LMFDB - Embedded newform 2640.2.d.i.529.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2640,2,Mod(529,2640)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2640, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0, 1, 0]))

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

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

chi := DirichletCharacter("2640.529");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2640 = 2^{4} \cdot 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2640.d (of order $2$, degree $1$, 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:	$21.0805061336$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.350464.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 $ x^6 - 2x^5 + 2x^4 + 2x^3 + 4x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 165)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			529.5
Root			$1.45161 + 1.45161i$ of defining polynomial
Character	$\chi$	$=$	2640.529
Dual form			2640.2.d.i.529.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{3} +(0.311108 - 2.21432i) q^{5} +4.90321i q^{7} -1.00000 q^{9} +O(q^{10})$	$q+1.00000i q^{3} +(0.311108 - 2.21432i) q^{5} +4.90321i q^{7} -1.00000 q^{9} +1.00000 q^{11} +4.14764i q^{13} +(2.21432 + 0.311108i) q^{15} +5.33185i q^{17} -5.18421 q^{19} -4.90321 q^{21} -4.00000i q^{23} +(-4.80642 - 1.37778i) q^{25} -1.00000i q^{27} -1.80642 q^{29} -2.62222 q^{31} +1.00000i q^{33} +(10.8573 + 1.52543i) q^{35} -5.80642i q^{37} -4.14764 q^{39} +1.80642 q^{41} -4.90321i q^{43} +(-0.311108 + 2.21432i) q^{45} +7.05086i q^{47} -17.0415 q^{49} -5.33185 q^{51} -7.18421i q^{53} +(0.311108 - 2.21432i) q^{55} -5.18421i q^{57} +1.67307 q^{59} +0.755569 q^{61} -4.90321i q^{63} +(9.18421 + 1.29036i) q^{65} -4.85728i q^{67} +4.00000 q^{69} -0.428639 q^{71} +12.7096i q^{73} +(1.37778 - 4.80642i) q^{75} +4.90321i q^{77} -6.42864 q^{79} +1.00000 q^{81} +2.90321i q^{83} +(11.8064 + 1.65878i) q^{85} -1.80642i q^{87} -0.622216 q^{89} -20.3368 q^{91} -2.62222i q^{93} +(-1.61285 + 11.4795i) q^{95} +2.75557i q^{97} -1.00000 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{5} - 6 q^{9}+O(q^{10}) $ 6 * q + 2 * q^5 - 6 * q^9	$ 6 q + 2 q^{5} - 6 q^{9} + 6 q^{11} - 4 q^{19} - 16 q^{21} - 2 q^{25} + 16 q^{29} - 16 q^{31} + 12 q^{35} - 12 q^{39} - 16 q^{41} - 2 q^{45} - 22 q^{49} + 8 q^{51} + 2 q^{55} - 16 q^{59} + 4 q^{61} + 28 q^{65} + 24 q^{69} + 24 q^{71} + 8 q^{75} - 12 q^{79} + 6 q^{81} + 44 q^{85} - 4 q^{89} - 16 q^{91} + 44 q^{95} - 6 q^{99}+O(q^{100}) $ 6 * q + 2 * q^5 - 6 * q^9 + 6 * q^11 - 4 * q^19 - 16 * q^21 - 2 * q^25 + 16 * q^29 - 16 * q^31 + 12 * q^35 - 12 * q^39 - 16 * q^41 - 2 * q^45 - 22 * q^49 + 8 * q^51 + 2 * q^55 - 16 * q^59 + 4 * q^61 + 28 * q^65 + 24 * q^69 + 24 * q^71 + 8 * q^75 - 12 * q^79 + 6 * q^81 + 44 * q^85 - 4 * q^89 - 16 * q^91 + 44 * q^95 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2640\mathbb{Z}\right)^\times$.

$n$	$661$	$881$	$991$	$1057$	$1201$
$\chi(n)$	$1$	$1$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$		0			0
$5$	0.311108	−	2.21432i	0.139132	−	0.990274i
$5$	0.311108	−	2.21432i	0.139132	−	0.990274i
$6$		0			0
$7$			4.90321i			1.85324i	0.375999	+	0.926620i	$0.377300\pi$
$7$			4.90321i			1.85324i	−0.375999	+	0.926620i	$0.622700\pi$
$8$		0			0
$9$	−1.00000			−0.333333
$10$		0			0
$11$	1.00000			0.301511
$11$	1.00000			0.301511
$12$		0			0
$13$			4.14764i			1.15035i	0.818031	+	0.575175i	$0.195066\pi$
$13$			4.14764i			1.15035i	−0.818031	+	0.575175i	$0.804934\pi$
$14$		0			0
$15$	2.21432	+	0.311108i	0.571735	+	0.0803277i
$16$		0			0
$17$			5.33185i			1.29316i	0.762845	+	0.646582i	$0.223802\pi$
$17$			5.33185i			1.29316i	−0.762845	+	0.646582i	$0.776198\pi$
$18$		0			0
$19$	−5.18421			−1.18934			−0.594669	−	0.803970i	$-0.702717\pi$
$19$	−5.18421			−1.18934			−0.594669	+	0.803970i	$0.702717\pi$
$20$		0			0
$21$	−4.90321			−1.06997
$22$		0			0
$23$		−	4.00000i		−	0.834058i	−0.908893	−	0.417029i	$-0.863071\pi$
$23$		−	4.00000i		−	0.834058i	0.908893	−	0.417029i	$-0.136929\pi$
$24$		0			0
$25$	−4.80642	−	1.37778i	−0.961285	−	0.275557i
$26$		0			0
$27$		−	1.00000i		−	0.192450i
$28$		0			0
$29$	−1.80642			−0.335444			−0.167722	−	0.985834i	$-0.553641\pi$
$29$	−1.80642			−0.335444			−0.167722	+	0.985834i	$0.553641\pi$
$30$		0			0
$31$	−2.62222			−0.470964			−0.235482	−	0.971879i	$-0.575667\pi$
$31$	−2.62222			−0.470964			−0.235482	+	0.971879i	$0.575667\pi$
$32$		0			0
$33$			1.00000i			0.174078i
$34$		0			0
$35$	10.8573	+	1.52543i	1.83522	+	0.257844i
$36$		0			0
$37$		−	5.80642i		−	0.954570i	−0.878749	−	0.477285i	$-0.841621\pi$
