LMFDB - Embedded newform 552.2.f.c.277.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(277,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))

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

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

chi := DirichletCharacter("552.277");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.f (of order $2$, degree $1$, 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:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 4 x^{16} - 2 x^{15} + 5 x^{14} + 2 x^{13} + 6 x^{12} + 24 x^{11} - 12 x^{10} - 88 x^{9} + \cdots + 512 $ x^18 - 4x^16 - 2x^15 + 5x^14 + 2x^13 + 6x^12 + 24x^11 - 12x^10 - 88x^9 - 24x^8 + 96x^7 + 48x^6 + 32x^5 + 160x^4 - 128x^3 - 512*x^2 + 512
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			277.4
Root			$-0.809892 - 1.15934i$ of defining polynomial
Character	$\chi$	$=$	552.277
Dual form			552.2.f.c.277.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.15934 + 0.809892i) q^{2} -1.00000i q^{3} +(0.688150 - 1.87788i) q^{4} -3.56420i q^{5} +(0.809892 + 1.15934i) q^{6} -2.96155 q^{7} +(0.723081 + 2.73444i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(-1.15934 + 0.809892i) q^{2} -1.00000i q^{3} +(0.688150 - 1.87788i) q^{4} -3.56420i q^{5} +(0.809892 + 1.15934i) q^{6} -2.96155 q^{7} +(0.723081 + 2.73444i) q^{8} -1.00000 q^{9} +(2.88661 + 4.13212i) q^{10} -2.43741i q^{11} +(-1.87788 - 0.688150i) q^{12} -2.03973i q^{13} +(3.43345 - 2.39853i) q^{14} -3.56420 q^{15} +(-3.05290 - 2.58453i) q^{16} +2.92323 q^{17} +(1.15934 - 0.809892i) q^{18} +5.23284i q^{19} +(-6.69315 - 2.45270i) q^{20} +2.96155i q^{21} +(1.97404 + 2.82579i) q^{22} -1.00000 q^{23} +(2.73444 - 0.723081i) q^{24} -7.70349 q^{25} +(1.65196 + 2.36475i) q^{26} +1.00000i q^{27} +(-2.03799 + 5.56144i) q^{28} -0.531515i q^{29} +(4.13212 - 2.88661i) q^{30} -10.1583 q^{31} +(5.63255 + 0.523843i) q^{32} -2.43741 q^{33} +(-3.38903 + 2.36750i) q^{34} +10.5555i q^{35} +(-0.688150 + 1.87788i) q^{36} +9.71912i q^{37} +(-4.23803 - 6.06665i) q^{38} -2.03973 q^{39} +(9.74607 - 2.57720i) q^{40} -3.68527 q^{41} +(-2.39853 - 3.43345i) q^{42} +1.24541i q^{43} +(-4.57717 - 1.67730i) q^{44} +3.56420i q^{45} +(1.15934 - 0.809892i) q^{46} +4.08428 q^{47} +(-2.58453 + 3.05290i) q^{48} +1.77077 q^{49} +(8.93099 - 6.23900i) q^{50} -2.92323i q^{51} +(-3.83038 - 1.40364i) q^{52} -13.3601i q^{53} +(-0.809892 - 1.15934i) q^{54} -8.68739 q^{55} +(-2.14144 - 8.09817i) q^{56} +5.23284 q^{57} +(0.430470 + 0.616208i) q^{58} -9.85521i q^{59} +(-2.45270 + 6.69315i) q^{60} -14.6238i q^{61} +(11.7769 - 8.22711i) q^{62} +2.96155 q^{63} +(-6.95431 + 3.95444i) q^{64} -7.27000 q^{65} +(2.82579 - 1.97404i) q^{66} +3.93132i q^{67} +(2.01162 - 5.48949i) q^{68} +1.00000i q^{69} +(-8.54884 - 12.2375i) q^{70} +5.93337 q^{71} +(-0.723081 - 2.73444i) q^{72} +3.85533 q^{73} +(-7.87143 - 11.2678i) q^{74} +7.70349i q^{75} +(9.82667 + 3.60098i) q^{76} +7.21849i q^{77} +(2.36475 - 1.65196i) q^{78} -7.13941 q^{79} +(-9.21178 + 10.8811i) q^{80} +1.00000 q^{81} +(4.27249 - 2.98467i) q^{82} +13.1885i q^{83} +(5.56144 + 2.03799i) q^{84} -10.4190i q^{85} +(-1.00865 - 1.44385i) q^{86} -0.531515 q^{87} +(6.66494 - 1.76244i) q^{88} -10.0810 q^{89} +(-2.88661 - 4.13212i) q^{90} +6.04076i q^{91} +(-0.688150 + 1.87788i) q^{92} +10.1583i q^{93} +(-4.73508 + 3.30783i) q^{94} +18.6509 q^{95} +(0.523843 - 5.63255i) q^{96} +9.43058 q^{97} +(-2.05292 + 1.43413i) q^{98} +2.43741i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 8 q^{4} + 8 q^{7} - 6 q^{8} - 18 q^{9}+O(q^{10}) $ 18 * q - 8 * q^4 + 8 * q^7 - 6 * q^8 - 18 * q^9	$ 18 q - 8 q^{4} + 8 q^{7} - 6 q^{8} - 18 q^{9} + 12 q^{10} - 4 q^{12} - 14 q^{14} + 8 q^{15} + 12 q^{16} - 8 q^{17} - 16 q^{20} - 30 q^{22} - 18 q^{23} + 6 q^{24} - 22 q^{25} + 8 q^{26} - 2 q^{28} + 4 q^{30} - 44 q^{31} + 10 q^{32} - 24 q^{33} + 18 q^{34} + 8 q^{36} - 20 q^{38} - 8 q^{39} + 40 q^{40} + 28 q^{41} + 6 q^{42} - 26 q^{44} + 42 q^{49} + 60 q^{50} - 36 q^{52} + 40 q^{55} - 2 q^{56} + 12 q^{57} + 52 q^{58} + 16 q^{60} + 24 q^{62} - 8 q^{63} + 16 q^{64} - 104 q^{65} + 2 q^{66} + 54 q^{68} - 48 q^{70} - 24 q^{71} + 6 q^{72} + 12 q^{73} - 22 q^{74} - 4 q^{78} + 8 q^{79} - 32 q^{80} + 18 q^{81} - 20 q^{82} + 34 q^{84} + 12 q^{87} + 10 q^{88} + 24 q^{89} - 12 q^{90} + 8 q^{92} - 56 q^{94} - 16 q^{95} - 30 q^{96} + 12 q^{97} - 48 q^{98}+O(q^{100}) $ 18 * q - 8 * q^4 + 8 * q^7 - 6 * q^8 - 18 * q^9 + 12 * q^10 - 4 * q^12 - 14 * q^14 + 8 * q^15 + 12 * q^16 - 8 * q^17 - 16 * q^20 - 30 * q^22 - 18 * q^23 + 6 * q^24 - 22 * q^25 + 8 * q^26 - 2 * q^28 + 4 * q^30 - 44 * q^31 + 10 * q^32 - 24 * q^33 + 18 * q^34 + 8 * q^36 - 20 * q^38 - 8 * q^39 + 40 * q^40 + 28 * q^41 + 6 * q^42 - 26 * q^44 + 42 * q^49 + 60 * q^50 - 36 * q^52 + 40 * q^55 - 2 * q^56 + 12 * q^57 + 52 * q^58 + 16 * q^60 + 24 * q^62 - 8 * q^63 + 16 * q^64 - 104 * q^65 + 2 * q^66 + 54 * q^68 - 48 * q^70 - 24 * q^71 + 6 * q^72 + 12 * q^73 - 22 * q^74 - 4 * q^78 + 8 * q^79 - 32 * q^80 + 18 * q^81 - 20 * q^82 + 34 * q^84 + 12 * q^87 + 10 * q^88 + 24 * q^89 - 12 * q^90 + 8 * q^92 - 56 * q^94 - 16 * q^95 - 30 * q^96 + 12 * q^97 - 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$1$	$1$	$-1$	$1$

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 $

$2$	−1.15934	+	0.809892i	−0.819779	+	0.572680i
$2$	−1.15934	+	0.809892i	−0.819779	+	0.572680i
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	0.688150	−	1.87788i	0.344075	−	0.938942i
$5$		−	3.56420i		−	1.59396i	−0.604008	−	0.796978i	$-0.706430\pi$
$5$		−	3.56420i		−	1.59396i	0.604008	−	0.796978i	$-0.293570\pi$
$6$	0.809892	+	1.15934i	0.330637	+	0.473300i
$7$	−2.96155			−1.11936			−0.559680	−	0.828709i	$-0.689076\pi$
$7$	−2.96155			−1.11936			−0.559680	+	0.828709i	$0.689076\pi$
$8$	0.723081	+	2.73444i	0.255648	+	0.966770i
$9$	−1.00000			−0.333333
$10$	2.88661	+	4.13212i	0.912827	+	1.30669i
$11$		−	2.43741i		−	0.734906i	−0.930042	−	0.367453i	$-0.880230\pi$
$11$		−	2.43741i		−	0.734906i	0.930042	−	0.367453i	$-0.119770\pi$
$12$	−1.87788	−	0.688150i	−0.542098	−	0.198652i
$13$		−	2.03973i		−	0.565720i	−0.959161	−	0.282860i	$-0.908717\pi$
$13$		−	2.03973i		−	0.565720i	0.959161	−	0.282860i	$-0.0912831\pi$
$14$	3.43345	−	2.39853i	0.917628	−	0.641035i
$15$	−3.56420			−0.920271
$16$	−3.05290	−	2.58453i	−0.763225	−	0.646133i
$17$	2.92323			0.708988			0.354494	−	0.935058i	$-0.384653\pi$
$17$	2.92323			0.708988			0.354494	+	0.935058i	$0.384653\pi$
$18$	1.15934	−	0.809892i	0.273260	−	0.190893i
$19$			5.23284i			1.20050i	0.799814	+	0.600248i	$0.204931\pi$
$19$			5.23284i			1.20050i	−0.799814	+	0.600248i	$0.795069\pi$
$20$	−6.69315	−	2.45270i	−1.49663	−	0.548441i
$21$			2.96155i			0.646263i
$22$	1.97404	+	2.82579i	0.420866	+	0.602460i
$23$	−1.00000			−0.208514
$23$	−1.00000			−0.208514
$24$	2.73444	−	0.723081i	0.558165	−	0.147598i
$25$	−7.70349			−1.54070
$26$	1.65196	+	2.36475i	0.323976	+	0.463765i
$27$			1.00000i			0.192450i
$28$	−2.03799	+	5.56144i	−0.385144	+	1.05101i
$29$		−	0.531515i		−	0.0986999i	−0.998782	−	0.0493500i	$-0.984285\pi$
$29$		−	0.531515i		−	0.0986999i	0.998782	−	0.0493500i	$-0.0157150\pi$
$30$	4.13212	−	2.88661i	0.754419	−	0.527021i
$31$	−10.1583			−1.82448			−0.912241	−	0.409654i	$-0.865649\pi$
$31$	−10.1583			−1.82448			−0.912241	+	0.409654i	$0.865649\pi$
$32$	5.63255	+	0.523843i	0.995703	+	0.0926032i
$33$	−2.43741			−0.424298
$34$	−3.38903	+	2.36750i	−0.581214	+	0.406023i
$35$			10.5555i			1.78421i
$36$	−0.688150	+	1.87788i	−0.114692	+	0.312981i
$37$			9.71912i			1.59781i	0.601455	+	0.798907i	$0.294588\pi$
$37$			9.71912i			1.59781i	−0.601455	+	0.798907i	$0.705412\pi$
$38$	−4.23803	−	6.06665i	−0.687500	−	0.984141i
$39$	−2.03973			−0.326618
$40$	9.74607	−	2.57720i	1.54099	−	0.407491i
$41$	−3.68527			−0.575542			−0.287771	−	0.957699i	$-0.592914\pi$
$41$	−3.68527			−0.575542			−0.287771	+	0.957699i	$0.592914\pi$
$42$	−2.39853	−	3.43345i	−0.370102	−	0.529793i
$43$			1.24541i			0.189923i	0.995481	+	0.0949615i	$0.0302728\pi$
$43$			1.24541i			0.189923i	−0.995481	+	0.0949615i	$0.969727\pi$
$44$	−4.57717	−	1.67730i	−0.690034	−	0.252863i
