LMFDB - Embedded newform 1950.2.i.ba.451.1

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			451.1
Root			$-1.58114 - 2.73861i$ of defining polynomial
Character	$\chi$	$=$	1950.451
Dual form			1950.2.i.ba.601.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{6} +(-1.58114 - 2.73861i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(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} +(0.0811388 + 3.60464i) q^{13} +3.16228 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-0.418861 - 0.725489i) q^{17} +1.00000 q^{18} +(1.58114 + 2.73861i) q^{19} -3.16228 q^{21} +(-1.50000 - 2.59808i) q^{22} +(-1.08114 + 1.87259i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-3.16228 - 1.73205i) q^{26} -1.00000 q^{27} +(-1.58114 + 2.73861i) q^{28} +(-2.16228 + 3.74517i) q^{29} +2.83772 q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.50000 + 2.59808i) q^{33} +0.837722 q^{34} +(-0.500000 + 0.866025i) q^{36} +(4.24342 - 7.34981i) q^{37} -3.16228 q^{38} +(3.16228 + 1.73205i) q^{39} +(-4.74342 + 8.21584i) q^{41} +(1.58114 - 2.73861i) q^{42} +(0.581139 + 1.00656i) q^{43} +3.00000 q^{44} +(-1.08114 - 1.87259i) q^{46} +6.00000 q^{47} +(0.500000 + 0.866025i) q^{48} +(-1.50000 + 2.59808i) q^{49} -0.837722 q^{51} +(3.08114 - 1.87259i) q^{52} +0.837722 q^{53} +(0.500000 - 0.866025i) q^{54} +(-1.58114 - 2.73861i) q^{56} +3.16228 q^{57} +(-2.16228 - 3.74517i) q^{58} +(3.00000 + 5.19615i) q^{59} +(2.24342 + 3.88571i) q^{61} +(-1.41886 + 2.45754i) q^{62} +(-1.58114 + 2.73861i) q^{63} +1.00000 q^{64} -3.00000 q^{66} +(-2.00000 + 3.46410i) q^{67} +(-0.418861 + 0.725489i) q^{68} +(1.08114 + 1.87259i) q^{69} +(7.08114 + 12.2649i) q^{71} +(-0.500000 - 0.866025i) q^{72} +11.3246 q^{73} +(4.24342 + 7.34981i) q^{74} +(1.58114 - 2.73861i) q^{76} +9.48683 q^{77} +(-3.08114 + 1.87259i) q^{78} +2.83772 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-4.74342 - 8.21584i) q^{82} +11.6491 q^{83} +(1.58114 + 2.73861i) q^{84} -1.16228 q^{86} +(2.16228 + 3.74517i) q^{87} +(-1.50000 + 2.59808i) q^{88} +(0.418861 - 0.725489i) q^{89} +(9.74342 - 5.92164i) q^{91} +2.16228 q^{92} +(1.41886 - 2.45754i) q^{93} +(-3.00000 + 5.19615i) q^{94} -1.00000 q^{96} +(-8.66228 - 15.0035i) 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 $\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times$.

$n$	$301$	$1301$	$1327$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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	−0.993172	−	0.116657i	$-0.962782\pi$
$7$	−1.58114	−	2.73861i	−0.597614	−	1.03510i	0.395558	−	0.918441i	$-0.370551\pi$
$8$	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	−0.998526	−	0.0542666i	$-0.982718\pi$
$11$	−1.50000	+	2.59808i	−0.452267	+	0.783349i	0.546259	+	0.837616i	$0.316051\pi$
$12$	−1.00000			−0.288675
$13$	0.0811388	+	3.60464i	0.0225039	+	0.999747i
$13$	0.0811388	+	3.60464i	0.0225039	+	0.999747i
$14$	3.16228			0.845154
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.418861	−	0.725489i	−0.101589	−	0.175957i	0.810751	−	0.585392i	$-0.199059\pi$
$17$	−0.418861	−	0.725489i	−0.101589	−	0.175957i	−0.912339	+	0.409435i	$0.865726\pi$
$18$	1.00000			0.235702
$19$	1.58114	+	2.73861i	0.362738	+	0.628281i	0.988410	−	0.151805i	$-0.0485086\pi$
$19$	1.58114	+	2.73861i	0.362738	+	0.628281i	−0.625672	+	0.780086i	$0.715175\pi$
$20$		0			0
$21$	−3.16228			−0.690066
$22$	−1.50000	−	2.59808i	−0.319801	−	0.553912i
$23$	−1.08114	+	1.87259i	−0.225433	+	0.390461i	−0.956449	−	0.291899i	$-0.905713\pi$
$23$	−1.08114	+	1.87259i	−0.225433	+	0.390461i	0.731016	+	0.682360i	$0.239046\pi$
$24$	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
$29$	−2.16228	+	3.74517i	−0.401525	+	0.695461i	−0.993910	−	0.110193i	$-0.964853\pi$
$29$	−2.16228	+	3.74517i	−0.401525	+	0.695461i	0.592385	+	0.805655i	$0.298186\pi$
$30$		0			0
$31$	2.83772			0.509670			0.254835	−	0.966985i	$-0.417979\pi$
$31$	2.83772			0.509670			0.254835	+	0.966985i	$0.417979\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	1.50000	+	2.59808i	0.261116	+	0.452267i
$34$	0.837722			0.143668
$35$		0			0
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	4.24342	−	7.34981i	0.697613	−	1.20830i	−0.271678	−	0.962388i	$-0.587579\pi$
$37$	4.24342	−	7.34981i	0.697613	−	1.20830i	0.969292	−	0.245914i	$-0.0790880\pi$
$38$	−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	0.211336	+	0.977414i	$0.432219\pi$
$41$	−4.74342	+	8.21584i	−0.740797	+	1.28310i	−0.952133	+	0.305685i	$0.901115\pi$
$42$	1.58114	−	2.73861i	0.243975	−	0.422577i
$43$	0.581139	+	1.00656i	0.0886228	+	0.153499i	0.906929	−	0.421283i	$-0.138420\pi$
$43$	0.581139	+	1.00656i	0.0886228	+	0.153499i	−0.818306	+	0.574782i	$0.805087\pi$
$44$	3.00000			0.452267
$45$		0			0
$46$	−1.08114	−	1.87259i	−0.159405	−	0.276098i
$47$	6.00000			0.875190			0.437595	−	0.899172i	$-0.355830\pi$
$47$	6.00000			0.875190			0.437595	+	0.899172i	$0.355830\pi$
$48$	0.500000	+	0.866025i	0.0721688	+	0.125000i
$49$	−1.50000	+	2.59808i	−0.214286	+	0.371154i
$50$		0			0
$51$	−0.837722			−0.117305
$52$	3.08114	−	1.87259i	0.427277	−	0.259681i
$53$	0.837722			0.115070			0.0575350	−	0.998343i	$-0.481676\pi$
$53$	0.837722			0.115070			0.0575350	+	0.998343i	$0.481676\pi$
$54$	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
$58$	−2.16228	−	3.74517i	−0.283921	−	0.491766i
$59$	3.00000	+	5.19615i	0.390567	+	0.676481i	0.992524	−	0.122047i	$-0.0389457\pi$
$59$	3.00000	+	5.19615i	0.390567	+	0.676481i	−0.601958	+	0.798528i	$0.705612\pi$
$60$		0			0
$61$	2.24342	+	3.88571i	0.287240	+	0.497514i	0.973150	−	0.230172i	$-0.0739289\pi$
$61$	2.24342	+	3.88571i	0.287240	+	0.497514i	−0.685910	+	0.727686i	$0.740596\pi$
$62$	−1.41886	+	2.45754i	−0.180196	+	0.312108i
$63$	−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	$-0.911904\pi$
$67$	−2.00000	+	3.46410i	−0.244339	+	0.423207i	0.717607	+	0.696449i	$0.245238\pi$
$68$	−0.418861	+	0.725489i	−0.0507944	+	0.0879784i
$69$	1.08114	+	1.87259i	0.130154	+	0.225433i
$70$		0			0
$71$	7.08114	+	12.2649i	0.840377	+	1.45557i	0.889577	+	0.456786i	$0.150999\pi$
$71$	7.08114	+	12.2649i	0.840377	+	1.45557i	−0.0492001	+	0.998789i	$0.515667\pi$
$72$	−0.500000	−	0.866025i	−0.0589256	−	0.102062i
$73$	11.3246			1.32544			0.662719	−	0.748868i	$-0.269402\pi$
$73$	11.3246			1.32544			0.662719	+	0.748868i	$0.269402\pi$
$74$	4.24342	+	7.34981i	0.493287	+	0.854398i
$75$		0			0
$76$	1.58114	−	2.73861i	0.181369	−	0.314140i
$77$	9.48683			1.08112
$78$	−3.08114	+	1.87259i	−0.348870	+	0.212029i
$79$	2.83772			0.319269			0.159634	−	0.987176i	$-0.448968\pi$
$79$	2.83772			0.319269			0.159634	+	0.987176i	$0.448968\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−4.74342	−	8.21584i	−0.523823	−	0.907288i
$83$	11.6491			1.27866			0.639328	−	0.768934i	$-0.279213\pi$
$83$	11.6491			1.27866			0.639328	+	0.768934i	$0.279213\pi$
$84$	1.58114	+	2.73861i	0.172516	+	0.298807i
$85$		0			0
$86$	−1.16228			−0.125332
$87$	2.16228	+	3.74517i	0.231820	+	0.401525i
$88$	−1.50000	+	2.59808i	−0.159901	+	0.276956i
$89$	0.418861	−	0.725489i	0.0443992	−	0.0769017i	−0.842972	−	0.537958i	$-0.819196\pi$
$89$	0.418861	−	0.725489i	0.0443992	−	0.0769017i	0.887371	+	0.461056i	$0.152529\pi$
$90$		0			0
$91$	9.74342	−	5.92164i	1.02139	−	0.620757i
$92$	2.16228			0.225433
$93$	1.41886	−	2.45754i	0.147129	−	0.254835i
$94$	−3.00000	+	5.19615i	−0.309426	+	0.535942i
