LMFDB - Embedded newform 1950.2.y.f.199.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1950,2,Mod(49,1950)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1950, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1950.49"); 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.y (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,2,0,-2,0,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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 $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 390)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1950.199
Dual form			1950.2.y.f.49.1

$q$-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} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{6} +(-1.00000 - 1.73205i) q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +(5.59808 + 3.23205i) q^{11} +1.00000i q^{12} +(-3.46410 - 1.00000i) q^{13} -2.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.46410 + 2.00000i) q^{17} +1.00000 q^{18} +(-6.46410 + 3.73205i) q^{19} +2.00000i q^{21} +(5.59808 - 3.23205i) q^{22} +(3.23205 + 1.86603i) q^{23} +(0.866025 + 0.500000i) q^{24} +(-2.59808 + 2.50000i) q^{26} -1.00000i q^{27} +(-1.00000 + 1.73205i) q^{28} +(0.133975 - 0.232051i) q^{29} -1.73205i q^{31} +(0.500000 + 0.866025i) q^{32} +(-3.23205 - 5.59808i) q^{33} +4.00000i q^{34} +(0.500000 - 0.866025i) q^{36} +(-4.59808 + 7.96410i) q^{37} +7.46410i q^{38} +(2.50000 + 2.59808i) q^{39} +(1.73205 + 1.00000i) q^{41} +(1.73205 + 1.00000i) q^{42} +(-10.3301 + 5.96410i) q^{43} -6.46410i q^{44} +(3.23205 - 1.86603i) q^{46} +3.53590 q^{47} +(0.866025 - 0.500000i) q^{48} +(1.50000 - 2.59808i) q^{49} +4.00000 q^{51} +(0.866025 + 3.50000i) q^{52} -0.928203i q^{53} +(-0.866025 - 0.500000i) q^{54} +(1.00000 + 1.73205i) q^{56} +7.46410 q^{57} +(-0.133975 - 0.232051i) q^{58} +(-7.33013 + 4.23205i) q^{59} +(5.19615 + 9.00000i) q^{61} +(-1.50000 - 0.866025i) q^{62} +(1.00000 - 1.73205i) q^{63} +1.00000 q^{64} -6.46410 q^{66} +(5.73205 - 9.92820i) q^{67} +(3.46410 + 2.00000i) q^{68} +(-1.86603 - 3.23205i) q^{69} +(-10.7321 + 6.19615i) q^{71} +(-0.500000 - 0.866025i) q^{72} +2.00000 q^{73} +(4.59808 + 7.96410i) q^{74} +(6.46410 + 3.73205i) q^{76} -12.9282i q^{77} +(3.50000 - 0.866025i) q^{78} +13.9282 q^{79} +(-0.500000 + 0.866025i) q^{81} +(1.73205 - 1.00000i) q^{82} +8.92820 q^{83} +(1.73205 - 1.00000i) q^{84} +11.9282i q^{86} +(-0.232051 + 0.133975i) q^{87} +(-5.59808 - 3.23205i) q^{88} +(0.464102 + 0.267949i) q^{89} +(1.73205 + 7.00000i) q^{91} -3.73205i q^{92} +(-0.866025 + 1.50000i) q^{93} +(1.76795 - 3.06218i) q^{94} -1.00000i q^{96} +(0.267949 + 0.464102i) q^{97} +(-1.50000 - 2.59808i) q^{98} +6.46410i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{4} - 4 q^{7} - 4 q^{8} + 2 q^{9} + 12 q^{11} - 8 q^{14} - 2 q^{16} + 4 q^{18} - 12 q^{19} + 12 q^{22} + 6 q^{23} - 4 q^{28} + 4 q^{29} + 2 q^{32} - 6 q^{33} + 2 q^{36} - 8 q^{37} + 10 q^{39}+ \cdots - 6 q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^4 - 4 * q^7 - 4 * q^8 + 2 * q^9 + 12 * q^11 - 8 * q^14 - 2 * q^16 + 4 * q^18 - 12 * q^19 + 12 * q^22 + 6 * q^23 - 4 * q^28 + 4 * q^29 + 2 * q^32 - 6 * q^33 + 2 * q^36 - 8 * q^37 + 10 * q^39 - 24 * q^43 + 6 * q^46 + 28 * q^47 + 6 * q^49 + 16 * q^51 + 4 * q^56 + 16 * q^57 - 4 * q^58 - 12 * q^59 - 6 * q^62 + 4 * q^63 + 4 * q^64 - 12 * q^66 + 16 * q^67 - 4 * q^69 - 36 * q^71 - 2 * q^72 + 8 * q^73 + 8 * q^74 + 12 * q^76 + 14 * q^78 + 28 * q^79 - 2 * q^81 + 8 * q^83 + 6 * q^87 - 12 * q^88 - 12 * q^89 + 14 * q^94 + 8 * q^97 - 6 * q^98

Character values

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

$n$	$301$	$1301$	$1327$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$

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
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	−0.866025	+	0.500000i	−0.353553	+	0.204124i
$7$	−1.00000	−	1.73205i	−0.377964	−	0.654654i	0.612801	−	0.790237i	$-0.290043\pi$
$7$	−1.00000	−	1.73205i	−0.377964	−	0.654654i	−0.990766	+	0.135583i	$0.956709\pi$
$8$	−1.00000			−0.353553
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$		0			0
$11$	5.59808	+	3.23205i	1.68788	+	0.974500i	0.956136	+	0.292925i	$0.0946285\pi$
$11$	5.59808	+	3.23205i	1.68788	+	0.974500i	0.731748	+	0.681575i	$0.238705\pi$
$12$			1.00000i			0.288675i
$13$	−3.46410	−	1.00000i	−0.960769	−	0.277350i
$13$	−3.46410	−	1.00000i	−0.960769	−	0.277350i
$14$	−2.00000			−0.534522
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.46410	+	2.00000i	−0.840168	+	0.485071i	−0.857321	−	0.514782i	$-0.827873\pi$
$17$	−3.46410	+	2.00000i	−0.840168	+	0.485071i	0.0171533	+	0.999853i	$0.494540\pi$
$18$	1.00000			0.235702
$19$	−6.46410	+	3.73205i	−1.48297	+	0.856191i	−0.999813	−	0.0193444i	$-0.993842\pi$
$19$	−6.46410	+	3.73205i	−1.48297	+	0.856191i	−0.483154	+	0.875536i	$0.660509\pi$
$20$		0			0
$21$			2.00000i			0.436436i
$22$	5.59808	−	3.23205i	1.19351	−	0.689076i
$23$	3.23205	+	1.86603i	0.673929	+	0.389093i	0.797564	−	0.603235i	$-0.206122\pi$
$23$	3.23205	+	1.86603i	0.673929	+	0.389093i	−0.123635	+	0.992328i	$0.539455\pi$
$24$	0.866025	+	0.500000i	0.176777	+	0.102062i
$25$		0			0
$26$	−2.59808	+	2.50000i	−0.509525	+	0.490290i
$27$		−	1.00000i		−	0.192450i
$28$	−1.00000	+	1.73205i	−0.188982	+	0.327327i
$29$	0.133975	−	0.232051i	0.0248785	−	0.0430908i	−0.853318	−	0.521391i	$-0.825413\pi$
$29$	0.133975	−	0.232051i	0.0248785	−	0.0430908i	0.878197	+	0.478300i	$0.158747\pi$
$30$		0			0
$31$		−	1.73205i		−	0.311086i	−0.987829	−	0.155543i	$-0.950287\pi$
$31$		−	1.73205i		−	0.311086i	0.987829	−	0.155543i	$-0.0497126\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−3.23205	−	5.59808i	−0.562628	−	0.974500i
$34$			4.00000i			0.685994i
$35$		0			0
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	−4.59808	+	7.96410i	−0.755919	+	1.30929i	0.188997	+	0.981978i	$0.439476\pi$
$37$	−4.59808	+	7.96410i	−0.755919	+	1.30929i	−0.944916	+	0.327313i	$0.893857\pi$
$38$			7.46410i			1.21084i
$39$	2.50000	+	2.59808i	0.400320	+	0.416025i
$40$		0			0
$41$	1.73205	+	1.00000i	0.270501	+	0.156174i	0.629115	−	0.777312i	$-0.283417\pi$
$41$	1.73205	+	1.00000i	0.270501	+	0.156174i	−0.358614	+	0.933486i	$0.616751\pi$
$42$	1.73205	+	1.00000i	0.267261	+	0.154303i
$43$	−10.3301	+	5.96410i	−1.57533	+	0.909517i	−0.579831	+	0.814736i	$0.696882\pi$
$43$	−10.3301	+	5.96410i	−1.57533	+	0.909517i	−0.995498	+	0.0947805i	$0.969785\pi$
$44$		−	6.46410i		−	0.974500i
$45$		0			0
$46$	3.23205	−	1.86603i	0.476540	−	0.275130i
$47$	3.53590			0.515764			0.257882	−	0.966176i	$-0.416975\pi$
$47$	3.53590			0.515764			0.257882	+	0.966176i	$0.416975\pi$
$48$	0.866025	−	0.500000i	0.125000	−	0.0721688i
$49$	1.50000	−	2.59808i	0.214286	−	0.371154i
$50$		0			0
$51$	4.00000			0.560112
$52$	0.866025	+	3.50000i	0.120096	+	0.485363i
$53$		−	0.928203i		−	0.127499i	−0.997966	−	0.0637493i	$-0.979694\pi$
$53$		−	0.928203i		−	0.127499i	0.997966	−	0.0637493i	$-0.0203058\pi$
$54$	−0.866025	−	0.500000i	−0.117851	−	0.0680414i
$55$		0			0
$56$	1.00000	+	1.73205i	0.133631	+	0.231455i
$57$	7.46410			0.988644
$58$	−0.133975	−	0.232051i	−0.0175917	−	0.0304698i
$59$	−7.33013	+	4.23205i	−0.954301	+	0.550966i	−0.894414	−	0.447239i	$-0.852407\pi$
$59$	−7.33013	+	4.23205i	−0.954301	+	0.550966i	−0.0598868	+	0.998205i	$0.519074\pi$
$60$		0			0
$61$	5.19615	+	9.00000i	0.665299	+	1.15233i	0.979204	+	0.202878i	$0.0650293\pi$
$61$	5.19615	+	9.00000i	0.665299	+	1.15233i	−0.313905	+	0.949454i	$0.601637\pi$
$62$	−1.50000	−	0.866025i	−0.190500	−	0.109985i
$63$	1.00000	−	1.73205i	0.125988	−	0.218218i
$64$	1.00000			0.125000
$65$		0			0
$66$	−6.46410			−0.795676
$67$	5.73205	−	9.92820i	0.700281	−	1.21292i	−0.268086	−	0.963395i	$-0.586391\pi$
$67$	5.73205	−	9.92820i	0.700281	−	1.21292i	0.968368	−	0.249528i	$-0.0802755\pi$
$68$	3.46410	+	2.00000i	0.420084	+	0.242536i
$69$	−1.86603	−	3.23205i	−0.224643	−	0.389093i