$45$			3.56420i			0.531319i
$46$	1.15934	−	0.809892i	0.170936	−	0.119412i
$47$	4.08428			0.595754			0.297877	−	0.954604i	$-0.403722\pi$
$47$	4.08428			0.595754			0.297877	+	0.954604i	$0.403722\pi$
$48$	−2.58453	+	3.05290i	−0.373045	+	0.440648i
$49$	1.77077			0.252966
$50$	8.93099	−	6.23900i	1.26303	−	0.882327i
$51$		−	2.92323i		−	0.409335i
$52$	−3.83038	−	1.40364i	−0.531178	−	0.194650i
$53$		−	13.3601i		−	1.83516i	−0.397556	−	0.917578i	$-0.630141\pi$
$53$		−	13.3601i		−	1.83516i	0.397556	−	0.917578i	$-0.369859\pi$
$54$	−0.809892	−	1.15934i	−0.110212	−	0.157767i
$55$	−8.68739			−1.17141
$56$	−2.14144	−	8.09817i	−0.286162	−	1.08216i
$57$	5.23284			0.693107
$58$	0.430470	+	0.616208i	0.0565235	+	0.0809121i
$59$		−	9.85521i		−	1.28304i	−0.767107	−	0.641520i	$-0.778304\pi$
$59$		−	9.85521i		−	1.28304i	0.767107	−	0.641520i	$-0.221696\pi$
$60$	−2.45270	+	6.69315i	−0.316643	+	0.864082i
$61$		−	14.6238i		−	1.87238i	−0.351494	−	0.936190i	$-0.614326\pi$
$61$		−	14.6238i		−	1.87238i	0.351494	−	0.936190i	$-0.385674\pi$
$62$	11.7769	−	8.22711i	1.49567	−	1.04484i
$63$	2.96155			0.373120
$64$	−6.95431	+	3.95444i	−0.869288	+	0.494305i
$65$	−7.27000			−0.901733
$66$	2.82579	−	1.97404i	0.347831	−	0.242987i
$67$			3.93132i			0.480287i	0.970737	+	0.240144i	$0.0771945\pi$
$67$			3.93132i			0.480287i	−0.970737	+	0.240144i	$0.922805\pi$
$68$	2.01162	−	5.48949i	0.243945	−	0.665699i
$69$			1.00000i			0.120386i
$70$	−8.54884	−	12.2375i	−1.02178	−	1.46266i
$71$	5.93337			0.704162			0.352081	−	0.935970i	$-0.385474\pi$
$71$	5.93337			0.704162			0.352081	+	0.935970i	$0.385474\pi$
$72$	−0.723081	−	2.73444i	−0.0852159	−	0.322257i
$73$	3.85533			0.451232			0.225616	−	0.974216i	$-0.427561\pi$
$73$	3.85533			0.451232			0.225616	+	0.974216i	$0.427561\pi$
$74$	−7.87143	−	11.2678i	−0.915036	−	1.30985i
$75$			7.70349i			0.889523i
$76$	9.82667	+	3.60098i	1.12720	+	0.413061i
$77$			7.21849i			0.822624i
$78$	2.36475	−	1.65196i	0.267755	−	0.187048i
$79$	−7.13941			−0.803247			−0.401623	−	0.915805i	$-0.631554\pi$
$79$	−7.13941			−0.803247			−0.401623	+	0.915805i	$0.631554\pi$
$80$	−9.21178	+	10.8811i	−1.02991	+	1.21655i
$81$	1.00000			0.111111
$82$	4.27249	−	2.98467i	0.471817	−	0.329602i
$83$			13.1885i			1.44763i	0.689996	+	0.723814i	$0.257612\pi$
$83$			13.1885i			1.44763i	−0.689996	+	0.723814i	$0.742388\pi$
$84$	5.56144	+	2.03799i	0.606803	+	0.222363i
$85$		−	10.4190i		−	1.13010i
$86$	−1.00865	−	1.44385i	−0.108765	−	0.155695i
$87$	−0.531515			−0.0569844
$88$	6.66494	−	1.76244i	0.710485	−	0.187877i
$89$	−10.0810			−1.06858			−0.534289	−	0.845302i	$-0.679421\pi$
$89$	−10.0810			−1.06858			−0.534289	+	0.845302i	$0.679421\pi$
$90$	−2.88661	−	4.13212i	−0.304276	−	0.435564i
$91$			6.04076i			0.633244i
$92$	−0.688150	+	1.87788i	−0.0717446	+	0.195783i
$93$			10.1583i			1.05336i
$94$	−4.73508	+	3.30783i	−0.488386	+	0.341176i
$95$	18.6509			1.91354
$96$	0.523843	−	5.63255i	0.0534645	−	0.574869i
$97$	9.43058			0.957530			0.478765	−	0.877943i	$-0.341085\pi$
$97$	9.43058			0.957530			0.478765	+	0.877943i	$0.341085\pi$
$98$	−2.05292	+	1.43413i	−0.207377	+	0.144869i
$99$			2.43741i			0.244969i
$100$	−5.30116	+	14.4663i	−0.530116	+	1.44663i
$101$		−	6.57301i		−	0.654039i	−0.945018	−	0.327020i	$-0.893956\pi$
$101$		−	6.57301i		−	0.654039i	0.945018	−	0.327020i	$-0.106044\pi$
$102$	2.36750	+	3.38903i	0.234418	+	0.335564i
$103$	−13.5855			−1.33862			−0.669309	−	0.742984i	$-0.733410\pi$
$103$	−13.5855			−1.33862			−0.669309	+	0.742984i	$0.733410\pi$
$104$	5.57752	−	1.47489i	0.546921	−	0.144625i
$105$	10.5555			1.03011
$106$	10.8203	+	15.4890i	1.05096	+	1.50442i
$107$		−	1.13589i		−	0.109810i	−0.998492	−	0.0549052i	$-0.982514\pi$
$107$		−	1.13589i		−	0.109810i	0.998492	−	0.0549052i	$-0.0174857\pi$
$108$	1.87788	+	0.688150i	0.180699	+	0.0662173i
$109$		−	11.9557i		−	1.14515i	−0.819853	−	0.572575i	$-0.805945\pi$
$109$		−	11.9557i		−	1.14515i	0.819853	−	0.572575i	$-0.194055\pi$
$110$	10.0717	−	7.03585i	0.960296	−	0.670842i
$111$	9.71912			0.922498
$112$	9.04130	+	7.65422i	0.854323	+	0.723256i
$113$	−7.70072			−0.724423			−0.362211	−	0.932096i	$-0.617978\pi$
$113$	−7.70072			−0.724423			−0.362211	+	0.932096i	$0.617978\pi$
$114$	−6.06665	+	4.23803i	−0.568194	+	0.396928i
$115$			3.56420i			0.332363i
$116$	−0.998124	−	0.365762i	−0.0926735	−	0.0339602i
$117$			2.03973i			0.188573i
$118$	7.98166	+	11.4256i	0.734771	+	1.05181i
$119$	−8.65729			−0.793613
$120$	−2.57720	−	9.74607i	−0.235265	−	0.889691i
$121$	5.05905			0.459914
$122$	11.8437	+	16.9539i	1.07227	+	1.53494i
$123$			3.68527i			0.332289i
$124$	−6.99043	+	19.0761i	−0.627759	+	1.71308i
$125$			9.63578i			0.861851i
$126$	−3.43345	+	2.39853i	−0.305876	+	0.213678i
$127$	16.3759			1.45313			0.726565	−	0.687098i	$-0.241116\pi$
$127$	16.3759			1.45313			0.726565	+	0.687098i	$0.241116\pi$
$128$	4.85976	−	10.2168i	0.429546	−	0.903045i
$129$	1.24541			0.109652
$130$	8.42842	−	5.88792i	0.739222	−	0.516404i
$131$		−	1.85086i		−	0.161710i	−0.996726	−	0.0808552i	$-0.974235\pi$
$131$		−	1.85086i		−	0.161710i	0.996726	−	0.0808552i	$-0.0257651\pi$
$132$	−1.67730	+	4.57717i	−0.145990	+	0.398391i
$133$		−	15.4973i		−	1.34379i
$134$	−3.18394	−	4.55775i	−0.275051	−	0.393729i
$135$	3.56420			0.306757
$136$	2.11373	+	7.99340i	0.181251	+	0.685429i
$137$	6.57501			0.561741			0.280870	−	0.959746i	$-0.409377\pi$
$137$	6.57501			0.561741			0.280870	+	0.959746i	$0.409377\pi$
$138$	−0.809892	−	1.15934i	−0.0689426	−	0.0986898i
$139$		−	19.0188i		−	1.61315i	−0.591129	−	0.806577i	$-0.701318\pi$
$139$		−	19.0188i		−	1.61315i	0.591129	−	0.806577i	$-0.298682\pi$
$140$	19.8221	+	7.26380i	1.67527	+	0.613903i
$141$		−	4.08428i		−	0.343959i
$142$	−6.87881	+	4.80539i	−0.577257	+	0.403259i
$143$	−4.97165			−0.415751
$144$	3.05290	+	2.58453i	0.254408	+	0.215378i
$145$	−1.89442			−0.157323
$146$	−4.46965	+	3.12240i	−0.369911	+	0.258412i
$147$		−	1.77077i		−	0.146050i
$148$	18.2514	+	6.68822i	1.50025	+	0.549768i
$149$			3.73487i			0.305972i	0.988228	+	0.152986i	$0.0488890\pi$
$149$			3.73487i			0.305972i	−0.988228	+	0.152986i	$0.951111\pi$
$150$	−6.23900	−	8.93099i	−0.509412	−	0.729212i
$151$	8.40368			0.683882			0.341941	−	0.939721i	$-0.388916\pi$
$151$	8.40368			0.683882			0.341941	+	0.939721i	$0.388916\pi$
$152$	−14.3089	+	3.78377i	−1.16060	+	0.306904i
$153$	−2.92323			−0.236329
$154$	−5.84620	−	8.36871i	−0.471100	−	0.674370i
$155$			36.2061i			2.90815i
$156$	−1.40364	+	3.83038i	−0.112381	+	0.306676i
$157$			13.0342i			1.04024i	0.854092	+	0.520121i	$0.174113\pi$
$157$			13.0342i			1.04024i	−0.854092	+	0.520121i	$0.825887\pi$
$158$	8.27702	−	5.78215i	0.658485	−	0.460003i
$159$	−13.3601			−1.05953
$160$	1.86708	−	20.0755i	0.147605	−	1.58711i
$161$	2.96155			0.233403
$162$	−1.15934	+	0.809892i	−0.0910866	+	0.0636311i
$163$		−	7.76344i		−	0.608080i	−0.952659	−	0.304040i	$-0.901664\pi$
$163$		−	7.76344i		−	0.608080i	0.952659	−	0.304040i	$-0.0983356\pi$
$164$	−2.53602	+	6.92051i	−0.198030	+	0.540401i
$165$			8.68739i			0.676313i
$166$	−10.6813	−	15.2900i	−0.829027	−	1.18673i
$167$	−12.8380			−0.993436			−0.496718	−	0.867912i	$-0.665462\pi$
$167$	−12.8380			−0.993436			−0.496718	+	0.867912i	$0.665462\pi$
$168$	−8.09817	+	2.14144i	−0.624787	+	0.165216i
$169$	8.83950			0.679961
$170$	8.43824	+	12.0792i	0.647184	+	0.926430i
$171$		−	5.23284i		−	0.400165i
$172$	2.33873	+	0.857028i	0.178327	+	0.0653478i
$173$		−	4.97498i		−	0.378241i	−0.981954	−	0.189120i	$-0.939436\pi$
$173$		−	4.97498i		−	0.378241i	0.981954	−	0.189120i	$-0.0605636\pi$
$174$	0.616208	−	0.430470i	0.0467146	−	0.0326338i
$175$	22.8143			1.72460
$176$	−6.29956	+	7.44115i	−0.474847	+	0.560898i
$177$	−9.85521			−0.740763
$178$	11.6873	−	8.16448i	0.875999	−	0.611954i
$179$		−	4.94416i		−	0.369544i	−0.982781	−	0.184772i	$-0.940845\pi$
$179$		−	4.94416i		−	0.369544i	0.982781	−	0.184772i	$-0.0591546\pi$
$180$	6.69315	+	2.45270i	0.498878	+	0.182814i
$181$		−	11.9833i		−	0.890708i	−0.895354	−	0.445354i	$-0.853078\pi$
$181$		−	11.9833i		−	0.890708i	0.895354	−	0.445354i	$-0.146922\pi$
$182$	−4.89236	−	7.00331i	−0.362646	−	0.519120i
$183$	−14.6238			−1.08102
