LMFDB - Embedded newform 1950.2.z.n.1849.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1950,2,Mod(1699,1950)]

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, 3, 4]))

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

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

chi := DirichletCharacter("1950.1699");

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.z (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$15.5708283941$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.1731891456.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 9x^{6} + 65x^{4} - 144x^{2} + 256 $ x^8 - 9x^6 + 65x^4 - 144*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 390)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1849.2
Root			$2.21837 + 1.28078i$ of defining polynomial
Character	$\chi$	$=$	1950.1849
Dual form			1950.2.z.n.1699.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{6} +(3.08440 + 1.78078i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{6} +(3.08440 + 1.78078i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(2.06155 + 3.57071i) q^{11} -1.00000i q^{12} +(-1.35234 - 3.34233i) q^{13} -3.56155 q^{14} +(-0.500000 - 0.866025i) q^{16} +(4.43674 + 2.56155i) q^{17} +1.00000i q^{18} +(-1.78078 + 3.08440i) q^{19} +3.56155 q^{21} +(-3.57071 - 2.06155i) q^{22} +(-6.65511 + 3.84233i) q^{23} +(0.500000 + 0.866025i) q^{24} +(2.84233 + 2.21837i) q^{26} -1.00000i q^{27} +(3.08440 - 1.78078i) q^{28} +(3.28078 + 5.68247i) q^{29} +5.68466 q^{31} +(0.866025 + 0.500000i) q^{32} +(3.57071 + 2.06155i) q^{33} -5.12311 q^{34} +(-0.500000 - 0.866025i) q^{36} +(-3.57071 + 2.06155i) q^{37} -3.56155i q^{38} +(-2.84233 - 2.21837i) q^{39} +(2.12311 + 3.67733i) q^{41} +(-3.08440 + 1.78078i) q^{42} +(-3.95042 - 2.28078i) q^{43} +4.12311 q^{44} +(3.84233 - 6.65511i) q^{46} -7.00000i q^{47} +(-0.866025 - 0.500000i) q^{48} +(2.84233 + 4.92306i) q^{49} +5.12311 q^{51} +(-3.57071 - 0.500000i) q^{52} +4.43845i q^{53} +(0.500000 + 0.866025i) q^{54} +(-1.78078 + 3.08440i) q^{56} +3.56155i q^{57} +(-5.68247 - 3.28078i) q^{58} +(5.28078 - 9.14657i) q^{59} +(-3.00000 + 5.19615i) q^{61} +(-4.92306 + 2.84233i) q^{62} +(3.08440 - 1.78078i) q^{63} -1.00000 q^{64} -4.12311 q^{66} +(-12.3376 + 7.12311i) q^{67} +(4.43674 - 2.56155i) q^{68} +(-3.84233 + 6.65511i) q^{69} +(2.43845 - 4.22351i) q^{71} +(0.866025 + 0.500000i) q^{72} -15.3693i q^{73} +(2.06155 - 3.57071i) q^{74} +(1.78078 + 3.08440i) q^{76} +14.6847i q^{77} +(3.57071 + 0.500000i) q^{78} -7.43845 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-3.67733 - 2.12311i) q^{82} +1.12311i q^{83} +(1.78078 - 3.08440i) q^{84} +4.56155 q^{86} +(5.68247 + 3.28078i) q^{87} +(-3.57071 + 2.06155i) q^{88} +(0.903882 + 1.56557i) q^{89} +(1.78078 - 12.7173i) q^{91} +7.68466i q^{92} +(4.92306 - 2.84233i) q^{93} +(3.50000 + 6.06218i) q^{94} +1.00000 q^{96} +(0.972638 + 0.561553i) q^{97} +(-4.92306 - 2.84233i) q^{98} +4.12311 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4} - 4 q^{6} + 4 q^{9}+O(q^{10}) $ 8 * q + 4 * q^4 - 4 * q^6 + 4 * q^9	$ 8 q + 4 q^{4} - 4 q^{6} + 4 q^{9} - 12 q^{14} - 4 q^{16} - 6 q^{19} + 12 q^{21} + 4 q^{24} - 2 q^{26} + 18 q^{29} - 4 q^{31} - 8 q^{34} - 4 q^{36} + 2 q^{39} - 16 q^{41} + 6 q^{46} - 2 q^{49} + 8 q^{51} + 4 q^{54} - 6 q^{56} + 34 q^{59} - 24 q^{61} - 8 q^{64} - 6 q^{69} + 36 q^{71} + 6 q^{76} - 76 q^{79} - 4 q^{81} + 6 q^{84} + 20 q^{86} - 34 q^{89} + 6 q^{91} + 28 q^{94} + 8 q^{96}+O(q^{100}) $ 8 * q + 4 * q^4 - 4 * q^6 + 4 * q^9 - 12 * q^14 - 4 * q^16 - 6 * q^19 + 12 * q^21 + 4 * q^24 - 2 * q^26 + 18 * q^29 - 4 * q^31 - 8 * q^34 - 4 * q^36 + 2 * q^39 - 16 * q^41 + 6 * q^46 - 2 * q^49 + 8 * q^51 + 4 * q^54 - 6 * q^56 + 34 * q^59 - 24 * q^61 - 8 * q^64 - 6 * q^69 + 36 * q^71 + 6 * q^76 - 76 * q^79 - 4 * q^81 + 6 * q^84 + 20 * q^86 - 34 * q^89 + 6 * q^91 + 28 * q^94 + 8 * q^96

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	−0.500000	+	0.866025i	−0.204124	+	0.353553i
$7$	3.08440	+	1.78078i	1.16579	+	0.673070i	0.952685	−	0.303959i	$-0.0983085\pi$
$7$	3.08440	+	1.78078i	1.16579	+	0.673070i	0.213107	+	0.977029i	$0.431642\pi$
$8$			1.00000i			0.353553i
$9$	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	$0.619824\pi$
$12$		−	1.00000i		−	0.288675i
$13$	−1.35234	−	3.34233i	−0.375073	−	0.926995i
$13$	−1.35234	−	3.34233i	−0.375073	−	0.926995i
$14$	−3.56155			−0.951865
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	4.43674	+	2.56155i	1.07607	+	0.621268i	0.929833	−	0.367982i	$-0.119951\pi$
$17$	4.43674	+	2.56155i	1.07607	+	0.621268i	0.146235	+	0.989250i	$0.453285\pi$
$18$			1.00000i			0.235702i
$19$	−1.78078	+	3.08440i	−0.408538	+	0.707609i	−0.994726	−	0.102566i	$-0.967295\pi$
$19$	−1.78078	+	3.08440i	−0.408538	+	0.707609i	0.586188	+	0.810175i	$0.300628\pi$
$20$		0			0
$21$	3.56155			0.777195
$22$	−3.57071	−	2.06155i	−0.761279	−	0.439525i
$23$	−6.65511	+	3.84233i	−1.38769	+	0.801181i	−0.993054	−	0.117658i	$-0.962461\pi$
$23$	−6.65511	+	3.84233i	−1.38769	+	0.801181i	−0.394632	+	0.918839i	$0.629128\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$		0			0
$26$	2.84233	+	2.21837i	0.557427	+	0.435058i
$27$		−	1.00000i		−	0.192450i
$28$	3.08440	−	1.78078i	0.582896	−	0.336535i
$29$	3.28078	+	5.68247i	0.609225	+	1.05521i	0.991368	+	0.131105i	$0.0418527\pi$
$29$	3.28078	+	5.68247i	0.609225	+	1.05521i	−0.382144	+	0.924103i	$0.624814\pi$
$30$		0			0
$31$	5.68466			1.02099			0.510497	−	0.859879i	$-0.329461\pi$
$31$	5.68466			1.02099			0.510497	+	0.859879i	$0.329461\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	3.57071	+	2.06155i	0.621582	+	0.358870i
$34$	−5.12311			−0.878605
$35$		0			0
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	−3.57071	+	2.06155i	−0.587022	+	0.338917i	−0.763919	−	0.645312i	$-0.776727\pi$
$37$	−3.57071	+	2.06155i	−0.587022	+	0.338917i	0.176897	+	0.984229i	$0.443394\pi$
$38$		−	3.56155i		−	0.577760i
$39$	−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	$0.725754\pi$
$42$	−3.08440	+	1.78078i	−0.475933	+	0.274780i
$43$	−3.95042	−	2.28078i	−0.602433	−	0.347815i	0.167565	−	0.985861i	$-0.446410\pi$
$43$	−3.95042	−	2.28078i	−0.602433	−	0.347815i	−0.769998	+	0.638046i	$0.779743\pi$
$44$	4.12311			0.621582
$45$		0			0
$46$	3.84233	−	6.65511i	0.566521	−	0.981242i
$47$		−	7.00000i		−	1.02105i	−0.859861	−	0.510527i	$-0.829450\pi$
$47$		−	7.00000i		−	1.02105i	0.859861	−	0.510527i	$-0.170550\pi$
$48$	−0.866025	−	0.500000i	−0.125000	−	0.0721688i
$49$	2.84233	+	4.92306i	0.406047	+	0.703294i
$50$		0			0
$51$	5.12311			0.717378
$52$	−3.57071	−	0.500000i	−0.495169	−	0.0693375i
$53$			4.43845i			0.609668i	0.952406	+	0.304834i	$0.0986009\pi$
$53$			4.43845i			0.609668i	−0.952406	+	0.304834i	$0.901399\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$		0			0
$56$	−1.78078	+	3.08440i	−0.237966	+	0.412170i
$57$			3.56155i			0.471739i
$58$	−5.68247	−	3.28078i	−0.746145	−	0.430787i
$59$	5.28078	−	9.14657i	0.687499	−	1.19078i	−0.285146	−	0.958484i	$-0.592042\pi$
$59$	5.28078	−	9.14657i	0.687499	−	1.19078i	0.972645	−	0.232298i	$-0.0746246\pi$
$60$		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	$0.292159\pi$
$62$	−4.92306	+	2.84233i	−0.625229	+	0.360976i
$63$	3.08440	−	1.78078i	0.388597	−	0.224357i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−4.12311			−0.507519