$70$		0			0
$71$	−10.7321	+	6.19615i	−1.27366	+	0.735348i	−0.975675	−	0.219222i	$-0.929648\pi$
$71$	−10.7321	+	6.19615i	−1.27366	+	0.735348i	−0.297985	+	0.954570i	$0.596315\pi$
$72$	−0.500000	−	0.866025i	−0.0589256	−	0.102062i
$73$	2.00000			0.234082			0.117041	−	0.993127i	$-0.462659\pi$
$73$	2.00000			0.234082			0.117041	+	0.993127i	$0.462659\pi$
$74$	4.59808	+	7.96410i	0.534516	+	0.925808i
$75$		0			0
$76$	6.46410	+	3.73205i	0.741483	+	0.428096i
$77$		−	12.9282i		−	1.47331i
$78$	3.50000	−	0.866025i	0.396297	−	0.0980581i
$79$	13.9282			1.56705			0.783523	−	0.621363i	$-0.213421\pi$
$79$	13.9282			1.56705			0.783523	+	0.621363i	$0.213421\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	1.73205	−	1.00000i	0.191273	−	0.110432i
$83$	8.92820			0.979998			0.489999	−	0.871723i	$-0.336997\pi$
$83$	8.92820			0.979998			0.489999	+	0.871723i	$0.336997\pi$
$84$	1.73205	−	1.00000i	0.188982	−	0.109109i
$85$		0			0
$86$			11.9282i			1.28625i
$87$	−0.232051	+	0.133975i	−0.0248785	+	0.0143636i
$88$	−5.59808	−	3.23205i	−0.596757	−	0.344538i
$89$	0.464102	+	0.267949i	0.0491947	+	0.0284026i	0.524396	−	0.851475i	$-0.324291\pi$
$89$	0.464102	+	0.267949i	0.0491947	+	0.0284026i	−0.475201	+	0.879877i	$0.657625\pi$
$90$		0			0
$91$	1.73205	+	7.00000i	0.181568	+	0.733799i
$92$		−	3.73205i		−	0.389093i
$93$	−0.866025	+	1.50000i	−0.0898027	+	0.155543i
$94$	1.76795	−	3.06218i	0.182350	−	0.315840i
$95$		0			0
$96$		−	1.00000i		−	0.102062i
$97$	0.267949	+	0.464102i	0.0272061	+	0.0471224i	0.879308	−	0.476254i	$-0.158006\pi$
$97$	0.267949	+	0.464102i	0.0272061	+	0.0471224i	−0.852102	+	0.523376i	$0.824672\pi$
$98$	−1.50000	−	2.59808i	−0.151523	−	0.262445i
$99$			6.46410i			0.649667i
$100$		0			0
$101$	−1.46410	+	2.53590i	−0.145684	+	0.252331i	−0.929628	−	0.368500i	$-0.879871\pi$
$101$	−1.46410	+	2.53590i	−0.145684	+	0.252331i	0.783944	+	0.620831i	$0.213205\pi$
$102$	2.00000	−	3.46410i	0.198030	−	0.342997i
$103$			11.8564i			1.16825i	0.811665	+	0.584123i	$0.198562\pi$
$103$			11.8564i			1.16825i	−0.811665	+	0.584123i	$0.801438\pi$
$104$	3.46410	+	1.00000i	0.339683	+	0.0980581i
$105$		0			0
$106$	−0.803848	−	0.464102i	−0.0780766	−	0.0450775i
$107$	6.80385	+	3.92820i	0.657753	+	0.379754i	0.791420	−	0.611273i	$-0.209342\pi$
$107$	6.80385	+	3.92820i	0.657753	+	0.379754i	−0.133667	+	0.991026i	$0.542675\pi$
$108$	−0.866025	+	0.500000i	−0.0833333	+	0.0481125i
$109$			15.8564i			1.51877i	0.650643	+	0.759384i	$0.274500\pi$
$109$			15.8564i			1.51877i	−0.650643	+	0.759384i	$0.725500\pi$
$110$		0			0
$111$	7.96410	−	4.59808i	0.755919	−	0.436430i
$112$	2.00000			0.188982
$113$	−0.696152	+	0.401924i	−0.0654885	+	0.0378098i	−0.532387	−	0.846501i	$-0.678705\pi$
$113$	−0.696152	+	0.401924i	−0.0654885	+	0.0378098i	0.466898	+	0.884311i	$0.345371\pi$
$114$	3.73205	−	6.46410i	0.349539	−	0.605419i
$115$		0			0
$116$	−0.267949			−0.0248785
$117$	−0.866025	−	3.50000i	−0.0800641	−	0.323575i
$118$			8.46410i			0.779184i
$119$	6.92820	+	4.00000i	0.635107	+	0.366679i
$120$		0			0
$121$	15.3923	+	26.6603i	1.39930	+	2.42366i
$122$	10.3923			0.940875
$123$	−1.00000	−	1.73205i	−0.0901670	−	0.156174i
$124$	−1.50000	+	0.866025i	−0.134704	+	0.0777714i
$125$		0			0
$126$	−1.00000	−	1.73205i	−0.0890871	−	0.154303i
$127$	4.26795	+	2.46410i	0.378719	+	0.218654i	0.677261	−	0.735743i	$-0.263167\pi$
$127$	4.26795	+	2.46410i	0.378719	+	0.218654i	−0.298542	+	0.954397i	$0.596500\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	11.9282			1.05022
$130$		0			0
$131$	−18.6603			−1.63035			−0.815177	−	0.579212i	$-0.803360\pi$
$131$	−18.6603			−1.63035			−0.815177	+	0.579212i	$0.803360\pi$
$132$	−3.23205	+	5.59808i	−0.281314	+	0.487250i
$133$	12.9282	+	7.46410i	1.12102	+	0.647220i
$134$	−5.73205	−	9.92820i	−0.495174	−	0.857666i
$135$		0			0
$136$	3.46410	−	2.00000i	0.297044	−	0.171499i
$137$	−1.23205	−	2.13397i	−0.105261	−	0.182318i	0.808584	−	0.588381i	$-0.200235\pi$
$137$	−1.23205	−	2.13397i	−0.105261	−	0.182318i	−0.913845	+	0.406063i	$0.866901\pi$
$138$	−3.73205			−0.317693
$139$	−6.46410	−	11.1962i	−0.548278	−	0.949645i	−0.998393	−	0.0566745i	$-0.981950\pi$
$139$	−6.46410	−	11.1962i	−0.548278	−	0.949645i	0.450115	−	0.892971i	$-0.351383\pi$
$140$		0			0
$141$	−3.06218	−	1.76795i	−0.257882	−	0.148888i
$142$			12.3923i			1.03994i
$143$	−16.1603	−	16.7942i	−1.35139	−	1.40440i
$144$	−1.00000			−0.0833333
$145$		0			0
$146$	1.00000	−	1.73205i	0.0827606	−	0.143346i
$147$	−2.59808	+	1.50000i	−0.214286	+	0.123718i
$148$	9.19615			0.755919
$149$	11.7224	−	6.76795i	0.960339	−	0.554452i	0.0640617	−	0.997946i	$-0.479595\pi$
$149$	11.7224	−	6.76795i	0.960339	−	0.554452i	0.896277	+	0.443494i	$0.146261\pi$
$150$		0			0
$151$		−	10.3923i		−	0.845714i	−0.906196	−	0.422857i	$-0.861027\pi$
$151$		−	10.3923i		−	0.845714i	0.906196	−	0.422857i	$-0.138973\pi$
$152$	6.46410	−	3.73205i	0.524308	−	0.302709i
$153$	−3.46410	−	2.00000i	−0.280056	−	0.161690i
$154$	−11.1962	−	6.46410i	−0.902212	−	0.520892i
$155$		0			0
$156$	1.00000	−	3.46410i	0.0800641	−	0.277350i
$157$		−	5.00000i		−	0.399043i	−0.979893	−	0.199522i	$-0.936061\pi$
$157$		−	5.00000i		−	0.399043i	0.979893	−	0.199522i	$-0.0639388\pi$
$158$	6.96410	−	12.0622i	0.554034	−	0.959615i
$159$	−0.464102	+	0.803848i	−0.0368057	+	0.0637493i
$160$		0			0
$161$		−	7.46410i		−	0.588254i
$162$	0.500000	+	0.866025i	0.0392837	+	0.0680414i
$163$	−7.52628	−	13.0359i	−0.589504	−	1.02105i	−0.994297	−	0.106642i	$-0.965990\pi$
$163$	−7.52628	−	13.0359i	−0.589504	−	1.02105i	0.404794	−	0.914408i	$-0.367343\pi$
$164$		−	2.00000i		−	0.156174i
$165$		0			0
$166$	4.46410	−	7.73205i	0.346481	−	0.600124i
$167$	−8.16025	+	14.1340i	−0.631459	+	1.09372i	0.355794	+	0.934564i	$0.384210\pi$
$167$	−8.16025	+	14.1340i	−0.631459	+	1.09372i	−0.987254	+	0.159155i	$0.949123\pi$
$168$		−	2.00000i		−	0.154303i
$169$	11.0000	+	6.92820i	0.846154	+	0.532939i
$170$		0			0
$171$	−6.46410	−	3.73205i	−0.494322	−	0.285397i
$172$	10.3301	+	5.96410i	0.787665	+	0.454758i
$173$	−9.46410	+	5.46410i	−0.719542	+	0.415428i	−0.814584	−	0.580045i	$-0.803035\pi$
$173$	−9.46410	+	5.46410i	−0.719542	+	0.415428i	0.0950419	+	0.995473i	$0.469701\pi$
$174$			0.267949i			0.0203132i
$175$		0			0
$176$	−5.59808	+	3.23205i	−0.421971	+	0.243625i
$177$	8.46410			0.636201
$178$	0.464102	−	0.267949i	0.0347859	−	0.0200836i
$179$	−9.86603	+	17.0885i	−0.737421	+	1.27725i	0.216231	+	0.976342i	$0.430623\pi$
$179$	−9.86603	+	17.0885i	−0.737421	+	1.27725i	−0.953653	+	0.300909i	$0.902710\pi$
$180$		0			0
$181$	−2.92820			−0.217652			−0.108826	−	0.994061i	$-0.534709\pi$
$181$	−2.92820			−0.217652			−0.108826	+	0.994061i	$0.534709\pi$
$182$	6.92820	+	2.00000i	0.513553	+	0.148250i
$183$		−	10.3923i		−	0.768221i
$184$	−3.23205	−	1.86603i	−0.238270	−	0.137565i
$185$		0			0
$186$	0.866025	+	1.50000i	0.0635001	+	0.109985i
$187$	−25.8564			−1.89081
$188$	−1.76795	−	3.06218i	−0.128941	−	0.223332i
$189$	−1.73205	+	1.00000i	−0.125988	+	0.0727393i
$190$		0			0
$191$	−10.7321	−	18.5885i	−0.776544	−	1.34501i	−0.933923	−	0.357475i	$-0.883638\pi$
$191$	−10.7321	−	18.5885i	−0.776544	−	1.34501i	0.157379	−	0.987538i	$-0.449696\pi$
$192$	−0.866025	−	0.500000i	−0.0625000	−	0.0360844i
$193$	5.66025	−	9.80385i	0.407434	−	0.705696i	−0.587167	−	0.809466i	$-0.699757\pi$
$193$	5.66025	−	9.80385i	0.407434	−	0.705696i	0.994601	+	0.103769i	$0.0330903\pi$
$194$	0.535898			0.0384753
$195$		0			0
$196$	−3.00000			−0.214286
$197$	−2.19615	+	3.80385i	−0.156469	+	0.271013i	−0.933593	−	0.358335i	$-0.883345\pi$
$197$	−2.19615	+	3.80385i	−0.156469	+	0.271013i	0.777124	+	0.629348i	$0.216678\pi$
$198$	5.59808	+	3.23205i	0.397838	+	0.229692i
$199$	−2.53590	−	4.39230i	−0.179765	−	0.311362i	0.762035	−	0.647536i	$-0.224200\pi$
$199$	−2.53590	−	4.39230i	−0.179765	−	0.311362i	−0.941800	+	0.336174i	$0.890867\pi$
$200$		0			0
$201$	−9.92820	+	5.73205i	−0.700281	+	0.404308i
