LMFDB - Embedded newform 2880.2.t.c.2161.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2880,2,Mod(721,2880)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2880, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("2880.721");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2880 = 2^{6} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2880.t (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:	$22.9969157821$
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:	$\Z[a_1, \ldots, a_{11}]$
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			2161.5
Root			$1.21331 + 0.726558i$ of defining polynomial
Character	$\chi$	$=$	2880.2161
Dual form			2880.2.t.c.721.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{5} -4.50961i q^{7} +O(q^{10})$	$q+(0.707107 + 0.707107i) q^{5} -4.50961i q^{7} +(-1.64080 - 1.64080i) q^{11} +(1.51857 - 1.51857i) q^{13} -1.45616 q^{17} +(2.67964 - 2.67964i) q^{19} +2.37423i q^{23} +1.00000i q^{25} +(-0.924966 + 0.924966i) q^{29} +7.20435 q^{31} +(3.18877 - 3.18877i) q^{35} +(-5.21123 - 5.21123i) q^{37} +6.41166i q^{41} +(-7.65800 - 7.65800i) q^{43} -2.51027 q^{47} -13.3366 q^{49} +(-1.50312 - 1.50312i) q^{53} -2.32045i q^{55} +(-5.31807 - 5.31807i) q^{59} +(-1.02169 + 1.02169i) q^{61} +2.14759 q^{65} +(-5.22745 + 5.22745i) q^{67} -1.92097i q^{71} -1.39412i q^{73} +(-7.39938 + 7.39938i) q^{77} -5.06317 q^{79} +(-2.44974 + 2.44974i) q^{83} +(-1.02966 - 1.02966i) q^{85} -9.36007i q^{89} +(-6.84817 - 6.84817i) q^{91} +3.78959 q^{95} +18.6313 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q - 8 q^{11} + 8 q^{19} + 16 q^{29} - 16 q^{37} - 8 q^{43} - 40 q^{47} - 16 q^{49} - 16 q^{53} - 8 q^{59} + 16 q^{61} - 40 q^{67} - 16 q^{77} - 16 q^{79} + 40 q^{83} - 16 q^{85} - 32 q^{91} + 32 q^{95}+O(q^{100}) $ 16 * q - 8 * q^11 + 8 * q^19 + 16 * q^29 - 16 * q^37 - 8 * q^43 - 40 * q^47 - 16 * q^49 - 16 * q^53 - 8 * q^59 + 16 * q^61 - 40 * q^67 - 16 * q^77 - 16 * q^79 + 40 * q^83 - 16 * q^85 - 32 * q^91 + 32 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2880\mathbb{Z}\right)^\times$.

$n$	$577$	$641$	$901$	$2431$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		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
$9$		0			0
$10$		0			0
$11$	−1.64080	−	1.64080i	−0.494721	−	0.494721i	0.415069	−	0.909790i	$-0.363757\pi$
$11$	−1.64080	−	1.64080i	−0.494721	−	0.494721i	−0.909790	+	0.415069i	$0.863757\pi$
$12$		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
$15$		0			0
$16$		0			0
$17$	−1.45616			−0.353170			−0.176585	−	0.984285i	$-0.556505\pi$
$17$	−1.45616			−0.353170			−0.176585	+	0.984285i	$0.556505\pi$
$18$		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
$21$		0			0
$22$		0			0
$23$			2.37423i			0.495061i	0.968880	+	0.247530i	$0.0796190\pi$
$23$			2.37423i			0.495061i	−0.968880	+	0.247530i	$0.920381\pi$
$24$		0			0
$25$			1.00000i			0.200000i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−0.924966	+	0.924966i	−0.171762	+	0.171762i	−0.787753	−	0.615991i	$-0.788756\pi$
$29$	−0.924966	+	0.924966i	−0.171762	+	0.171762i	0.615991	+	0.787753i	$0.288756\pi$
$30$		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
$33$		0			0
$34$		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
$39$		0			0
$40$		0			0
$41$			6.41166i			1.00133i	0.865640	+	0.500667i	$0.166912\pi$
$41$			6.41166i			1.00133i	−0.865640	+	0.500667i	$0.833088\pi$
$42$		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
$45$		0			0
$46$		0			0
$47$	−2.51027			−0.366161			−0.183081	−	0.983098i	$-0.558607\pi$
$47$	−2.51027			−0.366161			−0.183081	+	0.983098i	$0.558607\pi$
$48$		0			0
$49$	−13.3366			−1.90522
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−1.50312	−	1.50312i	−0.206470	−	0.206470i	0.596295	−	0.802765i	$-0.296639\pi$
$53$	−1.50312	−	1.50312i	−0.206470	−	0.206470i	−0.802765	+	0.596295i	$0.796639\pi$
$54$		0			0
$55$		−	2.32045i		−	0.312889i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−5.31807	−	5.31807i	−0.692353	−	0.692353i	0.270396	−	0.962749i	$-0.412845\pi$
$59$	−5.31807	−	5.31807i	−0.692353	−	0.692353i	−0.962749	+	0.270396i	$0.912845\pi$
$60$		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