$184$	−0.723081	−	2.73444i	−0.0533062	−	0.201585i
$185$	34.6408			2.54685
$186$	−8.22711	−	11.7769i	−0.603241	−	0.863526i
$187$		−	7.12511i		−	0.521039i
$188$	2.81060	−	7.66981i	0.204984	−	0.559378i
$189$		−	2.96155i		−	0.215421i
$190$	−21.6227	+	15.1052i	−1.56868	+	1.09585i
$191$	−14.8486			−1.07441			−0.537204	−	0.843452i	$-0.680520\pi$
$191$	−14.8486			−1.07441			−0.537204	+	0.843452i	$0.680520\pi$
$192$	3.95444	+	6.95431i	0.285387	+	0.501884i
$193$	20.6018			1.48295			0.741476	−	0.670979i	$-0.234126\pi$
$193$	20.6018			1.48295			0.741476	+	0.670979i	$0.234126\pi$
$194$	−10.9333	+	7.63775i	−0.784963	+	0.548358i
$195$			7.27000i			0.520616i
$196$	1.21855	−	3.32529i	0.0870395	−	0.237521i
$197$		−	13.4979i		−	0.961685i	−0.876807	−	0.480842i	$-0.840331\pi$
$197$		−	13.4979i		−	0.961685i	0.876807	−	0.480842i	$-0.159669\pi$
$198$	−1.97404	−	2.82579i	−0.140289	−	0.200820i
$199$	−25.7498			−1.82536			−0.912678	−	0.408679i	$-0.865990\pi$
$199$	−25.7498			−1.82536			−0.912678	+	0.408679i	$0.865990\pi$
$200$	−5.57025	−	21.0647i	−0.393876	−	1.48950i
$201$	3.93132			0.277294
$202$	5.32343	+	7.62037i	0.374555	+	0.536168i
$203$			1.57411i			0.110481i
$204$	−5.48949	−	2.01162i	−0.384341	−	0.140842i
$205$			13.1350i			0.917389i
$206$	15.7502	−	11.0028i	1.09737	−	0.766600i
$207$	1.00000			0.0695048
$208$	−5.27175	+	6.22709i	−0.365530	+	0.431771i
$209$	12.7546			0.882251
$210$	−12.2375	+	8.54884i	−0.844467	+	0.589926i
$211$			13.0782i			0.900344i	0.892942	+	0.450172i	$0.148637\pi$
$211$			13.0782i			0.900344i	−0.892942	+	0.450172i	$0.851363\pi$
$212$	−25.0888	−	9.19378i	−1.72311	−	0.631432i
$213$		−	5.93337i		−	0.406548i
$214$	0.919946	+	1.31688i	0.0628862	+	0.0900202i
$215$	4.43888			0.302729
$216$	−2.73444	+	0.723081i	−0.186055	+	0.0491994i
$217$	30.0842			2.04225
$218$	9.68283	+	13.8608i	0.655804	+	0.938769i
$219$		−	3.85533i		−	0.260519i
$220$	−5.97823	+	16.3139i	−0.403052	+	1.09988i
$221$		−	5.96261i		−	0.401089i
$222$	−11.2678	+	7.87143i	−0.756244	+	0.528296i
$223$	−1.68883			−0.113092			−0.0565462	−	0.998400i	$-0.518009\pi$
$223$	−1.68883			−0.113092			−0.0565462	+	0.998400i	$0.518009\pi$
$224$	−16.6811	−	1.55138i	−1.11455	−	0.103656i
$225$	7.70349			0.513566
$226$	8.92777	−	6.23675i	0.593866	−	0.414862i
$227$		−	1.74792i		−	0.116013i	−0.998316	−	0.0580066i	$-0.981526\pi$
$227$		−	1.74792i		−	0.116013i	0.998316	−	0.0580066i	$-0.0184744\pi$
$228$	3.60098	−	9.82667i	0.238481	−	0.650787i
$229$			7.42104i			0.490396i	0.969473	+	0.245198i	$0.0788530\pi$
$229$			7.42104i			0.490396i	−0.969473	+	0.245198i	$0.921147\pi$
$230$	−2.88661	−	4.13212i	−0.190338	−	0.272464i
$231$	7.21849			0.474942
$232$	1.45340	−	0.384329i	0.0954201	−	0.0252324i
$233$	−17.3726			−1.13812			−0.569058	−	0.822297i	$-0.692692\pi$
$233$	−17.3726			−1.13812			−0.569058	+	0.822297i	$0.692692\pi$
$234$	−1.65196	−	2.36475i	−0.107992	−	0.154588i
$235$		−	14.5572i		−	0.949606i
$236$	−18.5069	−	6.78187i	−1.20470	−	0.441462i
$237$			7.13941i			0.463755i
$238$	10.0368	−	7.01147i	0.650587	−	0.454486i
$239$	20.2068			1.30707			0.653536	−	0.756895i	$-0.273285\pi$
$239$	20.2068			1.30707			0.653536	+	0.756895i	$0.273285\pi$
$240$	10.8811	+	9.21178i	0.702374	+	0.594618i
$241$	−15.9279			−1.02601			−0.513004	−	0.858386i	$-0.671467\pi$
$241$	−15.9279			−1.02601			−0.513004	+	0.858386i	$0.671467\pi$
$242$	−5.86517	+	4.09728i	−0.377028	+	0.263383i
$243$		−	1.00000i		−	0.0641500i
$244$	−27.4617	−	10.0633i	−1.75806	−	0.644240i
$245$		−	6.31135i		−	0.403218i
$246$	−2.98467	−	4.27249i	−0.190296	−	0.272404i
$247$	10.6736			0.679144
$248$	−7.34526	−	27.7772i	−0.466425	−	1.76385i
$249$	13.1885			0.835788
$250$	−7.80394	−	11.1712i	−0.493565	−	0.706527i
$251$		−	28.4237i		−	1.79409i	−0.441938	−	0.897045i	$-0.645709\pi$
$251$		−	28.4237i		−	1.79409i	0.441938	−	0.897045i	$-0.354291\pi$
$252$	2.03799	−	5.56144i	0.128381	−	0.350338i
$253$			2.43741i			0.153238i
$254$	−18.9853	+	13.2627i	−1.19125	+	0.832179i
$255$	−10.4190			−0.652462
$256$	2.64037	+	15.7806i	0.165023	+	0.986290i
$257$	−4.70258			−0.293339			−0.146669	−	0.989186i	$-0.546855\pi$
$257$	−4.70258			−0.293339			−0.146669	+	0.989186i	$0.546855\pi$
$258$	−1.44385	+	1.00865i	−0.0898905	+	0.0627955i
$259$		−	28.7836i		−	1.78853i
$260$	−5.00286	+	13.6522i	−0.310264	+	0.846675i
$261$			0.531515i			0.0329000i
$262$	1.49900	+	2.14578i	0.0926083	+	0.132567i
$263$	−7.97324			−0.491651			−0.245826	−	0.969314i	$-0.579059\pi$
$263$	−7.97324			−0.491651			−0.245826	+	0.969314i	$0.579059\pi$
$264$	−1.76244	−	6.66494i	−0.108471	−	0.410199i
$265$	−47.6182			−2.92516
$266$	12.5511	+	17.9667i	0.769560	+	1.10161i
$267$			10.0810i			0.616944i
$268$	7.38257	+	2.70534i	0.450962	+	0.165255i
$269$			28.7702i			1.75415i	0.480353	+	0.877075i	$0.340509\pi$
$269$			28.7702i			1.75415i	−0.480353	+	0.877075i	$0.659491\pi$
$270$	−4.13212	+	2.88661i	−0.251473	+	0.175674i
$271$	10.1260			0.615112			0.307556	−	0.951530i	$-0.400489\pi$
$271$	10.1260			0.615112			0.307556	+	0.951530i	$0.400489\pi$
$272$	−8.92433	−	7.55519i	−0.541117	−	0.458101i
$273$	6.04076			0.365604
$274$	−7.62268	+	5.32504i	−0.460503	+	0.321698i
$275$			18.7765i			1.13227i
$276$	1.87788	+	0.688150i	0.113035	+	0.0414218i
$277$			16.3220i			0.980697i	0.871526	+	0.490348i	$0.163130\pi$
$277$			16.3220i			0.980697i	−0.871526	+	0.490348i	$0.836870\pi$
$278$	15.4032	+	22.0493i	0.923821	+	1.32243i
$279$	10.1583			0.608161
$280$	−28.8635	+	7.63251i	−1.72492	+	0.456130i
$281$	7.73296			0.461310			0.230655	−	0.973036i	$-0.425913\pi$
$281$	7.73296			0.461310			0.230655	+	0.973036i	$0.425913\pi$
$282$	3.30783	+	4.73508i	0.196978	+	0.281970i
$283$		−	21.1687i		−	1.25835i	−0.777265	−	0.629173i	$-0.783394\pi$
$283$		−	21.1687i		−	1.25835i	0.777265	−	0.629173i	$-0.216606\pi$
$284$	4.08305	−	11.1422i	0.242285	−	0.661167i
$285$		−	18.6509i		−	1.10478i
$286$	5.76385	−	4.02650i	0.340824	−	0.238092i
$287$	10.9141			0.644239
$288$	−5.63255	−	0.523843i	−0.331901	−	0.0308677i
$289$	−8.45471			−0.497336
$290$	2.19629	−	1.53428i	0.128970	−	0.0900960i
$291$		−	9.43058i		−	0.552830i
$292$	2.65305	−	7.23986i	0.155258	−	0.423681i
$293$		−	23.2022i		−	1.35549i	−0.735299	−	0.677743i	$-0.762958\pi$
$293$		−	23.2022i		−	1.35549i	0.735299	−	0.677743i	$-0.237042\pi$
$294$	1.43413	+	2.05292i	0.0836401	+	0.119729i
$295$	−35.1259			−2.04511
$296$	−26.5763	+	7.02771i	−1.54472	+	0.408477i
$297$	2.43741			0.141433
$298$	−3.02484	−	4.32999i	−0.175224	−	0.250830i
$299$			2.03973i			0.117961i
$300$	14.4663	+	5.30116i	0.835210	+	0.306063i
$301$		−	3.68834i		−	0.212592i
$302$	−9.74274	+	6.80607i	−0.560632	+	0.391645i
$303$	−6.57301			−0.377610
$304$	13.5244	−	15.9753i	0.775680	−	0.916248i
$305$	−52.1219			−2.98449
$306$	3.38903	−	2.36750i	0.193738	−	0.135341i
$307$			1.52569i			0.0870759i	0.999052	+	0.0435380i	$0.0138629\pi$
$307$			1.52569i			0.0870759i	−0.999052	+	0.0435380i	$0.986137\pi$
$308$	13.5555	+	4.96741i	0.772396	+	0.283044i
$309$			13.5855i			0.772852i
$310$	−29.3230	−	41.9753i	−1.66544	−	2.38404i
$311$	23.8043			1.34982			0.674909	−	0.737901i	$-0.264183\pi$
$311$	23.8043			1.34982			0.674909	+	0.737901i	$0.264183\pi$
$312$	−1.47489	−	5.57752i	−0.0834993	−	0.315765i
$313$	16.6423			0.940680			0.470340	−	0.882485i	$-0.344131\pi$
$313$	16.6423			0.940680			0.470340	+	0.882485i	$0.344131\pi$
$314$	−10.5563	−	15.1111i	−0.595726	−	0.852769i
$315$		−	10.5555i		−	0.594737i
$316$	−4.91299	+	13.4070i	−0.276377	+	0.754202i
$317$		−	13.3740i		−	0.751159i	−0.926790	−	0.375579i	$-0.877444\pi$
$317$		−	13.3740i		−	0.751159i	0.926790	−	0.375579i	$-0.122556\pi$
$318$	15.4890	−	10.8203i	0.868579	−	0.606770i
$319$	−1.29552			−0.0725351
$320$	14.0944	+	24.7865i	0.787901	+	1.38561i
$321$	−1.13589			−0.0633991
$322$	−3.43345	+	2.39853i	−0.191339	+	0.133665i
$323$			15.2968i			0.851137i
$324$	0.688150	−	1.87788i	0.0382306	−	0.104327i
$325$			15.7131i			0.871604i
$326$	6.28755	+	9.00049i	0.348235	+	0.498491i
$327$	−11.9557			−0.661152
$328$	−2.66475	−	10.0771i	−0.147136	−	0.556417i
$329$	−12.0958			−0.666863
$330$	−7.03585	−	10.0717i	−0.387311	−	0.554427i
$331$		−	26.6601i		−	1.46537i	−0.680568	−	0.732685i	$-0.738267\pi$
