LMFDB - Embedded newform 1134.2.l.d.269.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1134,2,Mod(215,1134)] 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("1134.215"); 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([5, 5])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [4,0,0,-4,0,0,8,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$9.05503558921$
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:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 378)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			269.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1134.269
Dual form			1134.2.l.d.215.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000i q^{2} -1.00000 q^{4} +(2.00000 + 1.73205i) q^{7} +1.00000i q^{8} +(2.59808 - 1.50000i) q^{11} +(-3.00000 + 1.73205i) q^{13} +(1.73205 - 2.00000i) q^{14} +1.00000 q^{16} +(-1.50000 - 2.59808i) q^{22} +(2.50000 + 4.33013i) q^{25} +(1.73205 + 3.00000i) q^{26} +(-2.00000 - 1.73205i) q^{28} +(7.79423 + 4.50000i) q^{29} +1.73205i q^{31} -1.00000i q^{32} +(4.00000 + 6.92820i) q^{37} +(-5.19615 - 9.00000i) q^{41} +(-2.00000 + 3.46410i) q^{43} +(-2.59808 + 1.50000i) q^{44} +10.3923 q^{47} +(1.00000 + 6.92820i) q^{49} +(4.33013 - 2.50000i) q^{50} +(3.00000 - 1.73205i) q^{52} +(5.19615 + 3.00000i) q^{53} +(-1.73205 + 2.00000i) q^{56} +(4.50000 - 7.79423i) q^{58} +5.19615 q^{59} -13.8564i q^{61} +1.73205 q^{62} -1.00000 q^{64} +2.00000 q^{67} -12.0000i q^{71} +(4.50000 + 2.59808i) q^{73} +(6.92820 - 4.00000i) q^{74} +(7.79423 + 1.50000i) q^{77} -13.0000 q^{79} +(-9.00000 + 5.19615i) q^{82} +(2.59808 - 4.50000i) q^{83} +(3.46410 + 2.00000i) q^{86} +(1.50000 + 2.59808i) q^{88} +(5.19615 + 9.00000i) q^{89} +(-9.00000 - 1.73205i) q^{91} -10.3923i q^{94} +(-7.50000 - 4.33013i) q^{97} +(6.92820 - 1.00000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} + 8 q^{7} - 12 q^{13} + 4 q^{16} - 6 q^{22} + 10 q^{25} - 8 q^{28} + 16 q^{37} - 8 q^{43} + 4 q^{49} + 12 q^{52} + 18 q^{58} - 4 q^{64} + 8 q^{67} + 18 q^{73} - 52 q^{79} - 36 q^{82} + 6 q^{88}+ \cdots - 30 q^{97}+O(q^{100}) $ 4 * q - 4 * q^4 + 8 * q^7 - 12 * q^13 + 4 * q^16 - 6 * q^22 + 10 * q^25 - 8 * q^28 + 16 * q^37 - 8 * q^43 + 4 * q^49 + 12 * q^52 + 18 * q^58 - 4 * q^64 + 8 * q^67 + 18 * q^73 - 52 * q^79 - 36 * q^82 + 6 * q^88 - 36 * q^91 - 30 * q^97

Character values

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

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

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$5$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$6$		0			0
$7$	2.00000	+	1.73205i	0.755929	+	0.654654i
$7$	2.00000	+	1.73205i	0.755929	+	0.654654i
$8$			1.00000i			0.353553i
$9$		0			0
$10$		0			0
$11$	2.59808	−	1.50000i	0.783349	−	0.452267i	−0.0542666	−	0.998526i	$-0.517282\pi$
$11$	2.59808	−	1.50000i	0.783349	−	0.452267i	0.837616	+	0.546259i	$0.183949\pi$
$12$		0			0
$13$	−3.00000	+	1.73205i	−0.832050	+	0.480384i	−0.854554	−	0.519362i	$-0.826170\pi$
$13$	−3.00000	+	1.73205i	−0.832050	+	0.480384i	0.0225039	+	0.999747i	$0.492836\pi$
$14$	1.73205	−	2.00000i	0.462910	−	0.534522i
$15$		0			0
$16$	1.00000			0.250000
$17$		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		0.500000	−	0.866025i	$-0.333333\pi$
$23$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$24$		0			0
$25$	2.50000	+	4.33013i	0.500000	+	0.866025i
$26$	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	0.998323	−	0.0578882i	$-0.0184367\pi$
$29$	7.79423	+	4.50000i	1.44735	+	0.835629i	0.449029	+	0.893517i	$0.351770\pi$
$30$		0			0
$31$			1.73205i			0.311086i	0.987829	+	0.155543i	$0.0497126\pi$
$31$			1.73205i			0.311086i	−0.987829	+	0.155543i	$0.950287\pi$
$32$		−	1.00000i		−	0.176777i
$33$		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	−0.911812	−	0.410608i	$-0.865317\pi$
$41$	−5.19615	−	9.00000i	−0.811503	−	1.40556i	0.100309	−	0.994956i	$-0.468017\pi$
$42$		0			0
$43$	−2.00000	+	3.46410i	−0.304997	+	0.528271i	−0.977261	−	0.212041i	$-0.931989\pi$
$43$	−2.00000	+	3.46410i	−0.304997	+	0.528271i	0.672264	+	0.740312i	$0.265322\pi$
$44$	−2.59808	+	1.50000i	−0.391675	+	0.226134i
$45$		0			0
$46$		0			0
$47$	10.3923			1.51587			0.757937	−	0.652328i	$-0.226208\pi$
$47$	10.3923			1.51587			0.757937	+	0.652328i	$0.226208\pi$
$48$		0			0
$49$	1.00000	+	6.92820i	0.142857	+	0.989743i
$50$	4.33013	−	2.50000i	0.612372	−	0.353553i
$51$		0			0
$52$	3.00000	−	1.73205i	0.416025	−	0.240192i
$53$	5.19615	+	3.00000i	0.713746	+	0.412082i	0.812447	−	0.583036i	$-0.198135\pi$
$53$	5.19615	+	3.00000i	0.713746	+	0.412082i	−0.0987002	+	0.995117i	$0.531468\pi$
$54$		0			0
$55$		0			0
$56$	−1.73205	+	2.00000i	−0.231455	+	0.267261i
$57$		0			0
$58$	4.50000	−	7.79423i	0.590879	−	1.02343i
$59$	5.19615			0.676481			0.338241	−	0.941060i	$-0.390168\pi$
$59$	5.19615			0.676481			0.338241	+	0.941060i	$0.390168\pi$
$60$		0			0
$61$		−	13.8564i		−	1.77413i	−0.461644	−	0.887066i	$-0.652740\pi$
$61$		−	13.8564i		−	1.77413i	0.461644	−	0.887066i	$-0.347260\pi$
$62$	1.73205			0.219971
$63$		0			0
$64$	−1.00000			−0.125000
$65$		0			0
$66$		0			0
$67$	2.00000			0.244339			0.122169	−	0.992509i	$-0.461015\pi$
$67$	2.00000			0.244339			0.122169	+	0.992509i	$0.461015\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	12.0000i		−	1.42414i	−0.702109	−	0.712069i	$-0.747758\pi$
$71$		−	12.0000i		−	1.42414i	0.702109	−	0.712069i	$-0.252242\pi$
