LMFDB - Embedded newform 1170.2.i.p.991.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1170,2,Mod(451,1170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1170, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1170.451");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1170.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:	$9.34249703649$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			991.2
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1170.991
Dual form			1170.2.i.p.451.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-0.133975 + 0.232051i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-0.133975 + 0.232051i) q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{10} +(0.866025 + 1.50000i) q^{11} +(3.59808 - 0.232051i) q^{13} -0.267949 q^{14} +(-0.500000 - 0.866025i) q^{16} +(3.46410 - 6.00000i) q^{17} +(-2.50000 + 4.33013i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(-0.866025 + 1.50000i) q^{22} +(3.46410 + 6.00000i) q^{23} +1.00000 q^{25} +(2.00000 + 3.00000i) q^{26} +(-0.133975 - 0.232051i) q^{28} +(1.26795 + 2.19615i) q^{29} -0.535898 q^{31} +(0.500000 - 0.866025i) q^{32} +6.92820 q^{34} +(-0.133975 + 0.232051i) q^{35} +(1.59808 + 2.76795i) q^{37} -5.00000 q^{38} -1.00000 q^{40} +(-3.46410 - 6.00000i) q^{41} +(-4.46410 + 7.73205i) q^{43} -1.73205 q^{44} +(-3.46410 + 6.00000i) q^{46} -0.464102 q^{47} +(3.46410 + 6.00000i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-1.59808 + 3.23205i) q^{52} +6.46410 q^{53} +(0.866025 + 1.50000i) q^{55} +(0.133975 - 0.232051i) q^{56} +(-1.26795 + 2.19615i) q^{58} +(1.73205 - 3.00000i) q^{59} +(-2.26795 + 3.92820i) q^{61} +(-0.267949 - 0.464102i) q^{62} +1.00000 q^{64} +(3.59808 - 0.232051i) q^{65} +(4.19615 + 7.26795i) q^{67} +(3.46410 + 6.00000i) q^{68} -0.267949 q^{70} +(6.46410 - 11.1962i) q^{71} -10.9282 q^{73} +(-1.59808 + 2.76795i) q^{74} +(-2.50000 - 4.33013i) q^{76} -0.464102 q^{77} +15.8564 q^{79} +(-0.500000 - 0.866025i) q^{80} +(3.46410 - 6.00000i) q^{82} -2.53590 q^{83} +(3.46410 - 6.00000i) q^{85} -8.92820 q^{86} +(-0.866025 - 1.50000i) q^{88} +(-2.59808 - 4.50000i) q^{89} +(-0.428203 + 0.866025i) q^{91} -6.92820 q^{92} +(-0.232051 - 0.401924i) q^{94} +(-2.50000 + 4.33013i) q^{95} +(-5.26795 + 9.12436i) q^{97} +(-3.46410 + 6.00000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{4} + 4 q^{5} - 4 q^{7} - 4 q^{8}+O(q^{10}) $ 4 * q + 2 * q^2 - 2 * q^4 + 4 * q^5 - 4 * q^7 - 4 * q^8	$ 4 q + 2 q^{2} - 2 q^{4} + 4 q^{5} - 4 q^{7} - 4 q^{8} + 2 q^{10} + 4 q^{13} - 8 q^{14} - 2 q^{16} - 10 q^{19} - 2 q^{20} + 4 q^{25} + 8 q^{26} - 4 q^{28} + 12 q^{29} - 16 q^{31} + 2 q^{32} - 4 q^{35} - 4 q^{37} - 20 q^{38} - 4 q^{40} - 4 q^{43} + 12 q^{47} + 2 q^{50} + 4 q^{52} + 12 q^{53} + 4 q^{56} - 12 q^{58} - 16 q^{61} - 8 q^{62} + 4 q^{64} + 4 q^{65} - 4 q^{67} - 8 q^{70} + 12 q^{71} - 16 q^{73} + 4 q^{74} - 10 q^{76} + 12 q^{77} + 8 q^{79} - 2 q^{80} - 24 q^{83} - 8 q^{86} + 26 q^{91} + 6 q^{94} - 10 q^{95} - 28 q^{97}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^4 + 4 * q^5 - 4 * q^7 - 4 * q^8 + 2 * q^10 + 4 * q^13 - 8 * q^14 - 2 * q^16 - 10 * q^19 - 2 * q^20 + 4 * q^25 + 8 * q^26 - 4 * q^28 + 12 * q^29 - 16 * q^31 + 2 * q^32 - 4 * q^35 - 4 * q^37 - 20 * q^38 - 4 * q^40 - 4 * q^43 + 12 * q^47 + 2 * q^50 + 4 * q^52 + 12 * q^53 + 4 * q^56 - 12 * q^58 - 16 * q^61 - 8 * q^62 + 4 * q^64 + 4 * q^65 - 4 * q^67 - 8 * q^70 + 12 * q^71 - 16 * q^73 + 4 * q^74 - 10 * q^76 + 12 * q^77 + 8 * q^79 - 2 * q^80 - 24 * q^83 - 8 * q^86 + 26 * q^91 + 6 * q^94 - 10 * q^95 - 28 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times$.

$n$	$911$	$937$	$1081$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$		0			0
$7$	−0.133975	+	0.232051i	−0.0506376	+	0.0877070i	−0.890233	−	0.455505i	$-0.849459\pi$
$7$	−0.133975	+	0.232051i	−0.0506376	+	0.0877070i	0.839596	+	0.543212i	$0.182792\pi$
$8$	−1.00000			−0.353553
$9$		0			0
$10$	0.500000	+	0.866025i	0.158114	+	0.273861i
$11$	0.866025	+	1.50000i	0.261116	+	0.452267i	0.966539	−	0.256520i	$-0.0825760\pi$
$11$	0.866025	+	1.50000i	0.261116	+	0.452267i	−0.705422	+	0.708787i	$0.749243\pi$
$12$		0			0
$13$	3.59808	−	0.232051i	0.997927	−	0.0643593i
$13$	3.59808	−	0.232051i	0.997927	−	0.0643593i
$14$	−0.267949			−0.0716124
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	3.46410	−	6.00000i	0.840168	−	1.45521i	−0.0495842	−	0.998770i	$-0.515790\pi$
$17$	3.46410	−	6.00000i	0.840168	−	1.45521i	0.889752	−	0.456444i	$-0.150877\pi$
$18$		0			0
$19$	−2.50000	+	4.33013i	−0.573539	+	0.993399i	0.422659	+	0.906289i	$0.361097\pi$
$19$	−2.50000	+	4.33013i	−0.573539	+	0.993399i	−0.996199	+	0.0871106i	$0.972237\pi$
$20$	−0.500000	+	0.866025i	−0.111803	+	0.193649i
$21$		0			0
$22$	−0.866025	+	1.50000i	−0.184637	+	0.319801i
$23$	3.46410	+	6.00000i	0.722315	+	1.25109i	0.960070	+	0.279761i	$0.0902553\pi$
$23$	3.46410	+	6.00000i	0.722315	+	1.25109i	−0.237754	+	0.971325i	$0.576411\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$	2.00000	+	3.00000i	0.392232	+	0.588348i
$27$		0			0
$28$	−0.133975	−	0.232051i	−0.0253188	−	0.0438535i
$29$	1.26795	+	2.19615i	0.235452	+	0.407815i	0.959404	−	0.282035i	$-0.0910095\pi$
$29$	1.26795	+	2.19615i	0.235452	+	0.407815i	−0.723952	+	0.689851i	$0.757676\pi$
$30$		0			0
$31$	−0.535898			−0.0962502			−0.0481251	−	0.998841i	$-0.515325\pi$
$31$	−0.535898			−0.0962502			−0.0481251	+	0.998841i	$0.515325\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$	6.92820			1.18818
$35$	−0.133975	+	0.232051i	−0.0226458	+	0.0392237i
$36$		0			0
$37$	1.59808	+	2.76795i	0.262722	+	0.455048i	0.966964	−	0.254912i	$-0.0820464\pi$
$37$	1.59808	+	2.76795i	0.262722	+	0.455048i	−0.704242	+	0.709960i	$0.748713\pi$
$38$	−5.00000			−0.811107
$39$		0			0
$40$	−1.00000			−0.158114
$41$	−3.46410	−	6.00000i	−0.541002	−	0.937043i	−0.998847	−	0.0480106i	$-0.984712\pi$
$41$	−3.46410	−	6.00000i	−0.541002	−	0.937043i	0.457845	−	0.889032i	$-0.348621\pi$
$42$		0			0
$43$	−4.46410	+	7.73205i	−0.680769	+	1.17913i	0.293977	+	0.955812i	$0.405021\pi$
$43$	−4.46410	+	7.73205i	−0.680769	+	1.17913i	−0.974746	+	0.223314i	$0.928312\pi$
$44$	−1.73205			−0.261116
$45$		0			0
$46$	−3.46410	+	6.00000i	−0.510754	+	0.884652i
$47$	−0.464102			−0.0676962			−0.0338481	−	0.999427i	$-0.510776\pi$
$47$	−0.464102			−0.0676962			−0.0338481	+	0.999427i	$0.510776\pi$
$48$		0			0
$49$	3.46410	+	6.00000i	0.494872	+	0.857143i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$		0			0
$52$	−1.59808	+	3.23205i	−0.221613	+	0.448205i
$53$	6.46410			0.887913			0.443956	−	0.896048i	$-0.353575\pi$
$53$	6.46410			0.887913			0.443956	+	0.896048i	$0.353575\pi$
$54$		0			0
$55$	0.866025	+	1.50000i	0.116775	+	0.202260i
$56$	0.133975	−	0.232051i	0.0179031	−	0.0310091i
$57$		0			0
$58$	−1.26795	+	2.19615i	−0.166490	+	0.288369i
$59$	1.73205	−	3.00000i	0.225494	−	0.390567i	−0.730974	−	0.682406i	$-0.760934\pi$
$59$	1.73205	−	3.00000i	0.225494	−	0.390567i	0.956467	+	0.291839i	$0.0942671\pi$
$60$		0			0
$61$	−2.26795	+	3.92820i	−0.290381	+	0.502955i	−0.973900	−	0.226978i	$-0.927115\pi$
$61$	−2.26795	+	3.92820i	−0.290381	+	0.502955i	0.683519	+	0.729933i	$0.260449\pi$
$62$	−0.267949	−	0.464102i	−0.0340296	−	0.0589410i
$63$		0			0
$64$	1.00000			0.125000
