LMFDB - Embedded newform 910.2.i.b.841.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [910,2,Mod(211,910)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(910, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("910.211");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$910 = 2 \cdot 5 \cdot 7 \cdot 13$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	910.i (of order $3$ , degree $2$ , minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.26638658394$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{2} - x + 1$ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$1$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			841.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	910.841
Dual form			910.2.i.b.211.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(0.500000 + 0.866025i) q^{6} +(-0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +(-0.500000 + 0.866025i) q^{10} +1.00000 q^{12} +(-3.50000 + 0.866025i) q^{13} -1.00000 q^{14} +(0.500000 - 0.866025i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.50000 + 2.59808i) q^{17} +2.00000 q^{18} +(-4.00000 - 6.92820i) q^{19} +(0.500000 + 0.866025i) q^{20} +1.00000 q^{21} +(-3.00000 + 5.19615i) q^{23} +(0.500000 - 0.866025i) q^{24} +1.00000 q^{25} +(-1.00000 + 3.46410i) q^{26} -5.00000 q^{27} +(-0.500000 + 0.866025i) q^{28} +(-4.50000 + 7.79423i) q^{29} +(-0.500000 - 0.866025i) q^{30} -4.00000 q^{31} +(0.500000 + 0.866025i) q^{32} +3.00000 q^{34} +(0.500000 + 0.866025i) q^{35} +(1.00000 - 1.73205i) q^{36} +(-1.00000 + 1.73205i) q^{37} -8.00000 q^{38} +(1.00000 - 3.46410i) q^{39} +1.00000 q^{40} +(0.500000 - 0.866025i) q^{42} +(5.00000 + 8.66025i) q^{43} +(-1.00000 - 1.73205i) q^{45} +(3.00000 + 5.19615i) q^{46} +9.00000 q^{47} +(-0.500000 - 0.866025i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(0.500000 - 0.866025i) q^{50} -3.00000 q^{51} +(2.50000 + 2.59808i) q^{52} -12.0000 q^{53} +(-2.50000 + 4.33013i) q^{54} +(0.500000 + 0.866025i) q^{56} +8.00000 q^{57} +(4.50000 + 7.79423i) q^{58} +(-3.00000 - 5.19615i) q^{59} -1.00000 q^{60} +(-1.00000 - 1.73205i) q^{61} +(-2.00000 + 3.46410i) q^{62} +(1.00000 - 1.73205i) q^{63} +1.00000 q^{64} +(3.50000 - 0.866025i) q^{65} +(-7.00000 + 12.1244i) q^{67} +(1.50000 - 2.59808i) q^{68} +(-3.00000 - 5.19615i) q^{69} +1.00000 q^{70} +(-1.50000 - 2.59808i) q^{71} +(-1.00000 - 1.73205i) q^{72} -13.0000 q^{73} +(1.00000 + 1.73205i) q^{74} +(-0.500000 + 0.866025i) q^{75} +(-4.00000 + 6.92820i) q^{76} +(-2.50000 - 2.59808i) q^{78} -1.00000 q^{79} +(0.500000 - 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +9.00000 q^{83} +(-0.500000 - 0.866025i) q^{84} +(-1.50000 - 2.59808i) q^{85} +10.0000 q^{86} +(-4.50000 - 7.79423i) q^{87} +(6.00000 - 10.3923i) q^{89} -2.00000 q^{90} +(2.50000 + 2.59808i) q^{91} +6.00000 q^{92} +(2.00000 - 3.46410i) q^{93} +(4.50000 - 7.79423i) q^{94} +(4.00000 + 6.92820i) q^{95} -1.00000 q^{96} +(3.50000 + 6.06218i) q^{97} +(0.500000 + 0.866025i) q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$2 q + q^{2} - q^{3} - q^{4} - 2 q^{5} + q^{6} - q^{7} - 2 q^{8} + 2 q^{9} - q^{10} + 2 q^{12} - 7 q^{13} - 2 q^{14} + q^{15} - q^{16} + 3 q^{17} + 4 q^{18} - 8 q^{19} + q^{20} + 2 q^{21} - 6 q^{23}+ \cdots + q^{98}+O(q^{100})$ 2 * q + q^2 - q^3 - q^4 - 2 * q^5 + q^6 - q^7 - 2 * q^8 + 2 * q^9 - q^10 + 2 * q^12 - 7 * q^13 - 2 * q^14 + q^15 - q^16 + 3 * q^17 + 4 * q^18 - 8 * q^19 + q^20 + 2 * q^21 - 6 * q^23 + q^24 + 2 * q^25 - 2 * q^26 - 10 * q^27 - q^28 - 9 * q^29 - q^30 - 8 * q^31 + q^32 + 6 * q^34 + q^35 + 2 * q^36 - 2 * q^37 - 16 * q^38 + 2 * q^39 + 2 * q^40 + q^42 + 10 * q^43 - 2 * q^45 + 6 * q^46 + 18 * q^47 - q^48 - q^49 + q^50 - 6 * q^51 + 5 * q^52 - 24 * q^53 - 5 * q^54 + q^56 + 16 * q^57 + 9 * q^58 - 6 * q^59 - 2 * q^60 - 2 * q^61 - 4 * q^62 + 2 * q^63 + 2 * q^64 + 7 * q^65 - 14 * q^67 + 3 * q^68 - 6 * q^69 + 2 * q^70 - 3 * q^71 - 2 * q^72 - 26 * q^73 + 2 * q^74 - q^75 - 8 * q^76 - 5 * q^78 - 2 * q^79 + q^80 - q^81 + 18 * q^83 - q^84 - 3 * q^85 + 20 * q^86 - 9 * q^87 + 12 * q^89 - 4 * q^90 + 5 * q^91 + 12 * q^92 + 4 * q^93 + 9 * q^94 + 8 * q^95 - 2 * q^96 + 7 * q^97 + q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/910\mathbb{Z}\right)^\times$ .

$n$	$521$	$547$	$561$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i	−0.973494	−	0.228714i	$-0.926548\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i	0.684819	+	0.728714i	$0.259881\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	0.500000	+	0.866025i	0.204124	+	0.353553i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$8$	−1.00000			−0.353553
$9$	1.00000	+	1.73205i	0.333333	+	0.577350i
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$11$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$12$	1.00000			0.288675
$13$	−3.50000	+	0.866025i	−0.970725	+	0.240192i
$13$	−3.50000	+	0.866025i	−0.970725	+	0.240192i
$14$	−1.00000			−0.267261
$15$	0.500000	−	0.866025i	0.129099	−	0.223607i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.50000	+	2.59808i	0.363803	+	0.630126i	0.988583	−	0.150675i	$-0.0481447\pi$
$17$	1.50000	+	2.59808i	0.363803	+	0.630126i	−0.624780	+	0.780801i	$0.714811\pi$
$18$	2.00000			0.471405
$19$	−4.00000	−	6.92820i	−0.917663	−	1.58944i	−0.802955	−	0.596040i	$-0.796740\pi$
$19$	−4.00000	−	6.92820i	−0.917663	−	1.58944i	−0.114708	−	0.993399i	$-0.536593\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$	1.00000			0.218218
$22$		0			0
$23$	−3.00000	+	5.19615i	−0.625543	+	1.08347i	0.362892	+	0.931831i	$0.381789\pi$
$23$	−3.00000	+	5.19615i	−0.625543	+	1.08347i	−0.988436	+	0.151642i	$0.951544\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	1.00000			0.200000
$26$	−1.00000	+	3.46410i	−0.196116	+	0.679366i
$27$	−5.00000			−0.962250
$28$	−0.500000	+	0.866025i	−0.0944911	+	0.163663i
$29$	−4.50000	+	7.79423i	−0.835629	+	1.44735i	0.0578882	+	0.998323i	$0.481563\pi$
$29$	−4.50000	+	7.79423i	−0.835629	+	1.44735i	−0.893517	+	0.449029i	$0.851770\pi$
$30$	−0.500000	−	0.866025i	−0.0912871	−	0.158114i
$31$	−4.00000			−0.718421			−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000			−0.718421			−0.359211	+	0.933257i	$0.616954\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$	3.00000			0.514496
$35$	0.500000	+	0.866025i	0.0845154	+	0.146385i
$36$	1.00000	−	1.73205i	0.166667	−	0.288675i
$37$	−1.00000	+	1.73205i	−0.164399	+	0.284747i	−0.936442	−	0.350823i	$-0.885902\pi$
$37$	−1.00000	+	1.73205i	−0.164399	+	0.284747i	0.772043	+	0.635571i	$0.219235\pi$
$38$	−8.00000			−1.29777
$39$	1.00000	−	3.46410i	0.160128	−	0.554700i
$40$	1.00000			0.158114
$41$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$41$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$42$	0.500000	−	0.866025i	0.0771517	−	0.133631i
$43$	5.00000	+	8.66025i	0.762493	+	1.32068i	0.941562	+	0.336840i	$0.109358\pi$
$43$	5.00000	+	8.66025i	0.762493	+	1.32068i	−0.179069	+	0.983836i	$0.557309\pi$
$44$		0			0
$45$	−1.00000	−	1.73205i	−0.149071	−	0.258199i
$46$	3.00000	+	5.19615i	0.442326	+	0.766131i
$47$	9.00000			1.31278			0.656392	−	0.754420i	$-0.272082\pi$
$47$	9.00000			1.31278			0.656392	+	0.754420i	$0.272082\pi$
$48$	−0.500000	−	0.866025i	−0.0721688	−	0.125000i
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	0.500000	−	0.866025i	0.0707107	−	0.122474i
$51$	−3.00000			−0.420084
$52$	2.50000	+	2.59808i	0.346688	+	0.360288i
$53$	−12.0000			−1.64833			−0.824163	−	0.566352i	$-0.808354\pi$
$53$	−12.0000			−1.64833			−0.824163	+	0.566352i	$0.808354\pi$
$54$	−2.50000	+	4.33013i	−0.340207	+	0.589256i
$55$		0			0
$56$	0.500000	+	0.866025i	0.0668153	+	0.115728i
$57$	8.00000			1.05963
$58$	4.50000	+	7.79423i	0.590879	+	1.02343i
