LMFDB - Embedded newform 1950.2.z.o.1849.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1950, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("1950.1699");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$15.5708283941$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.3317760000.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 25x^{4} + 625 $ x^8 - 25*x^4 + 625
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1849.3
Root			$0.578737 - 2.15988i$ of defining polynomial
Character	$\chi$	$=$	1950.1849
Dual form			1950.2.z.o.1699.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{6} +(-2.73861 - 1.58114i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{6} +(-2.73861 - 1.58114i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(-1.50000 - 2.59808i) q^{11} -1.00000i q^{12} +(-3.60464 - 0.0811388i) q^{13} -3.16228 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.725489 - 0.418861i) q^{17} -1.00000i q^{18} +(-1.58114 + 2.73861i) q^{19} -3.16228 q^{21} +(-2.59808 - 1.50000i) q^{22} +(-1.87259 + 1.08114i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-3.16228 + 1.73205i) q^{26} -1.00000i q^{27} +(-2.73861 + 1.58114i) q^{28} +(2.16228 + 3.74517i) q^{29} +2.83772 q^{31} +(-0.866025 - 0.500000i) q^{32} +(-2.59808 - 1.50000i) q^{33} -0.837722 q^{34} +(-0.500000 - 0.866025i) q^{36} +(-7.34981 + 4.24342i) q^{37} +3.16228i q^{38} +(-3.16228 + 1.73205i) q^{39} +(-4.74342 - 8.21584i) q^{41} +(-2.73861 + 1.58114i) q^{42} +(-1.00656 - 0.581139i) q^{43} -3.00000 q^{44} +(-1.08114 + 1.87259i) q^{46} +6.00000i q^{47} +(-0.866025 - 0.500000i) q^{48} +(1.50000 + 2.59808i) q^{49} -0.837722 q^{51} +(-1.87259 + 3.08114i) q^{52} -0.837722i q^{53} +(-0.500000 - 0.866025i) q^{54} +(-1.58114 + 2.73861i) q^{56} +3.16228i q^{57} +(3.74517 + 2.16228i) q^{58} +(-3.00000 + 5.19615i) q^{59} +(2.24342 - 3.88571i) q^{61} +(2.45754 - 1.41886i) q^{62} +(-2.73861 + 1.58114i) q^{63} -1.00000 q^{64} -3.00000 q^{66} +(3.46410 - 2.00000i) q^{67} +(-0.725489 + 0.418861i) q^{68} +(-1.08114 + 1.87259i) q^{69} +(7.08114 - 12.2649i) q^{71} +(-0.866025 - 0.500000i) q^{72} -11.3246i q^{73} +(-4.24342 + 7.34981i) q^{74} +(1.58114 + 2.73861i) q^{76} +9.48683i q^{77} +(-1.87259 + 3.08114i) q^{78} -2.83772 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-8.21584 - 4.74342i) q^{82} -11.6491i q^{83} +(-1.58114 + 2.73861i) q^{84} -1.16228 q^{86} +(3.74517 + 2.16228i) q^{87} +(-2.59808 + 1.50000i) q^{88} +(-0.418861 - 0.725489i) q^{89} +(9.74342 + 5.92164i) q^{91} +2.16228i q^{92} +(2.45754 - 1.41886i) q^{93} +(3.00000 + 5.19615i) q^{94} -1.00000 q^{96} +(-15.0035 - 8.66228i) q^{97} +(2.59808 + 1.50000i) q^{98} -3.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4} + 4 q^{6} + 4 q^{9}+O(q^{10}) $ 8 * q + 4 * q^4 + 4 * q^6 + 4 * q^9	$ 8 q + 4 q^{4} + 4 q^{6} + 4 q^{9} - 12 q^{11} - 4 q^{16} - 4 q^{24} - 8 q^{29} + 48 q^{31} - 32 q^{34} - 4 q^{36} - 24 q^{44} + 4 q^{46} + 12 q^{49} - 32 q^{51} - 4 q^{54} - 24 q^{59} - 20 q^{61} - 8 q^{64} - 24 q^{66} + 4 q^{69} + 44 q^{71} + 4 q^{74} - 48 q^{79} - 4 q^{81} + 16 q^{86} - 16 q^{89} + 40 q^{91} + 24 q^{94} - 8 q^{96} - 24 q^{99}+O(q^{100}) $ 8 * q + 4 * q^4 + 4 * q^6 + 4 * q^9 - 12 * q^11 - 4 * q^16 - 4 * q^24 - 8 * q^29 + 48 * q^31 - 32 * q^34 - 4 * q^36 - 24 * q^44 + 4 * q^46 + 12 * q^49 - 32 * q^51 - 4 * q^54 - 24 * q^59 - 20 * q^61 - 8 * q^64 - 24 * q^66 + 4 * q^69 + 44 * q^71 + 4 * q^74 - 48 * q^79 - 4 * q^81 + 16 * q^86 - 16 * q^89 + 40 * q^91 + 24 * q^94 - 8 * q^96 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	0.500000	−	0.866025i	0.204124	−	0.353553i
$7$	−2.73861	−	1.58114i	−1.03510	−	0.597614i	−0.116657	−	0.993172i	$-0.537218\pi$
$7$	−2.73861	−	1.58114i	−1.03510	−	0.597614i	−0.918441	+	0.395558i	$0.870551\pi$
$8$		−	1.00000i		−	0.353553i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$		0			0
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	0.546259	−	0.837616i	$-0.316051\pi$
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	−0.998526	+	0.0542666i	$0.982718\pi$
$12$		−	1.00000i		−	0.288675i
$13$	−3.60464	−	0.0811388i	−0.999747	−	0.0225039i
$13$	−3.60464	−	0.0811388i	−0.999747	−	0.0225039i
$14$	−3.16228			−0.845154
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.725489	−	0.418861i	−0.175957	−	0.101589i	0.409435	−	0.912339i	$-0.365726\pi$
$17$	−0.725489	−	0.418861i	−0.175957	−	0.101589i	−0.585392	+	0.810751i	$0.699059\pi$
$18$		−	1.00000i		−	0.235702i
$19$	−1.58114	+	2.73861i	−0.362738	+	0.628281i	−0.988410	−	0.151805i	$-0.951491\pi$
$19$	−1.58114	+	2.73861i	−0.362738	+	0.628281i	0.625672	+	0.780086i	$0.284825\pi$
$20$		0			0
$21$	−3.16228			−0.690066
$22$	−2.59808	−	1.50000i	−0.553912	−	0.319801i
$23$	−1.87259	+	1.08114i	−0.390461	+	0.225433i	−0.682360	−	0.731016i	$-0.739046\pi$
$23$	−1.87259	+	1.08114i	−0.390461	+	0.225433i	0.291899	+	0.956449i	$0.405713\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$		0			0
$26$	−3.16228	+	1.73205i	−0.620174	+	0.339683i
$27$		−	1.00000i		−	0.192450i
$28$	−2.73861	+	1.58114i	−0.517549	+	0.298807i
$29$	2.16228	+	3.74517i	0.401525	+	0.695461i	0.993910	−	0.110193i	$-0.0351470\pi$
$29$	2.16228	+	3.74517i	0.401525	+	0.695461i	−0.592385	+	0.805655i	$0.701814\pi$
$30$		0			0
$31$	2.83772			0.509670			0.254835	−	0.966985i	$-0.417979\pi$
$31$	2.83772			0.509670			0.254835	+	0.966985i	$0.417979\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	−2.59808	−	1.50000i	−0.452267	−	0.261116i
$34$	−0.837722			−0.143668
$35$		0			0
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	−7.34981	+	4.24342i	−1.20830	+	0.697613i	−0.962388	−	0.271678i	$-0.912421\pi$
$37$	−7.34981	+	4.24342i	−1.20830	+	0.697613i	−0.245914	+	0.969292i	$0.579088\pi$
$38$			3.16228i			0.512989i
$39$	−3.16228	+	1.73205i	−0.506370	+	0.277350i
$40$		0			0
$41$	−4.74342	−	8.21584i	−0.740797	−	1.28310i	−0.952133	−	0.305685i	$-0.901115\pi$
$41$	−4.74342	−	8.21584i	−0.740797	−	1.28310i	0.211336	−	0.977414i	$-0.432219\pi$
$42$	−2.73861	+	1.58114i	−0.422577	+	0.243975i
$43$	−1.00656	−	0.581139i	−0.153499	−	0.0886228i	0.421283	−	0.906929i	$-0.361580\pi$
$43$	−1.00656	−	0.581139i	−0.153499	−	0.0886228i	−0.574782	+	0.818306i	$0.694913\pi$
$44$	−3.00000			−0.452267
$45$		0			0
$46$	−1.08114	+	1.87259i	−0.159405	+	0.276098i
$47$			6.00000i			0.875190i	0.899172	+	0.437595i	$0.144170\pi$
$47$			6.00000i			0.875190i	−0.899172	+	0.437595i	$0.855830\pi$
$48$	−0.866025	−	0.500000i	−0.125000	−	0.0721688i
$49$	1.50000	+	2.59808i	0.214286	+	0.371154i
$50$		0			0
$51$	−0.837722			−0.117305
$52$	−1.87259	+	3.08114i	−0.259681	+	0.427277i
$53$		−	0.837722i		−	0.115070i	−0.998343	−	0.0575350i	$-0.981676\pi$
$53$		−	0.837722i		−	0.115070i	0.998343	−	0.0575350i	$-0.0183241\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$		0			0
$56$	−1.58114	+	2.73861i	−0.211289	+	0.365963i
$57$			3.16228i			0.418854i
$58$	3.74517	+	2.16228i	0.491766	+	0.283921i
$59$	−3.00000	+	5.19615i	−0.390567	+	0.676481i	−0.992524	−	0.122047i	$-0.961054\pi$
$59$	−3.00000	+	5.19615i	−0.390567	+	0.676481i	0.601958	+	0.798528i	$0.294388\pi$
$60$		0			0
$61$	2.24342	−	3.88571i	0.287240	−	0.497514i	−0.685910	−	0.727686i	$-0.740596\pi$
$61$	2.24342	−	3.88571i	0.287240	−	0.497514i	0.973150	+	0.230172i	$0.0739289\pi$
$62$	2.45754	−	1.41886i	0.312108	−	0.180196i
$63$	−2.73861	+	1.58114i	−0.345033	+	0.199205i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−3.00000			−0.369274
$67$	3.46410	−	2.00000i	0.423207	−	0.244339i	−0.273241	−	0.961946i	$-0.588096\pi$
$67$	3.46410	−	2.00000i	0.423207	−	0.244339i	0.696449	+	0.717607i	$0.254762\pi$
$68$	−0.725489	+	0.418861i	−0.0879784	+	0.0507944i
$69$	−1.08114	+	1.87259i	−0.130154	+	0.225433i
$70$		0			0
