LMFDB - Embedded newform 320.2.l.a.241.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [320,2,Mod(81,320)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("320.81"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(320, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 3, 0])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$2.55521286468$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 4 x^{14} + 7 x^{12} - 8 x^{11} - 28 x^{10} + 28 x^{9} + 17 x^{8} + 56 x^{7} + \cdots + 256 $ x^16 - 4x^15 + 4x^14 + 7x^12 - 8x^11 - 28x^10 + 28x^9 + 17x^8 + 56x^7 - 112x^6 - 64x^5 + 112x^4 + 256x^2 - 512*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			241.1
Root			$1.21331 - 0.726558i$ of defining polynomial
Character	$\chi$	$=$	320.241
Dual form			320.2.l.a.81.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.82762 + 1.82762i) q^{3} +(-0.707107 - 0.707107i) q^{5} -4.50961i q^{7} -3.68037i q^{9} +(1.64080 + 1.64080i) q^{11} +(1.51857 - 1.51857i) q^{13} +2.58464 q^{15} +1.45616 q^{17} +(2.67964 - 2.67964i) q^{19} +(8.24183 + 8.24183i) q^{21} -2.37423i q^{23} +1.00000i q^{25} +(1.24345 + 1.24345i) q^{27} +(0.924966 - 0.924966i) q^{29} +7.20435 q^{31} -5.99752 q^{33} +(-3.18877 + 3.18877i) q^{35} +(-5.21123 - 5.21123i) q^{37} +5.55074i q^{39} -6.41166i q^{41} +(-7.65800 - 7.65800i) q^{43} +(-2.60241 + 2.60241i) q^{45} +2.51027 q^{47} -13.3366 q^{49} +(-2.66130 + 2.66130i) q^{51} +(1.50312 + 1.50312i) q^{53} -2.32045i q^{55} +9.79472i q^{57} +(5.31807 + 5.31807i) q^{59} +(-1.02169 + 1.02169i) q^{61} -16.5970 q^{63} -2.14759 q^{65} +(-5.22745 + 5.22745i) q^{67} +(4.33918 + 4.33918i) q^{69} +1.92097i q^{71} -1.39412i q^{73} +(-1.82762 - 1.82762i) q^{75} +(7.39938 - 7.39938i) q^{77} -5.06317 q^{79} +6.49599 q^{81} +(2.44974 - 2.44974i) q^{83} +(-1.02966 - 1.02966i) q^{85} +3.38097i q^{87} +9.36007i q^{89} +(-6.84817 - 6.84817i) q^{91} +(-13.1668 + 13.1668i) q^{93} -3.78959 q^{95} +18.6313 q^{97} +(6.03876 - 6.03876i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{11} + 8 q^{15} + 8 q^{19} - 24 q^{27} - 16 q^{29} - 16 q^{37} - 8 q^{43} + 40 q^{47} - 16 q^{49} + 32 q^{51} + 16 q^{53} + 8 q^{59} + 16 q^{61} - 40 q^{63} - 40 q^{67} + 16 q^{69} + 16 q^{77}+ \cdots + 8 q^{99}+O(q^{100}) $ 16 * q + 8 * q^11 + 8 * q^15 + 8 * q^19 - 24 * q^27 - 16 * q^29 - 16 * q^37 - 8 * q^43 + 40 * q^47 - 16 * q^49 + 32 * q^51 + 16 * q^53 + 8 * q^59 + 16 * q^61 - 40 * q^63 - 40 * q^67 + 16 * q^69 + 16 * q^77 - 16 * q^79 - 16 * q^81 - 40 * q^83 - 16 * q^85 - 32 * q^91 - 48 * q^93 - 32 * q^95 + 8 * q^99

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
$3$	−1.82762	+	1.82762i	−1.05518	+	1.05518i	−0.0567890	+	0.998386i	$0.518086\pi$
$3$	−1.82762	+	1.82762i	−1.05518	+	1.05518i	−0.998386	+	0.0567890i	$0.981914\pi$
$4$		0			0
$5$	−0.707107	−	0.707107i	−0.316228	−	0.316228i
$5$	−0.707107	−	0.707107i	−0.316228	−	0.316228i
$6$		0			0
$7$		−	4.50961i		−	1.70447i	−0.523158	−	0.852236i	$-0.675246\pi$
$7$		−	4.50961i		−	1.70447i	0.523158	−	0.852236i	$-0.324754\pi$
$8$		0			0
$9$		−	3.68037i		−	1.22679i
$10$		0			0
$11$	1.64080	+	1.64080i	0.494721	+	0.494721i	0.909790	−	0.415069i	$-0.136243\pi$
$11$	1.64080	+	1.64080i	0.494721	+	0.494721i	−0.415069	+	0.909790i	$0.636243\pi$
$12$		0			0
$13$	1.51857	−	1.51857i	0.421176	−	0.421176i	−0.464432	−	0.885609i	$-0.653742\pi$
$13$	1.51857	−	1.51857i	0.421176	−	0.421176i	0.885609	+	0.464432i	$0.153742\pi$
$14$		0			0
$15$	2.58464			0.667351
$16$		0			0
$17$	1.45616			0.353170			0.176585	−	0.984285i	$-0.443495\pi$
$17$	1.45616			0.353170			0.176585	+	0.984285i	$0.443495\pi$
$18$		0			0
$19$	2.67964	−	2.67964i	0.614752	−	0.614752i	−0.329428	−	0.944181i	$-0.606856\pi$
$19$	2.67964	−	2.67964i	0.614752	−	0.614752i	0.944181	+	0.329428i	$0.106856\pi$
$20$		0			0
$21$	8.24183	+	8.24183i	1.79852	+	1.79852i
$22$		0			0
$23$		−	2.37423i		−	0.495061i	−0.968880	−	0.247530i	$-0.920381\pi$
$23$		−	2.37423i		−	0.495061i	0.968880	−	0.247530i	$-0.0796190\pi$
$24$		0			0
$25$			1.00000i			0.200000i
$26$		0			0
$27$	1.24345	+	1.24345i	0.239303	+	0.239303i
$28$		0			0
$29$	0.924966	−	0.924966i	0.171762	−	0.171762i	−0.615991	−	0.787753i	$-0.711244\pi$
$29$	0.924966	−	0.924966i	0.171762	−	0.171762i	0.787753	+	0.615991i	$0.211244\pi$
$30$		0			0
$31$	7.20435			1.29394			0.646970	−	0.762515i	$-0.276036\pi$
$31$	7.20435			1.29394			0.646970	+	0.762515i	$0.276036\pi$
$32$		0			0
$33$	−5.99752			−1.04403
$34$		0			0
$35$	−3.18877	+	3.18877i	−0.539001	+	0.539001i
$36$		0			0
$37$	−5.21123	−	5.21123i	−0.856720	−	0.856720i	0.134230	−	0.990950i	$-0.457144\pi$
$37$	−5.21123	−	5.21123i	−0.856720	−	0.856720i	−0.990950	+	0.134230i	$0.957144\pi$
$38$		0			0
$39$			5.55074i			0.888830i
$40$		0			0
$41$		−	6.41166i		−	1.00133i	−0.865640	−	0.500667i	$-0.833088\pi$
$41$		−	6.41166i		−	1.00133i	0.865640	−	0.500667i	$-0.166912\pi$
$42$		0			0
$43$	−7.65800	−	7.65800i	−1.16783	−	1.16783i	−0.982716	−	0.185118i	$-0.940733\pi$
$43$	−7.65800	−	7.65800i	−1.16783	−	1.16783i	−0.185118	−	0.982716i	$-0.559267\pi$
$44$		0			0
$45$	−2.60241	+	2.60241i	−0.387945	+	0.387945i
$46$		0			0
$47$	2.51027			0.366161			0.183081	−	0.983098i	$-0.441393\pi$
$47$	2.51027			0.366161			0.183081	+	0.983098i	$0.441393\pi$
$48$		0			0
$49$	−13.3366			−1.90522
$50$		0			0
$51$	−2.66130	+	2.66130i	−0.372657	+	0.372657i
$52$		0			0
$53$	1.50312	+	1.50312i	0.206470	+	0.206470i	0.802765	−	0.596295i	$-0.203361\pi$
$53$	1.50312	+	1.50312i	0.206470	+	0.206470i	−0.596295	+	0.802765i	$0.703361\pi$
$54$		0			0
$55$		−	2.32045i		−	0.312889i
$56$		0			0
$57$			9.79472i			1.29734i
$58$		0			0
$59$	5.31807	+	5.31807i	0.692353	+	0.692353i	0.962749	−	0.270396i	$-0.0871546\pi$
$59$	5.31807	+	5.31807i	0.692353	+	0.692353i	−0.270396	+	0.962749i	$0.587155\pi$
$60$		0			0
$61$	−1.02169	+	1.02169i	−0.130815	+	0.130815i	−0.769483	−	0.638668i	$-0.779486\pi$
$61$	−1.02169	+	1.02169i	−0.130815	+	0.130815i	0.638668	+	0.769483i	$0.279486\pi$
$62$		0			0
$63$	−16.5970			−2.09103
$64$		0			0
$65$	−2.14759			−0.266375
$66$		0			0
$67$	−5.22745	+	5.22745i	−0.638635	+	0.638635i	−0.950219	−	0.311584i	$-0.899141\pi$
$67$	−5.22745	+	5.22745i	−0.638635	+	0.638635i	0.311584	+	0.950219i	$0.399141\pi$
$68$		0			0
$69$	4.33918	+	4.33918i	0.522376	+	0.522376i
$70$		0			0
