LMFDB - Embedded newform 232.5.j.a.17.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [232,5,Mod(17,232)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(232, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("232.17");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 232 = 2^{3} \cdot 29 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	232.j (of order $4$, degree $2$, 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:	$23.9818314355$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			17.8
Character	$\chi$	$=$	232.17
Dual form			232.5.j.a.41.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.44306 + 1.44306i) q^{3} +19.5814i q^{5} -11.8564 q^{7} +76.8352i q^{9} +O(q^{10})$	\(q+(-1.44306 + 1.44306i) q^{3} +19.5814i q^{5} -11.8564 q^{7} +76.8352i q^{9} +(-21.9124 + 21.9124i) q^{11} -112.822i q^{13} +(-28.2571 - 28.2571i) q^{15} +(-229.429 + 229.429i) q^{17} +(337.159 - 337.159i) q^{19} +(17.1094 - 17.1094i) q^{21} -562.916 q^{23} +241.568 q^{25} +(-227.765 - 227.765i) q^{27} +(-818.342 - 193.899i) q^{29} +(-254.261 + 254.261i) q^{31} -63.2417i q^{33} -232.164i q^{35} +(-172.056 - 172.056i) q^{37} +(162.808 + 162.808i) q^{39} +(-1758.55 - 1758.55i) q^{41} +(432.324 - 432.324i) q^{43} -1504.54 q^{45} +(-212.448 - 212.448i) q^{47} -2260.43 q^{49} -662.158i q^{51} -1206.52 q^{53} +(-429.077 - 429.077i) q^{55} +973.078i q^{57} -3541.27 q^{59} +(-3592.18 + 3592.18i) q^{61} -910.985i q^{63} +2209.22 q^{65} +3452.96i q^{67} +(812.319 - 812.319i) q^{69} -6204.90i q^{71} +(-3795.18 - 3795.18i) q^{73} +(-348.595 + 348.595i) q^{75} +(259.801 - 259.801i) q^{77} +(5293.20 - 5293.20i) q^{79} -5566.30 q^{81} +7520.17 q^{83} +(-4492.56 - 4492.56i) q^{85} +(1460.72 - 901.106i) q^{87} +(-4782.97 + 4782.97i) q^{89} +1337.66i q^{91} -733.825i q^{93} +(6602.06 + 6602.06i) q^{95} +(11660.0 + 11660.0i) q^{97} +(-1683.64 - 1683.64i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 16 q^{3} + 96 q^{7}+O(q^{10}) $ 30 * q - 16 * q^3 + 96 * q^7	$ 30 q - 16 q^{3} + 96 q^{7} - 240 q^{15} - 338 q^{17} - 936 q^{19} + 1400 q^{21} - 352 q^{23} - 2154 q^{25} + 2648 q^{27} + 500 q^{29} - 1896 q^{31} - 1862 q^{37} + 1088 q^{39} + 2854 q^{41} - 800 q^{43} + 4552 q^{45} - 696 q^{47} + 9698 q^{49} + 4584 q^{53} - 8560 q^{55} + 7144 q^{59} - 1070 q^{61} + 8672 q^{65} - 19352 q^{69} - 7942 q^{73} + 11072 q^{75} - 3048 q^{77} + 3560 q^{79} - 10398 q^{81} - 9848 q^{83} + 11968 q^{85} - 13704 q^{87} - 9634 q^{89} - 33160 q^{95} - 27582 q^{97} + 16480 q^{99}+O(q^{100}) $ 30 * q - 16 * q^3 + 96 * q^7 - 240 * q^15 - 338 * q^17 - 936 * q^19 + 1400 * q^21 - 352 * q^23 - 2154 * q^25 + 2648 * q^27 + 500 * q^29 - 1896 * q^31 - 1862 * q^37 + 1088 * q^39 + 2854 * q^41 - 800 * q^43 + 4552 * q^45 - 696 * q^47 + 9698 * q^49 + 4584 * q^53 - 8560 * q^55 + 7144 * q^59 - 1070 * q^61 + 8672 * q^65 - 19352 * q^69 - 7942 * q^73 + 11072 * q^75 - 3048 * q^77 + 3560 * q^79 - 10398 * q^81 - 9848 * q^83 + 11968 * q^85 - 13704 * q^87 - 9634 * q^89 - 33160 * q^95 - 27582 * q^97 + 16480 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/232\mathbb{Z}\right)^\times$.

$n$	$89$	$117$	$175$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.44306	+	1.44306i	−0.160339	+	0.160339i	−0.782717	−	0.622378i	$-0.786167\pi$
$3$	−1.44306	+	1.44306i	−0.160339	+	0.160339i	0.622378	+	0.782717i	$0.286167\pi$
$4$		0			0
$5$			19.5814i			0.783257i	0.920123	+	0.391629i	$0.128088\pi$
$5$			19.5814i			0.783257i	−0.920123	+	0.391629i	$0.871912\pi$
$6$		0			0
$7$	−11.8564			−0.241966			−0.120983	−	0.992655i	$-0.538605\pi$
$7$	−11.8564			−0.241966			−0.120983	+	0.992655i	$0.538605\pi$
$8$		0			0
$9$			76.8352i			0.948583i
$10$		0			0
$11$	−21.9124	+	21.9124i	−0.181094	+	0.181094i	−0.791833	−	0.610738i	$-0.790873\pi$
$11$	−21.9124	+	21.9124i	−0.181094	+	0.181094i	0.610738	+	0.791833i	$0.290873\pi$
$12$		0			0
$13$		−	112.822i		−	0.667586i	−0.942646	−	0.333793i	$-0.891671\pi$
$13$		−	112.822i		−	0.667586i	0.942646	−	0.333793i	$-0.108329\pi$
$14$		0			0
$15$	−28.2571	−	28.2571i	−0.125587	−	0.125587i
$16$		0			0
$17$	−229.429	+	229.429i	−0.793873	+	0.793873i	−0.982121	−	0.188248i	$-0.939719\pi$
$17$	−229.429	+	229.429i	−0.793873	+	0.793873i	0.188248	+	0.982121i	$0.439719\pi$
$18$		0			0
$19$	337.159	−	337.159i	0.933959	−	0.933959i	−0.0639917	−	0.997950i	$-0.520383\pi$
$19$	337.159	−	337.159i	0.933959	−	0.933959i	0.997950	+	0.0639917i	$0.0203831\pi$
$20$		0			0
$21$	17.1094	−	17.1094i	0.0387968	−	0.0387968i
$22$		0			0
$23$	−562.916			−1.06411			−0.532057	−	0.846709i	$-0.678581\pi$
$23$	−562.916			−1.06411			−0.532057	+	0.846709i	$0.678581\pi$
$24$		0			0
$25$	241.568			0.386508
$26$		0			0
$27$	−227.765	−	227.765i	−0.312435	−	0.312435i
$28$		0			0
$29$	−818.342	−	193.899i	−0.973059	−	0.230558i
$29$	−818.342	−	193.899i	−0.973059	−	0.230558i
$30$		0			0
$31$	−254.261	+	254.261i	−0.264579	+	0.264579i	−0.826911	−	0.562332i	$-0.809904\pi$
$31$	−254.261	+	254.261i	−0.264579	+	0.264579i	0.562332	+	0.826911i	$0.309904\pi$
$32$		0			0
$33$		−	63.2417i		−	0.0580732i
$34$		0			0
$35$		−	232.164i		−	0.189522i
$36$		0			0
$37$	−172.056	−	172.056i	−0.125680	−	0.125680i	0.641469	−	0.767149i	$-0.278325\pi$
$37$	−172.056	−	172.056i	−0.125680	−	0.125680i	−0.767149	+	0.641469i	$0.778325\pi$
$38$		0			0
$39$	162.808	+	162.808i	0.107040	+	0.107040i
$40$		0			0
$41$	−1758.55	−	1758.55i	−1.04613	−	1.04613i	−0.998883	−	0.0472503i	$-0.984954\pi$
$41$	−1758.55	−	1758.55i	−1.04613	−	1.04613i	−0.0472503	−	0.998883i	$-0.515046\pi$
$42$		0			0
$43$	432.324	−	432.324i	0.233815	−	0.233815i	−0.580468	−	0.814283i	$-0.697130\pi$
$43$	432.324	−	432.324i	0.233815	−	0.233815i	0.814283	+	0.580468i	$0.197130\pi$
$44$		0			0
$45$	−1504.54			−0.742984
$46$		0			0
$47$	−212.448	−	212.448i	−0.0961738	−	0.0961738i	0.657383	−	0.753557i	$-0.271663\pi$
$47$	−212.448	−	212.448i	−0.0961738	−	0.0961738i	−0.753557	+	0.657383i	$0.771663\pi$
$48$		0			0
$49$	−2260.43			−0.941452
$50$		0			0
$51$		−	662.158i		−	0.254578i
$52$		0			0
$53$	−1206.52			−0.429518			−0.214759	−	0.976667i	$-0.568897\pi$
$53$	−1206.52			−0.429518			−0.214759	+	0.976667i	$0.568897\pi$
$54$		0			0
$55$	−429.077	−	429.077i	−0.141843	−	0.141843i
$56$		0			0
$57$			973.078i			0.299501i
$58$		0			0
$59$	−3541.27			−1.01732			−0.508658	−	0.860969i	$-0.669858\pi$