$37$		−	5.80642i		−	0.954570i	0.878749	−	0.477285i	$-0.158379\pi$
$38$		0			0
$39$	−4.14764			−0.664154
$40$		0			0
$41$	1.80642			0.282116			0.141058	−	0.990001i	$-0.454950\pi$
$41$	1.80642			0.282116			0.141058	+	0.990001i	$0.454950\pi$
$42$		0			0
$43$		−	4.90321i		−	0.747733i	−0.927483	−	0.373866i	$-0.878032\pi$
$43$		−	4.90321i		−	0.747733i	0.927483	−	0.373866i	$-0.121968\pi$
$44$		0			0
$45$	−0.311108	+	2.21432i	−0.0463772	+	0.330091i
$46$		0			0
$47$			7.05086i			1.02847i	0.857648	+	0.514236i	$0.171925\pi$
$47$			7.05086i			1.02847i	−0.857648	+	0.514236i	$0.828075\pi$
$48$		0			0
$49$	−17.0415			−2.43450
$50$		0			0
$51$	−5.33185			−0.746609
$52$		0			0
$53$		−	7.18421i		−	0.986827i	−0.869795	−	0.493413i	$-0.835749\pi$
$53$		−	7.18421i		−	0.986827i	0.869795	−	0.493413i	$-0.164251\pi$
$54$		0			0
$55$	0.311108	−	2.21432i	0.0419498	−	0.298579i
$56$		0			0
$57$		−	5.18421i		−	0.686665i
$58$		0			0
$59$	1.67307			0.217815			0.108908	−	0.994052i	$-0.465265\pi$
$59$	1.67307			0.217815			0.108908	+	0.994052i	$0.465265\pi$
$60$		0			0
$61$	0.755569			0.0967407			0.0483703	−	0.998829i	$-0.484597\pi$
$61$	0.755569			0.0967407			0.0483703	+	0.998829i	$0.484597\pi$
$62$		0			0
$63$		−	4.90321i		−	0.617747i
$64$		0			0
$65$	9.18421	+	1.29036i	1.13916	+	0.160050i
$66$		0			0
$67$		−	4.85728i		−	0.593411i	−0.954969	−	0.296706i	$-0.904112\pi$
$67$		−	4.85728i		−	0.593411i	0.954969	−	0.296706i	$-0.0958880\pi$
$68$		0			0
$69$	4.00000			0.481543
$70$		0			0
$71$	−0.428639			−0.0508701			−0.0254351	−	0.999676i	$-0.508097\pi$
$71$	−0.428639			−0.0508701			−0.0254351	+	0.999676i	$0.508097\pi$
$72$		0			0
$73$			12.7096i			1.48755i	0.668430	+	0.743775i	$0.266967\pi$
$73$			12.7096i			1.48755i	−0.668430	+	0.743775i	$0.733033\pi$
$74$		0			0
$75$	1.37778	−	4.80642i	0.159093	−	0.554998i
$76$		0			0
$77$			4.90321i			0.558773i
$78$		0			0
$79$	−6.42864			−0.723278			−0.361639	−	0.932318i	$-0.617783\pi$
$79$	−6.42864			−0.723278			−0.361639	+	0.932318i	$0.617783\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$			2.90321i			0.318669i	0.987225	+	0.159334i	$0.0509348\pi$
$83$			2.90321i			0.318669i	−0.987225	+	0.159334i	$0.949065\pi$
$84$		0			0
$85$	11.8064	+	1.65878i	1.28059	+	0.179920i
$86$		0			0
$87$		−	1.80642i		−	0.193669i
$88$		0			0
$89$	−0.622216			−0.0659547			−0.0329774	−	0.999456i	$-0.510499\pi$
$89$	−0.622216			−0.0659547			−0.0329774	+	0.999456i	$0.510499\pi$
$90$		0			0
$91$	−20.3368			−2.13187
$92$		0			0
$93$		−	2.62222i		−	0.271911i
$94$		0			0
$95$	−1.61285	+	11.4795i	−0.165475	+	1.17777i
$96$		0			0
$97$			2.75557i			0.279786i	0.990167	+	0.139893i	$0.0446758\pi$
$97$			2.75557i			0.279786i	−0.990167	+	0.139893i	$0.955324\pi$
$98$		0			0
$99$	−1.00000			−0.100504
$100$		0			0
$101$	−17.8064			−1.77181			−0.885903	−	0.463871i	$-0.846460\pi$
$101$	−17.8064			−1.77181			−0.885903	+	0.463871i	$0.846460\pi$
$102$		0			0
$103$		−	4.94914i		−	0.487654i	−0.969819	−	0.243827i	$-0.921597\pi$
$103$		−	4.94914i		−	0.487654i	0.969819	−	0.243827i	$-0.0784029\pi$
$104$		0			0
$105$	−1.52543	+	10.8573i	−0.148866	+	1.05956i
$106$		0			0
$107$			11.1985i			1.08260i	0.840830	+	0.541300i	$0.182068\pi$
$107$			11.1985i			1.08260i	−0.840830	+	0.541300i	$0.817932\pi$
$108$		0			0
$109$	−15.7146			−1.50518			−0.752591	−	0.658488i	$-0.771196\pi$
$109$	−15.7146			−1.50518			−0.752591	+	0.658488i	$0.771196\pi$
$110$		0			0
$111$	5.80642			0.551121
$112$		0			0
$113$		−	1.76494i		−	0.166031i	−0.996548	−	0.0830156i	$-0.973545\pi$
$113$		−	1.76494i		−	0.166031i	0.996548	−	0.0830156i	$-0.0264551\pi$
$114$		0			0
$115$	−8.85728	−	1.24443i	−0.825946	−	0.116044i
$116$		0			0
$117$		−	4.14764i		−	0.383450i
$118$		0			0
$119$	−26.1432			−2.39654
$120$		0			0
$121$	1.00000			0.0909091
$122$		0			0
$123$			1.80642i			0.162880i
$124$		0			0
$125$	−4.54617	+	10.2143i	−0.406622	+	0.913597i
$126$		0			0
$127$			18.7096i			1.66021i	0.557606	+	0.830106i	$0.311720\pi$
$127$			18.7096i			1.66021i	−0.557606	+	0.830106i	$0.688280\pi$
$128$		0			0
$129$	4.90321			0.431704
$130$		0			0
$131$	1.24443			0.108726			0.0543632	−	0.998521i	$-0.482687\pi$
$131$	1.24443			0.108726			0.0543632	+	0.998521i	$0.482687\pi$
$132$		0			0
$133$		−	25.4193i		−	2.20413i
$134$		0			0
$135$	−2.21432	−	0.311108i	−0.190578	−	0.0267759i
$136$		0			0
$137$		−	18.7971i		−	1.60594i	−0.596019	−	0.802970i	$-0.703252\pi$
$137$		−	18.7971i		−	1.60594i	0.596019	−	0.802970i	$-0.296748\pi$
$138$		0			0
$139$	14.0415			1.19098			0.595492	−	0.803361i	$-0.296957\pi$
$139$	14.0415			1.19098			0.595492	+	0.803361i	$0.296957\pi$
$140$		0			0
$141$	−7.05086			−0.593789
