LMFDB - Embedded newform 1710.2.l.m.1261.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1710,2,Mod(1261,1710)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1710, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1710.1261"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1710.l (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,-2,0,-2,2,0,10,4,0,2,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$13.6544187456$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{17})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 5x^{2} + 4x + 16 $ x^4 - x^3 + 5x^2 + 4x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1261.1
Root			$-0.780776 - 1.35234i$ of defining polynomial
Character	$\chi$	$=$	1710.1261
Dual form			1710.2.l.m.1531.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +0.438447 q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{10} -1.00000 q^{11} +(1.00000 - 1.73205i) q^{13} +(-0.219224 - 0.379706i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.56155 + 4.43674i) q^{17} +(-2.50000 + 3.57071i) q^{19} -1.00000 q^{20} +(0.500000 + 0.866025i) q^{22} +(-2.34233 + 4.05703i) q^{23} +(-0.500000 + 0.866025i) q^{25} -2.00000 q^{26} +(-0.219224 + 0.379706i) q^{28} +(1.00000 - 1.73205i) q^{29} +10.2462 q^{31} +(-0.500000 + 0.866025i) q^{32} +(2.56155 - 4.43674i) q^{34} +(0.219224 + 0.379706i) q^{35} -4.68466 q^{37} +(4.34233 + 0.379706i) q^{38} +(0.500000 + 0.866025i) q^{40} +(-3.06155 - 5.30277i) q^{41} +(-1.56155 - 2.70469i) q^{43} +(0.500000 - 0.866025i) q^{44} +4.68466 q^{46} +(1.43845 - 2.49146i) q^{47} -6.80776 q^{49} +1.00000 q^{50} +(1.00000 + 1.73205i) q^{52} +(-3.78078 + 6.54850i) q^{53} +(-0.500000 - 0.866025i) q^{55} +0.438447 q^{56} -2.00000 q^{58} +(7.28078 + 12.6107i) q^{59} +(-2.56155 + 4.43674i) q^{61} +(-5.12311 - 8.87348i) q^{62} +1.00000 q^{64} +2.00000 q^{65} +(-4.71922 + 8.17394i) q^{67} -5.12311 q^{68} +(0.219224 - 0.379706i) q^{70} +(8.12311 + 14.0696i) q^{71} +(0.842329 + 1.45896i) q^{73} +(2.34233 + 4.05703i) q^{74} +(-1.84233 - 3.95042i) q^{76} -0.438447 q^{77} +(5.56155 + 9.63289i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-3.06155 + 5.30277i) q^{82} +10.8078 q^{83} +(-2.56155 + 4.43674i) q^{85} +(-1.56155 + 2.70469i) q^{86} -1.00000 q^{88} +(-1.34233 + 2.32498i) q^{89} +(0.438447 - 0.759413i) q^{91} +(-2.34233 - 4.05703i) q^{92} -2.87689 q^{94} +(-4.34233 - 0.379706i) q^{95} +(-0.842329 - 1.45896i) q^{97} +(3.40388 + 5.89570i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 2 q^{4} + 2 q^{5} + 10 q^{7} + 4 q^{8} + 2 q^{10} - 4 q^{11} + 4 q^{13} - 5 q^{14} - 2 q^{16} + 2 q^{17} - 10 q^{19} - 4 q^{20} + 2 q^{22} + 3 q^{23} - 2 q^{25} - 8 q^{26} - 5 q^{28} + 4 q^{29}+ \cdots - 7 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 - 2 * q^4 + 2 * q^5 + 10 * q^7 + 4 * q^8 + 2 * q^10 - 4 * q^11 + 4 * q^13 - 5 * q^14 - 2 * q^16 + 2 * q^17 - 10 * q^19 - 4 * q^20 + 2 * q^22 + 3 * q^23 - 2 * q^25 - 8 * q^26 - 5 * q^28 + 4 * q^29 + 8 * q^31 - 2 * q^32 + 2 * q^34 + 5 * q^35 + 6 * q^37 + 5 * q^38 + 2 * q^40 - 4 * q^41 + 2 * q^43 + 2 * q^44 - 6 * q^46 + 14 * q^47 + 14 * q^49 + 4 * q^50 + 4 * q^52 - 11 * q^53 - 2 * q^55 + 10 * q^56 - 8 * q^58 + 25 * q^59 - 2 * q^61 - 4 * q^62 + 4 * q^64 + 8 * q^65 - 23 * q^67 - 4 * q^68 + 5 * q^70 + 16 * q^71 - 9 * q^73 - 3 * q^74 + 5 * q^76 - 10 * q^77 + 14 * q^79 + 2 * q^80 - 4 * q^82 + 2 * q^83 - 2 * q^85 + 2 * q^86 - 4 * q^88 + 7 * q^89 + 10 * q^91 + 3 * q^92 - 28 * q^94 - 5 * q^95 + 9 * q^97 - 7 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times$.

$n$	$191$	$1027$	$1351$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$		0			0
$7$	0.438447			0.165717			0.0828587	−	0.996561i	$-0.473595\pi$
$7$	0.438447			0.165717			0.0828587	+	0.996561i	$0.473595\pi$
$8$	1.00000			0.353553
$9$		0			0
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$	−1.00000			−0.301511			−0.150756	−	0.988571i	$-0.548171\pi$
$11$	−1.00000			−0.301511			−0.150756	+	0.988571i	$0.548171\pi$
$12$		0			0
$13$	1.00000	−	1.73205i	0.277350	−	0.480384i	−0.693375	−	0.720577i	$-0.743877\pi$
$13$	1.00000	−	1.73205i	0.277350	−	0.480384i	0.970725	+	0.240192i	$0.0772105\pi$
$14$	−0.219224	−	0.379706i	−0.0585900	−	0.101481i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.56155	+	4.43674i	0.621268	+	1.07607i	0.989250	+	0.146235i	$0.0467154\pi$
$17$	2.56155	+	4.43674i	0.621268	+	1.07607i	−0.367982	+	0.929833i	$0.619951\pi$
$18$		0			0
$19$	−2.50000	+	3.57071i	−0.573539	+	0.819178i
$19$	−2.50000	+	3.57071i	−0.573539	+	0.819178i
$20$	−1.00000			−0.223607
$21$		0			0
$22$	0.500000	+	0.866025i	0.106600	+	0.184637i
$23$	−2.34233	+	4.05703i	−0.488409	+	0.845950i	−0.999911	−	0.0133324i	$-0.995756\pi$
$23$	−2.34233	+	4.05703i	−0.488409	+	0.845950i	0.511502	+	0.859282i	$0.329089\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−2.00000			−0.392232
$27$		0			0
$28$	−0.219224	+	0.379706i	−0.0414294	+	0.0717578i
$29$	1.00000	−	1.73205i	0.185695	−	0.321634i	−0.758115	−	0.652121i	$-0.773880\pi$
$29$	1.00000	−	1.73205i	0.185695	−	0.321634i	0.943811	+	0.330487i	$0.107213\pi$
$30$		0			0
$31$	10.2462			1.84027			0.920137	−	0.391597i	$-0.128077\pi$
$31$	10.2462			1.84027			0.920137	+	0.391597i	$0.128077\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$	2.56155	−	4.43674i	0.439303	−	0.760895i
$35$	0.219224	+	0.379706i	0.0370556	+	0.0641821i
$36$		0			0
$37$	−4.68466			−0.770153			−0.385077	−	0.922885i	$-0.625825\pi$
$37$	−4.68466			−0.770153			−0.385077	+	0.922885i	$0.625825\pi$
$38$	4.34233	+	0.379706i	0.704419	+	0.0615965i
$39$		0			0
$40$	0.500000	+	0.866025i	0.0790569	+	0.136931i
$41$	−3.06155	−	5.30277i	−0.478134	−	0.828153i	0.521552	−	0.853220i	$-0.325353\pi$
$41$	−3.06155	−	5.30277i	−0.478134	−	0.828153i	−0.999686	+	0.0250670i	$0.992020\pi$
$42$		0			0
$43$	−1.56155	−	2.70469i	−0.238135	−	0.412461i	0.722044	−	0.691847i	$-0.243203\pi$
$43$	−1.56155	−	2.70469i	−0.238135	−	0.412461i	−0.960179	+	0.279385i	$0.909869\pi$
$44$	0.500000	−	0.866025i	0.0753778	−	0.130558i
$45$		0			0
$46$	4.68466			0.690715
$47$	1.43845	−	2.49146i	0.209819	−	0.363417i	−0.741838	−	0.670579i	$-0.766046\pi$
$47$	1.43845	−	2.49146i	0.209819	−	0.363417i	0.951657	+	0.307161i	$0.0993792\pi$
$48$		0			0
$49$	−6.80776			−0.972538
$50$	1.00000			0.141421
$51$		0			0
$52$	1.00000	+	1.73205i	0.138675	+	0.240192i
$53$	−3.78078	+	6.54850i	−0.519330	+	0.899505i	0.480418	+	0.877040i	$0.340485\pi$
$53$	−3.78078	+	6.54850i	−0.519330	+	0.899505i	−0.999748	+	0.0224656i	$0.992848\pi$
$54$		0			0
$55$	−0.500000	−	0.866025i	−0.0674200	−	0.116775i
$56$	0.438447			0.0585900
$57$		0			0
$58$	−2.00000			−0.262613
$59$	7.28078	+	12.6107i	0.947876	+	1.64177i	0.749887	+	0.661566i	$0.230108\pi$
$59$	7.28078	+	12.6107i	0.947876	+	1.64177i	0.197989	+	0.980204i	$0.436559\pi$
$60$		0			0
$61$	−2.56155	+	4.43674i	−0.327973	+	0.568066i	−0.982110	−	0.188310i	$-0.939699\pi$
$61$	−2.56155	+	4.43674i	−0.327973	+	0.568066i	0.654136	+	0.756377i	$0.273032\pi$
$62$	−5.12311	−	8.87348i	−0.650635	−	1.12693i
$63$		0			0
$64$	1.00000			0.125000
$65$	2.00000			0.248069
$66$		0			0
$67$	−4.71922	+	8.17394i	−0.576545	+	0.998605i	0.419327	+	0.907835i	$0.362266\pi$
$67$	−4.71922	+	8.17394i	−0.576545	+	0.998605i	−0.995872	+	0.0907698i	$0.971067\pi$