$59$	−3.00000	−	5.19615i	−0.390567	−	0.676481i	0.601958	−	0.798528i	$-0.294388\pi$
$59$	−3.00000	−	5.19615i	−0.390567	−	0.676481i	−0.992524	+	0.122047i	$0.961054\pi$
$60$	−1.00000			−0.129099
$61$	−1.00000	−	1.73205i	−0.128037	−	0.221766i	0.794879	−	0.606768i	$-0.207534\pi$
$61$	−1.00000	−	1.73205i	−0.128037	−	0.221766i	−0.922916	+	0.385002i	$0.874201\pi$
$62$	−2.00000	+	3.46410i	−0.254000	+	0.439941i
$63$	1.00000	−	1.73205i	0.125988	−	0.218218i
$64$	1.00000			0.125000
$65$	3.50000	−	0.866025i	0.434122	−	0.107417i
$66$		0			0
$67$	−7.00000	+	12.1244i	−0.855186	+	1.48123i	0.0212861	+	0.999773i	$0.493224\pi$
$67$	−7.00000	+	12.1244i	−0.855186	+	1.48123i	−0.876472	+	0.481452i	$0.840109\pi$
$68$	1.50000	−	2.59808i	0.181902	−	0.315063i
$69$	−3.00000	−	5.19615i	−0.361158	−	0.625543i
$70$	1.00000			0.119523
$71$	−1.50000	−	2.59808i	−0.178017	−	0.308335i	0.763184	−	0.646181i	$-0.223635\pi$
$71$	−1.50000	−	2.59808i	−0.178017	−	0.308335i	−0.941201	+	0.337846i	$0.890302\pi$
$72$	−1.00000	−	1.73205i	−0.117851	−	0.204124i
$73$	−13.0000			−1.52153			−0.760767	−	0.649025i	$-0.775177\pi$
$73$	−13.0000			−1.52153			−0.760767	+	0.649025i	$0.775177\pi$
$74$	1.00000	+	1.73205i	0.116248	+	0.201347i
$75$	−0.500000	+	0.866025i	−0.0577350	+	0.100000i
$76$	−4.00000	+	6.92820i	−0.458831	+	0.794719i
$77$		0			0
$78$	−2.50000	−	2.59808i	−0.283069	−	0.294174i
$79$	−1.00000			−0.112509			−0.0562544	−	0.998416i	$-0.517916\pi$
$79$	−1.00000			−0.112509			−0.0562544	+	0.998416i	$0.517916\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	9.00000			0.987878			0.493939	−	0.869496i	$-0.335557\pi$
$83$	9.00000			0.987878			0.493939	+	0.869496i	$0.335557\pi$
$84$	−0.500000	−	0.866025i	−0.0545545	−	0.0944911i
$85$	−1.50000	−	2.59808i	−0.162698	−	0.281801i
$86$	10.0000			1.07833
$87$	−4.50000	−	7.79423i	−0.482451	−	0.835629i
$88$		0			0
$89$	6.00000	−	10.3923i	0.635999	−	1.10158i	−0.350304	−	0.936636i	$-0.613922\pi$
$89$	6.00000	−	10.3923i	0.635999	−	1.10158i	0.986303	−	0.164946i	$-0.0527450\pi$
$90$	−2.00000			−0.210819
$91$	2.50000	+	2.59808i	0.262071	+	0.272352i
$92$	6.00000			0.625543
$93$	2.00000	−	3.46410i	0.207390	−	0.359211i
$94$	4.50000	−	7.79423i	0.464140	−	0.803913i
$95$	4.00000	+	6.92820i	0.410391	+	0.710819i
$96$	−1.00000			−0.102062
$97$	3.50000	+	6.06218i	0.355371	+	0.615521i	0.987181	−	0.159602i	$-0.0510211\pi$
$97$	3.50000	+	6.06218i	0.355371	+	0.615521i	−0.631810	+	0.775123i	$0.717688\pi$
$98$	0.500000	+	0.866025i	0.0505076	+	0.0874818i
$99$		0			0
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$101$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$102$	−1.50000	+	2.59808i	−0.148522	+	0.257248i
$103$	−1.00000			−0.0985329			−0.0492665	−	0.998786i	$-0.515688\pi$
$103$	−1.00000			−0.0985329			−0.0492665	+	0.998786i	$0.515688\pi$
$104$	3.50000	−	0.866025i	0.343203	−	0.0849208i
$105$	−1.00000			−0.0975900
$106$	−6.00000	+	10.3923i	−0.582772	+	1.00939i
$107$	6.00000	−	10.3923i	0.580042	−	1.00466i	−0.415432	−	0.909624i	$-0.636370\pi$
$107$	6.00000	−	10.3923i	0.580042	−	1.00466i	0.995474	−	0.0950377i	$-0.0302972\pi$
$108$	2.50000	+	4.33013i	0.240563	+	0.416667i
$109$	−1.00000			−0.0957826			−0.0478913	−	0.998853i	$-0.515250\pi$
$109$	−1.00000			−0.0957826			−0.0478913	+	0.998853i	$0.515250\pi$
$110$		0			0
$111$	−1.00000	−	1.73205i	−0.0949158	−	0.164399i
$112$	1.00000			0.0944911
$113$	−3.00000	−	5.19615i	−0.282216	−	0.488813i	0.689714	−	0.724082i	$-0.257736\pi$
$113$	−3.00000	−	5.19615i	−0.282216	−	0.488813i	−0.971930	+	0.235269i	$0.924403\pi$
$114$	4.00000	−	6.92820i	0.374634	−	0.648886i
$115$	3.00000	−	5.19615i	0.279751	−	0.484544i
$116$	9.00000			0.835629
$117$	−5.00000	−	5.19615i	−0.462250	−	0.480384i
$118$	−6.00000			−0.552345
$119$	1.50000	−	2.59808i	0.137505	−	0.238165i
$120$	−0.500000	+	0.866025i	−0.0456435	+	0.0790569i
$121$	5.50000	+	9.52628i	0.500000	+	0.866025i
$122$	−2.00000			−0.181071
$123$		0			0
$124$	2.00000	+	3.46410i	0.179605	+	0.311086i
$125$	−1.00000			−0.0894427
$126$	−1.00000	−	1.73205i	−0.0890871	−	0.154303i
$127$	11.0000	−	19.0526i	0.976092	−	1.69064i	0.299809	−	0.953999i	$-0.403077\pi$
$127$	11.0000	−	19.0526i	0.976092	−	1.69064i	0.676283	−	0.736642i	$-0.263590\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−10.0000			−0.880451
$130$	1.00000	−	3.46410i	0.0877058	−	0.303822i
$131$	12.0000			1.04844			0.524222	−	0.851581i	$-0.324356\pi$
$131$	12.0000			1.04844			0.524222	+	0.851581i	$0.324356\pi$
$132$		0			0
$133$	−4.00000	+	6.92820i	−0.346844	+	0.600751i
$134$	7.00000	+	12.1244i	0.604708	+	1.04738i
$135$	5.00000			0.430331
$136$	−1.50000	−	2.59808i	−0.128624	−	0.222783i
$137$	−6.00000	−	10.3923i	−0.512615	−	0.887875i	−0.999893	−	0.0146279i	$-0.995344\pi$
$137$	−6.00000	−	10.3923i	−0.512615	−	0.887875i	0.487278	−	0.873247i	$-0.337990\pi$
$138$	−6.00000			−0.510754
$139$	−7.00000	−	12.1244i	−0.593732	−	1.02837i	−0.993724	−	0.111856i	$-0.964321\pi$
$139$	−7.00000	−	12.1244i	−0.593732	−	1.02837i	0.399992	−	0.916519i	$-0.369013\pi$
$140$	0.500000	−	0.866025i	0.0422577	−	0.0731925i
$141$	−4.50000	+	7.79423i	−0.378968	+	0.656392i
$142$	−3.00000			−0.251754
$143$		0			0
$144$	−2.00000			−0.166667
$145$	4.50000	−	7.79423i	0.373705	−	0.647275i
$146$	−6.50000	+	11.2583i	−0.537944	+	0.931746i
$147$	−0.500000	−	0.866025i	−0.0412393	−	0.0714286i
$148$	2.00000			0.164399
$149$	1.50000	+	2.59808i	0.122885	+	0.212843i	0.920904	−	0.389789i	$-0.127452\pi$
$149$	1.50000	+	2.59808i	0.122885	+	0.212843i	−0.798019	+	0.602632i	$0.794119\pi$
$150$	0.500000	+	0.866025i	0.0408248	+	0.0707107i
$151$	8.00000			0.651031			0.325515	−	0.945537i	$-0.394462\pi$
$151$	8.00000			0.651031			0.325515	+	0.945537i	$0.394462\pi$
$152$	4.00000	+	6.92820i	0.324443	+	0.561951i
$153$	−3.00000	+	5.19615i	−0.242536	+	0.420084i
$154$		0			0
$155$	4.00000			0.321288
$156$	−3.50000	+	0.866025i	−0.280224	+	0.0693375i
$157$	5.00000			0.399043			0.199522	−	0.979893i	$-0.436061\pi$
$157$	5.00000			0.399043			0.199522	+	0.979893i	$0.436061\pi$
$158$	−0.500000	+	0.866025i	−0.0397779	+	0.0688973i
$159$	6.00000	−	10.3923i	0.475831	−	0.824163i
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	6.00000			0.472866
$162$	0.500000	+	0.866025i	0.0392837	+	0.0680414i
$163$	2.00000	+	3.46410i	0.156652	+	0.271329i	0.933659	−	0.358162i	$-0.116597\pi$
$163$	2.00000	+	3.46410i	0.156652	+	0.271329i	−0.777007	+	0.629492i	$0.783263\pi$
$164$		0			0
$165$		0			0
$166$	4.50000	−	7.79423i	0.349268	−	0.604949i
$167$	−1.50000	+	2.59808i	−0.116073	+	0.201045i	−0.918208	−	0.396098i	$-0.870364\pi$
$167$	−1.50000	+	2.59808i	−0.116073	+	0.201045i	0.802135	+	0.597143i	$0.203697\pi$
$168$	−1.00000			−0.0771517
$169$	11.5000	−	6.06218i	0.884615	−	0.466321i
$170$	−3.00000			−0.230089
$171$	8.00000	−	13.8564i	0.611775	−	1.05963i
$172$	5.00000	−	8.66025i	0.381246	−	0.660338i
$173$	9.00000	+	15.5885i	0.684257	+	1.18517i	0.973670	+	0.227964i	$0.0732068\pi$
$173$	9.00000	+	15.5885i	0.684257	+	1.18517i	−0.289412	+	0.957205i	$0.593460\pi$
$174$	−9.00000			−0.682288
$175$	−0.500000	−	0.866025i	−0.0377964	−	0.0654654i
$176$		0			0
$177$	6.00000			0.450988
$178$	−6.00000	−	10.3923i	−0.449719	−	0.778936i
$179$	4.50000	−	7.79423i	0.336346	−	0.582568i	−0.647397	−	0.762153i	$-0.724142\pi$
$179$	4.50000	−	7.79423i	0.336346	−	0.582568i	0.983742	+	0.179585i	$0.0574756\pi$
$180$	−1.00000	+	1.73205i	−0.0745356	+	0.129099i
$181$	−22.0000			−1.63525			−0.817624	−	0.575753i	$-0.804709\pi$
$181$	−22.0000			−1.63525			−0.817624	+	0.575753i	$0.804709\pi$
$182$	3.50000	−	0.866025i	0.259437	−	0.0641941i
$183$	2.00000			0.147844
$184$	3.00000	−	5.19615i	0.221163	−	0.383065i
$185$	1.00000	−	1.73205i	0.0735215	−	0.127343i
