LMFDB - Embedded newform 464.3.l.c.17.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [464,3,Mod(17,464)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(464, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("464.17");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 464 = 2^{4} \cdot 29 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	464.l (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$12.6430842663$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 18x^{6} + 91x^{4} + 126x^{2} + 25 $ x^8 + 18x^6 + 91x^4 + 126*x^2 + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 29)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			17.1
Root			$2.35663i$ of defining polynomial
Character	$\chi$	$=$	464.17
Dual form			464.3.l.c.273.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.81178 + 3.81178i) q^{3} +3.14526i q^{5} -0.342313 q^{7} -20.0593i q^{9} +O(q^{10})$	\(q+(-3.81178 + 3.81178i) q^{3} +3.14526i q^{5} -0.342313 q^{7} -20.0593i q^{9} +(14.0269 - 14.0269i) q^{11} -11.5162i q^{13} +(-11.9890 - 11.9890i) q^{15} +(-6.37430 + 6.37430i) q^{17} +(6.11703 - 6.11703i) q^{19} +(1.30482 - 1.30482i) q^{21} -15.8623 q^{23} +15.1074 q^{25} +(42.1557 + 42.1557i) q^{27} +(25.6758 - 13.4817i) q^{29} +(-6.18103 + 6.18103i) q^{31} +106.935i q^{33} -1.07666i q^{35} +(24.2121 + 24.2121i) q^{37} +(43.8972 + 43.8972i) q^{39} +(-34.9536 - 34.9536i) q^{41} +(15.9908 - 15.9908i) q^{43} +63.0917 q^{45} +(-7.57643 - 7.57643i) q^{47} -48.8828 q^{49} -48.5949i q^{51} +62.1991 q^{53} +(44.1182 + 44.1182i) q^{55} +46.6336i q^{57} +21.4867 q^{59} +(13.1414 - 13.1414i) q^{61} +6.86658i q^{63} +36.2214 q^{65} -17.8272i q^{67} +(60.4635 - 60.4635i) q^{69} +53.0072i q^{71} +(5.93089 + 5.93089i) q^{73} +(-57.5859 + 57.5859i) q^{75} +(-4.80160 + 4.80160i) q^{77} +(81.6782 - 81.6782i) q^{79} -140.843 q^{81} +77.1462 q^{83} +(-20.0488 - 20.0488i) q^{85} +(-46.4812 + 149.259i) q^{87} +(27.4315 - 27.4315i) q^{89} +3.94215i q^{91} -47.1215i q^{93} +(19.2396 + 19.2396i) q^{95} +(48.7308 + 48.7308i) q^{97} +(-281.370 - 281.370i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{3} + 4 q^{7}+O(q^{10}) $ 8 * q + 2 * q^3 + 4 * q^7	$ 8 q + 2 q^{3} + 4 q^{7} + 6 q^{11} + 10 q^{15} + 12 q^{17} + 16 q^{19} - 36 q^{21} + 104 q^{25} + 98 q^{27} + 128 q^{29} + 10 q^{31} - 84 q^{37} + 90 q^{39} + 20 q^{41} + 190 q^{43} + 292 q^{45} - 58 q^{47} - 72 q^{49} + 252 q^{53} + 74 q^{55} + 40 q^{59} - 208 q^{61} + 36 q^{65} + 120 q^{69} - 188 q^{73} + 12 q^{75} + 180 q^{77} + 382 q^{79} - 124 q^{81} - 280 q^{83} + 32 q^{85} - 34 q^{87} - 64 q^{89} + 380 q^{95} - 44 q^{97} - 552 q^{99}+O(q^{100}) $ 8 * q + 2 * q^3 + 4 * q^7 + 6 * q^11 + 10 * q^15 + 12 * q^17 + 16 * q^19 - 36 * q^21 + 104 * q^25 + 98 * q^27 + 128 * q^29 + 10 * q^31 - 84 * q^37 + 90 * q^39 + 20 * q^41 + 190 * q^43 + 292 * q^45 - 58 * q^47 - 72 * q^49 + 252 * q^53 + 74 * q^55 + 40 * q^59 - 208 * q^61 + 36 * q^65 + 120 * q^69 - 188 * q^73 + 12 * q^75 + 180 * q^77 + 382 * q^79 - 124 * q^81 - 280 * q^83 + 32 * q^85 - 34 * q^87 - 64 * q^89 + 380 * q^95 - 44 * q^97 - 552 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/464\mathbb{Z}\right)^\times$.

$n$	$117$	$175$	$321$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−3.81178	+	3.81178i	−1.27059	+	1.27059i	−0.324816	+	0.945777i	$0.605302\pi$
$3$	−3.81178	+	3.81178i	−1.27059	+	1.27059i	−0.945777	+	0.324816i	$0.894698\pi$
$4$		0			0
$5$			3.14526i			0.629051i	0.949249	+	0.314526i	$0.101845\pi$
$5$			3.14526i			0.629051i	−0.949249	+	0.314526i	$0.898155\pi$
$6$		0			0
$7$	−0.342313			−0.0489019			−0.0244510	−	0.999701i	$-0.507784\pi$
$7$	−0.342313			−0.0489019			−0.0244510	+	0.999701i	$0.507784\pi$
$8$		0			0
$9$		−	20.0593i		−	2.22881i
$10$		0			0
$11$	14.0269	−	14.0269i	1.27517	−	1.27517i	0.331837	−	0.943337i	$-0.392332\pi$
$11$	14.0269	−	14.0269i	1.27517	−	1.27517i	0.943337	−	0.331837i	$-0.107668\pi$
$12$		0			0
$13$		−	11.5162i		−	0.885861i	−0.896556	−	0.442931i	$-0.853939\pi$
$13$		−	11.5162i		−	0.885861i	0.896556	−	0.442931i	$-0.146061\pi$
$14$		0			0
$15$	−11.9890	−	11.9890i	−0.799268	−	0.799268i
$16$		0			0
$17$	−6.37430	+	6.37430i	−0.374959	+	0.374959i	−0.869280	−	0.494321i	$-0.835417\pi$
$17$	−6.37430	+	6.37430i	−0.374959	+	0.374959i	0.494321	+	0.869280i	$0.335417\pi$
$18$		0			0
$19$	6.11703	−	6.11703i	0.321949	−	0.321949i	−0.527565	−	0.849514i	$-0.676895\pi$
$19$	6.11703	−	6.11703i	0.321949	−	0.321949i	0.849514	+	0.527565i	$0.176895\pi$
$20$		0			0
$21$	1.30482	−	1.30482i	0.0621345	−	0.0621345i
$22$		0			0
$23$	−15.8623			−0.689664			−0.344832	−	0.938664i	$-0.612064\pi$
$23$	−15.8623			−0.689664			−0.344832	+	0.938664i	$0.612064\pi$
$24$		0			0
$25$	15.1074			0.604295
$26$		0			0
$27$	42.1557	+	42.1557i	1.56132	+	1.56132i
$28$		0			0
$29$	25.6758	−	13.4817i	0.885371	−	0.464885i
$29$	25.6758	−	13.4817i	0.885371	−	0.464885i
$30$		0			0
$31$	−6.18103	+	6.18103i	−0.199388	+	0.199388i	−0.799738	−	0.600350i	$-0.795028\pi$
$31$	−6.18103	+	6.18103i	−0.199388	+	0.199388i	0.600350	+	0.799738i	$0.295028\pi$
$32$		0			0
$33$			106.935i			3.24045i
$34$		0			0
$35$		−	1.07666i		−	0.0307618i
$36$		0			0
$37$	24.2121	+	24.2121i	0.654381	+	0.654381i	0.954045	−	0.299664i	$-0.0968745\pi$
$37$	24.2121	+	24.2121i	0.654381	+	0.654381i	−0.299664	+	0.954045i	$0.596874\pi$
$38$		0			0
$39$	43.8972	+	43.8972i	1.12557	+	1.12557i
$40$		0			0
$41$	−34.9536	−	34.9536i	−0.852526	−	0.852526i	0.137917	−	0.990444i	$-0.455959\pi$
$41$	−34.9536	−	34.9536i	−0.852526	−	0.852526i	−0.990444	+	0.137917i	$0.955959\pi$
$42$		0			0
$43$	15.9908	−	15.9908i	0.371878	−	0.371878i	−0.496283	−	0.868161i	$-0.665302\pi$
$43$	15.9908	−	15.9908i	0.371878	−	0.371878i	0.868161	+	0.496283i	$0.165302\pi$
$44$		0			0
$45$	63.0917			1.40204
$46$		0			0
$47$	−7.57643	−	7.57643i	−0.161201	−	0.161201i	0.621898	−	0.783098i	$-0.286362\pi$
$47$	−7.57643	−	7.57643i	−0.161201	−	0.161201i	−0.783098	+	0.621898i	$0.786362\pi$
$48$		0			0
$49$	−48.8828			−0.997609
$50$		0			0
$51$		−	48.5949i		−	0.952840i
$52$		0			0
$53$	62.1991			1.17357			0.586784	−	0.809743i	$-0.300394\pi$
$53$	62.1991			1.17357			0.586784	+	0.809743i	$0.300394\pi$
$54$		0			0
$55$	44.1182	+	44.1182i	0.802150	+	0.802150i
$56$		0			0
$57$			46.6336i			0.818133i
$58$		0			0
$59$	21.4867			0.364182			0.182091	−	0.983282i	$-0.441713\pi$
