LMFDB - Embedded newform 1134.2.t.a.1025.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1134,2,Mod(593,1134)] 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("1134.593"); 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([1, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1134 = 2 \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1134.t (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,2,0,0,-10,0,0,0,0,0,12,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(14)] == traces)

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

Self dual:	no
Analytic conductor:	$9.05503558921$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 378)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1025.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1134.1025
Dual form			1134.2.t.a.593.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-2.50000 + 0.866025i) q^{7} -1.00000i q^{8} -3.00000i q^{11} +(3.00000 + 1.73205i) q^{13} +(2.59808 + 0.500000i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.50000 + 2.59808i) q^{22} -5.00000 q^{25} +(-1.73205 - 3.00000i) q^{26} +(-2.00000 - 1.73205i) q^{28} +(7.79423 - 4.50000i) q^{29} +(1.50000 - 0.866025i) q^{31} +(0.866025 - 0.500000i) q^{32} +(4.00000 + 6.92820i) q^{37} +(5.19615 - 9.00000i) q^{41} +(-2.00000 - 3.46410i) q^{43} +(2.59808 - 1.50000i) q^{44} +(5.19615 - 9.00000i) q^{47} +(5.50000 - 4.33013i) q^{49} +(4.33013 + 2.50000i) q^{50} +3.46410i q^{52} +(-5.19615 - 3.00000i) q^{53} +(0.866025 + 2.50000i) q^{56} -9.00000 q^{58} +(2.59808 + 4.50000i) q^{59} +(12.0000 + 6.92820i) q^{61} -1.73205 q^{62} -1.00000 q^{64} +(-1.00000 - 1.73205i) q^{67} +12.0000i q^{71} +(4.50000 + 2.59808i) q^{73} -8.00000i q^{74} +(2.59808 + 7.50000i) q^{77} +(6.50000 - 11.2583i) q^{79} +(-9.00000 + 5.19615i) q^{82} +(-2.59808 - 4.50000i) q^{83} +4.00000i q^{86} -3.00000 q^{88} +(-5.19615 - 9.00000i) q^{89} +(-9.00000 - 1.73205i) q^{91} +(-9.00000 + 5.19615i) q^{94} +(7.50000 - 4.33013i) q^{97} +(-6.92820 + 1.00000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} - 10 q^{7} + 12 q^{13} - 2 q^{16} - 6 q^{22} - 20 q^{25} - 8 q^{28} + 6 q^{31} + 16 q^{37} - 8 q^{43} + 22 q^{49} - 36 q^{58} + 48 q^{61} - 4 q^{64} - 4 q^{67} + 18 q^{73} + 26 q^{79} - 36 q^{82}+ \cdots + 30 q^{97}+O(q^{100}) $ 4 * q + 2 * q^4 - 10 * q^7 + 12 * q^13 - 2 * q^16 - 6 * q^22 - 20 * q^25 - 8 * q^28 + 6 * q^31 + 16 * q^37 - 8 * q^43 + 22 * q^49 - 36 * q^58 + 48 * q^61 - 4 * q^64 - 4 * q^67 + 18 * q^73 + 26 * q^79 - 36 * q^82 - 12 * q^88 - 36 * q^91 - 36 * q^94 + 30 * q^97

Character values

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

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		0			0			−	1.00000i	$-0.5\pi$
$5$		0			0				1.00000i	$0.5\pi$
$6$		0			0
$7$	−2.50000	+	0.866025i	−0.944911	+	0.327327i
$7$	−2.50000	+	0.866025i	−0.944911	+	0.327327i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$		0			0
$11$		−	3.00000i		−	0.904534i	−0.891883	−	0.452267i	$-0.850615\pi$
$11$		−	3.00000i		−	0.904534i	0.891883	−	0.452267i	$-0.149385\pi$
$12$		0			0
$13$	3.00000	+	1.73205i	0.832050	+	0.480384i	0.854554	−	0.519362i	$-0.173830\pi$
$13$	3.00000	+	1.73205i	0.832050	+	0.480384i	−0.0225039	+	0.999747i	$0.507164\pi$
$14$	2.59808	+	0.500000i	0.694365	+	0.133631i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$17$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$18$		0			0
$19$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$19$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$20$		0			0
$21$		0			0
$22$	−1.50000	+	2.59808i	−0.319801	+	0.553912i
$23$		0			0		1.00000			$0$
$23$		0			0		−1.00000			$\pi$
$24$		0			0
$25$	−5.00000			−1.00000
$26$	−1.73205	−	3.00000i	−0.339683	−	0.588348i
$27$		0			0
$28$	−2.00000	−	1.73205i	−0.377964	−	0.327327i
$29$	7.79423	−	4.50000i	1.44735	−	0.835629i	0.449029	−	0.893517i	$-0.351770\pi$
$29$	7.79423	−	4.50000i	1.44735	−	0.835629i	0.998323	+	0.0578882i	$0.0184367\pi$
$30$		0			0
$31$	1.50000	−	0.866025i	0.269408	−	0.155543i	−0.359211	−	0.933257i	$-0.616954\pi$
$31$	1.50000	−	0.866025i	0.269408	−	0.155543i	0.628619	+	0.777714i	$0.283621\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$		0			0
$34$		0			0
$35$		0			0
$36$		0			0
$37$	4.00000	+	6.92820i	0.657596	+	1.13899i	0.981236	+	0.192809i	$0.0617599\pi$
$37$	4.00000	+	6.92820i	0.657596	+	1.13899i	−0.323640	+	0.946180i	$0.604907\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	5.19615	−	9.00000i	0.811503	−	1.40556i	−0.100309	−	0.994956i	$-0.531983\pi$
$41$	5.19615	−	9.00000i	0.811503	−	1.40556i	0.911812	−	0.410608i	$-0.134683\pi$
$42$		0			0
$43$	−2.00000	−	3.46410i	−0.304997	−	0.528271i	0.672264	−	0.740312i	$-0.265322\pi$
$43$	−2.00000	−	3.46410i	−0.304997	−	0.528271i	−0.977261	+	0.212041i	$0.931989\pi$
$44$	2.59808	−	1.50000i	0.391675	−	0.226134i
$45$		0			0
$46$		0			0
$47$	5.19615	−	9.00000i	0.757937	−	1.31278i	−0.185964	−	0.982556i	$-0.559541\pi$
$47$	5.19615	−	9.00000i	0.757937	−	1.31278i	0.943901	−	0.330228i	$-0.107126\pi$
$48$		0			0
$49$	5.50000	−	4.33013i	0.785714	−	0.618590i
$50$	4.33013	+	2.50000i	0.612372	+	0.353553i
$51$		0			0
$52$			3.46410i			0.480384i
$53$	−5.19615	−	3.00000i	−0.713746	−	0.412082i	0.0987002	−	0.995117i	$-0.468532\pi$
$53$	−5.19615	−	3.00000i	−0.713746	−	0.412082i	−0.812447	+	0.583036i	$0.801865\pi$
$54$		0			0
$55$		0			0
$56$	0.866025	+	2.50000i	0.115728	+	0.334077i
$57$		0			0
$58$	−9.00000			−1.18176
$59$	2.59808	+	4.50000i	0.338241	+	0.585850i	0.984102	−	0.177605i	$-0.0568349\pi$
$59$	2.59808	+	4.50000i	0.338241	+	0.585850i	−0.645861	+	0.763455i	$0.723502\pi$
$60$		0			0
$61$	12.0000	+	6.92820i	1.53644	+	0.887066i	0.999043	+	0.0437377i	$0.0139266\pi$
$61$	12.0000	+	6.92820i	1.53644	+	0.887066i	0.537400	+	0.843328i	$0.319407\pi$
$62$	−1.73205			−0.219971
$63$		0			0
$64$	−1.00000			−0.125000
$65$		0			0
$66$		0			0
$67$	−1.00000	−	1.73205i	−0.122169	−	0.211604i	0.798454	−	0.602056i	$-0.205652\pi$
$67$	−1.00000	−	1.73205i	−0.122169	−	0.211604i	−0.920623	+	0.390453i	$0.872318\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			12.0000i			1.42414i	0.702109	+	0.712069i	$0.252242\pi$
$71$			12.0000i			1.42414i	−0.702109	+	0.712069i	$0.747758\pi$
$72$		0			0
$73$	4.50000	+	2.59808i	0.526685	+	0.304082i	0.739666	−	0.672975i	$-0.234984\pi$
$73$	4.50000	+	2.59808i	0.526685	+	0.304082i	−0.212980	+	0.977056i	$0.568317\pi$
