LMFDB - Embedded newform 1950.2.i.bf.601.1

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:	$\Q(\sqrt{-3}, \sqrt{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 10x^{2} + 100 $ x^4 + 10*x^2 + 100
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			601.1
Root			$-1.58114 + 2.73861i$ of defining polynomial
Character	$\chi$	$=$	1950.601
Dual form			1950.2.i.bf.451.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{6} +(-1.58114 + 2.73861i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(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} +(-1.58114 + 2.73861i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.50000 - 2.59808i) q^{11} +1.00000 q^{12} +(3.08114 - 1.87259i) q^{13} -3.16228 q^{14} +(-0.500000 - 0.866025i) q^{16} +(3.58114 - 6.20271i) q^{17} -1.00000 q^{18} +(-1.58114 + 2.73861i) q^{19} +3.16228 q^{21} +(1.50000 - 2.59808i) q^{22} +(-2.08114 - 3.60464i) q^{23} +(0.500000 + 0.866025i) q^{24} +(3.16228 + 1.73205i) q^{26} +1.00000 q^{27} +(-1.58114 - 2.73861i) q^{28} +(4.16228 + 7.20928i) q^{29} +9.16228 q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.50000 + 2.59808i) q^{33} +7.16228 q^{34} +(-0.500000 - 0.866025i) q^{36} +(5.24342 + 9.08186i) q^{37} -3.16228 q^{38} +(-3.16228 - 1.73205i) q^{39} +(4.74342 + 8.21584i) q^{41} +(1.58114 + 2.73861i) q^{42} +(2.58114 - 4.47066i) q^{43} +3.00000 q^{44} +(2.08114 - 3.60464i) q^{46} -6.00000 q^{47} +(-0.500000 + 0.866025i) q^{48} +(-1.50000 - 2.59808i) q^{49} -7.16228 q^{51} +(0.0811388 + 3.60464i) q^{52} -7.16228 q^{53} +(0.500000 + 0.866025i) q^{54} +(1.58114 - 2.73861i) q^{56} +3.16228 q^{57} +(-4.16228 + 7.20928i) q^{58} +(3.00000 - 5.19615i) q^{59} +(-7.24342 + 12.5460i) q^{61} +(4.58114 + 7.93477i) q^{62} +(-1.58114 - 2.73861i) q^{63} +1.00000 q^{64} -3.00000 q^{66} +(2.00000 + 3.46410i) q^{67} +(3.58114 + 6.20271i) q^{68} +(-2.08114 + 3.60464i) q^{69} +(3.91886 - 6.78767i) q^{71} +(0.500000 - 0.866025i) q^{72} +1.32456 q^{73} +(-5.24342 + 9.08186i) q^{74} +(-1.58114 - 2.73861i) q^{76} +9.48683 q^{77} +(-0.0811388 - 3.60464i) q^{78} +9.16228 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-4.74342 + 8.21584i) q^{82} +13.6491 q^{83} +(-1.58114 + 2.73861i) q^{84} +5.16228 q^{86} +(4.16228 - 7.20928i) q^{87} +(1.50000 + 2.59808i) q^{88} +(3.58114 + 6.20271i) q^{89} +(0.256584 + 11.3989i) q^{91} +4.16228 q^{92} +(-4.58114 - 7.93477i) q^{93} +(-3.00000 - 5.19615i) q^{94} -1.00000 q^{96} +(2.33772 - 4.04905i) q^{97} +(1.50000 - 2.59808i) q^{98} +3.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{6} - 4 q^{8} - 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^6 - 4 * q^8 - 2 * q^9	$ 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{6} - 4 q^{8} - 2 q^{9} - 6 q^{11} + 4 q^{12} + 6 q^{13} - 2 q^{16} + 8 q^{17} - 4 q^{18} + 6 q^{22} - 2 q^{23} + 2 q^{24} + 4 q^{27} + 4 q^{29} + 24 q^{31} + 2 q^{32} - 6 q^{33} + 16 q^{34} - 2 q^{36} + 2 q^{37} + 4 q^{43} + 12 q^{44} + 2 q^{46} - 24 q^{47} - 2 q^{48} - 6 q^{49} - 16 q^{51} - 6 q^{52} - 16 q^{53} + 2 q^{54} - 4 q^{58} + 12 q^{59} - 10 q^{61} + 12 q^{62} + 4 q^{64} - 12 q^{66} + 8 q^{67} + 8 q^{68} - 2 q^{69} + 22 q^{71} + 2 q^{72} - 20 q^{73} - 2 q^{74} + 6 q^{78} + 24 q^{79} - 2 q^{81} + 4 q^{83} + 8 q^{86} + 4 q^{87} + 6 q^{88} + 8 q^{89} + 20 q^{91} + 4 q^{92} - 12 q^{93} - 12 q^{94} - 4 q^{96} + 22 q^{97} + 6 q^{98} + 12 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^6 - 4 * q^8 - 2 * q^9 - 6 * q^11 + 4 * q^12 + 6 * q^13 - 2 * q^16 + 8 * q^17 - 4 * q^18 + 6 * q^22 - 2 * q^23 + 2 * q^24 + 4 * q^27 + 4 * q^29 + 24 * q^31 + 2 * q^32 - 6 * q^33 + 16 * q^34 - 2 * q^36 + 2 * q^37 + 4 * q^43 + 12 * q^44 + 2 * q^46 - 24 * q^47 - 2 * q^48 - 6 * q^49 - 16 * q^51 - 6 * q^52 - 16 * q^53 + 2 * q^54 - 4 * q^58 + 12 * q^59 - 10 * q^61 + 12 * q^62 + 4 * q^64 - 12 * q^66 + 8 * q^67 + 8 * q^68 - 2 * q^69 + 22 * q^71 + 2 * q^72 - 20 * q^73 - 2 * q^74 + 6 * q^78 + 24 * q^79 - 2 * q^81 + 4 * q^83 + 8 * q^86 + 4 * q^87 + 6 * q^88 + 8 * q^89 + 20 * q^91 + 4 * q^92 - 12 * q^93 - 12 * q^94 - 4 * q^96 + 22 * q^97 + 6 * q^98 + 12 * q^99

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
$7$	−1.58114	+	2.73861i	−0.597614	+	1.03510i	0.395558	+	0.918441i	$0.370551\pi$
$7$	−1.58114	+	2.73861i	−0.597614	+	1.03510i	−0.993172	+	0.116657i	$0.962782\pi$
$8$	−1.00000			−0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	0.546259	−	0.837616i	$-0.316051\pi$
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	−0.998526	+	0.0542666i	$0.982718\pi$
$12$	1.00000			0.288675
$13$	3.08114	−	1.87259i	0.854554	−	0.519362i
$13$	3.08114	−	1.87259i	0.854554	−	0.519362i
$14$	−3.16228			−0.845154
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	3.58114	−	6.20271i	0.868554	−	1.50438i	0.00507902	−	0.999987i	$-0.498383\pi$
$17$	3.58114	−	6.20271i	0.868554	−	1.50438i	0.863475	−	0.504392i	$-0.168283\pi$
$18$	−1.00000			−0.235702
$19$	−1.58114	+	2.73861i	−0.362738	+	0.628281i	−0.988410	−	0.151805i	$-0.951491\pi$
$19$	−1.58114	+	2.73861i	−0.362738	+	0.628281i	0.625672	+	0.780086i	$0.284825\pi$
$20$		0			0
$21$	3.16228			0.690066
$22$	1.50000	−	2.59808i	0.319801	−	0.553912i
$23$	−2.08114	−	3.60464i	−0.433947	−	0.751619i	0.563262	−	0.826279i	$-0.309546\pi$
$23$	−2.08114	−	3.60464i	−0.433947	−	0.751619i	−0.997209	+	0.0746596i	$0.976213\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$		0			0
$26$	3.16228	+	1.73205i	0.620174	+	0.339683i
$27$	1.00000			0.192450
$28$	−1.58114	−	2.73861i	−0.298807	−	0.517549i
$29$	4.16228	+	7.20928i	0.772916	+	1.33873i	0.935959	+	0.352110i	$0.114536\pi$
$29$	4.16228	+	7.20928i	0.772916	+	1.33873i	−0.163043	+	0.986619i	$0.552131\pi$
$30$		0			0
$31$	9.16228			1.64559			0.822797	−	0.568336i	$-0.192412\pi$
$31$	9.16228			1.64559			0.822797	+	0.568336i	$0.192412\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−1.50000	+	2.59808i	−0.261116	+	0.452267i
$34$	7.16228			1.22832
$35$		0			0
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	5.24342	+	9.08186i	0.862012	+	1.49305i	0.869983	+	0.493081i	$0.164129\pi$
$37$	5.24342	+	9.08186i	0.862012	+	1.49305i	−0.00797106	+	0.999968i	$0.502537\pi$
$38$	−3.16228			−0.512989
$39$	−3.16228	−	1.73205i	−0.506370	−	0.277350i
$40$		0			0
$41$	4.74342	+	8.21584i	0.740797	+	1.28310i	0.952133	+	0.305685i	$0.0988854\pi$
$41$	4.74342	+	8.21584i	0.740797	+	1.28310i	−0.211336	+	0.977414i	$0.567781\pi$
$42$	1.58114	+	2.73861i	0.243975	+	0.422577i
$43$	2.58114	−	4.47066i	0.393620	−	0.681770i	−0.599304	−	0.800522i	$-0.704556\pi$
$43$	2.58114	−	4.47066i	0.393620	−	0.681770i	0.992924	+	0.118752i	$0.0378893\pi$
$44$	3.00000			0.452267
$45$		0			0
$46$	2.08114	−	3.60464i	0.306847	−	0.531475i
$47$	−6.00000			−0.875190			−0.437595	−	0.899172i	$-0.644170\pi$
$47$	−6.00000			−0.875190			−0.437595	+	0.899172i	$0.644170\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	−1.50000	−	2.59808i	−0.214286	−	0.371154i
$50$		0			0
$51$	−7.16228			−1.00292
$52$	0.0811388	+	3.60464i	0.0112519	+	0.499873i
$53$	−7.16228			−0.983814			−0.491907	−	0.870648i	$-0.663700\pi$
$53$	−7.16228			−0.983814			−0.491907	+	0.870648i	$0.663700\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$		0			0
$56$	1.58114	−	2.73861i	0.211289	−	0.365963i
$57$	3.16228			0.418854
$58$	−4.16228	+	7.20928i	−0.546534	+	0.946624i
$59$	3.00000	−	5.19615i	0.390567	−	0.676481i	−0.601958	−	0.798528i	$-0.705612\pi$
$59$	3.00000	−	5.19615i	0.390567	−	0.676481i	0.992524	+	0.122047i	$0.0389457\pi$
$60$		0			0
$61$	−7.24342	+	12.5460i	−0.927424	+	1.60635i	−0.139810	+	0.990178i	$0.544649\pi$
$61$	−7.24342	+	12.5460i	−0.927424	+	1.60635i	−0.787615	+	0.616168i	$0.788684\pi$
$62$	4.58114	+	7.93477i	0.581805	+	1.00772i
$63$	−1.58114	−	2.73861i	−0.199205	−	0.345033i
$64$	1.00000			0.125000
$65$		0			0
$66$	−3.00000			−0.369274
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	0.961946	−	0.273241i	$-0.0880957\pi$
