LMFDB - Embedded newform 418.2.f.b.191.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(115,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("418.115");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.f (of order $5$, degree $4$, 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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			191.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	418.191
Dual form			418.2.f.b.267.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(3.11803 - 2.26538i) q^{5} +(0.190983 + 0.587785i) q^{7} +(0.309017 - 0.951057i) q^{8} +(2.42705 + 1.76336i) q^{9} +O(q^{10})$	\(q+(-0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(3.11803 - 2.26538i) q^{5} +(0.190983 + 0.587785i) q^{7} +(0.309017 - 0.951057i) q^{8} +(2.42705 + 1.76336i) q^{9} -3.85410 q^{10} +(2.54508 + 2.12663i) q^{11} +(-2.00000 - 1.45309i) q^{13} +(0.190983 - 0.587785i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(-3.30902 + 2.40414i) q^{17} +(-0.927051 - 2.85317i) q^{18} +(0.309017 - 0.951057i) q^{19} +(3.11803 + 2.26538i) q^{20} +(-0.809017 - 3.21644i) q^{22} +1.14590 q^{23} +(3.04508 - 9.37181i) q^{25} +(0.763932 + 2.35114i) q^{26} +(-0.500000 + 0.363271i) q^{28} +(0.381966 + 1.17557i) q^{29} +(4.61803 + 3.35520i) q^{31} +1.00000 q^{32} +4.09017 q^{34} +(1.92705 + 1.40008i) q^{35} +(-0.927051 + 2.85317i) q^{36} +(-2.85410 - 8.78402i) q^{37} +(-0.809017 + 0.587785i) q^{38} +(-1.19098 - 3.66547i) q^{40} +(3.23607 - 9.95959i) q^{41} -1.61803 q^{43} +(-1.23607 + 3.07768i) q^{44} +11.5623 q^{45} +(-0.927051 - 0.673542i) q^{46} +(-3.59017 + 11.0494i) q^{47} +(5.35410 - 3.88998i) q^{49} +(-7.97214 + 5.79210i) q^{50} +(0.763932 - 2.35114i) q^{52} +(-1.61803 - 1.17557i) q^{53} +(12.7533 + 0.865300i) q^{55} +0.618034 q^{56} +(0.381966 - 1.17557i) q^{58} +(-3.09017 - 9.51057i) q^{59} +(-8.16312 + 5.93085i) q^{61} +(-1.76393 - 5.42882i) q^{62} +(-0.572949 + 1.76336i) q^{63} +(-0.809017 - 0.587785i) q^{64} -9.52786 q^{65} -8.00000 q^{67} +(-3.30902 - 2.40414i) q^{68} +(-0.736068 - 2.26538i) q^{70} +(-6.85410 + 4.97980i) q^{71} +(2.42705 - 1.76336i) q^{72} +(-2.61803 - 8.05748i) q^{73} +(-2.85410 + 8.78402i) q^{74} +1.00000 q^{76} +(-0.763932 + 1.90211i) q^{77} +(9.70820 + 7.05342i) q^{79} +(-1.19098 + 3.66547i) q^{80} +(2.78115 + 8.55951i) q^{81} +(-8.47214 + 6.15537i) q^{82} +(-3.11803 + 2.26538i) q^{83} +(-4.87132 + 14.9924i) q^{85} +(1.30902 + 0.951057i) q^{86} +(2.80902 - 1.76336i) q^{88} -14.1803 q^{89} +(-9.35410 - 6.79615i) q^{90} +(0.472136 - 1.45309i) q^{91} +(0.354102 + 1.08981i) q^{92} +(9.39919 - 6.82891i) q^{94} +(-1.19098 - 3.66547i) q^{95} +(6.09017 + 4.42477i) q^{97} -6.61803 q^{98} +(2.42705 + 9.64932i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} - q^{4} + 8 q^{5} + 3 q^{7} - q^{8} + 3 q^{9}+O(q^{10}) $ 4 * q - q^2 - q^4 + 8 * q^5 + 3 * q^7 - q^8 + 3 * q^9	$ 4 q - q^{2} - q^{4} + 8 q^{5} + 3 q^{7} - q^{8} + 3 q^{9} - 2 q^{10} - q^{11} - 8 q^{13} + 3 q^{14} - q^{16} - 11 q^{17} + 3 q^{18} - q^{19} + 8 q^{20} - q^{22} + 18 q^{23} + q^{25} + 12 q^{26} - 2 q^{28} + 6 q^{29} + 14 q^{31} + 4 q^{32} - 6 q^{34} + q^{35} + 3 q^{36} + 2 q^{37} - q^{38} - 7 q^{40} + 4 q^{41} - 2 q^{43} + 4 q^{44} + 6 q^{45} + 3 q^{46} + 8 q^{47} + 8 q^{49} - 14 q^{50} + 12 q^{52} - 2 q^{53} + 13 q^{55} - 2 q^{56} + 6 q^{58} + 10 q^{59} - 17 q^{61} - 16 q^{62} - 9 q^{63} - q^{64} - 56 q^{65} - 32 q^{67} - 11 q^{68} + 6 q^{70} - 14 q^{71} + 3 q^{72} - 6 q^{73} + 2 q^{74} + 4 q^{76} - 12 q^{77} + 12 q^{79} - 7 q^{80} - 9 q^{81} - 16 q^{82} - 8 q^{83} + 23 q^{85} + 3 q^{86} + 9 q^{88} - 12 q^{89} - 24 q^{90} - 16 q^{91} - 12 q^{92} + 13 q^{94} - 7 q^{95} + 2 q^{97} - 22 q^{98} + 3 q^{99}+O(q^{100}) $ 4 * q - q^2 - q^4 + 8 * q^5 + 3 * q^7 - q^8 + 3 * q^9 - 2 * q^10 - q^11 - 8 * q^13 + 3 * q^14 - q^16 - 11 * q^17 + 3 * q^18 - q^19 + 8 * q^20 - q^22 + 18 * q^23 + q^25 + 12 * q^26 - 2 * q^28 + 6 * q^29 + 14 * q^31 + 4 * q^32 - 6 * q^34 + q^35 + 3 * q^36 + 2 * q^37 - q^38 - 7 * q^40 + 4 * q^41 - 2 * q^43 + 4 * q^44 + 6 * q^45 + 3 * q^46 + 8 * q^47 + 8 * q^49 - 14 * q^50 + 12 * q^52 - 2 * q^53 + 13 * q^55 - 2 * q^56 + 6 * q^58 + 10 * q^59 - 17 * q^61 - 16 * q^62 - 9 * q^63 - q^64 - 56 * q^65 - 32 * q^67 - 11 * q^68 + 6 * q^70 - 14 * q^71 + 3 * q^72 - 6 * q^73 + 2 * q^74 + 4 * q^76 - 12 * q^77 + 12 * q^79 - 7 * q^80 - 9 * q^81 - 16 * q^82 - 8 * q^83 + 23 * q^85 + 3 * q^86 + 9 * q^88 - 12 * q^89 - 24 * q^90 - 16 * q^91 - 12 * q^92 + 13 * q^94 - 7 * q^95 + 2 * q^97 - 22 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$3$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$3$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	3.11803	−	2.26538i	1.39443	−	1.01311i	0.399064	−	0.916923i	$-0.369335\pi$
$5$	3.11803	−	2.26538i	1.39443	−	1.01311i	0.995363	−	0.0961876i	$-0.0306649\pi$
$6$		0			0
$7$	0.190983	+	0.587785i	0.0721848	+	0.222162i	0.980640	−	0.195821i	$-0.0627372\pi$
$7$	0.190983	+	0.587785i	0.0721848	+	0.222162i	−0.908455	+	0.417983i	$0.862737\pi$
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	2.42705	+	1.76336i	0.809017	+	0.587785i
$10$	−3.85410			−1.21877
$11$	2.54508	+	2.12663i	0.767372	+	0.641202i
$11$	2.54508	+	2.12663i	0.767372	+	0.641202i
$12$		0			0
$13$	−2.00000	−	1.45309i	−0.554700	−	0.403013i	0.274815	−	0.961497i	$-0.411383\pi$
$13$	−2.00000	−	1.45309i	−0.554700	−	0.403013i	−0.829515	+	0.558484i	$0.811383\pi$
$14$	0.190983	−	0.587785i	0.0510424	−	0.157092i
$15$		0			0
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−3.30902	+	2.40414i	−0.802555	+	0.583090i	−0.911662	−	0.410940i	$-0.865201\pi$
$17$	−3.30902	+	2.40414i	−0.802555	+	0.583090i	0.109108	+	0.994030i	$0.465201\pi$
$18$	−0.927051	−	2.85317i	−0.218508	−	0.672499i
$19$	0.309017	−	0.951057i	0.0708934	−	0.218187i
$19$	0.309017	−	0.951057i	0.0708934	−	0.218187i
$20$	3.11803	+	2.26538i	0.697214	+	0.506555i
$21$		0			0
$22$	−0.809017	−	3.21644i	−0.172483	−	0.685747i
$23$	1.14590			0.238936			0.119468	−	0.992838i	$-0.461881\pi$
$23$	1.14590			0.238936			0.119468	+	0.992838i	$0.461881\pi$
$24$		0			0
$25$	3.04508	−	9.37181i	0.609017	−	1.87436i
$26$	0.763932	+	2.35114i	0.149819	+	0.461097i
$27$		0			0
$28$	−0.500000	+	0.363271i	−0.0944911	+	0.0686518i
$29$	0.381966	+	1.17557i	0.0709293	+	0.218298i	0.980237	−	0.197826i	$-0.0633882\pi$
$29$	0.381966	+	1.17557i	0.0709293	+	0.218298i	−0.909308	+	0.416124i	$0.863388\pi$
$30$		0			0
$31$	4.61803	+	3.35520i	0.829423	+	0.602611i	0.919396	−	0.393333i	$-0.128678\pi$
$31$	4.61803	+	3.35520i	0.829423	+	0.602611i	−0.0899727	+	0.995944i	$0.528678\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	4.09017			0.701458
$35$	1.92705	+	1.40008i	0.325731	+	0.236657i
$36$	−0.927051	+	2.85317i	−0.154508	+	0.475528i
$37$	−2.85410	−	8.78402i	−0.469211	−	1.44408i	−0.853608	−	0.520916i	$-0.825590\pi$
$37$	−2.85410	−	8.78402i	−0.469211	−	1.44408i	0.384396	−	0.923168i	$-0.374410\pi$
$38$	−0.809017	+	0.587785i	−0.131240	+	0.0953514i
$39$		0			0
$40$	−1.19098	−	3.66547i	−0.188311	−	0.579562i
$41$	3.23607	−	9.95959i	0.505389	−	1.55543i	−0.294727	−	0.955582i	$-0.595229\pi$
$41$	3.23607	−	9.95959i	0.505389	−	1.55543i	0.800116	−	0.599846i	$-0.204771\pi$
$42$		0			0
$43$	−1.61803			−0.246748			−0.123374	−	0.992360i	$-0.539371\pi$
$43$	−1.61803			−0.246748			−0.123374	+	0.992360i	$0.539371\pi$
$44$	−1.23607	+	3.07768i	−0.186344	+	0.463978i
$45$	11.5623			1.72361
$46$	−0.927051	−	0.673542i	−0.136686	−	0.0993083i
$47$	−3.59017	+	11.0494i	−0.523680	+	1.61172i	0.243231	+	0.969968i	$0.421793\pi$
$47$	−3.59017	+	11.0494i	−0.523680	+	1.61172i	−0.766911	+	0.641753i	$0.778207\pi$
$48$		0			0
$49$	5.35410	−	3.88998i	0.764872	−	0.555712i
$50$	−7.97214	+	5.79210i	−1.12743	+	0.819126i
$51$		0			0
$52$	0.763932	−	2.35114i	0.105938	−	0.326045i
$53$	−1.61803	−	1.17557i	−0.222254	−	0.161477i	0.471087	−	0.882087i	$-0.343862\pi$
$53$	−1.61803	−	1.17557i	−0.222254	−	0.161477i	−0.693341	+	0.720610i	$0.743862\pi$
$54$		0			0
$55$	12.7533	+	0.865300i	1.71965	+	0.116677i
$56$	0.618034			0.0825883
$57$		0			0
$58$	0.381966	−	1.17557i	0.0501546	−	0.154360i