$63$		0			0
$64$		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
$69$		0			0
$70$		0			0
$71$		−	1.92097i		−	0.227978i	−0.993482	−	0.113989i	$-0.963637\pi$
$71$		−	1.92097i		−	0.227978i	0.993482	−	0.113989i	$-0.0363628\pi$
$72$		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
$75$		0			0
$76$		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
$81$		0			0
$82$		0			0
$83$	−2.44974	+	2.44974i	−0.268894	+	0.268894i	−0.828654	−	0.559761i	$-0.810893\pi$
$83$	−2.44974	+	2.44974i	−0.268894	+	0.268894i	0.559761	+	0.828654i	$0.310893\pi$
$84$		0			0
$85$	−1.02966	−	1.02966i	−0.111682	−	0.111682i
$86$		0			0
$87$		0			0
$88$		0			0
$89$		−	9.36007i		−	0.992165i	−0.868275	−	0.496083i	$-0.834771\pi$
$89$		−	9.36007i		−	0.992165i	0.868275	−	0.496083i	$-0.165229\pi$
$90$		0			0
$91$	−6.84817	−	6.84817i	−0.717883	−	0.717883i
$92$		0			0
$93$		0			0
$94$		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
$99$		0			0
$100$		0			0
$101$	4.84108	+	4.84108i	0.481705	+	0.481705i	0.905676	−	0.423971i	$-0.139364\pi$
$101$	4.84108	+	4.84108i	0.481705	+	0.481705i	−0.423971	+	0.905676i	$0.639364\pi$
$102$		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
$105$		0			0
$106$		0			0
$107$	−10.1505	−	10.1505i	−0.981290	−	0.981290i	0.0185385	−	0.999828i	$-0.494099\pi$
$107$	−10.1505	−	10.1505i	−0.981290	−	0.981290i	−0.999828	+	0.0185385i	$0.994099\pi$
$108$		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
$111$		0			0
$112$		0			0
$113$	2.56039			0.240861			0.120431	−	0.992722i	$-0.461572\pi$
$113$	2.56039			0.240861			0.120431	+	0.992722i	$0.461572\pi$
$114$		0			0
$115$	−1.67883	+	1.67883i	−0.156552	+	0.156552i
$116$		0			0
$117$		0			0
$118$		0			0
$119$			6.56670i			0.601969i
$120$		0			0
$121$		−	5.61553i		−	0.510503i
$122$		0			0
$123$		0			0
$124$		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
$129$		0			0
$130$		0			0
$131$	5.20726	−	5.20726i	0.454960	−	0.454960i	−0.442037	−	0.896997i	$-0.645744\pi$
$131$	5.20726	−	5.20726i	0.454960	−	0.454960i	0.896997	+	0.442037i	$0.145744\pi$
$132$		0			0
$133$	−12.0841	−	12.0841i	−1.04783	−	1.04783i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		−	22.7563i		−	1.94420i	−0.234559	−	0.972102i	$-0.575365\pi$
$137$		−	22.7563i		−	1.94420i	0.234559	−	0.972102i	$-0.424635\pi$
$138$		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
$141$		0			0
$142$		0			0
$143$	−4.98336			−0.416729
$144$		0			0
$145$	−1.30810			−0.108632
$146$		0			0
$147$		0			0
$148$		0			0
$149$	12.9574	+	12.9574i	1.06151	+	1.06151i	0.997980	+	0.0635329i	$0.0202368\pi$
$149$	12.9574	+	12.9574i	1.06151	+	1.06151i	0.0635329	+	0.997980i	$0.479763\pi$
$150$		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
$153$		0			0
$154$		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
$159$		0			0
$160$		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
$165$		0			0
$166$		0			0
$167$		−	16.0686i		−	1.24343i	−0.783245	−	0.621714i	$-0.786437\pi$
$167$		−	16.0686i		−	1.24343i	0.783245	−	0.621714i	$-0.213563\pi$
$168$		0			0
$169$			8.38787i			0.645221i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−17.1133	+	17.1133i	−1.30110	+	1.30110i	−0.373453	+	0.927649i	$0.621826\pi$
$173$	−17.1133	+	17.1133i	−1.30110	+	1.30110i	−0.927649	+	0.373453i	$0.878174\pi$
$174$		0			0
$175$	4.50961			0.340894
$176$		0			0
$177$		0			0
$178$		0			0
$179$	1.04482	−	1.04482i	0.0780933	−	0.0780933i	−0.666981	−	0.745075i	$-0.732414\pi$
$179$	1.04482	−	1.04482i	0.0780933	−	0.0780933i	0.745075	+	0.666981i	$0.232414\pi$
$180$		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
$183$		0			0
$184$		0			0
$185$		−	7.36979i		−	0.541838i
$186$		0			0
$187$	2.38927	+	2.38927i	0.174721	+	0.174721i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	0.0667471			0.00482965			0.00241483	−	0.999997i	$-0.499231\pi$
$191$	0.0667471			0.00482965			0.00241483	+	0.999997i	$0.499231\pi$
$192$		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
$195$		0			0
$196$		0			0
$197$	−11.9289	−	11.9289i	−0.849899	−	0.849899i	0.140222	−	0.990120i	$-0.455218\pi$
$197$	−11.9289	−	11.9289i	−0.849899	−	0.849899i	−0.990120	+	0.140222i	$0.955218\pi$