$65$	3.59808	−	0.232051i	0.446286	−	0.0287824i
$66$		0			0
$67$	4.19615	+	7.26795i	0.512642	+	0.887921i	0.999893	+	0.0146593i	$0.00466637\pi$
$67$	4.19615	+	7.26795i	0.512642	+	0.887921i	−0.487251	+	0.873262i	$0.662000\pi$
$68$	3.46410	+	6.00000i	0.420084	+	0.727607i
$69$		0			0
$70$	−0.267949			−0.0320261
$71$	6.46410	−	11.1962i	0.767148	−	1.32874i	−0.171956	−	0.985105i	$-0.555009\pi$
$71$	6.46410	−	11.1962i	0.767148	−	1.32874i	0.939104	−	0.343634i	$-0.111658\pi$
$72$		0			0
$73$	−10.9282			−1.27905			−0.639525	−	0.768771i	$-0.720869\pi$
$73$	−10.9282			−1.27905			−0.639525	+	0.768771i	$0.720869\pi$
$74$	−1.59808	+	2.76795i	−0.185773	+	0.321768i
$75$		0			0
$76$	−2.50000	−	4.33013i	−0.286770	−	0.496700i
$77$	−0.464102			−0.0528893
$78$		0			0
$79$	15.8564			1.78399			0.891993	−	0.452050i	$-0.149307\pi$
$79$	15.8564			1.78399			0.891993	+	0.452050i	$0.149307\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$		0			0
$82$	3.46410	−	6.00000i	0.382546	−	0.662589i
$83$	−2.53590			−0.278351			−0.139176	−	0.990268i	$-0.544445\pi$
$83$	−2.53590			−0.278351			−0.139176	+	0.990268i	$0.544445\pi$
$84$		0			0
$85$	3.46410	−	6.00000i	0.375735	−	0.650791i
$86$	−8.92820			−0.962753
$87$		0			0
$88$	−0.866025	−	1.50000i	−0.0923186	−	0.159901i
$89$	−2.59808	−	4.50000i	−0.275396	−	0.476999i	0.694839	−	0.719165i	$-0.255475\pi$
$89$	−2.59808	−	4.50000i	−0.275396	−	0.476999i	−0.970235	+	0.242166i	$0.922142\pi$
$90$		0			0
$91$	−0.428203	+	0.866025i	−0.0448879	+	0.0907841i
$92$	−6.92820			−0.722315
$93$		0			0
$94$	−0.232051	−	0.401924i	−0.0239342	−	0.0414553i
$95$	−2.50000	+	4.33013i	−0.256495	+	0.444262i
$96$		0			0
$97$	−5.26795	+	9.12436i	−0.534879	+	0.926438i	0.464290	+	0.885683i	$0.346310\pi$
$97$	−5.26795	+	9.12436i	−0.534879	+	0.926438i	−0.999169	+	0.0407547i	$0.987024\pi$
$98$	−3.46410	+	6.00000i	−0.349927	+	0.606092i
$99$		0			0
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	−8.19615	−	14.1962i	−0.815548	−	1.41257i	−0.908934	−	0.416940i	$-0.863103\pi$
$101$	−8.19615	−	14.1962i	−0.815548	−	1.41257i	0.0933864	−	0.995630i	$-0.470231\pi$
$102$		0			0
$103$	−6.66025			−0.656254			−0.328127	−	0.944634i	$-0.606417\pi$
$103$	−6.66025			−0.656254			−0.328127	+	0.944634i	$0.606417\pi$
$104$	−3.59808	+	0.232051i	−0.352820	+	0.0227545i
$105$		0			0
$106$	3.23205	+	5.59808i	0.313925	+	0.543733i
$107$	4.26795	+	7.39230i	0.412598	+	0.714641i	0.995173	−	0.0981360i	$-0.0312880\pi$
$107$	4.26795	+	7.39230i	0.412598	+	0.714641i	−0.582575	+	0.812777i	$0.697955\pi$
$108$		0			0
$109$	−4.92820			−0.472036			−0.236018	−	0.971749i	$-0.575842\pi$
$109$	−4.92820			−0.472036			−0.236018	+	0.971749i	$0.575842\pi$
$110$	−0.866025	+	1.50000i	−0.0825723	+	0.143019i
$111$		0			0
$112$	0.267949			0.0253188
$113$	−6.00000	+	10.3923i	−0.564433	+	0.977626i	0.432670	+	0.901553i	$0.357572\pi$
$113$	−6.00000	+	10.3923i	−0.564433	+	0.977626i	−0.997102	+	0.0760733i	$0.975762\pi$
$114$		0			0
$115$	3.46410	+	6.00000i	0.323029	+	0.559503i
$116$	−2.53590			−0.235452
$117$		0			0
$118$	3.46410			0.318896
$119$	0.928203	+	1.60770i	0.0850883	+	0.147377i
$120$		0			0
$121$	4.00000	−	6.92820i	0.363636	−	0.629837i
$122$	−4.53590			−0.410661
$123$		0			0
$124$	0.267949	−	0.464102i	0.0240625	−	0.0416776i
$125$	1.00000			0.0894427
$126$		0			0
$127$	−9.59808	−	16.6244i	−0.851692	−	1.47517i	−0.879681	−	0.475565i	$-0.842244\pi$
$127$	−9.59808	−	16.6244i	−0.851692	−	1.47517i	0.0279892	−	0.999608i	$-0.491090\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		0			0
$130$	2.00000	+	3.00000i	0.175412	+	0.263117i
$131$	6.80385			0.594455			0.297227	−	0.954807i	$-0.403938\pi$
$131$	6.80385			0.594455			0.297227	+	0.954807i	$0.403938\pi$
$132$		0			0
$133$	−0.669873	−	1.16025i	−0.0580854	−	0.100607i
$134$	−4.19615	+	7.26795i	−0.362492	+	0.627855i
$135$		0			0
$136$	−3.46410	+	6.00000i	−0.297044	+	0.514496i
$137$	10.7321	−	18.5885i	0.916901	−	1.58812i	0.112807	−	0.993617i	$-0.464016\pi$
$137$	10.7321	−	18.5885i	0.916901	−	1.58812i	0.804094	−	0.594502i	$-0.202651\pi$
$138$		0			0
$139$	−2.03590	+	3.52628i	−0.172683	+	0.299095i	−0.939357	−	0.342941i	$-0.888577\pi$
$139$	−2.03590	+	3.52628i	−0.172683	+	0.299095i	0.766674	+	0.642036i	$0.221910\pi$
$140$	−0.133975	−	0.232051i	−0.0113229	−	0.0196119i
$141$		0			0
$142$	12.9282			1.08491
$143$	3.46410	+	5.19615i	0.289683	+	0.434524i
$144$		0			0
$145$	1.26795	+	2.19615i	0.105297	+	0.182381i
$146$	−5.46410	−	9.46410i	−0.452212	−	0.783255i
$147$		0			0
$148$	−3.19615			−0.262722
$149$	−0.464102	+	0.803848i	−0.0380207	+	0.0658538i	−0.884410	−	0.466712i	$-0.845439\pi$
$149$	−0.464102	+	0.803848i	−0.0380207	+	0.0658538i	0.846389	+	0.532565i	$0.178772\pi$
$150$		0			0
$151$	6.39230			0.520198			0.260099	−	0.965582i	$-0.416245\pi$
$151$	6.39230			0.520198			0.260099	+	0.965582i	$0.416245\pi$
$152$	2.50000	−	4.33013i	0.202777	−	0.351220i
$153$		0			0
$154$	−0.232051	−	0.401924i	−0.0186992	−	0.0323879i
$155$	−0.535898			−0.0430444
$156$		0			0
$157$	−17.0526			−1.36094			−0.680471	−	0.732775i	$-0.738225\pi$
$157$	−17.0526			−1.36094			−0.680471	+	0.732775i	$0.738225\pi$
$158$	7.92820	+	13.7321i	0.630734	+	1.09246i
$159$		0			0
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	−1.85641			−0.146305
$162$		0			0
$163$	8.00000	−	13.8564i	0.626608	−	1.08532i	−0.361619	−	0.932326i	$-0.617776\pi$
$163$	8.00000	−	13.8564i	0.626608	−	1.08532i	0.988227	−	0.152992i	$-0.0488907\pi$
$164$	6.92820			0.541002
$165$		0			0
$166$	−1.26795	−	2.19615i	−0.0984119	−	0.170454i
$167$	−6.23205	−	10.7942i	−0.482251	−	0.835282i	0.517542	−	0.855658i	$-0.326847\pi$
$167$	−6.23205	−	10.7942i	−0.482251	−	0.835282i	−0.999792	+	0.0203754i	$0.993514\pi$
$168$		0			0
$169$	12.8923	−	1.66987i	0.991716	−	0.128452i
$170$	6.92820			0.531369
$171$		0			0
$172$	−4.46410	−	7.73205i	−0.340385	−	0.589563i
$173$	−6.69615	+	11.5981i	−0.509099	+	0.881785i	0.490845	+	0.871247i	$0.336688\pi$
$173$	−6.69615	+	11.5981i	−0.509099	+	0.881785i	−0.999944	+	0.0105387i	$0.996645\pi$
$174$		0			0
$175$	−0.133975	+	0.232051i	−0.0101275	+	0.0175414i
$176$	0.866025	−	1.50000i	0.0652791	−	0.113067i
$177$		0			0
$178$	2.59808	−	4.50000i	0.194734	−	0.337289i
$179$	−5.19615	−	9.00000i	−0.388379	−	0.672692i	0.603853	−	0.797096i	$-0.293631\pi$
$179$	−5.19615	−	9.00000i	−0.388379	−	0.672692i	−0.992232	+	0.124404i	$0.960298\pi$
$180$		0			0
$181$	14.0000			1.04061			0.520306	−	0.853980i	$-0.325818\pi$
$181$	14.0000			1.04061			0.520306	+	0.853980i	$0.325818\pi$
$182$	−0.964102	+	0.0621778i	−0.0714640	+	0.00460893i
$183$		0			0
$184$	−3.46410	−	6.00000i	−0.255377	−	0.442326i
$185$	1.59808	+	2.76795i	0.117493	+	0.203504i
$186$		0			0
$187$	12.0000			0.877527
$188$	0.232051	−	0.401924i	0.0169240	−	0.0293133i
$189$		0			0
$190$	−5.00000			−0.362738
$191$	−3.00000	+	5.19615i	−0.217072	+	0.375980i	−0.953912	−	0.300088i	$-0.902984\pi$
$191$	−3.00000	+	5.19615i	−0.217072	+	0.375980i	0.736839	+	0.676068i	$0.236317\pi$
$192$		0			0
$193$	−10.9282	−	18.9282i	−0.786629	−	1.36248i	−0.928021	−	0.372528i	$-0.878491\pi$
$193$	−10.9282	−	18.9282i	−0.786629	−	1.36248i	0.141392	−	0.989954i	$-0.454842\pi$
$194$	−10.5359			−0.756433
$195$		0			0
$196$	−6.92820			−0.494872
$197$	−4.16025	−	7.20577i	−0.296406	−	0.513390i	0.678905	−	0.734226i	$-0.262455\pi$
