LMFDB - Embedded newform 378.2.k.a.269.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [378,2,Mod(215,378)] 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("378.215"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(378, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.k (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$3.01834519640$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			269.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	378.269
Dual form			378.2.k.a.215.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(0.500000 - 2.59808i) q^{7} +1.00000i q^{8} +(-2.59808 - 1.50000i) q^{11} -3.46410i q^{13} +(0.866025 + 2.50000i) q^{14} +(-0.500000 - 0.866025i) q^{16} +3.00000 q^{22} +(2.50000 - 4.33013i) q^{25} +(1.73205 + 3.00000i) q^{26} +(-2.00000 - 1.73205i) q^{28} -9.00000i q^{29} +(-1.50000 - 0.866025i) q^{31} +(0.866025 + 0.500000i) q^{32} +(4.00000 + 6.92820i) q^{37} +10.3923 q^{41} +4.00000 q^{43} +(-2.59808 + 1.50000i) q^{44} +(-5.19615 - 9.00000i) q^{47} +(-6.50000 - 2.59808i) q^{49} +5.00000i q^{50} +(-3.00000 - 1.73205i) q^{52} +(5.19615 + 3.00000i) q^{53} +(2.59808 + 0.500000i) q^{56} +(4.50000 + 7.79423i) q^{58} +(-2.59808 + 4.50000i) q^{59} +(-12.0000 + 6.92820i) q^{61} +1.73205 q^{62} -1.00000 q^{64} +(-1.00000 + 1.73205i) q^{67} -12.0000i q^{71} +(4.50000 + 2.59808i) q^{73} +(-6.92820 - 4.00000i) q^{74} +(-5.19615 + 6.00000i) q^{77} +(6.50000 + 11.2583i) q^{79} +(-9.00000 + 5.19615i) q^{82} -5.19615 q^{83} +(-3.46410 + 2.00000i) q^{86} +(1.50000 - 2.59808i) q^{88} +(5.19615 + 9.00000i) q^{89} +(-9.00000 - 1.73205i) q^{91} +(9.00000 + 5.19615i) q^{94} +8.66025i q^{97} +(6.92820 - 1.00000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} + 2 q^{7} - 2 q^{16} + 12 q^{22} + 10 q^{25} - 8 q^{28} - 6 q^{31} + 16 q^{37} + 16 q^{43} - 26 q^{49} - 12 q^{52} + 18 q^{58} - 48 q^{61} - 4 q^{64} - 4 q^{67} + 18 q^{73} + 26 q^{79} - 36 q^{82}+ \cdots + 36 q^{94}+O(q^{100}) $ 4 * q + 2 * q^4 + 2 * q^7 - 2 * q^16 + 12 * q^22 + 10 * q^25 - 8 * q^28 - 6 * q^31 + 16 * q^37 + 16 * q^43 - 26 * q^49 - 12 * q^52 + 18 * q^58 - 48 * q^61 - 4 * q^64 - 4 * q^67 + 18 * q^73 + 26 * q^79 - 36 * q^82 + 6 * q^88 - 36 * q^91 + 36 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−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		0.866025	−	0.500000i	$-0.166667\pi$
$5$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$6$		0			0
$7$	0.500000	−	2.59808i	0.188982	−	0.981981i
$7$	0.500000	−	2.59808i	0.188982	−	0.981981i
$8$			1.00000i			0.353553i
$9$		0			0
$10$		0			0
$11$	−2.59808	−	1.50000i	−0.783349	−	0.452267i	0.0542666	−	0.998526i	$-0.482718\pi$
$11$	−2.59808	−	1.50000i	−0.783349	−	0.452267i	−0.837616	+	0.546259i	$0.816051\pi$
$12$		0			0
$13$		−	3.46410i		−	0.960769i	−0.877058	−	0.480384i	$-0.840497\pi$
$13$		−	3.46410i		−	0.960769i	0.877058	−	0.480384i	$-0.159503\pi$
$14$	0.866025	+	2.50000i	0.231455	+	0.668153i
$15$		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
$22$	3.00000			0.639602
$23$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$23$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$24$		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
$29$		−	9.00000i		−	1.67126i	−0.549294	−	0.835629i	$-0.685103\pi$
$29$		−	9.00000i		−	1.67126i	0.549294	−	0.835629i	$-0.314897\pi$
$30$		0			0
$31$	−1.50000	−	0.866025i	−0.269408	−	0.155543i	0.359211	−	0.933257i	$-0.383046\pi$
$31$	−1.50000	−	0.866025i	−0.269408	−	0.155543i	−0.628619	+	0.777714i	$0.716379\pi$
$32$	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
$41$	10.3923			1.62301			0.811503	−	0.584349i	$-0.198650\pi$
$41$	10.3923			1.62301			0.811503	+	0.584349i	$0.198650\pi$
$42$		0			0
$43$	4.00000			0.609994			0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000			0.609994			0.304997	+	0.952353i	$0.401344\pi$
$44$	−2.59808	+	1.50000i	−0.391675	+	0.226134i
$45$		0			0
$46$		0			0
$47$	−5.19615	−	9.00000i	−0.757937	−	1.31278i	−0.943901	−	0.330228i	$-0.892874\pi$
$47$	−5.19615	−	9.00000i	−0.757937	−	1.31278i	0.185964	−	0.982556i	$-0.440459\pi$
$48$		0			0
$49$	−6.50000	−	2.59808i	−0.928571	−	0.371154i
$50$			5.00000i			0.707107i
$51$		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
$56$	2.59808	+	0.500000i	0.347183	+	0.0668153i
$57$		0			0
$58$	4.50000	+	7.79423i	0.590879	+	1.02343i
$59$	−2.59808	+	4.50000i	−0.338241	+	0.585850i	−0.984102	−	0.177605i	$-0.943165\pi$
$59$	−2.59808	+	4.50000i	−0.338241	+	0.585850i	0.645861	+	0.763455i	$0.276498\pi$