$67$	−12.3376	+	7.12311i	−1.50728	+	0.870226i	−0.507311	+	0.861763i	$0.669361\pi$
$67$	−12.3376	+	7.12311i	−1.50728	+	0.870226i	−0.999964	+	0.00846293i	$0.997306\pi$
$68$	4.43674	−	2.56155i	0.538034	−	0.310634i
$69$	−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	$0.0732141\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$		−	15.3693i		−	1.79884i	−0.437083	−	0.899421i	$-0.643988\pi$
$73$		−	15.3693i		−	1.79884i	0.437083	−	0.899421i	$-0.356012\pi$
$74$	2.06155	−	3.57071i	0.239651	−	0.415087i
$75$		0			0
$76$	1.78078	+	3.08440i	0.204269	+	0.353804i
$77$			14.6847i			1.67347i
$78$	3.57071	+	0.500000i	0.404304	+	0.0566139i
$79$	−7.43845			−0.836891			−0.418445	−	0.908242i	$-0.637425\pi$
$79$	−7.43845			−0.836891			−0.418445	+	0.908242i	$0.637425\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−3.67733	−	2.12311i	−0.406093	−	0.234458i
$83$			1.12311i			0.123277i	0.998099	+	0.0616384i	$0.0196326\pi$
$83$			1.12311i			0.123277i	−0.998099	+	0.0616384i	$0.980367\pi$
$84$	1.78078	−	3.08440i	0.194299	−	0.336535i
$85$		0			0
$86$	4.56155			0.491885
$87$	5.68247	+	3.28078i	0.609225	+	0.351736i
$88$	−3.57071	+	2.06155i	−0.380639	+	0.219762i
$89$	0.903882	+	1.56557i	0.0958113	+	0.165950i	0.909947	−	0.414725i	$-0.136122\pi$
$89$	0.903882	+	1.56557i	0.0958113	+	0.165950i	−0.814136	+	0.580675i	$0.802789\pi$
$90$		0			0
$91$	1.78078	−	12.7173i	0.186676	−	1.33313i
$92$			7.68466i			0.801181i
$93$	4.92306	−	2.84233i	0.510497	−	0.294736i
$94$	3.50000	+	6.06218i	0.360997	+	0.625266i
$95$		0			0
$96$	1.00000			0.102062
$97$	0.972638	+	0.561553i	0.0987564	+	0.0570170i	0.548565	−	0.836108i	$-0.315174\pi$
$97$	0.972638	+	0.561553i	0.0987564	+	0.0570170i	−0.449808	+	0.893125i	$0.648508\pi$
$98$	−4.92306	−	2.84233i	−0.497304	−	0.287119i
$99$	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	$0.508780\pi$
$102$	−4.43674	+	2.56155i	−0.439303	+	0.253632i
$103$			0.438447i			0.0432015i	0.999767	+	0.0216007i	$0.00687626\pi$
$103$			0.438447i			0.0432015i	−0.999767	+	0.0216007i	$0.993124\pi$
$104$	3.34233	−	1.35234i	0.327742	−	0.132608i
$105$		0			0
$106$	−2.21922	−	3.84381i	−0.215550	−	0.373344i
$107$	−1.73205	+	1.00000i	−0.167444	+	0.0966736i	−0.581380	−	0.813632i	$-0.697487\pi$
$107$	−1.73205	+	1.00000i	−0.167444	+	0.0966736i	0.413936	+	0.910306i	$0.364154\pi$
$108$	−0.866025	−	0.500000i	−0.0833333	−	0.0481125i
$109$	20.2462			1.93924			0.969618	−	0.244625i	$-0.0786650\pi$
$109$	20.2462			1.93924			0.969618	+	0.244625i	$0.0786650\pi$
$110$		0			0
$111$	−2.06155	+	3.57071i	−0.195674	+	0.338917i
$112$		−	3.56155i		−	0.336535i
$113$	3.19101	+	1.84233i	0.300185	+	0.173312i	0.642526	−	0.766264i	$-0.277887\pi$
$113$	3.19101	+	1.84233i	0.300185	+	0.173312i	−0.342341	+	0.939576i	$0.611220\pi$
$114$	−1.78078	−	3.08440i	−0.166785	−	0.288880i
$115$		0			0
$116$	6.56155			0.609225
$117$	−3.57071	−	0.500000i	−0.330113	−	0.0462250i
$118$			10.5616i			0.972270i
$119$	9.12311	+	15.8017i	0.836314	+	1.44854i
$120$		0			0
$121$	−3.00000	+	5.19615i	−0.272727	+	0.472377i
$122$		−	6.00000i		−	0.543214i
$123$	3.67733	+	2.12311i	0.331573	+	0.191434i
$124$	2.84233	−	4.92306i	0.255249	−	0.442104i
$125$		0			0
$126$	−1.78078	+	3.08440i	−0.158644	+	0.274780i
$127$	3.84381	−	2.21922i	0.341083	−	0.196924i	−0.319668	−	0.947530i	$-0.603571\pi$
$127$	3.84381	−	2.21922i	0.341083	−	0.196924i	0.660751	+	0.750605i	$0.270238\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−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	$0.413806\pi$
$132$	3.57071	−	2.06155i	0.310791	−	0.179435i
$133$	−10.9852	+	6.34233i	−0.952541	+	0.549950i
$134$	7.12311	−	12.3376i	0.615343	−	1.06580i
$135$		0			0
$136$	−2.56155	+	4.43674i	−0.219651	+	0.380447i
$137$	−7.62775	−	4.40388i	−0.651682	−	0.376249i	0.137418	−	0.990513i	$-0.456120\pi$
$137$	−7.62775	−	4.40388i	−0.651682	−	0.376249i	−0.789101	+	0.614264i	$0.789453\pi$
$138$		−	7.68466i		−	0.654162i
$139$	4.21922	−	7.30791i	0.357870	−	0.619849i	−0.629735	−	0.776810i	$-0.716836\pi$
$139$	4.21922	−	7.30791i	0.357870	−	0.619849i	0.987605	+	0.156961i	$0.0501698\pi$
$140$		0			0
$141$	−3.50000	−	6.06218i	−0.294753	−	0.510527i
$142$			4.87689i			0.409260i
$143$	9.14657	−	11.7192i	0.764875	−	0.980011i
$144$	−1.00000			−0.0833333
$145$		0			0
$146$	7.68466	+	13.3102i	0.635987	+	1.10156i
$147$	4.92306	+	2.84233i	0.406047	+	0.234431i
$148$			4.12311i			0.338917i
$149$	−11.4039	+	19.7521i	−0.934242	+	1.61816i	−0.158263	+	0.987397i	$0.550589\pi$
$149$	−11.4039	+	19.7521i	−0.934242	+	1.61816i	−0.775979	+	0.630758i	$0.782744\pi$
$150$		0			0
$151$	9.36932			0.762464			0.381232	−	0.924479i	$-0.375500\pi$
$151$	9.36932			0.762464			0.381232	+	0.924479i	$0.375500\pi$
$152$	−3.08440	−	1.78078i	−0.250177	−	0.144440i
$153$	4.43674	−	2.56155i	0.358689	−	0.207089i
$154$	−7.34233	−	12.7173i	−0.591662	−	1.02479i
$155$		0			0
$156$	−3.34233	+	1.35234i	−0.267601	+	0.108274i
$157$		−	22.1231i		−	1.76562i	−0.469734	−	0.882808i	$-0.655650\pi$
$157$		−	22.1231i		−	1.76562i	0.469734	−	0.882808i	$-0.344350\pi$
$158$	6.44188	−	3.71922i	0.512489	−	0.295886i
$159$	2.21922	+	3.84381i	0.175996	+	0.304834i
$160$		0			0
$161$	−27.3693			−2.15700
$162$	0.866025	+	0.500000i	0.0680414	+	0.0392837i
$163$	16.0748	+	9.28078i	1.25907	+	0.726927i	0.972894	−	0.231250i	$-0.0742814\pi$
$163$	16.0748	+	9.28078i	1.25907	+	0.726927i	0.286179	+	0.958176i	$0.407615\pi$
$164$	4.24621			0.331573
$165$		0			0
$166$	−0.561553	−	0.972638i	−0.0435850	−	0.0754913i
$167$	17.6403	−	10.1847i	1.36505	−	0.788113i	0.374760	−	0.927122i	$-0.377725\pi$
$167$	17.6403	−	10.1847i	1.36505	−	0.788113i	0.990291	+	0.139009i	$0.0443918\pi$
$168$			3.56155i			0.274780i
$169$	−9.34233	+	9.03996i	−0.718641	+	0.695382i
$170$		0			0
$171$	1.78078	+	3.08440i	0.136179	+	0.235870i
$172$	−3.95042	+	2.28078i	−0.301217	+	0.173908i
$173$	21.8040	+	12.5885i	1.65773	+	0.957089i	0.973760	+	0.227575i	$0.0730798\pi$
$173$	21.8040	+	12.5885i	1.65773	+	0.957089i	0.683966	+	0.729514i	$0.260254\pi$
$174$	−6.56155			−0.497430
$175$		0			0
$176$	2.06155	−	3.57071i	0.155395	−	0.269153i
$177$		−	10.5616i		−	0.793855i
$178$	−1.56557	−	0.903882i	−0.117344	−	0.0677488i
$179$	−0.157671	−	0.273094i	−0.0117849	−	0.0204120i	0.860073	−	0.510171i	$-0.170418\pi$
$179$	−0.157671	−	0.273094i	−0.0117849	−	0.0204120i	−0.871858	+	0.489759i	$0.837085\pi$
$180$		0			0
$181$	11.1231			0.826774			0.413387	−	0.910555i	$-0.364346\pi$
$181$	11.1231			0.826774			0.413387	+	0.910555i	$0.364346\pi$
$182$	4.81645	+	11.9039i	0.357019	+	0.882374i
$183$			6.00000i			0.443533i
$184$	−3.84233	−	6.65511i	−0.283260	−	0.490621i
$185$		0			0
$186$	−2.84233	+	4.92306i	−0.208410	+	0.360976i
$187$			21.1231i			1.54467i
$188$	−6.06218	−	3.50000i	−0.442130	−	0.255264i
$189$	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	$0.923463\pi$
$192$	−0.866025	+	0.500000i	−0.0625000	+	0.0360844i
$193$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$193$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$194$	−1.12311			−0.0806343
$195$		0			0
$196$	5.68466			0.406047
$197$	6.76172	−	3.90388i	0.481753	−	0.278140i	−0.239394	−	0.970923i	$-0.576949\pi$
$197$	6.76172	−	3.90388i	0.481753	−	0.278140i	0.721147	+	0.692782i	$0.243615\pi$
