LMFDB - Embedded newform 2640.2.d.i.529.6

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			529.6
Root			$-0.854638 - 0.854638i$ of defining polynomial
Character	$\chi$	$=$	2640.529
Dual form			2640.2.d.i.529.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{3} +(2.17009 + 0.539189i) q^{5} +0.290725i q^{7} -1.00000 q^{9} +O(q^{10})$	$q+1.00000i q^{3} +(2.17009 + 0.539189i) q^{5} +0.290725i q^{7} -1.00000 q^{9} +1.00000 q^{11} +6.97107i q^{13} +(-0.539189 + 2.17009i) q^{15} -4.78765i q^{17} +7.75872 q^{19} -0.290725 q^{21} -4.00000i q^{23} +(4.41855 + 2.34017i) q^{25} -1.00000i q^{27} +7.41855 q^{29} -6.34017 q^{31} +1.00000i q^{33} +(-0.156755 + 0.630898i) q^{35} +3.41855i q^{37} -6.97107 q^{39} -7.41855 q^{41} -0.290725i q^{43} +(-2.17009 - 0.539189i) q^{45} +5.26180i q^{47} +6.91548 q^{49} +4.78765 q^{51} +5.75872i q^{53} +(2.17009 + 0.539189i) q^{55} +7.75872i q^{57} +3.60197 q^{59} -6.68035 q^{61} -0.290725i q^{63} +(-3.75872 + 15.1278i) q^{65} +6.15676i q^{67} +4.00000 q^{69} +5.07838 q^{71} -1.12783i q^{73} +(-2.34017 + 4.41855i) q^{75} +0.290725i q^{77} -0.921622 q^{79} +1.00000 q^{81} -1.70928i q^{83} +(2.58145 - 10.3896i) q^{85} +7.41855i q^{87} -4.34017 q^{89} -2.02666 q^{91} -6.34017i q^{93} +(16.8371 + 4.18342i) q^{95} -4.68035i q^{97} -1.00000 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	2.17009	+	0.539189i	0.970492	+	0.241133i
$5$	2.17009	+	0.539189i	0.970492	+	0.241133i
$6$		0			0
$7$			0.290725i			0.109884i	0.998490	+	0.0549418i	$0.0174973\pi$
$7$			0.290725i			0.109884i	−0.998490	+	0.0549418i	$0.982503\pi$
$8$		0			0
$9$	−1.00000			−0.333333
$10$		0			0
$11$	1.00000			0.301511
$11$	1.00000			0.301511
$12$		0			0
$13$			6.97107i			1.93343i	0.255861	+	0.966714i	$0.417641\pi$
$13$			6.97107i			1.93343i	−0.255861	+	0.966714i	$0.582359\pi$
$14$		0			0
$15$	−0.539189	+	2.17009i	−0.139218	+	0.560314i
$16$		0			0
$17$		−	4.78765i		−	1.16118i	−0.814197	−	0.580588i	$-0.802823\pi$
$17$		−	4.78765i		−	1.16118i	0.814197	−	0.580588i	$-0.197177\pi$
$18$		0			0
$19$	7.75872			1.77997			0.889987	−	0.455987i	$-0.150714\pi$
$19$	7.75872			1.77997			0.889987	+	0.455987i	$0.150714\pi$
$20$		0			0
$21$	−0.290725			−0.0634413
$22$		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
$25$	4.41855	+	2.34017i	0.883710	+	0.468035i
$26$		0			0
$27$		−	1.00000i		−	0.192450i
$28$		0			0
$29$	7.41855			1.37759			0.688795	−	0.724956i	$-0.258140\pi$
$29$	7.41855			1.37759			0.688795	+	0.724956i	$0.258140\pi$
$30$		0			0
$31$	−6.34017			−1.13873			−0.569364	−	0.822085i	$-0.692811\pi$
$31$	−6.34017			−1.13873			−0.569364	+	0.822085i	$0.692811\pi$
$32$		0			0
$33$			1.00000i			0.174078i
$34$		0			0
$35$	−0.156755	+	0.630898i	−0.0264965	+	0.106641i
$36$		0			0
$37$			3.41855i			0.562006i	0.959707	+	0.281003i	$0.0906671\pi$
$37$			3.41855i			0.562006i	−0.959707	+	0.281003i	$0.909333\pi$
$38$		0			0
$39$	−6.97107			−1.11626
$40$		0			0
$41$	−7.41855			−1.15858			−0.579291	−	0.815120i	$-0.696671\pi$
$41$	−7.41855			−1.15858			−0.579291	+	0.815120i	$0.696671\pi$
$42$		0			0
$43$		−	0.290725i		−	0.0443351i	−0.999754	−	0.0221675i	$-0.992943\pi$
$43$		−	0.290725i		−	0.0443351i	0.999754	−	0.0221675i	$-0.00705673\pi$
$44$		0			0
$45$	−2.17009	−	0.539189i	−0.323497	−	0.0803775i
$46$		0			0
$47$			5.26180i			0.767512i	0.923435	+	0.383756i	$0.125370\pi$
$47$			5.26180i			0.767512i	−0.923435	+	0.383756i	$0.874630\pi$
$48$		0			0
$49$	6.91548			0.987926
$50$		0			0
$51$	4.78765			0.670406
$52$		0			0
$53$			5.75872i			0.791022i	0.918461	+	0.395511i	$0.129432\pi$
$53$			5.75872i			0.791022i	−0.918461	+	0.395511i	$0.870568\pi$
$54$		0			0
$55$	2.17009	+	0.539189i	0.292614	+	0.0727042i
$56$		0			0
$57$			7.75872i			1.02767i
$58$		0			0
$59$	3.60197			0.468936			0.234468	−	0.972124i	$-0.424665\pi$
$59$	3.60197			0.468936			0.234468	+	0.972124i	$0.424665\pi$
$60$		0			0
$61$	−6.68035			−0.855331			−0.427665	−	0.903937i	$-0.640664\pi$
$61$	−6.68035			−0.855331			−0.427665	+	0.903937i	$0.640664\pi$
$62$		0			0
$63$		−	0.290725i		−	0.0366279i
$64$		0			0
$65$	−3.75872	+	15.1278i	−0.466212	+	1.87638i
$66$		0			0
$67$			6.15676i			0.752167i	0.926586	+	0.376084i	$0.122729\pi$
$67$			6.15676i			0.752167i	−0.926586	+	0.376084i	$0.877271\pi$
$68$		0			0
$69$	4.00000			0.481543
$70$		0			0