$59$	21.4867			0.364182			0.182091	+	0.983282i	$0.441713\pi$
$60$		0			0
$61$	13.1414	−	13.1414i	0.215432	−	0.215432i	−0.591138	−	0.806570i	$-0.701321\pi$
$61$	13.1414	−	13.1414i	0.215432	−	0.215432i	0.806570	+	0.591138i	$0.201321\pi$
$62$		0			0
$63$			6.86658i			0.108993i
$64$		0			0
$65$	36.2214			0.557252
$66$		0			0
$67$		−	17.8272i		−	0.266078i	−0.991111	−	0.133039i	$-0.957526\pi$
$67$		−	17.8272i		−	0.266078i	0.991111	−	0.133039i	$-0.0424736\pi$
$68$		0			0
$69$	60.4635	−	60.4635i	0.876282	−	0.876282i
$70$		0			0
$71$			53.0072i			0.746580i	0.927715	+	0.373290i	$0.121770\pi$
$71$			53.0072i			0.746580i	−0.927715	+	0.373290i	$0.878230\pi$
$72$		0			0
$73$	5.93089	+	5.93089i	0.0812450	+	0.0812450i	0.746561	−	0.665316i	$-0.231703\pi$
$73$	5.93089	+	5.93089i	0.0812450	+	0.0812450i	−0.665316	+	0.746561i	$0.731703\pi$
$74$		0			0
$75$	−57.5859	+	57.5859i	−0.767813	+	0.767813i
$76$		0			0
$77$	−4.80160	+	4.80160i	−0.0623584	+	0.0623584i
$78$		0			0
$79$	81.6782	−	81.6782i	1.03390	−	1.03390i	0.0344966	−	0.999405i	$-0.489017\pi$
$79$	81.6782	−	81.6782i	1.03390	−	1.03390i	0.999405	−	0.0344966i	$-0.0109828\pi$
$80$		0			0
$81$	−140.843			−1.73880
$82$		0			0
$83$	77.1462			0.929472			0.464736	−	0.885449i	$-0.346149\pi$
$83$	77.1462			0.929472			0.464736	+	0.885449i	$0.346149\pi$
$84$		0			0
$85$	−20.0488	−	20.0488i	−0.235868	−	0.235868i
$86$		0			0
$87$	−46.4812	+	149.259i	−0.534267	+	1.71563i
$88$		0			0
$89$	27.4315	−	27.4315i	0.308219	−	0.308219i	−0.535999	−	0.844218i	$-0.680065\pi$
$89$	27.4315	−	27.4315i	0.308219	−	0.308219i	0.844218	+	0.535999i	$0.180065\pi$
$90$		0			0
$91$			3.94215i			0.0433203i
$92$		0			0
$93$		−	47.1215i		−	0.506683i
$94$		0			0
$95$	19.2396	+	19.2396i	0.202522	+	0.202522i
$96$		0			0
$97$	48.7308	+	48.7308i	0.502379	+	0.502379i	0.912177	−	0.409797i	$-0.134401\pi$
$97$	48.7308	+	48.7308i	0.502379	+	0.502379i	−0.409797	+	0.912177i	$0.634401\pi$
$98$		0			0
$99$	−281.370	−	281.370i	−2.84213	−	2.84213i
$100$		0			0
$101$	−36.0686	+	36.0686i	−0.357115	+	0.357115i	−0.862748	−	0.505633i	$-0.831259\pi$
$101$	−36.0686	+	36.0686i	−0.357115	+	0.357115i	0.505633	+	0.862748i	$0.331259\pi$
$102$		0			0
$103$	38.7846			0.376549			0.188275	−	0.982116i	$-0.439711\pi$
$103$	38.7846			0.376549			0.188275	+	0.982116i	$0.439711\pi$
$104$		0			0
$105$	4.10400	+	4.10400i	0.0390857	+	0.0390857i
$106$		0			0
$107$	−100.580			−0.940004			−0.470002	−	0.882665i	$-0.655747\pi$
$107$	−100.580			−0.940004			−0.470002	+	0.882665i	$0.655747\pi$
$108$		0			0
$109$		−	43.4896i		−	0.398988i	−0.979899	−	0.199494i	$-0.936070\pi$
$109$		−	43.4896i		−	0.398988i	0.979899	−	0.199494i	$-0.0639298\pi$
$110$		0			0
$111$	−184.582			−1.66290
$112$		0			0
$113$	−106.279	−	106.279i	−0.940525	−	0.940525i	0.0578028	−	0.998328i	$-0.481591\pi$
$113$	−106.279	−	106.279i	−0.940525	−	0.940525i	−0.998328	+	0.0578028i	$0.981591\pi$
$114$		0			0
$115$		−	49.8909i		−	0.433834i
$116$		0			0
$117$	−231.007			−1.97442
$118$		0			0
$119$	2.18201	−	2.18201i	0.0183362	−	0.0183362i
$120$		0			0
$121$		−	272.508i		−	2.25214i
$122$		0			0
$123$	266.471			2.16643
$124$		0			0
$125$			126.148i			1.00918i
$126$		0			0
$127$	43.0879	−	43.0879i	0.339275	−	0.339275i	−0.516820	−	0.856094i	$-0.672884\pi$
$127$	43.0879	−	43.0879i	0.339275	−	0.339275i	0.856094	+	0.516820i	$0.172884\pi$
$128$		0			0
$129$			121.907i			0.945012i
$130$		0			0
$131$	−21.6703	−	21.6703i	−0.165422	−	0.165422i	0.619542	−	0.784964i	$-0.287318\pi$
$131$	−21.6703	−	21.6703i	−0.165422	−	0.165422i	−0.784964	+	0.619542i	$0.787318\pi$
$132$		0			0
$133$	−2.09394	+	2.09394i	−0.0157439	+	0.0157439i
$134$		0			0
$135$	−132.591	+	132.591i	−0.982152	+	0.982152i
$136$		0			0
$137$	64.9871	−	64.9871i	0.474359	−	0.474359i	−0.428963	−	0.903322i	$-0.641121\pi$
$137$	64.9871	−	64.9871i	0.474359	−	0.474359i	0.903322	+	0.428963i	$0.141121\pi$
$138$		0			0
$139$	73.6837			0.530099			0.265049	−	0.964235i	$-0.414612\pi$
$139$	73.6837			0.530099			0.265049	+	0.964235i	$0.414612\pi$
$140$		0			0
$141$	57.7594			0.409641
$142$		0			0
$143$	−161.537	−	161.537i	−1.12963	−	1.12963i
$144$		0			0
$145$	42.4033	+	80.7568i	0.292436	+	0.556944i
$146$		0			0
$147$	186.331	−	186.331i	1.26755	−	1.26755i
$148$		0			0
$149$			94.7514i			0.635915i	0.948105	+	0.317958i	$0.102997\pi$
$149$			94.7514i			0.635915i	−0.948105	+	0.317958i	$0.897003\pi$
$150$		0			0
$151$		−	174.343i		−	1.15459i	−0.816537	−	0.577293i	$-0.804109\pi$
$151$		−	174.343i		−	1.15459i	0.816537	−	0.577293i	$-0.195891\pi$
$152$		0			0
$153$	127.864	+	127.864i	0.835713	+	0.835713i
$154$		0			0
$155$	−19.4409	−	19.4409i	−0.125425	−	0.125425i
$156$		0			0
$157$	−204.862	−	204.862i	−1.30486	−	1.30486i	−0.925078	−	0.379777i	$-0.876001\pi$
$157$	−204.862	−	204.862i	−1.30486	−	1.30486i	−0.379777	−	0.925078i	$-0.623999\pi$
$158$		0			0
$159$	−237.089	+	237.089i	−1.49113	+	1.49113i
$160$		0			0
$161$	5.42987			0.0337259
$162$		0			0
$163$	128.935	+	128.935i	0.791012	+	0.791012i	0.981659	−	0.190647i	$-0.0610584\pi$
$163$	128.935	+	128.935i	0.791012	+	0.791012i	−0.190647	+	0.981659i	$0.561058\pi$
$164$		0			0
$165$	−336.338			−2.03841
$166$		0			0
$167$			266.891i			1.59815i	0.601230	+	0.799076i	$0.294678\pi$
$167$			266.891i			1.59815i	−0.601230	+	0.799076i	$0.705322\pi$
$168$		0			0
$169$	36.3773			0.215250
$170$		0			0
$171$	−122.704	−	122.704i	−0.717565	−	0.717565i
$172$		0			0
$173$			264.180i			1.52705i	0.645779	+	0.763525i	$0.276533\pi$
$173$			264.180i			1.52705i	−0.645779	+	0.763525i	$0.723467\pi$
$174$		0			0
$175$	−5.17145			−0.0295512
$176$		0			0
$177$	−81.9027	+	81.9027i	−0.462727	+	0.462727i
$178$		0			0
$179$		−	79.9849i		−	0.446843i	−0.974722	−	0.223421i	$-0.928277\pi$
$179$		−	79.9849i		−	0.446843i	0.974722	−	0.223421i	$-0.0717226\pi$
$180$		0			0
$181$	116.758			0.645074			0.322537	−	0.946557i	$-0.395464\pi$
$181$	116.758			0.645074			0.322537	+	0.946557i	$0.395464\pi$
$182$		0			0
$183$			100.184i			0.547454i
$184$		0			0
$185$	−76.1533	+	76.1533i	−0.411639	+	0.411639i
$186$		0			0
$187$			178.823i			0.956275i
$188$		0			0
$189$	−14.4305	−	14.4305i	−0.0763517	−	0.0763517i
$190$		0			0
$191$	60.0672	−	60.0672i	0.314488	−	0.314488i	−0.532157	−	0.846645i	$-0.678619\pi$
$191$	60.0672	−	60.0672i	0.314488	−	0.314488i	0.846645	+	0.532157i	$0.178619\pi$
