LMFDB - Embedded newform 390.2.i.b.211.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [390,2,Mod(61,390)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("390.61"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(390, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.i (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [2,-1,1,-1,2,1,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$3.11416567883$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			211.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	390.211
Dual form			390.2.i.b.61.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(0.500000 - 0.866025i) q^{6} +(1.50000 - 2.59808i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(-0.500000 - 0.866025i) q^{11} -1.00000 q^{12} +(2.50000 + 2.59808i) q^{13} -3.00000 q^{14} +(0.500000 + 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +1.00000 q^{18} +(2.50000 - 4.33013i) q^{19} +(-0.500000 + 0.866025i) q^{20} +3.00000 q^{21} +(-0.500000 + 0.866025i) q^{22} +(2.00000 + 3.46410i) q^{23} +(0.500000 + 0.866025i) q^{24} +1.00000 q^{25} +(1.00000 - 3.46410i) q^{26} -1.00000 q^{27} +(1.50000 + 2.59808i) q^{28} +(0.500000 - 0.866025i) q^{30} +10.0000 q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.500000 - 0.866025i) q^{33} +(1.50000 - 2.59808i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(0.500000 + 0.866025i) q^{37} -5.00000 q^{38} +(-1.00000 + 3.46410i) q^{39} +1.00000 q^{40} +(-3.00000 - 5.19615i) q^{41} +(-1.50000 - 2.59808i) q^{42} +(1.00000 - 1.73205i) q^{43} +1.00000 q^{44} +(-0.500000 + 0.866025i) q^{45} +(2.00000 - 3.46410i) q^{46} -9.00000 q^{47} +(0.500000 - 0.866025i) q^{48} +(-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^{54} +(-0.500000 - 0.866025i) q^{55} +(1.50000 - 2.59808i) q^{56} +5.00000 q^{57} +(-2.00000 + 3.46410i) q^{59} -1.00000 q^{60} +(1.00000 - 1.73205i) q^{61} +(-5.00000 - 8.66025i) q^{62} +(1.50000 + 2.59808i) q^{63} +1.00000 q^{64} +(2.50000 + 2.59808i) q^{65} -1.00000 q^{66} +(6.00000 + 10.3923i) q^{67} +(-2.00000 + 3.46410i) q^{69} -3.00000 q^{70} +(1.00000 - 1.73205i) q^{71} +(-0.500000 + 0.866025i) q^{72} -16.0000 q^{73} +(0.500000 - 0.866025i) q^{74} +(0.500000 + 0.866025i) q^{75} +(2.50000 + 4.33013i) q^{76} -3.00000 q^{77} +(3.50000 - 0.866025i) q^{78} -10.0000 q^{79} +(-0.500000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-3.00000 + 5.19615i) q^{82} +12.0000 q^{83} +(-1.50000 + 2.59808i) q^{84} -2.00000 q^{86} +(-0.500000 - 0.866025i) q^{88} +(-0.500000 - 0.866025i) q^{89} +1.00000 q^{90} +(10.5000 - 2.59808i) q^{91} -4.00000 q^{92} +(5.00000 + 8.66025i) q^{93} +(4.50000 + 7.79423i) q^{94} +(2.50000 - 4.33013i) q^{95} -1.00000 q^{96} +(-6.00000 + 10.3923i) q^{97} +(-1.00000 + 1.73205i) q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} + q^{3} - q^{4} + 2 q^{5} + q^{6} + 3 q^{7} + 2 q^{8} - q^{9} - q^{10} - q^{11} - 2 q^{12} + 5 q^{13} - 6 q^{14} + q^{15} - q^{16} + 2 q^{18} + 5 q^{19} - q^{20} + 6 q^{21} - q^{22}+ \cdots + 2 q^{99}+O(q^{100}) $ 2 * q - q^2 + q^3 - q^4 + 2 * q^5 + q^6 + 3 * q^7 + 2 * q^8 - q^9 - q^10 - q^11 - 2 * q^12 + 5 * q^13 - 6 * q^14 + q^15 - q^16 + 2 * q^18 + 5 * q^19 - q^20 + 6 * q^21 - q^22 + 4 * q^23 + q^24 + 2 * q^25 + 2 * q^26 - 2 * q^27 + 3 * q^28 + q^30 + 20 * q^31 - q^32 + q^33 + 3 * q^35 - q^36 + q^37 - 10 * q^38 - 2 * q^39 + 2 * q^40 - 6 * q^41 - 3 * q^42 + 2 * q^43 + 2 * q^44 - q^45 + 4 * q^46 - 18 * q^47 + q^48 - 2 * q^49 - q^50 - 7 * q^52 - 26 * q^53 + q^54 - q^55 + 3 * q^56 + 10 * q^57 - 4 * q^59 - 2 * q^60 + 2 * q^61 - 10 * q^62 + 3 * q^63 + 2 * q^64 + 5 * q^65 - 2 * q^66 + 12 * q^67 - 4 * q^69 - 6 * q^70 + 2 * q^71 - q^72 - 32 * q^73 + q^74 + q^75 + 5 * q^76 - 6 * q^77 + 7 * q^78 - 20 * q^79 - q^80 - q^81 - 6 * q^82 + 24 * q^83 - 3 * q^84 - 4 * q^86 - q^88 - q^89 + 2 * q^90 + 21 * q^91 - 8 * q^92 + 10 * q^93 + 9 * q^94 + 5 * q^95 - 2 * q^96 - 12 * q^97 - 2 * q^98 + 2 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$.

$n$	$131$	$157$	$301$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	0.500000	−	0.866025i	0.204124	−	0.353553i
$7$	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
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.500000	−	0.866025i	−0.158114	−	0.273861i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i	0.780750	−	0.624844i	$-0.214837\pi$
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i	−0.931505	+	0.363727i	$0.881504\pi$
$12$	−1.00000			−0.288675
$13$	2.50000	+	2.59808i	0.693375	+	0.720577i
$13$	2.50000	+	2.59808i	0.693375	+	0.720577i
$14$	−3.00000			−0.801784
$15$	0.500000	+	0.866025i	0.129099	+	0.223607i
$16$	−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	$0.166667\pi$
$18$	1.00000			0.235702
$19$	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
$21$	3.00000			0.654654
$22$	−0.500000	+	0.866025i	−0.106600	+	0.184637i
$23$	2.00000	+	3.46410i	0.417029	+	0.722315i	0.995639	−	0.0932891i	$-0.0297381\pi$
$23$	2.00000	+	3.46410i	0.417029	+	0.722315i	−0.578610	+	0.815604i	$0.696405\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	1.00000			0.200000
$26$	1.00000	−	3.46410i	0.196116	−	0.679366i
$27$	−1.00000			−0.192450
$28$	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	$0.833333\pi$
$30$	0.500000	−	0.866025i	0.0912871	−	0.158114i
$31$	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
$33$	0.500000	−	0.866025i	0.0870388	−	0.150756i
$34$		0			0
$35$	1.50000	−	2.59808i	0.253546	−	0.439155i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	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
$39$	−1.00000	+	3.46410i	−0.160128	+	0.554700i
$40$	1.00000			0.158114
$41$	−3.00000	−	5.19615i	−0.468521	−	0.811503i	0.530831	−	0.847477i	$-0.321880\pi$
$41$	−3.00000	−	5.19615i	−0.468521	−	0.811503i	−0.999353	+	0.0359748i	$0.988546\pi$
$42$	−1.50000	−	2.59808i	−0.231455	−	0.400892i
$43$	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
$45$	−0.500000	+	0.866025i	−0.0745356	+	0.129099i
$46$	2.00000	−	3.46410i	0.294884	−	0.510754i
$47$	−9.00000			−1.31278			−0.656392	−	0.754420i	$-0.727918\pi$
$47$	−9.00000			−1.31278			−0.656392	+	0.754420i	$0.727918\pi$
$48$	0.500000	−	0.866025i	0.0721688	−	0.125000i
$49$	−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	$-0.851293\pi$
$53$	−13.0000			−1.78569			−0.892844	+	0.450367i	$0.851293\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$	−0.500000	−	0.866025i	−0.0674200	−	0.116775i
$56$	1.50000	−	2.59808i	0.200446	−	0.347183i
$57$	5.00000			0.662266
$58$		0			0
$59$	−2.00000	+	3.46410i	−0.260378	+	0.450988i	−0.966342	−	0.257260i	$-0.917180\pi$
