LMFDB - Embedded newform 320.3.r.a.271.4

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			271.4
Character	$\chi$	$=$	320.271
Dual form			320.3.r.a.111.4

$q$-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 $\left(\mathbb{Z}/320\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.58103	−	2.58103i	−0.860343	−	0.860343i	0.131035	−	0.991378i	$-0.458170\pi$
$3$	−2.58103	−	2.58103i	−0.860343	−	0.860343i	−0.991378	+	0.131035i	$0.958170\pi$
$4$		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	−0.474109	−	0.880466i	$-0.657230\pi$
$11$	4.46992	−	4.46992i	0.406357	−	0.406357i	0.880466	+	0.474109i	$0.157230\pi$
$12$		0			0
$13$	11.7702	−	11.7702i	0.905400	−	0.905400i	−0.0904968	−	0.995897i	$-0.528845\pi$
$13$	11.7702	−	11.7702i	0.905400	−	0.905400i	0.995897	+	0.0904968i	$0.0288455\pi$
$14$		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	0.276351	−	0.961057i	$-0.410875\pi$
$19$	−13.0094	−	13.0094i	−0.684706	−	0.684706i	−0.961057	+	0.276351i	$0.910875\pi$
$20$		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	−0.481395	−	0.876504i	$-0.659870\pi$
$29$	11.4582	−	11.4582i	0.395109	−	0.395109i	0.876504	+	0.481395i	$0.159870\pi$
$30$		0			0
$31$			29.5161i			0.952132i	0.879410	+	0.476066i	$0.157938\pi$
$31$			29.5161i			0.952132i	−0.879410	+	0.476066i	$0.842062\pi$
$32$		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	−0.983709	−	0.179768i	$-0.942465\pi$
$37$	−43.0487	−	43.0487i	−1.16348	−	1.16348i	−0.179768	−	0.983709i	$-0.557535\pi$
$38$		0			0
$39$	−60.7584			−1.55791
$40$		0			0
$41$			25.9263i			0.632348i	0.948701	+	0.316174i	$0.102398\pi$
$41$			25.9263i			0.632348i	−0.948701	+	0.316174i	$0.897602\pi$
$42$		0			0
$43$	11.0580	−	11.0580i	0.257162	−	0.257162i	−0.566737	−	0.823899i	$-0.691794\pi$
$43$	11.0580	−	11.0580i	0.257162	−	0.257162i	0.823899	+	0.566737i	$0.191794\pi$
$44$		0			0
$45$	−6.83592	+	6.83592i	−0.151909	+	0.151909i
$46$		0			0
$47$		−	72.9849i		−	1.55287i	−0.630197	−	0.776435i	$-0.717026\pi$
$47$		−	72.9849i		−	1.55287i	0.630197	−	0.776435i	$-0.282974\pi$
$48$		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	0.0642539	−	0.997934i	$-0.479533\pi$
$53$	−49.4850	−	49.4850i	−0.933680	−	0.933680i	−0.997934	+	0.0642539i	$0.979533\pi$
$54$		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	−0.392050	−	0.919944i	$-0.628234\pi$
$59$	31.1457	−	31.1457i	0.527894	−	0.527894i	0.919944	+	0.392050i	$0.128234\pi$
$60$		0			0
$61$	13.9327	−	13.9327i	0.228405	−	0.228405i	−0.583621	−	0.812026i	$-0.698365\pi$
$61$	13.9327	−	13.9327i	0.228405	−	0.228405i	0.812026	+	0.583621i	$0.198365\pi$
$62$		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	0.999986	−	0.00529076i	$-0.00168411\pi$
$67$	66.6446	+	66.6446i	0.994695	+	0.994695i	−0.00529076	+	0.999986i	$0.501684\pi$
$68$		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	$-0.756173\pi$
$73$		−	101.216i		−	1.38652i	0.720686	−	0.693262i	$-0.243827\pi$
$74$		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	$-0.873870\pi$
$79$		−	60.9820i		−	0.771924i	0.922515	−	0.385962i	$-0.126130\pi$
$80$		0			0
$81$	101.219			1.24962
$82$		0			0
$83$	33.6610	+	33.6610i	0.405555	+	0.405555i	0.880185	−	0.474630i	$-0.157418\pi$
$83$	33.6610	+	33.6610i	0.405555	+	0.405555i	−0.474630	+	0.880185i	$0.657418\pi$