$198$	−3.57071	+	2.06155i	−0.253760	+	0.146508i
$199$	5.56155	−	9.63289i	0.394248	−	0.682858i	−0.598757	−	0.800931i	$-0.704338\pi$
$199$	5.56155	−	9.63289i	0.394248	−	0.682858i	0.993005	+	0.118073i	$0.0376718\pi$
$200$		0			0
$201$	−7.12311	+	12.3376i	−0.502425	+	0.870226i
$202$	−14.8290	−	8.56155i	−1.04337	−	0.602389i
$203$			23.3693i			1.64020i
$204$	2.56155	−	4.43674i	0.179345	−	0.310634i
$205$		0			0
$206$	−0.219224	−	0.379706i	−0.0152740	−	0.0264554i
$207$			7.68466i			0.534121i
$208$	−2.21837	+	2.84233i	−0.153816	+	0.197080i
$209$	−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	$0.910012\pi$
$212$	3.84381	+	2.21922i	0.263994	+	0.152417i
$213$		−	4.87689i		−	0.334159i
$214$	1.00000	−	1.73205i	0.0683586	−	0.118401i
$215$		0			0
$216$	1.00000			0.0680414
$217$	17.5337	+	10.1231i	1.19027	+	0.687201i
$218$	−17.5337	+	10.1231i	−1.18753	+	0.685623i
$219$	−7.68466	−	13.3102i	−0.519281	−	0.899421i
$220$		0			0
$221$	2.56155	−	18.2931i	0.172309	−	1.23053i
$222$		−	4.12311i		−	0.276725i
$223$	−22.7766	+	13.1501i	−1.52524	+	0.880595i	−0.525683	+	0.850680i	$0.676190\pi$
$223$	−22.7766	+	13.1501i	−1.52524	+	0.880595i	−0.999552	+	0.0299151i	$0.990476\pi$
$224$	1.78078	+	3.08440i	0.118983	+	0.206085i
$225$		0			0
$226$	−3.68466			−0.245100
$227$	−17.3205	−	10.0000i	−1.14960	−	0.663723i	−0.200812	−	0.979630i	$-0.564358\pi$
$227$	−17.3205	−	10.0000i	−1.14960	−	0.663723i	−0.948790	+	0.315906i	$0.897691\pi$
$228$	3.08440	+	1.78078i	0.204269	+	0.117935i
$229$	7.75379			0.512385			0.256192	−	0.966626i	$-0.417532\pi$
$229$	7.75379			0.512385			0.256192	+	0.966626i	$0.417532\pi$
$230$		0			0
$231$	7.34233	+	12.7173i	0.483090	+	0.836736i
$232$	−5.68247	+	3.28078i	−0.373073	+	0.215394i
$233$		−	17.6847i		−	1.15856i	−0.815128	−	0.579280i	$-0.803334\pi$
$233$		−	17.6847i		−	1.15856i	0.815128	−	0.579280i	$-0.196666\pi$
$234$	3.34233	−	1.35234i	0.218495	−	0.0884055i
$235$		0			0
$236$	−5.28078	−	9.14657i	−0.343749	−	0.595391i
$237$	−6.44188	+	3.71922i	−0.418445	+	0.241590i
$238$	−15.8017	−	9.12311i	−1.02427	−	0.591363i
$239$	−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	−0.345198	−	0.938530i	$-0.612188\pi$
$241$	9.93845	−	17.2139i	0.640192	−	1.10884i	0.985390	−	0.170315i	$-0.0544784\pi$
$242$		−	6.00000i		−	0.385695i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	3.00000	+	5.19615i	0.192055	+	0.332650i
$245$		0			0
$246$	−4.24621			−0.270729
$247$	12.7173	+	1.78078i	0.809182	+	0.113308i
$248$			5.68466i			0.360976i
$249$	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	$0.167903\pi$
$252$		−	3.56155i		−	0.224357i
$253$	−27.4397	−	15.8423i	−1.72512	−	0.995999i
$254$	−2.21922	+	3.84381i	−0.139246	+	0.241182i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	1.24573	−	0.719224i	0.0777066	−	0.0448639i	−0.460643	−	0.887585i	$-0.652381\pi$
$257$	1.24573	−	0.719224i	0.0777066	−	0.0448639i	0.538350	+	0.842721i	$0.319048\pi$
$258$	3.95042	−	2.28078i	0.245942	−	0.141995i
$259$	−14.6847			−0.912460
$260$		0			0
$261$	6.56155			0.406150
$262$	−5.30277	+	3.06155i	−0.327606	+	0.189143i
$263$	−11.2583	+	6.50000i	−0.694218	+	0.400807i	−0.805190	−	0.593016i	$-0.797937\pi$
$263$	−11.2583	+	6.50000i	−0.694218	+	0.400807i	0.110972	+	0.993824i	$0.464604\pi$
$264$	−2.06155	+	3.57071i	−0.126880	+	0.219762i
$265$		0			0
$266$	6.34233	−	10.9852i	0.388873	−	0.673548i
$267$	1.56557	+	0.903882i	0.0958113	+	0.0553167i
$268$			14.2462i			0.870226i
$269$	−1.68466	+	2.91791i	−0.102715	+	0.177908i	−0.912803	−	0.408401i	$-0.866086\pi$
$269$	−1.68466	+	2.91791i	−0.102715	+	0.177908i	0.810087	+	0.586310i	$0.199420\pi$
$270$		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	$-0.598728\pi$
$272$		−	5.12311i		−	0.310634i
$273$	−4.81645	−	11.9039i	−0.291505	−	0.720456i
$274$	8.80776			0.532096
$275$		0			0
$276$	3.84233	+	6.65511i	0.231281	+	0.400591i
$277$	−0.866025	−	0.500000i	−0.0520344	−	0.0300421i	0.473757	−	0.880656i	$-0.342897\pi$
$277$	−0.866025	−	0.500000i	−0.0520344	−	0.0300421i	−0.525792	+	0.850613i	$0.676231\pi$
$278$			8.43845i			0.506104i
$279$	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	$0.502338\pi$
$282$	6.06218	+	3.50000i	0.360997	+	0.208422i
$283$	9.90599	−	5.71922i	0.588850	−	0.339973i	−0.175793	−	0.984427i	$-0.556249\pi$
$283$	9.90599	−	5.71922i	0.588850	−	0.339973i	0.764643	+	0.644455i	$0.222916\pi$
$284$	−2.43845	−	4.22351i	−0.144695	−	0.250619i
$285$		0			0
$286$	−2.06155	+	14.7224i	−0.121902	+	0.870556i
$287$			15.1231i			0.892689i
$288$	0.866025	−	0.500000i	0.0510310	−	0.0294628i
$289$	4.62311	+	8.00745i	0.271947	+	0.471027i
$290$		0			0
$291$	1.12311			0.0658376
$292$	−13.3102	−	7.68466i	−0.778922	−	0.449711i
$293$	21.5908	+	12.4654i	1.26135	+	0.728238i	0.973335	−	0.229389i	$-0.0736727\pi$
$293$	21.5908	+	12.4654i	1.26135	+	0.728238i	0.288011	+	0.957627i	$0.407006\pi$
$294$	−5.68466			−0.331536
$295$		0			0
$296$	−2.06155	−	3.57071i	−0.119825	−	0.207544i
$297$	3.57071	−	2.06155i	0.207194	−	0.119623i
$298$		−	22.8078i		−	1.32122i
$299$	21.8423	+	17.0474i	1.26317	+	0.985877i
$300$		0			0
$301$	−8.12311	−	14.0696i	−0.468208	−	0.810960i
$302$	−8.11407	+	4.68466i	−0.466912	+	0.269572i
$303$	14.8290	+	8.56155i	0.851906	+	0.491848i
$304$	3.56155			0.204269
$305$		0			0
$306$	−2.56155	+	4.43674i	−0.146434	+	0.253632i
$307$			15.6155i			0.891225i	0.895226	+	0.445613i	$0.147014\pi$
$307$			15.6155i			0.891225i	−0.895226	+	0.445613i	$0.852986\pi$
$308$	12.7173	+	7.34233i	0.724635	+	0.418368i
$309$	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	$0.678291\pi$
$312$	2.21837	−	2.84233i	0.125590	−	0.160915i
$313$			6.63068i			0.374788i	0.982285	+	0.187394i	$0.0600042\pi$
$313$			6.63068i			0.374788i	−0.982285	+	0.187394i	$0.939996\pi$
$314$	11.0616	+	19.1592i	0.624240	+	1.08121i
$315$		0			0
$316$	−3.71922	+	6.44188i	−0.209223	+	0.362384i
$317$			4.19224i			0.235459i	0.993046	+	0.117730i	$0.0375616\pi$
$317$			4.19224i			0.235459i	−0.993046	+	0.117730i	$0.962438\pi$
$318$	−3.84381	−	2.21922i	−0.215550	−	0.124448i
$319$	−13.5270	+	23.4294i	−0.757366	+	1.31180i
$320$		0			0
$321$	−1.00000	+	1.73205i	−0.0558146	+	0.0966736i
$322$	23.7025	−	13.6847i	1.32089	−	0.762616i
$323$	−15.8017	+	9.12311i	−0.879229	+	0.507623i
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	−18.5616			−1.02803
$327$	17.5337	−	10.1231i	0.969618	−	0.559809i
$328$	−3.67733	+	2.12311i	−0.203046	+	0.117229i
$329$	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	$-0.00553556\pi$
$332$	0.972638	+	0.561553i	0.0533804	+	0.0308192i
$333$			4.12311i			0.225945i
$334$	−10.1847	+	17.6403i	−0.557280	+	0.965237i
$335$		0			0
$336$	−1.78078	−	3.08440i	−0.0971493	−	0.168268i
$337$			6.00000i			0.326841i	0.986557	+	0.163420i	$0.0522527\pi$
$337$			6.00000i			0.326841i	−0.986557	+	0.163420i	$0.947747\pi$
$338$	3.57071	−	12.5000i	0.194221	−	0.679910i
$339$	3.68466			0.200123
$340$		0			0
$341$	11.7192	+	20.2983i	0.634632	+	1.09921i
$342$	−3.08440	−	1.78078i	−0.166785	−	0.0962934i
$343$		−	4.68466i		−	0.252948i
$344$	2.28078	−	3.95042i	0.122971	−	0.212992i
$345$		0			0
$346$	−25.1771			−1.35353
$347$	7.90084	+	4.56155i	0.424139	+	0.244877i	0.696847	−	0.717220i	$-0.254586\pi$
$347$	7.90084	+	4.56155i	0.424139	+	0.244877i	−0.272707	+	0.962097i	$0.587919\pi$
