LMFDB - Embedded newform 121.2.c.e.81.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [121,2,Mod(3,121)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(121, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("121.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 121 = 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	121.c (of order $5$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.966189864457$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 11)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			81.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	121.81
Dual form			121.2.c.e.3.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.61803 + 1.17557i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(0.618034 + 1.90211i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(-1.61803 + 1.17557i) q^{6} +(-0.618034 - 1.90211i) q^{7} +(1.61803 + 1.17557i) q^{9} +O(q^{10})$	\(q+(1.61803 + 1.17557i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(0.618034 + 1.90211i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(-1.61803 + 1.17557i) q^{6} +(-0.618034 - 1.90211i) q^{7} +(1.61803 + 1.17557i) q^{9} -2.00000 q^{10} -2.00000 q^{12} +(-3.23607 - 2.35114i) q^{13} +(1.23607 - 3.80423i) q^{14} +(-0.309017 - 0.951057i) q^{15} +(3.23607 - 2.35114i) q^{16} +(1.61803 - 1.17557i) q^{17} +(1.23607 + 3.80423i) q^{18} +(-1.61803 - 1.17557i) q^{20} +2.00000 q^{21} -1.00000 q^{23} +(-1.23607 + 3.80423i) q^{25} +(-2.47214 - 7.60845i) q^{26} +(-4.04508 + 2.93893i) q^{27} +(3.23607 - 2.35114i) q^{28} +(0.618034 - 1.90211i) q^{30} +(-5.66312 - 4.11450i) q^{31} +8.00000 q^{32} +4.00000 q^{34} +(1.61803 + 1.17557i) q^{35} +(-1.23607 + 3.80423i) q^{36} +(0.927051 + 2.85317i) q^{37} +(3.23607 - 2.35114i) q^{39} +(-2.47214 + 7.60845i) q^{41} +(3.23607 + 2.35114i) q^{42} -6.00000 q^{43} -2.00000 q^{45} +(-1.61803 - 1.17557i) q^{46} +(2.47214 - 7.60845i) q^{47} +(1.23607 + 3.80423i) q^{48} +(2.42705 - 1.76336i) q^{49} +(-6.47214 + 4.70228i) q^{50} +(0.618034 + 1.90211i) q^{51} +(2.47214 - 7.60845i) q^{52} +(4.85410 + 3.52671i) q^{53} -10.0000 q^{54} +(1.54508 + 4.75528i) q^{59} +(1.61803 - 1.17557i) q^{60} +(-9.70820 + 7.05342i) q^{61} +(-4.32624 - 13.3148i) q^{62} +(1.23607 - 3.80423i) q^{63} +(6.47214 + 4.70228i) q^{64} +4.00000 q^{65} -7.00000 q^{67} +(3.23607 + 2.35114i) q^{68} +(0.309017 - 0.951057i) q^{69} +(1.23607 + 3.80423i) q^{70} +(2.42705 - 1.76336i) q^{71} +(1.23607 + 3.80423i) q^{73} +(-1.85410 + 5.70634i) q^{74} +(-3.23607 - 2.35114i) q^{75} +8.00000 q^{78} +(8.09017 + 5.87785i) q^{79} +(-1.23607 + 3.80423i) q^{80} +(0.309017 + 0.951057i) q^{81} +(-12.9443 + 9.40456i) q^{82} +(4.85410 - 3.52671i) q^{83} +(1.23607 + 3.80423i) q^{84} +(-0.618034 + 1.90211i) q^{85} +(-9.70820 - 7.05342i) q^{86} +15.0000 q^{89} +(-3.23607 - 2.35114i) q^{90} +(-2.47214 + 7.60845i) q^{91} +(-0.618034 - 1.90211i) q^{92} +(5.66312 - 4.11450i) q^{93} +(12.9443 - 9.40456i) q^{94} +(-2.47214 + 7.60845i) q^{96} +(5.66312 + 4.11450i) q^{97} +6.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + q^{3} - 2 q^{4} - q^{5} - 2 q^{6} + 2 q^{7} + 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 + q^3 - 2 * q^4 - q^5 - 2 * q^6 + 2 * q^7 + 2 * q^9	$ 4 q + 2 q^{2} + q^{3} - 2 q^{4} - q^{5} - 2 q^{6} + 2 q^{7} + 2 q^{9} - 8 q^{10} - 8 q^{12} - 4 q^{13} - 4 q^{14} + q^{15} + 4 q^{16} + 2 q^{17} - 4 q^{18} - 2 q^{20} + 8 q^{21} - 4 q^{23} + 4 q^{25} + 8 q^{26} - 5 q^{27} + 4 q^{28} - 2 q^{30} - 7 q^{31} + 32 q^{32} + 16 q^{34} + 2 q^{35} + 4 q^{36} - 3 q^{37} + 4 q^{39} + 8 q^{41} + 4 q^{42} - 24 q^{43} - 8 q^{45} - 2 q^{46} - 8 q^{47} - 4 q^{48} + 3 q^{49} - 8 q^{50} - 2 q^{51} - 8 q^{52} + 6 q^{53} - 40 q^{54} - 5 q^{59} + 2 q^{60} - 12 q^{61} + 14 q^{62} - 4 q^{63} + 8 q^{64} + 16 q^{65} - 28 q^{67} + 4 q^{68} - q^{69} - 4 q^{70} + 3 q^{71} - 4 q^{73} + 6 q^{74} - 4 q^{75} + 32 q^{78} + 10 q^{79} + 4 q^{80} - q^{81} - 16 q^{82} + 6 q^{83} - 4 q^{84} + 2 q^{85} - 12 q^{86} + 60 q^{89} - 4 q^{90} + 8 q^{91} + 2 q^{92} + 7 q^{93} + 16 q^{94} + 8 q^{96} + 7 q^{97} + 24 q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 + q^3 - 2 * q^4 - q^5 - 2 * q^6 + 2 * q^7 + 2 * q^9 - 8 * q^10 - 8 * q^12 - 4 * q^13 - 4 * q^14 + q^15 + 4 * q^16 + 2 * q^17 - 4 * q^18 - 2 * q^20 + 8 * q^21 - 4 * q^23 + 4 * q^25 + 8 * q^26 - 5 * q^27 + 4 * q^28 - 2 * q^30 - 7 * q^31 + 32 * q^32 + 16 * q^34 + 2 * q^35 + 4 * q^36 - 3 * q^37 + 4 * q^39 + 8 * q^41 + 4 * q^42 - 24 * q^43 - 8 * q^45 - 2 * q^46 - 8 * q^47 - 4 * q^48 + 3 * q^49 - 8 * q^50 - 2 * q^51 - 8 * q^52 + 6 * q^53 - 40 * q^54 - 5 * q^59 + 2 * q^60 - 12 * q^61 + 14 * q^62 - 4 * q^63 + 8 * q^64 + 16 * q^65 - 28 * q^67 + 4 * q^68 - q^69 - 4 * q^70 + 3 * q^71 - 4 * q^73 + 6 * q^74 - 4 * q^75 + 32 * q^78 + 10 * q^79 + 4 * q^80 - q^81 - 16 * q^82 + 6 * q^83 - 4 * q^84 + 2 * q^85 - 12 * q^86 + 60 * q^89 - 4 * q^90 + 8 * q^91 + 2 * q^92 + 7 * q^93 + 16 * q^94 + 8 * q^96 + 7 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/121\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{5}\right)$

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 $

$2$	1.61803	+	1.17557i	1.14412	+	0.831254i	0.987688	−	0.156434i	$-0.0500000\pi$
$2$	1.61803	+	1.17557i	1.14412	+	0.831254i	0.156434	+	0.987688i	$0.450000\pi$
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i	−0.999773	−	0.0213149i	$-0.993215\pi$
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i	0.821362	+	0.570408i	$0.193215\pi$
$4$	0.618034	+	1.90211i	0.309017	+	0.951057i
$5$	−0.809017	+	0.587785i	−0.361803	+	0.262866i	−0.753804	−	0.657099i	$-0.771783\pi$
$5$	−0.809017	+	0.587785i	−0.361803	+	0.262866i	0.392000	+	0.919965i	$0.371783\pi$
$6$	−1.61803	+	1.17557i	−0.660560	+	0.479925i
$7$	−0.618034	−	1.90211i	−0.233595	−	0.718931i	−0.997305	−	0.0733714i	$-0.976624\pi$
$7$	−0.618034	−	1.90211i	−0.233595	−	0.718931i	0.763710	−	0.645560i	$-0.223376\pi$
$8$		0			0
$9$	1.61803	+	1.17557i	0.539345	+	0.391857i
$10$	−2.00000			−0.632456
$11$		0			0
$11$		0			0
$12$	−2.00000			−0.577350
$13$	−3.23607	−	2.35114i	−0.897524	−	0.652089i	0.0403050	−	0.999187i	$-0.487167\pi$
$13$	−3.23607	−	2.35114i	−0.897524	−	0.652089i	−0.937829	+	0.347098i	$0.887167\pi$
$14$	1.23607	−	3.80423i	0.330353	−	1.01672i
$15$	−0.309017	−	0.951057i	−0.0797878	−	0.245562i
$16$	3.23607	−	2.35114i	0.809017	−	0.587785i
$17$	1.61803	−	1.17557i	0.392431	−	0.285118i	−0.374020	−	0.927421i	$-0.622021\pi$
$17$	1.61803	−	1.17557i	0.392431	−	0.285118i	0.766451	+	0.642303i	$0.222021\pi$
$18$	1.23607	+	3.80423i	0.291344	+	0.896665i
$19$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$19$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$20$	−1.61803	−	1.17557i	−0.361803	−	0.262866i
$21$	2.00000			0.436436
$22$		0			0
$23$	−1.00000			−0.208514			−0.104257	−	0.994550i	$-0.533247\pi$
$23$	−1.00000			−0.208514			−0.104257	+	0.994550i	$0.533247\pi$
$24$		0			0
$25$	−1.23607	+	3.80423i	−0.247214	+	0.760845i
$26$	−2.47214	−	7.60845i	−0.484826	−	1.49214i
$27$	−4.04508	+	2.93893i	−0.778477	+	0.565597i
$28$	3.23607	−	2.35114i	0.611559	−	0.444324i
$29$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$29$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$30$	0.618034	−	1.90211i	0.112837	−	0.347277i
$31$	−5.66312	−	4.11450i	−1.01713	−	0.738985i	−0.0514344	−	0.998676i	$-0.516379\pi$
$31$	−5.66312	−	4.11450i	−1.01713	−	0.738985i	−0.965692	+	0.259691i	$0.916379\pi$
$32$	8.00000			1.41421
$33$		0			0
$34$	4.00000			0.685994
$35$	1.61803	+	1.17557i	0.273498	+	0.198708i
$36$	−1.23607	+	3.80423i	−0.206011	+	0.634038i
$37$	0.927051	+	2.85317i	0.152406	+	0.469058i	0.997889	−	0.0649448i	$-0.0206871\pi$
$37$	0.927051	+	2.85317i	0.152406	+	0.469058i	−0.845483	+	0.534003i	$0.820687\pi$
$38$		0			0
$39$	3.23607	−	2.35114i	0.518186	−	0.376484i
$40$		0			0
$41$	−2.47214	+	7.60845i	−0.386083	+	1.18824i	0.549609	+	0.835422i	$0.314777\pi$
$41$	−2.47214	+	7.60845i	−0.386083	+	1.18824i	−0.935692	+	0.352819i	$0.885223\pi$
$42$	3.23607	+	2.35114i	0.499336	+	0.362789i
$43$	−6.00000			−0.914991			−0.457496	−	0.889212i	$-0.651253\pi$
$43$	−6.00000			−0.914991			−0.457496	+	0.889212i	$0.651253\pi$
$44$		0			0
$45$	−2.00000			−0.298142
$46$	−1.61803	−	1.17557i	−0.238566	−	0.173328i
$47$	2.47214	−	7.60845i	0.360598	−	1.10981i	−0.592094	−	0.805869i	$-0.701699\pi$
$47$	2.47214	−	7.60845i	0.360598	−	1.10981i	0.952692	−	0.303938i	$-0.0983015\pi$
$48$	1.23607	+	3.80423i	0.178411	+	0.549093i
$49$	2.42705	−	1.76336i	0.346722	−	0.251908i
$50$	−6.47214	+	4.70228i	−0.915298	+	0.665003i
$51$	0.618034	+	1.90211i	0.0865421	+	0.266349i
$52$	2.47214	−	7.60845i	0.342824	−	1.05510i
