LMFDB - Embedded newform 1950.2.z.p.1699.1

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			1699.1
Root			$-0.578737 + 2.15988i$ of defining polynomial
Character	$\chi$	$=$	1950.1699
Dual form			1950.2.z.p.1849.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{6} +(-4.47066 + 2.58114i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(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} +(-4.47066 + 2.58114i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-0.500000 + 0.866025i) q^{11} -1.00000i q^{12} +(-1.87259 + 3.08114i) q^{13} +5.16228 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-4.47066 + 2.58114i) q^{17} -1.00000i q^{18} +(-0.581139 - 1.00656i) q^{19} +5.16228 q^{21} +(0.866025 - 0.500000i) q^{22} +(3.60464 + 2.08114i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(3.16228 - 1.73205i) q^{26} -1.00000i q^{27} +(-4.47066 - 2.58114i) q^{28} +(2.16228 - 3.74517i) q^{29} -7.16228 q^{31} +(0.866025 - 0.500000i) q^{32} +(0.866025 - 0.500000i) q^{33} +5.16228 q^{34} +(-0.500000 + 0.866025i) q^{36} +(5.33669 + 3.08114i) q^{37} +1.16228i q^{38} +(3.16228 - 1.73205i) q^{39} +(-2.58114 + 4.47066i) q^{41} +(-4.47066 - 2.58114i) q^{42} +(-2.73861 + 1.58114i) q^{43} -1.00000 q^{44} +(-2.08114 - 3.60464i) q^{46} -6.00000i q^{47} +(0.866025 - 0.500000i) q^{48} +(9.82456 - 17.0166i) q^{49} +5.16228 q^{51} +(-3.60464 - 0.0811388i) q^{52} -11.4868i q^{53} +(-0.500000 + 0.866025i) q^{54} +(2.58114 + 4.47066i) q^{56} +1.16228i q^{57} +(-3.74517 + 2.16228i) q^{58} +(5.00000 + 8.66025i) q^{59} +(-3.08114 - 5.33669i) q^{61} +(6.20271 + 3.58114i) q^{62} +(-4.47066 - 2.58114i) q^{63} -1.00000 q^{64} -1.00000 q^{66} +(-4.47066 - 2.58114i) q^{68} +(-2.08114 - 3.60464i) q^{69} +(4.24342 + 7.34981i) q^{71} +(0.866025 - 0.500000i) q^{72} -9.32456i q^{73} +(-3.08114 - 5.33669i) q^{74} +(0.581139 - 1.00656i) q^{76} -5.16228i q^{77} +(-3.60464 - 0.0811388i) q^{78} -5.48683 q^{79} +(-0.500000 + 0.866025i) q^{81} +(4.47066 - 2.58114i) q^{82} +9.00000i q^{83} +(2.58114 + 4.47066i) q^{84} +3.16228 q^{86} +(-3.74517 + 2.16228i) q^{87} +(0.866025 + 0.500000i) q^{88} +(3.74342 - 6.48379i) q^{89} +(0.418861 - 18.6081i) q^{91} +4.16228i q^{92} +(6.20271 + 3.58114i) q^{93} +(-3.00000 + 5.19615i) q^{94} -1.00000 q^{96} +(6.34325 - 3.66228i) q^{97} +(-17.0166 + 9.82456i) q^{98} -1.00000 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} - 4 q^{11} + 16 q^{14} - 4 q^{16} + 8 q^{19} + 16 q^{21} - 4 q^{24} - 8 q^{29} - 32 q^{31} + 16 q^{34} - 4 q^{36} - 8 q^{41} - 8 q^{44} - 4 q^{46} + 28 q^{49} + 16 q^{51} - 4 q^{54} + 8 q^{56} + 40 q^{59} - 12 q^{61} - 8 q^{64} - 8 q^{66} - 4 q^{69} - 4 q^{71} - 12 q^{74} - 8 q^{76} + 32 q^{79} - 4 q^{81} + 8 q^{84} - 8 q^{89} + 16 q^{91} - 24 q^{94} - 8 q^{96} - 8 q^{99}+O(q^{100}) $ 8 * q + 4 * q^4 + 4 * q^6 + 4 * q^9 - 4 * q^11 + 16 * q^14 - 4 * q^16 + 8 * q^19 + 16 * q^21 - 4 * q^24 - 8 * q^29 - 32 * q^31 + 16 * q^34 - 4 * q^36 - 8 * q^41 - 8 * q^44 - 4 * q^46 + 28 * q^49 + 16 * q^51 - 4 * q^54 + 8 * q^56 + 40 * q^59 - 12 * q^61 - 8 * q^64 - 8 * q^66 - 4 * q^69 - 4 * q^71 - 12 * q^74 - 8 * q^76 + 32 * q^79 - 4 * q^81 + 8 * q^84 - 8 * q^89 + 16 * q^91 - 24 * q^94 - 8 * q^96 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.866025	−	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
$7$	−4.47066	+	2.58114i	−1.68975	+	0.975579i	−0.735051	+	0.678012i	$0.762842\pi$
$7$	−4.47066	+	2.58114i	−1.68975	+	0.975579i	−0.954701	+	0.297567i	$0.903825\pi$
$8$		−	1.00000i		−	0.353553i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$		0			0
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i	−0.931505	−	0.363727i	$-0.881504\pi$
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i	0.780750	+	0.624844i	$0.214837\pi$
$12$		−	1.00000i		−	0.288675i
$13$	−1.87259	+	3.08114i	−0.519362	+	0.854554i
$13$	−1.87259	+	3.08114i	−0.519362	+	0.854554i
$14$	5.16228			1.37968
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−4.47066	+	2.58114i	−1.08430	+	0.626018i	−0.932052	−	0.362325i	$-0.881983\pi$
$17$	−4.47066	+	2.58114i	−1.08430	+	0.626018i	−0.152243	+	0.988343i	$0.548650\pi$
$18$		−	1.00000i		−	0.235702i
$19$	−0.581139	−	1.00656i	−0.133322	−	0.230921i	0.791633	−	0.610997i	$-0.209231\pi$
$19$	−0.581139	−	1.00656i	−0.133322	−	0.230921i	−0.924955	+	0.380076i	$0.875898\pi$
$20$		0			0
$21$	5.16228			1.12650
$22$	0.866025	−	0.500000i	0.184637	−	0.106600i
$23$	3.60464	+	2.08114i	0.751619	+	0.433947i	0.826279	−	0.563262i	$-0.190454\pi$
$23$	3.60464	+	2.08114i	0.751619	+	0.433947i	−0.0746596	+	0.997209i	$0.523787\pi$
$24$	−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
$28$	−4.47066	−	2.58114i	−0.844876	−	0.487789i
$29$	2.16228	−	3.74517i	0.401525	−	0.695461i	−0.592385	−	0.805655i	$-0.701814\pi$
$29$	2.16228	−	3.74517i	0.401525	−	0.695461i	0.993910	+	0.110193i	$0.0351470\pi$
$30$		0			0
$31$	−7.16228			−1.28638			−0.643192	−	0.765705i	$-0.722390\pi$
$31$	−7.16228			−1.28638			−0.643192	+	0.765705i	$0.722390\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	0.866025	−	0.500000i	0.150756	−	0.0870388i
$34$	5.16228			0.885323
$35$		0			0
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	5.33669	+	3.08114i	0.877346	+	0.506536i	0.869783	−	0.493435i	$-0.164259\pi$
$37$	5.33669	+	3.08114i	0.877346	+	0.506536i	0.00756376	+	0.999971i	$0.497592\pi$
$38$			1.16228i			0.188546i
$39$	3.16228	−	1.73205i	0.506370	−	0.277350i
$40$		0			0
$41$	−2.58114	+	4.47066i	−0.403106	+	0.698200i	−0.994099	−	0.108476i	$-0.965403\pi$
$41$	−2.58114	+	4.47066i	−0.403106	+	0.698200i	0.590993	+	0.806677i	$0.298736\pi$
$42$	−4.47066	−	2.58114i	−0.689838	−	0.398278i
$43$	−2.73861	+	1.58114i	−0.417635	+	0.241121i	−0.694065	−	0.719913i	$-0.744182\pi$
$43$	−2.73861	+	1.58114i	−0.417635	+	0.241121i	0.276430	+	0.961034i	$0.410849\pi$
$44$	−1.00000			−0.150756
$45$		0			0
$46$	−2.08114	−	3.60464i	−0.306847	−	0.531475i
$47$		−	6.00000i		−	0.875190i	−0.899172	−	0.437595i	$-0.855830\pi$
$47$		−	6.00000i		−	0.875190i	0.899172	−	0.437595i	$-0.144170\pi$
$48$	0.866025	−	0.500000i	0.125000	−	0.0721688i
$49$	9.82456	−	17.0166i	1.40351	−	2.43095i
$50$		0			0
$51$	5.16228			0.722863
$52$	−3.60464	−	0.0811388i	−0.499873	−	0.0112519i
$53$		−	11.4868i		−	1.57784i	−0.614497	−	0.788919i	$-0.710641\pi$
$53$		−	11.4868i		−	1.57784i	0.614497	−	0.788919i	$-0.289359\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$		0			0
$56$	2.58114	+	4.47066i	0.344919	+	0.597418i
$57$			1.16228i			0.153947i
$58$	−3.74517	+	2.16228i	−0.491766	+	0.283921i
$59$	5.00000	+	8.66025i	0.650945	+	1.12747i	0.982894	+	0.184172i	$0.0589603\pi$
$59$	5.00000	+	8.66025i	0.650945	+	1.12747i	−0.331949	+	0.943297i	$0.607706\pi$
$60$		0			0
$61$	−3.08114	−	5.33669i	−0.394499	−	0.683293i	0.598538	−	0.801095i	$-0.295749\pi$
$61$	−3.08114	−	5.33669i	−0.394499	−	0.683293i	−0.993037	+	0.117802i	$0.962415\pi$
$62$	6.20271	+	3.58114i	0.787746	+	0.454805i
$63$	−4.47066	−	2.58114i	−0.563251	−	0.325193i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−1.00000			−0.123091
$67$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$67$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$68$	−4.47066	−	2.58114i	−0.542148	−	0.313009i
$69$	−2.08114	−	3.60464i	−0.250540	−	0.433947i
$70$		0			0
$71$	4.24342	+	7.34981i	0.503601	+	0.872262i	0.999991	+	0.00416295i	$0.00132511\pi$
$71$	4.24342	+	7.34981i	0.503601	+	0.872262i	−0.496390	+	0.868099i	$0.665342\pi$
$72$	0.866025	−	0.500000i	0.102062	−	0.0589256i
$73$		−	9.32456i		−	1.09136i	−0.837995	−	0.545678i	$-0.816272\pi$
$73$		−	9.32456i		−	1.09136i	0.837995	−	0.545678i	$-0.183728\pi$
$74$	−3.08114	−	5.33669i	−0.358175	−	0.620377i
$75$		0			0
