	8.61534			0.276479			0.138240	−	0.990399i	$-0.455856\pi$
$971$	8.61534			0.276479			0.138240	+	0.990399i	$0.455856\pi$
$972$		0			0
$973$		0			0
$974$	13.8095	+	46.1642i	0.442486	+	1.47920i
$975$		0			0
$976$	−21.6932	+	50.1684i	−0.694382	+	1.60585i
$977$			35.8715i			1.14763i	0.818985	+	0.573815i	$0.194537\pi$
$977$			35.8715i			1.14763i	−0.818985	+	0.573815i	$0.805463\pi$
$978$		0			0
$979$		−	27.0790i		−	0.865447i
$980$		0			0
$981$		0			0
$982$	−46.0698	+	13.7813i	−1.47015	+	0.439779i
$983$	41.0633			1.30971			0.654857	−	0.755752i	$-0.272729\pi$
$983$	41.0633			1.30971			0.654857	+	0.755752i	$0.272729\pi$
$984$		0			0
$985$	−12.6858			−0.404205
$986$	−0.929247	+	0.277974i	−0.0295933	+	0.00885251i
$987$		0			0
$988$	12.5363	+	19.0790i	0.398834	+	0.606983i
$989$			42.8125i			1.36136i
$990$		0			0
$991$			25.6707i			0.815456i	0.913103	+	0.407728i	$0.133679\pi$
$991$			25.6707i			0.815456i	−0.913103	+	0.407728i	$0.866321\pi$
$992$	−43.0578	−	5.08100i	−1.36709	−	0.161322i
$993$		0			0
$994$		0			0
$995$	20.0223			0.634750
$996$		0			0
$997$	2.45065			0.0776130			0.0388065	−	0.999247i	$-0.487644\pi$
$997$	2.45065			0.0776130			0.0388065	+	0.999247i	$0.487644\pi$
$998$	−2.17715	−	7.27806i	−0.0689166	−	0.230383i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1764.2.e.g.1079.2		12
3.2	odd	2	inner	1764.2.e.g.1079.11		12
4.3	odd	2	inner	1764.2.e.g.1079.12		12
7.6	odd	2		252.2.e.a.71.2	yes	12
12.11	even	2	inner	1764.2.e.g.1079.1		12
21.20	even	2		252.2.e.a.71.11	yes	12
28.27	even	2		252.2.e.a.71.12	yes	12
56.13	odd	2		4032.2.h.h.575.11		12
56.27	even	2		4032.2.h.h.575.12		12
84.83	odd	2		252.2.e.a.71.1	✓	12
168.83	odd	2		4032.2.h.h.575.2		12
168.125	even	2		4032.2.h.h.575.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.e.a.71.1	✓	12	84.83	odd	2
252.2.e.a.71.2	yes	12	7.6	odd	2
252.2.e.a.71.11	yes	12	21.20	even	2
252.2.e.a.71.12	yes	12	28.27	even	2
1764.2.e.g.1079.1		12	12.11	even	2	inner
1764.2.e.g.1079.2		12	1.1	even	1	trivial
1764.2.e.g.1079.11		12	3.2	odd	2	inner
1764.2.e.g.1079.12		12	4.3	odd	2	inner
4032.2.h.h.575.1		12	168.125	even	2
4032.2.h.h.575.2		12	168.83	odd	2
4032.2.h.h.575.11		12	56.13	odd	2
4032.2.h.h.575.12		12	56.27	even	2

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:	\( N \)	\(=\)	\( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1764.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.35489 + 0.405301i) q^{2} +(1.67146 - 1.09828i) q^{4} +3.31339i q^{5} +(-1.81951 + 2.16549i) q^{8} +O(q^{10})\)	\(q+(-1.35489 + 0.405301i) q^{2} +(1.67146 - 1.09828i) q^{4} +3.31339i q^{5} +(-1.81951 + 2.16549i) q^{8} +(-1.34292 - 4.48929i) q^{10} -4.72761 q^{11} +4.97858 q^{13} +(1.58757 - 3.67146i) q^{16} +0.484966i q^{17} +2.29273i q^{19} +(3.63903 + 5.53821i) q^{20} +(6.40539 - 1.91611i) q^{22} +7.97002 q^{23} -5.97858 q^{25} +(-6.74543 + 2.01782i) q^{26} -1.41421i q^{29} +7.66442i q^{31} +(-0.662933 + 5.61788i) q^{32} +(-0.196558 - 0.657077i) q^{34} -2.39312 q^{37} +(-0.929247 - 3.10640i) q^{38} +(-7.17513 - 6.02877i) q^{40} +6.55580i q^{41} +5.37169i q^{43} +(-7.90201 + 5.19223i) q^{44} +(-10.7985 + 3.23026i) q^{46} -6.21280 q^{47} +(8.10032 - 2.42313i) q^{50} +(8.32150 - 5.46787i) q^{52} +1.00023i q^{53} -15.6644i q^{55} +(0.573183 + 1.91611i) q^{58} -1.38392 q^{59} -13.6644 q^{61} +(-3.10640 - 10.3845i) q^{62} +(-1.37873 - 7.88030i) q^{64} +16.4960i q^{65} +3.27131i q^{67} +(0.532628 + 0.810603i) q^{68} +3.34369 q^{71} +2.10038 q^{73} +(3.24241 - 0.969933i) q^{74} +(2.51806 + 3.83221i) q^{76} -12.0575i q^{79} +(12.1650 + 5.26024i) q^{80} +(-2.65708 - 8.88240i) q^{82} +3.24241 q^{83} -1.60688 q^{85} +(-2.17715 - 7.27806i) q^{86} +(8.60195 - 10.2376i) q^{88} +5.72784i q^{89} +(13.3216 - 8.75330i) q^{92} +(8.41767 - 2.51806i) q^{94} -7.59672 q^{95} -12.0575 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 8 q^{4}+O(q^{10}) \) 12 * q + 8 * q^4	\( 12 q + 8 q^{4} + 8 q^{10} - 20 q^{16} + 20 q^{22} - 12 q^{25} + 16 q^{34} + 8 q^{37} - 8 q^{40} - 36 q^{46} + 16 q^{52} + 4 q^{58} - 56 q^{61} - 16 q^{64} - 72 q^{76} - 56 q^{82} - 56 q^{85} + 28 q^{88} + 24 q^{94}+O(q^{100}) \) 12 * q + 8 * q^4 + 8 * q^10 - 20 * q^16 + 20 * q^22 - 12 * q^25 + 16 * q^34 + 8 * q^37 - 8 * q^40 - 36 * q^46 + 16 * q^52 + 4 * q^58 - 56 * q^61 - 16 * q^64 - 72 * q^76 - 56 * q^82 - 56 * q^85 + 28 * q^88 + 24 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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