$53$	4.85410	+	3.52671i	0.666762	+	0.484431i	0.868940	−	0.494918i	$-0.164802\pi$
$53$	4.85410	+	3.52671i	0.666762	+	0.484431i	−0.202178	+	0.979349i	$0.564802\pi$
$54$	−10.0000			−1.36083
$55$		0			0
$56$		0			0
$57$		0			0
$58$		0			0
$59$	1.54508	+	4.75528i	0.201153	+	0.619085i	0.999849	+	0.0173510i	$0.00552328\pi$
$59$	1.54508	+	4.75528i	0.201153	+	0.619085i	−0.798697	+	0.601734i	$0.794477\pi$
$60$	1.61803	−	1.17557i	0.208887	−	0.151765i
$61$	−9.70820	+	7.05342i	−1.24301	+	0.903098i	−0.997795	−	0.0663709i	$-0.978858\pi$
$61$	−9.70820	+	7.05342i	−1.24301	+	0.903098i	−0.245213	+	0.969469i	$0.578858\pi$
$62$	−4.32624	−	13.3148i	−0.549433	−	1.69098i
$63$	1.23607	−	3.80423i	0.155730	−	0.479287i
$64$	6.47214	+	4.70228i	0.809017	+	0.587785i
$65$	4.00000			0.496139
$66$		0			0
$67$	−7.00000			−0.855186			−0.427593	−	0.903971i	$-0.640638\pi$
$67$	−7.00000			−0.855186			−0.427593	+	0.903971i	$0.640638\pi$
$68$	3.23607	+	2.35114i	0.392431	+	0.285118i
$69$	0.309017	−	0.951057i	0.0372013	−	0.114494i
$70$	1.23607	+	3.80423i	0.147738	+	0.454692i
$71$	2.42705	−	1.76336i	0.288038	−	0.209272i	−0.434378	−	0.900731i	$-0.643032\pi$
$71$	2.42705	−	1.76336i	0.288038	−	0.209272i	0.722416	+	0.691459i	$0.243032\pi$
$72$		0			0
$73$	1.23607	+	3.80423i	0.144671	+	0.445251i	0.996969	−	0.0778060i	$-0.0247915\pi$
$73$	1.23607	+	3.80423i	0.144671	+	0.445251i	−0.852298	+	0.523057i	$0.824791\pi$
$74$	−1.85410	+	5.70634i	−0.215535	+	0.663348i
$75$	−3.23607	−	2.35114i	−0.373669	−	0.271486i
$76$		0			0
$77$		0			0
$78$	8.00000			0.905822
$79$	8.09017	+	5.87785i	0.910215	+	0.661310i	0.941069	−	0.338214i	$-0.109823\pi$
$79$	8.09017	+	5.87785i	0.910215	+	0.661310i	−0.0308541	+	0.999524i	$0.509823\pi$
$80$	−1.23607	+	3.80423i	−0.138197	+	0.425325i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	−12.9443	+	9.40456i	−1.42946	+	1.03856i
$83$	4.85410	−	3.52671i	0.532807	−	0.387107i	−0.288600	−	0.957450i	$-0.593190\pi$
$83$	4.85410	−	3.52671i	0.532807	−	0.387107i	0.821407	+	0.570343i	$0.193190\pi$
$84$	1.23607	+	3.80423i	0.134866	+	0.415075i
$85$	−0.618034	+	1.90211i	−0.0670352	+	0.206313i
$86$	−9.70820	−	7.05342i	−1.04686	−	0.760590i
$87$		0			0
$88$		0			0
$89$	15.0000			1.59000			0.794998	−	0.606612i	$-0.207472\pi$
$89$	15.0000			1.59000			0.794998	+	0.606612i	$0.207472\pi$
$90$	−3.23607	−	2.35114i	−0.341112	−	0.247832i
$91$	−2.47214	+	7.60845i	−0.259150	+	0.797582i
$92$	−0.618034	−	1.90211i	−0.0644345	−	0.198309i
$93$	5.66312	−	4.11450i	0.587238	−	0.426653i
$94$	12.9443	−	9.40456i	1.33510	−	0.970007i
$95$		0			0
$96$	−2.47214	+	7.60845i	−0.252311	+	0.776534i
$97$	5.66312	+	4.11450i	0.575003	+	0.417764i	0.836919	−	0.547327i	$-0.184354\pi$
$97$	5.66312	+	4.11450i	0.575003	+	0.417764i	−0.261916	+	0.965091i	$0.584354\pi$
$98$	6.00000			0.606092
$99$		0			0
$100$	−8.00000			−0.800000
$101$	−1.61803	−	1.17557i	−0.161000	−	0.116974i	0.504368	−	0.863489i	$-0.331726\pi$
$101$	−1.61803	−	1.17557i	−0.161000	−	0.116974i	−0.665368	+	0.746515i	$0.731726\pi$
$102$	−1.23607	+	3.80423i	−0.122389	+	0.376675i
$103$	−4.94427	−	15.2169i	−0.487174	−	1.49937i	−0.828808	−	0.559533i	$-0.810980\pi$
$103$	−4.94427	−	15.2169i	−0.487174	−	1.49937i	0.341634	−	0.939833i	$-0.389020\pi$
$104$		0			0
$105$	−1.61803	+	1.17557i	−0.157904	+	0.114724i
$106$	3.70820	+	11.4127i	0.360173	+	1.10850i
$107$	5.56231	−	17.1190i	0.537728	−	1.65496i	−0.199950	−	0.979806i	$-0.564078\pi$
$107$	5.56231	−	17.1190i	0.537728	−	1.65496i	0.737679	−	0.675152i	$-0.235922\pi$
$108$	−8.09017	−	5.87785i	−0.778477	−	0.565597i
$109$	10.0000			0.957826			0.478913	−	0.877862i	$-0.341031\pi$
$109$	10.0000			0.957826			0.478913	+	0.877862i	$0.341031\pi$
$110$		0			0
$111$	−3.00000			−0.284747
$112$	−6.47214	−	4.70228i	−0.611559	−	0.444324i
$113$	2.78115	−	8.55951i	0.261629	−	0.805211i	−0.730822	−	0.682568i	$-0.760863\pi$
$113$	2.78115	−	8.55951i	0.261629	−	0.805211i	0.992451	−	0.122643i	$-0.0391369\pi$
$114$		0			0
$115$	0.809017	−	0.587785i	0.0754412	−	0.0548113i
$116$		0			0
$117$	−2.47214	−	7.60845i	−0.228549	−	0.703402i
$118$	−3.09017	+	9.51057i	−0.284473	+	0.875518i
$119$	−3.23607	−	2.35114i	−0.296650	−	0.215529i
$120$		0			0
$121$		0			0
$122$	−24.0000			−2.17286
$123$	−6.47214	−	4.70228i	−0.583573	−	0.423990i
$124$	4.32624	−	13.3148i	0.388508	−	1.19570i
$125$	−2.78115	−	8.55951i	−0.248754	−	0.765586i
$126$	6.47214	−	4.70228i	0.576584	−	0.418913i
$127$	−6.47214	+	4.70228i	−0.574309	+	0.417260i	−0.836668	−	0.547710i	$-0.815500\pi$
$127$	−6.47214	+	4.70228i	−0.574309	+	0.417260i	0.262359	+	0.964970i	$0.415500\pi$
$128$		0			0
$129$	1.85410	−	5.70634i	0.163245	−	0.502415i
$130$	6.47214	+	4.70228i	0.567644	+	0.412417i
$131$	−18.0000			−1.57267			−0.786334	−	0.617802i	$-0.788023\pi$
$131$	−18.0000			−1.57267			−0.786334	+	0.617802i	$0.788023\pi$
$132$		0			0
$133$		0			0
$134$	−11.3262	−	8.22899i	−0.978438	−	0.710877i
$135$	1.54508	−	4.75528i	0.132980	−	0.409270i
$136$		0			0
$137$	5.66312	−	4.11450i	0.483833	−	0.351525i	−0.318975	−	0.947763i	$-0.603339\pi$
$137$	5.66312	−	4.11450i	0.483833	−	0.351525i	0.802808	+	0.596238i	$0.203339\pi$
$138$	1.61803	−	1.17557i	0.137736	−	0.100071i
$139$	3.09017	+	9.51057i	0.262105	+	0.806676i	0.992346	+	0.123486i	$0.0394076\pi$
$139$	3.09017	+	9.51057i	0.262105	+	0.806676i	−0.730241	+	0.683189i	$0.760592\pi$
$140$	−1.23607	+	3.80423i	−0.104467	+	0.321516i
$141$	6.47214	+	4.70228i	0.545052	+	0.396004i
$142$	6.00000			0.503509
$143$		0			0
$144$	8.00000			0.666667
$145$		0			0
$146$	−2.47214	+	7.60845i	−0.204595	+	0.629680i
$147$	0.927051	+	2.85317i	0.0764619	+	0.235325i
$148$	−4.85410	+	3.52671i	−0.399005	+	0.289894i
$149$	8.09017	−	5.87785i	0.662773	−	0.481532i	−0.204826	−	0.978798i	$-0.565663\pi$
$149$	8.09017	−	5.87785i	0.662773	−	0.481532i	0.867598	+	0.497266i	$0.165663\pi$
$150$	−2.47214	−	7.60845i	−0.201849	−	0.621228i
$151$	0.618034	−	1.90211i	0.0502949	−	0.154792i	−0.922755	−	0.385388i	$-0.874068\pi$
$151$	0.618034	−	1.90211i	0.0502949	−	0.154792i	0.973050	+	0.230596i	$0.0740676\pi$
$152$		0			0
$153$	4.00000			0.323381
$154$		0			0
$155$	7.00000			0.562254
$156$	6.47214	+	4.70228i	0.518186	+	0.376484i
$157$	−2.16312	+	6.65740i	−0.172636	+	0.531318i	−0.999518	−	0.0310576i	$-0.990112\pi$
$157$	−2.16312	+	6.65740i	−0.172636	+	0.531318i	0.826882	+	0.562376i	$0.190112\pi$
$158$	6.18034	+	19.0211i	0.491681	+	1.51324i
$159$	−4.85410	+	3.52671i	−0.384955	+	0.279686i
$160$	−6.47214	+	4.70228i	−0.511667	+	0.371748i
$161$	0.618034	+	1.90211i	0.0487079	+	0.149908i
$162$	−0.618034	+	1.90211i	−0.0485573	+	0.149444i
$163$	−3.23607	−	2.35114i	−0.253468	−	0.184156i	0.453794	−	0.891107i	$-0.350070\pi$
$163$	−3.23607	−	2.35114i	−0.253468	−	0.184156i	−0.707263	+	0.706951i	$0.750070\pi$
$164$	−16.0000			−1.24939
$165$		0			0
$166$	12.0000			0.931381
$167$	9.70820	+	7.05342i	0.751243	+	0.545810i	0.896212	−	0.443626i	$-0.146308\pi$
$167$	9.70820	+	7.05342i	0.751243	+	0.545810i	−0.144969	+	0.989436i	$0.546308\pi$
$168$		0			0
$169$	0.927051	+	2.85317i	0.0713116	+	0.219475i
$170$	−3.23607	+	2.35114i	−0.248195	+	0.180324i
$171$		0			0
$172$	−3.70820	−	11.4127i	−0.282748	−	0.870209i
$173$	−1.85410	+	5.70634i	−0.140965	+	0.433845i	−0.996470	−	0.0839492i	$-0.973247\pi$
$173$	−1.85410	+	5.70634i	−0.140965	+	0.433845i	0.855505	+	0.517794i	$0.173247\pi$
$174$		0			0
$175$	8.00000			0.604743
$176$		0			0
$177$	−5.00000			−0.375823
$178$	24.2705	+	17.6336i	1.81915	+	1.32169i
$179$	−4.63525	+	14.2658i	−0.346455	+	1.06628i	0.614345	+	0.789038i	$0.289420\pi$
$179$	−4.63525	+	14.2658i	−0.346455	+	1.06628i	−0.960800	+	0.277242i	$0.910580\pi$
$180$	−1.23607	−	3.80423i	−0.0921311	−	0.283550i
$181$	−5.66312	+	4.11450i	−0.420936	+	0.305828i	−0.778014	−	0.628246i	$-0.783773\pi$
$181$	−5.66312	+	4.11450i	−0.420936	+	0.305828i	0.357078	+	0.934075i	$0.383773\pi$
$182$	−12.9443	+	9.40456i	−0.959493	+	0.697113i
$183$	−3.70820	−	11.4127i	−0.274118	−	0.843649i
$184$		0			0
$185$	−2.42705	−	1.76336i	−0.178440	−	0.129644i
$186$	14.0000			1.02653
$187$		0			0
$188$	16.0000			1.16692
$189$	8.09017	+	5.87785i	0.588473	+	0.427551i
$190$		0			0
$191$	5.25329	+	16.1680i	0.380115	+	1.16987i	0.939963	+	0.341277i	$0.110860\pi$
$191$	5.25329	+	16.1680i	0.380115	+	1.16987i	−0.559848	+	0.828595i	$0.689140\pi$
$192$	−6.47214	+	4.70228i	−0.467086	+	0.339358i
$193$	−3.23607	+	2.35114i	−0.232937	+	0.169239i	−0.698131	−	0.715970i	$-0.745985\pi$
$193$	−3.23607	+	2.35114i	−0.232937	+	0.169239i	0.465194	+	0.885209i	$0.345985\pi$
$194$	4.32624	+	13.3148i	0.310606	+	0.955946i
$195$	−1.23607	+	3.80423i	−0.0885167	+	0.272426i
$196$	4.85410	+	3.52671i	0.346722	+	0.251908i
