LMFDB - Embedded newform 1560.2.bg.f.841.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1560,2,Mod(601,1560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1560, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 2]))

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

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

chi := DirichletCharacter("1560.601");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1560 = 2^{3} \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1560.bg (of order $3$, degree $2$, 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:	$12.4566627153$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{17})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 5x^{2} + 4x + 16 $ x^4 - x^3 + 5x^2 + 4x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			841.1
Root			$1.28078 - 2.21837i$ of defining polynomial
Character	$\chi$	$=$	1560.841
Dual form			1560.2.bg.f.601.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{3} +1.00000 q^{5} +(-2.28078 - 3.95042i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{3} +1.00000 q^{5} +(-2.28078 - 3.95042i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(-0.219224 + 0.379706i) q^{11} +(-2.84233 - 2.21837i) q^{13} +(0.500000 - 0.866025i) q^{15} +(1.00000 + 1.73205i) q^{17} +(-1.56155 - 2.70469i) q^{19} -4.56155 q^{21} +(-0.219224 + 0.379706i) q^{23} +1.00000 q^{25} -1.00000 q^{27} +(-4.34233 + 7.52113i) q^{29} -4.12311 q^{31} +(0.219224 + 0.379706i) q^{33} +(-2.28078 - 3.95042i) q^{35} +(-0.219224 + 0.379706i) q^{37} +(-3.34233 + 1.35234i) q^{39} +(1.00000 - 1.73205i) q^{41} +(-1.06155 - 1.83866i) q^{43} +(-0.500000 - 0.866025i) q^{45} +2.43845 q^{47} +(-6.90388 + 11.9579i) q^{49} +2.00000 q^{51} -7.12311 q^{53} +(-0.219224 + 0.379706i) q^{55} -3.12311 q^{57} +(-4.34233 - 7.52113i) q^{59} +(0.842329 + 1.45896i) q^{61} +(-2.28078 + 3.95042i) q^{63} +(-2.84233 - 2.21837i) q^{65} +(3.28078 - 5.68247i) q^{67} +(0.219224 + 0.379706i) q^{69} +8.56155 q^{73} +(0.500000 - 0.866025i) q^{75} +2.00000 q^{77} -17.2462 q^{79} +(-0.500000 + 0.866025i) q^{81} +13.3693 q^{83} +(1.00000 + 1.73205i) q^{85} +(4.34233 + 7.52113i) q^{87} +(-1.00000 + 1.73205i) q^{89} +(-2.28078 + 16.2880i) q^{91} +(-2.06155 + 3.57071i) q^{93} +(-1.56155 - 2.70469i) q^{95} +(-6.28078 - 10.8786i) q^{97} +0.438447 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} + 4 q^{5} - 5 q^{7} - 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^3 + 4 * q^5 - 5 * q^7 - 2 * q^9	$ 4 q + 2 q^{3} + 4 q^{5} - 5 q^{7} - 2 q^{9} - 5 q^{11} + q^{13} + 2 q^{15} + 4 q^{17} + 2 q^{19} - 10 q^{21} - 5 q^{23} + 4 q^{25} - 4 q^{27} - 5 q^{29} + 5 q^{33} - 5 q^{35} - 5 q^{37} - q^{39} + 4 q^{41} + 4 q^{43} - 2 q^{45} + 18 q^{47} - 7 q^{49} + 8 q^{51} - 12 q^{53} - 5 q^{55} + 4 q^{57} - 5 q^{59} - 9 q^{61} - 5 q^{63} + q^{65} + 9 q^{67} + 5 q^{69} + 26 q^{73} + 2 q^{75} + 8 q^{77} - 36 q^{79} - 2 q^{81} + 4 q^{83} + 4 q^{85} + 5 q^{87} - 4 q^{89} - 5 q^{91} + 2 q^{95} - 21 q^{97} + 10 q^{99}+O(q^{100}) $ 4 * q + 2 * q^3 + 4 * q^5 - 5 * q^7 - 2 * q^9 - 5 * q^11 + q^13 + 2 * q^15 + 4 * q^17 + 2 * q^19 - 10 * q^21 - 5 * q^23 + 4 * q^25 - 4 * q^27 - 5 * q^29 + 5 * q^33 - 5 * q^35 - 5 * q^37 - q^39 + 4 * q^41 + 4 * q^43 - 2 * q^45 + 18 * q^47 - 7 * q^49 + 8 * q^51 - 12 * q^53 - 5 * q^55 + 4 * q^57 - 5 * q^59 - 9 * q^61 - 5 * q^63 + q^65 + 9 * q^67 + 5 * q^69 + 26 * q^73 + 2 * q^75 + 8 * q^77 - 36 * q^79 - 2 * q^81 + 4 * q^83 + 4 * q^85 + 5 * q^87 - 4 * q^89 - 5 * q^91 + 2 * q^95 - 21 * q^97 + 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1560\mathbb{Z}\right)^\times$.

$n$	$391$	$521$	$781$	$937$	$1081$
$\chi(n)$	$1$	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$		0			0
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$		0			0
$7$	−2.28078	−	3.95042i	−0.862052	−	1.49312i	−0.869944	−	0.493150i	$-0.835845\pi$
$7$	−2.28078	−	3.95042i	−0.862052	−	1.49312i	0.00789196	−	0.999969i	$-0.497488\pi$
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	−0.219224	+	0.379706i	−0.0660984	+	0.114486i	−0.897181	−	0.441664i	$-0.854388\pi$
$11$	−0.219224	+	0.379706i	−0.0660984	+	0.114486i	0.831082	+	0.556149i	$0.187722\pi$
$12$		0			0
$13$	−2.84233	−	2.21837i	−0.788320	−	0.615265i
$13$	−2.84233	−	2.21837i	−0.788320	−	0.615265i
$14$		0			0
$15$	0.500000	−	0.866025i	0.129099	−	0.223607i
$16$		0			0
$17$	1.00000	+	1.73205i	0.242536	+	0.420084i	0.961436	−	0.275029i	$-0.0886875\pi$
$17$	1.00000	+	1.73205i	0.242536	+	0.420084i	−0.718900	+	0.695113i	$0.755354\pi$
$18$		0			0
$19$	−1.56155	−	2.70469i	−0.358245	−	0.620498i	0.629423	−	0.777063i	$-0.283291\pi$
$19$	−1.56155	−	2.70469i	−0.358245	−	0.620498i	−0.987668	+	0.156565i	$0.949958\pi$
$20$		0			0
$21$	−4.56155			−0.995412
$22$		0			0
$23$	−0.219224	+	0.379706i	−0.0457113	+	0.0791743i	−0.887976	−	0.459890i	$-0.847889\pi$
$23$	−0.219224	+	0.379706i	−0.0457113	+	0.0791743i	0.842265	+	0.539064i	$0.181222\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	−4.34233	+	7.52113i	−0.806350	+	1.39664i	0.109025	+	0.994039i	$0.465227\pi$
$29$	−4.34233	+	7.52113i	−0.806350	+	1.39664i	−0.915376	+	0.402601i	$0.868106\pi$
$30$		0			0
$31$	−4.12311			−0.740532			−0.370266	−	0.928926i	$-0.620733\pi$
$31$	−4.12311			−0.740532			−0.370266	+	0.928926i	$0.620733\pi$
$32$		0			0
$33$	0.219224	+	0.379706i	0.0381619	+	0.0660984i
$34$		0			0
$35$	−2.28078	−	3.95042i	−0.385522	−	0.667743i
$36$		0			0
$37$	−0.219224	+	0.379706i	−0.0360401	+	0.0624233i	−0.883483	−	0.468463i	$-0.844808\pi$
$37$	−0.219224	+	0.379706i	−0.0360401	+	0.0624233i	0.847443	+	0.530887i	$0.178141\pi$
$38$		0			0
$39$	−3.34233	+	1.35234i	−0.535201	+	0.216548i
$40$		0			0
$41$	1.00000	−	1.73205i	0.156174	−	0.270501i	−0.777312	−	0.629115i	$-0.783417\pi$
$41$	1.00000	−	1.73205i	0.156174	−	0.270501i	0.933486	+	0.358614i	$0.116751\pi$
$42$		0			0
$43$	−1.06155	−	1.83866i	−0.161885	−	0.280394i	0.773660	−	0.633602i	$-0.218424\pi$
$43$	−1.06155	−	1.83866i	−0.161885	−	0.280394i	−0.935545	+	0.353208i	$0.885091\pi$
$44$		0			0
$45$	−0.500000	−	0.866025i	−0.0745356	−	0.129099i
$46$		0			0
$47$	2.43845			0.355684			0.177842	−	0.984059i	$-0.443088\pi$
$47$	2.43845			0.355684			0.177842	+	0.984059i	$0.443088\pi$
$48$		0			0
$49$	−6.90388	+	11.9579i	−0.986269	+	1.70827i
$50$		0			0
$51$	2.00000			0.280056
$52$		0			0
$53$	−7.12311			−0.978434			−0.489217	−	0.872162i	$-0.662717\pi$
$53$	−7.12311			−0.978434			−0.489217	+	0.872162i	$0.662717\pi$
$54$		0			0
$55$	−0.219224	+	0.379706i	−0.0295601	+	0.0511996i
$56$		0			0
$57$	−3.12311			−0.413665
$58$		0			0