$198$		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
$201$		0			0
$202$		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
$207$		0			0
$208$		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
$213$		0			0
$214$		0			0
$215$		−	10.8301i		−	0.738603i
$216$		0			0
$217$		−	32.4888i		−	2.20548i
$218$		0			0
$219$		0			0
$220$		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
$225$		0			0
$226$		0			0
$227$	−8.06331	+	8.06331i	−0.535181	+	0.535181i	−0.922110	−	0.386929i	$-0.873536\pi$
$227$	−8.06331	+	8.06331i	−0.535181	+	0.535181i	0.386929	+	0.922110i	$0.373536\pi$
$228$		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
$231$		0			0
$232$		0			0
$233$		−	26.0672i		−	1.70772i	−0.520502	−	0.853860i	$-0.674255\pi$
$233$		−	26.0672i		−	1.70772i	0.520502	−	0.853860i	$-0.325745\pi$
$234$		0			0
$235$	−1.77503	−	1.77503i	−0.115790	−	0.115790i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	5.12209			0.331320			0.165660	−	0.986183i	$-0.447025\pi$
$239$	5.12209			0.331320			0.165660	+	0.986183i	$0.447025\pi$
$240$		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
$243$		0			0
$244$		0			0
$245$	−9.43037	−	9.43037i	−0.602484	−	0.602484i
$246$		0			0
$247$		−	8.13847i		−	0.517838i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−19.8270	−	19.8270i	−1.25147	−	1.25147i	−0.955061	−	0.296408i	$-0.904211\pi$
$251$	−19.8270	−	19.8270i	−1.25147	−	1.25147i	−0.296408	−	0.955061i	$-0.595789\pi$
$252$		0			0
$253$	3.89564	−	3.89564i	0.244917	−	0.244917i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	24.2494			1.51264			0.756319	−	0.654203i	$-0.226996\pi$
$257$	24.2494			1.51264			0.756319	+	0.654203i	$0.226996\pi$
$258$		0			0
$259$	−23.5006	+	23.5006i	−1.46026	+	1.46026i
$260$		0			0
$261$		0			0
$262$		0			0
$263$			22.5680i			1.39160i	0.718234	+	0.695802i	$0.244951\pi$
$263$			22.5680i			1.39160i	−0.718234	+	0.695802i	$0.755049\pi$
$264$		0			0
$265$		−	2.12574i		−	0.130583i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	5.10558	−	5.10558i	0.311293	−	0.311293i	−0.534117	−	0.845410i	$-0.679356\pi$
$269$	5.10558	−	5.10558i	0.311293	−	0.311293i	0.845410	+	0.534117i	$0.179356\pi$
$270$		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
$273$		0			0
$274$		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
$279$		0			0
$280$		0			0
$281$		−	0.477460i		−	0.0284829i	−0.999899	−	0.0142414i	$-0.995467\pi$
$281$		−	0.477460i		−	0.0284829i	0.999899	−	0.0142414i	$-0.00453334\pi$
$282$		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
$285$		0			0
$286$		0			0
$287$	28.9141			1.70674
$288$		0			0
$289$	−14.8796			−0.875271
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−7.46638	−	7.46638i	−0.436190	−	0.436190i	0.454537	−	0.890728i	$-0.349805\pi$
$293$	−7.46638	−	7.46638i	−0.436190	−	0.436190i	−0.890728	+	0.454537i	$0.849805\pi$
$294$		0			0
$295$		−	7.52088i		−	0.437883i
$296$		0			0
$297$		0			0
$298$		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
$303$		0			0
$304$		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
$309$		0			0
$310$		0			0
$311$			20.4404i			1.15907i	0.814948	+	0.579534i	$0.196765\pi$
$311$			20.4404i			1.15907i	−0.814948	+	0.579534i	$0.803235\pi$
$312$		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
$315$		0			0
$316$		0			0
$317$	16.2241	−	16.2241i	0.911234	−	0.911234i	−0.0851350	−	0.996369i	$-0.527132\pi$
$317$	16.2241	−	16.2241i	0.911234	−	0.911234i	0.996369	+	0.0851350i	$0.0271322\pi$
$318$		0			0
$319$	3.03537			0.169948
$320$		0			0
$321$		0			0
$322$		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
$327$		0			0
$328$		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
$333$		0			0
$334$		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
$339$		0			0
$340$		0			0
$341$	−11.8209	−	11.8209i	−0.640139	−	0.640139i
$342$		0			0
$343$			28.5754i			1.54292i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−4.07531	−	4.07531i	−0.218774	−	0.218774i	0.589208	−	0.807982i	$-0.299440\pi$
$347$	−4.07531	−	4.07531i	−0.218774	−	0.218774i	−0.807982	+	0.589208i	$0.799440\pi$
$348$		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
