LMFDB - Embedded newform 1950.2.z.o.1849.4

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			1849.4
Root			$-0.578737 + 2.15988i$ of defining polynomial
Character	$\chi$	$=$	1950.1849
Dual form			1950.2.z.o.1699.4

$q$-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} +(1.87259 + 3.08114i) q^{13} +3.16228 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-6.20271 - 3.58114i) q^{17} -1.00000i q^{18} +(1.58114 - 2.73861i) q^{19} +3.16228 q^{21} +(-2.59808 - 1.50000i) q^{22} +(3.60464 - 2.08114i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(3.16228 + 1.73205i) q^{26} -1.00000i q^{27} +(2.73861 - 1.58114i) q^{28} +(-4.16228 - 7.20928i) q^{29} +9.16228 q^{31} +(-0.866025 - 0.500000i) q^{32} +(-2.59808 - 1.50000i) q^{33} -7.16228 q^{34} +(-0.500000 - 0.866025i) q^{36} +(9.08186 - 5.24342i) q^{37} -3.16228i q^{38} +(3.16228 + 1.73205i) q^{39} +(4.74342 + 8.21584i) q^{41} +(2.73861 - 1.58114i) q^{42} +(4.47066 + 2.58114i) q^{43} -3.00000 q^{44} +(2.08114 - 3.60464i) q^{46} +6.00000i q^{47} +(-0.866025 - 0.500000i) q^{48} +(1.50000 + 2.59808i) q^{49} -7.16228 q^{51} +(3.60464 - 0.0811388i) q^{52} -7.16228i q^{53} +(-0.500000 - 0.866025i) q^{54} +(1.58114 - 2.73861i) q^{56} -3.16228i q^{57} +(-7.20928 - 4.16228i) q^{58} +(-3.00000 + 5.19615i) q^{59} +(-7.24342 + 12.5460i) q^{61} +(7.93477 - 4.58114i) q^{62} +(2.73861 - 1.58114i) q^{63} -1.00000 q^{64} -3.00000 q^{66} +(3.46410 - 2.00000i) q^{67} +(-6.20271 + 3.58114i) q^{68} +(2.08114 - 3.60464i) q^{69} +(3.91886 - 6.78767i) q^{71} +(-0.866025 - 0.500000i) q^{72} +1.32456i q^{73} +(5.24342 - 9.08186i) q^{74} +(-1.58114 - 2.73861i) q^{76} -9.48683i q^{77} +(3.60464 - 0.0811388i) q^{78} -9.16228 q^{79} +(-0.500000 - 0.866025i) q^{81} +(8.21584 + 4.74342i) q^{82} +13.6491i q^{83} +(1.58114 - 2.73861i) q^{84} +5.16228 q^{86} +(-7.20928 - 4.16228i) q^{87} +(-2.59808 + 1.50000i) q^{88} +(-3.58114 - 6.20271i) q^{89} +(0.256584 + 11.3989i) q^{91} -4.16228i q^{92} +(7.93477 - 4.58114i) q^{93} +(3.00000 + 5.19615i) q^{94} -1.00000 q^{96} +(-4.04905 - 2.33772i) 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	0.918441	−	0.395558i	$-0.129449\pi$
$7$	2.73861	+	1.58114i	1.03510	+	0.597614i	0.116657	+	0.993172i	$0.462782\pi$
$8$		−	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
$13$	1.87259	+	3.08114i	0.519362	+	0.854554i
$13$	1.87259	+	3.08114i	0.519362	+	0.854554i
$14$	3.16228			0.845154
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−6.20271	−	3.58114i	−1.50438	−	0.868554i	−0.999987	−	0.00507902i	$-0.998383\pi$
$17$	−6.20271	−	3.58114i	−1.50438	−	0.868554i	−0.504392	−	0.863475i	$-0.668283\pi$
$18$		−	1.00000i		−	0.235702i
$19$	1.58114	−	2.73861i	0.362738	−	0.628281i	−0.625672	−	0.780086i	$-0.715175\pi$
$19$	1.58114	−	2.73861i	0.362738	−	0.628281i	0.988410	+	0.151805i	$0.0485086\pi$
$20$		0			0
$21$	3.16228			0.690066
$22$	−2.59808	−	1.50000i	−0.553912	−	0.319801i
$23$	3.60464	−	2.08114i	0.751619	−	0.433947i	−0.0746596	−	0.997209i	$-0.523787\pi$
$23$	3.60464	−	2.08114i	0.751619	−	0.433947i	0.826279	+	0.563262i	$0.190454\pi$
$24$	−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
$29$	−4.16228	−	7.20928i	−0.772916	−	1.33873i	−0.935959	−	0.352110i	$-0.885464\pi$
$29$	−4.16228	−	7.20928i	−0.772916	−	1.33873i	0.163043	−	0.986619i	$-0.447869\pi$
$30$		0			0
$31$	9.16228			1.64559			0.822797	−	0.568336i	$-0.192412\pi$
$31$	9.16228			1.64559			0.822797	+	0.568336i	$0.192412\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	−2.59808	−	1.50000i	−0.452267	−	0.261116i
$34$	−7.16228			−1.22832
$35$		0			0
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	9.08186	−	5.24342i	1.49305	−	0.862012i	0.493081	−	0.869983i	$-0.335871\pi$
$37$	9.08186	−	5.24342i	1.49305	−	0.862012i	0.999968	+	0.00797106i	$0.00253729\pi$
$38$		−	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	$0.0988854\pi$
$41$	4.74342	+	8.21584i	0.740797	+	1.28310i	−0.211336	+	0.977414i	$0.567781\pi$
$42$	2.73861	−	1.58114i	0.422577	−	0.243975i
$43$	4.47066	+	2.58114i	0.681770	+	0.393620i	0.800522	−	0.599304i	$-0.204556\pi$
$43$	4.47066	+	2.58114i	0.681770	+	0.393620i	−0.118752	+	0.992924i	$0.537889\pi$
$44$	−3.00000			−0.452267
$45$		0			0
$46$	2.08114	−	3.60464i	0.306847	−	0.531475i
$47$			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
$51$	−7.16228			−1.00292
$52$	3.60464	−	0.0811388i	0.499873	−	0.0112519i
$53$		−	7.16228i		−	0.983814i	−0.870648	−	0.491907i	$-0.836300\pi$
$53$		−	7.16228i		−	0.983814i	0.870648	−	0.491907i	$-0.163700\pi$
$54$	−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
$58$	−7.20928	−	4.16228i	−0.946624	−	0.546534i
$59$	−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
$61$	−7.24342	+	12.5460i	−0.927424	+	1.60635i	−0.139810	+	0.990178i	$0.544649\pi$
$61$	−7.24342	+	12.5460i	−0.927424	+	1.60635i	−0.787615	+	0.616168i	$0.788684\pi$
$62$	7.93477	−	4.58114i	1.00772	−	0.581805i
$63$	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	$0.254762\pi$
$68$	−6.20271	+	3.58114i	−0.752190	+	0.434277i
$69$	2.08114	−	3.60464i	0.250540	−	0.433947i
$70$		0			0
$71$	3.91886	−	6.78767i	0.465083	−	0.805548i	−0.534122	−	0.845407i	$-0.679358\pi$
$71$	3.91886	−	6.78767i	0.465083	−	0.805548i	0.999205	+	0.0398596i	$0.0126911\pi$
$72$	−0.866025	−	0.500000i	−0.102062	−	0.0589256i
$73$			1.32456i			0.155027i	0.996991	+	0.0775137i	$0.0246982\pi$
$73$			1.32456i			0.155027i	−0.996991	+	0.0775137i	$0.975302\pi$
$74$	5.24342	−	9.08186i	0.609535	−	1.05575i
$75$		0			0
$76$	−1.58114	−	2.73861i	−0.181369	−	0.314140i
$77$		−	9.48683i		−	1.08112i
$78$	3.60464	−	0.0811388i	0.408145	−	0.00918716i
$79$	−9.16228			−1.03084			−0.515418	−	0.856939i	$-0.672363\pi$
$79$	−9.16228			−1.03084			−0.515418	+	0.856939i	$0.672363\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	8.21584	+	4.74342i	0.907288	+	0.523823i
$83$			13.6491i			1.49818i	0.662466	+	0.749092i	$0.269510\pi$
$83$			13.6491i			1.49818i	−0.662466	+	0.749092i	$0.730490\pi$
$84$	1.58114	−	2.73861i	0.172516	−	0.298807i
$85$		0			0
$86$	5.16228			0.556663
$87$	−7.20928	−	4.16228i	−0.772916	−	0.446243i
$88$	−2.59808	+	1.50000i	−0.276956	+	0.159901i
$89$	−3.58114	−	6.20271i	−0.379600	−	0.657486i	0.611404	−	0.791319i	$-0.290605\pi$
$89$	−3.58114	−	6.20271i	−0.379600	−	0.657486i	−0.991004	+	0.133832i	$0.957272\pi$
$90$		0			0
$91$	0.256584	+	11.3989i	0.0268973	+	1.19493i
$92$		−	4.16228i		−	0.433947i
$93$	7.93477	−	4.58114i	0.822797	−	0.475042i
$94$	3.00000	+	5.19615i	0.309426	+	0.535942i
$95$		0			0
$96$	−1.00000			−0.102062
$97$	−4.04905	−	2.33772i	−0.411119	−	0.237360i	0.280151	−	0.959956i	$-0.409615\pi$
$97$	−4.04905	−	2.33772i	−0.411119	−	0.237360i	−0.691270	+	0.722596i	$0.742949\pi$
$98$	2.59808	+	1.50000i	0.262445	+	0.151523i
$99$	−3.00000			−0.301511
$100$		0			0
$101$	8.32456	+	14.4186i	0.828324	+	1.43470i	0.899352	+	0.437225i	$0.144039\pi$
$101$	8.32456	+	14.4186i	0.828324	+	1.43470i	−0.0710278	+	0.997474i	$0.522628\pi$
$102$	−6.20271	+	3.58114i	−0.614160	+	0.354586i