$95$		0			0
$96$	−1.00000			−0.102062
$97$	−8.66228	−	15.0035i	−0.879521	−	1.52338i	−0.851867	−	0.523758i	$-0.824530\pi$
$97$	−8.66228	−	15.0035i	−0.879521	−	1.52338i	−0.0276537	−	0.999618i	$-0.508804\pi$
$98$	−1.50000	−	2.59808i	−0.151523	−	0.262445i
$99$	3.00000			0.301511
$100$		0			0
$101$	−4.32456	+	7.49035i	−0.430309	+	0.745318i	−0.996900	−	0.0786819i	$-0.974929\pi$
$101$	−4.32456	+	7.49035i	−0.430309	+	0.745318i	0.566590	+	0.824000i	$0.308262\pi$
$102$	0.418861	−	0.725489i	0.0414734	−	0.0718341i
$103$	−5.48683			−0.540634			−0.270317	−	0.962771i	$-0.587128\pi$
$103$	−5.48683			−0.540634			−0.270317	+	0.962771i	$0.587128\pi$
$104$	0.0811388	+	3.60464i	0.00795632	+	0.353464i
$105$		0			0
$106$	−0.418861	+	0.725489i	−0.0406834	+	0.0704657i
$107$	3.00000	−	5.19615i	0.290021	−	0.502331i	−0.683793	−	0.729676i	$-0.739671\pi$
$107$	3.00000	−	5.19615i	0.290021	−	0.502331i	0.973814	+	0.227345i	$0.0730044\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	−10.4868			−1.00446			−0.502228	−	0.864735i	$-0.667486\pi$
$109$	−10.4868			−1.00446			−0.502228	+	0.864735i	$0.667486\pi$
$110$		0			0
$111$	−4.24342	−	7.34981i	−0.402767	−	0.697613i
$112$	3.16228			0.298807
$113$	5.16228	+	8.94133i	0.485626	+	0.841129i	0.999864	−	0.0165186i	$-0.00525828\pi$
$113$	5.16228	+	8.94133i	0.485626	+	0.841129i	−0.514237	+	0.857648i	$0.671925\pi$
$114$	−1.58114	+	2.73861i	−0.148087	+	0.256495i
$115$		0			0
$116$	4.32456			0.401525
$117$	3.08114	−	1.87259i	0.284851	−	0.173121i
$118$	−6.00000			−0.552345
$119$	−1.32456	+	2.29420i	−0.121422	+	0.210309i
$120$		0			0
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$	−4.48683			−0.406219
$123$	4.74342	+	8.21584i	0.427699	+	0.740797i
$124$	−1.41886	−	2.45754i	−0.127417	−	0.220694i
$125$		0			0
$126$	−1.58114	−	2.73861i	−0.140859	−	0.243975i
$127$	−10.1623	+	17.6016i	−0.901756	+	1.56189i	−0.0765432	+	0.997066i	$0.524388\pi$
$127$	−10.1623	+	17.6016i	−0.901756	+	1.56189i	−0.825213	+	0.564822i	$0.808945\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	1.16228			0.102333
$130$		0			0
$131$	16.3246			1.42628			0.713142	−	0.701020i	$-0.247272\pi$
$131$	16.3246			1.42628			0.713142	+	0.701020i	$0.247272\pi$
$132$	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
$136$	−0.418861	−	0.725489i	−0.0359170	−	0.0622102i
$137$	−6.00000	−	10.3923i	−0.512615	−	0.887875i	−0.999893	−	0.0146279i	$-0.995344\pi$
$137$	−6.00000	−	10.3923i	−0.512615	−	0.887875i	0.487278	−	0.873247i	$-0.337990\pi$
$138$	−2.16228			−0.184065
$139$	2.83772	+	4.91508i	0.240692	+	0.416892i	0.960912	−	0.276855i	$-0.0892921\pi$
$139$	2.83772	+	4.91508i	0.240692	+	0.416892i	−0.720219	+	0.693747i	$0.755959\pi$
$140$		0			0
$141$	3.00000	−	5.19615i	0.252646	−	0.437595i
$142$	−14.1623			−1.18847
$143$	−9.48683	−	5.19615i	−0.793329	−	0.434524i
$144$	1.00000			0.0833333
$145$		0			0
$146$	−5.66228	+	9.80735i	−0.468613	+	0.811662i
$147$	1.50000	+	2.59808i	0.123718	+	0.214286i
$148$	−8.48683			−0.697613
$149$	3.41886	+	5.92164i	0.280084	+	0.485120i	0.971405	−	0.237428i	$-0.0763043\pi$
$149$	3.41886	+	5.92164i	0.280084	+	0.485120i	−0.691321	+	0.722548i	$0.742971\pi$
$150$		0			0
$151$	9.81139			0.798439			0.399220	−	0.916855i	$-0.369281\pi$
$151$	9.81139			0.798439			0.399220	+	0.916855i	$0.369281\pi$
$152$	1.58114	+	2.73861i	0.128247	+	0.222131i
$153$	−0.418861	+	0.725489i	−0.0338629	+	0.0586523i
$154$	−4.74342	+	8.21584i	−0.382235	+	0.662051i
$155$		0			0
$156$	−0.0811388	−	3.60464i	−0.00649631	−	0.288602i
$157$	−16.1623			−1.28989			−0.644945	−	0.764229i	$-0.723120\pi$
$157$	−16.1623			−1.28989			−0.644945	+	0.764229i	$0.723120\pi$
$158$	−1.41886	+	2.45754i	−0.112879	+	0.195511i
$159$	0.418861	−	0.725489i	0.0332179	−	0.0575350i
$160$		0			0
$161$	6.83772			0.538888
$162$	−0.500000	−	0.866025i	−0.0392837	−	0.0680414i
$163$	7.90569	+	13.6931i	0.619222	+	1.07252i	0.989628	+	0.143654i	$0.0458851\pi$
$163$	7.90569	+	13.6931i	0.619222	+	1.07252i	−0.370406	+	0.928870i	$0.620782\pi$
$164$	9.48683			0.740797
$165$		0			0
$166$	−5.82456	+	10.0884i	−0.452073	+	0.783014i
$167$	4.08114	−	7.06874i	0.315808	−	0.546996i	−0.663801	−	0.747909i	$-0.731058\pi$
$167$	4.08114	−	7.06874i	0.315808	−	0.546996i	0.979609	+	0.200914i	$0.0643911\pi$
$168$	−3.16228			−0.243975
$169$	−12.9868	+	0.584952i	−0.998987	+	0.0449963i
$170$		0			0
$171$	1.58114	−	2.73861i	0.120913	−	0.209427i
$172$	0.581139	−	1.00656i	0.0443114	−	0.0767496i
$173$	−0.837722	−	1.45098i	−0.0636909	−	0.110316i	0.832422	−	0.554143i	$-0.186954\pi$
$173$	−0.837722	−	1.45098i	−0.0636909	−	0.110316i	−0.896113	+	0.443827i	$0.853620\pi$
$174$	−4.32456			−0.327844
$175$		0			0
$176$	−1.50000	−	2.59808i	−0.113067	−	0.195837i
$177$	6.00000			0.450988
$178$	0.418861	+	0.725489i	0.0313950	+	0.0543777i
$179$	−11.8246	+	20.4807i	−0.883809	+	1.53080i	−0.0367358	+	0.999325i	$0.511696\pi$
$179$	−11.8246	+	20.4807i	−0.883809	+	1.53080i	−0.847073	+	0.531477i	$0.821637\pi$
$180$		0			0
$181$	12.8114			0.952263			0.476131	−	0.879374i	$-0.342039\pi$
$181$	12.8114			0.952263			0.476131	+	0.879374i	$0.342039\pi$
$182$	0.256584	+	11.3989i	0.0190192	+	0.844940i
$183$	4.48683			0.331676
$184$	−1.08114	+	1.87259i	−0.0797026	+	0.138049i
$185$		0			0
$186$	1.41886	+	2.45754i	0.104036	+	0.180196i
$187$	2.51317			0.183781
$188$	−3.00000	−	5.19615i	−0.218797	−	0.378968i
$189$	1.58114	+	2.73861i	0.115011	+	0.199205i
$190$		0			0
$191$	−7.91886	−	13.7159i	−0.572989	−	0.992446i	−0.996257	−	0.0864411i	$-0.972451\pi$
$191$	−7.91886	−	13.7159i	−0.572989	−	0.992446i	0.423268	−	0.906004i	$-0.360883\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	−8.66228	+	15.0035i	−0.623524	+	1.07998i	0.365300	+	0.930890i	$0.380966\pi$
$193$	−8.66228	+	15.0035i	−0.623524	+	1.07998i	−0.988824	+	0.149086i	$0.952367\pi$
$194$	17.3246			1.24383
$195$		0			0
$196$	3.00000			0.214286
$197$	−3.00000	+	5.19615i	−0.213741	+	0.370211i	−0.952882	−	0.303340i	$-0.901898\pi$
$197$	−3.00000	+	5.19615i	−0.213741	+	0.370211i	0.739141	+	0.673550i	$0.235232\pi$
$198$	−1.50000	+	2.59808i	−0.106600	+	0.184637i
$199$	−4.41886	−	7.65369i	−0.313245	−	0.542556i	0.665818	−	0.746114i	$-0.268083\pi$
$199$	−4.41886	−	7.65369i	−0.313245	−	0.542556i	−0.979063	+	0.203558i	$0.934749\pi$
$200$		0			0
$201$	2.00000	+	3.46410i	0.141069	+	0.244339i
$202$	−4.32456	−	7.49035i	−0.304275	−	0.527019i
$203$	13.6754			0.959828
$204$	0.418861	+	0.725489i	0.0293261	+	0.0507944i
$205$		0			0
$206$	2.74342	−	4.75174i	0.191143	−	0.331069i
$207$	2.16228			0.150289
$208$	−3.16228	−	1.73205i	−0.219265	−	0.120096i
$209$	−9.48683			−0.656218
$210$		0			0
$211$	−6.58114	+	11.3989i	−0.453064	+	0.784730i	−0.998575	−	0.0533737i	$-0.983003\pi$
$211$	−6.58114	+	11.3989i	−0.453064	+	0.784730i	0.545510	+	0.838104i	$0.316336\pi$
$212$	−0.418861	−	0.725489i	−0.0287675	−	0.0498268i
$213$	14.1623			0.970383
$214$	3.00000	+	5.19615i	0.205076	+	0.355202i
$215$		0			0
$216$	−1.00000			−0.0680414
$217$	−4.48683	−	7.77142i	−0.304586	−	0.527559i
$218$	5.24342	−	9.08186i	0.355129	−	0.615101i
$219$	5.66228	−	9.80735i	0.382621	−	0.662719i
$220$		0			0
$221$	2.58114	−	1.56871i	0.173626	−	0.105523i
$222$	8.48683			0.569599
$223$	13.0680	−	22.6344i	0.875096	−	1.51571i	0.0184358	−	0.999830i	$-0.494131\pi$
$223$	13.0680	−	22.6344i	0.875096	−	1.51571i	0.856660	−	0.515881i	$-0.172535\pi$
$224$	−1.58114	+	2.73861i	−0.105644	+	0.182981i
