LMFDB - Embedded newform 396.2.j.b.37.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [396,2,Mod(37,396)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(396, base_ring=CyclotomicField(10))

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("396.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 396 = 2^{2} \cdot 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	396.j (of order $5$, degree $4$, 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:	$3.16207592004$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 132)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			37.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	396.37
Dual form			396.2.j.b.289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30902 + 0.951057i) q^{5} +(0.0729490 + 0.224514i) q^{7} +O(q^{10})$	$q+(-1.30902 + 0.951057i) q^{5} +(0.0729490 + 0.224514i) q^{7} +(0.809017 + 3.21644i) q^{11} +(3.42705 + 2.48990i) q^{13} +(-0.118034 + 0.0857567i) q^{17} +(-2.11803 + 6.51864i) q^{19} +5.00000 q^{23} +(-0.736068 + 2.26538i) q^{25} +(-0.618034 - 1.90211i) q^{29} +(-2.73607 - 1.98787i) q^{31} +(-0.309017 - 0.224514i) q^{35} +(0.690983 + 2.12663i) q^{37} +(2.69098 - 8.28199i) q^{41} -2.52786 q^{43} +(-2.95492 + 9.09429i) q^{47} +(5.61803 - 4.08174i) q^{49} +(5.35410 + 3.88998i) q^{53} +(-4.11803 - 3.44095i) q^{55} +(-3.64590 - 11.2209i) q^{59} +(8.78115 - 6.37988i) q^{61} -6.85410 q^{65} -4.38197 q^{67} +(-11.7812 + 8.55951i) q^{71} +(-4.85410 - 14.9394i) q^{73} +(-0.663119 + 0.416272i) q^{77} +(7.04508 + 5.11855i) q^{79} +(-1.42705 + 1.03681i) q^{83} +(0.0729490 - 0.224514i) q^{85} +5.18034 q^{89} +(-0.309017 + 0.951057i) q^{91} +(-3.42705 - 10.5474i) q^{95} +(-12.1631 - 8.83702i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 3 q^{5} + 7 q^{7}+O(q^{10}) $ 4 * q - 3 * q^5 + 7 * q^7	$ 4 q - 3 q^{5} + 7 q^{7} + q^{11} + 7 q^{13} + 4 q^{17} - 4 q^{19} + 20 q^{23} + 6 q^{25} + 2 q^{29} - 2 q^{31} + q^{35} + 5 q^{37} + 13 q^{41} - 28 q^{43} - 23 q^{47} + 18 q^{49} + 8 q^{53} - 12 q^{55} - 28 q^{59} + 15 q^{61} - 14 q^{65} - 22 q^{67} - 27 q^{71} - 6 q^{73} + 13 q^{77} + 17 q^{79} + q^{83} + 7 q^{85} - 24 q^{89} + q^{91} - 7 q^{95} - 33 q^{97}+O(q^{100}) $ 4 * q - 3 * q^5 + 7 * q^7 + q^11 + 7 * q^13 + 4 * q^17 - 4 * q^19 + 20 * q^23 + 6 * q^25 + 2 * q^29 - 2 * q^31 + q^35 + 5 * q^37 + 13 * q^41 - 28 * q^43 - 23 * q^47 + 18 * q^49 + 8 * q^53 - 12 * q^55 - 28 * q^59 + 15 * q^61 - 14 * q^65 - 22 * q^67 - 27 * q^71 - 6 * q^73 + 13 * q^77 + 17 * q^79 + q^83 + 7 * q^85 - 24 * q^89 + q^91 - 7 * q^95 - 33 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/396\mathbb{Z}\right)^\times$.

$n$	$145$	$199$	$353$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−1.30902	+	0.951057i	−0.585410	+	0.425325i	−0.840670	−	0.541547i	$-0.817839\pi$
$5$	−1.30902	+	0.951057i	−0.585410	+	0.425325i	0.255260	+	0.966872i	$0.417839\pi$
$6$		0			0
$7$	0.0729490	+	0.224514i	0.0275721	+	0.0848583i	0.963896	−	0.266280i	$-0.0857946\pi$
$7$	0.0729490	+	0.224514i	0.0275721	+	0.0848583i	−0.936324	+	0.351138i	$0.885795\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	0.809017	+	3.21644i	0.243928	+	0.969793i
$11$	0.809017	+	3.21644i	0.243928	+	0.969793i
$12$		0			0
$13$	3.42705	+	2.48990i	0.950493	+	0.690574i	0.950923	−	0.309426i	$-0.100137\pi$
$13$	3.42705	+	2.48990i	0.950493	+	0.690574i	−0.000430477		1.00000i	$0.500137\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.118034	+	0.0857567i	−0.0286274	+	0.0207991i	−0.602007	−	0.798491i	$-0.705632\pi$
$17$	−0.118034	+	0.0857567i	−0.0286274	+	0.0207991i	0.573380	+	0.819290i	$0.305632\pi$
$18$		0			0
$19$	−2.11803	+	6.51864i	−0.485910	+	1.49548i	0.344748	+	0.938695i	$0.387964\pi$
$19$	−2.11803	+	6.51864i	−0.485910	+	1.49548i	−0.830658	+	0.556783i	$0.812036\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	5.00000			1.04257			0.521286	−	0.853382i	$-0.325452\pi$
$23$	5.00000			1.04257			0.521286	+	0.853382i	$0.325452\pi$
$24$		0			0
$25$	−0.736068	+	2.26538i	−0.147214	+	0.453077i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−0.618034	−	1.90211i	−0.114766	−	0.353214i	0.877132	−	0.480249i	$-0.159454\pi$
$29$	−0.618034	−	1.90211i	−0.114766	−	0.353214i	−0.991898	+	0.127036i	$0.959454\pi$
$30$		0			0
$31$	−2.73607	−	1.98787i	−0.491412	−	0.357032i	0.314315	−	0.949319i	$-0.398225\pi$
$31$	−2.73607	−	1.98787i	−0.491412	−	0.357032i	−0.805727	+	0.592287i	$0.798225\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−0.309017	−	0.224514i	−0.0522334	−	0.0379498i
$36$		0			0
$37$	0.690983	+	2.12663i	0.113597	+	0.349615i	0.991652	−	0.128945i	$-0.0411589\pi$
$37$	0.690983	+	2.12663i	0.113597	+	0.349615i	−0.878055	+	0.478560i	$0.841159\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	2.69098	−	8.28199i	0.420261	−	1.29343i	−0.487199	−	0.873291i	$-0.661981\pi$
$41$	2.69098	−	8.28199i	0.420261	−	1.29343i	0.907460	−	0.420139i	$-0.138019\pi$
$42$		0			0
$43$	−2.52786			−0.385496			−0.192748	−	0.981248i	$-0.561740\pi$
$43$	−2.52786			−0.385496			−0.192748	+	0.981248i	$0.561740\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−2.95492	+	9.09429i	−0.431019	+	1.32654i	0.466093	+	0.884736i	$0.345661\pi$
$47$	−2.95492	+	9.09429i	−0.431019	+	1.32654i	−0.897112	+	0.441803i	$0.854339\pi$
$48$		0			0
$49$	5.61803	−	4.08174i	0.802576	−	0.583106i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	5.35410	+	3.88998i	0.735442	+	0.534330i	0.891280	−	0.453452i	$-0.149808\pi$
$53$	5.35410	+	3.88998i	0.735442	+	0.534330i	−0.155838	+	0.987783i	$0.549808\pi$
$54$		0			0
$55$	−4.11803	−	3.44095i	−0.555276	−	0.463978i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−3.64590	−	11.2209i	−0.474655	−	1.46084i	−0.846422	−	0.532513i	$-0.821248\pi$
$59$	−3.64590	−	11.2209i	−0.474655	−	1.46084i	0.371766	−	0.928326i	$-0.378752\pi$
$60$		0			0
$61$	8.78115	−	6.37988i	1.12431	−	0.816860i	0.139454	−	0.990228i	$-0.455465\pi$
$61$	8.78115	−	6.37988i	1.12431	−	0.816860i	0.984857	+	0.173368i	$0.0554651\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−6.85410			−0.850147
$66$		0			0
$67$	−4.38197			−0.535342			−0.267671	−	0.963510i	$-0.586254\pi$
$67$	−4.38197			−0.535342			−0.267671	+	0.963510i	$0.586254\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−11.7812	+	8.55951i	−1.39817	+	1.01583i	−0.403253	+	0.915089i	$0.632120\pi$
