LMFDB - Embedded newform 1170.2.i.j.991.1

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:	$2$
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:	no (minimal twist has level 390)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			991.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1170.991
Dual form			1170.2.i.j.451.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(1.50000 - 2.59808i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(1.50000 - 2.59808i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{10} +(0.500000 + 0.866025i) q^{11} +(2.50000 + 2.59808i) q^{13} +3.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.50000 - 4.33013i) q^{19} +(0.500000 - 0.866025i) q^{20} +(-0.500000 + 0.866025i) q^{22} +(-2.00000 - 3.46410i) q^{23} +1.00000 q^{25} +(-1.00000 + 3.46410i) q^{26} +(1.50000 + 2.59808i) q^{28} +10.0000 q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.50000 + 2.59808i) q^{35} +(0.500000 + 0.866025i) q^{37} +5.00000 q^{38} +1.00000 q^{40} +(3.00000 + 5.19615i) q^{41} +(1.00000 - 1.73205i) q^{43} -1.00000 q^{44} +(2.00000 - 3.46410i) q^{46} +9.00000 q^{47} +(-1.00000 - 1.73205i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-3.50000 + 0.866025i) q^{52} +13.0000 q^{53} +(-0.500000 - 0.866025i) q^{55} +(-1.50000 + 2.59808i) q^{56} +(2.00000 - 3.46410i) q^{59} +(1.00000 - 1.73205i) q^{61} +(5.00000 + 8.66025i) q^{62} +1.00000 q^{64} +(-2.50000 - 2.59808i) q^{65} +(6.00000 + 10.3923i) q^{67} -3.00000 q^{70} +(-1.00000 + 1.73205i) q^{71} -16.0000 q^{73} +(-0.500000 + 0.866025i) q^{74} +(2.50000 + 4.33013i) q^{76} +3.00000 q^{77} -10.0000 q^{79} +(0.500000 + 0.866025i) q^{80} +(-3.00000 + 5.19615i) q^{82} -12.0000 q^{83} +2.00000 q^{86} +(-0.500000 - 0.866025i) q^{88} +(0.500000 + 0.866025i) q^{89} +(10.5000 - 2.59808i) q^{91} +4.00000 q^{92} +(4.50000 + 7.79423i) q^{94} +(-2.50000 + 4.33013i) q^{95} +(-6.00000 + 10.3923i) q^{97} +(1.00000 - 1.73205i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{4} - 2 q^{5} + 3 q^{7} - 2 q^{8}+O(q^{10}) $ 2 * q + q^2 - q^4 - 2 * q^5 + 3 * q^7 - 2 * q^8	$ 2 q + q^{2} - q^{4} - 2 q^{5} + 3 q^{7} - 2 q^{8} - q^{10} + q^{11} + 5 q^{13} + 6 q^{14} - q^{16} + 5 q^{19} + q^{20} - q^{22} - 4 q^{23} + 2 q^{25} - 2 q^{26} + 3 q^{28} + 20 q^{31} + q^{32} - 3 q^{35} + q^{37} + 10 q^{38} + 2 q^{40} + 6 q^{41} + 2 q^{43} - 2 q^{44} + 4 q^{46} + 18 q^{47} - 2 q^{49} + q^{50} - 7 q^{52} + 26 q^{53} - q^{55} - 3 q^{56} + 4 q^{59} + 2 q^{61} + 10 q^{62} + 2 q^{64} - 5 q^{65} + 12 q^{67} - 6 q^{70} - 2 q^{71} - 32 q^{73} - q^{74} + 5 q^{76} + 6 q^{77} - 20 q^{79} + q^{80} - 6 q^{82} - 24 q^{83} + 4 q^{86} - q^{88} + q^{89} + 21 q^{91} + 8 q^{92} + 9 q^{94} - 5 q^{95} - 12 q^{97} + 2 q^{98}+O(q^{100}) $ 2 * q + q^2 - q^4 - 2 * q^5 + 3 * q^7 - 2 * q^8 - q^10 + q^11 + 5 * q^13 + 6 * q^14 - q^16 + 5 * q^19 + q^20 - q^22 - 4 * q^23 + 2 * q^25 - 2 * q^26 + 3 * q^28 + 20 * q^31 + q^32 - 3 * q^35 + q^37 + 10 * q^38 + 2 * q^40 + 6 * q^41 + 2 * q^43 - 2 * q^44 + 4 * q^46 + 18 * q^47 - 2 * q^49 + q^50 - 7 * q^52 + 26 * q^53 - q^55 - 3 * q^56 + 4 * q^59 + 2 * q^61 + 10 * q^62 + 2 * q^64 - 5 * q^65 + 12 * q^67 - 6 * q^70 - 2 * q^71 - 32 * q^73 - q^74 + 5 * q^76 + 6 * q^77 - 20 * q^79 + q^80 - 6 * q^82 - 24 * q^83 + 4 * q^86 - q^88 + q^89 + 21 * q^91 + 8 * q^92 + 9 * q^94 - 5 * q^95 - 12 * q^97 + 2 * q^98

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
$7$	1.50000	−	2.59808i	0.566947	−	0.981981i	−0.429919	−	0.902867i	$-0.641458\pi$
$7$	1.50000	−	2.59808i	0.566947	−	0.981981i	0.996866	−	0.0791130i	$-0.0252088\pi$
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−0.500000	−	0.866025i	−0.158114	−	0.273861i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i	0.931505	−	0.363727i	$-0.118496\pi$
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i	−0.780750	+	0.624844i	$0.785163\pi$
$12$		0			0
$13$	2.50000	+	2.59808i	0.693375	+	0.720577i
$13$	2.50000	+	2.59808i	0.693375	+	0.720577i
$14$	3.00000			0.801784
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$17$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$18$		0			0
$19$	2.50000	−	4.33013i	0.573539	−	0.993399i	−0.422659	−	0.906289i	$-0.638903\pi$
$19$	2.50000	−	4.33013i	0.573539	−	0.993399i	0.996199	−	0.0871106i	$-0.0277634\pi$
$20$	0.500000	−	0.866025i	0.111803	−	0.193649i
$21$		0			0
$22$	−0.500000	+	0.866025i	−0.106600	+	0.184637i
$23$	−2.00000	−	3.46410i	−0.417029	−	0.722315i	0.578610	−	0.815604i	$-0.303595\pi$
$23$	−2.00000	−	3.46410i	−0.417029	−	0.722315i	−0.995639	+	0.0932891i	$0.970262\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$	−1.00000	+	3.46410i	−0.196116	+	0.679366i
$27$		0			0
$28$	1.50000	+	2.59808i	0.283473	+	0.490990i
$29$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$29$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$30$		0			0
$31$	10.0000			1.79605			0.898027	−	0.439941i	$-0.145001\pi$
$31$	10.0000			1.79605			0.898027	+	0.439941i	$0.145001\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$		0			0
$35$	−1.50000	+	2.59808i	−0.253546	+	0.439155i
$36$		0			0
$37$	0.500000	+	0.866025i	0.0821995	+	0.142374i	0.904194	−	0.427121i	$-0.140472\pi$
$37$	0.500000	+	0.866025i	0.0821995	+	0.142374i	−0.821995	+	0.569495i	$0.807139\pi$
$38$	5.00000			0.811107
$39$		0			0
$40$	1.00000			0.158114
$41$	3.00000	+	5.19615i	0.468521	+	0.811503i	0.999353	−	0.0359748i	$-0.0114536\pi$
$41$	3.00000	+	5.19615i	0.468521	+	0.811503i	−0.530831	+	0.847477i	$0.678120\pi$
$42$		0			0
$43$	1.00000	−	1.73205i	0.152499	−	0.264135i	−0.779647	−	0.626219i	$-0.784601\pi$
$43$	1.00000	−	1.73205i	0.152499	−	0.264135i	0.932145	+	0.362084i	$0.117935\pi$
$44$	−1.00000			−0.150756
$45$		0			0
$46$	2.00000	−	3.46410i	0.294884	−	0.510754i
$47$	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			0
$49$	−1.00000	−	1.73205i	−0.142857	−	0.247436i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$		0			0
$52$	−3.50000	+	0.866025i	−0.485363	+	0.120096i
$53$	13.0000			1.78569			0.892844	−	0.450367i	$-0.148707\pi$
$53$	13.0000			1.78569			0.892844	+	0.450367i	$0.148707\pi$
$54$		0			0
$55$	−0.500000	−	0.866025i	−0.0674200	−	0.116775i
$56$	−1.50000	+	2.59808i	−0.200446	+	0.347183i
$57$		0			0
$58$		0			0
$59$	2.00000	−	3.46410i	0.260378	−	0.450988i	−0.705965	−	0.708247i	$-0.749486\pi$
$59$	2.00000	−	3.46410i	0.260378	−	0.450988i	0.966342	+	0.257260i	$0.0828195\pi$
$60$		0			0
$61$	1.00000	−	1.73205i	0.128037	−	0.221766i	−0.794879	−	0.606768i	$-0.792466\pi$
$61$	1.00000	−	1.73205i	0.128037	−	0.221766i	0.922916	+	0.385002i	$0.125799\pi$
$62$	5.00000	+	8.66025i	0.635001	+	1.09985i
$63$		0			0
$64$	1.00000			0.125000
$65$	−2.50000	−	2.59808i	−0.310087	−	0.322252i
$66$		0			0
$67$	6.00000	+	10.3923i	0.733017	+	1.26962i	0.955588	+	0.294706i	$0.0952216\pi$
$67$	6.00000	+	10.3923i	0.733017	+	1.26962i	−0.222571	+	0.974916i	$0.571445\pi$
$68$		0			0
$69$		0			0
$70$	−3.00000			−0.358569
$71$	−1.00000	+	1.73205i	−0.118678	+	0.205557i	−0.919244	−	0.393688i	$-0.871199\pi$