$197$	−2.00000			−0.142494			−0.0712470	−	0.997459i	$-0.522698\pi$
$197$	−2.00000			−0.142494			−0.0712470	+	0.997459i	$0.522698\pi$
$198$		0			0
$199$		0			0			−	1.00000i	$-0.5\pi$
$199$		0			0				1.00000i	$0.5\pi$
$200$		0			0
$201$	2.16312	−	6.65740i	0.152575	−	0.469576i
$202$	−1.23607	−	3.80423i	−0.0869694	−	0.267664i
$203$		0			0
$204$	−3.23607	+	2.35114i	−0.226570	+	0.164613i
$205$	−2.47214	−	7.60845i	−0.172661	−	0.531397i
$206$	9.88854	−	30.4338i	0.688967	−	2.12042i
$207$	−1.61803	−	1.17557i	−0.112461	−	0.0817078i
$208$	−16.0000			−1.10940
$209$		0			0
$210$	−4.00000			−0.276026
$211$	−9.70820	−	7.05342i	−0.668340	−	0.485578i	0.201129	−	0.979565i	$-0.435539\pi$
$211$	−9.70820	−	7.05342i	−0.668340	−	0.485578i	−0.869469	+	0.493987i	$0.835539\pi$
$212$	−3.70820	+	11.4127i	−0.254680	+	0.783826i
$213$	0.927051	+	2.85317i	0.0635205	+	0.195496i
$214$	29.1246	−	21.1603i	1.99092	−	1.44649i
$215$	4.85410	−	3.52671i	0.331047	−	0.240520i
$216$		0			0
$217$	−4.32624	+	13.3148i	−0.293684	+	0.903867i
$218$	16.1803	+	11.7557i	1.09587	+	0.796197i
$219$	−4.00000			−0.270295
$220$		0			0
$221$	−8.00000			−0.538138
$222$	−4.85410	−	3.52671i	−0.325786	−	0.236697i
$223$	5.87132	−	18.0701i	0.393173	−	1.21006i	−0.537203	−	0.843453i	$-0.680519\pi$
$223$	5.87132	−	18.0701i	0.393173	−	1.21006i	0.930375	−	0.366608i	$-0.119481\pi$
$224$	−4.94427	−	15.2169i	−0.330353	−	1.01672i
$225$	−6.47214	+	4.70228i	−0.431476	+	0.313485i
$226$	14.5623	−	10.5801i	0.968670	−	0.703780i
$227$	5.56231	+	17.1190i	0.369183	+	1.13623i	0.947320	+	0.320289i	$0.103780\pi$
$227$	5.56231	+	17.1190i	0.369183	+	1.13623i	−0.578137	+	0.815940i	$0.696220\pi$
$228$		0			0
$229$	−12.1353	−	8.81678i	−0.801920	−	0.582629i	0.109557	−	0.993981i	$-0.465057\pi$
$229$	−12.1353	−	8.81678i	−0.801920	−	0.582629i	−0.911477	+	0.411351i	$0.865057\pi$
$230$	2.00000			0.131876
$231$		0			0
$232$		0			0
$233$	−19.4164	−	14.1068i	−1.27201	−	0.924170i	−0.272730	−	0.962090i	$-0.587927\pi$
$233$	−19.4164	−	14.1068i	−1.27201	−	0.924170i	−0.999281	+	0.0379203i	$0.987927\pi$
$234$	4.94427	−	15.2169i	0.323217	−	0.994760i
$235$	2.47214	+	7.60845i	0.161264	+	0.496321i
$236$	−8.09017	+	5.87785i	−0.526625	+	0.382616i
$237$	−8.09017	+	5.87785i	−0.525513	+	0.381808i
$238$	−2.47214	−	7.60845i	−0.160245	−	0.493183i
$239$	−9.27051	+	28.5317i	−0.599659	+	1.84556i	−0.0696477	+	0.997572i	$0.522188\pi$
$239$	−9.27051	+	28.5317i	−0.599659	+	1.84556i	−0.530012	+	0.847990i	$0.677812\pi$
$240$	−3.23607	−	2.35114i	−0.208887	−	0.151765i
$241$	−8.00000			−0.515325			−0.257663	−	0.966235i	$-0.582952\pi$
$241$	−8.00000			−0.515325			−0.257663	+	0.966235i	$0.582952\pi$
$242$		0			0
$243$	−16.0000			−1.02640
$244$	−19.4164	−	14.1068i	−1.24301	−	0.903098i
$245$	−0.927051	+	2.85317i	−0.0592271	+	0.182282i
$246$	−4.94427	−	15.2169i	−0.315235	−	0.970194i
$247$		0			0
$248$		0			0
$249$	1.85410	+	5.70634i	0.117499	+	0.361625i
$250$	5.56231	−	17.1190i	0.351791	−	1.08270i
$251$	18.6074	+	13.5191i	1.17449	+	0.853316i	0.991539	−	0.129807i	$-0.0414357\pi$
$251$	18.6074	+	13.5191i	1.17449	+	0.853316i	0.182949	+	0.983122i	$0.441436\pi$
$252$	8.00000			0.503953
$253$		0			0
$254$	−16.0000			−1.00393
$255$	−1.61803	−	1.17557i	−0.101325	−	0.0736171i
$256$	4.94427	−	15.2169i	0.309017	−	0.951057i
$257$	−0.618034	−	1.90211i	−0.0385519	−	0.118651i	0.929928	−	0.367740i	$-0.119869\pi$
$257$	−0.618034	−	1.90211i	−0.0385519	−	0.118651i	−0.968480	+	0.249090i	$0.919869\pi$
$258$	9.70820	−	7.05342i	0.604406	−	0.439127i
$259$	4.85410	−	3.52671i	0.301619	−	0.219139i
$260$	2.47214	+	7.60845i	0.153315	+	0.471856i
$261$		0			0
$262$	−29.1246	−	21.1603i	−1.79932	−	1.30729i
$263$	14.0000			0.863277			0.431638	−	0.902047i	$-0.357936\pi$
$263$	14.0000			0.863277			0.431638	+	0.902047i	$0.357936\pi$
$264$		0			0
$265$	−6.00000			−0.368577
$266$		0			0
$267$	−4.63525	+	14.2658i	−0.283673	+	0.873056i
$268$	−4.32624	−	13.3148i	−0.264267	−	0.813330i
$269$	−8.09017	+	5.87785i	−0.493266	+	0.358379i	−0.806439	−	0.591317i	$-0.798608\pi$
$269$	−8.09017	+	5.87785i	−0.493266	+	0.358379i	0.313173	+	0.949696i	$0.398608\pi$
$270$	8.09017	−	5.87785i	0.492352	−	0.357715i
$271$	−8.65248	−	26.6296i	−0.525600	−	1.61763i	−0.763125	−	0.646250i	$-0.776336\pi$
$271$	−8.65248	−	26.6296i	−0.525600	−	1.61763i	0.237525	−	0.971381i	$-0.423664\pi$
$272$	2.47214	−	7.60845i	0.149895	−	0.461330i
$273$	−6.47214	−	4.70228i	−0.391711	−	0.284595i
$274$	14.0000			0.845771
$275$		0			0
$276$	2.00000			0.120386
$277$	1.61803	+	1.17557i	0.0972182	+	0.0706332i	0.635332	−	0.772239i	$-0.280863\pi$
$277$	1.61803	+	1.17557i	0.0972182	+	0.0706332i	−0.538114	+	0.842872i	$0.680863\pi$
$278$	−6.18034	+	19.0211i	−0.370672	+	1.14081i
$279$	−4.32624	−	13.3148i	−0.259005	−	0.797136i
$280$		0			0
$281$	14.5623	−	10.5801i	0.868714	−	0.631158i	−0.0615273	−	0.998105i	$-0.519597\pi$
$281$	14.5623	−	10.5801i	0.868714	−	0.631158i	0.930242	+	0.366947i	$0.119597\pi$
$282$	4.94427	+	15.2169i	0.294427	+	0.906153i
$283$	1.23607	−	3.80423i	0.0734766	−	0.226138i	−0.907573	−	0.419894i	$-0.862067\pi$
$283$	1.23607	−	3.80423i	0.0734766	−	0.226138i	0.981050	+	0.193756i	$0.0620672\pi$
$284$	4.85410	+	3.52671i	0.288038	+	0.209272i
$285$		0			0
$286$		0			0
$287$	16.0000			0.944450
$288$	12.9443	+	9.40456i	0.762749	+	0.554169i
$289$	−4.01722	+	12.3637i	−0.236307	+	0.727279i
$290$		0			0
$291$	−5.66312	+	4.11450i	−0.331978	+	0.241196i
$292$	−6.47214	+	4.70228i	−0.378753	+	0.275180i
$293$	7.41641	+	22.8254i	0.433271	+	1.33347i	0.894848	+	0.446371i	$0.147284\pi$
$293$	7.41641	+	22.8254i	0.433271	+	1.33347i	−0.461577	+	0.887100i	$0.652716\pi$
$294$	−1.85410	+	5.70634i	−0.108133	+	0.332800i
$295$	−4.04508	−	2.93893i	−0.235514	−	0.171111i
$296$		0			0
$297$		0			0
$298$	20.0000			1.15857
$299$	3.23607	+	2.35114i	0.187147	+	0.135970i
$300$	2.47214	−	7.60845i	0.142729	−	0.439274i
$301$	3.70820	+	11.4127i	0.213737	+	0.657816i
$302$	3.23607	−	2.35114i	0.186215	−	0.135293i
$303$	1.61803	−	1.17557i	0.0929536	−	0.0675348i
$304$		0			0
$305$	3.70820	−	11.4127i	0.212331	−	0.653488i
$306$	6.47214	+	4.70228i	0.369987	+	0.268812i
$307$	8.00000			0.456584			0.228292	−	0.973593i	$-0.426686\pi$
$307$	8.00000			0.456584			0.228292	+	0.973593i	$0.426686\pi$
$308$		0			0
$309$	16.0000			0.910208
$310$	11.3262	+	8.22899i	0.643287	+	0.467375i
$311$	3.70820	−	11.4127i	0.210273	−	0.647154i	−0.789183	−	0.614159i	$-0.789495\pi$
$311$	3.70820	−	11.4127i	0.210273	−	0.647154i	0.999456	−	0.0329949i	$-0.0105045\pi$
$312$		0			0
$313$	0.809017	−	0.587785i	0.0457283	−	0.0332236i	−0.564686	−	0.825306i	$-0.691003\pi$
$313$	0.809017	−	0.587785i	0.0457283	−	0.0332236i	0.610415	+	0.792082i	$0.291003\pi$
$314$	−11.3262	+	8.22899i	−0.639177	+	0.464389i
$315$	1.23607	+	3.80423i	0.0696445	+	0.214344i
$316$	−6.18034	+	19.0211i	−0.347671	+	1.07002i
$317$	−10.5172	−	7.64121i	−0.590706	−	0.429173i	0.251862	−	0.967763i	$-0.418957\pi$
$317$	−10.5172	−	7.64121i	−0.590706	−	0.429173i	−0.842568	+	0.538590i	$0.818957\pi$
$318$	−12.0000			−0.672927
$319$		0			0
$320$	−8.00000			−0.447214
$321$	14.5623	+	10.5801i	0.812789	+	0.590526i
$322$	−1.23607	+	3.80423i	−0.0688834	+	0.212001i
$323$		0			0
$324$	−1.61803	+	1.17557i	−0.0898908	+	0.0653095i
$325$	12.9443	−	9.40456i	0.718019	−	0.521671i
$326$	−2.47214	−	7.60845i	−0.136919	−	0.421393i
$327$	−3.09017	+	9.51057i	−0.170887	+	0.525935i
$328$		0			0
$329$	−16.0000			−0.882109
$330$		0			0
$331$	7.00000			0.384755			0.192377	−	0.981321i	$-0.438380\pi$
$331$	7.00000			0.384755			0.192377	+	0.981321i	$0.438380\pi$
$332$	9.70820	+	7.05342i	0.532807	+	0.387107i
$333$	−1.85410	+	5.70634i	−0.101604	+	0.312705i
$334$	7.41641	+	22.8254i	0.405808	+	1.24895i
$335$	5.66312	−	4.11450i	0.309409	−	0.224799i
$336$	6.47214	−	4.70228i	0.353084	−	0.256531i
$337$	−6.79837	−	20.9232i	−0.370331	−	1.13976i	−0.946575	−	0.322484i	$-0.895482\pi$
$337$	−6.79837	−	20.9232i	−0.370331	−	1.13976i	0.576244	−	0.817278i	$-0.304518\pi$
$338$	−1.85410	+	5.70634i	−0.100850	+	0.310384i
$339$	7.28115	+	5.29007i	0.395458	+	0.287317i
$340$	−4.00000			−0.216930
$341$		0			0
$342$		0			0
$343$	−16.1803	−	11.7557i	−0.873656	−	0.634748i
$344$		0			0
$345$	0.309017	+	0.951057i	0.0166369	+	0.0512032i
$346$	−9.70820	+	7.05342i	−0.521916	+	0.379194i
$347$	−22.6525	+	16.4580i	−1.21605	+	0.883511i	−0.995766	−	0.0919250i	$-0.970698\pi$
$347$	−22.6525	+	16.4580i	−1.21605	+	0.883511i	−0.220283	+	0.975436i	$0.570698\pi$
$348$		0			0
$349$	9.27051	−	28.5317i	0.496239	−	1.52727i	−0.318778	−	0.947829i	$-0.603272\pi$
$349$	9.27051	−	28.5317i	0.496239	−	1.52727i	0.815017	−	0.579437i	$-0.196728\pi$
$350$	12.9443	+	9.40456i	0.691900	+	0.502695i
$351$	20.0000			1.06752
