LMFDB - Embedded newform 116.2.e.b.75.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [116,2,Mod(75,116)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(116, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("116.75");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 116 = 2^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	116.e (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.926264663447$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{14})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 49 $ x^4 + 49
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			75.2
Root			$1.87083 + 1.87083i$ of defining polynomial
Character	$\chi$	$=$	116.75
Dual form			116.2.e.b.99.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.00000i) q^{2} +(1.87083 + 1.87083i) q^{3} -2.00000i q^{4} +3.00000i q^{5} -3.74166 q^{6} -3.74166i q^{7} +(2.00000 + 2.00000i) q^{8} +4.00000i q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.00000i) q^{2} +(1.87083 + 1.87083i) q^{3} -2.00000i q^{4} +3.00000i q^{5} -3.74166 q^{6} -3.74166i q^{7} +(2.00000 + 2.00000i) q^{8} +4.00000i q^{9} +(-3.00000 - 3.00000i) q^{10} +(-1.87083 - 1.87083i) q^{11} +(3.74166 - 3.74166i) q^{12} -1.00000i q^{13} +(3.74166 + 3.74166i) q^{14} +(-5.61249 + 5.61249i) q^{15} -4.00000 q^{16} +(-2.00000 + 2.00000i) q^{17} +(-4.00000 - 4.00000i) q^{18} +(3.74166 + 3.74166i) q^{19} +6.00000 q^{20} +(7.00000 - 7.00000i) q^{21} +3.74166 q^{22} -7.48331i q^{23} +7.48331i q^{24} -4.00000 q^{25} +(1.00000 + 1.00000i) q^{26} +(-1.87083 + 1.87083i) q^{27} -7.48331 q^{28} +(5.00000 - 2.00000i) q^{29} -11.2250i q^{30} +(-1.87083 - 1.87083i) q^{31} +(4.00000 - 4.00000i) q^{32} -7.00000i q^{33} -4.00000i q^{34} +11.2250 q^{35} +8.00000 q^{36} -7.48331 q^{38} +(1.87083 - 1.87083i) q^{39} +(-6.00000 + 6.00000i) q^{40} +(1.00000 + 1.00000i) q^{41} +14.0000i q^{42} +(1.87083 + 1.87083i) q^{43} +(-3.74166 + 3.74166i) q^{44} -12.0000 q^{45} +(7.48331 + 7.48331i) q^{46} +(-5.61249 + 5.61249i) q^{47} +(-7.48331 - 7.48331i) q^{48} -7.00000 q^{49} +(4.00000 - 4.00000i) q^{50} -7.48331 q^{51} -2.00000 q^{52} -11.0000 q^{53} -3.74166i q^{54} +(5.61249 - 5.61249i) q^{55} +(7.48331 - 7.48331i) q^{56} +14.0000i q^{57} +(-3.00000 + 7.00000i) q^{58} +7.48331i q^{59} +(11.2250 + 11.2250i) q^{60} +(6.00000 - 6.00000i) q^{61} +3.74166 q^{62} +14.9666 q^{63} +8.00000i q^{64} +3.00000 q^{65} +(7.00000 + 7.00000i) q^{66} -14.9666 q^{67} +(4.00000 + 4.00000i) q^{68} +(14.0000 - 14.0000i) q^{69} +(-11.2250 + 11.2250i) q^{70} -3.74166 q^{71} +(-8.00000 + 8.00000i) q^{72} +(4.00000 + 4.00000i) q^{73} +(-7.48331 - 7.48331i) q^{75} +(7.48331 - 7.48331i) q^{76} +(-7.00000 + 7.00000i) q^{77} +3.74166i q^{78} +(-5.61249 - 5.61249i) q^{79} -12.0000i q^{80} +5.00000 q^{81} -2.00000 q^{82} -7.48331i q^{83} +(-14.0000 - 14.0000i) q^{84} +(-6.00000 - 6.00000i) q^{85} -3.74166 q^{86} +(13.0958 + 5.61249i) q^{87} -7.48331i q^{88} +(-3.00000 + 3.00000i) q^{89} +(12.0000 - 12.0000i) q^{90} -3.74166 q^{91} -14.9666 q^{92} -7.00000i q^{93} -11.2250i q^{94} +(-11.2250 + 11.2250i) q^{95} +14.9666 q^{96} +(-5.00000 - 5.00000i) q^{97} +(7.00000 - 7.00000i) q^{98} +(7.48331 - 7.48331i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 8 q^{8}+O(q^{10}) $ 4 * q - 4 * q^2 + 8 * q^8	$ 4 q - 4 q^{2} + 8 q^{8} - 12 q^{10} - 16 q^{16} - 8 q^{17} - 16 q^{18} + 24 q^{20} + 28 q^{21} - 16 q^{25} + 4 q^{26} + 20 q^{29} + 16 q^{32} + 32 q^{36} - 24 q^{40} + 4 q^{41} - 48 q^{45} - 28 q^{49} + 16 q^{50} - 8 q^{52} - 44 q^{53} - 12 q^{58} + 24 q^{61} + 12 q^{65} + 28 q^{66} + 16 q^{68} + 56 q^{69} - 32 q^{72} + 16 q^{73} - 28 q^{77} + 20 q^{81} - 8 q^{82} - 56 q^{84} - 24 q^{85} - 12 q^{89} + 48 q^{90} - 20 q^{97} + 28 q^{98}+O(q^{100}) $ 4 * q - 4 * q^2 + 8 * q^8 - 12 * q^10 - 16 * q^16 - 8 * q^17 - 16 * q^18 + 24 * q^20 + 28 * q^21 - 16 * q^25 + 4 * q^26 + 20 * q^29 + 16 * q^32 + 32 * q^36 - 24 * q^40 + 4 * q^41 - 48 * q^45 - 28 * q^49 + 16 * q^50 - 8 * q^52 - 44 * q^53 - 12 * q^58 + 24 * q^61 + 12 * q^65 + 28 * q^66 + 16 * q^68 + 56 * q^69 - 32 * q^72 + 16 * q^73 - 28 * q^77 + 20 * q^81 - 8 * q^82 - 56 * q^84 - 24 * q^85 - 12 * q^89 + 48 * q^90 - 20 * q^97 + 28 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/116\mathbb{Z}\right)^\times$.

$n$	$59$	$89$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.00000	+	1.00000i	−0.707107	+	0.707107i
$2$	−1.00000	+	1.00000i	−0.707107	+	0.707107i
$3$	1.87083	+	1.87083i	1.08012	+	1.08012i	0.996497	+	0.0836263i	$0.0266502\pi$
$3$	1.87083	+	1.87083i	1.08012	+	1.08012i	0.0836263	+	0.996497i	$0.473350\pi$
$4$		−	2.00000i		−	1.00000i
$5$			3.00000i			1.34164i	0.741620	+	0.670820i	$0.234058\pi$
$5$			3.00000i			1.34164i	−0.741620	+	0.670820i	$0.765942\pi$
$6$	−3.74166			−1.52753
$7$		−	3.74166i		−	1.41421i	−0.707107	−	0.707107i	$-0.750000\pi$
$7$		−	3.74166i		−	1.41421i	0.707107	−	0.707107i	$-0.250000\pi$
$8$	2.00000	+	2.00000i	0.707107	+	0.707107i
$9$			4.00000i			1.33333i
$10$	−3.00000	−	3.00000i	−0.948683	−	0.948683i
$11$	−1.87083	−	1.87083i	−0.564076	−	0.564076i	0.366387	−	0.930463i	$-0.380595\pi$
$11$	−1.87083	−	1.87083i	−0.564076	−	0.564076i	−0.930463	+	0.366387i	$0.880595\pi$
$12$	3.74166	−	3.74166i	1.08012	−	1.08012i
$13$		−	1.00000i		−	0.277350i	−0.990338	−	0.138675i	$-0.955716\pi$
$13$		−	1.00000i		−	0.277350i	0.990338	−	0.138675i	$-0.0442844\pi$
$14$	3.74166	+	3.74166i	1.00000	+	1.00000i
$15$	−5.61249	+	5.61249i	−1.44914	+	1.44914i
$16$	−4.00000			−1.00000
$17$	−2.00000	+	2.00000i	−0.485071	+	0.485071i	−0.906747	−	0.421676i	$-0.861442\pi$
$17$	−2.00000	+	2.00000i	−0.485071	+	0.485071i	0.421676	+	0.906747i	$0.361442\pi$
$18$	−4.00000	−	4.00000i	−0.942809	−	0.942809i
$19$	3.74166	+	3.74166i	0.858395	+	0.858395i	0.991149	−	0.132754i	$-0.0423820\pi$
$19$	3.74166	+	3.74166i	0.858395	+	0.858395i	−0.132754	+	0.991149i	$0.542382\pi$
$20$	6.00000			1.34164
$21$	7.00000	−	7.00000i	1.52753	−	1.52753i
$22$	3.74166			0.797724
$23$		−	7.48331i		−	1.56038i	−0.625543	−	0.780189i	$-0.715123\pi$
$23$		−	7.48331i		−	1.56038i	0.625543	−	0.780189i	$-0.284877\pi$
$24$			7.48331i			1.52753i
$25$	−4.00000			−0.800000
$26$	1.00000	+	1.00000i	0.196116	+	0.196116i
$27$	−1.87083	+	1.87083i	−0.360041	+	0.360041i
$28$	−7.48331			−1.41421
$29$	5.00000	−	2.00000i	0.928477	−	0.371391i
$29$	5.00000	−	2.00000i	0.928477	−	0.371391i
$30$		−	11.2250i		−	2.04939i
$31$	−1.87083	−	1.87083i	−0.336011	−	0.336011i	0.518853	−	0.854864i	$-0.326359\pi$
$31$	−1.87083	−	1.87083i	−0.336011	−	0.336011i	−0.854864	+	0.518853i	$0.826359\pi$
$32$	4.00000	−	4.00000i	0.707107	−	0.707107i
$33$		−	7.00000i		−	1.21854i
$34$		−	4.00000i		−	0.685994i
$35$	11.2250			1.89737
$36$	8.00000			1.33333
$37$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$37$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$38$	−7.48331			−1.21395
$39$	1.87083	−	1.87083i	0.299572	−	0.299572i
$40$	−6.00000	+	6.00000i	−0.948683	+	0.948683i
$41$	1.00000	+	1.00000i	0.156174	+	0.156174i	0.780869	−	0.624695i	$-0.214777\pi$
$41$	1.00000	+	1.00000i	0.156174	+	0.156174i	−0.624695	+	0.780869i	$0.714777\pi$
$42$			14.0000i			2.16025i
$43$	1.87083	+	1.87083i	0.285299	+	0.285299i	0.835218	−	0.549919i	$-0.185341\pi$
$43$	1.87083	+	1.87083i	0.285299	+	0.285299i	−0.549919	+	0.835218i	$0.685341\pi$
$44$	−3.74166	+	3.74166i	−0.564076	+	0.564076i
$45$	−12.0000			−1.78885
$46$	7.48331	+	7.48331i	1.10335	+	1.10335i
$47$	−5.61249	+	5.61249i	−0.818665	+	0.818665i	−0.985915	−	0.167249i	$-0.946511\pi$
$47$	−5.61249	+	5.61249i	−0.818665	+	0.818665i	0.167249	+	0.985915i	$0.446511\pi$
$48$	−7.48331	−	7.48331i	−1.08012	−	1.08012i
$49$	−7.00000			−1.00000
$50$	4.00000	−	4.00000i	0.565685	−	0.565685i
$51$	−7.48331			−1.04787
$52$	−2.00000			−0.277350
$53$	−11.0000			−1.51097			−0.755483	−	0.655168i	$-0.772598\pi$
$53$	−11.0000			−1.51097			−0.755483	+	0.655168i	$0.772598\pi$
$54$		−	3.74166i		−	0.509175i
$55$	5.61249	−	5.61249i	0.756787	−	0.756787i
