LMFDB - Embedded newform 448.4.j.b.335.43

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [448,4,Mod(111,448)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(448, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 2]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("448.111");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$N$	$=$	$448 = 2^{6} \cdot 7$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	448.j (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:	$26.4328556826$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$44$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			335.43
Character	$\chi$	$=$	448.335
Dual form			448.4.j.b.111.43

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(6.75145 - 6.75145i) q^{3} +(10.7426 - 10.7426i) q^{5} +(-7.90955 - 16.7463i) q^{7} -64.1641i q^{9} +(-5.28964 + 5.28964i) q^{11} +(50.4866 + 50.4866i) q^{13} -145.056i q^{15} +17.6955i q^{17} +(63.5461 - 63.5461i) q^{19} +(-166.463 - 59.6609i) q^{21} -7.51181 q^{23} -105.807i q^{25} +(-250.911 - 250.911i) q^{27} +(-153.894 + 153.894i) q^{29} +60.8015 q^{31} +71.4254i q^{33} +(-264.868 - 94.9298i) q^{35} +(129.137 + 129.137i) q^{37} +681.716 q^{39} -48.6217 q^{41} +(-123.020 + 123.020i) q^{43} +(-689.289 - 689.289i) q^{45} +254.748 q^{47} +(-217.878 + 264.912i) q^{49} +(119.470 + 119.470i) q^{51} +(498.959 + 498.959i) q^{53} +113.649i q^{55} -858.056i q^{57} +(-122.203 - 122.203i) q^{59} +(228.300 + 228.300i) q^{61} +(-1074.51 + 507.509i) q^{63} +1084.72 q^{65} +(-360.174 - 360.174i) q^{67} +(-50.7156 + 50.7156i) q^{69} -605.544 q^{71} -913.990 q^{73} +(-714.350 - 714.350i) q^{75} +(130.421 + 46.7433i) q^{77} +885.306i q^{79} -1655.60 q^{81} +(108.532 - 108.532i) q^{83} +(190.095 + 190.095i) q^{85} +2078.01i q^{87} +269.774 q^{89} +(446.138 - 1244.79i) q^{91} +(410.498 - 410.498i) q^{93} -1365.30i q^{95} -1452.58i q^{97} +(339.405 + 339.405i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$88 q + 4 q^{7} - 112 q^{11} + 52 q^{21} - 160 q^{23} + 528 q^{29} - 476 q^{35} - 896 q^{37} + 8 q^{39} - 40 q^{43} - 1376 q^{49} - 1504 q^{51} - 1560 q^{53} - 8 q^{65} - 648 q^{67} + 456 q^{71} + 292 q^{77}+ \cdots - 7592 q^{99}+O(q^{100})$ 88 * q + 4 * q^7 - 112 * q^11 + 52 * q^21 - 160 * q^23 + 528 * q^29 - 476 * q^35 - 896 * q^37 + 8 * q^39 - 40 * q^43 - 1376 * q^49 - 1504 * q^51 - 1560 * q^53 - 8 * q^65 - 648 * q^67 + 456 * q^71 + 292 * q^77 - 1952 * q^81 + 496 * q^85 + 1964 * q^91 - 112 * q^93 - 7592 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/448\mathbb{Z}\right)^\times$ .

$n$	$127$	$129$	$197$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{4}\right)$