$74$		−	8.00000i		−	0.929981i
$75$		0			0
$76$		0			0
$77$	2.59808	+	7.50000i	0.296078	+	0.854704i
$78$		0			0
$79$	6.50000	−	11.2583i	0.731307	−	1.26666i	−0.225018	−	0.974355i	$-0.572244\pi$
$79$	6.50000	−	11.2583i	0.731307	−	1.26666i	0.956325	−	0.292306i	$-0.0944227\pi$
$80$		0			0
$81$		0			0
$82$	−9.00000	+	5.19615i	−0.993884	+	0.573819i
$83$	−2.59808	−	4.50000i	−0.285176	−	0.493939i	0.687476	−	0.726207i	$-0.258719\pi$
$83$	−2.59808	−	4.50000i	−0.285176	−	0.493939i	−0.972652	+	0.232268i	$0.925385\pi$
$84$		0			0
$85$		0			0
$86$			4.00000i			0.431331i
$87$		0			0
$88$	−3.00000			−0.319801
$89$	−5.19615	−	9.00000i	−0.550791	−	0.953998i	−0.998218	−	0.0596775i	$-0.980993\pi$
$89$	−5.19615	−	9.00000i	−0.550791	−	0.953998i	0.447427	−	0.894321i	$-0.352341\pi$
$90$		0			0
$91$	−9.00000	−	1.73205i	−0.943456	−	0.181568i
$92$		0			0
$93$		0			0
$94$	−9.00000	+	5.19615i	−0.928279	+	0.535942i
$95$		0			0
$96$		0			0
$97$	7.50000	−	4.33013i	0.761510	−	0.439658i	−0.0683279	−	0.997663i	$-0.521766\pi$
$97$	7.50000	−	4.33013i	0.761510	−	0.439658i	0.829837	+	0.558005i	$0.188433\pi$
$98$	−6.92820	+	1.00000i	−0.699854	+	0.101015i
$99$		0			0
$100$	−2.50000	−	4.33013i	−0.250000	−	0.433013i
$101$	−5.19615			−0.517036			−0.258518	−	0.966006i	$-0.583234\pi$
$101$	−5.19615			−0.517036			−0.258518	+	0.966006i	$0.583234\pi$
$102$		0			0
$103$		−	17.3205i		−	1.70664i	−0.521387	−	0.853320i	$-0.674585\pi$
$103$		−	17.3205i		−	1.70664i	0.521387	−	0.853320i	$-0.325415\pi$
$104$	1.73205	−	3.00000i	0.169842	−	0.294174i
$105$		0			0
$106$	3.00000	+	5.19615i	0.291386	+	0.504695i
$107$	10.3923	−	6.00000i	1.00466	−	0.580042i	0.0950377	−	0.995474i	$-0.469703\pi$
$107$	10.3923	−	6.00000i	1.00466	−	0.580042i	0.909624	+	0.415432i	$0.136370\pi$
$108$		0			0
$109$	4.00000	−	6.92820i	0.383131	−	0.663602i	−0.608377	−	0.793648i	$-0.708179\pi$
$109$	4.00000	−	6.92820i	0.383131	−	0.663602i	0.991508	+	0.130046i	$0.0415126\pi$
$110$		0			0
$111$		0			0
$112$	0.500000	−	2.59808i	0.0472456	−	0.245495i
$113$	10.3923	+	6.00000i	0.977626	+	0.564433i	0.901553	−	0.432670i	$-0.142428\pi$
$113$	10.3923	+	6.00000i	0.977626	+	0.564433i	0.0760733	+	0.997102i	$0.475762\pi$
$114$		0			0
$115$		0			0
$116$	7.79423	+	4.50000i	0.723676	+	0.417815i
$117$		0			0
$118$		−	5.19615i		−	0.478345i
$119$		0			0
$120$		0			0
$121$	2.00000			0.181818
$122$	−6.92820	−	12.0000i	−0.627250	−	1.08643i
$123$		0			0
$124$	1.50000	+	0.866025i	0.134704	+	0.0777714i
$125$		0			0
$126$		0			0
$127$	8.00000			0.709885			0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000			0.709885			0.354943	+	0.934888i	$0.384500\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$		0			0
$130$		0			0
$131$	−15.5885			−1.36197			−0.680985	−	0.732297i	$-0.738448\pi$
$131$	−15.5885			−1.36197			−0.680985	+	0.732297i	$0.738448\pi$
$132$		0			0
$133$		0			0
$134$			2.00000i			0.172774i
$135$		0			0
$136$		0			0
$137$			12.0000i			1.02523i	0.858619	+	0.512615i	$0.171323\pi$
$137$			12.0000i			1.02523i	−0.858619	+	0.512615i	$0.828677\pi$
$138$		0			0
$139$	6.00000	+	3.46410i	0.508913	+	0.293821i	0.732387	−	0.680889i	$-0.238406\pi$
$139$	6.00000	+	3.46410i	0.508913	+	0.293821i	−0.223474	+	0.974710i	$0.571740\pi$
$140$		0			0
$141$		0			0
$142$	6.00000	−	10.3923i	0.503509	−	0.872103i
$143$	5.19615	−	9.00000i	0.434524	−	0.752618i
$144$		0			0
$145$		0			0
$146$	−2.59808	−	4.50000i	−0.215018	−	0.372423i
$147$		0			0
$148$	−4.00000	+	6.92820i	−0.328798	+	0.569495i
$149$		−	15.0000i		−	1.22885i	−0.788976	−	0.614424i	$-0.789388\pi$
$149$		−	15.0000i		−	1.22885i	0.788976	−	0.614424i	$-0.210612\pi$
$150$		0			0
$151$	−23.0000			−1.87171			−0.935857	−	0.352381i	$-0.885372\pi$
$151$	−23.0000			−1.87171			−0.935857	+	0.352381i	$0.885372\pi$
$152$		0			0
$153$		0			0
$154$	1.50000	−	7.79423i	0.120873	−	0.628077i
$155$		0			0
$156$		0			0
$157$	−9.00000	+	5.19615i	−0.718278	+	0.414698i	−0.814119	−	0.580699i	$-0.802779\pi$
$157$	−9.00000	+	5.19615i	−0.718278	+	0.414698i	0.0958404	+	0.995397i	$0.469446\pi$
$158$	−11.2583	+	6.50000i	−0.895665	+	0.517112i
$159$		0			0
$160$		0			0
$161$		0			0
$162$		0			0
$163$	5.00000	+	8.66025i	0.391630	+	0.678323i	0.992665	−	0.120900i	$-0.0385779\pi$
$163$	5.00000	+	8.66025i	0.391630	+	0.678323i	−0.601035	+	0.799223i	$0.705245\pi$
$164$	10.3923			0.811503
$165$		0			0
$166$			5.19615i			0.403300i
$167$	5.19615	−	9.00000i	0.402090	−	0.696441i	−0.591888	−	0.806020i	$-0.701617\pi$
$167$	5.19615	−	9.00000i	0.402090	−	0.696441i	0.993978	+	0.109580i	$0.0349504\pi$
$168$		0			0
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$		0			0
$171$		0			0
$172$	2.00000	−	3.46410i	0.152499	−	0.264135i
$173$	−12.9904	+	22.5000i	−0.987640	+	1.71064i	−0.358082	+	0.933690i	$0.616569\pi$
$173$	−12.9904	+	22.5000i	−0.987640	+	1.71064i	−0.629558	+	0.776953i	$0.716764\pi$
$174$		0			0
$175$	12.5000	−	4.33013i	0.944911	−	0.327327i
$176$	2.59808	+	1.50000i	0.195837	+	0.113067i
$177$		0			0
$178$			10.3923i			0.778936i
$179$	−7.79423	−	4.50000i	−0.582568	−	0.336346i	0.179585	−	0.983742i	$-0.442524\pi$
$179$	−7.79423	−	4.50000i	−0.582568	−	0.336346i	−0.762153	+	0.647397i	$0.775858\pi$
$180$		0			0
$181$		−	20.7846i		−	1.54491i	−0.635071	−	0.772454i	$-0.719029\pi$
$181$		−	20.7846i		−	1.54491i	0.635071	−	0.772454i	$-0.280971\pi$
$182$	6.92820	+	6.00000i	0.513553	+	0.444750i
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$		0			0
$188$	10.3923			0.757937
$189$		0			0
$190$		0			0
$191$	5.19615	+	3.00000i	0.375980	+	0.217072i	0.676068	−	0.736839i	$-0.263683\pi$
$191$	5.19615	+	3.00000i	0.375980	+	0.217072i	−0.300088	+	0.953912i	$0.597016\pi$
$192$		0			0
$193$	5.50000	+	9.52628i	0.395899	+	0.685717i	0.993215	−	0.116289i	$-0.0370998\pi$
$193$	5.50000	+	9.52628i	0.395899	+	0.685717i	−0.597317	+	0.802005i	$0.703766\pi$
$194$	−8.66025			−0.621770
$195$		0			0
$196$	6.50000	+	2.59808i	0.464286	+	0.185577i
$197$			15.0000i			1.06871i	0.845262	+	0.534353i	$0.179445\pi$
$197$			15.0000i			1.06871i	−0.845262	+	0.534353i	$0.820555\pi$
$198$		0			0
$199$	1.50000	+	0.866025i	0.106332	+	0.0613909i	0.552223	−	0.833696i	$-0.313780\pi$
$199$	1.50000	+	0.866025i	0.106332	+	0.0613909i	−0.445891	+	0.895087i	$0.647113\pi$
$200$			5.00000i			0.353553i
$201$		0			0
$202$	4.50000	+	2.59808i	0.316619	+	0.182800i
$203$	−15.5885	+	18.0000i	−1.09410	+	1.26335i
$204$		0			0
$205$		0			0
$206$	−8.66025	+	15.0000i	−0.603388	+	1.04510i
$207$		0			0