$71$	5.07838			0.602693			0.301346	−	0.953515i	$-0.402564\pi$
$71$	5.07838			0.602693			0.301346	+	0.953515i	$0.402564\pi$
$72$		0			0
$73$		−	1.12783i		−	0.132002i	−0.997820	−	0.0660010i	$-0.978976\pi$
$73$		−	1.12783i		−	0.132002i	0.997820	−	0.0660010i	$-0.0210241\pi$
$74$		0			0
$75$	−2.34017	+	4.41855i	−0.270220	+	0.510210i
$76$		0			0
$77$			0.290725i			0.0331311i
$78$		0			0
$79$	−0.921622			−0.103691			−0.0518453	−	0.998655i	$-0.516510\pi$
$79$	−0.921622			−0.103691			−0.0518453	+	0.998655i	$0.516510\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$		−	1.70928i		−	0.187617i	−0.995590	−	0.0938087i	$-0.970096\pi$
$83$		−	1.70928i		−	0.187617i	0.995590	−	0.0938087i	$-0.0299042\pi$
$84$		0			0
$85$	2.58145	−	10.3896i	0.279997	−	1.12691i
$86$		0			0
$87$			7.41855i			0.795352i
$88$		0			0
$89$	−4.34017			−0.460057			−0.230029	−	0.973184i	$-0.573882\pi$
$89$	−4.34017			−0.460057			−0.230029	+	0.973184i	$0.573882\pi$
$90$		0			0
$91$	−2.02666			−0.212452
$92$		0			0
$93$		−	6.34017i		−	0.657445i
$94$		0			0
$95$	16.8371	+	4.18342i	1.72745	+	0.429210i
$96$		0			0
$97$		−	4.68035i		−	0.475217i	−0.971361	−	0.237609i	$-0.923636\pi$
$97$		−	4.68035i		−	0.475217i	0.971361	−	0.237609i	$-0.0763635\pi$
$98$		0			0
$99$	−1.00000			−0.100504
$100$		0			0
$101$	−8.58145			−0.853886			−0.426943	−	0.904279i	$-0.640410\pi$
$101$	−8.58145			−0.853886			−0.426943	+	0.904279i	$0.640410\pi$
$102$		0			0
$103$		−	6.73820i		−	0.663935i	−0.943291	−	0.331968i	$-0.892288\pi$
$103$		−	6.73820i		−	0.663935i	0.943291	−	0.331968i	$-0.107712\pi$
$104$		0			0
$105$	−0.630898	−	0.156755i	−0.0615693	−	0.0152978i
$106$		0			0
$107$			12.2329i			1.18260i	0.806453	+	0.591298i	$0.201384\pi$
$107$			12.2329i			1.18260i	−0.806453	+	0.591298i	$0.798616\pi$
$108$		0			0
$109$	6.31351			0.604725			0.302362	−	0.953193i	$-0.402225\pi$
$109$	6.31351			0.604725			0.302362	+	0.953193i	$0.402225\pi$
$110$		0			0
$111$	−3.41855			−0.324474
$112$		0			0
$113$		−	16.4969i		−	1.55190i	−0.630794	−	0.775950i	$-0.717271\pi$
$113$		−	16.4969i		−	1.55190i	0.630794	−	0.775950i	$-0.282729\pi$
$114$		0			0
$115$	2.15676	−	8.68035i	0.201118	−	0.809446i
$116$		0			0
$117$		−	6.97107i		−	0.644476i
$118$		0			0
$119$	1.39189			0.127594
$120$		0			0
$121$	1.00000			0.0909091
$122$		0			0
$123$		−	7.41855i		−	0.668908i
$124$		0			0
$125$	8.32684	+	7.46081i	0.744775	+	0.667315i
$126$		0			0
$127$			4.87217i			0.432336i	0.976356	+	0.216168i	$0.0693558\pi$
$127$			4.87217i			0.432336i	−0.976356	+	0.216168i	$0.930644\pi$
$128$		0			0
$129$	0.290725			0.0255969
$130$		0			0
$131$	8.68035			0.758405			0.379203	−	0.925314i	$-0.376198\pi$
$131$	8.68035			0.758405			0.379203	+	0.925314i	$0.376198\pi$
$132$		0			0
$133$			2.25565i			0.195590i
$134$		0			0
$135$	0.539189	−	2.17009i	0.0464060	−	0.186771i
$136$		0			0
$137$			12.5958i			1.07613i	0.842902	+	0.538067i	$0.180845\pi$
$137$			12.5958i			1.07613i	−0.842902	+	0.538067i	$0.819155\pi$
$138$		0			0
$139$	−9.91548			−0.841020			−0.420510	−	0.907288i	$-0.638149\pi$
$139$	−9.91548			−0.841020			−0.420510	+	0.907288i	$0.638149\pi$
$140$		0			0
$141$	−5.26180			−0.443123
$142$		0			0
$143$			6.97107i			0.582950i
$144$		0			0
$145$	16.0989	+	4.00000i	1.33694	+	0.332182i
$146$		0			0
$147$			6.91548i			0.570379i
$148$		0			0
$149$	1.26180			0.103370			0.0516851	−	0.998663i	$-0.483541\pi$
$149$	1.26180			0.103370			0.0516851	+	0.998663i	$0.483541\pi$
$150$		0			0
$151$	−1.60197			−0.130366			−0.0651832	−	0.997873i	$-0.520763\pi$
$151$	−1.60197			−0.130366			−0.0651832	+	0.997873i	$0.520763\pi$
$152$		0			0
$153$			4.78765i			0.387059i
$154$		0			0
$155$	−13.7587	−	3.41855i	−1.10513	−	0.274585i
$156$		0			0
$157$			7.10504i			0.567044i	0.958966	+	0.283522i	$0.0915029\pi$
$157$			7.10504i			0.567044i	−0.958966	+	0.283522i	$0.908497\pi$
$158$		0			0
$159$	−5.75872			−0.456696
$160$		0			0
$161$	1.16290			0.0916492
$162$		0			0
$163$			22.9360i			1.79649i	0.439499	+	0.898243i	$0.355156\pi$
$163$			22.9360i			1.79649i	−0.439499	+	0.898243i	$0.644844\pi$
$164$		0			0
$165$	−0.539189	+	2.17009i	−0.0419758	+	0.168941i
$166$		0			0
$167$			4.81432i			0.372543i	0.982498	+	0.186271i	$0.0596404\pi$
$167$			4.81432i			0.372543i	−0.982498	+	0.186271i	$0.940360\pi$
$168$		0			0
$169$	−35.5958			−2.73814
$170$		0			0