$72$		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	$0.568317\pi$
$74$	6.92820	−	4.00000i	0.805387	−	0.464991i
$75$		0			0
$76$		0			0
$77$	7.79423	+	1.50000i	0.888235	+	0.170941i
$78$		0			0
$79$	−13.0000			−1.46261			−0.731307	−	0.682048i	$-0.761089\pi$
$79$	−13.0000			−1.46261			−0.731307	+	0.682048i	$0.761089\pi$
$80$		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	$-0.741281\pi$
$83$	2.59808	−	4.50000i	0.285176	−	0.493939i	0.972652	+	0.232268i	$0.0746146\pi$
$84$		0			0
$85$		0			0
$86$	3.46410	+	2.00000i	0.373544	+	0.215666i
$87$		0			0
$88$	1.50000	+	2.59808i	0.159901	+	0.276956i
$89$	5.19615	+	9.00000i	0.550791	+	0.953998i	0.998218	+	0.0596775i	$0.0190072\pi$
$89$	5.19615	+	9.00000i	0.550791	+	0.953998i	−0.447427	+	0.894321i	$0.647659\pi$
$90$		0			0
$91$	−9.00000	−	1.73205i	−0.943456	−	0.181568i
$92$		0			0
$93$		0			0
$94$		−	10.3923i		−	1.07188i
$95$		0			0
$96$		0			0
$97$	−7.50000	−	4.33013i	−0.761510	−	0.439658i	0.0683279	−	0.997663i	$-0.478234\pi$
$97$	−7.50000	−	4.33013i	−0.761510	−	0.439658i	−0.829837	+	0.558005i	$0.811567\pi$
$98$	6.92820	−	1.00000i	0.699854	−	0.101015i
$99$		0			0
$100$	−2.50000	−	4.33013i	−0.250000	−	0.433013i
$101$	−2.59808	−	4.50000i	−0.258518	−	0.447767i	0.707327	−	0.706887i	$-0.249901\pi$
$101$	−2.59808	−	4.50000i	−0.258518	−	0.447767i	−0.965845	+	0.259120i	$0.916568\pi$
$102$		0			0
$103$	15.0000	+	8.66025i	1.47799	+	0.853320i	0.999691	−	0.0248745i	$-0.00791862\pi$
$103$	15.0000	+	8.66025i	1.47799	+	0.853320i	0.478303	+	0.878195i	$0.341252\pi$
$104$	−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	−0.909624	−	0.415432i	$-0.863630\pi$
$107$	−10.3923	+	6.00000i	−1.00466	+	0.580042i	−0.0950377	+	0.995474i	$0.530297\pi$
$108$		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
$112$	2.00000	+	1.73205i	0.188982	+	0.163663i
$113$	10.3923	−	6.00000i	0.977626	−	0.564433i	0.0760733	−	0.997102i	$-0.475762\pi$
$113$	10.3923	−	6.00000i	0.977626	−	0.564433i	0.901553	+	0.432670i	$0.142428\pi$
$114$		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
$121$	−1.00000	+	1.73205i	−0.0909091	+	0.157459i
$122$	−13.8564			−1.25450
$123$		0			0
$124$		−	1.73205i		−	0.155543i
$125$		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	$0.384500\pi$
$128$			1.00000i			0.0883883i
$129$		0			0
$130$		0			0
$131$	−7.79423	+	13.5000i	−0.680985	+	1.17950i	0.293696	+	0.955899i	$0.405115\pi$
$131$	−7.79423	+	13.5000i	−0.680985	+	1.17950i	−0.974681	+	0.223602i	$0.928219\pi$
$132$		0			0
$133$		0			0
$134$		−	2.00000i		−	0.172774i
$135$		0			0
$136$		0			0
$137$	−10.3923	+	6.00000i	−0.887875	+	0.512615i	−0.873247	−	0.487278i	$-0.837990\pi$
$137$	−10.3923	+	6.00000i	−0.887875	+	0.512615i	−0.0146279	+	0.999893i	$0.504656\pi$
$138$		0			0
$139$	−6.00000	+	3.46410i	−0.508913	+	0.293821i	−0.732387	−	0.680889i	$-0.761594\pi$
$139$	−6.00000	+	3.46410i	−0.508913	+	0.293821i	0.223474	+	0.974710i	$0.428260\pi$
$140$		0			0
$141$		0			0
$142$	−12.0000			−1.00702
$143$	−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
$149$	−12.9904	−	7.50000i	−1.06421	−	0.614424i	−0.137619	−	0.990485i	$-0.543945\pi$
$149$	−12.9904	−	7.50000i	−1.06421	−	0.614424i	−0.926595	+	0.376061i	$0.877278\pi$
$150$		0			0
$151$	11.5000	+	19.9186i	0.935857	+	1.62095i	0.773099	+	0.634285i	$0.218706\pi$
$151$	11.5000	+	19.9186i	0.935857	+	1.62095i	0.162758	+	0.986666i	$0.447961\pi$
$152$		0			0
$153$		0			0
$154$	1.50000	−	7.79423i	0.120873	−	0.628077i
$155$		0			0
$156$		0			0
$157$		−	10.3923i		−	0.829396i	−0.909959	−	0.414698i	$-0.863887\pi$
$157$		−	10.3923i		−	0.829396i	0.909959	−	0.414698i	$-0.136113\pi$
$158$			13.0000i			1.03422i
$159$		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	$0.705245\pi$
$164$	5.19615	+	9.00000i	0.405751	+	0.702782i
$165$		0			0
$166$	−4.50000	−	2.59808i	−0.349268	−	0.201650i
$167$	−5.19615	−	9.00000i	−0.402090	−	0.696441i	0.591888	−	0.806020i	$-0.298383\pi$
$167$	−5.19615	−	9.00000i	−0.402090	−	0.696441i	−0.993978	+	0.109580i	$0.965050\pi$
$168$		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
$173$	−25.9808			−1.97528			−0.987640	−	0.156737i	$-0.949903\pi$
$173$	−25.9808			−1.97528			−0.987640	+	0.156737i	$0.949903\pi$
$174$		0			0
$175$	−2.50000	+	12.9904i	−0.188982	+	0.981981i
$176$	2.59808	−	1.50000i	0.195837	−	0.113067i
$177$		0			0
$178$	9.00000	−	5.19615i	0.674579	−	0.389468i
$179$	7.79423	+	4.50000i	0.582568	+	0.336346i	0.762153	−	0.647397i	$-0.224142\pi$
$179$	7.79423	+	4.50000i	0.582568	+	0.336346i	−0.179585	+	0.983742i	$0.557476\pi$
$180$		0			0
$181$		−	20.7846i		−	1.54491i	−0.635071	−	0.772454i	$-0.719029\pi$
$181$		−	20.7846i		−	1.54491i	0.635071	−	0.772454i	$-0.280971\pi$
$182$	−1.73205	+	9.00000i	−0.128388	+	0.667124i
$183$		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
$191$			6.00000i			0.434145i	0.976156	+	0.217072i	$0.0696508\pi$
$191$			6.00000i			0.434145i	−0.976156	+	0.217072i	$0.930349\pi$
$192$		0			0
$193$	−11.0000			−0.791797			−0.395899	−	0.918294i	$-0.629567\pi$
$193$	−11.0000			−0.791797			−0.395899	+	0.918294i	$0.629567\pi$
$194$	−4.33013	+	7.50000i	−0.310885	+	0.538469i
$195$		0			0
$196$	−1.00000	−	6.92820i	−0.0714286	−	0.494872i
$197$		−	15.0000i		−	1.06871i	−0.845262	−	0.534353i	$-0.820555\pi$
$197$		−	15.0000i		−	1.06871i	0.845262	−	0.534353i	$-0.179445\pi$
$198$		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	$0.647113\pi$
$200$	−4.33013	+	2.50000i	−0.306186	+	0.176777i
$201$		0			0