$142$		0			0
$143$			4.14764i			0.346843i
$144$		0			0
$145$	−0.561993	+	4.00000i	−0.0466709	+	0.332182i
$146$		0			0
$147$		−	17.0415i		−	1.40556i
$148$		0			0
$149$	3.05086			0.249936			0.124968	−	0.992161i	$-0.460117\pi$
$149$	3.05086			0.249936			0.124968	+	0.992161i	$0.460117\pi$
$150$		0			0
$151$	0.326929			0.0266051			0.0133026	−	0.999912i	$-0.495766\pi$
$151$	0.326929			0.0266051			0.0133026	+	0.999912i	$0.495766\pi$
$152$		0			0
$153$		−	5.33185i		−	0.431055i
$154$		0			0
$155$	−0.815792	+	5.80642i	−0.0655260	+	0.466383i
$156$		0			0
$157$			19.9081i			1.58884i	0.607367	+	0.794421i	$0.292226\pi$
$157$			19.9081i			1.58884i	−0.607367	+	0.794421i	$0.707774\pi$
$158$		0			0
$159$	7.18421			0.569745
$160$		0			0
$161$	19.6128			1.54571
$162$		0			0
$163$		−	12.1748i		−	0.953607i	−0.879010	−	0.476804i	$-0.841795\pi$
$163$		−	12.1748i		−	0.953607i	0.879010	−	0.476804i	$-0.158205\pi$
$164$		0			0
$165$	2.21432	+	0.311108i	0.172385	+	0.0242197i
$166$		0			0
$167$			13.0049i			1.00635i	0.864184	+	0.503176i	$0.167835\pi$
$167$			13.0049i			1.00635i	−0.864184	+	0.503176i	$0.832165\pi$
$168$		0			0
$169$	−4.20294			−0.323303
$170$		0			0
$171$	5.18421			0.396446
$172$		0			0
$173$			13.8938i			1.05633i	0.849142	+	0.528165i	$0.177120\pi$
$173$			13.8938i			1.05633i	−0.849142	+	0.528165i	$0.822880\pi$
$174$		0			0
$175$	6.75557	−	23.5669i	0.510673	−	1.78149i
$176$		0			0
$177$			1.67307i			0.125756i
$178$		0			0
$179$	12.8573			0.960998			0.480499	−	0.876995i	$-0.340456\pi$
$179$	12.8573			0.960998			0.480499	+	0.876995i	$0.340456\pi$
$180$		0			0
$181$	0.917502			0.0681974			0.0340987	−	0.999418i	$-0.489144\pi$
$181$	0.917502			0.0681974			0.0340987	+	0.999418i	$0.489144\pi$
$182$		0			0
$183$			0.755569i			0.0558532i
$184$		0			0
$185$	−12.8573	−	1.80642i	−0.945286	−	0.132811i
$186$		0			0
$187$			5.33185i			0.389904i
$188$		0			0
$189$	4.90321			0.356656
$190$		0			0
$191$	−14.3684			−1.03966			−0.519831	−	0.854269i	$-0.674005\pi$
$191$	−14.3684			−1.03966			−0.519831	+	0.854269i	$0.674005\pi$
$192$		0			0
$193$		−	11.7605i		−	0.846539i	−0.906004	−	0.423269i	$-0.860882\pi$
$193$		−	11.7605i		−	0.846539i	0.906004	−	0.423269i	$-0.139118\pi$
$194$		0			0
$195$	−1.29036	+	9.18421i	−0.0924049	+	0.657695i
$196$		0			0
$197$			3.82071i			0.272215i	0.990694	+	0.136107i	$0.0434592\pi$
$197$			3.82071i			0.272215i	−0.990694	+	0.136107i	$0.956541\pi$
$198$		0			0
$199$	−13.7146			−0.972199			−0.486100	−	0.873903i	$-0.661581\pi$
$199$	−13.7146			−0.972199			−0.486100	+	0.873903i	$0.661581\pi$
$200$		0			0
$201$	4.85728			0.342606
$202$		0			0
$203$		−	8.85728i		−	0.621659i
$204$		0			0
$205$	0.561993	−	4.00000i	0.0392513	−	0.279372i
$206$		0			0
$207$			4.00000i			0.278019i
$208$		0			0
$209$	−5.18421			−0.358599
$210$		0			0
$211$	−1.95851			−0.134830			−0.0674148	−	0.997725i	$-0.521475\pi$
$211$	−1.95851			−0.134830			−0.0674148	+	0.997725i	$0.521475\pi$
$212$		0			0
$213$		−	0.428639i		−	0.0293699i
$214$		0			0
$215$	−10.8573	−	1.52543i	−0.740460	−	0.104033i
$216$		0			0
$217$		−	12.8573i		−	0.872809i
$218$		0			0
$219$	−12.7096			−0.858838
$220$		0			0
$221$	−22.1146			−1.48759
$222$		0			0
$223$			26.0098i			1.74175i	0.491506	+	0.870874i	$0.336446\pi$
$223$			26.0098i			1.74175i	−0.491506	+	0.870874i	$0.663554\pi$
$224$		0			0
$225$	4.80642	+	1.37778i	0.320428	+	0.0918523i
$226$		0			0
$227$		−	6.34122i		−	0.420882i	−0.977607	−	0.210441i	$-0.932510\pi$
$227$		−	6.34122i		−	0.420882i	0.977607	−	0.210441i	$-0.0674899\pi$
$228$		0			0
$229$	23.3274			1.54152			0.770759	−	0.637127i	$-0.219877\pi$
$229$	23.3274			1.54152			0.770759	+	0.637127i	$0.219877\pi$
$230$		0			0
$231$	−4.90321			−0.322608
$232$		0			0
$233$		−	1.42372i		−	0.0932708i	−0.998912	−	0.0466354i	$-0.985150\pi$
$233$		−	1.42372i		−	0.0932708i	0.998912	−	0.0466354i	$-0.0148499\pi$
$234$		0			0
$235$	15.6128	+	2.19358i	1.01847	+	0.143093i
$236$		0			0
$237$		−	6.42864i		−	0.417585i
$238$		0			0
$239$	−18.9590			−1.22636			−0.613178	−	0.789945i	$-0.710109\pi$
$239$	−18.9590			−1.22636			−0.613178	+	0.789945i	$0.710109\pi$
$240$		0			0
$241$	−1.34614			−0.0867126			−0.0433563	−	0.999060i	$-0.513805\pi$
$241$	−1.34614			−0.0867126			−0.0433563	+	0.999060i	$0.513805\pi$
$242$		0			0
$243$			1.00000i			0.0641500i
$244$		0			0
$245$	−5.30174	+	37.7353i	−0.338716	+	2.41082i
$246$		0			0
$247$		−	21.5022i		−	1.36816i
$248$		0			0
$249$	−2.90321			−0.183984
$250$		0			0
$251$	−1.08250			−0.0683267			−0.0341633	−	0.999416i	$-0.510877\pi$
$251$	−1.08250			−0.0683267			−0.0341633	+	0.999416i	$0.510877\pi$
$252$		0			0
$253$		−	4.00000i		−	0.251478i