$225$		0			0
$226$	−10.3246			−0.686779
$227$	10.9868	+	19.0298i	0.729222	+	1.26305i	0.957213	+	0.289386i	$0.0934510\pi$
$227$	10.9868	+	19.0298i	0.729222	+	1.26305i	−0.227991	+	0.973663i	$0.573216\pi$
$228$	−1.58114	−	2.73861i	−0.104713	−	0.181369i
$229$	−16.4868			−1.08948			−0.544740	−	0.838605i	$-0.683372\pi$
$229$	−16.4868			−1.08948			−0.544740	+	0.838605i	$0.683372\pi$
$230$		0			0
$231$	4.74342	−	8.21584i	0.312094	−	0.540562i
$232$	−2.16228	+	3.74517i	−0.141960	+	0.245883i
$233$	−13.6754			−0.895908			−0.447954	−	0.894057i	$-0.647847\pi$
$233$	−13.6754			−0.895908			−0.447954	+	0.894057i	$0.647847\pi$
$234$	0.0811388	+	3.60464i	0.00530421	+	0.235643i
$235$		0			0
$236$	3.00000	−	5.19615i	0.195283	−	0.338241i
$237$	1.41886	−	2.45754i	0.0921649	−	0.159634i
$238$	−1.32456	−	2.29420i	−0.0858582	−	0.148711i
$239$	18.4868			1.19581			0.597907	−	0.801566i	$-0.295999\pi$
$239$	18.4868			1.19581			0.597907	+	0.801566i	$0.295999\pi$
$240$		0			0
$241$	−4.00000	−	6.92820i	−0.257663	−	0.446285i	0.707953	−	0.706260i	$-0.249619\pi$
$241$	−4.00000	−	6.92820i	−0.257663	−	0.446285i	−0.965615	+	0.259975i	$0.916286\pi$
$242$	−2.00000			−0.128565
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	2.24342	−	3.88571i	0.143620	−	0.248757i
$245$		0			0
$246$	−9.48683			−0.604858
$247$	−9.74342	+	5.92164i	−0.619959	+	0.376785i
$248$	2.83772			0.180196
$249$	5.82456	−	10.0884i	0.369116	−	0.639328i
$250$		0			0
$251$	−7.50000	−	12.9904i	−0.473396	−	0.819946i	0.526140	−	0.850398i	$-0.323639\pi$
$251$	−7.50000	−	12.9904i	−0.473396	−	0.819946i	−0.999536	+	0.0304521i	$0.990305\pi$
$252$	3.16228			0.199205
$253$	−3.24342	−	5.61776i	−0.203912	−	0.353186i
$254$	−10.1623	−	17.6016i	−0.637638	−	1.10442i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−12.9057	+	22.3533i	−0.805035	+	1.39436i	0.111232	+	0.993794i	$0.464520\pi$
$257$	−12.9057	+	22.3533i	−0.805035	+	1.39436i	−0.916267	+	0.400567i	$0.868813\pi$
$258$	−0.581139	+	1.00656i	−0.0361801	+	0.0626658i
$259$	−26.8377			−1.66761
$260$		0			0
$261$	4.32456			0.267683
$262$	−8.16228	+	14.1375i	−0.504267	+	0.873416i
$263$	−0.243416	+	0.421610i	−0.0150097	+	0.0259976i	−0.873433	−	0.486945i	$-0.838111\pi$
$263$	−0.243416	+	0.421610i	−0.0150097	+	0.0259976i	0.858423	+	0.512942i	$0.171445\pi$
$264$	1.50000	+	2.59808i	0.0923186	+	0.159901i
$265$		0			0
$266$	5.00000	+	8.66025i	0.306570	+	0.530994i
$267$	−0.418861	−	0.725489i	−0.0256339	−	0.0443992i
$268$	4.00000			0.244339
$269$	6.41886	+	11.1178i	0.391365	+	0.677864i	0.992630	−	0.121186i	$-0.0386697\pi$
$269$	6.41886	+	11.1178i	0.391365	+	0.677864i	−0.601265	+	0.799050i	$0.705336\pi$
$270$		0			0
$271$	−0.162278	+	0.281073i	−0.00985767	+	0.0170740i	−0.870912	−	0.491439i	$-0.836471\pi$
$271$	−0.162278	+	0.281073i	−0.00985767	+	0.0170740i	0.861054	+	0.508513i	$0.169805\pi$
$272$	0.837722			0.0507944
$273$	−0.256584	−	11.3989i	−0.0155291	−	0.689891i
$274$	12.0000			0.724947
$275$		0			0
$276$	1.08114	−	1.87259i	0.0650769	−	0.112717i
$277$	−4.40569	−	7.63089i	−0.264713	−	0.458496i	0.702776	−	0.711411i	$-0.251944\pi$
$277$	−4.40569	−	7.63089i	−0.264713	−	0.458496i	−0.967488	+	0.252916i	$0.918610\pi$
$278$	−5.67544			−0.340391
$279$	−1.41886	−	2.45754i	−0.0849450	−	0.147129i
$280$		0			0
$281$	−21.4868			−1.28180			−0.640898	−	0.767626i	$-0.721438\pi$
$281$	−21.4868			−1.28180			−0.640898	+	0.767626i	$0.721438\pi$
$282$	3.00000	+	5.19615i	0.178647	+	0.309426i
$283$	−9.74342	+	16.8761i	−0.579186	+	1.00318i	0.416387	+	0.909187i	$0.363296\pi$
$283$	−9.74342	+	16.8761i	−0.579186	+	1.00318i	−0.995573	+	0.0939921i	$0.970037\pi$
$284$	7.08114	−	12.2649i	0.420188	−	0.727787i
$285$		0			0
$286$	9.24342	−	5.61776i	0.546575	−	0.332185i
$287$	30.0000			1.77084
$288$	−0.500000	+	0.866025i	−0.0294628	+	0.0510310i
$289$	8.14911	−	14.1147i	0.479359	−	0.830275i
$290$		0			0
$291$	−17.3246			−1.01558
$292$	−5.66228	−	9.80735i	−0.331360	−	0.573932i
$293$	10.7434	+	18.6081i	0.627637	+	1.08710i	0.988025	+	0.154297i	$0.0493111\pi$
$293$	10.7434	+	18.6081i	0.627637	+	1.08710i	−0.360387	+	0.932803i	$0.617356\pi$
$294$	−3.00000			−0.174964
$295$		0			0
$296$	4.24342	−	7.34981i	0.246644	−	0.427199i
$297$	1.50000	−	2.59808i	0.0870388	−	0.150756i
$298$	−6.83772			−0.396099
$299$	−6.83772	−	3.74517i	−0.395436	−	0.216589i
$300$		0			0
$301$	1.83772	−	3.18303i	0.105925	−	0.183467i
$302$	−4.90569	+	8.49691i	−0.282291	+	0.488942i
$303$	4.32456	+	7.49035i	0.248439	+	0.430309i
$304$	−3.16228			−0.181369
$305$		0			0
$306$	−0.418861	−	0.725489i	−0.0239447	−	0.0414734i
$307$	−16.6491			−0.950215			−0.475107	−	0.879928i	$-0.657591\pi$
$307$	−16.6491			−0.950215			−0.475107	+	0.879928i	$0.657591\pi$
$308$	−4.74342	−	8.21584i	−0.270281	−	0.468141i
$309$	−2.74342	+	4.75174i	−0.156068	+	0.270317i
$310$		0			0
$311$	−6.48683			−0.367835			−0.183917	−	0.982942i	$-0.558878\pi$
$311$	−6.48683			−0.367835			−0.183917	+	0.982942i	$0.558878\pi$
$312$	3.16228	+	1.73205i	0.179029	+	0.0980581i
$313$	−7.64911			−0.432353			−0.216177	−	0.976354i	$-0.569359\pi$
$313$	−7.64911			−0.432353			−0.216177	+	0.976354i	$0.569359\pi$
$314$	8.08114	−	13.9969i	0.456045	−	0.789893i
$315$		0			0
$316$	−1.41886	−	2.45754i	−0.0798172	−	0.138247i
$317$	31.8114			1.78671			0.893353	−	0.449356i	$-0.148347\pi$
$317$	31.8114			1.78671			0.893353	+	0.449356i	$0.148347\pi$
$318$	0.418861	+	0.725489i	0.0234886	+	0.0406834i
$319$	−6.48683	−	11.2355i	−0.363193	−	0.629069i
$320$		0			0
$321$	−3.00000	−	5.19615i	−0.167444	−	0.290021i
$322$	−3.41886	+	5.92164i	−0.190526	+	0.330000i
$323$	1.32456	−	2.29420i	0.0737002	−	0.127653i
$324$	1.00000			0.0555556
$325$		0			0
$326$	−15.8114			−0.875712
$327$	−5.24342	+	9.08186i	−0.289962	+	0.502228i
$328$	−4.74342	+	8.21584i	−0.261911	+	0.453644i
$329$	−9.48683	−	16.4317i	−0.523026	−	0.905908i
$330$		0			0
$331$	7.58114	+	13.1309i	0.416697	+	0.721741i	0.995605	−	0.0936524i	$-0.0298543\pi$
$331$	7.58114	+	13.1309i	0.416697	+	0.721741i	−0.578908	+	0.815393i	$0.696521\pi$
$332$	−5.82456	−	10.0884i	−0.319664	−	0.553674i
$333$	−8.48683			−0.465076
$334$	4.08114	+	7.06874i	0.223310	+	0.386784i
$335$		0			0
$336$	1.58114	−	2.73861i	0.0862582	−	0.149404i
$337$	4.00000			0.217894			0.108947	−	0.994048i	$-0.465252\pi$
$337$	4.00000			0.217894			0.108947	+	0.994048i	$0.465252\pi$
$338$	5.98683	−	11.5394i	0.325641	−	0.627661i
$339$	10.3246			0.560753
$340$		0			0
$341$	−4.25658	+	7.37262i	−0.230507	+	0.399250i
$342$	1.58114	+	2.73861i	0.0854982	+	0.148087i
$343$	−12.6491			−0.682988
$344$	0.581139	+	1.00656i	0.0313329	+	0.0542702i
$345$		0			0
$346$	1.67544			0.0900725
$347$	0.662278	+	1.14710i	0.0355529	+	0.0615795i	0.883254	−	0.468894i	$-0.155347\pi$
$347$	0.662278	+	1.14710i	0.0355529	+	0.0615795i	−0.847701	+	0.530474i	$0.822014\pi$
$348$	2.16228	−	3.74517i	0.115910	−	0.200762i
$349$	17.7302	−	30.7097i	0.949078	−	1.64385i	0.201707	−	0.979446i	$-0.435351\pi$
$349$	17.7302	−	30.7097i	0.949078	−	1.64385i	0.747372	−	0.664406i	$-0.231315\pi$
$350$		0			0
$351$	−0.0811388	−	3.60464i	−0.00433087	−	0.192401i
$352$	3.00000			0.159901
$353$	−9.90569	+	17.1572i	−0.527227	+	0.913184i	0.472270	+	0.881454i	$0.343435\pi$
$353$	−9.90569	+	17.1572i	−0.527227	+	0.913184i	−0.999496	+	0.0317296i	$0.989898\pi$
$354$	−3.00000	+	5.19615i	−0.159448	+	0.276172i
$355$		0			0
$356$	−0.837722			−0.0443992