$59$	−2.00000	+	3.46410i	−0.260378	+	0.450988i	0.705965	+	0.708247i	$0.250514\pi$
$60$	−1.00000			−0.129099
$61$	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
$63$	1.50000	+	2.59808i	0.188982	+	0.327327i
$64$	1.00000			0.125000
$65$	2.50000	+	2.59808i	0.310087	+	0.322252i
$66$	−1.00000			−0.123091
$67$	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
$69$	−2.00000	+	3.46410i	−0.240772	+	0.417029i
$70$	−3.00000			−0.358569
$71$	1.00000	−	1.73205i	0.118678	−	0.205557i	−0.800566	−	0.599245i	$-0.795468\pi$
$71$	1.00000	−	1.73205i	0.118678	−	0.205557i	0.919244	+	0.393688i	$0.128801\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	−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
$75$	0.500000	+	0.866025i	0.0577350	+	0.100000i
$76$	2.50000	+	4.33013i	0.286770	+	0.496700i
$77$	−3.00000			−0.341882
$78$	3.50000	−	0.866025i	0.396297	−	0.0980581i
$79$	−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
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−3.00000	+	5.19615i	−0.331295	+	0.573819i
$83$	12.0000			1.31717			0.658586	−	0.752506i	$-0.271155\pi$
$83$	12.0000			1.31717			0.658586	+	0.752506i	$0.271155\pi$
$84$	−1.50000	+	2.59808i	−0.163663	+	0.283473i
$85$		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	0.838308	−	0.545197i	$-0.183545\pi$
$89$	−0.500000	−	0.866025i	−0.0529999	−	0.0917985i	−0.891308	+	0.453398i	$0.850212\pi$
$90$	1.00000			0.105409
$91$	10.5000	−	2.59808i	1.10070	−	0.272352i
$92$	−4.00000			−0.417029
$93$	5.00000	+	8.66025i	0.518476	+	0.898027i
$94$	4.50000	+	7.79423i	0.464140	+	0.803913i
$95$	2.50000	−	4.33013i	0.256495	−	0.444262i
$96$	−1.00000			−0.102062
$97$	−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
$99$	1.00000			0.100504
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	−2.00000	−	3.46410i	−0.199007	−	0.344691i	0.749199	−	0.662344i	$-0.230438\pi$
$101$	−2.00000	−	3.46410i	−0.199007	−	0.344691i	−0.948207	+	0.317653i	$0.897105\pi$
$102$		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
$105$	3.00000			0.292770
$106$	6.50000	+	11.2583i	0.631336	+	1.09351i
$107$	3.00000	+	5.19615i	0.290021	+	0.502331i	0.973814	−	0.227345i	$-0.0730044\pi$
$107$	3.00000	+	5.19615i	0.290021	+	0.502331i	−0.683793	+	0.729676i	$0.739671\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	−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
$111$	−0.500000	+	0.866025i	−0.0474579	+	0.0821995i
$112$	−3.00000			−0.283473
$113$	−8.00000	+	13.8564i	−0.752577	+	1.30350i	0.193993	+	0.981003i	$0.437856\pi$
$113$	−8.00000	+	13.8564i	−0.752577	+	1.30350i	−0.946570	+	0.322498i	$0.895477\pi$
$114$	−2.50000	−	4.33013i	−0.234146	−	0.405554i
$115$	2.00000	+	3.46410i	0.186501	+	0.323029i
$116$		0			0
$117$	−3.50000	+	0.866025i	−0.323575	+	0.0800641i
$118$	4.00000			0.368230
$119$		0			0
$120$	0.500000	+	0.866025i	0.0456435	+	0.0790569i
$121$	5.00000	−	8.66025i	0.454545	−	0.787296i
$122$	−2.00000			−0.181071
$123$	3.00000	−	5.19615i	0.270501	−	0.468521i
$124$	−5.00000	+	8.66025i	−0.449013	+	0.777714i
$125$	1.00000			0.0894427
$126$	1.50000	−	2.59808i	0.133631	−	0.231455i
$127$	−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
$129$	2.00000			0.176090
$130$	1.00000	−	3.46410i	0.0877058	−	0.303822i
$131$	−15.0000			−1.31056			−0.655278	−	0.755388i	$-0.727449\pi$
$131$	−15.0000			−1.31056			−0.655278	+	0.755388i	$0.727449\pi$
$132$	0.500000	+	0.866025i	0.0435194	+	0.0753778i
$133$	−7.50000	−	12.9904i	−0.650332	−	1.12641i
$134$	6.00000	−	10.3923i	0.518321	−	0.897758i
$135$	−1.00000			−0.0860663
$136$		0			0
$137$	−8.00000	+	13.8564i	−0.683486	+	1.18383i	0.290424	+	0.956898i	$0.406204\pi$
$137$	−8.00000	+	13.8564i	−0.683486	+	1.18383i	−0.973910	+	0.226935i	$0.927130\pi$
$138$	4.00000			0.340503
$139$	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
$141$	−4.50000	−	7.79423i	−0.378968	−	0.656392i
$142$	−2.00000			−0.167836
$143$	1.00000	−	3.46410i	0.0836242	−	0.289683i
$144$	1.00000			0.0833333
$145$		0			0
$146$	8.00000	+	13.8564i	0.662085	+	1.14676i
$147$	1.00000	−	1.73205i	0.0824786	−	0.142857i
$148$	−1.00000			−0.0821995
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	−0.716578	−	0.697507i	$-0.754293\pi$
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	0.962348	+	0.271821i	$0.0876260\pi$
$150$	0.500000	−	0.866025i	0.0408248	−	0.0707107i
$151$	−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
$156$	−2.50000	−	2.59808i	−0.200160	−	0.208013i
$157$	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
$159$	−6.50000	−	11.2583i	−0.515484	−	0.892844i
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	12.0000			0.945732
$162$	−0.500000	+	0.866025i	−0.0392837	+	0.0680414i
$163$	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
$165$	0.500000	−	0.866025i	0.0389249	−	0.0674200i
$166$	−6.00000	−	10.3923i	−0.465690	−	0.806599i
$167$	6.50000	+	11.2583i	0.502985	+	0.871196i	0.999994	+	0.00345033i	$0.00109828\pi$
$167$	6.50000	+	11.2583i	0.502985	+	0.871196i	−0.497009	+	0.867745i	$0.665568\pi$
$168$	3.00000			0.231455
$169$	−0.500000	+	12.9904i	−0.0384615	+	0.999260i
$170$		0			0
$171$	2.50000	+	4.33013i	0.191180	+	0.331133i
$172$	1.00000	+	1.73205i	0.0762493	+	0.132068i
$173$	4.50000	−	7.79423i	0.342129	−	0.592584i	−0.642699	−	0.766119i	$-0.722185\pi$
$173$	4.50000	−	7.79423i	0.342129	−	0.592584i	0.984828	+	0.173534i	$0.0555188\pi$
$174$		0			0
$175$	1.50000	−	2.59808i	0.113389	−	0.196396i
$176$	−0.500000	+	0.866025i	−0.0376889	+	0.0652791i
$177$	−4.00000			−0.300658
$178$	−0.500000	+	0.866025i	−0.0374766	+	0.0649113i
$179$	−6.00000	−	10.3923i	−0.448461	−	0.776757i	0.549825	−	0.835280i	$-0.314694\pi$
$179$	−6.00000	−	10.3923i	−0.448461	−	0.776757i	−0.998286	+	0.0585225i	$0.981361\pi$
$180$	−0.500000	−	0.866025i	−0.0372678	−	0.0645497i
$181$	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
$183$	2.00000			0.147844
$184$	2.00000	+	3.46410i	0.147442	+	0.255377i
$185$	0.500000	+	0.866025i	0.0367607	+	0.0636715i
$186$	5.00000	−	8.66025i	0.366618	−	0.635001i
$187$		0			0
$188$	4.50000	−	7.79423i	0.328196	−	0.568453i
$189$	−1.50000	+	2.59808i	−0.109109	+	0.188982i
$190$	−5.00000			−0.362738
$191$	9.00000	−	15.5885i	0.651217	−	1.12794i	−0.331611	−	0.943416i	$-0.607592\pi$
$191$	9.00000	−	15.5885i	0.651217	−	1.12794i	0.982828	−	0.184525i	$-0.0590746\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	−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
$195$	−1.00000	+	3.46410i	−0.0716115	+	0.248069i
$196$	2.00000			0.142857
$197$	7.50000	+	12.9904i	0.534353	+	0.925526i	0.999194	+	0.0401324i	$0.0127780\pi$
$197$	7.50000	+	12.9904i	0.534353	+	0.925526i	−0.464841	+	0.885394i	$0.653889\pi$