$254$		0			0
$255$	−1.65878	+	11.8064i	−0.103877	+	0.739347i
$256$		0			0
$257$			0.133353i			0.00831834i	0.999991	+	0.00415917i	$0.00132391\pi$
$257$			0.133353i			0.00831834i	−0.999991	+	0.00415917i	$0.998676\pi$
$258$		0			0
$259$	28.4701			1.76905
$260$		0			0
$261$	1.80642			0.111815
$262$		0			0
$263$			0.147643i			0.00910407i	0.999990	+	0.00455203i	$0.00144896\pi$
$263$			0.147643i			0.00910407i	−0.999990	+	0.00455203i	$0.998551\pi$
$264$		0			0
$265$	−15.9081	−	2.23506i	−0.977229	−	0.137299i
$266$		0			0
$267$		−	0.622216i		−	0.0380790i
$268$		0			0
$269$	26.8573			1.63752			0.818759	−	0.574138i	$-0.194663\pi$
$269$	26.8573			1.63752			0.818759	+	0.574138i	$0.194663\pi$
$270$		0			0
$271$	−3.08250			−0.187248			−0.0936242	−	0.995608i	$-0.529845\pi$
$271$	−3.08250			−0.187248			−0.0936242	+	0.995608i	$0.529845\pi$
$272$		0			0
$273$		−	20.3368i		−	1.23084i
$274$		0			0
$275$	−4.80642	−	1.37778i	−0.289838	−	0.0830835i
$276$		0			0
$277$			8.70964i			0.523311i	0.965161	+	0.261656i	$0.0842685\pi$
$277$			8.70964i			0.523311i	−0.965161	+	0.261656i	$0.915732\pi$
$278$		0			0
$279$	2.62222			0.156988
$280$		0			0
$281$	−20.3783			−1.21567			−0.607833	−	0.794065i	$-0.707961\pi$
$281$	−20.3783			−1.21567			−0.607833	+	0.794065i	$0.707961\pi$
$282$		0			0
$283$			6.32248i			0.375833i	0.982185	+	0.187916i	$0.0601734\pi$
$283$			6.32248i			0.375833i	−0.982185	+	0.187916i	$0.939827\pi$
$284$		0			0
$285$	−11.4795	−	1.61285i	−0.679987	−	0.0955369i
$286$		0			0
$287$			8.85728i			0.522829i
$288$		0			0
$289$	−11.4286			−0.672273
$290$		0			0
$291$	−2.75557			−0.161534
$292$		0			0
$293$			16.6780i			0.974339i	0.873308	+	0.487169i	$0.161971\pi$
$293$			16.6780i			0.974339i	−0.873308	+	0.487169i	$0.838029\pi$
$294$		0			0
$295$	0.520505	−	3.70471i	0.0303050	−	0.215697i
$296$		0			0
$297$		−	1.00000i		−	0.0580259i
$298$		0			0
$299$	16.5906			0.959458
$300$		0			0
$301$	24.0415			1.38573
$302$		0			0
$303$		−	17.8064i		−	1.02295i
$304$		0			0
$305$	0.235063	−	1.67307i	0.0134597	−	0.0957998i
$306$		0			0
$307$		−	9.58565i		−	0.547082i	−0.961860	−	0.273541i	$-0.911805\pi$
$307$		−	9.58565i		−	0.547082i	0.961860	−	0.273541i	$-0.0881949\pi$
$308$		0			0
$309$	4.94914			0.281547
$310$		0			0
$311$	−14.5303			−0.823941			−0.411970	−	0.911197i	$-0.635159\pi$
$311$	−14.5303			−0.823941			−0.411970	+	0.911197i	$0.635159\pi$
$312$		0			0
$313$		−	21.0321i		−	1.18881i	−0.804167	−	0.594403i	$-0.797388\pi$
$313$		−	21.0321i		−	1.18881i	0.804167	−	0.594403i	$-0.202612\pi$
$314$		0			0
$315$	−10.8573	−	1.52543i	−0.611738	−	0.0859481i
$316$		0			0
$317$			0.990632i			0.0556394i	0.999613	+	0.0278197i	$0.00885643\pi$
$317$			0.990632i			0.0556394i	−0.999613	+	0.0278197i	$0.991144\pi$
$318$		0			0
$319$	−1.80642			−0.101140
$320$		0			0
$321$	−11.1985			−0.625039
$322$		0			0
$323$		−	27.6414i		−	1.53801i
$324$		0			0
$325$	5.71456	−	19.9353i	0.316987	−	1.10581i
$326$		0			0
$327$		−	15.7146i		−	0.869017i
$328$		0			0
$329$	−34.5718			−1.90601
$330$		0			0
$331$	17.5812			0.966350			0.483175	−	0.875524i	$-0.339483\pi$
$331$	17.5812			0.966350			0.483175	+	0.875524i	$0.339483\pi$
$332$		0			0
$333$			5.80642i			0.318190i
$334$		0			0
$335$	−10.7556	−	1.51114i	−0.587639	−	0.0825623i
$336$		0			0
$337$			3.16992i			0.172676i	0.996266	+	0.0863382i	$0.0275166\pi$
$337$			3.16992i			0.172676i	−0.996266	+	0.0863382i	$0.972483\pi$
$338$		0			0
$339$	1.76494			0.0958582
$340$		0			0
$341$	−2.62222			−0.142001
$342$		0			0
$343$		−	49.2355i		−	2.65847i
$344$		0			0
$345$	1.24443	−	8.85728i	0.0669979	−	0.476860i
$346$		0			0
$347$			4.97634i			0.267144i	0.991039	+	0.133572i	$0.0426447\pi$
$347$			4.97634i			0.267144i	−0.991039	+	0.133572i	$0.957355\pi$
$348$		0			0
$349$	−18.2034			−0.974407			−0.487203	−	0.873289i	$-0.661983\pi$
$349$	−18.2034			−0.974407			−0.487203	+	0.873289i	$0.661983\pi$
$350$		0			0
$351$	4.14764			0.221385
$352$		0			0
$353$			22.4099i			1.19276i	0.802703	+	0.596379i	$0.203395\pi$
$353$			22.4099i			1.19276i	−0.802703	+	0.596379i	$0.796605\pi$
$354$		0			0
$355$	−0.133353	+	0.949145i	−0.00707765	+	0.0503754i
$356$		0			0
$357$		−	26.1432i		−	1.38364i
$358$		0			0
$359$	21.3274			1.12562			0.562809	−	0.826587i	$-0.309721\pi$
$359$	21.3274			1.12562			0.562809	+	0.826587i	$0.309721\pi$
$360$		0			0
$361$	7.87601			0.414527
$362$		0			0
$363$			1.00000i			0.0524864i
$364$		0			0
$365$	28.1432	+	3.95407i	1.47308	+	0.206965i
$366$		0			0
$367$			35.1338i			1.83397i	0.398921	+	0.916985i	$0.369385\pi$
$367$			35.1338i			1.83397i	−0.398921	+	0.916985i	$0.630615\pi$
$368$		0			0