$348$	5.68247	−	3.28078i	0.304612	−	0.175868i
$349$	−12.2462	−	21.2111i	−0.655525	−	1.13540i	−0.981762	−	0.190114i	$-0.939114\pi$
$349$	−12.2462	−	21.2111i	−0.655525	−	1.13540i	0.326237	−	0.945288i	$-0.394219\pi$
$350$		0			0
$351$	−3.34233	+	1.35234i	−0.178400	+	0.0721828i
$352$			4.12311i			0.219762i
$353$	27.5931	−	15.9309i	1.46863	−	0.847915i	0.469249	−	0.883066i	$-0.344525\pi$
$353$	27.5931	−	15.9309i	1.46863	−	0.847915i	0.999382	+	0.0351511i	$0.0111913\pi$
$354$	5.28078	+	9.14657i	0.280670	+	0.486135i
$355$		0			0
$356$	1.80776			0.0958113
$357$	15.8017	+	9.12311i	0.836314	+	0.482846i
$358$	0.273094	+	0.157671i	0.0144335	+	0.00833316i
$359$	−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
$362$	−9.63289	+	5.56155i	−0.506294	+	0.292309i
$363$			6.00000i			0.314918i
$364$	−10.1231	−	7.90084i	−0.530595	−	0.414117i
$365$		0			0
$366$	−3.00000	−	5.19615i	−0.156813	−	0.271607i
$367$	17.7470	−	10.2462i	0.926384	−	0.534848i	0.0407177	−	0.999171i	$-0.487036\pi$
$367$	17.7470	−	10.2462i	0.926384	−	0.534848i	0.885666	+	0.464323i	$0.153702\pi$
$368$	6.65511	+	3.84233i	0.346922	+	0.200295i
$369$	4.24621			0.221049
$370$		0			0
$371$	−7.90388	+	13.6899i	−0.410349	+	0.710746i
$372$		−	5.68466i		−	0.294736i
$373$	4.49661	+	2.59612i	0.232826	+	0.134422i	0.611875	−	0.790955i	$-0.290416\pi$
$373$	4.49661	+	2.59612i	0.232826	+	0.134422i	−0.379049	+	0.925376i	$0.623749\pi$
$374$	−10.5616	−	18.2931i	−0.546125	−	0.945916i
$375$		0			0
$376$	7.00000			0.360997
$377$	14.5560	−	18.6501i	0.749670	−	0.960529i
$378$			3.56155i			0.183187i
$379$	−2.65767	−	4.60322i	−0.136515	−	0.236452i	0.789660	−	0.613545i	$-0.210257\pi$
$379$	−2.65767	−	4.60322i	−0.136515	−	0.236452i	−0.926175	+	0.377093i	$0.876924\pi$
$380$		0			0
$381$	2.21922	−	3.84381i	0.113694	−	0.196924i
$382$		−	19.1231i		−	0.978423i
$383$	−18.0201	−	10.4039i	−0.920782	−	0.531614i	−0.0368973	−	0.999319i	$-0.511747\pi$
$383$	−18.0201	−	10.4039i	−0.920782	−	0.531614i	−0.883884	+	0.467706i	$0.845081\pi$
$384$	0.500000	−	0.866025i	0.0255155	−	0.0441942i
$385$		0			0
$386$		0			0
$387$	−3.95042	+	2.28078i	−0.200811	+	0.115938i
$388$	0.972638	−	0.561553i	0.0493782	−	0.0285085i
$389$	−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
$392$	−4.92306	+	2.84233i	−0.248652	+	0.143559i
$393$	5.30277	−	3.06155i	0.267489	−	0.154435i
$394$	−3.90388	+	6.76172i	−0.196675	+	0.340651i
$395$		0			0
$396$	2.06155	−	3.57071i	0.103597	−	0.179435i
$397$	−10.2857	−	5.93845i	−0.516224	−	0.298042i	0.219164	−	0.975688i	$-0.429667\pi$
$397$	−10.2857	−	5.93845i	−0.516224	−	0.298042i	−0.735388	+	0.677646i	$0.763000\pi$
$398$			11.1231i			0.557551i
$399$	−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	$0.935915\pi$
$402$		−	14.2462i		−	0.710536i
$403$	−7.68762	−	19.0000i	−0.382947	−	0.946457i
$404$	17.1231			0.851906
$405$		0			0
$406$	−11.6847	−	20.2384i	−0.579900	−	1.00442i
$407$	−14.7224	−	8.50000i	−0.729764	−	0.421329i
$408$			5.12311i			0.253632i
$409$	0.903882	−	1.56557i	0.0446941	−	0.0774124i	−0.842813	−	0.538207i	$-0.819102\pi$
$409$	0.903882	−	1.56557i	0.0446941	−	0.0774124i	0.887507	+	0.460794i	$0.152435\pi$
$410$		0			0
$411$	−8.80776			−0.434455
$412$	0.379706	+	0.219224i	0.0187068	+	0.0108004i
$413$	32.5760	−	18.8078i	1.60296	−	0.925470i
$414$	−3.84233	−	6.65511i	−0.188840	−	0.327081i
$415$		0			0
$416$	0.500000	−	3.57071i	0.0245145	−	0.175069i
$417$		−	8.43845i		−	0.413233i
$418$	12.7173	−	7.34233i	0.622023	−	0.359125i
$419$	−0.246211	−	0.426450i	−0.0120282	−	0.0208335i	0.859949	−	0.510381i	$-0.170495\pi$
$419$	−0.246211	−	0.426450i	−0.0120282	−	0.0208335i	−0.871977	+	0.489547i	$0.837162\pi$
$420$		0			0
$421$	0.492423			0.0239992			0.0119996	−	0.999928i	$-0.496180\pi$
$421$	0.492423			0.0239992			0.0119996	+	0.999928i	$0.496180\pi$
$422$	6.00231	+	3.46543i	0.292188	+	0.168695i
$423$	−6.06218	−	3.50000i	−0.294753	−	0.170176i
$424$	−4.43845			−0.215550
$425$		0			0
$426$	2.43845	+	4.22351i	0.118143	+	0.204630i
$427$	−18.5064	+	10.6847i	−0.895586	+	0.517067i
$428$			2.00000i			0.0966736i
$429$	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	$-0.389384\pi$
$432$	−0.866025	+	0.500000i	−0.0416667	+	0.0240563i
$433$	−26.6204	−	15.3693i	−1.27930	−	0.738602i	−0.302578	−	0.953125i	$-0.597847\pi$
$433$	−26.6204	−	15.3693i	−1.27930	−	0.738602i	−0.976719	+	0.214523i	$0.931180\pi$
$434$	−20.2462			−0.971849
$435$		0			0
$436$	10.1231	−	17.5337i	0.484809	−	0.839714i
$437$		−	27.3693i		−	1.30925i
$438$	13.3102	+	7.68466i	0.635987	+	0.367187i
$439$	8.43845	+	14.6158i	0.402745	+	0.697575i	0.994056	−	0.108869i	$-0.0347228\pi$
$439$	8.43845	+	14.6158i	0.402745	+	0.697575i	−0.591311	+	0.806444i	$0.701389\pi$
$440$		0			0
$441$	5.68466			0.270698
$442$	6.92820	+	17.1231i	0.329541	+	0.814463i
$443$		−	4.87689i		−	0.231708i	−0.993266	−	0.115854i	$-0.963039\pi$
$443$		−	4.87689i		−	0.231708i	0.993266	−	0.115854i	$-0.0369605\pi$
$444$	2.06155	+	3.57071i	0.0978370	+	0.169459i
$445$		0			0
$446$	13.1501	−	22.7766i	0.622675	−	1.07850i
$447$			22.8078i			1.07877i
$448$	−3.08440	−	1.78078i	−0.145724	−	0.0841338i
$449$	12.5885	−	21.8040i	0.594090	−	1.02899i	−0.399585	−	0.916696i	$-0.630846\pi$
$449$	12.5885	−	21.8040i	0.594090	−	1.02899i	0.993675	−	0.112298i	$-0.0358210\pi$
$450$		0			0
$451$	−8.75379	+	15.1620i	−0.412200	+	0.713951i
$452$	3.19101	−	1.84233i	0.150092	−	0.0866559i
$453$	8.11407	−	4.68466i	0.381232	−	0.220104i
$454$	20.0000			0.938647
$455$		0			0
$456$	−3.56155			−0.166785
$457$	−3.25088	+	1.87689i	−0.152070	+	0.0877974i	−0.574104	−	0.818782i	$-0.694649\pi$
$457$	−3.25088	+	1.87689i	−0.152070	+	0.0877974i	0.422034	+	0.906580i	$0.361316\pi$
$458$	−6.71498	+	3.87689i	−0.313770	+	0.181155i
$459$	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	$0.219193\pi$
$462$	−12.7173	−	7.34233i	−0.591662	−	0.341596i
$463$			33.6155i			1.56225i	0.624377	+	0.781123i	$0.285353\pi$
$463$			33.6155i			1.56225i	−0.624377	+	0.781123i	$0.714647\pi$
$464$	3.28078	−	5.68247i	0.152306	−	0.263802i
$465$		0			0
$466$	8.84233	+	15.3154i	0.409613	+	0.709471i
$467$		−	39.8617i		−	1.84458i	−0.386497	−	0.922291i	$-0.626315\pi$
$467$		−	39.8617i		−	1.84458i	0.386497	−	0.922291i	$-0.373685\pi$
$468$	−2.21837	+	2.84233i	−0.102544	+	0.131387i
$469$	−50.7386			−2.34289
$470$		0			0
$471$	−11.0616	−	19.1592i	−0.509689	−	0.882808i
$472$	9.14657	+	5.28078i	0.421005	+	0.243067i
$473$		−	18.8078i		−	0.864782i
$474$	3.71922	−	6.44188i	0.170830	−	0.295886i
$475$		0			0
$476$	18.2462			0.836314
$477$	3.84381	+	2.21922i	0.175996	+	0.101611i
$478$	11.5782	−	6.68466i	0.529573	−	0.305749i
$479$	−10.8769	−	18.8393i	−0.496978	−	0.860791i	0.503016	−	0.864277i	$-0.332224\pi$
$479$	−10.8769	−	18.8393i	−0.496978	−	0.860791i	−0.999994	+	0.00348601i	$0.998890\pi$
$480$		0			0
$481$	11.7192	+	9.14657i	0.534351	+	0.417048i
$482$			19.8769i			0.905368i
$483$	−23.7025	+	13.6847i	−1.07850	+	0.622674i
$484$	3.00000	+	5.19615i	0.136364	+	0.236189i
$485$		0			0
$486$	1.00000			0.0453609
$487$	−20.8314	−	12.0270i	−0.943959	−	0.544995i	−0.0527597	−	0.998607i	$-0.516802\pi$
$487$	−20.8314	−	12.0270i	−0.943959	−	0.544995i	−0.891199	+	0.453612i	$0.850135\pi$
$488$	−5.19615	−	3.00000i	−0.235219	−	0.135804i
$489$	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	$0.671596\pi$