$202$	1.46410	+	2.53590i	0.103014	+	0.178425i
$203$	−0.535898			−0.0376127
$204$	−2.00000	−	3.46410i	−0.140028	−	0.242536i
$205$		0			0
$206$	10.2679	+	5.92820i	0.715402	+	0.413037i
$207$			3.73205i			0.259395i
$208$	2.59808	−	2.50000i	0.180144	−	0.173344i
$209$	−48.2487			−3.33743
$210$		0			0
$211$	5.66025	−	9.80385i	0.389668	−	0.674925i	−0.602737	−	0.797940i	$-0.705923\pi$
$211$	5.66025	−	9.80385i	0.389668	−	0.674925i	0.992405	+	0.123015i	$0.0392564\pi$
$212$	−0.803848	+	0.464102i	−0.0552085	+	0.0318746i
$213$	12.3923			0.849107
$214$	6.80385	−	3.92820i	0.465101	−	0.268526i
$215$		0			0
$216$			1.00000i			0.0680414i
$217$	−3.00000	+	1.73205i	−0.203653	+	0.117579i
$218$	13.7321	+	7.92820i	0.930052	+	0.536966i
$219$	−1.73205	−	1.00000i	−0.117041	−	0.0675737i
$220$		0			0
$221$	14.0000	−	3.46410i	0.941742	−	0.233021i
$222$		−	9.19615i		−	0.617205i
$223$	−10.2679	+	17.7846i	−0.687593	+	1.19095i	0.285022	+	0.958521i	$0.407999\pi$
$223$	−10.2679	+	17.7846i	−0.687593	+	1.19095i	−0.972614	+	0.232424i	$0.925334\pi$
$224$	1.00000	−	1.73205i	0.0668153	−	0.115728i
$225$		0			0
$226$			0.803848i			0.0534711i
$227$	−8.19615	−	14.1962i	−0.543998	−	0.942232i	−0.998669	−	0.0515725i	$-0.983577\pi$
$227$	−8.19615	−	14.1962i	−0.543998	−	0.942232i	0.454672	−	0.890659i	$-0.349757\pi$
$228$	−3.73205	−	6.46410i	−0.247161	−	0.428096i
$229$			7.85641i			0.519166i	0.965721	+	0.259583i	$0.0835851\pi$
$229$			7.85641i			0.519166i	−0.965721	+	0.259583i	$0.916415\pi$
$230$		0			0
$231$	−6.46410	+	11.1962i	−0.425307	+	0.736653i
$232$	−0.133975	+	0.232051i	−0.00879586	+	0.0152349i
$233$		−	6.12436i		−	0.401220i	−0.979671	−	0.200610i	$-0.935708\pi$
$233$		−	6.12436i		−	0.401220i	0.979671	−	0.200610i	$-0.0642924\pi$
$234$	−3.46410	−	1.00000i	−0.226455	−	0.0653720i
$235$		0			0
$236$	7.33013	+	4.23205i	0.477151	+	0.275483i
$237$	−12.0622	−	6.96410i	−0.783523	−	0.452367i
$238$	6.92820	−	4.00000i	0.449089	−	0.259281i
$239$			16.3923i			1.06033i	0.847894	+	0.530165i	$0.177870\pi$
$239$			16.3923i			1.06033i	−0.847894	+	0.530165i	$0.822130\pi$
$240$		0			0
$241$	15.3564	−	8.86603i	0.989193	−	0.571111i	0.0841601	−	0.996452i	$-0.473179\pi$
$241$	15.3564	−	8.86603i	0.989193	−	0.571111i	0.905033	+	0.425341i	$0.139846\pi$
$242$	30.7846			1.97891
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	5.19615	−	9.00000i	0.332650	−	0.576166i
$245$		0			0
$246$	−2.00000			−0.127515
$247$	26.1244	−	6.46410i	1.66225	−	0.411301i
$248$			1.73205i			0.109985i
$249$	−7.73205	−	4.46410i	−0.489999	−	0.282901i
$250$		0			0
$251$	−7.86603	−	13.6244i	−0.496499	−	0.859962i	0.503493	−	0.863999i	$-0.332048\pi$
$251$	−7.86603	−	13.6244i	−0.496499	−	0.859962i	−0.999992	+	0.00403776i	$0.998715\pi$
$252$	−2.00000			−0.125988
$253$	12.0622	+	20.8923i	0.758343	+	1.31349i
$254$	4.26795	−	2.46410i	0.267795	−	0.154611i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	4.62436	+	2.66987i	0.288459	+	0.166542i	0.637247	−	0.770660i	$-0.280073\pi$
$257$	4.62436	+	2.66987i	0.288459	+	0.166542i	−0.348787	+	0.937202i	$0.613407\pi$
$258$	5.96410	−	10.3301i	0.371309	−	0.643126i
$259$	18.3923			1.14284
$260$		0			0
$261$	0.267949			0.0165856
$262$	−9.33013	+	16.1603i	−0.576417	+	0.998384i
$263$	5.30385	+	3.06218i	0.327049	+	0.188822i	0.654530	−	0.756036i	$-0.272866\pi$
$263$	5.30385	+	3.06218i	0.327049	+	0.188822i	−0.327481	+	0.944858i	$0.606200\pi$
$264$	3.23205	+	5.59808i	0.198919	+	0.344538i
$265$		0			0
$266$	12.9282	−	7.46410i	0.792679	−	0.457653i
$267$	−0.267949	−	0.464102i	−0.0163982	−	0.0284026i
$268$	−11.4641			−0.700281
$269$	6.00000	+	10.3923i	0.365826	+	0.633630i	0.988908	−	0.148527i	$-0.0474530\pi$
$269$	6.00000	+	10.3923i	0.365826	+	0.633630i	−0.623082	+	0.782157i	$0.714120\pi$
$270$		0			0
$271$	1.03590	+	0.598076i	0.0629263	+	0.0363305i	0.531133	−	0.847288i	$-0.321766\pi$
$271$	1.03590	+	0.598076i	0.0629263	+	0.0363305i	−0.468207	+	0.883619i	$0.655100\pi$
$272$		−	4.00000i		−	0.242536i
$273$	2.00000	−	6.92820i	0.121046	−	0.419314i
$274$	−2.46410			−0.148862
$275$		0			0
$276$	−1.86603	+	3.23205i	−0.112322	+	0.194547i
$277$	−3.40192	+	1.96410i	−0.204402	+	0.118011i	−0.598707	−	0.800968i	$-0.704319\pi$
$277$	−3.40192	+	1.96410i	−0.204402	+	0.118011i	0.394305	+	0.918980i	$0.370985\pi$
$278$	−12.9282			−0.775382
$279$	1.50000	−	0.866025i	0.0898027	−	0.0518476i
$280$		0			0
$281$		−	8.92820i		−	0.532612i	−0.963889	−	0.266306i	$-0.914197\pi$
$281$		−	8.92820i		−	0.532612i	0.963889	−	0.266306i	$-0.0858032\pi$
$282$	−3.06218	+	1.76795i	−0.182350	+	0.105280i
$283$	−8.59808	−	4.96410i	−0.511103	−	0.295085i	0.222184	−	0.975005i	$-0.428681\pi$
$283$	−8.59808	−	4.96410i	−0.511103	−	0.295085i	−0.733287	+	0.679920i	$0.762015\pi$
$284$	10.7321	+	6.19615i	0.636830	+	0.367674i
$285$		0			0
$286$	−22.6244	+	5.59808i	−1.33781	+	0.331021i
$287$		−	4.00000i		−	0.236113i
$288$	−0.500000	+	0.866025i	−0.0294628	+	0.0510310i
$289$	−0.500000	+	0.866025i	−0.0294118	+	0.0509427i
$290$		0			0
$291$		−	0.535898i		−	0.0314149i
$292$	−1.00000	−	1.73205i	−0.0585206	−	0.101361i
$293$	15.9282	+	27.5885i	0.930536	+	1.61173i	0.782408	+	0.622767i	$0.213991\pi$
$293$	15.9282	+	27.5885i	0.930536	+	1.61173i	0.148128	+	0.988968i	$0.452675\pi$
$294$			3.00000i			0.174964i
$295$		0			0
$296$	4.59808	−	7.96410i	0.267258	−	0.462904i
$297$	3.23205	−	5.59808i	0.187543	−	0.324833i
$298$		−	13.5359i		−	0.784114i
$299$	−9.33013	−	9.69615i	−0.539575	−	0.560743i
$300$		0			0
$301$	20.6603	+	11.9282i	1.19084	+	0.687530i
$302$	−9.00000	−	5.19615i	−0.517892	−	0.299005i
$303$	2.53590	−	1.46410i	0.145684	−	0.0841104i
$304$		−	7.46410i		−	0.428096i
$305$		0			0
$306$	−3.46410	+	2.00000i	−0.198030	+	0.114332i
$307$	−19.4641			−1.11087			−0.555437	−	0.831558i	$-0.687449\pi$
$307$	−19.4641			−1.11087			−0.555437	+	0.831558i	$0.687449\pi$
$308$	−11.1962	+	6.46410i	−0.637960	+	0.368326i
$309$	5.92820	−	10.2679i	0.337244	−	0.584123i
$310$		0			0
$311$	−28.3923			−1.60998			−0.804990	−	0.593288i	$-0.797829\pi$
$311$	−28.3923			−1.60998			−0.804990	+	0.593288i	$0.797829\pi$
$312$	−2.50000	−	2.59808i	−0.141535	−	0.147087i
$313$			28.0000i			1.58265i	0.611393	+	0.791327i	$0.290609\pi$
$313$			28.0000i			1.58265i	−0.611393	+	0.791327i	$0.709391\pi$
$314$	−4.33013	−	2.50000i	−0.244363	−	0.141083i
$315$		0			0
$316$	−6.96410	−	12.0622i	−0.391761	−	0.678551i
$317$	−14.5359			−0.816417			−0.408209	−	0.912889i	$-0.633846\pi$
$317$	−14.5359			−0.816417			−0.408209	+	0.912889i	$0.633846\pi$
$318$	0.464102	+	0.803848i	0.0260255	+	0.0450775i
$319$	1.50000	−	0.866025i	0.0839839	−	0.0484881i
$320$		0			0
$321$	−3.92820	−	6.80385i	−0.219251	−	0.379754i
$322$	−6.46410	−	3.73205i	−0.360230	−	0.207979i
$323$	14.9282	−	25.8564i	0.830627	−	1.43869i
$324$	1.00000			0.0555556
$325$		0			0
$326$	−15.0526			−0.833684
$327$	7.92820	−	13.7321i	0.438431	−	0.759384i
$328$	−1.73205	−	1.00000i	−0.0956365	−	0.0552158i
$329$	−3.53590	−	6.12436i	−0.194940	−	0.337647i
$330$		0			0
$331$	−14.5359	+	8.39230i	−0.798965	+	0.461283i	−0.843109	−	0.537742i	$-0.819277\pi$
$331$	−14.5359	+	8.39230i	−0.798965	+	0.461283i	0.0441440	+	0.999025i	$0.485944\pi$
$332$	−4.46410	−	7.73205i	−0.244999	−	0.424351i
$333$	−9.19615			−0.503946
$334$	8.16025	+	14.1340i	0.446509	+	0.773377i
$335$		0			0
$336$	−1.73205	−	1.00000i	−0.0944911	−	0.0545545i
$337$			9.32051i			0.507720i	0.967241	+	0.253860i	$0.0817003\pi$
$337$			9.32051i			0.507720i	−0.967241	+	0.253860i	$0.918300\pi$
$338$	11.5000	−	6.06218i	0.625518	−	0.329739i
$339$	0.803848			0.0436590
$340$		0			0
$341$	5.59808	−	9.69615i	0.303153	−	0.525076i
$342$	−6.46410	+	3.73205i	−0.349539	+	0.201806i
$343$	−20.0000			−1.07990
$344$	10.3301	−	5.96410i	0.556963	−	0.321563i
$345$		0			0
$346$			10.9282i			0.587504i
$347$	1.39230	−	0.803848i	0.0747428	−	0.0431528i	−0.462163	−	0.886795i	$-0.652926\pi$