$186$	−2.00000	−	3.46410i	−0.146647	−	0.254000i
$187$		0			0
$188$	−4.50000	−	7.79423i	−0.328196	−	0.568453i
$189$	2.50000	+	4.33013i	0.181848	+	0.314970i
$190$	8.00000			0.580381
$191$	−7.50000	−	12.9904i	−0.542681	−	0.939951i	−0.998749	−	0.0500060i	$-0.984076\pi$
$191$	−7.50000	−	12.9904i	−0.542681	−	0.939951i	0.456068	−	0.889945i	$-0.349257\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	−7.00000	+	12.1244i	−0.503871	+	0.872730i	0.496119	+	0.868255i	$0.334758\pi$
$193$	−7.00000	+	12.1244i	−0.503871	+	0.872730i	−0.999990	+	0.00447566i	$0.998575\pi$
$194$	7.00000			0.502571
$195$	−1.00000	+	3.46410i	−0.0716115	+	0.248069i
$196$	1.00000			0.0714286
$197$	−6.00000	+	10.3923i	−0.427482	+	0.740421i	−0.996649	−	0.0818013i	$-0.973933\pi$
$197$	−6.00000	+	10.3923i	−0.427482	+	0.740421i	0.569166	+	0.822222i	$0.307266\pi$
$198$		0			0
$199$	8.00000	+	13.8564i	0.567105	+	0.982255i	0.996850	+	0.0793045i	$0.0252700\pi$
$199$	8.00000	+	13.8564i	0.567105	+	0.982255i	−0.429745	+	0.902950i	$0.641397\pi$
$200$	−1.00000			−0.0707107
$201$	−7.00000	−	12.1244i	−0.493742	−	0.855186i
$202$		0			0
$203$	9.00000			0.631676
$204$	1.50000	+	2.59808i	0.105021	+	0.181902i
$205$		0			0
$206$	−0.500000	+	0.866025i	−0.0348367	+	0.0603388i
$207$	−12.0000			−0.834058
$208$	1.00000	−	3.46410i	0.0693375	−	0.240192i
$209$		0			0
$210$	−0.500000	+	0.866025i	−0.0345033	+	0.0597614i
$211$	0.500000	−	0.866025i	0.0344214	−	0.0596196i	−0.848301	−	0.529514i	$-0.822374\pi$
$211$	0.500000	−	0.866025i	0.0344214	−	0.0596196i	0.882723	+	0.469894i	$0.155708\pi$
$212$	6.00000	+	10.3923i	0.412082	+	0.713746i
$213$	3.00000			0.205557
$214$	−6.00000	−	10.3923i	−0.410152	−	0.710403i
$215$	−5.00000	−	8.66025i	−0.340997	−	0.590624i
$216$	5.00000			0.340207
$217$	2.00000	+	3.46410i	0.135769	+	0.235159i
$218$	−0.500000	+	0.866025i	−0.0338643	+	0.0586546i
$219$	6.50000	−	11.2583i	0.439229	−	0.760767i
$220$		0			0
$221$	−7.50000	−	7.79423i	−0.504505	−	0.524297i
$222$	−2.00000			−0.134231
$223$	−8.50000	+	14.7224i	−0.569202	+	0.985887i	0.427443	+	0.904042i	$0.359414\pi$
$223$	−8.50000	+	14.7224i	−0.569202	+	0.985887i	−0.996645	+	0.0818447i	$0.973919\pi$
$224$	0.500000	−	0.866025i	0.0334077	−	0.0578638i
$225$	1.00000	+	1.73205i	0.0666667	+	0.115470i
$226$	−6.00000			−0.399114
$227$	−6.00000	−	10.3923i	−0.398234	−	0.689761i	0.595274	−	0.803523i	$-0.297043\pi$
$227$	−6.00000	−	10.3923i	−0.398234	−	0.689761i	−0.993508	+	0.113761i	$0.963710\pi$
$228$	−4.00000	−	6.92820i	−0.264906	−	0.458831i
$229$	2.00000			0.132164			0.0660819	−	0.997814i	$-0.478950\pi$
$229$	2.00000			0.132164			0.0660819	+	0.997814i	$0.478950\pi$
$230$	−3.00000	−	5.19615i	−0.197814	−	0.342624i
$231$		0			0
$232$	4.50000	−	7.79423i	0.295439	−	0.511716i
$233$	18.0000			1.17922			0.589610	−	0.807688i	$-0.299282\pi$
$233$	18.0000			1.17922			0.589610	+	0.807688i	$0.299282\pi$
$234$	−7.00000	+	1.73205i	−0.457604	+	0.113228i
$235$	−9.00000			−0.587095
$236$	−3.00000	+	5.19615i	−0.195283	+	0.338241i
$237$	0.500000	−	0.866025i	0.0324785	−	0.0562544i
$238$	−1.50000	−	2.59808i	−0.0972306	−	0.168408i
$239$	21.0000			1.35838			0.679189	−	0.733964i	$-0.262332\pi$
$239$	21.0000			1.35838			0.679189	+	0.733964i	$0.262332\pi$
$240$	0.500000	+	0.866025i	0.0322749	+	0.0559017i
$241$	−13.0000	−	22.5167i	−0.837404	−	1.45043i	−0.892058	−	0.451920i	$-0.850739\pi$
$241$	−13.0000	−	22.5167i	−0.837404	−	1.45043i	0.0546547	−	0.998505i	$-0.482594\pi$
$242$	11.0000			0.707107
$243$	−8.00000	−	13.8564i	−0.513200	−	0.888889i
$244$	−1.00000	+	1.73205i	−0.0640184	+	0.110883i
$245$	0.500000	−	0.866025i	0.0319438	−	0.0553283i
$246$		0			0
$247$	20.0000	+	20.7846i	1.27257	+	1.32249i
$248$	4.00000			0.254000
$249$	−4.50000	+	7.79423i	−0.285176	+	0.493939i
$250$	−0.500000	+	0.866025i	−0.0316228	+	0.0547723i
$251$	−9.00000	−	15.5885i	−0.568075	−	0.983935i	−0.996756	−	0.0804789i	$-0.974355\pi$
$251$	−9.00000	−	15.5885i	−0.568075	−	0.983935i	0.428681	−	0.903456i	$-0.358978\pi$
$252$	−2.00000			−0.125988
$253$		0			0
$254$	−11.0000	−	19.0526i	−0.690201	−	1.19546i
$255$	3.00000			0.187867
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−9.00000	+	15.5885i	−0.561405	+	0.972381i	0.435970	+	0.899961i	$0.356405\pi$
$257$	−9.00000	+	15.5885i	−0.561405	+	0.972381i	−0.997374	+	0.0724199i	$0.976928\pi$
$258$	−5.00000	+	8.66025i	−0.311286	+	0.539164i
$259$	2.00000			0.124274
$260$	−2.50000	−	2.59808i	−0.155043	−	0.161126i
$261$	−18.0000			−1.11417
$262$	6.00000	−	10.3923i	0.370681	−	0.642039i
$263$	−9.00000	+	15.5885i	−0.554964	+	0.961225i	0.442943	+	0.896550i	$0.353935\pi$
$263$	−9.00000	+	15.5885i	−0.554964	+	0.961225i	−0.997906	+	0.0646755i	$0.979399\pi$
$264$		0			0
$265$	12.0000			0.737154
$266$	4.00000	+	6.92820i	0.245256	+	0.424795i
$267$	6.00000	+	10.3923i	0.367194	+	0.635999i
$268$	14.0000			0.855186
$269$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$269$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$270$	2.50000	−	4.33013i	0.152145	−	0.263523i
$271$	−13.0000	+	22.5167i	−0.789694	+	1.36779i	0.136461	+	0.990645i	$0.456427\pi$
$271$	−13.0000	+	22.5167i	−0.789694	+	1.36779i	−0.926155	+	0.377144i	$0.876906\pi$
$272$	−3.00000			−0.181902
$273$	−3.50000	+	0.866025i	−0.211830	+	0.0524142i
$274$	−12.0000			−0.724947
$275$		0			0
$276$	−3.00000	+	5.19615i	−0.180579	+	0.312772i
$277$	2.00000	+	3.46410i	0.120168	+	0.208138i	0.919834	−	0.392308i	$-0.128323\pi$
$277$	2.00000	+	3.46410i	0.120168	+	0.208138i	−0.799666	+	0.600446i	$0.794990\pi$
$278$	−14.0000			−0.839664
$279$	−4.00000	−	6.92820i	−0.239474	−	0.414781i
$280$	−0.500000	−	0.866025i	−0.0298807	−	0.0517549i
$281$	27.0000			1.61068			0.805342	−	0.592810i	$-0.201981\pi$
$281$	27.0000			1.61068			0.805342	+	0.592810i	$0.201981\pi$
$282$	4.50000	+	7.79423i	0.267971	+	0.464140i
$283$	−10.0000	+	17.3205i	−0.594438	+	1.02960i	0.399188	+	0.916869i	$0.369292\pi$
$283$	−10.0000	+	17.3205i	−0.594438	+	1.02960i	−0.993626	+	0.112728i	$0.964041\pi$
$284$	−1.50000	+	2.59808i	−0.0890086	+	0.154167i
$285$	−8.00000			−0.473879
$286$		0			0
$287$		0			0
$288$	−1.00000	+	1.73205i	−0.0589256	+	0.102062i
$289$	4.00000	−	6.92820i	0.235294	−	0.407541i
$290$	−4.50000	−	7.79423i	−0.264249	−	0.457693i
$291$	−7.00000			−0.410347
$292$	6.50000	+	11.2583i	0.380384	+	0.658844i
$293$	4.50000	+	7.79423i	0.262893	+	0.455344i	0.967009	−	0.254741i	$-0.0819901\pi$
$293$	4.50000	+	7.79423i	0.262893	+	0.455344i	−0.704117	+	0.710084i	$0.748657\pi$
$294$	−1.00000			−0.0583212
$295$	3.00000	+	5.19615i	0.174667	+	0.302532i
$296$	1.00000	−	1.73205i	0.0581238	−	0.100673i
$297$		0			0
$298$	3.00000			0.173785
$299$	6.00000	−	20.7846i	0.346989	−	1.20201i
$300$	1.00000			0.0577350
$301$	5.00000	−	8.66025i	0.288195	−	0.499169i
$302$	4.00000	−	6.92820i	0.230174	−	0.398673i
$303$		0			0
$304$	8.00000			0.458831
$305$	1.00000	+	1.73205i	0.0572598	+	0.0991769i
$306$	3.00000	+	5.19615i	0.171499	+	0.297044i
$307$	−16.0000			−0.913168			−0.456584	−	0.889680i	$-0.650927\pi$
$307$	−16.0000			−0.913168			−0.456584	+	0.889680i	$0.650927\pi$
$308$		0			0
$309$	0.500000	−	0.866025i	0.0284440	−	0.0492665i
$310$	2.00000	−	3.46410i	0.113592	−	0.196748i
$311$		0			0			−	1.00000i	$-0.5\pi$
$311$		0			0				1.00000i	$0.5\pi$
$312$	−1.00000	+	3.46410i	−0.0566139	+	0.196116i
$313$	26.0000			1.46961			0.734803	−	0.678280i	$-0.237274\pi$
$313$	26.0000			1.46961			0.734803	+	0.678280i	$0.237274\pi$
$314$	2.50000	−	4.33013i	0.141083	−	0.244363i
$315$	−1.00000	+	1.73205i	−0.0563436	+	0.0975900i
$316$	0.500000	+	0.866025i	0.0281272	+	0.0487177i
$317$	−30.0000			−1.68497			−0.842484	−	0.538721i	$-0.818908\pi$
$317$	−30.0000			−1.68497			−0.842484	+	0.538721i	$0.818908\pi$