$60$		0			0
$61$	−12.0000	+	6.92820i	−1.53644	+	0.887066i	−0.537400	+	0.843328i	$0.680593\pi$
$61$	−12.0000	+	6.92820i	−1.53644	+	0.887066i	−0.999043	+	0.0437377i	$0.986073\pi$
$62$	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	−0.920623	−	0.390453i	$-0.872318\pi$
$67$	−1.00000	+	1.73205i	−0.122169	+	0.211604i	0.798454	+	0.602056i	$0.205652\pi$
$68$		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
$77$	−5.19615	+	6.00000i	−0.592157	+	0.683763i
$78$		0			0
$79$	6.50000	+	11.2583i	0.731307	+	1.26666i	0.956325	+	0.292306i	$0.0944227\pi$
$79$	6.50000	+	11.2583i	0.731307	+	1.26666i	−0.225018	+	0.974355i	$0.572244\pi$
$80$		0			0
$81$		0			0
$82$	−9.00000	+	5.19615i	−0.993884	+	0.573819i
$83$	−5.19615			−0.570352			−0.285176	−	0.958475i	$-0.592052\pi$
$83$	−5.19615			−0.570352			−0.285176	+	0.958475i	$0.592052\pi$
$84$		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
$94$	9.00000	+	5.19615i	0.928279	+	0.535942i
$95$		0			0
$96$		0			0
$97$			8.66025i			0.879316i	0.898165	+	0.439658i	$0.144900\pi$
$97$			8.66025i			0.879316i	−0.898165	+	0.439658i	$0.855100\pi$
$98$	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	−0.965845	−	0.259120i	$-0.916568\pi$
$101$	−2.59808	+	4.50000i	−0.258518	+	0.447767i	0.707327	+	0.706887i	$0.249901\pi$
$102$		0			0
$103$	−15.0000	+	8.66025i	−1.47799	+	0.853320i	−0.999691	−	0.0248745i	$-0.992081\pi$
$103$	−15.0000	+	8.66025i	−1.47799	+	0.853320i	−0.478303	+	0.878195i	$0.658748\pi$
$104$	3.46410			0.339683
$105$		0			0
$106$	−6.00000			−0.582772
$107$	−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
$112$	−2.50000	+	0.866025i	−0.236228	+	0.0818317i
$113$			12.0000i			1.12887i	0.825479	+	0.564433i	$0.190905\pi$
$113$			12.0000i			1.12887i	−0.825479	+	0.564433i	$0.809095\pi$
$114$		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
$122$	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
$131$	−7.79423	−	13.5000i	−0.680985	−	1.17950i	−0.974681	−	0.223602i	$-0.928219\pi$
$131$	−7.79423	−	13.5000i	−0.680985	−	1.17950i	0.293696	−	0.955899i	$-0.405115\pi$
$132$		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	$-0.162010\pi$
$137$	10.3923	+	6.00000i	0.887875	+	0.512615i	0.0146279	+	0.999893i	$0.495344\pi$
$138$		0			0
$139$		−	6.92820i		−	0.587643i	−0.955860	−	0.293821i	$-0.905073\pi$
$139$		−	6.92820i		−	0.587643i	0.955860	−	0.293821i	$-0.0949270\pi$
$140$		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
$146$	−5.19615			−0.430037
$147$		0			0
$148$	8.00000			0.657596
$149$	12.9904	−	7.50000i	1.06421	−	0.614424i	0.137619	−	0.990485i	$-0.456055\pi$
$149$	12.9904	−	7.50000i	1.06421	−	0.614424i	0.926595	+	0.376061i	$0.122722\pi$
$150$		0			0
$151$	11.5000	−	19.9186i	0.935857	−	1.62095i	0.162758	−	0.986666i	$-0.447961\pi$
$151$	11.5000	−	19.9186i	0.935857	−	1.62095i	0.773099	−	0.634285i	$-0.218706\pi$
$152$		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	$-0.197221\pi$
$157$	9.00000	+	5.19615i	0.718278	+	0.414698i	−0.0958404	+	0.995397i	$0.530554\pi$
$158$	−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	$0.705245\pi$
$164$	5.19615	−	9.00000i	0.405751	−	0.702782i
$165$		0			0
$166$	4.50000	−	2.59808i	0.349268	−	0.201650i
$167$	10.3923			0.804181			0.402090	−	0.915600i	$-0.368284\pi$
$167$	10.3923			0.804181			0.402090	+	0.915600i	$0.368284\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$		0			0
$171$		0			0
$172$	2.00000	−	3.46410i	0.152499	−	0.264135i
$173$	12.9904	+	22.5000i	0.987640	+	1.71064i	0.629558	+	0.776953i	$0.283236\pi$
$173$	12.9904	+	22.5000i	0.987640	+	1.71064i	0.358082	+	0.933690i	$0.383431\pi$
$174$		0			0
$175$	−10.0000	−	8.66025i	−0.755929	−	0.654654i
$176$			3.00000i			0.226134i
$177$		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	$-0.280971\pi$
$182$	8.66025	−	3.00000i	0.641941	−	0.222375i
$183$		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	−0.300088	−	0.953912i	$-0.597016\pi$
$191$	5.19615	−	3.00000i	0.375980	−	0.217072i	0.676068	+	0.736839i	$0.263683\pi$
$192$		0			0
$193$	5.50000	−	9.52628i	0.395899	−	0.685717i	−0.597317	−	0.802005i	$-0.703766\pi$
$193$	5.50000	−	9.52628i	0.395899	−	0.685717i	0.993215	+	0.116289i	$0.0370998\pi$
$194$	−4.33013	−	7.50000i	−0.310885	−	0.538469i
$195$		0			0
$196$	−5.50000	+	4.33013i	−0.392857	+	0.309295i
$197$		−	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
$202$		−	5.19615i		−	0.365600i
$203$	−23.3827	−	4.50000i	−1.64114	−	0.315838i
$204$		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
