LMFDB - Embedded newform 1170.2.i.o.451.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1170,2,Mod(451,1170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1170, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("1170.451");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1170.i (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:	$9.34249703649$
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:	no (minimal twist has level 390)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			451.1
Root			$1.28078 + 2.21837i$ of defining polynomial
Character	$\chi$	$=$	1170.451
Dual form			1170.2.i.o.991.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(-1.78078 - 3.08440i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(-1.78078 - 3.08440i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{10} +(-2.06155 + 3.57071i) q^{11} +(-3.34233 - 1.35234i) q^{13} -3.56155 q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.56155 + 4.43674i) q^{17} +(1.78078 + 3.08440i) q^{19} +(0.500000 + 0.866025i) q^{20} +(2.06155 + 3.57071i) q^{22} +(-3.84233 + 6.65511i) q^{23} +1.00000 q^{25} +(-2.84233 + 2.21837i) q^{26} +(-1.78078 + 3.08440i) q^{28} +(3.28078 - 5.68247i) q^{29} +5.68466 q^{31} +(0.500000 + 0.866025i) q^{32} +5.12311 q^{34} +(1.78078 + 3.08440i) q^{35} +(-2.06155 + 3.57071i) q^{37} +3.56155 q^{38} +1.00000 q^{40} +(-2.12311 + 3.67733i) q^{41} +(-2.28078 - 3.95042i) q^{43} +4.12311 q^{44} +(3.84233 + 6.65511i) q^{46} -7.00000 q^{47} +(-2.84233 + 4.92306i) q^{49} +(0.500000 - 0.866025i) q^{50} +(0.500000 + 3.57071i) q^{52} -4.43845 q^{53} +(2.06155 - 3.57071i) q^{55} +(1.78078 + 3.08440i) q^{56} +(-3.28078 - 5.68247i) q^{58} +(5.28078 + 9.14657i) q^{59} +(-3.00000 - 5.19615i) q^{61} +(2.84233 - 4.92306i) q^{62} +1.00000 q^{64} +(3.34233 + 1.35234i) q^{65} +(-7.12311 + 12.3376i) q^{67} +(2.56155 - 4.43674i) q^{68} +3.56155 q^{70} +(-2.43845 - 4.22351i) q^{71} -15.3693 q^{73} +(2.06155 + 3.57071i) q^{74} +(1.78078 - 3.08440i) q^{76} +14.6847 q^{77} +7.43845 q^{79} +(0.500000 - 0.866025i) q^{80} +(2.12311 + 3.67733i) q^{82} -1.12311 q^{83} +(-2.56155 - 4.43674i) q^{85} -4.56155 q^{86} +(2.06155 - 3.57071i) q^{88} +(0.903882 - 1.56557i) q^{89} +(1.78078 + 12.7173i) q^{91} +7.68466 q^{92} +(-3.50000 + 6.06218i) q^{94} +(-1.78078 - 3.08440i) q^{95} +(-0.561553 - 0.972638i) q^{97} +(2.84233 + 4.92306i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{4} - 4 q^{5} - 3 q^{7} - 4 q^{8}+O(q^{10}) $ 4 * q + 2 * q^2 - 2 * q^4 - 4 * q^5 - 3 * q^7 - 4 * q^8	$ 4 q + 2 q^{2} - 2 q^{4} - 4 q^{5} - 3 q^{7} - 4 q^{8} - 2 q^{10} - q^{13} - 6 q^{14} - 2 q^{16} + 2 q^{17} + 3 q^{19} + 2 q^{20} - 3 q^{23} + 4 q^{25} + q^{26} - 3 q^{28} + 9 q^{29} - 2 q^{31} + 2 q^{32} + 4 q^{34} + 3 q^{35} + 6 q^{38} + 4 q^{40} + 8 q^{41} - 5 q^{43} + 3 q^{46} - 28 q^{47} + q^{49} + 2 q^{50} + 2 q^{52} - 26 q^{53} + 3 q^{56} - 9 q^{58} + 17 q^{59} - 12 q^{61} - q^{62} + 4 q^{64} + q^{65} - 12 q^{67} + 2 q^{68} + 6 q^{70} - 18 q^{71} - 12 q^{73} + 3 q^{76} + 34 q^{77} + 38 q^{79} + 2 q^{80} - 8 q^{82} + 12 q^{83} - 2 q^{85} - 10 q^{86} - 17 q^{89} + 3 q^{91} + 6 q^{92} - 14 q^{94} - 3 q^{95} + 6 q^{97} - q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^4 - 4 * q^5 - 3 * q^7 - 4 * q^8 - 2 * q^10 - q^13 - 6 * q^14 - 2 * q^16 + 2 * q^17 + 3 * q^19 + 2 * q^20 - 3 * q^23 + 4 * q^25 + q^26 - 3 * q^28 + 9 * q^29 - 2 * q^31 + 2 * q^32 + 4 * q^34 + 3 * q^35 + 6 * q^38 + 4 * q^40 + 8 * q^41 - 5 * q^43 + 3 * q^46 - 28 * q^47 + q^49 + 2 * q^50 + 2 * q^52 - 26 * q^53 + 3 * q^56 - 9 * q^58 + 17 * q^59 - 12 * q^61 - q^62 + 4 * q^64 + q^65 - 12 * q^67 + 2 * q^68 + 6 * q^70 - 18 * q^71 - 12 * q^73 + 3 * q^76 + 34 * q^77 + 38 * q^79 + 2 * q^80 - 8 * q^82 + 12 * q^83 - 2 * q^85 - 10 * q^86 - 17 * q^89 + 3 * q^91 + 6 * q^92 - 14 * q^94 - 3 * q^95 + 6 * q^97 - q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times$.

$n$	$911$	$937$	$1081$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$		0			0
$7$	−1.78078	−	3.08440i	−0.673070	−	1.16579i	−0.977029	−	0.213107i	$-0.931642\pi$
$7$	−1.78078	−	3.08440i	−0.673070	−	1.16579i	0.303959	−	0.952685i	$-0.401692\pi$
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	−2.06155	+	3.57071i	−0.621582	+	1.07661i	0.367610	+	0.929980i	$0.380176\pi$
$11$	−2.06155	+	3.57071i	−0.621582	+	1.07661i	−0.989191	+	0.146631i	$0.953157\pi$
$12$		0			0
$13$	−3.34233	−	1.35234i	−0.926995	−	0.375073i
$13$	−3.34233	−	1.35234i	−0.926995	−	0.375073i
$14$	−3.56155			−0.951865
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.56155	+	4.43674i	0.621268	+	1.07607i	0.989250	+	0.146235i	$0.0467154\pi$
$17$	2.56155	+	4.43674i	0.621268	+	1.07607i	−0.367982	+	0.929833i	$0.619951\pi$
$18$		0			0
$19$	1.78078	+	3.08440i	0.408538	+	0.707609i	0.994726	−	0.102566i	$-0.0327054\pi$
$19$	1.78078	+	3.08440i	0.408538	+	0.707609i	−0.586188	+	0.810175i	$0.699372\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$		0			0
$22$	2.06155	+	3.57071i	0.439525	+	0.761279i
$23$	−3.84233	+	6.65511i	−0.801181	+	1.38769i	0.117658	+	0.993054i	$0.462461\pi$
$23$	−3.84233	+	6.65511i	−0.801181	+	1.38769i	−0.918839	+	0.394632i	$0.870872\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$	−2.84233	+	2.21837i	−0.557427	+	0.435058i
$27$		0			0
$28$	−1.78078	+	3.08440i	−0.336535	+	0.582896i
$29$	3.28078	−	5.68247i	0.609225	−	1.05521i	−0.382144	−	0.924103i	$-0.624814\pi$
$29$	3.28078	−	5.68247i	0.609225	−	1.05521i	0.991368	−	0.131105i	$-0.0418527\pi$
$30$		0			0
$31$	5.68466			1.02099			0.510497	−	0.859879i	$-0.329461\pi$
$31$	5.68466			1.02099			0.510497	+	0.859879i	$0.329461\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$	5.12311			0.878605
$35$	1.78078	+	3.08440i	0.301006	+	0.521358i
$36$		0			0
$37$	−2.06155	+	3.57071i	−0.338917	+	0.587022i	−0.984229	−	0.176897i	$-0.943394\pi$
$37$	−2.06155	+	3.57071i	−0.338917	+	0.587022i	0.645312	+	0.763919i	$0.276727\pi$
$38$	3.56155			0.577760
$39$		0			0
$40$	1.00000			0.158114
$41$	−2.12311	+	3.67733i	−0.331573	+	0.574302i	−0.982821	−	0.184564i	$-0.940913\pi$
$41$	−2.12311	+	3.67733i	−0.331573	+	0.574302i	0.651247	+	0.758866i	$0.274246\pi$
$42$		0			0
$43$	−2.28078	−	3.95042i	−0.347815	−	0.602433i	0.638046	−	0.769998i	$-0.279743\pi$
$43$	−2.28078	−	3.95042i	−0.347815	−	0.602433i	−0.985861	+	0.167565i	$0.946410\pi$
$44$	4.12311			0.621582
$45$		0			0
$46$	3.84233	+	6.65511i	0.566521	+	0.981242i
$47$	−7.00000			−1.02105			−0.510527	−	0.859861i	$-0.670550\pi$
$47$	−7.00000			−1.02105			−0.510527	+	0.859861i	$0.670550\pi$
$48$		0			0
$49$	−2.84233	+	4.92306i	−0.406047	+	0.703294i
$50$	0.500000	−	0.866025i	0.0707107	−	0.122474i
$51$		0			0
$52$	0.500000	+	3.57071i	0.0693375	+	0.495169i
$53$	−4.43845			−0.609668			−0.304834	−	0.952406i	$-0.598601\pi$
$53$	−4.43845			−0.609668			−0.304834	+	0.952406i	$0.598601\pi$
$54$		0			0
$55$	2.06155	−	3.57071i	0.277980	−	0.481475i
$56$	1.78078	+	3.08440i	0.237966	+	0.412170i
$57$		0			0
$58$	−3.28078	−	5.68247i	−0.430787	−	0.746145i
$59$	5.28078	+	9.14657i	0.687499	+	1.19078i	0.972645	+	0.232298i	$0.0746246\pi$
$59$	5.28078	+	9.14657i	0.687499	+	1.19078i	−0.285146	+	0.958484i	$0.592042\pi$
$60$		0			0
$61$	−3.00000	−	5.19615i	−0.384111	−	0.665299i	0.607535	−	0.794293i	$-0.292159\pi$
$61$	−3.00000	−	5.19615i	−0.384111	−	0.665299i	−0.991645	+	0.128994i	$0.958825\pi$