$369$	−1.80642			−0.0940387
$370$		0			0
$371$	35.2257			1.82883
$372$		0			0
$373$		−	17.0049i		−	0.880481i	−0.897880	−	0.440241i	$-0.854893\pi$
$373$		−	17.0049i		−	0.880481i	0.897880	−	0.440241i	$-0.145107\pi$
$374$		0			0
$375$	−10.2143	−	4.54617i	−0.527465	−	0.234763i
$376$		0			0
$377$		−	7.49240i		−	0.385878i
$378$		0			0
$379$	2.36842			0.121657			0.0608287	−	0.998148i	$-0.480626\pi$
$379$	2.36842			0.121657			0.0608287	+	0.998148i	$0.480626\pi$
$380$		0			0
$381$	−18.7096			−0.958524
$382$		0			0
$383$		−	1.21585i		−	0.0621271i	−0.999517	−	0.0310635i	$-0.990111\pi$
$383$		−	1.21585i		−	0.0621271i	0.999517	−	0.0310635i	$-0.00988942\pi$
$384$		0			0
$385$	10.8573	+	1.52543i	0.553338	+	0.0777430i
$386$		0			0
$387$			4.90321i			0.249244i
$388$		0			0
$389$	−2.26671			−0.114927			−0.0574633	−	0.998348i	$-0.518301\pi$
$389$	−2.26671			−0.114927			−0.0574633	+	0.998348i	$0.518301\pi$
$390$		0			0
$391$	21.3274			1.07857
$392$		0			0
$393$			1.24443i			0.0627733i
$394$		0			0
$395$	−2.00000	+	14.2351i	−0.100631	+	0.716244i
$396$		0			0
$397$			18.4889i			0.927929i	0.885854	+	0.463965i	$0.153574\pi$
$397$			18.4889i			0.927929i	−0.885854	+	0.463965i	$0.846426\pi$
$398$		0			0
$399$	25.4193			1.27256
$400$		0			0
$401$	17.5625			0.877028			0.438514	−	0.898724i	$-0.355505\pi$
$401$	17.5625			0.877028			0.438514	+	0.898724i	$0.355505\pi$
$402$		0			0
$403$		−	10.8760i		−	0.541773i
$404$		0			0
$405$	0.311108	−	2.21432i	0.0154591	−	0.110030i
$406$		0			0
$407$		−	5.80642i		−	0.287814i
$408$		0			0
$409$	21.3461			1.05550			0.527749	−	0.849400i	$-0.323036\pi$
$409$	21.3461			1.05550			0.527749	+	0.849400i	$0.323036\pi$
$410$		0			0
$411$	18.7971			0.927190
$412$		0			0
$413$			8.20342i			0.403664i
$414$		0			0
$415$	6.42864	+	0.903212i	0.315570	+	0.0443369i
$416$		0			0
$417$			14.0415i			0.687615i
$418$		0			0
$419$	28.8573			1.40977			0.704885	−	0.709321i	$-0.250999\pi$
$419$	28.8573			1.40977			0.704885	+	0.709321i	$0.250999\pi$
$420$		0			0
$421$	−35.4893			−1.72964			−0.864822	−	0.502078i	$-0.832569\pi$
$421$	−35.4893			−1.72964			−0.864822	+	0.502078i	$0.832569\pi$
$422$		0			0
$423$		−	7.05086i		−	0.342824i
$424$		0			0
$425$	7.34614	−	25.6271i	0.356340	−	1.24310i
$426$		0			0
$427$			3.70471i			0.179284i
$428$		0			0
$429$	−4.14764			−0.200250
$430$		0			0
$431$	−9.24443			−0.445289			−0.222644	−	0.974900i	$-0.571469\pi$
$431$	−9.24443			−0.445289			−0.222644	+	0.974900i	$0.571469\pi$
$432$		0			0
$433$		−	6.28544i		−	0.302059i	−0.988529	−	0.151030i	$-0.951741\pi$
$433$		−	6.28544i		−	0.302059i	0.988529	−	0.151030i	$-0.0482589\pi$
$434$		0			0
$435$	−4.00000	−	0.561993i	−0.191785	−	0.0269455i
$436$		0			0
$437$			20.7368i			0.991977i
$438$		0			0
$439$	−36.5303			−1.74350			−0.871749	−	0.489952i	$-0.837014\pi$
$439$	−36.5303			−1.74350			−0.871749	+	0.489952i	$0.837014\pi$
$440$		0			0
$441$	17.0415			0.811499
$442$		0			0
$443$			38.2766i			1.81857i	0.416170	+	0.909287i	$0.363372\pi$
$443$			38.2766i			1.81857i	−0.416170	+	0.909287i	$0.636628\pi$
$444$		0			0
$445$	−0.193576	+	1.37778i	−0.00917639	+	0.0653132i
$446$		0			0
$447$			3.05086i			0.144300i
$448$		0			0
$449$	31.8479			1.50300			0.751498	−	0.659735i	$-0.229332\pi$
$449$	31.8479			1.50300			0.751498	+	0.659735i	$0.229332\pi$
$450$		0			0
$451$	1.80642			0.0850612
$452$		0			0
$453$			0.326929i			0.0153605i
$454$		0			0
$455$	−6.32693	+	45.0321i	−0.296611	+	2.11114i
$456$		0			0
$457$		−	1.39207i		−	0.0651185i	−0.999470	−	0.0325592i	$-0.989634\pi$
$457$		−	1.39207i		−	0.0651185i	0.999470	−	0.0325592i	$-0.0103658\pi$
$458$		0			0
$459$	5.33185			0.248870
$460$		0			0
$461$	−7.70471			−0.358844			−0.179422	−	0.983772i	$-0.557423\pi$
$461$	−7.70471			−0.358844			−0.179422	+	0.983772i	$0.557423\pi$
$462$		0			0
$463$		−	4.68244i		−	0.217611i	−0.994063	−	0.108806i	$-0.965297\pi$
$463$		−	4.68244i		−	0.217611i	0.994063	−	0.108806i	$-0.0347026\pi$
$464$		0			0
$465$	−5.80642	−	0.815792i	−0.269266	−	0.0378314i
$466$		0			0
$467$			12.8573i			0.594964i	0.954727	+	0.297482i	$0.0961468\pi$
$467$			12.8573i			0.594964i	−0.954727	+	0.297482i	$0.903853\pi$
$468$		0			0
$469$	23.8163			1.09973
$470$		0			0
$471$	−19.9081			−0.917318
$472$		0			0
$473$		−	4.90321i		−	0.225450i
$474$		0			0
$475$	24.9175	+	7.14272i	1.14329	+	0.327731i
$476$		0			0
$477$			7.18421i			0.328942i
$478$		0			0
$479$	8.38715			0.383219			0.191609	−	0.981471i	$-0.438629\pi$
$479$	8.38715			0.383219			0.191609	+	0.981471i	$0.438629\pi$
$480$		0			0
$481$	24.0830			1.09809
$482$		0			0
$483$			19.6128i			0.892415i
$484$		0			0
$485$	6.10171	+	0.857279i	0.277064	+	0.0389270i