$71$	−11.7812	+	8.55951i	−1.39817	+	1.01583i	−0.994913	+	0.100738i	$0.967880\pi$
$72$		0			0
$73$	−4.85410	−	14.9394i	−0.568130	−	1.74852i	−0.658464	−	0.752612i	$-0.728794\pi$
$73$	−4.85410	−	14.9394i	−0.568130	−	1.74852i	0.0903348	−	0.995911i	$-0.471206\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.663119	+	0.416272i	−0.0755694	+	0.0474386i
$78$		0			0
$79$	7.04508	+	5.11855i	0.792634	+	0.575882i	0.908744	−	0.417354i	$-0.137043\pi$
$79$	7.04508	+	5.11855i	0.792634	+	0.575882i	−0.116110	+	0.993236i	$0.537043\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−1.42705	+	1.03681i	−0.156639	+	0.113805i	−0.663344	−	0.748315i	$-0.730863\pi$
$83$	−1.42705	+	1.03681i	−0.156639	+	0.113805i	0.506705	+	0.862120i	$0.330863\pi$
$84$		0			0
$85$	0.0729490	−	0.224514i	0.00791243	−	0.0243520i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	5.18034			0.549115			0.274557	−	0.961571i	$-0.411469\pi$
$89$	5.18034			0.549115			0.274557	+	0.961571i	$0.411469\pi$
$90$		0			0
$91$	−0.309017	+	0.951057i	−0.0323938	+	0.0996978i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−3.42705	−	10.5474i	−0.351608	−	1.08214i
$96$		0			0
$97$	−12.1631	−	8.83702i	−1.23498	−	0.897264i	−0.237724	−	0.971333i	$-0.576402\pi$
$97$	−12.1631	−	8.83702i	−1.23498	−	0.897264i	−0.997253	+	0.0740689i	$0.976402\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	13.1353	+	9.54332i	1.30701	+	0.949596i	0.999998	−	0.00211067i	$-0.000671847\pi$
$101$	13.1353	+	9.54332i	1.30701	+	0.949596i	0.307009	+	0.951707i	$0.400672\pi$
$102$		0			0
$103$	−2.90983	−	8.95554i	−0.286714	−	0.882415i	−0.985880	−	0.167455i	$-0.946445\pi$
$103$	−2.90983	−	8.95554i	−0.286714	−	0.882415i	0.699166	−	0.714960i	$-0.253555\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	4.83688	−	14.8864i	0.467599	−	1.43912i	−0.388085	−	0.921623i	$-0.626863\pi$
$107$	4.83688	−	14.8864i	0.467599	−	1.43912i	0.855684	−	0.517498i	$-0.173137\pi$
$108$		0			0
$109$	8.94427			0.856706			0.428353	−	0.903612i	$-0.359094\pi$
$109$	8.94427			0.856706			0.428353	+	0.903612i	$0.359094\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	2.45492	−	7.55545i	0.230939	−	0.710757i	−0.766695	−	0.642011i	$-0.778100\pi$
$113$	2.45492	−	7.55545i	0.230939	−	0.710757i	0.997634	−	0.0687459i	$-0.0218998\pi$
$114$		0			0
$115$	−6.54508	+	4.75528i	−0.610332	+	0.443432i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−0.0278640	−	0.0202444i	−0.00255429	−	0.00185580i
$120$		0			0
$121$	−9.69098	+	5.20431i	−0.880998	+	0.473119i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−3.69098	−	11.3597i	−0.330132	−	1.01604i
$126$		0			0
$127$	−1.38197	+	1.00406i	−0.122630	+	0.0890957i	−0.647410	−	0.762142i	$-0.724148\pi$
$127$	−1.38197	+	1.00406i	−0.122630	+	0.0890957i	0.524780	+	0.851238i	$0.324148\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	2.14590			0.187488			0.0937440	−	0.995596i	$-0.470116\pi$
$131$	2.14590			0.187488			0.0937440	+	0.995596i	$0.470116\pi$
$132$		0			0
$133$	−1.61803			−0.140301
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−11.5172	+	8.36775i	−0.983983	+	0.714905i	−0.958595	−	0.284772i	$-0.908082\pi$
$137$	−11.5172	+	8.36775i	−0.983983	+	0.714905i	−0.0253875	+	0.999678i	$0.508082\pi$
$138$		0			0
$139$	3.57295	+	10.9964i	0.303054	+	0.932703i	0.980396	+	0.197035i	$0.0631314\pi$
$139$	3.57295	+	10.9964i	0.303054	+	0.932703i	−0.677343	+	0.735668i	$0.736869\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−5.23607	+	13.0373i	−0.437862	+	1.09023i
$144$		0			0
$145$	2.61803	+	1.90211i	0.217416	+	0.157962i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	17.9894	−	13.0700i	1.47375	−	1.07074i	0.494239	−	0.869326i	$-0.335447\pi$
$149$	17.9894	−	13.0700i	1.47375	−	1.07074i	0.979506	−	0.201413i	$-0.0645533\pi$
$150$		0			0
$151$	1.38197	−	4.25325i	0.112463	−	0.346125i	−0.878947	−	0.476920i	$-0.841753\pi$
$151$	1.38197	−	4.25325i	0.112463	−	0.346125i	0.991409	+	0.130795i	$0.0417531\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	5.47214			0.439533
$156$		0			0
$157$	−0.708204	+	2.17963i	−0.0565208	+	0.173953i	−0.975331	−	0.220745i	$-0.929151\pi$
$157$	−0.708204	+	2.17963i	−0.0565208	+	0.173953i	0.918811	+	0.394699i	$0.129151\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	0.364745	+	1.12257i	0.0287459	+	0.0884709i
$162$		0			0
$163$	10.2082	+	7.41669i	0.799568	+	0.580920i	0.910787	−	0.412876i	$-0.135476\pi$
$163$	10.2082	+	7.41669i	0.799568	+	0.580920i	−0.111219	+	0.993796i	$0.535476\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	3.69098	+	2.68166i	0.285617	+	0.207513i	0.721364	−	0.692557i	$-0.243516\pi$
$167$	3.69098	+	2.68166i	0.285617	+	0.207513i	−0.435747	+	0.900069i	$0.643516\pi$
$168$		0			0
$169$	1.52786	+	4.70228i	0.117528	+	0.361714i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−7.82624	+	24.0867i	−0.595018	+	1.83128i	−0.0403806	+	0.999184i	$0.512857\pi$
$173$	−7.82624	+	24.0867i	−0.595018	+	1.83128i	−0.554637	+	0.832092i	$0.687143\pi$
$174$		0			0
$175$	−0.562306			−0.0425063
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−4.54508	+	13.9883i	−0.339716	+	1.04554i	0.624637	+	0.780915i	$0.285247\pi$
$179$	−4.54508	+	13.9883i	−0.339716	+	1.04554i	−0.964352	+	0.264622i	$0.914753\pi$
$180$		0			0
$181$	−4.04508	+	2.93893i	−0.300669	+	0.218449i	−0.727882	−	0.685702i	$-0.759495\pi$
$181$	−4.04508	+	2.93893i	−0.300669	+	0.218449i	0.427213	+	0.904151i	$0.359495\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−2.92705	−	2.12663i	−0.215201	−	0.156353i
$186$		0			0
$187$	−0.371323	−	0.310271i	−0.0271538	−	0.0226892i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	1.39919	+	4.30625i	0.101242	+	0.311590i	0.988830	−	0.149048i	$-0.0476208\pi$
$191$	1.39919	+	4.30625i	0.101242	+	0.311590i	−0.887588	+	0.460637i	$0.847621\pi$
$192$		0			0
$193$	5.50000	−	3.99598i	0.395899	−	0.287637i	−0.371970	−	0.928245i	$-0.621317\pi$
$193$	5.50000	−	3.99598i	0.395899	−	0.287637i	0.767868	+	0.640608i	$0.221317\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−3.67376			−0.261745			−0.130872	−	0.991399i	$-0.541778\pi$
$197$	−3.67376			−0.261745			−0.130872	+	0.991399i	$0.541778\pi$
$198$		0			0