$84$		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	$0.180968\pi$
$89$			95.8337i			1.07678i	−0.842695	+	0.538391i	$0.819032\pi$
$90$		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	0.960641	−	0.277792i	$-0.0896028\pi$
$101$	68.9677	+	68.9677i	0.682849	+	0.682849i	−0.277792	+	0.960641i	$0.589603\pi$
$102$		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	−0.0320513	+	0.999486i	$0.510204\pi$
$107$	−110.375	+	110.375i	−1.03154	+	1.03154i	−0.999486	+	0.0320513i	$0.989796\pi$
$108$		0			0
$109$	27.4144	−	27.4144i	0.251508	−	0.251508i	−0.570080	−	0.821589i	$-0.693088\pi$
$109$	27.4144	−	27.4144i	0.251508	−	0.251508i	0.821589	+	0.570080i	$0.193088\pi$
$110$		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	$-0.960681\pi$
$127$		−	31.2953i		−	0.246420i	0.992381	−	0.123210i	$-0.0393188\pi$
$128$		0			0
$129$	−57.0819			−0.442495
$130$		0			0
$131$	−137.756	−	137.756i	−1.05157	−	1.05157i	−0.998596	−	0.0529731i	$-0.983130\pi$
$131$	−137.756	−	137.756i	−1.05157	−	1.05157i	−0.0529731	−	0.998596i	$-0.516870\pi$
$132$		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	$0.100283\pi$
$137$			84.9022i			0.619724i	−0.950782	+	0.309862i	$0.899717\pi$
$138$		0			0
$139$	116.290	−	116.290i	0.836616	−	0.836616i	−0.151796	−	0.988412i	$-0.548506\pi$
$139$	116.290	−	116.290i	0.836616	−	0.836616i	0.988412	+	0.151796i	$0.0485056\pi$
$140$		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	0.839725	−	0.543012i	$-0.182716\pi$
$149$	44.2103	+	44.2103i	0.296714	+	0.296714i	−0.543012	+	0.839725i	$0.682716\pi$
$150$		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	−0.0160678	−	0.999871i	$-0.505115\pi$
$157$	154.457	−	154.457i	0.983803	−	0.983803i	0.999871	+	0.0160678i	$0.00511475\pi$
$158$		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	−0.920588	−	0.390536i	$-0.872290\pi$
$163$	−213.713	−	213.713i	−1.31112	−	1.31112i	−0.390536	−	0.920588i	$-0.627710\pi$
$164$		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	−0.777240	−	0.629205i	$-0.783381\pi$
$173$	−25.6101	+	25.6101i	−0.148035	+	0.148035i	0.629205	+	0.777240i	$0.283381\pi$
$174$		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	0.829923	−	0.557877i	$-0.188384\pi$
$179$	48.6962	+	48.6962i	0.272046	+	0.272046i	−0.557877	+	0.829923i	$0.688384\pi$
$180$		0			0
$181$	−151.332	−	151.332i	−0.836088	−	0.836088i	0.152254	−	0.988341i	$-0.451347\pi$
$181$	−151.332	−	151.332i	−0.836088	−	0.836088i	−0.988341	+	0.152254i	$0.951347\pi$
$182$		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	$0.132259\pi$
$191$			154.194i			0.807301i	−0.914913	+	0.403650i	$0.867741\pi$
$192$		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	0.974262	−	0.225418i	$-0.0723748\pi$
$197$	147.522	+	147.522i	0.748844	+	0.748844i	−0.225418	+	0.974262i	$0.572375\pi$
$198$		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	0.514721	−	0.857357i	$-0.327895\pi$
$211$	−72.2962	−	72.2962i	−0.342636	−	0.342636i	−0.857357	+	0.514721i	$0.827895\pi$
$212$		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	$-0.891430\pi$
$223$		−	149.191i		−	0.669017i	0.942393	−	0.334509i	$-0.108570\pi$
$224$		0			0
$225$	−21.6171			−0.0960758
$226$		0			0
$227$	58.3020	+	58.3020i	0.256837	+	0.256837i	0.823766	−	0.566929i	$-0.191869\pi$
$227$	58.3020	+	58.3020i	0.256837	+	0.256837i	−0.566929	+	0.823766i	$0.691869\pi$