$197$	−4.16025	−	7.20577i	−0.296406	−	0.513390i	−0.975311	+	0.220836i	$0.929121\pi$
$198$		0			0
$199$	−1.00000	+	1.73205i	−0.0708881	+	0.122782i	−0.899291	−	0.437351i	$-0.855917\pi$
$199$	−1.00000	+	1.73205i	−0.0708881	+	0.122782i	0.828403	+	0.560133i	$0.189250\pi$
$200$	−1.00000			−0.0707107
$201$		0			0
$202$	8.19615	−	14.1962i	0.576679	−	0.998838i
$203$	−0.679492			−0.0476910
$204$		0			0
$205$	−3.46410	−	6.00000i	−0.241943	−	0.419058i
$206$	−3.33013	−	5.76795i	−0.232021	−	0.401872i
$207$		0			0
$208$	−2.00000	−	3.00000i	−0.138675	−	0.208013i
$209$	−8.66025			−0.599042
$210$		0			0
$211$	−12.8923	−	22.3301i	−0.887543	−	1.53727i	−0.842771	−	0.538272i	$-0.819077\pi$
$211$	−12.8923	−	22.3301i	−0.887543	−	1.53727i	−0.0447718	−	0.998997i	$-0.514256\pi$
$212$	−3.23205	+	5.59808i	−0.221978	+	0.384477i
$213$		0			0
$214$	−4.26795	+	7.39230i	−0.291751	+	0.505328i
$215$	−4.46410	+	7.73205i	−0.304449	+	0.527321i
$216$		0			0
$217$	0.0717968	−	0.124356i	0.00487388	−	0.00844181i
$218$	−2.46410	−	4.26795i	−0.166890	−	0.289062i
$219$		0			0
$220$	−1.73205			−0.116775
$221$	11.0718	−	22.3923i	0.744770	−	1.50627i
$222$		0			0
$223$	2.40192	+	4.16025i	0.160845	+	0.278591i	0.935172	−	0.354194i	$-0.115245\pi$
$223$	2.40192	+	4.16025i	0.160845	+	0.278591i	−0.774327	+	0.632785i	$0.781912\pi$
$224$	0.133975	+	0.232051i	0.00895155	+	0.0155045i
$225$		0			0
$226$	−12.0000			−0.798228
$227$	−4.73205	+	8.19615i	−0.314077	+	0.543998i	−0.979241	−	0.202700i	$-0.935028\pi$
$227$	−4.73205	+	8.19615i	−0.314077	+	0.543998i	0.665164	+	0.746698i	$0.268362\pi$
$228$		0			0
$229$	2.00000			0.132164			0.0660819	−	0.997814i	$-0.478950\pi$
$229$	2.00000			0.132164			0.0660819	+	0.997814i	$0.478950\pi$
$230$	−3.46410	+	6.00000i	−0.228416	+	0.395628i
$231$		0			0
$232$	−1.26795	−	2.19615i	−0.0832449	−	0.144184i
$233$	10.3923			0.680823			0.340411	−	0.940277i	$-0.389434\pi$
$233$	10.3923			0.680823			0.340411	+	0.940277i	$0.389434\pi$
$234$		0			0
$235$	−0.464102			−0.0302747
$236$	1.73205	+	3.00000i	0.112747	+	0.195283i
$237$		0			0
$238$	−0.928203	+	1.60770i	−0.0601665	+	0.104211i
$239$	15.4641			1.00029			0.500145	−	0.865942i	$-0.333280\pi$
$239$	15.4641			1.00029			0.500145	+	0.865942i	$0.333280\pi$
$240$		0			0
$241$	3.50000	−	6.06218i	0.225455	−	0.390499i	−0.731001	−	0.682376i	$-0.760947\pi$
$241$	3.50000	−	6.06218i	0.225455	−	0.390499i	0.956456	+	0.291877i	$0.0942799\pi$
$242$	8.00000			0.514259
$243$		0			0
$244$	−2.26795	−	3.92820i	−0.145191	−	0.251477i
$245$	3.46410	+	6.00000i	0.221313	+	0.383326i
$246$		0			0
$247$	−7.99038	+	16.1603i	−0.508416	+	1.02825i
$248$	0.535898			0.0340296
$249$		0			0
$250$	0.500000	+	0.866025i	0.0316228	+	0.0547723i
$251$	2.59808	−	4.50000i	0.163989	−	0.284037i	−0.772307	−	0.635250i	$-0.780897\pi$
$251$	2.59808	−	4.50000i	0.163989	−	0.284037i	0.936296	+	0.351212i	$0.114230\pi$
$252$		0			0
$253$	−6.00000	+	10.3923i	−0.377217	+	0.653359i
$254$	9.59808	−	16.6244i	0.602237	−	1.04310i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−7.26795	−	12.5885i	−0.453362	−	0.785246i	0.545230	−	0.838286i	$-0.316442\pi$
$257$	−7.26795	−	12.5885i	−0.453362	−	0.785246i	−0.998592	+	0.0530400i	$0.983109\pi$
$258$		0			0
$259$	−0.856406			−0.0532145
$260$	−1.59808	+	3.23205i	−0.0991085	+	0.200443i
$261$		0			0
$262$	3.40192	+	5.89230i	0.210172	+	0.364028i
$263$	15.2321	+	26.3827i	0.939248	+	1.62683i	0.766877	+	0.641794i	$0.221810\pi$
$263$	15.2321	+	26.3827i	0.939248	+	1.62683i	0.172371	+	0.985032i	$0.444857\pi$
$264$		0			0
$265$	6.46410			0.397087
$266$	0.669873	−	1.16025i	0.0410725	−	0.0711397i
$267$		0			0
$268$	−8.39230			−0.512642
$269$	12.9282	−	22.3923i	0.788246	−	1.36528i	−0.138794	−	0.990321i	$-0.544323\pi$
$269$	12.9282	−	22.3923i	0.788246	−	1.36528i	0.927040	−	0.374962i	$-0.122344\pi$
$270$		0			0
$271$	−9.66025	−	16.7321i	−0.586819	−	1.01640i	−0.994646	−	0.103341i	$-0.967047\pi$
$271$	−9.66025	−	16.7321i	−0.586819	−	1.01640i	0.407827	−	0.913059i	$-0.366287\pi$
$272$	−6.92820			−0.420084
$273$		0			0
$274$	21.4641			1.29669
$275$	0.866025	+	1.50000i	0.0522233	+	0.0904534i
$276$		0			0
$277$	6.79423	−	11.7679i	0.408226	−	0.707068i	−0.586465	−	0.809974i	$-0.699481\pi$
$277$	6.79423	−	11.7679i	0.408226	−	0.707068i	0.994691	+	0.102907i	$0.0328143\pi$
$278$	−4.07180			−0.244210
$279$		0			0
$280$	0.133975	−	0.232051i	0.00800651	−	0.0138677i
$281$	1.85641			0.110744			0.0553720	−	0.998466i	$-0.482366\pi$
$281$	1.85641			0.110744			0.0553720	+	0.998466i	$0.482366\pi$
$282$		0			0
$283$	−5.73205	−	9.92820i	−0.340735	−	0.590170i	0.643834	−	0.765165i	$-0.277343\pi$
$283$	−5.73205	−	9.92820i	−0.340735	−	0.590170i	−0.984569	+	0.174994i	$0.944009\pi$
$284$	6.46410	+	11.1962i	0.383574	+	0.664369i
$285$		0			0
$286$	−2.76795	+	5.59808i	−0.163672	+	0.331021i
$287$	1.85641			0.109580
$288$		0			0
$289$	−15.5000	−	26.8468i	−0.911765	−	1.57922i
$290$	−1.26795	+	2.19615i	−0.0744565	+	0.128963i
$291$		0			0
$292$	5.46410	−	9.46410i	0.319762	−	0.553845i
$293$	3.69615	−	6.40192i	0.215932	−	0.374004i	−0.737629	−	0.675206i	$-0.764055\pi$
$293$	3.69615	−	6.40192i	0.215932	−	0.374004i	0.953560	+	0.301202i	$0.0973879\pi$
$294$		0			0
$295$	1.73205	−	3.00000i	0.100844	−	0.174667i
$296$	−1.59808	−	2.76795i	−0.0928863	−	0.160884i
$297$		0			0
$298$	−0.928203			−0.0537694
$299$	13.8564	+	20.7846i	0.801337	+	1.20201i
$300$		0			0
$301$	−1.19615	−	2.07180i	−0.0689451	−	0.119416i
$302$	3.19615	+	5.53590i	0.183918	+	0.318555i
$303$		0			0
$304$	5.00000			0.286770
$305$	−2.26795	+	3.92820i	−0.129862	+	0.224928i
$306$		0			0
$307$	−28.9282			−1.65102			−0.825510	−	0.564388i	$-0.809112\pi$
$307$	−28.9282			−1.65102			−0.825510	+	0.564388i	$0.809112\pi$
$308$	0.232051	−	0.401924i	0.0132223	−	0.0229017i
$309$		0			0
$310$	−0.267949	−	0.464102i	−0.0152185	−	0.0263592i
$311$	−20.7846			−1.17859			−0.589294	−	0.807919i	$-0.700594\pi$
$311$	−20.7846			−1.17859			−0.589294	+	0.807919i	$0.700594\pi$
$312$		0			0
$313$	30.3923			1.71787			0.858937	−	0.512081i	$-0.171125\pi$
$313$	30.3923			1.71787			0.858937	+	0.512081i	$0.171125\pi$
$314$	−8.52628	−	14.7679i	−0.481166	−	0.833404i
$315$		0			0
$316$	−7.92820	+	13.7321i	−0.445996	+	0.772488i
$317$	−6.46410			−0.363060			−0.181530	−	0.983385i	$-0.558105\pi$
$317$	−6.46410			−0.363060			−0.181530	+	0.983385i	$0.558105\pi$
$318$		0			0
$319$	−2.19615	+	3.80385i	−0.122961	+	0.212975i
$320$	1.00000			0.0559017
$321$		0			0
$322$	−0.928203	−	1.60770i	−0.0517267	−	0.0895933i
$323$	17.3205	+	30.0000i	0.963739	+	1.66924i
$324$		0			0
$325$	3.59808	−	0.232051i	0.199585	−	0.0128719i
$326$	16.0000			0.886158
$327$		0			0
$328$	3.46410	+	6.00000i	0.191273	+	0.331295i
$329$	0.0621778	−	0.107695i	0.00342797	−	0.00593743i
$330$		0			0
$331$	−0.535898	+	0.928203i	−0.0294556	+	0.0510187i	−0.880377	−	0.474274i	$-0.842711\pi$
$331$	−0.535898	+	0.928203i	−0.0294556	+	0.0510187i	0.850922	+	0.525292i	$0.176044\pi$
$332$	1.26795	−	2.19615i	0.0695878	−	0.120530i
$333$		0			0
$334$	6.23205	−	10.7942i	0.341003	−	0.590634i
$335$	4.19615	+	7.26795i	0.229260	+	0.397090i
$336$		0			0
$337$	6.39230			0.348211			0.174106	−	0.984727i	$-0.444297\pi$
$337$	6.39230			0.348211			0.174106	+	0.984727i	$0.444297\pi$
$338$	7.89230	+	10.3301i	0.429285	+	0.561885i
$339$		0			0