$318$	−6.00000	−	10.3923i	−0.336463	−	0.582772i
$319$		0			0
$320$	−1.00000			−0.0559017
$321$	6.00000	+	10.3923i	0.334887	+	0.580042i
$322$	3.00000	−	5.19615i	0.167183	−	0.289570i
$323$	12.0000	−	20.7846i	0.667698	−	1.15649i
$324$	1.00000			0.0555556
$325$	−3.50000	+	0.866025i	−0.194145	+	0.0480384i
$326$	4.00000			0.221540
$327$	0.500000	−	0.866025i	0.0276501	−	0.0478913i
$328$		0			0
$329$	−4.50000	−	7.79423i	−0.248093	−	0.429710i
$330$		0			0
$331$	−10.0000	−	17.3205i	−0.549650	−	0.952021i	−0.998298	−	0.0583130i	$-0.981428\pi$
$331$	−10.0000	−	17.3205i	−0.549650	−	0.952021i	0.448649	−	0.893708i	$-0.351905\pi$
$332$	−4.50000	−	7.79423i	−0.246970	−	0.427764i
$333$	−4.00000			−0.219199
$334$	1.50000	+	2.59808i	0.0820763	+	0.142160i
$335$	7.00000	−	12.1244i	0.382451	−	0.662424i
$336$	−0.500000	+	0.866025i	−0.0272772	+	0.0472456i
$337$	−22.0000			−1.19842			−0.599208	−	0.800593i	$-0.704518\pi$
$337$	−22.0000			−1.19842			−0.599208	+	0.800593i	$0.704518\pi$
$338$	0.500000	−	12.9904i	0.0271964	−	0.706584i
$339$	6.00000			0.325875
$340$	−1.50000	+	2.59808i	−0.0813489	+	0.140900i
$341$		0			0
$342$	−8.00000	−	13.8564i	−0.432590	−	0.749269i
$343$	1.00000			0.0539949
$344$	−5.00000	−	8.66025i	−0.269582	−	0.466930i
$345$	3.00000	+	5.19615i	0.161515	+	0.279751i
$346$	18.0000			0.967686
$347$	−6.00000	−	10.3923i	−0.322097	−	0.557888i	0.658824	−	0.752297i	$-0.271054\pi$
$347$	−6.00000	−	10.3923i	−0.322097	−	0.557888i	−0.980921	+	0.194409i	$0.937721\pi$
$348$	−4.50000	+	7.79423i	−0.241225	+	0.417815i
$349$	−7.00000	+	12.1244i	−0.374701	+	0.649002i	−0.990282	−	0.139072i	$-0.955588\pi$
$349$	−7.00000	+	12.1244i	−0.374701	+	0.649002i	0.615581	+	0.788074i	$0.288921\pi$
$350$	−1.00000			−0.0534522
$351$	17.5000	−	4.33013i	0.934081	−	0.231125i
$352$		0			0
$353$	−9.00000	+	15.5885i	−0.479022	+	0.829690i	−0.999711	−	0.0240566i	$-0.992342\pi$
$353$	−9.00000	+	15.5885i	−0.479022	+	0.829690i	0.520689	+	0.853746i	$0.325675\pi$
$354$	3.00000	−	5.19615i	0.159448	−	0.276172i
$355$	1.50000	+	2.59808i	0.0796117	+	0.137892i
$356$	−12.0000			−0.635999
$357$	1.50000	+	2.59808i	0.0793884	+	0.137505i
$358$	−4.50000	−	7.79423i	−0.237832	−	0.411938i
$359$	3.00000			0.158334			0.0791670	−	0.996861i	$-0.474774\pi$
$359$	3.00000			0.158334			0.0791670	+	0.996861i	$0.474774\pi$
$360$	1.00000	+	1.73205i	0.0527046	+	0.0912871i
$361$	−22.5000	+	38.9711i	−1.18421	+	2.05111i
$362$	−11.0000	+	19.0526i	−0.578147	+	1.00138i
$363$	−11.0000			−0.577350
$364$	1.00000	−	3.46410i	0.0524142	−	0.181568i
$365$	13.0000			0.680451
$366$	1.00000	−	1.73205i	0.0522708	−	0.0905357i
$367$	−8.50000	+	14.7224i	−0.443696	+	0.768505i	−0.997960	−	0.0638362i	$-0.979666\pi$
$367$	−8.50000	+	14.7224i	−0.443696	+	0.768505i	0.554264	+	0.832341i	$0.313000\pi$
$368$	−3.00000	−	5.19615i	−0.156386	−	0.270868i
$369$		0			0
$370$	−1.00000	−	1.73205i	−0.0519875	−	0.0900450i
$371$	6.00000	+	10.3923i	0.311504	+	0.539542i
$372$	−4.00000			−0.207390
$373$	2.00000	+	3.46410i	0.103556	+	0.179364i	0.913147	−	0.407630i	$-0.133645\pi$
$373$	2.00000	+	3.46410i	0.103556	+	0.179364i	−0.809591	+	0.586994i	$0.800311\pi$
$374$		0			0
$375$	0.500000	−	0.866025i	0.0258199	−	0.0447214i
$376$	−9.00000			−0.464140
$377$	9.00000	−	31.1769i	0.463524	−	1.60569i
$378$	5.00000			0.257172
$379$	12.5000	−	21.6506i	0.642082	−	1.11212i	−0.342885	−	0.939377i	$-0.611404\pi$
$379$	12.5000	−	21.6506i	0.642082	−	1.11212i	0.984967	−	0.172741i	$-0.0552624\pi$
$380$	4.00000	−	6.92820i	0.205196	−	0.355409i
$381$	11.0000	+	19.0526i	0.563547	+	0.976092i
$382$	−15.0000			−0.767467
$383$	7.50000	+	12.9904i	0.383232	+	0.663777i	0.991522	−	0.129937i	$-0.0414776\pi$
$383$	7.50000	+	12.9904i	0.383232	+	0.663777i	−0.608290	+	0.793715i	$0.708144\pi$
$384$	0.500000	+	0.866025i	0.0255155	+	0.0441942i
$385$		0			0
$386$	7.00000	+	12.1244i	0.356291	+	0.617113i
$387$	−10.0000	+	17.3205i	−0.508329	+	0.880451i
$388$	3.50000	−	6.06218i	0.177686	−	0.307760i
$389$	6.00000			0.304212			0.152106	−	0.988364i	$-0.451394\pi$
$389$	6.00000			0.304212			0.152106	+	0.988364i	$0.451394\pi$
$390$	2.50000	+	2.59808i	0.126592	+	0.131559i
$391$	−18.0000			−0.910299
$392$	0.500000	−	0.866025i	0.0252538	−	0.0437409i
$393$	−6.00000	+	10.3923i	−0.302660	+	0.524222i
$394$	6.00000	+	10.3923i	0.302276	+	0.523557i
$395$	1.00000			0.0503155
$396$		0			0
$397$	−1.00000	−	1.73205i	−0.0501886	−	0.0869291i	0.839840	−	0.542834i	$-0.182649\pi$
$397$	−1.00000	−	1.73205i	−0.0501886	−	0.0869291i	−0.890028	+	0.455905i	$0.849316\pi$
$398$	16.0000			0.802008
$399$	−4.00000	−	6.92820i	−0.200250	−	0.346844i
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	1.50000	−	2.59808i	0.0749064	−	0.129742i	−0.826139	−	0.563466i	$-0.809468\pi$
$401$	1.50000	−	2.59808i	0.0749064	−	0.129742i	0.901046	+	0.433724i	$0.142801\pi$
$402$	−14.0000			−0.698257
$403$	14.0000	−	3.46410i	0.697390	−	0.172559i
$404$		0			0
$405$	0.500000	−	0.866025i	0.0248452	−	0.0430331i
$406$	4.50000	−	7.79423i	0.223331	−	0.386821i
$407$		0			0
$408$	3.00000			0.148522
$409$	8.00000	+	13.8564i	0.395575	+	0.685155i	0.993174	−	0.116639i	$-0.0372122\pi$
$409$	8.00000	+	13.8564i	0.395575	+	0.685155i	−0.597600	+	0.801795i	$0.703879\pi$
$410$		0			0
$411$	12.0000			0.591916
$412$	0.500000	+	0.866025i	0.0246332	+	0.0426660i
$413$	−3.00000	+	5.19615i	−0.147620	+	0.255686i
$414$	−6.00000	+	10.3923i	−0.294884	+	0.510754i
$415$	−9.00000			−0.441793
$416$	−2.50000	−	2.59808i	−0.122573	−	0.127381i
$417$	14.0000			0.685583
$418$		0			0
$419$	−12.0000	+	20.7846i	−0.586238	+	1.01539i	0.408481	+	0.912767i	$0.366058\pi$
$419$	−12.0000	+	20.7846i	−0.586238	+	1.01539i	−0.994720	+	0.102628i	$0.967275\pi$
$420$	0.500000	+	0.866025i	0.0243975	+	0.0422577i
$421$	−37.0000			−1.80327			−0.901635	−	0.432498i	$-0.857632\pi$
$421$	−37.0000			−1.80327			−0.901635	+	0.432498i	$0.857632\pi$
$422$	−0.500000	−	0.866025i	−0.0243396	−	0.0421575i
$423$	9.00000	+	15.5885i	0.437595	+	0.757937i
$424$	12.0000			0.582772
$425$	1.50000	+	2.59808i	0.0727607	+	0.126025i
$426$	1.50000	−	2.59808i	0.0726752	−	0.125877i
$427$	−1.00000	+	1.73205i	−0.0483934	+	0.0838198i
$428$	−12.0000			−0.580042
$429$		0			0
$430$	−10.0000			−0.482243
$431$	1.50000	−	2.59808i	0.0722525	−	0.125145i	−0.827636	−	0.561266i	$-0.810315\pi$
$431$	1.50000	−	2.59808i	0.0722525	−	0.125145i	0.899888	+	0.436121i	$0.143648\pi$
$432$	2.50000	−	4.33013i	0.120281	−	0.208333i
$433$	17.0000	+	29.4449i	0.816968	+	1.41503i	0.907906	+	0.419173i	$0.137680\pi$
$433$	17.0000	+	29.4449i	0.816968	+	1.41503i	−0.0909384	+	0.995857i	$0.528987\pi$
$434$	4.00000			0.192006
$435$	4.50000	+	7.79423i	0.215758	+	0.373705i
$436$	0.500000	+	0.866025i	0.0239457	+	0.0414751i
$437$	48.0000			2.29615
$438$	−6.50000	−	11.2583i	−0.310582	−	0.537944i
$439$	−4.00000	+	6.92820i	−0.190910	+	0.330665i	−0.945552	−	0.325471i	$-0.894477\pi$
$439$	−4.00000	+	6.92820i	−0.190910	+	0.330665i	0.754642	+	0.656136i	$0.227810\pi$
$440$		0			0
$441$	−2.00000			−0.0952381
$442$	−10.5000	+	2.59808i	−0.499434	+	0.123578i
$443$	42.0000			1.99548			0.997740	−	0.0671913i	$-0.0214038\pi$
$443$	42.0000			1.99548			0.997740	+	0.0671913i	$0.0214038\pi$
$444$	−1.00000	+	1.73205i	−0.0474579	+	0.0821995i
$445$	−6.00000	+	10.3923i	−0.284427	+	0.492642i
$446$	8.50000	+	14.7224i	0.402487	+	0.697127i
$447$	−3.00000			−0.141895
$448$	−0.500000	−	0.866025i	−0.0236228	−	0.0409159i
$449$	10.5000	+	18.1865i	0.495526	+	0.858276i	0.999987	−	0.00515887i	$-0.00164213\pi$
$449$	10.5000	+	18.1865i	0.495526	+	0.858276i	−0.504461	+	0.863434i	$0.668309\pi$
$450$	2.00000			0.0942809
$451$		0			0
$452$	−3.00000	+	5.19615i	−0.141108	+	0.244406i