$198$	−0.500000	−	0.866025i	−0.0355335	−	0.0615457i
$199$	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
$201$	−6.00000	+	10.3923i	−0.423207	+	0.733017i
$202$	−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
$207$	−4.00000			−0.278019
$208$	1.00000	−	3.46410i	0.0693375	−	0.240192i
$209$	−5.00000			−0.345857
$210$	−1.50000	−	2.59808i	−0.103510	−	0.179284i
$211$	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
$213$	2.00000			0.137038
$214$	3.00000	−	5.19615i	0.205076	−	0.355202i
$215$	1.00000	−	1.73205i	0.0681994	−	0.118125i
$216$	−1.00000			−0.0680414
$217$	15.0000	−	25.9808i	1.01827	−	1.76369i
$218$	5.00000	+	8.66025i	0.338643	+	0.586546i
$219$	−8.00000	−	13.8564i	−0.540590	−	0.936329i
$220$	1.00000			0.0674200
$221$		0			0
$222$	1.00000			0.0671156
$223$	−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
$225$	−0.500000	+	0.866025i	−0.0333333	+	0.0577350i
$226$	16.0000			1.06430
$227$	10.0000	−	17.3205i	0.663723	−	1.14960i	−0.315906	−	0.948790i	$-0.602309\pi$
$227$	10.0000	−	17.3205i	0.663723	−	1.14960i	0.979630	−	0.200812i	$-0.0643581\pi$
$228$	−2.50000	+	4.33013i	−0.165567	+	0.286770i
$229$	−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
$231$	−1.50000	−	2.59808i	−0.0986928	−	0.170941i
$232$		0			0
$233$	10.0000			0.655122			0.327561	−	0.944830i	$-0.393773\pi$
$233$	10.0000			0.655122			0.327561	+	0.944830i	$0.393773\pi$
$234$	2.50000	+	2.59808i	0.163430	+	0.169842i
$235$	−9.00000			−0.587095
$236$	−2.00000	−	3.46410i	−0.130189	−	0.225494i
$237$	−5.00000	−	8.66025i	−0.324785	−	0.562544i
$238$		0			0
$239$	−2.00000			−0.129369			−0.0646846	−	0.997906i	$-0.520604\pi$
$239$	−2.00000			−0.129369			−0.0646846	+	0.997906i	$0.520604\pi$
$240$	0.500000	−	0.866025i	0.0322749	−	0.0559017i
$241$	−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
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	1.00000	+	1.73205i	0.0640184	+	0.110883i
$245$	−1.00000	−	1.73205i	−0.0638877	−	0.110657i
$246$	−6.00000			−0.382546
$247$	17.5000	−	4.33013i	1.11350	−	0.275519i
$248$	10.0000			0.635001
$249$	6.00000	+	10.3923i	0.380235	+	0.658586i
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$	−5.50000	+	9.52628i	−0.347157	+	0.601293i	−0.985743	−	0.168257i	$-0.946186\pi$
$251$	−5.50000	+	9.52628i	−0.347157	+	0.601293i	0.638586	+	0.769550i	$0.279520\pi$
$252$	−3.00000			−0.188982
$253$	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	$0.102578\pi$
$257$	12.0000	+	20.7846i	0.748539	+	1.29651i	−0.199983	+	0.979799i	$0.564089\pi$
$258$	−1.00000	−	1.73205i	−0.0622573	−	0.107833i
$259$	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	0.816066	−	0.577959i	$-0.196151\pi$
$263$	−1.50000	−	2.59808i	−0.0924940	−	0.160204i	−0.908560	+	0.417755i	$0.862817\pi$
$264$	0.500000	−	0.866025i	0.0307729	−	0.0533002i
$265$	−13.0000			−0.798584
$266$	−7.50000	+	12.9904i	−0.459855	+	0.796491i
$267$	0.500000	−	0.866025i	0.0305995	−	0.0529999i
$268$	−12.0000			−0.733017
$269$	10.0000	−	17.3205i	0.609711	−	1.05605i	−0.381577	−	0.924337i	$-0.624619\pi$
$269$	10.0000	−	17.3205i	0.609711	−	1.05605i	0.991288	−	0.131713i	$-0.0420477\pi$
$270$	0.500000	+	0.866025i	0.0304290	+	0.0527046i
$271$	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
$273$	7.50000	+	7.79423i	0.453921	+	0.471728i
$274$	16.0000			0.966595
$275$	−0.500000	−	0.866025i	−0.0301511	−	0.0522233i
$276$	−2.00000	−	3.46410i	−0.120386	−	0.208514i
$277$	−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
$279$	−5.00000	+	8.66025i	−0.299342	+	0.518476i
$280$	1.50000	−	2.59808i	0.0896421	−	0.155265i
$281$	10.0000			0.596550			0.298275	−	0.954480i	$-0.403589\pi$
$281$	10.0000			0.596550			0.298275	+	0.954480i	$0.403589\pi$
$282$	−4.50000	+	7.79423i	−0.267971	+	0.464140i
$283$	−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
$285$	5.00000			0.296174
$286$	−3.50000	+	0.866025i	−0.206959	+	0.0512092i
$287$	−18.0000			−1.06251
$288$	−0.500000	−	0.866025i	−0.0294628	−	0.0510310i
$289$	8.50000	+	14.7224i	0.500000	+	0.866025i
$290$		0			0
$291$	−12.0000			−0.703452
$292$	8.00000	−	13.8564i	0.468165	−	0.810885i
$293$	−6.50000	+	11.2583i	−0.379734	+	0.657719i	−0.991023	−	0.133689i	$-0.957318\pi$
$293$	−6.50000	+	11.2583i	−0.379734	+	0.657719i	0.611289	+	0.791407i	$0.290651\pi$
$294$	−2.00000			−0.116642
$295$	−2.00000	+	3.46410i	−0.116445	+	0.201688i
$296$	0.500000	+	0.866025i	0.0290619	+	0.0503367i
$297$	0.500000	+	0.866025i	0.0290129	+	0.0502519i
$298$	−6.00000			−0.347571
$299$	−4.00000	+	13.8564i	−0.231326	+	0.801337i
$300$	−1.00000			−0.0577350
$301$	−3.00000	−	5.19615i	−0.172917	−	0.299501i
$302$	3.00000	+	5.19615i	0.172631	+	0.299005i
$303$	2.00000	−	3.46410i	0.114897	−	0.199007i
$304$	−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
$309$	−4.50000	−	7.79423i	−0.255996	−	0.443398i
$310$	−5.00000	−	8.66025i	−0.283981	−	0.491869i
$311$	−12.0000			−0.680458			−0.340229	−	0.940343i	$-0.610505\pi$
$311$	−12.0000			−0.680458			−0.340229	+	0.940343i	$0.610505\pi$
$312$	−1.00000	+	3.46410i	−0.0566139	+	0.196116i
$313$	−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
$315$	1.50000	+	2.59808i	0.0845154	+	0.146385i
$316$	5.00000	−	8.66025i	0.281272	−	0.487177i
$317$	19.0000			1.06715			0.533573	−	0.845754i	$-0.320849\pi$
$317$	19.0000			1.06715			0.533573	+	0.845754i	$0.320849\pi$
$318$	−6.50000	+	11.2583i	−0.364502	+	0.631336i
$319$		0			0
$320$	1.00000			0.0559017
$321$	−3.00000	+	5.19615i	−0.167444	+	0.290021i
$322$	−6.00000	−	10.3923i	−0.334367	−	0.579141i
$323$		0			0
$324$	1.00000			0.0555556
$325$	2.50000	+	2.59808i	0.138675	+	0.144115i
$326$	−20.0000			−1.10770
$327$	−5.00000	−	8.66025i	−0.276501	−	0.478913i
$328$	−3.00000	−	5.19615i	−0.165647	−	0.286910i
$329$	−13.5000	+	23.3827i	−0.744279	+	1.28913i
$330$	−1.00000			−0.0550482
$331$	−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
$333$	−1.00000			−0.0547997
$334$	6.50000	−	11.2583i	0.355664	−	0.616028i
$335$	6.00000	+	10.3923i	0.327815	+	0.567792i
$336$	−1.50000	−	2.59808i	−0.0818317	−	0.141737i
$337$	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
$339$	−16.0000			−0.869001
$340$		0			0
$341$	−5.00000	−	8.66025i	−0.270765	−	0.468979i
$342$	2.50000	−	4.33013i	0.135185	−	0.234146i
$343$	15.0000			0.809924
$344$	1.00000	−	1.73205i	0.0539164	−	0.0933859i
$345$	−2.00000	+	3.46410i	−0.107676	+	0.186501i
$346$	−9.00000			−0.483843
$347$	14.0000	−	24.2487i	0.751559	−	1.30174i	−0.195507	−	0.980702i	$-0.562635\pi$
$347$	14.0000	−	24.2487i	0.751559	−	1.30174i	0.947067	−	0.321037i	$-0.104031\pi$
$348$		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
$351$	−2.50000	−	2.59808i	−0.133440	−	0.138675i
$352$	1.00000			0.0533002