$56$	7.48331	−	7.48331i	1.00000	−	1.00000i
$57$			14.0000i			1.85435i
$58$	−3.00000	+	7.00000i	−0.393919	+	0.919145i
$59$			7.48331i			0.974245i	0.873334	+	0.487122i	$0.161953\pi$
$59$			7.48331i			0.974245i	−0.873334	+	0.487122i	$0.838047\pi$
$60$	11.2250	+	11.2250i	1.44914	+	1.44914i
$61$	6.00000	−	6.00000i	0.768221	−	0.768221i	−0.209572	−	0.977793i	$-0.567207\pi$
$61$	6.00000	−	6.00000i	0.768221	−	0.768221i	0.977793	+	0.209572i	$0.0672070\pi$
$62$	3.74166			0.475191
$63$	14.9666			1.88562
$64$			8.00000i			1.00000i
$65$	3.00000			0.372104
$66$	7.00000	+	7.00000i	0.861640	+	0.861640i
$67$	−14.9666			−1.82846			−0.914232	−	0.405190i	$-0.867205\pi$
$67$	−14.9666			−1.82846			−0.914232	+	0.405190i	$0.867205\pi$
$68$	4.00000	+	4.00000i	0.485071	+	0.485071i
$69$	14.0000	−	14.0000i	1.68540	−	1.68540i
$70$	−11.2250	+	11.2250i	−1.34164	+	1.34164i
$71$	−3.74166			−0.444053			−0.222027	−	0.975041i	$-0.571267\pi$
$71$	−3.74166			−0.444053			−0.222027	+	0.975041i	$0.571267\pi$
$72$	−8.00000	+	8.00000i	−0.942809	+	0.942809i
$73$	4.00000	+	4.00000i	0.468165	+	0.468165i	0.901319	−	0.433155i	$-0.142600\pi$
$73$	4.00000	+	4.00000i	0.468165	+	0.468165i	−0.433155	+	0.901319i	$0.642600\pi$
$74$		0			0
$75$	−7.48331	−	7.48331i	−0.864099	−	0.864099i
$76$	7.48331	−	7.48331i	0.858395	−	0.858395i
$77$	−7.00000	+	7.00000i	−0.797724	+	0.797724i
$78$			3.74166i			0.423659i
$79$	−5.61249	−	5.61249i	−0.631454	−	0.631454i	0.316979	−	0.948433i	$-0.397332\pi$
$79$	−5.61249	−	5.61249i	−0.631454	−	0.631454i	−0.948433	+	0.316979i	$0.897332\pi$
$80$		−	12.0000i		−	1.34164i
$81$	5.00000			0.555556
$82$	−2.00000			−0.220863
$83$		−	7.48331i		−	0.821401i	−0.911770	−	0.410700i	$-0.865284\pi$
$83$		−	7.48331i		−	0.821401i	0.911770	−	0.410700i	$-0.134716\pi$
$84$	−14.0000	−	14.0000i	−1.52753	−	1.52753i
$85$	−6.00000	−	6.00000i	−0.650791	−	0.650791i
$86$	−3.74166			−0.403473
$87$	13.0958	+	5.61249i	1.40402	+	0.601722i
$88$		−	7.48331i		−	0.797724i
$89$	−3.00000	+	3.00000i	−0.317999	+	0.317999i	−0.847998	−	0.529999i	$-0.822192\pi$
$89$	−3.00000	+	3.00000i	−0.317999	+	0.317999i	0.529999	+	0.847998i	$0.322192\pi$
$90$	12.0000	−	12.0000i	1.26491	−	1.26491i
$91$	−3.74166			−0.392232
$92$	−14.9666			−1.56038
$93$		−	7.00000i		−	0.725866i
$94$		−	11.2250i		−	1.15777i
$95$	−11.2250	+	11.2250i	−1.15166	+	1.15166i
$96$	14.9666			1.52753
$97$	−5.00000	−	5.00000i	−0.507673	−	0.507673i	0.406138	−	0.913812i	$-0.366875\pi$
$97$	−5.00000	−	5.00000i	−0.507673	−	0.507673i	−0.913812	+	0.406138i	$0.866875\pi$
$98$	7.00000	−	7.00000i	0.707107	−	0.707107i
$99$	7.48331	−	7.48331i	0.752101	−	0.752101i
$100$			8.00000i			0.800000i
$101$	−4.00000	+	4.00000i	−0.398015	+	0.398015i	−0.877532	−	0.479517i	$-0.840812\pi$
$101$	−4.00000	+	4.00000i	−0.398015	+	0.398015i	0.479517	+	0.877532i	$0.340812\pi$
$102$	7.48331	−	7.48331i	0.740959	−	0.740959i
$103$			11.2250i			1.10603i	0.833172	+	0.553015i	$0.186523\pi$
$103$			11.2250i			1.10603i	−0.833172	+	0.553015i	$0.813477\pi$
$104$	2.00000	−	2.00000i	0.196116	−	0.196116i
$105$	21.0000	+	21.0000i	2.04939	+	2.04939i
$106$	11.0000	−	11.0000i	1.06841	−	1.06841i
$107$		−	3.74166i		−	0.361720i	−0.983509	−	0.180860i	$-0.942112\pi$
$107$		−	3.74166i		−	0.361720i	0.983509	−	0.180860i	$-0.0578880\pi$
$108$	3.74166	+	3.74166i	0.360041	+	0.360041i
$109$			1.00000i			0.0957826i	0.998853	+	0.0478913i	$0.0152501\pi$
$109$			1.00000i			0.0957826i	−0.998853	+	0.0478913i	$0.984750\pi$
$110$			11.2250i			1.07026i
$111$		0			0
$112$			14.9666i			1.41421i
$113$	−1.00000	−	1.00000i	−0.0940721	−	0.0940721i	0.658505	−	0.752577i	$-0.271189\pi$
$113$	−1.00000	−	1.00000i	−0.0940721	−	0.0940721i	−0.752577	+	0.658505i	$0.771189\pi$
$114$	−14.0000	−	14.0000i	−1.31122	−	1.31122i
$115$	22.4499			2.09347
$116$	−4.00000	−	10.0000i	−0.371391	−	0.928477i
$117$	4.00000			0.369800
$118$	−7.48331	−	7.48331i	−0.688895	−	0.688895i
$119$	7.48331	+	7.48331i	0.685994	+	0.685994i
$120$	−22.4499			−2.04939
$121$		−	4.00000i		−	0.363636i
$122$			12.0000i			1.08643i
$123$			3.74166i			0.337374i
$124$	−3.74166	+	3.74166i	−0.336011	+	0.336011i
$125$			3.00000i			0.268328i
$126$	−14.9666	+	14.9666i	−1.33333	+	1.33333i
$127$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$127$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$128$	−8.00000	−	8.00000i	−0.707107	−	0.707107i
$129$			7.00000i			0.616316i
$130$	−3.00000	+	3.00000i	−0.263117	+	0.263117i
$131$	7.48331	−	7.48331i	0.653820	−	0.653820i	−0.300090	−	0.953911i	$-0.597017\pi$
$131$	7.48331	−	7.48331i	0.653820	−	0.653820i	0.953911	+	0.300090i	$0.0970169\pi$
$132$	−14.0000			−1.21854
$133$	14.0000	−	14.0000i	1.21395	−	1.21395i
$134$	14.9666	−	14.9666i	1.29292	−	1.29292i
$135$	−5.61249	−	5.61249i	−0.483046	−	0.483046i
$136$	−8.00000			−0.685994
$137$	8.00000	−	8.00000i	0.683486	−	0.683486i	−0.277298	−	0.960784i	$-0.589439\pi$
$137$	8.00000	−	8.00000i	0.683486	−	0.683486i	0.960784	+	0.277298i	$0.0894389\pi$
$138$			28.0000i			2.38352i
$139$			7.48331i			0.634726i	0.948304	+	0.317363i	$0.102797\pi$
$139$			7.48331i			0.634726i	−0.948304	+	0.317363i	$0.897203\pi$
$140$		−	22.4499i		−	1.89737i
$141$	−21.0000			−1.76852
$142$	3.74166	−	3.74166i	0.313993	−	0.313993i
$143$	−1.87083	+	1.87083i	−0.156447	+	0.156447i
$144$		−	16.0000i		−	1.33333i
$145$	6.00000	+	15.0000i	0.498273	+	1.24568i
$146$	−8.00000			−0.662085
$147$	−13.0958	−	13.0958i	−1.08012	−	1.08012i
$148$		0			0
$149$			21.0000i			1.72039i	0.509968	+	0.860194i	$0.329657\pi$
$149$			21.0000i			1.72039i	−0.509968	+	0.860194i	$0.670343\pi$
$150$	14.9666			1.22202
$151$	−3.74166			−0.304492			−0.152246	−	0.988343i	$-0.548651\pi$
$151$	−3.74166			−0.304492			−0.152246	+	0.988343i	$0.548651\pi$
$152$			14.9666i			1.21395i
$153$	−8.00000	−	8.00000i	−0.646762	−	0.646762i
$154$		−	14.0000i		−	1.12815i
$155$	5.61249	−	5.61249i	0.450806	−	0.450806i
$156$	−3.74166	−	3.74166i	−0.299572	−	0.299572i
$157$	5.00000	+	5.00000i	0.399043	+	0.399043i	0.877896	−	0.478852i	$-0.158947\pi$
$157$	5.00000	+	5.00000i	0.399043	+	0.399043i	−0.478852	+	0.877896i	$0.658947\pi$
$158$	11.2250			0.893011
$159$	−20.5791	−	20.5791i	−1.63203	−	1.63203i
$160$	12.0000	+	12.0000i	0.948683	+	0.948683i
$161$	−28.0000			−2.20671
$162$	−5.00000	+	5.00000i	−0.392837	+	0.392837i
$163$	−9.35414	+	9.35414i	−0.732673	+	0.732673i	−0.971149	−	0.238475i	$-0.923352\pi$
$163$	−9.35414	+	9.35414i	−0.732673	+	0.732673i	0.238475	+	0.971149i	$0.423352\pi$
$164$	2.00000	−	2.00000i	0.156174	−	0.156174i
$165$	21.0000			1.63485
$166$	7.48331	+	7.48331i	0.580818	+	0.580818i
$167$	3.74166			0.289538			0.144769	−	0.989465i	$-0.453756\pi$
$167$	3.74166			0.289538			0.144769	+	0.989465i	$0.453756\pi$
$168$	28.0000			2.16025
$169$	12.0000			0.923077
$170$	12.0000			0.920358
$171$	−14.9666	+	14.9666i	−1.14453	+	1.14453i
$172$	3.74166	−	3.74166i	0.285299	−	0.285299i
$173$		−	16.0000i		−	1.21646i	−0.793762	−	0.608229i	$-0.791880\pi$
$173$		−	16.0000i		−	1.21646i	0.793762	−	0.608229i	$-0.208120\pi$
$174$	−18.7083	+	7.48331i	−1.41827	+	0.567309i
$175$			14.9666i			1.13137i
$176$	7.48331	+	7.48331i	0.564076	+	0.564076i
$177$	−14.0000	+	14.0000i	−1.05230	+	1.05230i
$178$		−	6.00000i		−	0.449719i
$179$	−18.7083			−1.39832			−0.699162	−	0.714964i	$-0.746443\pi$
$179$	−18.7083			−1.39832			−0.699162	+	0.714964i	$0.746443\pi$
$180$			24.0000i			1.78885i
$181$	17.0000			1.26360			0.631800	−	0.775131i	$-0.282316\pi$
$181$	17.0000			1.26360			0.631800	+	0.775131i	$0.282316\pi$
$182$	3.74166	−	3.74166i	0.277350	−	0.277350i
$183$	22.4499			1.65955
$184$	14.9666	−	14.9666i	1.10335	−	1.10335i
$185$		0			0
$186$	7.00000	+	7.00000i	0.513265	+	0.513265i
$187$	7.48331			0.547234
$188$	11.2250	+	11.2250i	0.818665	+	0.818665i
$189$	7.00000	+	7.00000i	0.509175	+	0.509175i
$190$		−	22.4499i		−	1.62869i
$191$	7.48331	+	7.48331i	0.541474	+	0.541474i	0.923961	−	0.382487i	$-0.124932\pi$
$191$	7.48331	+	7.48331i	0.541474	+	0.541474i	−0.382487	+	0.923961i	$0.624932\pi$