$71$	−1.00000	+	1.73205i	−0.118678	+	0.205557i	0.800566	+	0.599245i	$0.204532\pi$
$72$		0			0
$73$	−16.0000			−1.87266			−0.936329	−	0.351123i	$-0.885800\pi$
$73$	−16.0000			−1.87266			−0.936329	+	0.351123i	$0.885800\pi$
$74$	−0.500000	+	0.866025i	−0.0581238	+	0.100673i
$75$		0			0
$76$	2.50000	+	4.33013i	0.286770	+	0.496700i
$77$	3.00000			0.341882
$78$		0			0
$79$	−10.0000			−1.12509			−0.562544	−	0.826767i	$-0.690177\pi$
$79$	−10.0000			−1.12509			−0.562544	+	0.826767i	$0.690177\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$		0			0
$82$	−3.00000	+	5.19615i	−0.331295	+	0.573819i
$83$	−12.0000			−1.31717			−0.658586	−	0.752506i	$-0.728845\pi$
$83$	−12.0000			−1.31717			−0.658586	+	0.752506i	$0.728845\pi$
$84$		0			0
$85$		0			0
$86$	2.00000			0.215666
$87$		0			0
$88$	−0.500000	−	0.866025i	−0.0533002	−	0.0923186i
$89$	0.500000	+	0.866025i	0.0529999	+	0.0917985i	0.891308	−	0.453398i	$-0.149788\pi$
$89$	0.500000	+	0.866025i	0.0529999	+	0.0917985i	−0.838308	+	0.545197i	$0.816455\pi$
$90$		0			0
$91$	10.5000	−	2.59808i	1.10070	−	0.272352i
$92$	4.00000			0.417029
$93$		0			0
$94$	4.50000	+	7.79423i	0.464140	+	0.803913i
$95$	−2.50000	+	4.33013i	−0.256495	+	0.444262i
$96$		0			0
$97$	−6.00000	+	10.3923i	−0.609208	+	1.05518i	0.382164	+	0.924095i	$0.375179\pi$
$97$	−6.00000	+	10.3923i	−0.609208	+	1.05518i	−0.991371	+	0.131084i	$0.958154\pi$
$98$	1.00000	−	1.73205i	0.101015	−	0.174964i
$99$		0			0
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	2.00000	+	3.46410i	0.199007	+	0.344691i	0.948207	−	0.317653i	$-0.102895\pi$
$101$	2.00000	+	3.46410i	0.199007	+	0.344691i	−0.749199	+	0.662344i	$0.769562\pi$
$102$		0			0
$103$	−9.00000			−0.886796			−0.443398	−	0.896325i	$-0.646227\pi$
$103$	−9.00000			−0.886796			−0.443398	+	0.896325i	$0.646227\pi$
$104$	−2.50000	−	2.59808i	−0.245145	−	0.254762i
$105$		0			0
$106$	6.50000	+	11.2583i	0.631336	+	1.09351i
$107$	−3.00000	−	5.19615i	−0.290021	−	0.502331i	0.683793	−	0.729676i	$-0.260329\pi$
$107$	−3.00000	−	5.19615i	−0.290021	−	0.502331i	−0.973814	+	0.227345i	$0.926996\pi$
$108$		0			0
$109$	−10.0000			−0.957826			−0.478913	−	0.877862i	$-0.658969\pi$
$109$	−10.0000			−0.957826			−0.478913	+	0.877862i	$0.658969\pi$
$110$	0.500000	−	0.866025i	0.0476731	−	0.0825723i
$111$		0			0
$112$	−3.00000			−0.283473
$113$	8.00000	−	13.8564i	0.752577	−	1.30350i	−0.193993	−	0.981003i	$-0.562144\pi$
$113$	8.00000	−	13.8564i	0.752577	−	1.30350i	0.946570	−	0.322498i	$-0.104523\pi$
$114$		0			0
$115$	2.00000	+	3.46410i	0.186501	+	0.323029i
$116$		0			0
$117$		0			0
$118$	4.00000			0.368230
$119$		0			0
$120$		0			0
$121$	5.00000	−	8.66025i	0.454545	−	0.787296i
$122$	2.00000			0.181071
$123$		0			0
$124$	−5.00000	+	8.66025i	−0.449013	+	0.777714i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−2.50000	−	4.33013i	−0.221839	−	0.384237i	0.733527	−	0.679660i	$-0.237873\pi$
$127$	−2.50000	−	4.33013i	−0.221839	−	0.384237i	−0.955366	+	0.295423i	$0.904539\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		0			0
$130$	1.00000	−	3.46410i	0.0877058	−	0.303822i
$131$	15.0000			1.31056			0.655278	−	0.755388i	$-0.272551\pi$
$131$	15.0000			1.31056			0.655278	+	0.755388i	$0.272551\pi$
$132$		0			0
$133$	−7.50000	−	12.9904i	−0.650332	−	1.12641i
$134$	−6.00000	+	10.3923i	−0.518321	+	0.897758i
$135$		0			0
$136$		0			0
$137$	8.00000	−	13.8564i	0.683486	−	1.18383i	−0.290424	−	0.956898i	$-0.593796\pi$
$137$	8.00000	−	13.8564i	0.683486	−	1.18383i	0.973910	−	0.226935i	$-0.0728704\pi$
$138$		0			0
$139$	4.50000	−	7.79423i	0.381685	−	0.661098i	−0.609618	−	0.792695i	$-0.708677\pi$
$139$	4.50000	−	7.79423i	0.381685	−	0.661098i	0.991303	+	0.131597i	$0.0420106\pi$
$140$	−1.50000	−	2.59808i	−0.126773	−	0.219578i
$141$		0			0
$142$	−2.00000			−0.167836
$143$	−1.00000	+	3.46410i	−0.0836242	+	0.289683i
$144$		0			0
$145$		0			0
$146$	−8.00000	−	13.8564i	−0.662085	−	1.14676i
$147$		0			0
$148$	−1.00000			−0.0821995
$149$	−3.00000	+	5.19615i	−0.245770	+	0.425685i	−0.962348	−	0.271821i	$-0.912374\pi$
$149$	−3.00000	+	5.19615i	−0.245770	+	0.425685i	0.716578	+	0.697507i	$0.245707\pi$
$150$		0			0
$151$	−6.00000			−0.488273			−0.244137	−	0.969741i	$-0.578505\pi$
$151$	−6.00000			−0.488273			−0.244137	+	0.969741i	$0.578505\pi$
$152$	−2.50000	+	4.33013i	−0.202777	+	0.351220i
$153$		0			0
$154$	1.50000	+	2.59808i	0.120873	+	0.209359i
$155$	−10.0000			−0.803219
$156$		0			0
$157$	1.00000			0.0798087			0.0399043	−	0.999204i	$-0.487295\pi$
$157$	1.00000			0.0798087			0.0399043	+	0.999204i	$0.487295\pi$
$158$	−5.00000	−	8.66025i	−0.397779	−	0.688973i
$159$		0			0
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	−12.0000			−0.945732
$162$		0			0
$163$	10.0000	−	17.3205i	0.783260	−	1.35665i	−0.146772	−	0.989170i	$-0.546888\pi$
$163$	10.0000	−	17.3205i	0.783260	−	1.35665i	0.930033	−	0.367477i	$-0.119778\pi$
$164$	−6.00000			−0.468521
$165$		0			0
$166$	−6.00000	−	10.3923i	−0.465690	−	0.806599i
$167$	−6.50000	−	11.2583i	−0.502985	−	0.871196i	−0.999994	−	0.00345033i	$-0.998902\pi$
$167$	−6.50000	−	11.2583i	−0.502985	−	0.871196i	0.497009	−	0.867745i	$-0.334432\pi$
$168$		0			0
$169$	−0.500000	+	12.9904i	−0.0384615	+	0.999260i
$170$		0			0
$171$		0			0
$172$	1.00000	+	1.73205i	0.0762493	+	0.132068i
$173$	−4.50000	+	7.79423i	−0.342129	+	0.592584i	−0.984828	−	0.173534i	$-0.944481\pi$
$173$	−4.50000	+	7.79423i	−0.342129	+	0.592584i	0.642699	+	0.766119i	$0.277815\pi$
$174$		0			0
$175$	1.50000	−	2.59808i	0.113389	−	0.196396i
$176$	0.500000	−	0.866025i	0.0376889	−	0.0652791i
$177$		0			0
$178$	−0.500000	+	0.866025i	−0.0374766	+	0.0649113i
$179$	6.00000	+	10.3923i	0.448461	+	0.776757i	0.998286	−	0.0585225i	$-0.0186389\pi$
$179$	6.00000	+	10.3923i	0.448461	+	0.776757i	−0.549825	+	0.835280i	$0.685306\pi$
$180$		0			0
$181$	6.00000			0.445976			0.222988	−	0.974821i	$-0.428419\pi$
$181$	6.00000			0.445976			0.222988	+	0.974821i	$0.428419\pi$
$182$	7.50000	+	7.79423i	0.555937	+	0.577747i
$183$		0			0
$184$	2.00000	+	3.46410i	0.147442	+	0.255377i
$185$	−0.500000	−	0.866025i	−0.0367607	−	0.0636715i
$186$		0			0
$187$		0			0
$188$	−4.50000	+	7.79423i	−0.328196	+	0.568453i
$189$		0			0
$190$	−5.00000			−0.362738
$191$	−9.00000	+	15.5885i	−0.651217	+	1.12794i	0.331611	+	0.943416i	$0.392408\pi$
$191$	−9.00000	+	15.5885i	−0.651217	+	1.12794i	−0.982828	+	0.184525i	$0.940925\pi$
$192$		0			0
$193$	−8.00000	−	13.8564i	−0.575853	−	0.997406i	−0.995948	−	0.0899262i	$-0.971337\pi$
$193$	−8.00000	−	13.8564i	−0.575853	−	0.997406i	0.420096	−	0.907480i	$-0.361996\pi$
$194$	−12.0000			−0.861550
$195$		0			0
$196$	2.00000			0.142857
$197$	−7.50000	−	12.9904i	−0.534353	−	0.925526i	−0.999194	−	0.0401324i	$-0.987222\pi$
$197$	−7.50000	−	12.9904i	−0.534353	−	0.925526i	0.464841	−	0.885394i	$-0.346111\pi$
$198$		0			0
$199$	1.00000	−	1.73205i	0.0708881	−	0.122782i	−0.828403	−	0.560133i	$-0.810750\pi$
$199$	1.00000	−	1.73205i	0.0708881	−	0.122782i	0.899291	+	0.437351i	$0.144083\pi$
$200$	−1.00000			−0.0707107
$201$		0			0
$202$	−2.00000	+	3.46410i	−0.140720	+	0.243733i
