LMFDB - Embedded newform 120.2.d.b.109.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [120,2,Mod(109,120)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(120, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("120.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$120 = 2^{3} \cdot 3 \cdot 5$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	120.d (of order $2$ , degree $1$ , minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.958204824255$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.839056.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{6} + 6x^{4} + 8x^{2} + 1$ x^6 + 6x^4 + 8x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$2^{2}$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			109.6
Root			$1.32132i$ of defining polynomial
Character	$\chi$	$=$	120.109
Dual form			120.2.d.b.109.5

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.34067 + 0.450129i) q^{2} -1.00000 q^{3} +(1.59477 + 1.20695i) q^{4} +(0.254102 + 2.22158i) q^{5} +(-1.34067 - 0.450129i) q^{6} -2.64265i q^{7} +(1.59477 + 2.33596i) q^{8} +1.00000 q^{9} +(-0.659335 + 3.09278i) q^{10} -1.51363i q^{11} +(-1.59477 - 1.20695i) q^{12} -3.87086 q^{13} +(1.18953 - 3.54291i) q^{14} +(-0.254102 - 2.22158i) q^{15} +(1.08656 + 3.84959i) q^{16} -3.31415i q^{17} +(1.34067 + 0.450129i) q^{18} -7.08582i q^{19} +(-2.27610 + 3.84959i) q^{20} +2.64265i q^{21} +(0.681331 - 2.02927i) q^{22} +4.82778i q^{23} +(-1.59477 - 2.33596i) q^{24} +(-4.87086 + 1.12902i) q^{25} +(-5.18953 - 1.74239i) q^{26} -1.00000 q^{27} +(3.18953 - 4.21441i) q^{28} +2.18513i q^{29} +(0.659335 - 3.09278i) q^{30} -7.36266 q^{31} +(-0.276098 + 5.65011i) q^{32} +1.51363i q^{33} +(1.49180 - 4.44317i) q^{34} +(5.87086 - 0.671502i) q^{35} +(1.59477 + 1.20695i) q^{36} +7.87086 q^{37} +(3.18953 - 9.49971i) q^{38} +3.87086 q^{39} +(-4.78430 + 4.13648i) q^{40} +8.72532 q^{41} +(-1.18953 + 3.54291i) q^{42} -1.01641 q^{43} +(1.82687 - 2.41389i) q^{44} +(0.254102 + 2.22158i) q^{45} +(-2.17313 + 6.47244i) q^{46} +7.08582i q^{47} +(-1.08656 - 3.84959i) q^{48} +0.0164068 q^{49} +(-7.03840 - 0.678887i) q^{50} +3.31415i q^{51} +(-6.17313 - 4.67192i) q^{52} -4.50820 q^{53} +(-1.34067 - 0.450129i) q^{54} +(3.36266 - 0.384617i) q^{55} +(6.17313 - 4.21441i) q^{56} +7.08582i q^{57} +(-0.983593 + 2.92953i) q^{58} +6.79893i q^{59} +(2.27610 - 3.84959i) q^{60} -3.60104i q^{61} +(-9.87086 - 3.31415i) q^{62} -2.64265i q^{63} +(-2.91344 + 7.45063i) q^{64} +(-0.983593 - 8.59945i) q^{65} +(-0.681331 + 2.02927i) q^{66} +1.01641 q^{67} +(4.00000 - 5.28530i) q^{68} -4.82778i q^{69} +(8.17313 + 1.74239i) q^{70} -6.72532 q^{71} +(1.59477 + 2.33596i) q^{72} +15.5146i q^{73} +(10.5522 + 3.54291i) q^{74} +(4.87086 - 1.12902i) q^{75} +(8.55220 - 11.3002i) q^{76} -4.00000 q^{77} +(5.18953 + 1.74239i) q^{78} +7.36266 q^{79} +(-8.27610 + 3.39208i) q^{80} +1.00000 q^{81} +(11.6977 + 3.92752i) q^{82} -7.74173 q^{83} +(-3.18953 + 4.21441i) q^{84} +(7.36266 - 0.842131i) q^{85} +(-1.36266 - 0.457515i) q^{86} -2.18513i q^{87} +(3.53579 - 2.41389i) q^{88} -14.7581 q^{89} +(-0.659335 + 3.09278i) q^{90} +10.2293i q^{91} +(-5.82687 + 7.69919i) q^{92} +7.36266 q^{93} +(-3.18953 + 9.49971i) q^{94} +(15.7417 - 1.80052i) q^{95} +(0.276098 - 5.65011i) q^{96} -11.1444i q^{97} +(0.0219960 + 0.00738516i) q^{98} -1.51363i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$6 q + q^{2} - 6 q^{3} + q^{4} - q^{6} + q^{8} + 6 q^{9} - 11 q^{10} - q^{12} + 8 q^{13} - 10 q^{14} + q^{16} + q^{18} + 9 q^{20} - 10 q^{22} - q^{24} + 2 q^{25} - 14 q^{26} - 6 q^{27} + 2 q^{28}+ \cdots - 21 q^{98}+O(q^{100})$ 6 * q + q^2 - 6 * q^3 + q^4 - q^6 + q^8 + 6 * q^9 - 11 * q^10 - q^12 + 8 * q^13 - 10 * q^14 + q^16 + q^18 + 9 * q^20 - 10 * q^22 - q^24 + 2 * q^25 - 14 * q^26 - 6 * q^27 + 2 * q^28 + 11 * q^30 - 16 * q^31 + 21 * q^32 + 12 * q^34 + 4 * q^35 + q^36 + 16 * q^37 + 2 * q^38 - 8 * q^39 - 3 * q^40 - 4 * q^41 + 10 * q^42 + 22 * q^44 - 2 * q^46 - q^48 - 6 * q^49 - 15 * q^50 - 26 * q^52 - 24 * q^53 - q^54 - 8 * q^55 + 26 * q^56 - 12 * q^58 - 9 * q^60 - 28 * q^62 - 23 * q^64 - 12 * q^65 + 10 * q^66 + 24 * q^68 + 38 * q^70 + 16 * q^71 + q^72 + 18 * q^74 - 2 * q^75 + 6 * q^76 - 24 * q^77 + 14 * q^78 + 16 * q^79 - 27 * q^80 + 6 * q^81 + 50 * q^82 + 16 * q^83 - 2 * q^84 + 16 * q^85 + 20 * q^86 - 18 * q^88 - 20 * q^89 - 11 * q^90 - 46 * q^92 + 16 * q^93 - 2 * q^94 + 32 * q^95 - 21 * q^96 - 21 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/120\mathbb{Z}\right)^\times$ .

$n$	$31$	$41$	$61$	$97$
$\chi(n)$	$1$	$1$	$-1$	$-1$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	1.34067	+	0.450129i	0.947994	+	0.318290i
$2$	1.34067	+	0.450129i	0.947994	+	0.318290i
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	1.59477	+	1.20695i	0.797384	+	0.603473i
$5$	0.254102	+	2.22158i	0.113638	+	0.993522i
$5$	0.254102	+	2.22158i	0.113638	+	0.993522i
$6$	−1.34067	−	0.450129i	−0.547324	−	0.183765i
$7$		−	2.64265i		−	0.998827i	−0.866364	−	0.499414i	$-0.833549\pi$
$7$		−	2.64265i		−	0.998827i	0.866364	−	0.499414i	$-0.166451\pi$
$8$	1.59477	+	2.33596i	0.563835	+	0.825887i
$9$	1.00000			0.333333
$10$	−0.659335	+	3.09278i	−0.208500	+	0.978022i
$11$		−	1.51363i		−	0.456377i	−0.973617	−	0.228189i	$-0.926720\pi$
$11$		−	1.51363i		−	0.456377i	0.973617	−	0.228189i	$-0.0732803\pi$
$12$	−1.59477	−	1.20695i	−0.460370	−	0.348415i
$13$	−3.87086			−1.07358			−0.536792	−	0.843714i	$-0.680364\pi$
$13$	−3.87086			−1.07358			−0.536792	+	0.843714i	$0.680364\pi$
$14$	1.18953	−	3.54291i	0.317916	−	0.946882i
$15$	−0.254102	−	2.22158i	−0.0656088	−	0.573610i
$16$	1.08656	+	3.84959i	0.271641	+	0.962399i
$17$		−	3.31415i		−	0.803800i	−0.915684	−	0.401900i	$-0.868350\pi$
$17$		−	3.31415i		−	0.803800i	0.915684	−	0.401900i	$-0.131650\pi$
$18$	1.34067	+	0.450129i	0.315998	+	0.106097i
$19$		−	7.08582i		−	1.62560i	−0.582545	−	0.812799i	$-0.697943\pi$
$19$		−	7.08582i		−	1.62560i	0.582545	−	0.812799i	$-0.302057\pi$
$20$	−2.27610	+	3.84959i	−0.508951	+	0.860796i
$21$			2.64265i			0.576673i
$22$	0.681331	−	2.02927i	0.145260	−	0.432643i
$23$			4.82778i			1.00666i	0.864094	+	0.503331i	$0.167892\pi$
$23$			4.82778i			1.00666i	−0.864094	+	0.503331i	$0.832108\pi$
$24$	−1.59477	−	2.33596i	−0.325530	−	0.476826i
$25$	−4.87086	+	1.12902i	−0.974173	+	0.225803i
$26$	−5.18953	−	1.74239i	−1.01775	−	0.341711i
$27$	−1.00000			−0.192450
$28$	3.18953	−	4.21441i	0.602765	−	0.796448i
$29$			2.18513i			0.405769i	0.979203	+	0.202885i	$0.0650316\pi$
$29$			2.18513i			0.405769i	−0.979203	+	0.202885i	$0.934968\pi$
$30$	0.659335	−	3.09278i	0.120377	−	0.564661i
$31$	−7.36266			−1.32237			−0.661187	−	0.750222i	$-0.729947\pi$
$31$	−7.36266			−1.32237			−0.661187	+	0.750222i	$0.729947\pi$
$32$	−0.276098	+	5.65011i	−0.0488076	+	0.998808i
$33$			1.51363i			0.263490i
$34$	1.49180	−	4.44317i	0.255841	−	0.761997i
$35$	5.87086	−	0.671502i	0.992357	−	0.113504i
$36$	1.59477	+	1.20695i	0.265795	+	0.201158i
$37$	7.87086			1.29396			0.646981	−	0.762506i	$-0.276031\pi$
$37$	7.87086			1.29396			0.646981	+	0.762506i	$0.276031\pi$
$38$	3.18953	−	9.49971i	0.517411	−	1.54106i
$39$	3.87086			0.619834
$40$	−4.78430	+	4.13648i	−0.756464	+	0.654035i
$41$	8.72532			1.36267			0.681333	−	0.731973i	$-0.261400\pi$
$41$	8.72532			1.36267			0.681333	+	0.731973i	$0.261400\pi$
$42$	−1.18953	+	3.54291i	−0.183549	+	0.546683i
$43$	−1.01641			−0.155001			−0.0775003	−	0.996992i	$-0.524694\pi$
$43$	−1.01641			−0.155001			−0.0775003	+	0.996992i	$0.524694\pi$
$44$	1.82687	−	2.41389i	0.275411	−	0.363908i
$45$	0.254102	+	2.22158i	0.0378792	+	0.331174i
$46$	−2.17313	+	6.47244i	−0.320410	+	0.954309i
$47$			7.08582i			1.03357i	0.856114	+	0.516786i	$0.172872\pi$
$47$			7.08582i			1.03357i	−0.856114	+	0.516786i	$0.827128\pi$
$48$	−1.08656	−	3.84959i	−0.156832	−	0.555641i
$49$	0.0164068			0.00234382
$50$	−7.03840	−	0.678887i	−0.995380	−	0.0960091i
$51$			3.31415i			0.464074i
$52$	−6.17313	−	4.67192i	−0.856059	−	0.647879i
$53$	−4.50820			−0.619249			−0.309625	−	0.950859i	$-0.600203\pi$
$53$	−4.50820			−0.619249			−0.309625	+	0.950859i	$0.600203\pi$
$54$	−1.34067	−	0.450129i	−0.182441	−	0.0612549i