$68$	−5.12311			−0.621268
$69$		0			0
$70$	0.219224	−	0.379706i	0.0262022	−	0.0453836i
$71$	8.12311	+	14.0696i	0.964035	+	1.66976i	0.712185	+	0.701992i	$0.247706\pi$
$71$	8.12311	+	14.0696i	0.964035	+	1.66976i	0.251850	+	0.967766i	$0.418961\pi$
$72$		0			0
$73$	0.842329	+	1.45896i	0.0985872	+	0.170758i	0.911100	−	0.412185i	$-0.135234\pi$
$73$	0.842329	+	1.45896i	0.0985872	+	0.170758i	−0.812513	+	0.582943i	$0.801901\pi$
$74$	2.34233	+	4.05703i	0.272290	+	0.471621i
$75$		0			0
$76$	−1.84233	−	3.95042i	−0.211330	−	0.453144i
$77$	−0.438447			−0.0499657
$78$		0			0
$79$	5.56155	+	9.63289i	0.625724	+	1.08379i	0.988400	+	0.151870i	$0.0485295\pi$
$79$	5.56155	+	9.63289i	0.625724	+	1.08379i	−0.362677	+	0.931915i	$0.618137\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$		0			0
$82$	−3.06155	+	5.30277i	−0.338092	+	0.585592i
$83$	10.8078			1.18631			0.593153	−	0.805090i	$-0.297883\pi$
$83$	10.8078			1.18631			0.593153	+	0.805090i	$0.297883\pi$
$84$		0			0
$85$	−2.56155	+	4.43674i	−0.277839	+	0.481232i
$86$	−1.56155	+	2.70469i	−0.168387	+	0.291654i
$87$		0			0
$88$	−1.00000			−0.106600
$89$	−1.34233	+	2.32498i	−0.142287	+	0.246448i	−0.928357	−	0.371689i	$-0.878779\pi$
$89$	−1.34233	+	2.32498i	−0.142287	+	0.246448i	0.786071	+	0.618137i	$0.212112\pi$
$90$		0			0
$91$	0.438447	−	0.759413i	0.0459618	−	0.0796081i
$92$	−2.34233	−	4.05703i	−0.244205	−	0.422975i
$93$		0			0
$94$	−2.87689			−0.296729
$95$	−4.34233	−	0.379706i	−0.445514	−	0.0389571i
$96$		0			0
$97$	−0.842329	−	1.45896i	−0.0855256	−	0.148135i	0.820089	−	0.572235i	$-0.193924\pi$
$97$	−0.842329	−	1.45896i	−0.0855256	−	0.148135i	−0.905615	+	0.424101i	$0.860590\pi$
$98$	3.40388	+	5.89570i	0.343844	+	0.595555i
$99$		0			0
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	5.00000	−	8.66025i	0.497519	−	0.861727i	−0.502477	−	0.864590i	$-0.667578\pi$
$101$	5.00000	−	8.66025i	0.497519	−	0.861727i	0.999996	+	0.00286291i	$0.000911295\pi$
$102$		0			0
$103$	−5.80776			−0.572256			−0.286128	−	0.958191i	$-0.592368\pi$
$103$	−5.80776			−0.572256			−0.286128	+	0.958191i	$0.592368\pi$
$104$	1.00000	−	1.73205i	0.0980581	−	0.169842i
$105$		0			0
$106$	7.56155			0.734443
$107$	−2.24621			−0.217149			−0.108575	−	0.994088i	$-0.534629\pi$
$107$	−2.24621			−0.217149			−0.108575	+	0.994088i	$0.534629\pi$
$108$		0			0
$109$	7.12311	+	12.3376i	0.682270	+	1.18173i	0.974286	+	0.225313i	$0.0723404\pi$
$109$	7.12311	+	12.3376i	0.682270	+	1.18173i	−0.292017	+	0.956413i	$0.594326\pi$
$110$	−0.500000	+	0.866025i	−0.0476731	+	0.0825723i
$111$		0			0
$112$	−0.219224	−	0.379706i	−0.0207147	−	0.0358789i
$113$	16.8078			1.58114			0.790571	−	0.612371i	$-0.209784\pi$
$113$	16.8078			1.58114			0.790571	+	0.612371i	$0.209784\pi$
$114$		0			0
$115$	−4.68466			−0.436847
$116$	1.00000	+	1.73205i	0.0928477	+	0.160817i
$117$		0			0
$118$	7.28078	−	12.6107i	0.670250	−	1.16091i
$119$	1.12311	+	1.94528i	0.102955	+	0.178323i
$120$		0			0
$121$	−10.0000			−0.909091
$122$	5.12311			0.463824
$123$		0			0
$124$	−5.12311	+	8.87348i	−0.460068	+	0.796862i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	7.78078	−	13.4767i	0.690432	−	1.19586i	−0.281264	−	0.959630i	$-0.590754\pi$
$127$	7.78078	−	13.4767i	0.690432	−	1.19586i	0.971696	−	0.236233i	$-0.0759130\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	−1.00000	−	1.73205i	−0.0877058	−	0.151911i
$131$	−8.06155	−	13.9630i	−0.704341	−	1.21995i	−0.966929	−	0.255046i	$-0.917909\pi$
$131$	−8.06155	−	13.9630i	−0.704341	−	1.21995i	0.262588	−	0.964908i	$-0.415424\pi$
$132$		0			0
$133$	−1.09612	+	1.56557i	−0.0950455	+	0.135752i
$134$	9.43845			0.815358
$135$		0			0
$136$	2.56155	+	4.43674i	0.219651	+	0.380447i
$137$	−2.71922	+	4.70983i	−0.232319	+	0.402388i	−0.958490	−	0.285126i	$-0.907965\pi$
$137$	−2.71922	+	4.70983i	−0.232319	+	0.402388i	0.726171	+	0.687514i	$0.241298\pi$
$138$		0			0
$139$	−4.40388	+	7.62775i	−0.373532	+	0.646977i	−0.990106	−	0.140320i	$-0.955187\pi$
$139$	−4.40388	+	7.62775i	−0.373532	+	0.646977i	0.616574	+	0.787297i	$0.288520\pi$
$140$	−0.438447			−0.0370556
$141$		0			0
$142$	8.12311	−	14.0696i	0.681676	−	1.18070i
$143$	−1.00000	+	1.73205i	−0.0836242	+	0.144841i
$144$		0			0
$145$	2.00000			0.166091
$146$	0.842329	−	1.45896i	0.0697117	−	0.120744i
$147$		0			0
$148$	2.34233	−	4.05703i	0.192538	−	0.333486i
$149$	8.00000	+	13.8564i	0.655386	+	1.13516i	0.981797	+	0.189933i	$0.0608272\pi$
$149$	8.00000	+	13.8564i	0.655386	+	1.13516i	−0.326411	+	0.945228i	$0.605840\pi$
$150$		0			0
$151$	20.4924			1.66765			0.833825	−	0.552029i	$-0.186146\pi$
$151$	20.4924			1.66765			0.833825	+	0.552029i	$0.186146\pi$
$152$	−2.50000	+	3.57071i	−0.202777	+	0.289623i
$153$		0			0
$154$	0.219224	+	0.379706i	0.0176655	+	0.0305976i
$155$	5.12311	+	8.87348i	0.411498	+	0.712735i
$156$		0			0
$157$	−1.21922	−	2.11176i	−0.0973046	−	0.168537i	0.813263	−	0.581896i	$-0.197689\pi$
$157$	−1.21922	−	2.11176i	−0.0973046	−	0.168537i	−0.910568	+	0.413359i	$0.864355\pi$
$158$	5.56155	−	9.63289i	0.442453	−	0.766352i
$159$		0			0
$160$	−1.00000			−0.0790569
$161$	−1.02699	+	1.77879i	−0.0809380	+	0.140189i
$162$		0			0
$163$	17.0540			1.33577			0.667885	−	0.744264i	$-0.267200\pi$
$163$	17.0540			1.33577			0.667885	+	0.744264i	$0.267200\pi$
$164$	6.12311			0.478134
$165$		0			0
$166$	−5.40388	−	9.35980i	−0.419423	−	0.726461i
$167$	0.342329	−	0.592932i	0.0264902	−	0.0458824i	−0.852476	−	0.522766i	$-0.824900\pi$
$167$	0.342329	−	0.592932i	0.0264902	−	0.0458824i	0.878967	+	0.476883i	$0.158234\pi$
$168$		0			0
$169$	4.50000	+	7.79423i	0.346154	+	0.599556i
$170$	5.12311			0.392924
$171$		0			0
$172$	3.12311			0.238135
$173$	−2.90388	−	5.02967i	−0.220778	−	0.382399i	0.734266	−	0.678861i	$-0.237526\pi$
$173$	−2.90388	−	5.02967i	−0.220778	−	0.382399i	−0.955044	+	0.296463i	$0.904193\pi$
$174$		0			0
$175$	−0.219224	+	0.379706i	−0.0165717	+	0.0287031i
$176$	0.500000	+	0.866025i	0.0376889	+	0.0652791i
$177$		0			0
$178$	2.68466			0.201224
$179$	−11.4924			−0.858984			−0.429492	−	0.903071i	$-0.641307\pi$
$179$	−11.4924			−0.858984			−0.429492	+	0.903071i	$0.641307\pi$
$180$		0			0
$181$	−10.6847	+	18.5064i	−0.794184	+	1.37557i	0.129171	+	0.991622i	$0.458768\pi$
$181$	−10.6847	+	18.5064i	−0.794184	+	1.37557i	−0.923356	+	0.383945i	$0.874565\pi$
$182$	−0.876894			−0.0649997
$183$		0			0
$184$	−2.34233	+	4.05703i	−0.172679	+	0.299088i
$185$	−2.34233	−	4.05703i	−0.172211	−	0.298279i
$186$		0			0
$187$	−2.56155	−	4.43674i	−0.187319	−	0.324447i
$188$	1.43845	+	2.49146i	0.104910	+	0.181709i
$189$		0			0
$190$	1.84233	+	3.95042i	0.133657	+	0.286594i
$191$	5.36932			0.388510			0.194255	−	0.980951i	$-0.437771\pi$
$191$	5.36932			0.388510			0.194255	+	0.980951i	$0.437771\pi$
$192$		0			0
$193$	−12.8078	−	22.1837i	−0.921923	−	1.59682i	−0.796436	−	0.604722i	$-0.793284\pi$
$193$	−12.8078	−	22.1837i	−0.921923	−	1.59682i	−0.125487	−	0.992095i	$-0.540049\pi$
$194$	−0.842329	+	1.45896i	−0.0604757	+	0.104747i
$195$		0			0
$196$	3.40388	−	5.89570i	0.243134	−	0.421121i
$197$	−14.4384			−1.02870			−0.514348	−	0.857581i	$-0.671966\pi$
$197$	−14.4384			−1.02870			−0.514348	+	0.857581i	$0.671966\pi$
$198$		0			0
$199$	1.43845	−	2.49146i	0.101969	−	0.176615i	−0.810527	−	0.585701i	$-0.800819\pi$