$103$		−	13.4868i		−	1.32890i	−0.747334	−	0.664449i	$-0.768666\pi$
$103$		−	13.4868i		−	1.32890i	0.747334	−	0.664449i	$-0.231334\pi$
$104$	3.08114	−	1.87259i	0.302131	−	0.183622i
$105$		0			0
$106$	−3.58114	−	6.20271i	−0.347831	−	0.602461i
$107$	−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
$109$	−8.48683			−0.812891			−0.406446	−	0.913675i	$-0.633232\pi$
$109$	−8.48683			−0.812891			−0.406446	+	0.913675i	$0.633232\pi$
$110$		0			0
$111$	5.24342	−	9.08186i	0.497683	−	0.862012i
$112$		−	3.16228i		−	0.298807i
$113$	2.01312	+	1.16228i	0.189379	+	0.109338i	0.591692	−	0.806164i	$-0.298460\pi$
$113$	2.01312	+	1.16228i	0.189379	+	0.109338i	−0.402313	+	0.915502i	$0.631794\pi$
$114$	−1.58114	−	2.73861i	−0.148087	−	0.256495i
$115$		0			0
$116$	−8.32456			−0.772916
$117$	3.60464	−	0.0811388i	0.333249	−	0.00750129i
$118$			6.00000i			0.552345i
$119$	−11.3246	−	19.6147i	−1.03812	−	1.79808i
$120$		0			0
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$			14.4868i			1.31158i
$123$	8.21584	+	4.74342i	0.740797	+	0.427699i
$124$	4.58114	−	7.93477i	0.411398	−	0.712563i
$125$		0			0
$126$	1.58114	−	2.73861i	0.140859	−	0.243975i
$127$	6.64713	−	3.83772i	0.589837	−	0.340543i	−0.175196	−	0.984534i	$-0.556056\pi$
$127$	6.64713	−	3.83772i	0.589837	−	0.340543i	0.765033	+	0.643991i	$0.222723\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	5.16228			0.454513
$130$		0			0
$131$	3.67544			0.321125			0.160563	−	0.987026i	$-0.448669\pi$
$131$	3.67544			0.321125			0.160563	+	0.987026i	$0.448669\pi$
$132$	−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
$136$	−3.58114	+	6.20271i	−0.307080	+	0.531878i
$137$	−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	$0.837990\pi$
$138$		−	4.16228i		−	0.354317i
$139$	−9.16228	+	15.8695i	−0.777134	+	1.34604i	0.156453	+	0.987685i	$0.449994\pi$
$139$	−9.16228	+	15.8695i	−0.777134	+	1.34604i	−0.933587	+	0.358351i	$0.883339\pi$
$140$		0			0
$141$	3.00000	+	5.19615i	0.252646	+	0.437595i
$142$		−	7.83772i		−	0.657727i
$143$	5.19615	−	9.48683i	0.434524	−	0.793329i
$144$	−1.00000			−0.0833333
$145$		0			0
$146$	0.662278	+	1.14710i	0.0548105	+	0.0949346i
$147$	2.59808	+	1.50000i	0.214286	+	0.123718i
$148$		−	10.4868i		−	0.862012i
$149$	−6.58114	+	11.3989i	−0.539148	+	0.933832i	0.459802	+	0.888021i	$0.347920\pi$
$149$	−6.58114	+	11.3989i	−0.539148	+	0.933832i	−0.998950	+	0.0458102i	$0.985413\pi$
$150$		0			0
$151$	−21.8114			−1.77499			−0.887493	−	0.460822i	$-0.847555\pi$
$151$	−21.8114			−1.77499			−0.887493	+	0.460822i	$0.847555\pi$
$152$	−2.73861	−	1.58114i	−0.222131	−	0.128247i
$153$	−6.20271	+	3.58114i	−0.501460	+	0.289518i
$154$	−4.74342	−	8.21584i	−0.382235	−	0.662051i
$155$		0			0
$156$	3.08114	−	1.87259i	0.246689	−	0.149927i
$157$		−	9.83772i		−	0.785136i	−0.919723	−	0.392568i	$-0.871587\pi$
$157$		−	9.83772i		−	0.785136i	0.919723	−	0.392568i	$-0.128413\pi$
$158$	−7.93477	+	4.58114i	−0.631256	+	0.364456i
$159$	−3.58114	−	6.20271i	−0.284003	−	0.491907i
$160$		0			0
$161$	13.1623			1.03733
$162$	−0.866025	−	0.500000i	−0.0680414	−	0.0392837i
$163$	13.6931	+	7.90569i	1.07252	+	0.619222i	0.928870	−	0.370406i	$-0.120782\pi$
$163$	13.6931	+	7.90569i	1.07252	+	0.619222i	0.143654	+	0.989628i	$0.454115\pi$
$164$	9.48683			0.740797
$165$		0			0
$166$	6.82456	+	11.8205i	0.529688	+	0.917447i
$167$	−1.59151	+	0.918861i	−0.123155	+	0.0711036i	−0.560312	−	0.828282i	$-0.689319\pi$
$167$	−1.59151	+	0.918861i	−0.123155	+	0.0711036i	0.437157	+	0.899385i	$0.355985\pi$
$168$		−	3.16228i		−	0.243975i
$169$	−5.98683	+	11.5394i	−0.460526	+	0.887646i
$170$		0			0
$171$	−1.58114	−	2.73861i	−0.120913	−	0.209427i
$172$	4.47066	−	2.58114i	0.340885	−	0.196810i
$173$	12.4054	+	7.16228i	0.943167	+	0.544538i	0.890952	−	0.454098i	$-0.150038\pi$
$173$	12.4054	+	7.16228i	0.943167	+	0.544538i	0.0522155	+	0.998636i	$0.483372\pi$
$174$	−8.32456			−0.631083
$175$		0			0
$176$	−1.50000	+	2.59808i	−0.113067	+	0.195837i
$177$			6.00000i			0.450988i
$178$	−6.20271	−	3.58114i	−0.464913	−	0.268418i
$179$	−0.824555	−	1.42817i	−0.0616302	−	0.106747i	0.833564	−	0.552423i	$-0.186297\pi$
$179$	−0.824555	−	1.42817i	−0.0616302	−	0.106747i	−0.895194	+	0.445676i	$0.852963\pi$
$180$		0			0
$181$	−18.8114			−1.39824			−0.699120	−	0.715005i	$-0.746425\pi$
$181$	−18.8114			−1.39824			−0.699120	+	0.715005i	$0.746425\pi$
$182$	5.92164	+	9.74342i	0.438941	+	0.722230i
$183$			14.4868i			1.07090i
$184$	−2.08114	−	3.60464i	−0.153424	−	0.265737i
$185$		0			0
$186$	4.58114	−	7.93477i	0.335905	−	0.581805i
$187$			21.4868i			1.57127i
$188$	5.19615	+	3.00000i	0.378968	+	0.218797i
$189$	1.58114	−	2.73861i	0.115011	−	0.199205i
$190$		0			0
$191$	−11.0811	+	19.1931i	−0.801803	+	1.38876i	0.116625	+	0.993176i	$0.462792\pi$
$191$	−11.0811	+	19.1931i	−0.801803	+	1.38876i	−0.918428	+	0.395588i	$0.870541\pi$
$192$	−0.866025	+	0.500000i	−0.0625000	+	0.0360844i
$193$	−4.04905	+	2.33772i	−0.291457	+	0.168273i	−0.638599	−	0.769540i	$-0.720486\pi$
$193$	−4.04905	+	2.33772i	−0.291457	+	0.168273i	0.347142	+	0.937813i	$0.387152\pi$
$194$	−4.67544			−0.335677
$195$		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
$199$	7.58114	−	13.1309i	0.537413	−	0.930826i	−0.461630	−	0.887073i	$-0.652735\pi$
$199$	7.58114	−	13.1309i	0.537413	−	0.930826i	0.999042	−	0.0437533i	$-0.0139316\pi$
$200$		0			0
$201$	2.00000	−	3.46410i	0.141069	−	0.244339i
$202$	14.4186	+	8.32456i	1.01449	+	0.585714i
$203$		−	26.3246i		−	1.84762i
$204$	−3.58114	+	6.20271i	−0.250730	+	0.434277i
$205$		0			0
$206$	−6.74342	−	11.6799i	−0.469836	−	0.813780i
$207$		−	4.16228i		−	0.289298i
$208$	1.73205	−	3.16228i	0.120096	−	0.219265i
$209$	−9.48683			−0.656218
$210$		0			0
$211$	−3.41886	−	5.92164i	−0.235364	−	0.407663i	0.724014	−	0.689785i	$-0.242295\pi$
$211$	−3.41886	−	5.92164i	−0.235364	−	0.407663i	−0.959378	+	0.282122i	$0.908962\pi$
$212$	−6.20271	−	3.58114i	−0.426004	−	0.245954i
$213$		−	7.83772i		−	0.537032i
$214$	−3.00000	+	5.19615i	−0.205076	+	0.355202i
$215$		0			0
$216$	−1.00000			−0.0680414
$217$	25.0919	+	14.4868i	1.70335	+	0.983430i
$218$	−7.34981	+	4.24342i	−0.497792	+	0.287400i
$219$	0.662278	+	1.14710i	0.0447526	+	0.0775137i
$220$		0			0
$221$	−0.581139	−	25.8174i	−0.0390916	−	1.73667i
$222$		−	10.4868i		−	0.703830i
$223$	−15.7062	+	9.06797i	−1.05176	+	0.607236i	−0.923143	−	0.384457i	$-0.874389\pi$
$223$	−15.7062	+	9.06797i	−1.05176	+	0.607236i	−0.128621	+	0.991694i	$0.541055\pi$
$224$	−1.58114	−	2.73861i	−0.105644	−	0.182981i
$225$		0			0
$226$	2.32456			0.154627
$227$	−13.8336	−	7.98683i	−0.918168	−	0.530105i	−0.0351181	−	0.999383i	$-0.511181\pi$
$227$	−13.8336	−	7.98683i	−0.918168	−	0.530105i	−0.883050	+	0.469278i	$0.844514\pi$
$228$	−2.73861	−	1.58114i	−0.181369	−	0.104713i
$229$	−2.48683			−0.164335			−0.0821673	−	0.996619i	$-0.526184\pi$
$229$	−2.48683			−0.164335			−0.0821673	+	0.996619i	$0.526184\pi$
$230$		0			0
$231$	−4.74342	−	8.21584i	−0.312094	−	0.540562i
$232$	−7.20928	+	4.16228i	−0.473312	+	0.273267i