$55$	3.36266	−	0.384617i	0.453421	−	0.0518617i
$56$	6.17313	−	4.21441i	0.824919	−	0.563174i
$57$			7.08582i			0.938539i
$58$	−0.983593	+	2.92953i	−0.129152	+	0.384667i
$59$			6.79893i			0.885145i	0.896733	+	0.442573i	$0.145934\pi$
$59$			6.79893i			0.885145i	−0.896733	+	0.442573i	$0.854066\pi$
$60$	2.27610	−	3.84959i	0.293843	−	0.496981i
$61$		−	3.60104i		−	0.461065i	−0.973065	−	0.230533i	$-0.925953\pi$
$61$		−	3.60104i		−	0.461065i	0.973065	−	0.230533i	$-0.0740469\pi$
$62$	−9.87086	−	3.31415i	−1.25360	−	0.420898i
$63$		−	2.64265i		−	0.332942i
$64$	−2.91344	+	7.45063i	−0.364180	+	0.931329i
$65$	−0.983593	−	8.59945i	−0.122000	−	1.06663i
$66$	−0.681331	+	2.02927i	−0.0838660	+	0.249786i
$67$	1.01641			0.124174			0.0620869	−	0.998071i	$-0.480224\pi$
$67$	1.01641			0.124174			0.0620869	+	0.998071i	$0.480224\pi$
$68$	4.00000	−	5.28530i	0.485071	−	0.640937i
$69$		−	4.82778i		−	0.581197i
$70$	8.17313	+	1.74239i	0.976876	+	0.208255i
$71$	−6.72532			−0.798149			−0.399074	−	0.916919i	$-0.630669\pi$
$71$	−6.72532			−0.798149			−0.399074	+	0.916919i	$0.630669\pi$
$72$	1.59477	+	2.33596i	0.187945	+	0.275296i
$73$			15.5146i			1.81585i	0.419132	+	0.907925i	$0.362334\pi$
$73$			15.5146i			1.81585i	−0.419132	+	0.907925i	$0.637666\pi$
$74$	10.5522	+	3.54291i	1.22667	+	0.411855i
$75$	4.87086	−	1.12902i	0.562439	−	0.130368i
$76$	8.55220	−	11.3002i	0.981004	−	1.29622i
$77$	−4.00000			−0.455842
$78$	5.18953	+	1.74239i	0.587599	+	0.197287i
$79$	7.36266			0.828364			0.414182	−	0.910194i	$-0.364068\pi$
$79$	7.36266			0.828364			0.414182	+	0.910194i	$0.364068\pi$
$80$	−8.27610	+	3.39208i	−0.925296	+	0.379246i
$81$	1.00000			0.111111
$82$	11.6977	+	3.92752i	1.29180	+	0.433723i
$83$	−7.74173			−0.849765			−0.424883	−	0.905248i	$-0.639685\pi$
$83$	−7.74173			−0.849765			−0.424883	+	0.905248i	$0.639685\pi$
$84$	−3.18953	+	4.21441i	−0.348007	+	0.459830i
$85$	7.36266	−	0.842131i	0.798593	−	0.0913420i
$86$	−1.36266	−	0.457515i	−0.146940	−	0.0493351i
$87$		−	2.18513i		−	0.234271i
$88$	3.53579	−	2.41389i	0.376916	−	0.257322i
$89$	−14.7581			−1.56436			−0.782180	−	0.623053i	$-0.785892\pi$
$89$	−14.7581			−1.56436			−0.782180	+	0.623053i	$0.785892\pi$
$90$	−0.659335	+	3.09278i	−0.0695000	+	0.326007i
$91$			10.2293i			1.07233i
$92$	−5.82687	+	7.69919i	−0.607493	+	0.802696i
$93$	7.36266			0.763472
$94$	−3.18953	+	9.49971i	−0.328975	+	0.979820i
$95$	15.7417	−	1.80052i	1.61507	−	0.184729i
$96$	0.276098	−	5.65011i	0.0281791	−	0.576662i
$97$		−	11.1444i		−	1.13154i	−0.824563	−	0.565769i	$-0.808579\pi$
$97$		−	11.1444i		−	1.13154i	0.824563	−	0.565769i	$-0.191421\pi$
$98$	0.0219960	+	0.00738516i	0.00222193	+	0.000746014i
$99$		−	1.51363i		−	0.152126i
$100$	−9.13056	−	4.07835i	−0.913056	−	0.407835i
$101$		−	13.3295i		−	1.32633i	−0.748471	−	0.663167i	$-0.769212\pi$
$101$		−	13.3295i		−	1.32633i	0.748471	−	0.663167i	$-0.230788\pi$
$102$	−1.49180	+	4.44317i	−0.147710	+	0.439939i
$103$		−	0.958386i		−	0.0944326i	−0.998885	−	0.0472163i	$-0.984965\pi$
$103$		−	0.958386i		−	0.0944326i	0.998885	−	0.0472163i	$-0.0150350\pi$
$104$	−6.17313	−	9.04219i	−0.605325	−	0.886660i
$105$	−5.87086	+	0.671502i	−0.572938	+	0.0655318i
$106$	−6.04399	−	2.02927i	−0.587044	−	0.197101i
$107$	4.00000			0.386695			0.193347	−	0.981130i	$-0.438066\pi$
$107$	4.00000			0.386695			0.193347	+	0.981130i	$0.438066\pi$
$108$	−1.59477	−	1.20695i	−0.153457	−	0.116138i
$109$		−	0.769233i		−	0.0736792i	−0.999321	−	0.0368396i	$-0.988271\pi$
$109$		−	0.769233i		−	0.0736792i	0.999321	−	0.0368396i	$-0.0117291\pi$
$110$	4.68133	+	0.997991i	0.446347	+	0.0951547i
$111$	−7.87086			−0.747069
$112$	10.1731	−	2.87141i	0.961270	−	0.271322i
$113$		−	14.4585i		−	1.36014i	−0.733146	−	0.680071i	$-0.761949\pi$
$113$		−	14.4585i		−	1.36014i	0.733146	−	0.680071i	$-0.238051\pi$
$114$	−3.18953	+	9.49971i	−0.298727	+	0.889729i
$115$	−10.7253	+	1.22675i	−1.00014	+	0.114395i
$116$	−2.63734	+	3.48478i	−0.244871	+	0.323554i
$117$	−3.87086			−0.357862
$118$	−3.06040	+	9.11509i	−0.281733	+	0.839112i
$119$	−8.75814			−0.802857
$120$	4.78430	−	4.13648i	0.436745	−	0.377607i
$121$	8.70892			0.791720
$122$	1.62093	−	4.82778i	0.146752	−	0.437087i
$123$	−8.72532			−0.786736
$124$	−11.7417	−	8.88633i	−1.05444	−	0.798016i
$125$	−3.74590	−	10.5341i	−0.335043	−	0.942203i
$126$	1.18953	−	3.54291i	0.105972	−	0.315627i
$127$		−	11.5290i		−	1.02303i	−0.859274	−	0.511516i	$-0.829084\pi$
$127$		−	11.5290i		−	1.02303i	0.859274	−	0.511516i	$-0.170916\pi$
$128$	−7.25969	+	8.67738i	−0.641672	+	0.766979i
$129$	1.01641			0.0894896
$130$	2.55220	−	11.9717i	0.223842	−	1.04999i
$131$			7.37270i			0.644156i	0.946713	+	0.322078i	$0.104381\pi$
$131$			7.37270i			0.644156i	−0.946713	+	0.322078i	$0.895619\pi$
$132$	−1.82687	+	2.41389i	−0.159009	+	0.210102i
$133$	−18.7253			−1.62369
$134$	1.36266	+	0.457515i	0.117716	+	0.0395232i
$135$	−0.254102	−	2.22158i	−0.0218696	−	0.191203i
$136$	7.74173	−	5.28530i	0.663848	−	0.453211i
$137$			3.88792i			0.332167i	0.986112	+	0.166084i	$0.0531122\pi$
$137$			3.88792i			0.332167i	−0.986112	+	0.166084i	$0.946888\pi$
$138$	2.17313	−	6.47244i	0.184989	−	0.550971i
$139$			14.6291i			1.24083i	0.784275	+	0.620414i	$0.213035\pi$
$139$			14.6291i			1.24083i	−0.784275	+	0.620414i	$0.786965\pi$
$140$	10.1731	+	6.01493i	0.859786	+	0.508354i
$141$		−	7.08582i		−	0.596733i
$142$	−9.01641	−	3.02727i	−0.756640	−	0.254042i
$143$			5.85907i			0.489960i
$144$	1.08656	+	3.84959i	0.0905470	+	0.320800i
$145$	−4.85446	+	0.555246i	−0.403141	+	0.0461107i
$146$	−6.98359	+	20.7999i	−0.577966	+	1.72141i
$147$	−0.0164068			−0.00135321
$148$	12.5522	+	9.49971i	1.03178	+	0.780871i
$149$			11.0715i			0.907010i	0.891254	+	0.453505i	$0.149827\pi$
$149$			11.0715i			0.907010i	−0.891254	+	0.453505i	$0.850173\pi$
$150$	7.03840	+	0.678887i	0.574683	+	0.0554309i
$151$	0.637339			0.0518659			0.0259329	−	0.999664i	$-0.491744\pi$
$151$	0.637339			0.0518659			0.0259329	+	0.999664i	$0.491744\pi$
$152$	16.5522	−	11.3002i	1.34256	−	0.916569i
$153$		−	3.31415i		−	0.267933i
$154$	−5.36266	−	1.80052i	−0.432136	−	0.145090i
$155$	−1.87086	−	16.3568i	−0.150271	−	1.31381i
$156$	6.17313	+	4.67192i	0.494246	+	0.374053i
$157$	−0.129135			−0.0103061			−0.00515306	−	0.999987i	$-0.501640\pi$
$157$	−0.129135			−0.0103061			−0.00515306	+	0.999987i	$0.501640\pi$
$158$	9.87086	+	3.31415i	0.785284	+	0.263660i
$159$	4.50820			0.357524
$160$	−12.6224	+	0.822329i	−0.997885	+	0.0650108i
$161$	12.7581			1.00548
$162$	1.34067	+	0.450129i	0.105333	+	0.0353655i
$163$	19.4835			1.52606			0.763031	−	0.646362i	$-0.223710\pi$
$163$	19.4835			1.52606			0.763031	+	0.646362i	$0.223710\pi$
$164$	13.9149	+	10.5310i	1.08657	+	0.822332i
$165$	−3.36266	+	0.384617i	−0.261783	+	0.0299424i
$166$	−10.3791	−	3.48478i	−0.805572	−	0.270471i
$167$		−	1.80052i		−	0.139328i	−0.997571	−	0.0696641i	$-0.977807\pi$
$167$		−	1.80052i		−	0.139328i	0.997571	−	0.0696641i	$-0.0221928\pi$
$168$	−6.17313	+	4.21441i	−0.476267	+	0.325149i
$169$	1.98359			0.152584
$170$	10.2499	+	2.18513i	0.786134	+	0.167592i
$171$		−	7.08582i		−	0.541866i
$172$	−1.62093	−	1.22675i	−0.123595	−	0.0935386i
$173$	23.2335			1.76641			0.883206	−	0.468985i	$-0.155380\pi$
$173$	23.2335			1.76641			0.883206	+	0.468985i	$0.155380\pi$
$174$	0.983593	−	2.92953i	0.0745660	−	0.222087i
$175$	2.98359	+	12.8720i	0.225538	+	0.973031i
$176$	5.82687	−	1.64466i	0.439217	−	0.123971i
$177$		−	6.79893i		−	0.511039i
$178$	−19.7857	−	6.64307i	−1.48300	−	0.497919i
$179$			2.85664i			0.213515i	0.994285	+	0.106757i	$0.0340468\pi$
$179$			2.85664i			0.213515i	−0.994285	+	0.106757i	$0.965953\pi$
$180$	−2.27610	+	3.84959i	−0.169650	+	0.286932i
$181$			5.28530i			0.392853i	0.980519	+	0.196427i	$0.0629337\pi$
$181$			5.28530i			0.392853i	−0.980519	+	0.196427i	$0.937066\pi$
$182$	−4.60453	+	13.7141i	−0.341310	+	1.01656i
$183$			3.60104i			0.266196i
$184$	−11.2775	+	7.69919i	−0.831390	+	0.567592i
$185$	2.00000	+	17.4858i	0.147043	+	1.28558i
$186$	9.87086	+	3.31415i	0.723767	+	0.243005i
$187$	−5.01641			−0.366836
$188$	−8.55220	+	11.3002i	−0.623733	+	0.824154i
$189$			2.64265i			0.192224i