$351$		0			0
$352$		0			0
$353$	−1.34919			−0.0718103			−0.0359052	−	0.999355i	$-0.511431\pi$
$353$	−1.34919			−0.0718103			−0.0359052	+	0.999355i	$0.511431\pi$
$354$		0			0
$355$	1.35833	−	1.35833i	0.0720929	−	0.0720929i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			23.2192i			1.22546i	0.790291	+	0.612732i	$0.209929\pi$
$359$			23.2192i			1.22546i	−0.790291	+	0.612732i	$0.790071\pi$
$360$		0			0
$361$			4.63903i			0.244159i
$362$		0			0
$363$		0			0
$364$		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
$369$		0			0
$370$		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
$375$		0			0
$376$		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
$381$		0			0
$382$		0			0
$383$	21.9051			1.11930			0.559650	−	0.828729i	$-0.310936\pi$
$383$	21.9051			1.11930			0.559650	+	0.828729i	$0.310936\pi$
$384$		0			0
$385$	−10.4643			−0.533310
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−4.48844	−	4.48844i	−0.227573	−	0.227573i	0.584105	−	0.811678i	$-0.301446\pi$
$389$	−4.48844	−	4.48844i	−0.227573	−	0.227573i	−0.811678	+	0.584105i	$0.801446\pi$
$390$		0			0
$391$		−	3.45725i		−	0.174841i
$392$		0			0
$393$		0			0
$394$		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
$399$		0			0
$400$		0			0
$401$	−24.9259			−1.24474			−0.622371	−	0.782722i	$-0.713830\pi$
$401$	−24.9259			−1.24474			−0.622371	+	0.782722i	$0.713830\pi$
$402$		0			0
$403$	10.9403	−	10.9403i	0.544977	−	0.544977i
$404$		0			0
$405$		0			0
$406$		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
$411$		0			0
$412$		0			0
$413$	−23.9824	+	23.9824i	−1.18010	+	1.18010i
$414$		0			0
$415$	−3.46445			−0.170063
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−17.2979	+	17.2979i	−0.845060	+	0.845060i	−0.989512	−	0.144452i	$-0.953858\pi$
$419$	−17.2979	+	17.2979i	−0.845060	+	0.845060i	0.144452	+	0.989512i	$0.453858\pi$
$420$		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
$423$		0			0
$424$		0			0
$425$		−	1.45616i		−	0.0706341i
$426$		0			0
$427$	4.60744	+	4.60744i	0.222970	+	0.222970i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	28.3769			1.36687			0.683433	−	0.730013i	$-0.260486\pi$
$431$	28.3769			1.36687			0.683433	+	0.730013i	$0.260486\pi$
$432$		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
$435$		0			0
$436$		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
$441$		0			0
$442$		0			0
$443$	−13.1232	−	13.1232i	−0.623504	−	0.623504i	0.322922	−	0.946426i	$-0.395335\pi$
$443$	−13.1232	−	13.1232i	−0.623504	−	0.623504i	−0.946426	+	0.322922i	$0.895335\pi$
$444$		0			0
$445$	6.61857	−	6.61857i	0.313750	−	0.313750i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	14.3902			0.679116			0.339558	−	0.940585i	$-0.389723\pi$
$449$	14.3902			0.679116			0.339558	+	0.940585i	$0.389723\pi$
$450$		0			0
$451$	10.5203	−	10.5203i	0.495380	−	0.495380i
$452$		0			0
$453$		0			0
$454$		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
$459$		0			0
$460$		0			0
$461$	−19.8046	+	19.8046i	−0.922393	+	0.922393i	−0.997198	−	0.0748050i	$-0.976167\pi$
$461$	−19.8046	+	19.8046i	−0.922393	+	0.922393i	0.0748050	+	0.997198i	$0.476167\pi$
$462$		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
$465$		0			0
$466$		0			0
$467$	19.8105	−	19.8105i	0.916722	−	0.916722i	−0.0800671	−	0.996789i	$-0.525513\pi$
$467$	19.8105	−	19.8105i	0.916722	−	0.916722i	0.996789	+	0.0800671i	$0.0255135\pi$
$468$		0			0
$469$	23.5738	+	23.5738i	1.08853	+	1.08853i
$470$		0			0
$471$		0			0
$472$		0			0
$473$			25.1306i			1.15550i
$474$		0			0
$475$	2.67964	+	2.67964i	0.122950	+	0.122950i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	21.0378			0.961243			0.480621	−	0.876928i	$-0.340411\pi$
$479$	21.0378			0.961243			0.480621	+	0.876928i	$0.340411\pi$
$480$		0			0
$481$	−15.8273			−0.721661
$482$		0			0
$483$		0			0
$484$		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
$489$		0			0
$490$		0			0
$491$	−5.95681	−	5.95681i	−0.268827	−	0.268827i	0.559801	−	0.828627i	$-0.310878\pi$
$491$	−5.95681	−	5.95681i	−0.268827	−	0.268827i	−0.828627	+	0.559801i	$0.810878\pi$
$492$		0			0
$493$	1.34690	−	1.34690i	0.0606612	−	0.0606612i
$494$		0			0
$495$		0			0
