LMFDB - Embedded newform 105.2.i.a.16.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,2,Mod(16,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("105.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	105.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:	$0.838429221223$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			16.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	105.16
Dual form			105.2.i.a.46.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{3} +(1.00000 + 1.73205i) q^{4} +(0.500000 - 0.866025i) q^{5} +(2.50000 - 0.866025i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{3} +(1.00000 + 1.73205i) q^{4} +(0.500000 - 0.866025i) q^{5} +(2.50000 - 0.866025i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(1.00000 - 1.73205i) q^{12} -1.00000 q^{13} -1.00000 q^{15} +(-2.00000 + 3.46410i) q^{16} +(-3.00000 - 5.19615i) q^{17} +(-2.50000 + 4.33013i) q^{19} +2.00000 q^{20} +(-2.00000 - 1.73205i) q^{21} +(-3.00000 + 5.19615i) q^{23} +(-0.500000 - 0.866025i) q^{25} +1.00000 q^{27} +(4.00000 + 3.46410i) q^{28} -6.00000 q^{29} +(-2.50000 - 4.33013i) q^{31} +(0.500000 - 2.59808i) q^{35} -2.00000 q^{36} +(3.50000 - 6.06218i) q^{37} +(0.500000 + 0.866025i) q^{39} +12.0000 q^{41} -1.00000 q^{43} +(0.500000 + 0.866025i) q^{45} +(-3.00000 + 5.19615i) q^{47} +4.00000 q^{48} +(5.50000 - 4.33013i) q^{49} +(-3.00000 + 5.19615i) q^{51} +(-1.00000 - 1.73205i) q^{52} +5.00000 q^{57} +(3.00000 + 5.19615i) q^{59} +(-1.00000 - 1.73205i) q^{60} +(-1.00000 + 1.73205i) q^{61} +(-0.500000 + 2.59808i) q^{63} -8.00000 q^{64} +(-0.500000 + 0.866025i) q^{65} +(3.50000 + 6.06218i) q^{67} +(6.00000 - 10.3923i) q^{68} +6.00000 q^{69} +12.0000 q^{71} +(-5.50000 - 9.52628i) q^{73} +(-0.500000 + 0.866025i) q^{75} -10.0000 q^{76} +(6.50000 - 11.2583i) q^{79} +(2.00000 + 3.46410i) q^{80} +(-0.500000 - 0.866025i) q^{81} -12.0000 q^{83} +(1.00000 - 5.19615i) q^{84} -6.00000 q^{85} +(3.00000 + 5.19615i) q^{87} +(-3.00000 + 5.19615i) q^{89} +(-2.50000 + 0.866025i) q^{91} -12.0000 q^{92} +(-2.50000 + 4.33013i) q^{93} +(2.50000 + 4.33013i) q^{95} -10.0000 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{3} + 2 q^{4} + q^{5} + 5 q^{7} - q^{9}+O(q^{10}) $ 2 * q - q^3 + 2 * q^4 + q^5 + 5 * q^7 - q^9	$ 2 q - q^{3} + 2 q^{4} + q^{5} + 5 q^{7} - q^{9} + 2 q^{12} - 2 q^{13} - 2 q^{15} - 4 q^{16} - 6 q^{17} - 5 q^{19} + 4 q^{20} - 4 q^{21} - 6 q^{23} - q^{25} + 2 q^{27} + 8 q^{28} - 12 q^{29} - 5 q^{31} + q^{35} - 4 q^{36} + 7 q^{37} + q^{39} + 24 q^{41} - 2 q^{43} + q^{45} - 6 q^{47} + 8 q^{48} + 11 q^{49} - 6 q^{51} - 2 q^{52} + 10 q^{57} + 6 q^{59} - 2 q^{60} - 2 q^{61} - q^{63} - 16 q^{64} - q^{65} + 7 q^{67} + 12 q^{68} + 12 q^{69} + 24 q^{71} - 11 q^{73} - q^{75} - 20 q^{76} + 13 q^{79} + 4 q^{80} - q^{81} - 24 q^{83} + 2 q^{84} - 12 q^{85} + 6 q^{87} - 6 q^{89} - 5 q^{91} - 24 q^{92} - 5 q^{93} + 5 q^{95} - 20 q^{97}+O(q^{100}) $ 2 * q - q^3 + 2 * q^4 + q^5 + 5 * q^7 - q^9 + 2 * q^12 - 2 * q^13 - 2 * q^15 - 4 * q^16 - 6 * q^17 - 5 * q^19 + 4 * q^20 - 4 * q^21 - 6 * q^23 - q^25 + 2 * q^27 + 8 * q^28 - 12 * q^29 - 5 * q^31 + q^35 - 4 * q^36 + 7 * q^37 + q^39 + 24 * q^41 - 2 * q^43 + q^45 - 6 * q^47 + 8 * q^48 + 11 * q^49 - 6 * q^51 - 2 * q^52 + 10 * q^57 + 6 * q^59 - 2 * q^60 - 2 * q^61 - q^63 - 16 * q^64 - q^65 + 7 * q^67 + 12 * q^68 + 12 * q^69 + 24 * q^71 - 11 * q^73 - q^75 - 20 * q^76 + 13 * q^79 + 4 * q^80 - q^81 - 24 * q^83 + 2 * q^84 - 12 * q^85 + 6 * q^87 - 6 * q^89 - 5 * q^91 - 24 * q^92 - 5 * q^93 + 5 * q^95 - 20 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$2$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	1.00000	+	1.73205i	0.500000	+	0.866025i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$		0			0
$7$	2.50000	−	0.866025i	0.944911	−	0.327327i
$7$	2.50000	−	0.866025i	0.944911	−	0.327327i
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$11$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$12$	1.00000	−	1.73205i	0.288675	−	0.500000i
$13$	−1.00000			−0.277350			−0.138675	−	0.990338i	$-0.544284\pi$
$13$	−1.00000			−0.277350			−0.138675	+	0.990338i	$0.544284\pi$
$14$		0			0
$15$	−1.00000			−0.258199
$16$	−2.00000	+	3.46410i	−0.500000	+	0.866025i
$17$	−3.00000	−	5.19615i	−0.727607	−	1.26025i	−0.957892	−	0.287129i	$-0.907299\pi$
$17$	−3.00000	−	5.19615i	−0.727607	−	1.26025i	0.230285	−	0.973123i	$-0.426034\pi$
$18$		0			0
$19$	−2.50000	+	4.33013i	−0.573539	+	0.993399i	0.422659	+	0.906289i	$0.361097\pi$
$19$	−2.50000	+	4.33013i	−0.573539	+	0.993399i	−0.996199	+	0.0871106i	$0.972237\pi$
$20$	2.00000			0.447214
$21$	−2.00000	−	1.73205i	−0.436436	−	0.377964i
$22$		0			0
$23$	−3.00000	+	5.19615i	−0.625543	+	1.08347i	0.362892	+	0.931831i	$0.381789\pi$
$23$	−3.00000	+	5.19615i	−0.625543	+	1.08347i	−0.988436	+	0.151642i	$0.951544\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$	1.00000			0.192450
$28$	4.00000	+	3.46410i	0.755929	+	0.654654i
$29$	−6.00000			−1.11417			−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000			−1.11417			−0.557086	+	0.830455i	$0.688081\pi$
$30$		0			0
$31$	−2.50000	−	4.33013i	−0.449013	−	0.777714i	0.549309	−	0.835619i	$-0.314891\pi$
$31$	−2.50000	−	4.33013i	−0.449013	−	0.777714i	−0.998322	+	0.0579057i	$0.981558\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	0.500000	−	2.59808i	0.0845154	−	0.439155i
$36$	−2.00000			−0.333333
$37$	3.50000	−	6.06218i	0.575396	−	0.996616i	−0.420602	−	0.907245i	$-0.638181\pi$
$37$	3.50000	−	6.06218i	0.575396	−	0.996616i	0.995998	−	0.0893706i	$-0.0284856\pi$
$38$		0			0
$39$	0.500000	+	0.866025i	0.0800641	+	0.138675i
$40$		0			0
$41$	12.0000			1.87409			0.937043	−	0.349215i	$-0.113552\pi$
$41$	12.0000			1.87409			0.937043	+	0.349215i	$0.113552\pi$
$42$		0			0
$43$	−1.00000			−0.152499			−0.0762493	−	0.997089i	$-0.524294\pi$
$43$	−1.00000			−0.152499			−0.0762493	+	0.997089i	$0.524294\pi$
$44$		0			0
$45$	0.500000	+	0.866025i	0.0745356	+	0.129099i
$46$		0			0
$47$	−3.00000	+	5.19615i	−0.437595	+	0.757937i	−0.997503	−	0.0706177i	$-0.977503\pi$
$47$	−3.00000	+	5.19615i	−0.437595	+	0.757937i	0.559908	+	0.828554i	$0.310836\pi$
$48$	4.00000			0.577350
$49$	5.50000	−	4.33013i	0.785714	−	0.618590i
$50$		0			0
$51$	−3.00000	+	5.19615i	−0.420084	+	0.727607i
$52$	−1.00000	−	1.73205i	−0.138675	−	0.240192i
$53$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$53$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	5.00000			0.662266
$58$		0			0
$59$	3.00000	+	5.19615i	0.390567	+	0.676481i	0.992524	−	0.122047i	$-0.0389457\pi$
$59$	3.00000	+	5.19615i	0.390567	+	0.676481i	−0.601958	+	0.798528i	$0.705612\pi$
$60$	−1.00000	−	1.73205i	−0.129099	−	0.223607i
$61$	−1.00000	+	1.73205i	−0.128037	+	0.221766i	−0.922916	−	0.385002i	$-0.874201\pi$
$61$	−1.00000	+	1.73205i	−0.128037	+	0.221766i	0.794879	+	0.606768i	$0.207534\pi$
$62$		0			0
$63$	−0.500000	+	2.59808i	−0.0629941	+	0.327327i
$64$	−8.00000			−1.00000
$65$	−0.500000	+	0.866025i	−0.0620174	+	0.107417i
$66$		0			0
$67$	3.50000	+	6.06218i	0.427593	+	0.740613i	0.996659	−	0.0816792i	$-0.0260283\pi$