$233$			26.3246i			1.72458i	0.506416	+	0.862289i	$0.330970\pi$
$233$			26.3246i			1.72458i	−0.506416	+	0.862289i	$0.669030\pi$
$234$	3.08114	−	1.87259i	0.201420	−	0.122415i
$235$		0			0
$236$	3.00000	+	5.19615i	0.195283	+	0.338241i
$237$	−7.93477	+	4.58114i	−0.515418	+	0.297577i
$238$	−19.6147	−	11.3246i	−1.27143	−	0.734062i
$239$	0.486833			0.0314906			0.0157453	−	0.999876i	$-0.494988\pi$
$239$	0.486833			0.0314906			0.0157453	+	0.999876i	$0.494988\pi$
$240$		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
$244$	7.24342	+	12.5460i	0.463712	+	0.803173i
$245$		0			0
$246$	9.48683			0.604858
$247$	11.3989	−	0.256584i	0.725293	−	0.0163260i
$248$		−	9.16228i		−	0.581805i
$249$	6.82456	+	11.8205i	0.432489	+	0.749092i
$250$		0			0
$251$	−7.50000	+	12.9904i	−0.473396	+	0.819946i	−0.999536	−	0.0304521i	$-0.990305\pi$
$251$	−7.50000	+	12.9904i	−0.473396	+	0.819946i	0.526140	+	0.850398i	$0.323639\pi$
$252$		−	3.16228i		−	0.199205i
$253$	−10.8139	−	6.24342i	−0.679865	−	0.392520i
$254$	3.83772	−	6.64713i	0.240800	−	0.417078i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−5.03281	+	2.90569i	−0.313938	+	0.181252i	−0.648687	−	0.761055i	$-0.724682\pi$
$257$	−5.03281	+	2.90569i	−0.313938	+	0.181252i	0.334749	+	0.942307i	$0.391348\pi$
$258$	4.47066	−	2.58114i	0.278331	−	0.160695i
$259$	33.1623			2.06060
$260$		0			0
$261$	−8.32456			−0.515277
$262$	3.18303	−	1.83772i	0.196648	−	0.113535i
$263$	16.0101	−	9.24342i	0.987223	−	0.569973i	0.0827800	−	0.996568i	$-0.473620\pi$
$263$	16.0101	−	9.24342i	0.987223	−	0.569973i	0.904443	+	0.426594i	$0.140287\pi$
$264$	−1.50000	+	2.59808i	−0.0923186	+	0.159901i
$265$		0			0
$266$	5.00000	−	8.66025i	0.306570	−	0.530994i
$267$	−6.20271	−	3.58114i	−0.379600	−	0.219162i
$268$		−	4.00000i		−	0.244339i
$269$	−9.58114	+	16.5950i	−0.584172	+	1.01182i	0.410806	+	0.911723i	$0.365247\pi$
$269$	−9.58114	+	16.5950i	−0.584172	+	1.01182i	−0.994978	+	0.100093i	$0.968086\pi$
$270$		0			0
$271$	6.16228	+	10.6734i	0.374332	+	0.648362i	0.990227	−	0.139467i	$-0.0445388\pi$
$271$	6.16228	+	10.6734i	0.374332	+	0.648362i	−0.615895	+	0.787828i	$0.711205\pi$
$272$			7.16228i			0.434277i
$273$	5.92164	+	9.74342i	0.358394	+	0.589698i
$274$	−12.0000			−0.724947
$275$		0			0
$276$	−2.08114	−	3.60464i	−0.125270	−	0.216974i
$277$	19.7552	+	11.4057i	1.18698	+	0.685302i	0.957618	−	0.288040i	$-0.0930037\pi$
$277$	19.7552	+	11.4057i	1.18698	+	0.685302i	0.229359	+	0.973342i	$0.426337\pi$
$278$			18.3246i			1.09903i
$279$	4.58114	−	7.93477i	0.274266	−	0.475042i
$280$		0			0
$281$	−2.51317			−0.149923			−0.0749615	−	0.997186i	$-0.523883\pi$
$281$	−2.51317			−0.149923			−0.0749615	+	0.997186i	$0.523883\pi$
$282$	5.19615	+	3.00000i	0.309426	+	0.178647i
$283$	−0.444416	+	0.256584i	−0.0264178	+	0.0152523i	−0.513151	−	0.858299i	$-0.671522\pi$
$283$	−0.444416	+	0.256584i	−0.0264178	+	0.0152523i	0.486733	+	0.873551i	$0.338188\pi$
$284$	−3.91886	−	6.78767i	−0.232542	−	0.402774i
$285$		0			0
$286$	−0.243416	−	10.8139i	−0.0143935	−	0.639440i
$287$			30.0000i			1.77084i
$288$	−0.866025	+	0.500000i	−0.0510310	+	0.0294628i
$289$	17.1491	+	29.7031i	1.00877	+	1.74724i
$290$		0			0
$291$	−4.67544			−0.274079
$292$	1.14710	+	0.662278i	0.0671289	+	0.0387569i
$293$	−2.17647	−	1.25658i	−0.127151	−	0.0734104i	0.435076	−	0.900394i	$-0.356722\pi$
$293$	−2.17647	−	1.25658i	−0.127151	−	0.0734104i	−0.562226	+	0.826984i	$0.690055\pi$
$294$	3.00000			0.174964
$295$		0			0
$296$	−5.24342	−	9.08186i	−0.304767	−	0.527873i
$297$	−2.59808	+	1.50000i	−0.150756	+	0.0870388i
$298$			13.1623i			0.762470i
$299$	13.1623	+	7.20928i	0.761194	+	0.416923i
$300$		0			0
$301$	8.16228	+	14.1375i	0.470466	+	0.814871i
$302$	−18.8892	+	10.9057i	−1.08695	+	0.627552i
$303$	14.4186	+	8.32456i	0.828324	+	0.478233i
$304$	−3.16228			−0.181369
$305$		0			0
$306$	−3.58114	+	6.20271i	−0.204720	+	0.354586i
$307$			8.64911i			0.493631i	0.969063	+	0.246815i	$0.0793841\pi$
$307$			8.64911i			0.493631i	−0.969063	+	0.246815i	$0.920616\pi$
$308$	−8.21584	−	4.74342i	−0.468141	−	0.270281i
$309$	−6.74342	−	11.6799i	−0.383620	−	0.664449i
$310$		0			0
$311$	12.4868			0.708063			0.354032	−	0.935233i	$-0.384811\pi$
$311$	12.4868			0.708063			0.354032	+	0.935233i	$0.384811\pi$
$312$	1.73205	−	3.16228i	0.0980581	−	0.179029i
$313$		−	17.6491i		−	0.997587i	−0.866721	−	0.498793i	$-0.833777\pi$
$313$		−	17.6491i		−	0.997587i	0.866721	−	0.498793i	$-0.166223\pi$
$314$	−4.91886	−	8.51972i	−0.277587	−	0.480795i
$315$		0			0
$316$	−4.58114	+	7.93477i	−0.257709	+	0.446365i
$317$			0.188612i			0.0105935i	0.999986	+	0.00529674i	$0.00168601\pi$
$317$			0.188612i			0.0105935i	−0.999986	+	0.00529674i	$0.998314\pi$
$318$	−6.20271	−	3.58114i	−0.347831	−	0.200820i
$319$	−12.4868	+	21.6278i	−0.699128	+	1.21093i
$320$		0			0
$321$	−3.00000	+	5.19615i	−0.167444	+	0.290021i
$322$	11.3989	−	6.58114i	0.635234	−	0.366753i
$323$	−19.6147	+	11.3246i	−1.09139	+	0.630115i
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	15.8114			0.875712
$327$	−7.34981	+	4.24342i	−0.406446	+	0.234661i
$328$	8.21584	−	4.74342i	0.453644	−	0.261911i
$329$	−9.48683	+	16.4317i	−0.523026	+	0.905908i
$330$		0			0
$331$	4.41886	−	7.65369i	0.242883	−	0.420685i	−0.718652	−	0.695370i	$-0.755240\pi$
$331$	4.41886	−	7.65369i	0.242883	−	0.420685i	0.961534	+	0.274685i	$0.0885737\pi$
$332$	11.8205	+	6.82456i	0.648733	+	0.374546i
$333$		−	10.4868i		−	0.574675i
$334$	−0.918861	+	1.59151i	−0.0502778	+	0.0870838i
$335$		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	$0.965252\pi$
$338$	0.584952	+	12.9868i	0.0318172	+	0.706391i
$339$	2.32456			0.126253
$340$		0			0
$341$	−13.7434	−	23.8043i	−0.744248	−	1.28907i
$342$	−2.73861	−	1.58114i	−0.148087	−	0.0854982i
$343$		−	12.6491i		−	0.682988i
$344$	2.58114	−	4.47066i	0.139166	−	0.241042i
$345$		0			0
$346$	14.3246			0.770093
$347$	−9.80735	−	5.66228i	−0.526486	−	0.303967i	0.213098	−	0.977031i	$-0.431645\pi$
$347$	−9.80735	−	5.66228i	−0.526486	−	0.303967i	−0.739584	+	0.673064i	$0.764978\pi$
$348$	−7.20928	+	4.16228i	−0.386458	+	0.223122i
$349$	10.7302	+	18.5853i	0.574377	+	0.994850i	0.996109	+	0.0881297i	$0.0280890\pi$
$349$	10.7302	+	18.5853i	0.574377	+	0.994850i	−0.421732	+	0.906721i	$0.638578\pi$
$350$		0			0
$351$	3.08114	−	1.87259i	0.164459	−	0.0999513i
$352$			3.00000i			0.159901i
$353$	10.2290	−	5.90569i	0.544433	−	0.314328i	−0.202441	−	0.979295i	$-0.564887\pi$
$353$	10.2290	−	5.90569i	0.544433	−	0.314328i	0.746874	+	0.664966i	$0.231554\pi$
$354$	3.00000	+	5.19615i	0.159448	+	0.276172i
$355$		0			0
$356$	−7.16228			−0.379600
$357$	−19.6147	−	11.3246i	−1.03812	−	0.599359i
$358$	−1.42817	−	0.824555i	−0.0754812	−	0.0435791i
$359$	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
$362$	−16.2911	+	9.40569i	−0.856243	+	0.494352i
$363$		−	2.00000i		−	0.104973i
$364$	10.0000	+	5.47723i	0.524142	+	0.287085i
$365$		0			0
$366$	7.24342	+	12.5460i	0.378619	+	0.655788i
$367$	−5.75830	+	3.32456i	−0.300581	+	0.173540i	−0.642704	−	0.766115i	$-0.722187\pi$