$59$	−3.09017	−	9.51057i	−0.402306	−	1.23817i	−0.923124	−	0.384502i	$-0.874373\pi$
$59$	−3.09017	−	9.51057i	−0.402306	−	1.23817i	0.520818	−	0.853668i	$-0.325627\pi$
$60$		0			0
$61$	−8.16312	+	5.93085i	−1.04518	+	0.759368i	−0.971290	−	0.237898i	$-0.923541\pi$
$61$	−8.16312	+	5.93085i	−1.04518	+	0.759368i	−0.0738903	+	0.997266i	$0.523541\pi$
$62$	−1.76393	−	5.42882i	−0.224020	−	0.689461i
$63$	−0.572949	+	1.76336i	−0.0721848	+	0.222162i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−9.52786			−1.18179
$66$		0			0
$67$	−8.00000			−0.977356			−0.488678	−	0.872464i	$-0.662521\pi$
$67$	−8.00000			−0.977356			−0.488678	+	0.872464i	$0.662521\pi$
$68$	−3.30902	−	2.40414i	−0.401277	−	0.291545i
$69$		0			0
$70$	−0.736068	−	2.26538i	−0.0879770	−	0.270765i
$71$	−6.85410	+	4.97980i	−0.813432	+	0.590993i	−0.914824	−	0.403853i	$-0.867671\pi$
$71$	−6.85410	+	4.97980i	−0.813432	+	0.590993i	0.101391	+	0.994847i	$0.467671\pi$
$72$	2.42705	−	1.76336i	0.286031	−	0.207813i
$73$	−2.61803	−	8.05748i	−0.306418	−	0.943057i	−0.979144	−	0.203166i	$-0.934877\pi$
$73$	−2.61803	−	8.05748i	−0.306418	−	0.943057i	0.672727	−	0.739891i	$-0.265123\pi$
$74$	−2.85410	+	8.78402i	−0.331783	+	1.02112i
$75$		0			0
$76$	1.00000			0.114708
$77$	−0.763932	+	1.90211i	−0.0870581	+	0.216766i
$78$		0			0
$79$	9.70820	+	7.05342i	1.09226	+	0.793572i	0.979779	−	0.200082i	$-0.0641209\pi$
$79$	9.70820	+	7.05342i	1.09226	+	0.793572i	0.112479	+	0.993654i	$0.464121\pi$
$80$	−1.19098	+	3.66547i	−0.133156	+	0.409812i
$81$	2.78115	+	8.55951i	0.309017	+	0.951057i
$82$	−8.47214	+	6.15537i	−0.935591	+	0.679747i
$83$	−3.11803	+	2.26538i	−0.342249	+	0.248658i	−0.745610	−	0.666383i	$-0.767842\pi$
$83$	−3.11803	+	2.26538i	−0.342249	+	0.248658i	0.403361	+	0.915041i	$0.367842\pi$
$84$		0			0
$85$	−4.87132	+	14.9924i	−0.528369	+	1.62615i
$86$	1.30902	+	0.951057i	0.141155	+	0.102555i
$87$		0			0
$88$	2.80902	−	1.76336i	0.299442	−	0.187974i
$89$	−14.1803			−1.50311			−0.751557	−	0.659669i	$-0.770697\pi$
$89$	−14.1803			−1.50311			−0.751557	+	0.659669i	$0.770697\pi$
$90$	−9.35410	−	6.79615i	−0.986009	−	0.716377i
$91$	0.472136	−	1.45309i	0.0494933	−	0.152325i
$92$	0.354102	+	1.08981i	0.0369177	+	0.113621i
$93$		0			0
$94$	9.39919	−	6.82891i	0.969452	−	0.704348i
$95$	−1.19098	−	3.66547i	−0.122192	−	0.376069i
$96$		0			0
$97$	6.09017	+	4.42477i	0.618363	+	0.449267i	0.852349	−	0.522973i	$-0.175177\pi$
$97$	6.09017	+	4.42477i	0.618363	+	0.449267i	−0.233986	+	0.972240i	$0.575177\pi$
$98$	−6.61803			−0.668522
$99$	2.42705	+	9.64932i	0.243928	+	0.969793i
$100$	9.85410			0.985410
$101$	−1.11803	−	0.812299i	−0.111249	−	0.0808268i	0.530770	−	0.847516i	$-0.321903\pi$
$101$	−1.11803	−	0.812299i	−0.111249	−	0.0808268i	−0.642019	+	0.766689i	$0.721903\pi$
$102$		0			0
$103$	2.29180	+	7.05342i	0.225817	+	0.694994i	0.998208	+	0.0598462i	$0.0190610\pi$
$103$	2.29180	+	7.05342i	0.225817	+	0.694994i	−0.772390	+	0.635148i	$0.780939\pi$
$104$	−2.00000	+	1.45309i	−0.196116	+	0.142487i
$105$		0			0
$106$	0.618034	+	1.90211i	0.0600288	+	0.184750i
$107$	−2.85410	+	8.78402i	−0.275916	+	0.849184i	0.713059	+	0.701104i	$0.247309\pi$
$107$	−2.85410	+	8.78402i	−0.275916	+	0.849184i	−0.988975	+	0.148079i	$0.952691\pi$
$108$		0			0
$109$	1.70820			0.163616			0.0818081	−	0.996648i	$-0.473931\pi$
$109$	1.70820			0.163616			0.0818081	+	0.996648i	$0.473931\pi$
$110$	−9.80902	−	8.19624i	−0.935253	−	0.781481i
$111$		0			0
$112$	−0.500000	−	0.363271i	−0.0472456	−	0.0343259i
$113$	−4.23607	+	13.0373i	−0.398496	+	1.22644i	0.527710	+	0.849425i	$0.323051\pi$
$113$	−4.23607	+	13.0373i	−0.398496	+	1.22644i	−0.926205	+	0.377019i	$0.876949\pi$
$114$		0			0
$115$	3.57295	−	2.59590i	0.333179	−	0.242069i
$116$	−1.00000	+	0.726543i	−0.0928477	+	0.0674578i
$117$	−2.29180	−	7.05342i	−0.211877	−	0.652089i
$118$	−3.09017	+	9.51057i	−0.284473	+	0.875518i
$119$	−2.04508	−	1.48584i	−0.187473	−	0.136207i
$120$		0			0
$121$	1.95492	+	10.8249i	0.177720	+	0.984081i
$122$	10.0902			0.913521
$123$		0			0
$124$	−1.76393	+	5.42882i	−0.158406	+	0.487523i
$125$	−5.78115	−	17.7926i	−0.517082	−	1.59141i
$126$	1.50000	−	1.08981i	0.133631	−	0.0970883i
$127$	4.23607	−	3.07768i	0.375890	−	0.273100i	−0.383759	−	0.923433i	$-0.625371\pi$
$127$	4.23607	−	3.07768i	0.375890	−	0.273100i	0.759649	+	0.650333i	$0.225371\pi$
$128$	0.309017	+	0.951057i	0.0273135	+	0.0840623i
$129$		0			0
$130$	7.70820	+	5.60034i	0.676054	+	0.491182i
$131$	−6.32624			−0.552726			−0.276363	−	0.961053i	$-0.589129\pi$
$131$	−6.32624			−0.552726			−0.276363	+	0.961053i	$0.589129\pi$
$132$		0			0
$133$	0.618034			0.0535903
$134$	6.47214	+	4.70228i	0.559107	+	0.406215i
$135$		0			0
$136$	1.26393	+	3.88998i	0.108381	+	0.333563i
$137$	13.4443	−	9.76784i	1.14862	−	0.834522i	0.160325	−	0.987064i	$-0.448746\pi$
$137$	13.4443	−	9.76784i	1.14862	−	0.834522i	0.988297	+	0.152542i	$0.0487459\pi$
$138$		0			0
$139$	−5.97214	−	18.3803i	−0.506550	−	1.55900i	−0.798149	−	0.602460i	$-0.794187\pi$
$139$	−5.97214	−	18.3803i	−0.506550	−	1.55900i	0.291599	−	0.956541i	$-0.405813\pi$
$140$	−0.736068	+	2.26538i	−0.0622091	+	0.191460i
$141$		0			0
$142$	8.47214			0.710966
$143$	−2.00000	−	7.95148i	−0.167248	−	0.664936i
$144$	−3.00000			−0.250000
$145$	3.85410	+	2.80017i	0.320066	+	0.232541i
$146$	−2.61803	+	8.05748i	−0.216670	+	0.666842i
$147$		0			0
$148$	7.47214	−	5.42882i	0.614206	−	0.446247i
$149$	−10.8541	+	7.88597i	−0.889203	+	0.646044i	−0.935670	−	0.352876i	$-0.885204\pi$
$149$	−10.8541	+	7.88597i	−0.889203	+	0.646044i	0.0464673	+	0.998920i	$0.485204\pi$
$150$		0			0
$151$	−4.38197	+	13.4863i	−0.356599	+	1.09750i	0.598477	+	0.801140i	$0.295773\pi$
$151$	−4.38197	+	13.4863i	−0.356599	+	1.09750i	−0.955076	+	0.296360i	$0.904227\pi$
$152$	−0.809017	−	0.587785i	−0.0656199	−	0.0476757i
$153$	−12.2705			−0.992012
$154$	1.73607	−	1.08981i	0.139896	−	0.0878197i
$155$	22.0000			1.76708
$156$		0			0
$157$	0.135255	−	0.416272i	0.0107945	−	0.0332221i	−0.945514	−	0.325581i	$-0.894440\pi$
$157$	0.135255	−	0.416272i	0.0107945	−	0.0332221i	0.956309	+	0.292359i	$0.0944401\pi$
$158$	−3.70820	−	11.4127i	−0.295009	−	0.907944i
$159$		0			0
$160$	3.11803	−	2.26538i	0.246502	−	0.179094i
$161$	0.218847	+	0.673542i	0.0172476	+	0.0530825i
$162$	2.78115	−	8.55951i	0.218508	−	0.672499i
$163$	−20.2984	−	14.7476i	−1.58989	−	1.15512i	−0.904096	−	0.427329i	$-0.859455\pi$
$163$	−20.2984	−	14.7476i	−1.58989	−	1.15512i	−0.685795	−	0.727795i	$-0.740545\pi$
$164$	10.4721			0.817736
$165$		0			0
$166$	3.85410			0.299136
$167$	−6.47214	−	4.70228i	−0.500829	−	0.363874i	0.308505	−	0.951223i	$-0.400171\pi$
$167$	−6.47214	−	4.70228i	−0.500829	−	0.363874i	−0.809334	+	0.587349i	$0.800171\pi$
$168$		0			0
$169$	−2.12868	−	6.55139i	−0.163744	−	0.503953i
$170$	12.7533	−	9.26581i	0.978133	−	0.710655i
$171$	2.42705	−	1.76336i	0.185601	−	0.134847i
$172$	−0.500000	−	1.53884i	−0.0381246	−	0.117336i
$173$	−6.00000	+	18.4661i	−0.456172	+	1.40395i	0.413583	+	0.910467i	$0.364277\pi$
$173$	−6.00000	+	18.4661i	−0.456172	+	1.40395i	−0.869754	+	0.493485i	$0.835723\pi$
$174$		0			0
$175$	6.09017			0.460374
$176$	−3.30902	−	0.224514i	−0.249427	−	0.0169234i
$177$		0			0
$178$	11.4721	+	8.33499i	0.859873	+	0.624734i
$179$	2.23607	−	6.88191i	0.167132	−	0.514378i	−0.832055	−	0.554692i	$-0.812836\pi$
$179$	2.23607	−	6.88191i	0.167132	−	0.514378i	0.999187	+	0.0403143i	$0.0128359\pi$
$180$	3.57295	+	10.9964i	0.266312	+	0.819624i
$181$	10.2361	−	7.43694i	0.760841	−	0.552783i	−0.138327	−	0.990387i	$-0.544173\pi$
$181$	10.2361	−	7.43694i	0.760841	−	0.552783i	0.899168	+	0.437603i	$0.144173\pi$
$182$	−1.23607	+	0.898056i	−0.0916235	+	0.0665683i
$183$		0			0
$184$	0.354102	−	1.08981i	0.0261047	−	0.0803421i
$185$	−28.7984	−	20.9232i	−2.11730	−	1.53831i
$186$		0			0
$187$	−13.5344	−	0.918300i	−0.989736	−	0.0671528i
$188$	−11.6180			−0.847332
$189$		0			0
$190$	−1.19098	+	3.66547i	−0.0864030	+	0.265921i
$191$	2.95492	+	9.09429i	0.213810	+	0.658040i	0.999236	+	0.0390841i	$0.0124440\pi$
$191$	2.95492	+	9.09429i	0.213810	+	0.658040i	−0.785426	+	0.618956i	$0.787556\pi$
$192$		0			0
