LMFDB - Embedded newform 1134.2.g.f.163.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1134,2,Mod(163,1134)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1134.163"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1134, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1134 = 2 \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1134.g (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [2,1,0,-1,-3,0,5] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$9.05503558921$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			163.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1134.163
Dual form			1134.2.g.f.487.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.50000 + 2.59808i) q^{5} +(2.50000 - 0.866025i) q^{7} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{10} +(-1.50000 - 2.59808i) q^{11} +5.00000 q^{13} +(0.500000 - 2.59808i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.50000 + 2.59808i) q^{17} +(-2.50000 + 4.33013i) q^{19} +3.00000 q^{20} -3.00000 q^{22} +(-1.50000 + 2.59808i) q^{23} +(-2.00000 - 3.46410i) q^{25} +(2.50000 - 4.33013i) q^{26} +(-2.00000 - 1.73205i) q^{28} +3.00000 q^{29} +(2.00000 + 3.46410i) q^{31} +(0.500000 + 0.866025i) q^{32} +3.00000 q^{34} +(-1.50000 + 7.79423i) q^{35} +(3.50000 - 6.06218i) q^{37} +(2.50000 + 4.33013i) q^{38} +(1.50000 - 2.59808i) q^{40} +9.00000 q^{41} +11.0000 q^{43} +(-1.50000 + 2.59808i) q^{44} +(1.50000 + 2.59808i) q^{46} +(5.50000 - 4.33013i) q^{49} -4.00000 q^{50} +(-2.50000 - 4.33013i) q^{52} +(-1.50000 - 2.59808i) q^{53} +9.00000 q^{55} +(-2.50000 + 0.866025i) q^{56} +(1.50000 - 2.59808i) q^{58} +(6.00000 + 10.3923i) q^{59} +(-1.00000 + 1.73205i) q^{61} +4.00000 q^{62} +1.00000 q^{64} +(-7.50000 + 12.9904i) q^{65} +(2.00000 + 3.46410i) q^{67} +(1.50000 - 2.59808i) q^{68} +(6.00000 + 5.19615i) q^{70} +(-5.50000 - 9.52628i) q^{73} +(-3.50000 - 6.06218i) q^{74} +5.00000 q^{76} +(-6.00000 - 5.19615i) q^{77} +(-4.00000 + 6.92820i) q^{79} +(-1.50000 - 2.59808i) q^{80} +(4.50000 - 7.79423i) q^{82} -3.00000 q^{83} -9.00000 q^{85} +(5.50000 - 9.52628i) q^{86} +(1.50000 + 2.59808i) q^{88} +(7.50000 - 12.9904i) q^{89} +(12.5000 - 4.33013i) q^{91} +3.00000 q^{92} +(-7.50000 - 12.9904i) q^{95} -1.00000 q^{97} +(-1.00000 - 6.92820i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{4} - 3 q^{5} + 5 q^{7} - 2 q^{8} + 3 q^{10} - 3 q^{11} + 10 q^{13} + q^{14} - q^{16} + 3 q^{17} - 5 q^{19} + 6 q^{20} - 6 q^{22} - 3 q^{23} - 4 q^{25} + 5 q^{26} - 4 q^{28} + 6 q^{29}+ \cdots - 2 q^{98}+O(q^{100}) $ 2 * q + q^2 - q^4 - 3 * q^5 + 5 * q^7 - 2 * q^8 + 3 * q^10 - 3 * q^11 + 10 * q^13 + q^14 - q^16 + 3 * q^17 - 5 * q^19 + 6 * q^20 - 6 * q^22 - 3 * q^23 - 4 * q^25 + 5 * q^26 - 4 * q^28 + 6 * q^29 + 4 * q^31 + q^32 + 6 * q^34 - 3 * q^35 + 7 * q^37 + 5 * q^38 + 3 * q^40 + 18 * q^41 + 22 * q^43 - 3 * q^44 + 3 * q^46 + 11 * q^49 - 8 * q^50 - 5 * q^52 - 3 * q^53 + 18 * q^55 - 5 * q^56 + 3 * q^58 + 12 * q^59 - 2 * q^61 + 8 * q^62 + 2 * q^64 - 15 * q^65 + 4 * q^67 + 3 * q^68 + 12 * q^70 - 11 * q^73 - 7 * q^74 + 10 * q^76 - 12 * q^77 - 8 * q^79 - 3 * q^80 + 9 * q^82 - 6 * q^83 - 18 * q^85 + 11 * q^86 + 3 * q^88 + 15 * q^89 + 25 * q^91 + 6 * q^92 - 15 * q^95 - 2 * q^97 - 2 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.50000	+	2.59808i	−0.670820	+	1.16190i	0.306851	+	0.951757i	$0.400725\pi$
$5$	−1.50000	+	2.59808i	−0.670820	+	1.16190i	−0.977672	+	0.210138i	$0.932609\pi$
$6$		0			0
$7$	2.50000	−	0.866025i	0.944911	−	0.327327i
$7$	2.50000	−	0.866025i	0.944911	−	0.327327i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	1.50000	+	2.59808i	0.474342	+	0.821584i
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	0.546259	−	0.837616i	$-0.316051\pi$
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	−0.998526	+	0.0542666i	$0.982718\pi$
$12$		0			0
$13$	5.00000			1.38675			0.693375	−	0.720577i	$-0.256123\pi$
$13$	5.00000			1.38675			0.693375	+	0.720577i	$0.256123\pi$
$14$	0.500000	−	2.59808i	0.133631	−	0.694365i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.50000	+	2.59808i	0.363803	+	0.630126i	0.988583	−	0.150675i	$-0.0481447\pi$
$17$	1.50000	+	2.59808i	0.363803	+	0.630126i	−0.624780	+	0.780801i	$0.714811\pi$
$18$		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	$0.972237\pi$
$20$	3.00000			0.670820
$21$		0			0
$22$	−3.00000			−0.639602
$23$	−1.50000	+	2.59808i	−0.312772	+	0.541736i	−0.978961	−	0.204046i	$-0.934591\pi$
$23$	−1.50000	+	2.59808i	−0.312772	+	0.541736i	0.666190	+	0.745782i	$0.267924\pi$
$24$		0			0
$25$	−2.00000	−	3.46410i	−0.400000	−	0.692820i
$26$	2.50000	−	4.33013i	0.490290	−	0.849208i
$27$		0			0
$28$	−2.00000	−	1.73205i	−0.377964	−	0.327327i
$29$	3.00000			0.557086			0.278543	−	0.960424i	$-0.410149\pi$
$29$	3.00000			0.557086			0.278543	+	0.960424i	$0.410149\pi$
$30$		0			0
$31$	2.00000	+	3.46410i	0.359211	+	0.622171i	0.987829	−	0.155543i	$-0.0497126\pi$
$31$	2.00000	+	3.46410i	0.359211	+	0.622171i	−0.628619	+	0.777714i	$0.716379\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$	3.00000			0.514496
$35$	−1.50000	+	7.79423i	−0.253546	+	1.31747i
$36$		0			0
$37$	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	$-0.0284856\pi$
$38$	2.50000	+	4.33013i	0.405554	+	0.702439i
$39$		0			0
$40$	1.50000	−	2.59808i	0.237171	−	0.410792i
$41$	9.00000			1.40556			0.702782	−	0.711405i	$-0.251941\pi$
$41$	9.00000			1.40556			0.702782	+	0.711405i	$0.251941\pi$
$42$		0			0
$43$	11.0000			1.67748			0.838742	−	0.544529i	$-0.183292\pi$
$43$	11.0000			1.67748			0.838742	+	0.544529i	$0.183292\pi$
$44$	−1.50000	+	2.59808i	−0.226134	+	0.391675i
$45$		0			0
$46$	1.50000	+	2.59808i	0.221163	+	0.383065i
$47$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$47$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$48$		0			0
$49$	5.50000	−	4.33013i	0.785714	−	0.618590i
$50$	−4.00000			−0.565685
$51$		0			0
$52$	−2.50000	−	4.33013i	−0.346688	−	0.600481i
$53$	−1.50000	−	2.59808i	−0.206041	−	0.356873i	0.744423	−	0.667708i	$-0.232725\pi$
$53$	−1.50000	−	2.59808i	−0.206041	−	0.356873i	−0.950464	+	0.310835i	$0.899391\pi$
$54$		0			0
$55$	9.00000			1.21356
$56$	−2.50000	+	0.866025i	−0.334077	+	0.115728i
$57$		0			0
$58$	1.50000	−	2.59808i	0.196960	−	0.341144i
$59$	6.00000	+	10.3923i	0.781133	+	1.35296i	0.931282	+	0.364299i	$0.118692\pi$
$59$	6.00000	+	10.3923i	0.781133	+	1.35296i	−0.150148	+	0.988663i	$0.547975\pi$
$60$		0			0
$61$	−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	$0.207534\pi$
$62$	4.00000			0.508001
$63$		0			0
$64$	1.00000			0.125000
$65$	−7.50000	+	12.9904i	−0.930261	+	1.61126i
$66$		0			0
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	0.961946	−	0.273241i	$-0.0880957\pi$
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	−0.717607	+	0.696449i	$0.754762\pi$
$68$	1.50000	−	2.59808i	0.181902	−	0.315063i
$69$		0			0
$70$	6.00000	+	5.19615i	0.717137	+	0.621059i
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		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	$-0.389279\pi$
$74$	−3.50000	−	6.06218i	−0.406867	−	0.704714i
$75$		0			0
$76$	5.00000			0.573539
$77$	−6.00000	−	5.19615i	−0.683763	−	0.592157i
$78$		0			0
$79$	−4.00000	+	6.92820i	−0.450035	+	0.779484i	−0.998388	−	0.0567635i	$-0.981922\pi$