$71$			1.92097i			0.227978i	0.993482	+	0.113989i	$0.0363628\pi$
$71$			1.92097i			0.227978i	−0.993482	+	0.113989i	$0.963637\pi$
$72$		0			0
$73$		−	1.39412i		−	0.163169i	−0.996666	−	0.0815847i	$-0.974002\pi$
$73$		−	1.39412i		−	0.163169i	0.996666	−	0.0815847i	$-0.0259981\pi$
$74$		0			0
$75$	−1.82762	−	1.82762i	−0.211035	−	0.211035i
$76$		0			0
$77$	7.39938	−	7.39938i	0.843237	−	0.843237i
$78$		0			0
$79$	−5.06317			−0.569651			−0.284825	−	0.958579i	$-0.591936\pi$
$79$	−5.06317			−0.569651			−0.284825	+	0.958579i	$0.591936\pi$
$80$		0			0
$81$	6.49599			0.721777
$82$		0			0
$83$	2.44974	−	2.44974i	0.268894	−	0.268894i	−0.559761	−	0.828654i	$-0.689107\pi$
$83$	2.44974	−	2.44974i	0.268894	−	0.268894i	0.828654	+	0.559761i	$0.189107\pi$
$84$		0			0
$85$	−1.02966	−	1.02966i	−0.111682	−	0.111682i
$86$		0			0
$87$			3.38097i			0.362478i
$88$		0			0
$89$			9.36007i			0.992165i	0.868275	+	0.496083i	$0.165229\pi$
$89$			9.36007i			0.992165i	−0.868275	+	0.496083i	$0.834771\pi$
$90$		0			0
$91$	−6.84817	−	6.84817i	−0.717883	−	0.717883i
$92$		0			0
$93$	−13.1668	+	13.1668i	−1.36533	+	1.36533i
$94$		0			0
$95$	−3.78959			−0.388803
$96$		0			0
$97$	18.6313			1.89172			0.945859	−	0.324579i	$-0.105223\pi$
$97$	18.6313			1.89172			0.945859	+	0.324579i	$0.105223\pi$
$98$		0			0
$99$	6.03876	−	6.03876i	0.606918	−	0.606918i
$100$		0			0
$101$	−4.84108	−	4.84108i	−0.481705	−	0.481705i	0.423971	−	0.905676i	$-0.360636\pi$
$101$	−4.84108	−	4.84108i	−0.481705	−	0.481705i	−0.905676	+	0.423971i	$0.860636\pi$
$102$		0			0
$103$			9.12540i			0.899153i	0.893242	+	0.449576i	$0.148425\pi$
$103$			9.12540i			0.899153i	−0.893242	+	0.449576i	$0.851575\pi$
$104$		0			0
$105$		−	11.6557i		−	1.13748i
$106$		0			0
$107$	10.1505	+	10.1505i	0.981290	+	0.981290i	0.999828	−	0.0185385i	$-0.00590132\pi$
$107$	10.1505	+	10.1505i	0.981290	+	0.981290i	−0.0185385	+	0.999828i	$0.505901\pi$
$108$		0			0
$109$	1.35489	−	1.35489i	0.129775	−	0.129775i	−0.639236	−	0.769011i	$-0.720749\pi$
$109$	1.35489	−	1.35489i	0.129775	−	0.129775i	0.769011	+	0.639236i	$0.220749\pi$
$110$		0			0
$111$	19.0483			1.80798
$112$		0			0
$113$	−2.56039			−0.240861			−0.120431	−	0.992722i	$-0.538428\pi$
$113$	−2.56039			−0.240861			−0.120431	+	0.992722i	$0.538428\pi$
$114$		0			0
$115$	−1.67883	+	1.67883i	−0.156552	+	0.156552i
$116$		0			0
$117$	−5.58891	−	5.58891i	−0.516695	−	0.516695i
$118$		0			0
$119$		−	6.56670i		−	0.601969i
$120$		0			0
$121$		−	5.61553i		−	0.510503i
$122$		0			0
$123$	11.7181	+	11.7181i	1.05658	+	1.05658i
$124$		0			0
$125$	0.707107	−	0.707107i	0.0632456	−	0.0632456i
$126$		0			0
$127$	−13.7354			−1.21882			−0.609409	−	0.792856i	$-0.708593\pi$
$127$	−13.7354			−1.21882			−0.609409	+	0.792856i	$0.708593\pi$
$128$		0			0
$129$	27.9918			2.46454
$130$		0			0
$131$	−5.20726	+	5.20726i	−0.454960	+	0.454960i	−0.896997	−	0.442037i	$-0.854256\pi$
$131$	−5.20726	+	5.20726i	−0.454960	+	0.454960i	0.442037	+	0.896997i	$0.354256\pi$
$132$		0			0
$133$	−12.0841	−	12.0841i	−1.04783	−	1.04783i
$134$		0			0
$135$		−	1.75851i		−	0.151348i
$136$		0			0
$137$			22.7563i			1.94420i	0.234559	+	0.972102i	$0.424635\pi$
$137$			22.7563i			1.94420i	−0.234559	+	0.972102i	$0.575365\pi$
$138$		0			0
$139$	−6.28085	−	6.28085i	−0.532734	−	0.532734i	0.388651	−	0.921385i	$-0.372941\pi$
$139$	−6.28085	−	6.28085i	−0.532734	−	0.532734i	−0.921385	+	0.388651i	$0.872941\pi$
$140$		0			0
$141$	−4.58782	+	4.58782i	−0.386364	+	0.386364i
$142$		0			0
$143$	4.98336			0.416729
$144$		0			0
$145$	−1.30810			−0.108632
$146$		0			0
$147$	24.3741	−	24.3741i	2.01034	−	2.01034i
$148$		0			0
$149$	−12.9574	−	12.9574i	−1.06151	−	1.06151i	−0.997980	−	0.0635329i	$-0.979763\pi$
$149$	−12.9574	−	12.9574i	−1.06151	−	1.06151i	−0.0635329	−	0.997980i	$-0.520237\pi$
$150$		0			0
$151$		−	14.3417i		−	1.16711i	−0.812073	−	0.583555i	$-0.801661\pi$
$151$		−	14.3417i		−	1.16711i	0.812073	−	0.583555i	$-0.198339\pi$
$152$		0			0
$153$		−	5.35920i		−	0.433266i
$154$		0			0
$155$	−5.09425	−	5.09425i	−0.409180	−	0.409180i
$156$		0			0
$157$	−2.10564	+	2.10564i	−0.168049	+	0.168049i	−0.786121	−	0.618073i	$-0.787914\pi$
$157$	−2.10564	+	2.10564i	−0.168049	+	0.168049i	0.618073	+	0.786121i	$0.287914\pi$
$158$		0			0
$159$	−5.49426			−0.435723
$160$		0			0
$161$	−10.7068			−0.843817
$162$		0			0
$163$	5.34004	−	5.34004i	0.418265	−	0.418265i	−0.466341	−	0.884605i	$-0.654428\pi$
$163$	5.34004	−	5.34004i	0.418265	−	0.418265i	0.884605	+	0.466341i	$0.154428\pi$
$164$		0			0
$165$	4.24089	+	4.24089i	0.330153	+	0.330153i
$166$		0			0
$167$			16.0686i			1.24343i	0.783245	+	0.621714i	$0.213563\pi$
$167$			16.0686i			1.24343i	−0.783245	+	0.621714i	$0.786437\pi$
$168$		0			0
$169$			8.38787i			0.645221i
$170$		0			0
$171$	−9.86207	−	9.86207i	−0.754171	−	0.754171i
$172$		0			0
$173$	17.1133	−	17.1133i	1.30110	−	1.30110i	0.373453	−	0.927649i	$-0.378174\pi$
$173$	17.1133	−	17.1133i	1.30110	−	1.30110i	0.927649	−	0.373453i	$-0.121826\pi$
$174$		0			0
$175$	4.50961			0.340894
$176$		0			0
$177$	−19.4388			−1.46111
$178$		0			0
$179$	−1.04482	+	1.04482i	−0.0780933	+	0.0780933i	−0.745075	−	0.666981i	$-0.767586\pi$
$179$	−1.04482	+	1.04482i	−0.0780933	+	0.0780933i	0.666981	+	0.745075i	$0.267586\pi$
$180$		0			0
$181$	11.9886	+	11.9886i	0.891104	+	0.891104i	0.994627	−	0.103523i	$-0.0330115\pi$
$181$	11.9886	+	11.9886i	0.891104	+	0.891104i	−0.103523	+	0.994627i	$0.533012\pi$
$182$		0			0
$183$		−	3.73453i		−	0.276065i
$184$		0			0
$185$			7.36979i			0.541838i
$186$		0			0
$187$	2.38927	+	2.38927i	0.174721	+	0.174721i
$188$		0			0
$189$	5.60748	−	5.60748i	0.407884	−	0.407884i
$190$		0			0
$191$	−0.0667471			−0.00482965			−0.00241483	−	0.999997i	$-0.500769\pi$
$191$	−0.0667471			−0.00482965			−0.00241483	+	0.999997i	$0.500769\pi$
$192$		0			0
$193$	−1.09895			−0.0791039			−0.0395520	−	0.999218i	$-0.512593\pi$
$193$	−1.09895			−0.0791039			−0.0395520	+	0.999218i	$0.512593\pi$
$194$		0			0
$195$	3.92497	−	3.92497i	0.281073	−	0.281073i
$196$		0			0
$197$	11.9289	+	11.9289i	0.849899	+	0.849899i	0.990120	−	0.140222i	$-0.0447815\pi$
$197$	11.9289	+	11.9289i	0.849899	+	0.849899i	−0.140222	+	0.990120i	$0.544782\pi$
$198$		0			0
$199$			11.0397i			0.782584i	0.920267	+	0.391292i	$0.127972\pi$
$199$			11.0397i			0.782584i	−0.920267	+	0.391292i	$0.872028\pi$
$200$		0			0
$201$		−	19.1076i		−	1.34774i