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	−0.717607	+	0.696449i	$0.754762\pi$
$68$	3.58114	+	6.20271i	0.434277	+	0.752190i
$69$	−2.08114	+	3.60464i	−0.250540	+	0.433947i
$70$		0			0
$71$	3.91886	−	6.78767i	0.465083	−	0.805548i	−0.534122	−	0.845407i	$-0.679358\pi$
$71$	3.91886	−	6.78767i	0.465083	−	0.805548i	0.999205	+	0.0398596i	$0.0126911\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	1.32456			0.155027			0.0775137	−	0.996991i	$-0.475302\pi$
$73$	1.32456			0.155027			0.0775137	+	0.996991i	$0.475302\pi$
$74$	−5.24342	+	9.08186i	−0.609535	+	1.05575i
$75$		0			0
$76$	−1.58114	−	2.73861i	−0.181369	−	0.314140i
$77$	9.48683			1.08112
$78$	−0.0811388	−	3.60464i	−0.00918716	−	0.408145i
$79$	9.16228			1.03084			0.515418	−	0.856939i	$-0.327637\pi$
$79$	9.16228			1.03084			0.515418	+	0.856939i	$0.327637\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−4.74342	+	8.21584i	−0.523823	+	0.907288i
$83$	13.6491			1.49818			0.749092	−	0.662466i	$-0.230490\pi$
$83$	13.6491			1.49818			0.749092	+	0.662466i	$0.230490\pi$
$84$	−1.58114	+	2.73861i	−0.172516	+	0.298807i
$85$		0			0
$86$	5.16228			0.556663
$87$	4.16228	−	7.20928i	0.446243	−	0.772916i
$88$	1.50000	+	2.59808i	0.159901	+	0.276956i
$89$	3.58114	+	6.20271i	0.379600	+	0.657486i	0.991004	−	0.133832i	$-0.0427283\pi$
$89$	3.58114	+	6.20271i	0.379600	+	0.657486i	−0.611404	+	0.791319i	$0.709395\pi$
$90$		0			0
$91$	0.256584	+	11.3989i	0.0268973	+	1.19493i
$92$	4.16228			0.433947
$93$	−4.58114	−	7.93477i	−0.475042	−	0.822797i
$94$	−3.00000	−	5.19615i	−0.309426	−	0.535942i
$95$		0			0
$96$	−1.00000			−0.102062
$97$	2.33772	−	4.04905i	0.237360	−	0.411119i	−0.722596	−	0.691270i	$-0.757051\pi$
$97$	2.33772	−	4.04905i	0.237360	−	0.411119i	0.959956	+	0.280151i	$0.0903847\pi$
$98$	1.50000	−	2.59808i	0.151523	−	0.262445i
$99$	3.00000			0.301511
$100$		0			0
$101$	8.32456	+	14.4186i	0.828324	+	1.43470i	0.899352	+	0.437225i	$0.144039\pi$
$101$	8.32456	+	14.4186i	0.828324	+	1.43470i	−0.0710278	+	0.997474i	$0.522628\pi$
$102$	−3.58114	−	6.20271i	−0.354586	−	0.614160i
$103$	−13.4868			−1.32890			−0.664449	−	0.747334i	$-0.731334\pi$
$103$	−13.4868			−1.32890			−0.664449	+	0.747334i	$0.731334\pi$
$104$	−3.08114	+	1.87259i	−0.302131	+	0.183622i
$105$		0			0
$106$	−3.58114	−	6.20271i	−0.347831	−	0.602461i
$107$	−3.00000	−	5.19615i	−0.290021	−	0.502331i	0.683793	−	0.729676i	$-0.260329\pi$
$107$	−3.00000	−	5.19615i	−0.290021	−	0.502331i	−0.973814	+	0.227345i	$0.926996\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	8.48683			0.812891			0.406446	−	0.913675i	$-0.366768\pi$
$109$	8.48683			0.812891			0.406446	+	0.913675i	$0.366768\pi$
$110$		0			0
$111$	5.24342	−	9.08186i	0.497683	−	0.862012i
$112$	3.16228			0.298807
$113$	1.16228	−	2.01312i	0.109338	−	0.189379i	−0.806164	−	0.591692i	$-0.798460\pi$
$113$	1.16228	−	2.01312i	0.109338	−	0.189379i	0.915502	+	0.402313i	$0.131794\pi$
$114$	1.58114	+	2.73861i	0.148087	+	0.256495i
$115$		0			0
$116$	−8.32456			−0.772916
$117$	0.0811388	+	3.60464i	0.00750129	+	0.333249i
$118$	6.00000			0.552345
$119$	11.3246	+	19.6147i	1.03812	+	1.79808i
$120$		0			0
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$	−14.4868			−1.31158
$123$	4.74342	−	8.21584i	0.427699	−	0.740797i
$124$	−4.58114	+	7.93477i	−0.411398	+	0.712563i
$125$		0			0
$126$	1.58114	−	2.73861i	0.140859	−	0.243975i
$127$	3.83772	+	6.64713i	0.340543	+	0.589837i	0.984534	−	0.175196i	$-0.0560558\pi$
$127$	3.83772	+	6.64713i	0.340543	+	0.589837i	−0.643991	+	0.765033i	$0.722723\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−5.16228			−0.454513
$130$		0			0
$131$	3.67544			0.321125			0.160563	−	0.987026i	$-0.448669\pi$
$131$	3.67544			0.321125			0.160563	+	0.987026i	$0.448669\pi$
$132$	−1.50000	−	2.59808i	−0.130558	−	0.226134i
$133$	−5.00000	−	8.66025i	−0.433555	−	0.750939i
$134$	−2.00000	+	3.46410i	−0.172774	+	0.299253i
$135$		0			0
$136$	−3.58114	+	6.20271i	−0.307080	+	0.531878i
$137$	6.00000	−	10.3923i	0.512615	−	0.887875i	−0.487278	−	0.873247i	$-0.662010\pi$
$137$	6.00000	−	10.3923i	0.512615	−	0.887875i	0.999893	−	0.0146279i	$-0.00465636\pi$
$138$	−4.16228			−0.354317
$139$	9.16228	−	15.8695i	0.777134	−	1.34604i	−0.156453	−	0.987685i	$-0.550006\pi$
$139$	9.16228	−	15.8695i	0.777134	−	1.34604i	0.933587	−	0.358351i	$-0.116661\pi$
$140$		0			0
$141$	3.00000	+	5.19615i	0.252646	+	0.437595i
$142$	7.83772			0.657727
$143$	−9.48683	−	5.19615i	−0.793329	−	0.434524i
$144$	1.00000			0.0833333
$145$		0			0
$146$	0.662278	+	1.14710i	0.0548105	+	0.0949346i
$147$	−1.50000	+	2.59808i	−0.123718	+	0.214286i
$148$	−10.4868			−0.862012
$149$	6.58114	−	11.3989i	0.539148	−	0.933832i	−0.459802	−	0.888021i	$-0.652080\pi$
$149$	6.58114	−	11.3989i	0.539148	−	0.933832i	0.998950	−	0.0458102i	$-0.0145870\pi$
$150$		0			0
$151$	−21.8114			−1.77499			−0.887493	−	0.460822i	$-0.847555\pi$
$151$	−21.8114			−1.77499			−0.887493	+	0.460822i	$0.847555\pi$
$152$	1.58114	−	2.73861i	0.128247	−	0.222131i
$153$	3.58114	+	6.20271i	0.289518	+	0.501460i
$154$	4.74342	+	8.21584i	0.382235	+	0.662051i
$155$		0			0
$156$	3.08114	−	1.87259i	0.246689	−	0.149927i
$157$	9.83772			0.785136			0.392568	−	0.919723i	$-0.371587\pi$
$157$	9.83772			0.785136			0.392568	+	0.919723i	$0.371587\pi$
$158$	4.58114	+	7.93477i	0.364456	+	0.631256i
$159$	3.58114	+	6.20271i	0.284003	+	0.491907i
$160$		0			0
$161$	13.1623			1.03733
$162$	0.500000	−	0.866025i	0.0392837	−	0.0680414i
$163$	7.90569	−	13.6931i	0.619222	−	1.07252i	−0.370406	−	0.928870i	$-0.620782\pi$
$163$	7.90569	−	13.6931i	0.619222	−	1.07252i	0.989628	−	0.143654i	$-0.0458851\pi$
$164$	−9.48683			−0.740797
$165$		0			0
$166$	6.82456	+	11.8205i	0.529688	+	0.917447i
$167$	−0.918861	−	1.59151i	−0.0711036	−	0.123155i	0.828282	−	0.560312i	$-0.189319\pi$
$167$	−0.918861	−	1.59151i	−0.0711036	−	0.123155i	−0.899385	+	0.437157i	$0.855985\pi$
$168$	−3.16228			−0.243975
$169$	5.98683	−	11.5394i	0.460526	−	0.887646i
$170$		0			0
$171$	−1.58114	−	2.73861i	−0.120913	−	0.209427i
$172$	2.58114	+	4.47066i	0.196810	+	0.340885i
$173$	7.16228	−	12.4054i	0.544538	−	0.943167i	−0.454098	−	0.890952i	$-0.650038\pi$
$173$	7.16228	−	12.4054i	0.544538	−	0.943167i	0.998636	−	0.0522155i	$-0.0166283\pi$
$174$	8.32456			0.631083
$175$		0			0
$176$	−1.50000	+	2.59808i	−0.113067	+	0.195837i
$177$	−6.00000			−0.450988
$178$	−3.58114	+	6.20271i	−0.268418	+	0.464913i
$179$	0.824555	+	1.42817i	0.0616302	+	0.106747i	0.895194	−	0.445676i	$-0.147037\pi$
$179$	0.824555	+	1.42817i	0.0616302	+	0.106747i	−0.833564	+	0.552423i	$0.813703\pi$
$180$		0			0
$181$	−18.8114			−1.39824			−0.699120	−	0.715005i	$-0.746425\pi$
$181$	−18.8114			−1.39824			−0.699120	+	0.715005i	$0.746425\pi$
$182$	−9.74342	+	5.92164i	−0.722230	+	0.438941i
$183$	14.4868			1.07090
$184$	2.08114	+	3.60464i	0.153424	+	0.265737i
$185$		0			0
$186$	4.58114	−	7.93477i	0.335905	−	0.581805i
$187$	−21.4868			−1.57127
$188$	3.00000	−	5.19615i	0.218797	−	0.378968i
$189$	−1.58114	+	2.73861i	−0.115011	+	0.199205i
$190$		0			0
$191$	−11.0811	+	19.1931i	−0.801803	+	1.38876i	0.116625	+	0.993176i	$0.462792\pi$
$191$	−11.0811	+	19.1931i	−0.801803	+	1.38876i	−0.918428	+	0.395588i	$0.870541\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	2.33772	+	4.04905i	0.168273	+	0.291457i	0.937813	−	0.347142i	$-0.112848\pi$
$193$	2.33772	+	4.04905i	0.168273	+	0.291457i	−0.769540	+	0.638599i	$0.779514\pi$
$194$	4.67544			0.335677
$195$		0			0
$196$	3.00000			0.214286
$197$	3.00000	+	5.19615i	0.213741	+	0.370211i	0.952882	−	0.303340i	$-0.0981018\pi$
$197$	3.00000	+	5.19615i	0.213741	+	0.370211i	−0.739141	+	0.673550i	$0.764768\pi$
$198$	1.50000	+	2.59808i	0.106600	+	0.184637i
$199$	−7.58114	+	13.1309i	−0.537413	+	0.930826i	0.461630	+	0.887073i	$0.347265\pi$
$199$	−7.58114	+	13.1309i	−0.537413	+	0.930826i	−0.999042	+	0.0437533i	$0.986068\pi$
$200$		0			0