$199$	1.43845	−	2.49146i	0.101969	−	0.176615i	0.912496	+	0.409086i	$0.134152\pi$
$200$	−0.500000	+	0.866025i	−0.0353553	+	0.0612372i
$201$		0			0
$202$	−10.0000			−0.703598
$203$	0.438447	−	0.759413i	0.0307730	−	0.0533003i
$204$		0			0
$205$	3.06155	−	5.30277i	0.213828	−	0.370361i
$206$	2.90388	+	5.02967i	0.202323	+	0.350434i
$207$		0			0
$208$	−2.00000			−0.138675
$209$	2.50000	−	3.57071i	0.172929	−	0.246991i
$210$		0			0
$211$	1.65767	+	2.87117i	0.114119	+	0.197659i	0.917427	−	0.397904i	$-0.130262\pi$
$211$	1.65767	+	2.87117i	0.114119	+	0.197659i	−0.803308	+	0.595563i	$0.796929\pi$
$212$	−3.78078	−	6.54850i	−0.259665	−	0.449753i
$213$		0			0
$214$	1.12311	+	1.94528i	0.0767739	+	0.132976i
$215$	1.56155	−	2.70469i	0.106497	−	0.184458i
$216$		0			0
$217$	4.49242			0.304966
$218$	7.12311	−	12.3376i	0.482438	−	0.835606i
$219$		0			0
$220$	1.00000			0.0674200
$221$	10.2462			0.689235
$222$		0			0
$223$	−5.65767	−	9.79937i	−0.378866	−	0.656215i	0.612032	−	0.790833i	$-0.290352\pi$
$223$	−5.65767	−	9.79937i	−0.378866	−	0.656215i	−0.990897	+	0.134619i	$0.957019\pi$
$224$	−0.219224	+	0.379706i	−0.0146475	+	0.0253702i
$225$		0			0
$226$	−8.40388	−	14.5560i	−0.559018	−	0.968247i
$227$	−19.9309			−1.32286			−0.661429	−	0.750008i	$-0.730050\pi$
$227$	−19.9309			−1.32286			−0.661429	+	0.750008i	$0.730050\pi$
$228$		0			0
$229$	12.8769			0.850929			0.425465	−	0.904975i	$-0.360111\pi$
$229$	12.8769			0.850929			0.425465	+	0.904975i	$0.360111\pi$
$230$	2.34233	+	4.05703i	0.154449	+	0.267513i
$231$		0			0
$232$	1.00000	−	1.73205i	0.0656532	−	0.113715i
$233$	1.15767	+	2.00514i	0.0758415	+	0.131361i	0.901452	−	0.432879i	$-0.142502\pi$
$233$	1.15767	+	2.00514i	0.0758415	+	0.131361i	−0.825610	+	0.564241i	$0.809169\pi$
$234$		0			0
$235$	2.87689			0.187668
$236$	−14.5616			−0.947876
$237$		0			0
$238$	1.12311	−	1.94528i	0.0728001	−	0.126094i
$239$	−18.2462			−1.18025			−0.590125	−	0.807312i	$-0.700921\pi$
$239$	−18.2462			−1.18025			−0.590125	+	0.807312i	$0.700921\pi$
$240$		0			0
$241$	4.28078	−	7.41452i	0.275749	−	0.477611i	−0.694575	−	0.719421i	$-0.744407\pi$
$241$	4.28078	−	7.41452i	0.275749	−	0.477611i	0.970324	+	0.241809i	$0.0777408\pi$
$242$	5.00000	+	8.66025i	0.321412	+	0.556702i
$243$		0			0
$244$	−2.56155	−	4.43674i	−0.163987	−	0.284033i
$245$	−3.40388	−	5.89570i	−0.217466	−	0.376662i
$246$		0			0
$247$	3.68466	+	7.90084i	0.234449	+	0.502718i
$248$	10.2462			0.650635
$249$		0			0
$250$	0.500000	+	0.866025i	0.0316228	+	0.0547723i
$251$	12.9654	−	22.4568i	0.818371	−	1.41746i	−0.0885109	−	0.996075i	$-0.528211\pi$
$251$	12.9654	−	22.4568i	0.818371	−	1.41746i	0.906882	−	0.421385i	$-0.138456\pi$
$252$		0			0
$253$	2.34233	−	4.05703i	0.147261	−	0.255063i
$254$	−15.5616			−0.976419
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	6.52699	−	11.3051i	0.407142	−	0.705191i	−0.587426	−	0.809278i	$-0.699859\pi$
$257$	6.52699	−	11.3051i	0.407142	−	0.705191i	0.994568	+	0.104087i	$0.0331920\pi$
$258$		0			0
$259$	−2.05398			−0.127628
$260$	−1.00000	+	1.73205i	−0.0620174	+	0.107417i
$261$		0			0
$262$	−8.06155	+	13.9630i	−0.498044	+	0.862638i
$263$	−1.09612	−	1.89853i	−0.0675895	−	0.117068i	0.830250	−	0.557391i	$-0.188197\pi$
$263$	−1.09612	−	1.89853i	−0.0675895	−	0.117068i	−0.897840	+	0.440322i	$0.854864\pi$
$264$		0			0
$265$	−7.56155			−0.464502
$266$	1.90388	+	0.166481i	0.116734	+	0.0102076i
$267$		0			0
$268$	−4.71922	−	8.17394i	−0.288272	−	0.499303i
$269$	2.00000	+	3.46410i	0.121942	+	0.211210i	0.920534	−	0.390664i	$-0.127754\pi$
$269$	2.00000	+	3.46410i	0.121942	+	0.211210i	−0.798591	+	0.601874i	$0.794421\pi$
$270$		0			0
$271$	4.12311	+	7.14143i	0.250461	+	0.433811i	0.963653	−	0.267158i	$-0.0860845\pi$
$271$	4.12311	+	7.14143i	0.250461	+	0.433811i	−0.713192	+	0.700969i	$0.752751\pi$
$272$	2.56155	−	4.43674i	0.155317	−	0.269017i
$273$		0			0
$274$	5.43845			0.328549
$275$	0.500000	−	0.866025i	0.0301511	−	0.0522233i
$276$		0			0
$277$	4.24621			0.255130			0.127565	−	0.991830i	$-0.459284\pi$
$277$	4.24621			0.255130			0.127565	+	0.991830i	$0.459284\pi$
$278$	8.80776			0.528255
$279$		0			0
$280$	0.219224	+	0.379706i	0.0131011	+	0.0226918i
$281$	4.18466	−	7.24804i	0.249636	−	0.432382i	−0.713789	−	0.700361i	$-0.753022\pi$
$281$	4.18466	−	7.24804i	0.249636	−	0.432382i	0.963425	+	0.267979i	$0.0863558\pi$
$282$		0			0
$283$	9.71922	+	16.8342i	0.577748	+	1.00069i	0.995737	+	0.0922367i	$0.0294016\pi$
$283$	9.71922	+	16.8342i	0.577748	+	1.00069i	−0.417989	+	0.908452i	$0.637265\pi$
$284$	−16.2462			−0.964035
$285$		0			0
$286$	2.00000			0.118262
$287$	−1.34233	−	2.32498i	−0.0792352	−	0.137239i
$288$		0			0
$289$	−4.62311	+	8.00745i	−0.271947	+	0.471027i
$290$	−1.00000	−	1.73205i	−0.0587220	−	0.101710i
$291$		0			0
$292$	−1.68466			−0.0985872
$293$	−23.5616			−1.37648			−0.688240	−	0.725483i	$-0.741617\pi$
$293$	−23.5616			−1.37648			−0.688240	+	0.725483i	$0.741617\pi$
$294$		0			0
$295$	−7.28078	+	12.6107i	−0.423903	+	0.734222i
$296$	−4.68466			−0.272290
$297$		0			0
$298$	8.00000	−	13.8564i	0.463428	−	0.802680i
$299$	4.68466	+	8.11407i	0.270921	+	0.469249i
$300$		0			0
$301$	−0.684658	−	1.18586i	−0.0394631	−	0.0683520i
$302$	−10.2462	−	17.7470i	−0.589603	−	1.02122i
$303$		0			0
$304$	4.34233	+	0.379706i	0.249050	+	0.0217777i
$305$	−5.12311			−0.293348
$306$		0			0
$307$	11.9654	+	20.7247i	0.682903	+	1.18282i	0.974091	+	0.226157i	$0.0726164\pi$
$307$	11.9654	+	20.7247i	0.682903	+	1.18282i	−0.291187	+	0.956666i	$0.594050\pi$
$308$	0.219224	−	0.379706i	0.0124914	−	0.0216358i
$309$		0			0
$310$	5.12311	−	8.87348i	0.290973	−	0.503980i
$311$	−4.00000			−0.226819			−0.113410	−	0.993548i	$-0.536177\pi$
$311$	−4.00000			−0.226819			−0.113410	+	0.993548i	$0.536177\pi$
$312$		0			0
$313$	−2.15767	+	3.73720i	−0.121959	+	0.211239i	−0.920540	−	0.390648i	$-0.872251\pi$
$313$	−2.15767	+	3.73720i	−0.121959	+	0.211239i	0.798581	+	0.601887i	$0.205584\pi$
$314$	−1.21922	+	2.11176i	−0.0688048	+	0.119173i
$315$		0			0
$316$	−11.1231			−0.625724
$317$	9.34233	−	16.1814i	0.524717	−	0.908837i	−0.474868	−	0.880057i	$-0.657504\pi$
$317$	9.34233	−	16.1814i	0.524717	−	0.908837i	0.999586	−	0.0287805i	$-0.00916237\pi$
$318$		0			0
$319$	−1.00000	+	1.73205i	−0.0559893	+	0.0969762i
$320$	0.500000	+	0.866025i	0.0279508	+	0.0484123i
$321$		0			0
$322$	2.05398			0.114464
$323$	−22.2462	−	1.94528i	−1.23781	−	0.108238i
$324$		0			0
$325$	1.00000	+	1.73205i	0.0554700	+	0.0960769i
$326$	−8.52699	−	14.7692i	−0.472266	−	0.817989i
$327$		0			0
$328$	−3.06155	−	5.30277i	−0.169046	−	0.292796i
$329$	0.630683	−	1.09238i	0.0347707	−	0.0602246i
$330$		0			0
$331$	23.4924			1.29126			0.645630	−	0.763650i	$-0.276595\pi$
$331$	23.4924			1.29126			0.645630	+	0.763650i	$0.276595\pi$
$332$	−5.40388	+	9.35980i	−0.296577	+	0.513686i
$333$		0			0
$334$	−0.684658			−0.0374628
$335$	−9.43845			−0.515677
$336$		0			0
$337$	−10.5270	−	18.2333i	−0.573442	−	0.993230i	−0.996209	−	0.0869917i	$-0.972275\pi$
$337$	−10.5270	−	18.2333i	−0.573442	−	0.993230i	0.422767	−	0.906238i	$-0.361059\pi$
$338$	4.50000	−	7.79423i	0.244768	−	0.423950i
$339$		0			0
$340$	−2.56155	−	4.43674i	−0.138920	−	0.240616i
$341$	−10.2462			−0.554863
$342$		0			0
$343$	−6.05398			−0.326884
$344$	−1.56155	−	2.70469i	−0.0841933	−	0.145827i
$345$		0			0
