LMFDB - Embedded newform 1950.2.i.bi.601.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1950,2,Mod(451,1950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1950, 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("1950.451");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1950.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:	$15.5708283941$
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			601.2
Root			$1.28078 - 2.21837i$ of defining polynomial
Character	$\chi$	$=$	1950.601
Dual form			1950.2.i.bi.451.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{6} +(1.78078 - 3.08440i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{6} +(1.78078 - 3.08440i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(2.06155 + 3.57071i) q^{11} -1.00000 q^{12} +(3.34233 - 1.35234i) q^{13} +3.56155 q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.56155 - 4.43674i) q^{17} -1.00000 q^{18} +(1.78078 - 3.08440i) q^{19} +3.56155 q^{21} +(-2.06155 + 3.57071i) q^{22} +(-3.84233 - 6.65511i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(2.84233 + 2.21837i) q^{26} -1.00000 q^{27} +(1.78078 + 3.08440i) q^{28} +(-3.28078 - 5.68247i) q^{29} +5.68466 q^{31} +(0.500000 - 0.866025i) q^{32} +(-2.06155 + 3.57071i) q^{33} +5.12311 q^{34} +(-0.500000 - 0.866025i) q^{36} +(2.06155 + 3.57071i) q^{37} +3.56155 q^{38} +(2.84233 + 2.21837i) q^{39} +(2.12311 + 3.67733i) q^{41} +(1.78078 + 3.08440i) q^{42} +(2.28078 - 3.95042i) q^{43} -4.12311 q^{44} +(3.84233 - 6.65511i) q^{46} -7.00000 q^{47} +(0.500000 - 0.866025i) q^{48} +(-2.84233 - 4.92306i) q^{49} +5.12311 q^{51} +(-0.500000 + 3.57071i) q^{52} -4.43845 q^{53} +(-0.500000 - 0.866025i) q^{54} +(-1.78078 + 3.08440i) q^{56} +3.56155 q^{57} +(3.28078 - 5.68247i) q^{58} +(-5.28078 + 9.14657i) q^{59} +(-3.00000 + 5.19615i) q^{61} +(2.84233 + 4.92306i) q^{62} +(1.78078 + 3.08440i) q^{63} +1.00000 q^{64} -4.12311 q^{66} +(7.12311 + 12.3376i) q^{67} +(2.56155 + 4.43674i) q^{68} +(3.84233 - 6.65511i) q^{69} +(2.43845 - 4.22351i) q^{71} +(0.500000 - 0.866025i) q^{72} +15.3693 q^{73} +(-2.06155 + 3.57071i) q^{74} +(1.78078 + 3.08440i) q^{76} +14.6847 q^{77} +(-0.500000 + 3.57071i) q^{78} +7.43845 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-2.12311 + 3.67733i) q^{82} -1.12311 q^{83} +(-1.78078 + 3.08440i) q^{84} +4.56155 q^{86} +(3.28078 - 5.68247i) q^{87} +(-2.06155 - 3.57071i) q^{88} +(-0.903882 - 1.56557i) q^{89} +(1.78078 - 12.7173i) q^{91} +7.68466 q^{92} +(2.84233 + 4.92306i) q^{93} +(-3.50000 - 6.06218i) q^{94} +1.00000 q^{96} +(0.561553 - 0.972638i) q^{97} +(2.84233 - 4.92306i) q^{98} -4.12311 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{6} + 3 q^{7} - 4 q^{8} - 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^6 + 3 * q^7 - 4 * q^8 - 2 * q^9	$ 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{6} + 3 q^{7} - 4 q^{8} - 2 q^{9} - 4 q^{12} + q^{13} + 6 q^{14} - 2 q^{16} + 2 q^{17} - 4 q^{18} + 3 q^{19} + 6 q^{21} - 3 q^{23} - 2 q^{24} - q^{26} - 4 q^{27} + 3 q^{28} - 9 q^{29} - 2 q^{31} + 2 q^{32} + 4 q^{34} - 2 q^{36} + 6 q^{38} - q^{39} - 8 q^{41} + 3 q^{42} + 5 q^{43} + 3 q^{46} - 28 q^{47} + 2 q^{48} + q^{49} + 4 q^{51} - 2 q^{52} - 26 q^{53} - 2 q^{54} - 3 q^{56} + 6 q^{57} + 9 q^{58} - 17 q^{59} - 12 q^{61} - q^{62} + 3 q^{63} + 4 q^{64} + 12 q^{67} + 2 q^{68} + 3 q^{69} + 18 q^{71} + 2 q^{72} + 12 q^{73} + 3 q^{76} + 34 q^{77} - 2 q^{78} + 38 q^{79} - 2 q^{81} + 8 q^{82} + 12 q^{83} - 3 q^{84} + 10 q^{86} + 9 q^{87} + 17 q^{89} + 3 q^{91} + 6 q^{92} - q^{93} - 14 q^{94} + 4 q^{96} - 6 q^{97} - q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^6 + 3 * q^7 - 4 * q^8 - 2 * q^9 - 4 * q^12 + q^13 + 6 * q^14 - 2 * q^16 + 2 * q^17 - 4 * q^18 + 3 * q^19 + 6 * q^21 - 3 * q^23 - 2 * q^24 - q^26 - 4 * q^27 + 3 * q^28 - 9 * q^29 - 2 * q^31 + 2 * q^32 + 4 * q^34 - 2 * q^36 + 6 * q^38 - q^39 - 8 * q^41 + 3 * q^42 + 5 * q^43 + 3 * q^46 - 28 * q^47 + 2 * q^48 + q^49 + 4 * q^51 - 2 * q^52 - 26 * q^53 - 2 * q^54 - 3 * q^56 + 6 * q^57 + 9 * q^58 - 17 * q^59 - 12 * q^61 - q^62 + 3 * q^63 + 4 * q^64 + 12 * q^67 + 2 * q^68 + 3 * q^69 + 18 * q^71 + 2 * q^72 + 12 * q^73 + 3 * q^76 + 34 * q^77 - 2 * q^78 + 38 * q^79 - 2 * q^81 + 8 * q^82 + 12 * q^83 - 3 * q^84 + 10 * q^86 + 9 * q^87 + 17 * q^89 + 3 * q^91 + 6 * q^92 - q^93 - 14 * q^94 + 4 * q^96 - 6 * q^97 - q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times$.

$n$	$301$	$1301$	$1327$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	−0.500000	+	0.866025i	−0.204124	+	0.353553i
$7$	1.78078	−	3.08440i	0.673070	−	1.16579i	−0.303959	−	0.952685i	$-0.598308\pi$
$7$	1.78078	−	3.08440i	0.673070	−	1.16579i	0.977029	−	0.213107i	$-0.0683582\pi$
$8$	−1.00000			−0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	2.06155	+	3.57071i	0.621582	+	1.07661i	0.989191	+	0.146631i	$0.0468429\pi$
$11$	2.06155	+	3.57071i	0.621582	+	1.07661i	−0.367610	+	0.929980i	$0.619824\pi$
$12$	−1.00000			−0.288675
$13$	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	−0.367982	−	0.929833i	$-0.619951\pi$
$17$	2.56155	−	4.43674i	0.621268	−	1.07607i	0.989250	−	0.146235i	$-0.0467154\pi$
$18$	−1.00000			−0.235702
$19$	1.78078	−	3.08440i	0.408538	−	0.707609i	−0.586188	−	0.810175i	$-0.699372\pi$
$19$	1.78078	−	3.08440i	0.408538	−	0.707609i	0.994726	+	0.102566i	$0.0327054\pi$
$20$		0			0
$21$	3.56155			0.777195
$22$	−2.06155	+	3.57071i	−0.439525	+	0.761279i
$23$	−3.84233	−	6.65511i	−0.801181	−	1.38769i	−0.918839	−	0.394632i	$-0.870872\pi$
$23$	−3.84233	−	6.65511i	−0.801181	−	1.38769i	0.117658	−	0.993054i	$-0.462461\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$		0			0
$26$	2.84233	+	2.21837i	0.557427	+	0.435058i
$27$	−1.00000			−0.192450
$28$	1.78078	+	3.08440i	0.336535	+	0.582896i
$29$	−3.28078	−	5.68247i	−0.609225	−	1.05521i	−0.991368	−	0.131105i	$-0.958147\pi$
$29$	−3.28078	−	5.68247i	−0.609225	−	1.05521i	0.382144	−	0.924103i	$-0.375186\pi$
$30$		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
$33$	−2.06155	+	3.57071i	−0.358870	+	0.621582i
$34$	5.12311			0.878605
$35$		0			0
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	2.06155	+	3.57071i	0.338917	+	0.587022i	0.984229	−	0.176897i	$-0.0566060\pi$
$37$	2.06155	+	3.57071i	0.338917	+	0.587022i	−0.645312	+	0.763919i	$0.723273\pi$
$38$	3.56155			0.577760
$39$	2.84233	+	2.21837i	0.455137	+	0.355223i
$40$		0			0
$41$	2.12311	+	3.67733i	0.331573	+	0.574302i	0.982821	−	0.184564i	$-0.0590872\pi$
$41$	2.12311	+	3.67733i	0.331573	+	0.574302i	−0.651247	+	0.758866i	$0.725754\pi$
$42$	1.78078	+	3.08440i	0.274780	+	0.475933i
$43$	2.28078	−	3.95042i	0.347815	−	0.602433i	−0.638046	−	0.769998i	$-0.720257\pi$
$43$	2.28078	−	3.95042i	0.347815	−	0.602433i	0.985861	+	0.167565i	$0.0535903\pi$
$44$	−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	$0.670550\pi$
$48$	0.500000	−	0.866025i	0.0721688	−	0.125000i
$49$	−2.84233	−	4.92306i	−0.406047	−	0.703294i
$50$		0			0
$51$	5.12311			0.717378
$52$	−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	$0.598601\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$		0			0
$56$	−1.78078	+	3.08440i	−0.237966	+	0.412170i
$57$	3.56155			0.471739
