LMFDB - Embedded newform 2640.2.d.h.529.4

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			529.4
Root			$0.403032 - 0.403032i$ of defining polynomial
Character	$\chi$	$=$	2640.529
Dual form			2640.2.d.h.529.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{3} +(-1.48119 - 1.67513i) q^{5} -1.19394i q^{7} -1.00000 q^{9} +O(q^{10})$	$q+1.00000i q^{3} +(-1.48119 - 1.67513i) q^{5} -1.19394i q^{7} -1.00000 q^{9} -1.00000 q^{11} -0.806063i q^{13} +(1.67513 - 1.48119i) q^{15} +3.76845i q^{17} -5.35026 q^{19} +1.19394 q^{21} +4.00000i q^{23} +(-0.612127 + 4.96239i) q^{25} -1.00000i q^{27} +4.31265 q^{29} -0.962389 q^{31} -1.00000i q^{33} +(-2.00000 + 1.76845i) q^{35} +1.61213i q^{37} +0.806063 q^{39} +9.08840 q^{41} +4.41819i q^{43} +(1.48119 + 1.67513i) q^{45} -12.3127i q^{47} +5.57452 q^{49} -3.76845 q^{51} -1.42548i q^{53} +(1.48119 + 1.67513i) q^{55} -5.35026i q^{57} +13.2750 q^{59} -0.0752228 q^{61} +1.19394i q^{63} +(-1.35026 + 1.19394i) q^{65} +2.70052i q^{67} -4.00000 q^{69} +14.0508 q^{71} +10.7308i q^{73} +(-4.96239 - 0.612127i) q^{75} +1.19394i q^{77} +13.9756 q^{79} +1.00000 q^{81} -9.89446i q^{83} +(6.31265 - 5.58181i) q^{85} +4.31265i q^{87} -16.8872 q^{89} -0.962389 q^{91} -0.962389i q^{93} +(7.92478 + 8.96239i) q^{95} +11.4763i q^{97} +1.00000 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - 12 q^{19} + 8 q^{21} - 2 q^{25} - 16 q^{29} + 16 q^{31} - 12 q^{35} + 4 q^{39} + 16 q^{41} - 2 q^{45} + 10 q^{49} - 2 q^{55} + 16 q^{59} - 44 q^{61} + 12 q^{65} - 24 q^{69} + 24 q^{71} - 8 q^{75} - 20 q^{79} + 6 q^{81} - 4 q^{85} - 36 q^{89} + 16 q^{91} + 4 q^{95} + 6 q^{99}+O(q^{100}) $ 6 * q + 2 * q^5 - 6 * q^9 - 6 * q^11 - 12 * q^19 + 8 * q^21 - 2 * q^25 - 16 * q^29 + 16 * q^31 - 12 * q^35 + 4 * q^39 + 16 * q^41 - 2 * q^45 + 10 * q^49 - 2 * q^55 + 16 * q^59 - 44 * q^61 + 12 * q^65 - 24 * q^69 + 24 * q^71 - 8 * q^75 - 20 * q^79 + 6 * q^81 - 4 * q^85 - 36 * q^89 + 16 * q^91 + 4 * 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
$5$	−1.48119	−	1.67513i	−0.662410	−	0.749141i
$5$	−1.48119	−	1.67513i	−0.662410	−	0.749141i
$6$		0			0
$7$		−	1.19394i		−	0.451266i	−0.974212	−	0.225633i	$-0.927555\pi$
$7$		−	1.19394i		−	0.451266i	0.974212	−	0.225633i	$-0.0724450\pi$
$8$		0			0
$9$	−1.00000			−0.333333
$10$		0			0
$11$	−1.00000			−0.301511
$11$	−1.00000			−0.301511
$12$		0			0
$13$		−	0.806063i		−	0.223562i	−0.993733	−	0.111781i	$-0.964345\pi$
$13$		−	0.806063i		−	0.223562i	0.993733	−	0.111781i	$-0.0356555\pi$
$14$		0			0
$15$	1.67513	−	1.48119i	0.432517	−	0.382443i
$16$		0			0
$17$			3.76845i			0.913984i	0.889471	+	0.456992i	$0.151073\pi$
$17$			3.76845i			0.913984i	−0.889471	+	0.456992i	$0.848927\pi$
$18$		0			0
$19$	−5.35026			−1.22743			−0.613717	−	0.789526i	$-0.710326\pi$
$19$	−5.35026			−1.22743			−0.613717	+	0.789526i	$0.710326\pi$
$20$		0			0
$21$	1.19394			0.260538
$22$		0			0
$23$			4.00000i			0.834058i	0.908893	+	0.417029i	$0.136929\pi$
$23$			4.00000i			0.834058i	−0.908893	+	0.417029i	$0.863071\pi$
$24$		0			0
$25$	−0.612127	+	4.96239i	−0.122425	+	0.992478i
$26$		0			0
$27$		−	1.00000i		−	0.192450i
$28$		0			0
$29$	4.31265			0.800839			0.400420	−	0.916332i	$-0.368864\pi$
$29$	4.31265			0.800839			0.400420	+	0.916332i	$0.368864\pi$
$30$		0			0
$31$	−0.962389			−0.172850			−0.0864250	−	0.996258i	$-0.527544\pi$
$31$	−0.962389			−0.172850			−0.0864250	+	0.996258i	$0.527544\pi$
$32$		0			0
$33$		−	1.00000i		−	0.174078i
$34$		0			0
$35$	−2.00000	+	1.76845i	−0.338062	+	0.298923i
$36$		0			0
$37$			1.61213i			0.265032i	0.991181	+	0.132516i	$0.0423056\pi$
$37$			1.61213i			0.265032i	−0.991181	+	0.132516i	$0.957694\pi$
$38$		0			0
$39$	0.806063			0.129073
$40$		0			0
$41$	9.08840			1.41937			0.709685	−	0.704520i	$-0.248837\pi$
$41$	9.08840			1.41937			0.709685	+	0.704520i	$0.248837\pi$
$42$		0			0
$43$			4.41819i			0.673768i	0.941546	+	0.336884i	$0.109373\pi$
$43$			4.41819i			0.673768i	−0.941546	+	0.336884i	$0.890627\pi$
$44$		0			0
$45$	1.48119	+	1.67513i	0.220803	+	0.249714i
$46$		0			0
$47$		−	12.3127i		−	1.79598i	−0.440011	−	0.897992i	$-0.645026\pi$
$47$		−	12.3127i		−	1.79598i	0.440011	−	0.897992i	$-0.354974\pi$
$48$		0			0
$49$	5.57452			0.796359
$50$		0			0
$51$	−3.76845			−0.527689
$52$		0			0
$53$		−	1.42548i		−	0.195805i	−0.995196	−	0.0979027i	$-0.968787\pi$
$53$		−	1.42548i		−	0.195805i	0.995196	−	0.0979027i	$-0.0312134\pi$
$54$		0			0
$55$	1.48119	+	1.67513i	0.199724	+	0.225875i
$56$		0			0
$57$		−	5.35026i		−	0.708659i