$62$	2.84233	−	4.92306i	0.360976	−	0.625229i
$63$		0			0
$64$	1.00000			0.125000
$65$	3.34233	+	1.35234i	0.414565	+	0.167738i
$66$		0			0
$67$	−7.12311	+	12.3376i	−0.870226	+	1.50728i	−0.00846293	+	0.999964i	$0.502694\pi$
$67$	−7.12311	+	12.3376i	−0.870226	+	1.50728i	−0.861763	+	0.507311i	$0.830639\pi$
$68$	2.56155	−	4.43674i	0.310634	−	0.538034i
$69$		0			0
$70$	3.56155			0.425687
$71$	−2.43845	−	4.22351i	−0.289390	−	0.501239i	0.684274	−	0.729225i	$-0.260119\pi$
$71$	−2.43845	−	4.22351i	−0.289390	−	0.501239i	−0.973664	+	0.227986i	$0.926786\pi$
$72$		0			0
$73$	−15.3693			−1.79884			−0.899421	−	0.437083i	$-0.856012\pi$
$73$	−15.3693			−1.79884			−0.899421	+	0.437083i	$0.856012\pi$
$74$	2.06155	+	3.57071i	0.239651	+	0.415087i
$75$		0			0
$76$	1.78078	−	3.08440i	0.204269	−	0.353804i
$77$	14.6847			1.67347
$78$		0			0
$79$	7.43845			0.836891			0.418445	−	0.908242i	$-0.362575\pi$
$79$	7.43845			0.836891			0.418445	+	0.908242i	$0.362575\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$		0			0
$82$	2.12311	+	3.67733i	0.234458	+	0.406093i
$83$	−1.12311			−0.123277			−0.0616384	−	0.998099i	$-0.519633\pi$
$83$	−1.12311			−0.123277			−0.0616384	+	0.998099i	$0.519633\pi$
$84$		0			0
$85$	−2.56155	−	4.43674i	−0.277839	−	0.481232i
$86$	−4.56155			−0.491885
$87$		0			0
$88$	2.06155	−	3.57071i	0.219762	−	0.380639i
$89$	0.903882	−	1.56557i	0.0958113	−	0.165950i	−0.814136	−	0.580675i	$-0.802789\pi$
$89$	0.903882	−	1.56557i	0.0958113	−	0.165950i	0.909947	+	0.414725i	$0.136122\pi$
$90$		0			0
$91$	1.78078	+	12.7173i	0.186676	+	1.33313i
$92$	7.68466			0.801181
$93$		0			0
$94$	−3.50000	+	6.06218i	−0.360997	+	0.625266i
$95$	−1.78078	−	3.08440i	−0.182704	−	0.316452i
$96$		0			0
$97$	−0.561553	−	0.972638i	−0.0570170	−	0.0987564i	0.836108	−	0.548565i	$-0.184826\pi$
$97$	−0.561553	−	0.972638i	−0.0570170	−	0.0987564i	−0.893125	+	0.449808i	$0.851492\pi$
$98$	2.84233	+	4.92306i	0.287119	+	0.497304i
$99$		0			0
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	−8.56155	+	14.8290i	−0.851906	+	1.47555i	0.0275793	+	0.999620i	$0.491220\pi$
$101$	−8.56155	+	14.8290i	−0.851906	+	1.47555i	−0.879486	+	0.475925i	$0.842113\pi$
$102$		0			0
$103$	0.438447			0.0432015			0.0216007	−	0.999767i	$-0.493124\pi$
$103$	0.438447			0.0432015			0.0216007	+	0.999767i	$0.493124\pi$
$104$	3.34233	+	1.35234i	0.327742	+	0.132608i
$105$		0			0
$106$	−2.21922	+	3.84381i	−0.215550	+	0.373344i
$107$	1.00000	−	1.73205i	0.0966736	−	0.167444i	−0.813632	−	0.581380i	$-0.802513\pi$
$107$	1.00000	−	1.73205i	0.0966736	−	0.167444i	0.910306	+	0.413936i	$0.135846\pi$
$108$		0			0
$109$	−20.2462			−1.93924			−0.969618	−	0.244625i	$-0.921335\pi$
$109$	−20.2462			−1.93924			−0.969618	+	0.244625i	$0.921335\pi$
$110$	−2.06155	−	3.57071i	−0.196561	−	0.340454i
$111$		0			0
$112$	3.56155			0.336535
$113$	−1.84233	−	3.19101i	−0.173312	−	0.300185i	0.766264	−	0.642526i	$-0.222113\pi$
$113$	−1.84233	−	3.19101i	−0.173312	−	0.300185i	−0.939576	+	0.342341i	$0.888780\pi$
$114$		0			0
$115$	3.84233	−	6.65511i	0.358299	−	0.620592i
$116$	−6.56155			−0.609225
$117$		0			0
$118$	10.5616			0.972270
$119$	9.12311	−	15.8017i	0.836314	−	1.44854i
$120$		0			0
$121$	−3.00000	−	5.19615i	−0.272727	−	0.472377i
$122$	−6.00000			−0.543214
$123$		0			0
$124$	−2.84233	−	4.92306i	−0.255249	−	0.442104i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	2.21922	−	3.84381i	0.196924	−	0.341083i	−0.750605	−	0.660751i	$-0.770238\pi$
$127$	2.21922	−	3.84381i	0.196924	−	0.341083i	0.947530	+	0.319668i	$0.103571\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$		0			0
$130$	2.84233	−	2.21837i	0.249289	−	0.194564i
$131$	−6.12311			−0.534978			−0.267489	−	0.963561i	$-0.586194\pi$
$131$	−6.12311			−0.534978			−0.267489	+	0.963561i	$0.586194\pi$
$132$		0			0
$133$	6.34233	−	10.9852i	0.549950	−	0.952541i
$134$	7.12311	+	12.3376i	0.615343	+	1.06580i
$135$		0			0
$136$	−2.56155	−	4.43674i	−0.219651	−	0.380447i
$137$	−4.40388	−	7.62775i	−0.376249	−	0.651682i	0.614264	−	0.789101i	$-0.289453\pi$
$137$	−4.40388	−	7.62775i	−0.376249	−	0.651682i	−0.990513	+	0.137418i	$0.956120\pi$
$138$		0			0
$139$	−4.21922	−	7.30791i	−0.357870	−	0.619849i	0.629735	−	0.776810i	$-0.283164\pi$
$139$	−4.21922	−	7.30791i	−0.357870	−	0.619849i	−0.987605	+	0.156961i	$0.949830\pi$
$140$	1.78078	−	3.08440i	0.150503	−	0.260679i
$141$		0			0
$142$	−4.87689			−0.409260
$143$	11.7192	−	9.14657i	0.980011	−	0.764875i
$144$		0			0
$145$	−3.28078	+	5.68247i	−0.272454	+	0.471904i
$146$	−7.68466	+	13.3102i	−0.635987	+	1.10156i
$147$		0			0
$148$	4.12311			0.338917
$149$	−11.4039	−	19.7521i	−0.934242	−	1.61816i	−0.775979	−	0.630758i	$-0.782744\pi$
$149$	−11.4039	−	19.7521i	−0.934242	−	1.61816i	−0.158263	−	0.987397i	$-0.550589\pi$
$150$		0			0
$151$	9.36932			0.762464			0.381232	−	0.924479i	$-0.375500\pi$
$151$	9.36932			0.762464			0.381232	+	0.924479i	$0.375500\pi$
$152$	−1.78078	−	3.08440i	−0.144440	−	0.250177i
$153$		0			0
$154$	7.34233	−	12.7173i	0.591662	−	1.02479i
$155$	−5.68466			−0.456603
$156$		0			0
$157$	22.1231			1.76562			0.882808	−	0.469734i	$-0.155650\pi$
$157$	22.1231			1.76562			0.882808	+	0.469734i	$0.155650\pi$
$158$	3.71922	−	6.44188i	0.295886	−	0.512489i
$159$		0			0
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	27.3693			2.15700
$162$		0			0
$163$	9.28078	+	16.0748i	0.726927	+	1.25907i	0.958176	+	0.286179i	$0.0923853\pi$
$163$	9.28078	+	16.0748i	0.726927	+	1.25907i	−0.231250	+	0.972894i	$0.574281\pi$
$164$	4.24621			0.331573
$165$		0			0
$166$	−0.561553	+	0.972638i	−0.0435850	+	0.0754913i
$167$	−10.1847	+	17.6403i	−0.788113	+	1.36505i	0.139009	+	0.990291i	$0.455608\pi$
$167$	−10.1847	+	17.6403i	−0.788113	+	1.36505i	−0.927122	+	0.374760i	$0.877725\pi$
$168$		0			0
$169$	9.34233	+	9.03996i	0.718641	+	0.695382i
$170$	−5.12311			−0.392924
$171$		0			0
$172$	−2.28078	+	3.95042i	−0.173908	+	0.301217i
$173$	−12.5885	−	21.8040i	−0.957089	−	1.65773i	−0.729514	−	0.683966i	$-0.760254\pi$
$173$	−12.5885	−	21.8040i	−0.957089	−	1.65773i	−0.227575	−	0.973760i	$-0.573080\pi$
$174$		0			0
$175$	−1.78078	−	3.08440i	−0.134614	−	0.233158i
$176$	−2.06155	−	3.57071i	−0.155395	−	0.269153i
$177$		0			0
$178$	−0.903882	−	1.56557i	−0.0677488	−	0.117344i
$179$	−0.157671	+	0.273094i	−0.0117849	+	0.0204120i	−0.871858	−	0.489759i	$-0.837085\pi$
$179$	−0.157671	+	0.273094i	−0.0117849	+	0.0204120i	0.860073	+	0.510171i	$0.170418\pi$
$180$		0			0
$181$	11.1231			0.826774			0.413387	−	0.910555i	$-0.364346\pi$
$181$	11.1231			0.826774			0.413387	+	0.910555i	$0.364346\pi$
$182$	11.9039	+	4.81645i	0.882374	+	0.357019i
$183$		0			0
$184$	3.84233	−	6.65511i	0.283260	−	0.490621i
$185$	2.06155	−	3.57071i	0.151568	−	0.262524i
$186$		0			0
$187$	−21.1231			−1.54467
$188$	3.50000	+	6.06218i	0.255264	+	0.442130i
$189$		0			0
$190$	−3.56155			−0.258382
$191$	9.56155	+	16.5611i	0.691850	+	1.19832i	0.971231	+	0.238139i	$0.0765373\pi$
$191$	9.56155	+	16.5611i	0.691850	+	1.19832i	−0.279381	+	0.960180i	$0.590129\pi$
$192$		0			0
$193$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$193$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$194$	−1.12311			−0.0806343
$195$		0			0
$196$	5.68466			0.406047
$197$	−3.90388	+	6.76172i	−0.278140	+	0.481753i	−0.970923	−	0.239394i	$-0.923051\pi$
$197$	−3.90388	+	6.76172i	−0.278140	+	0.481753i	0.692782	+	0.721147i	$0.256385\pi$
$198$		0			0
