LMFDB - Embedded newform 320.3.r.a.111.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [320,3,Mod(111,320)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(320, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

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

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

chi := DirichletCharacter("320.111");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 320 = 2^{6} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	320.r (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:	$8.71936845953$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			111.4
Character	$\chi$	$=$	320.111
Dual form			320.3.r.a.271.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.58103 + 2.58103i) q^{3} +(1.58114 - 1.58114i) q^{5} -0.523915 q^{7} -4.32341i q^{9} +O(q^{10})$	\(q+(-2.58103 + 2.58103i) q^{3} +(1.58114 - 1.58114i) q^{5} -0.523915 q^{7} -4.32341i q^{9} +(4.46992 + 4.46992i) q^{11} +(11.7702 + 11.7702i) q^{13} +8.16193i q^{15} -23.7830 q^{17} +(-13.0094 + 13.0094i) q^{19} +(1.35224 - 1.35224i) q^{21} -31.0831 q^{23} -5.00000i q^{25} +(-12.0704 - 12.0704i) q^{27} +(11.4582 + 11.4582i) q^{29} -29.5161i q^{31} -23.0740 q^{33} +(-0.828383 + 0.828383i) q^{35} +(-43.0487 + 43.0487i) q^{37} -60.7584 q^{39} -25.9263i q^{41} +(11.0580 + 11.0580i) q^{43} +(-6.83592 - 6.83592i) q^{45} +72.9849i q^{47} -48.7255 q^{49} +(61.3847 - 61.3847i) q^{51} +(-49.4850 + 49.4850i) q^{53} +14.1351 q^{55} -67.1553i q^{57} +(31.1457 + 31.1457i) q^{59} +(13.9327 + 13.9327i) q^{61} +2.26510i q^{63} +37.2206 q^{65} +(66.6446 - 66.6446i) q^{67} +(80.2262 - 80.2262i) q^{69} +34.5733 q^{71} +101.216i q^{73} +(12.9051 + 12.9051i) q^{75} +(-2.34186 - 2.34186i) q^{77} +60.9820i q^{79} +101.219 q^{81} +(33.6610 - 33.6610i) q^{83} +(-37.6043 + 37.6043i) q^{85} -59.1477 q^{87} -95.8337i q^{89} +(-6.16659 - 6.16659i) q^{91} +(76.1819 + 76.1819i) q^{93} +41.1394i q^{95} +135.831 q^{97} +(19.3253 - 19.3253i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q - 32 q^{11} + 32 q^{19} + 128 q^{23} + 96 q^{27} + 32 q^{29} - 96 q^{37} - 384 q^{39} - 96 q^{43} + 224 q^{49} + 256 q^{51} - 160 q^{53} + 352 q^{59} - 32 q^{61} - 160 q^{67} + 96 q^{69} - 256 q^{71} + 224 q^{77} - 288 q^{81} + 480 q^{83} + 160 q^{85} + 384 q^{91} + 96 q^{93} - 608 q^{99}+O(q^{100}) $ 32 * q - 32 * q^11 + 32 * q^19 + 128 * q^23 + 96 * q^27 + 32 * q^29 - 96 * q^37 - 384 * q^39 - 96 * q^43 + 224 * q^49 + 256 * q^51 - 160 * q^53 + 352 * q^59 - 32 * q^61 - 160 * q^67 + 96 * q^69 - 256 * q^71 + 224 * q^77 - 288 * q^81 + 480 * q^83 + 160 * q^85 + 384 * q^91 + 96 * q^93 - 608 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/320\mathbb{Z}\right)^\times$.

$n$	$191$	$257$	$261$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.58103	+	2.58103i	−0.860343	+	0.860343i	−0.991378	−	0.131035i	$-0.958170\pi$
$3$	−2.58103	+	2.58103i	−0.860343	+	0.860343i	0.131035	+	0.991378i	$0.458170\pi$
$4$		0			0
$5$	1.58114	−	1.58114i	0.316228	−	0.316228i
$5$	1.58114	−	1.58114i	0.316228	−	0.316228i
$6$		0			0
$7$	−0.523915			−0.0748450			−0.0374225	−	0.999300i	$-0.511915\pi$
$7$	−0.523915			−0.0748450			−0.0374225	+	0.999300i	$0.511915\pi$
$8$		0			0
$9$		−	4.32341i		−	0.480379i
$10$		0			0
$11$	4.46992	+	4.46992i	0.406357	+	0.406357i	0.880466	−	0.474109i	$-0.157230\pi$
$11$	4.46992	+	4.46992i	0.406357	+	0.406357i	−0.474109	+	0.880466i	$0.657230\pi$
$12$		0			0
$13$	11.7702	+	11.7702i	0.905400	+	0.905400i	0.995897	−	0.0904968i	$-0.0288455\pi$
$13$	11.7702	+	11.7702i	0.905400	+	0.905400i	−0.0904968	+	0.995897i	$0.528845\pi$
$14$		0			0
$15$			8.16193i			0.544129i
$16$		0			0
$17$	−23.7830			−1.39900			−0.699501	−	0.714632i	$-0.746594\pi$
$17$	−23.7830			−1.39900			−0.699501	+	0.714632i	$0.746594\pi$
$18$		0			0
$19$	−13.0094	+	13.0094i	−0.684706	+	0.684706i	−0.961057	−	0.276351i	$-0.910875\pi$
$19$	−13.0094	+	13.0094i	−0.684706	+	0.684706i	0.276351	+	0.961057i	$0.410875\pi$
$20$		0			0
$21$	1.35224	−	1.35224i	0.0643924	−	0.0643924i
$22$		0			0
$23$	−31.0831			−1.35144			−0.675719	−	0.737160i	$-0.736167\pi$
$23$	−31.0831			−1.35144			−0.675719	+	0.737160i	$0.736167\pi$
$24$		0			0
$25$		−	5.00000i		−	0.200000i
$26$		0			0
$27$	−12.0704	−	12.0704i	−0.447052	−	0.447052i
$28$		0			0
$29$	11.4582	+	11.4582i	0.395109	+	0.395109i	0.876504	−	0.481395i	$-0.159870\pi$
$29$	11.4582	+	11.4582i	0.395109	+	0.395109i	−0.481395	+	0.876504i	$0.659870\pi$
$30$		0			0
$31$		−	29.5161i		−	0.952132i	−0.879410	−	0.476066i	$-0.842062\pi$
$31$		−	29.5161i		−	0.952132i	0.879410	−	0.476066i	$-0.157938\pi$
$32$		0			0
$33$	−23.0740			−0.699212
$34$		0			0
$35$	−0.828383	+	0.828383i	−0.0236681	+	0.0236681i
$36$		0			0
$37$	−43.0487	+	43.0487i	−1.16348	+	1.16348i	−0.179768	+	0.983709i	$0.557535\pi$
$37$	−43.0487	+	43.0487i	−1.16348	+	1.16348i	−0.983709	+	0.179768i	$0.942465\pi$
$38$		0			0
$39$	−60.7584			−1.55791
$40$		0			0
$41$		−	25.9263i		−	0.632348i	−0.948701	−	0.316174i	$-0.897602\pi$
$41$		−	25.9263i		−	0.632348i	0.948701	−	0.316174i	$-0.102398\pi$
$42$		0			0
$43$	11.0580	+	11.0580i	0.257162	+	0.257162i	0.823899	−	0.566737i	$-0.191794\pi$
$43$	11.0580	+	11.0580i	0.257162	+	0.257162i	−0.566737	+	0.823899i	$0.691794\pi$
$44$		0			0
$45$	−6.83592	−	6.83592i	−0.151909	−	0.151909i
$46$		0			0
$47$			72.9849i			1.55287i	0.630197	+	0.776435i	$0.282974\pi$
$47$			72.9849i			1.55287i	−0.630197	+	0.776435i	$0.717026\pi$
$48$		0			0
$49$	−48.7255			−0.994398
$50$		0			0
$51$	61.3847	−	61.3847i	1.20362	−	1.20362i
$52$		0			0
$53$	−49.4850	+	49.4850i	−0.933680	+	0.933680i	−0.997934	−	0.0642539i	$-0.979533\pi$
$53$	−49.4850	+	49.4850i	−0.933680	+	0.933680i	0.0642539	+	0.997934i	$0.479533\pi$
$54$		0			0
$55$	14.1351			0.257002
$56$		0			0
$57$		−	67.1553i		−	1.17816i
$58$		0			0
$59$	31.1457	+	31.1457i	0.527894	+	0.527894i	0.919944	−	0.392050i	$-0.128234\pi$
$59$	31.1457	+	31.1457i	0.527894	+	0.527894i	−0.392050	+	0.919944i	$0.628234\pi$
$60$		0			0
$61$	13.9327	+	13.9327i	0.228405	+	0.228405i	0.812026	−	0.583621i	$-0.198365\pi$
$61$	13.9327	+	13.9327i	0.228405	+	0.228405i	−0.583621	+	0.812026i	$0.698365\pi$
$62$		0			0
$63$			2.26510i			0.0359540i
$64$		0			0
$65$	37.2206			0.572625
$66$		0			0