$357$	1.32456	+	2.29420i	0.0701029	+	0.121422i
$358$	−11.8246	−	20.4807i	−0.624947	−	1.08244i
$359$	−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
$362$	−6.40569	+	11.0950i	−0.336676	+	0.583140i
$363$	2.00000			0.104973
$364$	−10.0000	−	5.47723i	−0.524142	−	0.287085i
$365$		0			0
$366$	−2.24342	+	3.88571i	−0.117265	+	0.203109i
$367$	−9.32456	+	16.1506i	−0.486738	+	0.843055i	−0.999884	−	0.0152467i	$-0.995147\pi$
$367$	−9.32456	+	16.1506i	−0.486738	+	0.843055i	0.513146	+	0.858301i	$0.328480\pi$
$368$	−1.08114	−	1.87259i	−0.0563583	−	0.0976154i
$369$	9.48683			0.493865
$370$		0			0
$371$	−1.32456	−	2.29420i	−0.0687675	−	0.119109i
$372$	−2.83772			−0.147129
$373$	−5.24342	−	9.08186i	−0.271494	−	0.470241i	0.697751	−	0.716341i	$-0.254184\pi$
$373$	−5.24342	−	9.08186i	−0.271494	−	0.470241i	−0.969245	+	0.246100i	$0.920851\pi$
$374$	−1.25658	+	2.17647i	−0.0649764	+	0.112542i
$375$		0			0
$376$	6.00000			0.309426
$377$	−13.6754	−	7.49035i	−0.704321	−	0.385773i
$378$	−3.16228			−0.162650
$379$	−1.00000	+	1.73205i	−0.0513665	+	0.0889695i	−0.890565	−	0.454855i	$-0.849691\pi$
$379$	−1.00000	+	1.73205i	−0.0513665	+	0.0889695i	0.839199	+	0.543825i	$0.183024\pi$
$380$		0			0
$381$	10.1623	+	17.6016i	0.520629	+	0.901756i
$382$	15.8377			0.810328
$383$	−1.08114	−	1.87259i	−0.0552436	−	0.0956847i	0.837081	−	0.547079i	$-0.184260\pi$
$383$	−1.08114	−	1.87259i	−0.0552436	−	0.0956847i	−0.892325	+	0.451394i	$0.850927\pi$
$384$	0.500000	+	0.866025i	0.0255155	+	0.0441942i
$385$		0			0
$386$	−8.66228	−	15.0035i	−0.440898	−	0.763658i
$387$	0.581139	−	1.00656i	0.0295409	−	0.0511664i
$388$	−8.66228	+	15.0035i	−0.439761	+	0.761688i
$389$	−28.3246			−1.43611			−0.718056	−	0.695985i	$-0.754968\pi$
$389$	−28.3246			−1.43611			−0.718056	+	0.695985i	$0.754968\pi$
$390$		0			0
$391$	1.81139			0.0916058
$392$	−1.50000	+	2.59808i	−0.0757614	+	0.131223i
$393$	8.16228	−	14.1375i	0.411732	−	0.713142i
$394$	−3.00000	−	5.19615i	−0.151138	−	0.261778i
$395$		0			0
$396$	−1.50000	−	2.59808i	−0.0753778	−	0.130558i
$397$	−5.83772	−	10.1112i	−0.292987	−	0.507468i	0.681528	−	0.731792i	$-0.261316\pi$
$397$	−5.83772	−	10.1112i	−0.292987	−	0.507468i	−0.974515	+	0.224324i	$0.927983\pi$
$398$	8.83772			0.442995
$399$	−5.00000	−	8.66025i	−0.250313	−	0.433555i
$400$		0			0
$401$	−8.16228	+	14.1375i	−0.407605	+	0.705992i	−0.994621	−	0.103583i	$-0.966969\pi$
$401$	−8.16228	+	14.1375i	−0.407605	+	0.705992i	0.587016	+	0.809575i	$0.300303\pi$
$402$	−4.00000			−0.199502
$403$	0.230249	+	10.2290i	0.0114695	+	0.509541i
$404$	8.64911			0.430309
$405$		0			0
$406$	−6.83772	+	11.8433i	−0.339350	+	0.587772i
$407$	12.7302	+	22.0494i	0.631015	+	1.09295i
$408$	−0.837722			−0.0414734
$409$	−15.1623	−	26.2618i	−0.749726	−	1.29856i	−0.947954	−	0.318408i	$-0.896852\pi$
$409$	−15.1623	−	26.2618i	−0.749726	−	1.29856i	0.198227	−	0.980156i	$-0.436482\pi$
$410$		0			0
$411$	−12.0000			−0.591916
$412$	2.74342	+	4.75174i	0.135158	+	0.234101i
$413$	9.48683	−	16.4317i	0.466817	−	0.808550i
$414$	−1.08114	+	1.87259i	−0.0531351	+	0.0920326i
$415$		0			0
$416$	3.08114	−	1.87259i	0.151065	−	0.0918112i
$417$	5.67544			0.277928
$418$	4.74342	−	8.21584i	0.232008	−	0.401850i
$419$	−4.50000	+	7.79423i	−0.219839	+	0.380773i	−0.954759	−	0.297382i	$-0.903887\pi$
$419$	−4.50000	+	7.79423i	−0.219839	+	0.380773i	0.734919	+	0.678155i	$0.237220\pi$
$420$		0			0
$421$	28.1623			1.37255			0.686273	−	0.727344i	$-0.259246\pi$
$421$	28.1623			1.37255			0.686273	+	0.727344i	$0.259246\pi$
$422$	−6.58114	−	11.3989i	−0.320365	−	0.554888i
$423$	−3.00000	−	5.19615i	−0.145865	−	0.252646i
$424$	0.837722			0.0406834
$425$		0			0
$426$	−7.08114	+	12.2649i	−0.343082	+	0.594236i
$427$	7.09431	−	12.2877i	0.343318	−	0.594643i
$428$	−6.00000			−0.290021
$429$	−9.24342	+	5.61776i	−0.446276	+	0.271228i
$430$		0			0
$431$	12.2434	−	21.2062i	0.589745	−	1.02147i	−0.404521	−	0.914529i	$-0.632562\pi$
$431$	12.2434	−	21.2062i	0.589745	−	1.02147i	0.994266	−	0.106939i	$-0.0341049\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	−17.3114	−	29.9842i	−0.831932	−	1.44095i	−0.896504	−	0.443036i	$-0.853901\pi$
$433$	−17.3114	−	29.9842i	−0.831932	−	1.44095i	0.0645717	−	0.997913i	$-0.479432\pi$
$434$	8.97367			0.430750
$435$		0			0
$436$	5.24342	+	9.08186i	0.251114	+	0.434942i
$437$	−6.83772			−0.327093
$438$	5.66228	+	9.80735i	0.270554	+	0.468613i
$439$	18.3246	−	31.7391i	0.874583	−	1.51482i	0.0173773	−	0.999849i	$-0.494468\pi$
$439$	18.3246	−	31.7391i	0.874583	−	1.51482i	0.857206	−	0.514974i	$-0.172198\pi$
$440$		0			0
$441$	3.00000			0.142857
$442$	0.0679718	+	3.01969i	0.00323309	+	0.143632i
$443$	9.00000			0.427603			0.213801	−	0.976877i	$-0.431415\pi$
$443$	9.00000			0.427603			0.213801	+	0.976877i	$0.431415\pi$
$444$	−4.24342	+	7.34981i	−0.201384	+	0.348807i
$445$		0			0
$446$	13.0680	+	22.6344i	0.618786	+	1.07177i
$447$	6.83772			0.323413
$448$	−1.58114	−	2.73861i	−0.0747018	−	0.129387i
$449$	−1.25658	−	2.17647i	−0.0593018	−	0.102714i	0.834850	−	0.550477i	$-0.185554\pi$
$449$	−1.25658	−	2.17647i	−0.0593018	−	0.102714i	−0.894152	+	0.447763i	$0.852221\pi$
$450$		0			0
$451$	−14.2302	−	24.6475i	−0.670076	−	1.16061i
$452$	5.16228	−	8.94133i	0.242813	−	0.420565i
$453$	4.90569	−	8.49691i	0.230490	−	0.399220i
$454$	−21.9737			−1.03128
$455$		0			0
$456$	3.16228			0.148087
$457$	−5.17544	+	8.96413i	−0.242097	+	0.419324i	−0.961311	−	0.275464i	$-0.911169\pi$
$457$	−5.17544	+	8.96413i	−0.242097	+	0.419324i	0.719214	+	0.694788i	$0.244502\pi$
$458$	8.24342	−	14.2780i	0.385190	−	0.667168i
$459$	0.418861	+	0.725489i	0.0195508	+	0.0338629i
$460$		0			0
$461$	8.58114	+	14.8630i	0.399663	+	0.692237i	0.993684	−	0.112212i	$-0.0357937\pi$
$461$	8.58114	+	14.8630i	0.399663	+	0.692237i	−0.594021	+	0.804450i	$0.702460\pi$
$462$	4.74342	+	8.21584i	0.220684	+	0.382235i
$463$	−4.51317			−0.209745			−0.104872	−	0.994486i	$-0.533443\pi$
$463$	−4.51317			−0.209745			−0.104872	+	0.994486i	$0.533443\pi$
$464$	−2.16228	−	3.74517i	−0.100381	−	0.173865i
$465$		0			0
$466$	6.83772	−	11.8433i	0.316751	−	0.548629i
$467$	3.00000			0.138823			0.0694117	−	0.997588i	$-0.477888\pi$
$467$	3.00000			0.138823			0.0694117	+	0.997588i	$0.477888\pi$
$468$	−3.16228	−	1.73205i	−0.146176	−	0.0800641i
$469$	12.6491			0.584082
$470$		0			0
$471$	−8.08114	+	13.9969i	−0.372359	+	0.644945i
$472$	3.00000	+	5.19615i	0.138086	+	0.239172i
$473$	−3.48683			−0.160325
$474$	1.41886	+	2.45754i	0.0651705	+	0.112879i
$475$		0			0
$476$	2.64911			0.121422
$477$	−0.418861	−	0.725489i	−0.0191783	−	0.0332179i
$478$	−9.24342	+	16.0101i	−0.422784	+	0.732283i
$479$	6.83772	−	11.8433i	0.312424	−	0.541133i	−0.666463	−	0.745538i	$-0.732193\pi$
$479$	6.83772	−	11.8433i	0.312424	−	0.541133i	0.978886	+	0.204405i	$0.0655259\pi$
$480$		0			0
$481$	26.8377	+	14.6996i	1.22369	+	0.670245i
$482$	8.00000			0.364390
$483$	3.41886	−	5.92164i	0.155564	−	0.269444i
$484$	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	0.827976	−	0.560764i	$-0.189493\pi$
$487$	−1.58114	−	2.73861i	−0.0716482	−	0.124098i	−0.899624	+	0.436666i	$0.856159\pi$
$488$	2.24342	+	3.88571i	0.101555	+	0.175898i
$489$	15.8114			0.715016
$490$		0			0
$491$	10.9868	−	19.0298i	0.495829	−	0.858801i	−0.504160	−	0.863611i	$-0.668198\pi$
$491$	10.9868	−	19.0298i	0.495829	−	0.858801i	0.999988	+	0.00480977i	$0.00153100\pi$
$492$	4.74342	−	8.21584i	0.213850	−	0.370399i