$346$	−2.90388	+	5.02967i	−0.156114	+	0.270397i
$347$	0.842329	+	1.45896i	0.0452186	+	0.0783209i	0.887749	−	0.460328i	$-0.152268\pi$
$347$	0.842329	+	1.45896i	0.0452186	+	0.0783209i	−0.842530	+	0.538649i	$0.818935\pi$
$348$		0			0
$349$	−14.2462			−0.762582			−0.381291	−	0.924455i	$-0.624520\pi$
$349$	−14.2462			−0.762582			−0.381291	+	0.924455i	$0.624520\pi$
$350$	0.438447			0.0234360
$351$		0			0
$352$	0.500000	−	0.866025i	0.0266501	−	0.0461593i
$353$	−24.1771			−1.28682			−0.643408	−	0.765523i	$-0.722480\pi$
$353$	−24.1771			−1.28682			−0.643408	+	0.765523i	$0.722480\pi$
$354$		0			0
$355$	−8.12311	+	14.0696i	−0.431130	+	0.746739i
$356$	−1.34233	−	2.32498i	−0.0711433	−	0.123224i
$357$		0			0
$358$	5.74621	+	9.95273i	0.303697	+	0.526018i
$359$	7.56155	+	13.0970i	0.399083	+	0.691233i	0.993613	−	0.112841i	$-0.0359950\pi$
$359$	7.56155	+	13.0970i	0.399083	+	0.691233i	−0.594530	+	0.804074i	$0.702662\pi$
$360$		0			0
$361$	−6.50000	−	17.8536i	−0.342105	−	0.939662i
$362$	21.3693			1.12315
$363$		0			0
$364$	0.438447	+	0.759413i	0.0229809	+	0.0398040i
$365$	−0.842329	+	1.45896i	−0.0440895	+	0.0763653i
$366$		0			0
$367$	8.87689	−	15.3752i	0.463370	−	0.802581i	−0.535756	−	0.844373i	$-0.679973\pi$
$367$	8.87689	−	15.3752i	0.463370	−	0.802581i	0.999126	+	0.0417921i	$0.0133067\pi$
$368$	4.68466			0.244205
$369$		0			0
$370$	−2.34233	+	4.05703i	−0.121772	+	0.210915i
$371$	−1.65767	+	2.87117i	−0.0860620	+	0.149064i
$372$		0			0
$373$	−35.8078			−1.85406			−0.927028	−	0.374992i	$-0.877645\pi$
$373$	−35.8078			−1.85406			−0.927028	+	0.374992i	$0.877645\pi$
$374$	−2.56155	+	4.43674i	−0.132455	+	0.229418i
$375$		0			0
$376$	1.43845	−	2.49146i	0.0741822	−	0.128487i
$377$	−2.00000	−	3.46410i	−0.103005	−	0.178410i
$378$		0			0
$379$	−0.492423			−0.0252940			−0.0126470	−	0.999920i	$-0.504026\pi$
$379$	−0.492423			−0.0252940			−0.0126470	+	0.999920i	$0.504026\pi$
$380$	2.50000	−	3.57071i	0.128247	−	0.183174i
$381$		0			0
$382$	−2.68466	−	4.64996i	−0.137359	−	0.237913i
$383$	2.56155	+	4.43674i	0.130889	+	0.226707i	0.924020	−	0.382345i	$-0.124883\pi$
$383$	2.56155	+	4.43674i	0.130889	+	0.226707i	−0.793130	+	0.609052i	$0.791550\pi$
$384$		0			0
$385$	−0.219224	−	0.379706i	−0.0111727	−	0.0193516i
$386$	−12.8078	+	22.1837i	−0.651898	+	1.12912i
$387$		0			0
$388$	1.68466			0.0855256
$389$	−9.56155	+	16.5611i	−0.484790	+	0.839681i	−0.999847	−	0.0174749i	$-0.994437\pi$
$389$	−9.56155	+	16.5611i	−0.484790	+	0.839681i	0.515057	+	0.857156i	$0.327771\pi$
$390$		0			0
$391$	−24.0000			−1.21373
$392$	−6.80776			−0.343844
$393$		0			0
$394$	7.21922	+	12.5041i	0.363699	+	0.629946i
$395$	−5.56155	+	9.63289i	−0.279832	+	0.484683i
$396$		0			0
$397$	−14.1501	−	24.5087i	−0.710173	−	1.23006i	−0.964792	−	0.263014i	$-0.915283\pi$
$397$	−14.1501	−	24.5087i	−0.710173	−	1.23006i	0.254619	−	0.967041i	$-0.418050\pi$
$398$	−2.87689			−0.144206
$399$		0			0
$400$	1.00000			0.0500000
$401$	13.9654	+	24.1888i	0.697401	+	1.20793i	0.969365	+	0.245626i	$0.0789934\pi$
$401$	13.9654	+	24.1888i	0.697401	+	1.20793i	−0.271964	+	0.962307i	$0.587673\pi$
$402$		0			0
$403$	10.2462	−	17.7470i	0.510400	−	0.884039i
$404$	5.00000	+	8.66025i	0.248759	+	0.430864i
$405$		0			0
$406$	−0.876894			−0.0435195
$407$	4.68466			0.232210
$408$		0			0
$409$	−10.5000	+	18.1865i	−0.519192	+	0.899266i	0.480560	+	0.876962i	$0.340434\pi$
$409$	−10.5000	+	18.1865i	−0.519192	+	0.899266i	−0.999751	+	0.0223042i	$0.992900\pi$
$410$	−6.12311			−0.302399
$411$		0			0
$412$	2.90388	−	5.02967i	0.143064	−	0.247794i
$413$	3.19224	+	5.52911i	0.157080	+	0.272070i
$414$		0			0
$415$	5.40388	+	9.35980i	0.265266	+	0.459454i
$416$	1.00000	+	1.73205i	0.0490290	+	0.0849208i
$417$		0			0
$418$	−4.34233	−	0.379706i	−0.212390	−	0.0185720i
$419$	17.5616			0.857938			0.428969	−	0.903319i	$-0.358877\pi$
$419$	17.5616			0.857938			0.428969	+	0.903319i	$0.358877\pi$
$420$		0			0
$421$	−16.2462	−	28.1393i	−0.791792	−	1.37142i	−0.924856	−	0.380316i	$-0.875815\pi$
$421$	−16.2462	−	28.1393i	−0.791792	−	1.37142i	0.133065	−	0.991107i	$-0.457518\pi$
$422$	1.65767	−	2.87117i	0.0806942	−	0.139766i
$423$		0			0
$424$	−3.78078	+	6.54850i	−0.183611	+	0.318023i
$425$	−5.12311			−0.248507
$426$		0			0
$427$	−1.12311	+	1.94528i	−0.0543509	+	0.0941385i
$428$	1.12311	−	1.94528i	0.0542874	−	0.0940285i
$429$		0			0
$430$	−3.12311			−0.150610
$431$	−3.68466	+	6.38202i	−0.177484	+	0.307411i	−0.941018	−	0.338356i	$-0.890129\pi$
$431$	−3.68466	+	6.38202i	−0.177484	+	0.307411i	0.763534	+	0.645767i	$0.223462\pi$
$432$		0			0
$433$	18.3693	−	31.8166i	0.882773	−	1.52901i	0.0345280	−	0.999404i	$-0.489007\pi$
$433$	18.3693	−	31.8166i	0.882773	−	1.52901i	0.848245	−	0.529604i	$-0.177659\pi$
$434$	−2.24621	−	3.89055i	−0.107822	−	0.186752i
$435$		0			0
$436$	−14.2462			−0.682270
$437$	−8.63068	−	18.5064i	−0.412862	−	0.885280i
$438$		0			0
$439$	8.24621	+	14.2829i	0.393570	+	0.681684i	0.992918	−	0.118806i	$-0.0379065\pi$
$439$	8.24621	+	14.2829i	0.393570	+	0.681684i	−0.599347	+	0.800489i	$0.704573\pi$
$440$	−0.500000	−	0.866025i	−0.0238366	−	0.0412861i
$441$		0			0
$442$	−5.12311	−	8.87348i	−0.243681	−	0.422068i
$443$	16.9654	−	29.3850i	0.806052	−	1.39612i	−0.109526	−	0.993984i	$-0.534933\pi$
$443$	16.9654	−	29.3850i	0.806052	−	1.39612i	0.915578	−	0.402139i	$-0.131733\pi$
$444$		0			0
$445$	−2.68466			−0.127265
$446$	−5.65767	+	9.79937i	−0.267898	+	0.464014i
$447$		0			0
$448$	0.438447			0.0207147
$449$	−29.0000			−1.36859			−0.684297	−	0.729203i	$-0.739891\pi$
$449$	−29.0000			−1.36859			−0.684297	+	0.729203i	$0.739891\pi$
$450$		0			0
$451$	3.06155	+	5.30277i	0.144163	+	0.249697i
$452$	−8.40388	+	14.5560i	−0.395285	+	0.684654i
$453$		0			0
$454$	9.96543	+	17.2606i	0.467701	+	0.810082i
$455$	0.876894			0.0411094
$456$		0			0
$457$	7.05398			0.329971			0.164986	−	0.986296i	$-0.447242\pi$
$457$	7.05398			0.329971			0.164986	+	0.986296i	$0.447242\pi$
$458$	−6.43845	−	11.1517i	−0.300849	−	0.521086i
$459$		0			0
$460$	2.34233	−	4.05703i	0.109212	−	0.189160i
$461$	−19.4924	−	33.7619i	−0.907853	−	1.57245i	−0.817042	−	0.576579i	$-0.804387\pi$
$461$	−19.4924	−	33.7619i	−0.907853	−	1.57245i	−0.0908110	−	0.995868i	$-0.528946\pi$
$462$		0			0
$463$	−19.5616			−0.909102			−0.454551	−	0.890721i	$-0.650200\pi$
$463$	−19.5616			−0.909102			−0.454551	+	0.890721i	$0.650200\pi$
$464$	−2.00000			−0.0928477
$465$		0			0
$466$	1.15767	−	2.00514i	0.0536281	−	0.0928865i
$467$	−16.5616			−0.766377			−0.383189	−	0.923670i	$-0.625174\pi$
$467$	−16.5616			−0.766377			−0.383189	+	0.923670i	$0.625174\pi$
$468$		0			0
$469$	−2.06913	+	3.58384i	−0.0955436	+	0.165486i
$470$	−1.43845	−	2.49146i	−0.0663506	−	0.114923i
$471$		0			0
$472$	7.28078	+	12.6107i	0.335125	+	0.580453i
$473$	1.56155	+	2.70469i	0.0718003	+	0.124362i
$474$		0			0
$475$	−1.84233	−	3.95042i	−0.0845319	−	0.181258i
$476$	−2.24621			−0.102955
$477$		0			0
$478$	9.12311	+	15.8017i	0.417281	+	0.722752i
$479$	14.6847	−	25.4346i	0.670959	−	1.16214i	−0.306673	−	0.951815i	$-0.599216\pi$
$479$	14.6847	−	25.4346i	0.670959	−	1.16214i	0.977632	−	0.210321i	$-0.0674508\pi$
$480$		0			0
$481$	−4.68466	+	8.11407i	−0.213602	+	0.369970i
$482$	−8.56155			−0.389968
$483$		0			0
$484$	5.00000	−	8.66025i	0.227273	−	0.393648i
$485$	0.842329	−	1.45896i	0.0382482	−	0.0662478i