$67$	66.6446	−	66.6446i	0.994695	−	0.994695i	−0.00529076	−	0.999986i	$-0.501684\pi$
$67$	66.6446	−	66.6446i	0.994695	−	0.994695i	0.999986	+	0.00529076i	$0.00168411\pi$
$68$		0			0
$69$	80.2262	−	80.2262i	1.16270	−	1.16270i
$70$		0			0
$71$	34.5733			0.486948			0.243474	−	0.969907i	$-0.421713\pi$
$71$	34.5733			0.486948			0.243474	+	0.969907i	$0.421713\pi$
$72$		0			0
$73$			101.216i			1.38652i	0.720686	+	0.693262i	$0.243827\pi$
$73$			101.216i			1.38652i	−0.720686	+	0.693262i	$0.756173\pi$
$74$		0			0
$75$	12.9051	+	12.9051i	0.172069	+	0.172069i
$76$		0			0
$77$	−2.34186	−	2.34186i	−0.0304138	−	0.0304138i
$78$		0			0
$79$			60.9820i			0.771924i	0.922515	+	0.385962i	$0.126130\pi$
$79$			60.9820i			0.771924i	−0.922515	+	0.385962i	$0.873870\pi$
$80$		0			0
$81$	101.219			1.24962
$82$		0			0
$83$	33.6610	−	33.6610i	0.405555	−	0.405555i	−0.474630	−	0.880185i	$-0.657418\pi$
$83$	33.6610	−	33.6610i	0.405555	−	0.405555i	0.880185	+	0.474630i	$0.157418\pi$
$84$		0			0
$85$	−37.6043	+	37.6043i	−0.442403	+	0.442403i
$86$		0			0
$87$	−59.1477			−0.679859
$88$		0			0
$89$		−	95.8337i		−	1.07678i	−0.842695	−	0.538391i	$-0.819032\pi$
$89$		−	95.8337i		−	1.07678i	0.842695	−	0.538391i	$-0.180968\pi$
$90$		0			0
$91$	−6.16659	−	6.16659i	−0.0677647	−	0.0677647i
$92$		0			0
$93$	76.1819	+	76.1819i	0.819160	+	0.819160i
$94$		0			0
$95$			41.1394i			0.433046i
$96$		0			0
$97$	135.831			1.40032			0.700159	−	0.713987i	$-0.253113\pi$
$97$	135.831			1.40032			0.700159	+	0.713987i	$0.253113\pi$
$98$		0			0
$99$	19.3253	−	19.3253i	0.195205	−	0.195205i
$100$		0			0
$101$	68.9677	−	68.9677i	0.682849	−	0.682849i	−0.277792	−	0.960641i	$-0.589603\pi$
$101$	68.9677	−	68.9677i	0.682849	−	0.682849i	0.960641	+	0.277792i	$0.0896028\pi$
$102$		0			0
$103$	22.2239			0.215766			0.107883	−	0.994164i	$-0.465593\pi$
$103$	22.2239			0.215766			0.107883	+	0.994164i	$0.465593\pi$
$104$		0			0
$105$		−	4.27616i		−	0.0407253i
$106$		0			0
$107$	−110.375	−	110.375i	−1.03154	−	1.03154i	−0.999486	−	0.0320513i	$-0.989796\pi$
$107$	−110.375	−	110.375i	−1.03154	−	1.03154i	−0.0320513	−	0.999486i	$-0.510204\pi$
$108$		0			0
$109$	27.4144	+	27.4144i	0.251508	+	0.251508i	0.821589	−	0.570080i	$-0.193088\pi$
$109$	27.4144	+	27.4144i	0.251508	+	0.251508i	−0.570080	+	0.821589i	$0.693088\pi$
$110$		0			0
$111$		−	222.220i		−	2.00198i
$112$		0			0
$113$	−153.139			−1.35521			−0.677605	−	0.735426i	$-0.736982\pi$
$113$	−153.139			−1.35521			−0.677605	+	0.735426i	$0.736982\pi$
$114$		0			0
$115$	−49.1466	+	49.1466i	−0.427362	+	0.427362i
$116$		0			0
$117$	50.8874	−	50.8874i	0.434935	−	0.434935i
$118$		0			0
$119$	12.4603			0.104708
$120$		0			0
$121$		−	81.0396i		−	0.669749i
$122$		0			0
$123$	66.9165	+	66.9165i	0.544036	+	0.544036i
$124$		0			0
$125$	−7.90569	−	7.90569i	−0.0632456	−	0.0632456i
$126$		0			0
$127$			31.2953i			0.246420i	0.992381	+	0.123210i	$0.0393188\pi$
$127$			31.2953i			0.246420i	−0.992381	+	0.123210i	$0.960681\pi$
$128$		0			0
$129$	−57.0819			−0.442495
$130$		0			0
$131$	−137.756	+	137.756i	−1.05157	+	1.05157i	−0.0529731	+	0.998596i	$0.516870\pi$
$131$	−137.756	+	137.756i	−1.05157	+	1.05157i	−0.998596	+	0.0529731i	$0.983130\pi$
$132$		0			0
$133$	6.81582	−	6.81582i	0.0512468	−	0.0512468i
$134$		0			0
$135$	−38.1700			−0.282740
$136$		0			0
$137$		−	84.9022i		−	0.619724i	−0.950782	−	0.309862i	$-0.899717\pi$
$137$		−	84.9022i		−	0.619724i	0.950782	−	0.309862i	$-0.100283\pi$
$138$		0			0
$139$	116.290	+	116.290i	0.836616	+	0.836616i	0.988412	−	0.151796i	$-0.0485056\pi$
$139$	116.290	+	116.290i	0.836616	+	0.836616i	−0.151796	+	0.988412i	$0.548506\pi$
$140$		0			0
$141$	−188.376	−	188.376i	−1.33600	−	1.33600i
$142$		0			0
$143$			105.224i			0.735831i
$144$		0			0
$145$	36.2339			0.249889
$146$		0			0
$147$	125.762	−	125.762i	0.855523	−	0.855523i
$148$		0			0
$149$	44.2103	−	44.2103i	0.296714	−	0.296714i	−0.543012	−	0.839725i	$-0.682716\pi$
$149$	44.2103	−	44.2103i	0.296714	−	0.296714i	0.839725	+	0.543012i	$0.182716\pi$
$150$		0			0
$151$	84.6340			0.560490			0.280245	−	0.959929i	$-0.409584\pi$
$151$	84.6340			0.560490			0.280245	+	0.959929i	$0.409584\pi$
$152$		0			0
$153$			102.824i			0.672051i
$154$		0			0
$155$	−46.6690	−	46.6690i	−0.301091	−	0.301091i
$156$		0			0
$157$	154.457	+	154.457i	0.983803	+	0.983803i	0.999871	−	0.0160678i	$-0.00511475\pi$
$157$	154.457	+	154.457i	0.983803	+	0.983803i	−0.0160678	+	0.999871i	$0.505115\pi$
$158$		0			0
$159$		−	255.444i		−	1.60657i
$160$		0			0
$161$	16.2849			0.101148
$162$		0			0
$163$	−213.713	+	213.713i	−1.31112	+	1.31112i	−0.390536	+	0.920588i	$0.627710\pi$
$163$	−213.713	+	213.713i	−1.31112	+	1.31112i	−0.920588	+	0.390536i	$0.872290\pi$
$164$		0			0
$165$	−36.4832	+	36.4832i	−0.221110	+	0.221110i
$166$		0			0
$167$	276.894			1.65805			0.829024	−	0.559213i	$-0.188896\pi$
$167$	276.894			1.65805			0.829024	+	0.559213i	$0.188896\pi$
$168$		0			0
$169$			108.075i			0.639498i
$170$		0			0
$171$	56.2450	+	56.2450i	0.328918	+	0.328918i
$172$		0			0
$173$	−25.6101	−	25.6101i	−0.148035	−	0.148035i	0.629205	−	0.777240i	$-0.283381\pi$
$173$	−25.6101	−	25.6101i	−0.148035	−	0.148035i	−0.777240	+	0.629205i	$0.783381\pi$
$174$		0			0
$175$			2.61958i			0.0149690i
$176$		0			0
$177$	−160.776			−0.908340
$178$		0			0
$179$	48.6962	−	48.6962i	0.272046	−	0.272046i	−0.557877	−	0.829923i	$-0.688384\pi$
$179$	48.6962	−	48.6962i	0.272046	−	0.272046i	0.829923	+	0.557877i	$0.188384\pi$
$180$		0			0
$181$	−151.332	+	151.332i	−0.836088	+	0.836088i	−0.988341	−	0.152254i	$-0.951347\pi$
$181$	−151.332	+	151.332i	−0.836088	+	0.836088i	0.152254	+	0.988341i	$0.451347\pi$
$182$		0			0
$183$	−71.9214			−0.393013
$184$		0			0
$185$			136.132i			0.735848i
$186$		0			0
$187$	−106.308	−	106.308i	−0.568493	−	0.568493i
$188$		0			0
$189$	6.32387	+	6.32387i	0.0334596	+	0.0334596i
$190$		0			0
$191$		−	154.194i		−	0.807301i	−0.914913	−	0.403650i	$-0.867741\pi$
$191$		−	154.194i		−	0.807301i	0.914913	−	0.403650i	$-0.132259\pi$
$192$		0			0
$193$	168.855			0.874896			0.437448	−	0.899244i	$-0.355882\pi$
$193$	168.855			0.874896			0.437448	+	0.899244i	$0.355882\pi$
$194$		0			0
$195$	−96.0675	+	96.0675i	−0.492654	+	0.492654i
$196$		0			0
$197$	147.522	−	147.522i	0.748844	−	0.748844i	−0.225418	−	0.974262i	$-0.572375\pi$