$59$	−4.34233	−	7.52113i	−0.565323	−	0.979168i	−0.997020	−	0.0771494i	$-0.975418\pi$
$59$	−4.34233	−	7.52113i	−0.565323	−	0.979168i	0.431696	−	0.902019i	$-0.357915\pi$
$60$		0			0
$61$	0.842329	+	1.45896i	0.107849	+	0.186800i	0.914899	−	0.403683i	$-0.132270\pi$
$61$	0.842329	+	1.45896i	0.107849	+	0.186800i	−0.807050	+	0.590484i	$0.798937\pi$
$62$		0			0
$63$	−2.28078	+	3.95042i	−0.287351	+	0.497706i
$64$		0			0
$65$	−2.84233	−	2.21837i	−0.352548	−	0.275155i
$66$		0			0
$67$	3.28078	−	5.68247i	0.400811	−	0.694224i	−0.593013	−	0.805193i	$-0.702062\pi$
$67$	3.28078	−	5.68247i	0.400811	−	0.694224i	0.993824	+	0.110968i	$0.0353952\pi$
$68$		0			0
$69$	0.219224	+	0.379706i	0.0263914	+	0.0457113i
$70$		0			0
$71$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$71$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$72$		0			0
$73$	8.56155			1.00205			0.501027	−	0.865432i	$-0.332956\pi$
$73$	8.56155			1.00205			0.501027	+	0.865432i	$0.332956\pi$
$74$		0			0
$75$	0.500000	−	0.866025i	0.0577350	−	0.100000i
$76$		0			0
$77$	2.00000			0.227921
$78$		0			0
$79$	−17.2462			−1.94035			−0.970175	−	0.242405i	$-0.922064\pi$
$79$	−17.2462			−1.94035			−0.970175	+	0.242405i	$0.922064\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	13.3693			1.46747			0.733737	−	0.679434i	$-0.237775\pi$
$83$	13.3693			1.46747			0.733737	+	0.679434i	$0.237775\pi$
$84$		0			0
$85$	1.00000	+	1.73205i	0.108465	+	0.187867i
$86$		0			0
$87$	4.34233	+	7.52113i	0.465547	+	0.806350i
$88$		0			0
$89$	−1.00000	+	1.73205i	−0.106000	+	0.183597i	−0.914146	−	0.405385i	$-0.867138\pi$
$89$	−1.00000	+	1.73205i	−0.106000	+	0.183597i	0.808146	+	0.588982i	$0.200471\pi$
$90$		0			0
$91$	−2.28078	+	16.2880i	−0.239090	+	1.70745i
$92$		0			0
$93$	−2.06155	+	3.57071i	−0.213773	+	0.370266i
$94$		0			0
$95$	−1.56155	−	2.70469i	−0.160212	−	0.277495i
$96$		0			0
$97$	−6.28078	−	10.8786i	−0.637716	−	1.10456i	−0.985933	−	0.167143i	$-0.946546\pi$
$97$	−6.28078	−	10.8786i	−0.637716	−	1.10456i	0.348216	−	0.937414i	$-0.386787\pi$
$98$		0			0
$99$	0.438447			0.0440656
$100$		0			0
$101$	4.12311	−	7.14143i	0.410264	−	0.710599i	−0.584654	−	0.811283i	$-0.698770\pi$
$101$	4.12311	−	7.14143i	0.410264	−	0.710599i	0.994918	+	0.100684i	$0.0321031\pi$
$102$		0			0
$103$	0.561553			0.0553314			0.0276657	−	0.999617i	$-0.491193\pi$
$103$	0.561553			0.0553314			0.0276657	+	0.999617i	$0.491193\pi$
$104$		0			0
$105$	−4.56155			−0.445162
$106$		0			0
$107$	5.56155	−	9.63289i	0.537656	−	0.931247i	−0.461374	−	0.887206i	$-0.652643\pi$
$107$	5.56155	−	9.63289i	0.537656	−	0.931247i	0.999030	−	0.0440411i	$-0.0140233\pi$
$108$		0			0
$109$	−2.80776			−0.268935			−0.134468	−	0.990918i	$-0.542932\pi$
$109$	−2.80776			−0.268935			−0.134468	+	0.990918i	$0.542932\pi$
$110$		0			0
$111$	0.219224	+	0.379706i	0.0208078	+	0.0360401i
$112$		0			0
$113$	−9.34233	−	16.1814i	−0.878852	−	1.52222i	−0.852602	−	0.522562i	$-0.824976\pi$
$113$	−9.34233	−	16.1814i	−0.878852	−	1.52222i	−0.0262509	−	0.999655i	$-0.508357\pi$
$114$		0			0
$115$	−0.219224	+	0.379706i	−0.0204427	+	0.0354078i
$116$		0			0
$117$	−0.500000	+	3.57071i	−0.0462250	+	0.330113i
$118$		0			0
$119$	4.56155	−	7.90084i	0.418157	−	0.724269i
$120$		0			0
$121$	5.40388	+	9.35980i	0.491262	+	0.850891i
$122$		0			0
$123$	−1.00000	−	1.73205i	−0.0901670	−	0.156174i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	4.84233	−	8.38716i	0.429687	−	0.744240i	−0.567158	−	0.823609i	$-0.691957\pi$
$127$	4.84233	−	8.38716i	0.429687	−	0.744240i	0.996845	+	0.0793688i	$0.0252905\pi$
$128$		0			0
$129$	−2.12311			−0.186929
$130$		0			0
$131$	1.56155			0.136434			0.0682168	−	0.997671i	$-0.478269\pi$
$131$	1.56155			0.136434			0.0682168	+	0.997671i	$0.478269\pi$
$132$		0			0
$133$	−7.12311	+	12.3376i	−0.617652	+	1.06980i
$134$		0			0
$135$	−1.00000			−0.0860663
$136$		0			0
$137$	0.219224	+	0.379706i	0.0187295	+	0.0324405i	0.875238	−	0.483692i	$-0.160705\pi$
$137$	0.219224	+	0.379706i	0.0187295	+	0.0324405i	−0.856509	+	0.516133i	$0.827371\pi$
$138$		0			0
$139$	−1.40388	−	2.43160i	−0.119076	−	0.206245i	0.800326	−	0.599565i	$-0.204660\pi$
$139$	−1.40388	−	2.43160i	−0.119076	−	0.206245i	−0.919402	+	0.393320i	$0.871326\pi$
$140$		0			0
$141$	1.21922	−	2.11176i	0.102677	−	0.177842i
$142$		0			0
$143$	1.46543	−	0.592932i	0.122546	−	0.0495834i
$144$		0			0
$145$	−4.34233	+	7.52113i	−0.360611	+	0.624596i
$146$		0			0
$147$	6.90388	+	11.9579i	0.569423	+	0.986269i
$148$		0			0
$149$	−7.46543	−	12.9305i	−0.611592	−	1.05931i	−0.990972	−	0.134068i	$-0.957196\pi$
$149$	−7.46543	−	12.9305i	−0.611592	−	1.05931i	0.379380	−	0.925241i	$-0.376137\pi$
$150$		0			0
$151$	16.0000			1.30206			0.651031	−	0.759051i	$-0.274337\pi$
$151$	16.0000			1.30206			0.651031	+	0.759051i	$0.274337\pi$
$152$		0			0
$153$	1.00000	−	1.73205i	0.0808452	−	0.140028i
$154$		0			0
$155$	−4.12311			−0.331176
$156$		0			0
$157$	−5.24621			−0.418693			−0.209347	−	0.977841i	$-0.567134\pi$
$157$	−5.24621			−0.418693			−0.209347	+	0.977841i	$0.567134\pi$
$158$		0			0
$159$	−3.56155	+	6.16879i	−0.282450	+	0.489217i
$160$		0			0
$161$	2.00000			0.157622
$162$		0			0
$163$	−5.93845	−	10.2857i	−0.465135	−	0.805638i	0.534073	−	0.845439i	$-0.320661\pi$
$163$	−5.93845	−	10.2857i	−0.465135	−	0.805638i	−0.999208	+	0.0398011i	$0.987328\pi$
$164$		0			0
$165$	0.219224	+	0.379706i	0.0170665	+	0.0295601i
$166$		0			0
$167$	−12.7808	+	22.1370i	−0.989006	+	1.71301i	−0.366440	+	0.930442i	$0.619424\pi$
$167$	−12.7808	+	22.1370i	−0.989006	+	1.71301i	−0.622566	+	0.782567i	$0.713910\pi$
$168$		0			0
$169$	3.15767	+	12.6107i	0.242898	+	0.970052i
$170$		0			0
$171$	−1.56155	+	2.70469i	−0.119415	+	0.206833i
$172$		0			0
$173$	2.00000	+	3.46410i	0.152057	+	0.263371i	0.931984	−	0.362500i	$-0.118077\pi$
$173$	2.00000	+	3.46410i	0.152057	+	0.263371i	−0.779926	+	0.625871i	$0.784744\pi$
$174$		0			0
$175$	−2.28078	−	3.95042i	−0.172410	−	0.298624i
$176$		0			0
$177$	−8.68466			−0.652779
$178$		0			0
$179$	4.90388	−	8.49377i	0.366533	−	0.634854i	−0.622488	−	0.782630i	$-0.713878\pi$
$179$	4.90388	−	8.49377i	0.366533	−	0.634854i	0.989021	+	0.147775i	$0.0472112\pi$
$180$		0			0
$181$	5.12311			0.380797			0.190399	−	0.981707i	$-0.439022\pi$
$181$	5.12311			0.380797			0.190399	+	0.981707i	$0.439022\pi$
$182$		0			0
$183$	1.68466			0.124534
$184$		0			0
$185$	−0.219224	+	0.379706i	−0.0161176	+	0.0279166i
$186$		0			0
$187$	−0.876894			−0.0641249
$188$		0			0
$189$	2.28078	+	3.95042i	0.165902	+	0.287351i
$190$		0			0
$191$	−10.0000	−	17.3205i	−0.723575	−	1.25327i	−0.959558	−	0.281511i	$-0.909164\pi$