$171$	−7.75872			−0.593324
$172$		0			0
$173$		−	12.8865i		−	0.979746i	−0.871794	−	0.489873i	$-0.837043\pi$
$173$		−	12.8865i		−	0.979746i	0.871794	−	0.489873i	$-0.162957\pi$
$174$		0			0
$175$	−0.680346	+	1.28458i	−0.0514293	+	0.0971052i
$176$		0			0
$177$			3.60197i			0.270741i
$178$		0			0
$179$	1.84324			0.137771			0.0688853	−	0.997625i	$-0.478056\pi$
$179$	1.84324			0.137771			0.0688853	+	0.997625i	$0.478056\pi$
$180$		0			0
$181$	10.2823			0.764278			0.382139	−	0.924105i	$-0.375187\pi$
$181$	10.2823			0.764278			0.382139	+	0.924105i	$0.375187\pi$
$182$		0			0
$183$		−	6.68035i		−	0.493825i
$184$		0			0
$185$	−1.84324	+	7.41855i	−0.135518	+	0.545423i
$186$		0			0
$187$		−	4.78765i		−	0.350108i
$188$		0			0
$189$	0.290725			0.0211471
$190$		0			0
$191$	11.5174			0.833373			0.416687	−	0.909050i	$-0.363191\pi$
$191$	11.5174			0.833373			0.416687	+	0.909050i	$0.363191\pi$
$192$		0			0
$193$			3.86603i			0.278283i	0.990273	+	0.139141i	$0.0444343\pi$
$193$			3.86603i			0.278283i	−0.990273	+	0.139141i	$0.955566\pi$
$194$		0			0
$195$	−15.1278	−	3.75872i	−1.08333	−	0.269168i
$196$		0			0
$197$			8.57304i			0.610804i	0.952224	+	0.305402i	$0.0987908\pi$
$197$			8.57304i			0.610804i	−0.952224	+	0.305402i	$0.901209\pi$
$198$		0			0
$199$	8.31351			0.589329			0.294665	−	0.955601i	$-0.404792\pi$
$199$	8.31351			0.589329			0.294665	+	0.955601i	$0.404792\pi$
$200$		0			0
$201$	−6.15676			−0.434264
$202$		0			0
$203$			2.15676i			0.151375i
$204$		0			0
$205$	−16.0989	−	4.00000i	−1.12440	−	0.279372i
$206$		0			0
$207$			4.00000i			0.278019i
$208$		0			0
$209$	7.75872			0.536682
$210$		0			0
$211$	−25.9155			−1.78410			−0.892048	−	0.451941i	$-0.850732\pi$
$211$	−25.9155			−1.78410			−0.892048	+	0.451941i	$0.850732\pi$
$212$		0			0
$213$			5.07838i			0.347965i
$214$		0			0
$215$	0.156755	−	0.630898i	0.0106906	−	0.0430269i
$216$		0			0
$217$		−	1.84324i		−	0.125128i
$218$		0			0
$219$	1.12783			0.0762114
$220$		0			0
$221$	33.3751			2.24505
$222$		0			0
$223$			9.62863i			0.644781i	0.946607	+	0.322390i	$0.104486\pi$
$223$			9.62863i			0.644781i	−0.946607	+	0.322390i	$0.895514\pi$
$224$		0			0
$225$	−4.41855	−	2.34017i	−0.294570	−	0.156012i
$226$		0			0
$227$		−	18.3896i		−	1.22056i	−0.792185	−	0.610281i	$-0.791057\pi$
$227$		−	18.3896i		−	1.22056i	0.792185	−	0.610281i	$-0.208943\pi$
$228$		0			0
$229$	−17.1506			−1.13334			−0.566672	−	0.823943i	$-0.691769\pi$
$229$	−17.1506			−1.13334			−0.566672	+	0.823943i	$0.691769\pi$
$230$		0			0
$231$	−0.290725			−0.0191283
$232$		0			0
$233$		−	4.10731i		−	0.269079i	−0.990908	−	0.134539i	$-0.957045\pi$
$233$		−	4.10731i		−	0.269079i	0.990908	−	0.134539i	$-0.0429555\pi$
$234$		0			0
$235$	−2.83710	+	11.4186i	−0.185072	+	0.744864i
$236$		0			0
$237$		−	0.921622i		−	0.0598658i
$238$		0			0
$239$	−4.36683			−0.282467			−0.141234	−	0.989976i	$-0.545107\pi$
$239$	−4.36683			−0.282467			−0.141234	+	0.989976i	$0.545107\pi$
$240$		0			0
$241$	−5.20394			−0.335215			−0.167608	−	0.985854i	$-0.553604\pi$
$241$	−5.20394			−0.335215			−0.167608	+	0.985854i	$0.553604\pi$
$242$		0			0
$243$			1.00000i			0.0641500i
$244$		0			0
$245$	15.0072	+	3.72875i	0.958774	+	0.238221i
$246$		0			0
$247$			54.0866i			3.44145i
$248$		0			0
$249$	1.70928			0.108321
$250$		0			0
$251$	8.28231			0.522775			0.261388	−	0.965234i	$-0.415820\pi$
$251$	8.28231			0.522775			0.261388	+	0.965234i	$0.415820\pi$
$252$		0			0
$253$		−	4.00000i		−	0.251478i
$254$		0			0
$255$	10.3896	+	2.58145i	0.650623	+	0.161657i
$256$		0			0
$257$		−	11.0205i		−	0.687441i	−0.939072	−	0.343721i	$-0.888313\pi$
$257$		−	11.0205i		−	0.687441i	0.939072	−	0.343721i	$-0.111687\pi$
$258$		0			0
$259$	−0.993857			−0.0617553
$260$		0			0
$261$	−7.41855			−0.459197
$262$		0			0
$263$			2.97107i			0.183204i	0.995796	+	0.0916020i	$0.0291988\pi$
$263$			2.97107i			0.183204i	−0.995796	+	0.0916020i	$0.970801\pi$
$264$		0			0
$265$	−3.10504	+	12.4969i	−0.190741	+	0.767680i
$266$		0			0
$267$		−	4.34017i		−	0.265614i
$268$		0			0
$269$	15.8432			0.965980			0.482990	−	0.875626i	$-0.339551\pi$
$269$	15.8432			0.965980			0.482990	+	0.875626i	$0.339551\pi$
$270$		0			0
$271$	6.28231			0.381623			0.190812	−	0.981627i	$-0.438888\pi$
$271$	6.28231			0.381623			0.190812	+	0.981627i	$0.438888\pi$
$272$		0			0