$59$	−3541.27			−1.01732			−0.508658	+	0.860969i	$0.669858\pi$
$60$		0			0
$61$	−3592.18	+	3592.18i	−0.965380	+	0.965380i	−0.999420	−	0.0340403i	$-0.989163\pi$
$61$	−3592.18	+	3592.18i	−0.965380	+	0.965380i	0.0340403	+	0.999420i	$0.489163\pi$
$62$		0			0
$63$		−	910.985i		−	0.229525i
$64$		0			0
$65$	2209.22			0.522891
$66$		0			0
$67$			3452.96i			0.769205i	0.923082	+	0.384603i	$0.125662\pi$
$67$			3452.96i			0.769205i	−0.923082	+	0.384603i	$0.874338\pi$
$68$		0			0
$69$	812.319	−	812.319i	0.170619	−	0.170619i
$70$		0			0
$71$		−	6204.90i		−	1.23089i	−0.788181	−	0.615443i	$-0.788977\pi$
$71$		−	6204.90i		−	1.23089i	0.788181	−	0.615443i	$-0.211023\pi$
$72$		0			0
$73$	−3795.18	−	3795.18i	−0.712175	−	0.712175i	0.254815	−	0.966990i	$-0.417985\pi$
$73$	−3795.18	−	3795.18i	−0.712175	−	0.712175i	−0.966990	+	0.254815i	$0.917985\pi$
$74$		0			0
$75$	−348.595	+	348.595i	−0.0619725	+	0.0619725i
$76$		0			0
$77$	259.801	−	259.801i	0.0438188	−	0.0438188i
$78$		0			0
$79$	5293.20	−	5293.20i	0.848134	−	0.848134i	−0.141766	−	0.989900i	$-0.545278\pi$
$79$	5293.20	−	5293.20i	0.848134	−	0.848134i	0.989900	+	0.141766i	$0.0452781\pi$
$80$		0			0
$81$	−5566.30			−0.848391
$82$		0			0
$83$	7520.17			1.09162			0.545810	−	0.837909i	$-0.316222\pi$
$83$	7520.17			1.09162			0.545810	+	0.837909i	$0.316222\pi$
$84$		0			0
$85$	−4492.56	−	4492.56i	−0.621807	−	0.621807i
$86$		0			0
$87$	1460.72	−	901.106i	0.192987	−	0.119052i
$88$		0			0
$89$	−4782.97	+	4782.97i	−0.603834	+	0.603834i	−0.941328	−	0.337493i	$-0.890421\pi$
$89$	−4782.97	+	4782.97i	−0.603834	+	0.603834i	0.337493	+	0.941328i	$0.390421\pi$
$90$		0			0
$91$			1337.66i			0.161533i
$92$		0			0
$93$		−	733.825i		−	0.0848450i
$94$		0			0
$95$	6602.06	+	6602.06i	0.731530	+	0.731530i
$96$		0			0
$97$	11660.0	+	11660.0i	1.23924	+	1.23924i	0.960313	+	0.278925i	$0.0899781\pi$
$97$	11660.0	+	11660.0i	1.23924	+	1.23924i	0.278925	+	0.960313i	$0.410022\pi$
$98$		0			0
$99$	−1683.64	−	1683.64i	−0.171783	−	0.171783i
$100$		0			0
$101$	−2619.31	+	2619.31i	−0.256769	+	0.256769i	−0.823739	−	0.566969i	$-0.808116\pi$
$101$	−2619.31	+	2619.31i	−0.256769	+	0.256769i	0.566969	+	0.823739i	$0.308116\pi$
$102$		0			0
$103$	8970.66			0.845570			0.422785	−	0.906230i	$-0.361052\pi$
$103$	8970.66			0.845570			0.422785	+	0.906230i	$0.361052\pi$
$104$		0			0
$105$	335.026	+	335.026i	0.0303879	+	0.0303879i
$106$		0			0
$107$	−15349.5			−1.34069			−0.670344	−	0.742050i	$-0.733853\pi$
$107$	−15349.5			−1.34069			−0.670344	+	0.742050i	$0.733853\pi$
$108$		0			0
$109$			4928.86i			0.414852i	0.978251	+	0.207426i	$0.0665087\pi$
$109$			4928.86i			0.414852i	−0.978251	+	0.207426i	$0.933491\pi$
$110$		0			0
$111$	496.573			0.0403029
$112$		0			0
$113$	−4987.25	−	4987.25i	−0.390575	−	0.390575i	0.484317	−	0.874892i	$-0.339068\pi$
$113$	−4987.25	−	4987.25i	−0.390575	−	0.390575i	−0.874892	+	0.484317i	$0.839068\pi$
$114$		0			0
$115$		−	11022.7i		−	0.833475i
$116$		0			0
$117$	8668.70			0.633260
$118$		0			0
$119$	2720.20	−	2720.20i	0.192091	−	0.192091i
$120$		0			0
$121$			13680.7i			0.934410i
$122$		0			0
$123$	5075.37			0.335473
$124$		0			0
$125$			16968.6i			1.08599i
$126$		0			0
$127$	12003.2	−	12003.2i	0.744200	−	0.744200i	−0.229183	−	0.973383i	$-0.573605\pi$
$127$	12003.2	−	12003.2i	0.744200	−	0.744200i	0.973383	+	0.229183i	$0.0736055\pi$
$128$		0			0
$129$			1247.73i			0.0749795i
$130$		0			0
$131$	19292.7	+	19292.7i	1.12422	+	1.12422i	0.991101	+	0.133116i	$0.0424982\pi$
$131$	19292.7	+	19292.7i	1.12422	+	1.12422i	0.133116	+	0.991101i	$0.457502\pi$
$132$		0			0
$133$	−3997.48	+	3997.48i	−0.225987	+	0.225987i
$134$		0			0
$135$	4459.96	−	4459.96i	0.244717	−	0.244717i
$136$		0			0
$137$	5008.06	−	5008.06i	0.266826	−	0.266826i	−0.560994	−	0.827820i	$-0.689581\pi$
$137$	5008.06	−	5008.06i	0.266826	−	0.266826i	0.827820	+	0.560994i	$0.189581\pi$
$138$		0			0
$139$	25717.8			1.33108			0.665539	−	0.746363i	$-0.268202\pi$
$139$	25717.8			1.33108			0.665539	+	0.746363i	$0.268202\pi$
$140$		0			0
$141$	613.148			0.0308409
$142$		0			0
$143$	2472.20	+	2472.20i	0.120896	+	0.120896i
$144$		0			0
$145$	3796.82	−	16024.3i	0.180586	−	0.762155i
$146$		0			0
$147$	3261.92	−	3261.92i	0.150952	−	0.150952i
$148$		0			0
$149$		−	15550.2i		−	0.700429i	−0.936670	−	0.350214i	$-0.886109\pi$
$149$		−	15550.2i		−	0.700429i	0.936670	−	0.350214i	$-0.113891\pi$
$150$		0			0
$151$			15235.4i			0.668190i	0.942539	+	0.334095i	$0.108431\pi$
$151$			15235.4i			0.668190i	−0.942539	+	0.334095i	$0.891569\pi$
$152$		0			0
$153$	−17628.2	−	17628.2i	−0.753054	−	0.753054i
$154$		0			0
$155$	−4978.79	−	4978.79i	−0.207234	−	0.207234i
$156$		0			0
$157$	8575.88	+	8575.88i	0.347920	+	0.347920i	0.859334	−	0.511414i	$-0.170878\pi$
$157$	8575.88	+	8575.88i	0.347920	+	0.347920i	−0.511414	+	0.859334i	$0.670878\pi$
$158$		0			0
$159$	1741.07	−	1741.07i	0.0688687	−	0.0688687i
$160$		0			0
$161$	6674.13			0.257480
$162$		0			0
$163$	8210.78	+	8210.78i	0.309036	+	0.309036i	0.844536	−	0.535500i	$-0.179877\pi$
$163$	8210.78	+	8210.78i	0.309036	+	0.309036i	−0.535500	+	0.844536i	$0.679877\pi$
$164$		0			0
$165$	1238.36			0.0454862
$166$		0			0
$167$		−	16733.4i		−	0.600001i	−0.953939	−	0.300001i	$-0.903013\pi$
$167$		−	16733.4i		−	0.600001i	0.953939	−	0.300001i	$-0.0969869\pi$
$168$		0			0
$169$	15832.2			0.554329
$170$		0			0
$171$	25905.7	+	25905.7i	0.885937	+	0.885937i
$172$		0			0
$173$			27855.0i			0.930702i	0.885126	+	0.465351i	$0.154072\pi$
$173$			27855.0i			0.930702i	−0.885126	+	0.465351i	$0.845928\pi$
$174$		0			0
$175$	−2864.11			−0.0935220
$176$		0			0
$177$	5110.25	−	5110.25i	0.163116	−	0.163116i
$178$		0			0
$179$			32431.9i			1.01220i	0.862475	+	0.506100i	$0.168913\pi$
$179$			32431.9i			1.01220i	−0.862475	+	0.506100i	$0.831087\pi$
$180$		0			0
$181$	−31725.3			−0.968386			−0.484193	−	0.874961i	$-0.660887\pi$
$181$	−31725.3			−0.968386			−0.484193	+	0.874961i	$0.660887\pi$
$182$		0			0
$183$		−	10367.4i		−	0.309577i
$184$		0			0
$185$	3369.10	−	3369.10i	0.0984398	−	0.0984398i
$186$		0			0
$187$		−	10054.7i		−	0.287532i
$188$		0			0
$189$	2700.46	+	2700.46i	0.0755987	+	0.0755987i
$190$		0			0
$191$	−14826.0	+	14826.0i	−0.406403	+	0.406403i	−0.880482	−	0.474079i	$-0.842781\pi$
$191$	−14826.0	+	14826.0i	−0.406403	+	0.406403i	0.474079	+	0.880482i	$0.342781\pi$
$192$		0			0