$228$		0			0
$229$	−103.062	−	103.062i	−0.450053	−	0.450053i	0.445319	−	0.895372i	$-0.353090\pi$
$229$	−103.062	−	103.062i	−0.450053	−	0.450053i	−0.895372	+	0.445319i	$0.853090\pi$
$230$		0			0
$231$	12.0888			0.0523325
$232$		0			0
$233$		−	2.62372i		−	0.0112606i	−0.999984	−	0.00563030i	$-0.998208\pi$
$233$		−	2.62372i		−	0.0112606i	0.999984	−	0.00563030i	$-0.00179219\pi$
$234$		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	$-0.758270\pi$
$239$		−	329.102i		−	1.37700i	0.725238	−	0.688499i	$-0.241730\pi$
$240$		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	−0.927447	−	0.373954i	$-0.878002\pi$
$251$	−138.927	+	138.927i	−0.553494	+	0.553494i	0.373954	+	0.927447i	$0.378002\pi$
$252$		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	−0.742139	−	0.670246i	$-0.766189\pi$
$269$	−19.3394	+	19.3394i	−0.0718938	+	0.0718938i	0.670246	+	0.742139i	$0.266189\pi$
$270$		0			0
$271$			153.877i			0.567811i	0.958852	+	0.283905i	$0.0916302\pi$
$271$			153.877i			0.567811i	−0.958852	+	0.283905i	$0.908370\pi$
$272$		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	0.854745	−	0.519048i	$-0.173713\pi$
$277$	92.9882	+	92.9882i	0.335698	+	0.335698i	−0.519048	+	0.854745i	$0.673713\pi$
$278$		0			0
$279$	−127.610			−0.457384
$280$		0			0
$281$			304.434i			1.08339i	0.840574	+	0.541697i	$0.182218\pi$
$281$			304.434i			1.08339i	−0.840574	+	0.541697i	$0.817782\pi$
$282$		0			0
$283$	−121.458	+	121.458i	−0.429179	+	0.429179i	−0.888349	−	0.459170i	$-0.848147\pi$
$283$	−121.458	+	121.458i	−0.429179	+	0.429179i	0.459170	+	0.888349i	$0.348147\pi$
$284$		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	0.868527	−	0.495643i	$-0.165067\pi$
$293$	109.255	+	109.255i	0.372884	+	0.372884i	−0.495643	+	0.868527i	$0.665067\pi$
$294$		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	0.634756	−	0.772713i	$-0.281101\pi$
$307$	−42.3527	−	42.3527i	−0.137957	−	0.137957i	−0.772713	+	0.634756i	$0.781101\pi$
$308$		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	$0.0349511\pi$
$313$			68.5980i			0.219163i	−0.993978	+	0.109581i	$0.965049\pi$
$314$		0			0
$315$	3.58144	−	3.58144i	0.0113697	−	0.0113697i
$316$		0			0
$317$	282.399	−	282.399i	0.890848	−	0.890848i	−0.103755	−	0.994603i	$-0.533086\pi$
$317$	282.399	−	282.399i	0.890848	−	0.890848i	0.994603	+	0.103755i	$0.0330859\pi$
$318$		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	0.0662731	−	0.997802i	$-0.478889\pi$
$331$	352.209	−	352.209i	1.06407	−	1.06407i	0.997802	−	0.0662731i	$-0.0211108\pi$
$332$		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	−0.619569	−	0.784943i	$-0.712692\pi$
$347$	57.3848	−	57.3848i	0.165374	−	0.165374i	0.784943	+	0.619569i	$0.212692\pi$
$348$		0			0
$349$	388.384	−	388.384i	1.11285	−	1.11285i	0.120084	−	0.992764i	$-0.461683\pi$
$349$	388.384	−	388.384i	1.11285	−	1.11285i	0.992764	−	0.120084i	$-0.0383165\pi$
$350$		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	$0.0138400\pi$
$367$			31.9040i			0.0869318i	−0.999055	+	0.0434659i	$0.986160\pi$
$368$		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	0.877871	−	0.478898i	$-0.158963\pi$
$373$	148.817	+	148.817i	0.398973	+	0.398973i	−0.478898	+	0.877871i	$0.658963\pi$
$374$		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	−0.322214	−	0.946667i	$-0.604427\pi$