$67$	3.50000	+	6.06218i	0.427593	+	0.740613i	−0.569066	+	0.822292i	$0.692695\pi$
$68$	6.00000	−	10.3923i	0.727607	−	1.26025i
$69$	6.00000			0.722315
$70$		0			0
$71$	12.0000			1.42414			0.712069	−	0.702109i	$-0.247758\pi$
$71$	12.0000			1.42414			0.712069	+	0.702109i	$0.247758\pi$
$72$		0			0
$73$	−5.50000	−	9.52628i	−0.643726	−	1.11497i	−0.984594	−	0.174855i	$-0.944054\pi$
$73$	−5.50000	−	9.52628i	−0.643726	−	1.11497i	0.340868	−	0.940111i	$-0.389279\pi$
$74$		0			0
$75$	−0.500000	+	0.866025i	−0.0577350	+	0.100000i
$76$	−10.0000			−1.14708
$77$		0			0
$78$		0			0
$79$	6.50000	−	11.2583i	0.731307	−	1.26666i	−0.225018	−	0.974355i	$-0.572244\pi$
$79$	6.50000	−	11.2583i	0.731307	−	1.26666i	0.956325	−	0.292306i	$-0.0944227\pi$
$80$	2.00000	+	3.46410i	0.223607	+	0.387298i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	−12.0000			−1.31717			−0.658586	−	0.752506i	$-0.728845\pi$
$83$	−12.0000			−1.31717			−0.658586	+	0.752506i	$0.728845\pi$
$84$	1.00000	−	5.19615i	0.109109	−	0.566947i
$85$	−6.00000			−0.650791
$86$		0			0
$87$	3.00000	+	5.19615i	0.321634	+	0.557086i
$88$		0			0
$89$	−3.00000	+	5.19615i	−0.317999	+	0.550791i	−0.980071	−	0.198650i	$-0.936344\pi$
$89$	−3.00000	+	5.19615i	−0.317999	+	0.550791i	0.662071	+	0.749441i	$0.269678\pi$
$90$		0			0
$91$	−2.50000	+	0.866025i	−0.262071	+	0.0907841i
$92$	−12.0000			−1.25109
$93$	−2.50000	+	4.33013i	−0.259238	+	0.449013i
$94$		0			0
$95$	2.50000	+	4.33013i	0.256495	+	0.444262i
$96$		0			0
$97$	−10.0000			−1.01535			−0.507673	−	0.861550i	$-0.669494\pi$
$97$	−10.0000			−1.01535			−0.507673	+	0.861550i	$0.669494\pi$
$98$		0			0
$99$		0			0
$100$	1.00000	−	1.73205i	0.100000	−	0.173205i
$101$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$101$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$102$		0			0
$103$	0.500000	−	0.866025i	0.0492665	−	0.0853320i	−0.840341	−	0.542059i	$-0.817645\pi$
$103$	0.500000	−	0.866025i	0.0492665	−	0.0853320i	0.889607	+	0.456727i	$0.150978\pi$
$104$		0			0
$105$	−2.50000	+	0.866025i	−0.243975	+	0.0845154i
$106$		0			0
$107$	−9.00000	+	15.5885i	−0.870063	+	1.50699i	−0.00813215	+	0.999967i	$0.502589\pi$
$107$	−9.00000	+	15.5885i	−0.870063	+	1.50699i	−0.861931	+	0.507026i	$0.830745\pi$
$108$	1.00000	+	1.73205i	0.0962250	+	0.166667i
$109$	3.50000	+	6.06218i	0.335239	+	0.580651i	0.983531	−	0.180741i	$-0.0578495\pi$
$109$	3.50000	+	6.06218i	0.335239	+	0.580651i	−0.648292	+	0.761392i	$0.724516\pi$
$110$		0			0
$111$	−7.00000			−0.664411
$112$	−2.00000	+	10.3923i	−0.188982	+	0.981981i
$113$	18.0000			1.69330			0.846649	−	0.532152i	$-0.178617\pi$
$113$	18.0000			1.69330			0.846649	+	0.532152i	$0.178617\pi$
$114$		0			0
$115$	3.00000	+	5.19615i	0.279751	+	0.484544i
$116$	−6.00000	−	10.3923i	−0.557086	−	0.964901i
$117$	0.500000	−	0.866025i	0.0462250	−	0.0800641i
$118$		0			0
$119$	−12.0000	−	10.3923i	−1.10004	−	0.952661i
$120$		0			0
$121$	5.50000	−	9.52628i	0.500000	−	0.866025i
$122$		0			0
$123$	−6.00000	−	10.3923i	−0.541002	−	0.937043i
$124$	5.00000	−	8.66025i	0.449013	−	0.777714i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	11.0000			0.976092			0.488046	−	0.872818i	$-0.337710\pi$
$127$	11.0000			0.976092			0.488046	+	0.872818i	$0.337710\pi$
$128$		0			0
$129$	0.500000	+	0.866025i	0.0440225	+	0.0762493i
$130$		0			0
$131$	3.00000	−	5.19615i	0.262111	−	0.453990i	−0.704692	−	0.709514i	$-0.748915\pi$
$131$	3.00000	−	5.19615i	0.262111	−	0.453990i	0.966803	+	0.255524i	$0.0822479\pi$
$132$		0			0
$133$	−2.50000	+	12.9904i	−0.216777	+	1.12641i
$134$		0			0
$135$	0.500000	−	0.866025i	0.0430331	−	0.0745356i
$136$		0			0
$137$	−3.00000	−	5.19615i	−0.256307	−	0.443937i	0.708942	−	0.705266i	$-0.249173\pi$
$137$	−3.00000	−	5.19615i	−0.256307	−	0.443937i	−0.965250	+	0.261329i	$0.915839\pi$
$138$		0			0
$139$	5.00000			0.424094			0.212047	−	0.977259i	$-0.431987\pi$
$139$	5.00000			0.424094			0.212047	+	0.977259i	$0.431987\pi$
$140$	5.00000	−	1.73205i	0.422577	−	0.146385i
$141$	6.00000			0.505291
$142$		0			0
$143$		0			0
$144$	−2.00000	−	3.46410i	−0.166667	−	0.288675i
$145$	−3.00000	+	5.19615i	−0.249136	+	0.431517i
$146$		0			0
$147$	−6.50000	−	2.59808i	−0.536111	−	0.214286i
$148$	14.0000			1.15079
$149$	12.0000	−	20.7846i	0.983078	−	1.70274i	0.332896	−	0.942964i	$-0.391974\pi$
$149$	12.0000	−	20.7846i	0.983078	−	1.70274i	0.650183	−	0.759778i	$-0.274692\pi$
$150$		0			0
$151$	8.00000	+	13.8564i	0.651031	+	1.12762i	0.982873	+	0.184284i	$0.0589965\pi$
$151$	8.00000	+	13.8564i	0.651031	+	1.12762i	−0.331842	+	0.943335i	$0.607670\pi$
$152$		0			0
$153$	6.00000			0.485071
$154$		0			0
$155$	−5.00000			−0.401610
$156$	−1.00000	+	1.73205i	−0.0800641	+	0.138675i
$157$	5.00000	+	8.66025i	0.399043	+	0.691164i	0.993608	−	0.112884i	$-0.0360089\pi$
$157$	5.00000	+	8.66025i	0.399043	+	0.691164i	−0.594565	+	0.804048i	$0.702676\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−3.00000	+	15.5885i	−0.236433	+	1.22854i
$162$		0			0
$163$	2.00000	−	3.46410i	0.156652	−	0.271329i	−0.777007	−	0.629492i	$-0.783263\pi$
$163$	2.00000	−	3.46410i	0.156652	−	0.271329i	0.933659	+	0.358162i	$0.116597\pi$
$164$	12.0000	+	20.7846i	0.937043	+	1.62301i
$165$		0			0
$166$		0			0
$167$	12.0000			0.928588			0.464294	−	0.885681i	$-0.346308\pi$
$167$	12.0000			0.928588			0.464294	+	0.885681i	$0.346308\pi$
$168$		0			0
$169$	−12.0000			−0.923077
$170$		0			0
$171$	−2.50000	−	4.33013i	−0.191180	−	0.331133i
$172$	−1.00000	−	1.73205i	−0.0762493	−	0.132068i
$173$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$173$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$174$		0			0
$175$	−2.00000	−	1.73205i	−0.151186	−	0.130931i
$176$		0			0
$177$	3.00000	−	5.19615i	0.225494	−	0.390567i
$178$		0			0
$179$	−9.00000	−	15.5885i	−0.672692	−	1.16514i	−0.977138	−	0.212607i	$-0.931805\pi$
$179$	−9.00000	−	15.5885i	−0.672692	−	1.16514i	0.304446	−	0.952529i	$-0.401529\pi$
$180$	−1.00000	+	1.73205i	−0.0745356	+	0.129099i
$181$	−7.00000			−0.520306			−0.260153	−	0.965567i	$-0.583773\pi$
$181$	−7.00000			−0.520306			−0.260153	+	0.965567i	$0.583773\pi$
$182$		0			0
$183$	2.00000			0.147844
$184$		0			0
$185$	−3.50000	−	6.06218i	−0.257325	−	0.445700i
$186$		0			0
$187$		0			0
$188$	−12.0000			−0.875190
$189$	2.50000	−	0.866025i	0.181848	−	0.0629941i
$190$		0			0
$191$	3.00000	−	5.19615i	0.217072	−	0.375980i	−0.736839	−	0.676068i	$-0.763683\pi$
$191$	3.00000	−	5.19615i	0.217072	−	0.375980i	0.953912	+	0.300088i	$0.0970159\pi$
$192$	4.00000	+	6.92820i	0.288675	+	0.500000i
$193$	−2.50000	−	4.33013i	−0.179954	−	0.311689i	0.761911	−	0.647682i	$-0.224262\pi$
$193$	−2.50000	−	4.33013i	−0.179954	−	0.311689i	−0.941865	+	0.335993i	$0.890928\pi$
$194$		0			0
$195$	1.00000			0.0716115
$196$	13.0000	+	5.19615i	0.928571	+	0.371154i
$197$	6.00000			0.427482			0.213741	−	0.976890i	$-0.431435\pi$
$197$	6.00000			0.427482			0.213741	+	0.976890i	$0.431435\pi$
$198$		0			0
$199$	8.00000	+	13.8564i	0.567105	+	0.982255i	0.996850	+	0.0793045i	$0.0252700\pi$
$199$	8.00000	+	13.8564i	0.567105	+	0.982255i	−0.429745	+	0.902950i	$0.641397\pi$
$200$		0			0