$211$	−2.00000			−0.137686			−0.0688428	−	0.997628i	$-0.521931\pi$
$211$	−2.00000			−0.137686			−0.0688428	+	0.997628i	$0.521931\pi$
$212$	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
$218$			8.00000i			0.541828i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		−	5.19615i		−	0.347960i	−0.984749	−	0.173980i	$-0.944337\pi$
$223$		−	5.19615i		−	0.347960i	0.984749	−	0.173980i	$-0.0556628\pi$
$224$	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	0.00759708	+	0.999971i	$0.497582\pi$
$227$	−12.9904	+	22.5000i	−0.862202	+	1.49338i	−0.869799	+	0.493406i	$0.835752\pi$
$228$		0			0
$229$	6.00000	−	3.46410i	0.396491	−	0.228914i	−0.288478	−	0.957487i	$-0.593149\pi$
$229$	6.00000	−	3.46410i	0.396491	−	0.228914i	0.684969	+	0.728572i	$0.259816\pi$
$230$		0			0
$231$		0			0
$232$	9.00000			0.590879
$233$	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
$236$	2.59808	+	4.50000i	0.169120	+	0.292925i
$237$		0			0
$238$		0			0
$239$			12.0000i			0.776215i	0.921614	+	0.388108i	$0.126871\pi$
$239$			12.0000i			0.776215i	−0.921614	+	0.388108i	$0.873129\pi$
$240$		0			0
$241$	−10.5000	−	6.06218i	−0.676364	−	0.390499i	0.122119	−	0.992515i	$-0.461031\pi$
$241$	−10.5000	−	6.06218i	−0.676364	−	0.390499i	−0.798484	+	0.602016i	$0.794364\pi$
$242$	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	$-0.805996\pi$
$251$	−25.9808			−1.63989			−0.819946	+	0.572441i	$0.805996\pi$
$252$		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
$257$	−10.3923	−	18.0000i	−0.648254	−	1.12281i	−0.983540	−	0.180693i	$-0.942166\pi$
$257$	−10.3923	−	18.0000i	−0.648254	−	1.12281i	0.335285	−	0.942117i	$-0.391167\pi$
$258$		0			0
$259$	20.0000	−	6.92820i	1.24274	−	0.430498i
$260$		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	$-0.0681817\pi$
$263$	20.7846	+	12.0000i	1.28163	+	0.739952i	0.304487	+	0.952517i	$0.401515\pi$
$264$		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	−0.999597	−	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
$274$	−12.0000			−0.724947
$275$	−12.9904	+	7.50000i	−0.783349	+	0.452267i
$276$		0			0
$277$	−7.00000	+	12.1244i	−0.420589	+	0.728482i	−0.995997	−	0.0893846i	$-0.971510\pi$
$277$	−7.00000	+	12.1244i	−0.420589	+	0.728482i	0.575408	+	0.817867i	$0.304843\pi$
$278$	3.46410	+	6.00000i	0.207763	+	0.359856i
$279$		0			0
$280$		0			0
$281$			6.00000i			0.357930i	0.983855	+	0.178965i	$0.0572749\pi$
$281$			6.00000i			0.357930i	−0.983855	+	0.178965i	$0.942725\pi$
$282$		0			0
$283$	6.00000	+	3.46410i	0.356663	+	0.205919i	0.667616	−	0.744506i	$-0.267315\pi$
$283$	6.00000	+	3.46410i	0.356663	+	0.205919i	−0.310953	+	0.950425i	$0.600648\pi$
$284$	−10.3923	−	6.00000i	−0.616670	−	0.356034i
$285$		0			0
$286$		−	10.3923i		−	0.614510i
$287$	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
$293$	5.19615			0.303562			0.151781	−	0.988414i	$-0.451499\pi$
$293$	5.19615			0.303562			0.151781	+	0.988414i	$0.451499\pi$
$294$		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
$301$	2.00000	−	10.3923i	0.115278	−	0.599002i
$302$			23.0000i			1.32350i
$303$		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	$0.835437\pi$
$308$	2.59808	+	7.50000i	0.148039	+	0.427352i
$309$		0			0
$310$		0			0
$311$	15.5885	−	27.0000i	0.883940	−	1.53103i	0.0370169	−	0.999315i	$-0.488214\pi$
$311$	15.5885	−	27.0000i	0.883940	−	1.53103i	0.846923	−	0.531715i	$-0.178452\pi$
$312$		0			0
$313$	−18.0000	+	10.3923i	−1.01742	+	0.587408i	−0.913356	−	0.407163i	$-0.866518\pi$
$313$	−18.0000	+	10.3923i	−1.01742	+	0.587408i	−0.104065	+	0.994571i	$0.533185\pi$
$314$	−10.3923			−0.586472
$315$		0			0
$316$	13.0000			0.731307
$317$	7.79423	−	4.50000i	0.437767	−	0.252745i	−0.264883	−	0.964281i	$-0.585333\pi$
$317$	7.79423	−	4.50000i	0.437767	−	0.252745i	0.702650	+	0.711535i	$0.252000\pi$
$318$		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
$326$	−8.66025	−	5.00000i	−0.479647	−	0.276924i
$327$		0			0
$328$			10.3923i			0.573819i
$329$	−25.9808	+	9.00000i	−1.43237	+	0.496186i
$330$		0			0
$331$	−14.0000	−	24.2487i	−0.769510	−	1.33283i	−0.937829	−	0.347097i	$-0.887167\pi$
$331$	−14.0000	−	24.2487i	−0.769510	−	1.33283i	0.168320	−	0.985732i	$-0.446166\pi$
$332$	−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
$337$	13.0000			0.708155			0.354078	−	0.935216i	$-0.384795\pi$
$337$	13.0000			0.708155			0.354078	+	0.935216i	$0.384795\pi$
$338$	−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
$344$			4.00000i			0.215666i
$345$		0			0