$197$	147.522	−	147.522i	0.748844	−	0.748844i	0.974262	+	0.225418i	$0.0723748\pi$
$198$		0			0
$199$	147.488			0.741145			0.370572	−	0.928804i	$-0.379162\pi$
$199$	147.488			0.741145			0.370572	+	0.928804i	$0.379162\pi$
$200$		0			0
$201$			344.023i			1.71156i
$202$		0			0
$203$	−6.00311	−	6.00311i	−0.0295720	−	0.0295720i
$204$		0			0
$205$	−40.9931	−	40.9931i	−0.199966	−	0.199966i
$206$		0			0
$207$			134.385i			0.649202i
$208$		0			0
$209$	−116.302			−0.556469
$210$		0			0
$211$	−72.2962	+	72.2962i	−0.342636	+	0.342636i	−0.857357	−	0.514721i	$-0.827895\pi$
$211$	−72.2962	+	72.2962i	−0.342636	+	0.342636i	0.514721	+	0.857357i	$0.327895\pi$
$212$		0			0
$213$	−89.2347	+	89.2347i	−0.418942	+	0.418942i
$214$		0			0
$215$	34.9684			0.162644
$216$		0			0
$217$			15.4639i			0.0712623i
$218$		0			0
$219$	−261.242	−	261.242i	−1.19289	−	1.19289i
$220$		0			0
$221$	−279.931	−	279.931i	−1.26666	−	1.26666i
$222$		0			0
$223$			149.191i			0.669017i	0.942393	+	0.334509i	$0.108570\pi$
$223$			149.191i			0.669017i	−0.942393	+	0.334509i	$0.891430\pi$
$224$		0			0
$225$	−21.6171			−0.0960758
$226$		0			0
$227$	58.3020	−	58.3020i	0.256837	−	0.256837i	−0.566929	−	0.823766i	$-0.691869\pi$
$227$	58.3020	−	58.3020i	0.256837	−	0.256837i	0.823766	+	0.566929i	$0.191869\pi$
$228$		0			0
$229$	−103.062	+	103.062i	−0.450053	+	0.450053i	−0.895372	−	0.445319i	$-0.853090\pi$
$229$	−103.062	+	103.062i	−0.450053	+	0.450053i	0.445319	+	0.895372i	$0.353090\pi$
$230$		0			0
$231$	12.0888			0.0523325
$232$		0			0
$233$			2.62372i			0.0112606i	0.999984	+	0.00563030i	$0.00179219\pi$
$233$			2.62372i			0.0112606i	−0.999984	+	0.00563030i	$0.998208\pi$
$234$		0			0
$235$	115.399	+	115.399i	0.491061	+	0.491061i
$236$		0			0
$237$	−157.396	−	157.396i	−0.664119	−	0.664119i
$238$		0			0
$239$			329.102i			1.37700i	0.725238	+	0.688499i	$0.241730\pi$
$239$			329.102i			1.37700i	−0.725238	+	0.688499i	$0.758270\pi$
$240$		0			0
$241$	288.189			1.19581			0.597903	−	0.801568i	$-0.296001\pi$
$241$	288.189			1.19581			0.597903	+	0.801568i	$0.296001\pi$
$242$		0			0
$243$	−152.615	+	152.615i	−0.628045	+	0.628045i
$244$		0			0
$245$	−77.0418	+	77.0418i	−0.314456	+	0.314456i
$246$		0			0
$247$	−306.247			−1.23986
$248$		0			0
$249$			173.760i			0.697832i
$250$		0			0
$251$	−138.927	−	138.927i	−0.553494	−	0.553494i	0.373954	−	0.927447i	$-0.378002\pi$
$251$	−138.927	−	138.927i	−0.553494	−	0.553494i	−0.927447	+	0.373954i	$0.878002\pi$
$252$		0			0
$253$	−138.939	−	138.939i	−0.549165	−	0.549165i
$254$		0			0
$255$		−	194.115i		−	0.761237i
$256$		0			0
$257$	−263.976			−1.02714			−0.513572	−	0.858046i	$-0.671678\pi$
$257$	−263.976			−1.02714			−0.513572	+	0.858046i	$0.671678\pi$
$258$		0			0
$259$	22.5538	−	22.5538i	0.0870805	−	0.0870805i
$260$		0			0
$261$	49.5384	−	49.5384i	0.189802	−	0.189802i
$262$		0			0
$263$	−38.2536			−0.145451			−0.0727256	−	0.997352i	$-0.523170\pi$
$263$	−38.2536			−0.145451			−0.0727256	+	0.997352i	$0.523170\pi$
$264$		0			0
$265$			156.485i			0.590511i
$266$		0			0
$267$	247.349	+	247.349i	0.926402	+	0.926402i
$268$		0			0
$269$	−19.3394	−	19.3394i	−0.0718938	−	0.0718938i	0.670246	−	0.742139i	$-0.266189\pi$
$269$	−19.3394	−	19.3394i	−0.0718938	−	0.0718938i	−0.742139	+	0.670246i	$0.766189\pi$
$270$		0			0
$271$		−	153.877i		−	0.567811i	−0.958852	−	0.283905i	$-0.908370\pi$
$271$		−	153.877i		−	0.567811i	0.958852	−	0.283905i	$-0.0916302\pi$
$272$		0			0
$273$	31.8323			0.116602
$274$		0			0
$275$	22.3496	−	22.3496i	0.0812713	−	0.0812713i
$276$		0			0
$277$	92.9882	−	92.9882i	0.335698	−	0.335698i	−0.519048	−	0.854745i	$-0.673713\pi$
$277$	92.9882	−	92.9882i	0.335698	−	0.335698i	0.854745	+	0.519048i	$0.173713\pi$
$278$		0			0
$279$	−127.610			−0.457384
$280$		0			0
$281$		−	304.434i		−	1.08339i	−0.840574	−	0.541697i	$-0.817782\pi$
$281$		−	304.434i		−	1.08339i	0.840574	−	0.541697i	$-0.182218\pi$
$282$		0			0
$283$	−121.458	−	121.458i	−0.429179	−	0.429179i	0.459170	−	0.888349i	$-0.348147\pi$
$283$	−121.458	−	121.458i	−0.429179	−	0.429179i	−0.888349	+	0.459170i	$0.848147\pi$
$284$		0			0
$285$	−106.182	−	106.182i	−0.372568	−	0.372568i
$286$		0			0
$287$			13.5832i			0.0473281i
$288$		0			0
$289$	276.632			0.957205
$290$		0			0
$291$	−350.583	+	350.583i	−1.20475	+	1.20475i
$292$		0			0
$293$	109.255	−	109.255i	0.372884	−	0.372884i	−0.495643	−	0.868527i	$-0.665067\pi$
$293$	109.255	−	109.255i	0.372884	−	0.372884i	0.868527	+	0.495643i	$0.165067\pi$
$294$		0			0
$295$	98.4915			0.333870
$296$		0			0
$297$		−	107.908i		−	0.363325i
$298$		0			0
$299$	−365.854	−	365.854i	−1.22359	−	1.22359i
$300$		0			0
$301$	−5.79344	−	5.79344i	−0.0192473	−	0.0192473i
$302$		0			0
$303$			356.015i			1.17497i
$304$		0			0
$305$	44.0591			0.144456
$306$		0			0
$307$	−42.3527	+	42.3527i	−0.137957	+	0.137957i	−0.772713	−	0.634756i	$-0.781101\pi$
$307$	−42.3527	+	42.3527i	−0.137957	+	0.137957i	0.634756	+	0.772713i	$0.281101\pi$
$308$		0			0
$309$	−57.3605	+	57.3605i	−0.185633	+	0.185633i
$310$		0			0
$311$	60.4736			0.194449			0.0972245	−	0.995262i	$-0.469004\pi$
$311$	60.4736			0.194449			0.0972245	+	0.995262i	$0.469004\pi$
$312$		0			0
$313$		−	68.5980i		−	0.219163i	−0.993978	−	0.109581i	$-0.965049\pi$
$313$		−	68.5980i		−	0.219163i	0.993978	−	0.109581i	$-0.0349511\pi$
$314$		0			0
$315$	3.58144	+	3.58144i	0.0113697	+	0.0113697i
$316$		0			0
$317$	282.399	+	282.399i	0.890848	+	0.890848i	0.994603	−	0.103755i	$-0.0330859\pi$
$317$	282.399	+	282.399i	0.890848	+	0.890848i	−0.103755	+	0.994603i	$0.533086\pi$
$318$		0			0
$319$			102.434i			0.321110i
$320$		0			0
$321$	569.759			1.77495
$322$		0			0
$323$	309.403	−	309.403i	0.957904	−	0.957904i
$324$		0			0
$325$	58.8510	−	58.8510i	0.181080	−	0.181080i
$326$		0			0
$327$	−141.515			−0.432767
$328$		0			0
$329$		−	38.2379i		−	0.116225i
$330$		0			0
$331$	352.209	+	352.209i	1.06407	+	1.06407i	0.997802	+	0.0662731i	$0.0211108\pi$
$331$	352.209	+	352.209i	1.06407	+	1.06407i	0.0662731	+	0.997802i	$0.478889\pi$
$332$		0			0
$333$	186.117	+	186.117i	0.558910	+	0.558910i
$334$		0			0
$335$		−	210.749i		−	0.629101i
$336$		0			0
$337$	−508.699			−1.50949			−0.754747	−	0.656016i	$-0.772240\pi$
$337$	−508.699			−1.50949			−0.754747	+	0.656016i	$0.772240\pi$
$338$		0			0
$339$	395.255	−	395.255i	1.16594	−	1.16594i