$353$	18.0000	+	31.1769i	0.958043	+	1.65938i	0.727245	+	0.686378i	$0.240800\pi$
$353$	18.0000	+	31.1769i	0.958043	+	1.65938i	0.230799	+	0.973002i	$0.425866\pi$
$354$	2.00000	+	3.46410i	0.106299	+	0.184115i
$355$	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	$-0.145579\pi$
$359$	34.0000			1.79445			0.897226	+	0.441572i	$0.145579\pi$
$360$	−0.500000	+	0.866025i	−0.0263523	+	0.0456435i
$361$	−3.00000	−	5.19615i	−0.157895	−	0.273482i
$362$	−3.00000	−	5.19615i	−0.157676	−	0.273104i
$363$	10.0000			0.524864
$364$	−3.00000	+	10.3923i	−0.157243	+	0.544705i
$365$	−16.0000			−0.837478
$366$	−1.00000	−	1.73205i	−0.0522708	−	0.0905357i
$367$		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
$369$	6.00000			0.312348
$370$	0.500000	−	0.866025i	0.0259938	−	0.0450225i
$371$	−19.5000	+	33.7750i	−1.01239	+	1.75351i
$372$	−10.0000			−0.518476
$373$	−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
$375$	0.500000	+	0.866025i	0.0258199	+	0.0447214i
$376$	−9.00000			−0.464140
$377$		0			0
$378$	3.00000			0.154303
$379$	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
$381$	2.50000	−	4.33013i	0.128079	−	0.221839i
$382$	−18.0000			−0.920960
$383$	14.0000	−	24.2487i	0.715367	−	1.23905i	−0.247451	−	0.968900i	$-0.579593\pi$
$383$	14.0000	−	24.2487i	0.715367	−	1.23905i	0.962818	−	0.270151i	$-0.0870736\pi$
$384$	0.500000	−	0.866025i	0.0255155	−	0.0441942i
$385$	−3.00000			−0.152894
$386$	−8.00000	+	13.8564i	−0.407189	+	0.705273i
$387$	1.00000	+	1.73205i	0.0508329	+	0.0880451i
$388$	−6.00000	−	10.3923i	−0.304604	−	0.527589i
$389$	−16.0000			−0.811232			−0.405616	−	0.914044i	$-0.632943\pi$
$389$	−16.0000			−0.811232			−0.405616	+	0.914044i	$0.632943\pi$
$390$	3.50000	−	0.866025i	0.177229	−	0.0438529i
$391$		0			0
$392$	−1.00000	−	1.73205i	−0.0505076	−	0.0874818i
$393$	−7.50000	−	12.9904i	−0.378325	−	0.655278i
$394$	7.50000	−	12.9904i	0.377845	−	0.654446i
$395$	−10.0000			−0.503155
$396$	−0.500000	+	0.866025i	−0.0251259	+	0.0435194i
$397$	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
$399$	7.50000	−	12.9904i	0.375470	−	0.650332i
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	−12.5000	−	21.6506i	−0.624220	−	1.08118i	−0.988691	−	0.149966i	$-0.952083\pi$
$401$	−12.5000	−	21.6506i	−0.624220	−	1.08118i	0.364471	−	0.931215i	$-0.381250\pi$
$402$	12.0000			0.598506
$403$	25.0000	+	25.9808i	1.24534	+	1.29419i
$404$	4.00000			0.199007
$405$	−0.500000	−	0.866025i	−0.0248452	−	0.0430331i
$406$		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
$411$	−16.0000			−0.789222
$412$	4.50000	−	7.79423i	0.221699	−	0.383994i
$413$	6.00000	+	10.3923i	0.295241	+	0.511372i
$414$	2.00000	+	3.46410i	0.0982946	+	0.170251i
$415$	12.0000			0.589057
$416$	−3.50000	+	0.866025i	−0.171602	+	0.0424604i
$417$	9.00000			0.440732
$418$	2.50000	+	4.33013i	0.122279	+	0.211793i
$419$	14.0000	+	24.2487i	0.683945	+	1.18463i	0.973767	+	0.227547i	$0.0730704\pi$
$419$	14.0000	+	24.2487i	0.683945	+	1.18463i	−0.289822	+	0.957080i	$0.593596\pi$
$420$	−1.50000	+	2.59808i	−0.0731925	+	0.126773i
$421$	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
$423$	4.50000	−	7.79423i	0.218797	−	0.378968i
$424$	−13.0000			−0.631336
$425$		0			0
$426$	−1.00000	−	1.73205i	−0.0484502	−	0.0839181i
$427$	−3.00000	−	5.19615i	−0.145180	−	0.251459i
$428$	−6.00000			−0.290021
$429$	3.50000	−	0.866025i	0.168982	−	0.0418121i
$430$	−2.00000			−0.0964486
$431$	−18.0000	−	31.1769i	−0.867029	−	1.50174i	−0.865018	−	0.501741i	$-0.832693\pi$
$431$	−18.0000	−	31.1769i	−0.867029	−	1.50174i	−0.00201168	−	0.999998i	$-0.500640\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	−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
$438$	−8.00000	+	13.8564i	−0.382255	+	0.662085i
$439$	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
$441$	2.00000			0.0952381
$442$		0			0
$443$	−18.0000			−0.855206			−0.427603	−	0.903967i	$-0.640642\pi$
$443$	−18.0000			−0.855206			−0.427603	+	0.903967i	$0.640642\pi$
$444$	−0.500000	−	0.866025i	−0.0237289	−	0.0410997i
$445$	−0.500000	−	0.866025i	−0.0237023	−	0.0410535i
$446$	−5.50000	+	9.52628i	−0.260433	+	0.451082i
$447$	6.00000			0.283790
$448$	1.50000	−	2.59808i	0.0708683	−	0.122748i
$449$	7.50000	−	12.9904i	0.353947	−	0.613054i	−0.632990	−	0.774160i	$-0.718173\pi$
$449$	7.50000	−	12.9904i	0.353947	−	0.613054i	0.986937	+	0.161106i	$0.0515060\pi$
$450$	1.00000			0.0471405
$451$	−3.00000	+	5.19615i	−0.141264	+	0.244677i
$452$	−8.00000	−	13.8564i	−0.376288	−	0.651751i
$453$	−3.00000	−	5.19615i	−0.140952	−	0.244137i
$454$	−20.0000			−0.938647
$455$	10.5000	−	2.59808i	0.492248	−	0.121800i
$456$	5.00000			0.234146
$457$	−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	−0.691800	−	0.722089i	$-0.743182\pi$
$461$	6.00000	−	10.3923i	0.279448	−	0.484018i	0.971248	+	0.238071i	$0.0765153\pi$
$462$	−1.50000	+	2.59808i	−0.0697863	+	0.120873i
$463$	−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
$465$	5.00000	+	8.66025i	0.231869	+	0.401610i
$466$	−5.00000	−	8.66025i	−0.231621	−	0.401179i
$467$	−36.0000			−1.66588			−0.832941	−	0.553362i	$-0.813345\pi$
$467$	−36.0000			−1.66588			−0.832941	+	0.553362i	$0.813345\pi$
$468$	1.00000	−	3.46410i	0.0462250	−	0.160128i
$469$	36.0000			1.66233
$470$	4.50000	+	7.79423i	0.207570	+	0.359521i
$471$	0.500000	+	0.866025i	0.0230388	+	0.0399043i
$472$	−2.00000	+	3.46410i	−0.0920575	+	0.159448i
$473$	−2.00000			−0.0919601
$474$	−5.00000	+	8.66025i	−0.229658	+	0.397779i
$475$	2.50000	−	4.33013i	0.114708	−	0.198680i
$476$		0			0
$477$	6.50000	−	11.2583i	0.297615	−	0.515484i
$478$	1.00000	+	1.73205i	0.0457389	+	0.0792222i
$479$	4.00000	+	6.92820i	0.182765	+	0.316558i	0.942821	−	0.333300i	$-0.108162\pi$
$479$	4.00000	+	6.92820i	0.182765	+	0.316558i	−0.760056	+	0.649857i	$0.774829\pi$
$480$	−1.00000			−0.0456435
$481$	−1.00000	+	3.46410i	−0.0455961	+	0.157949i
$482$	15.0000			0.683231
$483$	6.00000	+	10.3923i	0.273009	+	0.472866i
$484$	5.00000	+	8.66025i	0.227273	+	0.393648i
$485$	−6.00000	+	10.3923i	−0.272446	+	0.471890i
$486$	−1.00000			−0.0453609
$487$	−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
$489$	20.0000			0.904431
$490$	−1.00000	+	1.73205i	−0.0451754	+	0.0782461i
$491$	−12.5000	−	21.6506i	−0.564117	−	0.977079i	−0.997131	−	0.0756923i	$-0.975883\pi$
$491$	−12.5000	−	21.6506i	−0.564117	−	0.977079i	0.433014	−	0.901387i	$-0.357450\pi$
$492$	3.00000	+	5.19615i	0.135250	+	0.234261i
$493$		0			0
$494$	−12.5000	−	12.9904i	−0.562402	−	0.584465i
$495$	1.00000			0.0449467
$496$	−5.00000	−	8.66025i	−0.224507	−	0.388857i
$497$	−3.00000	−	5.19615i	−0.134568	−	0.233079i
$498$	6.00000	−	10.3923i	0.268866	−	0.465690i