$202$	−4.50000	+	2.59808i	−0.316619	+	0.182800i
$203$	7.79423	+	22.5000i	0.547048	+	1.57919i
$204$		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	0.898392	−	0.439194i	$-0.144736\pi$
$211$	1.00000	+	1.73205i	0.0688428	+	0.119239i	−0.829549	+	0.558433i	$0.811403\pi$
$212$	−5.19615	−	3.00000i	−0.356873	−	0.206041i
$213$		0			0
$214$	6.00000	+	10.3923i	0.410152	+	0.710403i
$215$		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	$-0.277671\pi$
$223$	4.50000	+	2.59808i	0.301342	+	0.173980i	−0.341703	+	0.939808i	$0.611004\pi$
$224$	1.73205	−	2.00000i	0.115728	−	0.133631i
$225$		0			0
$226$	−6.00000	−	10.3923i	−0.399114	−	0.691286i
$227$	−12.9904	−	22.5000i	−0.862202	−	1.49338i	−0.869799	−	0.493406i	$-0.835752\pi$
$227$	−12.9904	−	22.5000i	−0.862202	−	1.49338i	0.00759708	−	0.999971i	$-0.497582\pi$
$228$		0			0
$229$	−6.00000	−	3.46410i	−0.396491	−	0.228914i	0.288478	−	0.957487i	$-0.406851\pi$
$229$	−6.00000	−	3.46410i	−0.396491	−	0.228914i	−0.684969	+	0.728572i	$0.740184\pi$
$230$		0			0
$231$		0			0
$232$	−4.50000	+	7.79423i	−0.295439	+	0.511716i
$233$	15.5885	−	9.00000i	1.02123	−	0.589610i	0.106773	−	0.994283i	$-0.465948\pi$
$233$	15.5885	−	9.00000i	1.02123	−	0.589610i	0.914461	+	0.404674i	$0.132615\pi$
$234$		0			0
$235$		0			0
$236$	−5.19615			−0.338241
$237$		0			0
$238$		0			0
$239$	10.3923	−	6.00000i	0.672222	−	0.388108i	−0.124696	−	0.992195i	$-0.539796\pi$
$239$	10.3923	−	6.00000i	0.672222	−	0.388108i	0.796918	+	0.604087i	$0.206462\pi$
$240$		0			0
$241$	10.5000	−	6.06218i	0.676364	−	0.390499i	−0.122119	−	0.992515i	$-0.538969\pi$
$241$	10.5000	−	6.06218i	0.676364	−	0.390499i	0.798484	+	0.602016i	$0.205636\pi$
$242$	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
$248$	−1.73205			−0.109985
$249$		0			0
$250$		0			0
$251$	−25.9808			−1.63989			−0.819946	−	0.572441i	$-0.805996\pi$
$251$	−25.9808			−1.63989			−0.819946	+	0.572441i	$0.805996\pi$
$252$		0			0
$253$		0			0
$254$		−	8.00000i		−	0.501965i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−10.3923	+	18.0000i	−0.648254	+	1.12281i	0.335285	+	0.942117i	$0.391167\pi$
$257$	−10.3923	+	18.0000i	−0.648254	+	1.12281i	−0.983540	+	0.180693i	$0.942166\pi$
$258$		0			0
$259$	−4.00000	+	20.7846i	−0.248548	+	1.29149i
$260$		0			0
$261$		0			0
$262$	13.5000	+	7.79423i	0.834033	+	0.481529i
$263$	−20.7846	+	12.0000i	−1.28163	+	0.739952i	−0.977147	−	0.212565i	$-0.931818\pi$
$263$	−20.7846	+	12.0000i	−1.28163	+	0.739952i	−0.304487	+	0.952517i	$0.598485\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	−2.00000			−0.122169
$269$	−7.79423	+	13.5000i	−0.475223	+	0.823110i	−0.999597	−	0.0283781i	$-0.990966\pi$
$269$	−7.79423	+	13.5000i	−0.475223	+	0.823110i	0.524375	+	0.851488i	$0.324299\pi$
$270$		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
$275$	12.9904	+	7.50000i	0.783349	+	0.452267i
$276$		0			0
$277$	−7.00000	−	12.1244i	−0.420589	−	0.728482i	0.575408	−	0.817867i	$-0.304843\pi$
$277$	−7.00000	−	12.1244i	−0.420589	−	0.728482i	−0.995997	+	0.0893846i	$0.971510\pi$
$278$	3.46410	+	6.00000i	0.207763	+	0.359856i
$279$		0			0
$280$		0			0
$281$	−5.19615	−	3.00000i	−0.309976	−	0.178965i	0.336939	−	0.941526i	$-0.390608\pi$
$281$	−5.19615	−	3.00000i	−0.309976	−	0.178965i	−0.646916	+	0.762561i	$0.723942\pi$
$282$		0			0
$283$		−	6.92820i		−	0.411839i	−0.978569	−	0.205919i	$-0.933982\pi$
$283$		−	6.92820i		−	0.411839i	0.978569	−	0.205919i	$-0.0660185\pi$
$284$			12.0000i			0.712069i
$285$		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
$292$	−4.50000	−	2.59808i	−0.263343	−	0.152041i
$293$	−2.59808	−	4.50000i	−0.151781	−	0.262893i	0.780101	−	0.625653i	$-0.215168\pi$
$293$	−2.59808	−	4.50000i	−0.151781	−	0.262893i	−0.931882	+	0.362761i	$0.881834\pi$
$294$		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
$301$	−10.0000	+	3.46410i	−0.576390	+	0.199667i
$302$	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	$0.835437\pi$
$308$	−7.79423	−	1.50000i	−0.444117	−	0.0854704i
$309$		0			0
$310$		0			0
$311$	−31.1769			−1.76788			−0.883940	−	0.467600i	$-0.845119\pi$
$311$	−31.1769			−1.76788			−0.883940	+	0.467600i	$0.845119\pi$
$312$		0			0
$313$		−	20.7846i		−	1.17482i	−0.809291	−	0.587408i	$-0.800148\pi$
$313$		−	20.7846i		−	1.17482i	0.809291	−	0.587408i	$-0.199852\pi$
$314$	−10.3923			−0.586472
$315$		0			0
$316$	13.0000			0.731307
$317$			9.00000i			0.505490i	0.967533	+	0.252745i	$0.0813334\pi$
$317$			9.00000i			0.505490i	−0.967533	+	0.252745i	$0.918667\pi$
$318$		0			0
$319$	27.0000			1.51171
$320$		0			0
$321$		0			0
$322$		0			0
$323$		0			0
$324$		0			0
$325$	−15.0000	−	8.66025i	−0.832050	−	0.480384i
$326$	8.66025	−	5.00000i	0.479647	−	0.276924i
$327$		0			0
$328$	9.00000	−	5.19615i	0.496942	−	0.286910i
$329$	20.7846	+	18.0000i	1.14589	+	0.992372i
$330$		0			0
$331$	28.0000			1.53902			0.769510	−	0.638635i	$-0.220501\pi$
$331$	28.0000			1.53902			0.769510	+	0.638635i	$0.220501\pi$
$332$	−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	0.632882	−	0.774248i	$-0.281872\pi$
$337$	−6.50000	−	11.2583i	−0.354078	−	0.613280i	−0.986960	+	0.160968i	$0.948538\pi$
$338$	0.866025	+	0.500000i	0.0471056	+	0.0271964i
$339$		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
$346$			25.9808i			1.39673i
$347$		−	3.00000i		−	0.161048i	−0.996753	−	0.0805242i	$-0.974341\pi$
$347$		−	3.00000i		−	0.161048i	0.996753	−	0.0805242i	$-0.0256594\pi$
$348$		0			0
$349$	−24.0000	−	13.8564i	−1.28469	−	0.741716i	−0.306988	−	0.951713i	$-0.599321\pi$