$486$		0			0
$487$	−6.93087			−0.314068			−0.157034	−	0.987593i	$-0.550193\pi$
$487$	−6.93087			−0.314068			−0.157034	+	0.987593i	$0.550193\pi$
$488$	−2.56155	+	4.43674i	−0.115956	+	0.200842i
$489$		0			0
$490$	−3.40388	+	5.89570i	−0.153772	+	0.266340i
$491$	−4.58854	−	7.94759i	−0.207078	−	0.358670i	0.743715	−	0.668497i	$-0.233062\pi$
$491$	−4.58854	−	7.94759i	−0.207078	−	0.358670i	−0.950793	+	0.309827i	$0.899729\pi$
$492$		0			0
$493$	10.2462			0.461466
$494$	5.00000	−	7.14143i	0.224961	−	0.321308i
$495$		0			0
$496$	−5.12311	−	8.87348i	−0.230034	−	0.398431i
$497$	3.56155	+	6.16879i	0.159757	+	0.276708i
$498$		0			0
$499$	−14.5000	−	25.1147i	−0.649109	−	1.12429i	−0.983336	−	0.181797i	$-0.941809\pi$
$499$	−14.5000	−	25.1147i	−0.649109	−	1.12429i	0.334227	−	0.942493i	$-0.391525\pi$
$500$	0.500000	−	0.866025i	0.0223607	−	0.0387298i
$501$		0			0
$502$	−25.9309			−1.15735
$503$	13.7116	−	23.7493i	0.611372	−	1.05893i	−0.379637	−	0.925135i	$-0.623951\pi$
$503$	13.7116	−	23.7493i	0.611372	−	1.05893i	0.991009	−	0.133792i	$-0.0427154\pi$
$504$		0			0
$505$	10.0000			0.444994
$506$	−4.68466			−0.208258
$507$		0			0
$508$	7.78078	+	13.4767i	0.345216	+	0.597932i
$509$	−0.438447	+	0.759413i	−0.0194338	+	0.0336604i	−0.875579	−	0.483075i	$-0.839520\pi$
$509$	−0.438447	+	0.759413i	−0.0194338	+	0.0336604i	0.856145	+	0.516736i	$0.172853\pi$
$510$		0			0
$511$	0.369317	+	0.639676i	0.0163376	+	0.0282976i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−13.0540			−0.575786
$515$	−2.90388	−	5.02967i	−0.127960	−	0.221634i
$516$		0			0
$517$	−1.43845	+	2.49146i	−0.0632628	+	0.109574i
$518$	1.02699	+	1.77879i	0.0451232	+	0.0781558i
$519$		0			0
$520$	2.00000			0.0877058
$521$	22.8078			0.999226			0.499613	−	0.866249i	$-0.333476\pi$
$521$	22.8078			0.999226			0.499613	+	0.866249i	$0.333476\pi$
$522$		0			0
$523$	−7.31534	+	12.6705i	−0.319878	+	0.554044i	−0.980462	−	0.196707i	$-0.936975\pi$
$523$	−7.31534	+	12.6705i	−0.319878	+	0.554044i	0.660585	+	0.750752i	$0.270308\pi$
$524$	16.1231			0.704341
$525$		0			0
$526$	−1.09612	+	1.89853i	−0.0477930	+	0.0827799i
$527$	26.2462	+	45.4598i	1.14330	+	1.98026i
$528$		0			0
$529$	0.526988	+	0.912769i	0.0229125	+	0.0396856i
$530$	3.78078	+	6.54850i	0.164226	+	0.284449i
$531$		0			0
$532$	−0.807764	−	1.73205i	−0.0350210	−	0.0750939i
$533$	−12.2462			−0.530442
$534$		0			0
$535$	−1.12311	−	1.94528i	−0.0485561	−	0.0841016i
$536$	−4.71922	+	8.17394i	−0.203839	+	0.353060i
$537$		0			0
$538$	2.00000	−	3.46410i	0.0862261	−	0.149348i
$539$	6.80776			0.293231
$540$		0			0
$541$	14.2462	−	24.6752i	0.612492	−	1.06087i	−0.378326	−	0.925672i	$-0.623500\pi$
$541$	14.2462	−	24.6752i	0.612492	−	1.06087i	0.990819	−	0.135196i	$-0.0431664\pi$
$542$	4.12311	−	7.14143i	0.177103	−	0.306751i
$543$		0			0
$544$	−5.12311			−0.219651
$545$	−7.12311	+	12.3376i	−0.305120	+	0.528484i
$546$		0			0
$547$	2.43845	−	4.22351i	0.104260	−	0.180584i	−0.809175	−	0.587567i	$-0.800086\pi$
$547$	2.43845	−	4.22351i	0.104260	−	0.180584i	0.913436	+	0.406983i	$0.133419\pi$
$548$	−2.71922	−	4.70983i	−0.116159	−	0.201194i
$549$		0			0
$550$	−1.00000			−0.0426401
$551$	3.68466	+	7.90084i	0.156972	+	0.336587i
$552$		0			0
$553$	2.43845	+	4.22351i	0.103693	+	0.179602i
$554$	−2.12311	−	3.67733i	−0.0902021	−	0.156235i
$555$		0			0
$556$	−4.40388	−	7.62775i	−0.186766	−	0.323489i
$557$	20.8348	−	36.0868i	0.882797	−	1.52905i	0.0345785	−	0.999402i	$-0.488991\pi$
$557$	20.8348	−	36.0868i	0.882797	−	1.52905i	0.848218	−	0.529647i	$-0.177676\pi$
$558$		0			0
$559$	−6.24621			−0.264187
$560$	0.219224	−	0.379706i	0.00926389	−	0.0160455i
$561$		0			0
$562$	−8.36932			−0.353038
$563$	−21.3002			−0.897696			−0.448848	−	0.893608i	$-0.648166\pi$
$563$	−21.3002			−0.897696			−0.448848	+	0.893608i	$0.648166\pi$
$564$		0			0
$565$	8.40388	+	14.5560i	0.353554	+	0.612373i
$566$	9.71922	−	16.8342i	0.408529	−	0.707594i
$567$		0			0
$568$	8.12311	+	14.0696i	0.340838	+	0.590349i
$569$	11.1771			0.468568			0.234284	−	0.972168i	$-0.424726\pi$
$569$	11.1771			0.468568			0.234284	+	0.972168i	$0.424726\pi$
$570$		0			0
$571$	−4.80776			−0.201199			−0.100599	−	0.994927i	$-0.532076\pi$
$571$	−4.80776			−0.201199			−0.100599	+	0.994927i	$0.532076\pi$
$572$	−1.00000	−	1.73205i	−0.0418121	−	0.0724207i
$573$		0			0
$574$	−1.34233	+	2.32498i	−0.0560277	+	0.0970429i
$575$	−2.34233	−	4.05703i	−0.0976819	−	0.169190i
$576$		0			0
$577$	−16.3153			−0.679217			−0.339608	−	0.940567i	$-0.610295\pi$
$577$	−16.3153			−0.679217			−0.339608	+	0.940567i	$0.610295\pi$
$578$	9.24621			0.384592
$579$		0			0
$580$	−1.00000	+	1.73205i	−0.0415227	+	0.0719195i
$581$	4.73863			0.196592
$582$		0			0
$583$	3.78078	−	6.54850i	0.156584	−	0.271211i
$584$	0.842329	+	1.45896i	0.0348558	+	0.0603721i
$585$		0			0
$586$	11.7808	+	20.4049i	0.486659	+	0.842919i
$587$	13.3693	+	23.1563i	0.551811	+	0.955764i	0.998144	+	0.0608975i	$0.0193963\pi$
$587$	13.3693	+	23.1563i	0.551811	+	0.955764i	−0.446333	+	0.894867i	$0.647270\pi$
$588$		0			0
$589$	−25.6155	+	36.5863i	−1.05547	+	1.50751i
$590$	14.5616			0.599490
$591$		0			0
$592$	2.34233	+	4.05703i	0.0962691	+	0.166743i
$593$	12.7732	−	22.1238i	0.524532	−	0.908517i	−0.475060	−	0.879954i	$-0.657573\pi$
$593$	12.7732	−	22.1238i	0.524532	−	0.908517i	0.999592	−	0.0285632i	$-0.00909317\pi$
$594$		0			0
$595$	−1.12311	+	1.94528i	−0.0460428	+	0.0797485i
$596$	−16.0000			−0.655386
$597$		0			0
$598$	4.68466	−	8.11407i	0.191570	−	0.331809i
$599$	−16.2462	+	28.1393i	−0.663802	+	1.14974i	0.315806	+	0.948824i	$0.397725\pi$
$599$	−16.2462	+	28.1393i	−0.663802	+	1.14974i	−0.979609	+	0.200915i	$0.935608\pi$
$600$		0			0
$601$	−11.6307			−0.474425			−0.237213	−	0.971458i	$-0.576234\pi$
$601$	−11.6307			−0.474425			−0.237213	+	0.971458i	$0.576234\pi$
$602$	−0.684658	+	1.18586i	−0.0279046	+	0.0483322i
$603$		0			0
$604$	−10.2462	+	17.7470i	−0.416912	+	0.722113i
$605$	−5.00000	−	8.66025i	−0.203279	−	0.352089i
$606$		0			0
$607$	10.1922			0.413690			0.206845	−	0.978374i	$-0.433680\pi$
$607$	10.1922			0.413690			0.206845	+	0.978374i	$0.433680\pi$
$608$	−1.84233	−	3.95042i	−0.0747163	−	0.160211i
$609$		0			0
$610$	2.56155	+	4.43674i	0.103714	+	0.179638i
$611$	−2.87689	−	4.98293i	−0.116387	−	0.201588i
$612$		0			0
$613$	−15.3423	−	26.5737i	−0.619671	−	1.07330i	−0.989546	−	0.144220i	$-0.953933\pi$
$613$	−15.3423	−	26.5737i	−0.619671	−	1.07330i	0.369875	−	0.929082i	$-0.379401\pi$
$614$	11.9654	−	20.7247i	0.482886	−	0.836382i
$615$		0			0
$616$	−0.438447			−0.0176655
$617$	3.59612	−	6.22866i	0.144774	−	0.250756i	−0.784514	−	0.620111i	$-0.787088\pi$
$617$	3.59612	−	6.22866i	0.144774	−	0.250756i	0.929289	+	0.369354i	$0.120421\pi$
$618$		0			0
$619$	26.0540			1.04720			0.523599	−	0.851965i	$-0.324589\pi$
$619$	26.0540			1.04720			0.523599	+	0.851965i	$0.324589\pi$
$620$	−10.2462			−0.411498
$621$		0			0
$622$	2.00000	+	3.46410i	0.0801927	+	0.138898i
$623$	−0.588540	+	1.01938i	−0.0235794	+	0.0408407i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	4.31534			0.172476
$627$		0			0
$628$	2.43845			0.0973046
$629$	−12.0000	−	20.7846i	−0.478471	−	0.828737i
$630$		0			0
$631$	−2.12311	+	3.67733i	−0.0845195	+	0.146392i	−0.905186	−	0.425015i	$-0.860269\pi$
$631$	−2.12311	+	3.67733i	−0.0845195	+	0.146392i	0.820667	+	0.571407i	$0.193602\pi$