$201$	2.00000	−	3.46410i	0.141069	−	0.244339i
$202$	−8.32456	+	14.4186i	−0.585714	+	1.01449i
$203$	−26.3246			−1.84762
$204$	3.58114	−	6.20271i	0.250730	−	0.434277i
$205$		0			0
$206$	−6.74342	−	11.6799i	−0.469836	−	0.813780i
$207$	4.16228			0.289298
$208$	−3.16228	−	1.73205i	−0.219265	−	0.120096i
$209$	9.48683			0.656218
$210$		0			0
$211$	−3.41886	−	5.92164i	−0.235364	−	0.407663i	0.724014	−	0.689785i	$-0.242295\pi$
$211$	−3.41886	−	5.92164i	−0.235364	−	0.407663i	−0.959378	+	0.282122i	$0.908962\pi$
$212$	3.58114	−	6.20271i	0.245954	−	0.426004i
$213$	−7.83772			−0.537032
$214$	3.00000	−	5.19615i	0.205076	−	0.355202i
$215$		0			0
$216$	−1.00000			−0.0680414
$217$	−14.4868	+	25.0919i	−0.983430	+	1.70335i
$218$	4.24342	+	7.34981i	0.287400	+	0.497792i
$219$	−0.662278	−	1.14710i	−0.0447526	−	0.0775137i
$220$		0			0
$221$	−0.581139	−	25.8174i	−0.0390916	−	1.73667i
$222$	10.4868			0.703830
$223$	9.06797	+	15.7062i	0.607236	+	1.05176i	0.991694	+	0.128621i	$0.0410552\pi$
$223$	9.06797	+	15.7062i	0.607236	+	1.05176i	−0.384457	+	0.923143i	$0.625611\pi$
$224$	1.58114	+	2.73861i	0.105644	+	0.182981i
$225$		0			0
$226$	2.32456			0.154627
$227$	7.98683	−	13.8336i	0.530105	−	0.918168i	−0.469278	−	0.883050i	$-0.655486\pi$
$227$	7.98683	−	13.8336i	0.530105	−	0.918168i	0.999383	−	0.0351181i	$-0.0111807\pi$
$228$	−1.58114	+	2.73861i	−0.104713	+	0.181369i
$229$	2.48683			0.164335			0.0821673	−	0.996619i	$-0.473816\pi$
$229$	2.48683			0.164335			0.0821673	+	0.996619i	$0.473816\pi$
$230$		0			0
$231$	−4.74342	−	8.21584i	−0.312094	−	0.540562i
$232$	−4.16228	−	7.20928i	−0.273267	−	0.473312i
$233$	26.3246			1.72458			0.862289	−	0.506416i	$-0.169030\pi$
$233$	26.3246			1.72458			0.862289	+	0.506416i	$0.169030\pi$
$234$	−3.08114	+	1.87259i	−0.201420	+	0.122415i
$235$		0			0
$236$	3.00000	+	5.19615i	0.195283	+	0.338241i
$237$	−4.58114	−	7.93477i	−0.297577	−	0.515418i
$238$	−11.3246	+	19.6147i	−0.734062	+	1.27143i
$239$	−0.486833			−0.0314906			−0.0157453	−	0.999876i	$-0.505012\pi$
$239$	−0.486833			−0.0314906			−0.0157453	+	0.999876i	$0.505012\pi$
$240$		0			0
$241$	−4.00000	+	6.92820i	−0.257663	+	0.446285i	−0.965615	−	0.259975i	$-0.916286\pi$
$241$	−4.00000	+	6.92820i	−0.257663	+	0.446285i	0.707953	+	0.706260i	$0.249619\pi$
$242$	2.00000			0.128565
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−7.24342	−	12.5460i	−0.463712	−	0.803173i
$245$		0			0
$246$	9.48683			0.604858
$247$	0.256584	+	11.3989i	0.0163260	+	0.725293i
$248$	−9.16228			−0.581805
$249$	−6.82456	−	11.8205i	−0.432489	−	0.749092i
$250$		0			0
$251$	−7.50000	+	12.9904i	−0.473396	+	0.819946i	−0.999536	−	0.0304521i	$-0.990305\pi$
$251$	−7.50000	+	12.9904i	−0.473396	+	0.819946i	0.526140	+	0.850398i	$0.323639\pi$
$252$	3.16228			0.199205
$253$	−6.24342	+	10.8139i	−0.392520	+	0.679865i
$254$	−3.83772	+	6.64713i	−0.240800	+	0.417078i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−2.90569	−	5.03281i	−0.181252	−	0.313938i	0.761055	−	0.648687i	$-0.224682\pi$
$257$	−2.90569	−	5.03281i	−0.181252	−	0.313938i	−0.942307	+	0.334749i	$0.891348\pi$
$258$	−2.58114	−	4.47066i	−0.160695	−	0.278331i
$259$	−33.1623			−2.06060
$260$		0			0
$261$	−8.32456			−0.515277
$262$	1.83772	+	3.18303i	0.113535	+	0.196648i
$263$	−9.24342	−	16.0101i	−0.569973	−	0.987223i	−0.996568	−	0.0827800i	$-0.973620\pi$
$263$	−9.24342	−	16.0101i	−0.569973	−	0.987223i	0.426594	−	0.904443i	$-0.359713\pi$
$264$	1.50000	−	2.59808i	0.0923186	−	0.159901i
$265$		0			0
$266$	5.00000	−	8.66025i	0.306570	−	0.530994i
$267$	3.58114	−	6.20271i	0.219162	−	0.379600i
$268$	−4.00000			−0.244339
$269$	9.58114	−	16.5950i	0.584172	−	1.01182i	−0.410806	−	0.911723i	$-0.634753\pi$
$269$	9.58114	−	16.5950i	0.584172	−	1.01182i	0.994978	−	0.100093i	$-0.0319141\pi$
$270$		0			0
$271$	6.16228	+	10.6734i	0.374332	+	0.648362i	0.990227	−	0.139467i	$-0.0445388\pi$
$271$	6.16228	+	10.6734i	0.374332	+	0.648362i	−0.615895	+	0.787828i	$0.711205\pi$
$272$	−7.16228			−0.434277
$273$	9.74342	−	5.92164i	0.589698	−	0.358394i
$274$	12.0000			0.724947
$275$		0			0
$276$	−2.08114	−	3.60464i	−0.125270	−	0.216974i
$277$	−11.4057	+	19.7552i	−0.685302	+	1.18698i	0.288040	+	0.957618i	$0.406996\pi$
$277$	−11.4057	+	19.7552i	−0.685302	+	1.18698i	−0.973342	+	0.229359i	$0.926337\pi$
$278$	18.3246			1.09903
$279$	−4.58114	+	7.93477i	−0.274266	+	0.475042i
$280$		0			0
$281$	−2.51317			−0.149923			−0.0749615	−	0.997186i	$-0.523883\pi$
$281$	−2.51317			−0.149923			−0.0749615	+	0.997186i	$0.523883\pi$
$282$	−3.00000	+	5.19615i	−0.178647	+	0.309426i
$283$	0.256584	+	0.444416i	0.0152523	+	0.0264178i	0.873551	−	0.486733i	$-0.161812\pi$
$283$	0.256584	+	0.444416i	0.0152523	+	0.0264178i	−0.858299	+	0.513151i	$0.828478\pi$
$284$	3.91886	+	6.78767i	0.232542	+	0.402774i
$285$		0			0
$286$	−0.243416	−	10.8139i	−0.0143935	−	0.639440i
$287$	−30.0000			−1.77084
$288$	0.500000	+	0.866025i	0.0294628	+	0.0510310i
$289$	−17.1491	−	29.7031i	−1.00877	−	1.74724i
$290$		0			0
$291$	−4.67544			−0.274079
$292$	−0.662278	+	1.14710i	−0.0387569	+	0.0671289i
$293$	−1.25658	+	2.17647i	−0.0734104	+	0.127151i	−0.900394	−	0.435076i	$-0.856722\pi$
$293$	−1.25658	+	2.17647i	−0.0734104	+	0.127151i	0.826984	+	0.562226i	$0.190055\pi$
$294$	−3.00000			−0.174964
$295$		0			0
$296$	−5.24342	−	9.08186i	−0.304767	−	0.527873i
$297$	−1.50000	−	2.59808i	−0.0870388	−	0.150756i
$298$	13.1623			0.762470
$299$	−13.1623	−	7.20928i	−0.761194	−	0.416923i
$300$		0			0
$301$	8.16228	+	14.1375i	0.470466	+	0.814871i
$302$	−10.9057	−	18.8892i	−0.627552	−	1.08695i
$303$	8.32456	−	14.4186i	0.478233	−	0.828324i
$304$	3.16228			0.181369
$305$		0			0
$306$	−3.58114	+	6.20271i	−0.204720	+	0.354586i
$307$	−8.64911			−0.493631			−0.246815	−	0.969063i	$-0.579384\pi$
$307$	−8.64911			−0.493631			−0.246815	+	0.969063i	$0.579384\pi$
$308$	−4.74342	+	8.21584i	−0.270281	+	0.468141i
$309$	6.74342	+	11.6799i	0.383620	+	0.664449i
$310$		0			0
$311$	12.4868			0.708063			0.354032	−	0.935233i	$-0.384811\pi$
$311$	12.4868			0.708063			0.354032	+	0.935233i	$0.384811\pi$
$312$	3.16228	+	1.73205i	0.179029	+	0.0980581i
$313$	−17.6491			−0.997587			−0.498793	−	0.866721i	$-0.666223\pi$
$313$	−17.6491			−0.997587			−0.498793	+	0.866721i	$0.666223\pi$
$314$	4.91886	+	8.51972i	0.277587	+	0.480795i
$315$		0			0
$316$	−4.58114	+	7.93477i	−0.257709	+	0.446365i
$317$	−0.188612			−0.0105935			−0.00529674	−	0.999986i	$-0.501686\pi$
$317$	−0.188612			−0.0105935			−0.00529674	+	0.999986i	$0.501686\pi$
$318$	−3.58114	+	6.20271i	−0.200820	+	0.347831i
$319$	12.4868	−	21.6278i	0.699128	−	1.21093i
$320$		0			0
$321$	−3.00000	+	5.19615i	−0.167444	+	0.290021i
$322$	6.58114	+	11.3989i	0.366753	+	0.635234i
$323$	11.3246	+	19.6147i	0.630115	+	1.09139i
$324$	1.00000			0.0555556
$325$		0			0
$326$	15.8114			0.875712
$327$	−4.24342	−	7.34981i	−0.234661	−	0.406446i
$328$	−4.74342	−	8.21584i	−0.261911	−	0.453644i
$329$	9.48683	−	16.4317i	0.523026	−	0.905908i
$330$		0			0
$331$	4.41886	−	7.65369i	0.242883	−	0.420685i	−0.718652	−	0.695370i	$-0.755240\pi$
$331$	4.41886	−	7.65369i	0.242883	−	0.420685i	0.961534	+	0.274685i	$0.0885737\pi$
$332$	−6.82456	+	11.8205i	−0.374546	+	0.648733i
$333$	−10.4868			−0.574675
$334$	0.918861	−	1.59151i	0.0502778	−	0.0870838i
$335$		0			0
$336$	−1.58114	−	2.73861i	−0.0862582	−	0.149404i
$337$	−4.00000			−0.217894			−0.108947	−	0.994048i	$-0.534748\pi$
$337$	−4.00000			−0.217894			−0.108947	+	0.994048i	$0.534748\pi$
$338$	12.9868	−	0.584952i	0.706391	−	0.0318172i
$339$	−2.32456			−0.126253
$340$		0			0
$341$	−13.7434	−	23.8043i	−0.744248	−	1.28907i
$342$	1.58114	−	2.73861i	0.0854982	−	0.148087i
$343$	−12.6491			−0.682988
$344$	−2.58114	+	4.47066i	−0.139166	+	0.241042i
$345$		0			0
$346$	14.3246			0.770093
$347$	5.66228	−	9.80735i	0.303967	−	0.526486i	−0.673064	−	0.739584i	$-0.735022\pi$
$347$	5.66228	−	9.80735i	0.303967	−	0.526486i	0.977031	+	0.213098i	$0.0683554\pi$