$492$	3.67733	−	2.12311i	0.165787	−	0.0957170i
$493$			33.6155i			1.51397i
$494$	−11.9039	+	4.81645i	−0.535581	+	0.216702i
$495$		0			0
$496$	−2.84233	−	4.92306i	−0.127624	−	0.221052i
$497$	15.0423	−	8.68466i	0.674738	−	0.389560i
$498$	−0.972638	−	0.561553i	−0.0435850	−	0.0251638i
$499$	−4.00000			−0.179065			−0.0895323	−	0.995984i	$-0.528537\pi$
$499$	−4.00000			−0.179065			−0.0895323	+	0.995984i	$0.528537\pi$
$500$		0			0
$501$	10.1847	−	17.6403i	0.455017	−	0.788113i
$502$		−	0.123106i		−	0.00549447i
$503$	5.14941	+	2.97301i	0.229601	+	0.132560i	0.610388	−	0.792103i	$-0.291014\pi$
$503$	5.14941	+	2.97301i	0.229601	+	0.132560i	−0.380787	+	0.924663i	$0.624347\pi$
$504$	1.78078	+	3.08440i	0.0793221	+	0.137390i
$505$		0			0
$506$	31.6847			1.40855
$507$	−3.57071	+	12.5000i	−0.158581	+	0.555144i
$508$		−	4.43845i		−	0.196924i
$509$	−14.7732	−	25.5879i	−0.654811	−	1.13417i	−0.981941	−	0.189186i	$-0.939415\pi$
$509$	−14.7732	−	25.5879i	−0.654811	−	1.13417i	0.327131	−	0.944979i	$-0.393918\pi$
$510$		0			0
$511$	27.3693	−	47.4050i	1.21075	−	2.09708i
$512$		−	1.00000i		−	0.0441942i
$513$	3.08440	+	1.78078i	0.136179	+	0.0786232i
$514$	−0.719224	+	1.24573i	−0.0317236	+	0.0549469i
$515$		0			0
$516$	−2.28078	+	3.95042i	−0.100406	+	0.173908i
$517$	24.9950	−	14.4309i	1.09928	−	0.634669i
$518$	12.7173	−	7.34233i	0.558766	−	0.322603i
$519$	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	$0.634225\pi$
$522$	−5.68247	+	3.28078i	−0.248715	+	0.143596i
$523$	−7.96071	+	4.59612i	−0.348098	+	0.200974i	−0.663847	−	0.747868i	$-0.731077\pi$
$523$	−7.96071	+	4.59612i	−0.348098	+	0.200974i	0.315749	+	0.948843i	$0.397744\pi$
$524$	3.06155	−	5.30277i	0.133745	−	0.231652i
$525$		0			0
$526$	6.50000	−	11.2583i	0.283413	−	0.490887i
$527$	25.2213	+	14.5616i	1.09866	+	0.634311i
$528$		−	4.12311i		−	0.179435i
$529$	18.0270	−	31.2237i	0.783782	−	1.35755i
$530$		0			0
$531$	−5.28078	−	9.14657i	−0.229166	−	0.396927i
$532$			12.6847i			0.549950i
$533$	9.41967	−	12.0691i	0.408011	−	0.522772i
$534$	−1.80776			−0.0782296
$535$		0			0
$536$	−7.12311	−	12.3376i	−0.307671	−	0.532902i
$537$	−0.273094	−	0.157671i	−0.0117849	−	0.00680400i
$538$		−	3.36932i		−	0.145262i
$539$	−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	$0.518010\pi$
$542$	27.8662	+	16.0885i	1.19695	+	0.691062i
$543$	9.63289	−	5.56155i	0.413387	−	0.238669i
$544$	2.56155	+	4.43674i	0.109826	+	0.190224i
$545$		0			0
$546$	10.1231	+	7.90084i	0.433229	+	0.338125i
$547$		−	35.6155i		−	1.52281i	−0.648276	−	0.761405i	$-0.724510\pi$
$547$		−	35.6155i		−	1.52281i	0.648276	−	0.761405i	$-0.275490\pi$
$548$	−7.62775	+	4.40388i	−0.325841	+	0.188125i
$549$	3.00000	+	5.19615i	0.128037	+	0.221766i
$550$		0			0
$551$	−23.3693			−0.995566
$552$	−6.65511	−	3.84233i	−0.283260	−	0.163540i
$553$	−22.9431	−	13.2462i	−0.975640	−	0.563286i
$554$	1.00000			0.0424859
$555$		0			0
$556$	−4.21922	−	7.30791i	−0.178935	−	0.309924i
$557$	3.84381	−	2.21922i	0.162867	−	0.0940315i	−0.416351	−	0.909204i	$-0.636691\pi$
$557$	3.84381	−	2.21922i	0.162867	−	0.0940315i	0.579218	+	0.815172i	$0.303358\pi$
$558$			5.68466i			0.240651i
$559$	−2.28078	+	16.2880i	−0.0964666	+	0.688909i
$560$		0			0
$561$	10.5616	+	18.2931i	0.445909	+	0.772337i
$562$	0.213225	−	0.123106i	0.00899436	−	0.00519290i
$563$	−28.5657	−	16.4924i	−1.20390	−	0.695073i	−0.242481	−	0.970156i	$-0.577961\pi$
$563$	−28.5657	−	16.4924i	−1.20390	−	0.695073i	−0.961420	+	0.275083i	$0.911295\pi$
$564$	−7.00000			−0.294753
$565$		0			0
$566$	−5.71922	+	9.90599i	−0.240397	+	0.416380i
$567$		−	3.56155i		−	0.149571i
$568$	4.22351	+	2.43845i	0.177215	+	0.102315i
$569$	−9.58854	−	16.6078i	−0.401973	−	0.696237i	0.591991	−	0.805944i	$-0.298342\pi$
$569$	−9.58854	−	16.6078i	−0.401973	−	0.696237i	−0.993964	+	0.109707i	$0.965009\pi$
$570$		0			0
$571$	11.3153			0.473532			0.236766	−	0.971567i	$-0.423912\pi$
$571$	11.3153			0.473532			0.236766	+	0.971567i	$0.423912\pi$
$572$	−5.57586	−	13.7808i	−0.233138	−	0.576203i
$573$			19.1231i			0.798879i
$574$	−7.56155	−	13.0970i	−0.315613	−	0.546658i
$575$		0			0
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$		−	8.73863i		−	0.363794i	−0.983318	−	0.181897i	$-0.941776\pi$
$577$		−	8.73863i		−	0.363794i	0.983318	−	0.181897i	$-0.0582238\pi$
$578$	−8.00745	−	4.62311i	−0.333066	−	0.192296i
$579$		0			0
$580$		0			0
$581$	−2.00000	+	3.46410i	−0.0829740	+	0.143715i
$582$	−0.972638	+	0.561553i	−0.0403171	+	0.0232771i
$583$	−15.8484	+	9.15009i	−0.656375	+	0.378958i
$584$	15.3693			0.635987
$585$		0			0
$586$	−24.9309			−1.02988
$587$	20.5714	−	11.8769i	0.849072	−	0.490212i	−0.0112657	−	0.999937i	$-0.503586\pi$
$587$	20.5714	−	11.8769i	0.849072	−	0.490212i	0.860338	+	0.509725i	$0.170253\pi$
$588$	4.92306	−	2.84233i	0.203024	−	0.117216i
$589$	−10.1231	+	17.5337i	−0.417115	+	0.722465i
$590$		0			0
$591$	3.90388	−	6.76172i	0.160584	−	0.278140i
$592$	3.57071	+	2.06155i	0.146755	+	0.0847293i
$593$		−	12.1771i		−	0.500053i	−0.968239	−	0.250026i	$-0.919561\pi$
$593$		−	12.1771i		−	0.500053i	0.968239	−	0.250026i	$-0.0804393\pi$
$594$	−2.06155	+	3.57071i	−0.0845865	+	0.146508i
$595$		0			0
$596$	11.4039	+	19.7521i	0.467121	+	0.809078i
$597$		−	11.1231i		−	0.455238i
$598$	−27.4397	−	3.84233i	−1.12209	−	0.157125i
$599$	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	0.955193	+	0.295984i	$0.0956476\pi$
$601$	17.9924	+	31.1638i	0.733926	+	1.27120i	−0.221267	+	0.975213i	$0.571019\pi$
$602$	14.0696	+	8.12311i	0.573435	+	0.331073i
$603$			14.2462i			0.580151i
$604$	4.68466	−	8.11407i	0.190616	−	0.330157i
$605$		0			0
$606$	−17.1231			−0.695579
$607$	−25.4813	−	14.7116i	−1.03425	−	0.597127i	−0.116054	−	0.993243i	$-0.537025\pi$
$607$	−25.4813	−	14.7116i	−1.03425	−	0.597127i	−0.918201	+	0.396116i	$0.870358\pi$
$608$	−3.08440	+	1.78078i	−0.125089	+	0.0722200i
$609$	11.6847	+	20.2384i	0.473486	+	0.820102i
$610$		0			0
$611$	−23.3963	+	9.46641i	−0.946513	+	0.382970i
$612$		−	5.12311i		−	0.207089i
$613$	24.3553	−	14.0616i	0.983702	−	0.567941i	0.0803164	−	0.996769i	$-0.474407\pi$
$613$	24.3553	−	14.0616i	0.983702	−	0.567941i	0.903386	+	0.428829i	$0.141074\pi$
$614$	−7.80776	−	13.5234i	−0.315096	−	0.545762i
$615$		0			0
$616$	−14.6847			−0.591662
$617$	−36.1000	−	20.8423i	−1.45333	−	0.839081i	−0.454662	−	0.890664i	$-0.650240\pi$
$617$	−36.1000	−	20.8423i	−1.45333	−	0.839081i	−0.998669	+	0.0515837i	$0.983573\pi$
$618$	−0.379706	−	0.219224i	−0.0152740	−	0.00881847i
$619$	16.4384			0.660717			0.330358	−	0.943856i	$-0.392830\pi$
$619$	16.4384			0.660717			0.330358	+	0.943856i	$0.392830\pi$
$620$		0			0
$621$	3.84233	+	6.65511i	0.154187	+	0.267060i
$622$	16.2281	−	9.36932i	0.650689	−	0.375675i
$623$			6.43845i			0.257951i
$624$	−0.500000	+	3.57071i	−0.0200160	+	0.142943i
$625$		0			0
$626$	−3.31534	−	5.74234i	−0.132508	−	0.229510i
$627$	−12.7173	+	7.34233i	−0.507880	+	0.293224i
$628$	−19.1592	−	11.0616i	−0.764534	−	0.441404i
$629$	−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	$-0.0389791\pi$
$632$		−	7.43845i		−	0.295886i
$633$	−6.00231	−	3.46543i	−0.238570	−	0.137739i
$634$	−2.09612	−	3.63058i	−0.0832475	−	0.144189i
$635$		0			0
$636$	4.43845			0.175996
$637$	12.6107	−	16.1577i	0.499653	−	0.640190i
$638$		−	27.0540i		−	1.07108i
$639$	−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	$0.0672337\pi$