$499$	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
$501$	−6.50000	+	11.2583i	−0.290399	+	0.502985i
$502$	11.0000			0.490954
$503$	0.500000	−	0.866025i	0.0222939	−	0.0386142i	−0.854663	−	0.519183i	$-0.826236\pi$
$503$	0.500000	−	0.866025i	0.0222939	−	0.0386142i	0.876957	+	0.480569i	$0.159570\pi$
$504$	1.50000	+	2.59808i	0.0668153	+	0.115728i
$505$	−2.00000	−	3.46410i	−0.0889988	−	0.154150i
$506$	−4.00000			−0.177822
$507$	−11.5000	+	6.06218i	−0.510733	+	0.269231i
$508$	5.00000			0.221839
$509$	−9.00000	−	15.5885i	−0.398918	−	0.690946i	0.594675	−	0.803966i	$-0.297281\pi$
$509$	−9.00000	−	15.5885i	−0.398918	−	0.690946i	−0.993593	+	0.113020i	$0.963948\pi$
$510$		0			0
$511$	−24.0000	+	41.5692i	−1.06170	+	1.83891i
$512$	1.00000			0.0441942
$513$	−2.50000	+	4.33013i	−0.110378	+	0.191180i
$514$	12.0000	−	20.7846i	0.529297	−	0.916770i
$515$	−9.00000			−0.396587
$516$	−1.00000	+	1.73205i	−0.0440225	+	0.0762493i
$517$	4.50000	+	7.79423i	0.197910	+	0.342790i
$518$	−1.50000	−	2.59808i	−0.0659062	−	0.114153i
$519$	9.00000			0.395056
$520$	2.50000	+	2.59808i	0.109632	+	0.113933i
$521$	33.0000			1.44576			0.722878	−	0.690976i	$-0.242819\pi$
$521$	33.0000			1.44576			0.722878	+	0.690976i	$0.242819\pi$
$522$		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
$525$	3.00000			0.130931
$526$	−1.50000	+	2.59808i	−0.0654031	+	0.113282i
$527$		0			0
$528$	−1.00000			−0.0435194
$529$	3.50000	−	6.06218i	0.152174	−	0.263573i
$530$	6.50000	+	11.2583i	0.282342	+	0.489031i
$531$	−2.00000	−	3.46410i	−0.0867926	−	0.150329i
$532$	15.0000			0.650332
$533$	6.00000	−	20.7846i	0.259889	−	0.900281i
$534$	−1.00000			−0.0432742
$535$	3.00000	+	5.19615i	0.129701	+	0.224649i
$536$	6.00000	+	10.3923i	0.259161	+	0.448879i
$537$	6.00000	−	10.3923i	0.258919	−	0.448461i
$538$	−20.0000			−0.862261
$539$	−1.00000	+	1.73205i	−0.0430730	+	0.0746047i
$540$	0.500000	−	0.866025i	0.0215166	−	0.0372678i
$541$	−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
$543$	3.00000	+	5.19615i	0.128742	+	0.222988i
$544$		0			0
$545$	−10.0000			−0.428353
$546$	3.00000	−	10.3923i	0.128388	−	0.444750i
$547$	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
$549$	1.00000	+	1.73205i	0.0426790	+	0.0739221i
$550$	−0.500000	+	0.866025i	−0.0213201	+	0.0369274i
$551$		0			0
$552$	−2.00000	+	3.46410i	−0.0851257	+	0.147442i
$553$	−15.0000	+	25.9808i	−0.637865	+	1.10481i
$554$	23.0000			0.977176
$555$	−0.500000	+	0.866025i	−0.0212238	+	0.0367607i
$556$	4.50000	+	7.79423i	0.190843	+	0.330549i
$557$	1.50000	+	2.59808i	0.0635570	+	0.110084i	0.896053	−	0.443947i	$-0.146422\pi$
$557$	1.50000	+	2.59808i	0.0635570	+	0.110084i	−0.832496	+	0.554031i	$0.813089\pi$
$558$	10.0000			0.423334
$559$	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	$0.335447\pi$
$563$	−12.0000	+	20.7846i	−0.505740	+	0.875967i	−0.999978	+	0.00664037i	$0.997886\pi$
$564$	9.00000			0.378968
$565$	−8.00000	+	13.8564i	−0.336563	+	0.582943i
$566$	−1.00000	+	1.73205i	−0.0420331	+	0.0728035i
$567$	−3.00000			−0.125988
$568$	1.00000	−	1.73205i	0.0419591	−	0.0726752i
$569$	5.50000	+	9.52628i	0.230572	+	0.399362i	0.957977	−	0.286846i	$-0.0926069\pi$
$569$	5.50000	+	9.52628i	0.230572	+	0.399362i	−0.727405	+	0.686209i	$0.759274\pi$
$570$	−2.50000	−	4.33013i	−0.104713	−	0.181369i
$571$	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
$573$	18.0000			0.751961
$574$	9.00000	+	15.5885i	0.375653	+	0.650650i
$575$	2.00000	+	3.46410i	0.0834058	+	0.144463i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	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
$579$	8.00000	−	13.8564i	0.332469	−	0.575853i
$580$		0			0
$581$	18.0000	−	31.1769i	0.746766	−	1.29344i
$582$	6.00000	+	10.3923i	0.248708	+	0.430775i
$583$	6.50000	+	11.2583i	0.269202	+	0.466272i
$584$	−16.0000			−0.662085
$585$	−3.50000	+	0.866025i	−0.144707	+	0.0358057i
$586$	13.0000			0.537025
$587$	9.00000	+	15.5885i	0.371470	+	0.643404i	0.989792	−	0.142520i	$-0.0455206\pi$
$587$	9.00000	+	15.5885i	0.371470	+	0.643404i	−0.618322	+	0.785925i	$0.712187\pi$
$588$	1.00000	+	1.73205i	0.0412393	+	0.0714286i
$589$	25.0000	−	43.3013i	1.03011	−	1.78420i
$590$	4.00000			0.164677
$591$	−7.50000	+	12.9904i	−0.308509	+	0.534353i
$592$	0.500000	−	0.866025i	0.0205499	−	0.0355934i
$593$	28.0000			1.14982			0.574911	−	0.818216i	$-0.305037\pi$
$593$	28.0000			1.14982			0.574911	+	0.818216i	$0.305037\pi$
$594$	0.500000	−	0.866025i	0.0205152	−	0.0355335i
$595$		0			0
$596$	3.00000	+	5.19615i	0.122885	+	0.212843i
$597$	2.00000			0.0818546
$598$	14.0000	−	3.46410i	0.572503	−	0.141658i
$599$	−30.0000			−1.22577			−0.612883	−	0.790173i	$-0.709990\pi$
$599$	−30.0000			−1.22577			−0.612883	+	0.790173i	$0.709990\pi$
$600$	0.500000	+	0.866025i	0.0204124	+	0.0353553i
$601$	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
$603$	−12.0000			−0.488678
$604$	3.00000	−	5.19615i	0.122068	−	0.211428i
$605$	5.00000	−	8.66025i	0.203279	−	0.352089i
$606$	−4.00000			−0.162489
$607$	−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
$615$	3.00000	−	5.19615i	0.120972	−	0.209529i
$616$	−3.00000			−0.120873
$617$	3.00000	−	5.19615i	0.120775	−	0.209189i	−0.799298	−	0.600935i	$-0.794795\pi$
$617$	3.00000	−	5.19615i	0.120775	−	0.209189i	0.920074	+	0.391745i	$0.128129\pi$
$618$	−4.50000	+	7.79423i	−0.181017	+	0.313530i
$619$	−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
$621$	−2.00000	−	3.46410i	−0.0802572	−	0.139010i
$622$	6.00000	+	10.3923i	0.240578	+	0.416693i
$623$	−3.00000			−0.120192
$624$	3.50000	−	0.866025i	0.140112	−	0.0346688i
$625$	1.00000			0.0400000
$626$	17.0000	+	29.4449i	0.679457	+	1.17685i
$627$	−2.50000	−	4.33013i	−0.0998404	−	0.172929i
$628$	−0.500000	+	0.866025i	−0.0199522	+	0.0345582i
$629$		0			0
$630$	1.50000	−	2.59808i	0.0597614	−	0.103510i
$631$	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
$633$	−7.50000	+	12.9904i	−0.298098	+	0.516321i
$634$	−9.50000	−	16.4545i	−0.377293	−	0.653491i
$635$	−2.50000	−	4.33013i	−0.0992095	−	0.171836i
$636$	13.0000			0.515484
$637$	2.00000	−	6.92820i	0.0792429	−	0.274505i
$638$		0			0
$639$	1.00000	+	1.73205i	0.0395594	+	0.0685189i
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	4.50000	−	7.79423i	0.177739	−	0.307854i	−0.763367	−	0.645966i	$-0.776455\pi$
$641$	4.50000	−	7.79423i	0.177739	−	0.307854i	0.941106	+	0.338112i	$0.109788\pi$
$642$	6.00000			0.236801
$643$	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
$645$	2.00000			0.0787499
$646$		0			0
$647$	−4.50000	−	7.79423i	−0.176913	−	0.306423i	0.763908	−	0.645325i	$-0.223278\pi$
$647$	−4.50000	−	7.79423i	−0.176913	−	0.306423i	−0.940822	+	0.338902i	$0.889945\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	4.00000			0.157014