$348$	4.16228	+	7.20928i	0.223122	+	0.386458i
$349$	−10.7302	−	18.5853i	−0.574377	−	0.994850i	−0.996109	−	0.0881297i	$-0.971911\pi$
$349$	−10.7302	−	18.5853i	−0.574377	−	0.994850i	0.421732	−	0.906721i	$-0.361422\pi$
$350$		0			0
$351$	3.08114	−	1.87259i	0.164459	−	0.0999513i
$352$	−3.00000			−0.159901
$353$	−5.90569	−	10.2290i	−0.314328	−	0.544433i	0.664966	−	0.746874i	$-0.268446\pi$
$353$	−5.90569	−	10.2290i	−0.314328	−	0.544433i	−0.979295	+	0.202441i	$0.935113\pi$
$354$	−3.00000	−	5.19615i	−0.159448	−	0.276172i
$355$		0			0
$356$	−7.16228			−0.379600
$357$	11.3246	−	19.6147i	0.599359	−	1.03812i
$358$	−0.824555	+	1.42817i	−0.0435791	+	0.0754812i
$359$	−12.0000			−0.633336			−0.316668	−	0.948536i	$-0.602564\pi$
$359$	−12.0000			−0.633336			−0.316668	+	0.948536i	$0.602564\pi$
$360$		0			0
$361$	4.50000	+	7.79423i	0.236842	+	0.410223i
$362$	−9.40569	−	16.2911i	−0.494352	−	0.856243i
$363$	−2.00000			−0.104973
$364$	−10.0000	−	5.47723i	−0.524142	−	0.287085i
$365$		0			0
$366$	7.24342	+	12.5460i	0.378619	+	0.655788i
$367$	−3.32456	−	5.75830i	−0.173540	−	0.300581i	0.766115	−	0.642704i	$-0.222187\pi$
$367$	−3.32456	−	5.75830i	−0.173540	−	0.300581i	−0.939655	+	0.342123i	$0.888854\pi$
$368$	−2.08114	+	3.60464i	−0.108487	+	0.187905i
$369$	−9.48683			−0.493865
$370$		0			0
$371$	11.3246	−	19.6147i	0.587942	−	1.01834i
$372$	9.16228			0.475042
$373$	−4.24342	+	7.34981i	−0.219716	+	0.380559i	−0.954721	−	0.297503i	$-0.903846\pi$
$373$	−4.24342	+	7.34981i	−0.219716	+	0.380559i	0.735005	+	0.678061i	$0.237180\pi$
$374$	−10.7434	−	18.6081i	−0.555529	−	0.962204i
$375$		0			0
$376$	6.00000			0.309426
$377$	26.3246	+	14.4186i	1.35578	+	0.742593i
$378$	−3.16228			−0.162650
$379$	−1.00000	−	1.73205i	−0.0513665	−	0.0889695i	0.839199	−	0.543825i	$-0.183024\pi$
$379$	−1.00000	−	1.73205i	−0.0513665	−	0.0889695i	−0.890565	+	0.454855i	$0.849691\pi$
$380$		0			0
$381$	3.83772	−	6.64713i	0.196612	−	0.340543i
$382$	−22.1623			−1.13392
$383$	−2.08114	+	3.60464i	−0.106341	+	0.184188i	−0.914285	−	0.405071i	$-0.867247\pi$
$383$	−2.08114	+	3.60464i	−0.106341	+	0.184188i	0.807944	+	0.589259i	$0.200580\pi$
$384$	0.500000	−	0.866025i	0.0255155	−	0.0441942i
$385$		0			0
$386$	−2.33772	+	4.04905i	−0.118987	+	0.206091i
$387$	2.58114	+	4.47066i	0.131207	+	0.227257i
$388$	2.33772	+	4.04905i	0.118680	+	0.205560i
$389$	−15.6754			−0.794777			−0.397388	−	0.917651i	$-0.630083\pi$
$389$	−15.6754			−0.794777			−0.397388	+	0.917651i	$0.630083\pi$
$390$		0			0
$391$	−29.8114			−1.50763
$392$	1.50000	+	2.59808i	0.0757614	+	0.131223i
$393$	−1.83772	−	3.18303i	−0.0927008	−	0.160563i
$394$	−3.00000	+	5.19615i	−0.151138	+	0.261778i
$395$		0			0
$396$	−1.50000	+	2.59808i	−0.0753778	+	0.130558i
$397$	12.1623	−	21.0657i	0.610407	−	1.05726i	−0.380765	−	0.924672i	$-0.624339\pi$
$397$	12.1623	−	21.0657i	0.610407	−	1.05726i	0.991172	−	0.132584i	$-0.0423275\pi$
$398$	−15.1623			−0.760016
$399$	−5.00000	+	8.66025i	−0.250313	+	0.433555i
$400$		0			0
$401$	−1.83772	−	3.18303i	−0.0917715	−	0.158953i	0.816485	−	0.577366i	$-0.195920\pi$
$401$	−1.83772	−	3.18303i	−0.0917715	−	0.158953i	−0.908257	+	0.418414i	$0.862586\pi$
$402$	4.00000			0.199502
$403$	28.2302	−	17.1572i	1.40625	−	0.854659i
$404$	−16.6491			−0.828324
$405$		0			0
$406$	−13.1623	−	22.7977i	−0.653233	−	1.13143i
$407$	15.7302	−	27.2456i	0.779720	−	1.35051i
$408$	7.16228			0.354586
$409$	−8.83772	+	15.3074i	−0.436997	+	0.756901i	−0.997456	−	0.0712807i	$-0.977291\pi$
$409$	−8.83772	+	15.3074i	−0.436997	+	0.756901i	0.560459	+	0.828182i	$0.310625\pi$
$410$		0			0
$411$	−12.0000			−0.591916
$412$	6.74342	−	11.6799i	0.332224	−	0.575429i
$413$	9.48683	+	16.4317i	0.466817	+	0.808550i
$414$	2.08114	+	3.60464i	0.102282	+	0.177158i
$415$		0			0
$416$	−0.0811388	−	3.60464i	−0.00397816	−	0.176732i
$417$	−18.3246			−0.897357
$418$	4.74342	+	8.21584i	0.232008	+	0.401850i
$419$	−4.50000	−	7.79423i	−0.219839	−	0.380773i	0.734919	−	0.678155i	$-0.237220\pi$
$419$	−4.50000	−	7.79423i	−0.219839	−	0.380773i	−0.954759	+	0.297382i	$0.903887\pi$
$420$		0			0
$421$	21.8377			1.06431			0.532153	−	0.846648i	$-0.321383\pi$
$421$	21.8377			1.06431			0.532153	+	0.846648i	$0.321383\pi$
$422$	3.41886	−	5.92164i	0.166428	−	0.288261i
$423$	3.00000	−	5.19615i	0.145865	−	0.252646i
$424$	7.16228			0.347831
$425$		0			0
$426$	−3.91886	−	6.78767i	−0.189869	−	0.328864i
$427$	−22.9057	−	39.6738i	−1.10848	−	1.91995i
$428$	6.00000			0.290021
$429$	0.243416	+	10.8139i	0.0117523	+	0.522101i
$430$		0			0
$431$	2.75658	+	4.77454i	0.132780	+	0.229982i	0.924747	−	0.380582i	$-0.124276\pi$
$431$	2.75658	+	4.77454i	0.132780	+	0.229982i	−0.791967	+	0.610564i	$0.790943\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	−14.3114	+	24.7881i	−0.687761	+	1.19124i	0.284799	+	0.958587i	$0.408073\pi$
$433$	−14.3114	+	24.7881i	−0.687761	+	1.19124i	−0.972560	+	0.232650i	$0.925260\pi$
$434$	−28.9737			−1.39078
$435$		0			0
$436$	−4.24342	+	7.34981i	−0.203223	+	0.351992i
$437$	13.1623			0.629637
$438$	0.662278	−	1.14710i	0.0316449	−	0.0548105i
$439$	5.67544	+	9.83016i	0.270874	+	0.469168i	0.969086	−	0.246723i	$-0.0793539\pi$
$439$	5.67544	+	9.83016i	0.270874	+	0.469168i	−0.698212	+	0.715891i	$0.746021\pi$
$440$		0			0
$441$	3.00000			0.142857
$442$	22.0680	−	13.4120i	1.04967	−	0.637943i
$443$	−9.00000			−0.427603			−0.213801	−	0.976877i	$-0.568585\pi$
$443$	−9.00000			−0.427603			−0.213801	+	0.976877i	$0.568585\pi$
$444$	5.24342	+	9.08186i	0.248842	+	0.431006i
$445$		0			0
$446$	−9.06797	+	15.7062i	−0.429381	+	0.743710i
$447$	−13.1623			−0.622554
$448$	−1.58114	+	2.73861i	−0.0747018	+	0.129387i
$449$	−10.7434	+	18.6081i	−0.507013	+	0.878173i	0.492954	+	0.870055i	$0.335917\pi$
$449$	−10.7434	+	18.6081i	−0.507013	+	0.878173i	−0.999967	+	0.00811713i	$0.997416\pi$
$450$		0			0
$451$	14.2302	−	24.6475i	0.670076	−	1.16061i
$452$	1.16228	+	2.01312i	0.0546689	+	0.0946894i
$453$	10.9057	+	18.8892i	0.512394	+	0.887493i
$454$	15.9737			0.749681
$455$		0			0
$456$	−3.16228			−0.148087
$457$	17.8246	+	30.8730i	0.833798	+	1.44418i	0.895006	+	0.446055i	$0.147171\pi$
$457$	17.8246	+	30.8730i	0.833798	+	1.44418i	−0.0612082	+	0.998125i	$0.519495\pi$
$458$	1.24342	+	2.15366i	0.0581010	+	0.100634i
$459$	3.58114	−	6.20271i	0.167153	−	0.289518i
$460$		0			0
$461$	5.41886	−	9.38574i	0.252382	−	0.437138i	−0.711799	−	0.702383i	$-0.752120\pi$
$461$	5.41886	−	9.38574i	0.252382	−	0.437138i	0.964181	+	0.265245i	$0.0854529\pi$
$462$	4.74342	−	8.21584i	0.220684	−	0.382235i
$463$	23.4868			1.09153			0.545763	−	0.837940i	$-0.316240\pi$
$463$	23.4868			1.09153			0.545763	+	0.837940i	$0.316240\pi$
$464$	4.16228	−	7.20928i	0.193229	−	0.334682i
$465$		0			0
$466$	13.1623	+	22.7977i	0.609731	+	1.05608i
$467$	−3.00000			−0.138823			−0.0694117	−	0.997588i	$-0.522112\pi$
$467$	−3.00000			−0.138823			−0.0694117	+	0.997588i	$0.522112\pi$
$468$	−3.16228	−	1.73205i	−0.146176	−	0.0800641i
$469$	−12.6491			−0.584082
$470$		0			0
$471$	−4.91886	−	8.51972i	−0.226649	−	0.392568i
$472$	−3.00000	+	5.19615i	−0.138086	+	0.239172i
$473$	−15.4868			−0.712085
$474$	4.58114	−	7.93477i	0.210419	−	0.364456i
$475$		0			0
$476$	−22.6491			−1.03812
$477$	3.58114	−	6.20271i	0.163969	−	0.284003i
$478$	−0.243416	−	0.421610i	−0.0111336	−	0.0192840i
$479$	13.1623	+	22.7977i	0.601400	+	1.04166i	0.992609	+	0.121353i	$0.0387234\pi$
$479$	13.1623	+	22.7977i	0.601400	+	1.04166i	−0.391210	+	0.920302i	$0.627943\pi$
$480$		0			0
$481$	33.1623	+	18.1637i	1.51207	+	0.828195i
$482$	−8.00000			−0.364390
$483$	−6.58114	−	11.3989i	−0.299452	−	0.518666i
$484$	1.00000	+	1.73205i	0.0454545	+	0.0787296i
$485$		0			0
$486$	−1.00000			−0.0453609
$487$	−1.58114	+	2.73861i	−0.0716482	+	0.124098i	−0.899624	−	0.436666i	$-0.856159\pi$
$487$	−1.58114	+	2.73861i	−0.0716482	+	0.124098i	0.827976	+	0.560764i	$0.189493\pi$
$488$	7.24342	−	12.5460i	0.327894	−	0.567929i