$642$		−	2.00000i		−	0.0789337i
$643$	−33.1222	−	19.1231i	−1.30621	−	0.754142i	−0.324750	−	0.945800i	$-0.605280\pi$
$643$	−33.1222	−	19.1231i	−1.30621	−	0.754142i	−0.981462	+	0.191658i	$0.938613\pi$
$644$	−13.6847	+	23.7025i	−0.539251	+	0.934010i
$645$		0			0
$646$	9.12311	−	15.8017i	0.358944	−	0.621709i
$647$	1.77879	−	1.02699i	0.0699316	−	0.0403751i	−0.464626	−	0.885507i	$-0.653811\pi$
$647$	1.77879	−	1.02699i	0.0699316	−	0.0403751i	0.534558	+	0.845132i	$0.320478\pi$
$648$	0.866025	−	0.500000i	0.0340207	−	0.0196419i
$649$	43.5464			1.70935
$650$		0			0
$651$	20.2462			0.793512
$652$	16.0748	−	9.28078i	0.629537	−	0.363463i
$653$	−35.0207	+	20.2192i	−1.37047	+	0.791239i	−0.990987	−	0.133961i	$-0.957230\pi$
$653$	−35.0207	+	20.2192i	−1.37047	+	0.791239i	−0.379480	+	0.925200i	$0.623897\pi$
$654$	−10.1231	+	17.5337i	−0.395845	+	0.685623i
$655$		0			0
$656$	2.12311	−	3.67733i	0.0828933	−	0.143575i
$657$	−13.3102	−	7.68466i	−0.519281	−	0.299807i
$658$			24.9309i			0.971906i
$659$	15.5270	−	26.8935i	0.604846	−	1.04762i	−0.387230	−	0.921983i	$-0.626568\pi$
$659$	15.5270	−	26.8935i	0.604846	−	1.04762i	0.992076	−	0.125640i	$-0.0400985\pi$
$660$		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	$0.760802\pi$
$662$			18.7386i			0.728298i
$663$	−6.92820	−	17.1231i	−0.269069	−	0.665006i
$664$	−1.12311			−0.0435850
$665$		0			0
$666$	−2.06155	−	3.57071i	−0.0798835	−	0.138362i
$667$	−43.6679	−	25.2116i	−1.69083	−	0.976199i
$668$		−	20.3693i		−	0.788113i
$669$	−13.1501	+	22.7766i	−0.508412	+	0.880595i
$670$		0			0
$671$	−24.7386			−0.955024
$672$	3.08440	+	1.78078i	0.118983	+	0.0686949i
$673$	36.5863	−	21.1231i	1.41030	−	0.814236i	0.414882	−	0.909875i	$-0.363823\pi$
$673$	36.5863	−	21.1231i	1.41030	−	0.814236i	0.995416	+	0.0956394i	$0.0304896\pi$
$674$	−3.00000	−	5.19615i	−0.115556	−	0.200148i
$675$		0			0
$676$	3.15767	+	12.6107i	0.121449	+	0.485026i
$677$			28.8769i			1.10983i	0.831907	+	0.554915i	$0.187249\pi$
$677$			28.8769i			1.10983i	−0.831907	+	0.554915i	$0.812751\pi$
$678$	−3.19101	+	1.84233i	−0.122550	+	0.0707542i
$679$	2.00000	+	3.46410i	0.0767530	+	0.132940i
$680$		0			0
$681$	−20.0000			−0.766402
$682$	−20.2983	−	11.7192i	−0.777262	−	0.448752i
$683$	−7.68762	−	4.43845i	−0.294158	−	0.169832i	0.345657	−	0.938361i	$-0.387656\pi$
$683$	−7.68762	−	4.43845i	−0.294158	−	0.169832i	−0.639816	+	0.768528i	$0.720989\pi$
$684$	3.56155			0.136179
$685$		0			0
$686$	2.34233	+	4.05703i	0.0894305	+	0.154898i
$687$	6.71498	−	3.87689i	0.256192	−	0.147913i
$688$			4.56155i			0.173908i
$689$	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	$0.732109\pi$
$692$	21.8040	−	12.5885i	0.828863	−	0.478545i
$693$	12.7173	+	7.34233i	0.483090	+	0.278912i
$694$	−9.12311			−0.346308
$695$		0			0
$696$	−3.28078	+	5.68247i	−0.124358	+	0.215394i
$697$			21.7538i			0.823984i
$698$	21.2111	+	12.2462i	0.802850	+	0.463526i
$699$	−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	$0.394060\pi$
$702$	2.21837	−	2.84233i	0.0837270	−	0.107277i
$703$		−	14.6847i		−	0.553842i
$704$	−2.06155	−	3.57071i	−0.0776977	−	0.134576i
$705$		0			0
$706$	−15.9309	+	27.5931i	−0.599566	+	1.03848i
$707$			60.9848i			2.29357i
$708$	−9.14657	−	5.28078i	−0.343749	−	0.198464i
$709$	8.87689	−	15.3752i	0.333379	−	0.577429i	−0.649793	−	0.760111i	$-0.725145\pi$
$709$	8.87689	−	15.3752i	0.333379	−	0.577429i	0.983172	+	0.182682i	$0.0584779\pi$
$710$		0			0
$711$	−3.71922	+	6.44188i	−0.139482	+	0.241590i
$712$	−1.56557	+	0.903882i	−0.0586722	+	0.0338744i
$713$	−37.8320	+	21.8423i	−1.41682	+	0.818002i
$714$	−18.2462			−0.682847
$715$		0			0
$716$	−0.315342			−0.0117849
$717$	−11.5782	+	6.68466i	−0.432395	+	0.249643i
$718$	4.22351	−	2.43845i	0.157620	−	0.0910020i
$719$	−10.4924	+	18.1734i	−0.391301	+	0.677754i	−0.992621	−	0.121254i	$-0.961308\pi$
$719$	−10.4924	+	18.1734i	−0.391301	+	0.677754i	0.601320	+	0.799008i	$0.294642\pi$
$720$		0			0
$721$	−0.780776	+	1.35234i	−0.0290776	+	0.0503639i
$722$	−5.46925	−	3.15767i	−0.203544	−	0.117516i
$723$		−	19.8769i		−	0.739230i
$724$	5.56155	−	9.63289i	0.206693	−	0.358004i
$725$		0			0
$726$	−3.00000	−	5.19615i	−0.111340	−	0.192847i
$727$			23.4233i			0.868722i	0.900739	+	0.434361i	$0.143026\pi$
$727$			23.4233i			0.868722i	−0.900739	+	0.434361i	$0.856974\pi$
$728$	12.7173	+	1.78078i	0.471334	+	0.0660000i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	−11.6847	−	20.2384i	−0.432173	−	0.748545i
$732$	5.19615	+	3.00000i	0.192055	+	0.110883i
$733$			48.9309i			1.80730i	0.428269	+	0.903651i	$0.359124\pi$
$733$			48.9309i			1.80730i	−0.428269	+	0.903651i	$0.640876\pi$
$734$	−10.2462	+	17.7470i	−0.378195	+	0.655052i
$735$		0			0
$736$	−7.68466			−0.283260
$737$	−50.8691	−	29.3693i	−1.87379	−	1.08183i
$738$	−3.67733	+	2.12311i	−0.135364	+	0.0781526i
$739$	21.2732	+	36.8463i	0.782547	+	1.35541i	0.930453	+	0.366410i	$0.119413\pi$
$739$	21.2732	+	36.8463i	0.782547	+	1.35541i	−0.147906	+	0.989001i	$0.547253\pi$
$740$		0			0
$741$	11.9039	−	4.81645i	0.437300	−	0.176937i
$742$		−	15.8078i		−	0.580321i
$743$	−27.8662	+	16.0885i	−1.02231	+	0.590231i	−0.914772	−	0.403970i	$-0.867630\pi$
$743$	−27.8662	+	16.0885i	−1.02231	+	0.590231i	−0.107538	+	0.994201i	$0.534297\pi$
$744$	2.84233	+	4.92306i	0.104205	+	0.180488i
$745$		0			0
$746$	−5.19224			−0.190101
$747$	0.972638	+	0.561553i	0.0355870	+	0.0205461i
$748$	18.2931	+	10.5616i	0.668864	+	0.386169i
$749$	−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	$0.814783\pi$
$752$	−6.06218	+	3.50000i	−0.221065	+	0.127632i
$753$			0.123106i			0.00448622i
$754$	−3.28078	+	23.4294i	−0.119479	+	0.853250i
$755$		0			0
$756$	−1.78078	−	3.08440i	−0.0647662	−	0.112178i
$757$	−28.9454	+	16.7116i	−1.05204	+	0.607395i	−0.923220	−	0.384273i	$-0.874452\pi$
$757$	−28.9454	+	16.7116i	−1.05204	+	0.607395i	−0.128820	+	0.991668i	$0.541119\pi$
$758$	4.60322	+	2.65767i	0.167197	+	0.0965309i
$759$	−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	$0.230151\pi$
$762$			4.43845i			0.160788i
$763$	62.4473	+	36.0540i	2.26074	+	1.30524i
$764$	9.56155	+	16.5611i	0.345925	+	0.599159i
$765$		0			0
$766$	20.8078			0.751815
$767$	−37.7123	−	5.28078i	−1.36171	−	0.190678i
$768$			1.00000i			0.0360844i
$769$	−22.8423	−	39.5641i	−0.823715	−	1.42672i	−0.902897	−	0.429857i	$-0.858564\pi$
$769$	−22.8423	−	39.5641i	−0.823715	−	1.42672i	0.0791816	−	0.996860i	$-0.474769\pi$
$770$		0			0
$771$	0.719224	−	1.24573i	0.0259022	−	0.0448639i
$772$		0			0
$773$	18.3399	+	10.5885i	0.659640	+	0.380843i	0.792140	−	0.610340i	$-0.208967\pi$
$773$	18.3399	+	10.5885i	0.659640	+	0.380843i	−0.132500	+	0.991183i	$0.542300\pi$
$774$	2.28078	−	3.95042i	0.0819808	−	0.141995i
$775$		0			0
$776$	−0.561553	+	0.972638i	−0.0201586	+	0.0349157i
$777$	−12.7173	+	7.34233i	−0.456230	+	0.263405i
$778$	16.5012	−	9.52699i	0.591598	−	0.341559i
$779$	−15.1231			−0.541841
$780$		0			0
$781$	20.1080			0.719519
$782$	34.0948	−	19.6847i	1.21923	−	0.703922i
$783$	5.68247	−	3.28078i	0.203075	−	0.117245i
$784$	2.84233	−	4.92306i	0.101512	−	0.175824i
$785$		0			0
$786$	−3.06155	+	5.30277i	−0.109202	+	0.189143i
$787$	37.8320	+	21.8423i	1.34857	+	0.778595i	0.988046	−	0.154157i	$-0.0492661\pi$
$787$	37.8320	+	21.8423i	1.34857	+	0.778595i	0.360520	+	0.932752i	$0.382599\pi$