$367$	−5.75830	+	3.32456i	−0.300581	+	0.173540i	0.342123	+	0.939655i	$0.388854\pi$
$368$	−3.60464	−	2.08114i	−0.187905	−	0.108487i
$369$	9.48683			0.493865
$370$		0			0
$371$	11.3246	−	19.6147i	0.587942	−	1.01834i
$372$		−	9.16228i		−	0.475042i
$373$	−7.34981	−	4.24342i	−0.380559	−	0.219716i	0.297503	−	0.954721i	$-0.403846\pi$
$373$	−7.34981	−	4.24342i	−0.380559	−	0.219716i	−0.678061	+	0.735005i	$0.737180\pi$
$374$	10.7434	+	18.6081i	0.555529	+	0.962204i
$375$		0			0
$376$	6.00000			0.309426
$377$	14.4186	−	26.3246i	0.742593	−	1.35578i
$378$		−	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
$381$	3.83772	−	6.64713i	0.196612	−	0.340543i
$382$			22.1623i			1.13392i
$383$	−3.60464	−	2.08114i	−0.184188	−	0.106341i	0.405071	−	0.914285i	$-0.367247\pi$
$383$	−3.60464	−	2.08114i	−0.184188	−	0.106341i	−0.589259	+	0.807944i	$0.700580\pi$
$384$	−0.500000	+	0.866025i	−0.0255155	+	0.0441942i
$385$		0			0
$386$	−2.33772	+	4.04905i	−0.118987	+	0.206091i
$387$	4.47066	−	2.58114i	0.227257	−	0.131207i
$388$	−4.04905	+	2.33772i	−0.205560	+	0.118680i
$389$	15.6754			0.794777			0.397388	−	0.917651i	$-0.369917\pi$
$389$	15.6754			0.794777			0.397388	+	0.917651i	$0.369917\pi$
$390$		0			0
$391$	−29.8114			−1.50763
$392$	2.59808	−	1.50000i	0.131223	−	0.0757614i
$393$	3.18303	−	1.83772i	0.160563	−	0.0927008i
$394$	3.00000	−	5.19615i	0.151138	−	0.261778i
$395$		0			0
$396$	−1.50000	+	2.59808i	−0.0753778	+	0.130558i
$397$	−21.0657	−	12.1623i	−1.05726	−	0.610407i	−0.132584	−	0.991172i	$-0.542328\pi$
$397$	−21.0657	−	12.1623i	−1.05726	−	0.610407i	−0.924672	+	0.380765i	$0.875661\pi$
$398$		−	15.1623i		−	0.760016i
$399$	5.00000	−	8.66025i	0.250313	−	0.433555i
$400$		0			0
$401$	−1.83772	−	3.18303i	−0.0917715	−	0.158953i	0.816485	−	0.577366i	$-0.195920\pi$
$401$	−1.83772	−	3.18303i	−0.0917715	−	0.158953i	−0.908257	+	0.418414i	$0.862586\pi$
$402$		−	4.00000i		−	0.199502i
$403$	17.1572	+	28.2302i	0.854659	+	1.40625i
$404$	16.6491			0.828324
$405$		0			0
$406$	−13.1623	−	22.7977i	−0.653233	−	1.13143i
$407$	−27.2456	−	15.7302i	−1.35051	−	0.779720i
$408$			7.16228i			0.354586i
$409$	8.83772	−	15.3074i	0.436997	−	0.756901i	−0.560459	−	0.828182i	$-0.689375\pi$
$409$	8.83772	−	15.3074i	0.436997	−	0.756901i	0.997456	+	0.0712807i	$0.0227086\pi$
$410$		0			0
$411$	−12.0000			−0.591916
$412$	−11.6799	−	6.74342i	−0.575429	−	0.332224i
$413$	−16.4317	+	9.48683i	−0.808550	+	0.466817i
$414$	−2.08114	−	3.60464i	−0.102282	−	0.177158i
$415$		0			0
$416$	−0.0811388	−	3.60464i	−0.00397816	−	0.176732i
$417$			18.3246i			0.897357i
$418$	−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
$421$	21.8377			1.06431			0.532153	−	0.846648i	$-0.321383\pi$
$421$	21.8377			1.06431			0.532153	+	0.846648i	$0.321383\pi$
$422$	−5.92164	−	3.41886i	−0.288261	−	0.166428i
$423$	5.19615	+	3.00000i	0.252646	+	0.145865i
$424$	−7.16228			−0.347831
$425$		0			0
$426$	−3.91886	−	6.78767i	−0.189869	−	0.328864i
$427$	−39.6738	+	22.9057i	−1.91995	+	1.10848i
$428$			6.00000i			0.290021i
$429$	−0.243416	−	10.8139i	−0.0117523	−	0.522101i
$430$		0			0
$431$	2.75658	+	4.77454i	0.132780	+	0.229982i	0.924747	−	0.380582i	$-0.124276\pi$
$431$	2.75658	+	4.77454i	0.132780	+	0.229982i	−0.791967	+	0.610564i	$0.790943\pi$
$432$	−0.866025	+	0.500000i	−0.0416667	+	0.0240563i
$433$	−24.7881	−	14.3114i	−1.19124	−	0.687761i	−0.232650	−	0.972560i	$-0.574740\pi$
$433$	−24.7881	−	14.3114i	−1.19124	−	0.687761i	−0.958587	+	0.284799i	$0.908073\pi$
$434$	28.9737			1.39078
$435$		0			0
$436$	−4.24342	+	7.34981i	−0.203223	+	0.351992i
$437$		−	13.1623i		−	0.629637i
$438$	1.14710	+	0.662278i	0.0548105	+	0.0316449i
$439$	−5.67544	−	9.83016i	−0.270874	−	0.469168i	0.698212	−	0.715891i	$-0.253979\pi$
$439$	−5.67544	−	9.83016i	−0.270874	−	0.469168i	−0.969086	+	0.246723i	$0.920646\pi$
$440$		0			0
$441$	3.00000			0.142857
$442$	−13.4120	−	22.0680i	−0.637943	−	1.04967i
$443$		−	9.00000i		−	0.427603i	−0.976877	−	0.213801i	$-0.931415\pi$
$443$		−	9.00000i		−	0.427603i	0.976877	−	0.213801i	$-0.0685846\pi$
$444$	−5.24342	−	9.08186i	−0.248842	−	0.431006i
$445$		0			0
$446$	−9.06797	+	15.7062i	−0.429381	+	0.743710i
$447$			13.1623i			0.622554i
$448$	−2.73861	−	1.58114i	−0.129387	−	0.0747018i
$449$	10.7434	−	18.6081i	0.507013	−	0.878173i	−0.492954	−	0.870055i	$-0.664083\pi$
$449$	10.7434	−	18.6081i	0.507013	−	0.878173i	0.999967	−	0.00811713i	$-0.00258379\pi$
$450$		0			0
$451$	14.2302	−	24.6475i	0.670076	−	1.16061i
$452$	2.01312	−	1.16228i	0.0946894	−	0.0546689i
$453$	−18.8892	+	10.9057i	−0.887493	+	0.512394i
$454$	−15.9737			−0.749681
$455$		0			0
$456$	−3.16228			−0.148087
$457$	30.8730	−	17.8246i	1.44418	−	0.833798i	0.446055	−	0.895006i	$-0.352829\pi$
$457$	30.8730	−	17.8246i	1.44418	−	0.833798i	0.998125	+	0.0612082i	$0.0194954\pi$
$458$	−2.15366	+	1.24342i	−0.100634	+	0.0581010i
$459$	−3.58114	+	6.20271i	−0.167153	+	0.289518i
$460$		0			0
$461$	5.41886	−	9.38574i	0.252382	−	0.437138i	−0.711799	−	0.702383i	$-0.752120\pi$
$461$	5.41886	−	9.38574i	0.252382	−	0.437138i	0.964181	+	0.265245i	$0.0854529\pi$
$462$	−8.21584	−	4.74342i	−0.382235	−	0.220684i
$463$			23.4868i			1.09153i	0.837940	+	0.545763i	$0.183760\pi$
$463$			23.4868i			1.09153i	−0.837940	+	0.545763i	$0.816240\pi$
$464$	−4.16228	+	7.20928i	−0.193229	+	0.334682i
$465$		0			0
$466$	13.1623	+	22.7977i	0.609731	+	1.05608i
$467$			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
$471$	−4.91886	−	8.51972i	−0.226649	−	0.392568i
$472$	5.19615	+	3.00000i	0.239172	+	0.138086i
$473$		−	15.4868i		−	0.712085i
$474$	−4.58114	+	7.93477i	−0.210419	+	0.364456i
$475$		0			0
$476$	−22.6491			−1.03812
$477$	−6.20271	−	3.58114i	−0.284003	−	0.163969i
$478$	0.421610	−	0.243416i	0.0192840	−	0.0111336i
$479$	−13.1623	−	22.7977i	−0.601400	−	1.04166i	−0.992609	−	0.121353i	$-0.961277\pi$
$479$	−13.1623	−	22.7977i	−0.601400	−	1.04166i	0.391210	−	0.920302i	$-0.372057\pi$
$480$		0			0
$481$	33.1623	+	18.1637i	1.51207	+	0.828195i
$482$			8.00000i			0.364390i
$483$	11.3989	−	6.58114i	0.518666	−	0.299452i
$484$	−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	0.560764	−	0.827976i	$-0.310507\pi$
$487$	2.73861	+	1.58114i	0.124098	+	0.0716482i	−0.436666	+	0.899624i	$0.643841\pi$
$488$	12.5460	+	7.24342i	0.567929	+	0.327894i
$489$	15.8114			0.715016
$490$		0			0
$491$	−7.98683	−	13.8336i	−0.360441	−	0.624302i	0.627593	−	0.778542i	$-0.284040\pi$
$491$	−7.98683	−	13.8336i	−0.360441	−	0.624302i	−0.988033	+	0.154240i	$0.950707\pi$
$492$	8.21584	−	4.74342i	0.370399	−	0.213850i
$493$			59.6228i			2.68527i
$494$	9.74342	−	5.92164i	0.438377	−	0.266427i
$495$		0			0
$496$	−4.58114	−	7.93477i	−0.205699	−	0.356281i
$497$	21.4645	−	12.3925i	0.962814	−	0.555881i
$498$	11.8205	+	6.82456i	0.529688	+	0.305816i
$499$	−8.18861			−0.366573			−0.183286	−	0.983060i	$-0.558674\pi$
$499$	−8.18861			−0.366573			−0.183286	+	0.983060i	$0.558674\pi$
$500$		0			0
$501$	−0.918861	+	1.59151i	−0.0410517	+	0.0711036i
$502$			15.0000i			0.669483i