$58$	3.28078	−	5.68247i	0.430787	−	0.746145i
$59$	−5.28078	+	9.14657i	−0.687499	+	1.19078i	0.285146	+	0.958484i	$0.407958\pi$
$59$	−5.28078	+	9.14657i	−0.687499	+	1.19078i	−0.972645	+	0.232298i	$0.925375\pi$
$60$		0			0
$61$	−3.00000	+	5.19615i	−0.384111	+	0.665299i	−0.991645	−	0.128994i	$-0.958825\pi$
$61$	−3.00000	+	5.19615i	−0.384111	+	0.665299i	0.607535	+	0.794293i	$0.292159\pi$
$62$	2.84233	+	4.92306i	0.360976	+	0.625229i
$63$	1.78078	+	3.08440i	0.224357	+	0.388597i
$64$	1.00000			0.125000
$65$		0			0
$66$	−4.12311			−0.507519
$67$	7.12311	+	12.3376i	0.870226	+	1.50728i	0.861763	+	0.507311i	$0.169361\pi$
$67$	7.12311	+	12.3376i	0.870226	+	1.50728i	0.00846293	+	0.999964i	$0.497306\pi$
$68$	2.56155	+	4.43674i	0.310634	+	0.538034i
$69$	3.84233	−	6.65511i	0.462562	−	0.801181i
$70$		0			0
$71$	2.43845	−	4.22351i	0.289390	−	0.501239i	−0.684274	−	0.729225i	$-0.739881\pi$
$71$	2.43845	−	4.22351i	0.289390	−	0.501239i	0.973664	+	0.227986i	$0.0732141\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	15.3693			1.79884			0.899421	−	0.437083i	$-0.143988\pi$
$73$	15.3693			1.79884			0.899421	+	0.437083i	$0.143988\pi$
$74$	−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
$78$	−0.500000	+	3.57071i	−0.0566139	+	0.404304i
$79$	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			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−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	$0.519633\pi$
$84$	−1.78078	+	3.08440i	−0.194299	+	0.336535i
$85$		0			0
$86$	4.56155			0.491885
$87$	3.28078	−	5.68247i	0.351736	−	0.609225i
$88$	−2.06155	−	3.57071i	−0.219762	−	0.380639i
$89$	−0.903882	−	1.56557i	−0.0958113	−	0.165950i	0.814136	−	0.580675i	$-0.197211\pi$
$89$	−0.903882	−	1.56557i	−0.0958113	−	0.165950i	−0.909947	+	0.414725i	$0.863878\pi$
$90$		0			0
$91$	1.78078	−	12.7173i	0.186676	−	1.33313i
$92$	7.68466			0.801181
$93$	2.84233	+	4.92306i	0.294736	+	0.510497i
$94$	−3.50000	−	6.06218i	−0.360997	−	0.625266i
$95$		0			0
$96$	1.00000			0.102062
$97$	0.561553	−	0.972638i	0.0570170	−	0.0987564i	−0.836108	−	0.548565i	$-0.815174\pi$
$97$	0.561553	−	0.972638i	0.0570170	−	0.0987564i	0.893125	+	0.449808i	$0.148508\pi$
$98$	2.84233	−	4.92306i	0.287119	−	0.497304i
$99$	−4.12311			−0.414388
$100$		0			0
$101$	8.56155	+	14.8290i	0.851906	+	1.47555i	0.879486	+	0.475925i	$0.157887\pi$
$101$	8.56155	+	14.8290i	0.851906	+	1.47555i	−0.0275793	+	0.999620i	$0.508780\pi$
$102$	2.56155	+	4.43674i	0.253632	+	0.439303i
$103$	−0.438447			−0.0432015			−0.0216007	−	0.999767i	$-0.506876\pi$
$103$	−0.438447			−0.0432015			−0.0216007	+	0.999767i	$0.506876\pi$
$104$	−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	0.910306	−	0.413936i	$-0.135846\pi$
$107$	1.00000	+	1.73205i	0.0966736	+	0.167444i	−0.813632	+	0.581380i	$0.802513\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	−20.2462			−1.93924			−0.969618	−	0.244625i	$-0.921335\pi$
$109$	−20.2462			−1.93924			−0.969618	+	0.244625i	$0.921335\pi$
$110$		0			0
$111$	−2.06155	+	3.57071i	−0.195674	+	0.338917i
$112$	−3.56155			−0.336535
$113$	−1.84233	+	3.19101i	−0.173312	+	0.300185i	−0.939576	−	0.342341i	$-0.888780\pi$
$113$	−1.84233	+	3.19101i	−0.173312	+	0.300185i	0.766264	+	0.642526i	$0.222113\pi$
$114$	1.78078	+	3.08440i	0.166785	+	0.288880i
$115$		0			0
$116$	6.56155			0.609225
$117$	−0.500000	+	3.57071i	−0.0462250	+	0.330113i
$118$	−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
$123$	−2.12311	+	3.67733i	−0.191434	+	0.331573i
$124$	−2.84233	+	4.92306i	−0.255249	+	0.442104i
$125$		0			0
$126$	−1.78078	+	3.08440i	−0.158644	+	0.274780i
$127$	−2.21922	−	3.84381i	−0.196924	−	0.341083i	0.750605	−	0.660751i	$-0.229762\pi$
$127$	−2.21922	−	3.84381i	−0.196924	−	0.341083i	−0.947530	+	0.319668i	$0.896429\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	4.56155			0.401622
$130$		0			0
$131$	6.12311			0.534978			0.267489	−	0.963561i	$-0.413806\pi$
$131$	6.12311			0.534978			0.267489	+	0.963561i	$0.413806\pi$
$132$	−2.06155	−	3.57071i	−0.179435	−	0.310791i
$133$	−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	−0.990513	−	0.137418i	$-0.956120\pi$
$137$	−4.40388	+	7.62775i	−0.376249	+	0.651682i	0.614264	+	0.789101i	$0.289453\pi$
$138$	7.68466			0.654162
$139$	−4.21922	+	7.30791i	−0.357870	+	0.619849i	−0.987605	−	0.156961i	$-0.949830\pi$
$139$	−4.21922	+	7.30791i	−0.357870	+	0.619849i	0.629735	+	0.776810i	$0.283164\pi$
$140$		0			0
$141$	−3.50000	−	6.06218i	−0.294753	−	0.510527i
$142$	4.87689			0.409260
$143$	11.7192	+	9.14657i	0.980011	+	0.764875i
$144$	1.00000			0.0833333
$145$		0			0
$146$	7.68466	+	13.3102i	0.635987	+	1.10156i
$147$	2.84233	−	4.92306i	0.234431	−	0.406047i
$148$	−4.12311			−0.338917
$149$	11.4039	−	19.7521i	0.934242	−	1.61816i	0.158263	−	0.987397i	$-0.449411\pi$
$149$	11.4039	−	19.7521i	0.934242	−	1.61816i	0.775979	−	0.630758i	$-0.217256\pi$
$150$		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
$153$	2.56155	+	4.43674i	0.207089	+	0.358689i
$154$	7.34233	+	12.7173i	0.591662	+	1.02479i
$155$		0			0
$156$	−3.34233	+	1.35234i	−0.267601	+	0.108274i
$157$	−22.1231			−1.76562			−0.882808	−	0.469734i	$-0.844350\pi$
$157$	−22.1231			−1.76562			−0.882808	+	0.469734i	$0.844350\pi$
$158$	3.71922	+	6.44188i	0.295886	+	0.512489i
$159$	−2.21922	−	3.84381i	−0.175996	−	0.304834i
$160$		0			0
$161$	−27.3693			−2.15700
$162$	0.500000	−	0.866025i	0.0392837	−	0.0680414i
$163$	−9.28078	+	16.0748i	−0.726927	+	1.25907i	0.231250	+	0.972894i	$0.425719\pi$
$163$	−9.28078	+	16.0748i	−0.726927	+	1.25907i	−0.958176	+	0.286179i	$0.907615\pi$
$164$	−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	−0.927122	−	0.374760i	$-0.877725\pi$
$167$	−10.1847	−	17.6403i	−0.788113	−	1.36505i	0.139009	−	0.990291i	$-0.455608\pi$
$168$	−3.56155			−0.274780
$169$	9.34233	−	9.03996i	0.718641	−	0.695382i
$170$		0			0
$171$	1.78078	+	3.08440i	0.136179	+	0.235870i
$172$	2.28078	+	3.95042i	0.173908	+	0.301217i
$173$	−12.5885	+	21.8040i	−0.957089	+	1.65773i	−0.227575	+	0.973760i	$0.573080\pi$
$173$	−12.5885	+	21.8040i	−0.957089	+	1.65773i	−0.729514	+	0.683966i	$0.760254\pi$
$174$	6.56155			0.497430
$175$		0			0
$176$	2.06155	−	3.57071i	0.155395	−	0.269153i
$177$	−10.5616			−0.793855
$178$	0.903882	−	1.56557i	0.0677488	−	0.117344i
$179$	0.157671	+	0.273094i	0.0117849	+	0.0204120i	0.871858	−	0.489759i	$-0.162915\pi$
$179$	0.157671	+	0.273094i	0.0117849	+	0.0204120i	−0.860073	+	0.510171i	$0.829582\pi$
$180$		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
$183$	−6.00000			−0.443533
$184$	3.84233	+	6.65511i	0.283260	+	0.490621i
$185$		0			0
$186$	−2.84233	+	4.92306i	−0.208410	+	0.360976i
$187$	21.1231			1.54467
$188$	3.50000	−	6.06218i	0.255264	−	0.442130i
$189$	−1.78078	+	3.08440i	−0.129532	+	0.224357i
$190$		0			0
$191$	−9.56155	+	16.5611i	−0.691850	+	1.19832i	0.279381	+	0.960180i	$0.409871\pi$
$191$	−9.56155	+	16.5611i	−0.691850	+	1.19832i	−0.971231	+	0.238139i	$0.923463\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$193$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$194$	1.12311			0.0806343
$195$		0			0
$196$	5.68466			0.406047
$197$	−3.90388	−	6.76172i	−0.278140	−	0.481753i	0.692782	−	0.721147i	$-0.256385\pi$