$79$	−4.00000	+	6.92820i	−0.450035	+	0.779484i	0.548352	+	0.836247i	$0.315255\pi$
$80$	−1.50000	−	2.59808i	−0.167705	−	0.290474i
$81$		0			0
$82$	4.50000	−	7.79423i	0.496942	−	0.860729i
$83$	−3.00000			−0.329293			−0.164646	−	0.986353i	$-0.552648\pi$
$83$	−3.00000			−0.329293			−0.164646	+	0.986353i	$0.552648\pi$
$84$		0			0
$85$	−9.00000			−0.976187
$86$	5.50000	−	9.52628i	0.593080	−	1.02725i
$87$		0			0
$88$	1.50000	+	2.59808i	0.159901	+	0.276956i
$89$	7.50000	−	12.9904i	0.794998	−	1.37698i	−0.127842	−	0.991795i	$-0.540805\pi$
$89$	7.50000	−	12.9904i	0.794998	−	1.37698i	0.922840	−	0.385183i	$-0.125862\pi$
$90$		0			0
$91$	12.5000	−	4.33013i	1.31036	−	0.453921i
$92$	3.00000			0.312772
$93$		0			0
$94$		0			0
$95$	−7.50000	−	12.9904i	−0.769484	−	1.33278i
$96$		0			0
$97$	−1.00000			−0.101535			−0.0507673	−	0.998711i	$-0.516167\pi$
$97$	−1.00000			−0.101535			−0.0507673	+	0.998711i	$0.516167\pi$
$98$	−1.00000	−	6.92820i	−0.101015	−	0.699854i
$99$		0			0
$100$	−2.00000	+	3.46410i	−0.200000	+	0.346410i
$101$	−1.50000	−	2.59808i	−0.149256	−	0.258518i	0.781697	−	0.623658i	$-0.214354\pi$
$101$	−1.50000	−	2.59808i	−0.149256	−	0.258518i	−0.930953	+	0.365140i	$0.881021\pi$
$102$		0			0
$103$	−2.50000	+	4.33013i	−0.246332	+	0.426660i	−0.962505	−	0.271263i	$-0.912559\pi$
$103$	−2.50000	+	4.33013i	−0.246332	+	0.426660i	0.716173	+	0.697923i	$0.245892\pi$
$104$	−5.00000			−0.490290
$105$		0			0
$106$	−3.00000			−0.291386
$107$	−7.50000	+	12.9904i	−0.725052	+	1.25583i	0.233900	+	0.972261i	$0.424851\pi$
$107$	−7.50000	+	12.9904i	−0.725052	+	1.25583i	−0.958952	+	0.283567i	$0.908482\pi$
$108$		0			0
$109$	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	$0.724516\pi$
$110$	4.50000	−	7.79423i	0.429058	−	0.743151i
$111$		0			0
$112$	−0.500000	+	2.59808i	−0.0472456	+	0.245495i
$113$	−15.0000			−1.41108			−0.705541	−	0.708669i	$-0.749296\pi$
$113$	−15.0000			−1.41108			−0.705541	+	0.708669i	$0.749296\pi$
$114$		0			0
$115$	−4.50000	−	7.79423i	−0.419627	−	0.726816i
$116$	−1.50000	−	2.59808i	−0.139272	−	0.241225i
$117$		0			0
$118$	12.0000			1.10469
$119$	6.00000	+	5.19615i	0.550019	+	0.476331i
$120$		0			0
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$	1.00000	+	1.73205i	0.0905357	+	0.156813i
$123$		0			0
$124$	2.00000	−	3.46410i	0.179605	−	0.311086i
$125$	−3.00000			−0.268328
$126$		0			0
$127$	−16.0000			−1.41977			−0.709885	−	0.704317i	$-0.751253\pi$
$127$	−16.0000			−1.41977			−0.709885	+	0.704317i	$0.751253\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$		0			0
$130$	7.50000	+	12.9904i	0.657794	+	1.13933i
$131$	1.50000	−	2.59808i	0.131056	−	0.226995i	−0.793028	−	0.609185i	$-0.791497\pi$
$131$	1.50000	−	2.59808i	0.131056	−	0.226995i	0.924084	+	0.382190i	$0.124830\pi$
$132$		0			0
$133$	−2.50000	+	12.9904i	−0.216777	+	1.12641i
$134$	4.00000			0.345547
$135$		0			0
$136$	−1.50000	−	2.59808i	−0.128624	−	0.222783i
$137$	1.50000	+	2.59808i	0.128154	+	0.221969i	0.922961	−	0.384893i	$-0.125762\pi$
$137$	1.50000	+	2.59808i	0.128154	+	0.221969i	−0.794808	+	0.606861i	$0.792428\pi$
$138$		0			0
$139$	5.00000			0.424094			0.212047	−	0.977259i	$-0.431987\pi$
$139$	5.00000			0.424094			0.212047	+	0.977259i	$0.431987\pi$
$140$	7.50000	−	2.59808i	0.633866	−	0.219578i
$141$		0			0
$142$		0			0
$143$	−7.50000	−	12.9904i	−0.627182	−	1.08631i
$144$		0			0
$145$	−4.50000	+	7.79423i	−0.373705	+	0.647275i
$146$	−11.0000			−0.910366
$147$		0			0
$148$	−7.00000			−0.575396
$149$	−1.50000	+	2.59808i	−0.122885	+	0.212843i	−0.920904	−	0.389789i	$-0.872548\pi$
$149$	−1.50000	+	2.59808i	−0.122885	+	0.212843i	0.798019	+	0.602632i	$0.205881\pi$
$150$		0			0
$151$	−5.50000	−	9.52628i	−0.447584	−	0.775238i	0.550645	−	0.834740i	$-0.314382\pi$
$151$	−5.50000	−	9.52628i	−0.447584	−	0.775238i	−0.998228	+	0.0595022i	$0.981049\pi$
$152$	2.50000	−	4.33013i	0.202777	−	0.351220i
$153$		0			0
$154$	−7.50000	+	2.59808i	−0.604367	+	0.209359i
$155$	−12.0000			−0.963863
$156$		0			0
$157$	−7.00000	−	12.1244i	−0.558661	−	0.967629i	−0.997609	−	0.0691164i	$-0.977982\pi$
$157$	−7.00000	−	12.1244i	−0.558661	−	0.967629i	0.438948	−	0.898513i	$-0.355351\pi$
$158$	4.00000	+	6.92820i	0.318223	+	0.551178i
$159$		0			0
$160$	−3.00000			−0.237171
$161$	−1.50000	+	7.79423i	−0.118217	+	0.614271i
$162$		0			0
$163$	−8.50000	+	14.7224i	−0.665771	+	1.15315i	0.313304	+	0.949653i	$0.398564\pi$
$163$	−8.50000	+	14.7224i	−0.665771	+	1.15315i	−0.979076	+	0.203497i	$0.934769\pi$
$164$	−4.50000	−	7.79423i	−0.351391	−	0.608627i
$165$		0			0
$166$	−1.50000	+	2.59808i	−0.116423	+	0.201650i
$167$	−3.00000			−0.232147			−0.116073	−	0.993241i	$-0.537031\pi$
$167$	−3.00000			−0.232147			−0.116073	+	0.993241i	$0.537031\pi$
$168$		0			0
$169$	12.0000			0.923077
$170$	−4.50000	+	7.79423i	−0.345134	+	0.597790i
$171$		0			0
$172$	−5.50000	−	9.52628i	−0.419371	−	0.726372i
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	−0.729155	−	0.684349i	$-0.760087\pi$
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	0.957241	+	0.289292i	$0.0934200\pi$
$174$		0			0
$175$	−8.00000	−	6.92820i	−0.604743	−	0.523723i
$176$	3.00000			0.226134
$177$		0			0
$178$	−7.50000	−	12.9904i	−0.562149	−	0.973670i
$179$	1.50000	+	2.59808i	0.112115	+	0.194189i	0.916623	−	0.399753i	$-0.130904\pi$
$179$	1.50000	+	2.59808i	0.112115	+	0.194189i	−0.804508	+	0.593942i	$0.797571\pi$
$180$		0			0
$181$	−10.0000			−0.743294			−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000			−0.743294			−0.371647	+	0.928374i	$0.621207\pi$
$182$	2.50000	−	12.9904i	0.185312	−	0.962911i
$183$		0			0
$184$	1.50000	−	2.59808i	0.110581	−	0.191533i
$185$	10.5000	+	18.1865i	0.771975	+	1.33710i
$186$		0			0
$187$	4.50000	−	7.79423i	0.329073	−	0.569970i
$188$		0			0
$189$		0			0
$190$	−15.0000			−1.08821
$191$	6.00000	−	10.3923i	0.434145	−	0.751961i	−0.563081	−	0.826402i	$-0.690384\pi$
$191$	6.00000	−	10.3923i	0.434145	−	0.751961i	0.997225	+	0.0744412i	$0.0237173\pi$
$192$		0			0
$193$	−7.00000	−	12.1244i	−0.503871	−	0.872730i	−0.999990	−	0.00447566i	$-0.998575\pi$
$193$	−7.00000	−	12.1244i	−0.503871	−	0.872730i	0.496119	−	0.868255i	$-0.334758\pi$
$194$	−0.500000	+	0.866025i	−0.0358979	+	0.0621770i
$195$		0			0
$196$	−6.50000	−	2.59808i	−0.464286	−	0.185577i
$197$	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
$199$	3.50000	+	6.06218i	0.248108	+	0.429736i	0.963001	−	0.269498i	$-0.0868577\pi$
$199$	3.50000	+	6.06218i	0.248108	+	0.429736i	−0.714893	+	0.699234i	$0.753524\pi$
$200$	2.00000	+	3.46410i	0.141421	+	0.244949i
$201$		0			0
$202$	−3.00000			−0.211079
$203$	7.50000	−	2.59808i	0.526397	−	0.182349i
$204$		0			0
$205$	−13.5000	+	23.3827i	−0.942881	+	1.63312i
$206$	2.50000	+	4.33013i	0.174183	+	0.301694i
$207$		0			0
$208$	−2.50000	+	4.33013i	−0.173344	+	0.300240i
$209$	15.0000			1.03757
$210$		0			0
$211$	5.00000			0.344214			0.172107	−	0.985078i	$-0.444942\pi$
$211$	5.00000			0.344214			0.172107	+	0.985078i	$0.444942\pi$
$212$	−1.50000	+	2.59808i	−0.103020	+	0.178437i
$213$		0			0
$214$	7.50000	+	12.9904i	0.512689	+	0.888004i
$215$	−16.5000	+	28.5788i	−1.12529	+	1.94906i
$216$		0			0
$217$	8.00000	+	6.92820i	0.543075	+	0.470317i
$218$	7.00000			0.474100
$219$		0			0