$273$		−	2.02666i		−	0.122659i
$274$		0			0
$275$	4.41855	+	2.34017i	0.266449	+	0.141118i
$276$		0			0
$277$		−	5.12783i		−	0.308101i	−0.988063	−	0.154051i	$-0.950768\pi$
$277$		−	5.12783i		−	0.308101i	0.988063	−	0.154051i	$-0.0492319\pi$
$278$		0			0
$279$	6.34017			0.379576
$280$		0			0
$281$	21.8888			1.30578			0.652889	−	0.757454i	$-0.273557\pi$
$281$	21.8888			1.30578			0.652889	+	0.757454i	$0.273557\pi$
$282$		0			0
$283$		−	25.9649i		−	1.54345i	−0.635954	−	0.771727i	$-0.719393\pi$
$283$		−	25.9649i		−	1.54345i	0.635954	−	0.771727i	$-0.280607\pi$
$284$		0			0
$285$	−4.18342	+	16.8371i	−0.247804	+	0.997344i
$286$		0			0
$287$		−	2.15676i		−	0.127309i
$288$		0			0
$289$	−5.92162			−0.348331
$290$		0			0
$291$	4.68035			0.274367
$292$		0			0
$293$			10.4163i			0.608526i	0.952588	+	0.304263i	$0.0984101\pi$
$293$			10.4163i			0.608526i	−0.952588	+	0.304263i	$0.901590\pi$
$294$		0			0
$295$	7.81658	+	1.94214i	0.455099	+	0.113076i
$296$		0			0
$297$		−	1.00000i		−	0.0580259i
$298$		0			0
$299$	27.8843			1.61259
$300$		0			0
$301$	0.0845208			0.00487170
$302$		0			0
$303$		−	8.58145i		−	0.492991i
$304$		0			0
$305$	−14.4969	−	3.60197i	−0.830092	−	0.206248i
$306$		0			0
$307$		−	29.0700i		−	1.65911i	−0.558425	−	0.829555i	$-0.688594\pi$
$307$		−	29.0700i		−	1.65911i	0.558425	−	0.829555i	$-0.311406\pi$
$308$		0			0
$309$	6.73820			0.383323
$310$		0			0
$311$	−5.44521			−0.308770			−0.154385	−	0.988011i	$-0.549340\pi$
$311$	−5.44521			−0.308770			−0.154385	+	0.988011i	$0.549340\pi$
$312$		0			0
$313$			25.0928i			1.41833i	0.705044	+	0.709163i	$0.250927\pi$
$313$			25.0928i			1.41833i	−0.705044	+	0.709163i	$0.749073\pi$
$314$		0			0
$315$	0.156755	−	0.630898i	0.00883217	−	0.0355471i
$316$		0			0
$317$		−	21.1773i		−	1.18943i	−0.803935	−	0.594717i	$-0.797264\pi$
$317$		−	21.1773i		−	1.18943i	0.803935	−	0.594717i	$-0.202736\pi$
$318$		0			0
$319$	7.41855			0.415359
$320$		0			0
$321$	−12.2329			−0.682772
$322$		0			0
$323$		−	37.1461i		−	2.06686i
$324$		0			0
$325$	−16.3135	+	30.8020i	−0.904911	+	1.70859i
$326$		0			0
$327$			6.31351i			0.349138i
$328$		0			0
$329$	−1.52973			−0.0843369
$330$		0			0
$331$	6.70701			0.368650			0.184325	−	0.982865i	$-0.440990\pi$
$331$	6.70701			0.368650			0.184325	+	0.982865i	$0.440990\pi$
$332$		0			0
$333$		−	3.41855i		−	0.187335i
$334$		0			0
$335$	−3.31965	+	13.3607i	−0.181372	+	0.729973i
$336$		0			0
$337$		−	23.7503i		−	1.29376i	−0.762591	−	0.646881i	$-0.776073\pi$
$337$		−	23.7503i		−	1.29376i	0.762591	−	0.646881i	$-0.223927\pi$
$338$		0			0
$339$	16.4969			0.895990
$340$		0			0
$341$	−6.34017			−0.343340
$342$		0			0
$343$			4.04557i			0.218440i
$344$		0			0
$345$	8.68035	+	2.15676i	0.467334	+	0.116116i
$346$		0			0
$347$		−	31.1689i		−	1.67323i	−0.547790	−	0.836616i	$-0.684531\pi$
$347$		−	31.1689i		−	1.67323i	0.547790	−	0.836616i	$-0.315469\pi$
$348$		0			0
$349$	−11.0472			−0.591342			−0.295671	−	0.955290i	$-0.595543\pi$
$349$	−11.0472			−0.591342			−0.295671	+	0.955290i	$0.595543\pi$
$350$		0			0
$351$	6.97107			0.372088
$352$		0			0
$353$		−	27.4329i		−	1.46011i	−0.683390	−	0.730054i	$-0.739495\pi$
$353$		−	27.4329i		−	1.46011i	0.683390	−	0.730054i	$-0.260505\pi$
$354$		0			0
$355$	11.0205	+	2.73820i	0.584908	+	0.145329i
$356$		0			0
$357$			1.39189i			0.0736666i
$358$		0			0
$359$	−19.1506			−1.01073			−0.505365	−	0.862905i	$-0.668642\pi$
$359$	−19.1506			−1.01073			−0.505365	+	0.862905i	$0.668642\pi$
$360$		0			0
$361$	41.1978			2.16830
$362$		0			0
$363$			1.00000i			0.0524864i
$364$		0			0
$365$	0.608111	−	2.44748i	0.0318300	−	0.128107i
$366$		0			0
$367$		−	14.5692i		−	0.760504i	−0.924883	−	0.380252i	$-0.875837\pi$
$367$		−	14.5692i		−	0.760504i	0.924883	−	0.380252i	$-0.124163\pi$
$368$		0			0
$369$	7.41855			0.386194
$370$		0			0
$371$	−1.67420			−0.0869203
$372$		0			0
$373$		−	8.81432i		−	0.456388i	−0.973616	−	0.228194i	$-0.926718\pi$
$373$		−	8.81432i		−	0.456388i	0.973616	−	0.228194i	$-0.0732820\pi$
$374$		0			0
$375$	−7.46081	+	8.32684i	−0.385275	+	0.429996i
$376$		0			0
$377$			51.7152i			2.66347i
$378$		0			0
$379$	−23.5174			−1.20801			−0.604005	−	0.796980i	$-0.706429\pi$
$379$	−23.5174			−1.20801			−0.604005	+	0.796980i	$0.706429\pi$
$380$		0			0
$381$	−4.87217			−0.249609
$382$		0			0
$383$			19.3028i			0.986329i	0.869936	+	0.493164i	$0.164160\pi$