$208$	−3.00000	+	1.73205i	−0.208013	+	0.120096i
$209$		0			0
$210$		0			0
$211$	1.00000	−	1.73205i	0.0688428	−	0.119239i	−0.829549	−	0.558433i	$-0.811403\pi$
$211$	1.00000	−	1.73205i	0.0688428	−	0.119239i	0.898392	+	0.439194i	$0.144736\pi$
$212$		−	6.00000i		−	0.412082i
$213$		0			0
$214$	−12.0000			−0.820303
$215$		0			0
$216$		0			0
$217$	−3.00000	+	3.46410i	−0.203653	+	0.235159i
$218$	−6.92820	+	4.00000i	−0.469237	+	0.270914i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−4.50000	+	2.59808i	−0.301342	+	0.173980i	−0.643046	−	0.765828i	$-0.722329\pi$
$223$	−4.50000	+	2.59808i	−0.301342	+	0.173980i	0.341703	+	0.939808i	$0.388996\pi$
$224$	−1.73205	+	2.00000i	−0.115728	+	0.133631i
$225$		0			0
$226$	−6.00000	−	10.3923i	−0.399114	−	0.691286i
$227$	−25.9808			−1.72440			−0.862202	−	0.506565i	$-0.830915\pi$
$227$	−25.9808			−1.72440			−0.862202	+	0.506565i	$0.830915\pi$
$228$		0			0
$229$			6.92820i			0.457829i	0.973447	+	0.228914i	$0.0735176\pi$
$229$			6.92820i			0.457829i	−0.973447	+	0.228914i	$0.926482\pi$
$230$		0			0
$231$		0			0
$232$	−4.50000	−	7.79423i	−0.295439	−	0.511716i
$233$	−15.5885	+	9.00000i	−1.02123	+	0.589610i	−0.914461	−	0.404674i	$-0.867385\pi$
$233$	−15.5885	+	9.00000i	−1.02123	+	0.589610i	−0.106773	+	0.994283i	$0.534052\pi$
$234$		0			0
$235$		0			0
$236$	−2.59808	+	4.50000i	−0.169120	+	0.292925i
$237$		0			0
$238$		0			0
$239$	10.3923	+	6.00000i	0.672222	+	0.388108i	0.796918	−	0.604087i	$-0.206462\pi$
$239$	10.3923	+	6.00000i	0.672222	+	0.388108i	−0.124696	+	0.992195i	$0.539796\pi$
$240$		0			0
$241$			12.1244i			0.780998i	0.920603	+	0.390499i	$0.127698\pi$
$241$			12.1244i			0.780998i	−0.920603	+	0.390499i	$0.872302\pi$
$242$	−1.73205	−	1.00000i	−0.111340	−	0.0642824i
$243$		0			0
$244$			13.8564i			0.887066i
$245$		0			0
$246$		0			0
$247$		0			0
$248$	−0.866025	−	1.50000i	−0.0549927	−	0.0952501i
$249$		0			0
$250$		0			0
$251$	25.9808			1.63989			0.819946	−	0.572441i	$-0.194004\pi$
$251$	25.9808			1.63989			0.819946	+	0.572441i	$0.194004\pi$
$252$		0			0
$253$		0			0
$254$	−6.92820	−	4.00000i	−0.434714	−	0.250982i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−20.7846			−1.29651			−0.648254	−	0.761424i	$-0.724501\pi$
$257$	−20.7846			−1.29651			−0.648254	+	0.761424i	$0.724501\pi$
$258$		0			0
$259$	−16.0000	−	13.8564i	−0.994192	−	0.860995i
$260$		0			0
$261$		0			0
$262$	13.5000	+	7.79423i	0.834033	+	0.481529i
$263$			24.0000i			1.47990i	0.672660	+	0.739952i	$0.265152\pi$
$263$			24.0000i			1.47990i	−0.672660	+	0.739952i	$0.734848\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	1.00000	−	1.73205i	0.0610847	−	0.105802i
$269$	7.79423	−	13.5000i	0.475223	−	0.823110i	−0.524375	−	0.851488i	$-0.675701\pi$
$269$	7.79423	−	13.5000i	0.475223	−	0.823110i	0.999597	+	0.0283781i	$0.00903423\pi$
$270$		0			0
$271$	3.00000	−	1.73205i	0.182237	−	0.105215i	−0.406106	−	0.913826i	$-0.633114\pi$
$271$	3.00000	−	1.73205i	0.182237	−	0.105215i	0.588343	+	0.808611i	$0.299780\pi$
$272$		0			0
$273$		0			0
$274$	6.00000	−	10.3923i	0.362473	−	0.627822i
$275$			15.0000i			0.904534i
$276$		0			0
$277$	14.0000			0.841178			0.420589	−	0.907251i	$-0.361823\pi$
$277$	14.0000			0.841178			0.420589	+	0.907251i	$0.361823\pi$
$278$	−3.46410	−	6.00000i	−0.207763	−	0.359856i
$279$		0			0
$280$		0			0
$281$	−5.19615	+	3.00000i	−0.309976	+	0.178965i	−0.646916	−	0.762561i	$-0.723942\pi$
$281$	−5.19615	+	3.00000i	−0.309976	+	0.178965i	0.336939	+	0.941526i	$0.390608\pi$
$282$		0			0
$283$	−6.00000	+	3.46410i	−0.356663	+	0.205919i	−0.667616	−	0.744506i	$-0.732685\pi$
$283$	−6.00000	+	3.46410i	−0.356663	+	0.205919i	0.310953	+	0.950425i	$0.399352\pi$
$284$	−10.3923	+	6.00000i	−0.616670	+	0.356034i
$285$		0			0
$286$	−9.00000	+	5.19615i	−0.532181	+	0.307255i
$287$	−5.19615	+	27.0000i	−0.306719	+	1.59376i
$288$		0			0
$289$	8.50000	+	14.7224i	0.500000	+	0.866025i
$290$		0			0
$291$		0			0
$292$			5.19615i			0.304082i
$293$	2.59808	−	4.50000i	0.151781	−	0.262893i	−0.780101	−	0.625653i	$-0.784832\pi$
$293$	2.59808	−	4.50000i	0.151781	−	0.262893i	0.931882	+	0.362761i	$0.118166\pi$
$294$		0			0
$295$		0			0
$296$	6.92820	−	4.00000i	0.402694	−	0.232495i
$297$		0			0
$298$	−7.50000	+	12.9904i	−0.434463	+	0.752513i
$299$		0			0
$300$		0			0
$301$	8.00000	+	6.92820i	0.461112	+	0.399335i
$302$	19.9186	+	11.5000i	1.14619	+	0.661751i
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$			17.3205i			0.988534i	0.869310	+	0.494267i	$0.164563\pi$
$307$			17.3205i			0.988534i	−0.869310	+	0.494267i	$0.835437\pi$
$308$	−5.19615	+	6.00000i	−0.296078	+	0.341882i
$309$		0			0
$310$		0			0
$311$	−15.5885	−	27.0000i	−0.883940	−	1.53103i	−0.846923	−	0.531715i	$-0.821548\pi$
$311$	−15.5885	−	27.0000i	−0.883940	−	1.53103i	−0.0370169	−	0.999315i	$-0.511786\pi$
$312$		0			0
$313$	18.0000	+	10.3923i	1.01742	+	0.587408i	0.913356	−	0.407163i	$-0.133482\pi$
$313$	18.0000	+	10.3923i	1.01742	+	0.587408i	0.104065	+	0.994571i	$0.466815\pi$
$314$	10.3923			0.586472
$315$		0			0
$316$	13.0000			0.731307
$317$	7.79423	+	4.50000i	0.437767	+	0.252745i	0.702650	−	0.711535i	$-0.252000\pi$
$317$	7.79423	+	4.50000i	0.437767	+	0.252745i	−0.264883	+	0.964281i	$0.585333\pi$
$318$		0			0
$319$	−13.5000	−	23.3827i	−0.755855	−	1.30918i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		0			0
$324$		0			0
$325$	−15.0000	−	8.66025i	−0.832050	−	0.480384i
$326$		−	10.0000i		−	0.553849i
$327$		0			0
$328$	−9.00000	−	5.19615i	−0.496942	−	0.286910i
$329$	−5.19615	+	27.0000i	−0.286473	+	1.48856i
$330$		0			0
$331$	−14.0000	+	24.2487i	−0.769510	+	1.33283i	0.168320	+	0.985732i	$0.446166\pi$
$331$	−14.0000	+	24.2487i	−0.769510	+	1.33283i	−0.937829	+	0.347097i	$0.887167\pi$
$332$	2.59808	−	4.50000i	0.142588	−	0.246970i
$333$		0			0
$334$	−9.00000	+	5.19615i	−0.492458	+	0.284321i
$335$		0			0
$336$		0			0
$337$	−6.50000	+	11.2583i	−0.354078	+	0.613280i	−0.986960	−	0.160968i	$-0.948538\pi$
$337$	−6.50000	+	11.2583i	−0.354078	+	0.613280i	0.632882	+	0.774248i	$0.281872\pi$
$338$			1.00000i			0.0543928i
$339$		0			0
$340$		0			0
$341$	−2.59808	−	4.50000i	−0.140694	−	0.243689i
$342$		0			0
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$	−3.46410	+	2.00000i	−0.186772	+	0.107833i
$345$		0			0
$346$	22.5000	−	12.9904i	1.20961	−	0.698367i
$347$	2.59808	−	1.50000i	0.139472	−	0.0805242i	−0.428640	−	0.903475i	$-0.641007\pi$
$347$	2.59808	−	1.50000i	0.139472	−	0.0805242i	0.568112	+	0.822951i	$0.307674\pi$
