LMFDB - Embedded newform 1950.2.bc.b.751.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1950,2,Mod(751,1950)]

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, 5]))

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

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

chi := DirichletCharacter("1950.751");

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.bc (of order $6$, 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 $\Q(\zeta_{6})$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 390)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			751.2
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1950.751
Dual form			1950.2.bc.b.901.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$301$	$1301$	$1327$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	−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
$6$	−0.866025	−	0.500000i	−0.353553	−	0.204124i
$7$	1.73205	+	1.00000i	0.654654	+	0.377964i	0.790237	−	0.612801i	$-0.209957\pi$
$7$	1.73205	+	1.00000i	0.654654	+	0.377964i	−0.135583	+	0.990766i	$0.543291\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	5.59808	−	3.23205i	1.68788	−	0.974500i	0.731748	−	0.681575i	$-0.238705\pi$
$11$	5.59808	−	3.23205i	1.68788	−	0.974500i	0.956136	−	0.292925i	$-0.0946285\pi$
$12$	−1.00000			−0.288675
$13$	−1.00000	−	3.46410i	−0.277350	−	0.960769i
$13$	−1.00000	−	3.46410i	−0.277350	−	0.960769i
$14$	2.00000			0.534522
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.00000	+	3.46410i	−0.485071	+	0.840168i	−0.999853	−	0.0171533i	$-0.994540\pi$
$17$	−2.00000	+	3.46410i	−0.485071	+	0.840168i	0.514782	+	0.857321i	$0.327873\pi$
$18$			1.00000i			0.235702i
$19$	6.46410	+	3.73205i	1.48297	+	0.856191i	0.999813	−	0.0193444i	$-0.00615788\pi$
$19$	6.46410	+	3.73205i	1.48297	+	0.856191i	0.483154	+	0.875536i	$0.339491\pi$
$20$		0			0
$21$		−	2.00000i		−	0.436436i
$22$	3.23205	−	5.59808i	0.689076	−	1.19351i
$23$	1.86603	+	3.23205i	0.389093	+	0.673929i	0.992328	−	0.123635i	$-0.0394551\pi$
$23$	1.86603	+	3.23205i	0.389093	+	0.673929i	−0.603235	+	0.797564i	$0.706122\pi$
$24$	−0.866025	+	0.500000i	−0.176777	+	0.102062i
$25$		0			0
$26$	−2.59808	−	2.50000i	−0.509525	−	0.490290i
$27$	1.00000			0.192450
$28$	1.73205	−	1.00000i	0.327327	−	0.188982i
$29$	−0.133975	−	0.232051i	−0.0248785	−	0.0430908i	0.853318	−	0.521391i	$-0.174587\pi$
$29$	−0.133975	−	0.232051i	−0.0248785	−	0.0430908i	−0.878197	+	0.478300i	$0.841253\pi$
$30$		0			0
$31$			1.73205i			0.311086i	0.987829	+	0.155543i	$0.0497126\pi$
$31$			1.73205i			0.311086i	−0.987829	+	0.155543i	$0.950287\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	−5.59808	−	3.23205i	−0.974500	−	0.562628i
$34$			4.00000i			0.685994i
$35$		0			0
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$	−7.96410	+	4.59808i	−1.30929	+	0.755919i	−0.981978	−	0.188997i	$-0.939476\pi$
$37$	−7.96410	+	4.59808i	−1.30929	+	0.755919i	−0.327313	+	0.944916i	$0.606143\pi$
$38$	7.46410			1.21084
$39$	−2.50000	+	2.59808i	−0.400320	+	0.416025i
$40$		0			0
$41$	1.73205	−	1.00000i	0.270501	−	0.156174i	−0.358614	−	0.933486i	$-0.616751\pi$
$41$	1.73205	−	1.00000i	0.270501	−	0.156174i	0.629115	+	0.777312i	$0.283417\pi$
$42$	−1.00000	−	1.73205i	−0.154303	−	0.267261i
$43$	5.96410	−	10.3301i	0.909517	−	1.57533i	0.0947805	−	0.995498i	$-0.469785\pi$
$43$	5.96410	−	10.3301i	0.909517	−	1.57533i	0.814736	−	0.579831i	$-0.196882\pi$
$44$		−	6.46410i		−	0.974500i
$45$		0			0
$46$	3.23205	+	1.86603i	0.476540	+	0.275130i
$47$		−	3.53590i		−	0.515764i	−0.966176	−	0.257882i	$-0.916975\pi$
$47$		−	3.53590i		−	0.515764i	0.966176	−	0.257882i	$-0.0830245\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	−1.50000	−	2.59808i	−0.214286	−	0.371154i
$50$		0			0
$51$	4.00000			0.560112
$52$	−3.50000	−	0.866025i	−0.485363	−	0.120096i
$53$	−0.928203			−0.127499			−0.0637493	−	0.997966i	$-0.520306\pi$
$53$	−0.928203			−0.127499			−0.0637493	+	0.997966i	$0.520306\pi$
$54$	0.866025	−	0.500000i	0.117851	−	0.0680414i
$55$		0			0
$56$	1.00000	−	1.73205i	0.133631	−	0.231455i
$57$		−	7.46410i		−	0.988644i
$58$	−0.232051	−	0.133975i	−0.0304698	−	0.0175917i
$59$	7.33013	+	4.23205i	0.954301	+	0.550966i	0.894414	−	0.447239i	$-0.147593\pi$
$59$	7.33013	+	4.23205i	0.954301	+	0.550966i	0.0598868	+	0.998205i	$0.480926\pi$
$60$		0			0
$61$	5.19615	−	9.00000i	0.665299	−	1.15233i	−0.313905	−	0.949454i	$-0.601637\pi$
$61$	5.19615	−	9.00000i	0.665299	−	1.15233i	0.979204	−	0.202878i	$-0.0650293\pi$
$62$	0.866025	+	1.50000i	0.109985	+	0.190500i
$63$	−1.73205	+	1.00000i	−0.218218	+	0.125988i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−6.46410			−0.795676
$67$	9.92820	−	5.73205i	1.21292	−	0.700281i	0.249528	−	0.968368i	$-0.419724\pi$
$67$	9.92820	−	5.73205i	1.21292	−	0.700281i	0.963395	+	0.268086i	$0.0863912\pi$
$68$	2.00000	+	3.46410i	0.242536	+	0.420084i
$69$	1.86603	−	3.23205i	0.224643	−	0.389093i
$70$		0			0
$71$	−10.7321	−	6.19615i	−1.27366	−	0.735348i	−0.297985	−	0.954570i	$-0.596315\pi$
$71$	−10.7321	−	6.19615i	−1.27366	−	0.735348i	−0.975675	+	0.219222i	$0.929648\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$			2.00000i			0.234082i	0.993127	+	0.117041i	$0.0373409\pi$
$73$			2.00000i			0.234082i	−0.993127	+	0.117041i	$0.962659\pi$
$74$	−4.59808	+	7.96410i	−0.534516	+	0.925808i
$75$		0			0
$76$	6.46410	−	3.73205i	0.741483	−	0.428096i
$77$	12.9282			1.47331
$78$	−0.866025	+	3.50000i	−0.0980581	+	0.396297i
$79$	−13.9282			−1.56705			−0.783523	−	0.621363i	$-0.786579\pi$
$79$	−13.9282			−1.56705			−0.783523	+	0.621363i	$0.786579\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	1.00000	−	1.73205i	0.110432	−	0.191273i
$83$			8.92820i			0.979998i	0.871723	+	0.489999i	$0.163003\pi$
$83$			8.92820i			0.979998i	−0.871723	+	0.489999i	$0.836997\pi$
$84$	−1.73205	−	1.00000i	−0.188982	−	0.109109i
$85$		0			0
$86$		−	11.9282i		−	1.28625i
$87$	−0.133975	+	0.232051i	−0.0143636	+	0.0248785i
$88$	−3.23205	−	5.59808i	−0.344538	−	0.596757i
$89$	−0.464102	+	0.267949i	−0.0491947	+	0.0284026i	−0.524396	−	0.851475i	$-0.675709\pi$
$89$	−0.464102	+	0.267949i	−0.0491947	+	0.0284026i	0.475201	+	0.879877i	$0.342375\pi$
$90$		0			0
$91$	1.73205	−	7.00000i	0.181568	−	0.733799i
$92$	3.73205			0.389093
$93$	1.50000	−	0.866025i	0.155543	−	0.0898027i
$94$	−1.76795	−	3.06218i	−0.182350	−	0.315840i
$95$		0			0
$96$			1.00000i			0.102062i
$97$	−0.464102	−	0.267949i	−0.0471224	−	0.0272061i	0.476254	−	0.879308i	$-0.341994\pi$
$97$	−0.464102	−	0.267949i	−0.0471224	−	0.0272061i	−0.523376	+	0.852102i	$0.675328\pi$
$98$	−2.59808	−	1.50000i	−0.262445	−	0.151523i
$99$			6.46410i			0.649667i
$100$		0			0
$101$	−1.46410	−	2.53590i	−0.145684	−	0.252331i	0.783944	−	0.620831i	$-0.213205\pi$
$101$	−1.46410	−	2.53590i	−0.145684	−	0.252331i	−0.929628	+	0.368500i	$0.879871\pi$
$102$	3.46410	−	2.00000i	0.342997	−	0.198030i
$103$	11.8564			1.16825			0.584123	−	0.811665i	$-0.301438\pi$
$103$	11.8564			1.16825			0.584123	+	0.811665i	$0.301438\pi$