$489$	−15.8114			−0.715016
$490$		0			0
$491$	−7.98683	−	13.8336i	−0.360441	−	0.624302i	0.627593	−	0.778542i	$-0.284040\pi$
$491$	−7.98683	−	13.8336i	−0.360441	−	0.624302i	−0.988033	+	0.154240i	$0.950707\pi$
$492$	4.74342	+	8.21584i	0.213850	+	0.370399i
$493$	59.6228			2.68527
$494$	−9.74342	+	5.92164i	−0.438377	+	0.266427i
$495$		0			0
$496$	−4.58114	−	7.93477i	−0.205699	−	0.356281i
$497$	12.3925	+	21.4645i	0.555881	+	0.962814i
$498$	6.82456	−	11.8205i	0.305816	−	0.529688i
$499$	8.18861			0.366573			0.183286	−	0.983060i	$-0.441326\pi$
$499$	8.18861			0.366573			0.183286	+	0.983060i	$0.441326\pi$
$500$		0			0
$501$	−0.918861	+	1.59151i	−0.0410517	+	0.0711036i
$502$	−15.0000			−0.669483
$503$	−7.40569	+	12.8270i	−0.330204	+	0.571929i	−0.982552	−	0.185990i	$-0.940451\pi$
$503$	−7.40569	+	12.8270i	−0.330204	+	0.571929i	0.652348	+	0.757920i	$0.273784\pi$
$504$	1.58114	+	2.73861i	0.0704295	+	0.121988i
$505$		0			0
$506$	−12.4868			−0.555107
$507$	−12.9868	+	0.584952i	−0.576766	+	0.0259786i
$508$	−7.67544			−0.340543
$509$	−21.3925	−	37.0529i	−0.948207	−	1.64234i	−0.749199	−	0.662345i	$-0.769561\pi$
$509$	−21.3925	−	37.0529i	−0.948207	−	1.64234i	−0.199008	−	0.979998i	$-0.563772\pi$
$510$		0			0
$511$	−2.09431	+	3.62744i	−0.0926466	+	0.160469i
$512$	−1.00000			−0.0441942
$513$	−1.58114	+	2.73861i	−0.0698090	+	0.120913i
$514$	2.90569	−	5.03281i	0.128165	−	0.221988i
$515$		0			0
$516$	2.58114	−	4.47066i	0.113628	−	0.196810i
$517$	9.00000	+	15.5885i	0.395820	+	0.685580i
$518$	−16.5811	−	28.7194i	−0.728533	−	1.26186i
$519$	−14.3246			−0.628778
$520$		0			0
$521$	4.64911			0.203681			0.101841	−	0.994801i	$-0.467527\pi$
$521$	4.64911			0.203681			0.101841	+	0.994801i	$0.467527\pi$
$522$	−4.16228	−	7.20928i	−0.182178	−	0.315541i
$523$	2.48683	+	4.30732i	0.108742	+	0.188346i	0.915261	−	0.402862i	$-0.131985\pi$
$523$	2.48683	+	4.30732i	0.108742	+	0.188346i	−0.806519	+	0.591208i	$0.798651\pi$
$524$	−1.83772	+	3.18303i	−0.0802813	+	0.139051i
$525$		0			0
$526$	9.24342	−	16.0101i	0.403032	−	0.698072i
$527$	32.8114	−	56.8310i	1.42929	−	2.47560i
$528$	3.00000			0.130558
$529$	2.83772	−	4.91508i	0.123379	−	0.213699i
$530$		0			0
$531$	3.00000	+	5.19615i	0.130189	+	0.225494i
$532$	10.0000			0.433555
$533$	30.0000	+	16.4317i	1.29944	+	0.711735i
$534$	7.16228			0.309942
$535$		0			0
$536$	−2.00000	−	3.46410i	−0.0863868	−	0.149626i
$537$	0.824555	−	1.42817i	0.0355822	−	0.0616302i
$538$	19.1623			0.826144
$539$	−4.50000	+	7.79423i	−0.193829	+	0.335721i
$540$		0			0
$541$	−0.811388			−0.0348843			−0.0174422	−	0.999848i	$-0.505552\pi$
$541$	−0.811388			−0.0348843			−0.0174422	+	0.999848i	$0.505552\pi$
$542$	−6.16228	+	10.6734i	−0.264692	+	0.458461i
$543$	9.40569	+	16.2911i	0.403637	+	0.699120i
$544$	−3.58114	−	6.20271i	−0.153540	−	0.265939i
$545$		0			0
$546$	10.0000	+	5.47723i	0.427960	+	0.234404i
$547$	−30.1359			−1.28852			−0.644260	−	0.764807i	$-0.722835\pi$
$547$	−30.1359			−1.28852			−0.644260	+	0.764807i	$0.722835\pi$
$548$	6.00000	+	10.3923i	0.256307	+	0.443937i
$549$	−7.24342	−	12.5460i	−0.309141	−	0.535449i
$550$		0			0
$551$	−26.3246			−1.12146
$552$	2.08114	−	3.60464i	0.0885792	−	0.153424i
$553$	−14.4868	+	25.0919i	−0.616043	+	1.06702i
$554$	−22.8114			−0.969163
$555$		0			0
$556$	9.16228	+	15.8695i	0.388567	+	0.673018i
$557$	9.48683	+	16.4317i	0.401970	+	0.696232i	0.993964	−	0.109710i	$-0.0349923\pi$
$557$	9.48683	+	16.4317i	0.401970	+	0.696232i	−0.591994	+	0.805943i	$0.701659\pi$
$558$	−9.16228			−0.387870
$559$	−0.418861	−	18.6081i	−0.0177159	−	0.787041i
$560$		0			0
$561$	10.7434	+	18.6081i	0.453587	+	0.785636i
$562$	−1.25658	−	2.17647i	−0.0530058	−	0.0918087i
$563$	1.98683	−	3.44130i	0.0837350	−	0.145033i	−0.821116	−	0.570761i	$-0.806648\pi$
$563$	1.98683	−	3.44130i	0.0837350	−	0.145033i	0.904851	+	0.425727i	$0.139982\pi$
$564$	−6.00000			−0.252646
$565$		0			0
$566$	−0.256584	+	0.444416i	−0.0107850	+	0.0186802i
$567$	3.16228			0.132803
$568$	−3.91886	+	6.78767i	−0.164432	+	0.284804i
$569$	−15.4868	−	26.8240i	−0.649242	−	1.12452i	−0.983304	−	0.181969i	$-0.941753\pi$
$569$	−15.4868	−	26.8240i	−0.649242	−	1.12452i	0.334062	−	0.942551i	$-0.391580\pi$
$570$		0			0
$571$	−19.6754			−0.823392			−0.411696	−	0.911321i	$-0.635063\pi$
$571$	−19.6754			−0.823392			−0.411696	+	0.911321i	$0.635063\pi$
$572$	9.24342	−	5.61776i	0.386487	−	0.234890i
$573$	22.1623			0.925842
$574$	−15.0000	−	25.9808i	−0.626088	−	1.08442i
$575$		0			0
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−43.0000			−1.79011			−0.895057	−	0.445952i	$-0.852865\pi$
$577$	−43.0000			−1.79011			−0.895057	+	0.445952i	$0.852865\pi$
$578$	17.1491	−	29.7031i	0.713309	−	1.23549i
$579$	2.33772	−	4.04905i	0.0971524	−	0.168273i
$580$		0			0
$581$	−21.5811	+	37.3796i	−0.895337	+	1.55077i
$582$	−2.33772	−	4.04905i	−0.0969017	−	0.167839i
$583$	10.7434	+	18.6081i	0.444947	+	0.770671i
$584$	−1.32456			−0.0548105
$585$		0			0
$586$	−2.51317			−0.103818
$587$	10.5000	+	18.1865i	0.433381	+	0.750639i	0.997162	−	0.0752860i	$-0.0239870\pi$
$587$	10.5000	+	18.1865i	0.433381	+	0.750639i	−0.563781	+	0.825925i	$0.690654\pi$
$588$	−1.50000	−	2.59808i	−0.0618590	−	0.107143i
$589$	−14.4868	+	25.0919i	−0.596920	+	1.03389i
$590$		0			0
$591$	3.00000	−	5.19615i	0.123404	−	0.213741i
$592$	5.24342	−	9.08186i	0.215503	−	0.373262i
$593$	1.16228			0.0477290			0.0238645	−	0.999715i	$-0.492403\pi$
$593$	1.16228			0.0477290			0.0238645	+	0.999715i	$0.492403\pi$
$594$	1.50000	−	2.59808i	0.0615457	−	0.106600i
$595$		0			0
$596$	6.58114	+	11.3989i	0.269574	+	0.466916i
$597$	15.1623			0.620551
$598$	−0.337722	−	15.0035i	−0.0138105	−	0.613539i
$599$	32.8114			1.34064			0.670318	−	0.742074i	$-0.266157\pi$
$599$	32.8114			1.34064			0.670318	+	0.742074i	$0.266157\pi$
$600$		0			0
$601$	3.64911	+	6.32045i	0.148850	+	0.257816i	0.930803	−	0.365522i	$-0.119109\pi$
$601$	3.64911	+	6.32045i	0.148850	+	0.257816i	−0.781952	+	0.623338i	$0.785776\pi$
$602$	−8.16228	+	14.1375i	−0.332670	+	0.576201i
$603$	−4.00000			−0.162893
$604$	10.9057	−	18.8892i	0.443746	−	0.768591i
$605$		0			0
$606$	16.6491			0.676324
$607$	−11.8377	+	20.5035i	−0.480478	+	0.832213i	−0.999749	−	0.0223969i	$-0.992870\pi$
$607$	−11.8377	+	20.5035i	−0.480478	+	0.832213i	0.519271	+	0.854610i	$0.326204\pi$
$608$	1.58114	+	2.73861i	0.0641236	+	0.111065i
$609$	13.1623	+	22.7977i	0.533362	+	0.923811i
$610$		0			0
$611$	−18.4868	+	11.2355i	−0.747897	+	0.454541i
$612$	−7.16228			−0.289518
$613$	−14.8377	−	25.6997i	−0.599290	−	1.03800i	−0.992926	−	0.118734i	$-0.962116\pi$
$613$	−14.8377	−	25.6997i	−0.599290	−	1.03800i	0.393636	−	0.919266i	$-0.371217\pi$
$614$	−4.32456	−	7.49035i	−0.174525	−	0.302286i
$615$		0			0
$616$	−9.48683			−0.382235
$617$	−1.64911	+	2.85634i	−0.0663907	+	0.114992i	−0.897310	−	0.441401i	$-0.854482\pi$
$617$	−1.64911	+	2.85634i	−0.0663907	+	0.114992i	0.830919	+	0.556393i	$0.187815\pi$
$618$	−6.74342	+	11.6799i	−0.271260	+	0.469836i
$619$	8.00000			0.321547			0.160774	−	0.986991i	$-0.448601\pi$
$619$	8.00000			0.321547			0.160774	+	0.986991i	$0.448601\pi$
$620$		0			0
$621$	−2.08114	−	3.60464i	−0.0835132	−	0.144649i
$622$	6.24342	+	10.8139i	0.250338	+	0.433598i
$623$	−22.6491			−0.907417
$624$	0.0811388	+	3.60464i	0.00324815	+	0.144301i
$625$		0			0
$626$	−8.82456	−	15.2846i	−0.352700	−	0.610895i
$627$	−4.74342	−	8.21584i	−0.189434	−	0.328109i
$628$	−4.91886	+	8.51972i	−0.196284	+	0.339974i
$629$	75.1096			2.99482
$630$		0			0
$631$	−17.6491	+	30.5692i	−0.702600	+	1.21694i	0.264951	+	0.964262i	$0.414644\pi$
$631$	−17.6491	+	30.5692i	−0.702600	+	1.21694i	−0.967551	+	0.252677i	$0.918689\pi$
$632$	−9.16228			−0.364456
$633$	−3.41886	+	5.92164i	−0.135888	+	0.235364i
$634$	−0.0943058	−	0.163343i	−0.00374536	−	0.00648716i
$635$		0			0
$636$	−7.16228			−0.284003
$637$	−9.48683	−	5.19615i	−0.375882	−	0.205879i