$201$	3.50000	−	6.06218i	0.246871	−	0.427593i
$202$		0			0
$203$	−15.0000	+	5.19615i	−1.05279	+	0.364698i
$204$	−12.0000			−0.840168
$205$	6.00000	−	10.3923i	0.419058	−	0.725830i
$206$		0			0
$207$	−3.00000	−	5.19615i	−0.208514	−	0.361158i
$208$	2.00000	−	3.46410i	0.138675	−	0.240192i
$209$		0			0
$210$		0			0
$211$	−4.00000			−0.275371			−0.137686	−	0.990476i	$-0.543966\pi$
$211$	−4.00000			−0.275371			−0.137686	+	0.990476i	$0.543966\pi$
$212$		0			0
$213$	−6.00000	−	10.3923i	−0.411113	−	0.712069i
$214$		0			0
$215$	−0.500000	+	0.866025i	−0.0340997	+	0.0590624i
$216$		0			0
$217$	−10.0000	−	8.66025i	−0.678844	−	0.587896i
$218$		0			0
$219$	−5.50000	+	9.52628i	−0.371656	+	0.643726i
$220$		0			0
$221$	3.00000	+	5.19615i	0.201802	+	0.349531i
$222$		0			0
$223$	−4.00000			−0.267860			−0.133930	−	0.990991i	$-0.542760\pi$
$223$	−4.00000			−0.267860			−0.133930	+	0.990991i	$0.542760\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	−6.00000	−	10.3923i	−0.398234	−	0.689761i	0.595274	−	0.803523i	$-0.297043\pi$
$227$	−6.00000	−	10.3923i	−0.398234	−	0.689761i	−0.993508	+	0.113761i	$0.963710\pi$
$228$	5.00000	+	8.66025i	0.331133	+	0.573539i
$229$	−14.5000	+	25.1147i	−0.958187	+	1.65963i	−0.231287	+	0.972886i	$0.574293\pi$
$229$	−14.5000	+	25.1147i	−0.958187	+	1.65963i	−0.726900	+	0.686743i	$0.759040\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−3.00000	+	5.19615i	−0.196537	+	0.340411i	−0.947403	−	0.320043i	$-0.896303\pi$
$233$	−3.00000	+	5.19615i	−0.196537	+	0.340411i	0.750867	+	0.660454i	$0.229636\pi$
$234$		0			0
$235$	3.00000	+	5.19615i	0.195698	+	0.338960i
$236$	−6.00000	+	10.3923i	−0.390567	+	0.676481i
$237$	−13.0000			−0.844441
$238$		0			0
$239$	−6.00000			−0.388108			−0.194054	−	0.980991i	$-0.562164\pi$
$239$	−6.00000			−0.388108			−0.194054	+	0.980991i	$0.562164\pi$
$240$	2.00000	−	3.46410i	0.129099	−	0.223607i
$241$	−1.00000	−	1.73205i	−0.0644157	−	0.111571i	0.832019	−	0.554747i	$-0.187185\pi$
$241$	−1.00000	−	1.73205i	−0.0644157	−	0.111571i	−0.896435	+	0.443176i	$0.853852\pi$
$242$		0			0
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−4.00000			−0.256074
$245$	−1.00000	−	6.92820i	−0.0638877	−	0.442627i
$246$		0			0
$247$	2.50000	−	4.33013i	0.159071	−	0.275519i
$248$		0			0
$249$	6.00000	+	10.3923i	0.380235	+	0.658586i
$250$		0			0
$251$	−18.0000			−1.13615			−0.568075	−	0.822977i	$-0.692312\pi$
$251$	−18.0000			−1.13615			−0.568075	+	0.822977i	$0.692312\pi$
$252$	−5.00000	+	1.73205i	−0.314970	+	0.109109i
$253$		0			0
$254$		0			0
$255$	3.00000	+	5.19615i	0.187867	+	0.325396i
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$	6.00000	−	10.3923i	0.374270	−	0.648254i	−0.615948	−	0.787787i	$-0.711227\pi$
$257$	6.00000	−	10.3923i	0.374270	−	0.648254i	0.990217	+	0.139533i	$0.0445601\pi$
$258$		0			0
$259$	3.50000	−	18.1865i	0.217479	−	1.13006i
$260$	−2.00000			−0.124035
$261$	3.00000	−	5.19615i	0.185695	−	0.321634i
$262$		0			0
$263$	6.00000	+	10.3923i	0.369976	+	0.640817i	0.989561	−	0.144112i	$-0.0460326\pi$
$263$	6.00000	+	10.3923i	0.369976	+	0.640817i	−0.619586	+	0.784929i	$0.712699\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	6.00000			0.367194
$268$	−7.00000	+	12.1244i	−0.427593	+	0.740613i
$269$	9.00000	+	15.5885i	0.548740	+	0.950445i	0.998361	+	0.0572259i	$0.0182255\pi$
$269$	9.00000	+	15.5885i	0.548740	+	0.950445i	−0.449622	+	0.893219i	$0.648441\pi$
$270$		0			0
$271$	8.00000	−	13.8564i	0.485965	−	0.841717i	−0.513905	−	0.857847i	$-0.671801\pi$
$271$	8.00000	−	13.8564i	0.485965	−	0.841717i	0.999870	+	0.0161307i	$0.00513477\pi$
$272$	24.0000			1.45521
$273$	2.00000	+	1.73205i	0.121046	+	0.104828i
$274$		0			0
$275$		0			0
$276$	6.00000	+	10.3923i	0.361158	+	0.625543i
$277$	−11.5000	−	19.9186i	−0.690968	−	1.19679i	−0.971521	−	0.236953i	$-0.923851\pi$
$277$	−11.5000	−	19.9186i	−0.690968	−	1.19679i	0.280553	−	0.959839i	$-0.409482\pi$
$278$		0			0
$279$	5.00000			0.299342
$280$		0			0
$281$	−24.0000			−1.43172			−0.715860	−	0.698244i	$-0.753965\pi$
$281$	−24.0000			−1.43172			−0.715860	+	0.698244i	$0.753965\pi$
$282$		0			0
$283$	−5.50000	−	9.52628i	−0.326941	−	0.566279i	0.654962	−	0.755662i	$-0.272685\pi$
$283$	−5.50000	−	9.52628i	−0.326941	−	0.566279i	−0.981903	+	0.189383i	$0.939351\pi$
$284$	12.0000	+	20.7846i	0.712069	+	1.23334i
$285$	2.50000	−	4.33013i	0.148087	−	0.256495i
$286$		0			0
$287$	30.0000	−	10.3923i	1.77084	−	0.613438i
$288$		0			0
$289$	−9.50000	+	16.4545i	−0.558824	+	0.967911i
$290$		0			0
$291$	5.00000	+	8.66025i	0.293105	+	0.507673i
$292$	11.0000	−	19.0526i	0.643726	−	1.11497i
$293$	12.0000			0.701047			0.350524	−	0.936554i	$-0.386004\pi$
$293$	12.0000			0.701047			0.350524	+	0.936554i	$0.386004\pi$
$294$		0			0
$295$	6.00000			0.349334
$296$		0			0
$297$		0			0
$298$		0			0
$299$	3.00000	−	5.19615i	0.173494	−	0.300501i
$300$	−2.00000			−0.115470
$301$	−2.50000	+	0.866025i	−0.144098	+	0.0499169i
$302$		0			0
$303$		0			0
$304$	−10.0000	−	17.3205i	−0.573539	−	0.993399i
$305$	1.00000	+	1.73205i	0.0572598	+	0.0991769i
$306$		0			0
$307$	−7.00000			−0.399511			−0.199756	−	0.979846i	$-0.564015\pi$
$307$	−7.00000			−0.399511			−0.199756	+	0.979846i	$0.564015\pi$
$308$		0			0
$309$	−1.00000			−0.0568880
$310$		0			0
$311$	−6.00000	−	10.3923i	−0.340229	−	0.589294i	0.644246	−	0.764818i	$-0.277171\pi$
$311$	−6.00000	−	10.3923i	−0.340229	−	0.589294i	−0.984475	+	0.175525i	$0.943838\pi$
$312$		0			0
$313$	−8.50000	+	14.7224i	−0.480448	+	0.832161i	−0.999748	−	0.0224310i	$-0.992859\pi$
$313$	−8.50000	+	14.7224i	−0.480448	+	0.832161i	0.519300	+	0.854592i	$0.326193\pi$
$314$		0			0
$315$	2.00000	+	1.73205i	0.112687	+	0.0975900i
$316$	26.0000			1.46261
$317$	−3.00000	+	5.19615i	−0.168497	+	0.291845i	−0.937892	−	0.346929i	$-0.887225\pi$
$317$	−3.00000	+	5.19615i	−0.168497	+	0.291845i	0.769395	+	0.638774i	$0.220558\pi$
$318$		0			0
$319$		0			0
$320$	−4.00000	+	6.92820i	−0.223607	+	0.387298i
$321$	18.0000			1.00466
$322$		0			0
$323$	30.0000			1.66924
$324$	1.00000	−	1.73205i	0.0555556	−	0.0962250i
$325$	0.500000	+	0.866025i	0.0277350	+	0.0480384i
$326$		0			0
$327$	3.50000	−	6.06218i	0.193550	−	0.335239i
$328$		0			0
$329$	−3.00000	+	15.5885i	−0.165395	+	0.859419i
$330$		0			0
$331$	−11.5000	+	19.9186i	−0.632097	+	1.09482i	0.355025	+	0.934857i	$0.384472\pi$
$331$	−11.5000	+	19.9186i	−0.632097	+	1.09482i	−0.987122	+	0.159968i	$0.948861\pi$
$332$	−12.0000	−	20.7846i	−0.658586	−	1.14070i
$333$	3.50000	+	6.06218i	0.191799	+	0.332205i
$334$		0			0
$335$	7.00000			0.382451
$336$	10.0000	−	3.46410i	0.545545	−	0.188982i
$337$	−13.0000			−0.708155			−0.354078	−	0.935216i	$-0.615205\pi$
$337$	−13.0000			−0.708155			−0.354078	+	0.935216i	$0.615205\pi$
$338$		0			0
$339$	−9.00000	−	15.5885i	−0.488813	−	0.846649i
$340$	−6.00000	−	10.3923i	−0.325396	−	0.563602i
$341$		0			0
$342$		0			0
$343$	10.0000	−	15.5885i	0.539949	−	0.841698i
$344$		0			0
$345$	3.00000	−	5.19615i	0.161515	−	0.279751i
$346$		0			0
$347$	12.0000	+	20.7846i	0.644194	+	1.11578i	0.984487	+	0.175457i	$0.0561403\pi$
$347$	12.0000	+	20.7846i	0.644194	+	1.11578i	−0.340293	+	0.940319i	$0.610526\pi$