$503$	−12.8270	−	7.40569i	−0.571929	−	0.330204i	0.185990	−	0.982552i	$-0.440451\pi$
$503$	−12.8270	−	7.40569i	−0.571929	−	0.330204i	−0.757920	+	0.652348i	$0.773784\pi$
$504$	−1.58114	−	2.73861i	−0.0704295	−	0.121988i
$505$		0			0
$506$	−12.4868			−0.555107
$507$	0.584952	+	12.9868i	0.0259786	+	0.576766i
$508$		−	7.67544i		−	0.340543i
$509$	21.3925	+	37.0529i	0.948207	+	1.64234i	0.749199	+	0.662345i	$0.230439\pi$
$509$	21.3925	+	37.0529i	0.948207	+	1.64234i	0.199008	+	0.979998i	$0.436228\pi$
$510$		0			0
$511$	−2.09431	+	3.62744i	−0.0926466	+	0.160469i
$512$			1.00000i			0.0441942i
$513$	−2.73861	−	1.58114i	−0.120913	−	0.0698090i
$514$	−2.90569	+	5.03281i	−0.128165	+	0.221988i
$515$		0			0
$516$	2.58114	−	4.47066i	0.113628	−	0.196810i
$517$	15.5885	−	9.00000i	0.685580	−	0.395820i
$518$	28.7194	−	16.5811i	1.26186	−	0.728533i
$519$	14.3246			0.628778
$520$		0			0
$521$	4.64911			0.203681			0.101841	−	0.994801i	$-0.467527\pi$
$521$	4.64911			0.203681			0.101841	+	0.994801i	$0.467527\pi$
$522$	−7.20928	+	4.16228i	−0.315541	+	0.182178i
$523$	−4.30732	+	2.48683i	−0.188346	+	0.108742i	−0.591208	−	0.806519i	$-0.701349\pi$
$523$	−4.30732	+	2.48683i	−0.188346	+	0.108742i	0.402862	+	0.915261i	$0.368015\pi$
$524$	1.83772	−	3.18303i	0.0802813	−	0.139051i
$525$		0			0
$526$	9.24342	−	16.0101i	0.403032	−	0.698072i
$527$	−56.8310	−	32.8114i	−2.47560	−	1.42929i
$528$			3.00000i			0.130558i
$529$	−2.83772	+	4.91508i	−0.123379	+	0.213699i
$530$		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
$534$	−7.16228			−0.309942
$535$		0			0
$536$	−2.00000	−	3.46410i	−0.0863868	−	0.149626i
$537$	−1.42817	−	0.824555i	−0.0616302	−	0.0355822i
$538$			19.1623i			0.826144i
$539$	4.50000	−	7.79423i	0.193829	−	0.335721i
$540$		0			0
$541$	−0.811388			−0.0348843			−0.0174422	−	0.999848i	$-0.505552\pi$
$541$	−0.811388			−0.0348843			−0.0174422	+	0.999848i	$0.505552\pi$
$542$	10.6734	+	6.16228i	0.458461	+	0.264692i
$543$	−16.2911	+	9.40569i	−0.699120	+	0.403637i
$544$	3.58114	+	6.20271i	0.153540	+	0.265939i
$545$		0			0
$546$	10.0000	+	5.47723i	0.427960	+	0.234404i
$547$			30.1359i			1.28852i	0.764807	+	0.644260i	$0.222835\pi$
$547$			30.1359i			1.28852i	−0.764807	+	0.644260i	$0.777165\pi$
$548$	−10.3923	+	6.00000i	−0.443937	+	0.256307i
$549$	7.24342	+	12.5460i	0.309141	+	0.535449i
$550$		0			0
$551$	−26.3246			−1.12146
$552$	−3.60464	−	2.08114i	−0.153424	−	0.0885792i
$553$	−25.0919	−	14.4868i	−1.06702	−	0.616043i
$554$	22.8114			0.969163
$555$		0			0
$556$	9.16228	+	15.8695i	0.388567	+	0.673018i
$557$	16.4317	−	9.48683i	0.696232	−	0.401970i	−0.109710	−	0.993964i	$-0.534992\pi$
$557$	16.4317	−	9.48683i	0.696232	−	0.401970i	0.805943	+	0.591994i	$0.201659\pi$
$558$		−	9.16228i		−	0.387870i
$559$	0.418861	+	18.6081i	0.0177159	+	0.787041i
$560$		0			0
$561$	10.7434	+	18.6081i	0.453587	+	0.785636i
$562$	−2.17647	+	1.25658i	−0.0918087	+	0.0530058i
$563$	3.44130	+	1.98683i	0.145033	+	0.0837350i	0.570761	−	0.821116i	$-0.306648\pi$
$563$	3.44130	+	1.98683i	0.145033	+	0.0837350i	−0.425727	+	0.904851i	$0.639982\pi$
$564$	6.00000			0.252646
$565$		0			0
$566$	−0.256584	+	0.444416i	−0.0107850	+	0.0186802i
$567$		−	3.16228i		−	0.132803i
$568$	−6.78767	−	3.91886i	−0.284804	−	0.164432i
$569$	15.4868	+	26.8240i	0.649242	+	1.12452i	0.983304	+	0.181969i	$0.0582470\pi$
$569$	15.4868	+	26.8240i	0.649242	+	1.12452i	−0.334062	+	0.942551i	$0.608420\pi$
$570$		0			0
$571$	−19.6754			−0.823392			−0.411696	−	0.911321i	$-0.635063\pi$
$571$	−19.6754			−0.823392			−0.411696	+	0.911321i	$0.635063\pi$
$572$	−5.61776	−	9.24342i	−0.234890	−	0.386487i
$573$			22.1623i			0.925842i
$574$	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	$0.647135\pi$
$578$	29.7031	+	17.1491i	1.23549	+	0.713309i
$579$	−2.33772	+	4.04905i	−0.0971524	+	0.168273i
$580$		0			0
$581$	−21.5811	+	37.3796i	−0.895337	+	1.55077i
$582$	−4.04905	+	2.33772i	−0.167839	+	0.0969017i
$583$	−18.6081	+	10.7434i	−0.770671	+	0.444947i
$584$	1.32456			0.0548105
$585$		0			0
$586$	−2.51317			−0.103818
$587$	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
$589$	14.4868	−	25.0919i	0.596920	−	1.03389i
$590$		0			0
$591$	3.00000	−	5.19615i	0.123404	−	0.213741i
$592$	−9.08186	−	5.24342i	−0.373262	−	0.215503i
$593$			1.16228i			0.0477290i	0.999715	+	0.0238645i	$0.00759703\pi$
$593$			1.16228i			0.0477290i	−0.999715	+	0.0238645i	$0.992403\pi$
$594$	−1.50000	+	2.59808i	−0.0615457	+	0.106600i
$595$		0			0
$596$	6.58114	+	11.3989i	0.269574	+	0.466916i
$597$		−	15.1623i		−	0.620551i
$598$	15.0035	−	0.337722i	0.613539	−	0.0138105i
$599$	−32.8114			−1.34064			−0.670318	−	0.742074i	$-0.733843\pi$
$599$	−32.8114			−1.34064			−0.670318	+	0.742074i	$0.733843\pi$
$600$		0			0
$601$	3.64911	+	6.32045i	0.148850	+	0.257816i	0.930803	−	0.365522i	$-0.119109\pi$
$601$	3.64911	+	6.32045i	0.148850	+	0.257816i	−0.781952	+	0.623338i	$0.785776\pi$
$602$	14.1375	+	8.16228i	0.576201	+	0.332670i
$603$		−	4.00000i		−	0.162893i
$604$	−10.9057	+	18.8892i	−0.443746	+	0.768591i
$605$		0			0
$606$	16.6491			0.676324
$607$	20.5035	+	11.8377i	0.832213	+	0.480478i	0.854610	−	0.519271i	$-0.173796\pi$
$607$	20.5035	+	11.8377i	0.832213	+	0.480478i	−0.0223969	+	0.999749i	$0.507130\pi$
$608$	−2.73861	+	1.58114i	−0.111065	+	0.0641236i
$609$	−13.1623	−	22.7977i	−0.533362	−	0.923811i
$610$		0			0
$611$	−18.4868	+	11.2355i	−0.747897	+	0.454541i
$612$			7.16228i			0.289518i
$613$	25.6997	−	14.8377i	1.03800	−	0.599290i	0.118734	−	0.992926i	$-0.462116\pi$
$613$	25.6997	−	14.8377i	1.03800	−	0.599290i	0.919266	+	0.393636i	$0.128783\pi$
$614$	4.32456	+	7.49035i	0.174525	+	0.302286i
$615$		0			0
$616$	−9.48683			−0.382235
$617$	2.85634	+	1.64911i	0.114992	+	0.0663907i	0.556393	−	0.830919i	$-0.312185\pi$
$617$	2.85634	+	1.64911i	0.114992	+	0.0663907i	−0.441401	+	0.897310i	$0.645518\pi$
$618$	−11.6799	−	6.74342i	−0.469836	−	0.271260i
$619$	−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
$621$	−2.08114	−	3.60464i	−0.0835132	−	0.144649i
$622$	10.8139	−	6.24342i	0.433598	−	0.250338i
$623$		−	22.6491i		−	0.907417i
$624$	−0.0811388	−	3.60464i	−0.00324815	−	0.144301i
$625$		0			0
$626$	−8.82456	−	15.2846i	−0.352700	−	0.610895i
$627$	−8.21584	+	4.74342i	−0.328109	+	0.189434i
$628$	−8.51972	−	4.91886i	−0.339974	−	0.196284i
$629$	−75.1096			−2.99482
$630$		0			0
$631$	−17.6491	+	30.5692i	−0.702600	+	1.21694i	0.264951	+	0.964262i	$0.414644\pi$
$631$	−17.6491	+	30.5692i	−0.702600	+	1.21694i	−0.967551	+	0.252677i	$0.918689\pi$
$632$			9.16228i			0.364456i
$633$	−5.92164	−	3.41886i	−0.235364	−	0.135888i
$634$	0.0943058	+	0.163343i	0.00374536	+	0.00648716i
$635$		0			0
$636$	−7.16228			−0.284003
$637$	−5.19615	+	9.48683i	−0.205879	+	0.375882i
$638$			24.9737i			0.988717i
$639$	−3.91886	−	6.78767i	−0.155028	−	0.268516i
$640$		0			0
$641$	24.9737	−	43.2557i	0.986400	−	1.70850i	0.350861	−	0.936428i	$-0.385889\pi$
$641$	24.9737	−	43.2557i	0.986400	−	1.70850i	0.635540	−	0.772068i	$-0.280778\pi$
$642$			6.00000i			0.236801i