$190$	21.9149	+	4.67192i	1.58987	+	0.338937i
$191$	−5.96719			−0.431770			−0.215885	−	0.976419i	$-0.569264\pi$
$191$	−5.96719			−0.431770			−0.215885	+	0.976419i	$0.569264\pi$
$192$	2.91344	−	7.45063i	0.210259	−	0.537703i
$193$		−	14.9409i		−	1.07547i	−0.843115	−	0.537733i	$-0.819281\pi$
$193$		−	14.9409i		−	1.07547i	0.843115	−	0.537733i	$-0.180719\pi$
$194$	5.01641	−	14.9409i	0.360157	−	1.07269i
$195$	0.983593	+	8.59945i	0.0704366	+	0.615819i
$196$	0.0261649	+	0.0198021i	0.00186892	+	0.00141443i
$197$	−3.23353			−0.230379			−0.115190	−	0.993344i	$-0.536748\pi$
$197$	−3.23353			−0.230379			−0.115190	+	0.993344i	$0.536748\pi$
$198$	0.681331	−	2.02927i	0.0484201	−	0.144214i
$199$	8.12080			0.575668			0.287834	−	0.957680i	$-0.407065\pi$
$199$	8.12080			0.575668			0.287834	+	0.957680i	$0.407065\pi$
$200$	−10.4052	−	9.57764i	−0.735761	−	0.677241i
$201$	−1.01641			−0.0716918
$202$	6.00000	−	17.8704i	0.422159	−	1.25736i
$203$	5.77454			0.405293
$204$	−4.00000	+	5.28530i	−0.280056	+	0.370045i
$205$	2.21712	+	19.3840i	0.154850	+	1.35384i
$206$	0.431398	−	1.28488i	0.0300569	−	0.0895215i
$207$			4.82778i			0.335554i
$208$	−4.20594	−	14.9013i	−0.291630	−	1.03322i
$209$	−10.7253			−0.741886
$210$	−8.17313	−	1.74239i	−0.563999	−	0.120236i
$211$		−	13.7141i		−	0.944119i	−0.881567	−	0.472059i	$-0.843511\pi$
$211$		−	13.7141i		−	0.944119i	0.881567	−	0.472059i	$-0.156489\pi$
$212$	−7.18953	−	5.44116i	−0.493779	−	0.373700i
$213$	6.72532			0.460812
$214$	5.36266	+	1.80052i	0.366584	+	0.123081i
$215$	−0.258271	−	2.25803i	−0.0176139	−	0.153997i
$216$	−1.59477	−	2.33596i	−0.108510	−	0.158942i
$217$			19.4569i			1.32082i
$218$	0.346255	−	1.03128i	0.0234513	−	0.0698474i
$219$		−	15.5146i		−	1.04838i
$220$	5.82687	+	3.44518i	0.392848	+	0.232274i
$221$			12.8286i			0.862947i
$222$	−10.5522	−	3.54291i	−0.708217	−	0.237784i
$223$		−	9.84472i		−	0.659251i	−0.944112	−	0.329626i	$-0.893077\pi$
$223$		−	9.84472i		−	0.659251i	0.944112	−	0.329626i	$-0.106923\pi$
$224$	14.9313	+	0.729629i	0.997637	+	0.0487504i
$225$	−4.87086	+	1.12902i	−0.324724	+	0.0752677i
$226$	6.50820	−	19.3840i	0.432919	−	1.28941i
$227$	5.70892			0.378914			0.189457	−	0.981889i	$-0.439327\pi$
$227$	5.70892			0.378914			0.189457	+	0.981889i	$0.439327\pi$
$228$	−8.55220	+	11.3002i	−0.566383	+	0.748376i
$229$			0.769233i			0.0508324i	0.999677	+	0.0254162i	$0.00809109\pi$
$229$			0.769233i			0.0508324i	−0.999677	+	0.0254162i	$0.991909\pi$
$230$	−14.9313	−	3.18312i	−0.984538	−	0.209889i
$231$	4.00000			0.263181
$232$	−5.10439	+	3.48478i	−0.335120	+	0.228787i
$233$			18.4008i			1.20548i	0.797939	+	0.602739i	$0.205924\pi$
$233$			18.4008i			1.20548i	−0.797939	+	0.602739i	$0.794076\pi$
$234$	−5.18953	−	1.74239i	−0.339250	−	0.113904i
$235$	−15.7417	+	1.80052i	−1.02688	+	0.117453i
$236$	−8.20594	+	10.8427i	−0.534161	+	0.705800i
$237$	−7.36266			−0.478256
$238$	−11.7417	−	3.94229i	−0.761103	−	0.255541i
$239$	−10.0328			−0.648969			−0.324484	−	0.945891i	$-0.605191\pi$
$239$	−10.0328			−0.648969			−0.324484	+	0.945891i	$0.605191\pi$
$240$	8.27610	−	3.39208i	0.534220	−	0.218958i
$241$	10.7581			0.692992			0.346496	−	0.938051i	$-0.387371\pi$
$241$	10.7581			0.692992			0.346496	+	0.938051i	$0.387371\pi$
$242$	11.6757	+	3.92014i	0.750545	+	0.251996i
$243$	−1.00000			−0.0641500
$244$	4.34625	−	5.74281i	0.278240	−	0.367646i
$245$	0.00416898	+	0.0364490i	0.000266347	+	0.00232864i
$246$	−11.6977	−	3.92752i	−0.745820	−	0.250410i
$247$			27.4282i			1.74522i
$248$	−11.7417	−	17.1989i	−0.745601	−	1.09213i
$249$	7.74173			0.490612
$250$	−0.280267	−	15.8089i	−0.0177256	−	0.999843i
$251$		−	12.6580i		−	0.798966i	−0.916741	−	0.399483i	$-0.869190\pi$
$251$		−	12.6580i		−	0.798966i	0.916741	−	0.399483i	$-0.130810\pi$
$252$	3.18953	−	4.21441i	0.200922	−	0.265483i
$253$	7.30749			0.459418
$254$	5.18953	−	15.4565i	0.325620	−	0.969827i
$255$	−7.36266	+	0.842131i	−0.461068	+	0.0527363i
$256$	−13.6388	+	8.36566i	−0.852422	+	0.522854i
$257$			13.3110i			0.830316i	0.909749	+	0.415158i	$0.136274\pi$
$257$			13.3110i			0.830316i	−0.909749	+	0.415158i	$0.863726\pi$
$258$	1.36266	+	0.457515i	0.0848356	+	0.0284836i
$259$		−	20.7999i		−	1.29244i
$260$	8.81047	−	14.9013i	0.546402	−	0.924137i
$261$			2.18513i			0.135256i
$262$	−3.31867	+	9.88432i	−0.205028	+	0.610656i
$263$		−	18.4256i		−	1.13617i	−0.822969	−	0.568087i	$-0.807684\pi$
$263$		−	18.4256i		−	1.13617i	0.822969	−	0.568087i	$-0.192316\pi$
$264$	−3.53579	+	2.41389i	−0.217613	+	0.148565i
$265$	−1.14554	−	10.0153i	−0.0703701	−	0.615238i
$266$	−25.1044	−	8.42882i	−1.53925	−	0.516804i
$267$	14.7581			0.903183
$268$	1.62093	+	1.22675i	0.0990142	+	0.0749356i
$269$			3.86940i			0.235921i	0.993018	+	0.117961i	$0.0376357\pi$
$269$			3.86940i			0.235921i	−0.993018	+	0.117961i	$0.962364\pi$
$270$	0.659335	−	3.09278i	0.0401258	−	0.188220i
$271$	−17.3955			−1.05670			−0.528350	−	0.849027i	$-0.677189\pi$
$271$	−17.3955			−1.05670			−0.528350	+	0.849027i	$0.677189\pi$
$272$	12.7581	−	3.60104i	0.773576	−	0.218345i
$273$		−	10.2293i		−	0.619108i
$274$	−1.75007	+	5.21240i	−0.105725	+	0.314893i
$275$	1.70892	+	7.37270i	0.103052	+	0.444591i
$276$	5.82687	−	7.69919i	0.350737	−	0.463437i
$277$	−0.887271			−0.0533110			−0.0266555	−	0.999645i	$-0.508486\pi$
$277$	−0.887271			−0.0533110			−0.0266555	+	0.999645i	$0.508486\pi$
$278$	−6.58501	+	19.6128i	−0.394943	+	1.17630i
$279$	−7.36266			−0.440791
$280$	10.9313	+	12.6432i	0.653268	+	0.755577i
$281$	−13.4835			−0.804356			−0.402178	−	0.915562i	$-0.631747\pi$
$281$	−13.4835			−0.804356			−0.402178	+	0.915562i	$0.631747\pi$
$282$	3.18953	−	9.49971i	0.189934	−	0.565699i
$283$	28.4342			1.69024			0.845120	−	0.534577i	$-0.179529\pi$
$283$	28.4342			1.69024			0.845120	+	0.534577i	$0.179529\pi$
$284$	−10.7253	−	8.11710i	−0.636431	−	0.481661i
$285$	−15.7417	+	1.80052i	−0.932460	+	0.106653i
$286$	−2.63734	+	7.85505i	−0.155949	+	0.464479i
$287$		−	23.0580i		−	1.36107i
$288$	−0.276098	+	5.65011i	−0.0162692	+	0.332936i
$289$	6.01641			0.353906
$290$	−6.75814	−	1.44073i	−0.396851	−	0.0846029i
$291$			11.1444i			0.653294i
$292$	−18.7253	+	24.7422i	−1.09582	+	1.44793i
$293$	7.99166			0.466878			0.233439	−	0.972371i	$-0.425002\pi$
$293$	7.99166			0.466878			0.233439	+	0.972371i	$0.425002\pi$
$294$	−0.0219960	−	0.00738516i	−0.00128283	−	0.000430711i
$295$	−15.1044	+	1.72762i	−0.879412	+	0.100586i
$296$	12.5522	+	18.3860i	0.729582	+	1.06867i
$297$			1.51363i			0.0878299i
$298$	−4.98359	+	14.8431i	−0.288692	+	0.859840i
$299$		−	18.6877i		−	1.08074i
$300$	9.13056	+	4.07835i	0.527153	+	0.235464i
$301$			2.68601i			0.154819i
$302$	0.854458	+	0.286885i	0.0491685	+	0.0165084i
$303$			13.3295i			0.765760i
$304$	27.2775	−	7.69919i	1.56447	−	0.441579i
$305$	8.00000	−	0.915029i	0.458079	−	0.0523944i
$306$	1.49180	−	4.44317i	0.0852803	−	0.253999i
$307$	−17.4506			−0.995961			−0.497980	−	0.867188i	$-0.665925\pi$
$307$	−17.4506			−0.995961			−0.497980	+	0.867188i	$0.665925\pi$
$308$	−6.37907	−	4.82778i	−0.363481	−	0.275088i
$309$			0.958386i			0.0545207i
$310$	4.85446	−	22.7711i	0.275715	−	1.29331i
$311$	21.4506			1.21635			0.608177	−	0.793801i	$-0.291901\pi$
$311$	21.4506			1.21635			0.608177	+	0.793801i	$0.291901\pi$
$312$	6.17313	+	9.04219i	0.349485	+	0.511913i
$313$		−	7.73879i		−	0.437422i	−0.975790	−	0.218711i	$-0.929815\pi$
$313$		−	7.73879i		−	0.437422i	0.975790	−	0.218711i	$-0.0701853\pi$
$314$	−0.173127	−	0.0581276i	−0.00977014	−	0.00328033i
$315$	5.87086	−	0.671502i	0.330786	−	0.0378348i
$316$	11.7417	+	8.88633i	0.660524	+	0.499895i
$317$	−11.2335			−0.630938			−0.315469	−	0.948936i	$-0.602162\pi$
$317$	−11.2335			−0.630938			−0.315469	+	0.948936i	$0.602162\pi$
$318$	6.04399	+	2.02927i	0.338930	+	0.113796i
$319$	3.30749			0.185184
$320$	−17.2925	−	4.57922i	−0.966680	−	0.255986i
$321$	−4.00000			−0.223258
$322$	17.1044	+	5.74281i	0.953190	+	0.320034i
$323$	−23.4835			−1.30665
$324$	1.59477	+	1.20695i	0.0885982	+	0.0670525i
$325$	18.8545	−	4.37027i	1.04586	−	0.242419i
$326$	26.1208	+	8.77008i	1.44670	+	0.485730i
$327$			0.769233i			0.0425387i
$328$	13.9149	+	20.3820i	0.768319	+	1.12541i
$329$	18.7253			1.03236