$348$	−6.00000	+	10.3923i	−0.321634	+	0.557086i
$349$	26.0000			1.39175			0.695874	−	0.718164i	$-0.255017\pi$
$349$	26.0000			1.39175			0.695874	+	0.718164i	$0.255017\pi$
$350$		0			0
$351$	−1.00000			−0.0533761
$352$		0			0
$353$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$353$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$354$		0			0
$355$	6.00000	−	10.3923i	0.318447	−	0.551566i
$356$	−12.0000			−0.635999
$357$	−3.00000	+	15.5885i	−0.158777	+	0.825029i
$358$		0			0
$359$	3.00000	−	5.19615i	0.158334	−	0.274242i	−0.775934	−	0.630814i	$-0.782721\pi$
$359$	3.00000	−	5.19615i	0.158334	−	0.274242i	0.934268	+	0.356572i	$0.116054\pi$
$360$		0			0
$361$	−3.00000	−	5.19615i	−0.157895	−	0.273482i
$362$		0			0
$363$	−11.0000			−0.577350
$364$	−4.00000	−	3.46410i	−0.209657	−	0.181568i
$365$	−11.0000			−0.575766
$366$		0			0
$367$	9.50000	+	16.4545i	0.495896	+	0.858917i	0.999989	−	0.00473247i	$-0.00150640\pi$
$367$	9.50000	+	16.4545i	0.495896	+	0.858917i	−0.504093	+	0.863649i	$0.668173\pi$
$368$	−12.0000	−	20.7846i	−0.625543	−	1.08347i
$369$	−6.00000	+	10.3923i	−0.312348	+	0.541002i
$370$		0			0
$371$		0			0
$372$	−10.0000			−0.518476
$373$	−8.50000	+	14.7224i	−0.440113	+	0.762299i	−0.997697	−	0.0678218i	$-0.978395\pi$
$373$	−8.50000	+	14.7224i	−0.440113	+	0.762299i	0.557584	+	0.830120i	$0.311728\pi$
$374$		0			0
$375$	0.500000	+	0.866025i	0.0258199	+	0.0447214i
$376$		0			0
$377$	6.00000			0.309016
$378$		0			0
$379$	−25.0000			−1.28416			−0.642082	−	0.766636i	$-0.721929\pi$
$379$	−25.0000			−1.28416			−0.642082	+	0.766636i	$0.721929\pi$
$380$	−5.00000	+	8.66025i	−0.256495	+	0.444262i
$381$	−5.50000	−	9.52628i	−0.281774	−	0.488046i
$382$		0			0
$383$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$383$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	0.500000	−	0.866025i	0.0254164	−	0.0440225i
$388$	−10.0000	−	17.3205i	−0.507673	−	0.879316i
$389$	−6.00000	−	10.3923i	−0.304212	−	0.526911i	0.672874	−	0.739758i	$-0.265060\pi$
$389$	−6.00000	−	10.3923i	−0.304212	−	0.526911i	−0.977086	+	0.212847i	$0.931726\pi$
$390$		0			0
$391$	36.0000			1.82060
$392$		0			0
$393$	−6.00000			−0.302660
$394$		0			0
$395$	−6.50000	−	11.2583i	−0.327050	−	0.566468i
$396$		0			0
$397$	−14.5000	+	25.1147i	−0.727734	+	1.26047i	0.230105	+	0.973166i	$0.426093\pi$
$397$	−14.5000	+	25.1147i	−0.727734	+	1.26047i	−0.957839	+	0.287307i	$0.907240\pi$
$398$		0			0
$399$	12.5000	−	4.33013i	0.625783	−	0.216777i
$400$	4.00000			0.200000
$401$	−12.0000	+	20.7846i	−0.599251	+	1.03793i	0.393680	+	0.919247i	$0.371202\pi$
$401$	−12.0000	+	20.7846i	−0.599251	+	1.03793i	−0.992932	+	0.118686i	$0.962132\pi$
$402$		0			0
$403$	2.50000	+	4.33013i	0.124534	+	0.215699i
$404$		0			0
$405$	−1.00000			−0.0496904
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−2.50000	−	4.33013i	−0.123617	−	0.214111i	0.797574	−	0.603220i	$-0.206116\pi$
$409$	−2.50000	−	4.33013i	−0.123617	−	0.214111i	−0.921192	+	0.389109i	$0.872783\pi$
$410$		0			0
$411$	−3.00000	+	5.19615i	−0.147979	+	0.256307i
$412$	2.00000			0.0985329
$413$	12.0000	+	10.3923i	0.590481	+	0.511372i
$414$		0			0
$415$	−6.00000	+	10.3923i	−0.294528	+	0.510138i
$416$		0			0
$417$	−2.50000	−	4.33013i	−0.122426	−	0.212047i
$418$		0			0
$419$	−30.0000			−1.46560			−0.732798	−	0.680446i	$-0.761786\pi$
$419$	−30.0000			−1.46560			−0.732798	+	0.680446i	$0.761786\pi$
$420$	−4.00000	−	3.46410i	−0.195180	−	0.169031i
$421$	−7.00000			−0.341159			−0.170580	−	0.985344i	$-0.554564\pi$
$421$	−7.00000			−0.341159			−0.170580	+	0.985344i	$0.554564\pi$
$422$		0			0
$423$	−3.00000	−	5.19615i	−0.145865	−	0.252646i
$424$		0			0
$425$	−3.00000	+	5.19615i	−0.145521	+	0.252050i
$426$		0			0
$427$	−1.00000	+	5.19615i	−0.0483934	+	0.251459i
$428$	−36.0000			−1.74013
$429$		0			0
$430$		0			0
$431$	−3.00000	−	5.19615i	−0.144505	−	0.250290i	0.784683	−	0.619897i	$-0.212826\pi$
$431$	−3.00000	−	5.19615i	−0.144505	−	0.250290i	−0.929188	+	0.369607i	$0.879492\pi$
$432$	−2.00000	+	3.46410i	−0.0962250	+	0.166667i
$433$	29.0000			1.39365			0.696826	−	0.717241i	$-0.254595\pi$
$433$	29.0000			1.39365			0.696826	+	0.717241i	$0.254595\pi$
$434$		0			0
$435$	6.00000			0.287678
$436$	−7.00000	+	12.1244i	−0.335239	+	0.580651i
$437$	−15.0000	−	25.9808i	−0.717547	−	1.24283i
$438$		0			0
$439$	14.0000	−	24.2487i	0.668184	−	1.15733i	−0.310228	−	0.950662i	$-0.600405\pi$
$439$	14.0000	−	24.2487i	0.668184	−	1.15733i	0.978412	−	0.206666i	$-0.0662612\pi$
$440$		0			0
$441$	1.00000	+	6.92820i	0.0476190	+	0.329914i
$442$		0			0
$443$	18.0000	−	31.1769i	0.855206	−	1.48126i	−0.0212481	−	0.999774i	$-0.506764\pi$
$443$	18.0000	−	31.1769i	0.855206	−	1.48126i	0.876454	−	0.481486i	$-0.159903\pi$
$444$	−7.00000	−	12.1244i	−0.332205	−	0.575396i
$445$	3.00000	+	5.19615i	0.142214	+	0.246321i
$446$		0			0
$447$	−24.0000			−1.13516
$448$	−20.0000	+	6.92820i	−0.944911	+	0.327327i
$449$	30.0000			1.41579			0.707894	−	0.706319i	$-0.249646\pi$
$449$	30.0000			1.41579			0.707894	+	0.706319i	$0.249646\pi$
$450$		0			0
$451$		0			0
$452$	18.0000	+	31.1769i	0.846649	+	1.46644i
$453$	8.00000	−	13.8564i	0.375873	−	0.651031i
$454$		0			0
$455$	−0.500000	+	2.59808i	−0.0234404	+	0.121800i
$456$		0			0
$457$	−5.50000	+	9.52628i	−0.257279	+	0.445621i	−0.965512	−	0.260358i	$-0.916159\pi$
$457$	−5.50000	+	9.52628i	−0.257279	+	0.445621i	0.708233	+	0.705979i	$0.249493\pi$
$458$		0			0
$459$	−3.00000	−	5.19615i	−0.140028	−	0.242536i
$460$	−6.00000	+	10.3923i	−0.279751	+	0.484544i
$461$	−6.00000			−0.279448			−0.139724	−	0.990190i	$-0.544622\pi$
$461$	−6.00000			−0.279448			−0.139724	+	0.990190i	$0.544622\pi$
$462$		0			0
$463$	−7.00000			−0.325318			−0.162659	−	0.986682i	$-0.552007\pi$
$463$	−7.00000			−0.325318			−0.162659	+	0.986682i	$0.552007\pi$
$464$	12.0000	−	20.7846i	0.557086	−	0.964901i
$465$	2.50000	+	4.33013i	0.115935	+	0.200805i
$466$		0			0
$467$	−15.0000	+	25.9808i	−0.694117	+	1.20225i	0.276360	+	0.961054i	$0.410872\pi$
$467$	−15.0000	+	25.9808i	−0.694117	+	1.20225i	−0.970477	+	0.241192i	$0.922462\pi$
$468$	2.00000			0.0924500
$469$	14.0000	+	12.1244i	0.646460	+	0.559851i
$470$		0			0
$471$	5.00000	−	8.66025i	0.230388	−	0.399043i
$472$		0			0
$473$		0			0
$474$		0			0
$475$	5.00000			0.229416
$476$	6.00000	−	31.1769i	0.275010	−	1.42899i
$477$		0			0
$478$		0			0
$479$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$479$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$480$		0			0
$481$	−3.50000	+	6.06218i	−0.159586	+	0.276412i
$482$		0			0
$483$	15.0000	−	5.19615i	0.682524	−	0.236433i
$484$	22.0000			1.00000
$485$	−5.00000	+	8.66025i	−0.227038	+	0.393242i
$486$		0			0
$487$	3.50000	+	6.06218i	0.158600	+	0.274703i	0.934364	−	0.356320i	$-0.115969\pi$
$487$	3.50000	+	6.06218i	0.158600	+	0.274703i	−0.775764	+	0.631023i	$0.782635\pi$
$488$		0			0
$489$	−4.00000			−0.180886
$490$		0			0
$491$	−12.0000			−0.541552			−0.270776	−	0.962642i	$-0.587280\pi$
$491$	−12.0000			−0.541552			−0.270776	+	0.962642i	$0.587280\pi$
$492$	12.0000	−	20.7846i	0.541002	−	0.937043i