$199$	17.9443			1.27204			0.636018	−	0.771674i	$-0.280580\pi$
$199$	17.9443			1.27204			0.636018	+	0.771674i	$0.280580\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	0.381966	−	0.277515i	0.0268088	−	0.0194777i
$204$		0			0
$205$	4.35410	+	13.4005i	0.304104	+	0.935935i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−22.6803	−	1.53884i	−1.56883	−	0.106444i
$210$		0			0
$211$	7.20820	+	5.23707i	0.496233	+	0.360535i	0.807576	−	0.589763i	$-0.200779\pi$
$211$	7.20820	+	5.23707i	0.496233	+	0.360535i	−0.311343	+	0.950298i	$0.600779\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	3.30902	−	2.40414i	0.225673	−	0.163961i
$216$		0			0
$217$	0.246711	−	0.759299i	0.0167478	−	0.0515446i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−0.618034			−0.0415735
$222$		0			0
$223$	0.635255	−	1.95511i	0.0425398	−	0.130924i	−0.927531	−	0.373746i	$-0.878073\pi$
$223$	0.635255	−	1.95511i	0.0425398	−	0.130924i	0.970071	+	0.242822i	$0.0780731\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	1.07295	+	3.30220i	0.0712141	+	0.219175i	0.980329	−	0.197371i	$-0.0632405\pi$
$227$	1.07295	+	3.30220i	0.0712141	+	0.219175i	−0.909115	+	0.416546i	$0.863240\pi$
$228$		0			0
$229$	14.0902	+	10.2371i	0.931105	+	0.676487i	0.946263	−	0.323398i	$-0.104825\pi$
$229$	14.0902	+	10.2371i	0.931105	+	0.676487i	−0.0151584	+	0.999885i	$0.504825\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	19.2533	+	13.9883i	1.26132	+	0.916406i	0.998822	−	0.0485250i	$-0.0154521\pi$
$233$	19.2533	+	13.9883i	1.26132	+	0.916406i	0.262503	+	0.964931i	$0.415452\pi$
$234$		0			0
$235$	−4.78115	−	14.7149i	−0.311888	−	0.959893i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	6.10081	−	18.7764i	0.394629	−	1.21454i	−0.534621	−	0.845092i	$-0.679546\pi$
$239$	6.10081	−	18.7764i	0.394629	−	1.21454i	0.929250	−	0.369451i	$-0.120454\pi$
$240$		0			0
$241$	−0.763932			−0.0492092			−0.0246046	−	0.999697i	$-0.507833\pi$
$241$	−0.763932			−0.0492092			−0.0246046	+	0.999697i	$0.507833\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−3.47214	+	10.6861i	−0.221827	+	0.682712i
$246$		0			0
$247$	−23.4894	+	17.0660i	−1.49459	+	1.08588i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−5.11803	−	3.71847i	−0.323047	−	0.234708i	0.414427	−	0.910082i	$-0.363982\pi$
$251$	−5.11803	−	3.71847i	−0.323047	−	0.234708i	−0.737475	+	0.675375i	$0.763982\pi$
$252$		0			0
$253$	4.04508	+	16.0822i	0.254312	+	1.01108i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−3.35410	−	10.3229i	−0.209223	−	0.643923i	−0.999513	−	0.0311900i	$-0.990070\pi$
$257$	−3.35410	−	10.3229i	−0.209223	−	0.643923i	0.790290	−	0.612733i	$-0.209930\pi$
$258$		0			0
$259$	−0.427051	+	0.310271i	−0.0265357	+	0.0192793i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	22.7426			1.40237			0.701186	−	0.712979i	$-0.252654\pi$
$263$	22.7426			1.40237			0.701186	+	0.712979i	$0.252654\pi$
$264$		0			0
$265$	−10.7082			−0.657800
$266$		0			0
$267$		0			0
$268$		0			0
$269$	1.14590	−	0.832544i	0.0698666	−	0.0507611i	−0.552304	−	0.833643i	$-0.686251\pi$
$269$	1.14590	−	0.832544i	0.0698666	−	0.0507611i	0.622170	+	0.782882i	$0.286251\pi$
$270$		0			0
$271$	−4.20820	−	12.9515i	−0.255630	−	0.786749i	−0.993705	−	0.112030i	$-0.964265\pi$
$271$	−4.20820	−	12.9515i	−0.255630	−	0.786749i	0.738075	−	0.674719i	$-0.235735\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−7.88197	−	0.534785i	−0.475300	−	0.0322487i
$276$		0			0
$277$	−5.20820	−	3.78398i	−0.312931	−	0.227357i	0.420222	−	0.907421i	$-0.361952\pi$
$277$	−5.20820	−	3.78398i	−0.312931	−	0.227357i	−0.733153	+	0.680064i	$0.761952\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	14.7082	−	10.6861i	0.877418	−	0.637481i	−0.0551492	−	0.998478i	$-0.517563\pi$
$281$	14.7082	−	10.6861i	0.877418	−	0.637481i	0.932567	+	0.360997i	$0.117563\pi$
$282$		0			0
$283$	7.61803	−	23.4459i	0.452845	−	1.39371i	−0.420801	−	0.907153i	$-0.638251\pi$
$283$	7.61803	−	23.4459i	0.452845	−	1.39371i	0.873647	−	0.486561i	$-0.161749\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	2.05573			0.121346
$288$		0			0
$289$	−5.24671	+	16.1477i	−0.308630	+	0.949866i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−5.48936	−	16.8945i	−0.320692	−	0.986987i	−0.973348	−	0.229333i	$-0.926345\pi$
$293$	−5.48936	−	16.8945i	−0.320692	−	0.986987i	0.652656	−	0.757654i	$-0.273655\pi$
$294$		0			0
$295$	15.4443	+	11.2209i	0.899200	+	0.653307i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	17.1353	+	12.4495i	0.990957	+	0.719973i
$300$		0			0
$301$	−0.184405	−	0.567541i	−0.0106289	−	0.0327125i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−5.42705	+	16.7027i	−0.310752	+	0.956396i
$306$		0			0
$307$	−31.7426			−1.81165			−0.905824	−	0.423654i	$-0.860747\pi$
$307$	−31.7426			−1.81165			−0.905824	+	0.423654i	$0.860747\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−1.39919	+	4.30625i	−0.0793406	+	0.244185i	−0.982857	−	0.184367i	$-0.940976\pi$
$311$	−1.39919	+	4.30625i	−0.0793406	+	0.244185i	0.903517	+	0.428553i	$0.140976\pi$
$312$		0			0
$313$	−8.42705	+	6.12261i	−0.476325	+	0.346070i	−0.799901	−	0.600132i	$-0.795115\pi$
$313$	−8.42705	+	6.12261i	−0.476325	+	0.346070i	0.323576	+	0.946202i	$0.395115\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−21.2254	−	15.4212i	−1.19214	−	0.866139i	−0.198650	−	0.980071i	$-0.563656\pi$
$317$	−21.2254	−	15.4212i	−1.19214	−	0.866139i	−0.993489	+	0.113931i	$0.963656\pi$
$318$		0			0
$319$	5.61803	−	3.52671i	0.314550	−	0.197458i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−0.309017	−	0.951057i	−0.0171942	−	0.0529182i
$324$		0			0
$325$	−8.16312	+	5.93085i	−0.452808	+	0.328985i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−2.25735			−0.124452
$330$		0			0
$331$	11.9443			0.656517			0.328258	−	0.944588i	$-0.393538\pi$
$331$	11.9443			0.656517			0.328258	+	0.944588i	$0.393538\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	5.73607	−	4.16750i	0.313395	−	0.227695i
$336$		0			0
$337$	−3.76393	−	11.5842i	−0.205034	−	0.631031i	−0.999712	−	0.0239993i	$-0.992360\pi$
$337$	−3.76393	−	11.5842i	−0.205034	−	0.631031i	0.794678	−	0.607032i	$-0.207640\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	4.18034	−	10.4086i	0.226378	−	0.563658i
$342$		0			0