$191$	−10.0000	−	17.3205i	−0.723575	−	1.25327i	0.235983	−	0.971757i	$-0.424169\pi$
$192$		0			0
$193$	−9.52699	+	16.5012i	−0.685768	+	1.18778i	0.287427	+	0.957802i	$0.407200\pi$
$193$	−9.52699	+	16.5012i	−0.685768	+	1.18778i	−0.973195	+	0.229982i	$0.926133\pi$
$194$		0			0
$195$	−3.34233	+	1.35234i	−0.239349	+	0.0968434i
$196$		0			0
$197$	4.00000	−	6.92820i	0.284988	−	0.493614i	−0.687618	−	0.726073i	$-0.741344\pi$
$197$	4.00000	−	6.92820i	0.284988	−	0.493614i	0.972606	+	0.232458i	$0.0746770\pi$
$198$		0			0
$199$	−4.71922	−	8.17394i	−0.334537	−	0.579435i	0.648859	−	0.760909i	$-0.275247\pi$
$199$	−4.71922	−	8.17394i	−0.334537	−	0.579435i	−0.983396	+	0.181474i	$0.941913\pi$
$200$		0			0
$201$	−3.28078	−	5.68247i	−0.231408	−	0.400811i
$202$		0			0
$203$	39.6155			2.78046
$204$		0			0
$205$	1.00000	−	1.73205i	0.0698430	−	0.120972i
$206$		0			0
$207$	0.438447			0.0304742
$208$		0			0
$209$	1.36932			0.0947176
$210$		0			0
$211$	−11.5270	+	19.9653i	−0.793551	+	1.37447i	0.130205	+	0.991487i	$0.458436\pi$
$211$	−11.5270	+	19.9653i	−0.793551	+	1.37447i	−0.923755	+	0.382983i	$0.874897\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−1.06155	−	1.83866i	−0.0723973	−	0.125396i
$216$		0			0
$217$	9.40388	+	16.2880i	0.638377	+	1.10570i
$218$		0			0
$219$	4.28078	−	7.41452i	0.289268	−	0.501027i
$220$		0			0
$221$	1.00000	−	7.14143i	0.0672673	−	0.480384i
$222$		0			0
$223$	11.8078	−	20.4516i	0.790706	−	1.36954i	−0.134824	−	0.990870i	$-0.543047\pi$
$223$	11.8078	−	20.4516i	0.790706	−	1.36954i	0.925530	−	0.378674i	$-0.123620\pi$
$224$		0			0
$225$	−0.500000	−	0.866025i	−0.0333333	−	0.0577350i
$226$		0			0
$227$	−0.315342	−	0.546188i	−0.0209300	−	0.0362517i	0.855371	−	0.518016i	$-0.173329\pi$
$227$	−0.315342	−	0.546188i	−0.0209300	−	0.0362517i	−0.876301	+	0.481765i	$0.839996\pi$
$228$		0			0
$229$	−28.7386			−1.89910			−0.949551	−	0.313612i	$-0.898461\pi$
$229$	−28.7386			−1.89910			−0.949551	+	0.313612i	$0.898461\pi$
$230$		0			0
$231$	1.00000	−	1.73205i	0.0657952	−	0.113961i
$232$		0			0
$233$	16.0540			1.05173			0.525865	−	0.850568i	$-0.323742\pi$
$233$	16.0540			1.05173			0.525865	+	0.850568i	$0.323742\pi$
$234$		0			0
$235$	2.43845			0.159067
$236$		0			0
$237$	−8.62311	+	14.9357i	−0.560131	+	0.970175i
$238$		0			0
$239$	4.00000			0.258738			0.129369	−	0.991596i	$-0.458705\pi$
$239$	4.00000			0.258738			0.129369	+	0.991596i	$0.458705\pi$
$240$		0			0
$241$	14.4654	+	25.0549i	0.931801	+	1.61393i	0.780242	+	0.625478i	$0.215096\pi$
$241$	14.4654	+	25.0549i	0.931801	+	1.61393i	0.151558	+	0.988448i	$0.451571\pi$
$242$		0			0
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$		0			0
$245$	−6.90388	+	11.9579i	−0.441073	+	0.763961i
$246$		0			0
$247$	−1.56155	+	11.1517i	−0.0993592	+	0.709567i
$248$		0			0
$249$	6.68466	−	11.5782i	0.423623	−	0.733737i
$250$		0			0
$251$	−3.21922	−	5.57586i	−0.203196	−	0.351945i	0.746361	−	0.665542i	$-0.231799\pi$
$251$	−3.21922	−	5.57586i	−0.203196	−	0.351945i	−0.949556	+	0.313597i	$0.898466\pi$
$252$		0			0
$253$	−0.0961180	−	0.166481i	−0.00604288	−	0.0104666i
$254$		0			0
$255$	2.00000			0.125245
$256$		0			0
$257$	−6.21922	+	10.7720i	−0.387945	+	0.671940i	−0.992173	−	0.124872i	$-0.960148\pi$
$257$	−6.21922	+	10.7720i	−0.387945	+	0.671940i	0.604228	+	0.796811i	$0.293481\pi$
$258$		0			0
$259$	2.00000			0.124274
$260$		0			0
$261$	8.68466			0.537567
$262$		0			0
$263$	12.4654	−	21.5908i	0.768652	−	1.33134i	−0.169643	−	0.985506i	$-0.554261\pi$
$263$	12.4654	−	21.5908i	0.768652	−	1.33134i	0.938294	−	0.345838i	$-0.112405\pi$
$264$		0			0
$265$	−7.12311			−0.437569
$266$		0			0
$267$	1.00000	+	1.73205i	0.0611990	+	0.106000i
$268$		0			0
$269$	−4.12311	−	7.14143i	−0.251390	−	0.435421i	0.712519	−	0.701653i	$-0.247554\pi$
$269$	−4.12311	−	7.14143i	−0.251390	−	0.435421i	−0.963909	+	0.266233i	$0.914221\pi$
$270$		0			0
$271$	11.8693	−	20.5583i	0.721010	−	1.24883i	−0.239586	−	0.970875i	$-0.577012\pi$
$271$	11.8693	−	20.5583i	0.721010	−	1.24883i	0.960595	−	0.277950i	$-0.0896550\pi$
$272$		0			0
$273$	12.9654	+	10.1192i	0.784704	+	0.612443i
$274$		0			0
$275$	−0.219224	+	0.379706i	−0.0132197	+	0.0228972i
$276$		0			0
$277$	−7.78078	−	13.4767i	−0.467502	−	0.809736i	0.531809	−	0.846864i	$-0.321512\pi$
$277$	−7.78078	−	13.4767i	−0.467502	−	0.809736i	−0.999311	+	0.0371279i	$0.988179\pi$
$278$		0			0
$279$	2.06155	+	3.57071i	0.123422	+	0.213773i
$280$		0			0
$281$	25.8617			1.54278			0.771391	−	0.636361i	$-0.219561\pi$
$281$	25.8617			1.54278			0.771391	+	0.636361i	$0.219561\pi$
$282$		0			0
$283$	−1.50000	+	2.59808i	−0.0891657	+	0.154440i	−0.907159	−	0.420789i	$-0.861753\pi$
$283$	−1.50000	+	2.59808i	−0.0891657	+	0.154440i	0.817993	+	0.575228i	$0.195087\pi$
$284$		0			0
$285$	−3.12311			−0.184997
$286$		0			0
$287$	−9.12311			−0.538520
$288$		0			0
$289$	6.50000	−	11.2583i	0.382353	−	0.662255i
$290$		0			0
$291$	−12.5616			−0.736371
$292$		0			0
$293$	2.43845	+	4.22351i	0.142456	+	0.246740i	0.928421	−	0.371530i	$-0.121167\pi$
$293$	2.43845	+	4.22351i	0.142456	+	0.246740i	−0.785965	+	0.618271i	$0.787834\pi$
$294$		0			0
$295$	−4.34233	−	7.52113i	−0.252820	−	0.437897i
$296$		0			0
$297$	0.219224	−	0.379706i	0.0127206	−	0.0220328i
$298$		0			0
$299$	1.46543	−	0.592932i	0.0847483	−	0.0342901i
$300$		0			0
$301$	−4.84233	+	8.38716i	−0.279107	+	0.483428i
$302$		0			0
$303$	−4.12311	−	7.14143i	−0.236866	−	0.410264i
$304$		0			0
$305$	0.842329	+	1.45896i	0.0482316	+	0.0835396i
$306$		0			0
$307$	13.9309			0.795077			0.397538	−	0.917586i	$-0.369865\pi$
$307$	13.9309			0.795077			0.397538	+	0.917586i	$0.369865\pi$
$308$		0			0
$309$	0.280776	−	0.486319i	0.0159728	−	0.0276657i
$310$		0			0
$311$	19.3693			1.09833			0.549167	−	0.835713i	$-0.314945\pi$
$311$	19.3693			1.09833			0.549167	+	0.835713i	$0.314945\pi$
$312$		0			0
$313$	23.0540			1.30309			0.651544	−	0.758611i	$-0.274122\pi$
$313$	23.0540			1.30309			0.651544	+	0.758611i	$0.274122\pi$
$314$		0			0
$315$	−2.28078	+	3.95042i	−0.128507	+	0.222581i
$316$		0			0
$317$	18.2462			1.02481			0.512405	−	0.858744i	$-0.328755\pi$
$317$	18.2462			1.02481			0.512405	+	0.858744i	$0.328755\pi$
$318$		0			0
$319$	−1.90388	−	3.29762i	−0.106597	−	0.184631i
$320$		0			0
$321$	−5.56155	−	9.63289i	−0.310416	−	0.537656i
$322$		0			0
$323$	3.12311	−	5.40938i	0.173774	−	0.300986i
$324$		0			0
$325$	−2.84233	−	2.21837i	−0.157664	−	0.123053i
$326$		0			0
$327$	−1.40388	+	2.43160i	−0.0776349	+	0.134468i
$328$		0			0
$329$	−5.56155	−	9.63289i	−0.306618	−	0.531079i
$330$		0			0
$331$	−2.71922	−	4.70983i	−0.149462	−	0.258876i	0.781567	−	0.623822i	$-0.214421\pi$