$493$	18.0000	+	31.1769i	0.810679	+	1.40414i
$494$		0			0
$495$		0			0
$496$	20.0000			0.898027
$497$	30.0000	−	10.3923i	1.34568	−	0.466159i
$498$		0			0
$499$	−8.50000	+	14.7224i	−0.380512	+	0.659067i	−0.991136	−	0.132855i	$-0.957586\pi$
$499$	−8.50000	+	14.7224i	−0.380512	+	0.659067i	0.610623	+	0.791921i	$0.290919\pi$
$500$	−1.00000	−	1.73205i	−0.0447214	−	0.0774597i
$501$	−6.00000	−	10.3923i	−0.268060	−	0.464294i
$502$		0			0
$503$	−6.00000			−0.267527			−0.133763	−	0.991013i	$-0.542706\pi$
$503$	−6.00000			−0.267527			−0.133763	+	0.991013i	$0.542706\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	6.00000	+	10.3923i	0.266469	+	0.461538i
$508$	11.0000	+	19.0526i	0.488046	+	0.845321i
$509$	9.00000	−	15.5885i	0.398918	−	0.690946i	−0.594675	−	0.803966i	$-0.702719\pi$
$509$	9.00000	−	15.5885i	0.398918	−	0.690946i	0.993593	+	0.113020i	$0.0360525\pi$
$510$		0			0
$511$	−22.0000	−	19.0526i	−0.973223	−	0.842836i
$512$		0			0
$513$	−2.50000	+	4.33013i	−0.110378	+	0.191180i
$514$		0			0
$515$	−0.500000	−	0.866025i	−0.0220326	−	0.0381616i
$516$	−1.00000	+	1.73205i	−0.0440225	+	0.0762493i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	12.0000	+	20.7846i	0.525730	+	0.910590i	0.999551	+	0.0299693i	$0.00954094\pi$
$521$	12.0000	+	20.7846i	0.525730	+	0.910590i	−0.473821	+	0.880621i	$0.657126\pi$
$522$		0			0
$523$	21.5000	−	37.2391i	0.940129	−	1.62835i	0.174908	−	0.984585i	$-0.444037\pi$
$523$	21.5000	−	37.2391i	0.940129	−	1.62835i	0.765222	−	0.643767i	$-0.222629\pi$
$524$	12.0000			0.524222
$525$	−0.500000	+	2.59808i	−0.0218218	+	0.113389i
$526$		0			0
$527$	−15.0000	+	25.9808i	−0.653410	+	1.13174i
$528$		0			0
$529$	−6.50000	−	11.2583i	−0.282609	−	0.489493i
$530$		0			0
$531$	−6.00000			−0.260378
$532$	−25.0000	+	8.66025i	−1.08389	+	0.375470i
$533$	−12.0000			−0.519778
$534$		0			0
$535$	9.00000	+	15.5885i	0.389104	+	0.673948i
$536$		0			0
$537$	−9.00000	+	15.5885i	−0.388379	+	0.672692i
$538$		0			0
$539$		0			0
$540$	2.00000			0.0860663
$541$	9.50000	−	16.4545i	0.408437	−	0.707433i	−0.586278	−	0.810110i	$-0.699407\pi$
$541$	9.50000	−	16.4545i	0.408437	−	0.707433i	0.994715	+	0.102677i	$0.0327407\pi$
$542$		0			0
$543$	3.50000	+	6.06218i	0.150199	+	0.260153i
$544$		0			0
$545$	7.00000			0.299847
$546$		0			0
$547$	8.00000			0.342055			0.171028	−	0.985266i	$-0.445291\pi$
$547$	8.00000			0.342055			0.171028	+	0.985266i	$0.445291\pi$
$548$	6.00000	−	10.3923i	0.256307	−	0.443937i
$549$	−1.00000	−	1.73205i	−0.0426790	−	0.0739221i
$550$		0			0
$551$	15.0000	−	25.9808i	0.639021	−	1.10682i
$552$		0			0
$553$	6.50000	−	33.7750i	0.276408	−	1.43626i
$554$		0			0
$555$	−3.50000	+	6.06218i	−0.148567	+	0.257325i
$556$	5.00000	+	8.66025i	0.212047	+	0.367277i
$557$	−9.00000	−	15.5885i	−0.381342	−	0.660504i	0.609912	−	0.792469i	$-0.291205\pi$
$557$	−9.00000	−	15.5885i	−0.381342	−	0.660504i	−0.991254	+	0.131965i	$0.957871\pi$
$558$		0			0
$559$	1.00000			0.0422955
$560$	8.00000	+	6.92820i	0.338062	+	0.292770i
$561$		0			0
$562$		0			0
$563$	9.00000	+	15.5885i	0.379305	+	0.656975i	0.990961	−	0.134148i	$-0.0428299\pi$
$563$	9.00000	+	15.5885i	0.379305	+	0.656975i	−0.611656	+	0.791123i	$0.709497\pi$
$564$	6.00000	+	10.3923i	0.252646	+	0.437595i
$565$	9.00000	−	15.5885i	0.378633	−	0.655811i
$566$		0			0
$567$	−2.00000	−	1.73205i	−0.0839921	−	0.0727393i
$568$		0			0
$569$	12.0000	−	20.7846i	0.503066	−	0.871336i	−0.496928	−	0.867792i	$-0.665539\pi$
$569$	12.0000	−	20.7846i	0.503066	−	0.871336i	0.999994	−	0.00354413i	$-0.00112814\pi$
$570$		0			0
$571$	3.50000	+	6.06218i	0.146470	+	0.253694i	0.929921	−	0.367760i	$-0.119875\pi$
$571$	3.50000	+	6.06218i	0.146470	+	0.253694i	−0.783450	+	0.621455i	$0.786542\pi$
$572$		0			0
$573$	−6.00000			−0.250654
$574$		0			0
$575$	6.00000			0.250217
$576$	4.00000	−	6.92820i	0.166667	−	0.288675i
$577$	3.50000	+	6.06218i	0.145707	+	0.252372i	0.929636	−	0.368478i	$-0.120121\pi$
$577$	3.50000	+	6.06218i	0.145707	+	0.252372i	−0.783930	+	0.620850i	$0.786788\pi$
$578$		0			0
$579$	−2.50000	+	4.33013i	−0.103896	+	0.179954i
$580$	−12.0000			−0.498273
$581$	−30.0000	+	10.3923i	−1.24461	+	0.431145i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	−0.500000	−	0.866025i	−0.0206725	−	0.0358057i
$586$		0			0
$587$	−18.0000			−0.742940			−0.371470	−	0.928445i	$-0.621146\pi$
$587$	−18.0000			−0.742940			−0.371470	+	0.928445i	$0.621146\pi$
$588$	−2.00000	−	13.8564i	−0.0824786	−	0.571429i
$589$	25.0000			1.03011
$590$		0			0
$591$	−3.00000	−	5.19615i	−0.123404	−	0.213741i
$592$	14.0000	+	24.2487i	0.575396	+	0.996616i
$593$	−18.0000	+	31.1769i	−0.739171	+	1.28028i	0.213697	+	0.976900i	$0.431449\pi$
$593$	−18.0000	+	31.1769i	−0.739171	+	1.28028i	−0.952869	+	0.303383i	$0.901884\pi$
$594$		0			0
$595$	−15.0000	+	5.19615i	−0.614940	+	0.213021i
$596$	48.0000			1.96616
$597$	8.00000	−	13.8564i	0.327418	−	0.567105i
$598$		0			0
$599$	−6.00000	−	10.3923i	−0.245153	−	0.424618i	0.717021	−	0.697051i	$-0.245505\pi$
$599$	−6.00000	−	10.3923i	−0.245153	−	0.424618i	−0.962175	+	0.272433i	$0.912172\pi$
$600$		0			0
$601$	−1.00000			−0.0407909			−0.0203954	−	0.999792i	$-0.506493\pi$
$601$	−1.00000			−0.0407909			−0.0203954	+	0.999792i	$0.506493\pi$
$602$		0			0
$603$	−7.00000			−0.285062
$604$	−16.0000	+	27.7128i	−0.651031	+	1.12762i
$605$	−5.50000	−	9.52628i	−0.223607	−	0.387298i
$606$		0			0
$607$	9.50000	−	16.4545i	0.385593	−	0.667867i	−0.606258	−	0.795268i	$-0.707330\pi$
$607$	9.50000	−	16.4545i	0.385593	−	0.667867i	0.991851	+	0.127401i	$0.0406635\pi$
$608$		0			0
$609$	12.0000	+	10.3923i	0.486265	+	0.421117i
$610$		0			0
$611$	3.00000	−	5.19615i	0.121367	−	0.210214i
$612$	6.00000	+	10.3923i	0.242536	+	0.420084i
$613$	−19.0000	−	32.9090i	−0.767403	−	1.32918i	−0.938967	−	0.344008i	$-0.888215\pi$
$613$	−19.0000	−	32.9090i	−0.767403	−	1.32918i	0.171564	−	0.985173i	$-0.445118\pi$
$614$		0			0
$615$	−12.0000			−0.483887
$616$		0			0
$617$	−42.0000			−1.69086			−0.845428	−	0.534089i	$-0.820655\pi$
$617$	−42.0000			−1.69086			−0.845428	+	0.534089i	$0.820655\pi$
$618$		0			0
$619$	−17.5000	−	30.3109i	−0.703384	−	1.21830i	−0.967271	−	0.253744i	$-0.918338\pi$
$619$	−17.5000	−	30.3109i	−0.703384	−	1.21830i	0.263887	−	0.964554i	$-0.414995\pi$
$620$	−5.00000	−	8.66025i	−0.200805	−	0.347804i
$621$	−3.00000	+	5.19615i	−0.120386	+	0.208514i
$622$		0			0
$623$	−3.00000	+	15.5885i	−0.120192	+	0.624538i
$624$	−4.00000			−0.160128
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$		0			0
$628$	−10.0000	+	17.3205i	−0.399043	+	0.691164i
$629$	−42.0000			−1.67465
$630$		0			0
$631$	−40.0000			−1.59237			−0.796187	−	0.605050i	$-0.793153\pi$
$631$	−40.0000			−1.59237			−0.796187	+	0.605050i	$0.793153\pi$
$632$		0			0
$633$	2.00000	+	3.46410i	0.0794929	+	0.137686i
$634$		0			0
$635$	5.50000	−	9.52628i	0.218261	−	0.378039i
$636$		0			0
$637$	−5.50000	+	4.33013i	−0.217918	+	0.171566i
$638$		0			0
$639$	−6.00000	+	10.3923i	−0.237356	+	0.411113i
$640$		0			0
$641$	15.0000	+	25.9808i	0.592464	+	1.02618i	0.993899	+	0.110291i	$0.0351782\pi$
$641$	15.0000	+	25.9808i	0.592464	+	1.02618i	−0.401435	+	0.915888i	$0.631488\pi$