$330$	−4.68133	−	0.997991i	−0.257699	−	0.0549376i
$331$			8.00084i			0.439766i	0.975526	+	0.219883i	$0.0705676\pi$
$331$			8.00084i			0.439766i	−0.975526	+	0.219883i	$0.929432\pi$
$332$	−12.3463	−	9.34385i	−0.677589	−	0.512810i
$333$	7.87086			0.431321
$334$	0.810466	−	2.41389i	0.0443467	−	0.132082i
$335$	0.258271	+	2.25803i	0.0141108	+	0.123369i
$336$	−10.1731	+	2.87141i	−0.554990	+	0.156648i
$337$		−	21.5692i		−	1.17495i	−0.809243	−	0.587474i	$-0.800123\pi$
$337$		−	21.5692i		−	1.17495i	0.809243	−	0.587474i	$-0.199877\pi$
$338$	2.65933	+	0.892874i	0.144649	+	0.0485659i
$339$			14.4585i			0.785279i
$340$	12.7581	+	7.54333i	0.691907	+	0.409095i
$341$			11.1444i			0.603501i
$342$	3.18953	−	9.49971i	0.172470	−	0.513685i
$343$		−	18.5419i		−	1.00117i
$344$	−1.62093	−	2.37429i	−0.0873948	−	0.128013i
$345$	10.7253	−	1.22675i	0.577432	−	0.0660459i
$346$	31.1484	+	10.4581i	1.67455	+	0.562231i
$347$	−21.7089			−1.16540			−0.582698	−	0.812689i	$-0.698003\pi$
$347$	−21.7089			−1.16540			−0.582698	+	0.812689i	$0.698003\pi$
$348$	2.63734	−	3.48478i	0.141376	−	0.186804i
$349$		−	24.7422i		−	1.32442i	−0.749318	−	0.662211i	$-0.769618\pi$
$349$		−	24.7422i		−	1.32442i	0.749318	−	0.662211i	$-0.230382\pi$
$350$	−1.79406	+	18.6000i	−0.0958965	+	0.994213i
$351$	3.87086			0.206611
$352$	8.55220	+	0.417910i	0.455834	+	0.0222747i
$353$		−	3.31415i		−	0.176394i	−0.996103	−	0.0881972i	$-0.971889\pi$
$353$		−	3.31415i		−	0.176394i	0.996103	−	0.0881972i	$-0.0281106\pi$
$354$	3.06040	−	9.11509i	0.162658	−	0.484462i
$355$	−1.70892	−	14.9409i	−0.0906998	−	0.792979i
$356$	−23.5358	−	17.8123i	−1.24739	−	0.944048i
$357$	8.75814			0.463530
$358$	−1.28586	+	3.82979i	−0.0679596	+	0.202411i
$359$	16.7581			0.884461			0.442230	−	0.896902i	$-0.354187\pi$
$359$	16.7581			0.884461			0.442230	+	0.896902i	$0.354187\pi$
$360$	−4.78430	+	4.13648i	−0.252155	+	0.218012i
$361$	−31.2088			−1.64257
$362$	−2.37907	+	7.08582i	−0.125041	+	0.372422i
$363$	−8.70892			−0.457100
$364$	−12.3463	+	16.3134i	−0.647120	+	0.855055i
$365$	−34.4671	+	3.94229i	−1.80409	+	0.206349i
$366$	−1.62093	+	4.82778i	−0.0847275	+	0.252352i
$367$			28.5324i			1.48938i	0.667411	+	0.744690i	$0.267403\pi$
$367$			28.5324i			1.48938i	−0.667411	+	0.744690i	$0.732597\pi$
$368$	−18.5850	+	5.24569i	−0.968811	+	0.273451i
$369$	8.72532			0.454222
$370$	−5.18953	+	24.3428i	−0.269791	+	1.26552i
$371$			11.9136i			0.618523i
$372$	11.7417	+	8.88633i	0.608780	+	0.460735i
$373$	−37.5798			−1.94581			−0.972904	−	0.231211i	$-0.925731\pi$
$373$	−37.5798			−1.94581			−0.972904	+	0.231211i	$0.925731\pi$
$374$	−6.72532	−	2.25803i	−0.347758	−	0.116760i
$375$	3.74590	+	10.5341i	0.193437	+	0.543981i
$376$	−16.5522	+	11.3002i	−0.853614	+	0.582765i
$377$		−	8.45836i		−	0.435628i
$378$	−1.18953	+	3.54291i	−0.0611830	+	0.182228i
$379$			6.74456i			0.346445i	0.984883	+	0.173222i	$0.0554179\pi$
$379$			6.74456i			0.346445i	−0.984883	+	0.173222i	$0.944582\pi$
$380$	27.2775	+	16.1280i	1.39931	+	0.827349i
$381$			11.5290i			0.590648i
$382$	−8.00000	−	2.68601i	−0.409316	−	0.137428i
$383$		−	21.8312i		−	1.11552i	−0.830001	−	0.557762i	$-0.811660\pi$
$383$		−	21.8312i		−	1.11552i	0.830001	−	0.557762i	$-0.188340\pi$
$384$	7.25969	−	8.67738i	0.370470	−	0.442816i
$385$	−1.01641	−	8.88633i	−0.0518009	−	0.452889i
$386$	6.72532	−	20.0307i	0.342310	−	1.01954i
$387$	−1.01641			−0.0516669
$388$	13.4506	−	17.7727i	0.682853	−	0.902270i
$389$		−	8.81344i		−	0.446859i	−0.974720	−	0.223429i	$-0.928275\pi$
$389$		−	8.81344i		−	0.446859i	0.974720	−	0.223429i	$-0.0717252\pi$
$390$	−2.55220	+	11.9717i	−0.129235	+	0.606212i
$391$	16.0000			0.809155
$392$	0.0261649	+	0.0383256i	0.00132153	+	0.00193573i
$393$		−	7.37270i		−	0.371904i
$394$	−4.33508	−	1.45551i	−0.218398	−	0.0733273i
$395$	1.87086	+	16.3568i	0.0941334	+	0.822998i
$396$	1.82687	−	2.41389i	0.0918038	−	0.121303i
$397$	0.821644			0.0412372			0.0206186	−	0.999787i	$-0.493436\pi$
$397$	0.821644			0.0412372			0.0206186	+	0.999787i	$0.493436\pi$
$398$	10.8873	+	3.65541i	0.545730	+	0.183229i
$399$	18.7253			0.937439
$400$	−9.63876	−	17.5241i	−0.481938	−	0.876205i
$401$	−12.7253			−0.635472			−0.317736	−	0.948179i	$-0.602923\pi$
$401$	−12.7253			−0.635472			−0.317736	+	0.948179i	$0.602923\pi$
$402$	−1.36266	−	0.457515i	−0.0679634	−	0.0228188i
$403$	28.4999			1.41968
$404$	16.0880	−	21.2574i	0.800407	−	1.05760i
$405$	0.254102	+	2.22158i	0.0126264	+	0.110391i
$406$	7.74173	+	2.59929i	0.384216	+	0.129001i
$407$		−	11.9136i		−	0.590535i
$408$	−7.74173	+	5.28530i	−0.383273	+	0.261661i
$409$	−2.25827			−0.111664			−0.0558321	−	0.998440i	$-0.517781\pi$
$409$	−2.25827			−0.111664			−0.0558321	+	0.998440i	$0.517781\pi$
$410$	−5.75291	+	26.9855i	−0.284116	+	1.33272i
$411$		−	3.88792i		−	0.191777i
$412$	1.15672	−	1.52840i	0.0569875	−	0.0752990i
$413$	17.9672			0.884107
$414$	−2.17313	+	6.47244i	−0.106803	+	0.318103i
$415$	−1.96719	−	17.1989i	−0.0965654	−	0.844261i
$416$	1.06874	−	21.8708i	0.0523991	−	1.07231i
$417$		−	14.6291i		−	0.716392i
$418$	−14.3791	−	4.82778i	−0.703303	−	0.236135i
$419$			33.4579i			1.63453i	0.576264	+	0.817263i	$0.304510\pi$
$419$			33.4579i			1.63453i	−0.576264	+	0.817263i	$0.695490\pi$
$420$	−10.1731	−	6.01493i	−0.496398	−	0.293498i
$421$		−	11.3398i		−	0.552669i	−0.961061	−	0.276335i	$-0.910880\pi$
$421$		−	11.3398i		−	0.552669i	0.961061	−	0.276335i	$-0.0891198\pi$
$422$	6.17313	−	18.3860i	0.300503	−	0.895018i
$423$			7.08582i			0.344524i
$424$	−7.18953	−	10.5310i	−0.349155	−	0.511430i
$425$	3.74173	+	16.1428i	0.181501	+	0.783040i
$426$	9.01641	+	3.02727i	0.436846	+	0.146671i
$427$	−9.51627			−0.460525
$428$	6.37907	+	4.82778i	0.308344	+	0.233360i
$429$		−	5.85907i		−	0.282878i
$430$	0.670152	−	3.14352i	0.0323176	−	0.151594i
$431$	10.6597			0.513459			0.256730	−	0.966483i	$-0.417355\pi$
$431$	10.6597			0.513459			0.256730	+	0.966483i	$0.417355\pi$
$432$	−1.08656	−	3.84959i	−0.0522773	−	0.185214i
$433$			26.5132i			1.27414i	0.770805	+	0.637072i	$0.219854\pi$
$433$			26.5132i			1.27414i	−0.770805	+	0.637072i	$0.780146\pi$
$434$	−8.75814	+	26.0852i	−0.420404	+	1.25213i
$435$	4.85446	−	0.555246i	0.232753	−	0.0266220i
$436$	0.928423	−	1.22675i	0.0444634	−	0.0587506i
$437$	34.2088			1.63643
$438$	6.98359	−	20.7999i	0.333689	−	0.993859i
$439$	−32.8789			−1.56923			−0.784613	−	0.619986i	$-0.787138\pi$
$439$	−32.8789			−1.56923			−0.784613	+	0.619986i	$0.787138\pi$
$440$	6.26111	+	7.24167i	0.298487	+	0.345233i
$441$	0.0164068			0.000781274
$442$	−5.77454	+	17.1989i	−0.274667	+	0.818068i
$443$	−5.70892			−0.271239			−0.135619	−	0.990761i	$-0.543302\pi$
$443$	−5.70892			−0.271239			−0.135619	+	0.990761i	$0.543302\pi$
$444$	−12.5522	−	9.49971i	−0.595701	−	0.450836i
$445$	−3.75007	−	32.7864i	−0.177770	−	1.55423i
$446$	4.43140	−	13.1985i	0.209833	−	0.624966i
$447$		−	11.0715i		−	0.523662i
$448$	19.6894	+	7.69919i	0.930237	+	0.363753i
$449$	2.00000			0.0943858			0.0471929	−	0.998886i	$-0.484972\pi$
$449$	2.00000			0.0943858			0.0471929	+	0.998886i	$0.484972\pi$
$450$	−7.03840	−	0.678887i	−0.331793	−	0.0320030i
$451$		−	13.2069i		−	0.621890i
$452$	17.4506	−	23.0580i	0.820809	−	1.08456i
$453$	−0.637339			−0.0299448
$454$	7.65375	+	2.56975i	0.359208	+	0.120604i
$455$	−22.7253	+	2.59929i	−1.06538	+	0.121857i
$456$	−16.5522	+	11.3002i	−0.775128	+	0.529182i
$457$			3.94229i			0.184413i	0.995740	+	0.0922064i	$0.0293920\pi$
$457$			3.94229i			0.184413i	−0.995740	+	0.0922064i	$0.970608\pi$
$458$	−0.346255	+	1.03128i	−0.0161794	+	0.0481888i
$459$			3.31415i			0.154691i
$460$	−18.5850	−	10.9885i	−0.866531	−	0.512342i
$461$		−	33.8969i		−	1.57874i	−0.613920	−	0.789369i	$-0.710408\pi$
$461$		−	33.8969i		−	1.57874i	0.613920	−	0.789369i	$-0.289592\pi$
$462$	5.36266	+	1.80052i	0.249494	+	0.0837677i
$463$			22.8688i			1.06280i	0.847120	+	0.531402i	$0.178335\pi$
$463$			22.8688i			1.06280i	−0.847120	+	0.531402i	$0.821665\pi$
$464$	−8.41188	+	2.37429i	−0.390512	+	0.110224i
$465$	1.87086	+	16.3568i	0.0867593	+	0.758527i
$466$	−8.28275	+	24.6693i	−0.383691	+	1.14278i
$467$	15.7417			0.728440			0.364220	−	0.931313i	$-0.381336\pi$