$632$	5.56155	+	9.63289i	0.221227	+	0.383176i
$633$		0			0
$634$	−18.6847			−0.742063
$635$	15.5616			0.617541
$636$		0			0
$637$	−6.80776	+	11.7914i	−0.269733	+	0.467192i
$638$	2.00000			0.0791808
$639$		0			0
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	3.71922	+	6.44188i	0.146900	+	0.254439i	0.930080	−	0.367356i	$-0.119737\pi$
$641$	3.71922	+	6.44188i	0.146900	+	0.254439i	−0.783180	+	0.621795i	$0.786404\pi$
$642$		0			0
$643$	11.2808	+	19.5389i	0.444870	+	0.770538i	0.998043	−	0.0625284i	$-0.0199164\pi$
$643$	11.2808	+	19.5389i	0.444870	+	0.770538i	−0.553173	+	0.833067i	$0.686583\pi$
$644$	−1.02699	−	1.77879i	−0.0404690	−	0.0700943i
$645$		0			0
$646$	9.43845	+	20.2384i	0.371351	+	0.796270i
$647$	−3.17708			−0.124904			−0.0624520	−	0.998048i	$-0.519892\pi$
$647$	−3.17708			−0.124904			−0.0624520	+	0.998048i	$0.519892\pi$
$648$		0			0
$649$	−7.28078	−	12.6107i	−0.285795	−	0.495012i
$650$	1.00000	−	1.73205i	0.0392232	−	0.0679366i
$651$		0			0
$652$	−8.52699	+	14.7692i	−0.333943	+	0.578406i
$653$	5.06913			0.198370			0.0991852	−	0.995069i	$-0.468376\pi$
$653$	5.06913			0.198370			0.0991852	+	0.995069i	$0.468376\pi$
$654$		0			0
$655$	8.06155	−	13.9630i	0.314991	−	0.545580i
$656$	−3.06155	+	5.30277i	−0.119534	+	0.207038i
$657$		0			0
$658$	−1.26137			−0.0491732
$659$	9.46543	−	16.3946i	0.368721	−	0.638643i	−0.620645	−	0.784092i	$-0.713129\pi$
$659$	9.46543	−	16.3946i	0.368721	−	0.638643i	0.989366	+	0.145448i	$0.0464624\pi$
$660$		0			0
$661$	19.9309	−	34.5213i	0.775221	−	1.34272i	−0.159449	−	0.987206i	$-0.550972\pi$
$661$	19.9309	−	34.5213i	0.775221	−	1.34272i	0.934670	−	0.355516i	$-0.115695\pi$
$662$	−11.7462	−	20.3450i	−0.456529	−	0.790732i
$663$		0			0
$664$	10.8078			0.419423
$665$	−1.90388	−	0.166481i	−0.0738294	−	0.00645586i
$666$		0			0
$667$	4.68466	+	8.11407i	0.181391	+	0.314178i
$668$	0.342329	+	0.592932i	0.0132451	+	0.0229412i
$669$		0			0
$670$	4.71922	+	8.17394i	0.182320	+	0.315787i
$671$	2.56155	−	4.43674i	0.0988876	−	0.171278i
$672$		0			0
$673$	46.1080			1.77733			0.888665	−	0.458556i	$-0.151633\pi$
$673$	46.1080			1.77733			0.888665	+	0.458556i	$0.151633\pi$
$674$	−10.5270	+	18.2333i	−0.405484	+	0.702320i
$675$		0			0
$676$	−9.00000			−0.346154
$677$	23.1771			0.890768			0.445384	−	0.895340i	$-0.353067\pi$
$677$	23.1771			0.890768			0.445384	+	0.895340i	$0.353067\pi$
$678$		0			0
$679$	−0.369317	−	0.639676i	−0.0141731	−	0.0245485i
$680$	−2.56155	+	4.43674i	−0.0982311	+	0.170141i
$681$		0			0
$682$	5.12311	+	8.87348i	0.196174	+	0.339783i
$683$	−28.0000			−1.07139			−0.535695	−	0.844411i	$-0.679950\pi$
$683$	−28.0000			−1.07139			−0.535695	+	0.844411i	$0.679950\pi$
$684$		0			0
$685$	−5.43845			−0.207792
$686$	3.02699	+	5.24290i	0.115571	+	0.200175i
$687$		0			0
$688$	−1.56155	+	2.70469i	−0.0595336	+	0.103115i
$689$	7.56155	+	13.0970i	0.288072	+	0.498956i
$690$		0			0
$691$	−21.0691			−0.801507			−0.400754	−	0.916186i	$-0.631252\pi$
$691$	−21.0691			−0.801507			−0.400754	+	0.916186i	$0.631252\pi$
$692$	5.80776			0.220778
$693$		0			0
$694$	0.842329	−	1.45896i	0.0319744	−	0.0553813i
$695$	−8.80776			−0.334098
$696$		0			0
$697$	15.6847	−	27.1666i	0.594099	−	1.02901i
$698$	7.12311	+	12.3376i	0.269614	+	0.466984i
$699$		0			0
$700$	−0.219224	−	0.379706i	−0.00828587	−	0.0143516i
$701$	3.24621	+	5.62260i	0.122608	+	0.212363i	0.920795	−	0.390046i	$-0.127541\pi$
$701$	3.24621	+	5.62260i	0.122608	+	0.212363i	−0.798188	+	0.602409i	$0.794208\pi$
$702$		0			0
$703$	11.7116	−	16.7276i	0.441713	−	0.630892i
$704$	−1.00000			−0.0376889
$705$		0			0
$706$	12.0885	+	20.9380i	0.454958	+	0.788011i
$707$	2.19224	−	3.79706i	0.0824475	−	0.142803i
$708$		0			0
$709$	20.0000	−	34.6410i	0.751116	−	1.30097i	−0.196167	−	0.980571i	$-0.562849\pi$
$709$	20.0000	−	34.6410i	0.751116	−	1.30097i	0.947282	−	0.320400i	$-0.103817\pi$
$710$	16.2462			0.609709
$711$		0			0
$712$	−1.34233	+	2.32498i	−0.0503059	+	0.0871324i
$713$	−24.0000	+	41.5692i	−0.898807	+	1.55678i
$714$		0			0
$715$	−2.00000			−0.0747958
$716$	5.74621	−	9.95273i	0.214746	−	0.371951i
$717$		0			0
$718$	7.56155	−	13.0970i	0.282195	−	0.488775i
$719$	7.43845	+	12.8838i	0.277407	+	0.480483i	0.970740	−	0.240134i	$-0.0771915\pi$
$719$	7.43845	+	12.8838i	0.277407	+	0.480483i	−0.693332	+	0.720618i	$0.743858\pi$
$720$		0			0
$721$	−2.54640			−0.0948328
$722$	−12.2116	+	14.5560i	−0.454470	+	0.541716i
$723$		0			0
$724$	−10.6847	−	18.5064i	−0.397092	−	0.687784i
$725$	1.00000	+	1.73205i	0.0371391	+	0.0643268i
$726$		0			0
$727$	4.00000	+	6.92820i	0.148352	+	0.256953i	0.930618	−	0.365991i	$-0.119270\pi$
$727$	4.00000	+	6.92820i	0.148352	+	0.256953i	−0.782267	+	0.622944i	$0.785937\pi$
$728$	0.438447	−	0.759413i	0.0162499	−	0.0281457i
$729$		0			0
$730$	1.68466			0.0623520
$731$	8.00000	−	13.8564i	0.295891	−	0.512498i
$732$		0			0
$733$	−26.9309			−0.994714			−0.497357	−	0.867546i	$-0.665696\pi$
$733$	−26.9309			−0.994714			−0.497357	+	0.867546i	$0.665696\pi$
$734$	−17.7538			−0.655304
$735$		0			0
$736$	−2.34233	−	4.05703i	−0.0863394	−	0.149544i
$737$	4.71922	−	8.17394i	0.173835	−	0.301091i
$738$		0			0
$739$	−9.37689	−	16.2413i	−0.344935	−	0.597444i	0.640407	−	0.768036i	$-0.278766\pi$
$739$	−9.37689	−	16.2413i	−0.344935	−	0.597444i	−0.985342	+	0.170591i	$0.945432\pi$
$740$	4.68466			0.172211
$741$		0			0
$742$	3.31534			0.121710
$743$	−9.21922	−	15.9682i	−0.338221	−	0.585815i	0.645878	−	0.763441i	$-0.276492\pi$
$743$	−9.21922	−	15.9682i	−0.338221	−	0.585815i	−0.984098	+	0.177626i	$0.943158\pi$
$744$		0			0
$745$	−8.00000	+	13.8564i	−0.293097	+	0.507659i
$746$	17.9039	+	31.0104i	0.655508	+	1.13537i
$747$		0			0
$748$	5.12311			0.187319
$749$	−0.984845			−0.0359855
$750$		0			0
$751$	17.4384	−	30.2043i	0.636338	−	1.10217i	−0.349892	−	0.936790i	$-0.613782\pi$
$751$	17.4384	−	30.2043i	0.636338	−	1.10217i	0.986230	−	0.165380i	$-0.0528849\pi$
$752$	−2.87689			−0.104910
$753$		0			0
$754$	−2.00000	+	3.46410i	−0.0728357	+	0.126155i
$755$	10.2462	+	17.7470i	0.372898	+	0.645878i
$756$		0			0
$757$	9.78078	+	16.9408i	0.355488	+	0.615724i	0.987201	−	0.159478i	$-0.0509812\pi$
$757$	9.78078	+	16.9408i	0.355488	+	0.615724i	−0.631713	+	0.775202i	$0.717648\pi$
$758$	0.246211	+	0.426450i	0.00894280	+	0.0154894i
$759$		0			0
$760$	−4.34233	−	0.379706i	−0.157513	−	0.0137734i
$761$	51.9848			1.88445			0.942225	−	0.334982i	$-0.108730\pi$
$761$	51.9848			1.88445			0.942225	+	0.334982i	$0.108730\pi$
$762$		0			0
$763$	3.12311	+	5.40938i	0.113064	+	0.195833i
$764$	−2.68466	+	4.64996i	−0.0971275	+	0.168230i
$765$		0			0
$766$	2.56155	−	4.43674i	0.0925527	−	0.160306i
$767$	29.1231			1.05157
$768$		0			0
$769$	−13.2462	+	22.9431i	−0.477671	+	0.827350i	−0.999672	−	0.0255946i	$-0.991852\pi$
$769$	−13.2462	+	22.9431i	−0.477671	+	0.827350i	0.522002	+	0.852944i	$0.325185\pi$
$770$	−0.219224	+	0.379706i	−0.00790027	+	0.0136837i
$771$		0			0
$772$	25.6155			0.921923
$773$	−7.15009	+	12.3843i	−0.257171	+	0.445433i	−0.965483	−	0.260466i	$-0.916124\pi$
$773$	−7.15009	+	12.3843i	−0.257171	+	0.445433i	0.708312	+	0.705900i	$0.249457\pi$
$774$		0			0
$775$	−5.12311	+	8.87348i	−0.184027	+	0.318745i
$776$	−0.842329	−	1.45896i	−0.0302379	−	0.0523735i
$777$		0			0
$778$	19.1231			0.685597