$58$		0			0
$59$	13.2750			1.72826			0.864131	−	0.503266i	$-0.167868\pi$
$59$	13.2750			1.72826			0.864131	+	0.503266i	$0.167868\pi$
$60$		0			0
$61$	−0.0752228			−0.00963129			−0.00481565	−	0.999988i	$-0.501533\pi$
$61$	−0.0752228			−0.00963129			−0.00481565	+	0.999988i	$0.501533\pi$
$62$		0			0
$63$			1.19394i			0.150422i
$64$		0			0
$65$	−1.35026	+	1.19394i	−0.167479	+	0.148090i
$66$		0			0
$67$			2.70052i			0.329921i	0.986300	+	0.164961i	$0.0527497\pi$
$67$			2.70052i			0.329921i	−0.986300	+	0.164961i	$0.947250\pi$
$68$		0			0
$69$	−4.00000			−0.481543
$70$		0			0
$71$	14.0508			1.66752			0.833761	−	0.552126i	$-0.186183\pi$
$71$	14.0508			1.66752			0.833761	+	0.552126i	$0.186183\pi$
$72$		0			0
$73$			10.7308i			1.25595i	0.778234	+	0.627975i	$0.216116\pi$
$73$			10.7308i			1.25595i	−0.778234	+	0.627975i	$0.783884\pi$
$74$		0			0
$75$	−4.96239	−	0.612127i	−0.573007	−	0.0706823i
$76$		0			0
$77$			1.19394i			0.136062i
$78$		0			0
$79$	13.9756			1.57237			0.786187	−	0.617989i	$-0.212052\pi$
$79$	13.9756			1.57237			0.786187	+	0.617989i	$0.212052\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$		−	9.89446i		−	1.08606i	−0.839714	−	0.543029i	$-0.817277\pi$
$83$		−	9.89446i		−	1.08606i	0.839714	−	0.543029i	$-0.182723\pi$
$84$		0			0
$85$	6.31265	−	5.58181i	0.684703	−	0.605432i
$86$		0			0
$87$			4.31265i			0.462365i
$88$		0			0
$89$	−16.8872			−1.79004			−0.895018	−	0.446030i	$-0.852837\pi$
$89$	−16.8872			−1.79004			−0.895018	+	0.446030i	$0.852837\pi$
$90$		0			0
$91$	−0.962389			−0.100886
$92$		0			0
$93$		−	0.962389i		−	0.0997950i
$94$		0			0
$95$	7.92478	+	8.96239i	0.813065	+	0.919522i
$96$		0			0
$97$			11.4763i			1.16524i	0.812745	+	0.582619i	$0.197972\pi$
$97$			11.4763i			1.16524i	−0.812745	+	0.582619i	$0.802028\pi$
$98$		0			0
$99$	1.00000			0.100504
$100$		0			0
$101$	10.7612			1.07078			0.535388	−	0.844606i	$-0.320166\pi$
$101$	10.7612			1.07078			0.535388	+	0.844606i	$0.320166\pi$
$102$		0			0
$103$			16.9380i			1.66895i	0.551049	+	0.834473i	$0.314228\pi$
$103$			16.9380i			1.66895i	−0.551049	+	0.834473i	$0.685772\pi$
$104$		0			0
$105$	−1.76845	−	2.00000i	−0.172583	−	0.195180i
$106$		0			0
$107$		−	8.28233i		−	0.800683i	−0.916366	−	0.400342i	$-0.868891\pi$
$107$		−	8.28233i		−	0.800683i	0.916366	−	0.400342i	$-0.131109\pi$
$108$		0			0
$109$	10.0000			0.957826			0.478913	−	0.877862i	$-0.341031\pi$
$109$	10.0000			0.957826			0.478913	+	0.877862i	$0.341031\pi$
$110$		0			0
$111$	−1.61213			−0.153016
$112$		0			0
$113$		−	2.26187i		−	0.212778i	−0.994325	−	0.106389i	$-0.966071\pi$
$113$		−	2.26187i		−	0.212778i	0.994325	−	0.106389i	$-0.0339289\pi$
$114$		0			0
$115$	6.70052	−	5.92478i	0.624827	−	0.552488i
$116$		0			0
$117$			0.806063i			0.0745206i
$118$		0			0
$119$	4.49929			0.412449
$120$		0			0
$121$	1.00000			0.0909091
$122$		0			0
$123$			9.08840i			0.819473i
$124$		0			0
$125$	9.21933	−	6.32487i	0.824602	−	0.565713i
$126$		0			0
$127$			13.8192i			1.22626i	0.789982	+	0.613130i	$0.210090\pi$
$127$			13.8192i			1.22626i	−0.789982	+	0.613130i	$0.789910\pi$
$128$		0			0
$129$	−4.41819			−0.389000
$130$		0			0
$131$	5.92478			0.517650			0.258825	−	0.965924i	$-0.416665\pi$
$131$	5.92478			0.517650			0.258825	+	0.965924i	$0.416665\pi$
$132$		0			0
$133$			6.38787i			0.553899i
$134$		0			0
$135$	−1.67513	+	1.48119i	−0.144172	+	0.127481i
$136$		0			0
$137$			3.35026i			0.286232i	0.989706	+	0.143116i	$0.0457122\pi$
$137$			3.35026i			0.286232i	−0.989706	+	0.143116i	$0.954288\pi$
$138$		0			0
$139$	−21.1998			−1.79814			−0.899072	−	0.437800i	$-0.855758\pi$
$139$	−21.1998			−1.79814			−0.899072	+	0.437800i	$0.855758\pi$
$140$		0			0
$141$	12.3127			1.03691
$142$		0			0
$143$			0.806063i			0.0674064i
$144$		0			0
$145$	−6.38787	−	7.22425i	−0.530484	−	0.599942i
$146$		0			0
$147$			5.57452i			0.459778i
$148$		0			0
$149$	−6.38787			−0.523315			−0.261657	−	0.965161i	$-0.584269\pi$
$149$	−6.38787			−0.523315			−0.261657	+	0.965161i	$0.584269\pi$
$150$		0			0
$151$	2.64974			0.215633			0.107816	−	0.994171i	$-0.465614\pi$
$151$	2.64974			0.215633			0.107816	+	0.994171i	$0.465614\pi$
$152$		0			0
$153$		−	3.76845i		−	0.304661i
$154$		0			0
$155$	1.42548	+	1.61213i	0.114498	+	0.129489i
$156$		0			0
$157$			1.61213i			0.128662i	0.997929	+	0.0643309i	$0.0204913\pi$
$157$			1.61213i			0.128662i	−0.997929	+	0.0643309i	$0.979509\pi$
$158$		0			0
$159$	1.42548			0.113048
$160$		0			0
$161$	4.77575			0.376382
$162$		0			0