$346$	−22.5000	−	12.9904i	−1.20961	−	0.698367i
$347$	2.59808	+	1.50000i	0.139472	+	0.0805242i	0.568112	−	0.822951i	$-0.307674\pi$
$347$	2.59808	+	1.50000i	0.139472	+	0.0805242i	−0.428640	+	0.903475i	$0.641007\pi$
$348$		0			0
$349$			27.7128i			1.48343i	0.670714	+	0.741716i	$0.265988\pi$
$349$			27.7128i			1.48343i	−0.670714	+	0.741716i	$0.734012\pi$
$350$	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	−0.693965	−	0.720009i	$-0.744138\pi$
$353$	5.19615	−	9.00000i	0.276563	−	0.479022i	0.970528	+	0.240987i	$0.0774711\pi$
$354$		0			0
$355$		0			0
$356$	10.3923			0.550791
$357$		0			0
$358$	−9.00000			−0.475665
$359$	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
$362$	10.3923	+	18.0000i	0.546207	+	0.946059i
$363$		0			0
$364$	−6.00000	+	6.92820i	−0.314485	+	0.363137i
$365$		0			0
$366$		0			0
$367$	9.00000	+	5.19615i	0.469796	+	0.271237i	0.716154	−	0.697942i	$-0.245901\pi$
$367$	9.00000	+	5.19615i	0.469796	+	0.271237i	−0.246358	+	0.969179i	$0.579234\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	10.3923	−	12.0000i	0.539542	−	0.623009i
$372$		0			0
$373$	2.00000	+	3.46410i	0.103556	+	0.179364i	0.913147	−	0.407630i	$-0.133645\pi$
$373$	2.00000	+	3.46410i	0.103556	+	0.179364i	−0.809591	+	0.586994i	$0.800311\pi$
$374$		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
$383$	−10.3923	−	18.0000i	−0.531022	−	0.919757i	−0.999345	−	0.0361995i	$-0.988475\pi$
$383$	−10.3923	−	18.0000i	−0.531022	−	0.919757i	0.468323	−	0.883558i	$-0.344859\pi$
$384$		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	$-0.406604\pi$
$389$	−7.79423	−	4.50000i	−0.395183	−	0.228159i	−0.684403	+	0.729103i	$0.739937\pi$
$390$		0			0
$391$		0			0
$392$	2.59808	−	6.50000i	0.131223	−	0.328300i
$393$		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	$0.125103\pi$
$398$	−1.73205			−0.0868199
$399$		0			0
$400$	−5.00000			−0.250000
$401$	25.9808	−	15.0000i	1.29742	−	0.749064i	0.317460	−	0.948272i	$-0.397170\pi$
$401$	25.9808	−	15.0000i	1.29742	−	0.749064i	0.979957	+	0.199207i	$0.0638367\pi$
$402$		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
$407$		−	24.0000i		−	1.18964i
$408$		0			0
$409$	6.00000	+	3.46410i	0.296681	+	0.171289i	0.640951	−	0.767582i	$-0.278540\pi$
$409$	6.00000	+	3.46410i	0.296681	+	0.171289i	−0.344270	+	0.938871i	$0.611874\pi$
$410$		0			0
$411$		0			0
$412$			17.3205i			0.853320i
$413$	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
$419$	31.1769			1.52309			0.761546	−	0.648111i	$-0.224441\pi$
$419$	31.1769			1.52309			0.761546	+	0.648111i	$0.224441\pi$
$420$		0			0
$421$	−10.0000			−0.487370			−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000			−0.487370			−0.243685	+	0.969854i	$0.578356\pi$
$422$	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
$427$	12.0000	+	34.6410i	0.580721	+	1.67640i
$428$			12.0000i			0.580042i
$429$		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	$-0.0940977\pi$
$434$	0.866025	−	4.50000i	0.0415705	−	0.216007i
$435$		0			0
$436$	−4.00000	−	6.92820i	−0.191565	−	0.331801i
$437$		0			0
$438$		0			0
$439$	13.5000	−	7.79423i	0.644320	−	0.371998i	−0.141957	−	0.989873i	$-0.545339\pi$
$439$	13.5000	−	7.79423i	0.644320	−	0.371998i	0.786277	+	0.617875i	$0.212006\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−23.3827	+	13.5000i	−1.11094	+	0.641404i	−0.939074	−	0.343715i	$-0.888315\pi$
$443$	−23.3827	+	13.5000i	−1.11094	+	0.641404i	−0.171871	+	0.985119i	$0.554981\pi$
$444$		0			0
$445$		0			0
$446$	2.59808	+	4.50000i	0.123022	+	0.213081i
$447$		0			0
$448$	−0.500000	+	2.59808i	−0.0236228	+	0.122748i
$449$		−	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
$454$		−	25.9808i		−	1.21934i
$455$		0			0
$456$		0			0
$457$	−11.0000	−	19.0526i	−0.514558	−	0.891241i	−0.999857	−	0.0168929i	$-0.994623\pi$
$457$	−11.0000	−	19.0526i	−0.514558	−	0.891241i	0.485299	−	0.874348i	$-0.338711\pi$
$458$	−3.46410	+	6.00000i	−0.161867	+	0.280362i
$459$		0			0
$460$		0			0
$461$	−15.5885			−0.726027			−0.363013	−	0.931784i	$-0.618252\pi$
$461$	−15.5885			−0.726027			−0.363013	+	0.931784i	$0.618252\pi$
$462$		0			0
$463$	5.00000			0.232370			0.116185	−	0.993228i	$-0.462933\pi$
$463$	5.00000			0.232370			0.116185	+	0.993228i	$0.462933\pi$
$464$	−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
$472$	−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
$479$	5.19615	−	9.00000i	0.237418	−	0.411220i	−0.722554	−	0.691314i	$-0.757032\pi$
$479$	5.19615	−	9.00000i	0.237418	−	0.411220i	0.959973	+	0.280094i	$0.0903655\pi$