$192$		0			0
$193$	155.411	−	155.411i	0.805241	−	0.805241i	−0.178669	−	0.983909i	$-0.557179\pi$
$193$	155.411	−	155.411i	0.805241	−	0.805241i	0.983909	+	0.178669i	$0.0571790\pi$
$194$		0			0
$195$	−138.068	+	138.068i	−0.708040	+	0.708040i
$196$		0			0
$197$	127.935			0.649415			0.324708	−	0.945814i	$-0.394734\pi$
$197$	127.935			0.649415			0.324708	+	0.945814i	$0.394734\pi$
$198$		0			0
$199$	365.503			1.83670			0.918349	−	0.395772i	$-0.129523\pi$
$199$	365.503			1.83670			0.918349	+	0.395772i	$0.129523\pi$
$200$		0			0
$201$	67.9535	+	67.9535i	0.338077	+	0.338077i
$202$		0			0
$203$	−8.78916	+	4.61496i	−0.0432963	+	0.0227338i
$204$		0			0
$205$	109.938	−	109.938i	0.536283	−	0.536283i
$206$		0			0
$207$			318.186i			1.53713i
$208$		0			0
$209$		−	171.606i		−	0.821082i
$210$		0			0
$211$	−235.633	−	235.633i	−1.11674	−	1.11674i	−0.992216	−	0.124527i	$-0.960259\pi$
$211$	−235.633	−	235.633i	−1.11674	−	1.11674i	−0.124527	−	0.992216i	$-0.539741\pi$
$212$		0			0
$213$	−202.052	−	202.052i	−0.948600	−	0.948600i
$214$		0			0
$215$	50.2950	+	50.2950i	0.233930	+	0.233930i
$216$		0			0
$217$	2.11585	−	2.11585i	0.00975047	−	0.00975047i
$218$		0			0
$219$	−45.2145			−0.206459
$220$		0			0
$221$	73.4077	+	73.4077i	0.332161	+	0.332161i
$222$		0			0
$223$	−404.109			−1.81215			−0.906074	−	0.423119i	$-0.860935\pi$
$223$	−404.109			−1.81215			−0.906074	+	0.423119i	$0.860935\pi$
$224$		0			0
$225$		−	303.044i		−	1.34686i
$226$		0			0
$227$	−12.2558			−0.0539905			−0.0269952	−	0.999636i	$-0.508594\pi$
$227$	−12.2558			−0.0539905			−0.0269952	+	0.999636i	$0.508594\pi$
$228$		0			0
$229$	207.308	+	207.308i	0.905275	+	0.905275i	0.995886	−	0.0906117i	$-0.0288822\pi$
$229$	207.308	+	207.308i	0.905275	+	0.905275i	−0.0906117	+	0.995886i	$0.528882\pi$
$230$		0			0
$231$		−	36.6053i		−	0.158464i
$232$		0			0
$233$	240.593			1.03259			0.516293	−	0.856412i	$-0.327311\pi$
$233$	240.593			1.03259			0.516293	+	0.856412i	$0.327311\pi$
$234$		0			0
$235$	23.8298	−	23.8298i	0.101403	−	0.101403i
$236$		0			0
$237$			622.679i			2.62734i
$238$		0			0
$239$	265.870			1.11243			0.556213	−	0.831040i	$-0.312254\pi$
$239$	265.870			1.11243			0.556213	+	0.831040i	$0.312254\pi$
$240$		0			0
$241$		−	423.682i		−	1.75802i	−0.476806	−	0.879008i	$-0.658206\pi$
$241$		−	423.682i		−	1.75802i	0.476806	−	0.879008i	$-0.341794\pi$
$242$		0			0
$243$	157.460	−	157.460i	0.647982	−	0.647982i
$244$		0			0
$245$		−	153.749i		−	0.627547i
$246$		0			0
$247$	−70.4449	−	70.4449i	−0.285202	−	0.285202i
$248$		0			0
$249$	−294.064	+	294.064i	−1.18098	+	1.18098i
$250$		0			0
$251$	211.437	−	211.437i	0.842379	−	0.842379i	−0.146789	−	0.989168i	$-0.546894\pi$
$251$	211.437	−	211.437i	0.842379	−	0.842379i	0.989168	+	0.146789i	$0.0468939\pi$
$252$		0			0
$253$	−222.499	+	222.499i	−0.879441	+	0.879441i
$254$		0			0
$255$	152.843			0.599385
$256$		0			0
$257$	158.690			0.617471			0.308735	−	0.951148i	$-0.400094\pi$
$257$	158.690			0.617471			0.308735	+	0.951148i	$0.400094\pi$
$258$		0			0
$259$	−8.28813	−	8.28813i	−0.0320005	−	0.0320005i
$260$		0			0
$261$	−270.433	−	515.038i	−1.03614	−	1.97333i
$262$		0			0
$263$	−40.2518	+	40.2518i	−0.153049	+	0.153049i	−0.779478	−	0.626429i	$-0.784516\pi$
$263$	−40.2518	+	40.2518i	−0.153049	+	0.153049i	0.626429	+	0.779478i	$0.284516\pi$
$264$		0			0
$265$			195.632i			0.738234i
$266$		0			0
$267$			209.126i			0.783242i
$268$		0			0
$269$	−141.040	−	141.040i	−0.524311	−	0.524311i	0.394559	−	0.918870i	$-0.370897\pi$
$269$	−141.040	−	141.040i	−0.524311	−	0.524311i	−0.918870	+	0.394559i	$0.870897\pi$
$270$		0			0
$271$	−24.3687	−	24.3687i	−0.0899215	−	0.0899215i	0.660715	−	0.750637i	$-0.270253\pi$
$271$	−24.3687	−	24.3687i	−0.0899215	−	0.0899215i	−0.750637	+	0.660715i	$0.770253\pi$
$272$		0			0
$273$	−15.0266	−	15.0266i	−0.0550425	−	0.0550425i
$274$		0			0
$275$	211.910	−	211.910i	0.770581	−	0.770581i
$276$		0			0
$277$	57.9976			0.209378			0.104689	−	0.994505i	$-0.466615\pi$
$277$	57.9976			0.209378			0.104689	+	0.994505i	$0.466615\pi$
$278$		0			0
$279$	123.987	+	123.987i	0.444399	+	0.444399i
$280$		0			0
$281$	−352.000			−1.25267			−0.626334	−	0.779554i	$-0.715446\pi$
$281$	−352.000			−1.25267			−0.626334	+	0.779554i	$0.715446\pi$
$282$		0			0
$283$		−	446.547i		−	1.57790i	−0.614455	−	0.788952i	$-0.710624\pi$
$283$		−	446.547i		−	1.57790i	0.614455	−	0.788952i	$-0.289376\pi$
$284$		0			0
$285$	−146.674			−0.514647
$286$		0			0
$287$	11.9651	+	11.9651i	0.0416902	+	0.0416902i
$288$		0			0
$289$			207.737i			0.718812i
$290$		0			0
$291$	−371.502			−1.27664
$292$		0			0
$293$	14.9522	−	14.9522i	0.0510313	−	0.0510313i	−0.681131	−	0.732162i	$-0.738511\pi$
$293$	14.9522	−	14.9522i	0.0510313	−	0.0510313i	0.732162	+	0.681131i	$0.238511\pi$
$294$		0			0
$295$			67.5813i			0.229089i
$296$		0			0
$297$	1182.63			3.98192
$298$		0			0
$299$			182.673i			0.610946i
$300$		0			0
$301$	−5.47385	+	5.47385i	−0.0181856	+	0.0181856i
$302$		0			0
$303$		−	274.971i		−	0.907496i
$304$		0			0
$305$	41.3330	+	41.3330i	0.135518	+	0.135518i
$306$		0			0
$307$	−10.2622	+	10.2622i	−0.0334274	+	0.0334274i	−0.723623	−	0.690196i	$-0.757525\pi$
$307$	−10.2622	+	10.2622i	−0.0334274	+	0.0334274i	0.690196	+	0.723623i	$0.257525\pi$
$308$		0			0
$309$	−147.838	+	147.838i	−0.478441	+	0.478441i
$310$		0			0
$311$	−325.442	+	325.442i	−1.04644	+	1.04644i	−0.0475694	+	0.998868i	$0.515148\pi$
$311$	−325.442	+	325.442i	−1.04644	+	1.04644i	−0.998868	+	0.0475694i	$0.984852\pi$
$312$		0			0
$313$	−279.640			−0.893417			−0.446709	−	0.894680i	$-0.647404\pi$
$313$	−279.640			−0.893417			−0.446709	+	0.894680i	$0.647404\pi$
$314$		0			0
$315$	−21.5971			−0.0685624
$316$		0			0
$317$	195.785	+	195.785i	0.617619	+	0.617619i	0.944920	−	0.327301i	$-0.106139\pi$
$317$	195.785	+	195.785i	0.617619	+	0.617619i	−0.327301	+	0.944920i	$0.606139\pi$
$318$		0			0
$319$	171.045	−	549.258i	0.536193	−	1.72181i
$320$		0			0
$321$	383.390	−	383.390i	1.19436	−	1.19436i
$322$		0			0
$323$			77.9836i			0.241435i
$324$		0			0
$325$		−	173.979i		−	0.535321i
$326$		0			0
$327$	165.773	+	165.773i	0.506951	+	0.506951i
$328$		0			0
$329$	2.59351	+	2.59351i	0.00788302	+	0.00788302i
$330$		0			0
$331$	−177.780	−	177.780i	−0.537100	−	0.537100i	0.385576	−	0.922676i	$-0.374003\pi$