$163$		−	0.312650i		−	0.0244887i	−0.999925	−	0.0122443i	$-0.996102\pi$
$163$		−	0.312650i		−	0.0244887i	0.999925	−	0.0122443i	$-0.00389759\pi$
$164$		0			0
$165$	−1.67513	+	1.48119i	−0.130409	+	0.115311i
$166$		0			0
$167$		−	0.493413i		−	0.0381815i	−0.999818	−	0.0190907i	$-0.993923\pi$
$167$		−	0.493413i		−	0.0381815i	0.999818	−	0.0190907i	$-0.00607714\pi$
$168$		0			0
$169$	12.3503			0.950020
$170$		0			0
$171$	5.35026			0.409145
$172$		0			0
$173$			23.3054i			1.77187i	0.463806	+	0.885937i	$0.346483\pi$
$173$			23.3054i			1.77187i	−0.463806	+	0.885937i	$0.653517\pi$
$174$		0			0
$175$	5.92478	+	0.730841i	0.447871	+	0.0552464i
$176$		0			0
$177$			13.2750i			0.997813i
$178$		0			0
$179$	−10.7005			−0.799795			−0.399897	−	0.916560i	$-0.630954\pi$
$179$	−10.7005			−0.799795			−0.399897	+	0.916560i	$0.630954\pi$
$180$		0			0
$181$	−7.79877			−0.579678			−0.289839	−	0.957075i	$-0.593602\pi$
$181$	−7.79877			−0.579678			−0.289839	+	0.957075i	$0.593602\pi$
$182$		0			0
$183$		−	0.0752228i		−	0.00556063i
$184$		0			0
$185$	2.70052	−	2.38787i	0.198546	−	0.175560i
$186$		0			0
$187$		−	3.76845i		−	0.275577i
$188$		0			0
$189$	−1.19394			−0.0868461
$190$		0			0
$191$	−1.29948			−0.0940268			−0.0470134	−	0.998894i	$-0.514970\pi$
$191$	−1.29948			−0.0940268			−0.0470134	+	0.998894i	$0.514970\pi$
$192$		0			0
$193$		−	8.59498i		−	0.618680i	−0.950951	−	0.309340i	$-0.899892\pi$
$193$		−	8.59498i		−	0.618680i	0.950951	−	0.309340i	$-0.100108\pi$
$194$		0			0
$195$	−1.19394	−	1.35026i	−0.0854996	−	0.0966943i
$196$		0			0
$197$		−	20.7064i		−	1.47527i	−0.675200	−	0.737635i	$-0.735943\pi$
$197$		−	20.7064i		−	1.47527i	0.675200	−	0.737635i	$-0.264057\pi$
$198$		0			0
$199$	5.55149			0.393535			0.196767	−	0.980450i	$-0.436956\pi$
$199$	5.55149			0.393535			0.196767	+	0.980450i	$0.436956\pi$
$200$		0			0
$201$	−2.70052			−0.190480
$202$		0			0
$203$		−	5.14903i		−	0.361391i
$204$		0			0
$205$	−13.4617	−	15.2243i	−0.940205	−	1.06331i
$206$		0			0
$207$		−	4.00000i		−	0.278019i
$208$		0			0
$209$	5.35026			0.370085
$210$		0			0
$211$	18.4993			1.27354			0.636772	−	0.771052i	$-0.280269\pi$
$211$	18.4993			1.27354			0.636772	+	0.771052i	$0.280269\pi$
$212$		0			0
$213$			14.0508i			0.962744i
$214$		0			0
$215$	7.40105	−	6.54420i	0.504747	−	0.446311i
$216$		0			0
$217$			1.14903i			0.0780013i
$218$		0			0
$219$	−10.7308			−0.725123
$220$		0			0
$221$	3.03761			0.204332
$222$		0			0
$223$			17.6121i			1.17940i	0.807624	+	0.589698i	$0.200753\pi$
$223$			17.6121i			1.17940i	−0.807624	+	0.589698i	$0.799247\pi$
$224$		0			0
$225$	0.612127	−	4.96239i	0.0408085	−	0.330826i
$226$		0			0
$227$			17.4314i			1.15696i	0.815696	+	0.578480i	$0.196354\pi$
$227$			17.4314i			1.15696i	−0.815696	+	0.578480i	$0.803646\pi$
$228$		0			0
$229$	−13.0738			−0.863942			−0.431971	−	0.901888i	$-0.642182\pi$
$229$	−13.0738			−0.863942			−0.431971	+	0.901888i	$0.642182\pi$
$230$		0			0
$231$	−1.19394			−0.0785553
$232$		0			0
$233$			13.8437i			0.906929i	0.891274	+	0.453465i	$0.149812\pi$
$233$			13.8437i			0.906929i	−0.891274	+	0.453465i	$0.850188\pi$
$234$		0			0
$235$	−20.6253	+	18.2374i	−1.34545	+	1.18968i
$236$		0			0
$237$			13.9756i			0.907810i
$238$		0			0
$239$	−12.3733			−0.800361			−0.400181	−	0.916436i	$-0.631053\pi$
$239$	−12.3733			−0.800361			−0.400181	+	0.916436i	$0.631053\pi$
$240$		0			0
$241$	−24.5501			−1.58141			−0.790705	−	0.612198i	$-0.790286\pi$
$241$	−24.5501			−1.58141			−0.790705	+	0.612198i	$0.790286\pi$
$242$		0			0
$243$			1.00000i			0.0641500i
$244$		0			0
$245$	−8.25694	−	9.33804i	−0.527517	−	0.596586i
$246$		0			0
$247$			4.31265i			0.274407i
$248$		0			0
$249$	9.89446			0.627036
$250$		0			0
$251$	−13.9003			−0.877382			−0.438691	−	0.898638i	$-0.644558\pi$
$251$	−13.9003			−0.877382			−0.438691	+	0.898638i	$0.644558\pi$
$252$		0			0
$253$		−	4.00000i		−	0.251478i
$254$		0			0
$255$	5.58181	+	6.31265i	0.349546	+	0.395313i
$256$		0			0
$257$		−	18.8872i		−	1.17815i	−0.808079	−	0.589075i	$-0.799492\pi$
$257$		−	18.8872i		−	1.17815i	0.808079	−	0.589075i	$-0.200508\pi$
$258$		0			0
$259$	1.92478			0.119600
$260$		0			0
$261$	−4.31265			−0.266946
$262$		0			0
$263$			20.8061i			1.28296i	0.767141	+	0.641478i	$0.221679\pi$
$263$			20.8061i			1.28296i	−0.767141	+	0.641478i	$0.778321\pi$
$264$		0			0
$265$	−2.38787	+	2.11142i	−0.146686	+	0.129703i
$266$		0			0
$267$		−	16.8872i		−	1.03348i
$268$		0			0
$269$	32.3996			1.97544			0.987720	−	0.156233i	$-0.0499351\pi$