$349$	−24.0000	−	13.8564i	−1.28469	−	0.741716i	−0.977702	+	0.209997i	$0.932655\pi$
$350$	12.9904	+	2.50000i	0.694365	+	0.133631i
$351$		0			0
$352$	−1.50000	−	2.59808i	−0.0799503	−	0.138478i
$353$	5.19615	+	9.00000i	0.276563	+	0.479022i	0.970528	−	0.240987i	$-0.0774711\pi$
$353$	5.19615	+	9.00000i	0.276563	+	0.479022i	−0.693965	+	0.720009i	$0.744138\pi$
$354$		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	−0.200026	−	0.979791i	$-0.564103\pi$
$359$	10.3923	−	6.00000i	0.548485	−	0.316668i	0.748511	+	0.663123i	$0.230769\pi$
$360$		0			0
$361$	−9.50000	+	16.4545i	−0.500000	+	0.866025i
$362$	−20.7846			−1.09241
$363$		0			0
$364$	9.00000	+	1.73205i	0.471728	+	0.0907841i
$365$		0			0
$366$		0			0
$367$	−9.00000	+	5.19615i	−0.469796	+	0.271237i	−0.716154	−	0.697942i	$-0.754099\pi$
$367$	−9.00000	+	5.19615i	−0.469796	+	0.271237i	0.246358	+	0.969179i	$0.420766\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	5.19615	+	15.0000i	0.269771	+	0.778761i
$372$		0			0
$373$	2.00000	−	3.46410i	0.103556	−	0.179364i	−0.809591	−	0.586994i	$-0.800311\pi$
$373$	2.00000	−	3.46410i	0.103556	−	0.179364i	0.913147	+	0.407630i	$0.133645\pi$
$374$		0			0
$375$		0			0
$376$			10.3923i			0.535942i
$377$	−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
$382$	6.00000			0.306987
$383$	−10.3923	+	18.0000i	−0.531022	+	0.919757i	0.468323	+	0.883558i	$0.344859\pi$
$383$	−10.3923	+	18.0000i	−0.531022	+	0.919757i	−0.999345	+	0.0361995i	$0.988475\pi$
$384$		0			0
$385$		0			0
$386$			11.0000i			0.559885i
$387$		0			0
$388$	7.50000	+	4.33013i	0.380755	+	0.219829i
$389$	7.79423	−	4.50000i	0.395183	−	0.228159i	−0.289220	−	0.957263i	$-0.593396\pi$
$389$	7.79423	−	4.50000i	0.395183	−	0.228159i	0.684403	+	0.729103i	$0.260063\pi$
$390$		0			0
$391$		0			0
$392$	−6.92820	+	1.00000i	−0.349927	+	0.0505076i
$393$		0			0
$394$	−15.0000			−0.755689
$395$		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
$401$	−25.9808	−	15.0000i	−1.29742	−	0.749064i	−0.317460	−	0.948272i	$-0.602830\pi$
$401$	−25.9808	−	15.0000i	−1.29742	−	0.749064i	−0.979957	+	0.199207i	$0.936163\pi$
$402$		0			0
$403$	−3.00000	−	5.19615i	−0.149441	−	0.258839i
$404$	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
$409$		−	6.92820i		−	0.342578i	−0.985221	−	0.171289i	$-0.945207\pi$
$409$		−	6.92820i		−	0.342578i	0.985221	−	0.171289i	$-0.0547931\pi$
$410$		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
$416$	1.73205	+	3.00000i	0.0849208	+	0.147087i
$417$		0			0
$418$		0			0
$419$	−15.5885	−	27.0000i	−0.761546	−	1.31904i	−0.942053	−	0.335463i	$-0.891107\pi$
$419$	−15.5885	−	27.0000i	−0.761546	−	1.31904i	0.180508	−	0.983574i	$-0.442226\pi$
$420$		0			0
$421$	5.00000	−	8.66025i	0.243685	−	0.422075i	−0.718076	−	0.695965i	$-0.754977\pi$
$421$	5.00000	−	8.66025i	0.243685	−	0.422075i	0.961761	+	0.273890i	$0.0883103\pi$
$422$	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
$427$	24.0000	−	27.7128i	1.16144	−	1.34112i
$428$	10.3923	−	6.00000i	0.502331	−	0.290021i
$429$		0			0
$430$		0			0
$431$	15.5885	+	9.00000i	0.750870	+	0.433515i	0.826008	−	0.563658i	$-0.190607\pi$
$431$	15.5885	+	9.00000i	0.750870	+	0.433515i	−0.0751385	+	0.997173i	$0.523940\pi$
$432$		0			0
$433$		−	12.1244i		−	0.582659i	−0.956623	−	0.291330i	$-0.905902\pi$
$433$		−	12.1244i		−	0.582659i	0.956623	−	0.291330i	$-0.0940977\pi$
$434$	3.46410	+	3.00000i	0.166282	+	0.144005i
$435$		0			0
$436$	−4.00000	+	6.92820i	−0.191565	+	0.331801i
$437$		0			0
$438$		0			0
$439$			15.5885i			0.743996i	0.928233	+	0.371998i	$0.121327\pi$
$439$			15.5885i			0.743996i	−0.928233	+	0.371998i	$0.878673\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$		−	27.0000i		−	1.28281i	−0.767203	−	0.641404i	$-0.778352\pi$
$443$		−	27.0000i		−	1.28281i	0.767203	−	0.641404i	$-0.221648\pi$
$444$		0			0
$445$		0			0
$446$	2.59808	−	4.50000i	0.123022	−	0.213081i
$447$		0			0
$448$	−2.00000	−	1.73205i	−0.0944911	−	0.0818317i
$449$		−	30.0000i		−	1.41579i	−0.706319	−	0.707894i	$-0.749646\pi$
$449$		−	30.0000i		−	1.41579i	0.706319	−	0.707894i	$-0.250354\pi$
$450$		0			0
$451$	−27.0000	−	15.5885i	−1.27138	−	0.734032i
$452$	−10.3923	+	6.00000i	−0.488813	+	0.282216i
$453$		0			0
$454$	−22.5000	+	12.9904i	−1.05598	+	0.609669i
$455$		0			0
$456$		0			0
$457$	22.0000			1.02912			0.514558	−	0.857455i	$-0.327956\pi$
$457$	22.0000			1.02912			0.514558	+	0.857455i	$0.327956\pi$
$458$	−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	$-0.715081\pi$
$461$	7.79423	−	13.5000i	0.363013	−	0.628758i	0.988455	+	0.151513i	$0.0484146\pi$
$462$		0			0
$463$	−2.50000	−	4.33013i	−0.116185	−	0.201238i	0.802068	−	0.597233i	$-0.203733\pi$
$463$	−2.50000	−	4.33013i	−0.116185	−	0.201238i	−0.918253	+	0.395995i	$0.870400\pi$
$464$	7.79423	+	4.50000i	0.361838	+	0.208907i
$465$		0			0
$466$	−9.00000	−	15.5885i	−0.416917	−	0.722121i
$467$	−2.59808	−	4.50000i	−0.120225	−	0.208235i	0.799632	−	0.600491i	$-0.205028\pi$
$467$	−2.59808	−	4.50000i	−0.120225	−	0.208235i	−0.919856	+	0.392256i	$0.871695\pi$
$468$		0			0
$469$	4.00000	+	3.46410i	0.184703	+	0.159957i
$470$		0			0
$471$		0			0
$472$			5.19615i			0.239172i
$473$			12.0000i			0.551761i
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$	−6.00000	−	10.3923i	−0.274434	−	0.475333i
$479$	5.19615	+	9.00000i	0.237418	+	0.411220i	0.959973	−	0.280094i	$-0.0903655\pi$
$479$	5.19615	+	9.00000i	0.237418	+	0.411220i	−0.722554	+	0.691314i	$0.757032\pi$