$197$	−3.90388	−	6.76172i	−0.278140	−	0.481753i	−0.970923	+	0.239394i	$0.923051\pi$
$198$	−2.06155	−	3.57071i	−0.146508	−	0.253760i
$199$	−5.56155	+	9.63289i	−0.394248	+	0.682858i	−0.993005	−	0.118073i	$-0.962328\pi$
$199$	−5.56155	+	9.63289i	−0.394248	+	0.682858i	0.598757	+	0.800931i	$0.295662\pi$
$200$		0			0
$201$	−7.12311	+	12.3376i	−0.502425	+	0.870226i
$202$	−8.56155	+	14.8290i	−0.602389	+	1.04337i
$203$	−23.3693			−1.64020
$204$	−2.56155	+	4.43674i	−0.179345	+	0.310634i
$205$		0			0
$206$	−0.219224	−	0.379706i	−0.0152740	−	0.0264554i
$207$	7.68466			0.534121
$208$	−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	0.721734	−	0.692171i	$-0.243345\pi$
$211$	−3.46543	−	6.00231i	−0.238570	−	0.413216i	−0.960304	+	0.278955i	$0.910012\pi$
$212$	2.21922	−	3.84381i	0.152417	−	0.263994i
$213$	4.87689			0.334159
$214$	−1.00000	+	1.73205i	−0.0683586	+	0.118401i
$215$		0			0
$216$	1.00000			0.0680414
$217$	10.1231	−	17.5337i	0.687201	−	1.19027i
$218$	−10.1231	−	17.5337i	−0.685623	−	1.18753i
$219$	7.68466	+	13.3102i	0.519281	+	0.899421i
$220$		0			0
$221$	2.56155	−	18.2931i	0.172309	−	1.23053i
$222$	−4.12311			−0.276725
$223$	−13.1501	−	22.7766i	−0.880595	−	1.52524i	−0.850680	−	0.525683i	$-0.823810\pi$
$223$	−13.1501	−	22.7766i	−0.880595	−	1.52524i	−0.0299151	−	0.999552i	$-0.509524\pi$
$224$	−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	0.315906	+	0.948790i	$0.397691\pi$
$227$	−10.0000	+	17.3205i	−0.663723	+	1.14960i	−0.979630	+	0.200812i	$0.935642\pi$
$228$	−1.78078	+	3.08440i	−0.117935	+	0.204269i
$229$	−7.75379			−0.512385			−0.256192	−	0.966626i	$-0.582468\pi$
$229$	−7.75379			−0.512385			−0.256192	+	0.966626i	$0.582468\pi$
$230$		0			0
$231$	7.34233	+	12.7173i	0.483090	+	0.836736i
$232$	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	$0.303334\pi$
$234$	−3.34233	+	1.35234i	−0.218495	+	0.0884055i
$235$		0			0
$236$	−5.28078	−	9.14657i	−0.343749	−	0.595391i
$237$	3.71922	+	6.44188i	0.241590	+	0.418445i
$238$	9.12311	−	15.8017i	0.591363	−	1.02427i
$239$	13.3693			0.864789			0.432395	−	0.901684i	$-0.357669\pi$
$239$	13.3693			0.864789			0.432395	+	0.901684i	$0.357669\pi$
$240$		0			0
$241$	9.93845	−	17.2139i	0.640192	−	1.10884i	−0.345198	−	0.938530i	$-0.612188\pi$
$241$	9.93845	−	17.2139i	0.640192	−	1.10884i	0.985390	−	0.170315i	$-0.0544784\pi$
$242$	−6.00000			−0.385695
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−3.00000	−	5.19615i	−0.192055	−	0.332650i
$245$		0			0
$246$	−4.24621			−0.270729
$247$	1.78078	−	12.7173i	0.113308	−	0.809182i
$248$	−5.68466			−0.360976
$249$	−0.561553	−	0.972638i	−0.0355870	−	0.0616384i
$250$		0			0
$251$	−0.0615528	+	0.106613i	−0.00388518	+	0.00672933i	−0.867961	−	0.496632i	$-0.834570\pi$
$251$	−0.0615528	+	0.106613i	−0.00388518	+	0.00672933i	0.864076	+	0.503361i	$0.167903\pi$
$252$	−3.56155			−0.224357
$253$	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	0.842721	−	0.538350i	$-0.180952\pi$
$257$	−0.719224	−	1.24573i	−0.0448639	−	0.0777066i	−0.887585	+	0.460643i	$0.847619\pi$
$258$	2.28078	+	3.95042i	0.141995	+	0.245942i
$259$	14.6847			0.912460
$260$		0			0
$261$	6.56155			0.406150
$262$	3.06155	+	5.30277i	0.189143	+	0.327606i
$263$	−6.50000	−	11.2583i	−0.400807	−	0.694218i	0.593016	−	0.805190i	$-0.297937\pi$
$263$	−6.50000	−	11.2583i	−0.400807	−	0.694218i	−0.993824	+	0.110972i	$0.964604\pi$
$264$	2.06155	−	3.57071i	0.126880	−	0.219762i
$265$		0			0
$266$	6.34233	−	10.9852i	0.388873	−	0.673548i
$267$	0.903882	−	1.56557i	0.0553167	−	0.0958113i
$268$	−14.2462			−0.870226
$269$	1.68466	−	2.91791i	0.102715	−	0.177908i	−0.810087	−	0.586310i	$-0.800580\pi$
$269$	1.68466	−	2.91791i	0.102715	−	0.177908i	0.912803	+	0.408401i	$0.133914\pi$
$270$		0			0
$271$	−16.0885	−	27.8662i	−0.977309	−	1.69275i	−0.672094	−	0.740466i	$-0.734605\pi$
$271$	−16.0885	−	27.8662i	−0.977309	−	1.69275i	−0.305215	−	0.952283i	$-0.598728\pi$
$272$	−5.12311			−0.310634
$273$	11.9039	−	4.81645i	0.720456	−	0.291505i
$274$	−8.80776			−0.532096
$275$		0			0
$276$	3.84233	+	6.65511i	0.231281	+	0.400591i
$277$	−0.500000	+	0.866025i	−0.0300421	+	0.0520344i	−0.880656	−	0.473757i	$-0.842897\pi$
$277$	−0.500000	+	0.866025i	−0.0300421	+	0.0520344i	0.850613	+	0.525792i	$0.176231\pi$
$278$	−8.43845			−0.506104
$279$	−2.84233	+	4.92306i	−0.170166	+	0.294736i
$280$		0			0
$281$	−0.246211			−0.0146877			−0.00734387	−	0.999973i	$-0.502338\pi$
$281$	−0.246211			−0.0146877			−0.00734387	+	0.999973i	$0.502338\pi$
$282$	3.50000	−	6.06218i	0.208422	−	0.360997i
$283$	5.71922	+	9.90599i	0.339973	+	0.588850i	0.984427	−	0.175793i	$-0.0562489\pi$
$283$	5.71922	+	9.90599i	0.339973	+	0.588850i	−0.644455	+	0.764643i	$0.722916\pi$
$284$	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
$288$	0.500000	+	0.866025i	0.0294628	+	0.0510310i
$289$	−4.62311	−	8.00745i	−0.271947	−	0.471027i
$290$		0			0
$291$	1.12311			0.0658376
$292$	−7.68466	+	13.3102i	−0.449711	+	0.778922i
$293$	−12.4654	+	21.5908i	−0.728238	+	1.26135i	0.229389	+	0.973335i	$0.426327\pi$
$293$	−12.4654	+	21.5908i	−0.728238	+	1.26135i	−0.957627	+	0.288011i	$0.907006\pi$
$294$	5.68466			0.331536
$295$		0			0
$296$	−2.06155	−	3.57071i	−0.119825	−	0.207544i
$297$	−2.06155	−	3.57071i	−0.119623	−	0.207194i
$298$	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
$303$	−8.56155	+	14.8290i	−0.491848	+	0.851906i
$304$	−3.56155			−0.204269
$305$		0			0
$306$	−2.56155	+	4.43674i	−0.146434	+	0.253632i
$307$	15.6155			0.891225			0.445613	−	0.895226i	$-0.352986\pi$
$307$	15.6155			0.891225			0.445613	+	0.895226i	$0.352986\pi$
$308$	−7.34233	+	12.7173i	−0.418368	+	0.724635i
$309$	−0.219224	−	0.379706i	−0.0124712	−	0.0216007i
$310$		0			0
$311$	−18.7386			−1.06257			−0.531285	−	0.847193i	$-0.678291\pi$
$311$	−18.7386			−1.06257			−0.531285	+	0.847193i	$0.678291\pi$
$312$	−2.84233	−	2.21837i	−0.160915	−	0.125590i
$313$	−6.63068			−0.374788			−0.187394	−	0.982285i	$-0.560004\pi$
$313$	−6.63068			−0.374788			−0.187394	+	0.982285i	$0.560004\pi$
$314$	−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	$0.462438\pi$
$318$	2.21922	−	3.84381i	0.124448	−	0.215550i
$319$	13.5270	−	23.4294i	0.757366	−	1.31180i
$320$		0			0
$321$	−1.00000	+	1.73205i	−0.0558146	+	0.0966736i
$322$	−13.6847	−	23.7025i	−0.762616	−	1.32089i
$323$	−9.12311	−	15.8017i	−0.507623	−	0.879229i
$324$	1.00000			0.0555556
$325$		0			0
$326$	−18.5616			−1.02803
$327$	−10.1231	−	17.5337i	−0.559809	−	0.969618i
$328$	−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	−0.484865	−	0.874589i	$-0.661131\pi$
$331$	9.36932	−	16.2281i	0.514984	−	0.891979i	0.999849	−	0.0173896i	$-0.00553556\pi$
$332$	0.561553	−	0.972638i	0.0308192	−	0.0533804i
$333$	−4.12311			−0.225945
$334$	10.1847	−	17.6403i	0.557280	−	0.965237i
$335$		0			0
$336$	−1.78078	−	3.08440i	−0.0971493	−	0.168268i
$337$	6.00000			0.326841			0.163420	−	0.986557i	$-0.447747\pi$
$337$	6.00000			0.326841			0.163420	+	0.986557i	$0.447747\pi$
$338$	12.5000	+	3.57071i	0.679910	+	0.194221i
$339$	−3.68466			−0.200123
$340$		0			0
$341$	11.7192	+	20.2983i	0.634632	+	1.09921i
$342$	−1.78078	+	3.08440i	−0.0962934	+	0.166785i