$496$		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
$501$		0			0
$502$		0			0
$503$			5.49759i			0.245125i	0.992461	+	0.122563i	$0.0391113\pi$
$503$			5.49759i			0.245125i	−0.992461	+	0.122563i	$0.960889\pi$
$504$		0			0
$505$			6.84632i			0.304657i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	4.37578	−	4.37578i	0.193953	−	0.193953i	−0.603449	−	0.797402i	$-0.706207\pi$
$509$	4.37578	−	4.37578i	0.193953	−	0.193953i	0.797402	+	0.603449i	$0.206207\pi$
$510$		0			0
$511$	−6.28693			−0.278118
$512$		0			0
$513$		0			0
$514$		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
$519$		0			0
$520$		0			0
$521$			33.8729i			1.48400i	0.670401	+	0.741999i	$0.266122\pi$
$521$			33.8729i			1.48400i	−0.670401	+	0.741999i	$0.733878\pi$
$522$		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
$525$		0			0
$526$		0			0
$527$	−10.4907			−0.456981
$528$		0			0
$529$	17.3630			0.754915
$530$		0			0
$531$		0			0
$532$		0			0
$533$	9.73658	+	9.73658i	0.421738	+	0.421738i
$534$		0			0
$535$		−	14.3550i		−	0.620622i
$536$		0			0
$537$		0			0
$538$		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
$543$		0			0
$544$		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
$549$		0			0
$550$		0			0
$551$			4.95716i			0.211182i
$552$		0			0
$553$			22.8329i			0.970953i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	30.2060	−	30.2060i	1.27987	−	1.27987i	0.339127	−	0.940741i	$-0.389868\pi$
$557$	30.2060	−	30.2060i	1.27987	−	1.27987i	0.940741	−	0.339127i	$-0.110132\pi$
$558$		0			0
$559$	−23.2585			−0.983729
$560$		0			0
$561$		0			0
$562$		0			0
$563$	2.86747	−	2.86747i	0.120850	−	0.120850i	−0.644095	−	0.764945i	$-0.722766\pi$
$563$	2.86747	−	2.86747i	0.120850	−	0.120850i	0.764945	+	0.644095i	$0.222766\pi$
$564$		0			0
$565$	1.81047	+	1.81047i	0.0761670	+	0.0761670i
$566$		0			0
$567$		0			0
$568$		0			0
$569$			35.8628i			1.50345i	0.659479	+	0.751723i	$0.270777\pi$
$569$			35.8628i			1.50345i	−0.659479	+	0.751723i	$0.729223\pi$
$570$		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			0
$574$		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
$579$		0			0
$580$		0			0
$581$	11.0474	+	11.0474i	0.458322	+	0.458322i
$582$		0			0
$583$			4.93265i			0.204290i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−11.4005	−	11.4005i	−0.470550	−	0.470550i	0.431542	−	0.902093i	$-0.357970\pi$
$587$	−11.4005	−	11.4005i	−0.470550	−	0.470550i	−0.902093	+	0.431542i	$0.857970\pi$
$588$		0			0
$589$	19.3051	−	19.3051i	0.795453	−	0.795453i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	35.0454			1.43914			0.719572	−	0.694418i	$-0.244338\pi$
$593$	35.0454			1.43914			0.719572	+	0.694418i	$0.244338\pi$
$594$		0			0
$595$	−4.64336	+	4.64336i	−0.190359	+	0.190359i
$596$		0			0
$597$		0			0
$598$		0			0
$599$		−	18.2753i		−	0.746707i	−0.927689	−	0.373354i	$-0.878208\pi$
$599$		−	18.2753i		−	0.746707i	0.927689	−	0.373354i	$-0.121792\pi$
$600$		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
$603$		0			0
$604$		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
$609$		0			0
$610$		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
$615$		0			0
$616$		0			0
$617$		−	31.8836i		−	1.28358i	−0.766879	−	0.641792i	$-0.778191\pi$
$617$		−	31.8836i		−	1.28358i	0.766879	−	0.641792i	$-0.221809\pi$
$618$		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
$621$		0			0
$622$		0			0
$623$	−42.2102			−1.69112
$624$		0			0
$625$	−1.00000			−0.0400000
$626$		0			0
$627$		0			0
$628$		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
$633$		0			0
$634$		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
$639$		0			0
$640$		0			0
$641$	−13.6348			−0.538540			−0.269270	−	0.963065i	$-0.586782\pi$
$641$	−13.6348			−0.538540			−0.269270	+	0.963065i	$0.586782\pi$
$642$		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
$645$		0			0
$646$		0			0
$647$		−	4.87972i		−	0.191841i	−0.995389	−	0.0959207i	$-0.969420\pi$
$647$		−	4.87972i		−	0.191841i	0.995389	−	0.0959207i	$-0.0305795\pi$
$648$		0			0
$649$			17.4518i			0.685043i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	10.2913	−	10.2913i	0.402731	−	0.402731i	−0.476463	−	0.879194i	$-0.658081\pi$