$76$	0.581139	−	1.00656i	0.0666612	−	0.115461i
$77$		−	5.16228i		−	0.588296i
$78$	−3.60464	−	0.0811388i	−0.408145	−	0.00918716i
$79$	−5.48683			−0.617317			−0.308658	−	0.951173i	$-0.599880\pi$
$79$	−5.48683			−0.617317			−0.308658	+	0.951173i	$0.599880\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	4.47066	−	2.58114i	0.493702	−	0.285039i
$83$			9.00000i			0.987878i	0.869496	+	0.493939i	$0.164443\pi$
$83$			9.00000i			0.987878i	−0.869496	+	0.493939i	$0.835557\pi$
$84$	2.58114	+	4.47066i	0.281625	+	0.487789i
$85$		0			0
$86$	3.16228			0.340997
$87$	−3.74517	+	2.16228i	−0.401525	+	0.231820i
$88$	0.866025	+	0.500000i	0.0923186	+	0.0533002i
$89$	3.74342	−	6.48379i	0.396801	−	0.687280i	−0.596528	−	0.802592i	$-0.703454\pi$
$89$	3.74342	−	6.48379i	0.396801	−	0.687280i	0.993329	+	0.115312i	$0.0367868\pi$
$90$		0			0
$91$	0.418861	−	18.6081i	0.0439086	−	1.95066i
$92$			4.16228i			0.433947i
$93$	6.20271	+	3.58114i	0.643192	+	0.371347i
$94$	−3.00000	+	5.19615i	−0.309426	+	0.535942i
$95$		0			0
$96$	−1.00000			−0.102062
$97$	6.34325	−	3.66228i	0.644060	−	0.371848i	−0.142117	−	0.989850i	$-0.545391\pi$
$97$	6.34325	−	3.66228i	0.644060	−	0.371848i	0.786177	+	0.618002i	$0.212058\pi$
$98$	−17.0166	+	9.82456i	−1.71894	+	0.992430i
$99$	−1.00000			−0.100504
$100$		0			0
$101$	−6.32456	+	10.9545i	−0.629317	+	1.09001i	0.358372	+	0.933579i	$0.383332\pi$
$101$	−6.32456	+	10.9545i	−0.629317	+	1.09001i	−0.987689	+	0.156430i	$0.950001\pi$
$102$	−4.47066	−	2.58114i	−0.442662	−	0.255571i
$103$		−	15.4868i		−	1.52596i	−0.646420	−	0.762981i	$-0.723735\pi$
$103$		−	15.4868i		−	1.52596i	0.646420	−	0.762981i	$-0.276265\pi$
$104$	3.08114	+	1.87259i	0.302131	+	0.183622i
$105$		0			0
$106$	−5.74342	+	9.94789i	−0.557850	+	0.966224i
$107$	−5.19615	−	3.00000i	−0.502331	−	0.290021i	0.227345	−	0.973814i	$-0.426996\pi$
$107$	−5.19615	−	3.00000i	−0.502331	−	0.290021i	−0.729676	+	0.683793i	$0.760329\pi$
$108$	0.866025	−	0.500000i	0.0833333	−	0.0481125i
$109$	7.83772			0.750718			0.375359	−	0.926880i	$-0.377519\pi$
$109$	7.83772			0.750718			0.375359	+	0.926880i	$0.377519\pi$
$110$		0			0
$111$	−3.08114	−	5.33669i	−0.292449	−	0.506536i
$112$		−	5.16228i		−	0.487789i
$113$	15.8695	−	9.16228i	1.49288	−	0.861915i	0.492913	−	0.870079i	$-0.335932\pi$
$113$	15.8695	−	9.16228i	1.49288	−	0.861915i	0.999967	+	0.00816393i	$0.00259869\pi$
$114$	0.581139	−	1.00656i	0.0544286	−	0.0942732i
$115$		0			0
$116$	4.32456			0.401525
$117$	−3.60464	−	0.0811388i	−0.333249	−	0.00750129i
$118$		−	10.0000i		−	0.920575i
$119$	13.3246	−	23.0788i	1.22146	−	2.11563i
$120$		0			0
$121$	5.00000	+	8.66025i	0.454545	+	0.787296i
$122$			6.16228i			0.557906i
$123$	4.47066	−	2.58114i	0.403106	−	0.232733i
$124$	−3.58114	−	6.20271i	−0.321596	−	0.557020i
$125$		0			0
$126$	2.58114	+	4.47066i	0.229946	+	0.398278i
$127$	−0.281073	−	0.162278i	−0.0249412	−	0.0143998i	0.487478	−	0.873136i	$-0.337917\pi$
$127$	−0.281073	−	0.162278i	−0.0249412	−	0.0143998i	−0.512419	+	0.858736i	$0.671250\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	3.16228			0.278423
$130$		0			0
$131$	−16.3246			−1.42628			−0.713142	−	0.701020i	$-0.752728\pi$
$131$	−16.3246			−1.42628			−0.713142	+	0.701020i	$0.752728\pi$
$132$	0.866025	+	0.500000i	0.0753778	+	0.0435194i
$133$	5.19615	+	3.00000i	0.450564	+	0.260133i
$134$		0			0
$135$		0			0
$136$	2.58114	+	4.47066i	0.221331	+	0.383356i
$137$	−14.4186	+	8.32456i	−1.23186	+	0.711215i	−0.967417	−	0.253187i	$-0.918521\pi$
$137$	−14.4186	+	8.32456i	−1.23186	+	0.711215i	−0.264443	+	0.964401i	$0.585188\pi$
$138$			4.16228i			0.354317i
$139$	−5.16228	−	8.94133i	−0.437859	−	0.758393i	0.559665	−	0.828719i	$-0.310930\pi$
$139$	−5.16228	−	8.94133i	−0.437859	−	0.758393i	−0.997524	+	0.0703252i	$0.977596\pi$
$140$		0			0
$141$	−3.00000	+	5.19615i	−0.252646	+	0.437595i
$142$		−	8.48683i		−	0.712199i
$143$	−1.73205	−	3.16228i	−0.144841	−	0.264443i
$144$	−1.00000			−0.0833333
$145$		0			0
$146$	−4.66228	+	8.07530i	−0.385853	+	0.668317i
$147$	−17.0166	+	9.82456i	−1.40351	+	0.810316i
$148$			6.16228i			0.506536i
$149$	6.41886	+	11.1178i	0.525854	+	0.910805i	0.999546	+	0.0301150i	$0.00958736\pi$
$149$	6.41886	+	11.1178i	0.525854	+	0.910805i	−0.473693	+	0.880690i	$0.657079\pi$
$150$		0			0
$151$	−9.48683			−0.772028			−0.386014	−	0.922493i	$-0.626148\pi$
$151$	−9.48683			−0.772028			−0.386014	+	0.922493i	$0.626148\pi$
$152$	−1.00656	+	0.581139i	−0.0816430	+	0.0471366i
$153$	−4.47066	−	2.58114i	−0.361432	−	0.208673i
$154$	−2.58114	+	4.47066i	−0.207994	+	0.360256i
$155$		0			0
$156$	3.08114	+	1.87259i	0.246689	+	0.149927i
$157$		−	14.4868i		−	1.15618i	−0.815975	−	0.578088i	$-0.803799\pi$
$157$		−	14.4868i		−	1.15618i	0.815975	−	0.578088i	$-0.196201\pi$
$158$	4.75174	+	2.74342i	0.378028	+	0.218254i
$159$	−5.74342	+	9.94789i	−0.455483	+	0.788919i
$160$		0			0
$161$	−21.4868			−1.69340
$162$	0.866025	−	0.500000i	0.0680414	−	0.0392837i
$163$	2.45754	−	1.41886i	0.192489	−	0.111134i	−0.400658	−	0.916228i	$-0.631218\pi$
$163$	2.45754	−	1.41886i	0.192489	−	0.111134i	0.593147	+	0.805094i	$0.297885\pi$
$164$	−5.16228			−0.403106
$165$		0			0
$166$	4.50000	−	7.79423i	0.349268	−	0.604949i
$167$	−12.5460	−	7.24342i	−0.970836	−	0.560512i	−0.0713450	−	0.997452i	$-0.522729\pi$
$167$	−12.5460	−	7.24342i	−0.970836	−	0.560512i	−0.899491	+	0.436939i	$0.856062\pi$
$168$		−	5.16228i		−	0.398278i
$169$	−5.98683	−	11.5394i	−0.460526	−	0.887646i
$170$		0			0
$171$	0.581139	−	1.00656i	0.0444408	−	0.0769737i
$172$	−2.73861	−	1.58114i	−0.208817	−	0.120561i
$173$	8.94133	−	5.16228i	0.679797	−	0.392481i	−0.119982	−	0.992776i	$-0.538284\pi$
$173$	8.94133	−	5.16228i	0.679797	−	0.392481i	0.799778	+	0.600295i	$0.204950\pi$
$174$	4.32456			0.327844
$175$		0			0
$176$	−0.500000	−	0.866025i	−0.0376889	−	0.0652791i
$177$		−	10.0000i		−	0.751646i
$178$	−6.48379	+	3.74342i	−0.485980	+	0.280581i
$179$	−5.82456	+	10.0884i	−0.435348	+	0.754044i	−0.997324	−	0.0731090i	$-0.976708\pi$
$179$	−5.82456	+	10.0884i	−0.435348	+	0.754044i	0.561976	+	0.827153i	$0.310041\pi$
$180$		0			0
$181$	26.1623			1.94463			0.972313	−	0.233681i	$-0.0750770\pi$
$181$	26.1623			1.94463			0.972313	+	0.233681i	$0.0750770\pi$
$182$	−9.66682	+	15.9057i	−0.716552	+	1.17901i
$183$			6.16228i			0.455529i
$184$	2.08114	−	3.60464i	0.153424	−	0.265737i
$185$		0			0
$186$	−3.58114	−	6.20271i	−0.262582	−	0.454805i
$187$		−	5.16228i		−	0.377503i
$188$	5.19615	−	3.00000i	0.378968	−	0.218797i
$189$	2.58114	+	4.47066i	0.187750	+	0.325193i
$190$		0			0
$191$	3.24342	+	5.61776i	0.234685	+	0.406487i	0.959181	−	0.282792i	$-0.0912607\pi$
$191$	3.24342	+	5.61776i	0.234685	+	0.406487i	−0.724496	+	0.689279i	$0.757927\pi$
$192$	0.866025	+	0.500000i	0.0625000	+	0.0360844i
$193$	−8.07530	−	4.66228i	−0.581273	−	0.335598i	0.180366	−	0.983600i	$-0.442272\pi$
$193$	−8.07530	−	4.66228i	−0.581273	−	0.335598i	−0.761639	+	0.648001i	$0.775605\pi$
$194$	−7.32456			−0.525872
$195$		0			0
$196$	19.6491			1.40351
$197$	5.19615	+	3.00000i	0.370211	+	0.213741i	0.673550	−	0.739141i	$-0.264768\pi$
$197$	5.19615	+	3.00000i	0.370211	+	0.213741i	−0.303340	+	0.952882i	$0.598102\pi$
$198$	0.866025	+	0.500000i	0.0615457	+	0.0355335i
$199$	−6.58114	−	11.3989i	−0.466525	−	0.808044i	0.532744	−	0.846276i	$-0.321161\pi$
$199$	−6.58114	−	11.3989i	−0.466525	−	0.808044i	−0.999269	+	0.0382320i	$0.987827\pi$
$200$		0			0
$201$		0			0
$202$	10.9545	−	6.32456i	0.770752	−	0.444994i
$203$			22.3246i			1.56688i
$204$	2.58114	+	4.47066i	0.180716	+	0.313009i
$205$		0			0
$206$	−7.74342	+	13.4120i	−0.539509	+	0.934458i
$207$			4.16228i			0.289298i
$208$	−1.73205	−	3.16228i	−0.120096	−	0.219265i
$209$	1.16228			0.0803964