$379$	236.667	−	236.667i	0.624452	−	0.624452i	0.946667	+	0.322214i	$0.104427\pi$
$380$		0			0
$381$	−80.7740	+	80.7740i	−0.212005	+	0.212005i
$382$		0			0
$383$			587.307i			1.53344i	0.641982	+	0.766720i	$0.278112\pi$
$383$			587.307i			1.53344i	−0.641982	+	0.766720i	$0.721888\pi$
$384$		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	0.309255	−	0.950979i	$-0.399920\pi$
$389$	−249.631	−	249.631i	−0.641724	−	0.641724i	−0.950979	+	0.309255i	$0.899920\pi$
$390$		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	−0.00543774	−	0.999985i	$-0.501731\pi$
$397$	394.835	−	394.835i	0.994547	−	0.994547i	0.999985	+	0.00543774i	$0.00173090\pi$
$398$		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	$0.127237\pi$
$409$			318.338i			0.778334i	−0.921167	+	0.389167i	$0.872763\pi$
$410$		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	0.542637	−	0.839967i	$-0.317426\pi$
$419$	−124.581	−	124.581i	−0.297330	−	0.297330i	−0.839967	+	0.542637i	$0.817426\pi$
$420$		0			0
$421$	−231.291	−	231.291i	−0.549385	−	0.549385i	0.376878	−	0.926263i	$-0.376998\pi$
$421$	−231.291	−	231.291i	−0.549385	−	0.549385i	−0.926263	+	0.376878i	$0.876998\pi$
$422$		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	$-0.917890\pi$
$431$		−	219.900i		−	0.510209i	0.966914	−	0.255104i	$-0.0821098\pi$
$432$		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	−0.580906	+	0.813970i	$0.697302\pi$
$443$	−617.930	+	617.930i	−1.39488	+	1.39488i	−0.813970	+	0.580906i	$0.802698\pi$
$444$		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	$0.0519333\pi$
$457$			148.461i			0.324861i	−0.986720	+	0.162430i	$0.948067\pi$
$458$		0			0
$459$	287.071	−	287.071i	0.625426	−	0.625426i
$460$		0			0
$461$	540.235	−	540.235i	1.17188	−	1.17188i	0.190114	−	0.981762i	$-0.439114\pi$
$461$	540.235	−	540.235i	1.17188	−	1.17188i	0.981762	−	0.190114i	$-0.0608857\pi$
$462$		0			0
$463$		−	177.274i		−	0.382880i	−0.981504	−	0.191440i	$-0.938684\pi$
$463$		−	177.274i		−	0.382880i	0.981504	−	0.191440i	$-0.0613158\pi$
$464$		0			0
$465$	240.908			0.518082
$466$		0			0
$467$	380.452	+	380.452i	0.814672	+	0.814672i	0.985330	−	0.170658i	$-0.0545894\pi$
$467$	380.452	+	380.452i	0.814672	+	0.814672i	−0.170658	+	0.985330i	$0.554589\pi$
$468$		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	$-0.746558\pi$
$479$		−	684.694i		−	1.42942i	0.699419	−	0.714712i	$-0.253442\pi$
$480$		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	−0.931711	−	0.363200i	$-0.881684\pi$
$491$	−279.139	+	279.139i	−0.568511	+	0.568511i	0.363200	+	0.931711i	$0.381684\pi$
$492$		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	0.779390	−	0.626539i	$-0.215529\pi$
$499$	76.2725	+	76.2725i	0.152851	+	0.152851i	−0.626539	+	0.779390i	$0.715529\pi$
$500$		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	−0.835862	−	0.548940i	$-0.815032\pi$
$509$	−146.043	+	146.043i	−0.286922	+	0.286922i	0.548940	+	0.835862i	$0.315032\pi$
$510$		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	$-0.782178\pi$
$521$		−	658.686i		−	1.26427i	0.774857	−	0.632136i	$-0.217822\pi$
$522$		0			0
$523$	388.573	−	388.573i	0.742970	−	0.742970i	−0.230179	−	0.973148i	$-0.573931\pi$
$523$	388.573	−	388.573i	0.742970	−	0.742970i	0.973148	+	0.230179i	$0.0739310\pi$
$524$		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	−0.545512	+	0.838103i	$0.683665\pi$