$192$	−14.9666	+	14.9666i	−1.08012	+	1.08012i
$193$	−5.00000	+	5.00000i	−0.359908	+	0.359908i	−0.863779	−	0.503871i	$-0.831909\pi$
$193$	−5.00000	+	5.00000i	−0.359908	+	0.359908i	0.503871	+	0.863779i	$0.331909\pi$
$194$	10.0000			0.717958
$195$	5.61249	+	5.61249i	0.401918	+	0.401918i
$196$			14.0000i			1.00000i
$197$	−12.0000			−0.854965			−0.427482	−	0.904024i	$-0.640599\pi$
$197$	−12.0000			−0.854965			−0.427482	+	0.904024i	$0.640599\pi$
$198$			14.9666i			1.06363i
$199$		−	11.2250i		−	0.795717i	−0.917447	−	0.397859i	$-0.869753\pi$
$199$		−	11.2250i		−	0.795717i	0.917447	−	0.397859i	$-0.130247\pi$
$200$	−8.00000	−	8.00000i	−0.565685	−	0.565685i
$201$	−28.0000	−	28.0000i	−1.97497	−	1.97497i
$202$		−	8.00000i		−	0.562878i
$203$	−7.48331	−	18.7083i	−0.525226	−	1.31306i
$204$			14.9666i			1.04787i
$205$	−3.00000	+	3.00000i	−0.209529	+	0.209529i
$206$	−11.2250	−	11.2250i	−0.782081	−	0.782081i
$207$	29.9333			2.08051
$208$			4.00000i			0.277350i
$209$		−	14.0000i		−	0.968400i
$210$	−42.0000			−2.89828
$211$	16.8375	−	16.8375i	1.15914	−	1.15914i	0.174477	−	0.984661i	$-0.444176\pi$
$211$	16.8375	−	16.8375i	1.15914	−	1.15914i	0.984661	−	0.174477i	$-0.0558235\pi$
$212$			22.0000i			1.51097i
$213$	−7.00000	−	7.00000i	−0.479632	−	0.479632i
$214$	3.74166	+	3.74166i	0.255774	+	0.255774i
$215$	−5.61249	+	5.61249i	−0.382768	+	0.382768i
$216$	−7.48331			−0.509175
$217$	−7.00000	+	7.00000i	−0.475191	+	0.475191i
$218$	−1.00000	−	1.00000i	−0.0677285	−	0.0677285i
$219$			14.9666i			1.01135i
$220$	−11.2250	−	11.2250i	−0.756787	−	0.756787i
$221$	2.00000	+	2.00000i	0.134535	+	0.134535i
$222$		0			0
$223$			11.2250i			0.751680i	0.926685	+	0.375840i	$0.122646\pi$
$223$			11.2250i			0.751680i	−0.926685	+	0.375840i	$0.877354\pi$
$224$	−14.9666	−	14.9666i	−1.00000	−	1.00000i
$225$		−	16.0000i		−	1.06667i
$226$	2.00000			0.133038
$227$		−	3.74166i		−	0.248343i	−0.992261	−	0.124171i	$-0.960373\pi$
$227$		−	3.74166i		−	0.248343i	0.992261	−	0.124171i	$-0.0396272\pi$
$228$	28.0000			1.85435
$229$	3.00000	+	3.00000i	0.198246	+	0.198246i	0.799248	−	0.601002i	$-0.205232\pi$
$229$	3.00000	+	3.00000i	0.198246	+	0.198246i	−0.601002	+	0.799248i	$0.705232\pi$
$230$	−22.4499	+	22.4499i	−1.48031	+	1.48031i
$231$	−26.1916			−1.72328
$232$	14.0000	+	6.00000i	0.919145	+	0.393919i
$233$	9.00000			0.589610			0.294805	−	0.955557i	$-0.404745\pi$
$233$	9.00000			0.589610			0.294805	+	0.955557i	$0.404745\pi$
$234$	−4.00000	+	4.00000i	−0.261488	+	0.261488i
$235$	−16.8375	−	16.8375i	−1.09835	−	1.09835i
$236$	14.9666			0.974245
$237$		−	21.0000i		−	1.36410i
$238$	−14.9666			−0.970143
$239$			7.48331i			0.484055i	0.970269	+	0.242028i	$0.0778125\pi$
$239$			7.48331i			0.484055i	−0.970269	+	0.242028i	$0.922188\pi$
$240$	22.4499	−	22.4499i	1.44914	−	1.44914i
$241$			15.0000i			0.966235i	0.875556	+	0.483117i	$0.160496\pi$
$241$			15.0000i			0.966235i	−0.875556	+	0.483117i	$0.839504\pi$
$242$	4.00000	+	4.00000i	0.257130	+	0.257130i
$243$	14.9666	+	14.9666i	0.960110	+	0.960110i
$244$	−12.0000	−	12.0000i	−0.768221	−	0.768221i
$245$		−	21.0000i		−	1.34164i
$246$	−3.74166	−	3.74166i	−0.238559	−	0.238559i
$247$	3.74166	−	3.74166i	0.238076	−	0.238076i
$248$		−	7.48331i		−	0.475191i
$249$	14.0000	−	14.0000i	0.887214	−	0.887214i
$250$	−3.00000	−	3.00000i	−0.189737	−	0.189737i
$251$	16.8375	+	16.8375i	1.06277	+	1.06277i	0.997893	+	0.0648777i	$0.0206657\pi$
$251$	16.8375	+	16.8375i	1.06277	+	1.06277i	0.0648777	+	0.997893i	$0.479334\pi$
$252$		−	29.9333i		−	1.88562i
$253$	−14.0000	+	14.0000i	−0.880172	+	0.880172i
$254$		0			0
$255$		−	22.4499i		−	1.40587i
$256$	16.0000			1.00000
$257$	3.00000			0.187135			0.0935674	−	0.995613i	$-0.470173\pi$
$257$	3.00000			0.187135			0.0935674	+	0.995613i	$0.470173\pi$
$258$	−7.00000	−	7.00000i	−0.435801	−	0.435801i
$259$		0			0
$260$		−	6.00000i		−	0.372104i
$261$	8.00000	+	20.0000i	0.495188	+	1.23797i
$262$			14.9666i			0.924641i
$263$	1.87083	+	1.87083i	0.115360	+	0.115360i	0.762430	−	0.647070i	$-0.224006\pi$
$263$	1.87083	+	1.87083i	0.115360	+	0.115360i	−0.647070	+	0.762430i	$0.724006\pi$
$264$	14.0000	−	14.0000i	0.861640	−	0.861640i
$265$		−	33.0000i		−	2.02717i
$266$			28.0000i			1.71679i
$267$	−11.2250			−0.686957
$268$			29.9333i			1.82846i
$269$	−2.00000	−	2.00000i	−0.121942	−	0.121942i	0.643502	−	0.765444i	$-0.277481\pi$
$269$	−2.00000	−	2.00000i	−0.121942	−	0.121942i	−0.765444	+	0.643502i	$0.777481\pi$
$270$	11.2250			0.683130
$271$	−1.87083	+	1.87083i	−0.113645	+	0.113645i	−0.761642	−	0.647998i	$-0.775607\pi$
$271$	−1.87083	+	1.87083i	−0.113645	+	0.113645i	0.647998	+	0.761642i	$0.275607\pi$
$272$	8.00000	−	8.00000i	0.485071	−	0.485071i
$273$	−7.00000	−	7.00000i	−0.423659	−	0.423659i
$274$			16.0000i			0.966595i
$275$	7.48331	+	7.48331i	0.451261	+	0.451261i
$276$	−28.0000	−	28.0000i	−1.68540	−	1.68540i
$277$	28.0000			1.68236			0.841178	−	0.540758i	$-0.181862\pi$
$277$	28.0000			1.68236			0.841178	+	0.540758i	$0.181862\pi$
$278$	−7.48331	−	7.48331i	−0.448819	−	0.448819i
$279$	7.48331	−	7.48331i	0.448014	−	0.448014i
$280$	22.4499	+	22.4499i	1.34164	+	1.34164i
$281$	17.0000			1.01413			0.507067	−	0.861906i	$-0.330729\pi$
$281$	17.0000			1.01413			0.507067	+	0.861906i	$0.330729\pi$
$282$	21.0000	−	21.0000i	1.25053	−	1.25053i
$283$	−7.48331			−0.444837			−0.222418	−	0.974951i	$-0.571395\pi$
$283$	−7.48331			−0.444837			−0.222418	+	0.974951i	$0.571395\pi$
$284$			7.48331i			0.444053i
$285$	−42.0000			−2.48787
$286$		−	3.74166i		−	0.221249i
$287$	3.74166	−	3.74166i	0.220863	−	0.220863i
$288$	16.0000	+	16.0000i	0.942809	+	0.942809i
$289$			9.00000i			0.529412i
$290$	−21.0000	−	9.00000i	−1.23316	−	0.528498i
$291$		−	18.7083i		−	1.09670i
$292$	8.00000	−	8.00000i	0.468165	−	0.468165i
$293$	−15.0000	+	15.0000i	−0.876309	+	0.876309i	−0.993151	−	0.116841i	$-0.962723\pi$
$293$	−15.0000	+	15.0000i	−0.876309	+	0.876309i	0.116841	+	0.993151i	$0.462723\pi$
$294$	26.1916			1.52753
$295$	−22.4499			−1.30709
$296$		0			0
$297$	7.00000			0.406181
$298$	−21.0000	−	21.0000i	−1.21650	−	1.21650i
$299$	−7.48331			−0.432771
$300$	−14.9666	+	14.9666i	−0.864099	+	0.864099i
$301$	7.00000	−	7.00000i	0.403473	−	0.403473i
$302$	3.74166	−	3.74166i	0.215308	−	0.215308i
$303$	−14.9666			−0.859810
$304$	−14.9666	−	14.9666i	−0.858395	−	0.858395i
$305$	18.0000	+	18.0000i	1.03068	+	1.03068i
$306$	16.0000			0.914659
$307$	9.35414	+	9.35414i	0.533869	+	0.533869i	0.921722	−	0.387852i	$-0.126783\pi$
$307$	9.35414	+	9.35414i	0.533869	+	0.533869i	−0.387852	+	0.921722i	$0.626783\pi$
$308$	14.0000	+	14.0000i	0.797724	+	0.797724i
$309$	−21.0000	+	21.0000i	−1.19465	+	1.19465i
$310$			11.2250i			0.637536i
$311$	7.48331	+	7.48331i	0.424340	+	0.424340i	0.886695	−	0.462355i	$-0.152995\pi$
$311$	7.48331	+	7.48331i	0.424340	+	0.424340i	−0.462355	+	0.886695i	$0.652995\pi$
$312$	7.48331			0.423659
$313$	−11.0000			−0.621757			−0.310878	−	0.950450i	$-0.600623\pi$
$313$	−11.0000			−0.621757			−0.310878	+	0.950450i	$0.600623\pi$
$314$	−10.0000			−0.564333
$315$			44.8999i			2.52982i
$316$	−11.2250	+	11.2250i	−0.631454	+	0.631454i
$317$	10.0000	+	10.0000i	0.561656	+	0.561656i	0.929778	−	0.368122i	$-0.119999\pi$
$317$	10.0000	+	10.0000i	0.561656	+	0.561656i	−0.368122	+	0.929778i	$0.619999\pi$
$318$	41.1582			2.30804
$319$	−13.0958	−	5.61249i	−0.733224	−	0.314239i
$320$	−24.0000			−1.34164
$321$	7.00000	−	7.00000i	0.390702	−	0.390702i
$322$	28.0000	−	28.0000i	1.56038	−	1.56038i
$323$	−14.9666			−0.832766
$324$		−	10.0000i		−	0.555556i
$325$			4.00000i			0.221880i
$326$		−	18.7083i		−	1.03616i
$327$	−1.87083	+	1.87083i	−0.103457	+	0.103457i
$328$			4.00000i			0.220863i
$329$	21.0000	+	21.0000i	1.15777	+	1.15777i
$330$	−21.0000	+	21.0000i	−1.15601	+	1.15601i
$331$	16.8375	−	16.8375i	0.925470	−	0.925470i	−0.0719387	−	0.997409i	$-0.522919\pi$
$331$	16.8375	−	16.8375i	0.925470	−	0.925470i	0.997409	+	0.0719387i	$0.0229186\pi$
$332$	−14.9666			−0.821401
$333$		0			0