$210$		0			0
$211$	6.41886	−	11.1178i	0.441893	−	0.765380i	−0.555937	−	0.831224i	$-0.687641\pi$
$211$	6.41886	−	11.1178i	0.441893	−	0.765380i	0.997830	+	0.0658437i	$0.0209739\pi$
$212$	9.94789	−	5.74342i	0.683224	−	0.394459i
$213$		−	8.48683i		−	0.581508i
$214$	3.00000	+	5.19615i	0.205076	+	0.355202i
$215$		0			0
$216$	−1.00000			−0.0680414
$217$	32.0201	−	18.4868i	2.17367	−	1.25497i
$218$	−6.78767	−	3.91886i	−0.459719	−	0.265419i
$219$	−4.66228	+	8.07530i	−0.315048	+	0.545678i
$220$		0			0
$221$	0.418861	−	18.6081i	0.0281757	−	1.25172i
$222$			6.16228i			0.413585i
$223$	−18.3271	−	10.5811i	−1.22727	−	0.708565i	−0.260813	−	0.965389i	$-0.583991\pi$
$223$	−18.3271	−	10.5811i	−1.22727	−	0.708565i	−0.966458	+	0.256824i	$0.917324\pi$
$224$	−2.58114	+	4.47066i	−0.172460	+	0.298709i
$225$		0			0
$226$	−18.3246			−1.21893
$227$	−8.07530	+	4.66228i	−0.535977	+	0.309446i	−0.743447	−	0.668795i	$-0.766810\pi$
$227$	−8.07530	+	4.66228i	−0.535977	+	0.309446i	0.207470	+	0.978241i	$0.433477\pi$
$228$	−1.00656	+	0.581139i	−0.0666612	+	0.0384869i
$229$	−18.8114			−1.24309			−0.621546	−	0.783378i	$-0.713495\pi$
$229$	−18.8114			−1.24309			−0.621546	+	0.783378i	$0.713495\pi$
$230$		0			0
$231$	−2.58114	+	4.47066i	−0.169826	+	0.294148i
$232$	−3.74517	−	2.16228i	−0.245883	−	0.141960i
$233$		−	2.32456i		−	0.152287i	−0.997097	−	0.0761433i	$-0.975739\pi$
$233$		−	2.32456i		−	0.152287i	0.997097	−	0.0761433i	$-0.0242607\pi$
$234$	3.08114	+	1.87259i	0.201420	+	0.122415i
$235$		0			0
$236$	−5.00000	+	8.66025i	−0.325472	+	0.563735i
$237$	4.75174	+	2.74342i	0.308658	+	0.178204i
$238$	−23.0788	+	13.3246i	−1.49598	+	0.863703i
$239$	8.48683			0.548968			0.274484	−	0.961592i	$-0.411493\pi$
$239$	8.48683			0.548968			0.274484	+	0.961592i	$0.411493\pi$
$240$		0			0
$241$	−14.6491	−	25.3730i	−0.943632	−	1.63442i	−0.758467	−	0.651711i	$-0.774051\pi$
$241$	−14.6491	−	25.3730i	−0.943632	−	1.63442i	−0.185165	−	0.982707i	$-0.559282\pi$
$242$		−	10.0000i		−	0.642824i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	3.08114	−	5.33669i	0.197250	−	0.341647i
$245$		0			0
$246$	−5.16228			−0.329135
$247$	4.18959	+	0.0943058i	0.266577	+	0.00600054i
$248$			7.16228i			0.454805i
$249$	4.50000	−	7.79423i	0.285176	−	0.493939i
$250$		0			0
$251$	−12.8246	−	22.2128i	−0.809479	−	1.40206i	−0.913225	−	0.407455i	$-0.866416\pi$
$251$	−12.8246	−	22.2128i	−0.809479	−	1.40206i	0.103747	−	0.994604i	$-0.466917\pi$
$252$		−	5.16228i		−	0.325193i
$253$	−3.60464	+	2.08114i	−0.226622	+	0.130840i
$254$	0.162278	+	0.281073i	0.0101822	+	0.0176361i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	18.6081	+	10.7434i	1.16074	+	0.670156i	0.951482	−	0.307704i	$-0.0995606\pi$
$257$	18.6081	+	10.7434i	1.16074	+	0.670156i	0.209262	+	0.977860i	$0.432894\pi$
$258$	−2.73861	−	1.58114i	−0.170499	−	0.0984374i
$259$	−31.8114			−1.97666
$260$		0			0
$261$	4.32456			0.267683
$262$	14.1375	+	8.16228i	0.873416	+	0.504267i
$263$	−1.87259	−	1.08114i	−0.115469	−	0.0666659i	0.441153	−	0.897432i	$-0.354569\pi$
$263$	−1.87259	−	1.08114i	−0.115469	−	0.0666659i	−0.556622	+	0.830766i	$0.687903\pi$
$264$	−0.500000	−	0.866025i	−0.0307729	−	0.0533002i
$265$		0			0
$266$	−3.00000	−	5.19615i	−0.183942	−	0.318597i
$267$	−6.48379	+	3.74342i	−0.396801	+	0.229093i
$268$		0			0
$269$	−12.5811	−	21.7912i	−0.767086	−	1.32863i	−0.939137	−	0.343543i	$-0.888373\pi$
$269$	−12.5811	−	21.7912i	−0.767086	−	1.32863i	0.172051	−	0.985088i	$-0.444961\pi$
$270$		0			0
$271$	−3.83772	+	6.64713i	−0.233125	+	0.403784i	−0.958726	−	0.284331i	$-0.908228\pi$
$271$	−3.83772	+	6.64713i	−0.233125	+	0.403784i	0.725601	+	0.688116i	$0.241562\pi$
$272$		−	5.16228i		−	0.313009i
$273$	−9.66682	+	15.9057i	−0.585062	+	0.962656i
$274$	16.6491			1.00581
$275$		0			0
$276$	2.08114	−	3.60464i	0.125270	−	0.216974i
$277$	2.15366	−	1.24342i	0.129401	−	0.0747097i	−0.433902	−	0.900960i	$-0.642864\pi$
$277$	2.15366	−	1.24342i	0.129401	−	0.0747097i	0.563303	+	0.826250i	$0.309530\pi$
$278$			10.3246i			0.619226i
$279$	−3.58114	−	6.20271i	−0.214397	−	0.371347i
$280$		0			0
$281$	10.8377			0.646524			0.323262	−	0.946309i	$-0.395220\pi$
$281$	10.8377			0.646524			0.323262	+	0.946309i	$0.395220\pi$
$282$	5.19615	−	3.00000i	0.309426	−	0.178647i
$283$	21.1834	+	12.2302i	1.25922	+	0.727013i	0.972924	−	0.231127i	$-0.0742414\pi$
$283$	21.1834	+	12.2302i	1.25922	+	0.727013i	0.286300	+	0.958140i	$0.407575\pi$
$284$	−4.24342	+	7.34981i	−0.251800	+	0.436131i
$285$		0			0
$286$	−0.0811388	+	3.60464i	−0.00479784	+	0.213147i
$287$		−	26.6491i		−	1.57305i
$288$	0.866025	+	0.500000i	0.0510310	+	0.0294628i
$289$	4.82456	−	8.35637i	0.283797	−	0.491551i
$290$		0			0
$291$	−7.32456			−0.429373
$292$	8.07530	−	4.66228i	0.472571	−	0.272839i
$293$	20.3402	−	11.7434i	1.18829	−	0.686058i	0.230370	−	0.973103i	$-0.426006\pi$
$293$	20.3402	−	11.7434i	1.18829	−	0.686058i	0.957917	+	0.287045i	$0.0926731\pi$
$294$	19.6491			1.14596
$295$		0			0
$296$	3.08114	−	5.33669i	0.179088	−	0.310189i
$297$	0.866025	+	0.500000i	0.0502519	+	0.0290129i
$298$		−	12.8377i		−	0.743669i
$299$	−13.1623	+	7.20928i	−0.761194	+	0.416923i
$300$		0			0
$301$	8.16228	−	14.1375i	0.470466	−	0.814871i
$302$	8.21584	+	4.74342i	0.472768	+	0.272953i
$303$	10.9545	−	6.32456i	0.629317	−	0.363336i
$304$	1.16228			0.0666612
$305$		0			0
$306$	2.58114	+	4.47066i	0.147554	+	0.255571i
$307$		0			0		1.00000			$0$
$307$		0			0		−1.00000			$\pi$
$308$	4.47066	−	2.58114i	0.254740	−	0.147074i
$309$	−7.74342	+	13.4120i	−0.440508	+	0.762981i
$310$		0			0
$311$	24.4868			1.38852			0.694260	−	0.719724i	$-0.255732\pi$
$311$	24.4868			1.38852			0.694260	+	0.719724i	$0.255732\pi$
$312$	−1.73205	−	3.16228i	−0.0980581	−	0.179029i
$313$			30.2982i			1.71256i	0.516515	+	0.856278i	$0.327229\pi$
$313$			30.2982i			1.71256i	−0.516515	+	0.856278i	$0.672771\pi$
$314$	−7.24342	+	12.5460i	−0.408770	+	0.708010i
$315$		0			0
$316$	−2.74342	−	4.75174i	−0.154329	−	0.267306i
$317$			17.8114i			1.00039i	0.865914	+	0.500194i	$0.166738\pi$
$317$			17.8114i			1.00039i	−0.865914	+	0.500194i	$0.833262\pi$
$318$	9.94789	−	5.74342i	0.557850	−	0.322075i
$319$	2.16228	+	3.74517i	0.121064	+	0.209690i
$320$		0			0
$321$	3.00000	+	5.19615i	0.167444	+	0.290021i
$322$	18.6081	+	10.7434i	1.03699	+	0.598707i
$323$	5.19615	+	3.00000i	0.289122	+	0.166924i
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	−2.83772			−0.157167
$327$	−6.78767	−	3.91886i	−0.375359	−	0.216714i
$328$	4.47066	+	2.58114i	0.246851	+	0.142520i
$329$	15.4868	+	26.8240i	0.853817	+	1.47885i
$330$		0			0
$331$	2.25658	+	3.90852i	0.124033	+	0.214832i	0.921355	−	0.388723i	$-0.127084\pi$
$331$	2.25658	+	3.90852i	0.124033	+	0.214832i	−0.797322	+	0.603555i	$0.793750\pi$
$332$	−7.79423	+	4.50000i	−0.427764	+	0.246970i
$333$			6.16228i			0.337691i
$334$	7.24342	+	12.5460i	0.396342	+	0.686485i
$335$		0			0
$336$	−2.58114	+	4.47066i	−0.140813	+	0.243895i
$337$			32.0000i			1.74315i	0.490261	+	0.871576i	$0.336901\pi$
$337$			32.0000i			1.74315i	−0.490261	+	0.871576i	$0.663099\pi$
$338$	−0.584952	+	12.9868i	−0.0318172	+	0.706391i
$339$	−18.3246			−0.995253
$340$		0			0
$341$	3.58114	−	6.20271i	0.193930	−	0.335896i
$342$	−1.00656	+	0.581139i	−0.0544286	+	0.0314244i
$343$			65.2982i			3.52577i
$344$	1.58114	+	2.73861i	0.0852493	+	0.147656i
$345$		0			0
$346$	−10.3246			−0.555052
$347$	16.1734	−	9.33772i	0.868234	−	0.501275i	0.00147310	−	0.999999i	$-0.499531\pi$
$347$	16.1734	−	9.33772i	0.868234	−	0.501275i	0.866761	+	0.498724i	$0.166198\pi$
$348$	−3.74517	−	2.16228i	−0.200762	−	0.115910i
$349$	−4.08114	+	7.06874i	−0.218458	+	0.378381i	−0.954337	−	0.298733i	$-0.903436\pi$
$349$	−4.08114	+	7.06874i	−0.218458	+	0.378381i	0.735878	+	0.677114i	$0.236769\pi$