$493$	3.62278			0.163162
$494$	−0.256584	−	11.3989i	−0.0115442	−	0.512859i
$495$		0			0
$496$	−1.41886	+	2.45754i	−0.0637087	+	0.110347i
$497$	22.3925	−	38.7850i	1.00444	−	1.73974i
$498$	5.82456	+	10.0884i	0.261005	+	0.452073i
$499$	39.8114			1.78220			0.891101	−	0.453805i	$-0.149934\pi$
$499$	39.8114			1.78220			0.891101	+	0.453805i	$0.149934\pi$
$500$		0			0
$501$	−4.08114	−	7.06874i	−0.182332	−	0.315808i
$502$	15.0000			0.669483
$503$	−8.40569	−	14.5591i	−0.374791	−	0.649158i	0.615504	−	0.788133i	$-0.288952\pi$
$503$	−8.40569	−	14.5591i	−0.374791	−	0.649158i	−0.990296	+	0.138976i	$0.955619\pi$
$504$	−1.58114	+	2.73861i	−0.0704295	+	0.121988i
$505$		0			0
$506$	6.48683			0.288375
$507$	−5.98683	+	11.5394i	−0.265885	+	0.512483i
$508$	20.3246			0.901756
$509$	13.3925	−	23.1965i	0.593613	−	1.02817i	−0.400128	−	0.916459i	$-0.631034\pi$
$509$	13.3925	−	23.1965i	0.593613	−	1.02817i	0.993741	−	0.111709i	$-0.0356325\pi$
$510$		0			0
$511$	−17.9057	−	31.0136i	−0.792101	−	1.37196i
$512$	1.00000			0.0441942
$513$	−1.58114	−	2.73861i	−0.0698090	−	0.120913i
$514$	−12.9057	−	22.3533i	−0.569246	−	0.985963i
$515$		0			0
$516$	−0.581139	−	1.00656i	−0.0255832	−	0.0443114i
$517$	−9.00000	+	15.5885i	−0.395820	+	0.685580i
$518$	13.4189	−	23.2421i	0.589591	−	1.02120i
$519$	−1.67544			−0.0735439
$520$		0			0
$521$	−20.6491			−0.904654			−0.452327	−	0.891852i	$-0.649406\pi$
$521$	−20.6491			−0.904654			−0.452327	+	0.891852i	$0.649406\pi$
$522$	−2.16228	+	3.74517i	−0.0946403	+	0.163922i
$523$	16.4868	−	28.5560i	0.720919	−	1.24867i	−0.239713	−	0.970844i	$-0.577053\pi$
$523$	16.4868	−	28.5560i	0.720919	−	1.24867i	0.960632	−	0.277824i	$-0.0896133\pi$
$524$	−8.16228	−	14.1375i	−0.356571	−	0.617599i
$525$		0			0
$526$	−0.243416	−	0.421610i	−0.0106135	−	0.0183831i
$527$	−1.18861	−	2.05874i	−0.0517767	−	0.0896799i
$528$	−3.00000			−0.130558
$529$	9.16228	+	15.8695i	0.398360	+	0.689980i
$530$		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
$534$	0.837722			0.0362518
$535$		0			0
$536$	−2.00000	+	3.46410i	−0.0863868	+	0.149626i
$537$	11.8246	+	20.4807i	0.510267	+	0.883809i
$538$	−12.8377			−0.553474
$539$	−4.50000	−	7.79423i	−0.193829	−	0.335721i
$540$		0			0
$541$	30.8114			1.32469			0.662343	−	0.749201i	$-0.269562\pi$
$541$	30.8114			1.32469			0.662343	+	0.749201i	$0.269562\pi$
$542$	−0.162278	−	0.281073i	−0.00697042	−	0.0120731i
$543$	6.40569	−	11.0950i	0.274895	−	0.476131i
$544$	−0.418861	+	0.725489i	−0.0179585	+	0.0311051i
$545$		0			0
$546$	10.0000	+	5.47723i	0.427960	+	0.234404i
$547$	−14.1359			−0.604409			−0.302205	−	0.953243i	$-0.597723\pi$
$547$	−14.1359			−0.604409			−0.302205	+	0.953243i	$0.597723\pi$
$548$	−6.00000	+	10.3923i	−0.256307	+	0.443937i
$549$	2.24342	−	3.88571i	0.0957467	−	0.165838i
$550$		0			0
$551$	−13.6754			−0.582594
$552$	1.08114	+	1.87259i	0.0460163	+	0.0797026i
$553$	−4.48683	−	7.77142i	−0.190800	−	0.330475i
$554$	8.81139			0.374360
$555$		0			0
$556$	2.83772	−	4.91508i	0.120346	−	0.208446i
$557$	9.48683	−	16.4317i	0.401970	−	0.696232i	−0.591994	−	0.805943i	$-0.701659\pi$
$557$	9.48683	−	16.4317i	0.401970	−	0.696232i	0.993964	+	0.109710i	$0.0349923\pi$
$558$	2.83772			0.120130
$559$	−3.58114	+	2.17647i	−0.151466	+	0.0920547i
$560$		0			0
$561$	1.25658	−	2.17647i	0.0530530	−	0.0918905i
$562$	10.7434	−	18.6081i	0.453184	−	0.784937i
$563$	16.9868	+	29.4221i	0.715910	+	1.23999i	0.962608	+	0.270899i	$0.0873211\pi$
$563$	16.9868	+	29.4221i	0.715910	+	1.23999i	−0.246698	+	0.969092i	$0.579346\pi$
$564$	−6.00000			−0.252646
$565$		0			0
$566$	−9.74342	−	16.8761i	−0.409546	−	0.709355i
$567$	3.16228			0.132803
$568$	7.08114	+	12.2649i	0.297118	+	0.514623i
$569$	3.48683	−	6.03937i	0.146176	−	0.253184i	−0.783635	−	0.621221i	$-0.786637\pi$
$569$	3.48683	−	6.03937i	0.146176	−	0.253184i	0.929811	+	0.368038i	$0.119970\pi$
$570$		0			0
$571$	−32.3246			−1.35274			−0.676370	−	0.736562i	$-0.736448\pi$
$571$	−32.3246			−1.35274			−0.676370	+	0.736562i	$0.736448\pi$
$572$	0.243416	+	10.8139i	0.0101778	+	0.452152i
$573$	−15.8377			−0.661630
$574$	−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	$-0.147135\pi$
$577$	43.0000			1.79011			0.895057	+	0.445952i	$0.147135\pi$
$578$	8.14911	+	14.1147i	0.338958	+	0.587093i
$579$	8.66228	+	15.0035i	0.359992	+	0.623524i
$580$		0			0
$581$	−18.4189	−	31.9024i	−0.764143	−	1.32353i
$582$	8.66228	−	15.0035i	0.359063	−	0.621915i
$583$	−1.25658	+	2.17647i	−0.0520424	+	0.0901400i
$584$	11.3246			0.468613
$585$		0			0
$586$	−21.4868			−0.887613
$587$	−10.5000	+	18.1865i	−0.433381	+	0.750639i	−0.997162	−	0.0752860i	$-0.976013\pi$
$587$	−10.5000	+	18.1865i	−0.433381	+	0.750639i	0.563781	+	0.825925i	$0.309346\pi$
$588$	1.50000	−	2.59808i	0.0618590	−	0.107143i
$589$	4.48683	+	7.77142i	0.184877	+	0.320216i
$590$		0			0
$591$	3.00000	+	5.19615i	0.123404	+	0.213741i
$592$	4.24342	+	7.34981i	0.174403	+	0.302075i
$593$	5.16228			0.211989			0.105995	−	0.994367i	$-0.466197\pi$
$593$	5.16228			0.211989			0.105995	+	0.994367i	$0.466197\pi$
$594$	1.50000	+	2.59808i	0.0615457	+	0.106600i
$595$		0			0
$596$	3.41886	−	5.92164i	0.140042	−	0.242560i
$597$	−8.83772			−0.361704
$598$	6.66228	−	4.04905i	0.272441	−	0.165578i
$599$	1.18861			0.0485654			0.0242827	−	0.999705i	$-0.492270\pi$
$599$	1.18861			0.0485654			0.0242827	+	0.999705i	$0.492270\pi$
$600$		0			0
$601$	−21.6491	+	37.4974i	−0.883086	+	1.52955i	−0.0351935	+	0.999381i	$0.511205\pi$
$601$	−21.6491	+	37.4974i	−0.883086	+	1.52955i	−0.847892	+	0.530169i	$0.822129\pi$
$602$	1.83772	+	3.18303i	0.0749000	+	0.129731i
$603$	4.00000			0.162893
$604$	−4.90569	−	8.49691i	−0.199610	−	0.345734i
$605$		0			0
$606$	−8.64911			−0.351346
$607$	18.1623	+	31.4580i	0.737184	+	1.27684i	0.953758	+	0.300574i	$0.0971783\pi$
$607$	18.1623	+	31.4580i	0.737184	+	1.27684i	−0.216574	+	0.976266i	$0.569488\pi$
$608$	1.58114	−	2.73861i	0.0641236	−	0.111065i
$609$	6.83772	−	11.8433i	0.277078	−	0.479914i
$610$		0			0
$611$	0.486833	+	21.6278i	0.0196952	+	0.874968i
$612$	0.837722			0.0338629
$613$	21.1623	−	36.6541i	0.854736	−	1.48045i	−0.0221531	−	0.999755i	$-0.507052\pi$
$613$	21.1623	−	36.6541i	0.854736	−	1.48045i	0.876889	−	0.480692i	$-0.159615\pi$
$614$	8.32456	−	14.4186i	0.335952	−	0.581885i
$615$		0			0
$616$	9.48683			0.382235
$617$	−23.6491	−	40.9615i	−0.952077	−	1.64905i	−0.740919	−	0.671594i	$-0.765610\pi$
$617$	−23.6491	−	40.9615i	−0.952077	−	1.64905i	−0.211158	−	0.977452i	$-0.567724\pi$
$618$	−2.74342	−	4.75174i	−0.110356	−	0.191143i
$619$	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
$621$	1.08114	−	1.87259i	0.0433846	−	0.0751443i
$622$	3.24342	−	5.61776i	0.130049	−	0.225252i
$623$	−2.64911			−0.106134
$624$	−3.08114	+	1.87259i	−0.123344	+	0.0749635i
$625$		0			0
$626$	3.82456	−	6.62432i	0.152860	−	0.264761i
$627$	−4.74342	+	8.21584i	−0.189434	+	0.328109i
$628$	8.08114	+	13.9969i	0.322473	+	0.558539i
$629$	−7.10961			−0.283479
$630$		0			0
$631$	7.64911	+	13.2486i	0.304506	+	0.527420i	0.977151	−	0.212545i	$-0.0681752\pi$
$631$	7.64911	+	13.2486i	0.304506	+	0.527420i	−0.672645	+	0.739965i	$0.734842\pi$
$632$	2.83772			0.112879
$633$	6.58114	+	11.3989i	0.261577	+	0.453064i
$634$	−15.9057	+	27.5495i	−0.631696	+	1.09413i
$635$		0			0
$636$	−0.837722			−0.0332179
$637$	−9.48683	−	5.19615i	−0.375882	−	0.205879i
$638$	12.9737			0.513632