$331$		−	26.6601i		−	1.46537i	0.680568	−	0.732685i	$-0.261733\pi$
$332$	24.7665	+	9.07568i	1.35924	+	0.498093i
$333$		−	9.71912i		−	0.532604i
$334$	14.8837	−	10.3974i	0.814398	−	0.568921i
$335$	14.0120			0.765557
$336$	7.65422	−	9.04130i	0.417572	−	0.493244i
$337$	−35.8549			−1.95314			−0.976571	−	0.215193i	$-0.930962\pi$
$337$	−35.8549			−1.95314			−0.976571	+	0.215193i	$0.930962\pi$
$338$	−10.2480	+	7.15904i	−0.557418	+	0.389400i
$339$			7.70072i			0.418246i
$340$	−19.5656	−	7.16982i	−1.06110	−	0.388838i
$341$			24.7599i			1.34082i
$342$	4.23803	+	6.06665i	0.229167	+	0.328047i
$343$	15.4866			0.836199
$344$	−3.40549	+	0.900531i	−0.183612	+	0.0485534i
$345$	3.56420			0.191890
$346$	4.02920	+	5.76771i	0.216611	+	0.310074i
$347$		−	17.1967i		−	0.923167i	−0.887097	−	0.461583i	$-0.847282\pi$
$347$		−	17.1967i		−	0.923167i	0.887097	−	0.461583i	$-0.152718\pi$
$348$	−0.365762	+	0.998124i	−0.0196069	+	0.0535051i
$349$		−	22.2110i		−	1.18893i	−0.804123	−	0.594463i	$-0.797365\pi$
$349$		−	22.2110i		−	1.18893i	0.804123	−	0.594463i	$-0.202635\pi$
$350$	−26.4495	+	18.4771i	−1.41379	+	0.987642i
$351$	2.03973			0.108873
$352$	1.27682	−	13.7288i	0.0680546	−	0.731748i
$353$	31.0510			1.65268			0.826340	−	0.563171i	$-0.190419\pi$
$353$	31.0510			1.65268			0.826340	+	0.563171i	$0.190419\pi$
$354$	11.4256	−	7.98166i	0.607262	−	0.424220i
$355$		−	21.1477i		−	1.12240i
$356$	−6.93721	+	18.9309i	−0.367671	+	1.00333i
$357$			8.65729i			0.458193i
$358$	4.00423	+	5.73197i	0.211630	+	0.302944i
$359$	26.4638			1.39671			0.698354	−	0.715752i	$-0.253916\pi$
$359$	26.4638			1.39671			0.698354	+	0.715752i	$0.253916\pi$
$360$	−9.74607	+	2.57720i	−0.513663	+	0.135830i
$361$	−8.38261			−0.441190
$362$	9.70514	+	13.8927i	0.510091	+	0.730184i
$363$		−	5.05905i		−	0.265531i
$364$	11.3439	+	4.15695i	0.594579	+	0.217884i
$365$		−	13.7411i		−	0.719245i
$366$	16.9539	−	11.8437i	0.886197	−	0.619078i
$367$	6.43248			0.335773			0.167886	−	0.985806i	$-0.446306\pi$
$367$	6.43248			0.335773			0.167886	+	0.985806i	$0.446306\pi$
$368$	3.05290	+	2.58453i	0.159143	+	0.134728i
$369$	3.68527			0.191847
$370$	−40.1606	+	28.0553i	−2.08785	+	1.45853i
$371$			39.5667i			2.05420i
$372$	19.0761	+	6.99043i	0.989049	+	0.362437i
$373$			16.6015i			0.859595i	0.902925	+	0.429798i	$0.141415\pi$
$373$			16.6015i			0.859595i	−0.902925	+	0.429798i	$0.858585\pi$
$374$	5.77057	+	8.26044i	0.298389	+	0.427137i
$375$	9.63578			0.497590
$376$	2.95327	+	11.1682i	0.152303	+	0.575957i
$377$	−1.08415			−0.0558365
$378$	2.39853	+	3.43345i	0.123367	+	0.176598i
$379$			1.90915i			0.0980664i	0.998797	+	0.0490332i	$0.0156140\pi$
$379$			1.90915i			0.0980664i	−0.998797	+	0.0490332i	$0.984386\pi$
$380$	12.8346	−	35.0242i	0.658401	−	1.79670i
$381$		−	16.3759i		−	0.838965i
$382$	17.2146	−	12.0258i	0.880777	−	0.615292i
$383$	−4.23311			−0.216302			−0.108151	−	0.994134i	$-0.534493\pi$
$383$	−4.23311			−0.216302			−0.108151	+	0.994134i	$0.534493\pi$
$384$	−10.2168	−	4.85976i	−0.521373	−	0.247998i
$385$	25.7281			1.31123
$386$	−23.8846	+	16.6853i	−1.21569	+	0.849257i
$387$		−	1.24541i		−	0.0633076i
$388$	6.48965	−	17.7095i	0.329462	−	0.899065i
$389$		−	4.89165i		−	0.248017i	−0.992281	−	0.124008i	$-0.960425\pi$
$389$		−	4.89165i		−	0.248017i	0.992281	−	0.124008i	$-0.0395749\pi$
$390$	−5.88792	−	8.42842i	−0.298146	−	0.426790i
$391$	−2.92323			−0.147834
$392$	1.28041	+	4.84205i	0.0646703	+	0.244560i
$393$	−1.85086			−0.0933636
$394$	10.9318	+	15.6487i	0.550738	+	0.788369i
$395$			25.4463i			1.28034i
$396$	4.57717	+	1.67730i	0.230011	+	0.0842876i
$397$		−	8.01576i		−	0.402299i	−0.979561	−	0.201150i	$-0.935532\pi$
$397$		−	8.01576i		−	0.402299i	0.979561	−	0.201150i	$-0.0644678\pi$
$398$	29.8529	−	20.8546i	1.49639	−	1.04535i
$399$	−15.4973			−0.775836
$400$	23.5180	+	19.9099i	1.17590	+	0.995497i
$401$	−15.7797			−0.788000			−0.394000	−	0.919110i	$-0.628909\pi$
$401$	−15.7797			−0.788000			−0.394000	+	0.919110i	$0.628909\pi$
$402$	−4.55775	+	3.18394i	−0.227320	+	0.158801i
$403$			20.7202i			1.03215i
$404$	−12.3434	−	4.52322i	−0.614105	−	0.225039i
$405$		−	3.56420i		−	0.177106i
$406$	−1.27486	−	1.82493i	−0.0632701	−	0.0905698i
$407$	23.6894			1.17424
$408$	7.99340	−	2.11373i	0.395732	−	0.104645i
$409$	−13.9920			−0.691861			−0.345931	−	0.938260i	$-0.612437\pi$
$409$	−13.9920			−0.691861			−0.345931	+	0.938260i	$0.612437\pi$
$410$	−10.6379	−	15.2280i	−0.525371	−	0.752057i
$411$		−	6.57501i		−	0.324321i
$412$	−9.34887	+	25.5120i	−0.460586	+	1.25689i
$413$			29.1867i			1.43618i
$414$	−1.15934	+	0.809892i	−0.0569786	+	0.0398040i
$415$	47.0064			2.30746
$416$	1.06850	−	11.4889i	0.0523874	−	0.563289i
$417$	−19.0188			−0.931355
$418$	−14.7869	+	10.3298i	−0.723251	+	0.505248i
$419$		−	8.95929i		−	0.437690i	−0.975760	−	0.218845i	$-0.929771\pi$
$419$		−	8.95929i		−	0.437690i	0.975760	−	0.218845i	$-0.0702289\pi$
$420$	7.26380	−	19.8221i	0.354437	−	0.967218i
$421$			31.5139i			1.53590i	0.640512	+	0.767948i	$0.278722\pi$
$421$			31.5139i			1.53590i	−0.640512	+	0.767948i	$0.721278\pi$
$422$	−10.5920	−	15.1622i	−0.515609	−	0.738083i
$423$	−4.08428			−0.198585
$424$	36.5325	−	9.66046i	1.77417	−	0.469153i
$425$	−22.5191			−1.09234
$426$	4.80539	+	6.87881i	0.232822	+	0.333280i
$427$			43.3090i			2.09587i
$428$	−2.13307	−	0.781661i	−0.103106	−	0.0377830i
$429$			4.97165i			0.240034i
$430$	−5.14618	+	3.59501i	−0.248171	+	0.173367i
$431$	−30.3868			−1.46368			−0.731841	−	0.681475i	$-0.761339\pi$
$431$	−30.3868			−1.46368			−0.731841	+	0.681475i	$0.761339\pi$
$432$	2.58453	−	3.05290i	0.124348	−	0.146883i
$433$	−23.6611			−1.13708			−0.568541	−	0.822655i	$-0.692492\pi$
$433$	−23.6611			−1.13708			−0.568541	+	0.822655i	$0.692492\pi$
$434$	−34.8779	+	24.3650i	−1.67419	+	1.16956i
$435$			1.89442i			0.0908307i
$436$	−22.4514	−	8.22733i	−1.07523	−	0.394017i
$437$		−	5.23284i		−	0.250321i
$438$	3.12240	+	4.46965i	0.149194	+	0.213568i
$439$	−9.19869			−0.439030			−0.219515	−	0.975609i	$-0.570447\pi$
$439$	−9.19869			−0.439030			−0.219515	+	0.975609i	$0.570447\pi$
$440$	−6.28169	−	23.7551i	−0.299468	−	1.13248i
$441$	−1.77077			−0.0843222
$442$	4.82907	+	6.91271i	0.229695	+	0.328804i
$443$			6.81948i			0.324003i	0.986791	+	0.162002i	$0.0517950\pi$
$443$			6.81948i			0.324003i	−0.986791	+	0.162002i	$0.948205\pi$
$444$	6.68822	−	18.2514i	0.317409	−	0.866172i
$445$			35.9305i			1.70327i
$446$	1.95793	−	1.36777i	0.0927107	−	0.0647657i
$447$	3.73487			0.176653
$448$	20.5955	−	11.7113i	0.973047	−	0.553305i
$449$	−15.9175			−0.751195			−0.375598	−	0.926783i	$-0.622563\pi$
$449$	−15.9175			−0.751195			−0.375598	+	0.926783i	$0.622563\pi$
$450$	−8.93099	+	6.23900i	−0.421011	+	0.294109i
$451$			8.98250i			0.422969i
$452$	−5.29925	+	14.4611i	−0.249256	+	0.680191i
$453$		−	8.40368i		−	0.394839i
$454$	1.41562	+	2.02643i	0.0664384	+	0.0951052i
$455$	21.5305			1.00936
$456$	3.78377	+	14.3089i	0.177191	+	0.670075i
$457$	27.5120			1.28696			0.643478	−	0.765464i	$-0.277491\pi$
$457$	27.5120			1.28696			0.643478	+	0.765464i	$0.277491\pi$
$458$	−6.01024	−	8.60352i	−0.280840	−	0.402016i
$459$			2.92323i			0.136445i
$460$	6.69315	+	2.45270i	0.312070	+	0.114358i
$461$			18.3180i			0.853154i	0.904451	+	0.426577i	$0.140281\pi$
$461$			18.3180i			0.853154i	−0.904451	+	0.426577i	$0.859719\pi$
$462$	−8.36871	+	5.84620i	−0.389348	+	0.271990i
$463$	−11.4591			−0.532547			−0.266274	−	0.963897i	$-0.585792\pi$
$463$	−11.4591			−0.532547			−0.266274	+	0.963897i	$0.585792\pi$
$464$	−1.37372	+	1.62266i	−0.0637733	+	0.0753302i
$465$	36.2061			1.67902
$466$	20.1408	−	14.0699i	0.933004	−	0.651777i
$467$		−	14.1175i		−	0.653282i	−0.945148	−	0.326641i	$-0.894083\pi$
$467$		−	14.1175i		−	0.653282i	0.945148	−	0.326641i	$-0.105917\pi$
$468$	3.83038	+	1.40364i	0.177059	+	0.0648834i
$469$		−	11.6428i		−	0.537614i
$470$	11.7897	+	16.8768i	0.543820	+	0.778467i
$471$	13.0342			0.600585
$472$	26.9485	−	7.12612i	1.24040	−	0.328006i
$473$	3.03557			0.139575
$474$	−5.78215	−	8.27702i	−0.265583	−	0.380176i
$475$		−	40.3111i		−	1.84960i
$476$	−5.95752	+	16.2574i	−0.273063	+	0.745157i
$477$			13.3601i			0.611719i