$788$		−	7.80776i		−	0.278140i
$789$	−6.50000	+	11.2583i	−0.231406	+	0.400807i
$790$		0			0
$791$	6.56155	+	11.3649i	0.233302	+	0.404091i
$792$			4.12311i			0.146508i
$793$	21.4243	+	3.00000i	0.760799	+	0.106533i
$794$	11.8769			0.421495
$795$		0			0
$796$	−5.56155	−	9.63289i	−0.197124	−	0.341429i
$797$	4.22351	+	2.43845i	0.149605	+	0.0863742i	0.572934	−	0.819602i	$-0.305805\pi$
$797$	4.22351	+	2.43845i	0.149605	+	0.0863742i	−0.423329	+	0.905976i	$0.639139\pi$
$798$		−	12.6847i		−	0.449032i
$799$	17.9309	−	31.0572i	0.634349	−	1.09872i
$800$		0			0
$801$	1.80776			0.0638742
$802$	10.9852	+	6.34233i	0.387902	+	0.223955i
$803$	54.8794	−	31.6847i	1.93665	−	1.11813i
$804$	7.12311	+	12.3376i	0.251213	+	0.435113i
$805$		0			0
$806$	16.1577	+	12.6107i	0.569130	+	0.444192i
$807$			3.36932i			0.118606i
$808$	−14.8290	+	8.56155i	−0.521684	+	0.301194i
$809$	9.24621	+	16.0149i	0.325079	+	0.563054i	0.981528	−	0.191316i	$-0.0612756\pi$
$809$	9.24621	+	16.0149i	0.325079	+	0.563054i	−0.656449	+	0.754370i	$0.727942\pi$
$810$		0			0
$811$	−22.5464			−0.791711			−0.395856	−	0.918313i	$-0.629552\pi$
$811$	−22.5464			−0.791711			−0.395856	+	0.918313i	$0.629552\pi$
$812$	20.2384	+	11.6847i	0.710229	+	0.410051i
$813$	−27.8662	−	16.0885i	−0.977309	−	0.564250i
$814$	17.0000			0.595850
$815$		0			0
$816$	−2.56155	−	4.43674i	−0.0896723	−	0.155317i
$817$	14.0696	−	8.12311i	0.492234	−	0.284191i
$818$			1.80776i			0.0632070i
$819$	−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	$0.762988\pi$
$822$	7.62775	−	4.40388i	0.266048	−	0.153603i
$823$	27.7596	+	16.0270i	0.967637	+	0.558666i	0.898515	−	0.438943i	$-0.144647\pi$
$823$	27.7596	+	16.0270i	0.967637	+	0.558666i	0.0691222	+	0.997608i	$0.477980\pi$
$824$	−0.438447			−0.0152740
$825$		0			0
$826$	−18.8078	+	32.5760i	−0.654406	+	1.13346i
$827$			11.7538i			0.408719i	0.978896	+	0.204360i	$0.0655112\pi$
$827$			11.7538i			0.408719i	−0.978896	+	0.204360i	$0.934489\pi$
$828$	6.65511	+	3.84233i	0.231281	+	0.133530i
$829$	26.8078	+	46.4324i	0.931072	+	1.61266i	0.781493	+	0.623915i	$0.214459\pi$
$829$	26.8078	+	46.4324i	0.931072	+	1.61266i	0.149580	+	0.988750i	$0.452208\pi$
$830$		0			0
$831$	−1.00000			−0.0346896
$832$	1.35234	+	3.34233i	0.0468841	+	0.115874i
$833$			29.1231i			1.00906i
$834$	4.21922	+	7.30791i	0.146100	+	0.253052i
$835$		0			0
$836$	−7.34233	+	12.7173i	−0.253940	+	0.439837i
$837$		−	5.68466i		−	0.196491i
$838$	0.426450	+	0.246211i	0.0147315	+	0.00850523i
$839$	−6.36932	+	11.0320i	−0.219893	+	0.380866i	−0.954775	−	0.297329i	$-0.903904\pi$
$839$	−6.36932	+	11.0320i	−0.219893	+	0.380866i	0.734882	+	0.678195i	$0.237238\pi$
$840$		0			0
$841$	−7.02699	+	12.1711i	−0.242310	+	0.419693i
$842$	−0.426450	+	0.246211i	−0.0146965	+	0.00848500i
$843$	−0.213225	+	0.123106i	−0.00734387	+	0.00423998i
$844$	−6.93087			−0.238570
$845$		0			0
$846$	7.00000			0.240665
$847$	−18.5064	+	10.6847i	−0.635886	+	0.367129i
$848$	3.84381	−	2.21922i	0.131997	−	0.0762085i
$849$	5.71922	−	9.90599i	0.196283	−	0.339973i
$850$		0			0
$851$	15.8423	−	27.4397i	0.543068	−	0.940621i
$852$	−4.22351	−	2.43845i	−0.144695	−	0.0835398i
$853$		−	51.3002i		−	1.75648i	−0.478216	−	0.878242i	$-0.658716\pi$
$853$		−	51.3002i		−	1.75648i	0.478216	−	0.878242i	$-0.341284\pi$
$854$	10.6847	−	18.5064i	0.365621	−	0.633275i
$855$		0			0
$856$	−1.00000	−	1.73205i	−0.0341793	−	0.0592003i
$857$			26.8078i			0.915736i	0.889020	+	0.457868i	$0.151387\pi$
$857$			26.8078i			0.915736i	−0.889020	+	0.457868i	$0.848613\pi$
$858$	5.57586	+	13.7808i	0.190357	+	0.470468i
$859$	46.7926			1.59654			0.798272	−	0.602298i	$-0.205748\pi$
$859$	46.7926			1.59654			0.798272	+	0.602298i	$0.205748\pi$
$860$		0			0
$861$	7.56155	+	13.0970i	0.257697	+	0.446344i
$862$	23.1563	+	13.3693i	0.788708	+	0.455361i
$863$			6.56155i			0.223358i	0.993744	+	0.111679i	$0.0356228\pi$
$863$			6.56155i			0.223358i	−0.993744	+	0.111679i	$0.964377\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$		0			0
$866$	30.7386			1.04454
$867$	8.00745	+	4.62311i	0.271947	+	0.157009i
$868$	17.5337	−	10.1231i	0.595134	−	0.343601i
$869$	−15.3348	−	26.5606i	−0.520196	−	0.901006i
$870$		0			0
$871$	40.4924	+	31.6034i	1.37203	+	1.07084i
$872$			20.2462i			0.685623i
$873$	0.972638	−	0.561553i	0.0329188	−	0.0190057i
$874$	13.6847	+	23.7025i	0.462890	+	0.801750i
$875$		0			0
$876$	−15.3693			−0.519281
$877$	10.8786	+	6.28078i	0.367345	+	0.212087i	0.672298	−	0.740281i	$-0.265307\pi$
$877$	10.8786	+	6.28078i	0.367345	+	0.212087i	−0.304953	+	0.952367i	$0.598641\pi$
$878$	−14.6158	−	8.43845i	−0.493260	−	0.284784i
$879$	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	$0.721452\pi$
$882$	−4.92306	+	2.84233i	−0.165768	+	0.0957062i
$883$			26.1771i			0.880929i	0.897770	+	0.440464i	$0.145186\pi$
$883$			26.1771i			0.880929i	−0.897770	+	0.440464i	$0.854814\pi$
$884$	−14.5616	−	11.3649i	−0.489758	−	0.382244i
$885$		0			0
$886$	2.43845	+	4.22351i	0.0819212	+	0.141892i
$887$	−35.6005	+	20.5540i	−1.19535	+	0.690135i	−0.959515	−	0.281658i	$-0.909116\pi$
$887$	−35.6005	+	20.5540i	−1.19535	+	0.690135i	−0.235834	+	0.971793i	$0.575782\pi$
$888$	−3.57071	−	2.06155i	−0.119825	−	0.0691812i
$889$	15.8078			0.530175
$890$		0			0
$891$	2.06155	−	3.57071i	0.0690646	−	0.119623i
$892$			26.3002i			0.880595i
$893$	21.5908	+	12.4654i	0.722507	+	0.417140i
$894$	−11.4039	−	19.7521i	−0.381403	−	0.660609i
$895$		0			0
$896$	3.56155			0.118983
$897$	27.4397	+	3.84233i	0.916186	+	0.128292i
$898$			25.1771i			0.840170i
$899$	18.6501	+	32.3029i	0.622015	+	1.07736i
$900$		0			0
$901$	−11.3693	+	19.6922i	−0.378767	+	0.656043i
$902$		−	17.5076i		−	0.582939i
$903$	−14.0696	−	8.12311i	−0.468208	−	0.270320i
$904$	−1.84233	+	3.19101i	−0.0612750	+	0.106131i
$905$		0			0
$906$	−4.68466	+	8.11407i	−0.155637	+	0.269572i
$907$	−35.4340	+	20.4579i	−1.17657	+	0.679292i	−0.955218	−	0.295902i	$-0.904380\pi$
$907$	−35.4340	+	20.4579i	−1.17657	+	0.679292i	−0.221350	+	0.975194i	$0.571046\pi$
$908$	−17.3205	+	10.0000i	−0.574801	+	0.331862i
$909$	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	$0.755146\pi$
$912$	3.08440	−	1.78078i	0.102135	−	0.0589674i
$913$	−4.01029	+	2.31534i	−0.132721	+	0.0766266i
$914$	1.87689	−	3.25088i	0.0620821	−	0.107529i
$915$		0			0
$916$	3.87689	−	6.71498i	0.128096	−	0.221869i
$917$	18.8861	+	10.9039i	0.623673	+	0.360078i
$918$			5.12311i			0.169088i
$919$	20.6847	−	35.8269i	0.682324	−	1.18182i	−0.291946	−	0.956435i	$-0.594303\pi$
$919$	20.6847	−	35.8269i	0.682324	−	1.18182i	0.974270	−	0.225385i	$-0.0723639\pi$
$920$		0			0
$921$	7.80776	+	13.5234i	0.257275	+	0.445613i
$922$		−	7.05398i		−	0.232310i
$923$	−17.4140	−	2.43845i	−0.573189	−	0.0802625i
$924$	14.6847			0.483090
$925$		0			0
$926$	−16.8078	−	29.1119i	−0.552337	−	0.956676i
$927$	0.379706	+	0.219224i	0.0124712	+	0.00720025i
$928$			6.56155i			0.215394i
$929$	−8.43845	+	14.6158i	−0.276856	+	0.479529i	−0.970602	−	0.240691i	$-0.922626\pi$
$929$	−8.43845	+	14.6158i	−0.276856	+	0.479529i	0.693745	+	0.720220i	$0.255959\pi$
$930$		0			0
$931$	−20.2462			−0.663543
$932$	−15.3154	−	8.84233i	−0.501671	−	0.289640i
$933$	−16.2281	+	9.36932i	−0.531285	+	0.306738i
$934$	19.9309	+	34.5213i	0.652158	+	1.12957i
$935$		0			0
$936$	0.500000	−	3.57071i	0.0163430	−	0.116712i