$348$		0			0
$349$	24.0000	−	13.8564i	1.28469	−	0.741716i	0.306988	−	0.951713i	$-0.400679\pi$
$349$	24.0000	−	13.8564i	1.28469	−	0.741716i	0.977702	+	0.209997i	$0.0673454\pi$
$350$	−12.9904	−	2.50000i	−0.694365	−	0.133631i
$351$		0			0
$352$	−1.50000	−	2.59808i	−0.0799503	−	0.138478i
$353$	10.3923			0.553127			0.276563	−	0.960996i	$-0.410804\pi$
$353$	10.3923			0.553127			0.276563	+	0.960996i	$0.410804\pi$
$354$		0			0
$355$		0			0
$356$	5.19615	−	9.00000i	0.275396	−	0.476999i
$357$		0			0
$358$	4.50000	+	7.79423i	0.237832	+	0.411938i
$359$	−10.3923	+	6.00000i	−0.548485	+	0.316668i	−0.748511	−	0.663123i	$-0.769231\pi$
$359$	−10.3923	+	6.00000i	−0.548485	+	0.316668i	0.200026	+	0.979791i	$0.435897\pi$
$360$		0			0
$361$	−9.50000	+	16.4545i	−0.500000	+	0.866025i
$362$	−10.3923	+	18.0000i	−0.546207	+	0.946059i
$363$		0			0
$364$	−3.00000	−	8.66025i	−0.157243	−	0.453921i
$365$		0			0
$366$		0			0
$367$		−	10.3923i		−	0.542474i	−0.962513	−	0.271237i	$-0.912567\pi$
$367$		−	10.3923i		−	0.542474i	0.962513	−	0.271237i	$-0.0874327\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	15.5885	+	3.00000i	0.809312	+	0.155752i
$372$		0			0
$373$	−4.00000			−0.207112			−0.103556	−	0.994624i	$-0.533022\pi$
$373$	−4.00000			−0.207112			−0.103556	+	0.994624i	$0.533022\pi$
$374$		0			0
$375$		0			0
$376$	−9.00000	−	5.19615i	−0.464140	−	0.267971i
$377$	31.1769			1.60569
$378$		0			0
$379$	−26.0000			−1.33553			−0.667765	−	0.744372i	$-0.732749\pi$
$379$	−26.0000			−1.33553			−0.667765	+	0.744372i	$0.732749\pi$
$380$		0			0
$381$		0			0
$382$	−3.00000	−	5.19615i	−0.153493	−	0.265858i
$383$	−20.7846			−1.06204			−0.531022	−	0.847358i	$-0.678192\pi$
$383$	−20.7846			−1.06204			−0.531022	+	0.847358i	$0.678192\pi$
$384$		0			0
$385$		0			0
$386$		−	11.0000i		−	0.559885i
$387$		0			0
$388$	7.50000	+	4.33013i	0.380755	+	0.219829i
$389$		−	9.00000i		−	0.456318i	−0.973624	−	0.228159i	$-0.926729\pi$
$389$		−	9.00000i		−	0.456318i	0.973624	−	0.228159i	$-0.0732706\pi$
$390$		0			0
$391$		0			0
$392$	−4.33013	−	5.50000i	−0.218704	−	0.277792i
$393$		0			0
$394$	7.50000	−	12.9904i	0.377845	−	0.654446i
$395$		0			0
$396$		0			0
$397$	21.0000	−	12.1244i	1.05396	−	0.608504i	0.130204	−	0.991487i	$-0.458437\pi$
$397$	21.0000	−	12.1244i	1.05396	−	0.608504i	0.923755	+	0.382983i	$0.125103\pi$
$398$	−0.866025	−	1.50000i	−0.0434099	−	0.0751882i
$399$		0			0
$400$	2.50000	−	4.33013i	0.125000	−	0.216506i
$401$		−	30.0000i		−	1.49813i	−0.662497	−	0.749064i	$-0.730503\pi$
$401$		−	30.0000i		−	1.49813i	0.662497	−	0.749064i	$-0.269497\pi$
$402$		0			0
$403$	6.00000			0.298881
$404$	−2.59808	−	4.50000i	−0.129259	−	0.223883i
$405$		0			0
$406$	22.5000	−	7.79423i	1.11666	−	0.386821i
$407$	20.7846	−	12.0000i	1.03025	−	0.594818i
$408$		0			0
$409$	−6.00000	+	3.46410i	−0.296681	+	0.171289i	−0.640951	−	0.767582i	$-0.721460\pi$
$409$	−6.00000	+	3.46410i	−0.296681	+	0.171289i	0.344270	+	0.938871i	$0.388126\pi$
$410$		0			0
$411$		0			0
$412$	15.0000	−	8.66025i	0.738997	−	0.426660i
$413$	−10.3923	−	9.00000i	−0.511372	−	0.442861i
$414$		0			0
$415$		0			0
$416$	3.46410			0.169842
$417$		0			0
$418$		0			0
$419$	15.5885	−	27.0000i	0.761546	−	1.31904i	−0.180508	−	0.983574i	$-0.557774\pi$
$419$	15.5885	−	27.0000i	0.761546	−	1.31904i	0.942053	−	0.335463i	$-0.108893\pi$
$420$		0			0
$421$	5.00000	+	8.66025i	0.243685	+	0.422075i	0.961761	−	0.273890i	$-0.0883103\pi$
$421$	5.00000	+	8.66025i	0.243685	+	0.422075i	−0.718076	+	0.695965i	$0.754977\pi$
$422$	−1.73205	+	1.00000i	−0.0843149	+	0.0486792i
$423$		0			0
$424$	−3.00000	+	5.19615i	−0.145693	+	0.252347i
$425$		0			0
$426$		0			0
$427$	−36.0000	−	6.92820i	−1.74216	−	0.335279i
$428$	10.3923	+	6.00000i	0.502331	+	0.290021i
$429$		0			0
$430$		0			0
$431$	−15.5885	−	9.00000i	−0.750870	−	0.433515i	0.0751385	−	0.997173i	$-0.476060\pi$
$431$	−15.5885	−	9.00000i	−0.750870	−	0.433515i	−0.826008	+	0.563658i	$0.809393\pi$
$432$		0			0
$433$		−	12.1244i		−	0.582659i	−0.956623	−	0.291330i	$-0.905902\pi$
$433$		−	12.1244i		−	0.582659i	0.956623	−	0.291330i	$-0.0940977\pi$
$434$	4.33013	−	1.50000i	0.207853	−	0.0720023i
$435$		0			0
$436$	8.00000			0.383131
$437$		0			0
$438$		0			0
$439$	−13.5000	−	7.79423i	−0.644320	−	0.371998i	0.141957	−	0.989873i	$-0.454661\pi$
$439$	−13.5000	−	7.79423i	−0.644320	−	0.371998i	−0.786277	+	0.617875i	$0.787994\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−23.3827	−	13.5000i	−1.11094	−	0.641404i	−0.171871	−	0.985119i	$-0.554981\pi$
$443$	−23.3827	−	13.5000i	−1.11094	−	0.641404i	−0.939074	+	0.343715i	$0.888315\pi$
$444$		0			0
$445$		0			0
$446$	5.19615			0.246045
$447$		0			0
$448$	2.50000	−	0.866025i	0.118114	−	0.0409159i
$449$			30.0000i			1.41579i	0.706319	+	0.707894i	$0.250354\pi$
$449$			30.0000i			1.41579i	−0.706319	+	0.707894i	$0.749646\pi$
$450$		0			0
$451$	−27.0000	−	15.5885i	−1.27138	−	0.734032i
$452$			12.0000i			0.564433i
$453$		0			0
$454$	22.5000	+	12.9904i	1.05598	+	0.609669i
$455$		0			0
$456$		0			0
$457$	−11.0000	+	19.0526i	−0.514558	+	0.891241i	0.485299	+	0.874348i	$0.338711\pi$
$457$	−11.0000	+	19.0526i	−0.514558	+	0.891241i	−0.999857	+	0.0168929i	$0.994623\pi$
$458$	3.46410	−	6.00000i	0.161867	−	0.280362i
$459$		0			0
$460$		0			0
$461$	−7.79423	−	13.5000i	−0.363013	−	0.628758i	0.625442	−	0.780271i	$-0.284919\pi$
$461$	−7.79423	−	13.5000i	−0.363013	−	0.628758i	−0.988455	+	0.151513i	$0.951585\pi$
$462$		0			0
$463$	−2.50000	+	4.33013i	−0.116185	+	0.201238i	−0.918253	−	0.395995i	$-0.870400\pi$
$463$	−2.50000	+	4.33013i	−0.116185	+	0.201238i	0.802068	+	0.597233i	$0.203733\pi$
$464$			9.00000i			0.417815i
$465$		0			0
$466$	18.0000			0.833834
$467$	2.59808	+	4.50000i	0.120225	+	0.208235i	0.919856	−	0.392256i	$-0.128305\pi$
$467$	2.59808	+	4.50000i	0.120225	+	0.208235i	−0.799632	+	0.600491i	$0.794972\pi$
$468$		0			0
$469$	4.00000	+	3.46410i	0.184703	+	0.159957i
$470$		0			0
$471$		0			0
$472$	4.50000	−	2.59808i	0.207129	−	0.119586i
$473$	−10.3923	+	6.00000i	−0.477839	+	0.275880i
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$	−6.00000	−	10.3923i	−0.274434	−	0.475333i
$479$	10.3923			0.474837			0.237418	−	0.971408i	$-0.423699\pi$
$479$	10.3923			0.474837			0.237418	+	0.971408i	$0.423699\pi$
$480$		0			0
$481$			27.7128i			1.26360i
$482$	6.06218	−	10.5000i	0.276125	−	0.478262i
$483$		0			0
$484$	1.00000	+	1.73205i	0.0454545	+	0.0787296i
$485$		0			0