$202$		0			0
$203$	−4.17123	−	4.17123i	−0.292763	−	0.292763i
$204$		0			0
$205$	−4.53373	+	4.53373i	−0.316649	+	0.316649i
$206$		0			0
$207$	−8.73803			−0.607335
$208$		0			0
$209$	8.79353			0.608261
$210$		0			0
$211$	8.59737	−	8.59737i	0.591868	−	0.591868i	−0.346268	−	0.938136i	$-0.612551\pi$
$211$	8.59737	−	8.59737i	0.591868	−	0.591868i	0.938136	+	0.346268i	$0.112551\pi$
$212$		0			0
$213$	−3.51080	−	3.51080i	−0.240556	−	0.240556i
$214$		0			0
$215$			10.8301i			0.738603i
$216$		0			0
$217$		−	32.4888i		−	2.20548i
$218$		0			0
$219$	2.54792	+	2.54792i	0.172172	+	0.172172i
$220$		0			0
$221$	2.21128	−	2.21128i	0.148747	−	0.148747i
$222$		0			0
$223$	21.4238			1.43465			0.717323	−	0.696741i	$-0.245367\pi$
$223$	21.4238			1.43465			0.717323	+	0.696741i	$0.245367\pi$
$224$		0			0
$225$	3.68037			0.245358
$226$		0			0
$227$	8.06331	−	8.06331i	0.535181	−	0.535181i	−0.386929	−	0.922110i	$-0.626464\pi$
$227$	8.06331	−	8.06331i	0.535181	−	0.535181i	0.922110	+	0.386929i	$0.126464\pi$
$228$		0			0
$229$	4.63169	+	4.63169i	0.306071	+	0.306071i	0.843383	−	0.537313i	$-0.180560\pi$
$229$	4.63169	+	4.63169i	0.306071	+	0.306071i	−0.537313	+	0.843383i	$0.680560\pi$
$230$		0			0
$231$			27.0465i			1.77953i
$232$		0			0
$233$			26.0672i			1.70772i	0.520502	+	0.853860i	$0.325745\pi$
$233$			26.0672i			1.70772i	−0.520502	+	0.853860i	$0.674255\pi$
$234$		0			0
$235$	−1.77503	−	1.77503i	−0.115790	−	0.115790i
$236$		0			0
$237$	9.25353	−	9.25353i	0.601081	−	0.601081i
$238$		0			0
$239$	−5.12209			−0.331320			−0.165660	−	0.986183i	$-0.552975\pi$
$239$	−5.12209			−0.331320			−0.165660	+	0.986183i	$0.552975\pi$
$240$		0			0
$241$	11.4987			0.740695			0.370347	−	0.928893i	$-0.379239\pi$
$241$	11.4987			0.740695			0.370347	+	0.928893i	$0.379239\pi$
$242$		0			0
$243$	−15.6025	+	15.6025i	−1.00090	+	1.00090i
$244$		0			0
$245$	9.43037	+	9.43037i	0.602484	+	0.602484i
$246$		0			0
$247$		−	8.13847i		−	0.517838i
$248$		0			0
$249$			8.95437i			0.567460i
$250$		0			0
$251$	19.8270	+	19.8270i	1.25147	+	1.25147i	0.955061	+	0.296408i	$0.0957889\pi$
$251$	19.8270	+	19.8270i	1.25147	+	1.25147i	0.296408	+	0.955061i	$0.404211\pi$
$252$		0			0
$253$	3.89564	−	3.89564i	0.244917	−	0.244917i
$254$		0			0
$255$	3.76365			0.235689
$256$		0			0
$257$	−24.2494			−1.51264			−0.756319	−	0.654203i	$-0.773004\pi$
$257$	−24.2494			−1.51264			−0.756319	+	0.654203i	$0.773004\pi$
$258$		0			0
$259$	−23.5006	+	23.5006i	−1.46026	+	1.46026i
$260$		0			0
$261$	−3.40422	−	3.40422i	−0.210716	−	0.210716i
$262$		0			0
$263$		−	22.5680i		−	1.39160i	−0.718234	−	0.695802i	$-0.755049\pi$
$263$		−	22.5680i		−	1.39160i	0.718234	−	0.695802i	$-0.244951\pi$
$264$		0			0
$265$		−	2.12574i		−	0.130583i
$266$		0			0
$267$	−17.1066	−	17.1066i	−1.04691	−	1.04691i
$268$		0			0
$269$	−5.10558	+	5.10558i	−0.311293	+	0.311293i	−0.845410	−	0.534117i	$-0.820644\pi$
$269$	−5.10558	+	5.10558i	−0.311293	+	0.311293i	0.534117	+	0.845410i	$0.320644\pi$
$270$		0			0
$271$	−6.67920			−0.405733			−0.202866	−	0.979206i	$-0.565026\pi$
$271$	−6.67920			−0.405733			−0.202866	+	0.979206i	$0.565026\pi$
$272$		0			0
$273$	25.0317			1.51498
$274$		0			0
$275$	−1.64080	+	1.64080i	−0.0989441	+	0.0989441i
$276$		0			0
$277$	−11.8524	−	11.8524i	−0.712141	−	0.712141i	0.254842	−	0.966983i	$-0.417977\pi$
$277$	−11.8524	−	11.8524i	−0.712141	−	0.712141i	−0.966983	+	0.254842i	$0.917977\pi$
$278$		0			0
$279$		−	26.5147i		−	1.58739i
$280$		0			0
$281$			0.477460i			0.0284829i	0.999899	+	0.0142414i	$0.00453334\pi$
$281$			0.477460i			0.0284829i	−0.999899	+	0.0142414i	$0.995467\pi$
$282$		0			0
$283$	0.482914	+	0.482914i	0.0287063	+	0.0287063i	0.721314	−	0.692608i	$-0.243538\pi$
$283$	0.482914	+	0.482914i	0.0287063	+	0.0287063i	−0.692608	+	0.721314i	$0.743538\pi$
$284$		0			0
$285$	6.92591	−	6.92591i	0.410256	−	0.410256i
$286$		0			0
$287$	−28.9141			−1.70674
$288$		0			0
$289$	−14.8796			−0.875271
$290$		0			0
$291$	−34.0508	+	34.0508i	−1.99609	+	1.99609i
$292$		0			0
$293$	7.46638	+	7.46638i	0.436190	+	0.436190i	0.890728	−	0.454537i	$-0.150195\pi$
$293$	7.46638	+	7.46638i	0.436190	+	0.436190i	−0.454537	+	0.890728i	$0.650195\pi$
$294$		0			0
$295$		−	7.52088i		−	0.437883i
$296$		0			0
$297$			4.08052i			0.236776i
$298$		0			0
$299$	−3.60544	−	3.60544i	−0.208508	−	0.208508i
$300$		0			0
$301$	−34.5346	+	34.5346i	−1.99054	+	1.99054i
$302$		0			0
$303$	17.6953			1.01657
$304$		0			0
$305$	1.44489			0.0827344
$306$		0			0
$307$	−2.39349	+	2.39349i	−0.136604	+	0.136604i	−0.772102	−	0.635498i	$-0.780795\pi$
$307$	−2.39349	+	2.39349i	−0.136604	+	0.136604i	0.635498	+	0.772102i	$0.280795\pi$
$308$		0			0
$309$	−16.6777	−	16.6777i	−0.948764	−	0.948764i
$310$		0			0
$311$		−	20.4404i		−	1.15907i	−0.814948	−	0.579534i	$-0.803235\pi$
$311$		−	20.4404i		−	1.15907i	0.814948	−	0.579534i	$-0.196765\pi$
$312$		0			0
$313$		−	2.46975i		−	0.139598i	−0.997561	−	0.0697992i	$-0.977764\pi$
$313$		−	2.46975i		−	0.139598i	0.997561	−	0.0697992i	$-0.0222359\pi$
$314$		0			0
$315$	11.7359	+	11.7359i	0.661241	+	0.661241i
$316$		0			0
$317$	−16.2241	+	16.2241i	−0.911234	+	0.911234i	−0.996369	−	0.0851350i	$-0.972868\pi$
$317$	−16.2241	+	16.2241i	−0.911234	+	0.911234i	0.0851350	+	0.996369i	$0.472868\pi$
$318$		0			0
$319$	3.03537			0.169948
$320$		0			0
$321$	−37.1026			−2.07086
$322$		0			0
$323$	3.90198	−	3.90198i	0.217112	−	0.217112i
$324$		0			0
$325$	1.51857	+	1.51857i	0.0842353	+	0.0842353i
$326$		0			0
$327$			4.95246i			0.273871i
$328$		0			0
$329$		−	11.3204i		−	0.624111i
$330$		0			0
$331$	−3.42340	−	3.42340i	−0.188167	−	0.188167i	0.606736	−	0.794903i	$-0.292479\pi$
$331$	−3.42340	−	3.42340i	−0.188167	−	0.188167i	−0.794903	+	0.606736i	$0.792479\pi$
$332$		0			0
$333$	−19.1792	+	19.1792i	−1.05102	+	1.05102i
$334$		0			0
$335$	7.39273			0.403908
$336$		0			0
$337$	−5.40017			−0.294166			−0.147083	−	0.989124i	$-0.546988\pi$
$337$	−5.40017			−0.294166			−0.147083	+	0.989124i	$0.546988\pi$
$338$		0			0
$339$	4.67941	−	4.67941i	0.254151	−	0.254151i
$340$		0			0
$341$	11.8209	+	11.8209i	0.640139	+	0.640139i
$342$		0			0
$343$			28.5754i			1.54292i
$344$		0			0
$345$		−	6.13653i		−	0.330379i
$346$		0			0
$347$	4.07531	+	4.07531i	0.218774	+	0.218774i	0.807982	−	0.589208i	$-0.200560\pi$
$347$	4.07531	+	4.07531i	0.218774	+	0.218774i	−0.589208	+	0.807982i	$0.700560\pi$