$203$		0			0
$204$		0			0
$205$	−3.00000	−	5.19615i	−0.209529	−	0.362915i
$206$	−4.50000	−	7.79423i	−0.313530	−	0.543050i
$207$		0			0
$208$	1.00000	−	3.46410i	0.0693375	−	0.240192i
$209$	5.00000			0.345857
$210$		0			0
$211$	7.50000	+	12.9904i	0.516321	+	0.894295i	0.999820	+	0.0189499i	$0.00603229\pi$
$211$	7.50000	+	12.9904i	0.516321	+	0.894295i	−0.483499	+	0.875345i	$0.660634\pi$
$212$	−6.50000	+	11.2583i	−0.446422	+	0.773225i
$213$		0			0
$214$	3.00000	−	5.19615i	0.205076	−	0.355202i
$215$	−1.00000	+	1.73205i	−0.0681994	+	0.118125i
$216$		0			0
$217$	15.0000	−	25.9808i	1.01827	−	1.76369i
$218$	−5.00000	−	8.66025i	−0.338643	−	0.586546i
$219$		0			0
$220$	1.00000			0.0674200
$221$		0			0
$222$		0			0
$223$	−5.50000	−	9.52628i	−0.368307	−	0.637927i	0.620994	−	0.783815i	$-0.286729\pi$
$223$	−5.50000	−	9.52628i	−0.368307	−	0.637927i	−0.989301	+	0.145889i	$0.953396\pi$
$224$	−1.50000	−	2.59808i	−0.100223	−	0.173591i
$225$		0			0
$226$	16.0000			1.06430
$227$	−10.0000	+	17.3205i	−0.663723	+	1.14960i	0.315906	+	0.948790i	$0.397691\pi$
$227$	−10.0000	+	17.3205i	−0.663723	+	1.14960i	−0.979630	+	0.200812i	$0.935642\pi$
$228$		0			0
$229$	−10.0000			−0.660819			−0.330409	−	0.943838i	$-0.607187\pi$
$229$	−10.0000			−0.660819			−0.330409	+	0.943838i	$0.607187\pi$
$230$	−2.00000	+	3.46410i	−0.131876	+	0.228416i
$231$		0			0
$232$		0			0
$233$	−10.0000			−0.655122			−0.327561	−	0.944830i	$-0.606227\pi$
$233$	−10.0000			−0.655122			−0.327561	+	0.944830i	$0.606227\pi$
$234$		0			0
$235$	−9.00000			−0.587095
$236$	2.00000	+	3.46410i	0.130189	+	0.225494i
$237$		0			0
$238$		0			0
$239$	2.00000			0.129369			0.0646846	−	0.997906i	$-0.479396\pi$
$239$	2.00000			0.129369			0.0646846	+	0.997906i	$0.479396\pi$
$240$		0			0
$241$	−7.50000	+	12.9904i	−0.483117	+	0.836784i	−0.999812	−	0.0193858i	$-0.993829\pi$
$241$	−7.50000	+	12.9904i	−0.483117	+	0.836784i	0.516695	+	0.856170i	$0.327162\pi$
$242$	10.0000			0.642824
$243$		0			0
$244$	1.00000	+	1.73205i	0.0640184	+	0.110883i
$245$	1.00000	+	1.73205i	0.0638877	+	0.110657i
$246$		0			0
$247$	17.5000	−	4.33013i	1.11350	−	0.275519i
$248$	−10.0000			−0.635001
$249$		0			0
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$	5.50000	−	9.52628i	0.347157	−	0.601293i	−0.638586	−	0.769550i	$-0.720480\pi$
$251$	5.50000	−	9.52628i	0.347157	−	0.601293i	0.985743	+	0.168257i	$0.0538138\pi$
$252$		0			0
$253$	2.00000	−	3.46410i	0.125739	−	0.217786i
$254$	2.50000	−	4.33013i	0.156864	−	0.271696i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−12.0000	−	20.7846i	−0.748539	−	1.29651i	−0.948523	−	0.316709i	$-0.897422\pi$
$257$	−12.0000	−	20.7846i	−0.748539	−	1.29651i	0.199983	−	0.979799i	$-0.435911\pi$
$258$		0			0
$259$	3.00000			0.186411
$260$	3.50000	−	0.866025i	0.217061	−	0.0537086i
$261$		0			0
$262$	7.50000	+	12.9904i	0.463352	+	0.802548i
$263$	1.50000	+	2.59808i	0.0924940	+	0.160204i	0.908560	−	0.417755i	$-0.137183\pi$
$263$	1.50000	+	2.59808i	0.0924940	+	0.160204i	−0.816066	+	0.577959i	$0.803849\pi$
$264$		0			0
$265$	−13.0000			−0.798584
$266$	7.50000	−	12.9904i	0.459855	−	0.796491i
$267$		0			0
$268$	−12.0000			−0.733017
$269$	−10.0000	+	17.3205i	−0.609711	+	1.05605i	0.381577	+	0.924337i	$0.375381\pi$
$269$	−10.0000	+	17.3205i	−0.609711	+	1.05605i	−0.991288	+	0.131713i	$0.957952\pi$
$270$		0			0
$271$	12.0000	+	20.7846i	0.728948	+	1.26258i	0.957328	+	0.289003i	$0.0933238\pi$
$271$	12.0000	+	20.7846i	0.728948	+	1.26258i	−0.228380	+	0.973572i	$0.573343\pi$
$272$		0			0
$273$		0			0
$274$	16.0000			0.966595
$275$	0.500000	+	0.866025i	0.0301511	+	0.0522233i
$276$		0			0
$277$	−11.5000	+	19.9186i	−0.690968	+	1.19679i	0.280553	+	0.959839i	$0.409482\pi$
$277$	−11.5000	+	19.9186i	−0.690968	+	1.19679i	−0.971521	+	0.236953i	$0.923851\pi$
$278$	9.00000			0.539784
$279$		0			0
$280$	1.50000	−	2.59808i	0.0896421	−	0.155265i
$281$	−10.0000			−0.596550			−0.298275	−	0.954480i	$-0.596411\pi$
$281$	−10.0000			−0.596550			−0.298275	+	0.954480i	$0.596411\pi$
$282$		0			0
$283$	−1.00000	−	1.73205i	−0.0594438	−	0.102960i	0.834772	−	0.550596i	$-0.185599\pi$
$283$	−1.00000	−	1.73205i	−0.0594438	−	0.102960i	−0.894216	+	0.447636i	$0.852266\pi$
$284$	−1.00000	−	1.73205i	−0.0593391	−	0.102778i
$285$		0			0
$286$	−3.50000	+	0.866025i	−0.206959	+	0.0512092i
$287$	18.0000			1.06251
$288$		0			0
$289$	8.50000	+	14.7224i	0.500000	+	0.866025i
$290$		0			0
$291$		0			0
$292$	8.00000	−	13.8564i	0.468165	−	0.810885i
$293$	6.50000	−	11.2583i	0.379734	−	0.657719i	−0.611289	−	0.791407i	$-0.709349\pi$
$293$	6.50000	−	11.2583i	0.379734	−	0.657719i	0.991023	+	0.133689i	$0.0426822\pi$
$294$		0			0
$295$	−2.00000	+	3.46410i	−0.116445	+	0.201688i
$296$	−0.500000	−	0.866025i	−0.0290619	−	0.0503367i
$297$		0			0
$298$	−6.00000			−0.347571
$299$	4.00000	−	13.8564i	0.231326	−	0.801337i
$300$		0			0
$301$	−3.00000	−	5.19615i	−0.172917	−	0.299501i
$302$	−3.00000	−	5.19615i	−0.172631	−	0.299005i
$303$		0			0
$304$	−5.00000			−0.286770
$305$	−1.00000	+	1.73205i	−0.0572598	+	0.0991769i
$306$		0			0
$307$	18.0000			1.02731			0.513657	−	0.857996i	$-0.328290\pi$
$307$	18.0000			1.02731			0.513657	+	0.857996i	$0.328290\pi$
$308$	−1.50000	+	2.59808i	−0.0854704	+	0.148039i
$309$		0			0
$310$	−5.00000	−	8.66025i	−0.283981	−	0.491869i
$311$	12.0000			0.680458			0.340229	−	0.940343i	$-0.389495\pi$
$311$	12.0000			0.680458			0.340229	+	0.940343i	$0.389495\pi$
$312$		0			0
$313$	−34.0000			−1.92179			−0.960897	−	0.276907i	$-0.910691\pi$
$313$	−34.0000			−1.92179			−0.960897	+	0.276907i	$0.910691\pi$
$314$	0.500000	+	0.866025i	0.0282166	+	0.0488726i
$315$		0			0
$316$	5.00000	−	8.66025i	0.281272	−	0.487177i
$317$	−19.0000			−1.06715			−0.533573	−	0.845754i	$-0.679151\pi$
$317$	−19.0000			−1.06715			−0.533573	+	0.845754i	$0.679151\pi$
$318$		0			0
$319$		0			0
$320$	−1.00000			−0.0559017
$321$		0			0
$322$	−6.00000	−	10.3923i	−0.334367	−	0.579141i
$323$		0			0
$324$		0			0
$325$	2.50000	+	2.59808i	0.138675	+	0.144115i
$326$	20.0000			1.10770
$327$		0			0
$328$	−3.00000	−	5.19615i	−0.165647	−	0.286910i
$329$	13.5000	−	23.3827i	0.744279	−	1.28913i
$330$		0			0
$331$	−14.0000	+	24.2487i	−0.769510	+	1.33283i	0.168320	+	0.985732i	$0.446166\pi$
$331$	−14.0000	+	24.2487i	−0.769510	+	1.33283i	−0.937829	+	0.347097i	$0.887167\pi$
$332$	6.00000	−	10.3923i	0.329293	−	0.570352i
$333$		0			0
$334$	6.50000	−	11.2583i	0.355664	−	0.616028i
$335$	−6.00000	−	10.3923i	−0.327815	−	0.567792i
$336$		0			0
$337$	2.00000			0.108947			0.0544735	−	0.998515i	$-0.482652\pi$
$337$	2.00000			0.108947			0.0544735	+	0.998515i	$0.482652\pi$
$338$	−11.5000	+	6.06218i	−0.625518	+	0.329739i
$339$		0			0
$340$		0			0
$341$	5.00000	+	8.66025i	0.270765	+	0.468979i
$342$		0			0
$343$	15.0000			0.809924
$344$	−1.00000	+	1.73205i	−0.0539164	+	0.0933859i
$345$		0			0
$346$	−9.00000			−0.483843
$347$	−14.0000	+	24.2487i	−0.751559	+	1.30174i	0.195507	+	0.980702i	$0.437365\pi$
$347$	−14.0000	+	24.2487i	−0.751559	+	1.30174i	−0.947067	+	0.321037i	$0.895969\pi$
$348$		0			0