$104$	−3.46410	+	1.00000i	−0.339683	+	0.0980581i
$105$		0			0
$106$	−0.803848	+	0.464102i	−0.0780766	+	0.0450775i
$107$	−3.92820	−	6.80385i	−0.379754	−	0.657753i	0.611273	−	0.791420i	$-0.290658\pi$
$107$	−3.92820	−	6.80385i	−0.379754	−	0.657753i	−0.991026	+	0.133667i	$0.957325\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$			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
$112$		−	2.00000i		−	0.188982i
$113$	0.401924	−	0.696152i	0.0378098	−	0.0654885i	−0.846501	−	0.532387i	$-0.821295\pi$
$113$	0.401924	−	0.696152i	0.0378098	−	0.0654885i	0.884311	+	0.466898i	$0.154629\pi$
$114$	−3.73205	−	6.46410i	−0.349539	−	0.605419i
$115$		0			0
$116$	−0.267949			−0.0248785
$117$	3.50000	+	0.866025i	0.323575	+	0.0800641i
$118$	8.46410			0.779184
$119$	−6.92820	+	4.00000i	−0.635107	+	0.366679i
$120$		0			0
$121$	15.3923	−	26.6603i	1.39930	−	2.42366i
$122$		−	10.3923i		−	0.940875i
$123$	−1.73205	−	1.00000i	−0.156174	−	0.0901670i
$124$	1.50000	+	0.866025i	0.134704	+	0.0777714i
$125$		0			0
$126$	−1.00000	+	1.73205i	−0.0890871	+	0.154303i
$127$	−2.46410	−	4.26795i	−0.218654	−	0.378719i	0.735743	−	0.677261i	$-0.236833\pi$
$127$	−2.46410	−	4.26795i	−0.218654	−	0.378719i	−0.954397	+	0.298542i	$0.903500\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	−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	$0.803360\pi$
$132$	−5.59808	+	3.23205i	−0.487250	+	0.281314i
$133$	7.46410	+	12.9282i	0.647220	+	1.12102i
$134$	5.73205	−	9.92820i	0.495174	−	0.857666i
$135$		0			0
$136$	3.46410	+	2.00000i	0.297044	+	0.171499i
$137$	2.13397	+	1.23205i	0.182318	+	0.105261i	0.588381	−	0.808584i	$-0.299765\pi$
$137$	2.13397	+	1.23205i	0.182318	+	0.105261i	−0.406063	+	0.913845i	$0.633099\pi$
$138$		−	3.73205i		−	0.317693i
$139$	6.46410	−	11.1962i	0.548278	−	0.949645i	−0.450115	−	0.892971i	$-0.648617\pi$
$139$	6.46410	−	11.1962i	0.548278	−	0.949645i	0.998393	−	0.0566745i	$-0.0180497\pi$
$140$		0			0
$141$	−3.06218	+	1.76795i	−0.257882	+	0.148888i
$142$	−12.3923			−1.03994
$143$	−16.7942	−	16.1603i	−1.40440	−	1.35139i
$144$	1.00000			0.0833333
$145$		0			0
$146$	1.00000	+	1.73205i	0.0827606	+	0.143346i
$147$	−1.50000	+	2.59808i	−0.123718	+	0.214286i
$148$			9.19615i			0.755919i
$149$	−11.7224	−	6.76795i	−0.960339	−	0.554452i	−0.0640617	−	0.997946i	$-0.520405\pi$
$149$	−11.7224	−	6.76795i	−0.960339	−	0.554452i	−0.896277	+	0.443494i	$0.853739\pi$
$150$		0			0
$151$			10.3923i			0.845714i	0.906196	+	0.422857i	$0.138973\pi$
$151$			10.3923i			0.845714i	−0.906196	+	0.422857i	$0.861027\pi$
$152$	3.73205	−	6.46410i	0.302709	−	0.524308i
$153$	−2.00000	−	3.46410i	−0.161690	−	0.280056i
$154$	11.1962	−	6.46410i	0.902212	−	0.520892i
$155$		0			0
$156$	1.00000	+	3.46410i	0.0800641	+	0.277350i
$157$	5.00000			0.399043			0.199522	−	0.979893i	$-0.436061\pi$
$157$	5.00000			0.399043			0.199522	+	0.979893i	$0.436061\pi$
$158$	−12.0622	+	6.96410i	−0.959615	+	0.554034i
$159$	0.464102	+	0.803848i	0.0368057	+	0.0637493i
$160$		0			0
$161$			7.46410i			0.588254i
$162$	−0.866025	−	0.500000i	−0.0680414	−	0.0392837i
$163$	−13.0359	−	7.52628i	−1.02105	−	0.589504i	−0.106642	−	0.994297i	$-0.534010\pi$
$163$	−13.0359	−	7.52628i	−1.02105	−	0.589504i	−0.914408	+	0.404794i	$0.867343\pi$
$164$		−	2.00000i		−	0.156174i
$165$		0			0
$166$	4.46410	+	7.73205i	0.346481	+	0.600124i
$167$	−14.1340	+	8.16025i	−1.09372	+	0.631459i	−0.934564	−	0.355794i	$-0.884210\pi$
$167$	−14.1340	+	8.16025i	−1.09372	+	0.631459i	−0.159155	+	0.987254i	$0.550877\pi$
$168$	−2.00000			−0.154303
$169$	−11.0000	+	6.92820i	−0.846154	+	0.532939i
$170$		0			0
$171$	−6.46410	+	3.73205i	−0.494322	+	0.285397i
$172$	−5.96410	−	10.3301i	−0.454758	−	0.787665i
$173$	5.46410	−	9.46410i	0.415428	−	0.719542i	−0.580045	−	0.814584i	$-0.696965\pi$
$173$	5.46410	−	9.46410i	0.415428	−	0.719542i	0.995473	+	0.0950419i	$0.0302985\pi$
$174$			0.267949i			0.0203132i
$175$		0			0
$176$	−5.59808	−	3.23205i	−0.421971	−	0.243625i
$177$		−	8.46410i		−	0.636201i
$178$	−0.267949	+	0.464102i	−0.0200836	+	0.0347859i
$179$	9.86603	+	17.0885i	0.737421	+	1.27725i	0.953653	+	0.300909i	$0.0972901\pi$
$179$	9.86603	+	17.0885i	0.737421	+	1.27725i	−0.216231	+	0.976342i	$0.569377\pi$
$180$		0			0
$181$	−2.92820			−0.217652			−0.108826	−	0.994061i	$-0.534709\pi$
$181$	−2.92820			−0.217652			−0.108826	+	0.994061i	$0.534709\pi$
$182$	−2.00000	−	6.92820i	−0.148250	−	0.513553i
$183$	−10.3923			−0.768221
$184$	3.23205	−	1.86603i	0.238270	−	0.137565i
$185$		0			0
$186$	0.866025	−	1.50000i	0.0635001	−	0.109985i
$187$			25.8564i			1.89081i
$188$	−3.06218	−	1.76795i	−0.223332	−	0.128941i
$189$	1.73205	+	1.00000i	0.125988	+	0.0727393i
$190$		0			0
$191$	−10.7321	+	18.5885i	−0.776544	+	1.34501i	0.157379	+	0.987538i	$0.449696\pi$
$191$	−10.7321	+	18.5885i	−0.776544	+	1.34501i	−0.933923	+	0.357475i	$0.883638\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	−9.80385	+	5.66025i	−0.705696	+	0.407434i	−0.809466	−	0.587167i	$-0.800243\pi$
$193$	−9.80385	+	5.66025i	−0.705696	+	0.407434i	0.103769	+	0.994601i	$0.466910\pi$
$194$	−0.535898			−0.0384753
$195$		0			0
$196$	−3.00000			−0.214286
$197$	−3.80385	+	2.19615i	−0.271013	+	0.156469i	−0.629348	−	0.777124i	$-0.716678\pi$
$197$	−3.80385	+	2.19615i	−0.271013	+	0.156469i	0.358335	+	0.933593i	$0.383345\pi$
$198$	3.23205	+	5.59808i	0.229692	+	0.397838i
$199$	2.53590	−	4.39230i	0.179765	−	0.311362i	−0.762035	−	0.647536i	$-0.775800\pi$
$199$	2.53590	−	4.39230i	0.179765	−	0.311362i	0.941800	+	0.336174i	$0.109133\pi$
$200$		0			0
$201$	−9.92820	−	5.73205i	−0.700281	−	0.404308i
$202$	−2.53590	−	1.46410i	−0.178425	−	0.103014i
$203$		−	0.535898i		−	0.0376127i
$204$	2.00000	−	3.46410i	0.140028	−	0.242536i
$205$		0			0
$206$	10.2679	−	5.92820i	0.715402	−	0.413037i
$207$	−3.73205			−0.259395
$208$	−2.50000	+	2.59808i	−0.173344	+	0.180144i
$209$	48.2487			3.33743
$210$		0			0
$211$	5.66025	+	9.80385i	0.389668	+	0.674925i	0.992405	−	0.123015i	$-0.0392564\pi$
$211$	5.66025	+	9.80385i	0.389668	+	0.674925i	−0.602737	+	0.797940i	$0.705923\pi$
$212$	−0.464102	+	0.803848i	−0.0318746	+	0.0552085i
$213$			12.3923i			0.849107i
$214$	−6.80385	−	3.92820i	−0.465101	−	0.268526i
$215$		0			0
$216$		−	1.00000i		−	0.0680414i
$217$	−1.73205	+	3.00000i	−0.117579	+	0.203653i
$218$	7.92820	+	13.7321i	0.536966	+	0.930052i
$219$	1.73205	−	1.00000i	0.117041	−	0.0675737i
$220$		0			0
$221$	14.0000	+	3.46410i	0.941742	+	0.233021i
$222$	9.19615			0.617205
$223$	17.7846	−	10.2679i	1.19095	−	0.687593i	0.232424	−	0.972614i	$-0.425334\pi$
$223$	17.7846	−	10.2679i	1.19095	−	0.687593i	0.958521	+	0.285022i	$0.0920008\pi$
$224$	−1.00000	−	1.73205i	−0.0668153	−	0.115728i
$225$		0			0
$226$		−	0.803848i		−	0.0534711i
$227$	14.1962	+	8.19615i	0.942232	+	0.543998i	0.890659	−	0.454672i	$-0.150243\pi$
$227$	14.1962	+	8.19615i	0.942232	+	0.543998i	0.0515725	+	0.998669i	$0.483577\pi$
$228$	−6.46410	−	3.73205i	−0.428096	−	0.247161i
$229$			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