$348$		0			0
$349$	1.55681	−	1.55681i	0.0833339	−	0.0833339i	−0.664211	−	0.747545i	$-0.731232\pi$
$349$	1.55681	−	1.55681i	0.0833339	−	0.0833339i	0.747545	+	0.664211i	$0.231232\pi$
$350$		0			0
$351$	3.77655			0.201577
$352$		0			0
$353$	1.34919			0.0718103			0.0359052	−	0.999355i	$-0.488569\pi$
$353$	1.34919			0.0718103			0.0359052	+	0.999355i	$0.488569\pi$
$354$		0			0
$355$	1.35833	−	1.35833i	0.0720929	−	0.0720929i
$356$		0			0
$357$	12.0014	+	12.0014i	0.635182	+	0.635182i
$358$		0			0
$359$		−	23.2192i		−	1.22546i	−0.790291	−	0.612732i	$-0.790071\pi$
$359$		−	23.2192i		−	1.22546i	0.790291	−	0.612732i	$-0.209929\pi$
$360$		0			0
$361$			4.63903i			0.244159i
$362$		0			0
$363$	10.2630	+	10.2630i	0.538670	+	0.538670i
$364$		0			0
$365$	−0.985792	+	0.985792i	−0.0515987	+	0.0515987i
$366$		0			0
$367$	5.16452			0.269586			0.134793	−	0.990874i	$-0.456963\pi$
$367$	5.16452			0.269586			0.134793	+	0.990874i	$0.456963\pi$
$368$		0			0
$369$	−23.5973			−1.22843
$370$		0			0
$371$	6.77849	−	6.77849i	0.351922	−	0.351922i
$372$		0			0
$373$	18.5056	+	18.5056i	0.958185	+	0.958185i	0.999160	−	0.0409750i	$-0.0130464\pi$
$373$	18.5056	+	18.5056i	0.958185	+	0.958185i	−0.0409750	+	0.999160i	$0.513046\pi$
$374$		0			0
$375$			2.58464i			0.133470i
$376$		0			0
$377$		−	2.80926i		−	0.144684i
$378$		0			0
$379$	13.5254	+	13.5254i	0.694754	+	0.694754i	0.963274	−	0.268520i	$-0.0865346\pi$
$379$	13.5254	+	13.5254i	0.694754	+	0.694754i	−0.268520	+	0.963274i	$0.586535\pi$
$380$		0			0
$381$	25.1030	−	25.1030i	1.28607	−	1.28607i
$382$		0			0
$383$	−21.9051			−1.11930			−0.559650	−	0.828729i	$-0.689064\pi$
$383$	−21.9051			−1.11930			−0.559650	+	0.828729i	$0.689064\pi$
$384$		0			0
$385$	−10.4643			−0.533310
$386$		0			0
$387$	−28.1843	+	28.1843i	−1.43269	+	1.43269i
$388$		0			0
$389$	4.48844	+	4.48844i	0.227573	+	0.227573i	0.811678	−	0.584105i	$-0.198554\pi$
$389$	4.48844	+	4.48844i	0.227573	+	0.227573i	−0.584105	+	0.811678i	$0.698554\pi$
$390$		0			0
$391$		−	3.45725i		−	0.174841i
$392$		0			0
$393$		−	19.0337i		−	0.960126i
$394$		0			0
$395$	3.58020	+	3.58020i	0.180139	+	0.180139i
$396$		0			0
$397$	11.7892	−	11.7892i	0.591682	−	0.591682i	−0.346404	−	0.938086i	$-0.612597\pi$
$397$	11.7892	−	11.7892i	0.591682	−	0.591682i	0.938086	+	0.346404i	$0.112597\pi$
$398$		0			0
$399$	44.1703			2.21128
$400$		0			0
$401$	24.9259			1.24474			0.622371	−	0.782722i	$-0.286170\pi$
$401$	24.9259			1.24474			0.622371	+	0.782722i	$0.286170\pi$
$402$		0			0
$403$	10.9403	−	10.9403i	0.544977	−	0.544977i
$404$		0			0
$405$	−4.59336	−	4.59336i	−0.228246	−	0.228246i
$406$		0			0
$407$		−	17.1012i		−	0.847675i
$408$		0			0
$409$		−	21.5355i		−	1.06486i	−0.846474	−	0.532430i	$-0.821279\pi$
$409$		−	21.5355i		−	1.06486i	0.846474	−	0.532430i	$-0.178721\pi$
$410$		0			0
$411$	−41.5898	−	41.5898i	−2.05148	−	2.05148i
$412$		0			0
$413$	23.9824	−	23.9824i	1.18010	−	1.18010i
$414$		0			0
$415$	−3.46445			−0.170063
$416$		0			0
$417$	22.9580			1.12426
$418$		0			0
$419$	17.2979	−	17.2979i	0.845060	−	0.845060i	−0.144452	−	0.989512i	$-0.546142\pi$
$419$	17.2979	−	17.2979i	0.845060	−	0.845060i	0.989512	+	0.144452i	$0.0461419\pi$
$420$		0			0
$421$	−19.4330	−	19.4330i	−0.947105	−	0.947105i	0.0515648	−	0.998670i	$-0.483579\pi$
$421$	−19.4330	−	19.4330i	−0.947105	−	0.947105i	−0.998670	+	0.0515648i	$0.983579\pi$
$422$		0			0
$423$		−	9.23874i		−	0.449203i
$424$		0			0
$425$			1.45616i			0.0706341i
$426$		0			0
$427$	4.60744	+	4.60744i	0.222970	+	0.222970i
$428$		0			0
$429$	−9.10767	+	9.10767i	−0.439723	+	0.439723i
$430$		0			0
$431$	−28.3769			−1.36687			−0.683433	−	0.730013i	$-0.739514\pi$
$431$	−28.3769			−1.36687			−0.683433	+	0.730013i	$0.739514\pi$
$432$		0			0
$433$	9.04007			0.434438			0.217219	−	0.976123i	$-0.430301\pi$
$433$	9.04007			0.434438			0.217219	+	0.976123i	$0.430301\pi$
$434$		0			0
$435$	2.39071	−	2.39071i	0.114626	−	0.114626i
$436$		0			0
$437$	−6.36208	−	6.36208i	−0.304340	−	0.304340i
$438$		0			0
$439$			28.2949i			1.35044i	0.737615	+	0.675221i	$0.235952\pi$
$439$			28.2949i			1.35044i	−0.737615	+	0.675221i	$0.764048\pi$
$440$		0			0
$441$			49.0834i			2.33731i
$442$		0			0
$443$	13.1232	+	13.1232i	0.623504	+	0.623504i	0.946426	−	0.322922i	$-0.104665\pi$
$443$	13.1232	+	13.1232i	0.623504	+	0.623504i	−0.322922	+	0.946426i	$0.604665\pi$
$444$		0			0
$445$	6.61857	−	6.61857i	0.313750	−	0.313750i
$446$		0			0
$447$	47.3624			2.24016
$448$		0			0
$449$	−14.3902			−0.679116			−0.339558	−	0.940585i	$-0.610277\pi$
$449$	−14.3902			−0.679116			−0.339558	+	0.940585i	$0.610277\pi$
$450$		0			0
$451$	10.5203	−	10.5203i	0.495380	−	0.495380i
$452$		0			0
$453$	26.2111	+	26.2111i	1.23151	+	1.23151i
$454$		0			0
$455$			9.68477i			0.454029i
$456$		0			0
$457$			4.54538i			0.212624i	0.994333	+	0.106312i	$0.0339042\pi$
$457$			4.54538i			0.212624i	−0.994333	+	0.106312i	$0.966096\pi$
$458$		0			0
$459$	1.81066	+	1.81066i	0.0845146	+	0.0845146i
$460$		0			0
$461$	19.8046	−	19.8046i	0.922393	−	0.922393i	−0.0748050	−	0.997198i	$-0.523833\pi$
$461$	19.8046	−	19.8046i	0.922393	−	0.922393i	0.997198	+	0.0748050i	$0.0238334\pi$
$462$		0			0
$463$	14.5997			0.678506			0.339253	−	0.940695i	$-0.389826\pi$
$463$	14.5997			0.678506			0.339253	+	0.940695i	$0.389826\pi$
$464$		0			0
$465$	18.6207			0.863513
$466$		0			0
$467$	−19.8105	+	19.8105i	−0.916722	+	0.916722i	−0.996789	−	0.0800671i	$-0.974487\pi$
$467$	−19.8105	+	19.8105i	−0.916722	+	0.916722i	0.0800671	+	0.996789i	$0.474487\pi$
$468$		0			0
$469$	23.5738	+	23.5738i	1.08853	+	1.08853i
$470$		0			0
$471$		−	7.69661i		−	0.354641i
$472$		0			0
$473$		−	25.1306i		−	1.15550i
$474$		0			0
$475$	2.67964	+	2.67964i	0.122950	+	0.122950i
$476$		0			0
$477$	5.53204	−	5.53204i	0.253295	−	0.253295i
$478$		0			0
$479$	−21.0378			−0.961243			−0.480621	−	0.876928i	$-0.659589\pi$
$479$	−21.0378			−0.961243			−0.480621	+	0.876928i	$0.659589\pi$
$480$		0			0
$481$	−15.8273			−0.721661
$482$		0			0
$483$	19.5680	−	19.5680i	0.890375	−	0.890375i
$484$		0			0
$485$	−13.1743	−	13.1743i	−0.598214	−	0.598214i
$486$		0			0
$487$			10.2724i			0.465485i	0.972538	+	0.232743i	$0.0747699\pi$
$487$			10.2724i			0.465485i	−0.972538	+	0.232743i	$0.925230\pi$
$488$		0			0
$489$			19.5191i			0.882685i
$490$		0			0