$350$		0			0
$351$	3.08114	+	1.87259i	0.164459	+	0.0999513i
$352$			1.00000i			0.0533002i
$353$	−5.92164	−	3.41886i	−0.315177	−	0.181968i	0.334064	−	0.942551i	$-0.391580\pi$
$353$	−5.92164	−	3.41886i	−0.315177	−	0.181968i	−0.649241	+	0.760583i	$0.724913\pi$
$354$	−5.00000	+	8.66025i	−0.265747	+	0.460287i
$355$		0			0
$356$	7.48683			0.396801
$357$	−23.0788	+	13.3246i	−1.22146	+	0.705210i
$358$	10.0884	−	5.82456i	0.533190	−	0.307837i
$359$	16.6491			0.878706			0.439353	−	0.898314i	$-0.355208\pi$
$359$	16.6491			0.878706			0.439353	+	0.898314i	$0.355208\pi$
$360$		0			0
$361$	8.82456	−	15.2846i	0.464450	−	0.804451i
$362$	−22.6572	−	13.0811i	−1.19084	−	0.687529i
$363$		−	10.0000i		−	0.524864i
$364$	16.3246	−	8.94133i	0.855639	−	0.468653i
$365$		0			0
$366$	3.08114	−	5.33669i	0.161054	−	0.278953i
$367$	−15.5885	−	9.00000i	−0.813711	−	0.469796i	0.0345320	−	0.999404i	$-0.489006\pi$
$367$	−15.5885	−	9.00000i	−0.813711	−	0.469796i	−0.848243	+	0.529607i	$0.822339\pi$
$368$	−3.60464	+	2.08114i	−0.187905	+	0.108487i
$369$	−5.16228			−0.268737
$370$		0			0
$371$	29.6491	+	51.3538i	1.53931	+	2.66615i
$372$			7.16228i			0.371347i
$373$	7.34981	−	4.24342i	0.380559	−	0.219716i	−0.297503	−	0.954721i	$-0.596154\pi$
$373$	7.34981	−	4.24342i	0.380559	−	0.219716i	0.678061	+	0.735005i	$0.262820\pi$
$374$	−2.58114	+	4.47066i	−0.133468	+	0.231173i
$375$		0			0
$376$	−6.00000			−0.309426
$377$	7.49035	+	13.6754i	0.385773	+	0.704321i
$378$		−	5.16228i		−	0.265519i
$379$	−7.64911	+	13.2486i	−0.392908	+	0.680537i	−0.992832	−	0.119520i	$-0.961864\pi$
$379$	−7.64911	+	13.2486i	−0.392908	+	0.680537i	0.599923	+	0.800057i	$0.295198\pi$
$380$		0			0
$381$	0.162278	+	0.281073i	0.00831374	+	0.0143998i
$382$		−	6.48683i		−	0.331895i
$383$	29.2587	−	16.8925i	1.49505	−	0.863168i	0.495067	−	0.868855i	$-0.335144\pi$
$383$	29.2587	−	16.8925i	1.49505	−	0.863168i	0.999984	+	0.00568717i	$0.00181029\pi$
$384$	−0.500000	−	0.866025i	−0.0255155	−	0.0441942i
$385$		0			0
$386$	4.66228	+	8.07530i	0.237304	+	0.411022i
$387$	−2.73861	−	1.58114i	−0.139212	−	0.0803738i
$388$	6.34325	+	3.66228i	0.322030	+	0.185924i
$389$	4.97367			0.252175			0.126087	−	0.992019i	$-0.459758\pi$
$389$	4.97367			0.252175			0.126087	+	0.992019i	$0.459758\pi$
$390$		0			0
$391$	−21.4868			−1.08664
$392$	−17.0166	−	9.82456i	−0.859470	−	0.496215i
$393$	14.1375	+	8.16228i	0.713142	+	0.411732i
$394$	−3.00000	−	5.19615i	−0.151138	−	0.261778i
$395$		0			0
$396$	−0.500000	−	0.866025i	−0.0251259	−	0.0435194i
$397$	−6.64713	+	3.83772i	−0.333610	+	0.192610i	−0.657443	−	0.753505i	$-0.728362\pi$
$397$	−6.64713	+	3.83772i	−0.333610	+	0.192610i	0.323833	+	0.946114i	$0.395028\pi$
$398$			13.1623i			0.659765i
$399$	−3.00000	−	5.19615i	−0.150188	−	0.260133i
$400$		0			0
$401$	14.8114	−	25.6541i	0.739645	−	1.28110i	−0.213010	−	0.977050i	$-0.568327\pi$
$401$	14.8114	−	25.6541i	0.739645	−	1.28110i	0.952655	−	0.304053i	$-0.0983401\pi$
$402$		0			0
$403$	13.4120	−	22.0680i	0.668099	−	1.09928i
$404$	−12.6491			−0.629317
$405$		0			0
$406$	11.1623	−	19.3336i	0.553975	−	0.959512i
$407$	−5.33669	+	3.08114i	−0.264530	+	0.152726i
$408$		−	5.16228i		−	0.255571i
$409$	15.1623	+	26.2618i	0.749726	+	1.29856i	0.947954	+	0.318408i	$0.103148\pi$
$409$	15.1623	+	26.2618i	0.749726	+	1.29856i	−0.198227	+	0.980156i	$0.563518\pi$
$410$		0			0
$411$	16.6491			0.821240
$412$	13.4120	−	7.74342i	0.660761	−	0.381491i
$413$	−44.7066	−	25.8114i	−2.19987	−	1.27010i
$414$	2.08114	−	3.60464i	0.102282	−	0.177158i
$415$		0			0
$416$	−0.0811388	+	3.60464i	−0.00397816	+	0.176732i
$417$			10.3246i			0.505596i
$418$	−1.00656	−	0.581139i	−0.0492326	−	0.0284244i
$419$	−16.8246	+	29.1410i	−0.821933	+	1.42363i	0.0823073	+	0.996607i	$0.473771\pi$
$419$	−16.8246	+	29.1410i	−0.821933	+	1.42363i	−0.904241	+	0.427023i	$0.859562\pi$
$420$		0			0
$421$	−5.18861			−0.252877			−0.126439	−	0.991974i	$-0.540355\pi$
$421$	−5.18861			−0.252877			−0.126439	+	0.991974i	$0.540355\pi$
$422$	−11.1178	+	6.41886i	−0.541206	+	0.312465i
$423$	5.19615	−	3.00000i	0.252646	−	0.145865i
$424$	−11.4868			−0.557850
$425$		0			0
$426$	−4.24342	+	7.34981i	−0.205594	+	0.356100i
$427$	27.5495	+	15.9057i	1.33321	+	0.769730i
$428$		−	6.00000i		−	0.290021i
$429$	−0.0811388	+	3.60464i	−0.00391742	+	0.174034i
$430$		0			0
$431$	−9.24342	+	16.0101i	−0.445240	+	0.771178i	−0.998069	−	0.0621168i	$-0.980215\pi$
$431$	−9.24342	+	16.0101i	−0.445240	+	0.771178i	0.552829	+	0.833295i	$0.313548\pi$
$432$	0.866025	+	0.500000i	0.0416667	+	0.0240563i
$433$	−27.6900	+	15.9868i	−1.33070	+	0.768278i	−0.985406	−	0.170218i	$-0.945553\pi$
$433$	−27.6900	+	15.9868i	−1.33070	+	0.768278i	−0.345290	+	0.938496i	$0.612220\pi$
$434$	−36.9737			−1.77479
$435$		0			0
$436$	3.91886	+	6.78767i	0.187679	+	0.325070i
$437$		−	4.83772i		−	0.231420i
$438$	8.07530	−	4.66228i	0.385853	−	0.222772i
$439$	5.67544	−	9.83016i	0.270874	−	0.469168i	−0.698212	−	0.715891i	$-0.746021\pi$
$439$	5.67544	−	9.83016i	0.270874	−	0.469168i	0.969086	+	0.246723i	$0.0793539\pi$
$440$		0			0
$441$	19.6491			0.935672
$442$	−9.66682	+	15.9057i	−0.459804	+	0.756557i
$443$			6.35089i			0.301740i	0.988554	+	0.150870i	$0.0482075\pi$
$443$			6.35089i			0.301740i	−0.988554	+	0.150870i	$0.951793\pi$
$444$	3.08114	−	5.33669i	0.146224	−	0.253268i
$445$		0			0
$446$	10.5811	+	18.3271i	0.501031	+	0.867812i
$447$		−	12.8377i		−	0.607203i
$448$	4.47066	−	2.58114i	0.211219	−	0.121947i
$449$	13.7434	+	23.8043i	0.648592	+	1.12339i	0.983459	+	0.181129i	$0.0579751\pi$
$449$	13.7434	+	23.8043i	0.648592	+	1.12339i	−0.334867	+	0.942265i	$0.608692\pi$
$450$		0			0
$451$	−2.58114	−	4.47066i	−0.121541	−	0.210515i
$452$	15.8695	+	9.16228i	0.746440	+	0.430957i
$453$	8.21584	+	4.74342i	0.386014	+	0.222865i
$454$	9.32456			0.437623
$455$		0			0
$456$	1.16228			0.0544286
$457$	14.1147	+	8.14911i	0.660257	+	0.381199i	0.792375	−	0.610035i	$-0.208844\pi$
$457$	14.1147	+	8.14911i	0.660257	+	0.381199i	−0.132118	+	0.991234i	$0.542178\pi$
$458$	16.2911	+	9.40569i	0.761235	+	0.439499i
$459$	2.58114	+	4.47066i	0.120477	+	0.208673i
$460$		0			0
$461$	−14.2302	−	24.6475i	−0.662769	−	1.14795i	−0.979885	−	0.199563i	$-0.936048\pi$
$461$	−14.2302	−	24.6475i	−0.662769	−	1.14795i	0.317116	−	0.948387i	$-0.397285\pi$
$462$	4.47066	−	2.58114i	0.207994	−	0.120085i
$463$		−	27.8114i		−	1.29250i	−0.763124	−	0.646252i	$-0.776335\pi$
$463$		−	27.8114i		−	1.29250i	0.763124	−	0.646252i	$-0.223665\pi$
$464$	2.16228	+	3.74517i	0.100381	+	0.173865i
$465$		0			0
$466$	−1.16228	+	2.01312i	−0.0538415	+	0.0932562i
$467$			35.6491i			1.64964i	0.565392	+	0.824822i	$0.308725\pi$
$467$			35.6491i			1.64964i	−0.565392	+	0.824822i	$0.691275\pi$
$468$	−1.73205	−	3.16228i	−0.0800641	−	0.146176i
$469$		0			0
$470$		0			0
$471$	−7.24342	+	12.5460i	−0.333759	+	0.578088i
$472$	8.66025	−	5.00000i	0.398621	−	0.230144i
$473$		−	3.16228i		−	0.145402i
$474$	−2.74342	−	4.75174i	−0.126009	−	0.218254i
$475$		0			0
$476$	26.6491			1.22146
$477$	9.94789	−	5.74342i	0.455483	−	0.262973i
$478$	−7.34981	−	4.24342i	−0.336173	−	0.194089i
$479$	−3.16228	+	5.47723i	−0.144488	+	0.250261i	−0.929182	−	0.369623i	$-0.879487\pi$
$479$	−3.16228	+	5.47723i	−0.144488	+	0.250261i	0.784694	+	0.619884i	$0.212820\pi$
$480$		0			0
$481$	−19.4868	+	10.6734i	−0.888523	+	0.486664i
$482$			29.2982i			1.33450i
$483$	18.6081	+	10.7434i	0.846700	+	0.488842i
$484$	−5.00000	+	8.66025i	−0.227273	+	0.393648i
$485$		0			0
$486$	−1.00000			−0.0453609
$487$	−10.8367	+	6.25658i	−0.491059	+	0.283513i	−0.725014	−	0.688735i	$-0.758167\pi$
$487$	−10.8367	+	6.25658i	−0.491059	+	0.283513i	0.233955	+	0.972247i	$0.424833\pi$