$232$	−0.232051	+	0.133975i	−0.0152349	+	0.00879586i
$233$	−6.12436			−0.401220			−0.200610	−	0.979671i	$-0.564292\pi$
$233$	−6.12436			−0.401220			−0.200610	+	0.979671i	$0.564292\pi$
$234$	3.46410	−	1.00000i	0.226455	−	0.0653720i
$235$		0			0
$236$	7.33013	−	4.23205i	0.477151	−	0.275483i
$237$	6.96410	+	12.0622i	0.452367	+	0.783523i
$238$	−4.00000	+	6.92820i	−0.259281	+	0.449089i
$239$			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	0.905033	−	0.425341i	$-0.139846\pi$
$241$	15.3564	+	8.86603i	0.989193	+	0.571111i	0.0841601	+	0.996452i	$0.473179\pi$
$242$		−	30.7846i		−	1.97891i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−5.19615	−	9.00000i	−0.332650	−	0.576166i
$245$		0			0
$246$	−2.00000			−0.127515
$247$	6.46410	−	26.1244i	0.411301	−	1.66225i
$248$	1.73205			0.109985
$249$	7.73205	−	4.46410i	0.489999	−	0.282901i
$250$		0			0
$251$	−7.86603	+	13.6244i	−0.496499	+	0.859962i	−0.999992	−	0.00403776i	$-0.998715\pi$
$251$	−7.86603	+	13.6244i	−0.496499	+	0.859962i	0.503493	+	0.863999i	$0.332048\pi$
$252$			2.00000i			0.125988i
$253$	20.8923	+	12.0622i	1.31349	+	0.758343i
$254$	−4.26795	−	2.46410i	−0.267795	−	0.154611i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−2.66987	−	4.62436i	−0.166542	−	0.288459i	0.770660	−	0.637247i	$-0.219927\pi$
$257$	−2.66987	−	4.62436i	−0.166542	−	0.288459i	−0.937202	+	0.348787i	$0.886593\pi$
$258$	−10.3301	+	5.96410i	−0.643126	+	0.371309i
$259$	−18.3923			−1.14284
$260$		0			0
$261$	0.267949			0.0165856
$262$	−16.1603	+	9.33013i	−0.998384	+	0.576417i
$263$	3.06218	+	5.30385i	0.188822	+	0.327049i	0.944858	−	0.327481i	$-0.106200\pi$
$263$	3.06218	+	5.30385i	0.188822	+	0.327049i	−0.756036	+	0.654530i	$0.772866\pi$
$264$	−3.23205	+	5.59808i	−0.198919	+	0.344538i
$265$		0			0
$266$	12.9282	+	7.46410i	0.792679	+	0.457653i
$267$	0.464102	+	0.267949i	0.0284026	+	0.0163982i
$268$		−	11.4641i		−	0.700281i
$269$	−6.00000	+	10.3923i	−0.365826	+	0.633630i	−0.988908	−	0.148527i	$-0.952547\pi$
$269$	−6.00000	+	10.3923i	−0.365826	+	0.633630i	0.623082	+	0.782157i	$0.285880\pi$
$270$		0			0
$271$	1.03590	−	0.598076i	0.0629263	−	0.0363305i	−0.468207	−	0.883619i	$-0.655100\pi$
$271$	1.03590	−	0.598076i	0.0629263	−	0.0363305i	0.531133	+	0.847288i	$0.321766\pi$
$272$	4.00000			0.242536
$273$	−6.92820	+	2.00000i	−0.419314	+	0.121046i
$274$	2.46410			0.148862
$275$		0			0
$276$	−1.86603	−	3.23205i	−0.112322	−	0.194547i
$277$	−1.96410	+	3.40192i	−0.118011	+	0.204402i	−0.918980	−	0.394305i	$-0.870985\pi$
$277$	−1.96410	+	3.40192i	−0.118011	+	0.204402i	0.800968	+	0.598707i	$0.204319\pi$
$278$		−	12.9282i		−	0.775382i
$279$	−1.50000	−	0.866025i	−0.0898027	−	0.0518476i
$280$		0			0
$281$			8.92820i			0.532612i	0.963889	+	0.266306i	$0.0858032\pi$
$281$			8.92820i			0.532612i	−0.963889	+	0.266306i	$0.914197\pi$
$282$	−1.76795	+	3.06218i	−0.105280	+	0.182350i
$283$	−4.96410	−	8.59808i	−0.295085	−	0.511103i	0.679920	−	0.733287i	$-0.262015\pi$
$283$	−4.96410	−	8.59808i	−0.295085	−	0.511103i	−0.975005	+	0.222184i	$0.928681\pi$
$284$	−10.7321	+	6.19615i	−0.636830	+	0.367674i
$285$		0			0
$286$	−22.6244	−	5.59808i	−1.33781	−	0.331021i
$287$	4.00000			0.236113
$288$	0.866025	−	0.500000i	0.0510310	−	0.0294628i
$289$	0.500000	+	0.866025i	0.0294118	+	0.0509427i
$290$		0			0
$291$			0.535898i			0.0314149i
$292$	1.73205	+	1.00000i	0.101361	+	0.0585206i
$293$	27.5885	+	15.9282i	1.61173	+	0.930536i	0.988968	+	0.148128i	$0.0473247\pi$
$293$	27.5885	+	15.9282i	1.61173	+	0.930536i	0.622767	+	0.782408i	$0.286009\pi$
$294$			3.00000i			0.174964i
$295$		0			0
$296$	4.59808	+	7.96410i	0.267258	+	0.462904i
$297$	5.59808	−	3.23205i	0.324833	−	0.187543i
$298$	−13.5359			−0.784114
$299$	9.33013	−	9.69615i	0.539575	−	0.560743i
$300$		0			0
$301$	20.6603	−	11.9282i	1.19084	−	0.687530i
$302$	5.19615	+	9.00000i	0.299005	+	0.517892i
$303$	−1.46410	+	2.53590i	−0.0841104	+	0.145684i
$304$		−	7.46410i		−	0.428096i
$305$		0			0
$306$	−3.46410	−	2.00000i	−0.198030	−	0.114332i
$307$			19.4641i			1.11087i	0.831558	+	0.555437i	$0.187449\pi$
$307$			19.4641i			1.11087i	−0.831558	+	0.555437i	$0.812551\pi$
$308$	6.46410	−	11.1962i	0.368326	−	0.637960i
$309$	−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	$0.797829\pi$
$312$	2.59808	+	2.50000i	0.147087	+	0.141535i
$313$	28.0000			1.58265			0.791327	−	0.611393i	$-0.209391\pi$
$313$	28.0000			1.58265			0.791327	+	0.611393i	$0.209391\pi$
$314$	4.33013	−	2.50000i	0.244363	−	0.141083i
$315$		0			0
$316$	−6.96410	+	12.0622i	−0.391761	+	0.678551i
$317$			14.5359i			0.816417i	0.912889	+	0.408209i	$0.133846\pi$
$317$			14.5359i			0.816417i	−0.912889	+	0.408209i	$0.866154\pi$
$318$	0.803848	+	0.464102i	0.0450775	+	0.0260255i
$319$	−1.50000	−	0.866025i	−0.0839839	−	0.0484881i
$320$		0			0
$321$	−3.92820	+	6.80385i	−0.219251	+	0.379754i
$322$	3.73205	+	6.46410i	0.207979	+	0.360230i
$323$	−25.8564	+	14.9282i	−1.43869	+	0.830627i
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	−15.0526			−0.833684
$327$	13.7321	−	7.92820i	0.759384	−	0.438431i
$328$	−1.00000	−	1.73205i	−0.0552158	−	0.0956365i
$329$	3.53590	−	6.12436i	0.194940	−	0.337647i
$330$		0			0
$331$	−14.5359	−	8.39230i	−0.798965	−	0.461283i	0.0441440	−	0.999025i	$-0.485944\pi$
$331$	−14.5359	−	8.39230i	−0.798965	−	0.461283i	−0.843109	+	0.537742i	$0.819277\pi$
$332$	7.73205	+	4.46410i	0.424351	+	0.244999i
$333$		−	9.19615i		−	0.503946i
$334$	−8.16025	+	14.1340i	−0.446509	+	0.773377i
$335$		0			0
$336$	−1.73205	+	1.00000i	−0.0944911	+	0.0545545i
$337$	−9.32051			−0.507720			−0.253860	−	0.967241i	$-0.581700\pi$
$337$	−9.32051			−0.507720			−0.253860	+	0.967241i	$0.581700\pi$
$338$	−6.06218	+	11.5000i	−0.329739	+	0.625518i
$339$	−0.803848			−0.0436590
$340$		0			0
$341$	5.59808	+	9.69615i	0.303153	+	0.525076i
$342$	−3.73205	+	6.46410i	−0.201806	+	0.349539i
$343$		−	20.0000i		−	1.07990i
$344$	−10.3301	−	5.96410i	−0.556963	−	0.321563i
$345$		0			0
$346$		−	10.9282i		−	0.587504i
$347$	0.803848	−	1.39230i	0.0431528	−	0.0747428i	−0.843642	−	0.536906i	$-0.819593\pi$
$347$	0.803848	−	1.39230i	0.0431528	−	0.0747428i	0.886795	+	0.462163i	$0.152926\pi$
$348$	0.133975	+	0.232051i	0.00718179	+	0.0124392i
$349$	18.5885	−	10.7321i	0.995017	−	0.574474i	0.0882471	−	0.996099i	$-0.471873\pi$
$349$	18.5885	−	10.7321i	0.995017	−	0.574474i	0.906770	+	0.421625i	$0.138540\pi$
$350$		0			0
$351$	−1.00000	−	3.46410i	−0.0533761	−	0.184900i
$352$	−6.46410			−0.344538
$353$	−1.73205	+	1.00000i	−0.0921878	+	0.0532246i	−0.545385	−	0.838186i	$-0.683617\pi$
$353$	−1.73205	+	1.00000i	−0.0921878	+	0.0532246i	0.453197	+	0.891410i	$0.350283\pi$
$354$	−4.23205	−	7.33013i	−0.224931	−	0.389592i
$355$		0			0
$356$			0.535898i			0.0284026i
$357$	6.92820	+	4.00000i	0.366679	+	0.211702i
$358$	17.0885	+	9.86603i	0.903153	+	0.521436i
$359$		−	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
$362$	−2.53590	+	1.46410i	−0.133284	+	0.0769515i
$363$	−30.7846			−1.61577
$364$	−5.19615	−	5.00000i	−0.272352	−	0.262071i
$365$		0			0