$480$		0			0
$481$	24.0000	−	13.8564i	1.09431	−	0.631798i
$482$	12.1244			0.552249
$483$		0			0
$484$	−2.00000			−0.0909091
$485$		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
$491$			36.0000i			1.62466i	0.583200	+	0.812329i	$0.301800\pi$
$491$			36.0000i			1.62466i	−0.583200	+	0.812329i	$0.698200\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$			1.73205i			0.0777714i
$497$	−31.1769	−	6.00000i	−1.39848	−	0.269137i
$498$		0			0
$499$	−8.00000	−	13.8564i	−0.358129	−	0.620298i	0.629519	−	0.776985i	$-0.283252\pi$
$499$	−8.00000	−	13.8564i	−0.358129	−	0.620298i	−0.987648	+	0.156687i	$0.949919\pi$
$500$		0			0
$501$		0			0
$502$	22.5000	−	12.9904i	1.00422	−	0.579789i
$503$	31.1769			1.39011			0.695055	−	0.718957i	$-0.255380\pi$
$503$	31.1769			1.39011			0.695055	+	0.718957i	$0.255380\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$		0			0
$508$	4.00000	−	6.92820i	0.177471	−	0.307389i
$509$	2.59808	+	4.50000i	0.115158	+	0.199459i	0.917843	−	0.396944i	$-0.129929\pi$
$509$	2.59808	+	4.50000i	0.115158	+	0.199459i	−0.802685	+	0.596403i	$0.796596\pi$
$510$		0			0
$511$	9.00000	−	10.3923i	0.398137	−	0.459728i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	18.0000	+	10.3923i	0.793946	+	0.458385i
$515$		0			0
$516$		0			0
$517$			31.1769i			1.37116i
$518$	−13.8564	+	16.0000i	−0.608816	+	0.703000i
$519$		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	$0.0198913\pi$
$524$	−15.5885			−0.680985
$525$		0			0
$526$	−24.0000			−1.04645
$527$		0			0
$528$		0			0
$529$	−11.5000	+	19.9186i	−0.500000	+	0.866025i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		−	36.0000i		−	1.55933i
$534$		0			0
$535$		0			0
$536$	−1.73205	−	1.00000i	−0.0748132	−	0.0431934i
$537$		0			0
$538$		−	15.5885i		−	0.672066i
$539$	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
$547$	14.0000			0.598597			0.299298	−	0.954160i	$-0.403247\pi$
$547$	14.0000			0.598597			0.299298	+	0.954160i	$0.403247\pi$
$548$	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
$553$	32.5000	−	11.2583i	1.38204	−	0.478753i
$554$		−	14.0000i		−	0.594803i
$555$		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
$563$	−15.5885	+	27.0000i	−0.656975	+	1.13791i	0.324420	+	0.945913i	$0.394831\pi$
$563$	−15.5885	+	27.0000i	−0.656975	+	1.13791i	−0.981395	+	0.192001i	$0.938502\pi$
$564$		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	−0.266090	−	0.963948i	$-0.585732\pi$
$569$	10.3923	−	6.00000i	0.435668	−	0.251533i	0.701758	+	0.712415i	$0.252399\pi$
$570$		0			0
$571$	2.00000	−	3.46410i	0.0836974	−	0.144968i	−0.821138	−	0.570730i	$-0.806660\pi$
$571$	2.00000	−	3.46410i	0.0836974	−	0.144968i	0.904835	+	0.425762i	$0.139994\pi$
$572$	5.19615	+	9.00000i	0.217262	+	0.376309i
$573$		0			0
$574$	9.00000	+	25.9808i	0.375653	+	1.08442i
$575$		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
$581$	−2.59808	+	13.5000i	−0.107786	+	0.560074i
$582$		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
$587$	−10.3923			−0.428936			−0.214468	−	0.976731i	$-0.568802\pi$
$587$	−10.3923			−0.428936			−0.214468	+	0.976731i	$0.568802\pi$
$588$		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
$596$		−	15.0000i		−	0.614424i
$597$		0			0
$598$		0			0
$599$	25.9808	+	15.0000i	1.06155	+	0.612883i	0.925859	−	0.377869i	$-0.123343\pi$
$599$	25.9808	+	15.0000i	1.06155	+	0.612883i	0.135686	+	0.990752i	$0.456676\pi$
$600$		0			0
$601$		−	34.6410i		−	1.41304i	−0.707695	−	0.706518i	$-0.750265\pi$
$601$		−	34.6410i		−	1.41304i	0.707695	−	0.706518i	$-0.249735\pi$
$602$	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	$-0.700296\pi$
$607$	−4.50000	+	2.59808i	−0.182649	+	0.105453i	0.405887	+	0.913923i	$0.366962\pi$
$608$		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
$616$	−6.00000	−	5.19615i	−0.241747	−	0.209359i
$617$			18.0000i			0.724653i	0.932051	+	0.362326i	$0.118017\pi$
$617$			18.0000i			0.724653i	−0.932051	+	0.362326i	$0.881983\pi$
$618$		0			0
$619$	30.0000	+	17.3205i	1.20580	+	0.696170i	0.961839	−	0.273615i	$-0.0882193\pi$
$619$	30.0000	+	17.3205i	1.20580	+	0.696170i	0.243962	+	0.969785i	$0.421553\pi$
$620$		0			0
$621$		0			0
$622$			31.1769i			1.25008i
$623$	25.9808	−	9.00000i	1.04090	−	0.360577i
$624$		0			0
$625$	−12.5000	−	21.6506i	−0.500000	−	0.866025i
$626$	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
$637$	−9.00000	+	22.5167i	−0.356593	+	0.892143i
$638$		−	27.0000i		−	1.06894i
$639$		0			0
$640$		0			0