$334$	−3.74166	+	3.74166i	−0.204734	+	0.204734i
$335$		−	44.8999i		−	2.45314i
$336$	−28.0000	+	28.0000i	−1.52753	+	1.52753i
$337$	−10.0000	−	10.0000i	−0.544735	−	0.544735i	0.380178	−	0.924913i	$-0.375863\pi$
$337$	−10.0000	−	10.0000i	−0.544735	−	0.544735i	−0.924913	+	0.380178i	$0.875863\pi$
$338$	−12.0000	+	12.0000i	−0.652714	+	0.652714i
$339$		−	3.74166i		−	0.203219i
$340$	−12.0000	+	12.0000i	−0.650791	+	0.650791i
$341$			7.00000i			0.379071i
$342$		−	29.9333i		−	1.61861i
$343$		0			0
$344$			7.48331i			0.403473i
$345$	42.0000	+	42.0000i	2.26120	+	2.26120i
$346$	16.0000	+	16.0000i	0.860165	+	0.860165i
$347$	3.74166			0.200863			0.100431	−	0.994944i	$-0.467978\pi$
$347$	3.74166			0.200863			0.100431	+	0.994944i	$0.467978\pi$
$348$	11.2250	−	26.1916i	0.601722	−	1.40402i
$349$	15.0000			0.802932			0.401466	−	0.915874i	$-0.368501\pi$
$349$	15.0000			0.802932			0.401466	+	0.915874i	$0.368501\pi$
$350$	−14.9666	−	14.9666i	−0.800000	−	0.800000i
$351$	1.87083	+	1.87083i	0.0998574	+	0.0998574i
$352$	−14.9666			−0.797724
$353$		−	36.0000i		−	1.91609i	−0.286623	−	0.958043i	$-0.592533\pi$
$353$		−	36.0000i		−	1.91609i	0.286623	−	0.958043i	$-0.407467\pi$
$354$		−	28.0000i		−	1.48818i
$355$		−	11.2250i		−	0.595760i
$356$	6.00000	+	6.00000i	0.317999	+	0.317999i
$357$			28.0000i			1.48192i
$358$	18.7083	−	18.7083i	0.988764	−	0.988764i
$359$	−5.61249	−	5.61249i	−0.296216	−	0.296216i	0.543314	−	0.839530i	$-0.317169\pi$
$359$	−5.61249	−	5.61249i	−0.296216	−	0.296216i	−0.839530	+	0.543314i	$0.817169\pi$
$360$	−24.0000	−	24.0000i	−1.26491	−	1.26491i
$361$			9.00000i			0.473684i
$362$	−17.0000	+	17.0000i	−0.893500	+	0.893500i
$363$	7.48331	−	7.48331i	0.392772	−	0.392772i
$364$			7.48331i			0.392232i
$365$	−12.0000	+	12.0000i	−0.628109	+	0.628109i
$366$	−22.4499	+	22.4499i	−1.17348	+	1.17348i
$367$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$367$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$368$			29.9333i			1.56038i
$369$	−4.00000	+	4.00000i	−0.208232	+	0.208232i
$370$		0			0
$371$			41.1582i			2.13683i
$372$	−14.0000			−0.725866
$373$	−21.0000			−1.08734			−0.543669	−	0.839299i	$-0.682965\pi$
$373$	−21.0000			−1.08734			−0.543669	+	0.839299i	$0.682965\pi$
$374$	−7.48331	+	7.48331i	−0.386953	+	0.386953i
$375$	−5.61249	+	5.61249i	−0.289828	+	0.289828i
$376$	−22.4499			−1.15777
$377$	−2.00000	−	5.00000i	−0.103005	−	0.257513i
$378$	−14.0000			−0.720082
$379$	22.4499	+	22.4499i	1.15318	+	1.15318i	0.985912	+	0.167264i	$0.0534932\pi$
$379$	22.4499	+	22.4499i	1.15318	+	1.15318i	0.167264	+	0.985912i	$0.446507\pi$
$380$	22.4499	+	22.4499i	1.15166	+	1.15166i
$381$		0			0
$382$	−14.9666			−0.765759
$383$	−26.1916			−1.33833			−0.669164	−	0.743115i	$-0.733348\pi$
$383$	−26.1916			−1.33833			−0.669164	+	0.743115i	$0.733348\pi$
$384$		−	29.9333i		−	1.52753i
$385$	−21.0000	−	21.0000i	−1.07026	−	1.07026i
$386$		−	10.0000i		−	0.508987i
$387$	−7.48331	+	7.48331i	−0.380398	+	0.380398i
$388$	−10.0000	+	10.0000i	−0.507673	+	0.507673i
$389$	8.00000	+	8.00000i	0.405616	+	0.405616i	0.880207	−	0.474591i	$-0.157404\pi$
$389$	8.00000	+	8.00000i	0.405616	+	0.405616i	−0.474591	+	0.880207i	$0.657404\pi$
$390$	−11.2250			−0.568399
$391$	14.9666	+	14.9666i	0.756895	+	0.756895i
$392$	−14.0000	−	14.0000i	−0.707107	−	0.707107i
$393$	28.0000			1.41241
$394$	12.0000	−	12.0000i	0.604551	−	0.604551i
$395$	16.8375	−	16.8375i	0.847184	−	0.847184i
$396$	−14.9666	−	14.9666i	−0.752101	−	0.752101i
$397$	−17.0000			−0.853206			−0.426603	−	0.904439i	$-0.640290\pi$
$397$	−17.0000			−0.853206			−0.426603	+	0.904439i	$0.640290\pi$
$398$	11.2250	+	11.2250i	0.562657	+	0.562657i
$399$	52.3832			2.62244
$400$	16.0000			0.800000
$401$	−23.0000			−1.14857			−0.574283	−	0.818657i	$-0.694719\pi$
$401$	−23.0000			−1.14857			−0.574283	+	0.818657i	$0.694719\pi$
$402$	56.0000			2.79303
$403$	−1.87083	+	1.87083i	−0.0931926	+	0.0931926i
$404$	8.00000	+	8.00000i	0.398015	+	0.398015i
$405$			15.0000i			0.745356i
$406$	26.1916	+	11.2250i	1.29987	+	0.557086i
$407$		0			0
$408$	−14.9666	−	14.9666i	−0.740959	−	0.740959i
$409$	−3.00000	+	3.00000i	−0.148340	+	0.148340i	−0.777376	−	0.629036i	$-0.783450\pi$
$409$	−3.00000	+	3.00000i	−0.148340	+	0.148340i	0.629036	+	0.777376i	$0.283450\pi$
$410$		−	6.00000i		−	0.296319i
$411$	29.9333			1.47650
$412$	22.4499			1.10603
$413$	28.0000			1.37779
$414$	−29.9333	+	29.9333i	−1.47114	+	1.47114i
$415$	22.4499			1.10202
$416$	−4.00000	−	4.00000i	−0.196116	−	0.196116i
$417$	−14.0000	+	14.0000i	−0.685583	+	0.685583i
$418$	14.0000	+	14.0000i	0.684762	+	0.684762i
$419$	18.7083			0.913960			0.456980	−	0.889477i	$-0.348931\pi$
$419$	18.7083			0.913960			0.456980	+	0.889477i	$0.348931\pi$
$420$	42.0000	−	42.0000i	2.04939	−	2.04939i
$421$	6.00000	+	6.00000i	0.292422	+	0.292422i	0.838036	−	0.545614i	$-0.183704\pi$
$421$	6.00000	+	6.00000i	0.292422	+	0.292422i	−0.545614	+	0.838036i	$0.683704\pi$
$422$			33.6749i			1.63927i
$423$	−22.4499	−	22.4499i	−1.09155	−	1.09155i
$424$	−22.0000	−	22.0000i	−1.06841	−	1.06841i
$425$	8.00000	−	8.00000i	0.388057	−	0.388057i
$426$	14.0000			0.678302
$427$	−22.4499	−	22.4499i	−1.08643	−	1.08643i
$428$	−7.48331			−0.361720
$429$	−7.00000			−0.337963
$430$		−	11.2250i		−	0.541316i
$431$		−	37.4166i		−	1.80229i	−0.433515	−	0.901146i	$-0.642727\pi$
$431$		−	37.4166i		−	1.80229i	0.433515	−	0.901146i	$-0.357273\pi$
$432$	7.48331	−	7.48331i	0.360041	−	0.360041i
$433$	−16.0000	−	16.0000i	−0.768911	−	0.768911i	0.209004	−	0.977915i	$-0.432978\pi$
$433$	−16.0000	−	16.0000i	−0.768911	−	0.768911i	−0.977915	+	0.209004i	$0.932978\pi$
$434$		−	14.0000i		−	0.672022i
$435$	−16.8375	+	39.2874i	−0.807294	+	1.88369i
$436$	2.00000			0.0957826
$437$	28.0000	−	28.0000i	1.33942	−	1.33942i
$438$	−14.9666	−	14.9666i	−0.715133	−	0.715133i
$439$	−37.4166			−1.78580			−0.892898	−	0.450259i	$-0.851332\pi$
$439$	−37.4166			−1.78580			−0.892898	+	0.450259i	$0.851332\pi$
$440$	22.4499			1.07026
$441$		−	28.0000i		−	1.33333i
$442$	−4.00000			−0.190261
$443$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$443$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$444$		0			0
$445$	−9.00000	−	9.00000i	−0.426641	−	0.426641i
$446$	−11.2250	−	11.2250i	−0.531518	−	0.531518i
$447$	−39.2874	+	39.2874i	−1.85823	+	1.85823i
$448$	29.9333			1.41421
$449$	27.0000	−	27.0000i	1.27421	−	1.27421i	0.330350	−	0.943858i	$-0.392833\pi$
$449$	27.0000	−	27.0000i	1.27421	−	1.27421i	0.943858	−	0.330350i	$-0.107167\pi$
$450$	16.0000	+	16.0000i	0.754247	+	0.754247i
$451$		−	3.74166i		−	0.176188i
$452$	−2.00000	+	2.00000i	−0.0940721	+	0.0940721i
$453$	−7.00000	−	7.00000i	−0.328889	−	0.328889i
$454$	3.74166	+	3.74166i	0.175605	+	0.175605i
$455$		−	11.2250i		−	0.526235i
$456$	−28.0000	+	28.0000i	−1.31122	+	1.31122i
$457$		−	28.0000i		−	1.30978i	−0.755722	−	0.654892i	$-0.772714\pi$
$457$		−	28.0000i		−	1.30978i	0.755722	−	0.654892i	$-0.227286\pi$
$458$	−6.00000			−0.280362
$459$		−	7.48331i		−	0.349291i
$460$		−	44.8999i		−	2.09347i
$461$	−19.0000	−	19.0000i	−0.884918	−	0.884918i	0.109111	−	0.994030i	$-0.465200\pi$
$461$	−19.0000	−	19.0000i	−0.884918	−	0.884918i	−0.994030	+	0.109111i	$0.965200\pi$
$462$	26.1916	−	26.1916i	1.21854	−	1.21854i
$463$	−7.48331			−0.347779			−0.173890	−	0.984765i	$-0.555634\pi$
$463$	−7.48331			−0.347779			−0.173890	+	0.984765i	$0.555634\pi$
$464$	−20.0000	+	8.00000i	−0.928477	+	0.371391i
$465$	21.0000			0.973852
$466$	−9.00000	+	9.00000i	−0.416917	+	0.416917i
$467$	−9.35414	−	9.35414i	−0.432858	−	0.432858i	0.456741	−	0.889600i	$-0.349016\pi$
$467$	−9.35414	−	9.35414i	−0.432858	−	0.432858i	−0.889600	+	0.456741i	$0.849016\pi$
$468$		−	8.00000i		−	0.369800i
$469$			56.0000i			2.58584i
$470$	33.6749			1.55331
$471$			18.7083i			0.862032i
$472$	−14.9666	+	14.9666i	−0.688895	+	0.688895i
$473$		−	7.00000i		−	0.321860i
$474$	21.0000	+	21.0000i	0.964562	+	0.964562i
$475$	−14.9666	−	14.9666i	−0.686716	−	0.686716i
$476$	14.9666	−	14.9666i	0.685994	−	0.685994i