$343$	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	−0.717220	−	0.696847i	$-0.754586\pi$
$347$	4.56155	−	7.90084i	0.244877	−	0.424139i	0.962097	+	0.272707i	$0.0879191\pi$
$348$	3.28078	+	5.68247i	0.175868	+	0.304612i
$349$	12.2462	+	21.2111i	0.655525	+	1.13540i	0.981762	+	0.190114i	$0.0608858\pi$
$349$	12.2462	+	21.2111i	0.655525	+	1.13540i	−0.326237	+	0.945288i	$0.605781\pi$
$350$		0			0
$351$	−3.34233	+	1.35234i	−0.178400	+	0.0721828i
$352$	4.12311			0.219762
$353$	15.9309	+	27.5931i	0.847915	+	1.46863i	0.883066	+	0.469249i	$0.155475\pi$
$353$	15.9309	+	27.5931i	0.847915	+	1.46863i	−0.0351511	+	0.999382i	$0.511191\pi$
$354$	−5.28078	−	9.14657i	−0.280670	−	0.486135i
$355$		0			0
$356$	1.80776			0.0958113
$357$	9.12311	−	15.8017i	0.482846	−	0.836314i
$358$	−0.157671	+	0.273094i	−0.00833316	+	0.0144335i
$359$	4.87689			0.257393			0.128696	−	0.991684i	$-0.458921\pi$
$359$	4.87689			0.257393			0.128696	+	0.991684i	$0.458921\pi$
$360$		0			0
$361$	3.15767	+	5.46925i	0.166193	+	0.287855i
$362$	5.56155	+	9.63289i	0.292309	+	0.506294i
$363$	−6.00000			−0.314918
$364$	10.1231	+	7.90084i	0.530595	+	0.414117i
$365$		0			0
$366$	−3.00000	−	5.19615i	−0.156813	−	0.271607i
$367$	−10.2462	−	17.7470i	−0.534848	−	0.926384i	−0.999171	−	0.0407177i	$-0.987036\pi$
$367$	−10.2462	−	17.7470i	−0.534848	−	0.926384i	0.464323	−	0.885666i	$-0.346298\pi$
$368$	−3.84233	+	6.65511i	−0.200295	+	0.346922i
$369$	−4.24621			−0.221049
$370$		0			0
$371$	−7.90388	+	13.6899i	−0.410349	+	0.710746i
$372$	−5.68466			−0.294736
$373$	−2.59612	+	4.49661i	−0.134422	+	0.232826i	−0.925376	−	0.379049i	$-0.876251\pi$
$373$	−2.59612	+	4.49661i	−0.134422	+	0.232826i	0.790955	+	0.611875i	$0.209584\pi$
$374$	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
$378$	−3.56155			−0.183187
$379$	2.65767	+	4.60322i	0.136515	+	0.236452i	0.926175	−	0.377093i	$-0.123076\pi$
$379$	2.65767	+	4.60322i	0.136515	+	0.236452i	−0.789660	+	0.613545i	$0.789743\pi$
$380$		0			0
$381$	2.21922	−	3.84381i	0.113694	−	0.196924i
$382$	−19.1231			−0.978423
$383$	10.4039	−	18.0201i	0.531614	−	0.920782i	−0.467706	−	0.883884i	$-0.654919\pi$
$383$	10.4039	−	18.0201i	0.531614	−	0.920782i	0.999319	−	0.0368973i	$-0.0117474\pi$
$384$	−0.500000	+	0.866025i	−0.0255155	+	0.0441942i
$385$		0			0
$386$		0			0
$387$	2.28078	+	3.95042i	0.115938	+	0.200811i
$388$	0.561553	+	0.972638i	0.0285085	+	0.0493782i
$389$	19.0540			0.966075			0.483037	−	0.875600i	$-0.339533\pi$
$389$	19.0540			0.966075			0.483037	+	0.875600i	$0.339533\pi$
$390$		0			0
$391$	−39.3693			−1.99099
$392$	2.84233	+	4.92306i	0.143559	+	0.248652i
$393$	3.06155	+	5.30277i	0.154435	+	0.267489i
$394$	3.90388	−	6.76172i	0.196675	−	0.340651i
$395$		0			0
$396$	2.06155	−	3.57071i	0.103597	−	0.179435i
$397$	−5.93845	+	10.2857i	−0.298042	+	0.516224i	−0.975688	−	0.219164i	$-0.929667\pi$
$397$	−5.93845	+	10.2857i	−0.298042	+	0.516224i	0.677646	+	0.735388i	$0.263000\pi$
$398$	−11.1231			−0.557551
$399$	6.34233	−	10.9852i	0.317514	−	0.549950i
$400$		0			0
$401$	−6.34233	−	10.9852i	−0.316721	−	0.548577i	0.663081	−	0.748548i	$-0.269248\pi$
$401$	−6.34233	−	10.9852i	−0.316721	−	0.548577i	−0.979802	+	0.199971i	$0.935915\pi$
$402$	−14.2462			−0.710536
$403$	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
$408$	−5.12311			−0.253632
$409$	−0.903882	+	1.56557i	−0.0446941	+	0.0774124i	−0.887507	−	0.460794i	$-0.847565\pi$
$409$	−0.903882	+	1.56557i	−0.0446941	+	0.0774124i	0.842813	+	0.538207i	$0.180898\pi$
$410$		0			0
$411$	−8.80776			−0.434455
$412$	0.219224	−	0.379706i	0.0108004	−	0.0187068i
$413$	18.8078	+	32.5760i	0.925470	+	1.60296i
$414$	3.84233	+	6.65511i	0.188840	+	0.327081i
$415$		0			0
$416$	0.500000	−	3.57071i	0.0245145	−	0.175069i
$417$	−8.43845			−0.413233
$418$	7.34233	+	12.7173i	0.359125	+	0.622023i
$419$	0.246211	+	0.426450i	0.0120282	+	0.0208335i	0.871977	−	0.489547i	$-0.162838\pi$
$419$	0.246211	+	0.426450i	0.0120282	+	0.0208335i	−0.859949	+	0.510381i	$0.829505\pi$
$420$		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
$423$	3.50000	−	6.06218i	0.170176	−	0.294753i
$424$	4.43845			0.215550
$425$		0			0
$426$	2.43845	+	4.22351i	0.118143	+	0.204630i
$427$	10.6847	+	18.5064i	0.517067	+	0.895586i
$428$	−2.00000			−0.0966736
$429$	−2.06155	+	14.7224i	−0.0995327	+	0.710806i
$430$		0			0
$431$	−13.3693	−	23.1563i	−0.643977	−	1.11540i	−0.984537	−	0.175178i	$-0.943950\pi$
$431$	−13.3693	−	23.1563i	−0.643977	−	1.11540i	0.340559	−	0.940223i	$-0.389384\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	15.3693	−	26.6204i	0.738602	−	1.27930i	−0.214523	−	0.976719i	$-0.568820\pi$
$433$	15.3693	−	26.6204i	0.738602	−	1.27930i	0.953125	−	0.302578i	$-0.0978471\pi$
$434$	20.2462			0.971849
$435$		0			0
$436$	10.1231	−	17.5337i	0.484809	−	0.839714i
$437$	−27.3693			−1.30925
$438$	−7.68466	+	13.3102i	−0.367187	+	0.635987i
$439$	−8.43845	−	14.6158i	−0.402745	−	0.697575i	0.591311	−	0.806444i	$-0.298611\pi$
$439$	−8.43845	−	14.6158i	−0.402745	−	0.697575i	−0.994056	+	0.108869i	$0.965277\pi$
$440$		0			0
$441$	5.68466			0.270698
$442$	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	$0.463039\pi$
$444$	−2.06155	−	3.57071i	−0.0978370	−	0.169459i
$445$		0			0
$446$	13.1501	−	22.7766i	0.622675	−	1.07850i
$447$	22.8078			1.07877
$448$	1.78078	−	3.08440i	0.0841338	−	0.145724i
$449$	−12.5885	+	21.8040i	−0.594090	+	1.02899i	0.399585	+	0.916696i	$0.369154\pi$
$449$	−12.5885	+	21.8040i	−0.594090	+	1.02899i	−0.993675	+	0.112298i	$0.964179\pi$
$450$		0			0
$451$	−8.75379	+	15.1620i	−0.412200	+	0.713951i
$452$	−1.84233	−	3.19101i	−0.0866559	−	0.150092i
$453$	4.68466	+	8.11407i	0.220104	+	0.381232i
$454$	−20.0000			−0.938647
$455$		0			0
$456$	−3.56155			−0.166785
$457$	1.87689	+	3.25088i	0.0877974	+	0.152070i	0.906580	−	0.422034i	$-0.138684\pi$
$457$	1.87689	+	3.25088i	0.0877974	+	0.152070i	−0.818782	+	0.574104i	$0.805351\pi$
$458$	−3.87689	−	6.71498i	−0.181155	−	0.313770i
$459$	−2.56155	+	4.43674i	−0.119563	+	0.207089i
$460$		0			0
$461$	−3.52699	+	6.10892i	−0.164268	+	0.284521i	−0.936395	−	0.350947i	$-0.885860\pi$
$461$	−3.52699	+	6.10892i	−0.164268	+	0.284521i	0.772127	+	0.635468i	$0.219193\pi$
$462$	−7.34233	+	12.7173i	−0.341596	+	0.591662i
$463$	−33.6155			−1.56225			−0.781123	−	0.624377i	$-0.785353\pi$
$463$	−33.6155			−1.56225			−0.781123	+	0.624377i	$0.785353\pi$
$464$	−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	$0.873685\pi$
$468$	−2.84233	−	2.21837i	−0.131387	−	0.102544i
$469$	50.7386			2.34289
$470$		0			0
$471$	−11.0616	−	19.1592i	−0.509689	−	0.882808i
$472$	5.28078	−	9.14657i	0.243067	−	0.421005i
$473$	18.8078			0.864782
$474$	−3.71922	+	6.44188i	−0.170830	+	0.295886i
$475$		0			0
$476$	18.2462			0.836314
$477$	2.21922	−	3.84381i	0.101611	−	0.175996i
$478$	6.68466	+	11.5782i	0.305749	+	0.529573i
$479$	10.8769	+	18.8393i	0.496978	+	0.860791i	0.999994	−	0.00348601i	$-0.00110963\pi$
$479$	10.8769	+	18.8393i	0.496978	+	0.860791i	−0.503016	+	0.864277i	$0.667776\pi$
$480$		0			0
$481$	11.7192	+	9.14657i	0.534351	+	0.417048i
$482$	19.8769			0.905368
$483$	−13.6847	−	23.7025i	−0.622674	−	1.07850i
$484$	−3.00000	−	5.19615i	−0.136364	−	0.236189i
$485$		0			0