$71$	7.08114	−	12.2649i	0.840377	−	1.45557i	−0.0492001	−	0.998789i	$-0.515667\pi$
$71$	7.08114	−	12.2649i	0.840377	−	1.45557i	0.889577	−	0.456786i	$-0.150999\pi$
$72$	−0.866025	−	0.500000i	−0.102062	−	0.0589256i
$73$		−	11.3246i		−	1.32544i	−0.748868	−	0.662719i	$-0.769402\pi$
$73$		−	11.3246i		−	1.32544i	0.748868	−	0.662719i	$-0.230598\pi$
$74$	−4.24342	+	7.34981i	−0.493287	+	0.854398i
$75$		0			0
$76$	1.58114	+	2.73861i	0.181369	+	0.314140i
$77$			9.48683i			1.08112i
$78$	−1.87259	+	3.08114i	−0.212029	+	0.348870i
$79$	−2.83772			−0.319269			−0.159634	−	0.987176i	$-0.551032\pi$
$79$	−2.83772			−0.319269			−0.159634	+	0.987176i	$0.551032\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−8.21584	−	4.74342i	−0.907288	−	0.523823i
$83$		−	11.6491i		−	1.27866i	−0.768934	−	0.639328i	$-0.779213\pi$
$83$		−	11.6491i		−	1.27866i	0.768934	−	0.639328i	$-0.220787\pi$
$84$	−1.58114	+	2.73861i	−0.172516	+	0.298807i
$85$		0			0
$86$	−1.16228			−0.125332
$87$	3.74517	+	2.16228i	0.401525	+	0.231820i
$88$	−2.59808	+	1.50000i	−0.276956	+	0.159901i
$89$	−0.418861	−	0.725489i	−0.0443992	−	0.0769017i	0.842972	−	0.537958i	$-0.180804\pi$
$89$	−0.418861	−	0.725489i	−0.0443992	−	0.0769017i	−0.887371	+	0.461056i	$0.847471\pi$
$90$		0			0
$91$	9.74342	+	5.92164i	1.02139	+	0.620757i
$92$			2.16228i			0.225433i
$93$	2.45754	−	1.41886i	0.254835	−	0.147129i
$94$	3.00000	+	5.19615i	0.309426	+	0.535942i
$95$		0			0
$96$	−1.00000			−0.102062
$97$	−15.0035	−	8.66228i	−1.52338	−	0.879521i	−0.999618	−	0.0276537i	$-0.991196\pi$
$97$	−15.0035	−	8.66228i	−1.52338	−	0.879521i	−0.523758	−	0.851867i	$-0.675470\pi$
$98$	2.59808	+	1.50000i	0.262445	+	0.151523i
$99$	−3.00000			−0.301511
$100$		0			0
$101$	−4.32456	−	7.49035i	−0.430309	−	0.745318i	0.566590	−	0.824000i	$-0.308262\pi$
$101$	−4.32456	−	7.49035i	−0.430309	−	0.745318i	−0.996900	+	0.0786819i	$0.974929\pi$
$102$	−0.725489	+	0.418861i	−0.0718341	+	0.0414734i
$103$			5.48683i			0.540634i	0.962771	+	0.270317i	$0.0871285\pi$
$103$			5.48683i			0.540634i	−0.962771	+	0.270317i	$0.912872\pi$
$104$	−0.0811388	+	3.60464i	−0.00795632	+	0.353464i
$105$		0			0
$106$	−0.418861	−	0.725489i	−0.0406834	−	0.0704657i
$107$	−5.19615	+	3.00000i	−0.502331	+	0.290021i	−0.729676	−	0.683793i	$-0.760329\pi$
$107$	−5.19615	+	3.00000i	−0.502331	+	0.290021i	0.227345	+	0.973814i	$0.426996\pi$
$108$	−0.866025	−	0.500000i	−0.0833333	−	0.0481125i
$109$	10.4868			1.00446			0.502228	−	0.864735i	$-0.332514\pi$
$109$	10.4868			1.00446			0.502228	+	0.864735i	$0.332514\pi$
$110$		0			0
$111$	−4.24342	+	7.34981i	−0.402767	+	0.697613i
$112$			3.16228i			0.298807i
$113$	−8.94133	−	5.16228i	−0.841129	−	0.485626i	0.0165186	−	0.999864i	$-0.494742\pi$
$113$	−8.94133	−	5.16228i	−0.841129	−	0.485626i	−0.857648	+	0.514237i	$0.828075\pi$
$114$	1.58114	+	2.73861i	0.148087	+	0.256495i
$115$		0			0
$116$	4.32456			0.401525
$117$	−1.87259	+	3.08114i	−0.173121	+	0.284851i
$118$			6.00000i			0.552345i
$119$	1.32456	+	2.29420i	0.121422	+	0.210309i
$120$		0			0
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$		−	4.48683i		−	0.406219i
$123$	−8.21584	−	4.74342i	−0.740797	−	0.427699i
$124$	1.41886	−	2.45754i	0.127417	−	0.220694i
$125$		0			0
$126$	−1.58114	+	2.73861i	−0.140859	+	0.243975i
$127$	17.6016	−	10.1623i	1.56189	−	0.901756i	0.564822	−	0.825213i	$-0.308945\pi$
$127$	17.6016	−	10.1623i	1.56189	−	0.901756i	0.997066	−	0.0765432i	$-0.0243883\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	−1.16228			−0.102333
$130$		0			0
$131$	16.3246			1.42628			0.713142	−	0.701020i	$-0.247272\pi$
$131$	16.3246			1.42628			0.713142	+	0.701020i	$0.247272\pi$
$132$	−2.59808	+	1.50000i	−0.226134	+	0.130558i
$133$	8.66025	−	5.00000i	0.750939	−	0.433555i
$134$	2.00000	−	3.46410i	0.172774	−	0.299253i
$135$		0			0
$136$	−0.418861	+	0.725489i	−0.0359170	+	0.0622102i
$137$	−10.3923	−	6.00000i	−0.887875	−	0.512615i	−0.0146279	−	0.999893i	$-0.504656\pi$
$137$	−10.3923	−	6.00000i	−0.887875	−	0.512615i	−0.873247	+	0.487278i	$0.837990\pi$
$138$			2.16228i			0.184065i
$139$	−2.83772	+	4.91508i	−0.240692	+	0.416892i	−0.960912	−	0.276855i	$-0.910708\pi$
$139$	−2.83772	+	4.91508i	−0.240692	+	0.416892i	0.720219	+	0.693747i	$0.244041\pi$
$140$		0			0
$141$	3.00000	+	5.19615i	0.252646	+	0.437595i
$142$		−	14.1623i		−	1.18847i
$143$	5.19615	+	9.48683i	0.434524	+	0.793329i
$144$	−1.00000			−0.0833333
$145$		0			0
$146$	−5.66228	−	9.80735i	−0.468613	−	0.811662i
$147$	2.59808	+	1.50000i	0.214286	+	0.123718i
$148$			8.48683i			0.697613i
$149$	−3.41886	+	5.92164i	−0.280084	+	0.485120i	−0.971405	−	0.237428i	$-0.923696\pi$
$149$	−3.41886	+	5.92164i	−0.280084	+	0.485120i	0.691321	+	0.722548i	$0.257029\pi$
$150$		0			0
$151$	9.81139			0.798439			0.399220	−	0.916855i	$-0.369281\pi$
$151$	9.81139			0.798439			0.399220	+	0.916855i	$0.369281\pi$
$152$	2.73861	+	1.58114i	0.222131	+	0.128247i
$153$	−0.725489	+	0.418861i	−0.0586523	+	0.0338629i
$154$	4.74342	+	8.21584i	0.382235	+	0.662051i
$155$		0			0
$156$	−0.0811388	+	3.60464i	−0.00649631	+	0.288602i
$157$		−	16.1623i		−	1.28989i	−0.764229	−	0.644945i	$-0.776880\pi$
$157$		−	16.1623i		−	1.28989i	0.764229	−	0.644945i	$-0.223120\pi$
$158$	−2.45754	+	1.41886i	−0.195511	+	0.112879i
$159$	−0.418861	−	0.725489i	−0.0332179	−	0.0575350i
$160$		0			0
$161$	6.83772			0.538888
$162$	−0.866025	−	0.500000i	−0.0680414	−	0.0392837i
$163$	−13.6931	−	7.90569i	−1.07252	−	0.619222i	−0.143654	−	0.989628i	$-0.545885\pi$
$163$	−13.6931	−	7.90569i	−1.07252	−	0.619222i	−0.928870	+	0.370406i	$0.879218\pi$
$164$	−9.48683			−0.740797
$165$		0			0
$166$	−5.82456	−	10.0884i	−0.452073	−	0.783014i
$167$	−7.06874	+	4.08114i	−0.546996	+	0.315808i	−0.747909	−	0.663801i	$-0.768942\pi$
$167$	−7.06874	+	4.08114i	−0.546996	+	0.315808i	0.200914	+	0.979609i	$0.435609\pi$
$168$			3.16228i			0.243975i
$169$	12.9868	+	0.584952i	0.998987	+	0.0449963i
$170$		0			0
$171$	1.58114	+	2.73861i	0.120913	+	0.209427i
$172$	−1.00656	+	0.581139i	−0.0767496	+	0.0443114i
$173$	1.45098	+	0.837722i	0.110316	+	0.0636909i	0.554143	−	0.832422i	$-0.313046\pi$
$173$	1.45098	+	0.837722i	0.110316	+	0.0636909i	−0.443827	+	0.896113i	$0.646380\pi$
$174$	4.32456			0.327844
$175$		0			0
$176$	−1.50000	+	2.59808i	−0.113067	+	0.195837i
$177$			6.00000i			0.450988i
$178$	−0.725489	−	0.418861i	−0.0543777	−	0.0313950i
$179$	11.8246	+	20.4807i	0.883809	+	1.53080i	0.847073	+	0.531477i	$0.178363\pi$
$179$	11.8246	+	20.4807i	0.883809	+	1.53080i	0.0367358	+	0.999325i	$0.488304\pi$
$180$		0			0
$181$	12.8114			0.952263			0.476131	−	0.879374i	$-0.342039\pi$
$181$	12.8114			0.952263			0.476131	+	0.879374i	$0.342039\pi$
$182$	11.3989	+	0.256584i	0.844940	+	0.0190192i
$183$		−	4.48683i		−	0.331676i
$184$	1.08114	+	1.87259i	0.0797026	+	0.138049i
$185$		0			0
$186$	1.41886	−	2.45754i	0.104036	−	0.180196i
$187$			2.51317i			0.183781i
$188$	5.19615	+	3.00000i	0.378968	+	0.218797i
$189$	−1.58114	+	2.73861i	−0.115011	+	0.199205i
$190$		0			0
$191$	−7.91886	+	13.7159i	−0.572989	+	0.992446i	0.423268	+	0.906004i	$0.360883\pi$
$191$	−7.91886	+	13.7159i	−0.572989	+	0.992446i	−0.996257	+	0.0864411i	$0.972451\pi$
$192$	−0.866025	+	0.500000i	−0.0625000	+	0.0360844i
$193$	−15.0035	+	8.66228i	−1.07998	+	0.623524i	−0.930890	−	0.365300i	$-0.880966\pi$
$193$	−15.0035	+	8.66228i	−1.07998	+	0.623524i	−0.149086	+	0.988824i	$0.547633\pi$
$194$	−17.3246			−1.24383
$195$		0			0
$196$	3.00000			0.214286
$197$	5.19615	−	3.00000i	0.370211	−	0.213741i	−0.303340	−	0.952882i	$-0.598102\pi$
$197$	5.19615	−	3.00000i	0.370211	−	0.213741i	0.673550	+	0.739141i	$0.264768\pi$
$198$	−2.59808	+	1.50000i	−0.184637	+	0.106600i
$199$	4.41886	−	7.65369i	0.313245	−	0.542556i	−0.665818	−	0.746114i	$-0.731917\pi$
$199$	4.41886	−	7.65369i	0.313245	−	0.542556i	0.979063	+	0.203558i	$0.0652506\pi$