$193$	−13810.9	+	13810.9i	−0.370772	+	0.370772i	−0.867758	−	0.496987i	$-0.834440\pi$
$193$	−13810.9	+	13810.9i	−0.370772	+	0.370772i	0.496987	+	0.867758i	$0.334440\pi$
$194$		0			0
$195$	−3188.02	+	3188.02i	−0.0838401	+	0.0838401i
$196$		0			0
$197$	−13543.4			−0.348975			−0.174487	−	0.984659i	$-0.555827\pi$
$197$	−13543.4			−0.348975			−0.174487	+	0.984659i	$0.555827\pi$
$198$		0			0
$199$	−41376.4			−1.04483			−0.522416	−	0.852690i	$-0.674969\pi$
$199$	−41376.4			−1.04483			−0.522416	+	0.852690i	$0.674969\pi$
$200$		0			0
$201$	−4982.82	−	4982.82i	−0.123334	−	0.123334i
$202$		0			0
$203$	9702.56	+	2298.94i	0.235448	+	0.0557872i
$204$		0			0
$205$	34434.9	−	34434.9i	0.819392	−	0.819392i
$206$		0			0
$207$		−	43251.8i		−	1.00940i
$208$		0			0
$209$			14775.9i			0.338269i
$210$		0			0
$211$	−16174.5	−	16174.5i	−0.363300	−	0.363300i	0.501726	−	0.865027i	$-0.332699\pi$
$211$	−16174.5	−	16174.5i	−0.363300	−	0.363300i	−0.865027	+	0.501726i	$0.832699\pi$
$212$		0			0
$213$	8954.01	+	8954.01i	0.197360	+	0.197360i
$214$		0			0
$215$	8465.52	+	8465.52i	0.183137	+	0.183137i
$216$		0			0
$217$	3014.61	−	3014.61i	0.0640193	−	0.0640193i
$218$		0			0
$219$	10953.3			0.228379
$220$		0			0
$221$	25884.7	+	25884.7i	0.529978	+	0.529978i
$222$		0			0
$223$	−61443.6			−1.23557			−0.617784	−	0.786348i	$-0.711969\pi$
$223$	−61443.6			−1.23557			−0.617784	+	0.786348i	$0.711969\pi$
$224$		0			0
$225$			18560.9i			0.366635i
$226$		0			0
$227$	−54881.1			−1.06505			−0.532526	−	0.846414i	$-0.678757\pi$
$227$	−54881.1			−1.06505			−0.532526	+	0.846414i	$0.678757\pi$
$228$		0			0
$229$	−32466.4	−	32466.4i	−0.619102	−	0.619102i	0.326199	−	0.945301i	$-0.394232\pi$
$229$	−32466.4	−	32466.4i	−0.619102	−	0.619102i	−0.945301	+	0.326199i	$0.894232\pi$
$230$		0			0
$231$			749.816i			0.0140518i
$232$		0			0
$233$	37392.0			0.688758			0.344379	−	0.938831i	$-0.388090\pi$
$233$	37392.0			0.688758			0.344379	+	0.938831i	$0.388090\pi$
$234$		0			0
$235$	4160.04	−	4160.04i	0.0753289	−	0.0753289i
$236$		0			0
$237$			15276.8i			0.271979i
$238$		0			0
$239$	−103303.			−1.80850			−0.904250	−	0.427004i	$-0.859569\pi$
$239$	−103303.			−1.80850			−0.904250	+	0.427004i	$0.859569\pi$
$240$		0			0
$241$		−	32461.4i		−	0.558899i	−0.960160	−	0.279449i	$-0.909848\pi$
$241$		−	32461.4i		−	0.558899i	0.960160	−	0.279449i	$-0.0901519\pi$
$242$		0			0
$243$	26481.4	−	26481.4i	0.448465	−	0.448465i
$244$		0			0
$245$		−	44262.4i		−	0.737399i
$246$		0			0
$247$	−38039.0	−	38039.0i	−0.623497	−	0.623497i
$248$		0			0
$249$	−10852.0	+	10852.0i	−0.175030	+	0.175030i
$250$		0			0
$251$	−17934.1	+	17934.1i	−0.284664	+	0.284664i	−0.834966	−	0.550302i	$-0.814513\pi$
$251$	−17934.1	+	17934.1i	−0.284664	+	0.284664i	0.550302	+	0.834966i	$0.314513\pi$
$252$		0			0
$253$	12334.9	−	12334.9i	0.192705	−	0.192705i
$254$		0			0
$255$	12966.0			0.199400
$256$		0			0
$257$	−56381.5			−0.853632			−0.426816	−	0.904339i	$-0.640365\pi$
$257$	−56381.5			−0.853632			−0.426816	+	0.904339i	$0.640365\pi$
$258$		0			0
$259$	2039.96	+	2039.96i	0.0304104	+	0.0304104i
$260$		0			0
$261$	14898.3	−	62877.5i	0.218703	−	0.923026i
$262$		0			0
$263$	−43756.1	+	43756.1i	−0.632597	+	0.632597i	−0.948719	−	0.316122i	$-0.897619\pi$
$263$	−43756.1	+	43756.1i	−0.632597	+	0.632597i	0.316122	+	0.948719i	$0.397619\pi$
$264$		0			0
$265$		−	23625.3i		−	0.336423i
$266$		0			0
$267$		−	13804.2i		−	0.193637i
$268$		0			0
$269$	−4020.00	−	4020.00i	−0.0555548	−	0.0555548i	0.678784	−	0.734338i	$-0.262507\pi$
$269$	−4020.00	−	4020.00i	−0.0555548	−	0.0555548i	−0.734338	+	0.678784i	$0.762507\pi$
$270$		0			0
$271$	−58185.7	−	58185.7i	−0.792279	−	0.792279i	0.189586	−	0.981864i	$-0.439286\pi$
$271$	−58185.7	−	58185.7i	−0.792279	−	0.792279i	−0.981864	+	0.189586i	$0.939286\pi$
$272$		0			0
$273$	−1930.31	−	1930.31i	−0.0259002	−	0.0259002i
$274$		0			0
$275$	−5293.33	+	5293.33i	−0.0699944	+	0.0699944i
$276$		0			0
$277$	−9090.10			−0.118470			−0.0592351	−	0.998244i	$-0.518866\pi$
$277$	−9090.10			−0.118470			−0.0592351	+	0.998244i	$0.518866\pi$
$278$		0			0
$279$	−19536.2	−	19536.2i	−0.250975	−	0.250975i
$280$		0			0
$281$	51749.1			0.655375			0.327687	−	0.944786i	$-0.393731\pi$
$281$	51749.1			0.655375			0.327687	+	0.944786i	$0.393731\pi$
$282$		0			0
$283$			132045.i			1.64872i	0.566063	+	0.824362i	$0.308466\pi$
$283$			132045.i			1.64872i	−0.566063	+	0.824362i	$0.691534\pi$
$284$		0			0
$285$	−19054.3			−0.234586
$286$		0			0
$287$	20850.0	+	20850.0i	0.253129	+	0.253129i
$288$		0			0
$289$		−	21754.7i		−	0.260469i
$290$		0			0
$291$	−33652.0			−0.397397
$292$		0			0
$293$	20123.6	−	20123.6i	0.234407	−	0.234407i	−0.580122	−	0.814529i	$-0.696995\pi$
$293$	20123.6	−	20123.6i	0.234407	−	0.234407i	0.814529	+	0.580122i	$0.196995\pi$
$294$		0			0
$295$		−	69343.2i		−	0.796820i
$296$		0			0
$297$	9981.76			0.113160
$298$		0			0
$299$			63509.3i			0.710387i
$300$		0			0
$301$	−5125.78	+	5125.78i	−0.0565754	+	0.0565754i
$302$		0			0
$303$		−	7559.60i		−	0.0823406i
$304$		0			0
$305$	−70340.0	−	70340.0i	−0.756141	−	0.756141i
$306$		0			0
$307$	−5050.32	+	5050.32i	−0.0535849	+	0.0535849i	−0.733391	−	0.679807i	$-0.762064\pi$
$307$	−5050.32	+	5050.32i	−0.0535849	+	0.0535849i	0.679807	+	0.733391i	$0.262064\pi$
$308$		0			0
$309$	−12945.2	+	12945.2i	−0.135578	+	0.135578i
$310$		0			0
$311$	−17448.6	+	17448.6i	−0.180402	+	0.180402i	−0.791531	−	0.611129i	$-0.790716\pi$
$311$	−17448.6	+	17448.6i	−0.180402	+	0.180402i	0.611129	+	0.791531i	$0.290716\pi$
$312$		0			0
$313$	23766.7			0.242595			0.121297	−	0.992616i	$-0.461295\pi$
$313$	23766.7			0.242595			0.121297	+	0.992616i	$0.461295\pi$
$314$		0			0
$315$	17838.4			0.179777
$316$		0			0
$317$	74834.8	+	74834.8i	0.744706	+	0.744706i	0.973480	−	0.228773i	$-0.0734715\pi$
$317$	74834.8	+	74834.8i	0.744706	+	0.744706i	−0.228773	+	0.973480i	$0.573471\pi$
$318$		0			0
$319$	22180.7	−	13683.1i	0.217968	−	0.134463i
$320$		0			0
$321$	22150.2	−	22150.2i	0.214965	−	0.214965i
$322$		0			0
$323$			154708.i			1.48289i
$324$		0			0
$325$		−	27254.1i		−	0.258027i
$326$		0			0
$327$	−7112.62	−	7112.62i	−0.0665172	−	0.0665172i
$328$		0			0
$329$	2518.86	+	2518.86i	0.0232708	+	0.0232708i
$330$		0			0
$331$	−92810.5	−	92810.5i	−0.847113	−	0.847113i	0.142659	−	0.989772i	$-0.454435\pi$