$477$		−	44.0000i		−	2.01462i
$478$	−7.48331	−	7.48331i	−0.342279	−	0.342279i
$479$	−13.0958	+	13.0958i	−0.598362	+	0.598362i	−0.939877	−	0.341514i	$-0.889060\pi$
$479$	−13.0958	+	13.0958i	−0.598362	+	0.598362i	0.341514	+	0.939877i	$0.389060\pi$
$480$			44.8999i			2.04939i
$481$		0			0
$482$	−15.0000	−	15.0000i	−0.683231	−	0.683231i
$483$	−52.3832	−	52.3832i	−2.38352	−	2.38352i
$484$	−8.00000			−0.363636
$485$	15.0000	−	15.0000i	0.681115	−	0.681115i
$486$	−29.9333			−1.35780
$487$			33.6749i			1.52596i	0.646424	+	0.762978i	$0.276264\pi$
$487$			33.6749i			1.52596i	−0.646424	+	0.762978i	$0.723736\pi$
$488$	24.0000			1.08643
$489$	−35.0000			−1.58275
$490$	21.0000	+	21.0000i	0.948683	+	0.948683i
$491$	16.8375	−	16.8375i	0.759864	−	0.759864i	−0.216434	−	0.976297i	$-0.569442\pi$
$491$	16.8375	−	16.8375i	0.759864	−	0.759864i	0.976297	+	0.216434i	$0.0694425\pi$
$492$	7.48331			0.337374
$493$	−6.00000	+	14.0000i	−0.270226	+	0.630528i
$494$			7.48331i			0.336690i
$495$	22.4499	+	22.4499i	1.00905	+	1.00905i
$496$	7.48331	+	7.48331i	0.336011	+	0.336011i
$497$			14.0000i			0.627986i
$498$			28.0000i			1.25471i
$499$	37.4166			1.67500			0.837498	−	0.546440i	$-0.184018\pi$
$499$	37.4166			1.67500			0.837498	+	0.546440i	$0.184018\pi$
$500$	6.00000			0.268328
$501$	7.00000	+	7.00000i	0.312737	+	0.312737i
$502$	−33.6749			−1.50299
$503$	−9.35414	+	9.35414i	−0.417081	+	0.417081i	−0.884196	−	0.467116i	$-0.845293\pi$
$503$	−9.35414	+	9.35414i	−0.417081	+	0.417081i	0.467116	+	0.884196i	$0.345293\pi$
$504$	29.9333	+	29.9333i	1.33333	+	1.33333i
$505$	−12.0000	−	12.0000i	−0.533993	−	0.533993i
$506$		−	28.0000i		−	1.24475i
$507$	22.4499	+	22.4499i	0.997037	+	0.997037i
$508$		0			0
$509$	−5.00000			−0.221621			−0.110811	−	0.993842i	$-0.535345\pi$
$509$	−5.00000			−0.221621			−0.110811	+	0.993842i	$0.535345\pi$
$510$	22.4499	+	22.4499i	0.994100	+	0.994100i
$511$	14.9666	−	14.9666i	0.662085	−	0.662085i
$512$	−16.0000	+	16.0000i	−0.707107	+	0.707107i
$513$	−14.0000			−0.618115
$514$	−3.00000	+	3.00000i	−0.132324	+	0.132324i
$515$	−33.6749			−1.48389
$516$	14.0000			0.616316
$517$	21.0000			0.923579
$518$		0			0
$519$	29.9333	−	29.9333i	1.31392	−	1.31392i
$520$	6.00000	+	6.00000i	0.263117	+	0.263117i
$521$		−	15.0000i		−	0.657162i	−0.944476	−	0.328581i	$-0.893430\pi$
$521$		−	15.0000i		−	0.657162i	0.944476	−	0.328581i	$-0.106570\pi$
$522$	−28.0000	−	12.0000i	−1.22553	−	0.525226i
$523$		−	44.8999i		−	1.96334i	−0.190601	−	0.981668i	$-0.561044\pi$
$523$		−	44.8999i		−	1.96334i	0.190601	−	0.981668i	$-0.438956\pi$
$524$	−14.9666	−	14.9666i	−0.653820	−	0.653820i
$525$	−28.0000	+	28.0000i	−1.22202	+	1.22202i
$526$	−3.74166			−0.163144
$527$	7.48331			0.325978
$528$			28.0000i			1.21854i
$529$	−33.0000			−1.43478
$530$	33.0000	+	33.0000i	1.43343	+	1.43343i
$531$	−29.9333			−1.29899
$532$	−28.0000	−	28.0000i	−1.21395	−	1.21395i
$533$	1.00000	−	1.00000i	0.0433148	−	0.0433148i
$534$	11.2250	−	11.2250i	0.485752	−	0.485752i
$535$	11.2250			0.485298
$536$	−29.9333	−	29.9333i	−1.29292	−	1.29292i
$537$	−35.0000	−	35.0000i	−1.51036	−	1.51036i
$538$	4.00000			0.172452
$539$	13.0958	+	13.0958i	0.564076	+	0.564076i
$540$	−11.2250	+	11.2250i	−0.483046	+	0.483046i
$541$	−4.00000	+	4.00000i	−0.171973	+	0.171973i	−0.787846	−	0.615872i	$-0.788804\pi$
$541$	−4.00000	+	4.00000i	−0.171973	+	0.171973i	0.615872	+	0.787846i	$0.288804\pi$
$542$		−	3.74166i		−	0.160718i
$543$	31.8041	+	31.8041i	1.36484	+	1.36484i
$544$			16.0000i			0.685994i
$545$	−3.00000			−0.128506
$546$	14.0000			0.599145
$547$			33.6749i			1.43984i	0.694059	+	0.719918i	$0.255820\pi$
$547$			33.6749i			1.43984i	−0.694059	+	0.719918i	$0.744180\pi$
$548$	−16.0000	−	16.0000i	−0.683486	−	0.683486i
$549$	24.0000	+	24.0000i	1.02430	+	1.02430i
$550$	−14.9666			−0.638179
$551$	26.1916	+	11.2250i	1.11580	+	0.478200i
$552$	56.0000			2.38352
$553$	−21.0000	+	21.0000i	−0.893011	+	0.893011i
$554$	−28.0000	+	28.0000i	−1.18961	+	1.18961i
$555$		0			0
$556$	14.9666			0.634726
$557$		−	28.0000i		−	1.18640i	−0.805056	−	0.593199i	$-0.797865\pi$
$557$		−	28.0000i		−	1.18640i	0.805056	−	0.593199i	$-0.202135\pi$
$558$			14.9666i			0.633588i
$559$	1.87083	−	1.87083i	0.0791276	−	0.0791276i
$560$	−44.8999			−1.89737
$561$	14.0000	+	14.0000i	0.591080	+	0.591080i
$562$	−17.0000	+	17.0000i	−0.717102	+	0.717102i
$563$	−9.35414	+	9.35414i	−0.394230	+	0.394230i	−0.876192	−	0.481962i	$-0.839924\pi$
$563$	−9.35414	+	9.35414i	−0.394230	+	0.394230i	0.481962	+	0.876192i	$0.339924\pi$
$564$			42.0000i			1.76852i
$565$	3.00000	−	3.00000i	0.126211	−	0.126211i
$566$	7.48331	−	7.48331i	0.314547	−	0.314547i
$567$		−	18.7083i		−	0.785674i
$568$	−7.48331	−	7.48331i	−0.313993	−	0.313993i
$569$	23.0000	+	23.0000i	0.964210	+	0.964210i	0.999381	−	0.0351711i	$-0.0111976\pi$
$569$	23.0000	+	23.0000i	0.964210	+	0.964210i	−0.0351711	+	0.999381i	$0.511198\pi$
$570$	42.0000	−	42.0000i	1.75919	−	1.75919i
$571$		0			0		1.00000			$0$
$571$		0			0		−1.00000			$\pi$
$572$	3.74166	+	3.74166i	0.156447	+	0.156447i
$573$			28.0000i			1.16972i
$574$			7.48331i			0.312348i
$575$			29.9333i			1.24830i
$576$	−32.0000			−1.33333
$577$	30.0000	+	30.0000i	1.24892	+	1.24892i	0.956199	+	0.292717i	$0.0945595\pi$
$577$	30.0000	+	30.0000i	1.24892	+	1.24892i	0.292717	+	0.956199i	$0.405441\pi$
$578$	−9.00000	−	9.00000i	−0.374351	−	0.374351i
$579$	−18.7083			−0.777490
$580$	30.0000	−	12.0000i	1.24568	−	0.498273i
$581$	−28.0000			−1.16164
$582$	18.7083	+	18.7083i	0.775483	+	0.775483i
$583$	20.5791	+	20.5791i	0.852300	+	0.852300i
$584$			16.0000i			0.662085i
$585$			12.0000i			0.496139i
$586$		−	30.0000i		−	1.23929i
$587$		−	22.4499i		−	0.926608i	−0.886199	−	0.463304i	$-0.846664\pi$
$587$		−	22.4499i		−	0.926608i	0.886199	−	0.463304i	$-0.153336\pi$
$588$	−26.1916	+	26.1916i	−1.08012	+	1.08012i
$589$		−	14.0000i		−	0.576860i
$590$	22.4499	−	22.4499i	0.924250	−	0.924250i
$591$	−22.4499	−	22.4499i	−0.923467	−	0.923467i
$592$		0			0
$593$		−	11.0000i		−	0.451716i	−0.974160	−	0.225858i	$-0.927481\pi$
$593$		−	11.0000i		−	0.451716i	0.974160	−	0.225858i	$-0.0725185\pi$
$594$	−7.00000	+	7.00000i	−0.287213	+	0.287213i
$595$	−22.4499	+	22.4499i	−0.920358	+	0.920358i
$596$	42.0000			1.72039
$597$	21.0000	−	21.0000i	0.859473	−	0.859473i
$598$	7.48331	−	7.48331i	0.306015	−	0.306015i
$599$	13.0958	+	13.0958i	0.535080	+	0.535080i	0.922080	−	0.387000i	$-0.126489\pi$
$599$	13.0958	+	13.0958i	0.535080	+	0.535080i	−0.387000	+	0.922080i	$0.626489\pi$
$600$		−	29.9333i		−	1.22202i
$601$	−19.0000	+	19.0000i	−0.775026	+	0.775026i	−0.978980	−	0.203954i	$-0.934621\pi$
$601$	−19.0000	+	19.0000i	−0.775026	+	0.775026i	0.203954	+	0.978980i	$0.434621\pi$
$602$			14.0000i			0.570597i
$603$		−	59.8665i		−	2.43795i
$604$			7.48331i			0.304492i
$605$	12.0000			0.487869
$606$	14.9666	−	14.9666i	0.607978	−	0.607978i
$607$	31.8041	−	31.8041i	1.29089	−	1.29089i	0.356650	−	0.934238i	$-0.383919\pi$
$607$	31.8041	−	31.8041i	1.29089	−	1.29089i	0.934238	−	0.356650i	$-0.116081\pi$
$608$	29.9333			1.21395
$609$	21.0000	−	49.0000i	0.850963	−	1.98558i
$610$	−36.0000			−1.45760
$611$	5.61249	+	5.61249i	0.227057	+	0.227057i
$612$	−16.0000	+	16.0000i	−0.646762	+	0.646762i
$613$		−	1.00000i		−	0.0403896i	−0.999796	−	0.0201948i	$-0.993571\pi$
$613$		−	1.00000i		−	0.0403896i	0.999796	−	0.0201948i	$-0.00642864\pi$
$614$	−18.7083			−0.755005
$615$	−11.2250			−0.452635
$616$	−28.0000			−1.12815
$617$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$617$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$618$		−	42.0000i		−	1.68949i
$619$	−31.8041	+	31.8041i	−1.27831	+	1.27831i	−0.336703	+	0.941611i	$0.609312\pi$
$619$	−31.8041	+	31.8041i	−1.27831	+	1.27831i	−0.941611	+	0.336703i	$0.890688\pi$
$620$	−11.2250	−	11.2250i	−0.450806	−	0.450806i
$621$	14.0000	+	14.0000i	0.561801	+	0.561801i
$622$	−14.9666			−0.600107
$623$	11.2250	+	11.2250i	0.449719	+	0.449719i
$624$	−7.48331	+	7.48331i	−0.299572	+	0.299572i