$653$	10.2913	−	10.2913i	0.402731	−	0.402731i	0.879194	+	0.476463i	$0.158081\pi$
$654$		0			0
$655$	7.36417			0.287742
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−21.9025	+	21.9025i	−0.853201	+	0.853201i	−0.990526	−	0.137325i	$-0.956149\pi$
$659$	−21.9025	+	21.9025i	−0.853201	+	0.853201i	0.137325	+	0.990526i	$0.456149\pi$
$660$		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
$663$		0			0
$664$		0			0
$665$		−	17.0895i		−	0.662704i
$666$		0			0
$667$	−2.19608	−	2.19608i	−0.0850326	−	0.0850326i
$668$		0			0
$669$		0			0
$670$		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
$675$		0			0
$676$		0			0
$677$	−5.17061	−	5.17061i	−0.198723	−	0.198723i	0.600730	−	0.799452i	$-0.294877\pi$
$677$	−5.17061	−	5.17061i	−0.198723	−	0.198723i	−0.799452	+	0.600730i	$0.794877\pi$
$678$		0			0
$679$		−	84.0196i		−	3.22438i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	26.5989	+	26.5989i	1.01778	+	1.01778i	0.999839	+	0.0179409i	$0.00571108\pi$
$683$	26.5989	+	26.5989i	1.01778	+	1.01778i	0.0179409	+	0.999839i	$0.494289\pi$
$684$		0			0
$685$	16.0912	−	16.0912i	0.614811	−	0.614811i
$686$		0			0
$687$		0			0
$688$		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
$693$		0			0
$694$		0			0
$695$		−	8.88246i		−	0.336931i
$696$		0			0
$697$		−	9.33640i		−	0.353641i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	15.2175	−	15.2175i	0.574756	−	0.574756i	−0.358698	−	0.933454i	$-0.616779\pi$
$701$	15.2175	−	15.2175i	0.574756	−	0.574756i	0.933454	+	0.358698i	$0.116779\pi$
$702$		0			0
$703$	−27.9285			−1.05334
$704$		0			0
$705$		0			0
$706$		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
$711$		0			0
$712$		0			0
$713$			17.1048i			0.640579i
$714$		0			0
$715$	−3.52377	−	3.52377i	−0.131781	−	0.131781i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	9.27351			0.345843			0.172922	−	0.984936i	$-0.444679\pi$
$719$	9.27351			0.345843			0.172922	+	0.984936i	$0.444679\pi$
$720$		0			0
$721$	41.1520			1.53258
$722$		0			0
$723$		0			0
$724$		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
$729$		0			0
$730$		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
$735$		0			0
$736$		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
$741$		0			0
$742$		0			0
$743$		−	22.3956i		−	0.821617i	−0.911722	−	0.410808i	$-0.865247\pi$
$743$		−	22.3956i		−	0.821617i	0.911722	−	0.410808i	$-0.134753\pi$
$744$		0			0
$745$			18.3245i			0.671360i
$746$		0			0
$747$		0			0
$748$		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
$753$		0			0
$754$		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
$759$		0			0
$760$		0			0
$761$		−	50.1874i		−	1.81929i	−0.415383	−	0.909647i	$-0.636352\pi$
$761$		−	50.1874i		−	1.81929i	0.415383	−	0.909647i	$-0.363648\pi$
$762$		0			0
$763$	−6.11004	−	6.11004i	−0.221198	−	0.221198i
$764$		0			0
$765$		0			0
$766$		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
$771$		0			0
$772$		0			0
$773$	37.5957	+	37.5957i	1.35222	+	1.35222i	0.883171	+	0.469052i	$0.155404\pi$
$773$	37.5957	+	37.5957i	1.35222	+	1.35222i	0.469052	+	0.883171i	$0.344596\pi$
$774$		0			0
$775$			7.20435i			0.258788i
$776$		0			0
$777$		0			0
$778$		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
$783$		0			0
$784$		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
$789$		0			0
$790$		0			0
$791$		−	11.5463i		−	0.410541i
$792$		0			0
$793$			3.10304i			0.110192i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−0.0562195	+	0.0562195i	−0.00199140	+	0.00199140i	−0.708102	−	0.706110i	$-0.750448\pi$
$797$	−0.0562195	+	0.0562195i	−0.00199140	+	0.00199140i	0.706110	+	0.708102i	$0.250448\pi$
$798$		0			0
$799$	3.65536			0.129317
$800$		0			0
$801$		0			0
$802$		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
$807$		0			0
$808$		0			0
$809$			3.59856i			0.126518i	0.997997	+	0.0632592i	$0.0201495\pi$
$809$			3.59856i			0.126518i	−0.997997	+	0.0632592i	$0.979851\pi$
$810$		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
$813$		0			0
$814$		0			0
$815$	7.55196			0.264534
$816$		0			0
$817$	−41.0414			−1.43586
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−14.7799	−	14.7799i	−0.515824	−	0.515824i	0.400481	−	0.916305i	$-0.368843\pi$