$638$	24.9737			0.988717
$639$	3.91886	+	6.78767i	0.155028	+	0.268516i
$640$		0			0
$641$	24.9737	−	43.2557i	0.986400	−	1.70850i	0.350861	−	0.936428i	$-0.385889\pi$
$641$	24.9737	−	43.2557i	0.986400	−	1.70850i	0.635540	−	0.772068i	$-0.280778\pi$
$642$	−6.00000			−0.236801
$643$	12.1623	−	21.0657i	0.479633	−	0.830749i	−0.520094	−	0.854109i	$-0.674103\pi$
$643$	12.1623	−	21.0657i	0.479633	−	0.830749i	0.999727	+	0.0233598i	$0.00743632\pi$
$644$	−6.58114	+	11.3989i	−0.259333	+	0.449178i
$645$		0			0
$646$	−11.3246	+	19.6147i	−0.445559	+	0.771730i
$647$	21.2434	+	36.7947i	0.835165	+	1.44655i	0.893896	+	0.448274i	$0.147961\pi$
$647$	21.2434	+	36.7947i	0.835165	+	1.44655i	−0.0587312	+	0.998274i	$0.518705\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	−18.0000			−0.706562
$650$		0			0
$651$	28.9737			1.13557
$652$	7.90569	+	13.6931i	0.309611	+	0.536262i
$653$	−4.74342	−	8.21584i	−0.185624	−	0.321511i	0.758162	−	0.652066i	$-0.226097\pi$
$653$	−4.74342	−	8.21584i	−0.185624	−	0.321511i	−0.943787	+	0.330555i	$0.892764\pi$
$654$	4.24342	−	7.34981i	0.165931	−	0.287400i
$655$		0			0
$656$	4.74342	−	8.21584i	0.185199	−	0.320775i
$657$	−0.662278	+	1.14710i	−0.0258379	+	0.0447526i
$658$	18.9737			0.739671
$659$	7.50000	−	12.9904i	0.292159	−	0.506033i	−0.682161	−	0.731202i	$-0.738960\pi$
$659$	7.50000	−	12.9904i	0.292159	−	0.506033i	0.974320	+	0.225168i	$0.0722932\pi$
$660$		0			0
$661$	−13.0000	−	22.5167i	−0.505641	−	0.875797i	−0.999979	−	0.00652642i	$-0.997923\pi$
$661$	−13.0000	−	22.5167i	−0.505641	−	0.875797i	0.494337	−	0.869270i	$-0.335411\pi$
$662$	8.83772			0.343488
$663$	−22.0680	+	13.4120i	−0.857049	+	0.520879i
$664$	−13.6491			−0.529688
$665$		0			0
$666$	−5.24342	−	9.08186i	−0.203178	−	0.351915i
$667$	17.3246	−	30.0070i	0.670809	−	1.16188i
$668$	1.83772			0.0711036
$669$	9.06797	−	15.7062i	0.350588	−	0.607236i
$670$		0			0
$671$	43.4605			1.67777
$672$	1.58114	−	2.73861i	0.0609938	−	0.105644i
$673$	−10.8246	−	18.7487i	−0.417256	−	0.722708i	0.578406	−	0.815749i	$-0.303675\pi$
$673$	−10.8246	−	18.7487i	−0.417256	−	0.722708i	−0.995662	+	0.0930403i	$0.970341\pi$
$674$	−2.00000	−	3.46410i	−0.0770371	−	0.133432i
$675$		0			0
$676$	7.00000	+	10.9545i	0.269231	+	0.421325i
$677$	−7.35089			−0.282518			−0.141259	−	0.989973i	$-0.545115\pi$
$677$	−7.35089			−0.282518			−0.141259	+	0.989973i	$0.545115\pi$
$678$	−1.16228	−	2.01312i	−0.0446370	−	0.0773136i
$679$	7.39253	+	12.8042i	0.283699	+	0.491381i
$680$		0			0
$681$	−15.9737			−0.612112
$682$	13.7434	−	23.8043i	0.526263	−	0.911514i
$683$	−23.4737	+	40.6576i	−0.898195	+	1.55572i	−0.0683948	+	0.997658i	$0.521788\pi$
$683$	−23.4737	+	40.6576i	−0.898195	+	1.55572i	−0.829800	+	0.558061i	$0.811546\pi$
$684$	3.16228			0.120913
$685$		0			0
$686$	−6.32456	−	10.9545i	−0.241473	−	0.418243i
$687$	−1.24342	−	2.15366i	−0.0474393	−	0.0821673i
$688$	−5.16228			−0.196810
$689$	−22.0680	+	13.4120i	−0.840723	+	0.510956i
$690$		0			0
$691$	−25.9737	−	44.9877i	−0.988085	−	1.71141i	−0.627333	−	0.778751i	$-0.715853\pi$
$691$	−25.9737	−	44.9877i	−0.988085	−	1.71141i	−0.360752	−	0.932662i	$-0.617480\pi$
$692$	7.16228	+	12.4054i	0.272269	+	0.471584i
$693$	−4.74342	+	8.21584i	−0.180187	+	0.312094i
$694$	11.3246			0.429874
$695$		0			0
$696$	−4.16228	+	7.20928i	−0.157771	+	0.273267i
$697$	67.9473			2.57369
$698$	10.7302	−	18.5853i	0.406146	−	0.703465i
$699$	−13.1623	−	22.7977i	−0.497843	−	0.862289i
$700$		0			0
$701$	34.4605			1.30156			0.650778	−	0.759268i	$-0.274443\pi$
$701$	34.4605			1.30156			0.650778	+	0.759268i	$0.274443\pi$
$702$	3.16228	+	1.73205i	0.119352	+	0.0653720i
$703$	−33.1623			−1.25074
$704$	−1.50000	−	2.59808i	−0.0565334	−	0.0979187i
$705$		0			0
$706$	5.90569	−	10.2290i	0.222264	−	0.384972i
$707$	−52.6491			−1.98007
$708$	3.00000	−	5.19615i	0.112747	−	0.195283i
$709$	−10.2434	+	17.7421i	−0.384700	+	0.666319i	−0.991727	−	0.128361i	$-0.959028\pi$
$709$	−10.2434	+	17.7421i	−0.384700	+	0.666319i	0.607028	+	0.794681i	$0.292362\pi$
$710$		0			0
$711$	−4.58114	+	7.93477i	−0.171806	+	0.297577i
$712$	−3.58114	−	6.20271i	−0.134209	−	0.232457i
$713$	−19.0680	−	33.0267i	−0.714101	−	1.23686i
$714$	22.6491			0.847622
$715$		0			0
$716$	−1.64911			−0.0616302
$717$	0.243416	+	0.421610i	0.00909056	+	0.0157453i
$718$	−6.00000	−	10.3923i	−0.223918	−	0.387837i
$719$	7.59431	−	13.1537i	0.283220	−	0.490551i	−0.688956	−	0.724803i	$-0.741931\pi$
$719$	7.59431	−	13.1537i	0.283220	−	0.490551i	0.972176	+	0.234252i	$0.0752641\pi$
$720$		0			0
$721$	21.3246	−	36.9352i	0.794168	−	1.37554i
$722$	−4.50000	+	7.79423i	−0.167473	+	0.290071i
$723$	8.00000			0.297523
$724$	9.40569	−	16.2911i	0.349560	−	0.605455i
$725$		0			0
$726$	−1.00000	−	1.73205i	−0.0371135	−	0.0642824i
$727$	−0.324555			−0.0120371			−0.00601855	−	0.999982i	$-0.501916\pi$
$727$	−0.324555			−0.0120371			−0.00601855	+	0.999982i	$0.501916\pi$
$728$	−0.256584	−	11.3989i	−0.00950962	−	0.422470i
$729$	1.00000			0.0370370
$730$		0			0
$731$	−18.4868	−	32.0201i	−0.683760	−	1.18431i
$732$	−7.24342	+	12.5460i	−0.267724	+	0.463712i
$733$	38.4868			1.42154			0.710772	−	0.703423i	$-0.248346\pi$
$733$	38.4868			1.42154			0.710772	+	0.703423i	$0.248346\pi$
$734$	3.32456	−	5.75830i	0.122712	−	0.212543i
$735$		0			0
$736$	−4.16228			−0.153424
$737$	6.00000	−	10.3923i	0.221013	−	0.382805i
$738$	−4.74342	−	8.21584i	−0.174608	−	0.302429i
$739$	15.6491	+	27.1051i	0.575662	+	0.997076i	0.995969	+	0.0896938i	$0.0285889\pi$
$739$	15.6491	+	27.1051i	0.575662	+	0.997076i	−0.420308	+	0.907382i	$0.638078\pi$
$740$		0			0
$741$	9.74342	−	5.92164i	0.357933	−	0.217537i
$742$	22.6491			0.831475
$743$	9.67544	+	16.7584i	0.354958	+	0.614805i	0.987111	−	0.160039i	$-0.0511620\pi$
$743$	9.67544	+	16.7584i	0.354958	+	0.614805i	−0.632153	+	0.774844i	$0.717829\pi$
$744$	4.58114	+	7.93477i	0.167953	+	0.290903i
$745$		0			0
$746$	−8.48683			−0.310725
$747$	−6.82456	+	11.8205i	−0.249697	+	0.432489i
$748$	10.7434	−	18.6081i	0.392818	−	0.680381i
$749$	18.9737			0.693283
$750$		0			0
$751$	15.1623	+	26.2618i	0.553279	+	0.958308i	0.998035	+	0.0626561i	$0.0199571\pi$
$751$	15.1623	+	26.2618i	0.553279	+	0.958308i	−0.444756	+	0.895652i	$0.646710\pi$
$752$	3.00000	+	5.19615i	0.109399	+	0.189484i
$753$	15.0000			0.546630
$754$	0.675445	+	30.0070i	0.0245982	+	1.09279i
$755$		0			0
$756$	−1.58114	−	2.73861i	−0.0575055	−	0.0996024i
$757$	−13.4868	−	23.3599i	−0.490187	−	0.849029i	0.509749	−	0.860323i	$-0.329738\pi$
$757$	−13.4868	−	23.3599i	−0.490187	−	0.849029i	−0.999936	+	0.0112939i	$0.996405\pi$
$758$	1.00000	−	1.73205i	0.0363216	−	0.0629109i
$759$	12.4868			0.453243
$760$		0			0
$761$	−5.23025	+	9.05906i	−0.189596	+	0.328391i	−0.945116	−	0.326736i	$-0.894051\pi$
$761$	−5.23025	+	9.05906i	−0.189596	+	0.328391i	0.755519	+	0.655126i	$0.227385\pi$
$762$	7.67544			0.278052
$763$	−13.4189	+	23.2421i	−0.485795	+	0.841422i
$764$	−11.0811	−	19.1931i	−0.400902	−	0.694382i
$765$		0			0
$766$	−4.16228			−0.150389
$767$	−0.486833	−	21.6278i	−0.0175785	−	0.780936i
$768$	1.00000			0.0360844
$769$	11.4868	+	19.8958i	0.414226	+	0.717460i	0.995347	−	0.0963570i	$-0.0307191\pi$
$769$	11.4868	+	19.8958i	0.414226	+	0.717460i	−0.581121	+	0.813817i	$0.697386\pi$
$770$		0			0
$771$	−2.90569	+	5.03281i	−0.104646	+	0.181252i
$772$	−4.67544			−0.168273
$773$	17.3246	−	30.0070i	0.623121	−	1.07928i	−0.365780	−	0.930701i	$-0.619198\pi$
$773$	17.3246	−	30.0070i	0.623121	−	1.07928i	0.988901	−	0.148576i	$-0.0474689\pi$
$774$	−2.58114	+	4.47066i	−0.0927771	+	0.160695i
$775$		0			0
$776$	−2.33772	+	4.04905i	−0.0839193	+	0.145353i
$777$	16.5811	+	28.7194i	0.594845	+	1.03030i
$778$	−7.83772	−	13.5753i	−0.280996	−	0.486699i
$779$	−30.0000			−1.07486
$780$		0			0
$781$	−23.5132			−0.841367
$782$	−14.9057	−	25.8174i	−0.533027	−	0.923229i
$783$	4.16228	+	7.20928i	0.148748	+	0.257639i
$784$	−1.50000	+	2.59808i	−0.0535714	+	0.0927884i
$785$		0			0