$331$	−92810.5	−	92810.5i	−0.847113	−	0.847113i	−0.989772	+	0.142659i	$0.954435\pi$
$332$		0			0
$333$	13220.0	−	13220.0i	0.119218	−	0.119218i
$334$		0			0
$335$	−67614.0			−0.602486
$336$		0			0
$337$	138576.	+	138576.i	1.22019	+	1.22019i	0.967563	+	0.252629i	$0.0812951\pi$
$337$	138576.	+	138576.i	1.22019	+	1.22019i	0.252629	+	0.967563i	$0.418705\pi$
$338$		0			0
$339$	14393.8			0.125249
$340$		0			0
$341$		−	11142.9i		−	0.0958277i
$342$		0			0
$343$	55267.5			0.469766
$344$		0			0
$345$	15906.4	+	15906.4i	0.133639	+	0.133639i
$346$		0			0
$347$			220172.i			1.82854i	0.405108	+	0.914269i	$0.367234\pi$
$347$			220172.i			1.82854i	−0.405108	+	0.914269i	$0.632766\pi$
$348$		0			0
$349$	−53756.0			−0.441343			−0.220671	−	0.975348i	$-0.570825\pi$
$349$	−53756.0			−0.441343			−0.220671	+	0.975348i	$0.570825\pi$
$350$		0			0
$351$	−25696.9	+	25696.9i	−0.208577	+	0.208577i
$352$		0			0
$353$			129390.i			1.03837i	0.854663	+	0.519184i	$0.173764\pi$
$353$			129390.i			1.03837i	−0.854663	+	0.519184i	$0.826236\pi$
$354$		0			0
$355$	121501.			0.964101
$356$		0			0
$357$			7850.79i			0.0615994i
$358$		0			0
$359$	109726.	−	109726.i	0.851374	−	0.851374i	−0.138928	−	0.990302i	$-0.544366\pi$
$359$	109726.	−	109726.i	0.851374	−	0.851374i	0.990302	+	0.138928i	$0.0443657\pi$
$360$		0			0
$361$		−	97031.5i		−	0.744558i
$362$		0			0
$363$	−19742.0	−	19742.0i	−0.149823	−	0.149823i
$364$		0			0
$365$	74315.0	−	74315.0i	0.557816	−	0.557816i
$366$		0			0
$367$	60580.9	−	60580.9i	0.449784	−	0.449784i	−0.445499	−	0.895282i	$-0.646974\pi$
$367$	60580.9	−	60580.9i	0.449784	−	0.449784i	0.895282	+	0.445499i	$0.146974\pi$
$368$		0			0
$369$	135119.	−	135119.i	0.992344	−	0.992344i
$370$		0			0
$371$	14304.9			0.103929
$372$		0			0
$373$	72996.7			0.524669			0.262335	−	0.964977i	$-0.415508\pi$
$373$	72996.7			0.524669			0.262335	+	0.964977i	$0.415508\pi$
$374$		0			0
$375$	−24486.7	−	24486.7i	−0.174127	−	0.174127i
$376$		0			0
$377$	−21876.1	+	92327.0i	−0.153917	+	0.649600i
$378$		0			0
$379$	−26846.7	+	26846.7i	−0.186901	+	0.186901i	−0.794355	−	0.607454i	$-0.792191\pi$
$379$	−26846.7	+	26846.7i	−0.186901	+	0.186901i	0.607454	+	0.794355i	$0.292191\pi$
$380$		0			0
$381$			34642.6i			0.238649i
$382$		0			0
$383$		−	258964.i		−	1.76539i	−0.469943	−	0.882697i	$-0.655726\pi$
$383$		−	258964.i		−	1.76539i	0.469943	−	0.882697i	$-0.344274\pi$
$384$		0			0
$385$	5087.28	+	5087.28i	0.0343214	+	0.0343214i
$386$		0			0
$387$	33217.7	+	33217.7i	0.221793	+	0.221793i
$388$		0			0
$389$	−79.0369	−	79.0369i	−0.000522313	−	0.000522313i	0.706846	−	0.707368i	$-0.250118\pi$
$389$	−79.0369	−	79.0369i	−0.000522313	−	0.000522313i	−0.707368	+	0.706846i	$0.750118\pi$
$390$		0			0
$391$	129149.	−	129149.i	0.844771	−	0.844771i
$392$		0			0
$393$	−55680.8			−0.360512
$394$		0			0
$395$	103649.	+	103649.i	0.664307	+	0.664307i
$396$		0			0
$397$	−4406.91			−0.0279610			−0.0139805	−	0.999902i	$-0.504450\pi$
$397$	−4406.91			−0.0279610			−0.0139805	+	0.999902i	$0.504450\pi$
$398$		0			0
$399$		−	11537.2i		−	0.0724692i
$400$		0			0
$401$	−31555.0			−0.196236			−0.0981181	−	0.995175i	$-0.531282\pi$
$401$	−31555.0			−0.196236			−0.0981181	+	0.995175i	$0.531282\pi$
$402$		0			0
$403$	28686.2	+	28686.2i	0.176629	+	0.176629i
$404$		0			0
$405$		−	108996.i		−	0.664509i
$406$		0			0
$407$	7540.33			0.0455199
$408$		0			0
$409$	−64953.9	+	64953.9i	−0.388292	+	0.388292i	−0.874078	−	0.485786i	$-0.838533\pi$
$409$	−64953.9	+	64953.9i	−0.388292	+	0.388292i	0.485786	+	0.874078i	$0.338533\pi$
$410$		0			0
$411$			14453.8i			0.0855655i
$412$		0			0
$413$	41986.6			0.246156
$414$		0			0
$415$			147256.i			0.855019i
$416$		0			0
$417$	−37112.2	+	37112.2i	−0.213424	+	0.213424i
$418$		0			0
$419$			236405.i			1.34657i	0.739384	+	0.673284i	$0.235117\pi$
$419$			236405.i			1.34657i	−0.739384	+	0.673284i	$0.764883\pi$
$420$		0			0
$421$	233705.	+	233705.i	1.31857	+	1.31857i	0.914908	+	0.403663i	$0.132263\pi$
$421$	233705.	+	233705.i	1.31857	+	1.31857i	0.403663	+	0.914908i	$0.367737\pi$
$422$		0			0
$423$	16323.5	−	16323.5i	0.0912288	−	0.0912288i
$424$		0			0
$425$	−55422.7	+	55422.7i	−0.306838	+	0.306838i
$426$		0			0
$427$	42590.2	−	42590.2i	0.233590	−	0.233590i
$428$		0			0
$429$	−7135.05			−0.0387688
$430$		0			0
$431$	171654.			0.924056			0.462028	−	0.886865i	$-0.347122\pi$
$431$	171654.			0.924056			0.462028	+	0.886865i	$0.347122\pi$
$432$		0			0
$433$	167542.	+	167542.i	0.893611	+	0.893611i	0.994861	−	0.101250i	$-0.0322843\pi$
$433$	167542.	+	167542.i	0.893611	+	0.893611i	−0.101250	+	0.994861i	$0.532284\pi$
$434$		0			0
$435$	17644.9	+	28603.0i	0.0932485	+	0.151159i
$436$		0			0
$437$	−189792.	+	189792.i	−0.993838	+	0.993838i
$438$		0			0
$439$		−	57526.1i		−	0.298494i	−0.988800	−	0.149247i	$-0.952315\pi$
$439$		−	57526.1i		−	0.298494i	0.988800	−	0.149247i	$-0.0476850\pi$
$440$		0			0
$441$		−	173680.i		−	0.893045i
$442$		0			0
$443$	−12796.0	−	12796.0i	−0.0652031	−	0.0652031i	0.673753	−	0.738956i	$-0.264681\pi$
$443$	−12796.0	−	12796.0i	−0.0652031	−	0.0652031i	−0.738956	+	0.673753i	$0.764681\pi$
$444$		0			0
$445$	−93657.4	−	93657.4i	−0.472958	−	0.472958i
$446$		0			0
$447$	22439.8	+	22439.8i	0.112306	+	0.112306i
$448$		0			0
$449$	−251422.	+	251422.i	−1.24713	+	1.24713i	−0.290146	+	0.956982i	$0.593704\pi$
$449$	−251422.	+	251422.i	−1.24713	+	1.24713i	−0.956982	+	0.290146i	$0.906296\pi$
$450$		0			0
$451$	77068.2			0.378898
$452$		0			0
$453$	−21985.5	−	21985.5i	−0.107137	−	0.107137i
$454$		0			0
$455$	−26193.3			−0.126522
$456$		0			0
$457$		−	369586.i		−	1.76963i	−0.465938	−	0.884817i	$-0.654283\pi$
$457$		−	369586.i		−	1.76963i	0.465938	−	0.884817i	$-0.345717\pi$
$458$		0			0
$459$	104512.			0.496067
$460$		0			0
$461$	16601.8	+	16601.8i	0.0781183	+	0.0781183i	0.745086	−	0.666968i	$-0.232408\pi$
$461$	16601.8	+	16601.8i	0.0781183	+	0.0781183i	−0.666968	+	0.745086i	$0.732408\pi$
$462$		0			0
$463$		−	126363.i		−	0.589464i	−0.955580	−	0.294732i	$-0.904770\pi$
$463$		−	126363.i		−	0.589464i	0.955580	−	0.294732i	$-0.0952304\pi$
$464$		0			0
$465$	14369.3			0.0664555
$466$		0			0
$467$	35640.0	−	35640.0i	0.163420	−	0.163420i	−0.620660	−	0.784080i	$-0.713135\pi$
$467$	35640.0	−	35640.0i	0.163420	−	0.163420i	0.784080	+	0.620660i	$0.213135\pi$
$468$		0			0
$469$		−	40939.6i		−	0.186122i
$470$		0			0
$471$	−24750.9			−0.111571
$472$		0			0