$486$		0			0
$487$	5.50000	−	9.52628i	0.249229	−	0.431677i	−0.714083	−	0.700061i	$-0.753156\pi$
$487$	5.50000	−	9.52628i	0.249229	−	0.431677i	0.963312	+	0.268384i	$0.0864896\pi$
$488$	6.92820	−	12.0000i	0.313625	−	0.543214i
$489$		0			0
$490$		0			0
$491$	31.1769	+	18.0000i	1.40699	+	0.812329i	0.995097	−	0.0989017i	$-0.0315329\pi$
$491$	31.1769	+	18.0000i	1.40699	+	0.812329i	0.411897	+	0.911230i	$0.364866\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$			1.73205i			0.0777714i
$497$	−10.3923	−	30.0000i	−0.466159	−	1.34568i
$498$		0			0
$499$	16.0000			0.716258			0.358129	−	0.933672i	$-0.383415\pi$
$499$	16.0000			0.716258			0.358129	+	0.933672i	$0.383415\pi$
$500$		0			0
$501$		0			0
$502$	−22.5000	−	12.9904i	−1.00422	−	0.579789i
$503$	−31.1769			−1.39011			−0.695055	−	0.718957i	$-0.744620\pi$
$503$	−31.1769			−1.39011			−0.695055	+	0.718957i	$0.744620\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$		0			0
$508$	4.00000	+	6.92820i	0.177471	+	0.307389i
$509$	5.19615			0.230315			0.115158	−	0.993347i	$-0.463263\pi$
$509$	5.19615			0.230315			0.115158	+	0.993347i	$0.463263\pi$
$510$		0			0
$511$	−13.5000	−	2.59808i	−0.597205	−	0.114932i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	18.0000	+	10.3923i	0.793946	+	0.458385i
$515$		0			0
$516$		0			0
$517$	−27.0000	−	15.5885i	−1.18746	−	0.685580i
$518$	6.92820	+	20.0000i	0.304408	+	0.878750i
$519$		0			0
$520$		0			0
$521$	10.3923	−	18.0000i	0.455295	−	0.788594i	−0.543410	−	0.839467i	$-0.682867\pi$
$521$	10.3923	−	18.0000i	0.455295	−	0.788594i	0.998705	+	0.0508731i	$0.0162004\pi$
$522$		0			0
$523$	33.0000	−	19.0526i	1.44299	−	0.833110i	0.444941	−	0.895560i	$-0.353225\pi$
$523$	33.0000	−	19.0526i	1.44299	−	0.833110i	0.998048	+	0.0624496i	$0.0198913\pi$
$524$	−7.79423	−	13.5000i	−0.340492	−	0.589750i
$525$		0			0
$526$	12.0000	−	20.7846i	0.523225	−	0.906252i
$527$		0			0
$528$		0			0
$529$	23.0000			1.00000
$530$		0			0
$531$		0			0
$532$		0			0
$533$	31.1769	−	18.0000i	1.35042	−	0.779667i
$534$		0			0
$535$		0			0
$536$	−1.73205	+	1.00000i	−0.0748132	+	0.0431934i
$537$		0			0
$538$	−13.5000	+	7.79423i	−0.582026	+	0.336033i
$539$	−12.9904	−	16.5000i	−0.559535	−	0.710705i
$540$		0			0
$541$	−19.0000	−	32.9090i	−0.816874	−	1.41487i	−0.907975	−	0.419025i	$-0.862372\pi$
$541$	−19.0000	−	32.9090i	−0.816874	−	1.41487i	0.0911008	−	0.995842i	$-0.470961\pi$
$542$	−3.46410			−0.148796
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−7.00000	−	12.1244i	−0.299298	−	0.518400i	0.676677	−	0.736280i	$-0.263419\pi$
$547$	−7.00000	−	12.1244i	−0.299298	−	0.518400i	−0.975976	+	0.217880i	$0.930086\pi$
$548$	−10.3923	+	6.00000i	−0.443937	+	0.256307i
$549$		0			0
$550$	7.50000	−	12.9904i	0.319801	−	0.553912i
$551$		0			0
$552$		0			0
$553$	−6.50000	+	33.7750i	−0.276408	+	1.43626i
$554$	−12.1244	−	7.00000i	−0.515115	−	0.297402i
$555$		0			0
$556$			6.92820i			0.293821i
$557$	18.1865	+	10.5000i	0.770588	+	0.444899i	0.833084	−	0.553146i	$-0.186573\pi$
$557$	18.1865	+	10.5000i	0.770588	+	0.444899i	−0.0624962	+	0.998045i	$0.519906\pi$
$558$		0			0
$559$		−	13.8564i		−	0.586064i
$560$		0			0
$561$		0			0
$562$	6.00000			0.253095
$563$	15.5885	+	27.0000i	0.656975	+	1.13791i	0.981395	+	0.192001i	$0.0614977\pi$
$563$	15.5885	+	27.0000i	0.656975	+	1.13791i	−0.324420	+	0.945913i	$0.605169\pi$
$564$		0			0
$565$		0			0
$566$	6.92820			0.291214
$567$		0			0
$568$	12.0000			0.503509
$569$	10.3923	+	6.00000i	0.435668	+	0.251533i	0.701758	−	0.712415i	$-0.252399\pi$
$569$	10.3923	+	6.00000i	0.435668	+	0.251533i	−0.266090	+	0.963948i	$0.585732\pi$
$570$		0			0
$571$	2.00000	+	3.46410i	0.0836974	+	0.144968i	0.904835	−	0.425762i	$-0.139994\pi$
$571$	2.00000	+	3.46410i	0.0836974	+	0.144968i	−0.821138	+	0.570730i	$0.806660\pi$
$572$	10.3923			0.434524
$573$		0			0
$574$	18.0000	−	20.7846i	0.751305	−	0.867533i
$575$		0			0
$576$		0			0
$577$	−7.50000	−	4.33013i	−0.312229	−	0.180266i	0.335694	−	0.941971i	$-0.391029\pi$
$577$	−7.50000	−	4.33013i	−0.312229	−	0.180266i	−0.647924	+	0.761705i	$0.724362\pi$
$578$		−	17.0000i		−	0.707107i
$579$		0			0
$580$		0			0
$581$	10.3923	+	9.00000i	0.431145	+	0.373383i
$582$		0			0
$583$	−9.00000	+	15.5885i	−0.372742	+	0.645608i
$584$	2.59808	−	4.50000i	0.107509	−	0.186211i
$585$		0			0
$586$	−4.50000	+	2.59808i	−0.185893	+	0.107326i
$587$	−5.19615	−	9.00000i	−0.214468	−	0.371470i	0.738640	−	0.674100i	$-0.235468\pi$
$587$	−5.19615	−	9.00000i	−0.214468	−	0.371470i	−0.953108	+	0.302631i	$0.902135\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−8.00000			−0.328798
$593$	−10.3923	−	18.0000i	−0.426761	−	0.739171i	0.569822	−	0.821768i	$-0.307012\pi$
$593$	−10.3923	−	18.0000i	−0.426761	−	0.739171i	−0.996583	+	0.0825966i	$0.973679\pi$
$594$		0			0
$595$		0			0
$596$	12.9904	−	7.50000i	0.532107	−	0.307212i
$597$		0			0
$598$		0			0
$599$	25.9808	−	15.0000i	1.06155	−	0.612883i	0.135686	−	0.990752i	$-0.456676\pi$
$599$	25.9808	−	15.0000i	1.06155	−	0.612883i	0.925859	+	0.377869i	$0.123343\pi$
$600$		0			0
$601$	−30.0000	+	17.3205i	−1.22373	+	0.706518i	−0.965710	−	0.259623i	$-0.916402\pi$
$601$	−30.0000	+	17.3205i	−1.22373	+	0.706518i	−0.258015	+	0.966141i	$0.583069\pi$
$602$	−3.46410	−	10.0000i	−0.141186	−	0.407570i
$603$		0			0
$604$	−11.5000	−	19.9186i	−0.467928	−	0.810476i
$605$		0			0
$606$		0			0
$607$		−	5.19615i		−	0.210905i	−0.994424	−	0.105453i	$-0.966371\pi$
$607$		−	5.19615i		−	0.210905i	0.994424	−	0.105453i	$-0.0336291\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	31.1769	−	18.0000i	1.26128	−	0.728202i
$612$		0			0
$613$	5.00000	−	8.66025i	0.201948	−	0.349784i	−0.747208	−	0.664590i	$-0.768606\pi$
$613$	5.00000	−	8.66025i	0.201948	−	0.349784i	0.949156	+	0.314806i	$0.101939\pi$
$614$	8.66025	−	15.0000i	0.349499	−	0.605351i
$615$		0			0
$616$	7.50000	−	2.59808i	0.302184	−	0.104679i
$617$	15.5885	+	9.00000i	0.627568	+	0.362326i	0.779809	−	0.626017i	$-0.215316\pi$
$617$	15.5885	+	9.00000i	0.627568	+	0.362326i	−0.152242	+	0.988343i	$0.548649\pi$
$618$		0			0
$619$		−	34.6410i		−	1.39234i	−0.717877	−	0.696170i	$-0.754886\pi$
$619$		−	34.6410i		−	1.39234i	0.717877	−	0.696170i	$-0.245114\pi$
$620$		0			0
$621$		0			0
$622$			31.1769i			1.25008i
$623$	20.7846	+	18.0000i	0.832718	+	0.721155i
$624$		0			0
$625$	25.0000			1.00000
$626$	−10.3923	−	18.0000i	−0.415360	−	0.719425i
$627$		0			0
$628$	−9.00000	−	5.19615i	−0.359139	−	0.207349i
$629$		0			0