$349$	−18.0000	−	31.1769i	−0.963518	−	1.66886i	−0.713545	−	0.700609i	$-0.752912\pi$
$349$	−18.0000	−	31.1769i	−0.963518	−	1.66886i	−0.249973	−	0.968253i	$-0.580422\pi$
$350$	3.00000			0.160357
$351$		0			0
$352$	1.00000			0.0533002
$353$	−18.0000	−	31.1769i	−0.958043	−	1.65938i	−0.727245	−	0.686378i	$-0.759200\pi$
$353$	−18.0000	−	31.1769i	−0.958043	−	1.65938i	−0.230799	−	0.973002i	$-0.574134\pi$
$354$		0			0
$355$	1.00000	−	1.73205i	0.0530745	−	0.0919277i
$356$	−1.00000			−0.0529999
$357$		0			0
$358$	−6.00000	+	10.3923i	−0.317110	+	0.549250i
$359$	−34.0000			−1.79445			−0.897226	−	0.441572i	$-0.854421\pi$
$359$	−34.0000			−1.79445			−0.897226	+	0.441572i	$0.854421\pi$
$360$		0			0
$361$	−3.00000	−	5.19615i	−0.157895	−	0.273482i
$362$	3.00000	+	5.19615i	0.157676	+	0.273104i
$363$		0			0
$364$	−3.00000	+	10.3923i	−0.157243	+	0.544705i
$365$	16.0000			0.837478
$366$		0			0
$367$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$367$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$368$	−2.00000	+	3.46410i	−0.104257	+	0.180579i
$369$		0			0
$370$	0.500000	−	0.866025i	0.0259938	−	0.0450225i
$371$	19.5000	−	33.7750i	1.01239	−	1.75351i
$372$		0			0
$373$	−5.00000	+	8.66025i	−0.258890	+	0.448411i	−0.965945	−	0.258748i	$-0.916690\pi$
$373$	−5.00000	+	8.66025i	−0.258890	+	0.448411i	0.707055	+	0.707159i	$0.250023\pi$
$374$		0			0
$375$		0			0
$376$	−9.00000			−0.464140
$377$		0			0
$378$		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
$382$	−18.0000			−0.920960
$383$	−14.0000	+	24.2487i	−0.715367	+	1.23905i	0.247451	+	0.968900i	$0.420407\pi$
$383$	−14.0000	+	24.2487i	−0.715367	+	1.23905i	−0.962818	+	0.270151i	$0.912926\pi$
$384$		0			0
$385$	−3.00000			−0.152894
$386$	8.00000	−	13.8564i	0.407189	−	0.705273i
$387$		0			0
$388$	−6.00000	−	10.3923i	−0.304604	−	0.527589i
$389$	16.0000			0.811232			0.405616	−	0.914044i	$-0.367057\pi$
$389$	16.0000			0.811232			0.405616	+	0.914044i	$0.367057\pi$
$390$		0			0
$391$		0			0
$392$	1.00000	+	1.73205i	0.0505076	+	0.0874818i
$393$		0			0
$394$	7.50000	−	12.9904i	0.377845	−	0.654446i
$395$	10.0000			0.503155
$396$		0			0
$397$	16.5000	−	28.5788i	0.828111	−	1.43433i	−0.0714068	−	0.997447i	$-0.522749\pi$
$397$	16.5000	−	28.5788i	0.828111	−	1.43433i	0.899518	−	0.436884i	$-0.143918\pi$
$398$	2.00000			0.100251
$399$		0			0
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	12.5000	+	21.6506i	0.624220	+	1.08118i	0.988691	+	0.149966i	$0.0479165\pi$
$401$	12.5000	+	21.6506i	0.624220	+	1.08118i	−0.364471	+	0.931215i	$0.618750\pi$
$402$		0			0
$403$	25.0000	+	25.9808i	1.24534	+	1.29419i
$404$	−4.00000			−0.199007
$405$		0			0
$406$		0			0
$407$	−0.500000	+	0.866025i	−0.0247841	+	0.0429273i
$408$		0			0
$409$	−8.50000	+	14.7224i	−0.420298	+	0.727977i	−0.995968	−	0.0897044i	$-0.971408\pi$
$409$	−8.50000	+	14.7224i	−0.420298	+	0.727977i	0.575670	+	0.817682i	$0.304741\pi$
$410$	3.00000	−	5.19615i	0.148159	−	0.256620i
$411$		0			0
$412$	4.50000	−	7.79423i	0.221699	−	0.383994i
$413$	−6.00000	−	10.3923i	−0.295241	−	0.511372i
$414$		0			0
$415$	12.0000			0.589057
$416$	3.50000	−	0.866025i	0.171602	−	0.0424604i
$417$		0			0
$418$	2.50000	+	4.33013i	0.122279	+	0.211793i
$419$	−14.0000	−	24.2487i	−0.683945	−	1.18463i	−0.973767	−	0.227547i	$-0.926930\pi$
$419$	−14.0000	−	24.2487i	−0.683945	−	1.18463i	0.289822	−	0.957080i	$-0.406404\pi$
$420$		0			0
$421$	20.0000			0.974740			0.487370	−	0.873195i	$-0.337956\pi$
$421$	20.0000			0.974740			0.487370	+	0.873195i	$0.337956\pi$
$422$	−7.50000	+	12.9904i	−0.365094	+	0.632362i
$423$		0			0
$424$	−13.0000			−0.631336
$425$		0			0
$426$		0			0
$427$	−3.00000	−	5.19615i	−0.145180	−	0.251459i
$428$	6.00000			0.290021
$429$		0			0
$430$	−2.00000			−0.0964486
$431$	18.0000	+	31.1769i	0.867029	+	1.50174i	0.865018	+	0.501741i	$0.167307\pi$
$431$	18.0000	+	31.1769i	0.867029	+	1.50174i	0.00201168	+	0.999998i	$0.499360\pi$
$432$		0			0
$433$	−8.00000	+	13.8564i	−0.384455	+	0.665896i	−0.991693	−	0.128624i	$-0.958944\pi$
$433$	−8.00000	+	13.8564i	−0.384455	+	0.665896i	0.607238	+	0.794520i	$0.292277\pi$
$434$	30.0000			1.44005
$435$		0			0
$436$	5.00000	−	8.66025i	0.239457	−	0.414751i
$437$	−20.0000			−0.956730
$438$		0			0
$439$	5.00000	+	8.66025i	0.238637	+	0.413331i	0.960323	−	0.278889i	$-0.0899661\pi$
$439$	5.00000	+	8.66025i	0.238637	+	0.413331i	−0.721686	+	0.692220i	$0.756633\pi$
$440$	0.500000	+	0.866025i	0.0238366	+	0.0412861i
$441$		0			0
$442$		0			0
$443$	18.0000			0.855206			0.427603	−	0.903967i	$-0.359358\pi$
$443$	18.0000			0.855206			0.427603	+	0.903967i	$0.359358\pi$
$444$		0			0
$445$	−0.500000	−	0.866025i	−0.0237023	−	0.0410535i
$446$	5.50000	−	9.52628i	0.260433	−	0.451082i
$447$		0			0
$448$	1.50000	−	2.59808i	0.0708683	−	0.122748i
$449$	−7.50000	+	12.9904i	−0.353947	+	0.613054i	−0.986937	−	0.161106i	$-0.948494\pi$
$449$	−7.50000	+	12.9904i	−0.353947	+	0.613054i	0.632990	+	0.774160i	$0.281827\pi$
$450$		0			0
$451$	−3.00000	+	5.19615i	−0.141264	+	0.244677i
$452$	8.00000	+	13.8564i	0.376288	+	0.651751i
$453$		0			0
$454$	−20.0000			−0.938647
$455$	−10.5000	+	2.59808i	−0.492248	+	0.121800i
$456$		0			0
$457$	−11.0000	−	19.0526i	−0.514558	−	0.891241i	−0.999857	−	0.0168929i	$-0.994623\pi$
$457$	−11.0000	−	19.0526i	−0.514558	−	0.891241i	0.485299	−	0.874348i	$-0.338711\pi$
$458$	−5.00000	−	8.66025i	−0.233635	−	0.404667i
$459$		0			0
$460$	−4.00000			−0.186501
$461$	−6.00000	+	10.3923i	−0.279448	+	0.484018i	−0.971248	−	0.238071i	$-0.923485\pi$
$461$	−6.00000	+	10.3923i	−0.279448	+	0.484018i	0.691800	+	0.722089i	$0.256818\pi$
$462$		0			0
$463$	−16.0000			−0.743583			−0.371792	−	0.928316i	$-0.621256\pi$
$463$	−16.0000			−0.743583			−0.371792	+	0.928316i	$0.621256\pi$
$464$		0			0
$465$		0			0
$466$	−5.00000	−	8.66025i	−0.231621	−	0.401179i
$467$	36.0000			1.66588			0.832941	−	0.553362i	$-0.186655\pi$
$467$	36.0000			1.66588			0.832941	+	0.553362i	$0.186655\pi$
$468$		0			0
$469$	36.0000			1.66233
$470$	−4.50000	−	7.79423i	−0.207570	−	0.359521i
$471$		0			0
$472$	−2.00000	+	3.46410i	−0.0920575	+	0.159448i
$473$	2.00000			0.0919601
$474$		0			0
$475$	2.50000	−	4.33013i	0.114708	−	0.198680i
$476$		0			0
$477$		0			0
$478$	1.00000	+	1.73205i	0.0457389	+	0.0792222i
$479$	−4.00000	−	6.92820i	−0.182765	−	0.316558i	0.760056	−	0.649857i	$-0.225171\pi$
$479$	−4.00000	−	6.92820i	−0.182765	−	0.316558i	−0.942821	+	0.333300i	$0.891838\pi$
$480$		0			0
$481$	−1.00000	+	3.46410i	−0.0455961	+	0.157949i
$482$	−15.0000			−0.683231
$483$		0			0
$484$	5.00000	+	8.66025i	0.227273	+	0.393648i
$485$	6.00000	−	10.3923i	0.272446	−	0.471890i
$486$		0			0
$487$	−17.5000	+	30.3109i	−0.793001	+	1.37352i	0.131100	+	0.991369i	$0.458149\pi$
$487$	−17.5000	+	30.3109i	−0.793001	+	1.37352i	−0.924101	+	0.382148i	$0.875184\pi$
$488$	−1.00000	+	1.73205i	−0.0452679	+	0.0784063i
$489$		0			0
$490$	−1.00000	+	1.73205i	−0.0451754	+	0.0782461i
$491$	12.5000	+	21.6506i	0.564117	+	0.977079i	0.997131	+	0.0756923i	$0.0241167\pi$
$491$	12.5000	+	21.6506i	0.564117	+	0.977079i	−0.433014	+	0.901387i	$0.642550\pi$