$641$	−36.3731	−	21.0000i	−1.43665	−	0.829450i	−0.439034	−	0.898470i	$-0.644679\pi$
$641$	−36.3731	−	21.0000i	−1.43665	−	0.829450i	−0.997615	+	0.0690201i	$0.978013\pi$
$642$		0			0
$643$			3.46410i			0.136611i	0.997664	+	0.0683054i	$0.0217592\pi$
$643$			3.46410i			0.136611i	−0.997664	+	0.0683054i	$0.978241\pi$
$644$		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
$650$	17.3205			0.679366
$651$		0			0
$652$	10.0000			0.391630
$653$	−25.9808	+	15.0000i	−1.01671	+	0.586995i	−0.913148	−	0.407628i	$-0.866356\pi$
$653$	−25.9808	+	15.0000i	−1.01671	+	0.586995i	−0.103558	+	0.994623i	$0.533023\pi$
$654$		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
$659$			15.0000i			0.584317i	0.956370	+	0.292159i	$0.0943735\pi$
$659$			15.0000i			0.584317i	−0.956370	+	0.292159i	$0.905627\pi$
$660$		0			0
$661$	9.00000	+	5.19615i	0.350059	+	0.202107i	0.664711	−	0.747100i	$-0.268554\pi$
$661$	9.00000	+	5.19615i	0.350059	+	0.202107i	−0.314652	+	0.949207i	$0.601888\pi$
$662$	24.2487	+	14.0000i	0.942453	+	0.544125i
$663$		0			0
$664$		−	5.19615i		−	0.201650i
$665$		0			0
$666$		0			0
$667$		0			0
$668$	5.19615	−	9.00000i	0.201045	−	0.348220i
$669$		0			0
$670$		0			0
$671$	41.5692			1.60476
$672$		0			0
$673$	−26.0000			−1.00223			−0.501113	−	0.865382i	$-0.667076\pi$
$673$	−26.0000			−1.00223			−0.501113	+	0.865382i	$0.667076\pi$
$674$	−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	$-0.263505\pi$
$677$	−7.79423	−	13.5000i	−0.299557	−	0.518847i	−0.976035	+	0.217616i	$0.930172\pi$
$678$		0			0
$679$	22.5000	+	4.33013i	0.863471	+	0.166175i
$680$		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
$686$	0.866025	−	18.5000i	0.0330650	−	0.706333i
$687$		0			0
$688$	−2.00000	−	3.46410i	−0.0762493	−	0.132068i
$689$	10.3923	−	18.0000i	0.395915	−	0.685745i
$690$		0			0
$691$	12.0000	−	6.92820i	0.456502	−	0.263561i	−0.254071	−	0.967186i	$-0.581770\pi$
$691$	12.0000	−	6.92820i	0.456502	−	0.263561i	0.710572	+	0.703624i	$0.248436\pi$
$692$	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
$700$	−12.5000	+	4.33013i	−0.472456	+	0.163663i
$701$			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
$706$			10.3923i			0.391120i
$707$	10.3923	+	9.00000i	0.390843	+	0.338480i
$708$		0			0
$709$	−2.00000	−	3.46410i	−0.0751116	−	0.130097i	0.826023	−	0.563636i	$-0.190598\pi$
$709$	−2.00000	−	3.46410i	−0.0751116	−	0.130097i	−0.901135	+	0.433539i	$0.857265\pi$
$710$		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
$722$		−	19.0000i		−	0.707107i
$723$		0			0
$724$	−18.0000	−	10.3923i	−0.668965	−	0.386227i
$725$	−38.9711	−	22.5000i	−1.44735	−	0.835629i
$726$		0			0
$727$			24.2487i			0.899335i	0.893196	+	0.449667i	$0.148458\pi$
$727$			24.2487i			0.899335i	−0.893196	+	0.449667i	$0.851542\pi$
$728$	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	$-0.584295\pi$
$733$	12.0000	−	6.92820i	0.443230	−	0.255899i	0.704967	+	0.709240i	$0.250962\pi$
$734$	−10.3923			−0.383587
$735$		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
$742$	−3.00000	+	15.5885i	−0.110133	+	0.572270i
$743$			6.00000i			0.220119i	0.993925	+	0.110059i	$0.0351041\pi$
$743$			6.00000i			0.220119i	−0.993925	+	0.110059i	$0.964896\pi$
$744$		0			0
$745$		0			0
$746$	−3.46410	−	2.00000i	−0.126830	−	0.0732252i
$747$		0			0
$748$		0			0
$749$	10.3923	+	30.0000i	0.379727	+	1.09618i
$750$		0			0
$751$	−2.00000	−	3.46410i	−0.0729810	−	0.126407i	0.827225	−	0.561870i	$-0.189918\pi$
$751$	−2.00000	−	3.46410i	−0.0729810	−	0.126407i	−0.900207	+	0.435463i	$0.856585\pi$
$752$	−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
$761$	20.7846	+	36.0000i	0.753442	+	1.30500i	0.946145	+	0.323742i	$0.104941\pi$
$761$	20.7846	+	36.0000i	0.753442	+	1.30500i	−0.192704	+	0.981257i	$0.561726\pi$
$762$		0			0
$763$	−16.0000	−	13.8564i	−0.579239	−	0.501636i
$764$		−	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
$769$			15.5885i			0.562134i	0.959688	+	0.281067i	$0.0906883\pi$
$769$			15.5885i			0.562134i	−0.959688	+	0.281067i	$0.909312\pi$
$770$		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	$-0.564554\pi$
$773$	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
$776$	−8.66025			−0.310885
$777$		0			0
$778$	9.00000			0.322666
$779$		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
$787$	−21.0000	−	12.1244i	−0.748569	−	0.432187i	0.0766075	−	0.997061i	$-0.475591\pi$
$787$	−21.0000	−	12.1244i	−0.748569	−	0.432187i	−0.825177	+	0.564875i	$0.808924\pi$
$788$	−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