$486$		0			0
$487$			9.83500i			0.445667i	0.974857	+	0.222833i	$0.0715306\pi$
$487$			9.83500i			0.445667i	−0.974857	+	0.222833i	$0.928469\pi$
$488$		0			0
$489$	12.1748			0.550565
$490$		0			0
$491$	32.9403			1.48657			0.743286	−	0.668973i	$-0.233266\pi$
$491$	32.9403			1.48657			0.743286	+	0.668973i	$0.233266\pi$
$492$		0			0
$493$		−	9.63158i		−	0.433785i
$494$		0			0
$495$	−0.311108	+	2.21432i	−0.0139833	+	0.0995263i
$496$		0			0
$497$		−	2.10171i		−	0.0942746i
$498$		0			0
$499$	−1.63158			−0.0730397			−0.0365199	−	0.999333i	$-0.511627\pi$
$499$	−1.63158			−0.0730397			−0.0365199	+	0.999333i	$0.511627\pi$
$500$		0			0
$501$	−13.0049			−0.581017
$502$		0			0
$503$		−	41.8622i		−	1.86654i	−0.359171	−	0.933272i	$-0.616941\pi$
$503$		−	41.8622i		−	1.86654i	0.359171	−	0.933272i	$-0.383059\pi$
$504$		0			0
$505$	−5.53972	+	39.4291i	−0.246514	+	1.75457i
$506$		0			0
$507$		−	4.20294i		−	0.186659i
$508$		0			0
$509$	38.8573			1.72232			0.861159	−	0.508335i	$-0.169739\pi$
$509$	38.8573			1.72232			0.861159	+	0.508335i	$0.169739\pi$
$510$		0			0
$511$	−62.3180			−2.75679
$512$		0			0
$513$			5.18421i			0.228888i
$514$		0			0
$515$	−10.9590	−	1.53972i	−0.482911	−	0.0678481i
$516$		0			0
$517$			7.05086i			0.310096i
$518$		0			0
$519$	−13.8938			−0.609872
$520$		0			0
$521$	11.1111			0.486785			0.243393	−	0.969928i	$-0.421740\pi$
$521$	11.1111			0.486785			0.243393	+	0.969928i	$0.421740\pi$
$522$		0			0
$523$		−	27.3002i		−	1.19375i	−0.802332	−	0.596877i	$-0.796408\pi$
$523$		−	27.3002i		−	1.19375i	0.802332	−	0.596877i	$-0.203592\pi$
$524$		0			0
$525$	23.5669	+	6.75557i	1.02854	+	0.294837i
$526$		0			0
$527$		−	13.9813i		−	0.609033i
$528$		0			0
$529$	7.00000			0.304348
$530$		0			0
$531$	−1.67307			−0.0726051
$532$		0			0
$533$			7.49240i			0.324532i
$534$		0			0
$535$	24.7971	+	3.48394i	1.07207	+	0.150624i
$536$		0			0
$537$			12.8573i			0.554833i
$538$		0			0
$539$	−17.0415			−0.734029
$540$		0			0
$541$	−16.1017			−0.692267			−0.346133	−	0.938185i	$-0.612506\pi$
$541$	−16.1017			−0.692267			−0.346133	+	0.938185i	$0.612506\pi$
$542$		0			0
$543$			0.917502i			0.0393738i
$544$		0			0
$545$	−4.88892	+	34.7971i	−0.209418	+	1.49054i
$546$		0			0
$547$			40.0370i			1.71186i	0.517091	+	0.855930i	$0.327015\pi$
$547$			40.0370i			1.71186i	−0.517091	+	0.855930i	$0.672985\pi$
$548$		0			0
$549$	−0.755569			−0.0322469
$550$		0			0
$551$	9.36488			0.398957
$552$		0			0
$553$		−	31.5210i		−	1.34041i
$554$		0			0
$555$	1.80642	−	12.8573i	0.0766784	−	0.545761i
$556$		0			0
$557$			28.2908i			1.19872i	0.800479	+	0.599361i	$0.204578\pi$
$557$			28.2908i			1.19872i	−0.800479	+	0.599361i	$0.795422\pi$
$558$		0			0
$559$	20.3368			0.860154
$560$		0			0
$561$	−5.33185			−0.225111
$562$		0			0
$563$			32.7926i			1.38204i	0.722834	+	0.691022i	$0.242839\pi$
$563$			32.7926i			1.38204i	−0.722834	+	0.691022i	$0.757161\pi$
$564$		0			0
$565$	−3.90813	−	0.549086i	−0.164416	−	0.0231002i
$566$		0			0
$567$			4.90321i			0.205916i
$568$		0			0
$569$	8.88586			0.372515			0.186257	−	0.982501i	$-0.440364\pi$
$569$	8.88586			0.372515			0.186257	+	0.982501i	$0.440364\pi$
$570$		0			0
$571$	10.6953			0.447586			0.223793	−	0.974637i	$-0.428156\pi$
$571$	10.6953			0.447586			0.223793	+	0.974637i	$0.428156\pi$
$572$		0			0
$573$		−	14.3684i		−	0.600249i
$574$		0			0
$575$	−5.51114	+	19.2257i	−0.229830	+	0.801767i
$576$		0			0
$577$			27.1338i			1.12960i	0.825229	+	0.564798i	$0.191046\pi$
$577$			27.1338i			1.12960i	−0.825229	+	0.564798i	$0.808954\pi$
$578$		0			0
$579$	11.7605			0.488749
$580$		0			0
$581$	−14.2351			−0.590570
$582$		0			0
$583$		−	7.18421i		−	0.297540i
$584$		0			0
$585$	−9.18421	−	1.29036i	−0.379720	−	0.0533500i
$586$		0			0
$587$		−	10.9590i		−	0.452326i	−0.974089	−	0.226163i	$-0.927382\pi$
$587$		−	10.9590i		−	0.452326i	0.974089	−	0.226163i	$-0.0726182\pi$
$588$		0			0
$589$	13.5941			0.560136
$590$		0			0
$591$	−3.82071			−0.157163
$592$		0			0
$593$		−	23.7003i		−	0.973253i	−0.873610	−	0.486627i	$-0.838227\pi$
$593$		−	23.7003i		−	0.973253i	0.873610	−	0.486627i	$-0.161773\pi$
$594$		0			0
$595$	−8.13335	+	57.8894i	−0.333435	+	2.37323i
$596$		0			0
$597$		−	13.7146i		−	0.561299i
$598$		0			0
$599$	41.7146			1.70441			0.852205	−	0.523208i	$-0.175265\pi$
$599$	41.7146			1.70441			0.852205	+	0.523208i	$0.175265\pi$
$600$		0			0
$601$	14.5906			0.595162			0.297581	−	0.954697i	$-0.403820\pi$
$601$	14.5906			0.595162			0.297581	+	0.954697i	$0.403820\pi$
$602$		0			0
$603$			4.85728i			0.197804i
$604$		0			0
$605$	0.311108	−	2.21432i	0.0126483	−	0.0900249i
$606$		0			0