$478$	−23.4267	+	16.3654i	−1.07151	+	0.748534i
$479$	24.8116			1.13367			0.566835	−	0.823831i	$-0.308168\pi$
$479$	24.8116			1.13367			0.566835	+	0.823831i	$0.308168\pi$
$480$	−20.0755	−	1.86708i	−0.916317	−	0.0852200i
$481$	19.8244			0.903914
$482$	18.4659	−	12.8999i	0.841099	−	0.587574i
$483$		−	2.96155i		−	0.134755i
$484$	3.48139	−	9.50031i	0.158245	−	0.431832i
$485$		−	33.6124i		−	1.52626i
$486$	0.809892	+	1.15934i	0.0367374	+	0.0525888i
$487$	5.90456			0.267561			0.133780	−	0.991011i	$-0.457288\pi$
$487$	5.90456			0.267561			0.133780	+	0.991011i	$0.457288\pi$
$488$	39.9878	−	10.5742i	1.81016	−	0.478670i
$489$	−7.76344			−0.351075
$490$	5.11151	+	7.31702i	0.230915	+	0.330549i
$491$		−	24.0837i		−	1.08688i	−0.839447	−	0.543441i	$-0.817121\pi$
$491$		−	24.0837i		−	1.08688i	0.839447	−	0.543441i	$-0.182879\pi$
$492$	6.92051	+	2.53602i	0.312001	+	0.114333i
$493$		−	1.55374i		−	0.0699771i
$494$	−12.3743	+	8.64445i	−0.556748	+	0.388932i
$495$	8.68739			0.390469
$496$	31.0122	+	26.2544i	1.39249	+	1.17886i
$497$	−17.5720			−0.788211
$498$	−15.2900	+	10.6813i	−0.685161	+	0.478639i
$499$			25.2750i			1.13146i	0.824589	+	0.565732i	$0.191406\pi$
$499$			25.2750i			1.13146i	−0.824589	+	0.565732i	$0.808594\pi$
$500$	18.0949	+	6.63087i	0.809228	+	0.296541i
$501$			12.8380i			0.573560i
$502$	23.0202	+	32.9529i	1.02744	+	1.47076i
$503$	5.18211			0.231059			0.115529	−	0.993304i	$-0.463144\pi$
$503$	5.18211			0.231059			0.115529	+	0.993304i	$0.463144\pi$
$504$	2.14144	+	8.09817i	0.0953873	+	0.360721i
$505$	−23.4275			−1.04251
$506$	−1.97404	−	2.82579i	−0.0877566	−	0.125622i
$507$		−	8.83950i		−	0.392576i
$508$	11.2691	−	30.7521i	0.499986	−	1.36441i
$509$		−	6.38289i		−	0.282917i	−0.989944	−	0.141458i	$-0.954821\pi$
$509$		−	6.38289i		−	0.282917i	0.989944	−	0.141458i	$-0.0451791\pi$
$510$	12.0792	−	8.43824i	0.534874	−	0.373652i
$511$	−11.4177			−0.505091
$512$	−15.8417	−	16.1567i	−0.700111	−	0.714034i
$513$	−5.23284			−0.231036
$514$	5.45190	−	3.80858i	0.240473	−	0.167989i
$515$			48.4214i			2.13370i
$516$	0.857028	−	2.33873i	0.0377286	−	0.102957i
$517$		−	9.95505i		−	0.437823i
$518$	23.3116	+	33.3701i	1.02425	+	1.46620i
$519$	−4.97498			−0.218377
$520$	−5.25680	−	19.8794i	−0.230526	−	0.871768i
$521$	29.0886			1.27440			0.637198	−	0.770700i	$-0.280093\pi$
$521$	29.0886			1.27440			0.637198	+	0.770700i	$0.280093\pi$
$522$	−0.430470	−	0.616208i	−0.0188412	−	0.0269707i
$523$			2.89819i			0.126729i	0.997990	+	0.0633644i	$0.0201830\pi$
$523$			2.89819i			0.126729i	−0.997990	+	0.0633644i	$0.979817\pi$
$524$	−3.47570	−	1.27367i	−0.151837	−	0.0556405i
$525$		−	22.8143i		−	0.995696i
$526$	9.24372	−	6.45746i	0.403045	−	0.281559i
$527$	−29.6950			−1.29354
$528$	7.44115	+	6.29956i	0.323835	+	0.274153i
$529$	1.00000			0.0434783
$530$	55.2057	−	38.5656i	2.39798	−	1.67518i
$531$			9.85521i			0.427680i
$532$	−29.1021	−	10.6645i	−1.26174	−	0.462364i
$533$			7.51696i			0.325596i
$534$	−8.16448	−	11.6873i	−0.353312	−	0.505758i
$535$	−4.04853			−0.175033
$536$	−10.7500	+	2.84266i	−0.464327	+	0.122784i
$537$	−4.94416			−0.213356
$538$	−23.3008	−	33.3545i	−1.00457	−	1.43802i
$539$		−	4.31607i		−	0.185906i
$540$	2.45270	−	6.69315i	0.105548	−	0.288027i
$541$			9.38250i			0.403385i	0.979449	+	0.201693i	$0.0646442\pi$
$541$			9.38250i			0.403385i	−0.979449	+	0.201693i	$0.935356\pi$
$542$	−11.7395	+	8.20099i	−0.504256	+	0.352263i
$543$	−11.9833			−0.514251
$544$	16.4652	+	1.53131i	0.705942	+	0.0656545i
$545$	−42.6125			−1.82532
$546$	−7.00331	+	4.89236i	−0.299714	+	0.209374i
$547$		−	2.87400i		−	0.122883i	−0.998111	−	0.0614417i	$-0.980430\pi$
$547$		−	2.87400i		−	0.122883i	0.998111	−	0.0614417i	$-0.0195698\pi$
$548$	4.52459	−	12.3471i	0.193281	−	0.527442i
$549$			14.6238i			0.624127i
$550$	−15.2070	−	21.7684i	−0.648427	−	0.928210i
$551$	2.78133			0.118489
$552$	−2.73444	+	0.723081i	−0.116385	+	0.0307764i
$553$	21.1437			0.899122
$554$	−13.2191	−	18.9228i	−0.561625	−	0.803955i
$555$		−	34.6408i		−	1.47042i
$556$	−35.7151	−	13.0878i	−1.51466	−	0.555046i
$557$			29.7699i			1.26139i	0.776030	+	0.630696i	$0.217230\pi$
$557$			29.7699i			1.26139i	−0.776030	+	0.630696i	$0.782770\pi$
$558$	−11.7769	+	8.22711i	−0.498557	+	0.348281i
$559$	2.54030			0.107443
$560$	27.2811	−	32.2250i	1.15284	−	1.36175i
$561$	−7.12511			−0.300822
$562$	−8.96515	+	6.26286i	−0.378172	+	0.264183i
$563$		−	35.8633i		−	1.51146i	−0.654884	−	0.755730i	$-0.727282\pi$
$563$		−	35.8633i		−	1.51146i	0.654884	−	0.755730i	$-0.272718\pi$
$564$	−7.66981	−	2.81060i	−0.322957	−	0.118348i
$565$			27.4469i			1.15470i
$566$	17.1443	+	24.5417i	0.720630	+	1.03157i
$567$	−2.96155			−0.124373
$568$	4.29031	+	16.2244i	0.180017	+	0.680763i
$569$	−13.2432			−0.555182			−0.277591	−	0.960699i	$-0.589536\pi$
$569$	−13.2432			−0.555182			−0.277591	+	0.960699i	$0.589536\pi$
$570$	15.1052	+	21.6227i	0.632687	+	0.905677i
$571$			18.5454i			0.776100i	0.921638	+	0.388050i	$0.126851\pi$
$571$			18.5454i			0.776100i	−0.921638	+	0.388050i	$0.873149\pi$
$572$	−3.42125	+	9.33619i	−0.143049	+	0.390366i
$573$			14.8486i			0.620310i
$574$	−12.6532	+	8.83924i	−0.528133	+	0.368943i
$575$	7.70349			0.321258
$576$	6.95431	−	3.95444i	0.289763	−	0.164768i
$577$	37.3304			1.55408			0.777042	−	0.629448i	$-0.216719\pi$
$577$	37.3304			1.55408			0.777042	+	0.629448i	$0.216719\pi$
$578$	9.80190	−	6.84740i	0.407705	−	0.284814i
$579$		−	20.6018i		−	0.856183i
$580$	−1.30365	+	3.55751i	−0.0541311	+	0.147718i
$581$		−	39.0584i		−	1.62042i
$582$	7.63775	+	10.9333i	0.316595	+	0.453199i
$583$	−32.5641			−1.34867
$584$	2.78772	+	10.5422i	0.115356	+	0.436238i
$585$	7.27000			0.300578
$586$	18.7913	+	26.8993i	0.776260	+	1.11120i
$587$		−	31.4701i		−	1.29891i	−0.760401	−	0.649454i	$-0.774997\pi$
$587$		−	31.4701i		−	1.29891i	0.760401	−	0.649454i	$-0.225003\pi$
$588$	−3.32529	−	1.21855i	−0.137133	−	0.0502523i
$589$		−	53.1567i		−	2.19028i
$590$	40.7230	−	28.4482i	1.67654	−	1.17119i
$591$	−13.4979			−0.555229
$592$	25.1194	−	29.6715i	1.03240	−	1.21949i
$593$	−11.0591			−0.454143			−0.227071	−	0.973878i	$-0.572915\pi$
$593$	−11.0591			−0.454143			−0.227071	+	0.973878i	$0.572915\pi$
$594$	−2.82579	+	1.97404i	−0.115944	+	0.0809957i
$595$			30.8563i			1.26498i
$596$	7.01365	+	2.57015i	0.287290	+	0.105277i
$597$			25.7498i			1.05387i
$598$	−1.65196	−	2.36475i	−0.0675537	−	0.0967017i
$599$	−8.73932			−0.357079			−0.178540	−	0.983933i	$-0.557137\pi$
$599$	−8.73932			−0.357079			−0.178540	+	0.983933i	$0.557137\pi$
$600$	−21.0647	+	5.57025i	−0.859964	+	0.227405i
$601$	1.24151			0.0506422			0.0253211	−	0.999679i	$-0.491939\pi$
$601$	1.24151			0.0506422			0.0253211	+	0.999679i	$0.491939\pi$
$602$	2.98715	+	4.27604i	0.121747	+	0.174279i
$603$		−	3.93132i		−	0.160096i
$604$	5.78300	−	15.7811i	0.235307	−	0.642125i
$605$		−	18.0315i		−	0.733083i
$606$	7.62037	−	5.32343i	0.309557	−	0.216250i
$607$	−20.1764			−0.818934			−0.409467	−	0.912325i	$-0.634285\pi$
$607$	−20.1764			−0.818934			−0.409467	+	0.912325i	$0.634285\pi$
$608$	−2.74118	+	29.4742i	−0.111170	+	1.19534i
$609$	1.57411			0.0637861
$610$	60.4272	−	42.2131i	2.44662	−	1.70916i
$611$		−	8.33084i		−	0.337030i
$612$	−2.01162	+	5.48949i	−0.0813151	+	0.221900i
$613$			38.6552i			1.56127i	0.624988	+	0.780634i	$0.285104\pi$
$613$			38.6552i			1.56127i	−0.624988	+	0.780634i	$0.714896\pi$
$614$	−1.23565	−	1.76880i	−0.0498666	−	0.0713830i
$615$	13.1350			0.529655
$616$	−19.7385	+	5.21956i	−0.795288	+	0.210302i
$617$	−26.9695			−1.08575			−0.542875	−	0.839814i	$-0.682664\pi$
$617$	−26.9695			−1.08575			−0.542875	+	0.839814i	$0.682664\pi$
$618$	−11.0028	−	15.7502i	−0.442597	−	0.633568i
$619$		−	29.6122i		−	1.19022i	−0.803646	−	0.595108i	$-0.797109\pi$
$619$		−	29.6122i		−	1.19022i	0.803646	−	0.595108i	$-0.202891\pi$
$620$	67.9909	+	24.9153i	2.73058	+	1.00062i
$621$		−	1.00000i		−	0.0401286i
$622$	−27.5973	+	19.2789i	−1.10655	+	0.773014i
$623$	29.8552			1.19612
$624$	6.22709	+	5.27175i	0.249283	+	0.211039i
$625$	−4.17365			−0.166946
$626$	−19.2942	+	13.4785i	−0.771150	+	0.538709i
$627$		−	12.7546i		−	0.509368i
$628$	24.4767	+	8.96949i	0.976728	+	0.357922i
$629$			28.4112i			1.13283i