$199$	−5.56155	−	9.63289i	−0.394248	−	0.682858i	0.598757	−	0.800931i	$-0.295662\pi$
$199$	−5.56155	−	9.63289i	−0.394248	−	0.682858i	−0.993005	+	0.118073i	$0.962328\pi$
$200$	−1.00000			−0.0707107
$201$		0			0
$202$	8.56155	+	14.8290i	0.602389	+	1.04337i
$203$	−23.3693			−1.64020
$204$		0			0
$205$	2.12311	−	3.67733i	0.148284	−	0.256836i
$206$	0.219224	−	0.379706i	0.0152740	−	0.0264554i
$207$		0			0
$208$	2.84233	−	2.21837i	0.197080	−	0.153816i
$209$	−14.6847			−1.01576
$210$		0			0
$211$	−3.46543	+	6.00231i	−0.238570	+	0.413216i	−0.960304	−	0.278955i	$-0.910012\pi$
$211$	−3.46543	+	6.00231i	−0.238570	+	0.413216i	0.721734	+	0.692171i	$0.243345\pi$
$212$	2.21922	+	3.84381i	0.152417	+	0.263994i
$213$		0			0
$214$	−1.00000	−	1.73205i	−0.0683586	−	0.118401i
$215$	2.28078	+	3.95042i	0.155548	+	0.269416i
$216$		0			0
$217$	−10.1231	−	17.5337i	−0.687201	−	1.19027i
$218$	−10.1231	+	17.5337i	−0.685623	+	1.18753i
$219$		0			0
$220$	−4.12311			−0.277980
$221$	−2.56155	−	18.2931i	−0.172309	−	1.23053i
$222$		0			0
$223$	13.1501	−	22.7766i	0.880595	−	1.52524i	0.0299151	−	0.999552i	$-0.490476\pi$
$223$	13.1501	−	22.7766i	0.880595	−	1.52524i	0.850680	−	0.525683i	$-0.176190\pi$
$224$	1.78078	−	3.08440i	0.118983	−	0.206085i
$225$		0			0
$226$	−3.68466			−0.245100
$227$	−10.0000	−	17.3205i	−0.663723	−	1.14960i	−0.979630	−	0.200812i	$-0.935642\pi$
$227$	−10.0000	−	17.3205i	−0.663723	−	1.14960i	0.315906	−	0.948790i	$-0.397691\pi$
$228$		0			0
$229$	−7.75379			−0.512385			−0.256192	−	0.966626i	$-0.582468\pi$
$229$	−7.75379			−0.512385			−0.256192	+	0.966626i	$0.582468\pi$
$230$	−3.84233	−	6.65511i	−0.253356	−	0.438825i
$231$		0			0
$232$	−3.28078	+	5.68247i	−0.215394	+	0.373073i
$233$	17.6847			1.15856			0.579280	−	0.815128i	$-0.303334\pi$
$233$	17.6847			1.15856			0.579280	+	0.815128i	$0.303334\pi$
$234$		0			0
$235$	7.00000			0.456630
$236$	5.28078	−	9.14657i	0.343749	−	0.595391i
$237$		0			0
$238$	−9.12311	−	15.8017i	−0.591363	−	1.02427i
$239$	−13.3693			−0.864789			−0.432395	−	0.901684i	$-0.642331\pi$
$239$	−13.3693			−0.864789			−0.432395	+	0.901684i	$0.642331\pi$
$240$		0			0
$241$	9.93845	+	17.2139i	0.640192	+	1.10884i	0.985390	+	0.170315i	$0.0544784\pi$
$241$	9.93845	+	17.2139i	0.640192	+	1.10884i	−0.345198	+	0.938530i	$0.612188\pi$
$242$	−6.00000			−0.385695
$243$		0			0
$244$	−3.00000	+	5.19615i	−0.192055	+	0.332650i
$245$	2.84233	−	4.92306i	0.181590	−	0.314523i
$246$		0			0
$247$	−1.78078	−	12.7173i	−0.113308	−	0.809182i
$248$	−5.68466			−0.360976
$249$		0			0
$250$	−0.500000	+	0.866025i	−0.0316228	+	0.0547723i
$251$	0.0615528	+	0.106613i	0.00388518	+	0.00672933i	0.867961	−	0.496632i	$-0.165430\pi$
$251$	0.0615528	+	0.106613i	0.00388518	+	0.00672933i	−0.864076	+	0.503361i	$0.832097\pi$
$252$		0			0
$253$	−15.8423	−	27.4397i	−0.995999	−	1.72512i
$254$	−2.21922	−	3.84381i	−0.139246	−	0.241182i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−0.719224	+	1.24573i	−0.0448639	+	0.0777066i	−0.887585	−	0.460643i	$-0.847619\pi$
$257$	−0.719224	+	1.24573i	−0.0448639	+	0.0777066i	0.842721	+	0.538350i	$0.180952\pi$
$258$		0			0
$259$	14.6847			0.912460
$260$	−0.500000	−	3.57071i	−0.0310087	−	0.221446i
$261$		0			0
$262$	−3.06155	+	5.30277i	−0.189143	+	0.327606i
$263$	−6.50000	+	11.2583i	−0.400807	+	0.694218i	−0.993824	−	0.110972i	$-0.964604\pi$
$263$	−6.50000	+	11.2583i	−0.400807	+	0.694218i	0.593016	+	0.805190i	$0.297937\pi$
$264$		0			0
$265$	4.43845			0.272652
$266$	−6.34233	−	10.9852i	−0.388873	−	0.673548i
$267$		0			0
$268$	14.2462			0.870226
$269$	−1.68466	−	2.91791i	−0.102715	−	0.177908i	0.810087	−	0.586310i	$-0.199420\pi$
$269$	−1.68466	−	2.91791i	−0.102715	−	0.177908i	−0.912803	+	0.408401i	$0.866086\pi$
$270$		0			0
$271$	−16.0885	+	27.8662i	−0.977309	+	1.69275i	−0.305215	+	0.952283i	$0.598728\pi$
$271$	−16.0885	+	27.8662i	−0.977309	+	1.69275i	−0.672094	+	0.740466i	$0.734605\pi$
$272$	−5.12311			−0.310634
$273$		0			0
$274$	−8.80776			−0.532096
$275$	−2.06155	+	3.57071i	−0.124316	+	0.215322i
$276$		0			0
$277$	0.500000	+	0.866025i	0.0300421	+	0.0520344i	0.880656	−	0.473757i	$-0.157103\pi$
$277$	0.500000	+	0.866025i	0.0300421	+	0.0520344i	−0.850613	+	0.525792i	$0.823769\pi$
$278$	−8.43845			−0.506104
$279$		0			0
$280$	−1.78078	−	3.08440i	−0.106422	−	0.184328i
$281$	0.246211			0.0146877			0.00734387	−	0.999973i	$-0.497662\pi$
$281$	0.246211			0.0146877			0.00734387	+	0.999973i	$0.497662\pi$
$282$		0			0
$283$	−5.71922	+	9.90599i	−0.339973	+	0.588850i	−0.984427	−	0.175793i	$-0.943751\pi$
$283$	−5.71922	+	9.90599i	−0.339973	+	0.588850i	0.644455	+	0.764643i	$0.277084\pi$
$284$	−2.43845	+	4.22351i	−0.144695	+	0.250619i
$285$		0			0
$286$	−2.06155	−	14.7224i	−0.121902	−	0.870556i
$287$	15.1231			0.892689
$288$		0			0
$289$	−4.62311	+	8.00745i	−0.271947	+	0.471027i
$290$	3.28078	+	5.68247i	0.192654	+	0.333686i
$291$		0			0
$292$	7.68466	+	13.3102i	0.449711	+	0.778922i
$293$	−12.4654	−	21.5908i	−0.728238	−	1.26135i	−0.957627	−	0.288011i	$-0.907006\pi$
$293$	−12.4654	−	21.5908i	−0.728238	−	1.26135i	0.229389	−	0.973335i	$-0.426327\pi$
$294$		0			0
$295$	−5.28078	−	9.14657i	−0.307459	−	0.532534i
$296$	2.06155	−	3.57071i	0.119825	−	0.207544i
$297$		0			0
$298$	−22.8078			−1.32122
$299$	21.8423	−	17.0474i	1.26317	−	0.985877i
$300$		0			0
$301$	−8.12311	+	14.0696i	−0.468208	+	0.810960i
$302$	4.68466	−	8.11407i	0.269572	−	0.466912i
$303$		0			0
$304$	−3.56155			−0.204269
$305$	3.00000	+	5.19615i	0.171780	+	0.297531i
$306$		0			0
$307$	−15.6155			−0.891225			−0.445613	−	0.895226i	$-0.647014\pi$
$307$	−15.6155			−0.891225			−0.445613	+	0.895226i	$0.647014\pi$
$308$	−7.34233	−	12.7173i	−0.418368	−	0.724635i
$309$		0			0
$310$	−2.84233	+	4.92306i	−0.161433	+	0.279611i
$311$	18.7386			1.06257			0.531285	−	0.847193i	$-0.321709\pi$
$311$	18.7386			1.06257			0.531285	+	0.847193i	$0.321709\pi$
$312$		0			0
$313$	6.63068			0.374788			0.187394	−	0.982285i	$-0.439996\pi$
$313$	6.63068			0.374788			0.187394	+	0.982285i	$0.439996\pi$
$314$	11.0616	−	19.1592i	0.624240	−	1.08121i
$315$		0			0
$316$	−3.71922	−	6.44188i	−0.209223	−	0.362384i
$317$	4.19224			0.235459			0.117730	−	0.993046i	$-0.462438\pi$
$317$	4.19224			0.235459			0.117730	+	0.993046i	$0.462438\pi$
$318$		0			0
$319$	13.5270	+	23.4294i	0.757366	+	1.31180i
$320$	−1.00000			−0.0559017
$321$		0			0
$322$	13.6847	−	23.7025i	0.762616	−	1.32089i
$323$	−9.12311	+	15.8017i	−0.507623	+	0.879229i
$324$		0			0
$325$	−3.34233	−	1.35234i	−0.185399	−	0.0750146i
$326$	18.5616			1.02803
$327$		0			0
$328$	2.12311	−	3.67733i	0.117229	−	0.203046i
$329$	12.4654	+	21.5908i	0.687242	+	1.19034i
$330$		0			0
$331$	9.36932	+	16.2281i	0.514984	+	0.891979i	0.999849	+	0.0173896i	$0.00553556\pi$
$331$	9.36932	+	16.2281i	0.514984	+	0.891979i	−0.484865	+	0.874589i	$0.661131\pi$
$332$	0.561553	+	0.972638i	0.0308192	+	0.0533804i
$333$		0			0
$334$	10.1847	+	17.6403i	0.557280	+	0.965237i
$335$	7.12311	−	12.3376i	0.389177	−	0.674074i
$336$		0			0
$337$	−6.00000			−0.326841			−0.163420	−	0.986557i	$-0.552253\pi$
$337$	−6.00000			−0.326841			−0.163420	+	0.986557i	$0.552253\pi$
$338$	12.5000	−	3.57071i	0.679910	−	0.194221i
$339$		0			0
$340$	−2.56155	+	4.43674i	−0.138920	+	0.240616i
$341$	−11.7192	+	20.2983i	−0.634632	+	1.09921i
$342$		0			0
$343$	−4.68466			−0.252948
$344$	2.28078	+	3.95042i	0.122971	+	0.212992i
$345$		0			0
$346$	−25.1771			−1.35353