$541$	−748.536	+	748.536i	−1.38362	+	1.38362i	−0.838103	+	0.545512i	$0.816335\pi$
$542$		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	−0.998853	−	0.0478789i	$-0.984754\pi$
$547$	−572.562	−	572.562i	−1.04673	−	1.04673i	−0.0478789	−	0.998853i	$-0.515246\pi$
$548$		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	−0.615489	−	0.788146i	$-0.711041\pi$
$557$	96.1701	−	96.1701i	0.172657	−	0.172657i	0.788146	+	0.615489i	$0.211041\pi$
$558$		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	0.966766	−	0.255664i	$-0.0822939\pi$
$563$	400.351	+	400.351i	0.711102	+	0.711102i	−0.255664	+	0.966766i	$0.582294\pi$
$564$		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	$-0.653331\pi$
$569$		−	1008.50i		−	1.77241i	0.463289	−	0.886207i	$-0.346669\pi$
$570$		0			0
$571$	246.717	−	246.717i	0.432079	−	0.432079i	−0.457256	−	0.889335i	$-0.651168\pi$
$571$	246.717	−	246.717i	0.432079	−	0.432079i	0.889335	+	0.457256i	$0.151168\pi$
$572$		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	−0.338325	−	0.941029i	$-0.609860\pi$
$587$	353.788	−	353.788i	0.602705	−	0.602705i	0.941029	+	0.338325i	$0.109860\pi$
$588$		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	$-0.910535\pi$
$601$		−	333.408i		−	0.554755i	0.960761	−	0.277377i	$-0.0894652\pi$
$602$		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	$0.111651\pi$
$607$			417.147i			0.687227i	−0.939111	+	0.343614i	$0.888349\pi$
$608$		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	0.769878	−	0.638191i	$-0.220317\pi$
$613$	80.7246	+	80.7246i	0.131688	+	0.131688i	−0.638191	+	0.769878i	$0.720317\pi$
$614$		0			0
$615$	211.608			0.344079
$616$		0			0
$617$			635.686i			1.03029i	0.857104	+	0.515143i	$0.172261\pi$
$617$			635.686i			1.03029i	−0.857104	+	0.515143i	$0.827739\pi$
$618$		0			0
$619$	252.958	−	252.958i	0.408656	−	0.408656i	−0.472614	−	0.881270i	$-0.656689\pi$
$619$	252.958	−	252.958i	0.408656	−	0.408656i	0.881270	+	0.472614i	$0.156689\pi$
$620$		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	0.998981	−	0.0451239i	$-0.0143683\pi$
$643$	613.330	+	613.330i	0.953858	+	0.953858i	−0.0451239	+	0.998981i	$0.514368\pi$
$644$		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	−0.903782	−	0.427992i	$-0.859221\pi$
$653$	−310.691	+	310.691i	−0.475790	+	0.475790i	0.427992	+	0.903782i	$0.359221\pi$
$654$		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	0.623049	−	0.782183i	$-0.285894\pi$
$659$	−104.870	−	104.870i	−0.159135	−	0.159135i	−0.782183	+	0.623049i	$0.785894\pi$
$660$		0			0
$661$	−288.246	−	288.246i	−0.436075	−	0.436075i	0.454614	−	0.890689i	$-0.349777\pi$
$661$	−288.246	−	288.246i	−0.436075	−	0.436075i	−0.890689	+	0.454614i	$0.849777\pi$
$662$		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	0.109598	−	0.993976i	$-0.465044\pi$
$677$	−598.724	−	598.724i	−0.884378	−	0.884378i	−0.993976	+	0.109598i	$0.965044\pi$
$678$		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	−0.737198	−	0.675676i	$-0.763852\pi$
$683$	−42.0197	+	42.0197i	−0.0615222	+	0.0615222i	0.675676	+	0.737198i	$0.263852\pi$
$684$		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	0.0307538	−	0.999527i	$-0.490209\pi$
$691$	−669.422	−	669.422i	−0.968773	−	0.968773i	−0.999527	+	0.0307538i	$0.990209\pi$