$200$		0			0
$201$	2.00000	−	3.46410i	0.141069	−	0.244339i
$202$	−7.49035	−	4.32456i	−0.527019	−	0.304275i
$203$		−	13.6754i		−	0.959828i
$204$	−0.418861	+	0.725489i	−0.0293261	+	0.0507944i
$205$		0			0
$206$	2.74342	+	4.75174i	0.191143	+	0.331069i
$207$			2.16228i			0.150289i
$208$	1.73205	+	3.16228i	0.120096	+	0.219265i
$209$	9.48683			0.656218
$210$		0			0
$211$	−6.58114	−	11.3989i	−0.453064	−	0.784730i	0.545510	−	0.838104i	$-0.316336\pi$
$211$	−6.58114	−	11.3989i	−0.453064	−	0.784730i	−0.998575	+	0.0533737i	$0.983003\pi$
$212$	−0.725489	−	0.418861i	−0.0498268	−	0.0287675i
$213$		−	14.1623i		−	0.970383i
$214$	−3.00000	+	5.19615i	−0.205076	+	0.355202i
$215$		0			0
$216$	−1.00000			−0.0680414
$217$	−7.77142	−	4.48683i	−0.527559	−	0.304586i
$218$	9.08186	−	5.24342i	0.615101	−	0.355129i
$219$	−5.66228	−	9.80735i	−0.382621	−	0.662719i
$220$		0			0
$221$	2.58114	+	1.56871i	0.173626	+	0.105523i
$222$			8.48683i			0.569599i
$223$	22.6344	−	13.0680i	1.51571	−	0.875096i	0.515881	−	0.856660i	$-0.327465\pi$
$223$	22.6344	−	13.0680i	1.51571	−	0.875096i	0.999830	−	0.0184358i	$-0.00586863\pi$
$224$	1.58114	+	2.73861i	0.105644	+	0.182981i
$225$		0			0
$226$	−10.3246			−0.686779
$227$	19.0298	+	10.9868i	1.26305	+	0.729222i	0.973663	−	0.227991i	$-0.0732156\pi$
$227$	19.0298	+	10.9868i	1.26305	+	0.729222i	0.289386	+	0.957213i	$0.406549\pi$
$228$	2.73861	+	1.58114i	0.181369	+	0.104713i
$229$	16.4868			1.08948			0.544740	−	0.838605i	$-0.316628\pi$
$229$	16.4868			1.08948			0.544740	+	0.838605i	$0.316628\pi$
$230$		0			0
$231$	4.74342	+	8.21584i	0.312094	+	0.540562i
$232$	3.74517	−	2.16228i	0.245883	−	0.141960i
$233$			13.6754i			0.895908i	0.894057	+	0.447954i	$0.147847\pi$
$233$			13.6754i			0.895908i	−0.894057	+	0.447954i	$0.852153\pi$
$234$	−0.0811388	+	3.60464i	−0.00530421	+	0.235643i
$235$		0			0
$236$	3.00000	+	5.19615i	0.195283	+	0.338241i
$237$	−2.45754	+	1.41886i	−0.159634	+	0.0921649i
$238$	2.29420	+	1.32456i	0.148711	+	0.0858582i
$239$	−18.4868			−1.19581			−0.597907	−	0.801566i	$-0.704001\pi$
$239$	−18.4868			−1.19581			−0.597907	+	0.801566i	$0.704001\pi$
$240$		0			0
$241$	−4.00000	+	6.92820i	−0.257663	+	0.446285i	−0.965615	−	0.259975i	$-0.916286\pi$
$241$	−4.00000	+	6.92820i	−0.257663	+	0.446285i	0.707953	+	0.706260i	$0.249619\pi$
$242$		−	2.00000i		−	0.128565i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	−2.24342	−	3.88571i	−0.143620	−	0.248757i
$245$		0			0
$246$	−9.48683			−0.604858
$247$	5.92164	−	9.74342i	0.376785	−	0.619959i
$248$		−	2.83772i		−	0.180196i
$249$	−5.82456	−	10.0884i	−0.369116	−	0.639328i
$250$		0			0
$251$	−7.50000	+	12.9904i	−0.473396	+	0.819946i	−0.999536	−	0.0304521i	$-0.990305\pi$
$251$	−7.50000	+	12.9904i	−0.473396	+	0.819946i	0.526140	+	0.850398i	$0.323639\pi$
$252$			3.16228i			0.199205i
$253$	5.61776	+	3.24342i	0.353186	+	0.203912i
$254$	10.1623	−	17.6016i	0.637638	−	1.10442i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	22.3533	−	12.9057i	1.39436	−	0.805035i	0.400567	−	0.916267i	$-0.368813\pi$
$257$	22.3533	−	12.9057i	1.39436	−	0.805035i	0.993794	+	0.111232i	$0.0354798\pi$
$258$	−1.00656	+	0.581139i	−0.0626658	+	0.0361801i
$259$	26.8377			1.66761
$260$		0			0
$261$	4.32456			0.267683
$262$	14.1375	−	8.16228i	0.873416	−	0.504267i
$263$	−0.421610	+	0.243416i	−0.0259976	+	0.0150097i	−0.512942	−	0.858423i	$-0.671445\pi$
$263$	−0.421610	+	0.243416i	−0.0259976	+	0.0150097i	0.486945	+	0.873433i	$0.338111\pi$
$264$	−1.50000	+	2.59808i	−0.0923186	+	0.159901i
$265$		0			0
$266$	5.00000	−	8.66025i	0.306570	−	0.530994i
$267$	−0.725489	−	0.418861i	−0.0443992	−	0.0256339i
$268$		−	4.00000i		−	0.244339i
$269$	−6.41886	+	11.1178i	−0.391365	+	0.677864i	−0.992630	−	0.121186i	$-0.961330\pi$
$269$	−6.41886	+	11.1178i	−0.391365	+	0.677864i	0.601265	+	0.799050i	$0.294664\pi$
$270$		0			0
$271$	−0.162278	−	0.281073i	−0.00985767	−	0.0170740i	0.861054	−	0.508513i	$-0.169805\pi$
$271$	−0.162278	−	0.281073i	−0.00985767	−	0.0170740i	−0.870912	+	0.491439i	$0.836471\pi$
$272$			0.837722i			0.0507944i
$273$	11.3989	+	0.256584i	0.689891	+	0.0155291i
$274$	−12.0000			−0.724947
$275$		0			0
$276$	1.08114	+	1.87259i	0.0650769	+	0.112717i
$277$	−7.63089	−	4.40569i	−0.458496	−	0.264713i	0.252916	−	0.967488i	$-0.418610\pi$
$277$	−7.63089	−	4.40569i	−0.458496	−	0.264713i	−0.711411	+	0.702776i	$0.751944\pi$
$278$			5.67544i			0.340391i
$279$	1.41886	−	2.45754i	0.0849450	−	0.147129i
$280$		0			0
$281$	−21.4868			−1.28180			−0.640898	−	0.767626i	$-0.721438\pi$
$281$	−21.4868			−1.28180			−0.640898	+	0.767626i	$0.721438\pi$
$282$	5.19615	+	3.00000i	0.309426	+	0.178647i
$283$	−16.8761	+	9.74342i	−1.00318	+	0.579186i	−0.909187	−	0.416387i	$-0.863296\pi$
$283$	−16.8761	+	9.74342i	−1.00318	+	0.579186i	−0.0939921	+	0.995573i	$0.529963\pi$
$284$	−7.08114	−	12.2649i	−0.420188	−	0.727787i
$285$		0			0
$286$	9.24342	+	5.61776i	0.546575	+	0.332185i
$287$			30.0000i			1.77084i
$288$	−0.866025	+	0.500000i	−0.0510310	+	0.0294628i
$289$	−8.14911	−	14.1147i	−0.479359	−	0.830275i
$290$		0			0
$291$	−17.3246			−1.01558
$292$	−9.80735	−	5.66228i	−0.573932	−	0.331360i
$293$	−18.6081	−	10.7434i	−1.08710	−	0.627637i	−0.154297	−	0.988025i	$-0.549311\pi$
$293$	−18.6081	−	10.7434i	−1.08710	−	0.627637i	−0.932803	+	0.360387i	$0.882644\pi$
$294$	3.00000			0.174964
$295$		0			0
$296$	4.24342	+	7.34981i	0.246644	+	0.427199i
$297$	−2.59808	+	1.50000i	−0.150756	+	0.0870388i
$298$			6.83772i			0.396099i
$299$	6.83772	−	3.74517i	0.395436	−	0.216589i
$300$		0			0
$301$	1.83772	+	3.18303i	0.105925	+	0.183467i
$302$	8.49691	−	4.90569i	0.488942	−	0.282291i
$303$	−7.49035	−	4.32456i	−0.430309	−	0.248439i
$304$	3.16228			0.181369
$305$		0			0
$306$	−0.418861	+	0.725489i	−0.0239447	+	0.0414734i
$307$		−	16.6491i		−	0.950215i	−0.879928	−	0.475107i	$-0.842409\pi$
$307$		−	16.6491i		−	0.950215i	0.879928	−	0.475107i	$-0.157591\pi$
$308$	8.21584	+	4.74342i	0.468141	+	0.270281i
$309$	2.74342	+	4.75174i	0.156068	+	0.270317i
$310$		0			0
$311$	−6.48683			−0.367835			−0.183917	−	0.982942i	$-0.558878\pi$
$311$	−6.48683			−0.367835			−0.183917	+	0.982942i	$0.558878\pi$
$312$	1.73205	+	3.16228i	0.0980581	+	0.179029i
$313$			7.64911i			0.432353i	0.976354	+	0.216177i	$0.0693587\pi$
$313$			7.64911i			0.432353i	−0.976354	+	0.216177i	$0.930641\pi$
$314$	−8.08114	−	13.9969i	−0.456045	−	0.789893i
$315$		0			0
$316$	−1.41886	+	2.45754i	−0.0798172	+	0.138247i
$317$			31.8114i			1.78671i	0.449356	+	0.893353i	$0.351653\pi$
$317$			31.8114i			1.78671i	−0.449356	+	0.893353i	$0.648347\pi$
$318$	−0.725489	−	0.418861i	−0.0406834	−	0.0234886i
$319$	6.48683	−	11.2355i	0.363193	−	0.629069i
$320$		0			0
$321$	−3.00000	+	5.19615i	−0.167444	+	0.290021i
$322$	5.92164	−	3.41886i	0.330000	−	0.190526i
$323$	2.29420	−	1.32456i	0.127653	−	0.0737002i
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	−15.8114			−0.875712
$327$	9.08186	−	5.24342i	0.502228	−	0.289962i
$328$	−8.21584	+	4.74342i	−0.453644	+	0.261911i
$329$	9.48683	−	16.4317i	0.523026	−	0.905908i
$330$		0			0
$331$	7.58114	−	13.1309i	0.416697	−	0.721741i	−0.578908	−	0.815393i	$-0.696521\pi$
$331$	7.58114	−	13.1309i	0.416697	−	0.721741i	0.995605	+	0.0936524i	$0.0298543\pi$
$332$	−10.0884	−	5.82456i	−0.553674	−	0.319664i
$333$			8.48683i			0.465076i
$334$	−4.08114	+	7.06874i	−0.223310	+	0.386784i
$335$		0			0
$336$	1.58114	+	2.73861i	0.0862582	+	0.149404i
$337$			4.00000i			0.217894i	0.994048	+	0.108947i	$0.0347479\pi$
$337$			4.00000i			0.217894i	−0.994048	+	0.108947i	$0.965252\pi$
$338$	11.5394	−	5.98683i	0.627661	−	0.325641i
$339$	−10.3246			−0.560753
$340$		0			0
$341$	−4.25658	−	7.37262i	−0.230507	−	0.399250i
$342$	2.73861	+	1.58114i	0.148087	+	0.0854982i
$343$			12.6491i			0.682988i