$366$	−9.00000	+	5.19615i	−0.470438	+	0.271607i
$367$	7.80385	+	13.5167i	0.407358	+	0.705564i	0.994593	−	0.103852i	$-0.0331170\pi$
$367$	7.80385	+	13.5167i	0.407358	+	0.705564i	−0.587235	+	0.809416i	$0.699784\pi$
$368$	1.86603	−	3.23205i	0.0972733	−	0.168482i
$369$			2.00000i			0.104116i
$370$		0			0
$371$	−1.60770	−	0.928203i	−0.0834674	−	0.0481899i
$372$		−	1.73205i		−	0.0898027i
$373$	−7.89230	+	13.6699i	−0.408648	+	0.707799i	−0.994739	−	0.102446i	$-0.967333\pi$
$373$	−7.89230	+	13.6699i	−0.408648	+	0.707799i	0.586090	+	0.810246i	$0.300666\pi$
$374$	12.9282	+	22.3923i	0.668501	+	1.15788i
$375$		0			0
$376$	−3.53590			−0.182350
$377$	−0.669873	+	0.696152i	−0.0345002	+	0.0358537i
$378$	2.00000			0.102869
$379$	24.1244	−	13.9282i	1.23918	−	0.715444i	0.270257	−	0.962788i	$-0.412891\pi$
$379$	24.1244	−	13.9282i	1.23918	−	0.715444i	0.968928	+	0.247344i	$0.0795579\pi$
$380$		0			0
$381$	−2.46410	+	4.26795i	−0.126240	+	0.218654i
$382$			21.4641i			1.09820i
$383$	−21.9904	−	12.6962i	−1.12366	−	0.648743i	−0.181324	−	0.983423i	$-0.558038\pi$
$383$	−21.9904	−	12.6962i	−1.12366	−	0.648743i	−0.942332	+	0.334680i	$0.891372\pi$
$384$	0.866025	+	0.500000i	0.0441942	+	0.0255155i
$385$		0			0
$386$	−5.66025	+	9.80385i	−0.288099	+	0.499003i
$387$	5.96410	+	10.3301i	0.303172	+	0.525110i
$388$	−0.464102	+	0.267949i	−0.0235612	+	0.0136031i
$389$	−23.7321			−1.20326			−0.601631	−	0.798774i	$-0.705482\pi$
$389$	−23.7321			−1.20326			−0.601631	+	0.798774i	$0.705482\pi$
$390$		0			0
$391$	−14.9282			−0.754952
$392$	−2.59808	+	1.50000i	−0.131223	+	0.0757614i
$393$	9.33013	+	16.1603i	0.470643	+	0.815177i
$394$	−2.19615	+	3.80385i	−0.110641	+	0.191635i
$395$		0			0
$396$	5.59808	+	3.23205i	0.281314	+	0.162417i
$397$	−10.5000	−	6.06218i	−0.526980	−	0.304252i	0.212806	−	0.977095i	$-0.431740\pi$
$397$	−10.5000	−	6.06218i	−0.526980	−	0.304252i	−0.739786	+	0.672843i	$0.765073\pi$
$398$		−	5.07180i		−	0.254226i
$399$	7.46410	−	12.9282i	0.373672	−	0.647220i
$400$		0			0
$401$	−27.7128	+	16.0000i	−1.38391	+	0.799002i	−0.992620	−	0.121265i	$-0.961305\pi$
$401$	−27.7128	+	16.0000i	−1.38391	+	0.799002i	−0.391292	+	0.920267i	$0.627972\pi$
$402$	−11.4641			−0.571777
$403$	6.00000	−	1.73205i	0.298881	−	0.0862796i
$404$	−2.92820			−0.145684
$405$		0			0
$406$	−0.267949	−	0.464102i	−0.0132981	−	0.0230330i
$407$	−29.7224	+	51.4808i	−1.47329	+	2.55181i
$408$		−	4.00000i		−	0.198030i
$409$	3.46410	+	2.00000i	0.171289	+	0.0988936i	0.583193	−	0.812333i	$-0.301803\pi$
$409$	3.46410	+	2.00000i	0.171289	+	0.0988936i	−0.411905	+	0.911227i	$0.635136\pi$
$410$		0			0
$411$		−	2.46410i		−	0.121545i
$412$	5.92820	−	10.2679i	0.292062	−	0.505866i
$413$	8.46410	+	14.6603i	0.416491	+	0.721384i
$414$	−3.23205	+	1.86603i	−0.158847	+	0.0917101i
$415$		0			0
$416$	−0.866025	+	3.50000i	−0.0424604	+	0.171602i
$417$	−12.9282			−0.633097
$418$	41.7846	−	24.1244i	2.04375	−	1.17996i
$419$	−11.1962	−	19.3923i	−0.546968	−	0.947376i	−0.998480	−	0.0551112i	$-0.982449\pi$
$419$	−11.1962	−	19.3923i	−0.546968	−	0.947376i	0.451512	−	0.892265i	$-0.350885\pi$
$420$		0			0
$421$		−	4.39230i		−	0.214068i	−0.994255	−	0.107034i	$-0.965865\pi$
$421$		−	4.39230i		−	0.214068i	0.994255	−	0.107034i	$-0.0341353\pi$
$422$	9.80385	+	5.66025i	0.477244	+	0.275537i
$423$	3.06218	+	1.76795i	0.148888	+	0.0859606i
$424$			0.928203i			0.0450775i
$425$		0			0
$426$	6.19615	+	10.7321i	0.300205	+	0.519970i
$427$	18.0000	−	10.3923i	0.871081	−	0.502919i
$428$	−7.85641			−0.379754
$429$	−5.59808	+	22.6244i	−0.270278	+	1.09231i
$430$		0			0
$431$	24.5885	−	14.1962i	1.18438	−	0.683805i	0.227360	−	0.973811i	$-0.426991\pi$
$431$	24.5885	−	14.1962i	1.18438	−	0.683805i	0.957025	+	0.290006i	$0.0936574\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	9.66025	−	16.7321i	0.464242	−	0.804091i	−0.534925	−	0.844900i	$-0.679660\pi$
$433$	9.66025	−	16.7321i	0.464242	−	0.804091i	0.999167	+	0.0408086i	$0.0129934\pi$
$434$			3.46410i			0.166282i
$435$		0			0
$436$	13.7321	+	7.92820i	0.657646	+	0.379692i
$437$			27.8564i			1.33255i
$438$	1.00000	−	1.73205i	0.0477818	−	0.0827606i
$439$	8.92820	+	15.4641i	0.426120	+	0.738061i	0.996524	−	0.0833027i	$-0.0265468\pi$
$439$	8.92820	+	15.4641i	0.426120	+	0.738061i	−0.570404	+	0.821364i	$0.693214\pi$
$440$		0			0
$441$	3.00000			0.142857
$442$	13.8564	−	4.00000i	0.659082	−	0.190261i
$443$	−16.3923			−0.778822			−0.389411	−	0.921064i	$-0.627321\pi$
$443$	−16.3923			−0.778822			−0.389411	+	0.921064i	$0.627321\pi$
$444$	7.96410	−	4.59808i	0.377960	−	0.218215i
$445$		0			0
$446$	10.2679	−	17.7846i	0.486201	−	0.842126i
$447$			13.5359i			0.640226i
$448$	−1.73205	−	1.00000i	−0.0818317	−	0.0472456i
$449$	−13.6077	−	7.85641i	−0.642187	−	0.370767i	0.143270	−	0.989684i	$-0.454238\pi$
$449$	−13.6077	−	7.85641i	−0.642187	−	0.370767i	−0.785456	+	0.618917i	$0.787572\pi$
$450$		0			0
$451$	6.46410	−	11.1962i	0.304383	−	0.527206i
$452$	−0.401924	−	0.696152i	−0.0189049	−	0.0327443i
$453$	9.00000	−	5.19615i	0.422857	−	0.244137i
$454$	16.3923			0.769329
$455$		0			0
$456$	−7.46410			−0.349539
$457$	−21.2487	+	12.2679i	−0.993973	+	0.573870i	−0.906459	−	0.422293i	$-0.861225\pi$
$457$	−21.2487	+	12.2679i	−0.993973	+	0.573870i	−0.0875134	+	0.996163i	$0.527892\pi$
$458$	3.92820	+	6.80385i	0.183553	+	0.317923i
$459$	−2.00000	+	3.46410i	−0.0933520	+	0.161690i
$460$		0			0
$461$	0.401924	+	0.232051i	0.0187195	+	0.0108077i	0.509331	−	0.860571i	$-0.329893\pi$
$461$	0.401924	+	0.232051i	0.0187195	+	0.0108077i	−0.490611	+	0.871379i	$0.663226\pi$
$462$	−11.1962	−	6.46410i	−0.520892	−	0.300737i
$463$			7.07180i			0.328654i	0.986406	+	0.164327i	$0.0525453\pi$
$463$			7.07180i			0.328654i	−0.986406	+	0.164327i	$0.947455\pi$
$464$	−0.133975	+	0.232051i	−0.00621961	+	0.0107727i
$465$		0			0
$466$	−5.30385	+	3.06218i	−0.245696	+	0.141853i
$467$	15.8564			0.733747			0.366873	−	0.930271i	$-0.380428\pi$
$467$	15.8564			0.733747			0.366873	+	0.930271i	$0.380428\pi$
$468$	2.50000	−	2.59808i	0.115563	−	0.120096i
$469$	22.9282			1.05873
$470$		0			0
$471$	−2.50000	−	4.33013i	−0.115194	−	0.199522i
$472$	4.23205	−	7.33013i	0.194796	−	0.337396i
$473$		−	77.1051i		−	3.54530i
$474$	12.0622	+	6.96410i	0.554034	+	0.319872i
$475$		0			0
$476$			8.00000i			0.366679i
$477$	0.464102	−	0.803848i	0.0212498	−	0.0368057i
$478$	8.19615	+	14.1962i	0.374883	+	0.649317i
$479$	4.73205	−	2.73205i	0.216213	−	0.124831i	−0.387983	−	0.921667i	$-0.626828\pi$
$479$	4.73205	−	2.73205i	0.216213	−	0.124831i	0.604195	+	0.796836i	$0.293495\pi$
$480$		0			0
$481$	23.8923	+	22.9904i	1.08940	+	1.04827i
$482$	17.7321			0.807673
$483$	6.46410	−	3.73205i	0.294127	−	0.169814i
$484$	−15.3923	−	26.6603i	−0.699650	−	1.21183i
$485$		0			0
$486$			1.00000i			0.0453609i
$487$	−20.0718	−	11.5885i	−0.909540	−	0.525123i	−0.0292568	−	0.999572i	$-0.509314\pi$
$487$	−20.0718	−	11.5885i	−0.909540	−	0.525123i	−0.880283	+	0.474449i	$0.842647\pi$
$488$	−9.00000	−	5.19615i	−0.407411	−	0.235219i
$489$			15.0526i			0.680700i
$490$		0			0