$193$	−1.61803	+	1.17557i	−0.116469	+	0.0846194i	−0.644495	−	0.764609i	$-0.722932\pi$
$193$	−1.61803	+	1.17557i	−0.116469	+	0.0846194i	0.528026	+	0.849228i	$0.322932\pi$
$194$	−2.32624	−	7.15942i	−0.167014	−	0.514017i
$195$		0			0
$196$	5.35410	+	3.88998i	0.382436	+	0.277856i
$197$	7.52786			0.536338			0.268169	−	0.963372i	$-0.413581\pi$
$197$	7.52786			0.536338			0.268169	+	0.963372i	$0.413581\pi$
$198$	3.70820	−	9.23305i	0.263531	−	0.656164i
$199$	4.61803			0.327364			0.163682	−	0.986513i	$-0.447663\pi$
$199$	4.61803			0.327364			0.163682	+	0.986513i	$0.447663\pi$
$200$	−7.97214	−	5.79210i	−0.563715	−	0.409563i
$201$		0			0
$202$	0.427051	+	1.31433i	0.0300472	+	0.0924758i
$203$	−0.618034	+	0.449028i	−0.0433775	+	0.0315156i
$204$		0			0
$205$	−12.4721	−	38.3853i	−0.871092	−	2.68094i
$206$	2.29180	−	7.05342i	0.159677	−	0.491435i
$207$	2.78115	+	2.02063i	0.193303	+	0.140443i
$208$	2.47214			0.171412
$209$	2.80902	−	1.76336i	0.194304	−	0.121974i
$210$		0			0
$211$	13.8541	+	10.0656i	0.953756	+	0.692944i	0.951692	−	0.307054i	$-0.0993432\pi$
$211$	13.8541	+	10.0656i	0.953756	+	0.692944i	0.00206355	+	0.999998i	$0.499343\pi$
$212$	0.618034	−	1.90211i	0.0424467	−	0.130638i
$213$		0			0
$214$	7.47214	−	5.42882i	0.510785	−	0.371107i
$215$	−5.04508	+	3.66547i	−0.344072	+	0.249983i
$216$		0			0
$217$	−1.09017	+	3.35520i	−0.0740056	+	0.227766i
$218$	−1.38197	−	1.00406i	−0.0935985	−	0.0680033i
$219$		0			0
$220$	3.11803	+	12.3965i	0.210218	+	0.835771i
$221$	10.1115			0.680170
$222$		0			0
$223$	1.38197	−	4.25325i	0.0925433	−	0.284819i	−0.894062	−	0.447943i	$-0.852157\pi$
$223$	1.38197	−	4.25325i	0.0925433	−	0.284819i	0.986606	+	0.163124i	$0.0521569\pi$
$224$	0.190983	+	0.587785i	0.0127606	+	0.0392731i
$225$	23.9164	−	17.3763i	1.59443	−	1.15842i
$226$	11.0902	−	8.05748i	0.737707	−	0.535976i
$227$	3.56231	+	10.9637i	0.236439	+	0.727683i	0.996927	+	0.0783320i	$0.0249594\pi$
$227$	3.56231	+	10.9637i	0.236439	+	0.727683i	−0.760489	+	0.649351i	$0.775041\pi$
$228$		0			0
$229$	0.454915	+	0.330515i	0.0300616	+	0.0218411i	0.602715	−	0.797957i	$-0.294086\pi$
$229$	0.454915	+	0.330515i	0.0300616	+	0.0218411i	−0.572653	+	0.819798i	$0.694086\pi$
$230$	−4.41641			−0.291209
$231$		0			0
$232$	1.23607			0.0811518
$233$	7.20820	+	5.23707i	0.472225	+	0.343092i	0.798308	−	0.602250i	$-0.205729\pi$
$233$	7.20820	+	5.23707i	0.472225	+	0.343092i	−0.326083	+	0.945341i	$0.605729\pi$
$234$	−2.29180	+	7.05342i	−0.149819	+	0.461097i
$235$	13.8369	+	42.5855i	0.902619	+	2.77797i
$236$	8.09017	−	5.87785i	0.526625	−	0.382616i
$237$		0			0
$238$	0.781153	+	2.40414i	0.0506346	+	0.155837i
$239$	4.88197	−	15.0251i	0.315788	−	0.971896i	−0.659641	−	0.751581i	$-0.729292\pi$
$239$	4.88197	−	15.0251i	0.315788	−	0.971896i	0.975429	−	0.220315i	$-0.0707085\pi$
$240$		0			0
$241$	9.05573			0.583331			0.291665	−	0.956520i	$-0.405791\pi$
$241$	9.05573			0.583331			0.291665	+	0.956520i	$0.405791\pi$
$242$	4.78115	−	9.90659i	0.307344	−	0.636820i
$243$		0			0
$244$	−8.16312	−	5.93085i	−0.522590	−	0.379684i
$245$	7.88197	−	24.2582i	0.503560	−	1.54980i
$246$		0			0
$247$	−2.00000	+	1.45309i	−0.127257	+	0.0924576i
$248$	4.61803	−	3.35520i	0.293245	−	0.213055i
$249$		0			0
$250$	−5.78115	+	17.7926i	−0.365632	+	1.12530i
$251$	18.8713	+	13.7108i	1.19115	+	0.865419i	0.993385	−	0.114831i	$-0.0366326\pi$
$251$	18.8713	+	13.7108i	1.19115	+	0.865419i	0.197762	+	0.980250i	$0.436633\pi$
$252$	−1.85410			−0.116797
$253$	2.91641	+	2.43690i	0.183353	+	0.153206i
$254$	−5.23607			−0.328540
$255$		0			0
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−1.76393	−	5.42882i	−0.110031	−	0.338641i	0.880847	−	0.473401i	$-0.156974\pi$
$257$	−1.76393	−	5.42882i	−0.110031	−	0.338641i	−0.990878	+	0.134760i	$0.956974\pi$
$258$		0			0
$259$	4.61803	−	3.35520i	0.286951	−	0.208482i
$260$	−2.94427	−	9.06154i	−0.182596	−	0.561973i
$261$	−1.14590	+	3.52671i	−0.0709293	+	0.218298i
$262$	5.11803	+	3.71847i	0.316193	+	0.229728i
$263$	−1.52786			−0.0942121			−0.0471061	−	0.998890i	$-0.515000\pi$
$263$	−1.52786			−0.0942121			−0.0471061	+	0.998890i	$0.515000\pi$
$264$		0			0
$265$	−7.70820			−0.473511
$266$	−0.500000	−	0.363271i	−0.0306570	−	0.0222736i
$267$		0			0
$268$	−2.47214	−	7.60845i	−0.151010	−	0.464760i
$269$	−13.2361	+	9.61657i	−0.807017	+	0.586332i	−0.912964	−	0.408039i	$-0.866213\pi$
$269$	−13.2361	+	9.61657i	−0.807017	+	0.586332i	0.105947	+	0.994372i	$0.466213\pi$
$270$		0			0
$271$	−4.35410	−	13.4005i	−0.264493	−	0.814025i	−0.991810	−	0.127724i	$-0.959233\pi$
$271$	−4.35410	−	13.4005i	−0.264493	−	0.814025i	0.727317	−	0.686302i	$-0.240767\pi$
$272$	1.26393	−	3.88998i	0.0766371	−	0.235865i
$273$		0			0
$274$	−16.6180			−1.00393
$275$	27.6803	−	17.3763i	1.66919	−	1.04783i
$276$		0			0
$277$	17.7984	+	12.9313i	1.06940	+	0.776965i	0.975804	−	0.218645i	$-0.0701637\pi$
$277$	17.7984	+	12.9313i	1.06940	+	0.776965i	0.0935962	+	0.995610i	$0.470164\pi$
$278$	−5.97214	+	18.3803i	−0.358185	+	1.10238i
$279$	5.29180	+	16.2865i	0.316812	+	0.975046i
$280$	1.92705	−	1.40008i	0.115163	−	0.0836711i
$281$	−17.0902	+	12.4167i	−1.01951	+	0.740720i	−0.966183	−	0.257857i	$-0.916984\pi$
$281$	−17.0902	+	12.4167i	−1.01951	+	0.740720i	−0.0533309	+	0.998577i	$0.516984\pi$
$282$		0			0
$283$	8.42705	−	25.9358i	0.500936	−	1.54172i	−0.306561	−	0.951851i	$-0.599178\pi$
$283$	8.42705	−	25.9358i	0.500936	−	1.54172i	0.807497	−	0.589872i	$-0.200822\pi$
$284$	−6.85410	−	4.97980i	−0.406716	−	0.295497i
$285$		0			0
$286$	−3.05573	+	7.60845i	−0.180689	+	0.449897i
$287$	6.47214			0.382038
$288$	2.42705	+	1.76336i	0.143015	+	0.103907i
$289$	−0.0835921	+	0.257270i	−0.00491718	+	0.0151335i
$290$	−1.47214	−	4.53077i	−0.0864468	−	0.266056i
$291$		0			0
$292$	6.85410	−	4.97980i	0.401106	−	0.291421i
$293$	−0.527864	−	1.62460i	−0.0308381	−	0.0949101i	0.934453	−	0.356087i	$-0.115889\pi$
$293$	−0.527864	−	1.62460i	−0.0308381	−	0.0949101i	−0.965291	+	0.261177i	$0.915889\pi$
$294$		0			0
$295$	−31.1803	−	22.6538i	−1.81539	−	1.31896i
$296$	−9.23607			−0.536836
$297$		0			0
$298$	13.4164			0.777192
$299$	−2.29180	−	1.66509i	−0.132538	−	0.0962945i
$300$		0			0
$301$	−0.309017	−	0.951057i	−0.0178114	−	0.0548180i
$302$	11.4721	−	8.33499i	0.660147	−	0.479625i
$303$		0			0
$304$	0.309017	+	0.951057i	0.0177233	+	0.0545468i
$305$	−12.0172	+	36.9852i	−0.688104	+	2.11777i
$306$	9.92705	+	7.21242i	0.567492	+	0.412307i
$307$	−19.4164			−1.10815			−0.554076	−	0.832466i	$-0.686928\pi$
$307$	−19.4164			−1.10815			−0.554076	+	0.832466i	$0.686928\pi$
$308$	−2.04508	−	0.138757i	−0.116530	−	0.00790643i
$309$		0			0
$310$	−17.7984	−	12.9313i	−1.01088	−	0.734447i
$311$	−10.2984	+	31.6951i	−0.583967	+	1.79727i	0.0194116	+	0.999812i	$0.493821\pi$
$311$	−10.2984	+	31.6951i	−0.583967	+	1.79727i	−0.603379	+	0.797455i	$0.706179\pi$
$312$		0			0
$313$	0.836881	−	0.608030i	0.0473033	−	0.0343679i	−0.563882	−	0.825855i	$-0.690693\pi$
$313$	0.836881	−	0.608030i	0.0473033	−	0.0343679i	0.611186	+	0.791487i	$0.290693\pi$
$314$	−0.354102	+	0.257270i	−0.0199831	+	0.0145186i
$315$	2.20820	+	6.79615i	0.124418	+	0.382920i
$316$	−3.70820	+	11.4127i	−0.208603	+	0.642013i
$317$	−12.4721	−	9.06154i	−0.700505	−	0.508947i	0.179592	−	0.983741i	$-0.442522\pi$
$317$	−12.4721	−	9.06154i	−0.700505	−	0.508947i	−0.880097	+	0.474795i	$0.842522\pi$
$318$		0			0
$319$	−1.52786	+	3.80423i	−0.0855440	+	0.212996i
$320$	−3.85410			−0.215451
$321$		0			0
$322$	0.218847	−	0.673542i	0.0121959	−	0.0375350i
$323$	1.26393	+	3.88998i	0.0703271	+	0.216444i
$324$	−7.28115	+	5.29007i	−0.404508	+	0.293893i
$325$	−19.7082	+	14.3188i	−1.09321	+	0.794267i
$326$	7.75329	+	23.8622i	0.429415	+	1.32160i
$327$		0			0
$328$	−8.47214	−	6.15537i	−0.467795	−	0.339873i
$329$	−7.18034			−0.395865
$330$		0			0
$331$	−16.4721			−0.905390			−0.452695	−	0.891665i	$-0.649537\pi$
$331$	−16.4721			−0.905390			−0.452695	+	0.891665i	$0.649537\pi$
$332$	−3.11803	−	2.26538i	−0.171124	−	0.124329i
$333$	8.56231	−	26.3521i	0.469211	−	1.44408i
$334$	2.47214	+	7.60845i	0.135269	+	0.416316i
$335$	−24.9443	+	18.1231i	−1.36285	+	0.990169i
$336$		0			0