$220$	−4.50000	−	7.79423i	−0.303390	−	0.525487i
$221$	7.50000	+	12.9904i	0.504505	+	0.873828i
$222$		0			0
$223$	17.0000			1.13840			0.569202	−	0.822198i	$-0.307252\pi$
$223$	17.0000			1.13840			0.569202	+	0.822198i	$0.307252\pi$
$224$	2.00000	+	1.73205i	0.133631	+	0.115728i
$225$		0			0
$226$	−7.50000	+	12.9904i	−0.498893	+	0.864107i
$227$	4.50000	+	7.79423i	0.298675	+	0.517321i	0.975833	−	0.218517i	$-0.0701218\pi$
$227$	4.50000	+	7.79423i	0.298675	+	0.517321i	−0.677158	+	0.735838i	$0.736789\pi$
$228$		0			0
$229$	−8.50000	+	14.7224i	−0.561696	+	0.972886i	0.435653	+	0.900115i	$0.356518\pi$
$229$	−8.50000	+	14.7224i	−0.561696	+	0.972886i	−0.997349	+	0.0727709i	$0.976816\pi$
$230$	−9.00000			−0.593442
$231$		0			0
$232$	−3.00000			−0.196960
$233$	13.5000	−	23.3827i	0.884414	−	1.53185i	0.0380310	−	0.999277i	$-0.487891\pi$
$233$	13.5000	−	23.3827i	0.884414	−	1.53185i	0.846383	−	0.532574i	$-0.178775\pi$
$234$		0			0
$235$		0			0
$236$	6.00000	−	10.3923i	0.390567	−	0.676481i
$237$		0			0
$238$	7.50000	−	2.59808i	0.486153	−	0.168408i
$239$	−27.0000			−1.74648			−0.873242	−	0.487286i	$-0.837987\pi$
$239$	−27.0000			−1.74648			−0.873242	+	0.487286i	$0.837987\pi$
$240$		0			0
$241$	−11.5000	−	19.9186i	−0.740780	−	1.28307i	−0.952141	−	0.305661i	$-0.901123\pi$
$241$	−11.5000	−	19.9186i	−0.740780	−	1.28307i	0.211360	−	0.977408i	$-0.432211\pi$
$242$	−1.00000	−	1.73205i	−0.0642824	−	0.111340i
$243$		0			0
$244$	2.00000			0.128037
$245$	3.00000	+	20.7846i	0.191663	+	1.32788i
$246$		0			0
$247$	−12.5000	+	21.6506i	−0.795356	+	1.37760i
$248$	−2.00000	−	3.46410i	−0.127000	−	0.219971i
$249$		0			0
$250$	−1.50000	+	2.59808i	−0.0948683	+	0.164317i
$251$	−12.0000			−0.757433			−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000			−0.757433			−0.378717	+	0.925513i	$0.623635\pi$
$252$		0			0
$253$	9.00000			0.565825
$254$	−8.00000	+	13.8564i	−0.501965	+	0.869428i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	7.50000	−	12.9904i	0.467837	−	0.810318i	−0.531487	−	0.847066i	$-0.678367\pi$
$257$	7.50000	−	12.9904i	0.467837	−	0.810318i	0.999325	+	0.0367485i	$0.0117000\pi$
$258$		0			0
$259$	3.50000	−	18.1865i	0.217479	−	1.13006i
$260$	15.0000			0.930261
$261$		0			0
$262$	−1.50000	−	2.59808i	−0.0926703	−	0.160510i
$263$	−4.50000	−	7.79423i	−0.277482	−	0.480613i	0.693276	−	0.720672i	$-0.256167\pi$
$263$	−4.50000	−	7.79423i	−0.277482	−	0.480613i	−0.970758	+	0.240059i	$0.922833\pi$
$264$		0			0
$265$	9.00000			0.552866
$266$	10.0000	+	8.66025i	0.613139	+	0.530994i
$267$		0			0
$268$	2.00000	−	3.46410i	0.122169	−	0.211604i
$269$	10.5000	+	18.1865i	0.640196	+	1.10885i	0.985389	+	0.170321i	$0.0544803\pi$
$269$	10.5000	+	18.1865i	0.640196	+	1.10885i	−0.345192	+	0.938532i	$0.612186\pi$
$270$		0			0
$271$	6.50000	−	11.2583i	0.394847	−	0.683895i	−0.598235	−	0.801321i	$-0.704131\pi$
$271$	6.50000	−	11.2583i	0.394847	−	0.683895i	0.993082	+	0.117426i	$0.0374643\pi$
$272$	−3.00000			−0.181902
$273$		0			0
$274$	3.00000			0.181237
$275$	−6.00000	+	10.3923i	−0.361814	+	0.626680i
$276$		0			0
$277$	3.50000	+	6.06218i	0.210295	+	0.364241i	0.951807	−	0.306699i	$-0.0992243\pi$
$277$	3.50000	+	6.06218i	0.210295	+	0.364241i	−0.741512	+	0.670940i	$0.765891\pi$
$278$	2.50000	−	4.33013i	0.149940	−	0.259704i
$279$		0			0
$280$	1.50000	−	7.79423i	0.0896421	−	0.465794i
$281$	−3.00000			−0.178965			−0.0894825	−	0.995988i	$-0.528521\pi$
$281$	−3.00000			−0.178965			−0.0894825	+	0.995988i	$0.528521\pi$
$282$		0			0
$283$	−4.00000	−	6.92820i	−0.237775	−	0.411839i	0.722300	−	0.691580i	$-0.243085\pi$
$283$	−4.00000	−	6.92820i	−0.237775	−	0.411839i	−0.960076	+	0.279741i	$0.909752\pi$
$284$		0			0
$285$		0			0
$286$	−15.0000			−0.886969
$287$	22.5000	−	7.79423i	1.32813	−	0.460079i
$288$		0			0
$289$	4.00000	−	6.92820i	0.235294	−	0.407541i
$290$	4.50000	+	7.79423i	0.264249	+	0.457693i
$291$		0			0
$292$	−5.50000	+	9.52628i	−0.321863	+	0.557483i
$293$	27.0000			1.57736			0.788678	−	0.614806i	$-0.210766\pi$
$293$	27.0000			1.57736			0.788678	+	0.614806i	$0.210766\pi$
$294$		0			0
$295$	−36.0000			−2.09600
$296$	−3.50000	+	6.06218i	−0.203433	+	0.352357i
$297$		0			0
$298$	1.50000	+	2.59808i	0.0868927	+	0.150503i
$299$	−7.50000	+	12.9904i	−0.433736	+	0.751253i
$300$		0			0
$301$	27.5000	−	9.52628i	1.58507	−	0.549086i
$302$	−11.0000			−0.632979
$303$		0			0
$304$	−2.50000	−	4.33013i	−0.143385	−	0.248350i
$305$	−3.00000	−	5.19615i	−0.171780	−	0.297531i
$306$		0			0
$307$	−28.0000			−1.59804			−0.799022	−	0.601302i	$-0.794649\pi$
$307$	−28.0000			−1.59804			−0.799022	+	0.601302i	$0.794649\pi$
$308$	−1.50000	+	7.79423i	−0.0854704	+	0.444117i
$309$		0			0
$310$	−6.00000	+	10.3923i	−0.340777	+	0.590243i
$311$	−12.0000	−	20.7846i	−0.680458	−	1.17859i	−0.974841	−	0.222900i	$-0.928448\pi$
$311$	−12.0000	−	20.7846i	−0.680458	−	1.17859i	0.294384	−	0.955687i	$-0.404886\pi$
$312$		0			0
$313$	−7.00000	+	12.1244i	−0.395663	+	0.685309i	−0.993186	−	0.116543i	$-0.962819\pi$
$313$	−7.00000	+	12.1244i	−0.395663	+	0.685309i	0.597522	+	0.801852i	$0.296152\pi$
$314$	−14.0000			−0.790066
$315$		0			0
$316$	8.00000			0.450035
$317$	15.0000	−	25.9808i	0.842484	−	1.45922i	−0.0453045	−	0.998973i	$-0.514426\pi$
$317$	15.0000	−	25.9808i	0.842484	−	1.45922i	0.887788	−	0.460252i	$-0.152241\pi$
$318$		0			0
$319$	−4.50000	−	7.79423i	−0.251952	−	0.436393i
$320$	−1.50000	+	2.59808i	−0.0838525	+	0.145237i
$321$		0			0
$322$	6.00000	+	5.19615i	0.334367	+	0.289570i
$323$	−15.0000			−0.834622
$324$		0			0
$325$	−10.0000	−	17.3205i	−0.554700	−	0.960769i
$326$	8.50000	+	14.7224i	0.470771	+	0.815400i
$327$		0			0
$328$	−9.00000			−0.496942
$329$		0			0
$330$		0			0
$331$	−10.0000	+	17.3205i	−0.549650	+	0.952021i	0.448649	+	0.893708i	$0.351905\pi$
$331$	−10.0000	+	17.3205i	−0.549650	+	0.952021i	−0.998298	+	0.0583130i	$0.981428\pi$
$332$	1.50000	+	2.59808i	0.0823232	+	0.142588i
$333$		0			0
$334$	−1.50000	+	2.59808i	−0.0820763	+	0.142160i
$335$	−12.0000			−0.655630
$336$		0			0
$337$	−25.0000			−1.36184			−0.680918	−	0.732359i	$-0.738419\pi$
$337$	−25.0000			−1.36184			−0.680918	+	0.732359i	$0.738419\pi$
$338$	6.00000	−	10.3923i	0.326357	−	0.565267i
$339$		0			0
$340$	4.50000	+	7.79423i	0.244047	+	0.422701i
$341$	6.00000	−	10.3923i	0.324918	−	0.562775i
$342$		0			0
$343$	10.0000	−	15.5885i	0.539949	−	0.841698i
$344$	−11.0000			−0.593080
$345$		0			0
$346$	−3.00000	−	5.19615i	−0.161281	−	0.279347i
$347$	−6.00000	−	10.3923i	−0.322097	−	0.557888i	0.658824	−	0.752297i	$-0.271054\pi$
$347$	−6.00000	−	10.3923i	−0.322097	−	0.557888i	−0.980921	+	0.194409i	$0.937721\pi$
$348$		0			0
$349$	5.00000			0.267644			0.133822	−	0.991005i	$-0.457275\pi$
$349$	5.00000			0.267644			0.133822	+	0.991005i	$0.457275\pi$
$350$	−10.0000	+	3.46410i	−0.534522	+	0.185164i
$351$		0			0
$352$	1.50000	−	2.59808i	0.0799503	−	0.138478i
$353$	−4.50000	−	7.79423i	−0.239511	−	0.414845i	0.721063	−	0.692869i	$-0.243654\pi$
$353$	−4.50000	−	7.79423i	−0.239511	−	0.414845i	−0.960574	+	0.278024i	$0.910320\pi$
$354$		0			0
$355$		0			0
$356$	−15.0000			−0.794998
$357$		0			0
$358$	3.00000			0.158555
$359$	7.50000	−	12.9904i	0.395835	−	0.685606i	−0.597372	−	0.801964i	$-0.703789\pi$
$359$	7.50000	−	12.9904i	0.395835	−	0.685606i	0.993207	+	0.116358i	$0.0371219\pi$