$492$		0			0
$493$		0			0
$494$	12.5000	+	12.9904i	0.562402	+	0.584465i
$495$		0			0
$496$	−5.00000	−	8.66025i	−0.224507	−	0.388857i
$497$	3.00000	+	5.19615i	0.134568	+	0.233079i
$498$		0			0
$499$	20.0000			0.895323			0.447661	−	0.894203i	$-0.352257\pi$
$499$	20.0000			0.895323			0.447661	+	0.894203i	$0.352257\pi$
$500$	0.500000	−	0.866025i	0.0223607	−	0.0387298i
$501$		0			0
$502$	11.0000			0.490954
$503$	−0.500000	+	0.866025i	−0.0222939	+	0.0386142i	−0.876957	−	0.480569i	$-0.840430\pi$
$503$	−0.500000	+	0.866025i	−0.0222939	+	0.0386142i	0.854663	+	0.519183i	$0.173764\pi$
$504$		0			0
$505$	−2.00000	−	3.46410i	−0.0889988	−	0.154150i
$506$	4.00000			0.177822
$507$		0			0
$508$	5.00000			0.221839
$509$	9.00000	+	15.5885i	0.398918	+	0.690946i	0.993593	−	0.113020i	$-0.0360525\pi$
$509$	9.00000	+	15.5885i	0.398918	+	0.690946i	−0.594675	+	0.803966i	$0.702719\pi$
$510$		0			0
$511$	−24.0000	+	41.5692i	−1.06170	+	1.83891i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	12.0000	−	20.7846i	0.529297	−	0.916770i
$515$	9.00000			0.396587
$516$		0			0
$517$	4.50000	+	7.79423i	0.197910	+	0.342790i
$518$	1.50000	+	2.59808i	0.0659062	+	0.114153i
$519$		0			0
$520$	2.50000	+	2.59808i	0.109632	+	0.113933i
$521$	−33.0000			−1.44576			−0.722878	−	0.690976i	$-0.757181\pi$
$521$	−33.0000			−1.44576			−0.722878	+	0.690976i	$0.757181\pi$
$522$		0			0
$523$	−3.00000	−	5.19615i	−0.131181	−	0.227212i	0.792951	−	0.609285i	$-0.208544\pi$
$523$	−3.00000	−	5.19615i	−0.131181	−	0.227212i	−0.924132	+	0.382073i	$0.875210\pi$
$524$	−7.50000	+	12.9904i	−0.327639	+	0.567487i
$525$		0			0
$526$	−1.50000	+	2.59808i	−0.0654031	+	0.113282i
$527$		0			0
$528$		0			0
$529$	3.50000	−	6.06218i	0.152174	−	0.263573i
$530$	−6.50000	−	11.2583i	−0.282342	−	0.489031i
$531$		0			0
$532$	15.0000			0.650332
$533$	−6.00000	+	20.7846i	−0.259889	+	0.900281i
$534$		0			0
$535$	3.00000	+	5.19615i	0.129701	+	0.224649i
$536$	−6.00000	−	10.3923i	−0.259161	−	0.448879i
$537$		0			0
$538$	−20.0000			−0.862261
$539$	1.00000	−	1.73205i	0.0430730	−	0.0746047i
$540$		0			0
$541$	−2.00000			−0.0859867			−0.0429934	−	0.999075i	$-0.513689\pi$
$541$	−2.00000			−0.0859867			−0.0429934	+	0.999075i	$0.513689\pi$
$542$	−12.0000	+	20.7846i	−0.515444	+	0.892775i
$543$		0			0
$544$		0			0
$545$	10.0000			0.428353
$546$		0			0
$547$	34.0000			1.45374			0.726868	−	0.686778i	$-0.240975\pi$
$547$	34.0000			1.45374			0.726868	+	0.686778i	$0.240975\pi$
$548$	8.00000	+	13.8564i	0.341743	+	0.591916i
$549$		0			0
$550$	−0.500000	+	0.866025i	−0.0213201	+	0.0369274i
$551$		0			0
$552$		0			0
$553$	−15.0000	+	25.9808i	−0.637865	+	1.10481i
$554$	−23.0000			−0.977176
$555$		0			0
$556$	4.50000	+	7.79423i	0.190843	+	0.330549i
$557$	−1.50000	−	2.59808i	−0.0635570	−	0.110084i	0.832496	−	0.554031i	$-0.186911\pi$
$557$	−1.50000	−	2.59808i	−0.0635570	−	0.110084i	−0.896053	+	0.443947i	$0.853578\pi$
$558$		0			0
$559$	7.00000	−	1.73205i	0.296068	−	0.0732579i
$560$	3.00000			0.126773
$561$		0			0
$562$	−5.00000	−	8.66025i	−0.210912	−	0.365311i
$563$	12.0000	−	20.7846i	0.505740	−	0.875967i	−0.494238	−	0.869326i	$-0.664553\pi$
$563$	12.0000	−	20.7846i	0.505740	−	0.875967i	0.999978	−	0.00664037i	$-0.00211371\pi$
$564$		0			0
$565$	−8.00000	+	13.8564i	−0.336563	+	0.582943i
$566$	1.00000	−	1.73205i	0.0420331	−	0.0728035i
$567$		0			0
$568$	1.00000	−	1.73205i	0.0419591	−	0.0726752i
$569$	−5.50000	−	9.52628i	−0.230572	−	0.399362i	0.727405	−	0.686209i	$-0.240726\pi$
$569$	−5.50000	−	9.52628i	−0.230572	−	0.399362i	−0.957977	+	0.286846i	$0.907393\pi$
$570$		0			0
$571$	7.00000			0.292941			0.146470	−	0.989215i	$-0.453209\pi$
$571$	7.00000			0.292941			0.146470	+	0.989215i	$0.453209\pi$
$572$	−2.50000	−	2.59808i	−0.104530	−	0.108631i
$573$		0			0
$574$	9.00000	+	15.5885i	0.375653	+	0.650650i
$575$	−2.00000	−	3.46410i	−0.0834058	−	0.144463i
$576$		0			0
$577$	18.0000			0.749350			0.374675	−	0.927156i	$-0.377754\pi$
$577$	18.0000			0.749350			0.374675	+	0.927156i	$0.377754\pi$
$578$	−8.50000	+	14.7224i	−0.353553	+	0.612372i
$579$		0			0
$580$		0			0
$581$	−18.0000	+	31.1769i	−0.746766	+	1.29344i
$582$		0			0
$583$	6.50000	+	11.2583i	0.269202	+	0.466272i
$584$	16.0000			0.662085
$585$		0			0
$586$	13.0000			0.537025
$587$	−9.00000	−	15.5885i	−0.371470	−	0.643404i	0.618322	−	0.785925i	$-0.287813\pi$
$587$	−9.00000	−	15.5885i	−0.371470	−	0.643404i	−0.989792	+	0.142520i	$0.954479\pi$
$588$		0			0
$589$	25.0000	−	43.3013i	1.03011	−	1.78420i
$590$	−4.00000			−0.164677
$591$		0			0
$592$	0.500000	−	0.866025i	0.0205499	−	0.0355934i
$593$	−28.0000			−1.14982			−0.574911	−	0.818216i	$-0.694963\pi$
$593$	−28.0000			−1.14982			−0.574911	+	0.818216i	$0.694963\pi$
$594$		0			0
$595$		0			0
$596$	−3.00000	−	5.19615i	−0.122885	−	0.212843i
$597$		0			0
$598$	14.0000	−	3.46410i	0.572503	−	0.141658i
$599$	30.0000			1.22577			0.612883	−	0.790173i	$-0.290010\pi$
$599$	30.0000			1.22577			0.612883	+	0.790173i	$0.290010\pi$
$600$		0			0
$601$	13.5000	+	23.3827i	0.550676	+	0.953800i	0.998226	+	0.0595404i	$0.0189635\pi$
$601$	13.5000	+	23.3827i	0.550676	+	0.953800i	−0.447549	+	0.894259i	$0.647703\pi$
$602$	3.00000	−	5.19615i	0.122271	−	0.211779i
$603$		0			0
$604$	3.00000	−	5.19615i	0.122068	−	0.211428i
$605$	−5.00000	+	8.66025i	−0.203279	+	0.352089i
$606$		0			0
$607$	−18.5000	+	32.0429i	−0.750892	+	1.30058i	0.196499	+	0.980504i	$0.437043\pi$
$607$	−18.5000	+	32.0429i	−0.750892	+	1.30058i	−0.947391	+	0.320079i	$0.896291\pi$
$608$	−2.50000	−	4.33013i	−0.101388	−	0.175610i
$609$		0			0
$610$	−2.00000			−0.0809776
$611$	22.5000	+	23.3827i	0.910253	+	0.945962i
$612$		0			0
$613$	−11.5000	−	19.9186i	−0.464481	−	0.804504i	0.534697	−	0.845044i	$-0.320426\pi$
$613$	−11.5000	−	19.9186i	−0.464481	−	0.804504i	−0.999178	+	0.0405396i	$0.987092\pi$
$614$	9.00000	+	15.5885i	0.363210	+	0.629099i
$615$		0			0
$616$	−3.00000			−0.120873
$617$	−3.00000	+	5.19615i	−0.120775	+	0.209189i	−0.920074	−	0.391745i	$-0.871871\pi$
$617$	−3.00000	+	5.19615i	−0.120775	+	0.209189i	0.799298	+	0.600935i	$0.205205\pi$
$618$		0			0
$619$	−31.0000			−1.24600			−0.622998	−	0.782224i	$-0.714085\pi$
$619$	−31.0000			−1.24600			−0.622998	+	0.782224i	$0.714085\pi$
$620$	5.00000	−	8.66025i	0.200805	−	0.347804i
$621$		0			0
$622$	6.00000	+	10.3923i	0.240578	+	0.416693i
$623$	3.00000			0.120192
$624$		0			0
$625$	1.00000			0.0400000
$626$	−17.0000	−	29.4449i	−0.679457	−	1.17685i
$627$		0			0
$628$	−0.500000	+	0.866025i	−0.0199522	+	0.0345582i
$629$		0			0
$630$		0			0
$631$	2.00000	−	3.46410i	0.0796187	−	0.137904i	−0.823467	−	0.567365i	$-0.807963\pi$
$631$	2.00000	−	3.46410i	0.0796187	−	0.137904i	0.903085	+	0.429461i	$0.141296\pi$
$632$	10.0000			0.397779
$633$		0			0
$634$	−9.50000	−	16.4545i	−0.377293	−	0.653491i
$635$	2.50000	+	4.33013i	0.0992095	+	0.171836i
$636$		0			0
$637$	2.00000	−	6.92820i	0.0792429	−	0.274505i
$638$		0			0
$639$		0			0
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	−4.50000	+	7.79423i	−0.177739	+	0.307854i	−0.941106	−	0.338112i	$-0.890212\pi$