$344$	−0.581139	+	1.00656i	−0.0313329	+	0.0542702i
$345$		0			0
$346$	1.67544			0.0900725
$347$	1.14710	+	0.662278i	0.0615795	+	0.0355529i	0.530474	−	0.847701i	$-0.322014\pi$
$347$	1.14710	+	0.662278i	0.0615795	+	0.0355529i	−0.468894	+	0.883254i	$0.655347\pi$
$348$	3.74517	−	2.16228i	0.200762	−	0.115910i
$349$	−17.7302	−	30.7097i	−0.949078	−	1.64385i	−0.747372	−	0.664406i	$-0.768685\pi$
$349$	−17.7302	−	30.7097i	−0.949078	−	1.64385i	−0.201707	−	0.979446i	$-0.564649\pi$
$350$		0			0
$351$	−0.0811388	+	3.60464i	−0.00433087	+	0.192401i
$352$			3.00000i			0.159901i
$353$	−17.1572	+	9.90569i	−0.913184	+	0.527227i	−0.881454	−	0.472270i	$-0.843435\pi$
$353$	−17.1572	+	9.90569i	−0.913184	+	0.527227i	−0.0317296	+	0.999496i	$0.510102\pi$
$354$	3.00000	+	5.19615i	0.159448	+	0.276172i
$355$		0			0
$356$	−0.837722			−0.0443992
$357$	2.29420	+	1.32456i	0.121422	+	0.0701029i
$358$	20.4807	+	11.8246i	1.08244	+	0.624947i
$359$	12.0000			0.633336			0.316668	−	0.948536i	$-0.397436\pi$
$359$	12.0000			0.633336			0.316668	+	0.948536i	$0.397436\pi$
$360$		0			0
$361$	4.50000	+	7.79423i	0.236842	+	0.410223i
$362$	11.0950	−	6.40569i	0.583140	−	0.336676i
$363$		−	2.00000i		−	0.104973i
$364$	10.0000	−	5.47723i	0.524142	−	0.287085i
$365$		0			0
$366$	−2.24342	−	3.88571i	−0.117265	−	0.203109i
$367$	16.1506	−	9.32456i	0.843055	−	0.486738i	−0.0152467	−	0.999884i	$-0.504853\pi$
$367$	16.1506	−	9.32456i	0.843055	−	0.486738i	0.858301	+	0.513146i	$0.171520\pi$
$368$	1.87259	+	1.08114i	0.0976154	+	0.0563583i
$369$	−9.48683			−0.493865
$370$		0			0
$371$	−1.32456	+	2.29420i	−0.0687675	+	0.119109i
$372$		−	2.83772i		−	0.147129i
$373$	9.08186	+	5.24342i	0.470241	+	0.271494i	0.716341	−	0.697751i	$-0.245816\pi$
$373$	9.08186	+	5.24342i	0.470241	+	0.271494i	−0.246100	+	0.969245i	$0.579149\pi$
$374$	1.25658	+	2.17647i	0.0649764	+	0.112542i
$375$		0			0
$376$	6.00000			0.309426
$377$	−7.49035	−	13.6754i	−0.385773	−	0.704321i
$378$			3.16228i			0.162650i
$379$	1.00000	+	1.73205i	0.0513665	+	0.0889695i	0.890565	−	0.454855i	$-0.150309\pi$
$379$	1.00000	+	1.73205i	0.0513665	+	0.0889695i	−0.839199	+	0.543825i	$0.816976\pi$
$380$		0			0
$381$	10.1623	−	17.6016i	0.520629	−	0.901756i
$382$			15.8377i			0.810328i
$383$	1.87259	+	1.08114i	0.0956847	+	0.0552436i	0.547079	−	0.837081i	$-0.315740\pi$
$383$	1.87259	+	1.08114i	0.0956847	+	0.0552436i	−0.451394	+	0.892325i	$0.649073\pi$
$384$	−0.500000	+	0.866025i	−0.0255155	+	0.0441942i
$385$		0			0
$386$	−8.66228	+	15.0035i	−0.440898	+	0.763658i
$387$	−1.00656	+	0.581139i	−0.0511664	+	0.0295409i
$388$	−15.0035	+	8.66228i	−0.761688	+	0.439761i
$389$	28.3246			1.43611			0.718056	−	0.695985i	$-0.245032\pi$
$389$	28.3246			1.43611			0.718056	+	0.695985i	$0.245032\pi$
$390$		0			0
$391$	1.81139			0.0916058
$392$	2.59808	−	1.50000i	0.131223	−	0.0757614i
$393$	14.1375	−	8.16228i	0.713142	−	0.411732i
$394$	3.00000	−	5.19615i	0.151138	−	0.261778i
$395$		0			0
$396$	−1.50000	+	2.59808i	−0.0753778	+	0.130558i
$397$	−10.1112	−	5.83772i	−0.507468	−	0.292987i	0.224324	−	0.974515i	$-0.427983\pi$
$397$	−10.1112	−	5.83772i	−0.507468	−	0.292987i	−0.731792	+	0.681528i	$0.761316\pi$
$398$		−	8.83772i		−	0.442995i
$399$	5.00000	−	8.66025i	0.250313	−	0.433555i
$400$		0			0
$401$	−8.16228	−	14.1375i	−0.407605	−	0.705992i	0.587016	−	0.809575i	$-0.300303\pi$
$401$	−8.16228	−	14.1375i	−0.407605	−	0.705992i	−0.994621	+	0.103583i	$0.966969\pi$
$402$		−	4.00000i		−	0.199502i
$403$	−10.2290	−	0.230249i	−0.509541	−	0.0114695i
$404$	−8.64911			−0.430309
$405$		0			0
$406$	−6.83772	−	11.8433i	−0.339350	−	0.587772i
$407$	22.0494	+	12.7302i	1.09295	+	0.631015i
$408$			0.837722i			0.0414734i
$409$	15.1623	−	26.2618i	0.749726	−	1.29856i	−0.198227	−	0.980156i	$-0.563518\pi$
$409$	15.1623	−	26.2618i	0.749726	−	1.29856i	0.947954	−	0.318408i	$-0.103148\pi$
$410$		0			0
$411$	−12.0000			−0.591916
$412$	4.75174	+	2.74342i	0.234101	+	0.135158i
$413$	16.4317	−	9.48683i	0.808550	−	0.466817i
$414$	1.08114	+	1.87259i	0.0531351	+	0.0920326i
$415$		0			0
$416$	3.08114	+	1.87259i	0.151065	+	0.0918112i
$417$			5.67544i			0.277928i
$418$	8.21584	−	4.74342i	0.401850	−	0.232008i
$419$	4.50000	+	7.79423i	0.219839	+	0.380773i	0.954759	−	0.297382i	$-0.0961133\pi$
$419$	4.50000	+	7.79423i	0.219839	+	0.380773i	−0.734919	+	0.678155i	$0.762780\pi$
$420$		0			0
$421$	28.1623			1.37255			0.686273	−	0.727344i	$-0.259246\pi$
$421$	28.1623			1.37255			0.686273	+	0.727344i	$0.259246\pi$
$422$	−11.3989	−	6.58114i	−0.554888	−	0.320365i
$423$	5.19615	+	3.00000i	0.252646	+	0.145865i
$424$	−0.837722			−0.0406834
$425$		0			0
$426$	−7.08114	−	12.2649i	−0.343082	−	0.594236i
$427$	−12.2877	+	7.09431i	−0.594643	+	0.343318i
$428$			6.00000i			0.290021i
$429$	9.24342	+	5.61776i	0.446276	+	0.271228i
$430$		0			0
$431$	12.2434	+	21.2062i	0.589745	+	1.02147i	0.994266	+	0.106939i	$0.0341049\pi$
$431$	12.2434	+	21.2062i	0.589745	+	1.02147i	−0.404521	+	0.914529i	$0.632562\pi$
$432$	−0.866025	+	0.500000i	−0.0416667	+	0.0240563i
$433$	29.9842	+	17.3114i	1.44095	+	0.831932i	0.997913	−	0.0645717i	$-0.0205681\pi$
$433$	29.9842	+	17.3114i	1.44095	+	0.831932i	0.443036	+	0.896504i	$0.353901\pi$
$434$	−8.97367			−0.430750
$435$		0			0
$436$	5.24342	−	9.08186i	0.251114	−	0.434942i
$437$		−	6.83772i		−	0.327093i
$438$	−9.80735	−	5.66228i	−0.468613	−	0.270554i
$439$	−18.3246	−	31.7391i	−0.874583	−	1.51482i	−0.857206	−	0.514974i	$-0.827802\pi$
$439$	−18.3246	−	31.7391i	−0.874583	−	1.51482i	−0.0173773	−	0.999849i	$-0.505532\pi$
$440$		0			0
$441$	3.00000			0.142857
$442$	3.01969	+	0.0679718i	0.143632	+	0.00323309i
$443$		−	9.00000i		−	0.427603i	−0.976877	−	0.213801i	$-0.931415\pi$
$443$		−	9.00000i		−	0.427603i	0.976877	−	0.213801i	$-0.0685846\pi$
$444$	4.24342	+	7.34981i	0.201384	+	0.348807i
$445$		0			0
$446$	13.0680	−	22.6344i	0.618786	−	1.07177i
$447$			6.83772i			0.323413i
$448$	2.73861	+	1.58114i	0.129387	+	0.0747018i
$449$	1.25658	−	2.17647i	0.0593018	−	0.102714i	−0.834850	−	0.550477i	$-0.814446\pi$
$449$	1.25658	−	2.17647i	0.0593018	−	0.102714i	0.894152	+	0.447763i	$0.147779\pi$
$450$		0			0
$451$	−14.2302	+	24.6475i	−0.670076	+	1.16061i
$452$	−8.94133	+	5.16228i	−0.420565	+	0.242813i
$453$	8.49691	−	4.90569i	0.399220	−	0.230490i
$454$	21.9737			1.03128
$455$		0			0
$456$	3.16228			0.148087
$457$	8.96413	−	5.17544i	0.419324	−	0.242097i	−0.275464	−	0.961311i	$-0.588831\pi$
$457$	8.96413	−	5.17544i	0.419324	−	0.242097i	0.694788	+	0.719214i	$0.255498\pi$
$458$	14.2780	−	8.24342i	0.667168	−	0.385190i
$459$	−0.418861	+	0.725489i	−0.0195508	+	0.0338629i
$460$		0			0
$461$	8.58114	−	14.8630i	0.399663	−	0.692237i	−0.594021	−	0.804450i	$-0.702460\pi$
$461$	8.58114	−	14.8630i	0.399663	−	0.692237i	0.993684	+	0.112212i	$0.0357937\pi$
$462$	8.21584	+	4.74342i	0.382235	+	0.220684i
$463$			4.51317i			0.209745i	0.994486	+	0.104872i	$0.0334434\pi$
$463$			4.51317i			0.209745i	−0.994486	+	0.104872i	$0.966557\pi$
$464$	2.16228	−	3.74517i	0.100381	−	0.173865i
$465$		0			0
$466$	6.83772	+	11.8433i	0.316751	+	0.548629i
$467$			3.00000i			0.138823i	0.997588	+	0.0694117i	$0.0221122\pi$
$467$			3.00000i			0.138823i	−0.997588	+	0.0694117i	$0.977888\pi$
$468$	1.73205	+	3.16228i	0.0800641	+	0.146176i
$469$	−12.6491			−0.584082
$470$		0			0
$471$	−8.08114	−	13.9969i	−0.372359	−	0.644945i
$472$	5.19615	+	3.00000i	0.239172	+	0.138086i
$473$			3.48683i			0.160325i
$474$	−1.41886	+	2.45754i	−0.0651705	+	0.112879i
$475$		0			0
$476$	2.64911			0.121422
$477$	−0.725489	−	0.418861i	−0.0332179	−	0.0191783i
$478$	−16.0101	+	9.24342i	−0.732283	+	0.422784i
$479$	−6.83772	−	11.8433i	−0.312424	−	0.541133i	0.666463	−	0.745538i	$-0.267807\pi$
$479$	−6.83772	−	11.8433i	−0.312424	−	0.541133i	−0.978886	+	0.204405i	$0.934474\pi$
$480$		0			0