$486$	1.00000			0.0453609
$487$	−12.0270	+	20.8314i	−0.544995	+	0.943959i	0.453612	+	0.891199i	$0.350135\pi$
$487$	−12.0270	+	20.8314i	−0.544995	+	0.943959i	−0.998607	+	0.0527597i	$0.983198\pi$
$488$	3.00000	−	5.19615i	0.135804	−	0.235219i
$489$	−18.5616			−0.839382
$490$		0			0
$491$	10.7808	+	18.6729i	0.486530	+	0.842694i	0.999880	−	0.0154850i	$-0.00492923\pi$
$491$	10.7808	+	18.6729i	0.486530	+	0.842694i	−0.513350	+	0.858179i	$0.671596\pi$
$492$	−2.12311	−	3.67733i	−0.0957170	−	0.165787i
$493$	−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
$498$	0.561553	−	0.972638i	0.0251638	−	0.0435850i
$499$	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			0
$501$	10.1847	−	17.6403i	0.455017	−	0.788113i
$502$	−0.123106			−0.00549447
$503$	−2.97301	+	5.14941i	−0.132560	+	0.229601i	−0.924663	−	0.380787i	$-0.875653\pi$
$503$	−2.97301	+	5.14941i	−0.132560	+	0.229601i	0.792103	+	0.610388i	$0.208986\pi$
$504$	−1.78078	−	3.08440i	−0.0793221	−	0.137390i
$505$		0			0
$506$	31.6847			1.40855
$507$	12.5000	+	3.57071i	0.555144	+	0.158581i
$508$	4.43845			0.196924
$509$	14.7732	+	25.5879i	0.654811	+	1.13417i	0.981941	+	0.189186i	$0.0605849\pi$
$509$	14.7732	+	25.5879i	0.654811	+	1.13417i	−0.327131	+	0.944979i	$0.606082\pi$
$510$		0			0
$511$	27.3693	−	47.4050i	1.21075	−	2.09708i
$512$	−1.00000			−0.0441942
$513$	−1.78078	+	3.08440i	−0.0786232	+	0.136179i
$514$	0.719224	−	1.24573i	0.0317236	−	0.0549469i
$515$		0			0
$516$	−2.28078	+	3.95042i	−0.100406	+	0.173908i
$517$	−14.4309	−	24.9950i	−0.634669	−	1.09928i
$518$	7.34233	+	12.7173i	0.322603	+	0.558766i
$519$	−25.1771			−1.10515
$520$		0			0
$521$	−18.6847			−0.818590			−0.409295	−	0.912402i	$-0.634225\pi$
$521$	−18.6847			−0.818590			−0.409295	+	0.912402i	$0.634225\pi$
$522$	3.28078	+	5.68247i	0.143596	+	0.248715i
$523$	−4.59612	−	7.96071i	−0.200974	−	0.348098i	0.747868	−	0.663847i	$-0.231077\pi$
$523$	−4.59612	−	7.96071i	−0.200974	−	0.348098i	−0.948843	+	0.315749i	$0.897744\pi$
$524$	−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
$528$	4.12311			0.179435
$529$	−18.0270	+	31.2237i	−0.783782	+	1.35755i
$530$		0			0
$531$	−5.28078	−	9.14657i	−0.229166	−	0.396927i
$532$	12.6847			0.549950
$533$	12.0691	+	9.41967i	0.522772	+	0.408011i
$534$	1.80776			0.0782296
$535$		0			0
$536$	−7.12311	−	12.3376i	−0.307671	−	0.532902i
$537$	−0.157671	+	0.273094i	−0.00680400	+	0.0117849i
$538$	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
$543$	5.56155	+	9.63289i	0.238669	+	0.413387i
$544$	−2.56155	−	4.43674i	−0.109826	−	0.190224i
$545$		0			0
$546$	10.1231	+	7.90084i	0.433229	+	0.338125i
$547$	−35.6155			−1.52281			−0.761405	−	0.648276i	$-0.775490\pi$
$547$	−35.6155			−1.52281			−0.761405	+	0.648276i	$0.775490\pi$
$548$	−4.40388	−	7.62775i	−0.188125	−	0.325841i
$549$	−3.00000	−	5.19615i	−0.128037	−	0.221766i
$550$		0			0
$551$	−23.3693			−0.995566
$552$	−3.84233	+	6.65511i	−0.163540	+	0.283260i
$553$	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	0.815172	−	0.579218i	$-0.196642\pi$
$557$	−2.21922	−	3.84381i	−0.0940315	−	0.162867i	−0.909204	+	0.416351i	$0.863309\pi$
$558$	−5.68466			−0.240651
$559$	2.28078	−	16.2880i	0.0964666	−	0.688909i
$560$		0			0
$561$	10.5616	+	18.2931i	0.445909	+	0.772337i
$562$	−0.123106	−	0.213225i	−0.00519290	−	0.00899436i
$563$	16.4924	−	28.5657i	0.695073	−	1.20390i	−0.275083	−	0.961420i	$-0.588705\pi$
$563$	16.4924	−	28.5657i	0.695073	−	1.20390i	0.970156	−	0.242481i	$-0.0779612\pi$
$564$	7.00000			0.294753
$565$		0			0
$566$	−5.71922	+	9.90599i	−0.240397	+	0.416380i
$567$	−3.56155			−0.149571
$568$	−2.43845	+	4.22351i	−0.102315	+	0.177215i
$569$	9.58854	+	16.6078i	0.401973	+	0.696237i	0.993964	−	0.109707i	$-0.0349914\pi$
$569$	9.58854	+	16.6078i	0.401973	+	0.696237i	−0.591991	+	0.805944i	$0.701658\pi$
$570$		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
$573$	−19.1231			−0.798879
$574$	7.56155	+	13.0970i	0.315613	+	0.546658i
$575$		0			0
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−8.73863			−0.363794			−0.181897	−	0.983318i	$-0.558224\pi$
$577$	−8.73863			−0.363794			−0.181897	+	0.983318i	$0.558224\pi$
$578$	4.62311	−	8.00745i	0.192296	−	0.333066i
$579$		0			0
$580$		0			0
$581$	−2.00000	+	3.46410i	−0.0829740	+	0.143715i
$582$	0.561553	+	0.972638i	0.0232771	+	0.0403171i
$583$	−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	0.509725	−	0.860338i	$-0.329747\pi$
$587$	−11.8769	−	20.5714i	−0.490212	−	0.849072i	−0.999937	+	0.0112657i	$0.996414\pi$
$588$	2.84233	+	4.92306i	0.117216	+	0.203024i
$589$	10.1231	−	17.5337i	0.417115	−	0.722465i
$590$		0			0
$591$	3.90388	−	6.76172i	0.160584	−	0.278140i
$592$	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	$0.419561\pi$
$594$	2.06155	−	3.57071i	0.0845865	−	0.146508i
$595$		0			0
$596$	11.4039	+	19.7521i	0.467121	+	0.809078i
$597$	−11.1231			−0.455238
$598$	3.84233	−	27.4397i	0.157125	−	1.12209i
$599$	−14.0000			−0.572024			−0.286012	−	0.958226i	$-0.592330\pi$
$599$	−14.0000			−0.572024			−0.286012	+	0.958226i	$0.592330\pi$
$600$		0			0
$601$	17.9924	+	31.1638i	0.733926	+	1.27120i	0.955193	+	0.295984i	$0.0956476\pi$
$601$	17.9924	+	31.1638i	0.733926	+	1.27120i	−0.221267	+	0.975213i	$0.571019\pi$
$602$	8.12311	−	14.0696i	0.331073	−	0.573435i
$603$	−14.2462			−0.580151
$604$	−4.68466	+	8.11407i	−0.190616	+	0.330157i
$605$		0			0
$606$	−17.1231			−0.695579
$607$	−14.7116	+	25.4813i	−0.597127	+	1.03425i	0.396116	+	0.918201i	$0.370358\pi$
$607$	−14.7116	+	25.4813i	−0.597127	+	1.03425i	−0.993243	+	0.116054i	$0.962975\pi$
$608$	−1.78078	−	3.08440i	−0.0722200	−	0.125089i
$609$	−11.6847	−	20.2384i	−0.473486	−	0.820102i
$610$		0			0
$611$	−23.3963	+	9.46641i	−0.946513	+	0.382970i
$612$	−5.12311			−0.207089
$613$	14.0616	+	24.3553i	0.567941	+	0.983702i	0.996769	+	0.0803164i	$0.0255931\pi$
$613$	14.0616	+	24.3553i	0.567941	+	0.983702i	−0.428829	+	0.903386i	$0.641074\pi$
$614$	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	0.0515837	+	0.998669i	$0.483573\pi$
$617$	−20.8423	+	36.1000i	−0.839081	+	1.45333i	−0.890664	+	0.454662i	$0.849760\pi$
$618$	0.219224	−	0.379706i	0.00881847	−	0.0152740i
$619$	−16.4384			−0.660717			−0.330358	−	0.943856i	$-0.607170\pi$
$619$	−16.4384			−0.660717			−0.330358	+	0.943856i	$0.607170\pi$
$620$		0			0
$621$	3.84233	+	6.65511i	0.154187	+	0.267060i
$622$	−9.36932	−	16.2281i	−0.375675	−	0.650689i
$623$	−6.43845			−0.257951
$624$	0.500000	−	3.57071i	0.0200160	−	0.142943i
$625$		0			0
$626$	−3.31534	−	5.74234i	−0.132508	−	0.229510i
$627$	7.34233	+	12.7173i	0.293224	+	0.507880i
$628$	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	−0.390470	−	0.920616i	$-0.627688\pi$
$631$	15.1231	−	26.1940i	0.602041	−	1.04277i	0.992512	−	0.122151i	$-0.0389791\pi$
$632$	−7.43845			−0.295886
$633$	3.46543	−	6.00231i	0.137739	−	0.238570i
$634$	2.09612	+	3.63058i	0.0832475	+	0.144189i
$635$		0			0
$636$	4.43845			0.175996
$637$	−16.1577	−	12.6107i	−0.640190	−	0.499653i
$638$	27.0540			1.07108
$639$	2.43845	+	4.22351i	0.0964635	+	0.167080i
$640$		0			0
$641$	7.78078	−	13.4767i	0.307322	−	0.532298i	−0.670453	−	0.741952i	$-0.733900\pi$
$641$	7.78078	−	13.4767i	0.307322	−	0.532298i	0.977776	+	0.209654i	$0.0672337\pi$