$352$		0			0
$353$	−21.0000			−1.11772			−0.558859	−	0.829263i	$-0.688761\pi$
$353$	−21.0000			−1.11772			−0.558859	+	0.829263i	$0.688761\pi$
$354$	−8.09017	−	5.87785i	−0.429988	−	0.312404i
$355$	−0.927051	+	2.85317i	−0.0492028	+	0.151431i
$356$	9.27051	+	28.5317i	0.491336	+	1.51218i
$357$	3.23607	−	2.35114i	0.171271	−	0.124436i
$358$	−24.2705	+	17.6336i	−1.28274	+	0.931962i
$359$	−6.18034	−	19.0211i	−0.326186	−	1.00390i	−0.970902	−	0.239475i	$-0.923025\pi$
$359$	−6.18034	−	19.0211i	−0.326186	−	1.00390i	0.644717	−	0.764422i	$-0.276975\pi$
$360$		0			0
$361$	15.3713	+	11.1679i	0.809017	+	0.587785i
$362$	−14.0000			−0.735824
$363$		0			0
$364$	−16.0000			−0.838628
$365$	−3.23607	−	2.35114i	−0.169384	−	0.123064i
$366$	7.41641	−	22.8254i	0.387662	−	1.19310i
$367$	−5.25329	−	16.1680i	−0.274219	−	0.843961i	−0.989425	−	0.145046i	$-0.953667\pi$
$367$	−5.25329	−	16.1680i	−0.274219	−	0.843961i	0.715205	−	0.698914i	$-0.246333\pi$
$368$	−3.23607	+	2.35114i	−0.168692	+	0.122562i
$369$	−12.9443	+	9.40456i	−0.673852	+	0.489582i
$370$	−1.85410	−	5.70634i	−0.0963902	−	0.296658i
$371$	3.70820	−	11.4127i	0.192520	−	0.592517i
$372$	11.3262	+	8.22899i	0.587238	+	0.426653i
$373$	−26.0000			−1.34623			−0.673114	−	0.739538i	$-0.735044\pi$
$373$	−26.0000			−1.34623			−0.673114	+	0.739538i	$0.735044\pi$
$374$		0			0
$375$	9.00000			0.464758
$376$		0			0
$377$		0			0
$378$	6.18034	+	19.0211i	0.317882	+	0.978341i
$379$	4.04508	−	2.93893i	0.207782	−	0.150963i	−0.479028	−	0.877800i	$-0.659011\pi$
$379$	4.04508	−	2.93893i	0.207782	−	0.150963i	0.686810	+	0.726837i	$0.259011\pi$
$380$		0			0
$381$	−2.47214	−	7.60845i	−0.126651	−	0.389793i
$382$	−10.5066	+	32.3359i	−0.537563	+	1.65445i
$383$	0.809017	+	0.587785i	0.0413388	+	0.0300344i	0.608263	−	0.793736i	$-0.291867\pi$
$383$	0.809017	+	0.587785i	0.0413388	+	0.0300344i	−0.566924	+	0.823770i	$0.691867\pi$
$384$		0			0
$385$		0			0
$386$	−8.00000			−0.407189
$387$	−9.70820	−	7.05342i	−0.493496	−	0.358546i
$388$	−4.32624	+	13.3148i	−0.219631	+	0.675956i
$389$	−4.63525	−	14.2658i	−0.235017	−	0.723307i	−0.997119	−	0.0758507i	$-0.975833\pi$
$389$	−4.63525	−	14.2658i	−0.235017	−	0.723307i	0.762102	−	0.647456i	$-0.224167\pi$
$390$	−6.47214	+	4.70228i	−0.327729	+	0.238109i
$391$	−1.61803	+	1.17557i	−0.0818275	+	0.0594512i
$392$		0			0
$393$	5.56231	−	17.1190i	0.280581	−	0.863540i
$394$	−3.23607	−	2.35114i	−0.163031	−	0.118449i
$395$	−10.0000			−0.503155
$396$		0			0
$397$	−2.00000			−0.100377			−0.0501886	−	0.998740i	$-0.515982\pi$
$397$	−2.00000			−0.100377			−0.0501886	+	0.998740i	$0.515982\pi$
$398$		0			0
$399$		0			0
$400$	4.94427	+	15.2169i	0.247214	+	0.760845i
$401$	−1.61803	+	1.17557i	−0.0808008	+	0.0587052i	−0.627452	−	0.778655i	$-0.715902\pi$
$401$	−1.61803	+	1.17557i	−0.0808008	+	0.0587052i	0.546652	+	0.837360i	$0.315902\pi$
$402$	11.3262	−	8.22899i	0.564901	−	0.410425i
$403$	8.65248	+	26.6296i	0.431011	+	1.32651i
$404$	1.23607	−	3.80423i	0.0614967	−	0.189267i
$405$	−0.809017	−	0.587785i	−0.0402004	−	0.0292073i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	24.2705	+	17.6336i	1.20010	+	0.871923i	0.994295	−	0.106670i	$-0.0340188\pi$
$409$	24.2705	+	17.6336i	1.20010	+	0.871923i	0.205805	+	0.978593i	$0.434019\pi$
$410$	4.94427	−	15.2169i	0.244180	−	0.751509i
$411$	2.16312	+	6.65740i	0.106699	+	0.328385i
$412$	25.8885	−	18.8091i	1.27544	−	0.926659i
$413$	8.09017	−	5.87785i	0.398091	−	0.289230i
$414$	−1.23607	−	3.80423i	−0.0607494	−	0.186968i
$415$	−1.85410	+	5.70634i	−0.0910143	+	0.280113i
$416$	−25.8885	−	18.8091i	−1.26929	−	0.922193i
$417$	−10.0000			−0.489702
$418$		0			0
$419$	20.0000			0.977064			0.488532	−	0.872546i	$-0.337533\pi$
$419$	20.0000			0.977064			0.488532	+	0.872546i	$0.337533\pi$
$420$	−3.23607	−	2.35114i	−0.157904	−	0.114724i
$421$	6.79837	−	20.9232i	0.331332	−	1.01974i	−0.637168	−	0.770725i	$-0.719894\pi$
$421$	6.79837	−	20.9232i	0.331332	−	1.01974i	0.968501	−	0.249012i	$-0.0801057\pi$
$422$	−7.41641	−	22.8254i	−0.361025	−	1.11112i
$423$	12.9443	−	9.40456i	0.629372	−	0.457266i
$424$		0			0
$425$	2.47214	+	7.60845i	0.119916	+	0.369064i
$426$	−1.85410	+	5.70634i	−0.0898315	+	0.276473i
$427$	19.4164	+	14.1068i	0.939626	+	0.682678i
$428$	36.0000			1.74013
$429$		0			0
$430$	12.0000			0.578691
$431$	14.5623	+	10.5801i	0.701442	+	0.509627i	0.880401	−	0.474229i	$-0.157273\pi$
$431$	14.5623	+	10.5801i	0.701442	+	0.509627i	−0.178960	+	0.983856i	$0.557273\pi$
$432$	−6.18034	+	19.0211i	−0.297352	+	0.915155i
$433$	−3.39919	−	10.4616i	−0.163354	−	0.502753i	0.835557	−	0.549404i	$-0.185145\pi$
$433$	−3.39919	−	10.4616i	−0.163354	−	0.502753i	−0.998911	+	0.0466507i	$0.985145\pi$
$434$	−22.6525	+	16.4580i	−1.08735	+	0.790009i
$435$		0			0
$436$	6.18034	+	19.0211i	0.295985	+	0.910947i
$437$		0			0
$438$	−6.47214	−	4.70228i	−0.309251	−	0.224684i
$439$	40.0000			1.90910			0.954548	−	0.298057i	$-0.0963387\pi$
$439$	40.0000			1.90910			0.954548	+	0.298057i	$0.0963387\pi$
$440$		0			0
$441$	6.00000			0.285714
$442$	−12.9443	−	9.40456i	−0.615696	−	0.447329i
$443$	−3.39919	+	10.4616i	−0.161500	+	0.497047i	−0.998761	−	0.0497566i	$-0.984155\pi$
$443$	−3.39919	+	10.4616i	−0.161500	+	0.497047i	0.837261	+	0.546803i	$0.184155\pi$
$444$	−1.85410	−	5.70634i	−0.0879918	−	0.270811i
$445$	−12.1353	+	8.81678i	−0.575266	+	0.417955i
$446$	30.7426	−	22.3358i	1.45571	−	1.05763i
$447$	3.09017	+	9.51057i	0.146160	+	0.449834i
$448$	4.94427	−	15.2169i	0.233595	−	0.718931i
$449$	−28.3156	−	20.5725i	−1.33630	−	0.970876i	−0.999571	−	0.0292722i	$-0.990681\pi$
$449$	−28.3156	−	20.5725i	−1.33630	−	0.970876i	−0.336724	−	0.941603i	$-0.609319\pi$
$450$	−16.0000			−0.754247
$451$		0			0
$452$	18.0000			0.846649
$453$	1.61803	+	1.17557i	0.0760219	+	0.0552331i
$454$	−11.1246	+	34.2380i	−0.522104	+	1.60687i
$455$	−2.47214	−	7.60845i	−0.115896	−	0.356690i
$456$		0			0
$457$	9.70820	−	7.05342i	0.454131	−	0.329945i	−0.337094	−	0.941471i	$-0.609444\pi$
$457$	9.70820	−	7.05342i	0.454131	−	0.329945i	0.791224	+	0.611526i	$0.209444\pi$
$458$	−9.27051	−	28.5317i	−0.433182	−	1.33320i
$459$	−3.09017	+	9.51057i	−0.144237	+	0.443915i
$460$	1.61803	+	1.17557i	0.0754412	+	0.0548113i
$461$	12.0000			0.558896			0.279448	−	0.960161i	$-0.409849\pi$
$461$	12.0000			0.558896			0.279448	+	0.960161i	$0.409849\pi$
$462$		0			0
$463$	−11.0000			−0.511213			−0.255607	−	0.966781i	$-0.582275\pi$
$463$	−11.0000			−0.511213			−0.255607	+	0.966781i	$0.582275\pi$
$464$		0			0
$465$	−2.16312	+	6.65740i	−0.100312	+	0.308729i
$466$	−14.8328	−	45.6507i	−0.687117	−	2.11473i
$467$	21.8435	−	15.8702i	1.01079	−	0.734385i	0.0464191	−	0.998922i	$-0.485219\pi$
$467$	21.8435	−	15.8702i	1.01079	−	0.734385i	0.964376	+	0.264537i	$0.0852190\pi$
$468$	12.9443	−	9.40456i	0.598349	−	0.434726i
$469$	4.32624	+	13.3148i	0.199767	+	0.614820i
$470$	−4.94427	+	15.2169i	−0.228062	+	0.701903i
$471$	−5.66312	−	4.11450i	−0.260943	−	0.189586i
$472$		0			0
$473$		0			0
$474$	−20.0000			−0.918630
$475$		0			0
$476$	2.47214	−	7.60845i	0.113310	−	0.348733i
$477$	3.70820	+	11.4127i	0.169787	+	0.522551i
$478$	−48.5410	+	35.2671i	−2.22021	+	1.61308i
$479$	−16.1803	+	11.7557i	−0.739299	+	0.537132i	−0.892491	−	0.451064i	$-0.851044\pi$
$479$	−16.1803	+	11.7557i	−0.739299	+	0.537132i	0.153193	+	0.988196i	$0.451044\pi$
$480$	−2.47214	−	7.60845i	−0.112837	−	0.347277i
$481$	3.70820	−	11.4127i	0.169080	−	0.520373i
$482$	−12.9443	−	9.40456i	−0.589595	−	0.428366i
$483$	−2.00000			−0.0910032
$484$		0			0
$485$	−7.00000			−0.317854
$486$	−25.8885	−	18.8091i	−1.17433	−	0.853199i
$487$	7.10739	−	21.8743i	0.322067	−	0.991219i	−0.650681	−	0.759351i	$-0.725516\pi$
$487$	7.10739	−	21.8743i	0.322067	−	0.991219i	0.972747	−	0.231868i	$-0.0744836\pi$
$488$		0			0
$489$	3.23607	−	2.35114i	0.146340	−	0.106322i
$490$	−4.85410	+	3.52671i	−0.219286	+	0.159321i
$491$	−2.47214	−	7.60845i	−0.111566	−	0.343365i	0.879649	−	0.475623i	$-0.157777\pi$
$491$	−2.47214	−	7.60845i	−0.111566	−	0.343365i	−0.991215	+	0.132258i	$0.957777\pi$
$492$	4.94427	−	15.2169i	0.222905	−	0.686031i
$493$		0			0
$494$		0			0
$495$		0			0
$496$	−28.0000			−1.25724
$497$	−4.85410	−	3.52671i	−0.217736	−	0.158195i
$498$	−3.70820	+	11.4127i	−0.166169	+	0.511414i
$499$	6.18034	+	19.0211i	0.276670	+	0.851503i	0.988773	+	0.149427i	$0.0477430\pi$
$499$	6.18034	+	19.0211i	0.276670	+	0.851503i	−0.712103	+	0.702075i	$0.752257\pi$
$500$	14.5623	−	10.5801i	0.651246	−	0.473158i
$501$	−9.70820	+	7.05342i	−0.433731	+	0.315124i
$502$	14.2148	+	43.7486i	0.634437	+	1.95260i
$503$	−8.03444	+	24.7275i	−0.358238	+	1.10254i	0.595870	+	0.803081i	$0.296807\pi$
$503$	−8.03444	+	24.7275i	−0.358238	+	1.10254i	−0.954108	+	0.299462i	$0.903193\pi$