$337$	−4.52786	−	13.9353i	−0.246648	−	0.759106i	−0.995361	−	0.0962111i	$-0.969328\pi$
$337$	−4.52786	−	13.9353i	−0.246648	−	0.759106i	0.748712	−	0.662895i	$-0.230672\pi$
$338$	−2.12868	+	6.55139i	−0.115785	+	0.356349i
$339$		0			0
$340$	−15.7639			−0.854919
$341$	4.61803	+	18.3601i	0.250081	+	0.994255i
$342$	−3.00000			−0.162221
$343$	6.80902	+	4.94704i	0.367652	+	0.267115i
$344$	−0.500000	+	1.53884i	−0.0269582	+	0.0829688i
$345$		0			0
$346$	15.7082	−	11.4127i	0.844478	−	0.613549i
$347$	−13.9271	+	10.1186i	−0.747643	+	0.543195i	−0.895095	−	0.445875i	$-0.852893\pi$
$347$	−13.9271	+	10.1186i	−0.747643	+	0.543195i	0.147452	+	0.989069i	$0.452893\pi$
$348$		0			0
$349$	9.66312	−	29.7400i	0.517255	−	1.59195i	−0.261887	−	0.965099i	$-0.584345\pi$
$349$	9.66312	−	29.7400i	0.517255	−	1.59195i	0.779141	−	0.626848i	$-0.215655\pi$
$350$	−4.92705	−	3.57971i	−0.263362	−	0.191344i
$351$		0			0
$352$	2.54508	+	2.12663i	0.135653	+	0.113350i
$353$	8.32624			0.443161			0.221580	−	0.975142i	$-0.428878\pi$
$353$	8.32624			0.443161			0.221580	+	0.975142i	$0.428878\pi$
$354$		0			0
$355$	−10.0902	+	31.0543i	−0.535531	+	1.64819i
$356$	−4.38197	−	13.4863i	−0.232244	−	0.714773i
$357$		0			0
$358$	−5.85410	+	4.25325i	−0.309399	+	0.224791i
$359$	0.534442	+	1.64484i	0.0282068	+	0.0868115i	0.964169	−	0.265289i	$-0.0854674\pi$
$359$	0.534442	+	1.64484i	0.0282068	+	0.0868115i	−0.935962	+	0.352101i	$0.885467\pi$
$360$	3.57295	−	10.9964i	0.188311	−	0.579562i
$361$	−0.809017	−	0.587785i	−0.0425798	−	0.0309361i
$362$	−12.6525			−0.664999
$363$		0			0
$364$	1.52786			0.0800818
$365$	−26.4164	−	19.1926i	−1.38270	−	1.00459i
$366$		0			0
$367$	0.371323	+	1.14281i	0.0193829	+	0.0596544i	0.960280	−	0.279038i	$-0.0900155\pi$
$367$	0.371323	+	1.14281i	0.0193829	+	0.0596544i	−0.940897	+	0.338692i	$0.890015\pi$
$368$	−0.927051	+	0.673542i	−0.0483259	+	0.0351108i
$369$	25.4164	−	18.4661i	1.32313	−	0.961307i
$370$	11.0000	+	33.8545i	0.571863	+	1.76001i
$371$	0.381966	−	1.17557i	0.0198307	−	0.0610326i
$372$		0			0
$373$	25.5967			1.32535			0.662675	−	0.748907i	$-0.269421\pi$
$373$	25.5967			1.32535			0.662675	+	0.748907i	$0.269421\pi$
$374$	10.4098	+	8.69827i	0.538279	+	0.449777i
$375$		0			0
$376$	9.39919	+	6.82891i	0.484726	+	0.352174i
$377$	0.944272	−	2.90617i	0.0486325	−	0.149675i
$378$		0			0
$379$	−1.23607	+	0.898056i	−0.0634925	+	0.0461300i	−0.619079	−	0.785329i	$-0.712494\pi$
$379$	−1.23607	+	0.898056i	−0.0634925	+	0.0461300i	0.555586	+	0.831459i	$0.312494\pi$
$380$	3.11803	−	2.26538i	0.159952	−	0.116212i
$381$		0			0
$382$	2.95492	−	9.09429i	0.151187	−	0.465305i
$383$	−14.9443	−	10.8576i	−0.763617	−	0.554800i	0.136401	−	0.990654i	$-0.456446\pi$
$383$	−14.9443	−	10.8576i	−0.763617	−	0.554800i	−0.900017	+	0.435854i	$0.856446\pi$
$384$		0			0
$385$	1.92705	+	7.66145i	0.0982116	+	0.390464i
$386$	2.00000			0.101797
$387$	−3.92705	−	2.85317i	−0.199623	−	0.145035i
$388$	−2.32624	+	7.15942i	−0.118097	+	0.363465i
$389$	2.35410	+	7.24518i	0.119358	+	0.367345i	0.992831	−	0.119527i	$-0.0381378\pi$
$389$	2.35410	+	7.24518i	0.119358	+	0.367345i	−0.873473	+	0.486872i	$0.838138\pi$
$390$		0			0
$391$	−3.79180	+	2.75490i	−0.191759	+	0.139321i
$392$	−2.04508	−	6.29412i	−0.103292	−	0.317901i
$393$		0			0
$394$	−6.09017	−	4.42477i	−0.306818	−	0.222917i
$395$	46.2492			2.32705
$396$	−8.42705	+	5.29007i	−0.423475	+	0.265836i
$397$	7.79837			0.391389			0.195695	−	0.980665i	$-0.437304\pi$
$397$	7.79837			0.391389			0.195695	+	0.980665i	$0.437304\pi$
$398$	−3.73607	−	2.71441i	−0.187272	−	0.136061i
$399$		0			0
$400$	3.04508	+	9.37181i	0.152254	+	0.468590i
$401$	2.76393	−	2.00811i	0.138024	−	0.100280i	−0.516631	−	0.856208i	$-0.672814\pi$
$401$	2.76393	−	2.00811i	0.138024	−	0.100280i	0.654655	+	0.755928i	$0.272814\pi$
$402$		0			0
$403$	−4.36068	−	13.4208i	−0.217221	−	0.668537i
$404$	0.427051	−	1.31433i	0.0212466	−	0.0653903i
$405$	28.0623	+	20.3885i	1.39443	+	1.01311i
$406$	0.763932			0.0379133
$407$	11.4164	−	28.4257i	0.565890	−	1.40901i
$408$		0			0
$409$	−19.1803	−	13.9353i	−0.948407	−	0.689058i	0.00202274	−	0.999998i	$-0.499356\pi$
$409$	−19.1803	−	13.9353i	−0.948407	−	0.689058i	−0.950430	+	0.310940i	$0.899356\pi$
$410$	−12.4721	+	38.3853i	−0.615955	+	1.89571i
$411$		0			0
$412$	−6.00000	+	4.35926i	−0.295599	+	0.214765i
$413$	5.00000	−	3.63271i	0.246034	−	0.178754i
$414$	−1.06231	−	3.26944i	−0.0522095	−	0.160684i
$415$	−4.59017	+	14.1271i	−0.225323	+	0.693472i
$416$	−2.00000	−	1.45309i	−0.0980581	−	0.0712434i
$417$		0			0
$418$	−3.30902	−	0.224514i	−0.161849	−	0.0109813i
$419$	12.6738			0.619154			0.309577	−	0.950874i	$-0.399813\pi$
$419$	12.6738			0.619154			0.309577	+	0.950874i	$0.399813\pi$
$420$		0			0
$421$	−7.65248	+	23.5519i	−0.372959	+	1.14785i	0.571887	+	0.820333i	$0.306212\pi$
$421$	−7.65248	+	23.5519i	−0.372959	+	1.14785i	−0.944845	+	0.327517i	$0.893788\pi$
$422$	−5.29180	−	16.2865i	−0.257601	−	0.792813i
$423$	−28.1976	+	20.4867i	−1.37101	+	0.996099i
$424$	−1.61803	+	1.17557i	−0.0785787	+	0.0570908i
$425$	12.4549	+	38.3323i	0.604152	+	1.85939i
$426$		0			0
$427$	−5.04508	−	3.66547i	−0.244149	−	0.177384i
$428$	−9.23607			−0.446442
$429$		0			0
$430$	6.23607			0.300730
$431$	22.5623	+	16.3925i	1.08679	+	0.789598i	0.978854	−	0.204560i	$-0.0655765\pi$
$431$	22.5623	+	16.3925i	1.08679	+	0.789598i	0.107934	+	0.994158i	$0.465576\pi$
$432$		0			0
$433$	−11.2918	−	34.7526i	−0.542649	−	1.67010i	−0.726515	−	0.687151i	$-0.758861\pi$
$433$	−11.2918	−	34.7526i	−0.542649	−	1.67010i	0.183866	−	0.982951i	$-0.441139\pi$
$434$	2.85410	−	2.07363i	0.137001	−	0.0995373i
$435$		0			0
$436$	0.527864	+	1.62460i	0.0252801	+	0.0778042i
$437$	0.354102	−	1.08981i	0.0169390	−	0.0521329i
$438$		0			0
$439$	−36.3607			−1.73540			−0.867700	−	0.497088i	$-0.834403\pi$
$439$	−36.3607			−1.73540			−0.867700	+	0.497088i	$0.834403\pi$
$440$	4.76393	−	11.8617i	0.227112	−	0.565485i
$441$	19.8541			0.945433
$442$	−8.18034	−	5.94336i	−0.389099	−	0.282697i
$443$	−0.809017	+	2.48990i	−0.0384376	+	0.118299i	−0.968434	−	0.249269i	$-0.919810\pi$
$443$	−0.809017	+	2.48990i	−0.0384376	+	0.118299i	0.929997	+	0.367568i	$0.119810\pi$
$444$		0			0
$445$	−44.2148	+	32.1239i	−2.09598	+	1.52282i
$446$	−3.61803	+	2.62866i	−0.171319	+	0.124470i
$447$		0			0
$448$	0.190983	−	0.587785i	0.00902310	−	0.0277702i
$449$	26.6525	+	19.3642i	1.25781	+	0.913851i	0.998648	−	0.0519833i	$-0.0165543\pi$
$449$	26.6525	+	19.3642i	1.25781	+	0.913851i	0.259160	+	0.965834i	$0.416554\pi$
$450$	−29.5623			−1.39358
$451$	29.4164	−	18.4661i	1.38516	−	0.869535i
$452$	−13.7082			−0.644780
$453$		0			0
$454$	3.56231	−	10.9637i	0.167187	−	0.514550i
$455$	−1.81966	−	5.60034i	−0.0853070	−	0.262548i
$456$		0			0
$457$	24.9164	−	18.1028i	1.16554	−	0.846815i	0.175072	−	0.984556i	$-0.443984\pi$
$457$	24.9164	−	18.1028i	1.16554	−	0.846815i	0.990468	+	0.137741i	$0.0439841\pi$
$458$	−0.173762	−	0.534785i	−0.00811937	−	0.0249888i
$459$		0			0
$460$	3.57295	+	2.59590i	0.166590	+	0.121034i
$461$	25.3820			1.18216			0.591078	−	0.806614i	$-0.298703\pi$
$461$	25.3820			1.18216			0.591078	+	0.806614i	$0.298703\pi$
$462$		0			0
$463$	−17.8541			−0.829750			−0.414875	−	0.909878i	$-0.636175\pi$
$463$	−17.8541			−0.829750			−0.414875	+	0.909878i	$0.636175\pi$
$464$	−1.00000	−	0.726543i	−0.0464238	−	0.0337289i
$465$		0			0
$466$	−2.75329	−	8.47375i	−0.127544	−	0.392539i
$467$	−3.35410	+	2.43690i	−0.155209	+	0.112766i	−0.662679	−	0.748903i	$-0.730581\pi$
$467$	−3.35410	+	2.43690i	−0.155209	+	0.112766i	0.507470	+	0.861669i	$0.330581\pi$
$468$	6.00000	−	4.35926i	0.277350	−	0.201507i
$469$	−1.52786	−	4.70228i	−0.0705502	−	0.217131i
$470$	13.8369	−	42.5855i	0.638248	−	1.96432i
$471$		0			0
$472$	−10.0000			−0.460287
$473$	−4.11803	−	3.44095i	−0.189347	−	0.158215i
$474$		0			0
$475$	−7.97214	−	5.79210i	−0.365787	−	0.265760i
$476$	0.781153	−	2.40414i	0.0358041	−	0.110194i
$477$	−1.85410	−	5.70634i	−0.0848935	−	0.261275i
$478$	−12.7812	+	9.28605i	−0.584596	+	0.424734i
$479$	−13.3992	+	9.73508i	−0.612224	+	0.444807i	−0.850197	−	0.526465i	$-0.823517\pi$
$479$	−13.3992	+	9.73508i	−0.612224	+	0.444807i	0.237972	+	0.971272i	$0.423517\pi$