$641$	−4.50000	+	7.79423i	−0.177739	+	0.307854i	0.763367	+	0.645966i	$0.223545\pi$
$642$		0			0
$643$	22.0000	−	38.1051i	0.867595	−	1.50272i	0.00314839	−	0.999995i	$-0.498998\pi$
$643$	22.0000	−	38.1051i	0.867595	−	1.50272i	0.864447	−	0.502724i	$-0.167669\pi$
$644$	6.00000	−	10.3923i	0.236433	−	0.409514i
$645$		0			0
$646$		0			0
$647$	4.50000	+	7.79423i	0.176913	+	0.306423i	0.940822	−	0.338902i	$-0.110055\pi$
$647$	4.50000	+	7.79423i	0.176913	+	0.306423i	−0.763908	+	0.645325i	$0.776722\pi$
$648$		0			0
$649$	4.00000			0.157014
$650$	−1.00000	+	3.46410i	−0.0392232	+	0.135873i
$651$		0			0
$652$	10.0000	+	17.3205i	0.391630	+	0.678323i
$653$	20.5000	+	35.5070i	0.802227	+	1.38950i	0.918147	+	0.396239i	$0.129685\pi$
$653$	20.5000	+	35.5070i	0.802227	+	1.38950i	−0.115920	+	0.993259i	$0.536982\pi$
$654$		0			0
$655$	−15.0000			−0.586098
$656$	3.00000	−	5.19615i	0.117130	−	0.202876i
$657$		0			0
$658$	27.0000			1.05257
$659$	2.00000	−	3.46410i	0.0779089	−	0.134942i	−0.824439	−	0.565951i	$-0.808509\pi$
$659$	2.00000	−	3.46410i	0.0779089	−	0.134942i	0.902348	+	0.431009i	$0.141842\pi$
$660$		0			0
$661$	−7.00000	−	12.1244i	−0.272268	−	0.471583i	0.697174	−	0.716902i	$-0.254441\pi$
$661$	−7.00000	−	12.1244i	−0.272268	−	0.471583i	−0.969442	+	0.245319i	$0.921107\pi$
$662$	−28.0000			−1.08825
$663$		0			0
$664$	12.0000			0.465690
$665$	7.50000	+	12.9904i	0.290838	+	0.503745i
$666$		0			0
$667$		0			0
$668$	13.0000			0.502985
$669$		0			0
$670$	6.00000	−	10.3923i	0.231800	−	0.401490i
$671$	2.00000			0.0772091
$672$		0			0
$673$	16.0000	+	27.7128i	0.616755	+	1.06825i	0.990074	+	0.140548i	$0.0448863\pi$
$673$	16.0000	+	27.7128i	0.616755	+	1.06825i	−0.373319	+	0.927703i	$0.621780\pi$
$674$	1.00000	+	1.73205i	0.0385186	+	0.0667161i
$675$		0			0
$676$	−11.0000	−	6.92820i	−0.423077	−	0.266469i
$677$	26.0000			0.999261			0.499631	−	0.866239i	$-0.333469\pi$
$677$	26.0000			0.999261			0.499631	+	0.866239i	$0.333469\pi$
$678$		0			0
$679$	18.0000	+	31.1769i	0.690777	+	1.19646i
$680$		0			0
$681$		0			0
$682$	−5.00000	+	8.66025i	−0.191460	+	0.331618i
$683$	−13.0000	+	22.5167i	−0.497431	+	0.861576i	−0.999996	−	0.00296369i	$-0.999057\pi$
$683$	−13.0000	+	22.5167i	−0.497431	+	0.861576i	0.502564	+	0.864540i	$0.332390\pi$
$684$		0			0
$685$	−8.00000	+	13.8564i	−0.305664	+	0.529426i
$686$	7.50000	+	12.9904i	0.286351	+	0.495975i
$687$		0			0
$688$	−2.00000			−0.0762493
$689$	32.5000	+	33.7750i	1.23815	+	1.28672i
$690$		0			0
$691$	−16.5000	−	28.5788i	−0.627690	−	1.08719i	−0.988014	−	0.154363i	$-0.950667\pi$
$691$	−16.5000	−	28.5788i	−0.627690	−	1.08719i	0.360325	−	0.932827i	$-0.382666\pi$
$692$	−4.50000	−	7.79423i	−0.171064	−	0.296292i
$693$		0			0
$694$	−28.0000			−1.06287
$695$	−4.50000	+	7.79423i	−0.170695	+	0.295652i
$696$		0			0
$697$		0			0
$698$	18.0000	−	31.1769i	0.681310	−	1.18006i
$699$		0			0
$700$	1.50000	+	2.59808i	0.0566947	+	0.0981981i
$701$	−4.00000			−0.151078			−0.0755390	−	0.997143i	$-0.524068\pi$
$701$	−4.00000			−0.151078			−0.0755390	+	0.997143i	$0.524068\pi$
$702$		0			0
$703$	5.00000			0.188579
$704$	0.500000	+	0.866025i	0.0188445	+	0.0326396i
$705$		0			0
$706$	18.0000	−	31.1769i	0.677439	−	1.17336i
$707$	12.0000			0.451306
$708$		0			0
$709$	−2.00000	+	3.46410i	−0.0751116	+	0.130097i	−0.901135	−	0.433539i	$-0.857265\pi$
$709$	−2.00000	+	3.46410i	−0.0751116	+	0.130097i	0.826023	+	0.563636i	$0.190598\pi$
$710$	2.00000			0.0750587
$711$		0			0
$712$	−0.500000	−	0.866025i	−0.0187383	−	0.0324557i
$713$	−20.0000	−	34.6410i	−0.749006	−	1.29732i
$714$		0			0
$715$	1.00000	−	3.46410i	0.0373979	−	0.129550i
$716$	−12.0000			−0.448461
$717$		0			0
$718$	−17.0000	−	29.4449i	−0.634434	−	1.09887i
$719$	18.0000	−	31.1769i	0.671287	−	1.16270i	−0.306253	−	0.951950i	$-0.599075\pi$
$719$	18.0000	−	31.1769i	0.671287	−	1.16270i	0.977539	−	0.210752i	$-0.0675914\pi$
$720$		0			0
$721$	−13.5000	+	23.3827i	−0.502766	+	0.870817i
$722$	3.00000	−	5.19615i	0.111648	−	0.193381i
$723$		0			0
$724$	−3.00000	+	5.19615i	−0.111494	+	0.193113i
$725$		0			0
$726$		0			0
$727$	−37.0000			−1.37225			−0.686127	−	0.727482i	$-0.740691\pi$
$727$	−37.0000			−1.37225			−0.686127	+	0.727482i	$0.740691\pi$
$728$	−10.5000	+	2.59808i	−0.389156	+	0.0962911i
$729$		0			0
$730$	8.00000	+	13.8564i	0.296093	+	0.512849i
$731$		0			0
$732$		0			0
$733$	−5.00000			−0.184679			−0.0923396	−	0.995728i	$-0.529435\pi$
$733$	−5.00000			−0.184679			−0.0923396	+	0.995728i	$0.529435\pi$
$734$		0			0
$735$		0			0
$736$	−4.00000			−0.147442
$737$	−6.00000	+	10.3923i	−0.221013	+	0.382805i
$738$		0			0
$739$	−17.5000	−	30.3109i	−0.643748	−	1.11500i	−0.984589	−	0.174883i	$-0.944045\pi$
$739$	−17.5000	−	30.3109i	−0.643748	−	1.11500i	0.340841	−	0.940121i	$-0.389288\pi$
$740$	1.00000			0.0367607
$741$		0			0
$742$	39.0000			1.43174
$743$	12.0000	+	20.7846i	0.440237	+	0.762513i	0.997707	−	0.0676840i	$-0.0215610\pi$
$743$	12.0000	+	20.7846i	0.440237	+	0.762513i	−0.557470	+	0.830197i	$0.688228\pi$
$744$		0			0
$745$	3.00000	−	5.19615i	0.109911	−	0.190372i
$746$	−10.0000			−0.366126
$747$		0			0
$748$		0			0
$749$	−18.0000			−0.657706
$750$		0			0
$751$	−22.0000	−	38.1051i	−0.802791	−	1.39048i	−0.917772	−	0.397108i	$-0.870014\pi$
$751$	−22.0000	−	38.1051i	−0.802791	−	1.39048i	0.114981	−	0.993368i	$-0.463319\pi$
$752$	−4.50000	−	7.79423i	−0.164098	−	0.284226i
$753$		0			0
$754$		0			0
$755$	6.00000			0.218362
$756$		0			0
$757$	−19.5000	−	33.7750i	−0.708740	−	1.22757i	−0.965325	−	0.261051i	$-0.915931\pi$
$757$	−19.5000	−	33.7750i	−0.708740	−	1.22757i	0.256585	−	0.966522i	$-0.417403\pi$
$758$	−0.500000	+	0.866025i	−0.0181608	+	0.0314555i
$759$		0			0
$760$	2.50000	−	4.33013i	0.0906845	−	0.157070i
$761$	22.5000	−	38.9711i	0.815624	−	1.41270i	−0.0932544	−	0.995642i	$-0.529727\pi$
$761$	22.5000	−	38.9711i	0.815624	−	1.41270i	0.908879	−	0.417061i	$-0.136940\pi$
$762$		0			0
$763$	−15.0000	+	25.9808i	−0.543036	+	0.940567i
$764$	−9.00000	−	15.5885i	−0.325609	−	0.563971i
$765$		0			0
$766$	−28.0000			−1.01168
$767$	14.0000	−	3.46410i	0.505511	−	0.125081i
$768$		0			0
$769$	13.0000	+	22.5167i	0.468792	+	0.811972i	0.999364	−	0.0356685i	$-0.0113561\pi$
$769$	13.0000	+	22.5167i	0.468792	+	0.811972i	−0.530572	+	0.847640i	$0.678023\pi$
$770$	−1.50000	−	2.59808i	−0.0540562	−	0.0936282i
$771$		0			0
$772$	16.0000			0.575853
$773$	−18.5000	+	32.0429i	−0.665399	+	1.15250i	0.313778	+	0.949496i	$0.398405\pi$
$773$	−18.5000	+	32.0429i	−0.665399	+	1.15250i	−0.979177	+	0.203008i	$0.934928\pi$
$774$		0			0
$775$	10.0000			0.359211
$776$	6.00000	−	10.3923i	0.215387	−	0.373062i
$777$		0			0
$778$	8.00000	+	13.8564i	0.286814	+	0.496776i
$779$	30.0000			1.07486
$780$		0			0
$781$	−2.00000			−0.0715656
$782$		0			0
$783$		0			0
$784$	−1.00000	+	1.73205i	−0.0357143	+	0.0618590i
$785$	−1.00000			−0.0356915
$786$		0			0
$787$	−8.00000	+	13.8564i	−0.285169	+	0.493928i	−0.972650	−	0.232275i	$-0.925383\pi$
$787$	−8.00000	+	13.8564i	−0.285169	+	0.493928i	0.687481	+	0.726202i	$0.258716\pi$
$788$	15.0000			0.534353