$480$		0			0
$481$	−24.0000	−	13.8564i	−1.09431	−	0.631798i
$482$	−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	$0.0864896\pi$
$488$	13.8564			0.627250
$489$		0			0
$490$		0			0
$491$	31.1769	−	18.0000i	1.40699	−	0.812329i	0.411897	−	0.911230i	$-0.364866\pi$
$491$	31.1769	−	18.0000i	1.40699	−	0.812329i	0.995097	+	0.0989017i	$0.0315329\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$			1.73205i			0.0777714i
$497$	20.7846	−	24.0000i	0.932317	−	1.07655i
$498$		0			0
$499$	−8.00000	+	13.8564i	−0.358129	+	0.620298i	−0.987648	−	0.156687i	$-0.949919\pi$
$499$	−8.00000	+	13.8564i	−0.358129	+	0.620298i	0.629519	+	0.776985i	$0.283252\pi$
$500$		0			0
$501$		0			0
$502$			25.9808i			1.15958i
$503$	31.1769			1.39011			0.695055	−	0.718957i	$-0.255380\pi$
$503$	31.1769			1.39011			0.695055	+	0.718957i	$0.255380\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$		0			0
$508$	−8.00000			−0.354943
$509$	2.59808	−	4.50000i	0.115158	−	0.199459i	−0.802685	−	0.596403i	$-0.796596\pi$
$509$	2.59808	−	4.50000i	0.115158	−	0.199459i	0.917843	+	0.396944i	$0.129929\pi$
$510$		0			0
$511$	4.50000	+	12.9904i	0.199068	+	0.574661i
$512$		−	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
$518$	20.7846	+	4.00000i	0.913223	+	0.175750i
$519$		0			0
$520$		0			0
$521$	−10.3923	+	18.0000i	−0.455295	+	0.788594i	−0.998705	−	0.0508731i	$-0.983800\pi$
$521$	−10.3923	+	18.0000i	−0.455295	+	0.788594i	0.543410	+	0.839467i	$0.317133\pi$
$522$		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
$529$	−11.5000	−	19.9186i	−0.500000	−	0.866025i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	31.1769	+	18.0000i	1.35042	+	0.779667i
$534$		0			0
$535$		0			0
$536$			2.00000i			0.0863868i
$537$		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	$-0.470961\pi$
$542$	−1.73205	−	3.00000i	−0.0743980	−	0.128861i
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−7.00000	+	12.1244i	−0.299298	+	0.518400i	−0.975976	−	0.217880i	$-0.930086\pi$
$547$	−7.00000	+	12.1244i	−0.299298	+	0.518400i	0.676677	+	0.736280i	$0.263419\pi$
$548$	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
$553$	−26.0000	−	22.5167i	−1.10563	−	0.957506i
$554$	−12.1244	+	7.00000i	−0.515115	+	0.297402i
$555$		0			0
$556$	6.00000	−	3.46410i	0.254457	−	0.146911i
$557$	−18.1865	−	10.5000i	−0.770588	−	0.444899i	0.0624962	−	0.998045i	$-0.480094\pi$
$557$	−18.1865	−	10.5000i	−0.770588	−	0.444899i	−0.833084	+	0.553146i	$0.813427\pi$
$558$		0			0
$559$		−	13.8564i		−	0.586064i
$560$		0			0
$561$		0			0
$562$	−3.00000	+	5.19615i	−0.126547	+	0.219186i
$563$	31.1769			1.31395			0.656975	−	0.753912i	$-0.271836\pi$
$563$	31.1769			1.31395			0.656975	+	0.753912i	$0.271836\pi$
$564$		0			0
$565$		0			0
$566$	−6.92820			−0.291214
$567$		0			0
$568$	12.0000			0.503509
$569$			12.0000i			0.503066i	0.967849	+	0.251533i	$0.0809347\pi$
$569$			12.0000i			0.503066i	−0.967849	+	0.251533i	$0.919065\pi$
$570$		0			0
$571$	−4.00000			−0.167395			−0.0836974	−	0.996491i	$-0.526673\pi$
$571$	−4.00000			−0.167395			−0.0836974	+	0.996491i	$0.526673\pi$
$572$	5.19615	−	9.00000i	0.217262	−	0.376309i
$573$		0			0
$574$	−27.0000	−	5.19615i	−1.12696	−	0.216883i
$575$		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	$0.724362\pi$
$578$	14.7224	−	8.50000i	0.612372	−	0.353553i
$579$		0			0
$580$		0			0
$581$	12.9904	−	4.50000i	0.538932	−	0.186691i
$582$		0			0
$583$	18.0000			0.745484
$584$	−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	$-0.764532\pi$
$587$	5.19615	−	9.00000i	0.214468	−	0.371470i	0.953108	+	0.302631i	$0.0978648\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	4.00000	+	6.92820i	0.164399	+	0.284747i
$593$	10.3923	+	18.0000i	0.426761	+	0.739171i	0.996583	−	0.0825966i	$-0.0263213\pi$
$593$	10.3923	+	18.0000i	0.426761	+	0.739171i	−0.569822	+	0.821768i	$0.692988\pi$
$594$		0			0
$595$		0			0
$596$	12.9904	+	7.50000i	0.532107	+	0.307212i
$597$		0			0
$598$		0			0
$599$		−	30.0000i		−	1.22577i	−0.790173	−	0.612883i	$-0.790010\pi$
$599$		−	30.0000i		−	1.22577i	0.790173	−	0.612883i	$-0.209990\pi$
$600$		0			0
$601$	30.0000	+	17.3205i	1.22373	+	0.706518i	0.965710	−	0.259623i	$-0.0835982\pi$
$601$	30.0000	+	17.3205i	1.22373	+	0.706518i	0.258015	+	0.966141i	$0.416931\pi$
$602$	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
$607$	4.50000	+	2.59808i	0.182649	+	0.105453i	0.588537	−	0.808470i	$-0.299704\pi$
$607$	4.50000	+	2.59808i	0.182649	+	0.105453i	−0.405887	+	0.913923i	$0.633038\pi$
$608$		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	$0.101939\pi$
$614$	17.3205			0.698999
$615$		0			0
$616$	−1.50000	+	7.79423i	−0.0604367	+	0.314038i
$617$	15.5885	−	9.00000i	0.627568	−	0.362326i	−0.152242	−	0.988343i	$-0.548649\pi$
$617$	15.5885	−	9.00000i	0.627568	−	0.362326i	0.779809	+	0.626017i	$0.215316\pi$
$618$		0			0
$619$	−30.0000	+	17.3205i	−1.20580	+	0.696170i	−0.961839	−	0.273615i	$-0.911781\pi$
$619$	−30.0000	+	17.3205i	−1.20580	+	0.696170i	−0.243962	+	0.969785i	$0.578447\pi$
$620$		0			0
$621$		0			0
$622$			31.1769i			1.25008i
$623$	−5.19615	+	27.0000i	−0.208179	+	1.08173i
$624$		0			0
$625$	−12.5000	+	21.6506i	−0.500000	+	0.866025i
$626$	−20.7846			−0.830720
$627$		0			0
$628$			10.3923i			0.414698i
$629$		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	$0.763510\pi$
$632$		−	13.0000i		−	0.517112i
$633$		0			0
$634$	9.00000			0.357436
$635$		0			0
$636$		0			0
$637$	−15.0000	−	19.0526i	−0.594322	−	0.754890i