$343$	2.66312	+	1.93487i	0.143795	+	0.104473i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−4.47214	+	3.24920i	−0.240077	+	0.174426i	−0.701318	−	0.712849i	$-0.747404\pi$
$347$	−4.47214	+	3.24920i	−0.240077	+	0.174426i	0.461241	+	0.887275i	$0.347404\pi$
$348$		0			0
$349$	5.96149	−	18.3476i	0.319111	−	0.982124i	−0.654918	−	0.755700i	$-0.727297\pi$
$349$	5.96149	−	18.3476i	0.319111	−	0.982124i	0.974029	−	0.226424i	$-0.0727033\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−32.9443			−1.75345			−0.876723	−	0.480995i	$-0.840276\pi$
$353$	−32.9443			−1.75345			−0.876723	+	0.480995i	$0.840276\pi$
$354$		0			0
$355$	7.28115	−	22.4091i	0.386443	−	1.18935i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−5.61803	−	17.2905i	−0.296508	−	0.912559i	−0.982711	−	0.185148i	$-0.940723\pi$
$359$	−5.61803	−	17.2905i	−0.296508	−	0.912559i	0.686202	−	0.727411i	$-0.259277\pi$
$360$		0			0
$361$	−22.6353	−	16.4455i	−1.19133	−	0.865551i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	20.5623	+	14.9394i	1.07628	+	0.781963i
$366$		0			0
$367$	−6.82624	−	21.0090i	−0.356327	−	1.09666i	−0.955236	−	0.295844i	$-0.904399\pi$
$367$	−6.82624	−	21.0090i	−0.356327	−	1.09666i	0.598909	−	0.800817i	$-0.295601\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−0.482779	+	1.48584i	−0.0250646	+	0.0771410i
$372$		0			0
$373$	22.4164			1.16068			0.580339	−	0.814375i	$-0.302920\pi$
$373$	22.4164			1.16068			0.580339	+	0.814375i	$0.302920\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	2.61803	−	8.05748i	0.134836	−	0.414981i
$378$		0			0
$379$	17.6074	−	12.7925i	0.904431	−	0.657108i	−0.0351693	−	0.999381i	$-0.511197\pi$
$379$	17.6074	−	12.7925i	0.904431	−	0.657108i	0.939600	+	0.342274i	$0.111197\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−4.04508	−	2.93893i	−0.206694	−	0.150172i	0.479623	−	0.877475i	$-0.340774\pi$
$383$	−4.04508	−	2.93893i	−0.206694	−	0.150172i	−0.686317	+	0.727303i	$0.740774\pi$
$384$		0			0
$385$	0.472136	−	1.17557i	0.0240623	−	0.0599126i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	1.66312	+	5.11855i	0.0843235	+	0.259521i	0.984325	−	0.176367i	$-0.0564345\pi$
$389$	1.66312	+	5.11855i	0.0843235	+	0.259521i	−0.900001	+	0.435888i	$0.856434\pi$
$390$		0			0
$391$	−0.590170	+	0.428784i	−0.0298462	+	0.0216845i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−14.0902			−0.708953
$396$		0			0
$397$	5.76393			0.289283			0.144642	−	0.989484i	$-0.453797\pi$
$397$	5.76393			0.289283			0.144642	+	0.989484i	$0.453797\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	4.97214	−	3.61247i	0.248297	−	0.180398i	−0.456675	−	0.889634i	$-0.650960\pi$
$401$	4.97214	−	3.61247i	0.248297	−	0.180398i	0.704972	+	0.709236i	$0.250960\pi$
$402$		0			0
$403$	−4.42705	−	13.6251i	−0.220527	−	0.678713i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−6.28115	+	3.94298i	−0.311345	+	0.195446i
$408$		0			0
$409$	−18.9443	−	13.7638i	−0.936734	−	0.680577i	0.0108983	−	0.999941i	$-0.496531\pi$
$409$	−18.9443	−	13.7638i	−0.936734	−	0.680577i	−0.947632	+	0.319364i	$0.896531\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	2.25329	−	1.63711i	0.110877	−	0.0805569i
$414$		0			0
$415$	0.881966	−	2.71441i	0.0432940	−	0.133245i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	11.7984			0.576388			0.288194	−	0.957572i	$-0.406945\pi$
$419$	11.7984			0.576388			0.288194	+	0.957572i	$0.406945\pi$
$420$		0			0
$421$	−2.68034	+	8.24924i	−0.130632	+	0.402043i	−0.994885	−	0.101014i	$-0.967791\pi$
$421$	−2.68034	+	8.24924i	−0.130632	+	0.402043i	0.864253	+	0.503057i	$0.167791\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−0.107391	−	0.330515i	−0.00520922	−	0.0160323i
$426$		0			0
$427$	2.07295	+	1.50609i	0.100317	+	0.0728846i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−24.6803	−	17.9313i	−1.18881	−	0.863721i	−0.195672	−	0.980669i	$-0.562689\pi$
$431$	−24.6803	−	17.9313i	−1.18881	−	0.863721i	−0.993138	+	0.116948i	$0.962689\pi$
$432$		0			0
$433$	−1.09017	−	3.35520i	−0.0523902	−	0.161241i	0.921438	−	0.388525i	$-0.127015\pi$
$433$	−1.09017	−	3.35520i	−0.0523902	−	0.161241i	−0.973828	+	0.227284i	$0.927015\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−10.5902	+	32.5932i	−0.506597	+	1.55914i
$438$		0			0
$439$	3.47214			0.165716			0.0828580	−	0.996561i	$-0.473595\pi$
$439$	3.47214			0.165716			0.0828580	+	0.996561i	$0.473595\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	6.09017	−	18.7436i	0.289353	−	0.890536i	−0.695707	−	0.718325i	$-0.744909\pi$
$443$	6.09017	−	18.7436i	0.289353	−	0.890536i	0.985060	−	0.172211i	$-0.0550910\pi$
$444$		0			0
$445$	−6.78115	+	4.92680i	−0.321457	+	0.233553i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	8.85410	+	6.43288i	0.417851	+	0.303586i	0.776773	−	0.629781i	$-0.216855\pi$
$449$	8.85410	+	6.43288i	0.417851	+	0.303586i	−0.358922	+	0.933368i	$0.616855\pi$
$450$		0			0
$451$	28.8156	+	1.95511i	1.35687	+	0.0920627i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−0.500000	−	1.53884i	−0.0234404	−	0.0721420i
$456$		0			0
$457$	−13.5902	+	9.87384i	−0.635721	+	0.461879i	−0.858378	−	0.513018i	$-0.828527\pi$
$457$	−13.5902	+	9.87384i	−0.635721	+	0.461879i	0.222656	+	0.974897i	$0.428527\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−16.2705			−0.757793			−0.378897	−	0.925439i	$-0.623696\pi$
$461$	−16.2705			−0.757793			−0.378897	+	0.925439i	$0.623696\pi$
$462$		0			0
$463$	16.0344			0.745184			0.372592	−	0.927995i	$-0.378469\pi$
$463$	16.0344			0.745184			0.372592	+	0.927995i	$0.378469\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−9.89919	+	7.19218i	−0.458080	+	0.332814i	−0.792778	−	0.609511i	$-0.791366\pi$
$467$	−9.89919	+	7.19218i	−0.458080	+	0.332814i	0.334698	+	0.942326i	$0.391366\pi$
$468$		0			0
$469$	−0.319660	−	0.983813i	−0.0147605	−	0.0454282i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−2.04508	−	8.13073i	−0.0940331	−	0.373851i
$474$		0			0
$475$	−13.2082	−	9.59632i	−0.606034	−	0.440309i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	21.2082	−	15.4087i	0.969028	−	0.704040i	0.0137978	−	0.999905i	$-0.495608\pi$
$479$	21.2082	−	15.4087i	0.969028	−	0.704040i	0.955230	+	0.295865i	$0.0956079\pi$
$480$		0			0