$473$			18946.5i			0.0846851i
$474$		0			0
$475$	81446.7	−	81446.7i	0.360983	−	0.360983i
$476$		0			0
$477$		−	92702.9i		−	0.407434i
$478$		0			0
$479$	−161558.	−	161558.i	−0.704139	−	0.704139i	0.261157	−	0.965296i	$-0.415896\pi$
$479$	−161558.	−	161558.i	−0.704139	−	0.704139i	−0.965296	+	0.261157i	$0.915896\pi$
$480$		0			0
$481$	−19411.7	+	19411.7i	−0.0839022	+	0.0839022i
$482$		0			0
$483$	−9631.14	+	9631.14i	−0.0412842	+	0.0412842i
$484$		0			0
$485$	−228319.	+	228319.i	−0.970642	+	0.970642i
$486$		0			0
$487$	−81974.4			−0.345637			−0.172819	−	0.984954i	$-0.555287\pi$
$487$	−81974.4			−0.345637			−0.172819	+	0.984954i	$0.555287\pi$
$488$		0			0
$489$	−23697.2			−0.0991014
$490$		0			0
$491$	154367.	+	154367.i	0.640313	+	0.640313i	0.950632	−	0.310319i	$-0.100436\pi$
$491$	154367.	+	154367.i	0.640313	+	0.640313i	−0.310319	+	0.950632i	$0.600436\pi$
$492$		0			0
$493$	232238.	−	143266.i	0.955519	−	0.589452i
$494$		0			0
$495$	32968.2	−	32968.2i	0.134550	−	0.134550i
$496$		0			0
$497$			73567.5i			0.297833i
$498$		0			0
$499$		−	94911.3i		−	0.381168i	−0.981671	−	0.190584i	$-0.938962\pi$
$499$		−	94911.3i		−	0.381168i	0.981671	−	0.190584i	$-0.0610382\pi$
$500$		0			0
$501$	24147.3	+	24147.3i	0.0962039	+	0.0962039i
$502$		0			0
$503$	−53627.4	−	53627.4i	−0.211958	−	0.211958i	0.593141	−	0.805099i	$-0.297888\pi$
$503$	−53627.4	−	53627.4i	−0.211958	−	0.211958i	−0.805099	+	0.593141i	$0.797888\pi$
$504$		0			0
$505$	−51289.7	−	51289.7i	−0.201117	−	0.201117i
$506$		0			0
$507$	−22846.7	+	22846.7i	−0.0888809	+	0.0888809i
$508$		0			0
$509$	−211778.			−0.817421			−0.408711	−	0.912664i	$-0.634021\pi$
$509$	−211778.			−0.817421			−0.408711	+	0.912664i	$0.634021\pi$
$510$		0			0
$511$	44997.0	+	44997.0i	0.172322	+	0.172322i
$512$		0			0
$513$	−153586.			−0.583602
$514$		0			0
$515$			175658.i			0.662299i
$516$		0			0
$517$	9310.50			0.0348331
$518$		0			0
$519$	−40196.3	−	40196.3i	−0.149228	−	0.149228i
$520$		0			0
$521$		−	78861.8i		−	0.290530i	−0.989393	−	0.145265i	$-0.953596\pi$
$521$		−	78861.8i		−	0.290530i	0.989393	−	0.145265i	$-0.0464035\pi$
$522$		0			0
$523$	212395.			0.776501			0.388250	−	0.921554i	$-0.373080\pi$
$523$	212395.			0.776501			0.388250	+	0.921554i	$0.373080\pi$
$524$		0			0
$525$	4133.07	−	4133.07i	0.0149953	−	0.0149953i
$526$		0			0
$527$		−	116670.i		−	0.420085i
$528$		0			0
$529$	37033.4			0.132337
$530$		0			0
$531$		−	272094.i		−	0.965008i
$532$		0			0
$533$	−198403.	+	198403.i	−0.698384	+	0.698384i
$534$		0			0
$535$		−	300566.i		−	1.05010i
$536$		0			0
$537$	−46801.0	−	46801.0i	−0.162296	−	0.162296i
$538$		0			0
$539$	49531.4	−	49531.4i	0.170492	−	0.170492i
$540$		0			0
$541$	−305518.	+	305518.i	−1.04386	+	1.04386i	−0.0448665	+	0.998993i	$0.514286\pi$
$541$	−305518.	+	305518.i	−1.04386	+	1.04386i	−0.998993	+	0.0448665i	$0.985714\pi$
$542$		0			0
$543$	45781.4	−	45781.4i	0.155270	−	0.155270i
$544$		0			0
$545$	−96514.2			−0.324936
$546$		0			0
$547$	−461199.			−1.54139			−0.770697	−	0.637202i	$-0.780092\pi$
$547$	−461199.			−1.54139			−0.770697	+	0.637202i	$0.780092\pi$
$548$		0			0
$549$	−276006.	−	276006.i	−0.915743	−	0.915743i
$550$		0			0
$551$	−341286.	+	210537.i	−1.12413	+	0.693465i
$552$		0			0
$553$	−62758.1	+	62758.1i	−0.205220	+	0.205220i
$554$		0			0
$555$			9723.60i			0.0315676i
$556$		0			0
$557$		−	342322.i		−	1.10338i	−0.834050	−	0.551689i	$-0.813984\pi$
$557$		−	342322.i		−	1.10338i	0.834050	−	0.551689i	$-0.186016\pi$
$558$		0			0
$559$	−48775.6	−	48775.6i	−0.156091	−	0.156091i
$560$		0			0
$561$	14509.5	+	14509.5i	0.0461027	+	0.0461027i
$562$		0			0
$563$	421770.	+	421770.i	1.33063	+	1.33063i	0.904803	+	0.425831i	$0.140018\pi$
$563$	421770.	+	421770.i	1.33063	+	1.33063i	0.425831	+	0.904803i	$0.359982\pi$
$564$		0			0
$565$	97657.6	−	97657.6i	0.305921	−	0.305921i
$566$		0			0
$567$	65996.0			0.205282
$568$		0			0
$569$	38821.9	+	38821.9i	0.119909	+	0.119909i	0.764515	−	0.644606i	$-0.222979\pi$
$569$	38821.9	+	38821.9i	0.119909	+	0.119909i	−0.644606	+	0.764515i	$0.722979\pi$
$570$		0			0
$571$	157460.			0.482947			0.241473	−	0.970407i	$-0.422369\pi$
$571$	157460.			0.482947			0.241473	+	0.970407i	$0.422369\pi$
$572$		0			0
$573$		−	42789.4i		−	0.130325i
$574$		0			0
$575$	−135982.			−0.411288
$576$		0			0
$577$	−26691.1	−	26691.1i	−0.0801706	−	0.0801706i	0.665884	−	0.746055i	$-0.268054\pi$
$577$	−26691.1	−	26691.1i	−0.0801706	−	0.0801706i	−0.746055	+	0.665884i	$0.768054\pi$
$578$		0			0
$579$		−	39859.7i		−	0.118899i
$580$		0			0
$581$	−89161.8			−0.264135
$582$		0			0
$583$	26437.7	−	26437.7i	0.0777833	−	0.0777833i
$584$		0			0
$585$			169746.i			0.496006i
$586$		0			0
$587$	44588.9			0.129405			0.0647024	−	0.997905i	$-0.479390\pi$
$587$	44588.9			0.129405			0.0647024	+	0.997905i	$0.479390\pi$
$588$		0			0
$589$			171453.i			0.494212i
$590$		0			0
$591$	19543.8	−	19543.8i	0.0559544	−	0.0559544i
$592$		0			0
$593$		−	125031.i		−	0.355557i	−0.984070	−	0.177779i	$-0.943109\pi$
$593$		−	125031.i		−	0.355557i	0.984070	−	0.177779i	$-0.0568911\pi$
$594$		0			0
$595$	53265.3	+	53265.3i	0.150456	+	0.150456i
$596$		0			0
$597$	59708.5	−	59708.5i	0.167528	−	0.167528i
$598$		0			0
$599$	−161672.	+	161672.i	−0.450590	+	0.450590i	−0.895550	−	0.444960i	$-0.853218\pi$
$599$	−161672.	+	161672.i	−0.450590	+	0.450590i	0.444960	+	0.895550i	$0.353218\pi$
$600$		0			0
$601$	−170639.	+	170639.i	−0.472421	+	0.472421i	−0.902697	−	0.430276i	$-0.858416\pi$
$601$	−170639.	+	170639.i	−0.472421	+	0.472421i	0.430276	+	0.902697i	$0.358416\pi$
$602$		0			0
$603$	−265309.			−0.729655
$604$		0			0
$605$	−267888.			−0.731883
$606$		0			0
$607$	−474790.	−	474790.i	−1.28862	−	1.28862i	−0.935627	−	0.352990i	$-0.885165\pi$
$607$	−474790.	−	474790.i	−1.28862	−	1.28862i	−0.352990	−	0.935627i	$-0.614835\pi$
$608$		0			0
$609$	−17318.8	+	10683.8i	−0.0466964	+	0.0288066i
$610$		0			0
$611$	−23968.8	+	23968.8i	−0.0642043	+	0.0642043i
$612$		0			0
$613$		−	219628.i		−	0.584477i	−0.956345	−	0.292238i	$-0.905600\pi$
$613$		−	219628.i		−	0.584477i	0.956345	−	0.292238i	$-0.0944001\pi$
$614$		0			0
$615$			99383.0i			0.262762i
$616$		0			0
$617$	−220605.	−	220605.i	−0.579490	−	0.579490i	0.355273	−	0.934763i	$-0.384388\pi$
$617$	−220605.	−	220605.i	−0.579490	−	0.579490i	−0.934763	+	0.355273i	$0.884388\pi$
$618$		0			0