$643$	21.0657	+	12.1623i	0.830749	+	0.479633i	0.854109	−	0.520094i	$-0.174103\pi$
$643$	21.0657	+	12.1623i	0.830749	+	0.479633i	−0.0233598	+	0.999727i	$0.507436\pi$
$644$	6.58114	−	11.3989i	0.259333	−	0.449178i
$645$		0			0
$646$	−11.3246	+	19.6147i	−0.445559	+	0.771730i
$647$	36.7947	−	21.2434i	1.44655	−	0.835165i	0.448274	−	0.893896i	$-0.352039\pi$
$647$	36.7947	−	21.2434i	1.44655	−	0.835165i	0.998274	+	0.0587312i	$0.0187055\pi$
$648$	−0.866025	+	0.500000i	−0.0340207	+	0.0196419i
$649$	18.0000			0.706562
$650$		0			0
$651$	28.9737			1.13557
$652$	13.6931	−	7.90569i	0.536262	−	0.309611i
$653$	8.21584	−	4.74342i	0.321511	−	0.185624i	−0.330555	−	0.943787i	$-0.607236\pi$
$653$	8.21584	−	4.74342i	0.321511	−	0.185624i	0.652066	+	0.758162i	$0.273903\pi$
$654$	−4.24342	+	7.34981i	−0.165931	+	0.287400i
$655$		0			0
$656$	4.74342	−	8.21584i	0.185199	−	0.320775i
$657$	1.14710	+	0.662278i	0.0447526	+	0.0258379i
$658$			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	$-0.335411\pi$
$662$		−	8.83772i		−	0.343488i
$663$	−13.4120	−	22.0680i	−0.520879	−	0.857049i
$664$	13.6491			0.529688
$665$		0			0
$666$	−5.24342	−	9.08186i	−0.203178	−	0.351915i
$667$	−30.0070	−	17.3246i	−1.16188	−	0.670809i
$668$			1.83772i			0.0711036i
$669$	−9.06797	+	15.7062i	−0.350588	+	0.607236i
$670$		0			0
$671$	43.4605			1.67777
$672$	−2.73861	−	1.58114i	−0.105644	−	0.0609938i
$673$	18.7487	−	10.8246i	0.722708	−	0.417256i	−0.0930403	−	0.995662i	$-0.529659\pi$
$673$	18.7487	−	10.8246i	0.722708	−	0.417256i	0.815749	+	0.578406i	$0.196325\pi$
$674$	2.00000	+	3.46410i	0.0770371	+	0.133432i
$675$		0			0
$676$	7.00000	+	10.9545i	0.269231	+	0.421325i
$677$			7.35089i			0.282518i	0.989973	+	0.141259i	$0.0451150\pi$
$677$			7.35089i			0.282518i	−0.989973	+	0.141259i	$0.954885\pi$
$678$	2.01312	−	1.16228i	0.0773136	−	0.0446370i
$679$	−7.39253	−	12.8042i	−0.283699	−	0.491381i
$680$		0			0
$681$	−15.9737			−0.612112
$682$	−23.8043	−	13.7434i	−0.911514	−	0.526263i
$683$	−40.6576	−	23.4737i	−1.55572	−	0.898195i	−0.997658	−	0.0683948i	$-0.978212\pi$
$683$	−40.6576	−	23.4737i	−1.55572	−	0.898195i	−0.558061	−	0.829800i	$-0.688454\pi$
$684$	−3.16228			−0.120913
$685$		0			0
$686$	−6.32456	−	10.9545i	−0.241473	−	0.418243i
$687$	−2.15366	+	1.24342i	−0.0821673	+	0.0474393i
$688$		−	5.16228i		−	0.196810i
$689$	22.0680	−	13.4120i	0.840723	−	0.510956i
$690$		0			0
$691$	−25.9737	−	44.9877i	−0.988085	−	1.71141i	−0.627333	−	0.778751i	$-0.715853\pi$
$691$	−25.9737	−	44.9877i	−0.988085	−	1.71141i	−0.360752	−	0.932662i	$-0.617480\pi$
$692$	12.4054	−	7.16228i	0.471584	−	0.272269i
$693$	−8.21584	−	4.74342i	−0.312094	−	0.180187i
$694$	−11.3246			−0.429874
$695$		0			0
$696$	−4.16228	+	7.20928i	−0.157771	+	0.273267i
$697$		−	67.9473i		−	2.57369i
$698$	18.5853	+	10.7302i	0.703465	+	0.406146i
$699$	13.1623	+	22.7977i	0.497843	+	0.862289i
$700$		0			0
$701$	34.4605			1.30156			0.650778	−	0.759268i	$-0.274443\pi$
$701$	34.4605			1.30156			0.650778	+	0.759268i	$0.274443\pi$
$702$	1.73205	−	3.16228i	0.0653720	−	0.119352i
$703$		−	33.1623i		−	1.25074i
$704$	1.50000	+	2.59808i	0.0565334	+	0.0979187i
$705$		0			0
$706$	5.90569	−	10.2290i	0.222264	−	0.384972i
$707$			52.6491i			1.98007i
$708$	5.19615	+	3.00000i	0.195283	+	0.112747i
$709$	10.2434	−	17.7421i	0.384700	−	0.666319i	−0.607028	−	0.794681i	$-0.707638\pi$
$709$	10.2434	−	17.7421i	0.384700	−	0.666319i	0.991727	+	0.128361i	$0.0409717\pi$
$710$		0			0
$711$	−4.58114	+	7.93477i	−0.171806	+	0.297577i
$712$	−6.20271	+	3.58114i	−0.232457	+	0.134209i
$713$	33.0267	−	19.0680i	1.23686	−	0.714101i
$714$	−22.6491			−0.847622
$715$		0			0
$716$	−1.64911			−0.0616302
$717$	0.421610	−	0.243416i	0.0157453	−	0.00909056i
$718$	10.3923	−	6.00000i	0.387837	−	0.223918i
$719$	−7.59431	+	13.1537i	−0.283220	+	0.490551i	−0.972176	−	0.234252i	$-0.924736\pi$
$719$	−7.59431	+	13.1537i	−0.283220	+	0.490551i	0.688956	+	0.724803i	$0.258069\pi$
$720$		0			0
$721$	21.3246	−	36.9352i	0.794168	−	1.37554i
$722$	7.79423	+	4.50000i	0.290071	+	0.167473i
$723$			8.00000i			0.297523i
$724$	−9.40569	+	16.2911i	−0.349560	+	0.605455i
$725$		0			0
$726$	−1.00000	−	1.73205i	−0.0371135	−	0.0642824i
$727$			0.324555i			0.0120371i	0.999982	+	0.00601855i	$0.00191577\pi$
$727$			0.324555i			0.0120371i	−0.999982	+	0.00601855i	$0.998084\pi$
$728$	11.3989	−	0.256584i	0.422470	−	0.00950962i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	−18.4868	−	32.0201i	−0.683760	−	1.18431i
$732$	12.5460	+	7.24342i	0.463712	+	0.267724i
$733$			38.4868i			1.42154i	0.703423	+	0.710772i	$0.251654\pi$
$733$			38.4868i			1.42154i	−0.703423	+	0.710772i	$0.748346\pi$
$734$	−3.32456	+	5.75830i	−0.122712	+	0.212543i
$735$		0			0
$736$	−4.16228			−0.153424
$737$	−10.3923	−	6.00000i	−0.382805	−	0.221013i
$738$	8.21584	−	4.74342i	0.302429	−	0.174608i
$739$	−15.6491	−	27.1051i	−0.575662	−	0.997076i	−0.995969	−	0.0896938i	$-0.971411\pi$
$739$	−15.6491	−	27.1051i	−0.575662	−	0.997076i	0.420308	−	0.907382i	$-0.361922\pi$
$740$		0			0
$741$	9.74342	−	5.92164i	0.357933	−	0.217537i
$742$		−	22.6491i		−	0.831475i
$743$	−16.7584	+	9.67544i	−0.614805	+	0.354958i	−0.774844	−	0.632153i	$-0.782171\pi$
$743$	−16.7584	+	9.67544i	−0.614805	+	0.354958i	0.160039	+	0.987111i	$0.448838\pi$
$744$	−4.58114	−	7.93477i	−0.167953	−	0.290903i
$745$		0			0
$746$	−8.48683			−0.310725
$747$	11.8205	+	6.82456i	0.432489	+	0.249697i
$748$	18.6081	+	10.7434i	0.680381	+	0.392818i
$749$	−18.9737			−0.693283
$750$		0			0
$751$	15.1623	+	26.2618i	0.553279	+	0.958308i	0.998035	+	0.0626561i	$0.0199571\pi$
$751$	15.1623	+	26.2618i	0.553279	+	0.958308i	−0.444756	+	0.895652i	$0.646710\pi$
$752$	5.19615	−	3.00000i	0.189484	−	0.109399i
$753$			15.0000i			0.546630i
$754$	−0.675445	−	30.0070i	−0.0245982	−	1.09279i
$755$		0			0
$756$	−1.58114	−	2.73861i	−0.0575055	−	0.0996024i
$757$	−23.3599	+	13.4868i	−0.849029	+	0.490187i	−0.860323	−	0.509749i	$-0.829738\pi$
$757$	−23.3599	+	13.4868i	−0.849029	+	0.490187i	0.0112939	+	0.999936i	$0.496405\pi$
$758$	1.73205	+	1.00000i	0.0629109	+	0.0363216i
$759$	−12.4868			−0.453243
$760$		0			0
$761$	−5.23025	+	9.05906i	−0.189596	+	0.328391i	−0.945116	−	0.326736i	$-0.894051\pi$
$761$	−5.23025	+	9.05906i	−0.189596	+	0.328391i	0.755519	+	0.655126i	$0.227385\pi$
$762$		−	7.67544i		−	0.278052i
$763$	−23.2421	−	13.4189i	−0.841422	−	0.485795i
$764$	11.0811	+	19.1931i	0.400902	+	0.694382i
$765$		0			0
$766$	−4.16228			−0.150389
$767$	−21.6278	+	0.486833i	−0.780936	+	0.0175785i
$768$			1.00000i			0.0360844i
$769$	−11.4868	−	19.8958i	−0.414226	−	0.717460i	0.581121	−	0.813817i	$-0.302614\pi$
$769$	−11.4868	−	19.8958i	−0.414226	−	0.717460i	−0.995347	+	0.0963570i	$0.969281\pi$
$770$		0			0
$771$	−2.90569	+	5.03281i	−0.104646	+	0.181252i
$772$			4.67544i			0.168273i
$773$	30.0070	+	17.3246i	1.07928	+	0.623121i	0.930701	−	0.365780i	$-0.119198\pi$
$773$	30.0070	+	17.3246i	1.07928	+	0.623121i	0.148576	+	0.988901i	$0.452531\pi$
$774$	2.58114	−	4.47066i	0.0927771	−	0.160695i