$453$	−4.00000	+	6.92820i	−0.187936	+	0.325515i
$454$	−12.0000			−0.563188
$455$	−2.50000	−	2.59808i	−0.117202	−	0.121800i
$456$	−8.00000			−0.374634
$457$	−4.00000	+	6.92820i	−0.187112	+	0.324088i	−0.944286	−	0.329125i	$-0.893246\pi$
$457$	−4.00000	+	6.92820i	−0.187112	+	0.324088i	0.757174	+	0.653213i	$0.226579\pi$
$458$	1.00000	−	1.73205i	0.0467269	−	0.0809334i
$459$	−7.50000	−	12.9904i	−0.350070	−	0.606339i
$460$	−6.00000			−0.279751
$461$	12.0000	+	20.7846i	0.558896	+	0.968036i	0.997589	+	0.0693989i	$0.0221081\pi$
$461$	12.0000	+	20.7846i	0.558896	+	0.968036i	−0.438693	+	0.898637i	$0.644559\pi$
$462$		0			0
$463$	26.0000			1.20832			0.604161	−	0.796862i	$-0.293508\pi$
$463$	26.0000			1.20832			0.604161	+	0.796862i	$0.293508\pi$
$464$	−4.50000	−	7.79423i	−0.208907	−	0.361838i
$465$	−2.00000	+	3.46410i	−0.0927478	+	0.160644i
$466$	9.00000	−	15.5885i	0.416917	−	0.722121i
$467$	36.0000			1.66588			0.832941	−	0.553362i	$-0.186655\pi$
$467$	36.0000			1.66588			0.832941	+	0.553362i	$0.186655\pi$
$468$	−2.00000	+	6.92820i	−0.0924500	+	0.320256i
$469$	14.0000			0.646460
$470$	−4.50000	+	7.79423i	−0.207570	+	0.359521i
$471$	−2.50000	+	4.33013i	−0.115194	+	0.199522i
$472$	3.00000	+	5.19615i	0.138086	+	0.239172i
$473$		0			0
$474$	−0.500000	−	0.866025i	−0.0229658	−	0.0397779i
$475$	−4.00000	−	6.92820i	−0.183533	−	0.317888i
$476$	−3.00000			−0.137505
$477$	−12.0000	−	20.7846i	−0.549442	−	0.951662i
$478$	10.5000	−	18.1865i	0.480259	−	0.831833i
$479$	−18.0000	+	31.1769i	−0.822441	+	1.42451i	0.0814184	+	0.996680i	$0.474055\pi$
$479$	−18.0000	+	31.1769i	−0.822441	+	1.42451i	−0.903859	+	0.427830i	$0.859278\pi$
$480$	1.00000			0.0456435
$481$	2.00000	−	6.92820i	0.0911922	−	0.315899i
$482$	−26.0000			−1.18427
$483$	−3.00000	+	5.19615i	−0.136505	+	0.236433i
$484$	5.50000	−	9.52628i	0.250000	−	0.433013i
$485$	−3.50000	−	6.06218i	−0.158927	−	0.275269i
$486$	−16.0000			−0.725775
$487$	2.00000	+	3.46410i	0.0906287	+	0.156973i	0.907776	−	0.419456i	$-0.137779\pi$
$487$	2.00000	+	3.46410i	0.0906287	+	0.156973i	−0.817147	+	0.576429i	$0.804446\pi$
$488$	1.00000	+	1.73205i	0.0452679	+	0.0784063i
$489$	−4.00000			−0.180886
$490$	−0.500000	−	0.866025i	−0.0225877	−	0.0391230i
$491$	−4.50000	+	7.79423i	−0.203082	+	0.351749i	−0.949520	−	0.313707i	$-0.898429\pi$
$491$	−4.50000	+	7.79423i	−0.203082	+	0.351749i	0.746438	+	0.665455i	$0.231763\pi$
$492$		0			0
$493$	−27.0000			−1.21602
$494$	28.0000	−	6.92820i	1.25978	−	0.311715i
$495$		0			0
$496$	2.00000	−	3.46410i	0.0898027	−	0.155543i
$497$	−1.50000	+	2.59808i	−0.0672842	+	0.116540i
$498$	4.50000	+	7.79423i	0.201650	+	0.349268i
$499$	29.0000			1.29822			0.649109	−	0.760695i	$-0.275142\pi$
$499$	29.0000			1.29822			0.649109	+	0.760695i	$0.275142\pi$
$500$	0.500000	+	0.866025i	0.0223607	+	0.0387298i
$501$	−1.50000	−	2.59808i	−0.0670151	−	0.116073i
$502$	−18.0000			−0.803379
$503$	−13.5000	−	23.3827i	−0.601935	−	1.04258i	−0.992528	−	0.122019i	$-0.961063\pi$
$503$	−13.5000	−	23.3827i	−0.601935	−	1.04258i	0.390593	−	0.920564i	$-0.372270\pi$
$504$	−1.00000	+	1.73205i	−0.0445435	+	0.0771517i
$505$		0			0
$506$		0			0
$507$	−0.500000	+	12.9904i	−0.0222058	+	0.576923i
$508$	−22.0000			−0.976092
$509$	3.00000	−	5.19615i	0.132973	−	0.230315i	−0.791849	−	0.610718i	$-0.790881\pi$
$509$	3.00000	−	5.19615i	0.132973	−	0.230315i	0.924821	+	0.380402i	$0.124214\pi$
$510$	1.50000	−	2.59808i	0.0664211	−	0.115045i
$511$	6.50000	+	11.2583i	0.287543	+	0.498039i
$512$	−1.00000			−0.0441942
$513$	20.0000	+	34.6410i	0.883022	+	1.52944i
$514$	9.00000	+	15.5885i	0.396973	+	0.687577i
$515$	1.00000			0.0440653
$516$	5.00000	+	8.66025i	0.220113	+	0.381246i
$517$		0			0
$518$	1.00000	−	1.73205i	0.0439375	−	0.0761019i
$519$	−18.0000			−0.790112
$520$	−3.50000	+	0.866025i	−0.153485	+	0.0379777i
$521$	−12.0000			−0.525730			−0.262865	−	0.964833i	$-0.584667\pi$
$521$	−12.0000			−0.525730			−0.262865	+	0.964833i	$0.584667\pi$
$522$	−9.00000	+	15.5885i	−0.393919	+	0.682288i
$523$	6.50000	−	11.2583i	0.284225	−	0.492292i	−0.688196	−	0.725525i	$-0.741597\pi$
$523$	6.50000	−	11.2583i	0.284225	−	0.492292i	0.972421	+	0.233233i	$0.0749303\pi$
$524$	−6.00000	−	10.3923i	−0.262111	−	0.453990i
$525$	1.00000			0.0436436
$526$	9.00000	+	15.5885i	0.392419	+	0.679689i
$527$	−6.00000	−	10.3923i	−0.261364	−	0.452696i
$528$		0			0
$529$	−6.50000	−	11.2583i	−0.282609	−	0.489493i
$530$	6.00000	−	10.3923i	0.260623	−	0.451413i
$531$	6.00000	−	10.3923i	0.260378	−	0.450988i
$532$	8.00000			0.346844
$533$		0			0
$534$	12.0000			0.519291
$535$	−6.00000	+	10.3923i	−0.259403	+	0.449299i
$536$	7.00000	−	12.1244i	0.302354	−	0.523692i
$537$	4.50000	+	7.79423i	0.194189	+	0.336346i
$538$		0			0
$539$		0			0
$540$	−2.50000	−	4.33013i	−0.107583	−	0.186339i
$541$	−10.0000			−0.429934			−0.214967	−	0.976621i	$-0.568964\pi$
$541$	−10.0000			−0.429934			−0.214967	+	0.976621i	$0.568964\pi$
$542$	13.0000	+	22.5167i	0.558398	+	0.967173i
$543$	11.0000	−	19.0526i	0.472055	−	0.817624i
$544$	−1.50000	+	2.59808i	−0.0643120	+	0.111392i
$545$	1.00000			0.0428353
$546$	−1.00000	+	3.46410i	−0.0427960	+	0.148250i
$547$	−40.0000			−1.71028			−0.855138	−	0.518400i	$-0.826528\pi$
$547$	−40.0000			−1.71028			−0.855138	+	0.518400i	$0.826528\pi$
$548$	−6.00000	+	10.3923i	−0.256307	+	0.443937i
$549$	2.00000	−	3.46410i	0.0853579	−	0.147844i
$550$		0			0
$551$	72.0000			3.06730
$552$	3.00000	+	5.19615i	0.127688	+	0.221163i
$553$	0.500000	+	0.866025i	0.0212622	+	0.0368271i
$554$	4.00000			0.169944
$555$	1.00000	+	1.73205i	0.0424476	+	0.0735215i
$556$	−7.00000	+	12.1244i	−0.296866	+	0.514187i
$557$	3.00000	−	5.19615i	0.127114	−	0.220168i	−0.795443	−	0.606028i	$-0.792762\pi$
$557$	3.00000	−	5.19615i	0.127114	−	0.220168i	0.922557	+	0.385860i	$0.126095\pi$
$558$	−8.00000			−0.338667
$559$	−25.0000	−	25.9808i	−1.05739	−	1.09887i
$560$	−1.00000			−0.0422577
$561$		0			0
$562$	13.5000	−	23.3827i	0.569463	−	0.986339i
$563$	−7.50000	−	12.9904i	−0.316087	−	0.547479i	0.663581	−	0.748105i	$-0.269036\pi$
$563$	−7.50000	−	12.9904i	−0.316087	−	0.547479i	−0.979668	+	0.200625i	$0.935703\pi$
$564$	9.00000			0.378968
$565$	3.00000	+	5.19615i	0.126211	+	0.218604i
$566$	10.0000	+	17.3205i	0.420331	+	0.728035i
$567$	1.00000			0.0419961
$568$	1.50000	+	2.59808i	0.0629386	+	0.109013i
$569$	−16.5000	+	28.5788i	−0.691716	+	1.19809i	0.279559	+	0.960128i	$0.409812\pi$
$569$	−16.5000	+	28.5788i	−0.691716	+	1.19809i	−0.971275	+	0.237959i	$0.923522\pi$
$570$	−4.00000	+	6.92820i	−0.167542	+	0.290191i
$571$	11.0000			0.460336			0.230168	−	0.973151i	$-0.426072\pi$
$571$	11.0000			0.460336			0.230168	+	0.973151i	$0.426072\pi$
$572$		0			0
$573$	15.0000			0.626634
$574$		0			0
$575$	−3.00000	+	5.19615i	−0.125109	+	0.216695i
$576$	1.00000	+	1.73205i	0.0416667	+	0.0721688i
$577$	14.0000			0.582828			0.291414	−	0.956597i	$-0.405874\pi$
$577$	14.0000			0.582828			0.291414	+	0.956597i	$0.405874\pi$
$578$	−4.00000	−	6.92820i	−0.166378	−	0.288175i
$579$	−7.00000	−	12.1244i	−0.290910	−	0.503871i
$580$	−9.00000			−0.373705
$581$	−4.50000	−	7.79423i	−0.186691	−	0.323359i
$582$	−3.50000	+	6.06218i	−0.145080	+	0.251285i
$583$		0			0
$584$	13.0000			0.537944
$585$	5.00000	+	5.19615i	0.206725	+	0.214834i
$586$	9.00000			0.371787
$587$	−7.50000	+	12.9904i	−0.309558	+	0.536170i	−0.978266	−	0.207355i	$-0.933514\pi$
$587$	−7.50000	+	12.9904i	−0.309558	+	0.536170i	0.668708	+	0.743525i	$0.266848\pi$
$588$	−0.500000	+	0.866025i	−0.0206197	+	0.0357143i
$589$	16.0000	+	27.7128i	0.659269	+	1.14189i
$590$	6.00000			0.247016
$591$	−6.00000	−	10.3923i	−0.246807	−	0.427482i
$592$	−1.00000	−	1.73205i	−0.0410997	−	0.0711868i
$593$	−45.0000			−1.84793			−0.923964	−	0.382479i	$-0.875070\pi$