$488$	−5.33669	+	3.08114i	−0.241581	+	0.139477i
$489$	−2.83772			−0.128326
$490$		0			0
$491$	3.33772	−	5.78110i	0.150629	−	0.260898i	−0.780830	−	0.624744i	$-0.785203\pi$
$491$	3.33772	−	5.78110i	0.150629	−	0.260898i	0.931459	+	0.363846i	$0.118537\pi$
$492$	4.47066	+	2.58114i	0.201553	+	0.116367i
$493$			22.3246i			1.00545i
$494$	−3.58114	−	2.17647i	−0.161123	−	0.0979239i
$495$		0			0
$496$	3.58114	−	6.20271i	0.160798	−	0.278510i
$497$	−37.9418	−	21.9057i	−1.70192	−	0.982605i
$498$	−7.79423	+	4.50000i	−0.349268	+	0.201650i
$499$	7.48683			0.335157			0.167578	−	0.985859i	$-0.446405\pi$
$499$	7.48683			0.335157			0.167578	+	0.985859i	$0.446405\pi$
$500$		0			0
$501$	7.24342	+	12.5460i	0.323612	+	0.560512i
$502$			25.6491i			1.14478i
$503$	4.49347	−	2.59431i	0.200354	−	0.115674i	−0.396467	−	0.918049i	$-0.629764\pi$
$503$	4.49347	−	2.59431i	0.200354	−	0.115674i	0.596821	+	0.802375i	$0.296430\pi$
$504$	−2.58114	+	4.47066i	−0.114973	+	0.199139i
$505$		0			0
$506$	4.16228			0.185036
$507$	−0.584952	+	12.9868i	−0.0259786	+	0.576766i
$508$		−	0.324555i		−	0.0143998i
$509$	13.7434	−	23.8043i	0.609166	−	1.05511i	−0.382212	−	0.924075i	$-0.624838\pi$
$509$	13.7434	−	23.8043i	0.609166	−	1.05511i	0.991378	−	0.131032i	$-0.0418291\pi$
$510$		0			0
$511$	24.0680	+	41.6870i	1.06470	+	1.84412i
$512$			1.00000i			0.0441942i
$513$	−1.00656	+	0.581139i	−0.0444408	+	0.0256579i
$514$	−10.7434	−	18.6081i	−0.473872	−	0.820770i
$515$		0			0
$516$	1.58114	+	2.73861i	0.0696058	+	0.120561i
$517$	5.19615	+	3.00000i	0.228527	+	0.131940i
$518$	27.5495	+	15.9057i	1.21045	+	0.698856i
$519$	−10.3246			−0.453198
$520$		0			0
$521$	20.6491			0.904654			0.452327	−	0.891852i	$-0.350594\pi$
$521$	20.6491			0.904654			0.452327	+	0.891852i	$0.350594\pi$
$522$	−3.74517	−	2.16228i	−0.163922	−	0.0946403i
$523$	11.2355	+	6.48683i	0.491295	+	0.283649i	0.725112	−	0.688631i	$-0.241788\pi$
$523$	11.2355	+	6.48683i	0.491295	+	0.283649i	−0.233816	+	0.972281i	$0.575121\pi$
$524$	−8.16228	−	14.1375i	−0.356571	−	0.617599i
$525$		0			0
$526$	1.08114	+	1.87259i	0.0471399	+	0.0816487i
$527$	32.0201	−	18.4868i	1.39482	−	0.805299i
$528$			1.00000i			0.0435194i
$529$	−2.83772	−	4.91508i	−0.123379	−	0.213699i
$530$		0			0
$531$	−5.00000	+	8.66025i	−0.216982	+	0.375823i
$532$			6.00000i			0.260133i
$533$	−8.94133	−	16.3246i	−0.387292	−	0.707095i
$534$	7.48683			0.323987
$535$		0			0
$536$		0			0
$537$	10.0884	−	5.82456i	0.435348	−	0.251348i
$538$			25.1623i			1.08482i
$539$	9.82456	+	17.0166i	0.423174	+	0.732958i
$540$		0			0
$541$	−20.4868			−0.880798			−0.440399	−	0.897802i	$-0.645163\pi$
$541$	−20.4868			−0.880798			−0.440399	+	0.897802i	$0.645163\pi$
$542$	6.64713	−	3.83772i	0.285519	−	0.164844i
$543$	−22.6572	−	13.0811i	−0.972313	−	0.561365i
$544$	−2.58114	+	4.47066i	−0.110665	+	0.191678i
$545$		0			0
$546$	16.3246	−	8.94133i	0.698626	−	0.382653i
$547$		−	16.5132i		−	0.706052i	−0.935614	−	0.353026i	$-0.885153\pi$
$547$		−	16.5132i		−	0.706052i	0.935614	−	0.353026i	$-0.114847\pi$
$548$	−14.4186	−	8.32456i	−0.615930	−	0.355607i
$549$	3.08114	−	5.33669i	0.131500	−	0.227764i
$550$		0			0
$551$	−5.02633			−0.214129
$552$	−3.60464	+	2.08114i	−0.153424	+	0.0885792i
$553$	24.5298	−	14.1623i	1.04311	−	0.602241i
$554$	−2.48683			−0.105655
$555$		0			0
$556$	5.16228	−	8.94133i	0.218929	−	0.379197i
$557$	34.3143	+	19.8114i	1.45394	+	0.839435i	0.998702	−	0.0509319i	$-0.0162191\pi$
$557$	34.3143	+	19.8114i	1.45394	+	0.839435i	0.455243	+	0.890367i	$0.349552\pi$
$558$			7.16228i			0.303203i
$559$	0.256584	−	11.3989i	0.0108523	−	0.482121i
$560$		0			0
$561$	−2.58114	+	4.47066i	−0.108976	+	0.188752i
$562$	−9.38574	−	5.41886i	−0.395914	−	0.228581i
$563$	29.4221	−	16.9868i	1.23999	−	0.715910i	0.270899	−	0.962608i	$-0.412679\pi$
$563$	29.4221	−	16.9868i	1.23999	−	0.715910i	0.969092	+	0.246698i	$0.0793456\pi$
$564$	−6.00000			−0.252646
$565$		0			0
$566$	−12.2302	−	21.1834i	−0.514076	−	0.890405i
$567$		−	5.16228i		−	0.216795i
$568$	7.34981	−	4.24342i	0.308391	−	0.178050i
$569$	1.16228	−	2.01312i	0.0487252	−	0.0843945i	−0.840634	−	0.541603i	$-0.817817\pi$
$569$	1.16228	−	2.01312i	0.0487252	−	0.0843945i	0.889359	+	0.457209i	$0.151151\pi$
$570$		0			0
$571$	−20.9737			−0.877721			−0.438860	−	0.898555i	$-0.644618\pi$
$571$	−20.9737			−0.877721			−0.438860	+	0.898555i	$0.644618\pi$
$572$	1.87259	−	3.08114i	0.0782968	−	0.128829i
$573$		−	6.48683i		−	0.270991i
$574$	−13.3246	+	23.0788i	−0.556156	+	0.963291i
$575$		0			0
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$			9.00000i			0.374675i	0.982296	+	0.187337i	$0.0599858\pi$
$577$			9.00000i			0.374675i	−0.982296	+	0.187337i	$0.940014\pi$
$578$	−8.35637	+	4.82456i	−0.347579	+	0.200675i
$579$	4.66228	+	8.07530i	0.193758	+	0.335598i
$580$		0			0
$581$	−23.2302	−	40.2360i	−0.963753	−	1.66927i
$582$	6.34325	+	3.66228i	0.262936	+	0.151806i
$583$	9.94789	+	5.74342i	0.411999	+	0.237868i
$584$	−9.32456			−0.385853
$585$		0			0
$586$	−23.4868			−0.970232
$587$	12.9904	+	7.50000i	0.536170	+	0.309558i	0.743525	−	0.668708i	$-0.233152\pi$
$587$	12.9904	+	7.50000i	0.536170	+	0.309558i	−0.207355	+	0.978266i	$0.566486\pi$
$588$	−17.0166	−	9.82456i	−0.701754	−	0.405158i
$589$	4.16228	+	7.20928i	0.171504	+	0.297053i
$590$		0			0
$591$	−3.00000	−	5.19615i	−0.123404	−	0.213741i
$592$	−5.33669	+	3.08114i	−0.219337	+	0.126634i
$593$		−	6.51317i		−	0.267464i	−0.991018	−	0.133732i	$-0.957304\pi$
$593$		−	6.51317i		−	0.267464i	0.991018	−	0.133732i	$-0.0426961\pi$
$594$	−0.500000	−	0.866025i	−0.0205152	−	0.0355335i
$595$		0			0
$596$	−6.41886	+	11.1178i	−0.262927	+	0.455403i
$597$			13.1623i			0.538696i
$598$	15.0035	+	0.337722i	0.613539	+	0.0138105i
$599$	0.486833			0.0198915			0.00994573	−	0.999951i	$-0.496834\pi$
$599$	0.486833			0.0198915			0.00994573	+	0.999951i	$0.496834\pi$
$600$		0			0
$601$	23.6491	−	40.9615i	0.964667	−	1.67085i	0.254161	−	0.967162i	$-0.418201\pi$
$601$	23.6491	−	40.9615i	0.964667	−	1.67085i	0.710506	−	0.703691i	$-0.248466\pi$
$602$	−14.1375	+	8.16228i	−0.576201	+	0.332670i
$603$		0			0
$604$	−4.74342	−	8.21584i	−0.193007	−	0.334298i
$605$		0			0
$606$	−12.6491			−0.513835
$607$	10.1112	−	5.83772i	0.410402	−	0.236946i	−0.280560	−	0.959836i	$-0.590520\pi$
$607$	10.1112	−	5.83772i	0.410402	−	0.236946i	0.690963	+	0.722891i	$0.257187\pi$
$608$	−1.00656	−	0.581139i	−0.0408215	−	0.0235683i
$609$	11.1623	−	19.3336i	0.452318	−	0.783438i
$610$		0			0
$611$	18.4868	+	11.2355i	0.747897	+	0.454541i
$612$		−	5.16228i		−	0.208673i
$613$	−19.8958	−	11.4868i	−0.803583	−	0.463949i	0.0411395	−	0.999153i	$-0.486901\pi$
$613$	−19.8958	−	11.4868i	−0.803583	−	0.463949i	−0.844722	+	0.535205i	$0.820235\pi$
$614$		0			0
$615$		0			0
$616$	−5.16228			−0.207994
$617$	−25.9808	+	15.0000i	−1.04595	+	0.603877i	−0.921512	−	0.388351i	$-0.873045\pi$
$617$	−25.9808	+	15.0000i	−1.04595	+	0.603877i	−0.124434	+	0.992228i	$0.539712\pi$
$618$	13.4120	−	7.74342i	0.539509	−	0.311486i
$619$	−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
$622$	−21.2062	−	12.2434i	−0.850292	−	0.490916i
$623$			38.6491i			1.54844i
$624$	−0.0811388	+	3.60464i	−0.00324815	+	0.144301i
$625$		0			0
$626$	15.1491	−	26.2390i	0.605480	−	1.04872i
$627$	−1.00656	−	0.581139i	−0.0401982	−	0.0232084i
$628$	12.5460	−	7.24342i	0.500639	−	0.289044i
$629$	−31.8114			−1.26840
$630$		0			0
$631$	7.64911	+	13.2486i	0.304506	+	0.527420i	0.977151	−	0.212545i	$-0.0681752\pi$
$631$	7.64911	+	13.2486i	0.304506	+	0.527420i	−0.672645	+	0.739965i	$0.734842\pi$
$632$			5.48683i			0.218254i
$633$	−11.1178	+	6.41886i	−0.441893	+	0.255127i
$634$	8.90569	−	15.4251i	0.353690	−	0.612610i
$635$		0			0
$636$	−11.4868			−0.455483