$340$	3.46410	+	6.00000i	0.187867	+	0.325396i
$341$	−0.464102	−	0.803848i	−0.0251325	−	0.0435308i
$342$		0			0
$343$	−3.73205			−0.201512
$344$	4.46410	−	7.73205i	0.240688	−	0.416884i
$345$		0			0
$346$	−13.3923			−0.719975
$347$	−4.73205	+	8.19615i	−0.254030	+	0.439993i	−0.964632	−	0.263602i	$-0.915089\pi$
$347$	−4.73205	+	8.19615i	−0.254030	+	0.439993i	0.710602	+	0.703594i	$0.248423\pi$
$348$		0			0
$349$	−8.73205	−	15.1244i	−0.467416	−	0.809588i	0.531891	−	0.846813i	$-0.321482\pi$
$349$	−8.73205	−	15.1244i	−0.467416	−	0.809588i	−0.999307	+	0.0372247i	$0.988148\pi$
$350$	−0.267949			−0.0143225
$351$		0			0
$352$	1.73205			0.0923186
$353$	2.19615	+	3.80385i	0.116889	+	0.202458i	0.918533	−	0.395343i	$-0.129374\pi$
$353$	2.19615	+	3.80385i	0.116889	+	0.202458i	−0.801644	+	0.597802i	$0.796041\pi$
$354$		0			0
$355$	6.46410	−	11.1962i	0.343079	−	0.594230i
$356$	5.19615			0.275396
$357$		0			0
$358$	5.19615	−	9.00000i	0.274625	−	0.475665i
$359$	−24.9282			−1.31566			−0.657830	−	0.753166i	$-0.728526\pi$
$359$	−24.9282			−1.31566			−0.657830	+	0.753166i	$0.728526\pi$
$360$		0			0
$361$	−3.00000	−	5.19615i	−0.157895	−	0.273482i
$362$	7.00000	+	12.1244i	0.367912	+	0.637242i
$363$		0			0
$364$	−0.535898	−	0.803848i	−0.0280887	−	0.0421331i
$365$	−10.9282			−0.572008
$366$		0			0
$367$	−4.80385	−	8.32051i	−0.250759	−	0.434327i	0.712976	−	0.701188i	$-0.247347\pi$
$367$	−4.80385	−	8.32051i	−0.250759	−	0.434327i	−0.963735	+	0.266861i	$0.914013\pi$
$368$	3.46410	−	6.00000i	0.180579	−	0.312772i
$369$		0			0
$370$	−1.59808	+	2.76795i	−0.0830800	+	0.143899i
$371$	−0.866025	+	1.50000i	−0.0449618	+	0.0778761i
$372$		0			0
$373$	−16.9282	+	29.3205i	−0.876509	+	1.51816i	−0.0213627	+	0.999772i	$0.506800\pi$
$373$	−16.9282	+	29.3205i	−0.876509	+	1.51816i	−0.855146	+	0.518387i	$0.826533\pi$
$374$	6.00000	+	10.3923i	0.310253	+	0.537373i
$375$		0			0
$376$	0.464102			0.0239342
$377$	5.07180	+	7.60770i	0.261211	+	0.391816i
$378$		0			0
$379$	0.500000	+	0.866025i	0.0256833	+	0.0444847i	0.878581	−	0.477593i	$-0.158491\pi$
$379$	0.500000	+	0.866025i	0.0256833	+	0.0444847i	−0.852898	+	0.522077i	$0.825157\pi$
$380$	−2.50000	−	4.33013i	−0.128247	−	0.222131i
$381$		0			0
$382$	−6.00000			−0.306987
$383$	−10.3923	+	18.0000i	−0.531022	+	0.919757i	0.468323	+	0.883558i	$0.344859\pi$
$383$	−10.3923	+	18.0000i	−0.531022	+	0.919757i	−0.999345	+	0.0361995i	$0.988475\pi$
$384$		0			0
$385$	−0.464102			−0.0236528
$386$	10.9282	−	18.9282i	0.556231	−	0.963420i
$387$		0			0
$388$	−5.26795	−	9.12436i	−0.267440	−	0.463219i
$389$	−1.85641			−0.0941235			−0.0470618	−	0.998892i	$-0.514986\pi$
$389$	−1.85641			−0.0941235			−0.0470618	+	0.998892i	$0.514986\pi$
$390$		0			0
$391$	48.0000			2.42746
$392$	−3.46410	−	6.00000i	−0.174964	−	0.303046i
$393$		0			0
$394$	4.16025	−	7.20577i	0.209591	−	0.363022i
$395$	15.8564			0.797822
$396$		0			0
$397$	−7.06218	+	12.2321i	−0.354441	+	0.613909i	−0.987022	−	0.160585i	$-0.948662\pi$
$397$	−7.06218	+	12.2321i	−0.354441	+	0.613909i	0.632582	+	0.774494i	$0.281995\pi$
$398$	−2.00000			−0.100251
$399$		0			0
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	−13.7942	−	23.8923i	−0.688851	−	1.19312i	−0.972210	−	0.234111i	$-0.924782\pi$
$401$	−13.7942	−	23.8923i	−0.688851	−	1.19312i	0.283359	−	0.959014i	$-0.408551\pi$
$402$		0			0
$403$	−1.92820	+	0.124356i	−0.0960506	+	0.00619460i
$404$	16.3923			0.815548
$405$		0			0
$406$	−0.339746	−	0.588457i	−0.0168613	−	0.0292046i
$407$	−2.76795	+	4.79423i	−0.137202	+	0.237641i
$408$		0			0
$409$	−12.8923	+	22.3301i	−0.637483	+	1.10415i	0.348500	+	0.937309i	$0.386691\pi$
$409$	−12.8923	+	22.3301i	−0.637483	+	1.10415i	−0.985983	+	0.166845i	$0.946642\pi$
$410$	3.46410	−	6.00000i	0.171080	−	0.296319i
$411$		0			0
$412$	3.33013	−	5.76795i	0.164064	−	0.284166i
$413$	0.464102	+	0.803848i	0.0228369	+	0.0395548i
$414$		0			0
$415$	−2.53590			−0.124482
$416$	1.59808	−	3.23205i	0.0783521	−	0.158464i
$417$		0			0
$418$	−4.33013	−	7.50000i	−0.211793	−	0.366837i
$419$	7.73205	+	13.3923i	0.377735	+	0.654257i	0.990732	−	0.135828i	$-0.0433696\pi$
$419$	7.73205	+	13.3923i	0.377735	+	0.654257i	−0.612997	+	0.790085i	$0.710036\pi$
$420$		0			0
$421$	14.9282			0.727556			0.363778	−	0.931486i	$-0.381487\pi$
$421$	14.9282			0.727556			0.363778	+	0.931486i	$0.381487\pi$
$422$	12.8923	−	22.3301i	0.627588	−	1.08701i
$423$		0			0
$424$	−6.46410			−0.313925
$425$	3.46410	−	6.00000i	0.168034	−	0.291043i
$426$		0			0
$427$	−0.607695	−	1.05256i	−0.0294084	−	0.0509369i
$428$	−8.53590			−0.412598
$429$		0			0
$430$	−8.92820			−0.430556
$431$	−18.9282	−	32.7846i	−0.911739	−	1.57918i	−0.811606	−	0.584205i	$-0.801406\pi$
$431$	−18.9282	−	32.7846i	−0.911739	−	1.57918i	−0.100133	−	0.994974i	$-0.531927\pi$
$432$		0			0
$433$	−0.535898	+	0.928203i	−0.0257536	+	0.0446066i	−0.878615	−	0.477531i	$-0.841532\pi$
$433$	−0.535898	+	0.928203i	−0.0257536	+	0.0446066i	0.852861	+	0.522137i	$0.174865\pi$
$434$	0.143594			0.00689271
$435$		0			0
$436$	2.46410	−	4.26795i	0.118009	−	0.204398i
$437$	−34.6410			−1.65710
$438$		0			0
$439$	9.73205	+	16.8564i	0.464485	+	0.804512i	0.999178	−	0.0405342i	$-0.0129060\pi$
$439$	9.73205	+	16.8564i	0.464485	+	0.804512i	−0.534693	+	0.845047i	$0.679573\pi$
$440$	−0.866025	−	1.50000i	−0.0412861	−	0.0715097i
$441$		0			0
$442$	24.9282	−	1.60770i	1.18571	−	0.0764703i
$443$	5.32051			0.252785			0.126392	−	0.991980i	$-0.459660\pi$
$443$	5.32051			0.252785			0.126392	+	0.991980i	$0.459660\pi$
$444$		0			0
$445$	−2.59808	−	4.50000i	−0.123161	−	0.213320i
$446$	−2.40192	+	4.16025i	−0.113734	+	0.196994i
$447$		0			0
$448$	−0.133975	+	0.232051i	−0.00632970	+	0.0109634i
$449$	−1.79423	+	3.10770i	−0.0846749	+	0.146661i	−0.905253	−	0.424874i	$-0.860318\pi$
$449$	−1.79423	+	3.10770i	−0.0846749	+	0.146661i	0.820578	+	0.571535i	$0.193652\pi$
$450$		0			0
$451$	6.00000	−	10.3923i	0.282529	−	0.489355i
$452$	−6.00000	−	10.3923i	−0.282216	−	0.488813i
$453$		0			0
$454$	−9.46410			−0.444172
$455$	−0.428203	+	0.866025i	−0.0200745	+	0.0405999i
$456$		0			0
$457$	11.0000	+	19.0526i	0.514558	+	0.891241i	0.999857	+	0.0168929i	$0.00537742\pi$
$457$	11.0000	+	19.0526i	0.514558	+	0.891241i	−0.485299	+	0.874348i	$0.661289\pi$
$458$	1.00000	+	1.73205i	0.0467269	+	0.0809334i
$459$		0			0
$460$	−6.92820			−0.323029
$461$	1.26795	−	2.19615i	0.0590543	−	0.102285i	−0.834987	−	0.550270i	$-0.814525\pi$
$461$	1.26795	−	2.19615i	0.0590543	−	0.102285i	0.894041	+	0.447985i	$0.147858\pi$
$462$		0			0
$463$	20.2487			0.941037			0.470519	−	0.882390i	$-0.344067\pi$
$463$	20.2487			0.941037			0.470519	+	0.882390i	$0.344067\pi$
$464$	1.26795	−	2.19615i	0.0588631	−	0.101954i
$465$		0			0
$466$	5.19615	+	9.00000i	0.240707	+	0.416917i
$467$	16.3923			0.758545			0.379273	−	0.925285i	$-0.376174\pi$
$467$	16.3923			0.758545			0.379273	+	0.925285i	$0.376174\pi$
$468$		0			0
$469$	−2.24871			−0.103836
$470$	−0.232051	−	0.401924i	−0.0107037	−	0.0185394i
$471$		0			0
$472$	−1.73205	+	3.00000i	−0.0797241	+	0.138086i
$473$	−15.4641			−0.711040
$474$		0			0
$475$	−2.50000	+	4.33013i	−0.114708	+	0.198680i
$476$	−1.85641			−0.0850883
$477$		0			0
$478$	7.73205	+	13.3923i	0.353656	+	0.612550i
$479$	−4.73205	−	8.19615i	−0.216213	−	0.374492i	0.737434	−	0.675419i	$-0.236037\pi$
$479$	−4.73205	−	8.19615i	−0.216213	−	0.374492i	−0.953647	+	0.300927i	$0.902704\pi$