$383$			19.3028i			0.986329i	−0.869936	+	0.493164i	$0.835840\pi$
$384$		0			0
$385$	−0.156755	+	0.630898i	−0.00798900	+	0.0321535i
$386$		0			0
$387$			0.290725i			0.0147784i
$388$		0			0
$389$	20.0410			1.01612			0.508060	−	0.861321i	$-0.330363\pi$
$389$	20.0410			1.01612			0.508060	+	0.861321i	$0.330363\pi$
$390$		0			0
$391$	−19.1506			−0.968488
$392$		0			0
$393$			8.68035i			0.437866i
$394$		0			0
$395$	−2.00000	−	0.496928i	−0.100631	−	0.0250032i
$396$		0			0
$397$			33.3607i			1.67433i	0.546954	+	0.837163i	$0.315787\pi$
$397$			33.3607i			1.67433i	−0.546954	+	0.837163i	$0.684213\pi$
$398$		0			0
$399$	−2.25565			−0.112924
$400$		0			0
$401$	−37.6475			−1.88003			−0.940014	−	0.341135i	$-0.889189\pi$
$401$	−37.6475			−1.88003			−0.940014	+	0.341135i	$0.889189\pi$
$402$		0			0
$403$		−	44.1978i		−	2.20165i
$404$		0			0
$405$	2.17009	+	0.539189i	0.107832	+	0.0267925i
$406$		0			0
$407$			3.41855i			0.169451i
$408$		0			0
$409$	25.2039			1.24625			0.623127	−	0.782120i	$-0.285862\pi$
$409$	25.2039			1.24625			0.623127	+	0.782120i	$0.285862\pi$
$410$		0			0
$411$	−12.5958			−0.621306
$412$		0			0
$413$			1.04718i			0.0515284i
$414$		0			0
$415$	0.921622	−	3.70928i	0.0452407	−	0.182081i
$416$		0			0
$417$		−	9.91548i		−	0.485563i
$418$		0			0
$419$	17.8432			0.871700			0.435850	−	0.900019i	$-0.356448\pi$
$419$	17.8432			0.871700			0.435850	+	0.900019i	$0.356448\pi$
$420$		0			0
$421$	−11.8120			−0.575684			−0.287842	−	0.957678i	$-0.592938\pi$
$421$	−11.8120			−0.575684			−0.287842	+	0.957678i	$0.592938\pi$
$422$		0			0
$423$		−	5.26180i		−	0.255837i
$424$		0			0
$425$	11.2039	−	21.1545i	0.543471	−	1.02614i
$426$		0			0
$427$		−	1.94214i		−	0.0939868i
$428$		0			0
$429$	−6.97107			−0.336566
$430$		0			0
$431$	−16.6803			−0.803464			−0.401732	−	0.915757i	$-0.631592\pi$
$431$	−16.6803			−0.803464			−0.401732	+	0.915757i	$0.631592\pi$
$432$		0			0
$433$		−	28.3135i		−	1.36066i	−0.732906	−	0.680330i	$-0.761836\pi$
$433$		−	28.3135i		−	1.36066i	0.732906	−	0.680330i	$-0.238164\pi$
$434$		0			0
$435$	−4.00000	+	16.0989i	−0.191785	+	0.771883i
$436$		0			0
$437$		−	31.0349i		−	1.48460i
$438$		0			0
$439$	−27.4452			−1.30989			−0.654944	−	0.755677i	$-0.727308\pi$
$439$	−27.4452			−1.30989			−0.654944	+	0.755677i	$0.727308\pi$
$440$		0			0
$441$	−6.91548			−0.329309
$442$		0			0
$443$		−	0.412408i		−	0.0195941i	−0.999952	−	0.00979704i	$-0.996881\pi$
$443$		−	0.412408i		−	0.0195941i	0.999952	−	0.00979704i	$-0.00311854\pi$
$444$		0			0
$445$	−9.41855	−	2.34017i	−0.446482	−	0.110935i
$446$		0			0
$447$			1.26180i			0.0596809i
$448$		0			0
$449$	−1.33403			−0.0629568			−0.0314784	−	0.999504i	$-0.510022\pi$
$449$	−1.33403			−0.0629568			−0.0314784	+	0.999504i	$0.510022\pi$
$450$		0			0
$451$	−7.41855			−0.349326
$452$		0			0
$453$		−	1.60197i		−	0.0752670i
$454$		0			0
$455$	−4.39803	−	1.09275i	−0.206183	−	0.0512291i
$456$		0			0
$457$		−	11.6514i		−	0.545030i	−0.962151	−	0.272515i	$-0.912145\pi$
$457$		−	11.6514i		−	0.545030i	0.962151	−	0.272515i	$-0.0878555\pi$
$458$		0			0
$459$	−4.78765			−0.223469
$460$		0			0
$461$	−2.05786			−0.0958440			−0.0479220	−	0.998851i	$-0.515260\pi$
$461$	−2.05786			−0.0958440			−0.0479220	+	0.998851i	$0.515260\pi$
$462$		0			0
$463$		−	28.7792i		−	1.33748i	−0.743494	−	0.668742i	$-0.766833\pi$
$463$		−	28.7792i		−	1.33748i	0.743494	−	0.668742i	$-0.233167\pi$
$464$		0			0
$465$	3.41855	−	13.7587i	0.158531	−	0.638046i
$466$		0			0
$467$			1.84324i			0.0852952i	0.999090	+	0.0426476i	$0.0135793\pi$
$467$			1.84324i			0.0852952i	−0.999090	+	0.0426476i	$0.986421\pi$
$468$		0			0
$469$	−1.78992			−0.0826509
$470$		0			0
$471$	−7.10504			−0.327383
$472$		0			0
$473$		−	0.290725i		−	0.0133675i
$474$		0			0
$475$	34.2823	+	18.1568i	1.57298	+	0.833089i
$476$		0			0
$477$		−	5.75872i		−	0.263674i
$478$		0			0
$479$	26.8371			1.22622			0.613109	−	0.789998i	$-0.289919\pi$
$479$	26.8371			1.22622			0.613109	+	0.789998i	$0.289919\pi$
$480$		0			0
$481$	−23.8310			−1.08660
$482$		0			0
$483$			1.16290i			0.0529137i
$484$		0			0
$485$	2.52359	−	10.1568i	0.114590	−	0.461195i
$486$		0			0
$487$			28.5646i			1.29439i	0.762326	+	0.647193i	$0.224057\pi$
$487$			28.5646i			1.29439i	−0.762326	+	0.647193i	$0.775943\pi$
$488$		0			0
$489$	−22.9360			−1.03720