$481$	−2.92705	+	9.00854i	−0.133462	+	0.410754i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	24.3262			1.10460
$486$		0			0
$487$	−10.9271	+	33.6300i	−0.495152	+	1.52392i	0.321568	+	0.946887i	$0.395790\pi$
$487$	−10.9271	+	33.6300i	−0.495152	+	1.52392i	−0.816720	+	0.577034i	$0.804210\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	7.13525	+	21.9601i	0.322010	+	0.991043i	0.972772	+	0.231762i	$0.0744492\pi$
$491$	7.13525	+	21.9601i	0.322010	+	0.991043i	−0.650763	+	0.759281i	$0.725551\pi$
$492$		0			0
$493$	0.236068	+	0.171513i	0.0106320	+	0.00772458i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−2.78115	−	2.02063i	−0.124752	−	0.0906375i
$498$		0			0
$499$	6.82624	+	21.0090i	0.305584	+	0.940492i	0.979459	+	0.201646i	$0.0646290\pi$
$499$	6.82624	+	21.0090i	0.305584	+	0.940492i	−0.673874	+	0.738846i	$0.735371\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	6.70820	−	20.6457i	0.299104	−	0.920548i	−0.682708	−	0.730691i	$-0.739198\pi$
$503$	6.70820	−	20.6457i	0.299104	−	0.920548i	0.981812	−	0.189856i	$-0.0608022\pi$
$504$		0			0
$505$	−26.2705			−1.16902
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−5.33688	+	16.4252i	−0.236553	+	0.728036i	0.760359	+	0.649504i	$0.225023\pi$
$509$	−5.33688	+	16.4252i	−0.236553	+	0.728036i	−0.996912	+	0.0785319i	$0.974977\pi$
$510$		0			0
$511$	3.00000	−	2.17963i	0.132712	−	0.0964210i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	12.3262	+	8.95554i	0.543159	+	0.394628i
$516$		0			0
$517$	−31.6418	−	2.14687i	−1.39161	−	0.0944193i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	1.23607	+	3.80423i	0.0541531	+	0.166666i	0.974475	−	0.224495i	$-0.0720734\pi$
$521$	1.23607	+	3.80423i	0.0541531	+	0.166666i	−0.920322	+	0.391162i	$0.872073\pi$
$522$		0			0
$523$	2.97214	−	2.15938i	0.129962	−	0.0944232i	−0.520905	−	0.853615i	$-0.674405\pi$
$523$	2.97214	−	2.15938i	0.129962	−	0.0944232i	0.650867	+	0.759191i	$0.274405\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	0.493422			0.0214938
$528$		0			0
$529$	2.00000			0.0869565
$530$		0			0
$531$		0			0
$532$		0			0
$533$	29.8435	−	21.6825i	1.29266	−	0.939175i
$534$		0			0
$535$	7.82624	+	24.0867i	0.338358	+	1.04136i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	17.6738	+	14.7679i	0.761263	+	0.636097i
$540$		0			0
$541$	23.8713	+	17.3435i	1.02631	+	0.745657i	0.967566	−	0.252617i	$-0.0812911\pi$
$541$	23.8713	+	17.3435i	1.02631	+	0.745657i	0.0587419	+	0.998273i	$0.481291\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−11.7082	+	8.50651i	−0.501524	+	0.364379i
$546$		0			0
$547$	−8.60739	+	26.4908i	−0.368025	+	1.13267i	0.580039	+	0.814588i	$0.303037\pi$
$547$	−8.60739	+	26.4908i	−0.368025	+	1.13267i	−0.948065	+	0.318077i	$0.896963\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	13.7082			0.583989
$552$		0			0
$553$	−0.635255	+	1.95511i	−0.0270138	+	0.0831399i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	1.44427	+	4.44501i	0.0611958	+	0.188341i	0.976981	−	0.213328i	$-0.0684302\pi$
$557$	1.44427	+	4.44501i	0.0611958	+	0.188341i	−0.915785	+	0.401669i	$0.868430\pi$
$558$		0			0
$559$	−8.66312	−	6.29412i	−0.366411	−	0.266213i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−22.5172	−	16.3597i	−0.948988	−	0.689480i	0.00157952	−	0.999999i	$-0.499497\pi$
$563$	−22.5172	−	16.3597i	−0.948988	−	0.689480i	−0.950567	+	0.310519i	$0.899497\pi$
$564$		0			0
$565$	3.97214	+	12.2250i	0.167109	+	0.514309i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−1.18034	+	3.63271i	−0.0494824	+	0.152291i	−0.972745	−	0.231879i	$-0.925513\pi$
$569$	−1.18034	+	3.63271i	−0.0494824	+	0.152291i	0.923262	+	0.384171i	$0.125513\pi$
$570$		0			0
$571$	13.6180			0.569897			0.284948	−	0.958543i	$-0.408024\pi$
$571$	13.6180			0.569897			0.284948	+	0.958543i	$0.408024\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−3.68034	+	11.3269i	−0.153481	+	0.472365i
$576$		0			0
$577$	24.3262	−	17.6740i	1.01271	−	0.735780i	0.0479378	−	0.998850i	$-0.484735\pi$
$577$	24.3262	−	17.6740i	1.01271	−	0.735780i	0.964777	+	0.263070i	$0.0847351\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−0.336881	−	0.244758i	−0.0139762	−	0.0101543i
$582$		0			0
$583$	−8.18034	+	20.3682i	−0.338795	+	0.843565i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−4.48936	−	13.8168i	−0.185296	−	0.570281i	0.814658	−	0.579942i	$-0.196925\pi$
$587$	−4.48936	−	13.8168i	−0.185296	−	0.570281i	−0.999953	+	0.00966085i	$0.996925\pi$
$588$		0			0
$589$	18.7533	−	13.6251i	0.772716	−	0.561411i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	19.6180			0.805616			0.402808	−	0.915284i	$-0.368034\pi$
$593$	19.6180			0.805616			0.402808	+	0.915284i	$0.368034\pi$
$594$		0			0
$595$	0.0557281			0.00228463
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−28.7984	+	20.9232i	−1.17667	+	0.854901i	−0.991792	−	0.127861i	$-0.959189\pi$
$599$	−28.7984	+	20.9232i	−1.17667	+	0.854901i	−0.184878	+	0.982762i	$0.559189\pi$
$600$		0			0
$601$	−2.19756	−	6.76340i	−0.0896404	−	0.275885i	0.896179	−	0.443692i	$-0.146331\pi$
$601$	−2.19756	−	6.76340i	−0.0896404	−	0.275885i	−0.985820	+	0.167807i	$0.946331\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	7.73607	−	16.0292i	0.314516	−	0.651680i
$606$		0			0
$607$	2.02786	+	1.47333i	0.0823085	+	0.0598006i	0.628178	−	0.778069i	$-0.283801\pi$
$607$	2.02786	+	1.47333i	0.0823085	+	0.0598006i	−0.545870	+	0.837870i	$0.683801\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−32.7705	+	23.8092i	−1.32575	+	0.963216i
$612$		0			0
$613$	−7.79837	+	24.0009i	−0.314973	+	0.969388i	0.660792	+	0.750569i	$0.270221\pi$
$613$	−7.79837	+	24.0009i	−0.314973	+	0.969388i	−0.975765	+	0.218819i	$0.929779\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−13.2918			−0.535108			−0.267554	−	0.963543i	$-0.586215\pi$
$617$	−13.2918			−0.535108			−0.267554	+	0.963543i	$0.586215\pi$
$618$		0			0
$619$	8.16312	−	25.1235i	0.328103	−	1.00980i	−0.641917	−	0.766774i	$-0.721861\pi$
$619$	8.16312	−	25.1235i	0.328103	−	1.00980i	0.970020	−	0.243024i	$-0.0781395\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	0.377901	+	1.16306i	0.0151403	+	0.0465970i
$624$		0			0
$625$	6.00000	+	4.35926i	0.240000	+	0.174370i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−0.263932	−	0.191758i	−0.0105237	−	0.00764589i
$630$		0			0