$491$	5.95681	+	5.95681i	0.268827	+	0.268827i	0.828627	−	0.559801i	$-0.189122\pi$
$491$	5.95681	+	5.95681i	0.268827	+	0.268827i	−0.559801	+	0.828627i	$0.689122\pi$
$492$		0			0
$493$	1.34690	−	1.34690i	0.0606612	−	0.0606612i
$494$		0			0
$495$	−8.54009			−0.383849
$496$		0			0
$497$	8.66284			0.388581
$498$		0			0
$499$	2.81466	−	2.81466i	0.126002	−	0.126002i	−0.641294	−	0.767295i	$-0.721602\pi$
$499$	2.81466	−	2.81466i	0.126002	−	0.126002i	0.767295	+	0.641294i	$0.221602\pi$
$500$		0			0
$501$	−29.3673	−	29.3673i	−1.31203	−	1.31203i
$502$		0			0
$503$		−	5.49759i		−	0.245125i	−0.992461	−	0.122563i	$-0.960889\pi$
$503$		−	5.49759i		−	0.245125i	0.992461	−	0.122563i	$-0.0391113\pi$
$504$		0			0
$505$			6.84632i			0.304657i
$506$		0			0
$507$	−15.3298	−	15.3298i	−0.680821	−	0.680821i
$508$		0			0
$509$	−4.37578	+	4.37578i	−0.193953	+	0.193953i	−0.797402	−	0.603449i	$-0.793793\pi$
$509$	−4.37578	+	4.37578i	−0.193953	+	0.193953i	0.603449	+	0.797402i	$0.293793\pi$
$510$		0			0
$511$	−6.28693			−0.278118
$512$		0			0
$513$	6.66402			0.294224
$514$		0			0
$515$	6.45263	−	6.45263i	0.284337	−	0.284337i
$516$		0			0
$517$	4.11887	+	4.11887i	0.181148	+	0.181148i
$518$		0			0
$519$			62.5532i			2.74578i
$520$		0			0
$521$		−	33.8729i		−	1.48400i	−0.670401	−	0.741999i	$-0.733878\pi$
$521$		−	33.8729i		−	1.48400i	0.670401	−	0.741999i	$-0.266122\pi$
$522$		0			0
$523$	−27.8060	−	27.8060i	−1.21587	−	1.21587i	−0.969065	−	0.246804i	$-0.920620\pi$
$523$	−27.8060	−	27.8060i	−1.21587	−	1.21587i	−0.246804	−	0.969065i	$-0.579380\pi$
$524$		0			0
$525$	−8.24183	+	8.24183i	−0.359703	+	0.359703i
$526$		0			0
$527$	10.4907			0.456981
$528$		0			0
$529$	17.3630			0.754915
$530$		0			0
$531$	19.5724	−	19.5724i	0.849372	−	0.849372i
$532$		0			0
$533$	−9.73658	−	9.73658i	−0.421738	−	0.421738i
$534$		0			0
$535$		−	14.3550i		−	0.620622i
$536$		0			0
$537$		−	3.81905i		−	0.164804i
$538$		0			0
$539$	−21.8827	−	21.8827i	−0.942553	−	0.942553i
$540$		0			0
$541$	3.03066	−	3.03066i	0.130298	−	0.130298i	−0.638950	−	0.769248i	$-0.720631\pi$
$541$	3.03066	−	3.03066i	0.130298	−	0.130298i	0.769248	+	0.638950i	$0.220631\pi$
$542$		0			0
$543$	−43.8211			−1.88054
$544$		0			0
$545$	−1.91611			−0.0820771
$546$		0			0
$547$	18.4783	−	18.4783i	0.790074	−	0.790074i	−0.191432	−	0.981506i	$-0.561313\pi$
$547$	18.4783	−	18.4783i	0.790074	−	0.790074i	0.981506	+	0.191432i	$0.0613131\pi$
$548$		0			0
$549$	3.76021	+	3.76021i	0.160482	+	0.160482i
$550$		0			0
$551$		−	4.95716i		−	0.211182i
$552$		0			0
$553$			22.8329i			0.970953i
$554$		0			0
$555$	−13.4691	−	13.4691i	−0.571734	−	0.571734i
$556$		0			0
$557$	−30.2060	+	30.2060i	−1.27987	+	1.27987i	−0.339127	+	0.940741i	$0.610132\pi$
$557$	−30.2060	+	30.2060i	−1.27987	+	1.27987i	−0.940741	+	0.339127i	$0.889868\pi$
$558$		0			0
$559$	−23.2585			−0.983729
$560$		0			0
$561$	−8.73334			−0.368722
$562$		0			0
$563$	−2.86747	+	2.86747i	−0.120850	+	0.120850i	−0.764945	−	0.644095i	$-0.777234\pi$
$563$	−2.86747	+	2.86747i	−0.120850	+	0.120850i	0.644095	+	0.764945i	$0.277234\pi$
$564$		0			0
$565$	1.81047	+	1.81047i	0.0761670	+	0.0761670i
$566$		0			0
$567$		−	29.2944i		−	1.23025i
$568$		0			0
$569$		−	35.8628i		−	1.50345i	−0.659479	−	0.751723i	$-0.729223\pi$
$569$		−	35.8628i		−	1.50345i	0.659479	−	0.751723i	$-0.270777\pi$
$570$		0			0
$571$	17.6509	+	17.6509i	0.738667	+	0.738667i	0.972320	−	0.233653i	$-0.0750679\pi$
$571$	17.6509	+	17.6509i	0.738667	+	0.738667i	−0.233653	+	0.972320i	$0.575068\pi$
$572$		0			0
$573$	0.121988	−	0.121988i	0.00509613	−	0.00509613i
$574$		0			0
$575$	2.37423			0.0990122
$576$		0			0
$577$	36.1387			1.50448			0.752238	−	0.658892i	$-0.228975\pi$
$577$	36.1387			1.50448			0.752238	+	0.658892i	$0.228975\pi$
$578$		0			0
$579$	2.00845	−	2.00845i	0.0834685	−	0.0834685i
$580$		0			0
$581$	−11.0474	−	11.0474i	−0.458322	−	0.458322i
$582$		0			0
$583$			4.93265i			0.204290i
$584$		0			0
$585$			7.90391i			0.326786i
$586$		0			0
$587$	11.4005	+	11.4005i	0.470550	+	0.470550i	0.902093	−	0.431542i	$-0.142030\pi$
$587$	11.4005	+	11.4005i	0.470550	+	0.470550i	−0.431542	+	0.902093i	$0.642030\pi$
$588$		0			0
$589$	19.3051	−	19.3051i	0.795453	−	0.795453i
$590$		0			0
$591$	−43.6029			−1.79358
$592$		0			0
$593$	−35.0454			−1.43914			−0.719572	−	0.694418i	$-0.755662\pi$
$593$	−35.0454			−1.43914			−0.719572	+	0.694418i	$0.755662\pi$
$594$		0			0
$595$	−4.64336	+	4.64336i	−0.190359	+	0.190359i
$596$		0			0
$597$	−20.1764	−	20.1764i	−0.825764	−	0.825764i
$598$		0			0
$599$			18.2753i			0.746707i	0.927689	+	0.373354i	$0.121792\pi$
$599$			18.2753i			0.746707i	−0.927689	+	0.373354i	$0.878208\pi$
$600$		0			0
$601$			0.480142i			0.0195854i	0.999952	+	0.00979269i	$0.00311716\pi$
$601$			0.480142i			0.0195854i	−0.999952	+	0.00979269i	$0.996883\pi$
$602$		0			0
$603$	19.2389	+	19.2389i	0.783470	+	0.783470i
$604$		0			0
$605$	−3.97078	+	3.97078i	−0.161435	+	0.161435i
$606$		0			0
$607$	38.6107			1.56716			0.783581	−	0.621290i	$-0.213391\pi$
$607$	38.6107			1.56716			0.783581	+	0.621290i	$0.213391\pi$
$608$		0			0
$609$	15.2468			0.617833
$610$		0			0
$611$	3.81204	−	3.81204i	0.154218	−	0.154218i
$612$		0			0
$613$	−5.53592	−	5.53592i	−0.223594	−	0.223594i	0.586416	−	0.810010i	$-0.300538\pi$
$613$	−5.53592	−	5.53592i	−0.223594	−	0.223594i	−0.810010	+	0.586416i	$0.800538\pi$
$614$		0			0
$615$		−	16.5718i		−	0.668241i
$616$		0			0
$617$			31.8836i			1.28358i	0.766879	+	0.641792i	$0.221809\pi$
$617$			31.8836i			1.28358i	−0.766879	+	0.641792i	$0.778191\pi$
$618$		0			0
$619$	29.4054	+	29.4054i	1.18190	+	1.18190i	0.979251	+	0.202650i	$0.0649553\pi$
$619$	29.4054	+	29.4054i	1.18190	+	1.18190i	0.202650	+	0.979251i	$0.435045\pi$
$620$		0			0
$621$	2.95224	−	2.95224i	0.118469	−	0.118469i
$622$		0			0
$623$	42.2102			1.69112
$624$		0			0
$625$	−1.00000			−0.0400000
$626$		0			0
$627$	−16.0712	+	16.0712i	−0.641822	+	0.641822i
$628$		0			0
$629$	−7.58837	−	7.58837i	−0.302568	−	0.302568i
$630$		0			0
$631$			30.7381i			1.22367i	0.790987	+	0.611833i	$0.209568\pi$
$631$			30.7381i			1.22367i	−0.790987	+	0.611833i	$0.790432\pi$
$632$		0			0
$633$			31.4254i			1.24905i
$634$		0			0
$635$	9.71239	+	9.71239i	0.385424	+	0.385424i
$636$		0			0
$637$	−20.2525	+	20.2525i	−0.802435	+	0.802435i
$638$		0			0
$639$	7.06989			0.279681
$640$		0			0