$480$		0			0
$481$	6.39230	+	9.58846i	0.291464	+	0.437196i
$482$	7.00000			0.318841
$483$		0			0
$484$	4.00000	+	6.92820i	0.181818	+	0.314918i
$485$	−5.26795	+	9.12436i	−0.239205	+	0.414316i
$486$		0			0
$487$	−14.7942	+	25.6244i	−0.670390	+	1.16115i	0.307403	+	0.951579i	$0.400540\pi$
$487$	−14.7942	+	25.6244i	−0.670390	+	1.16115i	−0.977793	+	0.209571i	$0.932793\pi$
$488$	2.26795	−	3.92820i	0.102665	−	0.177821i
$489$		0			0
$490$	−3.46410	+	6.00000i	−0.156492	+	0.271052i
$491$	15.5263	+	26.8923i	0.700691	+	1.21363i	0.968224	+	0.250084i	$0.0804582\pi$
$491$	15.5263	+	26.8923i	0.700691	+	1.21363i	−0.267533	+	0.963549i	$0.586208\pi$
$492$		0			0
$493$	17.5692			0.791278
$494$	−17.9904	+	1.16025i	−0.809426	+	0.0522023i
$495$		0			0
$496$	0.267949	+	0.464102i	0.0120313	+	0.0208388i
$497$	1.73205	+	3.00000i	0.0776931	+	0.134568i
$498$		0			0
$499$	−28.0000			−1.25345			−0.626726	−	0.779240i	$-0.715605\pi$
$499$	−28.0000			−1.25345			−0.626726	+	0.779240i	$0.715605\pi$
$500$	−0.500000	+	0.866025i	−0.0223607	+	0.0387298i
$501$		0			0
$502$	5.19615			0.231916
$503$	−13.6244	+	23.5981i	−0.607480	+	1.05219i	0.384174	+	0.923261i	$0.374486\pi$
$503$	−13.6244	+	23.5981i	−0.607480	+	1.05219i	−0.991654	+	0.128926i	$0.958847\pi$
$504$		0			0
$505$	−8.19615	−	14.1962i	−0.364724	−	0.631720i
$506$	−12.0000			−0.533465
$507$		0			0
$508$	19.1962			0.851692
$509$	−16.2679	−	28.1769i	−0.721064	−	1.24892i	−0.960574	−	0.278026i	$-0.910320\pi$
$509$	−16.2679	−	28.1769i	−0.721064	−	1.24892i	0.239509	−	0.970894i	$-0.423013\pi$
$510$		0			0
$511$	1.46410	−	2.53590i	0.0647680	−	0.112182i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	7.26795	−	12.5885i	0.320575	−	0.555253i
$515$	−6.66025			−0.293486
$516$		0			0
$517$	−0.401924	−	0.696152i	−0.0176766	−	0.0306167i
$518$	−0.428203	−	0.741670i	−0.0188142	−	0.0325871i
$519$		0			0
$520$	−3.59808	+	0.232051i	−0.157786	+	0.0101761i
$521$	−0.124356			−0.00544812			−0.00272406	−	0.999996i	$-0.500867\pi$
$521$	−0.124356			−0.00544812			−0.00272406	+	0.999996i	$0.500867\pi$
$522$		0			0
$523$	−17.3923	−	30.1244i	−0.760512	−	1.31725i	−0.942587	−	0.333961i	$-0.891614\pi$
$523$	−17.3923	−	30.1244i	−0.760512	−	1.31725i	0.182074	−	0.983285i	$-0.441719\pi$
$524$	−3.40192	+	5.89230i	−0.148614	+	0.257407i
$525$		0			0
$526$	−15.2321	+	26.3827i	−0.664149	+	1.15034i
$527$	−1.85641	+	3.21539i	−0.0808663	+	0.140065i
$528$		0			0
$529$	−12.5000	+	21.6506i	−0.543478	+	0.941332i
$530$	3.23205	+	5.59808i	0.140391	+	0.243165i
$531$		0			0
$532$	1.33975			0.0580854
$533$	−13.8564	−	20.7846i	−0.600188	−	0.900281i
$534$		0			0
$535$	4.26795	+	7.39230i	0.184520	+	0.319597i
$536$	−4.19615	−	7.26795i	−0.181246	−	0.313928i
$537$		0			0
$538$	25.8564			1.11475
$539$	−6.00000	+	10.3923i	−0.258438	+	0.447628i
$540$		0			0
$541$	−31.4641			−1.35275			−0.676374	−	0.736559i	$-0.736450\pi$
$541$	−31.4641			−1.35275			−0.676374	+	0.736559i	$0.736450\pi$
$542$	9.66025	−	16.7321i	0.414943	−	0.718703i
$543$		0			0
$544$	−3.46410	−	6.00000i	−0.148522	−	0.257248i
$545$	−4.92820			−0.211101
$546$		0			0
$547$	32.2487			1.37886			0.689428	−	0.724355i	$-0.257862\pi$
$547$	32.2487			1.37886			0.689428	+	0.724355i	$0.257862\pi$
$548$	10.7321	+	18.5885i	0.458450	+	0.794060i
$549$		0			0
$550$	−0.866025	+	1.50000i	−0.0369274	+	0.0639602i
$551$	−12.6795			−0.540165
$552$		0			0
$553$	−2.12436	+	3.67949i	−0.0903368	+	0.156468i
$554$	13.5885			0.577318
$555$		0			0
$556$	−2.03590	−	3.52628i	−0.0863413	−	0.149548i
$557$	8.30385	+	14.3827i	0.351845	+	0.609414i	0.986573	−	0.163322i	$-0.0522210\pi$
$557$	8.30385	+	14.3827i	0.351845	+	0.609414i	−0.634727	+	0.772736i	$0.718888\pi$
$558$		0			0
$559$	−14.2679	+	28.8564i	−0.603470	+	1.22050i
$560$	0.267949			0.0113229
$561$		0			0
$562$	0.928203	+	1.60770i	0.0391539	+	0.0678165i
$563$	7.26795	−	12.5885i	0.306308	−	0.530540i	−0.671244	−	0.741236i	$-0.734240\pi$
$563$	7.26795	−	12.5885i	0.306308	−	0.530540i	0.977552	+	0.210696i	$0.0675731\pi$
$564$		0			0
$565$	−6.00000	+	10.3923i	−0.252422	+	0.437208i
$566$	5.73205	−	9.92820i	0.240936	−	0.417314i
$567$		0			0
$568$	−6.46410	+	11.1962i	−0.271228	+	0.469780i
$569$	3.40192	+	5.89230i	0.142616	+	0.247018i	0.928481	−	0.371380i	$-0.121115\pi$
$569$	3.40192	+	5.89230i	0.142616	+	0.247018i	−0.785865	+	0.618398i	$0.787782\pi$
$570$		0			0
$571$	25.7846			1.07905			0.539526	−	0.841969i	$-0.318603\pi$
$571$	25.7846			1.07905			0.539526	+	0.841969i	$0.318603\pi$
$572$	−6.23205	+	0.401924i	−0.260575	+	0.0168053i
$573$		0			0
$574$	0.928203	+	1.60770i	0.0387425	+	0.0671039i
$575$	3.46410	+	6.00000i	0.144463	+	0.250217i
$576$		0			0
$577$	2.00000			0.0832611			0.0416305	−	0.999133i	$-0.486745\pi$
$577$	2.00000			0.0832611			0.0416305	+	0.999133i	$0.486745\pi$
$578$	15.5000	−	26.8468i	0.644715	−	1.11668i
$579$		0			0
$580$	−2.53590			−0.105297
$581$	0.339746	−	0.588457i	0.0140950	−	0.0244133i
$582$		0			0
$583$	5.59808	+	9.69615i	0.231849	+	0.401574i
$584$	10.9282			0.452212
$585$		0			0
$586$	7.39230			0.305373
$587$	3.92820	+	6.80385i	0.162134	+	0.280825i	0.935634	−	0.352972i	$-0.114829\pi$
$587$	3.92820	+	6.80385i	0.162134	+	0.280825i	−0.773500	+	0.633797i	$0.781496\pi$
$588$		0			0
$589$	1.33975	−	2.32051i	0.0552033	−	0.0956149i
$590$	3.46410			0.142615
$591$		0			0
$592$	1.59808	−	2.76795i	0.0656805	−	0.113762i
$593$	−30.9282			−1.27007			−0.635035	−	0.772484i	$-0.719014\pi$
$593$	−30.9282			−1.27007			−0.635035	+	0.772484i	$0.719014\pi$
$594$		0			0
$595$	0.928203	+	1.60770i	0.0380526	+	0.0659091i
$596$	−0.464102	−	0.803848i	−0.0190103	−	0.0329269i
$597$		0			0
$598$	−11.0718	+	22.3923i	−0.452759	+	0.915689i
$599$	−34.3923			−1.40523			−0.702616	−	0.711569i	$-0.747985\pi$
$599$	−34.3923			−1.40523			−0.702616	+	0.711569i	$0.747985\pi$
$600$		0			0
$601$	10.8923	+	18.8660i	0.444306	+	0.769561i	0.998004	−	0.0631568i	$-0.0201168\pi$
$601$	10.8923	+	18.8660i	0.444306	+	0.769561i	−0.553697	+	0.832718i	$0.686784\pi$
$602$	1.19615	−	2.07180i	0.0487515	−	0.0844401i
$603$		0			0
$604$	−3.19615	+	5.53590i	−0.130050	+	0.225253i
$605$	4.00000	−	6.92820i	0.162623	−	0.281672i
$606$		0			0
$607$	1.59808	−	2.76795i	0.0648639	−	0.112348i	−0.831770	−	0.555121i	$-0.812672\pi$
$607$	1.59808	−	2.76795i	0.0648639	−	0.112348i	0.896634	+	0.442773i	$0.146005\pi$
$608$	2.50000	+	4.33013i	0.101388	+	0.175610i
$609$		0			0
$610$	−4.53590			−0.183653
$611$	−1.66987	+	0.107695i	−0.0675558	+	0.00435688i
$612$		0			0
$613$	16.2583	+	28.1603i	0.656668	+	1.13738i	0.981473	+	0.191601i	$0.0613679\pi$
$613$	16.2583	+	28.1603i	0.656668	+	1.13738i	−0.324805	+	0.945781i	$0.605299\pi$
$614$	−14.4641	−	25.0526i	−0.583724	−	1.01104i
$615$		0			0
$616$	0.464102			0.0186992
$617$	6.12436	−	10.6077i	0.246557	−	0.427050i	−0.716011	−	0.698089i	$-0.754034\pi$
$617$	6.12436	−	10.6077i	0.246557	−	0.427050i	0.962568	+	0.271039i	$0.0873673\pi$
$618$		0			0
$619$	−25.9282			−1.04214			−0.521071	−	0.853513i	$-0.674467\pi$
$619$	−25.9282			−1.04214			−0.521071	+	0.853513i	$0.674467\pi$
$620$	0.267949	−	0.464102i	0.0107611	−	0.0186388i
$621$		0			0
$622$	−10.3923	−	18.0000i	−0.416693	−	0.721734i
$623$	1.39230			0.0557815
$624$		0			0
$625$	1.00000			0.0400000
$626$	15.1962	+	26.3205i	0.607360	+	1.05198i