$637$	34.0333	+	62.1359i	1.34845	+	2.46192i
$638$		−	4.32456i		−	0.171211i
$639$	−4.24342	+	7.34981i	−0.167867	+	0.290754i
$640$		0			0
$641$	−6.00000	−	10.3923i	−0.236986	−	0.410471i	0.722862	−	0.690992i	$-0.242826\pi$
$641$	−6.00000	−	10.3923i	−0.236986	−	0.410471i	−0.959848	+	0.280521i	$0.909493\pi$
$642$		−	6.00000i		−	0.236801i
$643$	−32.5823	+	18.8114i	−1.28492	+	0.741849i	−0.977743	−	0.209804i	$-0.932717\pi$
$643$	−32.5823	+	18.8114i	−1.28492	+	0.741849i	−0.307176	+	0.951653i	$0.599384\pi$
$644$	−10.7434	−	18.6081i	−0.423350	−	0.733264i
$645$		0			0
$646$	−3.00000	−	5.19615i	−0.118033	−	0.204440i
$647$	−16.8533	−	9.73025i	−0.662571	−	0.382536i	0.130685	−	0.991424i	$-0.458282\pi$
$647$	−16.8533	−	9.73025i	−0.662571	−	0.382536i	−0.793256	+	0.608888i	$0.791616\pi$
$648$	0.866025	+	0.500000i	0.0340207	+	0.0196419i
$649$	−10.0000			−0.392534
$650$		0			0
$651$	−36.9737			−1.44911
$652$	2.45754	+	1.41886i	0.0962447	+	0.0555669i
$653$	−15.4251	−	8.90569i	−0.603631	−	0.348507i	0.166837	−	0.985984i	$-0.446644\pi$
$653$	−15.4251	−	8.90569i	−0.603631	−	0.348507i	−0.770469	+	0.637478i	$0.779978\pi$
$654$	3.91886	+	6.78767i	0.153240	+	0.265419i
$655$		0			0
$656$	−2.58114	−	4.47066i	−0.100777	−	0.174550i
$657$	8.07530	−	4.66228i	0.315048	−	0.181893i
$658$		−	30.9737i		−	1.20748i
$659$	−4.17544	−	7.23208i	−0.162652	−	0.281722i	0.773167	−	0.634203i	$-0.218672\pi$
$659$	−4.17544	−	7.23208i	−0.162652	−	0.281722i	−0.935819	+	0.352481i	$0.885338\pi$
$660$		0			0
$661$	−11.3246	+	19.6147i	−0.440474	+	0.762924i	−0.997725	−	0.0674208i	$-0.978523\pi$
$661$	−11.3246	+	19.6147i	−0.440474	+	0.762924i	0.557250	+	0.830344i	$0.311856\pi$
$662$		−	4.51317i		−	0.175409i
$663$	−9.66682	+	15.9057i	−0.375428	+	0.617726i
$664$	9.00000			0.349268
$665$		0			0
$666$	3.08114	−	5.33669i	0.119392	−	0.206792i
$667$	15.5885	−	9.00000i	0.603587	−	0.348481i
$668$		−	14.4868i		−	0.560512i
$669$	10.5811	+	18.3271i	0.409090	+	0.708565i
$670$		0			0
$671$	6.16228			0.237892
$672$	4.47066	−	2.58114i	0.172460	−	0.0995696i
$673$	−12.4282	−	7.17544i	−0.479073	−	0.276593i	0.240957	−	0.970536i	$-0.422539\pi$
$673$	−12.4282	−	7.17544i	−0.479073	−	0.276593i	−0.720030	+	0.693943i	$0.755872\pi$
$674$	16.0000	−	27.7128i	0.616297	−	1.06746i
$675$		0			0
$676$	7.00000	−	10.9545i	0.269231	−	0.421325i
$677$		−	40.6491i		−	1.56227i	−0.624361	−	0.781136i	$-0.714640\pi$
$677$		−	40.6491i		−	1.56227i	0.624361	−	0.781136i	$-0.285360\pi$
$678$	15.8695	+	9.16228i	0.609466	+	0.351875i
$679$	−18.9057	+	32.7456i	−0.725534	+	1.25666i
$680$		0			0
$681$	9.32456			0.357318
$682$	−6.20271	+	3.58114i	−0.237514	+	0.137129i
$683$	14.7224	−	8.50000i	0.563338	−	0.325243i	−0.191146	−	0.981562i	$-0.561220\pi$
$683$	14.7224	−	8.50000i	0.563338	−	0.325243i	0.754484	+	0.656318i	$0.227887\pi$
$684$	1.16228			0.0444408
$685$		0			0
$686$	32.6491	−	56.5499i	1.24655	−	2.15909i
$687$	16.2911	+	9.40569i	0.621546	+	0.358850i
$688$		−	3.16228i		−	0.120561i
$689$	35.3925	+	21.5101i	1.34835	+	0.819469i
$690$		0			0
$691$	10.6754	−	18.4904i	0.406113	−	0.703408i	−0.588337	−	0.808616i	$-0.700217\pi$
$691$	10.6754	−	18.4904i	0.406113	−	0.703408i	0.994450	+	0.105207i	$0.0335506\pi$
$692$	8.94133	+	5.16228i	0.339898	+	0.196240i
$693$	4.47066	−	2.58114i	0.169826	−	0.0980494i
$694$	−18.6754			−0.708910
$695$		0			0
$696$	2.16228	+	3.74517i	0.0819609	+	0.141960i
$697$		−	26.6491i		−	1.00941i
$698$	7.06874	−	4.08114i	0.267556	−	0.154473i
$699$	−1.16228	+	2.01312i	−0.0439614	+	0.0761433i
$700$		0			0
$701$	−34.7851			−1.31381			−0.656907	−	0.753972i	$-0.728135\pi$
$701$	−34.7851			−1.31381			−0.656907	+	0.753972i	$0.728135\pi$
$702$	−1.73205	−	3.16228i	−0.0653720	−	0.119352i
$703$		−	7.16228i		−	0.270130i
$704$	0.500000	−	0.866025i	0.0188445	−	0.0326396i
$705$		0			0
$706$	3.41886	+	5.92164i	0.128671	+	0.222864i
$707$		−	65.2982i		−	2.45579i
$708$	8.66025	−	5.00000i	0.325472	−	0.187912i
$709$	−24.8925	−	43.1151i	−0.934858	−	1.61922i	−0.774886	−	0.632101i	$-0.782193\pi$
$709$	−24.8925	−	43.1151i	−0.934858	−	1.61922i	−0.159972	−	0.987121i	$-0.551141\pi$
$710$		0			0
$711$	−2.74342	−	4.75174i	−0.102886	−	0.178204i
$712$	−6.48379	−	3.74342i	−0.242990	−	0.140290i
$713$	−25.8174	−	14.9057i	−0.966870	−	0.558223i
$714$	26.6491			0.997318
$715$		0			0
$716$	−11.6491			−0.435348
$717$	−7.34981	−	4.24342i	−0.274484	−	0.158473i
$718$	−14.4186	−	8.32456i	−0.538096	−	0.310670i
$719$	−12.2434	−	21.2062i	−0.456602	−	0.790859i	0.542176	−	0.840265i	$-0.317600\pi$
$719$	−12.2434	−	21.2062i	−0.456602	−	0.790859i	−0.998779	+	0.0494062i	$0.984267\pi$
$720$		0			0
$721$	39.9737	+	69.2364i	1.48870	+	2.57850i
$722$	−15.2846	+	8.82456i	−0.568833	+	0.328416i
$723$			29.2982i			1.08961i
$724$	13.0811	+	22.6572i	0.486157	+	0.842048i
$725$		0			0
$726$	−5.00000	+	8.66025i	−0.185567	+	0.321412i
$727$			12.3246i			0.457092i	0.973533	+	0.228546i	$0.0733972\pi$
$727$			12.3246i			0.457092i	−0.973533	+	0.228546i	$0.926603\pi$
$728$	−18.6081	−	0.418861i	−0.689664	−	0.0155240i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	8.16228	−	14.1375i	0.301893	−	0.522894i
$732$	−5.33669	+	3.08114i	−0.197250	+	0.113882i
$733$		−	32.1096i		−	1.18600i	−0.805204	−	0.592998i	$-0.797944\pi$
$733$		−	32.1096i		−	1.18600i	0.805204	−	0.592998i	$-0.202056\pi$
$734$	9.00000	+	15.5885i	0.332196	+	0.575380i
$735$		0			0
$736$	4.16228			0.153424
$737$		0			0
$738$	4.47066	+	2.58114i	0.164567	+	0.0950130i
$739$	−6.67544	+	11.5622i	−0.245560	+	0.425323i	−0.962289	−	0.272029i	$-0.912305\pi$
$739$	−6.67544	+	11.5622i	−0.245560	+	0.425323i	0.716729	+	0.697352i	$0.245639\pi$
$740$		0			0
$741$	−3.58114	−	2.17647i	−0.131556	−	0.0799545i
$742$		−	59.2982i		−	2.17691i
$743$	−20.7846	−	12.0000i	−0.762513	−	0.440237i	0.0676840	−	0.997707i	$-0.478439\pi$
$743$	−20.7846	−	12.0000i	−0.762513	−	0.440237i	−0.830197	+	0.557470i	$0.811772\pi$
$744$	3.58114	−	6.20271i	0.131291	−	0.227403i
$745$		0			0
$746$	−8.48683			−0.310725
$747$	−7.79423	+	4.50000i	−0.285176	+	0.164646i
$748$	4.47066	−	2.58114i	0.163464	−	0.0943758i
$749$	30.9737			1.13175
$750$		0			0
$751$	17.4868	−	30.2881i	0.638104	−	1.10523i	−0.347745	−	0.937589i	$-0.613052\pi$
$751$	17.4868	−	30.2881i	0.638104	−	1.10523i	0.985849	−	0.167639i	$-0.0536142\pi$
$752$	5.19615	+	3.00000i	0.189484	+	0.109399i
$753$			25.6491i			0.934706i
$754$	0.350889	−	15.5885i	0.0127786	−	0.567698i
$755$		0			0
$756$	−2.58114	+	4.47066i	−0.0938751	+	0.162596i
$757$	−4.35293	−	2.51317i	−0.158210	−	0.0913426i	0.418805	−	0.908076i	$-0.362449\pi$
$757$	−4.35293	−	2.51317i	−0.158210	−	0.0913426i	−0.577015	+	0.816734i	$0.695783\pi$
$758$	13.2486	−	7.64911i	0.481213	−	0.277828i
$759$	4.16228			0.151081
$760$		0			0
$761$	18.4189	+	31.9024i	0.667683	+	1.15646i	0.978550	+	0.206008i	$0.0660472\pi$
$761$	18.4189	+	31.9024i	0.667683	+	1.15646i	−0.310867	+	0.950453i	$0.600619\pi$
$762$		−	0.324555i		−	0.0117574i
$763$	−35.0398	+	20.2302i	−1.26853	+	0.732384i
$764$	−3.24342	+	5.61776i	−0.117343	+	0.203244i
$765$		0			0
$766$	−33.7851			−1.22070
$767$	−36.0464	−	0.811388i	−1.30156	−	0.0292975i
$768$			1.00000i			0.0360844i
$769$	11.4868	−	19.8958i	0.414226	−	0.717460i	−0.581121	−	0.813817i	$-0.697386\pi$
$769$	11.4868	−	19.8958i	0.414226	−	0.717460i	0.995347	+	0.0963570i	$0.0307191\pi$
$770$		0			0
$771$	−10.7434	−	18.6081i	−0.386915	−	0.670156i
$772$		−	9.32456i		−	0.335598i
$773$	−24.2031	+	13.9737i	−0.870525	+	0.502598i	−0.867523	−	0.497398i	$-0.834289\pi$
$773$	−24.2031	+	13.9737i	−0.870525	+	0.502598i	−0.00300232	+	0.999995i	$0.500956\pi$
$774$	1.58114	+	2.73861i	0.0568329	+	0.0984374i
$775$		0			0
$776$	−3.66228	−	6.34325i	−0.131468	−	0.227709i
$777$	27.5495	+	15.9057i	0.988332	+	0.570614i