$504$		0			0
$505$	2.00000			0.0889988
$506$		0			0
$507$	−3.00000			−0.133235
$508$	−12.9443	−	9.40456i	−0.574309	−	0.417260i
$509$	4.63525	−	14.2658i	0.205454	−	0.632323i	−0.794240	−	0.607604i	$-0.792131\pi$
$509$	4.63525	−	14.2658i	0.205454	−	0.632323i	0.999694	−	0.0247189i	$-0.00786908\pi$
$510$	−1.23607	−	3.80423i	−0.0547340	−	0.168454i
$511$	6.47214	−	4.70228i	0.286310	−	0.208017i
$512$	25.8885	−	18.8091i	1.14412	−	0.831254i
$513$		0			0
$514$	1.23607	−	3.80423i	0.0545206	−	0.167797i
$515$	12.9443	+	9.40456i	0.570393	+	0.414415i
$516$	12.0000			0.528271
$517$		0			0
$518$	12.0000			0.527250
$519$	−4.85410	−	3.52671i	−0.213071	−	0.154805i
$520$		0			0
$521$	−0.927051	−	2.85317i	−0.0406148	−	0.125000i	0.928693	−	0.370849i	$-0.120933\pi$
$521$	−0.927051	−	2.85317i	−0.0406148	−	0.125000i	−0.969308	+	0.245849i	$0.920933\pi$
$522$		0			0
$523$	12.9443	−	9.40456i	0.566013	−	0.411233i	−0.267641	−	0.963519i	$-0.586244\pi$
$523$	12.9443	−	9.40456i	0.566013	−	0.411233i	0.833655	+	0.552286i	$0.186244\pi$
$524$	−11.1246	−	34.2380i	−0.485981	−	1.49570i
$525$	−2.47214	+	7.60845i	−0.107893	+	0.332060i
$526$	22.6525	+	16.4580i	0.987695	+	0.717602i
$527$	−14.0000			−0.609850
$528$		0			0
$529$	−22.0000			−0.956522
$530$	−9.70820	−	7.05342i	−0.421697	−	0.306381i
$531$	−3.09017	+	9.51057i	−0.134102	+	0.412723i
$532$		0			0
$533$	25.8885	−	18.8091i	1.12136	−	0.814714i
$534$	−24.2705	+	17.6336i	−1.05029	+	0.763079i
$535$	5.56231	+	17.1190i	0.240479	+	0.740120i
$536$		0			0
$537$	−12.1353	−	8.81678i	−0.523675	−	0.380472i
$538$	−20.0000			−0.862261
$539$		0			0
$540$	10.0000			0.430331
$541$	6.47214	+	4.70228i	0.278259	+	0.202167i	0.718158	−	0.695880i	$-0.244986\pi$
$541$	6.47214	+	4.70228i	0.278259	+	0.202167i	−0.439899	+	0.898047i	$0.644986\pi$
$542$	17.3050	−	53.2592i	0.743311	−	2.28768i
$543$	−2.16312	−	6.65740i	−0.0928283	−	0.285696i
$544$	12.9443	−	9.40456i	0.554981	−	0.403217i
$545$	−8.09017	+	5.87785i	−0.346545	+	0.251780i
$546$	−4.94427	−	15.2169i	−0.211595	−	0.651223i
$547$	2.47214	−	7.60845i	0.105701	−	0.325314i	−0.884193	−	0.467121i	$-0.845291\pi$
$547$	2.47214	−	7.60845i	0.105701	−	0.325314i	0.989894	+	0.141807i	$0.0452913\pi$
$548$	11.3262	+	8.22899i	0.483833	+	0.351525i
$549$	−24.0000			−1.02430
$550$		0			0
$551$		0			0
$552$		0			0
$553$	6.18034	−	19.0211i	0.262815	−	0.808861i
$554$	1.23607	+	3.80423i	0.0525155	+	0.161626i
$555$	2.42705	−	1.76336i	0.103023	−	0.0748503i
$556$	−16.1803	+	11.7557i	−0.686199	+	0.498553i
$557$	−0.618034	−	1.90211i	−0.0261869	−	0.0805951i	0.937109	−	0.349037i	$-0.113491\pi$
$557$	−0.618034	−	1.90211i	−0.0261869	−	0.0805951i	−0.963296	+	0.268442i	$0.913491\pi$
$558$	8.65248	−	26.6296i	0.366289	−	1.12732i
$559$	19.4164	+	14.1068i	0.821227	+	0.596656i
$560$	8.00000			0.338062
$561$		0			0
$562$	36.0000			1.51857
$563$	−3.23607	−	2.35114i	−0.136384	−	0.0990888i	0.517501	−	0.855682i	$-0.326862\pi$
$563$	−3.23607	−	2.35114i	−0.136384	−	0.0990888i	−0.653885	+	0.756594i	$0.726862\pi$
$564$	−4.94427	+	15.2169i	−0.208191	+	0.640747i
$565$	2.78115	+	8.55951i	0.117004	+	0.360101i
$566$	6.47214	−	4.70228i	0.272044	−	0.197652i
$567$	1.61803	−	1.17557i	0.0679510	−	0.0493693i
$568$		0			0
$569$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$569$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$570$		0			0
$571$	−28.0000			−1.17176			−0.585882	−	0.810397i	$-0.699252\pi$
$571$	−28.0000			−1.17176			−0.585882	+	0.810397i	$0.699252\pi$
$572$		0			0
$573$	−17.0000			−0.710185
$574$	25.8885	+	18.8091i	1.08057	+	0.785078i
$575$	1.23607	−	3.80423i	0.0515476	−	0.158647i
$576$	4.94427	+	15.2169i	0.206011	+	0.634038i
$577$	−26.6976	+	19.3969i	−1.11143	+	0.807504i	−0.982889	−	0.184200i	$-0.941031\pi$
$577$	−26.6976	+	19.3969i	−1.11143	+	0.807504i	−0.128545	+	0.991704i	$0.541031\pi$
$578$	−21.0344	+	15.2824i	−0.874917	+	0.635665i
$579$	−1.23607	−	3.80423i	−0.0513692	−	0.158098i
$580$		0			0
$581$	−9.70820	−	7.05342i	−0.402764	−	0.292625i
$582$	−14.0000			−0.580319
$583$		0			0
$584$		0			0
$585$	6.47214	+	4.70228i	0.267590	+	0.194415i
$586$	−14.8328	+	45.6507i	−0.612738	+	1.88581i
$587$	8.65248	+	26.6296i	0.357126	+	1.09912i	0.954767	+	0.297356i	$0.0961050\pi$
$587$	8.65248	+	26.6296i	0.357126	+	1.09912i	−0.597641	+	0.801764i	$0.703895\pi$
$588$	−4.85410	+	3.52671i	−0.200180	+	0.145439i
$589$		0			0
$590$	−3.09017	−	9.51057i	−0.127220	−	0.391544i
$591$	0.618034	−	1.90211i	0.0254225	−	0.0782425i
$592$	9.70820	+	7.05342i	0.399005	+	0.289894i
$593$	44.0000			1.80686			0.903432	−	0.428732i	$-0.141040\pi$
$593$	44.0000			1.80686			0.903432	+	0.428732i	$0.141040\pi$
$594$		0			0
$595$	4.00000			0.163984
$596$	16.1803	+	11.7557i	0.662773	+	0.481532i
$597$		0			0
$598$	2.47214	+	7.60845i	0.101093	+	0.311133i
$599$	−32.3607	+	23.5114i	−1.32222	+	0.960650i	−0.322320	+	0.946631i	$0.604463\pi$
$599$	−32.3607	+	23.5114i	−1.32222	+	0.960650i	−0.999902	+	0.0140193i	$0.995537\pi$
$600$		0			0
$601$	0.618034	+	1.90211i	0.0252101	+	0.0775888i	0.962870	−	0.269965i	$-0.0870123\pi$
$601$	0.618034	+	1.90211i	0.0252101	+	0.0775888i	−0.937660	+	0.347554i	$0.887012\pi$
$602$	−7.41641	+	22.8254i	−0.302270	+	0.930292i
$603$	−11.3262	−	8.22899i	−0.461240	−	0.335111i
$604$	4.00000			0.162758
$605$		0			0
$606$	4.00000			0.162489
$607$	17.7984	+	12.9313i	0.722414	+	0.524864i	0.887154	−	0.461473i	$-0.152679\pi$
$607$	17.7984	+	12.9313i	0.722414	+	0.524864i	−0.164741	+	0.986337i	$0.552679\pi$
$608$		0			0
$609$		0			0
$610$	19.4164	−	14.1068i	0.786147	−	0.571170i
$611$	−25.8885	+	18.8091i	−1.04734	+	0.760936i
$612$	2.47214	+	7.60845i	0.0999302	+	0.307553i
$613$	−4.94427	+	15.2169i	−0.199697	+	0.614605i	0.800192	+	0.599744i	$0.204731\pi$
$613$	−4.94427	+	15.2169i	−0.199697	+	0.614605i	−0.999890	+	0.0148615i	$0.995269\pi$
$614$	12.9443	+	9.40456i	0.522388	+	0.379537i
$615$	8.00000			0.322591
$616$		0			0
$617$	18.0000			0.724653			0.362326	−	0.932051i	$-0.381983\pi$
$617$	18.0000			0.724653			0.362326	+	0.932051i	$0.381983\pi$
$618$	25.8885	+	18.8091i	1.04139	+	0.756614i
$619$	−7.72542	+	23.7764i	−0.310511	+	0.955655i	0.667052	+	0.745011i	$0.267556\pi$
$619$	−7.72542	+	23.7764i	−0.310511	+	0.955655i	−0.977563	+	0.210643i	$0.932444\pi$
$620$	4.32624	+	13.3148i	0.173746	+	0.534735i
$621$	4.04508	−	2.93893i	0.162324	−	0.117935i
$622$	19.4164	−	14.1068i	0.778527	−	0.565633i
$623$	−9.27051	−	28.5317i	−0.371415	−	1.14310i
$624$	4.94427	−	15.2169i	0.197929	−	0.609164i
$625$	−8.89919	−	6.46564i	−0.355967	−	0.258626i
$626$	2.00000			0.0799361
$627$		0			0
$628$	−14.0000			−0.558661
$629$	4.85410	+	3.52671i	0.193546	+	0.140619i
$630$	−2.47214	+	7.60845i	−0.0984923	+	0.303128i
$631$	2.16312	+	6.65740i	0.0861124	+	0.265027i	0.984836	−	0.173489i	$-0.0555042\pi$
$631$	2.16312	+	6.65740i	0.0861124	+	0.265027i	−0.898723	+	0.438516i	$0.855504\pi$
$632$		0			0
$633$	9.70820	−	7.05342i	0.385866	−	0.280348i
$634$	−8.03444	−	24.7275i	−0.319088	−	0.982053i
$635$	2.47214	−	7.60845i	0.0981037	−	0.301932i
$636$	−9.70820	−	7.05342i	−0.384955	−	0.279686i
$637$	−12.0000			−0.475457
$638$		0			0
$639$	6.00000			0.237356
$640$		0			0
$641$	−10.1976	+	31.3849i	−0.402779	+	1.23963i	0.519956	+	0.854193i	$0.325948\pi$
$641$	−10.1976	+	31.3849i	−0.402779	+	1.23963i	−0.922735	+	0.385434i	$0.874052\pi$
$642$	11.1246	+	34.2380i	0.439053	+	1.35127i
$643$	−23.4615	+	17.0458i	−0.925231	+	0.672220i	−0.944821	−	0.327588i	$-0.893764\pi$
$643$	−23.4615	+	17.0458i	−0.925231	+	0.672220i	0.0195896	+	0.999808i	$0.493764\pi$
$644$	−3.23607	+	2.35114i	−0.127519	+	0.0926479i
$645$	1.85410	+	5.70634i	0.0730052	+	0.224687i
$646$		0			0
$647$	5.66312	+	4.11450i	0.222640	+	0.161758i	0.693514	−	0.720443i	$-0.256061\pi$
$647$	5.66312	+	4.11450i	0.222640	+	0.161758i	−0.470874	+	0.882200i	$0.656061\pi$
$648$		0			0
$649$		0			0
$650$	32.0000			1.25514
$651$	−11.3262	−	8.22899i	−0.443910	−	0.322520i
$652$	2.47214	−	7.60845i	0.0968163	−	0.297970i
$653$	−12.6697	−	38.9933i	−0.495804	−	1.52593i	−0.815701	−	0.578474i	$-0.803648\pi$
$653$	−12.6697	−	38.9933i	−0.495804	−	1.52593i	0.319897	−	0.947452i	$-0.396352\pi$
$654$	−16.1803	+	11.7557i	−0.632701	+	0.459684i
$655$	14.5623	−	10.5801i	0.568996	−	0.413400i
$656$	9.88854	+	30.4338i	0.386083	+	1.18824i
$657$	−2.47214	+	7.60845i	−0.0964472	+	0.296834i
$658$	−25.8885	−	18.8091i	−1.00924	−	0.733256i
$659$	10.0000			0.389545			0.194772	−	0.980848i	$-0.437603\pi$
$659$	10.0000			0.389545			0.194772	+	0.980848i	$0.437603\pi$
$660$		0			0
$661$	37.0000			1.43913			0.719567	−	0.694423i	$-0.244340\pi$
$661$	37.0000			1.43913			0.719567	+	0.694423i	$0.244340\pi$
$662$	11.3262	+	8.22899i	0.440207	+	0.319829i