$794$	−12.1244	+	21.0000i	−0.430277	+	0.745262i
$795$		0			0
$796$	1.50000	−	0.866025i	0.0531661	−	0.0306955i
$797$	15.5885			0.552171			0.276086	−	0.961133i	$-0.410963\pi$
$797$	15.5885			0.552171			0.276086	+	0.961133i	$0.410963\pi$
$798$		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
$806$		−	6.00000i		−	0.211341i
$807$		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	$0.941593\pi$
$812$	−15.5885	+	18.0000i	−0.547048	+	0.631676i
$813$		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
$821$	−28.5788	+	16.5000i	−0.997408	+	0.575854i	−0.907480	−	0.420094i	$-0.861997\pi$
$821$	−28.5788	+	16.5000i	−0.997408	+	0.575854i	−0.0899279	+	0.995948i	$0.528664\pi$
$822$		0			0
$823$	−5.50000	+	9.52628i	−0.191718	+	0.332065i	−0.945820	−	0.324692i	$-0.894739\pi$
$823$	−5.50000	+	9.52628i	−0.191718	+	0.332065i	0.754102	+	0.656758i	$0.228073\pi$
$824$	−8.66025	−	15.0000i	−0.301694	−	0.522550i
$825$		0			0
$826$	−13.5000	−	2.59808i	−0.469725	−	0.0903986i
$827$			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
$832$			3.46410i			0.120096i
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$	−27.0000	+	15.5885i	−0.932700	+	0.538494i
$839$	20.7846			0.717564			0.358782	−	0.933421i	$-0.383192\pi$
$839$	20.7846			0.717564			0.358782	+	0.933421i	$0.383192\pi$
$840$		0			0
$841$	−52.0000			−1.79310
$842$	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
$848$		−	6.00000i		−	0.206041i
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$		−	10.3923i		−	0.355826i	−0.984046	−	0.177913i	$-0.943065\pi$
$853$		−	10.3923i		−	0.355826i	0.984046	−	0.177913i	$-0.0569345\pi$
$854$	−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	−0.941023	−	0.338344i	$-0.890133\pi$
$857$	−5.19615	+	9.00000i	−0.177497	+	0.307434i	0.763525	+	0.645778i	$0.223467\pi$
$858$		0			0
$859$	−42.0000	+	24.2487i	−1.43302	+	0.827355i	−0.997350	−	0.0727505i	$-0.976822\pi$
$859$	−42.0000	+	24.2487i	−1.43302	+	0.827355i	−0.435671	+	0.900106i	$0.643489\pi$
$860$		0			0
$861$		0			0
$862$	−18.0000			−0.613082
$863$	−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
$866$	6.06218	+	10.5000i	0.206001	+	0.356805i
$867$		0			0
$868$	1.50000	+	4.33013i	0.0509133	+	0.146974i
$869$		−	39.0000i		−	1.32298i
$870$		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	0.848648	−	0.528958i	$-0.177417\pi$
$877$	−1.00000	−	1.73205i	−0.0337676	−	0.0584872i	−0.882415	+	0.470471i	$0.844084\pi$
$878$	−7.79423	+	13.5000i	−0.263042	+	0.455603i
$879$		0			0
$880$		0			0
$881$	−31.1769			−1.05038			−0.525188	−	0.850986i	$-0.676005\pi$
$881$	−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
$886$	13.5000	−	23.3827i	0.453541	−	0.785557i
$887$	−15.5885	−	27.0000i	−0.523409	−	0.906571i	−0.999629	−	0.0272449i	$-0.991327\pi$
$887$	−15.5885	−	27.0000i	−0.523409	−	0.906571i	0.476220	−	0.879326i	$-0.342007\pi$
$888$		0			0
$889$	4.00000	−	20.7846i	0.134156	−	0.697093i
$890$		0			0
$891$		0			0
$892$	−4.50000	−	2.59808i	−0.150671	−	0.0869900i
$893$		0			0
$894$		0			0
$895$		0			0
$896$	−0.866025	−	2.50000i	−0.0289319	−	0.0835191i
$897$		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
$902$	31.1769			1.03808
$903$		0			0
$904$	−12.0000			−0.399114
$905$		0			0
$906$		0			0
$907$	−11.0000	+	19.0526i	−0.365249	+	0.632630i	−0.988816	−	0.149140i	$-0.952349\pi$
$907$	−11.0000	+	19.0526i	−0.365249	+	0.632630i	0.623567	+	0.781770i	$0.285683\pi$
$908$	12.9904	+	22.5000i	0.431101	+	0.746689i
$909$		0			0
$910$		0			0
$911$			36.0000i			1.19273i	0.802712	+	0.596367i	$0.203390\pi$
$911$			36.0000i			1.19273i	−0.802712	+	0.596367i	$0.796610\pi$
$912$		0			0
$913$	13.5000	+	7.79423i	0.446785	+	0.257951i
$914$	19.0526	+	11.0000i	0.630203	+	0.363848i
$915$		0			0
$916$		−	6.92820i		−	0.228914i
$917$	−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
$923$	−41.5692			−1.36827
$924$		0			0
$925$	40.0000			1.31519
$926$	−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	0.974394	+	0.224848i	$0.0721885\pi$
$929$	20.7846	+	36.0000i	0.681921	+	1.18112i	−0.292473	+	0.956274i	$0.594478\pi$
$930$		0			0
$931$		0			0
$932$		−	18.0000i		−	0.589610i
$933$		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	$0.808553\pi$
$938$	−5.19615	−	1.00000i	−0.169660	−	0.0326512i
$939$		0			0
$940$		0			0
$941$	−2.59808	+	4.50000i	−0.0846949	+	0.146696i	−0.905261	−	0.424856i	$-0.860325\pi$
$941$	−2.59808	+	4.50000i	−0.0846949	+	0.146696i	0.820566	+	0.571551i	$0.193658\pi$
$942$		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	−0.621264	−	0.783601i	$-0.713381\pi$