$340$		0			0
$341$	131.935	−	131.935i	0.386905	−	0.386905i
$342$		0			0
$343$	51.1999			0.149271
$344$		0			0
$345$		−	253.698i		−	0.735355i
$346$		0			0
$347$	57.3848	+	57.3848i	0.165374	+	0.165374i	0.784943	−	0.619569i	$-0.212692\pi$
$347$	57.3848	+	57.3848i	0.165374	+	0.165374i	−0.619569	+	0.784943i	$0.712692\pi$
$348$		0			0
$349$	388.384	+	388.384i	1.11285	+	1.11285i	0.992764	+	0.120084i	$0.0383165\pi$
$349$	388.384	+	388.384i	1.11285	+	1.11285i	0.120084	+	0.992764i	$0.461683\pi$
$350$		0			0
$351$		−	284.142i		−	0.809522i
$352$		0			0
$353$	−207.523			−0.587883			−0.293942	−	0.955823i	$-0.594967\pi$
$353$	−207.523			−0.587883			−0.293942	+	0.955823i	$0.594967\pi$
$354$		0			0
$355$	54.6652	−	54.6652i	0.153986	−	0.153986i
$356$		0			0
$357$	−32.1603	+	32.1603i	−0.0900850	+	0.0900850i
$358$		0			0
$359$	161.216			0.449069			0.224534	−	0.974466i	$-0.427914\pi$
$359$	161.216			0.449069			0.224534	+	0.974466i	$0.427914\pi$
$360$		0			0
$361$			22.5108i			0.0623567i
$362$		0			0
$363$	209.165	+	209.165i	0.576213	+	0.576213i
$364$		0			0
$365$	160.037	+	160.037i	0.438457	+	0.438457i
$366$		0			0
$367$		−	31.9040i		−	0.0869318i	−0.999055	−	0.0434659i	$-0.986160\pi$
$367$		−	31.9040i		−	0.0869318i	0.999055	−	0.0434659i	$-0.0138400\pi$
$368$		0			0
$369$	−112.090			−0.303767
$370$		0			0
$371$	25.9260	−	25.9260i	0.0698813	−	0.0698813i
$372$		0			0
$373$	148.817	−	148.817i	0.398973	−	0.398973i	−0.478898	−	0.877871i	$-0.658963\pi$
$373$	148.817	−	148.817i	0.398973	−	0.398973i	0.877871	+	0.478898i	$0.158963\pi$
$374$		0			0
$375$	40.8096			0.108826
$376$		0			0
$377$			269.730i			0.715464i
$378$		0			0
$379$	236.667	+	236.667i	0.624452	+	0.624452i	0.946667	−	0.322214i	$-0.104427\pi$
$379$	236.667	+	236.667i	0.624452	+	0.624452i	−0.322214	+	0.946667i	$0.604427\pi$
$380$		0			0
$381$	−80.7740	−	80.7740i	−0.212005	−	0.212005i
$382$		0			0
$383$		−	587.307i		−	1.53344i	−0.641982	−	0.766720i	$-0.721888\pi$
$383$		−	587.307i		−	1.53344i	0.641982	−	0.766720i	$-0.278112\pi$
$384$		0			0
$385$	−7.40561			−0.0192354
$386$		0			0
$387$	47.8082	−	47.8082i	0.123535	−	0.123535i
$388$		0			0
$389$	−249.631	+	249.631i	−0.641724	+	0.641724i	−0.950979	−	0.309255i	$-0.899920\pi$
$389$	−249.631	+	249.631i	−0.641724	+	0.641724i	0.309255	+	0.950979i	$0.399920\pi$
$390$		0			0
$391$	739.249			1.89066
$392$		0			0
$393$		−	711.102i		−	1.80942i
$394$		0			0
$395$	96.4210	+	96.4210i	0.244104	+	0.244104i
$396$		0			0
$397$	394.835	+	394.835i	0.994547	+	0.994547i	0.999985	−	0.00543774i	$-0.00173090\pi$
$397$	394.835	+	394.835i	0.994547	+	0.994547i	−0.00543774	+	0.999985i	$0.501731\pi$
$398$		0			0
$399$			35.1837i			0.0881796i
$400$		0			0
$401$	300.343			0.748986			0.374493	−	0.927230i	$-0.377817\pi$
$401$	300.343			0.748986			0.374493	+	0.927230i	$0.377817\pi$
$402$		0			0
$403$	347.410	−	347.410i	0.862060	−	0.862060i
$404$		0			0
$405$	160.041	−	160.041i	0.395163	−	0.395163i
$406$		0			0
$407$	−384.848			−0.945573
$408$		0			0
$409$		−	318.338i		−	0.778334i	−0.921167	−	0.389167i	$-0.872763\pi$
$409$		−	318.338i		−	0.778334i	0.921167	−	0.389167i	$-0.127237\pi$
$410$		0			0
$411$	219.135	+	219.135i	0.533175	+	0.533175i
$412$		0			0
$413$	−16.3177	−	16.3177i	−0.0395102	−	0.0395102i
$414$		0			0
$415$		−	106.446i		−	0.256495i
$416$		0			0
$417$	−600.294			−1.43955
$418$		0			0
$419$	−124.581	+	124.581i	−0.297330	+	0.297330i	−0.839967	−	0.542637i	$-0.817426\pi$
$419$	−124.581	+	124.581i	−0.297330	+	0.297330i	0.542637	+	0.839967i	$0.317426\pi$
$420$		0			0
$421$	−231.291	+	231.291i	−0.549385	+	0.549385i	−0.926263	−	0.376878i	$-0.876998\pi$
$421$	−231.291	+	231.291i	−0.549385	+	0.549385i	0.376878	+	0.926263i	$0.376998\pi$
$422$		0			0
$423$	315.544			0.745966
$424$		0			0
$425$			118.915i			0.279800i
$426$		0			0
$427$	−7.29956	−	7.29956i	−0.0170950	−	0.0170950i
$428$		0			0
$429$	−271.586	−	271.586i	−0.633066	−	0.633066i
$430$		0			0
$431$			219.900i			0.510209i	0.966914	+	0.255104i	$0.0821098\pi$
$431$			219.900i			0.510209i	−0.966914	+	0.255104i	$0.917890\pi$
$432$		0			0
$433$	319.622			0.738158			0.369079	−	0.929398i	$-0.379673\pi$
$433$	319.622			0.738158			0.369079	+	0.929398i	$0.379673\pi$
$434$		0			0
$435$	−93.5207	+	93.5207i	−0.214990	+	0.214990i
$436$		0			0
$437$	404.372	−	404.372i	0.925336	−	0.925336i
$438$		0			0
$439$	−449.321			−1.02351			−0.511756	−	0.859131i	$-0.671005\pi$
$439$	−449.321			−1.02351			−0.511756	+	0.859131i	$0.671005\pi$
$440$		0			0
$441$			210.661i			0.477688i
$442$		0			0
$443$	−617.930	−	617.930i	−1.39488	−	1.39488i	−0.813970	−	0.580906i	$-0.802698\pi$
$443$	−617.930	−	617.930i	−1.39488	−	1.39488i	−0.580906	−	0.813970i	$-0.697302\pi$
$444$		0			0
$445$	−151.526	−	151.526i	−0.340509	−	0.340509i
$446$		0			0
$447$			228.216i			0.510551i
$448$		0			0
$449$	−386.181			−0.860091			−0.430046	−	0.902807i	$-0.641503\pi$
$449$	−386.181			−0.860091			−0.430046	+	0.902807i	$0.641503\pi$
$450$		0			0
$451$	115.889	−	115.889i	0.256959	−	0.256959i
$452$		0			0
$453$	−218.443	+	218.443i	−0.482213	+	0.482213i
$454$		0			0
$455$	−19.5005			−0.0428581
$456$		0			0
$457$		−	148.461i		−	0.324861i	−0.986720	−	0.162430i	$-0.948067\pi$
$457$		−	148.461i		−	0.324861i	0.986720	−	0.162430i	$-0.0519333\pi$
$458$		0			0
$459$	287.071	+	287.071i	0.625426	+	0.625426i
$460$		0			0
$461$	540.235	+	540.235i	1.17188	+	1.17188i	0.981762	+	0.190114i	$0.0608857\pi$
$461$	540.235	+	540.235i	1.17188	+	1.17188i	0.190114	+	0.981762i	$0.439114\pi$
$462$		0			0
$463$			177.274i			0.382880i	0.981504	+	0.191440i	$0.0613158\pi$
$463$			177.274i			0.382880i	−0.981504	+	0.191440i	$0.938684\pi$
$464$		0			0
$465$	240.908			0.518082
$466$		0			0
$467$	380.452	−	380.452i	0.814672	−	0.814672i	−0.170658	−	0.985330i	$-0.554589\pi$
$467$	380.452	−	380.452i	0.814672	−	0.814672i	0.985330	+	0.170658i	$0.0545894\pi$
$468$		0			0
$469$	−34.9161	+	34.9161i	−0.0744480	+	0.0744480i
$470$		0			0
$471$	−797.316			−1.69282
$472$		0			0
$473$			98.8566i			0.208999i
$474$		0			0
$475$	65.0470	+	65.0470i	0.136941	+	0.136941i
$476$		0			0
$477$	213.944	+	213.944i	0.448520	+	0.448520i
$478$		0			0
$479$			684.694i			1.42942i	0.699419	+	0.714712i	$0.253442\pi$
$479$			684.694i			1.42942i	−0.699419	+	0.714712i	$0.746558\pi$
$480$		0			0