$593$	−45.0000			−1.84793			−0.923964	+	0.382479i	$0.875070\pi$
$594$		0			0
$595$	−1.50000	+	2.59808i	−0.0614940	+	0.106511i
$596$	1.50000	−	2.59808i	0.0614424	−	0.106421i
$597$	−16.0000			−0.654836
$598$	−15.0000	−	15.5885i	−0.613396	−	0.637459i
$599$		0			0			−	1.00000i	$-0.5\pi$
$599$		0			0				1.00000i	$0.5\pi$
$600$	0.500000	−	0.866025i	0.0204124	−	0.0353553i
$601$	−7.00000	+	12.1244i	−0.285536	+	0.494563i	−0.972739	−	0.231903i	$-0.925505\pi$
$601$	−7.00000	+	12.1244i	−0.285536	+	0.494563i	0.687203	+	0.726465i	$0.258838\pi$
$602$	−5.00000	−	8.66025i	−0.203785	−	0.352966i
$603$	−28.0000			−1.14025
$604$	−4.00000	−	6.92820i	−0.162758	−	0.281905i
$605$	−5.50000	−	9.52628i	−0.223607	−	0.387298i
$606$		0			0
$607$	−11.5000	−	19.9186i	−0.466771	−	0.808470i	0.532509	−	0.846424i	$-0.321249\pi$
$607$	−11.5000	−	19.9186i	−0.466771	−	0.808470i	−0.999279	+	0.0379540i	$0.987916\pi$
$608$	4.00000	−	6.92820i	0.162221	−	0.280976i
$609$	−4.50000	+	7.79423i	−0.182349	+	0.315838i
$610$	2.00000			0.0809776
$611$	−31.5000	+	7.79423i	−1.27435	+	0.315321i
$612$	6.00000			0.242536
$613$	−22.0000	+	38.1051i	−0.888572	+	1.53905i	−0.0470071	+	0.998895i	$0.514968\pi$
$613$	−22.0000	+	38.1051i	−0.888572	+	1.53905i	−0.841564	+	0.540157i	$0.818365\pi$
$614$	−8.00000	+	13.8564i	−0.322854	+	0.559199i
$615$		0			0
$616$		0			0
$617$	−9.00000	−	15.5885i	−0.362326	−	0.627568i	0.626017	−	0.779809i	$-0.284684\pi$
$617$	−9.00000	−	15.5885i	−0.362326	−	0.627568i	−0.988343	+	0.152242i	$0.951351\pi$
$618$	−0.500000	−	0.866025i	−0.0201129	−	0.0348367i
$619$	−10.0000			−0.401934			−0.200967	−	0.979598i	$-0.564408\pi$
$619$	−10.0000			−0.401934			−0.200967	+	0.979598i	$0.564408\pi$
$620$	−2.00000	−	3.46410i	−0.0803219	−	0.139122i
$621$	15.0000	−	25.9808i	0.601929	−	1.04257i
$622$		0			0
$623$	−12.0000			−0.480770
$624$	2.50000	+	2.59808i	0.100080	+	0.104006i
$625$	1.00000			0.0400000
$626$	13.0000	−	22.5167i	0.519584	−	0.899947i
$627$		0			0
$628$	−2.50000	−	4.33013i	−0.0997609	−	0.172791i
$629$	−6.00000			−0.239236
$630$	1.00000	+	1.73205i	0.0398410	+	0.0690066i
$631$	−23.5000	−	40.7032i	−0.935520	−	1.62037i	−0.773704	−	0.633548i	$-0.781598\pi$
$631$	−23.5000	−	40.7032i	−0.935520	−	1.62037i	−0.161817	−	0.986821i	$-0.551735\pi$
$632$	1.00000			0.0397779
$633$	0.500000	+	0.866025i	0.0198732	+	0.0344214i
$634$	−15.0000	+	25.9808i	−0.595726	+	1.03183i
$635$	−11.0000	+	19.0526i	−0.436522	+	0.756078i
$636$	−12.0000			−0.475831
$637$	1.00000	−	3.46410i	0.0396214	−	0.137253i
$638$		0			0
$639$	3.00000	−	5.19615i	0.118678	−	0.205557i
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	16.5000	+	28.5788i	0.651711	+	1.12880i	0.982708	+	0.185164i	$0.0592817\pi$
$641$	16.5000	+	28.5788i	0.651711	+	1.12880i	−0.330997	+	0.943632i	$0.607385\pi$
$642$	12.0000			0.473602
$643$	0.500000	+	0.866025i	0.0197181	+	0.0341527i	0.875716	−	0.482826i	$-0.160390\pi$
$643$	0.500000	+	0.866025i	0.0197181	+	0.0341527i	−0.855998	+	0.516979i	$0.827056\pi$
$644$	−3.00000	−	5.19615i	−0.118217	−	0.204757i
$645$	10.0000			0.393750
$646$	−12.0000	−	20.7846i	−0.472134	−	0.817760i
$647$	1.50000	−	2.59808i	0.0589711	−	0.102141i	−0.835033	−	0.550200i	$-0.814551\pi$
$647$	1.50000	−	2.59808i	0.0589711	−	0.102141i	0.894004	+	0.448059i	$0.147885\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$		0			0
$650$	−1.00000	+	3.46410i	−0.0392232	+	0.135873i
$651$	−4.00000			−0.156772
$652$	2.00000	−	3.46410i	0.0783260	−	0.135665i
$653$	−3.00000	+	5.19615i	−0.117399	+	0.203341i	−0.918736	−	0.394872i	$-0.870789\pi$
$653$	−3.00000	+	5.19615i	−0.117399	+	0.203341i	0.801337	+	0.598213i	$0.204122\pi$
$654$	−0.500000	−	0.866025i	−0.0195515	−	0.0338643i
$655$	−12.0000			−0.468879
$656$		0			0
$657$	−13.0000	−	22.5167i	−0.507178	−	0.878459i
$658$	−9.00000			−0.350857
$659$	4.50000	+	7.79423i	0.175295	+	0.303620i	0.940263	−	0.340448i	$-0.110579\pi$
$659$	4.50000	+	7.79423i	0.175295	+	0.303620i	−0.764968	+	0.644068i	$0.777245\pi$
$660$		0			0
$661$	20.0000	−	34.6410i	0.777910	−	1.34738i	−0.155235	−	0.987878i	$-0.549613\pi$
$661$	20.0000	−	34.6410i	0.777910	−	1.34738i	0.933144	−	0.359502i	$-0.117053\pi$
$662$	−20.0000			−0.777322
$663$	10.5000	−	2.59808i	0.407786	−	0.100901i
$664$	−9.00000			−0.349268
$665$	4.00000	−	6.92820i	0.155113	−	0.268664i
$666$	−2.00000	+	3.46410i	−0.0774984	+	0.134231i
$667$	−27.0000	−	46.7654i	−1.04544	−	1.81076i
$668$	3.00000			0.116073
$669$	−8.50000	−	14.7224i	−0.328629	−	0.569202i
$670$	−7.00000	−	12.1244i	−0.270434	−	0.468405i
$671$		0			0
$672$	0.500000	+	0.866025i	0.0192879	+	0.0334077i
$673$	17.0000	−	29.4449i	0.655302	−	1.13502i	−0.326516	−	0.945192i	$-0.605875\pi$
$673$	17.0000	−	29.4449i	0.655302	−	1.13502i	0.981818	−	0.189824i	$-0.0607919\pi$
$674$	−11.0000	+	19.0526i	−0.423704	+	0.733877i
$675$	−5.00000			−0.192450
$676$	−11.0000	−	6.92820i	−0.423077	−	0.266469i
$677$	−27.0000			−1.03769			−0.518847	−	0.854867i	$-0.673639\pi$
$677$	−27.0000			−1.03769			−0.518847	+	0.854867i	$0.673639\pi$
$678$	3.00000	−	5.19615i	0.115214	−	0.199557i
$679$	3.50000	−	6.06218i	0.134318	−	0.232645i
$680$	1.50000	+	2.59808i	0.0575224	+	0.0996317i
$681$	12.0000			0.459841
$682$		0			0
$683$	−6.00000	−	10.3923i	−0.229584	−	0.397650i	0.728101	−	0.685470i	$-0.240403\pi$
$683$	−6.00000	−	10.3923i	−0.229584	−	0.397650i	−0.957685	+	0.287819i	$0.907070\pi$
$684$	−16.0000			−0.611775
$685$	6.00000	+	10.3923i	0.229248	+	0.397070i
$686$	0.500000	−	0.866025i	0.0190901	−	0.0330650i
$687$	−1.00000	+	1.73205i	−0.0381524	+	0.0660819i
$688$	−10.0000			−0.381246
$689$	42.0000	−	10.3923i	1.60007	−	0.395915i
$690$	6.00000			0.228416
$691$	−10.0000	+	17.3205i	−0.380418	+	0.658903i	−0.991122	−	0.132956i	$-0.957553\pi$
$691$	−10.0000	+	17.3205i	−0.380418	+	0.658903i	0.610704	+	0.791859i	$0.290887\pi$
$692$	9.00000	−	15.5885i	0.342129	−	0.592584i
$693$		0			0
$694$	−12.0000			−0.455514
$695$	7.00000	+	12.1244i	0.265525	+	0.459903i
$696$	4.50000	+	7.79423i	0.170572	+	0.295439i
$697$		0			0
$698$	7.00000	+	12.1244i	0.264954	+	0.458914i
$699$	−9.00000	+	15.5885i	−0.340411	+	0.589610i
$700$	−0.500000	+	0.866025i	−0.0188982	+	0.0327327i
$701$	21.0000			0.793159			0.396580	−	0.918000i	$-0.370197\pi$
$701$	21.0000			0.793159			0.396580	+	0.918000i	$0.370197\pi$
$702$	5.00000	−	17.3205i	0.188713	−	0.653720i
$703$	16.0000			0.603451
$704$		0			0
$705$	4.50000	−	7.79423i	0.169480	−	0.293548i
$706$	9.00000	+	15.5885i	0.338719	+	0.586679i
$707$		0			0
$708$	−3.00000	−	5.19615i	−0.112747	−	0.195283i
$709$	5.00000	+	8.66025i	0.187779	+	0.325243i	0.944509	−	0.328484i	$-0.106538\pi$
$709$	5.00000	+	8.66025i	0.187779	+	0.325243i	−0.756730	+	0.653727i	$0.773204\pi$
$710$	3.00000			0.112588
$711$	−1.00000	−	1.73205i	−0.0375029	−	0.0649570i
$712$	−6.00000	+	10.3923i	−0.224860	+	0.389468i
$713$	12.0000	−	20.7846i	0.449404	−	0.778390i
$714$	3.00000			0.112272
$715$		0			0
$716$	−9.00000			−0.336346
$717$	−10.5000	+	18.1865i	−0.392130	+	0.679189i
$718$	1.50000	−	2.59808i	0.0559795	−	0.0969593i
$719$	6.00000	+	10.3923i	0.223762	+	0.387568i	0.955947	−	0.293538i	$-0.0948328\pi$
$719$	6.00000	+	10.3923i	0.223762	+	0.387568i	−0.732185	+	0.681106i	$0.761499\pi$
$720$	2.00000			0.0745356
$721$	0.500000	+	0.866025i	0.0186210	+	0.0322525i
$722$	22.5000	+	38.9711i	0.837363	+	1.45036i
$723$	26.0000			0.966950
$724$	11.0000	+	19.0526i	0.408812	+	0.708083i
$725$	−4.50000	+	7.79423i	−0.167126	+	0.289470i
$726$	−5.50000	+	9.52628i	−0.204124	+	0.353553i
$727$	−37.0000			−1.37225			−0.686127	−	0.727482i	$-0.740691\pi$
$727$	−37.0000			−1.37225			−0.686127	+	0.727482i	$0.740691\pi$
$728$	−2.50000	−	2.59808i	−0.0926562	−	0.0962911i
$729$	13.0000			0.481481