$480$		0			0
$481$	−7.05573	+	21.7153i	−0.321714	+	0.990132i
$482$	−7.32624	−	5.32282i	−0.333701	−	0.242448i
$483$		0			0
$484$	−9.69098	+	5.20431i	−0.440499	+	0.236560i
$485$	29.0132			1.31742
$486$		0			0
$487$	7.85410	−	24.1724i	0.355903	−	1.09536i	−0.599581	−	0.800314i	$-0.704666\pi$
$487$	7.85410	−	24.1724i	0.355903	−	1.09536i	0.955484	−	0.295043i	$-0.0953341\pi$
$488$	3.11803	+	9.59632i	0.141147	+	0.434405i
$489$		0			0
$490$	−20.6353	+	14.9924i	−0.932206	+	0.677287i
$491$	−10.9894	−	33.8218i	−0.495943	−	1.52635i	−0.815482	−	0.578782i	$-0.803528\pi$
$491$	−10.9894	−	33.8218i	−0.495943	−	1.52635i	0.319540	−	0.947573i	$-0.396472\pi$
$492$		0			0
$493$	−4.09017	−	2.97168i	−0.184212	−	0.133838i
$494$	2.47214			0.111227
$495$	29.4271	+	24.5887i	1.32265	+	1.10518i
$496$	−5.70820			−0.256306
$497$	−4.23607	−	3.07768i	−0.190014	−	0.138053i
$498$		0			0
$499$	−7.19098	−	22.1316i	−0.321913	−	0.990745i	−0.972815	−	0.231584i	$-0.925609\pi$
$499$	−7.19098	−	22.1316i	−0.321913	−	0.990745i	0.650902	−	0.759161i	$-0.274391\pi$
$500$	15.1353	−	10.9964i	0.676869	−	0.491774i
$501$		0			0
$502$	−7.20820	−	22.1846i	−0.321718	−	0.990146i
$503$	8.47214	−	26.0746i	0.377754	−	1.16261i	−0.563848	−	0.825879i	$-0.690680\pi$
$503$	8.47214	−	26.0746i	0.377754	−	1.16261i	0.941602	−	0.336728i	$-0.109320\pi$
$504$	1.50000	+	1.08981i	0.0668153	+	0.0485442i
$505$	−5.32624			−0.237014
$506$	−0.927051	−	3.68571i	−0.0412124	−	0.163850i
$507$		0			0
$508$	4.23607	+	3.07768i	0.187945	+	0.136550i
$509$	7.09017	−	21.8213i	0.314266	−	0.967212i	−0.661789	−	0.749690i	$-0.730203\pi$
$509$	7.09017	−	21.8213i	0.314266	−	0.967212i	0.976055	−	0.217522i	$-0.0697974\pi$
$510$		0			0
$511$	4.23607	−	3.07768i	0.187393	−	0.136149i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$		0			0
$514$	−1.76393	+	5.42882i	−0.0778037	+	0.239455i
$515$	23.1246	+	16.8010i	1.01899	+	0.740341i
$516$		0			0
$517$	−32.6353	+	20.4867i	−1.43530	+	0.901005i
$518$	−5.70820			−0.250804
$519$		0			0
$520$	−2.94427	+	9.06154i	−0.129115	+	0.397375i
$521$	−1.76393	−	5.42882i	−0.0772793	−	0.237841i	0.904953	−	0.425512i	$-0.139906\pi$
$521$	−1.76393	−	5.42882i	−0.0772793	−	0.237841i	−0.982232	+	0.187671i	$0.939906\pi$
$522$	3.00000	−	2.17963i	0.131306	−	0.0953997i
$523$	19.1803	−	13.9353i	0.838698	−	0.609350i	−0.0833089	−	0.996524i	$-0.526549\pi$
$523$	19.1803	−	13.9353i	0.838698	−	0.609350i	0.922007	+	0.387174i	$0.126549\pi$
$524$	−1.95492	−	6.01661i	−0.0854009	−	0.262837i
$525$		0			0
$526$	1.23607	+	0.898056i	0.0538951	+	0.0391571i
$527$	−23.3475			−1.01703
$528$		0			0
$529$	−21.6869			−0.942909
$530$	6.23607	+	4.53077i	0.270877	+	0.196804i
$531$	9.27051	−	28.5317i	0.402306	−	1.23817i
$532$	0.190983	+	0.587785i	0.00828016	+	0.0254837i
$533$	−20.9443	+	15.2169i	−0.907197	+	0.659117i
$534$		0			0
$535$	11.0000	+	33.8545i	0.475571	+	1.46366i
$536$	−2.47214	+	7.60845i	−0.106780	+	0.328635i
$537$		0			0
$538$	16.3607			0.705359
$539$	21.8992	+	1.48584i	0.943265	+	0.0639997i
$540$		0			0
$541$	25.2533	+	18.3476i	1.08572	+	0.788824i	0.978672	−	0.205429i	$-0.0658590\pi$
$541$	25.2533	+	18.3476i	1.08572	+	0.788824i	0.107052	+	0.994253i	$0.465859\pi$
$542$	−4.35410	+	13.4005i	−0.187025	+	0.575603i
$543$		0			0
$544$	−3.30902	+	2.40414i	−0.141873	+	0.103077i
$545$	5.32624	−	3.86974i	0.228151	−	0.165761i
$546$		0			0
$547$	8.27051	−	25.4540i	0.353621	−	1.08833i	−0.603183	−	0.797603i	$-0.706101\pi$
$547$	8.27051	−	25.4540i	0.353621	−	1.08833i	0.956804	−	0.290732i	$-0.0938989\pi$
$548$	13.4443	+	9.76784i	0.574311	+	0.417261i
$549$	−30.2705			−1.29191
$550$	−32.6074	−	2.21238i	−1.39038	−	0.0943364i
$551$	1.23607			0.0526583
$552$		0			0
$553$	−2.29180	+	7.05342i	−0.0974571	+	0.299942i
$554$	−6.79837	−	20.9232i	−0.288835	−	0.888943i
$555$		0			0
$556$	15.6353	−	11.3597i	0.663083	−	0.481758i
$557$	−9.93363	−	30.5726i	−0.420901	−	1.29540i	−0.906865	−	0.421422i	$-0.861531\pi$
$557$	−9.93363	−	30.5726i	−0.420901	−	1.29540i	0.485963	−	0.873979i	$-0.338469\pi$
$558$	5.29180	−	16.2865i	0.224020	−	0.689461i
$559$	3.23607	+	2.35114i	0.136871	+	0.0994427i
$560$	−2.38197			−0.100656
$561$		0			0
$562$	21.1246			0.891088
$563$	8.85410	+	6.43288i	0.373156	+	0.271114i	0.758518	−	0.651652i	$-0.225924\pi$
$563$	8.85410	+	6.43288i	0.373156	+	0.271114i	−0.385362	+	0.922765i	$0.625924\pi$
$564$		0			0
$565$	16.3262	+	50.2470i	0.686850	+	2.11391i
$566$	−22.0623	+	16.0292i	−0.927348	+	0.673758i
$567$	−4.50000	+	3.26944i	−0.188982	+	0.137304i
$568$	2.61803	+	8.05748i	0.109850	+	0.338084i
$569$	1.90983	−	5.87785i	0.0800642	−	0.246412i	−0.903010	−	0.429619i	$-0.858648\pi$
$569$	1.90983	−	5.87785i	0.0800642	−	0.246412i	0.983074	+	0.183207i	$0.0586478\pi$
$570$		0			0
$571$	24.5066			1.02557			0.512784	−	0.858518i	$-0.328614\pi$
$571$	24.5066			1.02557			0.512784	+	0.858518i	$0.328614\pi$
$572$	6.94427	−	4.35926i	0.290355	−	0.182270i
$573$		0			0
$574$	−5.23607	−	3.80423i	−0.218549	−	0.158785i
$575$	3.48936	−	10.7391i	0.145516	−	0.447853i
$576$	−0.927051	−	2.85317i	−0.0386271	−	0.118882i
$577$	−26.2705	+	19.0866i	−1.09366	+	0.794587i	−0.980013	−	0.198934i	$-0.936252\pi$
$577$	−26.2705	+	19.0866i	−1.09366	+	0.794587i	−0.113643	+	0.993522i	$0.536252\pi$
$578$	0.218847	−	0.159002i	0.00910284	−	0.00661360i
$579$		0			0
$580$	−1.47214	+	4.53077i	−0.0611271	+	0.188130i
$581$	−1.92705	−	1.40008i	−0.0799475	−	0.0580853i
$582$		0			0
$583$	−1.61803	−	6.43288i	−0.0670121	−	0.266423i
$584$	−8.47214			−0.350579
$585$	−23.1246	−	16.8010i	−0.956085	−	0.694636i
$586$	−0.527864	+	1.62460i	−0.0218059	+	0.0671115i
$587$	0.583592	+	1.79611i	0.0240874	+	0.0741335i	0.962378	−	0.271715i	$-0.0875910\pi$
$587$	0.583592	+	1.79611i	0.0240874	+	0.0741335i	−0.938290	+	0.345849i	$0.887591\pi$
$588$		0			0
$589$	4.61803	−	3.35520i	0.190283	−	0.138249i
$590$	11.9098	+	36.6547i	0.490320	+	1.50905i
$591$		0			0
$592$	7.47214	+	5.42882i	0.307103	+	0.223123i
$593$	31.9098			1.31038			0.655190	−	0.755464i	$-0.272589\pi$
$593$	31.9098			1.31038			0.655190	+	0.755464i	$0.272589\pi$
$594$		0			0
$595$	−9.74265			−0.399410
$596$	−10.8541	−	7.88597i	−0.444601	−	0.323022i
$597$		0			0
$598$	0.875388	+	2.69417i	0.0357973	+	0.110173i
$599$	−12.2361	+	8.89002i	−0.499952	+	0.363237i	−0.808999	−	0.587810i	$-0.799990\pi$
$599$	−12.2361	+	8.89002i	−0.499952	+	0.363237i	0.309047	+	0.951047i	$0.399990\pi$
$600$		0			0
$601$	6.81966	+	20.9888i	0.278180	+	0.856149i	0.988361	+	0.152130i	$0.0486132\pi$
$601$	6.81966	+	20.9888i	0.278180	+	0.856149i	−0.710181	+	0.704019i	$0.751387\pi$
$602$	−0.309017	+	0.951057i	−0.0125946	+	0.0387622i
$603$	−19.4164	−	14.1068i	−0.790697	−	0.574475i
$604$	−14.1803			−0.576990
$605$	30.6180	+	29.3238i	1.24480	+	1.19218i
$606$		0			0
$607$	15.0344	+	10.9232i	0.610229	+	0.443357i	0.849495	−	0.527597i	$-0.176907\pi$
$607$	15.0344	+	10.9232i	0.610229	+	0.443357i	−0.239266	+	0.970954i	$0.576907\pi$
$608$	0.309017	−	0.951057i	0.0125323	−	0.0385704i
$609$		0			0
$610$	31.4615	−	22.8581i	1.27384	−	0.925498i
$611$	23.2361	−	16.8820i	0.940031	−	0.682972i
$612$	−3.79180	−	11.6699i	−0.153274	−	0.471730i
$613$	−3.70163	+	11.3924i	−0.149507	+	0.460136i	−0.997563	−	0.0697709i	$-0.977773\pi$
$613$	−3.70163	+	11.3924i	−0.149507	+	0.460136i	0.848056	+	0.529907i	$0.177773\pi$
$614$	15.7082	+	11.4127i	0.633932	+	0.460578i
$615$		0			0
$616$	1.57295	+	1.31433i	0.0633759	+	0.0529558i
$617$	30.9443			1.24577			0.622885	−	0.782314i	$-0.285961\pi$
$617$	30.9443			1.24577			0.622885	+	0.782314i	$0.285961\pi$
$618$		0			0
$619$	14.5557	−	44.7979i	0.585044	−	1.80058i	−0.0140491	−	0.999901i	$-0.504472\pi$
$619$	14.5557	−	44.7979i	0.585044	−	1.80058i	0.599093	−	0.800679i	$-0.295528\pi$
$620$	6.79837	+	20.9232i	0.273029	+	0.840298i
$621$		0			0
$622$	26.9615	−	19.5887i	1.08106	−	0.785434i
$623$	−2.70820	−	8.33499i	−0.108502	−	0.333935i
$624$		0			0
$625$	−18.4721	−	13.4208i	−0.738885	−	0.536832i
$626$	−1.03444			−0.0413446
$627$		0			0
$628$	0.437694			0.0174659
$629$	30.5623	+	22.2048i	1.21860	+	0.885364i
$630$	2.20820	−	6.79615i	0.0879770	−	0.270765i