$481$	26.8377	−	14.6996i	1.22369	−	0.670245i
$482$			8.00000i			0.364390i
$483$	5.92164	−	3.41886i	0.269444	−	0.155564i
$484$	−1.00000	−	1.73205i	−0.0454545	−	0.0787296i
$485$		0			0
$486$	−1.00000			−0.0453609
$487$	−2.73861	−	1.58114i	−0.124098	−	0.0716482i	0.436666	−	0.899624i	$-0.356159\pi$
$487$	−2.73861	−	1.58114i	−0.124098	−	0.0716482i	−0.560764	+	0.827976i	$0.689493\pi$
$488$	−3.88571	−	2.24342i	−0.175898	−	0.101555i
$489$	−15.8114			−0.715016
$490$		0			0
$491$	10.9868	+	19.0298i	0.495829	+	0.858801i	0.999988	−	0.00480977i	$-0.00153100\pi$
$491$	10.9868	+	19.0298i	0.495829	+	0.858801i	−0.504160	+	0.863611i	$0.668198\pi$
$492$	−8.21584	+	4.74342i	−0.370399	+	0.213850i
$493$		−	3.62278i		−	0.163162i
$494$	0.256584	−	11.3989i	0.0115442	−	0.512859i
$495$		0			0
$496$	−1.41886	−	2.45754i	−0.0637087	−	0.110347i
$497$	−38.7850	+	22.3925i	−1.73974	+	1.00444i
$498$	−10.0884	−	5.82456i	−0.452073	−	0.261005i
$499$	−39.8114			−1.78220			−0.891101	−	0.453805i	$-0.850066\pi$
$499$	−39.8114			−1.78220			−0.891101	+	0.453805i	$0.850066\pi$
$500$		0			0
$501$	−4.08114	+	7.06874i	−0.182332	+	0.315808i
$502$			15.0000i			0.669483i
$503$	14.5591	+	8.40569i	0.649158	+	0.374791i	0.788133	−	0.615504i	$-0.211048\pi$
$503$	14.5591	+	8.40569i	0.649158	+	0.374791i	−0.138976	+	0.990296i	$0.544381\pi$
$504$	1.58114	+	2.73861i	0.0704295	+	0.121988i
$505$		0			0
$506$	6.48683			0.288375
$507$	11.5394	−	5.98683i	0.512483	−	0.265885i
$508$		−	20.3246i		−	0.901756i
$509$	−13.3925	−	23.1965i	−0.593613	−	1.02817i	−0.993741	−	0.111709i	$-0.964368\pi$
$509$	−13.3925	−	23.1965i	−0.593613	−	1.02817i	0.400128	−	0.916459i	$-0.368966\pi$
$510$		0			0
$511$	−17.9057	+	31.0136i	−0.792101	+	1.37196i
$512$			1.00000i			0.0441942i
$513$	2.73861	+	1.58114i	0.120913	+	0.0698090i
$514$	12.9057	−	22.3533i	0.569246	−	0.985963i
$515$		0			0
$516$	−0.581139	+	1.00656i	−0.0255832	+	0.0443114i
$517$	15.5885	−	9.00000i	0.685580	−	0.395820i
$518$	23.2421	−	13.4189i	1.02120	−	0.589591i
$519$	1.67544			0.0735439
$520$		0			0
$521$	−20.6491			−0.904654			−0.452327	−	0.891852i	$-0.649406\pi$
$521$	−20.6491			−0.904654			−0.452327	+	0.891852i	$0.649406\pi$
$522$	3.74517	−	2.16228i	0.163922	−	0.0946403i
$523$	28.5560	−	16.4868i	1.24867	−	0.720919i	0.277824	−	0.960632i	$-0.410387\pi$
$523$	28.5560	−	16.4868i	1.24867	−	0.720919i	0.970844	+	0.239713i	$0.0770534\pi$
$524$	8.16228	−	14.1375i	0.356571	−	0.617599i
$525$		0			0
$526$	−0.243416	+	0.421610i	−0.0106135	+	0.0183831i
$527$	−2.05874	−	1.18861i	−0.0896799	−	0.0517767i
$528$			3.00000i			0.130558i
$529$	−9.16228	+	15.8695i	−0.398360	+	0.689980i
$530$		0			0
$531$	3.00000	+	5.19615i	0.130189	+	0.225494i
$532$		−	10.0000i		−	0.433555i
$533$	16.4317	+	30.0000i	0.711735	+	1.29944i
$534$	−0.837722			−0.0362518
$535$		0			0
$536$	−2.00000	−	3.46410i	−0.0863868	−	0.149626i
$537$	20.4807	+	11.8246i	0.883809	+	0.510267i
$538$			12.8377i			0.553474i
$539$	4.50000	−	7.79423i	0.193829	−	0.335721i
$540$		0			0
$541$	30.8114			1.32469			0.662343	−	0.749201i	$-0.269562\pi$
$541$	30.8114			1.32469			0.662343	+	0.749201i	$0.269562\pi$
$542$	−0.281073	−	0.162278i	−0.0120731	−	0.00697042i
$543$	11.0950	−	6.40569i	0.476131	−	0.274895i
$544$	0.418861	+	0.725489i	0.0179585	+	0.0311051i
$545$		0			0
$546$	10.0000	−	5.47723i	0.427960	−	0.234404i
$547$		−	14.1359i		−	0.604409i	−0.953243	−	0.302205i	$-0.902277\pi$
$547$		−	14.1359i		−	0.604409i	0.953243	−	0.302205i	$-0.0977226\pi$
$548$	−10.3923	+	6.00000i	−0.443937	+	0.256307i
$549$	−2.24342	−	3.88571i	−0.0957467	−	0.165838i
$550$		0			0
$551$	−13.6754			−0.582594
$552$	1.87259	+	1.08114i	0.0797026	+	0.0460163i
$553$	7.77142	+	4.48683i	0.330475	+	0.190800i
$554$	−8.81139			−0.374360
$555$		0			0
$556$	2.83772	+	4.91508i	0.120346	+	0.208446i
$557$	−16.4317	+	9.48683i	−0.696232	+	0.401970i	−0.805943	−	0.591994i	$-0.798341\pi$
$557$	−16.4317	+	9.48683i	−0.696232	+	0.401970i	0.109710	+	0.993964i	$0.465008\pi$
$558$		−	2.83772i		−	0.120130i
$559$	3.58114	+	2.17647i	0.151466	+	0.0920547i
$560$		0			0
$561$	1.25658	+	2.17647i	0.0530530	+	0.0918905i
$562$	−18.6081	+	10.7434i	−0.784937	+	0.453184i
$563$	−29.4221	−	16.9868i	−1.23999	−	0.715910i	−0.270899	−	0.962608i	$-0.587321\pi$
$563$	−29.4221	−	16.9868i	−1.23999	−	0.715910i	−0.969092	+	0.246698i	$0.920654\pi$
$564$	6.00000			0.252646
$565$		0			0
$566$	−9.74342	+	16.8761i	−0.409546	+	0.709355i
$567$			3.16228i			0.132803i
$568$	−12.2649	−	7.08114i	−0.514623	−	0.297118i
$569$	−3.48683	−	6.03937i	−0.146176	−	0.253184i	0.783635	−	0.621221i	$-0.213363\pi$
$569$	−3.48683	−	6.03937i	−0.146176	−	0.253184i	−0.929811	+	0.368038i	$0.880030\pi$
$570$		0			0
$571$	−32.3246			−1.35274			−0.676370	−	0.736562i	$-0.736448\pi$
$571$	−32.3246			−1.35274			−0.676370	+	0.736562i	$0.736448\pi$
$572$	10.8139	+	0.243416i	0.452152	+	0.0101778i
$573$			15.8377i			0.661630i
$574$	15.0000	+	25.9808i	0.626088	+	1.08442i
$575$		0			0
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$			43.0000i			1.79011i	0.445952	+	0.895057i	$0.352865\pi$
$577$			43.0000i			1.79011i	−0.445952	+	0.895057i	$0.647135\pi$
$578$	−14.1147	−	8.14911i	−0.587093	−	0.338958i
$579$	−8.66228	+	15.0035i	−0.359992	+	0.623524i
$580$		0			0
$581$	−18.4189	+	31.9024i	−0.764143	+	1.32353i
$582$	−15.0035	+	8.66228i	−0.621915	+	0.359063i
$583$	−2.17647	+	1.25658i	−0.0901400	+	0.0520424i
$584$	−11.3246			−0.468613
$585$		0			0
$586$	−21.4868			−0.887613
$587$	18.1865	−	10.5000i	0.750639	−	0.433381i	−0.0752860	−	0.997162i	$-0.523987\pi$
$587$	18.1865	−	10.5000i	0.750639	−	0.433381i	0.825925	+	0.563781i	$0.190654\pi$
$588$	2.59808	−	1.50000i	0.107143	−	0.0618590i
$589$	−4.48683	+	7.77142i	−0.184877	+	0.320216i
$590$		0			0
$591$	3.00000	−	5.19615i	0.123404	−	0.213741i
$592$	7.34981	+	4.24342i	0.302075	+	0.174403i
$593$		−	5.16228i		−	0.211989i	−0.994367	−	0.105995i	$-0.966197\pi$
$593$		−	5.16228i		−	0.211989i	0.994367	−	0.105995i	$-0.0338026\pi$
$594$	−1.50000	+	2.59808i	−0.0615457	+	0.106600i
$595$		0			0
$596$	3.41886	+	5.92164i	0.140042	+	0.242560i
$597$		−	8.83772i		−	0.361704i
$598$	4.04905	−	6.66228i	0.165578	−	0.272441i
$599$	−1.18861			−0.0485654			−0.0242827	−	0.999705i	$-0.507730\pi$
$599$	−1.18861			−0.0485654			−0.0242827	+	0.999705i	$0.507730\pi$
$600$		0			0
$601$	−21.6491	−	37.4974i	−0.883086	−	1.52955i	−0.847892	−	0.530169i	$-0.822129\pi$
$601$	−21.6491	−	37.4974i	−0.883086	−	1.52955i	−0.0351935	−	0.999381i	$-0.511205\pi$
$602$	3.18303	+	1.83772i	0.129731	+	0.0749000i
$603$		−	4.00000i		−	0.162893i
$604$	4.90569	−	8.49691i	0.199610	−	0.345734i
$605$		0			0
$606$	−8.64911			−0.351346
$607$	31.4580	+	18.1623i	1.27684	+	0.737184i	0.976266	−	0.216574i	$-0.0694884\pi$
$607$	31.4580	+	18.1623i	1.27684	+	0.737184i	0.300574	+	0.953758i	$0.402822\pi$
$608$	2.73861	−	1.58114i	0.111065	−	0.0641236i
$609$	−6.83772	−	11.8433i	−0.277078	−	0.479914i
$610$		0			0
$611$	0.486833	−	21.6278i	0.0196952	−	0.874968i
$612$			0.837722i			0.0338629i
$613$	36.6541	−	21.1623i	1.48045	−	0.854736i	0.480692	−	0.876889i	$-0.340385\pi$
$613$	36.6541	−	21.1623i	1.48045	−	0.854736i	0.999755	+	0.0221531i	$0.00705211\pi$
$614$	−8.32456	−	14.4186i	−0.335952	−	0.581885i
$615$		0			0
$616$	9.48683			0.382235
$617$	−40.9615	−	23.6491i	−1.64905	−	0.952077i	−0.977452	−	0.211158i	$-0.932276\pi$
$617$	−40.9615	−	23.6491i	−1.64905	−	0.952077i	−0.671594	−	0.740919i	$-0.734390\pi$
$618$	4.75174	+	2.74342i	0.191143	+	0.110356i
$619$	−8.00000			−0.321547			−0.160774	−	0.986991i	$-0.551399\pi$
$619$	−8.00000			−0.321547			−0.160774	+	0.986991i	$0.551399\pi$
$620$		0			0
$621$	1.08114	+	1.87259i	0.0433846	+	0.0751443i
$622$	−5.61776	+	3.24342i	−0.225252	+	0.130049i
$623$			2.64911i			0.106134i
$624$	3.08114	+	1.87259i	0.123344	+	0.0749635i