$692$		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	−0.402841	−	0.915270i	$-0.631977\pi$
$701$	359.212	−	359.212i	0.512428	−	0.512428i	0.915270	+	0.402841i	$0.131977\pi$
$702$		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	0.734760	−	0.678327i	$-0.237295\pi$
$709$	40.0114	+	40.0114i	0.0564335	+	0.0564335i	−0.678327	+	0.734760i	$0.737295\pi$
$710$		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	$0.299890\pi$
$719$			1163.07i			1.61763i	−0.588065	+	0.808814i	$0.700110\pi$
$720$		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	−0.795062	−	0.606528i	$-0.792562\pi$
$733$	−138.195	+	138.195i	−0.188533	+	0.188533i	0.606528	+	0.795062i	$0.292562\pi$
$734$		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	0.232437	−	0.972612i	$-0.425330\pi$
$739$	−546.989	−	546.989i	−0.740175	−	0.740175i	−0.972612	+	0.232437i	$0.925330\pi$
$740$		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	$0.0606845\pi$
$751$			284.619i			0.378987i	−0.981882	+	0.189493i	$0.939315\pi$
$752$		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	0.985652	−	0.168789i	$-0.0539856\pi$
$757$	618.365	+	618.365i	0.816863	+	0.816863i	−0.168789	+	0.985652i	$0.553986\pi$
$758$		0			0
$759$	717.210			0.944941
$760$		0			0
$761$			741.506i			0.974384i	0.873295	+	0.487192i	$0.161979\pi$
$761$			741.506i			0.974384i	−0.873295	+	0.487192i	$0.838021\pi$
$762$		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	0.723978	−	0.689823i	$-0.242312\pi$
$773$	26.4020	+	26.4020i	0.0341552	+	0.0341552i	−0.689823	+	0.723978i	$0.742312\pi$
$774$		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	0.751306	−	0.659954i	$-0.229424\pi$
$787$	71.8942	+	71.8942i	0.0913522	+	0.0913522i	−0.659954	+	0.751306i	$0.729424\pi$
$788$		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	−0.394047	−	0.919090i	$-0.628925\pi$
$797$	418.459	−	418.459i	0.525043	−	0.525043i	0.919090	+	0.394047i	$0.128925\pi$
$798$		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	$-0.919693\pi$
$809$		−	403.893i		−	0.499250i	0.968343	−	0.249625i	$-0.0803074\pi$
$810$		0			0
$811$	−535.387	+	535.387i	−0.660157	+	0.660157i	−0.955417	−	0.295260i	$-0.904594\pi$
$811$	−535.387	+	535.387i	−0.660157	+	0.660157i	0.295260	+	0.955417i	$0.404594\pi$
$812$		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	0.769561	−	0.638573i	$-0.220475\pi$
$821$	107.542	+	107.542i	0.130989	+	0.130989i	−0.638573	+	0.769561i	$0.720475\pi$
$822$		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	−0.333496	−	0.942752i	$-0.608228\pi$
$827$	503.855	−	503.855i	0.609256	−	0.609256i	0.942752	+	0.333496i	$0.108228\pi$
$828$		0			0
$829$	201.982	−	201.982i	0.243645	−	0.243645i	−0.574711	−	0.818356i	$-0.694886\pi$
$829$	201.982	−	201.982i	0.243645	−	0.243645i	0.818356	+	0.574711i	$0.194886\pi$
$830$		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	0.997962	+	0.0638118i	$0.0203257\pi$
$853$	905.693	+	905.693i	1.06177	+	1.06177i	0.0638118	+	0.997962i	$0.479674\pi$
$854$		0			0
$855$	177.862			0.208026
$856$		0			0
$857$		−	353.050i		−	0.411960i	−0.978556	−	0.205980i	$-0.933962\pi$
$857$		−	353.050i		−	0.411960i	0.978556	−	0.205980i	$-0.0660382\pi$
$858$		0			0
$859$	189.473	−	189.473i	0.220574	−	0.220574i	−0.588166	−	0.808740i	$-0.700150\pi$
$859$	189.473	−	189.473i	0.220574	−	0.220574i	0.808740	+	0.588166i	$0.200150\pi$