$491$	8.66025	+	15.0000i	0.390832	+	0.676941i	0.992559	−	0.121761i	$-0.0388541\pi$
$491$	8.66025	+	15.0000i	0.390832	+	0.676941i	−0.601728	+	0.798701i	$0.705521\pi$
$492$	−1.73205	+	1.00000i	−0.0780869	+	0.0450835i
$493$	1.07180			0.0482713
$494$	−7.46410	−	25.8564i	−0.335826	−	1.16333i
$495$		0			0
$496$	1.50000	−	0.866025i	0.0673520	−	0.0388857i
$497$	−12.3923	−	21.4641i	−0.555871	−	0.962797i
$498$	4.46410	−	7.73205i	0.200041	−	0.346481i
$499$		−	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
$502$			15.7321i			0.702156i
$503$	−15.5885	+	27.0000i	−0.695055	+	1.20387i	0.275107	+	0.961414i	$0.411287\pi$
$503$	−15.5885	+	27.0000i	−0.695055	+	1.20387i	−0.970162	+	0.242457i	$0.922047\pi$
$504$	1.00000	+	1.73205i	0.0445435	+	0.0771517i
$505$		0			0
$506$	24.1244			1.07246
$507$	11.5000	+	6.06218i	0.510733	+	0.269231i
$508$	−4.92820			−0.218654
$509$	1.20577	−	0.696152i	0.0534449	−	0.0308564i	−0.473039	−	0.881041i	$-0.656843\pi$
$509$	1.20577	−	0.696152i	0.0534449	−	0.0308564i	0.526484	+	0.850185i	$0.323510\pi$
$510$		0			0
$511$	−2.00000	+	3.46410i	−0.0884748	+	0.153243i
$512$			1.00000i			0.0441942i
$513$	6.46410	+	3.73205i	0.285397	+	0.164774i
$514$	−4.62436	−	2.66987i	−0.203972	−	0.117763i
$515$		0			0
$516$	−5.96410	+	10.3301i	−0.262555	+	0.454758i
$517$	−11.4282	−	19.7942i	−0.502612	−	0.870549i
$518$	−15.9282	+	9.19615i	−0.699845	+	0.404056i
$519$	−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	$0.623874\pi$
$522$	0.232051	−	0.133975i	0.0101566	−	0.00586391i
$523$	5.89230	+	10.2058i	0.257653	+	0.446267i	0.965613	−	0.259985i	$-0.0837177\pi$
$523$	5.89230	+	10.2058i	0.257653	+	0.446267i	−0.707960	+	0.706252i	$0.750384\pi$
$524$	−9.33013	+	16.1603i	−0.407588	+	0.705964i
$525$		0			0
$526$	5.30385	+	3.06218i	0.231259	+	0.133517i
$527$	−6.00000	−	3.46410i	−0.261364	−	0.150899i
$528$			6.46410i			0.281314i
$529$	4.53590	−	7.85641i	0.197213	−	0.341583i
$530$		0			0
$531$	−7.33013	+	4.23205i	−0.318100	+	0.183655i
$532$	14.9282			0.647220
$533$	−5.19615	−	5.00000i	−0.225070	−	0.216574i
$534$	0.535898			0.0231906
$535$		0			0
$536$	−5.73205	−	9.92820i	−0.247587	−	0.428833i
$537$	9.86603	−	17.0885i	0.425750	−	0.737421i
$538$			12.0000i			0.517357i
$539$	−16.7942	−	9.69615i	−0.723379	−	0.417643i
$540$		0			0
$541$		−	26.9282i		−	1.15773i	−0.815422	−	0.578867i	$-0.803495\pi$
$541$		−	26.9282i		−	1.15773i	0.815422	−	0.578867i	$-0.196505\pi$
$542$	0.598076	−	1.03590i	0.0256896	−	0.0444956i
$543$	1.46410	+	2.53590i	0.0628306	+	0.108826i
$544$	3.46410	−	2.00000i	0.148522	−	0.0857493i
$545$		0			0
$546$	−5.00000	+	5.19615i	−0.213980	+	0.222375i
$547$	−22.9282			−0.980339			−0.490170	−	0.871627i	$-0.663065\pi$
$547$	−22.9282			−0.980339			−0.490170	+	0.871627i	$0.663065\pi$
$548$	2.13397	−	1.23205i	0.0911589	−	0.0526306i
$549$	5.19615	+	9.00000i	0.221766	+	0.384111i
$550$		0			0
$551$		−	2.00000i		−	0.0852029i
$552$	−3.23205	−	1.86603i	−0.137565	−	0.0794233i
$553$	−24.1244	−	13.9282i	−1.02587	−	0.592287i
$554$			3.92820i			0.166893i
$555$		0			0
$556$	−6.46410	−	11.1962i	−0.274139	−	0.474823i
$557$	−15.3397	+	8.85641i	−0.649966	+	0.375258i	−0.788443	−	0.615108i	$-0.789113\pi$
$557$	−15.3397	+	8.85641i	−0.649966	+	0.375258i	0.138477	+	0.990366i	$0.455779\pi$
$558$	−1.73205			−0.0733236
$559$	−41.7487	−	10.3301i	−1.76578	−	0.436918i
$560$		0			0
$561$	22.3923	−	12.9282i	0.945404	−	0.545829i
$562$	4.46410	+	7.73205i	0.188307	+	0.326157i
$563$	−2.33975	+	4.05256i	−0.0986085	+	0.170795i	−0.911109	−	0.412166i	$-0.864772\pi$
$563$	−2.33975	+	4.05256i	−0.0986085	+	0.170795i	0.812500	+	0.582961i	$0.198106\pi$
$564$			3.53590i			0.148888i
$565$		0			0
$566$	−8.59808	−	4.96410i	−0.361404	−	0.208657i
$567$		−	2.00000i		−	0.0839921i
$568$	−6.19615	+	10.7321i	−0.259985	+	0.450307i
$569$	−14.6603	−	25.3923i	−0.614590	−	1.06450i	−0.990456	−	0.137827i	$-0.955988\pi$
$569$	−14.6603	−	25.3923i	−0.614590	−	1.06450i	0.375867	−	0.926674i	$-0.377345\pi$
$570$		0			0
$571$	−17.1769			−0.718832			−0.359416	−	0.933178i	$-0.617024\pi$
$571$	−17.1769			−0.718832			−0.359416	+	0.933178i	$0.617024\pi$
$572$	−22.3923	+	6.46410i	−0.936269	+	0.270278i
$573$	21.4641			0.896676
$574$	3.46410	−	2.00000i	0.144589	−	0.0834784i
$575$		0			0
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$		−	10.0000i		−	0.416305i	−0.978096	−	0.208153i	$-0.933255\pi$
$577$		−	10.0000i		−	0.416305i	0.978096	−	0.208153i	$-0.0667451\pi$
$578$	0.866025	+	0.500000i	0.0360219	+	0.0207973i
$579$	9.80385	+	5.66025i	0.407434	+	0.235232i
$580$		0			0
$581$	−8.92820	+	15.4641i	−0.370404	+	0.641559i
$582$	0.267949	+	0.464102i	0.0111069	+	0.0192376i
$583$	−5.19615	+	3.00000i	−0.215203	+	0.124247i
$584$	2.00000			0.0827606
$585$		0			0
$586$	31.8564			1.31598
$587$	2.07180	−	1.19615i	0.0855122	−	0.0493705i	−0.456634	−	0.889655i	$-0.650945\pi$
$587$	2.07180	−	1.19615i	0.0855122	−	0.0493705i	0.542146	+	0.840284i	$0.317612\pi$
$588$	1.50000	+	2.59808i	0.0618590	+	0.107143i
$589$	−6.46410	+	11.1962i	−0.266349	+	0.461329i
$590$		0			0
$591$	3.80385	+	2.19615i	0.156469	+	0.0903376i
$592$	7.96410	+	4.59808i	0.327323	+	0.188980i
$593$			45.1051i			1.85225i	0.377223	+	0.926123i	$0.376879\pi$
$593$			45.1051i			1.85225i	−0.377223	+	0.926123i	$0.623121\pi$
$594$	3.23205	−	5.59808i	0.132613	−	0.229692i
$595$		0			0
$596$	−11.7224	+	6.76795i	−0.480170	+	0.277226i
$597$	−5.07180			−0.207575
$598$	3.23205	−	13.0622i	0.132168	−	0.534152i
$599$	−10.3923			−0.424618			−0.212309	−	0.977203i	$-0.568098\pi$
$599$	−10.3923			−0.424618			−0.212309	+	0.977203i	$0.568098\pi$
$600$		0			0
$601$	9.89230	+	17.1340i	0.403516	+	0.698909i	0.994147	−	0.108032i	$-0.0344548\pi$
$601$	9.89230	+	17.1340i	0.403516	+	0.698909i	−0.590632	+	0.806941i	$0.701121\pi$
$602$	11.9282	−	20.6603i	0.486157	−	0.842049i
$603$			11.4641i			0.466854i
$604$	9.00000	+	5.19615i	0.366205	+	0.211428i
$605$		0			0
$606$			2.92820i			0.118950i
$607$	−9.58846	+	16.6077i	−0.389183	+	0.674086i	−0.992340	−	0.123537i	$-0.960576\pi$
$607$	−9.58846	+	16.6077i	−0.389183	+	0.674086i	0.603156	+	0.797623i	$0.293909\pi$
$608$	−3.73205	−	6.46410i	−0.151355	−	0.262154i
$609$	−0.464102	+	0.267949i	−0.0188063	+	0.0108578i
$610$		0			0
$611$	−12.2487	+	3.53590i	−0.495530	+	0.143047i
$612$	−4.00000			−0.161690
$613$	33.8205	−	19.5263i	1.36600	−	0.788659i	0.375583	−	0.926789i	$-0.377442\pi$
$613$	33.8205	−	19.5263i	1.36600	−	0.788659i	0.990414	+	0.138130i	$0.0441091\pi$
$614$	9.73205	+	16.8564i	0.392754	+	0.680269i
$615$		0			0
$616$		−	12.9282i		−	0.520892i
$617$	19.4545	+	11.2321i	0.783208	+	0.452185i	0.837566	−	0.546336i	$-0.183978\pi$
$617$	19.4545	+	11.2321i	0.783208	+	0.452185i	−0.0543580	+	0.998522i	$0.517311\pi$
$618$	−10.2679	−	5.92820i	−0.413037	−	0.238467i
$619$			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
$622$	−24.5885	+	14.1962i	−0.985907	+	0.569214i
$623$	−1.07180			−0.0429406
$624$	3.50000	+	0.866025i	0.140112	+	0.0346688i
$625$		0			0
$626$	24.2487	−	14.0000i	0.969173	−	0.559553i