$631$	5.41641	+	16.6700i	0.215624	+	0.663622i	0.999109	+	0.0422110i	$0.0134402\pi$
$631$	5.41641	+	16.6700i	0.215624	+	0.663622i	−0.783485	+	0.621411i	$0.786560\pi$
$632$	9.70820	−	7.05342i	0.386172	−	0.280570i
$633$		0			0
$634$	4.76393	+	14.6619i	0.189200	+	0.582297i
$635$	6.23607	−	19.1926i	0.247471	−	0.761637i
$636$		0			0
$637$	−16.3607			−0.648234
$638$	3.47214	−	2.17963i	0.137463	−	0.0862923i
$639$	−25.4164			−1.00546
$640$	3.11803	+	2.26538i	0.123251	+	0.0895472i
$641$	−10.6525	+	32.7849i	−0.420747	+	1.29493i	0.486260	+	0.873814i	$0.338361\pi$
$641$	−10.6525	+	32.7849i	−0.420747	+	1.29493i	−0.907008	+	0.421114i	$0.861639\pi$
$642$		0			0
$643$	26.4336	−	19.2052i	1.04244	−	0.757377i	0.0716801	−	0.997428i	$-0.477164\pi$
$643$	26.4336	−	19.2052i	1.04244	−	0.757377i	0.970760	+	0.240050i	$0.0771639\pi$
$644$	−0.572949	+	0.416272i	−0.0225774	+	0.0164034i
$645$		0			0
$646$	1.26393	−	3.88998i	0.0497287	−	0.153049i
$647$	−16.4721	−	11.9677i	−0.647586	−	0.470499i	0.214862	−	0.976644i	$-0.431070\pi$
$647$	−16.4721	−	11.9677i	−0.647586	−	0.470499i	−0.862448	+	0.506145i	$0.831070\pi$
$648$	9.00000			0.353553
$649$	12.3607	−	30.7768i	0.485199	−	1.20810i
$650$	24.3607			0.955504
$651$		0			0
$652$	7.75329	−	23.8622i	0.303642	−	0.934515i
$653$	−3.59017	−	11.0494i	−0.140494	−	0.432397i	0.855910	−	0.517125i	$-0.172998\pi$
$653$	−3.59017	−	11.0494i	−0.140494	−	0.432397i	−0.996404	+	0.0847283i	$0.972998\pi$
$654$		0			0
$655$	−19.7254	+	14.3314i	−0.770736	+	0.559973i
$656$	3.23607	+	9.95959i	0.126347	+	0.388857i
$657$	7.85410	−	24.1724i	0.306418	−	0.943057i
$658$	5.80902	+	4.22050i	0.226459	+	0.164532i
$659$	41.3050			1.60901			0.804506	−	0.593944i	$-0.202430\pi$
$659$	41.3050			1.60901			0.804506	+	0.593944i	$0.202430\pi$
$660$		0			0
$661$	−6.94427			−0.270101			−0.135050	−	0.990839i	$-0.543120\pi$
$661$	−6.94427			−0.270101			−0.135050	+	0.990839i	$0.543120\pi$
$662$	13.3262	+	9.68208i	0.517939	+	0.376305i
$663$		0			0
$664$	1.19098	+	3.66547i	0.0462191	+	0.142248i
$665$	1.92705	−	1.40008i	0.0747278	−	0.0542929i
$666$	−22.4164	+	16.2865i	−0.868618	+	0.631088i
$667$	0.437694	+	1.34708i	0.0169476	+	0.0521593i
$668$	2.47214	−	7.60845i	0.0956498	−	0.294380i
$669$		0			0
$670$	30.8328			1.19118
$671$	−33.3885	−	2.26538i	−1.28895	−	0.0874542i
$672$		0			0
$673$	−3.76393	−	2.73466i	−0.145089	−	0.105413i	0.512873	−	0.858465i	$-0.328581\pi$
$673$	−3.76393	−	2.73466i	−0.145089	−	0.105413i	−0.657962	+	0.753051i	$0.728581\pi$
$674$	−4.52786	+	13.9353i	−0.174407	+	0.536769i
$675$		0			0
$676$	5.57295	−	4.04898i	0.214344	−	0.155730i
$677$	−35.6525	+	25.9030i	−1.37024	+	0.995535i	−0.372517	+	0.928025i	$0.621505\pi$
$677$	−35.6525	+	25.9030i	−1.37024	+	0.995535i	−0.997719	+	0.0675095i	$0.978495\pi$
$678$		0			0
$679$	−1.43769	+	4.42477i	−0.0551736	+	0.169807i
$680$	12.7533	+	9.26581i	0.489066	+	0.355327i
$681$		0			0
$682$	7.05573	−	17.5680i	0.270178	−	0.672715i
$683$	16.8328			0.644090			0.322045	−	0.946724i	$-0.395630\pi$
$683$	16.8328			0.644090			0.322045	+	0.946724i	$0.395630\pi$
$684$	2.42705	+	1.76336i	0.0928006	+	0.0674236i
$685$	19.7918	−	60.9129i	0.756206	−	2.32736i
$686$	−2.60081	−	8.00448i	−0.0992995	−	0.305612i
$687$		0			0
$688$	1.30902	−	0.951057i	0.0499058	−	0.0362587i
$689$	1.52786	+	4.70228i	0.0582070	+	0.179143i
$690$		0			0
$691$	−22.2984	−	16.2007i	−0.848270	−	0.616304i	0.0763984	−	0.997077i	$-0.475658\pi$
$691$	−22.2984	−	16.2007i	−0.848270	−	0.616304i	−0.924669	+	0.380773i	$0.875658\pi$
$692$	−19.4164			−0.738101
$693$	−5.20820	+	3.26944i	−0.197843	+	0.124196i
$694$	17.2148			0.653464
$695$	−60.2599	−	43.7814i	−2.28579	−	1.66072i
$696$		0			0
$697$	13.2361	+	40.7364i	0.501352	+	1.54300i
$698$	−25.2984	+	18.3803i	−0.957558	+	0.695706i
$699$		0			0
$700$	1.88197	+	5.79210i	0.0711316	+	0.218921i
$701$	2.29837	−	7.07367i	0.0868084	−	0.267169i	−0.898224	−	0.439538i	$-0.855142\pi$
$701$	2.29837	−	7.07367i	0.0868084	−	0.267169i	0.985032	+	0.172369i	$0.0551422\pi$
$702$		0			0
$703$	−9.23607			−0.348345
$704$	−0.809017	−	3.21644i	−0.0304910	−	0.121224i
$705$		0			0
$706$	−6.73607	−	4.89404i	−0.253515	−	0.184190i
$707$	0.263932	−	0.812299i	0.00992619	−	0.0305497i
$708$		0			0
$709$	12.1180	−	8.80427i	0.455102	−	0.330651i	−0.336505	−	0.941682i	$-0.609245\pi$
$709$	12.1180	−	8.80427i	0.455102	−	0.330651i	0.791607	+	0.611031i	$0.209245\pi$
$710$	26.4164	−	19.1926i	0.991390	−	0.720287i
$711$	11.1246	+	34.2380i	0.417206	+	1.28403i
$712$	−4.38197	+	13.4863i	−0.164221	+	0.505421i
$713$	5.29180	+	3.84471i	0.198179	+	0.143986i
$714$		0			0
$715$	−24.2492	−	20.2622i	−0.906870	−	0.757764i
$716$	7.23607			0.270425
$717$		0			0
$718$	0.534442	−	1.64484i	0.0199452	−	0.0613850i
$719$	−16.0106	−	49.2757i	−0.597096	−	1.83767i	−0.544002	−	0.839084i	$-0.683092\pi$
$719$	−16.0106	−	49.2757i	−0.597096	−	1.83767i	−0.0530939	−	0.998590i	$-0.516908\pi$
$720$	−9.35410	+	6.79615i	−0.348607	+	0.253278i
$721$	−3.70820	+	2.69417i	−0.138101	+	0.100336i
$722$	0.309017	+	0.951057i	0.0115004	+	0.0353947i
$723$		0			0
$724$	10.2361	+	7.43694i	0.380420	+	0.276392i
$725$	12.1803			0.452366
$726$		0			0
$727$	−25.9098			−0.960942			−0.480471	−	0.877011i	$-0.659534\pi$
$727$	−25.9098			−0.960942			−0.480471	+	0.877011i	$0.659534\pi$
$728$	−1.23607	−	0.898056i	−0.0458117	−	0.0332842i
$729$	−8.34346	+	25.6785i	−0.309017	+	0.951057i
$730$	10.0902	+	31.0543i	0.373454	+	1.14937i
$731$	5.35410	−	3.88998i	0.198029	−	0.143876i
$732$		0			0
$733$	11.5729	+	35.6179i	0.427457	+	1.31558i	0.900622	+	0.434603i	$0.143111\pi$
$733$	11.5729	+	35.6179i	0.427457	+	1.31558i	−0.473166	+	0.880973i	$0.656889\pi$
$734$	0.371323	−	1.14281i	0.0137058	−	0.0421820i
$735$		0			0
$736$	1.14590			0.0422384
$737$	−20.3607	−	17.0130i	−0.749995	−	0.626683i
$738$	−31.4164			−1.15645
$739$	17.8262	+	12.9515i	0.655749	+	0.476429i	0.865225	−	0.501384i	$-0.167176\pi$
$739$	17.8262	+	12.9515i	0.655749	+	0.476429i	−0.209476	+	0.977814i	$0.567176\pi$
$740$	11.0000	−	33.8545i	0.404368	−	1.24452i
$741$		0			0
$742$	−1.00000	+	0.726543i	−0.0367112	+	0.0266722i
$743$	−24.0344	+	17.4620i	−0.881738	+	0.640620i	−0.933711	−	0.358028i	$-0.883449\pi$
$743$	−24.0344	+	17.4620i	−0.881738	+	0.640620i	0.0519726	+	0.998649i	$0.483449\pi$
$744$		0			0
$745$	−15.9787	+	49.1774i	−0.585415	+	1.80172i
$746$	−20.7082	−	15.0454i	−0.758181	−	0.550851i
$747$	−11.5623			−0.423043
$748$	−3.30902	−	13.1558i	−0.120990	−	0.481023i
$749$	−5.70820			−0.208573
$750$		0			0
$751$	−10.2705	+	31.6094i	−0.374776	+	1.15344i	0.568853	+	0.822439i	$0.307387\pi$
$751$	−10.2705	+	31.6094i	−0.374776	+	1.15344i	−0.943629	+	0.331004i	$0.892613\pi$
$752$	−3.59017	−	11.0494i	−0.130920	−	0.402930i
$753$		0			0
$754$	−2.47214	+	1.79611i	−0.0900299	+	0.0654105i
$755$	16.8885	+	51.9776i	0.614637	+	1.89166i
$756$		0			0
$757$	38.2705	+	27.8052i	1.39097	+	1.01060i	0.995759	+	0.0920032i	$0.0293270\pi$
$757$	38.2705	+	27.8052i	1.39097	+	1.01060i	0.395207	+	0.918592i	$0.370673\pi$
$758$	1.52786			0.0554945
$759$		0			0
$760$	−3.85410			−0.139803
$761$	−4.38197	−	3.18368i	−0.158846	−	0.115408i	0.505523	−	0.862813i	$-0.331300\pi$
$761$	−4.38197	−	3.18368i	−0.158846	−	0.115408i	−0.664369	+	0.747405i	$0.731300\pi$
$762$		0			0
$763$	0.326238	+	1.00406i	0.0118106	+	0.0363493i
$764$	−7.73607	+	5.62058i	−0.279881	+	0.203346i
$765$	−38.2599	+	27.7974i	−1.38329	+	1.00502i
$766$	5.70820	+	17.5680i	0.206246	+	0.634759i
$767$	−7.63932	+	23.5114i	−0.275840	+	0.848948i
$768$		0			0
$769$	−31.7426			−1.14467			−0.572335	−	0.820020i	$-0.693962\pi$
$769$	−31.7426			−1.14467			−0.572335	+	0.820020i	$0.693962\pi$
$770$	2.94427	−	7.33094i	0.106104	−	0.264189i
$771$		0			0
$772$	−1.61803	−	1.17557i	−0.0582343	−	0.0423097i
$773$	13.7082	−	42.1895i	0.493050	−	1.51745i	−0.326924	−	0.945051i	$-0.606012\pi$
$773$	13.7082	−	42.1895i	0.493050	−	1.51745i	0.819974	−	0.572401i	$-0.193988\pi$
$774$	1.50000	+	4.61653i	0.0539164	+	0.165938i
$775$	45.5066	−	33.0625i	1.63464	−	1.18764i
$776$	6.09017	−	4.42477i	0.218624	−	0.158840i
$777$		0			0
$778$	2.35410	−	7.24518i	0.0843986	−	0.259752i
$779$	−8.47214	−	6.15537i	−0.303546	−	0.220539i
$780$		0			0