$789$		0			0
$790$	5.00000	+	8.66025i	0.177892	+	0.308118i
$791$	−24.0000	−	41.5692i	−0.853342	−	1.47803i
$792$		0			0
$793$	7.00000	−	1.73205i	0.248577	−	0.0615069i
$794$	33.0000			1.17113
$795$		0			0
$796$	1.00000	+	1.73205i	0.0354441	+	0.0613909i
$797$	−7.00000	+	12.1244i	−0.247953	+	0.429467i	−0.962958	−	0.269653i	$-0.913091\pi$
$797$	−7.00000	+	12.1244i	−0.247953	+	0.429467i	0.715005	+	0.699119i	$0.246424\pi$
$798$		0			0
$799$		0			0
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$		0			0
$802$	−12.5000	+	21.6506i	−0.441390	+	0.764511i
$803$	−8.00000	−	13.8564i	−0.282314	−	0.488982i
$804$		0			0
$805$	12.0000			0.422944
$806$	−10.0000	+	34.6410i	−0.352235	+	1.22018i
$807$		0			0
$808$	−2.00000	−	3.46410i	−0.0703598	−	0.121867i
$809$	−9.00000	−	15.5885i	−0.316423	−	0.548061i	0.663316	−	0.748340i	$-0.269149\pi$
$809$	−9.00000	−	15.5885i	−0.316423	−	0.548061i	−0.979739	+	0.200279i	$0.935815\pi$
$810$		0			0
$811$	33.0000			1.15879			0.579393	−	0.815048i	$-0.303290\pi$
$811$	33.0000			1.15879			0.579393	+	0.815048i	$0.303290\pi$
$812$		0			0
$813$		0			0
$814$	−1.00000			−0.0350500
$815$	−10.0000	+	17.3205i	−0.350285	+	0.606711i
$816$		0			0
$817$	−5.00000	−	8.66025i	−0.174928	−	0.302984i
$818$	−17.0000			−0.594391
$819$		0			0
$820$	6.00000			0.209529
$821$	9.00000	+	15.5885i	0.314102	+	0.544041i	0.979246	−	0.202674i	$-0.0649632\pi$
$821$	9.00000	+	15.5885i	0.314102	+	0.544041i	−0.665144	+	0.746715i	$0.731630\pi$
$822$		0			0
$823$	2.50000	−	4.33013i	0.0871445	−	0.150939i	−0.819159	−	0.573567i	$-0.805559\pi$
$823$	2.50000	−	4.33013i	0.0871445	−	0.150939i	0.906303	+	0.422628i	$0.138892\pi$
$824$	9.00000			0.313530
$825$		0			0
$826$	6.00000	−	10.3923i	0.208767	−	0.361595i
$827$	30.0000			1.04320			0.521601	−	0.853189i	$-0.325335\pi$
$827$	30.0000			1.04320			0.521601	+	0.853189i	$0.325335\pi$
$828$		0			0
$829$	22.0000	+	38.1051i	0.764092	+	1.32345i	0.940726	+	0.339169i	$0.110146\pi$
$829$	22.0000	+	38.1051i	0.764092	+	1.32345i	−0.176634	+	0.984277i	$0.556521\pi$
$830$	6.00000	+	10.3923i	0.208263	+	0.360722i
$831$		0			0
$832$	2.50000	+	2.59808i	0.0866719	+	0.0900721i
$833$		0			0
$834$		0			0
$835$	6.50000	+	11.2583i	0.224942	+	0.389611i
$836$	−2.50000	+	4.33013i	−0.0864643	+	0.149761i
$837$		0			0
$838$	14.0000	−	24.2487i	0.483622	−	0.837658i
$839$	−27.0000	+	46.7654i	−0.932144	+	1.61452i	−0.152493	+	0.988304i	$0.548730\pi$
$839$	−27.0000	+	46.7654i	−0.932144	+	1.61452i	−0.779650	+	0.626215i	$0.784603\pi$
$840$		0			0
$841$	14.5000	−	25.1147i	0.500000	−	0.866025i
$842$	10.0000	+	17.3205i	0.344623	+	0.596904i
$843$		0			0
$844$	−15.0000			−0.516321
$845$	0.500000	−	12.9904i	0.0172005	−	0.446883i
$846$		0			0
$847$	−15.0000	−	25.9808i	−0.515406	−	0.892710i
$848$	−6.50000	−	11.2583i	−0.223211	−	0.386613i
$849$		0			0
$850$		0			0
$851$	2.00000	−	3.46410i	0.0685591	−	0.118748i
$852$		0			0
$853$	−14.0000			−0.479351			−0.239675	−	0.970853i	$-0.577041\pi$
$853$	−14.0000			−0.479351			−0.239675	+	0.970853i	$0.577041\pi$
$854$	3.00000	−	5.19615i	0.102658	−	0.177809i
$855$		0			0
$856$	3.00000	+	5.19615i	0.102538	+	0.177601i
$857$	18.0000			0.614868			0.307434	−	0.951569i	$-0.400530\pi$
$857$	18.0000			0.614868			0.307434	+	0.951569i	$0.400530\pi$
$858$		0			0
$859$	19.0000			0.648272			0.324136	−	0.946011i	$-0.394927\pi$
$859$	19.0000			0.648272			0.324136	+	0.946011i	$0.394927\pi$
$860$	−1.00000	−	1.73205i	−0.0340997	−	0.0590624i
$861$		0			0
$862$	−18.0000	+	31.1769i	−0.613082	+	1.06189i
$863$	48.0000			1.63394			0.816970	−	0.576681i	$-0.195652\pi$
$863$	48.0000			1.63394			0.816970	+	0.576681i	$0.195652\pi$
$864$		0			0
$865$	4.50000	−	7.79423i	0.153005	−	0.265012i
$866$	−16.0000			−0.543702
$867$		0			0
$868$	15.0000	+	25.9808i	0.509133	+	0.881845i
$869$	−5.00000	−	8.66025i	−0.169613	−	0.293779i
$870$		0			0
$871$	−12.0000	+	41.5692i	−0.406604	+	1.40852i
$872$	10.0000			0.338643
$873$		0			0
$874$	−10.0000	−	17.3205i	−0.338255	−	0.585875i
$875$	−1.50000	+	2.59808i	−0.0507093	+	0.0878310i
$876$		0			0
$877$	−19.0000	+	32.9090i	−0.641584	+	1.11126i	0.343495	+	0.939155i	$0.388389\pi$
$877$	−19.0000	+	32.9090i	−0.641584	+	1.11126i	−0.985079	+	0.172102i	$0.944944\pi$
$878$	−5.00000	+	8.66025i	−0.168742	+	0.292269i
$879$		0			0
$880$	−0.500000	+	0.866025i	−0.0168550	+	0.0291937i
$881$	2.50000	+	4.33013i	0.0842271	+	0.145886i	0.905062	−	0.425280i	$-0.139825\pi$
$881$	2.50000	+	4.33013i	0.0842271	+	0.145886i	−0.820834	+	0.571166i	$0.806491\pi$
$882$		0			0
$883$	42.0000			1.41341			0.706706	−	0.707507i	$-0.250180\pi$
$883$	42.0000			1.41341			0.706706	+	0.707507i	$0.250180\pi$
$884$		0			0
$885$		0			0
$886$	9.00000	+	15.5885i	0.302361	+	0.523704i
$887$	−6.50000	−	11.2583i	−0.218249	−	0.378018i	0.736024	−	0.676955i	$-0.236701\pi$
$887$	−6.50000	−	11.2583i	−0.218249	−	0.378018i	−0.954273	+	0.298938i	$0.903368\pi$
$888$		0			0
$889$	−15.0000			−0.503084
$890$	0.500000	−	0.866025i	0.0167600	−	0.0290292i
$891$		0			0
$892$	11.0000			0.368307
$893$	22.5000	−	38.9711i	0.752934	−	1.30412i
$894$		0			0
$895$	−6.00000	−	10.3923i	−0.200558	−	0.347376i
$896$	3.00000			0.100223
$897$		0			0
$898$	−15.0000			−0.500556
$899$		0			0
$900$		0			0
$901$		0			0
$902$	−6.00000			−0.199778
$903$		0			0
$904$	−8.00000	+	13.8564i	−0.266076	+	0.460857i
$905$	−6.00000			−0.199447
$906$		0			0
$907$	−21.0000	−	36.3731i	−0.697294	−	1.20775i	−0.969401	−	0.245481i	$-0.921054\pi$
$907$	−21.0000	−	36.3731i	−0.697294	−	1.20775i	0.272108	−	0.962267i	$-0.412279\pi$
$908$	−10.0000	−	17.3205i	−0.331862	−	0.574801i
$909$		0			0
$910$	−7.50000	−	7.79423i	−0.248623	−	0.258376i
$911$	−12.0000			−0.397578			−0.198789	−	0.980042i	$-0.563701\pi$
$911$	−12.0000			−0.397578			−0.198789	+	0.980042i	$0.563701\pi$
$912$		0			0
$913$	−6.00000	−	10.3923i	−0.198571	−	0.343935i
$914$	11.0000	−	19.0526i	0.363848	−	0.630203i
$915$		0			0
$916$	5.00000	−	8.66025i	0.165205	−	0.286143i
$917$	22.5000	−	38.9711i	0.743015	−	1.28694i
$918$		0			0
$919$	−17.0000	+	29.4449i	−0.560778	+	0.971296i	0.436650	+	0.899631i	$0.356165\pi$
$919$	−17.0000	+	29.4449i	−0.560778	+	0.971296i	−0.997429	+	0.0716652i	$0.977169\pi$
$920$	−2.00000	−	3.46410i	−0.0659380	−	0.114208i
$921$		0			0
$922$	−12.0000			−0.395199
$923$	−7.00000	+	1.73205i	−0.230408	+	0.0570111i
$924$		0			0
$925$	0.500000	+	0.866025i	0.0164399	+	0.0284747i
$926$	−8.00000	−	13.8564i	−0.262896	−	0.455350i
$927$		0			0
$928$		0			0
$929$	17.0000	−	29.4449i	0.557752	−	0.966055i	−0.439932	−	0.898031i	$-0.644997\pi$
$929$	17.0000	−	29.4449i	0.557752	−	0.966055i	0.997684	−	0.0680235i	$-0.0216693\pi$
$930$		0			0
$931$	−10.0000			−0.327737
$932$	5.00000	−	8.66025i	0.163780	−	0.283676i
$933$		0			0
$934$	18.0000	+	31.1769i	0.588978	+	1.02014i
$935$		0			0
$936$		0			0
$937$	−10.0000			−0.326686			−0.163343	−	0.986569i	$-0.552228\pi$
$937$	−10.0000			−0.326686			−0.163343	+	0.986569i	$0.552228\pi$
$938$	18.0000	+	31.1769i	0.587721	+	1.01796i
$939$		0			0
$940$	4.50000	−	7.79423i	0.146774	−	0.254220i