$779$	26.5885	+	2.32498i	0.952633	+	0.0833011i
$780$		0			0
$781$	−8.12311	−	14.0696i	−0.290668	−	0.503451i
$782$	12.0000	+	20.7846i	0.429119	+	0.743256i
$783$		0			0
$784$	3.40388	+	5.89570i	0.121567	+	0.210561i
$785$	1.21922	−	2.11176i	0.0435160	−	0.0753718i
$786$		0			0
$787$	8.56155			0.305186			0.152593	−	0.988289i	$-0.451238\pi$
$787$	8.56155			0.305186			0.152593	+	0.988289i	$0.451238\pi$
$788$	7.21922	−	12.5041i	0.257174	−	0.445439i
$789$		0			0
$790$	11.1231			0.395742
$791$	7.36932			0.262023
$792$		0			0
$793$	5.12311	+	8.87348i	0.181927	+	0.315106i
$794$	−14.1501	+	24.5087i	−0.502168	+	0.869781i
$795$		0			0
$796$	1.43845	+	2.49146i	0.0509844	+	0.0883076i
$797$	4.19224			0.148497			0.0742483	−	0.997240i	$-0.476344\pi$
$797$	4.19224			0.148497			0.0742483	+	0.997240i	$0.476344\pi$
$798$		0			0
$799$	14.7386			0.521415
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$		0			0
$802$	13.9654	−	24.1888i	0.493137	−	0.854138i
$803$	−0.842329	−	1.45896i	−0.0297252	−	0.0514855i
$804$		0			0
$805$	−2.05398			−0.0723931
$806$	−20.4924			−0.721815
$807$		0			0
$808$	5.00000	−	8.66025i	0.175899	−	0.304667i
$809$	−23.4384			−0.824052			−0.412026	−	0.911172i	$-0.635179\pi$
$809$	−23.4384			−0.824052			−0.412026	+	0.911172i	$0.635179\pi$
$810$		0			0
$811$	4.58854	−	7.94759i	0.161125	−	0.279077i	−0.774147	−	0.633006i	$-0.781821\pi$
$811$	4.58854	−	7.94759i	0.161125	−	0.279077i	0.935273	+	0.353928i	$0.115154\pi$
$812$	0.438447	+	0.759413i	0.0153865	+	0.0266502i
$813$		0			0
$814$	−2.34233	−	4.05703i	−0.0820986	−	0.142199i
$815$	8.52699	+	14.7692i	0.298687	+	0.517342i
$816$		0			0
$817$	13.5616	+	1.18586i	0.474459	+	0.0414881i
$818$	21.0000			0.734248
$819$		0			0
$820$	3.06155	+	5.30277i	0.106914	+	0.185181i
$821$	−7.00000	+	12.1244i	−0.244302	+	0.423143i	−0.961935	−	0.273278i	$-0.911892\pi$
$821$	−7.00000	+	12.1244i	−0.244302	+	0.423143i	0.717633	+	0.696421i	$0.245225\pi$
$822$		0			0
$823$	13.5885	−	23.5360i	0.473667	−	0.820415i	−0.525879	−	0.850560i	$-0.676263\pi$
$823$	13.5885	−	23.5360i	0.473667	−	0.820415i	0.999546	+	0.0301446i	$0.00959679\pi$
$824$	−5.80776			−0.202323
$825$		0			0
$826$	3.19224	−	5.52911i	0.111072	−	0.192383i
$827$	−15.9654	+	27.6529i	−0.555173	+	0.961587i	0.442718	+	0.896661i	$0.354014\pi$
$827$	−15.9654	+	27.6529i	−0.555173	+	0.961587i	−0.997890	+	0.0649260i	$0.979319\pi$
$828$		0			0
$829$	26.7386			0.928671			0.464336	−	0.885659i	$-0.346293\pi$
$829$	26.7386			0.928671			0.464336	+	0.885659i	$0.346293\pi$
$830$	5.40388	−	9.35980i	0.187571	−	0.324883i
$831$		0			0
$832$	1.00000	−	1.73205i	0.0346688	−	0.0600481i
$833$	−17.4384	−	30.2043i	−0.604206	−	1.04652i
$834$		0			0
$835$	0.684658			0.0236936
$836$	1.84233	+	3.95042i	0.0637183	+	0.136628i
$837$		0			0
$838$	−8.78078	−	15.2088i	−0.303327	−	0.525378i
$839$	1.24621	+	2.15850i	0.0430240	+	0.0745197i	0.886735	−	0.462277i	$-0.152967\pi$
$839$	1.24621	+	2.15850i	0.0430240	+	0.0745197i	−0.843712	+	0.536797i	$0.819634\pi$
$840$		0			0
$841$	12.5000	+	21.6506i	0.431034	+	0.746574i
$842$	−16.2462	+	28.1393i	−0.559881	+	0.969743i
$843$		0			0
$844$	−3.31534			−0.114119
$845$	−4.50000	+	7.79423i	−0.154805	+	0.268130i
$846$		0			0
$847$	−4.38447			−0.150652
$848$	7.56155			0.259665
$849$		0			0
$850$	2.56155	+	4.43674i	0.0878605	+	0.152179i
$851$	10.9730	−	19.0058i	0.376150	−	0.651511i
$852$		0			0
$853$	−0.369317	−	0.639676i	−0.0126452	−	0.0219021i	0.859634	−	0.510911i	$-0.170692\pi$
$853$	−0.369317	−	0.639676i	−0.0126452	−	0.0219021i	−0.872279	+	0.489009i	$0.837359\pi$
$854$	2.24621			0.0768638
$855$		0			0
$856$	−2.24621			−0.0767739
$857$	14.8963	+	25.8012i	0.508848	+	0.881351i	0.999947	+	0.0102472i	$0.00326184\pi$
$857$	14.8963	+	25.8012i	0.508848	+	0.881351i	−0.491099	+	0.871104i	$0.663405\pi$
$858$		0			0
$859$	−23.7462	+	41.1296i	−0.810210	+	1.40333i	0.102506	+	0.994732i	$0.467314\pi$
$859$	−23.7462	+	41.1296i	−0.810210	+	1.40333i	−0.912717	+	0.408593i	$0.866020\pi$
$860$	1.56155	+	2.70469i	0.0532485	+	0.0922291i
$861$		0			0
$862$	7.36932			0.251000
$863$	−52.3002			−1.78032			−0.890160	−	0.455649i	$-0.849407\pi$
$863$	−52.3002			−1.78032			−0.890160	+	0.455649i	$0.849407\pi$
$864$		0			0
$865$	2.90388	−	5.02967i	0.0987350	−	0.171014i
$866$	−36.7386			−1.24843
$867$		0			0
$868$	−2.24621	+	3.89055i	−0.0762414	+	0.132054i
$869$	−5.56155	−	9.63289i	−0.188663	−	0.326773i
$870$		0			0
$871$	9.43845	+	16.3479i	0.319810	+	0.553926i
$872$	7.12311	+	12.3376i	0.241219	+	0.417803i
$873$		0			0
$874$	−11.7116	+	16.7276i	−0.396152	+	0.565819i
$875$	−0.438447			−0.0148222
$876$		0			0
$877$	−8.90388	−	15.4220i	−0.300663	−	0.520763i	0.675623	−	0.737247i	$-0.263875\pi$
$877$	−8.90388	−	15.4220i	−0.300663	−	0.520763i	−0.976286	+	0.216484i	$0.930541\pi$
$878$	8.24621	−	14.2829i	0.278296	−	0.482023i
$879$		0			0
$880$	−0.500000	+	0.866025i	−0.0168550	+	0.0291937i
$881$	24.1231			0.812728			0.406364	−	0.913711i	$-0.366796\pi$
$881$	24.1231			0.812728			0.406364	+	0.913711i	$0.366796\pi$
$882$		0			0
$883$	4.40388	−	7.62775i	0.148202	−	0.256694i	−0.782361	−	0.622826i	$-0.785985\pi$
$883$	4.40388	−	7.62775i	0.148202	−	0.256694i	0.930563	+	0.366131i	$0.119318\pi$
$884$	−5.12311	+	8.87348i	−0.172309	+	0.298447i
$885$		0			0
$886$	−33.9309			−1.13993
$887$	−13.1231	+	22.7299i	−0.440631	+	0.763195i	−0.997736	−	0.0672468i	$-0.978579\pi$
$887$	−13.1231	+	22.7299i	−0.440631	+	0.763195i	0.557106	+	0.830442i	$0.311912\pi$
$888$		0			0
$889$	3.41146	−	5.90882i	0.114417	−	0.198176i
$890$	1.34233	+	2.32498i	0.0449950	+	0.0779336i
$891$		0			0
$892$	11.3153			0.378866
$893$	5.30019	+	11.3649i	0.177364	+	0.380313i
$894$		0			0
$895$	−5.74621	−	9.95273i	−0.192075	−	0.332683i
$896$	−0.219224	−	0.379706i	−0.00732375	−	0.0126851i
$897$		0			0
$898$	14.5000	+	25.1147i	0.483871	+	0.838090i
$899$	10.2462	−	17.7470i	0.341730	−	0.591894i
$900$		0			0
$901$	−38.7386			−1.29057
$902$	3.06155	−	5.30277i	0.101939	−	0.176563i
$903$		0			0
$904$	16.8078			0.559018
$905$	−21.3693			−0.710340
$906$		0			0
$907$	25.0885	+	43.4546i	0.833051	+	1.44289i	0.895607	+	0.444846i	$0.146741\pi$
$907$	25.0885	+	43.4546i	0.833051	+	1.44289i	−0.0625559	+	0.998041i	$0.519925\pi$
$908$	9.96543	−	17.2606i	0.330715	−	0.572814i
$909$		0			0
$910$	−0.438447	−	0.759413i	−0.0145344	−	0.0251743i
$911$	−12.3845			−0.410316			−0.205158	−	0.978729i	$-0.565771\pi$
$911$	−12.3845			−0.410316			−0.205158	+	0.978729i	$0.565771\pi$
$912$		0			0
$913$	−10.8078			−0.357685
$914$	−3.52699	−	6.10892i	−0.116662	−	0.202065i
$915$		0			0
$916$	−6.43845	+	11.1517i	−0.212732	+	0.368463i
$917$	−3.53457	−	6.12205i	−0.116722	−	0.202168i
$918$		0			0
$919$	20.2462			0.667861			0.333930	−	0.942598i	$-0.391625\pi$
$919$	20.2462			0.667861			0.333930	+	0.942598i	$0.391625\pi$
$920$	−4.68466			−0.154449
$921$		0			0
$922$	−19.4924	+	33.7619i	−0.641949	+	1.11189i
$923$	32.4924			1.06950
$924$		0			0
$925$	2.34233	−	4.05703i	0.0770153	−	0.133394i
$926$	9.78078	+	16.9408i	0.321416	+	0.556709i
$927$		0			0
$928$	1.00000	+	1.73205i	0.0328266	+	0.0568574i
$929$	−17.9924	−	31.1638i	−0.590312	−	1.02245i	−0.994190	−	0.107638i	$-0.965671\pi$
$929$	−17.9924	−	31.1638i	−0.590312	−	1.02245i	0.403878	−	0.914813i	$-0.367662\pi$
$930$		0			0
$931$	17.0194	−	24.3086i	0.557789	−	0.796682i