$775$		0			0
$776$	−2.33772	+	4.04905i	−0.0839193	+	0.145353i
$777$	28.7194	−	16.5811i	1.03030	−	0.594845i
$778$	13.5753	−	7.83772i	0.486699	−	0.280996i
$779$	30.0000			1.07486
$780$		0			0
$781$	−23.5132			−0.841367
$782$	−25.8174	+	14.9057i	−0.923229	+	0.533027i
$783$	−7.20928	+	4.16228i	−0.257639	+	0.148748i
$784$	1.50000	−	2.59808i	0.0535714	−	0.0927884i
$785$		0			0
$786$	1.83772	−	3.18303i	0.0655494	−	0.113535i
$787$	−11.6799	−	6.74342i	−0.416345	−	0.240377i	0.277167	−	0.960822i	$-0.410604\pi$
$787$	−11.6799	−	6.74342i	−0.416345	−	0.240377i	−0.693512	+	0.720445i	$0.743938\pi$
$788$		−	6.00000i		−	0.213741i
$789$	9.24342	−	16.0101i	0.329074	−	0.569973i
$790$		0			0
$791$	3.67544	+	6.36606i	0.130684	+	0.226351i
$792$			3.00000i			0.106600i
$793$	−52.2198	+	1.17544i	−1.85438	+	0.0417413i
$794$	−24.3246			−0.863246
$795$		0			0
$796$	−7.58114	−	13.1309i	−0.268706	−	0.465413i
$797$	47.2819	+	27.2982i	1.67481	+	0.966953i	0.964884	+	0.262678i	$0.0846056\pi$
$797$	47.2819	+	27.2982i	1.67481	+	0.966953i	0.709927	+	0.704275i	$0.248728\pi$
$798$		−	10.0000i		−	0.353996i
$799$	21.4868	−	37.2163i	0.760150	−	1.31662i
$800$		0			0
$801$	−7.16228			−0.253067
$802$	−3.18303	−	1.83772i	−0.112397	−	0.0648922i
$803$	3.44130	−	1.98683i	0.121441	−	0.0701138i
$804$	−2.00000	−	3.46410i	−0.0705346	−	0.122169i
$805$		0			0
$806$	28.9737	+	15.8695i	1.02055	+	0.558980i
$807$			19.1623i			0.674544i
$808$	14.4186	−	8.32456i	0.507243	−	0.292857i
$809$	−9.58114	−	16.5950i	−0.336855	−	0.583450i	0.646984	−	0.762503i	$-0.276030\pi$
$809$	−9.58114	−	16.5950i	−0.336855	−	0.583450i	−0.983839	+	0.179053i	$0.942697\pi$
$810$		0			0
$811$	18.6491			0.654859			0.327429	−	0.944876i	$-0.393818\pi$
$811$	18.6491			0.654859			0.327429	+	0.944876i	$0.393818\pi$
$812$	−22.7977	−	13.1623i	−0.800044	−	0.461905i
$813$	10.6734	+	6.16228i	0.374332	+	0.216121i
$814$	−31.4605			−1.10269
$815$		0			0
$816$	3.58114	+	6.20271i	0.125365	+	0.217138i
$817$	14.1375	−	8.16228i	0.494608	−	0.285562i
$818$		−	17.6754i		−	0.618007i
$819$	10.0000	+	5.47723i	0.349428	+	0.191390i
$820$		0			0
$821$	4.16228	+	7.20928i	0.145264	+	0.251605i	0.929472	−	0.368894i	$-0.120263\pi$
$821$	4.16228	+	7.20928i	0.145264	+	0.251605i	−0.784207	+	0.620499i	$0.786930\pi$
$822$	−10.3923	+	6.00000i	−0.362473	+	0.209274i
$823$	−13.1309	−	7.58114i	−0.457715	−	0.264262i	0.253368	−	0.967370i	$-0.418462\pi$
$823$	−13.1309	−	7.58114i	−0.457715	−	0.264262i	−0.711083	+	0.703108i	$0.751795\pi$
$824$	−13.4868			−0.469836
$825$		0			0
$826$	−9.48683	+	16.4317i	−0.330089	+	0.571731i
$827$			9.97367i			0.346818i	0.984850	+	0.173409i	$0.0554783\pi$
$827$			9.97367i			0.346818i	−0.984850	+	0.173409i	$0.944522\pi$
$828$	−3.60464	−	2.08114i	−0.125270	−	0.0723246i
$829$	16.4868	+	28.5560i	0.572611	+	0.991792i	0.996297	+	0.0859825i	$0.0274029\pi$
$829$	16.4868	+	28.5560i	0.572611	+	0.991792i	−0.423685	+	0.905809i	$0.639264\pi$
$830$		0			0
$831$	22.8114			0.791318
$832$	−1.87259	−	3.08114i	−0.0649203	−	0.106819i
$833$		−	21.4868i		−	0.744475i
$834$	9.16228	+	15.8695i	0.317264	+	0.549517i
$835$		0			0
$836$	−4.74342	+	8.21584i	−0.164054	+	0.284151i
$837$		−	9.16228i		−	0.316695i
$838$	7.79423	+	4.50000i	0.269247	+	0.155450i
$839$	16.8925	−	29.2587i	0.583195	−	1.01012i	−0.411903	−	0.911228i	$-0.635136\pi$
$839$	16.8925	−	29.2587i	0.583195	−	1.01012i	0.995098	−	0.0988953i	$-0.0315309\pi$
$840$		0			0
$841$	−20.1491	+	34.8993i	−0.694797	+	1.20342i
$842$	18.9120	−	10.9189i	0.651751	−	0.376289i
$843$	−2.17647	+	1.25658i	−0.0749615	+	0.0432790i
$844$	−6.83772			−0.235364
$845$		0			0
$846$	6.00000			0.206284
$847$	5.47723	−	3.16228i	0.188200	−	0.108657i
$848$	−6.20271	+	3.58114i	−0.213002	+	0.122977i
$849$	−0.256584	+	0.444416i	−0.00880592	+	0.0152523i
$850$		0			0
$851$	21.8246	−	37.8012i	0.748136	−	1.29581i
$852$	−6.78767	−	3.91886i	−0.232542	−	0.134258i
$853$			6.64911i			0.227661i	0.993500	+	0.113831i	$0.0363121\pi$
$853$			6.64911i			0.227661i	−0.993500	+	0.113831i	$0.963688\pi$
$854$	−22.9057	+	39.6738i	−0.783817	+	1.35761i
$855$		0			0
$856$	3.00000	+	5.19615i	0.102538	+	0.177601i
$857$			46.2719i			1.58062i	0.612709	+	0.790309i	$0.290080\pi$
$857$			46.2719i			1.58062i	−0.612709	+	0.790309i	$0.709920\pi$
$858$	−5.61776	−	9.24342i	−0.191787	−	0.315565i
$859$	−43.8114			−1.49483			−0.747413	−	0.664360i	$-0.768704\pi$
$859$	−43.8114			−1.49483			−0.747413	+	0.664360i	$0.768704\pi$
$860$		0			0
$861$	15.0000	+	25.9808i	0.511199	+	0.885422i
$862$	4.77454	+	2.75658i	0.162622	+	0.0938896i
$863$		−	37.4605i		−	1.27517i	−0.770380	−	0.637585i	$-0.779933\pi$
$863$		−	37.4605i		−	1.27517i	0.770380	−	0.637585i	$-0.220067\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$		0			0
$866$	−28.6228			−0.972642
$867$	29.7031	+	17.1491i	1.00877	+	0.582414i
$868$	25.0919	−	14.4868i	0.851676	−	0.491715i
$869$	13.7434	+	23.8043i	0.466213	+	0.807505i
$870$		0			0
$871$	12.6491	+	6.92820i	0.428599	+	0.234753i
$872$			8.48683i			0.287400i
$873$	−4.04905	+	2.33772i	−0.137040	+	0.0791199i
$874$	−6.58114	−	11.3989i	−0.222610	−	0.385572i
$875$		0			0
$876$	1.32456			0.0447526
$877$	−21.8140	−	12.5943i	−0.736606	−	0.425279i	0.0842282	−	0.996446i	$-0.473158\pi$
$877$	−21.8140	−	12.5943i	−0.736606	−	0.425279i	−0.820834	+	0.571167i	$0.806491\pi$
$878$	−9.83016	−	5.67544i	−0.331752	−	0.191537i
$879$	−2.51317			−0.0847670
$880$		0			0
$881$	−17.2302	−	29.8437i	−0.580502	−	1.00546i	−0.995420	−	0.0955999i	$-0.969523\pi$
$881$	−17.2302	−	29.8437i	−0.580502	−	1.00546i	0.414918	−	0.909859i	$-0.363810\pi$
$882$	2.59808	−	1.50000i	0.0874818	−	0.0505076i
$883$		−	8.64911i		−	0.291066i	−0.989353	−	0.145533i	$-0.953510\pi$
$883$		−	8.64911i		−	0.291066i	0.989353	−	0.145533i	$-0.0464897\pi$
$884$	−22.6491	−	12.4054i	−0.761772	−	0.417240i
$885$		0			0
$886$	−4.50000	−	7.79423i	−0.151180	−	0.261852i
$887$	−14.4186	+	8.32456i	−0.484128	+	0.279511i	−0.722135	−	0.691752i	$-0.756839\pi$
$887$	−14.4186	+	8.32456i	−0.484128	+	0.279511i	0.238007	+	0.971263i	$0.423506\pi$
$888$	−9.08186	−	5.24342i	−0.304767	−	0.175958i
$889$	24.2719			0.814053
$890$		0			0
$891$	−1.50000	+	2.59808i	−0.0502519	+	0.0870388i
$892$			18.1359i			0.607236i
$893$	16.4317	+	9.48683i	0.549865	+	0.317465i
$894$	6.58114	+	11.3989i	0.220106	+	0.381235i
$895$		0			0
$896$	−3.16228			−0.105644
$897$	15.0035	−	0.337722i	0.500952	−	0.0112762i
$898$		−	21.4868i		−	0.717025i
$899$	−38.1359	−	66.0534i	−1.27190	−	2.20300i
$900$		0			0
$901$	−25.6491	+	44.4256i	−0.854496	+	1.48003i
$902$		−	28.4605i		−	0.947631i
$903$	14.1375	+	8.16228i	0.470466	+	0.271624i
$904$	1.16228	−	2.01312i	0.0386568	−	0.0669555i
$905$		0			0
$906$	−10.9057	+	18.8892i	−0.362317	+	0.627552i
$907$	44.0268	−	25.4189i	1.46188	−	0.844019i	0.462786	−	0.886470i	$-0.346850\pi$
$907$	44.0268	−	25.4189i	1.46188	−	0.844019i	0.999099	+	0.0424506i	$0.0135165\pi$
$908$	−13.8336	+	7.98683i	−0.459084	+	0.265052i
$909$	16.6491			0.552216
$910$		0			0
$911$	−11.1359			−0.368950			−0.184475	−	0.982837i	$-0.559059\pi$