$269$	32.3996			1.97544			0.987720	+	0.156233i	$0.0499351\pi$
$270$		0			0
$271$	16.8265			1.02214			0.511069	−	0.859539i	$-0.329249\pi$
$271$	16.8265			1.02214			0.511069	+	0.859539i	$0.329249\pi$
$272$		0			0
$273$		−	0.962389i		−	0.0582464i
$274$		0			0
$275$	0.612127	−	4.96239i	0.0369126	−	0.299243i
$276$		0			0
$277$			16.9076i			1.01588i	0.861392	+	0.507941i	$0.169593\pi$
$277$			16.9076i			1.01588i	−0.861392	+	0.507941i	$0.830407\pi$
$278$		0			0
$279$	0.962389			0.0576167
$280$		0			0
$281$	5.61213			0.334791			0.167396	−	0.985890i	$-0.446464\pi$
$281$	5.61213			0.334791			0.167396	+	0.985890i	$0.446464\pi$
$282$		0			0
$283$			5.81924i			0.345918i	0.984929	+	0.172959i	$0.0553328\pi$
$283$			5.81924i			0.345918i	−0.984929	+	0.172959i	$0.944667\pi$
$284$		0			0
$285$	−8.96239	+	7.92478i	−0.530886	+	0.469423i
$286$		0			0
$287$		−	10.8510i		−	0.640512i
$288$		0			0
$289$	2.79877			0.164633
$290$		0			0
$291$	−11.4763			−0.672751
$292$		0			0
$293$			8.29218i			0.484434i	0.970222	+	0.242217i	$0.0778747\pi$
$293$			8.29218i			0.484434i	−0.970222	+	0.242217i	$0.922125\pi$
$294$		0			0
$295$	−19.6629	−	22.2374i	−1.14482	−	1.29471i
$296$		0			0
$297$			1.00000i			0.0580259i
$298$		0			0
$299$	3.22425			0.186463
$300$		0			0
$301$	5.27504			0.304048
$302$		0			0
$303$			10.7612i			0.618212i
$304$		0			0
$305$	0.111420	+	0.126008i	0.00637987	+	0.00721520i
$306$		0			0
$307$		−	25.6688i		−	1.46500i	−0.680770	−	0.732498i	$-0.738354\pi$
$307$		−	25.6688i		−	1.46500i	0.680770	−	0.732498i	$-0.261646\pi$
$308$		0			0
$309$	−16.9380			−0.963566
$310$		0			0
$311$	15.7235			0.891601			0.445800	−	0.895132i	$-0.352919\pi$
$311$	15.7235			0.891601			0.445800	+	0.895132i	$0.352919\pi$
$312$		0			0
$313$			26.8627i			1.51837i	0.650874	+	0.759186i	$0.274403\pi$
$313$			26.8627i			1.51837i	−0.650874	+	0.759186i	$0.725597\pi$
$314$		0			0
$315$	2.00000	−	1.76845i	0.112687	−	0.0996410i
$316$		0			0
$317$			0.710373i			0.0398985i	0.999801	+	0.0199492i	$0.00635046\pi$
$317$			0.710373i			0.0398985i	−0.999801	+	0.0199492i	$0.993650\pi$
$318$		0			0
$319$	−4.31265			−0.241462
$320$		0			0
$321$	8.28233			0.462275
$322$		0			0
$323$		−	20.1622i		−	1.12186i
$324$		0			0
$325$	4.00000	+	0.493413i	0.221880	+	0.0273696i
$326$		0			0
$327$			10.0000i			0.553001i
$328$		0			0
$329$	−14.7005			−0.810466
$330$		0			0
$331$	−0.962389			−0.0528977			−0.0264488	−	0.999650i	$-0.508420\pi$
$331$	−0.962389			−0.0528977			−0.0264488	+	0.999650i	$0.508420\pi$
$332$		0			0
$333$		−	1.61213i		−	0.0883440i
$334$		0			0
$335$	4.52373	−	4.00000i	0.247158	−	0.218543i
$336$		0			0
$337$			19.8192i			1.07962i	0.841786	+	0.539811i	$0.181504\pi$
$337$			19.8192i			1.07962i	−0.841786	+	0.539811i	$0.818496\pi$
$338$		0			0
$339$	2.26187			0.122848
$340$		0			0
$341$	0.962389			0.0521163
$342$		0			0
$343$		−	15.0132i		−	0.810635i
$344$		0			0
$345$	5.92478	+	6.70052i	0.318979	+	0.360744i
$346$		0			0
$347$		−	6.20711i		−	0.333215i	−0.986023	−	0.166608i	$-0.946719\pi$
$347$		−	6.20711i		−	0.333215i	0.986023	−	0.166608i	$-0.0532813\pi$
$348$		0			0
$349$	−4.44851			−0.238123			−0.119062	−	0.992887i	$-0.537989\pi$
$349$	−4.44851			−0.238123			−0.119062	+	0.992887i	$0.537989\pi$
$350$		0			0
$351$	−0.806063			−0.0430245
$352$		0			0
$353$		−	6.57452i		−	0.349926i	−0.984575	−	0.174963i	$-0.944019\pi$
$353$		−	6.57452i		−	0.349926i	0.984575	−	0.174963i	$-0.0559806\pi$
$354$		0			0
$355$	−20.8119	−	23.5369i	−1.10458	−	1.24921i
$356$		0			0
$357$			4.49929i			0.238128i
$358$		0			0
$359$	8.62530			0.455226			0.227613	−	0.973752i	$-0.426908\pi$
$359$	8.62530			0.455226			0.227613	+	0.973752i	$0.426908\pi$
$360$		0			0
$361$	9.62530			0.506595
$362$		0			0
$363$			1.00000i			0.0524864i
$364$		0			0
$365$	17.9756	−	15.8945i	0.940884	−	0.831954i
$366$		0			0
$367$		−	23.0132i		−	1.20128i	−0.799520	−	0.600639i	$-0.794913\pi$
$367$		−	23.0132i		−	1.20128i	0.799520	−	0.600639i	$-0.205087\pi$
$368$		0			0
$369$	−9.08840			−0.473123
$370$		0			0
$371$	−1.70194			−0.0883602
$372$		0			0
$373$		−	28.1925i		−	1.45975i	−0.683579	−	0.729877i	$-0.739577\pi$
$373$		−	28.1925i		−	1.45975i	0.683579	−	0.729877i	$-0.260423\pi$
$374$		0			0
$375$	6.32487	+	9.21933i	0.326615	+	0.476084i
$376$		0			0
$377$		−	3.47627i		−	0.179037i
$378$		0			0
$379$	3.74798			0.192521			0.0962605	−	0.995356i	$-0.469312\pi$
$379$	3.74798			0.192521			0.0962605	+	0.995356i	$0.469312\pi$
$380$		0			0
$381$	−13.8192			−0.707981
$382$		0			0