$630$	8.54884	+	12.2375i	0.340594	+	0.487553i
$631$	12.1567			0.483949			0.241974	−	0.970283i	$-0.422205\pi$
$631$	12.1567			0.483949			0.241974	+	0.970283i	$0.422205\pi$
$632$	−5.16237	−	19.5223i	−0.205348	−	0.776555i
$633$	13.0782			0.519814
$634$	10.8315	+	15.5051i	0.430174	+	0.615784i
$635$		−	58.3671i		−	2.31623i
$636$	−9.19378	+	25.0888i	−0.364557	+	0.994835i
$637$		−	3.61189i		−	0.143108i
$638$	1.50195	−	1.04923i	0.0594628	−	0.0415394i
$639$	−5.93337			−0.234721
$640$	−36.4146	−	17.3211i	−1.43942	−	0.684677i
$641$	28.8525			1.13960			0.569802	−	0.821782i	$-0.307020\pi$
$641$	28.8525			1.13960			0.569802	+	0.821782i	$0.307020\pi$
$642$	1.31688	−	0.919946i	0.0519732	−	0.0363074i
$643$			10.8818i			0.429136i	0.976709	+	0.214568i	$0.0688343\pi$
$643$			10.8818i			0.429136i	−0.976709	+	0.214568i	$0.931166\pi$
$644$	2.03799	−	5.56144i	0.0803081	−	0.219152i
$645$		−	4.43888i		−	0.174781i
$646$	−12.3888	−	17.7342i	−0.487429	−	0.697744i
$647$	26.9107			1.05797			0.528984	−	0.848632i	$-0.322573\pi$
$647$	26.9107			1.05797			0.528984	+	0.848632i	$0.322573\pi$
$648$	0.723081	+	2.73444i	0.0284053	+	0.107419i
$649$	−24.0212			−0.942913
$650$	−12.7259	−	18.2168i	−0.499150	−	0.714522i
$651$		−	30.0842i		−	1.17909i
$652$	−14.5788	−	5.34242i	−0.570952	−	0.209225i
$653$			36.4356i			1.42584i	0.701248	+	0.712918i	$0.252627\pi$
$653$			36.4356i			1.42584i	−0.701248	+	0.712918i	$0.747373\pi$
$654$	13.8608	−	9.68283i	0.541999	−	0.378629i
$655$	−6.59683			−0.257759
$656$	11.2507	+	9.52470i	0.439268	+	0.371877i
$657$	−3.85533			−0.150411
$658$	14.0232	−	9.79628i	0.546680	−	0.381899i
$659$			17.2668i			0.672621i	0.941751	+	0.336310i	$0.109179\pi$
$659$			17.2668i			0.672621i	−0.941751	+	0.336310i	$0.890821\pi$
$660$	16.3139	+	5.97823i	0.635018	+	0.232702i
$661$			25.0091i			0.972742i	0.873752	+	0.486371i	$0.161680\pi$
$661$			25.0091i			0.972742i	−0.873752	+	0.486371i	$0.838320\pi$
$662$	21.5918	+	30.9082i	0.839188	+	1.20128i
$663$	−5.96261			−0.231569
$664$	−36.0632	+	9.53636i	−1.39952	+	0.370083i
$665$	−55.2354			−2.14194
$666$	7.87143	+	11.2678i	0.305012	+	0.436618i
$667$			0.531515i			0.0205804i
$668$	−8.83449	+	24.1083i	−0.341817	+	0.932779i
$669$			1.68883i			0.0652939i
$670$	−16.2447	+	11.3482i	−0.627588	+	0.438419i
$671$	−35.6440			−1.37602
$672$	−1.55138	+	16.6811i	−0.0598460	+	0.643486i
$673$	−9.18765			−0.354158			−0.177079	−	0.984197i	$-0.556665\pi$
$673$	−9.18765			−0.354158			−0.177079	+	0.984197i	$0.556665\pi$
$674$	41.5682	−	29.0386i	1.60115	−	1.11853i
$675$		−	7.70349i		−	0.296508i
$676$	6.08290	−	16.5995i	0.233958	−	0.638444i
$677$			23.7154i			0.911458i	0.890119	+	0.455729i	$0.150621\pi$
$677$			23.7154i			0.911458i	−0.890119	+	0.455729i	$0.849379\pi$
$678$	−6.23675	−	8.92777i	−0.239521	−	0.342869i
$679$	−27.9291			−1.07182
$680$	28.4901	−	7.53376i	1.09254	−	0.288907i
$681$	−1.74792			−0.0669803
$682$	−20.0528	−	28.7052i	−0.767862	−	1.09918i
$683$			9.92760i			0.379869i	0.981797	+	0.189934i	$0.0608276\pi$
$683$			9.92760i			0.379869i	−0.981797	+	0.189934i	$0.939172\pi$
$684$	−9.82667	−	3.60098i	−0.375732	−	0.137687i
$685$		−	23.4346i		−	0.895390i
$686$	−17.9543	+	12.5425i	−0.685499	+	0.478875i
$687$	7.42104			0.283130
$688$	3.21880	−	3.80210i	0.122716	−	0.144954i
$689$	−27.2511			−1.03818
$690$	−4.13212	+	2.88661i	−0.157307	+	0.109891i
$691$		−	24.4468i		−	0.930001i	−0.885310	−	0.465001i	$-0.846054\pi$
$691$		−	24.4468i		−	0.930001i	0.885310	−	0.465001i	$-0.153946\pi$
$692$	−9.34244	−	3.42354i	−0.355146	−	0.130143i
$693$		−	7.21849i		−	0.274208i
$694$	13.9275	+	19.9369i	0.528679	+	0.756793i
$695$	−67.7867			−2.57130
$696$	−0.384329	−	1.45340i	−0.0145679	−	0.0550908i
$697$	−10.7729			−0.408053
$698$	17.9885	+	25.7501i	0.680874	+	0.974656i
$699$			17.3726i			0.657092i
$700$	15.6996	−	42.8425i	0.593391	−	1.61930i
$701$		−	18.4078i		−	0.695254i	−0.937633	−	0.347627i	$-0.886988\pi$
$701$		−	18.4078i		−	0.695254i	0.937633	−	0.347627i	$-0.113012\pi$
$702$	−2.36475	+	1.65196i	−0.0892516	+	0.0623493i
$703$	−50.8586			−1.91817
$704$	9.63858	+	16.9505i	0.363268	+	0.638845i
$705$	−14.5572			−0.548255
$706$	−35.9988	+	25.1480i	−1.35483	+	0.946457i
$707$			19.4663i			0.732105i
$708$	−6.78187	+	18.5069i	−0.254878	+	0.695534i
$709$		−	4.68978i		−	0.176129i	−0.996115	−	0.0880643i	$-0.971932\pi$
$709$		−	4.68978i		−	0.176129i	0.996115	−	0.0880643i	$-0.0280681\pi$
$710$	17.1274	+	24.5174i	0.642778	+	0.920123i
$711$	7.13941			0.267749
$712$	−7.28935	−	27.5657i	−0.273180	−	1.03307i
$713$	10.1583			0.380431
$714$	−7.01147	−	10.0368i	−0.262398	−	0.375617i
$715$			17.7200i			0.662689i
$716$	−9.28455	−	3.40232i	−0.346980	−	0.127151i
$717$		−	20.2068i		−	0.754638i
$718$	−30.6807	+	21.4329i	−1.14499	+	0.799867i
$719$	−51.4818			−1.91995			−0.959974	−	0.280088i	$-0.909636\pi$
$719$	−51.4818			−1.91995			−0.959974	+	0.280088i	$0.909636\pi$
$720$	9.21178	−	10.8811i	0.343303	−	0.405516i
$721$	40.2341			1.49840
$722$	9.71832	−	6.78901i	0.361678	−	0.252661i
$723$			15.9279i			0.592366i
$724$	−22.5032	−	8.24628i	−0.836324	−	0.306471i
$725$			4.09452i			0.152067i
$726$	4.09728	+	5.86517i	0.152064	+	0.217677i
$727$	47.5643			1.76406			0.882031	−	0.471192i	$-0.156176\pi$
$727$	47.5643			1.76406			0.882031	+	0.471192i	$0.156176\pi$
$728$	−16.5181	+	4.36796i	−0.612201	+	0.161887i
$729$	−1.00000			−0.0370370
$730$	11.1288	+	15.9307i	0.411897	+	0.589622i
$731$			3.64062i			0.134653i
$732$	−10.0633	+	27.4617i	−0.371952	+	1.01501i
$733$			17.7710i			0.656386i	0.944611	+	0.328193i	$0.106440\pi$
$733$			17.7710i			0.656386i	−0.944611	+	0.328193i	$0.893560\pi$
$734$	−7.45745	+	5.20961i	−0.275259	+	0.192290i
$735$	−6.31135			−0.232798
$736$	−5.63255	−	0.523843i	−0.207618	−	0.0193091i
$737$	9.58223			0.352966
$738$	−4.27249	+	2.98467i	−0.157272	+	0.109867i
$739$		−	32.2500i		−	1.18633i	−0.805079	−	0.593167i	$-0.797877\pi$
$739$		−	32.2500i		−	1.18633i	0.805079	−	0.593167i	$-0.202123\pi$
$740$	23.8381	−	65.0515i	0.876306	−	2.39134i
$741$		−	10.6736i		−	0.392104i
$742$	−32.0447	−	45.8713i	−1.17640	−	1.68399i
$743$	26.9499			0.988695			0.494348	−	0.869264i	$-0.335407\pi$
$743$	26.9499			0.988695			0.494348	+	0.869264i	$0.335407\pi$
$744$	−27.7772	+	7.34526i	−1.01836	+	0.269290i
$745$	13.3118			0.487707
$746$	−13.4455	−	19.2469i	−0.492273	−	0.704678i
$747$		−	13.1885i		−	0.482542i
$748$	−13.3801	−	4.90315i	−0.489226	−	0.179277i
$749$			3.36398i			0.122917i
$750$	−11.1712	+	7.80394i	−0.407914	+	0.284960i
$751$	−19.8607			−0.724728			−0.362364	−	0.932037i	$-0.618030\pi$
$751$	−19.8607			−0.724728			−0.362364	+	0.932037i	$0.618030\pi$
$752$	−12.4689	−	10.5560i	−0.454694	−	0.384936i
$753$	−28.4237			−1.03582
$754$	1.25690	−	0.878043i	0.0457736	−	0.0319764i
$755$		−	29.9524i		−	1.09008i
$756$	−5.56144	−	2.03799i	−0.202268	−	0.0741210i
$757$			30.1817i			1.09697i	0.836160	+	0.548486i	$0.184795\pi$
$757$			30.1817i			1.09697i	−0.836160	+	0.548486i	$0.815205\pi$
$758$	−1.54620	−	2.21336i	−0.0561606	−	0.0803927i
$759$	2.43741			0.0884722
$760$	13.4861	+	50.9996i	0.489192	+	1.84995i
$761$	34.3807			1.24630			0.623150	−	0.782102i	$-0.285852\pi$
$761$	34.3807			1.24630			0.623150	+	0.782102i	$0.285852\pi$
$762$	13.2627	+	18.9853i	0.480459	+	0.687766i
$763$			35.4074i			1.28183i
$764$	−10.2181	+	27.8840i	−0.369677	+	1.00881i
$765$			10.4190i			0.376699i
$766$	4.90762	−	3.42836i	0.177320	−	0.123872i
$767$	−20.1020			−0.725841
$768$	15.7806	−	2.64037i	0.569435	−	0.0952762i
$769$	53.5633			1.93154			0.965771	−	0.259394i	$-0.0835229\pi$
$769$	53.5633			1.93154			0.965771	+	0.259394i	$0.0835229\pi$
$770$	−29.8277	+	20.8370i	−1.07492	+	0.750913i
$771$			4.70258i			0.169359i
$772$	14.1772	−	38.6879i	0.510247	−	1.39241i
$773$			20.3049i			0.730318i	0.930945	+	0.365159i	$0.118985\pi$
$773$			20.3049i			0.730318i	−0.930945	+	0.365159i	$0.881015\pi$
$774$	1.00865	+	1.44385i	0.0362550	+	0.0518983i
$775$	78.2543			2.81098
$776$	6.81907	+	25.7873i	0.244790	+	0.925711i
$777$	−28.7836			−1.03261
$778$	3.96171	+	5.67110i	0.142034	+	0.203319i
$779$		−	19.2844i		−	0.690936i
$780$	13.6522	+	5.00286i	0.488828	+	0.179131i
$781$		−	14.4620i		−	0.517493i