$941$	−24.0000			−0.782378			−0.391189	−	0.920310i	$-0.627936\pi$
$941$	−24.0000			−0.782378			−0.391189	+	0.920310i	$0.627936\pi$
$942$		0			0
$943$	12.0000	−	20.7846i	0.390774	−	0.676840i
$944$	−4.00000			−0.130189
$945$		0			0
$946$	1.00000	+	1.73205i	0.0325128	+	0.0563138i
$947$	−19.0000	−	32.9090i	−0.617417	−	1.06940i	−0.989955	−	0.141381i	$-0.954846\pi$
$947$	−19.0000	−	32.9090i	−0.617417	−	1.06940i	0.372538	−	0.928017i	$-0.378488\pi$
$948$		0			0
$949$	−40.0000	−	41.5692i	−1.29845	−	1.34939i
$950$	5.00000			0.162221
$951$		0			0
$952$		0			0
$953$	11.0000	−	19.0526i	0.356325	−	0.617173i	−0.631019	−	0.775768i	$-0.717363\pi$
$953$	11.0000	−	19.0526i	0.356325	−	0.617173i	0.987344	+	0.158595i	$0.0506963\pi$
$954$		0			0
$955$	9.00000	−	15.5885i	0.291233	−	0.504431i
$956$	−1.00000	+	1.73205i	−0.0323423	+	0.0560185i
$957$		0			0
$958$	4.00000	−	6.92820i	0.129234	−	0.223840i
$959$	−24.0000	−	41.5692i	−0.775000	−	1.34234i
$960$		0			0
$961$	69.0000			2.22581
$962$	−3.50000	+	0.866025i	−0.112845	+	0.0279218i
$963$		0			0
$964$	−7.50000	−	12.9904i	−0.241559	−	0.418392i
$965$	8.00000	+	13.8564i	0.257529	+	0.446054i
$966$		0			0
$967$	7.00000			0.225105			0.112552	−	0.993646i	$-0.464097\pi$
$967$	7.00000			0.225105			0.112552	+	0.993646i	$0.464097\pi$
$968$	−5.00000	+	8.66025i	−0.160706	+	0.278351i
$969$		0			0
$970$	12.0000			0.385297
$971$	13.5000	−	23.3827i	0.433236	−	0.750386i	−0.563914	−	0.825833i	$-0.690705\pi$
$971$	13.5000	−	23.3827i	0.433236	−	0.750386i	0.997150	+	0.0754473i	$0.0240385\pi$
$972$		0			0
$973$	−13.5000	−	23.3827i	−0.432790	−	0.749614i
$974$	−35.0000			−1.12147
$975$		0			0
$976$	−2.00000			−0.0640184
$977$	24.0000	+	41.5692i	0.767828	+	1.32992i	0.938738	+	0.344631i	$0.111996\pi$
$977$	24.0000	+	41.5692i	0.767828	+	1.32992i	−0.170910	+	0.985287i	$0.554671\pi$
$978$		0			0
$979$	−0.500000	+	0.866025i	−0.0159801	+	0.0276783i
$980$	−2.00000			−0.0638877
$981$		0			0
$982$	−12.5000	+	21.6506i	−0.398891	+	0.690900i
$983$	−53.0000			−1.69044			−0.845219	−	0.534421i	$-0.820530\pi$
$983$	−53.0000			−1.69044			−0.845219	+	0.534421i	$0.820530\pi$
$984$		0			0
$985$	7.50000	+	12.9904i	0.238970	+	0.413908i
$986$		0			0
$987$		0			0
$988$	−5.00000	+	17.3205i	−0.159071	+	0.551039i
$989$	−8.00000			−0.254385
$990$		0			0
$991$	−19.0000	−	32.9090i	−0.603555	−	1.04539i	−0.992278	−	0.124033i	$-0.960417\pi$
$991$	−19.0000	−	32.9090i	−0.603555	−	1.04539i	0.388723	−	0.921355i	$-0.372916\pi$
$992$	5.00000	−	8.66025i	0.158750	−	0.274963i
$993$		0			0
$994$	−3.00000	+	5.19615i	−0.0951542	+	0.164812i
$995$	−1.00000	+	1.73205i	−0.0317021	+	0.0549097i
$996$		0			0
$997$	3.50000	−	6.06218i	0.110846	−	0.191991i	−0.805266	−	0.592914i	$-0.797977\pi$
$997$	3.50000	−	6.06218i	0.110846	−	0.191991i	0.916112	+	0.400923i	$0.131311\pi$
$998$	10.0000	+	17.3205i	0.316544	+	0.548271i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1170.2.i.j.991.1		2
3.2	odd	2		390.2.i.b.211.1	yes	2
13.9	even	3	inner	1170.2.i.j.451.1		2
15.2	even	4		1950.2.z.i.1849.2		4
15.8	even	4		1950.2.z.i.1849.1		4
15.14	odd	2		1950.2.i.o.601.1		2
39.2	even	12		5070.2.b.a.1351.1		2
39.11	even	12		5070.2.b.a.1351.2		2
39.23	odd	6		5070.2.a.c.1.1		1
39.29	odd	6		5070.2.a.q.1.1		1
39.35	odd	6		390.2.i.b.61.1	✓	2
195.74	odd	6		1950.2.i.o.451.1		2
195.113	even	12		1950.2.z.i.1699.2		4
195.152	even	12		1950.2.z.i.1699.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.i.b.61.1	✓	2	39.35	odd	6
390.2.i.b.211.1	yes	2	3.2	odd	2
1170.2.i.j.451.1		2	13.9	even	3	inner
1170.2.i.j.991.1		2	1.1	even	1	trivial
1950.2.i.o.451.1		2	195.74	odd	6
1950.2.i.o.601.1		2	15.14	odd	2
1950.2.z.i.1699.1		4	195.152	even	12
1950.2.z.i.1699.2		4	195.113	even	12
1950.2.z.i.1849.1		4	15.8	even	4
1950.2.z.i.1849.2		4	15.2	even	4
5070.2.a.c.1.1		1	39.23	odd	6
5070.2.a.q.1.1		1	39.29	odd	6
5070.2.b.a.1351.1		2	39.2	even	12
5070.2.b.a.1351.2		2	39.11	even	12

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)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(1.50000 - 2.59808i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(1.50000 - 2.59808i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{10} +(0.500000 + 0.866025i) q^{11} +(2.50000 + 2.59808i) q^{13} +3.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.50000 - 4.33013i) q^{19} +(0.500000 - 0.866025i) q^{20} +(-0.500000 + 0.866025i) q^{22} +(-2.00000 - 3.46410i) q^{23} +1.00000 q^{25} +(-1.00000 + 3.46410i) q^{26} +(1.50000 + 2.59808i) q^{28} +10.0000 q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.50000 + 2.59808i) q^{35} +(0.500000 + 0.866025i) q^{37} +5.00000 q^{38} +1.00000 q^{40} +(3.00000 + 5.19615i) q^{41} +(1.00000 - 1.73205i) q^{43} -1.00000 q^{44} +(2.00000 - 3.46410i) q^{46} +9.00000 q^{47} +(-1.00000 - 1.73205i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-3.50000 + 0.866025i) q^{52} +13.0000 q^{53} +(-0.500000 - 0.866025i) q^{55} +(-1.50000 + 2.59808i) q^{56} +(2.00000 - 3.46410i) q^{59} +(1.00000 - 1.73205i) q^{61} +(5.00000 + 8.66025i) q^{62} +1.00000 q^{64} +(-2.50000 - 2.59808i) q^{65} +(6.00000 + 10.3923i) q^{67} -3.00000 q^{70} +(-1.00000 + 1.73205i) q^{71} -16.0000 q^{73} +(-0.500000 + 0.866025i) q^{74} +(2.50000 + 4.33013i) q^{76} +3.00000 q^{77} -10.0000 q^{79} +(0.500000 + 0.866025i) q^{80} +(-3.00000 + 5.19615i) q^{82} -12.0000 q^{83} +2.00000 q^{86} +(-0.500000 - 0.866025i) q^{88} +(0.500000 + 0.866025i) q^{89} +(10.5000 - 2.59808i) q^{91} +4.00000 q^{92} +(4.50000 + 7.79423i) q^{94} +(-2.50000 + 4.33013i) q^{95} +(-6.00000 + 10.3923i) q^{97} +(1.00000 - 1.73205i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{4} - 2 q^{5} + 3 q^{7} - 2 q^{8}+O(q^{10}) \) 2 * q + q^2 - q^4 - 2 * q^5 + 3 * q^7 - 2 * q^8	\( 2 q + q^{2} - q^{4} - 2 q^{5} + 3 q^{7} - 2 q^{8} - q^{10} + q^{11} + 5 q^{13} + 6 q^{14} - q^{16} + 5 q^{19} + q^{20} - q^{22} - 4 q^{23} + 2 q^{25} - 2 q^{26} + 3 q^{28} + 20 q^{31} + q^{32} - 3 q^{35} + q^{37} + 10 q^{38} + 2 q^{40} + 6 q^{41} + 2 q^{43} - 2 q^{44} + 4 q^{46} + 18 q^{47} - 2 q^{49} + q^{50} - 7 q^{52} + 26 q^{53} - q^{55} - 3 q^{56} + 4 q^{59} + 2 q^{61} + 10 q^{62} + 2 q^{64} - 5 q^{65} + 12 q^{67} - 6 q^{70} - 2 q^{71} - 32 q^{73} - q^{74} + 5 q^{76} + 6 q^{77} - 20 q^{79} + q^{80} - 6 q^{82} - 24 q^{83} + 4 q^{86} - q^{88} + q^{89} + 21 q^{91} + 8 q^{92} + 9 q^{94} - 5 q^{95} - 12 q^{97} + 2 q^{98}+O(q^{100}) \) 2 * q + q^2 - q^4 - 2 * q^5 + 3 * q^7 - 2 * q^8 - q^10 + q^11 + 5 * q^13 + 6 * q^14 - q^16 + 5 * q^19 + q^20 - q^22 - 4 * q^23 + 2 * q^25 - 2 * q^26 + 3 * q^28 + 20 * q^31 + q^32 - 3 * q^35 + q^37 + 10 * q^38 + 2 * q^40 + 6 * q^41 + 2 * q^43 - 2 * q^44 + 4 * q^46 + 18 * q^47 - 2 * q^49 + q^50 - 7 * q^52 + 26 * q^53 - q^55 - 3 * q^56 + 4 * q^59 + 2 * q^61 + 10 * q^62 + 2 * q^64 - 5 * q^65 + 12 * q^67 - 6 * q^70 - 2 * q^71 - 32 * q^73 - q^74 + 5 * q^76 + 6 * q^77 - 20 * q^79 + q^80 - 6 * q^82 - 24 * q^83 + 4 * q^86 - q^88 + q^89 + 21 * q^91 + 8 * q^92 + 9 * q^94 - 5 * q^95 - 12 * q^97 + 2 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more