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
$3$	6.75145	−	6.75145i	1.29932	−	1.29932i	0.370474	−	0.928843i	$-0.379195\pi$
$3$	6.75145	−	6.75145i	1.29932	−	1.29932i	0.928843	−	0.370474i	$-0.120805\pi$
$4$		0			0
$5$	10.7426	−	10.7426i	0.960848	−	0.960848i	−0.0384144	−	0.999262i	$-0.512231\pi$
$5$	10.7426	−	10.7426i	0.960848	−	0.960848i	0.999262	+	0.0384144i	$0.0122307\pi$
$6$		0			0
$7$	−7.90955	−	16.7463i	−0.427076	−	0.904216i
$7$	−7.90955	−	16.7463i	−0.427076	−	0.904216i
$8$		0			0
$9$		−	64.1641i		−	2.37645i
$10$		0			0
$11$	−5.28964	+	5.28964i	−0.144990	+	0.144990i	−0.775876	−	0.630886i	$-0.782692\pi$
$11$	−5.28964	+	5.28964i	−0.144990	+	0.144990i	0.630886	+	0.775876i	$0.282692\pi$
$12$		0			0
$13$	50.4866	+	50.4866i	1.07711	+	1.07711i	0.996767	+	0.0803460i	$0.0256025\pi$
$13$	50.4866	+	50.4866i	1.07711	+	1.07711i	0.0803460	+	0.996767i	$0.474397\pi$
$14$		0			0
$15$		−	145.056i		−	2.49689i
$16$		0			0
$17$			17.6955i			0.252458i	0.992001	+	0.126229i	$0.0402874\pi$
$17$			17.6955i			0.252458i	−0.992001	+	0.126229i	$0.959713\pi$
$18$		0			0
$19$	63.5461	−	63.5461i	0.767288	−	0.767288i	−0.210340	−	0.977628i	$-0.567457\pi$
$19$	63.5461	−	63.5461i	0.767288	−	0.767288i	0.977628	+	0.210340i	$0.0674572\pi$
$20$		0			0
$21$	−166.463	−	59.6609i	−1.72977	−	0.619956i
$22$		0			0
$23$	−7.51181			−0.0681009			−0.0340504	−	0.999420i	$-0.510841\pi$
$23$	−7.51181			−0.0681009			−0.0340504	+	0.999420i	$0.510841\pi$
$24$		0			0
$25$		−	105.807i		−	0.846456i
$26$		0			0
$27$	−250.911	−	250.911i	−1.78844	−	1.78844i
$28$		0			0
$29$	−153.894	+	153.894i	−0.985425	+	0.985425i	−0.999895	−	0.0144699i	$-0.995394\pi$
$29$	−153.894	+	153.894i	−0.985425	+	0.985425i	0.0144699	+	0.999895i	$0.495394\pi$
$30$		0			0
$31$	60.8015			0.352267			0.176133	−	0.984366i	$-0.443641\pi$
$31$	60.8015			0.352267			0.176133	+	0.984366i	$0.443641\pi$
$32$		0			0
$33$			71.4254i			0.376775i
$34$		0			0
$35$	−264.868	−	94.9298i	−1.27917	−	0.458459i
$36$		0			0
$37$	129.137	+	129.137i	0.573784	+	0.573784i	0.933184	−	0.359399i	$-0.117018\pi$
$37$	129.137	+	129.137i	0.573784	+	0.573784i	−0.359399	+	0.933184i	$0.617018\pi$
$38$		0			0
$39$	681.716			2.79902
$40$		0			0
$41$	−48.6217			−0.185206			−0.0926029	−	0.995703i	$-0.529519\pi$
$41$	−48.6217			−0.185206			−0.0926029	+	0.995703i	$0.529519\pi$
$42$		0			0
$43$	−123.020	+	123.020i	−0.436289	+	0.436289i	−0.890761	−	0.454472i	$-0.849828\pi$
$43$	−123.020	+	123.020i	−0.436289	+	0.436289i	0.454472	+	0.890761i	$0.349828\pi$
$44$		0			0
$45$	−689.289	−	689.289i	−2.28340	−	2.28340i
$46$		0			0
$47$	254.748			0.790612			0.395306	−	0.918550i	$-0.370639\pi$
$47$	254.748			0.790612			0.395306	+	0.918550i	$0.370639\pi$
$48$		0			0
$49$	−217.878	+	264.912i	−0.635213	+	0.772337i
$50$		0			0
$51$	119.470	+	119.470i	0.328023	+	0.328023i
$52$		0			0
$53$	498.959	+	498.959i	1.29316	+	1.29316i	0.932823	+	0.360334i	$0.117337\pi$
$53$	498.959	+	498.959i	1.29316	+	1.29316i	0.360334	+	0.932823i	$0.382663\pi$
$54$		0			0
$55$			113.649i			0.278626i
$56$		0			0
$57$		−	858.056i		−	1.99390i
$58$		0			0
$59$	−122.203	−	122.203i	−0.269652	−	0.269652i	0.559308	−	0.828960i	$-0.311067\pi$
$59$	−122.203	−	122.203i	−0.269652	−	0.269652i	−0.828960	+	0.559308i	$0.811067\pi$
$60$		0			0
$61$	228.300	+	228.300i	0.479194	+	0.479194i	0.904874	−	0.425680i	$-0.139965\pi$
$61$	228.300	+	228.300i	0.479194	+	0.479194i	−0.425680	+	0.904874i	$0.639965\pi$
$62$		0			0
$63$	−1074.51	+	507.509i	−2.14882	+	1.01492i
$64$		0			0
$65$	1084.72			2.06988
$66$		0			0
$67$	−360.174	−	360.174i	−0.656750	−	0.656750i	0.297860	−	0.954610i	$-0.403727\pi$
$67$	−360.174	−	360.174i	−0.656750	−	0.656750i	−0.954610	+	0.297860i	$0.903727\pi$
$68$		0			0
$69$	−50.7156	+	50.7156i	−0.0884846	+	0.0884846i
$70$		0			0
$71$	−605.544			−1.01218			−0.506091	−	0.862480i	$-0.668910\pi$
$71$	−605.544			−1.01218			−0.506091	+	0.862480i	$0.668910\pi$
$72$		0			0
$73$	−913.990			−1.46540			−0.732702	−	0.680550i	$-0.761741\pi$
$73$	−913.990			−1.46540			−0.732702	+	0.680550i	$0.761741\pi$
$74$		0			0
$75$	−714.350	−	714.350i	−1.09981	−	1.09981i
$76$		0			0
$77$	130.421	+	46.7433i	0.193024	+	0.0691804i
$78$		0			0
$79$			885.306i			1.26082i	0.776263	+	0.630410i	$0.217113\pi$
$79$			885.306i			1.26082i	−0.776263	+	0.630410i	$0.782887\pi$
$80$		0			0
$81$	−1655.60			−2.27105
$82$		0			0
$83$	108.532	−	108.532i	0.143530	−	0.143530i	−0.631691	−	0.775221i	$-0.717639\pi$
$83$	108.532	−	108.532i	0.143530	−	0.143530i	0.775221	+	0.631691i	$0.217639\pi$
$84$		0			0
$85$	190.095	+	190.095i	0.242573	+	0.242573i
$86$		0			0
$87$			2078.01i			2.56076i
$88$		0			0
$89$	269.774			0.321304			0.160652	−	0.987011i	$-0.448640\pi$
$89$	269.774			0.321304			0.160652	+	0.987011i	$0.448640\pi$
$90$		0			0
$91$	446.138	−	1244.79i	0.513934	−	1.43395i
$92$		0			0
$93$	410.498	−	410.498i	0.457706	−	0.457706i
$94$		0			0
$95$		−	1365.30i		−	1.47449i
$96$		0			0
$97$		−	1452.58i		−	1.52049i	−0.649639	−	0.760243i	$-0.725080\pi$
$97$		−	1452.58i		−	1.52049i	0.649639	−	0.760243i	$-0.274920\pi$
$98$		0			0
$99$	339.405	+	339.405i	0.344560	+	0.344560i
$100$		0			0
$101$	−32.6448	+	32.6448i	−0.0321612	+	0.0321612i	−0.723004	−	0.690843i	$-0.757239\pi$
$101$	−32.6448	+	32.6448i	−0.0321612	+	0.0321612i	0.690843	+	0.723004i	$0.257239\pi$
$102$		0			0
$103$		−	1486.69i		−	1.42221i	−0.703086	−	0.711105i	$-0.748195\pi$
$103$		−	1486.69i		−	1.42221i	0.703086	−	0.711105i	$-0.251805\pi$
$104$		0			0
$105$	−2429.16	+	1147.33i	−2.25773	+	1.06636i
$106$		0			0
$107$	973.114	−	973.114i	0.879201	−	0.879201i	−0.114251	−	0.993452i	$-0.536447\pi$
$107$	973.114	−	973.114i	0.879201	−	0.879201i	0.993452	+	0.114251i	$0.0364468\pi$
$108$		0			0
$109$	266.730	−	266.730i	0.234386	−	0.234386i	−0.580134	−	0.814521i	$-0.697000\pi$
$109$	266.730	−	266.730i	0.234386	−	0.234386i	0.814521	+	0.580134i	$0.197000\pi$
$110$		0			0
$111$	1743.73			1.49106
$112$		0			0
$113$	93.8639			0.0781414			0.0390707	−	0.999236i	$-0.487560\pi$
$113$	93.8639			0.0781414			0.0390707	+	0.999236i	$0.487560\pi$
$114$		0			0
$115$	−80.6964	+	80.6964i	−0.0654346	+	0.0654346i
$116$		0			0
$117$	3239.43	−	3239.43i	2.55970	−	2.55970i
$118$		0			0
$119$	296.334	−	139.963i	0.228276	−	0.107819i
$120$		0			0
$121$			1275.04i			0.957956i
$122$		0			0
$123$	−328.267	+	328.267i	−0.240641	+	0.240641i
$124$		0			0
$125$	206.183	+	206.183i	0.147532	+	0.147532i
$126$		0			0
$127$		−	18.1807i		−	0.0127030i	−0.999980	−	0.00635148i	$-0.997978\pi$
$127$		−	18.1807i		−	0.0127030i	0.999980	−	0.00635148i	$-0.00202175\pi$
$128$		0			0
$129$			1661.13i			1.13376i
$130$		0			0
$131$	−989.922	+	989.922i	−0.660228	+	0.660228i	−0.955434	−	0.295206i	$-0.904612\pi$
$131$	−989.922	+	989.922i	−0.660228	+	0.660228i	0.295206	+	0.955434i	$0.404612\pi$
$132$		0			0
$133$	−1566.78	−	561.541i	−1.02148	−	0.366104i
$134$		0			0
$135$	−5390.88			−3.43684
$136$		0			0
$137$		−	2748.38i		−	1.71394i	−0.515363	−	0.856972i	$-0.672343\pi$
$137$		−	2748.38i		−	1.71394i	0.515363	−	0.856972i	$-0.327657\pi$
$138$		0			0
$139$	1356.64	+	1356.64i	0.827830	+	0.827830i	0.987216	−	0.159387i	$-0.0509516\pi$
$139$	1356.64	+	1356.64i	0.827830	+	0.827830i	−0.159387	+	0.987216i	$0.550952\pi$
$140$		0			0
$141$	1719.91	−	1719.91i	1.02726	−	1.02726i
$142$		0			0
$143$	−534.112			−0.312341
$144$		0			0
$145$			3306.44i			1.89369i
$146$		0			0
$147$	317.546	+	3259.53i	0.178169	+	1.82885i
$148$		0			0