$663$	2.47214	−	7.60845i	0.0960098	−	0.295488i
$664$		0			0
$665$		0			0
$666$	−9.70820	+	7.05342i	−0.376185	+	0.273315i
$667$		0			0
$668$	−7.41641	+	22.8254i	−0.286949	+	0.883140i
$669$	15.3713	+	11.1679i	0.594290	+	0.431777i
$670$	14.0000			0.540867
$671$		0			0
$672$	16.0000			0.617213
$673$	−11.3262	−	8.22899i	−0.436594	−	0.317204i	0.347686	−	0.937611i	$-0.386968\pi$
$673$	−11.3262	−	8.22899i	−0.436594	−	0.317204i	−0.784280	+	0.620407i	$0.786968\pi$
$674$	13.5967	−	41.8465i	0.523727	−	1.61187i
$675$	−6.18034	−	19.0211i	−0.237881	−	0.732124i
$676$	−4.85410	+	3.52671i	−0.186696	+	0.135643i
$677$	33.9787	−	24.6870i	1.30591	−	0.948798i	0.305913	−	0.952059i	$-0.401038\pi$
$677$	33.9787	−	24.6870i	1.30591	−	0.948798i	0.999995	+	0.00326161i	$0.00103820\pi$
$678$	5.56231	+	17.1190i	0.213619	+	0.657452i
$679$	4.32624	−	13.3148i	0.166026	−	0.510975i
$680$		0			0
$681$	−18.0000			−0.689761
$682$		0			0
$683$	−16.0000			−0.612223			−0.306111	−	0.951996i	$-0.599028\pi$
$683$	−16.0000			−0.612223			−0.306111	+	0.951996i	$0.599028\pi$
$684$		0			0
$685$	−2.16312	+	6.65740i	−0.0826485	+	0.254366i
$686$	−12.3607	−	38.0423i	−0.471933	−	1.45246i
$687$	12.1353	−	8.81678i	0.462989	−	0.336381i
$688$	−19.4164	+	14.1068i	−0.740244	+	0.537818i
$689$	−7.41641	−	22.8254i	−0.282543	−	0.869577i
$690$	−0.618034	+	1.90211i	−0.0235282	+	0.0724122i
$691$	−13.7533	−	9.99235i	−0.523200	−	0.380127i	0.294608	−	0.955618i	$-0.404811\pi$
$691$	−13.7533	−	9.99235i	−0.523200	−	0.380127i	−0.817808	+	0.575491i	$0.804811\pi$
$692$	−12.0000			−0.456172
$693$		0			0
$694$	−56.0000			−2.12573
$695$	−8.09017	−	5.87785i	−0.306878	−	0.222960i
$696$		0			0
$697$	4.94427	+	15.2169i	0.187278	+	0.576381i
$698$	48.5410	−	35.2671i	1.83730	−	1.33488i
$699$	19.4164	−	14.1068i	0.734396	−	0.533570i
$700$	4.94427	+	15.2169i	0.186876	+	0.575145i
$701$	0.618034	−	1.90211i	0.0233428	−	0.0718418i	−0.938707	−	0.344717i	$-0.887975\pi$
$701$	0.618034	−	1.90211i	0.0233428	−	0.0718418i	0.962049	+	0.272876i	$0.0879747\pi$
$702$	32.3607	+	23.5114i	1.22138	+	0.887381i
$703$		0			0
$704$		0			0
$705$	−8.00000			−0.301297
$706$	−33.9787	−	24.6870i	−1.27881	−	0.929107i
$707$	−1.23607	+	3.80423i	−0.0464871	+	0.143073i
$708$	−3.09017	−	9.51057i	−0.116136	−	0.357429i
$709$	20.2254	−	14.6946i	0.759582	−	0.551868i	−0.139200	−	0.990264i	$-0.544453\pi$
$709$	20.2254	−	14.6946i	0.759582	−	0.551868i	0.898782	+	0.438396i	$0.144453\pi$
$710$	−4.85410	+	3.52671i	−0.182171	+	0.132355i
$711$	6.18034	+	19.0211i	0.231781	+	0.713348i
$712$		0			0
$713$	5.66312	+	4.11450i	0.212085	+	0.154089i
$714$	8.00000			0.299392
$715$		0			0
$716$	−30.0000			−1.12115
$717$	−24.2705	−	17.6336i	−0.906399	−	0.658537i
$718$	12.3607	−	38.0423i	0.461296	−	1.41972i
$719$	4.63525	+	14.2658i	0.172866	+	0.532026i	0.999530	−	0.0306699i	$-0.00976407\pi$
$719$	4.63525	+	14.2658i	0.172866	+	0.532026i	−0.826664	+	0.562696i	$0.809764\pi$
$720$	−6.47214	+	4.70228i	−0.241202	+	0.175244i
$721$	−25.8885	+	18.8091i	−0.964140	+	0.700489i
$722$	11.7426	+	36.1401i	0.437016	+	1.34500i
$723$	2.47214	−	7.60845i	0.0919397	−	0.282961i
$724$	−11.3262	−	8.22899i	−0.420936	−	0.305828i
$725$		0			0
$726$		0			0
$727$	3.00000			0.111264			0.0556319	−	0.998451i	$-0.482283\pi$
$727$	3.00000			0.111264			0.0556319	+	0.998451i	$0.482283\pi$
$728$		0			0
$729$	4.01722	−	12.3637i	0.148786	−	0.457916i
$730$	−2.47214	−	7.60845i	−0.0914979	−	0.281601i
$731$	−9.70820	+	7.05342i	−0.359071	+	0.260880i
$732$	19.4164	−	14.1068i	0.717651	−	0.521404i
$733$	−11.1246	−	34.2380i	−0.410897	−	1.26461i	−0.915870	−	0.401475i	$-0.868498\pi$
$733$	−11.1246	−	34.2380i	−0.410897	−	1.26461i	0.504973	−	0.863135i	$-0.331502\pi$
$734$	10.5066	−	32.3359i	0.387805	−	1.19354i
$735$	−2.42705	−	1.76336i	−0.0895231	−	0.0650424i
$736$	−8.00000			−0.294884
$737$		0			0
$738$	−32.0000			−1.17794
$739$	−40.4508	−	29.3893i	−1.48801	−	1.08110i	−0.974864	−	0.222799i	$-0.928481\pi$
$739$	−40.4508	−	29.3893i	−1.48801	−	1.08110i	−0.513144	−	0.858302i	$-0.671519\pi$
$740$	1.85410	−	5.70634i	0.0681581	−	0.209769i
$741$		0			0
$742$	19.4164	−	14.1068i	0.712799	−	0.517879i
$743$	−3.23607	+	2.35114i	−0.118720	+	0.0862550i	−0.645561	−	0.763709i	$-0.723376\pi$
$743$	−3.23607	+	2.35114i	−0.118720	+	0.0862550i	0.526841	+	0.849964i	$0.323376\pi$
$744$		0			0
$745$	−3.09017	+	9.51057i	−0.113215	+	0.348440i
$746$	−42.0689	−	30.5648i	−1.54025	−	1.11906i
$747$	12.0000			0.439057
$748$		0			0
$749$	−36.0000			−1.31541
$750$	14.5623	+	10.5801i	0.531740	+	0.386332i
$751$	−7.10739	+	21.8743i	−0.259352	+	0.798205i	0.733588	+	0.679594i	$0.237844\pi$
$751$	−7.10739	+	21.8743i	−0.259352	+	0.798205i	−0.992941	+	0.118611i	$0.962156\pi$
$752$	−9.88854	−	30.4338i	−0.360598	−	1.10981i
$753$	−18.6074	+	13.5191i	−0.678091	+	0.492662i
$754$		0			0
$755$	0.618034	+	1.90211i	0.0224926	+	0.0692250i
$756$	−6.18034	+	19.0211i	−0.224777	+	0.691792i
$757$	17.7984	+	12.9313i	0.646893	+	0.469995i	0.862211	−	0.506549i	$-0.169079\pi$
$757$	17.7984	+	12.9313i	0.646893	+	0.469995i	−0.215318	+	0.976544i	$0.569079\pi$
$758$	10.0000			0.363216
$759$		0			0
$760$		0			0
$761$	−9.70820	−	7.05342i	−0.351922	−	0.255686i	0.397753	−	0.917493i	$-0.369790\pi$
$761$	−9.70820	−	7.05342i	−0.351922	−	0.255686i	−0.749675	+	0.661806i	$0.769790\pi$
$762$	4.94427	−	15.2169i	0.179112	−	0.551250i
$763$	−6.18034	−	19.0211i	−0.223743	−	0.688611i
$764$	−27.5066	+	19.9847i	−0.995153	+	0.723021i
$765$	−3.23607	+	2.35114i	−0.117000	+	0.0850057i
$766$	0.618034	+	1.90211i	0.0223305	+	0.0687261i
$767$	6.18034	−	19.0211i	0.223159	−	0.686813i
$768$	12.9443	+	9.40456i	0.467086	+	0.339358i
$769$	20.0000			0.721218			0.360609	−	0.932717i	$-0.382569\pi$
$769$	20.0000			0.721218			0.360609	+	0.932717i	$0.382569\pi$
$770$		0			0
$771$	2.00000			0.0720282
$772$	−6.47214	−	4.70228i	−0.232937	−	0.169239i
$773$	−1.85410	+	5.70634i	−0.0666874	+	0.205243i	−0.978847	−	0.204591i	$-0.934413\pi$
$773$	−1.85410	+	5.70634i	−0.0666874	+	0.205243i	0.912160	+	0.409834i	$0.134413\pi$
$774$	−7.41641	−	22.8254i	−0.266577	−	0.820440i
$775$	22.6525	−	16.4580i	0.813701	−	0.591188i
$776$		0			0
$777$	1.85410	+	5.70634i	0.0665155	+	0.204714i
$778$	9.27051	−	28.5317i	0.332364	−	1.02291i
$779$		0			0
$780$	−8.00000			−0.286446
$781$		0			0
$782$	−4.00000			−0.143040
$783$		0			0
$784$	3.70820	−	11.4127i	0.132436	−	0.407596i
$785$	−2.16312	−	6.65740i	−0.0772050	−	0.237613i
$786$	29.1246	−	21.1603i	1.03884	−	0.754762i
$787$	25.8885	−	18.8091i	0.922827	−	0.670473i	−0.0213991	−	0.999771i	$-0.506812\pi$
$787$	25.8885	−	18.8091i	0.922827	−	0.670473i	0.944226	+	0.329298i	$0.106812\pi$
$788$	−1.23607	−	3.80423i	−0.0440331	−	0.135520i
$789$	−4.32624	+	13.3148i	−0.154018	+	0.474019i
$790$	−16.1803	−	11.7557i	−0.575671	−	0.418249i
$791$	−18.0000			−0.640006
$792$		0			0
$793$	48.0000			1.70453
$794$	−3.23607	−	2.35114i	−0.114844	−	0.0834389i
$795$	1.85410	−	5.70634i	0.0657582	−	0.202383i
$796$		0			0
$797$	−42.8779	+	31.1526i	−1.51881	+	1.10348i	−0.556741	+	0.830686i	$0.687949\pi$
$797$	−42.8779	+	31.1526i	−1.51881	+	1.10348i	−0.962072	+	0.272796i	$0.912051\pi$
$798$		0			0
$799$	−4.94427	−	15.2169i	−0.174916	−	0.538335i
$800$	−9.88854	+	30.4338i	−0.349613	+	1.07600i
$801$	24.2705	+	17.6336i	0.857556	+	0.623051i
$802$	−4.00000			−0.141245
$803$		0			0
$804$	14.0000			0.493742
$805$	−1.61803	−	1.17557i	−0.0570282	−	0.0414334i
$806$	−17.3050	+	53.2592i	−0.609541	+	1.87597i
$807$	−3.09017	−	9.51057i	−0.108779	−	0.334788i
$808$		0			0
$809$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$809$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$810$	−0.618034	−	1.90211i	−0.0217155	−	0.0668334i
$811$	−11.7426	+	36.1401i	−0.412340	+	1.26905i	0.502268	+	0.864712i	$0.332499\pi$
$811$	−11.7426	+	36.1401i	−0.412340	+	1.26905i	−0.914609	+	0.404340i	$0.867501\pi$
$812$		0			0
$813$	28.0000			0.982003
$814$		0			0
$815$	4.00000			0.140114
$816$	6.47214	+	4.70228i	0.226570	+	0.164613i
$817$		0			0
$818$	18.5410	+	57.0634i	0.648272	+	1.99517i
$819$	−12.9443	+	9.40456i	−0.452309	+	0.328622i
$820$	12.9443	−	9.40456i	0.452034	−	0.328422i
$821$	6.79837	+	20.9232i	0.237265	+	0.730226i	0.996813	+	0.0797750i	$0.0254202\pi$
$821$	6.79837	+	20.9232i	0.237265	+	0.730226i	−0.759548	+	0.650451i	$0.774580\pi$
$822$	−4.32624	+	13.3148i	−0.150895	+	0.464407i
$823$	−31.5517	−	22.9236i	−1.09982	−	0.799067i	−0.118791	−	0.992919i	$-0.537902\pi$
$823$	−31.5517	−	22.9236i	−1.09982	−	0.799067i	−0.981031	+	0.193852i	$0.937902\pi$
$824$		0			0
$825$		0			0
$826$	20.0000			0.695889
$827$	42.0689	+	30.5648i	1.46288	+	1.06284i	0.982601	+	0.185726i	$0.0594638\pi$