$860$		0			0
$861$	−35.0586	+	35.0586i	−0.0407184	+	0.0407184i
$862$		0			0
$863$		−	1295.69i		−	1.50138i	−0.660655	−	0.750690i	$-0.729721\pi$
$863$		−	1295.69i		−	1.50138i	0.660655	−	0.750690i	$-0.270279\pi$
$864$		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	−0.0476178	+	0.998866i	$0.515163\pi$
$877$	−917.766	+	917.766i	−1.04648	+	1.04648i	−0.998866	+	0.0476178i	$0.984837\pi$
$878$		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	0.120508	−	0.992712i	$-0.461548\pi$
$883$	−770.156	−	770.156i	−0.872204	−	0.872204i	−0.992712	+	0.120508i	$0.961548\pi$
$884$		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	−0.356768	+	0.934193i	$0.616122\pi$
$907$	−1170.90	+	1170.90i	−1.29096	+	1.29096i	−0.934193	+	0.356768i	$0.883878\pi$
$908$		0			0
$909$	−298.176	+	298.176i	−0.328026	+	0.328026i
$910$		0			0
$911$			87.3440i			0.0958770i	0.998850	+	0.0479385i	$0.0152652\pi$
$911$			87.3440i			0.0958770i	−0.998850	+	0.0479385i	$0.984735\pi$
$912$		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	$0.204955\pi$
$937$			1124.98i			1.20062i	−0.799769	+	0.600308i	$0.795045\pi$
$938$		0			0
$939$	177.053	−	177.053i	0.188555	−	0.188555i
$940$		0			0
$941$	606.490	−	606.490i	0.644516	−	0.644516i	−0.307146	−	0.951662i	$-0.599374\pi$
$941$	606.490	−	606.490i	0.644516	−	0.644516i	0.951662	+	0.307146i	$0.0993741\pi$
$942$		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	0.503620	−	0.863925i	$-0.332001\pi$
$947$	−341.210	−	341.210i	−0.360306	−	0.360306i	−0.863925	+	0.503620i	$0.832001\pi$
$948$		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	$0.0485286\pi$
$953$			289.459i			0.303735i	−0.988401	+	0.151867i	$0.951471\pi$
$954$		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	−0.811042	−	0.584988i	$-0.801099\pi$
$971$	−219.499	+	219.499i	−0.226055	+	0.226055i	0.584988	+	0.811042i	$0.301099\pi$
$972$		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	$-0.839672\pi$
$991$		−	956.623i		−	0.965310i	0.875810	−	0.482655i	$-0.160328\pi$
$992$		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	0.116413	−	0.993201i	$-0.462861\pi$
$997$	−874.158	−	874.158i	−0.876788	−	0.876788i	−0.993201	+	0.116413i	$0.962861\pi$
$998$		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.271.4		32
4.3	odd	2		80.3.r.a.11.9	✓	32
8.3	odd	2		640.3.r.a.31.4		32
8.5	even	2		640.3.r.b.31.13		32
16.3	odd	4	inner	320.3.r.a.111.4		32
16.5	even	4		640.3.r.a.351.4		32
16.11	odd	4		640.3.r.b.351.13		32
16.13	even	4		80.3.r.a.51.9	yes	32
20.3	even	4		400.3.k.g.299.16		32
20.7	even	4		400.3.k.h.299.1		32
20.19	odd	2		400.3.r.f.251.8		32
80.13	odd	4		400.3.k.h.99.1		32
80.29	even	4		400.3.r.f.51.8		32
80.77	odd	4		400.3.k.g.99.16		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.3.r.a.11.9	✓	32	4.3	odd	2
80.3.r.a.51.9	yes	32	16.13	even	4
320.3.r.a.111.4		32	16.3	odd	4	inner
320.3.r.a.271.4		32	1.1	even	1	trivial
400.3.k.g.99.16		32	80.77	odd	4
400.3.k.g.299.16		32	20.3	even	4
400.3.k.h.99.1		32	80.13	odd	4
400.3.k.h.299.1		32	20.7	even	4
400.3.r.f.51.8		32	80.29	even	4
400.3.r.f.251.8		32	20.19	odd	2
640.3.r.a.31.4		32	8.3	odd	2
640.3.r.a.351.4		32	16.5	even	4
640.3.r.b.31.13		32	8.5	even	2
640.3.r.b.351.13		32	16.11	odd	4

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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