$331$	−2.71922	−	4.70983i	−0.149462	−	0.258876i	−0.931029	+	0.364946i	$0.881088\pi$
$332$		0			0
$333$	0.438447			0.0240268
$334$		0			0
$335$	3.28078	−	5.68247i	0.179248	−	0.310467i
$336$		0			0
$337$	−1.19224			−0.0649452			−0.0324726	−	0.999473i	$-0.510338\pi$
$337$	−1.19224			−0.0649452			−0.0324726	+	0.999473i	$0.510338\pi$
$338$		0			0
$339$	−18.6847			−1.01481
$340$		0			0
$341$	0.903882	−	1.56557i	0.0489480	−	0.0847803i
$342$		0			0
$343$	31.0540			1.67676
$344$		0			0
$345$	0.219224	+	0.379706i	0.0118026	+	0.0204427i
$346$		0			0
$347$	6.68466	+	11.5782i	0.358851	+	0.621549i	0.987769	−	0.155923i	$-0.0498352\pi$
$347$	6.68466	+	11.5782i	0.358851	+	0.621549i	−0.628918	+	0.777472i	$0.716502\pi$
$348$		0			0
$349$	4.15767	−	7.20130i	0.222555	−	0.385477i	−0.733028	−	0.680198i	$-0.761894\pi$
$349$	4.15767	−	7.20130i	0.222555	−	0.385477i	0.955583	+	0.294722i	$0.0952270\pi$
$350$		0			0
$351$	2.84233	+	2.21837i	0.151712	+	0.118408i
$352$		0			0
$353$	14.1231	−	24.4619i	0.751697	−	1.30198i	−0.195303	−	0.980743i	$-0.562569\pi$
$353$	14.1231	−	24.4619i	0.751697	−	1.30198i	0.947000	−	0.321234i	$-0.104098\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−4.56155	−	7.90084i	−0.241423	−	0.418157i
$358$		0			0
$359$	25.1231			1.32595			0.662973	−	0.748643i	$-0.269294\pi$
$359$	25.1231			1.32595			0.662973	+	0.748643i	$0.269294\pi$
$360$		0			0
$361$	4.62311	−	8.00745i	0.243321	−	0.421445i
$362$		0			0
$363$	10.8078			0.567260
$364$		0			0
$365$	8.56155			0.448132
$366$		0			0
$367$	12.0885	−	20.9380i	0.631017	−	1.09295i	−0.356328	−	0.934361i	$-0.615971\pi$
$367$	12.0885	−	20.9380i	0.631017	−	1.09295i	0.987344	−	0.158592i	$-0.0506954\pi$
$368$		0			0
$369$	−2.00000			−0.104116
$370$		0			0
$371$	16.2462	+	28.1393i	0.843461	+	1.46092i
$372$		0			0
$373$	4.62311	+	8.00745i	0.239375	+	0.414610i	0.960535	−	0.278158i	$-0.0897240\pi$
$373$	4.62311	+	8.00745i	0.239375	+	0.414610i	−0.721160	+	0.692769i	$0.756391\pi$
$374$		0			0
$375$	0.500000	−	0.866025i	0.0258199	−	0.0447214i
$376$		0			0
$377$	29.0270	−	11.7446i	1.49497	−	0.604880i
$378$		0			0
$379$	−11.0885	+	19.2059i	−0.569580	+	0.986542i	0.427027	+	0.904239i	$0.359561\pi$
$379$	−11.0885	+	19.2059i	−0.569580	+	0.986542i	−0.996607	+	0.0823029i	$0.973773\pi$
$380$		0			0
$381$	−4.84233	−	8.38716i	−0.248080	−	0.429687i
$382$		0			0
$383$	10.0270	+	17.3673i	0.512355	+	0.887425i	0.999897	+	0.0143257i	$0.00456018\pi$
$383$	10.0270	+	17.3673i	0.512355	+	0.887425i	−0.487542	+	0.873099i	$0.662106\pi$
$384$		0			0
$385$	2.00000			0.101929
$386$		0			0
$387$	−1.06155	+	1.83866i	−0.0539618	+	0.0934645i
$388$		0			0
$389$	−24.3002			−1.23207			−0.616034	−	0.787719i	$-0.711262\pi$
$389$	−24.3002			−1.23207			−0.616034	+	0.787719i	$0.711262\pi$
$390$		0			0
$391$	−0.876894			−0.0443465
$392$		0			0
$393$	0.780776	−	1.35234i	0.0393850	−	0.0682168i
$394$		0			0
$395$	−17.2462			−0.867751
$396$		0			0
$397$	1.93845	+	3.35749i	0.0972879	+	0.168508i	0.910561	−	0.413374i	$-0.135650\pi$
$397$	1.93845	+	3.35749i	0.0972879	+	0.168508i	−0.813273	+	0.581882i	$0.802317\pi$
$398$		0			0
$399$	7.12311	+	12.3376i	0.356601	+	0.617652i
$400$		0			0
$401$	11.1231	−	19.2658i	0.555461	−	0.962087i	−0.442406	−	0.896815i	$-0.645875\pi$
$401$	11.1231	−	19.2658i	0.555461	−	0.962087i	0.997867	−	0.0652725i	$-0.0207917\pi$
$402$		0			0
$403$	11.7192	+	9.14657i	0.583776	+	0.455623i
$404$		0			0
$405$	−0.500000	+	0.866025i	−0.0248452	+	0.0430331i
$406$		0			0
$407$	−0.0961180	−	0.166481i	−0.00476439	−	0.00825217i
$408$		0			0
$409$	−6.59612	−	11.4248i	−0.326157	−	0.564921i	0.655589	−	0.755118i	$-0.272420\pi$
$409$	−6.59612	−	11.4248i	−0.326157	−	0.564921i	−0.981746	+	0.190198i	$0.939087\pi$
$410$		0			0
$411$	0.438447			0.0216270
$412$		0			0
$413$	−19.8078	+	34.3081i	−0.974676	+	1.68819i
$414$		0			0
$415$	13.3693			0.656274
$416$		0			0
$417$	−2.80776			−0.137497
$418$		0			0
$419$	−3.43845	+	5.95557i	−0.167979	+	0.290948i	−0.937709	−	0.347421i	$-0.887057\pi$
$419$	−3.43845	+	5.95557i	−0.167979	+	0.290948i	0.769730	+	0.638369i	$0.220391\pi$
$420$		0			0
$421$	−15.1922			−0.740424			−0.370212	−	0.928947i	$-0.620715\pi$
$421$	−15.1922			−0.740424			−0.370212	+	0.928947i	$0.620715\pi$
$422$		0			0
$423$	−1.21922	−	2.11176i	−0.0592807	−	0.102677i
$424$		0			0
$425$	1.00000	+	1.73205i	0.0485071	+	0.0840168i
$426$		0			0
$427$	3.84233	−	6.65511i	0.185943	−	0.322063i
$428$		0			0
$429$	0.219224	−	1.56557i	0.0105842	−	0.0755864i
$430$		0			0
$431$	−10.2462	+	17.7470i	−0.493543	+	0.854841i	−0.999972	−	0.00744035i	$-0.997632\pi$
$431$	−10.2462	+	17.7470i	−0.493543	+	0.854841i	0.506430	+	0.862281i	$0.330965\pi$
$432$		0			0
$433$	15.2116	+	26.3473i	0.731025	+	1.26617i	0.956445	+	0.291911i	$0.0942911\pi$
$433$	15.2116	+	26.3473i	0.731025	+	1.26617i	−0.225420	+	0.974262i	$0.572376\pi$
$434$		0			0
$435$	4.34233	+	7.52113i	0.208199	+	0.360611i
$436$		0			0
$437$	1.36932			0.0655033
$438$		0			0
$439$	−12.6501	+	21.9106i	−0.603756	+	1.04574i	0.388491	+	0.921453i	$0.372997\pi$
$439$	−12.6501	+	21.9106i	−0.603756	+	1.04574i	−0.992247	+	0.124283i	$0.960337\pi$
$440$		0			0
$441$	13.8078			0.657513
$442$		0			0
$443$	−4.63068			−0.220010			−0.110005	−	0.993931i	$-0.535087\pi$
$443$	−4.63068			−0.220010			−0.110005	+	0.993931i	$0.535087\pi$
$444$		0			0
$445$	−1.00000	+	1.73205i	−0.0474045	+	0.0821071i
$446$		0			0
$447$	−14.9309			−0.706206
$448$		0			0
$449$	−1.68466	−	2.91791i	−0.0795039	−	0.137705i	0.823532	−	0.567270i	$-0.192000\pi$
$449$	−1.68466	−	2.91791i	−0.0795039	−	0.137705i	−0.903036	+	0.429565i	$0.858667\pi$
$450$		0			0
$451$	0.438447	+	0.759413i	0.0206457	+	0.0357594i
$452$		0			0
$453$	8.00000	−	13.8564i	0.375873	−	0.651031i
$454$		0			0
$455$	−2.28078	+	16.2880i	−0.106924	+	0.763593i
$456$		0			0
$457$	11.9654	−	20.7247i	0.559719	−	0.969462i	−0.437800	−	0.899072i	$-0.644242\pi$
$457$	11.9654	−	20.7247i	0.559719	−	0.969462i	0.997520	−	0.0703902i	$-0.0224244\pi$
$458$		0			0
$459$	−1.00000	−	1.73205i	−0.0466760	−	0.0808452i
$460$		0			0
$461$	3.09612	+	5.36263i	0.144201	+	0.249763i	0.929074	−	0.369893i	$-0.120606\pi$
$461$	3.09612	+	5.36263i	0.144201	+	0.249763i	−0.784874	+	0.619656i	$0.787272\pi$
$462$		0			0
$463$	−18.8078			−0.874071			−0.437035	−	0.899444i	$-0.643972\pi$
$463$	−18.8078			−0.874071			−0.437035	+	0.899444i	$0.643972\pi$
$464$		0			0
$465$	−2.06155	+	3.57071i	−0.0956022	+	0.165588i
$466$		0			0
$467$	−19.6155			−0.907698			−0.453849	−	0.891079i	$-0.649950\pi$
$467$	−19.6155			−0.907698			−0.453849	+	0.891079i	$0.649950\pi$
$468$		0			0
$469$	−29.9309			−1.38208
$470$		0			0