$625$	−29.0000			−1.16000
$626$	11.0000	−	11.0000i	0.439648	−	0.439648i
$627$	26.1916	−	26.1916i	1.04599	−	1.04599i
$628$	10.0000	−	10.0000i	0.399043	−	0.399043i
$629$		0			0
$630$	−44.8999	−	44.8999i	−1.78885	−	1.78885i
$631$	−41.1582			−1.63848			−0.819242	−	0.573448i	$-0.805605\pi$
$631$	−41.1582			−1.63848			−0.819242	+	0.573448i	$0.805605\pi$
$632$		−	22.4499i		−	0.893011i
$633$	63.0000			2.50403
$634$	−20.0000			−0.794301
$635$		0			0
$636$	−41.1582	+	41.1582i	−1.63203	+	1.63203i
$637$			7.00000i			0.277350i
$638$	18.7083	−	7.48331i	0.740668	−	0.296267i
$639$		−	14.9666i		−	0.592071i
$640$	24.0000	−	24.0000i	0.948683	−	0.948683i
$641$	−14.0000	+	14.0000i	−0.552967	+	0.552967i	−0.927296	−	0.374329i	$-0.877873\pi$
$641$	−14.0000	+	14.0000i	−0.552967	+	0.552967i	0.374329	+	0.927296i	$0.377873\pi$
$642$			14.0000i			0.552536i
$643$	11.2250			0.442670			0.221335	−	0.975198i	$-0.428959\pi$
$643$	11.2250			0.442670			0.221335	+	0.975198i	$0.428959\pi$
$644$			56.0000i			2.20671i
$645$	−21.0000			−0.826874
$646$	14.9666	−	14.9666i	0.588854	−	0.588854i
$647$	22.4499			0.882598			0.441299	−	0.897360i	$-0.354518\pi$
$647$	22.4499			0.882598			0.441299	+	0.897360i	$0.354518\pi$
$648$	10.0000	+	10.0000i	0.392837	+	0.392837i
$649$	14.0000	−	14.0000i	0.549548	−	0.549548i
$650$	−4.00000	−	4.00000i	−0.156893	−	0.156893i
$651$	−26.1916			−1.02653
$652$	18.7083	+	18.7083i	0.732673	+	0.732673i
$653$	19.0000	+	19.0000i	0.743527	+	0.743527i	0.973255	−	0.229728i	$-0.0737835\pi$
$653$	19.0000	+	19.0000i	0.743527	+	0.743527i	−0.229728	+	0.973255i	$0.573784\pi$
$654$		−	3.74166i		−	0.146310i
$655$	22.4499	+	22.4499i	0.877192	+	0.877192i
$656$	−4.00000	−	4.00000i	−0.156174	−	0.156174i
$657$	−16.0000	+	16.0000i	−0.624219	+	0.624219i
$658$	−42.0000			−1.63733
$659$	−5.61249	−	5.61249i	−0.218631	−	0.218631i	0.589290	−	0.807922i	$-0.299408\pi$
$659$	−5.61249	−	5.61249i	−0.218631	−	0.218631i	−0.807922	+	0.589290i	$0.799408\pi$
$660$		−	42.0000i		−	1.63485i
$661$	12.0000			0.466746			0.233373	−	0.972387i	$-0.425024\pi$
$661$	12.0000			0.466746			0.233373	+	0.972387i	$0.425024\pi$
$662$			33.6749i			1.30881i
$663$			7.48331i			0.290628i
$664$	14.9666	−	14.9666i	0.580818	−	0.580818i
$665$	42.0000	+	42.0000i	1.62869	+	1.62869i
$666$		0			0
$667$	−14.9666	−	37.4166i	−0.579510	−	1.44878i
$668$		−	7.48331i		−	0.289538i
$669$	−21.0000	+	21.0000i	−0.811907	+	0.811907i
$670$	44.8999	+	44.8999i	1.73463	+	1.73463i
$671$	−22.4499			−0.866670
$672$		−	56.0000i		−	2.16025i
$673$		−	11.0000i		−	0.424019i	−0.977268	−	0.212009i	$-0.931999\pi$
$673$		−	11.0000i		−	0.424019i	0.977268	−	0.212009i	$-0.0680008\pi$
$674$	20.0000			0.770371
$675$	7.48331	−	7.48331i	0.288033	−	0.288033i
$676$		−	24.0000i		−	0.923077i
$677$	−25.0000	−	25.0000i	−0.960828	−	0.960828i	0.0384331	−	0.999261i	$-0.487763\pi$
$677$	−25.0000	−	25.0000i	−0.960828	−	0.960828i	−0.999261	+	0.0384331i	$0.987763\pi$
$678$	3.74166	+	3.74166i	0.143697	+	0.143697i
$679$	−18.7083	+	18.7083i	−0.717958	+	0.717958i
$680$		−	24.0000i		−	0.920358i
$681$	7.00000	−	7.00000i	0.268241	−	0.268241i
$682$	−7.00000	−	7.00000i	−0.268044	−	0.268044i
$683$			29.9333i			1.14536i	0.819777	+	0.572682i	$0.194097\pi$
$683$			29.9333i			1.14536i	−0.819777	+	0.572682i	$0.805903\pi$
$684$	29.9333	+	29.9333i	1.14453	+	1.14453i
$685$	24.0000	+	24.0000i	0.916993	+	0.916993i
$686$		0			0
$687$			11.2250i			0.428259i
$688$	−7.48331	−	7.48331i	−0.285299	−	0.285299i
$689$			11.0000i			0.419067i
$690$	−84.0000			−3.19783
$691$		0			0		1.00000			$0$
$691$		0			0		−1.00000			$\pi$
$692$	−32.0000			−1.21646
$693$	−28.0000	−	28.0000i	−1.06363	−	1.06363i
$694$	−3.74166	+	3.74166i	−0.142031	+	0.142031i
$695$	−22.4499			−0.851575
$696$	14.9666	+	37.4166i	0.567309	+	1.41827i
$697$	−4.00000			−0.151511
$698$	−15.0000	+	15.0000i	−0.567758	+	0.567758i
$699$	16.8375	+	16.8375i	0.636851	+	0.636851i
$700$	29.9333			1.13137
$701$		−	25.0000i		−	0.944237i	−0.881535	−	0.472118i	$-0.843489\pi$
$701$		−	25.0000i		−	0.944237i	0.881535	−	0.472118i	$-0.156511\pi$
$702$	−3.74166			−0.141220
$703$		0			0
$704$	14.9666	−	14.9666i	0.564076	−	0.564076i
$705$		−	63.0000i		−	2.37272i
$706$	36.0000	+	36.0000i	1.35488	+	1.35488i
$707$	14.9666	+	14.9666i	0.562878	+	0.562878i
$708$	28.0000	+	28.0000i	1.05230	+	1.05230i
$709$		−	19.0000i		−	0.713560i	−0.934188	−	0.356780i	$-0.883875\pi$
$709$		−	19.0000i		−	0.713560i	0.934188	−	0.356780i	$-0.116125\pi$
$710$	11.2250	+	11.2250i	0.421266	+	0.421266i
$711$	22.4499	−	22.4499i	0.841939	−	0.841939i
$712$	−12.0000			−0.449719
$713$	−14.0000	+	14.0000i	−0.524304	+	0.524304i
$714$	−28.0000	−	28.0000i	−1.04787	−	1.04787i
$715$	−5.61249	−	5.61249i	−0.209895	−	0.209895i
$716$			37.4166i			1.39832i
$717$	−14.0000	+	14.0000i	−0.522840	+	0.522840i
$718$	11.2250			0.418912
$719$		−	11.2250i		−	0.418621i	−0.977849	−	0.209310i	$-0.932878\pi$
$719$		−	11.2250i		−	0.418621i	0.977849	−	0.209310i	$-0.0671219\pi$
$720$	48.0000			1.78885
$721$	42.0000			1.56416
$722$	−9.00000	−	9.00000i	−0.334945	−	0.334945i
$723$	−28.0624	+	28.0624i	−1.04365	+	1.04365i
$724$		−	34.0000i		−	1.26360i
$725$	−20.0000	+	8.00000i	−0.742781	+	0.297113i
$726$			14.9666i			0.555464i
$727$	−37.4166	−	37.4166i	−1.38770	−	1.38770i	−0.830122	−	0.557582i	$-0.811729\pi$
$727$	−37.4166	−	37.4166i	−1.38770	−	1.38770i	−0.557582	−	0.830122i	$-0.688271\pi$
$728$	−7.48331	−	7.48331i	−0.277350	−	0.277350i
$729$			41.0000i			1.51852i
$730$		−	24.0000i		−	0.888280i
$731$	−7.48331			−0.276780
$732$		−	44.8999i		−	1.65955i
$733$	24.0000	+	24.0000i	0.886460	+	0.886460i	0.994181	−	0.107721i	$-0.0343553\pi$
$733$	24.0000	+	24.0000i	0.886460	+	0.886460i	−0.107721	+	0.994181i	$0.534355\pi$
$734$		0			0
$735$	39.2874	−	39.2874i	1.44914	−	1.44914i
$736$	−29.9333	−	29.9333i	−1.10335	−	1.10335i
$737$	28.0000	+	28.0000i	1.03139	+	1.03139i
$738$		−	8.00000i		−	0.294484i
$739$	13.0958	+	13.0958i	0.481737	+	0.481737i	0.905686	−	0.423949i	$-0.139356\pi$
$739$	13.0958	+	13.0958i	0.481737	+	0.481737i	−0.423949	+	0.905686i	$0.639356\pi$
$740$		0			0
$741$	14.0000			0.514303
$742$	−41.1582	−	41.1582i	−1.51097	−	1.51097i
$743$	−18.7083	+	18.7083i	−0.686340	+	0.686340i	−0.961421	−	0.275081i	$-0.911295\pi$
$743$	−18.7083	+	18.7083i	−0.686340	+	0.686340i	0.275081	+	0.961421i	$0.411295\pi$
$744$	14.0000	−	14.0000i	0.513265	−	0.513265i
$745$	−63.0000			−2.30814
$746$	21.0000	−	21.0000i	0.768865	−	0.768865i
$747$	29.9333			1.09520
$748$		−	14.9666i		−	0.547234i
$749$	−14.0000			−0.511549
$750$		−	11.2250i		−	0.409878i
$751$	−29.9333	+	29.9333i	−1.09228	+	1.09228i	−0.0969953	+	0.995285i	$0.530923\pi$
$751$	−29.9333	+	29.9333i	−1.09228	+	1.09228i	−0.995285	+	0.0969953i	$0.969077\pi$
$752$	22.4499	−	22.4499i	0.818665	−	0.818665i
$753$			63.0000i			2.29585i
$754$	7.00000	+	3.00000i	0.254925	+	0.109254i
$755$		−	11.2250i		−	0.408519i
$756$	14.0000	−	14.0000i	0.509175	−	0.509175i
$757$	18.0000	−	18.0000i	0.654221	−	0.654221i	−0.299786	−	0.954007i	$-0.596915\pi$
$757$	18.0000	−	18.0000i	0.654221	−	0.654221i	0.954007	+	0.299786i	$0.0969151\pi$
$758$	−44.8999			−1.63084
$759$	−52.3832			−1.90139
$760$	−44.8999			−1.62869
$761$	12.0000			0.435000			0.217500	−	0.976060i	$-0.430210\pi$
$761$	12.0000			0.435000			0.217500	+	0.976060i	$0.430210\pi$
$762$		0			0
$763$	3.74166			0.135457
$764$	14.9666	−	14.9666i	0.541474	−	0.541474i
$765$	24.0000	−	24.0000i	0.867722	−	0.867722i
$766$	26.1916	−	26.1916i	0.946341	−	0.946341i
$767$	7.48331			0.270207
$768$	29.9333	+	29.9333i	1.08012	+	1.08012i
$769$	−22.0000	−	22.0000i	−0.793340	−	0.793340i	0.188695	−	0.982036i	$-0.439574\pi$
$769$	−22.0000	−	22.0000i	−0.793340	−	0.793340i	−0.982036	+	0.188695i	$0.939574\pi$
$770$	42.0000			1.51357
$771$	5.61249	+	5.61249i	0.202129	+	0.202129i
$772$	10.0000	+	10.0000i	0.359908	+	0.359908i
$773$	25.0000	−	25.0000i	0.899188	−	0.899188i	−0.0961768	−	0.995364i	$-0.530661\pi$
$773$	25.0000	−	25.0000i	0.899188	−	0.899188i	0.995364	+	0.0961768i	$0.0306614\pi$