$619$	−277923.	−	277923.i	−0.725343	−	0.725343i	0.244345	−	0.969688i	$-0.421427\pi$
$619$	−277923.	−	277923.i	−0.725343	−	0.725343i	−0.969688	+	0.244345i	$0.921427\pi$
$620$		0			0
$621$	128212.	+	128212.i	0.332466	+	0.332466i
$622$		0			0
$623$	56708.6	−	56708.6i	0.146108	−	0.146108i
$624$		0			0
$625$	−181290.			−0.464104
$626$		0			0
$627$	−21322.5	−	21322.5i	−0.0542379	−	0.0542379i
$628$		0			0
$629$	78949.4			0.199548
$630$		0			0
$631$		−	454313.i		−	1.14103i	−0.821288	−	0.570514i	$-0.806744\pi$
$631$		−	454313.i		−	1.14103i	0.821288	−	0.570514i	$-0.193256\pi$
$632$		0			0
$633$	46681.4			0.116503
$634$		0			0
$635$	235040.	+	235040.i	0.582900	+	0.582900i
$636$		0			0
$637$			255026.i			0.628500i
$638$		0			0
$639$	476755.			1.16760
$640$		0			0
$641$	−182466.	+	182466.i	−0.444085	+	0.444085i	−0.893382	−	0.449297i	$-0.851674\pi$
$641$	−182466.	+	182466.i	−0.444085	+	0.444085i	0.449297	+	0.893382i	$0.351674\pi$
$642$		0			0
$643$		−	310209.i		−	0.750294i	−0.926965	−	0.375147i	$-0.877592\pi$
$643$		−	310209.i		−	0.750294i	0.926965	−	0.375147i	$-0.122408\pi$
$644$		0			0
$645$	−24432.4			−0.0587282
$646$		0			0
$647$		−	51773.7i		−	0.123680i	−0.998086	−	0.0618402i	$-0.980303\pi$
$647$		−	51773.7i		−	0.123680i	0.998086	−	0.0618402i	$-0.0196969\pi$
$648$		0			0
$649$	77597.9	−	77597.9i	0.184230	−	0.184230i
$650$		0			0
$651$			8700.49i			0.0205296i
$652$		0			0
$653$	293919.	+	293919.i	0.689288	+	0.689288i	0.962075	−	0.272787i	$-0.0879453\pi$
$653$	293919.	+	293919.i	0.689288	+	0.689288i	−0.272787	+	0.962075i	$0.587945\pi$
$654$		0			0
$655$	−377778.	+	377778.i	−0.880550	+	0.880550i
$656$		0			0
$657$	291603.	−	291603.i	0.675556	−	0.675556i
$658$		0			0
$659$	−102773.	+	102773.i	−0.236652	+	0.236652i	−0.815462	−	0.578810i	$-0.803517\pi$
$659$	−102773.	+	102773.i	−0.236652	+	0.236652i	0.578810	+	0.815462i	$0.303517\pi$
$660$		0			0
$661$	−58746.4			−0.134456			−0.0672278	−	0.997738i	$-0.521415\pi$
$661$	−58746.4			−0.134456			−0.0672278	+	0.997738i	$0.521415\pi$
$662$		0			0
$663$	−74706.0			−0.169953
$664$		0			0
$665$	−78276.3	−	78276.3i	−0.177006	−	0.177006i
$666$		0			0
$667$	460658.	+	109149.i	1.03544	+	0.245340i
$668$		0			0
$669$	88666.5	−	88666.5i	0.198110	−	0.198110i
$670$		0			0
$671$		−	157427.i		−	0.349650i
$672$		0			0
$673$			348490.i			0.769414i	0.923039	+	0.384707i	$0.125698\pi$
$673$			348490.i			0.769414i	−0.923039	+	0.384707i	$0.874302\pi$
$674$		0			0
$675$	−55020.6	−	55020.6i	−0.120759	−	0.120759i
$676$		0			0
$677$	218259.	+	218259.i	0.476205	+	0.476205i	0.903916	−	0.427710i	$-0.140680\pi$
$677$	218259.	+	218259.i	0.476205	+	0.476205i	−0.427710	+	0.903916i	$0.640680\pi$
$678$		0			0
$679$	−138245.	−	138245.i	−0.299854	−	0.299854i
$680$		0			0
$681$	79196.4	−	79196.4i	0.170770	−	0.170770i
$682$		0			0
$683$	505430.			1.08348			0.541739	−	0.840547i	$-0.317766\pi$
$683$	505430.			1.08348			0.541739	+	0.840547i	$0.317766\pi$
$684$		0			0
$685$	98065.0	+	98065.0i	0.208993	+	0.208993i
$686$		0			0
$687$	93701.5			0.198533
$688$		0			0
$689$			136122.i			0.286740i
$690$		0			0
$691$	−618113.			−1.29453			−0.647265	−	0.762265i	$-0.724087\pi$
$691$	−618113.			−1.29453			−0.647265	+	0.762265i	$0.724087\pi$
$692$		0			0
$693$	19961.9	+	19961.9i	0.0415657	+	0.0415657i
$694$		0			0
$695$			503591.i			1.04258i
$696$		0			0
$697$	806926.			1.66099
$698$		0			0
$699$	−53958.7	+	53958.7i	−0.110435	+	0.110435i
$700$		0			0
$701$		−	924154.i		−	1.88065i	−0.340276	−	0.940326i	$-0.610520\pi$
$701$		−	924154.i		−	1.88065i	0.340276	−	0.940326i	$-0.389480\pi$
$702$		0			0
$703$	−116020.			−0.234760
$704$		0			0
$705$			12006.3i			0.0241564i
$706$		0			0
$707$	31055.4	−	31055.4i	0.0621296	−	0.0621296i
$708$		0			0
$709$		−	59957.4i		−	0.119275i	−0.998220	−	0.0596376i	$-0.981005\pi$
$709$		−	59957.4i		−	0.119275i	0.998220	−	0.0596376i	$-0.0189945\pi$
$710$		0			0
$711$	406704.	+	406704.i	0.804525	+	0.804525i
$712$		0			0
$713$	143127.	−	143127.i	0.281542	−	0.281542i
$714$		0			0
$715$	−48409.3	+	48409.3i	−0.0946927	+	0.0946927i
$716$		0			0
$717$	149072.	−	149072.i	0.289974	−	0.289974i
$718$		0			0
$719$	−603599.			−1.16759			−0.583795	−	0.811901i	$-0.698433\pi$
$719$	−603599.			−1.16759			−0.583795	+	0.811901i	$0.698433\pi$
$720$		0			0
$721$	−106359.			−0.204600
$722$		0			0
$723$	46843.6	+	46843.6i	0.0896135	+	0.0896135i
$724$		0			0
$725$	−197685.	−	46839.7i	−0.376095	−	0.0891124i
$726$		0			0
$727$	397177.	−	397177.i	0.751476	−	0.751476i	−0.223278	−	0.974755i	$-0.571676\pi$
$727$	397177.	−	397177.i	0.751476	−	0.751476i	0.974755	+	0.223278i	$0.0716759\pi$
$728$		0			0
$729$		−	374442.i		−	0.704578i
$730$		0			0
$731$			198375.i			0.371239i
$732$		0			0
$733$	397977.	+	397977.i	0.740712	+	0.740712i	0.972715	−	0.232003i	$-0.0745278\pi$
$733$	397977.	+	397977.i	0.740712	+	0.740712i	−0.232003	+	0.972715i	$0.574528\pi$
$734$		0			0
$735$	63873.1	+	63873.1i	0.118234	+	0.118234i
$736$		0			0
$737$	−75662.8	−	75662.8i	−0.139299	−	0.139299i
$738$		0			0
$739$	253564.	−	253564.i	0.464300	−	0.464300i	−0.435762	−	0.900062i	$-0.643521\pi$
$739$	253564.	−	253564.i	0.464300	−	0.464300i	0.900062	+	0.435762i	$0.143521\pi$
$740$		0			0
$741$	109785.			0.199943
$742$		0			0
$743$	606911.	+	606911.i	1.09938	+	1.09938i	0.994483	+	0.104895i	$0.0334508\pi$
$743$	606911.	+	606911.i	1.09938	+	1.09938i	0.104895	+	0.994483i	$0.466549\pi$
$744$		0			0
$745$	304496.			0.548616
$746$		0			0
$747$			577814.i			1.03549i
$748$		0			0
$749$	181990.			0.324402
$750$		0			0
$751$	351194.	+	351194.i	0.622683	+	0.622683i	0.946217	−	0.323534i	$-0.104871\pi$
$751$	351194.	+	351194.i	0.622683	+	0.622683i	−0.323534	+	0.946217i	$0.604871\pi$
$752$		0			0
$753$		−	51759.8i		−	0.0912856i
$754$		0			0
$755$	−298331.			−0.523365
$756$		0			0
$757$	−571530.	+	571530.i	−0.997349	+	0.997349i	−0.999996	−	0.00264799i	$-0.999157\pi$
$757$	−571530.	+	571530.i	−0.997349	+	0.997349i	0.00264799	+	0.999996i	$0.499157\pi$
$758$		0			0
$759$			35599.7i			0.0617964i
$760$		0			0
$761$	1.11748e6			1.92961			0.964805	−	0.262968i	$-0.0847013\pi$
$761$	1.11748e6			1.92961			0.964805	+	0.262968i	$0.0847013\pi$
$762$		0			0
$763$		−	58438.3i		−	0.100380i
$764$		0			0
$765$	345186.	−	345186.i	0.589835	−	0.589835i
$766$		0			0
$767$			399534.i			0.679145i
$768$		0			0