$471$	−2.62311	+	4.54335i	−0.120866	+	0.209347i
$472$		0			0
$473$	0.930870			0.0428014
$474$		0			0
$475$	−1.56155	−	2.70469i	−0.0716490	−	0.124100i
$476$		0			0
$477$	3.56155	+	6.16879i	0.163072	+	0.282450i
$478$		0			0
$479$	−17.9309	+	31.0572i	−0.819282	+	1.41904i	0.0869294	+	0.996214i	$0.472295\pi$
$479$	−17.9309	+	31.0572i	−0.819282	+	1.41904i	−0.906212	+	0.422824i	$0.861039\pi$
$480$		0			0
$481$	1.46543	−	0.592932i	0.0668181	−	0.0270354i
$482$		0			0
$483$	1.00000	−	1.73205i	0.0455016	−	0.0788110i
$484$		0			0
$485$	−6.28078	−	10.8786i	−0.285195	−	0.493973i
$486$		0			0
$487$	−1.31534	−	2.27824i	−0.0596038	−	0.103237i	0.834684	−	0.550729i	$-0.185650\pi$
$487$	−1.31534	−	2.27824i	−0.0596038	−	0.103237i	−0.894288	+	0.447493i	$0.852317\pi$
$488$		0			0
$489$	−11.8769			−0.537092
$490$		0			0
$491$	−14.2462	+	24.6752i	−0.642923	+	1.11357i	0.341855	+	0.939753i	$0.388945\pi$
$491$	−14.2462	+	24.6752i	−0.642923	+	1.11357i	−0.984777	+	0.173822i	$0.944388\pi$
$492$		0			0
$493$	−17.3693			−0.782275
$494$		0			0
$495$	0.438447			0.0197067
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−16.4924			−0.738302			−0.369151	−	0.929369i	$-0.620352\pi$
$499$	−16.4924			−0.738302			−0.369151	+	0.929369i	$0.620352\pi$
$500$		0			0
$501$	12.7808	+	22.1370i	0.571003	+	0.989006i
$502$		0			0
$503$	−4.31534	−	7.47439i	−0.192412	−	0.333267i	0.753637	−	0.657290i	$-0.228298\pi$
$503$	−4.31534	−	7.47439i	−0.192412	−	0.333267i	−0.946049	+	0.324024i	$0.894964\pi$
$504$		0			0
$505$	4.12311	−	7.14143i	0.183476	−	0.317789i
$506$		0			0
$507$	12.5000	+	3.57071i	0.555144	+	0.158581i
$508$		0			0
$509$	15.3423	−	26.5737i	0.680037	−	1.17786i	−0.294932	−	0.955518i	$-0.595297\pi$
$509$	15.3423	−	26.5737i	0.680037	−	1.17786i	0.974969	−	0.222340i	$-0.0713695\pi$
$510$		0			0
$511$	−19.5270	−	33.8217i	−0.863823	−	1.49619i
$512$		0			0
$513$	1.56155	+	2.70469i	0.0689442	+	0.119415i
$514$		0			0
$515$	0.561553			0.0247450
$516$		0			0
$517$	−0.534565	+	0.925894i	−0.0235101	+	0.0407208i
$518$		0			0
$519$	4.00000			0.175581
$520$		0			0
$521$	24.7386			1.08382			0.541910	−	0.840437i	$-0.317702\pi$
$521$	24.7386			1.08382			0.541910	+	0.840437i	$0.317702\pi$
$522$		0			0
$523$	−9.21922	+	15.9682i	−0.403129	+	0.698239i	−0.994102	−	0.108452i	$-0.965411\pi$
$523$	−9.21922	+	15.9682i	−0.403129	+	0.698239i	0.590973	+	0.806691i	$0.298744\pi$
$524$		0			0
$525$	−4.56155			−0.199082
$526$		0			0
$527$	−4.12311	−	7.14143i	−0.179605	−	0.311086i
$528$		0			0
$529$	11.4039	+	19.7521i	0.495821	+	0.858787i
$530$		0			0
$531$	−4.34233	+	7.52113i	−0.188441	+	0.326389i
$532$		0			0
$533$	−6.68466	+	2.70469i	−0.289545	+	0.117153i
$534$		0			0
$535$	5.56155	−	9.63289i	0.240447	−	0.416466i
$536$		0			0
$537$	−4.90388	−	8.49377i	−0.211618	−	0.366533i
$538$		0			0
$539$	−3.02699	−	5.24290i	−0.130382	−	0.225828i
$540$		0			0
$541$	43.0540			1.85103			0.925517	−	0.378705i	$-0.123630\pi$
$541$	43.0540			1.85103			0.925517	+	0.378705i	$0.123630\pi$
$542$		0			0
$543$	2.56155	−	4.43674i	0.109927	−	0.190399i
$544$		0			0
$545$	−2.80776			−0.120271
$546$		0			0
$547$	16.3153			0.697594			0.348797	−	0.937198i	$-0.386590\pi$
$547$	16.3153			0.697594			0.348797	+	0.937198i	$0.386590\pi$
$548$		0			0
$549$	0.842329	−	1.45896i	0.0359497	−	0.0622668i
$550$		0			0
$551$	27.1231			1.15548
$552$		0			0
$553$	39.3348	+	68.1298i	1.67268	+	2.89717i
$554$		0			0
$555$	0.219224	+	0.379706i	0.00930552	+	0.0161176i
$556$		0			0
$557$	−5.31534	+	9.20644i	−0.225218	+	0.390089i	−0.956385	−	0.292109i	$-0.905643\pi$
$557$	−5.31534	+	9.20644i	−0.225218	+	0.390089i	0.731167	+	0.682199i	$0.238976\pi$
$558$		0			0
$559$	−1.06155	+	7.58100i	−0.0448989	+	0.320642i
$560$		0			0
$561$	−0.438447	+	0.759413i	−0.0185113	+	0.0320624i
$562$		0			0
$563$	10.8078	+	18.7196i	0.455493	+	0.788937i	0.998716	−	0.0506512i	$-0.0161297\pi$
$563$	10.8078	+	18.7196i	0.455493	+	0.788937i	−0.543223	+	0.839588i	$0.682796\pi$
$564$		0			0
$565$	−9.34233	−	16.1814i	−0.393035	−	0.680756i
$566$		0			0
$567$	4.56155			0.191567
$568$		0			0
$569$	−14.4384	+	25.0081i	−0.605291	+	1.04840i	0.386714	+	0.922200i	$0.373610\pi$
$569$	−14.4384	+	25.0081i	−0.605291	+	1.04840i	−0.992005	+	0.126195i	$0.959723\pi$
$570$		0			0
$571$	−43.2311			−1.80916			−0.904582	−	0.426300i	$-0.859817\pi$
$571$	−43.2311			−1.80916			−0.904582	+	0.426300i	$0.859817\pi$
$572$		0			0
$573$	−20.0000			−0.835512
$574$		0			0
$575$	−0.219224	+	0.379706i	−0.00914226	+	0.0158349i
$576$		0			0
$577$	26.9848			1.12339			0.561697	−	0.827343i	$-0.310149\pi$
$577$	26.9848			1.12339			0.561697	+	0.827343i	$0.310149\pi$
$578$		0			0
$579$	9.52699	+	16.5012i	0.395928	+	0.685768i
$580$		0			0
$581$	−30.4924	−	52.8144i	−1.26504	−	2.19111i
$582$		0			0
$583$	1.56155	−	2.70469i	0.0646729	−	0.112017i
$584$		0			0
$585$	−0.500000	+	3.57071i	−0.0206725	+	0.147631i
$586$		0			0
$587$	20.6847	−	35.8269i	0.853747	−	1.47873i	−0.0240552	−	0.999711i	$-0.507658\pi$
$587$	20.6847	−	35.8269i	0.853747	−	1.47873i	0.877802	−	0.479023i	$-0.159009\pi$
$588$		0			0
$589$	6.43845	+	11.1517i	0.265292	+	0.459499i
$590$		0			0
$591$	−4.00000	−	6.92820i	−0.164538	−	0.284988i
$592$		0			0
$593$	−10.3002			−0.422978			−0.211489	−	0.977380i	$-0.567831\pi$
$593$	−10.3002			−0.422978			−0.211489	+	0.977380i	$0.567831\pi$
$594$		0			0
$595$	4.56155	−	7.90084i	0.187005	−	0.323903i
$596$		0			0
$597$	−9.43845			−0.386290
$598$		0			0
$599$	−21.3693			−0.873127			−0.436563	−	0.899674i	$-0.643805\pi$
$599$	−21.3693			−0.873127			−0.436563	+	0.899674i	$0.643805\pi$
$600$		0			0
$601$	24.4654	−	42.3754i	0.997966	−	1.72853i	0.443774	−	0.896139i	$-0.353639\pi$
$601$	24.4654	−	42.3754i	0.997966	−	1.72853i	0.554192	−	0.832389i	$-0.313027\pi$
$602$		0			0
$603$	−6.56155			−0.267207
$604$		0			0
$605$	5.40388	+	9.35980i	0.219699	+	0.380530i
$606$		0			0
$607$	3.31534	+	5.74234i	0.134566	+	0.233074i	0.925431	−	0.378915i	$-0.123703\pi$
$607$	3.31534	+	5.74234i	0.134566	+	0.233074i	−0.790866	+	0.611990i	$0.790369\pi$
$608$		0			0
$609$	19.8078	−	34.3081i	0.802651	−	1.39023i
$610$		0			0
$611$	−6.93087	−	5.40938i	−0.280393	−	0.218840i
$612$		0			0
$613$	−0.307764	+	0.533063i	−0.0124305	+	0.0215302i	−0.872174	−	0.489196i	$-0.837290\pi$
$613$	−0.307764	+	0.533063i	−0.0124305	+	0.0215302i	0.859743	+	0.510726i	$0.170624\pi$
$614$		0			0
$615$	−1.00000	−	1.73205i	−0.0403239	−	0.0698430i
$616$		0			0
$617$	−9.78078	−	16.9408i	−0.393759	−	0.682011i	0.599183	−	0.800612i	$-0.295492\pi$
$617$	−9.78078	−	16.9408i	−0.393759	−	0.682011i	−0.992942	+	0.118601i	$0.962159\pi$
$618$		0			0