$347$	1.39230	−	0.803848i	0.0747428	−	0.0431528i	0.536906	+	0.843642i	$0.319593\pi$
$348$	0.232051	+	0.133975i	0.0124392	+	0.00718179i
$349$	−18.5885	−	10.7321i	−0.995017	−	0.574474i	−0.0882471	−	0.996099i	$-0.528127\pi$
$349$	−18.5885	−	10.7321i	−0.995017	−	0.574474i	−0.906770	+	0.421625i	$0.861460\pi$
$350$		0			0
$351$	−1.00000	+	3.46410i	−0.0533761	+	0.184900i
$352$			6.46410i			0.344538i
$353$	1.00000	−	1.73205i	0.0532246	−	0.0921878i	−0.838186	−	0.545385i	$-0.816383\pi$
$353$	1.00000	−	1.73205i	0.0532246	−	0.0921878i	0.891410	+	0.453197i	$0.149717\pi$
$354$	4.23205	−	7.33013i	0.224931	−	0.389592i
$355$		0			0
$356$		−	0.535898i		−	0.0284026i
$357$	−4.00000	−	6.92820i	−0.211702	−	0.366679i
$358$	9.86603	+	17.0885i	0.521436	+	0.903153i
$359$		−	5.07180i		−	0.267679i	−0.991003	−	0.133840i	$-0.957269\pi$
$359$		−	5.07180i		−	0.267679i	0.991003	−	0.133840i	$-0.0427307\pi$
$360$		0			0
$361$	18.3564	−	31.7942i	0.966127	−	1.67338i
$362$	−1.46410	+	2.53590i	−0.0769515	+	0.133284i
$363$		−	30.7846i		−	1.61577i
$364$	5.19615	−	5.00000i	0.272352	−	0.262071i
$365$		0			0
$366$	−9.00000	−	5.19615i	−0.470438	−	0.271607i
$367$	−13.5167	−	7.80385i	−0.705564	−	0.407358i	0.103852	−	0.994593i	$-0.466883\pi$
$367$	−13.5167	−	7.80385i	−0.705564	−	0.407358i	−0.809416	+	0.587235i	$0.800216\pi$
$368$	−3.23205	+	1.86603i	−0.168482	+	0.0972733i
$369$			2.00000i			0.104116i
$370$		0			0
$371$	−1.60770	+	0.928203i	−0.0834674	+	0.0481899i
$372$	1.73205			0.0898027
$373$	13.6699	−	7.89230i	0.707799	−	0.408648i	−0.102446	−	0.994739i	$-0.532667\pi$
$373$	13.6699	−	7.89230i	0.707799	−	0.408648i	0.810246	+	0.586090i	$0.199334\pi$
$374$	−12.9282	+	22.3923i	−0.668501	+	1.15788i
$375$		0			0
$376$	−3.53590			−0.182350
$377$	−0.696152	+	0.669873i	−0.0358537	+	0.0345002i
$378$			2.00000i			0.102869i
$379$	−24.1244	−	13.9282i	−1.23918	−	0.715444i	−0.270257	−	0.962788i	$-0.587109\pi$
$379$	−24.1244	−	13.9282i	−1.23918	−	0.715444i	−0.968928	+	0.247344i	$0.920442\pi$
$380$		0			0
$381$	−2.46410	−	4.26795i	−0.126240	−	0.218654i
$382$	−21.4641			−1.09820
$383$	−12.6962	−	21.9904i	−0.648743	−	1.12366i	−0.983423	−	0.181324i	$-0.941962\pi$
$383$	−12.6962	−	21.9904i	−0.648743	−	1.12366i	0.334680	−	0.942332i	$-0.391372\pi$
$384$	−0.866025	+	0.500000i	−0.0441942	+	0.0255155i
$385$		0			0
$386$	−5.66025	−	9.80385i	−0.288099	−	0.499003i
$387$	−10.3301	−	5.96410i	−0.525110	−	0.303172i
$388$	0.267949	−	0.464102i	0.0136031	−	0.0235612i
$389$	23.7321			1.20326			0.601631	−	0.798774i	$-0.294518\pi$
$389$	23.7321			1.20326			0.601631	+	0.798774i	$0.294518\pi$
$390$		0			0
$391$	−14.9282			−0.754952
$392$	−1.50000	+	2.59808i	−0.0757614	+	0.131223i
$393$	16.1603	+	9.33013i	0.815177	+	0.470643i
$394$	2.19615	+	3.80385i	0.110641	+	0.191635i
$395$		0			0
$396$	5.59808	−	3.23205i	0.281314	−	0.162417i
$397$	6.06218	+	10.5000i	0.304252	+	0.526980i	0.977095	−	0.212806i	$-0.0682602\pi$
$397$	6.06218	+	10.5000i	0.304252	+	0.526980i	−0.672843	+	0.739786i	$0.734927\pi$
$398$	−5.07180			−0.254226
$399$	−7.46410	−	12.9282i	−0.373672	−	0.647220i
$400$		0			0
$401$	−27.7128	−	16.0000i	−1.38391	−	0.799002i	−0.391292	−	0.920267i	$-0.627972\pi$
$401$	−27.7128	−	16.0000i	−1.38391	−	0.799002i	−0.992620	+	0.121265i	$0.961305\pi$
$402$			11.4641i			0.571777i
$403$	−1.73205	+	6.00000i	−0.0862796	+	0.298881i
$404$	2.92820			0.145684
$405$		0			0
$406$	−0.267949	+	0.464102i	−0.0132981	+	0.0230330i
$407$	−51.4808	+	29.7224i	−2.55181	+	1.47329i
$408$	−4.00000			−0.198030
$409$	−3.46410	+	2.00000i	−0.171289	+	0.0988936i	−0.583193	−	0.812333i	$-0.698197\pi$
$409$	−3.46410	+	2.00000i	−0.171289	+	0.0988936i	0.411905	+	0.911227i	$0.364864\pi$
$410$		0			0
$411$			2.46410i			0.121545i
$412$	10.2679	−	5.92820i	0.505866	−	0.292062i
$413$	14.6603	+	8.46410i	0.721384	+	0.416491i
$414$	3.23205	+	1.86603i	0.158847	+	0.0917101i
$415$		0			0
$416$	−0.866025	−	3.50000i	−0.0424604	−	0.171602i
$417$			12.9282i			0.633097i
$418$	−24.1244	+	41.7846i	−1.17996	+	2.04375i
$419$	11.1962	−	19.3923i	0.546968	−	0.947376i	−0.451512	−	0.892265i	$-0.649115\pi$
$419$	11.1962	−	19.3923i	0.546968	−	0.947376i	0.998480	−	0.0551112i	$-0.0175513\pi$
$420$		0			0
$421$			4.39230i			0.214068i	0.994255	+	0.107034i	$0.0341353\pi$
$421$			4.39230i			0.214068i	−0.994255	+	0.107034i	$0.965865\pi$
$422$	−5.66025	−	9.80385i	−0.275537	−	0.477244i
$423$	1.76795	+	3.06218i	0.0859606	+	0.148888i
$424$			0.928203i			0.0450775i
$425$		0			0
$426$	6.19615	−	10.7321i	0.300205	−	0.519970i
$427$	10.3923	−	18.0000i	0.502919	−	0.871081i
$428$		−	7.85641i		−	0.379754i
$429$	5.59808	+	22.6244i	0.270278	+	1.09231i
$430$		0			0
$431$	24.5885	+	14.1962i	1.18438	+	0.683805i	0.957025	−	0.290006i	$-0.0936574\pi$
$431$	24.5885	+	14.1962i	1.18438	+	0.683805i	0.227360	+	0.973811i	$0.426991\pi$
$432$	0.866025	+	0.500000i	0.0416667	+	0.0240563i
$433$	−16.7321	+	9.66025i	−0.804091	+	0.464242i	−0.844900	−	0.534925i	$-0.820340\pi$
$433$	−16.7321	+	9.66025i	−0.804091	+	0.464242i	0.0408086	+	0.999167i	$0.487007\pi$
$434$			3.46410i			0.166282i
$435$		0			0
$436$	13.7321	−	7.92820i	0.657646	−	0.379692i
$437$	−27.8564			−1.33255
$438$	−1.73205	+	1.00000i	−0.0827606	+	0.0477818i
$439$	−8.92820	+	15.4641i	−0.426120	+	0.738061i	−0.996524	−	0.0833027i	$-0.973453\pi$
$439$	−8.92820	+	15.4641i	−0.426120	+	0.738061i	0.570404	+	0.821364i	$0.306786\pi$
$440$		0			0
$441$	3.00000			0.142857
$442$	4.00000	−	13.8564i	0.190261	−	0.659082i
$443$		−	16.3923i		−	0.778822i	−0.921064	−	0.389411i	$-0.872679\pi$
$443$		−	16.3923i		−	0.778822i	0.921064	−	0.389411i	$-0.127321\pi$
$444$	−7.96410	−	4.59808i	−0.377960	−	0.218215i
$445$		0			0
$446$	10.2679	+	17.7846i	0.486201	+	0.842126i
$447$	−13.5359			−0.640226
$448$	−1.00000	−	1.73205i	−0.0472456	−	0.0818317i
$449$	13.6077	−	7.85641i	0.642187	−	0.370767i	−0.143270	−	0.989684i	$-0.545762\pi$
$449$	13.6077	−	7.85641i	0.642187	−	0.370767i	0.785456	+	0.618917i	$0.212428\pi$
$450$		0			0
$451$	6.46410	+	11.1962i	0.304383	+	0.527206i
$452$	0.696152	+	0.401924i	0.0327443	+	0.0189049i
$453$	−5.19615	+	9.00000i	−0.244137	+	0.422857i
$454$	−16.3923			−0.769329
$455$		0			0
$456$	−7.46410			−0.349539
$457$	−12.2679	+	21.2487i	−0.573870	+	0.993973i	0.422293	+	0.906459i	$0.361225\pi$
$457$	−12.2679	+	21.2487i	−0.573870	+	0.993973i	−0.996163	+	0.0875134i	$0.972108\pi$
$458$	6.80385	+	3.92820i	0.317923	+	0.183553i
$459$	2.00000	+	3.46410i	0.0933520	+	0.161690i
$460$		0			0
$461$	0.401924	−	0.232051i	0.0187195	−	0.0108077i	−0.490611	−	0.871379i	$-0.663226\pi$
$461$	0.401924	−	0.232051i	0.0187195	−	0.0108077i	0.509331	+	0.860571i	$0.329893\pi$
$462$	6.46410	+	11.1962i	0.300737	+	0.520892i
$463$	7.07180			0.328654			0.164327	−	0.986406i	$-0.447455\pi$
$463$	7.07180			0.328654			0.164327	+	0.986406i	$0.447455\pi$
$464$	0.133975	+	0.232051i	0.00621961	+	0.0107727i
$465$		0			0
$466$	−5.30385	−	3.06218i	−0.245696	−	0.141853i
$467$		−	15.8564i		−	0.733747i	−0.930271	−	0.366873i	$-0.880428\pi$
$467$		−	15.8564i		−	0.733747i	0.930271	−	0.366873i	$-0.119572\pi$
$468$	−2.59808	+	2.50000i	−0.120096	+	0.115563i
$469$	−22.9282			−1.05873
$470$		0			0
$471$	−2.50000	+	4.33013i	−0.115194	+	0.199522i
$472$	7.33013	−	4.23205i	0.337396	−	0.194796i
$473$	−77.1051			−3.54530
$474$	−12.0622	+	6.96410i	−0.554034	+	0.319872i
$475$		0			0
$476$		−	8.00000i		−	0.366679i
$477$	0.803848	−	0.464102i	0.0368057	−	0.0212498i
$478$	14.1962	+	8.19615i	0.649317	+	0.374883i
$479$	−4.73205	−	2.73205i	−0.216213	−	0.124831i	0.387983	−	0.921667i	$-0.373172\pi$
$479$	−4.73205	−	2.73205i	−0.216213	−	0.124831i	−0.604195	+	0.796836i	$0.706505\pi$
$480$		0			0
$481$	23.8923	−	22.9904i	1.08940	−	1.04827i
$482$		−	17.7321i		−	0.807673i
$483$	−3.73205	+	6.46410i	−0.169814	+	0.294127i
$484$	15.3923	−	26.6603i	0.699650	−	1.21183i
$485$		0			0
$486$		−	1.00000i		−	0.0453609i
$487$	11.5885	+	20.0718i	0.525123	+	0.909540i	0.999572	+	0.0292568i	$0.00931407\pi$