$641$	13.6348			0.538540			0.269270	−	0.963065i	$-0.413218\pi$
$641$	13.6348			0.538540			0.269270	+	0.963065i	$0.413218\pi$
$642$		0			0
$643$	−14.9224	+	14.9224i	−0.588480	+	0.588480i	−0.937220	−	0.348740i	$-0.886610\pi$
$643$	−14.9224	+	14.9224i	−0.588480	+	0.588480i	0.348740	+	0.937220i	$0.386610\pi$
$644$		0			0
$645$	−19.7932	−	19.7932i	−0.779356	−	0.779356i
$646$		0			0
$647$			4.87972i			0.191841i	0.995389	+	0.0959207i	$0.0305795\pi$
$647$			4.87972i			0.191841i	−0.995389	+	0.0959207i	$0.969420\pi$
$648$		0			0
$649$			17.4518i			0.685043i
$650$		0			0
$651$	59.3771	+	59.3771i	2.32717	+	2.32717i
$652$		0			0
$653$	−10.2913	+	10.2913i	−0.402731	+	0.402731i	−0.879194	−	0.476463i	$-0.841919\pi$
$653$	−10.2913	+	10.2913i	−0.402731	+	0.402731i	0.476463	+	0.879194i	$0.341919\pi$
$654$		0			0
$655$	7.36417			0.287742
$656$		0			0
$657$	−5.13088			−0.200174
$658$		0			0
$659$	21.9025	−	21.9025i	0.853201	−	0.853201i	−0.137325	−	0.990526i	$-0.543851\pi$
$659$	21.9025	−	21.9025i	0.853201	−	0.853201i	0.990526	+	0.137325i	$0.0438505\pi$
$660$		0			0
$661$	5.40595	+	5.40595i	0.210267	+	0.210267i	0.804381	−	0.594114i	$-0.202497\pi$
$661$	5.40595	+	5.40595i	0.210267	+	0.210267i	−0.594114	+	0.804381i	$0.702497\pi$
$662$		0			0
$663$			8.08276i			0.313908i
$664$		0			0
$665$			17.0895i			0.662704i
$666$		0			0
$667$	−2.19608	−	2.19608i	−0.0850326	−	0.0850326i
$668$		0			0
$669$	−39.1546	+	39.1546i	−1.51380	+	1.51380i
$670$		0			0
$671$	−3.35280			−0.129433
$672$		0			0
$673$	35.3820			1.36388			0.681938	−	0.731410i	$-0.261138\pi$
$673$	35.3820			1.36388			0.681938	+	0.731410i	$0.261138\pi$
$674$		0			0
$675$	−1.24345	+	1.24345i	−0.0478605	+	0.0478605i
$676$		0			0
$677$	5.17061	+	5.17061i	0.198723	+	0.198723i	0.799452	−	0.600730i	$-0.205123\pi$
$677$	5.17061	+	5.17061i	0.198723	+	0.198723i	−0.600730	+	0.799452i	$0.705123\pi$
$678$		0			0
$679$		−	84.0196i		−	3.22438i
$680$		0			0
$681$			29.4733i			1.12942i
$682$		0			0
$683$	−26.5989	−	26.5989i	−1.01778	−	1.01778i	−0.999839	−	0.0179409i	$-0.994289\pi$
$683$	−26.5989	−	26.5989i	−1.01778	−	1.01778i	−0.0179409	−	0.999839i	$-0.505711\pi$
$684$		0			0
$685$	16.0912	−	16.0912i	0.614811	−	0.614811i
$686$		0			0
$687$	−16.9299			−0.645916
$688$		0			0
$689$	4.56520			0.173920
$690$		0			0
$691$	21.7989	−	21.7989i	0.829270	−	0.829270i	−0.158146	−	0.987416i	$-0.550552\pi$
$691$	21.7989	−	21.7989i	0.829270	−	0.829270i	0.987416	+	0.158146i	$0.0505516\pi$
$692$		0			0
$693$	−27.2324	−	27.2324i	−1.03447	−	1.03447i
$694$		0			0
$695$			8.88246i			0.336931i
$696$		0			0
$697$		−	9.33640i		−	0.353641i
$698$		0			0
$699$	−47.6409	−	47.6409i	−1.80194	−	1.80194i
$700$		0			0
$701$	−15.2175	+	15.2175i	−0.574756	+	0.574756i	−0.933454	−	0.358698i	$-0.883221\pi$
$701$	−15.2175	+	15.2175i	−0.574756	+	0.574756i	0.358698	+	0.933454i	$0.383221\pi$
$702$		0			0
$703$	−27.9285			−1.05334
$704$		0			0
$705$	6.48816			0.244358
$706$		0			0
$707$	−21.8313	+	21.8313i	−0.821052	+	0.821052i
$708$		0			0
$709$	4.87350	+	4.87350i	0.183028	+	0.183028i	0.792674	−	0.609646i	$-0.208688\pi$
$709$	4.87350	+	4.87350i	0.183028	+	0.183028i	−0.609646	+	0.792674i	$0.708688\pi$
$710$		0			0
$711$			18.6343i			0.698842i
$712$		0			0
$713$		−	17.1048i		−	0.640579i
$714$		0			0
$715$	−3.52377	−	3.52377i	−0.131781	−	0.131781i
$716$		0			0
$717$	9.36121	−	9.36121i	0.349601	−	0.349601i
$718$		0			0
$719$	−9.27351			−0.345843			−0.172922	−	0.984936i	$-0.555321\pi$
$719$	−9.27351			−0.345843			−0.172922	+	0.984936i	$0.555321\pi$
$720$		0			0
$721$	41.1520			1.53258
$722$		0			0
$723$	−21.0152	+	21.0152i	−0.781563	+	0.781563i
$724$		0			0
$725$	0.924966	+	0.924966i	0.0343524	+	0.0343524i
$726$		0			0
$727$			10.6056i			0.393341i	0.980470	+	0.196670i	$0.0630129\pi$
$727$			10.6056i			0.393341i	−0.980470	+	0.196670i	$0.936987\pi$
$728$		0			0
$729$		−	37.5430i		−	1.39048i
$730$		0			0
$731$	−11.1513	−	11.1513i	−0.412445	−	0.412445i
$732$		0			0
$733$	−29.6530	+	29.6530i	−1.09526	+	1.09526i	−0.100301	+	0.994957i	$0.531981\pi$
$733$	−29.6530	+	29.6530i	−1.09526	+	1.09526i	−0.994957	+	0.100301i	$0.968019\pi$
$734$		0			0
$735$	−34.4702			−1.27145
$736$		0			0
$737$	−17.1544			−0.631892
$738$		0			0
$739$	−30.8751	+	30.8751i	−1.13576	+	1.13576i	−0.146559	+	0.989202i	$0.546820\pi$
$739$	−30.8751	+	30.8751i	−1.13576	+	1.13576i	−0.989202	+	0.146559i	$0.953180\pi$
$740$		0			0
$741$	14.8740	+	14.8740i	0.546410	+	0.546410i
$742$		0			0
$743$			22.3956i			0.821617i	0.911722	+	0.410808i	$0.134753\pi$
$743$			22.3956i			0.821617i	−0.911722	+	0.410808i	$0.865247\pi$
$744$		0			0
$745$			18.3245i			0.671360i
$746$		0			0
$747$	−9.01594	−	9.01594i	−0.329876	−	0.329876i
$748$		0			0
$749$	45.7749	−	45.7749i	1.67258	−	1.67258i
$750$		0			0
$751$	−20.6448			−0.753341			−0.376670	−	0.926347i	$-0.622931\pi$
$751$	−20.6448			−0.753341			−0.376670	+	0.926347i	$0.622931\pi$
$752$		0			0
$753$	−72.4724			−2.64104
$754$		0			0
$755$	−10.1411	+	10.1411i	−0.369073	+	0.369073i
$756$		0			0
$757$	24.1323	+	24.1323i	0.877104	+	0.877104i	0.993234	−	0.116130i	$-0.0370490\pi$
$757$	24.1323	+	24.1323i	0.877104	+	0.877104i	−0.116130	+	0.993234i	$0.537049\pi$
$758$		0			0
$759$			14.2395i			0.516860i
$760$		0			0
$761$			50.1874i			1.81929i	0.415383	+	0.909647i	$0.363648\pi$
$761$			50.1874i			1.81929i	−0.415383	+	0.909647i	$0.636352\pi$
$762$		0			0
$763$	−6.11004	−	6.11004i	−0.221198	−	0.221198i
$764$		0			0
$765$	−3.78953	+	3.78953i	−0.137011	+	0.137011i
$766$		0			0
$767$	16.1517			0.583206
$768$		0			0
$769$	−28.6887			−1.03454			−0.517270	−	0.855822i	$-0.673052\pi$
$769$	−28.6887			−1.03454			−0.517270	+	0.855822i	$0.673052\pi$
$770$		0			0
$771$	44.3187	−	44.3187i	1.59610	−	1.59610i
$772$		0			0
$773$	−37.5957	−	37.5957i	−1.35222	−	1.35222i	−0.883171	−	0.469052i	$-0.844596\pi$
$773$	−37.5957	−	37.5957i	−1.35222	−	1.35222i	−0.469052	−	0.883171i	$-0.655404\pi$
$774$		0			0
$775$			7.20435i			0.258788i
$776$		0			0
$777$		−	85.9001i		−	3.08165i
$778$		0			0
$779$	−17.1810	−	17.1810i	−0.615572	−	0.615572i
$780$		0			0
$781$	−3.15194	+	3.15194i	−0.112785	+	0.112785i
$782$		0			0
$783$	2.30030			0.0822061
$784$		0			0
$785$	2.97783			0.106283
$786$		0			0
$787$	3.13285	−	3.13285i	0.111674	−	0.111674i	−0.649062	−	0.760736i	$-0.724838\pi$
$787$	3.13285	−	3.13285i	0.111674	−	0.111674i	0.760736	+	0.649062i	$0.224838\pi$