$149$	−1086.44	−	1086.44i	−0.597345	−	0.597345i	0.342260	−	0.939605i	$-0.388808\pi$
$149$	−1086.44	−	1086.44i	−0.597345	−	0.597345i	−0.939605	+	0.342260i	$0.888808\pi$
$150$		0			0
$151$	−270.825			−0.145957			−0.0729784	−	0.997334i	$-0.523250\pi$
$151$	−270.825			−0.145957			−0.0729784	+	0.997334i	$0.523250\pi$
$152$		0			0
$153$	1135.41			0.599953
$154$		0			0
$155$	653.166	−	653.166i	0.338475	−	0.338475i
$156$		0			0
$157$	−360.348	−	360.348i	−0.183178	−	0.183178i	0.609561	−	0.792739i	$-0.291346\pi$
$157$	−360.348	−	360.348i	−0.183178	−	0.183178i	−0.792739	+	0.609561i	$0.791346\pi$
$158$		0			0
$159$	6737.39			3.36044
$160$		0			0
$161$	59.4151	+	125.795i	0.0290842	+	0.0615779i
$162$		0			0
$163$	−1755.20	−	1755.20i	−0.843422	−	0.843422i	0.145880	−	0.989302i	$-0.453399\pi$
$163$	−1755.20	−	1755.20i	−0.843422	−	0.843422i	−0.989302	+	0.145880i	$0.953399\pi$
$164$		0			0
$165$	767.295	+	767.295i	0.362023	+	0.362023i
$166$		0			0
$167$			1281.85i			0.593968i	0.954882	+	0.296984i	$0.0959808\pi$
$167$			1281.85i			0.593968i	−0.954882	+	0.296984i	$0.904019\pi$
$168$		0			0
$169$			2900.80i			1.32035i
$170$		0			0
$171$	−4077.37	−	4077.37i	−1.82342	−	1.82342i
$172$		0			0
$173$	−54.8132	−	54.8132i	−0.0240888	−	0.0240888i	0.694960	−	0.719049i	$-0.255422\pi$
$173$	−54.8132	−	54.8132i	−0.0240888	−	0.0240888i	−0.719049	+	0.694960i	$0.755422\pi$
$174$		0			0
$175$	−1771.88	+	836.886i	−0.765379	+	0.361501i
$176$		0			0
$177$	−1650.10			−0.700727
$178$		0			0
$179$	1497.55	+	1497.55i	0.625320	+	0.625320i	0.946887	−	0.321567i	$-0.104210\pi$
$179$	1497.55	+	1497.55i	0.625320	+	0.625320i	−0.321567	+	0.946887i	$0.604210\pi$
$180$		0			0
$181$	3092.20	−	3092.20i	1.26984	−	1.26984i	0.323675	−	0.946168i	$-0.395082\pi$
$181$	3092.20	−	3092.20i	1.26984	−	1.26984i	0.946168	−	0.323675i	$-0.104918\pi$
$182$		0			0
$183$	3082.72			1.24525
$184$		0			0
$185$	2774.54			1.10264
$186$		0			0
$187$	−93.6027	−	93.6027i	−0.0366038	−	0.0366038i
$188$		0			0
$189$	−2217.24	+	6186.44i	−0.853337	+	2.38094i
$190$		0			0
$191$			880.871i			0.333705i	0.985982	+	0.166852i	$0.0533603\pi$
$191$			880.871i			0.333705i	−0.985982	+	0.166852i	$0.946640\pi$
$192$		0			0
$193$	4562.97			1.70181			0.850905	−	0.525319i	$-0.176054\pi$
$193$	4562.97			1.70181			0.850905	+	0.525319i	$0.176054\pi$
$194$		0			0
$195$	7323.40	−	7323.40i	2.68943	−	2.68943i
$196$		0			0
$197$	1121.88	+	1121.88i	0.405738	+	0.405738i	0.880249	−	0.474512i	$-0.157375\pi$
$197$	1121.88	+	1121.88i	0.405738	+	0.405738i	−0.474512	+	0.880249i	$0.657375\pi$
$198$		0			0
$199$			1396.02i			0.497293i	0.968594	+	0.248646i	$0.0799857\pi$
$199$			1396.02i			0.497293i	−0.968594	+	0.248646i	$0.920014\pi$
$200$		0			0
$201$	−4863.39			−1.70665
$202$		0			0
$203$	3794.38	+	1359.92i	1.31189	+	0.470186i
$204$		0			0
$205$	−522.324	+	522.324i	−0.177955	+	0.177955i
$206$		0			0
$207$			481.988i			0.161838i
$208$		0			0
$209$			672.272i			0.222498i
$210$		0			0
$211$	763.850	+	763.850i	0.249221	+	0.249221i	0.820651	−	0.571430i	$-0.193611\pi$
$211$	763.850	+	763.850i	0.249221	+	0.249221i	−0.571430	+	0.820651i	$0.693611\pi$
$212$		0			0
$213$	−4088.30	+	4088.30i	−1.31514	+	1.31514i
$214$		0			0
$215$			2643.12i			0.838415i
$216$		0			0
$217$	−480.913	−	1018.20i	−0.150445	−	0.318525i
$218$		0			0
$219$	−6170.76	+	6170.76i	−1.90402	+	1.90402i
$220$		0			0
$221$	−893.385	+	893.385i	−0.271926	+	0.271926i
$222$		0			0
$223$	−3793.85			−1.13926			−0.569631	−	0.821901i	$-0.692914\pi$
$223$	−3793.85			−1.13926			−0.569631	+	0.821901i	$0.692914\pi$
$224$		0			0
$225$	−6789.01			−2.01156
$226$		0			0
$227$	−1146.33	+	1146.33i	−0.335173	+	0.335173i	−0.854547	−	0.519374i	$-0.826165\pi$
$227$	−1146.33	+	1146.33i	−0.335173	+	0.335173i	0.519374	+	0.854547i	$0.326165\pi$
$228$		0			0
$229$	2144.18	−	2144.18i	0.618740	−	0.618740i	−0.326468	−	0.945208i	$-0.605859\pi$
$229$	2144.18	−	2144.18i	0.618740	−	0.618740i	0.945208	+	0.326468i	$0.105859\pi$
$230$		0			0
$231$	1196.11	−	564.943i	0.340686	−	0.160911i
$232$		0			0
$233$			614.860i			0.172879i	0.996257	+	0.0864395i	$0.0275489\pi$
$233$			614.860i			0.172879i	−0.996257	+	0.0864395i	$0.972451\pi$
$234$		0			0
$235$	2736.65	−	2736.65i	0.759657	−	0.759657i
$236$		0			0
$237$	5977.10	+	5977.10i	1.63820	+	1.63820i
$238$		0			0
$239$			4263.99i			1.15404i	0.816731	+	0.577018i	$0.195784\pi$
$239$			4263.99i			1.15404i	−0.816731	+	0.577018i	$0.804216\pi$
$240$		0			0
$241$			2731.19i			0.730006i	0.931006	+	0.365003i	$0.118932\pi$
$241$			2731.19i			0.730006i	−0.931006	+	0.365003i	$0.881068\pi$
$242$		0			0
$243$	−4403.08	+	4403.08i	−1.16238	+	1.16238i
$244$		0			0
$245$	505.266	+	5186.42i	0.131756	+	1.35244i
$246$		0			0
$247$	6416.45			1.65291
$248$		0			0
$249$		−	1465.50i		−	0.372981i
$250$		0			0
$251$	975.121	+	975.121i	0.245216	+	0.245216i	0.819004	−	0.573788i	$-0.194527\pi$
$251$	975.121	+	975.121i	0.245216	+	0.245216i	−0.573788	+	0.819004i	$0.694527\pi$
$252$		0			0
$253$	39.7348	−	39.7348i	0.00987393	−	0.00987393i
$254$		0			0
$255$	2566.84			0.630359
$256$		0			0
$257$			6513.55i			1.58095i	0.612495	+	0.790475i	$0.290166\pi$
$257$			6513.55i			1.58095i	−0.612495	+	0.790475i	$0.709834\pi$
$258$		0			0
$259$	1141.15	−	3183.99i	0.273776	−	0.763874i
$260$		0			0
$261$	9874.45	+	9874.45i	2.34181	+	2.34181i
$262$		0			0
$263$	−802.056			−0.188049			−0.0940245	−	0.995570i	$-0.529973\pi$
$263$	−802.056			−0.188049			−0.0940245	+	0.995570i	$0.529973\pi$
$264$		0			0
$265$	10720.2			2.48505
$266$		0			0
$267$	1821.37	−	1821.37i	0.417475	−	0.417475i
$268$		0			0
$269$	−2029.90	−	2029.90i	−0.460094	−	0.460094i	0.438592	−	0.898686i	$-0.355477\pi$
$269$	−2029.90	−	2029.90i	−0.460094	−	0.460094i	−0.898686	+	0.438592i	$0.855477\pi$
$270$		0			0
$271$	2449.85			0.549143			0.274572	−	0.961567i	$-0.411464\pi$
$271$	2449.85			0.549143			0.274572	+	0.961567i	$0.411464\pi$
$272$		0			0
$273$	−5392.07	−	11416.2i	−1.19539	−	2.53092i
$274$		0			0
$275$	559.681	+	559.681i	0.122727	+	0.122727i
$276$		0			0
$277$	−3804.74	−	3804.74i	−0.825288	−	0.825288i	0.161573	−	0.986861i	$-0.448343\pi$
$277$	−3804.74	−	3804.74i	−0.825288	−	0.825288i	−0.986861	+	0.161573i	$0.948343\pi$
$278$		0			0
$279$		−	3901.27i		−	0.837144i
$280$		0			0
$281$		−	5469.38i		−	1.16112i	−0.814216	−	0.580562i	$-0.802833\pi$
$281$		−	5469.38i		−	1.16112i	0.814216	−	0.580562i	$-0.197167\pi$
$282$		0			0
$283$	−2997.42	−	2997.42i	−0.629606	−	0.629606i	0.318363	−	0.947969i	$-0.396867\pi$
$283$	−2997.42	−	2997.42i	−0.629606	−	0.629606i	−0.947969	+	0.318363i	$0.896867\pi$
$284$		0			0
$285$	−9217.75	−	9217.75i	−1.91583	−	1.91583i
$286$		0			0
$287$	384.576	+	814.235i	0.0790970	+	0.167466i
$288$		0			0
$289$	4599.87			0.936265
$290$		0			0
$291$	−9807.02	−	9807.02i	−1.97559	−	1.97559i
$292$		0			0
$293$	−4777.03	+	4777.03i	−0.952482	+	0.952482i	−0.998921	−	0.0464390i	$-0.985213\pi$
$293$	−4777.03	+	4777.03i	−0.952482	+	0.952482i	0.0464390	+	0.998921i	$0.485213\pi$
$294$		0			0
$295$	−2625.56			−0.518190
$296$		0			0
$297$	2654.46			0.518611
$298$		0			0
$299$	−379.246	−	379.246i	−0.0733524	−	0.0733524i
$300$		0			0
$301$	3033.18	+	1087.10i	0.580828	+	0.208171i
$302$		0			0
$303$			440.799i			0.0835751i
$304$		0			0
$305$	4905.08			0.920866
$306$		0			0
$307$	−1382.11	+	1382.11i	−0.256941	+	0.256941i	−0.823809	−	0.566868i	$-0.808155\pi$
$307$	−1382.11	+	1382.11i	−0.256941	+	0.256941i	0.566868	+	0.823809i	$0.308155\pi$
$308$		0			0
$309$	−10037.3	−	10037.3i	−1.84790	−	1.84790i