$639$	7.08114	−	12.2649i	0.280126	−	0.485192i
$640$		0			0
$641$	−12.9737	−	22.4710i	−0.512429	−	0.887553i	−0.999896	−	0.0144117i	$-0.995412\pi$
$641$	−12.9737	−	22.4710i	−0.512429	−	0.887553i	0.487467	−	0.873141i	$-0.337921\pi$
$642$	6.00000			0.236801
$643$	−5.83772	−	10.1112i	−0.230217	−	0.398748i	0.727655	−	0.685944i	$-0.240610\pi$
$643$	−5.83772	−	10.1112i	−0.230217	−	0.398748i	−0.957872	+	0.287196i	$0.907277\pi$
$644$	−3.41886	−	5.92164i	−0.134722	−	0.233345i
$645$		0			0
$646$	1.32456	+	2.29420i	0.0521139	+	0.0902640i
$647$	−11.7566	+	20.3630i	−0.462199	+	0.800552i	−0.999070	−	0.0431121i	$-0.986273\pi$
$647$	−11.7566	+	20.3630i	−0.462199	+	0.800552i	0.536871	+	0.843664i	$0.319606\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	−18.0000			−0.706562
$650$		0			0
$651$	−8.97367			−0.351706
$652$	7.90569	−	13.6931i	0.309611	−	0.536262i
$653$	−4.74342	+	8.21584i	−0.185624	+	0.321511i	−0.943787	−	0.330555i	$-0.892764\pi$
$653$	−4.74342	+	8.21584i	−0.185624	+	0.321511i	0.758162	+	0.652066i	$0.226097\pi$
$654$	−5.24342	−	9.08186i	−0.205034	−	0.355129i
$655$		0			0
$656$	−4.74342	−	8.21584i	−0.185199	−	0.320775i
$657$	−5.66228	−	9.80735i	−0.220906	−	0.382621i
$658$	18.9737			0.739671
$659$	7.50000	+	12.9904i	0.292159	+	0.506033i	0.974320	−	0.225168i	$-0.0722932\pi$
$659$	7.50000	+	12.9904i	0.292159	+	0.506033i	−0.682161	+	0.731202i	$0.738960\pi$
$660$		0			0
$661$	−13.0000	+	22.5167i	−0.505641	+	0.875797i	0.494337	+	0.869270i	$0.335411\pi$
$661$	−13.0000	+	22.5167i	−0.505641	+	0.875797i	−0.999979	+	0.00652642i	$0.997923\pi$
$662$	−15.1623			−0.589299
$663$	−0.0679718	−	3.01969i	−0.00263981	−	0.117275i
$664$	11.6491			0.452073
$665$		0			0
$666$	4.24342	−	7.34981i	0.164429	−	0.284799i
$667$	−4.67544	−	8.09811i	−0.181034	−	0.313560i
$668$	−8.16228			−0.315808
$669$	−13.0680	−	22.6344i	−0.505237	−	0.875096i
$670$		0			0
$671$	−13.4605			−0.519637
$672$	1.58114	+	2.73861i	0.0609938	+	0.105644i
$673$	−1.82456	+	3.16022i	−0.0703314	+	0.121818i	−0.899047	−	0.437853i	$-0.855739\pi$
$673$	−1.82456	+	3.16022i	−0.0703314	+	0.121818i	0.828715	+	0.559671i	$0.189072\pi$
$674$	−2.00000	+	3.46410i	−0.0770371	+	0.133432i
$675$		0			0
$676$	7.00000	+	10.9545i	0.269231	+	0.421325i
$677$	32.6491			1.25481			0.627404	−	0.778694i	$-0.284118\pi$
$677$	32.6491			1.25481			0.627404	+	0.778694i	$0.284118\pi$
$678$	−5.16228	+	8.94133i	−0.198256	+	0.343390i
$679$	−27.3925	+	47.4452i	−1.05123	+	1.82078i
$680$		0			0
$681$	21.9737			0.842033
$682$	−4.25658	−	7.37262i	−0.162993	−	0.282312i
$683$	−14.4737	−	25.0691i	−0.553819	−	0.959243i	−0.997994	−	0.0633033i	$-0.979836\pi$
$683$	−14.4737	−	25.0691i	−0.553819	−	0.959243i	0.444175	−	0.895940i	$-0.353497\pi$
$684$	−3.16228			−0.120913
$685$		0			0
$686$	6.32456	−	10.9545i	0.241473	−	0.418243i
$687$	−8.24342	+	14.2780i	−0.314506	+	0.544740i
$688$	−1.16228			−0.0443114
$689$	0.0679718	+	3.01969i	0.00258952	+	0.115041i
$690$		0			0
$691$	11.9737	−	20.7390i	0.455500	−	0.788949i	−0.543217	−	0.839592i	$-0.682794\pi$
$691$	11.9737	−	20.7390i	0.455500	−	0.788949i	0.998717	+	0.0506436i	$0.0161273\pi$
$692$	−0.837722	+	1.45098i	−0.0318454	+	0.0551579i
$693$	−4.74342	−	8.21584i	−0.180187	−	0.312094i
$694$	−1.32456			−0.0502794
$695$		0			0
$696$	2.16228	+	3.74517i	0.0819609	+	0.141960i
$697$	7.94733			0.301027
$698$	17.7302	+	30.7097i	0.671100	+	1.16238i
$699$	−6.83772	+	11.8433i	−0.258626	+	0.447954i
$700$		0			0
$701$	−22.4605			−0.848321			−0.424161	−	0.905587i	$-0.639431\pi$
$701$	−22.4605			−0.848321			−0.424161	+	0.905587i	$0.639431\pi$
$702$	3.16228	+	1.73205i	0.119352	+	0.0653720i
$703$	26.8377			1.01220
$704$	−1.50000	+	2.59808i	−0.0565334	+	0.0979187i
$705$		0			0
$706$	−9.90569	−	17.1572i	−0.372806	−	0.645718i
$707$	27.3509			1.02864
$708$	−3.00000	−	5.19615i	−0.112747	−	0.195283i
$709$	−0.756584	−	1.31044i	−0.0284141	−	0.0492146i	0.851469	−	0.524405i	$-0.175712\pi$
$709$	−0.756584	−	1.31044i	−0.0284141	−	0.0492146i	−0.879883	+	0.475191i	$0.842379\pi$
$710$		0			0
$711$	−1.41886	−	2.45754i	−0.0532115	−	0.0921649i
$712$	0.418861	−	0.725489i	0.0156975	−	0.0271888i
$713$	−3.06797	+	5.31388i	−0.114896	+	0.199006i
$714$	−2.64911			−0.0991405
$715$		0			0
$716$	23.6491			0.883809
$717$	9.24342	−	16.0101i	0.345202	−	0.597907i
$718$	6.00000	−	10.3923i	0.223918	−	0.387837i
$719$	23.4057	+	40.5399i	0.872885	+	1.51188i	0.858999	+	0.511978i	$0.171087\pi$
$719$	23.4057	+	40.5399i	0.872885	+	1.51188i	0.0138864	+	0.999904i	$0.495580\pi$
$720$		0			0
$721$	8.67544	+	15.0263i	0.323090	+	0.559609i
$722$	4.50000	+	7.79423i	0.167473	+	0.290071i
$723$	−8.00000			−0.297523
$724$	−6.40569	−	11.0950i	−0.238066	−	0.412342i
$725$		0			0
$726$	−1.00000	+	1.73205i	−0.0371135	+	0.0642824i
$727$	−12.3246			−0.457092			−0.228546	−	0.973533i	$-0.573397\pi$
$727$	−12.3246			−0.457092			−0.228546	+	0.973533i	$0.573397\pi$
$728$	9.74342	−	5.92164i	0.361115	−	0.219471i
$729$	1.00000			0.0370370
$730$		0			0
$731$	0.486833	−	0.843219i	0.0180062	−	0.0311876i
$732$	−2.24342	−	3.88571i	−0.0829191	−	0.143620i
$733$	−19.5132			−0.720735			−0.360368	−	0.932810i	$-0.617349\pi$
$733$	−19.5132			−0.720735			−0.360368	+	0.932810i	$0.617349\pi$
$734$	−9.32456	−	16.1506i	−0.344176	−	0.596130i
$735$		0			0
$736$	2.16228			0.0797026
$737$	−6.00000	−	10.3923i	−0.221013	−	0.382805i
$738$	−4.74342	+	8.21584i	−0.174608	+	0.302429i
$739$	−9.64911	+	16.7127i	−0.354948	+	0.614788i	−0.987109	−	0.160049i	$-0.948835\pi$
$739$	−9.64911	+	16.7127i	−0.354948	+	0.614788i	0.632161	+	0.774837i	$0.282168\pi$
$740$		0			0
$741$	0.256584	+	11.3989i	0.00942583	+	0.418748i
$742$	2.64911			0.0972519
$743$	−22.3246	+	38.6673i	−0.819009	+	1.41856i	0.0874050	+	0.996173i	$0.472143\pi$
$743$	−22.3246	+	38.6673i	−0.819009	+	1.41856i	−0.906414	+	0.422391i	$0.861191\pi$
$744$	1.41886	−	2.45754i	0.0520180	−	0.0900978i
$745$		0			0
$746$	10.4868			0.383950
$747$	−5.82456	−	10.0884i	−0.213109	−	0.369116i
$748$	−1.25658	−	2.17647i	−0.0459452	−	0.0795795i
$749$	−18.9737			−0.693283
$750$		0			0
$751$	8.83772	−	15.3074i	0.322493	−	0.558574i	−0.658509	−	0.752573i	$-0.728812\pi$
$751$	8.83772	−	15.3074i	0.322493	−	0.558574i	0.981002	+	0.193999i	$0.0621458\pi$
$752$	−3.00000	+	5.19615i	−0.109399	+	0.189484i
$753$	−15.0000			−0.546630
$754$	13.3246	−	8.09811i	0.485252	−	0.294916i
$755$		0			0
$756$	1.58114	−	2.73861i	0.0575055	−	0.0996024i
$757$	−5.48683	+	9.50347i	−0.199422	+	0.345410i	−0.948341	−	0.317252i	$-0.897240\pi$
$757$	−5.48683	+	9.50347i	−0.199422	+	0.345410i	0.748919	+	0.662662i	$0.230573\pi$
$758$	−1.00000	−	1.73205i	−0.0363216	−	0.0629109i
$759$	−6.48683			−0.235457
$760$		0			0
$761$	23.2302	+	40.2360i	0.842096	+	1.45855i	0.888120	+	0.459613i	$0.152012\pi$
$761$	23.2302	+	40.2360i	0.842096	+	1.45855i	−0.0460237	+	0.998940i	$0.514655\pi$
$762$	−20.3246			−0.736281
$763$	16.5811	+	28.7194i	0.600278	+	1.03971i
$764$	−7.91886	+	13.7159i	−0.286494	+	0.496223i
$765$		0			0
$766$	2.16228			0.0781263
$767$	−18.4868	+	11.2355i	−0.667521	+	0.405691i
$768$	−1.00000			−0.0360844
$769$	−7.48683	+	12.9676i	−0.269982	+	0.467623i	−0.968857	−	0.247621i	$-0.920351\pi$
$769$	−7.48683	+	12.9676i	−0.269982	+	0.467623i	0.698875	+	0.715244i	$0.253684\pi$
$770$		0			0
$771$	12.9057	+	22.3533i	0.464787	+	0.805035i
$772$	17.3246			0.623524
$773$	−4.67544	−	8.09811i	−0.168164	−	0.291269i	0.769610	−	0.638514i	$-0.220451\pi$