$490$		0			0
$491$	−25.9877			−1.17281			−0.586405	−	0.810018i	$-0.699457\pi$
$491$	−25.9877			−1.17281			−0.586405	+	0.810018i	$0.699457\pi$
$492$		0			0
$493$		−	35.5174i		−	1.59963i
$494$		0			0
$495$	−2.17009	−	0.539189i	−0.0975381	−	0.0242347i
$496$		0			0
$497$			1.47641i			0.0662260i
$498$		0			0
$499$	−27.5174			−1.23185			−0.615925	−	0.787805i	$-0.711218\pi$
$499$	−27.5174			−1.23185			−0.615925	+	0.787805i	$0.711218\pi$
$500$		0			0
$501$	−4.81432			−0.215088
$502$		0			0
$503$		−	22.6576i		−	1.01025i	−0.863046	−	0.505125i	$-0.831446\pi$
$503$		−	22.6576i		−	1.01025i	0.863046	−	0.505125i	$-0.168554\pi$
$504$		0			0
$505$	−18.6225	−	4.62702i	−0.828690	−	0.205900i
$506$		0			0
$507$		−	35.5958i		−	1.58087i
$508$		0			0
$509$	27.8432			1.23413			0.617065	−	0.786912i	$-0.288322\pi$
$509$	27.8432			1.23413			0.617065	+	0.786912i	$0.288322\pi$
$510$		0			0
$511$	0.327887			0.0145049
$512$		0			0
$513$		−	7.75872i		−	0.342556i
$514$		0			0
$515$	3.63317	−	14.6225i	0.160096	−	0.644344i
$516$		0			0
$517$			5.26180i			0.231413i
$518$		0			0
$519$	12.8865			0.565657
$520$		0			0
$521$	29.7009			1.30122			0.650609	−	0.759413i	$-0.274514\pi$
$521$	29.7009			1.30122			0.650609	+	0.759413i	$0.274514\pi$
$522$		0			0
$523$		−	24.7565i		−	1.08252i	−0.840854	−	0.541262i	$-0.817947\pi$
$523$		−	24.7565i		−	1.08252i	0.840854	−	0.541262i	$-0.182053\pi$
$524$		0			0
$525$	−1.28458	−	0.680346i	−0.0560637	−	0.0296927i
$526$		0			0
$527$			30.3545i			1.32226i
$528$		0			0
$529$	7.00000			0.304348
$530$		0			0
$531$	−3.60197			−0.156312
$532$		0			0
$533$		−	51.7152i		−	2.24004i
$534$		0			0
$535$	−6.59583	+	26.5464i	−0.285162	+	1.14770i
$536$		0			0
$537$			1.84324i			0.0795419i
$538$		0			0
$539$	6.91548			0.297871
$540$		0			0
$541$	−12.5236			−0.538431			−0.269216	−	0.963080i	$-0.586764\pi$
$541$	−12.5236			−0.538431			−0.269216	+	0.963080i	$0.586764\pi$
$542$		0			0
$543$			10.2823i			0.441256i
$544$		0			0
$545$	13.7009	+	3.40417i	0.586881	+	0.145819i
$546$		0			0
$547$		−	14.2784i		−	0.610502i	−0.952272	−	0.305251i	$-0.901260\pi$
$547$		−	14.2784i		−	0.610502i	0.952272	−	0.305251i	$-0.0987404\pi$
$548$		0			0
$549$	6.68035			0.285110
$550$		0			0
$551$	57.5585			2.45207
$552$		0			0
$553$		−	0.267938i		−	0.0113939i
$554$		0			0
$555$	−7.41855	−	1.84324i	−0.314900	−	0.0782414i
$556$		0			0
$557$			3.57918i			0.151655i	0.997121	+	0.0758274i	$0.0241598\pi$
$557$			3.57918i			0.151655i	−0.997121	+	0.0758274i	$0.975840\pi$
$558$		0			0
$559$	2.02666			0.0857187
$560$		0			0
$561$	4.78765			0.202135
$562$		0			0
$563$		−	28.9588i		−	1.22047i	−0.792222	−	0.610234i	$-0.791076\pi$
$563$		−	28.9588i		−	1.22047i	0.792222	−	0.610234i	$-0.208924\pi$
$564$		0			0
$565$	8.89496	−	35.7998i	0.374214	−	1.50611i
$566$		0			0
$567$			0.290725i			0.0122093i
$568$		0			0
$569$	25.8264			1.08270			0.541350	−	0.840797i	$-0.317913\pi$
$569$	25.8264			1.08270			0.541350	+	0.840797i	$0.317913\pi$
$570$		0			0
$571$	−17.1194			−0.716425			−0.358213	−	0.933640i	$-0.616614\pi$
$571$	−17.1194			−0.716425			−0.358213	+	0.933640i	$0.616614\pi$
$572$		0			0
$573$			11.5174i			0.481148i
$574$		0			0
$575$	9.36069	−	17.6742i	0.390368	−	0.737065i
$576$		0			0
$577$		−	22.5692i		−	0.939567i	−0.882782	−	0.469783i	$-0.844332\pi$
$577$		−	22.5692i		−	0.939567i	0.882782	−	0.469783i	$-0.155668\pi$
$578$		0			0
$579$	−3.86603			−0.160667
$580$		0			0
$581$	0.496928			0.0206161
$582$		0			0
$583$			5.75872i			0.238502i
$584$		0			0
$585$	3.75872	−	15.1278i	0.155404	−	0.625459i
$586$		0			0
$587$			3.63317i			0.149957i	0.997185	+	0.0749784i	$0.0238888\pi$
$587$			3.63317i			0.149957i	−0.997185	+	0.0749784i	$0.976111\pi$
$588$		0			0
$589$	−49.1917			−2.02691
$590$		0			0
$591$	−8.57304			−0.352648
$592$		0			0
$593$			12.3051i			0.505310i	0.967556	+	0.252655i	$0.0813037\pi$
$593$			12.3051i			0.505310i	−0.967556	+	0.252655i	$0.918696\pi$
$594$		0			0
$595$	3.02052	+	0.750491i	0.123829	+	0.0307671i
$596$		0			0
$597$			8.31351i			0.340249i
$598$		0			0
$599$	19.6865			0.804368			0.402184	−	0.915559i	$-0.368251\pi$
$599$	19.6865			0.804368			0.402184	+	0.915559i	$0.368251\pi$
$600$		0			0
$601$	25.8843			1.05584			0.527921	−	0.849294i	$-0.322972\pi$
$601$	25.8843			1.05584			0.527921	+	0.849294i	$0.322972\pi$
$602$		0			0