$937$			29.2311i			0.954937i	0.878649	+	0.477468i	$0.158446\pi$
$937$			29.2311i			0.954937i	−0.878649	+	0.477468i	$0.841554\pi$
$938$	43.9409	−	25.3693i	1.43472	−	0.828338i
$939$	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	$0.503272\pi$
$942$	19.1592	+	11.0616i	0.624240	+	0.360405i
$943$	−28.2590	−	16.3153i	−0.920240	−	0.531301i
$944$	−10.5616			−0.343749
$945$		0			0
$946$	9.40388	+	16.2880i	0.305747	+	0.529569i
$947$	−12.0046	+	6.93087i	−0.390098	+	0.225223i	−0.682202	−	0.731163i	$-0.738978\pi$
$947$	−12.0046	+	6.93087i	−0.390098	+	0.225223i	0.292105	+	0.956386i	$0.405644\pi$
$948$			7.43845i			0.241590i
$949$	−51.3693	+	20.7846i	−1.66752	+	0.674697i
$950$		0			0
$951$	2.09612	+	3.63058i	0.0679713	+	0.117730i
$952$	−15.8017	+	9.12311i	−0.512135	+	0.295682i
$953$	−5.04280	−	2.91146i	−0.163352	−	0.0943114i	0.416095	−	0.909321i	$-0.363398\pi$
$953$	−5.04280	−	2.91146i	−0.163352	−	0.0943114i	−0.579447	+	0.815010i	$0.696732\pi$
$954$	−4.43845			−0.143700
$955$		0			0
$956$	−6.68466	+	11.5782i	−0.216197	+	0.374465i
$957$			27.0540i			0.874531i
$958$	18.8393	+	10.8769i	0.608671	+	0.351417i
$959$	−15.6847	−	27.1666i	−0.506484	−	0.877256i
$960$		0			0
$961$	1.31534			0.0424304
$962$	−14.7224	−	2.06155i	−0.474670	−	0.0664671i
$963$			2.00000i			0.0644491i
$964$	−9.93845	−	17.2139i	−0.320096	−	0.554422i
$965$		0			0
$966$	13.6847	−	23.7025i	0.440297	−	0.762616i
$967$		−	3.31534i		−	0.106614i	−0.998578	−	0.0533071i	$-0.983024\pi$
$967$		−	3.31534i		−	0.106614i	0.998578	−	0.0533071i	$-0.0169762\pi$
$968$	−5.19615	−	3.00000i	−0.167011	−	0.0964237i
$969$	−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	$0.0803971\pi$
$972$	−0.866025	+	0.500000i	−0.0277778	+	0.0160375i
$973$	26.0275	−	15.0270i	0.834404	−	0.481743i
$974$	24.0540			0.770739
$975$		0			0
$976$	6.00000			0.192055
$977$	−4.59010	+	2.65009i	−0.146850	+	0.0847840i	−0.571625	−	0.820515i	$-0.693687\pi$
$977$	−4.59010	+	2.65009i	−0.146850	+	0.0847840i	0.424775	+	0.905299i	$0.360353\pi$
$978$	−16.0748	+	9.28078i	−0.514015	+	0.296767i
$979$	−3.72680	+	6.45501i	−0.119109	+	0.206303i
$980$		0			0
$981$	10.1231	−	17.5337i	0.323206	−	0.559809i
$982$	−18.6729	−	10.7808i	−0.595875	−	0.344028i
$983$			23.8769i			0.761555i	0.924667	+	0.380777i	$0.124344\pi$
$983$			23.8769i			0.761555i	−0.924667	+	0.380777i	$0.875656\pi$
$984$	−2.12311	+	3.67733i	−0.0676821	+	0.117229i
$985$		0			0
$986$	−16.8078	−	29.1119i	−0.535268	−	0.927112i
$987$		−	24.9309i		−	0.793558i
$988$	7.90084	−	10.1231i	0.251359	−	0.322059i
$989$	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	$0.770110\pi$
$992$	4.92306	+	2.84233i	0.156307	+	0.0902440i
$993$		−	18.7386i		−	0.594653i
$994$	−8.68466	+	15.0423i	−0.275461	+	0.477112i
$995$		0			0
$996$	1.12311			0.0355870
$997$	28.1860	+	16.2732i	0.892660	+	0.515377i	0.874812	−	0.484463i	$-0.160985\pi$
$997$	28.1860	+	16.2732i	0.892660	+	0.515377i	0.0178482	+	0.999841i	$0.494318\pi$
$998$	3.46410	−	2.00000i	0.109654	−	0.0633089i
$999$	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.z.n.1849.2		8
5.2	odd	4		390.2.i.g.211.1	yes	4
5.3	odd	4		1950.2.i.bi.601.2		4
5.4	even	2	inner	1950.2.z.n.1849.3		8
13.9	even	3	inner	1950.2.z.n.1699.3		8
15.2	even	4		1170.2.i.o.991.1		4
65.2	even	12		5070.2.b.r.1351.2		4
65.9	even	6	inner	1950.2.z.n.1699.2		8
65.22	odd	12		390.2.i.g.61.1	✓	4
65.37	even	12		5070.2.b.r.1351.3		4
65.42	odd	12		5070.2.a.bi.1.2		2
65.48	odd	12		1950.2.i.bi.451.2		4
65.62	odd	12		5070.2.a.bb.1.1		2
195.152	even	12		1170.2.i.o.451.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.i.g.61.1	✓	4	65.22	odd	12
390.2.i.g.211.1	yes	4	5.2	odd	4
1170.2.i.o.451.1		4	195.152	even	12
1170.2.i.o.991.1		4	15.2	even	4
1950.2.i.bi.451.2		4	65.48	odd	12
1950.2.i.bi.601.2		4	5.3	odd	4
1950.2.z.n.1699.2		8	65.9	even	6	inner
1950.2.z.n.1699.3		8	13.9	even	3	inner
1950.2.z.n.1849.2		8	1.1	even	1	trivial
1950.2.z.n.1849.3		8	5.4	even	2	inner
5070.2.a.bb.1.1		2	65.62	odd	12
5070.2.a.bi.1.2		2	65.42	odd	12
5070.2.b.r.1351.2		4	65.2	even	12
5070.2.b.r.1351.3		4	65.37	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:	\( N \)	\(=\)	\( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1950.z (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{6} +(3.08440 + 1.78078i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{6} +(3.08440 + 1.78078i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(2.06155 + 3.57071i) q^{11} -1.00000i q^{12} +(-1.35234 - 3.34233i) q^{13} -3.56155 q^{14} +(-0.500000 - 0.866025i) q^{16} +(4.43674 + 2.56155i) q^{17} +1.00000i q^{18} +(-1.78078 + 3.08440i) q^{19} +3.56155 q^{21} +(-3.57071 - 2.06155i) q^{22} +(-6.65511 + 3.84233i) q^{23} +(0.500000 + 0.866025i) q^{24} +(2.84233 + 2.21837i) q^{26} -1.00000i q^{27} +(3.08440 - 1.78078i) q^{28} +(3.28078 + 5.68247i) q^{29} +5.68466 q^{31} +(0.866025 + 0.500000i) q^{32} +(3.57071 + 2.06155i) q^{33} -5.12311 q^{34} +(-0.500000 - 0.866025i) q^{36} +(-3.57071 + 2.06155i) q^{37} -3.56155i q^{38} +(-2.84233 - 2.21837i) q^{39} +(2.12311 + 3.67733i) q^{41} +(-3.08440 + 1.78078i) q^{42} +(-3.95042 - 2.28078i) q^{43} +4.12311 q^{44} +(3.84233 - 6.65511i) q^{46} -7.00000i q^{47} +(-0.866025 - 0.500000i) q^{48} +(2.84233 + 4.92306i) q^{49} +5.12311 q^{51} +(-3.57071 - 0.500000i) q^{52} +4.43845i q^{53} +(0.500000 + 0.866025i) q^{54} +(-1.78078 + 3.08440i) q^{56} +3.56155i q^{57} +(-5.68247 - 3.28078i) q^{58} +(5.28078 - 9.14657i) q^{59} +(-3.00000 + 5.19615i) q^{61} +(-4.92306 + 2.84233i) q^{62} +(3.08440 - 1.78078i) q^{63} -1.00000 q^{64} -4.12311 q^{66} +(-12.3376 + 7.12311i) q^{67} +(4.43674 - 2.56155i) q^{68} +(-3.84233 + 6.65511i) q^{69} +(2.43845 - 4.22351i) q^{71} +(0.866025 + 0.500000i) q^{72} -15.3693i q^{73} +(2.06155 - 3.57071i) q^{74} +(1.78078 + 3.08440i) q^{76} +14.6847i q^{77} +(3.57071 + 0.500000i) q^{78} -7.43845 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-3.67733 - 2.12311i) q^{82} +1.12311i q^{83} +(1.78078 - 3.08440i) q^{84} +4.56155 q^{86} +(5.68247 + 3.28078i) q^{87} +(-3.57071 + 2.06155i) q^{88} +(0.903882 + 1.56557i) q^{89} +(1.78078 - 12.7173i) q^{91} +7.68466i q^{92} +(4.92306 - 2.84233i) q^{93} +(3.50000 + 6.06218i) q^{94} +1.00000 q^{96} +(0.972638 + 0.561553i) q^{97} +(-4.92306 - 2.84233i) q^{98} +4.12311 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4} - 4 q^{6} + 4 q^{9}+O(q^{10}) \) 8 * q + 4 * q^4 - 4 * q^6 + 4 * q^9	\( 8 q + 4 q^{4} - 4 q^{6} + 4 q^{9} - 12 q^{14} - 4 q^{16} - 6 q^{19} + 12 q^{21} + 4 q^{24} - 2 q^{26} + 18 q^{29} - 4 q^{31} - 8 q^{34} - 4 q^{36} + 2 q^{39} - 16 q^{41} + 6 q^{46} - 2 q^{49} + 8 q^{51} + 4 q^{54} - 6 q^{56} + 34 q^{59} - 24 q^{61} - 8 q^{64} - 6 q^{69} + 36 q^{71} + 6 q^{76} - 76 q^{79} - 4 q^{81} + 6 q^{84} + 20 q^{86} - 34 q^{89} + 6 q^{91} + 28 q^{94} + 8 q^{96}+O(q^{100}) \) 8 * q + 4 * q^4 - 4 * q^6 + 4 * q^9 - 12 * q^14 - 4 * q^16 - 6 * q^19 + 12 * q^21 + 4 * q^24 - 2 * q^26 + 18 * q^29 - 4 * q^31 - 8 * q^34 - 4 * q^36 + 2 * q^39 - 16 * q^41 + 6 * q^46 - 2 * q^49 + 8 * q^51 + 4 * q^54 - 6 * q^56 + 34 * q^59 - 24 * q^61 - 8 * q^64 - 6 * q^69 + 36 * q^71 + 6 * q^76 - 76 * q^79 - 4 * q^81 + 6 * q^84 + 20 * q^86 - 34 * q^89 + 6 * q^91 + 28 * q^94 + 8 * q^96

Introduction

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