$778$	−4.30732	−	2.48683i	−0.154425	−	0.0891573i
$779$	6.00000			0.214972
$780$		0			0
$781$	−8.48683			−0.303683
$782$	18.6081	+	10.7434i	0.665426	+	0.384184i
$783$	−3.74517	−	2.16228i	−0.133842	−	0.0772735i
$784$	9.82456	+	17.0166i	0.350877	+	0.607737i
$785$		0			0
$786$	−8.16228	−	14.1375i	−0.291139	−	0.504267i
$787$	−26.3796	+	15.2302i	−0.940330	+	0.542900i	−0.890064	−	0.455836i	$-0.849340\pi$
$787$	−26.3796	+	15.2302i	−0.940330	+	0.542900i	−0.0502662	+	0.998736i	$0.516007\pi$
$788$			6.00000i			0.213741i
$789$	1.08114	+	1.87259i	0.0384896	+	0.0666659i
$790$		0			0
$791$	−47.2982	+	81.9229i	−1.68173	+	2.91284i
$792$			1.00000i			0.0355335i
$793$	22.2128	+	0.500000i	0.788799	+	0.0177555i
$794$	7.67544			0.272391
$795$		0			0
$796$	6.58114	−	11.3989i	0.233262	−	0.404022i
$797$	−21.9089	+	12.6491i	−0.776053	+	0.448054i	−0.835030	−	0.550205i	$-0.814550\pi$
$797$	−21.9089	+	12.6491i	−0.776053	+	0.448054i	0.0589766	+	0.998259i	$0.481216\pi$
$798$			6.00000i			0.212398i
$799$	15.4868	+	26.8240i	0.547885	+	0.948964i
$800$		0			0
$801$	7.48683			0.264534
$802$	−25.6541	+	14.8114i	−0.905877	+	0.523008i
$803$	8.07530	+	4.66228i	0.284971	+	0.164528i
$804$		0			0
$805$		0			0
$806$	−22.6491	+	12.4054i	−0.797781	+	0.436963i
$807$			25.1623i			0.885754i
$808$	10.9545	+	6.32456i	0.385376	+	0.222497i
$809$	−14.5811	+	25.2553i	−0.512646	+	0.887928i	0.487247	+	0.873264i	$0.338001\pi$
$809$	−14.5811	+	25.2553i	−0.512646	+	0.887928i	−0.999892	+	0.0146639i	$0.995332\pi$
$810$		0			0
$811$	−21.3509			−0.749731			−0.374866	−	0.927079i	$-0.622311\pi$
$811$	−21.3509			−0.749731			−0.374866	+	0.927079i	$0.622311\pi$
$812$	−19.3336	+	11.1623i	−0.678477	+	0.391719i
$813$	6.64713	−	3.83772i	0.233125	−	0.134595i
$814$	6.16228			0.215988
$815$		0			0
$816$	−2.58114	+	4.47066i	−0.0903579	+	0.156505i
$817$	3.18303	+	1.83772i	0.111360	+	0.0642938i
$818$		−	30.3246i		−	1.06027i
$819$	16.3246	−	8.94133i	0.570426	−	0.312435i
$820$		0			0
$821$	16.8114	−	29.1182i	0.586721	−	1.01623i	−0.407937	−	0.913010i	$-0.633752\pi$
$821$	16.8114	−	29.1182i	0.586721	−	1.01623i	0.994658	−	0.103221i	$-0.0329150\pi$
$822$	−14.4186	−	8.32456i	−0.502905	−	0.290352i
$823$	39.6738	−	22.9057i	1.38294	−	0.798442i	0.390436	−	0.920630i	$-0.372324\pi$
$823$	39.6738	−	22.9057i	1.38294	−	0.798442i	0.992507	+	0.122188i	$0.0389911\pi$
$824$	−15.4868			−0.539509
$825$		0			0
$826$	25.8114	+	44.7066i	0.898093	+	1.55554i
$827$		−	15.9737i		−	0.555459i	−0.960659	−	0.277729i	$-0.910418\pi$
$827$		−	15.9737i		−	0.555459i	0.960659	−	0.277729i	$-0.0895819\pi$
$828$	−3.60464	+	2.08114i	−0.125270	+	0.0723246i
$829$	17.8377	−	30.8958i	0.619530	−	1.07306i	−0.370042	−	0.929015i	$-0.620657\pi$
$829$	17.8377	−	30.8958i	0.619530	−	1.07306i	0.989572	−	0.144042i	$-0.0460100\pi$
$830$		0			0
$831$	−2.48683			−0.0862673
$832$	1.87259	−	3.08114i	0.0649203	−	0.106819i
$833$			101.434i			3.51449i
$834$	5.16228	−	8.94133i	0.178755	−	0.309613i
$835$		0			0
$836$	0.581139	+	1.00656i	0.0200991	+	0.0348127i
$837$			7.16228i			0.247565i
$838$	29.1410	−	16.8246i	1.00666	−	0.581195i
$839$	19.9189	+	34.5005i	0.687675	+	1.19109i	0.972588	+	0.232535i	$0.0747021\pi$
$839$	19.9189	+	34.5005i	0.687675	+	1.19109i	−0.284913	+	0.958554i	$0.591965\pi$
$840$		0			0
$841$	5.14911	+	8.91852i	0.177556	+	0.307535i
$842$	4.49347	+	2.59431i	0.154855	+	0.0894057i
$843$	−9.38574	−	5.41886i	−0.323262	−	0.186635i
$844$	12.8377			0.441893
$845$		0			0
$846$	−6.00000			−0.206284
$847$	−44.7066	−	25.8114i	−1.53614	−	0.886890i
$848$	9.94789	+	5.74342i	0.341612	+	0.197230i
$849$	−12.2302	−	21.1834i	−0.419741	−	0.727013i
$850$		0			0
$851$	12.8246	+	22.2128i	0.439620	+	0.761444i
$852$	7.34981	−	4.24342i	0.251800	−	0.145377i
$853$		−	34.0000i		−	1.16414i	−0.813139	−	0.582069i	$-0.802243\pi$
$853$		−	34.0000i		−	1.16414i	0.813139	−	0.582069i	$-0.197757\pi$
$854$	−15.9057	−	27.5495i	−0.544282	−	0.942723i
$855$		0			0
$856$	−3.00000	+	5.19615i	−0.102538	+	0.177601i
$857$			7.67544i			0.262188i	0.991370	+	0.131094i	$0.0418490\pi$
$857$			7.67544i			0.262188i	−0.991370	+	0.131094i	$0.958151\pi$
$858$	1.87259	−	3.08114i	0.0639291	−	0.105188i
$859$	−22.8377			−0.779213			−0.389607	−	0.920981i	$-0.627389\pi$
$859$	−22.8377			−0.779213			−0.389607	+	0.920981i	$0.627389\pi$
$860$		0			0
$861$	−13.3246	+	23.0788i	−0.454100	+	0.786524i
$862$	16.0101	−	9.24342i	0.545305	−	0.314832i
$863$		−	36.4868i		−	1.24203i	−0.783800	−	0.621013i	$-0.786721\pi$
$863$		−	36.4868i		−	1.24203i	0.783800	−	0.621013i	$-0.213279\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$		0			0
$866$	31.9737			1.08651
$867$	−8.35637	+	4.82456i	−0.283797	+	0.163850i
$868$	32.0201	+	18.4868i	1.08683	+	0.627484i
$869$	2.74342	−	4.75174i	0.0930640	−	0.161192i
$870$		0			0
$871$		0			0
$872$		−	7.83772i		−	0.265419i
$873$	6.34325	+	3.66228i	0.214687	+	0.123949i
$874$	−2.41886	+	4.18959i	−0.0818192	+	0.141715i
$875$		0			0
$876$	−9.32456			−0.315048
$877$	−46.9059	+	27.0811i	−1.58390	+	0.914465i	−0.589618	+	0.807683i	$0.700722\pi$
$877$	−46.9059	+	27.0811i	−1.58390	+	0.914465i	−0.994282	+	0.106783i	$0.965945\pi$
$878$	−9.83016	+	5.67544i	−0.331752	+	0.191537i
$879$	−23.4868			−0.792191
$880$		0			0
$881$	14.4189	−	24.9742i	0.485784	−	0.841402i	−0.514083	−	0.857741i	$-0.671868\pi$
$881$	14.4189	−	24.9742i	0.485784	−	0.841402i	0.999867	+	0.0163384i	$0.00520091\pi$
$882$	−17.0166	−	9.82456i	−0.572980	−	0.330810i
$883$			20.6491i			0.694898i	0.937699	+	0.347449i	$0.112952\pi$
$883$			20.6491i			0.694898i	−0.937699	+	0.347449i	$0.887048\pi$
$884$	16.3246	−	8.94133i	0.549054	−	0.300729i
$885$		0			0
$886$	3.17544	−	5.50003i	0.106681	−	0.184777i
$887$	−11.5166	−	6.64911i	−0.386689	−	0.223255i	0.294035	−	0.955795i	$-0.405002\pi$
$887$	−11.5166	−	6.64911i	−0.386689	−	0.223255i	−0.680725	+	0.732539i	$0.738335\pi$
$888$	−5.33669	+	3.08114i	−0.179088	+	0.103396i
$889$	1.67544			0.0561926
$890$		0			0
$891$	−0.500000	−	0.866025i	−0.0167506	−	0.0290129i
$892$		−	21.1623i		−	0.708565i
$893$	−6.03937	+	3.48683i	−0.202100	+	0.116682i
$894$	−6.41886	+	11.1178i	−0.214679	+	0.371835i
$895$		0			0
$896$	−5.16228			−0.172460
$897$	15.0035	+	0.337722i	0.500952	+	0.0112762i
$898$		−	27.4868i		−	0.917247i
$899$	−15.4868	+	26.8240i	−0.516515	+	0.894630i
$900$		0			0
$901$	29.6491	+	51.3538i	0.987755	+	1.71084i
$902$			5.16228i			0.171885i
$903$	−14.1375	+	8.16228i	−0.470466	+	0.271624i
$904$	−9.16228	−	15.8695i	−0.304733	−	0.527813i
$905$		0			0
$906$	−4.74342	−	8.21584i	−0.157589	−	0.272953i
$907$	−15.7062	−	9.06797i	−0.521515	−	0.301097i	0.216039	−	0.976385i	$-0.430686\pi$
$907$	−15.7062	−	9.06797i	−0.521515	−	0.301097i	−0.737554	+	0.675288i	$0.764019\pi$
$908$	−8.07530	−	4.66228i	−0.267988	−	0.154723i
$909$	−12.6491			−0.419545
$910$		0			0
$911$	−45.8377			−1.51867			−0.759336	−	0.650699i	$-0.774476\pi$
$911$	−45.8377			−1.51867			−0.759336	+	0.650699i	$0.774476\pi$
$912$	−1.00656	−	0.581139i	−0.0333306	−	0.0192434i
$913$	−7.79423	−	4.50000i	−0.257951	−	0.148928i
$914$	−8.14911	−	14.1147i	−0.269549	−	0.466872i
$915$		0			0
$916$	−9.40569	−	16.2911i	−0.310773	−	0.538274i
$917$	72.9816	−	42.1359i	2.41006	−	1.39145i
$918$		−	5.16228i		−	0.170381i
$919$	−2.74342	−	4.75174i	−0.0904970	−	0.156745i	0.817223	−	0.576321i	$-0.195512\pi$
$919$	−2.74342	−	4.75174i	−0.0904970	−	0.156745i	−0.907720	+	0.419576i	$0.862179\pi$
$920$		0			0
$921$		0			0
$922$			28.4605i			0.937297i
$923$	−30.5920	−	0.688612i	−1.00695	−	0.0226659i
$924$	−5.16228			−0.169826
$925$		0			0
$926$	−13.9057	+	24.0854i	−0.456969	+	0.791494i
$927$	13.4120	−	7.74342i	0.440508	−	0.254327i
$928$		−	4.32456i		−	0.141960i