$619$	−28.4233			−1.14243			−0.571214	−	0.820801i	$-0.693527\pi$
$619$	−28.4233			−1.14243			−0.571214	+	0.820801i	$0.693527\pi$
$620$		0			0
$621$	0.219224	−	0.379706i	0.00879714	−	0.0152371i
$622$		0			0
$623$	9.12311			0.365510
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	0.684658	−	1.18586i	0.0273426	−	0.0473588i
$628$		0			0
$629$	−0.876894			−0.0349641
$630$		0			0
$631$	−3.28078	−	5.68247i	−0.130606	−	0.226216i	0.793305	−	0.608825i	$-0.208359\pi$
$631$	−3.28078	−	5.68247i	−0.130606	−	0.226216i	−0.923910	+	0.382609i	$0.875026\pi$
$632$		0			0
$633$	11.5270	+	19.9653i	0.458157	+	0.793551i
$634$		0			0
$635$	4.84233	−	8.38716i	0.192162	−	0.332834i
$636$		0			0
$637$	46.1501	−	18.6729i	1.82853	−	0.739845i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−17.0000	−	29.4449i	−0.671460	−	1.16300i	−0.977490	−	0.210981i	$-0.932334\pi$
$641$	−17.0000	−	29.4449i	−0.671460	−	1.16300i	0.306031	−	0.952022i	$-0.400999\pi$
$642$		0			0
$643$	−24.0885	−	41.7226i	−0.949959	−	1.64538i	−0.745503	−	0.666502i	$-0.767791\pi$
$643$	−24.0885	−	41.7226i	−0.949959	−	1.64538i	−0.204456	−	0.978876i	$-0.565543\pi$
$644$		0			0
$645$	−2.12311			−0.0835972
$646$		0			0
$647$	−19.0540	+	33.0025i	−0.749089	+	1.29746i	0.199171	+	0.979965i	$0.436175\pi$
$647$	−19.0540	+	33.0025i	−0.749089	+	1.29746i	−0.948260	+	0.317496i	$0.897158\pi$
$648$		0			0
$649$	3.80776			0.149468
$650$		0			0
$651$	18.8078			0.737134
$652$		0			0
$653$	12.1231	−	20.9978i	0.474414	−	0.821709i	−0.525157	−	0.851005i	$-0.675993\pi$
$653$	12.1231	−	20.9978i	0.474414	−	0.821709i	0.999571	+	0.0292966i	$0.00932673\pi$
$654$		0			0
$655$	1.56155			0.0610149
$656$		0			0
$657$	−4.28078	−	7.41452i	−0.167009	−	0.289268i
$658$		0			0
$659$	−6.58854	−	11.4117i	−0.256653	−	0.444536i	0.708690	−	0.705520i	$-0.249286\pi$
$659$	−6.58854	−	11.4117i	−0.256653	−	0.444536i	−0.965343	+	0.260984i	$0.915953\pi$
$660$		0			0
$661$	7.28078	−	12.6107i	0.283189	−	0.490498i	−0.688979	−	0.724781i	$-0.741941\pi$
$661$	7.28078	−	12.6107i	0.283189	−	0.490498i	0.972168	+	0.234283i	$0.0752742\pi$
$662$		0			0
$663$	−5.68466	−	4.43674i	−0.220774	−	0.172309i
$664$		0			0
$665$	−7.12311	+	12.3376i	−0.276222	+	0.478431i
$666$		0			0
$667$	−1.90388	−	3.29762i	−0.0737186	−	0.127684i
$668$		0			0
$669$	−11.8078	−	20.4516i	−0.456515	−	0.790706i
$670$		0			0
$671$	−0.738634			−0.0285146
$672$		0			0
$673$	−10.1577	+	17.5936i	−0.391549	+	0.678184i	−0.992654	−	0.120987i	$-0.961394\pi$
$673$	−10.1577	+	17.5936i	−0.391549	+	0.678184i	0.601105	+	0.799170i	$0.294727\pi$
$674$		0			0
$675$	−1.00000			−0.0384900
$676$		0			0
$677$	−6.24621			−0.240061			−0.120031	−	0.992770i	$-0.538299\pi$
$677$	−6.24621			−0.240061			−0.120031	+	0.992770i	$0.538299\pi$
$678$		0			0
$679$	−28.6501	+	49.6234i	−1.09949	+	1.90437i
$680$		0			0
$681$	−0.630683			−0.0241678
$682$		0			0
$683$	−4.87689	−	8.44703i	−0.186609	−	0.323217i	0.757508	−	0.652825i	$-0.226416\pi$
$683$	−4.87689	−	8.44703i	−0.186609	−	0.323217i	−0.944118	+	0.329609i	$0.893083\pi$
$684$		0			0
$685$	0.219224	+	0.379706i	0.00837610	+	0.0145078i
$686$		0			0
$687$	−14.3693	+	24.8884i	−0.548224	+	0.949551i
$688$		0			0
$689$	20.2462	+	15.8017i	0.771319	+	0.601996i
$690$		0			0
$691$	−15.6501	+	27.1068i	−0.595358	+	1.03119i	0.398139	+	0.917325i	$0.369656\pi$
$691$	−15.6501	+	27.1068i	−0.595358	+	1.03119i	−0.993496	+	0.113864i	$0.963677\pi$
$692$		0			0
$693$	−1.00000	−	1.73205i	−0.0379869	−	0.0657952i
$694$		0			0
$695$	−1.40388	−	2.43160i	−0.0532523	−	0.0922357i
$696$		0			0
$697$	4.00000			0.151511
$698$		0			0
$699$	8.02699	−	13.9032i	0.303609	−	0.525865i
$700$		0			0
$701$	−23.3153			−0.880608			−0.440304	−	0.897849i	$-0.645129\pi$
$701$	−23.3153			−0.880608			−0.440304	+	0.897849i	$0.645129\pi$
$702$		0			0
$703$	1.36932			0.0516448
$704$		0			0
$705$	1.21922	−	2.11176i	0.0459186	−	0.0795334i
$706$		0			0
$707$	−37.6155			−1.41468
$708$		0			0
$709$	11.5961	+	20.0851i	0.435501	+	0.754310i	0.997336	−	0.0729388i	$-0.0232378\pi$
$709$	11.5961	+	20.0851i	0.435501	+	0.754310i	−0.561835	+	0.827249i	$0.689904\pi$
$710$		0			0
$711$	8.62311	+	14.9357i	0.323392	+	0.560131i
$712$		0			0
$713$	0.903882	−	1.56557i	0.0338506	−	0.0586310i
$714$		0			0
$715$	1.46543	−	0.592932i	0.0548042	−	0.0221744i
$716$		0			0
$717$	2.00000	−	3.46410i	0.0746914	−	0.129369i
$718$		0			0
$719$	−26.2462	−	45.4598i	−0.978819	−	1.69536i	−0.666711	−	0.745317i	$-0.732298\pi$
$719$	−26.2462	−	45.4598i	−0.978819	−	1.69536i	−0.312108	−	0.950047i	$-0.601035\pi$
$720$		0			0
$721$	−1.28078	−	2.21837i	−0.0476986	−	0.0826164i
$722$		0			0
$723$	28.9309			1.07595
$724$		0			0
$725$	−4.34233	+	7.52113i	−0.161270	+	0.279328i
$726$		0			0
$727$	−12.3153			−0.456751			−0.228375	−	0.973573i	$-0.573341\pi$
$727$	−12.3153			−0.456751			−0.228375	+	0.973573i	$0.573341\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	2.12311	−	3.67733i	0.0785259	−	0.136011i
$732$		0			0
$733$	−44.4233			−1.64081			−0.820406	−	0.571782i	$-0.806252\pi$
$733$	−44.4233			−1.64081			−0.820406	+	0.571782i	$0.806252\pi$
$734$		0			0
$735$	6.90388	+	11.9579i	0.254654	+	0.441073i
$736$		0			0
$737$	1.43845	+	2.49146i	0.0529859	+	0.0917742i
$738$		0			0
$739$	7.75379	−	13.4300i	0.285228	−	0.494029i	−0.687437	−	0.726244i	$-0.741264\pi$
$739$	7.75379	−	13.4300i	0.285228	−	0.494029i	0.972664	+	0.232215i	$0.0745974\pi$
$740$		0			0
$741$	8.87689	+	6.92820i	0.326101	+	0.254514i
$742$		0			0
$743$	2.09612	−	3.63058i	0.0768991	−	0.133193i	−0.825011	−	0.565116i	$-0.808831\pi$
$743$	2.09612	−	3.63058i	0.0768991	−	0.133193i	0.901911	+	0.431923i	$0.142165\pi$
$744$		0			0
$745$	−7.46543	−	12.9305i	−0.273512	−	0.473737i
$746$		0			0
$747$	−6.68466	−	11.5782i	−0.244579	−	0.423623i
$748$		0			0
$749$	−50.7386			−1.85395
$750$		0			0
$751$	7.02699	−	12.1711i	0.256418	−	0.444130i	−0.708861	−	0.705348i	$-0.750791\pi$
$751$	7.02699	−	12.1711i	0.256418	−	0.444130i	0.965280	+	0.261218i	$0.0841242\pi$
$752$		0			0
$753$	−6.43845			−0.234630
$754$		0			0
$755$	16.0000			0.582300
$756$		0			0
$757$	15.4924	−	26.8337i	0.563082	−	0.975286i	−0.434144	−	0.900844i	$-0.642949\pi$
$757$	15.4924	−	26.8337i	0.563082	−	0.975286i	0.997225	−	0.0744424i	$-0.0237177\pi$
$758$		0			0
$759$	−0.192236			−0.00697772
$760$		0			0
$761$	19.1231	+	33.1222i	0.693212	+	1.20068i	0.970780	+	0.239972i	$0.0771384\pi$
$761$	19.1231	+	33.1222i	0.693212	+	1.20068i	−0.277568	+	0.960706i	$0.589528\pi$
$762$		0			0
$763$	6.40388	+	11.0918i	0.231836	+	0.401552i
$764$		0			0
$765$	1.00000	−	1.73205i	0.0361551	−	0.0626224i
$766$		0			0
$767$	−4.34233	+	31.0104i	−0.156792	+	1.11972i