$786$	1.83772	−	3.18303i	0.0655494	−	0.113535i
$787$	6.74342	−	11.6799i	0.240377	−	0.416345i	−0.720445	−	0.693512i	$-0.756062\pi$
$787$	6.74342	−	11.6799i	0.240377	−	0.416345i	0.960822	+	0.277167i	$0.0893957\pi$
$788$	−6.00000			−0.213741
$789$	−9.24342	+	16.0101i	−0.329074	+	0.569973i
$790$		0			0
$791$	3.67544	+	6.36606i	0.130684	+	0.226351i
$792$	−3.00000			−0.106600
$793$	1.17544	+	52.2198i	0.0417413	+	1.85438i
$794$	24.3246			0.863246
$795$		0			0
$796$	−7.58114	−	13.1309i	−0.268706	−	0.465413i
$797$	−27.2982	+	47.2819i	−0.966953	+	1.67481i	−0.262678	+	0.964884i	$0.584606\pi$
$797$	−27.2982	+	47.2819i	−0.966953	+	1.67481i	−0.704275	+	0.709927i	$0.748728\pi$
$798$	−10.0000			−0.353996
$799$	−21.4868	+	37.2163i	−0.760150	+	1.31662i
$800$		0			0
$801$	−7.16228			−0.253067
$802$	1.83772	−	3.18303i	0.0648922	−	0.112397i
$803$	−1.98683	−	3.44130i	−0.0701138	−	0.121441i
$804$	2.00000	+	3.46410i	0.0705346	+	0.122169i
$805$		0			0
$806$	28.9737	+	15.8695i	1.02055	+	0.558980i
$807$	−19.1623			−0.674544
$808$	−8.32456	−	14.4186i	−0.292857	−	0.507243i
$809$	9.58114	+	16.5950i	0.336855	+	0.583450i	0.983839	−	0.179053i	$-0.0573035\pi$
$809$	9.58114	+	16.5950i	0.336855	+	0.583450i	−0.646984	+	0.762503i	$0.723970\pi$
$810$		0			0
$811$	18.6491			0.654859			0.327429	−	0.944876i	$-0.393818\pi$
$811$	18.6491			0.654859			0.327429	+	0.944876i	$0.393818\pi$
$812$	13.1623	−	22.7977i	0.461905	−	0.800044i
$813$	6.16228	−	10.6734i	0.216121	−	0.374332i
$814$	31.4605			1.10269
$815$		0			0
$816$	3.58114	+	6.20271i	0.125365	+	0.217138i
$817$	8.16228	+	14.1375i	0.285562	+	0.494608i
$818$	−17.6754			−0.618007
$819$	−10.0000	−	5.47723i	−0.349428	−	0.191390i
$820$		0			0
$821$	4.16228	+	7.20928i	0.145264	+	0.251605i	0.929472	−	0.368894i	$-0.120263\pi$
$821$	4.16228	+	7.20928i	0.145264	+	0.251605i	−0.784207	+	0.620499i	$0.786930\pi$
$822$	−6.00000	−	10.3923i	−0.209274	−	0.362473i
$823$	−7.58114	+	13.1309i	−0.264262	+	0.457715i	−0.967370	−	0.253368i	$-0.918462\pi$
$823$	−7.58114	+	13.1309i	−0.264262	+	0.457715i	0.703108	+	0.711083i	$0.251795\pi$
$824$	13.4868			0.469836
$825$		0			0
$826$	−9.48683	+	16.4317i	−0.330089	+	0.571731i
$827$	−9.97367			−0.346818			−0.173409	−	0.984850i	$-0.555478\pi$
$827$	−9.97367			−0.346818			−0.173409	+	0.984850i	$0.555478\pi$
$828$	−2.08114	+	3.60464i	−0.0723246	+	0.125270i
$829$	−16.4868	−	28.5560i	−0.572611	−	0.991792i	−0.996297	−	0.0859825i	$-0.972597\pi$
$829$	−16.4868	−	28.5560i	−0.572611	−	0.991792i	0.423685	−	0.905809i	$-0.360736\pi$
$830$		0			0
$831$	22.8114			0.791318
$832$	3.08114	−	1.87259i	0.106819	−	0.0649203i
$833$	−21.4868			−0.744475
$834$	−9.16228	−	15.8695i	−0.317264	−	0.549517i
$835$		0			0
$836$	−4.74342	+	8.21584i	−0.164054	+	0.284151i
$837$	9.16228			0.316695
$838$	4.50000	−	7.79423i	0.155450	−	0.269247i
$839$	−16.8925	+	29.2587i	−0.583195	+	1.01012i	0.411903	+	0.911228i	$0.364864\pi$
$839$	−16.8925	+	29.2587i	−0.583195	+	1.01012i	−0.995098	+	0.0988953i	$0.968469\pi$
$840$		0			0
$841$	−20.1491	+	34.8993i	−0.694797	+	1.20342i
$842$	10.9189	+	18.9120i	0.376289	+	0.651751i
$843$	1.25658	+	2.17647i	0.0432790	+	0.0749615i
$844$	6.83772			0.235364
$845$		0			0
$846$	6.00000			0.206284
$847$	3.16228	+	5.47723i	0.108657	+	0.188200i
$848$	3.58114	+	6.20271i	0.122977	+	0.213002i
$849$	0.256584	−	0.444416i	0.00880592	−	0.0152523i
$850$		0			0
$851$	21.8246	−	37.8012i	0.748136	−	1.29581i
$852$	3.91886	−	6.78767i	0.134258	−	0.232542i
$853$	6.64911			0.227661			0.113831	−	0.993500i	$-0.463688\pi$
$853$	6.64911			0.227661			0.113831	+	0.993500i	$0.463688\pi$
$854$	22.9057	−	39.6738i	0.783817	−	1.35761i
$855$		0			0
$856$	3.00000	+	5.19615i	0.102538	+	0.177601i
$857$	−46.2719			−1.58062			−0.790309	−	0.612709i	$-0.790080\pi$
$857$	−46.2719			−1.58062			−0.790309	+	0.612709i	$0.790080\pi$
$858$	−9.24342	+	5.61776i	−0.315565	+	0.191787i
$859$	43.8114			1.49483			0.747413	−	0.664360i	$-0.231296\pi$
$859$	43.8114			1.49483			0.747413	+	0.664360i	$0.231296\pi$
$860$		0			0
$861$	15.0000	+	25.9808i	0.511199	+	0.885422i
$862$	−2.75658	+	4.77454i	−0.0938896	+	0.162622i
$863$	−37.4605			−1.27517			−0.637585	−	0.770380i	$-0.720067\pi$
$863$	−37.4605			−1.27517			−0.637585	+	0.770380i	$0.720067\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$		0			0
$866$	−28.6228			−0.972642
$867$	−17.1491	+	29.7031i	−0.582414	+	1.00877i
$868$	−14.4868	−	25.0919i	−0.491715	−	0.851676i
$869$	−13.7434	−	23.8043i	−0.466213	−	0.807505i
$870$		0			0
$871$	12.6491	+	6.92820i	0.428599	+	0.234753i
$872$	−8.48683			−0.287400
$873$	2.33772	+	4.04905i	0.0791199	+	0.137040i
$874$	6.58114	+	11.3989i	0.222610	+	0.385572i
$875$		0			0
$876$	1.32456			0.0447526
$877$	12.5943	−	21.8140i	0.425279	−	0.736606i	−0.571167	−	0.820834i	$-0.693509\pi$
$877$	12.5943	−	21.8140i	0.425279	−	0.736606i	0.996446	+	0.0842282i	$0.0268425\pi$
$878$	−5.67544	+	9.83016i	−0.191537	+	0.331752i
$879$	2.51317			0.0847670
$880$		0			0
$881$	−17.2302	−	29.8437i	−0.580502	−	1.00546i	−0.995420	−	0.0955999i	$-0.969523\pi$
$881$	−17.2302	−	29.8437i	−0.580502	−	1.00546i	0.414918	−	0.909859i	$-0.363810\pi$
$882$	1.50000	+	2.59808i	0.0505076	+	0.0874818i
$883$	−8.64911			−0.291066			−0.145533	−	0.989353i	$-0.546490\pi$
$883$	−8.64911			−0.291066			−0.145533	+	0.989353i	$0.546490\pi$
$884$	22.6491	+	12.4054i	0.761772	+	0.417240i
$885$		0			0
$886$	−4.50000	−	7.79423i	−0.151180	−	0.261852i
$887$	−8.32456	−	14.4186i	−0.279511	−	0.484128i	0.691752	−	0.722135i	$-0.256839\pi$
$887$	−8.32456	−	14.4186i	−0.279511	−	0.484128i	−0.971263	+	0.238007i	$0.923506\pi$
$888$	−5.24342	+	9.08186i	−0.175958	+	0.304767i
$889$	−24.2719			−0.814053
$890$		0			0
$891$	−1.50000	+	2.59808i	−0.0502519	+	0.0870388i
$892$	−18.1359			−0.607236
$893$	9.48683	−	16.4317i	0.317465	−	0.549865i
$894$	−6.58114	−	11.3989i	−0.220106	−	0.381235i
$895$		0			0
$896$	−3.16228			−0.105644
$897$	0.337722	+	15.0035i	0.0112762	+	0.500952i
$898$	−21.4868			−0.717025
$899$	38.1359	+	66.0534i	1.27190	+	2.20300i
$900$		0			0
$901$	−25.6491	+	44.4256i	−0.854496	+	1.48003i
$902$	28.4605			0.947631
$903$	8.16228	−	14.1375i	0.271624	−	0.470466i
$904$	−1.16228	+	2.01312i	−0.0386568	+	0.0669555i
$905$		0			0
$906$	−10.9057	+	18.8892i	−0.362317	+	0.627552i
$907$	25.4189	+	44.0268i	0.844019	+	1.46188i	0.886470	+	0.462786i	$0.153150\pi$
$907$	25.4189	+	44.0268i	0.844019	+	1.46188i	−0.0424506	+	0.999099i	$0.513517\pi$
$908$	7.98683	+	13.8336i	0.265052	+	0.459084i
$909$	−16.6491			−0.552216
$910$		0			0
$911$	−11.1359			−0.368950			−0.184475	−	0.982837i	$-0.559059\pi$
$911$	−11.1359			−0.368950			−0.184475	+	0.982837i	$0.559059\pi$
$912$	−1.58114	−	2.73861i	−0.0523567	−	0.0906845i
$913$	−20.4737	−	35.4614i	−0.677579	−	1.17360i
$914$	−17.8246	+	30.8730i	−0.589584	+	1.02119i
$915$		0			0
$916$	−1.24342	+	2.15366i	−0.0410836	+	0.0711589i
$917$	−5.81139	+	10.0656i	−0.191909	+	0.332396i
$918$	7.16228			0.236390
$919$	−14.0680	+	24.3664i	−0.464060	+	0.803775i	−0.999159	−	0.0410146i	$-0.986941\pi$
$919$	−14.0680	+	24.3664i	−0.464060	+	0.803775i	0.535099	+	0.844789i	$0.320274\pi$
$920$		0			0
$921$	4.32456	+	7.49035i	0.142499	+	0.246815i
$922$	10.8377			0.356921
$923$	−0.635944	−	28.2522i	−0.0209323	−	0.929931i
$924$	9.48683			0.312094
$925$		0			0
$926$	11.7434	+	20.3402i	0.385913	+	0.668420i
$927$	6.74342	−	11.6799i	0.221483	−	0.383620i
$928$	8.32456			0.273267
$929$	−20.3246	+	35.2032i	−0.666827	+	1.15498i	0.311959	+	0.950095i	$0.399015\pi$
$929$	−20.3246	+	35.2032i	−0.666827	+	1.15498i	−0.978786	+	0.204883i	$0.934319\pi$
$930$		0			0
$931$	9.48683			0.310918
$932$	−13.1623	+	22.7977i	−0.431145	+	0.746765i
$933$	−6.24342	−	10.8139i	−0.204400	−	0.354032i
$934$	−1.50000	−	2.59808i	−0.0490815	−	0.0850117i
$935$		0			0
$936$	−0.0811388	−	3.60464i	−0.00265211	−	0.117821i
$937$	−29.6491			−0.968594			−0.484297	−	0.874904i	$-0.660925\pi$