$932$	−2.31534			−0.0758415
$933$		0			0
$934$	8.28078	+	14.3427i	0.270955	+	0.469308i
$935$	2.56155	−	4.43674i	0.0837717	−	0.145097i
$936$		0			0
$937$	25.0885	−	43.4546i	0.819607	−	1.41960i	−0.0863653	−	0.996264i	$-0.527525\pi$
$937$	25.0885	−	43.4546i	0.819607	−	1.41960i	0.905972	−	0.423337i	$-0.139141\pi$
$938$	4.13826			0.135119
$939$		0			0
$940$	−1.43845	+	2.49146i	−0.0469170	+	0.0812626i
$941$	−8.12311	+	14.0696i	−0.264806	+	0.458657i	−0.967513	−	0.252822i	$-0.918641\pi$
$941$	−8.12311	+	14.0696i	−0.264806	+	0.458657i	0.702707	+	0.711479i	$0.251974\pi$
$942$		0			0
$943$	28.6847			0.934101
$944$	7.28078	−	12.6107i	0.236969	−	0.410442i
$945$		0			0
$946$	1.56155	−	2.70469i	0.0507705	−	0.0879370i
$947$	28.2462	+	48.9239i	0.917879	+	1.58981i	0.802631	+	0.596475i	$0.203433\pi$
$947$	28.2462	+	48.9239i	0.917879	+	1.58981i	0.115247	+	0.993337i	$0.463234\pi$
$948$		0			0
$949$	3.36932			0.109373
$950$	−2.50000	+	3.57071i	−0.0811107	+	0.115849i
$951$		0			0
$952$	1.12311	+	1.94528i	0.0364001	+	0.0630468i
$953$	−7.84233	−	13.5833i	−0.254038	−	0.440007i	0.710596	−	0.703600i	$-0.248425\pi$
$953$	−7.84233	−	13.5833i	−0.254038	−	0.440007i	−0.964634	+	0.263594i	$0.915092\pi$
$954$		0			0
$955$	2.68466	+	4.64996i	0.0868735	+	0.150469i
$956$	9.12311	−	15.8017i	0.295062	−	0.511063i
$957$		0			0
$958$	−29.3693			−0.948880
$959$	−1.19224	+	2.06501i	−0.0384993	+	0.0666828i
$960$		0			0
$961$	73.9848			2.38661
$962$	9.36932			0.302079
$963$		0			0
$964$	4.28078	+	7.41452i	0.137875	+	0.238806i
$965$	12.8078	−	22.1837i	0.412297	−	0.714119i
$966$		0			0
$967$	−14.5616	−	25.2213i	−0.468268	−	0.811064i	0.531074	−	0.847325i	$-0.321788\pi$
$967$	−14.5616	−	25.2213i	−0.468268	−	0.811064i	−0.999342	+	0.0362613i	$0.988455\pi$
$968$	−10.0000			−0.321412
$969$		0			0
$970$	−1.68466			−0.0540911
$971$	8.96543	+	15.5286i	0.287714	+	0.498336i	0.973264	−	0.229690i	$-0.0737712\pi$
$971$	8.96543	+	15.5286i	0.287714	+	0.498336i	−0.685549	+	0.728026i	$0.740438\pi$
$972$		0			0
$973$	−1.93087	+	3.34436i	−0.0619008	+	0.107215i
$974$	3.46543	+	6.00231i	0.111040	+	0.192326i
$975$		0			0
$976$	5.12311			0.163987
$977$	30.3153			0.969874			0.484937	−	0.874549i	$-0.338843\pi$
$977$	30.3153			0.969874			0.484937	+	0.874549i	$0.338843\pi$
$978$		0			0
$979$	1.34233	−	2.32498i	0.0429010	−	0.0743068i
$980$	6.80776			0.217466
$981$		0			0
$982$	−4.58854	+	7.94759i	−0.146426	+	0.253618i
$983$	20.7808	+	35.9934i	0.662804	+	1.14801i	0.979876	+	0.199608i	$0.0639670\pi$
$983$	20.7808	+	35.9934i	0.662804	+	1.14801i	−0.317072	+	0.948401i	$0.602700\pi$
$984$		0			0
$985$	−7.21922	−	12.5041i	−0.230024	−	0.398413i
$986$	−5.12311	−	8.87348i	−0.163153	−	0.282589i
$987$		0			0
$988$	−8.68466	−	0.759413i	−0.276296	−	0.0241601i
$989$	14.6307			0.465229
$990$		0			0
$991$	4.19224	+	7.26117i	0.133171	+	0.230659i	0.924897	−	0.380217i	$-0.124151\pi$
$991$	4.19224	+	7.26117i	0.133171	+	0.230659i	−0.791726	+	0.610876i	$0.790817\pi$
$992$	−5.12311	+	8.87348i	−0.162659	+	0.281733i
$993$		0			0
$994$	3.56155	−	6.16879i	0.112966	−	0.195662i
$995$	2.87689			0.0912037
$996$		0			0
$997$	1.34233	−	2.32498i	0.0425120	−	0.0736329i	−0.843986	−	0.536364i	$-0.819797\pi$
$997$	1.34233	−	2.32498i	0.0425120	−	0.0736329i	0.886498	+	0.462732i	$0.153131\pi$
$998$	−14.5000	+	25.1147i	−0.458989	+	0.794993i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1710.2.l.m.1261.1		4
3.2	odd	2		190.2.e.c.121.2	yes	4
12.11	even	2		1520.2.q.h.881.1		4
15.2	even	4		950.2.j.f.349.2		8
15.8	even	4		950.2.j.f.349.3		8
15.14	odd	2		950.2.e.h.501.1		4
19.11	even	3	inner	1710.2.l.m.1531.1		4
57.11	odd	6		190.2.e.c.11.2	✓	4
57.26	odd	6		3610.2.a.k.1.1		2
57.50	even	6		3610.2.a.u.1.2		2
228.11	even	6		1520.2.q.h.961.1		4
285.68	even	12		950.2.j.f.49.2		8
285.182	even	12		950.2.j.f.49.3		8
285.239	odd	6		950.2.e.h.201.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.e.c.11.2	✓	4	57.11	odd	6
190.2.e.c.121.2	yes	4	3.2	odd	2
950.2.e.h.201.1		4	285.239	odd	6
950.2.e.h.501.1		4	15.14	odd	2
950.2.j.f.49.2		8	285.68	even	12
950.2.j.f.49.3		8	285.182	even	12
950.2.j.f.349.2		8	15.2	even	4
950.2.j.f.349.3		8	15.8	even	4
1520.2.q.h.881.1		4	12.11	even	2
1520.2.q.h.961.1		4	228.11	even	6
1710.2.l.m.1261.1		4	1.1	even	1	trivial
1710.2.l.m.1531.1		4	19.11	even	3	inner
3610.2.a.k.1.1		2	57.26	odd	6
3610.2.a.u.1.2		2	57.50	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1710.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +0.438447 q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{10} -1.00000 q^{11} +(1.00000 - 1.73205i) q^{13} +(-0.219224 - 0.379706i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.56155 + 4.43674i) q^{17} +(-2.50000 + 3.57071i) q^{19} -1.00000 q^{20} +(0.500000 + 0.866025i) q^{22} +(-2.34233 + 4.05703i) q^{23} +(-0.500000 + 0.866025i) q^{25} -2.00000 q^{26} +(-0.219224 + 0.379706i) q^{28} +(1.00000 - 1.73205i) q^{29} +10.2462 q^{31} +(-0.500000 + 0.866025i) q^{32} +(2.56155 - 4.43674i) q^{34} +(0.219224 + 0.379706i) q^{35} -4.68466 q^{37} +(4.34233 + 0.379706i) q^{38} +(0.500000 + 0.866025i) q^{40} +(-3.06155 - 5.30277i) q^{41} +(-1.56155 - 2.70469i) q^{43} +(0.500000 - 0.866025i) q^{44} +4.68466 q^{46} +(1.43845 - 2.49146i) q^{47} -6.80776 q^{49} +1.00000 q^{50} +(1.00000 + 1.73205i) q^{52} +(-3.78078 + 6.54850i) q^{53} +(-0.500000 - 0.866025i) q^{55} +0.438447 q^{56} -2.00000 q^{58} +(7.28078 + 12.6107i) q^{59} +(-2.56155 + 4.43674i) q^{61} +(-5.12311 - 8.87348i) q^{62} +1.00000 q^{64} +2.00000 q^{65} +(-4.71922 + 8.17394i) q^{67} -5.12311 q^{68} +(0.219224 - 0.379706i) q^{70} +(8.12311 + 14.0696i) q^{71} +(0.842329 + 1.45896i) q^{73} +(2.34233 + 4.05703i) q^{74} +(-1.84233 - 3.95042i) q^{76} -0.438447 q^{77} +(5.56155 + 9.63289i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-3.06155 + 5.30277i) q^{82} +10.8078 q^{83} +(-2.56155 + 4.43674i) q^{85} +(-1.56155 + 2.70469i) q^{86} -1.00000 q^{88} +(-1.34233 + 2.32498i) q^{89} +(0.438447 - 0.759413i) q^{91} +(-2.34233 - 4.05703i) q^{92} -2.87689 q^{94} +(-4.34233 - 0.379706i) q^{95} +(-0.842329 - 1.45896i) q^{97} +(3.40388 + 5.89570i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{4} + 2 q^{5} + 10 q^{7} + 4 q^{8} + 2 q^{10} - 4 q^{11} + 4 q^{13} - 5 q^{14} - 2 q^{16} + 2 q^{17} - 10 q^{19} - 4 q^{20} + 2 q^{22} + 3 q^{23} - 2 q^{25} - 8 q^{26} - 5 q^{28} + 4 q^{29}+ \cdots - 7 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^4 + 2 * q^5 + 10 * q^7 + 4 * q^8 + 2 * q^10 - 4 * q^11 + 4 * q^13 - 5 * q^14 - 2 * q^16 + 2 * q^17 - 10 * q^19 - 4 * q^20 + 2 * q^22 + 3 * q^23 - 2 * q^25 - 8 * q^26 - 5 * q^28 + 4 * q^29 + 8 * q^31 - 2 * q^32 + 2 * q^34 + 5 * q^35 + 6 * q^37 + 5 * q^38 + 2 * q^40 - 4 * q^41 + 2 * q^43 + 2 * q^44 - 6 * q^46 + 14 * q^47 + 14 * q^49 + 4 * q^50 + 4 * q^52 - 11 * q^53 - 2 * q^55 + 10 * q^56 - 8 * q^58 + 25 * q^59 - 2 * q^61 - 4 * q^62 + 4 * q^64 + 8 * q^65 - 23 * q^67 - 4 * q^68 + 5 * q^70 + 16 * q^71 - 9 * q^73 - 3 * q^74 + 5 * q^76 - 10 * q^77 + 14 * q^79 + 2 * q^80 - 4 * q^82 + 2 * q^83 - 2 * q^85 + 2 * q^86 - 4 * q^88 + 7 * q^89 + 10 * q^91 + 3 * q^92 - 28 * q^94 - 5 * q^95 + 9 * q^97 - 7 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

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