$310$		0			0
$311$			4113.03i			0.749931i	0.927039	+	0.374966i	$0.122346\pi$
$311$			4113.03i			0.749931i	−0.927039	+	0.374966i	$0.877654\pi$
$312$		0			0
$313$	1183.14			0.213659			0.106829	−	0.994277i	$-0.465930\pi$
$313$	1183.14			0.213659			0.106829	+	0.994277i	$0.465930\pi$
$314$		0			0
$315$	−6091.08	+	16995.0i	−1.08950	+	3.03988i
$316$		0			0
$317$	1538.47	−	1538.47i	0.272584	−	0.272584i	−0.557556	−	0.830140i	$-0.688261\pi$
$317$	1538.47	−	1538.47i	0.272584	−	0.272584i	0.830140	+	0.557556i	$0.188261\pi$
$318$		0			0
$319$		−	1628.08i		−	0.285753i
$320$		0			0
$321$		−	13139.9i		−	2.28472i
$322$		0			0
$323$	1124.48	+	1124.48i	0.193708	+	0.193708i
$324$		0			0
$325$	5341.84	−	5341.84i	0.911729	−	0.911729i
$326$		0			0
$327$		−	3601.63i		−	0.609084i
$328$		0			0
$329$	−2014.94	−	4266.08i	−0.337651	−	0.714884i
$330$		0			0
$331$	−1870.74	+	1870.74i	−0.310651	+	0.310651i	−0.845162	−	0.534511i	$-0.820496\pi$
$331$	−1870.74	+	1870.74i	−0.310651	+	0.310651i	0.534511	+	0.845162i	$0.320496\pi$
$332$		0			0
$333$	8285.97	−	8285.97i	1.36357	−	1.36357i
$334$		0			0
$335$	−7738.41			−1.26207
$336$		0			0
$337$	2561.19			0.413997			0.206999	−	0.978341i	$-0.433630\pi$
$337$	2561.19			0.413997			0.206999	+	0.978341i	$0.433630\pi$
$338$		0			0
$339$	633.717	−	633.717i	0.101530	−	0.101530i
$340$		0			0
$341$	−321.618	+	321.618i	−0.0510751	+	0.0510751i
$342$		0			0
$343$	6159.61	+	1553.32i	0.969644	+	0.244523i
$344$		0			0
$345$			1089.63i			0.170040i
$346$		0			0
$347$	7775.33	−	7775.33i	1.20289	−	1.20289i	0.229601	−	0.973285i	$-0.426258\pi$
$347$	7775.33	−	7775.33i	1.20289	−	1.20289i	0.973285	−	0.229601i	$-0.0737421\pi$
$348$		0			0
$349$	−5078.97	−	5078.97i	−0.778999	−	0.778999i	0.200661	−	0.979661i	$-0.435691\pi$
$349$	−5078.97	−	5078.97i	−0.778999	−	0.778999i	−0.979661	+	0.200661i	$0.935691\pi$
$350$		0			0
$351$		−	25335.3i		−	3.85271i
$352$		0			0
$353$			321.509i			0.0484764i	0.999706	+	0.0242382i	$0.00771602\pi$
$353$			321.509i			0.0484764i	−0.999706	+	0.0242382i	$0.992284\pi$
$354$		0			0
$355$	−6505.12	+	6505.12i	−0.972552	+	0.972552i
$356$		0			0
$357$	1055.73	−	2945.64i	0.156513	−	0.436694i
$358$		0			0
$359$	−8216.04			−1.20787			−0.603936	−	0.797033i	$-0.706402\pi$
$359$	−8216.04			−1.20787			−0.603936	+	0.797033i	$0.706402\pi$
$360$		0			0
$361$		−	1217.21i		−	0.177461i
$362$		0			0
$363$	8608.36	+	8608.36i	1.24469	+	1.24469i
$364$		0			0
$365$	−9818.64	+	9818.64i	−1.40803	+	1.40803i
$366$		0			0
$367$	−2600.73			−0.369910			−0.184955	−	0.982747i	$-0.559214\pi$
$367$	−2600.73			−0.369910			−0.184955	+	0.982747i	$0.559214\pi$
$368$		0			0
$369$			3119.77i			0.440132i
$370$		0			0
$371$	4409.18	−	12302.3i	0.617017	−	1.72157i
$372$		0			0
$373$	−1438.00	−	1438.00i	−0.199616	−	0.199616i	0.600219	−	0.799835i	$-0.295080\pi$
$373$	−1438.00	−	1438.00i	−0.199616	−	0.199616i	−0.799835	+	0.600219i	$0.795080\pi$
$374$		0			0
$375$	2784.07			0.383383
$376$		0			0
$377$	−15539.1			−2.12283
$378$		0			0
$379$	5788.76	−	5788.76i	0.784561	−	0.784561i	−0.196036	−	0.980597i	$-0.562807\pi$
$379$	5788.76	−	5788.76i	0.784561	−	0.784561i	0.980597	+	0.196036i	$0.0628069\pi$
$380$		0			0
$381$	−122.746	−	122.746i	−0.0165052	−	0.0165052i
$382$		0			0
$383$	−1861.45			−0.248344			−0.124172	−	0.992261i	$-0.539627\pi$
$383$	−1861.45			−0.248344			−0.124172	+	0.992261i	$0.539627\pi$
$384$		0			0
$385$	1903.20	−	898.913i	0.251938	−	0.118994i
$386$		0			0
$387$	7893.49	+	7893.49i	1.03682	+	1.03682i
$388$		0			0
$389$	−9938.04	−	9938.04i	−1.29532	−	1.29532i	−0.931451	−	0.363866i	$-0.881457\pi$
$389$	−9938.04	−	9938.04i	−1.29532	−	1.29532i	−0.363866	−	0.931451i	$-0.618543\pi$
$390$		0			0
$391$		−	132.925i		−	0.0171926i
$392$		0			0
$393$			13366.8i			1.71569i
$394$		0			0
$395$	9510.49	+	9510.49i	1.21146	+	1.21146i
$396$		0			0
$397$	2937.95	+	2937.95i	0.371414	+	0.371414i	0.867992	−	0.496578i	$-0.165410\pi$
$397$	2937.95	+	2937.95i	0.371414	+	0.371414i	−0.496578	+	0.867992i	$0.665410\pi$
$398$		0			0
$399$	−14369.3	+	6786.84i	−1.80292	+	0.851546i
$400$		0			0
$401$	575.655			0.0716879			0.0358440	−	0.999357i	$-0.488588\pi$
$401$	575.655			0.0716879			0.0358440	+	0.999357i	$0.488588\pi$
$402$		0			0
$403$	3069.66	+	3069.66i	0.379431	+	0.379431i
$404$		0			0
$405$	−17785.4	+	17785.4i	−2.18214	+	2.18214i
$406$		0			0
$407$	−1366.18			−0.166386
$408$		0			0
$409$	−1575.07			−0.190421			−0.0952105	−	0.995457i	$-0.530352\pi$
$409$	−1575.07			−0.190421			−0.0952105	+	0.995457i	$0.530352\pi$
$410$		0			0
$411$	−18555.6	−	18555.6i	−2.22696	−	2.22696i
$412$		0			0
$413$	−1079.88	+	3013.02i	−0.128662	+	0.358986i
$414$		0			0
$415$		−	2331.84i		−	0.275821i
$416$		0			0
$417$	18318.5			2.15123
$418$		0			0
$419$	−6534.27	+	6534.27i	−0.761862	+	0.761862i	−0.976659	−	0.214797i	$-0.931091\pi$
$419$	−6534.27	+	6534.27i	−0.761862	+	0.761862i	0.214797	+	0.976659i	$0.431091\pi$
$420$		0			0
$421$	5564.69	+	5564.69i	0.644196	+	0.644196i	0.951584	−	0.307388i	$-0.0994550\pi$
$421$	5564.69	+	5564.69i	0.644196	+	0.644196i	−0.307388	+	0.951584i	$0.599455\pi$
$422$		0			0
$423$		−	16345.6i		−	1.87885i
$424$		0			0
$425$	1872.30			0.213694
$426$		0			0
$427$	2017.43	−	5628.94i	0.228643	−	0.637948i
$428$		0			0
$429$	−3606.03	+	3606.03i	−0.405829	+	0.405829i
$430$		0			0
$431$			8245.08i			0.921465i	0.887539	+	0.460733i	$0.152413\pi$
$431$			8245.08i			0.921465i	−0.887539	+	0.460733i	$0.847587\pi$
$432$		0			0
$433$		−	6790.68i		−	0.753670i	−0.926280	−	0.376835i	$-0.877012\pi$
$433$		−	6790.68i		−	0.753670i	0.926280	−	0.376835i	$-0.122988\pi$
$434$		0			0
$435$	22323.2	+	22323.2i	2.46050	+	2.46050i
$436$		0			0
$437$	−477.346	+	477.346i	−0.0522530	+	0.0522530i
$438$		0			0
$439$		−	8798.44i		−	0.956553i	−0.878209	−	0.478276i	$-0.841262\pi$
$439$		−	8798.44i		−	0.956553i	0.878209	−	0.478276i	$-0.158738\pi$
$440$		0			0
$441$	16997.8	+	13979.9i	1.83542	+	1.50955i
$442$		0			0
$443$	−11899.1	+	11899.1i	−1.27617	+	1.27617i	−0.333374	+	0.942795i	$0.608187\pi$
$443$	−11899.1	+	11899.1i	−1.27617	+	1.27617i	−0.942795	+	0.333374i	$0.891813\pi$
$444$		0			0
$445$	2898.08	−	2898.08i	0.308724	−	0.308724i
$446$		0			0
$447$	−14670.1			−1.55228
$448$		0			0
$449$	−5778.61			−0.607370			−0.303685	−	0.952772i	$-0.598217\pi$
$449$	−5778.61			−0.607370			−0.303685	+	0.952772i	$0.598217\pi$
$450$		0			0
$451$	257.192	−	257.192i	0.0268529	−	0.0268529i
$452$		0			0
$453$	−1828.46	+	1828.46i	−0.189644	+	0.189644i
$454$		0			0
$455$	−8579.62	−	18165.0i	−0.883997	−	1.87162i
$456$		0			0
$457$			13073.2i			1.33816i	0.743190	+	0.669080i	$0.233312\pi$
$457$			13073.2i			1.33816i	−0.743190	+	0.669080i	$0.766688\pi$
$458$		0			0
$459$	4439.99	−	4439.99i	0.451506	−	0.451506i
$460$		0			0
$461$	4275.73	+	4275.73i	0.431976	+	0.431976i	0.889300	−	0.457324i	$-0.151192\pi$
$461$	4275.73	+	4275.73i	0.431976	+	0.431976i	−0.457324	+	0.889300i	$0.651192\pi$
$462$		0			0
$463$			7519.45i			0.754770i	0.926056	+	0.377385i	$0.123177\pi$
$463$			7519.45i			0.754770i	−0.926056	+	0.377385i	$0.876823\pi$
$464$		0			0
$465$		−	8819.64i		−	0.879572i
$466$		0			0
$467$	−6745.11	+	6745.11i	−0.668365	+	0.668365i	−0.957337	−	0.288972i	$-0.906686\pi$
$467$	−6745.11	+	6745.11i	−0.668365	+	0.668365i	0.288972	+	0.957337i	$0.406686\pi$
$468$		0			0
$469$	−3182.77	+	8880.40i	−0.313362	+	0.874326i
$470$		0			0
$471$	−4865.74			−0.476012
$472$		0			0
$473$		−	1301.47i		−	0.126515i
$474$		0			0