$347$	4.56155	+	7.90084i	0.244877	+	0.424139i	0.962097	−	0.272707i	$-0.0879191\pi$
$347$	4.56155	+	7.90084i	0.244877	+	0.424139i	−0.717220	+	0.696847i	$0.754586\pi$
$348$		0			0
$349$	12.2462	−	21.2111i	0.655525	−	1.13540i	−0.326237	−	0.945288i	$-0.605781\pi$
$349$	12.2462	−	21.2111i	0.655525	−	1.13540i	0.981762	−	0.190114i	$-0.0608858\pi$
$350$	−3.56155			−0.190373
$351$		0			0
$352$	−4.12311			−0.219762
$353$	15.9309	−	27.5931i	0.847915	−	1.46863i	−0.0351511	−	0.999382i	$-0.511191\pi$
$353$	15.9309	−	27.5931i	0.847915	−	1.46863i	0.883066	−	0.469249i	$-0.155475\pi$
$354$		0			0
$355$	2.43845	+	4.22351i	0.129419	+	0.224161i
$356$	−1.80776			−0.0958113
$357$		0			0
$358$	0.157671	+	0.273094i	0.00833316	+	0.0144335i
$359$	−4.87689			−0.257393			−0.128696	−	0.991684i	$-0.541079\pi$
$359$	−4.87689			−0.257393			−0.128696	+	0.991684i	$0.541079\pi$
$360$		0			0
$361$	3.15767	−	5.46925i	0.166193	−	0.287855i
$362$	5.56155	−	9.63289i	0.292309	−	0.506294i
$363$		0			0
$364$	10.1231	−	7.90084i	0.530595	−	0.414117i
$365$	15.3693			0.804467
$366$		0			0
$367$	10.2462	−	17.7470i	0.534848	−	0.926384i	−0.464323	−	0.885666i	$-0.653702\pi$
$367$	10.2462	−	17.7470i	0.534848	−	0.926384i	0.999171	−	0.0407177i	$-0.0129644\pi$
$368$	−3.84233	−	6.65511i	−0.200295	−	0.346922i
$369$		0			0
$370$	−2.06155	−	3.57071i	−0.107175	−	0.185633i
$371$	7.90388	+	13.6899i	0.410349	+	0.710746i
$372$		0			0
$373$	2.59612	+	4.49661i	0.134422	+	0.232826i	0.925376	−	0.379049i	$-0.123749\pi$
$373$	2.59612	+	4.49661i	0.134422	+	0.232826i	−0.790955	+	0.611875i	$0.790416\pi$
$374$	−10.5616	+	18.2931i	−0.546125	+	0.945916i
$375$		0			0
$376$	7.00000			0.360997
$377$	−18.6501	+	14.5560i	−0.960529	+	0.749670i
$378$		0			0
$379$	2.65767	−	4.60322i	0.136515	−	0.236452i	−0.789660	−	0.613545i	$-0.789743\pi$
$379$	2.65767	−	4.60322i	0.136515	−	0.236452i	0.926175	+	0.377093i	$0.123076\pi$
$380$	−1.78078	+	3.08440i	−0.0913519	+	0.158226i
$381$		0			0
$382$	19.1231			0.978423
$383$	10.4039	+	18.0201i	0.531614	+	0.920782i	0.999319	+	0.0368973i	$0.0117474\pi$
$383$	10.4039	+	18.0201i	0.531614	+	0.920782i	−0.467706	+	0.883884i	$0.654919\pi$
$384$		0			0
$385$	−14.6847			−0.748399
$386$		0			0
$387$		0			0
$388$	−0.561553	+	0.972638i	−0.0285085	+	0.0493782i
$389$	−19.0540			−0.966075			−0.483037	−	0.875600i	$-0.660467\pi$
$389$	−19.0540			−0.966075			−0.483037	+	0.875600i	$0.660467\pi$
$390$		0			0
$391$	−39.3693			−1.99099
$392$	2.84233	−	4.92306i	0.143559	−	0.248652i
$393$		0			0
$394$	3.90388	+	6.76172i	0.196675	+	0.340651i
$395$	−7.43845			−0.374269
$396$		0			0
$397$	5.93845	+	10.2857i	0.298042	+	0.516224i	0.975688	−	0.219164i	$-0.0703331\pi$
$397$	5.93845	+	10.2857i	0.298042	+	0.516224i	−0.677646	+	0.735388i	$0.737000\pi$
$398$	−11.1231			−0.557551
$399$		0			0
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	6.34233	−	10.9852i	0.316721	−	0.548577i	−0.663081	−	0.748548i	$-0.730752\pi$
$401$	6.34233	−	10.9852i	0.316721	−	0.548577i	0.979802	+	0.199971i	$0.0640848\pi$
$402$		0			0
$403$	−19.0000	−	7.68762i	−0.946457	−	0.382947i
$404$	17.1231			0.851906
$405$		0			0
$406$	−11.6847	+	20.2384i	−0.579900	+	1.00442i
$407$	−8.50000	−	14.7224i	−0.421329	−	0.729764i
$408$		0			0
$409$	−0.903882	−	1.56557i	−0.0446941	−	0.0774124i	0.842813	−	0.538207i	$-0.180898\pi$
$409$	−0.903882	−	1.56557i	−0.0446941	−	0.0774124i	−0.887507	+	0.460794i	$0.847565\pi$
$410$	−2.12311	−	3.67733i	−0.104853	−	0.181610i
$411$		0			0
$412$	−0.219224	−	0.379706i	−0.0108004	−	0.0187068i
$413$	18.8078	−	32.5760i	0.925470	−	1.60296i
$414$		0			0
$415$	1.12311			0.0551311
$416$	−0.500000	−	3.57071i	−0.0245145	−	0.175069i
$417$		0			0
$418$	−7.34233	+	12.7173i	−0.359125	+	0.622023i
$419$	−0.246211	+	0.426450i	−0.0120282	+	0.0208335i	−0.871977	−	0.489547i	$-0.837162\pi$
$419$	−0.246211	+	0.426450i	−0.0120282	+	0.0208335i	0.859949	+	0.510381i	$0.170495\pi$
$420$		0			0
$421$	0.492423			0.0239992			0.0119996	−	0.999928i	$-0.496180\pi$
$421$	0.492423			0.0239992			0.0119996	+	0.999928i	$0.496180\pi$
$422$	3.46543	+	6.00231i	0.168695	+	0.292188i
$423$		0			0
$424$	4.43845			0.215550
$425$	2.56155	+	4.43674i	0.124254	+	0.215213i
$426$		0			0
$427$	−10.6847	+	18.5064i	−0.517067	+	0.895586i
$428$	−2.00000			−0.0966736
$429$		0			0
$430$	4.56155			0.219978
$431$	13.3693	−	23.1563i	0.643977	−	1.11540i	−0.340559	−	0.940223i	$-0.610616\pi$
$431$	13.3693	−	23.1563i	0.643977	−	1.11540i	0.984537	−	0.175178i	$-0.0560502\pi$
$432$		0			0
$433$	−15.3693	−	26.6204i	−0.738602	−	1.27930i	−0.953125	−	0.302578i	$-0.902153\pi$
$433$	−15.3693	−	26.6204i	−0.738602	−	1.27930i	0.214523	−	0.976719i	$-0.431180\pi$
$434$	−20.2462			−0.971849
$435$		0			0
$436$	10.1231	+	17.5337i	0.484809	+	0.839714i
$437$	−27.3693			−1.30925
$438$		0			0
$439$	−8.43845	+	14.6158i	−0.402745	+	0.697575i	−0.994056	−	0.108869i	$-0.965277\pi$
$439$	−8.43845	+	14.6158i	−0.402745	+	0.697575i	0.591311	+	0.806444i	$0.298611\pi$
$440$	−2.06155	+	3.57071i	−0.0982807	+	0.170227i
$441$		0			0
$442$	−17.1231	−	6.92820i	−0.814463	−	0.329541i
$443$	4.87689			0.231708			0.115854	−	0.993266i	$-0.463039\pi$
$443$	4.87689			0.231708			0.115854	+	0.993266i	$0.463039\pi$
$444$		0			0
$445$	−0.903882	+	1.56557i	−0.0428481	+	0.0742151i
$446$	−13.1501	−	22.7766i	−0.622675	−	1.07850i
$447$		0			0
$448$	−1.78078	−	3.08440i	−0.0841338	−	0.145724i
$449$	12.5885	+	21.8040i	0.594090	+	1.02899i	0.993675	+	0.112298i	$0.0358210\pi$
$449$	12.5885	+	21.8040i	0.594090	+	1.02899i	−0.399585	+	0.916696i	$0.630846\pi$
$450$		0			0
$451$	−8.75379	−	15.1620i	−0.412200	−	0.713951i
$452$	−1.84233	+	3.19101i	−0.0866559	+	0.150092i
$453$		0			0
$454$	−20.0000			−0.938647
$455$	−1.78078	−	12.7173i	−0.0834841	−	0.596196i
$456$		0			0
$457$	−1.87689	+	3.25088i	−0.0877974	+	0.152070i	−0.906580	−	0.422034i	$-0.861316\pi$
$457$	−1.87689	+	3.25088i	−0.0877974	+	0.152070i	0.818782	+	0.574104i	$0.194649\pi$
$458$	−3.87689	+	6.71498i	−0.181155	+	0.313770i
$459$		0			0
$460$	−7.68466			−0.358299
$461$	3.52699	+	6.10892i	0.164268	+	0.284521i	0.936395	−	0.350947i	$-0.114140\pi$
$461$	3.52699	+	6.10892i	0.164268	+	0.284521i	−0.772127	+	0.635468i	$0.780807\pi$
$462$		0			0
$463$	33.6155			1.56225			0.781123	−	0.624377i	$-0.214647\pi$
$463$	33.6155			1.56225			0.781123	+	0.624377i	$0.214647\pi$
$464$	3.28078	+	5.68247i	0.152306	+	0.263802i
$465$		0			0
$466$	8.84233	−	15.3154i	0.409613	−	0.709471i
$467$	−39.8617			−1.84458			−0.922291	−	0.386497i	$-0.873685\pi$
$467$	−39.8617			−1.84458			−0.922291	+	0.386497i	$0.873685\pi$
$468$		0			0
$469$	50.7386			2.34289
$470$	3.50000	−	6.06218i	0.161443	−	0.279627i
$471$		0			0
$472$	−5.28078	−	9.14657i	−0.243067	−	0.421005i
$473$	18.8078			0.864782
$474$		0			0
$475$	1.78078	+	3.08440i	0.0817076	+	0.141522i
$476$	−18.2462			−0.836314
$477$		0			0
$478$	−6.68466	+	11.5782i	−0.305749	+	0.529573i
$479$	−10.8769	+	18.8393i	−0.496978	+	0.860791i	−0.999994	−	0.00348601i	$-0.998890\pi$
$479$	−10.8769	+	18.8393i	−0.496978	+	0.860791i	0.503016	+	0.864277i	$0.332224\pi$
$480$		0			0
$481$	11.7192	−	9.14657i	0.534351	−	0.417048i
$482$	19.8769			0.905368
$483$		0			0
$484$	−3.00000	+	5.19615i	−0.136364	+	0.236189i
$485$	0.561553	+	0.972638i	0.0254988	+	0.0441652i
$486$		0			0
$487$	12.0270	+	20.8314i	0.544995	+	0.943959i	0.998607	+	0.0527597i	$0.0168017\pi$