$360$		0			0
$361$	−3.00000	−	5.19615i	−0.157895	−	0.273482i
$362$	−5.00000	+	8.66025i	−0.262794	+	0.455173i
$363$		0			0
$364$	−10.0000	−	8.66025i	−0.524142	−	0.453921i
$365$	33.0000			1.72730
$366$		0			0
$367$	0.500000	+	0.866025i	0.0260998	+	0.0452062i	0.878780	−	0.477227i	$-0.158358\pi$
$367$	0.500000	+	0.866025i	0.0260998	+	0.0452062i	−0.852680	+	0.522433i	$0.825025\pi$
$368$	−1.50000	−	2.59808i	−0.0781929	−	0.135434i
$369$		0			0
$370$	21.0000			1.09174
$371$	−6.00000	−	5.19615i	−0.311504	−	0.269771i
$372$		0			0
$373$	−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	$0.311728\pi$
$374$	−4.50000	−	7.79423i	−0.232689	−	0.403030i
$375$		0			0
$376$		0			0
$377$	15.0000			0.772539
$378$		0			0
$379$	−16.0000			−0.821865			−0.410932	−	0.911666i	$-0.634797\pi$
$379$	−16.0000			−0.821865			−0.410932	+	0.911666i	$0.634797\pi$
$380$	−7.50000	+	12.9904i	−0.384742	+	0.666392i
$381$		0			0
$382$	−6.00000	−	10.3923i	−0.306987	−	0.531717i
$383$	−7.50000	+	12.9904i	−0.383232	+	0.663777i	−0.991522	−	0.129937i	$-0.958522\pi$
$383$	−7.50000	+	12.9904i	−0.383232	+	0.663777i	0.608290	+	0.793715i	$0.291856\pi$
$384$		0			0
$385$	22.5000	−	7.79423i	1.14671	−	0.397231i
$386$	−14.0000			−0.712581
$387$		0			0
$388$	0.500000	+	0.866025i	0.0253837	+	0.0439658i
$389$	4.50000	+	7.79423i	0.228159	+	0.395183i	0.957263	−	0.289220i	$-0.0933960\pi$
$389$	4.50000	+	7.79423i	0.228159	+	0.395183i	−0.729103	+	0.684403i	$0.760063\pi$
$390$		0			0
$391$	−9.00000			−0.455150
$392$	−5.50000	+	4.33013i	−0.277792	+	0.218704i
$393$		0			0
$394$	3.00000	−	5.19615i	0.151138	−	0.261778i
$395$	−12.0000	−	20.7846i	−0.603786	−	1.04579i
$396$		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	$0.907240\pi$
$398$	7.00000			0.350878
$399$		0			0
$400$	4.00000			0.200000
$401$	13.5000	−	23.3827i	0.674158	−	1.16768i	−0.302556	−	0.953131i	$-0.597840\pi$
$401$	13.5000	−	23.3827i	0.674158	−	1.16768i	0.976714	−	0.214544i	$-0.0688266\pi$
$402$		0			0
$403$	10.0000	+	17.3205i	0.498135	+	0.862796i
$404$	−1.50000	+	2.59808i	−0.0746278	+	0.129259i
$405$		0			0
$406$	1.50000	−	7.79423i	0.0744438	−	0.386821i
$407$	−21.0000			−1.04093
$408$		0			0
$409$	11.0000	+	19.0526i	0.543915	+	0.942088i	0.998674	+	0.0514740i	$0.0163919\pi$
$409$	11.0000	+	19.0526i	0.543915	+	0.942088i	−0.454759	+	0.890614i	$0.650275\pi$
$410$	13.5000	+	23.3827i	0.666717	+	1.15479i
$411$		0			0
$412$	5.00000			0.246332
$413$	24.0000	+	20.7846i	1.18096	+	1.02274i
$414$		0			0
$415$	4.50000	−	7.79423i	0.220896	−	0.382604i
$416$	2.50000	+	4.33013i	0.122573	+	0.212302i
$417$		0			0
$418$	7.50000	−	12.9904i	0.366837	−	0.635380i
$419$	3.00000			0.146560			0.0732798	−	0.997311i	$-0.476653\pi$
$419$	3.00000			0.146560			0.0732798	+	0.997311i	$0.476653\pi$
$420$		0			0
$421$	−31.0000			−1.51085			−0.755424	−	0.655237i	$-0.772569\pi$
$421$	−31.0000			−1.51085			−0.755424	+	0.655237i	$0.772569\pi$
$422$	2.50000	−	4.33013i	0.121698	−	0.210787i
$423$		0			0
$424$	1.50000	+	2.59808i	0.0728464	+	0.126174i
$425$	6.00000	−	10.3923i	0.291043	−	0.504101i
$426$		0			0
$427$	−1.00000	+	5.19615i	−0.0483934	+	0.251459i
$428$	15.0000			0.725052
$429$		0			0
$430$	16.5000	+	28.5788i	0.795701	+	1.37819i
$431$	−1.50000	−	2.59808i	−0.0722525	−	0.125145i	0.827636	−	0.561266i	$-0.189685\pi$
$431$	−1.50000	−	2.59808i	−0.0722525	−	0.125145i	−0.899888	+	0.436121i	$0.856352\pi$
$432$		0			0
$433$	14.0000			0.672797			0.336399	−	0.941720i	$-0.390791\pi$
$433$	14.0000			0.672797			0.336399	+	0.941720i	$0.390791\pi$
$434$	10.0000	−	3.46410i	0.480015	−	0.166282i
$435$		0			0
$436$	3.50000	−	6.06218i	0.167620	−	0.290326i
$437$	−7.50000	−	12.9904i	−0.358774	−	0.621414i
$438$		0			0
$439$	−4.00000	+	6.92820i	−0.190910	+	0.330665i	−0.945552	−	0.325471i	$-0.894477\pi$
$439$	−4.00000	+	6.92820i	−0.190910	+	0.330665i	0.754642	+	0.656136i	$0.227810\pi$
$440$	−9.00000			−0.429058
$441$		0			0
$442$	15.0000			0.713477
$443$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$443$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$444$		0			0
$445$	22.5000	+	38.9711i	1.06660	+	1.84741i
$446$	8.50000	−	14.7224i	0.402487	−	0.697127i
$447$		0			0
$448$	2.50000	−	0.866025i	0.118114	−	0.0409159i
$449$	−30.0000			−1.41579			−0.707894	−	0.706319i	$-0.750354\pi$
$449$	−30.0000			−1.41579			−0.707894	+	0.706319i	$0.750354\pi$
$450$		0			0
$451$	−13.5000	−	23.3827i	−0.635690	−	1.10105i
$452$	7.50000	+	12.9904i	0.352770	+	0.611016i
$453$		0			0
$454$	9.00000			0.422391
$455$	−7.50000	+	38.9711i	−0.351605	+	1.82700i
$456$		0			0
$457$	17.0000	−	29.4449i	0.795226	−	1.37737i	−0.127469	−	0.991843i	$-0.540685\pi$
$457$	17.0000	−	29.4449i	0.795226	−	1.37737i	0.922695	−	0.385530i	$-0.125981\pi$
$458$	8.50000	+	14.7224i	0.397179	+	0.687934i
$459$		0			0
$460$	−4.50000	+	7.79423i	−0.209814	+	0.363408i
$461$	−9.00000			−0.419172			−0.209586	−	0.977790i	$-0.567212\pi$
$461$	−9.00000			−0.419172			−0.209586	+	0.977790i	$0.567212\pi$
$462$		0			0
$463$	35.0000			1.62659			0.813294	−	0.581853i	$-0.197672\pi$
$463$	35.0000			1.62659			0.813294	+	0.581853i	$0.197672\pi$
$464$	−1.50000	+	2.59808i	−0.0696358	+	0.120613i
$465$		0			0
$466$	−13.5000	−	23.3827i	−0.625375	−	1.08318i
$467$	−1.50000	+	2.59808i	−0.0694117	+	0.120225i	−0.898642	−	0.438682i	$-0.855446\pi$
$467$	−1.50000	+	2.59808i	−0.0694117	+	0.120225i	0.829231	+	0.558906i	$0.188779\pi$
$468$		0			0
$469$	8.00000	+	6.92820i	0.369406	+	0.319915i
$470$		0			0
$471$		0			0
$472$	−6.00000	−	10.3923i	−0.276172	−	0.478345i
$473$	−16.5000	−	28.5788i	−0.758671	−	1.31406i
$474$		0			0
$475$	20.0000			0.917663
$476$	1.50000	−	7.79423i	0.0687524	−	0.357248i
$477$		0			0
$478$	−13.5000	+	23.3827i	−0.617476	+	1.06950i
$479$	−4.50000	−	7.79423i	−0.205610	−	0.356127i	0.744717	−	0.667381i	$-0.232585\pi$
$479$	−4.50000	−	7.79423i	−0.205610	−	0.356127i	−0.950327	+	0.311253i	$0.899251\pi$
$480$		0			0
$481$	17.5000	−	30.3109i	0.797931	−	1.38206i
$482$	−23.0000			−1.04762
$483$		0			0
$484$	−2.00000			−0.0909091
$485$	1.50000	−	2.59808i	0.0681115	−	0.117973i
$486$		0			0
$487$	15.5000	+	26.8468i	0.702372	+	1.21654i	0.967632	+	0.252367i	$0.0812090\pi$
$487$	15.5000	+	26.8468i	0.702372	+	1.21654i	−0.265260	+	0.964177i	$0.585458\pi$
$488$	1.00000	−	1.73205i	0.0452679	−	0.0784063i
$489$		0			0
$490$	19.5000	+	7.79423i	0.880920	+	0.352107i
$491$	39.0000			1.76005			0.880023	−	0.474932i	$-0.157527\pi$
$491$	39.0000			1.76005			0.880023	+	0.474932i	$0.157527\pi$
$492$		0			0
$493$	4.50000	+	7.79423i	0.202670	+	0.351034i
$494$	12.5000	+	21.6506i	0.562402	+	0.974108i
$495$		0			0
$496$	−4.00000			−0.179605
$497$		0			0
$498$		0			0
$499$	−5.50000	+	9.52628i	−0.246214	+	0.426455i	−0.962472	−	0.271380i	$-0.912520\pi$
$499$	−5.50000	+	9.52628i	−0.246214	+	0.426455i	0.716258	+	0.697835i	$0.245853\pi$
$500$	1.50000	+	2.59808i	0.0670820	+	0.116190i
$501$		0			0
$502$	−6.00000	+	10.3923i	−0.267793	+	0.463831i
$503$	12.0000			0.535054			0.267527	−	0.963550i	$-0.413794\pi$
$503$	12.0000			0.535054			0.267527	+	0.963550i	$0.413794\pi$
$504$		0			0
$505$	9.00000			0.400495
$506$	4.50000	−	7.79423i	0.200049	−	0.346496i
$507$		0			0
$508$	8.00000	+	13.8564i	0.354943	+	0.614779i