$475$	−6723.62	−	6723.62i	−0.649475	−	0.649475i
$476$		0			0
$477$	32015.3	−	32015.3i	3.07312	−	3.07312i
$478$		0			0
$479$	5722.39			0.545851			0.272925	−	0.962035i	$-0.412009\pi$
$479$	5722.39			0.545851			0.272925	+	0.962035i	$0.412009\pi$
$480$		0			0
$481$			13039.4i			1.23606i
$482$		0			0
$483$	1250.44	+	448.161i	0.117799	+	0.0422196i
$484$		0			0
$485$	−15604.5	−	15604.5i	−1.46096	−	1.46096i
$486$		0			0
$487$	14286.2			1.32930			0.664651	−	0.747154i	$-0.268580\pi$
$487$	14286.2			1.32930			0.664651	+	0.747154i	$0.268580\pi$
$488$		0			0
$489$	−23700.3			−2.19175
$490$		0			0
$491$	2041.06	−	2041.06i	0.187600	−	0.187600i	−0.607057	−	0.794658i	$-0.707650\pi$
$491$	2041.06	−	2041.06i	0.187600	−	0.187600i	0.794658	+	0.607057i	$0.207650\pi$
$492$		0			0
$493$	−2723.22	−	2723.22i	−0.248778	−	0.248778i
$494$		0			0
$495$	7292.18			0.662140
$496$		0			0
$497$	4789.58	+	10140.6i	0.432278	+	0.915230i
$498$		0			0
$499$	−8527.48	−	8527.48i	−0.765015	−	0.765015i	0.212209	−	0.977224i	$-0.431934\pi$
$499$	−8527.48	−	8527.48i	−0.765015	−	0.765015i	−0.977224	+	0.212209i	$0.931934\pi$
$500$		0			0
$501$	8654.36	+	8654.36i	0.771753	+	0.771753i
$502$		0			0
$503$			5920.19i			0.524788i	0.964961	+	0.262394i	$0.0845120\pi$
$503$			5920.19i			0.524788i	−0.964961	+	0.262394i	$0.915488\pi$
$504$		0			0
$505$			701.380i			0.0618039i
$506$		0			0
$507$	19584.6	+	19584.6i	1.71555	+	1.71555i
$508$		0			0
$509$	−6278.29	−	6278.29i	−0.546719	−	0.546719i	0.378771	−	0.925490i	$-0.376347\pi$
$509$	−6278.29	−	6278.29i	−0.546719	−	0.546719i	−0.925490	+	0.378771i	$0.876347\pi$
$510$		0			0
$511$	7229.26	+	15306.0i	0.625839	+	1.32504i
$512$		0			0
$513$	−31888.9			−2.74450
$514$		0			0
$515$	−15970.9	−	15970.9i	−1.36653	−	1.36653i
$516$		0			0
$517$	−1347.52	+	1347.52i	−0.114631	+	0.114631i
$518$		0			0
$519$	−740.137			−0.0625981
$520$		0			0
$521$	−6389.95			−0.537330			−0.268665	−	0.963234i	$-0.586582\pi$
$521$	−6389.95			−0.537330			−0.268665	+	0.963234i	$0.586582\pi$
$522$		0			0
$523$	14557.4	+	14557.4i	1.21711	+	1.21711i	0.968638	+	0.248475i	$0.0799295\pi$
$523$	14557.4	+	14557.4i	1.21711	+	1.21711i	0.248475	+	0.968638i	$0.420070\pi$
$524$		0			0
$525$	−6312.54	+	17612.9i	−0.524765	+	1.46417i
$526$		0			0
$527$			1075.91i			0.0889325i
$528$		0			0
$529$	−12110.6			−0.995362
$530$		0			0
$531$	−7841.05	+	7841.05i	−0.640815	+	0.640815i
$532$		0			0
$533$	−2454.75	−	2454.75i	−0.199488	−	0.199488i
$534$		0			0
$535$		−	20907.6i		−	1.68956i
$536$		0			0
$537$	20221.3			1.62498
$538$		0			0
$539$	−248.792	−	2553.78i	−0.0198817	−	0.204080i
$540$		0			0
$541$	−8616.54	+	8616.54i	−0.684758	+	0.684758i	−0.961068	−	0.276311i	$-0.910888\pi$
$541$	−8616.54	+	8616.54i	−0.684758	+	0.684758i	0.276311	+	0.961068i	$0.410888\pi$
$542$		0			0
$543$		−	41753.7i		−	3.29986i
$544$		0			0
$545$		−	5730.75i		−	0.450419i
$546$		0			0
$547$	−14849.2	−	14849.2i	−1.16071	−	1.16071i	−0.984321	−	0.176386i	$-0.943559\pi$
$547$	−14849.2	−	14849.2i	−1.16071	−	1.16071i	−0.176386	−	0.984321i	$-0.556441\pi$
$548$		0			0
$549$	14648.7	−	14648.7i	1.13878	−	1.13878i
$550$		0			0
$551$			19558.7i			1.51221i
$552$		0			0
$553$	14825.6	−	7002.38i	1.14005	−	0.538465i
$554$		0			0
$555$	18732.2	−	18732.2i	1.43268	−	1.43268i
$556$		0			0
$557$	−5671.99	+	5671.99i	−0.431472	+	0.431472i	−0.889129	−	0.457657i	$-0.848689\pi$
$557$	−5671.99	+	5671.99i	−0.431472	+	0.431472i	0.457657	+	0.889129i	$0.348689\pi$
$558$		0			0
$559$	−12421.8			−0.939866
$560$		0			0
$561$	−1263.91			−0.0951198
$562$		0			0
$563$	9834.31	−	9834.31i	0.736175	−	0.736175i	−0.235660	−	0.971836i	$-0.575725\pi$
$563$	9834.31	−	9834.31i	0.736175	−	0.736175i	0.971836	+	0.235660i	$0.0757252\pi$
$564$		0			0
$565$	1008.34	−	1008.34i	0.0750819	−	0.0750819i
$566$		0			0
$567$	13095.0	+	27725.2i	0.969912	+	2.05352i
$568$		0			0
$569$			6475.74i			0.477112i	0.971129	+	0.238556i	$0.0766741\pi$
$569$			6475.74i			0.477112i	−0.971129	+	0.238556i	$0.923326\pi$
$570$		0			0
$571$	−8459.33	+	8459.33i	−0.619986	+	0.619986i	−0.945528	−	0.325542i	$-0.894453\pi$
$571$	−8459.33	+	8459.33i	−0.619986	+	0.619986i	0.325542	+	0.945528i	$0.394453\pi$
$572$		0			0
$573$	5947.16	+	5947.16i	0.433588	+	0.433588i
$574$		0			0
$575$			794.802i			0.0576444i
$576$		0			0
$577$		−	20187.2i		−	1.45650i	−0.685310	−	0.728252i	$-0.740333\pi$
$577$		−	20187.2i		−	1.45650i	0.685310	−	0.728252i	$-0.259667\pi$
$578$		0			0
$579$	30806.6	−	30806.6i	2.21119	−	2.21119i
$580$		0			0
$581$	−2675.96	−	959.074i	−0.191080	−	0.0684838i
$582$		0			0
$583$	−5278.63			−0.374989
$584$		0			0
$585$		−	69599.8i		−	4.91897i
$586$		0			0
$587$	−1093.14	−	1093.14i	−0.0768631	−	0.0768631i	0.667630	−	0.744493i	$-0.267309\pi$
$587$	−1093.14	−	1093.14i	−0.0768631	−	0.0768631i	−0.744493	+	0.667630i	$0.767309\pi$
$588$		0			0
$589$	3863.70	−	3863.70i	0.270290	−	0.270290i
$590$		0			0
$591$	15148.6			1.05436
$592$		0			0
$593$		−	7713.84i		−	0.534181i	−0.963671	−	0.267091i	$-0.913938\pi$
$593$		−	7713.84i		−	0.534181i	0.963671	−	0.267091i	$-0.0860623\pi$
$594$		0			0
$595$	1679.83	−	4686.97i	0.115742	−	0.322936i
$596$		0			0
$597$	9425.16	+	9425.16i	0.646141	+	0.646141i
$598$		0			0
$599$	4556.07			0.310778			0.155389	−	0.987853i	$-0.450337\pi$
$599$	4556.07			0.310778			0.155389	+	0.987853i	$0.450337\pi$
$600$		0			0
$601$	21438.9			1.45509			0.727547	−	0.686058i	$-0.240660\pi$
$601$	21438.9			1.45509			0.727547	+	0.686058i	$0.240660\pi$
$602$		0			0
$603$	−23110.2	+	23110.2i	−1.56073	+	1.56073i
$604$		0			0
$605$	13697.2	+	13697.2i	0.920450	+	0.920450i
$606$		0			0
$607$	18799.0			1.25705			0.628523	−	0.777791i	$-0.283660\pi$
$607$	18799.0			1.25705			0.628523	+	0.777791i	$0.283660\pi$
$608$		0			0
$609$	34799.0	−	16436.1i	2.31548	−	1.09364i
$610$		0			0
$611$	12861.3	+	12861.3i	0.851578	+	0.851578i
$612$		0			0
$613$	2748.66	+	2748.66i	0.181105	+	0.181105i	0.791837	−	0.610732i	$-0.209125\pi$
$613$	2748.66	+	2748.66i	0.181105	+	0.181105i	−0.610732	+	0.791837i	$0.709125\pi$
$614$		0			0
$615$			7052.89i			0.462439i
$616$		0			0
$617$			6315.24i			0.412061i	0.978546	+	0.206031i	$0.0660547\pi$
$617$			6315.24i			0.412061i	−0.978546	+	0.206031i	$0.933945\pi$
$618$		0			0
$619$	−14106.2	−	14106.2i	−0.915955	−	0.915955i	0.0807768	−	0.996732i	$-0.474260\pi$
$619$	−14106.2	−	14106.2i	−0.915955	−	0.915955i	−0.996732	+	0.0807768i	$0.974260\pi$
$620$		0			0
$621$	1884.80	+	1884.80i	0.121794	+	0.121794i
$622$		0			0
$623$	−2133.79	−	4517.72i	−0.137221	−	0.290528i
$624$		0			0
$625$	17655.8			1.12997
$626$		0			0
$627$	4538.81	+	4538.81i	0.289095	+	0.289095i
$628$		0			0
$629$	−2285.14	+	2285.14i	−0.144856	+	0.144856i
$630$		0			0
$631$	−12921.9			−0.815232			−0.407616	−	0.913153i	$-0.633640\pi$
$631$	−12921.9			−0.815232			−0.407616	+	0.913153i	$0.633640\pi$
$632$		0			0
$633$	10314.2			0.647634
$634$		0			0
$635$	−195.308	−	195.308i	−0.0122056	−	0.0122056i
$636$		0			0
$637$	−24374.4	+	2374.58i	−1.51609	+	0.147699i
$638$		0			0
$639$			38854.2i			2.40540i
$640$		0			0
$641$	−2627.47			−0.161902			−0.0809509	−	0.996718i	$-0.525796\pi$
$641$	−2627.47			−0.161902			−0.0809509	+	0.996718i	$0.525796\pi$
$642$		0			0
$643$	365.321	−	365.321i	0.0224057	−	0.0224057i	−0.695815	−	0.718221i	$-0.744957\pi$
$643$	365.321	−	365.321i	0.0224057	−	0.0224057i	0.718221	+	0.695815i	$0.244957\pi$
$644$		0			0
$645$	17844.9	+	17844.9i	1.08937	+	1.08937i
$646$		0			0
$647$			28089.2i			1.70680i	0.521254	+	0.853402i	$0.325464\pi$