$627$		0			0
$628$	8.52628	−	14.7679i	0.340236	−	0.589305i
$629$	22.1436			0.882923
$630$		0			0
$631$	6.39230	−	11.0718i	0.254474	−	0.440761i	−0.710279	−	0.703920i	$-0.751431\pi$
$631$	6.39230	−	11.0718i	0.254474	−	0.440761i	0.964752	+	0.263159i	$0.0847645\pi$
$632$	−15.8564			−0.630734
$633$		0			0
$634$	−3.23205	−	5.59808i	−0.128361	−	0.222328i
$635$	−9.59808	−	16.6244i	−0.380888	−	0.659717i
$636$		0			0
$637$	13.8564	+	20.7846i	0.549011	+	0.823516i
$638$	−4.39230			−0.173893
$639$		0			0
$640$	0.500000	+	0.866025i	0.0197642	+	0.0342327i
$641$	−9.52628	+	16.5000i	−0.376265	+	0.651711i	−0.990516	−	0.137401i	$-0.956125\pi$
$641$	−9.52628	+	16.5000i	−0.376265	+	0.651711i	0.614250	+	0.789111i	$0.289459\pi$
$642$		0			0
$643$	−10.0000	+	17.3205i	−0.394362	+	0.683054i	−0.993019	−	0.117951i	$-0.962368\pi$
$643$	−10.0000	+	17.3205i	−0.394362	+	0.683054i	0.598658	+	0.801005i	$0.295701\pi$
$644$	0.928203	−	1.60770i	0.0365763	−	0.0633521i
$645$		0			0
$646$	−17.3205	+	30.0000i	−0.681466	+	1.18033i
$647$	−12.2321	−	21.1865i	−0.480892	−	0.832929i	0.518868	−	0.854854i	$-0.326354\pi$
$647$	−12.2321	−	21.1865i	−0.480892	−	0.832929i	−0.999760	+	0.0219258i	$0.993020\pi$
$648$		0			0
$649$	6.00000			0.235521
$650$	2.00000	+	3.00000i	0.0784465	+	0.117670i
$651$		0			0
$652$	8.00000	+	13.8564i	0.313304	+	0.542659i
$653$	2.76795	+	4.79423i	0.108318	+	0.187613i	0.915089	−	0.403252i	$-0.132120\pi$
$653$	2.76795	+	4.79423i	0.108318	+	0.187613i	−0.806771	+	0.590864i	$0.798787\pi$
$654$		0			0
$655$	6.80385			0.265848
$656$	−3.46410	+	6.00000i	−0.135250	+	0.234261i
$657$		0			0
$658$	0.124356			0.00484789
$659$	−11.1962	+	19.3923i	−0.436140	+	0.755417i	−0.997388	−	0.0722309i	$-0.976988\pi$
$659$	−11.1962	+	19.3923i	−0.436140	+	0.755417i	0.561248	+	0.827648i	$0.310321\pi$
$660$		0			0
$661$	11.9282	+	20.6603i	0.463953	+	0.803591i	0.999154	−	0.0411344i	$-0.0130972\pi$
$661$	11.9282	+	20.6603i	0.463953	+	0.803591i	−0.535200	+	0.844725i	$0.679764\pi$
$662$	−1.07180			−0.0416566
$663$		0			0
$664$	2.53590			0.0984119
$665$	−0.669873	−	1.16025i	−0.0259766	−	0.0449927i
$666$		0			0
$667$	−8.78461	+	15.2154i	−0.340141	+	0.589142i
$668$	12.4641			0.482251
$669$		0			0
$670$	−4.19615	+	7.26795i	−0.162112	+	0.280785i
$671$	−7.85641			−0.303293
$672$		0			0
$673$	21.8564	+	37.8564i	0.842503	+	1.45926i	0.887773	+	0.460282i	$0.152252\pi$
$673$	21.8564	+	37.8564i	0.842503	+	1.45926i	−0.0452700	+	0.998975i	$0.514415\pi$
$674$	3.19615	+	5.53590i	0.123111	+	0.213235i
$675$		0			0
$676$	−5.00000	+	12.0000i	−0.192308	+	0.461538i
$677$	−18.0000			−0.691796			−0.345898	−	0.938272i	$-0.612426\pi$
$677$	−18.0000			−0.691796			−0.345898	+	0.938272i	$0.612426\pi$
$678$		0			0
$679$	−1.41154	−	2.44486i	−0.0541700	−	0.0938253i
$680$	−3.46410	+	6.00000i	−0.132842	+	0.230089i
$681$		0			0
$682$	0.464102	−	0.803848i	0.0177714	−	0.0307809i
$683$	−3.33975	+	5.78461i	−0.127792	+	0.221342i	−0.922821	−	0.385230i	$-0.874122\pi$
$683$	−3.33975	+	5.78461i	−0.127792	+	0.221342i	0.795029	+	0.606571i	$0.207456\pi$
$684$		0			0
$685$	10.7321	−	18.5885i	0.410051	−	0.710228i
$686$	−1.86603	−	3.23205i	−0.0712452	−	0.123400i
$687$		0			0
$688$	8.92820			0.340385
$689$	23.2583	−	1.50000i	0.886072	−	0.0571454i
$690$		0			0
$691$	0.500000	+	0.866025i	0.0190209	+	0.0329452i	0.875379	−	0.483437i	$-0.160612\pi$
$691$	0.500000	+	0.866025i	0.0190209	+	0.0329452i	−0.856358	+	0.516382i	$0.827278\pi$
$692$	−6.69615	−	11.5981i	−0.254550	−	0.440893i
$693$		0			0
$694$	−9.46410			−0.359252
$695$	−2.03590	+	3.52628i	−0.0772260	+	0.133759i
$696$		0			0
$697$	−48.0000			−1.81813
$698$	8.73205	−	15.1244i	0.330513	−	0.572465i
$699$		0			0
$700$	−0.133975	−	0.232051i	−0.00506376	−	0.00877070i
$701$	16.3923			0.619129			0.309564	−	0.950878i	$-0.399817\pi$
$701$	16.3923			0.619129			0.309564	+	0.950878i	$0.399817\pi$
$702$		0			0
$703$	−15.9808			−0.602726
$704$	0.866025	+	1.50000i	0.0326396	+	0.0565334i
$705$		0			0
$706$	−2.19615	+	3.80385i	−0.0826533	+	0.143160i
$707$	4.39230			0.165190
$708$		0			0
$709$	25.6603	−	44.4449i	0.963691	−	1.66916i	0.250600	−	0.968091i	$-0.419372\pi$
$709$	25.6603	−	44.4449i	0.963691	−	1.66916i	0.713091	−	0.701071i	$-0.247294\pi$
$710$	12.9282			0.485187
$711$		0			0
$712$	2.59808	+	4.50000i	0.0973670	+	0.168645i
$713$	−1.85641	−	3.21539i	−0.0695230	−	0.120417i
$714$		0			0
$715$	3.46410	+	5.19615i	0.129550	+	0.194325i
$716$	10.3923			0.388379
$717$		0			0
$718$	−12.4641	−	21.5885i	−0.465156	−	0.805674i
$719$	−24.2487	+	42.0000i	−0.904324	+	1.56634i	−0.0825027	+	0.996591i	$0.526291\pi$
$719$	−24.2487	+	42.0000i	−0.904324	+	1.56634i	−0.821822	+	0.569745i	$0.807042\pi$
$720$		0			0
$721$	0.892305	−	1.54552i	0.0332312	−	0.0575581i
$722$	3.00000	−	5.19615i	0.111648	−	0.193381i
$723$		0			0
$724$	−7.00000	+	12.1244i	−0.260153	+	0.450598i
$725$	1.26795	+	2.19615i	0.0470905	+	0.0815631i
$726$		0			0
$727$	−17.0526			−0.632444			−0.316222	−	0.948685i	$-0.602415\pi$
$727$	−17.0526			−0.632444			−0.316222	+	0.948685i	$0.602415\pi$
$728$	0.428203	−	0.866025i	0.0158703	−	0.0320970i
$729$		0			0
$730$	−5.46410	−	9.46410i	−0.202235	−	0.350282i
$731$	30.9282	+	53.5692i	1.14392	+	1.98133i
$732$		0			0
$733$	15.9808			0.590263			0.295131	−	0.955457i	$-0.404637\pi$
$733$	15.9808			0.590263			0.295131	+	0.955457i	$0.404637\pi$
$734$	4.80385	−	8.32051i	0.177313	−	0.307116i
$735$		0			0
$736$	6.92820			0.255377
$737$	−7.26795	+	12.5885i	−0.267718	+	0.463702i
$738$		0			0
$739$	18.2846	+	31.6699i	0.672610	+	1.16500i	0.977161	+	0.212499i	$0.0681603\pi$
$739$	18.2846	+	31.6699i	0.672610	+	1.16500i	−0.304551	+	0.952496i	$0.598506\pi$
$740$	−3.19615			−0.117493
$741$		0			0
$742$	−1.73205			−0.0635856
$743$	−4.39230	−	7.60770i	−0.161138	−	0.279099i	0.774139	−	0.633016i	$-0.218183\pi$
$743$	−4.39230	−	7.60770i	−0.161138	−	0.279099i	−0.935277	+	0.353916i	$0.884850\pi$
$744$		0			0
$745$	−0.464102	+	0.803848i	−0.0170034	+	0.0294507i
$746$	−33.8564			−1.23957
$747$		0			0
$748$	−6.00000	+	10.3923i	−0.219382	+	0.379980i
$749$	−2.28719			−0.0835720
$750$		0			0
$751$	−0.196152	−	0.339746i	−0.00715770	−	0.0123975i	0.862424	−	0.506186i	$-0.168945\pi$
$751$	−0.196152	−	0.339746i	−0.00715770	−	0.0123975i	−0.869582	+	0.493788i	$0.835612\pi$
$752$	0.232051	+	0.401924i	0.00846202	+	0.0146567i
$753$		0			0
$754$	−4.05256	+	8.19615i	−0.147585	+	0.298486i
$755$	6.39230			0.232640
$756$		0			0
$757$	1.59808	+	2.76795i	0.0580831	+	0.100603i	0.893605	−	0.448854i	$-0.148168\pi$
$757$	1.59808	+	2.76795i	0.0580831	+	0.100603i	−0.835522	+	0.549457i	$0.814835\pi$
$758$	−0.500000	+	0.866025i	−0.0181608	+	0.0314555i
$759$		0			0
$760$	2.50000	−	4.33013i	0.0906845	−	0.157070i
$761$	5.25833	−	9.10770i	0.190614	−	0.330154i	−0.754840	−	0.655909i	$-0.772285\pi$
$761$	5.25833	−	9.10770i	0.190614	−	0.330154i	0.945454	+	0.325756i	$0.105619\pi$
$762$		0			0
$763$	0.660254	−	1.14359i	0.0239028	−	0.0414009i
$764$	−3.00000	−	5.19615i	−0.108536	−	0.187990i
$765$		0			0
$766$	−20.7846			−0.750978
$767$	5.53590	−	11.1962i	0.199890	−	0.404270i
$768$		0			0
$769$	−17.3923	−	30.1244i	−0.627183	−	1.08631i	−0.988114	−	0.153720i	$-0.950875\pi$
$769$	−17.3923	−	30.1244i	−0.627183	−	1.08631i	0.360932	−	0.932592i	$-0.382459\pi$
$770$	−0.232051	−	0.401924i	−0.00836253	−	0.0144843i