$773$	−4.67544	−	8.09811i	−0.168164	−	0.291269i	−0.937774	+	0.347245i	$0.887117\pi$
$774$	0.581139	+	1.00656i	0.0208886	+	0.0361801i
$775$		0			0
$776$	−8.66228	−	15.0035i	−0.310958	−	0.538594i
$777$	−13.4189	+	23.2421i	−0.481399	+	0.833807i
$778$	14.1623	−	24.5298i	0.507742	−	0.879435i
$779$	−30.0000			−1.07486
$780$		0			0
$781$	−42.4868			−1.52030
$782$	−0.905694	+	1.56871i	−0.0323876	+	0.0560969i
$783$	2.16228	−	3.74517i	0.0772735	−	0.133842i
$784$	−1.50000	−	2.59808i	−0.0535714	−	0.0927884i
$785$		0			0
$786$	8.16228	+	14.1375i	0.291139	+	0.504267i
$787$	2.74342	+	4.75174i	0.0977922	+	0.169381i	0.910771	−	0.412913i	$-0.135489\pi$
$787$	2.74342	+	4.75174i	0.0977922	+	0.169381i	−0.812978	+	0.582294i	$0.802155\pi$
$788$	6.00000			0.213741
$789$	0.243416	+	0.421610i	0.00866586	+	0.0150097i
$790$		0			0
$791$	16.3246	−	28.2750i	0.580434	−	1.00534i
$792$	3.00000			0.106600
$793$	−13.8246	+	8.40199i	−0.490924	+	0.298363i
$794$	11.6754			0.414346
$795$		0			0
$796$	−4.41886	+	7.65369i	−0.156622	+	0.271278i
$797$	−23.2982	−	40.3537i	−0.825265	−	1.42940i	−0.901716	−	0.432328i	$-0.857692\pi$
$797$	−23.2982	−	40.3537i	−0.825265	−	1.42940i	0.0764510	−	0.997073i	$-0.475641\pi$
$798$	10.0000			0.353996
$799$	−2.51317	−	4.35293i	−0.0889095	−	0.153996i
$800$		0			0
$801$	−0.837722			−0.0295995
$802$	−8.16228	−	14.1375i	−0.288220	−	0.499212i
$803$	−16.9868	+	29.4221i	−0.599452	+	1.03828i
$804$	2.00000	−	3.46410i	0.0705346	−	0.122169i
$805$		0			0
$806$	−8.97367	−	4.91508i	−0.316084	−	0.173126i
$807$	12.8377			0.451909
$808$	−4.32456	+	7.49035i	−0.152137	+	0.263510i
$809$	6.41886	−	11.1178i	0.225675	−	0.390881i	−0.730847	−	0.682542i	$-0.760875\pi$
$809$	6.41886	−	11.1178i	0.225675	−	0.390881i	0.956522	+	0.291661i	$0.0942079\pi$
$810$		0			0
$811$	−6.64911			−0.233482			−0.116741	−	0.993162i	$-0.537245\pi$
$811$	−6.64911			−0.233482			−0.116741	+	0.993162i	$0.537245\pi$
$812$	−6.83772	−	11.8433i	−0.239957	−	0.415618i
$813$	0.162278	+	0.281073i	0.00569133	+	0.00985767i
$814$	−25.4605			−0.892390
$815$		0			0
$816$	0.418861	−	0.725489i	0.0146631	−	0.0253972i
$817$	−1.83772	+	3.18303i	−0.0642938	+	0.111360i
$818$	30.3246			1.06027
$819$	−10.0000	−	5.47723i	−0.349428	−	0.191390i
$820$		0			0
$821$	−2.16228	+	3.74517i	−0.0754640	+	0.130708i	−0.901288	−	0.433221i	$-0.857377\pi$
$821$	−2.16228	+	3.74517i	−0.0754640	+	0.130708i	0.825824	+	0.563928i	$0.190710\pi$
$822$	6.00000	−	10.3923i	0.209274	−	0.362473i
$823$	4.41886	+	7.65369i	0.154032	+	0.266791i	0.932706	−	0.360637i	$-0.117441\pi$
$823$	4.41886	+	7.65369i	0.154032	+	0.266791i	−0.778674	+	0.627428i	$0.784108\pi$
$824$	−5.48683			−0.191143
$825$		0			0
$826$	9.48683	+	16.4317i	0.330089	+	0.571731i
$827$	−27.9737			−0.972740			−0.486370	−	0.873753i	$-0.661679\pi$
$827$	−27.9737			−0.972740			−0.486370	+	0.873753i	$0.661679\pi$
$828$	−1.08114	−	1.87259i	−0.0375722	−	0.0650769i
$829$	2.48683	−	4.30732i	0.0863713	−	0.149599i	−0.819603	−	0.572931i	$-0.805806\pi$
$829$	2.48683	−	4.30732i	0.0863713	−	0.149599i	0.905975	+	0.423332i	$0.139140\pi$
$830$		0			0
$831$	−8.81139			−0.305664
$832$	0.0811388	+	3.60464i	0.00281298	+	0.124968i
$833$	2.51317			0.0870761
$834$	−2.83772	+	4.91508i	−0.0982623	+	0.170195i
$835$		0			0
$836$	4.74342	+	8.21584i	0.164054	+	0.284151i
$837$	−2.83772			−0.0980860
$838$	−4.50000	−	7.79423i	−0.155450	−	0.269247i
$839$	17.8925	+	30.9908i	0.617719	+	1.06992i	0.989901	+	0.141760i	$0.0452763\pi$
$839$	17.8925	+	30.9908i	0.617719	+	1.06992i	−0.372182	+	0.928160i	$0.621390\pi$
$840$		0			0
$841$	5.14911	+	8.91852i	0.177556	+	0.307535i
$842$	−14.0811	+	24.3892i	−0.485268	+	0.840509i
$843$	−10.7434	+	18.6081i	−0.370023	+	0.640898i
$844$	13.1623			0.453064
$845$		0			0
$846$	6.00000			0.206284
$847$	3.16228	−	5.47723i	0.108657	−	0.188200i
$848$	−0.418861	+	0.725489i	−0.0143838	+	0.0249134i
$849$	9.74342	+	16.8761i	0.334393	+	0.579186i
$850$		0			0
$851$	9.17544	+	15.8923i	0.314530	+	0.544782i
$852$	−7.08114	−	12.2649i	−0.242596	−	0.420188i
$853$	18.6491			0.638533			0.319267	−	0.947665i	$-0.396563\pi$
$853$	18.6491			0.638533			0.319267	+	0.947665i	$0.396563\pi$
$854$	7.09431	+	12.2877i	0.242762	+	0.420476i
$855$		0			0
$856$	3.00000	−	5.19615i	0.102538	−	0.177601i
$857$	−42.2719			−1.44398			−0.721990	−	0.691903i	$-0.756772\pi$
$857$	−42.2719			−1.44398			−0.721990	+	0.691903i	$0.756772\pi$
$858$	−0.243416	−	10.8139i	−0.00831010	−	0.369181i
$859$	12.1886			0.415870			0.207935	−	0.978143i	$-0.433326\pi$
$859$	12.1886			0.415870			0.207935	+	0.978143i	$0.433326\pi$
$860$		0			0
$861$	15.0000	−	25.9808i	0.511199	−	0.885422i
$862$	12.2434	+	21.2062i	0.417012	+	0.722287i
$863$	−19.4605			−0.662443			−0.331222	−	0.943553i	$-0.607461\pi$
$863$	−19.4605			−0.662443			−0.331222	+	0.943553i	$0.607461\pi$
$864$	0.500000	+	0.866025i	0.0170103	+	0.0294628i
$865$		0			0
$866$	34.6228			1.17653
$867$	−8.14911	−	14.1147i	−0.276758	−	0.479359i
$868$	−4.48683	+	7.77142i	−0.152293	+	0.263779i
$869$	−4.25658	+	7.37262i	−0.144395	+	0.250099i
$870$		0			0
$871$	−12.6491	−	6.92820i	−0.428599	−	0.234753i
$872$	−10.4868			−0.355129
$873$	−8.66228	+	15.0035i	−0.293174	+	0.507792i
$874$	3.41886	−	5.92164i	0.115645	−	0.200303i
$875$		0			0
$876$	−11.3246			−0.382621
$877$	−28.4057	−	49.2001i	−0.959192	−	1.66137i	−0.724469	−	0.689307i	$-0.757915\pi$
$877$	−28.4057	−	49.2001i	−0.959192	−	1.66137i	−0.234723	−	0.972062i	$-0.575418\pi$
$878$	18.3246	+	31.7391i	0.618424	+	1.07114i
$879$	21.4868			0.724733
$880$		0			0
$881$	11.2302	−	19.4514i	0.378357	−	0.655333i	−0.612467	−	0.790496i	$-0.709823\pi$
$881$	11.2302	−	19.4514i	0.378357	−	0.655333i	0.990823	+	0.135163i	$0.0431559\pi$
$882$	−1.50000	+	2.59808i	−0.0505076	+	0.0874818i
$883$	−16.6491			−0.560287			−0.280144	−	0.959958i	$-0.590382\pi$
$883$	−16.6491			−0.560287			−0.280144	+	0.959958i	$0.590382\pi$
$884$	−2.64911	−	1.45098i	−0.0890992	−	0.0488017i
$885$		0			0
$886$	−4.50000	+	7.79423i	−0.151180	+	0.261852i
$887$	−4.32456	+	7.49035i	−0.145204	+	0.251501i	−0.929449	−	0.368950i	$-0.879717\pi$
$887$	−4.32456	+	7.49035i	−0.145204	+	0.251501i	0.784245	+	0.620452i	$0.213051\pi$
$888$	−4.24342	−	7.34981i	−0.142400	−	0.246644i
$889$	64.2719			2.15561
$890$		0			0
$891$	−1.50000	−	2.59808i	−0.0502519	−	0.0870388i
$892$	−26.1359			−0.875096
$893$	9.48683	+	16.4317i	0.317465	+	0.549865i
$894$	−3.41886	+	5.92164i	−0.114344	+	0.198049i
$895$		0			0
$896$	3.16228			0.105644
$897$	−6.66228	+	4.04905i	−0.222447	+	0.135194i
$898$	2.51317			0.0838655
$899$	−6.13594	+	10.6278i	−0.204645	+	0.354456i
$900$		0			0
$901$	−0.350889	−	0.607758i	−0.0116898	−	0.0202474i
$902$	28.4605			0.947631
$903$	−1.83772	−	3.18303i	−0.0611556	−	0.105925i
$904$	5.16228	+	8.94133i	0.171695	+	0.297384i
$905$		0			0
$906$	4.90569	+	8.49691i	0.162981	+	0.282291i
$907$	−28.5811	+	49.5040i	−0.949021	+	1.64375i	−0.201529	+	0.979483i	$0.564591\pi$
$907$	−28.5811	+	49.5040i	−0.949021	+	1.64375i	−0.747493	+	0.664270i	$0.768742\pi$
$908$	10.9868	−	19.0298i	0.364611	−	0.631525i
$909$	8.64911			0.286873
$910$		0			0
$911$	33.1359			1.09784			0.548921	−	0.835874i	$-0.315039\pi$
$911$	33.1359			1.09784			0.548921	+	0.835874i	$0.315039\pi$
$912$	−1.58114	+	2.73861i	−0.0523567	+	0.0906845i
$913$	−17.4737	+	30.2653i	−0.578294	+	1.00163i
$914$	−5.17544	−	8.96413i	−0.171188	−	0.296507i