$481$	−1013.38			−2.10682
$482$		0			0
$483$	−42.0317	+	42.0317i	−0.0870222	+	0.0870222i
$484$		0			0
$485$	214.767	−	214.767i	0.442819	−	0.442819i
$486$		0			0
$487$	−307.415			−0.631242			−0.315621	−	0.948885i	$-0.602213\pi$
$487$	−307.415			−0.631242			−0.315621	+	0.948885i	$0.602213\pi$
$488$		0			0
$489$		−	1103.20i		−	2.25603i
$490$		0			0
$491$	−279.139	−	279.139i	−0.568511	−	0.568511i	0.363200	−	0.931711i	$-0.381684\pi$
$491$	−279.139	−	279.139i	−0.568511	−	0.568511i	−0.931711	+	0.363200i	$0.881684\pi$
$492$		0			0
$493$	−272.510	−	272.510i	−0.552758	−	0.552758i
$494$		0			0
$495$		−	61.1120i		−	0.123459i
$496$		0			0
$497$	−18.1135			−0.0364456
$498$		0			0
$499$	76.2725	−	76.2725i	0.152851	−	0.152851i	−0.626539	−	0.779390i	$-0.715529\pi$
$499$	76.2725	−	76.2725i	0.152851	−	0.152851i	0.779390	+	0.626539i	$0.215529\pi$
$500$		0			0
$501$	−714.672	+	714.672i	−1.42649	+	1.42649i
$502$		0			0
$503$	−304.296			−0.604962			−0.302481	−	0.953155i	$-0.597815\pi$
$503$	−304.296			−0.604962			−0.302481	+	0.953155i	$0.597815\pi$
$504$		0			0
$505$		−	218.095i		−	0.431871i
$506$		0			0
$507$	−278.945	−	278.945i	−0.550188	−	0.550188i
$508$		0			0
$509$	−146.043	−	146.043i	−0.286922	−	0.286922i	0.548940	−	0.835862i	$-0.315032\pi$
$509$	−146.043	−	146.043i	−0.286922	−	0.286922i	−0.835862	+	0.548940i	$0.815032\pi$
$510$		0			0
$511$		−	53.0287i		−	0.103774i
$512$		0			0
$513$	314.058			0.612198
$514$		0			0
$515$	35.1391	−	35.1391i	0.0682312	−	0.0682312i
$516$		0			0
$517$	−326.237	+	326.237i	−0.631019	+	0.631019i
$518$		0			0
$519$	132.201			0.254722
$520$		0			0
$521$			658.686i			1.26427i	0.774857	+	0.632136i	$0.217822\pi$
$521$			658.686i			1.26427i	−0.774857	+	0.632136i	$0.782178\pi$
$522$		0			0
$523$	388.573	+	388.573i	0.742970	+	0.742970i	0.973148	−	0.230179i	$-0.0739310\pi$
$523$	388.573	+	388.573i	0.742970	+	0.742970i	−0.230179	+	0.973148i	$0.573931\pi$
$524$		0			0
$525$	−6.76120	−	6.76120i	−0.0128785	−	0.0128785i
$526$		0			0
$527$			701.982i			1.33203i
$528$		0			0
$529$	437.156			0.826382
$530$		0			0
$531$	134.656	−	134.656i	0.253589	−	0.253589i
$532$		0			0
$533$	305.158	−	305.158i	0.572528	−	0.572528i
$534$		0			0
$535$	−349.035			−0.652402
$536$		0			0
$537$			251.373i			0.468105i
$538$		0			0
$539$	−217.799	−	217.799i	−0.404080	−	0.404080i
$540$		0			0
$541$	−748.536	−	748.536i	−1.38362	−	1.38362i	−0.838103	−	0.545512i	$-0.816335\pi$
$541$	−748.536	−	748.536i	−1.38362	−	1.38362i	−0.545512	−	0.838103i	$-0.683665\pi$
$542$		0			0
$543$		−	781.184i		−	1.43864i
$544$		0			0
$545$	86.6920			0.159068
$546$		0			0
$547$	−572.562	+	572.562i	−1.04673	+	1.04673i	−0.0478789	+	0.998853i	$0.515246\pi$
$547$	−572.562	+	572.562i	−1.04673	+	1.04673i	−0.998853	+	0.0478789i	$0.984754\pi$
$548$		0			0
$549$	60.2369	−	60.2369i	0.109721	−	0.109721i
$550$		0			0
$551$	−298.128			−0.541067
$552$		0			0
$553$		−	31.9494i		−	0.0577747i
$554$		0			0
$555$	−351.360	−	351.360i	−0.633081	−	0.633081i
$556$		0			0
$557$	96.1701	+	96.1701i	0.172657	+	0.172657i	0.788146	−	0.615489i	$-0.211041\pi$
$557$	96.1701	+	96.1701i	0.172657	+	0.172657i	−0.615489	+	0.788146i	$0.711041\pi$
$558$		0			0
$559$			260.309i			0.465670i
$560$		0			0
$561$	548.769			0.978198
$562$		0			0
$563$	400.351	−	400.351i	0.711102	−	0.711102i	−0.255664	−	0.966766i	$-0.582294\pi$
$563$	400.351	−	400.351i	0.711102	−	0.711102i	0.966766	+	0.255664i	$0.0822939\pi$
$564$		0			0
$565$	−242.133	+	242.133i	−0.428555	+	0.428555i
$566$		0			0
$567$	−53.0301			−0.0935275
$568$		0			0
$569$			1008.50i			1.77241i	0.463289	+	0.886207i	$0.346669\pi$
$569$			1008.50i			1.77241i	−0.463289	+	0.886207i	$0.653331\pi$
$570$		0			0
$571$	246.717	+	246.717i	0.432079	+	0.432079i	0.889335	−	0.457256i	$-0.151168\pi$
$571$	246.717	+	246.717i	0.432079	+	0.432079i	−0.457256	+	0.889335i	$0.651168\pi$
$572$		0			0
$573$	397.980	+	397.980i	0.694555	+	0.694555i
$574$		0			0
$575$			155.415i			0.270287i
$576$		0			0
$577$	967.428			1.67665			0.838326	−	0.545170i	$-0.183535\pi$
$577$	967.428			1.67665			0.838326	+	0.545170i	$0.183535\pi$
$578$		0			0
$579$	−435.819	+	435.819i	−0.752710	+	0.752710i
$580$		0			0
$581$	−17.6355	+	17.6355i	−0.0303538	+	0.0303538i
$582$		0			0
$583$	−442.388			−0.758814
$584$		0			0
$585$		−	160.920i		−	0.275077i
$586$		0			0
$587$	353.788	+	353.788i	0.602705	+	0.602705i	0.941029	−	0.338325i	$-0.109860\pi$
$587$	353.788	+	353.788i	0.602705	+	0.602705i	−0.338325	+	0.941029i	$0.609860\pi$
$588$		0			0
$589$	383.987	+	383.987i	0.651930	+	0.651930i
$590$		0			0
$591$			761.518i			1.28852i
$592$		0			0
$593$	−526.354			−0.887612			−0.443806	−	0.896123i	$-0.646372\pi$
$593$	−526.354			−0.887612			−0.443806	+	0.896123i	$0.646372\pi$
$594$		0			0
$595$	19.7014	−	19.7014i	0.0331117	−	0.0331117i
$596$		0			0
$597$	−380.670	+	380.670i	−0.637638	+	0.637638i
$598$		0			0
$599$	−152.316			−0.254283			−0.127142	−	0.991885i	$-0.540580\pi$
$599$	−152.316			−0.254283			−0.127142	+	0.991885i	$0.540580\pi$
$600$		0			0
$601$			333.408i			0.554755i	0.960761	+	0.277377i	$0.0894652\pi$
$601$			333.408i			0.554755i	−0.960761	+	0.277377i	$0.910535\pi$
$602$		0			0
$603$	−288.132	−	288.132i	−0.477831	−	0.477831i
$604$		0			0
$605$	−128.135	−	128.135i	−0.211793	−	0.211793i
$606$		0			0
$607$		−	417.147i		−	0.687227i	−0.939111	−	0.343614i	$-0.888349\pi$
$607$		−	417.147i		−	0.687227i	0.939111	−	0.343614i	$-0.111651\pi$
$608$		0			0
$609$	30.9884			0.0508840
$610$		0			0
$611$	−859.047	+	859.047i	−1.40597	+	1.40597i
$612$		0			0
$613$	80.7246	−	80.7246i	0.131688	−	0.131688i	−0.638191	−	0.769878i	$-0.720317\pi$
$613$	80.7246	−	80.7246i	0.131688	−	0.131688i	0.769878	+	0.638191i	$0.220317\pi$
$614$		0			0
$615$	211.608			0.344079
$616$		0			0
$617$		−	635.686i		−	1.03029i	−0.857104	−	0.515143i	$-0.827739\pi$
$617$		−	635.686i		−	1.03029i	0.857104	−	0.515143i	$-0.172261\pi$
$618$		0			0
$619$	252.958	+	252.958i	0.408656	+	0.408656i	0.881270	−	0.472614i	$-0.156689\pi$
$619$	252.958	+	252.958i	0.408656	+	0.408656i	−0.472614	+	0.881270i	$0.656689\pi$
$620$		0			0
$621$	375.185	+	375.185i	0.604163	+	0.604163i
$622$		0			0
$623$			50.2087i			0.0805918i
$624$		0			0
$625$	−25.0000			−0.0400000
$626$		0			0
$627$	300.179	−	300.179i	0.478754	−	0.478754i