$603$		−	6.15676i		−	0.250722i
$604$		0			0
$605$	2.17009	+	0.539189i	0.0882266	+	0.0219211i
$606$		0			0
$607$		−	41.5357i		−	1.68588i	−0.538006	−	0.842941i	$-0.680822\pi$
$607$		−	41.5357i		−	1.68588i	0.538006	−	0.842941i	$-0.319178\pi$
$608$		0			0
$609$	−2.15676			−0.0873961
$610$		0			0
$611$	−36.6803			−1.48393
$612$		0			0
$613$		−	20.6453i		−	0.833855i	−0.908940	−	0.416927i	$-0.863107\pi$
$613$		−	20.6453i		−	0.833855i	0.908940	−	0.416927i	$-0.136893\pi$
$614$		0			0
$615$	4.00000	−	16.0989i	0.161296	−	0.649170i
$616$		0			0
$617$		−	8.69472i		−	0.350036i	−0.984565	−	0.175018i	$-0.944002\pi$
$617$		−	8.69472i		−	0.350036i	0.984565	−	0.175018i	$-0.0559984\pi$
$618$		0			0
$619$	2.65368			0.106661			0.0533303	−	0.998577i	$-0.483016\pi$
$619$	2.65368			0.106661			0.0533303	+	0.998577i	$0.483016\pi$
$620$		0			0
$621$	−4.00000			−0.160514
$622$		0			0
$623$		−	1.26180i		−	0.0505528i
$624$		0			0
$625$	14.0472	+	20.6803i	0.561887	+	0.827214i
$626$		0			0
$627$			7.75872i			0.309854i
$628$		0			0
$629$	16.3668			0.652588
$630$		0			0
$631$	10.6393			0.423544			0.211772	−	0.977319i	$-0.432077\pi$
$631$	10.6393			0.423544			0.211772	+	0.977319i	$0.432077\pi$
$632$		0			0
$633$		−	25.9155i		−	1.03005i
$634$		0			0
$635$	−2.62702	+	10.5730i	−0.104250	+	0.419578i
$636$		0			0
$637$			48.2083i			1.91008i
$638$		0			0
$639$	−5.07838			−0.200898
$640$		0			0
$641$	−35.8576			−1.41629			−0.708145	−	0.706067i	$-0.750468\pi$
$641$	−35.8576			−1.41629			−0.708145	+	0.706067i	$0.750468\pi$
$642$		0			0
$643$		−	12.2146i		−	0.481697i	−0.970563	−	0.240849i	$-0.922574\pi$
$643$		−	12.2146i		−	0.481697i	0.970563	−	0.240849i	$-0.0774258\pi$
$644$		0			0
$645$	0.630898	+	0.156755i	0.0248416	+	0.00617224i
$646$		0			0
$647$			25.9421i			1.01989i	0.860207	+	0.509945i	$0.170334\pi$
$647$			25.9421i			1.01989i	−0.860207	+	0.509945i	$0.829666\pi$
$648$		0			0
$649$	3.60197			0.141390
$650$		0			0
$651$	1.84324			0.0722424
$652$		0			0
$653$		−	14.3402i		−	0.561174i	−0.959829	−	0.280587i	$-0.909471\pi$
$653$		−	14.3402i		−	0.561174i	0.959829	−	0.280587i	$-0.0905292\pi$
$654$		0			0
$655$	18.8371	+	4.68035i	0.736026	+	0.182876i
$656$		0			0
$657$			1.12783i			0.0440007i
$658$		0			0
$659$	6.52359			0.254123			0.127062	−	0.991895i	$-0.459445\pi$
$659$	6.52359			0.254123			0.127062	+	0.991895i	$0.459445\pi$
$660$		0			0
$661$	3.16290			0.123022			0.0615112	−	0.998106i	$-0.480408\pi$
$661$	3.16290			0.123022			0.0615112	+	0.998106i	$0.480408\pi$
$662$		0			0
$663$			33.3751i			1.29618i
$664$		0			0
$665$	−1.21622	+	4.89496i	−0.0471631	+	0.189818i
$666$		0			0
$667$		−	29.6742i		−	1.14899i
$668$		0			0
$669$	−9.62863			−0.372264
$670$		0			0
$671$	−6.68035			−0.257892
$672$		0			0
$673$		−	18.4885i		−	0.712680i	−0.934356	−	0.356340i	$-0.884024\pi$
$673$		−	18.4885i		−	0.712680i	0.934356	−	0.356340i	$-0.115976\pi$
$674$		0			0
$675$	2.34017	−	4.41855i	0.0900733	−	0.170070i
$676$		0			0
$677$		−	15.0966i		−	0.580211i	−0.956995	−	0.290105i	$-0.906310\pi$
$677$		−	15.0966i		−	0.580211i	0.956995	−	0.290105i	$-0.0936903\pi$
$678$		0			0
$679$	1.36069			0.0522186
$680$		0			0
$681$	18.3896			0.704692
$682$		0			0
$683$			12.4657i			0.476988i	0.971144	+	0.238494i	$0.0766537\pi$
$683$			12.4657i			0.476988i	−0.971144	+	0.238494i	$0.923346\pi$
$684$		0			0
$685$	−6.79153	+	27.3340i	−0.259491	+	1.04438i
$686$		0			0
$687$		−	17.1506i		−	0.654337i
$688$		0			0
$689$	−40.1445			−1.52938
$690$		0			0
$691$	30.7214			1.16870			0.584348	−	0.811503i	$-0.301350\pi$
$691$	30.7214			1.16870			0.584348	+	0.811503i	$0.301350\pi$
$692$		0			0
$693$		−	0.290725i		−	0.0110437i
$694$		0			0
$695$	−21.5174	−	5.34632i	−0.816203	−	0.202797i
$696$		0			0
$697$			35.5174i			1.34532i
$698$		0			0
$699$	4.10731			0.155353
$700$		0			0
$701$	17.9955			0.679679			0.339840	−	0.940483i	$-0.389627\pi$
$701$	17.9955			0.679679			0.339840	+	0.940483i	$0.389627\pi$
$702$		0			0
$703$			26.5236i			1.00036i
$704$		0			0
$705$	−11.4186	−	2.83710i	−0.430047	−	0.106851i
$706$		0			0
$707$		−	2.49484i		−	0.0938281i
$708$		0			0
$709$	−23.5897			−0.885929			−0.442965	−	0.896539i	$-0.646073\pi$
$709$	−23.5897			−0.885929			−0.442965	+	0.896539i	$0.646073\pi$
$710$		0			0
$711$	0.921622			0.0345635
$712$		0			0
$713$			25.3607i			0.949765i
$714$		0			0