$631$	8.39261	+	25.8298i	0.334104	+	1.02827i	0.967161	+	0.254163i	$0.0817999\pi$
$631$	8.39261	+	25.8298i	0.334104	+	1.02827i	−0.633057	+	0.774105i	$0.718200\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	0.854102	−	2.62866i	0.0338940	−	0.104315i
$636$		0			0
$637$	29.4164			1.16552
$638$		0			0
$639$		0			0
$640$		0			0
$641$	8.17376	−	25.1563i	0.322844	−	0.993612i	−0.649560	−	0.760310i	$-0.725047\pi$
$641$	8.17376	−	25.1563i	0.322844	−	0.993612i	0.972404	−	0.233302i	$-0.0749531\pi$
$642$		0			0
$643$	−16.0623	+	11.6699i	−0.633436	+	0.460218i	−0.857589	−	0.514336i	$-0.828038\pi$
$643$	−16.0623	+	11.6699i	−0.633436	+	0.460218i	0.224153	+	0.974554i	$0.428038\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	11.5902	+	8.42075i	0.455657	+	0.331054i	0.791825	−	0.610748i	$-0.209131\pi$
$647$	11.5902	+	8.42075i	0.455657	+	0.331054i	−0.336168	+	0.941802i	$0.609131\pi$
$648$		0			0
$649$	33.1418	−	20.8047i	1.30093	−	0.816657i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	14.9549	+	46.0265i	0.585231	+	1.80116i	0.598341	+	0.801242i	$0.295827\pi$
$653$	14.9549	+	46.0265i	0.585231	+	1.80116i	−0.0131095	+	0.999914i	$0.504173\pi$
$654$		0			0
$655$	−2.80902	+	2.04087i	−0.109757	+	0.0797434i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−0.652476			−0.0254169			−0.0127084	−	0.999919i	$-0.504045\pi$
$659$	−0.652476			−0.0254169			−0.0127084	+	0.999919i	$0.504045\pi$
$660$		0			0
$661$	−42.0344			−1.63495			−0.817475	−	0.575964i	$-0.804627\pi$
$661$	−42.0344			−1.63495			−0.817475	+	0.575964i	$0.804627\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	2.11803	−	1.53884i	0.0821338	−	0.0596737i
$666$		0			0
$667$	−3.09017	−	9.51057i	−0.119652	−	0.368251i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	27.6246	+	23.0826i	1.06644	+	0.891095i
$672$		0			0
$673$	29.0795	+	21.1275i	1.12093	+	0.814406i	0.984350	−	0.176223i	$-0.0563879\pi$
$673$	29.0795	+	21.1275i	1.12093	+	0.814406i	0.136583	+	0.990629i	$0.456388\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−34.1803	+	24.8335i	−1.31366	+	0.954428i	−0.313669	+	0.949532i	$0.601558\pi$
$677$	−34.1803	+	24.8335i	−1.31366	+	0.954428i	−0.999988	+	0.00489547i	$0.998442\pi$
$678$		0			0
$679$	1.09675	−	3.37544i	0.0420893	−	0.129538i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−17.9443			−0.686618			−0.343309	−	0.939222i	$-0.611548\pi$
$683$	−17.9443			−0.686618			−0.343309	+	0.939222i	$0.611548\pi$
$684$		0			0
$685$	7.11803	−	21.9071i	0.271966	−	0.837026i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	8.66312	+	26.6623i	0.330039	+	1.01575i
$690$		0			0
$691$	18.7082	+	13.5923i	0.711694	+	0.517076i	0.883720	−	0.468017i	$-0.155031\pi$
$691$	18.7082	+	13.5923i	0.711694	+	0.517076i	−0.172026	+	0.985092i	$0.555031\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−15.1353	−	10.9964i	−0.574113	−	0.417117i
$696$		0			0
$697$	0.392609	+	1.20833i	0.0148711	+	0.0457686i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	8.62461	−	26.5438i	0.325747	−	1.00255i	−0.645355	−	0.763883i	$-0.723291\pi$
$701$	8.62461	−	26.5438i	0.325747	−	1.00255i	0.971102	−	0.238664i	$-0.0767094\pi$
$702$		0			0
$703$	−15.3262			−0.578040
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−1.18441	+	3.64522i	−0.0445441	+	0.137093i
$708$		0			0
$709$	28.5344	−	20.7315i	1.07163	−	0.778587i	0.0954283	−	0.995436i	$-0.469578\pi$
$709$	28.5344	−	20.7315i	1.07163	−	0.778587i	0.976205	+	0.216849i	$0.0695779\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−13.6803	−	9.93935i	−0.512333	−	0.372232i
$714$		0			0
$715$	−5.54508	−	22.0458i	−0.207374	−	0.824467i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	0.163119	+	0.502029i	0.00608331	+	0.0187225i	0.954052	−	0.299641i	$-0.0968668\pi$
$719$	0.163119	+	0.502029i	0.00608331	+	0.0187225i	−0.947969	+	0.318363i	$0.896867\pi$
$720$		0			0
$721$	1.79837	−	1.30660i	0.0669749	−	0.0486601i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	4.76393			0.176928
$726$		0			0
$727$	−48.9787			−1.81652			−0.908260	−	0.418406i	$-0.862589\pi$
$727$	−48.9787			−1.81652			−0.908260	+	0.418406i	$0.862589\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	0.298374	−	0.216781i	0.0110358	−	0.00801795i
$732$		0			0
$733$	15.9098	+	48.9654i	0.587643	+	1.80858i	0.588387	+	0.808579i	$0.299763\pi$
$733$	15.9098	+	48.9654i	0.587643	+	1.80858i	−0.000744089		1.00000i	$0.500237\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−3.54508	−	14.0943i	−0.130585	−	0.519171i
$738$		0			0
$739$	−31.1353	−	22.6211i	−1.14533	−	0.832130i	−0.157476	−	0.987523i	$-0.550336\pi$
$739$	−31.1353	−	22.6211i	−1.14533	−	0.832130i	−0.987853	+	0.155393i	$0.950336\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−30.5517	+	22.1971i	−1.12083	+	0.814332i	−0.984335	−	0.176309i	$-0.943584\pi$
$743$	−30.5517	+	22.1971i	−1.12083	+	0.814332i	−0.136497	+	0.990641i	$0.543584\pi$
$744$		0			0
$745$	−11.1180	+	34.2178i	−0.407333	+	1.25364i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	3.69505			0.135014
$750$		0			0
$751$	4.84752	−	14.9191i	0.176889	−	0.544407i	−0.822826	−	0.568293i	$-0.807604\pi$
$751$	4.84752	−	14.9191i	0.176889	−	0.544407i	0.999715	+	0.0238860i	$0.00760388\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	2.23607	+	6.88191i	0.0813788	+	0.250458i
$756$		0			0
$757$	−35.1697	−	25.5523i	−1.27826	−	0.928713i	−0.278765	−	0.960359i	$-0.589925\pi$
$757$	−35.1697	−	25.5523i	−1.27826	−	0.928713i	−0.999499	+	0.0316459i	$0.989925\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−28.8435	−	20.9560i	−1.04557	−	0.759654i	−0.0742086	−	0.997243i	$-0.523643\pi$
$761$	−28.8435	−	20.9560i	−1.04557	−	0.759654i	−0.971366	+	0.237588i	$0.923643\pi$
$762$		0			0
$763$	0.652476	+	2.00811i	0.0236212	+	0.0726986i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	15.4443	−	47.5326i	0.557660	−	1.71630i
$768$		0			0
$769$	9.97871			0.359842			0.179921	−	0.983681i	$-0.442416\pi$
$769$	9.97871			0.359842			0.179921	+	0.983681i	$0.442416\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	7.48936	−	23.0499i	0.269373	−	0.829046i	−0.721280	−	0.692644i	$-0.756446\pi$
$773$	7.48936	−	23.0499i	0.269373	−	0.829046i	0.990653	−	0.136403i	$-0.0435541\pi$
$774$		0			0