$487$	12.0270	+	20.8314i	0.544995	+	0.943959i	−0.453612	+	0.891199i	$0.649865\pi$
$488$	3.00000	+	5.19615i	0.135804	+	0.235219i
$489$		0			0
$490$	−2.84233	−	4.92306i	−0.128403	−	0.222401i
$491$	−10.7808	+	18.6729i	−0.486530	+	0.842694i	−0.999880	−	0.0154850i	$-0.995071\pi$
$491$	−10.7808	+	18.6729i	−0.486530	+	0.842694i	0.513350	+	0.858179i	$0.328404\pi$
$492$		0			0
$493$	33.6155			1.51397
$494$	−11.9039	−	4.81645i	−0.535581	−	0.216702i
$495$		0			0
$496$	−2.84233	+	4.92306i	−0.127624	+	0.221052i
$497$	−8.68466	+	15.0423i	−0.389560	+	0.674738i
$498$		0			0
$499$	4.00000			0.179065			0.0895323	−	0.995984i	$-0.471463\pi$
$499$	4.00000			0.179065			0.0895323	+	0.995984i	$0.471463\pi$
$500$	0.500000	+	0.866025i	0.0223607	+	0.0387298i
$501$		0			0
$502$	0.123106			0.00549447
$503$	−2.97301	−	5.14941i	−0.132560	−	0.229601i	0.792103	−	0.610388i	$-0.208986\pi$
$503$	−2.97301	−	5.14941i	−0.132560	−	0.229601i	−0.924663	+	0.380787i	$0.875653\pi$
$504$		0			0
$505$	8.56155	−	14.8290i	0.380984	−	0.659884i
$506$	−31.6847			−1.40855
$507$		0			0
$508$	−4.43845			−0.196924
$509$	−14.7732	+	25.5879i	−0.654811	+	1.13417i	0.327131	+	0.944979i	$0.393918\pi$
$509$	−14.7732	+	25.5879i	−0.654811	+	1.13417i	−0.981941	+	0.189186i	$0.939415\pi$
$510$		0			0
$511$	27.3693	+	47.4050i	1.21075	+	2.09708i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	0.719224	+	1.24573i	0.0317236	+	0.0549469i
$515$	−0.438447			−0.0193203
$516$		0			0
$517$	14.4309	−	24.9950i	0.634669	−	1.09928i
$518$	7.34233	−	12.7173i	0.322603	−	0.558766i
$519$		0			0
$520$	−3.34233	−	1.35234i	−0.146571	−	0.0593042i
$521$	18.6847			0.818590			0.409295	−	0.912402i	$-0.365775\pi$
$521$	18.6847			0.818590			0.409295	+	0.912402i	$0.365775\pi$
$522$		0			0
$523$	4.59612	−	7.96071i	0.200974	−	0.348098i	−0.747868	−	0.663847i	$-0.768923\pi$
$523$	4.59612	−	7.96071i	0.200974	−	0.348098i	0.948843	+	0.315749i	$0.102256\pi$
$524$	3.06155	+	5.30277i	0.133745	+	0.231652i
$525$		0			0
$526$	6.50000	+	11.2583i	0.283413	+	0.490887i
$527$	14.5616	+	25.2213i	0.634311	+	1.09866i
$528$		0			0
$529$	−18.0270	−	31.2237i	−0.783782	−	1.35755i
$530$	2.21922	−	3.84381i	0.0963969	−	0.166964i
$531$		0			0
$532$	−12.6847			−0.549950
$533$	12.0691	−	9.41967i	0.522772	−	0.408011i
$534$		0			0
$535$	−1.00000	+	1.73205i	−0.0432338	+	0.0748831i
$536$	7.12311	−	12.3376i	0.307671	−	0.532902i
$537$		0			0
$538$	−3.36932			−0.145262
$539$	−11.7192	−	20.2983i	−0.504783	−	0.874309i
$540$		0			0
$541$	−2.63068			−0.113102			−0.0565510	−	0.998400i	$-0.518010\pi$
$541$	−2.63068			−0.113102			−0.0565510	+	0.998400i	$0.518010\pi$
$542$	16.0885	+	27.8662i	0.691062	+	1.19695i
$543$		0			0
$544$	−2.56155	+	4.43674i	−0.109826	+	0.190224i
$545$	20.2462			0.867252
$546$		0			0
$547$	35.6155			1.52281			0.761405	−	0.648276i	$-0.224510\pi$
$547$	35.6155			1.52281			0.761405	+	0.648276i	$0.224510\pi$
$548$	−4.40388	+	7.62775i	−0.188125	+	0.325841i
$549$		0			0
$550$	2.06155	+	3.57071i	0.0879049	+	0.152256i
$551$	23.3693			0.995566
$552$		0			0
$553$	−13.2462	−	22.9431i	−0.563286	−	0.975640i
$554$	1.00000			0.0424859
$555$		0			0
$556$	−4.21922	+	7.30791i	−0.178935	+	0.309924i
$557$	−2.21922	+	3.84381i	−0.0940315	+	0.162867i	−0.909204	−	0.416351i	$-0.863309\pi$
$557$	−2.21922	+	3.84381i	−0.0940315	+	0.162867i	0.815172	+	0.579218i	$0.196642\pi$
$558$		0			0
$559$	2.28078	+	16.2880i	0.0964666	+	0.688909i
$560$	−3.56155			−0.150503
$561$		0			0
$562$	0.123106	−	0.213225i	0.00519290	−	0.00899436i
$563$	16.4924	+	28.5657i	0.695073	+	1.20390i	0.970156	+	0.242481i	$0.0779612\pi$
$563$	16.4924	+	28.5657i	0.695073	+	1.20390i	−0.275083	+	0.961420i	$0.588705\pi$
$564$		0			0
$565$	1.84233	+	3.19101i	0.0775074	+	0.134247i
$566$	5.71922	+	9.90599i	0.240397	+	0.416380i
$567$		0			0
$568$	2.43845	+	4.22351i	0.102315	+	0.177215i
$569$	−9.58854	+	16.6078i	−0.401973	+	0.696237i	−0.993964	−	0.109707i	$-0.965009\pi$
$569$	−9.58854	+	16.6078i	−0.401973	+	0.696237i	0.591991	+	0.805944i	$0.298342\pi$
$570$		0			0
$571$	11.3153			0.473532			0.236766	−	0.971567i	$-0.423912\pi$
$571$	11.3153			0.473532			0.236766	+	0.971567i	$0.423912\pi$
$572$	−13.7808	−	5.57586i	−0.576203	−	0.233138i
$573$		0			0
$574$	7.56155	−	13.0970i	0.315613	−	0.546658i
$575$	−3.84233	+	6.65511i	−0.160236	+	0.277537i
$576$		0			0
$577$	8.73863			0.363794			0.181897	−	0.983318i	$-0.441776\pi$
$577$	8.73863			0.363794			0.181897	+	0.983318i	$0.441776\pi$
$578$	4.62311	+	8.00745i	0.192296	+	0.333066i
$579$		0			0
$580$	6.56155			0.272454
$581$	2.00000	+	3.46410i	0.0829740	+	0.143715i
$582$		0			0
$583$	9.15009	−	15.8484i	0.378958	−	0.656375i
$584$	15.3693			0.635987
$585$		0			0
$586$	−24.9309			−1.02988
$587$	−11.8769	+	20.5714i	−0.490212	+	0.849072i	−0.999937	−	0.0112657i	$-0.996414\pi$
$587$	−11.8769	+	20.5714i	−0.490212	+	0.849072i	0.509725	+	0.860338i	$0.329747\pi$
$588$		0			0
$589$	10.1231	+	17.5337i	0.417115	+	0.722465i
$590$	−10.5616			−0.434812
$591$		0			0
$592$	−2.06155	−	3.57071i	−0.0847293	−	0.146755i
$593$	12.1771			0.500053			0.250026	−	0.968239i	$-0.419561\pi$
$593$	12.1771			0.500053			0.250026	+	0.968239i	$0.419561\pi$
$594$		0			0
$595$	−9.12311	+	15.8017i	−0.374011	+	0.647806i
$596$	−11.4039	+	19.7521i	−0.467121	+	0.809078i
$597$		0			0
$598$	−3.84233	−	27.4397i	−0.157125	−	1.12209i
$599$	14.0000			0.572024			0.286012	−	0.958226i	$-0.407670\pi$
$599$	14.0000			0.572024			0.286012	+	0.958226i	$0.407670\pi$
$600$		0			0
$601$	17.9924	−	31.1638i	0.733926	−	1.27120i	−0.221267	−	0.975213i	$-0.571019\pi$
$601$	17.9924	−	31.1638i	0.733926	−	1.27120i	0.955193	−	0.295984i	$-0.0956476\pi$
$602$	8.12311	+	14.0696i	0.331073	+	0.573435i
$603$		0			0
$604$	−4.68466	−	8.11407i	−0.190616	−	0.330157i
$605$	3.00000	+	5.19615i	0.121967	+	0.211254i
$606$		0			0
$607$	14.7116	+	25.4813i	0.597127	+	1.03425i	0.993243	+	0.116054i	$0.0370246\pi$
$607$	14.7116	+	25.4813i	0.597127	+	1.03425i	−0.396116	+	0.918201i	$0.629642\pi$
$608$	−1.78078	+	3.08440i	−0.0722200	+	0.125089i
$609$		0			0
$610$	6.00000			0.242933
$611$	23.3963	+	9.46641i	0.946513	+	0.382970i
$612$		0			0
$613$	−14.0616	+	24.3553i	−0.567941	+	0.983702i	0.428829	+	0.903386i	$0.358926\pi$
$613$	−14.0616	+	24.3553i	−0.567941	+	0.983702i	−0.996769	+	0.0803164i	$0.974407\pi$
$614$	−7.80776	+	13.5234i	−0.315096	+	0.545762i
$615$		0			0
$616$	−14.6847			−0.591662
$617$	−20.8423	−	36.1000i	−0.839081	−	1.45333i	−0.890664	−	0.454662i	$-0.849760\pi$
$617$	−20.8423	−	36.1000i	−0.839081	−	1.45333i	0.0515837	−	0.998669i	$-0.483573\pi$
$618$		0			0
$619$	−16.4384			−0.660717			−0.330358	−	0.943856i	$-0.607170\pi$
$619$	−16.4384			−0.660717			−0.330358	+	0.943856i	$0.607170\pi$
$620$	2.84233	+	4.92306i	0.114151	+	0.197715i
$621$		0			0
$622$	9.36932	−	16.2281i	0.375675	−	0.650689i
$623$	−6.43845			−0.257951
$624$		0			0
$625$	1.00000			0.0400000
$626$	3.31534	−	5.74234i	0.132508	−	0.229510i
$627$		0			0
$628$	−11.0616	−	19.1592i	−0.441404	−	0.764534i
$629$	−21.1231			−0.842233
$630$		0			0
$631$	15.1231	+	26.1940i	0.602041	+	1.04277i	0.992512	+	0.122151i	$0.0389791\pi$
$631$	15.1231	+	26.1940i	0.602041	+	1.04277i	−0.390470	+	0.920616i	$0.627688\pi$
$632$	−7.43845			−0.295886
$633$		0			0
$634$	2.09612	−	3.63058i	0.0832475	−	0.144189i
$635$	−2.21922	+	3.84381i	−0.0880672	+	0.152537i
$636$		0			0
$637$	16.1577	−	12.6107i	0.640190	−	0.499653i
$638$	27.0540			1.07108