$650$	1.00000	−	3.46410i	0.0392232	−	0.135873i
$651$	30.0000			1.17579
$652$	10.0000	+	17.3205i	0.391630	+	0.678323i
$653$	−20.5000	−	35.5070i	−0.802227	−	1.38950i	−0.918147	−	0.396239i	$-0.870315\pi$
$653$	−20.5000	−	35.5070i	−0.802227	−	1.38950i	0.115920	−	0.993259i	$-0.463018\pi$
$654$	−5.00000	+	8.66025i	−0.195515	+	0.338643i
$655$	−15.0000			−0.586098
$656$	−3.00000	+	5.19615i	−0.117130	+	0.202876i
$657$	8.00000	−	13.8564i	0.312110	−	0.540590i
$658$	27.0000			1.05257
$659$	−2.00000	+	3.46410i	−0.0779089	+	0.134942i	−0.902348	−	0.431009i	$-0.858158\pi$
$659$	−2.00000	+	3.46410i	−0.0779089	+	0.134942i	0.824439	+	0.565951i	$0.191491\pi$
$660$	0.500000	+	0.866025i	0.0194625	+	0.0337100i
$661$	−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
$666$	0.500000	+	0.866025i	0.0193746	+	0.0335578i
$667$		0			0
$668$	−13.0000			−0.502985
$669$	5.50000	−	9.52628i	0.212642	−	0.368307i
$670$	6.00000	−	10.3923i	0.231800	−	0.401490i
$671$	−2.00000			−0.0772091
$672$	−1.50000	+	2.59808i	−0.0578638	+	0.100223i
$673$	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
$675$	−1.00000			−0.0384900
$676$	−11.0000	−	6.92820i	−0.423077	−	0.266469i
$677$	−26.0000			−0.999261			−0.499631	−	0.866239i	$-0.666531\pi$
$677$	−26.0000			−0.999261			−0.499631	+	0.866239i	$0.666531\pi$
$678$	8.00000	+	13.8564i	0.307238	+	0.532152i
$679$	18.0000	+	31.1769i	0.690777	+	1.19646i
$680$		0			0
$681$	20.0000			0.766402
$682$	−5.00000	+	8.66025i	−0.191460	+	0.331618i
$683$	13.0000	−	22.5167i	0.497431	−	0.861576i	−0.502564	−	0.864540i	$-0.667610\pi$
$683$	13.0000	−	22.5167i	0.497431	−	0.861576i	0.999996	+	0.00296369i	$0.000943372\pi$
$684$	−5.00000			−0.191180
$685$	−8.00000	+	13.8564i	−0.305664	+	0.529426i
$686$	−7.50000	−	12.9904i	−0.286351	−	0.495975i
$687$	−5.00000	−	8.66025i	−0.190762	−	0.330409i
$688$	−2.00000			−0.0762493
$689$	−32.5000	−	33.7750i	−1.23815	−	1.28672i
$690$	4.00000			0.152277
$691$	−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
$693$	1.50000	−	2.59808i	0.0569803	−	0.0986928i
$694$	−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
$699$	5.00000	+	8.66025i	0.189117	+	0.327561i
$700$	1.50000	+	2.59808i	0.0566947	+	0.0981981i
$701$	4.00000			0.151078			0.0755390	−	0.997143i	$-0.475932\pi$
$701$	4.00000			0.151078			0.0755390	+	0.997143i	$0.475932\pi$
$702$	−1.00000	+	3.46410i	−0.0377426	+	0.130744i
$703$	5.00000			0.188579
$704$	−0.500000	−	0.866025i	−0.0188445	−	0.0326396i
$705$	−4.50000	−	7.79423i	−0.169480	−	0.293548i
$706$	18.0000	−	31.1769i	0.677439	−	1.17336i
$707$	−12.0000			−0.451306
$708$	2.00000	−	3.46410i	0.0751646	−	0.130189i
$709$	−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
$711$	5.00000	−	8.66025i	0.187515	−	0.324785i
$712$	−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
$717$	−1.00000	−	1.73205i	−0.0373457	−	0.0646846i
$718$	−17.0000	−	29.4449i	−0.634434	−	1.09887i
$719$	−18.0000	+	31.1769i	−0.671287	+	1.16270i	0.306253	+	0.951950i	$0.400925\pi$
$719$	−18.0000	+	31.1769i	−0.671287	+	1.16270i	−0.977539	+	0.210752i	$0.932409\pi$
$720$	1.00000			0.0372678
$721$	−13.5000	+	23.3827i	−0.502766	+	0.870817i
$722$	−3.00000	+	5.19615i	−0.111648	+	0.193381i
$723$	−15.0000			−0.557856
$724$	−3.00000	+	5.19615i	−0.111494	+	0.193113i
$725$		0			0
$726$	−5.00000	−	8.66025i	−0.185567	−	0.321412i
$727$	−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
$729$	1.00000			0.0370370
$730$	8.00000	+	13.8564i	0.296093	+	0.512849i
$731$		0			0
$732$	−1.00000	+	1.73205i	−0.0369611	+	0.0640184i
$733$	−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
$735$	1.00000	−	1.73205i	0.0368856	−	0.0638877i
$736$	−4.00000			−0.147442
$737$	6.00000	−	10.3923i	0.221013	−	0.382805i
$738$	−3.00000	−	5.19615i	−0.110432	−	0.191273i
$739$	−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
$741$	12.5000	+	12.9904i	0.459199	+	0.477214i
$742$	39.0000			1.43174
$743$	−12.0000	−	20.7846i	−0.440237	−	0.762513i	0.557470	−	0.830197i	$-0.311772\pi$
$743$	−12.0000	−	20.7846i	−0.440237	−	0.762513i	−0.997707	+	0.0676840i	$0.978439\pi$
$744$	5.00000	+	8.66025i	0.183309	+	0.317500i
$745$	3.00000	−	5.19615i	0.109911	−	0.190372i
$746$	10.0000			0.366126
$747$	−6.00000	+	10.3923i	−0.219529	+	0.380235i
$748$		0			0
$749$	18.0000			0.657706
$750$	0.500000	−	0.866025i	0.0182574	−	0.0316228i
$751$	−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
$753$	−11.0000			−0.400862
$754$		0			0
$755$	−6.00000			−0.218362
$756$	−1.50000	−	2.59808i	−0.0545545	−	0.0944911i
$757$	−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
$759$	4.00000			0.145191
$760$	2.50000	−	4.33013i	0.0906845	−	0.157070i
$761$	−22.5000	+	38.9711i	−0.815624	+	1.41270i	0.0932544	+	0.995642i	$0.470273\pi$
$761$	−22.5000	+	38.9711i	−0.815624	+	1.41270i	−0.908879	+	0.417061i	$0.863060\pi$
$762$	−5.00000			−0.181131
$763$	−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
$768$	−1.00000			−0.0360844
$769$	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
$771$	−12.0000	+	20.7846i	−0.432169	+	0.748539i
$772$	16.0000			0.575853
$773$	18.5000	−	32.0429i	0.665399	−	1.15250i	−0.313778	−	0.949496i	$-0.601595\pi$
$773$	18.5000	−	32.0429i	0.665399	−	1.15250i	0.979177	−	0.203008i	$-0.0650718\pi$
$774$	1.00000	−	1.73205i	0.0359443	−	0.0622573i
$775$	10.0000			0.359211
$776$	−6.00000	+	10.3923i	−0.215387	+	0.373062i
$777$	1.50000	+	2.59808i	0.0538122	+	0.0932055i
$778$	8.00000	+	13.8564i	0.286814	+	0.496776i
$779$	−30.0000			−1.07486
$780$	−2.50000	−	2.59808i	−0.0895144	−	0.0930261i
$781$	−2.00000			−0.0715656
$782$		0			0
$783$		0			0
$784$	−1.00000	+	1.73205i	−0.0357143	+	0.0618590i
$785$	1.00000			0.0356915
$786$	−7.50000	+	12.9904i	−0.267516	+	0.463352i
$787$	−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
$789$	1.50000	−	2.59808i	0.0534014	−	0.0924940i
$790$	5.00000	+	8.66025i	0.177892	+	0.308118i
$791$	24.0000	+	41.5692i	0.853342	+	1.47803i
$792$	1.00000			0.0355335
$793$	7.00000	−	1.73205i	0.248577	−	0.0615069i
$794$	−33.0000			−1.17113
$795$	−6.50000	−	11.2583i	−0.230531	−	0.399292i
$796$	1.00000	+	1.73205i	0.0354441	+	0.0613909i
$797$	7.00000	−	12.1244i	0.247953	−	0.429467i	−0.715005	−	0.699119i	$-0.753576\pi$
$797$	7.00000	−	12.1244i	0.247953	−	0.429467i	0.962958	+	0.269653i	$0.0869089\pi$
$798$	−15.0000			−0.530994
$799$		0			0
$800$	−0.500000	+	0.866025i	−0.0176777	+	0.0306186i
$801$	1.00000			0.0353333
$802$	−12.5000	+	21.6506i	−0.441390	+	0.764511i
$803$	8.00000	+	13.8564i	0.282314	+	0.488982i
$804$	−6.00000	−	10.3923i	−0.211604	−	0.366508i
$805$	12.0000			0.422944
$806$	10.0000	−	34.6410i	0.352235	−	1.22018i