$768$		0			0
$769$	10.9039	−	18.8861i	0.393204	−	0.681049i	−0.599666	−	0.800250i	$-0.704700\pi$
$769$	10.9039	−	18.8861i	0.393204	−	0.681049i	0.992870	+	0.119201i	$0.0380333\pi$
$770$		0			0
$771$	6.21922	+	10.7720i	0.223980	+	0.387945i
$772$		0			0
$773$	22.5616	+	39.0778i	0.811483	+	1.40553i	0.911826	+	0.410576i	$0.134672\pi$
$773$	22.5616	+	39.0778i	0.811483	+	1.40553i	−0.100344	+	0.994953i	$0.531994\pi$
$774$		0			0
$775$	−4.12311			−0.148106
$776$		0			0
$777$	1.00000	−	1.73205i	0.0358748	−	0.0621370i
$778$		0			0
$779$	−6.24621			−0.223794
$780$		0			0
$781$		0			0
$782$		0			0
$783$	4.34233	−	7.52113i	0.155182	−	0.268783i
$784$		0			0
$785$	−5.24621			−0.187245
$786$		0			0
$787$	−24.1847	−	41.8891i	−0.862090	−	1.49318i	−0.869908	−	0.493214i	$-0.835822\pi$
$787$	−24.1847	−	41.8891i	−0.862090	−	1.49318i	0.00781794	−	0.999969i	$-0.497511\pi$
$788$		0			0
$789$	−12.4654	−	21.5908i	−0.443781	−	0.768652i
$790$		0			0
$791$	−42.6155	+	73.8123i	−1.51523	+	2.62446i
$792$		0			0
$793$	0.842329	−	6.01543i	0.0299120	−	0.213614i
$794$		0			0
$795$	−3.56155	+	6.16879i	−0.126315	+	0.218784i
$796$		0			0
$797$	−25.6847	−	44.4871i	−0.909797	−	1.57582i	−0.814345	−	0.580381i	$-0.802904\pi$
$797$	−25.6847	−	44.4871i	−0.909797	−	1.57582i	−0.0954523	−	0.995434i	$-0.530430\pi$
$798$		0			0
$799$	2.43845	+	4.22351i	0.0862661	+	0.149417i
$800$		0			0
$801$	2.00000			0.0706665
$802$		0			0
$803$	−1.87689	+	3.25088i	−0.0662342	+	0.114721i
$804$		0			0
$805$	2.00000			0.0704907
$806$		0			0
$807$	−8.24621			−0.290280
$808$		0			0
$809$	25.5616	−	44.2739i	0.898696	−	1.55659i	0.0695342	−	0.997580i	$-0.477849\pi$
$809$	25.5616	−	44.2739i	0.898696	−	1.55659i	0.829162	−	0.559008i	$-0.188818\pi$
$810$		0			0
$811$	−36.8078			−1.29250			−0.646248	−	0.763128i	$-0.723663\pi$
$811$	−36.8078			−1.29250			−0.646248	+	0.763128i	$0.723663\pi$
$812$		0			0
$813$	−11.8693	−	20.5583i	−0.416275	−	0.721010i
$814$		0			0
$815$	−5.93845	−	10.2857i	−0.208015	−	0.360292i
$816$		0			0
$817$	−3.31534	+	5.74234i	−0.115989	+	0.200899i
$818$		0			0
$819$	15.2462	−	6.16879i	0.532746	−	0.215555i
$820$		0			0
$821$	3.34233	−	5.78908i	0.116648	−	0.202040i	−0.801789	−	0.597607i	$-0.796118\pi$
$821$	3.34233	−	5.78908i	0.116648	−	0.202040i	0.918437	+	0.395566i	$0.129452\pi$
$822$		0			0
$823$	−16.9309	−	29.3251i	−0.590173	−	1.02221i	−0.994209	−	0.107466i	$-0.965726\pi$
$823$	−16.9309	−	29.3251i	−0.590173	−	1.02221i	0.404036	−	0.914743i	$-0.367607\pi$
$824$		0			0
$825$	0.219224	+	0.379706i	0.00763239	+	0.0132197i
$826$		0			0
$827$	7.26137			0.252502			0.126251	−	0.991998i	$-0.459705\pi$
$827$	7.26137			0.252502			0.126251	+	0.991998i	$0.459705\pi$
$828$		0			0
$829$	−24.8423	+	43.0282i	−0.862810	+	1.49443i	0.00639587	+	0.999980i	$0.497964\pi$
$829$	−24.8423	+	43.0282i	−0.862810	+	1.49443i	−0.869206	+	0.494451i	$0.835369\pi$
$830$		0			0
$831$	−15.5616			−0.539824
$832$		0			0
$833$	−27.6155			−0.956821
$834$		0			0
$835$	−12.7808	+	22.1370i	−0.442297	+	0.766081i
$836$		0			0
$837$	4.12311			0.142515
$838$		0			0
$839$	5.87689	+	10.1791i	0.202893	+	0.351421i	0.949459	−	0.313890i	$-0.101632\pi$
$839$	5.87689	+	10.1791i	0.202893	+	0.351421i	−0.746566	+	0.665311i	$0.768299\pi$
$840$		0			0
$841$	−23.2116	−	40.2038i	−0.800402	−	1.38634i
$842$		0			0
$843$	12.9309	−	22.3969i	0.445363	−	0.771391i
$844$		0			0
$845$	3.15767	+	12.6107i	0.108627	+	0.433820i
$846$		0			0
$847$	24.6501	−	42.6952i	0.846987	−	1.46702i
$848$		0			0
$849$	1.50000	+	2.59808i	0.0514799	+	0.0891657i
$850$		0			0
$851$	−0.0961180	−	0.166481i	−0.00329488	−	0.00570690i
$852$		0			0
$853$	9.38447			0.321318			0.160659	−	0.987010i	$-0.448638\pi$
$853$	9.38447			0.321318			0.160659	+	0.987010i	$0.448638\pi$
$854$		0			0
$855$	−1.56155	+	2.70469i	−0.0534040	+	0.0924984i
$856$		0			0
$857$	−7.42329			−0.253575			−0.126787	−	0.991930i	$-0.540467\pi$
$857$	−7.42329			−0.253575			−0.126787	+	0.991930i	$0.540467\pi$
$858$		0			0
$859$	−18.8078			−0.641713			−0.320856	−	0.947128i	$-0.603971\pi$
$859$	−18.8078			−0.641713			−0.320856	+	0.947128i	$0.603971\pi$
$860$		0			0
$861$	−4.56155	+	7.90084i	−0.155457	+	0.269260i
$862$		0			0
$863$	1.69981			0.0578623			0.0289312	−	0.999581i	$-0.490790\pi$
$863$	1.69981			0.0578623			0.0289312	+	0.999581i	$0.490790\pi$
$864$		0			0
$865$	2.00000	+	3.46410i	0.0680020	+	0.117783i
$866$		0			0
$867$	−6.50000	−	11.2583i	−0.220752	−	0.382353i
$868$		0			0
$869$	3.78078	−	6.54850i	0.128254	−	0.222143i
$870$		0			0
$871$	−21.9309	+	8.87348i	−0.743099	+	0.300666i
$872$		0			0
$873$	−6.28078	+	10.8786i	−0.212572	+	0.368186i
$874$		0			0
$875$	−2.28078	−	3.95042i	−0.0771043	−	0.133549i
$876$		0			0
$877$	13.3423	+	23.1096i	0.450538	+	0.780355i	0.998419	−	0.0562008i	$-0.0178987\pi$
$877$	13.3423	+	23.1096i	0.450538	+	0.780355i	−0.547881	+	0.836556i	$0.684565\pi$
$878$		0			0
$879$	4.87689			0.164494
$880$		0			0
$881$	−20.4384	+	35.4004i	−0.688589	+	1.19267i	0.283706	+	0.958911i	$0.408436\pi$
$881$	−20.4384	+	35.4004i	−0.688589	+	1.19267i	−0.972294	+	0.233759i	$0.924897\pi$
$882$		0			0
$883$	20.1231			0.677196			0.338598	−	0.940931i	$-0.390047\pi$
$883$	20.1231			0.677196			0.338598	+	0.940931i	$0.390047\pi$
$884$		0			0
$885$	−8.68466			−0.291932
$886$		0			0
$887$	−22.3963	+	38.7915i	−0.751994	+	1.30249i	0.194860	+	0.980831i	$0.437575\pi$
$887$	−22.3963	+	38.7915i	−0.751994	+	1.30249i	−0.946855	+	0.321661i	$0.895759\pi$
$888$		0			0
$889$	−44.1771			−1.48165
$890$		0			0
$891$	−0.219224	−	0.379706i	−0.00734427	−	0.0127206i
$892$		0			0
$893$	−3.80776	−	6.59524i	−0.127422	−	0.220701i
$894$		0			0
$895$	4.90388	−	8.49377i	0.163919	−	0.283916i
$896$		0			0
$897$	0.219224	−	1.56557i	0.00731966	−	0.0522728i
$898$		0			0
$899$	17.9039	−	31.0104i	0.597128	−	1.03426i
$900$		0			0
$901$	−7.12311	−	12.3376i	−0.237305	−	0.411024i
$902$		0			0
$903$	4.84233	+	8.38716i	0.161143	+	0.279107i
$904$		0			0
$905$	5.12311			0.170298
$906$		0			0
$907$	−20.7808	+	35.9934i	−0.690014	+	1.19514i	0.281818	+	0.959468i	$0.409062\pi$
$907$	−20.7808	+	35.9934i	−0.690014	+	1.19514i	−0.971833	+	0.235672i	$0.924271\pi$
$908$		0			0
$909$	−8.24621			−0.273510
$910$		0			0
$911$	−3.61553			−0.119788			−0.0598939	−	0.998205i	$-0.519076\pi$
$911$	−3.61553			−0.119788			−0.0598939	+	0.998205i	$0.519076\pi$
$912$		0			0
$913$	−2.93087	+	5.07642i	−0.0969976	+	0.168005i
$914$		0			0
$915$	1.68466			0.0556931
$916$		0			0
$917$	−3.56155	−	6.16879i	−0.117613	−	0.203711i
$918$		0			0
$919$	16.4924	+	28.5657i	0.544035	+	0.942296i	0.998667	+	0.0516167i	$0.0164374\pi$