$331$	−177.780	−	177.780i	−0.537100	−	0.537100i	−0.922676	+	0.385576i	$0.874003\pi$
$332$		0			0
$333$	485.679	−	485.679i	1.45849	−	1.45849i
$334$		0			0
$335$	56.0712			0.167377
$336$		0			0
$337$	−312.630	−	312.630i	−0.927686	−	0.927686i	0.0698697	−	0.997556i	$-0.477742\pi$
$337$	−312.630	−	312.630i	−0.927686	−	0.927686i	−0.997556	+	0.0698697i	$0.977742\pi$
$338$		0			0
$339$	810.227			2.39005
$340$		0			0
$341$			173.402i			0.508509i
$342$		0			0
$343$	33.5066			0.0976869
$344$		0			0
$345$	190.173	+	190.173i	0.551226	+	0.551226i
$346$		0			0
$347$			307.039i			0.884840i	0.896808	+	0.442420i	$0.145880\pi$
$347$			307.039i			0.884840i	−0.896808	+	0.442420i	$0.854120\pi$
$348$		0			0
$349$	463.827			1.32902			0.664509	−	0.747280i	$-0.268641\pi$
$349$	463.827			1.32902			0.664509	+	0.747280i	$0.268641\pi$
$350$		0			0
$351$	485.473	−	485.473i	1.38311	−	1.38311i
$352$		0			0
$353$			322.072i			0.912385i	0.889881	+	0.456192i	$0.150787\pi$
$353$			322.072i			0.912385i	−0.889881	+	0.456192i	$0.849213\pi$
$354$		0			0
$355$	−166.721			−0.469637
$356$		0			0
$357$			16.6347i			0.0465957i
$358$		0			0
$359$	−410.933	+	410.933i	−1.14466	+	1.14466i	−0.157072	+	0.987587i	$0.550205\pi$
$359$	−410.933	+	410.933i	−1.14466	+	1.14466i	−0.987587	+	0.157072i	$0.949795\pi$
$360$		0			0
$361$			286.164i			0.792698i
$362$		0			0
$363$	1038.74	+	1038.74i	2.86155	+	2.86155i
$364$		0			0
$365$	−18.6542	+	18.6542i	−0.0511073	+	0.0511073i
$366$		0			0
$367$	−309.094	+	309.094i	−0.842218	+	0.842218i	−0.989147	−	0.146929i	$-0.953061\pi$
$367$	−309.094	+	309.094i	−0.842218	+	0.842218i	0.146929	+	0.989147i	$0.453061\pi$
$368$		0			0
$369$	−701.145	+	701.145i	−1.90012	+	1.90012i
$370$		0			0
$371$	−21.2916			−0.0573897
$372$		0			0
$373$	210.646			0.564734			0.282367	−	0.959306i	$-0.408880\pi$
$373$	210.646			0.564734			0.282367	+	0.959306i	$0.408880\pi$
$374$		0			0
$375$	−480.848	−	480.848i	−1.28226	−	1.28226i
$376$		0			0
$377$	−155.257	−	295.687i	−0.411824	−	0.784316i
$378$		0			0
$379$	229.599	−	229.599i	0.605803	−	0.605803i	−0.336043	−	0.941847i	$-0.609089\pi$
$379$	229.599	−	229.599i	0.605803	−	0.605803i	0.941847	+	0.336043i	$0.109089\pi$
$380$		0			0
$381$			328.483i			0.862160i
$382$		0			0
$383$			248.070i			0.647701i	0.946108	+	0.323851i	$0.104978\pi$
$383$			248.070i			0.647701i	−0.946108	+	0.323851i	$0.895022\pi$
$384$		0			0
$385$	−15.1023	−	15.1023i	−0.0392267	−	0.0392267i
$386$		0			0
$387$	−320.764	−	320.764i	−0.828847	−	0.828847i
$388$		0			0
$389$	78.1188	+	78.1188i	0.200820	+	0.200820i	0.800351	−	0.599532i	$-0.204646\pi$
$389$	78.1188	+	78.1188i	0.200820	+	0.200820i	−0.599532	+	0.800351i	$0.704646\pi$
$390$		0			0
$391$	101.111	−	101.111i	0.258596	−	0.258596i
$392$		0			0
$393$	165.204			0.420368
$394$		0			0
$395$	256.899	+	256.899i	0.650377	+	0.650377i
$396$		0			0
$397$	399.382			1.00600			0.503000	−	0.864287i	$-0.332230\pi$
$397$	399.382			1.00600			0.503000	+	0.864287i	$0.332230\pi$
$398$		0			0
$399$		−	15.9633i		−	0.0400083i
$400$		0			0
$401$	−585.895			−1.46109			−0.730543	−	0.682867i	$-0.760733\pi$
$401$	−585.895			−1.46109			−0.730543	+	0.682867i	$0.760733\pi$
$402$		0			0
$403$	71.1820	+	71.1820i	0.176630	+	0.176630i
$404$		0			0
$405$		−	442.986i		−	1.09379i
$406$		0			0
$407$	679.242			1.66890
$408$		0			0
$409$	243.027	−	243.027i	0.594198	−	0.594198i	−0.344564	−	0.938763i	$-0.611973\pi$
$409$	243.027	−	243.027i	0.594198	−	0.594198i	0.938763	+	0.344564i	$0.111973\pi$
$410$		0			0
$411$			495.433i			1.20543i
$412$		0			0
$413$	−7.35520			−0.0178092
$414$		0			0
$415$			242.645i			0.584686i
$416$		0			0
$417$	−280.866	+	280.866i	−0.673540	+	0.673540i
$418$		0			0
$419$			548.833i			1.30987i	0.755687	+	0.654933i	$0.227303\pi$
$419$			548.833i			1.30987i	−0.755687	+	0.654933i	$0.772697\pi$
$420$		0			0
$421$	−126.907	−	126.907i	−0.301442	−	0.301442i	0.540136	−	0.841578i	$-0.318373\pi$
$421$	−126.907	−	126.907i	−0.301442	−	0.301442i	−0.841578	+	0.540136i	$0.818373\pi$
$422$		0			0
$423$	−151.978	+	151.978i	−0.359286	+	0.359286i
$424$		0			0
$425$	−96.2989	+	96.2989i	−0.226586	+	0.226586i
$426$		0			0
$427$	−4.49847	+	4.49847i	−0.0105351	+	0.0105351i
$428$		0			0
$429$	1231.48			2.87059
$430$		0			0
$431$	−334.232			−0.775480			−0.387740	−	0.921769i	$-0.626744\pi$
$431$	−334.232			−0.775480			−0.387740	+	0.921769i	$0.626744\pi$
$432$		0			0
$433$	−321.593	−	321.593i	−0.742710	−	0.742710i	0.230389	−	0.973099i	$-0.426000\pi$
$433$	−321.593	−	321.593i	−0.742710	−	0.742710i	−0.973099	+	0.230389i	$0.926000\pi$
$434$		0			0
$435$	−469.459	−	146.195i	−1.07922	−	0.336081i
$436$		0			0
$437$	−97.0300	+	97.0300i	−0.222037	+	0.222037i
$438$		0			0
$439$			493.002i			1.12301i	0.827473	+	0.561506i	$0.189778\pi$
$439$			493.002i			1.12301i	−0.827473	+	0.561506i	$0.810222\pi$
$440$		0			0
$441$			980.556i			2.22348i
$442$		0			0
$443$	−305.073	−	305.073i	−0.688653	−	0.688653i	0.273281	−	0.961934i	$-0.411891\pi$
$443$	−305.073	−	305.073i	−0.688653	−	0.688653i	−0.961934	+	0.273281i	$0.911891\pi$
$444$		0			0
$445$	86.2791	+	86.2791i	0.193886	+	0.193886i
$446$		0			0
$447$	−361.171	−	361.171i	−0.807990	−	0.807990i
$448$		0			0
$449$	−604.469	+	604.469i	−1.34626	+	1.34626i	−0.456567	+	0.889689i	$0.650921\pi$
$449$	−604.469	+	604.469i	−1.34626	+	1.34626i	−0.889689	+	0.456567i	$0.849079\pi$
$450$		0			0
$451$	−980.582			−2.17424
$452$		0			0
$453$	664.556	+	664.556i	1.46701	+	1.46701i
$454$		0			0
$455$	−12.3991			−0.0272507
$456$		0			0
$457$		−	563.383i		−	1.23278i	−0.787439	−	0.616392i	$-0.788594\pi$
$457$		−	563.383i		−	1.23278i	0.787439	−	0.616392i	$-0.211406\pi$
$458$		0			0
$459$	−537.426			−1.17086
$460$		0			0
$461$	−371.986	−	371.986i	−0.806911	−	0.806911i	0.177254	−	0.984165i	$-0.443279\pi$
$461$	−371.986	−	371.986i	−0.806911	−	0.806911i	−0.984165	+	0.177254i	$0.943279\pi$
$462$		0			0
$463$			13.1023i			0.0282986i	0.999900	+	0.0141493i	$0.00450402\pi$
$463$			13.1023i			0.0282986i	−0.999900	+	0.0141493i	$0.995496\pi$
$464$		0			0
$465$	148.209			0.318729
$466$		0			0
$467$	192.103	−	192.103i	0.411356	−	0.411356i	−0.470854	−	0.882211i	$-0.656054\pi$
$467$	192.103	−	192.103i	0.411356	−	0.411356i	0.882211	+	0.470854i	$0.156054\pi$
$468$		0			0
$469$			6.10250i			0.0130117i
$470$		0			0
$471$	1561.78			3.31588
$472$		0			0
$473$		−	448.602i		−	0.948419i