$625$		0			0
$626$	3.82456	+	6.62432i	0.152860	+	0.264761i
$627$	8.21584	−	4.74342i	0.328109	−	0.189434i
$628$	−13.9969	−	8.08114i	−0.558539	−	0.322473i
$629$	7.10961			0.283479
$630$		0			0
$631$	7.64911	−	13.2486i	0.304506	−	0.527420i	−0.672645	−	0.739965i	$-0.734842\pi$
$631$	7.64911	−	13.2486i	0.304506	−	0.527420i	0.977151	+	0.212545i	$0.0681752\pi$
$632$			2.83772i			0.112879i
$633$	−11.3989	−	6.58114i	−0.453064	−	0.261577i
$634$	15.9057	+	27.5495i	0.631696	+	1.09413i
$635$		0			0
$636$	−0.837722			−0.0332179
$637$	−5.19615	−	9.48683i	−0.205879	−	0.375882i
$638$		−	12.9737i		−	0.513632i
$639$	−7.08114	−	12.2649i	−0.280126	−	0.485192i
$640$		0			0
$641$	−12.9737	+	22.4710i	−0.512429	+	0.887553i	0.487467	+	0.873141i	$0.337921\pi$
$641$	−12.9737	+	22.4710i	−0.512429	+	0.887553i	−0.999896	+	0.0144117i	$0.995412\pi$
$642$			6.00000i			0.236801i
$643$	10.1112	+	5.83772i	0.398748	+	0.230217i	0.685944	−	0.727655i	$-0.259390\pi$
$643$	10.1112	+	5.83772i	0.398748	+	0.230217i	−0.287196	+	0.957872i	$0.592723\pi$
$644$	3.41886	−	5.92164i	0.134722	−	0.233345i
$645$		0			0
$646$	1.32456	−	2.29420i	0.0521139	−	0.0902640i
$647$	20.3630	−	11.7566i	0.800552	−	0.462199i	−0.0431121	−	0.999070i	$-0.513727\pi$
$647$	20.3630	−	11.7566i	0.800552	−	0.462199i	0.843664	+	0.536871i	$0.180394\pi$
$648$	−0.866025	+	0.500000i	−0.0340207	+	0.0196419i
$649$	18.0000			0.706562
$650$		0			0
$651$	−8.97367			−0.351706
$652$	−13.6931	+	7.90569i	−0.536262	+	0.309611i
$653$	−8.21584	+	4.74342i	−0.321511	+	0.185624i	−0.652066	−	0.758162i	$-0.726097\pi$
$653$	−8.21584	+	4.74342i	−0.321511	+	0.185624i	0.330555	+	0.943787i	$0.392764\pi$
$654$	5.24342	−	9.08186i	0.205034	−	0.355129i
$655$		0			0
$656$	−4.74342	+	8.21584i	−0.185199	+	0.320775i
$657$	−9.80735	−	5.66228i	−0.382621	−	0.220906i
$658$		−	18.9737i		−	0.739671i
$659$	−7.50000	+	12.9904i	−0.292159	+	0.506033i	−0.974320	−	0.225168i	$-0.927707\pi$
$659$	−7.50000	+	12.9904i	−0.292159	+	0.506033i	0.682161	+	0.731202i	$0.261040\pi$
$660$		0			0
$661$	−13.0000	−	22.5167i	−0.505641	−	0.875797i	−0.999979	−	0.00652642i	$-0.997923\pi$
$661$	−13.0000	−	22.5167i	−0.505641	−	0.875797i	0.494337	−	0.869270i	$-0.335411\pi$
$662$		−	15.1623i		−	0.589299i
$663$	3.01969	+	0.0679718i	0.117275	+	0.00263981i
$664$	−11.6491			−0.452073
$665$		0			0
$666$	4.24342	+	7.34981i	0.164429	+	0.284799i
$667$	−8.09811	−	4.67544i	−0.313560	−	0.181034i
$668$			8.16228i			0.315808i
$669$	13.0680	−	22.6344i	0.505237	−	0.875096i
$670$		0			0
$671$	−13.4605			−0.519637
$672$	2.73861	+	1.58114i	0.105644	+	0.0609938i
$673$	−3.16022	+	1.82456i	−0.121818	+	0.0703314i	−0.559671	−	0.828715i	$-0.689072\pi$
$673$	−3.16022	+	1.82456i	−0.121818	+	0.0703314i	0.437853	+	0.899047i	$0.355739\pi$
$674$	2.00000	+	3.46410i	0.0770371	+	0.133432i
$675$		0			0
$676$	7.00000	−	10.9545i	0.269231	−	0.421325i
$677$			32.6491i			1.25481i	0.778694	+	0.627404i	$0.215882\pi$
$677$			32.6491i			1.25481i	−0.778694	+	0.627404i	$0.784118\pi$
$678$	−8.94133	+	5.16228i	−0.343390	+	0.198256i
$679$	27.3925	+	47.4452i	1.05123	+	1.82078i
$680$		0			0
$681$	21.9737			0.842033
$682$	−7.37262	−	4.25658i	−0.282312	−	0.162993i
$683$	25.0691	+	14.4737i	0.959243	+	0.553819i	0.895940	−	0.444175i	$-0.146503\pi$
$683$	25.0691	+	14.4737i	0.959243	+	0.553819i	0.0633033	+	0.997994i	$0.479836\pi$
$684$	3.16228			0.120913
$685$		0			0
$686$	6.32456	+	10.9545i	0.241473	+	0.418243i
$687$	14.2780	−	8.24342i	0.544740	−	0.314506i
$688$			1.16228i			0.0443114i
$689$	−0.0679718	+	3.01969i	−0.00258952	+	0.115041i
$690$		0			0
$691$	11.9737	+	20.7390i	0.455500	+	0.788949i	0.998717	−	0.0506436i	$-0.0161273\pi$
$691$	11.9737	+	20.7390i	0.455500	+	0.788949i	−0.543217	+	0.839592i	$0.682794\pi$
$692$	1.45098	−	0.837722i	0.0551579	−	0.0318454i
$693$	8.21584	+	4.74342i	0.312094	+	0.180187i
$694$	1.32456			0.0502794
$695$		0			0
$696$	2.16228	−	3.74517i	0.0819609	−	0.141960i
$697$			7.94733i			0.301027i
$698$	−30.7097	−	17.7302i	−1.16238	−	0.671100i
$699$	6.83772	+	11.8433i	0.258626	+	0.447954i
$700$		0			0
$701$	−22.4605			−0.848321			−0.424161	−	0.905587i	$-0.639431\pi$
$701$	−22.4605			−0.848321			−0.424161	+	0.905587i	$0.639431\pi$
$702$	1.73205	+	3.16228i	0.0653720	+	0.119352i
$703$		−	26.8377i		−	1.01220i
$704$	1.50000	+	2.59808i	0.0565334	+	0.0979187i
$705$		0			0
$706$	−9.90569	+	17.1572i	−0.372806	+	0.645718i
$707$			27.3509i			1.02864i
$708$	5.19615	+	3.00000i	0.195283	+	0.112747i
$709$	0.756584	−	1.31044i	0.0284141	−	0.0492146i	−0.851469	−	0.524405i	$-0.824288\pi$
$709$	0.756584	−	1.31044i	0.0284141	−	0.0492146i	0.879883	+	0.475191i	$0.157621\pi$
$710$		0			0
$711$	−1.41886	+	2.45754i	−0.0532115	+	0.0921649i
$712$	−0.725489	+	0.418861i	−0.0271888	+	0.0156975i
$713$	−5.31388	+	3.06797i	−0.199006	+	0.114896i
$714$	2.64911			0.0991405
$715$		0			0
$716$	23.6491			0.883809
$717$	−16.0101	+	9.24342i	−0.597907	+	0.345202i
$718$	10.3923	−	6.00000i	0.387837	−	0.223918i
$719$	−23.4057	+	40.5399i	−0.872885	+	1.51188i	−0.0138864	+	0.999904i	$0.504420\pi$
$719$	−23.4057	+	40.5399i	−0.872885	+	1.51188i	−0.858999	+	0.511978i	$0.828913\pi$
$720$		0			0
$721$	8.67544	−	15.0263i	0.323090	−	0.559609i
$722$	7.79423	+	4.50000i	0.290071	+	0.167473i
$723$			8.00000i			0.297523i
$724$	6.40569	−	11.0950i	0.238066	−	0.412342i
$725$		0			0
$726$	−1.00000	−	1.73205i	−0.0371135	−	0.0642824i
$727$		−	12.3246i		−	0.457092i	−0.973533	−	0.228546i	$-0.926603\pi$
$727$		−	12.3246i		−	0.457092i	0.973533	−	0.228546i	$-0.0733972\pi$
$728$	5.92164	−	9.74342i	0.219471	−	0.361115i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	0.486833	+	0.843219i	0.0180062	+	0.0311876i
$732$	−3.88571	−	2.24342i	−0.143620	−	0.0829191i
$733$			19.5132i			0.720735i	0.932810	+	0.360368i	$0.117349\pi$
$733$			19.5132i			0.720735i	−0.932810	+	0.360368i	$0.882651\pi$
$734$	9.32456	−	16.1506i	0.344176	−	0.596130i
$735$		0			0
$736$	2.16228			0.0797026
$737$	−10.3923	−	6.00000i	−0.382805	−	0.221013i
$738$	−8.21584	+	4.74342i	−0.302429	+	0.174608i
$739$	9.64911	+	16.7127i	0.354948	+	0.614788i	0.987109	−	0.160049i	$-0.0511651\pi$
$739$	9.64911	+	16.7127i	0.354948	+	0.614788i	−0.632161	+	0.774837i	$0.717832\pi$
$740$		0			0
$741$	0.256584	−	11.3989i	0.00942583	−	0.418748i
$742$			2.64911i			0.0972519i
$743$	−38.6673	+	22.3246i	−1.41856	+	0.819009i	−0.996173	−	0.0874050i	$-0.972143\pi$
$743$	−38.6673	+	22.3246i	−1.41856	+	0.819009i	−0.422391	+	0.906414i	$0.638809\pi$
$744$	−1.41886	−	2.45754i	−0.0520180	−	0.0900978i
$745$		0			0
$746$	10.4868			0.383950
$747$	−10.0884	−	5.82456i	−0.369116	−	0.213109i
$748$	2.17647	+	1.25658i	0.0795795	+	0.0459452i
$749$	18.9737			0.693283
$750$		0			0
$751$	8.83772	+	15.3074i	0.322493	+	0.558574i	0.981002	−	0.193999i	$-0.0621458\pi$
$751$	8.83772	+	15.3074i	0.322493	+	0.558574i	−0.658509	+	0.752573i	$0.728812\pi$
$752$	5.19615	−	3.00000i	0.189484	−	0.109399i
$753$			15.0000i			0.546630i
$754$	−13.3246	−	8.09811i	−0.485252	−	0.294916i
$755$		0			0
$756$	1.58114	+	2.73861i	0.0575055	+	0.0996024i
$757$	9.50347	−	5.48683i	0.345410	−	0.199422i	−0.317252	−	0.948341i	$-0.602760\pi$
$757$	9.50347	−	5.48683i	0.345410	−	0.199422i	0.662662	+	0.748919i	$0.269427\pi$
$758$	1.73205	+	1.00000i	0.0629109	+	0.0363216i
$759$	6.48683			0.235457
$760$		0			0
$761$	23.2302	−	40.2360i	0.842096	−	1.45855i	−0.0460237	−	0.998940i	$-0.514655\pi$
$761$	23.2302	−	40.2360i	0.842096	−	1.45855i	0.888120	−	0.459613i	$-0.152012\pi$
$762$		−	20.3246i		−	0.736281i
$763$	−28.7194	−	16.5811i	−1.03971	−	0.600278i
$764$	7.91886	+	13.7159i	0.286494	+	0.496223i
$765$		0			0
$766$	2.16228			0.0781263
$767$	11.2355	−	18.4868i	0.405691	−	0.667521i
$768$			1.00000i			0.0360844i
$769$	7.48683	+	12.9676i	0.269982	+	0.467623i	0.968857	−	0.247621i	$-0.0796489\pi$