$782$	3.38903	−	2.36750i	0.121191	−	0.0846617i
$783$	0.531515			0.0189948
$784$	−5.40597	−	4.57660i	−0.193070	−	0.163450i
$785$	46.4565			1.65810
$786$	2.14578	−	1.49900i	0.0765375	−	0.0534674i
$787$			18.9842i			0.676712i	0.941018	+	0.338356i	$0.109871\pi$
$787$			18.9842i			0.676712i	−0.941018	+	0.338356i	$0.890129\pi$
$788$	−25.3475	−	9.28858i	−0.902966	−	0.330892i
$789$			7.97324i			0.283855i
$790$	−20.6087	−	29.5009i	−0.733225	−	1.04960i
$791$	22.8060			0.810889
$792$	−6.66494	+	1.76244i	−0.236828	+	0.0626257i
$793$	−29.8285			−1.05924
$794$	6.49190	+	9.29301i	0.230389	+	0.329797i
$795$			47.6182i			1.68884i
$796$	−17.7198	+	48.3552i	−0.628060	+	1.71390i
$797$		−	20.0092i		−	0.708763i	−0.935101	−	0.354381i	$-0.884691\pi$
$797$		−	20.0092i		−	0.708763i	0.935101	−	0.354381i	$-0.115309\pi$
$798$	17.9667	−	12.5511i	0.636014	−	0.444306i
$799$	11.9393			0.422382
$800$	−43.3903	−	4.03542i	−1.53408	−	0.142674i
$801$	10.0810			0.356193
$802$	18.2941	−	12.7798i	0.645986	−	0.451272i
$803$		−	9.39700i		−	0.331613i
$804$	2.70534	−	7.38257i	0.0954100	−	0.260363i
$805$		−	10.5555i		−	0.372034i
$806$	−16.7811	−	24.0218i	−0.591089	−	0.846131i
$807$	28.7702			1.01276
$808$	17.9735	−	4.75282i	0.632306	−	0.167204i
$809$	23.5001			0.826221			0.413110	−	0.910681i	$-0.364442\pi$
$809$	23.5001			0.826221			0.413110	+	0.910681i	$0.364442\pi$
$810$	2.88661	+	4.13212i	0.101425	+	0.145188i
$811$			44.8610i			1.57528i	0.616135	+	0.787641i	$0.288698\pi$
$811$			44.8610i			1.57528i	−0.616135	+	0.787641i	$0.711302\pi$
$812$	2.95599	+	1.08322i	0.103735	+	0.0380137i
$813$		−	10.1260i		−	0.355135i
$814$	−27.4642	+	19.1859i	−0.962619	+	0.672465i
$815$	−27.6704			−0.969253
$816$	−7.55519	+	8.92433i	−0.264485	+	0.312414i
$817$	−6.51702			−0.228002
$818$	16.2216	−	11.3320i	0.567173	−	0.396215i
$819$		−	6.04076i		−	0.211081i
$820$	24.6660	+	9.03887i	0.861376	+	0.315651i
$821$		−	14.6906i		−	0.512707i	−0.966583	−	0.256353i	$-0.917479\pi$
$821$		−	14.6906i		−	0.512707i	0.966583	−	0.256353i	$-0.0825211\pi$
$822$	5.32504	+	7.62268i	0.185732	+	0.265872i
$823$	41.5102			1.44695			0.723477	−	0.690349i	$-0.242543\pi$
$823$	41.5102			1.44695			0.723477	+	0.690349i	$0.242543\pi$
$824$	−9.82342	−	37.1487i	−0.342215	−	1.29414i
$825$	18.7765			0.653715
$826$	−23.6381	−	33.8374i	−0.822473	−	1.17735i
$827$		−	17.4244i		−	0.605904i	−0.953006	−	0.302952i	$-0.902028\pi$
$827$		−	17.4244i		−	0.605904i	0.953006	−	0.302952i	$-0.0979722\pi$
$828$	0.688150	−	1.87788i	0.0239149	−	0.0652610i
$829$			52.6041i			1.82702i	0.406820	+	0.913508i	$0.366638\pi$
$829$			52.6041i			1.82702i	−0.406820	+	0.913508i	$0.633362\pi$
$830$	−54.4966	+	38.0701i	−1.89160	+	1.32143i
$831$	16.3220			0.566206
$832$	8.06600	+	14.1849i	0.279638	+	0.491774i
$833$	5.17636			0.179350
$834$	22.0493	−	15.4032i	0.763505	−	0.533368i
$835$			45.7572i			1.58349i
$836$	8.77705	−	23.9516i	0.303561	−	0.828383i
$837$		−	10.1583i		−	0.351122i
$838$	7.25605	+	10.3869i	0.250656	+	0.358809i
$839$	−33.0754			−1.14189			−0.570944	−	0.820989i	$-0.693423\pi$
$839$	−33.0754			−1.14189			−0.570944	+	0.820989i	$0.693423\pi$
$840$	7.63251	+	28.8635i	0.263347	+	0.995884i
$841$	28.7175			0.990258
$842$	−25.5229	−	36.5355i	−0.879577	−	1.25909i
$843$		−	7.73296i		−	0.266337i
$844$	24.5594	+	8.99980i	0.845370	+	0.309786i
$845$		−	31.5057i		−	1.08383i
$846$	4.73508	−	3.30783i	0.162795	−	0.113725i
$847$	−14.9826			−0.514809
$848$	−34.5297	+	40.7871i	−1.18576	+	1.40064i
$849$	−21.1687			−0.726507
$850$	26.1074	−	18.2380i	0.895475	−	0.625560i
$851$		−	9.71912i		−	0.333167i
$852$	−11.1422	−	4.08305i	−0.381725	−	0.139883i
$853$			5.89107i			0.201707i	0.994901	+	0.100853i	$0.0321573\pi$
$853$			5.89107i			0.201707i	−0.994901	+	0.100853i	$0.967843\pi$
$854$	−35.0756	−	50.2099i	−1.20026	−	1.71815i
$855$	−18.6509			−0.637846
$856$	3.10601	−	0.821339i	0.106161	−	0.0280728i
$857$	52.0417			1.77771			0.888855	−	0.458189i	$-0.151502\pi$
$857$	52.0417			1.77771			0.888855	+	0.458189i	$0.151502\pi$
$858$	−4.02650	−	5.76385i	−0.137463	−	0.196775i
$859$		−	36.3727i		−	1.24102i	−0.784198	−	0.620510i	$-0.786926\pi$
$859$		−	36.3727i		−	1.24102i	0.784198	−	0.620510i	$-0.213074\pi$
$860$	3.05462	−	8.33570i	0.104162	−	0.284245i
$861$		−	10.9141i		−	0.371951i
$862$	35.2287	−	24.6100i	1.19990	−	0.838221i
$863$	1.99253			0.0678264			0.0339132	−	0.999425i	$-0.489203\pi$
$863$	1.99253			0.0678264			0.0339132	+	0.999425i	$0.489203\pi$
$864$	−0.523843	+	5.63255i	−0.0178215	+	0.191623i
$865$	−17.7318			−0.602900
$866$	27.4314	−	19.1630i	0.932156	−	0.651184i
$867$			8.45471i			0.287137i
$868$	20.7025	−	56.4947i	0.702688	−	1.91756i
$869$			17.4016i			0.590310i
$870$	−1.53428	−	2.19629i	−0.0520169	−	0.0744611i
$871$	8.01884			0.271708
$872$	32.6921	−	8.64495i	1.10710	−	0.292755i
$873$	−9.43058			−0.319177
$874$	4.23803	+	6.06665i	0.143354	+	0.205208i
$875$		−	28.5368i		−	0.964721i
$876$	−7.23986	−	2.65305i	−0.244612	−	0.0896381i
$877$			17.4486i			0.589198i	0.955621	+	0.294599i	$0.0951861\pi$
$877$			17.4486i			0.589198i	−0.955621	+	0.294599i	$0.904814\pi$
$878$	10.6644	−	7.44995i	0.359907	−	0.251424i
$879$	−23.2022			−0.782591
$880$	26.5217	+	22.4529i	0.894047	+	0.756886i
$881$	28.5205			0.960879			0.480440	−	0.877028i	$-0.340477\pi$
$881$	28.5205			0.960879			0.480440	+	0.877028i	$0.340477\pi$
$882$	2.05292	−	1.43413i	0.0691255	−	0.0482896i
$883$			40.5481i			1.36455i	0.731094	+	0.682277i	$0.239010\pi$
$883$			40.5481i			1.36455i	−0.731094	+	0.682277i	$0.760990\pi$
$884$	−11.1971	−	4.10317i	−0.376599	−	0.138005i
$885$			35.1259i			1.18074i
$886$	−5.52304	−	7.90611i	−0.185550	−	0.265611i
$887$	44.0386			1.47867			0.739337	−	0.673336i	$-0.235139\pi$
$887$	44.0386			1.47867			0.739337	+	0.673336i	$0.235139\pi$
$888$	7.02771	+	26.5763i	0.235834	+	0.891843i
$889$	−48.4981			−1.62658
$890$	−29.0998	−	41.6558i	−0.975428	−	1.39630i
$891$		−	2.43741i		−	0.0816562i
$892$	−1.16217	+	3.17143i	−0.0389123	+	0.106187i
$893$			21.3724i			0.715200i
$894$	−4.32999	+	3.02484i	−0.144817	+	0.101166i
$895$	−17.6219			−0.589036
$896$	−14.3924	+	30.2575i	−0.480816	+	1.01083i
$897$	2.03973			0.0681047
$898$	18.4539	−	12.8915i	0.615814	−	0.430195i
$899$			5.39928i			0.180076i
$900$	5.30116	−	14.4663i	0.176705	−	0.482209i
$901$		−	39.0548i		−	1.30110i
$902$	−7.27485	−	10.4138i	−0.242226	−	0.346741i
$903$	−3.68834			−0.122740
$904$	−5.56824	−	21.0571i	−0.185197	−	0.700350i
$905$	−42.7107			−1.41975
$906$	6.80607	+	9.74274i	0.226117	+	0.323681i
$907$			0.259673i			0.00862231i	0.999991	+	0.00431116i	$0.00137229\pi$
$907$			0.259673i			0.00862231i	−0.999991	+	0.00431116i	$0.998628\pi$
$908$	−3.28238	−	1.20283i	−0.108930	−	0.0399173i
$909$			6.57301i			0.218013i
$910$	−24.9612	+	17.4373i	−0.827455	+	0.578042i
$911$	39.2729			1.30117			0.650584	−	0.759434i	$-0.274524\pi$
$911$	39.2729			1.30117			0.650584	+	0.759434i	$0.274524\pi$
$912$	−15.9753	−	13.5244i	−0.528996	−	0.447839i
$913$	32.1458			1.06387
$914$	−31.8958	+	22.2817i	−1.05502	+	0.737014i
$915$			52.1219i			1.72310i
$916$	13.9358	+	5.10679i	0.460453	+	0.168733i
$917$			5.48141i			0.181012i
$918$	−2.36750	−	3.38903i	−0.0781392	−	0.111855i
$919$	−57.1823			−1.88627			−0.943135	−	0.332409i	$-0.892138\pi$
$919$	−57.1823			−1.88627			−0.943135	+	0.332409i	$0.892138\pi$
$920$	−9.74607	+	2.57720i	−0.321319	+	0.0849679i
$921$	1.52569			0.0502733
$922$	−14.8356	−	21.2368i	−0.488584	−	0.699397i
$923$		−	12.1025i		−	0.398358i
$924$	4.96741	−	13.5555i	0.163416	−	0.445943i
$925$		−	74.8712i		−	2.46175i
$926$	13.2850	−	9.28059i	0.436571	−	0.304979i
$927$	13.5855			0.446206
$928$	0.278430	−	2.99378i	0.00913992	−	0.0982758i
$929$	−50.3176			−1.65087			−0.825433	−	0.564500i	$-0.809069\pi$
$929$	−50.3176			−1.65087			−0.825433	+	0.564500i	$0.809069\pi$
$930$	−41.9753	+	29.3230i	−1.37642	+	0.961540i
$931$			9.26613i			0.303685i
$932$	−11.9550	+	32.6237i	−0.391598	+	1.06863i
$933$		−	23.8043i		−	0.779318i
$934$	11.4337	+	16.3671i	0.374122	+	0.535547i
$935$	−25.3953			−0.830514
$936$	−5.57752	+	1.47489i	−0.182307	+	0.0482083i
$937$	−31.8614			−1.04087			−0.520433	−	0.853902i	$-0.674230\pi$