$788$		0			0
$789$	41.2457	+	41.2457i	1.46839	+	1.46839i
$790$		0			0
$791$			11.5463i			0.410541i
$792$		0			0
$793$			3.10304i			0.110192i
$794$		0			0
$795$	3.88503	+	3.88503i	0.137788	+	0.137788i
$796$		0			0
$797$	0.0562195	−	0.0562195i	0.00199140	−	0.00199140i	−0.706110	−	0.708102i	$-0.749552\pi$
$797$	0.0562195	−	0.0562195i	0.00199140	−	0.00199140i	0.708102	+	0.706110i	$0.249552\pi$
$798$		0			0
$799$	3.65536			0.129317
$800$		0			0
$801$	34.4485			1.21718
$802$		0			0
$803$	2.28748	−	2.28748i	0.0807233	−	0.0807233i
$804$		0			0
$805$	7.57088	+	7.57088i	0.266838	+	0.266838i
$806$		0			0
$807$		−	18.6621i		−	0.656937i
$808$		0			0
$809$		−	3.59856i		−	0.126518i	−0.997997	−	0.0632592i	$-0.979851\pi$
$809$		−	3.59856i		−	0.126518i	0.997997	−	0.0632592i	$-0.0201495\pi$
$810$		0			0
$811$	7.36274	+	7.36274i	0.258541	+	0.258541i	0.824460	−	0.565920i	$-0.191479\pi$
$811$	7.36274	+	7.36274i	0.258541	+	0.258541i	−0.565920	+	0.824460i	$0.691479\pi$
$812$		0			0
$813$	12.2070	−	12.2070i	0.428119	−	0.428119i
$814$		0			0
$815$	−7.55196			−0.264534
$816$		0			0
$817$	−41.0414			−1.43586
$818$		0			0
$819$	−25.2038	+	25.2038i	−0.880691	+	0.880691i
$820$		0			0
$821$	14.7799	+	14.7799i	0.515824	+	0.515824i	0.916305	−	0.400481i	$-0.131157\pi$
$821$	14.7799	+	14.7799i	0.515824	+	0.515824i	−0.400481	+	0.916305i	$0.631157\pi$
$822$		0			0
$823$			52.7544i			1.83890i	0.393203	+	0.919452i	$0.371367\pi$
$823$			52.7544i			1.83890i	−0.393203	+	0.919452i	$0.628633\pi$
$824$		0			0
$825$		−	5.99752i		−	0.208807i
$826$		0			0
$827$	−16.8883	−	16.8883i	−0.587265	−	0.587265i	0.349625	−	0.936890i	$-0.386309\pi$
$827$	−16.8883	−	16.8883i	−0.587265	−	0.587265i	−0.936890	+	0.349625i	$0.886309\pi$
$828$		0			0
$829$	−8.55974	+	8.55974i	−0.297292	+	0.297292i	−0.839952	−	0.542660i	$-0.817417\pi$
$829$	−8.55974	+	8.55974i	−0.297292	+	0.297292i	0.542660	+	0.839952i	$0.317417\pi$
$830$		0			0
$831$	43.3232			1.50287
$832$		0			0
$833$	−19.4201			−0.672868
$834$		0			0
$835$	11.3622	−	11.3622i	0.393206	−	0.393206i
$836$		0			0
$837$	8.95827	+	8.95827i	0.309643	+	0.309643i
$838$		0			0
$839$			17.5407i			0.605572i	0.953059	+	0.302786i	$0.0979168\pi$
$839$			17.5407i			0.605572i	−0.953059	+	0.302786i	$0.902083\pi$
$840$		0			0
$841$			27.2889i			0.940996i
$842$		0			0
$843$	−0.872614	−	0.872614i	−0.0300544	−	0.0300544i
$844$		0			0
$845$	5.93112	−	5.93112i	0.204037	−	0.204037i
$846$		0			0
$847$	−25.3238			−0.870137
$848$		0			0
$849$	−1.76516			−0.0605803
$850$		0			0
$851$	−12.3726	+	12.3726i	−0.424129	+	0.424129i
$852$		0			0
$853$	−15.3577	−	15.3577i	−0.525839	−	0.525839i	0.393490	−	0.919329i	$-0.371268\pi$
$853$	−15.3577	−	15.3577i	−0.525839	−	0.525839i	−0.919329	+	0.393490i	$0.871268\pi$
$854$		0			0
$855$			13.9471i			0.476980i
$856$		0			0
$857$		−	17.9553i		−	0.613341i	−0.951816	−	0.306671i	$-0.900785\pi$
$857$		−	17.9553i		−	0.613341i	0.951816	−	0.306671i	$-0.0992150\pi$
$858$		0			0
$859$	33.3048	+	33.3048i	1.13634	+	1.13634i	0.989100	+	0.147245i	$0.0470405\pi$
$859$	33.3048	+	33.3048i	1.13634	+	1.13634i	0.147245	+	0.989100i	$0.452960\pi$
$860$		0			0
$861$	52.8439	−	52.8439i	1.80091	−	1.80091i
$862$		0			0
$863$	32.3557			1.10140			0.550701	−	0.834703i	$-0.314361\pi$
$863$	32.3557			1.10140			0.550701	+	0.834703i	$0.314361\pi$
$864$		0			0
$865$	−24.2019			−0.822889
$866$		0			0
$867$	27.1942	−	27.1942i	0.923564	−	0.923564i
$868$		0			0
$869$	−8.30766	−	8.30766i	−0.281818	−	0.281818i
$870$		0			0
$871$			15.8765i			0.537956i
$872$		0			0
$873$		−	68.5699i		−	2.32074i
$874$		0			0
$875$	−3.18877	−	3.18877i	−0.107800	−	0.107800i
$876$		0			0
$877$	26.2297	−	26.2297i	0.885714	−	0.885714i	−0.108394	−	0.994108i	$-0.534571\pi$
$877$	26.2297	−	26.2297i	0.885714	−	0.885714i	0.994108	+	0.108394i	$0.0345707\pi$
$878$		0			0
$879$	−27.2914			−0.920515
$880$		0			0
$881$	−47.3359			−1.59479			−0.797394	−	0.603459i	$-0.793789\pi$
$881$	−47.3359			−1.59479			−0.797394	+	0.603459i	$0.793789\pi$
$882$		0			0
$883$	−8.08371	+	8.08371i	−0.272039	+	0.272039i	−0.829920	−	0.557882i	$-0.811614\pi$
$883$	−8.08371	+	8.08371i	−0.272039	+	0.272039i	0.557882	+	0.829920i	$0.311614\pi$
$884$		0			0
$885$	13.7453	+	13.7453i	0.462043	+	0.462043i
$886$		0			0
$887$			12.9255i			0.433994i	0.976172	+	0.216997i	$0.0696263\pi$
$887$			12.9255i			0.433994i	−0.976172	+	0.216997i	$0.930374\pi$
$888$		0			0
$889$			61.9412i			2.07744i
$890$		0			0
$891$	10.6586	+	10.6586i	0.357078	+	0.357078i
$892$		0			0
$893$	6.72664	−	6.72664i	0.225098	−	0.225098i
$894$		0			0
$895$	1.47760			0.0493906
$896$		0			0
$897$	13.1787			0.440025
$898$		0			0
$899$	6.66378	−	6.66378i	0.222250	−	0.222250i
$900$		0			0
$901$	2.18878	+	2.18878i	0.0729190	+	0.0729190i
$902$		0			0
$903$		−	126.232i		−	4.20074i
$904$		0			0
$905$		−	16.9544i		−	0.563584i
$906$		0			0
$907$	−16.4991	−	16.4991i	−0.547844	−	0.547844i	0.377973	−	0.925817i	$-0.376621\pi$
$907$	−16.4991	−	16.4991i	−0.547844	−	0.547844i	−0.925817	+	0.377973i	$0.876621\pi$
$908$		0			0
$909$	−17.8169	+	17.8169i	−0.590951	+	0.590951i
$910$		0			0
$911$	26.6745			0.883765			0.441883	−	0.897073i	$-0.354311\pi$
$911$	26.6745			0.883765			0.441883	+	0.897073i	$0.354311\pi$
$912$		0			0
$913$	8.03908			0.266055
$914$		0			0
$915$	−2.64071	+	2.64071i	−0.0872993	+	0.0872993i
$916$		0			0
$917$	23.4827	+	23.4827i	0.775467	+	0.775467i
$918$		0			0
$919$		−	57.7425i		−	1.90475i	−0.304932	−	0.952374i	$-0.598634\pi$
$919$		−	57.7425i		−	1.90475i	0.304932	−	0.952374i	$-0.401366\pi$
$920$		0			0
$921$		−	8.74878i		−	0.288282i
$922$		0			0
$923$	2.91714	+	2.91714i	0.0960188	+	0.0960188i
$924$		0			0
$925$	5.21123	−	5.21123i	0.171344	−	0.171344i
$926$		0			0
$927$	33.5848			1.10307
$928$		0			0
$929$	42.5386			1.39565			0.697823	−	0.716270i	$-0.254152\pi$
$929$	42.5386			1.39565			0.697823	+	0.716270i	$0.254152\pi$
$930$		0			0
$931$	−35.7372	+	35.7372i	−1.17124	+	1.17124i
$932$		0			0
$933$	37.3572	+	37.3572i	1.22302	+	1.22302i
$934$		0			0
$935$		−	3.37894i		−	0.110503i
$936$		0			0
$937$		−	16.6795i		−	0.544894i	−0.962171	−	0.272447i	$-0.912167\pi$
$937$		−	16.6795i		−	0.544894i	0.962171	−	0.272447i	$-0.0878330\pi$
$938$		0			0
$939$	4.51376	+	4.51376i	0.147301	+	0.147301i
$940$		0			0