$642$		0			0
$643$	−25.0000			−0.985904			−0.492952	−	0.870057i	$-0.664082\pi$
$643$	−25.0000			−0.985904			−0.492952	+	0.870057i	$0.664082\pi$
$644$	−30.0000	+	10.3923i	−1.18217	+	0.409514i
$645$	1.00000			0.0393750
$646$		0			0
$647$	12.0000	+	20.7846i	0.471769	+	0.817127i	0.999478	−	0.0322975i	$-0.0102824\pi$
$647$	12.0000	+	20.7846i	0.471769	+	0.817127i	−0.527710	+	0.849425i	$0.676949\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$	−2.50000	+	12.9904i	−0.0979827	+	0.509133i
$652$	8.00000			0.313304
$653$	12.0000	−	20.7846i	0.469596	−	0.813365i	−0.529799	−	0.848123i	$-0.677733\pi$
$653$	12.0000	−	20.7846i	0.469596	−	0.813365i	0.999396	+	0.0347583i	$0.0110661\pi$
$654$		0			0
$655$	−3.00000	−	5.19615i	−0.117220	−	0.203030i
$656$	−24.0000	+	41.5692i	−0.937043	+	1.62301i
$657$	11.0000			0.429151
$658$		0			0
$659$	36.0000			1.40236			0.701180	−	0.712984i	$-0.252657\pi$
$659$	36.0000			1.40236			0.701180	+	0.712984i	$0.252657\pi$
$660$		0			0
$661$	6.50000	+	11.2583i	0.252821	+	0.437898i	0.964301	−	0.264807i	$-0.0853084\pi$
$661$	6.50000	+	11.2583i	0.252821	+	0.437898i	−0.711481	+	0.702706i	$0.751975\pi$
$662$		0			0
$663$	3.00000	−	5.19615i	0.116510	−	0.201802i
$664$		0			0
$665$	10.0000	+	8.66025i	0.387783	+	0.335830i
$666$		0			0
$667$	18.0000	−	31.1769i	0.696963	−	1.20717i
$668$	12.0000	+	20.7846i	0.464294	+	0.804181i
$669$	2.00000	+	3.46410i	0.0773245	+	0.133930i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−31.0000			−1.19496			−0.597481	−	0.801883i	$-0.703832\pi$
$673$	−31.0000			−1.19496			−0.597481	+	0.801883i	$0.703832\pi$
$674$		0			0
$675$	−0.500000	−	0.866025i	−0.0192450	−	0.0333333i
$676$	−12.0000	−	20.7846i	−0.461538	−	0.799408i
$677$	9.00000	−	15.5885i	0.345898	−	0.599113i	−0.639618	−	0.768693i	$-0.720908\pi$
$677$	9.00000	−	15.5885i	0.345898	−	0.599113i	0.985517	+	0.169580i	$0.0542410\pi$
$678$		0			0
$679$	−25.0000	+	8.66025i	−0.959412	+	0.332350i
$680$		0			0
$681$	−6.00000	+	10.3923i	−0.229920	+	0.398234i
$682$		0			0
$683$	−9.00000	−	15.5885i	−0.344375	−	0.596476i	0.640865	−	0.767654i	$-0.278576\pi$
$683$	−9.00000	−	15.5885i	−0.344375	−	0.596476i	−0.985240	+	0.171178i	$0.945243\pi$
$684$	5.00000	−	8.66025i	0.191180	−	0.331133i
$685$	−6.00000			−0.229248
$686$		0			0
$687$	29.0000			1.10642
$688$	2.00000	−	3.46410i	0.0762493	−	0.132068i
$689$		0			0
$690$		0			0
$691$	−5.50000	+	9.52628i	−0.209230	+	0.362397i	−0.951472	−	0.307735i	$-0.900429\pi$
$691$	−5.50000	+	9.52628i	−0.209230	+	0.362397i	0.742242	+	0.670132i	$0.233762\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	2.50000	−	4.33013i	0.0948304	−	0.164251i
$696$		0			0
$697$	−36.0000	−	62.3538i	−1.36360	−	2.36182i
$698$		0			0
$699$	6.00000			0.226941
$700$	1.00000	−	5.19615i	0.0377964	−	0.196396i
$701$	6.00000			0.226617			0.113308	−	0.993560i	$-0.463855\pi$
$701$	6.00000			0.226617			0.113308	+	0.993560i	$0.463855\pi$
$702$		0			0
$703$	17.5000	+	30.3109i	0.660025	+	1.14320i
$704$		0			0
$705$	3.00000	−	5.19615i	0.112987	−	0.195698i
$706$		0			0
$707$		0			0
$708$	12.0000			0.450988
$709$	5.00000	−	8.66025i	0.187779	−	0.325243i	−0.756730	−	0.653727i	$-0.773204\pi$
$709$	5.00000	−	8.66025i	0.187779	−	0.325243i	0.944509	+	0.328484i	$0.106538\pi$
$710$		0			0
$711$	6.50000	+	11.2583i	0.243769	+	0.422220i
$712$		0			0
$713$	30.0000			1.12351
$714$		0			0
$715$		0			0
$716$	18.0000	−	31.1769i	0.672692	−	1.16514i
$717$	3.00000	+	5.19615i	0.112037	+	0.194054i
$718$		0			0
$719$	−3.00000	+	5.19615i	−0.111881	+	0.193784i	−0.916529	−	0.399969i	$-0.869021\pi$
$719$	−3.00000	+	5.19615i	−0.111881	+	0.193784i	0.804648	+	0.593753i	$0.202354\pi$
$720$	−4.00000			−0.149071
$721$	0.500000	−	2.59808i	0.0186210	−	0.0967574i
$722$		0			0
$723$	−1.00000	+	1.73205i	−0.0371904	+	0.0644157i
$724$	−7.00000	−	12.1244i	−0.260153	−	0.450598i
$725$	3.00000	+	5.19615i	0.111417	+	0.192980i
$726$		0			0
$727$	−7.00000			−0.259616			−0.129808	−	0.991539i	$-0.541436\pi$
$727$	−7.00000			−0.259616			−0.129808	+	0.991539i	$0.541436\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	3.00000	+	5.19615i	0.110959	+	0.192187i
$732$	2.00000	+	3.46410i	0.0739221	+	0.128037i
$733$	6.50000	−	11.2583i	0.240083	−	0.415836i	−0.720655	−	0.693294i	$-0.756159\pi$
$733$	6.50000	−	11.2583i	0.240083	−	0.415836i	0.960738	+	0.277458i	$0.0894920\pi$
$734$		0			0
$735$	−5.50000	+	4.33013i	−0.202871	+	0.159719i
$736$		0			0
$737$		0			0
$738$		0			0
$739$	3.50000	+	6.06218i	0.128750	+	0.223001i	0.923192	−	0.384338i	$-0.125570\pi$
$739$	3.50000	+	6.06218i	0.128750	+	0.223001i	−0.794443	+	0.607339i	$0.792237\pi$
$740$	7.00000	−	12.1244i	0.257325	−	0.445700i
$741$	−5.00000			−0.183680
$742$		0			0
$743$	−24.0000			−0.880475			−0.440237	−	0.897881i	$-0.645106\pi$
$743$	−24.0000			−0.880475			−0.440237	+	0.897881i	$0.645106\pi$
$744$		0			0
$745$	−12.0000	−	20.7846i	−0.439646	−	0.761489i
$746$		0			0
$747$	6.00000	−	10.3923i	0.219529	−	0.380235i
$748$		0			0
$749$	−9.00000	+	46.7654i	−0.328853	+	1.70877i
$750$		0			0
$751$	9.50000	−	16.4545i	0.346660	−	0.600433i	−0.638994	−	0.769212i	$-0.720649\pi$
$751$	9.50000	−	16.4545i	0.346660	−	0.600433i	0.985654	+	0.168779i	$0.0539825\pi$
$752$	−12.0000	−	20.7846i	−0.437595	−	0.757937i
$753$	9.00000	+	15.5885i	0.327978	+	0.568075i
$754$		0			0
$755$	16.0000			0.582300
$756$	4.00000	+	3.46410i	0.145479	+	0.125988i
$757$	50.0000			1.81728			0.908640	−	0.417579i	$-0.137121\pi$
$757$	50.0000			1.81728			0.908640	+	0.417579i	$0.137121\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	21.0000	−	36.3731i	0.761249	−	1.31852i	−0.180957	−	0.983491i	$-0.557920\pi$
$761$	21.0000	−	36.3731i	0.761249	−	1.31852i	0.942207	−	0.335032i	$-0.108747\pi$
$762$		0			0
$763$	14.0000	+	12.1244i	0.506834	+	0.438931i
$764$	12.0000			0.434145
$765$	3.00000	−	5.19615i	0.108465	−	0.187867i
$766$		0			0
$767$	−3.00000	−	5.19615i	−0.108324	−	0.187622i
$768$	−8.00000	+	13.8564i	−0.288675	+	0.500000i
$769$	−13.0000			−0.468792			−0.234396	−	0.972141i	$-0.575311\pi$
$769$	−13.0000			−0.468792			−0.234396	+	0.972141i	$0.575311\pi$
$770$		0			0
$771$	−12.0000			−0.432169
$772$	5.00000	−	8.66025i	0.179954	−	0.311689i
$773$	12.0000	+	20.7846i	0.431610	+	0.747570i	0.997012	−	0.0772449i	$-0.0246123\pi$
$773$	12.0000	+	20.7846i	0.431610	+	0.747570i	−0.565402	+	0.824815i	$0.691279\pi$
$774$		0			0
$775$	−2.50000	+	4.33013i	−0.0898027	+	0.155543i
$776$		0			0
$777$	−17.5000	+	6.06218i	−0.627809	+	0.217479i
$778$		0			0
$779$	−30.0000	+	51.9615i	−1.07486	+	1.86171i
$780$	1.00000	+	1.73205i	0.0358057	+	0.0620174i
$781$		0			0
$782$		0			0
$783$	−6.00000			−0.214423
$784$	4.00000	+	27.7128i	0.142857	+	0.989743i
$785$	10.0000			0.356915
$786$		0			0
$787$	14.0000	+	24.2487i	0.499046	+	0.864373i	0.999999	−	0.00110111i	$-0.000350496\pi$
$787$	14.0000	+	24.2487i	0.499046	+	0.864373i	−0.500953	+	0.865474i	$0.667017\pi$
$788$	6.00000	+	10.3923i	0.213741	+	0.370211i
$789$	6.00000	−	10.3923i	0.213606	−	0.369976i
$790$		0			0
$791$	45.0000	−	15.5885i	1.60002	−	0.554262i
$792$		0			0