$642$	−2.00000			−0.0789337
$643$	19.1231	−	33.1222i	0.754142	−	1.30621i	−0.191658	−	0.981462i	$-0.561387\pi$
$643$	19.1231	−	33.1222i	0.754142	−	1.30621i	0.945800	−	0.324750i	$-0.105280\pi$
$644$	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	0.845132	−	0.534558i	$-0.179522\pi$
$647$	−1.02699	−	1.77879i	−0.0403751	−	0.0699316i	−0.885507	+	0.464626i	$0.846189\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	−43.5464			−1.70935
$650$		0			0
$651$	20.2462			0.793512
$652$	−9.28078	−	16.0748i	−0.363463	−	0.629537i
$653$	−20.2192	−	35.0207i	−0.791239	−	1.37047i	−0.925200	−	0.379480i	$-0.876103\pi$
$653$	−20.2192	−	35.0207i	−0.791239	−	1.37047i	0.133961	−	0.990987i	$-0.457230\pi$
$654$	10.1231	−	17.5337i	0.395845	−	0.685623i
$655$		0			0
$656$	2.12311	−	3.67733i	0.0828933	−	0.143575i
$657$	−7.68466	+	13.3102i	−0.299807	+	0.519281i
$658$	−24.9309			−0.971906
$659$	−15.5270	+	26.8935i	−0.604846	+	1.04762i	0.387230	+	0.921983i	$0.373432\pi$
$659$	−15.5270	+	26.8935i	−0.604846	+	1.04762i	−0.992076	+	0.125640i	$0.959902\pi$
$660$		0			0
$661$	5.80776	+	10.0593i	0.225896	+	0.391263i	0.956588	−	0.291444i	$-0.0941358\pi$
$661$	5.80776	+	10.0593i	0.225896	+	0.391263i	−0.730692	+	0.682707i	$0.760802\pi$
$662$	18.7386			0.728298
$663$	17.1231	−	6.92820i	0.665006	−	0.269069i
$664$	1.12311			0.0435850
$665$		0			0
$666$	−2.06155	−	3.57071i	−0.0798835	−	0.138362i
$667$	−25.2116	+	43.6679i	−0.976199	+	1.69083i
$668$	20.3693			0.788113
$669$	13.1501	−	22.7766i	0.508412	−	0.880595i
$670$		0			0
$671$	−24.7386			−0.955024
$672$	1.78078	−	3.08440i	0.0686949	−	0.118983i
$673$	21.1231	+	36.5863i	0.814236	+	1.41030i	0.909875	+	0.414882i	$0.136177\pi$
$673$	21.1231	+	36.5863i	0.814236	+	1.41030i	−0.0956394	+	0.995416i	$0.530490\pi$
$674$	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	$0.312751\pi$
$678$	−1.84233	−	3.19101i	−0.0707542	−	0.122550i
$679$	−2.00000	−	3.46410i	−0.0767530	−	0.132940i
$680$		0			0
$681$	−20.0000			−0.766402
$682$	−11.7192	+	20.2983i	−0.448752	+	0.777262i
$683$	4.43845	−	7.68762i	0.169832	−	0.294158i	−0.768528	−	0.639816i	$-0.779011\pi$
$683$	4.43845	−	7.68762i	0.169832	−	0.294158i	0.938361	+	0.345657i	$0.112344\pi$
$684$	−3.56155			−0.136179
$685$		0			0
$686$	2.34233	+	4.05703i	0.0894305	+	0.154898i
$687$	−3.87689	−	6.71498i	−0.147913	−	0.256192i
$688$	−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	0.978940	−	0.204147i	$-0.0654419\pi$
$691$	8.21922	+	14.2361i	0.312674	+	0.541567i	−0.666266	+	0.745714i	$0.732109\pi$
$692$	−12.5885	−	21.8040i	−0.478545	−	0.828863i
$693$	−7.34233	+	12.7173i	−0.278912	+	0.483090i
$694$	9.12311			0.346308
$695$		0			0
$696$	−3.28078	+	5.68247i	−0.124358	+	0.215394i
$697$	21.7538			0.823984
$698$	−12.2462	+	21.2111i	−0.463526	+	0.802850i
$699$	8.84233	+	15.3154i	0.334448	+	0.579280i
$700$		0			0
$701$	17.3002			0.653419			0.326710	−	0.945125i	$-0.394060\pi$
$701$	17.3002			0.653419			0.326710	+	0.945125i	$0.394060\pi$
$702$	−2.84233	−	2.21837i	−0.107277	−	0.0837270i
$703$	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
$708$	5.28078	−	9.14657i	0.198464	−	0.343749i
$709$	−8.87689	+	15.3752i	−0.333379	+	0.577429i	−0.983172	−	0.182682i	$-0.941522\pi$
$709$	−8.87689	+	15.3752i	−0.333379	+	0.577429i	0.649793	+	0.760111i	$0.274855\pi$
$710$		0			0
$711$	−3.71922	+	6.44188i	−0.139482	+	0.241590i
$712$	0.903882	+	1.56557i	0.0338744	+	0.0586722i
$713$	−21.8423	−	37.8320i	−0.818002	−	1.41682i
$714$	18.2462			0.682847
$715$		0			0
$716$	−0.315342			−0.0117849
$717$	6.68466	+	11.5782i	0.249643	+	0.432395i
$718$	2.43845	+	4.22351i	0.0910020	+	0.157620i
$719$	10.4924	−	18.1734i	0.391301	−	0.677754i	−0.601320	−	0.799008i	$-0.705358\pi$
$719$	10.4924	−	18.1734i	0.391301	−	0.677754i	0.992621	+	0.121254i	$0.0386917\pi$
$720$		0			0
$721$	−0.780776	+	1.35234i	−0.0290776	+	0.0503639i
$722$	−3.15767	+	5.46925i	−0.117516	+	0.203544i
$723$	19.8769			0.739230
$724$	−5.56155	+	9.63289i	−0.206693	+	0.358004i
$725$		0			0
$726$	−3.00000	−	5.19615i	−0.111340	−	0.192847i
$727$	23.4233			0.868722			0.434361	−	0.900739i	$-0.356974\pi$
$727$	23.4233			0.868722			0.434361	+	0.900739i	$0.356974\pi$
$728$	−1.78078	+	12.7173i	−0.0660000	+	0.471334i
$729$	1.00000			0.0370370
$730$		0			0
$731$	−11.6847	−	20.2384i	−0.432173	−	0.748545i
$732$	3.00000	−	5.19615i	0.110883	−	0.192055i
$733$	−48.9309			−1.80730			−0.903651	−	0.428269i	$-0.859124\pi$
$733$	−48.9309			−1.80730			−0.903651	+	0.428269i	$0.859124\pi$
$734$	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
$738$	−2.12311	−	3.67733i	−0.0781526	−	0.135364i
$739$	−21.2732	−	36.8463i	−0.782547	−	1.35541i	−0.930453	−	0.366410i	$-0.880587\pi$
$739$	−21.2732	−	36.8463i	−0.782547	−	1.35541i	0.147906	−	0.989001i	$-0.452747\pi$
$740$		0			0
$741$	11.9039	−	4.81645i	0.437300	−	0.176937i
$742$	−15.8078			−0.580321
$743$	−16.0885	−	27.8662i	−0.590231	−	1.02231i	−0.994201	−	0.107538i	$-0.965703\pi$
$743$	−16.0885	−	27.8662i	−0.590231	−	1.02231i	0.403970	−	0.914772i	$-0.367630\pi$
$744$	−2.84233	−	4.92306i	−0.104205	−	0.180488i
$745$		0			0
$746$	−5.19224			−0.190101
$747$	0.561553	−	0.972638i	0.0205461	−	0.0355870i
$748$	−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	0.893677	−	0.448711i	$-0.148117\pi$
$751$	1.59612	+	2.76456i	0.0582432	+	0.100880i	−0.835434	+	0.549591i	$0.814783\pi$
$752$	3.50000	+	6.06218i	0.127632	+	0.221065i
$753$	−0.123106			−0.00448622
$754$	3.28078	−	23.4294i	0.119479	−	0.853250i
$755$		0			0
$756$	−1.78078	−	3.08440i	−0.0647662	−	0.112178i
$757$	16.7116	+	28.9454i	0.607395	+	1.05204i	0.991668	+	0.128820i	$0.0411188\pi$
$757$	16.7116	+	28.9454i	0.607395	+	1.05204i	−0.384273	+	0.923220i	$0.625548\pi$
$758$	−2.65767	+	4.60322i	−0.0965309	+	0.167197i
$759$	31.6847			1.15008
$760$		0			0
$761$	−5.46543	+	9.46641i	−0.198122	+	0.343157i	−0.947919	−	0.318510i	$-0.896818\pi$
$761$	−5.46543	+	9.46641i	−0.198122	+	0.343157i	0.749798	+	0.661667i	$0.230151\pi$
$762$	4.43845			0.160788
$763$	−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
$768$	−1.00000			−0.0360844
$769$	22.8423	+	39.5641i	0.823715	+	1.42672i	0.902897	+	0.429857i	$0.141436\pi$
$769$	22.8423	+	39.5641i	0.823715	+	1.42672i	−0.0791816	+	0.996860i	$0.525231\pi$
$770$		0			0
$771$	0.719224	−	1.24573i	0.0259022	−	0.0448639i
$772$		0			0
$773$	−10.5885	+	18.3399i	−0.380843	+	0.659640i	−0.991183	−	0.132500i	$-0.957700\pi$
$773$	−10.5885	+	18.3399i	−0.380843	+	0.659640i	0.610340	+	0.792140i	$0.291033\pi$
$774$	−2.28078	+	3.95042i	−0.0819808	+	0.141995i
$775$		0			0
$776$	−0.561553	+	0.972638i	−0.0201586	+	0.0349157i
$777$	7.34233	+	12.7173i	0.263405	+	0.456230i
$778$	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
$783$	3.28078	+	5.68247i	0.117245	+	0.203075i
$784$	−2.84233	+	4.92306i	−0.101512	+	0.175824i
$785$		0			0
$786$	−3.06155	+	5.30277i	−0.109202	+	0.189143i
$787$	21.8423	−	37.8320i	0.778595	−	1.34857i	−0.154157	−	0.988046i	$-0.549266\pi$
$787$	21.8423	−	37.8320i	0.778595	−	1.34857i	0.932752	−	0.360520i	$-0.117401\pi$
$788$	7.80776			0.278140
$789$	6.50000	−	11.2583i	0.231406	−	0.400807i
$790$		0			0