$467$	15.7417			0.728440			0.364220	+	0.931313i	$0.381336\pi$
$468$	−6.17313	−	4.67192i	−0.285353	−	0.215960i
$469$		−	2.68601i		−	0.124028i
$470$	−21.9149	−	4.67192i	−1.01086	−	0.215500i
$471$	0.129135			0.00595024
$472$	−15.8820	+	10.8427i	−0.731030	+	0.499076i
$473$			1.53847i			0.0707388i
$474$	−9.87086	−	3.31415i	−0.453384	−	0.152224i
$475$	8.00000	+	34.5140i	0.367065	+	1.58361i
$476$	−13.9672	−	10.5706i	−0.640185	−	0.484502i
$477$	−4.50820			−0.206416
$478$	−13.4506	−	4.51606i	−0.615218	−	0.206560i
$479$	−20.6925			−0.945465			−0.472732	−	0.881206i	$-0.656732\pi$
$479$	−20.6925			−0.945465			−0.472732	+	0.881206i	$0.656732\pi$
$480$	12.6224	−	0.822329i	0.576129	−	0.0375340i
$481$	−30.4671			−1.38918
$482$	14.4231	+	4.84255i	0.656952	+	0.220572i
$483$	−12.7581			−0.580515
$484$	13.8887	+	10.5112i	0.631304	+	0.477781i
$485$	24.7581	−	2.83180i	1.12421	−	0.128586i
$486$	−1.34067	−	0.450129i	−0.0608138	−	0.0204183i
$487$		−	30.8401i		−	1.39750i	−0.715366	−	0.698750i	$-0.753740\pi$
$487$		−	30.8401i		−	1.39750i	0.715366	−	0.698750i	$-0.246260\pi$
$488$	8.41188	−	5.74281i	0.380788	−	0.259965i
$489$	−19.4835			−0.881072
$490$	−0.0108175	+	0.0507425i	−0.000488687	+	0.00229231i
$491$		−	10.9737i		−	0.495238i	−0.968858	−	0.247619i	$-0.920352\pi$
$491$		−	10.9737i		−	0.495238i	0.968858	−	0.247619i	$-0.0796481\pi$
$492$	−13.9149	−	10.5310i	−0.627330	−	0.474774i
$493$	7.24186			0.326157
$494$	−12.3463	+	36.7721i	−0.555484	+	1.65445i
$495$	3.36266	−	0.384617i	0.151140	−	0.0172872i
$496$	−8.00000	−	28.3433i	−0.359211	−	1.27265i
$497$			17.7727i			0.797213i
$498$	10.3791	+	3.48478i	0.465097	+	0.156157i
$499$		−	3.71729i		−	0.166409i	−0.996533	−	0.0832044i	$-0.973485\pi$
$499$		−	3.71729i		−	0.166409i	0.996533	−	0.0832044i	$-0.0265154\pi$
$500$	6.74031	−	21.3206i	0.301436	−	0.953486i
$501$			1.80052i			0.0804412i
$502$	5.69774	−	16.9701i	0.254302	−	0.757414i
$503$			39.9451i			1.78107i	0.454919	+	0.890533i	$0.349668\pi$
$503$			39.9451i			1.78107i	−0.454919	+	0.890533i	$0.650332\pi$
$504$	6.17313	−	4.21441i	0.274973	−	0.187725i
$505$	29.6126	−	3.38705i	1.31774	−	0.150722i
$506$	9.79690	+	3.28932i	0.435525	+	0.146228i
$507$	−1.98359			−0.0880945
$508$	13.9149	−	18.3860i	0.617372	−	0.815749i
$509$			0.0728979i			0.00323114i	0.999999	+	0.00161557i	$0.000514253\pi$
$509$			0.0728979i			0.00323114i	−0.999999	+	0.00161557i	$0.999486\pi$
$510$	−10.2499	−	2.18513i	−0.453875	−	0.0967594i
$511$	40.9997			1.81372
$512$	−22.0506	+	5.07634i	−0.974510	+	0.224345i
$513$			7.08582i			0.312846i
$514$	−5.99166	+	17.8456i	−0.264281	+	0.787134i
$515$	2.12914	−	0.243528i	0.0938209	−	0.0107311i
$516$	1.62093	+	1.22675i	0.0713576	+	0.0540046i
$517$	10.7253			0.471699
$518$	9.36266	−	27.8857i	0.411372	−	1.22523i
$519$	−23.2335			−1.01984
$520$	18.5194	−	16.0118i	0.812129	−	0.702162i
$521$	−11.9672			−0.524292			−0.262146	−	0.965028i	$-0.584430\pi$
$521$	−11.9672			−0.524292			−0.262146	+	0.965028i	$0.584430\pi$
$522$	−0.983593	+	2.92953i	−0.0430507	+	0.128222i
$523$	−16.0656			−0.702501			−0.351250	−	0.936282i	$-0.614243\pi$
$523$	−16.0656			−0.702501			−0.351250	+	0.936282i	$0.614243\pi$
$524$	−8.89845	+	11.7577i	−0.388731	+	0.513639i
$525$	−2.98359	−	12.8720i	−0.130215	−	0.561779i
$526$	8.29392	−	24.7026i	0.361632	−	1.07709i
$527$			24.4010i			1.06292i
$528$	−5.82687	+	1.64466i	−0.253582	+	0.0715746i
$529$	−0.307491			−0.0133692
$530$	2.97241	−	13.9429i	0.129113	−	0.605640i
$531$			6.79893i			0.295048i
$532$	−29.8625	−	22.6004i	−1.29470	−	0.979854i
$533$	−33.7745			−1.46294
$534$	19.7857	+	6.64307i	0.856212	+	0.287474i
$535$	1.01641	+	8.88633i	0.0439431	+	0.384190i
$536$	1.62093	+	2.37429i	0.0700136	+	0.102554i
$537$		−	2.85664i		−	0.123273i
$538$	−1.74173	+	5.18757i	−0.0750913	+	0.223652i
$539$		−	0.0248338i		−	0.00106967i
$540$	2.27610	−	3.84959i	0.0979476	−	0.165660i
$541$			15.8559i			0.681698i	0.940118	+	0.340849i	$0.110715\pi$
$541$			15.8559i			0.681698i	−0.940118	+	0.340849i	$0.889285\pi$
$542$	−23.3215	−	7.83021i	−1.00174	−	0.336337i
$543$		−	5.28530i		−	0.226814i
$544$	18.7253	+	0.915029i	0.802842	+	0.0392316i
$545$	1.70892	−	0.195463i	0.0732019	−	0.00837274i
$546$	4.60453	−	13.7141i	0.197055	−	0.586910i
$547$	−4.95078			−0.211680			−0.105840	−	0.994383i	$-0.533753\pi$
$547$	−4.95078			−0.211680			−0.105840	+	0.994383i	$0.533753\pi$
$548$	−4.69251	+	6.20033i	−0.200454	+	0.264865i
$549$		−	3.60104i		−	0.153688i
$550$	−1.02759	+	10.6536i	−0.0438164	+	0.454269i
$551$	15.4835			0.659618
$552$	11.2775	−	7.69919i	0.480003	−	0.327699i
$553$		−	19.4569i		−	0.827393i
$554$	−1.18953	−	0.399387i	−0.0505385	−	0.0169683i
$555$	−2.00000	−	17.4858i	−0.0848953	−	0.742230i
$556$	−17.6566	+	23.3301i	−0.748806	+	0.989416i
$557$	1.26634			0.0536565			0.0268283	−	0.999640i	$-0.491459\pi$
$557$	1.26634			0.0536565			0.0268283	+	0.999640i	$0.491459\pi$
$558$	−9.87086	−	3.31415i	−0.417867	−	0.140299i
$559$	3.93437			0.166406
$560$	8.96408	+	21.8708i	0.378801	+	0.924211i
$561$	5.01641			0.211793
$562$	−18.0768	−	6.06930i	−0.762524	−	0.256018i
$563$	5.70892			0.240602			0.120301	−	0.992737i	$-0.461614\pi$
$563$	5.70892			0.240602			0.120301	+	0.992737i	$0.461614\pi$
$564$	8.55220	−	11.3002i	0.360112	−	0.475825i
$565$	32.1208	−	3.67393i	1.35133	−	0.154564i
$566$	38.1208	+	12.7991i	1.60234	+	0.537986i
$567$		−	2.64265i		−	0.110981i
$568$	−10.7253	−	15.7101i	−0.450025	−	0.659181i
$569$	2.75814			0.115627			0.0578135	−	0.998327i	$-0.481587\pi$
$569$	2.75814			0.115627			0.0578135	+	0.998327i	$0.481587\pi$
$570$	−21.9149	−	4.67192i	−0.917912	−	0.195685i
$571$			25.7735i			1.07859i	0.842118	+	0.539294i	$0.181309\pi$
$571$			25.7735i			1.07859i	−0.842118	+	0.539294i	$0.818691\pi$
$572$	−7.07158	+	9.34385i	−0.295677	+	0.390686i
$573$	5.96719			0.249283
$574$	10.3791	−	30.9130i	0.433214	−	1.29028i
$575$	−5.45065	−	23.5155i	−0.227308	−	0.980663i
$576$	−2.91344	+	7.45063i	−0.121393	+	0.310443i
$577$			32.7135i			1.36188i	0.732338	+	0.680941i	$0.238429\pi$
$577$			32.7135i			1.36188i	−0.732338	+	0.680941i	$0.761571\pi$
$578$	8.06599	+	2.70816i	0.335501	+	0.112645i
$579$			14.9409i			0.620921i
$580$	−8.41188	−	4.97358i	−0.349284	−	0.206517i
$581$			20.4587i			0.848769i
$582$	−5.01641	+	14.9409i	−0.207937	+	0.619319i
$583$			6.82376i			0.282611i
$584$	−36.2416	+	24.7422i	−1.49969	+	1.02384i
$585$	−0.983593	−	8.59945i	−0.0406666	−	0.355543i
$586$	10.7141	+	3.59728i	0.442597	+	0.148602i
$587$	43.4835			1.79475			0.897377	−	0.441264i	$-0.145470\pi$
$587$	43.4835			1.79475			0.897377	+	0.441264i	$0.145470\pi$
$588$	−0.0261649	−	0.0198021i	−0.00107902	−	0.000816623i
$589$			52.1705i			2.14965i
$590$	−21.0276	−	4.48277i	−0.865692	−	0.184553i
$591$	3.23353			0.133009
$592$	8.55220	+	30.2996i	0.351493	+	1.24531i
$593$			7.83021i			0.321548i	0.986991	+	0.160774i	$0.0513991\pi$
$593$			7.83021i			0.321548i	−0.986991	+	0.160774i	$0.948601\pi$
$594$	−0.681331	+	2.02927i	−0.0279553	+	0.0832622i
$595$	−2.22546	−	19.4569i	−0.0912348	−	0.797656i
$596$	−13.3627	+	17.6564i	−0.547356	+	0.723235i
$597$	−8.12080			−0.332362
$598$	8.41188	−	25.0539i	0.343987	−	1.02453i
$599$	32.7581			1.33846			0.669231	−	0.743055i	$-0.266624\pi$
$599$	32.7581			1.33846			0.669231	+	0.743055i	$0.266624\pi$
$600$	10.4052	+	9.57764i	0.424792	+	0.391005i
$601$	17.8074			0.726377			0.363189	−	0.931716i	$-0.381688\pi$
$601$	17.8074			0.726377			0.363189	+	0.931716i	$0.381688\pi$
$602$	−1.20905	+	3.60104i	−0.0492772	+	0.146767i
$603$	1.01641			0.0413913
$604$	1.01641	+	0.769233i	0.0413570	+	0.0312997i
$605$	2.21295	+	19.3476i	0.0899692	+	0.786591i
$606$	−6.00000	+	17.8704i	−0.243733	+	0.725935i
$607$			3.41188i			0.138484i	0.997600	+	0.0692420i	$0.0220581\pi$
$607$			3.41188i			0.138484i	−0.997600	+	0.0692420i	$0.977942\pi$
$608$	40.0357	+	1.95638i	1.62366	+	0.0793416i
$609$	−5.77454			−0.233996
$610$	11.1372	+	2.37429i	0.450932	+	0.0961321i
$611$		−	27.4282i		−	1.10963i
$612$	4.00000	−	5.28530i	0.161690	−	0.213646i
$613$	−36.6290			−1.47943			−0.739716	−	0.672920i	$-0.765040\pi$
$613$	−36.6290			−1.47943			−0.739716	+	0.672920i	$0.765040\pi$
$614$	−23.3955	−	7.85505i	−0.944165	−	0.317004i