$509$	−13.5000	+	23.3827i	−0.598377	+	1.03642i	0.394684	+	0.918817i	$0.370854\pi$
$509$	−13.5000	+	23.3827i	−0.598377	+	1.03642i	−0.993061	+	0.117602i	$0.962479\pi$
$510$		0			0
$511$	−22.0000	−	19.0526i	−0.973223	−	0.842836i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−7.50000	−	12.9904i	−0.330811	−	0.572981i
$515$	−7.50000	−	12.9904i	−0.330489	−	0.572425i
$516$		0			0
$517$		0			0
$518$	−14.0000	−	12.1244i	−0.615125	−	0.532714i
$519$		0			0
$520$	7.50000	−	12.9904i	0.328897	−	0.569666i
$521$	1.50000	+	2.59808i	0.0657162	+	0.113824i	0.897011	−	0.442007i	$-0.145733\pi$
$521$	1.50000	+	2.59808i	0.0657162	+	0.113824i	−0.831295	+	0.555831i	$0.812400\pi$
$522$		0			0
$523$	3.50000	−	6.06218i	0.153044	−	0.265081i	−0.779301	−	0.626650i	$-0.784426\pi$
$523$	3.50000	−	6.06218i	0.153044	−	0.265081i	0.932345	+	0.361569i	$0.117759\pi$
$524$	−3.00000			−0.131056
$525$		0			0
$526$	−9.00000			−0.392419
$527$	−6.00000	+	10.3923i	−0.261364	+	0.452696i
$528$		0			0
$529$	7.00000	+	12.1244i	0.304348	+	0.527146i
$530$	4.50000	−	7.79423i	0.195468	−	0.338560i
$531$		0			0
$532$	12.5000	−	4.33013i	0.541944	−	0.187735i
$533$	45.0000			1.94917
$534$		0			0
$535$	−22.5000	−	38.9711i	−0.972760	−	1.68487i
$536$	−2.00000	−	3.46410i	−0.0863868	−	0.149626i
$537$		0			0
$538$	21.0000			0.905374
$539$	−19.5000	−	7.79423i	−0.839924	−	0.335721i
$540$		0			0
$541$	−8.50000	+	14.7224i	−0.365444	+	0.632967i	−0.988847	−	0.148933i	$-0.952416\pi$
$541$	−8.50000	+	14.7224i	−0.365444	+	0.632967i	0.623404	+	0.781900i	$0.285749\pi$
$542$	−6.50000	−	11.2583i	−0.279199	−	0.483587i
$543$		0			0
$544$	−1.50000	+	2.59808i	−0.0643120	+	0.111392i
$545$	−21.0000			−0.899541
$546$		0			0
$547$	11.0000			0.470326			0.235163	−	0.971956i	$-0.424438\pi$
$547$	11.0000			0.470326			0.235163	+	0.971956i	$0.424438\pi$
$548$	1.50000	−	2.59808i	0.0640768	−	0.110984i
$549$		0			0
$550$	6.00000	+	10.3923i	0.255841	+	0.443129i
$551$	−7.50000	+	12.9904i	−0.319511	+	0.553409i
$552$		0			0
$553$	−4.00000	+	20.7846i	−0.170097	+	0.883852i
$554$	7.00000			0.297402
$555$		0			0
$556$	−2.50000	−	4.33013i	−0.106024	−	0.183638i
$557$	−1.50000	−	2.59808i	−0.0635570	−	0.110084i	0.832496	−	0.554031i	$-0.186911\pi$
$557$	−1.50000	−	2.59808i	−0.0635570	−	0.110084i	−0.896053	+	0.443947i	$0.853578\pi$
$558$		0			0
$559$	55.0000			2.32625
$560$	−6.00000	−	5.19615i	−0.253546	−	0.219578i
$561$		0			0
$562$	−1.50000	+	2.59808i	−0.0632737	+	0.109593i
$563$	−6.00000	−	10.3923i	−0.252870	−	0.437983i	0.711445	−	0.702742i	$-0.248041\pi$
$563$	−6.00000	−	10.3923i	−0.252870	−	0.437983i	−0.964315	+	0.264758i	$0.914708\pi$
$564$		0			0
$565$	22.5000	−	38.9711i	0.946582	−	1.63953i
$566$	−8.00000			−0.336265
$567$		0			0
$568$		0			0
$569$	15.0000	−	25.9808i	0.628833	−	1.08917i	−0.358954	−	0.933355i	$-0.616866\pi$
$569$	15.0000	−	25.9808i	0.628833	−	1.08917i	0.987786	−	0.155815i	$-0.0498003\pi$
$570$		0			0
$571$	−10.0000	−	17.3205i	−0.418487	−	0.724841i	0.577301	−	0.816532i	$-0.304106\pi$
$571$	−10.0000	−	17.3205i	−0.418487	−	0.724841i	−0.995788	+	0.0916910i	$0.970773\pi$
$572$	−7.50000	+	12.9904i	−0.313591	+	0.543155i
$573$		0			0
$574$	4.50000	−	23.3827i	0.187826	−	0.975974i
$575$	12.0000			0.500435
$576$		0			0
$577$	−5.50000	−	9.52628i	−0.228968	−	0.396584i	0.728535	−	0.685009i	$-0.240202\pi$
$577$	−5.50000	−	9.52628i	−0.228968	−	0.396584i	−0.957503	+	0.288425i	$0.906868\pi$
$578$	−4.00000	−	6.92820i	−0.166378	−	0.288175i
$579$		0			0
$580$	9.00000			0.373705
$581$	−7.50000	+	2.59808i	−0.311152	+	0.107786i
$582$		0			0
$583$	−4.50000	+	7.79423i	−0.186371	+	0.322804i
$584$	5.50000	+	9.52628i	0.227592	+	0.394200i
$585$		0			0
$586$	13.5000	−	23.3827i	0.557680	−	0.965930i
$587$	33.0000			1.36206			0.681028	−	0.732257i	$-0.261533\pi$
$587$	33.0000			1.36206			0.681028	+	0.732257i	$0.261533\pi$
$588$		0			0
$589$	−20.0000			−0.824086
$590$	−18.0000	+	31.1769i	−0.741048	+	1.28353i
$591$		0			0
$592$	3.50000	+	6.06218i	0.143849	+	0.249154i
$593$	−10.5000	+	18.1865i	−0.431183	+	0.746831i	−0.996976	−	0.0777165i	$-0.975237\pi$
$593$	−10.5000	+	18.1865i	−0.431183	+	0.746831i	0.565792	+	0.824548i	$0.308570\pi$
$594$		0			0
$595$	−22.5000	+	7.79423i	−0.922410	+	0.319532i
$596$	3.00000			0.122885
$597$		0			0
$598$	7.50000	+	12.9904i	0.306698	+	0.531216i
$599$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$599$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$600$		0			0
$601$	−1.00000			−0.0407909			−0.0203954	−	0.999792i	$-0.506493\pi$
$601$	−1.00000			−0.0407909			−0.0203954	+	0.999792i	$0.506493\pi$
$602$	5.50000	−	28.5788i	0.224163	−	1.16479i
$603$		0			0
$604$	−5.50000	+	9.52628i	−0.223792	+	0.387619i
$605$	3.00000	+	5.19615i	0.121967	+	0.211254i
$606$		0			0
$607$	21.5000	−	37.2391i	0.872658	−	1.51149i	0.0134214	−	0.999910i	$-0.495728\pi$
$607$	21.5000	−	37.2391i	0.872658	−	1.51149i	0.859237	−	0.511578i	$-0.170939\pi$
$608$	−5.00000			−0.202777
$609$		0			0
$610$	−6.00000			−0.242933
$611$		0			0
$612$		0			0
$613$	15.5000	+	26.8468i	0.626039	+	1.08433i	0.988339	+	0.152270i	$0.0486583\pi$
$613$	15.5000	+	26.8468i	0.626039	+	1.08433i	−0.362300	+	0.932062i	$0.618008\pi$
$614$	−14.0000	+	24.2487i	−0.564994	+	0.978598i
$615$		0			0
$616$	6.00000	+	5.19615i	0.241747	+	0.209359i
$617$	−3.00000			−0.120775			−0.0603877	−	0.998175i	$-0.519234\pi$
$617$	−3.00000			−0.120775			−0.0603877	+	0.998175i	$0.519234\pi$
$618$		0			0
$619$	9.50000	+	16.4545i	0.381837	+	0.661361i	0.991325	−	0.131434i	$-0.0419582\pi$
$619$	9.50000	+	16.4545i	0.381837	+	0.661361i	−0.609488	+	0.792796i	$0.708625\pi$
$620$	6.00000	+	10.3923i	0.240966	+	0.417365i
$621$		0			0
$622$	−24.0000			−0.962312
$623$	7.50000	−	38.9711i	0.300481	−	1.56135i
$624$		0			0
$625$	14.5000	−	25.1147i	0.580000	−	1.00459i
$626$	7.00000	+	12.1244i	0.279776	+	0.484587i
$627$		0			0
$628$	−7.00000	+	12.1244i	−0.279330	+	0.483814i
$629$	21.0000			0.837325
$630$		0			0
$631$	8.00000			0.318475			0.159237	−	0.987240i	$-0.449096\pi$
$631$	8.00000			0.318475			0.159237	+	0.987240i	$0.449096\pi$
$632$	4.00000	−	6.92820i	0.159111	−	0.275589i
$633$		0			0
$634$	−15.0000	−	25.9808i	−0.595726	−	1.03183i
$635$	24.0000	−	41.5692i	0.952411	−	1.64962i
$636$		0			0
$637$	27.5000	−	21.6506i	1.08959	−	0.857829i
$638$	−9.00000			−0.356313
$639$		0			0
$640$	1.50000	+	2.59808i	0.0592927	+	0.102698i
$641$	−22.5000	−	38.9711i	−0.888697	−	1.53927i	−0.841417	−	0.540386i	$-0.818278\pi$
$641$	−22.5000	−	38.9711i	−0.888697	−	1.53927i	−0.0472793	−	0.998882i	$-0.515055\pi$
$642$		0			0
$643$	29.0000			1.14365			0.571824	−	0.820376i	$-0.306236\pi$
$643$	29.0000			1.14365			0.571824	+	0.820376i	$0.306236\pi$
$644$	7.50000	−	2.59808i	0.295541	−	0.102379i
$645$		0			0
$646$	−7.50000	+	12.9904i	−0.295084	+	0.511100i
$647$	−1.50000	−	2.59808i	−0.0589711	−	0.102141i	0.835033	−	0.550200i	$-0.185449\pi$
$647$	−1.50000	−	2.59808i	−0.0589711	−	0.102141i	−0.894004	+	0.448059i	$0.852115\pi$
$648$		0			0
$649$	18.0000	−	31.1769i	0.706562	−	1.22380i
$650$	−20.0000			−0.784465
$651$		0			0
$652$	17.0000			0.665771
$653$	4.50000	−	7.79423i	0.176099	−	0.305012i	−0.764442	−	0.644692i	$-0.776986\pi$
$653$	4.50000	−	7.79423i	0.176099	−	0.305012i	0.940541	+	0.339680i	$0.110319\pi$
$654$		0			0