$791$	6.56155	+	11.3649i	0.233302	+	0.404091i
$792$	4.12311			0.146508
$793$	−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	−0.819602	−	0.572934i	$-0.805805\pi$
$797$	2.43845	−	4.22351i	0.0863742	−	0.149605i	0.905976	+	0.423329i	$0.139139\pi$
$798$	12.6847			0.449032
$799$	−17.9309	+	31.0572i	−0.634349	+	1.09872i
$800$		0			0
$801$	1.80776			0.0638742
$802$	6.34233	−	10.9852i	0.223955	−	0.387902i
$803$	31.6847	+	54.8794i	1.11813	+	1.93665i
$804$	−7.12311	−	12.3376i	−0.251213	−	0.435113i
$805$		0			0
$806$	16.1577	+	12.6107i	0.569130	+	0.444192i
$807$	3.36932			0.118606
$808$	−8.56155	−	14.8290i	−0.301194	−	0.521684i
$809$	−9.24621	−	16.0149i	−0.325079	−	0.563054i	0.656449	−	0.754370i	$-0.272058\pi$
$809$	−9.24621	−	16.0149i	−0.325079	−	0.563054i	−0.981528	+	0.191316i	$0.938724\pi$
$810$		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
$813$	16.0885	−	27.8662i	0.564250	−	0.977309i
$814$	−17.0000			−0.595850
$815$		0			0
$816$	−2.56155	−	4.43674i	−0.0896723	−	0.155317i
$817$	−8.12311	−	14.0696i	−0.284191	−	0.492234i
$818$	−1.80776			−0.0632070
$819$	10.1231	+	7.90084i	0.353730	+	0.276078i
$820$		0			0
$821$	6.28078	+	10.8786i	0.219201	+	0.379667i	0.954564	−	0.298007i	$-0.0963217\pi$
$821$	6.28078	+	10.8786i	0.219201	+	0.379667i	−0.735363	+	0.677673i	$0.762988\pi$
$822$	−4.40388	−	7.62775i	−0.153603	−	0.266048i
$823$	−16.0270	+	27.7596i	−0.558666	+	0.967637i	0.438943	+	0.898515i	$0.355353\pi$
$823$	−16.0270	+	27.7596i	−0.558666	+	0.967637i	−0.997608	+	0.0691222i	$0.977980\pi$
$824$	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	$0.434489\pi$
$828$	−3.84233	+	6.65511i	−0.133530	+	0.231281i
$829$	−26.8078	−	46.4324i	−0.931072	−	1.61266i	−0.781493	−	0.623915i	$-0.785541\pi$
$829$	−26.8078	−	46.4324i	−0.931072	−	1.61266i	−0.149580	−	0.988750i	$-0.547792\pi$
$830$		0			0
$831$	−1.00000			−0.0346896
$832$	3.34233	−	1.35234i	0.115874	−	0.0468841i
$833$	−29.1231			−1.00906
$834$	−4.21922	−	7.30791i	−0.146100	−	0.253052i
$835$		0			0
$836$	−7.34233	+	12.7173i	−0.253940	+	0.439837i
$837$	−5.68466			−0.196491
$838$	−0.246211	+	0.426450i	−0.00850523	+	0.0147315i
$839$	6.36932	−	11.0320i	0.219893	−	0.380866i	−0.734882	−	0.678195i	$-0.762762\pi$
$839$	6.36932	−	11.0320i	0.219893	−	0.380866i	0.954775	+	0.297329i	$0.0960958\pi$
$840$		0			0
$841$	−7.02699	+	12.1711i	−0.242310	+	0.419693i
$842$	0.246211	+	0.426450i	0.00848500	+	0.0146965i
$843$	−0.123106	−	0.213225i	−0.00423998	−	0.00734387i
$844$	6.93087			0.238570
$845$		0			0
$846$	7.00000			0.240665
$847$	10.6847	+	18.5064i	0.367129	+	0.635886i
$848$	2.21922	+	3.84381i	0.0762085	+	0.131997i
$849$	−5.71922	+	9.90599i	−0.196283	+	0.339973i
$850$		0			0
$851$	15.8423	−	27.4397i	0.543068	−	0.940621i
$852$	−2.43845	+	4.22351i	−0.0835398	+	0.144695i
$853$	51.3002			1.75648			0.878242	−	0.478216i	$-0.158716\pi$
$853$	51.3002			1.75648			0.878242	+	0.478216i	$0.158716\pi$
$854$	−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	$0.348613\pi$
$858$	−13.7808	+	5.57586i	−0.470468	+	0.190357i
$859$	−46.7926			−1.59654			−0.798272	−	0.602298i	$-0.794252\pi$
$859$	−46.7926			−1.59654			−0.798272	+	0.602298i	$0.794252\pi$
$860$		0			0
$861$	7.56155	+	13.0970i	0.257697	+	0.446344i
$862$	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	$0.535623\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$		0			0
$866$	30.7386			1.04454
$867$	4.62311	−	8.00745i	0.157009	−	0.271947i
$868$	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
$873$	0.561553	+	0.972638i	0.0190057	+	0.0329188i
$874$	−13.6847	−	23.7025i	−0.462890	−	0.801750i
$875$		0			0
$876$	−15.3693			−0.519281
$877$	6.28078	−	10.8786i	0.212087	−	0.367345i	−0.740281	−	0.672298i	$-0.765307\pi$
$877$	6.28078	−	10.8786i	0.212087	−	0.367345i	0.952367	+	0.304953i	$0.0986407\pi$
$878$	8.43845	−	14.6158i	0.284784	−	0.493260i
$879$	−24.9309			−0.840897
$880$		0			0
$881$	10.2192	+	17.7002i	0.344294	+	0.596335i	0.985225	−	0.171263i	$-0.0547848\pi$
$881$	10.2192	+	17.7002i	0.344294	+	0.596335i	−0.640931	+	0.767599i	$0.721452\pi$
$882$	2.84233	+	4.92306i	0.0957062	+	0.165768i
$883$	−26.1771			−0.880929			−0.440464	−	0.897770i	$-0.645186\pi$
$883$	−26.1771			−0.880929			−0.440464	+	0.897770i	$0.645186\pi$
$884$	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	0.971793	+	0.235834i	$0.0757822\pi$
$887$	20.5540	+	35.6005i	0.690135	+	1.19535i	−0.281658	+	0.959515i	$0.590884\pi$
$888$	2.06155	−	3.57071i	0.0691812	−	0.119825i
$889$	−15.8078			−0.530175
$890$		0			0
$891$	2.06155	−	3.57071i	0.0690646	−	0.119623i
$892$	26.3002			0.880595
$893$	−12.4654	+	21.5908i	−0.417140	+	0.722507i
$894$	11.4039	+	19.7521i	0.381403	+	0.660609i
$895$		0			0
$896$	3.56155			0.118983
$897$	3.84233	−	27.4397i	0.128292	−	0.916186i
$898$	−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
$903$	8.12311	−	14.0696i	0.270320	−	0.468208i
$904$	1.84233	−	3.19101i	0.0612750	−	0.106131i
$905$		0			0
$906$	−4.68466	+	8.11407i	−0.155637	+	0.269572i
$907$	20.4579	+	35.4340i	0.679292	+	1.17657i	0.975194	+	0.221350i	$0.0710463\pi$
$907$	20.4579	+	35.4340i	0.679292	+	1.17657i	−0.295902	+	0.955218i	$0.595620\pi$
$908$	−10.0000	−	17.3205i	−0.331862	−	0.574801i
$909$	−17.1231			−0.567938
$910$		0			0
$911$	−43.3693			−1.43689			−0.718445	−	0.695584i	$-0.755146\pi$
$911$	−43.3693			−1.43689			−0.718445	+	0.695584i	$0.755146\pi$
$912$	−1.78078	−	3.08440i	−0.0589674	−	0.102135i
$913$	−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
$918$	−5.12311			−0.169088
$919$	−20.6847	+	35.8269i	−0.682324	+	1.18182i	0.291946	+	0.956435i	$0.405697\pi$
$919$	−20.6847	+	35.8269i	−0.682324	+	1.18182i	−0.974270	+	0.225385i	$0.927636\pi$
$920$		0			0
$921$	7.80776	+	13.5234i	0.257275	+	0.445613i
$922$	−7.05398			−0.232310
$923$	2.43845	−	17.4140i	0.0802625	−	0.573189i
$924$	−14.6847			−0.483090
$925$		0			0
$926$	−16.8078	−	29.1119i	−0.552337	−	0.956676i
$927$	0.219224	−	0.379706i	0.00720025	−	0.0124712i
$928$	−6.56155			−0.215394
$929$	8.43845	−	14.6158i	0.276856	−	0.479529i	−0.693745	−	0.720220i	$-0.744041\pi$
$929$	8.43845	−	14.6158i	0.276856	−	0.479529i	0.970602	+	0.240691i	$0.0773740\pi$
$930$		0			0
$931$	−20.2462			−0.663543
$932$	−8.84233	+	15.3154i	−0.289640	+	0.501671i
$933$	−9.36932	−	16.2281i	−0.306738	−	0.531285i
$934$	−19.9309	−	34.5213i	−0.652158	−	1.12957i
$935$		0			0
$936$	0.500000	−	3.57071i	0.0163430	−	0.116712i
$937$	29.2311			0.954937			0.477468	−	0.878649i	$-0.341554\pi$
$937$	29.2311			0.954937			0.477468	+	0.878649i	$0.341554\pi$
$938$	25.3693	+	43.9409i	0.828338	+	1.43472i
$939$	−3.31534	−	5.74234i	−0.108192	−	0.187394i
$940$		0			0
$941$	−0.630683			−0.0205597			−0.0102798	−	0.999947i	$-0.503272\pi$
$941$	−0.630683			−0.0205597			−0.0102798	+	0.999947i	$0.503272\pi$
$942$	11.0616	−	19.1592i	0.360405	−	0.624240i
$943$	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	0.956386	−	0.292105i	$-0.0943556\pi$
$947$	6.93087	+	12.0046i	0.225223	+	0.390098i	−0.731163	+	0.682202i	$0.761022\pi$
$948$	−7.43845			−0.241590
$949$	51.3693	−	20.7846i	1.66752	−	0.674697i
$950$		0			0
$951$	2.09612	+	3.63058i	0.0679713	+	0.117730i
$952$	9.12311	+	15.8017i	0.295682	+	0.512135i