$615$	−2.21712	−	19.3840i	−0.0894029	−	0.781640i
$616$	−6.37907	−	9.34385i	−0.257020	−	0.376474i
$617$		−	40.3979i		−	1.62636i	−0.582012	−	0.813180i	$-0.697734\pi$
$617$		−	40.3979i		−	1.62636i	0.582012	−	0.813180i	$-0.302266\pi$
$618$	−0.431398	+	1.28488i	−0.0173534	+	0.0516853i
$619$			24.5172i			0.985430i	0.870191	+	0.492715i	$0.163996\pi$
$619$			24.5172i			0.985430i	−0.870191	+	0.492715i	$0.836004\pi$
$620$	16.7581	−	28.3433i	0.673023	−	1.13829i
$621$		−	4.82778i		−	0.193732i
$622$	28.7581	+	9.65557i	1.15310	+	0.387153i
$623$			39.0006i			1.56252i
$624$	4.20594	+	14.9013i	0.168372	+	0.596528i
$625$	22.4506	−	10.9986i	0.898026	−	0.439943i
$626$	3.48346	−	10.3751i	0.139227	−	0.414674i
$627$	10.7253			0.428328
$628$	−0.205941	−	0.155859i	−0.00821793	−	0.00621947i
$629$		−	26.0852i		−	1.04009i
$630$	8.17313	+	1.74239i	0.325625	+	0.0694185i
$631$	18.7805			0.747640			0.373820	−	0.927501i	$-0.378048\pi$
$631$	18.7805			0.747640			0.373820	+	0.927501i	$0.378048\pi$
$632$	11.7417	+	17.1989i	0.467061	+	0.684135i
$633$			13.7141i			0.545087i
$634$	−15.0604	−	5.05654i	−0.598125	−	0.200821i
$635$	25.6126	−	2.92953i	1.01640	−	0.116255i
$636$	7.18953	+	5.44116i	0.285084	+	0.215756i
$637$	−0.0635083			−0.00251629
$638$	4.43424	+	1.48880i	0.175553	+	0.0589421i
$639$	−6.72532			−0.266050
$640$	−21.1222	−	13.9231i	−0.834929	−	0.550358i
$641$	−15.5163			−0.612856			−0.306428	−	0.951894i	$-0.599134\pi$
$641$	−15.5163			−0.612856			−0.306428	+	0.951894i	$0.599134\pi$
$642$	−5.36266	−	1.80052i	−0.211647	−	0.0710608i
$643$	−17.4506			−0.688186			−0.344093	−	0.938936i	$-0.611814\pi$
$643$	−17.4506			−0.688186			−0.344093	+	0.938936i	$0.611814\pi$
$644$	20.3463	+	15.3984i	0.801755	+	0.606781i
$645$	0.258271	+	2.25803i	0.0101694	+	0.0889099i
$646$	−31.4835	−	10.5706i	−1.23870	−	0.415895i
$647$			13.1403i			0.516600i	0.966065	+	0.258300i	$0.0831624\pi$
$647$			13.1403i			0.516600i	−0.966065	+	0.258300i	$0.916838\pi$
$648$	1.59477	+	2.33596i	0.0626484	+	0.0917653i
$649$	10.2911			0.403960
$650$	27.2447	+	2.62788i	1.06863	+	0.103074i
$651$		−	19.4569i		−	0.762577i
$652$	31.0716	+	23.5155i	1.21686	+	0.920937i
$653$	14.7993			0.579141			0.289570	−	0.957157i	$-0.406488\pi$
$653$	14.7993			0.579141			0.289570	+	0.957157i	$0.406488\pi$
$654$	−0.346255	+	1.03128i	−0.0135396	+	0.0403264i
$655$	−16.3791	+	1.87342i	−0.639983	+	0.0732004i
$656$	9.48062	+	33.5890i	0.370156	+	1.31143i
$657$			15.5146i			0.605284i
$658$	25.1044	+	8.42882i	0.978671	+	0.328590i
$659$		−	7.99614i		−	0.311485i	−0.987798	−	0.155743i	$-0.950223\pi$
$659$		−	7.99614i		−	0.311485i	0.987798	−	0.155743i	$-0.0497771\pi$
$660$	−5.82687	−	3.44518i	−0.226811	−	0.134103i
$661$		−	0.915029i		−	0.0355905i	−0.999842	−	0.0177953i	$-0.994335\pi$
$661$		−	0.915029i		−	0.0355905i	0.999842	−	0.0177953i	$-0.00566470\pi$
$662$	−3.60142	+	10.7265i	−0.139973	+	0.416896i
$663$		−	12.8286i		−	0.498223i
$664$	−12.3463	−	18.0844i	−0.479128	−	0.701810i
$665$	−4.75814	−	41.5999i	−0.184513	−	1.61317i
$666$	10.5522	+	3.54291i	0.408889	+	0.137285i
$667$	−10.5494			−0.408473
$668$	2.17313	−	2.87141i	0.0840808	−	0.111098i
$669$			9.84472i			0.380619i
$670$	−0.670152	+	3.14352i	−0.0258902	+	0.121445i
$671$	−5.45065			−0.210420
$672$	−14.9313	−	0.729629i	−0.575986	−	0.0281461i
$673$			34.3978i			1.32594i	0.748647	+	0.662969i	$0.230704\pi$
$673$			34.3978i			1.32594i	−0.748647	+	0.662969i	$0.769296\pi$
$674$	9.70892	−	28.9170i	0.373973	−	1.11384i
$675$	4.87086	−	1.12902i	0.187480	−	0.0434559i
$676$	3.16337	+	2.39409i	0.121668	+	0.0920804i
$677$	−40.1676			−1.54377			−0.771884	−	0.635764i	$-0.780685\pi$
$677$	−40.1676			−1.54377			−0.771884	+	0.635764i	$0.780685\pi$
$678$	−6.50820	+	19.3840i	−0.249946	+	0.744439i
$679$	−29.4506			−1.13021
$680$	13.7089	+	15.8559i	0.525713	+	0.608046i
$681$	−5.70892			−0.218766
$682$	−5.01641	+	14.9409i	−0.192088	+	0.572115i
$683$	−33.2580			−1.27258			−0.636291	−	0.771449i	$-0.719532\pi$
$683$	−33.2580			−1.27258			−0.636291	+	0.771449i	$0.719532\pi$
$684$	8.55220	−	11.3002i	0.327001	−	0.432075i
$685$	−8.63734	+	0.987927i	−0.330016	+	0.0377468i
$686$	8.34625	−	24.8585i	0.318661	−	0.949101i
$687$		−	0.769233i		−	0.0293481i
$688$	−1.10439	−	3.91275i	−0.0421045	−	0.149172i
$689$	17.4506			0.664817
$690$	14.9313	+	3.18312i	0.568423	+	0.121179i
$691$		−	50.2241i		−	1.91062i	−0.295611	−	0.955308i	$-0.595523\pi$
$691$		−	50.2241i		−	1.91062i	0.295611	−	0.955308i	$-0.404477\pi$
$692$	37.0521	+	28.0416i	1.40851	+	1.06598i
$693$	−4.00000			−0.151947
$694$	−29.1044	−	9.77182i	−1.10479	−	0.370933i
$695$	−32.4999	+	3.71729i	−1.23279	+	0.141005i
$696$	5.10439	−	3.48478i	0.193481	−	0.132090i
$697$		−	28.9170i		−	1.09531i
$698$	11.1372	−	33.1710i	0.421549	−	1.25554i
$699$		−	18.4008i		−	0.695983i
$700$	−10.7777	+	24.1289i	−0.407357	+	0.911985i
$701$			23.7543i			0.897188i	0.893736	+	0.448594i	$0.148075\pi$
$701$			23.7543i			0.897188i	−0.893736	+	0.448594i	$0.851925\pi$
$702$	5.18953	+	1.74239i	0.195866	+	0.0657623i
$703$		−	55.7715i		−	2.10346i
$704$	11.2775	+	4.40987i	0.425037	+	0.166203i
$705$	15.7417	−	1.80052i	0.592868	−	0.0678114i
$706$	1.49180	−	4.44317i	0.0561445	−	0.167221i
$707$	−35.2252			−1.32478
$708$	8.20594	−	10.8427i	0.308398	−	0.407494i
$709$			36.3146i			1.36382i	0.731435	+	0.681911i	$0.238851\pi$
$709$			36.3146i			1.36382i	−0.731435	+	0.681911i	$0.761149\pi$
$710$	4.43424	−	20.7999i	0.166414	−	0.780608i
$711$	7.36266			0.276121
$712$	−23.5358	−	34.4744i	−0.882041	−	1.29198i
$713$		−	35.5453i		−	1.33118i
$714$	11.7417	+	3.94229i	0.439423	+	0.147537i
$715$	−13.0164	+	1.48880i	−0.486786	+	0.0556779i
$716$	−3.44780	+	4.55567i	−0.128851	+	0.170253i
$717$	10.0328			0.374682
$718$	22.4671	+	7.54333i	0.838463	+	0.281515i
$719$	−30.7253			−1.14586			−0.572931	−	0.819604i	$-0.694194\pi$
$719$	−30.7253			−1.14586			−0.572931	+	0.819604i	$0.694194\pi$
$720$	−8.27610	+	3.39208i	−0.308432	+	0.126415i
$721$	−2.53268			−0.0943219
$722$	−41.8405	−	14.0480i	−1.55714	−	0.522812i
$723$	−10.7581			−0.400099
$724$	−6.37907	+	8.42882i	−0.237076	+	0.313255i
$725$	−2.46705	−	10.6435i	−0.0916240	−	0.395289i
$726$	−11.6757	−	3.92014i	−0.433327	−	0.145490i
$727$		−	5.47445i		−	0.203036i	−0.994834	−	0.101518i	$-0.967630\pi$
$727$		−	5.47445i		−	0.203036i	0.994834	−	0.101518i	$-0.0323700\pi$
$728$	−23.8953	+	16.3134i	−0.885620	+	0.604615i
$729$	1.00000			0.0370370
$730$	−47.9833	−	10.2293i	−1.77594	−	0.378605i
$731$			3.36852i			0.124589i
$732$	−4.34625	+	5.74281i	−0.160642	+	0.212260i
$733$	17.1455			0.633285			0.316643	−	0.948545i	$-0.397444\pi$
$733$	17.1455			0.633285			0.316643	+	0.948545i	$0.397444\pi$
$734$	−12.8433	+	38.2524i	−0.474054	+	1.41192i
$735$	−0.00416898	−	0.0364490i	−0.000153775	−	0.00134444i
$736$	−27.2775	−	1.33294i	−1.00546	−	0.0491328i
$737$		−	1.53847i		−	0.0566701i
$738$	11.6977	+	3.92752i	0.430600	+	0.144574i
$739$		−	11.6019i		−	0.426782i	−0.976967	−	0.213391i	$-0.931549\pi$
$739$		−	11.6019i		−	0.426782i	0.976967	−	0.213391i	$-0.0684508\pi$
$740$	−17.9149	+	30.2996i	−0.658563	+	1.11384i
$741$		−	27.4282i		−	1.00760i
$742$	−5.36266	+	15.9721i	−0.196869	+	0.586356i
$743$		−	23.6613i		−	0.868048i	−0.900901	−	0.434024i	$-0.857093\pi$
$743$		−	23.6613i		−	0.868048i	0.900901	−	0.434024i	$-0.142907\pi$
$744$	11.7417	+	17.1989i	0.430473	+	0.630542i
$745$	−24.5962	+	2.81328i	−0.901135	+	0.103071i
$746$	−50.3819	−	16.9158i	−1.84461	−	0.619330i
$747$	−7.74173			−0.283255
$748$	−8.00000	−	6.05453i	−0.292509	−	0.221376i
$749$		−	10.5706i		−	0.386241i
$750$	0.280267	+	15.8089i	0.0102339	+	0.577260i
$751$	−11.4283			−0.417024			−0.208512	−	0.978020i	$-0.566862\pi$
$751$	−11.4283			−0.417024			−0.208512	+	0.978020i	$0.566862\pi$
$752$	−27.2775	+	7.69919i	−0.994709	+	0.280761i
$753$			12.6580i			0.461283i
$754$	3.80736	−	11.3398i	0.138656	−	0.412972i
$755$	0.161949	+	1.41590i	0.00589392	+	0.0515299i
$756$	−3.18953	+	4.21441i	−0.116002	+	0.153277i
$757$	19.1784			0.697049			0.348525	−	0.937300i	$-0.386683\pi$
$757$	19.1784			0.697049			0.348525	+	0.937300i	$0.386683\pi$
$758$	−3.03592	+	9.04219i	−0.110270	+	0.328427i