$638$		−	27.0000i		−	1.06894i
$639$		0			0
$640$		0			0
$641$	36.3731	−	21.0000i	1.43665	−	0.829450i	0.439034	−	0.898470i	$-0.355321\pi$
$641$	36.3731	−	21.0000i	1.43665	−	0.829450i	0.997615	+	0.0690201i	$0.0219873\pi$
$642$		0			0
$643$	3.00000	−	1.73205i	0.118308	−	0.0683054i	−0.439678	−	0.898155i	$-0.644907\pi$
$643$	3.00000	−	1.73205i	0.118308	−	0.0683054i	0.557986	+	0.829850i	$0.311574\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−5.19615	+	9.00000i	−0.204282	+	0.353827i	−0.949904	−	0.312543i	$-0.898819\pi$
$647$	−5.19615	+	9.00000i	−0.204282	+	0.353827i	0.745622	+	0.666369i	$0.232153\pi$
$648$		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
$653$	25.9808	+	15.0000i	1.01671	+	0.586995i	0.913148	−	0.407628i	$-0.133644\pi$
$653$	25.9808	+	15.0000i	1.01671	+	0.586995i	0.103558	+	0.994623i	$0.466977\pi$
$654$		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	0.225168	−	0.974320i	$-0.427707\pi$
$659$	−12.9904	−	7.50000i	−0.506033	−	0.292159i	−0.731202	+	0.682161i	$0.761040\pi$
$660$		0			0
$661$		−	10.3923i		−	0.404214i	−0.979363	−	0.202107i	$-0.935221\pi$
$661$		−	10.3923i		−	0.404214i	0.979363	−	0.202107i	$-0.0647788\pi$
$662$		−	28.0000i		−	1.08825i
$663$		0			0
$664$	4.50000	+	2.59808i	0.174634	+	0.100825i
$665$		0			0
$666$		0			0
$667$		0			0
$668$	5.19615	+	9.00000i	0.201045	+	0.348220i
$669$		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	−0.498886	−	0.866668i	$-0.666257\pi$
$673$	13.0000	−	22.5167i	0.501113	−	0.867953i	0.999999	−	0.00128586i	$-0.000409302\pi$
$674$	−11.2583	+	6.50000i	−0.433655	+	0.250371i
$675$		0			0
$676$	0.500000	−	0.866025i	0.0192308	−	0.0333087i
$677$	15.5885			0.599113			0.299557	−	0.954079i	$-0.403161\pi$
$677$	15.5885			0.599113			0.299557	+	0.954079i	$0.403161\pi$
$678$		0			0
$679$	−7.50000	−	21.6506i	−0.287824	−	0.830875i
$680$		0			0
$681$		0			0
$682$	4.50000	−	2.59808i	0.172314	−	0.0994855i
$683$	18.1865	+	10.5000i	0.695888	+	0.401771i	0.805814	−	0.592168i	$-0.201728\pi$
$683$	18.1865	+	10.5000i	0.695888	+	0.401771i	−0.109926	+	0.993940i	$0.535061\pi$
$684$		0			0
$685$		0			0
$686$	15.5885	+	10.0000i	0.595170	+	0.381802i
$687$		0			0
$688$	−2.00000	+	3.46410i	−0.0762493	+	0.132068i
$689$	−20.7846			−0.791831
$690$		0			0
$691$			13.8564i			0.527123i	0.964643	+	0.263561i	$0.0848971\pi$
$691$			13.8564i			0.527123i	−0.964643	+	0.263561i	$0.915103\pi$
$692$	25.9808			0.987640
$693$		0			0
$694$	−3.00000			−0.113878
$695$		0			0
$696$		0			0
$697$		0			0
$698$	−13.8564	+	24.0000i	−0.524473	+	0.908413i
$699$		0			0
$700$	2.50000	−	12.9904i	0.0944911	−	0.490990i
$701$			6.00000i			0.226617i	0.993560	+	0.113308i	$0.0361448\pi$
$701$			6.00000i			0.226617i	−0.993560	+	0.113308i	$0.963855\pi$
$702$		0			0
$703$		0			0
$704$	−2.59808	+	1.50000i	−0.0979187	+	0.0565334i
$705$		0			0
$706$	9.00000	−	5.19615i	0.338719	−	0.195560i
$707$	2.59808	−	13.5000i	0.0977107	−	0.507720i
$708$		0			0
$709$	4.00000			0.150223			0.0751116	−	0.997175i	$-0.476069\pi$
$709$	4.00000			0.150223			0.0751116	+	0.997175i	$0.476069\pi$
$710$		0			0
$711$		0			0
$712$	−9.00000	+	5.19615i	−0.337289	+	0.194734i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−7.79423	−	4.50000i	−0.291284	−	0.168173i
$717$		0			0
$718$	−6.00000	−	10.3923i	−0.223918	−	0.387837i
$719$	5.19615	+	9.00000i	0.193784	+	0.335643i	0.946501	−	0.322700i	$-0.104591\pi$
$719$	5.19615	+	9.00000i	0.193784	+	0.335643i	−0.752717	+	0.658344i	$0.771257\pi$
$720$		0			0
$721$	15.0000	+	43.3013i	0.558629	+	1.61262i
$722$	16.4545	+	9.50000i	0.612372	+	0.353553i
$723$		0			0
$724$			20.7846i			0.772454i
$725$			45.0000i			1.67126i
$726$		0			0
$727$	−21.0000	−	12.1244i	−0.778847	−	0.449667i	0.0571746	−	0.998364i	$-0.481791\pi$
$727$	−21.0000	−	12.1244i	−0.778847	−	0.449667i	−0.836021	+	0.548697i	$0.815124\pi$
$728$	1.73205	−	9.00000i	0.0641941	−	0.333562i
$729$		0			0
$730$		0			0
$731$		0			0
$732$		0			0
$733$	−12.0000	−	6.92820i	−0.443230	−	0.255899i	0.261737	−	0.965139i	$-0.415705\pi$
$733$	−12.0000	−	6.92820i	−0.443230	−	0.255899i	−0.704967	+	0.709240i	$0.749038\pi$
$734$	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
$742$	15.0000	−	5.19615i	0.550667	−	0.190757i
$743$	5.19615	−	3.00000i	0.190628	−	0.110059i	−0.401648	−	0.915794i	$-0.631563\pi$
$743$	5.19615	−	3.00000i	0.190628	−	0.110059i	0.592277	+	0.805735i	$0.298229\pi$
$744$		0			0
$745$		0			0
$746$	−3.46410	−	2.00000i	−0.126830	−	0.0732252i
$747$		0			0
$748$		0			0
$749$	−31.1769	−	6.00000i	−1.13918	−	0.219235i
$750$		0			0
$751$	−2.00000	+	3.46410i	−0.0729810	+	0.126407i	−0.900207	−	0.435463i	$-0.856585\pi$
$751$	−2.00000	+	3.46410i	−0.0729810	+	0.126407i	0.827225	+	0.561870i	$0.189918\pi$
$752$	10.3923			0.378968
$753$		0			0
$754$			31.1769i			1.13540i
$755$		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	$0.441831\pi$
$758$			26.0000i			0.944363i
$759$		0			0
$760$		0			0
$761$	20.7846	−	36.0000i	0.753442	−	1.30500i	−0.192704	−	0.981257i	$-0.561726\pi$
$761$	20.7846	−	36.0000i	0.753442	−	1.30500i	0.946145	−	0.323742i	$-0.104941\pi$
$762$		0			0
$763$	20.0000	−	6.92820i	0.724049	−	0.250818i
$764$		−	6.00000i		−	0.217072i
$765$		0			0
$766$	18.0000	+	10.3923i	0.650366	+	0.375489i
$767$	−15.5885	+	9.00000i	−0.562867	+	0.324971i
$768$		0			0
$769$	13.5000	−	7.79423i	0.486822	−	0.281067i	−0.236433	−	0.971648i	$-0.575978\pi$
$769$	13.5000	−	7.79423i	0.486822	−	0.281067i	0.723255	+	0.690581i	$0.242645\pi$