$774$		−	14.9666i		−	0.537964i
$775$	7.48331	+	7.48331i	0.268809	+	0.268809i
$776$		−	20.0000i		−	0.717958i
$777$		0			0
$778$	−16.0000			−0.573628
$779$			7.48331i			0.268118i
$780$	11.2250	−	11.2250i	0.401918	−	0.401918i
$781$	7.00000	+	7.00000i	0.250480	+	0.250480i
$782$	−29.9333			−1.07041
$783$	−5.61249	+	13.0958i	−0.200574	+	0.468006i
$784$	28.0000			1.00000
$785$	−15.0000	+	15.0000i	−0.535373	+	0.535373i
$786$	−28.0000	+	28.0000i	−0.998727	+	0.998727i
$787$	41.1582			1.46713			0.733566	−	0.679618i	$-0.237854\pi$
$787$	41.1582			1.46713			0.733566	+	0.679618i	$0.237854\pi$
$788$			24.0000i			0.854965i
$789$			7.00000i			0.249207i
$790$			33.6749i			1.19810i
$791$	−3.74166	+	3.74166i	−0.133038	+	0.133038i
$792$	29.9333			1.06363
$793$	−6.00000	−	6.00000i	−0.213066	−	0.213066i
$794$	17.0000	−	17.0000i	0.603307	−	0.603307i
$795$	61.7373	−	61.7373i	2.18960	−	2.18960i
$796$	−22.4499			−0.795717
$797$	−2.00000	+	2.00000i	−0.0708436	+	0.0708436i	−0.741641	−	0.670797i	$-0.765952\pi$
$797$	−2.00000	+	2.00000i	−0.0708436	+	0.0708436i	0.670797	+	0.741641i	$0.265952\pi$
$798$	−52.3832	+	52.3832i	−1.85435	+	1.85435i
$799$		−	22.4499i		−	0.794222i
$800$	−16.0000	+	16.0000i	−0.565685	+	0.565685i
$801$	−12.0000	−	12.0000i	−0.423999	−	0.423999i
$802$	23.0000	−	23.0000i	0.812158	−	0.812158i
$803$		−	14.9666i		−	0.528161i
$804$	−56.0000	+	56.0000i	−1.97497	+	1.97497i
$805$		−	84.0000i		−	2.96061i
$806$		−	3.74166i		−	0.131794i
$807$		−	7.48331i		−	0.263425i
$808$	−16.0000			−0.562878
$809$	−12.0000	−	12.0000i	−0.421898	−	0.421898i	0.463959	−	0.885857i	$-0.346428\pi$
$809$	−12.0000	−	12.0000i	−0.421898	−	0.421898i	−0.885857	+	0.463959i	$0.846428\pi$
$810$	−15.0000	−	15.0000i	−0.527046	−	0.527046i
$811$	33.6749			1.18249			0.591243	−	0.806493i	$-0.298637\pi$
$811$	33.6749			1.18249			0.591243	+	0.806493i	$0.298637\pi$
$812$	−37.4166	+	14.9666i	−1.31306	+	0.525226i
$813$	−7.00000			−0.245501
$814$		0			0
$815$	−28.0624	−	28.0624i	−0.982984	−	0.982984i
$816$	29.9333			1.04787
$817$			14.0000i			0.489798i
$818$		−	6.00000i		−	0.209785i
$819$		−	14.9666i		−	0.522976i
$820$	6.00000	+	6.00000i	0.209529	+	0.209529i
$821$		−	15.0000i		−	0.523504i	−0.965135	−	0.261752i	$-0.915700\pi$
$821$		−	15.0000i		−	0.523504i	0.965135	−	0.261752i	$-0.0843002\pi$
$822$	−29.9333	+	29.9333i	−1.04404	+	1.04404i
$823$	29.9333	+	29.9333i	1.04341	+	1.04341i	0.999014	+	0.0443937i	$0.0141356\pi$
$823$	29.9333	+	29.9333i	1.04341	+	1.04341i	0.0443937	+	0.999014i	$0.485864\pi$
$824$	−22.4499	+	22.4499i	−0.782081	+	0.782081i
$825$			28.0000i			0.974835i
$826$	−28.0000	+	28.0000i	−0.974245	+	0.974245i
$827$	−24.3208	+	24.3208i	−0.845716	+	0.845716i	−0.989595	−	0.143879i	$-0.954042\pi$
$827$	−24.3208	+	24.3208i	−0.845716	+	0.845716i	0.143879	+	0.989595i	$0.454042\pi$
$828$		−	59.8665i		−	2.08051i
$829$	−18.0000	+	18.0000i	−0.625166	+	0.625166i	−0.946848	−	0.321682i	$-0.895752\pi$
$829$	−18.0000	+	18.0000i	−0.625166	+	0.625166i	0.321682	+	0.946848i	$0.395752\pi$
$830$	−22.4499	+	22.4499i	−0.779249	+	0.779249i
$831$	52.3832	+	52.3832i	1.81715	+	1.81715i
$832$	8.00000			0.277350
$833$	14.0000	−	14.0000i	0.485071	−	0.485071i
$834$		−	28.0000i		−	0.969561i
$835$			11.2250i			0.388456i
$836$	−28.0000			−0.968400
$837$	7.00000			0.241955
$838$	−18.7083	+	18.7083i	−0.646267	+	0.646267i
$839$	5.61249	−	5.61249i	0.193765	−	0.193765i	−0.603556	−	0.797321i	$-0.706250\pi$
$839$	5.61249	−	5.61249i	0.193765	−	0.193765i	0.797321	+	0.603556i	$0.206250\pi$
$840$			84.0000i			2.89828i
$841$	21.0000	−	20.0000i	0.724138	−	0.689655i
$842$	−12.0000			−0.413547
$843$	31.8041	+	31.8041i	1.09539	+	1.09539i
$844$	−33.6749	−	33.6749i	−1.15914	−	1.15914i
$845$			36.0000i			1.23844i
$846$	44.8999			1.54369
$847$	−14.9666			−0.514259
$848$	44.0000			1.51097
$849$	−14.0000	−	14.0000i	−0.480479	−	0.480479i
$850$			16.0000i			0.548795i
$851$		0			0
$852$	−14.0000	+	14.0000i	−0.479632	+	0.479632i
$853$	19.0000	+	19.0000i	0.650548	+	0.650548i	0.953125	−	0.302577i	$-0.0978470\pi$
$853$	19.0000	+	19.0000i	0.650548	+	0.650548i	−0.302577	+	0.953125i	$0.597847\pi$
$854$	44.8999			1.53644
$855$	−44.8999	−	44.8999i	−1.53554	−	1.53554i
$856$	7.48331	−	7.48331i	0.255774	−	0.255774i
$857$	13.0000			0.444072			0.222036	−	0.975039i	$-0.428730\pi$
$857$	13.0000			0.444072			0.222036	+	0.975039i	$0.428730\pi$
$858$	7.00000	−	7.00000i	0.238976	−	0.238976i
$859$	−31.8041	+	31.8041i	−1.08514	+	1.08514i	−0.0891206	+	0.996021i	$0.528406\pi$
$859$	−31.8041	+	31.8041i	−1.08514	+	1.08514i	−0.996021	+	0.0891206i	$0.971594\pi$
$860$	11.2250	+	11.2250i	0.382768	+	0.382768i
$861$	14.0000			0.477119
$862$	37.4166	+	37.4166i	1.27441	+	1.27441i
$863$	48.6415			1.65578			0.827889	−	0.560892i	$-0.189542\pi$
$863$	48.6415			1.65578			0.827889	+	0.560892i	$0.189542\pi$
$864$			14.9666i			0.509175i
$865$	48.0000			1.63205
$866$	32.0000			1.08740
$867$	−16.8375	+	16.8375i	−0.571830	+	0.571830i
$868$	14.0000	+	14.0000i	0.475191	+	0.475191i
$869$			21.0000i			0.712376i
$870$	−22.4499	−	56.1249i	−0.761124	−	1.90281i
$871$			14.9666i			0.507125i
$872$	−2.00000	+	2.00000i	−0.0677285	+	0.0677285i
$873$	20.0000	−	20.0000i	0.676897	−	0.676897i
$874$			56.0000i			1.89423i
$875$	11.2250			0.379473
$876$	29.9333			1.01135
$877$	−47.0000			−1.58708			−0.793539	−	0.608520i	$-0.791764\pi$
$877$	−47.0000			−1.58708			−0.793539	+	0.608520i	$0.791764\pi$
$878$	37.4166	−	37.4166i	1.26275	−	1.26275i
$879$	−56.1249			−1.89304
$880$	−22.4499	+	22.4499i	−0.756787	+	0.756787i
$881$	−19.0000	+	19.0000i	−0.640126	+	0.640126i	−0.950586	−	0.310460i	$-0.899517\pi$
$881$	−19.0000	+	19.0000i	−0.640126	+	0.640126i	0.310460	+	0.950586i	$0.399517\pi$
$882$	28.0000	+	28.0000i	0.942809	+	0.942809i
$883$	11.2250			0.377750			0.188875	−	0.982001i	$-0.439516\pi$
$883$	11.2250			0.377750			0.188875	+	0.982001i	$0.439516\pi$
$884$	4.00000	−	4.00000i	0.134535	−	0.134535i
$885$	−42.0000	−	42.0000i	−1.41181	−	1.41181i
$886$		0			0
$887$	−9.35414	−	9.35414i	−0.314081	−	0.314081i	0.532407	−	0.846488i	$-0.321288\pi$
$887$	−9.35414	−	9.35414i	−0.314081	−	0.314081i	−0.846488	+	0.532407i	$0.821288\pi$
$888$		0			0
$889$		0			0
$890$	18.0000			0.603361
$891$	−9.35414	−	9.35414i	−0.313376	−	0.313376i
$892$	22.4499			0.751680
$893$	−42.0000			−1.40548
$894$		−	78.5748i		−	2.62793i
$895$		−	56.1249i		−	1.87605i
$896$	−29.9333	+	29.9333i	−1.00000	+	1.00000i
$897$	−14.0000	−	14.0000i	−0.467446	−	0.467446i
$898$			54.0000i			1.80200i
$899$	−13.0958	−	5.61249i	−0.436769	−	0.187187i
$900$	−32.0000			−1.06667
$901$	22.0000	−	22.0000i	0.732926	−	0.732926i
$902$	3.74166	+	3.74166i	0.124584	+	0.124584i
$903$	26.1916			0.871602
$904$		−	4.00000i		−	0.133038i
$905$			51.0000i			1.69530i
$906$	14.0000			0.465119
$907$	−14.9666	+	14.9666i	−0.496959	+	0.496959i	−0.910490	−	0.413531i	$-0.864295\pi$
$907$	−14.9666	+	14.9666i	−0.496959	+	0.496959i	0.413531	+	0.910490i	$0.364295\pi$
$908$	−7.48331			−0.248343
$909$	−16.0000	−	16.0000i	−0.530687	−	0.530687i
$910$	11.2250	+	11.2250i	0.372104	+	0.372104i
$911$	16.8375	−	16.8375i	0.557850	−	0.557850i	−0.370845	−	0.928695i	$-0.620932\pi$
$911$	16.8375	−	16.8375i	0.557850	−	0.557850i	0.928695	+	0.370845i	$0.120932\pi$
$912$		−	56.0000i		−	1.85435i
$913$	−14.0000	+	14.0000i	−0.463332	+	0.463332i
$914$	28.0000	+	28.0000i	0.926158	+	0.926158i
$915$			67.3498i			2.22652i
$916$	6.00000	−	6.00000i	0.198246	−	0.198246i
$917$	−28.0000	−	28.0000i	−0.924641	−	0.924641i
$918$	7.48331	+	7.48331i	0.246986	+	0.246986i
$919$		−	11.2250i		−	0.370278i	−0.982712	−	0.185139i	$-0.940727\pi$
$919$		−	11.2250i		−	0.370278i	0.982712	−	0.185139i	$-0.0592735\pi$
$920$	44.8999	+	44.8999i	1.48031	+	1.48031i
$921$			35.0000i			1.15329i
$922$	38.0000			1.25146
$923$			3.74166i			0.123158i
$924$			52.3832i			1.72328i
$925$		0			0
$926$	7.48331	−	7.48331i	0.245917	−	0.245917i
$927$	−44.8999			−1.47471
$928$	12.0000	−	28.0000i	0.393919	−	0.919145i