$807$	20.0000			0.704033
$808$	−2.00000	−	3.46410i	−0.0703598	−	0.121867i
$809$	9.00000	+	15.5885i	0.316423	+	0.548061i	0.979739	−	0.200279i	$-0.0641847\pi$
$809$	9.00000	+	15.5885i	0.316423	+	0.548061i	−0.663316	+	0.748340i	$0.730851\pi$
$810$	−0.500000	+	0.866025i	−0.0175682	+	0.0304290i
$811$	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
$813$	−12.0000	+	20.7846i	−0.420858	+	0.728948i
$814$	−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
$819$	−3.00000	+	10.3923i	−0.104828	+	0.363137i
$820$	6.00000			0.209529
$821$	−9.00000	−	15.5885i	−0.314102	−	0.544041i	0.665144	−	0.746715i	$-0.268370\pi$
$821$	−9.00000	−	15.5885i	−0.314102	−	0.544041i	−0.979246	+	0.202674i	$0.935037\pi$
$822$	8.00000	+	13.8564i	0.279032	+	0.483298i
$823$	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
$825$	0.500000	−	0.866025i	0.0174078	−	0.0301511i
$826$	6.00000	−	10.3923i	0.208767	−	0.361595i
$827$	−30.0000			−1.04320			−0.521601	−	0.853189i	$-0.674665\pi$
$827$	−30.0000			−1.04320			−0.521601	+	0.853189i	$0.674665\pi$
$828$	2.00000	−	3.46410i	0.0695048	−	0.120386i
$829$	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
$831$	−23.0000			−0.797861
$832$	2.50000	+	2.59808i	0.0866719	+	0.0900721i
$833$		0			0
$834$	−4.50000	−	7.79423i	−0.155822	−	0.269892i
$835$	6.50000	+	11.2583i	0.224942	+	0.389611i
$836$	2.50000	−	4.33013i	0.0864643	−	0.149761i
$837$	−10.0000			−0.345651
$838$	14.0000	−	24.2487i	0.483622	−	0.837658i
$839$	27.0000	−	46.7654i	0.932144	−	1.61452i	0.152493	−	0.988304i	$-0.451270\pi$
$839$	27.0000	−	46.7654i	0.932144	−	1.61452i	0.779650	−	0.626215i	$-0.215397\pi$
$840$	3.00000			0.103510
$841$	14.5000	−	25.1147i	0.500000	−	0.866025i
$842$	−10.0000	−	17.3205i	−0.344623	−	0.596904i
$843$	5.00000	+	8.66025i	0.172209	+	0.298275i
$844$	−15.0000			−0.516321
$845$	−0.500000	+	12.9904i	−0.0172005	+	0.446883i
$846$	−9.00000			−0.309426
$847$	−15.0000	−	25.9808i	−0.515406	−	0.892710i
$848$	6.50000	+	11.2583i	0.223211	+	0.386613i
$849$	1.00000	−	1.73205i	0.0343199	−	0.0594438i
$850$		0			0
$851$	−2.00000	+	3.46410i	−0.0685591	+	0.118748i
$852$	−1.00000	+	1.73205i	−0.0342594	+	0.0593391i
$853$	−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
$855$	2.50000	+	4.33013i	0.0854982	+	0.148087i
$856$	3.00000	+	5.19615i	0.102538	+	0.177601i
$857$	−18.0000			−0.614868			−0.307434	−	0.951569i	$-0.599470\pi$
$857$	−18.0000			−0.614868			−0.307434	+	0.951569i	$0.599470\pi$
$858$	−2.50000	−	2.59808i	−0.0853486	−	0.0886969i
$859$	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
$861$	−9.00000	−	15.5885i	−0.306719	−	0.531253i
$862$	−18.0000	+	31.1769i	−0.613082	+	1.06189i
$863$	−48.0000			−1.63394			−0.816970	−	0.576681i	$-0.804348\pi$
$863$	−48.0000			−1.63394			−0.816970	+	0.576681i	$0.804348\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$	4.50000	−	7.79423i	0.153005	−	0.265012i
$866$	16.0000			0.543702
$867$	−8.50000	+	14.7224i	−0.288675	+	0.500000i
$868$	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
$873$	−6.00000	−	10.3923i	−0.203069	−	0.351726i
$874$	−10.0000	−	17.3205i	−0.338255	−	0.585875i
$875$	1.50000	−	2.59808i	0.0507093	−	0.0878310i
$876$	16.0000			0.540590
$877$	−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
$879$	−13.0000			−0.438479
$880$	−0.500000	+	0.866025i	−0.0168550	+	0.0291937i
$881$	−2.50000	−	4.33013i	−0.0842271	−	0.145886i	0.820834	−	0.571166i	$-0.193509\pi$
$881$	−2.50000	−	4.33013i	−0.0842271	−	0.145886i	−0.905062	+	0.425280i	$0.860175\pi$
$882$	−1.00000	−	1.73205i	−0.0336718	−	0.0583212i
$883$	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
$885$	−4.00000			−0.134459
$886$	9.00000	+	15.5885i	0.302361	+	0.523704i
$887$	6.50000	+	11.2583i	0.218249	+	0.378018i	0.954273	−	0.298938i	$-0.0966323\pi$
$887$	6.50000	+	11.2583i	0.218249	+	0.378018i	−0.736024	+	0.676955i	$0.763299\pi$
$888$	−0.500000	+	0.866025i	−0.0167789	+	0.0290619i
$889$	−15.0000			−0.503084
$890$	−0.500000	+	0.866025i	−0.0167600	+	0.0290292i
$891$	−0.500000	+	0.866025i	−0.0167506	+	0.0290129i
$892$	11.0000			0.368307
$893$	−22.5000	+	38.9711i	−0.752934	+	1.30412i
$894$	−3.00000	−	5.19615i	−0.100335	−	0.173785i
$895$	−6.00000	−	10.3923i	−0.200558	−	0.347376i
$896$	−3.00000			−0.100223
$897$	−14.0000	+	3.46410i	−0.467446	+	0.115663i
$898$	−15.0000			−0.500556
$899$		0			0
$900$	−0.500000	−	0.866025i	−0.0166667	−	0.0288675i
$901$		0			0
$902$	6.00000			0.199778
$903$	3.00000	−	5.19615i	0.0998337	−	0.172917i
$904$	−8.00000	+	13.8564i	−0.266076	+	0.460857i
$905$	6.00000			0.199447
$906$	−3.00000	+	5.19615i	−0.0996683	+	0.172631i
$907$	−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
$909$	4.00000			0.132672
$910$	−7.50000	−	7.79423i	−0.248623	−	0.258376i
$911$	12.0000			0.397578			0.198789	−	0.980042i	$-0.436299\pi$
$911$	12.0000			0.397578			0.198789	+	0.980042i	$0.436299\pi$
$912$	−2.50000	−	4.33013i	−0.0827833	−	0.143385i
$913$	−6.00000	−	10.3923i	−0.198571	−	0.343935i
$914$	−11.0000	+	19.0526i	−0.363848	+	0.630203i
$915$	2.00000			0.0661180
$916$	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
$921$	9.00000	+	15.5885i	0.296560	+	0.513657i
$922$	−12.0000			−0.395199
$923$	7.00000	−	1.73205i	0.230408	−	0.0570111i
$924$	3.00000			0.0986928
$925$	0.500000	+	0.866025i	0.0164399	+	0.0284747i
$926$	8.00000	+	13.8564i	0.262896	+	0.455350i
$927$	4.50000	−	7.79423i	0.147799	−	0.255996i
$928$		0			0
$929$	−17.0000	+	29.4449i	−0.557752	+	0.966055i	0.439932	+	0.898031i	$0.355003\pi$
$929$	−17.0000	+	29.4449i	−0.557752	+	0.966055i	−0.997684	+	0.0680235i	$0.978331\pi$
$930$	5.00000	−	8.66025i	0.163956	−	0.283981i
$931$	−10.0000			−0.327737
$932$	−5.00000	+	8.66025i	−0.163780	+	0.283676i
$933$	−6.00000	−	10.3923i	−0.196431	−	0.340229i
$934$	18.0000	+	31.1769i	0.588978	+	1.02014i
$935$		0			0
$936$	−3.50000	+	0.866025i	−0.114401	+	0.0283069i
$937$	−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
$939$	−17.0000	−	29.4449i	−0.554774	−	0.960897i
$940$	4.50000	−	7.79423i	0.146774	−	0.254220i
$941$	24.0000			0.782378			0.391189	−	0.920310i	$-0.372064\pi$
$941$	24.0000			0.782378			0.391189	+	0.920310i	$0.372064\pi$
$942$	0.500000	−	0.866025i	0.0162909	−	0.0282166i
$943$	12.0000	−	20.7846i	0.390774	−	0.676840i
$944$	4.00000			0.130189
$945$	−1.50000	+	2.59808i	−0.0487950	+	0.0845154i
$946$	1.00000	+	1.73205i	0.0325128	+	0.0563138i
$947$	19.0000	+	32.9090i	0.617417	+	1.06940i	0.989955	+	0.141381i	$0.0451542\pi$
$947$	19.0000	+	32.9090i	0.617417	+	1.06940i	−0.372538	+	0.928017i	$0.621512\pi$
$948$	10.0000			0.324785
$949$	−40.0000	−	41.5692i	−1.29845	−	1.34939i
$950$	−5.00000			−0.162221
$951$	9.50000	+	16.4545i	0.308059	+	0.533573i