$655$	4.50000	+	7.79423i	0.175830	+	0.304546i
$656$	−4.50000	+	7.79423i	−0.175695	+	0.304314i
$657$		0			0
$658$		0			0
$659$	−39.0000			−1.51922			−0.759612	−	0.650376i	$-0.774611\pi$
$659$	−39.0000			−1.51922			−0.759612	+	0.650376i	$0.774611\pi$
$660$		0			0
$661$	−7.00000	−	12.1244i	−0.272268	−	0.471583i	0.697174	−	0.716902i	$-0.254441\pi$
$661$	−7.00000	−	12.1244i	−0.272268	−	0.471583i	−0.969442	+	0.245319i	$0.921107\pi$
$662$	10.0000	+	17.3205i	0.388661	+	0.673181i
$663$		0			0
$664$	3.00000			0.116423
$665$	−30.0000	−	25.9808i	−1.16335	−	1.00749i
$666$		0			0
$667$	−4.50000	+	7.79423i	−0.174241	+	0.301794i
$668$	1.50000	+	2.59808i	0.0580367	+	0.100523i
$669$		0			0
$670$	−6.00000	+	10.3923i	−0.231800	+	0.401490i
$671$	6.00000			0.231627
$672$		0			0
$673$	11.0000			0.424019			0.212009	−	0.977268i	$-0.431999\pi$
$673$	11.0000			0.424019			0.212009	+	0.977268i	$0.431999\pi$
$674$	−12.5000	+	21.6506i	−0.481482	+	0.833951i
$675$		0			0
$676$	−6.00000	−	10.3923i	−0.230769	−	0.399704i
$677$	3.00000	−	5.19615i	0.115299	−	0.199704i	−0.802600	−	0.596518i	$-0.796551\pi$
$677$	3.00000	−	5.19615i	0.115299	−	0.199704i	0.917899	+	0.396813i	$0.129884\pi$
$678$		0			0
$679$	−2.50000	+	0.866025i	−0.0959412	+	0.0332350i
$680$	9.00000			0.345134
$681$		0			0
$682$	−6.00000	−	10.3923i	−0.229752	−	0.397942i
$683$	−16.5000	−	28.5788i	−0.631355	−	1.09354i	−0.987275	−	0.159022i	$-0.949166\pi$
$683$	−16.5000	−	28.5788i	−0.631355	−	1.09354i	0.355920	−	0.934516i	$-0.384168\pi$
$684$		0			0
$685$	−9.00000			−0.343872
$686$	−8.50000	−	16.4545i	−0.324532	−	0.628235i
$687$		0			0
$688$	−5.50000	+	9.52628i	−0.209686	+	0.363186i
$689$	−7.50000	−	12.9904i	−0.285727	−	0.494894i
$690$		0			0
$691$	−10.0000	+	17.3205i	−0.380418	+	0.658903i	−0.991122	−	0.132956i	$-0.957553\pi$
$691$	−10.0000	+	17.3205i	−0.380418	+	0.658903i	0.610704	+	0.791859i	$0.290887\pi$
$692$	−6.00000			−0.228086
$693$		0			0
$694$	−12.0000			−0.455514
$695$	−7.50000	+	12.9904i	−0.284491	+	0.492753i
$696$		0			0
$697$	13.5000	+	23.3827i	0.511349	+	0.885682i
$698$	2.50000	−	4.33013i	0.0946264	−	0.163898i
$699$		0			0
$700$	−2.00000	+	10.3923i	−0.0755929	+	0.392792i
$701$	−6.00000			−0.226617			−0.113308	−	0.993560i	$-0.536145\pi$
$701$	−6.00000			−0.226617			−0.113308	+	0.993560i	$0.536145\pi$
$702$		0			0
$703$	17.5000	+	30.3109i	0.660025	+	1.14320i
$704$	−1.50000	−	2.59808i	−0.0565334	−	0.0979187i
$705$		0			0
$706$	−9.00000			−0.338719
$707$	−6.00000	−	5.19615i	−0.225653	−	0.195421i
$708$		0			0
$709$	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
$711$		0			0
$712$	−7.50000	+	12.9904i	−0.281074	+	0.486835i
$713$	−12.0000			−0.449404
$714$		0			0
$715$	45.0000			1.68290
$716$	1.50000	−	2.59808i	0.0560576	−	0.0970947i
$717$		0			0
$718$	−7.50000	−	12.9904i	−0.279898	−	0.484797i
$719$	19.5000	−	33.7750i	0.727227	−	1.25959i	−0.230823	−	0.972996i	$-0.574142\pi$
$719$	19.5000	−	33.7750i	0.727227	−	1.25959i	0.958051	−	0.286599i	$-0.0925247\pi$
$720$		0			0
$721$	−2.50000	+	12.9904i	−0.0931049	+	0.483787i
$722$	−6.00000			−0.223297
$723$		0			0
$724$	5.00000	+	8.66025i	0.185824	+	0.321856i
$725$	−6.00000	−	10.3923i	−0.222834	−	0.385961i
$726$		0			0
$727$	5.00000			0.185440			0.0927199	−	0.995692i	$-0.470444\pi$
$727$	5.00000			0.185440			0.0927199	+	0.995692i	$0.470444\pi$
$728$	−12.5000	+	4.33013i	−0.463281	+	0.160485i
$729$		0			0
$730$	16.5000	−	28.5788i	0.610692	−	1.05775i
$731$	16.5000	+	28.5788i	0.610275	+	1.05703i
$732$		0			0
$733$	−20.5000	+	35.5070i	−0.757185	+	1.31148i	0.187096	+	0.982342i	$0.440092\pi$
$733$	−20.5000	+	35.5070i	−0.757185	+	1.31148i	−0.944281	+	0.329141i	$0.893241\pi$
$734$	1.00000			0.0369107
$735$		0			0
$736$	−3.00000			−0.110581
$737$	6.00000	−	10.3923i	0.221013	−	0.382805i
$738$		0			0
$739$	−23.5000	−	40.7032i	−0.864461	−	1.49729i	−0.867581	−	0.497296i	$-0.834326\pi$
$739$	−23.5000	−	40.7032i	−0.864461	−	1.49729i	0.00311943	−	0.999995i	$-0.499007\pi$
$740$	10.5000	−	18.1865i	0.385988	−	0.668550i
$741$		0			0
$742$	−7.50000	+	2.59808i	−0.275334	+	0.0953784i
$743$	−3.00000			−0.110059			−0.0550297	−	0.998485i	$-0.517525\pi$
$743$	−3.00000			−0.110059			−0.0550297	+	0.998485i	$0.517525\pi$
$744$		0			0
$745$	−4.50000	−	7.79423i	−0.164867	−	0.285558i
$746$	8.50000	+	14.7224i	0.311207	+	0.539027i
$747$		0			0
$748$	−9.00000			−0.329073
$749$	−7.50000	+	38.9711i	−0.274044	+	1.42397i
$750$		0			0
$751$	−14.5000	+	25.1147i	−0.529113	+	0.916450i	0.470311	+	0.882501i	$0.344142\pi$
$751$	−14.5000	+	25.1147i	−0.529113	+	0.916450i	−0.999424	+	0.0339490i	$0.989192\pi$
$752$		0			0
$753$		0			0
$754$	7.50000	−	12.9904i	0.273134	−	0.473082i
$755$	33.0000			1.20099
$756$		0			0
$757$	14.0000			0.508839			0.254419	−	0.967094i	$-0.418116\pi$
$757$	14.0000			0.508839			0.254419	+	0.967094i	$0.418116\pi$
$758$	−8.00000	+	13.8564i	−0.290573	+	0.503287i
$759$		0			0
$760$	7.50000	+	12.9904i	0.272054	+	0.471211i
$761$	1.50000	−	2.59808i	0.0543750	−	0.0941802i	−0.837557	−	0.546350i	$-0.816017\pi$
$761$	1.50000	−	2.59808i	0.0543750	−	0.0941802i	0.891932	+	0.452170i	$0.149350\pi$
$762$		0			0
$763$	14.0000	+	12.1244i	0.506834	+	0.438931i
$764$	−12.0000			−0.434145
$765$		0			0
$766$	7.50000	+	12.9904i	0.270986	+	0.469362i
$767$	30.0000	+	51.9615i	1.08324	+	1.87622i
$768$		0			0
$769$	−1.00000			−0.0360609			−0.0180305	−	0.999837i	$-0.505740\pi$
$769$	−1.00000			−0.0360609			−0.0180305	+	0.999837i	$0.505740\pi$
$770$	4.50000	−	23.3827i	0.162169	−	0.842654i
$771$		0			0
$772$	−7.00000	+	12.1244i	−0.251936	+	0.436365i
$773$	10.5000	+	18.1865i	0.377659	+	0.654124i	0.990721	−	0.135910i	$-0.0433959\pi$
$773$	10.5000	+	18.1865i	0.377659	+	0.654124i	−0.613062	+	0.790034i	$0.710063\pi$
$774$		0			0
$775$	8.00000	−	13.8564i	0.287368	−	0.497737i
$776$	1.00000			0.0358979
$777$		0			0
$778$	9.00000			0.322666
$779$	−22.5000	+	38.9711i	−0.806146	+	1.39629i
$780$		0			0
$781$		0			0
$782$	−4.50000	+	7.79423i	−0.160920	+	0.278721i
$783$		0			0
$784$	1.00000	+	6.92820i	0.0357143	+	0.247436i
$785$	42.0000			1.49904
$786$		0			0
$787$	−22.0000	−	38.1051i	−0.784215	−	1.35830i	−0.929467	−	0.368906i	$-0.879732\pi$
$787$	−22.0000	−	38.1051i	−0.784215	−	1.35830i	0.145251	−	0.989395i	$-0.453601\pi$
$788$	−3.00000	−	5.19615i	−0.106871	−	0.185105i
$789$		0			0
$790$	−24.0000			−0.853882
$791$	−37.5000	+	12.9904i	−1.33335	+	0.461885i
$792$		0			0
$793$	−5.00000	+	8.66025i	−0.177555	+	0.307535i
$794$	14.5000	+	25.1147i	0.514586	+	0.891289i
$795$		0			0
$796$	3.50000	−	6.06218i	0.124054	−	0.214868i
$797$	27.0000			0.956389			0.478195	−	0.878254i	$-0.341291\pi$
$797$	27.0000			0.956389			0.478195	+	0.878254i	$0.341291\pi$
$798$		0			0
$799$		0			0
$800$	2.00000	−	3.46410i	0.0707107	−	0.122474i
$801$		0			0
$802$	−13.5000	−	23.3827i	−0.476702	−	0.825671i
$803$	−16.5000	+	28.5788i	−0.582272	+	1.00853i
$804$		0			0
$805$	−18.0000	−	15.5885i	−0.634417	−	0.549421i
$806$	20.0000			0.704470
$807$		0			0
$808$	1.50000	+	2.59808i	0.0527698	+	0.0914000i
$809$	19.5000	+	33.7750i	0.685583	+	1.18747i	0.973253	+	0.229736i	$0.0737862\pi$
$809$	19.5000	+	33.7750i	0.685583	+	1.18747i	−0.287670	+	0.957730i	$0.592880\pi$
$810$		0			0
$811$	20.0000			0.702295			0.351147	−	0.936320i	$-0.385792\pi$