$781$	−28.0344	−	1.90211i	−1.00315	−	0.0680630i
$782$	4.68692			0.167604
$783$		0			0
$784$	−2.04508	+	6.29412i	−0.0730387	+	0.224790i
$785$	−0.521286	−	1.60435i	−0.0186055	−	0.0572619i
$786$		0			0
$787$	31.5066	−	22.8909i	1.12309	−	0.815971i	0.138414	−	0.990374i	$-0.455800\pi$
$787$	31.5066	−	22.8909i	1.12309	−	0.815971i	0.984674	+	0.174403i	$0.0557996\pi$
$788$	2.32624	+	7.15942i	0.0828688	+	0.255044i
$789$		0			0
$790$	−37.4164	−	27.1846i	−1.33122	−	0.967185i
$791$	−8.47214			−0.301234
$792$	9.92705	+	0.673542i	0.352742	+	0.0239333i
$793$	24.9443			0.885797
$794$	−6.30902	−	4.58377i	−0.223899	−	0.162672i
$795$		0			0
$796$	1.42705	+	4.39201i	0.0505805	+	0.155671i
$797$	10.8541	−	7.88597i	0.384472	−	0.279335i	−0.378714	−	0.925514i	$-0.623634\pi$
$797$	10.8541	−	7.88597i	0.384472	−	0.279335i	0.763186	+	0.646178i	$0.223634\pi$
$798$		0			0
$799$	−14.6844	−	45.1940i	−0.519497	−	1.59885i
$800$	3.04508	−	9.37181i	0.107660	−	0.331343i
$801$	−34.4164	−	25.0050i	−1.21604	−	0.883508i
$802$	−3.41641			−0.120638
$803$	10.4721	−	26.0746i	0.369554	−	0.920151i
$804$		0			0
$805$	2.20820	+	1.60435i	0.0778290	+	0.0565461i
$806$	−4.36068	+	13.4208i	−0.153598	+	0.472727i
$807$		0			0
$808$	−1.11803	+	0.812299i	−0.0393323	+	0.0285766i
$809$	37.3885	−	27.1644i	1.31451	−	0.955048i	0.314528	−	0.949248i	$-0.398154\pi$
$809$	37.3885	−	27.1644i	1.31451	−	0.955048i	0.999983	−	0.00580010i	$-0.00184624\pi$
$810$	−10.7188	−	32.9892i	−0.376622	−	1.15912i
$811$	17.2361	−	53.0472i	0.605240	−	1.86274i	0.110109	−	0.993919i	$-0.464880\pi$
$811$	17.2361	−	53.0472i	0.605240	−	1.86274i	0.495131	−	0.868818i	$-0.335120\pi$
$812$	−0.618034	−	0.449028i	−0.0216887	−	0.0157578i
$813$		0			0
$814$	−25.9443	+	16.2865i	−0.909346	+	0.570841i
$815$	−96.7001			−3.38726
$816$		0			0
$817$	−0.500000	+	1.53884i	−0.0174928	+	0.0538373i
$818$	7.32624	+	22.5478i	0.256156	+	0.788367i
$819$	3.70820	−	2.69417i	0.129575	−	0.0941418i
$820$	32.6525	−	23.7234i	1.14027	−	0.828457i
$821$	−2.46556	−	7.58821i	−0.0860486	−	0.264830i	0.898769	−	0.438422i	$-0.144463\pi$
$821$	−2.46556	−	7.58821i	−0.0860486	−	0.264830i	−0.984818	+	0.173592i	$0.944463\pi$
$822$		0			0
$823$	7.97214	+	5.79210i	0.277891	+	0.201900i	0.717997	−	0.696046i	$-0.245059\pi$
$823$	7.97214	+	5.79210i	0.277891	+	0.201900i	−0.440106	+	0.897946i	$0.645059\pi$
$824$	7.41641			0.258363
$825$		0			0
$826$	−6.18034			−0.215042
$827$	30.0344	+	21.8213i	1.04440	+	0.758801i	0.971140	−	0.238512i	$-0.0766596\pi$
$827$	30.0344	+	21.8213i	1.04440	+	0.758801i	0.0732603	+	0.997313i	$0.476660\pi$
$828$	−1.06231	+	3.26944i	−0.0369177	+	0.113621i
$829$	4.34752	+	13.3803i	0.150996	+	0.464717i	0.997733	−	0.0672938i	$-0.0214365\pi$
$829$	4.34752	+	13.3803i	0.150996	+	0.464717i	−0.846737	+	0.532011i	$0.821436\pi$
$830$	12.0172	−	8.73102i	0.417124	−	0.303058i
$831$		0			0
$832$	0.763932	+	2.35114i	0.0264846	+	0.0815111i
$833$	−8.36475	+	25.7440i	−0.289821	+	0.891978i
$834$		0			0
$835$	−30.8328			−1.06701
$836$	2.54508	+	2.12663i	0.0880236	+	0.0735509i
$837$		0			0
$838$	−10.2533	−	7.44945i	−0.354194	−	0.257337i
$839$	7.76393	−	23.8949i	0.268041	−	0.824944i	−0.722937	−	0.690914i	$-0.757208\pi$
$839$	7.76393	−	23.8949i	0.268041	−	0.824944i	0.990977	−	0.134030i	$-0.0427919\pi$
$840$		0			0
$841$	22.2254	−	16.1477i	0.766394	−	0.556818i
$842$	20.0344	−	14.5559i	0.690432	−	0.501629i
$843$		0			0
$844$	−5.29180	+	16.2865i	−0.182151	+	0.560604i
$845$	−21.4787	−	15.6052i	−0.738890	−	0.536835i
$846$	34.8541			1.19831
$847$	−5.98936	+	3.21644i	−0.205797	+	0.110518i
$848$	2.00000			0.0686803
$849$		0			0
$850$	12.4549	−	38.3323i	0.427200	−	1.31479i
$851$	−3.27051	−	10.0656i	−0.112112	−	0.345044i
$852$		0			0
$853$	13.2533	−	9.62908i	0.453784	−	0.329693i	−0.337304	−	0.941396i	$-0.609515\pi$
$853$	13.2533	−	9.62908i	0.453784	−	0.329693i	0.791088	+	0.611702i	$0.209515\pi$
$854$	1.92705	+	5.93085i	0.0659423	+	0.202950i
$855$	3.57295	−	10.9964i	0.122192	−	0.376069i
$856$	7.47214	+	5.42882i	0.255392	+	0.185553i
$857$	32.8328			1.12155			0.560774	−	0.827969i	$-0.310504\pi$
$857$	32.8328			1.12155			0.560774	+	0.827969i	$0.310504\pi$
$858$		0			0
$859$	−19.6869			−0.671709			−0.335854	−	0.941914i	$-0.609025\pi$
$859$	−19.6869			−0.671709			−0.335854	+	0.941914i	$0.609025\pi$
$860$	−5.04508	−	3.66547i	−0.172036	−	0.124991i
$861$		0			0
$862$	−8.61803	−	26.5236i	−0.293531	−	0.903397i
$863$	−6.76393	+	4.91428i	−0.230247	+	0.167284i	−0.696927	−	0.717142i	$-0.745450\pi$
$863$	−6.76393	+	4.91428i	−0.230247	+	0.167284i	0.466680	+	0.884426i	$0.345450\pi$
$864$		0			0
$865$	23.1246	+	71.1702i	0.786260	+	2.41986i
$866$	−11.2918	+	34.7526i	−0.383711	+	1.18094i
$867$		0			0
$868$	−3.52786			−0.119744
$869$	9.70820	+	38.5973i	0.329328	+	1.30932i
$870$		0			0
$871$	16.0000	+	11.6247i	0.542139	+	0.393887i
$872$	0.527864	−	1.62460i	0.0178757	−	0.0550158i
$873$	6.97871	+	21.4783i	0.236194	+	0.726929i
$874$	−0.927051	+	0.673542i	−0.0313580	+	0.0227829i
$875$	9.35410	−	6.79615i	0.316226	−	0.229752i
$876$		0			0
$877$	−5.36068	+	16.4985i	−0.181017	+	0.557114i	−0.999857	−	0.0169082i	$-0.994618\pi$
$877$	−5.36068	+	16.4985i	−0.181017	+	0.557114i	0.818840	+	0.574022i	$0.194618\pi$
$878$	29.4164	+	21.3723i	0.992756	+	0.721279i
$879$		0			0
$880$	−10.8262	+	6.79615i	−0.364952	+	0.229098i
$881$	−10.9443			−0.368722			−0.184361	−	0.982859i	$-0.559022\pi$
$881$	−10.9443			−0.368722			−0.184361	+	0.982859i	$0.559022\pi$
$882$	−16.0623	−	11.6699i	−0.540846	−	0.392948i
$883$	−10.6976	+	32.9237i	−0.360002	+	1.10797i	0.593051	+	0.805165i	$0.297923\pi$
$883$	−10.6976	+	32.9237i	−0.360002	+	1.10797i	−0.953052	+	0.302806i	$0.902077\pi$
$884$	3.12461	+	9.61657i	0.105092	+	0.323440i
$885$		0			0
$886$	2.11803	−	1.53884i	0.0711567	−	0.0516984i
$887$	12.0344	+	37.0382i	0.404077	+	1.24362i	0.921663	+	0.387990i	$0.126831\pi$
$887$	12.0344	+	37.0382i	0.404077	+	1.24362i	−0.517586	+	0.855631i	$0.673169\pi$
$888$		0			0
$889$	2.61803	+	1.90211i	0.0878060	+	0.0637948i
$890$	54.6525			1.83196
$891$	−11.1246	+	27.6992i	−0.372689	+	0.927957i
$892$	4.47214			0.149738
$893$	9.39919	+	6.82891i	0.314532	+	0.228521i
$894$		0			0
$895$	−8.61803	−	26.5236i	−0.288069	−	0.886586i
$896$	−0.500000	+	0.363271i	−0.0167038	+	0.0121360i
$897$		0			0
$898$	−10.1803	−	31.3319i	−0.339722	−	1.04556i
$899$	−2.18034	+	6.71040i	−0.0727184	+	0.223804i
$900$	23.9164	+	17.3763i	0.797214	+	0.579210i
$901$	8.18034			0.272527
$902$	−34.6525	−	2.35114i	−1.15380	−	0.0782844i
$903$		0			0
$904$	11.0902	+	8.05748i	0.368854	+	0.267988i
$905$	15.0689	−	46.3773i	0.500907	−	1.54163i
$906$		0			0
$907$	−32.1246	+	23.3399i	−1.06668	+	0.774989i	−0.975313	−	0.220829i	$-0.929124\pi$
$907$	−32.1246	+	23.3399i	−1.06668	+	0.774989i	−0.0913676	+	0.995817i	$0.529124\pi$
$908$	−9.32624	+	6.77591i	−0.309502	+	0.224866i
$909$	−1.28115	−	3.94298i	−0.0424932	−	0.130781i
$910$	−1.81966	+	5.60034i	−0.0603211	+	0.185649i
$911$	9.70820	+	7.05342i	0.321647	+	0.233690i	0.736878	−	0.676026i	$-0.236299\pi$
$911$	9.70820	+	7.05342i	0.321647	+	0.233690i	−0.415231	+	0.909716i	$0.636299\pi$
$912$		0			0
$913$	−12.7533	−	0.865300i	−0.422072	−	0.0286372i
$914$	−30.7984			−1.01872
$915$		0			0
$916$	−0.173762	+	0.534785i	−0.00574126	+	0.0176698i
$917$	−1.20820	−	3.71847i	−0.0398984	−	0.122795i
$918$		0			0
$919$	7.73607	−	5.62058i	0.255189	−	0.185406i	−0.452834	−	0.891595i	$-0.649587\pi$
$919$	7.73607	−	5.62058i	0.255189	−	0.185406i	0.708024	+	0.706189i	$0.249587\pi$
$920$	−1.36475	−	4.20025i	−0.0449943	−	0.138478i
$921$		0			0
$922$	−20.5344	−	14.9191i	−0.676266	−	0.491336i
$923$	20.9443			0.689389
$924$		0			0
$925$	−91.0132			−2.99249
$926$	14.4443	+	10.4944i	0.474668	+	0.344867i
$927$	−6.87539	+	21.1603i	−0.225817	+	0.694994i
$928$	0.381966	+	1.17557i	0.0125386	+	0.0385900i
$929$	−28.1074	+	20.4212i	−0.922174	+	0.669998i	−0.944064	−	0.329762i	$-0.893031\pi$
$929$	−28.1074	+	20.4212i	−0.922174	+	0.669998i	0.0218905	+	0.999760i	$0.493031\pi$
$930$		0			0
$931$	−2.04508	−	6.29412i	−0.0670250	−	0.206282i
$932$	−2.75329	+	8.47375i	−0.0901870	+	0.277567i
$933$		0			0