$715$	−3.75872	+	15.1278i	−0.140568	+	0.565749i
$716$		0			0
$717$		−	4.36683i		−	0.163082i
$718$		0			0
$719$	24.5646			0.916106			0.458053	−	0.888925i	$-0.348547\pi$
$719$	24.5646			0.916106			0.458053	+	0.888925i	$0.348547\pi$
$720$		0			0
$721$	1.95896			0.0729556
$722$		0			0
$723$		−	5.20394i		−	0.193536i
$724$		0			0
$725$	32.7792	+	17.3607i	1.21739	+	0.644760i
$726$		0			0
$727$			8.51130i			0.315667i	0.987466	+	0.157833i	$0.0504509\pi$
$727$			8.51130i			0.315667i	−0.987466	+	0.157833i	$0.949549\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	−1.39189			−0.0514809
$732$		0			0
$733$		−	29.8615i		−	1.10296i	−0.834188	−	0.551480i	$-0.814063\pi$
$733$		−	29.8615i		−	1.10296i	0.834188	−	0.551480i	$-0.185937\pi$
$734$		0			0
$735$	−3.72875	+	15.0072i	−0.137537	+	0.553548i
$736$		0			0
$737$			6.15676i			0.226787i
$738$		0			0
$739$	−36.7526			−1.35197			−0.675983	−	0.736917i	$-0.736281\pi$
$739$	−36.7526			−1.35197			−0.675983	+	0.736917i	$0.736281\pi$
$740$		0			0
$741$	−54.0866			−1.98692
$742$		0			0
$743$			2.17501i			0.0797933i	0.999204	+	0.0398966i	$0.0127029\pi$
$743$			2.17501i			0.0797933i	−0.999204	+	0.0398966i	$0.987297\pi$
$744$		0			0
$745$	2.73820	+	0.680346i	0.100320	+	0.0249259i
$746$		0			0
$747$			1.70928i			0.0625391i
$748$		0			0
$749$	−3.55640			−0.129948
$750$		0			0
$751$	44.4580			1.62229			0.811147	−	0.584842i	$-0.198843\pi$
$751$	44.4580			1.62229			0.811147	+	0.584842i	$0.198843\pi$
$752$		0			0
$753$			8.28231i			0.301824i
$754$		0			0
$755$	−3.47641	−	0.863763i	−0.126519	−	0.0314356i
$756$		0			0
$757$			26.4247i			0.960422i	0.877153	+	0.480211i	$0.159440\pi$
$757$			26.4247i			0.960422i	−0.877153	+	0.480211i	$0.840560\pi$
$758$		0			0
$759$	4.00000			0.145191
$760$		0			0
$761$	−27.6163			−1.00109			−0.500546	−	0.865710i	$-0.666867\pi$
$761$	−27.6163			−1.00109			−0.500546	+	0.865710i	$0.666867\pi$
$762$		0			0
$763$			1.83549i			0.0664493i
$764$		0			0
$765$	−2.58145	+	10.3896i	−0.0933325	+	0.375638i
$766$		0			0
$767$			25.1096i			0.906654i
$768$		0			0
$769$	−27.8432			−1.00405			−0.502027	−	0.864852i	$-0.667412\pi$
$769$	−27.8432			−1.00405			−0.502027	+	0.864852i	$0.667412\pi$
$770$		0			0
$771$	11.0205			0.396894
$772$		0			0
$773$		−	18.0267i		−	0.648374i	−0.945993	−	0.324187i	$-0.894909\pi$
$773$		−	18.0267i		−	0.648374i	0.945993	−	0.324187i	$-0.105091\pi$
$774$		0			0
$775$	−28.0144	−	14.8371i	−1.00631	−	0.532964i
$776$		0			0
$777$		−	0.993857i		−	0.0356544i
$778$		0			0
$779$	−57.5585			−2.06225
$780$		0			0
$781$	5.07838			0.181719
$782$		0			0
$783$		−	7.41855i		−	0.265117i
$784$		0			0
$785$	−3.83096	+	15.4186i	−0.136733	+	0.550312i
$786$		0			0
$787$			35.6391i			1.27040i	0.772349	+	0.635199i	$0.219082\pi$
$787$			35.6391i			1.27040i	−0.772349	+	0.635199i	$0.780918\pi$
$788$		0			0
$789$	−2.97107			−0.105773
$790$		0			0
$791$	4.79606			0.170528
$792$		0			0
$793$		−	46.5692i		−	1.65372i
$794$		0			0
$795$	−12.4969	−	3.10504i	−0.443220	−	0.110124i
$796$		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)

\(f(q)\)	\(=\)	\(q+1.00000i q^{3} +(2.17009 + 0.539189i) q^{5} +0.290725i q^{7} -1.00000 q^{9} +O(q^{10})\)	\(q+1.00000i q^{3} +(2.17009 + 0.539189i) q^{5} +0.290725i q^{7} -1.00000 q^{9} +1.00000 q^{11} +6.97107i q^{13} +(-0.539189 + 2.17009i) q^{15} -4.78765i q^{17} +7.75872 q^{19} -0.290725 q^{21} -4.00000i q^{23} +(4.41855 + 2.34017i) q^{25} -1.00000i q^{27} +7.41855 q^{29} -6.34017 q^{31} +1.00000i q^{33} +(-0.156755 + 0.630898i) q^{35} +3.41855i q^{37} -6.97107 q^{39} -7.41855 q^{41} -0.290725i q^{43} +(-2.17009 - 0.539189i) q^{45} +5.26180i q^{47} +6.91548 q^{49} +4.78765 q^{51} +5.75872i q^{53} +(2.17009 + 0.539189i) q^{55} +7.75872i q^{57} +3.60197 q^{59} -6.68035 q^{61} -0.290725i q^{63} +(-3.75872 + 15.1278i) q^{65} +6.15676i q^{67} +4.00000 q^{69} +5.07838 q^{71} -1.12783i q^{73} +(-2.34017 + 4.41855i) q^{75} +0.290725i q^{77} -0.921622 q^{79} +1.00000 q^{81} -1.70928i q^{83} +(2.58145 - 10.3896i) q^{85} +7.41855i q^{87} -4.34017 q^{89} -2.02666 q^{91} -6.34017i q^{93} +(16.8371 + 4.18342i) q^{95} -4.68035i q^{97} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{5} - 6 q^{9}+O(q^{10}) \) 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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