$769$	−232516.	−	232516.i	−0.393188	−	0.393188i	0.482634	−	0.875822i	$-0.339680\pi$
$769$	−232516.	−	232516.i	−0.393188	−	0.393188i	−0.875822	+	0.482634i	$0.839680\pi$
$770$		0			0
$771$	81361.7	−	81361.7i	0.136871	−	0.136871i
$772$		0			0
$773$	250361.	−	250361.i	0.418995	−	0.418995i	−0.465862	−	0.884857i	$-0.654256\pi$
$773$	250361.	−	250361.i	0.418995	−	0.418995i	0.884857	+	0.465862i	$0.154256\pi$
$774$		0			0
$775$	−61421.1	+	61421.1i	−0.102262	+	0.102262i
$776$		0			0
$777$	−5887.54			−0.00975196
$778$		0			0
$779$	−1.18582e6			−1.95409
$780$		0			0
$781$	135964.	+	135964.i	0.222907	+	0.222907i
$782$		0			0
$783$	142226.	+	230553.i	0.231983	+	0.376052i
$784$		0			0
$785$	−167928.	+	167928.i	−0.272511	+	0.272511i
$786$		0			0
$787$			460158.i			0.742947i	0.928444	+	0.371474i	$0.121147\pi$
$787$			460158.i			0.742947i	−0.928444	+	0.371474i	$0.878853\pi$
$788$		0			0
$789$		−	126285.i		−	0.202860i
$790$		0			0
$791$	59130.7	+	59130.7i	0.0945061	+	0.0945061i
$792$		0			0
$793$	405277.	+	405277.i	0.644474	+	0.644474i
$794$		0			0
$795$	34092.7	+	34092.7i	0.0539419	+	0.0539419i
$796$		0			0
$797$	69919.0	−	69919.0i	0.110072	−	0.110072i	−0.649925	−	0.759998i	$-0.725200\pi$
$797$	69919.0	−	69919.0i	0.110072	−	0.110072i	0.759998	+	0.649925i	$0.225200\pi$
$798$		0			0
$799$	97483.6			0.152700
$800$		0			0
$801$	−367501.	−	367501.i	−0.572787	−	0.572787i
$802$		0			0
$803$	166323.			0.257942
$804$		0			0
$805$			130689.i			0.201673i
$806$		0			0
$807$	11602.2			0.0178153
$808$		0			0
$809$	461308.	+	461308.i	0.704845	+	0.704845i	0.965446	−	0.260601i	$-0.0839209\pi$
$809$	461308.	+	461308.i	0.704845	+	0.704845i	−0.260601	+	0.965446i	$0.583921\pi$
$810$		0			0
$811$		−	440479.i		−	0.669704i	−0.942271	−	0.334852i	$-0.891314\pi$
$811$		−	440479.i		−	0.669704i	0.942271	−	0.334852i	$-0.108686\pi$
$812$		0			0
$813$	167930.			0.254067
$814$		0			0
$815$	−160779.	+	160779.i	−0.242055	+	0.242055i
$816$		0			0
$817$		−	291524.i		−	0.436747i
$818$		0			0
$819$	−102779.			−0.153228
$820$		0			0
$821$			1.01894e6i			1.51169i	0.654752	+	0.755844i	$0.272773\pi$
$821$			1.01894e6i			1.51169i	−0.654752	+	0.755844i	$0.727227\pi$
$822$		0			0
$823$	−185208.	+	185208.i	−0.273439	+	0.273439i	−0.830483	−	0.557044i	$-0.811935\pi$
$823$	−185208.	+	185208.i	−0.273439	+	0.273439i	0.557044	+	0.830483i	$0.311935\pi$
$824$		0			0
$825$		−	15277.1i		−	0.0224457i
$826$		0			0
$827$	178013.	+	178013.i	0.260280	+	0.260280i	0.825168	−	0.564888i	$-0.191081\pi$
$827$	178013.	+	178013.i	0.260280	+	0.260280i	−0.564888	+	0.825168i	$0.691081\pi$
$828$		0			0
$829$	425057.	−	425057.i	0.618498	−	0.618498i	−0.326648	−	0.945146i	$-0.605919\pi$
$829$	425057.	−	425057.i	0.618498	−	0.618498i	0.945146	+	0.326648i	$0.105919\pi$
$830$		0			0
$831$	13117.5	−	13117.5i	0.0189955	−	0.0189955i
$832$		0			0
$833$	518608.	−	518608.i	0.747394	−	0.747394i
$834$		0			0
$835$	327665.			0.469955
$836$		0			0
$837$	115823.			0.165328
$838$		0			0
$839$	−582851.	−	582851.i	−0.828006	−	0.828006i	0.159235	−	0.987241i	$-0.449097\pi$
$839$	−582851.	−	582851.i	−0.828006	−	0.828006i	−0.987241	+	0.159235i	$0.949097\pi$
$840$		0			0
$841$	632087.	+	317352.i	0.893686	+	0.448692i
$842$		0			0
$843$	−74676.7	+	74676.7i	−0.105082	+	0.105082i
$844$		0			0
$845$			310017.i			0.434183i
$846$		0			0
$847$		−	162203.i		−	0.226096i
$848$		0			0
$849$	−190548.	−	190548.i	−0.264356	−	0.264356i
$850$		0			0
$851$	96853.1	+	96853.1i	0.133738	+	0.133738i
$852$		0			0
$853$	−391989.	−	391989.i	−0.538735	−	0.538735i	0.384422	−	0.923157i	$-0.374401\pi$
$853$	−391989.	−	391989.i	−0.538735	−	0.538735i	−0.923157	+	0.384422i	$0.874401\pi$
$854$		0			0
$855$	−507270.	+	507270.i	−0.693917	+	0.693917i
$856$		0			0
$857$	289645.			0.394371			0.197186	−	0.980366i	$-0.436820\pi$
$857$	289645.			0.394371			0.197186	+	0.980366i	$0.436820\pi$
$858$		0			0
$859$	−745869.	−	745869.i	−1.01083	−	1.01083i	−0.999941	−	0.0108848i	$-0.996535\pi$
$859$	−745869.	−	745869.i	−1.01083	−	1.01083i	−0.0108848	−	0.999941i	$-0.503465\pi$
$860$		0			0
$861$	−60175.4			−0.0811732
$862$		0			0
$863$		−	1.05873e6i		−	1.42156i	−0.703415	−	0.710779i	$-0.748343\pi$
$863$		−	1.05873e6i		−	1.42156i	0.703415	−	0.710779i	$-0.251657\pi$
$864$		0			0
$865$	−545440.			−0.728979
$866$		0			0
$867$	31393.2	+	31393.2i	0.0417635	+	0.0417635i
$868$		0			0
$869$			231974.i			0.307185i
$870$		0			0
$871$	389570.			0.513511
$872$		0			0
$873$	−895897.	+	895897.i	−1.17552	+	1.17552i
$874$		0			0
$875$		−	201186.i		−	0.262774i
$876$		0			0
$877$	1.23372e6			1.60404			0.802022	−	0.597294i	$-0.203758\pi$
$877$	1.23372e6			1.60404			0.802022	+	0.597294i	$0.203758\pi$
$878$		0			0
$879$			58079.0i			0.0751694i
$880$		0			0
$881$	770584.	−	770584.i	0.992815	−	0.992815i	−0.00715932	−	0.999974i	$-0.502279\pi$
$881$	770584.	−	770584.i	0.992815	−	0.992815i	0.999974	+	0.00715932i	$0.00227890\pi$
$882$		0			0
$883$		−	648837.i		−	0.832174i	−0.909325	−	0.416087i	$-0.863401\pi$
$883$		−	648837.i		−	0.832174i	0.909325	−	0.416087i	$-0.136599\pi$
$884$		0			0
$885$	100066.	+	100066.i	0.127762	+	0.127762i
$886$		0			0
$887$	620682.	−	620682.i	0.788900	−	0.788900i	−0.192414	−	0.981314i	$-0.561632\pi$
$887$	620682.	−	620682.i	0.788900	−	0.788900i	0.981314	+	0.192414i	$0.0616316\pi$
$888$		0			0
$889$	−142314.	+	142314.i	−0.180071	+	0.180071i
$890$		0			0
$891$	121971.	−	121971.i	0.153639	−	0.153639i
$892$		0			0
$893$	−143258.			−0.179645
$894$		0			0
$895$	−635063.			−0.792813
$896$		0			0
$897$	−91647.4	−	91647.4i	−0.113903	−	0.113903i
$898$		0			0
$899$	257373.	−	158771.i	0.318452	−	0.196450i
$900$		0			0
$901$	276810.	−	276810.i	0.340983	−	0.340983i
$902$		0			0
$903$		−	14793.6i		−	0.0181425i
$904$		0			0
$905$		−	621227.i		−	0.758495i
$906$		0			0
$907$	−396827.	−	396827.i	−0.482377	−	0.482377i	0.423513	−	0.905890i	$-0.360797\pi$
$907$	−396827.	−	396827.i	−0.482377	−	0.482377i	−0.905890	+	0.423513i	$0.860797\pi$
$908$		0			0
$909$	−201255.	−	201255.i	−0.243567	−	0.243567i
$910$		0			0
$911$	642878.	+	642878.i	0.774625	+	0.774625i	0.978911	−	0.204286i	$-0.0654872\pi$
$911$	642878.	+	642878.i	0.774625	+	0.774625i	−0.204286	+	0.978911i	$0.565487\pi$
$912$		0			0
$913$	−164785.	+	164785.i	−0.197686	+	0.197686i
$914$		0			0
$915$	203009.			0.242479
$916$		0			0
$917$	−228741.	−	228741.i	−0.272023	−	0.272023i
$918$		0			0