$647$			28089.2i			1.70680i	−0.521254	+	0.853402i	$0.674536\pi$
$648$		0			0
$649$	1292.82			0.0781936
$650$		0			0
$651$	−10121.2	−	3627.47i	−0.609340	−	0.218390i
$652$		0			0
$653$	−8988.84	+	8988.84i	−0.538684	+	0.538684i	−0.923142	−	0.384458i	$-0.874388\pi$
$653$	−8988.84	+	8988.84i	−0.538684	+	0.538684i	0.384458	+	0.923142i	$0.374388\pi$
$654$		0			0
$655$			21268.7i			1.26876i
$656$		0			0
$657$			58645.4i			3.48246i
$658$		0			0
$659$	−18384.3	−	18384.3i	−1.08672	−	1.08672i	−0.995864	−	0.0908590i	$-0.971039\pi$
$659$	−18384.3	−	18384.3i	−1.08672	−	1.08672i	−0.0908590	−	0.995864i	$-0.528961\pi$
$660$		0			0
$661$	8728.20	−	8728.20i	0.513597	−	0.513597i	−0.402030	−	0.915627i	$-0.631695\pi$
$661$	8728.20	−	8728.20i	0.513597	−	0.513597i	0.915627	+	0.402030i	$0.131695\pi$
$662$		0			0
$663$			12063.3i			0.706635i
$664$		0			0
$665$	−22863.7	+	10798.9i	−1.33326	+	0.629720i
$666$		0			0
$667$	1156.02	−	1156.02i	0.0671083	−	0.0671083i
$668$		0			0
$669$	−25614.0	+	25614.0i	−1.48026	+	1.48026i
$670$		0			0
$671$	−2415.25			−0.138956
$672$		0			0
$673$	−11763.2			−0.673758			−0.336879	−	0.941548i	$-0.609371\pi$
$673$	−11763.2			−0.673758			−0.336879	+	0.941548i	$0.609371\pi$
$674$		0			0
$675$	−26548.2	+	26548.2i	−1.51384	+	1.51384i
$676$		0			0
$677$	−2299.45	+	2299.45i	−0.130539	+	0.130539i	−0.769358	−	0.638818i	$-0.779423\pi$
$677$	−2299.45	+	2299.45i	−0.130539	+	0.130539i	0.638818	+	0.769358i	$0.279423\pi$
$678$		0			0
$679$	−24325.4	+	11489.3i	−1.37485	+	0.649363i
$680$		0			0
$681$			15478.7i			0.870992i
$682$		0			0
$683$	−22496.7	+	22496.7i	−1.26034	+	1.26034i	−0.309410	+	0.950929i	$0.600132\pi$
$683$	−22496.7	+	22496.7i	−1.26034	+	1.26034i	−0.950929	+	0.309410i	$0.899868\pi$
$684$		0			0
$685$	−29524.8	−	29524.8i	−1.64684	−	1.64684i
$686$		0			0
$687$		−	28952.6i		−	1.60788i
$688$		0			0
$689$			50381.5i			2.78575i
$690$		0			0
$691$	−7136.02	+	7136.02i	−0.392861	+	0.392861i	−0.875706	−	0.482845i	$-0.839603\pi$
$691$	−7136.02	+	7136.02i	−0.392861	+	0.392861i	0.482845	+	0.875706i	$0.339603\pi$
$692$		0			0
$693$	2999.24	−	8368.32i	0.164404	−	0.458710i
$694$		0			0
$695$	29147.6			1.59084
$696$		0			0
$697$		−	860.385i		−	0.0467567i
$698$		0			0
$699$	4151.19	+	4151.19i	0.224625	+	0.224625i
$700$		0			0
$701$	21007.7	−	21007.7i	1.13188	−	1.13188i	0.142017	−	0.989864i	$-0.454641\pi$
$701$	21007.7	−	21007.7i	1.13188	−	1.13188i	0.989864	−	0.142017i	$-0.0453588\pi$
$702$		0			0
$703$	16412.3			0.880515
$704$		0			0
$705$		−	36952.7i		−	1.97407i
$706$		0			0
$707$	804.885	+	288.474i	0.0428159	+	0.0153454i
$708$		0			0
$709$	920.048	+	920.048i	0.0487350	+	0.0487350i	0.731054	−	0.682319i	$-0.239029\pi$
$709$	920.048	+	920.048i	0.0487350	+	0.0487350i	−0.682319	+	0.731054i	$0.739029\pi$
$710$		0			0
$711$	56804.9			2.99627
$712$		0			0
$713$	−456.729			−0.0239897
$714$		0			0
$715$	−5737.75	+	5737.75i	−0.300112	+	0.300112i
$716$		0			0
$717$	28788.1	+	28788.1i	1.49946	+	1.49946i
$718$		0			0
$719$	−27809.1			−1.44242			−0.721212	−	0.692714i	$-0.756415\pi$
$719$	−27809.1			−1.44242			−0.721212	+	0.692714i	$0.756415\pi$
$720$		0			0
$721$	−24896.5	+	11759.0i	−1.28598	+	0.607391i
$722$		0			0
$723$	18439.5	+	18439.5i	0.948510	+	0.948510i
$724$		0			0
$725$	16283.0	+	16283.0i	0.834119	+	0.834119i
$726$		0			0
$727$		−	23899.8i		−	1.21925i	−0.792691	−	0.609624i	$-0.791320\pi$
$727$		−	23899.8i		−	1.21925i	0.792691	−	0.609624i	$-0.208680\pi$
$728$		0			0
$729$			14753.2i			0.749539i
$730$		0			0
$731$	−2176.91	−	2176.91i	−0.110145	−	0.110145i
$732$		0			0
$733$	−799.842	−	799.842i	−0.0403040	−	0.0403040i	0.686668	−	0.726972i	$-0.259073\pi$
$733$	−799.842	−	799.842i	−0.0403040	−	0.0403040i	−0.726972	+	0.686668i	$0.759073\pi$
$734$		0			0
$735$	38427.1	+	31604.5i	1.92844	+	1.58606i
$736$		0			0
$737$	3810.38			0.190444
$738$		0			0
$739$	−8049.79	−	8049.79i	−0.400699	−	0.400699i	0.477781	−	0.878479i	$-0.341441\pi$
$739$	−8049.79	−	8049.79i	−0.400699	−	0.400699i	−0.878479	+	0.477781i	$0.841441\pi$
$740$		0			0
$741$	43320.3	−	43320.3i	2.14766	−	2.14766i
$742$		0			0
$743$	−35083.7			−1.73229			−0.866147	−	0.499789i	$-0.833411\pi$
$743$	−35083.7			−1.73229			−0.866147	+	0.499789i	$0.833411\pi$
$744$		0			0
$745$	−23342.3			−1.14792
$746$		0			0
$747$	−6963.88	−	6963.88i	−0.341091	−	0.341091i
$748$		0			0
$749$	−23993.0	−	8599.17i	−1.17047	−	0.419502i
$750$		0			0
$751$		−	15178.6i		−	0.737518i	−0.929525	−	0.368759i	$-0.879783\pi$
$751$		−	15178.6i		−	0.737518i	0.929525	−	0.368759i	$-0.120217\pi$
$752$		0			0
$753$	13167.0			0.637225
$754$		0			0
$755$	−2909.37	+	2909.37i	−0.140242	+	0.140242i
$756$		0			0
$757$	4237.45	+	4237.45i	0.203451	+	0.203451i	0.801477	−	0.598026i	$-0.204048\pi$
$757$	4237.45	+	4237.45i	0.203451	+	0.203451i	−0.598026	+	0.801477i	$0.704048\pi$
$758$		0			0
$759$		−	536.534i		−	0.0256587i
$760$		0			0
$761$	12456.8			0.593378			0.296689	−	0.954974i	$-0.404118\pi$
$761$	12456.8			0.593378			0.296689	+	0.954974i	$0.404118\pi$
$762$		0			0
$763$	−6576.46	−	2357.03i	−0.312037	−	0.111835i
$764$		0			0
$765$	12197.3	−	12197.3i	0.576463	−	0.576463i
$766$		0			0
$767$		−	12339.2i		−	0.580892i
$768$		0			0
$769$			7576.59i			0.355291i	0.984095	+	0.177645i	$0.0568480\pi$
$769$			7576.59i			0.355291i	−0.984095	+	0.177645i	$0.943152\pi$
$770$		0			0
$771$	43975.9	+	43975.9i	2.05415	+	2.05415i
$772$		0			0
$773$	−13423.2	+	13423.2i	−0.624580	+	0.624580i	−0.946699	−	0.322119i	$-0.895605\pi$
$773$	−13423.2	+	13423.2i	−0.624580	+	0.624580i	0.322119	+	0.946699i	$0.395605\pi$
$774$		0			0
$775$		−	6433.22i		−	0.298178i
$776$		0			0
$777$	−13792.1	−	29201.0i	−0.636794	−	1.34824i
$778$		0			0
$779$	−3089.72	+	3089.72i	−0.142106	+	0.142106i
$780$		0			0
$781$	3203.11	−	3203.11i	0.146756	−	0.146756i
$782$		0			0
$783$	77227.3			3.52475
$784$		0			0
$785$	−7742.15			−0.352012
$786$		0			0
$787$	9970.27	−	9970.27i	0.451591	−	0.451591i	−0.444292	−	0.895882i	$-0.646545\pi$
$787$	9970.27	−	9970.27i	0.451591	−	0.451591i	0.895882	+	0.444292i	$0.146545\pi$
$788$		0			0
$789$	−5415.04	+	5415.04i	−0.244335	+	0.244335i
$790$		0			0
$791$	−742.422	−	1571.87i	−0.0333723	−	0.0706567i
$792$		0			0
$793$			23052.2i			1.03229i
$794$		0			0
$795$	72377.1	−	72377.1i	3.22887	−	3.22887i
$796$		0			0
$797$	24511.9	+	24511.9i	1.08941	+	1.08941i	0.995590	+	0.0938157i	$0.0299065\pi$
$797$	24511.9	+	24511.9i	1.08941	+	1.08941i	0.0938157	+	0.995590i	$0.470094\pi$
$798$		0			0
$799$			4507.88i			0.199596i
$800$		0			0
$801$		−	17309.8i		−	0.763561i
$802$		0			0
$803$	4834.68	−	4834.68i	0.212468	−	0.212468i
$804$		0			0
$805$	1989.64	+	713.094i	0.0871125	+	0.0312215i
$806$		0			0
$807$	−27409.5			−1.19562
$808$		0			0
$809$			34908.0i			1.51706i	0.651640	+	0.758529i	$0.274081\pi$
$809$			34908.0i			1.51706i	−0.651640	+	0.758529i	$0.725919\pi$
$810$		0			0
$811$	−12610.4	−	12610.4i	−0.546004	−	0.546004i	0.379278	−	0.925283i	$-0.376172\pi$
$811$	−12610.4	−	12610.4i	−0.546004	−	0.546004i	−0.925283	+	0.379278i	$0.876172\pi$
$812$		0			0
$813$	16540.0	−	16540.0i	0.713511	−	0.713511i
$814$		0			0
$815$	−37710.8			−1.62080
$816$		0			0
$817$			15634.9i			0.669519i
$818$		0			0
$819$	−79870.9	−	28626.0i	−3.40771	−	1.22134i
$820$		0			0
$821$	−23212.1	−	23212.1i	−0.986731	−	0.986731i	0.0131819	−	0.999913i	$-0.495804\pi$
$821$	−23212.1	−	23212.1i	−0.986731	−	0.986731i	−0.999913	+	0.0131819i	$0.995804\pi$
$822$		0			0
$823$	−13666.7			−0.578849			−0.289425	−	0.957201i	$-0.593464\pi$