$474$		0			0
$475$	92.4122	−	92.4122i	0.194552	−	0.194552i
$476$		0			0
$477$		−	1247.67i		−	2.61566i
$478$		0			0
$479$	−237.779	−	237.779i	−0.496407	−	0.496407i	0.413911	−	0.910317i	$-0.364163\pi$
$479$	−237.779	−	237.779i	−0.496407	−	0.496407i	−0.910317	+	0.413911i	$0.864163\pi$
$480$		0			0
$481$	278.831	−	278.831i	0.579691	−	0.579691i
$482$		0			0
$483$	−20.6975	+	20.6975i	−0.0428519	+	0.0428519i
$484$		0			0
$485$	−153.271	+	153.271i	−0.316022	+	0.316022i
$486$		0			0
$487$	754.182			1.54863			0.774314	−	0.632802i	$-0.218095\pi$
$487$	754.182			1.54863			0.774314	+	0.632802i	$0.218095\pi$
$488$		0			0
$489$	−982.943			−2.01011
$490$		0			0
$491$	−451.910	−	451.910i	−0.920388	−	0.920388i	0.0766690	−	0.997057i	$-0.475572\pi$
$491$	−451.910	−	451.910i	−0.920388	−	0.920388i	−0.997057	+	0.0766690i	$0.975572\pi$
$492$		0			0
$493$	−77.7288	+	249.601i	−0.157665	+	0.506290i
$494$		0			0
$495$	884.982	−	884.982i	1.78784	−	1.78784i
$496$		0			0
$497$		−	18.1451i		−	0.0365092i
$498$		0			0
$499$		−	292.373i		−	0.585918i	−0.956125	−	0.292959i	$-0.905360\pi$
$499$		−	292.373i		−	0.585918i	0.956125	−	0.292959i	$-0.0946399\pi$
$500$		0			0
$501$	−1017.33	−	1017.33i	−2.03060	−	2.03060i
$502$		0			0
$503$	−510.905	−	510.905i	−1.01572	−	1.01572i	−0.999875	−	0.0158408i	$-0.994958\pi$
$503$	−510.905	−	510.905i	−1.01572	−	1.01572i	−0.0158408	−	0.999875i	$-0.505042\pi$
$504$		0			0
$505$	−113.445	−	113.445i	−0.224644	−	0.224644i
$506$		0			0
$507$	−138.662	+	138.662i	−0.273496	+	0.273496i
$508$		0			0
$509$	−10.9652			−0.0215427			−0.0107714	−	0.999942i	$-0.503429\pi$
$509$	−10.9652			−0.0215427			−0.0107714	+	0.999942i	$0.503429\pi$
$510$		0			0
$511$	−2.03022	−	2.03022i	−0.00397304	−	0.00397304i
$512$		0			0
$513$	515.736			1.00533
$514$		0			0
$515$			121.987i			0.236869i
$516$		0			0
$517$	−212.548			−0.411118
$518$		0			0
$519$	−1006.99	−	1006.99i	−1.94026	−	1.94026i
$520$		0			0
$521$			93.8560i			0.180146i	0.995935	+	0.0900729i	$0.0287100\pi$
$521$			93.8560i			0.180146i	−0.995935	+	0.0900729i	$0.971290\pi$
$522$		0			0
$523$	−32.4183			−0.0619853			−0.0309926	−	0.999520i	$-0.509867\pi$
$523$	−32.4183			−0.0619853			−0.0309926	+	0.999520i	$0.509867\pi$
$524$		0			0
$525$	19.7124	−	19.7124i	0.0375475	−	0.0375475i
$526$		0			0
$527$		−	78.7995i		−	0.149525i
$528$		0			0
$529$	−277.388			−0.524364
$530$		0			0
$531$		−	431.009i		−	0.811694i
$532$		0			0
$533$	−402.532	+	402.532i	−0.755220	+	0.755220i
$534$		0			0
$535$		−	316.351i		−	0.591311i
$536$		0			0
$537$	304.885	+	304.885i	0.567756	+	0.567756i
$538$		0			0
$539$	−685.675	+	685.675i	−1.27212	+	1.27212i
$540$		0			0
$541$	−249.329	+	249.329i	−0.460867	+	0.460867i	−0.898940	−	0.438072i	$-0.855661\pi$
$541$	−249.329	+	249.329i	−0.460867	+	0.460867i	0.438072	+	0.898940i	$0.355661\pi$
$542$		0			0
$543$	−445.058	+	445.058i	−0.819627	+	0.819627i
$544$		0			0
$545$	136.786			0.250984
$546$		0			0
$547$	−387.586			−0.708566			−0.354283	−	0.935138i	$-0.615275\pi$
$547$	−387.586			−0.708566			−0.354283	+	0.935138i	$0.615275\pi$
$548$		0			0
$549$	−263.607	−	263.607i	−0.480159	−	0.480159i
$550$		0			0
$551$	74.5917	−	239.527i	0.135375	−	0.434714i
$552$		0			0
$553$	−27.9596	+	27.9596i	−0.0505598	+	0.0505598i
$554$		0			0
$555$		−	580.559i		−	1.04605i
$556$		0			0
$557$		−	352.548i		−	0.632941i	−0.948602	−	0.316471i	$-0.897502\pi$
$557$		−	352.548i		−	0.632941i	0.948602	−	0.316471i	$-0.102498\pi$
$558$		0			0
$559$	−184.153	−	184.153i	−0.329432	−	0.329432i
$560$		0			0
$561$	−681.636	−	681.636i	−1.21504	−	1.21504i
$562$		0			0
$563$	151.066	+	151.066i	0.268324	+	0.268324i	0.828425	−	0.560101i	$-0.189238\pi$
$563$	151.066	+	151.066i	0.268324	+	0.268324i	−0.560101	+	0.828425i	$0.689238\pi$
$564$		0			0
$565$	334.276	−	334.276i	0.591638	−	0.591638i
$566$		0			0
$567$	48.2123			0.0850306
$568$		0			0
$569$	431.698	+	431.698i	0.758697	+	0.758697i	0.976085	−	0.217389i	$-0.0697539\pi$
$569$	431.698	+	431.698i	0.758697	+	0.758697i	−0.217389	+	0.976085i	$0.569754\pi$
$570$		0			0
$571$	−66.0488			−0.115672			−0.0578361	−	0.998326i	$-0.518420\pi$
$571$	−66.0488			−0.115672			−0.0578361	+	0.998326i	$0.518420\pi$
$572$		0			0
$573$			457.926i			0.799172i
$574$		0			0
$575$	−239.637			−0.416760
$576$		0			0
$577$	−392.139	−	392.139i	−0.679616	−	0.679616i	0.280297	−	0.959913i	$-0.409567\pi$
$577$	−392.139	−	392.139i	−0.679616	−	0.679616i	−0.959913	+	0.280297i	$0.909567\pi$
$578$		0			0
$579$			1184.79i			2.04627i
$580$		0			0
$581$	−26.4082			−0.0454530
$582$		0			0
$583$	872.461	−	872.461i	1.49650	−	1.49650i
$584$		0			0
$585$		−	726.576i		−	1.24201i
$586$		0			0
$587$	−195.193			−0.332527			−0.166263	−	0.986081i	$-0.553170\pi$
$587$	−195.193			−0.332527			−0.166263	+	0.986081i	$0.553170\pi$
$588$		0			0
$589$			75.6192i			0.128386i
$590$		0			0
$591$	−487.659	+	487.659i	−0.825143	+	0.825143i
$592$		0			0
$593$		−	128.271i		−	0.216309i	−0.994134	−	0.108155i	$-0.965506\pi$
$593$		−	128.271i		−	0.216309i	0.994134	−	0.108155i	$-0.0344942\pi$
$594$		0			0
$595$	6.86298	+	6.86298i	0.0115344	+	0.0115344i
$596$		0			0
$597$	−1393.22	+	1393.22i	−2.33370	+	2.33370i
$598$		0			0
$599$	−717.619	+	717.619i	−1.19803	+	1.19803i	−0.223271	+	0.974756i	$0.571674\pi$
$599$	−717.619	+	717.619i	−1.19803	+	1.19803i	−0.974756	+	0.223271i	$0.928326\pi$
$600$		0			0
$601$	−9.96872	+	9.96872i	−0.0165869	+	0.0165869i	−0.715352	−	0.698765i	$-0.753733\pi$
$601$	−9.96872	+	9.96872i	−0.0165869	+	0.0165869i	0.698765	+	0.715352i	$0.253733\pi$
$602$		0			0
$603$	−357.602			−0.593038
$604$		0			0
$605$	857.109			1.41671
$606$		0			0
$607$	162.407	+	162.407i	0.267556	+	0.267556i	0.828115	−	0.560559i	$-0.189414\pi$
$607$	162.407	+	162.407i	0.267556	+	0.267556i	−0.560559	+	0.828115i	$0.689414\pi$
$608$		0			0
$609$	15.9111	−	51.0935i	0.0261267	−	0.0838974i
$610$		0			0
$611$	−87.2517	+	87.2517i	−0.142801	+	0.142801i
$612$		0			0
$613$			376.150i			0.613621i	0.951771	+	0.306811i	$0.0992619\pi$
$613$			376.150i			0.613621i	−0.951771	+	0.306811i	$0.900738\pi$
$614$		0			0
$615$			838.118i			1.36279i
$616$		0			0
$617$	373.217	+	373.217i	0.604889	+	0.604889i	0.941606	−	0.336717i	$-0.109316\pi$
$617$	373.217	+	373.217i	0.604889	+	0.604889i	−0.336717	+	0.941606i	$0.609316\pi$
$618$		0			0