$628$		0			0
$629$	1023.83	−	1023.83i	1.62771	−	1.62771i
$630$		0			0
$631$	−428.484			−0.679055			−0.339527	−	0.940596i	$-0.610267\pi$
$631$	−428.484			−0.679055			−0.339527	+	0.940596i	$0.610267\pi$
$632$		0			0
$633$		−	373.197i		−	0.589569i
$634$		0			0
$635$	49.4822	+	49.4822i	0.0779247	+	0.0779247i
$636$		0			0
$637$	−573.509	−	573.509i	−0.900328	−	0.900328i
$638$		0			0
$639$		−	149.475i		−	0.233920i
$640$		0			0
$641$	−919.482			−1.43445			−0.717225	−	0.696842i	$-0.754588\pi$
$641$	−919.482			−1.43445			−0.717225	+	0.696842i	$0.754588\pi$
$642$		0			0
$643$	613.330	−	613.330i	0.953858	−	0.953858i	−0.0451239	−	0.998981i	$-0.514368\pi$
$643$	613.330	−	613.330i	0.953858	−	0.953858i	0.998981	+	0.0451239i	$0.0143683\pi$
$644$		0			0
$645$	−90.2544	+	90.2544i	−0.139929	+	0.139929i
$646$		0			0
$647$	1118.15			1.72821			0.864105	−	0.503312i	$-0.167885\pi$
$647$	1118.15			1.72821			0.864105	+	0.503312i	$0.167885\pi$
$648$		0			0
$649$			278.438i			0.429026i
$650$		0			0
$651$	−39.9128	−	39.9128i	−0.0613100	−	0.0613100i
$652$		0			0
$653$	−310.691	−	310.691i	−0.475790	−	0.475790i	0.427992	−	0.903782i	$-0.359221\pi$
$653$	−310.691	−	310.691i	−0.475790	−	0.475790i	−0.903782	+	0.427992i	$0.859221\pi$
$654$		0			0
$655$			435.621i			0.665071i
$656$		0			0
$657$	437.599			0.666057
$658$		0			0
$659$	−104.870	+	104.870i	−0.159135	+	0.159135i	−0.782183	−	0.623049i	$-0.785894\pi$
$659$	−104.870	+	104.870i	−0.159135	+	0.159135i	0.623049	+	0.782183i	$0.285894\pi$
$660$		0			0
$661$	−288.246	+	288.246i	−0.436075	+	0.436075i	−0.890689	−	0.454614i	$-0.849777\pi$
$661$	−288.246	+	288.246i	−0.436075	+	0.436075i	0.454614	+	0.890689i	$0.349777\pi$
$662$		0			0
$663$	1445.02			2.17952
$664$		0			0
$665$		−	21.5535i		−	0.0324113i
$666$		0			0
$667$	−356.155	−	356.155i	−0.533965	−	0.533965i
$668$		0			0
$669$	−385.066	−	385.066i	−0.575584	−	0.575584i
$670$		0			0
$671$			124.556i			0.185628i
$672$		0			0
$673$	−765.186			−1.13698			−0.568489	−	0.822691i	$-0.692472\pi$
$673$	−765.186			−1.13698			−0.568489	+	0.822691i	$0.692472\pi$
$674$		0			0
$675$	−60.3520	+	60.3520i	−0.0894104	+	0.0894104i
$676$		0			0
$677$	−598.724	+	598.724i	−0.884378	+	0.884378i	−0.993976	−	0.109598i	$-0.965044\pi$
$677$	−598.724	+	598.724i	−0.884378	+	0.884378i	0.109598	+	0.993976i	$0.465044\pi$
$678$		0			0
$679$	−71.1638			−0.104807
$680$		0			0
$681$			300.958i			0.441935i
$682$		0			0
$683$	−42.0197	−	42.0197i	−0.0615222	−	0.0615222i	0.675676	−	0.737198i	$-0.263852\pi$
$683$	−42.0197	−	42.0197i	−0.0615222	−	0.0615222i	−0.737198	+	0.675676i	$0.763852\pi$
$684$		0			0
$685$	−134.242	−	134.242i	−0.195974	−	0.195974i
$686$		0			0
$687$		−	532.012i		−	0.774400i
$688$		0			0
$689$	−1164.90			−1.69071
$690$		0			0
$691$	−669.422	+	669.422i	−0.968773	+	0.968773i	−0.999527	−	0.0307538i	$-0.990209\pi$
$691$	−669.422	+	669.422i	−0.968773	+	0.968773i	0.0307538	+	0.999527i	$0.490209\pi$
$692$		0			0
$693$	−10.1248	+	10.1248i	−0.0146101	+	0.0146101i
$694$		0			0
$695$	367.740			0.529122
$696$		0			0
$697$			616.605i			0.884656i
$698$		0			0
$699$	−6.77190	−	6.77190i	−0.00968798	−	0.00968798i
$700$		0			0
$701$	359.212	+	359.212i	0.512428	+	0.512428i	0.915270	−	0.402841i	$-0.131977\pi$
$701$	359.212	+	359.212i	0.512428	+	0.512428i	−0.402841	+	0.915270i	$0.631977\pi$
$702$		0			0
$703$		−	1120.07i		−	1.59328i
$704$		0			0
$705$	−595.697			−0.844961
$706$		0			0
$707$	−36.1332	+	36.1332i	−0.0511078	+	0.0511078i
$708$		0			0
$709$	40.0114	−	40.0114i	0.0564335	−	0.0564335i	−0.678327	−	0.734760i	$-0.737295\pi$
$709$	40.0114	−	40.0114i	0.0564335	−	0.0564335i	0.734760	+	0.678327i	$0.237295\pi$
$710$		0			0
$711$	263.650			0.370816
$712$		0			0
$713$			917.450i			1.28675i
$714$		0			0
$715$	166.373	+	166.373i	0.232690	+	0.232690i
$716$		0			0
$717$	−849.423	−	849.423i	−1.18469	−	1.18469i
$718$		0			0
$719$		−	1163.07i		−	1.61763i	−0.588065	−	0.808814i	$-0.700110\pi$
$719$		−	1163.07i		−	1.61763i	0.588065	−	0.808814i	$-0.299890\pi$
$720$		0			0
$721$	−11.6434			−0.0161490
$722$		0			0
$723$	−743.825	+	743.825i	−1.02880	+	1.02880i
$724$		0			0
$725$	57.2908	−	57.2908i	0.0790218	−	0.0790218i
$726$		0			0
$727$	693.503			0.953924			0.476962	−	0.878924i	$-0.341738\pi$
$727$	693.503			0.953924			0.476962	+	0.878924i	$0.341738\pi$
$728$		0			0
$729$			123.162i			0.168947i
$730$		0			0
$731$	−262.992	−	262.992i	−0.359770	−	0.359770i
$732$		0			0
$733$	−138.195	−	138.195i	−0.188533	−	0.188533i	0.606528	−	0.795062i	$-0.292562\pi$
$733$	−138.195	−	138.195i	−0.188533	−	0.188533i	−0.795062	+	0.606528i	$0.792562\pi$
$734$		0			0
$735$		−	397.694i		−	0.541080i
$736$		0			0
$737$	595.792			0.808402
$738$		0			0
$739$	−546.989	+	546.989i	−0.740175	+	0.740175i	−0.972612	−	0.232437i	$-0.925330\pi$
$739$	−546.989	+	546.989i	−0.740175	+	0.740175i	0.232437	+	0.972612i	$0.425330\pi$
$740$		0			0
$741$	790.431	−	790.431i	1.06671	−	1.06671i
$742$		0			0
$743$	−369.647			−0.497506			−0.248753	−	0.968567i	$-0.580021\pi$
$743$	−369.647			−0.497506			−0.248753	+	0.968567i	$0.580021\pi$
$744$		0			0
$745$		−	139.805i		−	0.187658i
$746$		0			0
$747$	−145.531	−	145.531i	−0.194820	−	0.194820i
$748$		0			0
$749$	57.8269	+	57.8269i	0.0772054	+	0.0772054i
$750$		0			0
$751$		−	284.619i		−	0.378987i	−0.981882	−	0.189493i	$-0.939315\pi$
$751$		−	284.619i		−	0.378987i	0.981882	−	0.189493i	$-0.0606845\pi$
$752$		0			0
$753$	717.148			0.952388
$754$		0			0
$755$	133.818	−	133.818i	0.177242	−	0.177242i
$756$		0			0
$757$	618.365	−	618.365i	0.816863	−	0.816863i	−0.168789	−	0.985652i	$-0.553986\pi$
$757$	618.365	−	618.365i	0.816863	−	0.816863i	0.985652	+	0.168789i	$0.0539856\pi$
$758$		0			0
$759$	717.210			0.944941
$760$		0			0
$761$		−	741.506i		−	0.974384i	−0.873295	−	0.487192i	$-0.838021\pi$
$761$		−	741.506i		−	0.974384i	0.873295	−	0.487192i	$-0.161979\pi$
$762$		0			0
$763$	−14.3628	−	14.3628i	−0.0188242	−	0.0188242i
$764$		0			0
$765$	162.579	+	162.579i	0.212521	+	0.212521i
$766$		0			0
$767$			733.183i			0.955911i
$768$		0			0
$769$	1087.55			1.41424			0.707119	−	0.707094i	$-0.249994\pi$
$769$	1087.55			1.41424			0.707119	+	0.707094i	$0.249994\pi$
$770$		0			0
$771$	681.330	−	681.330i	0.883696	−	0.883696i
$772$		0			0