$937$	−29.6491			−0.968594			−0.484297	+	0.874904i	$0.660925\pi$
$938$	−6.32456	−	10.9545i	−0.206504	−	0.357676i
$939$	8.82456	+	15.2846i	0.287978	+	0.498793i
$940$		0			0
$941$	−12.0000			−0.391189			−0.195594	−	0.980685i	$-0.562664\pi$
$941$	−12.0000			−0.391189			−0.195594	+	0.980685i	$0.562664\pi$
$942$	4.91886	−	8.51972i	0.160265	−	0.277587i
$943$	19.7434	−	34.1966i	0.642934	−	1.11359i
$944$	−6.00000			−0.195283
$945$		0			0
$946$	−7.74342	−	13.4120i	−0.251760	−	0.436061i
$947$	−11.1754	−	19.3564i	−0.363153	−	0.629000i	0.625325	−	0.780365i	$-0.284966\pi$
$947$	−11.1754	−	19.3564i	−0.363153	−	0.629000i	−0.988478	+	0.151365i	$0.951633\pi$
$948$	9.16228			0.297577
$949$	4.08114	−	2.48035i	0.132479	−	0.0805154i
$950$		0			0
$951$	0.0943058	+	0.163343i	0.00305808	+	0.00529674i
$952$	−11.3246	−	19.6147i	−0.367031	−	0.635716i
$953$	−11.2302	+	19.4514i	−0.363783	+	0.630091i	−0.988580	−	0.150696i	$-0.951849\pi$
$953$	−11.2302	+	19.4514i	−0.363783	+	0.630091i	0.624797	+	0.780787i	$0.285182\pi$
$954$	7.16228			0.231887
$955$		0			0
$956$	0.243416	−	0.421610i	0.00787265	−	0.0136358i
$957$	−24.9737			−0.807284
$958$	−13.1623	+	22.7977i	−0.425254	+	0.736561i
$959$	18.9737	+	32.8634i	0.612692	+	1.06121i
$960$		0			0
$961$	52.9473			1.70798
$962$	0.850889	+	37.8012i	0.0274338	+	1.21876i
$963$	6.00000			0.193347
$964$	−4.00000	−	6.92820i	−0.128831	−	0.223142i
$965$		0			0
$966$	6.58114	−	11.3989i	0.211745	−	0.366753i
$967$	−15.0263			−0.483214			−0.241607	−	0.970374i	$-0.577675\pi$
$967$	−15.0263			−0.483214			−0.241607	+	0.970374i	$0.577675\pi$
$968$	−1.00000	+	1.73205i	−0.0321412	+	0.0556702i
$969$	11.3246	−	19.6147i	0.363797	−	0.630115i
$970$		0			0
$971$	−21.0000	+	36.3731i	−0.673922	+	1.16727i	0.302861	+	0.953035i	$0.402058\pi$
$971$	−21.0000	+	36.3731i	−0.673922	+	1.16727i	−0.976783	+	0.214232i	$0.931275\pi$
$972$	−0.500000	−	0.866025i	−0.0160375	−	0.0277778i
$973$	28.9737	+	50.1839i	0.928853	+	1.60882i
$974$	−3.16228			−0.101326
$975$		0			0
$976$	14.4868			0.463712
$977$	19.1623	+	33.1900i	0.613056	+	1.06184i	0.990722	+	0.135902i	$0.0433932\pi$
$977$	19.1623	+	33.1900i	0.613056	+	1.06184i	−0.377667	+	0.925942i	$0.623273\pi$
$978$	−7.90569	−	13.6931i	−0.252796	−	0.437856i
$979$	10.7434	−	18.6081i	0.343361	−	0.594719i
$980$		0			0
$981$	−4.24342	+	7.34981i	−0.135482	+	0.234661i
$982$	7.98683	−	13.8336i	0.254870	−	0.441448i
$983$	−21.2982			−0.679308			−0.339654	−	0.940550i	$-0.610310\pi$
$983$	−21.2982			−0.679308			−0.339654	+	0.940550i	$0.610310\pi$
$984$	−4.74342	+	8.21584i	−0.151215	+	0.261911i
$985$		0			0
$986$	29.8114	+	51.6348i	0.949388	+	1.64439i
$987$	−18.9737			−0.603938
$988$	−10.0000	−	5.47723i	−0.318142	−	0.174254i
$989$	−21.4868			−0.683242
$990$		0			0
$991$	−29.0680	−	50.3472i	−0.923375	−	1.59933i	−0.794155	−	0.607716i	$-0.792086\pi$
$991$	−29.0680	−	50.3472i	−0.923375	−	1.59933i	−0.129220	−	0.991616i	$-0.541247\pi$
$992$	4.58114	−	7.93477i	0.145451	−	0.251929i
$993$	−8.83772			−0.280457
$994$	−12.3925	+	21.4645i	−0.393067	+	0.680812i
$995$		0			0
$996$	13.6491			0.432489
$997$	−3.51317	+	6.08498i	−0.111263	+	0.192713i	−0.916280	−	0.400539i	$-0.868823\pi$
$997$	−3.51317	+	6.08498i	−0.111263	+	0.192713i	0.805017	+	0.593252i	$0.202156\pi$
$998$	4.09431	+	7.09155i	0.129603	+	0.224479i
$999$	5.24342	+	9.08186i	0.165894	+	0.287337i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1950.2.i.bf.601.1	yes	4
5.2	odd	4		1950.2.z.o.1849.1		8
5.3	odd	4		1950.2.z.o.1849.4		8
5.4	even	2		1950.2.i.ba.601.2	yes	4
13.9	even	3	inner	1950.2.i.bf.451.1	yes	4
65.9	even	6		1950.2.i.ba.451.2	✓	4
65.22	odd	12		1950.2.z.o.1699.4		8
65.48	odd	12		1950.2.z.o.1699.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1950.2.i.ba.451.2	✓	4	65.9	even	6
1950.2.i.ba.601.2	yes	4	5.4	even	2
1950.2.i.bf.451.1	yes	4	13.9	even	3	inner
1950.2.i.bf.601.1	yes	4	1.1	even	1	trivial
1950.2.z.o.1699.1		8	65.48	odd	12
1950.2.z.o.1699.4		8	65.22	odd	12
1950.2.z.o.1849.1		8	5.2	odd	4
1950.2.z.o.1849.4		8	5.3	odd	4

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)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{6} +(-1.58114 + 2.73861i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(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} +(-1.58114 + 2.73861i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.50000 - 2.59808i) q^{11} +1.00000 q^{12} +(3.08114 - 1.87259i) q^{13} -3.16228 q^{14} +(-0.500000 - 0.866025i) q^{16} +(3.58114 - 6.20271i) q^{17} -1.00000 q^{18} +(-1.58114 + 2.73861i) q^{19} +3.16228 q^{21} +(1.50000 - 2.59808i) q^{22} +(-2.08114 - 3.60464i) q^{23} +(0.500000 + 0.866025i) q^{24} +(3.16228 + 1.73205i) q^{26} +1.00000 q^{27} +(-1.58114 - 2.73861i) q^{28} +(4.16228 + 7.20928i) q^{29} +9.16228 q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.50000 + 2.59808i) q^{33} +7.16228 q^{34} +(-0.500000 - 0.866025i) q^{36} +(5.24342 + 9.08186i) q^{37} -3.16228 q^{38} +(-3.16228 - 1.73205i) q^{39} +(4.74342 + 8.21584i) q^{41} +(1.58114 + 2.73861i) q^{42} +(2.58114 - 4.47066i) q^{43} +3.00000 q^{44} +(2.08114 - 3.60464i) q^{46} -6.00000 q^{47} +(-0.500000 + 0.866025i) q^{48} +(-1.50000 - 2.59808i) q^{49} -7.16228 q^{51} +(0.0811388 + 3.60464i) q^{52} -7.16228 q^{53} +(0.500000 + 0.866025i) q^{54} +(1.58114 - 2.73861i) q^{56} +3.16228 q^{57} +(-4.16228 + 7.20928i) q^{58} +(3.00000 - 5.19615i) q^{59} +(-7.24342 + 12.5460i) q^{61} +(4.58114 + 7.93477i) q^{62} +(-1.58114 - 2.73861i) q^{63} +1.00000 q^{64} -3.00000 q^{66} +(2.00000 + 3.46410i) q^{67} +(3.58114 + 6.20271i) q^{68} +(-2.08114 + 3.60464i) q^{69} +(3.91886 - 6.78767i) q^{71} +(0.500000 - 0.866025i) q^{72} +1.32456 q^{73} +(-5.24342 + 9.08186i) q^{74} +(-1.58114 - 2.73861i) q^{76} +9.48683 q^{77} +(-0.0811388 - 3.60464i) q^{78} +9.16228 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-4.74342 + 8.21584i) q^{82} +13.6491 q^{83} +(-1.58114 + 2.73861i) q^{84} +5.16228 q^{86} +(4.16228 - 7.20928i) q^{87} +(1.50000 + 2.59808i) q^{88} +(3.58114 + 6.20271i) q^{89} +(0.256584 + 11.3989i) q^{91} +4.16228 q^{92} +(-4.58114 - 7.93477i) q^{93} +(-3.00000 - 5.19615i) q^{94} -1.00000 q^{96} +(2.33772 - 4.04905i) q^{97} +(1.50000 - 2.59808i) q^{98} +3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{6} - 4 q^{8} - 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^6 - 4 * q^8 - 2 * q^9	\( 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{6} - 4 q^{8} - 2 q^{9} - 6 q^{11} + 4 q^{12} + 6 q^{13} - 2 q^{16} + 8 q^{17} - 4 q^{18} + 6 q^{22} - 2 q^{23} + 2 q^{24} + 4 q^{27} + 4 q^{29} + 24 q^{31} + 2 q^{32} - 6 q^{33} + 16 q^{34} - 2 q^{36} + 2 q^{37} + 4 q^{43} + 12 q^{44} + 2 q^{46} - 24 q^{47} - 2 q^{48} - 6 q^{49} - 16 q^{51} - 6 q^{52} - 16 q^{53} + 2 q^{54} - 4 q^{58} + 12 q^{59} - 10 q^{61} + 12 q^{62} + 4 q^{64} - 12 q^{66} + 8 q^{67} + 8 q^{68} - 2 q^{69} + 22 q^{71} + 2 q^{72} - 20 q^{73} - 2 q^{74} + 6 q^{78} + 24 q^{79} - 2 q^{81} + 4 q^{83} + 8 q^{86} + 4 q^{87} + 6 q^{88} + 8 q^{89} + 20 q^{91} + 4 q^{92} - 12 q^{93} - 12 q^{94} - 4 q^{96} + 22 q^{97} + 6 q^{98} + 12 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^6 - 4 * q^8 - 2 * q^9 - 6 * q^11 + 4 * q^12 + 6 * q^13 - 2 * q^16 + 8 * q^17 - 4 * q^18 + 6 * q^22 - 2 * q^23 + 2 * q^24 + 4 * q^27 + 4 * q^29 + 24 * q^31 + 2 * q^32 - 6 * q^33 + 16 * q^34 - 2 * q^36 + 2 * q^37 + 4 * q^43 + 12 * q^44 + 2 * q^46 - 24 * q^47 - 2 * q^48 - 6 * q^49 - 16 * q^51 - 6 * q^52 - 16 * q^53 + 2 * q^54 - 4 * q^58 + 12 * q^59 - 10 * q^61 + 12 * q^62 + 4 * q^64 - 12 * q^66 + 8 * q^67 + 8 * q^68 - 2 * q^69 + 22 * q^71 + 2 * q^72 - 20 * q^73 - 2 * q^74 + 6 * q^78 + 24 * q^79 - 2 * q^81 + 4 * q^83 + 8 * q^86 + 4 * q^87 + 6 * q^88 + 8 * q^89 + 20 * q^91 + 4 * q^92 - 12 * q^93 - 12 * q^94 - 4 * q^96 + 22 * q^97 + 6 * q^98 + 12 * q^99

Introduction

L-functions

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