$911$	−11.1359			−0.368950			−0.184475	+	0.982837i	$0.559059\pi$
$912$	−2.73861	+	1.58114i	−0.0906845	+	0.0523567i
$913$	35.4614	−	20.4737i	1.17360	−	0.677579i
$914$	17.8246	−	30.8730i	0.589584	−	1.02119i
$915$		0			0
$916$	−1.24342	+	2.15366i	−0.0410836	+	0.0711589i
$917$	10.0656	+	5.81139i	0.332396	+	0.191909i
$918$			7.16228i			0.236390i
$919$	14.0680	−	24.3664i	0.464060	−	0.803775i	−0.535099	−	0.844789i	$-0.679726\pi$
$919$	14.0680	−	24.3664i	0.464060	−	0.803775i	0.999159	+	0.0410146i	$0.0130590\pi$
$920$		0			0
$921$	4.32456	+	7.49035i	0.142499	+	0.246815i
$922$		−	10.8377i		−	0.356921i
$923$	28.2522	−	0.635944i	0.929931	−	0.0209323i
$924$	−9.48683			−0.312094
$925$		0			0
$926$	11.7434	+	20.3402i	0.385913	+	0.668420i
$927$	−11.6799	−	6.74342i	−0.383620	−	0.221483i
$928$			8.32456i			0.273267i
$929$	20.3246	−	35.2032i	0.666827	−	1.15498i	−0.311959	−	0.950095i	$-0.600985\pi$
$929$	20.3246	−	35.2032i	0.666827	−	1.15498i	0.978786	−	0.204883i	$-0.0656814\pi$
$930$		0			0
$931$	9.48683			0.310918
$932$	22.7977	+	13.1623i	0.746765	+	0.431145i
$933$	10.8139	−	6.24342i	0.354032	−	0.204400i
$934$	1.50000	+	2.59808i	0.0490815	+	0.0850117i
$935$		0			0
$936$	−0.0811388	−	3.60464i	−0.00265211	−	0.117821i
$937$			29.6491i			0.968594i	0.874904	+	0.484297i	$0.160925\pi$
$937$			29.6491i			0.968594i	−0.874904	+	0.484297i	$0.839075\pi$
$938$	10.9545	−	6.32456i	0.357676	−	0.206504i
$939$	−8.82456	−	15.2846i	−0.287978	−	0.498793i
$940$		0			0
$941$	−12.0000			−0.391189			−0.195594	−	0.980685i	$-0.562664\pi$
$941$	−12.0000			−0.391189			−0.195594	+	0.980685i	$0.562664\pi$
$942$	−8.51972	−	4.91886i	−0.277587	−	0.160265i
$943$	34.1966	+	19.7434i	1.11359	+	0.642934i
$944$	6.00000			0.195283
$945$		0			0
$946$	−7.74342	−	13.4120i	−0.251760	−	0.436061i
$947$	−19.3564	+	11.1754i	−0.629000	+	0.363153i	−0.780365	−	0.625325i	$-0.784966\pi$
$947$	−19.3564	+	11.1754i	−0.629000	+	0.363153i	0.151365	+	0.988478i	$0.451633\pi$
$948$			9.16228i			0.297577i
$949$	−4.08114	+	2.48035i	−0.132479	+	0.0805154i
$950$		0			0
$951$	0.0943058	+	0.163343i	0.00305808	+	0.00529674i
$952$	−19.6147	+	11.3246i	−0.635716	+	0.367031i
$953$	−19.4514	−	11.2302i	−0.630091	−	0.363783i	0.150696	−	0.988580i	$-0.451849\pi$
$953$	−19.4514	−	11.2302i	−0.630091	−	0.363783i	−0.780787	+	0.624797i	$0.785182\pi$
$954$	−7.16228			−0.231887
$955$		0			0
$956$	0.243416	−	0.421610i	0.00787265	−	0.0136358i
$957$			24.9737i			0.807284i
$958$	−22.7977	−	13.1623i	−0.736561	−	0.425254i
$959$	−18.9737	−	32.8634i	−0.612692	−	1.06121i
$960$		0			0
$961$	52.9473			1.70798
$962$	37.8012	−	0.850889i	1.21876	−	0.0274338i
$963$			6.00000i			0.193347i
$964$	4.00000	+	6.92820i	0.128831	+	0.223142i
$965$		0			0
$966$	6.58114	−	11.3989i	0.211745	−	0.366753i
$967$			15.0263i			0.483214i	0.970374	+	0.241607i	$0.0776745\pi$
$967$			15.0263i			0.483214i	−0.970374	+	0.241607i	$0.922325\pi$
$968$	−1.73205	−	1.00000i	−0.0556702	−	0.0321412i
$969$	−11.3246	+	19.6147i	−0.363797	+	0.630115i
$970$		0			0
$971$	−21.0000	+	36.3731i	−0.673922	+	1.16727i	0.302861	+	0.953035i	$0.402058\pi$
$971$	−21.0000	+	36.3731i	−0.673922	+	1.16727i	−0.976783	+	0.214232i	$0.931275\pi$
$972$	−0.866025	+	0.500000i	−0.0277778	+	0.0160375i
$973$	−50.1839	+	28.9737i	−1.60882	+	0.928853i
$974$	3.16228			0.101326
$975$		0			0
$976$	14.4868			0.463712
$977$	33.1900	−	19.1623i	1.06184	−	0.613056i	0.135902	−	0.990722i	$-0.456607\pi$
$977$	33.1900	−	19.1623i	1.06184	−	0.613056i	0.925942	+	0.377667i	$0.123273\pi$
$978$	13.6931	−	7.90569i	0.437856	−	0.252796i
$979$	−10.7434	+	18.6081i	−0.343361	+	0.594719i
$980$		0			0
$981$	−4.24342	+	7.34981i	−0.135482	+	0.234661i
$982$	−13.8336	−	7.98683i	−0.441448	−	0.254870i
$983$		−	21.2982i		−	0.679308i	−0.940550	−	0.339654i	$-0.889690\pi$
$983$		−	21.2982i		−	0.679308i	0.940550	−	0.339654i	$-0.110310\pi$
$984$	4.74342	−	8.21584i	0.151215	−	0.261911i
$985$		0			0
$986$	29.8114	+	51.6348i	0.949388	+	1.64439i
$987$			18.9737i			0.603938i
$988$	5.47723	−	10.0000i	0.174254	−	0.318142i
$989$	21.4868			0.683242
$990$		0			0
$991$	−29.0680	−	50.3472i	−0.923375	−	1.59933i	−0.794155	−	0.607716i	$-0.792086\pi$
$991$	−29.0680	−	50.3472i	−0.923375	−	1.59933i	−0.129220	−	0.991616i	$-0.541247\pi$
$992$	−7.93477	−	4.58114i	−0.251929	−	0.145451i
$993$		−	8.83772i		−	0.280457i
$994$	12.3925	−	21.4645i	0.393067	−	0.680812i
$995$		0			0
$996$	13.6491			0.432489
$997$	6.08498	+	3.51317i	0.192713	+	0.111263i	0.593252	−	0.805017i	$-0.297844\pi$
$997$	6.08498	+	3.51317i	0.192713	+	0.111263i	−0.400539	+	0.916280i	$0.631177\pi$
$998$	−7.09155	+	4.09431i	−0.224479	+	0.129603i
$999$	−5.24342	−	9.08186i	−0.165894	−	0.287337i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1950.2.i.ba.451.2	✓	4	65.48	odd	12
1950.2.i.ba.601.2	yes	4	5.3	odd	4
1950.2.i.bf.451.1	yes	4	65.22	odd	12
1950.2.i.bf.601.1	yes	4	5.2	odd	4
1950.2.z.o.1699.1		8	13.9	even	3	inner
1950.2.z.o.1699.4		8	65.9	even	6	inner
1950.2.z.o.1849.1		8	5.4	even	2	inner
1950.2.z.o.1849.4		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} +(1.87259 + 3.08114i) q^{13} +3.16228 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-6.20271 - 3.58114i) q^{17} -1.00000i q^{18} +(1.58114 - 2.73861i) q^{19} +3.16228 q^{21} +(-2.59808 - 1.50000i) q^{22} +(3.60464 - 2.08114i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(3.16228 + 1.73205i) q^{26} -1.00000i q^{27} +(2.73861 - 1.58114i) q^{28} +(-4.16228 - 7.20928i) q^{29} +9.16228 q^{31} +(-0.866025 - 0.500000i) q^{32} +(-2.59808 - 1.50000i) q^{33} -7.16228 q^{34} +(-0.500000 - 0.866025i) q^{36} +(9.08186 - 5.24342i) q^{37} -3.16228i q^{38} +(3.16228 + 1.73205i) q^{39} +(4.74342 + 8.21584i) q^{41} +(2.73861 - 1.58114i) q^{42} +(4.47066 + 2.58114i) q^{43} -3.00000 q^{44} +(2.08114 - 3.60464i) q^{46} +6.00000i q^{47} +(-0.866025 - 0.500000i) q^{48} +(1.50000 + 2.59808i) q^{49} -7.16228 q^{51} +(3.60464 - 0.0811388i) q^{52} -7.16228i q^{53} +(-0.500000 - 0.866025i) q^{54} +(1.58114 - 2.73861i) q^{56} -3.16228i q^{57} +(-7.20928 - 4.16228i) q^{58} +(-3.00000 + 5.19615i) q^{59} +(-7.24342 + 12.5460i) q^{61} +(7.93477 - 4.58114i) q^{62} +(2.73861 - 1.58114i) q^{63} -1.00000 q^{64} -3.00000 q^{66} +(3.46410 - 2.00000i) q^{67} +(-6.20271 + 3.58114i) q^{68} +(2.08114 - 3.60464i) q^{69} +(3.91886 - 6.78767i) q^{71} +(-0.866025 - 0.500000i) q^{72} +1.32456i q^{73} +(5.24342 - 9.08186i) q^{74} +(-1.58114 - 2.73861i) q^{76} -9.48683i q^{77} +(3.60464 - 0.0811388i) q^{78} -9.16228 q^{79} +(-0.500000 - 0.866025i) q^{81} +(8.21584 + 4.74342i) q^{82} +13.6491i q^{83} +(1.58114 - 2.73861i) q^{84} +5.16228 q^{86} +(-7.20928 - 4.16228i) q^{87} +(-2.59808 + 1.50000i) q^{88} +(-3.58114 - 6.20271i) q^{89} +(0.256584 + 11.3989i) q^{91} -4.16228i q^{92} +(7.93477 - 4.58114i) q^{93} +(3.00000 + 5.19615i) q^{94} -1.00000 q^{96} +(-4.04905 - 2.33772i) 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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