$639$		0			0
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	−7.78078	−	13.4767i	−0.307322	−	0.532298i	0.670453	−	0.741952i	$-0.266100\pi$
$641$	−7.78078	−	13.4767i	−0.307322	−	0.532298i	−0.977776	+	0.209654i	$0.932766\pi$
$642$		0			0
$643$	−19.1231	−	33.1222i	−0.754142	−	1.30621i	−0.945800	−	0.324750i	$-0.894720\pi$
$643$	−19.1231	−	33.1222i	−0.754142	−	1.30621i	0.191658	−	0.981462i	$-0.438613\pi$
$644$	−13.6847	−	23.7025i	−0.539251	−	0.934010i
$645$		0			0
$646$	9.12311	+	15.8017i	0.358944	+	0.621709i
$647$	−1.02699	+	1.77879i	−0.0403751	+	0.0699316i	−0.885507	−	0.464626i	$-0.846189\pi$
$647$	−1.02699	+	1.77879i	−0.0403751	+	0.0699316i	0.845132	+	0.534558i	$0.179522\pi$
$648$		0			0
$649$	−43.5464			−1.70935
$650$	−2.84233	+	2.21837i	−0.111485	+	0.0870116i
$651$		0			0
$652$	9.28078	−	16.0748i	0.363463	−	0.629537i
$653$	−20.2192	+	35.0207i	−0.791239	+	1.37047i	0.133961	+	0.990987i	$0.457230\pi$
$653$	−20.2192	+	35.0207i	−0.791239	+	1.37047i	−0.925200	+	0.379480i	$0.876103\pi$
$654$		0			0
$655$	6.12311			0.239250
$656$	−2.12311	−	3.67733i	−0.0828933	−	0.143575i
$657$		0			0
$658$	24.9309			0.971906
$659$	15.5270	+	26.8935i	0.604846	+	1.04762i	0.992076	+	0.125640i	$0.0400985\pi$
$659$	15.5270	+	26.8935i	0.604846	+	1.04762i	−0.387230	+	0.921983i	$0.626568\pi$
$660$		0			0
$661$	5.80776	−	10.0593i	0.225896	−	0.391263i	−0.730692	−	0.682707i	$-0.760802\pi$
$661$	5.80776	−	10.0593i	0.225896	−	0.391263i	0.956588	+	0.291444i	$0.0941358\pi$
$662$	18.7386			0.728298
$663$		0			0
$664$	1.12311			0.0435850
$665$	−6.34233	+	10.9852i	−0.245945	+	0.425989i
$666$		0			0
$667$	25.2116	+	43.6679i	0.976199	+	1.69083i
$668$	20.3693			0.788113
$669$		0			0
$670$	−7.12311	−	12.3376i	−0.275190	−	0.476642i
$671$	24.7386			0.955024
$672$		0			0
$673$	−21.1231	+	36.5863i	−0.814236	+	1.41030i	0.0956394	+	0.995416i	$0.469510\pi$
$673$	−21.1231	+	36.5863i	−0.814236	+	1.41030i	−0.909875	+	0.414882i	$0.863823\pi$
$674$	−3.00000	+	5.19615i	−0.115556	+	0.200148i
$675$		0			0
$676$	3.15767	−	12.6107i	0.121449	−	0.485026i
$677$	28.8769			1.10983			0.554915	−	0.831907i	$-0.312751\pi$
$677$	28.8769			1.10983			0.554915	+	0.831907i	$0.312751\pi$
$678$		0			0
$679$	−2.00000	+	3.46410i	−0.0767530	+	0.132940i
$680$	2.56155	+	4.43674i	0.0982311	+	0.170141i
$681$		0			0
$682$	11.7192	+	20.2983i	0.448752	+	0.777262i
$683$	4.43845	+	7.68762i	0.169832	+	0.294158i	0.938361	−	0.345657i	$-0.112344\pi$
$683$	4.43845	+	7.68762i	0.169832	+	0.294158i	−0.768528	+	0.639816i	$0.779011\pi$
$684$		0			0
$685$	4.40388	+	7.62775i	0.168264	+	0.291441i
$686$	−2.34233	+	4.05703i	−0.0894305	+	0.154898i
$687$		0			0
$688$	4.56155			0.173908
$689$	14.8348	+	6.00231i	0.565159	+	0.228670i
$690$		0			0
$691$	8.21922	−	14.2361i	0.312674	−	0.541567i	−0.666266	−	0.745714i	$-0.732109\pi$
$691$	8.21922	−	14.2361i	0.312674	−	0.541567i	0.978940	+	0.204147i	$0.0654419\pi$
$692$	−12.5885	+	21.8040i	−0.478545	+	0.828863i
$693$		0			0
$694$	9.12311			0.346308
$695$	4.21922	+	7.30791i	0.160044	+	0.277205i
$696$		0			0
$697$	−21.7538			−0.823984
$698$	−12.2462	−	21.2111i	−0.463526	−	0.802850i
$699$		0			0
$700$	−1.78078	+	3.08440i	−0.0673070	+	0.116579i
$701$	−17.3002			−0.653419			−0.326710	−	0.945125i	$-0.605940\pi$
$701$	−17.3002			−0.653419			−0.326710	+	0.945125i	$0.605940\pi$
$702$		0			0
$703$	−14.6847			−0.553842
$704$	−2.06155	+	3.57071i	−0.0776977	+	0.134576i
$705$		0			0
$706$	−15.9309	−	27.5931i	−0.599566	−	1.03848i
$707$	60.9848			2.29357
$708$		0			0
$709$	−8.87689	−	15.3752i	−0.333379	−	0.577429i	0.649793	−	0.760111i	$-0.274855\pi$
$709$	−8.87689	−	15.3752i	−0.333379	−	0.577429i	−0.983172	+	0.182682i	$0.941522\pi$
$710$	4.87689			0.183027
$711$		0			0
$712$	−0.903882	+	1.56557i	−0.0338744	+	0.0586722i
$713$	−21.8423	+	37.8320i	−0.818002	+	1.41682i
$714$		0			0
$715$	−11.7192	+	9.14657i	−0.438274	+	0.342062i
$716$	0.315342			0.0117849
$717$		0			0
$718$	−2.43845	+	4.22351i	−0.0910020	+	0.157620i
$719$	−10.4924	−	18.1734i	−0.391301	−	0.677754i	0.601320	−	0.799008i	$-0.294642\pi$
$719$	−10.4924	−	18.1734i	−0.391301	−	0.677754i	−0.992621	+	0.121254i	$0.961308\pi$
$720$		0			0
$721$	−0.780776	−	1.35234i	−0.0290776	−	0.0503639i
$722$	−3.15767	−	5.46925i	−0.117516	−	0.203544i
$723$		0			0
$724$	−5.56155	−	9.63289i	−0.206693	−	0.358004i
$725$	3.28078	−	5.68247i	0.121845	−	0.211042i
$726$		0			0
$727$	−23.4233			−0.868722			−0.434361	−	0.900739i	$-0.643026\pi$
$727$	−23.4233			−0.868722			−0.434361	+	0.900739i	$0.643026\pi$
$728$	−1.78078	−	12.7173i	−0.0660000	−	0.471334i
$729$		0			0
$730$	7.68466	−	13.3102i	0.284422	−	0.492633i
$731$	11.6847	−	20.2384i	0.432173	−	0.748545i
$732$		0			0
$733$	48.9309			1.80730			0.903651	−	0.428269i	$-0.140876\pi$
$733$	48.9309			1.80730			0.903651	+	0.428269i	$0.140876\pi$
$734$	−10.2462	−	17.7470i	−0.378195	−	0.655052i
$735$		0			0
$736$	−7.68466			−0.283260
$737$	−29.3693	−	50.8691i	−1.08183	−	1.87379i
$738$		0			0
$739$	−21.2732	+	36.8463i	−0.782547	+	1.35541i	0.147906	+	0.989001i	$0.452747\pi$
$739$	−21.2732	+	36.8463i	−0.782547	+	1.35541i	−0.930453	+	0.366410i	$0.880587\pi$
$740$	−4.12311			−0.151568
$741$		0			0
$742$	15.8078			0.580321
$743$	−16.0885	+	27.8662i	−0.590231	+	1.02231i	0.403970	+	0.914772i	$0.367630\pi$
$743$	−16.0885	+	27.8662i	−0.590231	+	1.02231i	−0.994201	+	0.107538i	$0.965703\pi$
$744$		0			0
$745$	11.4039	+	19.7521i	0.417806	+	0.723661i
$746$	5.19224			0.190101
$747$		0			0
$748$	10.5616	+	18.2931i	0.386169	+	0.668864i
$749$	−7.12311			−0.260273
$750$		0			0
$751$	1.59612	−	2.76456i	0.0582432	−	0.100880i	−0.835434	−	0.549591i	$-0.814783\pi$
$751$	1.59612	−	2.76456i	0.0582432	−	0.100880i	0.893677	+	0.448711i	$0.148117\pi$
$752$	3.50000	−	6.06218i	0.127632	−	0.221065i
$753$		0			0
$754$	3.28078	+	23.4294i	0.119479	+	0.853250i
$755$	−9.36932			−0.340984
$756$		0			0
$757$	−16.7116	+	28.9454i	−0.607395	+	1.05204i	0.384273	+	0.923220i	$0.374452\pi$
$757$	−16.7116	+	28.9454i	−0.607395	+	1.05204i	−0.991668	+	0.128820i	$0.958881\pi$
$758$	−2.65767	−	4.60322i	−0.0965309	−	0.167197i
$759$		0			0
$760$	1.78078	+	3.08440i	0.0645955	+	0.111883i
$761$	5.46543	+	9.46641i	0.198122	+	0.343157i	0.947919	−	0.318510i	$-0.103182\pi$
$761$	5.46543	+	9.46641i	0.198122	+	0.343157i	−0.749798	+	0.661667i	$0.769849\pi$
$762$		0			0
$763$	36.0540	+	62.4473i	1.30524	+	2.26074i
$764$	9.56155	−	16.5611i	0.345925	−	0.599159i
$765$		0			0
$766$	20.8078			0.751815
$767$	−5.28078	−	37.7123i	−0.190678	−	1.36171i
$768$		0			0
$769$	22.8423	−	39.5641i	0.823715	−	1.42672i	−0.0791816	−	0.996860i	$-0.525231\pi$
$769$	22.8423	−	39.5641i	0.823715	−	1.42672i	0.902897	−	0.429857i	$-0.141436\pi$
$770$	−7.34233	+	12.7173i	−0.264599	+	0.458299i
$771$		0			0
$772$		0			0
$773$	−10.5885	−	18.3399i	−0.380843	−	0.659640i	0.610340	−	0.792140i	$-0.291033\pi$
$773$	−10.5885	−	18.3399i	−0.380843	−	0.659640i	−0.991183	+	0.132500i	$0.957700\pi$
$774$		0			0
$775$	5.68466			0.204199
$776$	0.561553	+	0.972638i	0.0201586	+	0.0349157i
$777$		0			0
$778$	−9.52699	+	16.5012i	−0.341559	+	0.591598i
$779$	−15.1231			−0.541841
$780$		0			0
$781$	20.1080			0.719519
$782$	−19.6847	+	34.0948i	−0.703922	+	1.21923i
$783$		0			0
$784$	−2.84233	−	4.92306i	−0.101512	−	0.175824i
$785$	−22.1231			−0.789607
$786$		0			0
$787$	−21.8423	−	37.8320i	−0.778595	−	1.34857i	−0.932752	−	0.360520i	$-0.882599\pi$