$771$		0			0
$772$	21.8564			0.786629
$773$	3.23205	−	5.59808i	0.116249	−	0.201349i	−0.802029	−	0.597284i	$-0.796246\pi$
$773$	3.23205	−	5.59808i	0.116249	−	0.201349i	0.918278	+	0.395936i	$0.129580\pi$
$774$		0			0
$775$	−0.535898			−0.0192500
$776$	5.26795	−	9.12436i	0.189108	−	0.327545i
$777$		0			0
$778$	−0.928203	−	1.60770i	−0.0332777	−	0.0576387i
$779$	34.6410			1.24114
$780$		0			0
$781$	22.3923			0.801260
$782$	24.0000	+	41.5692i	0.858238	+	1.48651i
$783$		0			0
$784$	3.46410	−	6.00000i	0.123718	−	0.214286i
$785$	−17.0526			−0.608632
$786$		0			0
$787$	−11.2679	+	19.5167i	−0.401659	+	0.695694i	−0.993926	−	0.110048i	$-0.964900\pi$
$787$	−11.2679	+	19.5167i	−0.401659	+	0.695694i	0.592267	+	0.805742i	$0.298233\pi$
$788$	8.32051			0.296406
$789$		0			0
$790$	7.92820	+	13.7321i	0.282073	+	0.488564i
$791$	−1.60770	−	2.78461i	−0.0571631	−	0.0990093i
$792$		0			0
$793$	−7.24871	+	14.6603i	−0.257409	+	0.520601i
$794$	−14.1244			−0.501255
$795$		0			0
$796$	−1.00000	−	1.73205i	−0.0354441	−	0.0613909i
$797$	6.46410	−	11.1962i	0.228970	−	0.396588i	−0.728533	−	0.685011i	$-0.759797\pi$
$797$	6.46410	−	11.1962i	0.228970	−	0.396588i	0.957503	+	0.288423i	$0.0931308\pi$
$798$		0			0
$799$	−1.60770	+	2.78461i	−0.0568762	+	0.0985124i
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$		0			0
$802$	13.7942	−	23.8923i	0.487091	−	0.843667i
$803$	−9.46410	−	16.3923i	−0.333981	−	0.578472i
$804$		0			0
$805$	−1.85641			−0.0654297
$806$	−1.07180	−	1.60770i	−0.0377524	−	0.0566286i
$807$		0			0
$808$	8.19615	+	14.1962i	0.288340	+	0.499419i
$809$	−18.0000	−	31.1769i	−0.632846	−	1.09612i	−0.986967	−	0.160922i	$-0.948553\pi$
$809$	−18.0000	−	31.1769i	−0.632846	−	1.09612i	0.354121	−	0.935200i	$-0.384780\pi$
$810$		0			0
$811$	3.14359			0.110386			0.0551932	−	0.998476i	$-0.482423\pi$
$811$	3.14359			0.110386			0.0551932	+	0.998476i	$0.482423\pi$
$812$	0.339746	−	0.588457i	0.0119227	−	0.0206508i
$813$		0			0
$814$	−5.53590			−0.194033
$815$	8.00000	−	13.8564i	0.280228	−	0.485369i
$816$		0			0
$817$	−22.3205	−	38.6603i	−0.780896	−	1.35255i
$818$	−25.7846			−0.901538
$819$		0			0
$820$	6.92820			0.241943
$821$	12.1244	+	21.0000i	0.423143	+	0.732905i	0.996245	−	0.0865789i	$-0.0275935\pi$
$821$	12.1244	+	21.0000i	0.423143	+	0.732905i	−0.573102	+	0.819484i	$0.694260\pi$
$822$		0			0
$823$	17.9904	−	31.1603i	0.627105	−	1.08618i	−0.361024	−	0.932556i	$-0.617573\pi$
$823$	17.9904	−	31.1603i	0.627105	−	1.08618i	0.988130	−	0.153622i	$-0.0490938\pi$
$824$	6.66025			0.232021
$825$		0			0
$826$	−0.464102	+	0.803848i	−0.0161482	+	0.0279694i
$827$	54.4974			1.89506			0.947531	−	0.319665i	$-0.103570\pi$
$827$	54.4974			1.89506			0.947531	+	0.319665i	$0.103570\pi$
$828$		0			0
$829$	−23.5167	−	40.7321i	−0.816767	−	1.41468i	−0.908052	−	0.418858i	$-0.862431\pi$
$829$	−23.5167	−	40.7321i	−0.816767	−	1.41468i	0.0912845	−	0.995825i	$-0.470903\pi$
$830$	−1.26795	−	2.19615i	−0.0440112	−	0.0762296i
$831$		0			0
$832$	3.59808	−	0.232051i	0.124741	−	0.00804491i
$833$	48.0000			1.66310
$834$		0			0
$835$	−6.23205	−	10.7942i	−0.215669	−	0.373550i
$836$	4.33013	−	7.50000i	0.149761	−	0.259393i
$837$		0			0
$838$	−7.73205	+	13.3923i	−0.267099	+	0.462629i
$839$	13.7321	−	23.7846i	0.474083	−	0.821136i	−0.525477	−	0.850808i	$-0.676113\pi$
$839$	13.7321	−	23.7846i	0.474083	−	0.821136i	0.999560	+	0.0296721i	$0.00944631\pi$
$840$		0			0
$841$	11.2846	−	19.5455i	0.389124	−	0.673983i
$842$	7.46410	+	12.9282i	0.257230	+	0.445535i
$843$		0			0
$844$	25.7846			0.887543
$845$	12.8923	−	1.66987i	0.443509	−	0.0574454i
$846$		0			0
$847$	1.07180	+	1.85641i	0.0368274	+	0.0637869i
$848$	−3.23205	−	5.59808i	−0.110989	−	0.192239i
$849$		0			0
$850$	6.92820			0.237635
$851$	−11.0718	+	19.1769i	−0.379536	+	0.657376i
$852$		0			0
$853$	−16.0000			−0.547830			−0.273915	−	0.961754i	$-0.588319\pi$
$853$	−16.0000			−0.547830			−0.273915	+	0.961754i	$0.588319\pi$
$854$	0.607695	−	1.05256i	0.0207949	−	0.0360178i
$855$		0			0
$856$	−4.26795	−	7.39230i	−0.145876	−	0.252664i
$857$	18.6795			0.638079			0.319040	−	0.947741i	$-0.396640\pi$
$857$	18.6795			0.638079			0.319040	+	0.947741i	$0.396640\pi$
$858$		0			0
$859$	29.9282			1.02114			0.510569	−	0.859837i	$-0.329435\pi$
$859$	29.9282			1.02114			0.510569	+	0.859837i	$0.329435\pi$
$860$	−4.46410	−	7.73205i	−0.152225	−	0.263661i
$861$		0			0
$862$	18.9282	−	32.7846i	0.644697	−	1.11665i
$863$	−46.6410			−1.58768			−0.793839	−	0.608128i	$-0.791921\pi$
$863$	−46.6410			−1.58768			−0.793839	+	0.608128i	$0.791921\pi$
$864$		0			0
$865$	−6.69615	+	11.5981i	−0.227676	+	0.394346i
$866$	−1.07180			−0.0364211
$867$		0			0
$868$	0.0717968	+	0.124356i	0.00243694	+	0.00422091i
$869$	13.7321	+	23.7846i	0.465828	+	0.806838i
$870$		0			0
$871$	16.7846	+	25.1769i	0.568725	+	0.853087i
$872$	4.92820			0.166890
$873$		0			0
$874$	−17.3205	−	30.0000i	−0.585875	−	1.01477i
$875$	−0.133975	+	0.232051i	−0.00452917	+	0.00784475i
$876$		0			0
$877$	−8.39230	+	14.5359i	−0.283388	+	0.490842i	−0.972217	−	0.234081i	$-0.924792\pi$
$877$	−8.39230	+	14.5359i	−0.283388	+	0.490842i	0.688829	+	0.724924i	$0.258125\pi$
$878$	−9.73205	+	16.8564i	−0.328441	+	0.568876i
$879$		0			0
$880$	0.866025	−	1.50000i	0.0291937	−	0.0505650i
$881$	−2.72243	−	4.71539i	−0.0917211	−	0.158866i	0.816514	−	0.577325i	$-0.195903\pi$
$881$	−2.72243	−	4.71539i	−0.0917211	−	0.158866i	−0.908235	+	0.418460i	$0.862570\pi$
$882$		0			0
$883$	40.5359			1.36414			0.682071	−	0.731286i	$-0.261080\pi$
$883$	40.5359			1.36414			0.682071	+	0.731286i	$0.261080\pi$
$884$	13.8564	+	20.7846i	0.466041	+	0.699062i
$885$		0			0
$886$	2.66025	+	4.60770i	0.0893730	+	0.154799i
$887$	−13.1603	−	22.7942i	−0.441878	−	0.765355i	0.555951	−	0.831215i	$-0.312354\pi$
$887$	−13.1603	−	22.7942i	−0.441878	−	0.765355i	−0.997829	+	0.0658599i	$0.979021\pi$
$888$		0			0
$889$	5.14359			0.172511
$890$	2.59808	−	4.50000i	0.0870877	−	0.150840i
$891$		0			0
$892$	−4.80385			−0.160845
$893$	1.16025	−	2.00962i	0.0388264	−	0.0672493i
$894$		0			0
$895$	−5.19615	−	9.00000i	−0.173688	−	0.300837i
$896$	−0.267949			−0.00895155
$897$		0			0
$898$	−3.58846			−0.119748
$899$	−0.679492	−	1.17691i	−0.0226623	−	0.0392523i
$900$		0			0
$901$	22.3923	−	38.7846i	0.745996	−	1.29210i
$902$	12.0000			0.399556
$903$		0			0
$904$	6.00000	−	10.3923i	0.199557	−	0.345643i
$905$	14.0000			0.465376
$906$		0			0
$907$	9.39230	+	16.2679i	0.311866	+	0.540168i	0.978766	−	0.204979i	$-0.0657125\pi$
$907$	9.39230	+	16.2679i	0.311866	+	0.540168i	−0.666900	+	0.745147i	$0.732379\pi$
$908$	−4.73205	−	8.19615i	−0.157039	−	0.271999i
$909$		0			0
$910$	−0.964102	+	0.0621778i	−0.0319597	+	0.00206117i
$911$	25.8564			0.856661			0.428330	−	0.903622i	$-0.359102\pi$
$911$	25.8564			0.856661			0.428330	+	0.903622i	$0.359102\pi$
$912$		0			0
$913$	−2.19615	−	3.80385i	−0.0726820	−	0.125889i
$914$	−11.0000	+	19.0526i	−0.363848	+	0.630203i
$915$		0			0
$916$	−1.00000	+	1.73205i	−0.0330409	+	0.0572286i
$917$	−0.911543	+	1.57884i	−0.0301018	+	0.0521378i
$918$		0			0
$919$	−29.9808	+	51.9282i	−0.988974	+	1.71295i	−0.366238	+	0.930521i	$0.619355\pi$
$919$	−29.9808	+	51.9282i	−0.988974	+	1.71295i	−0.622736	+	0.782432i	$0.713979\pi$
$920$	−3.46410	−	6.00000i	−0.114208	−	0.197814i
$921$		0			0
$922$	2.53590			0.0835154