$953$	2.91146	−	5.04280i	0.0943114	−	0.163352i	−0.815010	−	0.579447i	$-0.803268\pi$
$953$	2.91146	−	5.04280i	0.0943114	−	0.163352i	0.909321	+	0.416095i	$0.136602\pi$
$954$	4.43845			0.143700
$955$		0			0
$956$	−6.68466	+	11.5782i	−0.216197	+	0.374465i
$957$	27.0540			0.874531
$958$	−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
$963$	−2.00000			−0.0644491
$964$	9.93845	+	17.2139i	0.320096	+	0.554422i
$965$		0			0
$966$	13.6847	−	23.7025i	0.440297	−	0.762616i
$967$	−3.31534			−0.106614			−0.0533071	−	0.998578i	$-0.516976\pi$
$967$	−3.31534			−0.106614			−0.0533071	+	0.998578i	$0.516976\pi$
$968$	3.00000	−	5.19615i	0.0964237	−	0.167011i
$969$	9.12311	−	15.8017i	0.293076	−	0.507623i
$970$		0			0
$971$	8.34233	−	14.4493i	0.267718	−	0.463701i	−0.700554	−	0.713599i	$-0.747064\pi$
$971$	8.34233	−	14.4493i	0.267718	−	0.463701i	0.968272	+	0.249898i	$0.0803971\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	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	0.905299	−	0.424775i	$-0.139647\pi$
$977$	2.65009	+	4.59010i	0.0847840	+	0.146850i	−0.820515	+	0.571625i	$0.806313\pi$
$978$	−9.28078	−	16.0748i	−0.296767	−	0.514015i
$979$	3.72680	−	6.45501i	0.119109	−	0.206303i
$980$		0			0
$981$	10.1231	−	17.5337i	0.323206	−	0.559809i
$982$	−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	$0.624344\pi$
$984$	2.12311	−	3.67733i	0.0676821	−	0.117229i
$985$		0			0
$986$	−16.8078	−	29.1119i	−0.535268	−	0.927112i
$987$	−24.9309			−0.793558
$988$	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	0.947658	−	0.319286i	$-0.103443\pi$
$991$	6.21165	+	10.7589i	0.197319	+	0.341767i	−0.750339	+	0.661053i	$0.770110\pi$
$992$	2.84233	−	4.92306i	0.0902440	−	0.156307i
$993$	18.7386			0.594653
$994$	8.68466	−	15.0423i	0.275461	−	0.477112i
$995$		0			0
$996$	1.12311			0.0355870
$997$	16.2732	−	28.1860i	0.515377	−	0.892660i	−0.484463	−	0.874812i	$-0.660985\pi$
$997$	16.2732	−	28.1860i	0.515377	−	0.892660i	0.999841	−	0.0178482i	$-0.00568157\pi$
$998$	2.00000	+	3.46410i	0.0633089	+	0.109654i
$999$	−2.06155	−	3.57071i	−0.0652246	−	0.112972i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1950.2.i.bi.601.2		4
5.2	odd	4		1950.2.z.n.1849.2		8
5.3	odd	4		1950.2.z.n.1849.3		8
5.4	even	2		390.2.i.g.211.1	yes	4
13.9	even	3	inner	1950.2.i.bi.451.2		4
15.14	odd	2		1170.2.i.o.991.1		4
65.9	even	6		390.2.i.g.61.1	✓	4
65.22	odd	12		1950.2.z.n.1699.3		8
65.24	odd	12		5070.2.b.r.1351.3		4
65.29	even	6		5070.2.a.bi.1.2		2
65.48	odd	12		1950.2.z.n.1699.2		8
65.49	even	6		5070.2.a.bb.1.1		2
65.54	odd	12		5070.2.b.r.1351.2		4
195.74	odd	6		1170.2.i.o.451.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.i.g.61.1	✓	4	65.9	even	6
390.2.i.g.211.1	yes	4	5.4	even	2
1170.2.i.o.451.1		4	195.74	odd	6
1170.2.i.o.991.1		4	15.14	odd	2
1950.2.i.bi.451.2		4	13.9	even	3	inner
1950.2.i.bi.601.2		4	1.1	even	1	trivial
1950.2.z.n.1699.2		8	65.48	odd	12
1950.2.z.n.1699.3		8	65.22	odd	12
1950.2.z.n.1849.2		8	5.2	odd	4
1950.2.z.n.1849.3		8	5.3	odd	4
5070.2.a.bb.1.1		2	65.49	even	6
5070.2.a.bi.1.2		2	65.29	even	6
5070.2.b.r.1351.2		4	65.54	odd	12
5070.2.b.r.1351.3		4	65.24	odd	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:	\( N \)	\(=\)	\( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1950.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{6} +(1.78078 - 3.08440i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{6} +(1.78078 - 3.08440i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(2.06155 + 3.57071i) q^{11} -1.00000 q^{12} +(3.34233 - 1.35234i) q^{13} +3.56155 q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.56155 - 4.43674i) q^{17} -1.00000 q^{18} +(1.78078 - 3.08440i) q^{19} +3.56155 q^{21} +(-2.06155 + 3.57071i) q^{22} +(-3.84233 - 6.65511i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(2.84233 + 2.21837i) q^{26} -1.00000 q^{27} +(1.78078 + 3.08440i) q^{28} +(-3.28078 - 5.68247i) q^{29} +5.68466 q^{31} +(0.500000 - 0.866025i) q^{32} +(-2.06155 + 3.57071i) q^{33} +5.12311 q^{34} +(-0.500000 - 0.866025i) q^{36} +(2.06155 + 3.57071i) q^{37} +3.56155 q^{38} +(2.84233 + 2.21837i) q^{39} +(2.12311 + 3.67733i) q^{41} +(1.78078 + 3.08440i) q^{42} +(2.28078 - 3.95042i) q^{43} -4.12311 q^{44} +(3.84233 - 6.65511i) q^{46} -7.00000 q^{47} +(0.500000 - 0.866025i) q^{48} +(-2.84233 - 4.92306i) q^{49} +5.12311 q^{51} +(-0.500000 + 3.57071i) q^{52} -4.43845 q^{53} +(-0.500000 - 0.866025i) q^{54} +(-1.78078 + 3.08440i) q^{56} +3.56155 q^{57} +(3.28078 - 5.68247i) q^{58} +(-5.28078 + 9.14657i) q^{59} +(-3.00000 + 5.19615i) q^{61} +(2.84233 + 4.92306i) q^{62} +(1.78078 + 3.08440i) q^{63} +1.00000 q^{64} -4.12311 q^{66} +(7.12311 + 12.3376i) q^{67} +(2.56155 + 4.43674i) q^{68} +(3.84233 - 6.65511i) q^{69} +(2.43845 - 4.22351i) q^{71} +(0.500000 - 0.866025i) q^{72} +15.3693 q^{73} +(-2.06155 + 3.57071i) q^{74} +(1.78078 + 3.08440i) q^{76} +14.6847 q^{77} +(-0.500000 + 3.57071i) q^{78} +7.43845 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-2.12311 + 3.67733i) q^{82} -1.12311 q^{83} +(-1.78078 + 3.08440i) q^{84} +4.56155 q^{86} +(3.28078 - 5.68247i) q^{87} +(-2.06155 - 3.57071i) q^{88} +(-0.903882 - 1.56557i) q^{89} +(1.78078 - 12.7173i) q^{91} +7.68466 q^{92} +(2.84233 + 4.92306i) q^{93} +(-3.50000 - 6.06218i) q^{94} +1.00000 q^{96} +(0.561553 - 0.972638i) q^{97} +(2.84233 - 4.92306i) q^{98} -4.12311 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{6} + 3 q^{7} - 4 q^{8} - 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^6 + 3 * q^7 - 4 * q^8 - 2 * q^9	\( 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{6} + 3 q^{7} - 4 q^{8} - 2 q^{9} - 4 q^{12} + q^{13} + 6 q^{14} - 2 q^{16} + 2 q^{17} - 4 q^{18} + 3 q^{19} + 6 q^{21} - 3 q^{23} - 2 q^{24} - q^{26} - 4 q^{27} + 3 q^{28} - 9 q^{29} - 2 q^{31} + 2 q^{32} + 4 q^{34} - 2 q^{36} + 6 q^{38} - q^{39} - 8 q^{41} + 3 q^{42} + 5 q^{43} + 3 q^{46} - 28 q^{47} + 2 q^{48} + q^{49} + 4 q^{51} - 2 q^{52} - 26 q^{53} - 2 q^{54} - 3 q^{56} + 6 q^{57} + 9 q^{58} - 17 q^{59} - 12 q^{61} - q^{62} + 3 q^{63} + 4 q^{64} + 12 q^{67} + 2 q^{68} + 3 q^{69} + 18 q^{71} + 2 q^{72} + 12 q^{73} + 3 q^{76} + 34 q^{77} - 2 q^{78} + 38 q^{79} - 2 q^{81} + 8 q^{82} + 12 q^{83} - 3 q^{84} + 10 q^{86} + 9 q^{87} + 17 q^{89} + 3 q^{91} + 6 q^{92} - q^{93} - 14 q^{94} + 4 q^{96} - 6 q^{97} - q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^6 + 3 * q^7 - 4 * q^8 - 2 * q^9 - 4 * q^12 + q^13 + 6 * q^14 - 2 * q^16 + 2 * q^17 - 4 * q^18 + 3 * q^19 + 6 * q^21 - 3 * q^23 - 2 * q^24 - q^26 - 4 * q^27 + 3 * q^28 - 9 * q^29 - 2 * q^31 + 2 * q^32 + 4 * q^34 - 2 * q^36 + 6 * q^38 - q^39 - 8 * q^41 + 3 * q^42 + 5 * q^43 + 3 * q^46 - 28 * q^47 + 2 * q^48 + q^49 + 4 * q^51 - 2 * q^52 - 26 * q^53 - 2 * q^54 - 3 * q^56 + 6 * q^57 + 9 * q^58 - 17 * q^59 - 12 * q^61 - q^62 + 3 * q^63 + 4 * q^64 + 12 * q^67 + 2 * q^68 + 3 * q^69 + 18 * q^71 + 2 * q^72 + 12 * q^73 + 3 * q^76 + 34 * q^77 - 2 * q^78 + 38 * q^79 - 2 * q^81 + 8 * q^82 + 12 * q^83 - 3 * q^84 + 10 * q^86 + 9 * q^87 + 17 * q^89 + 3 * q^91 + 6 * q^92 - q^93 - 14 * q^94 + 4 * q^96 - 6 * q^97 - q^98

Introduction

L-functions

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