$773$	26.4020	−	26.4020i	0.0341552	−	0.0341552i	−0.689823	−	0.723978i	$-0.742312\pi$
$773$	26.4020	−	26.4020i	0.0341552	−	0.0341552i	0.723978	+	0.689823i	$0.242312\pi$
$774$		0			0
$775$	−147.580			−0.190426
$776$		0			0
$777$			116.424i			0.149838i
$778$		0			0
$779$	337.286	+	337.286i	0.432973	+	0.432973i
$780$		0			0
$781$	154.540	+	154.540i	0.197875	+	0.197875i
$782$		0			0
$783$		−	276.609i		−	0.353269i
$784$		0			0
$785$	488.436			0.622212
$786$		0			0
$787$	71.8942	−	71.8942i	0.0913522	−	0.0913522i	−0.659954	−	0.751306i	$-0.729424\pi$
$787$	71.8942	−	71.8942i	0.0913522	−	0.0913522i	0.751306	+	0.659954i	$0.229424\pi$
$788$		0			0
$789$	98.7337	−	98.7337i	0.125138	−	0.125138i
$790$		0			0
$791$	80.2317			0.101431
$792$		0			0
$793$			327.982i			0.413596i
$794$		0			0
$795$	−403.893	−	403.893i	−0.508042	−	0.508042i
$796$		0			0
$797$	418.459	+	418.459i	0.525043	+	0.525043i	0.919090	−	0.394047i	$-0.128925\pi$
$797$	418.459	+	418.459i	0.525043	+	0.525043i	−0.394047	+	0.919090i	$0.628925\pi$
$798$		0			0
$799$		−	1735.80i		−	2.17247i
$800$		0			0
$801$	−414.328			−0.517264
$802$		0			0
$803$	−452.429	+	452.429i	−0.563423	+	0.563423i
$804$		0			0
$805$	25.7487	−	25.7487i	0.0319859	−	0.0319859i
$806$		0			0
$807$	99.8312			0.123707
$808$		0			0
$809$			403.893i			0.499250i	0.968343	+	0.249625i	$0.0803074\pi$
$809$			403.893i			0.499250i	−0.968343	+	0.249625i	$0.919693\pi$
$810$		0			0
$811$	−535.387	−	535.387i	−0.660157	−	0.660157i	0.295260	−	0.955417i	$-0.404594\pi$
$811$	−535.387	−	535.387i	−0.660157	−	0.660157i	−0.955417	+	0.295260i	$0.904594\pi$
$812$		0			0
$813$	397.160	+	397.160i	0.488512	+	0.488512i
$814$		0			0
$815$			675.820i			0.829227i
$816$		0			0
$817$	−287.715			−0.352161
$818$		0			0
$819$	−26.6607	+	26.6607i	−0.0325527	+	0.0325527i
$820$		0			0
$821$	107.542	−	107.542i	0.130989	−	0.130989i	−0.638573	−	0.769561i	$-0.720475\pi$
$821$	107.542	−	107.542i	0.130989	−	0.130989i	0.769561	+	0.638573i	$0.220475\pi$
$822$		0			0
$823$	−227.398			−0.276304			−0.138152	−	0.990411i	$-0.544116\pi$
$823$	−227.398			−0.276304			−0.138152	+	0.990411i	$0.544116\pi$
$824$		0			0
$825$			115.370i			0.139842i
$826$		0			0
$827$	503.855	+	503.855i	0.609256	+	0.609256i	0.942752	−	0.333496i	$-0.108228\pi$
$827$	503.855	+	503.855i	0.609256	+	0.609256i	−0.333496	+	0.942752i	$0.608228\pi$
$828$		0			0
$829$	201.982	+	201.982i	0.243645	+	0.243645i	0.818356	−	0.574711i	$-0.194886\pi$
$829$	201.982	+	201.982i	0.243645	+	0.243645i	−0.574711	+	0.818356i	$0.694886\pi$
$830$		0			0
$831$			480.011i			0.577630i
$832$		0			0
$833$	1158.84			1.39116
$834$		0			0
$835$	437.808	−	437.808i	0.524321	−	0.524321i
$836$		0			0
$837$	−356.271	+	356.271i	−0.425652	+	0.425652i
$838$		0			0
$839$	28.6959			0.0342025			0.0171013	−	0.999854i	$-0.494556\pi$
$839$	28.6959			0.0342025			0.0171013	+	0.999854i	$0.494556\pi$
$840$		0			0
$841$		−	578.421i		−	0.687778i
$842$		0			0
$843$	785.753	+	785.753i	0.932091	+	0.932091i
$844$		0			0
$845$	170.882	+	170.882i	0.202227	+	0.202227i
$846$		0			0
$847$			42.4579i			0.0501273i
$848$		0			0
$849$	626.971			0.738482
$850$		0			0
$851$	1338.08	−	1338.08i	1.57237	−	1.57237i
$852$		0			0
$853$	905.693	−	905.693i	1.06177	−	1.06177i	0.0638118	−	0.997962i	$-0.479674\pi$
$853$	905.693	−	905.693i	1.06177	−	1.06177i	0.997962	−	0.0638118i	$-0.0203257\pi$
$854$		0			0
$855$	177.862			0.208026
$856$		0			0
$857$			353.050i			0.411960i	0.978556	+	0.205980i	$0.0660382\pi$
$857$			353.050i			0.411960i	−0.978556	+	0.205980i	$0.933962\pi$
$858$		0			0
$859$	189.473	+	189.473i	0.220574	+	0.220574i	0.808740	−	0.588166i	$-0.200150\pi$
$859$	189.473	+	189.473i	0.220574	+	0.220574i	−0.588166	+	0.808740i	$0.700150\pi$
$860$		0			0
$861$	−35.0586	−	35.0586i	−0.0407184	−	0.0407184i
$862$		0			0
$863$			1295.69i			1.50138i	0.660655	+	0.750690i	$0.270279\pi$
$863$			1295.69i			1.50138i	−0.660655	+	0.750690i	$0.729721\pi$
$864$		0			0
$865$	−80.9861			−0.0936256
$866$		0			0
$867$	−713.995	+	713.995i	−0.823524	+	0.823524i
$868$		0			0
$869$	−272.585	+	272.585i	−0.313676	+	0.313676i
$870$		0			0
$871$	1568.84			1.80119
$872$		0			0
$873$		−	587.252i		−	0.672683i
$874$		0			0
$875$	4.14191	+	4.14191i	0.00473361	+	0.00473361i
$876$		0			0
$877$	−917.766	−	917.766i	−1.04648	−	1.04648i	−0.998866	−	0.0476178i	$-0.984837\pi$
$877$	−917.766	−	917.766i	−1.04648	−	1.04648i	−0.0476178	−	0.998866i	$-0.515163\pi$
$878$		0			0
$879$			563.980i			0.641616i
$880$		0			0
$881$	98.4178			0.111711			0.0558557	−	0.998439i	$-0.482211\pi$
$881$	98.4178			0.111711			0.0558557	+	0.998439i	$0.482211\pi$
$882$		0			0
$883$	−770.156	+	770.156i	−0.872204	+	0.872204i	−0.992712	−	0.120508i	$-0.961548\pi$
$883$	−770.156	+	770.156i	−0.872204	+	0.872204i	0.120508	+	0.992712i	$0.461548\pi$
$884$		0			0
$885$	−254.209	+	254.209i	−0.287242	+	0.287242i
$886$		0			0
$887$	1112.42			1.25414			0.627070	−	0.778963i	$-0.284254\pi$
$887$	1112.42			1.25414			0.627070	+	0.778963i	$0.284254\pi$
$888$		0			0
$889$		−	16.3961i		−	0.0184433i
$890$		0			0
$891$	452.440	+	452.440i	0.507789	+	0.507789i
$892$		0			0
$893$	−949.490	−	949.490i	−1.06326	−	1.06326i
$894$		0			0
$895$		−	153.991i		−	0.172057i
$896$		0			0
$897$	1888.56			2.10542
$898$		0			0
$899$	338.200	−	338.200i	0.376196	−	0.376196i
$900$		0			0
$901$	1176.90	−	1176.90i	1.30622	−	1.30622i
$902$		0			0
$903$	29.9061			0.0331186
$904$		0			0
$905$			478.553i			0.528788i
$906$		0			0
$907$	−1170.90	−	1170.90i	−1.29096	−	1.29096i	−0.934193	−	0.356768i	$-0.883878\pi$
$907$	−1170.90	−	1170.90i	−1.29096	−	1.29096i	−0.356768	−	0.934193i	$-0.616122\pi$
$908$		0			0
$909$	−298.176	−	298.176i	−0.328026	−	0.328026i
$910$		0			0
$911$		−	87.3440i		−	0.0958770i	−0.998850	−	0.0479385i	$-0.984735\pi$
$911$		−	87.3440i		−	0.0958770i	0.998850	−	0.0479385i	$-0.0152652\pi$
$912$		0			0
$913$	300.925			0.329600
$914$		0			0
$915$	−113.718	+	113.718i	−0.124282	+	0.124282i
$916$		0			0
$917$	72.1722	−	72.1722i	0.0787047	−	0.0787047i
$918$		0			0
$919$	−1142.79			−1.24352			−0.621758	−	0.783210i	$-0.713581\pi$
$919$	−1142.79			−1.24352			−0.621758	+	0.783210i	$0.713581\pi$
$920$		0			0
$921$		−	218.627i		−	0.237380i
$922$		0			0
$923$	406.935	+	406.935i	0.440883	+	0.440883i
$924$		0			0
$925$	215.243	+	215.243i	0.232695	+	0.232695i