$923$	20.6603	−	41.7846i	0.680041	−	1.37536i
$924$		0			0
$925$	1.59808	+	2.76795i	0.0525444	+	0.0910096i
$926$	10.1244	+	17.5359i	0.332707	+	0.576265i
$927$		0			0
$928$	2.53590			0.0832449
$929$	−22.3923	+	38.7846i	−0.734668	+	1.27248i	0.220201	+	0.975454i	$0.429329\pi$
$929$	−22.3923	+	38.7846i	−0.734668	+	1.27248i	−0.954869	+	0.297027i	$0.904005\pi$
$930$		0			0
$931$	−34.6410			−1.13531
$932$	−5.19615	+	9.00000i	−0.170206	+	0.294805i
$933$		0			0
$934$	8.19615	+	14.1962i	0.268186	+	0.464512i
$935$	12.0000			0.392442
$936$		0			0
$937$	31.5692			1.03132			0.515661	−	0.856793i	$-0.327547\pi$
$937$	31.5692			1.03132			0.515661	+	0.856793i	$0.327547\pi$
$938$	−1.12436	−	1.94744i	−0.0367115	−	0.0635862i
$939$		0			0
$940$	0.232051	−	0.401924i	0.00756866	−	0.0131093i
$941$	−36.0000			−1.17357			−0.586783	−	0.809744i	$-0.699606\pi$
$941$	−36.0000			−1.17357			−0.586783	+	0.809744i	$0.699606\pi$
$942$		0			0
$943$	24.0000	−	41.5692i	0.781548	−	1.35368i
$944$	−3.46410			−0.112747
$945$		0			0
$946$	−7.73205	−	13.3923i	−0.251391	−	0.435421i
$947$	20.6603	+	35.7846i	0.671368	+	1.16284i	0.977516	+	0.210860i	$0.0676263\pi$
$947$	20.6603	+	35.7846i	0.671368	+	1.16284i	−0.306148	+	0.951984i	$0.599040\pi$
$948$		0			0
$949$	−39.3205	+	2.53590i	−1.27640	+	0.0823187i
$950$	−5.00000			−0.162221
$951$		0			0
$952$	−0.928203	−	1.60770i	−0.0300832	−	0.0521057i
$953$	27.0000	−	46.7654i	0.874616	−	1.51488i	0.0174443	−	0.999848i	$-0.494447\pi$
$953$	27.0000	−	46.7654i	0.874616	−	1.51488i	0.857171	−	0.515031i	$-0.172220\pi$
$954$		0			0
$955$	−3.00000	+	5.19615i	−0.0970777	+	0.168144i
$956$	−7.73205	+	13.3923i	−0.250072	+	0.433138i
$957$		0			0
$958$	4.73205	−	8.19615i	0.152886	−	0.264806i
$959$	2.87564	+	4.98076i	0.0928594	+	0.160837i
$960$		0			0
$961$	−30.7128			−0.990736
$962$	−5.10770	+	10.3301i	−0.164679	+	0.333057i
$963$		0			0
$964$	3.50000	+	6.06218i	0.112727	+	0.195250i
$965$	−10.9282	−	18.9282i	−0.351791	−	0.609320i
$966$		0			0
$967$	−25.5885			−0.822869			−0.411435	−	0.911439i	$-0.634972\pi$
$967$	−25.5885			−0.822869			−0.411435	+	0.911439i	$0.634972\pi$
$968$	−4.00000	+	6.92820i	−0.128565	+	0.222681i
$969$		0			0
$970$	−10.5359			−0.338287
$971$	−9.40192	+	16.2846i	−0.301722	+	0.522598i	−0.976526	−	0.215399i	$-0.930895\pi$
$971$	−9.40192	+	16.2846i	−0.301722	+	0.522598i	0.674804	+	0.737997i	$0.264228\pi$
$972$		0			0
$973$	−0.545517	−	0.944864i	−0.0174885	−	0.0302909i
$974$	−29.5885			−0.948075
$975$		0			0
$976$	4.53590			0.145191
$977$	−11.6603	−	20.1962i	−0.373045	−	0.646132i	0.616988	−	0.786973i	$-0.288353\pi$
$977$	−11.6603	−	20.1962i	−0.373045	−	0.646132i	−0.990032	+	0.140841i	$0.955019\pi$
$978$		0			0
$979$	4.50000	−	7.79423i	0.143821	−	0.249105i
$980$	−6.92820			−0.221313
$981$		0			0
$982$	−15.5263	+	26.8923i	−0.495463	+	0.858168i
$983$	−15.2487			−0.486358			−0.243179	−	0.969981i	$-0.578190\pi$
$983$	−15.2487			−0.486358			−0.243179	+	0.969981i	$0.578190\pi$
$984$		0			0
$985$	−4.16025	−	7.20577i	−0.132557	−	0.229595i
$986$	8.78461	+	15.2154i	0.279759	+	0.484557i
$987$		0			0
$988$	−10.0000	−	15.0000i	−0.318142	−	0.477214i
$989$	−61.8564			−1.96692
$990$		0			0
$991$	1.19615	+	2.07180i	0.0379970	+	0.0658128i	0.884399	−	0.466733i	$-0.154569\pi$
$991$	1.19615	+	2.07180i	0.0379970	+	0.0658128i	−0.846401	+	0.532545i	$0.821236\pi$
$992$	−0.267949	+	0.464102i	−0.00850740	+	0.0147352i
$993$		0			0
$994$	−1.73205	+	3.00000i	−0.0549373	+	0.0951542i
$995$	−1.00000	+	1.73205i	−0.0317021	+	0.0549097i
$996$		0			0
$997$	14.4019	−	24.9449i	0.456114	−	0.790012i	−0.542638	−	0.839967i	$-0.682574\pi$
$997$	14.4019	−	24.9449i	0.456114	−	0.790012i	0.998751	+	0.0499549i	$0.0159078\pi$
$998$	−14.0000	−	24.2487i	−0.443162	−	0.767580i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1170.2.i.p.991.2	yes	4
3.2	odd	2		1170.2.i.m.991.2	yes	4
13.9	even	3	inner	1170.2.i.p.451.2	yes	4
39.35	odd	6		1170.2.i.m.451.2	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1170.2.i.m.451.2	✓	4	39.35	odd	6
1170.2.i.m.991.2	yes	4	3.2	odd	2
1170.2.i.p.451.2	yes	4	13.9	even	3	inner
1170.2.i.p.991.2	yes	4	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1170.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-0.133975 + 0.232051i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-0.133975 + 0.232051i) q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{10} +(0.866025 + 1.50000i) q^{11} +(3.59808 - 0.232051i) q^{13} -0.267949 q^{14} +(-0.500000 - 0.866025i) q^{16} +(3.46410 - 6.00000i) q^{17} +(-2.50000 + 4.33013i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(-0.866025 + 1.50000i) q^{22} +(3.46410 + 6.00000i) q^{23} +1.00000 q^{25} +(2.00000 + 3.00000i) q^{26} +(-0.133975 - 0.232051i) q^{28} +(1.26795 + 2.19615i) q^{29} -0.535898 q^{31} +(0.500000 - 0.866025i) q^{32} +6.92820 q^{34} +(-0.133975 + 0.232051i) q^{35} +(1.59808 + 2.76795i) q^{37} -5.00000 q^{38} -1.00000 q^{40} +(-3.46410 - 6.00000i) q^{41} +(-4.46410 + 7.73205i) q^{43} -1.73205 q^{44} +(-3.46410 + 6.00000i) q^{46} -0.464102 q^{47} +(3.46410 + 6.00000i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-1.59808 + 3.23205i) q^{52} +6.46410 q^{53} +(0.866025 + 1.50000i) q^{55} +(0.133975 - 0.232051i) q^{56} +(-1.26795 + 2.19615i) q^{58} +(1.73205 - 3.00000i) q^{59} +(-2.26795 + 3.92820i) q^{61} +(-0.267949 - 0.464102i) q^{62} +1.00000 q^{64} +(3.59808 - 0.232051i) q^{65} +(4.19615 + 7.26795i) q^{67} +(3.46410 + 6.00000i) q^{68} -0.267949 q^{70} +(6.46410 - 11.1962i) q^{71} -10.9282 q^{73} +(-1.59808 + 2.76795i) q^{74} +(-2.50000 - 4.33013i) q^{76} -0.464102 q^{77} +15.8564 q^{79} +(-0.500000 - 0.866025i) q^{80} +(3.46410 - 6.00000i) q^{82} -2.53590 q^{83} +(3.46410 - 6.00000i) q^{85} -8.92820 q^{86} +(-0.866025 - 1.50000i) q^{88} +(-2.59808 - 4.50000i) q^{89} +(-0.428203 + 0.866025i) q^{91} -6.92820 q^{92} +(-0.232051 - 0.401924i) q^{94} +(-2.50000 + 4.33013i) q^{95} +(-5.26795 + 9.12436i) q^{97} +(-3.46410 + 6.00000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{4} + 4 q^{5} - 4 q^{7} - 4 q^{8}+O(q^{10}) \) 4 * q + 2 * q^2 - 2 * q^4 + 4 * q^5 - 4 * q^7 - 4 * q^8	\( 4 q + 2 q^{2} - 2 q^{4} + 4 q^{5} - 4 q^{7} - 4 q^{8} + 2 q^{10} + 4 q^{13} - 8 q^{14} - 2 q^{16} - 10 q^{19} - 2 q^{20} + 4 q^{25} + 8 q^{26} - 4 q^{28} + 12 q^{29} - 16 q^{31} + 2 q^{32} - 4 q^{35} - 4 q^{37} - 20 q^{38} - 4 q^{40} - 4 q^{43} + 12 q^{47} + 2 q^{50} + 4 q^{52} + 12 q^{53} + 4 q^{56} - 12 q^{58} - 16 q^{61} - 8 q^{62} + 4 q^{64} + 4 q^{65} - 4 q^{67} - 8 q^{70} + 12 q^{71} - 16 q^{73} + 4 q^{74} - 10 q^{76} + 12 q^{77} + 8 q^{79} - 2 q^{80} - 24 q^{83} - 8 q^{86} + 26 q^{91} + 6 q^{94} - 10 q^{95} - 28 q^{97}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^4 + 4 * q^5 - 4 * q^7 - 4 * q^8 + 2 * q^10 + 4 * q^13 - 8 * q^14 - 2 * q^16 - 10 * q^19 - 2 * q^20 + 4 * q^25 + 8 * q^26 - 4 * q^28 + 12 * q^29 - 16 * q^31 + 2 * q^32 - 4 * q^35 - 4 * q^37 - 20 * q^38 - 4 * q^40 - 4 * q^43 + 12 * q^47 + 2 * q^50 + 4 * q^52 + 12 * q^53 + 4 * q^56 - 12 * q^58 - 16 * q^61 - 8 * q^62 + 4 * q^64 + 4 * q^65 - 4 * q^67 - 8 * q^70 + 12 * q^71 - 16 * q^73 + 4 * q^74 - 10 * q^76 + 12 * q^77 + 8 * q^79 - 2 * q^80 - 24 * q^83 - 8 * q^86 + 26 * q^91 + 6 * q^94 - 10 * q^95 - 28 * q^97

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