$827$	42.0689	+	30.5648i	1.46288	+	1.06284i	0.480277	+	0.877117i	$0.340536\pi$
$828$	1.23607	−	3.80423i	0.0429563	−	0.132206i
$829$	7.72542	+	23.7764i	0.268315	+	0.825789i	0.990911	+	0.134518i	$0.0429487\pi$
$829$	7.72542	+	23.7764i	0.268315	+	0.825789i	−0.722596	+	0.691271i	$0.757051\pi$
$830$	−9.70820	+	7.05342i	−0.336977	+	0.244828i
$831$	−1.61803	+	1.17557i	−0.0561290	+	0.0407801i
$832$	−9.88854	−	30.4338i	−0.342824	−	1.05510i
$833$	1.85410	−	5.70634i	0.0642408	−	0.197713i
$834$	−16.1803	−	11.7557i	−0.560279	−	0.407067i
$835$	−12.0000			−0.415277
$836$		0			0
$837$	35.0000			1.20978
$838$	32.3607	+	23.5114i	1.11788	+	0.812188i
$839$	−1.54508	+	4.75528i	−0.0533423	+	0.164171i	−0.974179	−	0.225779i	$-0.927507\pi$
$839$	−1.54508	+	4.75528i	−0.0533423	+	0.164171i	0.920836	+	0.389949i	$0.127507\pi$
$840$		0			0
$841$	23.4615	−	17.0458i	0.809017	−	0.587785i
$842$	35.5967	−	25.8626i	1.22674	−	0.891282i
$843$	5.56231	+	17.1190i	0.191576	+	0.589610i
$844$	7.41641	−	22.8254i	0.255283	−	0.785681i
$845$	−2.42705	−	1.76336i	−0.0834931	−	0.0606613i
$846$	32.0000			1.10018
$847$		0			0
$848$	24.0000			0.824163
$849$	3.23607	+	2.35114i	0.111062	+	0.0806910i
$850$	−4.94427	+	15.2169i	−0.169587	+	0.521936i
$851$	−0.927051	−	2.85317i	−0.0317789	−	0.0978054i
$852$	−4.85410	+	3.52671i	−0.166299	+	0.120823i
$853$	−11.3262	+	8.22899i	−0.387803	+	0.281755i	−0.764555	−	0.644559i	$-0.777041\pi$
$853$	−11.3262	+	8.22899i	−0.387803	+	0.281755i	0.376752	+	0.926314i	$0.377041\pi$
$854$	14.8328	+	45.6507i	0.507569	+	1.56214i
$855$		0			0
$856$		0			0
$857$	8.00000			0.273275			0.136637	−	0.990621i	$-0.456370\pi$
$857$	8.00000			0.273275			0.136637	+	0.990621i	$0.456370\pi$
$858$		0			0
$859$	−15.0000			−0.511793			−0.255897	−	0.966704i	$-0.582371\pi$
$859$	−15.0000			−0.511793			−0.255897	+	0.966704i	$0.582371\pi$
$860$	9.70820	+	7.05342i	0.331047	+	0.240520i
$861$	−4.94427	+	15.2169i	−0.168500	+	0.518591i
$862$	11.1246	+	34.2380i	0.378906	+	1.16615i
$863$	−19.4164	+	14.1068i	−0.660942	+	0.480203i	−0.866981	−	0.498341i	$-0.833943\pi$
$863$	−19.4164	+	14.1068i	−0.660942	+	0.480203i	0.206039	+	0.978544i	$0.433943\pi$
$864$	−32.3607	+	23.5114i	−1.10093	+	0.799874i
$865$	−1.85410	−	5.70634i	−0.0630414	−	0.194021i
$866$	6.79837	−	20.9232i	0.231018	−	0.711001i
$867$	−10.5172	−	7.64121i	−0.357184	−	0.259509i
$868$	−28.0000			−0.950382
$869$		0			0
$870$		0			0
$871$	22.6525	+	16.4580i	0.767550	+	0.557658i
$872$		0			0
$873$	4.32624	+	13.3148i	0.146421	+	0.450637i
$874$		0			0
$875$	−14.5623	+	10.5801i	−0.492296	+	0.357674i
$876$	−2.47214	−	7.60845i	−0.0835257	−	0.257066i
$877$	−3.70820	+	11.4127i	−0.125217	+	0.385379i	−0.993941	−	0.109919i	$-0.964941\pi$
$877$	−3.70820	+	11.4127i	−0.125217	+	0.385379i	0.868723	+	0.495297i	$0.164941\pi$
$878$	64.7214	+	47.0228i	2.18424	+	1.58694i
$879$	−24.0000			−0.809500
$880$		0			0
$881$	−43.0000			−1.44871			−0.724353	−	0.689429i	$-0.757862\pi$
$881$	−43.0000			−1.44871			−0.724353	+	0.689429i	$0.757862\pi$
$882$	9.70820	+	7.05342i	0.326892	+	0.237501i
$883$	1.23607	−	3.80423i	0.0415970	−	0.128022i	−0.928101	−	0.372327i	$-0.878560\pi$
$883$	1.23607	−	3.80423i	0.0415970	−	0.128022i	0.969698	+	0.244305i	$0.0785598\pi$
$884$	−4.94427	−	15.2169i	−0.166294	−	0.511800i
$885$	4.04508	−	2.93893i	0.135974	−	0.0987909i
$886$	−17.7984	+	12.9313i	−0.597948	+	0.434435i
$887$	−6.79837	−	20.9232i	−0.228267	−	0.702534i	−0.997944	−	0.0640996i	$-0.979582\pi$
$887$	−6.79837	−	20.9232i	−0.228267	−	0.702534i	0.769676	−	0.638434i	$-0.220418\pi$
$888$		0			0
$889$	12.9443	+	9.40456i	0.434137	+	0.315419i
$890$	−30.0000			−1.00560
$891$		0			0
$892$	38.0000			1.27233
$893$		0			0
$894$	−6.18034	+	19.0211i	−0.206701	+	0.636162i
$895$	−4.63525	−	14.2658i	−0.154939	−	0.476855i
$896$		0			0
$897$	−3.23607	+	2.35114i	−0.108049	+	0.0785023i
$898$	−21.6312	−	66.5740i	−0.721842	−	2.22160i
$899$		0			0
$900$	−12.9443	−	9.40456i	−0.431476	−	0.313485i
$901$	12.0000			0.399778
$902$		0			0
$903$	−12.0000			−0.399335
$904$		0			0
$905$	2.16312	−	6.65740i	0.0719045	−	0.221299i
$906$	1.23607	+	3.80423i	0.0410656	+	0.126387i
$907$	9.70820	−	7.05342i	0.322356	−	0.234205i	−0.414824	−	0.909902i	$-0.636157\pi$
$907$	9.70820	−	7.05342i	0.322356	−	0.234205i	0.737180	+	0.675696i	$0.236157\pi$
$908$	−29.1246	+	21.1603i	−0.966534	+	0.702228i
$909$	−1.23607	−	3.80423i	−0.0409978	−	0.126178i
$910$	4.94427	−	15.2169i	0.163901	−	0.504435i
$911$	−9.70820	−	7.05342i	−0.321647	−	0.233690i	0.415231	−	0.909716i	$-0.363701\pi$
$911$	−9.70820	−	7.05342i	−0.321647	−	0.233690i	−0.736878	+	0.676026i	$0.763701\pi$
$912$		0			0
$913$		0			0
$914$	24.0000			0.793849
$915$	9.70820	+	7.05342i	0.320943	+	0.233179i
$916$	9.27051	−	28.5317i	0.306306	−	0.942714i
$917$	11.1246	+	34.2380i	0.367367	+	1.13064i
$918$	−16.1803	+	11.7557i	−0.534031	+	0.387996i
$919$	−8.09017	+	5.87785i	−0.266870	+	0.193892i	−0.713170	−	0.700991i	$-0.752741\pi$
$919$	−8.09017	+	5.87785i	−0.266870	+	0.193892i	0.446300	+	0.894883i	$0.352741\pi$
$920$		0			0
$921$	−2.47214	+	7.60845i	−0.0814596	+	0.250707i
$922$	19.4164	+	14.1068i	0.639445	+	0.464584i
$923$	−12.0000			−0.394985
$924$		0			0
$925$	−12.0000			−0.394558
$926$	−17.7984	−	12.9313i	−0.584891	−	0.424948i
$927$	9.88854	−	30.4338i	0.324782	−	0.999577i
$928$		0			0
$929$	24.2705	−	17.6336i	0.796290	−	0.578538i	−0.113534	−	0.993534i	$-0.536217\pi$
$929$	24.2705	−	17.6336i	0.796290	−	0.578538i	0.909823	+	0.414996i	$0.136217\pi$
$930$	−11.3262	+	8.22899i	−0.371402	+	0.269839i
$931$		0			0
$932$	14.8328	−	45.6507i	0.485865	−	1.49534i
$933$	9.70820	+	7.05342i	0.317832	+	0.230919i
$934$	54.0000			1.76693
$935$		0			0
$936$		0			0
$937$	−6.47214	−	4.70228i	−0.211435	−	0.153617i	0.477027	−	0.878888i	$-0.341714\pi$
$937$	−6.47214	−	4.70228i	−0.211435	−	0.153617i	−0.688463	+	0.725272i	$0.741714\pi$
$938$	−8.65248	+	26.6296i	−0.282513	+	0.869487i
$939$	0.309017	+	0.951057i	0.0100844	+	0.0310366i
$940$	−12.9443	+	9.40456i	−0.422196	+	0.306743i
$941$	−33.9787	+	24.6870i	−1.10767	+	0.804773i	−0.982296	−	0.187336i	$-0.940015\pi$
$941$	−33.9787	+	24.6870i	−1.10767	+	0.804773i	−0.125379	+	0.992109i	$0.540015\pi$
$942$	−4.32624	−	13.3148i	−0.140956	−	0.433819i
$943$	2.47214	−	7.60845i	0.0805038	−	0.247765i
$944$	16.1803	+	11.7557i	0.526625	+	0.382616i
$945$	−10.0000			−0.325300
$946$		0			0
$947$	−27.0000			−0.877382			−0.438691	−	0.898638i	$-0.644558\pi$
$947$	−27.0000			−0.877382			−0.438691	+	0.898638i	$0.644558\pi$
$948$	−16.1803	−	11.7557i	−0.525513	−	0.381808i
$949$	4.94427	−	15.2169i	0.160498	−	0.493962i
$950$		0			0
$951$	10.5172	−	7.64121i	0.341044	−	0.247783i
$952$		0			0
$953$	10.5066	+	32.3359i	0.340341	+	1.04746i	0.964031	+	0.265791i	$0.0856331\pi$
$953$	10.5066	+	32.3359i	0.340341	+	1.04746i	−0.623689	+	0.781672i	$0.714367\pi$
$954$	−7.41641	+	22.8254i	−0.240115	+	0.738998i
$955$	−13.7533	−	9.99235i	−0.445046	−	0.323345i
$956$	−60.0000			−1.94054
$957$		0			0
$958$	−40.0000			−1.29234
$959$	−11.3262	−	8.22899i	−0.365743	−	0.265728i
$960$	2.47214	−	7.60845i	0.0797878	−	0.245562i
$961$	5.56231	+	17.1190i	0.179429	+	0.552226i
$962$	19.4164	−	14.1068i	0.626010	−	0.454823i
$963$	29.1246	−	21.1603i	0.938527	−	0.681880i
$964$	−4.94427	−	15.2169i	−0.159244	−	0.490103i
$965$	1.23607	−	3.80423i	0.0397904	−	0.122462i
$966$	−3.23607	−	2.35114i	−0.104119	−	0.0756467i
$967$	−32.0000			−1.02905			−0.514525	−	0.857475i	$-0.672032\pi$
$967$	−32.0000			−1.02905			−0.514525	+	0.857475i	$0.672032\pi$
$968$		0			0
$969$		0			0
$970$	−11.3262	−	8.22899i	−0.363664	−	0.264217i
$971$	14.5238	−	44.6997i	0.466091	−	1.43448i	−0.391514	−	0.920172i	$-0.628049\pi$
$971$	14.5238	−	44.6997i	0.466091	−	1.43448i	0.857605	−	0.514308i	$-0.171951\pi$
$972$	−9.88854	−	30.4338i	−0.317175	−	0.976165i
$973$	16.1803	−	11.7557i	0.518718	−	0.376871i
$974$	37.2148	−	27.0381i	1.19244	−	0.866357i
$975$	4.94427	+	15.2169i	0.158343	+	0.487331i
$976$	−14.8328	+	45.6507i	−0.474787	+	1.46124i
$977$	21.8435	+	15.8702i	0.698834	+	0.507733i	0.879552	−	0.475802i	$-0.157842\pi$
$977$	21.8435	+	15.8702i	0.698834	+	0.507733i	−0.180718	+	0.983535i	$0.557842\pi$
$978$	8.00000			0.255812
$979$		0			0
$980$	−6.00000			−0.191663
$981$	16.1803	+	11.7557i	0.516598	+	0.375331i
$982$	4.94427	−	15.2169i	0.157778	−	0.485591i
$983$	12.0517	+	37.0912i	0.384388	+	1.18303i	0.936923	+	0.349536i	$0.113661\pi$
$983$	12.0517	+	37.0912i	0.384388	+	1.18303i	−0.552535	+	0.833490i	$0.686339\pi$
$984$		0			0
$985$	1.61803	−	1.17557i	0.0515548	−	0.0374568i
$986$		0			0
$987$	4.94427	−	15.2169i	0.157378	−	0.484359i
$988$		0			0
$989$	6.00000			0.190789
$990$		0			0
$991$	−8.00000			−0.254128			−0.127064	−	0.991894i	$-0.540555\pi$