$793$	1.00000	−	1.73205i	0.0355110	−	0.0615069i
$794$		0			0
$795$		0			0
$796$	−16.0000	+	27.7128i	−0.567105	+	0.982255i
$797$	18.0000			0.637593			0.318796	−	0.947823i	$-0.396721\pi$
$797$	18.0000			0.637593			0.318796	+	0.947823i	$0.396721\pi$
$798$		0			0
$799$	36.0000			1.27359
$800$		0			0
$801$	−3.00000	−	5.19615i	−0.106000	−	0.183597i
$802$		0			0
$803$		0			0
$804$	14.0000			0.493742
$805$	12.0000	+	10.3923i	0.422944	+	0.366281i
$806$		0			0
$807$	9.00000	−	15.5885i	0.316815	−	0.548740i
$808$		0			0
$809$	−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
$811$	−28.0000			−0.983213			−0.491606	−	0.870817i	$-0.663590\pi$
$811$	−28.0000			−0.983213			−0.491606	+	0.870817i	$0.663590\pi$
$812$	−24.0000	−	20.7846i	−0.842235	−	0.729397i
$813$	−16.0000			−0.561144
$814$		0			0
$815$	−2.00000	−	3.46410i	−0.0700569	−	0.121342i
$816$	−12.0000	−	20.7846i	−0.420084	−	0.727607i
$817$	2.50000	−	4.33013i	0.0874639	−	0.151492i
$818$		0			0
$819$	0.500000	−	2.59808i	0.0174714	−	0.0907841i
$820$	24.0000			0.838116
$821$	12.0000	−	20.7846i	0.418803	−	0.725388i	−0.577016	−	0.816733i	$-0.695783\pi$
$821$	12.0000	−	20.7846i	0.418803	−	0.725388i	0.995819	+	0.0913446i	$0.0291165\pi$
$822$		0			0
$823$	20.0000	+	34.6410i	0.697156	+	1.20751i	0.969448	+	0.245295i	$0.0788849\pi$
$823$	20.0000	+	34.6410i	0.697156	+	1.20751i	−0.272292	+	0.962215i	$0.587782\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−6.00000			−0.208640			−0.104320	−	0.994544i	$-0.533267\pi$
$827$	−6.00000			−0.208640			−0.104320	+	0.994544i	$0.533267\pi$
$828$	6.00000	−	10.3923i	0.208514	−	0.361158i
$829$	9.50000	+	16.4545i	0.329949	+	0.571488i	0.982501	−	0.186256i	$-0.0596352\pi$
$829$	9.50000	+	16.4545i	0.329949	+	0.571488i	−0.652553	+	0.757743i	$0.726302\pi$
$830$		0			0
$831$	−11.5000	+	19.9186i	−0.398931	+	0.690968i
$832$	8.00000			0.277350
$833$	−39.0000	−	15.5885i	−1.35127	−	0.540108i
$834$		0			0
$835$	6.00000	−	10.3923i	0.207639	−	0.359641i
$836$		0			0
$837$	−2.50000	−	4.33013i	−0.0864126	−	0.149671i
$838$		0			0
$839$	−30.0000			−1.03572			−0.517858	−	0.855467i	$-0.673270\pi$
$839$	−30.0000			−1.03572			−0.517858	+	0.855467i	$0.673270\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$		0			0
$843$	12.0000	+	20.7846i	0.413302	+	0.715860i
$844$	−4.00000	−	6.92820i	−0.137686	−	0.238479i
$845$	−6.00000	+	10.3923i	−0.206406	+	0.357506i
$846$		0			0
$847$	5.50000	−	28.5788i	0.188982	−	0.981981i
$848$		0			0
$849$	−5.50000	+	9.52628i	−0.188760	+	0.326941i
$850$		0			0
$851$	21.0000	+	36.3731i	0.719871	+	1.24685i
$852$	12.0000	−	20.7846i	0.411113	−	0.712069i
$853$	17.0000			0.582069			0.291034	−	0.956713i	$-0.406001\pi$
$853$	17.0000			0.582069			0.291034	+	0.956713i	$0.406001\pi$
$854$		0			0
$855$	−5.00000			−0.170996
$856$		0			0
$857$	−21.0000	−	36.3731i	−0.717346	−	1.24248i	−0.962048	−	0.272882i	$-0.912023\pi$
$857$	−21.0000	−	36.3731i	−0.717346	−	1.24248i	0.244701	−	0.969599i	$-0.421310\pi$
$858$		0			0
$859$	2.00000	−	3.46410i	0.0682391	−	0.118194i	−0.829887	−	0.557931i	$-0.811595\pi$
$859$	2.00000	−	3.46410i	0.0682391	−	0.118194i	0.898126	+	0.439738i	$0.144929\pi$
$860$	−2.00000			−0.0681994
$861$	−24.0000	−	20.7846i	−0.817918	−	0.708338i
$862$		0			0
$863$	3.00000	−	5.19615i	0.102121	−	0.176879i	−0.810437	−	0.585826i	$-0.800770\pi$
$863$	3.00000	−	5.19615i	0.102121	−	0.176879i	0.912558	+	0.408946i	$0.134104\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	19.0000			0.645274
$868$	5.00000	−	25.9808i	0.169711	−	0.881845i
$869$		0			0
$870$		0			0
$871$	−3.50000	−	6.06218i	−0.118593	−	0.205409i
$872$		0			0
$873$	5.00000	−	8.66025i	0.169224	−	0.293105i
$874$		0			0
$875$	−2.50000	+	0.866025i	−0.0845154	+	0.0292770i
$876$	−22.0000			−0.743311
$877$	−1.00000	+	1.73205i	−0.0337676	+	0.0584872i	−0.882415	−	0.470471i	$-0.844084\pi$
$877$	−1.00000	+	1.73205i	−0.0337676	+	0.0584872i	0.848648	+	0.528958i	$0.177417\pi$
$878$		0			0
$879$	−6.00000	−	10.3923i	−0.202375	−	0.350524i
$880$		0			0
$881$	12.0000			0.404290			0.202145	−	0.979356i	$-0.435209\pi$
$881$	12.0000			0.404290			0.202145	+	0.979356i	$0.435209\pi$
$882$		0			0
$883$	−31.0000			−1.04323			−0.521617	−	0.853180i	$-0.674671\pi$
$883$	−31.0000			−1.04323			−0.521617	+	0.853180i	$0.674671\pi$
$884$	−6.00000	+	10.3923i	−0.201802	+	0.349531i
$885$	−3.00000	−	5.19615i	−0.100844	−	0.174667i
$886$		0			0
$887$	−6.00000	+	10.3923i	−0.201460	+	0.348939i	−0.948999	−	0.315279i	$-0.897902\pi$
$887$	−6.00000	+	10.3923i	−0.201460	+	0.348939i	0.747539	+	0.664218i	$0.231235\pi$
$888$		0			0
$889$	27.5000	−	9.52628i	0.922320	−	0.319501i
$890$		0			0
$891$		0			0
$892$	−4.00000	−	6.92820i	−0.133930	−	0.231973i
$893$	−15.0000	−	25.9808i	−0.501956	−	0.869413i
$894$		0			0
$895$	−18.0000			−0.601674
$896$		0			0
$897$	−6.00000			−0.200334
$898$		0			0
$899$	15.0000	+	25.9808i	0.500278	+	0.866507i
$900$	1.00000	+	1.73205i	0.0333333	+	0.0577350i
$901$		0			0
$902$		0			0
$903$	2.00000	+	1.73205i	0.0665558	+	0.0576390i
$904$		0			0
$905$	−3.50000	+	6.06218i	−0.116344	+	0.201514i
$906$		0			0
$907$	15.5000	+	26.8468i	0.514669	+	0.891433i	0.999855	+	0.0170220i	$0.00541854\pi$
$907$	15.5000	+	26.8468i	0.514669	+	0.891433i	−0.485186	+	0.874411i	$0.661248\pi$
$908$	12.0000	−	20.7846i	0.398234	−	0.689761i
$909$		0			0
$910$		0			0
$911$	−18.0000			−0.596367			−0.298183	−	0.954509i	$-0.596381\pi$
$911$	−18.0000			−0.596367			−0.298183	+	0.954509i	$0.596381\pi$
$912$	−10.0000	+	17.3205i	−0.331133	+	0.573539i
$913$		0			0
$914$		0			0
$915$	1.00000	−	1.73205i	0.0330590	−	0.0572598i
$916$	−58.0000			−1.91637
$917$	3.00000	−	15.5885i	0.0990687	−	0.514776i
$918$		0			0
$919$	−23.5000	+	40.7032i	−0.775193	+	1.34267i	0.159492	+	0.987199i	$0.449014\pi$
$919$	−23.5000	+	40.7032i	−0.775193	+	1.34267i	−0.934686	+	0.355475i	$0.884319\pi$
$920$		0			0
$921$	3.50000	+	6.06218i	0.115329	+	0.199756i
$922$		0			0
$923$	−12.0000			−0.394985
$924$		0			0
$925$	−7.00000			−0.230159
$926$		0			0
$927$	0.500000	+	0.866025i	0.0164222	+	0.0284440i
$928$		0			0
$929$	6.00000	−	10.3923i	0.196854	−	0.340960i	−0.750653	−	0.660697i	$-0.770261\pi$
$929$	6.00000	−	10.3923i	0.196854	−	0.340960i	0.947507	+	0.319736i	$0.103594\pi$
$930$		0			0
$931$	5.00000	+	34.6410i	0.163868	+	1.13531i
$932$	−12.0000			−0.393073
$933$	−6.00000	+	10.3923i	−0.196431	+	0.340229i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	29.0000			0.947389			0.473694	−	0.880689i	$-0.342920\pi$
$937$	29.0000			0.947389			0.473694	+	0.880689i	$0.342920\pi$
$938$		0			0
$939$	17.0000			0.554774
$940$	−6.00000	+	10.3923i	−0.195698	+	0.338960i
$941$	15.0000	+	25.9808i	0.488986	+	0.846949i	0.999920	−	0.0126715i	$-0.00403357\pi$
$941$	15.0000	+	25.9808i	0.488986	+	0.846949i	−0.510934	+	0.859620i	$0.670700\pi$
$942$		0			0
$943$	−36.0000	+	62.3538i	−1.17232	+	2.03052i
$944$	−24.0000			−0.781133
$945$	0.500000	−	2.59808i	0.0162650	−	0.0845154i
$946$		0			0
$947$	−24.0000	+	41.5692i	−0.779895	+	1.35082i	0.152106	+	0.988364i	$0.451394\pi$
$947$	−24.0000	+	41.5692i	−0.779895	+	1.35082i	−0.932002	+	0.362454i	$0.881939\pi$