$929$	−2.32456	−	4.02625i	−0.0762662	−	0.132097i	0.825370	−	0.564592i	$-0.190967\pi$
$929$	−2.32456	−	4.02625i	−0.0762662	−	0.132097i	−0.901636	+	0.432495i	$0.857633\pi$
$930$		0			0
$931$	−22.8377			−0.748476
$932$	2.01312	−	1.16228i	0.0659421	−	0.0380717i
$933$	−21.2062	−	12.2434i	−0.694260	−	0.400831i
$934$	17.8246	−	30.8730i	0.583237	−	1.01020i
$935$		0			0
$936$	−0.0811388	+	3.60464i	−0.00265211	+	0.117821i
$937$		−	4.35089i		−	0.142137i	−0.997471	−	0.0710687i	$-0.977359\pi$
$937$		−	4.35089i		−	0.142137i	0.997471	−	0.0710687i	$-0.0226409\pi$
$938$		0			0
$939$	15.1491	−	26.2390i	0.494373	−	0.856278i
$940$		0			0
$941$	−20.6491			−0.673142			−0.336571	−	0.941658i	$-0.609267\pi$
$941$	−20.6491			−0.673142			−0.336571	+	0.941658i	$0.609267\pi$
$942$	12.5460	−	7.24342i	0.408770	−	0.236003i
$943$	−18.6081	+	10.7434i	−0.605965	+	0.349854i
$944$	−10.0000			−0.325472
$945$		0			0
$946$	−1.58114	+	2.73861i	−0.0514073	+	0.0890400i
$947$	−33.7294	−	19.4737i	−1.09606	−	0.632809i	−0.160875	−	0.986975i	$-0.551432\pi$
$947$	−33.7294	−	19.4737i	−1.09606	−	0.632809i	−0.935183	+	0.354166i	$0.884765\pi$
$948$			5.48683i			0.178204i
$949$	28.7302	+	17.4610i	0.932623	+	0.566809i
$950$		0			0
$951$	8.90569	−	15.4251i	0.288787	−	0.500194i
$952$	−23.0788	−	13.3246i	−0.747988	−	0.431851i
$953$	−43.0923	+	24.8794i	−1.39590	+	0.805922i	−0.993960	−	0.109746i	$-0.964996\pi$
$953$	−43.0923	+	24.8794i	−1.39590	+	0.805922i	−0.401937	+	0.915667i	$0.631663\pi$
$954$	−11.4868			−0.371900
$955$		0			0
$956$	4.24342	+	7.34981i	0.137242	+	0.237710i
$957$		−	4.32456i		−	0.139793i
$958$	5.47723	−	3.16228i	0.176961	−	0.102169i
$959$	42.9737	−	74.4326i	1.38769	−	2.40355i
$960$		0			0
$961$	20.2982			0.654781
$962$	22.2128	+	0.500000i	0.716169	+	0.0161206i
$963$		−	6.00000i		−	0.193347i
$964$	14.6491	−	25.3730i	0.471816	−	0.817209i
$965$		0			0
$966$	−10.7434	−	18.6081i	−0.345664	−	0.598707i
$967$		−	56.9737i		−	1.83215i	−0.401007	−	0.916075i	$-0.631340\pi$
$967$		−	56.9737i		−	1.83215i	0.401007	−	0.916075i	$-0.368660\pi$
$968$	8.66025	−	5.00000i	0.278351	−	0.160706i
$969$	−3.00000	−	5.19615i	−0.0963739	−	0.166924i
$970$		0			0
$971$	1.32456	+	2.29420i	0.0425070	+	0.0736243i	0.886496	−	0.462736i	$-0.153132\pi$
$971$	1.32456	+	2.29420i	0.0425070	+	0.0736243i	−0.843989	+	0.536360i	$0.819799\pi$
$972$	0.866025	+	0.500000i	0.0277778	+	0.0160375i
$973$	46.1576	+	26.6491i	1.47975	+	0.854331i
$974$	12.5132			0.400948
$975$		0			0
$976$	6.16228			0.197250
$977$	−6.03937	−	3.48683i	−0.193217	−	0.111554i	0.400271	−	0.916397i	$-0.368916\pi$
$977$	−6.03937	−	3.48683i	−0.193217	−	0.111554i	−0.593488	+	0.804843i	$0.702249\pi$
$978$	2.45754	+	1.41886i	0.0785835	+	0.0453702i
$979$	3.74342	+	6.48379i	0.119640	+	0.207223i
$980$		0			0
$981$	3.91886	+	6.78767i	0.125120	+	0.216714i
$982$	−5.78110	+	3.33772i	−0.184482	+	0.106511i
$983$			4.00000i			0.127580i	0.997963	+	0.0637901i	$0.0203188\pi$
$983$			4.00000i			0.127580i	−0.997963	+	0.0637901i	$0.979681\pi$
$984$	−2.58114	−	4.47066i	−0.0822837	−	0.142520i
$985$		0			0
$986$	11.1623	−	19.3336i	0.355479	−	0.615708i
$987$		−	30.9737i		−	0.985903i
$988$	2.01312	+	3.67544i	0.0640460	+	0.116931i
$989$	−13.1623			−0.418536
$990$		0			0
$991$	−19.5548	+	33.8699i	−0.621179	+	1.07591i	0.368088	+	0.929791i	$0.380013\pi$
$991$	−19.5548	+	33.8699i	−0.621179	+	1.07591i	−0.989267	+	0.146122i	$0.953321\pi$
$992$	−6.20271	+	3.58114i	−0.196936	+	0.113701i
$993$		−	4.51317i		−	0.143221i
$994$	21.9057	+	37.9418i	0.694806	+	1.20344i
$995$		0			0
$996$	9.00000			0.285176
$997$	−1.40537	+	0.811388i	−0.0445084	+	0.0256969i	−0.522089	−	0.852891i	$-0.674847\pi$
$997$	−1.40537	+	0.811388i	−0.0445084	+	0.0256969i	0.477581	+	0.878588i	$0.341514\pi$
$998$	−6.48379	−	3.74342i	−0.205241	−	0.118496i
$999$	3.08114	−	5.33669i	0.0974829	−	0.168845i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1950.2.z.p.1699.1		8
5.2	odd	4		1950.2.i.bd.451.1	yes	4
5.3	odd	4		1950.2.i.bc.451.2	✓	4
5.4	even	2	inner	1950.2.z.p.1699.4		8
13.3	even	3	inner	1950.2.z.p.1849.4		8
65.3	odd	12		1950.2.i.bc.601.2	yes	4
65.29	even	6	inner	1950.2.z.p.1849.1		8
65.42	odd	12		1950.2.i.bd.601.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1950.2.i.bc.451.2	✓	4	5.3	odd	4
1950.2.i.bc.601.2	yes	4	65.3	odd	12
1950.2.i.bd.451.1	yes	4	5.2	odd	4
1950.2.i.bd.601.1	yes	4	65.42	odd	12
1950.2.z.p.1699.1		8	1.1	even	1	trivial
1950.2.z.p.1699.4		8	5.4	even	2	inner
1950.2.z.p.1849.1		8	65.29	even	6	inner
1950.2.z.p.1849.4		8	13.3	even	3	inner

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)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{6} +(-4.47066 + 2.58114i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(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} +(-4.47066 + 2.58114i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-0.500000 + 0.866025i) q^{11} -1.00000i q^{12} +(-1.87259 + 3.08114i) q^{13} +5.16228 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-4.47066 + 2.58114i) q^{17} -1.00000i q^{18} +(-0.581139 - 1.00656i) q^{19} +5.16228 q^{21} +(0.866025 - 0.500000i) q^{22} +(3.60464 + 2.08114i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(3.16228 - 1.73205i) q^{26} -1.00000i q^{27} +(-4.47066 - 2.58114i) q^{28} +(2.16228 - 3.74517i) q^{29} -7.16228 q^{31} +(0.866025 - 0.500000i) q^{32} +(0.866025 - 0.500000i) q^{33} +5.16228 q^{34} +(-0.500000 + 0.866025i) q^{36} +(5.33669 + 3.08114i) q^{37} +1.16228i q^{38} +(3.16228 - 1.73205i) q^{39} +(-2.58114 + 4.47066i) q^{41} +(-4.47066 - 2.58114i) q^{42} +(-2.73861 + 1.58114i) q^{43} -1.00000 q^{44} +(-2.08114 - 3.60464i) q^{46} -6.00000i q^{47} +(0.866025 - 0.500000i) q^{48} +(9.82456 - 17.0166i) q^{49} +5.16228 q^{51} +(-3.60464 - 0.0811388i) q^{52} -11.4868i q^{53} +(-0.500000 + 0.866025i) q^{54} +(2.58114 + 4.47066i) q^{56} +1.16228i q^{57} +(-3.74517 + 2.16228i) q^{58} +(5.00000 + 8.66025i) q^{59} +(-3.08114 - 5.33669i) q^{61} +(6.20271 + 3.58114i) q^{62} +(-4.47066 - 2.58114i) q^{63} -1.00000 q^{64} -1.00000 q^{66} +(-4.47066 - 2.58114i) q^{68} +(-2.08114 - 3.60464i) q^{69} +(4.24342 + 7.34981i) q^{71} +(0.866025 - 0.500000i) q^{72} -9.32456i q^{73} +(-3.08114 - 5.33669i) q^{74} +(0.581139 - 1.00656i) q^{76} -5.16228i q^{77} +(-3.60464 - 0.0811388i) q^{78} -5.48683 q^{79} +(-0.500000 + 0.866025i) q^{81} +(4.47066 - 2.58114i) q^{82} +9.00000i q^{83} +(2.58114 + 4.47066i) q^{84} +3.16228 q^{86} +(-3.74517 + 2.16228i) q^{87} +(0.866025 + 0.500000i) q^{88} +(3.74342 - 6.48379i) q^{89} +(0.418861 - 18.6081i) q^{91} +4.16228i q^{92} +(6.20271 + 3.58114i) q^{93} +(-3.00000 + 5.19615i) q^{94} -1.00000 q^{96} +(6.34325 - 3.66228i) q^{97} +(-17.0166 + 9.82456i) q^{98} -1.00000 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	\( 8 q + 4 q^{4} + 4 q^{6} + 4 q^{9} - 4 q^{11} + 16 q^{14} - 4 q^{16} + 8 q^{19} + 16 q^{21} - 4 q^{24} - 8 q^{29} - 32 q^{31} + 16 q^{34} - 4 q^{36} - 8 q^{41} - 8 q^{44} - 4 q^{46} + 28 q^{49} + 16 q^{51} - 4 q^{54} + 8 q^{56} + 40 q^{59} - 12 q^{61} - 8 q^{64} - 8 q^{66} - 4 q^{69} - 4 q^{71} - 12 q^{74} - 8 q^{76} + 32 q^{79} - 4 q^{81} + 8 q^{84} - 8 q^{89} + 16 q^{91} - 24 q^{94} - 8 q^{96} - 8 q^{99}+O(q^{100}) \) 8 * q + 4 * q^4 + 4 * q^6 + 4 * q^9 - 4 * q^11 + 16 * q^14 - 4 * q^16 + 8 * q^19 + 16 * q^21 - 4 * q^24 - 8 * q^29 - 32 * q^31 + 16 * q^34 - 4 * q^36 - 8 * q^41 - 8 * q^44 - 4 * q^46 + 28 * q^49 + 16 * q^51 - 4 * q^54 + 8 * q^56 + 40 * q^59 - 12 * q^61 - 8 * q^64 - 8 * q^66 - 4 * q^69 - 4 * q^71 - 12 * q^74 - 8 * q^76 + 32 * q^79 - 4 * q^81 + 8 * q^84 - 8 * q^89 + 16 * q^91 - 24 * q^94 - 8 * q^96 - 8 * q^99

Introduction

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