$769$	7.48683	+	12.9676i	0.269982	+	0.467623i	−0.698875	+	0.715244i	$0.746316\pi$
$770$		0			0
$771$	12.9057	−	22.3533i	0.464787	−	0.805035i
$772$			17.3246i			0.623524i
$773$	8.09811	+	4.67544i	0.291269	+	0.168164i	0.638514	−	0.769610i	$-0.279549\pi$
$773$	8.09811	+	4.67544i	0.291269	+	0.168164i	−0.347245	+	0.937774i	$0.612883\pi$
$774$	−0.581139	+	1.00656i	−0.0208886	+	0.0361801i
$775$		0			0
$776$	−8.66228	+	15.0035i	−0.310958	+	0.538594i
$777$	23.2421	−	13.4189i	0.833807	−	0.481399i
$778$	24.5298	−	14.1623i	0.879435	−	0.507742i
$779$	30.0000			1.07486
$780$		0			0
$781$	−42.4868			−1.52030
$782$	1.56871	−	0.905694i	0.0560969	−	0.0323876i
$783$	3.74517	−	2.16228i	0.133842	−	0.0772735i
$784$	1.50000	−	2.59808i	0.0535714	−	0.0927884i
$785$		0			0
$786$	8.16228	−	14.1375i	0.291139	−	0.504267i
$787$	4.75174	+	2.74342i	0.169381	+	0.0977922i	0.582294	−	0.812978i	$-0.302155\pi$
$787$	4.75174	+	2.74342i	0.169381	+	0.0977922i	−0.412913	+	0.910771i	$0.635489\pi$
$788$		−	6.00000i		−	0.213741i
$789$	−0.243416	+	0.421610i	−0.00866586	+	0.0150097i
$790$		0			0
$791$	16.3246	+	28.2750i	0.580434	+	1.00534i
$792$			3.00000i			0.106600i
$793$	−8.40199	+	13.8246i	−0.298363	+	0.490924i
$794$	−11.6754			−0.414346
$795$		0			0
$796$	−4.41886	−	7.65369i	−0.156622	−	0.271278i
$797$	−40.3537	−	23.2982i	−1.42940	−	0.825265i	−0.432328	−	0.901716i	$-0.642308\pi$
$797$	−40.3537	−	23.2982i	−1.42940	−	0.825265i	−0.997073	+	0.0764510i	$0.975641\pi$
$798$		−	10.0000i		−	0.353996i
$799$	2.51317	−	4.35293i	0.0889095	−	0.153996i
$800$		0			0
$801$	−0.837722			−0.0295995
$802$	−14.1375	−	8.16228i	−0.499212	−	0.288220i
$803$	−29.4221	+	16.9868i	−1.03828	+	0.599452i
$804$	−2.00000	−	3.46410i	−0.0705346	−	0.122169i
$805$		0			0
$806$	−8.97367	+	4.91508i	−0.316084	+	0.173126i
$807$			12.8377i			0.451909i
$808$	−7.49035	+	4.32456i	−0.263510	+	0.152137i
$809$	−6.41886	−	11.1178i	−0.225675	−	0.390881i	0.730847	−	0.682542i	$-0.239125\pi$
$809$	−6.41886	−	11.1178i	−0.225675	−	0.390881i	−0.956522	+	0.291661i	$0.905792\pi$
$810$		0			0
$811$	−6.64911			−0.233482			−0.116741	−	0.993162i	$-0.537245\pi$
$811$	−6.64911			−0.233482			−0.116741	+	0.993162i	$0.537245\pi$
$812$	−11.8433	−	6.83772i	−0.415618	−	0.239957i
$813$	−0.281073	−	0.162278i	−0.00985767	−	0.00569133i
$814$	25.4605			0.892390
$815$		0			0
$816$	0.418861	+	0.725489i	0.0146631	+	0.0253972i
$817$	3.18303	−	1.83772i	0.111360	−	0.0642938i
$818$		−	30.3246i		−	1.06027i
$819$	10.0000	−	5.47723i	0.349428	−	0.191390i
$820$		0			0
$821$	−2.16228	−	3.74517i	−0.0754640	−	0.130708i	0.825824	−	0.563928i	$-0.190710\pi$
$821$	−2.16228	−	3.74517i	−0.0754640	−	0.130708i	−0.901288	+	0.433221i	$0.857377\pi$
$822$	−10.3923	+	6.00000i	−0.362473	+	0.209274i
$823$	−7.65369	−	4.41886i	−0.266791	−	0.154032i	0.360637	−	0.932706i	$-0.382559\pi$
$823$	−7.65369	−	4.41886i	−0.266791	−	0.154032i	−0.627428	+	0.778674i	$0.715892\pi$
$824$	5.48683			0.191143
$825$		0			0
$826$	9.48683	−	16.4317i	0.330089	−	0.571731i
$827$		−	27.9737i		−	0.972740i	−0.873753	−	0.486370i	$-0.838321\pi$
$827$		−	27.9737i		−	0.972740i	0.873753	−	0.486370i	$-0.161679\pi$
$828$	1.87259	+	1.08114i	0.0650769	+	0.0375722i
$829$	−2.48683	−	4.30732i	−0.0863713	−	0.149599i	0.819603	−	0.572931i	$-0.194194\pi$
$829$	−2.48683	−	4.30732i	−0.0863713	−	0.149599i	−0.905975	+	0.423332i	$0.860860\pi$
$830$		0			0
$831$	−8.81139			−0.305664
$832$	3.60464	+	0.0811388i	0.124968	+	0.00281298i
$833$		−	2.51317i		−	0.0870761i
$834$	2.83772	+	4.91508i	0.0982623	+	0.170195i
$835$		0			0
$836$	4.74342	−	8.21584i	0.164054	−	0.284151i
$837$		−	2.83772i		−	0.0980860i
$838$	7.79423	+	4.50000i	0.269247	+	0.155450i
$839$	−17.8925	+	30.9908i	−0.617719	+	1.06992i	0.372182	+	0.928160i	$0.378610\pi$
$839$	−17.8925	+	30.9908i	−0.617719	+	1.06992i	−0.989901	+	0.141760i	$0.954724\pi$
$840$		0			0
$841$	5.14911	−	8.91852i	0.177556	−	0.307535i
$842$	24.3892	−	14.0811i	0.840509	−	0.485268i
$843$	−18.6081	+	10.7434i	−0.640898	+	0.370023i
$844$	−13.1623			−0.453064
$845$		0			0
$846$	6.00000			0.206284
$847$	−5.47723	+	3.16228i	−0.188200	+	0.108657i
$848$	−0.725489	+	0.418861i	−0.0249134	+	0.0143838i
$849$	−9.74342	+	16.8761i	−0.334393	+	0.579186i
$850$		0			0
$851$	9.17544	−	15.8923i	0.314530	−	0.544782i
$852$	−12.2649	−	7.08114i	−0.420188	−	0.242596i
$853$		−	18.6491i		−	0.638533i	−0.947665	−	0.319267i	$-0.896563\pi$
$853$		−	18.6491i		−	0.638533i	0.947665	−	0.319267i	$-0.103437\pi$
$854$	−7.09431	+	12.2877i	−0.242762	+	0.420476i
$855$		0			0
$856$	3.00000	+	5.19615i	0.102538	+	0.177601i
$857$		−	42.2719i		−	1.44398i	−0.691903	−	0.721990i	$-0.743228\pi$
$857$		−	42.2719i		−	1.44398i	0.691903	−	0.721990i	$-0.256772\pi$
$858$	10.8139	+	0.243416i	0.369181	+	0.00831010i
$859$	−12.1886			−0.415870			−0.207935	−	0.978143i	$-0.566674\pi$
$859$	−12.1886			−0.415870			−0.207935	+	0.978143i	$0.566674\pi$
$860$		0			0
$861$	15.0000	+	25.9808i	0.511199	+	0.885422i
$862$	21.2062	+	12.2434i	0.722287	+	0.417012i
$863$			19.4605i			0.662443i	0.943553	+	0.331222i	$0.107461\pi$
$863$			19.4605i			0.662443i	−0.943553	+	0.331222i	$0.892539\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$		0			0
$866$	34.6228			1.17653
$867$	−14.1147	−	8.14911i	−0.479359	−	0.276758i
$868$	−7.77142	+	4.48683i	−0.263779	+	0.152293i
$869$	4.25658	+	7.37262i	0.144395	+	0.250099i
$870$		0			0
$871$	−12.6491	+	6.92820i	−0.428599	+	0.234753i
$872$		−	10.4868i		−	0.355129i
$873$	−15.0035	+	8.66228i	−0.507792	+	0.293174i
$874$	−3.41886	−	5.92164i	−0.115645	−	0.200303i
$875$		0			0
$876$	−11.3246			−0.382621
$877$	−49.2001	−	28.4057i	−1.66137	−	0.959192i	−0.972062	−	0.234723i	$-0.924582\pi$
$877$	−49.2001	−	28.4057i	−1.66137	−	0.959192i	−0.689307	−	0.724469i	$-0.742085\pi$
$878$	−31.7391	−	18.3246i	−1.07114	−	0.618424i
$879$	−21.4868			−0.724733
$880$		0			0
$881$	11.2302	+	19.4514i	0.378357	+	0.655333i	0.990823	−	0.135163i	$-0.0431559\pi$
$881$	11.2302	+	19.4514i	0.378357	+	0.655333i	−0.612467	+	0.790496i	$0.709823\pi$
$882$	2.59808	−	1.50000i	0.0874818	−	0.0505076i
$883$			16.6491i			0.560287i	0.959958	+	0.280144i	$0.0903821\pi$
$883$			16.6491i			0.560287i	−0.959958	+	0.280144i	$0.909618\pi$
$884$	2.64911	−	1.45098i	0.0890992	−	0.0488017i
$885$		0			0
$886$	−4.50000	−	7.79423i	−0.151180	−	0.261852i
$887$	7.49035	−	4.32456i	0.251501	−	0.145204i	−0.368950	−	0.929449i	$-0.620283\pi$
$887$	7.49035	−	4.32456i	0.251501	−	0.145204i	0.620452	+	0.784245i	$0.286949\pi$
$888$	7.34981	+	4.24342i	0.246644	+	0.142400i
$889$	−64.2719			−2.15561
$890$		0			0
$891$	−1.50000	+	2.59808i	−0.0502519	+	0.0870388i
$892$		−	26.1359i		−	0.875096i
$893$	−16.4317	−	9.48683i	−0.549865	−	0.317465i
$894$	3.41886	+	5.92164i	0.114344	+	0.198049i
$895$		0			0
$896$	3.16228			0.105644
$897$	4.04905	−	6.66228i	0.135194	−	0.222447i
$898$		−	2.51317i		−	0.0838655i
$899$	6.13594	+	10.6278i	0.204645	+	0.354456i
$900$		0			0
$901$	−0.350889	+	0.607758i	−0.0116898	+	0.0202474i
$902$			28.4605i			0.947631i
$903$	3.18303	+	1.83772i	0.105925	+	0.0611556i
$904$	−5.16228	+	8.94133i	−0.171695	+	0.297384i
$905$		0			0
$906$	4.90569	−	8.49691i	0.162981	−	0.282291i
$907$	49.5040	−	28.5811i	1.64375	−	0.949021i	0.664270	−	0.747493i	$-0.268742\pi$
$907$	49.5040	−	28.5811i	1.64375	−	0.949021i	0.979483	−	0.201529i	$-0.0645909\pi$
$908$	19.0298	−	10.9868i	0.631525	−	0.364611i
$909$	−8.64911			−0.286873
$910$		0			0
$911$	33.1359			1.09784			0.548921	−	0.835874i	$-0.315039\pi$
$911$	33.1359			1.09784			0.548921	+	0.835874i	$0.315039\pi$
$912$	2.73861	−	1.58114i	0.0906845	−	0.0523567i
$913$	−30.2653	+	17.4737i	−1.00163	+	0.578294i
$914$	5.17544	−	8.96413i	0.171188	−	0.296507i
$915$		0			0
$916$	8.24342	−	14.2780i	0.272370	−	0.471759i
$917$	−44.7066	−	25.8114i	−1.47634	−	0.852367i