$823$	−13666.7			−0.578849			−0.289425	+	0.957201i	$0.593464\pi$
$824$		0			0
$825$	7557.31			0.318923
$826$		0			0
$827$	19896.8	−	19896.8i	0.836615	−	0.836615i	−0.151796	−	0.988412i	$-0.548506\pi$
$827$	19896.8	−	19896.8i	0.836615	−	0.836615i	0.988412	+	0.151796i	$0.0485058\pi$
$828$		0			0
$829$	−29292.8	−	29292.8i	−1.22724	−	1.22724i	−0.965005	−	0.262233i	$-0.915541\pi$
$829$	−29292.8	−	29292.8i	−1.22724	−	1.22724i	−0.262233	−	0.965005i	$-0.584459\pi$
$830$		0			0
$831$	−51375.0			−2.14462
$832$		0			0
$833$	−4687.74	−	3855.45i	−0.194983	−	0.160364i
$834$		0			0
$835$	13770.4	+	13770.4i	0.570713	+	0.570713i
$836$		0			0
$837$	−15255.8	−	15255.8i	−0.630008	−	0.630008i
$838$		0			0
$839$			23024.9i			0.947447i	0.880674	+	0.473723i	$0.157090\pi$
$839$			23024.9i			0.947447i	−0.880674	+	0.473723i	$0.842910\pi$
$840$		0			0
$841$		−	22977.5i		−	0.942127i
$842$		0			0
$843$	−36926.2	−	36926.2i	−1.50867	−	1.50867i
$844$		0			0
$845$	31162.1	+	31162.1i	1.26865	+	1.26865i
$846$		0			0
$847$	21352.2	−	10085.0i	0.866199	−	0.409120i
$848$		0			0
$849$	−40473.9			−1.63611
$850$		0			0
$851$	−970.054	−	970.054i	−0.0390752	−	0.0390752i
$852$		0			0
$853$	19763.3	−	19763.3i	0.793298	−	0.793298i	−0.188730	−	0.982029i	$-0.560437\pi$
$853$	19763.3	−	19763.3i	0.793298	−	0.793298i	0.982029	+	0.188730i	$0.0604373\pi$
$854$		0			0
$855$	−87603.2			−3.50406
$856$		0			0
$857$	−20283.0			−0.808464			−0.404232	−	0.914656i	$-0.632461\pi$
$857$	−20283.0			−0.808464			−0.404232	+	0.914656i	$0.632461\pi$
$858$		0			0
$859$	30204.5	+	30204.5i	1.19973	+	1.19973i	0.974248	+	0.225478i	$0.0723945\pi$
$859$	30204.5	+	30204.5i	1.19973	+	1.19973i	0.225478	+	0.974248i	$0.427606\pi$
$860$		0			0
$861$	8093.71	+	2900.82i	0.320363	+	0.114819i
$862$		0			0
$863$			4343.51i			0.171326i	0.996324	+	0.0856632i	$0.0273009\pi$
$863$			4343.51i			0.171326i	−0.996324	+	0.0856632i	$0.972699\pi$
$864$		0			0
$865$	−1177.67			−0.0462914
$866$		0			0
$867$	31055.8	−	31055.8i	1.21650	−	1.21650i
$868$		0			0
$869$	−4682.95	−	4682.95i	−0.182806	−	0.182806i
$870$		0			0
$871$		−	36367.9i		−	1.41479i
$872$		0			0
$873$	−93203.5			−3.61336
$874$		0			0
$875$	1821.99	−	5083.62i	0.0703936	−	0.196409i
$876$		0			0
$877$	10248.6	−	10248.6i	0.394608	−	0.394608i	−0.481718	−	0.876326i	$-0.659987\pi$
$877$	10248.6	−	10248.6i	0.394608	−	0.394608i	0.876326	+	0.481718i	$0.159987\pi$
$878$		0			0
$879$			64503.8i			2.47515i
$880$		0			0
$881$		−	39067.0i		−	1.49399i	−0.664832	−	0.746993i	$-0.731497\pi$
$881$		−	39067.0i		−	1.49399i	0.664832	−	0.746993i	$-0.268503\pi$
$882$		0			0
$883$	33173.0	+	33173.0i	1.26428	+	1.26428i	0.948998	+	0.315283i	$0.102099\pi$
$883$	33173.0	+	33173.0i	1.26428	+	1.26428i	0.315283	+	0.948998i	$0.397901\pi$
$884$		0			0
$885$	−17726.3	+	17726.3i	−0.673292	+	0.673292i
$886$		0			0
$887$			31068.0i			1.17606i	0.808841	+	0.588028i	$0.200095\pi$
$887$			31068.0i			1.17606i	−0.808841	+	0.588028i	$0.799905\pi$
$888$		0			0
$889$	−304.460	+	143.801i	−0.0114862	+	0.00542513i
$890$		0			0
$891$	8757.52	−	8757.52i	0.329279	−	0.329279i
$892$		0			0
$893$	16188.2	−	16188.2i	0.606627	−	0.606627i
$894$		0			0
$895$	32175.2			1.20167
$896$		0			0
$897$	−5120.92			−0.190616
$898$		0			0
$899$	−9356.97	+	9356.97i	−0.347133	+	0.347133i
$900$		0			0
$901$	−8829.32	+	8829.32i	−0.326468	+	0.326468i
$902$		0			0
$903$	27817.8	−	13138.8i	1.02516	−	0.484200i
$904$		0			0
$905$		−	66436.6i		−	2.44025i
$906$		0			0
$907$	−7883.36	+	7883.36i	−0.288603	+	0.288603i	−0.836528	−	0.547925i	$-0.815418\pi$
$907$	−7883.36	+	7883.36i	−0.288603	+	0.288603i	0.547925	+	0.836528i	$0.315418\pi$
$908$		0			0
$909$	2094.62	+	2094.62i	0.0764293	+	0.0764293i
$910$		0			0
$911$		−	54680.2i		−	1.98862i	−0.106517	−	0.994311i	$-0.533970\pi$
$911$		−	54680.2i		−	1.98862i	0.106517	−	0.994311i	$-0.466030\pi$
$912$		0			0
$913$			1148.19i			0.0416207i
$914$		0			0
$915$	33116.4	−	33116.4i	1.19650	−	1.19650i
$916$		0			0
$917$	24407.4	+	8747.70i	0.878956	+	0.315021i
$918$		0			0
$919$	−3540.65			−0.127090			−0.0635448	−	0.997979i	$-0.520241\pi$
$919$	−3540.65			−0.127090			−0.0635448	+	0.997979i	$0.520241\pi$
$920$		0			0
$921$			18662.4i			0.667696i
$922$		0			0
$923$	−30571.9	−	30571.9i	−1.09023	−	1.09023i
$924$		0			0
$925$	13663.6	−	13663.6i	0.485683	−	0.485683i
$926$		0			0
$927$	−95391.9			−3.37981
$928$		0			0
$929$		−	16349.4i		−	0.577404i	−0.957419	−	0.288702i	$-0.906776\pi$
$929$		−	16349.4i		−	0.577404i	0.957419	−	0.288702i	$-0.0932236\pi$
$930$		0			0
$931$	2988.81	+	30679.4i	0.105214	+	1.08000i
$932$		0			0
$933$	27768.9	+	27768.9i	0.974398	+	0.974398i
$934$		0			0
$935$	−2011.07			−0.0703413
$936$		0			0
$937$	−9033.40			−0.314950			−0.157475	−	0.987523i	$-0.550335\pi$
$937$	−9033.40			−0.314950			−0.157475	+	0.987523i	$0.550335\pi$
$938$		0			0
$939$	7987.93	−	7987.93i	0.277611	−	0.277611i
$940$		0			0
$941$	15317.5	+	15317.5i	0.530644	+	0.530644i	0.920764	−	0.390120i	$-0.127566\pi$
$941$	15317.5	+	15317.5i	0.530644	+	0.530644i	−0.390120	+	0.920764i	$0.627566\pi$
$942$		0			0
$943$	365.237			0.0126127
$944$		0			0
$945$	42639.5	+	90277.4i	1.46779	+	3.10764i
$946$		0			0
$947$	−15099.6	−	15099.6i	−0.518131	−	0.518131i	0.398875	−	0.917005i	$-0.369401\pi$
$947$	−15099.6	−	15099.6i	−0.518131	−	0.518131i	−0.917005	+	0.398875i	$0.869401\pi$
$948$		0			0
$949$	−46144.3	−	46144.3i	−1.57841	−	1.57841i
$950$		0			0
$951$		−	20773.8i		−	0.708345i
$952$		0			0
$953$			29129.5i			0.990133i	0.868855	+	0.495067i	$0.164856\pi$
$953$			29129.5i			0.990133i	−0.868855	+	0.495067i	$0.835144\pi$
$954$		0			0
$955$	9462.85	+	9462.85i	0.320639	+	0.320639i
$956$		0			0
$957$	−10991.9	−	10991.9i	−0.371284	−	0.371284i
$958$		0			0
$959$	−46025.3	+	21738.5i	−1.54977	+	0.731984i
$960$		0			0
$961$	−26094.2			−0.875908
$962$		0			0
$963$	−62439.0	−	62439.0i	−2.08937	−	2.08937i
$964$		0			0
$965$	49018.1	−	49018.1i	1.63518	−	1.63518i
$966$		0			0
$967$	43742.0			1.45465			0.727325	−	0.686293i	$-0.240763\pi$
$967$	43742.0			1.45465			0.727325	+	0.686293i	$0.240763\pi$
$968$		0			0
$969$	15183.7			0.503375
$970$		0			0
$971$	8883.28	+	8883.28i	0.293592	+	0.293592i	0.838498	−	0.544905i	$-0.183434\pi$
$971$	8883.28	+	8883.28i	0.293592	+	0.293592i	−0.544905	+	0.838498i	$0.683434\pi$
$972$		0			0
$973$	11988.3	−	33449.0i	0.394991	−	1.10208i
$974$		0			0
$975$		−	72130.3i		−	2.36925i
$976$		0			0
$977$	307.596			0.0100725			0.00503627	−	0.999987i	$-0.498397\pi$
$977$	307.596			0.0100725			0.00503627	+	0.999987i	$0.498397\pi$
$978$		0			0
$979$	−1427.01	+	1427.01i	−0.0465857	+	0.0465857i
$980$		0			0
$981$	−17114.5	−	17114.5i	−0.557007	−	0.557007i
$982$		0			0
$983$			29915.4i			0.970653i	0.874333	+	0.485327i	$0.161299\pi$
$983$			29915.4i			0.970653i	−0.874333	+	0.485327i	$0.838701\pi$
$984$		0			0
$985$	24103.7			0.779704
$986$		0			0
$987$	−42406.0	−	15198.5i	−1.36758	−	0.490144i
$988$		0			0
$989$	924.106	−	924.106i	0.0297117	−	0.0297117i
$990$		0			0
$991$			40094.7i			1.28522i	0.766195	+	0.642609i	$0.222148\pi$
$991$			40094.7i			1.28522i	−0.766195	+	0.642609i	$0.777852\pi$
$992$		0			0
$993$			25260.5i			0.807267i
$994$		0			0
$995$	14996.9	+	14996.9i	0.477823	+	0.477823i
$996$		0			0
$997$	−28430.3	+	28430.3i	−0.903107	+	0.903107i	−0.995704	−	0.0925966i	$-0.970483\pi$
$997$	−28430.3	+	28430.3i	−0.903107	+	0.903107i	0.0925966	+	0.995704i	$0.470483\pi$
$998$		0			0
$999$		−	64804.0i		−	2.05236i