$487$	11.5885	+	20.0718i	0.525123	+	0.909540i	−0.474449	+	0.880283i	$0.657353\pi$
$488$	−5.19615	−	9.00000i	−0.235219	−	0.407411i
$489$			15.0526i			0.680700i
$490$		0			0
$491$	8.66025	−	15.0000i	0.390832	−	0.676941i	−0.601728	−	0.798701i	$-0.705521\pi$
$491$	8.66025	−	15.0000i	0.390832	−	0.676941i	0.992559	+	0.121761i	$0.0388541\pi$
$492$	−1.00000	+	1.73205i	−0.0450835	+	0.0780869i
$493$			1.07180i			0.0482713i
$494$	7.46410	−	25.8564i	0.335826	−	1.16333i
$495$		0			0
$496$	1.50000	+	0.866025i	0.0673520	+	0.0388857i
$497$	21.4641	+	12.3923i	0.962797	+	0.555871i
$498$	−7.73205	+	4.46410i	−0.346481	+	0.200041i
$499$		−	6.53590i		−	0.292587i	−0.989241	−	0.146293i	$-0.953266\pi$
$499$		−	6.53590i		−	0.292587i	0.989241	−	0.146293i	$-0.0467344\pi$
$500$		0			0
$501$	14.1340	−	8.16025i	0.631459	−	0.364573i
$502$	−15.7321			−0.702156
$503$	27.0000	−	15.5885i	1.20387	−	0.695055i	0.242457	−	0.970162i	$-0.422047\pi$
$503$	27.0000	−	15.5885i	1.20387	−	0.695055i	0.961414	+	0.275107i	$0.0887134\pi$
$504$	−1.00000	+	1.73205i	−0.0445435	+	0.0771517i
$505$		0			0
$506$	24.1244			1.07246
$507$	−6.06218	−	11.5000i	−0.269231	−	0.510733i
$508$		−	4.92820i		−	0.218654i
$509$	−1.20577	−	0.696152i	−0.0534449	−	0.0308564i	0.473039	−	0.881041i	$-0.343157\pi$
$509$	−1.20577	−	0.696152i	−0.0534449	−	0.0308564i	−0.526484	+	0.850185i	$0.676490\pi$
$510$		0			0
$511$	−2.00000	−	3.46410i	−0.0884748	−	0.153243i
$512$	−1.00000			−0.0441942
$513$	3.73205	+	6.46410i	0.164774	+	0.285397i
$514$	4.62436	−	2.66987i	0.203972	−	0.117763i
$515$		0			0
$516$	−5.96410	−	10.3301i	−0.262555	−	0.454758i
$517$	19.7942	+	11.4282i	0.870549	+	0.502612i
$518$	9.19615	−	15.9282i	0.404056	−	0.699845i
$519$	10.9282			0.479695
$520$		0			0
$521$	−17.3205			−0.758825			−0.379413	−	0.925228i	$-0.623874\pi$
$521$	−17.3205			−0.758825			−0.379413	+	0.925228i	$0.623874\pi$
$522$	0.133975	−	0.232051i	0.00586391	−	0.0101566i
$523$	10.2058	+	5.89230i	0.446267	+	0.257653i	0.706252	−	0.707960i	$-0.250384\pi$
$523$	10.2058	+	5.89230i	0.446267	+	0.257653i	−0.259985	+	0.965613i	$0.583718\pi$
$524$	9.33013	+	16.1603i	0.407588	+	0.705964i
$525$		0			0
$526$	5.30385	−	3.06218i	0.231259	−	0.133517i
$527$	3.46410	+	6.00000i	0.150899	+	0.261364i
$528$	6.46410			0.281314
$529$	−4.53590	−	7.85641i	−0.197213	−	0.341583i
$530$		0			0
$531$	−7.33013	−	4.23205i	−0.318100	−	0.183655i
$532$		−	14.9282i		−	0.647220i
$533$	−5.00000	−	5.19615i	−0.216574	−	0.225070i
$534$	−0.535898			−0.0231906
$535$		0			0
$536$	−5.73205	+	9.92820i	−0.247587	+	0.428833i
$537$	17.0885	−	9.86603i	0.737421	−	0.425750i
$538$	12.0000			0.517357
$539$	16.7942	−	9.69615i	0.723379	−	0.417643i
$540$		0			0
$541$			26.9282i			1.15773i	0.815422	+	0.578867i	$0.196505\pi$
$541$			26.9282i			1.15773i	−0.815422	+	0.578867i	$0.803495\pi$
$542$	1.03590	−	0.598076i	0.0444956	−	0.0256896i
$543$	2.53590	+	1.46410i	0.108826	+	0.0628306i
$544$	−3.46410	−	2.00000i	−0.148522	−	0.0857493i
$545$		0			0
$546$	−5.00000	−	5.19615i	−0.213980	−	0.222375i
$547$			22.9282i			0.980339i	0.871627	+	0.490170i	$0.163065\pi$
$547$			22.9282i			0.980339i	−0.871627	+	0.490170i	$0.836935\pi$
$548$	−1.23205	+	2.13397i	−0.0526306	+	0.0911589i
$549$	−5.19615	+	9.00000i	−0.221766	+	0.384111i
$550$		0			0
$551$			2.00000i			0.0852029i
$552$	1.86603	+	3.23205i	0.0794233	+	0.137565i
$553$	−13.9282	−	24.1244i	−0.592287	−	1.02587i
$554$			3.92820i			0.166893i
$555$		0			0
$556$	−6.46410	+	11.1962i	−0.274139	+	0.474823i
$557$	−8.85641	+	15.3397i	−0.375258	+	0.649966i	−0.990366	−	0.138477i	$-0.955779\pi$
$557$	−8.85641	+	15.3397i	−0.375258	+	0.649966i	0.615108	+	0.788443i	$0.289113\pi$
$558$		−	1.73205i		−	0.0733236i
$559$	41.7487	−	10.3301i	1.76578	−	0.436918i
$560$		0			0
$561$	22.3923	+	12.9282i	0.945404	+	0.545829i
$562$	−7.73205	−	4.46410i	−0.326157	−	0.188307i
$563$	4.05256	−	2.33975i	0.170795	−	0.0986085i	−0.412166	−	0.911109i	$-0.635228\pi$
$563$	4.05256	−	2.33975i	0.170795	−	0.0986085i	0.582961	+	0.812500i	$0.301894\pi$
$564$			3.53590i			0.148888i
$565$		0			0
$566$	−8.59808	+	4.96410i	−0.361404	+	0.208657i
$567$	2.00000			0.0839921
$568$	10.7321	−	6.19615i	0.450307	−	0.259985i
$569$	14.6603	−	25.3923i	0.614590	−	1.06450i	−0.375867	−	0.926674i	$-0.622655\pi$
$569$	14.6603	−	25.3923i	0.614590	−	1.06450i	0.990456	−	0.137827i	$-0.0440118\pi$
$570$		0			0
$571$	−17.1769			−0.718832			−0.359416	−	0.933178i	$-0.617024\pi$
$571$	−17.1769			−0.718832			−0.359416	+	0.933178i	$0.617024\pi$
$572$	−6.46410	+	22.3923i	−0.270278	+	0.936269i
$573$			21.4641i			0.896676i
$574$	−3.46410	−	2.00000i	−0.144589	−	0.0834784i
$575$		0			0
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	10.0000			0.416305			0.208153	−	0.978096i	$-0.433255\pi$
$577$	10.0000			0.416305			0.208153	+	0.978096i	$0.433255\pi$
$578$	0.500000	+	0.866025i	0.0207973	+	0.0360219i
$579$	−9.80385	+	5.66025i	−0.407434	+	0.235232i
$580$		0			0
$581$	−8.92820	−	15.4641i	−0.370404	−	0.641559i
$582$	−0.464102	−	0.267949i	−0.0192376	−	0.0111069i
$583$	3.00000	−	5.19615i	0.124247	−	0.215203i
$584$	−2.00000			−0.0827606
$585$		0			0
$586$	31.8564			1.31598
$587$	1.19615	−	2.07180i	0.0493705	−	0.0855122i	−0.840284	−	0.542146i	$-0.817612\pi$
$587$	1.19615	−	2.07180i	0.0493705	−	0.0855122i	0.889655	+	0.456634i	$0.150945\pi$
$588$	2.59808	+	1.50000i	0.107143	+	0.0618590i
$589$	6.46410	+	11.1962i	0.266349	+	0.461329i
$590$		0			0
$591$	3.80385	−	2.19615i	0.156469	−	0.0903376i
$592$	−4.59808	−	7.96410i	−0.188980	−	0.327323i
$593$	45.1051			1.85225			0.926123	−	0.377223i	$-0.123121\pi$
$593$	45.1051			1.85225			0.926123	+	0.377223i	$0.123121\pi$
$594$	−3.23205	−	5.59808i	−0.132613	−	0.229692i
$595$		0			0
$596$	−11.7224	−	6.76795i	−0.480170	−	0.277226i
$597$			5.07180i			0.207575i
$598$	−13.0622	+	3.23205i	−0.534152	+	0.132168i
$599$	10.3923			0.424618			0.212309	−	0.977203i	$-0.431902\pi$
$599$	10.3923			0.424618			0.212309	+	0.977203i	$0.431902\pi$
$600$		0			0
$601$	9.89230	−	17.1340i	0.403516	−	0.698909i	−0.590632	−	0.806941i	$-0.701121\pi$
$601$	9.89230	−	17.1340i	0.403516	−	0.698909i	0.994147	+	0.108032i	$0.0344548\pi$
$602$	20.6603	−	11.9282i	0.842049	−	0.486157i
$603$	11.4641			0.466854
$604$	−9.00000	+	5.19615i	−0.366205	+	0.211428i
$605$		0			0
$606$		−	2.92820i		−	0.118950i
$607$	−16.6077	+	9.58846i	−0.674086	+	0.389183i	−0.797623	−	0.603156i	$-0.793909\pi$
$607$	−16.6077	+	9.58846i	−0.674086	+	0.389183i	0.123537	+	0.992340i	$0.460576\pi$
$608$	−6.46410	−	3.73205i	−0.262154	−	0.151355i
$609$	0.464102	+	0.267949i	0.0188063	+	0.0108578i
$610$		0			0
$611$	−12.2487	−	3.53590i	−0.495530	−	0.143047i
$612$			4.00000i			0.161690i
$613$	−19.5263	+	33.8205i	−0.788659	+	1.36600i	0.138130	+	0.990414i	$0.455891\pi$
$613$	−19.5263	+	33.8205i	−0.788659	+	1.36600i	−0.926789	+	0.375583i	$0.877442\pi$
$614$	−9.73205	+	16.8564i	−0.392754	+	0.680269i
$615$		0			0
$616$			12.9282i			0.520892i
$617$	−11.2321	−	19.4545i	−0.452185	−	0.783208i	0.546336	−	0.837566i	$-0.316022\pi$
$617$	−11.2321	−	19.4545i	−0.452185	−	0.783208i	−0.998522	+	0.0543580i	$0.982689\pi$
$618$	−5.92820	−	10.2679i	−0.238467	−	0.413037i
$619$			24.2487i			0.974638i	0.873224	+	0.487319i	$0.162025\pi$
$619$			24.2487i			0.974638i	−0.873224	+	0.487319i	$0.837975\pi$
$620$		0			0
$621$	1.86603	−	3.23205i	0.0748810	−	0.129698i
$622$	−14.1962	+	24.5885i	−0.569214	+	0.985907i
$623$		−	1.07180i		−	0.0429406i
$624$	−3.50000	+	0.866025i	−0.140112	+	0.0346688i
$625$		0			0
$626$	24.2487	+	14.0000i	0.969173	+	0.559553i
$627$	41.7846	+	24.1244i	1.66872	+	0.963434i
$628$	−4.33013	+	2.50000i	−0.172791	+	0.0997609i
$629$		−	36.7846i		−	1.46670i
$630$		0			0
$631$	27.2487	−	15.7321i	1.08475	−	0.626283i	0.152579	−	0.988291i	$-0.451242\pi$
$631$	27.2487	−	15.7321i	1.08475	−	0.626283i	0.932175	+	0.362008i	$0.117909\pi$