$383$			1.76257i			0.0900632i	0.998986	+	0.0450316i	$0.0143389\pi$
$383$			1.76257i			0.0900632i	−0.998986	+	0.0450316i	$0.985661\pi$
$384$		0			0
$385$	2.00000	−	1.76845i	0.101929	−	0.0901287i
$386$		0			0
$387$		−	4.41819i		−	0.224589i
$388$		0			0
$389$	−6.52373			−0.330766			−0.165383	−	0.986229i	$-0.552886\pi$
$389$	−6.52373			−0.330766			−0.165383	+	0.986229i	$0.552886\pi$
$390$		0			0
$391$	−15.0738			−0.762315
$392$		0			0
$393$			5.92478i			0.298865i
$394$		0			0
$395$	−20.7005	−	23.4109i	−1.04156	−	1.17793i
$396$		0			0
$397$		−	23.6991i		−	1.18942i	−0.803939	−	0.594712i	$-0.797266\pi$
$397$		−	23.6991i		−	1.18942i	0.803939	−	0.594712i	$-0.202734\pi$
$398$		0			0
$399$	−6.38787			−0.319794
$400$		0			0
$401$	8.88717			0.443804			0.221902	−	0.975069i	$-0.428774\pi$
$401$	8.88717			0.443804			0.221902	+	0.975069i	$0.428774\pi$
$402$		0			0
$403$			0.775746i			0.0386427i
$404$		0			0
$405$	−1.48119	−	1.67513i	−0.0736011	−	0.0832379i
$406$		0			0
$407$		−	1.61213i		−	0.0799102i
$408$		0			0
$409$	4.85097			0.239865			0.119932	−	0.992782i	$-0.461732\pi$
$409$	4.85097			0.239865			0.119932	+	0.992782i	$0.461732\pi$
$410$		0			0
$411$	−3.35026			−0.165256
$412$		0			0
$413$		−	15.8496i		−	0.779906i
$414$		0			0
$415$	−16.5745	+	14.6556i	−0.813611	+	0.719416i
$416$		0			0
$417$		−	21.1998i		−	1.03816i
$418$		0			0
$419$	−10.7005			−0.522755			−0.261377	−	0.965237i	$-0.584177\pi$
$419$	−10.7005			−0.522755			−0.261377	+	0.965237i	$0.584177\pi$
$420$		0			0
$421$	−30.6009			−1.49139			−0.745697	−	0.666285i	$-0.767884\pi$
$421$	−30.6009			−1.49139			−0.745697	+	0.666285i	$0.767884\pi$
$422$		0			0
$423$			12.3127i			0.598662i
$424$		0			0
$425$	−18.7005	−	2.30677i	−0.907109	−	0.111895i
$426$		0			0
$427$			0.0898112i			0.00434627i
$428$		0			0
$429$	−0.806063			−0.0389171
$430$		0			0
$431$	5.92478			0.285386			0.142693	−	0.989767i	$-0.454424\pi$
$431$	5.92478			0.285386			0.142693	+	0.989767i	$0.454424\pi$
$432$		0			0
$433$			16.0000i			0.768911i	0.923144	+	0.384455i	$0.125611\pi$
$433$			16.0000i			0.768911i	−0.923144	+	0.384455i	$0.874389\pi$
$434$		0			0
$435$	7.22425	−	6.38787i	0.346376	−	0.306275i
$436$		0			0
$437$		−	21.4010i		−	1.02375i
$438$		0			0
$439$	5.35026			0.255354			0.127677	−	0.991816i	$-0.459248\pi$
$439$	5.35026			0.255354			0.127677	+	0.991816i	$0.459248\pi$
$440$		0			0
$441$	−5.57452			−0.265453
$442$		0			0
$443$			19.6873i			0.935374i	0.883894	+	0.467687i	$0.154913\pi$
$443$			19.6873i			0.935374i	−0.883894	+	0.467687i	$0.845087\pi$
$444$		0			0
$445$	25.0132	+	28.2882i	1.18574	+	1.34099i
$446$		0			0
$447$		−	6.38787i		−	0.302136i
$448$		0			0
$449$	31.3357			1.47882			0.739411	−	0.673254i	$-0.235104\pi$
$449$	31.3357			1.47882			0.739411	+	0.673254i	$0.235104\pi$
$450$		0			0
$451$	−9.08840			−0.427956
$452$		0			0
$453$			2.64974i			0.124496i
$454$		0			0
$455$	1.42548	+	1.61213i	0.0668277	+	0.0755777i
$456$		0			0
$457$		−	37.5936i		−	1.75855i	−0.476312	−	0.879276i	$-0.658027\pi$
$457$		−	37.5936i		−	1.75855i	0.476312	−	0.879276i	$-0.341973\pi$
$458$		0			0
$459$	3.76845			0.175896
$460$		0			0
$461$	17.9854			0.837664			0.418832	−	0.908064i	$-0.362440\pi$
$461$	17.9854			0.837664			0.418832	+	0.908064i	$0.362440\pi$
$462$		0			0
$463$			39.0132i			1.81310i	0.422103	+	0.906548i	$0.361292\pi$
$463$			39.0132i			1.81310i	−0.422103	+	0.906548i	$0.638708\pi$
$464$		0			0
$465$	−1.61213	+	1.42548i	−0.0747606	+	0.0661053i
$466$		0			0
$467$		−	14.5501i		−	0.673297i	−0.941630	−	0.336649i	$-0.890707\pi$
$467$		−	14.5501i		−	0.673297i	0.941630	−	0.336649i	$-0.109293\pi$
$468$		0			0
$469$	3.22425			0.148882
$470$		0			0
$471$	−1.61213			−0.0742829
$472$		0			0
$473$		−	4.41819i		−	0.203149i
$474$		0			0
$475$	3.27504	−	26.5501i	0.150269	−	1.21820i
$476$		0			0
$477$			1.42548i			0.0652685i
$478$		0			0
$479$	28.6253			1.30792			0.653962	−	0.756528i	$-0.273106\pi$
$479$	28.6253			1.30792			0.653962	+	0.756528i	$0.273106\pi$
$480$		0			0
$481$	1.29948			0.0592510
$482$		0			0
$483$			4.77575i			0.217304i
$484$		0			0
$485$	19.2243	−	16.9986i	0.872928	−	0.771866i
$486$		0			0
$487$		−	1.44992i		−	0.0657022i	−0.999460	−	0.0328511i	$-0.989541\pi$
$487$		−	1.44992i		−	0.0657022i	0.999460	−	0.0328511i	$-0.0104587\pi$
$488$		0			0
$489$	0.312650			0.0141385
$490$		0			0
$491$	8.00000			0.361035			0.180517	−	0.983572i	$-0.442223\pi$
$491$	8.00000			0.361035			0.180517	+	0.983572i	$0.442223\pi$
$492$		0			0