$730$	6.50000	−	11.2583i	0.240576	−	0.416689i
$731$	−15.0000	+	25.9808i	−0.554795	+	0.960933i
$732$	−1.00000	−	1.73205i	−0.0369611	−	0.0640184i
$733$	5.00000			0.184679			0.0923396	−	0.995728i	$-0.470565\pi$
$733$	5.00000			0.184679			0.0923396	+	0.995728i	$0.470565\pi$
$734$	8.50000	+	14.7224i	0.313741	+	0.543415i
$735$	0.500000	+	0.866025i	0.0184428	+	0.0319438i
$736$	−6.00000			−0.221163
$737$		0			0
$738$		0			0
$739$	−5.50000	+	9.52628i	−0.202321	+	0.350430i	−0.949276	−	0.314445i	$-0.898182\pi$
$739$	−5.50000	+	9.52628i	−0.202321	+	0.350430i	0.746955	+	0.664875i	$0.231515\pi$
$740$	−2.00000			−0.0735215
$741$	−28.0000	+	6.92820i	−1.02861	+	0.254514i
$742$	12.0000			0.440534
$743$	21.0000	−	36.3731i	0.770415	−	1.33440i	−0.166920	−	0.985970i	$-0.553382\pi$
$743$	21.0000	−	36.3731i	0.770415	−	1.33440i	0.937336	−	0.348428i	$-0.113284\pi$
$744$	−2.00000	+	3.46410i	−0.0733236	+	0.127000i
$745$	−1.50000	−	2.59808i	−0.0549557	−	0.0951861i
$746$	4.00000			0.146450
$747$	9.00000	+	15.5885i	0.329293	+	0.570352i
$748$		0			0
$749$	−12.0000			−0.438470
$750$	−0.500000	−	0.866025i	−0.0182574	−	0.0316228i
$751$	−16.0000	+	27.7128i	−0.583848	+	1.01125i	0.411170	+	0.911559i	$0.365120\pi$
$751$	−16.0000	+	27.7128i	−0.583848	+	1.01125i	−0.995018	+	0.0996961i	$0.968213\pi$
$752$	−4.50000	+	7.79423i	−0.164098	+	0.284226i
$753$	18.0000			0.655956
$754$	−22.5000	−	23.3827i	−0.819402	−	0.851547i
$755$	−8.00000			−0.291150
$756$	2.50000	−	4.33013i	0.0909241	−	0.157485i
$757$	17.0000	−	29.4449i	0.617876	−	1.07019i	−0.371997	−	0.928234i	$-0.621327\pi$
$757$	17.0000	−	29.4449i	0.617876	−	1.07019i	0.989873	−	0.141958i	$-0.0453398\pi$
$758$	−12.5000	−	21.6506i	−0.454020	−	0.786386i
$759$		0			0
$760$	−4.00000	−	6.92820i	−0.145095	−	0.251312i
$761$	3.00000	+	5.19615i	0.108750	+	0.188360i	0.915264	−	0.402854i	$-0.131982\pi$
$761$	3.00000	+	5.19615i	0.108750	+	0.188360i	−0.806514	+	0.591215i	$0.798649\pi$
$762$	22.0000			0.796976
$763$	0.500000	+	0.866025i	0.0181012	+	0.0313522i
$764$	−7.50000	+	12.9904i	−0.271340	+	0.469975i
$765$	3.00000	−	5.19615i	0.108465	−	0.187867i
$766$	15.0000			0.541972
$767$	15.0000	+	15.5885i	0.541619	+	0.562867i
$768$	1.00000			0.0360844
$769$	14.0000	−	24.2487i	0.504853	−	0.874431i	−0.495131	−	0.868818i	$-0.664880\pi$
$769$	14.0000	−	24.2487i	0.504853	−	0.874431i	0.999984	−	0.00561275i	$-0.00178660\pi$
$770$		0			0
$771$	−9.00000	−	15.5885i	−0.324127	−	0.561405i
$772$	14.0000			0.503871
$773$	−22.5000	−	38.9711i	−0.809269	−	1.40169i	−0.913371	−	0.407128i	$-0.866530\pi$
$773$	−22.5000	−	38.9711i	−0.809269	−	1.40169i	0.104102	−	0.994567i	$-0.466803\pi$
$774$	10.0000	+	17.3205i	0.359443	+	0.622573i
$775$	−4.00000			−0.143684
$776$	−3.50000	−	6.06218i	−0.125643	−	0.217620i
$777$	−1.00000	+	1.73205i	−0.0358748	+	0.0621370i
$778$	3.00000	−	5.19615i	0.107555	−	0.186291i
$779$		0			0
$780$	3.50000	−	0.866025i	0.125320	−	0.0310087i
$781$		0			0
$782$	−9.00000	+	15.5885i	−0.321839	+	0.557442i
$783$	22.5000	−	38.9711i	0.804084	−	1.39272i
$784$	−0.500000	−	0.866025i	−0.0178571	−	0.0309295i
$785$	−5.00000			−0.178458
$786$	6.00000	+	10.3923i	0.214013	+	0.370681i
$787$	27.5000	+	47.6314i	0.980269	+	1.69788i	0.661320	+	0.750104i	$0.269997\pi$
$787$	27.5000	+	47.6314i	0.980269	+	1.69788i	0.318950	+	0.947772i	$0.396670\pi$
$788$	12.0000			0.427482
$789$	−9.00000	−	15.5885i	−0.320408	−	0.554964i
$790$	0.500000	−	0.866025i	0.0177892	−	0.0308118i
$791$	−3.00000	+	5.19615i	−0.106668	+	0.184754i
$792$		0			0
$793$	5.00000	+	5.19615i	0.177555	+	0.184521i
$794$	−2.00000			−0.0709773
$795$	−6.00000	+	10.3923i	−0.212798	+	0.368577i
$796$	8.00000	−	13.8564i	0.283552	−	0.491127i
$797$	−13.5000	−	23.3827i	−0.478195	−	0.828257i	0.521493	−	0.853256i	$-0.325375\pi$
$797$	−13.5000	−	23.3827i	−0.478195	−	0.828257i	−0.999687	+	0.0249984i	$0.992042\pi$
$798$	−8.00000			−0.283197
$799$	13.5000	+	23.3827i	0.477596	+	0.827220i
$800$	0.500000	+	0.866025i	0.0176777	+	0.0306186i
$801$	24.0000			0.847998
$802$	−1.50000	−	2.59808i	−0.0529668	−	0.0917413i
$803$		0			0
$804$	−7.00000	+	12.1244i	−0.246871	+	0.427593i
$805$	−6.00000			−0.211472
$806$	4.00000	−	13.8564i	0.140894	−	0.488071i
$807$		0			0
$808$		0			0
$809$	−9.00000	+	15.5885i	−0.316423	+	0.548061i	−0.979739	−	0.200279i	$-0.935815\pi$
$809$	−9.00000	+	15.5885i	−0.316423	+	0.548061i	0.663316	+	0.748340i	$0.269149\pi$
$810$	−0.500000	−	0.866025i	−0.0175682	−	0.0304290i
$811$	2.00000			0.0702295			0.0351147	−	0.999383i	$-0.488820\pi$
$811$	2.00000			0.0702295			0.0351147	+	0.999383i	$0.488820\pi$
$812$	−4.50000	−	7.79423i	−0.157919	−	0.273524i
$813$	−13.0000	−	22.5167i	−0.455930	−	0.789694i
$814$		0			0
$815$	−2.00000	−	3.46410i	−0.0700569	−	0.121342i
$816$	1.50000	−	2.59808i	0.0525105	−	0.0909509i
$817$	40.0000	−	69.2820i	1.39942	−	2.42387i
$818$	16.0000			0.559427
$819$	−2.00000	+	6.92820i	−0.0698857	+	0.242091i
$820$		0			0
$821$	−7.50000	+	12.9904i	−0.261752	+	0.453367i	−0.966708	−	0.255884i	$-0.917634\pi$
$821$	−7.50000	+	12.9904i	−0.261752	+	0.453367i	0.704956	+	0.709251i	$0.250967\pi$
$822$	6.00000	−	10.3923i	0.209274	−	0.362473i
$823$	−7.00000	−	12.1244i	−0.244005	−	0.422628i	0.717847	−	0.696201i	$-0.245128\pi$
$823$	−7.00000	−	12.1244i	−0.244005	−	0.422628i	−0.961851	+	0.273573i	$0.911795\pi$
$824$	1.00000			0.0348367
$825$		0			0
$826$	3.00000	+	5.19615i	0.104383	+	0.180797i
$827$	18.0000			0.625921			0.312961	−	0.949766i	$-0.398679\pi$
$827$	18.0000			0.625921			0.312961	+	0.949766i	$0.398679\pi$
$828$	6.00000	+	10.3923i	0.208514	+	0.361158i
$829$	−25.0000	+	43.3013i	−0.868286	+	1.50392i	−0.00453881	+	0.999990i	$0.501445\pi$
$829$	−25.0000	+	43.3013i	−0.868286	+	1.50392i	−0.863747	+	0.503926i	$0.831889\pi$
$830$	−4.50000	+	7.79423i	−0.156197	+	0.270542i
$831$	−4.00000			−0.138758
$832$	−3.50000	+	0.866025i	−0.121341	+	0.0300240i
$833$	−3.00000			−0.103944
$834$	7.00000	−	12.1244i	0.242390	−	0.419832i
$835$	1.50000	−	2.59808i	0.0519096	−	0.0899101i
$836$		0			0
$837$	20.0000			0.691301
$838$	12.0000	+	20.7846i	0.414533	+	0.717992i
$839$	−6.00000	−	10.3923i	−0.207143	−	0.358782i	0.743670	−	0.668546i	$-0.233083\pi$
$839$	−6.00000	−	10.3923i	−0.207143	−	0.358782i	−0.950813	+	0.309764i	$0.899750\pi$
$840$	1.00000			0.0345033
$841$	−26.0000	−	45.0333i	−0.896552	−	1.55287i
$842$	−18.5000	+	32.0429i	−0.637552	+	1.10427i
$843$	−13.5000	+	23.3827i	−0.464965	+	0.805342i
$844$	−1.00000			−0.0344214
$845$	−11.5000	+	6.06218i	−0.395612	+	0.208545i
$846$	18.0000			0.618853
$847$	5.50000	−	9.52628i	0.188982	−	0.327327i
$848$	6.00000	−	10.3923i	0.206041	−	0.356873i
$849$	−10.0000	−	17.3205i	−0.343199	−	0.594438i
$850$	3.00000			0.102899
$851$	−6.00000	−	10.3923i	−0.205677	−	0.356244i
$852$	−1.50000	−	2.59808i	−0.0513892	−	0.0890086i
$853$	−1.00000			−0.0342393			−0.0171197	−	0.999853i	$-0.505450\pi$
$853$	−1.00000			−0.0342393			−0.0171197	+	0.999853i	$0.505450\pi$
$854$	1.00000	+	1.73205i	0.0342193	+	0.0592696i
$855$	−8.00000	+	13.8564i	−0.273594	+	0.473879i
$856$	−6.00000	+	10.3923i	−0.205076	+	0.355202i
$857$	−45.0000			−1.53717			−0.768585	−	0.639747i	$-0.779039\pi$
$857$	−45.0000			−1.53717			−0.768585	+	0.639747i	$0.779039\pi$
$858$		0			0
$859$	20.0000			0.682391			0.341196	−	0.939992i	$-0.389168\pi$
$859$	20.0000			0.682391			0.341196	+	0.939992i	$0.389168\pi$
$860$	−5.00000	+	8.66025i	−0.170499	+	0.295312i
$861$		0			0
$862$	−1.50000	−	2.59808i	−0.0510902	−	0.0884908i
$863$	54.0000			1.83818			0.919091	−	0.394046i	$-0.128925\pi$
$863$	54.0000			1.83818			0.919091	+	0.394046i	$0.128925\pi$
$864$	−2.50000	−	4.33013i	−0.0850517	−	0.147314i
$865$	−9.00000	−	15.5885i	−0.306009	−	0.530023i
$866$	34.0000			1.15537