$811$	20.0000			0.702295			0.351147	+	0.936320i	$0.385792\pi$
$812$	−6.00000	−	5.19615i	−0.210559	−	0.182349i
$813$		0			0
$814$	−10.5000	+	18.1865i	−0.368025	+	0.637438i
$815$	−25.5000	−	44.1673i	−0.893226	−	1.54711i
$816$		0			0
$817$	−27.5000	+	47.6314i	−0.962103	+	1.66641i
$818$	22.0000			0.769212
$819$		0			0
$820$	27.0000			0.942881
$821$	−27.0000	+	46.7654i	−0.942306	+	1.63212i	−0.181250	+	0.983437i	$0.558014\pi$
$821$	−27.0000	+	46.7654i	−0.942306	+	1.63212i	−0.761056	+	0.648686i	$0.775319\pi$
$822$		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	$0.587782\pi$
$824$	2.50000	−	4.33013i	0.0870916	−	0.150847i
$825$		0			0
$826$	30.0000	−	10.3923i	1.04383	−	0.361595i
$827$	24.0000			0.834562			0.417281	−	0.908778i	$-0.362983\pi$
$827$	24.0000			0.834562			0.417281	+	0.908778i	$0.362983\pi$
$828$		0			0
$829$	−20.5000	−	35.5070i	−0.711994	−	1.23321i	−0.964107	−	0.265513i	$-0.914459\pi$
$829$	−20.5000	−	35.5070i	−0.711994	−	1.23321i	0.252113	−	0.967698i	$-0.418875\pi$
$830$	−4.50000	−	7.79423i	−0.156197	−	0.270542i
$831$		0			0
$832$	5.00000			0.173344
$833$	19.5000	+	7.79423i	0.675635	+	0.270054i
$834$		0			0
$835$	4.50000	−	7.79423i	0.155729	−	0.269730i
$836$	−7.50000	−	12.9904i	−0.259393	−	0.449282i
$837$		0			0
$838$	1.50000	−	2.59808i	0.0518166	−	0.0897491i
$839$	39.0000			1.34643			0.673215	−	0.739447i	$-0.264913\pi$
$839$	39.0000			1.34643			0.673215	+	0.739447i	$0.264913\pi$
$840$		0			0
$841$	−20.0000			−0.689655
$842$	−15.5000	+	26.8468i	−0.534165	+	0.925201i
$843$		0			0
$844$	−2.50000	−	4.33013i	−0.0860535	−	0.149049i
$845$	−18.0000	+	31.1769i	−0.619219	+	1.07252i
$846$		0			0
$847$	1.00000	−	5.19615i	0.0343604	−	0.178542i
$848$	3.00000			0.103020
$849$		0			0
$850$	−6.00000	−	10.3923i	−0.205798	−	0.356453i
$851$	10.5000	+	18.1865i	0.359935	+	0.623426i
$852$		0			0
$853$	17.0000			0.582069			0.291034	−	0.956713i	$-0.406001\pi$
$853$	17.0000			0.582069			0.291034	+	0.956713i	$0.406001\pi$
$854$	4.00000	+	3.46410i	0.136877	+	0.118539i
$855$		0			0
$856$	7.50000	−	12.9904i	0.256345	−	0.444002i
$857$	−16.5000	−	28.5788i	−0.563629	−	0.976235i	−0.997176	−	0.0751033i	$-0.976071\pi$
$857$	−16.5000	−	28.5788i	−0.563629	−	0.976235i	0.433546	−	0.901131i	$-0.357262\pi$
$858$		0			0
$859$	−5.50000	+	9.52628i	−0.187658	+	0.325032i	−0.944469	−	0.328601i	$-0.893423\pi$
$859$	−5.50000	+	9.52628i	−0.187658	+	0.325032i	0.756811	+	0.653633i	$0.226756\pi$
$860$	33.0000			1.12529
$861$		0			0
$862$	−3.00000			−0.102180
$863$	7.50000	−	12.9904i	0.255303	−	0.442198i	−0.709675	−	0.704529i	$-0.751158\pi$
$863$	7.50000	−	12.9904i	0.255303	−	0.442198i	0.964978	+	0.262332i	$0.0844915\pi$
$864$		0			0
$865$	9.00000	+	15.5885i	0.306009	+	0.530023i
$866$	7.00000	−	12.1244i	0.237870	−	0.412002i
$867$		0			0
$868$	2.00000	−	10.3923i	0.0678844	−	0.352738i
$869$	24.0000			0.814144
$870$		0			0
$871$	10.0000	+	17.3205i	0.338837	+	0.586883i
$872$	−3.50000	−	6.06218i	−0.118525	−	0.205291i
$873$		0			0
$874$	−15.0000			−0.507383
$875$	−7.50000	+	2.59808i	−0.253546	+	0.0878310i
$876$		0			0
$877$	21.5000	−	37.2391i	0.726003	−	1.25747i	−0.232556	−	0.972583i	$-0.574709\pi$
$877$	21.5000	−	37.2391i	0.726003	−	1.25747i	0.958560	−	0.284892i	$-0.0919577\pi$
$878$	4.00000	+	6.92820i	0.134993	+	0.233816i
$879$		0			0
$880$	−4.50000	+	7.79423i	−0.151695	+	0.262743i
$881$	−6.00000			−0.202145			−0.101073	−	0.994879i	$-0.532227\pi$
$881$	−6.00000			−0.202145			−0.101073	+	0.994879i	$0.532227\pi$
$882$		0			0
$883$	−4.00000			−0.134611			−0.0673054	−	0.997732i	$-0.521440\pi$
$883$	−4.00000			−0.134611			−0.0673054	+	0.997732i	$0.521440\pi$
$884$	7.50000	−	12.9904i	0.252252	−	0.436914i
$885$		0			0
$886$		0			0
$887$	−19.5000	+	33.7750i	−0.654746	+	1.13405i	0.327212	+	0.944951i	$0.393891\pi$
$887$	−19.5000	+	33.7750i	−0.654746	+	1.13405i	−0.981957	+	0.189102i	$0.939442\pi$
$888$		0			0
$889$	−40.0000	+	13.8564i	−1.34156	+	0.464729i
$890$	45.0000			1.50840
$891$		0			0
$892$	−8.50000	−	14.7224i	−0.284601	−	0.492943i
$893$		0			0
$894$		0			0
$895$	−9.00000			−0.300837
$896$	0.500000	−	2.59808i	0.0167038	−	0.0867956i
$897$		0			0
$898$	−15.0000	+	25.9808i	−0.500556	+	0.866989i
$899$	6.00000	+	10.3923i	0.200111	+	0.346603i
$900$		0			0
$901$	4.50000	−	7.79423i	0.149917	−	0.259663i
$902$	−27.0000			−0.899002
$903$		0			0
$904$	15.0000			0.498893
$905$	15.0000	−	25.9808i	0.498617	−	0.863630i
$906$		0			0
$907$	−8.50000	−	14.7224i	−0.282238	−	0.488850i	0.689698	−	0.724097i	$-0.257743\pi$
$907$	−8.50000	−	14.7224i	−0.282238	−	0.488850i	−0.971936	+	0.235247i	$0.924410\pi$
$908$	4.50000	−	7.79423i	0.149338	−	0.258661i
$909$		0			0
$910$	30.0000	+	25.9808i	0.994490	+	0.861254i
$911$	−9.00000			−0.298183			−0.149092	−	0.988823i	$-0.547635\pi$
$911$	−9.00000			−0.298183			−0.149092	+	0.988823i	$0.547635\pi$
$912$		0			0
$913$	4.50000	+	7.79423i	0.148928	+	0.257951i
$914$	−17.0000	−	29.4449i	−0.562310	−	0.973950i
$915$		0			0
$916$	17.0000			0.561696
$917$	1.50000	−	7.79423i	0.0495344	−	0.257388i
$918$		0			0
$919$	0.500000	−	0.866025i	0.0164935	−	0.0285675i	−0.857661	−	0.514216i	$-0.828083\pi$
$919$	0.500000	−	0.866025i	0.0164935	−	0.0285675i	0.874154	+	0.485648i	$0.161416\pi$
$920$	4.50000	+	7.79423i	0.148361	+	0.256968i
$921$		0			0
$922$	−4.50000	+	7.79423i	−0.148200	+	0.256689i
$923$		0			0
$924$		0			0
$925$	−28.0000			−0.920634
$926$	17.5000	−	30.3109i	0.575086	−	0.996078i
$927$		0			0
$928$	1.50000	+	2.59808i	0.0492399	+	0.0852860i
$929$	−9.00000	+	15.5885i	−0.295280	+	0.511441i	−0.975050	−	0.221985i	$-0.928746\pi$
$929$	−9.00000	+	15.5885i	−0.295280	+	0.511441i	0.679770	+	0.733426i	$0.262080\pi$
$930$		0			0
$931$	5.00000	+	34.6410i	0.163868	+	1.13531i
$932$	−27.0000			−0.884414
$933$		0			0
$934$	1.50000	+	2.59808i	0.0490815	+	0.0850117i
$935$	13.5000	+	23.3827i	0.441497	+	0.764696i
$936$		0			0
$937$	−34.0000			−1.11073			−0.555366	−	0.831606i	$-0.687422\pi$
$937$	−34.0000			−1.11073			−0.555366	+	0.831606i	$0.687422\pi$
$938$	10.0000	−	3.46410i	0.326512	−	0.113107i
$939$		0			0
$940$		0			0
$941$	27.0000	+	46.7654i	0.880175	+	1.52451i	0.851146	+	0.524929i	$0.175908\pi$
$941$	27.0000	+	46.7654i	0.880175	+	1.52451i	0.0290288	+	0.999579i	$0.490759\pi$
$942$		0			0
$943$	−13.5000	+	23.3827i	−0.439620	+	0.761445i
$944$	−12.0000			−0.390567
$945$		0			0
$946$	−33.0000			−1.07292
$947$	−6.00000	+	10.3923i	−0.194974	+	0.337705i	−0.946892	−	0.321552i	$-0.895796\pi$
$947$	−6.00000	+	10.3923i	−0.194974	+	0.337705i	0.751918	+	0.659256i	$0.229129\pi$
$948$		0			0
$949$	−27.5000	−	47.6314i	−0.892688	−	1.54618i
$950$	10.0000	−	17.3205i	0.324443	−	0.561951i
$951$		0			0
$952$	−6.00000	−	5.19615i	−0.194461	−	0.168408i
$953$	6.00000			0.194359			0.0971795	−	0.995267i	$-0.469018\pi$
$953$	6.00000			0.194359			0.0971795	+	0.995267i	$0.469018\pi$
$954$		0			0
$955$	18.0000	+	31.1769i	0.582466	+	1.00886i
$956$	13.5000	+	23.3827i	0.436621	+	0.756250i
$957$		0			0
$958$	−9.00000			−0.290777
$959$	6.00000	+	5.19615i	0.193750	+	0.167793i
$960$		0			0
$961$	7.50000	−	12.9904i	0.241935	−	0.419045i
$962$	−17.5000	−	30.3109i	−0.564223	−	0.977262i
$963$		0			0
$964$	−11.5000	+	19.9186i	−0.370390	+	0.641534i
$965$	42.0000			1.35203
$966$		0			0