$607$		−	19.9826i		−	0.811071i	−0.914079	−	0.405535i	$-0.867085\pi$
$607$		−	19.9826i		−	0.811071i	0.914079	−	0.405535i	$-0.132915\pi$
$608$		0			0
$609$	8.85728			0.358915
$610$		0			0
$611$	−29.2444			−1.18310
$612$		0			0
$613$			19.0781i			0.770555i	0.922801	+	0.385278i	$0.125894\pi$
$613$			19.0781i			0.770555i	−0.922801	+	0.385278i	$0.874106\pi$
$614$		0			0
$615$	4.00000	+	0.561993i	0.161296	+	0.0226617i
$616$		0			0
$617$			39.3590i			1.58454i	0.610174	+	0.792268i	$0.291100\pi$
$617$			39.3590i			1.58454i	−0.610174	+	0.792268i	$0.708900\pi$
$618$		0			0
$619$	−23.0923			−0.928160			−0.464080	−	0.885793i	$-0.653615\pi$
$619$	−23.0923			−0.928160			−0.464080	+	0.885793i	$0.653615\pi$
$620$		0			0
$621$	−4.00000			−0.160514
$622$		0			0
$623$		−	3.05086i		−	0.122230i
$624$		0			0
$625$	21.2034	+	13.2444i	0.848137	+	0.529777i
$626$		0			0
$627$		−	5.18421i		−	0.207037i
$628$		0			0
$629$	30.9590			1.23442
$630$		0			0
$631$	25.5111			1.01558			0.507791	−	0.861480i	$-0.330462\pi$
$631$	25.5111			1.01558			0.507791	+	0.861480i	$0.330462\pi$
$632$		0			0
$633$		−	1.95851i		−	0.0778439i
$634$		0			0
$635$	41.4291	+	5.82071i	1.64406	+	0.230988i
$636$		0			0
$637$		−	70.6820i		−	2.80052i
$638$		0			0
$639$	0.428639			0.0169567
$640$		0			0
$641$	−6.25380			−0.247010			−0.123505	−	0.992344i	$-0.539414\pi$
$641$	−6.25380			−0.247010			−0.123505	+	0.992344i	$0.539414\pi$
$642$		0			0
$643$		−	6.84743i		−	0.270036i	−0.990843	−	0.135018i	$-0.956891\pi$
$643$		−	6.84743i		−	0.270036i	0.990843	−	0.135018i	$-0.0431093\pi$
$644$		0			0
$645$	1.52543	−	10.8573i	0.0600637	−	0.427505i
$646$		0			0
$647$			20.2953i			0.797890i	0.916975	+	0.398945i	$0.130624\pi$
$647$			20.2953i			0.797890i	−0.916975	+	0.398945i	$0.869376\pi$
$648$		0			0
$649$	1.67307			0.0656738
$650$		0			0
$651$	12.8573			0.503916
$652$		0			0
$653$		−	10.6222i		−	0.415679i	−0.978163	−	0.207840i	$-0.933357\pi$
$653$		−	10.6222i		−	0.415679i	0.978163	−	0.207840i	$-0.0666432\pi$
$654$		0			0
$655$	0.387152	−	2.75557i	0.0151273	−	0.107669i
$656$		0			0
$657$		−	12.7096i		−	0.495850i
$658$		0			0
$659$	10.1017			0.393507			0.196753	−	0.980453i	$-0.436960\pi$
$659$	10.1017			0.393507			0.196753	+	0.980453i	$0.436960\pi$
$660$		0			0
$661$	21.6128			0.840642			0.420321	−	0.907375i	$-0.361917\pi$
$661$	21.6128			0.840642			0.420321	+	0.907375i	$0.361917\pi$
$662$		0			0
$663$		−	22.1146i		−	0.858861i
$664$		0			0
$665$	−56.2864	−	7.90813i	−2.18269	−	0.306664i
$666$		0			0
$667$			7.22570i			0.279780i
$668$		0			0
$669$	−26.0098			−1.00560
$670$		0			0
$671$	0.755569			0.0291684
$672$		0			0
$673$			10.2208i			0.393982i	0.980405	+	0.196991i	$0.0631170\pi$
$673$			10.2208i			0.393982i	−0.980405	+	0.196991i	$0.936883\pi$
$674$		0			0
$675$	−1.37778	+	4.80642i	−0.0530309	+	0.184999i
$676$		0			0
$677$		−	13.9224i		−	0.535082i	−0.963546	−	0.267541i	$-0.913789\pi$
$677$		−	13.9224i		−	0.535082i	0.963546	−	0.267541i	$-0.0862111\pi$
$678$		0			0
$679$	−13.5111			−0.518510
$680$		0			0
$681$	6.34122			0.242996
$682$		0			0
$683$			10.3970i			0.397830i	0.980017	+	0.198915i	$0.0637418\pi$
$683$			10.3970i			0.397830i	−0.980017	+	0.198915i	$0.936258\pi$
$684$		0			0
$685$	−41.6227	−	5.84791i	−1.59032	−	0.223437i
$686$		0			0
$687$			23.3274i			0.889996i
$688$		0			0
$689$	29.7975			1.13520
$690$		0			0
$691$	0.977725			0.0371944			0.0185972	−	0.999827i	$-0.494080\pi$
$691$	0.977725			0.0371944			0.0185972	+	0.999827i	$0.494080\pi$
$692$		0			0
$693$		−	4.90321i		−	0.186258i
$694$		0			0
$695$	4.36842	−	31.0923i	0.165703	−	1.17940i
$696$		0			0
$697$			9.63158i			0.364822i
$698$		0			0
$699$	1.42372			0.0538499
$700$		0			0
$701$	48.9688			1.84953			0.924764	−	0.380542i	$-0.124263\pi$
$701$	48.9688			1.84953			0.924764	+	0.380542i	$0.124263\pi$
$702$		0			0
$703$			30.1017i			1.13531i
$704$		0			0
$705$	−2.19358	+	15.6128i	−0.0826149	+	0.588014i
$706$		0			0
$707$		−	87.3087i		−	3.28358i
$708$		0			0
$709$	37.2672			1.39960			0.699799	−	0.714340i	$-0.253273\pi$
$709$	37.2672			1.39960			0.699799	+	0.714340i	$0.253273\pi$
$710$		0			0
$711$	6.42864			0.241093
$712$		0			0
$713$			10.4889i			0.392811i
$714$		0			0
$715$	9.18421	+	1.29036i	0.343470	+	0.0482569i
$716$		0			0
$717$		−	18.9590i		−	0.708036i
$718$		0			0
$719$	5.83500			0.217609			0.108804	−	0.994063i	$-0.465298\pi$
$719$	5.83500			0.217609			0.108804	+	0.994063i	$0.465298\pi$
$720$		0			0
$721$	24.2667			0.903739
$722$		0			0
$723$		−	1.34614i		−	0.0500635i
$724$		0			0
$725$	8.68244	+	2.48886i	0.322458	+	0.0924340i
$726$		0			0
$727$		−	46.8385i		−	1.73715i	−0.495562	−	0.868573i	$-0.665038\pi$