$991$	−8.00000			−0.254128			−0.127064	+	0.991894i	$0.540555\pi$
$992$	−45.3050	−	32.9160i	−1.43843	−	1.04508i
$993$	−2.16312	+	6.65740i	−0.0686445	+	0.211266i
$994$	−3.70820	−	11.4127i	−0.117617	−	0.361988i
$995$		0			0
$996$	−9.70820	+	7.05342i	−0.307616	+	0.223496i
$997$	11.7426	+	36.1401i	0.371893	+	1.14457i	0.945551	+	0.325475i	$0.105524\pi$
$997$	11.7426	+	36.1401i	0.371893	+	1.14457i	−0.573657	+	0.819095i	$0.694476\pi$
$998$	−12.3607	+	38.0423i	−0.391270	+	1.20421i
$999$	−12.1353	−	8.81678i	−0.383942	−	0.278951i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	121.2.c.e.81.1		4
11.2	odd	10		121.2.c.a.27.1		4
11.3	even	5	inner	121.2.c.e.3.1		4
11.4	even	5	inner	121.2.c.e.9.1		4
11.5	even	5		11.2.a.a.1.1	✓	1
11.6	odd	10		121.2.a.d.1.1		1
11.7	odd	10		121.2.c.a.9.1		4
11.8	odd	10		121.2.c.a.3.1		4
11.9	even	5	inner	121.2.c.e.27.1		4
11.10	odd	2		121.2.c.a.81.1		4
33.5	odd	10		99.2.a.d.1.1		1
33.17	even	10		1089.2.a.b.1.1		1
44.27	odd	10		176.2.a.b.1.1		1
44.39	even	10		1936.2.a.i.1.1		1
55.27	odd	20		275.2.b.a.199.1		2
55.38	odd	20		275.2.b.a.199.2		2
55.39	odd	10		3025.2.a.a.1.1		1
55.49	even	10		275.2.a.b.1.1		1
77.5	odd	30		539.2.e.g.67.1		2
77.6	even	10		5929.2.a.h.1.1		1
77.16	even	15		539.2.e.h.67.1		2
77.27	odd	10		539.2.a.a.1.1		1
77.38	odd	30		539.2.e.g.177.1		2
77.60	even	15		539.2.e.h.177.1		2
88.5	even	10		704.2.a.h.1.1		1
88.27	odd	10		704.2.a.c.1.1		1
88.61	odd	10		7744.2.a.x.1.1		1
88.83	even	10		7744.2.a.k.1.1		1
99.5	odd	30		891.2.e.b.298.1		2
99.16	even	15		891.2.e.k.595.1		2
99.38	odd	30		891.2.e.b.595.1		2
99.49	even	15		891.2.e.k.298.1		2
132.71	even	10		1584.2.a.g.1.1		1
143.38	even	10		1859.2.a.b.1.1		1
165.38	even	20		2475.2.c.a.199.1		2
165.104	odd	10		2475.2.a.a.1.1		1
165.137	even	20		2475.2.c.a.199.2		2
176.5	even	20		2816.2.c.j.1409.2		2
176.27	odd	20		2816.2.c.f.1409.1		2
176.93	even	20		2816.2.c.j.1409.1		2
176.115	odd	20		2816.2.c.f.1409.2		2
187.16	even	10		3179.2.a.a.1.1		1
209.170	odd	10		3971.2.a.b.1.1		1
220.27	even	20		4400.2.b.h.4049.1		2
220.159	odd	10		4400.2.a.i.1.1		1
220.203	even	20		4400.2.b.h.4049.2		2
231.104	even	10		4851.2.a.t.1.1		1
253.137	odd	10		5819.2.a.a.1.1		1
264.5	odd	10		6336.2.a.br.1.1		1
264.203	even	10		6336.2.a.bu.1.1		1
308.27	even	10		8624.2.a.j.1.1		1
319.115	even	10		9251.2.a.d.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.2.a.a.1.1	✓	1	11.5	even	5
99.2.a.d.1.1		1	33.5	odd	10
121.2.a.d.1.1		1	11.6	odd	10
121.2.c.a.3.1		4	11.8	odd	10
121.2.c.a.9.1		4	11.7	odd	10
121.2.c.a.27.1		4	11.2	odd	10
121.2.c.a.81.1		4	11.10	odd	2
121.2.c.e.3.1		4	11.3	even	5	inner
121.2.c.e.9.1		4	11.4	even	5	inner
121.2.c.e.27.1		4	11.9	even	5	inner
121.2.c.e.81.1		4	1.1	even	1	trivial
176.2.a.b.1.1		1	44.27	odd	10
275.2.a.b.1.1		1	55.49	even	10
275.2.b.a.199.1		2	55.27	odd	20
275.2.b.a.199.2		2	55.38	odd	20
539.2.a.a.1.1		1	77.27	odd	10
539.2.e.g.67.1		2	77.5	odd	30
539.2.e.g.177.1		2	77.38	odd	30
539.2.e.h.67.1		2	77.16	even	15
539.2.e.h.177.1		2	77.60	even	15
704.2.a.c.1.1		1	88.27	odd	10
704.2.a.h.1.1		1	88.5	even	10
891.2.e.b.298.1		2	99.5	odd	30
891.2.e.b.595.1		2	99.38	odd	30
891.2.e.k.298.1		2	99.49	even	15
891.2.e.k.595.1		2	99.16	even	15
1089.2.a.b.1.1		1	33.17	even	10
1584.2.a.g.1.1		1	132.71	even	10
1859.2.a.b.1.1		1	143.38	even	10
1936.2.a.i.1.1		1	44.39	even	10
2475.2.a.a.1.1		1	165.104	odd	10
2475.2.c.a.199.1		2	165.38	even	20
2475.2.c.a.199.2		2	165.137	even	20
2816.2.c.f.1409.1		2	176.27	odd	20
2816.2.c.f.1409.2		2	176.115	odd	20
2816.2.c.j.1409.1		2	176.93	even	20
2816.2.c.j.1409.2		2	176.5	even	20
3025.2.a.a.1.1		1	55.39	odd	10
3179.2.a.a.1.1		1	187.16	even	10
3971.2.a.b.1.1		1	209.170	odd	10
4400.2.a.i.1.1		1	220.159	odd	10
4400.2.b.h.4049.1		2	220.27	even	20
4400.2.b.h.4049.2		2	220.203	even	20
4851.2.a.t.1.1		1	231.104	even	10
5819.2.a.a.1.1		1	253.137	odd	10
5929.2.a.h.1.1		1	77.6	even	10
6336.2.a.br.1.1		1	264.5	odd	10
6336.2.a.bu.1.1		1	264.203	even	10
7744.2.a.k.1.1		1	88.83	even	10
7744.2.a.x.1.1		1	88.61	odd	10
8624.2.a.j.1.1		1	308.27	even	10
9251.2.a.d.1.1		1	319.115	even	10

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:	\( N \)	\(=\)	\( 121 = 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	121.c (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.61803 + 1.17557i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(0.618034 + 1.90211i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(-1.61803 + 1.17557i) q^{6} +(-0.618034 - 1.90211i) q^{7} +(1.61803 + 1.17557i) q^{9} +O(q^{10})\)	\(q+(1.61803 + 1.17557i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(0.618034 + 1.90211i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(-1.61803 + 1.17557i) q^{6} +(-0.618034 - 1.90211i) q^{7} +(1.61803 + 1.17557i) q^{9} -2.00000 q^{10} -2.00000 q^{12} +(-3.23607 - 2.35114i) q^{13} +(1.23607 - 3.80423i) q^{14} +(-0.309017 - 0.951057i) q^{15} +(3.23607 - 2.35114i) q^{16} +(1.61803 - 1.17557i) q^{17} +(1.23607 + 3.80423i) q^{18} +(-1.61803 - 1.17557i) q^{20} +2.00000 q^{21} -1.00000 q^{23} +(-1.23607 + 3.80423i) q^{25} +(-2.47214 - 7.60845i) q^{26} +(-4.04508 + 2.93893i) q^{27} +(3.23607 - 2.35114i) q^{28} +(0.618034 - 1.90211i) q^{30} +(-5.66312 - 4.11450i) q^{31} +8.00000 q^{32} +4.00000 q^{34} +(1.61803 + 1.17557i) q^{35} +(-1.23607 + 3.80423i) q^{36} +(0.927051 + 2.85317i) q^{37} +(3.23607 - 2.35114i) q^{39} +(-2.47214 + 7.60845i) q^{41} +(3.23607 + 2.35114i) q^{42} -6.00000 q^{43} -2.00000 q^{45} +(-1.61803 - 1.17557i) q^{46} +(2.47214 - 7.60845i) q^{47} +(1.23607 + 3.80423i) q^{48} +(2.42705 - 1.76336i) q^{49} +(-6.47214 + 4.70228i) q^{50} +(0.618034 + 1.90211i) q^{51} +(2.47214 - 7.60845i) q^{52} +(4.85410 + 3.52671i) q^{53} -10.0000 q^{54} +(1.54508 + 4.75528i) q^{59} +(1.61803 - 1.17557i) q^{60} +(-9.70820 + 7.05342i) q^{61} +(-4.32624 - 13.3148i) q^{62} +(1.23607 - 3.80423i) q^{63} +(6.47214 + 4.70228i) q^{64} +4.00000 q^{65} -7.00000 q^{67} +(3.23607 + 2.35114i) q^{68} +(0.309017 - 0.951057i) q^{69} +(1.23607 + 3.80423i) q^{70} +(2.42705 - 1.76336i) q^{71} +(1.23607 + 3.80423i) q^{73} +(-1.85410 + 5.70634i) q^{74} +(-3.23607 - 2.35114i) q^{75} +8.00000 q^{78} +(8.09017 + 5.87785i) q^{79} +(-1.23607 + 3.80423i) q^{80} +(0.309017 + 0.951057i) q^{81} +(-12.9443 + 9.40456i) q^{82} +(4.85410 - 3.52671i) q^{83} +(1.23607 + 3.80423i) q^{84} +(-0.618034 + 1.90211i) q^{85} +(-9.70820 - 7.05342i) q^{86} +15.0000 q^{89} +(-3.23607 - 2.35114i) q^{90} +(-2.47214 + 7.60845i) q^{91} +(-0.618034 - 1.90211i) q^{92} +(5.66312 - 4.11450i) q^{93} +(12.9443 - 9.40456i) q^{94} +(-2.47214 + 7.60845i) q^{96} +(5.66312 + 4.11450i) q^{97} +6.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + q^{3} - 2 q^{4} - q^{5} - 2 q^{6} + 2 q^{7} + 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 + q^3 - 2 * q^4 - q^5 - 2 * q^6 + 2 * q^7 + 2 * q^9	\( 4 q + 2 q^{2} + q^{3} - 2 q^{4} - q^{5} - 2 q^{6} + 2 q^{7} + 2 q^{9} - 8 q^{10} - 8 q^{12} - 4 q^{13} - 4 q^{14} + q^{15} + 4 q^{16} + 2 q^{17} - 4 q^{18} - 2 q^{20} + 8 q^{21} - 4 q^{23} + 4 q^{25} + 8 q^{26} - 5 q^{27} + 4 q^{28} - 2 q^{30} - 7 q^{31} + 32 q^{32} + 16 q^{34} + 2 q^{35} + 4 q^{36} - 3 q^{37} + 4 q^{39} + 8 q^{41} + 4 q^{42} - 24 q^{43} - 8 q^{45} - 2 q^{46} - 8 q^{47} - 4 q^{48} + 3 q^{49} - 8 q^{50} - 2 q^{51} - 8 q^{52} + 6 q^{53} - 40 q^{54} - 5 q^{59} + 2 q^{60} - 12 q^{61} + 14 q^{62} - 4 q^{63} + 8 q^{64} + 16 q^{65} - 28 q^{67} + 4 q^{68} - q^{69} - 4 q^{70} + 3 q^{71} - 4 q^{73} + 6 q^{74} - 4 q^{75} + 32 q^{78} + 10 q^{79} + 4 q^{80} - q^{81} - 16 q^{82} + 6 q^{83} - 4 q^{84} + 2 q^{85} - 12 q^{86} + 60 q^{89} - 4 q^{90} + 8 q^{91} + 2 q^{92} + 7 q^{93} + 16 q^{94} + 8 q^{96} + 7 q^{97} + 24 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 + q^3 - 2 * q^4 - q^5 - 2 * q^6 + 2 * q^7 + 2 * q^9 - 8 * q^10 - 8 * q^12 - 4 * q^13 - 4 * q^14 + q^15 + 4 * q^16 + 2 * q^17 - 4 * q^18 - 2 * q^20 + 8 * q^21 - 4 * q^23 + 4 * q^25 + 8 * q^26 - 5 * q^27 + 4 * q^28 - 2 * q^30 - 7 * q^31 + 32 * q^32 + 16 * q^34 + 2 * q^35 + 4 * q^36 - 3 * q^37 + 4 * q^39 + 8 * q^41 + 4 * q^42 - 24 * q^43 - 8 * q^45 - 2 * q^46 - 8 * q^47 - 4 * q^48 + 3 * q^49 - 8 * q^50 - 2 * q^51 - 8 * q^52 + 6 * q^53 - 40 * q^54 - 5 * q^59 + 2 * q^60 - 12 * q^61 + 14 * q^62 - 4 * q^63 + 8 * q^64 + 16 * q^65 - 28 * q^67 + 4 * q^68 - q^69 - 4 * q^70 + 3 * q^71 - 4 * q^73 + 6 * q^74 - 4 * q^75 + 32 * q^78 + 10 * q^79 + 4 * q^80 - q^81 - 16 * q^82 + 6 * q^83 - 4 * q^84 + 2 * q^85 - 12 * q^86 + 60 * q^89 - 4 * q^90 + 8 * q^91 + 2 * q^92 + 7 * q^93 + 16 * q^94 + 8 * q^96 + 7 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more