$934$	4.14590			0.135658
$935$	−44.2812	+	27.7974i	−1.44815	+	0.909073i
$936$	−7.41641			−0.242413
$937$	17.6353	+	12.8128i	0.576119	+	0.418575i	0.837323	−	0.546709i	$-0.184120\pi$
$937$	17.6353	+	12.8128i	0.576119	+	0.418575i	−0.261204	+	0.965284i	$0.584120\pi$
$938$	−1.52786	+	4.70228i	−0.0498865	+	0.153535i
$939$		0			0
$940$	−36.2254	+	26.3193i	−1.18154	+	0.858441i
$941$	6.52786	−	4.74277i	0.212802	−	0.154610i	−0.476278	−	0.879295i	$-0.658015\pi$
$941$	6.52786	−	4.74277i	0.212802	−	0.154610i	0.689081	+	0.724685i	$0.258015\pi$
$942$		0			0
$943$	3.70820	−	11.4127i	0.120756	−	0.371648i
$944$	8.09017	+	5.87785i	0.263313	+	0.191308i
$945$		0			0
$946$	1.30902	+	5.20431i	0.0425598	+	0.169207i
$947$	−50.0344			−1.62590			−0.812950	−	0.582333i	$-0.802140\pi$
$947$	−50.0344			−1.62590			−0.812950	+	0.582333i	$0.802140\pi$
$948$		0			0
$949$	−6.47214	+	19.9192i	−0.210094	+	0.646604i
$950$	3.04508	+	9.37181i	0.0987956	+	0.304062i
$951$		0			0
$952$	−2.04508	+	1.48584i	−0.0662816	+	0.0481564i
$953$	−6.47214	−	19.9192i	−0.209653	−	0.645246i	−0.999490	−	0.0319290i	$-0.989835\pi$
$953$	−6.47214	−	19.9192i	−0.209653	−	0.645246i	0.789837	−	0.613317i	$-0.210165\pi$
$954$	−1.85410	+	5.70634i	−0.0600288	+	0.184750i
$955$	29.8156	+	21.6623i	0.964810	+	0.700975i
$956$	15.7984			0.510956
$957$		0			0
$958$	16.5623			0.535104
$959$	8.30902	+	6.03685i	0.268312	+	0.194940i
$960$		0			0
$961$	0.489357	+	1.50609i	0.0157857	+	0.0485834i
$962$	18.4721	−	13.4208i	0.595566	−	0.432704i
$963$	−22.4164	+	16.2865i	−0.722359	+	0.524824i
$964$	2.79837	+	8.61251i	0.0901296	+	0.277390i
$965$	−2.38197	+	7.33094i	−0.0766782	+	0.235991i
$966$		0			0
$967$	−0.201626			−0.00648386			−0.00324193	−	0.999995i	$-0.501032\pi$
$967$	−0.201626			−0.00648386			−0.00324193	+	0.999995i	$0.501032\pi$
$968$	10.8992	+	1.48584i	0.350313	+	0.0477567i
$969$		0			0
$970$	−23.4721	−	17.0535i	−0.753645	−	0.547555i
$971$	−7.90983	+	24.3440i	−0.253839	+	0.781235i	0.740218	+	0.672367i	$0.234722\pi$
$971$	−7.90983	+	24.3440i	−0.253839	+	0.781235i	−0.994056	+	0.108867i	$0.965278\pi$
$972$		0			0
$973$	9.66312	−	7.02067i	0.309785	−	0.225072i
$974$	−20.5623	+	14.9394i	−0.658859	+	0.478689i
$975$		0			0
$976$	3.11803	−	9.59632i	0.0998058	−	0.307171i
$977$	7.00000	+	5.08580i	0.223950	+	0.162709i	0.694103	−	0.719876i	$-0.255801\pi$
$977$	7.00000	+	5.08580i	0.223950	+	0.162709i	−0.470153	+	0.882585i	$0.655801\pi$
$978$		0			0
$979$	−36.0902	−	30.1563i	−1.15345	−	0.963799i
$980$	25.5066			0.814778
$981$	4.14590	+	3.01217i	0.132368	+	0.0961712i
$982$	−10.9894	+	33.8218i	−0.350684	+	1.07930i
$983$	5.72949	+	17.6336i	0.182742	+	0.562423i	0.999902	−	0.0139880i	$-0.00445268\pi$
$983$	5.72949	+	17.6336i	0.182742	+	0.562423i	−0.817160	+	0.576411i	$0.804453\pi$
$984$		0			0
$985$	23.4721	−	17.0535i	0.747884	−	0.543370i
$986$	1.56231	+	4.80828i	0.0497540	+	0.153127i
$987$		0			0
$988$	−2.00000	−	1.45309i	−0.0636285	−	0.0462288i
$989$	−1.85410			−0.0589570
$990$	−9.35410	−	37.1895i	−0.297293	−	1.18196i
$991$	−39.7082			−1.26137			−0.630686	−	0.776038i	$-0.717227\pi$
$991$	−39.7082			−1.26137			−0.630686	+	0.776038i	$0.717227\pi$
$992$	4.61803	+	3.35520i	0.146623	+	0.106528i
$993$		0			0
$994$	1.61803	+	4.97980i	0.0513209	+	0.157950i
$995$	14.3992	−	10.4616i	0.456485	−	0.331656i
$996$		0			0
$997$	1.84346	+	5.67358i	0.0583829	+	0.179684i	0.975995	−	0.217793i	$-0.0698858\pi$
$997$	1.84346	+	5.67358i	0.0583829	+	0.179684i	−0.917612	+	0.397477i	$0.869886\pi$
$998$	−7.19098	+	22.1316i	−0.227627	+	0.700563i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.f.b.191.1	✓	4
11.3	even	5	inner	418.2.f.b.267.1	yes	4
11.5	even	5		4598.2.a.bh.1.1		2
11.6	odd	10		4598.2.a.z.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.f.b.191.1	✓	4	1.1	even	1	trivial
418.2.f.b.267.1	yes	4	11.3	even	5	inner
4598.2.a.z.1.1		2	11.6	odd	10
4598.2.a.bh.1.1		2	11.5	even	5

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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(3.11803 - 2.26538i) q^{5} +(0.190983 + 0.587785i) q^{7} +(0.309017 - 0.951057i) q^{8} +(2.42705 + 1.76336i) q^{9} +O(q^{10})\)	\(q+(-0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(3.11803 - 2.26538i) q^{5} +(0.190983 + 0.587785i) q^{7} +(0.309017 - 0.951057i) q^{8} +(2.42705 + 1.76336i) q^{9} -3.85410 q^{10} +(2.54508 + 2.12663i) q^{11} +(-2.00000 - 1.45309i) q^{13} +(0.190983 - 0.587785i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(-3.30902 + 2.40414i) q^{17} +(-0.927051 - 2.85317i) q^{18} +(0.309017 - 0.951057i) q^{19} +(3.11803 + 2.26538i) q^{20} +(-0.809017 - 3.21644i) q^{22} +1.14590 q^{23} +(3.04508 - 9.37181i) q^{25} +(0.763932 + 2.35114i) q^{26} +(-0.500000 + 0.363271i) q^{28} +(0.381966 + 1.17557i) q^{29} +(4.61803 + 3.35520i) q^{31} +1.00000 q^{32} +4.09017 q^{34} +(1.92705 + 1.40008i) q^{35} +(-0.927051 + 2.85317i) q^{36} +(-2.85410 - 8.78402i) q^{37} +(-0.809017 + 0.587785i) q^{38} +(-1.19098 - 3.66547i) q^{40} +(3.23607 - 9.95959i) q^{41} -1.61803 q^{43} +(-1.23607 + 3.07768i) q^{44} +11.5623 q^{45} +(-0.927051 - 0.673542i) q^{46} +(-3.59017 + 11.0494i) q^{47} +(5.35410 - 3.88998i) q^{49} +(-7.97214 + 5.79210i) q^{50} +(0.763932 - 2.35114i) q^{52} +(-1.61803 - 1.17557i) q^{53} +(12.7533 + 0.865300i) q^{55} +0.618034 q^{56} +(0.381966 - 1.17557i) q^{58} +(-3.09017 - 9.51057i) q^{59} +(-8.16312 + 5.93085i) q^{61} +(-1.76393 - 5.42882i) q^{62} +(-0.572949 + 1.76336i) q^{63} +(-0.809017 - 0.587785i) q^{64} -9.52786 q^{65} -8.00000 q^{67} +(-3.30902 - 2.40414i) q^{68} +(-0.736068 - 2.26538i) q^{70} +(-6.85410 + 4.97980i) q^{71} +(2.42705 - 1.76336i) q^{72} +(-2.61803 - 8.05748i) q^{73} +(-2.85410 + 8.78402i) q^{74} +1.00000 q^{76} +(-0.763932 + 1.90211i) q^{77} +(9.70820 + 7.05342i) q^{79} +(-1.19098 + 3.66547i) q^{80} +(2.78115 + 8.55951i) q^{81} +(-8.47214 + 6.15537i) q^{82} +(-3.11803 + 2.26538i) q^{83} +(-4.87132 + 14.9924i) q^{85} +(1.30902 + 0.951057i) q^{86} +(2.80902 - 1.76336i) q^{88} -14.1803 q^{89} +(-9.35410 - 6.79615i) q^{90} +(0.472136 - 1.45309i) q^{91} +(0.354102 + 1.08981i) q^{92} +(9.39919 - 6.82891i) q^{94} +(-1.19098 - 3.66547i) q^{95} +(6.09017 + 4.42477i) q^{97} -6.61803 q^{98} +(2.42705 + 9.64932i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} - q^{4} + 8 q^{5} + 3 q^{7} - q^{8} + 3 q^{9}+O(q^{10}) \) 4 * q - q^2 - q^4 + 8 * q^5 + 3 * q^7 - q^8 + 3 * q^9	\( 4 q - q^{2} - q^{4} + 8 q^{5} + 3 q^{7} - q^{8} + 3 q^{9} - 2 q^{10} - q^{11} - 8 q^{13} + 3 q^{14} - q^{16} - 11 q^{17} + 3 q^{18} - q^{19} + 8 q^{20} - q^{22} + 18 q^{23} + q^{25} + 12 q^{26} - 2 q^{28} + 6 q^{29} + 14 q^{31} + 4 q^{32} - 6 q^{34} + q^{35} + 3 q^{36} + 2 q^{37} - q^{38} - 7 q^{40} + 4 q^{41} - 2 q^{43} + 4 q^{44} + 6 q^{45} + 3 q^{46} + 8 q^{47} + 8 q^{49} - 14 q^{50} + 12 q^{52} - 2 q^{53} + 13 q^{55} - 2 q^{56} + 6 q^{58} + 10 q^{59} - 17 q^{61} - 16 q^{62} - 9 q^{63} - q^{64} - 56 q^{65} - 32 q^{67} - 11 q^{68} + 6 q^{70} - 14 q^{71} + 3 q^{72} - 6 q^{73} + 2 q^{74} + 4 q^{76} - 12 q^{77} + 12 q^{79} - 7 q^{80} - 9 q^{81} - 16 q^{82} - 8 q^{83} + 23 q^{85} + 3 q^{86} + 9 q^{88} - 12 q^{89} - 24 q^{90} - 16 q^{91} - 12 q^{92} + 13 q^{94} - 7 q^{95} + 2 q^{97} - 22 q^{98} + 3 q^{99}+O(q^{100}) \) 4 * q - q^2 - q^4 + 8 * q^5 + 3 * q^7 - q^8 + 3 * q^9 - 2 * q^10 - q^11 - 8 * q^13 + 3 * q^14 - q^16 - 11 * q^17 + 3 * q^18 - q^19 + 8 * q^20 - q^22 + 18 * q^23 + q^25 + 12 * q^26 - 2 * q^28 + 6 * q^29 + 14 * q^31 + 4 * q^32 - 6 * q^34 + q^35 + 3 * q^36 + 2 * q^37 - q^38 - 7 * q^40 + 4 * q^41 - 2 * q^43 + 4 * q^44 + 6 * q^45 + 3 * q^46 + 8 * q^47 + 8 * q^49 - 14 * q^50 + 12 * q^52 - 2 * q^53 + 13 * q^55 - 2 * q^56 + 6 * q^58 + 10 * q^59 - 17 * q^61 - 16 * q^62 - 9 * q^63 - q^64 - 56 * q^65 - 32 * q^67 - 11 * q^68 + 6 * q^70 - 14 * q^71 + 3 * q^72 - 6 * q^73 + 2 * q^74 + 4 * q^76 - 12 * q^77 + 12 * q^79 - 7 * q^80 - 9 * q^81 - 16 * q^82 - 8 * q^83 + 23 * q^85 + 3 * q^86 + 9 * q^88 - 12 * q^89 - 24 * q^90 - 16 * q^91 - 12 * q^92 + 13 * q^94 - 7 * q^95 + 2 * q^97 - 22 * q^98 + 3 * q^99

Introduction

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