$775$	6.51722	−	4.73504i	0.234105	−	0.170088i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	48.2877	+	35.0831i	1.73009	+	1.25698i
$780$		0			0
$781$	−37.0623	−	30.9686i	−1.32619	−	1.10814i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−1.14590	−	3.52671i	−0.0408989	−	0.125874i
$786$		0			0
$787$	−12.7082	+	9.23305i	−0.452999	+	0.329123i	−0.790779	−	0.612102i	$-0.790324\pi$
$787$	−12.7082	+	9.23305i	−0.452999	+	0.329123i	0.337780	+	0.941225i	$0.390324\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	1.87539			0.0666811
$792$		0			0
$793$	45.9787			1.63275
$794$		0			0
$795$		0			0
$796$		0			0
$797$	21.0902	−	15.3229i	0.747052	−	0.542765i	−0.147860	−	0.989008i	$-0.547238\pi$
$797$	21.0902	−	15.3229i	0.747052	−	0.542765i	0.894912	+	0.446243i	$0.147238\pi$
$798$		0			0
$799$	−0.431116	−	1.32684i	−0.0152518	−	0.0469402i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	44.1246	−	27.6992i	1.55712	−	0.977482i
$804$		0			0
$805$	−1.54508	−	1.12257i	−0.0544571	−	0.0395654i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	31.0172	−	22.5353i	1.09051	−	0.792300i	0.111023	−	0.993818i	$-0.464587\pi$
$809$	31.0172	−	22.5353i	1.09051	−	0.792300i	0.979485	+	0.201518i	$0.0645874\pi$
$810$		0			0
$811$	−3.80902	+	11.7229i	−0.133753	+	0.411648i	−0.995394	−	0.0958694i	$-0.969437\pi$
$811$	−3.80902	+	11.7229i	−0.133753	+	0.411648i	0.861641	+	0.507518i	$0.169437\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−20.4164			−0.715156
$816$		0			0
$817$	5.35410	−	16.4782i	0.187316	−	0.576500i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−8.07295	−	24.8460i	−0.281748	−	0.867131i	−0.987355	−	0.158527i	$-0.949325\pi$
$821$	−8.07295	−	24.8460i	−0.281748	−	0.867131i	0.705607	−	0.708604i	$-0.250675\pi$
$822$		0			0
$823$	−14.6631	−	10.6534i	−0.511124	−	0.371353i	0.302126	−	0.953268i	$-0.402304\pi$
$823$	−14.6631	−	10.6534i	−0.511124	−	0.371353i	−0.813250	+	0.581915i	$0.802304\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−39.3607	−	28.5972i	−1.36870	−	0.994422i	−0.997837	−	0.0657367i	$-0.979060\pi$
$827$	−39.3607	−	28.5972i	−1.36870	−	0.994422i	−0.370868	−	0.928686i	$-0.620940\pi$
$828$		0			0
$829$	4.15654	+	12.7925i	0.144363	+	0.444303i	0.996928	−	0.0783173i	$-0.0249547\pi$
$829$	4.15654	+	12.7925i	0.144363	+	0.444303i	−0.852566	+	0.522620i	$0.824955\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−0.313082	+	0.963568i	−0.0108477	+	0.0333857i
$834$		0			0
$835$	−7.38197			−0.255463
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−1.42047	+	4.37177i	−0.0490402	+	0.150930i	−0.972578	−	0.232578i	$-0.925284\pi$
$839$	−1.42047	+	4.37177i	−0.0490402	+	0.150930i	0.923538	+	0.383508i	$0.125284\pi$
$840$		0			0
$841$	20.2254	−	14.6946i	0.697428	−	0.506711i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−6.47214	−	4.70228i	−0.222648	−	0.161763i
$846$		0			0
$847$	−1.87539	−	1.79611i	−0.0644391	−	0.0617151i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	3.45492	+	10.6331i	0.118433	+	0.364499i
$852$		0			0
$853$	10.8090	−	7.85321i	0.370094	−	0.268889i	−0.387156	−	0.922014i	$-0.626543\pi$
$853$	10.8090	−	7.85321i	0.370094	−	0.268889i	0.757250	+	0.653125i	$0.226543\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	29.1803			0.996781			0.498391	−	0.866953i	$-0.333925\pi$
$857$	29.1803			0.996781			0.498391	+	0.866953i	$0.333925\pi$
$858$		0			0
$859$	−58.1246			−1.98319			−0.991593	−	0.129395i	$-0.958696\pi$
$859$	−58.1246			−1.98319			−0.991593	+	0.129395i	$0.958696\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	15.0344	−	10.9232i	0.511778	−	0.371829i	−0.301719	−	0.953397i	$-0.597561\pi$
$863$	15.0344	−	10.9232i	0.511778	−	0.371829i	0.813498	+	0.581568i	$0.197561\pi$
$864$		0			0
$865$	−12.6631	−	38.9731i	−0.430559	−	1.32512i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−10.7639	+	26.8011i	−0.365141	+	0.909165i
$870$		0			0
$871$	−15.0172	−	10.9106i	−0.508839	−	0.369693i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	2.28115	−	1.65735i	0.0771170	−	0.0560288i
$876$		0			0
$877$	7.28773	−	22.4293i	0.246089	−	0.757385i	−0.749366	−	0.662156i	$-0.769642\pi$
$877$	7.28773	−	22.4293i	0.246089	−	0.757385i	0.995455	−	0.0952289i	$-0.0303583\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−22.5066			−0.758266			−0.379133	−	0.925342i	$-0.623778\pi$
$881$	−22.5066			−0.758266			−0.379133	+	0.925342i	$0.623778\pi$
$882$		0			0
$883$	−11.2016	+	34.4751i	−0.376965	+	1.16018i	0.565179	+	0.824968i	$0.308807\pi$
$883$	−11.2016	+	34.4751i	−0.376965	+	1.16018i	−0.942144	+	0.335210i	$0.891193\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	8.81559	+	27.1316i	0.295999	+	0.910990i	0.982884	+	0.184225i	$0.0589774\pi$
$887$	8.81559	+	27.1316i	0.295999	+	0.910990i	−0.686885	+	0.726766i	$0.741023\pi$
$888$		0			0
$889$	−0.326238	−	0.237026i	−0.0109417	−	0.00794959i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−53.0238	−	38.5240i	−1.77437	−	1.28916i
$894$		0			0
$895$	−7.35410	−	22.6336i	−0.245821	−	0.756558i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−2.09017	+	6.43288i	−0.0697111	+	0.214549i
$900$		0			0
$901$	−0.965558			−0.0321674
$902$		0			0
$903$		0			0
$904$		0			0
$905$	2.50000	−	7.69421i	0.0831028	−	0.255764i
$906$		0			0
$907$	3.45492	−	2.51014i	0.114719	−	0.0833479i	−0.528947	−	0.848655i	$-0.677413\pi$
$907$	3.45492	−	2.51014i	0.114719	−	0.0833479i	0.643665	+	0.765307i	$0.277413\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	16.0451	+	11.6574i	0.531597	+	0.386228i	0.820955	−	0.570993i	$-0.193442\pi$
$911$	16.0451	+	11.6574i	0.531597	+	0.386228i	−0.289358	+	0.957221i	$0.593442\pi$
$912$		0			0
$913$	−4.48936	−	3.75123i	−0.148576	−	0.124147i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	0.156541	+	0.481784i	0.00516944	+	0.0159099i
$918$		0			0
$919$	1.28115	−	0.930812i	0.0422613	−	0.0307047i	−0.566454	−	0.824093i	$-0.691685\pi$
$919$	1.28115	−	0.930812i	0.0422613	−	0.0307047i	0.608715	+	0.793389i	$0.291685\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−61.6869			−2.03045
$924$		0			0
$925$	−5.32624			−0.175126
$926$		0			0
$927$		0			0
$928$		0			0
$929$	6.66312	−	4.84104i	0.218610	−	0.158829i	−0.473091	−	0.881014i	$-0.656862\pi$
$929$	6.66312	−	4.84104i	0.218610	−	0.158829i	0.691701	+	0.722184i	$0.256862\pi$