$630$		0			0
$631$	−37.0000			−1.47295			−0.736473	−	0.676467i	$-0.763510\pi$
$631$	−37.0000			−1.47295			−0.736473	+	0.676467i	$0.763510\pi$
$632$	−11.2583	−	6.50000i	−0.447832	−	0.258556i
$633$		0			0
$634$	−4.50000	−	7.79423i	−0.178718	−	0.309548i
$635$		0			0
$636$		0			0
$637$	24.0000	−	3.46410i	0.950915	−	0.137253i
$638$			27.0000i			1.06894i
$639$		0			0
$640$		0			0
$641$		−	42.0000i		−	1.65890i	−0.558581	−	0.829450i	$-0.688654\pi$
$641$		−	42.0000i		−	1.65890i	0.558581	−	0.829450i	$-0.311346\pi$
$642$		0			0
$643$	−3.00000	−	1.73205i	−0.118308	−	0.0683054i	0.439678	−	0.898155i	$-0.355093\pi$
$643$	−3.00000	−	1.73205i	−0.118308	−	0.0683054i	−0.557986	+	0.829850i	$0.688426\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	5.19615	−	9.00000i	0.204282	−	0.353827i	−0.745622	−	0.666369i	$-0.767847\pi$
$647$	5.19615	−	9.00000i	0.204282	−	0.353827i	0.949904	+	0.312543i	$0.101181\pi$
$648$		0			0
$649$	13.5000	−	7.79423i	0.529921	−	0.305950i
$650$	8.66025	+	15.0000i	0.339683	+	0.588348i
$651$		0			0
$652$	−5.00000	+	8.66025i	−0.195815	+	0.339162i
$653$			30.0000i			1.17399i	0.809590	+	0.586995i	$0.199689\pi$
$653$			30.0000i			1.17399i	−0.809590	+	0.586995i	$0.800311\pi$
$654$		0			0
$655$		0			0
$656$	5.19615	+	9.00000i	0.202876	+	0.351391i
$657$		0			0
$658$	18.0000	−	20.7846i	0.701713	−	0.810268i
$659$	−12.9904	+	7.50000i	−0.506033	+	0.292159i	−0.731202	−	0.682161i	$-0.761040\pi$
$659$	−12.9904	+	7.50000i	−0.506033	+	0.292159i	0.225168	+	0.974320i	$0.427707\pi$
$660$		0			0
$661$	−9.00000	+	5.19615i	−0.350059	+	0.202107i	−0.664711	−	0.747100i	$-0.731446\pi$
$661$	−9.00000	+	5.19615i	−0.350059	+	0.202107i	0.314652	+	0.949207i	$0.398112\pi$
$662$	24.2487	−	14.0000i	0.942453	−	0.544125i
$663$		0			0
$664$	−4.50000	+	2.59808i	−0.174634	+	0.100825i
$665$		0			0
$666$		0			0
$667$		0			0
$668$	10.3923			0.402090
$669$		0			0
$670$		0			0
$671$	20.7846	−	36.0000i	0.802381	−	1.38976i
$672$		0			0
$673$	13.0000	+	22.5167i	0.501113	+	0.867953i	0.999999	+	0.00128586i	$0.000409302\pi$
$673$	13.0000	+	22.5167i	0.501113	+	0.867953i	−0.498886	+	0.866668i	$0.666257\pi$
$674$	11.2583	−	6.50000i	0.433655	−	0.250371i
$675$		0			0
$676$	0.500000	−	0.866025i	0.0192308	−	0.0333087i
$677$	7.79423	−	13.5000i	0.299557	−	0.518847i	−0.676478	−	0.736463i	$-0.736495\pi$
$677$	7.79423	−	13.5000i	0.299557	−	0.518847i	0.976035	+	0.217616i	$0.0698279\pi$
$678$		0			0
$679$	−15.0000	+	17.3205i	−0.575647	+	0.664700i
$680$		0			0
$681$		0			0
$682$			5.19615i			0.198971i
$683$	−18.1865	−	10.5000i	−0.695888	−	0.401771i	0.109926	−	0.993940i	$-0.464939\pi$
$683$	−18.1865	−	10.5000i	−0.695888	−	0.401771i	−0.805814	+	0.592168i	$0.798272\pi$
$684$		0			0
$685$		0			0
$686$	16.4545	−	8.50000i	0.628235	−	0.324532i
$687$		0			0
$688$	4.00000			0.152499
$689$	−10.3923	−	18.0000i	−0.395915	−	0.685745i
$690$		0			0
$691$	−12.0000	−	6.92820i	−0.456502	−	0.263561i	0.254071	−	0.967186i	$-0.418230\pi$
$691$	−12.0000	−	6.92820i	−0.456502	−	0.263561i	−0.710572	+	0.703624i	$0.751564\pi$
$692$	−25.9808			−0.987640
$693$		0			0
$694$	−3.00000			−0.113878
$695$		0			0
$696$		0			0
$697$		0			0
$698$	−27.7128			−1.04895
$699$		0			0
$700$	10.0000	+	8.66025i	0.377964	+	0.327327i
$701$		−	6.00000i		−	0.226617i	−0.993560	−	0.113308i	$-0.963855\pi$
$701$		−	6.00000i		−	0.226617i	0.993560	−	0.113308i	$-0.0361448\pi$
$702$		0			0
$703$		0			0
$704$			3.00000i			0.113067i
$705$		0			0
$706$	−9.00000	−	5.19615i	−0.338719	−	0.195560i
$707$	12.9904	−	4.50000i	0.488554	−	0.169240i
$708$		0			0
$709$	−2.00000	+	3.46410i	−0.0751116	+	0.130097i	−0.901135	−	0.433539i	$-0.857265\pi$
$709$	−2.00000	+	3.46410i	−0.0751116	+	0.130097i	0.826023	+	0.563636i	$0.190598\pi$
$710$		0			0
$711$		0			0
$712$	−9.00000	+	5.19615i	−0.337289	+	0.194734i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		−	9.00000i		−	0.336346i
$717$		0			0
$718$	12.0000			0.447836
$719$	−5.19615	−	9.00000i	−0.193784	−	0.335643i	0.752717	−	0.658344i	$-0.228743\pi$
$719$	−5.19615	−	9.00000i	−0.193784	−	0.335643i	−0.946501	+	0.322700i	$0.895409\pi$
$720$		0			0
$721$	15.0000	+	43.3013i	0.558629	+	1.61262i
$722$	16.4545	−	9.50000i	0.612372	−	0.353553i
$723$		0			0
$724$	18.0000	−	10.3923i	0.668965	−	0.386227i
$725$	−38.9711	+	22.5000i	−1.44735	+	0.835629i
$726$		0			0
$727$	21.0000	−	12.1244i	0.778847	−	0.449667i	−0.0571746	−	0.998364i	$-0.518209\pi$
$727$	21.0000	−	12.1244i	0.778847	−	0.449667i	0.836021	+	0.548697i	$0.184876\pi$
$728$	−1.73205	+	9.00000i	−0.0641941	+	0.333562i
$729$		0			0
$730$		0			0
$731$		0			0
$732$		0			0
$733$			13.8564i			0.511798i	0.966704	+	0.255899i	$0.0823715\pi$
$733$			13.8564i			0.511798i	−0.966704	+	0.255899i	$0.917629\pi$
$734$	−5.19615	+	9.00000i	−0.191793	+	0.332196i
$735$		0			0
$736$		0			0
$737$	−5.19615	+	3.00000i	−0.191403	+	0.110506i
$738$		0			0
$739$	−13.0000	+	22.5167i	−0.478213	+	0.828289i	−0.999688	−	0.0249776i	$-0.992049\pi$
$739$	−13.0000	+	22.5167i	−0.478213	+	0.828289i	0.521475	+	0.853266i	$0.325382\pi$
$740$		0			0
$741$		0			0
$742$	−12.0000	−	10.3923i	−0.440534	−	0.381514i
$743$	5.19615	+	3.00000i	0.190628	+	0.110059i	0.592277	−	0.805735i	$-0.298229\pi$
$743$	5.19615	+	3.00000i	0.190628	+	0.110059i	−0.401648	+	0.915794i	$0.631563\pi$
$744$		0			0
$745$		0			0
$746$	3.46410	+	2.00000i	0.126830	+	0.0732252i
$747$		0			0
$748$		0			0
$749$	−20.7846	+	24.0000i	−0.759453	+	0.876941i
$750$		0			0
$751$	4.00000			0.145962			0.0729810	−	0.997333i	$-0.476749\pi$
$751$	4.00000			0.145962			0.0729810	+	0.997333i	$0.476749\pi$
$752$	5.19615	+	9.00000i	0.189484	+	0.328196i
$753$		0			0
$754$	−27.0000	−	15.5885i	−0.983282	−	0.567698i
$755$		0			0
$756$		0			0
$757$	10.0000			0.363456			0.181728	−	0.983349i	$-0.441831\pi$
$757$	10.0000			0.363456			0.181728	+	0.983349i	$0.441831\pi$
$758$	22.5167	+	13.0000i	0.817842	+	0.472181i
$759$		0			0
$760$		0			0
$761$	41.5692			1.50688			0.753442	−	0.657515i	$-0.228392\pi$
$761$	41.5692			1.50688			0.753442	+	0.657515i	$0.228392\pi$
$762$		0			0
$763$	−4.00000	+	20.7846i	−0.144810	+	0.752453i
$764$			6.00000i			0.217072i
$765$		0			0
$766$	18.0000	+	10.3923i	0.650366	+	0.375489i
$767$			18.0000i			0.649942i
$768$		0			0
$769$	−13.5000	−	7.79423i	−0.486822	−	0.281067i	0.236433	−	0.971648i	$-0.424022\pi$
$769$	−13.5000	−	7.79423i	−0.486822	−	0.281067i	−0.723255	+	0.690581i	$0.757355\pi$
$770$		0			0
$771$		0			0