$937$	−31.8614			−1.04087			−0.520433	+	0.853902i	$0.674230\pi$
$938$	9.42940	+	13.4980i	0.307881	+	0.440725i
$939$		−	16.6423i		−	0.543102i
$940$	−27.3367	−	10.0175i	−0.891625	−	0.326736i
$941$		−	4.21697i		−	0.137469i	−0.997635	−	0.0687347i	$-0.978104\pi$
$941$		−	4.21697i		−	0.137469i	0.997635	−	0.0687347i	$-0.0218962\pi$
$942$	−15.1111	+	10.5563i	−0.492347	+	0.343943i
$943$	3.68527			0.120009
$944$	−25.4711	+	30.0870i	−0.829015	+	0.979247i
$945$	−10.5555			−0.343372
$946$	−3.51926	+	2.45848i	−0.114421	+	0.0799321i
$947$		−	23.8696i		−	0.775659i	−0.921731	−	0.387829i	$-0.873225\pi$
$947$		−	23.8696i		−	0.775659i	0.921731	−	0.387829i	$-0.126775\pi$
$948$	13.4070	+	4.91299i	0.435439	+	0.159566i
$949$		−	7.86384i		−	0.255271i
$950$	32.6477	+	46.7344i	1.05923	+	1.51627i
$951$	−13.3740			−0.433682
$952$	−6.25993	−	23.6728i	−0.202885	−	0.767241i
$953$	41.5476			1.34586			0.672929	−	0.739707i	$-0.265036\pi$
$953$	41.5476			1.34586			0.672929	+	0.739707i	$0.265036\pi$
$954$	−10.8203	−	15.4890i	−0.350319	−	0.501474i
$955$			52.9234i			1.71256i
$956$	13.9053	−	37.9461i	0.449731	−	1.22727i
$957$			1.29552i			0.0418782i
$958$	−28.7651	+	20.0947i	−0.929359	+	0.649230i
$959$	−19.4722			−0.628790
$960$	24.7865	−	14.0944i	0.799981	−	0.454895i
$961$	72.1907			2.32873
$962$	−22.9833	+	16.0556i	−0.741010	+	0.517654i
$963$			1.13589i			0.0366035i
$964$	−10.9608	+	29.9108i	−0.353024	+	0.963362i
$965$		−	73.4290i		−	2.36376i
$966$	2.39853	+	3.43345i	0.0771715	+	0.110469i
$967$	37.3284			1.20040			0.600200	−	0.799850i	$-0.295088\pi$
$967$	37.3284			1.20040			0.600200	+	0.799850i	$0.295088\pi$
$968$	3.65810	+	13.8337i	0.117576	+	0.444631i
$969$	15.2968			0.491404
$970$	27.2224	+	38.9683i	0.874059	+	1.25120i
$971$		−	6.88969i		−	0.221101i	−0.993871	−	0.110550i	$-0.964739\pi$
$971$		−	6.88969i		−	0.221101i	0.993871	−	0.110550i	$-0.0352613\pi$
$972$	−1.87788	−	0.688150i	−0.0602332	−	0.0220724i
$973$			56.3251i			1.80570i
$974$	−6.84540	+	4.78205i	−0.219341	+	0.153227i
$975$	15.7131			0.503221
$976$	−37.7956	+	44.6448i	−1.20981	+	1.42905i
$977$	−17.1500			−0.548676			−0.274338	−	0.961633i	$-0.588459\pi$
$977$	−17.1500			−0.548676			−0.274338	+	0.961633i	$0.588459\pi$
$978$	9.00049	−	6.28755i	0.287804	−	0.201054i
$979$			24.5714i			0.785305i
$980$	−11.8520	−	4.34316i	−0.378598	−	0.138737i
$981$			11.9557i			0.381716i
$982$	19.5052	+	27.9213i	0.622436	+	0.891004i
$983$	−23.8672			−0.761244			−0.380622	−	0.924731i	$-0.624290\pi$
$983$	−23.8672			−0.761244			−0.380622	+	0.924731i	$0.624290\pi$
$984$	−10.0771	+	2.66475i	−0.321247	+	0.0849490i
$985$	−48.1091			−1.53288
$986$	1.25836	+	1.80132i	0.0400745	+	0.0573657i
$987$			12.0958i			0.385013i
$988$	7.34503	−	20.0438i	0.233677	−	0.637677i
$989$		−	1.24541i		−	0.0396017i
$990$	−10.0717	+	7.03585i	−0.320099	+	0.223614i
$991$	−4.08890			−0.129888			−0.0649441	−	0.997889i	$-0.520687\pi$
$991$	−4.08890			−0.129888			−0.0649441	+	0.997889i	$0.520687\pi$
$992$	−57.2170	−	5.32134i	−1.81664	−	0.168953i
$993$	−26.6601			−0.846032
$994$	20.3719	−	14.2314i	0.646159	−	0.451392i
$995$			91.7774i			2.90954i
$996$	9.07568	−	24.7665i	0.287574	−	0.784756i
$997$		−	52.7237i		−	1.66978i	−0.550420	−	0.834888i	$-0.685532\pi$
$997$		−	52.7237i		−	1.66978i	0.550420	−	0.834888i	$-0.314468\pi$
$998$	−20.4700	−	29.3024i	−0.647967	−	0.927550i
$999$	−9.71912			−0.307499

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.f.c.277.4	yes	18
4.3	odd	2		2208.2.f.c.1105.10		18
8.3	odd	2		2208.2.f.c.1105.9		18
8.5	even	2	inner	552.2.f.c.277.3	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.f.c.277.3	✓	18	8.5	even	2	inner
552.2.f.c.277.4	yes	18	1.1	even	1	trivial
2208.2.f.c.1105.9		18	8.3	odd	2
2208.2.f.c.1105.10		18	4.3	odd	2

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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.15934 + 0.809892i) q^{2} -1.00000i q^{3} +(0.688150 - 1.87788i) q^{4} -3.56420i q^{5} +(0.809892 + 1.15934i) q^{6} -2.96155 q^{7} +(0.723081 + 2.73444i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(-1.15934 + 0.809892i) q^{2} -1.00000i q^{3} +(0.688150 - 1.87788i) q^{4} -3.56420i q^{5} +(0.809892 + 1.15934i) q^{6} -2.96155 q^{7} +(0.723081 + 2.73444i) q^{8} -1.00000 q^{9} +(2.88661 + 4.13212i) q^{10} -2.43741i q^{11} +(-1.87788 - 0.688150i) q^{12} -2.03973i q^{13} +(3.43345 - 2.39853i) q^{14} -3.56420 q^{15} +(-3.05290 - 2.58453i) q^{16} +2.92323 q^{17} +(1.15934 - 0.809892i) q^{18} +5.23284i q^{19} +(-6.69315 - 2.45270i) q^{20} +2.96155i q^{21} +(1.97404 + 2.82579i) q^{22} -1.00000 q^{23} +(2.73444 - 0.723081i) q^{24} -7.70349 q^{25} +(1.65196 + 2.36475i) q^{26} +1.00000i q^{27} +(-2.03799 + 5.56144i) q^{28} -0.531515i q^{29} +(4.13212 - 2.88661i) q^{30} -10.1583 q^{31} +(5.63255 + 0.523843i) q^{32} -2.43741 q^{33} +(-3.38903 + 2.36750i) q^{34} +10.5555i q^{35} +(-0.688150 + 1.87788i) q^{36} +9.71912i q^{37} +(-4.23803 - 6.06665i) q^{38} -2.03973 q^{39} +(9.74607 - 2.57720i) q^{40} -3.68527 q^{41} +(-2.39853 - 3.43345i) q^{42} +1.24541i q^{43} +(-4.57717 - 1.67730i) q^{44} +3.56420i q^{45} +(1.15934 - 0.809892i) q^{46} +4.08428 q^{47} +(-2.58453 + 3.05290i) q^{48} +1.77077 q^{49} +(8.93099 - 6.23900i) q^{50} -2.92323i q^{51} +(-3.83038 - 1.40364i) q^{52} -13.3601i q^{53} +(-0.809892 - 1.15934i) q^{54} -8.68739 q^{55} +(-2.14144 - 8.09817i) q^{56} +5.23284 q^{57} +(0.430470 + 0.616208i) q^{58} -9.85521i q^{59} +(-2.45270 + 6.69315i) q^{60} -14.6238i q^{61} +(11.7769 - 8.22711i) q^{62} +2.96155 q^{63} +(-6.95431 + 3.95444i) q^{64} -7.27000 q^{65} +(2.82579 - 1.97404i) q^{66} +3.93132i q^{67} +(2.01162 - 5.48949i) q^{68} +1.00000i q^{69} +(-8.54884 - 12.2375i) q^{70} +5.93337 q^{71} +(-0.723081 - 2.73444i) q^{72} +3.85533 q^{73} +(-7.87143 - 11.2678i) q^{74} +7.70349i q^{75} +(9.82667 + 3.60098i) q^{76} +7.21849i q^{77} +(2.36475 - 1.65196i) q^{78} -7.13941 q^{79} +(-9.21178 + 10.8811i) q^{80} +1.00000 q^{81} +(4.27249 - 2.98467i) q^{82} +13.1885i q^{83} +(5.56144 + 2.03799i) q^{84} -10.4190i q^{85} +(-1.00865 - 1.44385i) q^{86} -0.531515 q^{87} +(6.66494 - 1.76244i) q^{88} -10.0810 q^{89} +(-2.88661 - 4.13212i) q^{90} +6.04076i q^{91} +(-0.688150 + 1.87788i) q^{92} +10.1583i q^{93} +(-4.73508 + 3.30783i) q^{94} +18.6509 q^{95} +(0.523843 - 5.63255i) q^{96} +9.43058 q^{97} +(-2.05292 + 1.43413i) q^{98} +2.43741i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 8 q^{4} + 8 q^{7} - 6 q^{8} - 18 q^{9}+O(q^{10}) \) 18 * q - 8 * q^4 + 8 * q^7 - 6 * q^8 - 18 * q^9	\( 18 q - 8 q^{4} + 8 q^{7} - 6 q^{8} - 18 q^{9} + 12 q^{10} - 4 q^{12} - 14 q^{14} + 8 q^{15} + 12 q^{16} - 8 q^{17} - 16 q^{20} - 30 q^{22} - 18 q^{23} + 6 q^{24} - 22 q^{25} + 8 q^{26} - 2 q^{28} + 4 q^{30} - 44 q^{31} + 10 q^{32} - 24 q^{33} + 18 q^{34} + 8 q^{36} - 20 q^{38} - 8 q^{39} + 40 q^{40} + 28 q^{41} + 6 q^{42} - 26 q^{44} + 42 q^{49} + 60 q^{50} - 36 q^{52} + 40 q^{55} - 2 q^{56} + 12 q^{57} + 52 q^{58} + 16 q^{60} + 24 q^{62} - 8 q^{63} + 16 q^{64} - 104 q^{65} + 2 q^{66} + 54 q^{68} - 48 q^{70} - 24 q^{71} + 6 q^{72} + 12 q^{73} - 22 q^{74} - 4 q^{78} + 8 q^{79} - 32 q^{80} + 18 q^{81} - 20 q^{82} + 34 q^{84} + 12 q^{87} + 10 q^{88} + 24 q^{89} - 12 q^{90} + 8 q^{92} - 56 q^{94} - 16 q^{95} - 30 q^{96} + 12 q^{97} - 48 q^{98}+O(q^{100}) \) 18 * q - 8 * q^4 + 8 * q^7 - 6 * q^8 - 18 * q^9 + 12 * q^10 - 4 * q^12 - 14 * q^14 + 8 * q^15 + 12 * q^16 - 8 * q^17 - 16 * q^20 - 30 * q^22 - 18 * q^23 + 6 * q^24 - 22 * q^25 + 8 * q^26 - 2 * q^28 + 4 * q^30 - 44 * q^31 + 10 * q^32 - 24 * q^33 + 18 * q^34 + 8 * q^36 - 20 * q^38 - 8 * q^39 + 40 * q^40 + 28 * q^41 + 6 * q^42 - 26 * q^44 + 42 * q^49 + 60 * q^50 - 36 * q^52 + 40 * q^55 - 2 * q^56 + 12 * q^57 + 52 * q^58 + 16 * q^60 + 24 * q^62 - 8 * q^63 + 16 * q^64 - 104 * q^65 + 2 * q^66 + 54 * q^68 - 48 * q^70 - 24 * q^71 + 6 * q^72 + 12 * q^73 - 22 * q^74 - 4 * q^78 + 8 * q^79 - 32 * q^80 + 18 * q^81 - 20 * q^82 + 34 * q^84 + 12 * q^87 + 10 * q^88 + 24 * q^89 - 12 * q^90 + 8 * q^92 - 56 * q^94 - 16 * q^95 - 30 * q^96 + 12 * q^97 - 48 * q^98

Introduction

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