$947$	−7.79423	+	4.50000i	−0.253278	+	0.146230i	0.367986	+	0.929831i	$0.380047\pi$
$948$		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	$0.0941672\pi$
$953$			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
$958$			10.3923i			0.335760i
$959$	20.7846	−	24.0000i	0.671170	−	0.775000i
$960$		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
$967$	56.0000			1.80084			0.900419	−	0.435023i	$-0.143260\pi$
$967$	56.0000			1.80084			0.900419	+	0.435023i	$0.143260\pi$
$968$	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
$974$			11.0000i			0.352463i
$975$		0			0
$976$	12.0000	+	6.92820i	0.384111	+	0.221766i
$977$	−15.5885	−	9.00000i	−0.498719	−	0.287936i	0.229465	−	0.973317i	$-0.426302\pi$
$977$	−15.5885	−	9.00000i	−0.498719	−	0.287936i	−0.728184	+	0.685381i	$0.759636\pi$
$978$		0			0
$979$		−	31.1769i		−	0.996419i
$980$		0			0
$981$		0			0
$982$	−18.0000	−	31.1769i	−0.574403	−	0.994895i
$983$	10.3923	−	18.0000i	0.331463	−	0.574111i	−0.651336	−	0.758790i	$-0.725791\pi$
$983$	10.3923	−	18.0000i	0.331463	−	0.574111i	0.982799	+	0.184679i	$0.0591244\pi$
$984$		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
$994$	30.0000	−	10.3923i	0.951542	−	0.329624i
$995$		0			0
$996$		0			0
$997$	33.0000	+	19.0526i	1.04512	+	0.603401i	0.921279	−	0.388901i	$-0.127145\pi$
$997$	33.0000	+	19.0526i	1.04512	+	0.603401i	0.123841	+	0.992302i	$0.460479\pi$
$998$	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	378.2.k.a.269.1	yes	4
3.2	odd	2	inner	378.2.k.a.269.2	yes	4
7.3	odd	6		2646.2.d.c.2645.2		4
7.4	even	3		2646.2.d.c.2645.1		4
7.5	odd	6	inner	378.2.k.a.215.2	yes	4
9.2	odd	6		1134.2.t.a.1025.1		4
9.4	even	3		1134.2.l.d.269.1		4
9.5	odd	6		1134.2.l.d.269.2		4
9.7	even	3		1134.2.t.a.1025.2		4
21.5	even	6	inner	378.2.k.a.215.1	✓	4
21.11	odd	6		2646.2.d.c.2645.3		4
21.17	even	6		2646.2.d.c.2645.4		4
63.5	even	6		1134.2.t.a.593.2		4
63.40	odd	6		1134.2.t.a.593.1		4
63.47	even	6		1134.2.l.d.215.2		4
63.61	odd	6		1134.2.l.d.215.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.k.a.215.1	✓	4	21.5	even	6	inner
378.2.k.a.215.2	yes	4	7.5	odd	6	inner
378.2.k.a.269.1	yes	4	1.1	even	1	trivial
378.2.k.a.269.2	yes	4	3.2	odd	2	inner
1134.2.l.d.215.1		4	63.61	odd	6
1134.2.l.d.215.2		4	63.47	even	6
1134.2.l.d.269.1		4	9.4	even	3
1134.2.l.d.269.2		4	9.5	odd	6
1134.2.t.a.593.1		4	63.40	odd	6
1134.2.t.a.593.2		4	63.5	even	6
1134.2.t.a.1025.1		4	9.2	odd	6
1134.2.t.a.1025.2		4	9.7	even	3
2646.2.d.c.2645.1		4	7.4	even	3
2646.2.d.c.2645.2		4	7.3	odd	6
2646.2.d.c.2645.3		4	21.11	odd	6
2646.2.d.c.2645.4		4	21.17	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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(0.500000 - 2.59808i) q^{7} +1.00000i q^{8} +(-2.59808 - 1.50000i) q^{11} -3.46410i q^{13} +(0.866025 + 2.50000i) q^{14} +(-0.500000 - 0.866025i) q^{16} +3.00000 q^{22} +(2.50000 - 4.33013i) q^{25} +(1.73205 + 3.00000i) q^{26} +(-2.00000 - 1.73205i) q^{28} -9.00000i q^{29} +(-1.50000 - 0.866025i) q^{31} +(0.866025 + 0.500000i) q^{32} +(4.00000 + 6.92820i) q^{37} +10.3923 q^{41} +4.00000 q^{43} +(-2.59808 + 1.50000i) q^{44} +(-5.19615 - 9.00000i) q^{47} +(-6.50000 - 2.59808i) q^{49} +5.00000i q^{50} +(-3.00000 - 1.73205i) q^{52} +(5.19615 + 3.00000i) q^{53} +(2.59808 + 0.500000i) q^{56} +(4.50000 + 7.79423i) q^{58} +(-2.59808 + 4.50000i) q^{59} +(-12.0000 + 6.92820i) q^{61} +1.73205 q^{62} -1.00000 q^{64} +(-1.00000 + 1.73205i) q^{67} -12.0000i q^{71} +(4.50000 + 2.59808i) q^{73} +(-6.92820 - 4.00000i) q^{74} +(-5.19615 + 6.00000i) q^{77} +(6.50000 + 11.2583i) q^{79} +(-9.00000 + 5.19615i) q^{82} -5.19615 q^{83} +(-3.46410 + 2.00000i) q^{86} +(1.50000 - 2.59808i) q^{88} +(5.19615 + 9.00000i) q^{89} +(-9.00000 - 1.73205i) q^{91} +(9.00000 + 5.19615i) q^{94} +8.66025i q^{97} +(6.92820 - 1.00000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} + 2 q^{7} - 2 q^{16} + 12 q^{22} + 10 q^{25} - 8 q^{28} - 6 q^{31} + 16 q^{37} + 16 q^{43} - 26 q^{49} - 12 q^{52} + 18 q^{58} - 48 q^{61} - 4 q^{64} - 4 q^{67} + 18 q^{73} + 26 q^{79} - 36 q^{82}+ \cdots + 36 q^{94}+O(q^{100}) \) 4 * q + 2 * q^4 + 2 * q^7 - 2 * q^16 + 12 * q^22 + 10 * q^25 - 8 * q^28 - 6 * q^31 + 16 * q^37 + 16 * q^43 - 26 * q^49 - 12 * q^52 + 18 * q^58 - 48 * q^61 - 4 * q^64 - 4 * q^67 + 18 * q^73 + 26 * q^79 - 36 * q^82 + 6 * q^88 - 36 * q^91 + 36 * q^94

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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