$948$	−13.0000	−	22.5167i	−0.422220	−	0.731307i
$949$	5.50000	+	9.52628i	0.178538	+	0.309236i
$950$		0			0
$951$	6.00000			0.194563
$952$		0			0
$953$	−24.0000			−0.777436			−0.388718	−	0.921357i	$-0.627082\pi$
$953$	−24.0000			−0.777436			−0.388718	+	0.921357i	$0.627082\pi$
$954$		0			0
$955$	−3.00000	−	5.19615i	−0.0970777	−	0.168144i
$956$	−6.00000	−	10.3923i	−0.194054	−	0.336111i
$957$		0			0
$958$		0			0
$959$	−12.0000	−	10.3923i	−0.387500	−	0.335585i
$960$	8.00000			0.258199
$961$	3.00000	−	5.19615i	0.0967742	−	0.167618i
$962$		0			0
$963$	−9.00000	−	15.5885i	−0.290021	−	0.502331i
$964$	2.00000	−	3.46410i	0.0644157	−	0.111571i
$965$	−5.00000			−0.160956
$966$		0			0
$967$	−55.0000			−1.76868			−0.884340	−	0.466843i	$-0.845391\pi$
$967$	−55.0000			−1.76868			−0.884340	+	0.466843i	$0.845391\pi$
$968$		0			0
$969$	−15.0000	−	25.9808i	−0.481869	−	0.834622i
$970$		0			0
$971$	12.0000	−	20.7846i	0.385098	−	0.667010i	−0.606685	−	0.794943i	$-0.707501\pi$
$971$	12.0000	−	20.7846i	0.385098	−	0.667010i	0.991783	+	0.127933i	$0.0408342\pi$
$972$	−2.00000			−0.0641500
$973$	12.5000	−	4.33013i	0.400732	−	0.138817i
$974$		0			0
$975$	0.500000	−	0.866025i	0.0160128	−	0.0277350i
$976$	−4.00000	−	6.92820i	−0.128037	−	0.221766i
$977$	6.00000	+	10.3923i	0.191957	+	0.332479i	0.945899	−	0.324462i	$-0.105183\pi$
$977$	6.00000	+	10.3923i	0.191957	+	0.332479i	−0.753942	+	0.656941i	$0.771850\pi$
$978$		0			0
$979$		0			0
$980$	11.0000	−	8.66025i	0.351382	−	0.276642i
$981$	−7.00000			−0.223493
$982$		0			0
$983$	−9.00000	−	15.5885i	−0.287055	−	0.497195i	0.686050	−	0.727554i	$-0.259343\pi$
$983$	−9.00000	−	15.5885i	−0.287055	−	0.497195i	−0.973106	+	0.230360i	$0.926010\pi$
$984$		0			0
$985$	3.00000	−	5.19615i	0.0955879	−	0.165563i
$986$		0			0
$987$	15.0000	−	5.19615i	0.477455	−	0.165395i
$988$	10.0000			0.318142
$989$	3.00000	−	5.19615i	0.0953945	−	0.165228i
$990$		0			0
$991$	21.5000	+	37.2391i	0.682970	+	1.18294i	0.974070	+	0.226246i	$0.0726454\pi$
$991$	21.5000	+	37.2391i	0.682970	+	1.18294i	−0.291100	+	0.956693i	$0.594021\pi$
$992$		0			0
$993$	23.0000			0.729883
$994$		0			0
$995$	16.0000			0.507234
$996$	−12.0000	+	20.7846i	−0.380235	+	0.658586i
$997$	15.5000	+	26.8468i	0.490890	+	0.850246i	0.999945	−	0.0104877i	$-0.00333839\pi$
$997$	15.5000	+	26.8468i	0.490890	+	0.850246i	−0.509055	+	0.860734i	$0.670005\pi$
$998$		0			0
$999$	3.50000	−	6.06218i	0.110735	−	0.191799i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.2.i.a.16.1	✓	2
3.2	odd	2		315.2.j.b.226.1		2
4.3	odd	2		1680.2.bg.m.961.1		2
5.2	odd	4		525.2.r.b.499.1		4
5.3	odd	4		525.2.r.b.499.2		4
5.4	even	2		525.2.i.c.226.1		2
7.2	even	3		735.2.a.e.1.1		1
7.3	odd	6		735.2.i.c.361.1		2
7.4	even	3	inner	105.2.i.a.46.1	yes	2
7.5	odd	6		735.2.a.d.1.1		1
7.6	odd	2		735.2.i.c.226.1		2
21.2	odd	6		2205.2.a.f.1.1		1
21.5	even	6		2205.2.a.d.1.1		1
21.11	odd	6		315.2.j.b.46.1		2
28.11	odd	6		1680.2.bg.m.1201.1		2
35.4	even	6		525.2.i.c.151.1		2
35.9	even	6		3675.2.a.h.1.1		1
35.18	odd	12		525.2.r.b.424.1		4
35.19	odd	6		3675.2.a.i.1.1		1
35.32	odd	12		525.2.r.b.424.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.i.a.16.1	✓	2	1.1	even	1	trivial
105.2.i.a.46.1	yes	2	7.4	even	3	inner
315.2.j.b.46.1		2	21.11	odd	6
315.2.j.b.226.1		2	3.2	odd	2
525.2.i.c.151.1		2	35.4	even	6
525.2.i.c.226.1		2	5.4	even	2
525.2.r.b.424.1		4	35.18	odd	12
525.2.r.b.424.2		4	35.32	odd	12
525.2.r.b.499.1		4	5.2	odd	4
525.2.r.b.499.2		4	5.3	odd	4
735.2.a.d.1.1		1	7.5	odd	6
735.2.a.e.1.1		1	7.2	even	3
735.2.i.c.226.1		2	7.6	odd	2
735.2.i.c.361.1		2	7.3	odd	6
1680.2.bg.m.961.1		2	4.3	odd	2
1680.2.bg.m.1201.1		2	28.11	odd	6
2205.2.a.d.1.1		1	21.5	even	6
2205.2.a.f.1.1		1	21.2	odd	6
3675.2.a.h.1.1		1	35.9	even	6
3675.2.a.i.1.1		1	35.19	odd	6

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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	105.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{3} +(1.00000 + 1.73205i) q^{4} +(0.500000 - 0.866025i) q^{5} +(2.50000 - 0.866025i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{3} +(1.00000 + 1.73205i) q^{4} +(0.500000 - 0.866025i) q^{5} +(2.50000 - 0.866025i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(1.00000 - 1.73205i) q^{12} -1.00000 q^{13} -1.00000 q^{15} +(-2.00000 + 3.46410i) q^{16} +(-3.00000 - 5.19615i) q^{17} +(-2.50000 + 4.33013i) q^{19} +2.00000 q^{20} +(-2.00000 - 1.73205i) q^{21} +(-3.00000 + 5.19615i) q^{23} +(-0.500000 - 0.866025i) q^{25} +1.00000 q^{27} +(4.00000 + 3.46410i) q^{28} -6.00000 q^{29} +(-2.50000 - 4.33013i) q^{31} +(0.500000 - 2.59808i) q^{35} -2.00000 q^{36} +(3.50000 - 6.06218i) q^{37} +(0.500000 + 0.866025i) q^{39} +12.0000 q^{41} -1.00000 q^{43} +(0.500000 + 0.866025i) q^{45} +(-3.00000 + 5.19615i) q^{47} +4.00000 q^{48} +(5.50000 - 4.33013i) q^{49} +(-3.00000 + 5.19615i) q^{51} +(-1.00000 - 1.73205i) q^{52} +5.00000 q^{57} +(3.00000 + 5.19615i) q^{59} +(-1.00000 - 1.73205i) q^{60} +(-1.00000 + 1.73205i) q^{61} +(-0.500000 + 2.59808i) q^{63} -8.00000 q^{64} +(-0.500000 + 0.866025i) q^{65} +(3.50000 + 6.06218i) q^{67} +(6.00000 - 10.3923i) q^{68} +6.00000 q^{69} +12.0000 q^{71} +(-5.50000 - 9.52628i) q^{73} +(-0.500000 + 0.866025i) q^{75} -10.0000 q^{76} +(6.50000 - 11.2583i) q^{79} +(2.00000 + 3.46410i) q^{80} +(-0.500000 - 0.866025i) q^{81} -12.0000 q^{83} +(1.00000 - 5.19615i) q^{84} -6.00000 q^{85} +(3.00000 + 5.19615i) q^{87} +(-3.00000 + 5.19615i) q^{89} +(-2.50000 + 0.866025i) q^{91} -12.0000 q^{92} +(-2.50000 + 4.33013i) q^{93} +(2.50000 + 4.33013i) q^{95} -10.0000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{3} + 2 q^{4} + q^{5} + 5 q^{7} - q^{9}+O(q^{10}) \) 2 * q - q^3 + 2 * q^4 + q^5 + 5 * q^7 - q^9	\( 2 q - q^{3} + 2 q^{4} + q^{5} + 5 q^{7} - q^{9} + 2 q^{12} - 2 q^{13} - 2 q^{15} - 4 q^{16} - 6 q^{17} - 5 q^{19} + 4 q^{20} - 4 q^{21} - 6 q^{23} - q^{25} + 2 q^{27} + 8 q^{28} - 12 q^{29} - 5 q^{31} + q^{35} - 4 q^{36} + 7 q^{37} + q^{39} + 24 q^{41} - 2 q^{43} + q^{45} - 6 q^{47} + 8 q^{48} + 11 q^{49} - 6 q^{51} - 2 q^{52} + 10 q^{57} + 6 q^{59} - 2 q^{60} - 2 q^{61} - q^{63} - 16 q^{64} - q^{65} + 7 q^{67} + 12 q^{68} + 12 q^{69} + 24 q^{71} - 11 q^{73} - q^{75} - 20 q^{76} + 13 q^{79} + 4 q^{80} - q^{81} - 24 q^{83} + 2 q^{84} - 12 q^{85} + 6 q^{87} - 6 q^{89} - 5 q^{91} - 24 q^{92} - 5 q^{93} + 5 q^{95} - 20 q^{97}+O(q^{100}) \) 2 * q - q^3 + 2 * q^4 + q^5 + 5 * q^7 - q^9 + 2 * q^12 - 2 * q^13 - 2 * q^15 - 4 * q^16 - 6 * q^17 - 5 * q^19 + 4 * q^20 - 4 * q^21 - 6 * q^23 - q^25 + 2 * q^27 + 8 * q^28 - 12 * q^29 - 5 * q^31 + q^35 - 4 * q^36 + 7 * q^37 + q^39 + 24 * q^41 - 2 * q^43 + q^45 - 6 * q^47 + 8 * q^48 + 11 * q^49 - 6 * q^51 - 2 * q^52 + 10 * q^57 + 6 * q^59 - 2 * q^60 - 2 * q^61 - q^63 - 16 * q^64 - q^65 + 7 * q^67 + 12 * q^68 + 12 * q^69 + 24 * q^71 - 11 * q^73 - q^75 - 20 * q^76 + 13 * q^79 + 4 * q^80 - q^81 - 24 * q^83 + 2 * q^84 - 12 * q^85 + 6 * q^87 - 6 * q^89 - 5 * q^91 - 24 * q^92 - 5 * q^93 + 5 * q^95 - 20 * q^97

Introduction

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