$632$	−13.9282			−0.554034
$633$	−9.80385	+	5.66025i	−0.389668	+	0.224975i
$634$	−7.26795	+	12.5885i	−0.288647	+	0.499952i
$635$		0			0
$636$	0.928203			0.0368057
$637$	−7.79423	+	7.50000i	−0.308819	+	0.297161i
$638$		−	1.73205i		−	0.0685725i
$639$	−10.7321	−	6.19615i	−0.424553	−	0.245116i
$640$		0			0
$641$	−0.0717968	−	0.124356i	−0.00283580	−	0.00491175i	0.864604	−	0.502454i	$-0.167569\pi$
$641$	−0.0717968	−	0.124356i	−0.00283580	−	0.00491175i	−0.867440	+	0.497542i	$0.834236\pi$
$642$	−7.85641			−0.310068
$643$	10.2679	+	17.7846i	0.404928	+	0.701357i	0.994313	−	0.106496i	$-0.0339631\pi$
$643$	10.2679	+	17.7846i	0.404928	+	0.701357i	−0.589385	+	0.807852i	$0.700630\pi$
$644$	−6.46410	+	3.73205i	−0.254721	+	0.147063i
$645$		0			0
$646$	−14.9282	−	25.8564i	−0.587342	−	1.01731i
$647$	11.5359	+	6.66025i	0.453523	+	0.261842i	0.709317	−	0.704890i	$-0.249004\pi$
$647$	11.5359	+	6.66025i	0.453523	+	0.261842i	−0.255794	+	0.966731i	$0.582337\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	−54.7128			−2.14767
$650$		0			0
$651$	3.46410			0.135769
$652$	−7.52628	+	13.0359i	−0.294752	+	0.510525i
$653$	3.67949	+	2.12436i	0.143990	+	0.0831325i	0.570264	−	0.821461i	$-0.306841\pi$
$653$	3.67949	+	2.12436i	0.143990	+	0.0831325i	−0.426274	+	0.904594i	$0.640174\pi$
$654$	−7.92820	−	13.7321i	−0.310017	−	0.536966i
$655$		0			0
$656$	−1.73205	+	1.00000i	−0.0676252	+	0.0390434i
$657$	1.00000	+	1.73205i	0.0390137	+	0.0675737i
$658$	−7.07180			−0.275687
$659$	−0.133975	−	0.232051i	−0.00521891	−	0.00903942i	0.863404	−	0.504513i	$-0.168328\pi$
$659$	−0.133975	−	0.232051i	−0.00521891	−	0.00903942i	−0.868623	+	0.495473i	$0.834995\pi$
$660$		0			0
$661$	−7.51666	−	4.33975i	−0.292364	−	0.168797i	0.346643	−	0.937997i	$-0.387321\pi$
$661$	−7.51666	−	4.33975i	−0.292364	−	0.168797i	−0.639008	+	0.769200i	$0.720655\pi$
$662$			16.7846i			0.652352i
$663$	−13.8564	−	4.00000i	−0.538138	−	0.155347i
$664$	−8.92820			−0.346481
$665$		0			0
$666$	−4.59808	+	7.96410i	−0.178172	+	0.308603i
$667$	0.866025	−	0.500000i	0.0335326	−	0.0193601i
$668$	16.3205			0.631459
$669$	17.7846	−	10.2679i	0.687593	−	0.396982i
$670$		0			0
$671$			67.1769i			2.59334i
$672$	−1.73205	+	1.00000i	−0.0668153	+	0.0385758i
$673$	27.7128	+	16.0000i	1.06825	+	0.616755i	0.927703	−	0.373319i	$-0.121780\pi$
$673$	27.7128	+	16.0000i	1.06825	+	0.616755i	0.140548	+	0.990074i	$0.455114\pi$
$674$	8.07180	+	4.66025i	0.310914	+	0.179506i
$675$		0			0
$676$	0.500000	−	12.9904i	0.0192308	−	0.499630i
$677$			32.3923i			1.24494i	0.782645	+	0.622469i	$0.213870\pi$
$677$			32.3923i			1.24494i	−0.782645	+	0.622469i	$0.786130\pi$
$678$	0.401924	−	0.696152i	0.0154358	−	0.0267356i
$679$	0.535898	−	0.928203i	0.0205659	−	0.0356212i
$680$		0			0
$681$			16.3923i			0.628154i
$682$	−5.59808	−	9.69615i	−0.214361	−	0.371285i
$683$	20.3923	+	35.3205i	0.780290	+	1.35150i	0.931773	+	0.363042i	$0.118262\pi$
$683$	20.3923	+	35.3205i	0.780290	+	1.35150i	−0.151483	+	0.988460i	$0.548405\pi$
$684$			7.46410i			0.285397i
$685$		0			0
$686$	−10.0000	+	17.3205i	−0.381802	+	0.661300i
$687$	3.92820	−	6.80385i	0.149870	−	0.259583i
$688$		−	11.9282i		−	0.454758i
$689$	−0.928203	+	3.21539i	−0.0353617	+	0.122497i
$690$		0			0
$691$	−23.5359	−	13.5885i	−0.895348	−	0.516929i	−0.0196598	−	0.999807i	$-0.506258\pi$
$691$	−23.5359	−	13.5885i	−0.895348	−	0.516929i	−0.875688	+	0.482877i	$0.839592\pi$
$692$	9.46410	+	5.46410i	0.359771	+	0.207714i
$693$	11.1962	−	6.46410i	0.425307	−	0.245551i
$694$		−	1.60770i		−	0.0610273i
$695$		0			0
$696$	0.232051	−	0.133975i	0.00879586	−	0.00507829i
$697$	−8.00000			−0.303022
$698$	−18.5885	+	10.7321i	−0.703583	+	0.406214i
$699$	−3.06218	+	5.30385i	−0.115822	+	0.200610i
$700$		0			0
$701$	−0.267949			−0.0101203			−0.00506015	−	0.999987i	$-0.501611\pi$
$701$	−0.267949			−0.0101203			−0.00506015	+	0.999987i	$0.501611\pi$
$702$	2.50000	+	2.59808i	0.0943564	+	0.0980581i
$703$		−	68.6410i		−	2.58884i
$704$	5.59808	+	3.23205i	0.210985	+	0.121812i
$705$		0			0
$706$	−1.00000	−	1.73205i	−0.0376355	−	0.0651866i
$707$	5.85641			0.220253
$708$	−4.23205	−	7.33013i	−0.159050	−	0.275483i
$709$	19.8564	−	11.4641i	0.745723	−	0.430543i	−0.0784234	−	0.996920i	$-0.524989\pi$
$709$	19.8564	−	11.4641i	0.745723	−	0.430543i	0.824146	+	0.566377i	$0.191655\pi$
$710$		0			0
$711$	6.96410	+	12.0622i	0.261174	+	0.452367i
$712$	−0.464102	−	0.267949i	−0.0173929	−	0.0100418i
$713$	3.23205	−	5.59808i	0.121041	−	0.209650i
$714$	−8.00000			−0.299392
$715$		0			0
$716$	19.7321			0.737421
$717$	8.19615	−	14.1962i	0.306091	−	0.530165i
$718$	−4.39230	−	2.53590i	−0.163919	−	0.0946389i
$719$	−17.3205	−	30.0000i	−0.645946	−	1.11881i	−0.984082	−	0.177714i	$-0.943130\pi$
$719$	−17.3205	−	30.0000i	−0.645946	−	1.11881i	0.338136	−	0.941097i	$-0.390204\pi$
$720$		0			0
$721$	20.5359	−	11.8564i	0.764797	−	0.441556i
$722$	−18.3564	−	31.7942i	−0.683155	−	1.18326i
$723$	−17.7321			−0.659462
$724$	1.46410	+	2.53590i	0.0544129	+	0.0942459i
$725$		0			0
$726$	−26.6603	−	15.3923i	−0.989455	−	0.571262i
$727$		−	31.7128i		−	1.17616i	−0.808802	−	0.588082i	$-0.799883\pi$
$727$		−	31.7128i		−	1.17616i	0.808802	−	0.588082i	$-0.200117\pi$
$728$	−1.73205	−	7.00000i	−0.0641941	−	0.259437i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	23.8564	−	41.3205i	0.882361	−	1.52829i
$732$	−9.00000	+	5.19615i	−0.332650	+	0.192055i
$733$	−50.9282			−1.88108			−0.940538	−	0.339688i	$-0.889678\pi$
$733$	−50.9282			−1.88108			−0.940538	+	0.339688i	$0.889678\pi$
$734$	−13.5167	+	7.80385i	−0.498909	+	0.288045i
$735$		0			0
$736$			3.73205i			0.137565i
$737$	64.1769	−	37.0526i	2.36399	−	1.36485i
$738$	1.73205	+	1.00000i	0.0637577	+	0.0368105i
$739$	16.7321	+	9.66025i	0.615498	+	0.355358i	0.775114	−	0.631821i	$-0.217692\pi$
$739$	16.7321	+	9.66025i	0.615498	+	0.355358i	−0.159616	+	0.987179i	$0.551026\pi$
$740$		0			0
$741$	−25.8564	−	7.46410i	−0.949859	−	0.274201i
$742$			1.85641i			0.0681508i
$743$	−20.2321	+	35.0429i	−0.742242	+	1.28560i	0.209230	+	0.977866i	$0.432904\pi$
$743$	−20.2321	+	35.0429i	−0.742242	+	1.28560i	−0.951472	+	0.307734i	$0.900429\pi$
$744$	0.866025	−	1.50000i	0.0317500	−	0.0549927i
$745$		0			0
$746$		−	15.7846i		−	0.577916i
$747$	4.46410	+	7.73205i	0.163333	+	0.282901i
$748$	12.9282	+	22.3923i	0.472702	+	0.818744i
$749$		−	15.7128i		−	0.574134i
$750$		0			0
$751$	−7.03590	+	12.1865i	−0.256744	+	0.444693i	−0.965368	−	0.260893i	$-0.915983\pi$
$751$	−7.03590	+	12.1865i	−0.256744	+	0.444693i	0.708624	+	0.705586i	$0.249316\pi$
$752$	−1.76795	+	3.06218i	−0.0644705	+	0.111666i
$753$			15.7321i			0.573308i
$754$	0.232051	+	0.937822i	0.00845079	+	0.0341535i
$755$		0			0
$756$	1.73205	+	1.00000i	0.0629941	+	0.0363696i
$757$	15.5885	+	9.00000i	0.566572	+	0.327111i	0.755779	−	0.654827i	$-0.227258\pi$
$757$	15.5885	+	9.00000i	0.566572	+	0.327111i	−0.189207	+	0.981937i	$0.560592\pi$
$758$	−24.1244	+	13.9282i	−0.876236	+	0.505895i
$759$		−	24.1244i		−	0.875659i
$760$		0			0
$761$	4.39230	−	2.53590i	0.159221	−	0.0919262i	−0.418272	−	0.908322i	$-0.637364\pi$
$761$	4.39230	−	2.53590i	0.159221	−	0.0919262i	0.577493	+	0.816395i	$0.304031\pi$
$762$	−4.92820			−0.178530
$763$	27.4641	−	15.8564i	0.994267	−	0.574040i
$764$	−10.7321	+	18.5885i	−0.388272	+	0.672507i
$765$		0			0
$766$	−25.3923			−0.917461
$767$	29.6244	−	7.33013i	1.06967	−	0.264676i
$768$			1.00000i			0.0360844i
$769$	10.0359	+	5.79423i	0.361904	+	0.208945i	0.669916	−	0.742437i	$-0.266330\pi$
$769$	10.0359	+	5.79423i	0.361904	+	0.208945i	−0.308012	+	0.951383i	$0.599664\pi$
$770$		0			0
$771$	−2.66987	−	4.62436i	−0.0961531	−	0.166542i
$772$	−11.3205			−0.407434
$773$	−13.8564	−	24.0000i	−0.498380	−	0.863220i	0.501618	−	0.865089i	$-0.332738\pi$
$773$	−13.8564	−	24.0000i	−0.498380	−	0.863220i	−0.999998	+	0.00186926i	$0.999405\pi$
$774$	−10.3301	+	5.96410i	−0.371309	+	0.214375i
$775$		0			0