$493$			16.2520i			0.731954i
$494$		0			0
$495$	−1.48119	−	1.67513i	−0.0665747	−	0.0752915i
$496$		0			0
$497$		−	16.7757i		−	0.752495i
$498$		0			0
$499$	30.7005			1.37434			0.687172	−	0.726495i	$-0.258852\pi$
$499$	30.7005			1.37434			0.687172	+	0.726495i	$0.258852\pi$
$500$		0			0
$501$	0.493413			0.0220441
$502$		0			0
$503$		−	19.7586i		−	0.880993i	−0.897754	−	0.440496i	$-0.854802\pi$
$503$		−	19.7586i		−	0.880993i	0.897754	−	0.440496i	$-0.145198\pi$
$504$		0			0
$505$	−15.9394	−	18.0263i	−0.709292	−	0.802162i
$506$		0			0
$507$			12.3503i			0.548494i
$508$		0			0
$509$	−22.1016			−0.979635			−0.489817	−	0.871825i	$-0.662937\pi$
$509$	−22.1016			−0.979635			−0.489817	+	0.871825i	$0.662937\pi$
$510$		0			0
$511$	12.8119			0.566767
$512$		0			0
$513$			5.35026i			0.236220i
$514$		0			0
$515$	28.3733	−	25.0884i	1.25028	−	1.10553i
$516$		0			0
$517$			12.3127i			0.541510i
$518$		0			0
$519$	−23.3054			−1.02299
$520$		0			0
$521$	−22.8119			−0.999409			−0.499705	−	0.866196i	$-0.666558\pi$
$521$	−22.8119			−0.999409			−0.499705	+	0.866196i	$0.666558\pi$
$522$		0			0
$523$		−	12.2677i		−	0.536431i	−0.963359	−	0.268216i	$-0.913566\pi$
$523$		−	12.2677i		−	0.536431i	0.963359	−	0.268216i	$-0.0864339\pi$
$524$		0			0
$525$	−0.730841	+	5.92478i	−0.0318965	+	0.258578i
$526$		0			0
$527$		−	3.62672i		−	0.157982i
$528$		0			0
$529$	7.00000			0.304348
$530$		0			0
$531$	−13.2750			−0.576088
$532$		0			0
$533$		−	7.32582i		−	0.317317i
$534$		0			0
$535$	−13.8740	+	12.2677i	−0.599825	+	0.530381i
$536$		0			0
$537$		−	10.7005i		−	0.461762i
$538$		0			0
$539$	−5.57452			−0.240111
$540$		0			0
$541$	−5.22425			−0.224608			−0.112304	−	0.993674i	$-0.535823\pi$
$541$	−5.22425			−0.224608			−0.112304	+	0.993674i	$0.535823\pi$
$542$		0			0
$543$		−	7.79877i		−	0.334677i
$544$		0			0
$545$	−14.8119	−	16.7513i	−0.634474	−	0.717547i
$546$		0			0
$547$			17.9697i			0.768328i	0.923265	+	0.384164i	$0.125510\pi$
$547$			17.9697i			0.768328i	−0.923265	+	0.384164i	$0.874490\pi$
$548$		0			0
$549$	0.0752228			0.00321043
$550$		0			0
$551$	−23.0738			−0.982977
$552$		0			0
$553$		−	16.6859i		−	0.709558i
$554$		0			0
$555$	2.38787	+	2.70052i	0.101360	+	0.114631i
$556$		0			0
$557$			15.8700i			0.672434i	0.941784	+	0.336217i	$0.109148\pi$
$557$			15.8700i			0.672434i	−0.941784	+	0.336217i	$0.890852\pi$
$558$		0			0
$559$	3.56134			0.150629
$560$		0			0
$561$	3.76845			0.159104
$562$		0			0
$563$			31.6688i			1.33468i	0.744753	+	0.667340i	$0.232567\pi$
$563$			31.6688i			1.33468i	−0.744753	+	0.667340i	$0.767433\pi$
$564$		0			0
$565$	−3.78892	+	3.35026i	−0.159401	+	0.140947i
$566$		0			0
$567$		−	1.19394i		−	0.0501406i
$568$		0			0
$569$	24.3127			1.01924			0.509620	−	0.860400i	$-0.329786\pi$
$569$	24.3127			1.01924			0.509620	+	0.860400i	$0.329786\pi$
$570$		0			0
$571$	−8.05079			−0.336915			−0.168457	−	0.985709i	$-0.553879\pi$
$571$	−8.05079			−0.336915			−0.168457	+	0.985709i	$0.553879\pi$
$572$		0			0
$573$		−	1.29948i		−	0.0542864i
$574$		0			0
$575$	−19.8496	−	2.44851i	−0.827784	−	0.102110i
$576$		0			0
$577$		−	44.5355i		−	1.85404i	−0.375016	−	0.927018i	$-0.622363\pi$
$577$		−	44.5355i		−	1.85404i	0.375016	−	0.927018i	$-0.377637\pi$
$578$		0			0
$579$	8.59498			0.357195
$580$		0			0
$581$	−11.8134			−0.490101
$582$		0			0
$583$			1.42548i			0.0590375i
$584$		0			0
$585$	1.35026	−	1.19394i	0.0558265	−	0.0493632i
$586$		0			0
$587$			15.4763i			0.638774i	0.947624	+	0.319387i	$0.103477\pi$
$587$			15.4763i			0.638774i	−0.947624	+	0.319387i	$0.896523\pi$
$588$		0			0
$589$	5.14903			0.212162
$590$		0			0
$591$	20.7064			0.851748
$592$		0			0
$593$			9.53102i			0.391392i	0.980665	+	0.195696i	$0.0626966\pi$
$593$			9.53102i			0.391392i	−0.980665	+	0.195696i	$0.937303\pi$
$594$		0			0
$595$	−6.66433	−	7.53690i	−0.273211	−	0.308983i
$596$		0			0
$597$			5.55149i			0.227207i
$598$		0			0
$599$	−25.5515			−1.04401			−0.522003	−	0.852944i	$-0.674815\pi$
$599$	−25.5515			−1.04401			−0.522003	+	0.852944i	$0.674815\pi$
$600$		0			0
$601$	12.0263			0.490565			0.245282	−	0.969452i	$-0.421119\pi$
$601$	12.0263			0.490565			0.245282	+	0.969452i	$0.421119\pi$
$602$		0			0
$603$		−	2.70052i		−	0.109974i
$604$		0			0
$605$	−1.48119	−	1.67513i	−0.0602191	−	0.0681038i
$606$		0			0
$607$			6.86670i			0.278711i	0.990242	+	0.139355i	$0.0445030\pi$
$607$			6.86670i			0.278711i	−0.990242	+	0.139355i	$0.955497\pi$
$608$		0			0
$609$	5.14903			0.208649
$610$		0			0
$611$	−9.92478			−0.401514
$612$		0			0