$952$		0			0
$953$	−11.0000	+	19.0526i	−0.356325	+	0.617173i	−0.987344	−	0.158595i	$-0.949304\pi$
$953$	−11.0000	+	19.0526i	−0.356325	+	0.617173i	0.631019	+	0.775768i	$0.282637\pi$
$954$	−13.0000			−0.420891
$955$	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
$960$	0.500000	+	0.866025i	0.0161374	+	0.0279508i
$961$	69.0000			2.22581
$962$	3.50000	−	0.866025i	0.112845	−	0.0279218i
$963$	−6.00000			−0.193347
$964$	−7.50000	−	12.9904i	−0.241559	−	0.418392i
$965$	−8.00000	−	13.8564i	−0.257529	−	0.446054i
$966$	6.00000	−	10.3923i	0.193047	−	0.334367i
$967$	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	−0.997150	−	0.0754473i	$-0.975962\pi$
$971$	−13.5000	+	23.3827i	−0.433236	+	0.750386i	0.563914	+	0.825833i	$0.309295\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	−13.5000	−	23.3827i	−0.432790	−	0.749614i
$974$	35.0000			1.12147
$975$	−1.00000	+	3.46410i	−0.0320256	+	0.110940i
$976$	−2.00000			−0.0640184
$977$	−24.0000	−	41.5692i	−0.767828	−	1.32992i	−0.938738	−	0.344631i	$-0.888004\pi$
$977$	−24.0000	−	41.5692i	−0.767828	−	1.32992i	0.170910	−	0.985287i	$-0.445329\pi$
$978$	−10.0000	−	17.3205i	−0.319765	−	0.553849i
$979$	−0.500000	+	0.866025i	−0.0159801	+	0.0276783i
$980$	2.00000			0.0638877
$981$	5.00000	−	8.66025i	0.159638	−	0.276501i
$982$	−12.5000	+	21.6506i	−0.398891	+	0.690900i
$983$	53.0000			1.69044			0.845219	−	0.534421i	$-0.179470\pi$
$983$	53.0000			1.69044			0.845219	+	0.534421i	$0.179470\pi$
$984$	3.00000	−	5.19615i	0.0956365	−	0.165647i
$985$	7.50000	+	12.9904i	0.238970	+	0.413908i
$986$		0			0
$987$	−27.0000			−0.859419
$988$	−5.00000	+	17.3205i	−0.159071	+	0.551039i
$989$	8.00000			0.254385
$990$	−0.500000	−	0.866025i	−0.0158910	−	0.0275241i
$991$	−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
$993$	−28.0000			−0.888553
$994$	−3.00000	+	5.19615i	−0.0951542	+	0.164812i
$995$	1.00000	−	1.73205i	0.0317021	−	0.0549097i
$996$	−12.0000			−0.380235
$997$	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
$999$	−0.500000	−	0.866025i	−0.0158193	−	0.0273998i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	390.2.i.b.211.1	yes	2
3.2	odd	2		1170.2.i.j.991.1		2
5.2	odd	4		1950.2.z.i.1849.2		4
5.3	odd	4		1950.2.z.i.1849.1		4
5.4	even	2		1950.2.i.o.601.1		2
13.2	odd	12		5070.2.b.a.1351.1		2
13.3	even	3		5070.2.a.q.1.1		1
13.9	even	3	inner	390.2.i.b.61.1	✓	2
13.10	even	6		5070.2.a.c.1.1		1
13.11	odd	12		5070.2.b.a.1351.2		2
39.35	odd	6		1170.2.i.j.451.1		2
65.9	even	6		1950.2.i.o.451.1		2
65.22	odd	12		1950.2.z.i.1699.1		4
65.48	odd	12		1950.2.z.i.1699.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.i.b.61.1	✓	2	13.9	even	3	inner
390.2.i.b.211.1	yes	2	1.1	even	1	trivial
1170.2.i.j.451.1		2	39.35	odd	6
1170.2.i.j.991.1		2	3.2	odd	2
1950.2.i.o.451.1		2	65.9	even	6
1950.2.i.o.601.1		2	5.4	even	2
1950.2.z.i.1699.1		4	65.22	odd	12
1950.2.z.i.1699.2		4	65.48	odd	12
1950.2.z.i.1849.1		4	5.3	odd	4
1950.2.z.i.1849.2		4	5.2	odd	4
5070.2.a.c.1.1		1	13.10	even	6
5070.2.a.q.1.1		1	13.3	even	3
5070.2.b.a.1351.1		2	13.2	odd	12
5070.2.b.a.1351.2		2	13.11	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	390.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(0.500000 - 0.866025i) q^{6} +(1.50000 - 2.59808i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(-0.500000 - 0.866025i) q^{11} -1.00000 q^{12} +(2.50000 + 2.59808i) q^{13} -3.00000 q^{14} +(0.500000 + 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +1.00000 q^{18} +(2.50000 - 4.33013i) q^{19} +(-0.500000 + 0.866025i) q^{20} +3.00000 q^{21} +(-0.500000 + 0.866025i) q^{22} +(2.00000 + 3.46410i) q^{23} +(0.500000 + 0.866025i) q^{24} +1.00000 q^{25} +(1.00000 - 3.46410i) q^{26} -1.00000 q^{27} +(1.50000 + 2.59808i) q^{28} +(0.500000 - 0.866025i) q^{30} +10.0000 q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.500000 - 0.866025i) q^{33} +(1.50000 - 2.59808i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(0.500000 + 0.866025i) q^{37} -5.00000 q^{38} +(-1.00000 + 3.46410i) q^{39} +1.00000 q^{40} +(-3.00000 - 5.19615i) q^{41} +(-1.50000 - 2.59808i) q^{42} +(1.00000 - 1.73205i) q^{43} +1.00000 q^{44} +(-0.500000 + 0.866025i) q^{45} +(2.00000 - 3.46410i) q^{46} -9.00000 q^{47} +(0.500000 - 0.866025i) q^{48} +(-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^{54} +(-0.500000 - 0.866025i) q^{55} +(1.50000 - 2.59808i) q^{56} +5.00000 q^{57} +(-2.00000 + 3.46410i) q^{59} -1.00000 q^{60} +(1.00000 - 1.73205i) q^{61} +(-5.00000 - 8.66025i) q^{62} +(1.50000 + 2.59808i) q^{63} +1.00000 q^{64} +(2.50000 + 2.59808i) q^{65} -1.00000 q^{66} +(6.00000 + 10.3923i) q^{67} +(-2.00000 + 3.46410i) q^{69} -3.00000 q^{70} +(1.00000 - 1.73205i) q^{71} +(-0.500000 + 0.866025i) q^{72} -16.0000 q^{73} +(0.500000 - 0.866025i) q^{74} +(0.500000 + 0.866025i) q^{75} +(2.50000 + 4.33013i) q^{76} -3.00000 q^{77} +(3.50000 - 0.866025i) q^{78} -10.0000 q^{79} +(-0.500000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-3.00000 + 5.19615i) q^{82} +12.0000 q^{83} +(-1.50000 + 2.59808i) q^{84} -2.00000 q^{86} +(-0.500000 - 0.866025i) q^{88} +(-0.500000 - 0.866025i) q^{89} +1.00000 q^{90} +(10.5000 - 2.59808i) q^{91} -4.00000 q^{92} +(5.00000 + 8.66025i) q^{93} +(4.50000 + 7.79423i) q^{94} +(2.50000 - 4.33013i) q^{95} -1.00000 q^{96} +(-6.00000 + 10.3923i) q^{97} +(-1.00000 + 1.73205i) q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + q^{3} - q^{4} + 2 q^{5} + q^{6} + 3 q^{7} + 2 q^{8} - q^{9} - q^{10} - q^{11} - 2 q^{12} + 5 q^{13} - 6 q^{14} + q^{15} - q^{16} + 2 q^{18} + 5 q^{19} - q^{20} + 6 q^{21} - q^{22}+ \cdots + 2 q^{99}+O(q^{100}) \) 2 * q - q^2 + q^3 - q^4 + 2 * q^5 + q^6 + 3 * q^7 + 2 * q^8 - q^9 - q^10 - q^11 - 2 * q^12 + 5 * q^13 - 6 * q^14 + q^15 - q^16 + 2 * q^18 + 5 * q^19 - q^20 + 6 * q^21 - q^22 + 4 * q^23 + q^24 + 2 * q^25 + 2 * q^26 - 2 * q^27 + 3 * q^28 + q^30 + 20 * q^31 - q^32 + q^33 + 3 * q^35 - q^36 + q^37 - 10 * q^38 - 2 * q^39 + 2 * q^40 - 6 * q^41 - 3 * q^42 + 2 * q^43 + 2 * q^44 - q^45 + 4 * q^46 - 18 * q^47 + q^48 - 2 * q^49 - q^50 - 7 * q^52 - 26 * q^53 + q^54 - q^55 + 3 * q^56 + 10 * q^57 - 4 * q^59 - 2 * q^60 + 2 * q^61 - 10 * q^62 + 3 * q^63 + 2 * q^64 + 5 * q^65 - 2 * q^66 + 12 * q^67 - 4 * q^69 - 6 * q^70 + 2 * q^71 - q^72 - 32 * q^73 + q^74 + q^75 + 5 * q^76 - 6 * q^77 + 7 * q^78 - 20 * q^79 - q^80 - q^81 - 6 * q^82 + 24 * q^83 - 3 * q^84 - 4 * q^86 - q^88 - q^89 + 2 * q^90 + 21 * q^91 - 8 * q^92 + 10 * q^93 + 9 * q^94 + 5 * q^95 - 2 * q^96 - 12 * q^97 - 2 * q^98 + 2 * q^99

Introduction

L-functions

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Database

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