$619$	196.763	+	196.763i	0.317872	+	0.317872i	0.847949	−	0.530077i	$-0.177837\pi$
$619$	196.763	+	196.763i	0.317872	+	0.317872i	−0.530077	+	0.847949i	$0.677837\pi$
$620$		0			0
$621$	−668.685	−	668.685i	−1.07679	−	1.07679i
$622$		0			0
$623$	−9.39017	+	9.39017i	−0.0150725	+	0.0150725i
$624$		0			0
$625$	−19.0833			−0.0305333
$626$		0			0
$627$	654.125	+	654.125i	1.04326	+	1.04326i
$628$		0			0
$629$	−308.670			−0.490732
$630$		0			0
$631$		−	335.146i		−	0.531135i	−0.964092	−	0.265567i	$-0.914441\pi$
$631$		−	335.146i		−	0.531135i	0.964092	−	0.265567i	$-0.0855592\pi$
$632$		0			0
$633$	1796.36			2.83785
$634$		0			0
$635$	135.522	+	135.522i	0.213421	+	0.213421i
$636$		0			0
$637$			562.944i			0.883743i
$638$		0			0
$639$	1063.29			1.66399
$640$		0			0
$641$	−343.144	+	343.144i	−0.535326	+	0.535326i	−0.922152	−	0.386827i	$-0.873571\pi$
$641$	−343.144	+	343.144i	−0.535326	+	0.535326i	0.386827	+	0.922152i	$0.373571\pi$
$642$		0			0
$643$			561.006i			0.872482i	0.899830	+	0.436241i	$0.143690\pi$
$643$			561.006i			0.872482i	−0.899830	+	0.436241i	$0.856310\pi$
$644$		0			0
$645$	−383.427			−0.594461
$646$		0			0
$647$		−	930.722i		−	1.43852i	−0.694741	−	0.719260i	$-0.744481\pi$
$647$		−	930.722i		−	1.43852i	0.694741	−	0.719260i	$-0.255519\pi$
$648$		0			0
$649$	301.393	−	301.393i	0.464395	−	0.464395i
$650$		0			0
$651$			16.1303i			0.0247777i
$652$		0			0
$653$	168.866	+	168.866i	0.258600	+	0.258600i	0.824484	−	0.565885i	$-0.191465\pi$
$653$	168.866	+	168.866i	0.258600	+	0.258600i	−0.565885	+	0.824484i	$0.691465\pi$
$654$		0			0
$655$	68.1585	−	68.1585i	0.104059	−	0.104059i
$656$		0			0
$657$	118.970	−	118.970i	0.181080	−	0.181080i
$658$		0			0
$659$	414.083	−	414.083i	0.628350	−	0.628350i	−0.319303	−	0.947653i	$-0.603449\pi$
$659$	414.083	−	414.083i	0.628350	−	0.628350i	0.947653	+	0.319303i	$0.103449\pi$
$660$		0			0
$661$	−732.973			−1.10888			−0.554442	−	0.832222i	$-0.687068\pi$
$661$	−732.973			−1.10888			−0.554442	+	0.832222i	$0.687068\pi$
$662$		0			0
$663$	−559.628			−0.844084
$664$		0			0
$665$	−6.58598	−	6.58598i	−0.00990374	−	0.00990374i
$666$		0			0
$667$	−407.276	+	213.850i	−0.610608	+	0.320614i
$668$		0			0
$669$	1540.37	−	1540.37i	2.30250	−	2.30250i
$670$		0			0
$671$		−	368.666i		−	0.549427i
$672$		0			0
$673$			503.554i			0.748223i	0.927384	+	0.374112i	$0.122052\pi$
$673$			503.554i			0.748223i	−0.927384	+	0.374112i	$0.877948\pi$
$674$		0			0
$675$	636.862	+	636.862i	0.943499	+	0.943499i
$676$		0			0
$677$	257.461	+	257.461i	0.380298	+	0.380298i	0.871209	−	0.490912i	$-0.163336\pi$
$677$	257.461	+	257.461i	0.380298	+	0.380298i	−0.490912	+	0.871209i	$0.663336\pi$
$678$		0			0
$679$	−16.6812	−	16.6812i	−0.0245673	−	0.0245673i
$680$		0			0
$681$	46.7165	−	46.7165i	0.0685999	−	0.0685999i
$682$		0			0
$683$	840.114			1.23004			0.615018	−	0.788513i	$-0.289149\pi$
$683$	840.114			1.23004			0.615018	+	0.788513i	$0.289149\pi$
$684$		0			0
$685$	204.401	+	204.401i	0.298396	+	0.298396i
$686$		0			0
$687$	−1580.42			−2.30047
$688$		0			0
$689$		−	716.297i		−	1.03962i
$690$		0			0
$691$	347.277			0.502571			0.251286	−	0.967913i	$-0.419147\pi$
$691$	347.277			0.502571			0.251286	+	0.967913i	$0.419147\pi$
$692$		0			0
$693$	96.3169	+	96.3169i	0.138985	+	0.138985i
$694$		0			0
$695$			231.754i			0.333459i
$696$		0			0
$697$	445.609			0.639325
$698$		0			0
$699$	−917.087	+	917.087i	−1.31200	+	1.31200i
$700$		0			0
$701$			384.210i			0.548088i	0.961717	+	0.274044i	$0.0883615\pi$
$701$			384.210i			0.548088i	−0.961717	+	0.274044i	$0.911639\pi$
$702$		0			0
$703$	296.212			0.421355
$704$		0			0
$705$			181.668i			0.257685i
$706$		0			0
$707$	12.3468	−	12.3468i	0.0174636	−	0.0174636i
$708$		0			0
$709$			689.774i			0.972883i	0.873713	+	0.486442i	$0.161705\pi$
$709$			689.774i			0.972883i	−0.873713	+	0.486442i	$0.838295\pi$
$710$		0			0
$711$	−1638.41	−	1638.41i	−2.30437	−	2.30437i
$712$		0			0
$713$	98.0452	−	98.0452i	0.137511	−	0.137511i
$714$		0			0
$715$	508.074	−	508.074i	0.710593	−	0.710593i
$716$		0			0
$717$	−1013.44	+	1013.44i	−1.41344	+	1.41344i
$718$		0			0
$719$	1313.45			1.82677			0.913387	−	0.407092i	$-0.133457\pi$
$719$	1313.45			1.82677			0.913387	+	0.407092i	$0.133457\pi$
$720$		0			0
$721$	−13.2765			−0.0184140
$722$		0			0
$723$	1614.98	+	1614.98i	2.23372	+	2.23372i
$724$		0			0
$725$	387.893	−	203.672i	0.535025	−	0.280928i
$726$		0			0
$727$	−767.639	+	767.639i	−1.05590	+	1.05590i	−0.0575571	+	0.998342i	$0.518331\pi$
$727$	−767.639	+	767.639i	−1.05590	+	1.05590i	−0.998342	+	0.0575571i	$0.981669\pi$
$728$		0			0
$729$		−	67.1807i		−	0.0921546i
$730$		0			0
$731$			203.860i			0.278878i
$732$		0			0
$733$	−640.227	−	640.227i	−0.873434	−	0.873434i	0.119411	−	0.992845i	$-0.461899\pi$
$733$	−640.227	−	640.227i	−0.873434	−	0.873434i	−0.992845	+	0.119411i	$0.961899\pi$
$734$		0			0
$735$	586.057	+	586.057i	0.797357	+	0.797357i
$736$		0			0
$737$	−250.061	−	250.061i	−0.339296	−	0.339296i
$738$		0			0
$739$	126.689	−	126.689i	0.171433	−	0.171433i	−0.616175	−	0.787609i	$-0.711319\pi$
$739$	126.689	−	126.689i	0.171433	−	0.171433i	0.787609	+	0.616175i	$0.211319\pi$
$740$		0			0
$741$	537.041			0.724752
$742$		0			0
$743$	−547.079	−	547.079i	−0.736310	−	0.736310i	0.235551	−	0.971862i	$-0.424310\pi$
$743$	−547.079	−	547.079i	−0.736310	−	0.736310i	−0.971862	+	0.235551i	$0.924310\pi$
$744$		0			0
$745$	−298.017			−0.400023
$746$		0			0
$747$		−	1547.50i		−	2.07162i
$748$		0			0
$749$	34.4300			0.0459680
$750$		0			0
$751$	819.975	+	819.975i	1.09184	+	1.09184i	0.995332	+	0.0965128i	$0.0307689\pi$
$751$	819.975	+	819.975i	1.09184	+	1.09184i	0.0965128	+	0.995332i	$0.469231\pi$
$752$		0			0
$753$			1611.90i			2.14064i
$754$		0			0
$755$	548.352			0.726294
$756$		0			0
$757$	499.757	−	499.757i	0.660181	−	0.660181i	−0.295242	−	0.955423i	$-0.595400\pi$
$757$	499.757	−	499.757i	0.660181	−	0.660181i	0.955423	+	0.295242i	$0.0954003\pi$
$758$		0			0
$759$		−	1696.23i		−	2.23482i
$760$		0			0
$761$	1105.01			1.45205			0.726023	−	0.687670i	$-0.241367\pi$
$761$	1105.01			1.45205			0.726023	+	0.687670i	$0.241367\pi$
$762$		0			0
$763$			14.8871i			0.0195113i
$764$		0			0
$765$	−402.165	+	402.165i	−0.525707	+	0.525707i
$766$		0			0
$767$		−	247.445i		−	0.322615i
$768$		0			0
$769$	−379.661	−	379.661i	−0.493707	−	0.493707i	0.415765	−	0.909472i	$-0.363514\pi$