$613$			7.25457i			0.293009i	0.989210	+	0.146505i	$0.0468023\pi$
$613$			7.25457i			0.293009i	−0.989210	+	0.146505i	$0.953198\pi$
$614$		0			0
$615$	15.2243	−	13.4617i	0.613901	−	0.542827i
$616$		0			0
$617$			38.3634i			1.54445i	0.635347	+	0.772227i	$0.280857\pi$
$617$			38.3634i			1.54445i	−0.635347	+	0.772227i	$0.719143\pi$
$618$		0			0
$619$	−29.6893			−1.19331			−0.596656	−	0.802497i	$-0.703504\pi$
$619$	−29.6893			−1.19331			−0.596656	+	0.802497i	$0.703504\pi$
$620$		0			0
$621$	4.00000			0.160514
$622$		0			0
$623$			20.1622i			0.807782i
$624$		0			0
$625$	−24.2506	−	6.07522i	−0.970024	−	0.243009i
$626$		0			0
$627$			5.35026i			0.213669i
$628$		0			0
$629$	−6.07522			−0.242235
$630$		0			0
$631$	19.6991			0.784209			0.392105	−	0.919921i	$-0.371747\pi$
$631$	19.6991			0.784209			0.392105	+	0.919921i	$0.371747\pi$
$632$		0			0
$633$			18.4993i			0.735281i
$634$		0			0
$635$	23.1490	−	20.4690i	0.918641	−	0.812287i
$636$		0			0
$637$		−	4.49341i		−	0.178036i
$638$		0			0
$639$	−14.0508			−0.555840
$640$		0			0
$641$	−31.4372			−1.24170			−0.620848	−	0.783931i	$-0.713212\pi$
$641$	−31.4372			−1.24170			−0.620848	+	0.783931i	$0.713212\pi$
$642$		0			0
$643$		−	34.4894i		−	1.36013i	−0.733151	−	0.680065i	$-0.761951\pi$
$643$		−	34.4894i		−	1.36013i	0.733151	−	0.680065i	$-0.238049\pi$
$644$		0			0
$645$	6.54420	+	7.40105i	0.257678	+	0.291416i
$646$		0			0
$647$			5.61213i			0.220635i	0.993896	+	0.110318i	$0.0351868\pi$
$647$			5.61213i			0.220635i	−0.993896	+	0.110318i	$0.964813\pi$
$648$		0			0
$649$	−13.2750			−0.521091
$650$		0			0
$651$	−1.14903			−0.0450341
$652$		0			0
$653$		−	4.06537i		−	0.159090i	−0.996831	−	0.0795452i	$-0.974653\pi$
$653$		−	4.06537i		−	0.159090i	0.996831	−	0.0795452i	$-0.0253468\pi$
$654$		0			0
$655$	−8.77575	−	9.92478i	−0.342897	−	0.387793i
$656$		0			0
$657$		−	10.7308i		−	0.418650i
$658$		0			0
$659$	11.3747			0.443095			0.221548	−	0.975150i	$-0.428889\pi$
$659$	11.3747			0.443095			0.221548	+	0.975150i	$0.428889\pi$
$660$		0			0
$661$	−42.4749			−1.65208			−0.826040	−	0.563611i	$-0.809412\pi$
$661$	−42.4749			−1.65208			−0.826040	+	0.563611i	$0.809412\pi$
$662$		0			0
$663$			3.03761i			0.117971i
$664$		0			0
$665$	10.7005	−	9.46168i	0.414949	−	0.366908i
$666$		0			0
$667$			17.2506i			0.667946i
$668$		0			0
$669$	−17.6121			−0.680924
$670$		0			0
$671$	0.0752228			0.00290394
$672$		0			0
$673$			14.8813i			0.573631i	0.957986	+	0.286816i	$0.0925967\pi$
$673$			14.8813i			0.573631i	−0.957986	+	0.286816i	$0.907403\pi$
$674$		0			0
$675$	4.96239	+	0.612127i	0.191002	+	0.0235608i
$676$		0			0
$677$		−	27.7685i		−	1.06723i	−0.845728	−	0.533614i	$-0.820833\pi$
$677$		−	27.7685i		−	1.06723i	0.845728	−	0.533614i	$-0.179167\pi$
$678$		0			0
$679$	13.7019			0.525832
$680$		0			0
$681$	−17.4314			−0.667971
$682$		0			0
$683$		−	25.4617i		−	0.974264i	−0.873328	−	0.487132i	$-0.838043\pi$
$683$		−	25.4617i		−	0.974264i	0.873328	−	0.487132i	$-0.161957\pi$
$684$		0			0
$685$	5.61213	−	4.96239i	0.214428	−	0.189603i
$686$		0			0
$687$		−	13.0738i		−	0.498797i
$688$		0			0
$689$	−1.14903			−0.0437746
$690$		0			0
$691$	−43.6991			−1.66239			−0.831196	−	0.555979i	$-0.812343\pi$
$691$	−43.6991			−1.66239			−0.831196	+	0.555979i	$0.812343\pi$
$692$		0			0
$693$		−	1.19394i		−	0.0453539i
$694$		0			0
$695$	31.4010	+	35.5125i	1.19111	+	1.34706i
$696$		0			0
$697$			34.2492i			1.29728i
$698$		0			0
$699$	−13.8437			−0.523616
$700$		0			0
$701$	7.01317			0.264884			0.132442	−	0.991191i	$-0.457718\pi$
$701$	7.01317			0.264884			0.132442	+	0.991191i	$0.457718\pi$
$702$		0			0
$703$		−	8.62530i		−	0.325309i
$704$		0			0
$705$	−18.2374	−	20.6253i	−0.686861	−	0.776794i
$706$		0			0
$707$		−	12.8481i		−	0.483204i
$708$		0			0
$709$	−45.6747			−1.71535			−0.857674	−	0.514194i	$-0.828091\pi$
$709$	−45.6747			−1.71535			−0.857674	+	0.514194i	$0.828091\pi$
$710$		0			0
$711$	−13.9756			−0.524125
$712$		0			0
$713$		−	3.84955i		−	0.144167i
$714$		0			0
$715$	1.35026	−	1.19394i	0.0504969	−	0.0446507i
$716$		0			0
$717$		−	12.3733i		−	0.462089i
$718$		0			0
$719$	16.2520			0.606098			0.303049	−	0.952975i	$-0.401995\pi$
$719$	16.2520			0.606098			0.303049	+	0.952975i	$0.401995\pi$
$720$		0			0
$721$	20.2228			0.753138
$722$		0			0
$723$		−	24.5501i		−	0.913027i
$724$		0			0
$725$	−2.63989	+	21.4010i	−0.0980430	+	0.794815i
$726$		0			0
$727$		−	15.2243i		−	0.564636i	−0.959321	−	0.282318i	$-0.908897\pi$