$930$		0			0
$931$	14.7082	+	45.2672i	0.482042	+	1.48357i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	0.781153	+	0.0530006i	0.0255464	+	0.00173330i
$936$		0			0
$937$	−6.19098	−	4.49801i	−0.202251	−	0.146944i	0.482050	−	0.876144i	$-0.339892\pi$
$937$	−6.19098	−	4.49801i	−0.202251	−	0.146944i	−0.684301	+	0.729200i	$0.739892\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−13.8262	+	10.0453i	−0.450722	+	0.327469i	−0.789881	−	0.613260i	$-0.789858\pi$
$941$	−13.8262	+	10.0453i	−0.450722	+	0.327469i	0.339158	+	0.940729i	$0.389858\pi$
$942$		0			0
$943$	13.4549	−	41.4100i	0.438152	−	1.34849i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	32.9230			1.06985			0.534927	−	0.844899i	$-0.320339\pi$
$947$	32.9230			1.06985			0.534927	+	0.844899i	$0.320339\pi$
$948$		0			0
$949$	20.5623	−	63.2843i	0.667481	−	2.05429i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	18.5967	+	57.2349i	0.602408	+	1.85402i	0.513714	+	0.857961i	$0.328269\pi$
$953$	18.5967	+	57.2349i	0.602408	+	1.85402i	0.0886937	+	0.996059i	$0.471731\pi$
$954$		0			0
$955$	−5.92705	−	4.30625i	−0.191795	−	0.139347i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−2.71885	−	1.97536i	−0.0877962	−	0.0637876i
$960$		0			0
$961$	−6.04508	−	18.6049i	−0.195003	−	0.600157i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−3.39919	+	10.4616i	−0.109424	+	0.336772i
$966$		0			0
$967$	46.1591			1.48438			0.742188	−	0.670192i	$-0.233788\pi$
$967$	46.1591			1.48438			0.742188	+	0.670192i	$0.233788\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	13.7426	−	42.2955i	0.441022	−	1.35733i	−0.445765	−	0.895150i	$-0.647068\pi$
$971$	13.7426	−	42.2955i	0.441022	−	1.35733i	0.886787	−	0.462178i	$-0.152932\pi$
$972$		0			0
$973$	−2.20820	+	1.60435i	−0.0707918	+	0.0514332i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−16.8435	−	12.2375i	−0.538870	−	0.391512i	0.284795	−	0.958588i	$-0.408074\pi$
$977$	−16.8435	−	12.2375i	−0.538870	−	0.391512i	−0.823665	+	0.567076i	$0.808074\pi$
$978$		0			0
$979$	4.19098	+	16.6623i	0.133944	+	0.532528i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	4.43769	+	13.6578i	0.141540	+	0.435617i	0.996550	−	0.0829957i	$-0.0264488\pi$
$983$	4.43769	+	13.6578i	0.141540	+	0.435617i	−0.855009	+	0.518612i	$0.826449\pi$
$984$		0			0
$985$	4.80902	−	3.49396i	0.153228	−	0.111327i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−12.6393			−0.401907
$990$		0			0
$991$	33.1459			1.05291			0.526457	−	0.850202i	$-0.323520\pi$
$991$	33.1459			1.05291			0.526457	+	0.850202i	$0.323520\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−23.4894	+	17.0660i	−0.744663	+	0.541029i
$996$		0			0
$997$	10.0279	+	30.8626i	0.317586	+	0.977428i	0.974677	+	0.223617i	$0.0717865\pi$
$997$	10.0279	+	30.8626i	0.317586	+	0.977428i	−0.657091	+	0.753811i	$0.728213\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	396.2.j.b.37.1		4
3.2	odd	2		132.2.i.a.37.1	yes	4
11.3	even	5	inner	396.2.j.b.289.1		4
11.5	even	5		4356.2.a.r.1.2		2
11.6	odd	10		4356.2.a.w.1.2		2
12.11	even	2		528.2.y.i.433.1		4
33.2	even	10		1452.2.i.f.1237.1		4
33.5	odd	10		1452.2.a.l.1.1		2
33.8	even	10		1452.2.i.g.1213.1		4
33.14	odd	10		132.2.i.a.25.1	✓	4
33.17	even	10		1452.2.a.m.1.1		2
33.20	odd	10		1452.2.i.c.1237.1		4
33.26	odd	10		1452.2.i.c.493.1		4
33.29	even	10		1452.2.i.f.493.1		4
33.32	even	2		1452.2.i.g.565.1		4
132.47	even	10		528.2.y.i.289.1		4
132.71	even	10		5808.2.a.bq.1.1		2
132.83	odd	10		5808.2.a.bn.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
132.2.i.a.25.1	✓	4	33.14	odd	10
132.2.i.a.37.1	yes	4	3.2	odd	2
396.2.j.b.37.1		4	1.1	even	1	trivial
396.2.j.b.289.1		4	11.3	even	5	inner
528.2.y.i.289.1		4	132.47	even	10
528.2.y.i.433.1		4	12.11	even	2
1452.2.a.l.1.1		2	33.5	odd	10
1452.2.a.m.1.1		2	33.17	even	10
1452.2.i.c.493.1		4	33.26	odd	10
1452.2.i.c.1237.1		4	33.20	odd	10
1452.2.i.f.493.1		4	33.29	even	10
1452.2.i.f.1237.1		4	33.2	even	10
1452.2.i.g.565.1		4	33.32	even	2
1452.2.i.g.1213.1		4	33.8	even	10
4356.2.a.r.1.2		2	11.5	even	5
4356.2.a.w.1.2		2	11.6	odd	10
5808.2.a.bn.1.1		2	132.83	odd	10
5808.2.a.bq.1.1		2	132.71	even	10

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:	\( N \)	\(=\)	\( 396 = 2^{2} \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	396.j (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.30902 + 0.951057i) q^{5} +(0.0729490 + 0.224514i) q^{7} +O(q^{10})\)	\(q+(-1.30902 + 0.951057i) q^{5} +(0.0729490 + 0.224514i) q^{7} +(0.809017 + 3.21644i) q^{11} +(3.42705 + 2.48990i) q^{13} +(-0.118034 + 0.0857567i) q^{17} +(-2.11803 + 6.51864i) q^{19} +5.00000 q^{23} +(-0.736068 + 2.26538i) q^{25} +(-0.618034 - 1.90211i) q^{29} +(-2.73607 - 1.98787i) q^{31} +(-0.309017 - 0.224514i) q^{35} +(0.690983 + 2.12663i) q^{37} +(2.69098 - 8.28199i) q^{41} -2.52786 q^{43} +(-2.95492 + 9.09429i) q^{47} +(5.61803 - 4.08174i) q^{49} +(5.35410 + 3.88998i) q^{53} +(-4.11803 - 3.44095i) q^{55} +(-3.64590 - 11.2209i) q^{59} +(8.78115 - 6.37988i) q^{61} -6.85410 q^{65} -4.38197 q^{67} +(-11.7812 + 8.55951i) q^{71} +(-4.85410 - 14.9394i) q^{73} +(-0.663119 + 0.416272i) q^{77} +(7.04508 + 5.11855i) q^{79} +(-1.42705 + 1.03681i) q^{83} +(0.0729490 - 0.224514i) q^{85} +5.18034 q^{89} +(-0.309017 + 0.951057i) q^{91} +(-3.42705 - 10.5474i) q^{95} +(-12.1631 - 8.83702i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 3 q^{5} + 7 q^{7}+O(q^{10}) \) 4 * q - 3 * q^5 + 7 * q^7	\( 4 q - 3 q^{5} + 7 q^{7} + q^{11} + 7 q^{13} + 4 q^{17} - 4 q^{19} + 20 q^{23} + 6 q^{25} + 2 q^{29} - 2 q^{31} + q^{35} + 5 q^{37} + 13 q^{41} - 28 q^{43} - 23 q^{47} + 18 q^{49} + 8 q^{53} - 12 q^{55} - 28 q^{59} + 15 q^{61} - 14 q^{65} - 22 q^{67} - 27 q^{71} - 6 q^{73} + 13 q^{77} + 17 q^{79} + q^{83} + 7 q^{85} - 24 q^{89} + q^{91} - 7 q^{95} - 33 q^{97}+O(q^{100}) \) 4 * q - 3 * q^5 + 7 * q^7 + q^11 + 7 * q^13 + 4 * q^17 - 4 * q^19 + 20 * q^23 + 6 * q^25 + 2 * q^29 - 2 * q^31 + q^35 + 5 * q^37 + 13 * q^41 - 28 * q^43 - 23 * q^47 + 18 * q^49 + 8 * q^53 - 12 * q^55 - 28 * q^59 + 15 * q^61 - 14 * q^65 - 22 * q^67 - 27 * q^71 - 6 * q^73 + 13 * q^77 + 17 * q^79 + q^83 + 7 * q^85 - 24 * q^89 + q^91 - 7 * q^95 - 33 * q^97

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