$929$	−40.0000			−1.31236			−0.656179	−	0.754606i	$-0.727828\pi$
$929$	−40.0000			−1.31236			−0.656179	+	0.754606i	$0.727828\pi$
$930$	−21.0000	+	21.0000i	−0.688617	+	0.688617i
$931$	−26.1916	−	26.1916i	−0.858395	−	0.858395i
$932$		−	18.0000i		−	0.589610i
$933$			28.0000i			0.916679i
$934$	18.7083			0.612154
$935$			22.4499i			0.734192i
$936$	8.00000	+	8.00000i	0.261488	+	0.261488i
$937$			32.0000i			1.04539i	0.852518	+	0.522697i	$0.175074\pi$
$937$			32.0000i			1.04539i	−0.852518	+	0.522697i	$0.824926\pi$
$938$	−56.0000	−	56.0000i	−1.82846	−	1.82846i
$939$	−20.5791	−	20.5791i	−0.671574	−	0.671574i
$940$	−33.6749	+	33.6749i	−1.09835	+	1.09835i
$941$		−	15.0000i		−	0.488986i	−0.969651	−	0.244493i	$-0.921378\pi$
$941$		−	15.0000i		−	0.488986i	0.969651	−	0.244493i	$-0.0786215\pi$
$942$	−18.7083	−	18.7083i	−0.609549	−	0.609549i
$943$	7.48331	−	7.48331i	0.243690	−	0.243690i
$944$		−	29.9333i		−	0.974245i
$945$	−21.0000	+	21.0000i	−0.683130	+	0.683130i
$946$	7.00000	+	7.00000i	0.227590	+	0.227590i
$947$	−28.0624	−	28.0624i	−0.911906	−	0.911906i	0.0845157	−	0.996422i	$-0.473066\pi$
$947$	−28.0624	−	28.0624i	−0.911906	−	0.911906i	−0.996422	+	0.0845157i	$0.973066\pi$
$948$	−42.0000			−1.36410
$949$	4.00000	−	4.00000i	0.129845	−	0.129845i
$950$	29.9333			0.971163
$951$			37.4166i			1.21332i
$952$			29.9333i			0.970143i
$953$	−51.0000			−1.65205			−0.826026	−	0.563632i	$-0.809404\pi$
$953$	−51.0000			−1.65205			−0.826026	+	0.563632i	$0.809404\pi$
$954$	44.0000	+	44.0000i	1.42455	+	1.42455i
$955$	−22.4499	+	22.4499i	−0.726463	+	0.726463i
$956$	14.9666			0.484055
$957$	−14.0000	−	35.0000i	−0.452556	−	1.13139i
$958$		−	26.1916i		−	0.846212i
$959$	−29.9333	−	29.9333i	−0.966595	−	0.966595i
$960$	−44.8999	−	44.8999i	−1.44914	−	1.44914i
$961$		−	24.0000i		−	0.774194i
$962$		0			0
$963$	14.9666			0.482293
$964$	30.0000			0.966235
$965$	−15.0000	−	15.0000i	−0.482867	−	0.482867i
$966$	104.766			3.37080
$967$	31.8041	−	31.8041i	1.02275	−	1.02275i	0.0230154	−	0.999735i	$-0.492673\pi$
$967$	31.8041	−	31.8041i	1.02275	−	1.02275i	0.999735	−	0.0230154i	$-0.00732668\pi$
$968$	8.00000	−	8.00000i	0.257130	−	0.257130i
$969$	−28.0000	−	28.0000i	−0.899490	−	0.899490i
$970$			30.0000i			0.963242i
$971$	−29.9333	−	29.9333i	−0.960604	−	0.960604i	0.0386489	−	0.999253i	$-0.487695\pi$
$971$	−29.9333	−	29.9333i	−0.960604	−	0.960604i	−0.999253	+	0.0386489i	$0.987695\pi$
$972$	29.9333	−	29.9333i	0.960110	−	0.960110i
$973$	28.0000			0.897639
$974$	−33.6749	−	33.6749i	−1.07901	−	1.07901i
$975$	−7.48331	+	7.48331i	−0.239658	+	0.239658i
$976$	−24.0000	+	24.0000i	−0.768221	+	0.768221i
$977$	13.0000			0.415907			0.207953	−	0.978139i	$-0.433320\pi$
$977$	13.0000			0.415907			0.207953	+	0.978139i	$0.433320\pi$
$978$	35.0000	−	35.0000i	1.11918	−	1.11918i
$979$	11.2250			0.358752
$980$	−42.0000			−1.34164
$981$	−4.00000			−0.127710
$982$			33.6749i			1.07461i
$983$	28.0624	−	28.0624i	0.895053	−	0.895053i	−0.0999409	−	0.994993i	$-0.531865\pi$
$983$	28.0624	−	28.0624i	0.895053	−	0.895053i	0.994993	+	0.0999409i	$0.0318654\pi$
$984$	−7.48331	+	7.48331i	−0.238559	+	0.238559i
$985$		−	36.0000i		−	1.14706i
$986$	−8.00000	−	20.0000i	−0.254772	−	0.636930i
$987$			78.5748i			2.50106i
$988$	−7.48331	−	7.48331i	−0.238076	−	0.238076i
$989$	14.0000	−	14.0000i	0.445174	−	0.445174i
$990$	−44.8999			−1.42701
$991$	−3.74166			−0.118858			−0.0594288	−	0.998233i	$-0.518928\pi$
$991$	−3.74166			−0.118858			−0.0594288	+	0.998233i	$0.518928\pi$
$992$	−14.9666			−0.475191
$993$	63.0000			1.99924
$994$	−14.0000	−	14.0000i	−0.444053	−	0.444053i
$995$	33.6749			1.06757
$996$	−28.0000	−	28.0000i	−0.887214	−	0.887214i
$997$	−12.0000	+	12.0000i	−0.380044	+	0.380044i	−0.871118	−	0.491074i	$-0.836604\pi$
$997$	−12.0000	+	12.0000i	−0.380044	+	0.380044i	0.491074	+	0.871118i	$0.336604\pi$
$998$	−37.4166	+	37.4166i	−1.18440	+	1.18440i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	116.2.e.b.75.2	yes	4
4.3	odd	2	inner	116.2.e.b.75.1	✓	4
29.12	odd	4	inner	116.2.e.b.99.1	yes	4
116.99	even	4	inner	116.2.e.b.99.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
116.2.e.b.75.1	✓	4	4.3	odd	2	inner
116.2.e.b.75.2	yes	4	1.1	even	1	trivial
116.2.e.b.99.1	yes	4	29.12	odd	4	inner
116.2.e.b.99.2	yes	4	116.99	even	4	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:	\( N \)	\(=\)	\( 116 = 2^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	116.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{2} +(1.87083 + 1.87083i) q^{3} -2.00000i q^{4} +3.00000i q^{5} -3.74166 q^{6} -3.74166i q^{7} +(2.00000 + 2.00000i) q^{8} +4.00000i q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.00000i) q^{2} +(1.87083 + 1.87083i) q^{3} -2.00000i q^{4} +3.00000i q^{5} -3.74166 q^{6} -3.74166i q^{7} +(2.00000 + 2.00000i) q^{8} +4.00000i q^{9} +(-3.00000 - 3.00000i) q^{10} +(-1.87083 - 1.87083i) q^{11} +(3.74166 - 3.74166i) q^{12} -1.00000i q^{13} +(3.74166 + 3.74166i) q^{14} +(-5.61249 + 5.61249i) q^{15} -4.00000 q^{16} +(-2.00000 + 2.00000i) q^{17} +(-4.00000 - 4.00000i) q^{18} +(3.74166 + 3.74166i) q^{19} +6.00000 q^{20} +(7.00000 - 7.00000i) q^{21} +3.74166 q^{22} -7.48331i q^{23} +7.48331i q^{24} -4.00000 q^{25} +(1.00000 + 1.00000i) q^{26} +(-1.87083 + 1.87083i) q^{27} -7.48331 q^{28} +(5.00000 - 2.00000i) q^{29} -11.2250i q^{30} +(-1.87083 - 1.87083i) q^{31} +(4.00000 - 4.00000i) q^{32} -7.00000i q^{33} -4.00000i q^{34} +11.2250 q^{35} +8.00000 q^{36} -7.48331 q^{38} +(1.87083 - 1.87083i) q^{39} +(-6.00000 + 6.00000i) q^{40} +(1.00000 + 1.00000i) q^{41} +14.0000i q^{42} +(1.87083 + 1.87083i) q^{43} +(-3.74166 + 3.74166i) q^{44} -12.0000 q^{45} +(7.48331 + 7.48331i) q^{46} +(-5.61249 + 5.61249i) q^{47} +(-7.48331 - 7.48331i) q^{48} -7.00000 q^{49} +(4.00000 - 4.00000i) q^{50} -7.48331 q^{51} -2.00000 q^{52} -11.0000 q^{53} -3.74166i q^{54} +(5.61249 - 5.61249i) q^{55} +(7.48331 - 7.48331i) q^{56} +14.0000i q^{57} +(-3.00000 + 7.00000i) q^{58} +7.48331i q^{59} +(11.2250 + 11.2250i) q^{60} +(6.00000 - 6.00000i) q^{61} +3.74166 q^{62} +14.9666 q^{63} +8.00000i q^{64} +3.00000 q^{65} +(7.00000 + 7.00000i) q^{66} -14.9666 q^{67} +(4.00000 + 4.00000i) q^{68} +(14.0000 - 14.0000i) q^{69} +(-11.2250 + 11.2250i) q^{70} -3.74166 q^{71} +(-8.00000 + 8.00000i) q^{72} +(4.00000 + 4.00000i) q^{73} +(-7.48331 - 7.48331i) q^{75} +(7.48331 - 7.48331i) q^{76} +(-7.00000 + 7.00000i) q^{77} +3.74166i q^{78} +(-5.61249 - 5.61249i) q^{79} -12.0000i q^{80} +5.00000 q^{81} -2.00000 q^{82} -7.48331i q^{83} +(-14.0000 - 14.0000i) q^{84} +(-6.00000 - 6.00000i) q^{85} -3.74166 q^{86} +(13.0958 + 5.61249i) q^{87} -7.48331i q^{88} +(-3.00000 + 3.00000i) q^{89} +(12.0000 - 12.0000i) q^{90} -3.74166 q^{91} -14.9666 q^{92} -7.00000i q^{93} -11.2250i q^{94} +(-11.2250 + 11.2250i) q^{95} +14.9666 q^{96} +(-5.00000 - 5.00000i) q^{97} +(7.00000 - 7.00000i) q^{98} +(7.48331 - 7.48331i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 8 q^{8}+O(q^{10}) \) 4 * q - 4 * q^2 + 8 * q^8	\( 4 q - 4 q^{2} + 8 q^{8} - 12 q^{10} - 16 q^{16} - 8 q^{17} - 16 q^{18} + 24 q^{20} + 28 q^{21} - 16 q^{25} + 4 q^{26} + 20 q^{29} + 16 q^{32} + 32 q^{36} - 24 q^{40} + 4 q^{41} - 48 q^{45} - 28 q^{49} + 16 q^{50} - 8 q^{52} - 44 q^{53} - 12 q^{58} + 24 q^{61} + 12 q^{65} + 28 q^{66} + 16 q^{68} + 56 q^{69} - 32 q^{72} + 16 q^{73} - 28 q^{77} + 20 q^{81} - 8 q^{82} - 56 q^{84} - 24 q^{85} - 12 q^{89} + 48 q^{90} - 20 q^{97} + 28 q^{98}+O(q^{100}) \) 4 * q - 4 * q^2 + 8 * q^8 - 12 * q^10 - 16 * q^16 - 8 * q^17 - 16 * q^18 + 24 * q^20 + 28 * q^21 - 16 * q^25 + 4 * q^26 + 20 * q^29 + 16 * q^32 + 32 * q^36 - 24 * q^40 + 4 * q^41 - 48 * q^45 - 28 * q^49 + 16 * q^50 - 8 * q^52 - 44 * q^53 - 12 * q^58 + 24 * q^61 + 12 * q^65 + 28 * q^66 + 16 * q^68 + 56 * q^69 - 32 * q^72 + 16 * q^73 - 28 * q^77 + 20 * q^81 - 8 * q^82 - 56 * q^84 - 24 * q^85 - 12 * q^89 + 48 * q^90 - 20 * q^97 + 28 * q^98

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