$919$	−1.24610e6			−1.47544			−0.737722	−	0.675104i	$-0.764099\pi$
$919$	−1.24610e6			−1.47544			−0.737722	+	0.675104i	$0.764099\pi$
$920$		0			0
$921$		−	14575.8i		−	0.0171836i
$922$		0			0
$923$	−700049.			−0.821722
$924$		0			0
$925$	−41563.1	−	41563.1i	−0.0485763	−	0.0485763i
$926$		0			0
$927$			689262.i			0.802093i
$928$		0			0
$929$	−614954.			−0.712543			−0.356272	−	0.934382i	$-0.615952\pi$
$929$	−614954.			−0.712543			−0.356272	+	0.934382i	$0.615952\pi$
$930$		0			0
$931$	−762123.	+	762123.i	−0.879278	+	0.879278i
$932$		0			0
$933$		−	50358.7i		−	0.0578510i
$934$		0			0
$935$	196886.			0.225211
$936$		0			0
$937$			712283.i			0.811285i	0.914032	+	0.405643i	$0.132952\pi$
$937$			712283.i			0.811285i	−0.914032	+	0.405643i	$0.867048\pi$
$938$		0			0
$939$	−34296.7	+	34296.7i	−0.0388975	+	0.0388975i
$940$		0			0
$941$		−	1.25922e6i		−	1.42207i	−0.703157	−	0.711035i	$-0.748227\pi$
$941$		−	1.25922e6i		−	1.42207i	0.703157	−	0.711035i	$-0.251773\pi$
$942$		0			0
$943$	989916.	+	989916.i	1.11320	+	1.11320i
$944$		0			0
$945$	−52878.9	+	52878.9i	−0.0592132	+	0.0592132i
$946$		0			0
$947$	−440536.	+	440536.i	−0.491226	+	0.491226i	−0.908692	−	0.417466i	$-0.862918\pi$
$947$	−440536.	+	440536.i	−0.491226	+	0.491226i	0.417466	+	0.908692i	$0.362918\pi$
$948$		0			0
$949$	−428180.	+	428180.i	−0.475438	+	0.475438i
$950$		0			0
$951$	−215981.			−0.238812
$952$		0			0
$953$	−842173.			−0.927290			−0.463645	−	0.886021i	$-0.653459\pi$
$953$	−842173.			−0.927290			−0.463645	+	0.886021i	$0.653459\pi$
$954$		0			0
$955$	−290314.	−	290314.i	−0.318318	−	0.318318i
$956$		0			0
$957$	−12262.5	+	51753.3i	−0.0133892	+	0.0565086i
$958$		0			0
$959$	−59377.3	+	59377.3i	−0.0645630	+	0.0645630i
$960$		0			0
$961$			794224.i			0.859996i
$962$		0			0
$963$		−	1.17938e6i		−	1.27175i
$964$		0			0
$965$	−270437.	−	270437.i	−0.290410	−	0.290410i
$966$		0			0
$967$	−84007.8	−	84007.8i	−0.0898393	−	0.0898393i	0.660759	−	0.750598i	$-0.270235\pi$
$967$	−84007.8	−	84007.8i	−0.0898393	−	0.0898393i	−0.750598	+	0.660759i	$0.770235\pi$
$968$		0			0
$969$	−223253.	−	223253.i	−0.237766	−	0.237766i
$970$		0			0
$971$	−585178.	+	585178.i	−0.620654	+	0.620654i	−0.945699	−	0.325044i	$-0.894621\pi$
$971$	−585178.	+	585178.i	−0.620654	+	0.620654i	0.325044	+	0.945699i	$0.394621\pi$
$972$		0			0
$973$	−304919.			−0.322076
$974$		0			0
$975$	39329.2	+	39329.2i	0.0413719	+	0.0413719i
$976$		0			0
$977$	−1.08922e6			−1.14110			−0.570552	−	0.821261i	$-0.693271\pi$
$977$	−1.08922e6			−1.14110			−0.570552	+	0.821261i	$0.693271\pi$
$978$		0			0
$979$		−	209613.i		−	0.218702i
$980$		0			0
$981$	−378710.			−0.393522
$982$		0			0
$983$	1.18313e6	+	1.18313e6i	1.22440	+	1.22440i	0.966052	+	0.258349i	$0.0831786\pi$
$983$	1.18313e6	+	1.18313e6i	1.22440	+	1.22440i	0.258349	+	0.966052i	$0.416821\pi$
$984$		0			0
$985$		−	265198.i		−	0.273337i
$986$		0			0
$987$	−7269.71			−0.00746247
$988$		0			0
$989$	−243362.	+	243362.i	−0.248806	+	0.248806i
$990$		0			0
$991$			312996.i			0.318707i	0.987222	+	0.159353i	$0.0509409\pi$
$991$			312996.i			0.318707i	−0.987222	+	0.159353i	$0.949059\pi$
$992$		0			0
$993$	267861.			0.271651
$994$		0			0
$995$		−	810210.i		−	0.818373i
$996$		0			0
$997$	−721709.	+	721709.i	−0.726058	+	0.726058i	−0.969832	−	0.243774i	$-0.921615\pi$
$997$	−721709.	+	721709.i	−0.726058	+	0.726058i	0.243774	+	0.969832i	$0.421615\pi$
$998$		0			0
$999$			78376.6i			0.0785336i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	232.5.j.a.17.8	✓	30
29.12	odd	4	inner	232.5.j.a.41.8	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
232.5.j.a.17.8	✓	30	1.1	even	1	trivial
232.5.j.a.41.8	yes	30	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:	\( N \)	\(=\)	\( 232 = 2^{3} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	232.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.44306 + 1.44306i) q^{3} +19.5814i q^{5} -11.8564 q^{7} +76.8352i q^{9} +O(q^{10})\)	\(q+(-1.44306 + 1.44306i) q^{3} +19.5814i q^{5} -11.8564 q^{7} +76.8352i q^{9} +(-21.9124 + 21.9124i) q^{11} -112.822i q^{13} +(-28.2571 - 28.2571i) q^{15} +(-229.429 + 229.429i) q^{17} +(337.159 - 337.159i) q^{19} +(17.1094 - 17.1094i) q^{21} -562.916 q^{23} +241.568 q^{25} +(-227.765 - 227.765i) q^{27} +(-818.342 - 193.899i) q^{29} +(-254.261 + 254.261i) q^{31} -63.2417i q^{33} -232.164i q^{35} +(-172.056 - 172.056i) q^{37} +(162.808 + 162.808i) q^{39} +(-1758.55 - 1758.55i) q^{41} +(432.324 - 432.324i) q^{43} -1504.54 q^{45} +(-212.448 - 212.448i) q^{47} -2260.43 q^{49} -662.158i q^{51} -1206.52 q^{53} +(-429.077 - 429.077i) q^{55} +973.078i q^{57} -3541.27 q^{59} +(-3592.18 + 3592.18i) q^{61} -910.985i q^{63} +2209.22 q^{65} +3452.96i q^{67} +(812.319 - 812.319i) q^{69} -6204.90i q^{71} +(-3795.18 - 3795.18i) q^{73} +(-348.595 + 348.595i) q^{75} +(259.801 - 259.801i) q^{77} +(5293.20 - 5293.20i) q^{79} -5566.30 q^{81} +7520.17 q^{83} +(-4492.56 - 4492.56i) q^{85} +(1460.72 - 901.106i) q^{87} +(-4782.97 + 4782.97i) q^{89} +1337.66i q^{91} -733.825i q^{93} +(6602.06 + 6602.06i) q^{95} +(11660.0 + 11660.0i) q^{97} +(-1683.64 - 1683.64i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 16 q^{3} + 96 q^{7}+O(q^{10}) \) 30 * q - 16 * q^3 + 96 * q^7	\( 30 q - 16 q^{3} + 96 q^{7} - 240 q^{15} - 338 q^{17} - 936 q^{19} + 1400 q^{21} - 352 q^{23} - 2154 q^{25} + 2648 q^{27} + 500 q^{29} - 1896 q^{31} - 1862 q^{37} + 1088 q^{39} + 2854 q^{41} - 800 q^{43} + 4552 q^{45} - 696 q^{47} + 9698 q^{49} + 4584 q^{53} - 8560 q^{55} + 7144 q^{59} - 1070 q^{61} + 8672 q^{65} - 19352 q^{69} - 7942 q^{73} + 11072 q^{75} - 3048 q^{77} + 3560 q^{79} - 10398 q^{81} - 9848 q^{83} + 11968 q^{85} - 13704 q^{87} - 9634 q^{89} - 33160 q^{95} - 27582 q^{97} + 16480 q^{99}+O(q^{100}) \) 30 * q - 16 * q^3 + 96 * q^7 - 240 * q^15 - 338 * q^17 - 936 * q^19 + 1400 * q^21 - 352 * q^23 - 2154 * q^25 + 2648 * q^27 + 500 * q^29 - 1896 * q^31 - 1862 * q^37 + 1088 * q^39 + 2854 * q^41 - 800 * q^43 + 4552 * q^45 - 696 * q^47 + 9698 * q^49 + 4584 * q^53 - 8560 * q^55 + 7144 * q^59 - 1070 * q^61 + 8672 * q^65 - 19352 * q^69 - 7942 * q^73 + 11072 * q^75 - 3048 * q^77 + 3560 * q^79 - 10398 * q^81 - 9848 * q^83 + 11968 * q^85 - 13704 * q^87 - 9634 * q^89 - 33160 * q^95 - 27582 * q^97 + 16480 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more