$727$		−	46.8385i		−	1.73715i	0.495562	−	0.868573i	$-0.334962\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	26.1432			0.966941
$732$		0			0
$733$		−	45.2083i		−	1.66981i	−0.550395	−	0.834904i	$-0.685523\pi$
$733$		−	45.2083i		−	1.66981i	0.550395	−	0.834904i	$-0.314477\pi$
$734$		0			0
$735$	−37.7353	−	5.30174i	−1.39189	−	0.195558i
$736$		0			0
$737$		−	4.85728i		−	0.178920i
$738$		0			0
$739$	5.65433			0.207998			0.103999	−	0.994577i	$-0.466836\pi$
$739$	5.65433			0.207998			0.103999	+	0.994577i	$0.466836\pi$
$740$		0			0
$741$	21.5022			0.789905
$742$		0			0
$743$		−	4.50622i		−	0.165317i	−0.996578	−	0.0826585i	$-0.973659\pi$
$743$		−	4.50622i		−	0.165317i	0.996578	−	0.0826585i	$-0.0263411\pi$
$744$		0			0
$745$	0.949145	−	6.75557i	0.0347740	−	0.247505i
$746$		0			0
$747$		−	2.90321i		−	0.106223i
$748$		0			0
$749$	−54.9086			−2.00632
$750$		0			0
$751$	−47.5121			−1.73374			−0.866870	−	0.498534i	$-0.833872\pi$
$751$	−47.5121			−1.73374			−0.866870	+	0.498534i	$0.833872\pi$
$752$		0			0
$753$		−	1.08250i		−	0.0394484i
$754$		0			0
$755$	0.101710	−	0.723926i	0.00370161	−	0.0263464i
$756$		0			0
$757$			46.6637i			1.69602i	0.529979	+	0.848011i	$0.322200\pi$
$757$			46.6637i			1.69602i	−0.529979	+	0.848011i	$0.677800\pi$
$758$		0			0
$759$	4.00000			0.145191
$760$		0			0
$761$	14.9304			0.541227			0.270613	−	0.962688i	$-0.412773\pi$
$761$	14.9304			0.541227			0.270613	+	0.962688i	$0.412773\pi$
$762$		0			0
$763$		−	77.0518i		−	2.78946i
$764$		0			0
$765$	−11.8064	−	1.65878i	−0.426862	−	0.0599733i
$766$		0			0
$767$			6.93930i			0.250564i
$768$		0			0
$769$	−38.8573			−1.40123			−0.700615	−	0.713540i	$-0.747091\pi$
$769$	−38.8573			−1.40123			−0.700615	+	0.713540i	$0.747091\pi$
$770$		0			0
$771$	−0.133353			−0.00480259
$772$		0			0
$773$		−	36.3368i		−	1.30694i	−0.756951	−	0.653471i	$-0.773312\pi$
$773$		−	36.3368i		−	1.30694i	0.756951	−	0.653471i	$-0.226688\pi$
$774$		0			0
$775$	12.6035	+	3.61285i	0.452730	+	0.129777i
$776$		0			0
$777$			28.4701i			1.02136i
$778$		0			0
$779$	−9.36488			−0.335532
$780$		0			0
$781$	−0.428639			−0.0153379
$782$		0			0
$783$			1.80642i			0.0645563i
$784$		0			0
$785$	44.0830	+	6.19358i	1.57339	+	0.221058i
$786$		0			0
$787$		−	33.5482i		−	1.19586i	−0.801547	−	0.597932i	$-0.795989\pi$
$787$		−	33.5482i		−	1.19586i	0.801547	−	0.597932i	$-0.204011\pi$
$788$		0			0
$789$	−0.147643			−0.00525624
$790$		0			0
$791$	8.65386			0.307696
$792$		0			0
$793$			3.13383i			0.111286i
$794$		0			0
$795$	2.23506	−	15.9081i	0.0792695	−	0.564203i
$796$		0			0

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:	\( N \)	\(=\)	\( 2640 = 2^{4} \cdot 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2640.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{3} +(0.311108 - 2.21432i) q^{5} +4.90321i q^{7} -1.00000 q^{9} +O(q^{10})\)	\(q+1.00000i q^{3} +(0.311108 - 2.21432i) q^{5} +4.90321i q^{7} -1.00000 q^{9} +1.00000 q^{11} +4.14764i q^{13} +(2.21432 + 0.311108i) q^{15} +5.33185i q^{17} -5.18421 q^{19} -4.90321 q^{21} -4.00000i q^{23} +(-4.80642 - 1.37778i) q^{25} -1.00000i q^{27} -1.80642 q^{29} -2.62222 q^{31} +1.00000i q^{33} +(10.8573 + 1.52543i) q^{35} -5.80642i q^{37} -4.14764 q^{39} +1.80642 q^{41} -4.90321i q^{43} +(-0.311108 + 2.21432i) q^{45} +7.05086i q^{47} -17.0415 q^{49} -5.33185 q^{51} -7.18421i q^{53} +(0.311108 - 2.21432i) q^{55} -5.18421i q^{57} +1.67307 q^{59} +0.755569 q^{61} -4.90321i q^{63} +(9.18421 + 1.29036i) q^{65} -4.85728i q^{67} +4.00000 q^{69} -0.428639 q^{71} +12.7096i q^{73} +(1.37778 - 4.80642i) q^{75} +4.90321i q^{77} -6.42864 q^{79} +1.00000 q^{81} +2.90321i q^{83} +(11.8064 + 1.65878i) q^{85} -1.80642i q^{87} -0.622216 q^{89} -20.3368 q^{91} -2.62222i q^{93} +(-1.61285 + 11.4795i) q^{95} +2.75557i q^{97} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{5} - 6 q^{9}+O(q^{10}) \) 6 * q + 2 * q^5 - 6 * q^9	\( 6 q + 2 q^{5} - 6 q^{9} + 6 q^{11} - 4 q^{19} - 16 q^{21} - 2 q^{25} + 16 q^{29} - 16 q^{31} + 12 q^{35} - 12 q^{39} - 16 q^{41} - 2 q^{45} - 22 q^{49} + 8 q^{51} + 2 q^{55} - 16 q^{59} + 4 q^{61} + 28 q^{65} + 24 q^{69} + 24 q^{71} + 8 q^{75} - 12 q^{79} + 6 q^{81} + 44 q^{85} - 4 q^{89} - 16 q^{91} + 44 q^{95} - 6 q^{99}+O(q^{100}) \) 6 * q + 2 * q^5 - 6 * q^9 + 6 * q^11 - 4 * q^19 - 16 * q^21 - 2 * q^25 + 16 * q^29 - 16 * q^31 + 12 * q^35 - 12 * q^39 - 16 * q^41 - 2 * q^45 - 22 * q^49 + 8 * q^51 + 2 * q^55 - 16 * q^59 + 4 * q^61 + 28 * q^65 + 24 * q^69 + 24 * q^71 + 8 * q^75 - 12 * q^79 + 6 * q^81 + 44 * q^85 - 4 * q^89 - 16 * q^91 + 44 * q^95 - 6 * q^99

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