$776$	−0.267949	−	0.464102i	−0.00961882	−	0.0166603i
$777$	−15.9282	−	9.19615i	−0.571421	−	0.329910i
$778$	11.8660	−	20.5526i	0.425418	−	0.736845i
$779$	−14.9282			−0.534858
$780$		0			0
$781$	−80.1051			−2.86639
$782$	−7.46410	+	12.9282i	−0.266916	+	0.462312i
$783$	−0.232051	−	0.133975i	−0.00829282	−	0.00478786i
$784$	1.50000	+	2.59808i	0.0535714	+	0.0927884i
$785$		0			0
$786$	16.1603	−	9.33013i	0.576417	−	0.332795i
$787$	0.866025	+	1.50000i	0.0308705	+	0.0534692i	0.881048	−	0.473027i	$-0.156839\pi$
$787$	0.866025	+	1.50000i	0.0308705	+	0.0534692i	−0.850177	+	0.526496i	$0.823505\pi$
$788$	4.39230			0.156469
$789$	−3.06218	−	5.30385i	−0.109016	−	0.188822i
$790$		0			0
$791$	1.39230	+	0.803848i	0.0495047	+	0.0285815i
$792$		−	6.46410i		−	0.229692i
$793$	−9.00000	−	36.3731i	−0.319599	−	1.29165i
$794$	12.1244			0.430277
$795$		0			0
$796$	−2.53590	+	4.39230i	−0.0898825	+	0.155681i
$797$	−8.78461	+	5.07180i	−0.311167	+	0.179652i	−0.647449	−	0.762109i	$-0.724164\pi$
$797$	−8.78461	+	5.07180i	−0.311167	+	0.179652i	0.336282	+	0.941761i	$0.390831\pi$
$798$	−14.9282			−0.528453
$799$	−12.2487	+	7.07180i	−0.433328	+	0.250182i
$800$		0			0
$801$			0.535898i			0.0189350i
$802$	−27.7128	+	16.0000i	−0.978573	+	0.564980i
$803$	11.1962	+	6.46410i	0.395104	+	0.228113i
$804$	9.92820	+	5.73205i	0.350141	+	0.202154i
$805$		0			0
$806$	4.33013	+	4.50000i	0.152522	+	0.158506i
$807$		−	12.0000i		−	0.422420i
$808$	1.46410	−	2.53590i	0.0515069	−	0.0892126i
$809$	−21.3923	+	37.0526i	−0.752113	+	1.30270i	0.194683	+	0.980866i	$0.437632\pi$
$809$	−21.3923	+	37.0526i	−0.752113	+	1.30270i	−0.946797	+	0.321832i	$0.895701\pi$
$810$		0			0
$811$			40.7846i			1.43214i	0.698028	+	0.716071i	$0.254061\pi$
$811$			40.7846i			1.43214i	−0.698028	+	0.716071i	$0.745939\pi$
$812$	0.267949	+	0.464102i	0.00940317	+	0.0162868i
$813$	−0.598076	−	1.03590i	−0.0209754	−	0.0363305i
$814$			59.4449i			2.08354i
$815$		0			0
$816$	−2.00000	+	3.46410i	−0.0700140	+	0.121268i
$817$	44.5167	−	77.1051i	1.55744	−	2.69757i
$818$			4.00000i			0.139857i
$819$	−5.19615	+	5.00000i	−0.181568	+	0.174714i
$820$		0			0
$821$	12.6506	+	7.30385i	0.441510	+	0.254906i	0.704238	−	0.709964i	$-0.251289\pi$
$821$	12.6506	+	7.30385i	0.441510	+	0.254906i	−0.262728	+	0.964870i	$0.584622\pi$
$822$	2.13397	+	1.23205i	0.0744309	+	0.0429727i
$823$	−33.9282	+	19.5885i	−1.18266	+	0.682811i	−0.956629	−	0.291309i	$-0.905909\pi$
$823$	−33.9282	+	19.5885i	−1.18266	+	0.682811i	−0.226034	+	0.974119i	$0.572576\pi$
$824$		−	11.8564i		−	0.413037i
$825$		0			0
$826$	14.6603	−	8.46410i	0.510095	−	0.294504i
$827$	−17.3205			−0.602293			−0.301147	−	0.953578i	$-0.597369\pi$
$827$	−17.3205			−0.602293			−0.301147	+	0.953578i	$0.597369\pi$
$828$	3.23205	−	1.86603i	0.112322	−	0.0648489i
$829$	8.26795	−	14.3205i	0.287158	−	0.497372i	−0.685972	−	0.727628i	$-0.740623\pi$
$829$	8.26795	−	14.3205i	0.287158	−	0.497372i	0.973130	+	0.230256i	$0.0739563\pi$
$830$		0			0
$831$	3.92820			0.136268
$832$	−3.46410	−	1.00000i	−0.120096	−	0.0346688i
$833$			12.0000i			0.415775i
$834$	11.1962	+	6.46410i	0.387691	+	0.223834i
$835$		0			0
$836$	24.1244	+	41.7846i	0.834358	+	1.44515i
$837$	−1.73205			−0.0598684
$838$	−11.1962	−	19.3923i	−0.386765	−	0.669896i
$839$	37.7321	−	21.7846i	1.30266	−	0.752088i	0.321796	−	0.946809i	$-0.395713\pi$
$839$	37.7321	−	21.7846i	1.30266	−	0.752088i	0.980859	+	0.194721i	$0.0623800\pi$
$840$		0			0
$841$	14.4641	+	25.0526i	0.498762	+	0.863881i
$842$	3.80385	+	2.19615i	0.131089	+	0.0756844i
$843$	−4.46410	+	7.73205i	−0.153752	+	0.266306i
$844$	−11.3205			−0.389668
$845$		0			0
$846$	3.53590			0.121567
$847$	30.7846	−	53.3205i	1.05777	−	1.83211i
$848$	0.803848	+	0.464102i	0.0276042	+	0.0159373i
$849$	4.96410	+	8.59808i	0.170368	+	0.295085i
$850$		0			0
$851$	−29.7224	+	17.1603i	−1.01887	+	0.588246i
$852$	−6.19615	−	10.7321i	−0.212277	−	0.367674i
$853$	43.8372			1.50096			0.750478	−	0.660895i	$-0.229823\pi$
$853$	43.8372			1.50096			0.750478	+	0.660895i	$0.229823\pi$
$854$	−10.3923	−	18.0000i	−0.355617	−	0.615947i
$855$		0			0
$856$	−6.80385	−	3.92820i	−0.232551	−	0.134263i
$857$			24.5167i			0.837473i	0.908108	+	0.418737i	$0.137527\pi$
$857$			24.5167i			0.837473i	−0.908108	+	0.418737i	$0.862473\pi$
$858$	22.3923	+	6.46410i	0.764461	+	0.220681i
$859$	35.1769			1.20022			0.600110	−	0.799917i	$-0.295123\pi$
$859$	35.1769			1.20022			0.600110	+	0.799917i	$0.295123\pi$
$860$		0			0
$861$	−2.00000	+	3.46410i	−0.0681598	+	0.118056i
$862$	24.5885	−	14.1962i	0.837486	−	0.483523i
$863$	35.5359			1.20966			0.604828	−	0.796356i	$-0.293242\pi$
$863$	35.5359			1.20966			0.604828	+	0.796356i	$0.293242\pi$
$864$	0.866025	−	0.500000i	0.0294628	−	0.0170103i
$865$		0			0
$866$			19.3205i			0.656538i
$867$	0.866025	−	0.500000i	0.0294118	−	0.0169809i
$868$	3.00000	+	1.73205i	0.101827	+	0.0587896i
$869$	77.9711	+	45.0167i	2.64499	+	1.52709i
$870$		0			0
$871$	−29.7846	+	28.6603i	−1.00921	+	0.971116i
$872$		−	15.8564i		−	0.536966i
$873$	−0.267949	+	0.464102i	−0.00906871	+	0.0157075i
$874$	−13.9282	+	24.1244i	−0.471129	+	0.816019i
$875$		0			0
$876$			2.00000i			0.0675737i
$877$	−1.93782	−	3.35641i	−0.0654356	−	0.113338i	0.831452	−	0.555597i	$-0.187510\pi$
$877$	−1.93782	−	3.35641i	−0.0654356	−	0.113338i	−0.896887	+	0.442260i	$0.854177\pi$
$878$	8.92820	+	15.4641i	0.301312	+	0.521888i
$879$		−	31.8564i		−	1.07449i
$880$		0			0
$881$	7.00000	−	12.1244i	0.235836	−	0.408480i	−0.723679	−	0.690136i	$-0.757551\pi$
$881$	7.00000	−	12.1244i	0.235836	−	0.408480i	0.959515	+	0.281656i	$0.0908839\pi$
$882$	1.50000	−	2.59808i	0.0505076	−	0.0874818i
$883$		−	29.9282i		−	1.00716i	−0.863947	−	0.503582i	$-0.832015\pi$
$883$		−	29.9282i		−	1.00716i	0.863947	−	0.503582i	$-0.167985\pi$
$884$	−10.0000	−	10.3923i	−0.336336	−	0.349531i
$885$		0			0
$886$	−14.1962	−	8.19615i	−0.476929	−	0.275355i
$887$	−12.2321	−	7.06218i	−0.410712	−	0.237125i	0.280384	−	0.959888i	$-0.409538\pi$
$887$	−12.2321	−	7.06218i	−0.410712	−	0.237125i	−0.691096	+	0.722763i	$0.742872\pi$
$888$	−7.96410	+	4.59808i	−0.267258	+	0.154301i
$889$		−	9.85641i		−	0.330573i
$890$		0			0
$891$	−5.59808	+	3.23205i	−0.187543	+	0.108278i
$892$	20.5359			0.687593
$893$	−22.8564	+	13.1962i	−0.764860	+	0.441592i
$894$	−6.76795	+	11.7224i	−0.226354	+	0.392057i
$895$		0			0
$896$	−2.00000			−0.0668153
$897$	3.23205	+	13.0622i	0.107915	+	0.436133i
$898$		−	15.7128i		−	0.524343i
$899$	−0.401924	−	0.232051i	−0.0134049	−	0.00773933i
$900$		0			0
$901$	1.85641	+	3.21539i	0.0618459	+	0.107120i
$902$	12.9282			0.430462
$903$	−11.9282	−	20.6603i	−0.396946	−	0.687530i
$904$	0.696152	−	0.401924i	0.0231537	−	0.0133678i
$905$		0			0
$906$	5.19615	+	9.00000i	0.172631	+	0.299005i
$907$	18.0622	+	10.4282i	0.599745	+	0.346263i	0.768941	−	0.639320i	$-0.220784\pi$
$907$	18.0622	+	10.4282i	0.599745	+	0.346263i	−0.169196	+	0.985582i	$0.554117\pi$
$908$	−8.19615	+	14.1962i	−0.271999	+	0.471116i
$909$	−2.92820			−0.0971224
$910$		0			0
$911$	24.2487			0.803396			0.401698	−	0.915772i	$-0.368420\pi$
$911$	24.2487			0.803396			0.401698	+	0.915772i	$0.368420\pi$
$912$	−3.73205	+	6.46410i	−0.123581	+	0.214048i
$913$	49.9808	+	28.8564i	1.65412	+	0.955008i
$914$	12.2679	+	21.2487i	0.405788	+	0.702845i
$915$		0			0
$916$	6.80385	−	3.92820i	0.224805	−	0.129791i
$917$	18.6603	+	32.3205i	0.616216	+	1.06732i
$918$	4.00000			0.132020
$919$	7.32051	+	12.6795i	0.241481	+	0.418258i	0.961136	−	0.276074i	$-0.0890334\pi$
$919$	7.32051	+	12.6795i	0.241481	+	0.418258i	−0.719655	+	0.694332i	$0.755700\pi$
$920$		0			0
$921$	16.8564	+	9.73205i	0.555437	+	0.320682i
$922$		−	0.464102i		−	0.0152844i
$923$	43.3731	−	10.7321i	1.42764	−	0.353250i
$924$	12.9282			0.425307
$925$		0			0
$926$	3.53590	−	6.12436i	0.116197	−	0.201259i
$927$	−10.2679	+	5.92820i	−0.337244	+	0.194708i
$928$	0.267949			0.00879586
$929$	5.32051	−	3.07180i	0.174560	−	0.100782i	−0.410174	−	0.912007i	$-0.634532\pi$