$967$	−49.0000			−1.57573			−0.787867	−	0.615846i	$-0.788815\pi$
$967$	−49.0000			−1.57573			−0.787867	+	0.615846i	$0.788815\pi$
$968$	−1.00000	+	1.73205i	−0.0321412	+	0.0556702i
$969$		0			0
$970$	−1.50000	−	2.59808i	−0.0481621	−	0.0834192i
$971$	−13.5000	+	23.3827i	−0.433236	+	0.750386i	−0.997150	−	0.0754473i	$-0.975962\pi$
$971$	−13.5000	+	23.3827i	−0.433236	+	0.750386i	0.563914	+	0.825833i	$0.309295\pi$
$972$		0			0
$973$	12.5000	−	4.33013i	0.400732	−	0.138817i
$974$	31.0000			0.993304
$975$		0			0
$976$	−1.00000	−	1.73205i	−0.0320092	−	0.0554416i
$977$	3.00000	+	5.19615i	0.0959785	+	0.166240i	0.910017	−	0.414572i	$-0.136069\pi$
$977$	3.00000	+	5.19615i	0.0959785	+	0.166240i	−0.814038	+	0.580812i	$0.802735\pi$
$978$		0			0
$979$	−45.0000			−1.43821
$980$	16.5000	−	12.9904i	0.527073	−	0.414963i
$981$		0			0
$982$	19.5000	−	33.7750i	0.622270	−	1.07780i
$983$	−10.5000	−	18.1865i	−0.334898	−	0.580060i	0.648567	−	0.761157i	$-0.275369\pi$
$983$	−10.5000	−	18.1865i	−0.334898	−	0.580060i	−0.983465	+	0.181097i	$0.942035\pi$
$984$		0			0
$985$	−9.00000	+	15.5885i	−0.286764	+	0.496690i
$986$	9.00000			0.286618
$987$		0			0
$988$	25.0000			0.795356
$989$	−16.5000	+	28.5788i	−0.524669	+	0.908754i
$990$		0			0
$991$	−14.5000	−	25.1147i	−0.460608	−	0.797796i	0.538384	−	0.842700i	$-0.319035\pi$
$991$	−14.5000	−	25.1147i	−0.460608	−	0.797796i	−0.998991	+	0.0449040i	$0.985702\pi$
$992$	−2.00000	+	3.46410i	−0.0635001	+	0.109985i
$993$		0			0
$994$		0			0
$995$	−21.0000			−0.665745
$996$		0			0
$997$	−20.5000	−	35.5070i	−0.649242	−	1.12452i	−0.983304	−	0.181968i	$-0.941753\pi$
$997$	−20.5000	−	35.5070i	−0.649242	−	1.12452i	0.334063	−	0.942551i	$-0.391580\pi$
$998$	5.50000	+	9.52628i	0.174099	+	0.301549i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1134.2.g.f.163.1		2
3.2	odd	2		1134.2.g.d.163.1		2
7.2	even	3		7938.2.a.o.1.1		1
7.4	even	3	inner	1134.2.g.f.487.1		2
7.5	odd	6		7938.2.a.c.1.1		1
9.2	odd	6		126.2.e.b.121.1	yes	2
9.4	even	3		378.2.h.b.289.1		2
9.5	odd	6		126.2.h.a.79.1	yes	2
9.7	even	3		378.2.e.a.37.1		2
21.2	odd	6		7938.2.a.r.1.1		1
21.5	even	6		7938.2.a.bd.1.1		1
21.11	odd	6		1134.2.g.d.487.1		2
36.7	odd	6		3024.2.q.a.2305.1		2
36.11	even	6		1008.2.q.e.625.1		2
36.23	even	6		1008.2.t.c.961.1		2
36.31	odd	6		3024.2.t.f.289.1		2
63.2	odd	6		882.2.f.e.589.1		2
63.4	even	3		378.2.e.a.235.1		2
63.5	even	6		882.2.f.a.295.1		2
63.11	odd	6		126.2.h.a.67.1	yes	2
63.13	odd	6		2646.2.h.f.667.1		2
63.16	even	3		2646.2.f.e.1765.1		2
63.20	even	6		882.2.e.h.373.1		2
63.23	odd	6		882.2.f.e.295.1		2
63.25	even	3		378.2.h.b.361.1		2
63.31	odd	6		2646.2.e.e.2125.1		2
63.32	odd	6		126.2.e.b.25.1	✓	2
63.34	odd	6		2646.2.e.e.1549.1		2
63.38	even	6		882.2.h.e.67.1		2
63.40	odd	6		2646.2.f.i.883.1		2
63.41	even	6		882.2.h.e.79.1		2
63.47	even	6		882.2.f.a.589.1		2
63.52	odd	6		2646.2.h.f.361.1		2
63.58	even	3		2646.2.f.e.883.1		2
63.59	even	6		882.2.e.h.655.1		2
63.61	odd	6		2646.2.f.i.1765.1		2
252.11	even	6		1008.2.t.c.193.1		2
252.67	odd	6		3024.2.q.a.2881.1		2
252.95	even	6		1008.2.q.e.529.1		2
252.151	odd	6		3024.2.t.f.1873.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.b.25.1	✓	2	63.32	odd	6
126.2.e.b.121.1	yes	2	9.2	odd	6
126.2.h.a.67.1	yes	2	63.11	odd	6
126.2.h.a.79.1	yes	2	9.5	odd	6
378.2.e.a.37.1		2	9.7	even	3
378.2.e.a.235.1		2	63.4	even	3
378.2.h.b.289.1		2	9.4	even	3
378.2.h.b.361.1		2	63.25	even	3
882.2.e.h.373.1		2	63.20	even	6
882.2.e.h.655.1		2	63.59	even	6
882.2.f.a.295.1		2	63.5	even	6
882.2.f.a.589.1		2	63.47	even	6
882.2.f.e.295.1		2	63.23	odd	6
882.2.f.e.589.1		2	63.2	odd	6
882.2.h.e.67.1		2	63.38	even	6
882.2.h.e.79.1		2	63.41	even	6
1008.2.q.e.529.1		2	252.95	even	6
1008.2.q.e.625.1		2	36.11	even	6
1008.2.t.c.193.1		2	252.11	even	6
1008.2.t.c.961.1		2	36.23	even	6
1134.2.g.d.163.1		2	3.2	odd	2
1134.2.g.d.487.1		2	21.11	odd	6
1134.2.g.f.163.1		2	1.1	even	1	trivial
1134.2.g.f.487.1		2	7.4	even	3	inner
2646.2.e.e.1549.1		2	63.34	odd	6
2646.2.e.e.2125.1		2	63.31	odd	6
2646.2.f.e.883.1		2	63.58	even	3
2646.2.f.e.1765.1		2	63.16	even	3
2646.2.f.i.883.1		2	63.40	odd	6
2646.2.f.i.1765.1		2	63.61	odd	6
2646.2.h.f.361.1		2	63.52	odd	6
2646.2.h.f.667.1		2	63.13	odd	6
3024.2.q.a.2305.1		2	36.7	odd	6
3024.2.q.a.2881.1		2	252.67	odd	6
3024.2.t.f.289.1		2	36.31	odd	6
3024.2.t.f.1873.1		2	252.151	odd	6
7938.2.a.c.1.1		1	7.5	odd	6
7938.2.a.o.1.1		1	7.2	even	3
7938.2.a.r.1.1		1	21.2	odd	6
7938.2.a.bd.1.1		1	21.5	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:	\( N \)	\(=\)	\( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1134.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.50000 + 2.59808i) q^{5} +(2.50000 - 0.866025i) q^{7} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{10} +(-1.50000 - 2.59808i) q^{11} +5.00000 q^{13} +(0.500000 - 2.59808i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.50000 + 2.59808i) q^{17} +(-2.50000 + 4.33013i) q^{19} +3.00000 q^{20} -3.00000 q^{22} +(-1.50000 + 2.59808i) q^{23} +(-2.00000 - 3.46410i) q^{25} +(2.50000 - 4.33013i) q^{26} +(-2.00000 - 1.73205i) q^{28} +3.00000 q^{29} +(2.00000 + 3.46410i) q^{31} +(0.500000 + 0.866025i) q^{32} +3.00000 q^{34} +(-1.50000 + 7.79423i) q^{35} +(3.50000 - 6.06218i) q^{37} +(2.50000 + 4.33013i) q^{38} +(1.50000 - 2.59808i) q^{40} +9.00000 q^{41} +11.0000 q^{43} +(-1.50000 + 2.59808i) q^{44} +(1.50000 + 2.59808i) q^{46} +(5.50000 - 4.33013i) q^{49} -4.00000 q^{50} +(-2.50000 - 4.33013i) q^{52} +(-1.50000 - 2.59808i) q^{53} +9.00000 q^{55} +(-2.50000 + 0.866025i) q^{56} +(1.50000 - 2.59808i) q^{58} +(6.00000 + 10.3923i) q^{59} +(-1.00000 + 1.73205i) q^{61} +4.00000 q^{62} +1.00000 q^{64} +(-7.50000 + 12.9904i) q^{65} +(2.00000 + 3.46410i) q^{67} +(1.50000 - 2.59808i) q^{68} +(6.00000 + 5.19615i) q^{70} +(-5.50000 - 9.52628i) q^{73} +(-3.50000 - 6.06218i) q^{74} +5.00000 q^{76} +(-6.00000 - 5.19615i) q^{77} +(-4.00000 + 6.92820i) q^{79} +(-1.50000 - 2.59808i) q^{80} +(4.50000 - 7.79423i) q^{82} -3.00000 q^{83} -9.00000 q^{85} +(5.50000 - 9.52628i) q^{86} +(1.50000 + 2.59808i) q^{88} +(7.50000 - 12.9904i) q^{89} +(12.5000 - 4.33013i) q^{91} +3.00000 q^{92} +(-7.50000 - 12.9904i) q^{95} -1.00000 q^{97} +(-1.00000 - 6.92820i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{4} - 3 q^{5} + 5 q^{7} - 2 q^{8} + 3 q^{10} - 3 q^{11} + 10 q^{13} + q^{14} - q^{16} + 3 q^{17} - 5 q^{19} + 6 q^{20} - 6 q^{22} - 3 q^{23} - 4 q^{25} + 5 q^{26} - 4 q^{28} + 6 q^{29}+ \cdots - 2 q^{98}+O(q^{100}) \) 2 * q + q^2 - q^4 - 3 * q^5 + 5 * q^7 - 2 * q^8 + 3 * q^10 - 3 * q^11 + 10 * q^13 + q^14 - q^16 + 3 * q^17 - 5 * q^19 + 6 * q^20 - 6 * q^22 - 3 * q^23 - 4 * q^25 + 5 * q^26 - 4 * q^28 + 6 * q^29 + 4 * q^31 + q^32 + 6 * q^34 - 3 * q^35 + 7 * q^37 + 5 * q^38 + 3 * q^40 + 18 * q^41 + 22 * q^43 - 3 * q^44 + 3 * q^46 + 11 * q^49 - 8 * q^50 - 5 * q^52 - 3 * q^53 + 18 * q^55 - 5 * q^56 + 3 * q^58 + 12 * q^59 - 2 * q^61 + 8 * q^62 + 2 * q^64 - 15 * q^65 + 4 * q^67 + 3 * q^68 + 12 * q^70 - 11 * q^73 - 7 * q^74 + 10 * q^76 - 12 * q^77 - 8 * q^79 - 3 * q^80 + 9 * q^82 - 6 * q^83 - 18 * q^85 + 11 * q^86 + 3 * q^88 + 15 * q^89 + 25 * q^91 + 6 * q^92 - 15 * q^95 - 2 * q^97 - 2 * q^98

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