$627$	−24.1244	−	41.7846i	−0.963434	−	1.66872i
$628$	2.50000	−	4.33013i	0.0997609	−	0.172791i
$629$		−	36.7846i		−	1.46670i
$630$		0			0
$631$	27.2487	+	15.7321i	1.08475	+	0.626283i	0.932175	−	0.362008i	$-0.117909\pi$
$631$	27.2487	+	15.7321i	1.08475	+	0.626283i	0.152579	+	0.988291i	$0.451242\pi$
$632$			13.9282i			0.554034i
$633$	5.66025	−	9.80385i	0.224975	−	0.389668i
$634$	7.26795	+	12.5885i	0.288647	+	0.499952i
$635$		0			0
$636$	0.928203			0.0368057
$637$	−7.50000	+	7.79423i	−0.297161	+	0.308819i
$638$	−1.73205			−0.0685725
$639$	10.7321	−	6.19615i	0.424553	−	0.245116i
$640$		0			0
$641$	−0.0717968	+	0.124356i	−0.00283580	+	0.00491175i	−0.867440	−	0.497542i	$-0.834236\pi$
$641$	−0.0717968	+	0.124356i	−0.00283580	+	0.00491175i	0.864604	+	0.502454i	$0.167569\pi$
$642$			7.85641i			0.310068i
$643$	17.7846	+	10.2679i	0.701357	+	0.404928i	0.807852	−	0.589385i	$-0.200630\pi$
$643$	17.7846	+	10.2679i	0.701357	+	0.404928i	−0.106496	+	0.994313i	$0.533963\pi$
$644$	6.46410	+	3.73205i	0.254721	+	0.147063i
$645$		0			0
$646$	−14.9282	+	25.8564i	−0.587342	+	1.01731i
$647$	−6.66025	−	11.5359i	−0.261842	−	0.453523i	0.704890	−	0.709317i	$-0.250996\pi$
$647$	−6.66025	−	11.5359i	−0.261842	−	0.453523i	−0.966731	+	0.255794i	$0.917663\pi$
$648$	−0.866025	+	0.500000i	−0.0340207	+	0.0196419i
$649$	54.7128			2.14767
$650$		0			0
$651$	3.46410			0.135769
$652$	−13.0359	+	7.52628i	−0.510525	+	0.294752i
$653$	2.12436	+	3.67949i	0.0831325	+	0.143990i	0.904594	−	0.426274i	$-0.140174\pi$
$653$	2.12436	+	3.67949i	0.0831325	+	0.143990i	−0.821461	+	0.570264i	$0.806841\pi$
$654$	7.92820	−	13.7321i	0.310017	−	0.536966i
$655$		0			0
$656$	−1.73205	−	1.00000i	−0.0676252	−	0.0390434i
$657$	−1.73205	−	1.00000i	−0.0675737	−	0.0390137i
$658$		−	7.07180i		−	0.275687i
$659$	0.133975	−	0.232051i	0.00521891	−	0.00903942i	−0.863404	−	0.504513i	$-0.831672\pi$
$659$	0.133975	−	0.232051i	0.00521891	−	0.00903942i	0.868623	+	0.495473i	$0.165005\pi$
$660$		0			0
$661$	−7.51666	+	4.33975i	−0.292364	+	0.168797i	−0.639008	−	0.769200i	$-0.720655\pi$
$661$	−7.51666	+	4.33975i	−0.292364	+	0.168797i	0.346643	+	0.937997i	$0.387321\pi$
$662$	−16.7846			−0.652352
$663$	−4.00000	−	13.8564i	−0.155347	−	0.538138i
$664$	8.92820			0.346481
$665$		0			0
$666$	−4.59808	−	7.96410i	−0.178172	−	0.308603i
$667$	0.500000	−	0.866025i	0.0193601	−	0.0335326i
$668$			16.3205i			0.631459i
$669$	−17.7846	−	10.2679i	−0.687593	−	0.396982i
$670$		0			0
$671$		−	67.1769i		−	2.59334i
$672$	−1.00000	+	1.73205i	−0.0385758	+	0.0668153i
$673$	16.0000	+	27.7128i	0.616755	+	1.06825i	0.990074	+	0.140548i	$0.0448863\pi$
$673$	16.0000	+	27.7128i	0.616755	+	1.06825i	−0.373319	+	0.927703i	$0.621780\pi$
$674$	−8.07180	+	4.66025i	−0.310914	+	0.179506i
$675$		0			0
$676$	0.500000	+	12.9904i	0.0192308	+	0.499630i
$677$	−32.3923			−1.24494			−0.622469	−	0.782645i	$-0.713870\pi$
$677$	−32.3923			−1.24494			−0.622469	+	0.782645i	$0.713870\pi$
$678$	−0.696152	+	0.401924i	−0.0267356	+	0.0154358i
$679$	−0.535898	−	0.928203i	−0.0205659	−	0.0356212i
$680$		0			0
$681$		−	16.3923i		−	0.628154i
$682$	9.69615	+	5.59808i	0.371285	+	0.214361i
$683$	35.3205	+	20.3923i	1.35150	+	0.780290i	0.988460	−	0.151483i	$-0.0484049\pi$
$683$	35.3205	+	20.3923i	1.35150	+	0.780290i	0.363042	+	0.931773i	$0.381738\pi$
$684$			7.46410i			0.285397i
$685$		0			0
$686$	−10.0000	−	17.3205i	−0.381802	−	0.661300i
$687$	6.80385	−	3.92820i	0.259583	−	0.149870i
$688$	−11.9282			−0.454758
$689$	0.928203	+	3.21539i	0.0353617	+	0.122497i
$690$		0			0
$691$	−23.5359	+	13.5885i	−0.895348	+	0.516929i	−0.875688	−	0.482877i	$-0.839592\pi$
$691$	−23.5359	+	13.5885i	−0.895348	+	0.516929i	−0.0196598	+	0.999807i	$0.506258\pi$
$692$	−5.46410	−	9.46410i	−0.207714	−	0.359771i
$693$	−6.46410	+	11.1962i	−0.245551	+	0.425307i
$694$		−	1.60770i		−	0.0610273i
$695$		0			0
$696$	0.232051	+	0.133975i	0.00879586	+	0.00507829i
$697$			8.00000i			0.303022i
$698$	10.7321	−	18.5885i	0.406214	−	0.703583i
$699$	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	$0.501611\pi$
$702$	−2.59808	−	2.50000i	−0.0980581	−	0.0943564i
$703$	−68.6410			−2.58884
$704$	−5.59808	+	3.23205i	−0.210985	+	0.121812i
$705$		0			0
$706$	−1.00000	+	1.73205i	−0.0376355	+	0.0651866i
$707$		−	5.85641i		−	0.220253i
$708$	−7.33013	−	4.23205i	−0.275483	−	0.159050i
$709$	−19.8564	−	11.4641i	−0.745723	−	0.430543i	0.0784234	−	0.996920i	$-0.475011\pi$
$709$	−19.8564	−	11.4641i	−0.745723	−	0.430543i	−0.824146	+	0.566377i	$0.808345\pi$
$710$		0			0
$711$	6.96410	−	12.0622i	0.261174	−	0.452367i
$712$	0.267949	+	0.464102i	0.0100418	+	0.0173929i
$713$	−5.59808	+	3.23205i	−0.209650	+	0.121041i
$714$	8.00000			0.299392
$715$		0			0
$716$	19.7321			0.737421
$717$	14.1962	−	8.19615i	0.530165	−	0.306091i
$718$	−2.53590	−	4.39230i	−0.0946389	−	0.163919i
$719$	17.3205	−	30.0000i	0.645946	−	1.11881i	−0.338136	−	0.941097i	$-0.609796\pi$
$719$	17.3205	−	30.0000i	0.645946	−	1.11881i	0.984082	−	0.177714i	$-0.0568702\pi$
$720$		0			0
$721$	20.5359	+	11.8564i	0.764797	+	0.441556i
$722$	31.7942	+	18.3564i	1.18326	+	0.683155i
$723$		−	17.7321i		−	0.659462i
$724$	−1.46410	+	2.53590i	−0.0544129	+	0.0942459i
$725$		0			0
$726$	−26.6603	+	15.3923i	−0.989455	+	0.571262i
$727$	31.7128			1.17616			0.588082	−	0.808802i	$-0.299883\pi$
$727$	31.7128			1.17616			0.588082	+	0.808802i	$0.299883\pi$
$728$	−7.00000	−	1.73205i	−0.259437	−	0.0641941i
$729$	1.00000			0.0370370
$730$		0			0
$731$	23.8564	+	41.3205i	0.882361	+	1.52829i
$732$	−5.19615	+	9.00000i	−0.192055	+	0.332650i
$733$		−	50.9282i		−	1.88108i	−0.339688	−	0.940538i	$-0.610322\pi$
$733$		−	50.9282i		−	1.88108i	0.339688	−	0.940538i	$-0.389678\pi$
$734$	13.5167	+	7.80385i	0.498909	+	0.288045i
$735$		0			0
$736$		−	3.73205i		−	0.137565i
$737$	37.0526	−	64.1769i	1.36485	−	2.36399i
$738$	1.00000	+	1.73205i	0.0368105	+	0.0637577i
$739$	−16.7321	+	9.66025i	−0.615498	+	0.355358i	−0.775114	−	0.631821i	$-0.782308\pi$
$739$	−16.7321	+	9.66025i	−0.615498	+	0.355358i	0.159616	+	0.987179i	$0.448974\pi$
$740$		0			0
$741$	−25.8564	+	7.46410i	−0.949859	+	0.274201i
$742$	−1.85641			−0.0681508
$743$	35.0429	−	20.2321i	1.28560	−	0.742242i	0.307734	−	0.951472i	$-0.400429\pi$
$743$	35.0429	−	20.2321i	1.28560	−	0.742242i	0.977866	+	0.209230i	$0.0670958\pi$
$744$	−0.866025	−	1.50000i	−0.0317500	−	0.0549927i
$745$		0			0
$746$			15.7846i			0.577916i
$747$	−7.73205	−	4.46410i	−0.282901	−	0.163333i
$748$	22.3923	+	12.9282i	0.818744	+	0.472702i
$749$		−	15.7128i		−	0.574134i
$750$		0			0
$751$	−7.03590	−	12.1865i	−0.256744	−	0.444693i	0.708624	−	0.705586i	$-0.249316\pi$
$751$	−7.03590	−	12.1865i	−0.256744	−	0.444693i	−0.965368	+	0.260893i	$0.915983\pi$
$752$	−3.06218	+	1.76795i	−0.111666	+	0.0644705i
$753$	15.7321			0.573308
$754$	−0.232051	+	0.937822i	−0.00845079	+	0.0341535i
$755$		0			0
$756$	1.73205	−	1.00000i	0.0629941	−	0.0363696i
$757$	−9.00000	−	15.5885i	−0.327111	−	0.566572i	0.654827	−	0.755779i	$-0.272742\pi$