$821$	−14.7799	−	14.7799i	−0.515824	−	0.515824i	−0.916305	+	0.400481i	$0.868843\pi$
$822$		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
$825$		0			0
$826$		0			0
$827$	16.8883	+	16.8883i	0.587265	+	0.587265i	0.936890	−	0.349625i	$-0.113691\pi$
$827$	16.8883	+	16.8883i	0.587265	+	0.587265i	−0.349625	+	0.936890i	$0.613691\pi$
$828$		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
$831$		0			0
$832$		0			0
$833$	19.4201			0.672868
$834$		0			0
$835$	11.3622	−	11.3622i	0.393206	−	0.393206i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		−	17.5407i		−	0.605572i	−0.953059	−	0.302786i	$-0.902083\pi$
$839$		−	17.5407i		−	0.605572i	0.953059	−	0.302786i	$-0.0979168\pi$
$840$		0			0
$841$			27.2889i			0.940996i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−5.93112	+	5.93112i	−0.204037	+	0.204037i
$846$		0			0
$847$	−25.3238			−0.870137
$848$		0			0
$849$		0			0
$850$		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
$855$		0			0
$856$		0			0
$857$			17.9553i			0.613341i	0.951816	+	0.306671i	$0.0992150\pi$
$857$			17.9553i			0.613341i	−0.951816	+	0.306671i	$0.900785\pi$
$858$		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
$861$		0			0
$862$		0			0
$863$	−32.3557			−1.10140			−0.550701	−	0.834703i	$-0.685639\pi$
$863$	−32.3557			−1.10140			−0.550701	+	0.834703i	$0.685639\pi$
$864$		0			0
$865$	−24.2019			−0.822889
$866$		0			0
$867$		0			0
$868$		0			0
$869$	8.30766	+	8.30766i	0.281818	+	0.281818i
$870$		0			0
$871$			15.8765i			0.537956i
$872$		0			0
$873$		0			0
$874$		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
$879$		0			0
$880$		0			0
$881$	47.3359			1.59479			0.797394	−	0.603459i	$-0.206211\pi$
$881$	47.3359			1.59479			0.797394	+	0.603459i	$0.206211\pi$
$882$		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
$885$		0			0
$886$		0			0
$887$		−	12.9255i		−	0.433994i	−0.976172	−	0.216997i	$-0.930374\pi$
$887$		−	12.9255i		−	0.433994i	0.976172	−	0.216997i	$-0.0696263\pi$
$888$		0			0
$889$			61.9412i			2.07744i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−6.72664	+	6.72664i	−0.225098	+	0.225098i
$894$		0			0
$895$	1.47760			0.0493906
$896$		0			0
$897$		0			0
$898$		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
$903$		0			0
$904$		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
$909$		0			0
$910$		0			0
$911$	−26.6745			−0.883765			−0.441883	−	0.897073i	$-0.645689\pi$
$911$	−26.6745			−0.883765			−0.441883	+	0.897073i	$0.645689\pi$
$912$		0			0
$913$	8.03908			0.266055
$914$		0			0
$915$		0			0
$916$		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
$921$		0			0
$922$		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
$927$		0			0
$928$		0			0
$929$	−42.5386			−1.39565			−0.697823	−	0.716270i	$-0.745848\pi$
$929$	−42.5386			−1.39565			−0.697823	+	0.716270i	$0.745848\pi$
$930$		0			0
$931$	−35.7372	+	35.7372i	−1.17124	+	1.17124i
$932$		0			0
$933$		0			0
$934$		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
$939$		0			0
$940$		0			0
$941$	−9.63152	+	9.63152i	−0.313979	+	0.313979i	−0.846449	−	0.532470i	$-0.821264\pi$
$941$	−9.63152	+	9.63152i	−0.313979	+	0.313979i	0.532470	+	0.846449i	$0.321264\pi$
$942$		0			0
$943$	−15.2227			−0.495721
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−3.44034	+	3.44034i	−0.111796	+	0.111796i	−0.760792	−	0.648996i	$-0.775189\pi$
$947$	−3.44034	+	3.44034i	−0.111796	+	0.111796i	0.648996	+	0.760792i	$0.275189\pi$
$948$		0			0
$949$	−2.11707	−	2.11707i	−0.0687231	−	0.0687231i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	17.6965i		−	0.573247i	−0.958043	−	0.286623i	$-0.907467\pi$
$953$		−	17.6965i		−	0.573247i	0.958043	−	0.286623i	$-0.0925328\pi$
$954$		0			0
$955$	0.0471973	+	0.0471973i	0.00152727	+	0.00152727i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−102.622			−3.31384
$960$		0			0
$961$	20.9027			0.674281
$962$		0			0
$963$		0			0
$964$		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
$969$		0			0
$970$		0			0
$971$	−14.3135	−	14.3135i	−0.459340	−	0.459340i	0.439098	−	0.898439i	$-0.355298\pi$