$918$			0.837722i			0.0276490i
$919$	−8.06797	+	13.9741i	−0.266138	+	0.460964i	−0.967861	−	0.251485i	$-0.919081\pi$
$919$	−8.06797	+	13.9741i	−0.266138	+	0.460964i	0.701723	+	0.712450i	$0.252414\pi$
$920$		0			0
$921$	−8.32456	−	14.4186i	−0.274303	−	0.475107i
$922$		−	17.1623i		−	0.565210i
$923$	−26.5201	+	43.6359i	−0.872920	+	1.43629i
$924$	9.48683			0.312094
$925$		0			0
$926$	2.25658	+	3.90852i	0.0741559	+	0.128442i
$927$	4.75174	+	2.74342i	0.156068	+	0.0901056i
$928$		−	4.32456i		−	0.141960i
$929$	7.67544	−	13.2943i	0.251823	−	0.436171i	−0.712205	−	0.701972i	$-0.752303\pi$
$929$	7.67544	−	13.2943i	0.251823	−	0.436171i	0.964028	+	0.265801i	$0.0856365\pi$
$930$		0			0
$931$	−9.48683			−0.310918
$932$	11.8433	+	6.83772i	0.387940	+	0.223977i
$933$	−5.61776	+	3.24342i	−0.183917	+	0.106185i
$934$	1.50000	+	2.59808i	0.0490815	+	0.0850117i
$935$		0			0
$936$	3.08114	+	1.87259i	0.100710	+	0.0612074i
$937$			4.35089i			0.142137i	0.997471	+	0.0710687i	$0.0226409\pi$
$937$			4.35089i			0.142137i	−0.997471	+	0.0710687i	$0.977359\pi$
$938$	−10.9545	+	6.32456i	−0.357676	+	0.206504i
$939$	3.82456	+	6.62432i	0.124810	+	0.216177i
$940$		0			0
$941$	−12.0000			−0.391189			−0.195594	−	0.980685i	$-0.562664\pi$
$941$	−12.0000			−0.391189			−0.195594	+	0.980685i	$0.562664\pi$
$942$	−13.9969	−	8.08114i	−0.456045	−	0.263298i
$943$	17.7649	+	10.2566i	0.578506	+	0.334000i
$944$	6.00000			0.195283
$945$		0			0
$946$	1.74342	+	3.01969i	0.0566834	+	0.0981785i
$947$	−41.2653	+	23.8246i	−1.34094	+	0.774194i	−0.986946	−	0.161052i	$-0.948511\pi$
$947$	−41.2653	+	23.8246i	−1.34094	+	0.774194i	−0.353998	+	0.935246i	$0.615178\pi$
$948$			2.83772i			0.0921649i
$949$	−0.918861	+	40.8209i	−0.0298275	+	1.32510i
$950$		0			0
$951$	15.9057	+	27.5495i	0.515777	+	0.893353i
$952$	2.29420	−	1.32456i	0.0743554	−	0.0429291i
$953$	29.8437	+	17.2302i	0.966731	+	0.558143i	0.898238	−	0.439509i	$-0.144848\pi$
$953$	29.8437	+	17.2302i	0.966731	+	0.558143i	0.0684931	+	0.997652i	$0.478181\pi$
$954$	−0.837722			−0.0271223
$955$		0			0
$956$	−9.24342	+	16.0101i	−0.298953	+	0.517803i
$957$		−	12.9737i		−	0.419379i
$958$	−11.8433	−	6.83772i	−0.382639	−	0.220917i
$959$	18.9737	+	32.8634i	0.612692	+	1.06121i
$960$		0			0
$961$	−22.9473			−0.740237
$962$	15.8923	−	26.1491i	0.512389	−	0.843081i
$963$			6.00000i			0.193347i
$964$	4.00000	+	6.92820i	0.128831	+	0.223142i
$965$		0			0
$966$	3.41886	−	5.92164i	0.110000	−	0.190526i
$967$			52.9737i			1.70352i	0.523934	+	0.851759i	$0.324464\pi$
$967$			52.9737i			1.70352i	−0.523934	+	0.851759i	$0.675536\pi$
$968$	−1.73205	−	1.00000i	−0.0556702	−	0.0321412i
$969$	1.32456	−	2.29420i	0.0425508	−	0.0737002i
$970$		0			0
$971$	−21.0000	+	36.3731i	−0.673922	+	1.16727i	0.302861	+	0.953035i	$0.402058\pi$
$971$	−21.0000	+	36.3731i	−0.673922	+	1.16727i	−0.976783	+	0.214232i	$0.931275\pi$
$972$	−0.866025	+	0.500000i	−0.0277778	+	0.0160375i
$973$	15.5428	−	8.97367i	0.498281	−	0.287683i
$974$	−3.16228			−0.101326
$975$		0			0
$976$	−4.48683			−0.143620
$977$	22.2356	−	12.8377i	0.711379	−	0.410715i	−0.100192	−	0.994968i	$-0.531946\pi$
$977$	22.2356	−	12.8377i	0.711379	−	0.410715i	0.811572	+	0.584253i	$0.198612\pi$
$978$	−13.6931	+	7.90569i	−0.437856	+	0.252796i
$979$	−1.25658	+	2.17647i	−0.0401606	+	0.0695602i
$980$		0			0
$981$	5.24342	−	9.08186i	0.167409	−	0.289962i
$982$	19.0298	+	10.9868i	0.607264	+	0.350604i
$983$			29.2982i			0.934468i	0.884134	+	0.467234i	$0.154749\pi$
$983$			29.2982i			0.934468i	−0.884134	+	0.467234i	$0.845251\pi$
$984$	−4.74342	+	8.21584i	−0.151215	+	0.261911i
$985$		0			0
$986$	−1.81139	−	3.13742i	−0.0576864	−	0.0999157i
$987$		−	18.9737i		−	0.603938i
$988$	−5.47723	−	10.0000i	−0.174254	−	0.318142i
$989$	2.51317			0.0799141
$990$		0			0
$991$	−6.93203	−	12.0066i	−0.220203	−	0.381403i	0.734666	−	0.678429i	$-0.237339\pi$
$991$	−6.93203	−	12.0066i	−0.220203	−	0.381403i	−0.954870	+	0.297026i	$0.904005\pi$
$992$	−2.45754	−	1.41886i	−0.0780270	−	0.0450489i
$993$		−	15.1623i		−	0.481160i
$994$	−22.3925	+	38.7850i	−0.710248	+	1.23019i
$995$		0			0
$996$	−11.6491			−0.369116
$997$	38.9483	+	22.4868i	1.23351	+	0.712165i	0.967759	−	0.251878i	$-0.0810480\pi$
$997$	38.9483	+	22.4868i	1.23351	+	0.712165i	0.265747	+	0.964043i	$0.414381\pi$
$998$	−34.4777	+	19.9057i	−1.09137	+	0.630104i
$999$	4.24342	+	7.34981i	0.134256	+	0.232538i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1950.2.i.ba.451.1	✓	4	65.48	odd	12
1950.2.i.ba.601.1	yes	4	5.3	odd	4
1950.2.i.bf.451.2	yes	4	65.22	odd	12
1950.2.i.bf.601.2	yes	4	5.2	odd	4
1950.2.z.o.1699.2		8	13.9	even	3	inner
1950.2.z.o.1699.3		8	65.9	even	6	inner
1950.2.z.o.1849.2		8	5.4	even	2	inner
1950.2.z.o.1849.3		8	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{6} +(-2.73861 - 1.58114i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{6} +(-2.73861 - 1.58114i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(-1.50000 - 2.59808i) q^{11} -1.00000i q^{12} +(-3.60464 - 0.0811388i) q^{13} -3.16228 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.725489 - 0.418861i) q^{17} -1.00000i q^{18} +(-1.58114 + 2.73861i) q^{19} -3.16228 q^{21} +(-2.59808 - 1.50000i) q^{22} +(-1.87259 + 1.08114i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-3.16228 + 1.73205i) q^{26} -1.00000i q^{27} +(-2.73861 + 1.58114i) q^{28} +(2.16228 + 3.74517i) q^{29} +2.83772 q^{31} +(-0.866025 - 0.500000i) q^{32} +(-2.59808 - 1.50000i) q^{33} -0.837722 q^{34} +(-0.500000 - 0.866025i) q^{36} +(-7.34981 + 4.24342i) q^{37} +3.16228i q^{38} +(-3.16228 + 1.73205i) q^{39} +(-4.74342 - 8.21584i) q^{41} +(-2.73861 + 1.58114i) q^{42} +(-1.00656 - 0.581139i) q^{43} -3.00000 q^{44} +(-1.08114 + 1.87259i) q^{46} +6.00000i q^{47} +(-0.866025 - 0.500000i) q^{48} +(1.50000 + 2.59808i) q^{49} -0.837722 q^{51} +(-1.87259 + 3.08114i) q^{52} -0.837722i q^{53} +(-0.500000 - 0.866025i) q^{54} +(-1.58114 + 2.73861i) q^{56} +3.16228i q^{57} +(3.74517 + 2.16228i) q^{58} +(-3.00000 + 5.19615i) q^{59} +(2.24342 - 3.88571i) q^{61} +(2.45754 - 1.41886i) q^{62} +(-2.73861 + 1.58114i) q^{63} -1.00000 q^{64} -3.00000 q^{66} +(3.46410 - 2.00000i) q^{67} +(-0.725489 + 0.418861i) q^{68} +(-1.08114 + 1.87259i) q^{69} +(7.08114 - 12.2649i) q^{71} +(-0.866025 - 0.500000i) q^{72} -11.3246i q^{73} +(-4.24342 + 7.34981i) q^{74} +(1.58114 + 2.73861i) q^{76} +9.48683i q^{77} +(-1.87259 + 3.08114i) q^{78} -2.83772 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-8.21584 - 4.74342i) q^{82} -11.6491i q^{83} +(-1.58114 + 2.73861i) q^{84} -1.16228 q^{86} +(3.74517 + 2.16228i) q^{87} +(-2.59808 + 1.50000i) q^{88} +(-0.418861 - 0.725489i) q^{89} +(9.74342 + 5.92164i) q^{91} +2.16228i q^{92} +(2.45754 - 1.41886i) q^{93} +(3.00000 + 5.19615i) q^{94} -1.00000 q^{96} +(-15.0035 - 8.66228i) q^{97} +(2.59808 + 1.50000i) q^{98} -3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4} + 4 q^{6} + 4 q^{9}+O(q^{10}) \) 8 * q + 4 * q^4 + 4 * q^6 + 4 * q^9	\( 8 q + 4 q^{4} + 4 q^{6} + 4 q^{9} - 12 q^{11} - 4 q^{16} - 4 q^{24} - 8 q^{29} + 48 q^{31} - 32 q^{34} - 4 q^{36} - 24 q^{44} + 4 q^{46} + 12 q^{49} - 32 q^{51} - 4 q^{54} - 24 q^{59} - 20 q^{61} - 8 q^{64} - 24 q^{66} + 4 q^{69} + 44 q^{71} + 4 q^{74} - 48 q^{79} - 4 q^{81} + 16 q^{86} - 16 q^{89} + 40 q^{91} + 24 q^{94} - 8 q^{96} - 24 q^{99}+O(q^{100}) \) 8 * q + 4 * q^4 + 4 * q^6 + 4 * q^9 - 12 * q^11 - 4 * q^16 - 4 * q^24 - 8 * q^29 + 48 * q^31 - 32 * q^34 - 4 * q^36 - 24 * q^44 + 4 * q^46 + 12 * q^49 - 32 * q^51 - 4 * q^54 - 24 * q^59 - 20 * q^61 - 8 * q^64 - 24 * q^66 + 4 * q^69 + 44 * q^71 + 4 * q^74 - 48 * q^79 - 4 * q^81 + 16 * q^86 - 16 * q^89 + 40 * q^91 + 24 * q^94 - 8 * q^96 - 24 * q^99

Introduction

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