$915$		0			0
$916$	8.24342	+	14.2780i	0.272370	+	0.471759i
$917$	−25.8114	−	44.7066i	−0.852367	−	1.47634i
$918$	−0.837722			−0.0276490
$919$	8.06797	+	13.9741i	0.266138	+	0.460964i	0.967861	−	0.251485i	$-0.0809190\pi$
$919$	8.06797	+	13.9741i	0.266138	+	0.460964i	−0.701723	+	0.712450i	$0.747586\pi$
$920$		0			0
$921$	−8.32456	+	14.4186i	−0.274303	+	0.475107i
$922$	−17.1623			−0.565210
$923$	−43.6359	+	26.5201i	−1.43629	+	0.872920i
$924$	−9.48683			−0.312094
$925$		0			0
$926$	2.25658	−	3.90852i	0.0741559	−	0.128442i
$927$	2.74342	+	4.75174i	0.0901056	+	0.156068i
$928$	4.32456			0.141960
$929$	−7.67544	−	13.2943i	−0.251823	−	0.436171i	0.712205	−	0.701972i	$-0.247697\pi$
$929$	−7.67544	−	13.2943i	−0.251823	−	0.436171i	−0.964028	+	0.265801i	$0.914363\pi$
$930$		0			0
$931$	−9.48683			−0.310918
$932$	6.83772	+	11.8433i	0.223977	+	0.387940i
$933$	−3.24342	+	5.61776i	−0.106185	+	0.183917i
$934$	−1.50000	+	2.59808i	−0.0490815	+	0.0850117i
$935$		0			0
$936$	3.08114	−	1.87259i	0.100710	−	0.0612074i
$937$	4.35089			0.142137			0.0710687	−	0.997471i	$-0.477359\pi$
$937$	4.35089			0.142137			0.0710687	+	0.997471i	$0.477359\pi$
$938$	−6.32456	+	10.9545i	−0.206504	+	0.357676i
$939$	−3.82456	+	6.62432i	−0.124810	+	0.216177i
$940$		0			0
$941$	−12.0000			−0.391189			−0.195594	−	0.980685i	$-0.562664\pi$
$941$	−12.0000			−0.391189			−0.195594	+	0.980685i	$0.562664\pi$
$942$	−8.08114	−	13.9969i	−0.263298	−	0.456045i
$943$	−10.2566	−	17.7649i	−0.334000	−	0.578506i
$944$	−6.00000			−0.195283
$945$		0			0
$946$	1.74342	−	3.01969i	0.0566834	−	0.0981785i
$947$	23.8246	−	41.2653i	0.774194	−	1.34094i	−0.161052	−	0.986946i	$-0.551489\pi$
$947$	23.8246	−	41.2653i	0.774194	−	1.34094i	0.935246	−	0.353998i	$-0.115178\pi$
$948$	−2.83772			−0.0921649
$949$	0.918861	+	40.8209i	0.0298275	+	1.32510i
$950$		0			0
$951$	15.9057	−	27.5495i	0.515777	−	0.893353i
$952$	−1.32456	+	2.29420i	−0.0429291	+	0.0743554i
$953$	−17.2302	−	29.8437i	−0.558143	−	0.966731i	−0.997652	−	0.0684931i	$-0.978181\pi$
$953$	−17.2302	−	29.8437i	−0.558143	−	0.966731i	0.439509	−	0.898238i	$-0.355152\pi$
$954$	0.837722			0.0271223
$955$		0			0
$956$	−9.24342	−	16.0101i	−0.298953	−	0.517803i
$957$	−12.9737			−0.419379
$958$	6.83772	+	11.8433i	0.220917	+	0.382639i
$959$	−18.9737	+	32.8634i	−0.612692	+	1.06121i
$960$		0			0
$961$	−22.9473			−0.740237
$962$	−26.1491	+	15.8923i	−0.843081	+	0.512389i
$963$	−6.00000			−0.193347
$964$	−4.00000	+	6.92820i	−0.128831	+	0.223142i
$965$		0			0
$966$	3.41886	+	5.92164i	0.110000	+	0.190526i
$967$	52.9737			1.70352			0.851759	−	0.523934i	$-0.175536\pi$
$967$	52.9737			1.70352			0.851759	+	0.523934i	$0.175536\pi$
$968$	1.00000	+	1.73205i	0.0321412	+	0.0556702i
$969$	−1.32456	−	2.29420i	−0.0425508	−	0.0737002i
$970$		0			0
$971$	−21.0000	−	36.3731i	−0.673922	−	1.16727i	−0.976783	−	0.214232i	$-0.931275\pi$
$971$	−21.0000	−	36.3731i	−0.673922	−	1.16727i	0.302861	−	0.953035i	$-0.402058\pi$
$972$	0.500000	−	0.866025i	0.0160375	−	0.0277778i
$973$	8.97367	−	15.5428i	0.287683	−	0.498281i
$974$	3.16228			0.101326
$975$		0			0
$976$	−4.48683			−0.143620
$977$	−12.8377	+	22.2356i	−0.410715	+	0.711379i	−0.994968	−	0.100192i	$-0.968054\pi$
$977$	−12.8377	+	22.2356i	−0.410715	+	0.711379i	0.584253	+	0.811572i	$0.301388\pi$
$978$	−7.90569	+	13.6931i	−0.252796	+	0.437856i
$979$	1.25658	+	2.17647i	0.0401606	+	0.0695602i
$980$		0			0
$981$	5.24342	+	9.08186i	0.167409	+	0.289962i
$982$	10.9868	+	19.0298i	0.350604	+	0.607264i
$983$	−29.2982			−0.934468			−0.467234	−	0.884134i	$-0.654749\pi$
$983$	−29.2982			−0.934468			−0.467234	+	0.884134i	$0.654749\pi$
$984$	4.74342	+	8.21584i	0.151215	+	0.261911i
$985$		0			0
$986$	−1.81139	+	3.13742i	−0.0576864	+	0.0999157i
$987$	−18.9737			−0.603938
$988$	10.0000	+	5.47723i	0.318142	+	0.174254i
$989$	−2.51317			−0.0799141
$990$		0			0
$991$	−6.93203	+	12.0066i	−0.220203	+	0.381403i	−0.954870	−	0.297026i	$-0.904005\pi$
$991$	−6.93203	+	12.0066i	−0.220203	+	0.381403i	0.734666	+	0.678429i	$0.237339\pi$
$992$	−1.41886	−	2.45754i	−0.0450489	−	0.0780270i
$993$	15.1623			0.481160
$994$	22.3925	+	38.7850i	0.710248	+	1.23019i
$995$		0			0
$996$	−11.6491			−0.369116
$997$	22.4868	+	38.9483i	0.712165	+	1.23351i	0.964043	+	0.265747i	$0.0856186\pi$
$997$	22.4868	+	38.9483i	0.712165	+	1.23351i	−0.251878	+	0.967759i	$0.581048\pi$
$998$	−19.9057	+	34.4777i	−0.630104	+	1.09137i
$999$	−4.24342	+	7.34981i	−0.134256	+	0.232538i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1950.2.i.ba.451.1	✓	4
5.2	odd	4		1950.2.z.o.1699.2		8
5.3	odd	4		1950.2.z.o.1699.3		8
5.4	even	2		1950.2.i.bf.451.2	yes	4
13.3	even	3	inner	1950.2.i.ba.601.1	yes	4
65.3	odd	12		1950.2.z.o.1849.2		8
65.29	even	6		1950.2.i.bf.601.2	yes	4
65.42	odd	12		1950.2.z.o.1849.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1950.2.i.ba.451.1	✓	4	1.1	even	1	trivial
1950.2.i.ba.601.1	yes	4	13.3	even	3	inner
1950.2.i.bf.451.2	yes	4	5.4	even	2
1950.2.i.bf.601.2	yes	4	65.29	even	6
1950.2.z.o.1699.2		8	5.2	odd	4
1950.2.z.o.1699.3		8	5.3	odd	4
1950.2.z.o.1849.2		8	65.3	odd	12
1950.2.z.o.1849.3		8	65.42	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1950.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{6} +(-1.58114 - 2.73861i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(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} +(0.0811388 + 3.60464i) q^{13} +3.16228 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-0.418861 - 0.725489i) q^{17} +1.00000 q^{18} +(1.58114 + 2.73861i) q^{19} -3.16228 q^{21} +(-1.50000 - 2.59808i) q^{22} +(-1.08114 + 1.87259i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-3.16228 - 1.73205i) q^{26} -1.00000 q^{27} +(-1.58114 + 2.73861i) q^{28} +(-2.16228 + 3.74517i) q^{29} +2.83772 q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.50000 + 2.59808i) q^{33} +0.837722 q^{34} +(-0.500000 + 0.866025i) q^{36} +(4.24342 - 7.34981i) q^{37} -3.16228 q^{38} +(3.16228 + 1.73205i) q^{39} +(-4.74342 + 8.21584i) q^{41} +(1.58114 - 2.73861i) q^{42} +(0.581139 + 1.00656i) q^{43} +3.00000 q^{44} +(-1.08114 - 1.87259i) q^{46} +6.00000 q^{47} +(0.500000 + 0.866025i) q^{48} +(-1.50000 + 2.59808i) q^{49} -0.837722 q^{51} +(3.08114 - 1.87259i) q^{52} +0.837722 q^{53} +(0.500000 - 0.866025i) q^{54} +(-1.58114 - 2.73861i) q^{56} +3.16228 q^{57} +(-2.16228 - 3.74517i) q^{58} +(3.00000 + 5.19615i) q^{59} +(2.24342 + 3.88571i) q^{61} +(-1.41886 + 2.45754i) q^{62} +(-1.58114 + 2.73861i) q^{63} +1.00000 q^{64} -3.00000 q^{66} +(-2.00000 + 3.46410i) q^{67} +(-0.418861 + 0.725489i) q^{68} +(1.08114 + 1.87259i) q^{69} +(7.08114 + 12.2649i) q^{71} +(-0.500000 - 0.866025i) q^{72} +11.3246 q^{73} +(4.24342 + 7.34981i) q^{74} +(1.58114 - 2.73861i) q^{76} +9.48683 q^{77} +(-3.08114 + 1.87259i) q^{78} +2.83772 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-4.74342 - 8.21584i) q^{82} +11.6491 q^{83} +(1.58114 + 2.73861i) q^{84} -1.16228 q^{86} +(2.16228 + 3.74517i) q^{87} +(-1.50000 + 2.59808i) q^{88} +(0.418861 - 0.725489i) q^{89} +(9.74342 - 5.92164i) q^{91} +2.16228 q^{92} +(1.41886 - 2.45754i) q^{93} +(-3.00000 + 5.19615i) q^{94} -1.00000 q^{96} +(-8.66228 - 15.0035i) 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

Modular forms

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Database

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