$929$	5.32051	−	3.07180i	0.174560	−	0.100782i	0.584734	+	0.811225i	$0.301199\pi$
$930$		0			0
$931$			22.3923i			0.733878i
$932$	−5.30385	+	3.06218i	−0.173733	+	0.100305i
$933$	24.5885	+	14.1962i	0.804990	+	0.464761i
$934$	−13.7321	−	7.92820i	−0.449326	−	0.259419i
$935$		0			0
$936$	0.866025	+	3.50000i	0.0283069	+	0.114401i
$937$		−	24.6410i		−	0.804987i	−0.915423	−	0.402493i	$-0.868144\pi$
$937$		−	24.6410i		−	0.804987i	0.915423	−	0.402493i	$-0.131856\pi$
$938$	−11.4641	+	19.8564i	−0.374316	+	0.648335i
$939$	14.0000	−	24.2487i	0.456873	−	0.791327i
$940$		0			0
$941$		−	14.7846i		−	0.481965i	−0.970530	−	0.240982i	$-0.922530\pi$
$941$		−	14.7846i		−	0.481965i	0.970530	−	0.240982i	$-0.0774696\pi$
$942$	2.50000	+	4.33013i	0.0814544	+	0.141083i
$943$	3.73205	+	6.46410i	0.121532	+	0.210500i
$944$		−	8.46410i		−	0.275483i
$945$		0			0
$946$	−38.5526	+	66.7750i	−1.25345	+	2.17104i
$947$	−4.73205	+	8.19615i	−0.153771	+	0.266339i	−0.932611	−	0.360884i	$-0.882475\pi$
$947$	−4.73205	+	8.19615i	−0.153771	+	0.266339i	0.778840	+	0.627223i	$0.215808\pi$
$948$			13.9282i			0.452367i
$949$	−6.92820	−	2.00000i	−0.224899	−	0.0649227i
$950$		0			0
$951$	12.5885	+	7.26795i	0.408209	+	0.235679i
$952$	−6.92820	−	4.00000i	−0.224544	−	0.129641i
$953$	10.6244	−	6.13397i	0.344157	−	0.198699i	−0.317952	−	0.948107i	$-0.602995\pi$
$953$	10.6244	−	6.13397i	0.344157	−	0.198699i	0.662109	+	0.749408i	$0.269662\pi$
$954$		−	0.928203i		−	0.0300517i
$955$		0			0
$956$	14.1962	−	8.19615i	0.459136	−	0.265083i
$957$	−1.73205			−0.0559893
$958$	−4.73205	+	2.73205i	−0.152886	+	0.0882686i
$959$	−2.46410	+	4.26795i	−0.0795700	+	0.137819i
$960$		0			0
$961$	28.0000			0.903226
$962$	−7.96410	−	32.1865i	−0.256773	−	1.03774i
$963$			7.85641i			0.253169i
$964$	−15.3564	−	8.86603i	−0.494597	−	0.285555i
$965$		0			0
$966$	3.73205	+	6.46410i	0.120077	+	0.207979i
$967$	41.4641			1.33340			0.666698	−	0.745328i	$-0.267707\pi$
$967$	41.4641			1.33340			0.666698	+	0.745328i	$0.267707\pi$
$968$	−15.3923	−	26.6603i	−0.494727	−	0.856893i
$969$	−25.8564	+	14.9282i	−0.830627	+	0.479563i
$970$		0			0
$971$	−2.26795	−	3.92820i	−0.0727820	−	0.126062i	0.827338	−	0.561705i	$-0.189854\pi$
$971$	−2.26795	−	3.92820i	−0.0727820	−	0.126062i	−0.900120	+	0.435643i	$0.856521\pi$
$972$	−0.866025	−	0.500000i	−0.0277778	−	0.0160375i
$973$	−12.9282	+	22.3923i	−0.414459	+	0.717864i
$974$	23.1769			0.742636
$975$		0			0
$976$	−10.3923			−0.332650
$977$	−6.30385	+	10.9186i	−0.201678	+	0.349316i	−0.949069	−	0.315068i	$-0.897973\pi$
$977$	−6.30385	+	10.9186i	−0.201678	+	0.349316i	0.747391	+	0.664384i	$0.231306\pi$
$978$	13.0359	+	7.52628i	0.416842	+	0.240664i
$979$	1.73205	+	3.00000i	0.0553566	+	0.0958804i
$980$		0			0
$981$	−13.7321	+	7.92820i	−0.438431	+	0.253128i
$982$	−8.66025	−	15.0000i	−0.276360	−	0.478669i
$983$	−36.6077			−1.16760			−0.583802	−	0.811896i	$-0.698436\pi$
$983$	−36.6077			−1.16760			−0.583802	+	0.811896i	$0.698436\pi$
$984$	1.00000	+	1.73205i	0.0318788	+	0.0552158i
$985$		0			0
$986$	0.928203	+	0.535898i	0.0295600	+	0.0170665i
$987$			7.07180i			0.225098i
$988$	−18.6603	−	19.3923i	−0.593662	−	0.616951i
$989$	−44.5167			−1.41555
$990$		0			0
$991$	26.4282	−	45.7750i	0.839520	−	1.45409i	−0.0507774	−	0.998710i	$-0.516170\pi$
$991$	26.4282	−	45.7750i	0.839520	−	1.45409i	0.890297	−	0.455381i	$-0.150497\pi$
$992$	1.50000	−	0.866025i	0.0476250	−	0.0274963i
$993$	16.7846			0.532643
$994$	21.4641	−	12.3923i	0.680800	−	0.393060i
$995$		0			0
$996$			8.92820i			0.282901i
$997$	30.8038	−	17.7846i	0.975568	−	0.563244i	0.0746386	−	0.997211i	$-0.476220\pi$
$997$	30.8038	−	17.7846i	0.975568	−	0.563244i	0.900929	+	0.433966i	$0.142886\pi$
$998$	−5.66025	−	3.26795i	−0.179172	−	0.103445i
$999$	7.96410	+	4.59808i	0.251973	+	0.145477i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1950.2.y.f.199.1		4
5.2	odd	4		1950.2.bc.b.901.2		4
5.3	odd	4		390.2.bb.b.121.1	✓	4
5.4	even	2		1950.2.y.c.199.2		4
13.10	even	6		1950.2.y.c.49.2		4
15.8	even	4		1170.2.bs.e.901.2		4
65.23	odd	12		390.2.bb.b.361.1	yes	4
65.33	even	12		5070.2.a.y.1.1		2
65.43	odd	12		5070.2.b.o.1351.2		4
65.48	odd	12		5070.2.b.o.1351.3		4
65.49	even	6	inner	1950.2.y.f.49.1		4
65.58	even	12		5070.2.a.bg.1.2		2
65.62	odd	12		1950.2.bc.b.751.2		4
195.23	even	12		1170.2.bs.e.361.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.bb.b.121.1	✓	4	5.3	odd	4
390.2.bb.b.361.1	yes	4	65.23	odd	12
1170.2.bs.e.361.2		4	195.23	even	12
1170.2.bs.e.901.2		4	15.8	even	4
1950.2.y.c.49.2		4	13.10	even	6
1950.2.y.c.199.2		4	5.4	even	2
1950.2.y.f.49.1		4	65.49	even	6	inner
1950.2.y.f.199.1		4	1.1	even	1	trivial
1950.2.bc.b.751.2		4	65.62	odd	12
1950.2.bc.b.901.2		4	5.2	odd	4
5070.2.a.y.1.1		2	65.33	even	12
5070.2.a.bg.1.2		2	65.58	even	12
5070.2.b.o.1351.2		4	65.43	odd	12
5070.2.b.o.1351.3		4	65.48	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1950.y (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{6} +(-1.00000 - 1.73205i) q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +(5.59808 + 3.23205i) q^{11} +1.00000i q^{12} +(-3.46410 - 1.00000i) q^{13} -2.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.46410 + 2.00000i) q^{17} +1.00000 q^{18} +(-6.46410 + 3.73205i) q^{19} +2.00000i q^{21} +(5.59808 - 3.23205i) q^{22} +(3.23205 + 1.86603i) q^{23} +(0.866025 + 0.500000i) q^{24} +(-2.59808 + 2.50000i) q^{26} -1.00000i q^{27} +(-1.00000 + 1.73205i) q^{28} +(0.133975 - 0.232051i) q^{29} -1.73205i q^{31} +(0.500000 + 0.866025i) q^{32} +(-3.23205 - 5.59808i) q^{33} +4.00000i q^{34} +(0.500000 - 0.866025i) q^{36} +(-4.59808 + 7.96410i) q^{37} +7.46410i q^{38} +(2.50000 + 2.59808i) q^{39} +(1.73205 + 1.00000i) q^{41} +(1.73205 + 1.00000i) q^{42} +(-10.3301 + 5.96410i) q^{43} -6.46410i q^{44} +(3.23205 - 1.86603i) q^{46} +3.53590 q^{47} +(0.866025 - 0.500000i) q^{48} +(1.50000 - 2.59808i) q^{49} +4.00000 q^{51} +(0.866025 + 3.50000i) q^{52} -0.928203i q^{53} +(-0.866025 - 0.500000i) q^{54} +(1.00000 + 1.73205i) q^{56} +7.46410 q^{57} +(-0.133975 - 0.232051i) q^{58} +(-7.33013 + 4.23205i) q^{59} +(5.19615 + 9.00000i) q^{61} +(-1.50000 - 0.866025i) q^{62} +(1.00000 - 1.73205i) q^{63} +1.00000 q^{64} -6.46410 q^{66} +(5.73205 - 9.92820i) q^{67} +(3.46410 + 2.00000i) q^{68} +(-1.86603 - 3.23205i) q^{69} +(-10.7321 + 6.19615i) q^{71} +(-0.500000 - 0.866025i) q^{72} +2.00000 q^{73} +(4.59808 + 7.96410i) q^{74} +(6.46410 + 3.73205i) q^{76} -12.9282i q^{77} +(3.50000 - 0.866025i) q^{78} +13.9282 q^{79} +(-0.500000 + 0.866025i) q^{81} +(1.73205 - 1.00000i) q^{82} +8.92820 q^{83} +(1.73205 - 1.00000i) q^{84} +11.9282i q^{86} +(-0.232051 + 0.133975i) q^{87} +(-5.59808 - 3.23205i) q^{88} +(0.464102 + 0.267949i) q^{89} +(1.73205 + 7.00000i) q^{91} -3.73205i q^{92} +(-0.866025 + 1.50000i) q^{93} +(1.76795 - 3.06218i) q^{94} -1.00000i q^{96} +(0.267949 + 0.464102i) q^{97} +(-1.50000 - 2.59808i) q^{98} +6.46410i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{4} - 4 q^{7} - 4 q^{8} + 2 q^{9} + 12 q^{11} - 8 q^{14} - 2 q^{16} + 4 q^{18} - 12 q^{19} + 12 q^{22} + 6 q^{23} - 4 q^{28} + 4 q^{29} + 2 q^{32} - 6 q^{33} + 2 q^{36} - 8 q^{37} + 10 q^{39}+ \cdots - 6 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^4 - 4 * q^7 - 4 * q^8 + 2 * q^9 + 12 * q^11 - 8 * q^14 - 2 * q^16 + 4 * q^18 - 12 * q^19 + 12 * q^22 + 6 * q^23 - 4 * q^28 + 4 * q^29 + 2 * q^32 - 6 * q^33 + 2 * q^36 - 8 * q^37 + 10 * q^39 - 24 * q^43 + 6 * q^46 + 28 * q^47 + 6 * q^49 + 16 * q^51 + 4 * q^56 + 16 * q^57 - 4 * q^58 - 12 * q^59 - 6 * q^62 + 4 * q^63 + 4 * q^64 - 12 * q^66 + 16 * q^67 - 4 * q^69 - 36 * q^71 - 2 * q^72 + 8 * q^73 + 8 * q^74 + 12 * q^76 + 14 * q^78 + 28 * q^79 - 2 * q^81 + 8 * q^83 + 6 * q^87 - 12 * q^88 - 12 * q^89 + 14 * q^94 + 8 * q^97 - 6 * q^98

Introduction

L-functions

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