$971$	−14.3135	−	14.3135i	−0.459340	−	0.459340i	−0.898439	+	0.439098i	$0.855298\pi$
$972$		0			0
$973$	−28.3241	+	28.3241i	−0.908030	+	0.908030i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−48.1433			−1.54024			−0.770120	−	0.637900i	$-0.779804\pi$
$977$	−48.1433			−1.54024			−0.770120	+	0.637900i	$0.779804\pi$
$978$		0			0
$979$	−15.3580	+	15.3580i	−0.490845	+	0.490845i
$980$		0			0
$981$		0			0
$982$		0			0
$983$			0.791292i			0.0252383i	0.999920	+	0.0126191i	$0.00401690\pi$
$983$			0.791292i			0.0252383i	−0.999920	+	0.0126191i	$0.995983\pi$
$984$		0			0
$985$		−	16.8700i		−	0.537523i
$986$		0			0
$987$		0			0
$988$		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
$993$		0			0
$994$		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
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2880.2.t.c.2161.5		16
3.2	odd	2		320.2.l.a.241.1		16
4.3	odd	2		720.2.t.c.181.6		16
12.11	even	2		80.2.l.a.21.3	✓	16
15.2	even	4		1600.2.q.h.49.8		16
15.8	even	4		1600.2.q.g.49.1		16
15.14	odd	2		1600.2.l.i.1201.8		16
16.3	odd	4		720.2.t.c.541.6		16
16.13	even	4	inner	2880.2.t.c.721.8		16
24.5	odd	2		640.2.l.a.481.8		16
24.11	even	2		640.2.l.b.481.1		16
48.5	odd	4		640.2.l.a.161.8		16
48.11	even	4		640.2.l.b.161.1		16
48.29	odd	4		320.2.l.a.81.1		16
48.35	even	4		80.2.l.a.61.3	yes	16
60.23	odd	4		400.2.q.h.149.1		16
60.47	odd	4		400.2.q.g.149.8		16
60.59	even	2		400.2.l.h.101.6		16
96.29	odd	8		5120.2.a.t.1.2		8
96.35	even	8		5120.2.a.v.1.7		8
96.77	odd	8		5120.2.a.u.1.7		8
96.83	even	8		5120.2.a.s.1.2		8
240.29	odd	4		1600.2.l.i.401.8		16
240.77	even	4		1600.2.q.g.849.1		16
240.83	odd	4		400.2.q.g.349.8		16
240.173	even	4		1600.2.q.h.849.8		16
240.179	even	4		400.2.l.h.301.6		16
240.227	odd	4		400.2.q.h.349.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.l.a.21.3	✓	16	12.11	even	2
80.2.l.a.61.3	yes	16	48.35	even	4
320.2.l.a.81.1		16	48.29	odd	4
320.2.l.a.241.1		16	3.2	odd	2
400.2.l.h.101.6		16	60.59	even	2
400.2.l.h.301.6		16	240.179	even	4
400.2.q.g.149.8		16	60.47	odd	4
400.2.q.g.349.8		16	240.83	odd	4
400.2.q.h.149.1		16	60.23	odd	4
400.2.q.h.349.1		16	240.227	odd	4
640.2.l.a.161.8		16	48.5	odd	4
640.2.l.a.481.8		16	24.5	odd	2
640.2.l.b.161.1		16	48.11	even	4
640.2.l.b.481.1		16	24.11	even	2
720.2.t.c.181.6		16	4.3	odd	2
720.2.t.c.541.6		16	16.3	odd	4
1600.2.l.i.401.8		16	240.29	odd	4
1600.2.l.i.1201.8		16	15.14	odd	2
1600.2.q.g.49.1		16	15.8	even	4
1600.2.q.g.849.1		16	240.77	even	4
1600.2.q.h.49.8		16	15.2	even	4
1600.2.q.h.849.8		16	240.173	even	4
2880.2.t.c.721.8		16	16.13	even	4	inner
2880.2.t.c.2161.5		16	1.1	even	1	trivial
5120.2.a.s.1.2		8	96.83	even	8
5120.2.a.t.1.2		8	96.29	odd	8
5120.2.a.u.1.7		8	96.77	odd	8
5120.2.a.v.1.7		8	96.35	even	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2880.t (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{5} -4.50961i q^{7} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{5} -4.50961i q^{7} +(-1.64080 - 1.64080i) q^{11} +(1.51857 - 1.51857i) q^{13} -1.45616 q^{17} +(2.67964 - 2.67964i) q^{19} +2.37423i q^{23} +1.00000i q^{25} +(-0.924966 + 0.924966i) q^{29} +7.20435 q^{31} +(3.18877 - 3.18877i) q^{35} +(-5.21123 - 5.21123i) q^{37} +6.41166i q^{41} +(-7.65800 - 7.65800i) q^{43} -2.51027 q^{47} -13.3366 q^{49} +(-1.50312 - 1.50312i) q^{53} -2.32045i q^{55} +(-5.31807 - 5.31807i) q^{59} +(-1.02169 + 1.02169i) q^{61} +2.14759 q^{65} +(-5.22745 + 5.22745i) q^{67} -1.92097i q^{71} -1.39412i q^{73} +(-7.39938 + 7.39938i) q^{77} -5.06317 q^{79} +(-2.44974 + 2.44974i) q^{83} +(-1.02966 - 1.02966i) q^{85} -9.36007i q^{89} +(-6.84817 - 6.84817i) q^{91} +3.78959 q^{95} +18.6313 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q - 8 q^{11} + 8 q^{19} + 16 q^{29} - 16 q^{37} - 8 q^{43} - 40 q^{47} - 16 q^{49} - 16 q^{53} - 8 q^{59} + 16 q^{61} - 40 q^{67} - 16 q^{77} - 16 q^{79} + 40 q^{83} - 16 q^{85} - 32 q^{91} + 32 q^{95}+O(q^{100}) \) 16 * q - 8 * q^11 + 8 * q^19 + 16 * q^29 - 16 * q^37 - 8 * q^43 - 40 * q^47 - 16 * q^49 - 16 * q^53 - 8 * q^59 + 16 * q^61 - 40 * q^67 - 16 * q^77 - 16 * q^79 + 40 * q^83 - 16 * q^85 - 32 * q^91 + 32 * q^95

Introduction

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