$757$	−9.00000	−	15.5885i	−0.327111	−	0.566572i	−0.981937	+	0.189207i	$0.939408\pi$
$758$	13.9282	−	24.1244i	0.505895	−	0.876236i
$759$		−	24.1244i		−	0.875659i
$760$		0			0
$761$	4.39230	+	2.53590i	0.159221	+	0.0919262i	0.577493	−	0.816395i	$-0.304031\pi$
$761$	4.39230	+	2.53590i	0.159221	+	0.0919262i	−0.418272	+	0.908322i	$0.637364\pi$
$762$			4.92820i			0.178530i
$763$	−15.8564	+	27.4641i	−0.574040	+	0.994267i
$764$	10.7321	+	18.5885i	0.388272	+	0.672507i
$765$		0			0
$766$	−25.3923			−0.917461
$767$	7.33013	−	29.6244i	0.264676	−	1.06967i
$768$	1.00000			0.0360844
$769$	−10.0359	+	5.79423i	−0.361904	+	0.208945i	−0.669916	−	0.742437i	$-0.733670\pi$
$769$	−10.0359	+	5.79423i	−0.361904	+	0.208945i	0.308012	+	0.951383i	$0.400336\pi$
$770$		0			0
$771$	−2.66987	+	4.62436i	−0.0961531	+	0.166542i
$772$			11.3205i			0.407434i
$773$	−24.0000	−	13.8564i	−0.863220	−	0.498380i	0.00186926	−	0.999998i	$-0.499405\pi$
$773$	−24.0000	−	13.8564i	−0.863220	−	0.498380i	−0.865089	+	0.501618i	$0.832738\pi$
$774$	10.3301	+	5.96410i	0.371309	+	0.214375i
$775$		0			0
$776$	−0.267949	+	0.464102i	−0.00961882	+	0.0166603i
$777$	9.19615	+	15.9282i	0.329910	+	0.571421i
$778$	−20.5526	+	11.8660i	−0.736845	+	0.425418i
$779$	14.9282			0.534858
$780$		0			0
$781$	−80.1051			−2.86639
$782$	−12.9282	+	7.46410i	−0.462312	+	0.266916i
$783$	−0.133975	−	0.232051i	−0.00478786	−	0.00829282i
$784$	−1.50000	+	2.59808i	−0.0535714	+	0.0927884i
$785$		0			0
$786$	16.1603	+	9.33013i	0.576417	+	0.332795i
$787$	−1.50000	−	0.866025i	−0.0534692	−	0.0308705i	0.473027	−	0.881048i	$-0.343161\pi$
$787$	−1.50000	−	0.866025i	−0.0534692	−	0.0308705i	−0.526496	+	0.850177i	$0.676495\pi$
$788$			4.39230i			0.156469i
$789$	3.06218	−	5.30385i	0.109016	−	0.188822i
$790$		0			0
$791$	1.39230	−	0.803848i	0.0495047	−	0.0285815i
$792$	6.46410			0.229692
$793$	−36.3731	−	9.00000i	−1.29165	−	0.319599i
$794$	−12.1244			−0.430277
$795$		0			0
$796$	−2.53590	−	4.39230i	−0.0898825	−	0.155681i
$797$	−5.07180	+	8.78461i	−0.179652	+	0.311167i	−0.941761	−	0.336282i	$-0.890831\pi$
$797$	−5.07180	+	8.78461i	−0.179652	+	0.311167i	0.762109	+	0.647449i	$0.224164\pi$
$798$		−	14.9282i		−	0.528453i
$799$	12.2487	+	7.07180i	0.433328	+	0.250182i
$800$		0			0
$801$		−	0.535898i		−	0.0189350i
$802$	−16.0000	+	27.7128i	−0.564980	+	0.978573i
$803$	6.46410	+	11.1962i	0.228113	+	0.395104i
$804$	−9.92820	+	5.73205i	−0.350141	+	0.202154i
$805$		0			0
$806$	4.33013	−	4.50000i	0.152522	−	0.158506i
$807$	12.0000			0.422420
$808$	−2.53590	+	1.46410i	−0.0892126	+	0.0515069i
$809$	21.3923	+	37.0526i	0.752113	+	1.30270i	0.946797	+	0.321832i	$0.104299\pi$
$809$	21.3923	+	37.0526i	0.752113	+	1.30270i	−0.194683	+	0.980866i	$0.562368\pi$
$810$		0			0
$811$		−	40.7846i		−	1.43214i	−0.698028	−	0.716071i	$-0.745939\pi$
$811$		−	40.7846i		−	1.43214i	0.698028	−	0.716071i	$-0.254061\pi$
$812$	−0.464102	−	0.267949i	−0.0162868	−	0.00940317i
$813$	−1.03590	−	0.598076i	−0.0363305	−	0.0209754i
$814$			59.4449i			2.08354i
$815$		0			0
$816$	−2.00000	−	3.46410i	−0.0700140	−	0.121268i
$817$	77.1051	−	44.5167i	2.69757	−	1.55744i
$818$	4.00000			0.139857
$819$	5.19615	+	5.00000i	0.181568	+	0.174714i
$820$		0			0
$821$	12.6506	−	7.30385i	0.441510	−	0.254906i	−0.262728	−	0.964870i	$-0.584622\pi$
$821$	12.6506	−	7.30385i	0.441510	−	0.254906i	0.704238	+	0.709964i	$0.251289\pi$
$822$	−1.23205	−	2.13397i	−0.0429727	−	0.0744309i
$823$	19.5885	−	33.9282i	0.682811	−	1.18266i	−0.291309	−	0.956629i	$-0.594091\pi$
$823$	19.5885	−	33.9282i	0.682811	−	1.18266i	0.974119	−	0.226034i	$-0.0725760\pi$
$824$		−	11.8564i		−	0.413037i
$825$		0			0
$826$	14.6603	+	8.46410i	0.510095	+	0.294504i
$827$			17.3205i			0.602293i	0.953578	+	0.301147i	$0.0973693\pi$
$827$			17.3205i			0.602293i	−0.953578	+	0.301147i	$0.902631\pi$
$828$	−1.86603	+	3.23205i	−0.0648489	+	0.112322i
$829$	−8.26795	−	14.3205i	−0.287158	−	0.497372i	0.685972	−	0.727628i	$-0.259377\pi$
$829$	−8.26795	−	14.3205i	−0.287158	−	0.497372i	−0.973130	+	0.230256i	$0.926044\pi$
$830$		0			0
$831$	3.92820			0.136268
$832$	1.00000	+	3.46410i	0.0346688	+	0.120096i
$833$	12.0000			0.415775
$834$	−11.1962	+	6.46410i	−0.387691	+	0.223834i
$835$		0			0
$836$	24.1244	−	41.7846i	0.834358	−	1.44515i
$837$			1.73205i			0.0598684i
$838$	−19.3923	−	11.1962i	−0.669896	−	0.386765i
$839$	−37.7321	−	21.7846i	−1.30266	−	0.752088i	−0.321796	−	0.946809i	$-0.604287\pi$
$839$	−37.7321	−	21.7846i	−1.30266	−	0.752088i	−0.980859	+	0.194721i	$0.937620\pi$
$840$		0			0
$841$	14.4641	−	25.0526i	0.498762	−	0.863881i
$842$	−2.19615	−	3.80385i	−0.0756844	−	0.131089i
$843$	7.73205	−	4.46410i	0.266306	−	0.153752i
$844$	11.3205			0.389668
$845$		0			0
$846$	3.53590			0.121567
$847$	53.3205	−	30.7846i	1.83211	−	1.05777i
$848$	0.464102	+	0.803848i	0.0159373	+	0.0276042i
$849$	−4.96410	+	8.59808i	−0.170368	+	0.295085i
$850$		0			0
$851$	−29.7224	−	17.1603i	−1.01887	−	0.588246i
$852$	10.7321	+	6.19615i	0.367674	+	0.212277i
$853$			43.8372i			1.50096i	0.660895	+	0.750478i	$0.270177\pi$
$853$			43.8372i			1.50096i	−0.660895	+	0.750478i	$0.729823\pi$
$854$	10.3923	−	18.0000i	0.355617	−	0.615947i
$855$		0			0
$856$	−6.80385	+	3.92820i	−0.232551	+	0.134263i
$857$	−24.5167			−0.837473			−0.418737	−	0.908108i	$-0.637527\pi$
$857$	−24.5167			−0.837473			−0.418737	+	0.908108i	$0.637527\pi$
$858$	6.46410	+	22.3923i	0.220681	+	0.764461i
$859$	−35.1769			−1.20022			−0.600110	−	0.799917i	$-0.704877\pi$
$859$	−35.1769			−1.20022			−0.600110	+	0.799917i	$0.704877\pi$
$860$		0			0
$861$	−2.00000	−	3.46410i	−0.0681598	−	0.118056i
$862$	14.1962	−	24.5885i	0.483523	−	0.837486i
$863$			35.5359i			1.20966i	0.796356	+	0.604828i	$0.206758\pi$
$863$			35.5359i			1.20966i	−0.796356	+	0.604828i	$0.793242\pi$
$864$	−0.866025	−	0.500000i	−0.0294628	−	0.0170103i
$865$		0			0
$866$		−	19.3205i		−	0.656538i
$867$	0.500000	−	0.866025i	0.0169809	−	0.0294118i
$868$	1.73205	+	3.00000i	0.0587896	+	0.101827i
$869$	−77.9711	+	45.0167i	−2.64499	+	1.52709i
$870$		0			0
$871$	−29.7846	−	28.6603i	−1.00921	−	0.971116i
$872$	15.8564			0.536966
$873$	0.464102	−	0.267949i	0.0157075	−	0.00906871i
$874$	13.9282	+	24.1244i	0.471129	+	0.816019i
$875$		0			0
$876$		−	2.00000i		−	0.0675737i
$877$	3.35641	+	1.93782i	0.113338	+	0.0654356i	0.555597	−	0.831452i	$-0.312490\pi$
$877$	3.35641	+	1.93782i	0.113338	+	0.0654356i	−0.442260	+	0.896887i	$0.645823\pi$
$878$	15.4641	+	8.92820i	0.521888	+	0.301312i
$879$		−	31.8564i		−	1.07449i
$880$		0			0
$881$	7.00000	+	12.1244i	0.235836	+	0.408480i	0.959515	−	0.281656i	$-0.0908839\pi$
$881$	7.00000	+	12.1244i	0.235836	+	0.408480i	−0.723679	+	0.690136i	$0.757551\pi$
$882$	2.59808	−	1.50000i	0.0874818	−	0.0505076i
$883$	−29.9282			−1.00716			−0.503582	−	0.863947i	$-0.667985\pi$
$883$	−29.9282			−1.00716			−0.503582	+	0.863947i	$0.667985\pi$
$884$	10.0000	−	10.3923i	0.336336	−	0.349531i
$885$		0			0
$886$	−14.1962	+	8.19615i	−0.476929	+	0.275355i
$887$	7.06218	+	12.2321i	0.237125	+	0.410712i	0.959888	−	0.280384i	$-0.0904617\pi$