Display

a_p

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p

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a_n

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a_n

instead) (See

a_n

instead) Display

a_n

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n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	448.4.j.b.335.43		88
4.3	odd	2		112.4.j.b.27.5	✓	88
7.6	odd	2	inner	448.4.j.b.335.2		88
16.3	odd	4	inner	448.4.j.b.111.2		88
16.13	even	4		112.4.j.b.83.6	yes	88
28.27	even	2		112.4.j.b.27.6	yes	88
112.13	odd	4		112.4.j.b.83.5	yes	88
112.83	even	4	inner	448.4.j.b.111.43		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.4.j.b.27.5	✓	88	4.3	odd	2
112.4.j.b.27.6	yes	88	28.27	even	2
112.4.j.b.83.5	yes	88	112.13	odd	4
112.4.j.b.83.6	yes	88	16.13	even	4
448.4.j.b.111.2		88	16.3	odd	4	inner
448.4.j.b.111.43		88	112.83	even	4	inner
448.4.j.b.335.2		88	7.6	odd	2	inner
448.4.j.b.335.43		88	1.1	even	1	trivial

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

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Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	448.4.j.b.335.43

Level	$448$
Weight	$4$
Character	448.335
Analytic conductor	$26.433$
Analytic rank	$0$
Dimension	$88$
Inner twists	$4$