$926$		0			0
$927$		−	96.0832i		−	0.103650i
$928$		0			0
$929$	−506.684			−0.545408			−0.272704	−	0.962098i	$-0.587918\pi$
$929$	−506.684			−0.545408			−0.272704	+	0.962098i	$0.587918\pi$
$930$		0			0
$931$	633.890	−	633.890i	0.680870	−	0.680870i
$932$		0			0
$933$	−156.084	+	156.084i	−0.167293	+	0.167293i
$934$		0			0
$935$	−336.176			−0.359547
$936$		0			0
$937$		−	1124.98i		−	1.20062i	−0.799769	−	0.600308i	$-0.795045\pi$
$937$		−	1124.98i		−	1.20062i	0.799769	−	0.600308i	$-0.204955\pi$
$938$		0			0
$939$	177.053	+	177.053i	0.188555	+	0.188555i
$940$		0			0
$941$	606.490	+	606.490i	0.644516	+	0.644516i	0.951662	−	0.307146i	$-0.0993741\pi$
$941$	606.490	+	606.490i	0.644516	+	0.644516i	−0.307146	+	0.951662i	$0.599374\pi$
$942$		0			0
$943$			805.868i			0.854579i
$944$		0			0
$945$	19.9978			0.0211617
$946$		0			0
$947$	−341.210	+	341.210i	−0.360306	+	0.360306i	−0.863925	−	0.503620i	$-0.832001\pi$
$947$	−341.210	+	341.210i	−0.360306	+	0.360306i	0.503620	+	0.863925i	$0.332001\pi$
$948$		0			0
$949$	−1191.33	+	1191.33i	−1.25536	+	1.25536i
$950$		0			0
$951$	−1457.76			−1.53287
$952$		0			0
$953$		−	289.459i		−	0.303735i	−0.988401	−	0.151867i	$-0.951471\pi$
$953$		−	289.459i		−	0.303735i	0.988401	−	0.151867i	$-0.0485286\pi$
$954$		0			0
$955$	−243.803	−	243.803i	−0.255291	−	0.255291i
$956$		0			0
$957$	−264.386	−	264.386i	−0.276265	−	0.276265i
$958$		0			0
$959$			44.4815i			0.0463832i
$960$		0			0
$961$	89.8005			0.0934448
$962$		0			0
$963$	−477.195	+	477.195i	−0.495529	+	0.495529i
$964$		0			0
$965$	266.983	−	266.983i	0.276666	−	0.276666i
$966$		0			0
$967$	−1503.09			−1.55439			−0.777193	−	0.629262i	$-0.783357\pi$
$967$	−1503.09			−1.55439			−0.777193	+	0.629262i	$0.783357\pi$
$968$		0			0
$969$			1597.16i			1.64825i
$970$		0			0
$971$	−219.499	−	219.499i	−0.226055	−	0.226055i	0.584988	−	0.811042i	$-0.301099\pi$
$971$	−219.499	−	219.499i	−0.226055	−	0.226055i	−0.811042	+	0.584988i	$0.801099\pi$
$972$		0			0
$973$	−60.9259	−	60.9259i	−0.0626165	−	0.0626165i
$974$		0			0
$975$			303.792i			0.311582i
$976$		0			0
$977$	−334.950			−0.342836			−0.171418	−	0.985198i	$-0.554835\pi$
$977$	−334.950			−0.342836			−0.171418	+	0.985198i	$0.554835\pi$
$978$		0			0
$979$	428.369	−	428.369i	0.437558	−	0.437558i
$980$		0			0
$981$	118.524	−	118.524i	0.120819	−	0.120819i
$982$		0			0
$983$	−972.818			−0.989642			−0.494821	−	0.868995i	$-0.664766\pi$
$983$	−972.818			−0.989642			−0.494821	+	0.868995i	$0.664766\pi$
$984$		0			0
$985$		−	466.506i		−	0.473610i
$986$		0			0
$987$	98.6931	+	98.6931i	0.0999930	+	0.0999930i
$988$		0			0
$989$	−343.716	−	343.716i	−0.347539	−	0.347539i
$990$		0			0
$991$			956.623i			0.965310i	0.875810	+	0.482655i	$0.160328\pi$
$991$			956.623i			0.965310i	−0.875810	+	0.482655i	$0.839672\pi$
$992$		0			0
$993$	−1818.12			−1.83094
$994$		0			0
$995$	233.199	−	233.199i	0.234371	−	0.234371i
$996$		0			0
$997$	−874.158	+	874.158i	−0.876788	+	0.876788i	−0.993201	−	0.116413i	$-0.962861\pi$
$997$	−874.158	+	874.158i	−0.876788	+	0.876788i	0.116413	+	0.993201i	$0.462861\pi$
$998$		0			0
$999$	1039.23			1.04027

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	320.3.r.a.111.4		32
4.3	odd	2		80.3.r.a.51.9	yes	32
8.3	odd	2		640.3.r.a.351.4		32
8.5	even	2		640.3.r.b.351.13		32
16.3	odd	4		640.3.r.b.31.13		32
16.5	even	4		80.3.r.a.11.9	✓	32
16.11	odd	4	inner	320.3.r.a.271.4		32
16.13	even	4		640.3.r.a.31.4		32
20.3	even	4		400.3.k.h.99.1		32
20.7	even	4		400.3.k.g.99.16		32
20.19	odd	2		400.3.r.f.51.8		32
80.37	odd	4		400.3.k.h.299.1		32
80.53	odd	4		400.3.k.g.299.16		32
80.69	even	4		400.3.r.f.251.8		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.3.r.a.11.9	✓	32	16.5	even	4
80.3.r.a.51.9	yes	32	4.3	odd	2
320.3.r.a.111.4		32	1.1	even	1	trivial
320.3.r.a.271.4		32	16.11	odd	4	inner
400.3.k.g.99.16		32	20.7	even	4
400.3.k.g.299.16		32	80.53	odd	4
400.3.k.h.99.1		32	20.3	even	4
400.3.k.h.299.1		32	80.37	odd	4
400.3.r.f.51.8		32	20.19	odd	2
400.3.r.f.251.8		32	80.69	even	4
640.3.r.a.31.4		32	16.13	even	4
640.3.r.a.351.4		32	8.3	odd	2
640.3.r.b.31.13		32	16.3	odd	4
640.3.r.b.351.13		32	8.5	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 320 = 2^{6} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	320.r (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.58103 + 2.58103i) q^{3} +(1.58114 - 1.58114i) q^{5} -0.523915 q^{7} -4.32341i q^{9} +O(q^{10})\)	\(q+(-2.58103 + 2.58103i) q^{3} +(1.58114 - 1.58114i) q^{5} -0.523915 q^{7} -4.32341i q^{9} +(4.46992 + 4.46992i) q^{11} +(11.7702 + 11.7702i) q^{13} +8.16193i q^{15} -23.7830 q^{17} +(-13.0094 + 13.0094i) q^{19} +(1.35224 - 1.35224i) q^{21} -31.0831 q^{23} -5.00000i q^{25} +(-12.0704 - 12.0704i) q^{27} +(11.4582 + 11.4582i) q^{29} -29.5161i q^{31} -23.0740 q^{33} +(-0.828383 + 0.828383i) q^{35} +(-43.0487 + 43.0487i) q^{37} -60.7584 q^{39} -25.9263i q^{41} +(11.0580 + 11.0580i) q^{43} +(-6.83592 - 6.83592i) q^{45} +72.9849i q^{47} -48.7255 q^{49} +(61.3847 - 61.3847i) q^{51} +(-49.4850 + 49.4850i) q^{53} +14.1351 q^{55} -67.1553i q^{57} +(31.1457 + 31.1457i) q^{59} +(13.9327 + 13.9327i) q^{61} +2.26510i q^{63} +37.2206 q^{65} +(66.6446 - 66.6446i) q^{67} +(80.2262 - 80.2262i) q^{69} +34.5733 q^{71} +101.216i q^{73} +(12.9051 + 12.9051i) q^{75} +(-2.34186 - 2.34186i) q^{77} +60.9820i q^{79} +101.219 q^{81} +(33.6610 - 33.6610i) q^{83} +(-37.6043 + 37.6043i) q^{85} -59.1477 q^{87} -95.8337i q^{89} +(-6.16659 - 6.16659i) q^{91} +(76.1819 + 76.1819i) q^{93} +41.1394i q^{95} +135.831 q^{97} +(19.3253 - 19.3253i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q - 32 q^{11} + 32 q^{19} + 128 q^{23} + 96 q^{27} + 32 q^{29} - 96 q^{37} - 384 q^{39} - 96 q^{43} + 224 q^{49} + 256 q^{51} - 160 q^{53} + 352 q^{59} - 32 q^{61} - 160 q^{67} + 96 q^{69} - 256 q^{71} + 224 q^{77} - 288 q^{81} + 480 q^{83} + 160 q^{85} + 384 q^{91} + 96 q^{93} - 608 q^{99}+O(q^{100}) \) 32 * q - 32 * q^11 + 32 * q^19 + 128 * q^23 + 96 * q^27 + 32 * q^29 - 96 * q^37 - 384 * q^39 - 96 * q^43 + 224 * q^49 + 256 * q^51 - 160 * q^53 + 352 * q^59 - 32 * q^61 - 160 * q^67 + 96 * q^69 - 256 * q^71 + 224 * q^77 - 288 * q^81 + 480 * q^83 + 160 * q^85 + 384 * q^91 + 96 * q^93 - 608 * q^99

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