$887$	7.06218	+	12.2321i	0.237125	+	0.410712i	−0.722763	+	0.691096i	$0.757128\pi$
$888$	4.59808	−	7.96410i	0.154301	−	0.267258i
$889$		−	9.85641i		−	0.330573i
$890$		0			0
$891$	−5.59808	−	3.23205i	−0.187543	−	0.108278i
$892$		−	20.5359i		−	0.687593i
$893$	13.1962	−	22.8564i	0.441592	−	0.764860i
$894$	6.76795	+	11.7224i	0.226354	+	0.392057i
$895$		0			0
$896$	−2.00000			−0.0668153
$897$	−13.0622	−	3.23205i	−0.436133	−	0.107915i
$898$	−15.7128			−0.524343
$899$	0.401924	−	0.232051i	0.0134049	−	0.00773933i
$900$		0			0
$901$	1.85641	−	3.21539i	0.0618459	−	0.107120i
$902$		−	12.9282i		−	0.430462i
$903$	−20.6603	−	11.9282i	−0.687530	−	0.396946i
$904$	−0.696152	−	0.401924i	−0.0231537	−	0.0133678i
$905$		0			0
$906$	5.19615	−	9.00000i	0.172631	−	0.299005i
$907$	−10.4282	−	18.0622i	−0.346263	−	0.599745i	0.639320	−	0.768941i	$-0.279216\pi$
$907$	−10.4282	−	18.0622i	−0.346263	−	0.599745i	−0.985582	+	0.169196i	$0.945883\pi$
$908$	14.1962	−	8.19615i	0.471116	−	0.271999i
$909$	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	$0.368420\pi$
$912$	−6.46410	+	3.73205i	−0.214048	+	0.123581i
$913$	28.8564	+	49.9808i	0.955008	+	1.65412i
$914$	−12.2679	+	21.2487i	−0.405788	+	0.702845i
$915$		0			0
$916$	6.80385	+	3.92820i	0.224805	+	0.129791i
$917$	−32.3205	−	18.6603i	−1.06732	−	0.616216i
$918$			4.00000i			0.132020i
$919$	−7.32051	+	12.6795i	−0.241481	+	0.418258i	−0.961136	−	0.276074i	$-0.910967\pi$
$919$	−7.32051	+	12.6795i	−0.241481	+	0.418258i	0.719655	+	0.694332i	$0.244300\pi$
$920$		0			0
$921$	16.8564	−	9.73205i	0.555437	−	0.320682i
$922$	0.464102			0.0152844
$923$	−10.7321	+	43.3731i	−0.353250	+	1.42764i
$924$	−12.9282			−0.425307
$925$		0			0
$926$	3.53590	+	6.12436i	0.116197	+	0.201259i
$927$	−5.92820	+	10.2679i	−0.194708	+	0.337244i
$928$			0.267949i			0.00879586i
$929$	−5.32051	−	3.07180i	−0.174560	−	0.100782i	0.410174	−	0.912007i	$-0.365468\pi$
$929$	−5.32051	−	3.07180i	−0.174560	−	0.100782i	−0.584734	+	0.811225i	$0.698801\pi$
$930$		0			0
$931$		−	22.3923i		−	0.733878i
$932$	−3.06218	+	5.30385i	−0.100305	+	0.173733i
$933$	14.1962	+	24.5885i	0.464761	+	0.804990i
$934$	13.7321	−	7.92820i	0.449326	−	0.259419i
$935$		0			0
$936$	0.866025	−	3.50000i	0.0283069	−	0.114401i
$937$	24.6410			0.804987			0.402493	−	0.915423i	$-0.368144\pi$
$937$	24.6410			0.804987			0.402493	+	0.915423i	$0.368144\pi$
$938$	19.8564	−	11.4641i	0.648335	−	0.374316i
$939$	−14.0000	−	24.2487i	−0.456873	−	0.791327i
$940$		0			0
$941$			14.7846i			0.481965i	0.970530	+	0.240982i	$0.0774696\pi$
$941$			14.7846i			0.481965i	−0.970530	+	0.240982i	$0.922530\pi$
$942$	−4.33013	−	2.50000i	−0.141083	−	0.0814544i
$943$	6.46410	+	3.73205i	0.210500	+	0.121532i
$944$		−	8.46410i		−	0.275483i
$945$		0			0
$946$	−38.5526	−	66.7750i	−1.25345	−	2.17104i
$947$	−8.19615	+	4.73205i	−0.266339	+	0.153771i	−0.627223	−	0.778840i	$-0.715808\pi$
$947$	−8.19615	+	4.73205i	−0.266339	+	0.153771i	0.360884	+	0.932611i	$0.382475\pi$
$948$	13.9282			0.452367
$949$	6.92820	−	2.00000i	0.224899	−	0.0649227i
$950$		0			0
$951$	12.5885	−	7.26795i	0.408209	−	0.235679i
$952$	4.00000	+	6.92820i	0.129641	+	0.224544i
$953$	−6.13397	+	10.6244i	−0.198699	+	0.344157i	−0.948107	−	0.317952i	$-0.897005\pi$
$953$	−6.13397	+	10.6244i	−0.198699	+	0.344157i	0.749408	+	0.662109i	$0.230338\pi$
$954$		−	0.928203i		−	0.0300517i
$955$		0			0
$956$	14.1962	+	8.19615i	0.459136	+	0.265083i
$957$			1.73205i			0.0559893i
$958$	2.73205	−	4.73205i	0.0882686	−	0.152886i
$959$	2.46410	+	4.26795i	0.0795700	+	0.137819i
$960$		0			0
$961$	28.0000			0.903226
$962$	32.1865	+	7.96410i	1.03774	+	0.256773i
$963$	7.85641			0.253169
$964$	15.3564	−	8.86603i	0.494597	−	0.285555i
$965$		0			0
$966$	3.73205	−	6.46410i	0.120077	−	0.207979i
$967$		−	41.4641i		−	1.33340i	−0.745328	−	0.666698i	$-0.767707\pi$
$967$		−	41.4641i		−	1.33340i	0.745328	−	0.666698i	$-0.232293\pi$
$968$	−26.6603	−	15.3923i	−0.856893	−	0.494727i
$969$	25.8564	+	14.9282i	0.830627	+	0.479563i
$970$		0			0
$971$	−2.26795	+	3.92820i	−0.0727820	+	0.126062i	−0.900120	−	0.435643i	$-0.856521\pi$
$971$	−2.26795	+	3.92820i	−0.0727820	+	0.126062i	0.827338	+	0.561705i	$0.189854\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	22.3923	−	12.9282i	0.717864	−	0.414459i
$974$	−23.1769			−0.742636
$975$		0			0
$976$	−10.3923			−0.332650
$977$	−10.9186	+	6.30385i	−0.349316	+	0.201678i	−0.664384	−	0.747391i	$-0.731306\pi$
$977$	−10.9186	+	6.30385i	−0.349316	+	0.201678i	0.315068	+	0.949069i	$0.397973\pi$
$978$	7.52628	+	13.0359i	0.240664	+	0.416842i
$979$	−1.73205	+	3.00000i	−0.0553566	+	0.0958804i
$980$		0			0
$981$	−13.7321	−	7.92820i	−0.438431	−	0.253128i
$982$	15.0000	+	8.66025i	0.478669	+	0.276360i
$983$		−	36.6077i		−	1.16760i	−0.811896	−	0.583802i	$-0.801564\pi$
$983$		−	36.6077i		−	1.16760i	0.811896	−	0.583802i	$-0.198436\pi$
$984$	−1.00000	+	1.73205i	−0.0318788	+	0.0552158i
$985$		0			0
$986$	0.928203	−	0.535898i	0.0295600	−	0.0170665i
$987$	−7.07180			−0.225098
$988$	−19.3923	−	18.6603i	−0.616951	−	0.593662i
$989$	44.5167			1.41555
$990$		0			0
$991$	26.4282	+	45.7750i	0.839520	+	1.45409i	0.890297	+	0.455381i	$0.150497\pi$
$991$	26.4282	+	45.7750i	0.839520	+	1.45409i	−0.0507774	+	0.998710i	$0.516170\pi$
$992$	0.866025	−	1.50000i	0.0274963	−	0.0476250i
$993$			16.7846i			0.532643i
$994$	−21.4641	−	12.3923i	−0.680800	−	0.393060i
$995$		0			0
$996$		−	8.92820i		−	0.282901i
$997$	17.7846	−	30.8038i	0.563244	−	0.975568i	−0.433966	−	0.900929i	$-0.642886\pi$
$997$	17.7846	−	30.8038i	0.563244	−	0.975568i	0.997211	−	0.0746386i	$-0.0237803\pi$
$998$	−3.26795	−	5.66025i	−0.103445	−	0.179172i
$999$	−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.bc.b.751.2		4
5.2	odd	4		1950.2.y.f.49.1		4
5.3	odd	4		1950.2.y.c.49.2		4
5.4	even	2		390.2.bb.b.361.1	yes	4
13.4	even	6	inner	1950.2.bc.b.901.2		4
15.14	odd	2		1170.2.bs.e.361.2		4
65.4	even	6		390.2.bb.b.121.1	✓	4
65.17	odd	12		1950.2.y.c.199.2		4
65.24	odd	12		5070.2.a.bg.1.2		2
65.29	even	6		5070.2.b.o.1351.2		4
65.43	odd	12		1950.2.y.f.199.1		4
65.49	even	6		5070.2.b.o.1351.3		4
65.54	odd	12		5070.2.a.y.1.1		2
195.134	odd	6		1170.2.bs.e.901.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.bb.b.121.1	✓	4	65.4	even	6
390.2.bb.b.361.1	yes	4	5.4	even	2
1170.2.bs.e.361.2		4	15.14	odd	2
1170.2.bs.e.901.2		4	195.134	odd	6
1950.2.y.c.49.2		4	5.3	odd	4
1950.2.y.c.199.2		4	65.17	odd	12
1950.2.y.f.49.1		4	5.2	odd	4
1950.2.y.f.199.1		4	65.43	odd	12
1950.2.bc.b.751.2		4	1.1	even	1	trivial
1950.2.bc.b.901.2		4	13.4	even	6	inner
5070.2.a.y.1.1		2	65.54	odd	12
5070.2.a.bg.1.2		2	65.24	odd	12
5070.2.b.o.1351.2		4	65.29	even	6
5070.2.b.o.1351.3		4	65.49	even	6

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.bc (of order \(6\), degree \(2\), minimal)

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

Introduction

L-functions

Modular forms

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Database

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