$919$	16.4924	+	28.5657i	0.544035	+	0.942296i	−0.454632	+	0.890679i	$0.650229\pi$
$920$		0			0
$921$	6.96543	−	12.0645i	0.229519	−	0.397538i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−0.219224	+	0.379706i	−0.00720803	+	0.0124847i
$926$		0			0
$927$	−0.280776	−	0.486319i	−0.00922191	−	0.0159728i
$928$		0			0
$929$	25.6155	+	44.3674i	0.840418	+	1.45565i	0.889542	+	0.456854i	$0.151024\pi$
$929$	25.6155	+	44.3674i	0.840418	+	1.45565i	−0.0491233	+	0.998793i	$0.515643\pi$
$930$		0			0
$931$	43.1231			1.41330
$932$		0			0
$933$	9.68466	−	16.7743i	0.317061	−	0.549167i
$934$		0			0
$935$	−0.876894			−0.0286775
$936$		0			0
$937$	−7.75379			−0.253305			−0.126653	−	0.991947i	$-0.540423\pi$
$937$	−7.75379			−0.253305			−0.126653	+	0.991947i	$0.540423\pi$
$938$		0			0
$939$	11.5270	−	19.9653i	0.376169	−	0.651544i
$940$		0			0
$941$	−34.3542			−1.11991			−0.559957	−	0.828522i	$-0.689182\pi$
$941$	−34.3542			−1.11991			−0.559957	+	0.828522i	$0.689182\pi$
$942$		0			0
$943$	0.438447	+	0.759413i	0.0142778	+	0.0247299i
$944$		0			0
$945$	2.28078	+	3.95042i	0.0741937	+	0.128507i
$946$		0			0
$947$	−27.6847	+	47.9512i	−0.899631	+	1.55821i	−0.0716636	+	0.997429i	$0.522831\pi$
$947$	−27.6847	+	47.9512i	−0.899631	+	1.55821i	−0.827967	+	0.560777i	$0.810503\pi$
$948$		0			0
$949$	−24.3348	−	18.9927i	−0.789939	−	0.616529i
$950$		0			0
$951$	9.12311	−	15.8017i	0.295837	−	0.512405i
$952$		0			0
$953$	−20.9039	−	36.2066i	−0.677143	−	1.17285i	−0.975838	−	0.218498i	$-0.929884\pi$
$953$	−20.9039	−	36.2066i	−0.677143	−	1.17285i	0.298694	−	0.954349i	$-0.403449\pi$
$954$		0			0
$955$	−10.0000	−	17.3205i	−0.323592	−	0.560478i
$956$		0			0
$957$	−3.80776			−0.123088
$958$		0			0
$959$	1.00000	−	1.73205i	0.0322917	−	0.0559308i
$960$		0			0
$961$	−14.0000			−0.451613
$962$		0			0
$963$	−11.1231			−0.358437
$964$		0			0
$965$	−9.52699	+	16.5012i	−0.306685	+	0.531193i
$966$		0			0
$967$	−6.24621			−0.200865			−0.100432	−	0.994944i	$-0.532023\pi$
$967$	−6.24621			−0.200865			−0.100432	+	0.994944i	$0.532023\pi$
$968$		0			0
$969$	−3.12311	−	5.40938i	−0.100329	−	0.173774i
$970$		0			0
$971$	−1.75379	−	3.03765i	−0.0562818	−	0.0974829i	0.836512	−	0.547949i	$-0.184591\pi$
$971$	−1.75379	−	3.03765i	−0.0562818	−	0.0974829i	−0.892794	+	0.450466i	$0.851258\pi$
$972$		0			0
$973$	−6.40388	+	11.0918i	−0.205299	+	0.355588i
$974$		0			0
$975$	−3.34233	+	1.35234i	−0.107040	+	0.0433097i
$976$		0			0
$977$	−26.1501	+	45.2933i	−0.836616	+	1.44906i	0.0560926	+	0.998426i	$0.482136\pi$
$977$	−26.1501	+	45.2933i	−0.836616	+	1.44906i	−0.892708	+	0.450635i	$0.851198\pi$
$978$		0			0
$979$	−0.438447	−	0.759413i	−0.0140128	−	0.0242709i
$980$		0			0
$981$	1.40388	+	2.43160i	0.0448225	+	0.0776349i
$982$		0			0
$983$	21.8078			0.695560			0.347780	−	0.937576i	$-0.386936\pi$
$983$	21.8078			0.695560			0.347780	+	0.937576i	$0.386936\pi$
$984$		0			0
$985$	4.00000	−	6.92820i	0.127451	−	0.220751i
$986$		0			0
$987$	−11.1231			−0.354052
$988$		0			0
$989$	0.930870			0.0295999
$990$		0			0
$991$	−11.6577	+	20.1917i	−0.370318	+	0.641410i	−0.989614	−	0.143748i	$-0.954085\pi$
$991$	−11.6577	+	20.1917i	−0.370318	+	0.641410i	0.619296	+	0.785157i	$0.287418\pi$
$992$		0			0
$993$	−5.43845			−0.172584
$994$		0			0
$995$	−4.71922	−	8.17394i	−0.149609	−	0.259131i
$996$		0			0
$997$	16.7732	+	29.0520i	0.531213	+	0.920087i	0.999336	+	0.0364243i	$0.0115968\pi$
$997$	16.7732	+	29.0520i	0.531213	+	0.920087i	−0.468124	+	0.883663i	$0.655070\pi$
$998$		0			0
$999$	0.219224	−	0.379706i	0.00693593	−	0.0120134i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1560.2.bg.f.841.1	yes	4
13.3	even	3	inner	1560.2.bg.f.601.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1560.2.bg.f.601.1	✓	4	13.3	even	3	inner
1560.2.bg.f.841.1	yes	4	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1560 = 2^{3} \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1560.bg (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{3} +1.00000 q^{5} +(-2.28078 - 3.95042i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{3} +1.00000 q^{5} +(-2.28078 - 3.95042i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(-0.219224 + 0.379706i) q^{11} +(-2.84233 - 2.21837i) q^{13} +(0.500000 - 0.866025i) q^{15} +(1.00000 + 1.73205i) q^{17} +(-1.56155 - 2.70469i) q^{19} -4.56155 q^{21} +(-0.219224 + 0.379706i) q^{23} +1.00000 q^{25} -1.00000 q^{27} +(-4.34233 + 7.52113i) q^{29} -4.12311 q^{31} +(0.219224 + 0.379706i) q^{33} +(-2.28078 - 3.95042i) q^{35} +(-0.219224 + 0.379706i) q^{37} +(-3.34233 + 1.35234i) q^{39} +(1.00000 - 1.73205i) q^{41} +(-1.06155 - 1.83866i) q^{43} +(-0.500000 - 0.866025i) q^{45} +2.43845 q^{47} +(-6.90388 + 11.9579i) q^{49} +2.00000 q^{51} -7.12311 q^{53} +(-0.219224 + 0.379706i) q^{55} -3.12311 q^{57} +(-4.34233 - 7.52113i) q^{59} +(0.842329 + 1.45896i) q^{61} +(-2.28078 + 3.95042i) q^{63} +(-2.84233 - 2.21837i) q^{65} +(3.28078 - 5.68247i) q^{67} +(0.219224 + 0.379706i) q^{69} +8.56155 q^{73} +(0.500000 - 0.866025i) q^{75} +2.00000 q^{77} -17.2462 q^{79} +(-0.500000 + 0.866025i) q^{81} +13.3693 q^{83} +(1.00000 + 1.73205i) q^{85} +(4.34233 + 7.52113i) q^{87} +(-1.00000 + 1.73205i) q^{89} +(-2.28078 + 16.2880i) q^{91} +(-2.06155 + 3.57071i) q^{93} +(-1.56155 - 2.70469i) q^{95} +(-6.28078 - 10.8786i) q^{97} +0.438447 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} + 4 q^{5} - 5 q^{7} - 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^3 + 4 * q^5 - 5 * q^7 - 2 * q^9	\( 4 q + 2 q^{3} + 4 q^{5} - 5 q^{7} - 2 q^{9} - 5 q^{11} + q^{13} + 2 q^{15} + 4 q^{17} + 2 q^{19} - 10 q^{21} - 5 q^{23} + 4 q^{25} - 4 q^{27} - 5 q^{29} + 5 q^{33} - 5 q^{35} - 5 q^{37} - q^{39} + 4 q^{41} + 4 q^{43} - 2 q^{45} + 18 q^{47} - 7 q^{49} + 8 q^{51} - 12 q^{53} - 5 q^{55} + 4 q^{57} - 5 q^{59} - 9 q^{61} - 5 q^{63} + q^{65} + 9 q^{67} + 5 q^{69} + 26 q^{73} + 2 q^{75} + 8 q^{77} - 36 q^{79} - 2 q^{81} + 4 q^{83} + 4 q^{85} + 5 q^{87} - 4 q^{89} - 5 q^{91} + 2 q^{95} - 21 q^{97} + 10 q^{99}+O(q^{100}) \) 4 * q + 2 * q^3 + 4 * q^5 - 5 * q^7 - 2 * q^9 - 5 * q^11 + q^13 + 2 * q^15 + 4 * q^17 + 2 * q^19 - 10 * q^21 - 5 * q^23 + 4 * q^25 - 4 * q^27 - 5 * q^29 + 5 * q^33 - 5 * q^35 - 5 * q^37 - q^39 + 4 * q^41 + 4 * q^43 - 2 * q^45 + 18 * q^47 - 7 * q^49 + 8 * q^51 - 12 * q^53 - 5 * q^55 + 4 * q^57 - 5 * q^59 - 9 * q^61 - 5 * q^63 + q^65 + 9 * q^67 + 5 * q^69 + 26 * q^73 + 2 * q^75 + 8 * q^77 - 36 * q^79 - 2 * q^81 + 4 * q^83 + 4 * q^85 + 5 * q^87 - 4 * q^89 - 5 * q^91 + 2 * q^95 - 21 * q^97 + 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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