$727$		−	15.2243i		−	0.564636i	0.959321	−	0.282318i	$-0.0911034\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	−16.6497			−0.615813
$732$		0			0
$733$			43.5066i			1.60695i	0.595337	+	0.803476i	$0.297019\pi$
$733$			43.5066i			1.60695i	−0.595337	+	0.803476i	$0.702981\pi$
$734$		0			0
$735$	9.33804	−	8.25694i	0.344439	−	0.304562i
$736$		0			0
$737$		−	2.70052i		−	0.0994751i
$738$		0			0
$739$	−7.02302			−0.258346			−0.129173	−	0.991622i	$-0.541232\pi$
$739$	−7.02302			−0.258346			−0.129173	+	0.991622i	$0.541232\pi$
$740$		0			0
$741$	−4.31265			−0.158429
$742$		0			0
$743$		−	2.94192i		−	0.107929i	−0.998543	−	0.0539643i	$-0.982814\pi$
$743$		−	2.94192i		−	0.107929i	0.998543	−	0.0539643i	$-0.0171857\pi$
$744$		0			0
$745$	9.46168	+	10.7005i	0.346649	+	0.392037i
$746$		0			0
$747$			9.89446i			0.362019i
$748$		0			0
$749$	−9.88858			−0.361321
$750$		0			0
$751$	−24.1016			−0.879479			−0.439739	−	0.898125i	$-0.644929\pi$
$751$	−24.1016			−0.879479			−0.439739	+	0.898125i	$0.644929\pi$
$752$		0			0
$753$		−	13.9003i		−	0.506557i
$754$		0			0
$755$	−3.92478	−	4.43866i	−0.142837	−	0.161539i
$756$		0			0
$757$		−	16.3127i		−	0.592893i	−0.955049	−	0.296447i	$-0.904198\pi$
$757$		−	16.3127i		−	0.592893i	0.955049	−	0.296447i	$-0.0958017\pi$
$758$		0			0
$759$	4.00000			0.145191
$760$		0			0
$761$	−5.08840			−0.184454			−0.0922271	−	0.995738i	$-0.529399\pi$
$761$	−5.08840			−0.184454			−0.0922271	+	0.995738i	$0.529399\pi$
$762$		0			0
$763$		−	11.9394i		−	0.432234i
$764$		0			0
$765$	−6.31265	+	5.58181i	−0.228234	+	0.201811i
$766$		0			0
$767$		−	10.7005i		−	0.386374i
$768$		0			0
$769$	−2.10157			−0.0757846			−0.0378923	−	0.999282i	$-0.512064\pi$
$769$	−2.10157			−0.0757846			−0.0378923	+	0.999282i	$0.512064\pi$
$770$		0			0
$771$	18.8872			0.680205
$772$		0			0
$773$		−	46.0625i		−	1.65675i	−0.560171	−	0.828377i	$-0.689264\pi$
$773$		−	46.0625i		−	1.65675i	0.560171	−	0.828377i	$-0.310736\pi$
$774$		0			0
$775$	0.589104	−	4.77575i	0.0211612	−	0.171550i
$776$		0			0
$777$			1.92478i			0.0690510i
$778$		0			0
$779$	−48.6253			−1.74218
$780$		0			0
$781$	−14.0508			−0.502777
$782$		0			0
$783$		−	4.31265i		−	0.154122i
$784$		0			0
$785$	2.70052	−	2.38787i	0.0963858	−	0.0852268i
$786$		0			0
$787$			26.0303i			0.927881i	0.885866	+	0.463940i	$0.153565\pi$
$787$			26.0303i			0.927881i	−0.885866	+	0.463940i	$0.846435\pi$
$788$		0			0
$789$	−20.8061			−0.740715
$790$		0			0
$791$	−2.70052			−0.0960196
$792$		0			0
$793$			0.0606343i			0.00215319i
$794$		0			0
$795$	−2.11142	−	2.38787i	−0.0748843	−	0.0846891i
$796$		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)

\(f(q)\)	\(=\)	\(q+1.00000i q^{3} +(-1.48119 - 1.67513i) q^{5} -1.19394i q^{7} -1.00000 q^{9} +O(q^{10})\)	\(q+1.00000i q^{3} +(-1.48119 - 1.67513i) q^{5} -1.19394i q^{7} -1.00000 q^{9} -1.00000 q^{11} -0.806063i q^{13} +(1.67513 - 1.48119i) q^{15} +3.76845i q^{17} -5.35026 q^{19} +1.19394 q^{21} +4.00000i q^{23} +(-0.612127 + 4.96239i) q^{25} -1.00000i q^{27} +4.31265 q^{29} -0.962389 q^{31} -1.00000i q^{33} +(-2.00000 + 1.76845i) q^{35} +1.61213i q^{37} +0.806063 q^{39} +9.08840 q^{41} +4.41819i q^{43} +(1.48119 + 1.67513i) q^{45} -12.3127i q^{47} +5.57452 q^{49} -3.76845 q^{51} -1.42548i q^{53} +(1.48119 + 1.67513i) q^{55} -5.35026i q^{57} +13.2750 q^{59} -0.0752228 q^{61} +1.19394i q^{63} +(-1.35026 + 1.19394i) q^{65} +2.70052i q^{67} -4.00000 q^{69} +14.0508 q^{71} +10.7308i q^{73} +(-4.96239 - 0.612127i) q^{75} +1.19394i q^{77} +13.9756 q^{79} +1.00000 q^{81} -9.89446i q^{83} +(6.31265 - 5.58181i) q^{85} +4.31265i q^{87} -16.8872 q^{89} -0.962389 q^{91} -0.962389i q^{93} +(7.92478 + 8.96239i) q^{95} +11.4763i q^{97} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{5} - 6 q^{9}+O(q^{10}) \) 6 * q + 2 * q^5 - 6 * q^9	\( 6 q + 2 q^{5} - 6 q^{9} - 6 q^{11} - 12 q^{19} + 8 q^{21} - 2 q^{25} - 16 q^{29} + 16 q^{31} - 12 q^{35} + 4 q^{39} + 16 q^{41} - 2 q^{45} + 10 q^{49} - 2 q^{55} + 16 q^{59} - 44 q^{61} + 12 q^{65} - 24 q^{69} + 24 q^{71} - 8 q^{75} - 20 q^{79} + 6 q^{81} - 4 q^{85} - 36 q^{89} + 16 q^{91} + 4 q^{95} + 6 q^{99}+O(q^{100}) \) 6 * q + 2 * q^5 - 6 * q^9 - 6 * q^11 - 12 * q^19 + 8 * q^21 - 2 * q^25 - 16 * q^29 + 16 * q^31 - 12 * q^35 + 4 * q^39 + 16 * q^41 - 2 * q^45 + 10 * q^49 - 2 * q^55 + 16 * q^59 - 44 * q^61 + 12 * q^65 - 24 * q^69 + 24 * q^71 - 8 * q^75 - 20 * q^79 + 6 * q^81 - 4 * q^85 - 36 * q^89 + 16 * q^91 + 4 * q^95 + 6 * q^99

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