$770$		0			0
$771$		0			0
$772$	11.0000			0.395899
$773$	20.7846	−	36.0000i	0.747570	−	1.29483i	−0.201414	−	0.979506i	$-0.564554\pi$
$773$	20.7846	−	36.0000i	0.747570	−	1.29483i	0.948984	−	0.315324i	$-0.102113\pi$
$774$		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
$781$	−18.0000	−	31.1769i	−0.644091	−	1.11560i
$782$		0			0
$783$		0			0
$784$	1.00000	+	6.92820i	0.0357143	+	0.247436i
$785$		0			0
$786$		0			0
$787$			24.2487i			0.864373i	0.901784	+	0.432187i	$0.142258\pi$
$787$			24.2487i			0.864373i	−0.901784	+	0.432187i	$0.857742\pi$
$788$			15.0000i			0.534353i
$789$		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
$794$	−12.1244	−	21.0000i	−0.430277	−	0.745262i
$795$		0			0
$796$	−1.50000	−	0.866025i	−0.0531661	−	0.0306955i
$797$	−7.79423	−	13.5000i	−0.276086	−	0.478195i	0.694323	−	0.719664i	$-0.255704\pi$
$797$	−7.79423	−	13.5000i	−0.276086	−	0.478195i	−0.970408	+	0.241469i	$0.922371\pi$
$798$		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
$803$	15.5885			0.550105
$804$		0			0
$805$		0			0
$806$	−5.19615	+	3.00000i	−0.183027	+	0.105670i
$807$		0			0
$808$	4.50000	−	2.59808i	0.158309	−	0.0914000i
$809$	−5.19615	−	3.00000i	−0.182687	−	0.105474i	0.405868	−	0.913932i	$-0.366969\pi$
$809$	−5.19615	−	3.00000i	−0.182687	−	0.105474i	−0.588555	+	0.808458i	$0.700303\pi$
$810$		0			0
$811$			10.3923i			0.364923i	0.983213	+	0.182462i	$0.0584065\pi$
$811$			10.3923i			0.364923i	−0.983213	+	0.182462i	$0.941593\pi$
$812$	−7.79423	−	22.5000i	−0.273524	−	0.789595i
$813$		0			0
$814$	12.0000	−	20.7846i	0.420600	−	0.728500i
$815$		0			0
$816$		0			0
$817$		0			0
$818$	−6.92820			−0.242239
$819$		0			0
$820$		0			0
$821$		−	33.0000i		−	1.15171i	−0.817553	−	0.575854i	$-0.804670\pi$
$821$		−	33.0000i		−	1.15171i	0.817553	−	0.575854i	$-0.195330\pi$
$822$		0			0
$823$	11.0000			0.383436			0.191718	−	0.981450i	$-0.438594\pi$
$823$	11.0000			0.383436			0.191718	+	0.981450i	$0.438594\pi$
$824$	−8.66025	+	15.0000i	−0.301694	+	0.522550i
$825$		0			0
$826$	9.00000	−	10.3923i	0.313150	−	0.361595i
$827$			3.00000i			0.104320i	0.998639	+	0.0521601i	$0.0166106\pi$
$827$			3.00000i			0.104320i	−0.998639	+	0.0521601i	$0.983389\pi$
$828$		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	$-0.950141\pi$
$839$	−10.3923	+	18.0000i	−0.358782	+	0.621429i	0.628975	+	0.777425i	$0.283475\pi$
$840$		0			0
$841$	26.0000	+	45.0333i	0.896552	+	1.55287i
$842$	−8.66025	−	5.00000i	−0.298452	−	0.172311i
$843$		0			0
$844$	−1.00000	−	1.73205i	−0.0344214	−	0.0596196i
$845$		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	$-0.276399\pi$
$853$	9.00000	+	5.19615i	0.308154	+	0.177913i	−0.337946	+	0.941165i	$0.609732\pi$
$854$	−27.7128	−	24.0000i	−0.948313	−	0.821263i
$855$		0			0
$856$	−6.00000	−	10.3923i	−0.205076	−	0.355202i
$857$	−5.19615	−	9.00000i	−0.177497	−	0.307434i	0.763525	−	0.645778i	$-0.223467\pi$
$857$	−5.19615	−	9.00000i	−0.177497	−	0.307434i	−0.941023	+	0.338344i	$0.890133\pi$
$858$		0			0
$859$	42.0000	+	24.2487i	1.43302	+	0.827355i	0.997350	−	0.0727505i	$-0.0231777\pi$
$859$	42.0000	+	24.2487i	1.43302	+	0.827355i	0.435671	+	0.900106i	$0.356511\pi$
$860$		0			0
$861$		0			0
$862$	9.00000	−	15.5885i	0.306541	−	0.530945i
$863$	−5.19615	+	3.00000i	−0.176879	+	0.102121i	−0.585826	−	0.810437i	$-0.699230\pi$
$863$	−5.19615	+	3.00000i	−0.176879	+	0.102121i	0.408946	+	0.912558i	$0.365896\pi$
$864$		0			0
$865$		0			0
$866$	−12.1244			−0.412002
$867$		0			0
$868$	3.00000	−	3.46410i	0.101827	−	0.117579i
$869$	−33.7750	+	19.5000i	−1.14574	+	0.661492i
$870$		0			0
$871$	−6.00000	+	3.46410i	−0.203302	+	0.117377i
$872$	6.92820	+	4.00000i	0.234619	+	0.135457i
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−1.00000	+	1.73205i	−0.0337676	+	0.0584872i	−0.882415	−	0.470471i	$-0.844084\pi$
$877$	−1.00000	+	1.73205i	−0.0337676	+	0.0584872i	0.848648	+	0.528958i	$0.177417\pi$
$878$	15.5885			0.526085
$879$		0			0
$880$		0			0
$881$	−31.1769			−1.05038			−0.525188	−	0.850986i	$-0.676005\pi$
$881$	−31.1769			−1.05038			−0.525188	+	0.850986i	$0.676005\pi$
$882$		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
$886$	−27.0000			−0.907083
$887$	−15.5885	+	27.0000i	−0.523409	+	0.906571i	0.476220	+	0.879326i	$0.342007\pi$
$887$	−15.5885	+	27.0000i	−0.523409	+	0.906571i	−0.999629	+	0.0272449i	$0.991327\pi$
$888$		0			0
$889$	16.0000	+	13.8564i	0.536623	+	0.464729i
$890$		0			0
$891$		0			0
$892$	−4.50000	−	2.59808i	−0.150671	−	0.0869900i
$893$		0			0
$894$		0			0
$895$		0			0
$896$	−1.73205	+	2.00000i	−0.0578638	+	0.0668153i
$897$		0			0
$898$	−30.0000			−1.00111
$899$	−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
$907$	−11.0000	−	19.0526i	−0.365249	−	0.632630i	0.623567	−	0.781770i	$-0.285683\pi$
$907$	−11.0000	−	19.0526i	−0.365249	−	0.632630i	−0.988816	+	0.149140i	$0.952349\pi$
$908$	12.9904	+	22.5000i	0.431101	+	0.746689i
$909$		0			0
$910$		0			0
$911$	−31.1769	−	18.0000i	−1.03294	−	0.596367i	−0.115113	−	0.993352i	$-0.536723\pi$
$911$	−31.1769	−	18.0000i	−1.03294	−	0.596367i	−0.917825	+	0.396986i	$0.870056\pi$
$912$		0			0
$913$		−	15.5885i		−	0.515903i
$914$		−	22.0000i		−	0.727695i
$915$		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
$922$	−13.5000	−	7.79423i	−0.444599	−	0.256689i
$923$	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
$929$	−41.5692			−1.36384			−0.681921	−	0.731426i	$-0.738855\pi$