$769$	−379.661	−	379.661i	−0.493707	−	0.493707i	−0.909472	+	0.415765i	$0.863514\pi$
$770$		0			0
$771$	−604.891	+	604.891i	−0.784554	+	0.784554i
$772$		0			0
$773$	−912.108	+	912.108i	−1.17996	+	1.17996i	−0.200204	+	0.979754i	$0.564160\pi$
$773$	−912.108	+	912.108i	−1.17996	+	1.17996i	−0.979754	+	0.200204i	$0.935840\pi$
$774$		0			0
$775$	−93.3791	+	93.3791i	−0.120489	+	0.120489i
$776$		0			0
$777$	63.1850			0.0813192
$778$		0			0
$779$	−427.624			−0.548940
$780$		0			0
$781$	743.527	+	743.527i	0.952019	+	0.952019i
$782$		0			0
$783$	1650.71	+	514.051i	2.10819	+	0.656514i
$784$		0			0
$785$	644.344	−	644.344i	0.820821	−	0.820821i
$786$		0			0
$787$			1254.47i			1.59399i	0.603984	+	0.796996i	$0.293579\pi$
$787$			1254.47i			1.59399i	−0.603984	+	0.796996i	$0.706421\pi$
$788$		0			0
$789$		−	306.862i		−	0.388925i
$790$		0			0
$791$	36.3809	+	36.3809i	0.0459935	+	0.0459935i
$792$		0			0
$793$	−151.339	−	151.339i	−0.190843	−	0.190843i
$794$		0			0
$795$	−745.706	−	745.706i	−0.937995	−	0.937995i
$796$		0			0
$797$	222.524	−	222.524i	0.279202	−	0.279202i	−0.553588	−	0.832790i	$-0.686742\pi$
$797$	222.524	−	222.524i	0.279202	−	0.279202i	0.832790	+	0.553588i	$0.186742\pi$
$798$		0			0
$799$	96.5889			0.120887
$800$		0			0
$801$	−550.257	−	550.257i	−0.686963	−	0.686963i
$802$		0			0
$803$	166.384			0.207203
$804$		0			0
$805$			17.0783i			0.0212153i
$806$		0			0
$807$	1075.22			1.33237
$808$		0			0
$809$	−393.131	−	393.131i	−0.485947	−	0.485947i	0.421078	−	0.907025i	$-0.361652\pi$
$809$	−393.131	−	393.131i	−0.485947	−	0.485947i	−0.907025	+	0.421078i	$0.861652\pi$
$810$		0			0
$811$		−	1199.23i		−	1.47870i	−0.673320	−	0.739351i	$-0.735132\pi$
$811$		−	1199.23i		−	1.47870i	0.673320	−	0.739351i	$-0.264868\pi$
$812$		0			0
$813$	185.776			0.228507
$814$		0			0
$815$	−405.533	+	405.533i	−0.497587	+	0.497587i
$816$		0			0
$817$		−	195.632i		−	0.239452i
$818$		0			0
$819$	79.0768			0.0965529
$820$		0			0
$821$			1035.60i			1.26139i	0.776032	+	0.630693i	$0.217229\pi$
$821$			1035.60i			1.26139i	−0.776032	+	0.630693i	$0.782771\pi$
$822$		0			0
$823$	738.936	−	738.936i	0.897857	−	0.897857i	−0.0973894	−	0.995246i	$-0.531049\pi$
$823$	738.936	−	738.936i	0.897857	−	0.897857i	0.995246	+	0.0973894i	$0.0310492\pi$
$824$		0			0
$825$			1615.51i			1.95819i
$826$		0			0
$827$	−38.9897	−	38.9897i	−0.0471459	−	0.0471459i	0.683141	−	0.730287i	$-0.260614\pi$
$827$	−38.9897	−	38.9897i	−0.0471459	−	0.0471459i	−0.730287	+	0.683141i	$0.760614\pi$
$828$		0			0
$829$	562.619	−	562.619i	0.678672	−	0.678672i	−0.281028	−	0.959700i	$-0.590675\pi$
$829$	562.619	−	562.619i	0.678672	−	0.678672i	0.959700	+	0.281028i	$0.0906752\pi$
$830$		0			0
$831$	−221.074	+	221.074i	−0.266034	+	0.266034i
$832$		0			0
$833$	311.594	−	311.594i	0.374062	−	0.374062i
$834$		0			0
$835$	−839.442			−1.00532
$836$		0			0
$837$	−521.132			−0.622619
$838$		0			0
$839$	−42.1944	−	42.1944i	−0.0502913	−	0.0502913i	0.681514	−	0.731805i	$-0.261322\pi$
$839$	−42.1944	−	42.1944i	−0.0502913	−	0.0502913i	−0.731805	+	0.681514i	$0.761322\pi$
$840$		0			0
$841$	477.489	−	692.304i	0.567764	−	0.823191i
$842$		0			0
$843$	1341.75	−	1341.75i	1.59163	−	1.59163i
$844$		0			0
$845$			114.416i			0.135403i
$846$		0			0
$847$			93.2833i			0.110134i
$848$		0			0
$849$	1702.14	+	1702.14i	2.00487	+	2.00487i
$850$		0			0
$851$	−384.059	−	384.059i	−0.451303	−	0.451303i
$852$		0			0
$853$	−946.645	−	946.645i	−1.10978	−	1.10978i	−0.993178	−	0.116604i	$-0.962799\pi$
$853$	−946.645	−	946.645i	−1.10978	−	1.10978i	−0.116604	−	0.993178i	$-0.537201\pi$
$854$		0			0
$855$	385.934	−	385.934i	0.451385	−	0.451385i
$856$		0			0
$857$	390.149			0.455250			0.227625	−	0.973749i	$-0.426904\pi$
$857$	390.149			0.455250			0.227625	+	0.973749i	$0.426904\pi$
$858$		0			0
$859$	−579.404	−	579.404i	−0.674510	−	0.674510i	0.284242	−	0.958752i	$-0.408258\pi$
$859$	−579.404	−	579.404i	−0.674510	−	0.674510i	−0.958752	+	0.284242i	$0.908258\pi$
$860$		0			0
$861$	−91.2165			−0.105943
$862$		0			0
$863$			1539.24i			1.78360i	0.452434	+	0.891798i	$0.350556\pi$
$863$			1539.24i			1.78360i	−0.452434	+	0.891798i	$0.649444\pi$
$864$		0			0
$865$	−830.912			−0.960592
$866$		0			0
$867$	−791.846	−	791.846i	−0.913317	−	0.913317i
$868$		0			0
$869$		−	2291.39i		−	2.63681i
$870$		0			0
$871$	−205.302			−0.235708
$872$		0			0
$873$	977.507	−	977.507i	1.11971	−	1.11971i
$874$		0			0
$875$		−	43.1821i		−	0.0493510i
$876$		0			0
$877$	−909.345			−1.03688			−0.518441	−	0.855114i	$-0.673487\pi$
$877$	−909.345			−1.03688			−0.518441	+	0.855114i	$0.673487\pi$
$878$		0			0
$879$			113.989i			0.129680i
$880$		0			0
$881$	949.796	−	949.796i	1.07809	−	1.07809i	0.0814077	−	0.996681i	$-0.474058\pi$
$881$	949.796	−	949.796i	1.07809	−	1.07809i	0.996681	−	0.0814077i	$-0.0259416\pi$
$882$		0			0
$883$			226.833i			0.256889i	0.991717	+	0.128445i	$0.0409985\pi$
$883$			226.833i			0.256889i	−0.991717	+	0.128445i	$0.959002\pi$
$884$		0			0
$885$	−257.605	−	257.605i	−0.291079	−	0.291079i
$886$		0			0
$887$	575.636	−	575.636i	0.648969	−	0.648969i	−0.303775	−	0.952744i	$-0.598247\pi$
$887$	575.636	−	575.636i	0.648969	−	0.648969i	0.952744	+	0.303775i	$0.0982470\pi$
$888$		0			0
$889$	−14.7496	+	14.7496i	−0.0165912	+	0.0165912i
$890$		0			0
$891$	−1975.59	+	1975.59i	−2.21727	+	2.21727i
$892$		0			0
$893$	−92.6906			−0.103797
$894$		0			0
$895$	251.573			0.281087
$896$		0			0
$897$	−696.309	−	696.309i	−0.776264	−	0.776264i
$898$		0			0
$899$	−75.3721	+	242.033i	−0.0838399	+	0.269225i
$900$		0			0
$901$	−396.476	+	396.476i	−0.440040	+	0.440040i
$902$		0			0
$903$		−	41.7302i		−	0.0462129i
$904$		0			0
$905$			367.235i			0.405785i
$906$		0			0
$907$	−123.661	−	123.661i	−0.136341	−	0.136341i	0.635643	−	0.771983i	$-0.280735\pi$
$907$	−123.661	−	123.661i	−0.136341	−	0.136341i	−0.771983	+	0.635643i	$0.780735\pi$
$908$		0			0
$909$	723.512	+	723.512i	0.795943	+	0.795943i
$910$		0			0
$911$	22.7492	+	22.7492i	0.0249716	+	0.0249716i	0.719482	−	0.694511i	$-0.244379\pi$
$911$	22.7492	+	22.7492i	0.0249716	+	0.0249716i	−0.694511	+	0.719482i	$0.744379\pi$
$912$		0			0
$913$	1082.12	−	1082.12i	1.18524	−	1.18524i
$914$		0			0
$915$	−315.104			−0.344376
$916$		0			0
$917$	7.41802	+	7.41802i	0.00808944	+	0.00808944i
$918$		0			0
$919$	1114.91			1.21318			0.606591	−	0.795014i	$-0.292537\pi$