$787$	−21.8423	−	37.8320i	−0.778595	−	1.34857i	0.154157	−	0.988046i	$-0.450734\pi$
$788$	7.80776			0.278140
$789$		0			0
$790$	−3.71922	+	6.44188i	−0.132324	+	0.229192i
$791$	−6.56155	+	11.3649i	−0.233302	+	0.404091i
$792$		0			0
$793$	3.00000	+	21.4243i	0.106533	+	0.760799i
$794$	11.8769			0.421495
$795$		0			0
$796$	−5.56155	+	9.63289i	−0.197124	+	0.341429i
$797$	2.43845	+	4.22351i	0.0863742	+	0.149605i	0.905976	−	0.423329i	$-0.139139\pi$
$797$	2.43845	+	4.22351i	0.0863742	+	0.149605i	−0.819602	+	0.572934i	$0.805805\pi$
$798$		0			0
$799$	−17.9309	−	31.0572i	−0.634349	−	1.09872i
$800$	0.500000	+	0.866025i	0.0176777	+	0.0306186i
$801$		0			0
$802$	−6.34233	−	10.9852i	−0.223955	−	0.387902i
$803$	31.6847	−	54.8794i	1.11813	−	1.93665i
$804$		0			0
$805$	−27.3693			−0.964642
$806$	−16.1577	+	12.6107i	−0.569130	+	0.444192i
$807$		0			0
$808$	8.56155	−	14.8290i	0.301194	−	0.521684i
$809$	9.24621	−	16.0149i	0.325079	−	0.563054i	−0.656449	−	0.754370i	$-0.727942\pi$
$809$	9.24621	−	16.0149i	0.325079	−	0.563054i	0.981528	+	0.191316i	$0.0612756\pi$
$810$		0			0
$811$	−22.5464			−0.791711			−0.395856	−	0.918313i	$-0.629552\pi$
$811$	−22.5464			−0.791711			−0.395856	+	0.918313i	$0.629552\pi$
$812$	11.6847	+	20.2384i	0.410051	+	0.710229i
$813$		0			0
$814$	−17.0000			−0.595850
$815$	−9.28078	−	16.0748i	−0.325091	−	0.563075i
$816$		0			0
$817$	8.12311	−	14.0696i	0.284191	−	0.492234i
$818$	−1.80776			−0.0632070
$819$		0			0
$820$	−4.24621			−0.148284
$821$	−6.28078	+	10.8786i	−0.219201	+	0.379667i	−0.954564	−	0.298007i	$-0.903678\pi$
$821$	−6.28078	+	10.8786i	−0.219201	+	0.379667i	0.735363	+	0.677673i	$0.237012\pi$
$822$		0			0
$823$	16.0270	+	27.7596i	0.558666	+	0.967637i	0.997608	+	0.0691222i	$0.0220198\pi$
$823$	16.0270	+	27.7596i	0.558666	+	0.967637i	−0.438943	+	0.898515i	$0.644647\pi$
$824$	−0.438447			−0.0152740
$825$		0			0
$826$	−18.8078	−	32.5760i	−0.654406	−	1.13346i
$827$	11.7538			0.408719			0.204360	−	0.978896i	$-0.434489\pi$
$827$	11.7538			0.408719			0.204360	+	0.978896i	$0.434489\pi$
$828$		0			0
$829$	−26.8078	+	46.4324i	−0.931072	+	1.61266i	−0.149580	+	0.988750i	$0.547792\pi$
$829$	−26.8078	+	46.4324i	−0.931072	+	1.61266i	−0.781493	+	0.623915i	$0.785541\pi$
$830$	0.561553	−	0.972638i	0.0194918	−	0.0337608i
$831$		0			0
$832$	−3.34233	−	1.35234i	−0.115874	−	0.0468841i
$833$	−29.1231			−1.00906
$834$		0			0
$835$	10.1847	−	17.6403i	0.352455	−	0.610469i
$836$	7.34233	+	12.7173i	0.253940	+	0.439837i
$837$		0			0
$838$	0.246211	+	0.426450i	0.00850523	+	0.0147315i
$839$	−6.36932	−	11.0320i	−0.219893	−	0.380866i	0.734882	−	0.678195i	$-0.237238\pi$
$839$	−6.36932	−	11.0320i	−0.219893	−	0.380866i	−0.954775	+	0.297329i	$0.903904\pi$
$840$		0			0
$841$	−7.02699	−	12.1711i	−0.242310	−	0.419693i
$842$	0.246211	−	0.426450i	0.00848500	−	0.0146965i
$843$		0			0
$844$	6.93087			0.238570
$845$	−9.34233	−	9.03996i	−0.321386	−	0.310984i
$846$		0			0
$847$	−10.6847	+	18.5064i	−0.367129	+	0.635886i
$848$	2.21922	−	3.84381i	0.0762085	−	0.131997i
$849$		0			0
$850$	5.12311			0.175721
$851$	−15.8423	−	27.4397i	−0.543068	−	0.940621i
$852$		0			0
$853$	−51.3002			−1.75648			−0.878242	−	0.478216i	$-0.841284\pi$
$853$	−51.3002			−1.75648			−0.878242	+	0.478216i	$0.841284\pi$
$854$	10.6847	+	18.5064i	0.365621	+	0.633275i
$855$		0			0
$856$	−1.00000	+	1.73205i	−0.0341793	+	0.0592003i
$857$	26.8078			0.915736			0.457868	−	0.889020i	$-0.348613\pi$
$857$	26.8078			0.915736			0.457868	+	0.889020i	$0.348613\pi$
$858$		0			0
$859$	−46.7926			−1.59654			−0.798272	−	0.602298i	$-0.794252\pi$
$859$	−46.7926			−1.59654			−0.798272	+	0.602298i	$0.794252\pi$
$860$	2.28078	−	3.95042i	0.0777738	−	0.134708i
$861$		0			0
$862$	−13.3693	−	23.1563i	−0.455361	−	0.788708i
$863$	−6.56155			−0.223358			−0.111679	−	0.993744i	$-0.535623\pi$
$863$	−6.56155			−0.223358			−0.111679	+	0.993744i	$0.535623\pi$
$864$		0			0
$865$	12.5885	+	21.8040i	0.428023	+	0.741358i
$866$	−30.7386			−1.04454
$867$		0			0
$868$	−10.1231	+	17.5337i	−0.343601	+	0.595134i
$869$	−15.3348	+	26.5606i	−0.520196	+	0.901006i
$870$		0			0
$871$	40.4924	−	31.6034i	1.37203	−	1.07084i
$872$	20.2462			0.685623
$873$		0			0
$874$	−13.6847	+	23.7025i	−0.462890	+	0.801750i
$875$	1.78078	+	3.08440i	0.0602012	+	0.104272i
$876$		0			0
$877$	−6.28078	−	10.8786i	−0.212087	−	0.367345i	0.740281	−	0.672298i	$-0.234693\pi$
$877$	−6.28078	−	10.8786i	−0.212087	−	0.367345i	−0.952367	+	0.304953i	$0.901359\pi$
$878$	8.43845	+	14.6158i	0.284784	+	0.493260i
$879$		0			0
$880$	2.06155	+	3.57071i	0.0694949	+	0.120369i
$881$	−10.2192	+	17.7002i	−0.344294	+	0.596335i	−0.985225	−	0.171263i	$-0.945215\pi$
$881$	−10.2192	+	17.7002i	−0.344294	+	0.596335i	0.640931	+	0.767599i	$0.278548\pi$
$882$		0			0
$883$	26.1771			0.880929			0.440464	−	0.897770i	$-0.354814\pi$
$883$	26.1771			0.880929			0.440464	+	0.897770i	$0.354814\pi$
$884$	−14.5616	+	11.3649i	−0.489758	+	0.382244i
$885$		0			0
$886$	2.43845	−	4.22351i	0.0819212	−	0.141892i
$887$	20.5540	−	35.6005i	0.690135	−	1.19535i	−0.281658	−	0.959515i	$-0.590884\pi$
$887$	20.5540	−	35.6005i	0.690135	−	1.19535i	0.971793	−	0.235834i	$-0.0757822\pi$
$888$		0			0
$889$	−15.8078			−0.530175
$890$	0.903882	+	1.56557i	0.0302982	+	0.0524780i
$891$		0			0
$892$	−26.3002			−0.880595
$893$	−12.4654	−	21.5908i	−0.417140	−	0.722507i
$894$		0			0
$895$	0.157671	−	0.273094i	0.00527035	−	0.00912852i
$896$	−3.56155			−0.118983
$897$		0			0
$898$	25.1771			0.840170
$899$	18.6501	−	32.3029i	0.622015	−	1.07736i
$900$		0			0
$901$	−11.3693	−	19.6922i	−0.378767	−	0.656043i
$902$	−17.5076			−0.582939
$903$		0			0
$904$	1.84233	+	3.19101i	0.0612750	+	0.106131i
$905$	−11.1231			−0.369745
$906$		0			0
$907$	−20.4579	+	35.4340i	−0.679292	+	1.17657i	0.295902	+	0.955218i	$0.404380\pi$
$907$	−20.4579	+	35.4340i	−0.679292	+	1.17657i	−0.975194	+	0.221350i	$0.928954\pi$
$908$	−10.0000	+	17.3205i	−0.331862	+	0.574801i
$909$		0			0
$910$	−11.9039	−	4.81645i	−0.394610	−	0.159664i
$911$	43.3693			1.43689			0.718445	−	0.695584i	$-0.244854\pi$
$911$	43.3693			1.43689			0.718445	+	0.695584i	$0.244854\pi$
$912$		0			0
$913$	2.31534	−	4.01029i	0.0766266	−	0.132721i
$914$	1.87689	+	3.25088i	0.0620821	+	0.107529i
$915$		0			0
$916$	3.87689	+	6.71498i	0.128096	+	0.221869i
$917$	10.9039	+	18.8861i	0.360078	+	0.623673i
$918$		0			0
$919$	−20.6847	−	35.8269i	−0.682324	−	1.18182i	−0.974270	−	0.225385i	$-0.927636\pi$
$919$	−20.6847	−	35.8269i	−0.682324	−	1.18182i	0.291946	−	0.956435i	$-0.405697\pi$
$920$	−3.84233	+	6.65511i	−0.126678	+	0.219412i
$921$		0			0
$922$	7.05398			0.232310
$923$	2.43845	+	17.4140i	0.0802625	+	0.573189i
$924$		0			0
$925$	−2.06155	+	3.57071i	−0.0677834	+	0.117404i
$926$	16.8078	−	29.1119i	0.552337	−	0.956676i
$927$		0			0
$928$	6.56155			0.215394
$929$	−8.43845	−	14.6158i	−0.276856	−	0.479529i	0.693745	−	0.720220i	$-0.255959\pi$
$929$	−8.43845	−	14.6158i	−0.276856	−	0.479529i	−0.970602	+	0.240691i	$0.922626\pi$
$930$		0			0
$931$	−20.2462			−0.663543
$932$	−8.84233	−	15.3154i	−0.289640	−	0.501671i
$933$		0			0
$934$	−19.9309	+	34.5213i	−0.652158	+	1.12957i
$935$	21.1231			0.690799
$936$		0			0
$937$	−29.2311			−0.954937			−0.477468	−	0.878649i	$-0.658446\pi$
$937$	−29.2311			−0.954937			−0.477468	+	0.878649i	$0.658446\pi$
$938$	25.3693	−	43.9409i	0.828338	−	1.43472i
$939$		0			0
$940$	−3.50000	−	6.06218i	−0.114157	−	0.197726i