$759$	−7.30749			−0.265245
$760$	29.3103	+	33.9007i	1.06320	+	1.22971i
$761$	4.03281			0.146189			0.0730947	−	0.997325i	$-0.476712\pi$
$761$	4.03281			0.146189			0.0730947	+	0.997325i	$0.476712\pi$
$762$	−5.18953	+	15.4565i	−0.187997	+	0.559930i
$763$	−2.03281			−0.0735928
$764$	−9.51627	−	7.20207i	−0.344287	−	0.260562i
$765$	7.36266	−	0.842131i	0.266198	−	0.0304473i
$766$	9.82687	−	29.2684i	0.355059	−	1.05751i
$767$		−	26.3177i		−	0.950279i
$768$	13.6388	−	8.36566i	0.492146	−	0.301870i
$769$	2.95078			0.106408			0.0532039	−	0.998584i	$-0.483057\pi$
$769$	2.95078			0.106408			0.0532039	+	0.998584i	$0.483057\pi$
$770$	2.63734	−	12.3711i	0.0950431	−	0.445824i
$771$		−	13.3110i		−	0.479383i
$772$	18.0328	−	23.8272i	0.649015	−	0.857560i
$773$	−45.2663			−1.62812			−0.814059	−	0.580783i	$-0.802747\pi$
$773$	−45.2663			−1.62812			−0.814059	+	0.580783i	$0.802747\pi$
$774$	−1.36266	−	0.457515i	−0.0489798	−	0.0164450i
$775$	35.8625	−	8.31256i	1.28822	−	0.298596i
$776$	26.0328	−	17.7727i	0.934524	−	0.638002i
$777$			20.7999i			0.746193i
$778$	3.96719	−	11.8159i	0.142231	−	0.423619i
$779$		−	61.8260i		−	2.21515i
$780$	−8.81047	+	14.9013i	−0.315465	+	0.533551i
$781$			10.1797i			0.364257i
$782$	21.4506	+	7.20207i	0.767074	+	0.257546i
$783$		−	2.18513i		−	0.0780903i
$784$	0.0178270	+	0.0631594i	0.000636678	+	0.00225569i
$785$	−0.0328135	−	0.286885i	−0.00117116	−	0.0102394i
$786$	3.31867	−	9.88432i	0.118373	−	0.352562i
$787$	52.9997			1.88924			0.944618	−	0.328171i	$-0.106432\pi$
$787$	52.9997			1.88924			0.944618	+	0.328171i	$0.106432\pi$
$788$	−5.15672	−	3.90269i	−0.183701	−	0.139028i
$789$			18.4256i			0.655970i
$790$	−4.85446	+	22.7711i	−0.172714	+	0.810159i
$791$	−38.2088			−1.35855
$792$	3.53579	−	2.41389i	0.125639	−	0.0857739i
$793$			13.9391i			0.494993i
$794$	1.10155	+	0.369846i	0.0390926	+	0.0131254i
$795$	1.14554	+	10.0153i	0.0406282	+	0.355208i
$796$	12.9508	+	9.80136i	0.459028	+	0.347400i
$797$	−16.5738			−0.587075			−0.293538	−	0.955948i	$-0.594833\pi$
$797$	−16.5738			−0.587075			−0.293538	+	0.955948i	$0.594833\pi$
$798$	25.1044	+	8.42882i	0.888686	+	0.298377i
$799$	23.4835			0.830785
$800$	−5.03423	−	27.8327i	−0.177987	−	0.984033i
$801$	−14.7581			−0.521453
$802$	−17.0604	−	5.72804i	−0.602424	−	0.202264i
$803$	23.4835			0.828713
$804$	−1.62093	−	1.22675i	−0.0571659	−	0.0432641i
$805$	3.24186	+	28.3433i	0.114261	+	0.998969i
$806$	38.2088	+	12.8286i	1.34585	+	0.451869i
$807$		−	3.86940i		−	0.136209i
$808$	31.1372	−	21.2574i	1.09540	−	0.747834i
$809$	37.5491			1.32016			0.660078	−	0.751197i	$-0.270523\pi$
$809$	37.5491			1.32016			0.660078	+	0.751197i	$0.270523\pi$
$810$	−0.659335	+	3.09278i	−0.0231667	+	0.108669i
$811$			32.1102i			1.12754i	0.825931	+	0.563771i	$0.190650\pi$
$811$			32.1102i			1.12754i	−0.825931	+	0.563771i	$0.809350\pi$
$812$	9.20905	+	6.96956i	0.323174	+	0.244584i
$813$	17.3955			0.610086
$814$	5.36266	−	15.9721i	0.187961	−	0.559824i
$815$	4.95078	+	43.2841i	0.173418	+	1.51618i
$816$	−12.7581	+	3.60104i	−0.446624	+	0.126061i
$817$			7.20207i			0.251969i
$818$	−3.02759	−	1.01651i	−0.105857	−	0.0355416i
$819$			10.2293i			0.357442i
$820$	−19.8597	+	33.5890i	−0.693530	+	1.17298i
$821$			29.3809i			1.02540i	0.858568	+	0.512699i	$0.171354\pi$
$821$			29.3809i			1.02540i	−0.858568	+	0.512699i	$0.828646\pi$
$822$	1.75007	−	5.21240i	0.0610406	−	0.181803i
$823$			28.3866i			0.989495i	0.869037	+	0.494748i	$0.164740\pi$
$823$			28.3866i			0.989495i	−0.869037	+	0.494748i	$0.835260\pi$
$824$	2.23875	−	1.52840i	0.0779907	−	0.0532444i
$825$	−1.70892	−	7.37270i	−0.0594968	−	0.256684i
$826$	24.0880	+	8.08756i	0.838128	+	0.281402i
$827$	1.45065			0.0504439			0.0252219	−	0.999682i	$-0.491971\pi$
$827$	1.45065			0.0504439			0.0252219	+	0.999682i	$0.491971\pi$
$828$	−5.82687	+	7.69919i	−0.202498	+	0.267565i
$829$		−	37.4621i		−	1.30111i	−0.759458	−	0.650556i	$-0.774536\pi$
$829$		−	37.4621i		−	1.30111i	0.759458	−	0.650556i	$-0.225464\pi$
$830$	5.10439	−	23.9435i	0.177176	−	0.831089i
$831$	0.887271			0.0307791
$832$	11.2775	−	28.8404i	0.390978	−	0.999860i
$833$		−	0.0543744i		−	0.00188396i
$834$	6.58501	−	19.6128i	0.228020	−	0.679135i
$835$	4.00000	−	0.457515i	0.138426	−	0.0158329i
$836$	−17.1044	−	12.9449i	−0.591568	−	0.447708i
$837$	7.36266			0.254491
$838$	−15.0604	+	44.8559i	−0.520253	+	1.54952i
$839$	48.7581			1.68332			0.841659	−	0.540010i	$-0.181579\pi$
$839$	48.7581			1.68332			0.841659	+	0.540010i	$0.181579\pi$
$840$	−10.9313	−	12.6432i	−0.377164	−	0.436233i
$841$	24.2252			0.835351
$842$	5.10439	−	15.2029i	0.175909	−	0.523927i
$843$	13.4835			0.464395
$844$	16.5522	−	21.8708i	0.569750	−	0.752825i
$845$	0.504034	+	4.40672i	0.0173393	+	0.151596i
$846$	−3.18953	+	9.49971i	−0.109658	+	0.326607i
$847$		−	23.0146i		−	0.790791i
$848$	−4.89845	−	17.3548i	−0.168213	−	0.595965i
$849$	−28.4342			−0.975861
$850$	−2.24993	+	23.3263i	−0.0771721	+	0.800086i
$851$			37.9988i			1.30258i
$852$	10.7253	+	8.11710i	0.367443	+	0.278087i
$853$	4.37073			0.149651			0.0748255	−	0.997197i	$-0.476160\pi$
$853$	4.37073			0.149651			0.0748255	+	0.997197i	$0.476160\pi$
$854$	−12.7581	−	4.28355i	−0.436574	−	0.146580i
$855$	15.7417	−	1.80052i	0.538356	−	0.0615764i
$856$	6.37907	+	9.34385i	0.218032	+	0.319366i
$857$		−	20.5130i		−	0.700712i	−0.936617	−	0.350356i	$-0.886061\pi$
$857$		−	20.5130i		−	0.700712i	0.936617	−	0.350356i	$-0.113939\pi$
$858$	2.63734	−	7.85505i	0.0900373	−	0.268167i
$859$			10.1131i			0.345054i	0.985005	+	0.172527i	$0.0551932\pi$
$859$			10.1131i			0.345054i	−0.985005	+	0.172527i	$0.944807\pi$
$860$	2.31344	−	3.91275i	0.0788877	−	0.133424i
$861$			23.0580i			0.785813i
$862$	14.2911	+	4.79824i	0.486756	+	0.163429i
$863$			13.2861i			0.452266i	0.974096	+	0.226133i	$0.0726083\pi$
$863$			13.2861i			0.452266i	−0.974096	+	0.226133i	$0.927392\pi$
$864$	0.276098	−	5.65011i	0.00939303	−	0.192221i
$865$	5.90368	+	51.6152i	0.200731	+	1.75497i
$866$	−11.9344	+	35.5453i	−0.405547	+	1.20788i
$867$	−6.01641			−0.204328
$868$	−23.4835	+	31.0293i	−0.797081	+	1.05320i
$869$		−	11.1444i		−	0.378047i
$870$	6.75814	+	1.44073i	0.229122	+	0.0488455i
$871$	−3.93437			−0.133311
$872$	1.79690	−	1.22675i	0.0608507	−	0.0415429i
$873$		−	11.1444i		−	0.377180i
$874$	45.8625	+	15.3984i	1.55132	+	0.520858i
$875$	−27.8381	+	9.89909i	−0.941098	+	0.334650i
$876$	18.7253	−	24.7422i	0.632670	−	0.835962i
$877$	−33.6454			−1.13612			−0.568062	−	0.822986i	$-0.692307\pi$
$877$	−33.6454			−1.13612			−0.568062	+	0.822986i	$0.692307\pi$
$878$	−44.0796	−	14.7998i	−1.48762	−	0.499468i
$879$	−7.99166			−0.269552
$880$	5.13436	+	12.5270i	0.173079	+	0.422284i
$881$	−32.7909			−1.10476			−0.552378	−	0.833594i	$-0.686279\pi$
$881$	−32.7909			−1.10476			−0.552378	+	0.833594i	$0.686279\pi$
$882$	0.0219960	+	0.00738516i	0.000740643	+	0.000248671i
$883$	−33.4506			−1.12570			−0.562852	−	0.826558i	$-0.690296\pi$
$883$	−33.4506			−1.12570			−0.562852	+	0.826558i	$0.690296\pi$
$884$	−15.4835	+	20.4587i	−0.520765	+	0.688100i
$885$	15.1044	−	1.72762i	0.507729	−	0.0580733i
$886$	−7.65375	−	2.56975i	−0.257133	−	0.0863325i
$887$			34.8924i			1.17157i	0.810466	+	0.585785i	$0.199214\pi$
$887$			34.8924i			1.17157i	−0.810466	+	0.585785i	$0.800786\pi$
$888$	−12.5522	−	18.3860i	−0.421224	−	0.616995i
$889$	−30.4671			−1.02183
$890$	9.73055	−	45.6436i	0.326169	−	1.52998i
$891$		−	1.51363i		−	0.0507086i
$892$	11.8820	−	15.7000i	0.397840	−	0.525676i
$893$	50.2088			1.68017
$894$	4.98359	−	14.8431i	0.166676	−	0.496429i
$895$	−6.34625	+	0.725876i	−0.212132	+	0.0242634i
$896$	22.9313	+	19.1848i	0.766080	+	0.640920i
$897$			18.6877i			0.623964i
$898$	2.68133	+	0.900259i	0.0894772	+	0.0300420i
$899$		−	16.0884i		−	0.536578i
$900$	−9.13056	−	4.07835i	−0.304352	−	0.135945i
$901$			14.9409i			0.497752i
$902$	5.94483	−	17.7061i	0.197941	−	0.589548i
$903$		−	2.68601i		−	0.0893847i
$904$	33.7745	−	23.0580i	1.12332	−	0.766896i
$905$	−11.7417	+	1.34300i	−0.390308	+	0.0446429i
$906$	−0.854458	−	0.286885i	−0.0283875	−	0.00953111i
$907$	30.9836			1.02879			0.514397	−	0.857552i	$-0.328016\pi$
$907$	30.9836			1.02879			0.514397	+	0.857552i	$0.328016\pi$