$929$	−41.5692			−1.36384			−0.681921	+	0.731426i	$0.738855\pi$
$930$		0			0
$931$		0			0
$932$	−15.5885	+	9.00000i	−0.510617	+	0.294805i
$933$		0			0
$934$	−4.50000	+	2.59808i	−0.147244	+	0.0850117i
$935$		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	$0.808553\pi$
$938$	3.46410	−	4.00000i	0.113107	−	0.130605i
$939$		0			0
$940$		0			0
$941$	5.19615			0.169390			0.0846949	−	0.996407i	$-0.473008\pi$
$941$	5.19615			0.169390			0.0846949	+	0.996407i	$0.473008\pi$
$942$		0			0
$943$		0			0
$944$	5.19615			0.169120
$945$		0			0
$946$	12.0000			0.390154
$947$		−	9.00000i		−	0.292461i	−0.989251	−	0.146230i	$-0.953286\pi$
$947$		−	9.00000i		−	0.292461i	0.989251	−	0.146230i	$-0.0467141\pi$
$948$		0			0
$949$	−18.0000			−0.584305
$950$		0			0
$951$		0			0
$952$		0			0
$953$			18.0000i			0.583077i	0.956559	+	0.291539i	$0.0941672\pi$
$953$			18.0000i			0.583077i	−0.956559	+	0.291539i	$0.905833\pi$
$954$		0			0
$955$		0			0
$956$	−10.3923	+	6.00000i	−0.336111	+	0.194054i
$957$		0			0
$958$	9.00000	−	5.19615i	0.290777	−	0.167880i
$959$	−31.1769	−	6.00000i	−1.00676	−	0.193750i
$960$		0			0
$961$	28.0000			0.903226
$962$	−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	−0.826951	−	0.562274i	$-0.809926\pi$
$967$	−28.0000	−	48.4974i	−0.900419	−	1.55957i	−0.0734686	−	0.997298i	$-0.523407\pi$
$968$	−1.73205	−	1.00000i	−0.0556702	−	0.0321412i
$969$		0			0
$970$		0			0
$971$	−15.5885	−	27.0000i	−0.500257	−	0.866471i	−1.00000		0.000297246i	$-0.999905\pi$
$971$	−15.5885	−	27.0000i	−0.500257	−	0.866471i	0.499743	−	0.866174i	$-0.333428\pi$
$972$		0			0
$973$	−18.0000	−	3.46410i	−0.577054	−	0.111054i
$974$	−9.52628	−	5.50000i	−0.305242	−	0.176231i
$975$		0			0
$976$		−	13.8564i		−	0.443533i
$977$			18.0000i			0.575871i	0.957650	+	0.287936i	$0.0929689\pi$
$977$			18.0000i			0.575871i	−0.957650	+	0.287936i	$0.907031\pi$
$978$		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
$983$	10.3923	+	18.0000i	0.331463	+	0.574111i	0.982799	−	0.184679i	$-0.0591244\pi$
$983$	10.3923	+	18.0000i	0.331463	+	0.574111i	−0.651336	+	0.758790i	$0.725791\pi$
$984$		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	$0.126111\pi$
$992$	1.73205			0.0549927
$993$		0			0
$994$	−24.0000	−	20.7846i	−0.761234	−	0.659248i
$995$		0			0
$996$		0			0
$997$	−33.0000	+	19.0526i	−1.04512	+	0.603401i	−0.921279	−	0.388901i	$-0.872855\pi$
$997$	−33.0000	+	19.0526i	−1.04512	+	0.603401i	−0.123841	+	0.992302i	$0.539521\pi$
$998$	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.l.d.269.1		4
3.2	odd	2	inner	1134.2.l.d.269.2		4
7.5	odd	6		1134.2.t.a.593.1		4
9.2	odd	6		378.2.k.a.269.2	yes	4
9.4	even	3		1134.2.t.a.1025.2		4
9.5	odd	6		1134.2.t.a.1025.1		4
9.7	even	3		378.2.k.a.269.1	yes	4
21.5	even	6		1134.2.t.a.593.2		4
63.5	even	6	inner	1134.2.l.d.215.2		4
63.11	odd	6		2646.2.d.c.2645.3		4
63.25	even	3		2646.2.d.c.2645.1		4
63.38	even	6		2646.2.d.c.2645.4		4
63.40	odd	6	inner	1134.2.l.d.215.1		4
63.47	even	6		378.2.k.a.215.1	✓	4
63.52	odd	6		2646.2.d.c.2645.2		4
63.61	odd	6		378.2.k.a.215.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.k.a.215.1	✓	4	63.47	even	6
378.2.k.a.215.2	yes	4	63.61	odd	6
378.2.k.a.269.1	yes	4	9.7	even	3
378.2.k.a.269.2	yes	4	9.2	odd	6
1134.2.l.d.215.1		4	63.40	odd	6	inner
1134.2.l.d.215.2		4	63.5	even	6	inner
1134.2.l.d.269.1		4	1.1	even	1	trivial
1134.2.l.d.269.2		4	3.2	odd	2	inner
1134.2.t.a.593.1		4	7.5	odd	6
1134.2.t.a.593.2		4	21.5	even	6
1134.2.t.a.1025.1		4	9.5	odd	6
1134.2.t.a.1025.2		4	9.4	even	3
2646.2.d.c.2645.1		4	63.25	even	3
2646.2.d.c.2645.2		4	63.52	odd	6
2646.2.d.c.2645.3		4	63.11	odd	6
2646.2.d.c.2645.4		4	63.38	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.l (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(2.00000 + 1.73205i) q^{7} +1.00000i q^{8} +(2.59808 - 1.50000i) q^{11} +(-3.00000 + 1.73205i) q^{13} +(1.73205 - 2.00000i) q^{14} +1.00000 q^{16} +(-1.50000 - 2.59808i) q^{22} +(2.50000 + 4.33013i) q^{25} +(1.73205 + 3.00000i) q^{26} +(-2.00000 - 1.73205i) q^{28} +(7.79423 + 4.50000i) q^{29} +1.73205i q^{31} -1.00000i q^{32} +(4.00000 + 6.92820i) q^{37} +(-5.19615 - 9.00000i) q^{41} +(-2.00000 + 3.46410i) q^{43} +(-2.59808 + 1.50000i) q^{44} +10.3923 q^{47} +(1.00000 + 6.92820i) q^{49} +(4.33013 - 2.50000i) q^{50} +(3.00000 - 1.73205i) q^{52} +(5.19615 + 3.00000i) q^{53} +(-1.73205 + 2.00000i) q^{56} +(4.50000 - 7.79423i) q^{58} +5.19615 q^{59} -13.8564i q^{61} +1.73205 q^{62} -1.00000 q^{64} +2.00000 q^{67} -12.0000i q^{71} +(4.50000 + 2.59808i) q^{73} +(6.92820 - 4.00000i) q^{74} +(7.79423 + 1.50000i) q^{77} -13.0000 q^{79} +(-9.00000 + 5.19615i) q^{82} +(2.59808 - 4.50000i) q^{83} +(3.46410 + 2.00000i) q^{86} +(1.50000 + 2.59808i) q^{88} +(5.19615 + 9.00000i) q^{89} +(-9.00000 - 1.73205i) q^{91} -10.3923i q^{94} +(-7.50000 - 4.33013i) q^{97} +(6.92820 - 1.00000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} + 8 q^{7} - 12 q^{13} + 4 q^{16} - 6 q^{22} + 10 q^{25} - 8 q^{28} + 16 q^{37} - 8 q^{43} + 4 q^{49} + 12 q^{52} + 18 q^{58} - 4 q^{64} + 8 q^{67} + 18 q^{73} - 52 q^{79} - 36 q^{82} + 6 q^{88}+ \cdots - 30 q^{97}+O(q^{100}) \) 4 * q - 4 * q^4 + 8 * q^7 - 12 * q^13 + 4 * q^16 - 6 * q^22 + 10 * q^25 - 8 * q^28 + 16 * q^37 - 8 * q^43 + 4 * q^49 + 12 * q^52 + 18 * q^58 - 4 * q^64 + 8 * q^67 + 18 * q^73 - 52 * q^79 - 36 * q^82 + 6 * q^88 - 36 * q^91 - 30 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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