$941$	0.630683			0.0205597			0.0102798	−	0.999947i	$-0.496728\pi$
$941$	0.630683			0.0205597			0.0102798	+	0.999947i	$0.496728\pi$
$942$		0			0
$943$	−16.3153	−	28.2590i	−0.531301	−	0.920240i
$944$	−10.5616			−0.343749
$945$		0			0
$946$	9.40388	−	16.2880i	0.305747	−	0.529569i
$947$	6.93087	−	12.0046i	0.225223	−	0.390098i	−0.731163	−	0.682202i	$-0.761022\pi$
$947$	6.93087	−	12.0046i	0.225223	−	0.390098i	0.956386	+	0.292105i	$0.0943556\pi$
$948$		0			0
$949$	51.3693	+	20.7846i	1.66752	+	0.674697i
$950$	3.56155			0.115552
$951$		0			0
$952$	−9.12311	+	15.8017i	−0.295682	+	0.512135i
$953$	2.91146	+	5.04280i	0.0943114	+	0.163352i	0.909321	−	0.416095i	$-0.136602\pi$
$953$	2.91146	+	5.04280i	0.0943114	+	0.163352i	−0.815010	+	0.579447i	$0.803268\pi$
$954$		0			0
$955$	−9.56155	−	16.5611i	−0.309405	−	0.535904i
$956$	6.68466	+	11.5782i	0.216197	+	0.374465i
$957$		0			0
$958$	10.8769	+	18.8393i	0.351417	+	0.608671i
$959$	−15.6847	+	27.1666i	−0.506484	+	0.877256i
$960$		0			0
$961$	1.31534			0.0424304
$962$	−2.06155	−	14.7224i	−0.0664671	−	0.474670i
$963$		0			0
$964$	9.93845	−	17.2139i	0.320096	−	0.554422i
$965$		0			0
$966$		0			0
$967$	3.31534			0.106614			0.0533071	−	0.998578i	$-0.483024\pi$
$967$	3.31534			0.106614			0.0533071	+	0.998578i	$0.483024\pi$
$968$	3.00000	+	5.19615i	0.0964237	+	0.167011i
$969$		0			0
$970$	1.12311			0.0360607
$971$	−8.34233	−	14.4493i	−0.267718	−	0.463701i	0.700554	−	0.713599i	$-0.252936\pi$
$971$	−8.34233	−	14.4493i	−0.267718	−	0.463701i	−0.968272	+	0.249898i	$0.919603\pi$
$972$		0			0
$973$	−15.0270	+	26.0275i	−0.481743	+	0.834404i
$974$	24.0540			0.770739
$975$		0			0
$976$	6.00000			0.192055
$977$	2.65009	−	4.59010i	0.0847840	−	0.146850i	−0.820515	−	0.571625i	$-0.806313\pi$
$977$	2.65009	−	4.59010i	0.0847840	−	0.146850i	0.905299	+	0.424775i	$0.139647\pi$
$978$		0			0
$979$	3.72680	+	6.45501i	0.119109	+	0.206303i
$980$	−5.68466			−0.181590
$981$		0			0
$982$	10.7808	+	18.6729i	0.344028	+	0.595875i
$983$	−23.8769			−0.761555			−0.380777	−	0.924667i	$-0.624344\pi$
$983$	−23.8769			−0.761555			−0.380777	+	0.924667i	$0.624344\pi$
$984$		0			0
$985$	3.90388	−	6.76172i	0.124388	−	0.215446i
$986$	16.8078	−	29.1119i	0.535268	−	0.927112i
$987$		0			0
$988$	−10.1231	+	7.90084i	−0.322059	+	0.251359i
$989$	35.0540			1.11465
$990$		0			0
$991$	6.21165	−	10.7589i	0.197319	−	0.341767i	−0.750339	−	0.661053i	$-0.770110\pi$
$991$	6.21165	−	10.7589i	0.197319	−	0.341767i	0.947658	+	0.319286i	$0.103443\pi$
$992$	2.84233	+	4.92306i	0.0902440	+	0.156307i
$993$		0			0
$994$	8.68466	+	15.0423i	0.275461	+	0.477112i
$995$	5.56155	+	9.63289i	0.176313	+	0.305383i
$996$		0			0
$997$	−16.2732	−	28.1860i	−0.515377	−	0.892660i	−0.999841	−	0.0178482i	$-0.994318\pi$
$997$	−16.2732	−	28.1860i	−0.515377	−	0.892660i	0.484463	−	0.874812i	$-0.339015\pi$
$998$	2.00000	−	3.46410i	0.0633089	−	0.109654i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1170.2.i.o.451.1		4
3.2	odd	2		390.2.i.g.61.1	✓	4
13.3	even	3	inner	1170.2.i.o.991.1		4
15.2	even	4		1950.2.z.n.1699.2		8
15.8	even	4		1950.2.z.n.1699.3		8
15.14	odd	2		1950.2.i.bi.451.2		4
39.17	odd	6		5070.2.a.bb.1.1		2
39.20	even	12		5070.2.b.r.1351.3		4
39.29	odd	6		390.2.i.g.211.1	yes	4
39.32	even	12		5070.2.b.r.1351.2		4
39.35	odd	6		5070.2.a.bi.1.2		2
195.29	odd	6		1950.2.i.bi.601.2		4
195.68	even	12		1950.2.z.n.1849.2		8
195.107	even	12		1950.2.z.n.1849.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.i.g.61.1	✓	4	3.2	odd	2
390.2.i.g.211.1	yes	4	39.29	odd	6
1170.2.i.o.451.1		4	1.1	even	1	trivial
1170.2.i.o.991.1		4	13.3	even	3	inner
1950.2.i.bi.451.2		4	15.14	odd	2
1950.2.i.bi.601.2		4	195.29	odd	6
1950.2.z.n.1699.2		8	15.2	even	4
1950.2.z.n.1699.3		8	15.8	even	4
1950.2.z.n.1849.2		8	195.68	even	12
1950.2.z.n.1849.3		8	195.107	even	12
5070.2.a.bb.1.1		2	39.17	odd	6
5070.2.a.bi.1.2		2	39.35	odd	6
5070.2.b.r.1351.2		4	39.32	even	12
5070.2.b.r.1351.3		4	39.20	even	12

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:	\( N \)	\(=\)	\( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1170.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(-1.78078 - 3.08440i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(-1.78078 - 3.08440i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{10} +(-2.06155 + 3.57071i) q^{11} +(-3.34233 - 1.35234i) q^{13} -3.56155 q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.56155 + 4.43674i) q^{17} +(1.78078 + 3.08440i) q^{19} +(0.500000 + 0.866025i) q^{20} +(2.06155 + 3.57071i) q^{22} +(-3.84233 + 6.65511i) q^{23} +1.00000 q^{25} +(-2.84233 + 2.21837i) q^{26} +(-1.78078 + 3.08440i) q^{28} +(3.28078 - 5.68247i) q^{29} +5.68466 q^{31} +(0.500000 + 0.866025i) q^{32} +5.12311 q^{34} +(1.78078 + 3.08440i) q^{35} +(-2.06155 + 3.57071i) q^{37} +3.56155 q^{38} +1.00000 q^{40} +(-2.12311 + 3.67733i) q^{41} +(-2.28078 - 3.95042i) q^{43} +4.12311 q^{44} +(3.84233 + 6.65511i) q^{46} -7.00000 q^{47} +(-2.84233 + 4.92306i) q^{49} +(0.500000 - 0.866025i) q^{50} +(0.500000 + 3.57071i) q^{52} -4.43845 q^{53} +(2.06155 - 3.57071i) q^{55} +(1.78078 + 3.08440i) q^{56} +(-3.28078 - 5.68247i) q^{58} +(5.28078 + 9.14657i) q^{59} +(-3.00000 - 5.19615i) q^{61} +(2.84233 - 4.92306i) q^{62} +1.00000 q^{64} +(3.34233 + 1.35234i) q^{65} +(-7.12311 + 12.3376i) q^{67} +(2.56155 - 4.43674i) q^{68} +3.56155 q^{70} +(-2.43845 - 4.22351i) q^{71} -15.3693 q^{73} +(2.06155 + 3.57071i) q^{74} +(1.78078 - 3.08440i) q^{76} +14.6847 q^{77} +7.43845 q^{79} +(0.500000 - 0.866025i) q^{80} +(2.12311 + 3.67733i) q^{82} -1.12311 q^{83} +(-2.56155 - 4.43674i) q^{85} -4.56155 q^{86} +(2.06155 - 3.57071i) q^{88} +(0.903882 - 1.56557i) q^{89} +(1.78078 + 12.7173i) q^{91} +7.68466 q^{92} +(-3.50000 + 6.06218i) q^{94} +(-1.78078 - 3.08440i) q^{95} +(-0.561553 - 0.972638i) q^{97} +(2.84233 + 4.92306i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{4} - 4 q^{5} - 3 q^{7} - 4 q^{8}+O(q^{10}) \) 4 * q + 2 * q^2 - 2 * q^4 - 4 * q^5 - 3 * q^7 - 4 * q^8	\( 4 q + 2 q^{2} - 2 q^{4} - 4 q^{5} - 3 q^{7} - 4 q^{8} - 2 q^{10} - q^{13} - 6 q^{14} - 2 q^{16} + 2 q^{17} + 3 q^{19} + 2 q^{20} - 3 q^{23} + 4 q^{25} + q^{26} - 3 q^{28} + 9 q^{29} - 2 q^{31} + 2 q^{32} + 4 q^{34} + 3 q^{35} + 6 q^{38} + 4 q^{40} + 8 q^{41} - 5 q^{43} + 3 q^{46} - 28 q^{47} + q^{49} + 2 q^{50} + 2 q^{52} - 26 q^{53} + 3 q^{56} - 9 q^{58} + 17 q^{59} - 12 q^{61} - q^{62} + 4 q^{64} + q^{65} - 12 q^{67} + 2 q^{68} + 6 q^{70} - 18 q^{71} - 12 q^{73} + 3 q^{76} + 34 q^{77} + 38 q^{79} + 2 q^{80} - 8 q^{82} + 12 q^{83} - 2 q^{85} - 10 q^{86} - 17 q^{89} + 3 q^{91} + 6 q^{92} - 14 q^{94} - 3 q^{95} + 6 q^{97} - q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^4 - 4 * q^5 - 3 * q^7 - 4 * q^8 - 2 * q^10 - q^13 - 6 * q^14 - 2 * q^16 + 2 * q^17 + 3 * q^19 + 2 * q^20 - 3 * q^23 + 4 * q^25 + q^26 - 3 * q^28 + 9 * q^29 - 2 * q^31 + 2 * q^32 + 4 * q^34 + 3 * q^35 + 6 * q^38 + 4 * q^40 + 8 * q^41 - 5 * q^43 + 3 * q^46 - 28 * q^47 + q^49 + 2 * q^50 + 2 * q^52 - 26 * q^53 + 3 * q^56 - 9 * q^58 + 17 * q^59 - 12 * q^61 - q^62 + 4 * q^64 + q^65 - 12 * q^67 + 2 * q^68 + 6 * q^70 - 18 * q^71 - 12 * q^73 + 3 * q^76 + 34 * q^77 + 38 * q^79 + 2 * q^80 - 8 * q^82 + 12 * q^83 - 2 * q^85 - 10 * q^86 - 17 * q^89 + 3 * q^91 + 6 * q^92 - 14 * q^94 - 3 * q^95 + 6 * q^97 - q^98

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