$772$	−5.50000	+	9.52628i	−0.197949	+	0.342858i
$773$	−20.7846	+	36.0000i	−0.747570	+	1.29483i	0.201414	+	0.979506i	$0.435446\pi$
$773$	−20.7846	+	36.0000i	−0.747570	+	1.29483i	−0.948984	+	0.315324i	$0.897887\pi$
$774$		0			0
$775$	−7.50000	+	4.33013i	−0.269408	+	0.155543i
$776$	−4.33013	−	7.50000i	−0.155443	−	0.269234i
$777$		0			0
$778$	−4.50000	+	7.79423i	−0.161333	+	0.279437i
$779$		0			0
$780$		0			0
$781$	36.0000			1.28818
$782$		0			0
$783$		0			0
$784$	1.00000	+	6.92820i	0.0357143	+	0.247436i
$785$		0			0
$786$		0			0
$787$	21.0000	−	12.1244i	0.748569	−	0.432187i	−0.0766075	−	0.997061i	$-0.524409\pi$
$787$	21.0000	−	12.1244i	0.748569	−	0.432187i	0.825177	+	0.564875i	$0.191076\pi$
$788$	−12.9904	+	7.50000i	−0.462763	+	0.267176i
$789$		0			0
$790$		0			0
$791$	−31.1769	−	6.00000i	−1.10852	−	0.213335i
$792$		0			0
$793$	24.0000	+	41.5692i	0.852265	+	1.47617i
$794$	−24.2487			−0.860555
$795$		0			0
$796$			1.73205i			0.0613909i
$797$	7.79423	−	13.5000i	0.276086	−	0.478195i	−0.694323	−	0.719664i	$-0.744296\pi$
$797$	7.79423	−	13.5000i	0.276086	−	0.478195i	0.970408	+	0.241469i	$0.0776293\pi$
$798$		0			0
$799$		0			0
$800$	−4.33013	+	2.50000i	−0.153093	+	0.0883883i
$801$		0			0
$802$	−15.0000	+	25.9808i	−0.529668	+	0.917413i
$803$	7.79423	−	13.5000i	0.275052	−	0.476405i
$804$		0			0
$805$		0			0
$806$	−5.19615	−	3.00000i	−0.183027	−	0.105670i
$807$		0			0
$808$			5.19615i			0.182800i
$809$	5.19615	+	3.00000i	0.182687	+	0.105474i	0.588555	−	0.808458i	$-0.299697\pi$
$809$	5.19615	+	3.00000i	0.182687	+	0.105474i	−0.405868	+	0.913932i	$0.633031\pi$
$810$		0			0
$811$			10.3923i			0.364923i	0.983213	+	0.182462i	$0.0584065\pi$
$811$			10.3923i			0.364923i	−0.983213	+	0.182462i	$0.941593\pi$
$812$	−23.3827	−	4.50000i	−0.820571	−	0.157919i
$813$		0			0
$814$	−24.0000			−0.841200
$815$		0			0
$816$		0			0
$817$		0			0
$818$	6.92820			0.242239
$819$		0			0
$820$		0			0
$821$	−28.5788	−	16.5000i	−0.997408	−	0.575854i	−0.0899279	−	0.995948i	$-0.528664\pi$
$821$	−28.5788	−	16.5000i	−0.997408	−	0.575854i	−0.907480	+	0.420094i	$0.861997\pi$
$822$		0			0
$823$	−5.50000	−	9.52628i	−0.191718	−	0.332065i	0.754102	−	0.656758i	$-0.228073\pi$
$823$	−5.50000	−	9.52628i	−0.191718	−	0.332065i	−0.945820	+	0.324692i	$0.894739\pi$
$824$	−17.3205			−0.603388
$825$		0			0
$826$	4.50000	+	12.9904i	0.156575	+	0.451993i
$827$		−	3.00000i		−	0.104320i	−0.998639	−	0.0521601i	$-0.983389\pi$
$827$		−	3.00000i		−	0.104320i	0.998639	−	0.0521601i	$-0.0166106\pi$
$828$		0			0
$829$	−27.0000	−	15.5885i	−0.937749	−	0.541409i	−0.0484949	−	0.998823i	$-0.515442\pi$
$829$	−27.0000	−	15.5885i	−0.937749	−	0.541409i	−0.889254	+	0.457414i	$0.848776\pi$
$830$		0			0
$831$		0			0
$832$	−3.00000	−	1.73205i	−0.104006	−	0.0600481i
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$	−27.0000	+	15.5885i	−0.932700	+	0.538494i
$839$	10.3923	+	18.0000i	0.358782	+	0.621429i	0.987758	−	0.155996i	$-0.0498587\pi$
$839$	10.3923	+	18.0000i	0.358782	+	0.621429i	−0.628975	+	0.777425i	$0.716525\pi$
$840$		0			0
$841$	26.0000	−	45.0333i	0.896552	−	1.55287i
$842$		−	10.0000i		−	0.344623i
$843$		0			0
$844$	2.00000			0.0688428
$845$		0			0
$846$		0			0
$847$	−5.00000	+	1.73205i	−0.171802	+	0.0595140i
$848$	5.19615	−	3.00000i	0.178437	−	0.103020i
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$	−9.00000	+	5.19615i	−0.308154	+	0.177913i	−0.646100	−	0.763253i	$-0.723601\pi$
$853$	−9.00000	+	5.19615i	−0.308154	+	0.177913i	0.337946	+	0.941165i	$0.390268\pi$
$854$	27.7128	+	24.0000i	0.948313	+	0.821263i
$855$		0			0
$856$	−6.00000	−	10.3923i	−0.205076	−	0.355202i
$857$	−10.3923			−0.354994			−0.177497	−	0.984121i	$-0.556800\pi$
$857$	−10.3923			−0.354994			−0.177497	+	0.984121i	$0.556800\pi$
$858$		0			0
$859$		−	48.4974i		−	1.65471i	−0.561679	−	0.827355i	$-0.689844\pi$
$859$		−	48.4974i		−	1.65471i	0.561679	−	0.827355i	$-0.310156\pi$
$860$		0			0
$861$		0			0
$862$	9.00000	+	15.5885i	0.306541	+	0.530945i
$863$	5.19615	−	3.00000i	0.176879	−	0.102121i	−0.408946	−	0.912558i	$-0.634104\pi$
$863$	5.19615	−	3.00000i	0.176879	−	0.102121i	0.585826	+	0.810437i	$0.300770\pi$
$864$		0			0
$865$		0			0
$866$	−6.06218	+	10.5000i	−0.206001	+	0.356805i
$867$		0			0
$868$	−4.50000	−	0.866025i	−0.152740	−	0.0293948i
$869$	−33.7750	−	19.5000i	−1.14574	−	0.661492i
$870$		0			0
$871$		−	6.92820i		−	0.234753i
$872$	−6.92820	−	4.00000i	−0.234619	−	0.135457i
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	2.00000			0.0675352			0.0337676	−	0.999430i	$-0.489249\pi$
$877$	2.00000			0.0675352			0.0337676	+	0.999430i	$0.489249\pi$
$878$	7.79423	+	13.5000i	0.263042	+	0.455603i
$879$		0			0
$880$		0			0
$881$	31.1769			1.05038			0.525188	−	0.850986i	$-0.323995\pi$
$881$	31.1769			1.05038			0.525188	+	0.850986i	$0.323995\pi$
$882$		0			0
$883$	−2.00000			−0.0673054			−0.0336527	−	0.999434i	$-0.510714\pi$
$883$	−2.00000			−0.0673054			−0.0336527	+	0.999434i	$0.510714\pi$
$884$		0			0
$885$		0			0
$886$	13.5000	+	23.3827i	0.453541	+	0.785557i
$887$	−31.1769			−1.04682			−0.523409	−	0.852081i	$-0.675340\pi$
$887$	−31.1769			−1.04682			−0.523409	+	0.852081i	$0.675340\pi$
$888$		0			0
$889$	−20.0000	+	6.92820i	−0.670778	+	0.232364i
$890$		0			0
$891$		0			0
$892$	−4.50000	−	2.59808i	−0.150671	−	0.0869900i
$893$		0			0
$894$		0			0
$895$		0			0
$896$	−2.59808	−	0.500000i	−0.0867956	−	0.0167038i
$897$		0			0
$898$	15.0000	−	25.9808i	0.500556	−	0.866989i
$899$	7.79423	−	13.5000i	0.259952	−	0.450250i
$900$		0			0
$901$		0			0
$902$	15.5885	+	27.0000i	0.519039	+	0.899002i
$903$		0			0
$904$	6.00000	−	10.3923i	0.199557	−	0.345643i
$905$		0			0
$906$		0			0
$907$	22.0000			0.730498			0.365249	−	0.930910i	$-0.380984\pi$
$907$	22.0000			0.730498			0.365249	+	0.930910i	$0.380984\pi$
$908$	−12.9904	−	22.5000i	−0.431101	−	0.746689i
$909$		0			0
$910$		0			0
$911$	−31.1769	+	18.0000i	−1.03294	+	0.596367i	−0.917825	−	0.396986i	$-0.870056\pi$
$911$	−31.1769	+	18.0000i	−1.03294	+	0.596367i	−0.115113	+	0.993352i	$0.536723\pi$
$912$		0			0
$913$	−13.5000	+	7.79423i	−0.446785	+	0.257951i
$914$	19.0526	−	11.0000i	0.630203	−	0.363848i
$915$		0			0
$916$	−6.00000	+	3.46410i	−0.198246	+	0.114457i
$917$	38.9711	−	13.5000i	1.28694	−	0.445809i
$918$		0			0
$919$	17.5000	+	30.3109i	0.577272	+	0.999864i	0.995791	+	0.0916559i	$0.0292160\pi$
$919$	17.5000	+	30.3109i	0.577272	+	0.999864i	−0.418519	+	0.908208i	$0.637451\pi$
$920$		0			0
$921$		0			0