$919$	1114.91			1.21318			0.606591	+	0.795014i	$0.292537\pi$
$920$		0			0
$921$		−	78.2346i		−	0.0849452i
$922$		0			0
$923$	610.441			0.661366
$924$		0			0
$925$	365.781	+	365.781i	0.395439	+	0.395439i
$926$		0			0
$927$		−	777.992i		−	0.839258i
$928$		0			0
$929$	−1298.02			−1.39722			−0.698611	−	0.715502i	$-0.746198\pi$
$929$	−1298.02			−1.39722			−0.698611	+	0.715502i	$0.746198\pi$
$930$		0			0
$931$	−299.018	+	299.018i	−0.321179	+	0.321179i
$932$		0			0
$933$		−	2481.03i		−	2.65919i
$934$		0			0
$935$	−562.446			−0.601546
$936$		0			0
$937$			965.994i			1.03094i	0.856907	+	0.515472i	$0.172383\pi$
$937$			965.994i			1.03094i	−0.856907	+	0.515472i	$0.827617\pi$
$938$		0			0
$939$	1065.92	−	1065.92i	1.13517	−	1.13517i
$940$		0			0
$941$			407.730i			0.433295i	0.976250	+	0.216647i	$0.0695121\pi$
$941$			407.730i			0.433295i	−0.976250	+	0.216647i	$0.930488\pi$
$942$		0			0
$943$	554.443	+	554.443i	0.587957	+	0.587957i
$944$		0			0
$945$	45.3875	−	45.3875i	0.0480291	−	0.0480291i
$946$		0			0
$947$	200.676	−	200.676i	0.211907	−	0.211907i	−0.593170	−	0.805077i	$-0.702124\pi$
$947$	200.676	−	200.676i	0.211907	−	0.211907i	0.805077	+	0.593170i	$0.202124\pi$
$948$		0			0
$949$	68.3012	−	68.3012i	0.0719718	−	0.0719718i
$950$		0			0
$951$	−1492.58			−1.56948
$952$		0			0
$953$	−955.349			−1.00246			−0.501232	−	0.865313i	$-0.667120\pi$
$953$	−955.349			−1.00246			−0.501232	+	0.865313i	$0.667120\pi$
$954$		0			0
$955$	188.927	+	188.927i	0.197829	+	0.197829i
$956$		0			0
$957$	1441.66	+	2745.64i	1.50644	+	2.86900i
$958$		0			0
$959$	−22.2460	+	22.2460i	−0.0231970	+	0.0231970i
$960$		0			0
$961$			884.590i			0.920489i
$962$		0			0
$963$			2017.58i			2.09509i
$964$		0			0
$965$	488.809	+	488.809i	0.506538	+	0.506538i
$966$		0			0
$967$	148.263	+	148.263i	0.153322	+	0.153322i	0.779600	−	0.626278i	$-0.215422\pi$
$967$	148.263	+	148.263i	0.153322	+	0.153322i	−0.626278	+	0.779600i	$0.715422\pi$
$968$		0			0
$969$	−297.256	−	297.256i	−0.306766	−	0.306766i
$970$		0			0
$971$	284.558	−	284.558i	0.293057	−	0.293057i	−0.545230	−	0.838287i	$-0.683558\pi$
$971$	284.558	−	284.558i	0.293057	−	0.293057i	0.838287	+	0.545230i	$0.183558\pi$
$972$		0			0
$973$	−25.2229			−0.0259228
$974$		0			0
$975$	663.171	+	663.171i	0.680175	+	0.680175i
$976$		0			0
$977$	−893.603			−0.914639			−0.457320	−	0.889302i	$-0.651190\pi$
$977$	−893.603			−0.914639			−0.457320	+	0.889302i	$0.651190\pi$
$978$		0			0
$979$		−	769.558i		−	0.786066i
$980$		0			0
$981$	−872.373			−0.889269
$982$		0			0
$983$	263.685	+	263.685i	0.268245	+	0.268245i	0.828393	−	0.560148i	$-0.189256\pi$
$983$	263.685	+	263.685i	0.268245	+	0.268245i	−0.560148	+	0.828393i	$0.689256\pi$
$984$		0			0
$985$			402.388i			0.408515i
$986$		0			0
$987$	−19.7718			−0.0200322
$988$		0			0
$989$	−253.650	+	253.650i	−0.256471	+	0.256471i
$990$		0			0
$991$			905.420i			0.913643i	0.889558	+	0.456821i	$0.151012\pi$
$991$			905.420i			0.913643i	−0.889558	+	0.456821i	$0.848988\pi$
$992$		0			0
$993$	1355.32			1.36487
$994$		0			0
$995$			1149.60i			1.15538i
$996$		0			0
$997$	1236.12	−	1236.12i	1.23984	−	1.23984i	0.279776	−	0.960065i	$-0.409740\pi$
$997$	1236.12	−	1236.12i	1.23984	−	1.23984i	0.960065	−	0.279776i	$-0.0902604\pi$
$998$		0			0
$999$			2041.36i			2.04340i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	464.3.l.c.17.1		8
4.3	odd	2		29.3.c.a.17.1	yes	8
12.11	even	2		261.3.f.a.46.4		8
29.12	odd	4	inner	464.3.l.c.273.1		8
116.99	even	4		29.3.c.a.12.1	✓	8
348.215	odd	4		261.3.f.a.244.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.3.c.a.12.1	✓	8	116.99	even	4
29.3.c.a.17.1	yes	8	4.3	odd	2
261.3.f.a.46.4		8	12.11	even	2
261.3.f.a.244.4		8	348.215	odd	4
464.3.l.c.17.1		8	1.1	even	1	trivial
464.3.l.c.273.1		8	29.12	odd	4	inner

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:	\( N \)	\(=\)	\( 464 = 2^{4} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	464.l (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-3.81178 + 3.81178i) q^{3} +3.14526i q^{5} -0.342313 q^{7} -20.0593i q^{9} +O(q^{10})\)	\(q+(-3.81178 + 3.81178i) q^{3} +3.14526i q^{5} -0.342313 q^{7} -20.0593i q^{9} +(14.0269 - 14.0269i) q^{11} -11.5162i q^{13} +(-11.9890 - 11.9890i) q^{15} +(-6.37430 + 6.37430i) q^{17} +(6.11703 - 6.11703i) q^{19} +(1.30482 - 1.30482i) q^{21} -15.8623 q^{23} +15.1074 q^{25} +(42.1557 + 42.1557i) q^{27} +(25.6758 - 13.4817i) q^{29} +(-6.18103 + 6.18103i) q^{31} +106.935i q^{33} -1.07666i q^{35} +(24.2121 + 24.2121i) q^{37} +(43.8972 + 43.8972i) q^{39} +(-34.9536 - 34.9536i) q^{41} +(15.9908 - 15.9908i) q^{43} +63.0917 q^{45} +(-7.57643 - 7.57643i) q^{47} -48.8828 q^{49} -48.5949i q^{51} +62.1991 q^{53} +(44.1182 + 44.1182i) q^{55} +46.6336i q^{57} +21.4867 q^{59} +(13.1414 - 13.1414i) q^{61} +6.86658i q^{63} +36.2214 q^{65} -17.8272i q^{67} +(60.4635 - 60.4635i) q^{69} +53.0072i q^{71} +(5.93089 + 5.93089i) q^{73} +(-57.5859 + 57.5859i) q^{75} +(-4.80160 + 4.80160i) q^{77} +(81.6782 - 81.6782i) q^{79} -140.843 q^{81} +77.1462 q^{83} +(-20.0488 - 20.0488i) q^{85} +(-46.4812 + 149.259i) q^{87} +(27.4315 - 27.4315i) q^{89} +3.94215i q^{91} -47.1215i q^{93} +(19.2396 + 19.2396i) q^{95} +(48.7308 + 48.7308i) q^{97} +(-281.370 - 281.370i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{3} + 4 q^{7}+O(q^{10}) \) 8 * q + 2 * q^3 + 4 * q^7	\( 8 q + 2 q^{3} + 4 q^{7} + 6 q^{11} + 10 q^{15} + 12 q^{17} + 16 q^{19} - 36 q^{21} + 104 q^{25} + 98 q^{27} + 128 q^{29} + 10 q^{31} - 84 q^{37} + 90 q^{39} + 20 q^{41} + 190 q^{43} + 292 q^{45} - 58 q^{47} - 72 q^{49} + 252 q^{53} + 74 q^{55} + 40 q^{59} - 208 q^{61} + 36 q^{65} + 120 q^{69} - 188 q^{73} + 12 q^{75} + 180 q^{77} + 382 q^{79} - 124 q^{81} - 280 q^{83} + 32 q^{85} - 34 q^{87} - 64 q^{89} + 380 q^{95} - 44 q^{97} - 552 q^{99}+O(q^{100}) \) 8 * q + 2 * q^3 + 4 * q^7 + 6 * q^11 + 10 * q^15 + 12 * q^17 + 16 * q^19 - 36 * q^21 + 104 * q^25 + 98 * q^27 + 128 * q^29 + 10 * q^31 - 84 * q^37 + 90 * q^39 + 20 * q^41 + 190 * q^43 + 292 * q^45 - 58 * q^47 - 72 * q^49 + 252 * q^53 + 74 * q^55 + 40 * q^59 - 208 * q^61 + 36 * q^65 + 120 * q^69 - 188 * q^73 + 12 * q^75 + 180 * q^77 + 382 * q^79 - 124 * q^81 - 280 * q^83 + 32 * q^85 - 34 * q^87 - 64 * q^89 + 380 * q^95 - 44 * q^97 - 552 * q^99

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