$867$	4.00000	+	6.92820i	0.135847	+	0.235294i
$868$	2.00000	−	3.46410i	0.0678844	−	0.117579i
$869$		0			0
$870$	9.00000			0.305129
$871$	14.0000	−	48.4974i	0.474372	−	1.64327i
$872$	1.00000			0.0338643
$873$	−7.00000	+	12.1244i	−0.236914	+	0.410347i
$874$	24.0000	−	41.5692i	0.811812	−	1.40610i
$875$	0.500000	+	0.866025i	0.0169031	+	0.0292770i
$876$	−13.0000			−0.439229
$877$	20.0000	+	34.6410i	0.675352	+	1.16974i	0.976366	+	0.216124i	$0.0693416\pi$
$877$	20.0000	+	34.6410i	0.675352	+	1.16974i	−0.301014	+	0.953620i	$0.597325\pi$
$878$	4.00000	+	6.92820i	0.134993	+	0.233816i
$879$	−9.00000			−0.303562
$880$		0			0
$881$	27.0000	−	46.7654i	0.909653	−	1.57557i	0.0951067	−	0.995467i	$-0.469681\pi$
$881$	27.0000	−	46.7654i	0.909653	−	1.57557i	0.814546	−	0.580098i	$-0.196986\pi$
$882$	−1.00000	+	1.73205i	−0.0336718	+	0.0583212i
$883$	−46.0000			−1.54802			−0.774012	−	0.633171i	$-0.781753\pi$
$883$	−46.0000			−1.54802			−0.774012	+	0.633171i	$0.781753\pi$
$884$	−3.00000	+	10.3923i	−0.100901	+	0.349531i
$885$	−6.00000			−0.201688
$886$	21.0000	−	36.3731i	0.705509	−	1.22198i
$887$	24.0000	−	41.5692i	0.805841	−	1.39576i	−0.109881	−	0.993945i	$-0.535047\pi$
$887$	24.0000	−	41.5692i	0.805841	−	1.39576i	0.915722	−	0.401813i	$-0.131620\pi$
$888$	1.00000	+	1.73205i	0.0335578	+	0.0581238i
$889$	−22.0000			−0.737856
$890$	6.00000	+	10.3923i	0.201120	+	0.348351i
$891$		0			0
$892$	17.0000			0.569202
$893$	−36.0000	−	62.3538i	−1.20469	−	2.08659i
$894$	−1.50000	+	2.59808i	−0.0501675	+	0.0868927i
$895$	−4.50000	+	7.79423i	−0.150418	+	0.260532i
$896$	−1.00000			−0.0334077
$897$	15.0000	+	15.5885i	0.500835	+	0.520483i
$898$	21.0000			0.700779
$899$	18.0000	−	31.1769i	0.600334	−	1.03981i
$900$	1.00000	−	1.73205i	0.0333333	−	0.0577350i
$901$	−18.0000	−	31.1769i	−0.599667	−	1.03865i
$902$		0			0
$903$	5.00000	+	8.66025i	0.166390	+	0.288195i
$904$	3.00000	+	5.19615i	0.0997785	+	0.172821i
$905$	22.0000			0.731305
$906$	4.00000	+	6.92820i	0.132891	+	0.230174i
$907$	−4.00000	+	6.92820i	−0.132818	+	0.230047i	−0.924762	−	0.380547i	$-0.875736\pi$
$907$	−4.00000	+	6.92820i	−0.132818	+	0.230047i	0.791944	+	0.610594i	$0.209069\pi$
$908$	−6.00000	+	10.3923i	−0.199117	+	0.344881i
$909$		0			0
$910$	−3.50000	+	0.866025i	−0.116024	+	0.0287085i
$911$	45.0000			1.49092			0.745458	−	0.666552i	$-0.232231\pi$
$911$	45.0000			1.49092			0.745458	+	0.666552i	$0.232231\pi$
$912$	−4.00000	+	6.92820i	−0.132453	+	0.229416i
$913$		0			0
$914$	4.00000	+	6.92820i	0.132308	+	0.229165i
$915$	−2.00000			−0.0661180
$916$	−1.00000	−	1.73205i	−0.0330409	−	0.0572286i
$917$	−6.00000	−	10.3923i	−0.198137	−	0.343184i
$918$	−15.0000			−0.495074
$919$	−2.50000	−	4.33013i	−0.0824674	−	0.142838i	0.821842	−	0.569716i	$-0.192947\pi$
$919$	−2.50000	−	4.33013i	−0.0824674	−	0.142838i	−0.904309	+	0.426878i	$0.859613\pi$
$920$	−3.00000	+	5.19615i	−0.0989071	+	0.171312i
$921$	8.00000	−	13.8564i	0.263609	−	0.456584i
$922$	24.0000			0.790398
$923$	7.50000	+	7.79423i	0.246866	+	0.256550i
$924$		0			0
$925$	−1.00000	+	1.73205i	−0.0328798	+	0.0569495i
$926$	13.0000	−	22.5167i	0.427207	−	0.739943i
$927$	−1.00000	−	1.73205i	−0.0328443	−	0.0568880i
$928$	−9.00000			−0.295439
$929$	12.0000	+	20.7846i	0.393707	+	0.681921i	0.992935	−	0.118657i	$-0.0378590\pi$
$929$	12.0000	+	20.7846i	0.393707	+	0.681921i	−0.599228	+	0.800578i	$0.704526\pi$
$930$	2.00000	+	3.46410i	0.0655826	+	0.113592i
$931$	8.00000			0.262189
$932$	−9.00000	−	15.5885i	−0.294805	−	0.510617i
$933$		0			0
$934$	18.0000	−	31.1769i	0.588978	−	1.02014i
$935$		0			0
$936$	5.00000	+	5.19615i	0.163430	+	0.169842i
$937$	41.0000			1.33941			0.669706	−	0.742627i	$-0.266420\pi$
$937$	41.0000			1.33941			0.669706	+	0.742627i	$0.266420\pi$
$938$	7.00000	−	12.1244i	0.228558	−	0.395874i
$939$	−13.0000	+	22.5167i	−0.424239	+	0.734803i
$940$	4.50000	+	7.79423i	0.146774	+	0.254220i
$941$	30.0000			0.977972			0.488986	−	0.872292i	$-0.337367\pi$
$941$	30.0000			0.977972			0.488986	+	0.872292i	$0.337367\pi$
$942$	2.50000	+	4.33013i	0.0814544	+	0.141083i
$943$		0			0
$944$	6.00000			0.195283
$945$	−2.50000	−	4.33013i	−0.0813250	−	0.140859i
$946$		0			0
$947$	−3.00000	+	5.19615i	−0.0974869	+	0.168852i	−0.910644	−	0.413192i	$-0.864414\pi$
$947$	−3.00000	+	5.19615i	−0.0974869	+	0.168852i	0.813157	+	0.582045i	$0.197747\pi$
$948$	−1.00000			−0.0324785
$949$	45.5000	−	11.2583i	1.47699	−	0.365461i
$950$	−8.00000			−0.259554
$951$	15.0000	−	25.9808i	0.486408	−	0.842484i
$952$	−1.50000	+	2.59808i	−0.0486153	+	0.0842041i
$953$	15.0000	+	25.9808i	0.485898	+	0.841599i	0.999869	−	0.0162081i	$-0.00515944\pi$
$953$	15.0000	+	25.9808i	0.485898	+	0.841599i	−0.513971	+	0.857808i	$0.671826\pi$
$954$	−24.0000			−0.777029
$955$	7.50000	+	12.9904i	0.242694	+	0.420359i
$956$	−10.5000	−	18.1865i	−0.339594	−	0.588195i
$957$		0			0
$958$	18.0000	+	31.1769i	0.581554	+	1.00728i
$959$	−6.00000	+	10.3923i	−0.193750	+	0.335585i
$960$	0.500000	−	0.866025i	0.0161374	−	0.0279508i
$961$	−15.0000			−0.483871
$962$	−5.00000	−	5.19615i	−0.161206	−	0.167531i
$963$	24.0000			0.773389
$964$	−13.0000	+	22.5167i	−0.418702	+	0.725213i
$965$	7.00000	−	12.1244i	0.225338	−	0.390297i
$966$	3.00000	+	5.19615i	0.0965234	+	0.167183i
$967$	−4.00000			−0.128631			−0.0643157	−	0.997930i	$-0.520486\pi$
$967$	−4.00000			−0.128631			−0.0643157	+	0.997930i	$0.520486\pi$
$968$	−5.50000	−	9.52628i	−0.176777	−	0.306186i
$969$	12.0000	+	20.7846i	0.385496	+	0.667698i
$970$	−7.00000			−0.224756
$971$	−12.0000	−	20.7846i	−0.385098	−	0.667010i	0.606685	−	0.794943i	$-0.292499\pi$
$971$	−12.0000	−	20.7846i	−0.385098	−	0.667010i	−0.991783	+	0.127933i	$0.959166\pi$
$972$	−8.00000	+	13.8564i	−0.256600	+	0.444444i
$973$	−7.00000	+	12.1244i	−0.224410	+	0.388689i
$974$	4.00000			0.128168
$975$	1.00000	−	3.46410i	0.0320256	−	0.110940i
$976$	2.00000			0.0640184
$977$	30.0000	−	51.9615i	0.959785	−	1.66240i	0.236768	−	0.971566i	$-0.423912\pi$
$977$	30.0000	−	51.9615i	0.959785	−	1.66240i	0.723017	−	0.690830i	$-0.242755\pi$
$978$	−2.00000	+	3.46410i	−0.0639529	+	0.110770i
$979$		0			0
$980$	−1.00000			−0.0319438
$981$	−1.00000	−	1.73205i	−0.0319275	−	0.0553001i
$982$	4.50000	+	7.79423i	0.143601	+	0.248724i
$983$	−24.0000			−0.765481			−0.382741	−	0.923856i	$-0.625020\pi$
$983$	−24.0000			−0.765481			−0.382741	+	0.923856i	$0.625020\pi$
$984$		0			0
$985$	6.00000	−	10.3923i	0.191176	−	0.331126i
$986$	−13.5000	+	23.3827i	−0.429928	+	0.744656i
$987$	9.00000			0.286473
$988$	8.00000	−	27.7128i	0.254514	−	0.881662i
$989$	−60.0000			−1.90789
$990$		0			0
$991$	−16.0000	+	27.7128i	−0.508257	+	0.880327i	0.491698	+	0.870766i	$0.336377\pi$
$991$	−16.0000	+	27.7128i	−0.508257	+	0.880327i	−0.999954	+	0.00956046i	$0.996957\pi$
$992$	−2.00000	−	3.46410i	−0.0635001	−	0.109985i
$993$	20.0000			0.634681
$994$	1.50000	+	2.59808i	0.0475771	+	0.0824060i
$995$	−8.00000	−	13.8564i	−0.253617	−	0.439278i
$996$	9.00000			0.285176
$997$	−1.00000	−	1.73205i	−0.0316703	−	0.0548546i	0.849756	−	0.527176i	$-0.176749\pi$
$997$	−1.00000	−	1.73205i	−0.0316703	−	0.0548546i	−0.881426	+	0.472322i	$0.843416\pi$
$998$	14.5000	−	25.1147i	0.458989	−	0.794993i
$999$	5.00000	−	8.66025i	0.158193	−	0.273998i

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	910.2.i.b.841.1	yes	2
13.3	even	3	inner	910.2.i.b.211.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
910.2.i.b.211.1	✓	2	13.3	even	3	inner
910.2.i.b.841.1	yes	2	1.1	even	1	trivial

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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	910.2.i.b.841.1

Level	$910$
Weight	$2$
Character	910.841
Analytic conductor	$7.266$
Analytic rank	$0$
Dimension	$2$
Inner twists	$2$