$908$	9.10439	+	6.89035i	0.302140	+	0.228664i
$909$		−	13.3295i		−	0.442112i
$910$	−31.6371	−	6.74456i	−1.04876	−	0.223580i
$911$	16.0000			0.530104			0.265052	−	0.964234i	$-0.414611\pi$
$911$	16.0000			0.530104			0.265052	+	0.964234i	$0.414611\pi$
$912$	−27.2775	+	7.69919i	−0.903249	+	0.254946i
$913$			11.7181i			0.387814i
$914$	−1.77454	+	5.28530i	−0.0586967	+	0.174822i
$915$	−8.00000	+	0.915029i	−0.264472	+	0.0302499i
$916$	−0.928423	+	1.22675i	−0.0306760	+	0.0405329i
$917$	19.4835			0.643400
$918$	−1.49180	+	4.44317i	−0.0492366	+	0.146646i
$919$	15.6043			0.514737			0.257368	−	0.966313i	$-0.417145\pi$
$919$	15.6043			0.514737			0.257368	+	0.966313i	$0.417145\pi$
$920$	−19.9700	−	23.0976i	−0.658392	−	0.761504i
$921$	17.4506			0.575018
$922$	15.2580	−	45.4444i	0.502496	−	1.49663i
$923$	26.0328			0.856880
$924$	6.37907	+	4.82778i	0.209856	+	0.158822i
$925$	−38.3379	+	8.88633i	−1.26054	+	0.292181i
$926$	−10.2939	+	30.6594i	−0.338279	+	1.00753i
$927$		−	0.958386i		−	0.0314775i
$928$	−12.3463	−	0.603310i	−0.405286	−	0.0198046i
$929$	38.9341			1.27739			0.638693	−	0.769461i	$-0.279475\pi$
$929$	38.9341			1.27739			0.638693	+	0.769461i	$0.279475\pi$
$930$	−4.85446	+	22.7711i	−0.159184	+	0.746693i
$931$		−	0.116255i		−	0.00381011i
$932$	−22.2088	+	29.3450i	−0.727473	+	0.961228i
$933$	−21.4506			−0.702263
$934$	21.1044	+	7.08582i	0.690557	+	0.231855i
$935$	−1.27468	−	11.1444i	−0.0416864	−	0.364460i
$936$	−6.17313	−	9.04219i	−0.201775	−	0.295553i
$937$		−	19.6027i		−	0.640393i	−0.947351	−	0.320197i	$-0.896251\pi$
$937$		−	19.6027i		−	0.640393i	0.947351	−	0.320197i	$-0.103749\pi$
$938$	1.20905	−	3.60104i	0.0394769	−	0.117578i
$939$			7.73879i			0.252546i
$940$	−27.2775	−	16.1280i	−0.889695	−	0.526038i
$941$		−	25.0476i		−	0.816530i	−0.912864	−	0.408265i	$-0.866134\pi$
$941$		−	25.0476i		−	0.816530i	0.912864	−	0.408265i	$-0.133866\pi$
$942$	0.173127	+	0.0581276i	0.00564079	+	0.00189390i
$943$			42.1240i			1.37175i
$944$	−26.1731	+	7.38747i	−0.851863	+	0.240442i
$945$	−5.87086	+	0.671502i	−0.190979	+	0.0218439i
$946$	−0.692509	+	2.06257i	−0.0225154	+	0.0670599i
$947$	7.93437			0.257832			0.128916	−	0.991655i	$-0.458850\pi$
$947$	7.93437			0.257832			0.128916	+	0.991655i	$0.458850\pi$
$948$	−11.7417	−	8.88633i	−0.381354	−	0.288615i
$949$		−	60.0550i		−	1.94947i
$950$	−4.81047	+	49.8728i	−0.156072	+	1.61809i
$951$	11.2335			0.364272
$952$	−13.9672	−	20.4587i	−0.452679	−	0.663069i
$953$		−	11.4809i		−	0.371903i	−0.982559	−	0.185952i	$-0.940463\pi$
$953$		−	11.4809i		−	0.371903i	0.982559	−	0.185952i	$-0.0595368\pi$
$954$	−6.04399	−	2.02927i	−0.195681	−	0.0657002i
$955$	−1.51627	−	13.2566i	−0.0490654	−	0.428974i
$956$	−16.0000	−	12.1091i	−0.517477	−	0.391635i
$957$	−3.30749			−0.106916
$958$	−27.7417	−	9.31431i	−0.896295	−	0.300932i
$959$	10.2744			0.331778
$960$	17.2925	+	4.57922i	0.558113	+	0.147794i
$961$	23.2088			0.748670
$962$	−40.8461	−	13.7141i	−1.31693	−	0.442161i
$963$	4.00000			0.128898
$964$	17.1567	+	12.9845i	0.552581	+	0.418202i
$965$	33.1924	−	3.79650i	1.06850	−	0.122214i
$966$	−17.1044	−	5.74281i	−0.550325	−	0.184772i
$967$		−	15.8993i		−	0.511285i	−0.966771	−	0.255643i	$-0.917713\pi$
$967$		−	15.8993i		−	0.511285i	0.966771	−	0.255643i	$-0.0822871\pi$
$968$	13.8887	+	20.3437i	0.446399	+	0.653871i
$969$	23.4835			0.754397
$970$	34.4671	+	7.34787i	1.10667	+	0.235926i
$971$			40.6600i			1.30484i	0.757857	+	0.652421i	$0.226246\pi$
$971$			40.6600i			1.30484i	−0.757857	+	0.652421i	$0.773754\pi$
$972$	−1.59477	−	1.20695i	−0.0511522	−	0.0387128i
$973$	38.6597			1.23937
$974$	13.8820	−	41.3463i	0.444809	−	1.32482i
$975$	−18.8545	+	4.37027i	−0.603826	+	0.139961i
$976$	13.8625	−	3.91275i	0.443729	−	0.125244i
$977$			26.5676i			0.849972i	0.905200	+	0.424986i	$0.139721\pi$
$977$			26.5676i			0.849972i	−0.905200	+	0.424986i	$0.860279\pi$
$978$	−26.1208	−	8.77008i	−0.835251	−	0.280436i
$979$			22.3384i			0.713938i
$980$	−0.0373434	+	0.0631594i	−0.00119289	+	0.00201755i
$981$		−	0.769233i		−	0.0245597i
$982$	4.93960	−	14.7121i	0.157629	−	0.469482i
$983$			9.88057i			0.315141i	0.987508	+	0.157571i	$0.0503662\pi$
$983$			9.88057i			0.315141i	−0.987508	+	0.157571i	$0.949634\pi$
$984$	−13.9149	−	20.3820i	−0.443589	−	0.649755i
$985$	−0.821644	−	7.18355i	−0.0261798	−	0.228887i
$986$	9.70892	+	3.25978i	0.309195	+	0.103812i
$987$	−18.7253			−0.596034
$988$	−33.1044	+	43.7416i	−1.05319	+	1.39161i
$989$		−	4.90699i		−	0.156033i
$990$	4.68133	+	0.997991i	0.148782	+	0.0317182i
$991$	−53.0549			−1.68534			−0.842672	−	0.538427i	$-0.819019\pi$
$991$	−53.0549			−1.68534			−0.842672	+	0.538427i	$0.819019\pi$
$992$	2.03281	−	41.5999i	0.0645419	−	1.32080i
$993$		−	8.00084i		−	0.253899i
$994$	−8.00000	+	23.8272i	−0.253745	+	0.755753i
$995$	2.06351	+	18.0410i	0.0654176	+	0.571939i
$996$	12.3463	+	9.34385i	0.391206	+	0.296071i
$997$	32.3051			1.02311			0.511556	−	0.859250i	$-0.329069\pi$
$997$	32.3051			1.02311			0.511556	+	0.859250i	$0.329069\pi$
$998$	1.67326	−	4.98364i	0.0529662	−	0.157754i
$999$	−7.87086			−0.249023

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	120.2.d.b.109.6	yes	6
3.2	odd	2		360.2.d.e.109.1		6
4.3	odd	2		480.2.d.b.49.4		6
5.2	odd	4		600.2.k.f.301.6		12
5.3	odd	4		600.2.k.f.301.7		12
5.4	even	2		120.2.d.a.109.1	✓	6
8.3	odd	2		480.2.d.a.49.3		6
8.5	even	2		120.2.d.a.109.2	yes	6
12.11	even	2		1440.2.d.f.1009.3		6
15.2	even	4		1800.2.k.u.901.7		12
15.8	even	4		1800.2.k.u.901.6		12
15.14	odd	2		360.2.d.f.109.6		6
16.3	odd	4		3840.2.f.m.769.12		12
16.5	even	4		3840.2.f.l.769.7		12
16.11	odd	4		3840.2.f.m.769.1		12
16.13	even	4		3840.2.f.l.769.6		12
20.3	even	4		2400.2.k.f.1201.11		12
20.7	even	4		2400.2.k.f.1201.2		12
20.19	odd	2		480.2.d.a.49.4		6
24.5	odd	2		360.2.d.f.109.5		6
24.11	even	2		1440.2.d.e.1009.4		6
40.3	even	4		2400.2.k.f.1201.5		12
40.13	odd	4		600.2.k.f.301.8		12
40.19	odd	2		480.2.d.b.49.3		6
40.27	even	4		2400.2.k.f.1201.8		12
40.29	even	2	inner	120.2.d.b.109.5	yes	6
40.37	odd	4		600.2.k.f.301.5		12
60.23	odd	4		7200.2.k.u.3601.9		12
60.47	odd	4		7200.2.k.u.3601.3		12
60.59	even	2		1440.2.d.e.1009.3		6
80.19	odd	4		3840.2.f.m.769.6		12
80.29	even	4		3840.2.f.l.769.12		12
80.59	odd	4		3840.2.f.m.769.7		12
80.69	even	4		3840.2.f.l.769.1		12
120.29	odd	2		360.2.d.e.109.2		6
120.53	even	4		1800.2.k.u.901.5		12
120.59	even	2		1440.2.d.f.1009.4		6
120.77	even	4		1800.2.k.u.901.8		12
120.83	odd	4		7200.2.k.u.3601.10		12
120.107	odd	4		7200.2.k.u.3601.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.2.d.a.109.1	✓	6	5.4	even	2
120.2.d.a.109.2	yes	6	8.5	even	2
120.2.d.b.109.5	yes	6	40.29	even	2	inner
120.2.d.b.109.6	yes	6	1.1	even	1	trivial
360.2.d.e.109.1		6	3.2	odd	2
360.2.d.e.109.2		6	120.29	odd	2
360.2.d.f.109.5		6	24.5	odd	2
360.2.d.f.109.6		6	15.14	odd	2
480.2.d.a.49.3		6	8.3	odd	2
480.2.d.a.49.4		6	20.19	odd	2
480.2.d.b.49.3		6	40.19	odd	2
480.2.d.b.49.4		6	4.3	odd	2
600.2.k.f.301.5		12	40.37	odd	4
600.2.k.f.301.6		12	5.2	odd	4
600.2.k.f.301.7		12	5.3	odd	4
600.2.k.f.301.8		12	40.13	odd	4
1440.2.d.e.1009.3		6	60.59	even	2
1440.2.d.e.1009.4		6	24.11	even	2
1440.2.d.f.1009.3		6	12.11	even	2
1440.2.d.f.1009.4		6	120.59	even	2
1800.2.k.u.901.5		12	120.53	even	4
1800.2.k.u.901.6		12	15.8	even	4
1800.2.k.u.901.7		12	15.2	even	4
1800.2.k.u.901.8		12	120.77	even	4
2400.2.k.f.1201.2		12	20.7	even	4
2400.2.k.f.1201.5		12	40.3	even	4
2400.2.k.f.1201.8		12	40.27	even	4
2400.2.k.f.1201.11		12	20.3	even	4
3840.2.f.l.769.1		12	80.69	even	4
3840.2.f.l.769.6		12	16.13	even	4
3840.2.f.l.769.7		12	16.5	even	4
3840.2.f.l.769.12		12	80.29	even	4
3840.2.f.m.769.1		12	16.11	odd	4
3840.2.f.m.769.6		12	80.19	odd	4
3840.2.f.m.769.7		12	80.59	odd	4
3840.2.f.m.769.12		12	16.3	odd	4
7200.2.k.u.3601.3		12	60.47	odd	4
7200.2.k.u.3601.4		12	120.107	odd	4
7200.2.k.u.3601.9		12	60.23	odd	4
7200.2.k.u.3601.10		12	120.83	odd	4

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 $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	120.2.d.b.109.6

Level	$120$
Weight	$2$
Character	120.109
Analytic conductor	$0.958$
Analytic rank	$0$
Dimension	$6$
Inner twists	$2$