$941$	9.63152	−	9.63152i	0.313979	−	0.313979i	−0.532470	−	0.846449i	$-0.678736\pi$
$941$	9.63152	−	9.63152i	0.313979	−	0.313979i	0.846449	+	0.532470i	$0.178736\pi$
$942$		0			0
$943$	−15.2227			−0.495721
$944$		0			0
$945$	−7.93018			−0.257969
$946$		0			0
$947$	3.44034	−	3.44034i	0.111796	−	0.111796i	−0.648996	−	0.760792i	$-0.724811\pi$
$947$	3.44034	−	3.44034i	0.111796	−	0.111796i	0.760792	+	0.648996i	$0.224811\pi$
$948$		0			0
$949$	−2.11707	−	2.11707i	−0.0687231	−	0.0687231i
$950$		0			0
$951$		−	59.3028i		−	1.92302i
$952$		0			0
$953$			17.6965i			0.573247i	0.958043	+	0.286623i	$0.0925328\pi$
$953$			17.6965i			0.573247i	−0.958043	+	0.286623i	$0.907467\pi$
$954$		0			0
$955$	0.0471973	+	0.0471973i	0.00152727	+	0.00152727i
$956$		0			0
$957$	−5.54750	+	5.54750i	−0.179325	+	0.179325i
$958$		0			0
$959$	102.622			3.31384
$960$		0			0
$961$	20.9027			0.674281
$962$		0			0
$963$	37.3577	−	37.3577i	1.20384	−	1.20384i
$964$		0			0
$965$	0.777073	+	0.777073i	0.0250149	+	0.0250149i
$966$		0			0
$967$			15.0023i			0.482442i	0.970470	+	0.241221i	$0.0775479\pi$
$967$			15.0023i			0.482442i	−0.970470	+	0.241221i	$0.922452\pi$
$968$		0			0
$969$			14.2627i			0.458183i
$970$		0			0
$971$	14.3135	+	14.3135i	0.459340	+	0.459340i	0.898439	−	0.439098i	$-0.144702\pi$
$971$	14.3135	+	14.3135i	0.459340	+	0.459340i	−0.439098	+	0.898439i	$0.644702\pi$
$972$		0			0
$973$	−28.3241	+	28.3241i	−0.908030	+	0.908030i
$974$		0			0
$975$	−5.55074			−0.177766
$976$		0			0
$977$	48.1433			1.54024			0.770120	−	0.637900i	$-0.220196\pi$
$977$	48.1433			1.54024			0.770120	+	0.637900i	$0.220196\pi$
$978$		0			0
$979$	−15.3580	+	15.3580i	−0.490845	+	0.490845i
$980$		0			0
$981$	−4.98651	−	4.98651i	−0.159207	−	0.159207i
$982$		0			0
$983$		−	0.791292i		−	0.0252383i	−0.999920	−	0.0126191i	$-0.995983\pi$
$983$		−	0.791292i		−	0.0252383i	0.999920	−	0.0126191i	$-0.00401690\pi$
$984$		0			0
$985$		−	16.8700i		−	0.537523i
$986$		0			0
$987$	20.6893	+	20.6893i	0.658547	+	0.658547i
$988$		0			0
$989$	−18.1818	+	18.1818i	−0.578149	+	0.578149i
$990$		0			0
$991$	60.2424			1.91366			0.956832	−	0.290643i	$-0.0938690\pi$
$991$	60.2424			1.91366			0.956832	+	0.290643i	$0.0938690\pi$
$992$		0			0
$993$	12.5133			0.397099
$994$		0			0
$995$	7.80625	−	7.80625i	0.247475	−	0.247475i
$996$		0			0
$997$	1.15773	+	1.15773i	0.0366655	+	0.0366655i	0.725202	−	0.688536i	$-0.241746\pi$
$997$	1.15773	+	1.15773i	0.0366655	+	0.0366655i	−0.688536	+	0.725202i	$0.741746\pi$
$998$		0			0
$999$		−	12.9598i		−	0.410031i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	320.2.l.a.241.1		16
3.2	odd	2		2880.2.t.c.2161.5		16
4.3	odd	2		80.2.l.a.21.3	✓	16
5.2	odd	4		1600.2.q.h.49.8		16
5.3	odd	4		1600.2.q.g.49.1		16
5.4	even	2		1600.2.l.i.1201.8		16
8.3	odd	2		640.2.l.b.481.1		16
8.5	even	2		640.2.l.a.481.8		16
12.11	even	2		720.2.t.c.181.6		16
16.3	odd	4		80.2.l.a.61.3	yes	16
16.5	even	4		640.2.l.a.161.8		16
16.11	odd	4		640.2.l.b.161.1		16
16.13	even	4	inner	320.2.l.a.81.1		16
20.3	even	4		400.2.q.h.149.1		16
20.7	even	4		400.2.q.g.149.8		16
20.19	odd	2		400.2.l.h.101.6		16
32.3	odd	8		5120.2.a.v.1.7		8
32.13	even	8		5120.2.a.u.1.7		8
32.19	odd	8		5120.2.a.s.1.2		8
32.29	even	8		5120.2.a.t.1.2		8
48.29	odd	4		2880.2.t.c.721.8		16
48.35	even	4		720.2.t.c.541.6		16
80.3	even	4		400.2.q.g.349.8		16
80.13	odd	4		1600.2.q.h.849.8		16
80.19	odd	4		400.2.l.h.301.6		16
80.29	even	4		1600.2.l.i.401.8		16
80.67	even	4		400.2.q.h.349.1		16
80.77	odd	4		1600.2.q.g.849.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.l.a.21.3	✓	16	4.3	odd	2
80.2.l.a.61.3	yes	16	16.3	odd	4
320.2.l.a.81.1		16	16.13	even	4	inner
320.2.l.a.241.1		16	1.1	even	1	trivial
400.2.l.h.101.6		16	20.19	odd	2
400.2.l.h.301.6		16	80.19	odd	4
400.2.q.g.149.8		16	20.7	even	4
400.2.q.g.349.8		16	80.3	even	4
400.2.q.h.149.1		16	20.3	even	4
400.2.q.h.349.1		16	80.67	even	4
640.2.l.a.161.8		16	16.5	even	4
640.2.l.a.481.8		16	8.5	even	2
640.2.l.b.161.1		16	16.11	odd	4
640.2.l.b.481.1		16	8.3	odd	2
720.2.t.c.181.6		16	12.11	even	2
720.2.t.c.541.6		16	48.35	even	4
1600.2.l.i.401.8		16	80.29	even	4
1600.2.l.i.1201.8		16	5.4	even	2
1600.2.q.g.49.1		16	5.3	odd	4
1600.2.q.g.849.1		16	80.77	odd	4
1600.2.q.h.49.8		16	5.2	odd	4
1600.2.q.h.849.8		16	80.13	odd	4
2880.2.t.c.721.8		16	48.29	odd	4
2880.2.t.c.2161.5		16	3.2	odd	2
5120.2.a.s.1.2		8	32.19	odd	8
5120.2.a.t.1.2		8	32.29	even	8
5120.2.a.u.1.7		8	32.13	even	8
5120.2.a.v.1.7		8	32.3	odd	8

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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-1.82762 + 1.82762i) q^{3} +(-0.707107 - 0.707107i) q^{5} -4.50961i q^{7} -3.68037i q^{9} +(1.64080 + 1.64080i) q^{11} +(1.51857 - 1.51857i) q^{13} +2.58464 q^{15} +1.45616 q^{17} +(2.67964 - 2.67964i) q^{19} +(8.24183 + 8.24183i) q^{21} -2.37423i q^{23} +1.00000i q^{25} +(1.24345 + 1.24345i) q^{27} +(0.924966 - 0.924966i) q^{29} +7.20435 q^{31} -5.99752 q^{33} +(-3.18877 + 3.18877i) q^{35} +(-5.21123 - 5.21123i) q^{37} +5.55074i q^{39} -6.41166i q^{41} +(-7.65800 - 7.65800i) q^{43} +(-2.60241 + 2.60241i) q^{45} +2.51027 q^{47} -13.3366 q^{49} +(-2.66130 + 2.66130i) q^{51} +(1.50312 + 1.50312i) q^{53} -2.32045i q^{55} +9.79472i q^{57} +(5.31807 + 5.31807i) q^{59} +(-1.02169 + 1.02169i) q^{61} -16.5970 q^{63} -2.14759 q^{65} +(-5.22745 + 5.22745i) q^{67} +(4.33918 + 4.33918i) q^{69} +1.92097i q^{71} -1.39412i q^{73} +(-1.82762 - 1.82762i) q^{75} +(7.39938 - 7.39938i) q^{77} -5.06317 q^{79} +6.49599 q^{81} +(2.44974 - 2.44974i) q^{83} +(-1.02966 - 1.02966i) q^{85} +3.38097i q^{87} +9.36007i q^{89} +(-6.84817 - 6.84817i) q^{91} +(-13.1668 + 13.1668i) q^{93} -3.78959 q^{95} +18.6313 q^{97} +(6.03876 - 6.03876i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{11} + 8 q^{15} + 8 q^{19} - 24 q^{27} - 16 q^{29} - 16 q^{37} - 8 q^{43} + 40 q^{47} - 16 q^{49} + 32 q^{51} + 16 q^{53} + 8 q^{59} + 16 q^{61} - 40 q^{63} - 40 q^{67} + 16 q^{69} + 16 q^{77}+ \cdots + 8 q^{99}+O(q^{100}) \) 16 * q + 8 * q^11 + 8 * q^15 + 8 * q^19 - 24 * q^27 - 16 * q^29 - 16 * q^37 - 8 * q^43 + 40 * q^47 - 16 * q^49 + 32 * q^51 + 16 * q^53 + 8 * q^59 + 16 * q^61 - 40 * q^63 - 40 * q^67 + 16 * q^69 + 16 * q^77 - 16 * q^79 - 16 * q^81 - 40 * q^83 - 16 * q^85 - 32 * q^91 - 48 * q^93 - 32 * q^95 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more