$922$			15.5885i			0.513378i
$923$	−20.7846	+	36.0000i	−0.684134	+	1.18495i
$924$		0			0
$925$	−20.0000	−	34.6410i	−0.657596	−	1.13899i
$926$	4.33013	−	2.50000i	0.142297	−	0.0821551i
$927$		0			0
$928$	4.50000	−	7.79423i	0.147720	−	0.255858i
$929$	−20.7846	+	36.0000i	−0.681921	+	1.18112i	0.292473	+	0.956274i	$0.405522\pi$
$929$	−20.7846	+	36.0000i	−0.681921	+	1.18112i	−0.974394	+	0.224848i	$0.927811\pi$
$930$		0			0
$931$		0			0
$932$	−15.5885	−	9.00000i	−0.510617	−	0.294805i
$933$		0			0
$934$		−	5.19615i		−	0.170023i
$935$		0			0
$936$		0			0
$937$			34.6410i			1.13167i	0.824518	+	0.565836i	$0.191447\pi$
$937$			34.6410i			1.13167i	−0.824518	+	0.565836i	$0.808553\pi$
$938$	−1.73205	−	5.00000i	−0.0565535	−	0.163256i
$939$		0			0
$940$		0			0
$941$	2.59808	+	4.50000i	0.0846949	+	0.146696i	0.905261	−	0.424856i	$-0.139675\pi$
$941$	2.59808	+	4.50000i	0.0846949	+	0.146696i	−0.820566	+	0.571551i	$0.806342\pi$
$942$		0			0
$943$		0			0
$944$	−5.19615			−0.169120
$945$		0			0
$946$	12.0000			0.390154
$947$	−7.79423	−	4.50000i	−0.253278	−	0.146230i	0.367986	−	0.929831i	$-0.380047\pi$
$947$	−7.79423	−	4.50000i	−0.253278	−	0.146230i	−0.621264	+	0.783601i	$0.713381\pi$
$948$		0			0
$949$	9.00000	+	15.5885i	0.292152	+	0.506023i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	18.0000i		−	0.583077i	−0.956559	−	0.291539i	$-0.905833\pi$
$953$		−	18.0000i		−	0.583077i	0.956559	−	0.291539i	$-0.0941672\pi$
$954$		0			0
$955$		0			0
$956$			12.0000i			0.388108i
$957$		0			0
$958$	−9.00000	−	5.19615i	−0.290777	−	0.167880i
$959$	−10.3923	−	30.0000i	−0.335585	−	0.968751i
$960$		0			0
$961$	−14.0000	+	24.2487i	−0.451613	+	0.782216i
$962$	13.8564	−	24.0000i	0.446748	−	0.773791i
$963$		0			0
$964$	−10.5000	+	6.06218i	−0.338182	+	0.195250i
$965$		0			0
$966$		0			0
$967$	−28.0000	+	48.4974i	−0.900419	+	1.55957i	−0.0734686	+	0.997298i	$0.523407\pi$
$967$	−28.0000	+	48.4974i	−0.900419	+	1.55957i	−0.826951	+	0.562274i	$0.809926\pi$
$968$		−	2.00000i		−	0.0642824i
$969$		0			0
$970$		0			0
$971$	15.5885	+	27.0000i	0.500257	+	0.866471i	1.00000		0.000297246i	$9.46163e-5\pi$
$971$	15.5885	+	27.0000i	0.500257	+	0.866471i	−0.499743	+	0.866174i	$0.666572\pi$
$972$		0			0
$973$	−18.0000	−	3.46410i	−0.577054	−	0.111054i
$974$	−9.52628	+	5.50000i	−0.305242	+	0.176231i
$975$		0			0
$976$	−12.0000	+	6.92820i	−0.384111	+	0.221766i
$977$	−15.5885	+	9.00000i	−0.498719	+	0.287936i	−0.728184	−	0.685381i	$-0.759636\pi$
$977$	−15.5885	+	9.00000i	−0.498719	+	0.287936i	0.229465	+	0.973317i	$0.426302\pi$
$978$		0			0
$979$	−27.0000	+	15.5885i	−0.862924	+	0.498209i
$980$		0			0
$981$		0			0
$982$	−18.0000	−	31.1769i	−0.574403	−	0.994895i
$983$	20.7846			0.662926			0.331463	−	0.943468i	$-0.392458\pi$
$983$	20.7846			0.662926			0.331463	+	0.943468i	$0.392458\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	4.00000	−	6.92820i	0.127064	−	0.220082i	−0.795474	−	0.605988i	$-0.792778\pi$
$991$	4.00000	−	6.92820i	0.127064	−	0.220082i	0.922538	+	0.385906i	$0.126111\pi$
$992$	0.866025	−	1.50000i	0.0274963	−	0.0476250i
$993$		0			0
$994$	−6.00000	+	31.1769i	−0.190308	+	0.988872i
$995$		0			0
$996$		0			0
$997$		−	38.1051i		−	1.20680i	−0.797438	−	0.603401i	$-0.793812\pi$
$997$		−	38.1051i		−	1.20680i	0.797438	−	0.603401i	$-0.206188\pi$
$998$	−13.8564	−	8.00000i	−0.438617	−	0.253236i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1134.2.t.a.1025.1		4
3.2	odd	2	inner	1134.2.t.a.1025.2		4
7.5	odd	6		1134.2.l.d.215.2		4
9.2	odd	6		1134.2.l.d.269.1		4
9.4	even	3		378.2.k.a.269.2	yes	4
9.5	odd	6		378.2.k.a.269.1	yes	4
9.7	even	3		1134.2.l.d.269.2		4
21.5	even	6		1134.2.l.d.215.1		4
63.4	even	3		2646.2.d.c.2645.3		4
63.5	even	6		378.2.k.a.215.2	yes	4
63.31	odd	6		2646.2.d.c.2645.4		4
63.32	odd	6		2646.2.d.c.2645.1		4
63.40	odd	6		378.2.k.a.215.1	✓	4
63.47	even	6	inner	1134.2.t.a.593.1		4
63.59	even	6		2646.2.d.c.2645.2		4
63.61	odd	6	inner	1134.2.t.a.593.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.k.a.215.1	✓	4	63.40	odd	6
378.2.k.a.215.2	yes	4	63.5	even	6
378.2.k.a.269.1	yes	4	9.5	odd	6
378.2.k.a.269.2	yes	4	9.4	even	3
1134.2.l.d.215.1		4	21.5	even	6
1134.2.l.d.215.2		4	7.5	odd	6
1134.2.l.d.269.1		4	9.2	odd	6
1134.2.l.d.269.2		4	9.7	even	3
1134.2.t.a.593.1		4	63.47	even	6	inner
1134.2.t.a.593.2		4	63.61	odd	6	inner
1134.2.t.a.1025.1		4	1.1	even	1	trivial
1134.2.t.a.1025.2		4	3.2	odd	2	inner
2646.2.d.c.2645.1		4	63.32	odd	6
2646.2.d.c.2645.2		4	63.59	even	6
2646.2.d.c.2645.3		4	63.4	even	3
2646.2.d.c.2645.4		4	63.31	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1134.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-2.50000 + 0.866025i) q^{7} -1.00000i q^{8} -3.00000i q^{11} +(3.00000 + 1.73205i) q^{13} +(2.59808 + 0.500000i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.50000 + 2.59808i) q^{22} -5.00000 q^{25} +(-1.73205 - 3.00000i) q^{26} +(-2.00000 - 1.73205i) q^{28} +(7.79423 - 4.50000i) q^{29} +(1.50000 - 0.866025i) q^{31} +(0.866025 - 0.500000i) q^{32} +(4.00000 + 6.92820i) q^{37} +(5.19615 - 9.00000i) q^{41} +(-2.00000 - 3.46410i) q^{43} +(2.59808 - 1.50000i) q^{44} +(5.19615 - 9.00000i) q^{47} +(5.50000 - 4.33013i) q^{49} +(4.33013 + 2.50000i) q^{50} +3.46410i q^{52} +(-5.19615 - 3.00000i) q^{53} +(0.866025 + 2.50000i) q^{56} -9.00000 q^{58} +(2.59808 + 4.50000i) q^{59} +(12.0000 + 6.92820i) q^{61} -1.73205 q^{62} -1.00000 q^{64} +(-1.00000 - 1.73205i) q^{67} +12.0000i q^{71} +(4.50000 + 2.59808i) q^{73} -8.00000i q^{74} +(2.59808 + 7.50000i) q^{77} +(6.50000 - 11.2583i) q^{79} +(-9.00000 + 5.19615i) q^{82} +(-2.59808 - 4.50000i) q^{83} +4.00000i q^{86} -3.00000 q^{88} +(-5.19615 - 9.00000i) q^{89} +(-9.00000 - 1.73205i) q^{91} +(-9.00000 + 5.19615i) q^{94} +(7.50000 - 4.33013i) q^{97} +(-6.92820 + 1.00000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} - 10 q^{7} + 12 q^{13} - 2 q^{16} - 6 q^{22} - 20 q^{25} - 8 q^{28} + 6 q^{31} + 16 q^{37} - 8 q^{43} + 22 q^{49} - 36 q^{58} + 48 q^{61} - 4 q^{64} - 4 q^{67} + 18 q^{73} + 26 q^{79} - 36 q^{82}+ \cdots + 30 q^{97}+O(q^{100}) \) 4 * q + 2 * q^4 - 10 * q^7 + 12 * q^13 - 2 * q^16 - 6 * q^22 - 20 * q^25 - 8 * q^28 + 6 * q^31 + 16 * q^37 - 8 * q^43 + 22 * q^49 - 36 * q^58 + 48 * q^61 - 4 * q^64 - 4 * q^67 + 18 * q^73 + 26 * q^79 - 36 * q^82 - 12 * q^88 - 36 * q^91 - 36 * q^94 + 30 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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